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You are given two containers, the first containing one litre of wine and the second one...

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Advance Math

You are given two containers, the first containing one litre ofwine and the second one litre of water. You also have a cup whichhas a capacity of r litres, where 0 < r < 1. You fill the cupfrom the first container and transfer the content to the secondcontainer, stirring thoroughly afterwards. Next, dip the cup in thesecond container and transfer r litres of liquid back to the firstcontainer. This operation is repeated again and again. Prove thatas the number of iterations n of the operation tends to infinity,the concentrations of wine in both containers tend to equal eachother.

Answer & Explanation Solved by verified expert
4.1 Ratings (689 Votes)
Conservation of the respective liquids would impliy that thevolume of wine in the barrel holding mostly water lets call itWa has to be equal to the volume of water in the barrel    See Answer
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