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Question 5 Your job is to determine a location for a Y-junction that minimizes the total distance to three sites. (a) Suppose the sites are at coordinates (0,4), (0, -4), and (10,0). The symmetry implies that the junction should lie on the positive x-axis, but we must still determine the x-coordinate. Find the point (x,0) that minimizes the sum of the distances to the three sites. Then use trigonometry to determine the angle formed by the segments connecting the three sites to the optimal junction. site A, (0,4) Junction, (x, 0) site C, (10, 0) site B, (0, -4) (b) Contrast the above with the scenario where the third site is much closer to the first two. In particular, suppose that the three sites are at (0,4), (0, –4), and (2,0) and find the point (x, 0) that is the minimum total distance from these three sites.

Question 5 Your job is to determine a location for a Y-junction that minimizes the total distance to three sites. (a) Suppose the sites are at coordinates (0,4), (0, -4), and (10,0). The symmetry implies that the junction should lie on the positive x-axis, but we must still determine the x-coordinate. Find the point (x,0) that minimizes the sum of the distances to the three sites. Then use trigonometry to determine the angle formed by the segments connecting the three sites to the optimal junction. site A, (0,4) Junction, (x, 0) site C, (10, 0) site B, (0, -4) (b) Contrast the above with the scenario where the third site is much closer to the first two. In particular, suppose that the three sites are at (0,4), (0, –4), and (2,0) and find the point (x, 0) that is the minimum total distance from these three sites.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Question 5 Your job is to determine a location for a Y-junction that minimizes the total distance to three sites. (a) Suppose the sites are at coordinates (0,4), (0, –4), and (10,0). The symmetry implies that the junction should lie on the positive x-axis, but we must still determine the x-coordinate. Find the point (x,0) that minimizes the sum of the distances to the three sites. Then use trigonometry to determine the angle formed by the segments connecting the three sites to the optimal junction. site A, (0, 4) Junction, (x, 0) site C, (10,0) site B, (0, -4) (b) Contrast the above with the scenario where the third site is much closer to the first two. In particular, suppose that the three sites are at (0,4), (0, –4), and (2,0) and find the point (x, 0) that is the minimum total distance from these three sites.
Transcribed Image Text:Question 5 Your job is to determine a location for a Y-junction that minimizes the total distance to three sites. (a) Suppose the sites are at coordinates (0,4), (0, –4), and (10,0). The symmetry implies that the junction should lie on the positive x-axis, but we must still determine the x-coordinate. Find the point (x,0) that minimizes the sum of the distances to the three sites. Then use trigonometry to determine the angle formed by the segments connecting the three sites to the optimal junction. site A, (0, 4) Junction, (x, 0) site C, (10,0) site B, (0, -4) (b) Contrast the above with the scenario where the third site is much closer to the first two. In particular, suppose that the three sites are at (0,4), (0, –4), and (2,0) and find the point (x, 0) that is the minimum total distance from these three sites.
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