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bbrid8590
20.12.2019 •
Mathematics
An oil refinery is located 1 km north of the north bank of a straight river that is 3 km wide. a pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 8 km east of the refinery. the cost of laying pipe is $500,000/km over land to a point p on the north bank and $1,000,000/km under the river to the tanks. to minimize the cost of the pipeline, how far downriver from the refinery should the point p be located?
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Ответ:
10√(x^2+ 1) + 5×(8- x) = C
5(2x)÷√(x^2 + 1) - 5 = 0
10x = 5√(x^2 + 1)
100x^2 = 25(x^2 + 1)
⇔75x^2 = 25
⇒ x=√(25÷75)
x ≈ √3/3 ( Let x = no of km downriver to P and C = cost. )
Ответ: