Final answer:
The diameter of the circle x^(2)+(y+6)^(2)=100 is 20 units.
Step-by-step explanation:
The equation x^(2)+(y+6)^(2)=100 represents a circle. In order to find the diameter of the circle, we need to determine the radius first. The equation is already in the standard form of a circle, (x - h)^(2) + (y - k)^(2) = r^(2), where (h, k) represents the center of the circle. From the given equation, we can see that the center of the circle is located at (0, -6) and the radius is √100 = 10. The diameter of a circle is twice the radius, so the diameter of this circle is 2 * 10 = 20 units.