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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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A university administrator was interested in determining if there was a difference in the distance students travel to get from c
eduard

Answer:

1) Fail to reject the Null hypothesis

2) We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.

Step-by-step explanation:

A university administrator wants to test if there is a difference between the distance men and women travel to class from their current residence. So, the hypothesis would be:

H_{o}: \mu_{F}-\mu_{M}=0\\\\ H_{a}: \mu_{F}-\mu_{M}\neq 0

The results of his tests are:

t-value = -1.05

p-value = 0.305

Degrees of freedom = df = 21

Based on this data we need to draw a conclusion about test. The significance level is not given, but the normally used levels of significance are 0.001, 0.005, 0.01 and 0.05

The rule of the thumb is:

  • If p-value is equal to or less than the significance level, then we reject the null hypothesis
  • If p-value is greater than the significance level, we fail to reject the null hypothesis.

No matter which significance level is used from the above mentioned significance levels, p-value will always be larger than it. Therefore, we fail to reject the null hypothesis.

Conclusion:

We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.

7 0
3 years ago
How do I do this? (Will give brainliest) (explanation if you could)
Liula [17]
Take a photo of your screen and chose either word or math
6 0
3 years ago
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If the data is spread out evenly, the measure of the center that is best to use is the what.
miss Akunina [59]

That would be the mean.

3 0
3 years ago
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WHAT IS X<br> PLEASE HELP 50 POINTS
Iteru [2.4K]

Answer:

x=52

Step-by-step explanation:

90+34

124

180 (sum of all interior angles) - 124

56

x+72+56=180 (straight line)

x+128=180

 -128  -128

x=52

*replace to verify*

52+72= 124

124+56= 180 (straight line)

4 0
2 years ago
Evaluate the expression for k = 2. –9 + 7k =
zhannawk [14.2K]

Answer:

k = 7/6

Step-by-step explanation:

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2 years ago
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