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
ira [324]
3 years ago
8

Use the surface integral in​ Stokes' Theorem to calculate the circulation of the field Bold Upper F equals x squared Bold i plus

4 x Bold j plus z squared Bold k around the curve​ C: the ellipse 16x squared plus 4 y squared equals 3 in the​ xy-plane, counterclockwise when viewed from above.
Mathematics
1 answer:
Alinara [238K]3 years ago
3 0

Answer:

The circulation of the field f(x) over curve C is Zero

Step-by-step explanation:

The function f(x)=(x^{2},4x,z^{2}) and curve C is ellipse of equation

16x^{2} + 4y^{2} = 3

Theory: Stokes Theorem is given by:

I= \int \int\limits {{Curl f\cdot \hat{N }} \, dx

Where, Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]

Also, f(x) = (F1,F2,F3)

\hat{N} = grad(g(x))

Using Stokes Theorem,

Surface is given by g(x) = 16x^{2} + 4y^{2} - 3

Therefore, tex]\hat{N} = grad(g(x))[/tex]

\hat{N} = grad(16x^{2} + 4y^{2} - 3)

\hat{N} = (32x,8y,0)

Now,  f(x)=(x^{2},4x,z^{2})

Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\F1&F2&F3\end{array}\right]

Curl f(x) = \left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\\frac{∂}{∂x} &\frac{∂}{∂y} &\frac{∂}{∂z} \\x^{2}&4x&z^{2}\end{array}\right]

Curl f(x) = (0,0,4)

Putting all values in Stokes Theorem,

I= \int \int\limits {Curl f\cdot \hat{N} } \, dx

I= \int \int\limits {(0,0,4)\cdot(32x,8y,0)} \, dx

I= \int \int\limits {(0,0,4)\cdot(32x,8y,0)} \, dx

I=0

Thus, The circulation of the field f(x) over curve C is Zero

You might be interested in
A High School is currently 700 students and increases at an annual rate of 3.5% per year
Cerrena [4.2K]

Answer:

f(t)  = 700(1.035)^t.

Step-by-step explanation:

Initial value is given as 700 students and this corresponds to time t = 0.

The growth factor is 1 plus 3.5% = 1.035.

The time t is in years.

7 0
3 years ago
So I have to finish this and I have no idea How to do it. Please Help.
Zina [86]

Answer:

25 bc I mena I did count the scares but then I took the ones that weren’t fully squares and counted them as a quarter and that’s what I got not sure don’t trust meh bc I just guess this

Step-by-step explanation:

8 0
3 years ago
In a random sample of 16 residents of the state of Washington, the mean waste recycled per person per day was 2.8 pounds with a
kakasveta [241]

Answer: The required confidence interval would be (2.72,2.89)

Step-by-step explanation:

Since we have given that

Mean = 2.8 pounds

Standard deviation = 0.24 pounds

n = sample size = 16

We need to find the 80% confidence interval for the mean waste.

z=1.341

So, the confidence interval will be

\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=(2.8\pm 1.341\times \dfrac{0.24}{\sqrt{16}})\\\\=(2.8\pm 1.314\times 0.06)\\\\=(2.8-0.07884,2.8+0.07884)\\\\=(2.72116,2.87884)

Hence, the required confidence interval would be (2.72,2.89)

4 0
3 years ago
Simplify by using the distributive property: ​
lesya692 [45]
12. 4(s+5)
4s+20

15. 2(3r-12)
6r-24

18. -3(16-3d)
9d-48
3 0
3 years ago
How many square inches does an "11x13" area encompass
Juliette [100K]
143 square inches         <span> </span>
3 0
4 years ago
Read 2 more answers
Other questions:
  • Emma sells jewelry online. She has found that when she sells each piece of jewelry for $20, she sells an average of 23 pieces of
    13·1 answer
  • Solve the system of equations and choose the correct answer from the list of options. x − y = 7 y = 3x + 12 2 over 19 comma 2 ov
    7·1 answer
  • The graph shows equivalent ratios. Frank plotted another point with a y-value of 18. What is the x-value of that point?
    6·1 answer
  • Suppose you got 3 out every 4 questions correct on your homework. How many total questions were on the homework if you got 12 qu
    13·1 answer
  • 5[x-3(x-3)]<br> Simplify
    7·1 answer
  • Slope intercept of (6,-2) and (12,1)
    9·1 answer
  • Story problem to represent 6 divided by 1/5
    11·1 answer
  • True or false question<br> please help
    10·2 answers
  • HELP ILL GIVE BRAINLIEST
    15·1 answer
  • Tell whether the ratios form a proportion.<br><br> 2/5,40/16
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!