Kia is printing packets of information. there are 23 pages in a packet, and she needs enough copies for 52 people. each package of paper contains 200 sheets. she estimates she needs 5 packages of paper to print the packets. will she have enough paper? explain.

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) = .

What is the missing statement in step 4? ? rts ? ? vtu and ? rtu ? ? vts ? rts ? ? rvs and ? rtu ? ? stv ? vrs ? ? vru and ? usr ? ? usv ? vur ? ? vus and ? uvs ? ? sru

What fraction is equivalent to 0.46464646··· a. 46⁄999 b. 46⁄100 c. 46⁄99 d. 23⁄50