BRAINLIEST AND 10 POINTS

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

4 0

Answer:

use the link but its answer D.

Step-by-step explanation:

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Lottie had a collection of 72 dishes that she really used she decided to keep one sixth of dishes and sell the rest in a garage

Serggg [28]

$\frac{1}{6} \: of \: 72 \\ = \: \frac{1}{6} \times 72 \\ \\ = \frac{72}{6} \\ = 12$

So, she kept 12 dishes.

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A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.00 m/s. The car is a distan

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3 years ago

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givi [52]

Use the divergence theorem. Let $R$ be the cylindrical region, then

$\displaystyle\iint_{\partial R}\mathbf F\cdot\mathbf n\,\mathrm dS=\iiint_R\nabla\cdot\mathbf F\,\mathrm dV$

(where $\mathbf n$ denotes the unit normal vector to $\partial R$ , but we don't need to worry about it now)

We have

$\mathrm{div }\mathbf F=(\nabla\cdot\mathbf F)(x,y,z)=\dfrac{\partial\mathbf F}{\partial x}+\dfrac{\partial\mathbf F}{\partial y}+\dfrac{\partial\mathbf F}{\partial z}$
$\nabla\cdot\mathbf F=3x^2+3y^2+3z^2$

For the solid $R$ with boundary $\partial R$ , we can set up the following volume integral in cylindrical coordinates for ease:

$\displaystyle3\iiint_R(x^2+y^2+z^2)\,\mathrm dV=3\int_{z=0}^{z=4}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=2}(r^2+z^2)r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$
$=\displaystyle6\pi\int_{z=0}^{z=4}\int_{r=0}^{r=2}(r^3+rz^2)\,\mathrm dr\,\mathrm dz$
$=\displaystyle12\pi\int_{z=0}^{z=4}(2+z^2)\,\mathrm dz$
$=352\pi$