In the diagram below, points a and b represent two lakes. how far apart are the lakes?

What is the equation in slope-intercept form of the linear function represented by the table? y -18 -1 -8 4 2 912 o y=-2x-6 o y=-2x+6 o y=2x-6 o y = 2x+6

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) = .

Find the value of x. give reasons to justify your solutions! c ∈ ae