Asking for help on this again because i reallu need it!!

Mathematics

1 answer:

shutvik [7]1 year ago

7 0

Answer:

5. 5.8

6. 6

7. 6

Step-by-step explanation:

5. mean - add all values and divide by the number of values

2 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 9 + 10 = 75

mean = 75/13 = 5.8

6. median - middle value of values written in ascending order.

2 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 9 + 10

median = 6

7. mode - value that occurs most times

mode = 6

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Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 = 9 and the sphere x2 y2 z2 =

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In Cartesian coordinates, the region is given by $-3\le x\le3$ , $-\sqrt{9-x^2}\le y\le\sqrt{9-x^2}$ , and $-\sqrt{16-x^2-y^2}\le z\le\sqrt{16-x^2-y^2}$ . Converting to cylindrical coordinates, using

$\begin{cases}\mathbf x(r,\theta,\zeta)=r\cos\theta\\\mathbf y(r,\theta,\zeta)=r\sin\theta\\\mathbf z(r,\theta,\zeta)=\zeta\end{cases}$

we get a Jacobian determinant of $r$ , and the region is given in cylindrical coordinates by $0\le\theta\le2\pi$ , $0\le r\le3$ , and $-\sqrt{16-r^2}\le z\le\sqrt{16-r^2}$ .

The volume is then

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{z=-\sqrt{16-r^2}}^{z=\sqrt{16-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\dfrac{4(64-7\sqrt7)\pi}3$