A power station is one side of the river that is one half kilometer wide. A factory is 5 kilometers downstream on the other side of the river. It costs Php 100.00 per meter to run the power lines on the land and Php 150.00 per meter to run underwater. Write the cost C of running the line from the power station to the factory as a function of x.
you don't say what x is
I assume it is the distance (in meters) from the factory to where the pipeline comes ashore. If so, then
C(x) = 100x + 150√((5000-x)^2 + 500^2)
Oh, I see we're getting into some mathematical humor now! Alright, let me try to "compute" a funny answer for you.
Okay, imagine this: the power lines are like a lost river camel trying to find its way to the factory oasis. On land, the camel is perfectly happy and costs only Php 100.00 per meter to operate, but as soon as it has to swim underwater like a mermaid, it needs an extra Php 150.00 per meter to buy a fashionable snorkel.
So, let's use our imagination for some math comedy now! We have two parts to our line, one that's the distance on land (x), and the other that's underwater (0.5 km - x). Don't worry, our camel-mermaid is a talented multitasker!
The cost C for running the line from the power station to the factory is then:
C = (100.00 * x) + (150.00 * (0.5 - x))
Got it? Our camel-mermaid is doing a little land adventure and a little underwater exploration to get the job done. Remember, math can be as fun as an underwater camel-mermaid!
To determine the cost C of running the power lines from the power station to the factory as a function of x, we need to consider the different scenarios for the line placement.
Let's define x as the location along the river at which the power lines cross to the other side. The value of x will represent the distance in kilometers from the power station, with x = 0 representing the power station itself, and x = 0.5 representing the farthest point across the river.
Scenario 1: Line runs entirely on land
In this case, the distance covered on land is x kilometers. Since the cost per meter on land is Php 100.00, the cost of running the line on land will be 100 * 1000 * x = 100000x Php.
Scenario 2: Line runs underwater
In this scenario, the line crosses the river and runs underwater from the power station to the factory. The total distance underwater is (5 - x) kilometers. Considering the cost per meter underwater is Php 150.00, the cost of running the line underwater will be 150 * 1000 * (5 - x) = 150000(5 - x) Php.
Scenario 3: Combination of land and underwater
In this scenario, the line runs on land for a distance of x kilometers and runs underwater for a distance of (5 - x) kilometers. Therefore, the total cost for this scenario will be the sum of the costs for each section:
C(x) = 100000x + 150000(5 - x) Php.
Thus, the cost C of running the line from the power station to the factory as a function of x is given by:
C(x) = 100000x + 150000(5 - x) Php.
To determine the cost C of running the power lines from the power station to the factory as a function of x, where x represents the distance from the power station, we need to consider the various sections of the line that will run on land and underwater.
Let's break down the problem step by step:
1. First, we need to find the length of the line running on land. Since the river is half a kilometer wide, the line will need to travel a distance of x + 0.5 kilometers to reach the other side of the river.
2. Next, we need to determine the length of the line running underwater. Using the Pythagorean theorem, we can find the length of the hypotenuse (the line underwater). Since the river is half a kilometer wide and the factory is 5 kilometers downstream, the total distance the line will have to travel underwater is √(x^2 + 0.5^2) kilometers.
3. Now, we can calculate the cost of the line running on land and underwater separately. The cost of the land portion is Php 100.00 per meter, so the cost for the land section is (x + 0.5) * 100.00.
4. Similarly, the cost of the underwater portion is Php 150.00 per meter, so the cost for the underwater section is √(x^2 + 0.5^2) * 150.00.
5. Finally, we can add the costs of the land and underwater sections to find the total cost C as a function of x:
C(x) = (x + 0.5) * 100.00 + √(x^2 + 0.5^2) * 150.00.
Therefore, the cost C of running the line from the power station to the factory as a function of x is given by C(x) = (x + 0.5) * 100.00 + √(x^2 + 0.5^2) * 150.00.