The volume of an empty container is 15 m³. If water is poured into the container at a rate of 2t + 2 m³ per minute where t is the time. What is the time needed to fill the container?
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If water is poured into the container at a rate of 2t + 2 m³ per minute where t is the time.
Think about what that rate represents:
It's in cubic metres per minute so that's
At the start t = 0 and V = 0. At the end V = 15 at (say) t = T
So integrate to get V in terms of t; put V = 15 (the constant of integration will come from t = V = 0) and solve for T
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