30 points, .
17. the colosseum in rome was the largest amphitheater built in the roman empir...
Mathematics, 29.06.2019 10:10 raymondleggett44
30 points, .
17. the colosseum in rome was the largest amphitheater built in the roman empire. the interior of the colosseum is a perfect circle. the roof of this enormous amphitheater was about 600 feet in diameter. if the center of the colosseum is assumed to be at origin, then write an equation for the circle that represents the roof of the colosseum. (justify)
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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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