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
allsm [11]
3 years ago
7

How do you solve this?

Mathematics
1 answer:
Tasya [4]3 years ago
8 0

Answer:

Step-by-step explanation:

You might be interested in
Whoever gets this correct gets brainliest
AlekseyPX

Answer:

More. Older

Likey

To vote

Less likely. younger

to

vote

8 0
3 years ago
WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Mars2501 [29]

Answer:

20

Step-by-step explanation:

20+20=40

7 0
2 years ago
Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find
Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk x^2+y^2\le3, I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere x^2+y^2+z^2=3.

a. Let C denote the hemispherical <u>c</u>ap z=\sqrt{3-x^2-y^2}, parameterized by

\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k

with 0\le u\le2\pi and 0\le v\le\frac\pi2. Take the normal vector to C to be

\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k

Then the upward flux of \vec F=(2z+2)\,\vec k through C is

\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du

\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du

=\boxed{2(3+2\sqrt3)\pi}

b. Let D be the disk that closes off the hemisphere C, parameterized by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

with 0\le u\le\sqrt3 and 0\le v\le2\pi. Take the normal to D to be

\vec s_v\times\vec s_u=-u\,\vec k

Then the downward flux of \vec F through D is

\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv

=\boxed{-6\pi}

c. The net flux is then \boxed{4\sqrt3\pi}.

d. By the divergence theorem, the flux of \vec F across the closed hemisphere H with boundary C\cup D is equal to the integral of \mathrm{div}\vec F over its interior:

\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV

We have

\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2

so the volume integral is

2\displaystyle\iiint_H\mathrm dV

which is 2 times the volume of the hemisphere H, so that the net flux is \boxed{4\sqrt3\pi}. Just to confirm, we could compute the integral in spherical coordinates:

\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi

4 0
3 years ago
A farmer has a sack of grain, a chicken and a fox. He has to get them across the river and he can't go around or fly but he does
snow_tiger [21]
<span>

</span><span>http://www.squiglysplayhouse.com/BrainTeasers/bt.php?id=119
 this should help</span>
7 0
3 years ago
Gary learned that the value of his car depreciates by 15% percent per year. Which of the following functions best describes the
Sever21 [200]
For this case we have that the original value of the car is:
 m dollars
 For the following year we have the value is:
 ((100-15) / (100)) m
 Rewriting we have:
 ((85) / (100)) m
 0.85m
 Answer:
 
the value of his car the year after the car is worth m dollars is:
 
B.f (m) = 0.85m
5 0
2 years ago
Other questions:
  • Please help I don’t know what the answer is
    9·2 answers
  • Emma is 9 1/4 years old . how many months is Emma please answer
    9·2 answers
  • It can burn but can have no heat it smokes but its not hot what is it?
    5·2 answers
  • What is the quotient?
    11·1 answer
  • Planes Q and R are parallel. Explain how you know lines a and b are skew.
    10·2 answers
  • Is there a strategy to approaching a problem like this?
    8·1 answer
  • Why is pie considered an irrational number A. it is a non-repeating decimal B. the decimal never terminates C. both A and B D. n
    13·2 answers
  • What is (4.81 times 10 Superscript 16 Baseline) (1.1 times 10 Superscript negative 4 Baseline) in scientific notation?
    8·2 answers
  • A small television costs $150. if the sales tax is 6%, what is the total cost
    7·1 answer
  • How can you use estimation to find<br> 92 +91 +92 +91 +9?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!