Find the 13th term of an arithmetic sequence where the common difference is six and starts with a1=2

Alake near the arctic circle is covered by a 222-meter-thick sheet of ice during the cold winter months. when spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. after 333 weeks, the sheet is only 1.251.251, point, 25 meters thick. let s(t)s(t)s, left parenthesis, t, right parenthesis denote the ice sheet's thickness sss (measured in meters) as a function of time ttt (measured in weeks).

Which situation can be modeled by the inequality 5 + 10w ≥ 45? a. you start with $5 and save $10 a week until you have at least $45. b.you start with 5 baseball cards and purchase 10 cards every week until you have at most 45 cards. c.you start with 5 water bottles and purchases cases of 10 water bottles each until you have a total of 45 water bottles. d.you spend $5 plus $10 per week until you have less than $45.

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) = .