Its about finding the equation of a circle from its general form equation:
x^2 + y^2 + 8x - 4y - 61 = 0
x^2 + 8x + 16 + y^2 - 4y + 4 = 61 + 16 + 4
(x + 4)^2 + (y - 2)^2 = 81
therefore the center is C(-4, 2), and the radius is 9
You are right about the domain
it is all real values of x except 4
So about the range we must make x subject of the formular so we know the values of y in which g(x) is defined
u
First let's find the GCF of 27, 36, and 72:
-->Find the factors of each number:
27: 1, 3, 9, 27
36: 1, 2, 3, 4, 9, 12, 18, 36
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
-->Now look for the factors they have in common.
1, 3, and 9
-->Now see which one is the biggest number in value
9
--> So therefore, 9 is the GCF
Now let's find the LCM of 7, 4, 10, and 12
-->Start listing all the multiples of of each number
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40... 420
7: 7, 14, 21, 28, 35, 42, 49, 56, 64, 70... 420
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120... 420
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120... 420
(sorry got bored of typing so I fast forwarded at the '...'s)
--> The least number in value that they have in common is the LCM of those numbers
The LCM is 420
*Just saying that took forever to do that LCM part but not way too long thank goodness :p