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Math Help - Transposing Equations Assistance Needed

  1. #1
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    Transposing Equations Assistance Needed

    Hi,

    I am hoping for a little assistance in transposing equations for use in engineering calculations. The equation in question is as below, yet I need to find the value of A:

    Qs = 0.2 x A (Δt x h x g / (t + 273)0.5

    Can anyone provide me with an explanation as to how I can transpose this equation to find the value of A?

    Many thanks,

    James
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  2. #2
    A Plied Mathematician
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    Two comments.

    1. Please type your equation in a more legible form. I can't tell the difference, for example, between your "variable x" and the multiplication operation.
    2. Are any of the quantities in your equation vectors or matrices?
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  3. #3
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    Apologies, there are no variable x's present in the equation. All 'x' shown represent multiplication. I have removed these for clarity below.

    Qs = 0.2 A (Δt h g / (t + 273)0.5

    There are also no equation vectors or matrices in the equation.

    Thanks

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  4. #4
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    Thanks for that clarification. One or two more are needed, however: what is the small 0.5 doing to the (t+273) ? Also, there's a left parenthesis between the A and the Δt. Where is its closing parenthesis supposed to be? These factors are crucial in helping you to solve your problem, which is why clear problem statements are so important.
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  5. #5
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    Apologies again...the 0.5 is from I gather supposed to represent multiplying the solution to the power of 0.5 (which is effectively square root?)

    And the right parathensis I had previously missed is located as following:

    Qs = 0.2 A (Δt h g / (t + 273))0.5

    I hope this makes a little more sense now.

    James
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  6. #6
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    So your equation is this, then:

    Qs = 0.2 A \sqrt{\dfrac{\Delta t\,h\,g}{t + 273}}.

    Is that right? Is the s a subscript of Q, or is it a variable?
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  7. #7
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    Im unsure whether the square root would also cover '0.2 A' as the '0.5' previously discussed appears to be positioned outside of both paranthesis?

    I have attached a pdf document of the original source equation (shown as equation 2.7 in page 2.59), hopefully this may assist.

    And yes the 's' is a subscript of Q

    Thanks,

    James
    Attached Thumbnails Attached Thumbnails Transposing Equations Assistance Needed-cibse-guide-b-extract.pdf  
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  8. #8
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    According to the pdf, the 0.2 does not belong under the square root. The correct equation is

    Q_{s} = 0.2 A \sqrt{\dfrac{\Delta t\,h\,g}{\bar{t} + 273}}.

    Now, if all you're doing is solving for A, you have a fairly straight-forward job ahead of you. It's basically one step to get this:

    A=\dfrac{Q_{s}}{0.2}\,\sqrt{\dfrac{\bar{t} + 273}{\Delta t\,h\,g}}.
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  9. #9
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    Thats excellent! Thanks very much for your assistance. However could I ask how the process of the transposing worked to produce the solution?

    Also, is there any particular reason as to why the division equation under the square root has flipped?

    Many thanks again
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  10. #10
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    This is basic algebra. In order to solve for A, which has the 0.2 and the square root multiplying it, I have to divide by those things. Hence, the 0.2 in the denominator of the solved expression. And, dividing by a fraction is the same as multiplying by the reciprocal (a fact that is unchanged by exponentiation, which is why I can do that under the square root sign), which is why the numerator and denominator are flipped in the solved expression.
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  11. #11
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    After reading through that alot of it has gone over my head..however I remain grateful for your help in any case!
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  12. #12
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    You're welcome!
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