A cabin in the shape of a square pyramid has a slant height of 12 feet and a base edge length of 14 feet. Paint for the cabin costs $1.25 per square foot. How much does it cost to paint the lateral faces of the cabin?

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) = .

Which value of y will make the inequality y< -1 false?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.