What is the answer to 243 x 1/3?

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) = .

Janet is rolling a number cube with the numbers one through six she record the numbers after each row if she rolls of keep 48 times how many times should she expect to roll a 4

Find the distance from the theater to the library. leave your answer in simplest radical form if necessary. 12 √12 74 √74