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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
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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1 -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
Transcribed Image Text:1 -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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