(2 points) A 100 ft wire is attached at its ends to the tops of two 40 ft poles that are positioned 95 ft apart. The equation that describes the cable is of the form $a cosh(frac{x}{a}) + c$. (a) Find $a=$ and $c=$ (b) How high above the ground is the middle of the wire?
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(a) The figure shows a telephone wire hanging between two poles at $x=-b$ and $x=b .$ It takes the shape of a catenary with equation $y=c+a \cosh (x / a) .$ Find the length of the wire. (b) Suppose two telephone poles are 50 $\mathrm{ft}$ apart and the length of the wire between the poles is 51 $\mathrm{ft}$ . If the lowest point of the wire must be 20 $\mathrm{ft}$ above the ground, how high up on each pole should the wire be attached?
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