SOLUTION: One of the longest crude oil pipelines in the world is the one from Edmonton, Alberta, to Buffalo, New York, a distance of 2858 km. In In one region, the pipeline follows the path

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Question 1195590: One of the longest crude oil pipelines in the world is the one from Edmonton, Alberta, to Buffalo, New York, a distance of 2858 km. In In one region, the pipeline follows the path given by y=2x+20, where each unit on the grid represents 1 km. A town in that region is centred at (50,5) and has a radius of 5 km. New bylaws require that the pipeline not be within 55 km of an urban area.
a) How close does the pipeline come to the town?
b) Does the pipeline need to be rerouted?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One of the longest crude oil pipelines in the world is the one from Edmonton, Alberta, to Buffalo, New York, a distance of 2858 km. In In one region, the pipeline follows the path given by y=2x+20, where each unit on the grid represents 1 km. A town in that region is centred at (50,5) and has a radius of 5 km. New bylaws require that the pipeline not be within 55 km of an urban area.
a) How close does the pipeline come to the town?
----
y=2x+20 --> 2x - y + 20 = 0
Distance for the center at (50,5) = |2*50 -1*5 + 20|/sqrt(2^2 + 1^2)
= 115/sqrt(5) = ~51.43 km
Minus the 5 km radius ---> 46.43 kms
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b) Does the pipeline need to be rerouted?
Obviously, it does.