A power company has a power plant on a river that is 900 feet wide. To lay a new

Question

A power company has a power plant on a river that is 900 feet wide. To lay a new cable from the plant to a city 2 mi downstream on the opposite side costs $200 per foot across the river and $110 per foot across the land. (Recall 1 mile = 5280 feet.) Suppose 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 distance x. C(x)= NOTE: When entering answers you may enter values raised to powers such as 102 instead of 100.

Explanation / Answer

Total amount of cable = amount across river + amount across land Total amount of cable = amount across river + (10560-x) Pythagorean theorem: x^2 + 900^2 = (amount across river)^2 amount across river = (x^2+900^2)^(1/2) Total amount of cable = (x^2+900^2)^(1/2) + (10560-x) Cost of cable = $200(amount across river) + $110(amount across land) Cost of cable = 200(x^2+900^2)^(1/2) + 110(10560-x) This can be expanded/simplified to: Cost of cable = 200 sqrt(x^2 + 810000) - 100x + 1161600

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