1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jeka94
3 years ago
8

Use the divergence theorem to calculate the outward flux of f=r|r|f=r|r| where r=⟨x,y,z⟩r=⟨x,y,z⟩ across ss: the hemisphere z=16

−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√z=16−x2−y2 and the disk x2+y2≤16x2+y2≤16 in the xyxy-plane.
Mathematics
1 answer:
yuradex [85]3 years ago
7 0

With \mathbf f=\mathbf r (?) you have divergence

\nabla\cdot\mathbf f=\dfrac{\partial x}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial z}{\partial z}=3

Then by the divergence theorem, the flux is

\displaystyle\iint_S\mathbf f\cdot\mathrm d\mathbf S=3\iiint_R\mathrm dV

where R denotes the interior of the region with boundary S.

Convert to spherical coordinates to set up the volume integral as

\displaystyle3\int_{\varphi=0}^{\varphi=\pi/2}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=4}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

=\displaystyle6\pi\left(\int_0^4\rho^2\,\mathrm d\rho\right)\left(\int_0^{\pi/2}\sin\varphi\,\mathrm d\varphi\right)

=128\pi

You might be interested in
I need help with Number 7 please!!!
olga2289 [7]

Answer:

8.06 ft or \sqrt{65}  ft

Step-by-step explanation:

Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you \sqrt{65}  ft per side. This can be approximated to 8.06 ft.

8 0
2 years ago
Read 2 more answers
Between x=2 and x=3, which function has a greater average rate of change than f(x)=2^x has?
maxonik [38]

Answer: f(3)

Step-by-step explanation:

First find the formula for the rate of change by taking the derivative of 2^x. Let f(x) equal some hypothetical y-value, then take the natural log of both sides.

y=2^x\\\ln(y)=x \ln(2)

Implicitly differentiate the left side and take the derivative of the right side

\frac{y'}{y} =\ln(2)

Multiply both sides by 'y' which was defined as 2^x

y'=\ln(2)*2^x

Plug in x = 2 and x = 3 to see which slope is larger

y'=\ln(2)*2^2=4\ln(2)\\y'=\ln(2)*2^3=8\ln(2)

4 0
3 years ago
7 with the exponent of 3 times 9 with the exponent of 4 minus 2
gayaneshka [121]

Answer:

Step-by-step explanation:

7 with exp 3 times 9 with exp 4 minus 2=

343 times 6561 minus 2=

2250421

4 0
2 years ago
The figure shows the movement of a pedestrian as she walks from point B to point E. Write a formula for function d(t) for each s
levacccp [35]

Answer:

crxr utcug UFC tvuyvuyv tvuycrcfgvugvihtc

Step-by-step explanation:

TT good uvjobihcygc r

8 0
2 years ago
Read 2 more answers
Can u please help me with 27
Pachacha [2.7K]
The answer would be 237.375. To get this answer, you will first use the formula given for each unit. First, you will do the first unit by putting 8 to the third power, or basically 8x8x8. After you get the product 512, you will then do the next unit. Do that one by doing 6.5 to the third power, or as followed, 6.5x6.5x6.5. Once you get the product 274.625, you will then subtract that from 512. You will then receive the answer 237.375.
5 0
3 years ago
Other questions:
  • Use substitution to solve each system of equations<br> c-5d=2 <br> 2c+d=4
    12·2 answers
  • GEOMETRY PROBLEM THAT I CAN NEVER GET
    7·1 answer
  • What is the sum of 5(−3.4k−7) (3k 21) =
    5·1 answer
  • Classify the triangle by the measure of its sides.Explain.
    10·1 answer
  • I’ll give brainliest help
    10·1 answer
  • The graph shows how a store sells peppers by weight at a constant price per pound
    12·1 answer
  • (vii) log32 8=m<br> Again please
    7·1 answer
  • In the figure shown, what fractional part of the circle is shaded?
    9·2 answers
  • What is the equation of the line that has a slope of -4 and goes through (-1,6) ?
    10·1 answer
  • Which division problem does the number line below best illustrate?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!