![ashanti93](/avatars/37113.jpg)
ashanti93
18.07.2019 •
Mathematics
An oil refinery is located 1 km north of 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 9 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? (round your answer to two decimal places.)
km
Solved
Show answers
More tips
- S Style and Beauty 5 Tips for Choosing the Best Ugg Boots...
- H Health and Medicine How to Treat the Flu: A Comprehensive Guide...
- H Health and Medicine Effective Ways to Treat Colic in Infants...
- C Computers and Internet IMHO: What is it, why is it important, and how to use it?...
- F Food and Cooking How to Calculate the Gender of Your Child with Blood?...
- S Style and Beauty How to Get Rid of Under Eye Bruises?...
- C Cities and Countries What time does the Metro open in Moscow?...
- W Work and Career Where can you learn to be a flight attendant?...
- H Health and Medicine What are Electronic Cigarettes? The Ultimate Guide...
- C Computers and Internet Where are passwords stored in Opera?...
Answers on questions: Mathematics
- M Mathematics According to a survey, in a certain county 57% of all workers have a workplace retirement plan, 70% have health insurance, and 82% have at least one of the benefits. We select...
- M Mathematics Point P (1,5) is the image of P(- 3, 1) under a translation Determine the translation....
- M Mathematics Use the law of cosines to find the value of cose. Round your answer to two decimal places. 5.7 10.2 9.8...
- M Mathematics Choose the correct conic section to fit the equation. x 2 + y 2 = 9 Circle Ellipse Parabola Hyperbola...
- M Mathematics A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining...
- M Mathematics 3.25x + (–0.4y) + 1 2x + 1 5y Enter the equivalent expression into the response box....
- M Mathematics The half life of a certain tranquilizer in the bloodstream is 30 hours. How long will it take for the drug to decay to 80% of the original dosage...
- M Mathematics Lila has gained a lot of weight recently she works out and watches her intake but she s still gaining weight when she visited the doctor she told her that she had a problem...
- M Mathematics Expand and simplily 32.1 (321)...
- M Mathematics The distribution of the scores on a certain exam is N(40,5), which means that the exam scores are Normally distributed with a mean of 40 and standard deviation of 5. a. Sketch...
Ответ:
7.86 km
Step-by-step explanation:
Let x represent the distance point P lies east of the refinery. (We assume this direction is downriver from the refinery.)
The cost of laying pipe to P from the refinery (in millions of $) will be ...
0.5√(1² +x²)
The cost of laying pipe under the river from P to the storage facility will be ...
1.0√(2² +(9-x)²) = √(85 -18x +x²)
We want to minimize the total cost c. That total cost is ...
c = 0.5√(x² +1) +√(x² -18x +85)
The minimum value is best found using technology. (Differentiating c with respect to x results in a messy radical equation that has no algebraic solution.) A graphing calculator shows it to be at about x ≈ 7.86 km.
Point P should be located about 7.86 km downriver from the refinery.
Ответ: