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authorsijanec <sijanecantonluka@gmail.com>2020-11-22 01:04:56 +0100
committersijanec <sijanecantonluka@gmail.com>2020-11-22 01:04:56 +0100
commita0fc471bf8c89eb32b77bd144027d70a54c7f243 (patch)
treef8f9a49c0e901de036127eb9cd01a113db730887
parentoiv končna (diff)
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diff --git a/mat/domace_naloge/17/2 b/mat/domace_naloge/17/2
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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[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{amsmath}
+\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[ddMMyyyy]{datetime}
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\usepackage{xcolor}
+\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}{Pitagorov izrek }
+\newcommand{\predmdn}{mat}
+\newcommand{\stevilkadn}{17}
+\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}}
+}
+% \renewcommand\abstractname{Povzetek}
+% \date{17. november 2020}
+% \renewcommand\contentsname{Kazalo vsebine}
+% \renewcommand\figurename{Slika}
+% \renewcommand\abstractname{Povzetek}
+\newcommand{\iic}{I\textsuperscript{2}C }
+% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
+\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 vključujoč snov \textit{\snovdn}, ki nam jo je bil profesor naročil 20. novembra 2020, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbiral naključno.
+\end{abstract}
+\tableofcontents
+\section{Učni list \textit{\snovdn --- 1} (tri naloge)} % 6, 10, 14
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \setcounter{enumi}{5}
+ \begin{multicols}{2}
+ \item Štirje okrogli kovanci s polmerom 2,4 cm se med seboj dotikajo tako, kakor kaže risba na desni. Kolikšna je razdalja ned središčema levega in desnega kovanca?
+ $$\sqrt{(\cm{2,4}\cdot2)^2-\cm{2,4}^2}=
+ \SI[parse-numbers=false]{\sqrt{17,28}}{\centi\meter}\tilde=\cm{4,156922}$$
+ \vfill\null\columnbreak
+ \begin{center}
+ \begin{tikzpicture}[scale=.6]
+ \tkzDefPoint(0,2.4){A} \tkzDefPoint(0,-2.4){B}
+ \tkzDefPoint(0,0){M} \tkzDefPoint(4.156922,0){C}
+ \tkzDefPoint(-4.156922,0){D}
+ \tkzDefMidPoint(A,C) \tkzGetPoint{rC}
+ \tkzDefMidPoint(A,D) \tkzGetPoint{rD}
+ \tkzDrawCircle[fill=yellow](A,M)
+ \tkzDrawCircle[fill=yellow](B,M)
+ \tkzDrawCircle[fill=yellow](C,rC)
+ \tkzDrawCircle[fill=yellow](D,rD)
+ \end{tikzpicture}
+ \end{center}
+ \end{multicols}
+ \setcounter{enumi}{9}
+ \item Težiščnici na kateti pravokotnega trikotnika merita 5 cm in $\sqrt{40}$ cm. Izračunaj dolžino hipotenuze.
+ $$
+ t_a=\sqrt{\left(\frac{a}{2}\right)^2+b^2}
+ =\sqrt{40}=\sqrt{\frac{a^2}{4}+b^2}\wedge
+ t_b=\sqrt{\left(\frac{b}{2}\right)^2+a^2}=5
+ =\sqrt{\frac{b^2}{4}+a^2} \rightarrow
+ $$
+ $$
+ {t_a}^2=\frac{a^2}{4}+b^2=25\wedge{t_b}^2=\frac{b^2}{4}+a^2=40\rightarrow
+ 100=a^2+4b^2\wedge160=b^2+4a^2\rightarrow
+ $$
+ \begin{multicols}{2}
+ $$
+ \begin{tabular}{ccccc}
+ 100 & = & a^2 & + & 4b^2 \\
+ \hcancel[black]{160} & = & 4a^2 & + & b^2
+ \end{tabular}
+ $$
+ $$
+
+ $$
+ \end{multicols}
+% \item
+% \begin{enumerate}[label=\textbf{\xslalph*)}]
+% \item Rombu s stranico 8 cm in s kotom 60\degree je včrtan krog. Izračunaj polmer tega kroga.
+% \item Rombu z diagonalama 5 cm in 6 cm je včrtan krog. Izračunaj polmer tega kroga.
+% \end{enumerate}
+ \setcounter{enumi}{13}
+ \item Ali obstaja pravokotnik, ki ima obseg enak vsoti dolžin diagonal?
+
+ Ne. (Razen če je vsaj ena stranica dolga 0)
+\end{enumerate}
+\section{Učni list \textit{\snovdn --- 2} (dve nalogi)} % 3, 10, 11
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \setcounter{enumi}{2}
+ \item V krožnico s polmerom $R$ so včrtane tri enako velike manjše krožnice, kjer se vsaka dotika večje krožnice in dvah manjših. Izračunaj polmer manjše krožnice.
+ \setcounter{enumi}{9}
+ \item[\textbf{*10.}] Ali je mogoče v kvadrat s stranico dolžine 60 cm včrtati pet enako velikih kvadratov s stranico 22 cm tako, da se ti med seboj ne prekrivajo?
+ \setcounter{enumi}{10}
+ \item Izračunaj vsoto ploščin vseh osenčenih likov v kvadratu s stranico dolžine 2. Nalogo rešite brez uporabe računala. Osenčeni liki so dve polovici kroga s premerom 2 in dva kroga. Kroga se dotikata obeh polkrogov in stranice kvadrata. \textsuperscript{(Matura OR marec 2020)}
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}
+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/domace\_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace\_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/domace\_naloge/\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/17/dokument.aux b/mat/domace_naloge/17/dokument.aux
new file mode 100644
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--- /dev/null
+++ b/mat/domace_naloge/17/dokument.aux
@@ -0,0 +1,25 @@
+\relax
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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+\AtEndDocument{\ifx\hyper@anchor\@undefined
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+\fi}
+\fi}
+\global\let\hyper@last\relax
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\@nameuse{bbl@beforestart}
+\catcode `"\active
+\babel@aux{slovene}{}
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+\@writefile{toc}{\contentsline {section}{\numberline {1}Učni list \textit {Pitagorov izrek --- 1} (tri naloge)}{1}{section.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {2}Učni list \textit {Pitagorov izrek --- 2} (dve nalogi)}{2}{section.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {3}Zaključek}{2}{section.3}\protected@file@percent }
diff --git a/mat/domace_naloge/17/dokument.log b/mat/domace_naloge/17/dokument.log
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diff --git a/mat/domace_naloge/17/dokument.out b/mat/domace_naloge/17/dokument.out
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+\BOOKMARK [1][-]{section.1}{Ucni list Pitagorov izrek \204 1 \(tri naloge\)}{}% 1
+\BOOKMARK [1][-]{section.2}{Ucni list Pitagorov izrek \204 2 \(dve nalogi\)}{}% 2
+\BOOKMARK [1][-]{section.3}{Zakljucek}{}% 3
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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[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{amsmath}
+\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[ddMMyyyy]{datetime}
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\usepackage{xcolor}
+\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}{Pitagorov izrek }
+\newcommand{\predmdn}{mat}
+\newcommand{\stevilkadn}{17}
+\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}}
+}
+% \renewcommand\abstractname{Povzetek}
+% \date{17. november 2020}
+% \renewcommand\contentsname{Kazalo vsebine}
+% \renewcommand\figurename{Slika}
+% \renewcommand\abstractname{Povzetek}
+\newcommand{\iic}{I\textsuperscript{2}C }
+% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
+\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 vključujoč snov \textit{\snovdn}, ki nam jo je bil profesor naročil 20. novembra 2020, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbiral naključno.
+\end{abstract}
+\tableofcontents
+\section{Učni list \textit{\snovdn --- 1} (tri naloge)} % 6, 10, 14
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \setcounter{enumi}{5}
+ \begin{multicols}{2}
+ \item Štirje okrogli kovanci s polmerom 2,4 cm se med seboj dotikajo tako, kakor kaže risba na desni. Kolikšna je razdalja ned središčema levega in desnega kovanca?
+ $$\sqrt{(\cm{2,4}\cdot2)^2-\cm{2,4}^2}=
+ \SI[parse-numbers=false]{\sqrt{17,28}}{\centi\meter}\tilde=\cm{4,156922}$$
+ \vfill\null\columnbreak
+ \begin{center}
+ \begin{tikzpicture}[scale=.6]
+ \tkzDefPoint(0,2.4){A} \tkzDefPoint(0,-2.4){B}
+ \tkzDefPoint(0,0){M} \tkzDefPoint(4.156922,0){C}
+ \tkzDefPoint(-4.156922,0){D}
+ \tkzDefMidPoint(A,C) \tkzGetPoint{rC}
+ \tkzDefMidPoint(A,D) \tkzGetPoint{rD}
+ \tkzDrawCircle[fill=yellow](A,M)
+ \tkzDrawCircle[fill=yellow](B,M)
+ \tkzDrawCircle[fill=yellow](C,rC)
+ \tkzDrawCircle[fill=yellow](D,rD)
+ \end{tikzpicture}
+ \end{center}
+ \end{multicols}
+ \setcounter{enumi}{9}
+ \item Težiščnici na kateti pravokotnega trikotnika merita 5 cm in $\sqrt{40}$ cm. Izračunaj dolžino hipotenuze.
+ $$
+ t_a=\sqrt{\left(\frac{a}{2}\right)^2+b^2}=\sqrt{40}\cm{}
+ =\sqrt{\frac{a^2}{4}+b^2}\wedge
+ t_b=\sqrt{\left(\frac{b}{2}\right)^2+a^2}=\cm{5}
+ =\sqrt{\frac{b^2}{4}+a^2} \rightarrow
+ $$
+ $$
+ {t_a}^2=\frac{a^2}{4}+b^2=\cm{25}\wedge{t_b}^2=\frac{b^2}{4}+a^2=\cm{40}\rightarrow\cm{100}=a^2+4b^2\wedge\cm{160}=b^2+4a^2\rightarrow
+ $$
+ Rešimo sistem enačb $\cm{100}=a^2+4b^2$ in $\cm{160}=4a^2+b^2$.
+ $$a=6\wedgeb=\pm4\rightarrow c=\sqrt{a^2+b^2}=\sqrt{52}\cm{}\tilde=\cm{7,21}$$
+% \item
+% \begin{enumerate}[label=\textbf{\xslalph*)}]
+% \item Rombu s stranico 8 cm in s kotom 60\degree je včrtan krog. Izračunaj polmer tega kroga.
+% \item Rombu z diagonalama 5 cm in 6 cm je včrtan krog. Izračunaj polmer tega kroga.
+% \end{enumerate}
+ \setcounter{enumi}{13}
+ \item Ali obstaja pravokotnik, ki ima obseg enak vsoti dolžin diagonal?
+
+ Ne. (Obstaja sicer zgolj takrat, ko je vsaj ena stranica dolga 0)
+\end{enumerate}
+\section{Učni list \textit{\snovdn --- 2} (dve nalogi)} % 3, 10, 11
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \setcounter{enumi}{2}
+ \item V krožnico s polmerom $R$ so včrtane tri enako velike manjše krožnice, kjer se vsaka dotika večje krožnice in dvah manjših. Izračunaj polmer manjše krožnice.
+ \begin{itemize}
+ \item Težišče enakostraničnega trikotnika, katerega oglišča so središča manjših krogov, je enako težišču velikega kroga.
+ \item Težišče razpolavlja težiščnico na dva dela, kjer je prvi dolg za dvakratnik dolžine drugega.
+ \item Ker je težiščnica v enakokrakem trikotniku višina, lahko uporabimo kratko formulo za višino kot formulo za težiščnico.
+ \end{itemize}
+ $$\rightarrow R=\frac{t_{ežiščnica}}{3}\cdot2+r_{\text{manjši}}
+ =\frac{r_{\text{manjši}\cdot\sqrt{3}}}{3}\cdot2+r_{\text{manjši}}
+ \rightarrow r_{\text{manjši}}=\frac{R\cdot3}{3+\sqrt{3}}$$
+ \setcounter{enumi}{9}
+ \item[\textbf{*10.}] Ali je mogoče v kvadrat s stranico dolžine 60 cm včrtati pet enako velikih kvadratov s stranico 22 cm tako, da se ti med seboj ne prekrivajo?
+
+ Ja. Hipotenuza velikega kvadrata je približno \cm{84,852814}, vsota hipotenuz dveh manjših kvadratov pa je približno \cm{62,225397}. Razlika zadošča za eno stranico in celo več (približno \cm{22,627415}). Če torej male kvadrate postavimo v oglišča večjega kvadrata, lahko v sredini zarišemo še en mali kvadrat, le da mora biti rotiran za \ang{45} ($\pm$ nekaj\degree).
+
+ %\begin{tikzpicture}[scale=0.1]
+ % \tkzDefPoint(0,0){A} \tkzDefPoint(60,0){B} \tkzDefPoint(60,60){C}
+ % \tkzDefPoint(0,60){D}
+ % \tkzDefPoint(22,60){2260} \tkzDefPoint(0,60-22){06022}
+ % \tkzDefPoint(22,60-22){226022}
+ % \tkzDrawPolygon[fill=blue!30, opacity=.3](D,2260,226022,06022)
+ % \tkzDrawSegment[dim={$\cm{22}$,6pt,transform shape}](D,2260)
+ % \tkzDefPoint(60-22,60){602260} \tkzDefPoint(60-22,60-22){60226022}
+ % \tkzDefPoint(60,60-22){606022}
+ % \tkzDrawPolygon[fill=blue!30, opacity=.3](60226022,606022,C,602260)
+ % \tkzDefPoint(0,22){022} \tkzDefPoint(22,22){2222} \tkzDefPoint(22,0){220}
+ % \tkzDrawPolygon[fill=blue!30, opacity=.3](A,220,2222,022)
+ % \tkzDefPoint(60-22,0){60220} \tkzDefPoint(60,22){6022}
+ % \tkzDefPoint(60-22,22){602222}
+ % \tkzDrawPolygon[fill=blue!30, opacity=.3](60220,B,6022,602222)
+ % \tkzInterLC(2222,A)(2222,A) \tkzGetPoints{U}{X} \tkzCompass(2222,X)
+ % \tkzDrawSegment[dim={$\cm{60}$,6pt,transform shape}](A,B)
+ % \tkzDrawPolygon[fill=red!30, opacity=.30](A,B,C,D)
+ % \tkzMarkRightAngles(D,A,B A,B,C B,C,D C,D,A)
+ % \tkzLabelPoints(A,B,C,D) \tkzDrawPoints(A,B,C,D)
+ %\end{tikzpicture}
+ \setcounter{enumi}{10}
+ % \item Izračunaj vsoto ploščin vseh osenčenih likov v kvadratu s stranico dolžine 2. Nalogo rešite brez uporabe računala. Osenčeni liki so dve polovici kroga s premerom 2 in dva kroga. Kroga se dotikata obeh polkrogov in stranice kvadrata. \textsuperscript{(Matura OR marec 2020)}
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}
+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/domace\_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace\_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/domace\_naloge/\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/17/dokument.toc b/mat/domace_naloge/17/dokument.toc
new file mode 100644
index 0000000..a34cf3e
--- /dev/null
+++ b/mat/domace_naloge/17/dokument.toc
@@ -0,0 +1,5 @@
+\babel@toc {slovene}{}
+\babel@toc {slovene}{}
+\contentsline {section}{\numberline {1}Učni list \textit {Pitagorov izrek --- 1} (tri naloge)}{1}{section.1}%
+\contentsline {section}{\numberline {2}Učni list \textit {Pitagorov izrek --- 2} (dve nalogi)}{2}{section.2}%
+\contentsline {section}{\numberline {3}Zaključek}{2}{section.3}%
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