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Finding errors

  • Thread starter lemon
  • Start date
  • #1
200
0

Homework Statement


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



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?
 
Last edited:

Answers and Replies

  • #2
648
2
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.
 
  • #3
200
0
Thank you
 

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