He is running at a speed of 28 feet per second.
At what rate is the player’s
distance from home plate decreasing?
18)
A potter places a cylindrical lump of clay on her wheel.
Before she begins to shape it, it
has a radius of 10 inches and a height of 4 inches.
Assuming that no clay is lost in the
shaping process (and that the cylindrical lump stays cylindrical throughout the process)

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how fast is the height of the lump of clay changing when the radius is 7.5 inches, given
the radius is shrinking by 1.2 inches per minute?
19)
The celebrated actress,
D.R. Amaqueen, is exactly 6 feet tall.
Tonight she delivers a
stirring soliloquy on stage.
For dramatic effect she is illuminated only by a single
footlight, which is at the same level as the floor of the stage.
24 feet behind the footlight
is the vertical backdrop of the stage.
As Amaqueen nears the climax of her soliloquy, she
begins walking towards the audience (and toward the footlight) at 2 feet per second.
When she is 8 feet from the footlight, at what rate is her shadow on the backdrop
increasing in height?
(Hint:
Make a diagram, and use similar triangles to start!)
20)
Refer back to the very first problem we did involving a taxicab.
This time, give the
westbound cab a quarter mile head start.
Keep everything else the same.
When the
northbound cab has gone ½ a mile from its starting position, how fast is the distance
between the two cabs increasing?
21)
A solution drains through a filter-funnel at a rate of 10cc/minute.
From the center point
of its mouth to its apex, the funnel is 10 cm.
At its mouth it is 12cm in diameter.
How
fast is the solution-level dropping when there are 200 cc left in the funnel?
(Assume that
the funnel is a right circular cone).
For reference, the volume of a cone is given by V =
h
r
2
3
1
.
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