Tutorial Exercise The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = √10 + t, y = 7+1t, where x and y are measured in centimeters. The temperature function satisfies Tx(4, 8) = 4 and Ty(4, 8) : = 1. How fast is the temperature rising on the bug's path after 6 seconds? Step 1 dT We know that the rate of change of the temperature is given by dt aT dx ax dt aT dy + ay dt Using x = √10 + t and y = 7 + 1½t, we have dx dt and dy dt
Tutorial Exercise The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = √10 + t, y = 7+1t, where x and y are measured in centimeters. The temperature function satisfies Tx(4, 8) = 4 and Ty(4, 8) : = 1. How fast is the temperature rising on the bug's path after 6 seconds? Step 1 dT We know that the rate of change of the temperature is given by dt aT dx ax dt aT dy + ay dt Using x = √10 + t and y = 7 + 1½t, we have dx dt and dy dt
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Question
![Tutorial Exercise
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = √10 + t, y = 7+1t, where x and y are measured in
centimeters. The temperature function satisfies Tx(4, 8) = 4 and Ty(4, 8) :
=
1. How fast is the temperature rising on the bug's path after 6 seconds?
Step 1
dT
We know that the rate of change of the temperature is given by
dt
aT dx
ax dt
aT dy
+
ay dt
Using x = √10 + t and y = 7 + 1½t,
we have
dx
dt
and
dy
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e533fec-51fd-4870-9b3f-7eb1d9840991%2Fb142266e-e6ca-487e-a179-2245f9d03be1%2Fkkc54oj_processed.png&w=3840&q=75)
Transcribed Image Text:Tutorial Exercise
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = √10 + t, y = 7+1t, where x and y are measured in
centimeters. The temperature function satisfies Tx(4, 8) = 4 and Ty(4, 8) :
=
1. How fast is the temperature rising on the bug's path after 6 seconds?
Step 1
dT
We know that the rate of change of the temperature is given by
dt
aT dx
ax dt
aT dy
+
ay dt
Using x = √10 + t and y = 7 + 1½t,
we have
dx
dt
and
dy
dt
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