Find the coordinates of the center and the measure of the diameter for a circle whose equation is (x + 8)2 + (y - 4)2 = 81

3-12. write each answer with a reasonable number of figures. find the absolute uncertainty and percent relative uncertainty for each answer. (a) [12.41 (±0.09) + 4.16 (±0.01)] x 7.068 2 (±0.000 4) =? (b) [3.26 (±0.10) x 8.47 (±0.05)] - 0.18 (±0.06) =? (c) 6.843 (±0.008) x 104 + [2.09 (±0.04)- 1.63 (±0.01)] =?

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) = .

There are three bags: a (contains 2 white and 4 red balls), b (8 white, 4 red) and c (1 white 3 red). you select one ball at random from each bag, observe that exactly two are white, but forget which ball came from which bag. what is the probability that you selected a white ball from bag a?