author: sijanec <sijanecantonluka@gmail.com> 2020-10-07 22:39:00 +0200
committer: sijanec <sijanecantonluka@gmail.com> 2020-10-07 22:39:00 +0200
commit: 076d0a47416fe33e6f495030effeb80cfff588ce (patch)
tree: fa6ad0e25905f5755c4bc501268e8de5597f62dc /mat/domace_naloge/9
parent: fizika, 1. dn (diff)
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9 files changed, 2196 insertions, 0 deletions
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diff --git a/mat/domace_naloge/9/dokument.out b/mat/domace_naloge/9/dokument.out
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+\BOOKMARK [1][-]{section.1}{Ucni list Trikotniki \204 1 \040\205 nalode 1 \205 11 \(3 sode in 3 lihe, po en primer\)}{}% 1
+\BOOKMARK [1][-]{section.2}{Zakljucek}{}% 2
+\BOOKMARK [1][-]{section.3}{Razhro\235cevalne informacije}{}% 3
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+% !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}
diff --git a/mat/domace_naloge/9/dokument.toc b/mat/domace_naloge/9/dokument.toc
new file mode 100644
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--- /dev/null
+++ b/mat/domace_naloge/9/dokument.toc
@@ -0,0 +1,3 @@
+\contentsline {section}{\numberline {1}Učni list \textit {Trikotniki --- 1 } -- nalode 1 -- 11 (3 sode in 3 lihe, po en primer)}{1}{section.1}%
+\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}%
+\contentsline {section}{\numberline {3}Razhroščevalne informacije}{2}{section.3}%
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+! Package siunitx Error: Misplaced sign token '180-'.
+
+For immediate help type H <return>.
+ ...                                              
+                                                  
+l.131 ...tranji kot tega kota je torej $\ang{180-}
+                                                  \ang{23}=\ang(157)$. Torej...
+
+
+! Package siunitx Error: Token '(' forbidden in restricted numerical input.
+
+For immediate help type H <return>.
+ ...                                              
+                                                  
+l.131 ...a kota je torej $\ang{180-}\ang{23}=\ang(
+                                                  157)$. Torej je lahko to z...
+
+
+! Package siunitx Error: Invalid numerical input '('.
+
+For immediate help type H <return>.
+ ...                                              
+                                                  
+l.131 ...a kota je torej $\ang{180-}\ang{23}=\ang(
+                                                  157)$. Torej je lahko to z...
+
+
+Overfull \hbox (16.2744pt too wide) detected at line 138
+[][] \OT1/cmr/m/n/10 = \U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OMS/cmsy/m/n/10 ^^@ [
+][] ^^@ [][] \OT1/cmr/m/n/10 + \U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OMS/cmsy/m/n/
+10 ^^@ [][] \OT1/cmr/m/n/10 + \U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OT1/cmr/m/n/10
+ = 3 \OMS/cmsy/m/n/10 ^^A \U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OMS/cmsy/m/n/10 ^^
+@ [][] ! [][] \OT1/cmr/m/n/10 = 3\U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OMS/cmsy/m/
+n/10 ! \U/msa/m/n/10 ]\OML/cmm/m/it/10 B \OT1/cmr/m/n/10 = [] = [][] \OMS/cmsy/
+m/n/10 ! \U/msa/m/n/10 ]\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 = [][] \OMS/cmsy/m/n
+/10 ^ \U/msa/m/n/10 ]\OML/cmm/m/it/10 C \OT1/cmr/m/n/10 = [][]
+[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]
+
+Package hyperref Warning: Composite letter `\textasciicaron+c'
+(hyperref)                not defined in PD1 encoding,
+(hyperref)                removing `\textasciicaron' on input line 201.
+
+
+Package hyperref Warning: Composite letter `\textasciicaron+c'
+(hyperref)                not defined in PD1 encoding,
+(hyperref)                removing `\textasciicaron' on input line 209.
+
+(|date -Ins) [2] (./dokument.aux) )
+(see the transcript file for additional information){/usr/share/texmf/fonts/enc
+/dvips/cm-super/cm-super-ts1.enc}</usr/share/texlive/texmf-dist/fonts/type1/pub
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+sfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts
+/cm/cmbx9.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmb
+xti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.
+pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></u
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+-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb></usr/share/texlive/texmf-dist/fo
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+sfonts/symbols/msam10.pfb></usr/share/texmf/fonts/type1/public/cm-super/sfrm100
+0.pfb>
+Output written on dokument.pdf (2 pages, 168435 bytes).
+SyncTeX written on dokument.synctex.gz.
+Transcript written on dokument.log.
author	sijanec <sijanecantonluka@gmail.com>	2020-10-07 22:39:00 +0200
committer	sijanec <sijanecantonluka@gmail.com>	2020-10-07 22:39:00 +0200
commit	076d0a47416fe33e6f495030effeb80cfff588ce (patch)
tree	fa6ad0e25905f5755c4bc501268e8de5597f62dc /mat/domace_naloge/9
parent	fizika, 1. dn (diff)
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