Mathematics, 16.12.2020 19:40 maddie0533

80% of all castles had been preserved. if there were 135 castles in all, how many had not been preserved?

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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) = .

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80% of all castles had been preserved. if there were 135 castles in all, how many had not been prese...