Hugh made a recipe that yields 5 1/4 cups if each serving is 1/2 cup, which expression will high determine the number of servings his recipe will yield

Given a: b and b: c, find a: b: c. write the ratio in simplest form. a: b=6: 10 and b: c=21: 33

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) = .

Assume that y varies inversely with x. if y=1.6 when x=0.5 find x when y=3.2