PointQ′(prime)is the image of Q(-4,7)Q(−4,7)Q, left parenthesis, minus, 4, comma, 7, right parenthesis under a translation by 44
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Answer:
The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.
Step-by-step explanation:
At first we assume that north and east directions both represent positive quantities. Let suppose that and
. If both ghosts moves at constant velocity such that
and
, then the final positions of both ghosts are, respectively:
Ghost A
(Eq. 1)
Ghost B
(Eq. 2)
Where is the time, measured in hours.
Then, the equations of motion of each ghost are, respectively:
Ghost A
Ghost B
Then, the distance between both ghosts is:
(Eq. 3)
The magnitude of the relative is represented by the following Pythagorean identity:
Then, we find the rate of change of the relative distance (), measured in kilometers per hour, by implicit differentiation:
(Eq. 4)
If we know that , then the rate of change of the relative distance at 10 PM is:
The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.