In order to build a highway, it is necessary to fill a section of a valley where

Question

In order to build a highway, it is necessary to fill a section of a valley where the grades (slopes) of the sides are p% and 9%, where ?-9 and q = 6 (see figure). The top of the filled region will have the shape of a parabolic arc that is tangent to the two slopes at the points A and B. The horizontal distances from A to the y-axis and from B to the y-axis are both 500 feet. 500 ft 500 ft- Highway Nat drewn to seale (a) Find the coordinates of A (x, y) = ( |-500.45 | X Find the coordinates of B (x, y) 500.30 (b) Find a quadratic function y = ax2 + bx + c for -500 x 500 that describes the top of the filled region. (c) Construct a table giving the depths d of the fill for x =-500, -400,-300,-200,-100, 0, 100, 200, 300, 400, and 500" (Round your answers to two decimal places.) X1-500 -400 -300 -200 -100 0 x 100 200 300 400 500

Explanation / Answer

(a) slope of the side where A is "p" = 9

slope = tan =y/x=9

we know x= 500.45

so y=9*500.45=4504.05

A (x,y)=(500.45,4504.05)

for x= 500.3

B(x,y)=(500.3,4502.7)

(b) more information will be needed to solve afterward

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