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Solve this system of equations. 12x − 18y = 27 4x − 6y = 10

Suzanne began a trip with 18 1/2 gallons of gas in the gas tank of her car if she hughes 17 3/4 gallons on the trip how many gallons does she have left once she finish the trip

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) = .