Aheap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters.

Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.

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The volume of a cube of edge e is given by:

In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.

Now, for the rate of change, we need to apply the implicit differentiation, thus:

Volume decreases at a rate of 4 cubic meters per minute, thus:

The rate of change of an edge is . Then:

The rate of change is of -0.0533 cubic meters per minute.

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step-by-step explanation: