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
lapo4ka [179]
3 years ago
7

Consider the following region R and the vector field F. a. Compute the​ two-dimensional curl of the vector field. b. Evaluate bo

th integrals in​ Green's Theorem and check for consistency. Bold Upper F equals left angle negative x comma negative y right angle​; Upper R equals StartSet (x comma y ): x squared plus y squared less than or equals 5 EndSet a. The​ two-dimensional curl is 0. ​(Type an exact​ answer.) b. Set up the integral over the region R. Write the integral using polar​ coordinates, with r as the radius and theta as the angle. Integral from 0 to nothing Integral from 0 to nothing (nothing )r font size decreased by 3 dr font size decreased by 3 d theta ​(Type exact​ answers.)
Mathematics
1 answer:
Shalnov [3]3 years ago
7 0

Looks like we're given

\vec F(x,y)=\langle-x,-y\rangle

which in three dimensions could be expressed as

\vec F(x,y)=\langle-x,-y,0\rangle

and this has curl

\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle

which confirms the two-dimensional curl is 0.

It also looks like the region R is the disk x^2+y^2\le5. Green's theorem says the integral of \vec F along the boundary of R is equal to the integral of the two-dimensional curl of \vec F over the interior of R:

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of R by

\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle

\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt

with 0\le t\le2\pi. Then

\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt

=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0

You might be interested in
Which inequality explains why these three segments cannot be used to construct a triangle?​
Anna11 [10]

Answer:

Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side. Iliana cannot construct a triangle because the sum of the two smaller sides will be greater than the third side.

5 0
2 years ago
A TV has a listed price of $608.98 before tax. If the sales tax rate is 9.75%, find the total cost of the TV with sales tax incl
Juliette [100K]

Answer:

the total cost is $705.77

Step-by-step explanation:

3 0
2 years ago
Can somebody help me please first person to asnwer gets brainliest
garri49 [273]

Answer:

a= 15

a18= 267

Step-by-step explanation:

5 0
2 years ago
Which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8
Gnom [1K]
The correct equation is 8.7 + b = 54.6
because it is given that measure of side a is 8.7cm, in all other equations the values of a is different.
from the first equation we can find the value of b, that is
b = 54.6 - 8.7 = 45.9
so, value of b is 45.9cm
5 0
2 years ago
Find the 16th term for the sequence a (n)=3-2n.
Scilla [17]
In the expression given, the "n" is referring to a certain term, in this case, it would be the 16th term. So in order to find the 16th term, all you have to do is substitute n as 16 in the expression, so the answer is a(n)=3-2(16)=3-32=-29. So the 16th term of the sequence is -29.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Frank finished 65% of his math homework before dinner. If this amount represents 26 problems,How many problems will Frank need t
    14·1 answer
  • You are making fruit baskets using 54 apples, 36 oranges, and 73 bananas. a. Explain why you cannot make identical fruit baskets
    11·1 answer
  • Find the slope of the line through (–9, –10) and (–2, –5). A. –five-sevenths B. seven-fifths C. five-sevenths D. –negative seven
    12·1 answer
  • Target sells 24 bottles of water for $3, and 36 bottles of water for $4. Which is the better buy and by how much?
    14·1 answer
  • The value 5pi/24 is a solution for the equation 4 cos^2 (4x)-3=0. True or false
    12·1 answer
  • WHY ISNT ANYBODY ANSWERING MY QUESTION PS HELP MEEEEE I ALWAYS GIVE BRAINLIEST 5 STARS andddd offer 25 pointsssssssssss plsss he
    14·1 answer
  • 1.Choose the best description for ∠1 and ∠2 in the following figure.
    5·1 answer
  • What is the surface area of the pyramid? 3 6​
    12·1 answer
  • Find the value of x,
    8·1 answer
  • (02.06)A local store has a puppy that weighs 56 ounces. How many pounds does the puppy weigh, given that 1 pound = 16 ounces? (I
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!