Which of the following relations is a function? A. (5, 10), (-9, 3), (-1, 8), (-1,-6)
B. (10,5), (3, -9), (8,-1), (10,-6)
C. (-1, 10),(-9, 3), (-1, 8), (-9,-6)
D. (5, 10).(-9,3), (-1,8), (-6, 10)

Consider the reaction 2x2y2+z2⇌2x2y2z which has a rate law of rate= k[x2y2][z2] select a possible mechanism for the reaction.

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) = .

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