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Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. a. Start counting time with t = 0 at noon and express the dis- tance s between the ships as a function of t. b. How rapidly was the distance between the ships changing at noon? One hour later? c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? d. Graph s and ds/dt together as functions of t for -1 SIS3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). e. The graph of ds/dt looks as if it might have a horizontal as- ymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t0o. What is this value? What is its relation to the ships' individual speeds?

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. a. Start counting time with t = 0 at noon and express the dis- tance s between the ships as a function of t. b. How rapidly was the distance between the ships changing at noon? One hour later? c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? d. Graph s and ds/dt together as functions of t for -1 SIS3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). e. The graph of ds/dt looks as if it might have a horizontal as- ymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t0o. What is this value? What is its relation to the ships' individual speeds?

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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Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. a. Start counting time with t = 0 at noon and express the dis- tance s between the ships as a function of t. b. How rapidly was the distance between the ships changing at noon? One hour later? c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? d. Graph s and ds/dt together as functions of t for -1 SIS3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). e. The graph of ds/dt looks as if it might have a horizontal as- ymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t0o. What is this value? What is its relation to the ships' individual speeds?
Transcribed Image Text:Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (nautical miles per hour; a nautical mile is 2000 yd) and continued to do so all day. Ship B was sailing east at 8 knots and continued to do so all day. a. Start counting time with t = 0 at noon and express the dis- tance s between the ships as a function of t. b. How rapidly was the distance between the ships changing at noon? One hour later? c. The visibility that day was 5 nautical miles. Did the ships ever sight each other? d. Graph s and ds/dt together as functions of t for -1 SIS3, using different colors if possible. Compare the graphs and reconcile what you see with your answers in parts (b) and (c). e. The graph of ds/dt looks as if it might have a horizontal as- ymptote in the first quadrant. This in turn suggests that ds/dt approaches a limiting value as t0o. What is this value? What is its relation to the ships' individual speeds?
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