The profit of a cell-phone manufacturer is found by the function y = -2x^2 + 108x + 75 , where x is the cost of the cell phone. At what price should the manufacturer sell the phone to maximize its profits? What will the maximum profit be?

To determine the number of deer in a forest a forest ranger tags 280 and releases them back

Find the constant of variation for the relation and use it to write an equation for the statement. then solve the equation.

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) = .