Math 1A – Chapter 4 Test II– Fall ’04 Name__________________________
Show your work for credit. Write all responses on separate paper.
1. Blanca is running around a circular track of radius r = 30 meters at a speed of 3 meters/sec. Recall that the linear speed v is related to the angular speed ω by v = ωr. a. What is Blanca’s angular velocity, ω? b. Recall that Blanca’s position at time t can be modeled by the parametric equations . If Blanca starts at a bench on the east side of the track and heads north around the track, what is a parameterization of her position at time t? c.
Write a formula for the d. Find the rate of change of Blanca’s distance from the bench when t = 1.
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2.
A paper cup has the shape of a cone with height 8 cm
and radius 2 cm (at the top). I water
is poured into the cup at a rate of 2 cm3/s, how fast is the water
levelrising when the water is 6 cm deep? |
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3.
Find the point on the ellipse which is closest to the point (3,5).
4. An observer stands at a point P, 10 meters above a track. Two runners start at a point S in the figure and run along the track. One runner runs twice as fast as the other. Find the maximum value of the observer’s angle of sight θ between the runners. |
5.
Use
6. Consider
a. Explain why g satisfies the conditions of the mean value theorem on .
b. Set up an equation to find the point(s) in which, by the mean value theorem are guaranteed to exist.
c.
Use