Is -32 an irrational number

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) = .

Whoever gets this right gets the ! the half life of a soul smelling substance is 4 years. if you have 8 oz of this strange substance, how much of it will you have after 20 years? show work.

What is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?