The english alphabet has 20 letters more than one-fourth the number of letters in the greek alphabet. the english alphabet has 26 letters. which of the following equations would you use to find the number of letters, g, in the greek alphabet?

Sal is tiling his entryway. the floor plan is drawn on a unit grid. each unit length represents 1 foot. tile costs $1.35 per square foot. how much will sal pay to tile his entryway? round your answer to the nearest cent.

In the geometric progression –3, 12, −48… what term is 3,072?

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) = .