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puteri [66]
2 years ago
7

Find the two small as possible solutions ​

Mathematics
2 answers:
solong [7]2 years ago
6 0

Answer:  \bold{b)\quad \dfrac{5}{6},\ \dfrac{25}{6}}

<u>Step-by-step explanation:</u>

12cos\bigg(\dfrac{2\pi}{5}x\bigg)+10=16\\\\\\12cos\bigg(\dfrac{2\pi}{5}x\bigg)=6\\\\\\cos\bigg(\dfrac{2\pi}{5}x\bigg)=\dfrac{1}{2}\\\\\\cos^{-1}\bigg[cos\bigg(\dfrac{2\pi}{5}x\bigg)\bigg]=cos^{-1}\bigg(\dfrac{1}{2}\bigg)

\text{Use the Unit Circle to determine when}\ cos=\dfrac{1}{2}\quad \rightarrow \quad\text{at}\ \dfrac{\pi}{3}\ and \ \dfrac{5\pi}{3}\\\\\\\dfrac{2\pi}{5}x=\dfrac{\pi}{3}\qquad and\qquad \dfrac{2\pi}{5}x=\dfrac{5\pi}{3}\\\\\\\bigg(\dfrac{5}{2\pi}\bigg)\dfrac{2\pi}{5}x=\dfrac{\pi}{3}\bigg(\dfrac{5}{2\pi}\bigg)\quad and\quad \bigg(\dfrac{5}{2\pi}\bigg)\dfrac{2\pi}{5}x=\dfrac{5\pi}{3}\bigg(\dfrac{5}{2\pi}\bigg)\\\\\\.\qquad \qquad \large\boxed{x=\dfrac{5}{6}\qquad and \qquad x=\dfrac{25}{6}}

Alla [95]2 years ago
5 0

Answer:

○ b. \displaystyle \frac{5}{6}, \frac{25}{6}

Explanation:

<em>See my above explanation</em>

I am joyous to assist you anytime. ☺️

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