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anonymous

  • one year ago

How can I solve this for x? ... cos(pi*x) = 4x^2 - 1

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  1. nincompoop
    • one year ago
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    |dw:1439590609138:dw|

  2. nincompoop
    • one year ago
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    |dw:1439590681521:dw|

  3. anonymous
    • one year ago
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    Ohhh but then how would you know that they intersect at those points (i mean at the x-intercepts) ?

  4. xapproachesinfinity
    • one year ago
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    do intermediate value thm

  5. anonymous
    • one year ago
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    Ohhh right right!! Can you help me out with it?

  6. xapproachesinfinity
    • one year ago
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    eh lol you want exact numbers that may not be a good way

  7. anonymous
    • one year ago
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    No no haha not exact numbers xD lol just lead me in the right way and I'll take it from there

  8. xapproachesinfinity
    • one year ago
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    what i meant is that IVT that proves that in an interval there exist a solution not helpful to determine those solution so you need a different way as your question is asking to solve..

  9. anonymous
    • one year ago
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    Hmm, well I'm actually trying to solve a different question but I need to find the intersection of the 2 graphs (y=cos(pi*x) and y=4x^2-1) in order to solve it... I'm looking for the area of the enclosed region.

  10. xapproachesinfinity
    • one year ago
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    enclosed region |dw:1439591365383:dw|

  11. xapproachesinfinity
    • one year ago
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    http://prntscr.com/84qa1x

  12. anonymous
    • one year ago
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    Exactly! And I'm not sure how to find the intersection points of the 2 graphs... |dw:1439591506353:dw| I usually set the 2 equations to equal each other, but it doesn't work with this problem

  13. anonymous
    • one year ago
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    Is there any way to find it without using a calculator?

  14. xapproachesinfinity
    • one year ago
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    yeah that work with simple equations lol

  15. anonymous
    • one year ago
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    So not with this one?

  16. xapproachesinfinity
    • one year ago
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    i guess not with simple algebra no? could be with some advanced maneuver that uses calculus and different other stuff haha

  17. xapproachesinfinity
    • one year ago
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    yeah it is x=-+1/2 the graph shows the same

  18. anonymous
    • one year ago
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    Ok, the thing is, I have a Calculus final exam in a couple days and I was wondering how to go about such a question cuz we're not allowed to use calculators either...

  19. anonymous
    • one year ago
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    Refer to the attachment.

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  20. anonymous
    • one year ago
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    But I guess in that case such a question wouldn't appear on an exam then, right?

  21. xapproachesinfinity
    • one year ago
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    i don't think you gonna have some problem of this sort without giving those points this needs some program haha

  22. anonymous
    • one year ago
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    @robtobey it doesn't open the file :/

  23. anonymous
    • one year ago
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    Haha good! Relief xD lol

  24. xapproachesinfinity
    • one year ago
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    you don;t have file opener of that time you need mathematica or something

  25. xapproachesinfinity
    • one year ago
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    of that type*

  26. anonymous
    • one year ago
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    Yeah, whats mathematica?

  27. xapproachesinfinity
    • one year ago
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    a language or something hhh they solve problems with it i don't know either lol

  28. anonymous
    • one year ago
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    Sorry. I intended to post a pdf file.

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  29. xapproachesinfinity
    • one year ago
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    http://prntscr.com/84qeo7

  30. xapproachesinfinity
    • one year ago
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    mathematica is an environment i guess right @robtobey

  31. anonymous
    • one year ago
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    Now I see it :) thanks! That makes sense...

  32. xapproachesinfinity
    • one year ago
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    that was IVT usage by wolfram

  33. anonymous
    • one year ago
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    I wish it showed the solution too, but I guess you gotta go pro for that XD haha

  34. xapproachesinfinity
    • one year ago
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    it has solution x=+-1/2 ?

  35. anonymous
    • one year ago
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    yeah, i mean the step-by-step solution

  36. xapproachesinfinity
    • one year ago
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    what steps? how it used IVT?

  37. anonymous
    • one year ago
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    mhmm

  38. xapproachesinfinity
    • one year ago
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    you could choose the interval [0,1] and do iterations of the thm or may be newtons method

  39. xapproachesinfinity
    • one year ago
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    that would lead to one solution close to 0.5 use symmetry then to get -0.5 that;s a lot of work

  40. anonymous
    • one year ago
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    Hmm right, I'll give that try later on And yeah its a lots of work for just finding the intersection points to then finally get to work out the area between the 2 curves... it wouldn't be reasonable to get a question like this on the exam...

  41. xapproachesinfinity
    • one year ago
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    newton's method works good lead straight to the answer more quickly

  42. anonymous
    • one year ago
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    Yeah, I gotta review that again, it was from last term and I tend to forget math really soon xD hahaha

  43. anonymous
    • one year ago
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    But thank you all for the help! I appreciate it :)

  44. xapproachesinfinity
    • one year ago
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    i just use wolfram or any other program with this stuff in exam they will give you the intersection point if this sort of question pops up

  45. anonymous
    • one year ago
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    Mhmm, hopefully it doesn't show up on the exam at all - just don't like it xD lol

  46. xapproachesinfinity
    • one year ago
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    lol depends on the prof

  47. anonymous
    • one year ago
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    He's cruel and nice at the same time - pretty unpredictable xD haha

  48. anonymous
    • one year ago
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    Anyways wish me luck! :D Im really nervous lol

  49. xapproachesinfinity
    • one year ago
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    yeah bonne chance :)

  50. anonymous
    • one year ago
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    Merci beaucoup Monsieur ;D haha

  51. xapproachesinfinity
    • one year ago
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    de rien haha

  52. anonymous
    • one year ago
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    lol

  53. xapproachesinfinity
    • one year ago
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    حظا سعيدا

  54. anonymous
    • one year ago
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    Thats Arabic! :O haha awesome!

  55. xapproachesinfinity
    • one year ago
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    yeah it is :) Arabic is tough little bit

  56. anonymous
    • one year ago
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    Yeah, I almost learned to speak it when I was little but then forgot it after a while of not working on it :/

  57. anonymous
    • one year ago
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    But I still remember some words and can still read :D

  58. xapproachesinfinity
    • one year ago
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    oh good :) i understand french but i don't speak it fluently due to luck of practice too haha

  59. anonymous
    • one year ago
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    Same here! I understand French and German a lot better than speaking them xD French, in particular, I've studied for over 6 years and yet can't speak it xD such a shame hahaha

  60. xapproachesinfinity
    • one year ago
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    eh what shame lol i studied french for over 14 years i even studied math with french but outside school i never practiced speaking it

  61. anonymous
    • one year ago
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    Btw,

  62. anonymous
    • one year ago
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    Hahaha wow!! Lets just admit its a tough language xD

  63. xapproachesinfinity
    • one year ago
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    eh perhaps it is

  64. xapproachesinfinity
    • one year ago
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    eh haha forgot that

  65. anonymous
    • one year ago
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    Mmhm it sure is xD lol

  66. anonymous
    • one year ago
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    Lol

  67. xapproachesinfinity
    • one year ago
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    haha could be lack of interest too i never had intereest in it

  68. anonymous
    • one year ago
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    Could be... But for me, it has always been a dream to be able to speak French - it just sounds so nice xD haha

  69. xapproachesinfinity
    • one year ago
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    haha language of romance restudy it xD

  70. anonymous
    • one year ago
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    Lol true xD certainly does sound romantic xD and I definitely will... once my schedule gets a bit lighter xD lol

  71. nincompoop
    • one year ago
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    sorry I was at work so we can solve for their intersection points manually cos(pi*x) = 4x^2 - 1 means cos(pi x = 0 4x^2 -1 = 0

  72. anonymous
    • one year ago
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    Refer to the attachment from the Mathematica 9 program. Sort of a proof for the first quadrant.

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