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A train is moving west along a long straight track toward a station. An observer is located at a point 0.75 miles directly south of the train station with a camera (see figure below). 0.75 me (a) Let x represent the distance of the train to the station. Express x in terms of e (b) (c) The observer notices that when the train is 2.5 miles from the station, he is having to rotate his camera at a rate of 0.06 radians minute to keep the train in focus. Write an appropriate mathematical statement for each of these two pieces of information using the variables defined in this problem. Use Leibniz notation for any derivatives. Use implicit differentiation to find d when the train is 2.5 miles from the station means what about x? the observer rotating his camera 0.06 radians per minute means what about the angle ? (d) How fast is the train traveling at the instant described in part (c)? Give your answer to the nearest miles per hour.

A train is moving west along a long straight track toward a station. An observer is located at a point 0.75 miles directly south of the train station with a camera (see figure below). 0.75 me (a) Let x represent the distance of the train to the station. Express x in terms of e (b) (c) The observer notices that when the train is 2.5 miles from the station, he is having to rotate his camera at a rate of 0.06 radians minute to keep the train in focus. Write an appropriate mathematical statement for each of these two pieces of information using the variables defined in this problem. Use Leibniz notation for any derivatives. Use implicit differentiation to find d when the train is 2.5 miles from the station means what about x? the observer rotating his camera 0.06 radians per minute means what about the angle ? (d) How fast is the train traveling at the instant described in part (c)? Give your answer to the nearest miles per hour.

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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A train is moving west along a long straight track toward a station. An observer is located at a point 0.75 miles directly south of the train station with a camera (see figure below). Station 0.75 miles Observer -Train (a) Let x represent the distance of the train to the station. Express x in terms of 0. X = dx (b) Use implicit differentiation to find dt (c) The observer notices that when the train is 2.5 miles from the station, he is having to rotate his camera at a rate of 0.06 radians per minute to keep the train in focus. Write an appropriate mathematical statement for each of these two pieces of information using the variables defined in this problem. Use Leibniz notation for any derivatives. = when the train is 2.5 miles from the station means what about x? the observer rotating his camera 0.06 radians per minute means what about the angle 0? (d) How fast is the train traveling at the instant described in part (c)? Give your answer to the nearest miles per hour.
Transcribed Image Text:A train is moving west along a long straight track toward a station. An observer is located at a point 0.75 miles directly south of the train station with a camera (see figure below). Station 0.75 miles Observer -Train (a) Let x represent the distance of the train to the station. Express x in terms of 0. X = dx (b) Use implicit differentiation to find dt (c) The observer notices that when the train is 2.5 miles from the station, he is having to rotate his camera at a rate of 0.06 radians per minute to keep the train in focus. Write an appropriate mathematical statement for each of these two pieces of information using the variables defined in this problem. Use Leibniz notation for any derivatives. = when the train is 2.5 miles from the station means what about x? the observer rotating his camera 0.06 radians per minute means what about the angle 0? (d) How fast is the train traveling at the instant described in part (c)? Give your answer to the nearest miles per hour.
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