If P= c^3b^2/cd andpercentage error in c,b,d are1% 2% and 3% respectively , calculate the % error in P
Answers
Explanation:
Answer:
The percentage error in P is 13%.
Explanation:
Given that,
P=a^3b^2(\sqrt{c}d)P=a
3
b
2
(
c
d)
a = 1%
b= 3%
c=4%
d=2%
The percentage error in P
\dfrac{\Delta P}{P}\times100=[3\times\dfrac{\Delta a}{a}+2\times\dfrac{\Delta b}{b}+\dfrac{1}{2}\dfrac{\Delta C}{C}+\dfrac{\Delta d}{d}]\times100
P
ΔP
×100=[3×
a
Δa
+2×
b
Δb
+
2
1
C
ΔC
+
d
Δd
]×100
\dfrac{\Delta P}{P}\times100=[3\times\dfrac{1}{100}+2\times\dfrac{3}{100}+\dfrac{1}{2}\times\dfrac{4}{100}+\dfrac{2}{100}]\toimes100
P
ΔP
×100=[3×
100
1
+2×
100
3
+
2
1
×
100
4
+
100
2
]\toimes100
\dfrac{\Delta P}{P}\times100=[\dfrac{3+6+2+2}{100}]\times100
P
ΔP
×100=[
100
3+6+2+2
]×100
\dfrac{\Delta P}{P}\times100=[\dfrac{13}{100}]\times100
P
ΔP
×100=[
100
13
]×100
\dfrac{\Delta P}{P}\times100=13\%
P
ΔP
×100=13%
Hence, The percentage error in P is 13%.