Apaper cone has an e-inch slant height and an r-inch base radius. in terms of the quantities e and r, write a formula for the lateral area of the cone. in other words, find the area of the circular sector obtained by cutting the cone from base to vertex and flattening it out.

If lmn=xyz, which congruences are true by cpctc? check all that apply

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) = .

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