The circumference of a circle changes from 20 to 4 after a dilation. What was the scale factor of the dilation?

a. StartFraction 1 Over 25 EndFraction

b. One-fifth

c. 5

d. 25

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Ответ:

kobrien9146

14.12.2020

Mathematics

$\begin{aligned} \cos 4x + \cos 2x & = 2 - 2\sin^2(2x) - 2\sin^2 x \end{aligned}$ left-hand side: manipulate cos 4x to get: $\begin{aligned} \text{lhs} & = \cos 4x + \cos 2x \\ & = \cos\big[2(2x)\big] + \cos 2x \end{aligned}$ now we use cosine double angle identity as follows. we use the sine version of the cosine double angle identity because the right-hand side is exclusively in sine. $\begin{aligned} \cos 2x & = 1 - 2\sin^2 x \end{aligned}$ also $\begin{aligned} \cos\big[2(2x)\big] & = 1 - 2\sin^2 (2x) \end{aligned}$ so $\begin{aligned} \text{lhs} & = \cos\big[2(2x)\big] + \cos 2x \\ & = 1 - 2\sin^2 (2x) + 1 - 2\sin^2 x \\ & = 1 + 1 - 2\sin^2 (2x) - 2\sin^2 x \\ & = 2 - 2\sin^2(2x) - 2\sin^2 x\\ & = \text{rhs} \end{aligned}$

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