Pipe is going to be laid from point A to point B and going through point C as shown in the picture. Distances are in miles and as indicated in the picture. The position of point C is up to the pipe layers but point C must lie on the straight line shown in the picture. Laying the pipe from point A to point C involves laying the pipe under water and costs 3 million dollars per mile. Laying the pipe from point C to point B involves laying the pipe over land and costs 1 million dollars per mile. Find the value of x in the picture to minimize the total cost of laying the pipe. Assume the angle that looks like a right angle is a right angle. CB = 4- x. Clx) = 2k Jx²+4 +K (4-x) A 2 B
Pipe is going to be laid from point A to point B and going through point C as shown in the picture. Distances are in miles and as indicated in the picture. The position of point C is up to the pipe layers but point C must lie on the straight line shown in the picture. Laying the pipe from point A to point C involves laying the pipe under water and costs 3 million dollars per mile. Laying the pipe from point C to point B involves laying the pipe over land and costs 1 million dollars per mile. Find the value of x in the picture to minimize the total cost of laying the pipe. Assume the angle that looks like a right angle is a right angle. CB = 4- x. Clx) = 2k Jx²+4 +K (4-x) A 2 B
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Text on Educational Website:**
Pipe is going to be laid from point A to point B and go through point C, as shown in the picture. Distances are in miles and as indicated in the picture. The position of point C is up to the pipe layers, but point C must lie on the straight line shown in the picture.
Laying the pipe from point A to point C involves laying the pipe underwater and costs 3 million dollars per mile. Laying the pipe from point C to point B involves laying the pipe over land and costs 1 million dollars per mile. Find the value of x in the picture to minimize the total cost of laying the pipe. Assume the angle that looks like a right angle is a right angle. CB = 4 - x.
\[ C(x) = 2k \sqrt{x^2 + 4} + k(4-x) \]
**Diagram Explanation:**
The diagram illustrates a right triangle with a horizontal line extending from point A to point B. Point A is at the top of the vertical side of the triangle, which is labeled "2" miles. Point B lies 6 miles horizontally from point A along the x-axis. An adjustable point C lies on the x-axis between point A and point B.
- The horizontal distance from the origin (x=0) to point C is labeled as "x."
- The horizontal distance from point C to point B is labeled as "4 - x."
- The hypotenuse of the right triangle (from point A to point C) represents the underwater pipe section.
- The segment from point C to B represents the land pipe section.
The task involves optimizing the position of point C to minimize the total cost of the pipeline, taking into consideration the different costs associated with underwater and land segments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff26050af-8cf2-44aa-a499-323c21b5df7b%2F33c7b89d-8fd1-4c11-a4af-a28b0e4c877f%2Fz4va75h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text on Educational Website:**
Pipe is going to be laid from point A to point B and go through point C, as shown in the picture. Distances are in miles and as indicated in the picture. The position of point C is up to the pipe layers, but point C must lie on the straight line shown in the picture.
Laying the pipe from point A to point C involves laying the pipe underwater and costs 3 million dollars per mile. Laying the pipe from point C to point B involves laying the pipe over land and costs 1 million dollars per mile. Find the value of x in the picture to minimize the total cost of laying the pipe. Assume the angle that looks like a right angle is a right angle. CB = 4 - x.
\[ C(x) = 2k \sqrt{x^2 + 4} + k(4-x) \]
**Diagram Explanation:**
The diagram illustrates a right triangle with a horizontal line extending from point A to point B. Point A is at the top of the vertical side of the triangle, which is labeled "2" miles. Point B lies 6 miles horizontally from point A along the x-axis. An adjustable point C lies on the x-axis between point A and point B.
- The horizontal distance from the origin (x=0) to point C is labeled as "x."
- The horizontal distance from point C to point B is labeled as "4 - x."
- The hypotenuse of the right triangle (from point A to point C) represents the underwater pipe section.
- The segment from point C to B represents the land pipe section.
The task involves optimizing the position of point C to minimize the total cost of the pipeline, taking into consideration the different costs associated with underwater and land segments.
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