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djyliett [7]
3 years ago
12

Use the divergence theorem to find the outward flux of the vector field F(xyz)= 4x^2 i + 4y^2 j + 3z^2 k across the boundary of

the rectangular prism: 0
Mathematics
1 answer:
Pavel [41]3 years ago
5 0

\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z

Let S be the surface of the rectangular prism bounded by the planes x=0, x=a, y=0, y=b, z=0, and z=c. By the divergence theorem, the integral of \vec F over S is given by the integral of \nabla\cdot\vec F over the interior of S (call it R):

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}

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grandymaker [24]

Answer:

-5 and -5.5;

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Step-by-step explanation:

Two negative addends, can be added together to give -10.5.

For example:

(-5) + (-5.5) = -5 - 5.5 = -10.5

Also, it is possible for one of the addends to be negative while the other is positive, and their sum will give us -10.5.

For example:

The sum of -12.5 and 2 will give us -10.5.

We are adding a positive and a negative number here. As usual, we will subtract the smaller number from the bigger number, while the result will carry the sign of the bigger number, which in this case is negative sign.

Thus:

(-12.5) + (2) = -10.5

4 0
3 years ago
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nordsb [41]
A
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8 0
2 years ago
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malfutka [58]

Simplify for -5/8*2/3= -5/12

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6 0
3 years ago
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lyudmila [28]

For this case we have the following number:

600,000

We can rewrite this number as the product of two numbers.

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Then, rewriting in words we have:

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Answer:

Rewriting 600,000 we have:

600,000 = sixty - ten thousands

4 0
3 years ago
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Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is _____.
Bond [772]

Answer:

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Step-by-step explanation:

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d = | 2.4 - 1.3 | = | 1.1 | = 1.1 units

7 0
2 years ago
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