The cables of a suspension bridge are in the shape of a parabola. The pillars supporting the cable are 600ft. apart and 90.ft above the road. The lowest height of the cable is 10 ft above the road. What is the height of the cable from the road at a point 150 feet from the center?

Step-by-step explanation:

Equation of The Parabola

The situation presented in the question requires the modeling of a cable of suspension as the equation of a parabola. We can find the exact parameters of the equation by using the dimensions provided in the problem.

Let's place the pillars at each side of the line x=0, where the cable reaches its minimum height. The point (0,10) belongs to the curve. Each pillar is located at x=300 ft and x=-300 ft and the height of the cable is 90 ft. It means we have two more points (300,90) and (-300,90). Now we have enough data, we'll use the general formula for a parabola

We only need to find the values of a, b, and c. Let's use the point (0,10)

Solving for c

The equation is now

Using (300,90)

Rearranging

Using (-300,90)

Rearranging

Subtracting the last two equations

Now we can find the value of a by solving

The model is now complete:

Now we find the height at x=150 ft

astronomers is your final answer! : )