If T (x, y) is the temperature at a point (x, y) on a thin metalplate in the xy-plane
Chapter 13, Problem 69(choose chapter or problem)
If \(T(x,y)\) is the temperature at a point \((x,y)\) on a thin metal plate in the \(xy\)-plane, then the level curves of \(T\) are called, isothermal curves. All points on such a curve are at the same temperature. Suppose that a plate occupies the first quadrant and \(T(x,y)=xy\).
(a) Sketch the isothermal curves on which \(T=1,T=2\), and \(T=3\).
(b) An ant, initially at \((1,4)\), wants to walk on the plate so that the temperature along its path remains constant. What path should the ant take and what is the temperature along that path?
Equation Transcription:
Text Transcription:
T(x,y)
(x,y)
xy
T
T(x,y)=xy
T=1,T=2
T=3
(1,4)
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