Mathematics
Mathematics, 27.10.2020 22:20, avision42

Answer all parts please.


Answer all parts please.

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Answers: 3

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Prove (a) cosh2(x) āˆ’ sinh2(x) = 1 and (b) 1 āˆ’ tanh 2(x) = sech 2(x). solution (a) cosh2(x) āˆ’ sinh2(x) = ex + eāˆ’x 2 2 āˆ’ 2 = e2x + 2 + eāˆ’2x 4 āˆ’ = 4 = . (b) we start with the identity proved in part (a): cosh2(x) āˆ’ sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 āˆ’ sinh2(x) cosh2(x) = 1 or 1 āˆ’ tanh 2(x) = .
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You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?
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