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Really complicated solve for x problem please help

  1. Apr 19, 2010 #1
    really complicated "solve for x" problem.. please help..

    1. The problem statement, all variables and given/known data
    [This is the final step in a "critical thinking" problem assigned as extra practice/intense application] Find the value of x, for the given equation, when f(x) = [tex]\frac{49}{6}[/tex][tex]\pi[/tex]


    f(x) = [tex]\left(x\right)[/tex][tex]\times[/tex][tex]\sqrt{49-x^2}[/tex] + 49sin[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex]



    2. Relevant equations
    (This is where I need help, I have tried moving around the values, sqaring both sides, applying e and ln; my T.A. could only think of plugging f(x) into a graphing calculator and tracing to y = [tex]\frac{49}{6}[/tex][tex]\pi[/tex])
    *A big question I have is if trig-substitution (aside from integration) can be used, or another method I am not "equipped with," with simplifications.



    3. The attempt at a solution
    This is what is left after integrating a problem, the answer should be ~1.85 (from graphing/tracing). I tried simplifying using regular relationships:

    sin[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex] = [tex]\frac{1}{6}\pi[/tex] - [tex]\left(x\sqrt{49-x^2}\right)\div49[/tex]
     
  2. jcsd
  3. Apr 19, 2010 #2

    Mark44

    Staff: Mentor

    Re: really complicated "solve for x" problem.. please help..

    You're not going to be able to solve this by algebraic means. The simplest approach is to graph the function and see what value of x gives a y value of 49pi/6.
     
  4. Apr 19, 2010 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi phys-lexic! :wink:

    Try the obvious substitution. :smile:
     
  5. Apr 19, 2010 #4
    Re: really complicated "solve for x" problem.. please help..

    I understand algebraic means won't help, which is why I'm posting this question.

    Trig-substitution is what I was thinking, but is that applicable when not integrating? (We were only introduced to trig-substitutions with integrals, for obvious reasons)
     
  6. Apr 19, 2010 #5

    tiny-tim

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    Science Advisor
    Homework Helper

    Yes!! You can always substitute, if you think it will make the problem easier. :smile:
     
  7. Apr 19, 2010 #6
    Re: really complicated "solve for x" problem.. please help..

    Would be a lot simpler if there was only a way to make that first term go to zero...
     
  8. Apr 19, 2010 #7
    Re: really complicated "solve for x" problem.. please help..

    If f(x)=y, substitute Sqrt[a^2-x^2]=dy/dx, then it reduces to the standard form dy/dx +Py=Q
     
  9. Apr 19, 2010 #8
    Re: really complicated "solve for x" problem.. please help..

    Aah.. I tried it out a few times and ended up going in circles. Thankyou anyways everyone, now I know why this question is "way harder than the exam would be."
     
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