3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:3. Suppose that the temperature on a metal plate is given by the function T with
T(x, y) = 100 - (x² +4y²)
where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now
suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the
point (1, 4) to the point (5, 6).
(a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6)
in one minute at a constant speed.
(b) What can you say about
dr
dt
and
dy
dt
for every value of t?
(c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi-
encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.
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