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In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. The radius r of the circle is increasing at the rate of 30 r(t) = %3D V2t +4 ft/min t min after the rupture occurs. 1. To integrate r'(t), we'll want to use the method of integration by substitution. What expression could we let u be in our substitution? What is the corresponding expression for du? 2. Find the general antiderivative of r'(t) using your u from the previous part. 3. Since the rupture occurred at t = 0, we can assume that for that brief instant, r(0) = 0. Using this initial value, find r(t). %3D 4. What is the radius of the polluted area 16 min after the rupture occurred? 5. Recall that the oil slick is circular. What is the area of this circle 16 min after the rupture occurred? (Round your answer to the nearest square foot.)

In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. The radius r of the circle is increasing at the rate of 30 r(t) = %3D V2t +4 ft/min t min after the rupture occurs. 1. To integrate r'(t), we'll want to use the method of integration by substitution. What expression could we let u be in our substitution? What is the corresponding expression for du? 2. Find the general antiderivative of r'(t) using your u from the previous part. 3. Since the rupture occurred at t = 0, we can assume that for that brief instant, r(0) = 0. Using this initial value, find r(t). %3D 4. What is the radius of the polluted area 16 min after the rupture occurred? 5. Recall that the oil slick is circular. What is the area of this circle 16 min after the rupture occurred? (Round your answer to the nearest square foot.)

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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In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. The radius r of the circle is increasing at the rate of 30 "(t) = V2t +4 ft/min t min after the rupture occurs. 1. To integrate r'(t), we'll want to use the method of integration by substitution. What expression could we let u be in our substitution? What is the corresponding expression for du? 2. Find the general antiderivative of r'(t) using your u from the previous part. 3. Since the rupture occurred at t = 0, we can assume that for that brief instant, r(0) = 0. Using this initial value, find r(t). 4. What is the radius of the polluted area 16 min after the rupture occurred? 5. Recall that the oil slick is circular. What is the area of this circle 16 min after the rupture occurred? (Round your answer to the nearest square foot.) MacBook Air 000 000 F4 F7 F8 F9
Transcribed Image Text:In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape. The radius r of the circle is increasing at the rate of 30 "(t) = V2t +4 ft/min t min after the rupture occurs. 1. To integrate r'(t), we'll want to use the method of integration by substitution. What expression could we let u be in our substitution? What is the corresponding expression for du? 2. Find the general antiderivative of r'(t) using your u from the previous part. 3. Since the rupture occurred at t = 0, we can assume that for that brief instant, r(0) = 0. Using this initial value, find r(t). 4. What is the radius of the polluted area 16 min after the rupture occurred? 5. Recall that the oil slick is circular. What is the area of this circle 16 min after the rupture occurred? (Round your answer to the nearest square foot.) MacBook Air 000 000 F4 F7 F8 F9
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