A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 2 miles downstream on the opposite side costs $225 per foot across the river and $150 per foot along the land.
Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P
Directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x.
A) $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )$
B) $C ( x ) = 225 ( 600 - x ) + 150 ( 2 - x )$
C) $C ( x ) = 150 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 225 ( 10,560 - x )$
D) $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 10,560 - x )$

Question

A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 2 miles downstream on the opposite side costs $225 per foot across the river and $150 per foot along the land.
Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P
Directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x. 
A) $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )$ 
B) $C ( x ) = 225 ( 600 - x ) + 150 ( 2 - x )$ 
C) $C ( x ) = 150 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 225 ( 10,560 - x )$ 
D) $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 10,560 - x )$

Quizplus · Accepted Answer

The cost of laying the cable consists of two parts: the cost of the cable across the river and the cost of the cable along the land. The cost of the cable across the river depends on the distance x from the point P directly opposite the plant to the point Q on the opposite side of the river. This cost is given by the formula:

$225 	imes 	ext{distance across the river} = 225 	imes \sqrt{x^2 + 600^2}$

The cost of the cable along the land is simply the product of the cost per foot and the length of this part of the cable. The length of this part is the distance from Q to the end point, which is $2 - x$ miles. Therefore, the cost of this part is:

$150 	imes 	ext{distance along the land} = 150 	imes (2 - x) 	imes 5280$

Adding these two costs together, we get:

$C(x) = 225 \sqrt{x^2 + 600^2} + 150 (2 - x) 	imes 5280$

Simplifying this expression, we get:

$C(x) = 225 \sqrt{x^2 + 360000} + 792000 (2 - x)$

This matches choice D.

A Power Plant Is Located on a River That Is C(x)=225x2+6002+150(2−x)C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )C(x)=225x2+6002​+150(2−x)

A Power Plant Is Located on a River That Is $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )$