Find the coordinate of the point P that divides the directed line segment from A to B in the given ratio. Round the
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Answer:
4.11 miles.
Step-by-step explanation:
In the image that I am going to attach we can see the description of the statement in a graph, now, the right triangle is formed, and we can apply Pythagoras, and the hypotenuse would be equal to:
(5 ^ 2 + x ^ 2) ^ (1/2)
The speed is equal to:
V = d / t, therefore the time is t = d / V, the total time would then be:
total time = (5 ^ 2 + x ^ 2) ^ (1/2) / 3 + (7-x) / 6
we derive with respect to x, and we are left with:
dt / dx = x / (3 * (5 ^ 2 + x ^ 2) ^ (1/2)) - 1/6 = 0
x / (3 * (5 ^ 2 + x ^ 2) ^ (1/2)) = 1/6
6x / (3 = (5 ^ 2 + x ^ 2) ^ (1/2)
(2 * x) ^ 2 = (5 ^ 2 + x ^ 2)
4 * x ^ 2 = 25 + x ^ 2
3 * x ^ 2 = 25
x ^ 2 = 25/3
x = 2.88
now we replace
7 - x = 7 - 2.89 = 4.11
In other words, the answer is 4.11 miles.
