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Problem #4: The temperature at a point (x, y) on a rectangular metal plate is given by 100 T(x, y) 6x +y (a) Find the rate of change of T at the point (3, 4) in the direction of the vector (-3,-4) (b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest. (c) What is the maximum rate of change of T at the point (3, 4)?

Problem #4: The temperature at a point (x, y) on a rectangular metal plate is given by 100 T(x, y) 6x +y (a) Find the rate of change of T at the point (3, 4) in the direction of the vector (-3,-4) (b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest. (c) What is the maximum rate of change of T at the point (3, 4)?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter16: Temperature And The Kinetic Theory Of Gases
Section: Chapter Questions
Problem 14OQ: An ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900...
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The temperature at a point (x, y) on a rectangular metal plate is given by

T(x, y)  =  
100
6x2 + y2
(a) Find the rate of change of T at the point (3, 4) in the direction of the vector (−3, −4)
(b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest.
(c) What is the maximum rate of change of T at the point (3, 4)?
Problem #4: The temperature at a point (x, y) on a rectangular metal plate is given by 100 T(x, y) 6x- + y (a) Find the rate of change of T at the point (3, 4) in the direction of the vector (-3,-4) (b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest. (c) What is the maximum rate of change of T at the point (3, 4)? Problem #4(a): Round your answer to 4 decimals. Enter your answer symbolically, as in these examples Enter the components of the unit vector separated with a comma. Problem #4(b): Problem #4(c): Round your answer to 4 decimals. Just Save Your work has been saved! (Back to Admin Page) Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) Your Mark: 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c)
Transcribed Image Text:Problem #4: The temperature at a point (x, y) on a rectangular metal plate is given by 100 T(x, y) 6x- + y (a) Find the rate of change of T at the point (3, 4) in the direction of the vector (-3,-4) (b) At the point (3, 4), find a unit vector in the direction in which the temperature increases the fastest. (c) What is the maximum rate of change of T at the point (3, 4)? Problem #4(a): Round your answer to 4 decimals. Enter your answer symbolically, as in these examples Enter the components of the unit vector separated with a comma. Problem #4(b): Problem #4(c): Round your answer to 4 decimals. Just Save Your work has been saved! (Back to Admin Page) Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) Your Mark: 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c) 4(a) 4(b) 4(c)
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