Given two concentric circles (circles that have the same center point), with the inner circle having a radius of r1 and the outer one having a radius of

r2 as shown, give a dilation that would map the inner circle onto the outer

circle. Specify both the center of dilation and the scale factor.

The center of dilation has a coordinate of and the scale factor is . The transformation formula is .

Two circles are concentric when they share the same center () but they have different radii (), where corresponds to the radius of the smaller circle. By analytic geometry we know that circles are modeled after this formula:

    (1)

If we assume that the center of dilation is the center of both circles and the dilation use a scale factor of . Then, we have the following expression:

    (2)

The center of dilation has a coordinate of and the scale factor is . The transformation formula is .

To learn more on dilations, we kindly invite to check this verified question:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

70.30

step-by-step explanation: