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Mathematics, 28.05.2020 02:09 supermkimbrel
Out of fifty students, twenty five are taking Math Competition classes and 29 are taking Geometry. Given that 12 are taking History and no math classes and nineteen students are in both math classes. How many are in at least one math class?
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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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Out of fifty students, twenty five are taking Math Competition classes and 29 are taking Geometry. G...
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