91Ó°ÊÓ

A tank in the form of a right-circular cylinder of radius \(2\) feet and height \(10\) feet is standing on end. If the tank is initially full of water and water leaks from a circular hole of radius \(12\) inch at its bottom, determine a differential equation for the height h of the water at time \(t > 0\). Ignore friction and contraction of water at the hole.

In Problems \(15\) and \(16\) interpret each statement as a differential equation.

On the graph of \(y = \phi (x)\) the slope of the tangent line at a point \(P(x,y)\) is the square of the distance from \(P(x,y)\) to the origin.