Element X decays radioactively with a half life of 7 minutes. If there are 500 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 21 grams?

Consider the line y = -3/-2 x +6. find the equation of the line that is perpendicular to this line and passes through the point (-9,-3). find the equation of the line that is parallel to this line and passes through the point (-9,-3).

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

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) = .