A power station and a factory are on opposite sides of a river 50 feet wide. A power line must be run from the station to the factory. It costs 25 dollars per foot to run the cable in the river and $15 per foot on land. Express the total cost as a function of x, where x represents the distance downstream from the power station to the point where the cable touches land.

Question

A power station and a factory are on opposite sides of a river 50 feet wide. A power line must be run from the station to the factory. It costs 25 dollars per foot to run the cable in the river and $15 per foot on land. Express the total cost as a function of x, where x represents the distance downstream from the power station to the point where the cable touches land.

Answer 1

assume the line goes on the same side L, the n crosses.

cost=15L+25sqrt(50^2+(L-x)^2 )
Where L is the distance downstream to the factory.
So what is dcost/dx ?

check my thinking.

Answer 2

i have a similar question but instead of 50 its 60 aqnd 15 is 20

Answer 3

To express the total cost as a function of x, let's break down the distance into two parts: the distance in the river and the distance on land.

Let's assume that x is the distance downstream from the power station to the point where the cable touches the land. This means the remaining distance from the end of the river to the factory is (50 - x).

The cost of running the cable in the river is $25 per foot, and since the river is a constant width of 50 feet, the cost in the river is (25 * 50) = $1250.

The cost of running the cable on land is $15 per foot, and the distance on land is (50 - x) feet. So, the cost on land is (15 * (50 - x)) = (750 - 15x) dollars.

Therefore, the total cost, C(x), can be expressed as the sum of the cost in the river and the cost on land:

C(x) = $1250 + (750 - 15x)

Simplifying further:

C(x) = $2000 - 15x

Thus, the total cost as a function of x is C(x) = $2000 - 15x.