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Physics algebra problem.

  1. Aug 11, 2009 #1
    How would you solve cl *ml *(TL-TF)= cg*mg*(TF-TG)

    for TF?

    The text gives it as

    Tf= cl*ml*TL+cg*mg*Tg / cl*ml+cg*mg


    If you are wondering the basic equation is for method of mixtures

    Thank you.
     
  2. jcsd
  3. Aug 11, 2009 #2

    Doc Al

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    First thing to do is multiply it out to get rid of the parentheses. Hint: a*(x - y) = a*x - a*y.

    Then collect all the terms with the Tf factor to one side.
     
  4. Aug 11, 2009 #3
    Hmmm, thanks for the help but, I'm still not getting it. Here is what I'm trying so far. Sorry algebra has never been my strong point. :(


    cl* ml*TL-ml*TF = cg* mg* TF - mg *TG

    then TF/1= cg * mg* TF-mg*TG / cl *ml*TL-ml ----- I think this is where I screw it up


    then: TF/TF = cg * mg -mg * TG / cl * ml* TL-ml


    as you can see I'm probably doing this all wrong and am getting myself confused.
     
  5. Aug 11, 2009 #4

    berkeman

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    You lost some terms right off the bat there. Check your first line -- you didn't distribute the cl*ml across both terms in the parenthesis on the left-hand side (LHS). And you made the same error on the RHS.
     
  6. Aug 11, 2009 #5

    Doc Al

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    No shortcuts: a*b*(x - y) = a*b*x - a*b*y
     
  7. Aug 11, 2009 #6
    Soo.... the first line would look more like:

    cl*ml*TL- cl*ml*TF = cg*mg*TF-cg*mg*TG?
     
  8. Aug 11, 2009 #7

    Doc Al

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    Now you're cooking!
     
  9. Aug 11, 2009 #8
    lol..

    So I'm probably gonna screw up again ,but would the next line be TF = cg x mg x TF - cg x mg x TG / cl x ml x TL - cl x ml ?
     
  10. Aug 11, 2009 #9

    Doc Al

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    Do the second step that I suggested: Starting with your new first line, move all the terms that contain TF to the left and all others to the right.
     
  11. Aug 11, 2009 #10
    By doing that I get: TF= cg x mg x TG / Cl x ML x TL- CL x ML


    Once again my algebra skills are really lacking so bare with me.
     
  12. Aug 11, 2009 #11

    Doc Al

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    Just move the terms to one side. Don't divide by anything yet. (One step at a time.)
     
  13. Aug 11, 2009 #12
    But both sides are filled with variables, don't you have to clear one side to be able to have the side clear for TF?
     
  14. Aug 11, 2009 #13

    Doc Al

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    No. In your equation in post #6 there are 4 terms (each with multiple factors, like a*b*c). Two of them contain Tf and two do not. Move things around so that the two Tf terms are on the left side and the others are on the right.
     
  15. Aug 11, 2009 #14
    Ok, I see so cl*ml*TL- cl*ml*TF = cg*mg*TF-cg*mg*TG becomes:

    cl*ml*TF+cg*mg*TF= cg*mg*TG+cl*ml*TL?
     
  16. Aug 11, 2009 #15

    Doc Al

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    Looks good. Now you can take the left hand side and factor out the TF, adding in the correct parentheses. It will be wise to put parentheses around the right hand side too.
     
  17. Aug 11, 2009 #16
    What do you mean like this?

    (cl*ml)(TF)+(cg*mg)(TF)= (cg*mg)(TG)+(cl*ml)(TL)

    then

    TF/TF = TF= (cg*mg)(TG)+(cl*ml)(TL) / (cl*ml)+(cg*mg)


    Looks like I got it ehhhh? I really appreciate your help, I hope I can remember this
     
  18. Aug 11, 2009 #17

    Redbelly98

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    I think you have the right idea in your head, but you have written things down rather sloppily ... in essence, wrongly.

    For starters,
    TF/TF = TF​
    is simply not true. Forget the TF/TF here.

    Can you add parantheses, in two places, to make this a correct statement? Maybe use square parantheses [], in order not to confuse distinguish them with the regular () kind.

    As written, this equation means

    TF = [(cg*mg)(TG)] + [(cl*ml)(TL) / (cl*ml)] + [(cg*mg)]

    which probably isn't what you meant.
     
  19. Aug 12, 2009 #18

    Doc Al

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    As Redbelly98 says, it looks like you've got the right idea, but you need to be more careful when writing it out. Here's the outline of what I had in mind:

    Starting with something like this:
    a*X + b*X = c*Y + d*Z

    Factor out the X, adding in parentheses as needed:
    (a + b)*X = (c*Y + d*Z)

    Solve for X and you're done.
     
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