Difference between revisions of "User talk:Bobthesmartypants/Sandbox"
(→yay) |
(→solution reflection) |
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Line 351: | Line 351: | ||
label("$C$",dir(0),dir(0)); | label("$C$",dir(0),dir(0)); | ||
label("$C'$",dir(30),dir(30));</asy> | label("$C'$",dir(30),dir(30));</asy> | ||
+ | |||
+ | |||
+ | <asy> | ||
+ | for(int i = 0; i < 60; ++i){ | ||
+ | draw((0,0)--dir(6*i)); | ||
+ | draw(dir(6*i)--dir(6*i+6),linetype("8 8")); | ||
+ | } | ||
+ | draw(1.2*dir(3)--1.2*dir(177)); | ||
+ | label("Diagram not to Scale",dir(-90),dir(-90));</asy> |
Revision as of 17:13, 11 May 2014
Contents
Bobthesmartypants's Sandbox
Solution 1
First, continue to hit at . Also continue to hit at .
We have that . Because , we have .
Similarly, because , we have .
Therefore, .
We also have that because is a parallelogram, and .
Therefore, . This means that , so .
Therefore, .
Solution 2
Note that is rational and is not divisible by nor because .
This means the decimal representation of is a repeating decimal.
Let us set as the block that repeats in the repeating decimal: .
( written without the overline used to signify one number so won't confuse with notation for repeating decimal)
The fractional representation of this repeating decimal would be .
Taking the reciprocal of both sides you get .
Multiplying both sides by gives .
Since we divide on both sides of the equation to get .
Because is not divisible by (therefore ) since and is prime, it follows that .
Picture 1
Picture 2
physics problem
Solution
inscribed triangle
moar images
yay
solution reflection