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

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Me solve this problem, and someone clearly explain to me how to solve it.1.) use the value of the discriminant to determine if the given trinomials has 2 real solutions, 1 real solution, or no real solutions.a.  x2  − 4x  − 7 = 0b. 4r2  + 11r  − 3 = 0c. 3m2  + 7 = 0d.  t2  + 2t  + 1 = 0

Simplify (2^5/3^2)^4 a. 2^20/3^8 b. 2^9/3^8 c. 8^5/12^2 d. 2/3^2