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LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150,0) and (150, 0) and that a ship is traveling on a path with coordinates (x, 75), (see the figure below). Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 seconds = 1 microseconds).

LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150,0) and (150, 0) and that a ship is traveling on a path with coordinates (x, 75), (see the figure below). Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 seconds = 1 microseconds).

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Trigonometric Functions: Right Triangle Approach
Section5.1: Angle Measure
Problem 4E: Object A is travelling along a circle of radius 2, and Object B is travelling along a circle of...
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LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150,0) and (150, 0) and that a ship is traveling on a path with coordinates (x, 75), (see the figure below). Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 seconds = 1 microseconds). -150 150 -75 -75 <-150 75 150
Transcribed Image Text:LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150,0) and (150, 0) and that a ship is traveling on a path with coordinates (x, 75), (see the figure below). Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 seconds = 1 microseconds). -150 150 -75 -75 <-150 75 150
Use rotation of axes to show that the equation 2x² - 72xy + 23y² - 80x - 60y = 125 represents a hyperbola. Then: 1. Find the XY-coordinates of the foci. 2. Find the xy-coordinates of the foci. 3. Find the xy-coordinates of the vertices. 4. Find the equations of the asymptotes in the xy-coordinate system. 5. Find the eccentricity of the hyperbola.
Transcribed Image Text:Use rotation of axes to show that the equation 2x² - 72xy + 23y² - 80x - 60y = 125 represents a hyperbola. Then: 1. Find the XY-coordinates of the foci. 2. Find the xy-coordinates of the foci. 3. Find the xy-coordinates of the vertices. 4. Find the equations of the asymptotes in the xy-coordinate system. 5. Find the eccentricity of the hyperbola.
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