I have done similar questions but this one does not give a value for r. Should I give it any value?
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I have done similar questions but this one does not give a value for r. Should I give it any value?
No need...Quote:
Originally Posted by Stuck Man
$\displaystyle relative\ error=\frac{absolute\ error}{exact\ value\ of\ that\ being\ measured}$
$\displaystyle =\displaystyle\huge\frac{{\pi}r^2-{\pi}\left(r-\frac{r}{400}\right)^2}{{\pi}r^2}=\frac{{\pi}r^2-{\pi}r^2\left(1-\frac{1}{400}\right)^2}{{\pi}r^2}$
or
$\displaystyle \displaystyle\huge\frac{{\pi}\left(r+\frac{r}{400} \right)^2-{\pi}r^2}{{\pi}r^2}=\frac{{\pi}r^2\left(1+\frac{1} {400}\right)^2-{\pi}r^2}{{\pi}r^2}$
which may be factorised, removing $\displaystyle r$ and $\displaystyle \pi}$ completely.
Those parameters are needed for the "absolute" error,
but not for the "relative" error.
Ok. In general is the absolute error either +ve or -ve? Is an error bound always positive? Wikipedia seems to muddle these things up.
It would be positive,Quote:
Originally Posted by Stuck Man
however that's because the modulus is taken,
which doesn't mean we get the same error here if the radius is lower by 0.25%
or if it's higher by 0.25% from it's nominal value.
To calculate the absolute error you've taken the minimum value of r so you must also take the minimum value of pi which is 3.1415. This will get the answer in the book. Part b is done similarly for pi=3.14159.
There is much more work than this. I know how to do it though.
