Question

In the formula $z = \sqrt{\frac{tx^3}{y}}$ $x$ is subjected to an increase of $2\%$ and $t$ is subjected to an decrease of $0.1\%$. Calculate, approx- imately, the percentage change needed in $y$ to ensure that $z$ remains unchanged.

Name: in the formula z sqrtfractx3y x is subjected to an increase of 2 and t is subjected to an decrease of 01 calculate approx imately the percentage change needed in y to ensure that z remains u 87384
Uploaded: 2024-01-29T04:49:17-08:00
Duration: 1 min 40 s
Channel: Khushbu Rani
Description: in the formula z sqrtfractx3y x is subjected to an increase of 2 and t is subjected to an decrease of 01 calculate approx imately the percentage change needed in y to ensure that z remains u 87384

          In the formula
$z = \sqrt{\frac{tx^3}{y}}$
$x$ is subjected to an increase of $2\%$ and $t$ is subjected to an decrease of $0.1\%$. Calculate, approx- imately, the percentage change needed in $y$ to ensure that $z$ remains unchanged.

$in the formula z sqrtfractx3y x is subjected to an increase of 2 and t is subjected to an decrease of 01 calculate approx imately the percentage change needed in y to ensure that z remains u 87384$

Added by Andrew P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Khushbu Rani

01/29/2024

Step 1

We can rewrite this as $z = t^{1/2} x^{3/2} y^{-1/2}$. To find the percentage change, we use the concept of relative change or logarithmic differentiation. Take the natural logarithm of both sides: $\ln z = \ln(t^{1/2} x^{3/2} y^{-1/2})$ $\ln z = \frac{1}{2} \ln Show more…

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In the formula $z = \sqrt{\frac{tx^3}{y}}$ $x$ is subjected to an increase of $2\%$ and $t$ is subjected to an decrease of $0.1\%$. Calculate, approx- imately, the percentage change needed in $y$ to ensure that $z$ remains unchanged.