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Ant on a metal plate. The temperature at a point ( x, y) on a metal...

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Basic Math

Ant on a metal plate. The temperature at a point ( x, y) on ametal plate is T(x, y) = 4x2 - 4xy + y2 . Anant on the plate walks around the circle of radius 10 centered atthe origin.

a) What are the highest and lowest temperatures encountered bythe ant?

b) Suppose the ant has changed its trajectory and is walkingaround the circle of radius 5. Is the highest temperatureencountered by the ant greater or less compared to the one in parta)?

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