Question

if p=3c²-6c², find the percentage error in p at c=1 if the error in c is 0.05​

Answer 1

Answer:

It's right mate which is written above... xd....

Answer 2

Answer:

 The percentage error in p at c = 1 is $10\%$.

Step-by-step explanation:

Given,

The equation: $p = 3c^{2} -6c^{2}$

The error in c, δc = $0.05$

The percentage error in p at c = $1$ is =?

As we know,

• The percentage error is defined as the ratio of change in error to the error multiplied by 100.
• Percentage error = $\frac{\d\delta p}{p} \times 100$  -------equation (a)

Here,

• δp = change in error

Firstly, we have to calculate the value of δp, by partial differentiation of the given equation:

• $p = 3c^{2} -6c^{2}$

Differentiating the equation concerning c, we get:

• $\frac{\delta p}{\delta c} = 6c -12c$
• ${\delta p} = (6c -12c)\delta c$

After putting the value of δc and at c= 1, we get:

• ${\delta p} = (6(1) -12(1))0.05$
• ${\delta p} = -0.3$

Now, the value of p at c = $1$;

• $p = 3c^{2} -6c^{2}$
• $p = 3(1)^{2} -6(1)^{2}$
• $p = 3 - 6$
• $p = -3$

After putting these values in equation (a), we get:

• Percentage error = $\frac{-0.3}{-3} \times 100$ = $10\%$

Hence, the percentage error in p = $10\%$.