Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (11,0)(11,0) in the ??xy-plane, Springfield is at (0,2)(0,2), and Shelbyville is at (0,−2)(0,−2). The cable runs from Centerville to some point (?,0)(x,0) on the ?x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (?,0)(x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (11,0)(11,0) in the ??xy-plane, Springfield is at (0,2)(0,2), and Shelbyville is at (0,−2)(0,−2). The cable runs from Centerville to some point (?,0)(x,0) on the ?x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (?,0)(x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
. Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y-shaped configuation. Centerville is located at (11,0)(11,0) in the ??xy-plane, Springfield is at (0,2)(0,2), and Shelbyville is at (0,−2)(0,−2). The cable runs from Centerville to some point (?,0)(x,0) on the ?x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (?,0)(x,0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
Transcribed Image Text:To solve this problem we need to minimize the following function of x:
\( f(x) = \underline{\hspace{50px}} \)
We find that \( f(x) \) has a critical number at \( x = \underline{\hspace{50px}} \)
To verify that \( f(x) \) has a minimum at this critical number we compute the second derivative \( f''(x) \) and find that its value at the critical number is \( \underline{\hspace{50px}} \), a positive number.
Thus the minimum length of cable needed is \( \underline{\hspace{50px}} \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
