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Calculus cost function question?
Write the cost as a function of the distance x labeled in the figure. Show work.?
-A road from city A to city B must cross a strip of private land and a strip of public land as shown in the figure. It costs $73,000 per mile to build a road on public land, but it costs 35% more to build the road on private land.
Here is the diagram photo:
http://i217.photobucket.com/albums/cc274/christopher15012/pic.jpg
If x is the height along that central line, then use pythagorean theorem to write expressions for the length in the private area and the length in the public area:
1^2 + x^2 = A(x)^2
1^2 + (3-x)^2 = B(x)^2
where A(x) and B(x) are the hypotenuses of the two relevant right triangles.
so A(x) = square root of (1+x^2)
and B(x) = square root of (10 - 6x + x^2)
Then just write a function for the total cost:
Cost(x) = 73000*B(x) + 73000*1.35*A(x)
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