The general equation of the circle is:

(h,k) is the center of the circle and r is the radius. We are given the coordinates of the center. So we can write the equation of the circle as:

In order to complete the equation, we need the radius of the circle. Using the given point we can find the radius. Using the point in the above equation, we get:

Thus the value of r² is 125. Using the value in equation of the circle, we get:

The radius of the circle is √125.
Divide each set to see if the answers are identical:
A: 3/2 = 1.5
6/3 = 3
Answers are not the same so this is not proportional.
B: 20/4 = 5
24 /6 = 4
Answers are not the same so this is not proportional.
C: 27/9 = 3
81/27 = 3
Answers are the same so this is proportional.
D: 8/2 = 4
16/8 = 2
Answers are not the same so this is not proportional.
The answer is C.
1. The time taken for the water to fall that much is 0.2 s
2. The initial speed of the water is 4 m/s
<h3>1. How to determine the time </h3>
- Height (h) = 20 cm = 20 / 100 = 0.2 m
- Acceleration due to gravity (g) = 9.8 m/s²
- Time (t) =?
h = ½gt²
0.2 = ½ × 9.8 × t²
0.2 = 4.9 × t²
Divide both side by 4.9
t² = 0.2 / 4.9
Take the square root of both side
t = √(0.2 / 4.9)
t = 0.2 s
<h3>2. How to determine the initial speed</h3>
- Horizontal distance (s) = 80 cm = 80 / 100 = 0.8 m
- Time (t) = 0.2 s
- Initial speed (u) =?
s = ut
Divide both sides by t
u = s / t
u = 0.8 / 0.2
u = 4 m/s
Learn more about motion under gravity:
brainly.com/question/20385439
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