Aball is dropped from 81 feet. it hits the ground and bounces up 1/3 as high as it fell. this is true for each successive bounce. what height does the ball reach on its 4th bounce?

Describe what moves you could use to create the transformation of the original image shown at right

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) = .

For g(x) = 5x - 3 and h(x) = [tex]\sqrt{x}[/tex], find (g · h)(4)