Question
The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.
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Answer to a math question The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.
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Solution:
The formula for the volume of a cube is given by V=s^3 Taking the derivative of the equation with respect to t, \frac{\differentialD V}{\differentialD t}=3s^2\frac{\differentialD s}{\differentialD t} \frac{\differentialD s}{\differentialD t}=\frac{\frac{\differentialD V}{\differentialD t}}{3s^2} Substituting values, \frac{\differentialD s}{\differentialD t}=\frac{10}{3\left(2\right)^2} \frac{\differentialD s}{\differentialD t}=\frac{5}{6}\operatorname{m/s}
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