The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and 128 m high. The parabola y equals 0.00035 x squared gives a good fit to the shape of the cables, where StartAbsoluteValue x EndAbsoluteValue less than or equals 605, and x and y are measured in meters. Approximate the length of the cables that stretch between the tops of the two towers.

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

Compute the first order derivative of y as follows:

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

Now, let

Plug in the solved integrals in Arc Length and solve as follows:

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

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step-by-step explanation: