About Experts Sitemap - Group 182 - Page 9 2012-07-20
Geometry: Conversion - Cubic Meter to Ton, 1 cubic meter, conversion
1 cubic meter, conversion: Hello Hashim, A cubic meter is a unit of volume, while a ton is a unit of mass. You may not convert from one to the other, unless if you are dealing with a specific substance (e.g. 1 cubic meter of water has a mass of 1 ton). Thanks for asking, Azee...
Geometry: Circumference - Exactitude of Pi, straight line segments, circumference of a circle
Geometry: Circumference - Exactitude of Pi, straight line segments, circumference of a circle, differential equations
Geometry: hi, coordinate geometry, wrong numbers
coordinate geometry, wrong numbers, linear equations: Hi hi, The order of the coordinates is irrelevant, as long as it is consistent. Whether (-3,7) or (5,-1) is taken as the first point, the end result will be the same. (The importance lies in the difference between the two values.) a=(y2-y1)/(x2-x1)...
Geometry: Irrational/Rational Circumference, pi
pi: Hi Shikhin, You said that if we take a line whose length is rational and bend it to form a circle, the circumference will be rational. Then will in such a case, the diamter become irrational??? Because of the irrational value of pi, the diameter would...
Geometry: Proofs - Isosceles Triangle, isosceles triangle, angle measures
isosceles triangle, angle measures, prrof: Hi Robert, It seems as though your reason for statement 3 is mismatched. I think you should first state that the angle measures are 90 degrees (definition of perpendicular). Afterwards you can mention that the angles are congruent (90 degrees congruent...
Geometry: Properties of Triangles, radians, sine law
radians, sine law, cosine law: Hello Kishore, For Q1, you haven t actually asked the question. You ve given me the setup, but you haven t asked me what you re required to find. I can t help you. It should follow as no surprise that I have no idea what your calculations mean. I ve...
Geometry: Roots of an Equation, eq 2, asymptotic behaviour
eq 2, asymptotic behaviour, factor x: Hi Shikhin! Allow me to begin by stating that the ideal strategy is to cancel the common factor. This gives you the actual roots with no extra clutter. Although equations 1 and 2 are essentially mathematically equal, the subtle difference lies in their...
Geometry: Square Roots, square roots, square root of x
square roots, square root of x, conjecture: Hey Cody! The square root of x will be greater than x when x is between 0 and 1 inclusively. √(1/2)=1/√2=0.707... 1/2 √0.1=0.316... 0.1 √0=0, which is not less than 0 √1=1, which is not less than 1. Thanks for...
Geometry: Supplementary & Complementary Angles, complementary angles, note spelling
complementary angles, note spelling, suppliment: Hi Jim! The supplement (note spelling) of the complement (note spelling) is not 180-90-x, but 180-(90-x). This simplifies to 90+x. Setting up the full equation, we obtain: 180-x=2(90+x)-36 180-x=180+2x-36 -x=2x-36 -3x=-36 x=12 The difficulty in...
Geometry: Volumes and Areas, cylinder, prism
cylinder, prism: Hi Alex, For a rectangular prism, volume can be calculated by multiplying all three dimensions. Lateral area is found by finding the area of the four lateral faces, which are all rectangle. It can be calculated by (l+w)h. Total surface area is 2(lw+lh+lw)....
Geometry: Basic Trig - Airplane, sine, sin
sine, sin: Hi Akire, Sketch the ground. Sketch the diagonal at 25 degrees to the ground. Connect the diagonal to the ground. You now have a right triangle. A right triangle means you can do basic trigonometric operations, such as sin, cos, and tan. You know...
Geometry: Circles and solids., right triangle, chord length
right triangle, chord length, groun: I forgot to send the picture with my response. I wish that could be attached at first, but I have to wait until I have previewed it at first. This is not to you, but to the people who run it, and I think they read the answers. They should have a box to...
Geometry: Complementary Angles, quadratic, typo
quadratic, typo: Hi Mike! As written, there is no solution to the quadratic equation. Assuming there is a typo and it s supposed to be positive 2x², the equation becomes 2x²+8x-64=0 x²+4x-32=0 Which can be factored as (x+8)(x-4)=0 Therefore x=-8, and x=4. ...
Geometry: convert cubic meter to cubic foot, cubic meter, cubic foot
cubic meter, cubic foot, cubic meters: I believe a meter is 39.37 inchese. Divide this by 12 to convert that to feet. It should be around 3.28 or so. Since we are dealing with cubic feet and cubic meters, we need to divide by the number we got. A great place to do the conversion is...
Geometry: equations!, line segment, 7x
line segment, 7x, sr 2: I will use L() as the length of a line segment. 1. It is nown that L(AC) = 11x-20, L(AB) = 3x-8, and L(BC) = 6x+4. Since L(AC) = L(AB) + L(BC), we know that 11x-20 = 3x-8 + 6x+4, which is the same as 11x - 20 = 9x - 4. Adding 20-9x to both sides gives...
Geometry: Geometry, 3x, geometry
3x, geometry, c sqrt: The equations are (1) ab=3x-4, (2) ac = 40, and (3) ab = bc. Looking at 3, if b is not 0, we know that a = c by dividing both sides by b. Using a = c and (2) ac = 40, we can see that a = c = sqrt(40). Equation (1) will tell us that b*sqrt(40) = 3x...
Geometry: Geometry, isosceles triangle, triangle share
isosceles triangle, triangle share, right angles: The triangle is an iscoeles triangle, and by definition, two of the sides are equal. Since the line is draw as a Median, it bisects the base, making the two bases equal. Since the two triangle share the inside line, we now have both triangles having...
Geometry: Geometry, kh, 3x
kh, 3x, geometry: If we know the length of HJ and JK, add them up and you get the length of KH. The lengths or HJ = 2x + 4 and the length of JK is 3x + 3. When HJ and JK are added together, you get KH, which is 22. The equation to solve is then 2x+4 + 3x+3 = 22. Combine...
Geometry: Geometry, base of the pyramid, hypoteneuse
base of the pyramid, hypoteneuse, right triangle: The area of a pyramid is known to be Ah/3 where A is the area of the base and h is the height. The area of the base is A = 2(1+√2)a² where a is the length of an edge. For this octagon, the area of the base is 4²2(1+√2) = 32(1+√2). ...
Geometry: Geometry help, geometry help, compliment
geometry help, compliment, complement: The angle is X. The complemt is 90-X. We are given that 3X = 2(90-X). This means that 3X = 180 - 2X, so add 2X to both sides of the equation. This gives 5X = 180, so now we can divide by 5. That is, X = 180/5 = 36. 3X = 108 and the complement...
Geometry: geometry, even integers, conjectures
even integers, conjectures, geometry: The list of positive, even integers is 2, 4, 6, 8, 10, 12, ... The sum is 2, 2+4=6 2+4+6=12 2+4+6+8=20 2+4+6+8+10=30 Use these values to form a difference table. i sum 1 2 2 6 (6-2)/(2-1) = 4 3 12 (12-6)/(3-2) = 6 (6-4)/(3-1) = 1 4 20 (20-12)/(4-3)...
Geometry: geometry conjectures, geometry conjectures, conjecture
geometry conjectures, conjecture: A conjecture is any statement that is either true or false. If one statement is found that is false, the conjecture is false. Suppose two numbers are 1 and -1. It is known that the sum is 0. The sum is not greater than the larger number since 0...
Geometry: Math, volume of a shere, spherical tank
volume of a shere, spherical tank, volume of a sphere: I don t know of any particular job that uses this, but it is sometimes needed in various places. The volume of a sphere is V = 4πr³. The derivative of this is the surface area, A = 12πr². Perhaps somebody wants to calculate how much water it...
Geometry: Math problem, 44j, integer solution
44j, integer solution, squareroot: I didn t find an integer solution, but I did find that given a value of x, the equations can be solved. From the last equation, H = 44/K. The first equation HJ=3(x+2), after putting H = 44/K in, becomes 44J/K = 3(x+2). Multiplying both sides by K gives...
Geometry: math, trig laws, trig identities
trig laws, trig identities, tana: There are some trig laws that are proved in almost any book on trig. The first one is sin(2A) = 2sinAcosA. The completes the first line. Now if we multiply that by cosA/cosA, we get the next line, 2sinAcos²A/cosA. For the 3rd line, note that two more...
Geometry: math, c cos, sinc
c cos, sinc, xz: The equation is sin(2A) + sin(2B) + sin(2C) = 2•sinA•cosA + 2sin(B+C)•cos(B-C). First, it is a comon identity that 1) sin(A+B) = sinA•cosB + sinB•cosA, so sin(2A) = 2sinA•cosA; and 2) cos(B-C) = cosB•cosC + sinB•sinC; and 3) sin²(A) + cos²(A) = 1....
Geometry: In need of help., ef, df
ef, df, geometry: Yes, DE + EF = DF, so just put in the values. DE is 5x + 13, EF is 6, and DF is 7x - 25. That gives 5x + 13 + 6 = 7x - 25. Add 13+6 and get 19, so now the equation is 5x + 19 = 7x - 25. Add -5x + 25 to both sides of the equation and get 44 = 2x....
Geometry: Pythagorean Theorem, right triangle, combining like terms
right triangle, combining like terms, quadratic formula: For a right triangle, we know that a² + b² = c². Putting in what we re given for a, b, and c gives us (x-2)² + (x-4)² = 10². Multiplying this out gives x² - 4x + 4 + x² - 8x + 16 = 100. Combining like terms gives 2x² - 12x - 80 = 0. The coefficients...
Geometry: pump tank, pump tank, water discharge
pump tank, water discharge, minimum distance: Since the diameter is 40 inches, the radius is 20 inches. That makes the area πr² in.², which is π(20)² in² = 400π in². From http://www.belden.com/pdfs/TechInfo/TechUnitConversion.htm I can see that a gallon is 231.0 in². This makes 50...
Geometry: More questions!, volume of a frustum, slant height
volume of a frustum, slant height, lateral area: 1) If d = 4, 2r = d = r = d/2 = 4/2 = 2. The height h is 15, so take 15c, where c is the length of the perimeter of that circle. The length of the perimiter is c = 2(pi)r = 4pi. The answer, then, is 15*4pi. 2) The area of the bae is 36, the height is...
Geometry: ratios??, hypoteneuse, paint program
hypoteneuse, paint program, angle measure: I have no way of accessing that picture. When I want to send pictures, they need to be put in a JPG file by a drawing language. I will send back a basic JPG file which was created in my Paint program and saved as a JPG file. Note that the file extension...
Geometry: Segment Addition Postulate., st rt, graph paper
st rt, graph paper, collinear: Let XY, YZ, and XZ be lines. The Segment Addition Postulate says that if XY + YZ = XZ, then Y is between the points X and Z. Using the posutlate for RS, ST, and TW, we know that RS + ST = RT. Since RS=2w+1 and ST=w-1, RS+ST=3w. Since RT = 18 and...
Geometry: Systems of Equations - Complementary Angles, complementary angles, math problem
complementary angles, math problem, p 90: Hello Ted, Complementary angles sum to 90 degrees. L+M=90, N+P=90. You have two variables in two equations. Set up the system and solve for the variables. Finally, plug them in to find the angle measures. L+M=90 (y-2)+(2x+3)=90 2x+y=90-3+2 y=89-2x...
Geometry: segment addition postulate, 44j, line segment
44j, line segment, integer solution: I didn t find an integer solution, but I did find that given a value of x, the equations can be solved. From the last equation, H = 44/K. The first equation HJ=3(x+2), after putting H = 44/K in, becomes 44J/K = 3(x+2). Multiplying both sides by K gives...
Geometry: Triangular Prism, volume, surface area
volume, surface area, lateral area: Hi Fatima! Assuming you have the three sides of the triangle and the prisms height... [a=side 1 of triangle b=side 2 of triangle c=side 3 of triangle h=height of prism s=(a+b+c)/2 (semi-perimeter of triangle) z=area of triangle] The triangle s...
Geometry: trigonmetry, 6a, 3a
6a, 3a, sina: I m not sure what sinA6A is. Is it suppose to be sin6A? I don t see how that is possible. It looks like the question should be prove that (sinA•sin2A + sin3A•sin6A)/(sinA•cos2A + sin3A.cos6A) = 5tanA . I don t follow where the equations came from,...
Geometry: Various, longest side of a right triangle, side of a right triangle
longest side of a right triangle, side of a right triangle, town c: Hi Bongiwe, Unless if you don t know what a square is (in which case tell me), I can t make it much simpler than I already have. A square s area is found by multiplying the length of one side by itself. To find the cube s surface area, multiply one square...
Geometry: Area - Equil. Triangle, radical
radical: Hi Cathy! I ll take the radius to be what you said it is, that is the distance from the centre of the triangle to a vertex. Draw one radius and one altitude. Focus on the smallest right triangle. Its hypotenuse is the radius r, its base (b) is half...
Geometry: Cone - Polyhedron?, polyhedron, circular base
polyhedron, circular base, polyhedrons: Hey Heather, A cone is not a polyhedron. It is a circular cross-section of a pyramid, but still not a polyhedron. Polyhedrons are, by definition, comprised to polygons joined at their edges. Polygons are, by definition, closed 2-dimensional figures...
Geometry: Counterexmaples - Months, information results, geometry
information results, geometry, conclusion: Hi Jesse, You re trying to show an example where the same given information results in a different conclusion. It is not January, but it is [any month other than January or June] would be an appropriate counterexample. Thanks for asking, Azee...
Geometry: chords with rotation in side plane, side plane, inch radius
side plane, inch radius: It sound like we re rotating a plane in a cyllinder, which is equivalant to rotating a line in a circle. If 90 deg gives you a view of the full width and 0 degrees gives you a width of 0, that sounds like the sin() wave. That is because sin(0)=0 and...
Geometry: Diagonals, diagonals, multiplications
diagonals, multiplications, polygon: Note that the diagonal can t be drawn to the same corner or either adjacent corner. The number of corners left is n-3, so that total is n(n-3), but that counts them all twice, since there is a point at either end that is a corner. The answer, then, is...
Geometry: Diagonals of Quadrilaterals, quadrilaterals, diagonals
quadrilaterals, diagonals, quadrilateral: Hi Alex, A diagonal joins two non-adjacent vertices (2 corners that aren t connected by a line). Quadrilaterals have 2 diagonals. When drawing a diagonal, it connects two sides together by a third. This forms a triangle. The diagonal does this on both...
Geometry: Factoring, difference of squares, difference of 2 squares
difference of squares, difference of 2 squares, binomial: Hey Sierra! The basic principle of factoring is to turn a sum into a product of sums. It is a form of decomposition which allows for things such as cancellation. Obvious example: 12/4 (3)(4)/4 Cancel the 4s 3 thus, 12/4=3 There is simple factoring...
Geometry: Geometry, allexperts, geometry
allexperts, geometry, civil engineering: In doing drawings of what is being produced. When several things are manufactured, a drawing is needed. In doing the drawing, geometry can come in very useful. I found a page in AllExperts that has several questions on geometry and engineering. It is...
Geometry: Geometry, area of a rectangle, area of a square
area of a rectangle, area of a square, geometry: The area of a rectangle is the height times the width. A square is a special rectangle where the height = width. This known, the area of the square is the width*width, or widht². Since the width is the length of the side, and the length of a side...
Geometry: geometry question, geometry question, bottom right
geometry question, bottom right, right angle: If two lines in a triangle are congruent, the opposing angels are congruent. One of these angles is given, so the other has the same value. Now that all of the angles in a trianle are known, add them all together. This will give 180 degrees. Once this...
Geometry: Interior Angles of a Hexagon, interior angles, angles of a hexagon
interior angles, angles of a hexagon, six sided figure: Hi Mariaha, To my understanding, you re trying to find the value of x, where x is an angle measure. (I m going to ignore the x=10, because that s where you lose me.) In order to find the sum of the interior angles, you can use the formula: total=180(n-2),...
Geometry: math, greatest common divisor, congruent squares
greatest common divisor, congruent squares, canvas: That question is the same as asking for the greatest common divisor of 150 and 180. It is known that 150 = 2*3*5*5 and 180 = 2*2*3*3*5, so the numbers in common are 2,3, and 5. That is only one of each, and 2*3*5=30. This means to divide the canvas in...
Geometry: math, diameter of a circle, hypoteneuse
diameter of a circle, hypoteneuse, right triangle: I m not sure I understand the question, but I ll take a shot at it. Yes, if the radius is the hypoteneuse of a triangle and the corner is on the edge of the circle. That makes the triangle into a right triangle since an angle in a circle is always one...
Geometry: perimeter of triangle, hypoteneuse c, perimeter of triangle
hypoteneuse c, perimeter of triangle, right triangle: The area A of a triangle is A = bh/2 where b is the base and h is the height. If the area is 84 and the base is 14, this gives the 84 = 14h/2, so h=12. Since that is what is given as the height, it is a right triangle. Knowing this, the hypoteneuse c...
Geometry: I am doing a project for Geometry class, geometry class, right triangles
geometry class, right triangles, mathematicians: Enineers, landsapers, constructionists, physicists, mathematicians, and chemists are some of the occupations that frequently use polygons. The most common one is with right triangles and finding the third side given the length of the other two. ...
Geometry: question, 32h, number 32
32h, number 32, square inches: The area is WH where W is the width and H is the height, so we have A = WH. The number 576 is A, and is known to be 64*9 = (2^6)(3^2). The number 32 is W, and is known to be 2^5. So we have 576 = 32H. or (2^6)(3^2) = (2^5)H, so 2(3^2) = H, so H = 18....
Geometry: Science Fair Project, conservation of momentum, expiriment
conservation of momentum, expiriment, parabolics: Hi Noah, When the ball goes down the ramp at 20 degrees, due to the direction of its momentum, it will try to mount the next ramp at 20 degrees. If the angle of the second ramp is more than 20 degrees, momentum will be lost in climbing that ramp. If the...
Geometry: Science fair project answers, project answers, horizontal speed
project answers, horizontal speed, expiriment: There are some formulas that would be handy. The acceleration a is g•sin(A), where g is gravity and A is the angle of incline. Note that to solve for time t, use the formla d = at²/2, where a = g•sin(A) and d is the distance, which is the plank length....
Geometry: Solving equations involving vertical angles, vertical angles, solving equations
vertical angles, solving equations, vertex: I know two vertical angles share the same vertex. This means that they are equal. I don t know what type of equation that is being solved that involves vertical angles. Here is a reference to vertical angles://www.mathsisfun.com/geometry/vertical-angles.html...
Geometry: surface areas, volume of a cube, surface areas
volume of a cube, surface areas, relationship: If the volume is 8 times less, it is known that 8 = 2³, so the bigger cube has twice the side length to get 8 times the volume. With twice the dimensions, each side is twice as long and twice as wide. Since the area is the product of these two, the area...
Geometry: Trapezoid, angle measures, jklm
angle measures, jklm, acute angle: Hi Angel! The trapezoid you have proposed is completely acceptable. From the information given, there is not much to conclude. It isn t even possible to determine whether JM or KL is longer. The only thing you know for sure is that angle J is a right...
Geometry: Trigonometry - 0, 90 Degrees, sine, cosine
sine, cosine, tangent: Hi Riya! Draw a unit circle. 0 degrees is on the x-axis, so the sine is 0 and the cosine is 1. Similarly for 90 degrees, it is on the y-axis, so the sine is 1 and the cosine is 0. The other trig operators such as tangent and the reciprocals can be derived...
Geometry: Vectors - Dot and Cross Products, vector quantity, vector product
vector quantity, vector product, scalar quantity: Hi Zaheer! The dot product (aka scalar product) results in a scalar quantity. 2 vectors are combined and the result is a number that is the sum of the products of the like components. A regular number is a scalar. Thus a dot product gives a scalar....
Geometry: Volume - Water Tank, gallon
gallon: Hi Nelson, Your water tank has a radius of 5 feet, or 60 inches. πr² tells you the area of a disc inside your water tank is 11 309.73 square inches. Multiplied by the 36-inch drop, you have a volume of 407 150.41 cubic inches. There are 231 cubic...
Geometry: Angles of Inclination, angle of inclination, mathematical concept
angle of inclination, mathematical concept, course thanks: Hi Jordan! I understand your situation. I ll give you a couple of examples, but frankly, it s not like I use this on a day-to-day basis the way it might be drawn up in your textbook. For a project, I need to design a staircase. There are constraints...
Geometry: Contrapositive, Converse, and Inverse, converse, veracity
converse, veracity, geometry: Hey Jason, The inverse is the same statement, but with not in front of each part. If a figure does not have exactly three sides, then it is not a triangle. The converse flips the sentence s if-then relation. If a figure is a triangle, then it...
Geometry: Cylinder Radius, system of equations
system of equations: Hi Vivek! To solve this question, you need to make a system of equations in 2 variables using the equations for the area of the metal sheet and the volume of the cylinder. Use the equation of the volume of the cylinder to find height in terms of radius....
Geometry: complement and supplement
Hi Patrick! If I had to guess, I d say the 0.5 is relative, meaning the angle is half as large as its supplement, or something like that. The π/3 has to be radians. A radian is defined as the angle required for the arc length to equal the radius....
Geometry: Geometric Problem Solving, math, geometry
math, geometry, square: The square is AxA and the rectangle is HxV. The perimeter is P on both of them. The perimeter of the square is P = 4A and the perimeter of the rectangle is P = 2H + 2L, where H = height and L = length. It is given that H = 2A, so for the rectangle P...
Geometry: Geometry, law of detachment, two choices
law of detachment, two choices, true statements: Detachment: If p→q is a true statement and p is true, then q is true. Syllogism: If p→q and q→r are true statements, then p→r is a true statement. Detachment can be used where there are two choices to...
Geometry: Oval finding arc length and radius of 4 sections, math, oval
math, oval, length: To find the length of the outside, see the article http://en.wikipedia.org/wiki/Ellipse and almost half way down is the derivation of area and perimeter. To find the foci of the ellipse, see http://mathworld.wolfram.com/Ellipse.html To get a good guess,...
Geometry: Surface Area - Pyramid
Hi Sharon, As with all right pyramids (whose vertical faces are congruent isosceles or equilateral triangles), the surface area is the sum of the base area and the triangles area. The area of the triangles can be found by multiplying the base edge by...
Geometry: scale factor, math, drawing
math, drawing, scale: If standard graph paper (8.5 x 11 ) is used and this was for a floor plan, then I would used 1 = 2 as the scaling factor. In this way, the graph of the floor would be 4.25 by 5.5 and things on the floor could be put where they go. Now if the drawing...
Geometry: Triangle calculation, math, t rig
math, t rig, angles: Let the height be h, which is usually put on the y-axis when graphing. The width w, which is usually put on the x-axis when graphing, is given by the ratio of h:w which is 1:1. This ration says that whatever the value of h is, that same value is the...
Geometry: Algebra and Geometry, change, value
change, value, quarters: The complement of an angle is the angle needed to make 90°. Thus, the complement of 42° is 48° since 42° + 48° = 90°. If the angle is of measure x°, the complement is 90° - x°. The supplement of an angle is the angle needed to make 180°. Thus, the supplement...
Geometry: Angle Bisecting-Respectively, algebra, graph
algebra, graph, points of intersection: I ll send a picture of what I think it looks like. In the triangle ABC, we know that the angles at A and B are complementary to each other since C is a right angle. I didn t include E and F, as I believe one of them should have a non-zero x value, so its...
Geometry: Find circumference of cirlce with area, circle, radius
circle, radius, area: I will use sqrt() for the squareroot. Both the circumference and the area of a circle have equations in terms of the radius. The circumference is C = 2*pi*r and the area is A = pi*r^2. Solving for r given A leads to A/pi = r^2, so r = sqrt(A/pi)....
Geometry: geometry, math, algebra
math, algebra, area of a square: If 17 is the distance from the center of the square to the center of a side, then that 17 is half the width. This means the width is 2*17 = 34, and the area of that square is 34x34. I believe 34x34 is 1,156. That is probably correct, for if it were...
Geometry: geometry, math, geometry
math, geometry: I believe I ve got it. We have a line m, so lets turn it so it is vertical. If we have a set of points that are at a fixed distance d from m, then they make up to lines the are distance d from m, on on either side of m. If a and b, on m, are suppose...
Geometry: Mathematical Modelling, minor axes, xy plane
minor axes, xy plane, roof structure: Hi Anamjit, In 3-D, we have the x-, y-, and z-axes, the latter of which is conventionally used for height. Another important factor is when looking down on your building, what shape is it? If it is rectangular, then z=(-1/36)y²+36 would suffice. If you...
Geometry: Quadrilateral's Area from Side Lengths, quadrilateral, shubham
quadrilateral, shubham, diagonals: Hi Shubham, To my knowledge, you need insight on the shape of the quadrilateral. If you know a little bit more, the area can be solved for. If you know the length of a diagonal, you can subdivide the quadrilateral into two triangles and calculate their...
Geometry: Area - Regular Triangular Prism, triangular prism, right triangles
triangular prism, right triangles, lateral area: Hi Will! The lateral area would be equal to the base perimeter multiplied by the height of the prism. That means finding the length of each side of the the triangle, multiply that by three, and then by the height. As for the total surface area, it s...
Geometry: Area of Triangle Using Semiperimetre, finding the area of a triangle, area of triangle
finding the area of a triangle, area of triangle, area of a triangle: Hi Jillian! The subject line doens t match the question, and that has me confused. I m nearly certain this problem depends on the shape of the triangle. There is a formula for finding the area of a triangle from the length of its three sides (Hero s formula),...
Geometry: Areas of Regular Triangles, square root, radical
square root, radical: Hi Andrew! Multiplying square roots is really quite simple. When multiplying roots, multiply the stuff outside by the stuff outside, and the stuff inside by the stuff inside. For example: (2√5)(8√2)=(2)(8)(√5)(√2)=16√10...
Geometry: algebra, numerator and denominator, half hour
numerator and denominator, half hour, top and bottom: We start with 64 people. Now 1/8 of the people is 8 people, so 3/8 of the peopleis 3*8 = 24. Since 3/8 of the people left, we have 64 - 24 = 40 people left. It then states 1/5 of the people leave, so 1/5 f 40 is 8, so 8 people leave. We have 40 - 8 =...
Geometry: algebra, confidence interval, red 19
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...