Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 4 km from the nearest pointBon the shoreline, flies to a pointCon the shoreline, and then flies along the shoreline to its nesting areaD. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. PointsBandDare 12 km apart. Give your answers to two decimal places.

(a) In general, if it takes 1.3 times as much energy to fly over water as land, to what pointCshould the bird fly in order to minimize the total energy expended in returning to its nesting area?

(b) LetWandLdenote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratioW/Lin terms ofx, the distance fromBtoC.

I'm assuming (b) is reliant on (a), so here's my work for (a):

(the line) BC = L

(the line) AC = w = $\displaystyle \sqrt{L^2+16}$

e = 1.3w + (12-L)

e = 1.3$\displaystyle \sqrt{L^2+16}$ + 12 - L

$\displaystyle e' = \frac{1.3*L}{\sqrt{L^2+16}}-1$

Which gave me a minimum of like L = 6.08, which isn't correct. Where didgo wrong?