Newton's Cooling: Professor Westin lives in a two story house. One cold winter night the Professor's furnace (which is housed on the first floor) fails! Suppose each floor exchanges heat with it's environment according to Newton' Law of Cooling. Suppose the system discussed in class is a model for the temperature ₁ downstairs and the temperature 2 upstairs: *-3-71* 10 x' = -6 X (a) Determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = components, 2₁ (t) and r2(t), of your solution. 70 60 Use desmos to graph the 70 " 60 (b) Again, determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = but now assume the furnace does not simply die in an instant, but instead dies a slow death, supplying heat downstairs at the rate e-t. That is, solve the nonhomogeneous system wi 1 with F(t) = [0]. Use desmos to graph the components, x₁(1) and r2(t), of your solution.
Newton's Cooling: Professor Westin lives in a two story house. One cold winter night the Professor's furnace (which is housed on the first floor) fails! Suppose each floor exchanges heat with it's environment according to Newton' Law of Cooling. Suppose the system discussed in class is a model for the temperature ₁ downstairs and the temperature 2 upstairs: *-3-71* 10 x' = -6 X (a) Determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = components, 2₁ (t) and r2(t), of your solution. 70 60 Use desmos to graph the 70 " 60 (b) Again, determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = but now assume the furnace does not simply die in an instant, but instead dies a slow death, supplying heat downstairs at the rate e-t. That is, solve the nonhomogeneous system wi 1 with F(t) = [0]. Use desmos to graph the components, x₁(1) and r2(t), of your solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Newton's Cooling: Professor Westin lives in a two story house. One cold winter night the Professor's furnace
(which is housed on the first floor) fails! Suppose each floor exchanges heat with it's environment according to
Newton' Law of Cooling. Suppose the system discussed in class is a model for the temperature ₁ downstairs and
the temperature 2 upstairs:
*-3-71*
=
10
x'
=
-6
X
(a) Determine x(t) for times t> 0 if the temperatures at t = 0 are given by x =
components, 2₁ (t) and x2(t), of your solution.
70
60
Use desmos to graph the
70
"
60
(b) Again, determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = but now assume the
furnace does not simply die in an instant, but instead dies a slow death, supplying heat downstairs at the rate
e-t. That is, solve the nonhomogeneous system wi
1 with f(t) = [0]. Use desmos to graph the components, 2₁(1)
and r2(t), of your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeeb7c66-0798-43fa-9a0f-eb1dc3206797%2F4dbac4ea-bd42-4d9a-8930-879d53e32437%2Fx9vvbkl_processed.png&w=3840&q=75)
Transcribed Image Text:Newton's Cooling: Professor Westin lives in a two story house. One cold winter night the Professor's furnace
(which is housed on the first floor) fails! Suppose each floor exchanges heat with it's environment according to
Newton' Law of Cooling. Suppose the system discussed in class is a model for the temperature ₁ downstairs and
the temperature 2 upstairs:
*-3-71*
=
10
x'
=
-6
X
(a) Determine x(t) for times t> 0 if the temperatures at t = 0 are given by x =
components, 2₁ (t) and x2(t), of your solution.
70
60
Use desmos to graph the
70
"
60
(b) Again, determine x(t) for times t> 0 if the temperatures at t = 0 are given by x = but now assume the
furnace does not simply die in an instant, but instead dies a slow death, supplying heat downstairs at the rate
e-t. That is, solve the nonhomogeneous system wi
1 with f(t) = [0]. Use desmos to graph the components, 2₁(1)
and r2(t), of your solution.
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