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a) What is the coordinate of the city? What is the direct distance between the city and the station? b) The station, the town, and the city form a plane. Express the equations of this plane using the two distinct strategies we learned. c) Use Calculus concepts to answer this: during the time that the train traveled from the station to the town, what is the longest and the shortest distance to the city?

a) What is the coordinate of the city? What is the direct distance between the city and the station? b) The station, the town, and the city form a plane. Express the equations of this plane using the two distinct strategies we learned. c) Use Calculus concepts to answer this: during the time that the train traveled from the station to the town, what is the longest and the shortest distance to the city?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A space train departs from the station at (5, -2, 0) at 1:00 pm. For 2 hours, it has a velocity of (-1, 0, 7) kilometers per hour to reach a town. Then it turns to have the velocity of (0, 7, 1) kilometers per hour and runs for 3 hours to reach a city. Each unit is 1 km. a) What is the coordinate of the city? What is the direct distance between the city and the station? b) The station, the town, and the city form a plane. Express the equations of this plane using the two distinct strategies we learned. c) Use Calculus concepts to answer this: during the time that the train traveled from the station to the town, what is the longest and the shortest distance to the city?
Transcribed Image Text:A space train departs from the station at (5, -2, 0) at 1:00 pm. For 2 hours, it has a velocity of (-1, 0, 7) kilometers per hour to reach a town. Then it turns to have the velocity of (0, 7, 1) kilometers per hour and runs for 3 hours to reach a city. Each unit is 1 km. a) What is the coordinate of the city? What is the direct distance between the city and the station? b) The station, the town, and the city form a plane. Express the equations of this plane using the two distinct strategies we learned. c) Use Calculus concepts to answer this: during the time that the train traveled from the station to the town, what is the longest and the shortest distance to the city?
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