Plane Separation : Convex Triangle

If A,B,C are noncollinear in a metric geometry prove that triangle ABC is convex.

Geometry : Distance Function

Prove or disprove: If d0 and d1 are distance functions on S, s is > or = to 0 and t > 0 then sd0 +td1 is also a distance function on S.

Taxicab Distance and Triangle Inequality

Prove or disprove that the Taxicab distance dt satisfies the triangle inequality.

Geometry -- Rectangle

Q: If you have a string of Christmas lights that is 100 feet long, and, you want to hang it in the form of a rectangle that its length is twice its width or more; what is the range of the width? [Hint: This means that we need the lowest and highest values that the width can be.]

Straight Line and slope

a) Explain what is the y-intercept and which letter represents it in the equation y = mx +b. b) If a and b are positive numbers, what is all the information we can deduce about the relationship between the lines: L1: y = - ax + b and L2: y = (1/a)x + b?

Sine Rule in Triangles

Q: I know the length of two sides of a triangle. I know the degree of the hypotenuse. How do I figure out the length of the base. Example: The length of two sides is 144 inches. The angle is 22.5%. How long is the base?

Rotating Hyperbola : Is the Function an Hyperbola?

Is the function c(x)=(x^2+4)/x an hyperbola ? How would you rotate it 45 degrees in an anti clockwise direction ?

Simple Geometry : Line Segments and Constructing a Golden Triangle

Given a line segment of length 1 inch, how do I construct a line segment of squareroot(6), squareroot(7), squareroot(8), etc. Also, given a wire of total length 4236 feet, how do I construct a golden triangle from the wire?

Geometry Transformations Questions

1) A double reflection over two intersecting lines is the same as a single_____. 2)A double reflection over two parallel lines is the same as a single ______. Given the ordered pair (-3,5), give the coordinates of its image after each of the following tranformations: 1) A reflection over the line y=x _______ 2) A ref ...continues

Equation of a Frustum-Shaped Plate

What is/are the equation/s required to calculate dimensions and construction of a frustum shaped plate in its flat form before rolling into cone shape?