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agentx5

Yikes, need to find the area and the name for these parametric equations: x(t) = a cos(t) (2 cos(2 t)+1) y(t) = a sin(t) (2 cos(2 t)+1) What is...? I don't even...? How? I'll draw the graph....

  • one year ago
  • one year ago

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  1. agentx5
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    Cartesian? Check me please? x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4 |dw:1342133559037:dw|

    • one year ago
  2. agentx5
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    It looks like of like a D-orbital from chemistry, but it's got little lobes on the vertical, so that means it's probably more like some weird F-orbital. :-D Help?

    • one year ago
  3. agentx5
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    \[x^6+3 x^4 (y^2-3)+3 x^2 y^2 (y^2+2)+y^6 = y^4\]

    • one year ago
  4. agentx5
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    I just chose some arbitrary "a" constant to sub.

    • one year ago
  5. mahmit2012
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    |dw:1342133866479:dw|

    • one year ago
  6. agentx5
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    Is that \(\tan t\) @mahmit2012 ? Ty in advance btw, you always seem to be the one who's here to help when I get stuck on these challenge problems :D

    • one year ago
  7. mahmit2012
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    |dw:1342133990522:dw|

    • one year ago
  8. mahmit2012
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    |dw:1342134107025:dw|

    • one year ago
  9. mahmit2012
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    |dw:1342134151837:dw|

    • one year ago
  10. agentx5
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    \(x^2 + y^2 = \text{radius}^2\)

    • one year ago
  11. mahmit2012
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    |dw:1342134219662:dw|

    • one year ago
  12. mahmit2012
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    so a=1

    • one year ago
  13. asnaseer
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    you can see a graph of this using wolfram, e.g.: http://www.wolframalpha.com/input/?i=plot+%7Bx%3Da*cos%28t%29%282cos%282t%29%2B1%29%2C+y%3Da*sin%28t%29%282cos%282t%29%2B1%29%7D+when+a%3D3 your graph is correct :)

    • one year ago
  14. agentx5
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    \(\text{Area} = 3 \pi a^2\), correct ?

    • one year ago
  15. agentx5
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    Whoa cool link there, @asnaseer I didn't know you could do that with Wolfram, that's some pretty fancy syntax :D

    • one year ago
  16. agentx5
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    Does this graph actually have a name though? It's not as if I can just Google the image lol

    • one year ago
  17. mahmit2012
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    |dw:1342134548532:dw|

    • one year ago
  18. mahmit2012
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    |dw:1342134699157:dw|

    • one year ago
  19. mahmit2012
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    |dw:1342134862828:dw|

    • one year ago
  20. mahmit2012
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    |dw:1342134931824:dw|

    • one year ago
  21. agentx5
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    *reading & taking notes* :-3

    • one year ago
  22. mahmit2012
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    origin build with 1+cos2t=0 _> x=0 , y=0 common term between x , y

    • one year ago
  23. mahmit2012
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    |dw:1342135079515:dw|

    • one year ago
  24. mahmit2012
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    |dw:1342135156538:dw|

    • one year ago
  25. mahmit2012
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    is it clear?

    • one year ago
  26. mahmit2012
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    for exactly drawing d/dt=0 for x , y give you some critical points

    • one year ago
  27. agentx5
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    Clear, you are finding the polar lines, basically, where r = 0.

    • one year ago
  28. mahmit2012
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    |dw:1342135317896:dw|

    • one year ago
  29. agentx5
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    We just touched on polar stuff today, this question was from the "challenge" section of the written homework. The other curves have names that we discussed in the lecture like "carotid", "ellipse", and "circle" which are kind of obvious which is which.

    • one year ago
  30. agentx5
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    Yep! That looks like the other questions where we were asked to find the vertical and horizontal tangents

    • one year ago
  31. agentx5
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    dy/dt = 0 is for horizontal I believe

    • one year ago
  32. mahmit2012
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    |dw:1342135476935:dw|

    • one year ago
  33. mahmit2012
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    |dw:1342135505524:dw|

    • one year ago
  34. mahmit2012
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    interesting problem !

    • one year ago
  35. agentx5
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    Does this funky thing have a name though? :-D

    • one year ago
  36. mahmit2012
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    No! it has a nice shape .

    • one year ago
  37. agentx5
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    It just asks me to type in the "area" in the one text field. Which was correct yay! And then it has a text box under it for "name of curve". The others were easy, but this one I haven't got a clue. Maybe it's in the text, somewhere amidst all its pages but it's not easy to find.

    • one year ago
  38. agentx5
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    It kind of looks like... one of those things when you roll a circle within a circle

    • one year ago
  39. mahmit2012
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    Try to solve one by yourself then think it's so easy and sure after that enjoy with the figure.

    • one year ago
  40. agentx5
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    Well I'm not going to sweat it, the hard part is done. Who cares about the name, you're right :-D

    • one year ago
  41. mahmit2012
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    |dw:1342136059673:dw|

    • one year ago