A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle?

increased by a factor of 16
increased by a factor of 12
increased by a factor of 8
increased by a factor of 4

Increased by a factor of 4

Step-by-step explanation:

The original circumference is:

C1 = 2 * pi * r1

The new circumference is:

C2 = (2 * pi * r2)

"circumference that is 4 times larger than the original"

(2 * pi * r2) = 4 (2 * pi * r1)

Rewriting:

r2 = 4r1

The radius of the original circle is:

increased by a factor of 4

Hope this helps :)

4 yw:)

Step-by-step explanation:

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.

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered