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authorsijanec <anton@sijanec.eu>2021-01-18 00:22:45 +0100
committersijanec <anton@sijanec.eu>2021-01-18 00:22:45 +0100
commit9bd49030245472ef2000308bdab0f224c570de14 (patch)
tree192f0db0452acf4e56e3f6894a5d029e37e73f95 /mat/domace_naloge
parent23. domača naloga za matematiko (diff)
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-% !TeX encoding = UTF-8
-% !TeX spellcheck = sl_SI
-% do-vimlatex-onwrite
-\documentclass[]{article}
-\usepackage[utf8]{inputenc}
-\usepackage{etoolbox}
-\usepackage[hidelinks]{hyperref}
-\usepackage{xurl} % da breaka url
-\usepackage[a4paper, total={7in, 10in}]{geometry}
-\usepackage{graphicx}
-\usepackage{hologo}
-\usepackage{amssymb}
-\usepackage{calculator}
-\usepackage{pgfplots}
-\usepackage[inline]{enumitem}
-\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{datetime} % [ddMMyyyy]
-\usepackage{ccicons}
-\usepackage{chemformula}
-\usepackage{gensymb}
-\usepackage[normalem]{ulem}
-\usepackage[slovene]{babel}
-\usepackage{cancel}
-\usepackage{tabularx}
-\usepackage{xcolor}
-\usepackage{colortbl}
-\usepackage{exsheets}
-\usepackage{harpoon}
-\usepackage{readarray}
-\usepackage{forloop}
-\usepackage[nomessages]{fp}
-\usepackage{multirow}
-\newcolumntype{Y}{>{\centering\arraybackslash}X}
-% \usepackage{multienum} % weird with labels
-\usetikzlibrary{calc} %% not really needed............. idk.
-%\usetikzlibrary{external}
-% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
-%\tikzexternalize
-\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
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-\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
-\newcommand{\razhroscevanje}{1}
-\definecolor{codegreen}{rgb}{0,0.6,0}
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-\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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-\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
-\renewcommand{\dateseparator}{. }
-\settimeformat{hhmmsstime}
-\lstdefinestyle{mystyle}{
- backgroundcolor=\color{backcolour},
- commentstyle=\color{codegreen},
- keywordstyle=\color{magenta},
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- keepspaces=true,
- numbers=left,
- numbersep=5pt,
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- 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}{Podobni liki }
-\newcommand{\predmdn}{mat}
-\newcommand{\predmkaj}{domace\_naloge}
-\newcommand{\stevilkadn}{23}
-\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}
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-\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}}
-}
-\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
-\newcommand\vektor{\overrightarrow}
-\newcommand{\iic}{I\textsuperscript{2}C }
-\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{$0#2$}%
-\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 navodila in rešitve domačih nalog snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam. Kjer je bilo potrebno izbirati neke poljubne naloge, sem jih vselej izbral naključno.
-\end{abstracit}
-\paragraph{Navodilo naloge} vaje2: 65/424, ... 460 (izberi 2 sodi in 2 lihi nalogi)
-%\tableofcontents
-\begin{enumerate}[label=\textbf{\arabic*.}] % 453, 428, 442, 441
- \setcounter{enumi}{427}
- \item Na sliki je $\measuredangle DEA=\measuredangle ACB$, $|BC|=\cm{18}$, $|AD|=\cm{6}$, $|ED|=\cm{9}$, $|AE|=\cm{5}$, $|BE|=x$, $|DC|=y$. Koliko je $x+y$? % 428
- \begin{center}
- \begin{tikzpicture}[scale=.5]
- \tkzDefPoint(0,0){B} \tkzDefPoint(18,0){C} \tkzDefPoint(12,0){Ah} \tkzDefPoint(18-10,0){Ah2}
- \tkzInterCC(B,Ah)(C,Ah2) \tkzGetPoint{A}
- \tkzDrawPolygon[red!30, opacity=.3](A,B,C)
- \tkzDrawPoints(A,B,C) \tkzLabelPoints(A,B,C)
- \end{tikzpicture}
- \end{center}
- \setcounter{enumi}{440} % the holy setcounter (-;
- \item Pravokotni trikotnik $ABC$, katerega kateti sta dolgi \cm{24} in \cm{10}, je podoben trikotniku $MNK$ s hipotenuzo, dolgo \cm{130}. Izračunaj obseg trikotnika $MNK$. % 441
- $$
- h_{ABC}=\sqrt{\cm{24}^2+\cm{10}^2}=\cm{26} \rightarrow \cm{130}=k\cdot\cm{26}=5\cdot\cm{26} \rightarrow k=5
- $$$$
- O_{MNK}=O_{ABC}\cdot k=(\cm{24}+\cm{26}+\cm{10})\cdot k=\cm{60}\cdot5=\cm{300}
- $$
- \item Dani sta istosrediščni krožnici. Polmer manjše krožnice je enak četrtini polmera večje krožnice. Naj bo $AB$ premer večje krožnice. Iz točke $B$ narišemo tangento na manjšo krožnico. Ta tangenta seka večjo krožnico v točki $C$. Dolžina daljice $AC$ je enaka \cm{100}. Kolikšen je polmer večje krožnice? % 442
- \begin{multicols}{2}
- $$
- \bigtriangleup ABC \Tilde= \bigtriangleup OBT \wedge k = 0,5 \rightarrow |OT| = \cm{50}
- $$$$
- \rightarrow |OB| = \cm{200}
- $$
- \vfill\null\columnbreak
- \begin{tikzpicture}[scale=.8]
- \tkzDefPoint(0,0){O} \tkzDefPoint(1,0){M} \tkzDefPoint(4,0){B} \tkzDefPoint(-4,0){A}
- \tkzDefMidPoint(O,B) \tkzGetPoint{S} \tkzCompass(O,S) \tkzCompass(B,S) \tkzInterCC(O,M)(S,O) \tkzGetPoints{T}{X}
- \tkzInterLC(B,T)(O,A) \tkzGetPoints{C}{CX}
- \tkzDrawCircle(O,M) \tkzDrawCircle(O,B) \tkzDrawLine(A,B) \tkzDrawLine(B,C) \tkzDrawLine(A,C)
- \tkzDrawPoints(A,B,O,M,C,T) \tkzLabelPoints(A,B,O,M,C,T)
- \end{tikzpicture}
- \end{multicols}
-\end{enumerate}
-\section{Zaključek}
-Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
-\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.}
-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/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
-\if\razhroscevanje1
-\vfill
-\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}