isosceles triangle, triangle abc, lqj: I am sorry, but I am unable to solve this. ( It is not clear to me: Where the point D is and in what way it is related to the triangle ABC ? ) Ques. 2: Given Regular octagon JKLMNOPQ with diagonals LQ and QK, find measure of angle LKQ. In a regular...

Geometry: Geometry, rectangle abcd, perimeter of rectangle

rectangle abcd, perimeter of rectangle, area of rectangle: Jay-Jay, The first strategy for solving these logic questions is to find set up the original statements by drawing and labeling a diagram. Draw a rectangle and label it ABCD. Write A = 50 in.^2 and P = 30 in. Label the width, w. And label the length...

Geometry: Geometry, geometry index, google search

geometry index, google search, math examples: Sergey, This is an interesting question. I did a google search using the search term geometry in medicine. Much of it is at an advanced level. Here are a few websites that may be helpful: http://mathforum.org/library/topics/medicine/ or http://www.doctorsecrets.com/your-bones/type-of-fracture.htm...

Geometry: Geometry, tangent, caleb

tangent, caleb, clarification: Caleb, We may need some clarification. If the point from which you are drawing a tangent is 3 inches from the circle, then the length of the tangent from the point to the circle is 3 inches. Let me know if you have any other information for this problem...

Geometry: Geometry, hypotenuse of a right triangle, altitude to the hypotenuse

hypotenuse of a right triangle, altitude to the hypotenuse, mean proportional: Hello, Robert! Again I ll try this without a diagram. Hope you can follow my directions. Draw a horizontal line. The left end is A, the right end is B. Above the line, pick a point C (slightly left of center) so that angle ACB = 90¡Æ. ...

Geometry: Geometry, isosceles triangle, geometry teacher

isosceles triangle, geometry teacher, diagonals: Hello, Katie! If you make a sketch, you may be able to see the answer. The altitude to the base of an isosceles triangle is perpendicular to the base (of course), and it BISECTS the base. The diagonals of a rhombus bisect each other...

Geometry: Geometry, area of a regular hexagon, congruent figures

area of a regular hexagon, congruent figures, diagonals: Samarial, If there are 2 circles with the radius of 4, then the circles would be congruent b/c the circles would have the same shape and size. If there are 2 or more regular triangles with a radius of 4, then by definition of congruent figures, the triangles...

Geometry: Geometry, area of a rectangle, geometry 1

area of a rectangle, geometry 1, perimeter formula: Anthony, The maximum area of a rectangle with a given perimeter happens when the length and width are closest in value. This is from p.8 of http://www.pearsoned.ca/school/pearsonmath9/media/PM9_StudEd_Prac_Home_Ch02.pdf. See if you can make a table...

Geometry: Geometry, perimeter of a rectangle, area of a rectangle

perimeter of a rectangle, area of a rectangle, geometry 1: Hello, Clyde! 1) Perimeter of a rectangle is 100 feet Find the dimensions of the rectangle of maximum area. Sketch a rectangle. The length is L; the width is W. The perimeter is: 2L + 2W = 100 -- W = 50 - L [1] The area is: A =...

Geometry: Geometry, perpendicular bisector, congruent squares

perpendicular bisector, congruent squares, geometry questions: Hello, Ruchi! Whew! . . . A lot of problems! I ll do my best . . . 1) What is the area of a sector of a circle that has a diameter of 10 inches if the length of the arc is 10 inches ? The circle has a radius of 5 inches. Its area...

Geometry: Geometry, isosceles triangle, geometry question

isosceles triangle, geometry question, area of triangle: Hello, pnd! Doubt 1 . . . absolutely right ... *blush* The RADIUS is 12 ... so the base is 24. (slap head) Doubt 2 . . . Yes, AB is tangent to the circle. OE is a radius drawn to the point of tangency. And that radius is always perpendicular...

Geometry: Geometry, square root of 3, angled triangle

square root of 3, angled triangle, inscribed circle: Let ABC be the a right angled triangle with right angle at C. Suppose the hypotenuse is c units, then the side opposite to 30 degrees will be c/2 and the side opposite to 60 degrees will be (3^(1/2) / 2) * c ( i.e square root of 3 by 2 into c, 3^(1/2)...

Geometry: Geometry, line segment, right triangle

line segment, right triangle, pythagorus: Hello, pnd! Another diagram . . . Draw a horizontal line segment; P at the left, Q at the right. Mark its midpoint O. Draw a semicircle above PQ, using PO as its radius. Now try to sketch a square inscribed in the semicircle. Point A is on...

Geometry: Geometry, similar right triangles, rectangular sheet

similar right triangles, rectangular sheet, crease: Hello, pnd! I got it! (It took me a while to see what was going on.) Draw a rectangle, taller than it is wide. A in the upper-left, and letter it clockwise: B, C, D. Draw diagonal AC. Locate its midpoint, O. Through O, draw a line perpendicular...

Geometry: Geometry, perimeter of a rectangle, area of a rectangle

perimeter of a rectangle, area of a rectangle, vertex of a parabola: Hello, Jenna! A rectangle has a width (x) and a length (y). Its perimeter is made up of two widths and two lengths. So we have: 2x + 2y = 200 Solve for y: 2y = 200 - 2x ¡æ y = 100 - x The area of a rectangle is: Length ¡¿ Width...

Geometry: Geometry, circumference of a circle, triangle abc

circumference of a circle, triangle abc, right triangle: Hello, Janet! I hope you can follow my diagram. Draw a circle with center O. Inscribe square ABCD inside. Draw diagonal AC; it is also the diameter of the circle. The circumference of a circle is: C = ¥ð ¡¿ diameter So, we have: ¥ð D = ...

Geometry: Geometry, distance formula, y1

distance formula, y1, x1: Hello, Janae! Are you familiar with the Distance Formula? Given two points: P(x1, y1) and Q(x2, y2) the distance PQ is: d = ¡î[ (x2 - x1)©÷ + (y2 - y1)©÷ ] In our problem, we have: PQ = ¡î[(1 - 4)©÷ + (-6 + 4)©÷ ] = ¡î[ (-3)©÷...

Geometry: Geometry, segment st, bettween

segment st, bettween, tenth person: Hello, Victoria! You re the tenth person to ask this (or a similar) question. Are you all in the same class? And your teacher didn t explain it well? I m not sure what the Addition Postulate is, but we don t need itto answer the question....

Geometry: Geometry, horizontal diameter, left c

horizontal diameter, left c, trapezoid: Hello, Marie! I hope you can follow my diagram. The problem is kind of cute . Draw a circle; the center is O. Draw a horizontal diameter AB (through O), A on the left, B on the right. In the upper semicircle, draw a horizontal chord...

Geometry: Geometry, isosceles triangle, angled triangles

isosceles triangle, angled triangles, right triangle: The legs of a right triangle are 3 and 4. Find the length of the hypotenuse. It must be 5 since square of one leg + square of the other leg = square of the hypotenuse (Pythagoras Theorem ) Therefore 9 + 16 = square of Hypotenuse Therefore...

Geometry: Geometry, elementary geometry, angled triangle

elementary geometry, angled triangle, sides of a triangle: As far as I know there is no simple method in elementary geometry which will tell us whether a triangle will be acute angled, right angled or obtuse without constructing it. So the most obvious method would be to construct these triangles and check for...

Geometry: Geometry for an Accountant, square root function, logarithmic function

square root function, logarithmic function, rational function: Hi Starleana! An accountant would use a logarithmic function to determine something exponential, such as an interest rate. A square root function would work for determining how much it would cost to, for instance, re-tile a floor (because there are two...

Geometry: Geometry/Algebra, inch graph paper, axis ranges

inch graph paper, axis ranges, coordinate axis: ( I am not sure about what is the exact relavance of the reference to quarter inch graph paper here. It is not clear to me what is meant by (lines under the arrow) I am also not aware of what are the dimensions of this paper. ) The point at...

Geometry: Geometry - Area and ratio, similar triangle, similar triangles

similar triangle, similar triangles, sq inches: 1. The areas of the similar triangles will be in the proportion of squares of the ratio of any 2 corresponding sides. Let the required area be x squared inches. Then 90 / x = ( 15 / 9 )^2 ( Here (15/9)^2 means square of 15/9 ) ...

Geometry: Geometry: Area and Volume, square centimeters, cylindrical tank

square centimeters, cylindrical tank, area of circle: what is the area of a square television screen with 16 inch sides? Area of a square with each side equal to a is a*a So the area of the TV screen will be 16*16=256 square inches. the area of a square piece of cardboard is 81 square inches. what is...

Geometry: Geometry: angle of elevation, visual learner, word problem

visual learner, word problem, imageshack: Shane, I believe this question was addressed to another Expert , but I will try to clarify his answer as best as I can. The first thing I ask my students to do is to draw & label a picture of the word problem. If you are a visual learner then this may...

Geometry: Geometry - angles and circles, alternate angles, math homework

alternate angles, math homework, interior angle: 1. The two angles described by you are equal because they are alternate angles formed by a transversal (Walnut street) intersecting 2 parallel lines. So 2x+33=5x-15 So 33+15=5x-2x So 48=3x So x=16 So 5x-15=5(16)-15=80-15=65...

Geometry: Geometry - Circles inside circle, many circles, 1 5mm

many circles, 1 5mm, whole number: Justin, If you assume that the circles inside the big circle do not overlap, then you can divide the diameter of the big circle by the diameter of the small circle to get your answer. The answer will be a decimal. You must round to a whole number because...

Geometry: Geometry - Circles and Solids, square root of 2, circle radius

square root of 2, circle radius, word pie: (I have used Pi to denote the mathematical constant. * denotes multiplication, for the sake of clarity. You should not write it in your written answer. ^ to denotes exponentiation. i.e. x^2 is x squared , So you should write it a x superscript...

Geometry: Geometry: Conjectures, geometry conjectures, matter of luck

geometry conjectures, matter of luck, conjecture: Hello, Brandon! Basically, a conjecture is an unproved theory. Here s a simple example. (I hope it s simple enough!) Consider the numbers: 18, 63, 207, 3105 We find that ALL of them are divisible by 9. We also note that, for each number,...

Geometry: Geometry:Conjectures, geometry conjectures, odd integers

geometry conjectures, odd integers, even integers: A conjecture is essentially a guess. By observing some examples you are supposed to make an intelligent guess. Now let us see what can we guess when an odd number is multiplied by an even number. An even number is an integer which is divisible by 2....

Geometry: Geometry Constructions, geometry constructions, construction reference

geometry constructions, construction reference, cropcircles: Silvia, Here s a couple of links to websites which give step-by-step instructions on constructions with compass and straight-edge. Your question seems to fit the category: Construct an angle congruent to a given angle. URL: http://whistleralley.com/construction/reference.htm...

Geometry: Geometry and Core Classes 9th grade, homework problems, trigonometry class

homework problems, trigonometry class, homework assignments: I hope that I can help by looking at this from a student s perspective. I am currently in my first year of college. I think that I also have the perspective of a teacher since I student taught a trigonometry class as a senior in high school. As a student...

Geometry: Geometry, complements, skye, complement

skye, complement, geometry: Hello Skye, it s a pleasure to help you. First things first, translate the problem from English into Mathematics. Let s make an angle =(x). is means equals, and its complement means (90-x). Therefore... 3x=2(90-x) 3x=180-2x 5x=180 x=180/5 ...

Geometry: Geometry, complements, complementary angles, skye

complementary angles, skye, complement: Hello, Skye! We re expected to know what complementary angles are. Two angles are complements if their sum is 90°. Let x be one angle. Then: 90 - x is its complement (Do you see why?) Three times an angle is twice its complement. The equation...

Geometry: Geometry construction, angle bcd, geometry construction

angle bcd, geometry construction, construction lines: (A) Using the ruler draw a straight line. ( I have drawn it horizontally.) Mark a point on it as A. From A at a distance of 8.0 cm, mark another point on this line as B. ( I have taken it on the right hand side. ) Now with A as center...

Geometry: Geometry and Discrete Mathematics, geometry and discrete mathematics, pascal newton

geometry and discrete mathematics, pascal newton, course geometry: Without looking at the syllabus it will not be proper on my part to comment on your teacher s opinion. But in general 1. I don t agree that Discrete maths is like Physics. Discrete mathematics is quite close to theoritical Computer Science. ...

Geometry: Geometry examples, parallel straight lines, geometry help

parallel straight lines, geometry help, triangle abc: 1.Given: AB//DC To Prove: 1 is congruent or equal to 2 I need analysis, statements, and reasons Statements Reasons 1. AB//DC 1. Given 2. m 1 = m 2 2. AC is the transversal. ...

Geometry: Geometry: Finding the slope, finding the slope, parallel lines

finding the slope, parallel lines, negative comments: I would be glad to help! First, parallel lines have the same slope. So any line parallel to CD has the same slope as CD. The formula for slope when you have 2 points is: (y2 - y1)/(x2 - x1) FOLLOW UP: ----------------------------------- Judging...

Geometry: Geometry: find the slope of every line perpendicular to RS?, point of intersection, perpendicular slope

point of intersection, perpendicular slope, right question: I would be glad to help! Your math was perfect up until this point. -1/2/-7= -1*(-2)=2 -1/2/-7= -1*(-7/2)= 7/2 is correct. There is an easy way to find a perpendicular slope. All you do is flip the fraction and multiply by -1. This is called...

Geometry: Geometry Grade 10, fact quiz, line segments

fact quiz, line segments, radii of a circle: See whether the following 2 fit the requirements.? 1. Consider a Pyramid with triangular faces. Let the base be with the points A, B & C. Let O be the remaining vertex. Now consider the figure formed by the line segments OA, OB & OC. What is the area of...

Geometry: Geometry grade 12, picnic benches, geometry question

picnic benches, geometry question, concrete area: If I have unserstood the problem correctly, the dimensions of the larger square(?) are not required for our calculations. The answer is = 20 * 20 * (2/3) cu. ft. = 400 * (2/3) cu. ft. = 800/3 cu. ft. ( Please note 8 inches = 8 * (1/12) ft ...

Geometry: Geometry / hexagon, inscribed circle, sqrt

inscribed circle, sqrt, radii: I am not sure about what exactly you mean by the radius of the circle. This is because there are 2 radii involved here: 1. Radius of the inner circle ( inradius, also called the radius of the inscribed circle. ) is given by the formula r = a sqrt(3)/2...

Geometry: Geometry/kids, www aaamath, artist mondrian

www aaamath, artist mondrian, teaching geometry: Janset, This is a difficult question to answer. No matter what age the kid , geometry is great because it deals with shapes and objects with which kids are familiar. So there are many hands-on projects that you can do. I teach high-schoolers so to help...

Geometry: Geometry, kites, multiplication symbol, area of a triangle

multiplication symbol, area of a triangle, right angles: Let us draw a kite first. Let the kite have vertices ABCD with diagonals AC and BD intersecting at point O (these will be at right angles to each other), with side AB equal to side AD and side BC equal to side CD. Now let the length AC be d1 and lenght...

Geometry: Geometry - Mandala Logos, network logos, international baccalaureate

network logos, international baccalaureate, circle foundation: Well, I m don t have very much experience with mandala, but a few TV network logos are instances of these, including those of CBC and CBS. The Who Wants to Be a Millionaire Logo is a sort of mandala. Plextor, Inside Circle Foundation, Rainbow DJ Services,...

Geometry: Geometry Measurement, using algebra, sq feet

using algebra, sq feet, five feet: The area of the orginal square must be 484 sq. feet. There is no standard formula for solving this. I solved this using algebra. Let each side of the original square be x feet. So the original square s area must be = x*x sq. feet. After increasing...

Geometry: Geometry - Midpoint, midpoint formula, simple logic

midpoint formula, simple logic, yx: Hi C-Jay, Don t worry about getting stumped on this question. Working backwards with the midpoint formula [(X1+X2)/2, (Y1+Yx)/2] is one way to do this, but I prefer simple logic. It is quicker and easier. Here goes... Look only at the x-values for the...

Geometry: Geometry - Prism Volume, lwh, cubic inches

lwh, cubic inches, evelyn: Hi Evelyn! First, find the volume of the cube. Vcube=s^3 Vcube=6^3 Vcube=216 Now, find the volume of the rectangular box. Vrprism=lwh Vrprism=(10)(4)(4) Vrprism=160 And for the difference in volume: Vdiff=Vcube-Vrprism Vdiff=(216)-(160) Vdiff=56...

Geometry: Geometry Problem, geometry conjectures, similar polygons

geometry conjectures, similar polygons, geometry problem: Andrew Salazar, You need the following conjecture or theorem. If two similar polygons (or circles) have corresponding sides (or radii) in the ratio of m/n, then their areas are in the ratio of m2/m2. (Proportional Area Conjecture). (pg 614)There is a...

Geometry: Geometry Proof, angle bisector, isosceles triangle

angle bisector, isosceles triangle, geometry proof: Mark the point X on AD such that AX=AB And since DA=AB+CD, we must have XD=CD ...(1) Join XE. The triangles ABE and AXE must be congruent ...(2) (Since AB=AX by construction, AE...

Geometry: Geometry Proof, isosceles trapezoid, geometry proof

isosceles trapezoid, geometry proof, line segments: (This is result is actually true for any quadrilateral.) Let K,L,M & N be the mid-points of QR,RS,ST & TQ respectively. Join RT. This divides the quadrilateral into 2 triangles TQR & RST. Join K,L; L,M; M,N; N,K. In triangle TQR. N & K are mid-points...

Geometry: Geometry Proof, geometry proof, parallel state

geometry proof, parallel state, library thinkquest: Here is a hint: The tangents to the circle at both the endpoints of a diameter will both be perpendicular to the diameter and hence by using the result Theorem: In a plane, if two lines are perpendicular to the same line then the lines are parallel. ...

Geometry: Geometry Proof, geometry proof, angles of a triangle

geometry proof, angles of a triangle, triangle abc: If AB=AC, m ABC=m ACB Let m ABC=x, then m A=180-2*x. ...(1) (Since m A+x+x=180) In triangle DCB, m CDB=90 ( by construcyion) and m DBC=x, ( since it is same as m ABC) Therefore m DCB=180-(90-x) ( Angles of a triangle add up to 180) = 90-x...

Geometry: Geometry Proofs, segment ac, rhombus shape

segment ac, rhombus shape, triangle abc: Hello, Julia! Remember how to prove two triangles congruent? Three ways: s.a.s, a.s.a., s.s.s We have: AB = DC and AC = DB. [Given] And: BC = BC [Reflexive property] Therefore: triangle ABC is congruent to triangle DCB . . . by s.s.s....

Geometry: Geometry-perpendicular, indirect proof, proof method

indirect proof, proof method, right angles: We can prove this by the indirect proof method. In this method we start with the assumption that what we want to prove is not true. Then we try to show that by doing this we arrive at a contradiction. Thus our assumption that what we wanted to prove was...

Geometry: in Geometry pi, tenths hundredths thousandths, decimal approximation

tenths hundredths thousandths, decimal approximation, pi through the ages: Eileen, To change a decimal to a fraction, you need to remember the place value of the digits behind the decimal. The order is Ones. Tenths Hundredths Thousandths Ten Thousandths ... First let s rewrite the decimal as a mixed fraction. 3.14...

Geometry: Geometry problem, e mail address, geometry problem

e mail address, geometry problem, free web server: I am not sure whether I can help you with your easy problem. But All Experts service hides my e-mail address from you (and yours from me.) And I think they are doing the right thing. So the work around in your case could be: You can upload the diagram...

Geometry: Geometry proofs, geometry proofs, line ed

geometry proofs, line ed, side angle: AC = DC ( since C is midpoint of AD, given ) CB = CE ( since C is midpoint of BE, given ) m ACB=m DCE ( since they are opposite angles formed by the intersection of the lines AD and BE Hence by Side-Angle-Side postulate the 2 triangles must be congruent....

Geometry: Geometry - Quadratic Equations, numerator and denominator, divided by four

numerator and denominator, divided by four, quadratic equations: I m sorry, I misread your statement about needing work, I will go through the steps. In order to rationalize a fraction with more terms than just the radical in the denominator you must multiply by the conjugate. The conjugate is the polynomial with the...

Geometry: Geometry - Quadratic Equations, square root of 3, divided by four

square root of 3, divided by four, quadratic equations: I shall use your notation. When you have a+ b in the denominator, you need to multiply the denominator as well as the numerator by a- b . When you have denominator of the form a- b , you need to multiply the denominator as well as the numerator by a+...

Geometry: Geometry - Rhombus, angle measurements, enormous pleasure

angle measurements, enormous pleasure, imageshack: Hey Lizzie! Let s begin with the angle measurements. One property of a rhombus is that its diagonals are perpendicular to one another. Hence, m 1=90 degrees. Another property of a rhombus is that its diagonals bisect its vertices. m EAD=m 2=40 degrees....

Geometry: Geometry Riddle, perimeter of a rectangle, formula for perimeter of a rectangle

perimeter of a rectangle, formula for perimeter of a rectangle, length of a rectangle: Tracie, The first thing to do is to draw and label a rectangle with the given information. Let w = width. Since the length is 2in. more than twice it s width , then length = 2w + 2. The formula for Perimeter of a Rectangle is P = 2L + 2W. Now, substitute...

Geometry: Geometry - Segment Addition Postulate, transitive property of equality, equivalent length

transitive property of equality, equivalent length, congruence: Hello Steven, these are kinda tough. Firstly, the Segment Addition Postulate simply means that the sum of the parts equals the whole. Consider this: A---------------B----------C (Assuming B is between A and C.) AB+BC=AC. That s all that means. ...

Geometry: Geometry, Special Parallelograms, diagonals of a rectangle, special parallelograms

diagonals of a rectangle, special parallelograms, quadratic equation: Samantha, There is a theorem that states Diagonals of a Rectangle are Congruent . If AC & DB are diagonals, then you are correct to set the measures =. Good start. Now, let s solve the equation. Since there is an x^2, move all the terms to the...

Geometry: Geometry - Triangles, angle bisectors, geometry triangles

angle bisectors, geometry triangles, perpendicular bisectors: Hello, Trisha! With an equilateral triangle, it s quite easy. The middle point can be described in four ways. (1) The common intersection of the three medians. (2) The common intersection of the three altitudes. (3) The common intersection...

Geometry: Geometry theorems, geometry theorems, angled triangle

geometry theorems, angled triangle, triangle abc: 1. Actually you have asked 3 questions here. ( All three are Theorems which are extensions of Pythagoras Theorem ) These are generally stated as: 1.1 In an obtuse angled triangle the square on the side opposite to the obtuse angle is equal to...

Geometry: Geometry - transformations, triangle abc, geometry transformations

triangle abc, geometry transformations, dilation: Hello. 1. Quadrant 1. The image will take the point further away from the origin past (5,6) and onto the other side of it. You re still in Quadrant 1. 2. C. The dilation factor affects all sides, but decreasing the side lengths does nothing to the...

Geometry: Geometry Word Problem, word problem, 2 ways

word problem, 2 ways, side 1: I don t know why do you want use a square ? It is clearly mentioned in the question that the park has 3 sides which means it is a triangle. Now to find the perimeter you simply need to add all the 3 sides. There are 2 ways to do it. 1. Either convert...

Geometry: Geometry, straight line segment, segment bc

straight line segment, segment bc, triangle abc: Consider a triangle ABC. Now let us consider the side BC. The claim is BA + AC BC. Suppose this is not true. Then what this will mean ? It will mean that the straight line segment BC is not the shortest distance between B & C, (And that there is path...

Geometry: Golden Mean., concidence, answers to the questions

concidence, answers to the questions, phi: Hello Elizabeth Kearney. Instead of me trying to explain using this service (which won t allow for me to type proper expressions), I d like to direct you to a webpage I found that has the answers to the questions above, except for the why in dealing with...

Geometry: Graphing, slope intercept form, undefined slope

slope intercept form, undefined slope, y intercept: Sure thing! A. If you notice on part (c) above, I stated that a line with 0 slope is a horizontal line. If you look at a horizontal line on a graph, the vertical (or you could say the y) coordinates of each point on the line are all the same. B. A...

Geometry: Graphing, slope intercept form, slope intercept form of a line

slope intercept form, slope intercept form of a line, y intercept: I would be glad to help! I cant show you what the graph would look like, but I can give you the equations for the lines. You can then just plot points on a graph. a) The slope-intercept form of a line is: y = mx + b Where m is the slope, and b is...

Geometry: general, e mail address, 9th grade geometry

e mail address, 9th grade geometry, free e mail: I am sorry but I haven t seen many Educational CDs and hence can t comment on this. As far as on-line resources are concerned again whatever I know is limited to free resources only. In my opinion the best site for seeking extra help in mathematics...

Geometry: geo. symbol, right triangle, wavy line

right triangle, wavy line, srt: Hello, Krista! That wavy line (~) means similar to . Two figures are similar if they have the same SHAPE, but not necessarily the same size. Any two squares are similar. One could be a 3-by-3, the other could be 10-by-10. Draw a triangle...

Geometry: geomatry-tiling and tessellations, 10th grade geometry, geometry project

10th grade geometry, geometry project, library thinkquest: Please refer to the following links. Tessellations 1. Lot of links and information http://mathforum.org/sum95/suzanne/tess.intro.html 2. Some basics about the subject http://www.coolmath.com/tesspag1.htm 3. A good tutorial made by students ...

Geometry: geomerty, angle adc, angled triangles

angle adc, angled triangles, corresponding angles: To prove triangle ABC is similar to triangle DAC m(angle BAC) = 90 (since AB is a tangent to the circle at A) m(angle ADC) = 90 (As AOC is a diameter of the circle, angle ADC is an angle in the semi circle. Angle...

Geometry: geometric centres, autodesk corporation, cardboard sheet

autodesk corporation, cardboard sheet, finding center of gravity: As far as irregular shapes are concerned there is no simple formula for finding the position of center of gravity. But there is a procedure which is usually described in the Physics text books for finding center of gravity of irregular shaped plate...

Geometry: geometric centres, measure of central tendancy, math physics

measure of central tendancy, math physics, e mail: Well I know physics has some method of finding the measure of central tendancy but I m currently in that class and have not come across it yet. I can look it up but can not garentee that I can come up with a solid answer. Is this project for Math, Physics,...

Geometry: geometric formulas, area and perimeter, circumference of a circle

area and perimeter, circumference of a circle, area of a cylinder: A cylinder is a 3 dimensional object, which has surface area and volume but it has no perimeter. ( Perimeter is the length of boundary of a closed curve. e.g. the circumference of a circle is its perimeter.) The area of a cylinder is found by adding the...

Geometry: geometric means, square root of 4, dictnary

square root of 4, dictnary, geometric mean: Ashley, Mean refers to an average. A geometric mean is a way of averaging using a square root. To set up a geometric mean, you need to set up a proportion. [a/b = b/c]The geometric mean will appear twice in the proportion and always caddy-cornered...

Geometry: geometry, right angles, parallel sides

right angles, parallel sides, septagon: It seems to me you ve got the concept of a right angle, its just that when you think of a pentagon or a hexagon, you tend to think of regular ones. This is just because that s how we normally see them. Of course, you probably know that a pentagon is just...

Geometry: geometry, slope of a line, square roots

slope of a line, square roots, side ac: 1. It it is a square. You need to find the distances EF, FG, GH, HE if they are all equal then the figure is not a rectangle and not just a parallelogram. Then find the slopes of EF, FG, GH & HE, If the products of slopes of adjacent sides...

Geometry: geometry 10th grade level, area of a trapezoid, math faq

area of a trapezoid, math faq, parallel sides: I am sorry but the question is not clear to me. Please refer to the following web page for the formula for the area of the trapezoid. http://www.mathforum.org/dr.math/faq/formulas/faq.quad.html#trapezoid The formula is = sum of the lenghts of the parallel...

Geometry: geometry, square root of 3, rough sketch

square root of 3, rough sketch, equilateral triangle: Let the length of each side be x . (please draw a rough sketch for better understanding.) Join all the verices to the center. Now you will get 6 identical equilateral triangles. Now the distance between the opposite sides is equal to the sum of the...

Geometry: geometry, unit cubes, edge length

unit cubes, edge length, red paint: So we have a 10 by 10 by 10 cube. Making 1000 unit cubes in all. Now you can imagine there is cube inside with all sides 8 i.e. made up of 8 unit cube on each side. So this inner cube is having 8 * 8 * 8 = 512 unit cubes, and these are not visible from...

Geometry: geometry, mathematical term, string tie

mathematical term, string tie, tacks: The mathematical term for an oval is ellipse. Read the details of constructing an ellipse at the following links: 1. http://mathworld.wolfram.com/Ellipse.html (Here you can see a nice animation of the process of construction.) Else ...

Geometry: geometry, symbolic name, variable name

symbolic name, variable name, geometry: Of course the value of x can be different in different situations(problems). This concept is generally introduced in Algebra. The basic idea is in a problem we are asked to find certain value. But in the beginning this value is unknown and to this...

Geometry: geometry, sector of a circle, central angle

sector of a circle, central angle, cm 2: The total area of the circle corresponds to a central angle of 360 degrees. So when the angle is 360 degrees the area is Pi*r^2, where Pi is the mathematical costant 3.14 (Approx.), r^2 ( means r squared i.e. r multiplied by r ) The area of this circle...

Geometry: geometry, congruent triangles, left hand corner

congruent triangles, left hand corner, ratio form: What a good question! I m thinking I have a good answer for you to but you will have to bear with me because sometimes these problems are hard to answer just with words. If you have a piece of paper it would help greatly! First you make your regular hexagon,...

Geometry: geometry, intersecting planes, parallel planes

intersecting planes, parallel planes, two planes: Hi! Well the only way I can think of rays intersecting is when they come together to form an angle. To sketch that you make a V with arrowheads on the end of each one. The planes pose a tougher problem though because my scanner broke. I can tell you...

Geometry: geometry, slope intercept form, geometry

slope intercept form, geometry, graph: The required line is parallel to 2x+y=5. So it must have the same slope as this line. Now 2x+y=5 So y=-2x+5 Comparing with slope intercept form i.e. y=mx+c, the slope of this line is -2. So the required line also must be having slope = -2 Let P(x,y)...

Geometry: geometry, minus sign, geometry

minus sign, geometry: Hello Jessica Joe. First off, the full definition of |x| is as follows: |x| = x for x 0 |x| = -x for x 0 |x| = 0 for x=0 Usually this is written with the large bracket, but this website doesn t allow that. This is still accurate. The reason...

Geometry: geometry, surface area to volume ratio, dimensional representation

surface area to volume ratio, dimensional representation, perpendicular lines: Surface area = 6(s^2) volume = s^3. If s is tripled surface area becomes 18(s^2) and volume is 3(s^3). The surface area to volume ratio decreases with increased size. The only case in which your second scenario can be true is in three dimensions if the...

Geometry: geometry, area of a equilateral triangle, square root of 3

area of a equilateral triangle, square root of 3, triangle abc: Let us first note the following 2 results: I. The area of a equilateral triangle with each side equal to r , is given by r*[square root of (3)]/4 (This is a standard result, can be proved using the properties of a 30-60-90 triangle....

Geometry: geometry, triangle abc, angled triangle

triangle abc, angled triangle, scientific calculator: Let A denote a point on the top edge of the building. Let B denote the foot of the perpendicular from A. Let C denote the tip of the shadow of the building. triangle ABC is a right angled triangle, with right angle at B. Now tan(52)=opposite side/hypotenuse...

Geometry: geometry, area of an equilateral triangle, square root of 2

area of an equilateral triangle, square root of 2, area of a circle: 1. One side of a rectangle is 12 and the perimeter is 32. What is the area? If the side are x & y then the perimeter is the sum of all the sides = x + y + x + y = 2*(x+y) One of the sides is 12, so let x = 12 So 32 = 2*(12+y)...

Geometry: geometry, linear equation, line x

linear equation, line x, curve: Hello. First solve the linear equation for y, then set each equation equal to each other, and solve for x. 1/2x + 7/2 = -x^2 + 5 0 = -x^2 - 1/2x + 3/2 This can be factored into -1/2((x-1)(2x+3) So we have two x-coordinates, -1 and 3/2. The...

Geometry: geometry, secant, tangents

secant, tangents, polygon: I am sorry but except for question 3. , I don t know the answers. 1. 2. (I am not clear about what is expected here. But one answer that I can think of is:) equal 3. circumscribed ===========================================================...

Geometry: geometry, area of sphere, volume of sphere

area of sphere, volume of sphere, volume of a cone: 1. What is the volume of cube with edge 2? V=x*x*x=2*2*2=8 2. A rectangle solid with length 8 and width 2 has volume 48. find it height. V=lenght*widhth*height 48=8*2*height So 48=16*height So the height=48/16 ...

Geometry: geometry, area of a sphere, volume of a cube

area of a sphere, volume of a cube, right cylinder: true or false: 1. the lateral area of a prison is the sum of the areas of its bases. FALSE 2. if the volume of a cube is 1000, the length of each of its edges is 10. TRUE 3. all lateral faces of regular pyramids are congruent rectangles....

Geometry: geometry, segment bc, ba 5

segment bc, ba 5, geometry: I am sorry but I am unable to answer these. 1. If A is the center of the circle and BA=5, then B must be on the circle. So we can not draw a tangent from B, intersecting the circle at C. Looks like there is some mistake here. 2. The question...

Geometry: geometry, regular triangular pyramid, volume of a right cylinder

regular triangular pyramid, volume of a right cylinder, square pyramid: Please do not ask a question with too many subquestions. Please try to understand the priciples involved and ask doubts related to the concepts rather that asking me to do so many calculations. In subquestion 9. You are asking me to apply Theorem 12-11...

Geometry: geometry, geometry 2, question papers

geometry 2, question papers, sample question: I am sorry but I am not in a position to answer your question. But please do not misunderstand me, I do wish to help you, But consider the following points. 1. Everything in Geometry will never be known as it is a growing subject and mathematicians...

Geometry: geometry!, lateral surface area, regular triangular pyramid

lateral surface area, regular triangular pyramid, volume of a right cylinder: 1. find the lateral area of a regular triangular pyramid with base edge 3 in. and slant height 4 in. Lateral Surface area = (1/2)*(perimeter of the base)*(slant height) = (1/2)*(3+3+3)* 4 = (1/2)*9*4 = 18 sq. in. 2....

Geometry: geometry, diameter of a circle, geometry

diameter of a circle, geometry, radius: I m sorry but the terms you are using are not universal, I do not know what you mean by the height of the circle. If you mean the distance from the center of the circle to the outside, this is the radius. The diameter is two times the radius. I can not...

Geometry: geometry, graph paper, irregular shape

graph paper, irregular shape, geometric figures: What he has measured is the perimeter of the blob. Now he is forming a square with the same perimeter as the blob and finding the area of the square and claiming that this is a good approximation of the area of the blob. The contention that if 2 geometric...

Geometry: geometry, geometry 1, math homework

geometry 1, math homework, apothem: 1. This is most easily solved if thought of as 5 equal triangles. The area of one of these triangles is (1/2)bh or one half times the base times the height. The height is 4 and the base is 8tan(pi/5). If you are wondering where the pi/5 came from this is...

Geometry: geometry, angles of a triangle, triangle abc

angles of a triangle, triangle abc, corresponding angles: This can be easily proved using the result: If the respective angles of 2 triangles are are equal then they are similar. Both the new triangles formed here are right angled. They also share 1 angle each with the original triangle. And since the sum...

Geometry: geometry, mathart, mathforum

mathart, mathforum, tesselation: These are quite simple and interesting ideas but I can not explain them thru e-mail. I suggest you browse the following web pages to get a good idea of the topics. These pages have several examples and diagrams and further links. http://www.punahou.edu/acad/sanders/MathArt/MACch2sym.html...

Geometry: geometry, line of symmetry, mirror image

line of symmetry, mirror image, imaginary line: A translation is a shift horizontally, vertically, or both. A rotation is just as it sounds, you rotate the object around a point. A reflection gives a mirror image. A dilation decreases or increases the size of the object. If an object has a line of symmetry...

Geometry: geometry, radius of a sphere, cube root

radius of a sphere, cube root, pi: If the radius of a sphere is r then its volume is (4/3)*Pi*r^3 Here Pi is the well known mathematical constant. r^3 is to be read as r cubed . So (4/3)*Pi*r^3=113.04 m^3 Therefore r^3=(3/4)*(1/Pi)*(113.04) Therefore r=cube root of[(3/4)*(1/Pi)*(113.04)]...

Geometry: geometry, angled triangles, atenna

angled triangles, atenna, angles of elevation: What does respectively mean? Respectively is an adverb which means in the order given . e.g. John and Jack were 10 and 12 years old respectively. means John was 10 years old and Jack was 12 years old. Now consider: the angles of...

Geometry: geometry, wheel diameter, small wheels

wheel diameter, small wheels, radii: The radii of the larger wheels are 32 cm. So the diameter of the larger wheels must be 2*32=64 cms. But (diameter of the larger wheel)/(diameter of the smaller wheel) = 18 / 5 Therefore 64/(diameter of the smaller wheel)= 18 / 5 Therefore, (diameter...

Geometry: geometry, free webserver, prob

free webserver, prob, geometry: Sorry, I can t do that. (There are many problems that I already know and can t solve. So there is no assurance that I can solve yours.) What you may do alternatively is to make a webpage containing the picture of your problem and then put it...

Geometry: geometry, global positioning system, geometrical knowledge

global positioning system, geometrical knowledge, flower beds: Geometry is extensively used in all kinds of design jobs. Examples are architecture, interior, furniture. Even clothes are stitched using geometrical measurements as they have to take a 3 dimensional shape but are made from flat 2 dimensional cloth....

Geometry: geometry, solving equations, geometry

solving equations, geometry, variables: I am sorry but the question is not clear to me. Which variables are you referring to ? Generally the values of variables are found by solving equations. The equations to be solved will be different in different situations. These techniques are generally...

Geometry: geometry, branches of mathematics, different branches of mathematics

branches of mathematics, different branches of mathematics, famous persons: Congrats for finishing one of your subjects by self study in such a short time! I have no doubt you must be a genius. Ultimately all learning is self learning; others can only help, guide & motivate. I am glad you have realised this at a young age. ...

Geometry: geometry, pi radians, radius of a circle

pi radians, radius of a circle, radian measures: Suppose the radius of the circular building is r , Let the center of the circle (representing the building) be O. Let A be the point where you are standing. Let C & D be the points of contact of the 2 tangents. So ABOC will form a quadrilateral. We...

Geometry: geometry, area of a trapezoid, formula for area of a trapezoid

area of a trapezoid, formula for area of a trapezoid, 3 dimensional objects: (We use the term surface area for surfaces associated with 3-dimensional objects. A trapezoid is a 2-dimensional figure, so I assume what you want is the formula for area of a trapezoid.) If a and c are the lengths of the parallel sides and h is the...

Geometry: where did geometry come from?what..., library thinkquest, wikipedia

library thinkquest, wikipedia, geometry: Please visit the following links: ( I think the first one should be sufficient, others are having more details.) http://library.thinkquest.org/C006354/history.html http://en.wikipedia.org/wiki/Geometry http://www.math.wichita.edu/~pparker/classes/geomhist.htm...

Geometry: geometry, square root of 3, geometry

square root of 3, geometry, calculators: I am sorry, but the question is not clear to me. What is required here ? Under what topic in Geometry is this question has been asked? Do you want to know the value of 16*square root(3) ? If yes, then the answer is =16*1.732050808 =27.71281292 OR Is...

Geometry: geometry, definition of congruence, translations rotations and reflections

definition of congruence, translations rotations and reflections, rotations: Yes. (One of the definitions of congruence (in Geometry):) In Geometry two sets are called congruent if one can be transformed into the other by an isometry, i.e., a combination of translations, rotations and reflections. In other words, two sets are congruent...

Geometry: geometry, perpendicular bisectors, oblate spheroid

perpendicular bisectors, oblate spheroid, plane triangle: To Jill From Jay Subj Spherical Triangle I m going to disappoint you right off by not answering Part 2, since i d have to brush up on selfduality first. Now for part 1, which is just a point-of view theorem with a show-and-tell proof....

Geometry: geometry, circular base, tenths place

circular base, tenths place, amnt: Dawn, Are you working with surface area or volume? To fill the base of the pier with concrete, one would need cubic yards of concrete. To find the surface area of the pier one would need square yards of concrete. I m going to treat this as a surface...

Geometry: geometry, centimeters, circumference

centimeters, circumference, multiplication: The cicumference of the circle is Pi multiplied by the diameter of the circle. Threfore if the diameter is d and circumference is C C = Pi * d Pi is the mathematical constant Approximately equal to 22/7 or 3.14 here * ...

Geometry: geometry, toolbox area, trig function

toolbox area, trig function, apothem: Indre, The picture that you describe shows a circle inside of a pentagon. Now I am assuming that the pentagon is regular. That means that all the sides of the pentagon are = and all the angles of the pentagon are =. Now put a dot at the center of...

Geometry: geometry, similar right triangles, similar triangles

similar right triangles, similar triangles, direct proportion: To Laura From Jay Subj Cast a Giant Shadow (an old movie title) The sun is so far away that for our purposes its rays come to us all parallel. If you draw a simple picture with the person and the building sharing the same vertical line,...

Geometry: geometry, triangle abc, right triangles

triangle abc, right triangles, right triangle: To Dav From Jay Subj Perimeters i found a Euclidean proof, but it only works for polygons with the same number of sides. i will do it just for our triangles A and B as before. First get a board and pound in 3 nails at the corners...

Geometry: geometry, angled triangle, square root of 25

angled triangle, square root of 25, pythagoras theorem: If a rectange has legs of 5 units and 4 units, then its diagonal will have length of square root of ( 5*5 + 4*4) units. i.e. square root of ( 25 + 16 ), = square root of (41) units = 6.4 units ( The resoning is as follows: If you draw the diagonal you...

Geometry: geometry, geometrical constructions, school mathematics

geometrical constructions, school mathematics, geoboards: Everything is important; not only in Geometry but in mathematics in general! Imagine Mathematics to be a big structure like a building with muliple stories(floors). There is the foundation and then there are many many floors, each resting firmly on the ones...

Geometry: geometry, square root of 4, geometric mean

square root of 4, geometric mean, multiplication: If you want to know about Geometric mean , it is calculated as follows. If a and b are two numbers then their geometric mean is square root of (a*b), ( * is used to indicate multiplication ). e.g. Geometric mean of 4 and 9 is square root of (4*9),...

Geometry: geometry, square root of 3, square root of 2

square root of 3, square root of 2, sides of a right triangle: These questions are based on converse of the Pythagoras Theorem. (i.e. If the sum of the squares of two sides of a trianlge is equal to the square of the third side then the trianlge must be a right angled triangle. )The method to solve these is: square...

Geometry: geometry, cot pi, regular polygon

cot pi, regular polygon, inner radius: I assume by an Octagon you mean a regular octagon, i.e. an Octagon with all its sides equal. A regular octagon can be fitted in a circle. So consider a 13 x 13 square part of your basement. ( We can t have a bigger square here.) We can fit an octagon with...

Geometry: geometry, sides of a right triangle, trig functions

sides of a right triangle, trig functions, sides of a triangle: Hung, Try to draw this triangle as described: A right triangle with the right angle on the bottom left corner and label it as C. Then straight above it ( the top left corner) is labled as A. And then horizontal from C is labled as angle B. The...

Geometry: geometry, jewlery store, area of a rectangle

jewlery store, area of a rectangle, formula for the area of a rectangle: Samantha, A store is usually in the shape of a rectangle. The formula for the area of a rectangle is A = lenght * width or A=lw. Units are always squared. Now, substitute the measures that you were given into the formula and multiply. Since you...

Geometry: geometry, meeting at infinity, professional mathematician

meeting at infinity, professional mathematician, projective geometry: Dear friends from Jordan Let me clarify one thing at the outset: I am not a professional mathematician/teacher/researcher and desipte the name of this site, I can hardly call myself an expert of this vast subject. (I have mentioned the level of questions...

Geometry: geometry, math faq, dr math

math faq, dr math, axes: If the semi-axes of the ellipse are a and b then the area is given by: Area=Pi*a*b (Here Pi is the well known mathematical constant approximately equal to 3.14) You can find formulas related to ellipse at: http://www.mathforum.org/dr.math/faq/formulas/faq.ellipse.html...

Geometry: geometry, clarification, geometry

clarification, geometry, triangle: There is no unique answer to your problem. (Unless you have missed something ?) With the given information only thing one can deduce is that the triangle must have the height = 2*21/7=6, (with respect to the side 7) This is because the area of a trianlge...

Geometry: geometry, triangle inequality, whole numbers

triangle inequality, whole numbers, good answer: Elizabeth, I m sorry to have taken so long in getting back to you. I hope you have found an answer by now. Honestly, I am drawing a blank here. I will list some theorems that I hope will help you to discover the answer for yourself. First, Theorem:...

Geometry: geometry, geometry, segment

geometry, segment: Thais, You have not provided enough information to find the length of each segment. Here are some steps that will help you to start solving the problem: 1) Draw and label the segment; 2) Set up an equation based on what you see in the diagram; 3) Solve;...

Geometry: geometry, angled triangle, different shapes

angled triangle, different shapes, perimeter: Consider a right angled triangle with sides 3,4,5. Its perimeter is 3+4+5=12 and its area is (1/2)*3*4=(1/2)*12=6 sq. units. ( since the side with lenghts 3 & 4 are perpendicular to each other .) Compare it with a square with all its sides equal to 3....

Geometry: geometry, outer rectangle, landscape contractor

outer rectangle, landscape contractor, formula x: I am getting the width of the border larger than the length of the pool! (18.41 ft. approx. ) Here are my calculations: I assume a constant width. So after building the path we will still have a rectangle. Let us say the length of the new rectangle is...

Geometry: geometry, difference of squares, using algebra

difference of squares, using algebra, mathematical expressions: Yes, you are right * stands for multiplication. I forgot to mention that. This is a convention used in writing mathematical expressions in textual format and is used quite often on the net. I agree, if your son has not yet been taught algebra, then...

Geometry: geometry, e mail address, email adress

e mail address, email adress, questioners: No, I won t send you my e-mail address. This is in the best interest of both of us. Because when you send me an e-mail your e-mail address becomes known to me. Making free account and uploading diagrams is very easy. I had some questioners in the past who...

Geometry: geometry, box measures, sq inches

box measures, sq inches, wrapping paper: (Please note: We also need to know the length of the box, which is not mentioned here. I am assuming that the box has a square shaped base, i.e. the length is the same as the width.) Amount of wrapping paper required will be equal to the total surface area...

Geometry: geometry, radius of a circle, square root of 64

radius of a circle, square root of 64, square root of 8: 1. ( What are the co-ordinates of the second point ? I assumed them to be 7 and 4 ) The radius will be equal to half of the diameter. So let us find the distance KJ d(K,J) = square root of ( [7-(-1)]^2 + [4-4]^2 ) ( ^2 means square, i.e. raised...

Geometry: geometry, ecb, midpoint

ecb, midpoint, geometry: m- midpoint is not clear to me. The m that is written in front of the symbol refers to the word measure, i.e. m ECB=125 means measure of the angle ECB is 125 degees . (In absence of the diagrams understanding and solving the problems become difficult....

Geometry: geometry, x 90, multiplication

x 90, multiplication, supplement of an angle: Let the angle be x. So its complement will be 90-x and suppliment will be 180-x But we have been given 180-x-[3*(90-x)]=5 ( I am using * to denote multiplication ) Therefore 180-x-270+3*x=5 Therefore 2*x-90=5 Therefore 2*x=95 Therefore x=95/2=47.5...

Geometry: geometry, locus of points, vertices

locus of points, vertices, vertex: Consider the side joining (0,0) & (3,0) as the base. What is the lenght of this side ? It is 3. Now with respect to this side as the base, what the height of the triangle must be so as to have area equal to 2 ? Let us assume that the height is a . Then...

Geometry: geometry, rough sketches, line segment

rough sketches, line segment, locus of points: Showing the diagram is not possible here. But consider the two conditions independenly. 1. Locus in space of points that are equidistant from 2 given points. This wll be a plane passing thru the mid point of the 2 given points and this plane will be perpendicular...

Geometry: geometry, best guess, 4y

best guess, 4y, complement: Let x be the supplement and y be the complement. We know x=4y because of the problem statement. If the supplement is four times as large as the angle s complement, then the complement is 1/4 the supplement so (1/4)x+x=180 = 5/4x=180 and x=144 and y=36. So...

Geometry: geometry, corresponding angles, parallelograms

corresponding angles, parallelograms, side angle: Let the two parallelograms be ABCD and PQRS. (Please draw a rough labelled diagram to understand the argument. ) Let AB=PQ, BC=QR, m ABC=m PQR ( Given ) Join A,C & also P,R. The triangles ABC is congruent to triangle PQR. ...(1) ( Due to Side-Angle-Side...

Geometry: geometry, geometry conjectures, corresponding angles

geometry conjectures, corresponding angles, congruent figures: Mary, Let s look at the definition of congruent figures. A congruent figure has the same shape and size. Since the sizes are the same,then the corresponding angles are congruent and the corresponding sides are congruent. Here s an example: http://www.ocean.k12.wa.us/ilwacohi/mathDpt/geometry/conjectures.htm...

Geometry: geometry, y intercept, point c

y intercept, point c, coordinates: Hello, Smiley! 1. A line drawn through the point A(4,6), parallel to the line 2y = x-2, meets the y-axis at the point B. Calculate the coordinates of B. The given line is: y = ¨öx - 1 Its slope is: m = ¨ö We want the line through A(4,6)...

Geometry: geometry, reflexive property, math faq

reflexive property, math faq, mn pr: Danielle, For proofs, start with the given information. Then use any definitions, conjectures, or theorems that fit with the section in which you are working. Also be sure to mark the diagram. This can give hints too. I won t do the whole proof but...

Geometry: geometry, isosceles triangle, right triangle

isosceles triangle, right triangle, angle c: Hello, Gary! Hope you can follow my diagram . . . Angle A is at the top: A = 70¡ã. Sides AB and AC are equal: AB = AC = 12 and: m = BC We have: angle B = angle C = 55¡ã. Draw an altitude from vertex A, cutting BC at D....

Geometry: geometry, perimeter of a trapezoid, geometry 1

perimeter of a trapezoid, geometry 1, postage stamps: 1. Cindy bought $5.00 worth of postage stamps to mail letters and postcards. If she used all of the stamps, how many letters at 29 cents each and how many postcards at 19 cents each did she mail? She must have mailed 12 letters and 8 postcards,...

Geometry: geometry, geometry question, straight segments

geometry question, straight segments, circular cone: Hello again, Max! Yes, I m sure the curved region is considered a face. A face doesn t have to be a polygon, border by straight segments. After all, the base is a circle. I suppose a baby-talk definition of a face might be: a piece we...

Geometry: geometry, spere, decimals

spere, decimals, fractions: Hello, Nick! Of course, they are different answers. 4/3 ‚ 1.33 (but they are close ) It always better to use fractions. Enter: 4 € 3 into your calculator and let the calculator carry all the decimals. The same for pi . Don...

Geometry: geometry, geometry, arrow

geometry, arrow, logic: Hello, Tom! If you re dealing with Logic, you should have been taught the meaning of the symbols. ~p ¨ ~q means: not-p implies not-q There is no answer because it doesn t ask a question. It is just a statement. Example: If it...

Geometry: geometry, geometry proofs, angles

geometry proofs, angles: Hello, Rafael! Sorry, I don t understand the problem. What is the diagram? It says the measure of angle 1 = the measure of angle 2 . Exactly where are these angles? (or does it matter?) Then it says angle 1 = angle 2 . . . Isn t that...

Geometry: geometry, perimeter of a triangle, geometry questions

perimeter of a triangle, geometry questions, area of a rectangle: Hello, Regina! You re expected to know the basic definitions and formulas. 1. The area of a rectangle is: [Length] × [Width] Therefore, the area is: 12 × 10 = 120 square feet 2. The perimeter of any figure is the distance around , the...

Geometry: geometry, adjacent angles, geometry question

adjacent angles, geometry question, right triangles: Hello, Krista! Thank you for the diagram. Let E be the intersection of the two diagonals. We re expected to know that the diagonals of a rhombus are perpendicular and they divide the rhombus into four congruent right triangles. So if angle-1...

Geometry: geometry, collinear points, qr

collinear points, qr, pq: Hello, Dominique! Since you made a diagram for me, I assume you made one for yourself. We re told that: PQ = QR = RS ... and that QS = 6. Then QR and RS are each HALF of QS. Hence: QR = 3 and RS = 3 . . . and PQ = 3 That leaves:...

Geometry: geometry, isosceles triangle, triangle abc

isosceles triangle, triangle abc, distance formula: Hello, Teresa! I will assume you know the Distance Formula. A triangle is isosceles if two sides have the same length. Use the Distance Formula to find the lengths of AB, BC, and AC. AB = ¡î[(a-0)©÷ + (b-0)©÷ ] = ¡î(a©÷ + b©÷) BC = ¡î[(2x-a)©÷...

Geometry: geometry, kh, third person

kh, third person, geometry: Hello, Luke! You re the third person to ask about the addition postulate . I ve never heard that terms used before, but it s a very simple (and obvious) concept. We have a line: (H) ----- (J) ----- (K) Label segment HJ with 5x - 9 Label...

Geometry: geometry, triangular prism, geometry 1

triangular prism, geometry 1, word base: For better understanding, simply divide the problem into 2 parts. The first part is to obtain the area of the base figiure. (Triangle in this case). And then to obtain the volume by multiplying this area by the height (15 in this case) of...

Geometry: geometry, area of a trapezoid, b2

area of a trapezoid, b2, geometry: Hello, Jessica! You left out some information. I assume they gave us the AREA of the trapezoid. Your formula is correct: A = ½(B1 + B2)H So we have: ½[(3x+1) + 5x]·x = A Then we have: ½x(8x + 1) = A And if we know what A is, we...

Geometry: geometry, segment ac, segment bc

segment ac, segment bc, 6x: Hello, Victoria! I assume you have a sketch for this problem. [B] - - - [A} - - - [C] The segment BA is labeled 2x-6 The segment AC is labeled 6x-10 The whole segment BC is labeled 24 So we have: (2x - 6) + (6x - 10) = 24 Then: 8x -...

Geometry: geometry, negative reciprocals, slope of line

negative reciprocals, slope of line, slopes: Hello, Julie! Two lines are perpendicular if their slopes are negative reciprocals of each other. This means: (1) They have opposite signs and: (2) one is the flip-over of the other. If the slope of line J is 2, then the slope...

Geometry: geometry, geometry question, flat screen television

geometry question, flat screen television, right triangle: Hello, Celeste! The problem still doesn t make sense . . . ALL of those answer could be the height. Draw a rectangle (longer than it is high). Label the length (horizontal) with L . Label the height (vertical) with H . Draw a diagonal, label...

Geometry: geometry---- area, decimal approximation, calculating pi

decimal approximation, calculating pi, decimal expression: Dear niraj shah, This is a profound question that has kept mathematicians busy for centuries. And there are many books about pi. A simple definition is that pi is the ratio of the circumference of a circle to its diameter. This ratio is sometimes expressed...

Geometry: geometry area, surface area of a triangular prism, area of a triangular prism

surface area of a triangular prism, area of a triangular prism, area of regular polygons: Polygons are 2 dimensional figures and only have areas. ( not surface areas.) To find the area of a polygon we need to join all the verices to the center. This will divide the polygon into equal sized isosceles triangles. Now area of the polygon is...

Geometry: geometry-coordinate proofs, isosceles triangle, vertices of a square

isosceles triangle, vertices of a square, central axis: Hello, Kristine! How would you find one of the vertices of a square? The known vertices are A(-1,2a), B(a,2a), C(-a,0)? I think there s a typo . . . The first one looks like it should be: A(-a,2a) Did you plot the points yourself?...

Geometry: geometry formulas, circumference formula, geometry formulas

circumference formula, geometry formulas, discovery method: Its heartening to know that your are trying to help your son. You have written: need help with tips on how to remember which formulas to use ! I think generally, you don t have to remember when to use which formula . Memory is to be taxed only to...

Geometry: geometry help, basic geometry, dimensional geometry

basic geometry, dimensional geometry, anxious parents: I find it very difficult to answer questions of a general nature. But let me try. 1. Usually difficulties in mathematics have their roots in the maths taught in earlier classes. Mathematical topics have lots of interconections and dependancies. ...

Geometry: geometry help asap, geometry help, math coordinator

geometry help, math coordinator, shortest route: (I assume the diagram is as follows: The locations of schools A,D,H,K are on the same line one below the other. Similarly the the schools B,E,I,L are on the same line one below the other. The schools A,B are on the same horizontal line. Similarly...

Geometry: geometry help, isosceles triangle, adjacent angles

isosceles triangle, adjacent angles, angle abc: Let the consecutive vertices of the rhombus be ABCD. Since one of the angles is 100 degrees, the other angle must be 180 - 100 = 80 degrees. (Since in a rhombus adjacent angles are supplimentary. This is because the opposite sides are parallel.) Now...

Geometry: geometry level 3, compression ratio calculator, nissan 300zx

compression ratio calculator, nissan 300zx, compression ratios: I don t know anything about compression ratios and Nissans. But if compression ratio of 7.8 to 1 means that 7.8 cu. in. uncompressed becomes 1 cu. in. after comression. Then 3868 cu. in. compressed should be equal to 7.8 * 3868 cu. in uncompressed But,...

Geometry: geometry locus, perpendicular bisectors, perpendicular bisector

perpendicular bisectors, perpendicular bisector, orange lines: Alice, Here s a diagram that I drew of your problem: http://img207.imageshack.us/my.php?image=rectanglepqrswithtqae7.jpg. The length of the rectangle should be twice as long as the width. You will want to measure this with your ruler. TQ is in Green....

Geometry: geometry (would love to have tonight!!!!), abc triangle, different time zone

abc triangle, different time zone, triangle def: 1. a regular polygon with an exterior angle measuring 45 degrees: use that above to answer ^ *identify the kind of polygon... Octagon *find the mesasure of each interior angle... 180 - 45 = 135 Method: First find the interior...

Geometry: geometry plane....., complementry, angles

complementry, angles, geometry: Complimetary angles are angles which add uo to 90 degrees. If the smaller angle is x degrees the larger must be x+40 degrees. So x + x + 40 = 90 Therefore 2 * x = 50 Therefore x = 25 degrees So the larger angle must be 25+40=65 degrees. Hence...

Geometry: geometry problem, intermediate algebra level, geometry problem

intermediate algebra level, geometry problem, 5w: L=5W and the Perimeter (P) is 2L+2W. Using substitution P=10W+2W which is simplified to P=12W. Substituting in the measurement of the perimeter we get 48=12W. Solving this for W gives us W=4. Go back to the equation L=5W and put in 4 for W and we discover...

Geometry: geometry problem, geometry problem, rectangular field

geometry problem, rectangular field, imageshack: Shipra, Let s start with a diagram. Visit the following URL: http://img235.imageshack.us/my.php?image=rectanglewithl40mav8.jpg Now, the key to finding the width and the area is found in the cost of the fencing. The length of the fence is actually the perimeter...

Geometry: geometry problem, intial velocity, horizontal velocity

intial velocity, horizontal velocity, geometry problem: I am sorry, but I don t know what is meant by glide ratio ? This looks like a problem in mechanics. But I will definitely try to help. The outline of the solution should be: From what I remember you can treat the horizontal and vertical (downwards...

Geometry: geometry proof, definition of similar triangles, abc triangle

definition of similar triangles, abc triangle, geometry proof: Jessica, Let s break this conditional statement down into 2 parts:hypothesis(given) and conclusion(prove). And let s draw a picture(diagram) so that we can talk about the proof in specific terms. Now it s difficult for me to draw a triangle but here...

Geometry: geometry proofs, efo, mid point

efo, mid point, geometry: Here is the outline of the argument. Since EG congruent to KH, F is mid-point of EG and J is the mid-point of KH, we get EF congruent to KJ ...(1) EO congruent to KM ( Given ) ...(2) FO congruent to JM ( Given ) ...(3)...

Geometry: geometry proofs, point of tangency, center c

point of tangency, center c, circle c: Mariah, Sorry it has taken so long to respond. You can put a few more statements into your proof. Here s how I would work it out. Given: AB is the diamter of Circle C. DF & EG are tangents to Circle C. Prove: DF is parallel to EG S: & R: stand...

Geometry: geometry proofs!, alternate interior angles, parallel plan

alternate interior angles, parallel plan, parallel state: Hello. Given: two tangents to a circle at the endpoints of a diameter. To Prove: the two tnagents are parallel. Plan: use the definitions of tangents, endpoints, diameter, and parallel to show they are parallel. I won t do the proof for you,...

Geometry: geometry: pyramid question, isosceles triangles, rough diagram

isosceles triangles, rough diagram, aob: Here is the outline of the argument. ( Please draw a rough diagram. ) Let the vertext of the Pyramid be O, Let the base be ABCD. We are given that ABCD is a square and we want to prove that the isosceles triangles OAB, OBC, OCD, ODA are all congruent....

Geometry: geometry question, geometry question, using a compass

geometry question, using a compass, construction reference: Kara, Is this a construction problem with compass and straight-edge? or just in general? If you are not using a compass and straight-edge, then use these methods. For a segment, 1) Measure the segment with your ruler; 2) Divide the measurement by...

Geometry: geometry-solid-prism and cylinders, surface area of a cylinder, area of a cylinder

surface area of a cylinder, area of a cylinder, math faq: Volume of a cylinder with base radius r and height h is given by V=Pi*r*r*h ( = base area * height ) ( Pi is the well known mathematical constant, approximately equal to 3.14 or 22/7 ) So the volume must be = 22/7*7/11*7/11*11 cu. cm...

Geometry: geometry of surface area, isosceles triangles, triangular prisms

isosceles triangles, triangular prisms, square pyramids: 1. Triangular prisms (I assume you are having a regular triangular prism. i.e. all the faces are equal, the vertical edges are perpendicular to the base. The triangular faces at the top and the bottom are equilateral.) ...

Geometry: geometry surface area, area of a rectangle, rectangular prism

area of a rectangle, rectangular prism, rough sketch: You mean the bottom is 7inches by 5 inches and the height of the prism is 9 inches ? Now if you know that the area of a rectangle is the product of its length and breadth you can easly solve this problem. Here we have to total the surface areas of 6...

Geometry: geometry that my teacher dropped on us without showing how to do it....., angled triangle, line segments

angled triangle, line segments, geometric problems: While solving geometric problems it is always better to draw a rough figure first. Let us draw a semi-cirlce with some suitable scaling factor. ( Just draw a circle and draw one of its diameters. You may take the scaling factor as 1 ft = 1/4 inch.) Let...

Geometry: geometry triangles, geometry triangles, angle bisector

geometry triangles, angle bisector, external angles: (Allow me rephrase the statement we want to prove as:) To prove that if the lengths of two angle bisectors of a triangle are equal in length then such a triangle must be an isoceles triangle. (Please draw the figure to follow the proof give below)...

Geometry: geometry-trig, dangerous rocks, intermediate steps

dangerous rocks, intermediate steps, correct solution: Your answer is wrong. How do you say is not clear to me. sin(40)/y=sin(50)/668.8 ? By which rule ? If you have sine rule in mind then 668.8 is not the side opposite to angle 50. By applying sine rule you will get sin(40)/y=sin(90)/668.8 This...

Geometry: geometry word problem, horizontal side, bottom piece

horizontal side, bottom piece, efgh: 16 ft * 9 ft = 144 ft^2 ( * denotes multiplication, ft^2 is for square ft. ) So the required square msut have sides of 12 ft each. Now you need to know the dimensions of the 2 pieces. This is not easy to describe in e-mail. But I will try...

Geometry: geometry word terms, geometry class, words with their definitions

geometry class, words with their definitions, liking: Here are some net based Geometry glossaries choose the one that fits your liking and required depth of coverage. http://www.mathleague.com/help/geometry/geometry.htm http://www.e-zgeometry.com/geoglossary/ezglossary.htm http://www.math.psu.edu/geom/koltsova/glossary.html...

Geometry: geometry, pythagorean theorum, trapazoid

pythagorean theorum, trapazoid, imaginary line: Since the top and bottom , usually referred to as bases, are parallel, you know that they are always 12 ft. apart. Imagine the triangle formed by the 15 ft. side, a portion of the 18 ft. base, and an imaginary line 12 ft. long that is perpendicular to...

Geometry: geomtry, regular polygon, radius of a circle

regular polygon, radius of a circle, graph paper: Nicole, Your problem is best done on graph paper to help make you see the problem better. Remember, regular polygon means all the sides and all the angles are congruent(=). Also, the radius of a circle is a segment with the endpoints on the center...

Geometry: goemetry proving, geometry 1, transitive property

geometry 1, transitive property, congruence: Here is the outline of the argument. ( Please note: for the exact format of proof and the correct wording of the properties, please refer to your textbook and class notes since there is no standardisation in this part of geometry. ) 1. ab=7 ...

Geometry: goemetry, goemetry, epsb

goemetry, epsb, perimeter: Jay, Remember that a rhombus has 4 equal sides. Also, remember that perimeter is the distance around an object. Since the rhombus has 4 = sides, one can multipy the side length by 4 to obtain the perimeter. So a formula for the perimeter of a rhombus:...

Geometry: graphing a line using slope and y intercept, slope and y intercept, slope intercept form

slope and y intercept, slope intercept form, x intercept: If a line passes thru 2 points (x1,y1), (x2,y2), then its slope ( m ) is calculated by using the formula m=(y2-y1)/(x2-x1) ( Please note this formula fails for line which are parellel to the Y-axis.) The point at which this line intersects the Y-axis...

Geometry: HELP!!! ANS AS QUICK AS POSSIBLE, indian mathematician, kaprekar

indian mathematician, kaprekar, 4 digits: Please note this not a question on Geometry. Since you want the help urgently. I am venturing to answer, relying only on my memory. This number is called the Kaprekar s constant. ( Named after the Indian mathematician Kaprekar who found it) The...

Geometry: Hello, I'd be very thankful..., great mathematician, approximate formula

great mathematician, approximate formula, series expansion: 1- No, there is no formula to get the exact value, but But for large value of n the approximate value is computed by using the formula n! = (2*Pi)^(1/2)*n^((n+1)/2)*e^(-n) ( I have used ^ symbol to denote exponentiation ) 2- Half of the...

Geometry: Hexagon in a Circle, isosceles triangles, regular polygon

isosceles triangles, regular polygon, apothem: Hi Jessica! Trigonometry and a formula you may or may not have learned make this problem decently quick to solve. Every regular polygon (other than equilateral triangles and squares) may be divided into a (n) isosceles triangles, where (n) is the number...

Geometry: High School Geometry, interior angles, school geometry

interior angles, school geometry, tangents: Draw a circle and a diameter to it. Let the end points of the diameter be called A & B. Draw tangents at A and B. On the tangent at A, mark any point and call it X. on the tangent at B, mark any point and call it Y. Please ensure that Y is on the same...

Geometry: High school geometry project., rectangular parallelepiped, cambridge university press

rectangular parallelepiped, cambridge university press, first year engineering: If I have understood it correctly. Then the shape is like this: Take a circular slab of 2 1/4 inch dia and 3/4 inch thickness. On this are mounted two pices ( symmetrically ), one above and one below which are almost like rectangular parallelepiped (i.e....

Geometry: Make a half sphere using pi, non ferrous metals, inches millimeters

non ferrous metals, inches millimeters, diameter radius: Stephan, I m not able to find any formulas which completely answer your question. There are several online calculators which compute surface area and some which convert gauge into inches/millimeters. But nothing turns up that takes into account gauge and...

Geometry: hard polynomials, html study, divisor

html study, divisor, quotient: You mean to say that to get the first term in the quotient which is x^2 (=x^3/x), why we did not use -1 ? Is that the question ? To get an insight in the process Consider an example of long division: Suppose you want to divide 8242407 by 201. ( The...

Geometry: hard question, maximum height, time t

maximum height, time t: (t)=-(16t^2-30t)+6 h(t)=-(16t^2-30t+225/16)+6+225/16 (by adding and subtracting 225/16 to complete the square term.) h(t)=-[(4*t)^2-2*4t*15/4+(15/4)^2]+6+225/16 h(t)=-[(4*t-15/4)^2]+(96+225)/16 h(t)=-[(4*t-15/4)^2]+321/16 Now h(t) will be maximum,...

Geometry: hard trig problem, 80f, trig

80f, trig, dips: On the graph find the point where the value become greater than 80. Note the t value (i.e. x co-ordinate of this point) Note this value as say t0, now find the next point at which the graph dips below 80, note the x-coordinate of this point and call this...

Geometry: help!!!!!!!, class books, tenth grade

class books, tenth grade, classmate: Hello Debra. About the only thing I can suggest is to practice. Do other problems as well as the assigned problems. You can always get together with another classmate to work on problems, and this will help you out. Of course, you can send any problems...

Geometry: help, perpendicular bisector, sides of a rhombus

perpendicular bisector, sides of a rhombus, trigonometric ratios: ( I have already answered this but in case you have not received the earlier answer I repeat it here. The only difference here is the perimeter is 51.225 instead of the earlier 51.224993899463.) ===========================================================...

Geometry: help me, perpendicular bisector, perpendicular bisectors

perpendicular bisector, perpendicular bisectors, mathworld wolfram: Please draw a labeld rough sketch. Let ABCD be the vertices of the rhombus. Let AC be 20 and BD be 16. Let the point of intersection of AC & BD be M. Let the lenght of each side of the rhombus be equal to a and the lengths of the diagonals be p and...

Geometry: help need for examples, abc triangle, triangle def

abc triangle, triangle def, triangle abc: I am sorry but I am unable to answer your questions. I could not relate the first 4 problems to the given figures. (And then I gave up ). Are you sure the problems are referring to the figures you have uploaded at photobucket.com ? I have a few suggestions...

Geometry: help, abc triangle, triangle def

abc triangle, triangle def, triangle abc: 1. if M A=M D=110 and M B=M E=15, then triangle ABC is___________ to triangle DEF. Reason:_____________________ Similar: Because corresponding angles are equal. As m A=m D, m B=m E, and angles of a trianlge add upto 180, So m C=m F 2. if...

Geometry: hey, vertical sides, quarter circle

vertical sides, quarter circle, left edge: Hello, Bobby! I can t type a diagram for you, so I hope you can following my directions. Draw a 150 x 100 rectangle. Make the horizontal sides 150 and the vertical sides 100. On the top edge of the rectangle, attach another rectangle ...

Geometry: I am in a high school geometry course I have 4 questions, regular polygon, geometry course

regular polygon, geometry course, acute angles: 7)I cannot help with this one. 19) Complementry angles are two angles whose sum is 90 degrees, there are different ways of setting up this equation, but an easier one is 3A+A=90 which simplifies to 4A=90. Where A is the measure of angle A, solve this equation...

Geometry: Ice Hockey, winter olympics 2006, olympics 2006

winter olympics 2006, olympics 2006, geometry teacher: I am sorry, I am not aware of winter olympics sports. But try: http://library.thinkquest.org/3885/ About science behind olympics try: http://whyfiles.org/019olympic/ http://www.exploratorium.edu/hockey/ In general thinkquest site could be of help...

Geometry: Impossible Triangle, sine and cosine law, impossible triangle

sine and cosine law, impossible triangle, right triangles: Hey Trevor, A triangle with those dimensions may not exist because the sum of the 2 shorter sides is not greater than the third. (A previous answer goes into this in more detail, I believe.) Sine, Cosine and Tangent are primarily but not solely used for...

Geometry: Increase in Volume of a Cube, volume of a cube, quadratic equation

volume of a cube, quadratic equation, sqrt: Let the sides of the cube be x units. So the volume before increasing the the side was x^3 ...(1) ( ^ stands for exponentiation, i.e. x * x * x ) After the sides are increased by 0.39 the volume of the cube will be (x+0.39)^3 ...

Geometry: Infinity, infinite series, 123456789

infinite series, 123456789, infinite number: Hello. Infinities are interesting. For example, there are an infinite number of fractions between 1 and 2. But there are an infinite number of fractions between 1 and 3. Which infinity is larger? Common sense would say 1 to 3, but infinity equals infinity....

Geometry: Interactive tools for solving the sums., geometry ii, cube roots

geometry ii, cube roots, jitendra shah: I am sorry but I am not very knowledgeable about Geometry related softwares and their market. So I really can t comment on your querries and would liked to be excused; but 1. Apparently some of the leading Geometry softwares are 1. Cabrie Geometry...

Geometry: Intermediate Algebra, polynomial expression, intermediate algebra

polynomial expression, intermediate algebra, geometry: 54x^3+128 =2*[27x^3+64] =2*[(3*x)^3+(4)^3] =2*(3*x+2)*(9*x^2-3*x*4+4^2) (Using a^3+b^3=(a+b)*(a^2-a*b+b^2)) =2*(3*x+2)*(9*x^2-3*x*4+4^2) (x+2)^3-8*y^3 =(x+2)^3-(2*y)^3 =(x+2-2*y)*((x+2)^2+(x+2)*(2*y)+(2*y)^2) (Using a^3-b^3=(a-b)*(a^2+a*b+b^2))...

Geometry: Inverse Sin/Cos/Tan and Exponents, degree mode, angle measure

degree mode, angle measure, scientific notation: Jessica, The order that you type into your calculator depends upon the type/brand of calculator that you are using. One way to know whether you are receiving a correct answer is to type in a problem for which you are certain of the answer. Also since...

Geometry: Irregular Octagon, octogon shape, inscribed circle

octogon shape, inscribed circle, square frame: As I understand it, not only the bottom 3 sides but even the top 3 sides will also be equal. Only sides which will be longer ( by 40 -15 =25 ) will be the 2 sides along the 40 sides. So for calculation the remaining sides of the octagon we need to calculate...

Geometry: inches cubed to gallons, cubic inches to gallons, metric conversions

cubic inches to gallons, metric conversions, web based resources: Please note I am not good at the FPS system of units and I hence I have used web based resources to find the answer. The volume of your fish tank in cubic inches =20*12*10 =2400 I have used the following conversion calculator to convert 2400 cubic...

Geometry: indirect proof, indirect proof, sorry john

indirect proof, sorry john, speed limit: Hello, Ralph! I m not sure how to use an Indirect Proof with this problem, but I give it a try. Suppose we think John is innocent of speeding, that he drove at 55 mph to work (at most). To drive 60 miles at 55 mph, it would take: 60/55 hours....

Geometry: Why would the inverse function..., inverse function, arc

inverse function, arc, pi: If f(x)=y Then if, g(f(x)) = g(y) = x Then the function g() is called the inverse of function f() cos(x)=y Therefore arccos(cos(x))=arccos(y) x=arccos(y) ( As arccos() is the inverse function of cos() ) e.g. if cos(x)=1/2 arccos(cos(x))=arccos(1/2)...

Geometry: judging orchids, measure of central tendency, glossary glossary

measure of central tendency, glossary glossary, hawcc: Ms. Ingrid, This is an interesting application for the geometric mean. I will be sure to share this with my students. The geometric mean is: a type of average (measure of central tendency), which is defined as the n-th root of the product of all the...

Geometry: Lateral Area of a Rectangular Prism, area of a rectangle, lateral area

area of a rectangle, lateral area, s lateral: Hi Emily! l=10 w=6 h=4 la=lateral area By rectangular solid, I take it you mean rectangular prism. The lateral area is made up of four rectangular faces. (I m assuming by lateral you re excluding the bases.) The area of a rectangle is found...

Geometry: Lenght of sides of triangle, hypotenuse of right triangle, angle abc

hypotenuse of right triangle, angle abc, angle cab: If one angle is 15 degrees then the other one must be 75 degrees. ( It is not clear which angle is 15 degrees so I assume the angle at the base is 15 degrees and the side adjacent to it is 6.4 m, i.e. If the triangle is ABC I assume BC is the base...

Geometry: Length of Legs of Hypotenuse When angles to Hypotenuse are known, mathematical calculators, angled triangle

mathematical calculators, angled triangle, cosine of an angle: You mean the angles are not standard angles like, 30,45,60 or their submultiples like 15, 22 1/2 etc. In such a case one needs to use the trignometic tables. ( or mathematical calculators or Spreadsheet programs like e.g. Excel) to know the relationship between...

Geometry: Length of a Median, median, triangle

median, triangle, two sides: Hi Shreyasi! Draw them both and measure them. At any rate, the median hitting the smallest side must be the longest because its angle of origin is formed by the two largest sides. In order to retain a closed figure, these two sides must meet far from...

Geometry: Length of a side of a right triangle, side of a right triangle, sides of a right triangle

side of a right triangle, sides of a right triangle, perfect square: Hello. The Pythagorean Theorem is to be used. a^2 + b^2 = c^2, where a,b are the sides, and c is the hypoteneuse. 28^2 + b^2 = 32^2 b^2 = 240 240 is not a perfect square. When factored, sqrt(240) = 4*sqrt(15). This is supposed to be a...

Geometry: Length vs. Width, math team, math program

math team, math program, length and width of a rectangle: Personally, I think this discrepancy is more opinion than anything else. I always thought of length being the longer dimension as more of a general convention than a rule. I think both answers should be accepted. Out of curiosity, however, I consulted a...

Geometry: Lengths of Legs given Hypotenuse, equilateral triangle, right triangle

equilateral triangle, right triangle, hypotenuse: There is a theorem which says that in a 30-60-90 triangle the side opposite to 30 degrees is (1/2)* hypotensuse and the size opposite to 60 degrees is = square root (3)/2 * hypotenuse (The proof is quite simple, if you have 2 congruent 30-60-90 triangles...

Geometry: Line-Ellipse Intersection, intersection points, alpha pi

intersection points, alpha pi, point slope form: ( I am using * to denote multiplication and ^ to denote exponentiation.) We are given a line (x0,y0,alpha) I assume that it means that the line passes thru (x0,y0) and makes an angle of alpha with the x-axis. i.e. the equation of the line is given...

Geometry: Lines and Angles, lines and angles, x 120

lines and angles, x 120, multiplication: If the angle is x then its supplement must be x/2 ( Since x=2*(x/2), I am using * to denote multiplication.) But they add upto to 180 degrees. So we have x+(x/2)=180 Therefore (3/2)*x=180 Therefore 3*x=360 Therefore x=120 degrees, (And the supplimentary...

Geometry: Lines of Symetry, axis of symmetry, diagonals of a rectangle

axis of symmetry, diagonals of a rectangle, lines of symmetry: Dear Azar, An axis of symmetry is a line such that to every point of the figure on one side of the axis of symmetry, there is a corresponding point of the figure on the other side (similarly situated and at the same distance from the axis of symmetry.)...

Geometry: Locus and Equations of Lines, line segment, locus of points

line segment, locus of points, y1: Hi Will! This is on a plane, right? First, figure out what the locus will look like. It will be a line perpendicularly bisecting the line formed by joining points F and G. You must find the equation of the line FG. a=ΔY/ΔX a=((1)-(3))/((-2)-(6))...

Geometry: Locus - Fence, foot radius, foot area

foot radius, foot area, shaded areas: Hi Liz! I can t actually draw you a diagram here, but assuming the gate has SOME width, I can tell you how to draw it. First, deal with the 5 feet from the fence. Draw the fence and shade in the 5-foot area the treasure could be in. Next, measure an...

Geometry: Locus, vertices of a square, locus of points

vertices of a square, locus of points, s center: Hey Sarah, I d say it would be the summit of a pyramid whose base vertices are formed by those of the square. The topmost (or bottommost) vertex would be in line with the square s center. The actual locus formed is thus a giant line extending to infinity,...

Geometry: Logical Reasoning - Geometry, logical reasoning, qr

logical reasoning, qr, pq: Hello, Vanessa! I assume there is a diagram for this problem. [P]---[Q]---[R]---[S]------- We are told that: PQ = QR = RS. Since QS = 6, we conclude that: QR = 3 and RS = 3. Since PQ = QR, then PQ = 3. This leaves: 20 - 3 - 3...

Geometry: Logs, logarithm function, linear transformation

logarithm function, linear transformation, real numbers: (I assume by transform you mean linear transformation) No, logarithm function is not a linear trnasformation. For a function f(x), to be a transformation it should satisfy the condition f(a*x+b*y)=a*f(x)+b*f(y) For any real numbers a, b. So,...

Geometry: law of detachment and syllogism, law of syllogism, law of detachment

law of syllogism, law of detachment, question index: Gina, Let s look at Law of detachment first. If p and (p implies q), then we conclude q. Remember both parts of the hypothesis MUST BE TRUE. So, let s look at a couple of statements. p: This toy is a truck. q: This toy has 4 wheels. Rememeber...

Geometry: about law of detachment and syllogism., law of detachment, law of syllogism

law of detachment, law of syllogism, true example: Law of Detachment ( also known as Modus Ponens (MP) ) says that if p= q is true and p is true, then q must be true. example: If an angle is obtuse, then it cannot be acute. Angle A is obtuse. Therefore Angle A cannot be acute. The Law of Syllogism...

Geometry: length of the 400m track, 400m track, hw assignment

400m track, hw assignment, semicircle: Hello, bhaskar! Could you state the original problem? I don t understand what is asked for. You said that the track is 400 meters long. Then you ask for the length of the tracks. Isn t the answer: 400 meters ? I assume that this track...

Geometry: length of sides of triangle, right angle triangle, abc 90

right angle triangle, abc 90, spreadsheet program: I assume the base is the hypotenuse. Let ABC be the triangle with AC as the hypotenuse, So m( ABC)=90, and we need to know the lengths of side AB and side BC. sin( BAC) = length BC / lenght AC Therefore lenght BC = length AC * sin( BAC) ...(1) ...

Geometry: limits, sqrt, derivative of x

sqrt, derivative of x, denominator: This question cannot be solved by the elemetary methods you are trying. This type of a limit is called the Indeterminate form . These are generally not covered in the introductory part of Limits in Calculus. This is because calculating these limits ...

Geometry: limits, approaches infinity, limit x

approaches infinity, limit x, x limit: The limits you are trying to evaluate are not simple ones. In your book they might have been dicuseed under a topic called indeterminate forms OR l Hopital s rule. This requires a knowledge of differention. So this topic might be in chapter after differentioation....

Geometry: lines and area, cartesian coordinate plane, convex quadrilateral

cartesian coordinate plane, convex quadrilateral, 3rd quadrant: 1) the line y= 3-2x contains points in how many quadrants of the Cartesian coordinate plane? y = -2x + 3, Therefore this is a straight line which intersects X - axis at (3/2, 0), Y - axis at (0, 3) makes an angle with the postive...

Geometry: list of jobs that use geometry, global positioning system, geometrical knowledge

global positioning system, geometrical knowledge, flower beds: Geometry is extensively used in all kinds of design and construction activities. Examples are architecture, interior design, furniture. Engineers/technicians working in almost all types of technologies use geometry. Physicist, Astronomers need to know...

Geometry: locus, distance formula, locus of points

distance formula, locus of points, equation of a circle: Let (h,k) be any point on the locus. Then by using the distance formula we get, sqrt((h-(-1))^2+(k-3)^2)=6 ( I am using ^ to denote exponentiation ) Now squaring both the sides we get, ((h-(-1))^2+(k-3)^2)=36 But this nothing but the equation of...

Geometry: locus, angle bisector, point of intersection

angle bisector, point of intersection, problem states: When the problem states sides , do they mean both or what ? Yes, at least that is what I understand from the statement. Now points equidistant from both the sides of an angle are points on its bisector. But we want to find the locus of points equidistant...

Geometry: locus, perpendicular bisector, line segment

perpendicular bisector, line segment, locus of points: Hello, Will! The locus of point equidistanct from R and from S in a given triangle RST. What is the locus? The set of points equidistance from two points, R and S, is the perpendicular bisector of line segment RS. The locus of...

Geometry: locus math problem, 3 dimensional objects, math problem

3 dimensional objects, math problem, locus: (First the units part of the question.) Some of the commonly used units of distance are centimeter, inch etc. Now since none of these units have been specifically mentioned in the question, it means you have the freedom to choose any one that is convenient...

Geometry: locus, diameter of a circle, variable point

diameter of a circle, variable point, locus: Here is the solution: (Please, ignore the previous reply) Let Q(h,k) be any point on the locus. So the equation of the line passing thru this point will be y=(k/h)x ...(1) The point P(x,y) is on this line so it satisfies (1) By the definition...

Geometry: log equations, numerator, change of base formula

numerator, change of base formula, denominator: When you are using change of base, which is the new base you are taking ? Since nothing is mentioned I suppose you are taking base as 10. But this is of no help in simplifying the calculations here. Try taking the new base as 2 So the numerator will...

Geometry: logarithims, contenets, cell a1

contenets, cell a1, spreadsheet programs: Log is nothing but the exponent. e.g. a^x = y Then log y to the base a is x It is a common practice to use the base as 10. (At a slightly advance level you will be told that the the constant e is preferred over 10. You will get exposed to...

Geometry: logarithims, logarithm, different ways

logarithm, different ways, logs: Hello Paul. First you have to know the following identity: x^a=y = log[x]y=a, where [x] is the base of the logarithm Using this, you get log[x]112=5.2 log(112)/log(x) = 5.2 (these logs are now in base 10) log(112)/5.2 = log(x) 10^(log(112)/5.2)...

Geometry: MATH FORMULA, calculating volumes, math formula

calculating volumes, math formula, geometric shapes: I am sorry but the question is not clear to me. cubic yards is just a unit of volume. There are different formulas for calculating volumes of different geometric shapes. ( Just like there are different formulas for calculating areas of different geometric...

Geometry: MATH FORMULA, regular polygon, square root of 3

regular polygon, square root of 3, radius of a circle: If each side is a then the circumradius for an equilateral triangle will be = a /[square root of (3)] ( The general formula for a regular polygon with n sides is Circumradius = a * cosec(alpha/2)*(1/2), Where, alpha = 360 / n ) ...

Geometry: Math, tenth game, basketball games

tenth game, basketball games, game average: Let the scores in the 6th, 7th, .. etc. games be denoted by s6, s7,.. respectively. Let the average scores after 5th, 9th, 10th games be denoted by a5, a9, a10 respectively. Let the total score after 5th, 9th, 10th games be t5,t9,t10 So the given...

Geometry: Math for Elem Ed, outer diameter, inner diameter

outer diameter, inner diameter, volume of a cylinder: Hello, Diane! This requires knowledge of the geometry of a circle and the volume of a cylinder. I assume that the rope will completely fill the spool from a radius of 10 cm to a radius of 30 cm. [Note that the spool is 100 cm long.] The...

Geometry: Math - Geometry Word Probelm, swimming pool cover, area of a rectangle

swimming pool cover, area of a rectangle, geometry problems: With geometry problems it is helpful to draw pictures. Draw a picture of the pool that is 5 meters long and 3 meters wide. These dimensions mean that it is a rectangle. The per square meter gives us the clue that we are talking about area. The area of...

Geometry: Math Homework, math homework, complement of an angle

math homework, complement of an angle, complements: Hello, Kaitlyn! First, we have to know that complement and supplement mean. Two angles are complements if they add up to 90°. Two angles are supplements if they add up to 180°. Let X = the angle. The complement of this angle is: 90 - X (Do...

Geometry: Math Question, equation of an ellipse, math question

equation of an ellipse, math question, line thanks: Hello, Mohammed! I suppose there are many ways to do this. Here s one that I just came up with . . . The equation of an ellipse is: x©÷/a©÷ + y©÷/b©÷ = 1 Let s suppose that a b. The focal distance is given by: c = ¡î(a©÷ - b©÷) And...

Geometry: Math Question, minor axis, major axis

minor axis, major axis, math question: I would be glad to help! E = sqrt(1 - [b^2/a^2]) Where, E = eccentricity b = length of semi-minor axis a = length of semi-major axis If you look at the equation for eccentricity, the only time E can equal 1 is when b^2/a^2 equals 0. That would produce...

Geometry: Math, diophantine equation, school syllabus

diophantine equation, school syllabus, unexpected guests: Suppose initial plan was to serve the guests x sandwitches each, and after the arrival of 4 new guests, the host reduced the number of sandwitches by 2, So that the 15 guests now will receive y sandwitches each, We get the equation 11x - 2 = 15y ...

Geometry: Maths Problem, square root of 1, conversion factor

square root of 1, conversion factor, rectangular room: Damien, I confirmed that a 30% increase over 1462 sqft. yields 1913.60sqft. Next, the ratio of the original sides of what I am assuming is a rectangular room is 46/32 = 1.4375 (length/width). There is a theorem which states that if 2 figures are similar,...

Geometry: Maths Problem, square root of 1, correct shape

square root of 1, correct shape, x square: I am extremely, sorry But please ignore the answer sent to you earlier; as I found a flaw in it. The revised answer is as follows: Yes your answer of the revised area is correct. To maintain correct shape, one needs to keep the ratio of new length and breadth...

Geometry: Measuring height of flagpole, similarity of triangles, measuring height

similarity of triangles, measuring height, halyard: I am sorry but I haven t understood the question fully. I assume you have a pole whose length you want to measure by measuring the length of its shadow. You know your height and the length of your shadow. By similarity of triangles: Length of the pole...

Geometry: Medians, triangle abc, centroid

triangle abc, centroid, bk: We are given that K is the centroid of the triangle. Since centroid divides the medians in the ratio of 2:1 Therefore If FK is 3.40 Then BK must be 2 * 3.40 = 6.80 If EK is 1.63 Then AK must be 2 * 1.63 = 3.26 Hence AK + BK must be 3.26 + 6.80...

Geometry: Mid-point theorem, midpoint theorem, equilateral triangle

midpoint theorem, equilateral triangle, overview plan: To Jasleen From Jay Subj A three-sided plot. i m sorry Jasleen but i cannot answer your question properly for two reasons: 1. This is a simple tect editor and i can t draw in it. 2. i don t know what the Midpoint Theorem...

Geometry: Min and max of a volume, surface area of a cube, surface areas

surface area of a cube, surface areas, cubes: (I feel the question is not very clear. Can we assume that the dimensions of the cubes must be intergers ?) If that is the case, then we need to find 2 integers such that their cubes add up to 432. Let us write done all the cubes upto 432 No. Cube...

Geometry: math, lateral surface area, math faq

lateral surface area, math faq, mathforum: LSA & TSA are not standard abbreviations. But since you have mentioned areas etc. My guess is they stand for LSA - Lateral Surface area TSA - Total surface area One very good web page which will give you some of the useful formulas for Lateral & total...

Geometry: math, irrigation ditch, inner rectangle

irrigation ditch, inner rectangle, outer rectangle: (a) Let the width be x feet. So the lenght must be 2x-2 x*(2x-2)=420 2x^2-2x-420=0 x^2-x-210=0 x^2-15x+14x-210=0 x(x-15)+14(x-15)=0 (x-15)(x+14)=0 Therefore (x-15)=0 OR (x+14)=0 Therefore x=15 OR x=-14 But x is the width, so it can t be negative....

Geometry: math, trapezoid, factor x

trapezoid, factor x, common factor: Trapezoid s area = 1/2*6*(2x-1+x+7) ( 1/2*(sum of the bases)*height, As if you join to digonally opposite points you get 2 triangles with same height but different bases. ) = 3*(3x+6) = 9x+18 Rectangle s...

Geometry: math, minor arc, length of arc

minor arc, length of arc, area of a sector: Let the radius of the circle be r. Let the central angle of the sector be theta. So the area of the circle will be Pi*r^2 ( Pi stands for the well known mathematical constant approximately equal to 3.14. ^ denotes exponentiation. ) Now 360 degree...

Geometry: math, dimesions, quadratic equation

dimesions, quadratic equation, sqrt: Assume the width is x feet. Hence the length will be x+2. So the area will be x*(x+2) So since the total area of the room is 90 feet. Therefore x*(x+2)=90 Therefore x^2+2*x-90=0 (If a quadratic equation is of the form a*x^2+b*x+c=0, then its solutions...

Geometry: math, algebraic method, maximum value

algebraic method, maximum value, turning point: The minimum value of x^2 is 0, this is attained at x=0. So the maximum value of -x^2 will be 0 when x=0. So the maximum value of -x^2+10 will be 10 when x=0. So the co-ordinates of turning point will be (0,10). There is no general purely algebraic method...

Geometry: math, exponential function, brackets

exponential function, brackets, confusion: The source of confusion is the order in which oprations are to be performed, There is a difference in the value of -3^2, if it is interpreted as (-3)^2 then it will be 9 it wiil be -(3^2) otherwise ( So it will work out to -9) The best way...

Geometry: math, calculator spreadsheets, rate of depreciation

calculator spreadsheets, rate of depreciation, formula v: V=C(1-r)^t Therefore 6000=24000*(1-r)^5 Therefore 1/4=(1-r)^5 Therefore (1/4)^(1/5)=(1-r) (By taking 5th root of both the sides) Therefore r=1-(1/4)^(1/5) (1/4)^(1/5) can be computed using 1. calculator/Spreadsheets or ...

Geometry: math, pi radians, arc length

pi radians, arc length, degree 54: The formula is s=r*(theta) Where s is the arc length, r is the radius and theta is the angle corresponding to the arc. But in this formula the angle must be in a unit called radians. So in order to use the formula we need to convert 54 degrees into...

Geometry: math, 3rd quadrant, first quadrant

3rd quadrant, first quadrant, angled triangle: No the answer you have got can t be right as sin and cos values can never be more than 1 or less than -1. We are given sinx=8/17, But sin^2(x)+cos^2(x)=1 ( ^ is for exponentiation, so sin^2(x) is sine squared x ) Therefore 64 / 289 + cos^2(x)...

Geometry: math, population increase, populaton

population increase, populaton, math: Let us find the current population i.e. t=0 P(0)=954525.6668721 * 1.0212854293573^(0) =954525.6668721 * 1 =954525.6668721 Now find the population after 1 year P(1)=954525.6668721*1.0212854293573^(1) =974843.155524036 So to calculate...

Geometry: math, vertices of a triangle, upper case letters

vertices of a triangle, upper case letters, area of triangle: Area of a triangle with vertices at a(0,6), b(3,0) and c(11,0) Method 1: If the vertices of a triangle are (x1,y1), (x2,y2) and (x3,y3) then the area = absolute value of((1/2)*[x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)]) ( * denotes multiplication) If you...

Geometry: math, th root, 3x

th root, 3x, graphs: Try some typical points for which calculations should be easy to make manually. e.g. x^(1/4) means taking the 4 th root whereas x^(4) means the 4th power. Now if x=16, which is the 4th power of 2, so 3x^(1/4) will be 3(16)^(1/4) i.e. 3*2 =6, where as...

Geometry: math, logarithm function, log functions

logarithm function, log functions, log2: I am not clear about your comment: Here is the multiple choice reduced to the harder ones.4,2, and 10 are small numbers. I feel the if the numbers are small then it is easier to make the calculations mentally. Of course I assume the numbers 4,2,10...

Geometry: math, first quadrant, angled triangle

first quadrant, angled triangle, line segment: The point P must be in the first quadrant if OP is making an angle of 30 degrees with the X-axis. Let P have the co-ordinates (x,y). From the point P drop perpendicular on the X-axis. Let the foot of the perpendicular be Q. So the co-ordinates of Q will...

Geometry: math, angle aob, isosceles triangle

angle aob, isosceles triangle, cap alpha: Join CA and OA. Let angle ACO be alpha . Now since triangle OCA is an isosceles triangle, Angle CAO is lso alpha . In triangle CAP we have m(angle ACP)= alpha m(angle CAP)= alpha + 90 (Since OA perpendicular to AP) ...

Geometry: math, cos theta, unit circle

cos theta, unit circle, agle: Note the point is on the unit circle so after rotation also it will remain on the unit circle. Now if a point is on the unit circle and the line joining the origin to the point makes an angle of theta, then its co-ordinates are cos(theta) and sin(theta)....

Geometry: math, algebra concepts, tangent ratio

algebra concepts, tangent ratio, trignometry: Of course the rule is about signs only, why mix signs with values. Your book says if secA 0 then cosA o and then you give sec and cos values for A=5, which you will notice are both greater than zeros. So where is the problem ? It is exactly as your...

Geometry: math, cos theta, unit circle

cos theta, unit circle, quadrant: Without doing detailed calculations we can say that the answer is 240 degrees. Since the point is on the unit circle its x-co ordinate must be cos(theta) and y-co ordinate must be sin(theta). Since both sin(theta) and cos(theta) are negative we know...

Geometry: math, multiple choice, expression

multiple choice, expression, math: The question is asking you to compute the log value of sqrt(6) but the base is not given. So the data given is in sufficient. We have 2 unknowns and one equation. Now since you say the answer is 1.935, the modified question becomes, which number when...

Geometry: math, math faq, dr math

math faq, dr math, mathforum: 1. cos(90-x)=sin(x) Please note the above is applicable to 90 degrees and not for 180 degrees. 2. If you want a similar rules for 180 degrees, then they would be cos(180-x)= (-1)*cos(x) sin(180-x)=sin(x) tan(180-x)= sin(180-x)/cos(180-x)...

Geometry: math, sine law, exercises

sine law, exercises, triangle: Using the sine Law sin A / a = sin W / w ( = sin L /l) Therefore (1/4)/28=(3/7)/w Therefore w=(3/7)*4*28 =3*4*4 =48 Unless you have an exam round the corner, while you are getting introduced to the concepts, spend sufficient time on understanding...

Geometry: math, co ordinates, mid point

co ordinates, mid point, midpoint: Let the co-ordinates of B be (x,y). So by mid-point formula (6+x)/2 = 3 Therefore 6+x = 2*3 ( * denotes multiplication ) 6+x = 6 x = 0 ...(1) Also (8+y)/2=2 Therefore (8+y)=2*2 Therfore 8+y=4 Therefore y=-4 ...(2) Thus the co-ordinates...

Geometry: math, cos theta, complex fraction

cos theta, complex fraction, numerator: Yes it is indeed simple. All you need to to do is try a bit harder, and use paper and pencil rather than trying to solve the problem mentally. Multiply the denominator and numerator by cos(theta) [cos(theta)+1]/[1+{1/cos(theta)}] =cos(theta)*[cos(theta)+1]/...

Geometry: math, algbra, cos theta

algbra, cos theta, lcm: I really admire your efforts, but you should make several attempts before you ask others. Because in the end the answer doesn t matter but the number of attempts you make forces you to think more about the ideas involved and that really helps in the long...

Geometry: math, time duration, speed time

time duration, speed time, car travel: Let the beach be at a distance of x miles. For conveniece let us do all the calculations in minutes. So the total time for the round trip which is 1 hr 22.5 minutes is 60 + 22.5 = 82.5 minutes. ...(1) Also the speed of the bike is 9 miles /...

Geometry: math, square roots, siple

square roots, siple, pi: sin(pi/6)=1/2 tan(pi/4)=1 Hence the result 0, pi/6, pi/4, pi/3, pi/2 are standard angles and you should remeber the sin,cos, tan values of these angles One siple way to remember the sine values is write (0 to 4) 0 1 2 3 4 Then divide each...

Geometry: math, spread sheet program, decimal point

spread sheet program, decimal point, 60 minutes: It is not clear to me,how you find the degrees in this case. If you are using trignometric tables then I don t see any problem. If you are using a spread sheet program. You might have got the answer in degrees with some value after the decimal point....

Geometry: math, math

math: replacing cos(2 theta) by (1 - 2*sin^2(theta)) We get sin(theta)+3*(1-2*sin^2(theta))=1 Therefore sin(theta)+3-3*2*sin^2(theta)=1 Therefore 6*sin^2(theta)-sin(theta)+1-3=0 Therefore 6*sin^2(theta)-sin(theta)-2=0 Therefore (after factorising) (2*sin(theta)+1)(3*sin(theta)-2)=0...

Geometry: math, algebraic simplification, math 5

algebraic simplification, math 5, approximate values: Since the numbers 5,7 and 12 don t have any common factors, further algebraic simplification is not possible. So we need to take the approximate values and do the further calculations. 5^(1/2)=2.236067977 7^(1/2)=2.645751311 12^(1/2)=2.645751311 This...

Geometry: math, square root of 100, math faq

square root of 100, math faq, dr math: (The formula is based on Pythagoras Theorem.) Suppose the the lengths of the sides are l & b, then the diagonal is squre root of ( sum of the squares of l & b ) i.e. sqrt(l*l+b*b) ( I have given the exact formula for spreadsheets. Here * denotes...

Geometry: math, physical equations, lockheed martin

physical equations, lockheed martin, vegetable garden: To Angel From Jay Subj Veg garden Hoping that the garden is a rectangle: A rectangle has two sides equal to the length (20 ) and two sides equal to the width (15 ). We just add them up to get the perimeter (distance...

Geometry: math, similarity of triangles, math c

similarity of triangles, math c, acb: Sorry, I am not clear about this and hence can t explain. Is ther one more line which you have forgotten to describe ? Or there are just 3 lines joining AB,BC and AC ? one of the commonest area where proportions enter in geometry in similarity of triangles...

Geometry: math, elementary algebra, suppliment

elementary algebra, suppliment, multiplication: (I assume we are permitted to use elementary Algebra.) Let the angle be x , so its suppliment must be 180-x ( since an angle and its suppliment must add upto 180) But we are given that the suppliment is equal to 2*x+12, So, we have 180-x=2*x+12...

Geometry: math, cubic centimeters, cube 50

cubic centimeters, cube 50, prims: Hello, Gema! The wording is confusing . . . I don t understand base-10 blocks or that she used 50cm cubes to make the base . Is a cube 50 cm on its edges? Then how many were used in the base? Ten? Is a cube 10 cm on its edges? ...

Geometry: math, right triangle, straight highway

right triangle, straight highway, ac 8: Hello, Doris! If you make a sketch and a draw a few extra lines, the answer is quite clear. Draw a horizontal line; left end is A , right end is B . The midpoint is O . Label OA = OB = 6 From A , draw a line straight down to C ; AC =...

Geometry: math, similarity of triangles, java elements

similarity of triangles, java elements, undefined terms: I am not aware of this statement. But if you allow me to guess: This should mean something like If x=y and a=b then x/a=y/b This is true because x=y, Therefore x/a=y/a ...(1) (Assuming a not equal to zero) But a=b, Therefore y/a=y/b...

Geometry: math, math line, 4r

math line, 4r, 8r: The lengths of the 2 tangents drawn from a point P must be equal. (This can be proven easily. If O is the center of the circle, then draw OP, OA & OB. Now prove that triangles OAP and OBP are congruent. They have a common side OP, OA & OB are both...

Geometry: math, rectangle, gh

rectangle, gh, multiplication: Theorem: If two chords of a circle intersect inside or outside the circle when produced, then the rectangle formed by the two segments of one chord is equal in area to the rectangle formed by the two segments of the other chord. Using this theorem...

Geometry: math, simplest form, square root

simplest form, square root, expression: | a + ib | = square root of (a^2+b^2) (Here ^ denotes exponentiation, so a^2 means a squared ) Therefore |3-sqrt(-12)|=|3 - sqrt(-1*12)| =|3 - i*sqrt(12)| =|3 - i*sqrt(4*3)| =|3 - i*sqrt(4)*sqrt(3)| ...

Geometry: math, hypotenuse of a right triangle, altitude to the hypotenuse

hypotenuse of a right triangle, altitude to the hypotenuse, angled triangle: (If the 2 segments of the hypotenuse measure 9 and 16 the length of the hypotenuse must be 9+16=25 inches and not 15 inches as you have stated ? I have assumed it to be 25 inches in the following calculations ) Theorem: In a right-angled triangle,...

Geometry: math(geomentry), area of a rhombus, perimeter area

area of a rhombus, perimeter area, math faq: You mean How do you find the perimeter & area of a rhombus ? If each side is a then the perimeter (P) is P = 4*a If the lengths of the diagonals are p and q then the area (K) is given by K=(1/2)*p*q You can find commonly used formulas related...

Geometry: math -geometry, isosceles triangle theorem, geometry triangles

isosceles triangle theorem, geometry triangles, math geometry: Margaret, Let s remember a few definitions and theorems to help us with this problem. Isosceles Triangle is a triangle with 2 equal sides. Isosceles Triangle Theorem states that if 2 sides of a triangle are congruent then the opposite angles are congruent....

Geometry: math ratio, 12a, perimeter

12a, perimeter, triangle: Hello, Deirdrie! The sides are in the ratio 3:4:5 They must have lengths of: 3a, 4a, 5a ... for some number a. The perimeter is 204 cm, so we have: 3a + 4a + 5a = 204 and we have: 12a = 204 ¨ a = 17 Therefore, the three...

Geometry: math/science, word accuracy, precision and accuracy

word accuracy, precision and accuracy, accuracy and precision: No I am not quite sure. This kind of questions are always troublesome. But if I were in your situation I would do exactly as you are trying. i.e. If there are terms A and B and we are claiming them to be different then we should have something of type...

Geometry: math/trig, slope of line, slope of a line

slope of line, slope of a line, spreadsheet program: Slope of line passing thru (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1) So the slope of the given line is = (10-7)/(8-4)=3/4 Now the slope of a line making an angle of (theta) with X-axis is also given by tan(theta) So we have, tan(theta)=3/4 So theta=tan^(-1)...

Geometry: math, square root of 3, b1 b2

square root of 3, b1 b2, unit vectors: I do not know the method of finding answer to your question. But if converting the above equation from the parametric form to the regular form is acceptable then please read furhter. The parametric form that I am familiar with is : if a line passes...

Geometry: mathematics, polygon names, math faq

polygon names, math faq, dr math: Please visit the following web page and links given there for a proposed scheme of naming polygons. This by Prof J H Conway who is a leading mathematician. http://www.mathforum.org/dr.math/faq/faq.polygon.names.html Of course if a figure is not used...

Geometry: mathematics(geometry), chris budd, space geometry

chris budd, space geometry, relativity 3: Dear friends, Please note I am not a professional teacher of Mathematics. 1- I don t know which particular theorem is called the Theorem of Circle , would you please let me know the statement of the same. 2- I am sorry but, I don t...

Geometry: mathematics, line segment, y2

line segment, y2, y1: Suppose the points are C and D which divide AB into three equal parts. This means C divides AB in the ratio of 1:2 and D divides AB in the ratio of 2:1. The co-ordinates of a point which divides a segment with end co-ordinates (x1,y1) and (x2,y2) in...

Geometry: maths-ellipse, minor axes, integral calculus

minor axes, integral calculus, formulae: There is no staraight forward formula. But you can calculate the area using integral calculus. This is done for convenience by converting the values to polar co-ordinates. Visit the following page for derivation: http://mathforum.org/library/drmath/view/53635.html...

Geometry: maths -geometry, adjacent angles, 9x

adjacent angles, 9x, q1: What is the sum of this 2 angles supposed to be ? ( It should be 180. ) So, 5x-4+4x-5=180 Therefore 5x+4x-4-5=180 Therefore 9x-9=180 Therefore 9x=180+9 Therefore 9x=189 Therefore x=21 So the angles must be 5*21-4 and 4*21-5 So the smaller angle...

Geometry: maths, geometry questions, correct answer

geometry questions, correct answer, maths: 1. Since 3x-5 is not zero when we substitute, x as 10. We can find the limit by simply calculating the value of (2x+5)/(3x-5), when x=10. So the limit will be 1, ( [2(10)+5]/[3(10)-5] ), i.e. (25/25=1). 2. Since when we substitute x=3...

Geometry: measurements, gallons to quarts, qt 5

gallons to quarts, qt 5, gal 4: Benita, To divide 11 gal 1 qt by 5, first convert the gallons to quarts. There are 4 qt. in a gallon. 11 gal * 4 qt/1 gal = 44 qt. Notice the gallons cancel out. Now, 44 qt. + 1 qt. = 45 qt. Now divide. 45 qt./5 = 9 qt. Keep asking questions!...

Geometry: mid point theorem, minimum wastage, similar triangles

minimum wastage, similar triangles, midpoint theorem: To Khubru From Jay Subj Desperate real-estate deal. This is a 1st-semester calculus problem, once we get all the area formulas set up. That is, it s not hard if we stick to the way it appears in the homework problems ! i ll explain......

Geometry: minimum area, bottom curve, integral problems

bottom curve, integral problems, integral symbol: Jeff, That info. helps! Okay, from your description the graph of y = cos x is from -pi/2 to pi/2 on the x-axis and from 0 to 1 on the y-axis. I can not determine the x-values or y-values of the rectangle from the description. I see 3 shaded...

Geometry: mostly surface area and volumn, lateral surface area, corresponding angle

lateral surface area, corresponding angle, volume of a cylinder: 1. B 2. B, AB parallel to CD, So slope of AB = slope of CD So (-6-4) /(x-4) = (6-2) / ( 3-5) Therefore -10/(x-4)=4/-2 Therefore -10/(x-4)=-2 Therefore -10=-2*x+8 Therefore -18=-2*x Therefore x = 9 ...

Geometry: NEED HELP!!!, vocabulary cards, theorems and postulates

vocabulary cards, theorems and postulates, study strategies: Aaron, It s hard to answer this question without knowing what your study strategies and habits are now. Geometry is very visual and yet it also uses a lot of vocabulary. I suggest that students take the time to make vocabulary cards. Be sure to put...

Geometry: Nearest Square Centimeter, square centimeter, multiple choice questions

square centimeter, multiple choice questions, cm 2: I am sorry but the question seems to be incomplete to me. Is there an accompanying diagram ? Anyway, it appears that you are supposed to find some area and the answer you get may not be exactly equal to the choices given. So you are supposed to round it....

Geometry: n-gons, consecutive angles, other additional information

consecutive angles, other additional information, alternate angles: I am sorry, but the question is not clear to me. But I have made some assumptions and tried to solve it. 1. You say you are shown a part of hexagon ? In that case it should have 6 sides, as only polygons with 6 sides are called hexagons. (...

Geometry: i need to find a name of a famous mathmatician, famous mathmatician, andrew wiles

famous mathmatician, andrew wiles, famous mathematicians: Of course I can give you names of several famous mathematicians. Here is one Prof Andrew Wiles You can get details of him at the following link http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Wiles.html (Please note: The link above is getting...

Geometry: i need help please!!!, finding the area of a circle, angled triangle

finding the area of a circle, angled triangle, outermost circle: Let the radius of the circle be r. So the cicumference of the outermost circle (length of rope) must be 2*pi*r. (Here pi denotes the well known mathematical constant approximatly equal to 3.14) Now the circumference of the next circle(length of rope)...

Geometry: I need help with a question, could you help me., quadratic formula, question the question

quadratic formula, question the question, multiplication: Hello, John! The equation seems to be: (2x)(4©÷x)/(2 - 2x) - 128 = 0 Then we have: 32x©÷/2(1-x) = 128 ¡æ 16x©÷/(1-x) = 128 And: 16x©÷ = 128(1 - x) Divide by 16: x©÷ = 8(1 - x) We have the quadratic: x©÷ + 8x - 8 = 0 This...

Geometry: i need help, theorems

theorems: Hello Vin Landolfi. The only thing that I can suggest is practice. Try to memorize all the theorems, and try to apply them to do extra problems. Any problem you have, you can send my way and I can check to see if you ve done it correctly. Steve ...

Geometry: I need to know how to solve something like this., weird shape, geometric problem

weird shape, geometric problem, symmetry: Looks like the same question was sent twice. Here is an additional suggestion. Try to use symmetry in reducing the comlexity of the area. e.g. is it possible to fold the figure in some way so that it becomes easier to find the area of this new shape,(...

Geometry: need these to study and help me with, similar polygons, corresponding angles

similar polygons, corresponding angles, equal angles: Hello Brandon, 1. Both blanks are congruent. Congruent means that all corresponding angles and sides are equal. 2. Length. Similar polygons have equal angles, but unequal sides. 3. Congruent. 4. The wording of this is incorrect. Two right...

Geometry: the notation for the length..., lower case, pq

lower case, pq, comma: l(PQ) (i.e. lower-case L followed by PQ in brackets.) But this differs from Text-Book to Text-Book, some books simply use PQ. Some authors also have a notation to denote this as distance between the points P & Q, which is written as d(P,Q). (Please...

Geometry: Oconstag, interior angles of a polygon, regular polygon

interior angles of a polygon, regular polygon, math math: Donald, The first thing we need to know about your octagon is whether it is a regular polygon or not? A regular polygon is a polygon with all sides congruent AND all angles congruent. If and only if this is a regular octagon, then we can use a formula...

Geometry: Octagon, building a deck, diameter

building a deck, diameter, radius: Hello. There is a formula to find the length. It is 1/2 * sqrt(4 + 2 * sqrt(2)) * s = R, where s is the length of the side, and R is the radius of the circle that is circumscribed around the outside of the octagon. In your problem, R = 14 feet....

Geometry: Orientation in the plane..., odd number, reflection

odd number, reflection, reflections: Hello. The first reflection will produce the objects reflection. A second can put it back, so the evens can be an identity. But because after each even number reflection, the object still has it s original orientation. So each successive reflection (all...

Geometry: octagon, sided polygon, regular polygon

sided polygon, regular polygon, pi radians: I am sorry the question is not clear to me. What is meant by 9 feet by 9 feet equal sided octagon ? I assume that you have a 9 feet by 9 feet square and you want to fit a regular octagon inside it. Now how do you wish to fit this octagon inside the...

Geometry: octagon, square root of 2

square root of 2: The length of the side of an octagon is equal to the length from flat side to flat side divided by (1+sqrt[2]). So if the distance from side to side is 10, then the length of each side (in a regular octagon) would be 10/(1+sqrt[2]). Where sqrt[2] means the...

Geometry: octagon, isosceles triangles, vertex angle

isosceles triangles, vertex angle, astronomy hobby: Hello, Bob! I believe we must use trigonometry for this one. Try to follow my sketch. I have a regular octagon; its diameter is 8 feet. Draw radii from the center to the eight vertices. We have eight identical isosceles triangles. Their equal sides...

Geometry: octagon, foot piece, thanks in advance

foot piece, thanks in advance, floor plan: Hello Steve. The wording of this question doesn t make much sense. The equal distance of the eight sides... the total divided by 8? Also, do you mean 9 square feet? Like, 9 feet by 9 feet? If so, do you want the octagon maximally fit into the 9 square...

Geometry: oil drum, oil drum, gallon oil

oil drum, gallon oil, tiny fraction: Hello, Sheila! We need more information . . . like the dimensions of the drum. If the oil drum is 8½ inches high, the drum is full . . . we have 280 gallons. If the drum is 100 feet high, then 8½ inches isn t very much. We d have a...

Geometry: oval arc, circumference of an ellipse, arc length

circumference of an ellipse, arc length, minor axis: Oval shape is called ellipse. The total arc length around a shape is called its circumference. You can find the formula for circumference of an ellipse at: http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html Let us use the 3rd formula given at the...

Geometry: Parabola, vertx, cordinates

vertx, cordinates, co ordinates: Since the curve passes thru (3,-5), substituting x=3 & y=-5, We get: -5 = a . 3^2 + c ( Here 3^2 means 3 (squared) ) So -5 = 9.a + c . . . (1) We know the vertex of a parabola x(squared)=4ay i.e. x^2=4ay is at (0,0). So let us try to...

Geometry: Parallelogram, internal angles, pqrs

internal angles, pqrs, pa 1: Hi Terry! Something is wrong here. How does SQR exist, and how is it congruent to QPS? You meant SRQ, right? And in the last hypothesis, what is A? Either way, I was able to find this to be a parallelogram because the OPPOSITE INTERNAL ANGLES ARE...

Geometry: Parallelograms, adjacent angles, adjacent angle

adjacent angles, adjacent angle, parallelogram: Because in a parallelogram adjacent angles are supplimentary,( i.e. they add upto 180.) So when one of the angles is 90, degrees its adjacent angle must be 180-90 = 90. We use the same argument to prove that the third angle must also be 90, since it is...

Geometry: Parallelograms - Planes, shape thanks, wingtips

shape thanks, wingtips, parallelogram: Azza, I must say that my response will be no better than your teacher s. Furthermore, I also don t know if you mean Cartesian-- or aeroplanes. An aeroplane, from a certain angle, can be perceived as a parallelogram if its tail is one vertex, the nose...

Geometry: Parallelograms, 4 generations, problems solutions

4 generations, problems solutions, test tomorrow: I am sorry but 1. I prefer to solve the problems rather than setting them. (solving problems is generally much easier!.) 2. Time is too short. 3. The topic is too vague. What sort of problems you are interested in ? At what lelvel ? Are you interested...

Geometry: Parametric equations and integration limits, parametric equation, involute

parametric equation, involute, parametric equations: To Mark From Jay Subj The dreaded Cow Curve. You gotta envy them cows, all they have to do is to eat up the nightshade. This is gonna be a little tedious, so fasten your seatbelt. To avoid some irrelevant algebra i assume that...

Geometry: Parrallelogram PQRS clarfying- Due Thursday, pair of vertical angles, interior angles

pair of vertical angles, interior angles, similar triangles: Gus, This is mostly an exercise in Algebra. Since you have the steps, I will try to tell you the reason for each step. I ve copied the steps from the website that you gave me.And I m numbering the steps.The reasons will be numbered for the steps ex: R1...

Geometry: Parts of an Angle, measuring angles, line segments

measuring angles, line segments, point of intersection: An angle has 3 parts. Two intersecting lines/line segments and the point of intersection (called the vertex of the angle.) The amount of rotation required to bring one of the line segments to coincide with the other is called the value the angle. The...

Geometry: Perimeter - Parallelogram, jklm, perimeter

jklm, perimeter, parallelogram: Hi Ralph! Let (JM=x). This way, we know that (JK=x+1), right? To find the perimeter, we need to add all four sides together. Because this is a parallelogram, there are two sides that have the measure of JM, and two that have the measure of JK. Let s...

Geometry: Perpendicular Bisector, hello mike, line x

hello mike, line x, vertical line: Hello, Mike? Did you make a sketch? The point A(-4,1) is 4 units to the left, 1 unit up. The vertical line x = 2 is the perpendicular bisector of AB. Since the bisector is vertical, AB must be horizontal. Hence, B is at the same height ; the...

Geometry: Perpendicular Bisectors and Altitudes, perpendicular bisectors, angles

perpendicular bisectors, angles, sx: Hi Kevin! Question 5 can be answered quite simply using the segment addition postulate. RX=RS+SX RX=(x+7)+(3x-11) RX=4x-4 As for question 7, I will not assume which sides are altitudes and which angles are bisected. Ask a follow-up with specifications...

Geometry: Perpendicular Bisectors, perpendicular bisector, perpendicular bisectors

perpendicular bisector, perpendicular bisectors, compass method: Paul, A perpendicular bisector can be a line, a ray, or a segment which divides another segment into 2 equal parts and also forms a right angle to that segment. Think of the red vertical line that passes through the blue lines on lined paper. The red...

Geometry: Perpendicular line Proofs, perpendicular line, bd

perpendicular line, bd, property of equality: Hello, Joe! DC is perpendicular to BD. [Given] Angle 2 = 90°. [Def. of perpendicular] Angle 1 = angle 2. [Given] Angle 1 = 90° [Transitive property of equality] Therefore, BA is perpendicular to BD. [Def. of perpendicular] I...

Geometry: Pi/ Perimeter, archimedes method of exhaustion, perimeter of a circle

archimedes method of exhaustion, perimeter of a circle, method of exhaustion: I am not sure about what is meant by method of Pi ? If you want to know the formula for perimeter of a circle when the radius is knwon,: C=2*Pi*r, ( Here, Pi is the well known mathematical constant which is approximately equal to 3.14 ( or 22/7), r is...

Geometry: Plane Geometry, unit vectors, plane geometry

unit vectors, plane geometry, dot product: If the 3 points on the plane are P1(x1,y1,z1),P2(x2,y2,z2) & P3(x3,y3,z3), then the equation of the plane can be found by expanding the following determinant and equating it to zero |(x-x1) (y-y1) (z-z1) | |(x2-x1) (y2-y1) (z2-z1) | |(x3-x1)...

Geometry: Plane Geometry, first quadrant, plane geometry

first quadrant, plane geometry, co ordinate geometry: ( Here we have to arrive at some relationship between the size of the side of the outer square (100) and the total number of squares formed. Since we don t know this relationship we need to use induction to arrive at the guess for the required...

Geometry: Plane Trigonometry, right triangle, degree sign

right triangle, degree sign, decimal place: Hello, Morris! Are you sure it says by logarithms ? It sounds like a very old book, from 1950 B.C. (before calculators). [In case the HTML code doesn t work, a warning: If something looks like &# 176 , it s a degree-sign.] I ll solve it in...

Geometry: Point (x,y) in a Closed Figure, ploygon, vertices

ploygon, vertices, xn: Hi Jack! I m sorry to say, but I don t fully understand your question. I gather you mean given the points of the vertices of the closed figure, how to test for point (x,y). I would do this by finding the domain and range of the figure, and then seeing...

Geometry: Polar coordinates, polar coordinates, conversion formulas

polar coordinates, conversion formulas, rcos: Hello, Sean! You need these conversion formulas: x = r¡¤cos¥è y = r¡¤sin¥è And just make the substitutions. Simplify and solve for r, if possible. Example: the line, y = x + 2 Substitute: r¡¤sin¥è = r¡¤cos¥è +...

Geometry: Polygons, isosceles triangle, uregina ca

isosceles triangle, uregina ca, equilateral triangles: The general answer is yes all equilateral triangles are isosceles. ------------------------------------------------------ But the answer will depend upon the definition given in your book. e.g. if your book says an isosceles triangle is one in which exactly...

Geometry: Polygons, j l heilbron, early civilizations

j l heilbron, early civilizations, civilized history: I am sorry, but I don t know the details you want. But in my opinion the best site for maths history is: http://www-history.mcs.st-and.ac.uk/~history/ You may also consider consulting printed books like: 1. Geometry Civilized: History, Culture, and...

Geometry: Polyhedron - Cone, what is a polyhedron, circular cone

what is a polyhedron, circular cone, ovals: Cheyenne! What is a polyhedron? Basically, it s a 3-D figure which has faces made up of polygons. What are polygons? Closed 2-D figures made up of straight lines (as opposed to curved lines, thus eliminating circles and ovals and the like). What are...

Geometry: Pre-Calculus, pre calculus, polynomial

pre calculus, polynomial, multiplication: The data given is not sufficient to find the height of the box. Assuming that the height of the box is x cms., we get the expression for the volume of the box as: V=10*15*x=150*x sq. cm. ( I am using * to denote multiplication. ) This is the required...

Geometry: Prisms, square centimeters, rectangular prism

square centimeters, rectangular prism, cubic cm: A. Find the surface area of the prism in square centimeters. This will be nothing but the total area of all the six surfaces We have 3 pairs of identical surfaces. = 60cm * 40cm + 60cm * 40cm + 40cm * 200cm + 40cm * 200cm...

Geometry: Probability, new york yankees, major league baseball

new york yankees, major league baseball, boston red sox: Kevin, If A and B are independent, then to find the probability of both events occurring multiply the probability of the events. For example, P(A and B) = P(A) * P(B). If you re-worded your question to What is the probability of Team A winning the...

Geometry: Probability, winning the lottery, cash prize

winning the lottery, cash prize, three ways: Hello, Chassity! An interesting question . . . I suppose if you had about 23 million dollars to spend, you could guarantee winning the jackpot. But if two other people had the same idea, you must split the winnings three ways. Then you...

Geometry: Probability, permutations and combinations, n factorial

permutations and combinations, n factorial, integers: The answer is chossing 4 out 6 which is also written as 6C4 We know nCr is equal to n! / (r!*(n-r)!) Therefore 6C4 = 6! / (4!*(6-4)!) (I am using * to denote multiplication this convention...

Geometry: Proof for bisected line in a trapezium, isosceles triangle, congruent triangles

isosceles triangle, congruent triangles, geometry books: To Alan From Jay Subj Bisecting up a storm This will be a modern style proof, marked (E) where it touches Euclid somewhere. Let the vertexes of trapezium T be (CCW) ABCD, with AD || BC and BC AD. If AB || CD , T...

Geometry: Proof required, boa poa, cop 3

boa poa, cop 3, aop: I think there is a mistake in the problem. The problem says BO bisects the angle between AO and BO. This is clearly impossible. So I assume the statement should read as BO bisects the angle between AO and CO. Let the BOA = COB = x degrees. We are...

Geometry: Proofs, old text books, initial doubts

old text books, initial doubts, geometric proofs: (Sorry, I don t know what is exactly meant by a worksite.) I am assuming you are looking for websites which will accept proofs from you and will check them automatically thru software ? I am not aware of any such sites. (Even if such sites exist...

Geometry: Proofs, ask dr math, school mates

ask dr math, school mates, thinkquest: Eventhough I am interested in helping you, Geometry (especially proofs part) is very difficult to teach/ explain simply thru e-mails ( that too without the help of diagrams.) Additionally this part of mathematics is also not quite standardised, so the...

Geometry: Proofs, definitions and postulates, problem definitions

definitions and postulates, problem definitions, rectangle: Hello. I can t really explain them in a different way than your teacher, but I can tell you this: Proofs use what you are given, then through a series of theorems, definitions, and postulates, you can conclude something, which is usually the point of...

Geometry: Proofs, reason number, cd 3

reason number, cd 3, cd 4: Substitution Property If a = b then either a or b may be substituted for the other in any equation. Subtraction Property If a = b and c = d, then a – b = c – d. So while going from statement 4. to statement 5. you have used subtraction property. (as...

Geometry: Proofs, explicit description, intersecting lines

explicit description, intersecting lines, opposite angles: Tsunami, I hate to disappoint you, but I don t have the diagram as you do. I m thus unable to answer the question. I m assuming there are intersecting lines creating vertically opposite angles, but give me an explicit description of the diagram and I...

Geometry: Proofs - Circle, intersection points, line segment

intersection points, line segment, perpendicular line: Hey Elizabeth, The most logical way I see this is that the side measuring root h is a radius. This bisects g, effectively making (r) and (s) radii as well. This way, the three lengths in question are equal, but (rs) definitely equals (h). As I do not...

Geometry: Proofs, Postulates, and Properties, answer key, postulates

answer key, postulates, arguement: Hi Sophie! The first two are undeniably given. Your teacher s answer key (or reasoning) is wrong. JK is congruent to MN because of the TRANSITIVE axiom (or postulate or property, it s all the same). This essentially means that things that are equal to...

Geometry: Proofs, math faq, mail message

math faq, mail message, dr math: Sorry, I am not able to explain this with a single e-mail message. But you will find several intersting links below. http://www.mathforum.org/dr.math/faq/faq.proof.html Of course, you are welcome to ask for further guidance. But if the doubts are...

Geometry: Proportion problem within a triangle, simplist terms, drafting program

simplist terms, drafting program, dimentions: I am sorry, but the question is not clear to me. What kind of shape you are trying to build ? Is it a Pyramid ? The part about steps between A & B, that graduate in equal proportion between D & C is also not clear. Have you tried using some drafting program...

Geometry: Proving Statements, angles of a triangle, straight angles

angles of a triangle, straight angles, straight angle: Out line of the proof: Simply join any pair of diagonally oposite vertices. This will divide the quadrilateral in 2 triangles. Now the the sum of the angles of the quadrilateral is equal to sum of the angles of these 2 triangles. But sum of the angles...

Geometry: Proving, angle bcd, math faq

angle bcd, math faq, dr math: Red, Here s an image of the angles that you describe: http://img63.imageshack.us/my.php?image=angleacewith2interiorraysbs0.jpg. Notice the first thing to do is to MARK THE DIAGRAM. I ve put single arcs to show Angle ACD = Angle BCE. I ve put double...

Geometry: Pythagoreom Theorem, isosceles triangle, hypotenuse

isosceles triangle, hypotenuse, abd: Let the triangle be ABC, with AB=AC=x and BC=y, Drop a perpendicular from A on BC, meeting BC at D. Now BD=DC, as triangle ABD & ADC are congruent. And both must be right angled. The perimeter of ABC is 32. Therefore 2*x+y=32 ...(1) In triangle...

Geometry: parallel lines, alternate interior angles, e mail address

alternate interior angles, e mail address, uregina ca: It is clear from what we are asked to prove, the authors of your textbook exclude paralleograms from their definition of a trapezoid ( also called trapezium ). We are using the indirect method of proof. This is alos known as Reductio ad absurdum ....

Geometry: parts of similar triangles, corresponding angles, similar triangles

corresponding angles, similar triangles, dg: Since the triangle KJL~the triangle EDC. We have triangle MJL~the triangle GDC (This can been proved easily as the corresponding angles are equal.) So MJ/GD=JL/DC Therefore X/2=4/(6-x) Therefore X*(6-X)=8 Therefore 6*X-X*X=8 Therefore X*X-6*X+8=0...

Geometry: perimeter of an octagon, isosceles triangles, angle aob

isosceles triangles, angle aob, law of cosines: Hello, Mike! Try to duplicate my diagram. Sketch a regular octagon. Label the vertices A, B, C, D, E, F, G, H (in that order). Draw diagonals: AE, BF, CG, DH. Label the center O. And we have eight isosceles triangles. Consider triangle AOB....

Geometry: You are playing golf on the..., mathematical constant, playing golf

mathematical constant, playing golf, 3 feet: Area of the inner circle with 2 feet radius will be = Pi * 2 * 2 (Here Pi is the well known mathematical constant, approximately = 22/7 ) = Pi * 4 sq. feet. The area of the 4 the hole = Pi * 20*3 * 20*3 ( 1 yard = 3 feet...

Geometry: You are playing golf on the..., mathematical constant, playing golf

mathematical constant, playing golf, 3 feet: Area of the inner circle with 2 feet radius will be = Pi * 2 * 2 (Here Pi is the well known mathematical constant, approximately = 22/7 ) = Pi * 4 sq. feet. The area of the 4 the hole = Pi * 20*3 * 20*3 ( 1 yard = 3 feet...

Geometry: please help...S.O.S, y2, y1

y2, y1, x1: ( I am not sure about Find an equatio in x and y part of the question. I think they want to know the co-ordinates of the point which satisfy the given condition.) According to section formula: The co-ordinates of the point which divides the line joining...

Geometry: pls help me..........., perpendicular bisector, sides of a rhombus

perpendicular bisector, sides of a rhombus, trigonometry lessons: Please draw a rough sketch. Let ABCD be the vertices of the rhombus. Let AC be 20 and BD be 16. Let the point of intersection of AC & BD be M. We know all the sides of a rhombus are all equal. Since the perimeter is 51.224993899463 We get each side of...

Geometry: pls help me..........., geometry conjectures, picture of a rhombus

geometry conjectures, picture of a rhombus, obtuse angles: Hung, First, there are a few theorems which pertain to your problem. 1) Opposite angles of a parallelogram are congruent. 2) Diagonals of a rhombus are perpendicular and bisect each other. 3) Diagonals of a rhombus bisect the angles of the rhombus....

Geometry: poloygons, area of a hexagon, math faq

area of a hexagon, math faq, mathforum: I assume you mean a regular hexagon, i.e. a Hexagon with all its sides and angles equal. The formula is Area = 3a^2 sqrt(3)/2 Here a is length of each side. ^ is exponentiation, i.e. a^2 is a squared . If you have a irregular hexagon, there is no...

Geometry: polygon & its area...., pakistan currency, note rs

pakistan currency, note rs, octagon: If I have understood the question correctly we have been ( indirectly ) given the perimeter of an octagon and from this we are supposed to find the area of that octagon. Let each side of the octagon be s (Let us convert everthing into paisas) So 8*s*10=4000...

Geometry: polygon & its area...., square root of 3, equilateral triangles

square root of 3, equilateral triangles, inradius: This is will be twice the inradius of the hexagon. The inradius will be square root of(3)/2* 16 Threfore the required answer must be 16*square root of(3) mms. (It is easy to derive the above formula. Join all the vertices to the center of the...

Geometry: polygons, regular dodecagon, equilateral triangles

regular dodecagon, equilateral triangles, interior angles: Kitty, Think of tilings on the floor. The tiles must meet at one point, a vertex. If you have tiles that are all squares, then you know each corner must be 90 degrees. So 4 squares around one vertex would equal 360 degrees. Now, going around a vertex...

Geometry: pool/billiards, jpl nasa, saturn jpl

jpl nasa, saturn jpl, pool billiards: I am sorry but I don t have any definite idea about what you are looking for. (Are you looking for ideas on how to trace the lines along which the ball travels ?) In any case please try: 1. http://www.jimloy.com/billiard/kick.htm There is lot of...

Geometry: pool border, area of a rectangle, rectangle area

area of a rectangle, rectangle area, landscape contractor: Jackie, The first thing I tell my students to do is to draw a picture and label. You will draw a rectangle inside of a rectangle. Just like a picture frame. The inside rectangle is the pool in this word problem. Label the length and width. The outside...

Geometry: postulate/theorem on lines and planes, two planes, true statement

two planes, true statement, theorems: Hello Glen Pratt. There is a big difference. If you say that you must go to the store tomorrow, you don t necessarily have to go. You could go to the library, or bank, or whatever. This isn t exactly what the theorems say, but this is for explanation...

Geometry: postulates & theorems in geometry, mathworld wolfram, java elements

mathworld wolfram, java elements, mathematical theorems: ( As per: http://mathworld.wolfram.com/Postulate.html ) A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of Euclidean geometry, for example,...

Geometry: practicl geometry, surface area of a right cylinder, base diameter

surface area of a right cylinder, base diameter, exponentiation: (Seems to be a duplicate question ? Anyway here is the answer) The diameter d = 16 mm So the radius r = 8 mm The surface area of the sphere will be S = 4 * Pi * r^2 ( * denotes multiplication here. ^ denotes exponentiation 4 into Pi into r squared...

Geometry: practicl geometry, base diameter, simplification

base diameter, simplification, multiplication: Let the diameter of the sphere be d and volume be V1 So V1 = 4/3*Pi*(d/2)^3 ...(1) ( * denotes multiplication, Pi is the well known mathematical constant, (d/2)^3 means cube of (d/2), If d is the diameter the radius must be...

Geometry: practicl geometry, equilateral triangle, equilateral triangles

equilateral triangle, equilateral triangles, square root of 3: Join all the vertices of the base hexagon to its center. You will get 6 equilateral triangles all congruent to each other. Now let us find the area of one of these 6 triangles. If the side of an equilateral triangle is a its area is = 1/2 * a * (3^(1/2))/2...

Geometry: practicl geometry, surface area of a cube, sq inches

surface area of a cube, sq inches, sq foot: The total surface area of a cube will be 6 times the area of a single face, since a cube has 6 equal faces (all squares) So S = 6 * 10 * 10 = 600 sq inches But the answer is required in sq. feet so s = 600 / 144 sq. feet ( as 1 sq foot = 12...

Geometry: practicl geometry, volume of a cylinder, cylindrical container

volume of a cylinder, cylindrical container, volume of water: The volume of a cylinder = (Pi * r^2) * h ...(1) (Where Pi is the well known mathematical constant approximately equal to 3.14 or 22/7, * denotes multiplication, and let h be the height of the cylinder.) = (Area of the base)...

Geometry: practicl geometry, right cylinder, surface area

right cylinder, surface area, s1: The surface area of the bottom is S1 = Pi * r^2 ( Pi into r squared, where Pi is the well known mathematical constant apporoximately equal to 3.14 or 22/7, r is the radius of the base.) So S1 = 3.14 * 12 * 12 mm squared = 3.14 * 144 mm squared ...

Geometry: practicl geometry, surface area of a right cylinder, base diameter

surface area of a right cylinder, base diameter, exponentiation: The diameter d = 16 mm So the radius r = 8 mm The surface area of the sphere will be S = 4 * Pi * r^2 ( * denotes multiplication here. ^ denotes exponentiation 4 into Pi into r squared , here Pi is the well known amthematical constant approx....

Geometry: pre calculus inequality question, interval 1, critical points

interval 1, critical points, inequality: Karen, To solve this inequality, you want to make a sign chart. First, we can determine where the function is undefined. Remember, one can NOT divide by 0. So the denominator can NOT be 0. So set x-5 not equal to 0. ( I can t insert the not...

Geometry: problem solving, centimeters to meters, rectangular pieces

centimeters to meters, rectangular pieces, square meters: Hello. Let s first convert 60 centimeters and 30 centimeters to meters. Area = length * width So the area of each board is .6m * .3m = .18m^2 There are 50 boards: .18m^2 * 50 = 9m^2 So the total area of all the wood to be painted is 8...

Geometry: process of asking questions, geocities tripod, free space

geocities tripod, free space, key word: No there is no way to do it on allexperts.com (as far as I know). The work around is: upload your figures to some web server and send me a link to it in the question. There are many sites which offer you free space on their site. e.g. geocities, tripod...

Geometry: another proof, alternate interior angles, congruent triangle

alternate interior angles, congruent triangle, traingles: The outline of the argument is as follows: 1.AB//CD and BD is the transversal. So using the result: When a pair of parallel lines is cut by a transversal the alternate interior angles are congruent.( For proof see: http://library.thinkquest.org/2647/geometry/angle/proof6.htm...

Geometry: another proof, congruent triangle, parallel pairs

congruent triangle, parallel pairs, corresponding angles: To Julie From Jay Subj Halving a parallelogram. This proof is a one trick pony in that you beat it to death with this result from Euclid: Theorem: a transversal cuts a parallel line-pair in equal corresponding angles. So,...

Geometry: A proof were I know what to do, but cant get there, congruent segments, side splitter

congruent segments, side splitter, cd 1: You are on the right track and have almost finished the proof. You have written AE/EB=AD/CD ...(1) But since AE=EB We have AE/EB=1 ...(2) So AC/CD=1 (From (1) & (2)) Hence AC=CD, i.e D bisects A...

Geometry: proof of perpendicular line, img photobucket, complementary angles

img photobucket, complementary angles, triangle abc: To Julie From Jay Subj Lines that pass in the night. Not enough given here, Julie, i don t know what angles 1 and 2 are yet. For instance, here s a scenario where the conclusion would be true: L, M meet in C. A is a point on...

Geometry: proof, isosceles triangle, vertex angle

isosceles triangle, vertex angle, triangle abc: To Prove: m ACD = m BCD Consider the triangles ACD and BCD We will prove that these 2 are congruent. AC = BC (Given) m DAC = m DBC (Since the triangle ABC is an isosceles triangle) m CDA = m CDB (Since CD is perpendicular...

Geometry: proofs, interior angles, column proofs

interior angles, column proofs, math faq: Here are some links for details about proofs http://www.mathforum.org/dr.math/faq/faq.proof.html Basic concepts related to parallel lines http://library.thinkquest.org/20991/geo/parallel.html#transversal How to build 2 column proofs http://www.mathforum.org/library/drmath/view/54693.html...

Geometry: proofs, prime numbers, positive integer

prime numbers, positive integer, primes: Before proving the main result let us note: When any positive integer is divided by 4 there are only 4 possibilities for the remainder viz. 0,1,2 and 3. Alternatively, this fact can be expressed as: Every integer is of one of the 4 following forms...

Geometry: proofs, definition of congruent triangles, corresponding angles

definition of congruent triangles, corresponding angles, corresponding sides: As far as I know there is nothing to prove here. (Or may be I have not understood the question.) By definition two congruent triangles will have their corresponding sides and corresponding angles equal. Alternatively, we start from...

Geometry: proofs, area of triangle, area of a triangle

area of triangle, area of a triangle, absolute value: slope of JA=[-1-(-2)]/[8-2]=1/6 slope of ME=[2-3]/[3-9]=(-1)/(-6)=1/6 slope of JE=[2-(-2)]/[3-2]=4 slope of AM=[3-(-1)]/[9-6]=4 Since the slopes of opposite sides are equal, the opposite sides are parallel. So the quadrilateral must be a parallelogram....

Geometry: proofs, congruent angles, triangle abc

congruent angles, triangle abc, right angles: Please read my earlier answer. Please name the altitude, angles and triangles you have in mind so that there is no communication gap. Finally I repeat the result you are using is applicable when the angles belong to the same triangle and it can t be used...

Geometry: proofs, column proofs, true hope

column proofs, true hope: I m guessing that you mean two column proofs; the first column are statements that are true and the second column is the reason that it s true. The reason can be a theorem, postulate, or definition. One statement (except the very first one) is a result of...

Geometry: proofs, alternate interior angles, point of tangency

alternate interior angles, point of tangency, horizontal diameter: Hello, Krista! I ll sketch out the proof. I hope you can supply the details. Let s see if I describe my diagram. Draw a circle. Label its center O. Draw a horizontal diameter. Label the left end A, the right end B. Draw vertical...

Geometry: proofs, congruent triangles, line bc

congruent triangles, line bc, line cd: Hello, Ryan! I assume we have a quadrilateral ABCD. Draw diagonal AC, dividing it into two triangles: ABC and ADC. We are told that: AB = CD and BC = DA. We know that; AC = AC. The two triangles are congruent (by s.s.s.) Therefore: angle...

Geometry: proofs in geometry related question, proofs in geometry, angled triangle

proofs in geometry, angled triangle, inradius: What you want to calculate is called the inradius of the triangle. The formulas for calculating it can be found at: http://www.saltire.com/applets/pythag/incircle.html OR http://www.ilovemaths.com/3circlestriangle.htm As you must have noticed, it is better...

Geometry: proofs and medians, indirect proofs, sides of a triangle

indirect proofs, sides of a triangle, line segment: About proofs, visit the following web page for a series of articles about various aspects of proofs. http://mathforum.org/dr.math/faq/faq.proof.html http://www.cut-the-knot.org/proofs/index.shtml Notes on methods of proof http://www.math.csusb.edu/notes/proofs/pfnot/pfnot.html...

Geometry: proofs, induction proofs, odd integer

induction proofs, odd integer, integer solutions: I am sorry but these are not questions pertaining to Geometry. You need to ask an expert in Number Theory for solutions to such problems. But here are some quick answers to some of your questions. 1. What you are asked to prove is not true. Simpley...

Geometry: proportional parts conjecture, discovering geometry conjectures, angle bisectors

discovering geometry conjectures, angle bisectors, geometry textbook: Sasha, It sounds as if you are using the Discovering Geometry textbook or something similar. The key word in the name of the conjecture is proportional. Someone has placed the Discovering Geometry conjectures online with the blanks filled in. ...

Geometry: proportional segments under ratio and proportion in geometry, ratio and proportion, proportional segments

ratio and proportion, proportional segments, danilo: Hello, Danilo! Let x = smaller number. 145 - x = larger number The smaller is decreased by 2: x - 2 The larger is increased by 1: (145 - x) + 1 = 146 - x Their ratio is 2/7: (x - 2)/(146 - x) = 2/7 Cross-multiply: 7(x - 2) ...

Geometry: prove, isosceles triangle, triangle abc

isosceles triangle, triangle abc, rough sketch: Let ABC be the triangle. Let m ABC=m ACB. Here is the ouline of the argument. Please draw a rough sketch to understand it. Let AM be the altitude. You want to prove. BM=MC. For proving this you should prove, triangle ABM is congruent with triangle...

Geometry: proving bc=ef, using compass, lockheed martin

using compass, lockheed martin, line ac: To Leslee From Jay Subj ABCDEF Well Leslee, the result doesn t follow from what you gave, there must be something missing somewhere. Example: Make AC and DF opposite sides of a rectangle. Let B = midpoint of AC. Using compass...

Geometry: pyramids, slant height, edge lateral

slant height, edge lateral, angled triangle: Please draw a (rough) figure of the Pyramid. For simplifying the discussion let us name the various vertices as follow: Let A,B,C,D be the vertices of the square at the base of the square Pyramid. Let P be the remaining vertex. Let M be the center of the...

Geometry: pythagoras, right angle triangle, hypotenuse

right angle triangle, hypotenuse, memory lane: I am glad to know you want to recollect the proof. The one you have in mind is the most popular amongst the texbook writers. But mathematicians have found several different proofs. ( Of the order of hundreds!) Here is a link to a web page containing 69...

Geometry: Q #23 stoneman douglas regional competition Florida, constant of proportionality, stoneman douglas

constant of proportionality, stoneman douglas, slant surface: The sureface area of a pyramid is given by S=(1/2)*p*s Where p is the perimeter of the base s is the slant height ...(1) The voume of a pyramid is given by V=(1/3)*A*h Where A is the area of the base and h is the height ...

Geometry: Questions about Geometry theorems, geometry theorems, secant

geometry theorems, secant, e mail: 1. I am sorry but I can t answer questions about proofs because in geometry there is no standardization about which properties are treated as axioms/postulates and which are considered as theorems. You will find a variation in different...

Geometry: Questions for math portion of teachers certification exam, home rents, gallon containers

home rents, gallon containers, distance between two cities: Jammie, This follow-up is for question#6. In this problem, you need to convert from inches to miles. The conversion factor is 1/2 in. to 25 mi. Since we have decimals in the problem, change 1/2in. to 0.5in. So let s muliply. 8.5 in. * 25mi/0.5in....

Geometry: quadratic formula/imaginary numbers, square root of 1, square root of 4

square root of 1, square root of 4, x square: 3*x^2+72=0 Mutiplying both the sides by 4 we get, x^2+24=0 x^2=-24 x= square root of (-1*24) OR x=(-1)*[square root of (-1*24)] Therefore x=[square root of(-1)]*[square root of (24)] OR x=(-1)*[square root of(-1)]*[square root of (24)] Therefore...

Geometry: quadratic formula/imaginary numbers, square root of 1, square root of 4

square root of 1, square root of 4, x square: 3*x^2+72=0 Multiplying both the sides by 4 we get, x^2+24=0 x^2=-24 x= square root of (-1*24) OR x=(-1)*[square root of (-1*24)] Therefore x=[square root of(-1)]*[square root of (24)] OR x=(-1)*[square root of(-1)]*[square root of (24)] Therefore...

Geometry: Another question, exact mechanism, key word

exact mechanism, key word, servers: No as far as I know, you can t attach a diagram here. What you may try 1. Try to draw the diagram and upload it to some server ( there are many servers where free webspace is available ) and pass me the link to it in the question. There are...

Geometry: question about an answer i got, secant, mean proportional

secant, mean proportional, code numbers: Hello, Krista! Sorry about that . . . Sometimes the code-numbers don t work here (don t know why). That circle-C is supposed to be exponent 2 (squared). And the !ae is suppose to be a arrow pointing to the right. Here s what I wrote: So...

Geometry: question, qr, pq

qr, pq, geometry: 8. if AB=PQ, BC=QR, m B=70, and m Q=110 which is longer, AC or PR? PR reason: The side opposite to the greater angle will be longer when the sides containing the angles are congruent. ( Please recheck the question...

Geometry: Some questions with geometry, surface area of a pyramid, surface area of a regular pyramid

surface area of a pyramid, surface area of a regular pyramid, square pyramid: Lucas, A square has 4 congruent sides. To find the perimeter of as square, use the formula P = 4*s. P stands for perimeter and s stands for the length of the side. Use the Perimeter and the slant height and plug into L = .5Pl to find the surface...

Geometry: Radian measures, radians to degrees, radian measure

radians to degrees, radian measure, radian measures: To convert from radians to degrees multiply by 180/pi. To convert from degrees to radians multiply by pi/180. Setting up this specific case we get: (3pi/4)(180/pi) The pi s cancel and four goes into 180 forty-five times, so you then have 3*45 which...

Geometry: Radical Expressions, sq rt, simplifying radicals

sq rt, simplifying radicals, radical expressions: Jaedon, There are several strategies for simplifying radicals.These strategies will work most of the time but not all of the time. So here goes: 1st: Is the RADICAND (the # under the radical) a perfect square? Is yes, take the sq.rt. If no, try the...

Geometry: Rate of Water, decent size, three dimensions

decent size, three dimensions, water water: Hi Aleksandar, I need to make several assumptions in order to interpret this question and answer it. This drain must be completely cylindrical, right? Also this 200 mm/sec. refers to the increase in depth, right? If so, calculate the capacity in three...

Geometry: Ratio and Proportion, right angle triangle, triangle ade

right angle triangle, triangle ade, area of trapezoid: Since AB=BC and ABC is right angled neither AB nor BC can be the hypotenuse. So AC must be the hypotenuse, and hence angle ABC must be the right angle. Area of the triangle ABC = 1/2 * 3 * 3 = 4.5 square units ...(1) ( As B...

Geometry: Ratios as Percentages, watching tv, darius

watching tv, darius, ratios: Hi Darius, By definition percent means for every one hundred. The symbol is thus a 1 with a 0 in either side. Anyway, 100% represents the whole. When your whole is not 100, you need to make it so. In this case (from what I gather based on your question)...

Geometry: Rectangle Solve problem, color triangle, vertical angles

color triangle, vertical angles, diagonals: Shea, You know Angle CBD is 55 degrees. Since Angle CBA is a right angle then Angle DBA is 35 degrees. Now since DA || CB then alt. int. angles are =. So... Angle BDA = 55 since Angle CBD = 55. Next highlight Triangle DAB & Triangle CBA. Triangle...

Geometry: Rectangular Solid with Cubes, blue face, rectangular block

blue face, rectangular block, cubes: Hello, Tamra! This is an exercise in imagination (geometric). We have eight cubes, each has one blue face. We put them together in a rectangular block. We can always turn the blocks so its blue face is showing. So we can always have 8 blue faces...

Geometry: Reflection Upon a Line, graph paper, image points

graph paper, image points, midpoint: Hi Will, Draw this out on graph paper to find the actual coordinates of the image points. From that, notice a pattern in the original coordinates and its image s. Although you could find the distance between a point and a line, it would not really be...

Geometry: Rhombus, angle bisector, isosceles triangle

angle bisector, isosceles triangle, geometrical problem: When you want to solve a geometrical problem involving proofs always start by drawing a rough digram. Here is the outline of the proof. Let ABCD be a rhombus. Join A, C ( i.e. draw the diagonal AC ). We will prove that AC is in fact the angle bisector...

Geometry: Rhombus' Diagonal, height of a triangle, square centimeters

height of a triangle, square centimeters, right triangles: Hi Ray! Rhombus diagonals intersect at a right angle. Knowing this, basic trig will guide you to the answer. If the rhombus has an angle of 120, then its small angle is 60. Go ahead: draw in the second diagonal. You will find it to bisect your 120...

Geometry: Rhombus Diagonals, geometry quadrilaterals, sides of a rhombus

geometry quadrilaterals, sides of a rhombus, diagonals: Dawna Natale, First thing to do is to draw a rhombus. Remember that all sides of a rhombus are =. So mark each side with a dash to show that they are =. Here s a picture of a rhombus: http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rhombus.php...

Geometry: Rhombus, diagonals, turms

diagonals, turms, rhombus: Let p & q be the lengths of the diagonals of the rhombus. There is a property about area of the rhombus which gives the area in turms of the length of its diagonals. The area of the rhombus = (1/2)*p*q ...(1) Let the shorter diagonal be p,...

Geometry: Rotating, value of pi, approximate value

value of pi, approximate value, circumference: Circumference of the ball will be 2*Pi*r=2*3.14*3 cm =6*3.14cm =18.84 cm (Taking approximate value of Pi as 3.14) So the ball will cove 16.84 cm distance when it makes one rotation. So to cover 1-m slope it will have to rotate 100 cm / 18.84 cm...

Geometry: Round the following numbers..., place hope, left hand side

place hope, left hand side, decimal place: (a) 4,256,000 = 4.256 * 10^6 (b) 2783 = 2.783 * 10^3 (c) 0.01020 = 1.020 * 10^(-2) (d) 0.00006279 = 6.279 * 10^(-5) Now by round to three figures if it means including the digit on the left hand side of the decimal then the...

Geometry: radians and degrees, radians to degrees, non euclidean geometry

radians to degrees, non euclidean geometry, inches to centimeters: Hello. Both radians and degrees used to measure angles, just like inches and centimeters are used to measure length. There are conversions for inches to centimeters, so they are different in their origin and where they are used. But if you have one,...

Geometry: radius and circumference, circumference of a circle, value of pi

circumference of a circle, value of pi, area of a circle: 1. Area of a circle is found by using the formula A=Pi*r*r ( Here r denotes the radius and Pi is the well known mathematical constant and * denotes multiplication.) So we have Pi*r*r=20*3.14 Therefore r*r=20*3.14/Pi Therefore ( after taking...

Geometry: radius, building a privacy fence, foot span

building a privacy fence, foot span, fence posts: Hello. Now I see what you are saying. I checked out this site: http://www.elyriafence.com/GN17.html to see what scalloped fence meant. The dip would be in the fence itself, not in the ground like I thought. I ll direct you to a site that will help...

Geometry: reducing the area of a circle, diameter of a circle, area of a circle

diameter of a circle, area of a circle, square inches: Hello, Jan! We must be careful . . . The diameter is measured in (say) inches. But the area is measured in square inches. We can do this algebraically . . . The original diameter is D. Then the area of the circle is: A = π(½D)² =...

Geometry: reflections, 3rd quadrant, perpendicular axes

3rd quadrant, perpendicular axes, co ordinate geometry: [I have myself not studied geomtry thru transformations in my studies. I got introduced to them only when I was trying to understand some of the algorithms related to computer graphics. But at that level they use Matrix operations to perform the transformations...

Geometry: related rates, cubic centimeters, center of the sphere

cubic centimeters, center of the sphere, volume of a sphere: (I assume you are learning Calculus and are familiar with the basic notations.) The rate of change is the derivative with respect to time. Let the variable r denote the radius of the sphere. We have been given: dr/dt ( i.e. the rate of change...

Geometry: It is required..., area of rectangle, area of triangle

area of rectangle, area of triangle, rstu: We are given a triangle having an angle of 90 degress at R. It is given that one of the vertices of the required rectangle has to be R. Now since the required rectangle or its part can t be out side the given triangle, so 2 of the sides of the required...

Geometry: The rhombus, rhombus, best guess

rhombus, best guess, parallelogram: I have never heard this before in my career as a student and now as a mathematician. If I had to venture a guess (this is a pure guess on my part), I d guess it means that every square can be called a rectangle (I think that s the way I heard it) and every...

Geometry: right angles of triangles, right triangle, angles of triangles

right triangle, angles of triangles, triagle: Jenn, First thing to do is to draw a right triangle and label the given measures. Ex: | | 20 | ---- 48 Now,when you said the side is 20 , I put it as the height. Where you place the values in the triangle does...

Geometry: Segment Add. Postulate Again!, cb 4, final answer

cb 4, final answer, segment: Hi Laura, I agree with you in that my method seems easier. From what I gather, I ve done nothing wrong, other than not emphasizing the answer enough. The question asks for the length of CB. (4/9)(27)=AC. The following calculation solves for CB, i.e....

Geometry: Segment Addition Postulate, geometry homework, line segment

geometry homework, line segment, mbc: Hello Laura, Firstly, the segment addtition postulate states that the sum of the parts equals the whole (I describe this further in a previous answer). Allow me to draw a diagram. A----C-----B mAC+mBC=mAB, according to the segment addition postulate....

Geometry: Segment Addition Postulate, horizontal line, 3x

horizontal line, 3x, segment: Hello, Andy! You are right . . . it s quite simple. Draw a horizontal line. Label the left end H , the right end K . Locate point J somewhere in between. Above the segment HJ, write 2x + 4 Above the segment JK, write 3x + 3 Below the line,...

Geometry: Segment and Angle Addition Postulate, library thinkquest, postulates

library thinkquest, postulates, k12: Segment addition postulate can be found at: http://library.advanced.org/10030/2segmen.htm Angle addition postulate along with a digram can be found at: http://library.thinkquest.org/10030/3anglead.htm Digrams about both the postulates can be found...

Geometry: Segment and Angle Addition Postulates, angle measures, line segment

angle measures, line segment, azb: Hi Akhira, Questioner Steven asked about the addition postulate before, so browse through my past answers for that. Consider the following: A / / / / / Z_______________B | | | | C The angle addition postulate...

Geometry: Shadows, circular shadow, vertical axis

circular shadow, vertical axis, bottom surface: I don t know of any everyday object which will fit the requirements. But we can make such an object as follows: Consider a cylinder with height = diameter. (You may take a cylinderical piece of cork if you actully want to make a model.) Now when viewed...

Geometry: Similar FIgures, similar figures, perimeters

similar figures, perimeters, perimeter: Let the triangles be ABC and DEF. Since they are equiangular they must be similar. So the ratio of their corresponding sides must be equal. So length(AB)/length(DE) = length(BC)/length(EF) = length(CA)/length(FD) ...

Geometry: Similar Triangles, triangle def, similar triangles

triangle def, similar triangles, triangle abc: Let the triangles be ABC and DEF, with AM and DN as the medians. We are given AB/DE=AC/DF=AM/DN We want to prove that the triangles ABC and DEF are similar. Construction: Produce AM to P such that MP = AM Join CP. Produce DN to Q such that NQ...

Geometry: Similarity - Areas, perimeter area, lateral area

perimeter area, lateral area, volume volume: Hey Courtney, The ratio of their areas will be the square of the ratio of their sides. Why? Consider this. If you have a 2 by 2 square, its area is 4. A 6 by 6 square would have an area of 36. If I ask you what is the scale factor of the 6 by 6 square...

Geometry: Similarity Transformations, similarity transformations, dimension volume

similarity transformations, dimension volume, cross section: Hi Mark, Logically, a dinosaur twice as tall would be much more voluminous. This is because (k=scale factor) side:area:volume=k:k^2:k^3. Radius is in one dimension. Volume is in three. R/r=k^3, where (r) is small radius and (R) is big radius, what you...

Geometry: Similarity, corresponding angles, similarity

corresponding angles, similarity, corresponding sides: No, I did not use the term. Similarity for me is a mathematical term. Two figures are Similar means that they are having same shape but not necessarily the same size. So when 2 objects ate similar then their corresponding sides are having the same ratio...

Geometry: Sin,Cos,Tan, spread sheet programs, spread sheet program

spread sheet programs, spread sheet program, maths physics: I am sorry, but the question is not clear to me. Do you mean you want to know the values of sin, cos, tan etc. for different angles ? If that is the case then 1. I am an old timer. In our days, we were not having access to calculators in school. But our...

Geometry: Sin,Cos,Tan, inverse cosine, trig function

inverse cosine, trig function, horizontal side: Ashley, Trig. questions are best solved by drawing a picture. When you see it, then your brain can usually fiqure it out. It s difficult to draw here but it would help if you drew a right triangle. The vertical line is the building; the horizontal line...

Geometry: Solving a triangle, angles of a triangle, cosine rule

angles of a triangle, cosine rule, right triangle: You need to use the cosine rule. Let the known sides be a and b and the included angle be C so (I am using ^ to denote exponentiation, i.e. c^2 is to be read as c squared ) c^2=a^2+b^2-2*a*b*cos(C) c^2=(424)^2+(63)^2-2*424*53*cos(66) Now...

Geometry: Solving a triangle, isoceles triangle, angled triangle

isoceles triangle, angled triangle, right triangles: Above Water(in Air) O - - - - -+ - - - - - /| / | Under Water / | / | - - - - - P D Q...

Geometry: Special Parallelograms, consecutive angles, special parallelograms

consecutive angles, special parallelograms, opposite angles: Hey Richard, A), B), and C) are definitely correct. I m assuming by D) you mean consecutive ANGLES are complementary. That would be false because a parallelogram s consecutive angles are supplementary. The answer, by process of elimination or reasoning,...

Geometry: Sq FT of a circle, circumference of a circle, area of a circle

circumference of a circle, area of a circle, sq footage: Hello, John! We re expected to know the formula for the circumference of a circle: C = 2 ð r where r is the radius. If we re given C, we can solve for r: r = C/2ð We re supposed to know the formula for the area of a circle: A =...

Geometry: Square footage of a circle, radius of a circle, square footage of a circle

radius of a circle, square footage of a circle, sq ft: If the radius of a circle is r , then its diameter is 2*r and area is Pi*r*r ( Pi is the well known mathematical constant approximately equal to 3.14 ) What we have been given is the diameter. So we have, 2*r=50 ft Therefore r=25 ft Therefore ...

Geometry: Square units, dissection theory, vector arithmetic

dissection theory, vector arithmetic, vector notation: Hello Samantha. First of all, when dealing with area the units are always square. Length is one dimensional, so the units have no exponent; area is two dimensional, since it relies on one length spanning another length; volume is three dimensional, since...

Geometry: Squared, area of a rectangle, geometrical figures

area of a rectangle, geometrical figures, square root: No. It means the figure has the same area as that of a square with each side equal to square root of 14 feet. There can be several geometrical figures with area equal to 14 feet squared. e.g. A rectangle with sides as 2 feet and 7 feet has the area...

Geometry: Squares, perimeter of a square, area of a square

perimeter of a square, area of a square, squares: Hey Janine! By definition, a square has four equal sides. To find the length of one side of a square, calculate the following (where s is side and p is perimeter): s=p/4 s=(152)/4 s=38 Now to find the area of a square, multiply the side length by...

Geometry: Stuck on Geometry, regular triangular pyramid, isosceles triangles

regular triangular pyramid, isosceles triangles, volume of a rectangle: Hello, Tiffany! You re expected to know the appropriate formulas. 1. The volume of a rectangular solid is: Length x Width x Height. 2. A regular triangular pyramid has three sides which are congruent isosceles triangles. The...

Geometry: Study Help, kinesthetic learner, vocabulary flashcards

kinesthetic learner, vocabulary flashcards, visual learners: Cynthia, This is a very good question. I will share with you those things that I share with my sophomores and their parents. It s not anything spectacular but works(most of the time) when students use these methods. These suggestions are not intended to...

Geometry: Studying Geometry, intersection points, graphing calculator

intersection points, graphing calculator, happy holidays: Hi Trisha! Take what you ve learned in class and condense it into a few equations, formulae, theorems, and notions. After that, make up problems and solve them! For instance, find the intersection points of y=5x-104 and y=x^2-8x+1. I wrote that up here...