How do you find the amount of sugar in the tank after t minutes if a tank contains 1640 liters of pure water and a solution that contains 0.09 kg of sugar per liter enters a tank at the rate 5 l/min the solution is mixed and drains from the tank at the same rate?
This needs a bit of calculus and some thought.
The overall gain rate is just the difference between above gain and loss rates:
Rearranging this to integrate, we have
which leads to
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To find the amount of sugar in the tank after t minutes, you can use the formula:
Amount of sugar = Initial amount of sugar + (Rate of sugar solution in - Rate of sugar solution out) * t
Given: Initial amount of sugar = 1640 liters * 0.09 kg/liter Rate of sugar solution in = 5 liters/minute * 0.09 kg/liter Rate of sugar solution out = 5 liters/minute * (Amount of sugar in tank / Total volume of tank)
Substitute the values into the formula and solve for the amount of sugar in the tank after t minutes.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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