MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 6 Week 6

See the coversheet for instructions and the point value of each problem.

1. 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?
2. 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 $$25\,\mathrm{km/hour}$$.
1. Draw and label a diagram illustrating this scenario.
2. How fast is the distance between the ships changing at 3:00pm? (Do not try to simplify your answer.)
3. 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 $$12\,\mathrm{m}^3/\mathrm{min}$$.
1. Draw and label a diagram illustrating this scenario.
2. How fast is the water level rising when it is $$2\,\mathrm{m}$$ deep? (Do not try to simplify your answer.)
4. 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 $$0.06\, \mathrm{rad/s}$$.
1. Draw and label a diagram illustrating this scenario.
2. Find the rate at which the area of the traingle is increasing when the angle between the sides of fixed length is $$\pi/3$$.