Solving for Error in Y: A Math Problem

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AI Thread Summary
To find the error in the quantity Y defined as Y = (4a^3 b) / (5c^2 √d), the discussion emphasizes the need to apply the rules for combining percentage errors, particularly considering the powers of the variables involved. The user initially calculated a total percentage error of 5% but expressed confusion about the methodology. It is clarified that for terms raised to powers, the percentage errors should be multiplied by the respective powers before summing them. Additionally, there is a technical issue with LaTeX formatting that affects the display of the mathematical expressions. The discussion highlights the importance of correctly applying error propagation rules in mathematical problems.
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Homework Statement


\[<br /> \[<br /> \begin{array}{l}<br /> {\rm{A quantity Y is given by:}} \\ <br /> Y = \frac{{4a^3 b}}{{\left( {5c^2 \sqrt {\rm{d}} } \right)}} \\ <br /> {\rm{Find the error in Y given the following errors in a, b, c, and d:}} \\ <br /> a \pm 1\% ,{\rm{ }}b \pm 0.5\% ,{\rm{ }}c \pm 2\% ,\,{\rm{ }}d \pm 1.5\% \\ <br /> \end{array}<br /> \]<br /> \

Homework Equations


Given above

The Attempt at a Solution


I plugged the numbers into this equation and got 0.1632993162
This is not correct.
I added all the percentage errors together to get 5%. Then asked myself why I did that anyway.
Don't know how to solve this problem. I know how to find percentage errors but these are already given.
please help. Thank you

And also - My LaTex is not working properly - It doesn't recognize the spaces between the words from MathType. Anyone know why?
 
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When you combine errors in a formula containing powers with the terms multiplied and divided you add the percentage errors of all the terms, but with the additional factor that if a term is squared the % error is doubled, if it's cubed the % error is 3 times. etc etc.
You can probably find a proof of this online.
 
Thank you
 
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