A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hundred and twenty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe