A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01^2, where i refers to the height. in feet, of the bridge at a location of z 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?
Do not round your answer until your end result. When finding the length of the bridge round to the nearest tenth of a foot
To find the length of the bridge, we need to determine the distance between the x-intercepts of the parabola.
First, let's set the equation h = 40 - 0.01z^2 to zero to find the x-intercepts:
0 = 40 - 0.01z^2
0.01z^2 = 40
z^2 = 40/0.01
z^2 = 4000
z = ±√4000
z = ± 63.2
Therefore, the x-intercepts are at z = -63.2 and z = 63.2 feet from the middle of the bridge.
The length of the bridge is the distance between these two points:
Length = 2 * 63.2
Length = 126.4 feet
The length of the bridge is 126.4 feet.