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A cube has an edge of 5 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.

A cube has an edge of 5 feet. The edge is increasing at the rate of 2 feet per minute-example-1
User Renato Mefi
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1 Answer

18 votes
18 votes

INFORMATION:

We know that:

- A cube has an edge of 5 feet

- The edge is increasing at the rate of 2 feet per minute

And we must express the volume of the cube as a function of m, the number of minutes elapsed

STEP BY STEP EXPLANATION:

First, we need to use that the volume of a cube of edge e is given by:


V=e^3

Second, we can find an expression for the variation of the edge in terms of the time. The edge starts at 5 feet, and increases at the rate of 2 feet per minute


e(m)=5+2m

Finally, replacing the function for the edge variation in the formula for the volume of a cube


V(m)=(5+2m)^3

ANSWER:

The expression for the volume of the cube as a function of m is:


V(m)=(5+2m)^3

User Max Barfuss
by
3.2k points
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