Question

A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01x2, where h refers to the height, in feet, of the bridge at a location of x feet from the middle of the bridge. The bridge starts and ends at the x-intercepts of the parabola. What is the length of this bridge?

Answer 1

Answer:

The length of the bridge is 126.492 feet.

Step-by-step explanation:

Let $h(x) = 40-0.01\cdot x^{2}$, where $x$ is the position from the middle of the bridge, measured in feet, and $h(x)$ is the height of the bridge at a location of x feet, measured in feet. In this case, the length of the bridge is represented by the distance between the x-intercepts of the parabola, which we now find by factorization:

$40-0.01\cdot x^{2} = 0$ (Eq. 1)

$x^{2} = \frac{40}{0.01}$

$x =\pm \sqrt{\frac{40}{0.01} }$

$x = \pm 63.246\,ft$

Given that the parabola is symmetrical with respect to y-axis, then the length is two times the magnitude of the value found above, that is:

$l = 2\cdot (63.246\,ft)$

$l = 126.492\,ft$

The length of the bridge is 126.492 feet.