A company manufactures and sells book cases. The selling price $54.90 per book case. The total cost function is linear and cost amount is $50,000 for 2000 book cases and $32,120 for 800 book cases. 1. Write the equation for revenue
2. Write the equation for total cost
3. Find the break even point

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) = .