If a diver of mass stands at the end of a diving board with length and linear density , then the board takes on the shape of a curve , where Here, and are positive constants that depend on the material of the board, and is the acceleration due to gravity.

(a) Find an expression for the shape of the curve (in other words, determine the equation for .

(b) Using , find the distance below the horizontal at the end of the board.

Distance below horizontal at the end =

You can earn partial credit on this problem.