Related Rates Example 1 2 2 4 9 45 x y   Given that...

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3.7 Related Rates Example 1 2 2 4 9 45 x y . Given that 2 dx dt , find dy dt when x = 3. Example 2 Oil spilled from a ruptured tanker spreads in a circular pattern whose radius is constantly increasing at 2 ft/sec. How fast is the area of the spill increasing when the radius of the spill is 60 ft? Example 3a
A spherical balloon is inflated with helium at a rate of 3 in 200 . How fast is the balloon’s radius increasing at
the moment the radius is 5 inches? Example 3b A spherical cell is growing at a constant rate of 400 µm 3 /day (1 µm= 10 -6 m). At what rate is the radius increasing at the moment the radius is 10 µm? Example 4a Water runs into a tank, which is shaped like an upside-down cone at a rate of 9 3 ft min . The height of the water is twice the radius of the top of the water level at all times. How fast is the water level rising when the water is 6 feet deep?

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