The cable between the two towers of a power line hangs in the shape of the curve
where T is the tension in the cable at its lowest point and w is the weight of the cable per unit length. This curve is called a catenary.
(a) Suppose the cable stretches between the points x = -T /w and x = T /w. Find an expression for the "sag" in the cable. (That is, find the difference between the height of the cable at the highest and lowest points.)
(b) Show that the shape of the cable satisfies the equation
