1. ## calc hw problem

( a ) Aa telephone wire hangs between two poles at x = - b and x = b. It takes the shape of a catenary with equation y = c + 7a cosh ( x / 7a ). Find the length of the wire.

( b ) Suppose two telephone poles are 50 ft apart and the length of the wire between the poles is 51 ft. If the lowest point of the wire must be 22 ft above the ground, how high up on each pole should the wire be attached? Round your answer to two decimal places.

I dunno how to do this.

2. Originally Posted by jamessmith
( a ) Aa telephone wire hangs between two poles at x = - b and x = b. It takes the shape of a catenary with equation y = c + 7a cosh ( x / 7a ). Find the length of the wire.

( b ) Suppose two telephone poles are 50 ft apart Mr F says: Taking the turning to be at x = 0 this lets you calculate the value of b.

and the length of the wire between the poles is 51 ft.

If the lowest point of the wire must be 22 ft above the ground, Mr F says: Therefore the y-coordinate of the turning point is y = 22.

how high up on each pole should the wire be attached? Round your answer to two decimal places.

I dunno how to do this.
(a) Are you familiar with the arclength formula? Do you know how to differentiate cosh? Do you know how to substitute the derivative intot the formula and simply. Please post all the work you can do and state where you get stuck.

(b) The turning point of $\displaystyle y = c + 7a \cosh \left(\frac{x}{7a}\right)$ is at (0, 22). Use this fact to get an equation with a and c in it. Make a the subject and substitute into $\displaystyle y = c + 7a \cosh \left(\frac{x}{7a}\right)$.

Now substitute this expression for y (and your value of b) into $\displaystyle 51 = \int_{-b}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$ and solve for c. (You will need to use technology to do this).

Substitute your value for b and c (and hence a) into $\displaystyle y = c + 7a \cosh \left(\frac{b}{7a}\right)$ and solve for y. If you need more help please post everything you've done and state exactly where you're stuck.