Given , aa2), , ), , c2), and , d2), find a general formula in terms of a1, a2, , , c1, c2, d1, and
d2 that will let us determine whether ab and cd are perpendicular.

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) = .

Find the length of the normal and the angle it makes with the positive x-axis. (see pictured below)

The table below shows the number of free throw shots attempted and the number of shots made for the five starting players on the basketball team during practice. each player's goal is to make 80% of her shots.