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is centered at the apex of a right square pyramid with base length 
and height 
The volume of the space where the sphere overlaps with the pyramid can be expressed in the form 
Find 
+1 w
is written in decimal form with n being a natural number, that it's decimal either terminates or is eventually periodic.
and 
Prove that
Let and 
Prove that
Let 
and 
Prove that
Let and 
Prove that
be the roots of 
with 
and 
.![$[|3 \alpha |] + [|6 \beta|] +
[|9 \gamma |]$](http://latex.artofproblemsolving.com/9/f/f/9ffb5118d94f0e2fb84a411b47ec91c122985673.png)
is equal to
such that 
where degrees are used.
be real numbers such that 
Prove that
Let be real numbers such that 
Prove that
Let be real numbers such that 
Prove that
)
)
:
Volume of a right square pyramid with base length 
and height 
.
![\[\begin{cases}
3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\
2x+\dfrac{1}{x-y}=4
\end{cases}\]](http://latex.artofproblemsolving.com/e/b/f/ebf41764f74c98da66dc31c48975f27bd734c334.png)
and 
Prove that
Let 
Prove that
