Part 2: Identify the center and radius of each. Then sketch the graph.
1 answer:
Answer:
See below for graphs
- (2, -3), r = 2 (blue)
- (-3, -1), r = 1 (green)
- (3, -1), r = 3 (purple)
- (4, 1), r = 3 (red)
Step-by-step explanation:
I like to solve a set of problems like this once, then use a calculator or spreadsheet to crunch the numbers.
We can start with the general form of the equation for a circle:
x^2 +y^2 +ax +by +c = 0
Completing the square gives ...
(x^2 +ax +(a/2)^2) +(y^2 +by +(b/2)^2) = (a/2)^2 +(b/2)^2 -c
(x +(a/2))^2 +(y +(b/2))^2 = (a/2)^2 +(b/2)^2 -c
Comparing this to the standard form formula ...
(x -h)^2 + (y -k)^2 = r^2
we see the relations are ...
- h = -a/2
- k = -b/2
- r = √((a/2)² +(b/2)² -c)
where (h, k) is the center and r is the radius.
Then your circle centers and radii are ...
- (h, k) = (-(-4)/2, -6/2) = (2, -3); r = √(4+9-9) = 2
- (h, k) = (-6/2, -2/2) = (-3, -1); r = √(9+1-9) = 1
- (h, k) = (-(-6)/2, -2/2) = (3, -1); r = √(9+1-1) = 3
- (h, k) = (-(-8)/2, -(-2)/2) = (4, 1); r = √(16+1-8) = 3
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Hey there! Hello!
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You can see that I added a zero onto the end of the 8.2. This just evens out the amount of numbers and makes the problem easier to visualize while keeping the amount the same.
From the result of the problem, Emily gained 1.95 pounds in two months.
I hope this helped you out! Feel free to ask me any additional questions if you have any. :-)
The easiest way to solve this problem is by subtracting one value from the other. In order to find how much weight Emily gained in two months, we need to find the difference between her initial weight and how much she weighed at the end of two months:
You can see that I added a zero onto the end of the 8.2. This just evens out the amount of numbers and makes the problem easier to visualize while keeping the amount the same.
From the result of the problem, Emily gained 1.95 pounds in two months.
I hope this helped you out! Feel free to ask me any additional questions if you have any. :-)