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Math Help - Help......Please!

  1. #1
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    Help......Please!

    Been at this for hours..

    the temperature ,P, of a conductor at time, t, is given by

    P=P^0[1-e-^-t/T]

    Where P^0 is the initial temperature and T is a constant.

    Express T in terms of P,P^0 and t and determine its value when p^0 = 190, P= 20 and t = 40

    Any help would be much appreciated...Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    \dfrac{P}{P_0} = 1-e^{-t/T}

    Subtract 1 from both sides: \dfrac{P}{P_0} -1 = -e^{-t/T}

    Multiply through by -1: 1 -\dfrac{P}{P_0} = e^{-t/T}

    Can you finish off? (use logs)
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  3. #3
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    Thanks very much for the help and the hint....

    Hopefully I have it sussed!
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  4. #4
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    e^(i*pi)'s Avatar
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    If you want to check your answers I've put mine in a spoiler

    Spoiler:
    T = -\dfrac{t}{\ln \left(1 - \dfrac{P}{P_0}\right)}

    T = -\dfrac{40}{\ln \left(1 - \dfrac{20}{190}\right)} \approx  359.6

    Your answer will have whatever unit t is in
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  5. #5
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    Thanks for the spoiler, Matches what I had thankfully!

    I am stuck with final question - After this hopefully thats me done with algebra!!

    Show using factor theorem,that 2x-1 is a factor of...

    2x^4-x^3-6x^2+5x-1

    and hence express 2x^4-x^3-6x^2+5x-1 as a product of a linear & cubic factor

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  6. #6
    Super Member Quacky's Avatar
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    let  f(x)=2x^4-x^3-6x^2+5x-1
    If 2x-1 is a factor, f(\frac{1}{2}) = 0. That is to say, when x = 0.5, the quartic should equal 0.
    Then, once you've proven that, take out a factor of (2x-1).
    <br />
2x^4-x^3-6x^2+5x-1=(2x-1)(x^3... ....+1)
    Can you find the x^2 and x coefficients?
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  7. #7
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    Thanks, so would I be right in saying..

    f(0.5)=2(0.5)^4-(0.5)^2-6(0.5)^2+5(0.5)-1??
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  8. #8
    Super Member Quacky's Avatar
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    Quote Originally Posted by scott6162 View Post
    Thanks, so would I be right in saying..

    f(0.5)=2(0.5)^4-(0.5)^3-6(0.5)^2+5(0.5)-1??
    Just a small typing mistake, but I'm confident you have the right idea. If that is equal to 0 (and you'll have to test it) then you've proven that (2x-1) is a factor. You then need to factorize the expression, and I've started you off in my above post.
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