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October 24, 2014

October 24, 2014

Posted by **Anom** on Wednesday, October 31, 2012 at 2:36pm.

Is the answer 2.1? Can you some list their steps?

- Calculus -
**Reiny**, Wednesday, October 31, 2012 at 4:19pmMake a sketch, mark the well as W and the point on the shore closest to W as A, label the refinery as R

Place P somewhere between A and R.

They will lay the pipeline from R to P along the shore, then directly through the water to W

let AP=x , the PR = 4-x, and AW=4

by Pythagoras:

WP = √(9-x^2) or (9-x^2(^(1/2)

cost = 1(4-x) + 2(9-x^2)^(1/2) , the actual money units don't matter as long as they are in the ratio 1 : 2

d(cost)/dx = -1 + (1/2)(9 - x^2)^(-1/2) (-2x)

= 0 for a min of cost

1 = x/√(9-x^2)

x = √(9-x^2)

square both sides

x^2 = 9-x^2

2x^2 = 9

x^2 = 4.5

x = √4.5 = appr 2.12

So they should aim for a point P which is 2.12 miles from A or 1.88 miles from R

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