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diff --git a/mat/domace_naloge/4.tex b/mat/domace_naloge/4.tex new file mode 100644 index 0000000..8a02b8e --- /dev/null +++ b/mat/domace_naloge/4.tex @@ -0,0 +1,119 @@ +% do-vimlatex-onwrite +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage{siunitx} +\usepackage[slovene]{babel} +\usepackage[inline]{enumitem} +\usepackage[a4paper, total={7in, 10in}]{geometry} +\usepackage{hologo} +\usepackage[hidelinks,unicode]{hyperref} +\usepackage{datetime} +\usepackage{tkz-euclide} +\usepackage{amssymb} +\usepackage{multicol} +\usepackage{listings} +\usepackage{xcolor} +% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction} % frac način +% \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=symbol} % poševnica način +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction} % na -1 način +\settimeformat{hhmmsstime} +\newcommand{\razhroscevanje}{0} +\newcommand{\razhroscevanjeg}{0} % grafično razhroščevanje +\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 +\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} +\newcommand{\cm}[1]{ + \SI[parse-numbers=false]{#1}{\centi\meter} +} +\newcommand{\m}[1]{ + \SI[parse-numbers=false]{#1}{\meter} +} +\newcommand{\kvm}[1]{ + \SI[parse-numbers=false]{#1}{\meter\squared} +} +\newcommand{\kvcm}[1]{ + \SI[parse-numbers=false]{#1}{\centi\meter\squared} +} +\newcommand{\herod}{ + \text{herod} +} +\title{Domača naloga} +\author{Anton Luka Šijanec, 3. a} +\begin{document} +\maketitle +\begin{abstract} +Rešitev domače naloge, naročene 20. januarja 2022. Navodilo: \textbf{Mat3:} 43 / 3, 4, 9, 10. Ker na 43. strani sploh ni nalog 9 in 10, predvidevam, da je imel profesor v mislih naloge s strani 59. +\end{abstract} +% \tableofcontents +\section{Naloge in rešitve} +\begin{enumerate}[label=\textbf{\arabic*.}] + \setcounter{enumi}{2} + \item Marko je na dvorišču narisal trikotnik, katerega stranice so bile dolge \m{5}, \m{8} in \cm{12}, Tadeja pa je narisala trikotnik, katerega stranice so bile dolge \m{5}, \m{8} in \cm{9}. Kateri trikotnik je imel večjo ploščino? Za koliko? + $$ + s = \frac{a+b+c}{2} \wedge s_M = \m{12,5} \wedge s_T = \m{11} \Rightarrow + S = \sqrt{s(s-a)(s-b)(s-c)} \wedge S_M = \kvm{210,9375} \wedge S_T = \kvm{396} + $$ + Tadejin je večji za \kvm{185,0625}. + \item Stranici romboida sta dolgi \cm{52} in \cm{32}, diagonala pa \cm{44}. Kolikšna je njegova ploščina? + $$ + s = \frac{\cm{52}+\cm{32}+\cm{44}}{2} \wedge + S=2\sqrt{s(s-\cm{52})(s-\cm{32})(s-\cm{44})}=\kvcm{1402,16974721} + $$ + \setcounter{enumi}{8} + \item Stranice trikotnika so dolge \cm{5}, \cm{6} in \cm{7}. Koliko so veliki notranji koti tega trikotnika? Kolikšen je polmer trikotniku očrtane krožnice? Kolikšna je ploščina trikotnika? + $$ + \gamma=\arccos\left(\frac{a^2+b^2-c^2}{2ab}\right)=\ang{78,463} \wedge + \alpha=\ang{57,122} \wedge \beta=\ang{44,415} + $$$$ + R=\frac{c}{\sin\gamma}=2R + \wedge R=\frac{\frac{\cm{7}}{\sin\ang{78,463}}}{2}=\cm{3,572} + $$$$ + S=\herod(\cm{5}, \cm{6}, \cm{7})=\kvcm{14,6969} + $$ + \item Koliko sta dolgi najdaljša in najkrajša višina trikotnika, ki ima stranice dolge \cm{8}, \cm{11} in \cm{14}? + $$ + v_a=\frac{2\herod(a, b, c)}{\cm{8}}=\cm{10,978} \wedge + v_b=\frac{2\herod(a, b, c)}{\cm{11}}=\cm{7,984} \wedge + v_c=\frac{2\herod(a, b, c)}{\cm{14}}=\cm{6,273} + $$ +\end{enumerate} +\section{Zaključek} +\hologo{LaTeX} izvorna koda dokumenta je objavljena na \url{https://git.sijanec.eu/sijanec/sola-gimb-3}. Za izdelavo dokumenta je potreben \texttt{TeXLive 2020}. +\if\razhroscevanje1 +\vfill +\section*{Razhroščevalne informacije} +Konec generiranja dokumenta \today\ ob \currenttime. + +Dokument se je generiral R0qK1KR2 \SI{}{\second}. % aaasecgeninsaaa +\fi +\end{document} |