Answer:
A point 5.103km from B
Step-by-step explanation:
Let x be the distance from B to C. Thus, the distance from the island to C is given as;
√(x²+5²) = √(x²+25)
Mow, the distance from C to D will be equal to 13-x
Hence the total distance travelled will now be;
√(x²+25) + 13-x
Let's say k is the energy per km it takes to fly over land. Thus, total energy is given as;
E(x) = 1.4k√(x²+25) + k(13-x)
Mow, let's find the derivative of E(x);
E'(x) = 1.4k(1/2)(2x)[(x²+25)^(-1/2)] + k(-1)
Thus;
E'(x) = 1.4kx/(√(x²+25)) - k
Simplifying this to get;
E'(x) = [1.4kx - k(√(x²+25))]/[√(x²+25)]
Now, to find the distance, it will be at E'(x) = 0
Thus;
[1.4kx - k(√(x²+25))]/[√(x²+25)] = 0
Multiply both sides by [√(x²+25)] to obtain;
[1.4kx - k(√(x²+25))] = 0
(divide each term by k) to obtain ;
1.4x - (√(x²+25)) = 0
1.4x = (√(x²+25))
Square both sides;
1.4²x² = x²+25
1.96x² = x² + 25
1.96x² - x² = 25
0.96 x² = 25
x² = 25/0.96
x² = 26.042
x = √26.042
x = 5.103km
