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Standard XII

Mathematics

Average Rate of Change

The length x ...

Question

The length $x$ of a rectangle is increasing at the rate of $4 c m / s$ and the width $y$ is decreasing at the rate of $3 c m / s$ . When $x = 5 c m$ and $y = 6 c m$ , then the rate of change of the perimeter is

1 c m / s

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2 c m / s

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4 c m / s

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0.5 c m / s

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Solution

The correct option is B $2 c m / s$
Perimeter of the rectangle
$P = 2 (x + y) \Rightarrow \frac{d P}{d t} = 2 (\frac{d x}{d t} + \frac{d y}{d t}) \Rightarrow \frac{d P}{d t} = 2 (4 - 3) = 2 c m / s$

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The length x of a rectangle is increasing at the rate of 4 cm/s and the width y is decreasing at the rate of 3 cm/s. When x=5 cm and y=6 cm, then the rate of change of the perimeter is

The correct option is B 2 cm/sPerimeter of the rectangle P=2(x+y)⇒dPdt=2(dxdt+dydt)⇒dPdt=2(4−3)=2 cm/s

The length $x$ of a rectangle is increasing at the rate of $4 c m / s$ and the width $y$ is decreasing at the rate of $3 c m / s$ . When $x = 5 c m$ and $y = 6 c m$ , then the rate of change of the perimeter is

The correct option is B $2 c m / s$
Perimeter of the rectangle
$P = 2 (x + y) \Rightarrow \frac{d P}{d t} = 2 (\frac{d x}{d t} + \frac{d y}{d t}) \Rightarrow \frac{d P}{d t} = 2 (4 - 3) = 2 c m / s$