Alicia is programming computerized robotic arms to cut burlap for the 4 of July placemats.

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) = .

Ellen makes and sells bookmarks. she graphs the number of bookmarks sold compared to the total money earned. why is the rate of change for the function graphed to the left?

What would be the reasons for lines 3 and 4? a. addition property; subtraction property b. addition property; solve c. substitution property; subtraction property d. substitution property; prove