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Airida [17]
3 years ago
12

Verify that the divergence theorem is true for the vector field f on the region

Mathematics
1 answer:
timofeeve [1]3 years ago
5 0
\mathbf f(x,y,z)=3x\,\mathbf i+xy\,\mathbf j+4xz\,\mathbf k
\implies\nabla\cdot\mathbf f(x,y,z)=3+x+4x=3+5x

\displaystyle\iint_{\partial E}\mathbf f(x,y,z)\,\mathrm dS=\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV
=\displaystyle\int_{z=0}^{z=3}\int_{y=0}^{y=3}\int_{x=0}^{x=3}(3+5x)\,\mathrm dx\,\mathrm dy\,\mathrm dz
=\displaystyle9\int_0^3(3+5x)\,\mathrm dx
=\dfrac{567}2
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The average number of ice cream cones sold in a weekend is 60. On Friday, 67 cones were sold and on Saturday, 59 cones were sold
Anastaziya [24]

The average would be each number of cones sold per day added, and divided by the number of days (3). So this can be translated into the equation (67 + 59 + x)/3 = 60/1. Simplified, that is 67 + 59 + x = 180, then 126 + x = 180, then x = 54.

You can check by adding 67 + 59 + 54, which is 180, and divide by 3 days which is 60. So 54 cones were sold on Sunday.

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3 years ago
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IRISSAK [1]

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Step-by-step explanation:

6 0
3 years ago
What is 118/200 simplified?
algol13
<span>- Find the GCD (or HCF) of numerator and denominator
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Anastasy [175]

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3 0
2 years ago
A Square has a length of 9 feet. Find the area and perimeter.
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