Which expression gives the closest estimate of 268 + 524?
2 answers:
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Use the distance formula to find 2 sides. O through A and O through B.
distance formula is in the image.
OA
root[(x2-x1)^2+(y2-y1)^2]
root[(4-0)^2+(0-0)^2]
root[16]
4
OB
root[(x2-x1)^2+(y2-y1)^2]
root[(0-6)^2+(6-0)^2]
root[36+36]
root[72]
6root[2]
multiply the two numbers and divide by 2.
4 * 6root[2]
24root[2]
24root[2]/2
12root[2]
distance formula is in the image.
OA
root[(x2-x1)^2+(y2-y1)^2]
root[(4-0)^2+(0-0)^2]
root[16]
4
OB
root[(x2-x1)^2+(y2-y1)^2]
root[(0-6)^2+(6-0)^2]
root[36+36]
root[72]
6root[2]
multiply the two numbers and divide by 2.
4 * 6root[2]
24root[2]
24root[2]/2
12root[2]
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
