Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Best_Mathematician

  • one year ago

Calculus challenge

  • This Question is Closed
  1. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The type of bread chosen for this special calculus toast isn't the square sandwich shape, but the kind that is curved across the top. Imagine that the toast is composed of the curved part sitting atop the rectangular portion. The equation of the curved part of the toast is x2/4 + y2 = 1, and it sits directly and perfectly on top of a rectangle of height 3 inches. a) What are the equations of the rectangular boundaries? b) Graph the toast boundaries, making certain to include screen shots of the boundary equations, Window settings, and the graph. c) How would you find the length of the curve

  2. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  3. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then

  4. modphysnoob
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    once you find two x values , they are your answer for a)

  5. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is x two negative values

  6. modphysnoob
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is x squred?

  7. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya here is the equation again \[\frac{ x^2 }{ 4 } + y^2 = 1\]

  8. modphysnoob
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ahh, that's different, this is ellipse x^2/4 + (y-3)^2 = 1

  9. modphysnoob
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now plug in y=3, x^2/4=1 x^2=4 x=2,-2 that's your part a

  10. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sweet ur r doing grt go ahead

  11. modphysnoob
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    part b is graphing,

  12. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here's the graph, done without benefit of the above

    1 Attachment
  13. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i wud just graph that right

  14. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh thx @dlipson1 can u go further

  15. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?

  16. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey hey hey never mind...i know how to find the length of the curve thanks..but i dont knw do i need to find length of whole curve or just the bread as in ur graph

  17. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, the rectangle is trivial (is the side along the x-axis included?), the top is just half the ellipse, that's the only real calculus (integration) you have to do.

  18. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so from negative 2 to 2...right

  19. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy

  20. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya and what kinda graphing calculator r u using dude

  21. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.padowan.dk/ and Google --> http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

  22. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thx...getting my next question...i wud give u a lot of awards but unfortunately this site doesnt aloow lol

  23. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "Graph" (from padowan.dk) gives me the curve length of 4.882, then +3+3 +4 for the entire perimeter.

  24. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sweet thanks

  25. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey @dlipson1 one more thing, how wud we find area on top of the toast

  26. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1-x^2/4)... hmm, do we need substitution here?

  27. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do u need the derivative...i have it

  28. Best_Mathematician
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -x/(4y-12)....now wht to do

  29. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm not sure dy/dx helps. I set up the integral, thought about a trig. substitution, multiplied through by the 2 (as sqrt(4)) to get int(sqrt(4-x^2))dx, which I found here, but I think there must be an easier way (like polar coordinates): http://answers.yahoo.com/question/index?qid=20071231235113AAAAfuP

  30. dlipson1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is almost the same problem: http://www.youtube.com/watch?v=PSlsj0IP8R8

  31. 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.