An inextensible cable of length L > a and uniform mass density σ per unit length is suspended between the points (x, z) = (0, 0) and (x, z) = (a, 0) with z in the (upward) vertical direction, and gravity acting downwards. (a) What is the total gravitational potential energy of the cable? (b) Assume that the curve formed by the cable is a function of the horizontal distance x, i.e. z = = f(x). Derive the equation satisfied by f(x). (c) Find the resulting f(x) satisfying the boundary conditions and the length constraint.