Find the path followed by a heat seeking particle

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1. Some bacteria can sense the "nutritional gradient" and will move in the direction of higher concentration of nutrients. Imagine that such a bacteria is placed at the point P(10, 10) in a dish in which the nutrition concentration is given by by N(x, y) =400 - 2x²-y². Sketch the path of the bacteria as it swims towards higher concentrations.

2. The temperature field in the neighborhood of (π / 4, 0) is given by T(x, y) = square root 2 e^-y cos (x). Find the path followed by a heat seeking particle originating at (π / 4, 0).

Reference no: EM131008588

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