See the coversheet for instructions and the point value of each problem.
 The radius of a spherical cell is observed to decrease at a rate
of \(2\) units/second when that radius is \(30\) units long. How fast is
the volume of the cell decreasing at that point?
 At noon, ship \(A\) is 100 km
directly south of ship \(B\). Ship \(A\) is sailing west at \(35\,
\mathrm{km/hour}\) and ship \(B\) is sailing east at \(25\,\mathrm{km/hour}\).
 Draw and label a diagram illustrating this
scenario.
 How fast is the distance between the ships changing at
3:00pm? (Do not try to simplify your answer.)

A trough is \(10\, \mathrm{m}\) long and its ends have the
shape of isosceles triangles that are \(5\, \mathrm{m}\) across at the top
and have a height of \(3\, \mathrm{m}\). The trough is being filled with
water at a rate of \(12\,\mathrm{m}^3/\mathrm{min}\).
 Draw and label a diagram illustrating this
scenario.
 How fast is the water level rising when it is
\(2\,\mathrm{m}\) deep? (Do not try to simplify your
answer.)
 Two sides of a triangle are \(3\,
\mathrm{m}\) and \(5\, \mathrm{m}\) in length and the angle
between them is increasing at a rate of \(0.06\,
\mathrm{rad/s}\).
 Draw and label a diagram illustrating this
scenario.
 Find the rate at which the area of the traingle is
increasing when the angle between the sides of fixed length is
\(\pi/3\).
Last modified: Thu Sep 28 14:36:38 UTC 2017