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natulia [17]
3 years ago
5

A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3

cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 8 cubic meters.
Mathematics
1 answer:
inna [77]3 years ago
4 0

Answer:

-1/4 meter per minute

Step-by-step explanation:

Since, the volume of a cube,

V=r^3

Where, r is the edge of the cube,

Differentiating with respect to t ( time )

\frac{dV}{dt}=3r^2\frac{dr}{dt}

Given, \frac{dV}{dt}=-3\text{ cubic meters per minute}

Also, V = 8 ⇒ r = ∛8 = 2,

By substituting the values,

-3=3(2)^2 \frac{dr}{dt}

-3=12\frac{dr}{dt}

\implies \frac{dr}{dt}=-\frac{3}{12}=-\frac{1}{4}

Hence, the rate of change of an edge is -1/4 meter per minute.

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Jobisdone [24]

Answer:

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Step by step Explanation:

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8 0
3 years ago
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Xelga [282]
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3 years ago
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