over 
.
are real number satisfying
show that the equation 
has at least one real root.
be real numbers. Find the ranges of 
converges.
converge?
,where 
,
it is positiv integer number.
to find the third side 
He uses logarithms as follows. He finds 
and doubles it; adds to that the double of 
subtracts the sum of the logarithms of 
and 
divides the result by 
and takes the anti-logarithm. Although his method may be open to suspicion his computation is accurate. What are the necessary and sufficient conditions on the triangle that this method should yield the correct result?
![\[ f(x) = \sum_{i=0}^{i=n} a_i x^{n - i}\]](http://latex.artofproblemsolving.com/0/0/5/0050577825cfc0208f72081efbfa8df9db902378.png)
be a polynomial of degree 
and 
are odd, prove that 
has no rational roots.
is positive, then ![\[ \log_e (1 + 1/x) > 1 / (1 + x).\]](http://latex.artofproblemsolving.com/f/3/0/f30f05414aace0d4c5ce8549afb430bfff34ccfc.png)
does the sequence 
defined by the initial condition 
and the recursion 
have 
for all 
Y by samrocksnature
In a convex quadrilateral 
, the lengths of the sides 
and 
are equal to 
cm, and the measures of angles 
and 
are equal to 
and 
degrees, respectively. Find the length of the diagonal 
.
, the lengths of the sides 
and 
are equal to 
cm, and the measures of angles 
and 
are equal to 
and 
degrees, respectively. Find the length of the diagonal 
.This post has been edited 4 times. Last edited by parmenides51, Jun 6, 2021, 5:17 AM
Reason: latex
Reason: latex
,
,
,
on a circle, so 
.
