Seven of the 10 children at art camp make an average of 8 paintings. the remaining children make an average of 12 paintings. what is the average number of paintings made by children at the art camp? enter your answer in the box.

Which of the following would be a good name for the function that takes the weight of a box and returns the energy needed to lift it?

Is the power produced directly proportional to the wind speed, give reasons for your answer?

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) = .