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?
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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.