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Answer on Calculus Question for sofia

Question #17513

QUESTION 4
A controller spots two planes at the same altitude flying toward each other (see figure). Their
flight paths are
0
20 SW
and
0
45 SE
. One plane is 150 miles from point P with a speed of
375 miles per hour. The other is 190 miles from point P with a speed of 450 miles per hour.

a) Find parametric equations for the path of each plane where
t
is the time in hours, with
0t 
corresponding to the time at which the air traffic controller spots the planes.
b) Use the result in part (a) to write the distance between the planes as a function of
t
.
c) Use a graphing utility to graph the function in part (b). When will the distance
between the planes be minimum? If the planes must keep a separation of at least 3
miles, is the requirement met?
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