Explanation Given: Two devices A and B are placed with a distance of 2000 feet in between them. A is placed to the west of B and an explosive is detonated to the west of B at a distance of 200 feet. Another explosive is detonated to the north of B at an unknown distance. Formula used: Equation of an hyperbola: Center at ( 0 , 0 ) , and major axis along x -axis: “An equation of the hyperbola with center at ( 0 , 0 ) , foci at ( ± c , 0 ) , and vertices at ( ± a , 0 ) is x 2 a 2 − y 2 b 2 = 1 where a > b > 0 and b 2 = c 2 − a 2 .” Calculation: The distance between the devices A and B is 2000 ft. Consider the center of the devices as origin. Then the devices are placed at the point of ( − 2000 2 , 0 2 ) and ( 2000 2 , 0 2 ) . Thus, the devices are placed at A ( − 1000 , 0 ) and B ( 1000 , 0 ) where device A is to west of the device B . Since the explosive is detonated 200 feet to the west of B , the point the detonation is ( 1000 , 0 ) − ( 200 , 0 ) . That is, D 1 = ( 800 , 0 ) . Since the explosive is detonated y feet to the north of B , the point the detonation is ( 1000 , 0 ) + ( 0 , y ) . That is, D 2 = ( 1000 , y ) . Now sketch the detonations with the above information as shown in below Figure 1. From Figure 1, the vertices are at A ( − 1000 , 0 ) and B ( 1000 , 0 ) and focus is D 1 ( 800 , 0 ) . Note that the focus is of the form ( c , 0 ) . As the focus lies on the positive x -axis, the major axis is along the x -axis. Then the values of a and c are 800 and 1000, respectively. Thus, the equation of the hyperbola is of the form, x 2 a 2 − y 2 b 2 = 1 where a = 800 and c = 1000

College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)

7th Edition

ISBN: 9780134111315

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter 7, Problem 23RE

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The distance to the north at which the site of the second explosion should be chosen so that the difference recorded by the devices for the second detonation is the same as that recorded for the first detonation.

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Chapter 7, Problem 22RE

Chapter 7, Problem 1CT

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Chapter 7 Solutions

College Algebra Enhanced with Graphing Utilities (7th Edition) (Sullivan Enhanced with Graphing Utilities Series)

Ch. 7.2 - The formula for the distance d from to is ...Ch. 7.2 - Prob. 2AYU Ch. 7.2 - Prob. 3AYU Ch. 7.2 - Prob. 4AYU Ch. 7.2 - Prob. 5AYU Ch. 7.2 - Prob. 6AYU Ch. 7.2 - Prob. 7AYU Ch. 7.2 - Prob. 8AYU Ch. 7.2 - Prob. 9AYU Ch. 7.2 - Prob. 10AYU

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