Find an explicit formula for the geometric sequence 3, 15, 75, 375, Note: the first term should be a(1).
a(n)

Two variables, x and y, vary inversely, and x=12 when y=4. what is the value of y when x=3?

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) = .

Solve the triangle. a = 21°, c = 105°, c = 5