Answer: ![\bold{b)\quad \dfrac{5}{6},\ \dfrac{25}{6}}](https://tex.z-dn.net/?f=%5Cbold%7Bb%29%5Cquad%20%5Cdfrac%7B5%7D%7B6%7D%2C%5C%20%5Cdfrac%7B25%7D%7B6%7D%7D)
<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)](https://tex.z-dn.net/?f=12cos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%5Cbigg%29%2B10%3D16%5C%5C%5C%5C%5C%5C12cos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%5Cbigg%29%3D6%5C%5C%5C%5C%5C%5Ccos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%5Cbigg%29%3D%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5C%5Ccos%5E%7B-1%7D%5Cbigg%5Bcos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%5Cbigg%29%5Cbigg%5D%3Dcos%5E%7B-1%7D%5Cbigg%28%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29)
![\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}}](https://tex.z-dn.net/?f=%5Ctext%7BUse%20the%20Unit%20Circle%20to%20determine%20when%7D%5C%20cos%3D%5Cdfrac%7B1%7D%7B2%7D%5Cquad%20%5Crightarrow%20%5Cquad%5Ctext%7Bat%7D%5C%20%5Cdfrac%7B%5Cpi%7D%7B3%7D%5C%20and%20%5C%20%5Cdfrac%7B5%5Cpi%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%5Cqquad%20and%5Cqquad%20%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%3D%5Cdfrac%7B5%5Cpi%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5Cbigg%28%5Cdfrac%7B5%7D%7B2%5Cpi%7D%5Cbigg%29%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%5Cbigg%28%5Cdfrac%7B5%7D%7B2%5Cpi%7D%5Cbigg%29%5Cquad%20and%5Cquad%20%5Cbigg%28%5Cdfrac%7B5%7D%7B2%5Cpi%7D%5Cbigg%29%5Cdfrac%7B2%5Cpi%7D%7B5%7Dx%3D%5Cdfrac%7B5%5Cpi%7D%7B3%7D%5Cbigg%28%5Cdfrac%7B5%7D%7B2%5Cpi%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Clarge%5Cboxed%7Bx%3D%5Cdfrac%7B5%7D%7B6%7D%5Cqquad%20and%20%5Cqquad%20x%3D%5Cdfrac%7B25%7D%7B6%7D%7D)
Answer:
the answer is c
Step-by-step explanation:
i hope this helps
Answer: I need more details plz
Step-by-step explanation:
Answer:
The ratio of their volumes is 27/64
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
The scale factor is 3/4
step 2
Find the ratio of their volumes
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
![(\frac{3}{4})^{3}=\frac{27}{64}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B3%7D%3D%5Cfrac%7B27%7D%7B64%7D)
I hope this helps you
2x and 8x+40 complementary angles
their sum is 180
2x+8x+40=180
10x=140
x=14