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.
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To express the total cost as a function of x, we need to consider two scenarios: when x is less than or equal to 50 (where the cable is in the river), and when x is greater than 50 (where the cable is on land).
When x is less than or equal to 50, the cable is in the river. The cost per foot in the river is $25. Therefore, the cost in the river is 25x dollars.
When x is greater than 50, the cable is on land. The cost per foot on land is $15. The distance on land is (x - 50) feet. Therefore, the cost on land is 15(x - 50) dollars.
To find the total cost, we add the cost in the river and the cost on land:
Total cost = Cost in the river + Cost on land
Total cost = 25x + 15(x - 50)
Total cost = 25x + 15x - 750
Total cost = 40x - 750
Therefore, the total cost is a function of x and can be expressed as:
Total cost = 40x - 750.