What is the sum of the geometric series in which a1 = −5, r = 3, and an = −405? a hint on how to solve is attached! r ≠ 1, where a1 is the first term and r is the common ratio.

In the triangles, bc =de and ac fe.if the mzc is greater than the mze, then ab isdfelth

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) = .

Present age of man is 45 years, 5 years back his age was 4 times age of his son what is present age of his son?