Question

7) The two towers on a suspension bridge will be 50 feet high and 300 feet apart. The two supporting cables are connected at the top of the towers and hang in a curve that is a parabola. At the center of the bridge, the parabola will be 5 feet above the road. Write an equation for the parabola, then determine the height of the main cable 100 feet from the center

Answer 1

Answer:

f(x) = x^2/500 + 5

f(100) = 100^2/500+5 = 25

Cable is 25 feet above road 100 feet from center of bridge.

Step-by-step explanation:

Assume towers are 50 feet above the road and the road is flat and level.

Tower bases are (-150,0) and (150,0).

Tower tops are (-150,50) and (150,50).

Center of bridge at roadway is (0,0).

Minimum height of parabola is (0,5).

f(x) = ax^2 + bx + c

The parabola is symmetrical about the y axis so b = 0

Constant term c = 5.

f(0)=5

f(150)=f(-150)=50.

a × 150^2 + 5 = 50

a = 45/(150^2) = 5/(50^2) = 1/500

f(x) = x^2/500 + 5

f(150) = 150^2/500+5 = 50✔

f(100) = 100^2/500+5 = 25