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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) = .

Joe has a rectangular chicken coop. the length of the coop is 4 feet less than twice the width. the area of the chicken coop is 510 square feet. what is the length of the chicken coup?

20 points for the answer. this is for real , don't put random ! a rectangle has a length of 4 centimeters and a width of 7 centimeters. what is the effect on the perimeter when the dimensions are multiplied by 5? the perimeter is increased by a factor of 5. the perimeter is increased by a factor of 20. the perimeter is increased by a factor of 25. the perimeter is increased by a factor of 100.