Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Insanity

  • 3 years ago

1) Find the flux of the vector field F(x,y,z) = (e^-y) i - (y) j + (x sinz) k across σ wit outward orientation where σ is the portion of the elliptic cylinder r(u,v) = (2cos v) i + (sin v) j + (u) k with 0 ≤ u ≤ 5, 0 ≤ v ≤ 2pi. 2) Find the work done by the force field F(x, y, z) = (x + y) i + (xy) j - (z^2) k on a particle that moves along line segments from (0,0,0) to (1,3,1) to (2,-1,4).

  • This Question is Closed
  1. Mathematics_pro
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry wat 2 high 4 me

  2. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits{\int\limits{s F dS}} = ∫∫∫v ∇·F dV\] \[∇·F = x \cos(z) - 1\] \[= ∫∫∫v x \cos(z) - 1 dx dy dz\] \[v: x² + 4y² ≤ 4 ; 0 ≤ z ≤ 5\] let u = x , v = 2y , z = z ∂(u,v)/∂(x,y) = 2 = 1/2 ∫∫∫v u cos(z) - 1 du dv dz v: u² + v² ≤ 4 ; 0 ≤ z ≤ 5 let u = r cos(theta) ; v = r sin(theta) z = z \[\frac{∂(u,v)}{∂(r,θ)} = r\] \[= 1/2 ∫∫∫ (r \cos(θ) \cos(z) - 1) r dr dθ dz\] \[{(r,θ,z) | 0 ≤ r ≤ 2 ; 0 ≤ θ ≤ 2π ; 0 ≤ z ≤ 5}\] \[= 1/3 ∫∫ (4 \cos(θ) \cos(z) - 3) dθ dz\] \[{(θ,z) | 0 ≤ θ ≤ 2π ; 0 ≤ z ≤ 5}\] \[= -2π ∫ dz\](z) | 0 ≤ z ≤ 5 \[= -10π\]

  3. Mathematics_pro
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh 2 smaalllllllll

  4. Insanity
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you know the second one

  5. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is the first one right? or u dont know tha answer?

  6. Insanity
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im just checking what i got wrong on my hw and yeah the answer is right

  7. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh ok im thinkin

  8. Insanity
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    k thanks lana :)

  9. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (0,0,0) -->> (1,3,1) x = t y = 3t z = t dx =dt........ dy = 3 dt...... dz = dt work done is integration of F.dr int{ (x + y)dx + (xy)dy - (z^2) dz

  10. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now substitute x=t y=3t and z=t and the dx dy and dz values in terms of dt

  11. lalaly
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then integrate

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.