Problema Solution
some radio stations extend their broadcast range by installing a translator- a remote device that receives the signal and retransmits it. A station with a broadcast range given by x^2+y^2=1600, where x and y are in miles, installs a translator with a broadcast area bounded by x^2+y^2-70y+600=0. Find the greatest distance from the transmitter that the signal can be received
Answer provided by our tutors
to answer this problem correctly may require specialized knowledge of broadcast transmission ranges and such information should be included in the problem statement
we make the following assumption: the relay transmitter location must fall somewhere within the radius that bounds the broadcast station
the broadcast station equation defines a circle with radius of sqrt(1600) = 400 miles
x^2 + y^2 - 70y + 600 = 0
factors to the following circular equation:
x^2 + (y-35)^2 = 625
the relay transmitter equation defines a circle with radius of 25 miles
the maximum distance that the signal could be received, based on the assumptions that we are making, is the sum of their radii: 400 + 25 = 425 miles