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diff --git a/mat/domace_naloge/17/2 b/mat/domace_naloge/17/2 new file mode 100644 index 0000000..1db662b --- /dev/null +++ b/mat/domace_naloge/17/2 @@ -0,0 +1,216 @@ +% !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 index 0000000..d45d4d7 --- /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}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} 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+\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}% diff --git a/mat/domace_naloge/17/stderr.log b/mat/domace_naloge/17/stderr.log new file mode 100644 index 0000000..cc36dfe --- /dev/null +++ b/mat/domace_naloge/17/stderr.log @@ -0,0 +1 @@ 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