A rectangular garden has length and width as given by the expressions below. Length: 4 − 7(3x + 4y) Width: 3x(−2y) Write a simplified expression for the perimeter of the rectangle.

Given a circle with measures of (c, d, and r) and a circle with measures of (c', d', and r'), what is d if c c' = 12 and d' = 0.50? a) 3 b) 6 c) 12 d) 24

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) = .

The area (a) of a circle with a radius of r is given by the formula and its diameter (d) is given by d=2r. arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.