Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathstina Group Title

At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    find the gradient of the surface

    • 2 years ago
  2. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    <2,-1,2>

    • 2 years ago
  3. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    grad f=<2x, -1, 2z>

    • 2 years ago
  4. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • 2 years ago
  5. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ok, now since we can't plug in anything that will change y, let's multiply the gradient by a scalar to get the j-component equal to 2 like it is for the plane

    • 2 years ago
  6. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    multiply by -2

    • 2 years ago
  7. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    right, and so we get?

    • 2 years ago
  8. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    grad f=<-4x,2y, -4z>

    • 2 years ago
  9. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    grad f=<-4x,2,-4z> that y can't just appear from nowhere

    • 2 years ago
  10. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so what value of x makes the i-components equal for the plane and grad f ? what value of z makes the k-components equal?

    • 2 years ago
  11. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x=1/2and z= 3/2 ???

    • 2 years ago
  12. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    from the equation as we have it we need x=-1/4 and z=-3/4

    • 2 years ago
  13. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok.

    • 2 years ago
  14. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    that's all then... boring problem

    • 2 years ago
  15. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    why qns with sphere have 2 sets of points?

    • 2 years ago
  16. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    hm... seems strange that y does not matter. Maybe I messed this one up :P

    • 2 years ago
  17. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    sorry? what do you mean?

    • 2 years ago
  18. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    for qns with sphere has 2 sets of points as ans why?

    • 2 years ago
  19. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    what do you mean it has 2 sets of points?

    • 2 years ago
  20. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the ans fot this qn is (-1/4, -2,-3/4)

    • 2 years ago
  21. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    the way we did it it looks like y does not matter, so (-1/4,y,-3/4) seems strange that y does not matter though, maybe I made a mistake... not sure

    • 2 years ago
  22. mathstina Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so the point for y is 0 or -1?

    • 2 years ago
  23. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    neither, the result says y can be anything, so just write y=y

    • 2 years ago
  24. amistre64 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    isnt y a function if x and z to begin with? y = x^2 + z^2; therefore y=1/4

    • 2 years ago
    • Attachments:

See more questions >>>

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.