september 26

  • A brine tank of volume \(V\) get an influx of \(p\%\) brine at the rate \(r\), which mixes instantaneously and flows away at the same rate \(r\). If the tank was filled with fresh water initially, when it will have the concentration \(q\)?
  • A graph of a function \(y\) has the property that the area of the triangle formed by the \(x\)-axis, segment \([(x,0),(x,y)]\) and the tangent line to the graph of \(y\) at \((x,y)\) has constant area \(S\). Find this function.
  • A boy walks along the \(x\) axis pulling a stone on a rope of length \(1\). Find the trace left by the stone.
  • In a social network, the users randomly share gossips, so that at any minute each user has on average \(1\) exchange. If at noon just \(1\%\) of the users knew a hot new story, when it will be known to \(99\%\) of the network?

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