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emmasim [6.3K]
3 years ago
14

Find the exact circumference of a circle with the given radius. 5 inches C = 2.5π in. 10π in. 25π in.

Mathematics
1 answer:
docker41 [41]3 years ago
5 0
The circumference, C, of a given circle may be calculated through the equation,
         
                                   C = 2πr

where r is the radius. 

Substituting the known values from the given in this item,
                                    C = 2(π)(5 in)
                                    <em>C = 10π in</em>

Thus, the answer is this item is the second choice. 
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Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

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Where the point (h,k)  is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121

Add 10x to both sides:

x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121

Make two groups for variable "x" and variable "y":

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Add (\frac{10}{2})^2=5^2 inside the parentheses of "x".

Add  (\frac{20}{2})^2=10^2  inside the parentheses of "y".

Add 5^2 and 10^2 to the right side of the equation.

Then:

(x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4

Rewriting, you get that the equation of the circle in center-radius form is:

 (x+5)^2+(y-10)^2=2^2

You can observe that the radius of the circle is:

r=2

And the center is:

(h,k)=(-5,10)

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