<h2>
Answer:</h2>
<em><u>Distance of the pipeline down the shoreline should be = 3.34 miles</u></em>
<h2>
Step-by-step explanation:</h2>
In the question,
Distance of the Resort, R, from the point, P = 5 miles
Distance of the Fresh Source of water, X, from P = 10 miles
Also, if,
Cost of laying pipeline on land = 1
then,
Cost of laying pipeline in water = 1.8
So,
Using Pythagoras theorem in triangle PRX, we get,
Length of pipe in water, LR is,
So,
<u>Total cost, C, of laying the pipeline</u> is,
On differentiating it w.r.t x, we get,
<em><u>Therefore, the distance of the pipeline down the shoreline should be,</u></em>
<em><u>x = 3.34 miles to minimize the construction cost.</u></em>