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
Fittoniya [83]
4 years ago
15

Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of

f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 10 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2
Mathematics
1 answer:
Flura [38]4 years ago
6 0
\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+10\,\mathbf k
\implies\nabla\cdot\mathbf f(x,y,z)=1+1+0=2

By the divergence theorem, the surface integral along S is equivalent to the triple integral over the region R bounded by S:

\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=2\iiint_R\mathrm dV

Convert to cylindrical coordinates, setting

\begin{cases}x=r\cos\theta\\y=Y\\z=r\sin\theta\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dY

The triple integral is then equivalent to

=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{Y=0}^{Y=2-r\cos\theta}r\,\mathrm dY\,\mathrm dr\,\mathrm\theta
=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r(2-r\cos\theta)\,\mathrm dr\,\mathrm\theta
=\displaystyle\frac23\int_{\theta=0}^{\theta=2\pi}(3-\cos\theta)\,\mathrm dr\,\mathrm\theta
=4\pi
You might be interested in
Write two ratios that are equivalent to 9/12
sergij07 [2.7K]
3/4 and 18/24 because if you divide 9 and 12 by 3 you get 3/4 and when you multiply 9/12 by 2 you get 18/24
5 0
4 years ago
Read 2 more answers
1 cm - 125 miles
s344n2d4d5 [400]

Answer:

412.5

Step-by-step explanation:

If 1cm = 125 miles, then 3.3cm = 412.5

3 0
3 years ago
Which statement best explains the value of 16-(-3)
Alja [10]

Answer: 48

Step-by-step explanation:

It is the negative of 16 times the negative of 3.

Not sure if this is the answer but I hope it helps!

3 0
3 years ago
Read 2 more answers
Which represents the inverse of the function f(x) = 4x?
fiasKO [112]

Answer:

<h3>h(x) = 1/2x </h3>

  • f(x) = 4x
  • 4x/2=2x

<h3>So,h(x) = 1/2x</h3>
6 0
3 years ago
Find the x - and y -intercepts of the graph of the linear equation -4x+8y=-16 .
Sav [38]

Answer:

  • x: (4, 0)
  • y: (0, -2)

Step-by-step explanation:

To find the x-intercept, set y=0 and solve for x. That will mean dividing by the coefficient of x:

  -4x +0 = -16

  x = -16/-4 = 4 . . . . the x-intercept

__

To find the y-intercept, set x=0 and solve for y. That will mean dividing by the coefficient of y:

  0 +8y = -16

  y = -16/8 = -2 . . . . the y-intercept

__

The x- and y-intercepts are (4, 0) and (0, -2), respectively.

_____

<em>Additional comment</em>

The standard form equation of a line, ax+by=c, is especially nice for finding the intercepts, as they are always (c/a, 0) and (0, c/b). Once you see this, you can do a question like this in your head.

6 0
3 years ago
Other questions:
  • ILL GIVE BRAINLIEST TO WHOEVER Can answer this I’ve been stuck on this for a while :(( solve for x
    14·2 answers
  • How to find the fraction equivalent of each. show your work
    13·1 answer
  • Order the fractions from least to greatest 2/3 2/9 5/6 11/8
    7·1 answer
  • Find the GCF of 18a and 20ab (and please explain why your answer is what it is)
    8·2 answers
  • ..............,...............
    14·2 answers
  • If an object is dropped from a height of 144 feet, the function h(t) = -16t2 + 144 gives the height of the object after t second
    5·2 answers
  • 6) Stanton ate 32 jelly beans. This is 8 times the
    13·1 answer
  • Bill measures the circumference of a circular fish pond to be 28ft.
    6·1 answer
  • Alternate exterior angles ​
    6·1 answer
  • Plz help-<br> I don't wanna fail math-<br> again...
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!