at a grocery store , one pound of grapes cost $2.25 . in the following expressions, p presents any number of pounds of grapes. what expression represent the cost , in dollars, of pm pounds of grapes?

2x - 20 = 32 20 - 3x = 8 6x - 8 = 16 -13 - 3x = -10

Aquantity with an initial value of 3900 decays exponentially at a rate of 35% every hour. what is the value of the quantity after 0.5 days, to the nearest hundredth?

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) = .