The radius of a cylindrical gift box is (2x+3) in. the height of the gift box is three times the radius. what is the surface area of the cylinder? write your answer as a polynomial form.

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) = .

Scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. the professor teaching the class declares that a score of 70 or higher is required for a grade of at least “c.” using the 68-95-99.7 rule, what percentage of students failed to earn a grade of at least “c”?

Azul has 4 green picks and no orange picks.you add orange picks so that there are 2 orange picks for every 1 green pick.how many picks are there now.