The graph of the equation
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Chapter 11 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Navigation 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 with coordinates (150,0)and (150,0)and that a ship is traveling on a path with coordinates (x,75), as shown in the figure. 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 second).arrow_forwardNavigation 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 with coordinates 150,0 and 150,0 and that a ship is traveling on a hyperbolic path with coordinates x,75 (see figure). (a) 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 second). (b) Determine the distance between the port and station A. (c) Find a linear equation that approximates the ship’s path as it travels far away from the shore.arrow_forwardSonic boom The position of a sonic boom caused by the faster-than-sound aircraft is one branch of the hyperbola y2x2=25 in the coordinate system shown. How wide is the hyperbola 5 miles from its vertex?arrow_forward
- 37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions. Foci (5,0), length of transverse axis:6arrow_forwardThe graph of the equation x2=4py is a parabola with focus F(__, __) and directrix y = ____. So the graph of x2=12y is a parabola with focus F(__, __) and directrix y = ____.arrow_forwardProperty of a Hyperbola Use the figure to show that d2d1=2a.arrow_forward
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