On their next training run, Pepe averaged a speed of 23 2 3 of a mile in 5 minutes, while Paula averaged 14 1 4 of a mile in 2 minutes. If Pepe and Paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?

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) = .

The value of cos 30° is the same as which of the following?

Which pair of numbers is relatively prime? a. 105 and 128 b. 130 and 273 c. 205 and 350 d. 273 and 333