The length x of a rectangle is decreasing at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given that the length $x$ is decreasing at the rate of $3 	ext{ cm/min}$,so $\frac{dx}{dt} = -3 	ext{ cm/min}$.Given that the width $y$ is incre

Vedclass · Accepted Answer

$-2 	ext{ cm/min}$

Vedclass · Answer

(A) Given that the length $x$ is decreasing at the rate of $3 	ext{ cm/min}$,so $\frac{dx}{dt} = -3 	ext{ cm/min}$.Given that the width $y$ is increasing at the rate of $2 	ext{ cm/min}$,so $\frac{dy}{dt} = 2 	ext{ cm/min}$.The perimeter $P$ of a rectangle is given by the formula $P = 2(x + y)$.To find the rate of change of the perimeter with respect to time $t$,we differentiate $P$ with respect to $t$:$\frac{dP}{dt} = 2 \left( \frac{dx}{dt} + \frac{dy}{dt} ight)$.Substituting the given values:$\frac{dP}{dt} = 2(-3 + 2) = 2(-1) = -2 	ext{ cm/min}$.Thus,the rate of change of the perimeter is $-2 	ext{ cm/min}$.

The length $x$ of a rectangle is decreasing at the rate of $3 \text{ cm/min}$ and the width $y$ is increasing at the rate of $2 \text{ cm/min}$. When $x = 10 \text{ cm}$ and $y = 6 \text{ cm}$,find the rate of change of the perimeter.

Similar Questions

The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

If $x \log x \frac{dy}{dx} + y = \log x^2$ and $y(e) = 0$, then $y(e^2) = $

How many tripeptides can be prepared by linking the amino acids glycine,alanine and phenylalanine?

Two monoatomic ideal gases $1$ and $2$ of molecular masses $M_1$ and $M_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas $1$ to that in gas $2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module