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For z = a2x3 y1/2,where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12%, respectively, then the percentage error for 'z' will be _______ %.
Correct answer is '18'. Can you explain this answer?
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For z = a2x3y1/2,where a is a constant. If percentage error in measure...
Calculation of Percentage Error in z
Given: z = a2x3y1/2
To find: Percentage error in z
Formula: Percentage Error = (Error/Measurement) x 100%
For x: Error in x = 4% of x
For y: Error in y = 12% of y
Calculation:
Let us assume that x and y are measured as x0 and y0, respectively.
Therefore, we can write:
z0 = a2x03y01/2
Now, let's consider the percentage error in z:
Percentage Error in z = [(Δz/z0) x 100%]
where Δz is the error in z.
We can write:
Δz = z - z0
= a2x3y1/2 - a2x03y01/2
= a2(x3y1/2 - x03y01/2)
Now, let's calculate the percentage error in z:
Percentage Error in z = [(Δz/z0) x 100%]
= [a2(x3y1/2 - x03y01/2)/(a2x03y01/2) x 100%]
= [(x3y1/2 - x03y01/2)/x03y01/2) x 100%]
= [(x3/x03) x (y1/2/y01/2) - 1] x 100%
= [(1 + Δx/x)3 x (1 + Δy/y)1/2 - 1] x 100%
where Δx = 4% of x0 and Δy = 12% of y
Given: z = a2x3y1/2
To find: Percentage error in z
Formula: Percentage Error = (Error/Measurement) x 100%
For x: Error in x = 4% of x
For y: Error in y = 12% of y
Calculation:
Let us assume that x and y are measured as x0 and y0, respectively.
Therefore, we can write:
z0 = a2x03y01/2
Now, let's consider the percentage error in z:
Percentage Error in z = [(Δz/z0) x 100%]
where Δz is the error in z.
We can write:
Δz = z - z0
= a2x3y1/2 - a2x03y01/2
= a2(x3y1/2 - x03y01/2)
Now, let's calculate the percentage error in z:
Percentage Error in z = [(Δz/z0) x 100%]
= [a2(x3y1/2 - x03y01/2)/(a2x03y01/2) x 100%]
= [(x3y1/2 - x03y01/2)/x03y01/2) x 100%]
= [(x3/x03) x (y1/2/y01/2) - 1] x 100%
= [(1 + Δx/x)3 x (1 + Δy/y)1/2 - 1] x 100%
where Δx = 4% of x0 and Δy = 12% of y
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For z = a2x3y1/2,where a is a constant. If percentage error in measurement of x and y are 4% and 12%, respectively, then the percentage error for z will be _______ %.Correct answer is '18'. Can you explain this answer?
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