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Question

The given equation, (x + 6)^2 + (y + 4)^2 = 36, represents a circle in a 2D plane. This equation suggests that the center of the circle, which symbolizes the source of the radio signal, is located at (-6, -4). The radius of the circle, which refers to the range of the radio signal, is the square root of 36, i.e., 6 units. Therefore, the radio signals extend to an area within this radius.

The equation indicates that the signal is spreading out in all directions from the source, to a distance of 6 units, similar to how sound waves spread out from a source. The coordinates are in reference to a central point, which is often taken to be the receiver in signal theory. Thus, the receiver must be within a 6 unit radius to receive the signals normally. If the receiver were to move beyond the 6 unit range, the power would need to be increased as per the inverse square law.

Answer 1

The equation (x + 6)^2 + (y + 4)^2 = 36 describes a circle on a 2D plane, with its center at (-6, -4) representing the source of a radio signal. The radius of the circle, 6 units, signifies the range of the signal. This means that the radio signals cover an area within this radius, spreading out in all directions like sound waves from a source. The coordinates are oriented around a central point, typically the receiver in signal theory. Therefore, the receiver must be within the 6 unit radius to properly receive the signals. Any movement beyond this range would require an increase in power as per the inverse square law.