Find the distance between (3,12) and (-5,-3)

In the diagram below what is the approximate length of the minor arc ab

What is the expression in factored form? -20x^2 - 12x a. 4x(5x+3) b. -4x(5x-3) c. -4(5x+3) d. -4x(5x+3)

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) = .