# Need help with Calculus 2 Project.

Looking for help on a certain project. I have posted the project in pdf format

http://home.ripway.com/2005-5/317800/proj1sum05.pdf

I have already solved the first problem (a), but problem b (finding the angle) doesn't make intuitive sense to me.If you all could be so kind, all ideas are greatly appreciated. Maybe if I understood the question better that would also help.

Well you are given the equation of the curve created by the cable. Thus you can find the tangent line to to curve at $x=\pm b$. Thus you can create a triangle using the tangent line as the hypotenuse, a pole as a vertical leg, and the horizontal line tangent to the minimum of the curve. Try drawing a picture.

number one....

man i don't even think I did number one right now....

Maybe you'll see it better if its translated.

A curve with equation y = 2acosh(x/a) intersects the x axis at x = -b, b. Find the arclength of the curve. All you need to do is integrate arclength for x = -50 to 50.

its the letter a....

I don't mind integrating it, but I just can't figure out what a is.....

Pyrrhus
Homework Helper
Have you read the problem? it states a is a positive constant...

Considering real valued functions, this means

$$\{ a \epsilon \Re | a > 0 \}$$

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since the distance of the poles from another is 100m, then this means there are poles at $x=\pm 50$. From then you can solve for $a$ since you know that $S = 20$ and you know what $b$ is.

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I end up with (a+20 = a cosh(50/a), I know that this in turn is the same as
[a + 20 = a (e^(50/a) + e^-50/a) all over 2). There are too many a's I still don't understand how to simplify, thank you for your help though.