A circle has an arc of length 20π that is intercepted by a central angle of 180°. What is the radius of the circle?

10π

Step-by-step explanation:

RULE:  The angle measure of the central angle is congruent to the measure of the intercepted arc.  

RULE:  Central Angle = Arc length

Given:  

Arc length (20 π) = central angle (180)

we know 180 degrees is a straight line, thus a semi-circle is created.  This would be the diameter.  

1/2 diameter is the radius.  20π/2 is the radius.  

10π

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

the correct answer is b.

this is because an open circle means < or > & since the line goes left it is < -3.

the next one has a filled circle so it can only be ≥ or ≤ and since the line goes right from 1 it is ≥ 1

hope that