Problema Solution
Emergency Broadcasts: The emergency broadcast system is designed to relay an emergency signal o all of the country. A signal is sent from station ESMB with broadcast area bounded by x^2+y^2=2500 (x and y in miles). The signal is relayed by a transmitter with range (x-24)^2+(y-33)^2=900. Determine the greatest distance from ESMB hat this signal can be received. Round your answer to one decimal place.
Answer provided by our tutors
the equation for broadcast, x^2+y^2=2500, defines a circle of radius sqrt(2500) = 50 miles
the equation for the relay transmitter, (x-24)^2+(y-33)^2=900, defines a circle of radius sqrt(900) = 30 miles
we assume the transmitter itself has to fall within the range of the broadcast signal radius, otherwise please provide specific information regarding the physics of such transmission schemes
based on these assumptions, the greatest signal path should be the sum of their radii: 50+30=80 miles