A small house was built on an island off a perfectly straight shoreline. The point B on the shoreline that is closest to the island is exactly 6 miles from the island. Eight miles east of B is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between B and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 6000 dollars per mile to lay the pipe under the water and 3750 dollars per mile to lay pipe on land. How far east of B should Q be located in order to minimize the total construction costs? underwater underground Find a formula for the cost of laying the pipe in terms of x C(x) = Find the value for x that will minimize the total cost.
A small house was built on an island off a perfectly straight shoreline. The point B on the shoreline that is closest to the island is exactly 6 miles from the island. Eight miles east of B is the closest source of fresh water to the island. A pipeline is to be built from the island to the source of fresh water by laying pipe underwater in a straight line from the island to a point Q on the shoreline between B and the water source, and then laying pipe on land along the shoreline from Q to the source. It costs 6000 dollars per mile to lay the pipe under the water and 3750 dollars per mile to lay pipe on land. How far east of B should Q be located in order to minimize the total construction costs? underwater underground Find a formula for the cost of laying the pipe in terms of x C(x) = Find the value for x that will minimize the total cost.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.2: Law Of Cosines
Problem 3ECP: In a softball game, a batter hits a ball to dead center field, a distance of 240 feet from home...
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Transcribed Image Text:A small house was built on an island off a
perfectly straight shoreline. The point B on the
shoreline that is closest to the island is exactly 6
miles from the island. Eight miles east of B is the
closest source of fresh water to the island. A
pipeline is to be built from the island to the
source of fresh water by laying pipe underwater
in a straight line from the island to a point Q on
the shoreline between B and the water source,
and then laying pipe on land along the shoreline
from Q to the source. It costs 6000 dollars per
mile to lay the pipe under the water and 3750
dollars per mile to lay pipe on land. How far east
of B should Q be located in order to minimize the
total construction costs?
underwater
underground
Find a formula for the cost of laying the pipe in
terms of x
C(x) =
Find the value for x that will minimize the total
cost.
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