Cellular phone networks use towers to transmit calls to a circular area. On a grid of a province, the coordinates that correspond to the location of the towers and the radius each covers are as follows: Tower 1 is at (-5, -3) and covers a 9 km radius; Tower 2 is at (3,6) and covers a 4 km radius; and Tower 3 is at (12, -3) and covers a 6 km radius.
a. What equation represents the transmission boundaries of each tower?
b. Which tower transmits calls to phones located at (12,2)?(-6,-7)?(2,8)?(1,3)?
c. If you were a cellular phone user, which cellular phone network will you subscribe to? Why?
Answers
The equation for each tower would be:
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2Tower 3 transmits calls to phones located at (12,2)
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)Tower 2 transmits calls to phones located at (2,8)
equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)Tower 2 transmits calls to phones located at (2,8)Tower 1 and 2 both transmits calls to phones located at (1,3).
Given:
Tower 1 is at (-5, -3) and covers a 9 km radius; Tower 2 is at (3,6) and covers a 4 km radius; and Tower 3 is at (12, -3) and covers a 6 km radius.
To find:
Equation representing the transmission boundaries of each tower.
Tower which transmits calls to phones located at (12,2)(-6,-7) ,(2,8) ,(1,3)
Solution:
a. The transmission boundaries of each tower can be represented by the equation of a circle, with the tower's location as the center of the circle and the radius as the distance from the center to the boundary. The equation for each tower would be:
Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2
Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2
Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2
b.
Tower 3 transmits calls to phones located at (12,2)
Tower 1 transmits calls to phones located at (-6,-7)
Tower 2 transmits calls to phones located at (2,8)
Tower 1 and 2 both transmits calls to phones located at (1,3)
c. The choice of cellular phone network would depend on the specific needs of the user. If the area the user frequently travels in is covered by all three towers, then the user would likely choose the network that offers the best service and coverage in terms of call quality, data speeds, and pricing. If the user frequently travels in an area that is only covered by a single tower, then the user would likely choose the network that operates that tower.
Therefore
Therefore The equation for each tower would be:
Therefore The equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2
Therefore The equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2
Therefore The equation for each tower would be:Tower 1: (x + 5)^2 + (y + 3)^2 <= 9^2Tower 2: (x - 3)^2 + (y - 6)^2 <= 4^2Tower 3: (x - 12)^2 + (y - (-3))^2 <= 6^2
Tower 3 transmits calls to phones located at (12,2)
Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)
Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)Tower 2 transmits calls to phones located at (2,8)
Tower 3 transmits calls to phones located at (12,2)Tower 1 transmits calls to phones located at (-6,-7)Tower 2 transmits calls to phones located at (2,8)Tower 1 and 2 both transmits calls to phones located at (1,3).
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