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author | sijanec <sijanecantonluka@gmail.com> | 2020-10-22 22:13:34 +0200 |
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committer | sijanec <sijanecantonluka@gmail.com> | 2020-10-22 22:13:34 +0200 |
commit | c45a26308a6e959dfa4c8367edae72db5041092c (patch) | |
tree | d452d86a796321aa4563fd80be81de160fd103d4 /mat/domace_naloge/13 | |
parent | domača naloga 12 za matematiko (diff) | |
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-rw-r--r-- | mat/domace_naloge/13/165a.tex | 24 | ||||
-rw-r--r-- | mat/domace_naloge/13/165b.tex | 25 | ||||
-rw-r--r-- | mat/domace_naloge/13/165cstresica.tex | 25 | ||||
-rw-r--r-- | mat/domace_naloge/13/dokument.aux | 23 | ||||
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-rw-r--r-- | mat/domace_naloge/13/dokument.tex | 180 | ||||
-rw-r--r-- | mat/domace_naloge/13/dokument.toc | 3 | ||||
-rw-r--r-- | mat/domace_naloge/13/stderr.log | 1 | ||||
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diff --git a/mat/domace_naloge/13/165a.tex b/mat/domace_naloge/13/165a.tex new file mode 100644 index 0000000..49e7202 --- /dev/null +++ b/mat/domace_naloge/13/165a.tex @@ -0,0 +1,24 @@ +\begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(30:4){C} \tkzDefPoint(10,0){VSH} + \tkzDrawLine(A,C) \tkzCompass(A,C) + \tkzLabelLine[above left](A,C){$b$} + \tkzInterCC(A,C)(C,A) \tkzGetPoints{K60X}{K60} + \tkzCompass(A,K60) \tkzCompass(C,K60) + \tkzDefMidPoint(C,K60) \tkzGetPoint{K30} + \tkzCompass(C,K30) \tkzCompass(K60,K30) + \tkzDrawLine(A,VSH) + \tkzLabelLine[above](A,K30){$c$}\tkzCompass(A,VSH) + \tkzInterCC(C,VSH)(VSH,C) \tkzGetPoints{PBX}{PB} \tkzDrawLine(C,VSH) + \tkzCompass(VSH,PB) \tkzCompass(VSH,PBX) + \tkzCompass(C,PB) \tkzCompass(C,PBX) + \tkzDrawLine(PB,PBX) \tkzInterLL(PB,PBX)(A,VSH) \tkzGetPoint{B} + \tkzDrawLine(C,B) \tkzDrawPolygon[fill=blue!30, opacity=.3](A,B,C) + \tkzLabelLine[below left](C,B){$a$} + \tkzCalcLength[cm](A,B)\tkzGetLength{ABl} + \tkzCalcLength[cm](B,C)\tkzGetLength{BCl} + \tkzDrawSegment[dim={\pgfmathprintnumber\ABl,-6pt,transform shape}](A,B) + \tkzDrawSegment[dim={\pgfmathprintnumber\BCl,6pt,transform shape}](C,B) + \tkzDrawPoints(A) \tkzLabelPoints(A,C,B) + \end{tikzpicture} +\end{center} diff --git a/mat/domace_naloge/13/165b.tex b/mat/domace_naloge/13/165b.tex new file mode 100644 index 0000000..e7eaf47 --- /dev/null +++ b/mat/domace_naloge/13/165b.tex @@ -0,0 +1,25 @@ +\begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(75:4){C} \tkzDefPoint(255:6){VSH} + \tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} + \tkzCompass(A,C) \tkzInterCC(A,C)(C,A) \tkzGetPoints{K60X}{K60} + \tkzCompass(A,K60) \tkzCompass(C,K60) + \tkzDefMidPoint(A,K60) \tkzGetPoint{K30} + \tkzCompass(A,K30) \tkzCompass(K60,K30) + \tkzInterLC(C,K30)(C,VSH) \tkzGetPoints{VSX}{VS} + \tkzCompass(C,VS) \tkzDrawLine(C,VS) + \tkzDrawLine(VS,A) \tkzInterCC(VS,A)(A,VS) \tkzGetPoints{PB}{PBX} + \tkzCompass(A,PBX) \tkzCompass(A,PB) + \tkzCompass(VS,PB) \tkzCompass(VS,PBX) + \tkzDrawLine(PB,PBX) \tkzInterLL(C,VS)(PB,PBX) \tkzGetPoint{B} + \tkzDrawPolygon[fill=blue!000030, opacity=0000.30000000](A,B,C) + \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$} + \tkzLabelLine[left](C,B){$a$} + \tkzCalcLength[cm](A,B) \tkzGetLength{ABl} + \tkzCalcLength[cm](C,B) \tkzGetLength{CBl} + \tkzDrawSegment[dim={\pgfmathprintnumber\ABl,-6pt,transform shape}](A,B) + \tkzDrawSegment[dim={\pgfmathprintnumber\CBl,6pt,transform shape}](C,B) + \tkzDrawPoints(A) \tkzLabelPoints[left](A,C,B) + \end{tikzpicture} +\end{center} + diff --git a/mat/domace_naloge/13/165cstresica.tex b/mat/domace_naloge/13/165cstresica.tex new file mode 100644 index 0000000..0bdab52 --- /dev/null +++ b/mat/domace_naloge/13/165cstresica.tex @@ -0,0 +1,25 @@ +\begin{center} % mogoce izgleda, kakor da imam obsesivno-kompulzivno + \begin{tikzpicture} % motnjo, ko pisem program takole v dveh stolpcih (: + \tkzDefPoint(0,0){C} \tkzDefPoint(285:4){B} + \tkzDrawLine(C,B) \tkzLabelLine[below left](C,B){$a$} + \tkzCompass(C,B) \tkzDefPoint(255:10){VH} + \tkzInterCC(C,B)(B,C) \tkzGetPoints{K60X}{K60} + \tkzCompass(C,K60) \tkzCompass(B,K60) \tkzCompass(C,VH) + \tkzDefMidPoint(K60,B) \tkzGetPoint{K30} + \tkzCompass(K60,K30) \tkzCompass(B,K30) + \tkzDrawLine(C,VH) \tkzDrawLine(VH,B) % od VisinaHelperja do tocke B + \tkzInterCC(VH,B)(B,VH) \tkzGetPoints{PB}{PBX} % perpendicular bisector + \tkzCompass(VH,PB) \tkzCompass(B,PB) + \tkzCompass(VH,PBX) \tkzCompass(B,PBX) + \tkzInterLL(C,VH)(PB,PBX) \tkzGetPoint{A} + \tkzDrawLine(A,B) \tkzLabelLine[above left](A,B){$c$} + \tkzDrawLine(PB,PBX) \tkzLabelLine[right](A,C){$b$} + \tkzCalcLength[cm](A,B) \tkzGetLength{ABl} + \tkzCalcLength[cm](A,C) \tkzGetLength{ACl} + \tkzDrawPolygon [fill=blue!30, opacity=.3](A,B,C) + \tkzDrawSegment [dim={\pgfmathprintnumber\ABl,-6pt,transform shape}](A,B) + \tkzDrawSegment [dim={\pgfmathprintnumber\ACl,6pt,transform shape}](A,C) + \tkzDrawPoints(C) \tkzLabelPoints(C,B,A) + \end{tikzpicture} +\end{center} + diff --git a/mat/domace_naloge/13/dokument.aux b/mat/domace_naloge/13/dokument.aux new file mode 100644 index 0000000..000788b --- /dev/null +++ b/mat/domace_naloge/13/dokument.aux @@ -0,0 +1,23 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\@writefile{toc}{\contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 29 --- Trikotnik}{1}{section.1}\protected@file@percent } +\@writefile{lol}{\contentsline {lstlisting}{165a.tex}{2}{lstlisting.-1}\protected@file@percent } +\@writefile{lol}{\contentsline {lstlisting}{165b.tex}{3}{lstlisting.-2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {2}Zaključek}{4}{section.2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {3}Razhroščevalne informacije}{4}{section.3}\protected@file@percent } diff --git a/mat/domace_naloge/13/dokument.dvi b/mat/domace_naloge/13/dokument.dvi Binary files differnew file mode 100644 index 0000000..00fac3a --- /dev/null +++ b/mat/domace_naloge/13/dokument.dvi diff --git a/mat/domace_naloge/13/dokument.log b/mat/domace_naloge/13/dokument.log new file mode 100644 index 0000000..a348642 --- /dev/null +++ b/mat/domace_naloge/13/dokument.log @@ -0,0 +1,1471 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded 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+\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 +\newcommand{\snovdn}{Trikotnik --- konstrukcije } +\newcommand{\predmdn}{mat} +\newcommand{\stevilkadn}{13} +\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} + \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{22. 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 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 22. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka in vaj. +\end{abstract} +\tableofcontents + +\section{Vaje \textit{Matematika 2}: stran 29 --- Trikotnik} +\begin{enumerate}[label=\textbf{\arabic*.}] + \setcounter{enumi}{164} + \item[\textbf{165.*}] Načrtaj trikotnik $ABC$ z dano vsoto dolžin stranic. Napiši postopek načrtovanja. + + % Nihče ni rekel, v katerem jeziku, zato bom postopek opisal kar v \hologo{LaTeX} jeziku \texttt{PGF/Ti\textit{k}Z}. Kako prikladno, ne? + \begin{enumerate}[label=\textbf{\xslalph*)}] % b č a d + \item $a+c=\cm{10}, \alpha=\ang{30}, b=\cm{4}$ + \input{165a} + \lstinputlisting[language=TeX]{165a.tex} + \item $a+c=\cm{10}, \gamma=\ang{30}, b=\cm{4}$ + \input{165b} + \lstinputlisting[language=TeX]{165b.tex} + \setcounter{enumii}{3} + \item $b+c=\cm{7}, v_b=\cm{3}, a=\cm{4}$ + % \input{165cstresica} % ne, to nalogo sem si kar v možganih izmislil... + % \lstinputlisting[language=TeX]{165cstresica.tex} + \item $a+b+c=\cm{12}, \alpha=\ang{30}, \beta=\ang{75}$ + % Nisem povsem prepričan, če smem uporabljati \textit{matematiko} \textsuperscript{(kaj sploh je to?)}, ampak nekako \textit{očitno} je, da so stranice trikotnika v razmerju $75:75:30$, torej je najkrajša dolga $\frac{1}{6}\cm{12}$. + %\begin{center} + % \begin{tikzpicture} + % \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){12} + % \tkz + % \tkzDrawPoints() + % \end{tikzpicture} + %\end{center} + \end{enumerate} + \item[\textbf{166.*}] Načrtaj trikotnik $ABC$ z dano razliko dolžin stranic. Napiši postopek načrtovanja. + \begin{enumerate}[label=\textbf{\xslalph*)}] % c b + \setcounter{enumii}{1} + \item $a-c=\cm{2}, \gamma=\ang{30}, v_a=\cm{4}$ + \item $b-c=\cm{1}, \gamma=\ang{60}, a=\cm{3}$ + \end{enumerate} +\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/\predmdn/domace_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/\predmdn/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" + +Dokument se je generiral aaasecgeninsaaa \SI{}{\second}. +\fi +% \item $$$$ +\end{document} diff --git a/mat/domace_naloge/13/dokument.toc b/mat/domace_naloge/13/dokument.toc new file mode 100644 index 0000000..f04652a --- /dev/null +++ b/mat/domace_naloge/13/dokument.toc @@ -0,0 +1,3 @@ +\contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 29 --- Trikotnik}{1}{section.1}% +\contentsline {section}{\numberline {2}Zaključek}{4}{section.2}% +\contentsline {section}{\numberline {3}Razhroščevalne informacije}{4}{section.3}% diff --git a/mat/domace_naloge/13/stderr.log b/mat/domace_naloge/13/stderr.log new file mode 100644 index 0000000..9378aea --- /dev/null +++ b/mat/domace_naloge/13/stderr.log @@ -0,0 +1 @@ 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