C, the median is 23 when you add 13 + 10. Then you divide 23 and 2.
Answer:
I = 91.125
Step-by-step explanation:
Given that:
where E is bounded by the cylinder
and the planes x = 0 , y = 9x and z = 0 in the first octant.
The initial activity to carry out is to determine the limits of the region
since curve z = 0 and
∴ ![z^2 = 81 - y^2](https://tex.z-dn.net/?f=z%5E2%20%3D%2081%20-%20y%5E2)
![z = \sqrt{81 - y^2}](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B81%20-%20y%5E2%7D)
Thus, z lies between 0 to ![\sqrt{81 - y^2}](https://tex.z-dn.net/?f=%5Csqrt%7B81%20-%20y%5E2%7D)
GIven curve x = 0 and y = 9x
![x =\dfrac{y}{9}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7By%7D%7B9%7D)
As such,x lies between 0 to ![\dfrac{y}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7B9%7D)
Given curve x = 0 ,
and z = 0,
y = 0 and
![y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9](https://tex.z-dn.net/?f=y%5E2%20%3D%2081%20%5C%5C%20%5C%5C%20y%20%3D%20%5Csqrt%7B81%7D%20%20%5C%5C%20%5C%5C%20%20y%20%3D%209)
∴ y lies between 0 and 9
Then ![I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%5Cint%5E%7B%5Cdfrac%7By%7D%7B9%7D%7D_%7Bx%3D0%7D%20%5Cint%5E%7B%5Csqrt%7B81-y%5E2%7D%7D_%7Bz%3D0%7D%20%5C%20zdzdxdy)
![I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%5Cint%5E%7B%5Cdfrac%7By%7D%7B9%7D%7D_%7Bx%3D0%7D%20%5Cbegin%20%7Bbmatrix%7D%20%5Cdfrac%7Bz%5E2%7D%7B2%7D%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%5E%20%7B%5Csqrt%20%7B%7B81-y%5E2%7D%7D%7D_%7B0%7D%20%5C%20dxdy)
![I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%5Cint%5E%7B%5Cdfrac%7By%7D%7B9%7D%7D_%7Bx%3D0%7D%20%5Cbegin%20%7Bbmatrix%7D%20%20%5Cdfrac%7B%28%5Csqrt%7B81%20-y%5E2%7D%29%5E2%20%7D%7B2%7D-0%20%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%20%5C%20dxdy)
![I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%5Cint%5E%7B%5Cdfrac%7By%7D%7B9%7D%7D_%7Bx%3D0%7D%20%5Cbegin%20%7Bbmatrix%7D%20%20%5Cdfrac%7B%7B81%20-y%5E2%7D%20%7D%7B2%7D%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%20%5C%20dxdy)
![I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%5Cdfrac%7B%7B81x%20-xy%5E2%7D%20%7D%7B2%7D%20%5Cend%20%7Bbmatrix%7D%20%5E%7B%5Cdfrac%7By%7D%7B9%7D%7D_%7B0%7D%20%20%20%20%5C%20dy)
![I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%5Cdfrac%7B%7B81%28%5Cdfrac%7By%7D%7B9%7D%29%20-%28%5Cdfrac%7By%7D%7B9%7D%29y%5E2%7D%20%7D%7B2%7D-0%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%20%5C%20dy)
![I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy](https://tex.z-dn.net/?f=I%20%3D%20%5Cint%5E9_%7By%3D0%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%5Cdfrac%7B%7B81%20%5C%20%20y%20-y%5E3%7D%20%7D%7B18%7D%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%20%5C%20dy)
![I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B1%7D%7B18%7D%20%5Cint%5E9_%7By%3D0%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%7B81%20%5C%20%20y%20-y%5E3%7D%20%20%5Cend%20%7Bbmatrix%7D%20%20%20%20%20%5C%20dy)
![I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B1%7D%7B18%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%7B81%20%5C%20%5Cdfrac%7By%5E2%7D%7B2%7D%20-%20%5Cdfrac%7By%5E4%7D%7B4%7D%7D%20%20%5Cend%20%7Bbmatrix%7D%5E9_0)
![I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B1%7D%7B18%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%20%7B40.5%20%5C%20%289%5E2%29%20-%20%5Cdfrac%7B9%5E4%7D%7B4%7D%7D%20%20%5Cend%20%7Bbmatrix%7D)
![I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B1%7D%7B18%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%203280.5%20-%201640.25%20%20%5Cend%20%7Bbmatrix%7D)
![I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}](https://tex.z-dn.net/?f=I%20%3D%20%5Cdfrac%7B1%7D%7B18%7D%20%20%5Cbegin%20%7Bbmatrix%7D%20%201640.25%20%20%5Cend%20%7Bbmatrix%7D)
I = 91.125
<u>Answer:</u>
Option D
<u>Step-by-step explanation:</u>
In this table, the constant of proportionality, which is just the number that each <em>x</em> value is multiplied by to get the corresponding <em>y</em> value, is 7. This is because, as shown by the first row of the table, 1*7=7, and, as shown by the third row of the table, 3*7=21. Therefore, in the second row of the table, <em>y</em> should be 14, as 2*7=14, while in the fourth row of the table, <em>y</em> should be 28, as 4*7=28.
<em>Hope this helps! Comment any questions. </em>
The distance is 8, since the x co-ordinate stays 5, the y co-ordinate goes from 10 to 2, which is an 8 distance