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Mathematics

1 answer:

stiks02 [169]3 years ago

4 0

Answer:

1, False

2, the sum of a number and two is 5 (n + 2 = 5)

2, 5n=2 (5 times a number is 2)

2, n÷2=5 (The quotient of a number and 2 is 5)

2, 5+2=n (5 added to 2 is a number)

The last one from number two that you put in number 3, x+2=5 (The sum of a number and two is five)

3, There are four terms.

Step-by-step explanation:

Hope it helps!

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alukav5142 [94]

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4 0

4 years ago

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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 =

marissa [1.9K]

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

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