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
taurus [48]
3 years ago
11

Determine whether or not the vector field is conservative. if it is, find a function f such that f = ∇f. if the vector field is

not conservative, enter none. f(x, y, z) = 3y2z3 i + 6xyz3 j + 9xy2z2 k
Mathematics
1 answer:
amm18123 years ago
7 0
\dfrac{\partial f}{\partial x}=3y^2z^3\implies f(x,y,z)=3xy^2z^3+g(y,z)

\dfrac{\partial f}{\partial y}=6xyz^3+\dfrac{\partial g}{\partial y}=6xyz^3
\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)

\dfrac{\partial f}{\partial z}=9xy^2z^2+\dfrac{\mathrm dh}{\mathrm dz}=9xy^2z^2
\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C

\implies f(x,y,z)=3xy^2z^3+C

The potential function exists, so \mathbf f is indeed conservative.
You might be interested in
A certificate of deposit has an annual simple interest rate of 5.25%. If $567 in interest is earned over a 6 year period, how mu
Scrat [10]
Find the the amount of interest per year. Since $567 were earned over 6 years, you divide the interest earned by the number of years it took to accumulate it:

$567/6 years = $94.5/year

Divide that by the interest rate which the interest rate needs to be in decimal form:

$94.5/.0525 = $1800
4 0
3 years ago
What is the answer to 9 over 15= 3 over 5
Ksenya-84 [330]

Answer:

2 25/100

Step-by-step explanation:

9 times 15 divided by 3 times 5

5 0
3 years ago
The scale drawing of a rectangular oty park measures 10.0 cm by 50 cm
satela [25.4K]
The answer is 2... I think idrk 2 second ago was I thinking abt Damon Salvatore bunt GOOD LUCK!!!
6 0
3 years ago
The diameter of a circle is 14 m. Find its area in terms of \piπ.
Lena [83]
43.96 is what i got! im sorry if i got it wrong
6 0
3 years ago
Read 2 more answers
Assuming that there are no hidden cubes, what is the front orthographic view of the diagram?
Makovka662 [10]

Answer:

the visible number of cubes is 7

Step-by-step explanation:

Assuming that there are no hidden cubes, the # of visible cubes is 7

7 0
2 years ago
Other questions:
  • Find the x- and y-intercepts. Put in ordered pairs. 5x+9y=18-(x+y)
    14·1 answer
  • Solve for y in simplest form: y^2+3y-4=0
    14·2 answers
  • What is the value of each digit in this number 58
    10·2 answers
  • Select all units that can be used for surface area.
    13·2 answers
  • (3x-4)^2(x-3) i need help simplyfind this equation
    10·1 answer
  • 900,000 divided by 1,000
    12·1 answer
  • Write the expression a 15 as a product of two exponents with the same base, one of
    9·1 answer
  • Convert 111110 base two to base eight​
    9·1 answer
  • Help!!! be quick
    7·1 answer
  • Pls help, i will give brainliest:
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!