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error analysis stuff
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Error Analysis/Practice
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5
Error Analysis/Practice
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1) a) 9 ± 2.24, 9 ± 24.9%
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b) 1 ± 2.24, 1 ± 224%
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c) 15 ± 2.24, 15 ± 14.9%; if c had no error, then it comes to ± 2.2360, so I would still round that to ± 2.24
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2) 120
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Error Analysis/error propagation
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Error Analysis/error propagation
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Z = X + Y OR Z = X - Y
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_________
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ΔZ = √ΔX² + ΔY²
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Z = X * Y OR Z = X / Y
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__________________
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_ΔZ_ = / ⎛_ΔX_⎞² + ⎛_ΔY_⎞²
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Z √ ⎝ X ⎠ ⎝ Y ⎠
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Z = Xⁿ
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ΔZ = n X⁽ⁿ⁻¹⁾ ΔX, i.e. _ΔZ_ = n _ΔX_
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Z X
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Z = 𝑓(X,Y,...)
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ΔZ² = ⎛_∂f(X,Y)_ ΔX⎞² + ⎛_∂f(X,Y)_ ΔY⎞² + ...
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⎝ ∂X ⎠ ⎝ ∂Y ⎠
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1) a) 9 ± 3, 9 ± 33%
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b) 1 ± 3, 1 ± 300%
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c) 15 ± 3.2, 15 ± 21.3%; if c had no error, then, 15 ± 3, 15 ± 20%
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2)
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