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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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What is the sum of two numbers a and b decreased by their product?
natka813 [3]

Answer:

(a+b) - (ab)

Step-by-step explanation:

sum of two numbers a and b decreased by their product

(a+b) - (ab)

8 0
3 years ago
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3/4 is added to x, the result is 9/8. What is the value of x?
KIM [24]

Answer:

x=3/8

Step-by-step explanation:

turn 3/4 into a fraction that has a denominator of 8 3/4x2= 6/8

To get it to 9/8 you add x which is 3/8

so 3/8+6/8 is 9/8

x=3/8

4 0
2 years ago
During a rainstorm a pail collects 1/3 of an inch of water in 5/6 of a minute. At what rate is the pail collecting water?
Delicious77 [7]

Answer:

2/5 of an inch per minute

Step-by-step explanation:

You can set up the rate as  \frac{1/3}{5/6}.  From here to find the amount of rain per minute, just multiply the numerator and denominator by 6/5 (The reciprocal of 5/6, so you can have one minute and see how much rains fills up in that time.)

You end with 2/5 of and inch per minute

4 0
3 years ago
What is 2.3w-7+8.1-3w
stepan [7]
2.0 w-1.1
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8 0
3 years ago
Find the 64th term of the arithmetic sequence -4, -21, -38, ...−4,−21,−38,
lisov135 [29]

a_{n} = a_{1} + d(n - 1)  ; a₁ is the first term, d is the difference between terms, and n is the term

-4, -21, -38, ...   ⇒   a₁ = -4, d = -17

a_{n} = -4 - 17(n - 1)

   = -4 - 17n + 17

   = 13 - 17n

a_{64} = 13 - 17(64)

    = 13 - 1088

    = 1075

Answer: 1075


5 0
3 years ago
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