What's the square root of 57?

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) = .

Samson is going shopping for sugar and butter to make three different kinds of cookies: lemon bars, peanut butter cookies, and sugar cookies. the recipe for lemon bars calls for 2 cups of flour, 2 cups of sugar, and 1 stick of butter. the peanut butter cookie recipe calls for 2 cups of flour, 4 cup of sugar and 2 stick of butter. the sugar cookie recipe calls for 1 cup of flour, 2 cups of sugar, and 2 sticks of butter. sampson has 13 cups of flour at home, and he buys 12 cups (6 pounds) of sugar and 10 sticks of butter. how many batches of each type of cookie can he make? samson can make batches of lemon bars, batches of peanut butter cookies, and batches of 09 cookies submit reset

Carly stated, “all pairs of rectangles are dilations.” which pair of rectangles would prove that carly’s statement is incorrect?