Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

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) = .

60 musicians applied for a job at a music school. 14 of the musicians play both guitar and drums. what is the probability that the applicant who gets the job plays drums or guitar?

Which set of lengths could represent the sides of a triangle? a. 3, 7, 10 b. 4, 5, 10 c. 6, 8, 14 d. 12, 6, 7