Sandy has four boxes filled with pink ribbons and yellow ribbons the table shows the number of pink and yellow ribbons in each box the fifth box has pink and yellow ribbons in the same proportion as sandy’s first floor box which tables could represent box no. 5

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) = .

Solve the triangle. a = 21°, c = 105°, c = 5

Can you me find the slope! (30 points)