Ashipping carton for a rolled-up poster has the shape of a triangular prism. each end of the carton is a triangle with a base 6 inches long and a height of 5 inches. the length of the carton is 32 inches. what is the volume of the carton?
a. 43 in3 b. 86 in3 c. 240 in3 d. 480 in3

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) = .