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?
Do not round your answer until your end result. when finding thelength of the bridge round to the nearest tenth of a foot
To find the length of the bridge, we first need to find the x-intercepts of the parabola. The x-intercepts occur when h=0, so we can set the equation h=40-0.01x^2 to 0 and solve for x:
0 = 40 - 0.01x^2
0.01x^2 = 40
x^2 = 4000
x = ±√4000
x = ± 63.25
Since the bridge starts and ends at the x-intercepts, the length of the bridge is 2*63.25 = 126.5 feet
Therefore, the length of the bridge is 126.5 feet.