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Quadratic Function : Word Problem

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Here is the word problem:

The cables supporting a straight-line suspension bridge are nearly parabolic in shape. Suppose that a suspension bridge is being designed with concrete supports 160 ft apart and with verticle cables 30 ft above road level at the midpoint of the bridge and 80 ft above the road level at a point 50 feet from the midpoint for the bridge. How long are the longest verticle cables?

I am unsure how to:
1) Find the distances between the cables (assuming they are the same)
2) Find the quadratic function that represents the curve cable.

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Solution Preview

The question is asking you the actual length of the cable which is given as:
l= integration (-x0 to +x0) [ sqrt(1 + (dy/dx)^2)dx]
where -x0 and +x0 are the end points of the cable = 160/2 = 80 ft.

If we consider the vertical ...

Solution Summary

A quadratic equation is gleaned from a word problem and integrated. The solution is concise.