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Math Help - Please simplify for me !!!?

  1. #1
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    Please simplify for me !!!?




    2 different sets of equations:

    F+2T=30
    (0.5F^ -0.5)/(0.5T^ -0.5)=1/2



    4F+2T=30
    (0.5F^ -0.5)/(0.5T^ -0.5)=2
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    F+2T=30
     <br />
\frac{{(0.5F)}^ \frac{-1}{2}}{{(0.5T)}^ \frac{-1}{2}}=\frac{1}{2}<br />
    If the above is your question
    Cancel 0.5 of numerator and denominator and your question becomes
     <br />
\sqrt{\frac{T}{F}} =\frac{1}{2}<br />
    Squaring both sides
     <br />
T=\frac{F}{4}<br />
    So
     <br />
T =\frac{30-2T}{4} <br />
    I think you can go ahead and solve this and next question
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  3. #3
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    Indices

    Hello schoolhelp
    Quote Originally Posted by schoolhelp View Post

    2 different sets of equations:

    F+2T=30
    (0.5F^ -0.5)/(0.5T^ -0.5)=1/2



    4F+2T=30
    (0.5F^ -0.5)/(0.5T^ -0.5)=2
    First of all, notice that in \frac{0.5F^{-0.5}}{0.5T^{-0.5}} you can cancel the initial 0.5's to get \frac{F^{-0.5}}{T^{-0.5}}

    Then you need to know that:

    • a^{-x} = \frac{1}{a^x}; and


    • a^{0.5}=\sqrt{a}

    So F^{-0.5} = \frac{1}{F^{0.5}}

    = \frac{1}{\sqrt{F}}

    Do the same with the denominator:

    T^{-0.5}=\frac{1}{\sqrt{T}}

    and now invert and multiply, and the second equation reads

    \frac{\sqrt{T}}{\sqrt{F}}=\frac{1}{2}

    \Rightarrow \frac{T}{F} = \frac{1}{4}

    \Rightarrow F=4T

    Substitute into the first equation and solve for T, and then F.

    Do the second problem in a similar way.

    OK now?

    Grandad
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