# 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?

### 2 Responses to september 26

1. Atyab Bhatti September 27, 2014 at 6:37 pm #

Do we have permission to use a graphing calculator on exam?

• yuliy September 29, 2014 at 11:02 pm #

Too late! Yes, but I consider them useless.