Let ABCDE be a regular pentagon, assume that each side has length 1. Let F be the intersection point of AD and EC. Using no trigonometry, show that |AF|/|FD| = (1+v 5)/2 %3D

Q: Determine the acute angle, in degree measurement, between the planes 2x+2y-1z = -3 and 5x+3y + 2z =…

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Q: For what values of h, b is in Span {v1,V2, V3} where 5 -4|, v3: %= 4 ,V2= 7

A: First we transfer this problem into a matrix then apply row reduction.

Q: Find the area of a triangle formed by the points (8, – 5), – 7) and (5, 1) by using Herones formula…

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Q: Find the area of the triangle with vertices: Q(-5,-1,-1), R(-6,-4,1), S(-9,-3,2).

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Q: AAOB is placed on a coordinate system so that A = (6, 12), B = (21, 3), and O=(0, 0). A segment, CD,…

A: Step 1:

Q: The points P: (-2,0,0), Q: (0,1,1) and R: (1,2,1) are givena. determine the angle in the triangle…

A: Solution  a) To determine the angle at corner Q in triangle ΔPQR, we can use the dot product…

Q: Use v=<3/5,4/5>,w=<-4/5, 3/5>, to verify the Parallelogram Law

A: The given vectors are

Q: The midpoint of AB is at (5, 0). If A = (4, 3), find B. B is:(

A: Consider the given information.

Q: in standard position, and the unit circle. The value of b can be written in t are whole numbers. ues…

A: we will find the required.

Q: Let a = ci + j and b = 16i + 12j. Find c π so that the angle between a and b is 6

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Q: Two points 0(0, 0) and A(3, √√3) with another point P form equilateral triangle. Find the…

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Q: Find an expression for the distance between (a, b) and (a, c) if b > c.

A: we have to find an expression for the distance between (a, b) and (a, c) if b>c.

Q: 8 units away from

A: Given that: Coordinates of A(0,0) and B(12,5)C is 8 units away from AB.

Q: Find a positive angle less than 360° or 2π that is coterminal with the given angle -150°.

A: Here the given angle is -150°. θ=-150°=-5π6=-5π6+2π=-5π+12π6=7π6

Q: -4x 2.) y = required:a) find the value of y if x = 1

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Q: Find the image of the circle Iz| = 3 under the stereographic projection in the sphere.

A: We let G be a sphere in Euclidean three space. We want to obtain a picture of the sphere on a flat…

Q: Find the area of the triangle with vertices: Q(0,2,-2), R(-1,3,-5), S(-3,-1,-8).

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Q: D W.

A: Two straight line are intersected by a point D.Two straight line is given.