Answer:
![\frac{4\sqrt{6}-\sqrt{15}}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Csqrt%7B6%7D-%5Csqrt%7B15%7D%7D%7B27%7D)
Step-by-step explanation:
![\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}\\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B6%7D%20%7D%7B8%2B%5Csqrt%7B10%7D%20%7D%20%5C%5C%5C%5C%5Cmathrm%7BMultiply%5C%3Aby%5C%3Athe%5C%3Aconjugate%7D%5C%3A%5Cfrac%7B8-%5Csqrt%7B10%7D%7D%7B8-%5Csqrt%7B10%7D%7D%5C%5C%3D%5Cfrac%7B%5Csqrt%7B6%7D%5Cleft%288-%5Csqrt%7B10%7D%5Cright%29%7D%7B%5Cleft%288%2B%5Csqrt%7B10%7D%5Cright%29%5Cleft%288-%5Csqrt%7B10%7D%5Cright%29%7D%5C%5C%5C%5C%5Csqrt%7B6%7D%5Cleft%288-%5Csqrt%7B10%7D%5Cright%29%3D8%5Csqrt%7B6%7D-2%5Csqrt%7B15%7D%5C%5C%5Cleft%288%2B%5Csqrt%7B10%7D%5Cright%29%5Cleft%288-%5Csqrt%7B10%7D%5Cright%29%3D54%5C%5C%5C%5C%3D%5Cfrac%7B8%5Csqrt%7B6%7D-2%5Csqrt%7B15%7D%7D%7B54%7D%5C%5C%5C%5C%5Cmathrm%7BFactor%7D%5C%3A8%5Csqrt%7B6%7D-2%5Csqrt%7B15%7D%3A%5Cquad%202%5Cleft%284%5Csqrt%7B6%7D-%5Csqrt%7B15%7D%5Cright%29%5C%5C%5C%5C%3D%5Cfrac%7B2%5Cleft%284%5Csqrt%7B6%7D-%5Csqrt%7B15%7D%5Cright%29%7D%7B54%7D%5C%5C)
![\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}](https://tex.z-dn.net/?f=%5Cmathrm%7BCancel%5C%3Athe%5C%3Acommon%5C%3Afactor%3A%7D%5C%3A2%5C%5C%5C%5C%3D%5Cfrac%7B4%5Csqrt%7B6%7D-%5Csqrt%7B15%7D%7D%7B27%7D)
Answer: I dont know the answer but i did some research and i got you some notes i hope they help!
Step-by-step explanation: :D
Answer:
8 pi
Step-by-step explanation:
When radius is
L = r * Θ = 2 * π/4 = 1.57079633 cm.
When radius is
L = r * Θ = 10 * π/4 = 7.85398163 cm.
ANSWER:
We know that,
Speed = Distance/Time
So, Time taken = 20kmh-¹/160km
Given:
![\dfrac{?}{5}+\dfrac{18}{20}=\dfrac{30}{20}](https://tex.z-dn.net/?f=%5Cdfrac%7B%3F%7D%7B5%7D%2B%5Cdfrac%7B18%7D%7B20%7D%3D%5Cdfrac%7B30%7D%7B20%7D)
To find:
The missing value.
Solution:
Let x be the missing value.
We have,
![\dfrac{x}{5}+\dfrac{18}{20}=\dfrac{30}{20}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%2B%5Cdfrac%7B18%7D%7B20%7D%3D%5Cdfrac%7B30%7D%7B20%7D)
![\dfrac{x}{5}+\dfrac{9}{10}=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%2B%5Cdfrac%7B9%7D%7B10%7D%3D%5Cdfrac%7B3%7D%7B2%7D)
Subtract
from both sides.
![\dfrac{x}{5}=\dfrac{3}{2}-\dfrac{9}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%3D%5Cdfrac%7B3%7D%7B2%7D-%5Cdfrac%7B9%7D%7B10%7D)
![\dfrac{x}{5}=\dfrac{15-9}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%3D%5Cdfrac%7B15-9%7D%7B10%7D)
![\dfrac{x}{5}=\dfrac{6}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%3D%5Cdfrac%7B6%7D%7B10%7D)
![\dfrac{x}{5}=\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B5%7D%3D%5Cdfrac%7B3%7D%7B5%7D)
Multiplying both sides by 5, we get
![x=3](https://tex.z-dn.net/?f=x%3D3)
So, the missing value is 3.
Therefore, the correct option is C.