An island is 4 miles offshore in a large bay. A water pipeline is to be...

 

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An island is 4 miles offshore in a large bay. A water pipeline is to be run from a water tank on the shore to the island, as in the figure. The pipeline costs 60 thousand dollars per mile in the ocean, and 40 thousand P dollars per mile on the land. What pipeline configuration will cost the least? Fill in the table below (2 pts for values, 2 pts for the formulas) Length of pipeline under water: Distance to P on shore (no pipeline there) 0° 20° 1. Angle (0, degrees) 40° Last angle that matters Formula (in) Island 4 mi Shore 10 mi Length of the pipeline on shore: Total Cost (in thousands) An island is 4 miles offshore in a large bay. A water pipeline is to be run from a water tank on the shore to the island, as in the figure. The pipeline costs 60 thousand dollars per mile in the ocean, and 40 thousand P dollars per mile on the land. What pipeline configuration will cost the least? Fill in the table below (2 pts for values, 2 pts for the formulas) Length of pipeline under water: Distance to P on shore (no pipeline there) 0° 20° 1. Angle (0, degrees) 40° Last angle that matters Formula (in) Island 4 mi Shore 10 mi Length of the pipeline on shore: Total Cost (in thousands)

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