The Library of Congress in Washington D. C. is considered the largest library in the world. They often receive boxes of books of books to be added to their collection. Since books can be quite heavy, they aren't shipped in big boxes. If, on average, each box contains about 8 books, how many books are received by the library in 6 boxes, 10 boxes, or n boxes? a. Use a table, a graph, and an equation to model this situation.

b. Identify the domain of the function

Do 12/14 and 8/10 have the same value? explain your answer.

Amanager recorded the number of bicycles sold by his company each quarter. his projected sales after t years is given by the expression below. which of the following statements best describes the expression? a. the initial sales of 575 bicycles increases at the rate of 4% over 4 quarters. b. the initial sales of 575 bicycles increases at the rate of 18% over 4 years. c. the initial sales of 575 bicycles increases at the rate of 4% over t quarters. d. the initial sales of 575 bicycles increases at the rate of 18% over t years.

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) = .