Math  /  Algebra

Question1 Points] DETAILS MY NOTES SCALCCC5 4.6.059.MI. PRACTICE ANOTHER
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 10 km east of the refinery. The cost of laying pipe is $200,000/km\$ 200,000 / \mathrm{km} over land to a point PP on the north bank and $400,000/km\$ 400,000 / \mathrm{km} under the river to the tanks. To minimize the cost of the pipeline, how far (in km) from the refinery should PP be located? (Round your answer to two decimal places.) \qquad km Need Help? Read It Master It Submit Answer

Studdy Solution
Calculate the numerical value:
x1043101.15478.8453 x \approx 10 - \sqrt{\frac{4}{3}} \approx 10 - 1.1547 \approx 8.8453
Round to two decimal places:
x8.85 x \approx 8.85
The point P P should be located approximately 8.85 \boxed{8.85} km from the refinery.

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