When full, one of the pools at Sapphire Island will hold 43,000 gallons. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute. Write and solve an equation that can be used to find h, the number of hours it will take to fill the pool from its current level.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .