If Z = A4, then the relative error introduced in Z is ..
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Correct question: Z = [A^4][B^(1/3)]/[C][D^(3/2)]
percentage error in A = 4%
percentage error in B = 2%
percentage error in C = 3%
percentage error in D = 1%
Given: Z = [A^4][B^(1/3)]/[C][D^(3/2)]
percentage error in A = 4%
percentage error in B = 2%
percentage error in C = 3%
percentage error in D = 1%
To find: Relative error of Z
Concept: ΔZ/Z = (4)ΔA/A + (1/3)ΔB/B + ΔC/C + (3/2)ΔD/D
Step by step explanation:
percentage error in A = 4%
percentage error in B = 2%
percentage error in C = 3%
percentage error in D = 1%
ΔA/A*100 = 4
ΔB/B*100 = 2
ΔC/C*100 = 3
ΔD/D*100 = 1
[ΔZ/Z]*100 = [(4)ΔA/A + (1/3)ΔB/B + ΔC/C + (3/2)ΔD/D]*100
Putting values in the above equation
[ΔZ/Z]*100 = 4(4) + 2/3 + 3 + 3/2
[ΔZ/Z]*100 = 16 + 2/3 +3 +3/2
[ΔZ/Z]*100 = 21.16%
% error measurement of Z is 21.16%
Hence, the relative error in Z is 21.16/100 = 0.2116
Answer: % error measurement of Z is 21.16%
Hence, the relative error in Z is 21.16/100 = 0.2116
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