A lighthouse is located on a small island 2 km away from the nearest point P...
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7. A police cruiser has a light on the roof rotating 6 revolutions per minute. The car is 30 feet away from a straight wall. How fast is the beam of light moving along the wall when it is 10 feet from the point on the wall nearest the car? A. 845 ft/sec B. 1257 ft/sec C. 987 ft/sec D. 1047 ft/sec
3.9 1. Balloons A spherical balloon is inflated and its volume increases at a rate of 15 in/min. What is the rate of change of its radius when the radius is 10 in? 2. Ladder against the wall A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.5 ft/s. How fast is the top of the ladder sliding down the wall...
The shortest distance across the water from an island dock (point D) to a straight shoreline is 9 miles. Let the closest point on the shoreline be A. An amphibious vehicle makes a trip from a depot at a point B on the shoreline that is 20 miles away from A. Suppose that it travels 20 – x miles toward A along the shoreline (where 0 ≤ x ≤ 20) to a point C, then strikes out across the water...
A woman is on a lake in a rowboat located 1 mi from the closest point P of a straight shoreline (see the accompanying figure). She wishes to get to point Q, 10mi along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 2mph and walk at a speed of 6 mph how should she pick the point R...
An offshore oil well must be connected by pipe to the refinery. The oil-well is 2 km off-shore. The refinery is on the coast, 3 km from the nearest point of land to the oil well. The coastline is perfectly straight. It costs $ S per kilometre to lay pipe along the shore, but U times as much per km to lay pipe undenwater. The pipe may be laid either straight to the refinery, or to an intermediate point on...
Related Rates 5. An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other. One plane is 225 miles from the point moving at 450 miles per hour. The other plane is 300 miles from the point moving at 600 miles per hour. a). At what rate is the distance between the planes decreasing? b). How much time does the air traffic controller have to get one...
(1 point) A street light is at the top of a 17 ft pole. A 6 ft tall girl walks along a straight path away trom the pole with a speed of 7 ft/sec At what rate is the tip of her shadow moving away from the light (ie away from the top of the pole) when the girl is 35 ft away from the pole? Answer How fast is her shadow lengthening? Answer
A small balloon is released at a point 60 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 10 feet per second, how fast (in feet per second) is the distance from the observer to the balloon increasing when the balloon is 80 feet high? 10 a
ornithologists have determined that some species o fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure....
Understanding Physical Science 14.5: A. A 10-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 2 feet from the wall? The top of the ladder is moving down at a rate of ___ feet/second when the foot of the ladder is 2 feet from the wall....