From 01c7750a88488b6f8876698363668cd6d4fa01d6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Wed, 5 Jan 2022 00:48:35 +0100
Subject: dn

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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}
+\title{Domača naloga}
+\author{Anton Luka Šijanec, 3. a}
+\begin{document}
+\maketitle
+\begin{abstract}
+Rešitev domače naloge, naročene 4. aprila 2021. Navodilo: V učbeniku na strani 49 pri nalogah od prve do devete naredi vsaj štiri primere.
+\end{abstract}
+% \tableofcontents
+\section{Naloge in rešitve}
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\item Izmeri dolžino in širino klopi ali mize in izračunaj ploščino. Rezultat zaokroži na kvadratni centimeter natančno.
+	$$\SI{75}{\centi\meter}\cdot\SI{175}{\centi\meter}=\SI{13125}{\centi\meter\squared}$$
+	\item Obseg romboida je \SI{70}{\centi\meter}, dolžini sosednjih stranic pa sta v razmerju $4:3$. Kolikšna je ploščina romboida, če je njegov ostri kot velik $\ang{60}$? Rezulat zaokroži na dve decimalni mesti.
+	$$a = \frac{\SI{70}{\centi\meter}}{7}\cdot3=\SI{40}{\centi\meter} \wedge b=\frac{\SI{70}{\centi\meter}}{7}\cdot3=\SI{30}{\centi\meter} \Rightarrow S = ab\sin\alpha = \SI{40}{\centi\meter}\SI{30}{\centi\meter}\sin\ang{60}=\SI{1039,23}{\centi\meter\squared}$$
+	\item Koliko je dolga diagonala pravokotnika, katerega obseg je \SI{22}{\centi\meter}, ploščina pa \SI{30}{\centi\meter\squared}?
+	$$a+b=\SI{11}{\centi\meter} \wedge ab=\SI{15}{\centi\meter\squared} \wedge \frac{\SI{30}{\centi\meter\squared}}{a}=\SI{11}{\centi\meter}-a=b \Rightarrow $$
+	Na tej točki je morebiti že prepozno. Očitno se nikoli nisem naučil osnov matematike.
+	\begin{lstlisting}[language=Python]
+sage: var("a m")
+(a, m)
+sage: e = 30*m**2/a==11*m-a
+sage: solve([e, e2], a, m)
+[[a == 5, m == 1], [a == 6, m == 1]]\end{lstlisting}
+	$$\Rightarrow a = \SI{5}{\centi\meter} \wedge b = \SI{6}{\centi\meter} \Rightarrow d = \sqrt{a^2+b^2}=\sqrt{\SI{25}{\centi\meter\squared}+\SI{36}{\centi\meter\squared}}=\sqrt{\SI{61}{\centi\meter\squared}} = \SI{7,810}{\centi\meter}$$
+	\item Diagonali pravokotnika sta dolgi \SI{10}{\centi\meter} in se sekata pod kotom \ang{60}. Izračunaj obseg in ploščino pravokotnika. Rezultat naj bo točen.
+	$$2\sin\ang{60}\cdot\SI{5}{\centi\meter}=b=\SI[parse-numbers = false]{5\sqrt{3}}{\centi\meter} \wedge 2\cos\ang{60}\cdot\SI{5}{\centi\meter}=a=\SI{5}{\centi\meter} \Rightarrow O = \SI[parse-numbers = false]{5+5\sqrt{3}}{\centi\meter} \wedge S = \SI[parse-numbers = false]{25\sqrt{3}}{\centi\meter\squared}$$
+	\item Dolžini stranic pravokotnika sta v razmerju $4:3$. Razpolovišča stranic pravokotnika določajo štirikotnik.
+	\begin{enumerate}[label=\xslalph*)]
+		\item Kolikšen del pravokotnika pokrije štirikotnik?
+		$$S_n=\frac{ef}{2}\sin\theta \wedge \sin\theta=\sin\ang{90}=1 \wedge e=3 \wedge f=4 \Rightarrow S_n=6 \rightarrow \frac{6}{S_z=a_zb_z=12}=\frac{1}{2}$$
+		\item Kolikšno je razmerje med obsegoma pravokotnika in štirikotnika?
+		$$a_n = \sqrt{\frac{4}{2}^2+\frac{3}{2}^2}=\sqrt{6,25}=2,5 \wedge \frac{4\cdot2,5=10}{2\cdot\left(4+3\right)=14}=\frac{5}{7}$$
+	\end{enumerate}
+	\item Ploščina romba, katerega ena izmed diagonal je dolga \SI{36}{\centi\meter}, je \SI{432}{\centi\meter\squared}. Koliko sta dolgi stranica in višina romba?
+	$$a=\sqrt{\left(\frac{\frac{2\cdot\SI{432}{\centi\meter\squared}}{\SI{36}{\centi\meter}}}{2}\right)^2+\left(\frac{\SI{36}{\centi\meter}}{2}\right)^2}=\SI[parse-numbers = false]{\sqrt{468}}{\centi\meter}$$
+	$$v_a=a\sin\alpha \wedge \alpha=2\cdot\left(\ang{90}-\arccos\frac{\SI{18}{\centi\meter}}{a}\right)=\ang{112,6} \Rightarrow o=\SI{19,969}{\centi\meter}$$
+	\item Ploščina romboida je \SI{108}{\centi\meter\squared}. Višina na daljšo stranico je dolga \SI{6}{\centi\meter}. Koliko sta dolgi stranici romboida, če sta njuni dolžini v razmerju $2:3$?
+	$$a=\frac{\SI{180}{\centi\meter\squared}}{\SI{6}{\centi\meter}}=\SI{30}{\centi\meter} \Rightarrow b=\SI{20}{\centi\meter}$$
+\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

