The volume of the empty space inside the cube is 513.5 cubic inches. If one ball has a volume of 8.2 cubic inches, what is the
total volume of the cube?

1. what is the measure of ∠abc? what is the measure of ∠abd?

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) = .

Interpret the following expression (5y^2-7)^3/(2y)^2