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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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PLEASE HELP ASAP!! CORRECT ANSWER ONLY PLEASE!!
Leona [35]
9x + 4 ≤ 58

=> 9x ≤ 58 - 4

=> 9x ≤ 54

=> x ≤ 54/9

=> x ≤ 6
______________

1/6x − 2 > 3

=> 1/6x > 3 + 2

=> 1/6x > 5

=> x > 5×6

=> x > 30
5 0
3 years ago
Read 2 more answers
A pair of corresponding side of two similar pentagons have length of 12cm and 28cm
ICE Princess25 [194]
The ratio of their areas = 12^2 / 28^2
5 0
3 years ago
Mrs.Zomoro is 36 years old and her son is 4.When will the mother be thrice as o old as her son?​
Arisa [49]

Answer:

12 years

Step-by-step explanation:

Represent the mother's age by m and the son's by 4.  Currently m = 36 years old.

In x years the mother will be three times as old as her son:

mother:  36 + x years old

son:  4 + x years old

The pertinent equation to solve is:

36 + x = 3(4 + x)

Performing the multiplication, we get:

36 + x = 12 + 3x, or

24 = 2x.  Then x = 12.

Check:  In 12 years, will the mother's age be 3 times the son's age?

Does 36 + 12 = 3(4 + 12)?

Does    48      = 48?  YES

The mother will be 3 times as old as her son in 12 years from now.

3 0
3 years ago
Two pumps connected in parallel fail indepen- dently of each other on any given day. The proba- bility that only the older pump
lions [1.4K]

Answer: 0.145

Step-by-step explanation:

Since,

the Probability of the older pump failing P(fail older) = 0.10

The probability of the newer pump failing P(fail newer) = 0.05

Therefore,

The Probability of the older pump not failing P(not fail older) = 1 - 0.1

P(not fail older) = 0.9

Also,

The probability of the newer pump not failing P(not fail newer) = 1 - 0.05 = 0.95

The probability of the pumping system failing = P(not fail older)* P(not fail newer) = 0.9*0.95

P(not fail system)= 0.855

Therefore,

The probability that the pumping system will fail = 1 - P(not fail system) = 1 - 0.855 = 0.145

The probability that the pumping system will fail one day is 0.145

3 0
3 years ago
The number that is multiplied by a power of 10 in scientific notation must be in between 1 and 10
vazorg [7]

Answer:

Thats false

Step-by-step explanation:

When you multiply by a power your basically multiplying that number b itself 10x except for 1

4 0
3 years ago
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