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