A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature at any point on the disk is given by T(x, y) = 50e 2a*-y" degrees Celsius, where x and y are measured in meters. (a) What shapes are the level curves of T? (b) Where on the disk is the temperature the greatest? What is the temperature at that point? (c) Find the direction of greatest temperature increase at the point (1, 1). (d) What is the rate of temperature change if you move away from the point (1, 1) in the direction of the point (2,0)?

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature at any
point on the disk is given by T(x,y)
= 50e 2a*-y degrees Celsius, where x and y are measured in meters.
(a) What shapes are the level curves of T?
(b) Where on the disk is the temperature the greatest? What is the temperature at that point?
(c) Find the direction of greatest temperature increase at the point (1, 1).
(d) What is the rate of temperature change if you move away from the point (1, 1) in the direction of the
point (2,0)?
Transcribed Image Text:A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature at any point on the disk is given by T(x,y) = 50e 2a*-y degrees Celsius, where x and y are measured in meters. (a) What shapes are the level curves of T? (b) Where on the disk is the temperature the greatest? What is the temperature at that point? (c) Find the direction of greatest temperature increase at the point (1, 1). (d) What is the rate of temperature change if you move away from the point (1, 1) in the direction of the point (2,0)?
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