An annulus(no giggling!) is a region in the plane bounded by two concentric circles. Suppose Sis an annulus with an inner circle radius of rand an outer circle of radius R. The radii are changing so that ris increasing at a constant rate of 7cm/minand Ris decreasing ata constant rate of1 cm/min. At 9:00 am it is known that ris 30 cm and Ris 80 cm.(a) Write a formula for P, the total perimeter of region S.(b) How fast is P changing at 9:00 am