Question 1115085
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The shoreline, the perpendicular distance of 1 mile from the shoreline to the island, and the path of the power line form a right triangle.  The length of the side of that triangle along the shore is (4-x).<br>
By the Pythagorean Theorem, the length of the part of the power line under water is {{{sqrt((4-x)^2+1^2) = sqrt(x^2-8x+17)}}}<br>
The total cost of the power line is $2000 for each mile along the shore and $6000 for each mile underwater:
{{{2000(x)+6000(sqrt(x^2-8x+17))}}}<br>
It clearly would not make sense, if you were trying to minimize the total cost of the power line, to run the line more than 4 miles along the shoreline.  So a reasonable domain would be x from 0 to 4.