Hey I got a project assigned for my Calc 3 class, and I was wondering what to do with the following:(adsbygoogle = window.adsbygoogle || []).push({});

A hanging cable has the shape

y = 1/c cosh(cx + b) + a

for some constants a,b,c with c>0. Suppose the ends are at P(0,10) and P2(30,5).

If the length of the cable is known to be 100 units then determine a,b,c and then plot the graph.

I know that dy/dx = sinh(cx + b), so the arc length formula would be:

100 = int(sqrt(1 + sinh(cx + b)^2)) from 0 to 30

but I'm having issues solving the equations in terms of a,b and c. I tried, and got an equation with lots of cosh's that myself and Maple could not solve or reduce.

Any advice?

Thanks alot!

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# Arc Length Problem

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