If a graphic designer is drawing a pattern of four concentric circles on a coordinate plane. The center of the circles is located at (-4, 3). The smallest circle has a radius of 3 units. If the radius of each circle is 4 units greater than the largest circle within it, then the equation of the fourth circle is...

See below.

Step-by-step explanation:

Let's first find the equation of the smallest circle. We know the center is at (-4,3) and the radius is 3 units. Recall the equation for a circle:

Where (h,k) is the center and r is the radius.

Plugging the numbers in, we get:

Each subsequent circle's radius is 4 units greater than the smallest circle. Importantly, note that the center will remain unchanged. The largest circle will have a radius of 3 + 4 + 4 + 4 = 15. We simply need to change the r:

Thus, equation for the fourth circle is:

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above