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August 27, 2014

August 27, 2014

Posted by **Anonymous** on Saturday, December 3, 2011 at 12:57am.

- Math -
**Steve**, Saturday, December 3, 2011 at 5:48pmDraw a diagram. Let x be the distance east to point P

on land:

d^2 = x^2 + 1^2

underwater

d^2 = 3^2 + (8-x)^2

cost is thus (in half-millions)

c = sqrt(x^2 + 1) + 2sqrt(9 + (8-x)^2)

dc/dx = x/sqrt(x^2+1) - 2(8-x)/sqrt(9+(8-x)^2)

to find where dc/dx = 0 we put all over a common denominator, and set the numerator to zero:

xsqrt(9+(8-x)^2) - 2(8-x)sqrt(x^2+1) = 0

x^2(9 + (8-x)^2) = 4(8-x)^2(x^2+1)

This is satisfied when x is about 6.3

So, P should be 6.3 km downriver from the refinery. Cost will be about $M26.55

Better check my math for the details.

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