Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section,cable runs from the top of one tower down to the roadway, just touching it there, and up again to the topof a second tower. The towers stand 40 inches apart. At a point between the towers and 12 inches along theroad from the base of one tower, the cable is 0.64 inches above the roadway. Find the height of the towers.
A)4 in.
B)4.5 in.
C)3.5 in.
D)6 in.

Question

Quizplus · Accepted Answer

The parabola is symmetric, so the vertex is at the midpoint between the towers, which is 20 inches from each tower. Using the point (12, 0.64) and the vertex form of a parabola, we can solve for the height of the towers. The equation is y = a(x - 20)^2. Substituting the point (12, 0.64) gives 0.64 = a(12 - 20)^2. Solving for a and using the vertex at (20, h) where h is the height of the towers, we find h = 4 inches.

Solve the Problem. -An Experimental Model for a Suspension Bridge Is Built in Is