An isosceles triangle has two sides of 18 centimeters. it’s height is 14 centimeters. what is the length of the base of the triangle?

Alake near the arctic circle is covered by a sheet of ice during the cold winter months. when spring arrives, the ice starts to melt. s(t) models the ice sheet's thickness (in meters) as a function of time tt (in weeks). s(t)=-0.25t+4

Sanya noticed that the temperature was falling at a steady rate of 1.4 degrees every hour from the time that she first checked her outdoor thermometer. by 6 a. m., the temperature had fallen 21 degrees. which expression can you use to find how many hours earlier she had first checked the thermometer?

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) = .