Answer:20% is the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
![sin(2\theta)=2sin\theta~cos\theta\\\\cos(2\theta)=cos^2\theta-sin^2\theta\\\\cos\theta=\frac{24}{25}\\\\sin^2\theta+cos^2\theta=1~=>sin\theta=\pm\sqrt{1-cos^2\theta}\\\\we ~will~ use~ the ~minus~ sign~because~sin\theta~is~negative~in~IV~cuadrant\\sin\theta=-\sqrt{1-{(\frac{24}{25})}^2}=-\frac{7}{25}](https://tex.z-dn.net/?f=sin%282%5Ctheta%29%3D2sin%5Ctheta~cos%5Ctheta%5C%5C%5C%5Ccos%282%5Ctheta%29%3Dcos%5E2%5Ctheta-sin%5E2%5Ctheta%5C%5C%5C%5Ccos%5Ctheta%3D%5Cfrac%7B24%7D%7B25%7D%5C%5C%5C%5Csin%5E2%5Ctheta%2Bcos%5E2%5Ctheta%3D1~%3D%3Esin%5Ctheta%3D%5Cpm%5Csqrt%7B1-cos%5E2%5Ctheta%7D%5C%5C%5C%5Cwe%20~will~%20use~%20the%20~minus~%20sign~because~sin%5Ctheta~is~negative~in~IV~cuadrant%5C%5Csin%5Ctheta%3D-%5Csqrt%7B1-%7B%28%5Cfrac%7B24%7D%7B25%7D%29%7D%5E2%7D%3D-%5Cfrac%7B7%7D%7B25%7D)
Now we cal calculate the quantities requested
![sin(2\theta)=2sin\theta cos\theta=2(-\frac{7}{25})\frac{24}{25}=-\frac{336}{625}\\\\](https://tex.z-dn.net/?f=sin%282%5Ctheta%29%3D2sin%5Ctheta%20cos%5Ctheta%3D2%28-%5Cfrac%7B7%7D%7B25%7D%29%5Cfrac%7B24%7D%7B25%7D%3D-%5Cfrac%7B336%7D%7B625%7D%5C%5C%5C%5C)
![cos(2\theta)=cos^2\theta-sin^2\theta=(\frac{24}{25})^2-(-\frac{7}{25})^2=\frac{527}{625}](https://tex.z-dn.net/?f=cos%282%5Ctheta%29%3Dcos%5E2%5Ctheta-sin%5E2%5Ctheta%3D%28%5Cfrac%7B24%7D%7B25%7D%29%5E2-%28-%5Cfrac%7B7%7D%7B25%7D%29%5E2%3D%5Cfrac%7B527%7D%7B625%7D)
![tan(2\theta)=\frac{sin(2\theta)}{cos(2\theta)}=\frac{-\frac{336}{625}}{\frac{527}{625}}=-\frac{336}{527}](https://tex.z-dn.net/?f=tan%282%5Ctheta%29%3D%5Cfrac%7Bsin%282%5Ctheta%29%7D%7Bcos%282%5Ctheta%29%7D%3D%5Cfrac%7B-%5Cfrac%7B336%7D%7B625%7D%7D%7B%5Cfrac%7B527%7D%7B625%7D%7D%3D-%5Cfrac%7B336%7D%7B527%7D)
So, that's
![{8}^{ \frac{1}{2} } \times {x}^{ \frac{1}{2} } \times {y}^{ \frac{3}{4} }](https://tex.z-dn.net/?f=%20%7B8%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%5Ctimes%20%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%5Ctimes%20%20%7By%7D%5E%7B%20%5Cfrac%7B3%7D%7B4%7D%20%7D%20)
*Helpful To Know
![{5}^{ \frac{1}{2} } = \sqrt{5} \\ {5}^{ \frac{1}{3} } = \sqrt[3]{5} \\ {5}^{ \frac{1}{4} } = \sqrt[4]{5} \\ {5}^{ \frac{3}{2} } = \sqrt{ {5}^{3} } \: \: or \: {( \sqrt{5} )}^{3}](https://tex.z-dn.net/?f=%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%5Csqrt%7B5%7D%20%5C%5C%20%20%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%20%3D%20%20%5Csqrt%5B3%5D%7B5%7D%20%20%5C%5C%20%7B5%7D%5E%7B%20%5Cfrac%7B1%7D%7B4%7D%20%7D%20%20%3D%20%20%5Csqrt%5B4%5D%7B5%7D%20%20%20%20%5C%5C%20%20%20%7B5%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%3D%20%20%5Csqrt%7B%20%7B5%7D%5E%7B3%7D%20%7D%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%20%7B%28%20%5Csqrt%7B5%7D%20%29%7D%5E%7B3%7D%20)
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*Assuming that you want to covert to radicals
![( \sqrt{8} )( \sqrt{x} )( \sqrt[4]{ {y}^{3} } )](https://tex.z-dn.net/?f=%28%20%5Csqrt%7B8%7D%20%29%28%20%5Csqrt%7Bx%7D%20%29%28%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B3%7D%20%7D%20%29)
*Simplify