Tammy, Eric, and Dan sent a total of 109 text messages over their cell phones during the weekend. Eric sent 5 more messages than Tammy. Dan sent 4 times as many messages as Eric. How many messages did they each send?

Question part points submissions used suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. of these 100 tickets, only 12 are winning tickets. the generalized pigeonhole principle guarantees that there must be a streak of at least l losing tickets in a row. find l.

If f(x) = 2x - 6 and g(x) = 3x + 9, find (f - g)(x). a. (f-g)(x) = x + 15 o o b. (f- g)(x) = -x - 15 o c. (f- g)(x) = 5x + 3 o d. (f- g)(x) = -x+3 submit

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) = .