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 top of a second
Tower. The towers stand 60 inches apart. At a point between the towers and 18 inches along the road from the
Base of one tower, the cable is 1.44 inches above the roadway. Find the height of the towers.
A) 11 in.
B) 9 in.
C) 8.5 in.
D) 9.5 in.

Question

Quizplus · Accepted Answer

The height of the towers can be found by using the vertex form of a parabolic equation, $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Since the towers are 60 inches apart and the cable touches the roadway exactly between them, the vertex is at the midpoint, 30 inches from each tower, and at the roadway level, making $k = 0$. The point (18, 1.44) gives us a way to solve for $a$ because it is 18 inches from one tower and 1.44 inches above the roadway. Plugging these values into the equation gives $1.44 = a(18 - 30)^2$, which simplifies to $1.44 = a(12)^2$, or $1.44 = 144a$. Solving for $a$ gives $a = 0.01$. To find the height of the towers, we use the fact that the towers are at the ends of the parabola, 30 inches from the vertex on either side. Plugging this into the equation with $a = 0.01$ and $x = 30$ (since the towers are 30 inches from the midpoint), we get $y = 0.01(30)^2 = 0.01(900) = 9$. Therefore, the towers are 9 inches tall.

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