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 = √3+t, y = 6 + centimeters. The temperature function satisfies Tx(4, 7) = 4 and T,(4, 7) = 3. How fast is the temperature rising on the bug's path after 13 seconds? Step 1 We know that the rate of change of the temperature is given by Using x = √3+ t and y = 6 + , we have 13 Step 3 dx dt We are given that T (4, 7) = 4 and T,(4, 7) = 3. dv = dT ƏT dx dt ax dt = du ƏT dy ay dt ду Step 2 To find x and y after 13 seconds, we substitute t = 13 into the above equations to obtain x = 4✔ 1 2√3+1 and dy dt = 1 13. 4 1 13 and y = 7✔ 7 t, where x and y are measured in. ₁
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 = √3+t, y = 6 + centimeters. The temperature function satisfies Tx(4, 7) = 4 and T,(4, 7) = 3. How fast is the temperature rising on the bug's path after 13 seconds? Step 1 We know that the rate of change of the temperature is given by Using x = √3+ t and y = 6 + , we have 13 Step 3 dx dt We are given that T (4, 7) = 4 and T,(4, 7) = 3. dv = dT ƏT dx dt ax dt = du ƏT dy ay dt ду Step 2 To find x and y after 13 seconds, we substitute t = 13 into the above equations to obtain x = 4✔ 1 2√3+1 and dy dt = 1 13. 4 1 13 and y = 7✔ 7 t, where x and y are measured in. ₁
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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-t, where x and y are measured in
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 = √3+ t, y = 6 +
centimeters. The temperature function satisfies Tx(4, 7) = 4 and Ty(4, 7) = 3. How fast is the temperature rising on the bug's path after 13 seconds?
13
Step 1
dT ƏT dx at dy
We know that the rate of change of the temperature is given by.
+
dt
ax dt
ay dt
Using x = √√3+ t and y = 6 + -t, we have
1
13
Step 2
dx
dt
We are given that Tx(4, 7) = 4 and T,(4, 7) = 3.
Step 3
dx
Also, after 13 seconds, we have = 4
dt
=
²/² (3+1)
=
12
To find x and y after 13 seconds, we substitute t = 13 into the above equations to obtain x =
1
2√3+t
X and = 7
dy
dt
1
and =
dt 13
dy
X
1
13
4 and y = 7✔
7
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