Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. if erica made $42.80 on monday, $64.20 on tuesday and $74.90 on wednesday, how many subscriptions did she sell in the three days? a. 32 b. 33 c. 34 d. 35

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) = .