Question

the curve is described by the cable of the suspension bridge given by y = hx^2 / 2L^2 - h/L x + 2h, where x is the distance measured from one end of the bridge, h and L are constant. what is the length of the bridge?

Answer 1

This is a quadratic equation. So its a parabola. As much as i understood from your description x is the length. Since it says that its starts beying mesured at one of the ends, it means at x=0 y=2h. At some point x=? y=0 you would be at the half of the hanging bridg, this x=? for which y=0 is half of your bridg length. Its a 0 of a quadratic equation. Find it, and later multiply your result by 2, and you have the answer (since parabola is symetric curve respect to x)

Answer 2

thanx