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One equation one unknown

  1. Feb 10, 2008 #1
    1. The problem statement, all variables and given/known data
    i want to find the value of k in the following equation:
    8.7-(0.75/k)=[e^(8k)](11.7-(0.75/k))


    2. Relevant equations



    3. The attempt at a solution

    i know i can use matlab but i dont have matlab and i dont even know how to do it on matlab; does anyone know how to do it on matlab?
    is there an alternative method to find k?

    thank you
     
  2. jcsd
  3. Feb 10, 2008 #2

    Dick

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    If you don't have any special tools, write the problem as f(k)=exp(8*k)*(11.7-.75/k)-(8.7-0.75/k). Now you want to find where f(k)=0. Now graph it and look for a zero, or just try different values of k until you find one where f(x) is positive and one where it's negative. E.g. f(0.03)<0 and f(0.04)>0. That means there is a root between 0.03 and 0.04. Try the midpoint k=0.035 and keep refining the interval containing the root until you get enough significant digits for the needs of the problem. This is called 'bisection'.
     
  4. Feb 10, 2008 #3
    yes i know that method but it takes too long and i'm lazy.
    i just need the answer without the working out so i dont want to take too much time finding the value for k.
     
  5. Feb 10, 2008 #4

    cristo

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    Well, you should just probably wait until you get to a computer with maple or matlab or whatever. Otherwise, you'll need to do it the long way!
     
  6. Feb 10, 2008 #5

    HallsofIvy

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    There is no simple formula for such a problem. You might be able use the Lambert W function, but I suspect just getting it into the right form for that would be much more work that the graph Dick suggested.
     
  7. Feb 11, 2008 #6
    yes but how do i type that into matlab and how do i find k using matlab? what do i type?
     
  8. Feb 11, 2008 #7

    EnumaElish

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  9. Feb 11, 2008 #8

    HallsofIvy

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