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These are problems involving rates of
change of related variables. The variables
usually have a relationship to time.
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Example 1
Example 2 Let
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Oil is running out of an inverted conical
tank at the rate of 3π m3/min. If the tank
has a radius of 2.5 m at the top and a
depth of 10 m, how fast is the depth of
the oil changing when it is 8 m.
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Example
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A balloon is rising vertically above a level
straight road at a constant rate of 1 ft/sec.
Just when the balloon is 65 ft above the
ground, a bicycle moving at a constant rate
of 17 ft/sec passes under it. How fast is the
distance between the bicycle and the balloon
increasing 3 seconds later?
x2 + y2 = z2
z
x
y
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A trough is 12 ft long and 3 ft across the top.
Its ends are isosceles triangles with altitudes
of three ft.
a) If water is being pumped
into the trough at 2 cubic
ft/min, how fast is the
level rising when its
height is 1 ft deep?
b) If the water is rising at a rate of 3/8 in/min
when h = 2, determine the rate at which
the water is being pumped into the trough.
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