An offshore oil well is 1 mile off the coast. The oil refinery is 4 miles down the coast. Laying pipe in the ocean is twice as expensive as laying it on land. Find x, and consider how finding x helps determine the most economical path for the pipe from the well to the oil refinery.   A diagonal line segment, a vertical line segment, and a horizontal line segment are given in the graph. The vertical line segment connects the point labeled Offshore oil well to the left most point of the horizontal line forming a right angle. The horizontal line segement then goes right and ends at the point labeled Refinery. The diagonal line segment is labeled √(x2 + 1), begins at the point labeled Offshore oil well, goes down and right, and ends at a point on the horizontal line segment. The part of the horizontal line segement between the intersection of the vertical and horizontal line segments and the intersection of the diagonal and horizontal line segments is labeled x. The distance between the intersection of the diagonal and horizontal line segments and the rightmost point of the horiztonal line sgement labled Refinery is labeled 4 − x. x =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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An offshore oil well is 1 mile off the coast. The oil refinery is 4 miles down the coast. Laying pipe in the ocean is twice as expensive as laying it on land. Find x, and consider how finding x helps determine the most economical path for the pipe from the well to the oil refinery.
 
A diagonal line segment, a vertical line segment, and a horizontal line segment are given in the graph.
  • The vertical line segment connects the point labeled Offshore oil well to the left most point of the horizontal line forming a right angle.
  • The horizontal line segement then goes right and ends at the point labeled Refinery.
  • The diagonal line segment is labeled √(x2 + 1), begins at the point labeled Offshore oil well, goes down and right, and ends at a point on the horizontal line segment.
  • The part of the horizontal line segement between the intersection of the vertical and horizontal line segments and the intersection of the diagonal and horizontal line segments is labeled x.
  • The distance between the intersection of the diagonal and horizontal line segments and the rightmost point of the horiztonal line sgement labled Refinery is labeled 4 − x.
x = 
 
 
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