(Solution Library) Two towns are located on the same side of a river; Town 1 is located at 1 mile from the river and Town 2 at 4 miles. A water pipeline
Question: Two towns are located on the same side of a river; Town 1 is located at 1 mile from the river and Town 2 at 4 miles. A water pipeline is to be built at point \(x\) along the river, as shown in the figure below, to supply water to both towns, and such that they use the least amount of pipeline. The total amount of pipeline \(P(x)\) to be used when the station is located at point \(\mathrm{x}\), is
\[P(x)=\sqrt{1+x^{2}}+\sqrt{4^{2}+(1-x)^{2}} \quad 0 \leq x \leq 4\]
- Give an explanation as to why this formula gives the total length of the pipeline
- How far from town 1 will the location be along the rives so that the amount of pipeline is the least to use?
Deliverable: Word Document 
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