Question

A suspension bridge has a cable shaped like a parabola. the bridge is supported by two towers. the towers are 132 meters apart. if the cable is 4 meters high when it is 44 meters from the center of the bridge, what is the height of one of the towers?

Answer 1

To find the height of one of the towers of the suspension bridge, use the equation of a parabola. Substitute the given values into the equation to find the values of a and c. Substitute the distance between the two towers into the equation to find the height of one of the towers.

Step-by-step explanation:

To find the height of one of the towers of the suspension bridge, we need to use the equation of a parabola. The equation of a parabola can be written in the form y = ax^2 + bx + c, where (x, y) are the coordinates of a point on the parabola, and a, b, and c are constants. In this case, the vertex of the parabola is the highest point on the cable, and the equation of the parabola can be written as y = ax^2 + c, where a and c are constants. Since we know the height of the cable (4 meters) when it is 44 meters from the center of the bridge, we can substitute these values into the equation to find the values of a and c.

Using the given values, we can write the equation as 4 = a(44^2) + c. Solving this equation will give us the values of a and c. Once we have the values of a and c, we can substitute the distance between the two towers (132 meters) into the equation to find the height of one of the towers.

Let's solve the equation:

1. Substitute the values of y, x, and c into the equation: 4 = a(44^2) + c
2. Substitute the value of c into the equation: 4 = a(44^2) + c
3. Solve the equation for a: a = (-c + 4) / (44^2)
4. Substitute the value of a into the equation: y = a*x^2 + c
5. Substitute the value of x into the equation: y = a*(132/2)^2 + c
6. Calculate the value of y
7. The height of one of the towers is the calculated value of y