# All Questions

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### Proof of Simson line theorem using barycentric coordinates.

Is there anybody who knows how to prove Simson line theorem using barycentric coordinates only?
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### Find expected step, on which half-normal RV exceeds a scalar value?

I have defined a following problem. Given is a non-negative integer variable (steps) $s\in[0,1,...)$, and a scalar random variable as a function of $s$ $R(s)$. Random variable is half-normally ...
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### simultaneous diagonalize

$A = \begin{pmatrix} 18 & -9 \\ -9 & 9 \end{pmatrix}$ $B = \begin{pmatrix} 3 & 2 \\ 2 & -2 \end{pmatrix}$ Find a real invertible matrix such as $P^tAP = I_2$ and $P^tBP$ is diagonal ...
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Lets say I have $C=\{00000, 01101, 10110, 11011\}$ I know the covering radii is given by $e=\frac{1}{2} (d-1)$ So in this example $e=1$. Regarding the covering radius, this is the definition I have. ...
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### Expressing a solution to a differential equation in a more compact form

We know that $Ae^{ikx}$ is a solution for $k \geq 0$ and $Be^{ikx}$ is a solution for $k \leq 0$. So does the $N$ here depend on whether or not $k \geq 0$ or $\leq 0$? Also I do not understand how ...
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### Proving statement for a tree-graph theory

So i need help with this: Let T be a tree. And degree of every vertice is an odd number. So i need to prove that there is an odd number of paths in that tree. So i basically need to prove that there ...
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### Compactly generated complete lattice is Heyting Algebra

Let $L$ be a lattice. $a\in L$ is said to be compact if whenever $a\leq \bigvee A$ for some $A\subseteq L$, then there is some finite subset $B\subseteq A$ such that $a\leq \bigvee B$. A lattice is ...
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### is the followng function $f$ surjective?

$f$ is a function from plane $V$ to $V$ mapping $x$ axis to plane $V$ defined by if $P(x,0)$ then $f(P) = (x,x^2)$ ? I am not so sure for my following answer : to show that $f$ is surjective, for ...
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### prove that a non constant linear functional from a normed linear space X is discontinuous if and only if Z(f) = {x in X | f(x) = 0} is dense in X.

I could prove that if Z(f) is dense in X then the functional must me discontinuous but I am not able to prove the other way round
### Is there any palindromic power of $2$?
My question is in the title: Is it possible to find $n≥4$ such that $2^n$ is a palindromic number (in base $10$)? A palindromic number is a number which is the same, independently from which ...