Difference between revisions of "2006 AMC 12A Problems/Problem 21"
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<math>S_1=\{(x,y)|\log_{10}(1+x^2+y^2)\le 1+\log_{10}(x+y)\}</math> | <math>S_1=\{(x,y)|\log_{10}(1+x^2+y^2)\le 1+\log_{10}(x+y)\}</math> | ||
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and | and | ||
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<math>S_2=\{(x,y)|\log_{10}(2+x^2+y^2)\le 2+\log_{10}(x+y)\}</math>. | <math>S_2=\{(x,y)|\log_{10}(2+x^2+y^2)\le 2+\log_{10}(x+y)\}</math>. | ||
Latest revision as of 16:35, 17 September 2023
Problem
Let and .
What is the ratio of the area of to the area of ?
Solution
Looking at the constraints of :
is a circle with a radius of . So, the area of is .
Looking at the constraints of :
is a circle with a radius of . So, the area of is .
So the desired ratio is .
See also
2006 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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