1. At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 18 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
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2. When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV14=C where C is a constant. Suppose that at a certain instant the volume is 410 cubic centimeters and the pressure is 75 kPa and is decreasing at a rate of 11 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
(Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )
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3. A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 8 km and climbs at an angle of 50 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 1 minutes later?
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4. Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 18 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V=1/3r2h.
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5. A particle is moving along the curve y=2*sqrt(5x+1). As the particle passes through the point (38), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.