Answer :

Given pv1.4 = constant and the decrease in v is.

Hence, we have

Δv = –0.005v

We have pv1.4 = constant

Taking log on both sides, we get

log(pv1.4) = log(constant)

log p + log v1.4 = 0 [ log(ab) = log a + log b]

log p + 1.4 log v = 0 [ log(am) = m log a]

On differentiating both sides with respect to v, we get

We know

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δv = –0.005v

Δp = (–1.4p)(–0.005)

Δp = 0.007p

The percentage error is,

Error = 0.007 × 100%

Error = 0.7%

Thus, the error in p corresponding to the decrease in v is 0.7%.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

If y = sin x and RD Sharma - Volume 1

Find the percentaRD Sharma - Volume 1

A circular metal RD Sharma - Volume 1

The radius of a sRD Sharma - Volume 1

The height of a cRD Sharma - Volume 1

Find the approximMathematics - Exemplar

Find the point onMathematics - Board Papers