Which ratios in the list below are equivalent. Select all that apply. a
24 : 12
b
14 : 28
c
10 : 5
d
18 : 2
e
9 : 4.5

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) = .

Aswimming pool measures 22ft by 12ft and is 4ft deep. if the pool is being filled at 2.5 cubic ft per minute, how long will it take to fill the pool?

Can you divide 25 into 4 equal groups? explain why or why not.