Parry Hampton

04/24/2024 · Escuela primaria

A power line is to be constructed from a power station at point \( A \) to an island at point C , which is 4 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 \( \$ 2800 \) per mile to lay the power line under water and \( \$ 2000 \) 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 \( \sqrt{16+\mathrm{x}^{2}} \).)