and 
Prove that
be real numbers such that 
Prove that
be non-negative real numbers such that 
.![\[
P = \frac{a}{a^2 + 2} + \frac{b}{b^2 + 2} + \frac{c}{c^2 + 2}.
\]](http://latex.artofproblemsolving.com/d/b/e/dbea7db769c4996fc081ee75837e177b298cffcb.png)
be a positive root of the equation 
.
(0<x<2π)
with domain ![$[0,2025]$](http://latex.artofproblemsolving.com/d/1/7/d17ac41d54c4b1888fb8bb43cf11b372691694a0.png)
satisfying 
and 
is strictly increasing on 
have local extrema at 
respectively. find 
. Here 
are constants .
be the region in the complex plane enclosed by curve 
for 
.
,
irreducible over 
?
from a distribution with probability density function (PDF) 
for 
,
has a prior distribution with PDF 
.
be the complete data vector. Denote the posterior PDF as 
,
,
.
be the current prior and update it using observation 
to obtain the new posterior:
from part (b) the same? Provide a proof or a counterexample.
,
be a non constant polynomial with real coefficients. Prove that the system of simultaneous equations —
has finitely many solutions 
.
Why we can't write 
as 
such that
Y by
In trapezoid 
, the bisector of angle 
intersects the base 
at point 
. Point 
is the midpoint of side 
. A straight line parallel to 
and passing through intersects side 
at point 
. It turned out that the angle 
is a straight line. Find the ratio 
.
, the bisector of angle 
intersects the base 
at point 
. Point 
is the midpoint of side 
. A straight line parallel to 
and passing through intersects side 
at point 
. It turned out that the angle 
is a straight line. Find the ratio 
.This post has been edited 1 time. Last edited by parmenides51, Feb 14, 2021, 10:49 AM
