A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01x^2, 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?
To find the length of the bridge, we need to find the distance between the x-intercepts of the parabola.
First, let's find the x-intercepts by setting h to zero:
0 = 40 - 0.01x^2
0.01x^2 = 40
x^2 = 4000
x = ±√4000
x = ± 63.25
The distance between the x-intercepts is:
2 * 63.25 = 126.5 feet
Therefore, the length of the bridge is 126.5 feet.