A power line is to be constructed from a power station at point A to an island at point C, which is 2 mi directly out in the water from a point B on the shore. Point B is 8 mi downshore from the power station at A. It costs $4200 per mile to lay the power line under water and $3000 per mile to lay the line under ground. At what point S downshore from A should the line come to the shore in order to minimize cost? Note that S could very well be B or A. (Hint: The length of CS is StartRoot 4 plus x squared EndRoot.)

The distance downshore from point A to point S that minimizes cost is 5.5 miles.

Step-by-step explanation:

We can define the value X as the length that the power line is lie underground across the shore.

Then the segment Y becomes:

Then, we can write the cost of the line (Z) as:

To optimize the cost function, we derive and equal to zero:

The distance downshore from point A to point S that minimizes cost is 5.5 miles.

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

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