Concept explainers
(a)
To write: an equation of the parabola with its vertex at the origin that models the road surface.
(a)
Answer to Problem 64E
The equation is
Explanation of Solution
Given information:
Roads are often designed with parabolic surface to allow rain to drain off. A particular road is 32 feet wide and 0.4 foot higher in the center than it is on the sides.
Calculation:
Find an equation that models the road surface.
The road is in the shape of a parabola with axis vertical.
We know that the standard equation of a parabola with axis vertical is given as
Now, since the vertex is given to be at
Thus, the equation reduces to
Also, we know that the points
Substituting the value of
Thus, substituting the value of
(b)
To find: the distance the center of the road.
(b)
Answer to Problem 64E
The road is 0.1 foot lower than in the middle at a distance of 8 feet from the center.
Explanation of Solution
Given information:
The road surface 0.1 feet lower than the center.
Calculation:
Find the distance from the center of the road where the road surface is 0.1 foot lower than in the middle.
Thus, we need to find the value of
Substituting the value of
Or
Thus, the road is 0.1 foot lower than in the middle at a distance of 8 feet from the center.
Chapter 10 Solutions
EBK PRECALCULUS W/LIMITS
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