SOLUTION: A car leaves an intersection traveling east. Its position t sec later is given by x = t^2 + t ft. At the same time, another car leaves the same intersection heading north, travel

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Question 517244: A car leaves an intersection traveling east. Its position t sec later is given by
x = t^2 + t
ft. At the same time, another car leaves the same intersection heading north, traveling
y = t^2 + 3t ft
in t sec. Find the rate at which the distance between the two cars will be changing 3 sec later.?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A car leaves an intersection traveling east. Its position t sec later is given by
x = t^2 + t
ft. At the same time, another car leaves the same intersection heading north, traveling
y = t^2 + 3t ft
in t sec. Find the rate at which the distance between the two cars will be changing 3 sec later.?
-----------
d%28t%29+=+sqrt%28%28t%5E2%2Bt%29%5E2+%2B+%28t%5E2%2B3t%29%5E2%29
= sqrt%282t%5E4+%2B+8t%5E3+%2B+10t%5E2%29
--------------
d'(t) =
d'(3) = (216 + 216 + 60)/(2(162 + 216 + 90))
= 492/936
= 41/78 ft/sec