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 8000 dollars per mile to lay the pipe under the water and 5000 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? B underwater x = 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
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 8000 dollars per mile to lay the pipe under the water and 5000 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? B underwater x = 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
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.4: The Trapezoid
Problem 24E: The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340...
Related questions
Question
100%
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 8000 dollars per mile to lay
the pipe under the water and 5000 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?
B
underwater
x =
underground
Find a formula for the cost of laying the pipe in terms of
C'(x) =
Find the value for x that will minimize the total cost.
A
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 2 steps with 1 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning