A drone, flying at a constant altitude, is designed to monitor an industrial area for signs of illegal emissions and toxic leaks. Environmentalists studying the area have determined that the concentration of pollution (in parts per million) above an emission site, at the altitude where the drone is flying, can be modeled by P(x,y)=e-(x^2+2y^2)/10000 where x and y are measured in meters, in a rectangular coordinate system, with the source of pollution at the origin. When the drone detects pollution on its patrol, it changes course and travels in the direction in which the concentration of pollution particles increases most rapidly. (a) Sketch several level curves of the pollution function, along with a possible path that the drone will follow to the source. (b) Suppose that the drone is located at the point (a, b) when it detects the presence of pollution. Find an equation describing the drone’s path to the source.
A drone, flying at a constant altitude, is designed to monitor an industrial area for signs of
illegal emissions and toxic leaks. Environmentalists studying the area have determined that
the concentration of pollution (in parts per million) above an emission site, at the altitude
where the drone is flying, can be modeled by
P(x,y)=e-(x^2+2y^2)/10000
where x and y are measured in meters, in a rectangular
of pollution at the origin. When the drone detects pollution on its patrol, it changes course
and travels in the direction in which the concentration of pollution particles increases most
rapidly.
(a) Sketch several level curves of the pollution function, along with a possible path that the
drone will follow to the source.
(b) Suppose that the drone is located at the point (a, b) when it detects the presence of
pollution. Find an equation describing the drone’s path to the source.
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