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Best_Mathematician

Calculus challenge

  • one year ago
  • one year ago

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  1. Best_Mathematician
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    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

    • one year ago
  2. Best_Mathematician
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    ok

    • one year ago
  3. Best_Mathematician
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    then

    • one year ago
  4. modphysnoob
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    once you find two x values , they are your answer for a)

    • one year ago
  5. Best_Mathematician
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    is x two negative values

    • one year ago
  6. modphysnoob
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    is x squred?

    • one year ago
  7. Best_Mathematician
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    ya here is the equation again \[\frac{ x^2 }{ 4 } + y^2 = 1\]

    • one year ago
  8. modphysnoob
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    ahh, that's different, this is ellipse x^2/4 + (y-3)^2 = 1

    • one year ago
  9. modphysnoob
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    now plug in y=3, x^2/4=1 x^2=4 x=2,-2 that's your part a

    • one year ago
  10. Best_Mathematician
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    sweet ur r doing grt go ahead

    • one year ago
  11. modphysnoob
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    part b is graphing,

    • one year ago
  12. dlipson1
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    Here's the graph, done without benefit of the above

    • one year ago
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  13. Best_Mathematician
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    i wud just graph that right

    • one year ago
  14. Best_Mathematician
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    oh thx @dlipson1 can u go further

    • one year ago
  15. dlipson1
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    Uh oh, I think that's a line integral, I'd have to look that up. Do you know anything about Stochastic Optimization?

    • one year ago
  16. Best_Mathematician
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    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

    • one year ago
  17. dlipson1
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    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.

    • one year ago
  18. Best_Mathematician
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    so from negative 2 to 2...right

    • one year ago
  19. dlipson1
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    Yeah, use the top half, y = sqrt(...), then (I just looked it up): Length = integral (sqrt(1+(y')^2))dy

    • one year ago
  20. Best_Mathematician
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    ya and what kinda graphing calculator r u using dude

    • one year ago
  21. dlipson1
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    http://www.padowan.dk/ and Google --> http://tutorial.math.lamar.edu/Classes/CalcII/ArcLength.aspx

    • one year ago
  22. Best_Mathematician
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    thx...getting my next question...i wud give u a lot of awards but unfortunately this site doesnt aloow lol

    • one year ago
  23. dlipson1
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    "Graph" (from padowan.dk) gives me the curve length of 4.882, then +3+3 +4 for the entire perimeter.

    • one year ago
  24. Best_Mathematician
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    sweet thanks

    • one year ago
  25. Best_Mathematician
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    hey @dlipson1 one more thing, how wud we find area on top of the toast

    • one year ago
  26. dlipson1
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    The rectangle + 2*integral (by symmetry) from 0 to 2 of y = sqrt(1-x^2/4)... hmm, do we need substitution here?

    • one year ago
  27. Best_Mathematician
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    do u need the derivative...i have it

    • one year ago
  28. Best_Mathematician
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    -x/(4y-12)....now wht to do

    • one year ago
  29. dlipson1
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    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

    • one year ago
  30. dlipson1
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    Here is almost the same problem: http://www.youtube.com/watch?v=PSlsj0IP8R8

    • one year ago
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