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diff --git a/mat/domace_naloge/11/dokument.tex b/mat/domace_naloge/11/dokument.tex new file mode 100644 index 0000000..6bf78f4 --- /dev/null +++ b/mat/domace_naloge/11/dokument.tex @@ -0,0 +1,271 @@ +% !TeX encoding = UTF-8 +% !TeX spellcheck = sl_SI +% do-vimlatex-onwrite +\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{dirtytalk} +\usepackage{csquotes} +\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{codered}{rgb}{1,0,0} +\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 +\newcommand{\snovdn}{Trikotnik } +\newcommand{\predmdn}{mat} +\newcommand{\stevilkadn}{11} +\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{19. 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 19. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učbenika. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno. +\end{abstract} +\tableofcontents + +\section{Učbenik \textit{Matematika 2}: Trikotnik --- stran 33} +\begin{enumerate}[label=\textbf{\arabic*.}] + \setcounter{enumi}{6} + \item Načrtaj trikotnik s podatki: $c=\cm{4}, t_a=\cm{5,5}, \beta=\ang{120}$. + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B} \tkzDefPoint(5.5,0){AH} + \tkzInterLC(A,B)(B,A) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(A,B) + \tkzDrawLine(A,AX) \tkzLabelLine[above, pos = 0.25](A,AX){$c$} \tkzCompass(B,AX) \tkzInterCC(B,AX)(AX,B) \tkzGetPoints{CH}{USELESS} + \tkzCompass(B,CH) \tkzCompass(AX,CH) + \tkzDrawLine(B,CH) \tkzLabelLine[above left](B,CH){$a$} + \tkzInterLC(B,CH)(A,AH) \tkzGetPoints{HA}{USELESS} + \tkzCompass(A,HA) \tkzInterLC(B,CH)(HA,B) \tkzGetPoints{BAGAIN}{C} + \tkzCompass(HA,C) \tkzDrawLine(A,C) \tkzLabelLine[below](A,C){$b$} + \tkzDrawPoints(A) \tkzLabelPoints(A,B,C) + \end{tikzpicture} + \end{center} + \newpage + \item Načrtaj trikotnike. + \begin{multicols}{4} + \begin{enumerate}[label=\color{black}\textbf{\xslalph*)}] + \item \color{codered} $$b=\cm{6}$$ $$v_b=\cm{4}$$ $$t_b=\cm{5}$$ % <&=& + \item \color{black} $$a=\cm{5}$$ $$v_a=\cm{3,5}$$ $$\gamma=\ang{75}$$ + \item $$c=\cm{6}$$ $$a=\cm{4}$$ $$t_a=\cm{5,5}$$ + \item $$b=\cm{5,5}$$ $$t_c=\cm{5}$$ $$\alpha=\ang{60}$$ + \end{enumerate} + \end{multicols} + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(69:6){C} + \tkzDefPoint(69:4){VH} \tkzDefPoint(69:-2){TH} + \tkzCompass(A,C) \tkzDrawLine(TH,C) \tkzLabelLine[below right](A,C){$b$} + \tkzDefMidPoint(A,C) \tkzGetPoint{ACM} + \tkzCompass(A,ACM) \tkzCompass(C,ACM) + \tkzDefMidPoint(A,ACM) \tkzGetPoint{AACMM} + \tkzInterLC(A,C)(A,AACMM) \tkzGetPoints{PH1}{PH2} + \tkzCompass(A,PH1) \tkzCompass(A,PH2) + \tkzInterCC(PH1,PH2)(PH2,PH1) \tkzGetPoints{USELESS}{V1} + \tkzCompass(PH1,V1)\tkzCompass(PH2,V1) + \tkzInterLC(A,V1)(A,VH) \tkzGetPoints{USELESS}{V} + \tkzCompass(A,V) \tkzInterLC(A,V)(V,V1) \tkzGetPoints{USELESS}{V1X} + \tkzDrawLine(A,V1X) \tkzCompass(V,V1X) \tkzInterCC(V1,V1X)(V1X,V1) + \tkzGetPoints{VP}{VPX} \tkzCompass(V1,VP) \tkzCompass(V1X,VP) + \tkzDrawLine(VPX,VP) \tkzInterLC(VP,VPX)(ACM,TH) \tkzGetPoints{USELE}{B} + \tkzCompass(ACM,B) \tkzDrawLine(B,C) \tkzLabelLine[below left](B,C){$a$} + \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$} + \tkzMarkRightAngles(PH1,A,V1 A,V,VP) + \tkzDrawPoints(A) \tkzLabelPoints(A,C,B) + \end{tikzpicture} + \end{center} + \item Načrtaj enakokraki trikotnik, katerega višina na osnovnico je dolga $\cm{3}$, kot ob osnovinci pa je velik $\ang{30}$. + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B} + \tkzDrawLine(A,B) \tkzLabelLine[above,pos=.4](A,B){$c$} \tkzCompass(A,B) + \tkzInterCC(A,B)(B,A) \tkzGetPoints{CL}{USELESS} + \tkzCompass(A,B) \tkzCompass(A,CL) + \tkzDefMidPoint(B,CL) \tkzGetPoint{K}\tkzCompass(B,K)\tkzCompass(CL,K) + \tkzDrawLine(A,K) + \tkzDefMidPoint(A,B) \tkzGetPoint{ABM} \tkzInterCC(A,B)(B,A) + \tkzGetPoints{ABP}{ABPX} \tkzCompass(A,ABP) \tkzCompass(B,ABP) + \tkzDrawLine(ABM,ABP) \tkzInterLL(ABPX,ABP)(A,K) \tkzGetPoint{C} + \tkzLabelLine[above left](A,C){$b$} + \tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$} + \tkzDrawPoints(A) \tkzLabelPoints(A) + \tkzLabelPoint[below left](B){$B$} \tkzLabelPoint[above left](C){$C$} + \end{tikzpicture} + \end{center} + \item Načrtaj pravokotni trikotnik s pravim kotom v oglišču $C$, katerega stranica $AC$ je dolga $\cm{4}$, simetrala kota pri $A$ pa $\cm{5}$. Nariši trikotniku včrtano krožnico. + + Na tem mestu naj povem, da je \textbf{simetrala kota poltrak} in nima dolžine! + Zato trikotnika ne morem načrtati, zakar tudi včrtanje stranice ni možno. )-: + \if\false1 + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(69:4){C} + \tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C) + \tkz + \tkzDrawPoints(A) \tkzLabelPoints(A,C) + \end{tikzpicture} + \end{center} + \fi + \newpage + \item Načrtaj trikotnik in trikotniku očrtano krožnico. + \begin{multicols}{4} + \begin{enumerate}[label=\color{black}\textbf{\xslalph*)}] + \item $$a=\cm{5}$$ $$b=\cm{4}$$ $$\alpha=\ang{75}$$ + \item \color{codered} $$b=\cm{3}$$ $$v_b=\cm{4}$$ $$\gamma=\ang{120}$$ + \item \color{black} $$a=\cm{4}$$ $$b=\cm{5}$$ $$\gamma=\ang{90}$$ + \item $$a=b=\cm{4}$$ $$c=6\cm$$ + \end{enumerate} + \end{multicols} + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(69:3){C} \tkzDefPoint(69:4){VHX} + \tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C) + \tkzInterLC(A,C)(C,A) \tkzGetPoints{A}{AX} + \tkzCompass(C,AX) \tkzDrawLine(A,AX) \tkzInterCC(AX,C)(C,AX) + \tkzGetPoints{BH}{BHX} \tkzCompass(AX,BH) \tkzCompass(C,BH) + \tkzDefMidPoint(A,C) \tkzGetPoint{ACM} \tkzCompass(A,ACM) + \tkzInterLC(A,C)(A,ACM) \tkzGetPoints{ACMX}{ACM} \tkzCompass(A,ACMX) + \tkzDrawLine(ACMX,AX)\tkzInterCC(ACMX,ACM)(ACM,ACMX) \tkzGetPoints{Y}{X} + \tkzCompass(ACM,X) \tkzCompass(ACMX,X) + \tkzInterLC(A,X)(A,VHX) \tkzGetPoints{USELESS}{VH} + \tkzCompass(A,VH) \tkzInterLC(A,X)(VH,A) \tkzGetPoints{A}{AXX} + \tkzCompass(VH,AXX) \tkzDrawLine(A,AXX) + \tkzInterCC(A,AXX)(AXX,A) \tkzGetPoints{V2}{V2X} + \tkzCompass(A,V2) \tkzCompass(AXX,V2) \tkzDrawLine(VH,V2) + \tkzInterLL(V2,V2X)(C,BH) \tkzGetPoint{B} \tkzDrawLine(C,B) + \tkzLabelLine[above left](C,B){$a$} + \tkzDrawLine(A,B) \tkzLabelLine[above left](A,B){$c$} + \tkzInterCC(C,B)(B,C) \tkzGetPoints{CBS}{CBSX} % krožnica + \tkzCompass(C,CBS) \tkzCompass(B,CBS) \tkzDrawLine(CBS,CBSX) + \tkzCompass(C,CBSX) \tkzCompass(B,CBSX) + \tkzInterCC(A,B)(B,A) \tkzGetPoints{ABS}{ABSX} + \tkzCompass(A,ABS) \tkzCompass(B,ABS) \tkzDrawLine(ABS,ABSX) + \tkzCompass(A,ABSX) \tkzCompass(B,ABSX) + \tkzInterLL(ABS,ABSX)(CBS,CBSX) \tkzGetPoint{S} + \tkzDrawPoints(A) \tkzLabelPoints(A,C,B) + \tkzMarkRightAngles(VH,A,C B,VH,A) + \tkzDrawCircle[fill = red!30,opacity=.3](S,A) + \tkzDrawPolygon[fill=blue!30,opacity=.3](A,B,C) % za razvidnost + \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/\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 sekund. +\fi +% \item $$$$ +\end{document} |