A bridge is sketched in the coordinate plane as a parabola represented by the equation h= 40-0.01x^2, where each refers to the height in feet of the bridge at location of x feet from the middle of the bridge. The bridge starts and ends at the 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 two x-intercepts of the parabola.
The x-intercepts occur when h=0, so we can set 40-0.01x^2=0 and solve for x:
0.01x^2 = 40
x^2 = 4000
x = ± 20√10
The length of the bridge is the distance between these two x-intercepts, which is:
length = 2 * |20√10 - (-20√10)|
length = 2 * 40√10
length = 80√10 feet
Therefore, the length of the bridge is 80√10 feet.