Question

The cables of a suspension bridge are in the shape of a parabola. If the towers supporting the cable are 500 feet apart and 100 feet high, and the cables touch the road surface midway between the towers, what is the height of the cable at a point 125 feet from the center of the bridge?

A) The cable is 25 feet from the road surface.
B) The cable is 100 feet from the road surface.
C) The cable is 50 feet from the road surface.
D) The cable is 75 feet from the road surface

Answer 1

The height of the cable at a point 125 feet from the center of the bridge is 25 feet from the road surface.

Step-by-step explanation:

To find the height of the suspension cable at a point 125 feet from the center of the bridge, we can use the fact that the cables are in the shape of a parabola. Since the cables touch the road surface midway between the towers, the lowest point of the parabola is the midpoint between the towers.

Since the towers are 500 feet apart and 100 feet high, the lowest point of the cable is 250 feet from each tower horizontally and 100 feet down vertically.

Using this information, we can set up a parabolic equation using the vertex form y = a(x-h)^2 + k, where (h,k) is the vertex. Plugging in the values h = 250, k = -100, and x = 125, we can solve for y. The height of the cable at a point 125 feet from the center of the bridge is 25 feet from the road surface.