Math 1210
Quiz 5
February 14th, 2014
Answer the following three (3) questions. The value of every question is
indicated at the beginning of it. You may use scratch paper, but you can
only turn in this sheet. Please write your answer in the space provided. You
have 25 minutes.
Name:
UID:
1. (10 points) Sand is pouring from a pipe at a rate of 16 cubic feet per second. If the
falling sand forms a conical pile on the ground whose altitude is always 14 of the diameter
of the base, how fast is the altitude increasing when the pile is 4 feet high? Refer to
figure 1 and use the fact that the volume is given by V = 13 πr2 h.
2. (10 points) The angle between the two equal sides of an isosceles triangle measures
θ = π3 rad and the two equal sides are a = 3cm long. How much does the length L of the
third side vary if θ increases 0.01rad? Recall that L = 2a tan 2θ .
3. (10 points) Find the maximum and the minimum values of the function
f (x) = sin x − cos x
over the interval [0, π]. Recall that sin π4 = sin π4 =
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