author: sijanec <sijanecantonluka@gmail.com> 2020-09-17 23:28:50 +0200
committer: sijanec <sijanecantonluka@gmail.com> 2020-09-17 23:28:50 +0200
commit: 597b821dd1b8e6e97adec2e779dff5e298adbc70 (patch)
tree: c1e32653fde0b3f44d116126f73a10d6821966b1
parent: peta matematična domača naloga! (diff)
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9 files changed, 2749 insertions, 0 deletions
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@@ -0,0 +1,3 @@
+\BOOKMARK [1][-]{section.1}{Ucbenik Matematika 1: Stran 19}{}% 1
+\BOOKMARK [1][-]{section.2}{Zbirka nalog Matematika 1: Stran 16}{}% 2
+\BOOKMARK [1][-]{section.3}{Zakljucek}{}% 3
diff --git a/mat/domace_naloge/6/dokument.pdf b/mat/domace_naloge/6/dokument.pdf
new file mode 100644
index 0000000..d5d6cd7
--- /dev/null
+++ b/mat/domace_naloge/6/dokument.pdf
diff --git a/mat/domace_naloge/6/dokument.synctex.gz b/mat/domace_naloge/6/dokument.synctex.gz
new file mode 100644
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diff --git a/mat/domace_naloge/6/dokument.tex b/mat/domace_naloge/6/dokument.tex
new file mode 100644
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--- /dev/null
+++ b/mat/domace_naloge/6/dokument.tex
@@ -0,0 +1,315 @@
+% !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}{0}
+\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}{6}
+\newcommand{\snovdn}{Skladnost trikotnikov }
+\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{17. september 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 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}}
+
+
+% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+
+\begin{abstract}
+	Ta dokument obsega naloge, naročene dijakom 16. septembra 2020, in njihove
+	rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so
+	iz učbenika in vaj/zbirke nalog.
+\end{abstract}
+% \tableofcontents
+
+\section{Učbenik \textit{Matematika 1}: Stran 19}
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\item Načrtaj kote, velike \ang[parse-numbers=false]{\textbf{105}}, \ang{150}, \ang{15}, \ang{135} in \ang{165}.
+		\begin{center}
+			\begin{tikzpicture}
+				\tkzDefPoint(-5,0){A} %%% kot 90 stopinj ˇˇˇ
+				\tkzDefPoint(5,0){B}
+				\tkzDefPoint(0,0){CHEATING0} \tkzDefPoint(0.05,0){CHEATING1} \tkzDefPoint(-0.05,0){CHEATING2}
+				\tkzInterCC(A,B)(B,A) \tkzGetPoints{C}{D}
+				\tkzDrawPoints(A) \tkzCompass(A,C) \tkzCompass(B,C) \tkzCompass(A,CHEATING1) \tkzCompass(B,CHEATING2) \tkzCompass(A,B)
+				\tkzDrawLine(A,B) \tkzDrawLine(CHEATING0,C) \tkzMarkAngle[mark=none](B,CHEATING0,C)
+				\tkzMarkRightAngles(B,CHEATING0,C)
+				%%% kot 60 stopinj ˇˇˇ
+				\tkzInterLC(CHEATING0,C)(CHEATING0,A) \tkzGetPoints{E}{F} \tkzCompass(CHEATING0,F)
+				\tkzInterCC(CHEATING0,F)(F,CHEATING0) \tkzGetPoints{G}{H} \tkzCompass(CHEATING0,G) \tkzCompass(F,G)
+				\tkzDrawLine(CHEATING0,G) \tkzMarkAngle[color=magenta, mark=none](F,CHEATING0,G)
+				%%% kot 60/2 stopinj ˇˇˇ
+				\tkzDrawLine(F,G) \tkzDefMidPoint(F,G) \tkzGetPoint{I} \tkzCompass(F,I) \tkzCompass(G,I)
+				\tkzMarkAngle[color=cyan,mark=none, size=1.1cm](F,CHEATING0,I)
+				%%% kot 60/2/2 stopinj = 15 stopinj ˇˇˇ
+				\tkzDefMidPoint(F,I) \tkzGetPoint{J} \tkzCompass(F,J) \tkzCompass(I,J)
+				\tkzMarkAngle[color=yellow,mark=none, size=1.2cm](F,CHEATING0,J)
+				%%% kot 105 stopinj = kot 90 stopinj + kot 15 stopinj ˇˇˇ
+				\tkzMarkAngle[color=red,mark=none, size=0.9cm](B,CHEATING0,J) \tkzDrawLine(CHEATING0,J)
+			\end{tikzpicture}
+		\end{center}
+	\item Načrtaj trikotnik, ki ima stranice dolge \SI{6}{\centi\meter}, \SI{4}{\centi\meter} in \SI{4,5}{\centi\meter}.
+
+	\item Načrtaj trikotnik z danimi podatki.
+		\begin{multicols}{4}
+			\noindent
+			\begin{enumerate}[label=\textbf{\xslalph*)}]
+				\item	$\mathbf{c=}\SI[parse-numbers=false, parse-units=false]{\mathbf{5}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{b=}\SI[parse-numbers=false, parse-units=false]{\mathbf{4}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{\alpha=}\ang[parse-numbers=false, parse-units=false]{\mathbf{75}}$
+				\item $a=\SI{6}{\centi\meter}$
+
+							$\beta=\ang{60}$
+
+							$\gamma=\ang{45}$
+				\item $c=\SI{5,5}{\centi\meter}$
+
+							$a=\SI{4}{\centi\meter}$
+
+							$\gamma=\ang{75}$
+				\item	$b=\SI{5}{\cm}$
+
+							$c=\SI{6,5}{\centi\meter}$
+
+							$\beta=\ang{60}$
+			\end{enumerate}
+		\end{multicols}
+		\begin{multicols}{2}
+			\noindent
+			\begin{center}
+				\begin{tikzpicture}
+					\tkzDefPoint(0,0){A}
+					\tkzDefPoint(5,0){B}
+					\tkzDefPoint(4,0){b}
+					\tkzDrawPoints(A) \tkzCompass(A,b) \tkzDrawLine(A,B) \tkzCompass(A,b)
+					\tkzDrawSegment[dim={$\SI{4,0}{\centi\meter}$,6pt,transform shape}](A,b)
+					\tkzInterCC(A,b)(b,A) \tkzGetPoints{D}{d} \tkzCompass(A,D) \tkzCompass(B,D) \tkzInterCC(D,A)(A,D)	\tkzGetPoints{e}{E}
+					\tkzCompass(A,E) \tkzCompass(D,E) \tkzDefMidPoint(E,D) \tkzGetPoint{F} \tkzCompass(D,F) \tkzCompass(E,F)
+					\tkzDefMidPoint(F,D) \tkzGetPoint{C} \tkzCompass(F,C) \tkzCompass(D,C) \tkzDrawLine(A,C) \tkzDrawLine(B,C)
+					\tkzLabelLine[below left](B,C){$a$} \tkzLabelLine[below right](C,A){$b$} \tkzLabelLine[below](A,B){$c$}
+					\tkzLabelPoints(A) \tkzLabelPoints[below left](B) \tkzLabelPoints[above right](C)
+					\tkzMarkAngle[mark=none](B,A,C) \tkzLabelAngle[pos=1.2](B,A,C){$\alpha$}
+				\end{tikzpicture}
+				\begin{tikzpicture}
+					\tkzDefPoint(0,0){A}
+					\tkzDefPoint(6,0){B}
+					\tkzDefPoint(4,0){a}
+					\tkzDefPoint(4.5+6,0){b}
+					\tkzDrawPoint(A)
+					\tkzCompass(A,B)
+					\tkzInterCC(A,a)(B,b) \tkzGetPoints{C}{c} \tkzCompass(A,C) \tkzCompass(B,C)
+					\tkzDrawLine(A,B) \tkzDrawLine(B,C) \tkzDrawLine(C,A)
+				\end{tikzpicture}
+			\end{center}
+		\end{multicols}
+	\item Načrtaj štirikotnik z danimi podatki. Pomagaj si s trikotnika, na katera diagonala razdeli štirikotnik
+		\begin{multicols}{6}
+			\noindent
+			\begin{enumerate}[label=\textbf{\xslalph*)}]
+				\item $\mathbf{a=}\SI[parse-numbers=false, parse-units=false]{\mathbf{5}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{b=}\SI[parse-numbers=false, parse-units=false]{\mathbf{3}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{c=}\SI[parse-numbers=false, parse-units=false]{\mathbf{4}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{d=}\SI[parse-numbers=false, parse-units=false]{\mathbf{4}}{\mathbf{\centi\meter}}$
+
+							$\mathbf{f=}\SI[parse-numbers=false, parse-units=false]{\mathbf{5}}{\mathbf{\centi\meter}}$
+				\item	$a=\SI{6}{\centi\meter}$
+				
+							$b=\SI{5}{\centi\meter}$
+
+							$d=\SI{4}{\centi\meter}$
+
+							$\alpha=\ang{120}$
+
+							$\delta=\ang{90}$
+				\item	$b=\SI{6}{\centi\meter}$
+
+							$c=\cm{2}$
+
+							$d=\cm{5}$
+
+							$\gamma=\ang{105}$
+
+							$\delta=\ang{75}$
+				\item	$a=\cm{7}$
+
+							$b=\cm{4}$
+
+							$c=\cm{5}$
+
+							$e=\cm{6}$
+
+							$f=\cm{5,5}$
+				\item	$d=c=\cm{3}$
+				
+							$a=d=\cm{5}$
+
+							$f=\cm{5,5}$
+				\item $a=\cm{5}$
+
+							$d=\cm{4}$
+
+							$e=\cm{6}$
+
+							$f=\cm{7}$
+
+							$\beta=\ang{60}$
+			\end{enumerate}
+		\end{multicols}
+		% \begin{center}
+			Štirikotnikov še nismo definirali. (-; Problem je v tem, da ne vem, med katerimi pari točk so določene stranice.
+		% \end{center}
+\end{enumerate}
+
+\section{Zbirka nalog \textit{Matematika 1}: Stran 16}
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\setcounter{enumi}{71}
+	\item Trikotnika $ABC$ in $A'B'C$ sta skladna. Točki $D$ in $D'$ ležita na stranicah $AB$ oziroma $A'B'$ tako, da sta kota $DCB$ in $D'C'B'$ skladna. Dokaži, da je $|AD|=|A'D'|$
+	\item Na sliki je $|AE|=|BG|$, kota $BAC$ in $FEG$ sta skladna, prav tako sta skladna kota $CBA$ in $EGF$. Dokaži, da sta trikotnika $ABC$ in $EGF$ skladna.
+	\item Točke $A, B, C, E$ in $F$ ležijo, kot kaže slika: $|AB|=|BC|, AF \bot BE, CE \bot BF$. Dokaži, da je $|AF|=|CE|$.
+		\begin{multicols}{2}
+			\begin{center}
+				\begin{tikzpicture}
+					\tkzDefPoint(0,0){B}
+					\tkzDefPoint(-5,0){C}
+					\tkzDefPoint(210:5){A}
+					%\tkzDefPoint(210:6){E}
+					\tkzDefLine[orthogonal=through A](B,A) \tkzGetPoint{f}
+					\tkzInterLL(A,f)(B,C)
+					\tkzGetPoint{F}
+					\tkzDefMidPoint(A,F) \tkzGetPoint{M}
+					\tkzDefLine[orthogonal=through M](B,F) \tkzGetPoint{e}
+					\tkzInterLL(C,e)(B,A) \tkzGetPoint{E}
+					\tkzDrawPoints(A,B,C,F,E)
+					\tkzLabelPoints(B,E,A) \tkzLabelPoints[above right](F,C)
+					\tkzDrawLine(B,F)	\tkzDrawLine[add = 0 and 0](C,E)
+					\tkzDrawLine(B,E)	\tkzDrawLine[add = 0 and 0](A,F)
+					\tkzMarkSegments[mark=|](C,B A,B) \tkzMarkSegments[mark=||](F,A E,C)
+					\tkzMarkAngles[mark=|||](C,B,A) \tkzLabelAngle[pos=2](C,B,A){$\beta$}
+					\tkzMarkRightAngles(B,A,F E,C,B)
+				\end{tikzpicture}
+			\end{center}
+			
+			Trikotnika $ABF$ in $EBC$ sta skladna zaradi dveh skladnih kotov in ene stranice, zato so vse njune stranice enako dolge.
+		\end{multicols}
+\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. Prej 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/6/dokument.toc b/mat/domace_naloge/6/dokument.toc
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@@ -0,0 +1,3 @@
+\contentsline {section}{\numberline {1}Učbenik \textit {Matematika 1}: Stran 19}{1}{section.1}%
+\contentsline {section}{\numberline {2}Zbirka nalog \textit {Matematika 1}: Stran 16}{2}{section.2}%
+\contentsline {section}{\numberline {3}Zaključek}{3}{section.3}%
diff --git a/mat/domace_naloge/6/stderr.log b/mat/domace_naloge/6/stderr.log
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+2020/01/24 3.02c tkz-obj-eu-show.tex
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+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character /).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character m).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character a).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character t).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character /).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character d).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character o).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character m).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character a).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character c).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+
+! \textfont 0 is undefined (character e).
+\Url@FormatString ...\Url@String \UrlRight \m@th $
+                                                  
+l.243 ...t/domace_naloge/\stevilkadn/dokument.pdf}
+                                                   in/ali \url{https://githu...
+(That makes 100 errors; please try again.)
+!  ==> Fatal error occurred, no output PDF file produced!
+Transcript written on dokument.log.
author	sijanec <sijanecantonluka@gmail.com>	2020-09-17 23:28:50 +0200
committer	sijanec <sijanecantonluka@gmail.com>	2020-09-17 23:28:50 +0200
commit	597b821dd1b8e6e97adec2e779dff5e298adbc70 (patch)
tree	c1e32653fde0b3f44d116126f73a10d6821966b1
parent	peta matematična domača naloga! (diff)
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