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Highway Design In order to build a highway, it is necessary to fill a section of a valley where the grades (slopes) of the sides are 9% and 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.
(a) Find the coordinates of A and B.
(b) Find a quadratic function
(c) Construct a table giving the depths d of the fill for
(d) What will be the lowest point on the completed highway? Will it be directly over the point where the two hillsides come together?
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Chapter 3 Solutions
Calculus
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