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
pochemuha
3 years ago
10

Se the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x2

yi + xy2j + 5xyzk, s is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x + 4y + z = 4. 1104 125​ incorrect: your answer is incorrect.
Mathematics
1 answer:
zalisa [80]3 years ago
7 0

f(x,y,z)=x^2y\,\vec\imath+xy^2\,\vec\jmath+5xyz\,\vec k

\implies\nabla\cdot f=2xy+2xy+5xy=9xy

The plane has intercepts in the x,y plane at (4, 0, 0) and (0, 1, 0), so the flux is given by (via the divergence theorem)

\displaystyle\iint_Sf\cdot\mathrm dS=9\int_{x=0}^{x=4}\int_{y=0}^{y=1}\int_{z=0}^{z=4-x-4y}xy\,\mathrm dz\,\mathrm dy\,\mathrm dx=-48

You might be interested in
Find the point of intersection (if any) of the following pairs of lines: a) x – 2y +1=0 2x + 3y – 7 = 0 b) x-2y+11=0 -x+2y-13 =
pychu [463]

Answer:

a) (11/7, 9/7)

b) There's no point of intersection

Step-by-step explanation:

a) x - 2y + 1 = 0

2x + 3y - 7 = 0

To find the point of intersection, we need to solve the system of equations  and the result will be the point of intersection (x,y)

x-2y+1=0\\x= 2y-1

Now we substitute x in the second equation:

2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7

Now we substitute y in our first equation.

x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7.

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

-x + 2y - 13 =0

We are going to follow the same procedure:

x-2y+11=0\\x=2y-11

-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2

Since this system of equations doesn't have a solution, the system has no point of intersection.

5 0
3 years ago
Joan has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $6390,
Gekata [30.6K]

It would be something that looks like this:

((6390 * 0.17)/365) x 3


3 0
3 years ago
Read 2 more answers
Will be MARKED AS BRAINLIEST :)Brenda walks dogs after school. She is planning to increase the rate that she charges by 20% in J
krek1111 [17]

Are there answer choices for this one because I got something kind of weird

3 0
3 years ago
Read 2 more answers
I need help please.
lorasvet [3.4K]

Answer:

may it help you..MARK ME AS BRAINLISTS PLS

5 0
3 years ago
What is the value of z for the equation
vitfil [10]
Z= -7
So your answer is number 2, -7
5 0
2 years ago
Other questions:
  • 1.find the quotient and remainder when 133 is divided by 85
    14·1 answer
  • Please answer asap thanks
    12·1 answer
  • Cat este 5 la puterea 5?
    12·1 answer
  • A box contains five red balls, six green ones, and nine yellow balls. Suppose you select one ball at random from the box and do
    10·1 answer
  • Let d be the (shortest) distance between 2 parallel lines with slope 6 whose -intercepts are 8 units apart. Find d^2.
    11·2 answers
  • 40000 is how much greater than 4000
    8·2 answers
  • What is the equation of the line that passes through the point <br> (−4,−3) and has a slope of 3/4?
    5·1 answer
  • 15 POINTS!
    9·2 answers
  • shamillia sent 60 text messages. 15% of those messages were to her mother. how many text messages did shamillia send to her moth
    9·1 answer
  • Leo is building a model
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!