Two parter part 2 use the foil method to solve 15-21 15: (k+5) (k-1) 16: (x-4) (x+8) 17: (q-3) (q-4) 18: (z-5) (z-9) 19: (t+2) (2t+1) 20: (5v-3) (2v+4) 21: (9-r) (2-3r)

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) = .

12 3 4 5 6 7 8 9 10time remaining01: 24: 54which graph represents this system? y=1/2x + 3 y= 3/2x -1

David leaves his house to go to school. he walks 200 meters west and 300 meters north. how far is david from his original starting point?