5) You plan to build a playing field in the shape of a rectangle with a semicircular region at each end, so that races can be held around the...

5) You plan to build a playing field in the shape of a rectangle with a semicircular region ateach end, so that races can be held around the perimeter of the field. If you want the totalperimeter of the field to be 1000 m, what dimensions should your field have to maximizethe area of the rectangular portion of the field?13) A metal cube dissolves in acid such that an edge of the cube decreases by 0.43 mm per minute.How fast is the volume of the cube changing when the edge is 8.9 mm?15) A company knows that unit cost C and unit revenue R from the production and sale of x units arerelated by C =R2/176,000 + 9330. Find the rate of change of revenue per unit when the cost per unit ischanging by $12 and the revenue is $4000.