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PtichkaEL [24]
3 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]3 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.
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10) Solve using any method<br> 10x+2y=42<br> 5x+y=20
KIM [24]

Answer:

no solutions

Step-by-step explanation:

10x+2y=42

5x+y=20

Multiply the second equation by -2 to use elimination

-2(5x+y)=20*-2

-10x -2y = -40

Add this to the first equation

10x+2y=42

-10x -2y = -40

--------------------------

0 = 2

This is never true.  This means there are no solutions

3 0
3 years ago
Read 2 more answers
Select the tables that show a proportional relationship between x and
forsale [732]

Answer:

213`334

Step-by-step explanation:

sry lol i want points i apologize

4 0
3 years ago
Mrs.Cranston bought five bottles of water for $0.90 each and 8 pounds of meat. She paid a total of $26.90 for these items, not i
Morgarella [4.7K]
Water = 5 bottles * $0.90 = $4.50
meat = 8 pounds * x amount.

Total = water + meat prices = $26.90
26.90 = $4.50 + 8x
22.40 = 8x
2.8 = x

The price per pound of meat is $2.80.
6 0
3 years ago
An epidemiologic survey of roller-skating injuries in Metroville, a city with a population of 100,000 (during the midpoint of th
Ahat [919]

Answer: c. \dfrac{90}{1800}\times100\%

Step-by-step explanation:

As per given , we have

Total number of residents injured from roller-skating =1,800

Total number of deaths from roller-skating = 90

Formula for Mortality rate : Mortaility\ rate= \dfrac{Deaths\ due \ to\ injury}{Tota\ injuries}

Then, the proportional mortality ratio (%) due to roller-skating was

=\dfrac{90}{1800}\times100\%

= 5%

Hence, the correct answer is c.\dfrac{90}{1800}\times100\%

8 0
3 years ago
Evaluate math pls help algebra
Free_Kalibri [48]

Answer:

A. -10

B. -1

C. 5

Step-by-step explanation:

A. 3x-4 = 3(-2)-4 = -10

B. 3x-4 = 3(1)-4 = -1

C. 3x-4 = 3(3)-4 = 5

3 0
3 years ago
Read 2 more answers
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