confidence interval, red 19, different colors: There are 40 marbles in the bag of each color, which makes 4*40=160 marbles. Of the 8+19+29+23=79 drawn, 19 were blue. This makes the expected fraction of blue be 19/79. So since there are 160 marbles in the bag, we would expect 19/79ths of them to be blue....

Geometry: Conics, exy, ellipse

exy, ellipse, coefficients: It is almost in standard form. The standard form s Ax² + Bx + Cy² + Dy + Exy + F = 0. If they say that it is a centered conice, that means the graph has a center. FOr this case, a has taken the place of x and b as taken the place of y. I believe for...

http://en.allexperts.com/q/Geometry-2060/2010/2/f/Area-Triangle-Using-Semiperimetre.htm

Geometry: geometry, geometry question, instantaneous change

geometry question, instantaneous change, dimensional object: The derivative of distance is speed, and the derivative of speed if acceleration. With spheres that are expanding, the surface area is the instantaneous change in voluem Since a globe is a three dimensional object, but the surface is only two dimensional,...

Geometry: help?!, surface area of a rectangular prism, area of a rectangular prism

surface area of a rectangular prism, area of a rectangular prism, lateral area: The rectanglular prism has 6 sides. Now on the surface, 2 of the sides are 18x12, 2 of them are 18x9, and 2 are 12x9. It is known that 18x12 = 216, 18x9 = 162, and 12x9 = 108. The sum of these gives the surface area of 3 sides. The surface are...

Geometry: math, friend glen, diagonals

friend glen, diagonals, bens: Ben walked straight along the diagonal. That means his distance was shorter and that he walked √(15²+8²) = √(225+64) = √289 = 17 km. Glen walked 7.5 meters down the lnger side, which means he had 7.5 meters go go, walked parallel...

Geometry: math, symmetric property, segment

symmetric property, segment, segments: If a line is cut in half, both segments of the line are equal. A piece of a bigger shape is a segment. Usually segment is used for a linear segment. However, a square could have part of it cut out as a segment of the square A circle could have part...

Geometry: Probability - Marbles, probabilistic view, red 19

probabilistic view, red 19, rounding error: Hi Allyson! From a purely probabilistic view, you would have to find the amount of marbles there were initially (8+19+29+23=79). Then you d take the number of blue marbles and divide that by the total (19/79=0.24). Multiply this number by the total marbles...

Geometry: Rectangles and Area, area of a rectangle, whole number

area of a rectangle, whole number, 2w: The smallest area can be found with calculus to be a square. Let w be the width. Since the area is 225, this makes the length 225/w. The total fencing is then F(w) = 2w + 2*225/w = 2w + 450/w. Taking the derivative gives F (w) = 2 - 450/w². Setting...

Geometry: Regular Figures, rudolf arnheim, equal angles

rudolf arnheim, equal angles, geometry 1: Hi Jean, Equal side measures means all the sides have the same length. A square is a regular figure, other rectangles are not (rhombi are not either, because they have equal sides but non-equal angles). A circle is a regular figure but an oval is not....

Geometry: Similarity - Globe, surface area

surface area: Hey Allyson! There is a formula. The scale factor (k) is defined as the ratio of one side to another. When dealing with a 2- or 3-dimensional quantity, the scale factor must be raised to the power of the number of dimensions. For instance, k=R/r, where...

Geometry: Basic Trig - Ladder Against Wall, geometry question, right triangle

geometry question, right triangle, hypotenuse: Hi William! The ladder forms a right triangle with the wall. Height 7, base x, hypotenuse h. You can set up the equation x²+7²=h². When the ladder is pulled out one foot from the wall, it is flat. This means that x+1=h. You have 2 unknowns in 2 equations....

Geometry: Calculate parts, cross sectional area, 1 728

cross sectional area, 1 728, cubic inches: If the drum is 14 wide, that is a 7 radius. The cross sectional area is a circle with area πr². That is 7²π, or 49π. Now since it is h = 33 long, the volume is hA. It can be seen that hA = 33x49π = 1617π = 5079.955321... 5080....

Geometry: Circle - Circumference, circumfrence of a circle, circle circumference

circumfrence of a circle, circle circumference, circumference of a circle: Hi Matt, The formula for the circumference of a circle is 2 x pi x radius. Pi has an approximate value of 3.14, so if your calculator does not have a pi button, you can type in that value. If you have other questions, please be extremely clear when you...

Geometry: Geometry, chape

Geometry: Geometry, chape

Geometry: Solids - Painting Cubes, cubes, paint

Geometry: Solids - Painting Cubes, cubes, paint, math

Geometry: Geometry, list of names, geometry

list of names, geometry, shape: Here is a list of names for some of the n sided figures : http://www.mathleague.com/help/geometry/polygons.htm As far as how many sides a figure can have, there is no end. Giving a figure with n number of points, take any two corners, add another...

Geometry: Geometry, hypoteneuse, equilateral triangle

hypoteneuse, equilateral triangle, 3s: An equilateralt triangle has all sides equal. This means that with a line straigth up the middle, the hypoteneuse is s long and the base side is s/2 long. Taking s² - (s/2)² gives 18². Thus, s² - s²/4 = 18², so 3s²/4 = 324, so s² = 1296/3, so s = 36/√3...

Geometry: geometry, three corners, medians

three corners, medians, conjecture: From what I understand, you want a conjecture about how far it is to the median given the length of the line. One end of this line is at the vertex of a triangle, and so it is a vertex of that angle. The other point is somewhere else on the line. ...

Geometry: geometry, congruent angles, obtuse angles

congruent angles, obtuse angles, quadralateral: The sum of the angle in a n-gon is (n-2)*180°. This can be seen to be true since a triangle has 3 sides, so the sum is 180° and a quadralateral has 4 sides, and the sum is 360°. For a pentagon, is would be (5-2)180 = 540°. Since there are two angles...

Geometry: geometry, obtuse angles, internal angles

obtuse angles, internal angles, congruent angles: Hullo Allyson, Good question! Let s see how we can tackle this. We know that a pentagon has 5 sides. So we can find the sum of all the internal angles of the pentagon using this formula, sum of internal angles of a polygon with n sides= 2*(n-2)*90...

Geometry: Inequalities in triangle, humble request, point thanks

humble request, point thanks, greater than the sum: Forget what I said before; I remember it vaguely, but lets not even go ther. I just figured it out! I send you a diagram to show what to do. Suppose P were moved closer to B. In fact, suppose that P was right almost on top of B. Then AP would be almost...

Geometry: Math dilemma, isosceles triangle, angles of a triangle

isosceles triangle, angles of a triangle, corresponding angles: Hi Nour, Excellent question :)). Geometry is my personal favorite! Here s how we do it. I have attached an image with this answer. Please go through it. In the image, consider the two triangles OBP and O B P angle OBP=angle OPB (since, OB=OP=R...

Geometry: Math dilemma, two circles, parallel lines

two circles, parallel lines, radii: The line goes through A. It forms 2 triangles. One is triangle OBA and the other is triangle O B A. Note that the angle at A is the same for both. Note that both triangles are isoceles triangle, so the far angle of each is the same as well. This means...

Geometry: maths, math, profession

math, profession, calculator: Because math is used in almost every profession there is and comes in handy. Nowadays it can be done with a calculator, but if you know the math, you know what the answer should be close to. Here is a good article to read. It is http://www.suzannesutton.com/why_math.htm...

Geometry: maths, area of a parallelogram, true height

area of a parallelogram, true height, maths: It is in the form of a parallelogram, with the width the same as width as the sign, so the width is 20 meters. The height, however, is changed by the angle of the sun. Take the agnle of elevation of the sun as Θ. It is known that tan(Θ) = 10/L,...

Geometry: Perpendicular Bisector - Definition, line segment, slope of the line

line segment, slope of the line, right angle: Hi Donald, A perpendicular bisector splits a line segment in two equal parts and is at a right angle to that line segment. The slope of the line segment can be anything, but the perpendicular bisector must be at a right angle to that (the line segment...

Geometry: Quadrilateral Inscribed in a Circle., angle adc, triangle abc

angle adc, triangle abc, angle abc: Hi Mark! The radius is given, allowing you to find diameter AC. ABC is a 30-60-90 triangle, so you can use those ratios or basic trig to find the lengths of AB and BC. ABD and BCD are also right triangles with a diameter of 10, and thus the lengths are...

Geometry: Quadrilateral and Triangle., geometric principles, right triangle

geometric principles, right triangle, abce: At first I assigned lengths to the two lines in the middle and the top line and the bottom line on the right, ending up with 6 variables. I nicely came up with 7 equations, and figured one of the equations must be an extra. Eliminating the varialbes one...

Geometry: Question Regarding Induction, induction proof, mr wilson

induction proof, mr wilson, exercise: The induction proof would say assume it is true at n = 1, and it is. The next step says that it is true for n = k. That is, a^(k-1) = 1. To finish this proof, it must be shown true for n = k+1. This would mean a^k would have to be shown to be 1....

Geometry: Scale, scale drawings, inches in a foot

scale drawings, inches in a foot, scale model: Hi Tanya, To find the scale of 1 in: 12 ft, only one type of unit must be used. There are 12 inches in a foot, and thus 144 inches in 12 feet. The scale is 1 in: 144 in, so 1:144. For the second question, simply divide 2.5 by 45 to get the scale: 1:18....

Geometry: Sides of a Dodecagon, isosceles triangles, base angles

isosceles triangles, base angles, internal angles: Hi Thomas! Find the centre of the dodecagon. Draw a line to every vertex. You have now separated the triangle into 12 equal isosceles triangles. To find the base angles, use the following formula. (sum of internal angles)=180(n-2). Divide this by 12...

Geometry: Similarity - Cylinder, higher dimensions, nine times

higher dimensions, nine times, surface area: Hey Travis, Dimensions are in 1-D, surface area is in 2-D. When you affect something in 1-D, the repercussions in higher dimensions will be that same scale factor risen to the power of the number of dimensions. In this example, it would be 3², which is...

Geometry: Solids - Painting Cubes, small cubes, painted faces

small cubes, painted faces, two faces: Hey Allyson! Begin by constructing your large cube. It will measure 5 by 5 by 5 small cubes. It will be easier to answer the questions if you work from the outside in. Cubes that have three faces painted will be the ones located on the corners. Cubes...

Geometry: scale factor, scale factor

scale factor: It says that if the length in each direction of a solid is multiplied by the same factor, the volume is multiplied by the factor cubed. Thus, if all the directions are multiplied by 5, the volume is multiplied by 5³. That is, 5*5*5. Now 5*5=25 and 25*5...

Geometry: Volume - Drum, radius, height

radius, height, cylinder: Hi Chris, The drum is a cylinder and the volume of a cylinder can be calculated by πr²h, where r is the radius (14/2=7) and h (33) is the height. This gives a volume of 5079.955 cubic inches, meaning you could fit 5079 blocks inside the drum. For...

Geometry: working backwards, hullo, travel time

hullo, travel time: Hullo Tyler! Let s see how we can tackle this question. Cost of a class further away is $150. Cost of a class in Detroit is $12 less than the cost of class farther away. So cost of a class in Detroit $(150-12) = $138. This is a 12 week course....

Geometry: Angles with Trig, sinx cosx, x 120

sinx cosx, x 120, trig: 1. 3sin²(4x) = (cos(4x) - 1) given that 0 = x 360. It is known that sin²x+cos²x=1, so 3sin²(4x) = 3(1-cos²(4x)). Putting this in the equation gives 3(1-cos²(4x)) = cos(4x) - 1. Letting y = cos(4x), this is 3(1-y²) = y - 1, so 0 = -3 + 3y² + y - 1...

Geometry: Area - Yield Sign, triangle, equilateral Pythagorean

triangle, equilateral Pythagorean, Pythagoras: Hey Jacqueline! The general way of doing this is as follows. Subdivide your equilateral triangle by drawing one altitude. You now have two equal right triangles. The base measures half of one side, so 31 cm. The hypotenuse is a full side, so 62 cm....

Geometry: Dodecagon, law of cosines

law of cosines: Hi Jerry! The idea here is fairly simple. From the centre of the [regular] dodecagon, draw a line to two adjacent vertices. You now have an isosceles triangle whose equal sides are the length of the radius of the circumcircle. You could form 12 isosceles...

Geometry: Geometry, area of a triangle, word problems

area of a triangle, word problems, whole number: It is known that the area of a triangle with base b and height h is A = bh/2. We are given that b=h, so this is A = b²/2. For A being at least 144, solve 144 = b²/2. This means, multiplying both sides by 2, that 288 = b². Since 17²=289, that...

Geometry: geometry, triangle abc, mp 90

triangle abc, mp 90, right triangle: To be isosceles, two of the sides must be equal. To find the square of the length of each side, take (y2-y2)²+(x2-x1)². If the lengths are equal, the squares will be equal as well. a) Len²(FG) = 85, Len²(FH) = 85, Len²(GH) = 68. It looks like (a). b)...

Geometry: geometry, volume of a pyramid, triangular pyramid

volume of a pyramid, triangular pyramid, isoceles triangle: The volume of a pyramid has the equation hA/3, where h is the height and A is the base area. The base is two back to back right triangles with base 6/2 = 3 and hypoteneuse 5. This means the other side is √(5²-3²) = √(25-9) = √16 = 4....

Geometry: geometry, isosceles trapezoids, using a compass

isosceles trapezoids, using a compass, quadralateral: A rhombus is a quadralateral with sides of equal length. Pick a point. From that point, use a compass to draw an arc. On the arc, choose 2 points. From both these points, without changing the compass, draw an arc from each of the 2 points chosen on the...

Geometry: Lateral Area of Triangular Prism, area of a triangular prism, lateral area

area of a triangular prism, lateral area, prisms: Hey Allie! As with all prisms, the lateral area (bases excluded) is equal to the base perimeter multiplied by the height. If you want the total surface area, you have to add the bases. For triangles, that s either base times half-height, or Hero s formula....

Geometry: PYTHAGORAS THEOREM, consecutive integers, set of integers

consecutive integers, set of integers, proofs of pythagoras theorem: 1. There is a proof that is known as Garfield s Proof . It is here: http://en.wikipedia.org/wiki/Pythagorean_theorem 2. A Pythagoras triplet is a set of integers that satisfies this condition. A few of them are (3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15,...

Geometry: radius of circle, hypotenuese, radius of circle

hypotenuese, radius of circle, two circles: I m not sure I understand the problem, but it looks like there are two circles which are tanget. There is a third circle that is tangent to both. There is a line that is tangent to all three circles. This given, draw the circle that has radius 36 right...

Geometry: Why are they similar?, vertex angles, isosceles triangles

vertex angles, isosceles triangles, isoceles triangle: That was the answer to the wrong question. If the vertex angles are similar, the other angles must be equal as well since the sum of all of the angles in a triangle is 180° and the other two angles in an isoceles triangle are equal. Two triangles...

Geometry: Trigonometry - Aircraft, Pythagoras, Pythagorean Theorem

Pythagoras, Pythagorean Theorem: Hi Ian! I m not sure how much of an effect the curvature of the Earth has. If you were to neglect that effect, you would end up with a right triangle between you, the horizon, and the aircraft. This distance to the plane would be the hypotenuse of the...

Geometry: Analytical, y intercept, variable point

y intercept, variable point, slope of the line: Since A is on the x axis and B is on the y axis and P is a point such that PA = b, PB = a, and AB = a+b, then ... Well, take a line AB and put P on that line. If the length of AP + PB = the length of AB, then P must to on that line as well. That...

Geometry: Circles and Pentagons, minor arc, internal angles

minor arc, internal angles, inscribed angle: Hey Kevin! To my understanding, finding the diagonal is not necessary. Begin by finding the measure of each of the internal angles of the pentagon. This can be done using the formula (180)(n-2)/n, where n is the number of sides. Every vertex of the pentagon...

Geometry: Conventions for Drawing Shapes, dimensional shape, carmine

dimensional shape, carmine, wrong way: Hi Carmine! It does not matter. In 2 or 3 dimensions, shapes can be drawn with any perspective, provided the necessary faces are shown. The only wrong way to draw a cube would be to draw it head on, which would just be a square (this is not actually...

Geometry: conic sections puzzler, 4y, conic sections

4y, conic sections, note x: The original problem is x² + y² + 4y + 2x - 20 = 0. This can be changed to x² + 2x + __ + y² + y + __ = 20. To complete the square means to find out what goes in those blanks to make the equation be (x+a)² + (y+b)² = c, and hopefully c will be a square...

Geometry: Evaluating pi value, verticle lines, archimedes method

verticle lines, archimedes method, circumference of a circle: Look at one side of a hexagon. It has two endpoint that are on the circle. It is known that the shortest distance between two points is a straight line. This is the same as one side of the hexagon to get between these two point. Using the same approach,...

Geometry: Far Arc Near Arc Formula, circle

circle: Hey Megan! The measure of an angle formed by two intersecting secants through a circle is equal to half the difference between the far arc and the near arc. This means if you have two secants who intersect outside the circle, take the large arc formed...

http://en.allexperts.com/q/Geometry-2060/2010/5/f/Far-Arc-Near-Arc.htm

Geometry: Geometry, area of an equilateral triangle, area of a hexagon

area of an equilateral triangle, area of a hexagon, circumference of a circle: 1) V = πr²h where r is the radius and h is the height. 2) C = 2πr where C is the circumference and r is the radius. 3) V = lwh where l is the length, w is the width, and h is the height. 4) A hexagon contains 6 equilateral triangle. The...

Geometry: Geometry Help, geometry help, parallelogram

geometry help, parallelogram, small font: 24. It looks upsidedown with small font, but I can still read it. The height of E is the same as the height of D, so for E, y = t. In the x direction, D has been shifted s units from the origin, so shift F s units from the origin in the x direction. This...

Geometry: geomerty-simplifying radicals, simplifying radicals, square root

simplifying radicals, square root: The factors of 200 are 2, 2, 2, 5, and 5 (2*2*2=8, 5*6=25, 8*25=200). There are 2-2 s and 2-5 s with a 2 left over. This makes it √2²√5²√2 = 2*5√2 = 10√2. Another approach is that 200 is 100*2, and that 10² = 100, so the...

Geometry: Isosceles Proof, angle-angle-side, AAS

angle-angle-side, AAS, ASA: Hi Lettie, Show that ABD and ACD are congruent probably refers to the triangles. The perpendicular line creates a right angle in each triangle. It is given that the vertex angle of each triangle is equal. As the length of the bisector is equal to itself,...

Geometry: math, surface area of a box, boxes

surface area of a box, boxes, alex: If the smaller box has length 12, the width is 12x and the height is 12y. If the larger box has length 48, and it is similar in shape to the smaller, this means it has width 48x and height 48y. Since the surface area of a box is 2WL + 2WH + 2HL. ...

Geometry: math help, ft rope, hypotenus

ft rope, hypotenus, diagnal: Since the forms a right triangle with the mast as the vertical line and the line from the base of the telephone pole to the point at which it is tied the horizontal line. Thus, given A=12 and B=4, the hypotenus (which is the length of the rope) is the √(A²+B²)....

Geometry: Trigonometry - Definitions, sin, cos

sin, cos, tan: Hi Pooja, sin, cos, and all the rest are trigonometric operators. They exist because of we have defined them to represent certain things. It all has to do with a right triangle. The sine of an angle is defined as the ratio of the opposite side over the...

Geometry: Proofs - Diameter Tangents, interior angles, right angles

interior angles, right angles, parallel state: Hi Kieara, I won t prove it formally for you, but the basic idea is as follows. Tangents, by definition, form right angles to a radius of the circle. Since a diameter is two radii back-to-back, and thus the same line, both tangents actually form right...

Geometry: PYTHAGORAS THEOREM, square route, irrational numbers

square route, irrational numbers: You can find information on irrational numbers www.mathsisfun.com/irrational-numbers.html As found down a few pages, there are other irrational numbers, such as π and e, but more than that, √3, √5, √6 (which is √2√3),...

Geometry: PYTHAGORAS THEOREM RELATED WORD PROBLEM, pythagorean triangles, word problem

pythagorean triangles, word problem: Here is a list of the first few Pythagorean triangles: ( 3 , 4 , 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73)...

Geometry: Triangles - Isosceles & Scalene, isosceles triangles, scalene triangles

isosceles triangles, scalene triangles, vertex angle: Hi KK, Isosceles triangles have exactly two equal sides. As a result, they have two equal angles (typically referred to as the base angles; the other is the vertex angle). Scalene triangles have no equal sides, and therefore no equal angles. Thanks...

Geometry: Trigonometric ratios, maclaurin series, trigonometric ratios

maclaurin series, trigonometric ratios, advanced math: If sin(A) = 0, 1, or √2/2, the angle can be found. For other values of sin(), cos() can be found since sin²(x) + cos²(x) = 1. However, in general, the only way I know of to find t is with a calculator. Now if you re into advanced math, read on ......

Geometry: Volume - Test Tube, cylinder, sphere

cylinder, sphere, hemisphere: Hey Tony! You have a cylinder with a hemisphere attached to it. Consider both solids separately. Find the volume of each, then add them. For both parts you need the radius, which is half the diameter, so 8. The hemisphere s volume can be found by...

Geometry: volume of cylinder(sort of), volume of cylinder, volume of a cone

volume of cylinder, volume of a cone, tall cone: The volume of a cone is bh/3 where b is the area of the base and h is the height. One way to view it is as the difference in volume of two cones. The 1st one has base that is 12 in diameter and the 2nd one has a base that is 8 in diameter. This means...

Geometry: 2foot round circle, area of a circle, 2r

area of a circle, 2r, circumference: By two foot round circle , it sounds like the circumference is two feet. Is there supposed to be a square in front of the feet? Is that question suppose to be how many square feet are in a two foot round circle? The area of a circle is πr² where...

Geometry: Area Formulae for Hexagons, hey rosie, dimensional solids

hey rosie, dimensional solids, area formulae: Hey Rosie, There is no formula for any irregular polygon s area. You d need to subdivide it into other polygons and add their areas. As for volume, a hexagon is two-dimensional, so it has an area. Three-dimensional solids, such as cubes or pyramids,...

Geometry: Two-Column Proofs, formal proof

formal proof: Hey Aimee! Proofs like this require a labelled diagram. I ll do my best to describe one. There is circle O with diameter PQ. There is line AB, tangent to the circle at P. On the other side, there is line CD, tangent to the circle at Q. You then need...

Geometry: Coordinate Geometry, coordinate geometry, line c

coordinate geometry, line c, 2b: To be concurrent, put both of them in the form of -c = .... For the 1st line, -c = ax + by. For the 2nd line, -c = (3a + 2b)/4. Now that we have both equal to -c, we can set them equal to each other, so ax + by = (3a + 2b)/4. This can be divided...

Geometry: Elementary Concepts, multiplication of integers, creative thoughts

multiplication of integers, creative thoughts, tim tim: I just thought of a different approach. Look at a number line in the hall. Mark some point on the line as 0. If someone says to go 5 feet, you would move from 0 to 5. If they said to move 4 more feet, you would move from 5 to 9, since 5+4 = 9. On this...

Geometry: Trigonometry Without a Calculator, trig table, home depot

Geometry: Trigonometry Without a Calculator, trig table, home depot, electrical reference

Geometry: Geometry 10th grade Similar triangles, similar triangles, jhg

similar triangles, jhg, fhl: The sides on JHG are 3, 4, and 6. This means its perimeter can be found as 3+4+6 (which you can do), and I ll call P. The length of KM is 6, and KM corresponds to JG, which has length 4. Since 6/4 = 3/2, triangle KLM is 3/2 as large as JHG. Since KLM...

Geometry: geometry, upper case letters, angle the choice

upper case letters, angle the choice, triangle abc: In geometry, an angle is usually named as ABC, where A is on one straight side and C is on the other with B being at the vertex of the angle. The choice of A and C is arbitrary. If D is on the same line as A, it can be said that ABC = DBC. If ABC...

Geometry: Multiplying & Dividing Negatives, multiplication of integers, mathematical explanation

multiplication of integers, mathematical explanation, creative thoughts: Hi Abhinav, Strictly speaking, one word: pragmatism. Because it works. The actual mathematical explanation is that any negative number has a -1 that can be factored out, and (-1)(-1)=1 is indeed the adopted convention. This isn t very helpful, I know....

Geometry: math question for work, cross sectional area, fuel point

cross sectional area, fuel point, math question: If the diameter of the tank is 10 , the radius is 5 . The circle is sideways (right?), so the area filled would be the area of a section of the circle minus the area of the triangle between the surface and the center. If the depth of liquid is d, the...

Geometry: Trigonometry, trigonometric ratios, right triangle

trigonometric ratios, right triangle, hypotenuse: If you have a protractor, draw angles of these sizes. Make a right triangle with the right angle on one of the sides. Measure the sides and divide to get the answer. The sin() is the opposite side over the hypotenuse. That tan() is the opposite side...

Geometry: Trigonometry Without a Calculator, trig tables, trigonometric table

trig tables, trigonometric table, trigonometric ratios: Hi Shameem, Without a calculator, you would need a trigonometric table. This is a table with angles down one column and sin, cos, tan, etc. each in their own column. These were used until the advent of computers. Trig tables were made by repeatedly applying...

Geometry: triangles within parrallelogram, parallelogram, triangles

parallelogram, triangles, angles: Seaking more in terms of geometry, they have all sides the same since the diagonal of a parallelogram is congruent to itself and the sides are congruent since it is a parallelogram. The far angles are also congruent since it is a parallelogram as well. ...

Geometry: Lottery Odds, lottery odds, chances of winning the lottery

lottery odds, chances of winning the lottery, winning the lottery: Hi Sterling, It all depends on the process by which the lottery runner selects the winning numbers. If they are chosen completely at random, then the odds are identical, no matter if someone plays the same numbers each time. If the numbers are even somewhat...

Geometry: Symmetric, Reflexive, and Commutative Properties, symmetric property of equality, commutative properties

symmetric property of equality, commutative properties, line segments and angles: Hey Autumn, These are all similar, so be sure you understand how to distinguish them. The symmetric property means that a relationship works both ways. The symmetric property of equality, for instance, stipulates that if a=b, then b=a. The reflexive...

Geometry: Diagonal of Prism, Pythagoras, Pythagorean Theorem

Pythagoras, Pythagorean Theorem: Hey Jeff, All this problem requires is two applications of the Pythagorean Theorem. I want you to see the triangle formed by the diagonal of the base (a 10 by 7 faces), the 2-unit depth, and the diagonal AB (AB is the hypotenuse of this triangle). Do...

Geometry: Geometry:Circles, geometry problems, circle theorems

geometry problems, circle theorems, secants: Hey Samantha, Question 2 is a direct application of the far arc-near arc formula (FANAF). Question 3 is a tad more involved. The tangent and the secant define three arcs, which put together form a circle, 360 degrees. The indicated arcs are 150 and...

Geometry: geometry, area of a square, 5w

area of a square, 5w, five feet: The field is L by W. The area is LW. Now if the sides were increased by 5, the area would be (L+5)(W+5). Multiplying this out gives LW + 5W + 5L + 25. Taking the difference in these areas gives 5W + 5L + 25. This difference is said to be 245, so we...

Geometry: Hyperbolas & Ellipses, focus, foci

focus, foci, eccentricity: Hi Shameem, Let s begin by defining what a circle is: the locus of points equidistant from a single point known as the centre. To draw a circle, you could attach a pen to a pin with a string of fixed length. Put the pin in the wall and move the pen as...

Geometry: Plotting an Isoceles Triangle, Pythagoras

Pythagoras: Hey Hope, Start by sketching the given points. This gives you a very rough idea of what to expect. Then examine the most reasonable point (for me this was (2,-15)). For the triangle to be isosceles, two of the inter-point distances must be identical....

Geometry: Proofs for Isosceles and Speed, proof by contradiction

proof by contradiction: Hi Sara, I ll say this informally. Consider the two triangles created by the altitude. An altitude is, by definition, perpendicular to the base, therefore the two angles formed at the altitude are 90 degrees. Isosceles triangles have equal non-base sides...

Geometry: Spherical Coordinate, spherical coordinate system, spherical coordinates

spherical coordinate system, spherical coordinates, arbitrary point: Hi Keyvan, I would say to convert the coordinates to rectangular, and then use the extended Pythagorean Theorem. I do not know of a more convenient way to calculate distances in spherical coordinates, and it seems like symmetry alone wouldn t help you...

Geometry: Sum of Integers from 1 to 100, classic question, integers

classic question, integers, midpoint: Hey Erica! Classic question. Count pairs of numbers whose sum is 100, and then the the midpoint. (Don t know what s going on with AllExperts lately, but I m emailing them right away about this. + is supposed to be a plus sign. Really sorry about the...

Geometry: Supplementary or Complementary, geometry question, complementary angles

geometry question, complementary angles, supplementary angles: Hamad, They are in the same plane. Picture a side view of a staircase. Or an inclined plane, with a railing coming up out of it. If this were a three-dimensional drawing, beta would almost certainly be a right angle. This is a simple geometry question...

Geometry: Various, rhombus, parallelogram

rhombus, parallelogram, locus: Hi Sara! (a) It s worded a bit weird, but I believe the locus in question is the bisector of that angle. (b) The plane situated midway between the other two planes. (c) The right bisector of line AB. 2) I ll say this informally. Tangents are by definition...

Geometry: Area of Triangle, area of triangle, area of a triangle

area of triangle, area of a triangle, 2bh: Hi C, The height is three times the base? No problem. h=3b. No need to guess anything now, just put this in your equation and solve for b! 27=bh/2 27=b(3b)/2 54=3b² 18=b² You get the idea. This is a ridiculously useful technique known as substitution....

Geometry: Finding Z, lengths, sum

lengths, sum: Put the values into the equation given and solve for z. That is, z-3 + z+4 = 4z+15, and solve for z. Now the left side is 2z-3+4, which is 2z+1. This gives 2z+1 = 4z+15. It gives LM = -10, MN = -3, and LN = -13, but that does work since -10 0 3 =...

Geometry: Pizzas, medium pizza, radius of a circle

Geometry: Pizzas, medium pizza, radius of a circle, large pizza

Geometry: Isosceles Trapezoid, law of cosines, basic trig

law of cosines, basic trig, basic trigonometry: Hey Space Man, Use the law of cosines to find the angle between a leg and the long base. Drop altitudes from the edges of the short base, so as to subdivide the trapezoid into a rectangle and two congruent right triangles. Use basic trig to find the base...

Geometry: Law of Sines, triangle

triangle: Hi David! What you need here is the law of sines. It states that the ratio of a side to the sine of its opposite angle is the same for all sides in the same triangle, i.e. a/sin(A)=b/sin(B)=c/sin(C) (lower case are sides, upper case are angles opposite...

Geometry: Maths, math, cyllinder

math, cyllinder, volumn: If the cyllinder is laying down, the volume is pi*r²*w, where r is the radius f the circle and w is the width from end to end on the straight side. If the cyllinder is standing up, the volume is pi*r²*h, where r is the radius of the circle and h is the...

Geometry: Pizzas, medium pizza, large pizza

medium pizza, large pizza, area of a circle: Hey Brianna, The area of a circle is found by A=πr², where r is the radius of the circle. Medium pizza (a): a=π(13.5²) a=182.25π Large pizza (A): A=π(16.25)² A=264.0625π a/A=(medium price)/(large price) ... Note:...

Geometry: Square Root Counterexample, funky stuff, conjecture

funky stuff, conjecture, square root: Hey Olivia, Take x to be any number between 0 and 1. Root x will be greater than x. If x=0 or if x=1, Root x will be equal to x. Funky stuff tends to happen when the numbers are less than 1, 0, or negative. Always a good idea to give those a try....

Geometry: segment addition postulate, geometry, points in a line

geometry, points in a line: So the line has the points Q, T, R, S, and V, in that order. The pieces would be QT, TR, RS, and SV. The total line, from Q to V, is 23. The first segment, from Q to T, is 8. This leaves 15 over the intervals TR, RS, and SV. If TR = RS = SV,...

Geometry: Area of Circle, diameter circle, area of circle

diameter circle, area of circle, area of a circle: Hi Chris, The area of a circle is given πr², where r is the radius, and π is the constant approximately equal to 3.14. Given the circle s diameter, you d need to divide it by 2, then plug it into the formula above. Thanks for asking, Azee...

Geometry: Area of a Triangle with Variable, finding the area of a triangle, area of a triangle

finding the area of a triangle, area of a triangle, how to find the area of a triangle: Hi Kiwi! The area of a triangle is half the product of the base and the height. If you want a numerical area, then you need both dimensions numerically. If the only information you have is what you have given me, then the result will be algebraic. ...

Geometry: Basic Trig - Ladder Against Building, basic trigonometry, foot ladder

basic trigonometry, foot ladder, right triangle: Hey Sharonett! The building, the ground, and the ladder form a right triangle. You need to use basic trigonometry to solve for the base of this triangle. This is done using the trig operator cosine, which is the ratio of the adjacent side to the hypotenuse....

Geometry: Coordinate Geometry - Linear Equations w/2 Variables, slope, intercept

slope, intercept: Hi Zachary! The line can be expressed by a number of equations, but the simplest one to find is the slope-intercept form, that is to say y=mx+b. To find the slope m, divide the rise by the run, that is the difference in y over the difference in x. (The...

Geometry: Finding the Equation of a Line, slope, intercept

slope, intercept, parallel: Hey Jolleen! Begin by finding the slope of the line. Parallel lines have identical slopes, so the line you seek shares the slope of the line between the two given points. It is equal to the difference in y divided by the difference in x. You know have...

http://en.allexperts.com/q/Geometry-2060/2011/1/f/Basic-Trig-Ladder-Against-1.htm

Geometry: Integers on a Circle, integer solution, modulus

integer solution, modulus: I can say that the points on the circle are integers are (-3,-4), (-4,-3), (-3,4), (4,-3), (3,-4), (-4,3), (3,4), and (4,3). I have never applied modulo to graphs, however, only integers. I will assume it is applied to x and y. When modulo n is done,...

Geometry: Length of a Chord, math, polygon

math, polygon, length: It is given that the radius is 10 and the circle is divided into 11 parts. Are these equal parts? If so, the interior angle for each is 360/11 = 33 1/3 degrees. If one triangle is looked at, but the interior angle in half to get two reflective right...

Geometry: Polygons - Internal Angles, internal angles, interior angles

internal angles, interior angles, camping tent: Hi Daisy, For an n-sided polygon, the sum of its interior angles is given by 180(n-2). From this equation, find the sum of the angles in the tent (ignoring the inner part). Then equate that to the sum of the individual angles in the tent. Solve for x...

Geometry: Rhombus, diagonal, perimeter

diagonal, perimeter, area rhombi: Hi Daisy, Rhombi have four equal sides, so their perimeter is simply the side length multiplied by four. The area, like that of a rectangle or any parallelogram, is the product of the base and the height. A cool property of rhombi is that their diagonals...

Geometry: Trig, math, algebra

math, algebra, quadratic: An x can factor out, giving x(x² - 6x - 10). To find the factors of x² - 6x - 10, use the quadratic equation. To use the quadratic, it is known that a=1, b=-6, and c=-10. The quadratic equation is x = (-b ± √(b²-4ac))/(2a). Putting in a, b, and...

Geometry: trapezium, math, geometry

math, geometry, trapezoid: Draw one diagonal, and this can be seen to divide the triangle into two triangles. Between n1 and p1, make the angle A1 and between n2 and p1, make the angle A2. Make p1 into the longer side and angle A1 between n1 and p1 and A2 between n2 and P1. Further,...

Geometry: Complementary Angles, complementary angles, algebraic expressions

complementary angles, algebraic expressions, degree sign: Hi Tyjane, Complementary angles sum to 90 degrees. This means angle A plus angle B equal 90 degrees, which means the sum of their algebraic expressions of x equals 90 degrees. (3x+2)+(x-4)=90 from which you can solve for x, and then plug it into angles...

Geometry: Determining Triangle Congruence, triangle congruence, internal angles

triangle congruence, internal angles, congruent segments: Hi Ian, PT=PT by the reflexive axiom, which is necessary to mention. Stating that IT is parallel to OP by hypothesis should precede the alternate internal angles conjecture. Your overall reasoning is correct. A note on semantics: for the alternate...

Geometry: Geometry, quadratic formual, surface area

quadratic formual, surface area, cm3: The height is 4x cm and the volume is π(15x^3 + 48x^2 + 36x)cm3. ai) Since the volume V = πr²h, the radius is given by r = V/(πh). Put in what V and h are to get r in terms of x. aii) The total surface area of a cyllinder is 2πrh...

Geometry: Geometry, triangle abc, angles in a triangle

triangle abc, angles in a triangle, 3x: It is known that the sum of the angles in a triangle is 180. This means that is we take m A = 2x, m B = 3x, and m C = 5x and add them up, we get 180. In other words, 2x + 3x + 5x = 180. This is the same as (2+3+5)x = 10x, so we have 10x = 180. To find...

Geometry: Geometry, algebra, cylinder

algebra, cylinder, area: The surface area I will assume to be the outside of the cyllinder, for the bottom is not on the surface, it is against a table. The area is then 2πrh, where r is the radius and h is the height. If this is 500*π cm², then set 500 π cm...

Geometry: Geometry, Sillogism and Detachment

Sillogism and Detachment: Using the Law of Detachment, we can say that X, Y, and Z or collinear since they meed the condition of the first statement (if three points are on a straight line). A good place to see the Law of Detachment and the Law of Sillogism is http://www.youtube.com/watch?v=zf3KCOrpcaI...

Geometry: Triangle question, trig, triangle

trig, triangle: It must be known what the angle is. If it is 45°, then both sides are the same, and that is C/√2, where C is the hypotenuse. If it is another angle, say T, then the legs are A = C*cos(T) and B = C*sin(T) where A is near angle T and B is on the opposite...

Geometry: Curve/Point, arc length, basics of geometry

arc length, basics of geometry, nth number: Hi Kevin, Strictly speaking, there are countable infinites and uncountable infinites. The natural numbers (1, 2, 3, 4,...) are countably infinite as we will never be able to stop counting them, but we know HOW to count them. There is a first number. ...

Geometry: Diameter and Circumference, arc length

arc length: Hi Daniel, Draw a circle of radius R centred at the origin. Treat it essentially as you would the unit circle. Every point on the circle has coordinates (Rcos(b), Rsin(b)), where b is the angle measured to the positive x-axis. Focus on the x-value, Rcos(b),...

Geometry: elementry algebra, line, slope

line, slope, y-intercept: Put the equation in the proper form, as in y = mx + b. For this one, just add x to either side, giving y = x + 5. When the equation is in the form y = mx + b, the slope is m and the y-intercept is b. This means the line has slope 1 and crosses the y-axis...

Geometry: Geometry, line segments, line segment

line segments, line segment, line ac: It is known that both line segments contain BC; let L(xy) be the length of xy. It is known L(AB) + L(BC) = L(AC) and L(BC) + L(CD) = L(BD). Thus, it can be said that L(AB) = L(AC) - L(BC), since L(AB) + L(BC) = L(AC); L(AC) - L(BC) = L(BD) - L(BC), since...

Geometry: mathematics, 7i, magnitude

7i, magnitude, greater than signs: Greater than signs are used for real nuumber. As far as magnitude goes, 7i has magnitude 7 and 2i has magnitude 2, so the magnitue of 7i is greater than the magnitude of 2i This also can be applied to the imaginary multiples in the numbers. Since 7...

Geometry: Octogon prism lenght, geometry, volume

geometry, volume, octagonal cone: Sorry, but I m from the US. I think are comma (,) and period (.) are the opposite of yours. The area of an octagon is 4r². The height of the octagonal pyramid is h. The volume of the octagonal pyramid is 4r²h. If you say the radius is 3.5 cm and the...

Geometry: Proving Lines Parallel, angles of a triangle, right angles

angles of a triangle, right angles, m6: Given angles 3 and 6 are right angles, since the lines are perpendicular at these points, and given that angle 4 is the same as angle 2, we know that angle 1 is the same as angle 5. This is because the angles of a triangle always add to 180, so m1 + m2 +...

Geometry: Surface Area, cyllinder surface area

cyllinder surface area: This sounds like we are generating a cyllinder with the center on the x-axis. It is known that the circumference of a circle with radius r is 2πr. The surface area of a cyllinder is 2πrh, where r is the radius and h is the height. Here, the...

Geometry: Tables, linear equation, absolute value

linear equation, absolute value, 3x: If y = -3x - 5 is given, looking at the x value being -4 gives -3(-4) - 5 = 12 - 5 = 7, and that is the y value. Checking x=0 gives y=-5, x=1 gives y=-8, and x=4 gives -17. To get the unknown y value, then, take -3(-2) - 5 = 6 - 5 = 1, and that is B....

Geometry: Triangle Congruency, triangle congruency, isosceles triangle

triangle congruency, isosceles triangle, segment bd: Hi Alex, As written, if BD splits the isosceles into two right triangles, angles ADB and CDB are by definition both right and therefore equal to each other. I know this isn t what you re asking, but I can t tell exactly what it is you are. If you can...

Geometry: triangles, acute triangle, orthocenter

acute triangle, orthocenter, point c: Yes. Lets put A at (-1,0) and B at (1,0). The point C must be chosen at (0,y) so that the distance from the orthocenter (which is on the y-axis) out to y is 2. I haven t looked into how to construct this, other than by geometry as seen in http://www.mathopenref.com/constorthocenter.html,...

Geometry: Angles of depression, trig, sin

trig, sin, tan: If the angle is 3°, and we call the height h with the other side being 10 miles, we have a slight problem. Is that 10 miles the actual distance, making it the hypotenuse, or is it the horizontal distance, making it the other leg of the triangle? The...

Geometry: Congruency Proof, triangle, bisect

triangle, bisect: Hi Kim, It is given that angle BAD is congruent to Angle CAD and therefore triangles BAD and CAD are congruent by AAS congruency. AD bisects BC is equivalent to saying AD and BC have the same measure. This follows by corresponding parts of congruent triangles....

Geometry: Geometry Homework I do not know where to start!, traijngles

traijngles: For the 1st one, I know how to do it if it is an equilateral triangle. The angles are all 60°. Contstructing the medians cuts all of the angle in half. This means that each of these lines intersects the far side at 90°. If the big triangle is cut in...

Geometry: Geomtry Using Similarity, quotients, quotient

quotients, quotient, similarity: Hi Angel, Once you ve converted all measurements to the same units, divide the width of the wall by the width of the mural. Then divide the height of the wall by the height of the mural. Take whichever of the two quotients is smallest. Multiply the other...

Geometry: help help help, set theory

set theory: Draw a circle and label it m. Since m - n, n must be inside the circle, so make a smaller circle for n inside of m. Since ~m - s, everywhere outside of m must be in s, as well as a small piece of the inside of m and inside n, since we don t know...

Geometry: math, cube, faces if each subcube exposed

cube, faces if each subcube exposed: There are 125 cubes, and 125 = 5*5*5, so each edge if 5 cubs long. The number with 3 faces painted red is the number of corners. Since the outside is made of squares, there is a top and a bottom. Since there are 4 corners to a square and two squares with...

Geometry: trigo, trig

trig: Use the formula cos 3a = cos 2a cos a - sin 2a sin a. Once this has been done, use sin 2a = 2 sin a cos a, cos 2a = cos²a - sin²a. 2 cos a (cos²a - sin²a) + 4 sin a (2 sin a cos a) 2 cos³a - 2 cos a sin²a + 8 sin²a cos a 2 cos³a + 6 cos a sin²a 2 cos³a...

Geometry: Trigonometry, angle of depression, basic trigonometry

angle of depression, basic trigonometry, right triangle: Hi Omn, Begin by drawing a diagram of the situation. The buildings are understood to be perpendicular to the ground, so you have a right triangle of height 8, base d (between buildings), and an angle of depression 30 degrees. This sits inside a larger...

Geometry: Diagonal of Cube, Pythagorean Theorem, Pythagoras

Pythagorean Theorem, Pythagoras, 30-60-90: Hi Gay, Knowing the properties of 45-45-90 and 30-60-90 triangles is very useful, but it is the trusty Pythagorean Theorem (a²+b²=c²) which will always come through for you. To begin, find the diagonal of the base of the cube. This is simple as it is...

Geometry: Diagonal of Cube, square root of 3, heighth

Geometry: Diagonal of Cube, square root of 3, heighth, 3a

Geometry: Isosceles-based Prism, total surface area, surface area

total surface area, surface area, area: Hey Patrycja, First off, all prisms have rectangular faces. Take the base, whatever shape if may be, and extrude it. The result will be a prism. Imagine a cake. Trace an isosceles triangle on the top. Now use a knife and cut all the way down the cake...

Geometry: Parabola - Bridge, vertex

vertex: Hi Allen! That question was asked 37 months ago today... And in retrospect, I don t know what I did to end up with that result. So here s a different method that gives a different - but most definitely correct - result. I am setting my bridge entirely...

Geometry: Surface Area, dimensional geometry, irregular shapes

dimensional geometry, irregular shapes, surface area: Hey Jen, Surface area, or simply area, is the expression of two-dimensional geometry. It is the product of two dimensions: height and length, though potentially nontrivial to compute when curves and irregular shapes are involved. Surface area with reference...

Geometry: Volume of a Triangular Prism, volume of a triangular prism, slant height

volume of a triangular prism, slant height, right triangle: I am sending along a drawing of a triangle, sides of length 1. Each of the six triangles that are sketched out are suppose to be of the same size, and all of them share the center point in common. A 30-60-90 degree triangle has edges 1 and root(3), with...

Geometry: Apex or Vertex?, cone

cone: Hi Elena, When I was first taught solids, the same question came up. My teacher hesitated, but gave the correct response: apex. Apexes (or the fun plural apices!), especially at that level only really appear in cones. In my opinion, being taught something...

Geometry: Circle and Pi, circle circumference, regular polygon

circle circumference, regular polygon, equilateral triangle: A circle can be thought of as being similar to a regular polygon. If an equilateral triangle has side of length A, the perimiter is 3A. The big radius from the center to a corner is A/2 and the radius from the center to a corner is (√3 - 1)A. The...

Geometry: Circle and Pi, circumference, diameter

circumference, diameter: Hi Apoorv, All circles are similar. They can be expanded or contracted, but all their relative properties remain the same. Consider equilateral triangles. They all have internal angles of 60 degrees. Or squares, they all have a diagonal equal to the...

Geometry: Eigenvalues of a 3 x 3 Matrix, characteristic equation

characteristic equation: Hi Mark, The characteristic equation of a 3x3 matrix is a polynomial of degree 3. The roots of this polynomial are the eigenvalues of the matrix. All third-degree polynomials have at least one real root (try drawing a cubic that doesn t cross the x-axis...)....

Geometry: Exponent Issue, fractional exponent, factor

fractional exponent, factor: Hi Ann! Almost anything mathematical can be featured in an exponent. Fractional exponents are fairly common. To simplify matters, you can think of the fractional exponent in the form of (power/root). For instance x^(3/2) is equivalent to the square root...

Geometry: Intersection of Angle and Perpendicular Bisectors of a Triangle, orthocenter, circumcenter

orthocenter, circumcenter, centroid: Hey Deni, The angle bisectors will cross at the incenter and the perpendicular bisectors will cross at the circumcenter. If the triangle is equilateral, the incenter and circumcenter are coincident, along with the centroid. If you d like more information,...

Geometry: Lateral Area - Triangular Prism, surface area of a triangular prism, area of a triangular prism

surface area of a triangular prism, area of a triangular prism, law of sines: Hi Cindy! The lateral area of a triangular prism (or any prism) is the base perimeter multiplied by the height, and the total surface area is the lateral area plus two base areas. The area of a triangle is given by the half the product of its base and...

Geometry: Math, math, area

math, area, error: The area of a circle is pi*r^2, so a half-circle has area pi(r^2)/2. Since 35^2 is 1225, the area is 1225*pi.2 = 612.5*pi. That works out to be around 1900 sq ft, and that is since the radius is given as 35, and that is only two places of accuracy. If...

Geometry: Math, math, surface area

math, surface area: I believe the lateral surface area is all the area except the base. That is, the four sides and the top. Two sides have area 20*13 = 260, two sides have area 5*13 = 65, and the top has area 5*20 = 100. This means the total area is 2(260) + 2(65) + 100 =...

Geometry: Maths Geometry, math, geometry

math, geometry: If APB is 120°, and since APO is congruent to BPO, this makes both angles 60°. Since PA is tangent to the circle, this makes PAO a right triangle. Since one angle of this right triangle is 60°, we have a 30°-60°-90° triangle, and it is known that the hypotenuse...

Geometry: Reducing Fractions, proper, improper

proper, improper: Hi Mackenzie, When reducing fractions, you need to divide by the greatest common divisor in the numerator and denominator. For instance, 4/6 reduces to 2/3, as both 4 and 6 are evenly divisible by 2. If the fraction is improper, the same rule applies;...

Geometry: Rotations, centre, center

centre, center: Hi Cathy! About O means point O is the centre of rotation. Consider the following. Place a pencil on your desk. Gently push down towards the table, on the eraser end. With your other hand, push the pencil point along the table. The result? The pencil...

Geometry: Similarity - Paint Can, scale factor, cylinder

scale factor, cylinder, volume: Hi Tien, Scale factors refers to the ratio of one-dimensional sides. This means for the smaller can, it would have a radius of 2 inches and a height of 6 inches. When dealing with areas, it is the square of the scale factor that is of interest, and with...

Geometry: Triangles, triangle abc, right triangles

triangle abc, right triangles, right triangle: Is this suppose to say, In a triangle ABC, AB is perpendicular to BC, b c, C=23° and ... ? What is, AD=abc/b^2-c^2 ? Is that suppose to be something like a^2 + b^2 = c^2 for right triangles? This is a right triangle, since AB is perpendicular to BC....

Geometry: word problem involving are and perimeter, math, algebra

math, algebra, area: Let the length of a rectangle is x and the width is y. The area is xy and the perimeter is 2x+2y. The 1st statement says that x = 4y. The 2nd statement says that 2x + 2y = 100. Putting the 1st into the 2nd gives 2(4y) + 2y = 100. Multiplying out the...

Geometry: analytical geometry, algebra, slope

algebra, slope, perpendicular: Slope is given by two points on a line. When the two points are (x1,y1) and (x2,y2), the slope is (y2-y1)/(x2-x1). For some examples ... ... if a line has slope 2, then the perpendicular line has slope -1/2; ... if a line has slope -1/3, then the perpendicular...

Geometry: Can you answer this?, math, algebra

math, algebra: The x coordinate of a point is the abcissa and the y coordinate is the ordinate. Since the line is at 45 degrees, the equation is given by y + 9/2 = x + 5/2. If the ordinate is 6, that means y is 6. The equation has y + 9/2, so in halves, we have 12/2...

Geometry: Congruency Cases - SSS, SAS, AAS, mathematical theorems, formal proof

mathematical theorems, formal proof, degrees of freedom: Hello Abhinav, The theorems can all be proven essentially by contradiction. However, they require diagrams that I cannot provide here. I leave it to you to research these proofs (Google should lead you well) if you so desire. While there are some mathematical...

Geometry: Geometry, geometry, parallel lines

geometry, parallel lines, crossing line: After drawing out what was talked about, I found someone who presents the subject very well. He is at http://www.mathplanet.com/education/geometry/perpendicular-and-parallel/angles,-parallel-lines-and-transversals It covers the relation between all...

Geometry: Geometry, algebra, triangles

algebra, triangles: That is since if any of these conditions are true, it can be shown that two triangles are congruent and therefore the rest of the rules can be seen to be true as far as S.S.S., S.A.S., and A.A.S. I have found that R.H.S. relates to a right triangle, a...

Geometry: geometry, geometry, circle

geometry, circle: It is known that if two angles in a circle are equal, the length of the arc s are also equal. That is, since B and C are congruent, this means that the circle sections AC and AB are congruent. If acr CB is added to AC, area ACB is gotten. If arc CB is...

Geometry: Internal Line Division, analytic geometry

analytic geometry: Hey John, If you draw the line, it looks something like this: P--O--------Q, with P being the lowest point and Q being the highest. Point O splits the line in a 1:4 ratio. The ratio that is higher up on the graph is 4, and the lower one is 1. The higher...

Geometry: Math, algebra, line

algebra, line: A line can be written as y = mx + b, where m is the slope and b is the y-intercept. Since we are given the slope is 2, that means that m is 2. Since we are given the y-intercept is -3, that means that b is -3. This makes the line into y = 2x - 3. ...

Geometry: Trigonometry, trig, sin

trig, sin, cos: In the attatched image, the top angle is B, the lower left angle is A, and the right angle is C. The side opposite angle A is a, the side opposite angle B is b, and the side opposite the right angle C is c. It could also be said that a^2 + b^2 = c^2. ...

Geometry: Volume and Area of Solids, algebra, lateral surface

algebra, lateral surface, prism: According to http://en.wikipedia.org/wiki/Triangular_prism a triangular prism has the top and bottom as triangles and the sides as rectrangles. The lateral area would be the sum of the lengths of three sides on a triangle times the height. So, if...

Geometry: Factor Completely, rectangular prism, lateral area

rectangular prism, lateral area, math teacher: Hey Kelly, The expression for volume can be factored into V=(xy)(x²-2xy+y²), and then into V=(xy)(x²-y²)². The parenthetical with the square corresponds to the side of the square, and the xy corresponds to the height. You can make another equation with...

Geometry: Finding the Exact Value of Trig Functions, trig function, quadrant ii

trig function, quadrant ii, trig functions: Hi Sarah, As the sine of an angle represents a y-value on the trig circle, it can have a different value in a different quadrant. sin(a)=sin(180-a). Because you are told that A and B are in quadrant 2, you need to use the large angle, i.e. 180 minus the...

Geometry: Finding the exact value for trig identities, trig function, trig identities

trig function, trig identities, quadrant ii: Use tan(x) = sin(x)/cos(x). Once this has been done, sin(A-B) = sinAcosB - sinBcosA and cos(A-B) = cosAcosB + sinAsinB. This is from http://www.ies.co.jp/math/java/trig/kahote/kahote.html which states that sin(A+B) = sin A cos B + cos A sin B sin(A-B)...

Geometry: geometry question, isosceles triangle, geometry question

isosceles triangle, geometry question, perimeter: If the legs are of equal length and each is 8 cm longer than the base, that means the length of the three sides is b, b+8, and b+8. The perimeter is the sum of all the side lengths. Add the lengths of the sides together, getting b + b+8 + b+8. That...

Geometry: Polynomials, monomial, binomial

monomial, binomial: Hi Nagesh, There are numerous properties that apply to functions where the exponents on x are all positive integers. (The domain being all real numbers and the Fundamental Theorem of Algebra are two such properties.) These properties fail to hold if we...

Geometry: Proving a Trigonometric Identity, half-angle formula, sin

half-angle formula, sin, cos: Hi Amanda! You ve almost got it. The half-angle formulas are sin^2 x = (1 - cos2x)/2 and cos^2 x = (1 + cos2x)/2. The divisions by 2 cancel each other, but you are still required to show them in your intermediate step. Thanks for asking, Azee...

Geometry: Quadratic Trigonometric Equation, arcsin, arcsine

arcsin, arcsine: Hi Danny, The sine of an angle represents the y-coordinate of a point on the unit circle. Provided θ is neither 90 degrees nor 270 degrees, there will be an angle in both quadrants I and II, or both quadrants III and IV. This gives rise to the identities...

Geometry: Quadratic Trigonometric Equation, sin, sine

sin, sine: Hi Kenny, Substitute sin(delta) with x. The equation becomes 2x²+x=1, or 2x²+x-1=0. This is a quadratic equation, and its roots are found to be x=-1 and x=1/2. This means that sin(delta)=-1, and sin(delta)=1/2. You should be able to find the possible...

Geometry: Solving Logarithmic Equations, change of base

change of base: Whoa Eddy, You re raising 64 to the power of x? Please explain your reasoning! Whenever you have a logarithm and you want to get rid of it, do the following. The base of the logarithm becomes the base of the exponent, and the argument of the logarithm...

Geometry: Solving for x, squareroot

squareroot: The x^2 terms can t be cancelled, for this would leave 64/[(1/x^2) + 1] = 16. However, that is a good place to start. Multiplying both sides by [(1/x^2) + 1]/16 gives 4 = (1/x^2) + 1. Subtracting 1 from both sides gives 3 = 1/x^2. Inverting both sides...

Geometry: Trigonometric Identities, trigonometric identities, correct question

trigonometric identities, correct question, sines and cosines: Hey Kyle! A strategy I find helpful with these problems is to break all the operators into sines and cosines. Refer to the definitions: (tan x)=(sin x)/(cos x), (csc x)=(1/sin x), (sec x=1)/(cos x), (cot x)=(1/tan x)=(cos x)/(sin x). For question 1, split...

Geometry: Turn rate determined by math function, spiraling robot

spiraling robot: EQUATION In polar coordinates, a sprial is given by r = a + bΘ where r is the radius and Θ is the angle. A place to look and see a spiral is http://en.wikipedia.org/wiki/Archimedean_spiral but that only speaks of the equation of a spiral, so read...

Geometry: 3D Object's Cost, volume, area

volume, area, perimeter: Hey Jim, The first thing you need to do is select the shape of the 3D object. You then need to create equations for its volume, surface area, and edges. (Ideally, these should all be in terms of a single variable.) Those equations must be multiplied...

Geometry: 3D vector, ellipse

ellipse: If r=(x,y), r1=(x1,y1), and r2 = (x2,y2), an ellipse is the set of all the points where the distance to r1 plus the distance to r2 is some constant k. The distance to a point r from r1 is √[(x-x1)²+(y-y1)²]. Similarly, the distance from r to...

Geometry: Basic Trigonometry, tangent, opposite

tangent, opposite, adjacent: Hi Bob, The key to solving both of these problems is reducing the situation to right triangles. Drawing a diagram is often very helpful. In the first problem, consider the tree as the height of a triangle, and Tim s distance from it as the base. We...

Geometry: Constant width curves, circle, radius

circle, radius, diameter: I believe this is true, but that is the most common place the radius and diameter are used. Perhaps they might be used in say, a shell of a snail. Here, the radius would be increasing as the outside if gone around, but I m not sure a diameter even makes...

Geometry: "Very Difficult Question in Geometry", degree polynomial, xy plane

degree polynomial, xy plane, quartic equation: All right Jazzzzzzz, here goes. In two dimensions, consider a 5m by 5m shed adjacent to an arbitrarily tall house. A 20m ladder touches the ground, the corner of the shed, and rests against the house. The question is: how high up does the ladder touch...

Geometry: Geometry, cone, surface area

cone, surface area, volume: The equation for the volume of a conve is V(r,h) = pi*r²h where r is the radius and h is the height. The surface area is pi*r² + pi*r*h. Note that the 1st term is the area of the bottom and the 2nd term is the area of the side. For this problem,...

Geometry: Given an Arc's length, how does its height vary with its width ?, circular arc, bottom corner

circular arc, bottom corner, plywood: It sounds like you re trying to cut letters out of plywood, one letter per piece. It sound like the sheet of plywood is 2440mm long, which is barealy over 96 inchese. That is the same as 8 feet. If sounds like this is the length and the width would then...

Geometry: Loci Help!, locus, circle

locus, circle, angle bisector: Hey Helen, If we re indeed in the plane (2-D) and not in space (3-D), then your statements regarding the angle bisector and circle are correct. Technically, the locus of points around both would be the intersection of points of the two loci. In the...

Geometry: sin(ab), trig identity, sines

trig identity, sines, cosine: Hey Adam, To my knowledge, there is no general identity that will give you a result with no ab product. This may be possible using complex numbers and Taylor series, but it will not pretty. It sure won t be as nice as a sum of sines. However if there...

Geometry: Standard Form of a Line, perpendicular

perpendicular: Hey Julia, Perpendicular lines have slopes that are negative reciprocals of one another. An approach you can take is to find the perpendicular slope, then find the slope-intercept form using the given point, and finally convert that into the standard form....

Geometry: triangles and trigonometry., trig, law of sines

trig, law of sines: Use the law of sines, which says a/sin(A) = b/sin(B) = c/sin(C). The sides used are the ones oppositve the angle. Let a = 23, so A = 54 degrees, b = x, so B = 64 degrees. Using the formula, we can say 23/sin(54 degrees) = x/sin(64 degrees). Multiplying...

Geometry: trigonometry, circumference of a circle, png format

circumference of a circle, png format, sexagesimal: For 1, sexagesimal uses 60 as the base and centesimal uses 100 as the base. I don t follow, for it seems like 60x would be 1 unit, where as 100 y would be 1 unit. This implies that 60x = 100y, so 250x = (25/6)100y = (1250/3)y. For 2, the answer is pi,...

Geometry: circular functions, trig

trig: Since the value of x is 3pi/4, the value of 7x is 21pi/4. Since there are 2pi degrees in a circle, and this is the same as 8pi/4, we can subtract 8pi/4 from the angle. This means that 21pi/4 is the same as 13pi/3, and that is the same aas 5pi/4. Since...

Geometry: Geometry, radius of moon, reflective triangles

radius of moon, reflective triangles, triangle abc: I can answer 2, but I ve thought about 1 and 3, coming up with no way to show it. Note that on 3, for any triangle with sides a, b, and c, b^2 + c^2 - 2*b*c*cosA = a^2. For 2, that generates two reflective right triangles. The center is from your eye...

Geometry: Isoceles Trapezoid Diagonal, Pythagorean Theorem, Pythagoras

Pythagorean Theorem, Pythagoras: Hi Ankur, Let a be the short base, b be the long base and c be the length of the equal sides. Draw the trapezoid s diagonal. Now draw the rectangle that shares that diagonal. The objective is to use the Pythagorean Theorem on this rectangle to solve...

Geometry: Loci Help! (illustrated), circle, intersect

circle, intersect: Hey Anna, In the diagram, BX is the angle bisector. The zero-point case is when the given distance of P is d0. No points fit the bill: the locus is null. The one-point case is when the given distance of P is d1. The locus consists only of the intersect...

Geometry: Mirrored Numbers - (Exact Replica of the Number) - Optics & Real Life Use ?, mirror glass, palindromic numbers

mirror glass, palindromic numbers, glass object: Hi Prashant, Mirrored Numbers are palindromic numbers containing the digits 0, 1, and 8. I don t believe this property has applications in physics or nature. The only real life applications I can think of would be aesthetic: a number on a window that...

Geometry: Negative Angles, Complement, degrees

Complement, degrees: Hi Lance, It would be a stretch to allow x to take on negative values. By definition, complementary angles sum to 90 degrees. An angle added to its complement will yield a right angle. In geometry, negative angles are not considered to be subtractions....

Geometry: Pi, exact value of pi, mathworld wolfram

exact value of pi, mathworld wolfram, algebra series: The distance will be a real number, but it can t be expressed as a fraction. It is known that pi can be calculated by an infinite sum of a(n)x^n where there is some expression to calculate a(n). Expressing pi is just like trying to write 1/3 in decimal...

Geometry: Quadractic Relations, triangle, right triangle

triangle, right triangle: Hi Michael, The area of a triangle is determined by A=bh/2. You know A=30, b=(x+6) and h=(x-1). Plug them into the area equation and rearrange to have an equation quadratic in x. Solve it and determine the appropriate x value(s) to select from the quadratic...

Geometry: Geometry Problem & Symbols?, pi, rounding

pi, rounding: Hi Miss Susan Wilson, You answered the first question correctly. Note that having found the measure of angle 2, you could then simply have subtracted it from 180 to get that of angle 1. However, solving it the way you have, when you re not pressed for...

Geometry: Proofs - Isosceles Triangle, isosceles, triangle

isosceles, triangle, proof: Hi Gilbert, By the definition of perpendicular, angles BDA and CDA are both 90 degrees. BD=BC (given) and AD=AD (reflexive axiom). Considering triangles ACD and BCD, they are congruent by SAS congruency. Therefore, by corresponding parts AB=AC. Now...

Geometry: Finding Endpoints, line segment, endpoint

line segment, endpoint, midpoints: THe midpoints is halfway between the two endpoints. If the other endpoint is (x,y), then (8+x)/2 = 3 and (2+y)/2 = 8. Multiplying both equations by 2 gives 8+x=6 for the 1st and 2+y=16 for the 2nd. Subtracting 8 from both sides on the x equation gives...

Geometry: Geometry, triangle, geometry

triangle, geometry: If D is the midpoint of BC, E were the midpoint of AB and F were the midpoint of AC, it would seem that the triangles CFD, AFC, AED, and BED would all have to be the same. This makes the length of BD the same as AD the same as DC, so CB would be twice AD....

Geometry: Geometry - Complement & Supplement, complement, supplements

complement, supplements: The angle has measure A. To have a complement, 0 = A = 90. The supplement is 180 - A. If 3/4 of this angle is take, it has measure 135 - 3A/4. To have a complement, we need 0 = 135 - 3A/4 = 90. Subtract 135 from each of the 3 terms and get -135...

Geometry: Length of a chord, algebra, circle cross section

algebra, circle cross section: This picture is a crosss-section of what is filled. A is the measure of the radius to the edge of the top of the fill line. The area of the light blue area is pi*r^2*(2A+pi)/(2*pi). The area of the dark blue area is ab, where a is half of the length...

Geometry: tangent, point of intersection, conic section

point of intersection, conic section, y 108: If the function is f(x) = Ax^n, the slope at x0 is nA(x0)^(n-1) and the point of intersection is (x0,A(x0)^n). Thus, to find the equation that passes through 2x^5 + 4x^3 + 6x at x = 2, the slope would be 5*2x^(5-1) + 3*4x^(3-1) + 6x^(1-1) = 10x^4 + 12x^2...

Geometry: Tangent to Conic Section, conic section, derivative function

conic section, derivative function, coordinates: Hey jazzzzzzz, Choose an appropriate interval where you can define the conic section as a function. Then compute its derivative function. This will give you the slope or directional vector towards that point. Using what you have just found along with...

Geometry: Year 12 Further Mathematics - Trigonometry, cube, pyramid

cube, pyramid, area: I m not sure what a trapezium is. The area of a trapezoid of width W with sides A and B that are parrallel is W(A+B)/2. As I read the question, it says, A car park is to be made by running a straight line on a bearing of 25 degrees until it meets the...

Geometry: Year 12 Further Mathematics - Trigonometry, area and perimeter, further mathematics

area and perimeter, further mathematics, parallel sides: 1. A hiker walks 3.2 km on a bearing of 120 degrees and then takes a bearing of 055 degrees and walks 6 km. What is his bearing from the start? Since 0 degrees is dues east, the 3.2 km would be 1.6 km to the west and 1.6√3 km to the north. He then...

Geometry: 8th grade made, histogram

histogram: Since if the shots are between 105 and 115 they are considered to be accurate, these need to be the cutoff points. Since that is 11 data points, put 11 data points in each bar below and above. That would make the next lower bar anything from 94 to 104,...

Geometry: Derivation of formula of frustum of a cone, geometry, surface of a cone

geometry, surface of a cone: It is known that the slanted surface area of a cone is pi*s*r, where pi is 3.14159265..., s is the length from the point on top to the bottom edge, and r is the radius of the circle at the bottom. It is known that the bottom surface area is pi*r^2. ...

Geometry: Distance Between Point and Line, trunk cable, orthogonal projection

trunk cable, orthogonal projection, cable company: Hi Nour, The shortest distance is the perpendicular distance. This can be computed by taking the orthogonal projection between H and a point on the cable onto a vector consisting of the cable itself. If you haven t seen how to do that by manipulating...

Geometry: Geometry, straight lines, ef

straight lines, ef, triangles: If the three straight lines are AB, CD, and EF, with points of intersection x on AB and CD, y on CD and EF, and z on AB and EF, then the intersection forms a triangle, and triangles are on a plane as long as x, y, and z are not on the same line. If the...

Geometry: geometry, algebra curve

algebra curve: A point on the curve is (x,y). The distance from (4,-3) to (x,y) is √[(x-4)²+(y+3)²] and the distance from (-1,-1) to (x,y) is √[(x+1)²+(y+1)²]. The 1st distance is 1/2 of the 2nd distance, so we have the equation √[(x-4)²+(y+3)²]...

Geometry: Intersections, drawings, possibilities

drawings, possibilities: Can 4 line segments have just 2 intersecting points? A line segment is a piece of a line. Draw one horizontal, and draw two of them vertical with the distance between them far enough so that the 4th line segment can be draw so that it also intersects the...

Geometry: Pythagorean Triples, right triangle, pythagorean triples

right triangle, pythagorean triples, perfect square: Hey SuperGeek, There are two options: (1) Both sides are legs (2) The longer side is the hypotenuse and the other is a leg. For case (1) to hold, we need 24²+51²=[perfect square]. For case (2) to hold, we need 51²-24²=[perfect square]. These formulas...

Geometry: 30°-60°-90° Triangle, sides of a triangle, cosine of an angle

sides of a triangle, cosine of an angle, hypotenuse: Hello, Recall that sin(x), by definition, is opposite over hypotenuse. sin(x)=opp/hyp Now substitute in the given information. Let s focus on the 30-degree angle and the hypotenuse of length 8. sin(30)=opp/(8) Rearrange to solve for opposite. ...

Geometry: Apex vs Vertex, isosceles triangle, 2d shape

isosceles triangle, 2d shape, intersection point: Hi Jane! A vertex is the intersection point of two lines. An apex is a summit point which may or may not be a vertex. The point of a cone is not a vertex, but it is an apex. The top vertex of a pyramid (the one not on the base) can be referred to as...

Geometry: Construction of Rhombus, angle measure, half the distance

angle measure, half the distance, diagonals: Hi Hamza, It depends on what information you are given. If you know the side length and an angle measure, construct the angle and measure off the sides. You now have three vertices. Reflect that to get the fourth. If you know the two diagonals, then...

Geometry: counter example?, counter examples

counter examples: I don t know what the queestion was either. A counter example is a case that shows an equation is untrue. I m not sure if there were any details of the problem, but here are two examples. 1. A rather simple case is suppose we had x quarts of water....

Geometry: Finding the Centroid of a Triangle, median, intersect

median, intersect: Hello Nina, Take a side and find its midpoint. It has coordinates ((x1+x2)/2, (y1+y2)/2); be careful with the parentheses (this is the average x- and the average y-value of the two points). Then find the equation of the line containing that midpoint and...

Geometry: Geometrical Representation, Vectors

Vectors: Hi Ana, I would be glad to help. Adding vectors geometrically requires drawing a parallelogram and constructing a diagonal. You can move vectors (as long as they same length and direction) and they will be the same unit vector. Notice AB, goes up two and...

Geometry: Geometry (involving variables), Triangle area, distributive property

Triangle area, distributive property, multiplying monomials: Yes, Alyaa, you are correct. The area of a triangle is (1/2)b x h. So, multiply (1/2)(6 - 2y)(13). Notice, 6 - 2y has an even constant and an even coefficient so you can easily take (1/2) of it, by dividing each by two, to get 3 - y. Now just multiply this...

Geometry: area between concentric polygons, area of a polygon, quadratic equation

area of a polygon, quadratic equation, parabola: It is not important how many sides the polygon has, it is always true. Given it has n sides, then it can also have n+1 sides. Given the last line, n would be allowed to increase indefinitely. Eventually, n will get so large that it appears to be a circle....

Geometry: Math help, right angles, isoceles triangles

right angles, isoceles triangles: I could work with your method, but this one is obvious to me. Since the angles at B and C are equal and angles BDA and CDA are right triangles, angle BAD and angle DAC are also both equal since the sum of angles in a triangle is always 180°. Given...

Geometry: Giant Wheel User Experiences, giant wheel, giant wheels

giant wheel, giant wheels, center axis: Hi Prashant, This would be quite the engineering feat. The simplest way would probably consist of building a multilevel platform to allow users to embark at different circles. However, they would not be able to transit from one circle to another, they...

Geometry: Tau, pi

pi: Hi AL, There are many pedagogical advantages of tau at the high school level. Beyond that, the advantages are primarily aesthetic. Furthermore, the difference between pi and tau is a factor of one half. It is not some weird factor like the square root...

Geometry: Triangle, trig class, equalateral triangle

trig class, equalateral triangle, square root of 3: James, Yes, that is the length from the midpoint of one side to the vertex. As far as books, I would suggest Euler s Gem: The Polyhedron Formula and the Birth of Topology David S. Richeson (Author) Or Polyhedra Peter R. Cromwell (Author) ...

Geometry: circle, geometery, area of a circle

geometery, area of a circle: The formulas both involve the area A = pi*r^2. For the 1st circle, since they give the diameter d as d = 32 , and 2r = d, then r = 16 . For the 2nd circle, since they give the outer circumference c of 120 , the equation is 2*pi*r = c. This means that...

Geometry: Circle Areas, diameter, circumference

diameter, circumference, radius: Hi Ed, You need to use C=2πr for to obtain the radius of the outer circle, and then A=πr² to find its area. You need to use d=2r to obtain the radius of the radius of the inner circle, and then A=πr² to find its area. Finally, find the...

Geometry: Dimensions of a Compound shape with only the area, Norman window

Norman window: Hey Chris, For a Norman window, the side of the square is equal to the diameter of the semicircle. We can therefore represent the area of each part in terms of a single parameter, x. This means we need to find an expression for the area of the square...

Geometry: Geometry, geometry, right angle triangle

geometry, right angle triangle: There is an angle between B1 and C1. Call it A. There is an angle between B2 and C2. Call it B. It is known that A1/C1 = sin(A), so A1 = C1*sin(A). It is known that B1/C1 = cos(A), so B1 = C1*cos(A). It is known that A2/C2 = sin(B), so A2 = C2*sin(B)....

Geometry: Geometry-prism, three dimensions geomtery

three dimensions geomtery: Since a prism has height, width, and depth, that is three parameters. Since volume is base on h = hight, w = width, and d = depth with some constant C, it is Chwd. If all three parameters are doubled, the volume is now C(2h)(2w)(2d) = 8Cwhd. Since the...

Geometry: Horizontal cylindrical tank volume at different levels, cylindrical tank, integral calculus

cylindrical tank, integral calculus, green triangle: D is the diameter, so r is the radius, and r = D/2. B is the height of the green area. The base of the green triangle has length 2F. It is known that F²+B²=r². Since B and r are known, F = √(r²-B²). This makes the area of each triangle be FB/2....

Geometry: I was asked by a friend to figure this out but cant, algebra

algebra: The equation would have h as the height and d as the distance, where d = 0 is at the center of the bridge. This would make h(0) = 30, h(60) = 0, and h(-60) = 0. If the equation h = A - Bd² is looked at, we want A = 30, since the bridge has height 30...

Geometry: Conics, algebra, solving equations

algebra, solving equations: First, keep only terms involving y on the left. This means to subtract off the other term from both sides, giving (y+1.7)² = 3.35 - (x+1.1)². Taking the squareroot of both sides gives y + 1.7 = ±√(3.35 - (x+1.1)²). Finally, subtract 1.7 from both...

Geometry: Geometry, trig

trig: The sides are a, b, and c, with c being the hypotenuse, a being the near side, and b being the far side. The angles area A, B, and C, where C is the right angle, A is opposite side a, and B is opposite side b. You have the length of c and an angle,...

Geometry: Geometry, geometry, trapezoidal area

geometry, trapezoidal area: 1.) It is known that if the edges of a rectangle are A and B, and the diagonal is C, then A²+B²=C². Since 17² = 289 and 15²= 225, 289 - 225 = 64, and that is 8². This means the other side is 8. The perimeter is the sum of the lengths of the sides, so...

Geometry: Geometry, minimize distance fly, spider

minimize distance fly, spider: The fly can go throught the air. To find the distance straight from one corner to the other, compute √(30²+20²+15²) = √(900+400+225) = √1525 = 5√61. To find the shortest distance the ant can crawl, spread the box out. If the side...

Geometry: Geometry, transformation

transformation: 1a.) If an object is rotated 180 degrees, the is halfway aroud. This means it can be rotated either in a clockwise or couterclockwise rotation. 1b.) If the object is rotated 360 degress, that is the same as not rotation the object at all. That is again...

Geometry: math, diameter of a circle, number pi

diameter of a circle, number pi, circumference: Given radius r, diameter d, and circumference c, the equations are c = 2p(pi)r and c = (pi)d. This is because d = 2r. The radius is found by finding 6.4/2, abd the circumference is found by finding 6.4(pi). The number pi is 3.1416 { rounded to four...

Geometry: SAT Triangle Question, isosceles, mean

isosceles, mean: Hey Jack, This is probably easier if you don t try to set up equations. Two non-congruent angles have a mean measure of 70, so they are 140 together, so the other angle is 180-140=40. Because the triangle is isosceles, two angles must measure 40, so the...

Geometry: Triangular prism, volume of a prism, bae

volume of a prism, bae, triangular prism: the volume of a prism is given by V = Ah/3 where A is the base area and h is the height. If V is 96 with the bae as 16, put these values in. This gives 96 = 16h/3. Multiply by both sides by 3/16 to get the height. Is it 18? That s what it looks like...

Geometry: 6-Sided Shape with Two Isosceles Trapezoids, isosceles trapezoids, isosceles trapezoid

isosceles trapezoids, isosceles trapezoid, 6 sided shape: Greetings Marco, The shape you wish to make can be made fairly simply by using a compass to preserve distances and draw parallel lines. I was able to do this just now by first drawing an isosceles trapezoid with the legs being equal to the short base,...

Geometry: Advanced Geometry, Heaxagonal Area, Volume

Heaxagonal Area, Volume: To approah this problem with no reafThe height h is different than the side s, which means the true volume is 3h(s²√3)/2. The surface area would be six rectanglar sides with area hs, so the total is 6hs. The base would have an area of the hexagon,...

Geometry: math, pi, diameter

pi, diameter, radius: The circumference of a circle c in relation to a diameter d is given by c = pi*d. The number pi is infinite, but usually 3.14 or 3.1416 is used. It depends how many places accuracy are desire (in the above example, the number of places is 3 for 3.14 and...

Geometry: Proofs - Isosceles Triangle, isosceles triangle, triangle abc

isosceles triangle, triangle abc, necessary proof: Hi Tony, Your penultimate step ( ABC = ACB) doesn t seem to follow. (I d also like to add that I don t have the diagram of the triangle, but I m assuming you have a triangle ABC with an altitude AD.) This can be solved using angle-side-angle congruency...

Geometry: Transformations, algebra, reflective line

algebra, reflective line: When reflected over a line x=7, the y value stays the same. IF x=8, the reflection is x=6; if x=10, the reflection is x=4. In other words, when x=7+a, the reflection is 7-a. As you said, if we take y = 4x and reflect it about the y axis, we just get y...

Geometry: Transformations, bisector, midpoint

bisector, midpoint, rotations: Hi Madison! Given the location of the image (A) and pre-image (B), the axis of reflection is the right bisector of the line AB. (To find the equation of the axis, find the midpoint of AB, then find the slope of AB. The axis you seek will have slope that...

Geometry: Angles - Cyclic Quadrilateral, inscribe

inscribe: Hi Mary, There are a number of equivalent statements for a quadrilateral inscribed in a circle (a cyclic quadrilateral). One of these is that the angle between one side and a diagonal is equal to the angle between the opposite side and the other diagonal....

Geometry: Concentric Circles, bd x, concentric circles

bd x, concentric circles, short leg: Hi Mary, Triangle ABE is similar to triangle BDE. Because the two triangles are similar, the ratio of side lengths is the same for both triangles. Thus the ratio of short leg to long leg is the same for both triangles. Triangle ABE s short leg is AB=8,...

Geometry: Cylinder Cut on a Slant's Surface Area, ellipse, semiminor

ellipse, semiminor, semimajor: Hi Kaye, The area of an ellipse is given by πab, where a is the semiminor axis (the shortest distance from centre to edge) and b is the semimajor axis (the longest distance from the centre to the edge). (A circle is a special case of the ellipse,...

Geometry: Finding the surface area of a polygon?, octagonal area

octagonal area: Take a square that is 1x1. Extend each side (√2)/2 away from the square at both ends. Connect the side extensions from the same corner at a 45° angle. The result is an octagon with each side having length 1. This octagon has 3 sections I will divide...

Geometry: Shape of Infinity, compactification, circle

compactification, circle: Hi James, Infinity denotes boundless growth. There is no associated geometric shape. A circle is no closer to being considered infinity than any other shape. Simply put, there is no such thing as the shape of infinity. Those who talk about the shape...

Geometry: Triangles - Area, Base, and Height, area of a triangle, quadratic equation

area of a triangle, quadratic equation, parallelogram: Hi Carissa! The area of a triangle is given by half the area of the parallelogram, that is A=bh/2, (A is area, b is base, h is height.) In the given problem, you can use the formula to make a quadratic equation in x and then solve it, selecting the appropriate...

Geometry: Calculating the weight of a cube, physics

physics: You have a cube that is 125 micrometers by 125 micrometers by 125 micrometers. It is made of a type of plastic called Mylar, who s density is 1.390 grams/cm³. Note that 125 micrometers is 1/80 of a centimeter since 80 * 125 = 10,000 and there are 10,000...

Geometry: Equation of a Line with Variable, integers, slope

integers, slope, graph: Hi Barbara, Formulas apply even when you have variables (letters). The delta y over delta x would still work. In this particular problem, both points have the same x-value: c. Hence every point on the line has the same x-value and the line s equation...

Geometry: Infinity/Space/Order, infinity space, cartesian coordinate system

infinity space, cartesian coordinate system, infinite positions: Hi James. Very interesting question. You need to be careful by how you define space. In any case, if I m understanding your question correctly, there s a fairly simple explanation. Before I begin, I want to make one thing absolutely clear. i Assuming...

Geometry: Math, piston force

piston force: If the rod is pointing straight up and down, call that angle 0. If the rod is pointing straight to the left or to the right, call that angle A. How far it goes in either direction would be a critical value. If it went from horizontal one way to horizontal...

Geometry: Minimizing volume, calculus, derivative

calculus, derivative, optimization: The volume of a can with height h and radius r is V = πr²h. The surface area is 2πrh on the side and πr² at one of the ends Since there are two ends, we need to add 2πr² to 2πrh, which is A = 2πr(r+h). It is known that A...

Geometry: Circle and Equilateral Triangle Areas, perimeter, Pythagorean Theorem

perimeter, Pythagorean Theorem: Hi Rangam, First, compute the area of a circle with circumference p. We need the circle s radius. The circumference is 2πr=p, so solving for r you obtain r=p/(2π). Area of a circle is πr², so the area of the circle is π(p/(2π))²,...

Geometry: Expansion of a shape with holes, metal, hole

metal, hole: Hi Eddie, i According to the information I have found on thermal expansion, all dimensions will expand by the same percentage. /i This is true and also applies to the dimensions of the holes themselves. The holes will expand. This may seem a bit...

Geometry: Submarine schematic: difficulty assessing size, vertical launch system, adobe photoshop cs4

vertical launch system, adobe photoshop cs4, teardrop shape: Hi Julian, It is quite difficult for me to assess the size here, but I have some estimates. They are quite different from yours. If each projectile is 533 mm (0.533 meters) in diameter, and the space between them is roughly the same, then the central...

Geometry: Applying Law of Sines and Cosines, air traffic controller, law of sines

air traffic controller, law of sines, law of sines and cosines: Hi Nichole, Both questions require the law of cosines, applied in nearly the same way. I ve attached an picture of how to do this. I hope it is clear enough. If not, feel free to ask a follow-up and I will explain in detail what I did. Thanks for...

Geometry: vectors. skew lines, direction vectors, string 1

Geometry: vectors. skew lines, direction vectors, string 1, parametric equations

Geometry: mathematics investigation, math, work

math, work: If a talbe needs a new edge, the length needed is the perimeter of tha table. If a house needs painted, sufrace area needs to be calculated to determine how much paint. For people putting the roads in place, the sufrace area is used to determine the...

Geometry: straight line, Lines, line segments

Lines, line segments, rays: Hello Larry, I would be happy to help you. Yes, it takes two points to determine a line. But, two points can also be a part of line segments and rays. If both points are endpoints, you have a line segment. A ray has one end point and continues infinitely...

Geometry: vectors. skew lines, algebra

algebra: To find the equation of the lines, note that it is the 1st point plus the difference times x. The equation of the 1st line is (3a, 3.3 - 2a, 2.4 - 0.5a). The equation of the 2nd line is (0.7 + 0.8b, 4b, 2.3 - 0.8b). For one to pass over another, find...

Geometry: parallel lines, limits

limits: By math, two parallel lines never intersect. Look at y=0 and y=1. They are parallel, but as x increases, the relative difference of 1 in y appears to get smaller when compared to the size of x. When it is said that 1/(1-x) converges to 0 as x goes...

Geometry: 3D rotation plane around defined axis (line), trig, rotation

trig, rotation: Make the line in the x-y plane y = -x/2 be the new x axis. To do this, z stays the same. This problem involves two stages. 1 The first is to find the new points with that line as the new x-axis. The angle of rotation would be the angle that has tan(A)...

Geometry: Geometry Net Plans, Pyramid

Pyramid: Hi Jo, You have the right dimensions, but in the wrong places. Consider the summit of one of the pyramids (say (0,0,6)). There is an edge that goes straight down, measuring 6. (From (0,0,6) to (0,0,0).) There are two edges that travel along the outside...

Geometry: find point, algebra, line

algebra, line, perpendicular: To be perpendicular to AB, we need the slope m from A to B. The slope of the perpendicular line would be -1/m. The slope from A to B is (yB-yA)/(xB-xA) = -4/4 = -1 = m. This makes -1/m = 1. The line through C with slope 1 is y-2 = x-1, and this can...

Geometry: Find Point Perpendicular to Line, Perpendicular, analytical geometry

Perpendicular, analytical geometry: Hello Fendi, If you are familiar with vectors, you can find the orthogonal projection of AC on AB, then add that to A to get a vector with the coordinates of D. Alternatively, if you know that parallel lines have slopes that are negative reciprocals,...

Geometry: Geometry, algebra, volume

algebra, volume: a)Since it is 40 cm long and 20 cm wide, that is 40x20 = 800 cm². Since the depth is 5 cm, take 5x800 to get the volume of cm³. b) The length of the cylinder is 4h. The volume of the cone is pi*r²h/3. The volume of the hemisphere is 4*pi*r³/6. These...

Geometry: Volume of gallons, volume

volume: The main reason I see for different answers is which type of stuff we re dealing with. On the web, I converted 100 in³ into liquid pints, dry pints, and pints in the United Kingdom. The answers were 3.4632 liquid pints, 2.9762 dry pints, and 2.8837 UK...

Geometry: Differentiate Points

Dear Fendi, This can be done readily if you have the equation of the line and the coordinates of the vertices. For the sake of illustration, let us suppose the line s equation is y=-x, or x+y=0. Then, for any point (x,y) calculate x+y (add the two coordinates)....

Geometry: agebra, algebra

algebra: Algebraic equations are in three different forms. Some are lines, some are parabolas, and some involve two variables. The lines are of the form y = mx + b. In these, m is the slope and b is the value at which the line crosses the y axis (where x=0)....

Geometry: Area of a triangle, algebra

algebra: That is because b/2 x h/2 = bh/4 since when multiplying fractions, both the numerator and denominator are multiplied. It is only addition where the same denominator is kept. Think about it 1/2 x 1/2 means half of a half, and that is 1/4. How about...

Geometry: This is a geometric puzzle, geometry

geometry: If this shape is 4 units by 4 units, then there are 8 squares that are 1/2 x 1/2, 18 squares that are 1 x 1, 9 squares that are 2 x 2, 4 squares that are 3 x 3, and 1 square that is 4x4. So, we take 8 + 18 + 9 + 4 + 1 = 40, so that sounds...

Geometry: line segment, Euclidean Geometry

Euclidean Geometry: In normal Euclidean geometry, a line is defined as being drawn straight between two points. No matter how much it is magnified, it is the set of all points defined by the line between the points. The width of a line is 0 and the length is infinity. All...

Geometry: math-geometric terms, geometry

geometry: The questions that are asked are only viewed at most once each day, and sometimes I skip a day. This might be a day late, but ... Two opposite sides are parallel. If the height is h, one side is a and the opposite parallel side is b, the area is h(a+b)/2....

Geometry: Maths, algebra

algebra: For a right triangle with one angle 60°, the other angle is 30°. This is known to be half of a triangle with all corners 60° and all sides equal. If the hypotenuse has length x, the short side has length x/2. This makes the other side have length sqrt(x²...

Geometry: Coordinate Geometry - Inverting, 3rd quadrant, vector algebra

3rd quadrant, vector algebra, coordinate geometry: Hi Prashant, Mapping a point (x,y) to (y,x) is equivalent to reflecting the point about the line y=x and is also equivalent to rotating the point 90 degrees about the origin. If you re interested in transformations in the plane, then mapping (x,y) to (y,x)...

Geometry: Geometry Help, Circles, midpoint formula

Circles, midpoint formula, coordinate geometry: Hello Meagan, i will be happy to offer assistance. Since the circle is O, O is the center. If you know the endpoints of the diameter, then use the midpoint formula to find the coordinates of the center. Midpoint Formula ( (x1 + x2)/2, (y1 + y2)/2) Basically,...

Geometry: HomeWork Help, geometry

geometry: (A), (B), and (C) can t be concluded. Take w = 50, so since x is the other angle in a right triangle, x = 40 Since the angle at B is cut in two, and z is the same as x, and is also 40. Since angle y is the same as w and is also one out of 3 angles that...

Geometry: Perpendicular Bisector, analytic geometry

analytic geometry: Hi Meagan, The perpendicular bisector of AB has the slope that is the negative reciprocal of that of AB, and it passes through the midpoint of AB. Find the slope of AB. (2-6)/(8-0)=-1/2 Take the negative reciprocal. -(-1/2)^(-1)=2 Find the midpoint...

Geometry: Microsoft Excel Column Name Updates, reply thanks, note column

reply thanks, note column, column name: Hi Prashant, It is a good idea for all the reasons you mentioned. Using a comma instead of a period would also be more fitting, depending on the region. The reason this is not currently in place is because many spreadsheets do not use a very high number...

Geometry: Octagonal Pyramid Surface Area, slant height, lateral area

slant height, lateral area, octagonal pyramid: Hi Gina, The total surface area of any pyramid is the sum of the base area and the lateral area. The lateral area is made up entirely of triangles. If you want the wood for the walls of the playhouse, you are only concerned with the area of those 8 triangles....

Geometry: the philosophy of number/lines, tally mark, blank sheet of paper

tally mark, blank sheet of paper, tally marks: I don t know of anyone who can say what the future holds, but I can say what has happened in the past. When numbers were first developed, they were positive integers. When addition and subtraction was introduced, it was seen that if you had 5 widgets and...

Geometry: Quick Word Problem, trig, triangle

trig, triangle, inscribed in a circle: To get a right triangle, the other point must involve a side going through the center of the circle. The length of the side going through the center is the length of the diameter, and that is twice the length of the radius. This means the length of that...

Geometry: Special segments in Triangles, Median, triangles

Median, triangles, geometry: Pam, I will be happy to help. The median divides the side into two congruents parts. Therefore, if BD is the median, AD is congruent to CD and so the measures are equal, making x + 3 = 2x - 17 Solving this equation (and please let me know if you...

Geometry: Subscript and Superscript Numbers,, superscript numbers, trigonometric values

superscript numbers, trigonometric values, chemistry physics: Hello Prashant, Subscripts and superscripts are merely a typographical thing. They are used in many conventions in mathematics and science. Every example you mentioned can be in a subscript or superscript. There really is no restriction on what can and...

Geometry: Annulus' Area, azeem hussain, right triangle

azeem hussain, right triangle, concentric circle: Hi Valerie, You don t find R and r. Consider (R²-r²) as a single unknown. The area of the annulus is given by Area=π(R²-r²). From the Pythagorean Theorem, R²-r²=18². Substitute that in to get Area=π(18²). This question can be very challenging...

Geometry: Area of Parallelogram, diagonal, bisect

diagonal, bisect, hero's formula: Hi Victoria, The diagonals of a parallelogram bisect each other. Draw the diagonals so as to subdivide the parallelogram into four triangles. Applying the laws of cosines and sines within these triangles, you can determine all the side measures. Finally,...

Geometry: Geometry Math Problem, trig

trig: It is known that the angle and its compliment add up to 90°. That means we can take the measure 5x and the measure 10x to get 90. So, 5x + 10x = 90 is the same as 15x = 90. Dividing both sides by 15 gives x = 90/15, and that is the same as x = 6....

Geometry: Angles Wider than 360 Degrees, sector of a circle, vertical angle

sector of a circle, vertical angle, javelin: Hi Gen! An angle represents the spread of two lines. By definition, a circle has 360 degrees (or a degree is a 360th of a circle). Therefore, whenever we have an angle of 360 degrees, we really have the two lines one on top of the other, which is identical...

Geometry: Cell Reference in Excel application., matrix mathematics, reply thanks

matrix mathematics, reply thanks, cell reference: Hi Prashant, A1=R1C1=1A=3. The letter always refers to the row and the number always refers to the column, but this is still a dangerous thing to do. Not wrong, but dangerous. Either way, there is still a convention that must be remembered (letter for...

Geometry: geometry, geometry, bisect

geometry, bisect, parallel: a) Since FG in halfway down the triangle, BC would be twice BF, and BF is 20. This makes BC 40. b) Sing GF is the bottom of the triangle that is half the size of ABC, GF is 1/2 of AC, so GF is 15. c) Since AD is the same as GF, and GF was just found...

Geometry: Quadratic Equations - Right Triangle, right angle triangle, right triangle

right angle triangle, right triangle, hypotenuse: Hey Brittany, If you re second-guessing your results, see if they satisfy both equations. If not, then you ve made a mistake. A straightforward way to solve this is below. Use the perimeter equation to solve for y. x+y+24=120 x+y=96 y=96-x Substitute...

Geometry: Complex Number Data in Excel Application., complex, imaginary

complex, imaginary, Excel: Hi Prashant, A number of the form a+bi can be entered in Excel as COMPLEX(a,b). There are special functions for operations on imaginary numbers, such as IMSUM, IMSUB, IMPROD, IMDIV, IMEXP. (Search for a function and type imaginary to see many others.)...

Geometry: Complex Number Variant., number arithmetic, horizontal axis

number arithmetic, horizontal axis, vertical axis: Hi Prashant, How the number is plotted on the graph has no bearing on the number itself. Operations on complex numbers will be completely untouched. Really, all this does is induce a reflection on all complex graphs. This reflection must be carried...

Geometry: English Alphabets/Characters/Letters Graphical Symbols., english alphabets, alphabet character

english alphabets, alphabet character, uppercase characters: Hi Prashant, Though this is not done in the English language, some languages use diacritics or other embellishments instead of entirely new letters. The reason this is not done in English is because combinations of vowels are used instead. This question...

Geometry: Mathematical Constants in Excel, uqam ca, mathematical constants

uqam ca, mathematical constants, excel spreadsheets: Hi Prashant, Pi is certainly a constant in Excel, and e can be obtained using EXP(1). Users can define their own functions, constants included. The usefulness depends on the frequency of use of the constant, but it s a nice feature to have. Thanks...

Geometry: Scientific Notation for Complex Numbers, scientific notations, mathematical computations

scientific notations, mathematical computations, reply thanks: Hi Prashant, All the operations you mentioned can be performed using real or complex numbers written in scientific notation. The justification is the same as above: scientific notation is merely a different way of writing the same number. Regards,...

Geometry: Asymptotes, assymptotes

assymptotes: The assymptote on for the graph F(x) = 1/x is at x = 0. For graphs with vertical assymptotes, they occur where x is undefined. That is the same as where the denominator of a faction is 0, for 1/0 is undefined. If the numerator of the fraction were also...

Geometry: Centuries, 100 centuries, reply thanks

100 centuries, reply thanks, names of numbers: Hi Prashant, 1. Names of numbers of years are typically named in base 10: year, decade (10 years), century, (100 years), millennium (1000 years). I do not know of a term for 100 centuries. 2. Yes, what you wrote above is correct. The Wikipedia article...

Geometry: Is Euclid's Parallel Posulate Undecideable from the other Axioms of Euclidean Geometry, parallel postulate, Euclid

parallel postulate, Euclid: Hi Justin, The parallel postulate cannot be proven using the other four axioms of Euclidean Geometry. For centuries people tried, but it was eventually found that the parallel postulate is indeed necessary. Also, be aware that undecidable does not...

Geometry: Geometry and Scale Factor, area

area: Hey Rebecca, In a scale transformation, the scale factor is the ratio of the new side length versus the old side length. (I say side length, but any one-dimensional length will work, provided you use the corresponding one in both figures.) For instance,...

Geometry: Spherical geometry, great circle, plane

great circle, plane, Euclidean: Hi Jeremy, i 1. If there are no parallel lines in spherical geometry, why are latitudes called parallels. Would not two lines of latitude equidistant from the equator to north and south be parallel? Even if they are circles. /i Line takes on a special...

Geometry: Analog Clock Design - Anticlockwise motion., analog clock, clock design

analog clock, clock design, clock manufacturers: Hello Prashant, This is another question that is a matter of convention. Clocks move as they do to mimic the movement of a shadow on a sundial, as viewed in the Northern Hemisphere. The clocks you mention here would likely not be accepted by consumers...

Geometry: Circles (and Zombies), circumference, radius

circumference, radius: Hey Caroline, The question is indeed asking for the circumference. However, C=2πr is the equation you need, not πr² (that would give you the area of the circle). Thus C=2π(49)=98π=307.88 So, Mrs. Greene will cover a distance of...

Geometry: Geometry, algebra, circumference of a circle

algebra, circumference of a circle: The formula given is for the area. Even that was done incorrectly, for 49 is 7^2 and doesn t need to be squared again. The correct answer would be the circumference of a circle C = 2πr. That is 2*π*7 = 14*π = 43.98..., which rounds to...

Geometry: Measurement Dimensions, relevant dimensions, length x width x height

relevant dimensions, length x width x height, filing cabinet: Hello Kenneth, Height refers to distance to the ground. Depth can refer to that, but it can also refer to the distance to the back (e.g. the depth of a filing cabinet). Many people use height and depth interchangeably. I would say height is more...

Geometry: Polygon Shaped Board games., board game rules, scrabble board

board game rules, scrabble board, snakes and ladders: Hello Prashant, Boards are often square or rectangular because of ease of construction and layout. Your question seems to imply that the number of sides of the board is the limiting factor in the number of players, but that generally is not the case. ...

Geometry: Cylinder Liquid Problem, circle, sector

circle, sector, area: Hello Nathanial, You need to find the volume of oil in the lying down cylinder. It takes the shape of a prism whose bases are truncated circles. You need to find the area of the truncated circle. On a Cartesian plane, draw a circle of radius 8 centred...

Geometry: Geometry: Lines in the coordinate plane, algebra, line

algebra, line, point-slope: Use the point-slope form of a line. That is, y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope. We are given (x1,y1) = (1,5). The standard line is y = mx + b, and we have y = -5x, so b=0 and m=-5. So, just take x1=1, y1=5, and m=-5 and...

Geometry: List of Points

Hi Fendi, Convert your list of points to polar coordinates (radius, angle). Sort the points by angle. Locate the first point, then add the remaining points in the sorted order, wrapping around the list if necessary. For example, in your picture the sorted...

Geometry: Right Triangle, trig, law of cosines

trig, law of cosines: When a right triangle is put in a circle, the hypotenuse is the diameter of the circle. This means that the triangle PSR is symmetric and the triangle RSQ is symmetric since PS, SQ, and SR are all radii of the circle. Using the law of cosines, the measure...

Geometry: Angle Properties of Circles, trig, circle

trig, circle, isosceles: Sorry, but I forgot to attach my picture with that problem. It had a line drawn at BO. It had angle CBD labeled as a, angle CAO labeled as b, angle AOD labeled as d, angle CBO labeled as e, and angle ABO labeled as f If you would like the actual attachment,...

Geometry: Applications of Trigonometry, trig

trig: The law of cosines says that a² = b² + c² - 2 * b * c * [cos A]. Since the b is known, c is known, and cos 60° is 1/2, that gives a² = 8² + 12² - 2*8*12/2 = 64 + 144 - 96 = 112. This means the value of a is the square root of 112. Using the law of sines,...

Geometry: CIRCLE, algebra, circle

algebra, circle: Since it touches both of the axis and is still in the 1st quadrant, that means it must be tangent to both of the axis. This means the radius of the circle that touches an axis is perpendicular to that axis. Since the radius is 4 and the circle is tangent...

Geometry: Geometry, geometry

geometry: Put the kite down so that the top and bottom are on the y axis. Slide the kite up or down so that the points on the side are on the x axis. I believe this makes the x-axis and y-axis be the diagonals of a kite. It is known that the axis are perpendicular....

Geometry: Geometry Planets, algebra, physics

algebra, physics: Let the orbit radius be O and the planet radius be P. The surface area with radius r is known to be 4*pi*r^2. The surface area of the orbit sphere would then be 4*pi*O^2. The surface area of the planet would then be 4*pi*P^2. Since we are dividing...

Geometry: Horizontal Cylindrical Tanks

Hello Tracy, This is a somewhat involved problem, but I have given an outline of the solution in a question that I was recently asked. You can see the steps of the solution here: http://en.allexperts.com/q/Geometry-2060/2014/1/cylinder-liquid-problem.htm...

Geometry: Surface Area of a Sphere as a Function of Radius

Hey Anne, How do you initially calculate the surface area of the sphere? The surface area of a sphere of radius r is given by A(r)=4πr². Hence the area decreases quadratically with the radius. So if the radius of the sphere decreases (or increases,...

Geometry: Pythagorean Theorem, quadratic, inequality

quadratic, inequality, quadratic formula: Hi Monica, You re told that JKL is a right triangle, but you don t know which side is the hypotenuse. For the moment, suppose that JL is the hypotenuse. Then set it up with the Pythagorean Theorem. JK²+KL²=JL² (3x-6)²+(2x+11)²=(20)² Expand all...

Geometry: Geometry, algebra, line

algebra, line: Let s change that to (3t+2, 2-t) and then call it (x,y). If y = 2-t, then we need to solve for t(x). Since we have x = 3t+2, 3t = x-2, so t = (x-2)/3. Putting this in the equation for y gives y = 2 - (x-2)/3. Multiplying out gives y = 2 - x/3 + 2/3....

Geometry: Triangle Side Length from Median Lengths, Hero's formula

Hero's formula: Hi Nathanial, Each median divides the triangle into two smaller triangles of equal area. If all three medians are drawn, because they intersect at a point, the triangle will be divided into six smaller triangles of equal area. A triangle s medians intersect...

Geometry: Volume of a Sphere, Cavalieri's principle

Cavalieri's principle: Hi Danielle, It s great that you re eager to learn where formulas come from. Unfortunately, this one is a bit difficult to see without the use of integral calculus (which you ll be taking a little ways down the road if you love math!). The result, however,...

Geometry: Circles - Arc Length and Area, Radius, arc length

Radius, arc length, area: Hello Caroline, For Problem 1, we must find the sum of the circumferences of the circles, but only the portions before the intersection. When an angle is formed at the center of the circle (such as the 80-degree and 100-degree angles), it subtends an arc...

Geometry: Formular to Calculate Area of a Shaded Portion

Hi John, This depends completely on what the shape is. If the shape is a rectangle or a triangle or circle (for instance) you will need to use the corresponding formula. If the shape is irregular, then you may be able to subdivide it into portions that...

Geometry: Geometry-circles, trigonometry

trigonometry: The outside of a circle is 2*pi*r. The total degrees in a circle are 360. This would make the total distance be [(360-80)/360]2*pi*6 + [(360-100)/360]2*pi*4. That reduces to (28/36)*12*pi + (26/36)*8*pi. That reduces more to (28/3 + 52/9)pi. For pi, use...

Geometry: Unit Circle, trigonometry, trig

trigonometry, trig: Hi J.D., Solving problems on the unit circle isn t too bad once you understand what s going on. On a Cartesian plane, the unit circle is a circle of radius 1 centered at the origin. All points on the circle have coordinates (x,y)=(cos t, sin t), where...

Geometry: Area of Rectangle that Intersects Circle, circle, area

circle, area, rectangle: Hi Janet, Your conclusion is indeed the correct one: the area of the rectangle is 25 square units, irrespective of where the point C lies on the arc. Proving this, however, is not a particularly easy task. I ll start with some motivating ideas, then I...

Geometry: Math, area

area: Let the triangle with sides of 2 be called A. Make a new triangle with one of the corners as a corner of A, one of the corners as the center of A, and one of the corners as the midpoint in one of the sides of A near the corner chosen. Drawing this...

Geometry: Perimeters and Areas, square, rectangle

square, rectangle: Hi Johnny, (1) A square with side length x has area x² and perimeter 4x. Using the given area, you can solve for x. x²=14400 √(x²)=√14400 x=120 Now multiply by 4 to get the perimeter of the square. (2) A rectangle with side lengths...

Geometry: Rotating around points other than the origin?, trigonometry

trigonometry: The point given will be taken to be (x,y). Take the point and subtract 1 from the y coordinate, giving (x,y-1). Convert (x,y-1) that to polar coordinates. Add on however much of a rotation to the angle. Convert that new point back to (x,y). That is,...

Geometry: math, geometry

geometry: I have seen characters misinterpreted by other PC s, but hopefully ° comes across as a degree symbol. For an n-sided polygon with uniform angles and sides, the measure of each angle is 180(n-2)°. Thus, the angles of a triangle add up too (3-2)180°...

Geometry: Math, rounding

rounding: If 20,000 is divided by 300, that is the same as 200 divided by 3 (dropping 00 from each). If is known the 200/3 = 66 2/3. In decimals, that is 66.66666666666666... Since 6 round up, cutting it off at some point would give 66.667 to the nearest 1000th,...

Geometry: Computing Factorial of a Number

Hi Prashant, There gamma function will be of interest to you. It is a function that agrees with the factorial on the positive integers, but is also defined over the reals and the complex numbers. For the factorial inverse, one could use the inverse...

Geometry: Polygon -> Polyhedron

Hello Eric, There are very few regular polyhedra whose faces are the regular polygon. What you are asking is closely related to the Platonic solids, of which the dodecahedron is one. The others are the tetrahedron, the cube, and the icosahedron. For...

Geometry: 3-D shapes and a net of the demention, geometry class, demention

geometry class, demention, hieght: I would assume that it means to draw the edges of the shape (meaning draw the shape but don t color in the faces) and label the height as 24, width as 6, and length as 18. Unfortunately draw a net is not a universally used idea so I can not be 100% sure....

Geometry: 3D shapes, mathworld wolfram, physical representations

mathworld wolfram, physical representations, 3d shapes: As such a hocky puck doen t become a cylinder, it is a cylinder. But I assume you want to know whether there is a certain threshold thickness beyond which a circular disc like object is called a cylinder and otherwise it is called a disc ? If this is indeed...

Geometry: 6 side 3d object, hexagonal base, fish tank

hexagonal base, fish tank, graph paper: I assume the tank is regular prism with hexagonal base. ( i.e. the sides (walls) of the tank are all vertical and the bottom cross section is identical to the top. In this case the volume of the tank will be area of the base multiplied by its height. So...

Geometry: 8ft across circle how many square sf., diameter of a circle, radius of a circle

diameter of a circle, radius of a circle, sq ft: If the radius of a circle is r then its area is given by = Pi * r * r ( Here Pi is the well known mathematical constant approximately equal to 3.14) We are given the diameter of a circle. But diameter is two times the radius. So the radius r of...

Geometry: Advanced Geometry, linear pair, rough diagram

linear pair, rough diagram, opposite angles: Becca, you have explained it well, and I think I have understood the question. The angles that you have described are called vertically opposite angles. Let us first draw a labeled rough diagram. Let the lines AB & CD intersect in a point O. We want...

Geometry: Advanced Math help!, sinx, advanced math

sinx, advanced math, exact solutions: 1/(csc x)(sec^2 x) (I assume both the terms are in the denominator ?) So 1/(csc x)(sec^2 x) =(1/(csc x)*(1/sec^2(x)) =(1/(1/sin(x)))*(1/(1/cos^2 (x))) (Since 1/sin(x)=csc(x) & ...

Geometry: AL construction of a right triangle., angled triangle, right triangle

angled triangle, right triangle, circular plate: I assume traditional tools means you are allowed to use a protractor( A semi circular plate with angles from 0 to 180 marked on it.) 1. Draw the knwon side of the triangle. Let us name it AB. 2. Since on of the angles of the right angled triangle...

Geometry: Algebra 1 and Calculus, slope and y intercept, slope y intercept

slope and y intercept, slope y intercept, slope intercept form: Hello, Chelsea! These are the EASIEST line problems you ll ever get . . . The formula is: y = mx + b where m is the slope and b is the y-intercept. All we have to do is drop in the numbers they give us. 1) slope: -2, y-intercept:...

Geometry: Algebraic Angles, interior angles, supplementary angles

interior angles, supplementary angles, angle measures: Hey Elizabeth! You know that the sum of the interior angles in a triangle is 180 degrees. Therefore, you can add the three given angle measures together and they ll equal 180. This, as shown below, will allow you to solve for X. 180=m BAC+m ABC+m BCA...

Geometry: Algebraic Angles, dividing by 2, 11x

dividing by 2, 11x, explicit details: Hey Ashton, This question gives you an algebraic equation with the variable on both sides of the equals sign. The variable needs to be isolated (made alone on one side of the equals sign). I ll walk you through this. Rest assured, my explicit details...

Geometry: Algebraic Equation, algebraic equation, xs

algebraic equation, xs, pleasure: Hi Abbi! First, simplify each side of the equals sign as much as possible. On the left, multiply (2x) and (-3) by -5, as shown below: 6-5(2x-3)=4x+7 6-10x+15=4x+7 Now, isolate the variable. Move all xs to the right, and everything else to the left....

Geometry: Algebraic Equations, sign changes, algebraic equations

sign changes, algebraic equations: Hi Liz! In algebraic equations, moving anything across the equals sign changes its sign. REMEMBER THIS! For the problem with (a) in it, the left side must be simplified before anything else can be done. 1/5(a+10)=-3 1/5a+2=-3 Now isolate (a). 1/5a+2=-3...

Geometry: Algebraic Perimeter - Carpet, perimeter of a rectangle, carpet

perimeter of a rectangle, carpet, sofia: Hello Sofia! I m honoured to be able to help you. The carpet s perimeter is 70 feet, with a width 3/4 the length. Let (x) equal the length. Because the width is 3/4 the length, (3x/4) or (0.75x) equals the width. Perimeter of a rectangle is twice the...

Geometry: Analytical Geometry - Functional and Standard Forms, slope intercept form, y intercept

slope intercept form, y intercept, analytical geometry: Hi Barbara! First, find the slope: a: a=ΔY/ΔX a=((-5)-(1))/((3)-(6)) a=-6/-3 a=2 Now for the slope-intercept form, y=ax+b. Choose a point to be (x,y). Let s use (6,1). y=ax+b (1)=(2)(6)+b 1=12+b b=-11 SOLUTION a): y=2x-11 For...

Geometry: Analytical Geometry - Isosceles Triangle, isosceles triangle, angle bisector

isosceles triangle, angle bisector, vertex angle: Hey Will, I ll tell you how to do this: 1. Graph the triangle. This can be done visually, but if you want the math, here it is. The base is the side that does not measure the same as the other 2. The formula for distance between 2 points is d=((ΔX)^2+(ΔY)^2)^1/2....

Geometry: Analytical Geometry - Midpoint, midpoint of a segment, analytical geometry

midpoint of a segment, analytical geometry, tiny mistake: Hey Emily! You re right for Q1, but you ve made a tiny mistake. 5+(-3)=2, not -2. The midpoint s coordinates are thus (1,5) (no negative). For Q2, you need to work backwards. The formula is the same, but the defined variables are in different places....

Geometry: Analytical Geometry - Perpendicular, y intercept, analytical geometry

y intercept, analytical geometry, infinite points: Hi Simon! You need a point on this perpendicular line to find the y-intercept. You know the slope is the negative reciprocal, but this line would intersect with the other perpendicularly at infinite points. In the problem, you ll usually have the coordinates...

Geometry: Angles and Arcs, length of an arc, degrees to radians conversion

length of an arc, degrees to radians conversion, conversion formula: Can you please specify what kind of help you need ? The basic formula for finding the length of an arc is s = r * (theta) ...(1) Where s is the arc length, r is the radius of the circle and theta is the angle subtended by the arc...

Geometry: Angles degree, interior angle, regular polygon

interior angle, regular polygon, angles: I m assuming you mean the degree of each interior angle of a regular polygon. The formula for determining this is 360(n-2)/n where n is the number of sides. So for a 5 sided polygon n=5 so the formula is 180(5-2)/5 which is 108. If this is not what you...

Geometry: Angles degree, regular polygons, angles

regular polygons, angles, pentagon: For regular polygons with number of sides n , each angle is =180*(n-2)/n degrees So for pentagon each angle will be =180*(5-2)/5 =180*3/5 =540/5 =108 degrees You can do the calculations on similar lines for n=6,7,8,9,10 and get the required answers....

Geometry: Applications of Geometry, grass seeds, rectangular garden

grass seeds, rectangular garden, types of geometry: Hi Akash, Geometry is really all around us and has virtually infinite real life applications. Perhaps you have a rectangular garden and you need to know its area to find out how many grass seeds you will need. Maybe you have to find the lateral area of...

Geometry: Area from Algebraic Perimeter, area of a rectangle, azeem

area of a rectangle, azeem, perimeter: Hi Ana, If the rectangle s perimeter is 200, then half its perimeter is 100. Half its perimeter equals the sum of the length and the width, as seen below. p=2(l+w) (200)=2(l+w) (200)/2=l+w 100=l+w The width equals (x), so the length must equal (100-x),...

Geometry: Area of geometrical shapes, lateral surface area, rectangular parallelepiped

lateral surface area, rectangular parallelepiped, surface area of a cube: The term lateral is generally not used in case of cubes. Instead, we simply talk about total surface area. If each side of a cube is a then the total surface area is given by T = 6*a^2 ( ^ denotes exponentiation, so it is to be read as 6 times a squared...

Geometry: Area of a hexagon, empty pop cans, area of a hexagon

empty pop cans, area of a hexagon, area of a regular hexagon: Let me make sure whether I have understood the problem correctly. In the equation 3x^2-3x+1 where x is the length of one side By x being the length of one side you mean the x is the number of cans on one side. So, in hexagon with each side...

Geometry: Area & Perimeter for 2-D and 3-D shapes, area and perimeter, area perimeter

area and perimeter, area perimeter, math faq: As per my knowledge the term perimeter is not applicable to solids. For all kinds of area / volume, perimeter formulas with figueres please visit the follwing web page http://www.mathforum.org/dr.math/faq/formulas/ and further links from this page....

Geometry: Area, Perimeter, and Circumference, area perimeter, handy crafts

area perimeter, handy crafts, tax calculations: Area is needed in calculation relatd to gardening, tailoring, handy crafts, property value (& relatd tax calculations). Area of floor is required in calculating the size of carpet required. One common application of perimeter calculation is in calculating...

Geometry: Area, Perimeter, and Circumference, area perimeter, volume of a box

area perimeter, volume of a box, advanced mathematics: Hello. Only when I m on here. No, actually those lessons may not be applied every day, but they are used in everyday life. The word problems found in those courses are not far from being real. Someone may have a garden with length 20 feet and width...

Geometry: Area of a Rhombus, area of a rhombus, perpendicular bisectors

area of a rhombus, perpendicular bisectors, right triangle: David, First draw a rhombus slanting to the right with diagonals. Label clockwise the vertices A,B,C,D. Label the intersection of the diagonals, E. This will help us to talk about the rhombus. You are correct that you will need to find the length of...

Geometry: Area of triangle using vertices, square root of 169, vector algebra

square root of 169, vector algebra, magnitude of vector: Method 1: Calculate hte lengths of all the 3 sides using the distance formula, and then apply the Hero s formula. ( If the sides are a , b and c and s=(a+b+c)/2, then the area = square root of (s*(s-a)*(s-b)*(s-c)) This will be generally lenghthy....

Geometry: Area and Volume Ratios, volume ratios, square roots

volume ratios, square roots, area and volume: I am sorry, Please ignore my earlier reply, which was sent to you by mistake. The answer is: If the radius of and the slant heights of the two cones are r1, s1 and r2, s2 respectively then the ratios of their areas will be [Pi * r1 ( r1 + s1 )]...

Geometry: Area, triagle, hieght

triagle, hieght, bottom base: The sum of the areas of the trapezoid and the smaller triangle must add up to the area of the bigger triangle. But as you claim they are not equal. Whenever we arrive at a situation where our conclusion has contradicting a axiom/postulate or proven...

Geometry: Areas of irregular shaped, different sized objects., maths problem, graph paper

maths problem, graph paper, vertical and horizontal lines: You are right, if you plot the figures on a graph paper with denser grid, ( i.e. vertical and horizontal lines are much closer) Then the errors will reduce. But if this is not possible in practice then approach is to do scaling, which will be the same thing...

Geometry: Areas and Perimeters, parallelograms, parallelogram

parallelograms, parallelogram, areas and perimeters: The question is not clear to me. There will be infinite parallellograms and trapeziums with total perimeter of 1000m. e.g. Consider the parallelograms alone: If a parallelogram has sides a & b then its perimeter will be 2*(a+b) Now 2*(a+b)=1000m gives...

Geometry: Areas of Regular Polygons, areas of regular polygons, cot pi

areas of regular polygons, cot pi, apothem: The question is not clear to me. (Or there are 2 questions ?) Question 1. Given apothem, find the radius and the perimeter of the polygon. ( What about the number of sides ? Is this information given in the question ?) Question 2. Given...

Geometry: ASA Postulate, equal angles, alternate angles

equal angles, alternate angles, rhombus: Hey Janet, The ASA Postulate may be used. Rhombi, by definition, have 4 sides of equal measure. Parallelism is also defined, but it is given to you too. Alternate angles are equal when lines are parallel, so you have 3 equal sides and actually 3 equal...

Geometry: ASAP-- THANK YOU SO MUCH, radius of earth, mars orbit

radius of earth, mars orbit, alpine meadow: Deb, I don t normally answer questions that appear to be homework questions. To help you get started though, I will show you how to set up the first question. Word Problems usually require a picture. Go to http://img75.imageshack.us/img75/7973/mountaindrawing3ve.png...

Geometry: addition postulate, distance formula, nq

distance formula, nq, 7x: The Segment Addition Postulate says that if C is between A and B, then AB=AC+BC. Your example really isn t a good example, so let me make up my own. Let B be between A and C so AB+BC=AC. Let AB=x+3, BC=2x-1 and AC=26. Using the Postulate, we have x+3+2x-1=26...

Geometry: addition postulate, measure 1, horizontal line

measure 1, horizontal line, sketch: Hello, Sam! I think we just need a sketch. Draw a horizontal line. Label the left end A , the right end C . Mark point B on the line (close to C than to A). We are told that AB = 5.3 ... label that segment. We are told that AC = 6.7 ... the...

Geometry: addition postulate, algebra distance formula, sq rt

algebra distance formula, sq rt, decimal approximation: Britiny, I need a little bit more information about your problem. Is MR and NQ on the same segment? Can you tell me the order of the points on the segment? Have you been told that there is a midpoint? Do you know if MR = NQ? All these things will...

Geometry: aep theorem, google search, exchange property

google search, exchange property, theorem states: Saiya, It is difficult to say exactly what AEP Theorem states since I do not know the context of the use of this theorem. I did a google search with the term: AEP Theorem . Here is one of the results: Asypmptotic Equipartition Property http://en.wikipedia.org/wiki/Asymptotic_equipartition_property...

Geometry: alegbra, supplementary angles, math math

supplementary angles, math math, correct answer: Matt, Def. supplementary angles--Two angles whose sum is 180 degrees. Ex: 30 degrees + 150 degrees = 180 degrees so 30 and 150 are supplementary angles. Suppose you know 2 angles are supplementary and 1 of those angles is 100 degrees. What is the supplement?...

Geometry: algebra with geometry, finding the slope, how to find the slope

finding the slope, how to find the slope, geometry: If you have a point (a,b) and a point (h,k) the formula for finding the slope is (b-k)/(a-h). It does not matter which you have first, the b or the k, as long as you have the corrisponding x-value first. So if you want to have the k first in the top, make...

Geometry: algebraic geometry, algebraic geometry, rectangle

algebraic geometry, rectangle, breadth: Let the side of the square be x Therefore one of the sides of the rectangle must be 2*x and the other side of the rectangle must be 2+x So the area of the rectangle must be 2*x*(x+2) Now the area of the square must be x^2 So 2*x*(x+2)-x^2=32 Therefore...

Geometry: algorithm... area ratio/length of sides, perimeter of triangle, area of rectangle

perimeter of triangle, area of rectangle, area of a rectangle: Don, I m sorry I misunderstood what you are wanting to do. Well, I think this is much easier. The formula for the area of a rectangle is A = length*width so A = L*W. Let s say you have a rectangle which has a length 3 less than twice the width...

Geometry: analytical geometry, equation of a vertical line, analytical geometry

equation of a vertical line, analytical geometry, equation of a horizontal line: Billy, This is an interesting question. Let s say that you have a rectangle 4 units long and 2 units high. Graph this rectangle with the bottom left corner on (0,0). Then the other 3 points of the rectangle could be (4,0), (4,2), & (0,2). Now, instead...

Geometry: angle of elevation, angle cab, right triangle

angle cab, right triangle, line ac: Hello, Terry! Do you draw MY diagram? Do you see that angle A (21 degrees) is in the lower left? Why are you working with 69 degrees? [That s up by the rock.] When I say height of the rock , I mean its thickness. [Look at my diagram.]...

Geometry: angle of elevation of a balloon, 23 degrees, angle of elevation

23 degrees, angle of elevation, balloon: Yes, Why not ? Go ahead and use the sine rule and solve it; if you think that is simpler. But please note you have to apply it to angles of the same triangle and the angles 23 degrees and 18 degrees in this case do not belong to the same triangle. So...

Geometry: angle whose sin is .0692, spreadsheet programs, scientific calculator

spreadsheet programs, scientific calculator, mathematical tables: Taking sine inverse of .0692, we get the angle as 0.069255348 in radians, OR 3.968039168 degrees. Please note sine inverse can be found by using mathematical tables or a scientific calculator or by using the asin() function available in spreadsheet programs....

Geometry: angles in a triangle, e mail address, angles of a triangle

e mail address, angles of a triangle, cosine rule: I am sorry but I haven t kept any backup of my previously answered questions. But let me try to answer your question: Let the triangle be having vertices A,B,C. Let the sides opposite these be a,b,c (i.e. AB=c, BC=a, AC=b etc.) Let us use the cosine rule...

Geometry: angles, angled triangle, spreadsheet programs

angled triangle, spreadsheet programs, scientific calculators: Yes there is a way of finding the angles if in a right angled triangle you know all the sides. This involves the use of trignometric ratios. I have included the explanation and I have given a formula to be used within Excel(Spreadsheet), So in case ...

Geometry: applying quadratic functions, formula x, quadratics

formula x, quadratics, quadratic functions: Hello Jeff. I m assuming you re the same Jeff that asked about the previous question about the apples in the orchard. If so, this question I can answer. If not, I can still answer this question. The sign in front of the x^2 coefficient is negative,...

Geometry: applying quadratic functions, fencing material, 880 yards

fencing material, 880 yards, step solution: Let one side of the rectangle be x and the other side be y. Now since the plot is rectangular and is having a river on one of the sides. So for the fencing purpose we need to cover only 3 of its sides. Let the river be on a side with length y. So...

Geometry: applying quadratic functions, rectangular garden, maximum area

rectangular garden, maximum area, quadratic functions: Let one side of the rectangle be x and the other side be y. So the perimeter of the garden will be 2*(x+y), this is given to be 30 yards ( * denotes multiplication ) So, 2*(x+y)=30 ...(1) So, (x+y)=15 So, y=15-x ...(2) So if the...

Geometry: area of equilateral triangle given only radius, area of equilateral triangle, area of an equilateral triangle

area of equilateral triangle, area of an equilateral triangle, triangle abc: 1. I assume by radius of the equilateral triangle, you mean the radius of the circumcircle of the triangle. (Circumcircle of a triangle is the circle which passes thru all the vertices of the triangle.) Let the veritices of the given equilateral ...

Geometry: area of a hot tub border, pi times, pi symbol

pi times, pi symbol, circumfrence: Assuming that the hot tub and border are both circular, the best way to find the area of the border is by finding the area of the circle with the outside edge of the border as it s circumfrence and then subtracting from that the area of the circle whose circumfrence...

Geometry: the area in the middle of the figure, sq meters, quadrilateral

sq meters, quadrilateral, degree angle: Extend the two sides of the larger square (the sides which are partly inside the smaller square ), so that they intresect the sides of the smaller square. Now we have made 4 parts of the smaller square. Notice that these 4 parts are congruent to each ...

Geometry: area and probably something relating to that, convex quadrilateral, perimeter of a rectangle

convex quadrilateral, perimeter of a rectangle, line segment: 1) a rectangle s width is 3 units, its length is (2x + 2) units, and its area is 48 sq. units. what is the value of x? 3 * (2x+2) = 48 ( * indicates multiplication ) Therefore 6x + 6 = 48 Therefore 6x = 42 Therefore x = 7 ...

Geometry: area of rhombus, equilateral triangle area, area of rhombus

equilateral triangle area, area of rhombus, area of triangle: Let the rhombus be ABCD, with m BCD=120 degrees and BD=10 . Let the diagonals AC and BD intersect each other at O. Now we need to use the following results. 1. Diagonals of rhombus bisect each other and are perpendicular to each other. The diagonals...

Geometry: area of a triangle, formula area of a triangle, area of a triangle

formula area of a triangle, area of a triangle, angled triangle: In a right angled triangle the sides containing the right angle can be considered as the base and the height of the triangle and then we can use the formula: Area of a triangle = (1/2)*base*height ...(1) But in this problem we are not given, the...

Geometry: area under curve, area under the curve, arbitrary point

area under the curve, arbitrary point, dependent variable: Consider the square formed by (0,0), (R,0), (R,R), (0,R) Let the points be named as O(0,0), A(R,0), B(R,R) and C(0,R). The given curve is a part of a circle with equation (x-R)^2 + (y-R)^2 = R^2 ...(1) ( Here ^ denotes exponentiation. ...

Geometry: area and volume, area of rectangle, jewlery store

area of rectangle, jewlery store, gymnasium floor: 1. Store space in a shopping mall is often rented by the square foot. What is the area of a rectangular jewlery store that is 12 feet wide and 18 feet long? Area of rectangle=length*width ( I am using * to indicate multiplication) =12feet*18feet =216sq.feet....

Geometry: areas of circle..., area of an equilateral triangle, square root of 3

area of an equilateral triangle, square root of 3, 3 circles: Let A, B & C be the centres of the 3 circles (coins). Join A,B; B,C & C,A. Now we have an equilateral tringle ABC with each side equal to 2 cm each. Now the required area is area of the triangle ABC minus the areas od 3 sectors of 3 circles having centres...

Geometry: areas of circle.., pythagoras theorem, square root of 64

pythagoras theorem, square root of 64, square root of 100: Let O be the cenre of the circle.Let P be the point at a distance of 10cm from O. From P draw tangents PA and PB. Join PO. Let us call the point of intersection of PO with the circle be X. Now what we are required to compute is the area bound by the...

Geometry: areas of rectangular prisms, surface area of a rectangular prism, rectangular prisms

surface area of a rectangular prism, rectangular prisms, area perimeter: Danielle, To find the surface area of a rectangular prism, you can use a couple of formulas to obtain the correct answer. The first one is a short-hand version of finding the area of each face and each base and adding them all together. Surface Area...

Geometry: areas, rectangles, perimeter

rectangles, perimeter, rectangle: This is a great question. Basically, what s going on is you re measuring two different attributes of the two rectangles. Think of each rectangle as two different gardens. The area is the amount of room it takes up. The perimeter is the length around the outside...

Geometry: Balloon Volumes, gum balls, tiny balls

gum balls, tiny balls, bubble gum: Hey Carl, Given how I ve been taught, I found each volume using (4/3)(pi)r^3. Nonetheless, I end up with the same answer: 1271.412037. I don t see why you re reducing for empty space . In theory, if the balloons were almost as malleable as liquid,...

Geometry: Basic Geometry, harward university, university mathematician

harward university, university mathematician, swiss mathematician: Both the questions are rather general and it would be difficult to give short / precise answers, but anyway let me try. 1) What s the point of proving and how do you prove? I mathematics when some one observes a pattern he/she forms what is...

Geometry: Bay/Bow window angles and line length, initial angles, equal angles

initial angles, equal angles, geometry skills: Sorry for the delay. I think I have understood roughly what a bay window is. ( Here is a link to a software (Bay 6) to calculate the required details. You can down load it and try the demo yourself. It talks about things like strings, facets,...

Geometry: Black O wall drawings, appstate edu, straight railway

appstate edu, straight railway, branch of geometry: I don t know much about this. But this is called perspective drawing. Here parallel lines are shown as intersecting in a point.( Like if you stand near a long and straight railway track, it looks as if the tracks meet at a point.) You can try the following...

Geometry: Calcuate the surface area..., surface area of a square pyramid, lateral surface area

surface area of a square pyramid, lateral surface area, slant height: Total surface Area of the Pyramid = Lateral Surface area + Surface area of the base = (1/2)*(perimeter of the base)*(slant height) + Area of the square at the base = (1/2)*(12+12+12+12)*11 ...

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

perimeter of a rectangle, area of a rectangle, area of a triangle: What is the value of x ? If it is specified, then by Pythagoras Theorem we get L*L + W*W = x*x ...(1) ( I am using * to denote multiplication. ) But we know L+W=100 ...(2), So we get, W=100-L ...

Geometry: Calculating a sprial's primiter (i.e. rolled carpet), pir 2, don donald

pir 2, don donald, diamater: Donald, Let me start by saying that I enjoyed reviewing your work. It is terrific to learn of someone who enjoys doing math. The Circumference of the rolled tube of carpet is actually the length of the carpet as you have indicated. I tell my students...

Geometry: Circle - Debate, azeem, sphere

azeem, sphere, orb: Hi Jacques! I totally agree with your perspective. Although a sphere has a radius, it is not based on a circle the way a cylinder is. Of course, the counter-argument, that a sphere is made up of infinite discs, is true. Nevertheless, I m behind your...

Geometry: Circle Definitions, circle definitions, dimensional measurement

circle definitions, dimensional measurement, foot diameter: Luke, Generally, when one names a circle by one-dimensional measurement, it is the diameter to which is referred (think of the barrel of a gun). In this case a 48-inch diameter would be a 4-foot diameter which would mean a 2-foot radius (d/2=r). Then...

Geometry: Circle Question, minor arc, circumference of circle

minor arc, circumference of circle, equilateral triangles: Hello, Gus! I need more information, like the size of circle Q. If it is the same size as circle P and its center is on the circumference of circle P, then I can work out the answer. Draw line from the center of circle P to the ends of the...

Geometry: Circle, radius of a circle, formula c

radius of a circle, formula c, dividing by 8: The formula used by you is correct but the answer obtained by me is different. c = square root of (4h(2R-h)) Therefore c = square root of (8h*R-4*h*h), (Here * denotes multiplication) Now squaring both sides c*c = 8*h*R - 4*h*h ...

Geometry: Circles, circumference of the earth, earth circumference

circumference of the earth, earth circumference, circumference and diameter: a. What is the Earth s circumference in nautical miles? Earth circumference will correspond to 360 degrees. But (1/60) degree arc of Earth s circumference = 1 nautical mile Therefore 1 degree arc of Earth s circumference ...

Geometry: Circles inside a circle, many circles, small circles

many circles, small circles, central angle: To Justin From Jay Subj Packin Circles UHOH, not too sure i got all the bases covered but here goes. The area ratio is (1.5/.6)^2 = 6.junk, so the max is = 6. Let s put the big circle at the centre of the standard (x,y) coordinates....

Geometry: Circles in a triangle, square root of 3, equlateral triangle

square root of 3, equlateral triangle, equalateral triangle: Let ABC be the given triangle. Let D,E & F be the centers of the 3 triangles, such that the circle with center at D touches the sides AB & AC; the circle with center at E touches the sides AB & BC; the circle with center at F touches...

Geometry: Circles, math faq, dr math

math faq, dr math, area of a circle: If the radius of the circle is r then the formula for calculation the area of the circle is Area = Pi * r * r ( Pi denotes the well known mathematical constant, approximatel equal to 3.14 or 22/7, * denotes multiplication. ) so if the radius...

Geometry: Circumference, circumference of a circle, radius of a circle

circumference of a circle, radius of a circle, math math: Roy, The formula for Circumference of a Circle is C = 2*pi*radius. Now set 12pi = 2*pi*r. Solve for r and you will have the answer to your question. Check these websites for more information: http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=fperim...

Geometry: Classify an angle, reflex angle, straight angle

reflex angle, straight angle, obtuse angle: The four type of angles are: 1. An ACUTE ANGLE is one whose measure is LESS THAN 90 DEGREES. 2. A RIGHT ANGLE is an angle whose measure is EXACTLY 90 DEGRRES 3. An OBTUSE ANGLE is one whose measure is GREATER THAN 90 AND LESS THAN 180 DEGREES ...

Geometry: Classifying Triangles, classifying triangles, triangle abc

classifying triangles, triangle abc, sq rt: LeShae, First, you will need to draw triangle ABC on graph paper. If a side is a vertical line or a horizontal line, then you can count the number of squares to find its length. If the side slants, then you must put the coordinates of the endpoints...

Geometry: Co-ordinate Geometry (The Circle), distance formula, co ordinate geometry

distance formula, co ordinate geometry, point 0: Alternatively, The equation of the circle with center at (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2 ...(I) ( I am using ^ to denote the exponentiation, hence (x-a)^2 is to be read as (x-a) squared ) But the center of the circle...

Geometry: Co-ordinate Geometry - Parallelogram, eye sores, co ordinate geometry

eye sores, co ordinate geometry, parallelogram: Hi JKMishra! The 4 equations you have given me are coincident: they are all the same line. There is no parallelogram here. If you know this to be untrue (e.g., you ve been given a diagram), then send me a follow-up with the four equations without A, B,...

Geometry: Compass and straightedge, constructing parallel lines, construction reference

constructing parallel lines, construction reference, mathforum: Rosy, A compass and a straight-edge are tools used to make constructions. To draw a thermometer, you will need to construct several parallel lines. It is difficult to draw anything here, so I will include a few websites for you to visit. Look for directions...

Geometry: Complement and Supplements, definition of complementary angles, math math

definition of complementary angles, math math, math topic: Stephanie, First, let s remember the definition of complementary angles. Complementary angles are 2 angles whose sum is 90 degrees. Ex: 30 degrees & 60 degrees are complementary angles b/c their sum is 90 degrees. 60 degrees is called the complement...

Geometry: Complement and Supplements, agles, 23 degrees

agles, 23 degrees, 3x: Complement of the angle is x+54, so the angle must be 90-(x+54) ...(1) ( Since the total of the angle and its complement must be 90 ) Suuplement of the angle is 118+3x, so the angle must be 180-(118+3x) ...(2) (...

Geometry: Complements and Supplements, angle measure, andle

angle measure, andle, complements: Hi Janine, The complement of the angle equals (90-x) while the supplement equals (180-x), where (x) is the angle measure in degrees. Under these circumstances... COMPLEMENT c=90-x c=90-(71) c=19 SUPPLEMENT s=180-x s=180-(71) s=109 The complement...

Geometry: Composite space figure, rectangular pyramid, composite space

rectangular pyramid, composite space, greek alphabet: Mel, Definitions: Let s start with composite space figure. AND....let s take the words separately. In math lingo, Composite means built from more than one thing; Space means that the figure you are working with is in 3-D which means it has...

Geometry: Congruent Triangles, congruent triangles, leg lengths

congruent triangles, leg lengths, square root: By Pythagoras theorem: Square of the Hypotenuse = sum of the squares of the remaining two sides. Square of Hypotenuse = 4*4 + 7*7 ( * denotes multiplication ) = 16 + 49 = 55 Hypotenuse...

Geometry: Construction, isosceles right triangle, constructing triangles

isosceles right triangle, constructing triangles, using a compass: Katie, Are you using a compass and straight-edge for your construction? First you need to know the area of the given triangle. For example, let s say the given right triangle is a 3,4,5 triangle. The Area = (1/2)*3*4=6. What are side lengths...

Geometry: Converting Square Centimetres to Square Feet, cell b5, square centimeter

cell b5, square centimeter, measurment: Hello Hitesh! A foot is equivalent to 30.48 centimetres. Therefore, you have to multiply 10 000 by 30.48 to give you the floor space in square centimetres. This gives you 304 800. I will assume the cages are rectangular to solve this problem. # of cages=floor...

Geometry: Coordinate geometry question, geometry question, coordinate geometry

geometry question, coordinate geometry, distance between 2 points: Distance between 2 points (x1,y1) and (x2,y2) is given by the distance formula = square root of ( (x2-x1)^2 + (y2-y1)^2 ) ...(1) ( ^ stands for exponentiation i.e. (x2-x1)^2 is square of (x2-x1) etc. ) Therefore...

Geometry: Coordinates, baby talk, coordinates

baby talk, coordinates, axis: Hello, Angie! A reflection of a point over the y-axis give a point which uses the y-axis as a mirror . The point (3,-5) will be reflected to (-3,-5). It is still at the same height (y = -5), but it is now 3 units to the left instead...

Geometry: Coordinates, math geometry, math math

math geometry, math math, math topic: JayJay, The best explanation with a great diagram can be found in the Glencoe textbook. Here s a link: http://www.glencoe.com/sec/math/geometry/geo/geo_04/ Under Lesson Resources click on Extra Examples . Then click on Chapter 9 - Transformations...

Geometry: Cubes, analytic geometry, equilateral triangle

analytic geometry, equilateral triangle, diagonals: Hello, pand! This is a classic problem ... with a trick answer. You can use all kinds of techniques to answer the question: analytic geometry, vectors, etc. Look at this solution . . . Those two diagonals meet at one vertex. Look at the...

Geometry: Cubic Bezier Curves, cubic bezier curves, bezier curve

cubic bezier curves, bezier curve, superposition of waves: To Nick From Jay Subj Cubic Bezier Curve in the Plane. Nick, this question has a very messy answer. It s: 1. Given x = u, solve the cubic u = x(t) for t. There may be 0, 1, 2, or 3 solutions even if the curve...

Geometry: calculating distance, homework question, car length

homework question, car length, olympic style: Jacques, This is an interesting application. You indicated that you can use your bow to help judge distance which made me think that often one does use some common tool as a reference for judging distance. For instance, when one learns to drive one learns...

Geometry: catapult building, foot arm, luck steve

foot arm, luck steve, counterweight: Hello Jacob. Because of forces, torque, and angles, you would be better off trying an expert in physics. I would guess that somewhere near the counterweight would be the ideal place to drill the hole, but physics will tell where the force will maximize...

Geometry: circle and area, math faq, dr math

math faq, dr math, area of a circle: If radius is r and Pi denotes the well known mathematical constant ( approximately equal to 3.14 or 22/7), the formula for the area of a circle is A=Pi*r*r The formula for circumferene is P=2*Pi*r (I am using * to denote multiplication) So in...

Geometry: circles, minor arc, secants

minor arc, secants, secant: The minor arcs DA, AC,CB & BD add up to 360 degrees So measure (minor arc DA) = 1/(1+2+5+7)*360 = 1/15*360 = 24 degrees measure(minor arc AC) = 2/(1+2+5+7)*360 = 2/15*360 ...

Geometry: circles, triangle oab, radius of a circle

triangle oab, radius of a circle, angled triangle: Let the length of the chord be c , let the radius of the circle be r , let the distance from center point of the chord to the edge of the circle be h , then the required formula is: r= (1/[2*h])*( ((c*c)/4) + [h*h] ) Here * denotes multiplication....

Geometry: circles and lines, numerator and denominator, exact coordinates

numerator and denominator, exact coordinates, sqrt: x^2+y^2=9 can be written as x^2+y^2=3^3 This is an equation of a circle with center at (0,0) and radius 3. x=y or y=x is an equation of a line making an angle of 45 degrees with the X-axis ans passing thru the origin. Clearly there will be 2 points...

Geometry: circles/tangents and secants, angled triangle, secants

angled triangle, secants, secant: Theorem: If PAB is a secant to a circle intersecting the circle at A and B and PT is a tangent segment, then PA * PB = PT^2 ( I am using * to denote multiplication and ^ to denote exponentiation i.e. PT^2 is to be read as PT squared ) Given:...

Geometry: circles, minor arc, tringles

minor arc, tringles, intercepts: You have almost solved it. (But I can t understand why do you say the radius has to be 3?) Let the radius be r ( and you don t need to know its actual value. In fact you if observe all the alternative answers above, you will notice that none of...

Geometry: circumference, 6th grade math, circumference of a circle

6th grade math, circumference of a circle, diameter of a circle: Every circle has a center, all the points on the circle are at the same distance from the center. This distance is called the radius of the circle. ( Plural of radius is radii ) ( Generally the letter r is used to denote the radius.) The half lines...

Geometry: circumference and value of pi, archimedes pi, archimedes method

archimedes pi, archimedes method, math pi: There are several web pages which describe the Archimedes method. (Some of the webpages have animations also!). The basic idea is to approximate the area of a circle with the help of inscribed and circumscribed regular polygons. Better approximations are...

Geometry: circumference, radius of a circle, button hole

radius of a circle, button hole, buttonhole: If the radius of a circle is r , then its cicumference is 2*Pi*r ( Here Pi is the well known mathematical constant, approximately equal to 3.14 ) If the radius of a circle is r , then its diameter is 2*r 1. We are given the value...

Geometry: college math 2, supplementary angle, complementary angle

supplementary angle, complementary angle, math 2: An angle and its complemetary must addup to 90, so complementary angle of 33 must be = 90-33 =57 degrees An angle and its supplementary angle must addup to 180, so the supplementary angle of 33 must be =180-33=147 ( Note that the supplementary angle and...

Geometry: two column proofs, corresponding angles, column proofs

corresponding angles, column proofs, perpendicular line: Hello Misty. I drew triangle MLP, and marked N as the midpoint of MP. This was the given. It was also given that triangle MLP is isosceles, so ML is congruent to LP, so I marked those as congruent. Since the triangle is isosceles, by definition angle...

Geometry: with a compass only!!, compass constructions, perpendicular bisectors

compass constructions, perpendicular bisectors, geometric constructions: The compass only constructions are known as Mascheroni constructions. Lorenzo Mascheroni an Italian mascheroni in 1797 proved that every straight-edge and compass construction can also be made by compass alone. Such constructions are also called Mohr-Mascheroni...

Geometry: complement and supplement, degree 54, complement of an angle

degree 54, complement of an angle: The complement of an angle x is 90 - x and the supplement is 180 - x. So complement of 35 degrees 20 will be = 90 - (35 degrees + 20 ) = 90 - 35 - 20 = 55 - 20 = 54 + 1 - 20 ( By writing 55 degrees as 54 degress + 1 degree)...

Geometry: congruent triangles and transformations, congruent triangles, class exercise

congruent triangles, class exercise, coordinate plane: First plot A, B, and C on a coordinate plane. A reflection over the x-axis gives you the opposite y value for each point (opposite meaning switch the sign). If we give the reflection of A the name A (and follow this pattern for the other points. Then A...

Geometry: construct a tetrahedron from..., math geometry, tetrahedron

math geometry, tetrahedron, tremors: Have you actually tried to make a tetrahedron by following the given instructions but have faild to make it ? I think the instructions are fairly simple and staight forward. May I know in which particular step you have problems ? In any case you may...

Geometry: continuing about 8-shape figure turning, boundary value, frame rate

boundary value, frame rate, eyesight: Well, it would depend on your eyesight, or if say you re using a camera, it would depend on the frame rate. If you spin it fast enough it will appear as a bumpy sphere, but not quite a perfect sphere. For a hyper n-gon, it will be the same. To truly answer...

Geometry: contructing triangles, point of intersection, bisector

point of intersection, bisector, detailed solution: The problem is how to construct an angle of 75 degrees, ( I hope you can manage the other part of marking 6 cm & 7 cm on the arms of the angle of 75 degrees, after it is constructed.) We can write 75=90-15 (Or = 60 + 15) So you will agree that...

Geometry: conversions, answer 7, decimal point

answer 7, decimal point, conversions: 10 cm = 1 dm So 1 cm =(1/10) dm i.e. you need to divide the cm value by 10. So 129 cm = 129*(1/10) dm = 12.9 dm But division by 10 means shifting the decimal point by one position to left. When you are given the value in cm just shift...

Geometry: convex quadrilateral, interior angles of a polygon, right angles

interior angles of a polygon, right angles, convex quadrilateral: Hannah, A convex quadrilateral can look like a rectangle but doesn t have to have 4 right angles. Now there s a formula for finding the sum of the interior angles of a polygon. The formula is (n-2)*180 degrees. n stands for the number of sides of the...

Geometry: coordinate geometry, coordinate geometry, locus of a point

coordinate geometry, locus of a point, directrix: Please refer to the diagram given at: http://www.mathacademy.com/pr/prime/articles/conics/index.asp ( I am referring to the 13th diagram given on this page, under tthe topic Eccentricity) Please note: There is an alternative definition of ellipse...

Geometry: coordinate geometry, y intercept, x intercept

y intercept, x intercept, coordinate geometry: x+y=8 Therefore y=-x+8 When the equation of a line is written in the y=m*x+c format, m is the slope and c is the y-intercept, x-intercemt can be found by substituting the value of y as 0. ( I have used * to indicate multiplication. ) So the slope...

Geometry: coordinate geometry, slope y intercept, slope intercept form

slope y intercept, slope intercept form, x intercept: To find these properties, take the equation and put it in slope intercept form (y=mx+b). Solving x+y=8 for y gives y=-x+8. In the form y=mx+b, m is the slope, y is the intercept, and to find the x intercept, let y=0 and solve for x so the slope is -1, y intercept...

Geometry: coordinate geometry, regular decagon, geometry 1

regular decagon, geometry 1, centemeters: A regular decagon has 10 sides all equal to each other. The perimeter of regular decagon is sum of these 10 equal lengths. So the length of each side of the regular decagon must be (1/10) th of 120 centemeters. So the answer must be 120/10 centimeters.,...

Geometry: coordinate proofs, isosceles trapezoid, algebraic manipulations

isosceles trapezoid, algebraic manipulations, first quadrant: (I am myself not very familiar with this topic of geometric proofs using co-ordinate geometry. But the general guidelines to reduce algebraic manipulations are: 1. One should take one of the vertex of the figure under consideration to be ...

Geometry: coordinate proofs, line segments, additive inverse

line segments, additive inverse, perpendicular lines: Hello. This is a cool problem. You need to know a few formulas to finish it up, but the main one is how to get the equation of a line using only the coordinates of two points. Let s say you have two points, (x1,y1) and (x2,y2). The formula for finding...

Geometry: correction, synthetic division, simpler method

synthetic division, simpler method, binomial: Please visit the following sites and you will understand the method: http://www.purplemath.com/modules/synthdiv.htm http://www.purplemath.com/modules/synthdiv2.htm http://mathforum.org/library/drmath/view/53056.html http://mathforum.org/library/drmath/view/56406.html...

Geometry: cosӨ = 1 + sin²Ө, quadratic equation, first solution

quadratic equation, first solution, bur: You mean, you want to solve the equation cos(theta)=1+sin^2(theta) ? ( I am using ^ to denote exponentiation.) Replace sin^2(theta) with 1-cos^2(theta) ( Since sin^2(theta) + cos^2(theta) = 1 ) So we get cos(theta)=1+1-cos^2(theta) Therefore,...

Geometry: coterminals, bus terminal, bus route

bus terminal, bus route, angles: Coterminus angles differ from each other by multiples of 360 degrees. So the angle which is coterminus with 427 degrees but between 0 to 360 degrees can be found by subtracting 360 from 427. So the answer is =427-360 =67 degrees (If...

Geometry: cube in a cone, axis of symmetry, square root of 2

axis of symmetry, square root of 2, rough sketch: Please draw a rough sketch. Let the height (and each of the sides ) of the cube be h . Now when it is fit inside a cone, the longest side would be the diagonal of its top face. Assume the half of the diagonal be a So from Pythagoras Theorem we...

Geometry: cubes, querry, bottom layer

querry, bottom layer, mathforum: I am sorry for the delay. This is can be easily demonstrated with a digram but I couldn t get the exact diagram I was looking for. Just think about where the 8 cubes will be ? How they will be placed ? They will be in 2 layers. The bottom layer will have...

Geometry: cubic feet, 3 dimensional shapes, three dimensional figures

3 dimensional shapes, three dimensional figures, volume formulas: Cubic feet is just a unit for measuring volume.(just as foot is a unit of measuring length and square foot is a unit of measuring area.) But as you may be aware the formula for finding the area of different geometric shapes are different. Similarly the formulas...

Geometry: cubic meters, line calculator, google search

line calculator, google search, cubic meter: I. 1 cubic meter = 35.3146667 cubic feet So just multiply the value of cubic meters by 35.3146667 Needless to say, if you don t need the accuracy upto so many decimals, then you may drop some of the digits from the end of this multiplier. II. For an...

Geometry: cyclic quadralaterals, angle bcd, cyclic quadrilateral

angle bcd, cyclic quadrilateral, arc of a circle: To prove that : The opposite angles of a cyclic quadrilateral are supplementary. (This follows readily from another theorem: The angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part...

Geometry: cylinder capacity, gallons to cubic inches, conversion calculator

gallons to cubic inches, conversion calculator, volume of a cylinder: Angie, Here s an image I drew with the information you provided: http://img247.imageshack.us/my.php?image=6000galcylinderhs8.jpg. I used an online conversion calculator to convert from gallons to cubic inches. The URL: http://www.onlineconversion.com/volume.htm....

Geometry: cylinder circumference + length, spiral stair case, circumference of a cylinder

spiral stair case, circumference of a cylinder, tuning coil: To Larry From Jay Subj The length of a simple helix. i had replied with: [ The secret to rectifying a cylindrical spiral is imagine it all unrolled to lie in a plane. For computing purposes, let s suppose: 1. The cylinder...

Geometry: Decagon Diameter, math faq, inscribed circle

math faq, inscribed circle, regular decagon: Formulas related to regular polygons can be found at: http://www.mathforum.org/dr.math/faq/formulas/faq.regpoly.html ============================================================ For a regular decagon we can inscribe a circle which touches all the 10 sides...

Geometry: Deck, tiffany, guidance

tiffany, guidance: Tiffany, This sounds like an interesting project; but, without more information I m not certain how to help you with the project. I googled geometric deck and found several articles which may provide you with some guidance. If you can provide me...

Geometry: Dividends - Multiples of 3, divisor, magic number

divisor, magic number, number 3: Hi Deanna! This question almost answers itself if you think about it. 3 is a factor of many numbers. For this example, let s use 12 and 36. A number that is divisible by 12 will also be divisible by 3 because its divisor, 12, is divisible by 3. Allow...

Geometry: Due to the unexpected cold..., original cost, cold weather

original cost, cold weather, arithmetic: 50% increase means, if the original cost was 100, now it will be 150. Now the current cost per pound and the original cost per pound must be in the same ratio as 150/100 So 150/100=0.60/(original cost per pound) So the original cost per pound=0.60*100/150...

Geometry: Duplicate Questions, question pool, answering the question

question pool, answering the question, questioner: Trisha, Please don t send duplicate questions to experts. I m going to assume this was an Internet mess-up, but it does get annoying when the same questioner asks the same question over and over. (I m really just answering the question so another expert...

Geometry: determining possible real roots, complex number, conjugates

complex number, conjugates, real numbers: Since this is an equation of 5th degree it must have 5 roots. There is a result which says that the sum of the roots must be equal to -(co-efficient of the term with x^(n-1)), i.e sum of the roots in the above case must be -(-4)=4. Now sum of a: complex...

Geometry: Can diagonals be the same?, isosceles trapezoid, graphic examples

isosceles trapezoid, graphic examples, diagonals: The answer is yes, provided 1 set of opposite sides are allowed to be equal. If the requirement is both the sets of opposite sides should be unequal then the answer is no . The required figure is called an isosceles trapezoid. The figure can be seen at the...

Geometry: If the diameter of a circle..., diameter of a circle, using algebra

diameter of a circle, using algebra, initial area: Let A1 be the area of the circle before increasing the diameter. Let A2 be the area of the circle after increasing the diameter by 45 percent. A1=Pi*r*r=Pi*(d/2)*(d/2) =(Pi*d^2)/4 ( Pi is the well known mathematical constant, *...

Geometry: diameters and pi, math faq, dr math

math faq, dr math, circumference: The circumferece c = d * Pi ...(1) (Where d is the diameter, and c is the circumference, I have used * to denote multiplication. This used only in writing e-mails etc., not to be used by your nephew. ) Hence,...

Geometry: difficult trigonometry, 3rd quadrant, first quadrant

3rd quadrant, first quadrant, 80f: In one part of the question they ask to the nearest tenth of an hour, the amount of time in 1 day that the air-conditioning is on in the building And later on they ask you to graph it only for 6 = t 17 This I felt was a source of confusion....

Geometry: dividing polynomials, dividing polynomials, hi thanks

dividing polynomials, hi thanks: a^2-a*b+b^2 ------------- a+b | a^3+b^3 a^3+a^2*b --------- -a^2*b+b^3 -a^2*b-a*b^2 ------------ a*b^2+b^3 a*b^2+b^3 --------- Alternatively, let...

Geometry: dodecahedrons, decagon, dodecahedron

decagon, dodecahedron, polyhedron: A dodecahedron is a polyhedron (a solid with 12 surfaces). Do you want to construct a decagon ( a polygon with 10 equal sides ) instead ? Please clarify. If you know how to fit a pentagon inside a circle just bisect the 5 arcs and you will get 5 more...

Geometry: Electrical Design, pi radians, degress

pi radians, degress, electrical design: (I think there is an error in the problem but here is the solution anyway) - - - - - - - - - - - - - - - - - - - - - - - - - - - If 3.14 Radians = 120 Degrees What Degrees will 5 Radians have ? Since 3.14 Radians = 120 Degrees Then 1 Radian = 120...

Geometry: Elevation, hundreth, flagpole

hundreth, flagpole, sun express: Draw a triangle joining the top of the flagpole, the foot of the flagpole and the tip of the shadow. Let the top of the flagpole be A , the foot be B and the tip of the shadow be C . Now angle of elevation is the ACB. So we have tan( ACB) =12/9=4/3. ...

Geometry: Ellipse - Eccentricity of 1, minor axis, major axis

minor axis, major axis, line thanks: Hi Mohammed! I would use logic to show this. If e=0, then the ellipse is really a circle, for both foci are superimposed. As the eccentricity increases from 0 to 1, the circle flattens out, forming an ellipse. The formula for calculating eccentricity...

Geometry: Engineering, arc of a circle, upper segment

arc of a circle, upper segment, millimeters: For any two intersecting chords in a circle, AB and CD with the intersection at E, AE(BE)=CE(DE). As with all geometry, a diagram helps a lot, so let me know if you need clarification. So the ends of the arc form a chord 12 mm long and a diameter perpendicularly...

Geometry: Equations of Circles, standard equation of a circle, equations of circles

standard equation of a circle, equations of circles, equation of a circle: Brittney, I m sorry to hear about your injury. But great job on teaching yourself! To go from the standard equation to the 2nd version is mostly Algebra. So here s an example given center (1,1) and radius 2. (x-1)^2 + (y -1)^2 = 2^2. First,...

Geometry: Equations and Inequalities, equations and inequalities, 11q

equations and inequalities, 11q, intermediate steps: solve this inequality: 3p-6 21 Adding 6 to both the sides we get, 3p-6+6 21+6 Therefore, 3p+(-6+6) 27 Therefore, 3p+0 27 Therefore, 3p 27 Multiplying both the sides by (1/3), we get 3p*(1/3) 27*(1/3) ( I have used * to denote the multiplication.)...