What is 12.357 in expanded form

Mathematics

1 answer:

Andrew [12]3 years ago

6 0

Answer:

10+2+0.3+0.05+0.007

Step-by-step explanation:

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Solve the equation 4*e+2=1 (mod5)

otez555 [7]

Here's a way to do it.

Let 4e +2 = 5n +1 . . . . . . for some integer n

Then e = (5n -1)/4 = n + (n -1)/4

We want (n-1)/4 to be an integer, so let it be integer m.

... m = (n -1)/4

... 4m = n -1

... 4m +1 = n

Substituting this into our expression for e gives

... e = (5(4m+1) -1)/4 = (20m +4)/4 = 5m +1

e = 5m+1 for any integer m

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4 years ago

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3 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

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