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-rw-r--r--mat/domace_naloge/20/dokument.aux33
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-rw-r--r--mat/domace_naloge/20/dokument.tex289
-rw-r--r--mat/domace_naloge/20/dokument.toc4
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+\BOOKMARK [1][-]{section.1}{Vaje Matematika 2: stran 50, dve sodi in dve lihi nalogi 317-336}{}% 1
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+\usepackage{filecontents}
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+\usepackage{tkz-euclide}
+\usepackage{dirtytalk}
+\usepackage{csquotes}
+\usepackage{listings}
+\usepackage{datetime} % [ddMMyyyy]
+\usepackage{ccicons}
+\usepackage{chemformula}
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+\usepackage[slovene]{babel}
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+\usepackage{xcolor}
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+\usepackage{harpoon}
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+ keywordstyle=\color{magenta},
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+ stringstyle=\color{codepurple},
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+ breaklines=true,
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+ keepspaces=true,
+ numbers=left,
+ numbersep=5pt,
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+ showstringspaces=false,
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+ tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
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+ \null
+ \vskip 2em%
+ \begin{center}%
+ \let \footnote \thanks
+ {\LARGE \@title \par}%
+ \vskip 1.5em%
+ {\large
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+ \begin{tabular}[t]{c}% <------
+ \@author% <------ Authors
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+ \vskip 1em%
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+ \par
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+\title{%
+ \snovdn --- \stevilkadn. domača naloga
+ \\
+ \large Matematika, Gimnazija Bežigrad}
+\author{\begin{tabular}{rl}
+ \textbf{Profesor:} & prof. Vilko Domajnko\\
+ \textbf{Avtor:} & Anton Luka Šijanec, 2. a
+% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
+\end{tabular}}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{$#2$}%
+\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
+% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+\begin{abstract}
+Ta dokument vsebuje domačo nalogo, ki zajema snov \textit{\snovdn}pri matematiki, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno.
+\end{abstract}
+\tableofcontents
+\section{Vaje \textit{Matematika 2}: stran 50, dve sodi in dve lihi nalogi 317-336}
+\begin{enumerate}[label=\textbf{\arabic*.}] % 318, 329, 320, 325
+ \if\false1
+ \setcounter{enumi}{317}
+ \item Nariši vektor $\vektor{a}$, dolg \cm{3}. Nariši še vektorje:
+ \footnote{Za sezname ne uporabljam več \texttt{enumerate}, ampak \texttt{tasks} (Deutsche Kvalität)}
+ \begin{primerTasks}(8)
+ \task $\displaystyle\frac{1}{3}\Vec{a}$ % a
+ \task $\displaystyle\frac{4}{5}\Vec{a}$ % b
+ \task $\displaystyle-\frac{3}{7}\Vec{a}$ % c
+ \task $\displaystyle-\frac{3}{4}\Vec{a}$ % č
+ \task $\displaystyle\frac{5}{4}\Vec{a}$ % d
+ \task $\displaystyle\frac{7}{5}\Vec{a}$ % e
+ \task $\displaystyle-\frac{3}{2}\Vec{a}$ % f
+ \task $\displaystyle-\frac{8}{5}\Vec{a}$ % g
+ \task $\displaystyle\sqrt{2}\Vec{a}$ % h
+ \task $\displaystyle\sqrt{5}\Vec{a}$ % i
+ \task $\displaystyle-\sqrt{7}\Vec{a}$ % j
+ \task $\displaystyle-\sqrt{10}\Vec{a}$ % k
+ \task $\displaystyle\frac{\sqrt{3}}{4}\Vec{a}$ % l
+ \task $\displaystyle\frac{\sqrt{6}}{7}\Vec{a}$ % m
+ \task $\displaystyle-\frac{\sqrt{12}}{3}\Vec{a}$ % n
+ \task $\displaystyle-\frac{\sqrt{15}}{8}\Vec{a}$ % o
+ \end{primerTasks}
+ \begin{center}
+ \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+ % 0
+ \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
+ \tkzDrawPoints[red](A,B) \tkzDrawSegments[vect](A,B)
+ \tkzLabelLine[above](A,B){$\Vec{a}$}
+ % a
+ \tkzDefPoint(30:3){aA}
+ \tkzDrawLine(A,aA) \tkzDrawLine(aA,B)
+ \tkzDefPoint(1,0){a1} \tkzDefPoint(30:1){a2} \tkzDefPoint(30:2){a3}
+ \tkzDefPoint(2,0){a4}
+ \tkzCompass(A,a2) \tkzCompass(a2,a3) \tkzDrawLine(a3,a4)
+ \tkzDrawLine(a1,a2) \tkzDrawPoints[red](a1) \tkzDrawSegment[vect](A,a1)
+ \tkzLabelLine[below](A,a1){$\frac{1}{3}\Vec{a}$}
+ % b
+ \tkzDefPoint(30:(3/5)){b1} \tkzDefPoint(30:(3/5)*2){b2}
+ \tkzDefPoint(30:(3/5)*3){b3} \tkzDefPoint(30:(3/5)*4){b4}
+ \tkzCompass(A,b1) \tkzCompass(b1,b2) \tkzCompass(b2,b3)
+ \tkzCompass(b3,b4) \tkzCompass(b4,aA)
+ \tkzDefPoint((3/5)*4,0){b5} \tkzDrawLine(b4,b5) \tkzDrawPoints[red](b5)
+ \tkzDrawSegments[vect](A,b5)
+ \tkzLabelLine[below](A,b5){$\frac{4}{5}\Vec{a}$}
+ \end{tikzpicture}
+ \end{center}
+ \fi
+ \setcounter{enumi}{318}
+ \item Nariši trikotnik $ABC$ s podatki $a=\cm{4}$, $b=\cm{6}$, $c=\cm{7}$. Nariši še $\displaystyle\frac{1}{3}\vektor{AC}+\sqrt{2}\vektor{AB}$. % 319
+ \begin{center}
+ \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+ \tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B}
+ \tkzDefPoint(6,0){bh} \tkzDefPoint(7-4,0){ah}
+ \tkzDefPoint(0,6){3h} \tkzDefPoint(0,4){2h} \tkzDefPoint(0,2){1h}
+ \tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$c$}
+ \tkzInterCC(A,bh)(B,ah) \tkzGetPoints{C}{CX}
+ \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C)
+ \tkzLabelLine[below right](A,C){$\vektor{AC}$}
+ \tkzDrawLine(A,3h) \tkzCompass(A,1h) \tkzCompass(1h,2h)
+ \tkzCompass(2h,3h) \tkzDrawLine(3h,C)
+ \tkzDefPointWith[colinear=at 1h](3h,C) \tkzGetPoint{Z}
+ \tkzInterLL(A,C)(1h,Z) \tkzGetPoint{T}
+ \tkzLabelLine[above](A,T){$\frac{1}{3}\vektor{AC}$}
+ % sedaj pa sqrt(2)AB
+ \tkzDefPoint(0,7){P} \tkzCompass(A,P)
+ \tkzDefPoint(7,7){K} \tkzDrawLine(B,K) \tkzDrawLine(P,K)
+ \tkzInterLC(A,B)(A,K) \tkzGetPoints{K2X}{K2} \tkzCompass(A,K2)
+ \tkzLabelLine[below](A,K2){$\sqrt{2}\vektor{AB}$}
+ % sedaj pa seštevek
+ \tkzDefPointWith[colinear=at B](A,C) \tkzGetPoint{S}
+ \tkzLabelLine[above left](A,S){$\frac{1}{3}\vektor{AC}+\sqrt{AB}$}
+ \tkzDrawSegments[vect](A,C A,T, A,K A,K2)
+ \tkzDrawSegments[red, vect](A,S)
+ \tkzMarkRightAngles(A,P,K P,K,B K,B,A B,A,P)
+ \tkzDrawPoints[red](A,B,C,T,K,K2,S) \tkzLabelPoints(A,B,C)
+ \end{tikzpicture}
+ \end{center}
+ \newpage
+ \item Nariši pravokotnik $ABCD$ s podatki: $a=\cm{6}$, $b=\cm{2}$. Nariši še $\displaystyle-\frac{3}{2}\vektor{AC}+\frac{\sqrt{2}}{2}\vektor{BC}$.
+ \begin{center}
+ \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+ \tkzDefPoint(0,0){A} \tkzDefPoint(6,2){C} \tkzDefPoint(6,0){B}
+ \tkzDefPoint(0,2){D}
+ \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D)
+ \tkzDefPoint(0,(2/3)){a1} \tkzDefPoint(0,(2/3)*2){a2}
+ \tkzCompass(A,a1) \tkzCompass(a1,a2) \tkzCompass(a2,D)
+ \tkzDefPointWith[colinear=at a1](D,C) \tkzGetPoint{Z}
+ \tkzInterLL(A,C)(a1,Z) \tkzGetPoint{V}
+ \tkzDrawLine(a1,V) \tkzLabelLine[above left](A,C){$\vektor{AC}$}
+ \tkzLabelLine[below](V,C){$-\frac{2}{3}\vektor{AC}$}
+ % zdaj pa še koren iz dve polovic vektorja BC
+ \tkzDefPoint(6-2,0){K} \tkzDefPoint(6-2,2){P}
+ \tkzCompass(B,K) \tkzCompass(C,P)
+ \tkzInterLC(C,B)(C,K) \tkzGetPoints{K2X}{K2}
+ \tkzDefMidPoint(C,K2) \tkzGetPoint{K22}
+ \tkzLabelLine[left](C,K22){$\frac{\sqrt{2}}{2}\vektor{CB}$}
+ \tkzDefPointWith[colinear=at K22](C,V) \tkzGetPoint{S}
+ \tkzDrawPoints[red](A,B,C,D,V,K2,K22,S) \tkzLabelPoints[](A,B,C,D)
+ \tkzDrawSegments[vect](A,C C,V C,K2 C,K22)
+ \tkzDrawSegments[vect, red](C,S)
+ \tkzMarkRightAngles(C,P,K P,K,B K,B,C B,C,P)
+ \end{tikzpicture}
+ \end{center}
+ \setcounter{enumi}{324}
+ \item Naj bo $\Vec{m}=2\Vec{a}+3\Vec{b}$ in $\Vec{n}=\Vec{a}-2\Vec{b}$. Izrazi vektor $2\Vec{m}-\frac{1}{2}\Vec{n}$ z vektorjema $\Vec{a}$ in $\Vec{b}$.
+ $$
+ 2\Vec{a}+3\Vec{b}-(\frac{1}{2}(\Vec{a}-2\Vec{b})) =
+ 2\Vec{a} + 3\Vec{b} - \frac{1}{2}\Vec{a} + \frac{1}{2} \cdot 2\Vec{b} =
+ 1\frac{1}{2}\Vec{a}+4\Vec{b}
+ $$
+ \setcounter{enumi}{328}
+ \item Nariši daljico $AB$, dolgo \cm{6}. Na njen nariši tako točno $M$, da velja $|AM|:|MB|=1:2$, in tako točno $N$, da velja $|AN|:|AB|=1:2$. Vektorja $\vektor{AM}$ in $\vektor{AN}$ izrazi z vektorjem $\vektor{AB}$.
+ \begin{center}
+ \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+ \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B}
+ \tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$AB$}
+ \tkzDefPoint(30:6){3h} \tkzDefPoint(30:4){2h} \tkzDefPoint(30:2){1h}
+ \tkzDrawLine(A,3h) \tkzDrawLine(3h,B)
+ \tkzCompass(A,1h) \tkzCompass(1h,2h) \tkzCompass(2h,3h)
+ \tkzDefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M)
+ \tkzDefMidPoint(A,B) \tkzGetPoint{N}
+ \tkzDrawPoints[red](A,B,M,N) \tkzLabelPoints[below left](A,B,M,N)
+ \tkzDrawSegments[vect](A,M A,N)
+ \end{tikzpicture}
+ \end{center}
+ $$
+ \vektor{AM} = \frac{1}{3}\vektor{AB}
+ $$
+ $$
+ \vektor{AN} = \frac{1}{2}\vektor{AB}
+ $$
+\end{enumerate}
+
+
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.}
+izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
+\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi
+\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
+
+\if\razhroscevanje1
+\section*{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
+
+Grafi imajo natančnost \functionSamples\space točk na graf.
+
+Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+% \item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}
diff --git a/mat/domace_naloge/20/dokument.toc b/mat/domace_naloge/20/dokument.toc
new file mode 100644
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+\babel@toc {slovene}{}
+\babel@toc {slovene}{}
+\contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 50, dve sodi in dve lihi nalogi 317-336}{1}{section.1}%
+\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}%
diff --git a/mat/domace_naloge/20/stderr.log b/mat/domace_naloge/20/stderr.log
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