Constructing a box. from a rectangular piece of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by cutting out identical squares of area x^2 from each corner and turning up the sides.

(a) show that the volume of the box is given by the function v(x)=x(20-2x)(30-2x).

(b) find all positive values of x such that v(x)> 0.