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.
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?
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1 answer