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
babunello [35]
3 years ago
10

Let m be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2+y2=49, 0≤z≤1, and a hemispher

ical cap defined by x2+y2+(z−1)2=49, z≥1. for the vector field f=(zx+z2y+8y, z3yx+5x, z4x2), compute ∬m(∇×f)⋅ds in any way you like.
Mathematics
1 answer:
maxonik [38]3 years ago
3 0

It seems that the boundary of M is the circle x^2+y^2=49 in the plane z=0. By Stokes' theorem,

\displaystyle\iint_M(\nabla\times\vec f)\cdot\mathrm d\vec S=\int_{\partial M}\vec f\cdot\mathrm d\vec r

Parameterize \partial M by

\vec r(t)=(7\cos t,7\sin t,0)

with 0\le t\le2\pi. Then the line integral is

\displaystyle\int_{\partial M}\vec f(x(t),y(t),z(t))\cdot\mathrm d\vec r=\int_0^{2\pi}(56\sin t,35\cos t,0)\cdot(-7\sin t,7\cos t,0)\,\mathrm dt

=\displaystyle\int_0^{2\pi}(245\cos^2t-392\sin^2t)\,\mathrm dt=\boxed{-147\pi}

You might be interested in
Solve for x -x + 2 = 4
andreev551 [17]

Answer:

-2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Simplify in Exponential form <br> First correct answer gets BRAINLIEST
svlad2 [7]

Answer:

Steps to simplifying fractions

Therefore, 9/9 simplified to lowest terms is 1/1.

Reduce 9/8 to lowest terms

9/8 is already in the simplest form. It can be written as 1.125 in decimal form (rounded to 6 decimal places).Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the product? Enter your answer as a fraction, in simplified form, in the box. −4/5⋅10/16
Pie
-40/80 = -1/2
since when you’re multiplying fraction, you multiply the top by the top number and bottom by the bottom number. So -4 • 10 is -40 and 5 • 16 is 80. -40/80, simplified is -1/2.
7 0
3 years ago
Read 2 more answers
What is 96-8c=20-12
galben [10]

Answer:

c = 11

Step-by-step explanation:

96 - 8c = 20 - 12 , that is

96 - 8c = 8 ( subtract 96 from both sides )

- 8c = - 88 ( divide both sides by - 8 )

c = 11

5 0
2 years ago
Help me please in my module​
Ghella [55]

Answer:

1.(b)

2.(b)

3. (d) 4cm

4.(a)

Explanation :

The polygons will have the same shape and size, but one may be a rotated, or be the mirror image of the other.Polygons are congruent when they have the same number of sides, and all corresponding sides and interior angles are congruent.

5 0
3 years ago
Other questions:
  • Betty had $40 in her pocket. She bought 12 identical bags of popcorn. Betty was left with $10 after buying the popcorn. What was
    5·2 answers
  • PLS HELP WILL MARK BRAINLEIST​
    6·2 answers
  • What is the percent increase from 5 to 9
    5·1 answer
  • Find the product<br> .<br> -1(6) =<br> 1
    5·1 answer
  • The Sugar Sweet Company is going to transport its sugar to market. It will cost
    6·1 answer
  • A binomial random variable X is defined as the number of successes achieved in the n trials of a Bernoulli process. Describe an
    9·1 answer
  • Volume equals length times width times height v=lwh<br> solve the equation for l
    9·1 answer
  • What is cosA ?<br><br><br><br> Enter your answer, as a simplified fraction, in the box.
    13·1 answer
  • What is the area of sector below
    13·1 answer
  • Flying against the wind, an airplane travels 2520 kilometers in 4 hours. Flying with the wind, the same plane travels 9450 kilom
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!