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Cost A company wishes to run a utility cable from point $A$ on the shore (see the figure below) to an installation at point $B$ on the island. The island is 6 miles...

Question

Cost A company wishes to run a utility cable from point $A$ on the shore (see the figure below) to an installation at point $B$ on the island. The island is 6 miles from the shore. Point $A$ is 9 miles from Point $C,$ the point on the shore closest to Point $B$ . It costs $\$ 400$ per mile to run the cable on land and $\$ 500$ per mile underwater. Assume that the cable starts at $A$ and runs along the shoreline, then angles and runs underwater to the island. Find the point at which the line shou

cost A company wishes to run a utility cable from point $A$ on the shore (see the figure below) to an installation at point $B$ on the island. The island is 6 miles from the shore. Point $A$ is 9 miles from Point $C,$ the point on the shore closest to Point $B$ . It costs $\$ 400$ per mile to run the cable on land and $\$ 500$ per mile underwater. Assume that the cable starts at $A$ and runs along the shoreline, then angles and runs underwater to the island. Find the point at which the line should begin to angle in order to yield the minimum total cost.



Answers

cost A company wishes to run a utility cable from point $A$ on the shore (see the figure below) to an installation at point $B$ on the island. The island is 6 miles from the shore. Point $A$ is 9 miles from Point $C,$ the point on the shore closest to Point $B$ . It costs $\$ 400$ per mile to run the cable on land and $\$ 500$ per mile underwater. Assume that the cable starts at $A$ and runs along the shoreline, then angles and runs underwater to the island. Find the point at which the line should begin to angle in order to yield the minimum total cost.


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