Mathematics, 20.09.2019 17:30 mamacita712
Consider the operation of counting the factors of a whole number. this function is usually called v. for example, the number 6 has as its factors: 1, 2, 3, 6, so v(6)=4. complete the following.
5) what can you say about a number m if v(m)=12?
6) find two number n and m such that v(nm)=v(n) x v(m). find two more. what can you say about the relationship between n and m?
Answers: 3
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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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Consider the operation of counting the factors of a whole number. this function is usually called v....
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