Juan is walking up a hill at 130 3/4 feet above sea level when he kicks a pebble. If the pebble falls to the base of the hill, which is 18.5 feet below sea level, what is the vertical distance that the pebble fell?

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.

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) = .

How many sides does a regular polygon have if each exterior angle measure is 45 degrees explain your answer, i really don't understand this.