[/quote]
,
be non-negative real numbers such that 
Prove that
be real numbers satisfying 
. Find the maximum value of![\[P = \dfrac{a(b+c)}{a^2+2bc+3} + \dfrac{b(a+c) }{b^2+2ca +3 } + \dfrac{c(a+b)}{c^2+2ab+3}.\]](http://latex.artofproblemsolving.com/7/b/2/7b2ec0a87ca05d3cb29da888a4dfa73e10f238f8.png)
and 
intersect at the point 
.
?
,
.
are chosen from 0 to 1. What is the probability that their positive difference is more than 
?
?
families, there are 
children respectively. If a random child from any of the families is chosen, what is the probability that the child has 
siblings? Express your answer as a common fraction.[/quote]
,
people, exactly 
such that 
.
,
lies on diagonal 
such that 
.
.
and 
. Prove that 
.
matrix whose entries come from the set 
is called a silver matrix if, for each 
,
-
.
;
.
such that: 
and 
and 
such that 
.
be the circumcenter of 
and let 
.
![\[ a_n=2^n+3^n+6^n -1,\ n\geq 1. \]](http://latex.artofproblemsolving.com/6/4/9/6499d8f992f3e72765cab1f3afe15df99d01b12a.png)
that satisfy the equation
Y by
Hi everyone!
So I am currently in grade 6, and if anyone could give any tips for getting high scores in math competition, that would be great!
I haven't been doing so well in AMC 8, and other competitions like Math Kangaroo, etc....
I feel like i'm stuck, so if anyone could give any resources that helped you learn and score better, could you share that with me?
Thank you so much!
( also how much time should i spend on math every day? )
So I am currently in grade 6, and if anyone could give any tips for getting high scores in math competition, that would be great!
I haven't been doing so well in AMC 8, and other competitions like Math Kangaroo, etc....
I feel like i'm stuck, so if anyone could give any resources that helped you learn and score better, could you share that with me?
Thank you so much!
( also how much time should i spend on math every day? )
