The relative error of the speed is the ratio of the absolute error and the actual length
The absolute error and the relative error are 1.24 and 0.62%,
The given parameters are:
[tex]\mathbf{S = 9.4L^{0.37}}[/tex]
[tex]\mathbf{L = 200 \pm 10}[/tex]
Start by calculating the absolute error:
Differentiate [tex]\mathbf{S = 9.4L^{0.37}}[/tex]
[tex]\mathbf{S'= 0.37 \times 9.4L^{-0.63} L'}[/tex]
So, we have:
[tex]\mathbf{S'= 0.37 \times 9.4 \times 200^{-0.63} \times 10}[/tex]
[tex]\mathbf{S'= 1.24}[/tex]
So, the relative error is:
[tex]\mathbf{R = \frac{S'}{L} \times 100\%}[/tex]
This gives
[tex]\mathbf{R = \frac{1.24}{200} \times 100\%}[/tex]
[tex]\mathbf{R = \frac{124\%}{200} }[/tex]
[tex]\mathbf{R = 0.62\% }[/tex]
Hence, the absolute error and the relative error are 1.24 and 0.62%, respectively.
Read more about errors at:
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