A power station is on one side of a river that is 3/4 mile wide, and a factory is 8 miles downstream on the other side of the river. It costs $24 per foot to run power lines over land and $30 per foot to run them under water.(1 mile = 5280 feet)
Write the total cost C to run power lines in term of x?
P.S. the diagram that went along with this had a ______ that represented 8-x and a slanted line that represented x "/"
Consider the point on shore that is closest to the station.
I can't tell from your explanation, but I will say that x is the distance from there to where the line comes ashore. That means 8-x is the rest of the way to the factory.
So, using the Pythagorean Theorem, the distance from the power station to where the line comes ashore is
d^2 = x^2 + (3/4)^2
So, the cost is
30d + 24(8-x)
= 30√(.75^2+x^2) + 24(8-x)
If I got x and 8-x mixed up, I'm sure you can make the fix...
To find the total cost C to run power lines, we need to consider two parts: the cost of running power lines over land and the cost of running power lines under the water.
Let's consider the length of power lines over land. From the diagram, we can see that the length is represented by (8 - x) miles. Since 1 mile is equal to 5280 feet, the length over land can be expressed as 5280 * (8 - x) feet.
Similarly, the length of power lines under the water is represented by x miles. So, the length underwater can be expressed as 5280 * x feet.
The cost to run power lines over land is $24 per foot, so the cost for the land part is 24 * 5280 * (8 - x) dollars.
The cost to run power lines under the water is $30 per foot, so the cost for the underwater part is 30 * 5280 * x dollars.
To find the total cost C, we add the cost over land and the cost underwater:
C = 24 * 5280 * (8 - x) + 30 * 5280 * x
Simplifying this expression gives us the total cost C in terms of x:
C = 126720(x - 8) + 158400x
C = 126720x - 1013760 + 158400x
C = 285120x - 1013760 dollars
Therefore, the total cost C to run power lines in terms of x is given by the equation:
C = 285120x - 1013760 dollars.
To determine the total cost C to run power lines, we need to consider the cost of running power lines over land and under water separately.
Let's analyze the situation step by step:
1. Over land:
The distance on land, represented by the dashed line, is 8 - x miles. Since 1 mile is equal to 5280 feet, the distance over land, in feet, will be (8 - x) * 5280 feet.
The cost of running power lines over land is $24 per foot, so the cost over land will be 24 * (8 - x) * 5280.
2. Through water:
The distance through water is x miles. In feet, this distance is x * 5280 feet.
The cost of running power lines under water is $30 per foot, so the cost underwater will be 30 * x * 5280.
Now, we can express the total cost C, in terms of x, by summing up the costs over land and under water:
C = 24 * (8 - x) * 5280 + 30 * x * 5280
Simplifying further, we have:
C = 126720 * (8 - x) + 158400 * x
C = 1013760 - 126720x + 158400x
C = 269760 + 31680x
Therefore, the total cost C to run power lines in terms of x is 269760 + 31680x.