About 20% of the time you sleep is spent in rapid eye movement (rem) sleep, which is associated
with dreaming. if an adult sleeps 7 to 8 hours, how much time is spent in rem sleep?

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) = .

Which of these tools or constructions is used to inscribe a hexagon inside a circle?

The base of a rectangular pyramid is 13 inches long and 12 inches wide. the height of the pyramid is 8 inches. what is the volume of the pyramid