(08.02)A pair of equations is shown below. x + y = 5
y = one halfx + 2

If the two equations are graphed, at what point do the lines representing the two equations intersect?

(2, 5)
(5, 2)
(2, 3)
(3, 2)

Draw a scaled copy of the circle using a scale factor of 2

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) = .

Whats four fifths to the first power