Q: Gravel is being dumped from a conveyor belt at a rate of
Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is...
See AnswerQ: A kite 100 ft above the ground moves horizontally at a speed
A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?
See AnswerQ: The sides of an equilateral triangle are increasing at a rate of
The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area of the triangle increasing when the sides are 30 cm long?
See AnswerQ: How fast is the angle between the ladder and the ground changing
How fast is the angle between the ladder and the ground changing in Example 2 when the bottom of the ladder is 6 ft from the wall? Data from Example 2: A ladder 10 ft long rests against a vertical wa...
See AnswerQ: The top of a ladder slides down a vertical wall at a
The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s. How long is...
See AnswerQ: According to the model we used to solve Example 2, what
According to the model we used to solve Example 2, what happens as the top of the ladder approaches the ground? Is the model appropriate for small values of y? Data from Example 2: A ladder 10 ft lon...
See AnswerQ: If the minute hand of a clock has length r (in
If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out area as a function of r.
See AnswerQ: A faucet is filling a hemispherical basin of diameter 60 cm with
A faucet is filling a hemispherical basin of diameter 60 cm with water at a rate of 2 L/min. Find the rate at which the water is rising in the basin when it is half full. [Use the following facts: 1 L...
See AnswerQ: Boyle’s Law states that when a sample of gas is compressed at
Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant...
See AnswerQ: When air expands adiabatically (without gaining or losing heat), its
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4 = C, where C is a constant. Suppose that at a certain instant the volume...
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