A rectangular swimming pool with dimensions 12 meters by 18 meters is surrounded by a pavement of uniform width x meters. Find the area of the pavement, A, as a function of x.

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) = .

Solve the following pair of equations for x and y: ax/b_ by /a= a +b; ax - by = 2ab

What is the slope of (0,32) and (100,212)