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diff --git a/mat/domace_naloge/9/dokument.tex b/mat/domace_naloge/9/dokument.tex new file mode 100644 index 0000000..4643428 --- /dev/null +++ b/mat/domace_naloge/9/dokument.tex @@ -0,0 +1,217 @@ +% !TeX encoding = UTF-8 +% !TeX spellcheck = sl_SI +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage{etoolbox} +\usepackage[hidelinks]{hyperref} +\usepackage[a4paper, total={7in, 10in}]{geometry} +\usepackage{graphicx} +\usepackage{hologo} +\usepackage{amssymb} +\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{listings} +% \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{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} + +\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 +\makeatletter +\newcommand{\stevilkadn}{9} +\newcommand{\snovdn}{Trikotniki --- 1 } +\newcommand{\cm}[1]{\SI{#1}{\centi\meter}} +\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{7. oktober 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 Fizika, 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}} + + +% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 +\begin{document} +\maketitle + +\begin{abstract} + + Ta dokument obsega naloge, naročene dijakom 6. oktobra 2020, in njihove + rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so + iz učnega lista z nalogami profesorja Domajnka. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno. +\end{abstract} +\tableofcontents + +\section{Učni list \textit{\snovdn} -- nalode 1 -- 11 (3 sode in 3 lihe, po en primer)} +\begin{enumerate}[label=\textbf{\arabic*.}] % 9, 1, 7, 8, 4, 2 + \item + \begin{enumerate}[label=\textbf{\xslalph*)}] + \setcounter{enumii}{3} + \item V enakokrakem trikotniku meri eden od zunanjih kotov \ang{23}. Izračunaj notranje kote tega trikotnika. + + Notranji kot tega kota je torej $\ang{180-}\ang{23}=\ang(157)$. Torej je lahko to zgolj kot med krakoma. Torej sta ostala kota velika vsak po: + $$\frac{\ang{180}-\ang{157}}{2}=\ang{11,5}$$ + \end{enumerate} + \item + \begin{enumerate}[label=\textbf{\xslalph*)}] + \setcounter{enumii}{2} + \item V trikotniku $ABC$ je notranji kot pri oglišču $A$ za \ang{12} manjši od kota pri oglišču $B$, kot pri oglišču $C$ je za \ang{18} manjši od kota pri oglišču $A$. Izračunaj notranje kote tega trikotnika. + $$\ang{180} = \measuredangle B-\ang{12}-\ang{18}+\measuredangle B-\ang{12}+\measuredangle B = 3 \cdot \measuredangle B-\ang{42} \rightarrow \ang{222}=3\measuredangle B \rightarrow \measuredangle B = \frac{222}{3} = \ang{74} \rightarrow \measuredangle A = \ang{62} \wedge \measuredangle C = \ang{44}$$ + \end{enumerate} + \setcounter{enumi}{3} + \item Naj bo $ABC$ pravokotni trikotnik: $\gamma=\ang{90}, \alpha=\ang{34}$. + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Pod kakšnim kotom se sekata simetrali kotov ob hipotenuzi? + $$\beta=\ang{180}-\alpha-\gamma=\ang{56} \rightarrow \measuredangle = \ang{180}-(\ang{180}-\ang{17}-\ang{28})=\ang{45}$$ + \end{enumerate} + \setcounter{enumi}{6} + \item V enakokrakem trikotniku $ABC$ je $\alpha=4\gamma$. + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Pod kakšnim kotom se sekata simetrali kotov ob osnovnici? + $$\alpha=\beta=\frac{\ang{180}}{9}\cdot4=\ang{80}\wedge + \gamma=\frac{\alpha}{4}=\ang{20}\rightarrow\measuredangle=\ang{180}-(\ang{180}-2\cdot\ang{40})=\ang{180}-\ang{100}=\ang{80}$$ + \end{enumerate} + \item + \begin{enumerate}[label=\textbf{\xslalph*)}] + \setcounter{enumii}{3} + \item Dokaži: Če je v trikotniku razlika dveh kotov večja od tretjega kota, je trikotnik topokoten. + $$\alpha-\beta>\gamma\rightarrow\alpha>\gamma+\beta\rightarrow + \alpha>\ang{180}-\alpha$$ + Pa denimo, da $\alpha \not> \ang{90}$: + $$\alpha = \ang{90} + \color{magenta} + \rightarrow\ang{90}>\ang{180}-\ang{90}\rightarrow\ang{90}>\ang{90} + \color{black}$$ + + Trditve v \color{magenta} magenti \color{black} ne držijo. $\alpha>\ang{90} \square$ + \end{enumerate} + \item Načrtaj trikotnik $ABC$ s podatki: $a=\cm{5}, b=\cm{6}, c=\cm{7}$. + \begin{enumerate}[label=\textbf{\xslalph*)}] + \setcounter{enumii}{3} + \item Trikotniku $ABC$ včrtaj krožnico. + \end{enumerate} + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){CHA} + \tkzDefPoint(7,0){B} \tkzDefPoint(2,0){CHB} + \tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$} + \tkzCompass(A,B) + \tkzInterCC(A,CHA)(B,CHB) \tkzGetPoints{C}{CBELOW} + \tkzCompass(A,C) \tkzCompass(B,C) + \tkzDrawLine(A,C) \tkzLabelLine[above](A,C){$b$} + \tkzDrawLine(B,C) \tkzLabelLine[above](B,C){$a$} + \tkzInterLC(A,B)(A,C) \tkzGetPoints{ABPK}{ABP} \tkzCompass(A,ABP) + \tkzInterLC(A,C)(C,B) \tkzGetPoints{ACP}{ACPK} \tkzCompass(C,ACP) + \tkzDrawLine(C,ABP) \tkzDrawLine(B,ACP) + \tkzDefMidPoint(ACP,B) \tkzGetPoint{CM} + \tkzCompass(ACP,CM) \tkzCompass(B,CM) + \tkzDefMidPoint(ABP,C) \tkzGetPoint{AM} + \tkzCompass(ABP,AM) \tkzCompass(C,AM) + \tkzDrawLine(A,AM) \tkzDrawLine(CM,C) + \tkzInterLL(C,CM)(AM,A) \tkzGetPoint{S} + \tkzInterLC(A,B)(S,A) \tkzGetPoints{AB1}{AB2} + \tkzCompass(S,AB1) \tkzCompass(S,AB2) + \tkzDefMidPoint(AB1,AB2) \tkzGetPoint{ABM} + \tkzCompass(AB1,ABM) \tkzCompass(AB2,ABM) + \tkzDrawLine[add = 0 and 0](S,ABM) \tkzLabelLine[right](S,ABM){$r$} + \tkzDrawCircle(S,ABM) + \tkzDrawPoints(A) \tkzLabelPoints(A,B,C) + \end{tikzpicture} + \end{center} +\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 mojem šolskem Git repozitoriju na +\url{https://github.com/sijanec/sola-gimb-2} v mapi +\href{https://github.com/sijanec/sola-gimb-2/tree/master/mat/domace_naloge/\stevilkadn/}{/mat/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/mat/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/mat/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: \input|"date -Ins" +\fi +% \item $$$$ +\end{document} |