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+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+% do-vimlatex-onwrite
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\usepackage{xurl} % da breaka url
+\usepackage[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{siunitx}
+\usepackage{multicol}
+\usepackage{tabularcalc}
+\usepackage{amsmath}
+\usepackage{float}
+\usepackage{tasks}
+\usepackage{filecontents}
+\usepackage{textcomp}
+\usepackage{tkz-euclide}
+\usepackage{dirtytalk}
+\usepackage{csquotes}
+\usepackage{listings}
+\usepackage{datetime} % [ddMMyyyy]
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+\usepackage{tabularx}
+\usepackage{xcolor}
+\usepackage{colortbl}
+\usepackage{exsheets}
+\usepackage{harpoon}
+\usepackage{readarray}
+\usepackage{forloop}
+\usepackage[nomessages]{fp}
+\usepackage{multirow}
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codered}{rgb}{1,0,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\renewcommand{\dateseparator}{. }
+\settimeformat{hhmmsstime}
+\lstdefinestyle{mystyle}{
+	backgroundcolor=\color{backcolour},   
+	commentstyle=\color{codegreen},
+	keywordstyle=\color{magenta},
+	numberstyle=\tiny\color{codegray},
+	stringstyle=\color{codepurple},
+	basicstyle=\ttfamily\footnotesize,
+	breakatwhitespace=false,         
+	breaklines=true,                 
+	captionpos=b,                    
+	keepspaces=true,                 
+	numbers=left,                    
+	numbersep=5pt,                  
+	showspaces=false,                
+	showstringspaces=false,
+	showtabs=false,                  
+	tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
+	\newpage
+	\null
+	\vskip 2em%
+	\begin{center}%
+		\let \footnote \thanks
+		{\LARGE \@title \par}%
+		\vskip 1.5em%
+		{\large
+			\lineskip .5em%
+			\begin{tabular}[t]{c}% <------
+				\@author%            <------ Authors
+			\end{tabular}\par}%    <------
+		\vskip 1em%
+		{\large \@date}%
+	\end{center}%
+	\par
+	\vskip 1.5em}
+%opening
+\newcommand{\snovdn}{Koreni poljubnih stopenj }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{29}
+\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
+\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
+\makeatletter
+\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
+\newcommand{\@xslalph}[1]{%
+	\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
+	\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
+	\or t\or u\or v\or z\or \v{z}
+	\else\@ctrerr\fi%
+}
+\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+	\frac{\text{#1}}{\text{#2}}
+}
+\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
+\newcommand\vektor{\overrightarrow}
+\newcommand{\iic}{I\textsuperscript{2}C }
+\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{$0#2$}%
+\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 navodila in rešitve domače naloge snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam.
+Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbiral naključno.
+\end{abstract}
+\paragraph{Navodilo naloge} \textbf{listi}: \textit{Koreni poljubnih stopenj} / 1, ... 10 (izberi tri sode in tri lihe, povsod po en primer)
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\item Izračunaj brez pomoči kalkulatorja:
+		\begin{enumerate}[label=\textbf{\xslalph*})]
+			\setcounter{enumii}{1}
+			\item $$\sqrt[3]{12,5\cdot10^{-5}}=\sqrt[3]{\frac{25}{2}\cdot\frac{1}{10^5}}=\sqrt[3]{\frac{1}{8000}}=\frac{1}{20}$$
+		\end{enumerate}
+	\setcounter{enumi}{2}
+	\item Izračunaj in poenostavi:
+		\begin{enumerate}[label=\textbf{\xslalph*})]
+			\setcounter{enumii}{4}
+			\item $$a\cdot\frac{\left(\sqrt[4]{a}+\sqrt[4]{b}\right)^2+\left(\sqrt[4]{a}-\sqrt[4]{b}\right)^2}{a+\sqrt{ab}}
+				=a\cdot\frac{\sqrt{a}+2\sqrt[4]{ab}+\sqrt{b}+\sqrt{a}-2\sqrt[4]{ab}+\sqrt{b}}{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}
+				=a\cdot\frac{2\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}=$$$$=\frac{a2}{\sqrt{2}}=2\sqrt{a}$$
+		\end{enumerate}
+	\item Poenostavi:
+		\begin{enumerate}[label=\textbf{\xslalph*})]
+			\setcounter{enumii}{7}
+			\item $$\frac{\sqrt[3]{x^2\cdot\sqrt[4]{xy^3}}}{\sqrt{x\sqrt{xy}}}
+				=\frac{\sqrt[3]{\sqrt[4]{x^2^4\cdot xy^3}}}{\sqrt{\sqrt{x^2\cdot xy}}}
+				=\frac{\sqrt[3]{\sqrt[4]{x^9y^3}}}{\sqrt{\sqrt{x^3y}}}
+				=\frac{\sqrt[12]{\left(x^3y\right)^3}}{\sqrt{\sqrt{x^3y}}}
+				=\frac{\sqrt[4]{x^3y}}{\sqrt[4]{x^3y}}
+				=1$$
+		\end{enumerate}
+	\setcounter{enumi}{7}
+	\item Zaprta kvadratna škatla z merami $\SI{6}{\deci\meter}\times\SI{9}{\deci\meter}\times\SI{30}{\deci\meter}$ ima enako površino kot kocka. Izračunaj dolžino kockinega roba (do milimetra natančno).
+		$$
+			\sqrt{
+				\frac{
+					2\left(\SI{30}{\deci\meter}\cdot\SI{6}{\deci\meter}\right)+
+					2\left(\SI{6}{\deci\meter}\cdot\SI{9}{\deci\meter}\right)+
+					2\left(\SI{9}{\deci\meter}\cdot\SI{30}{\deci\meter}\right)
+				}{6}
+			}
+			=\sqrt{\frac{\SI{1008}{\deci\meter\squared}}{6}}=\sqrt{\SI{168}{\deci\meter\squared}}=\SI{12,961481}{\deci\meter}
+		$$
+	\item \begin{enumerate}[label=\textbf{\xslalph*})]
+			\setcounter{enumii}{1}
+			\item Za koliko se mora povečati stranica kocke, da se bo njena prostornina s tem povečala za četrtino (prejšnje vrednosti)?
+			$$
+				\left(n+x\right)^2=x^2\cdot\frac{5}{4} \rightarrow n+x=\frac{\sqrt{5}x}{2} \rightarrow n=\frac{\sqrt{5}x}{2}-x
+			$$
+		\end{enumerate}
+	\item \begin{enumerate}[label=\textbf{\xslalph*})]
+			\setcounter{enumii}{1}
+			\item V veliki steklenici je 10 litrov vina. Iz nje izlijemo $x$ litrov vina in nato dolijemo $x$ litrov vode. Zatem ponovno izlijemo iz steklenice $x$ litrov te mešanice in za \say{nadomestek} spet dolijemo $x$ litrov vode. In zatem še enkrat tako. Tedaj je v sodu 5 litrov vina in 5 litrov vode. Izračuaj $x$. \small{\textit{Moj dedek v orehovi lupinici.}}
+				\def\de{\left(1-x\right)-x\left(\frac{1-x}{1}\right)}
+				$$
+					\left(\de\right)-x\frac{\de}{1}=\frac{1}{2}=1-x-x\left(1-x\right)-x\left(1-x-x\left(1-x\right)\right)=-x^3+3x^2-3x+1=
+				$$
+				$$
+					=-\left(x^3-1\right)+3x\left(x-1\right)=-\left(x-1\right)\cdot\left(x^2+x+1\right)+3x\left(x-1\right)
+					=-\left(x-1\right)\cdot\left(x^2+x+1-3x\right)=
+				$$
+				$$
+					-\left(x-1\right)\cdot\left(x^2-2x+1\right)=-\left(x-1\right)\cdot\left(x-1\right)^2=-\left(x-1\right)^3=\frac{1}{2}
+					\rightarrow \left(x-1\right)^3=\frac{-1}{2} \rightarrow x=-\frac{\sqrt[3]{4}}{2}+1
+				$$
+				Sedaj pa $x$ za pravilno vrednost še pomnožimo z 10 in dobimo $2,05299$, torej je, ker smo prej namesto \SI{10}{\liter} uporabili 1, rezultat \SI{2,05299}{\liter}.
+		\end{enumerate}
+\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
+\vfill
+\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}