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The equation (x + 9)² + (y - 4)² = 81 models the position and range of the source of a radio signal. Describe the position of the source and range of the signals.
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Answered by
Bot
The position of the source is (-9, 4), as this is the center of the circle. The range of the signal is 9 units, which is the square root of 81 (the radius of the circle). This means that any point within 9 units of the source will receive the radio signal.
Answered by
Bot
Yes, I can show you step-by-step how I got that answer.
We start with the given equation:
(x + 9)² + (y - 4)² = 81
We can recognize that this is the equation of a circle, with center (-9,4) and radius 9. To see this, we can rewrite the equation in standard form:
(x - (-9))² + (y - 4)² = 9²
Simplifying, we get:
(x + 9)² + (y - 4)² = 81
So the center of the circle is (-9,4) and the radius is 9.
The position of the radio source is the center of the circle (-9, 4).
The range of the signals is the distance from any point on the circle to the center (-9, 4), which is the radius of the circle, or 9 units. This means that any point within 9 units of the source will receive the radio signal.
We start with the given equation:
(x + 9)² + (y - 4)² = 81
We can recognize that this is the equation of a circle, with center (-9,4) and radius 9. To see this, we can rewrite the equation in standard form:
(x - (-9))² + (y - 4)² = 9²
Simplifying, we get:
(x + 9)² + (y - 4)² = 81
So the center of the circle is (-9,4) and the radius is 9.
The position of the radio source is the center of the circle (-9, 4).
The range of the signals is the distance from any point on the circle to the center (-9, 4), which is the radius of the circle, or 9 units. This means that any point within 9 units of the source will receive the radio signal.
Answered by
Bot
Sure, I can solve this equation using the same method.
First, we can recognize that this is the equation of a circle, with center (7,-2) and radius 8. To see this, we can rewrite the equation in standard form:
(x - 7)² + (y + 2)² = 8²
So the center of the circle is (7,-2) and the radius is 8.
The position of the radio source is the center of the circle (7, -2).
The range of the signals is the distance from any point on the circle to the center (7, -2), which is the radius of the circle, or 8 units. This means that any point within 8 units of the source will receive the radio signal.
First, we can recognize that this is the equation of a circle, with center (7,-2) and radius 8. To see this, we can rewrite the equation in standard form:
(x - 7)² + (y + 2)² = 8²
So the center of the circle is (7,-2) and the radius is 8.
The position of the radio source is the center of the circle (7, -2).
The range of the signals is the distance from any point on the circle to the center (7, -2), which is the radius of the circle, or 8 units. This means that any point within 8 units of the source will receive the radio signal.
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