From c14eb1497ed4cbc3dc391463c935bba8639d635f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Sun, 23 Jan 2022 22:36:07 +0100
Subject: dnmat

---
 mat/domace_naloge/4.tex | 119 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 119 insertions(+)
 create mode 100644 mat/domace_naloge/4.tex

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diff --git a/mat/domace_naloge/4.tex b/mat/domace_naloge/4.tex
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+% 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}
-- 
cgit v1.2.3

