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
weeeeeb [17]
4 years ago
15

Use the divergence theorem to calculate the surface integral z s ~f d~s ; that is, calculate the ux of ~f across s, where ~f = z

~i + y~j + zx~k; and s is the surface of the tetrahedron enclosed by the coordinate planes and the plane x a + y b + z c = 1 with a; b; c > 0.
Mathematics
1 answer:
MAXImum [283]4 years ago
7 0
By the divergence theorem,

\displaystyle\iint_S\mathbf f\cdot\mathrm d\mathbf S=\iiint_R(\nabla\cdot\mathbf f)\,\mathrm dV

where R is the solid whose boundary is S. We have

\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial zx}{\partial z}=1+x

so we set up the volume integral as

\displaystyle\iiint_R(\nabla\cdot\mathbf f)\,\mathrm dV=\int_{x=0}^{x=1/a}\int_{y=0}^{y=(1-ax)/b}\int_{z=0}^{z=(1-ax-by)/c}(1+x)\,\mathrm dz\,\mathrm dy\,\mathrm dx
=\dfrac{4a+1}{24a^2bc}
You might be interested in
Someone help me plzzz:((((
mash [69]

Step-by-step explanation:

OI= 3.2 cm (same as OH)

To find GI, use Pythagoras Theorem (a²+b²= c²)

6.8²+3.2²= 56.48

√56.48= 7.5 cm

hope it helps! please mark me brainliest

thank you! have a good day ahead

if u follow me, i will follow u back

3 0
3 years ago
Read 2 more answers
In a school there are 600 teachers ad 1200 students
8_murik_8 [283]

Answer:

Can you please give a clearer explanation of what is your question?

Step-by-step explanation:

8 0
3 years ago
Which set of numbers is the most reasonable to describe the temperature in alaska during the winter?
Zielflug [23.3K]
The rational numbers are the positive counting numbers: 1, 2, 3, 4, . . .

The whole number are the natural numbers plus 0: 0, 1, 2, 3, . . .

The irrational numbers are the numbers which cannot be expressed in the form a/b where a and b are integers. They are usually in the form of a non recurring and non terminating decimals.

The integers complices of both the negative and the positive whole numbers.

In winter, the temperature of Alaska usually drop to negative numbers.

Therefore, the <span>set of numbers is the most reasonable to describe the temperature in alaska during the winter is the set of integers.</span>
5 0
3 years ago
Read 2 more answers
In 10 seconds, Lauren counts 5 vehicles passing by her house. At that rate, how many vehicles would pass by in one hour?
Anna007 [38]
6 x 60 x 5 would be the equation and all of that put together would be 1,800 vehicles would pass by in an hour.
7 0
4 years ago
((PLEASE ANSWER WITH A B C or D))
natali 33 [55]

Answer:

  D.  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...

  Sin = Opposite/Hypotenuse

  sin(M) = ON/OM = 4(√3)/8 = (√3)/2

  M = sin⁻¹((√3)/2) = 60°

8 0
3 years ago
Other questions:
  • The box and whisker plot displays a set of data obtained from a marketing survey. Drag each item to the appropriate position on
    15·1 answer
  • Metric System Conversion. The thickness of a dollar bill is 0.10414 mm. Convert this value to inches.532
    15·1 answer
  • Two consecutive positive integers have a<br>product of 6. What are the integer?​
    12·2 answers
  • In the right triangle shown,
    5·1 answer
  • In a 30-60-90 triangle, the length of the hypotenuse is 17. Find the length of the side opposite the 30 degree angle.
    6·1 answer
  • A line passes through the point (–7, 5) and has a slope of One-half. Which is another point that the line passes through?
    11·2 answers
  • Plsss help I’ll give u brainlest and 10 points
    11·1 answer
  • In the equation y=1/2x-3, what is the y-intercept? *
    9·2 answers
  • (5 - 2i) + (-4 + 81)<br> O A. 5i<br> B. 7i<br> O c. 1-6<br> D. 1 + 6
    14·2 answers
  • 4. Give an example of a like term for each of the following: a. 144 b. -95 c. 200 d. h²​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!