Greyson is playing a game. If he picks a red marble he earns 3 points. If he picks a blue marble, he loses 4 points. How many points does Greyson have at the end of 6 turns if he picks : red, red, blue, blue, blue, red?

Question 5 spring semester final exam math evaluate

What is the distance between point a and b

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) = .