Charity is four times as old as her daughter. She is also six years younger than her husband. The sum of their ages ten years to come will be 117 years. How old is Charity today? ​

The random variable x represents the number of phone calls an author receives in a day, and it has a poisson distribution with a mean of 8.7 calls. what are the possible values of x

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) = .

Aconstruction worker has rope 9 m long he needs to cut it in pieces that are each 3 /5 m long how many such pieces can he cut without having any rope leftover?