The equation (x-7)^2 + (y-2)^2 = 64 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.
position is at (7,2)
If by range you mean the radius of the circle, then that would be 8.
(miles? km?)
To describe the position of the source of the radio signal, we can look at the equation (x-7)^2 + (y-2)^2 = 64. This equation represents a circle in the xy-plane.
The general equation for a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the coordinates of the center of the circle and r represents the radius.
Comparing this general form with our equation, we can see that the center of our circle is at the point (7, 2). Therefore, the position of the source of the radio signal is located at the coordinates (7, 2).
Now, let's discuss the range of the signals. In this particular equation, the radius of the circle is 8 (since 8^2 = 64). The radius represents the distance between the center of the circle and the edge of the circle.
So, the range of the signals from the source extends up to a distance of 8 units in all directions from the center. This means that any point within a radius of 8 units from the source (7, 2) will be within the range of the radio signals.
In summary, the position of the source of the radio signal is at coordinates (7, 2), and the range of the signals extends up to a distance of 8 units in all directions from the source.
To describe the position of the source and the range of the signals based on the equation (x-7)^2 + (y-2)^2 = 64, we can break it down step by step:
Step 1: Identify the center of the circle.
The equation is in the form (x-h)^2 + (y-k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle. In this case, the center of the circle is (7, 2).
Step 2: Determine the radius of the circle.
The radius of the circle is the square root of the value on the right side of the equation (r^2). In this case, the radius is √64 = 8.
Step 3: Describe the position of the source.
The position of the source is represented by the coordinates of the center of the circle, which is (7, 2). This implies that the source of the radio signal is located 7 units to the right and 2 units up from the origin (0, 0).
Step 4: Define the range of the signals.
The range of the signals is given by the radius of the circle, which is 8 units. This means that the radio signals can be received up to a distance of 8 units from the source.
In summary, the position of the source of the radio signal is located at (7, 2), and the range of the signals can be received within an 8-unit radius.