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Minimum-length roads A house is located at each corner of

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 51E Chapter 4.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 51E

Minimum-length roads A house is located at each corner of a square with side lengths of 1 mi. What is the length of the shortest road system with straight roads that connects all of the houses by roads (that is, a road system that allows one to drive from any house to any other house?)? (H ? int: Place two points inside the square at which roads meet.?) (S ? ource: Halmos. for Mathematicians Young and ? Old.)

Step-by-Step Solution:

Solution Step 1 Consider A BCD as the square and let the houses be located at each corner. Step 2 : Let E be the optimum point, located in th e middle of the road F G. Consider D as the sum of the individual distances to ea ch house from the point E. Therefore, As the shortest length of the roads to each house is to be found out therefore optimize the function D. In order to this, find the value of each road and after adding those find the minimum value for D . Each house is located at a distance of 1mile from its adjacent house. Therefore, Consider as the distance of IB such that . Also, Since E is located in the middle, Apply Pythagoras theorem to triangles AFH. It is clear from the diagram that, Therefore, Now substitute all the values into D,

Step 3 of 4

Chapter 4.4, Problem 51E is Solved
Step 4 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This full solution covers the following key subjects: roads, house, square, system, road. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 51E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 51E from 4.4 chapter was answered, more than 335 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Minimum-length roads A house is located at each corner of a square with side lengths of 1 mi. What is the length of the shortest road system with straight roads that connects all of the houses by roads (that is, a road system that allows one to drive from any house to any other house?)? (H ? int: Place two points inside the square at which roads meet.?) (S ? ource: Halmos. for Mathematicians Young and ? Old.)” is broken down into a number of easy to follow steps, and 78 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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