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
PtichkaEL [24]
2 years ago
8

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

ctor field is not conservative, enter dne.) f(x, y, z) = ye−xi + e−xj + 2zk
Mathematics
1 answer:
Akimi4 [234]2 years ago
8 0
A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is \mathbf 0. We have

\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k

so this vector field is not conservative.

- - -

Another way of determining the same result: We want to find a scalar function f(x,y,z) such that its gradient is equal to the given vector field, \mathbf f(x,y,z):

\nabla f(x,y,z)=\mathbf f(x,y,z)

For this to happen, we need to satisfy

\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}

From the first equation, integrating with respect to x yields

f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)

Note that g *must* be a function of y,z only.

Now differentiate with respect to y and we have

f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots

but this contradicts the assumption that g(y,z) is independent of x. So, the scalar potential function does not exist, and therefore the vector field is not conservative.
You might be interested in
The degree of the expression 4x^5y^m is 10 what is the value of m
Gala2k [10]

Answer: 5

Step-by-step explanation:

The degree is 5+m. Setting this equal to 10, we get m = 5.

4 0
1 year ago
Given the function w (x) = 9x + 8, evaluate w (5) . Explain all steps.
masya89 [10]

Hi there!

\large\boxed{w(5) = 53}

Evalute by substituting in 5 for x:

w(5) = 9(5) + 8

Simplify:

w(5) = 45 + 8 = 53

7 0
2 years ago
Read 2 more answers
Which is enough information to prove that s is parallel to T? Help faaast first answer gets brainliest!!!!
sdas [7]

Answer:

the answer you picked in the pictures is the correct one

6 0
2 years ago
I need help can anyone help me on this pls?
Ksenya-84 [330]

Answer:

Multiply 6 x 4 then add 10

or do the other way around

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Use the model to create zero pairs. What is an equivalent expression that has two terms?
ioda

Answer:

x+1

Step-by-step explanation:

just did it all you have to do is put that in and you got it write

6 0
3 years ago
Read 3 more answers
Other questions:
  • A box contains 4 red pencils and 6 black pencils. What fraction of the pencils are red write two equivalent fractions
    5·2 answers
  • Juno calculated the area of a square to be 4/9 square yard. Which shows the side length of the square?
    10·1 answer
  • Find the area of the figure <br> A)75in^2<br> B)70in^2<br> C)65in^2<br> D)80in^2
    10·1 answer
  • Sam is building a dog kennel. He wants the kennel to be 8 ft long and 4 ft wide. If a scale drawing of the kennels length is 2 i
    12·1 answer
  • Deep mixing is a ground improvement method developed for soft soils like​ clay, silt, and peat. Civil engineers investigated the
    11·1 answer
  • 50 POINTS I need a answer fast
    13·1 answer
  • The low temperature was 35f. this was 13f lower than the daytime high temperature. write an equation to determine whether the hi
    14·2 answers
  • If cot x = .78, what is tan x
    15·1 answer
  • What is definition of and INDEPENDENT Vairable?
    10·2 answers
  • Find the rate change
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!