A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow
rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = -1/200(x – 16)(x + 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet?
2 answers:
Remark.
The problem is a bit indistinct. Where exactly are the two edges of the road? I'm going to say that they are the x intercepts, but that may not be true. Certainly it does not have to be true at all.
Graph.
A graph has been made for you. The maximum is marked for you. It is an approximation The actual height can be more accurately found.
Height
y = (-1/200)(x - 16)(x + 16)
y = (-1/200)*(x^2 - 256)
The maximum height for this graph only is when x = 0.Other graphs require completing the square.
y = (-1/200) * (-256)
y = 1.28 exactly. I thought the graph might be rounding the answer. It is not.
You might be interested in
Answer:
Step-by-step explanation:
<u><em>The complete question is</em></u>
A cone and a triangular pyramid have a height of 9.3 m and their cross-sectional areas are equal at every level parallel to their respective bases. The radius of the base of the cone is 3 in and the other leg (not x) of the triangle base of the triangular pyramid is 3.3 in
What is the height, x, of the triangle base of the pyramid? Round to the nearest tenth
The picture of the question in the attached figure
we know that
If their cross-sectional areas are equal at every level parallel to their respective bases and the height is the same, then their volumes are equal
Equate the volume of the cone and the volume of the triangular pyramid
simplify
we have
substitute the given values
solve for x
