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 end at the x-intercepts of the parabola. What is the length of this bridge?
To find the length of the bridge, we first need to find the x-intercepts of the parabola.
Setting h = 0 in the equation h = 40 - 0.01x^2:
0 = 40 - 0.01x^2
0.01x^2 = 40
x^2 = 40/0.01
x^2 = 4000
x = ±√4000
x = ± 63.25
So, the x-intercepts occur at x = -63.25 and x = 63.25.
The length of the bridge is the distance between these two x-intercepts, which is 63.25 + 63.25 = 126.5 feet.
Therefore, the length of this bridge is 126.5 feet.