From 4016e34d4376f30b2f317b5627733178e12b9ce4 Mon Sep 17 00:00:00 2001 From: sijanec Date: Sun, 7 Feb 2021 01:04:27 +0100 Subject: =?UTF-8?q?24.=20doma=C4=8Da=20naloga=20za=20matematiko?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- mat/domace_naloge/24/dokument.aux | 36 + mat/domace_naloge/24/dokument.log | 2055 ++++++++++++++++++++++++++++++ mat/domace_naloge/24/dokument.out | 1 + mat/domace_naloge/24/dokument.pdf | Bin 0 -> 68493 bytes mat/domace_naloge/24/dokument.synctex.gz | Bin 0 -> 19759 bytes mat/domace_naloge/24/dokument.tex | 214 ++++ mat/domace_naloge/24/stderr.log | 1 + mat/domace_naloge/24/stdout.log | 960 ++++++++++++++ 8 files changed, 3267 insertions(+) create mode 100644 mat/domace_naloge/24/dokument.aux create mode 100644 mat/domace_naloge/24/dokument.log create mode 100644 mat/domace_naloge/24/dokument.out create mode 100644 mat/domace_naloge/24/dokument.pdf create mode 100644 mat/domace_naloge/24/dokument.synctex.gz 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\vskip 1.5em} +%opening +\newcommand{\snovdn}{Kotne funkcije } +\newcommand{\predmdn}{mat} +\newcommand{\predmkaj}{domace\_naloge} +\newcommand{\stevilkadn}{24} +\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}} +} +\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{abstract} +\paragraph{Navodilo naloge} \textbf{listi:} \textit{Kotne funkcije - 1} / 1, ... 15 (izberi štiri naloge) +%\tableofcontents +\begin{enumerate}[label=\textbf{\arabic*.}] % 8, 6, 14, 13 + % \item Felicijan stoji na hribu, ki se dviguje 244 metrov visoko nad barjem naokoli. Z vrha vidi v ravno črto poravnani hiši, kjer stanuje on, in hišo svoje prijateljice Gizelice. Svojo vidi pod vpadnim kotom % 6 + \setcounter{enumi}{5} + \item Stolp, visok 20 metrov, vidiš iz točke, ki leži v ravnini podnožja stolpa, pod kotom \ang{30}. Pod kakšnim kotom bi iz te točke videl dvakrat višji stolp, ki bi stal na istem mestu? + + \begin{multicols}{2} + \def\c{34.6410} + \begin{tikzpicture}[scale=.15] + \tkzDefPoint(0,0){Jaz} + \tkzDefPoint(\c,0){HisaJZ} \tkzDefPoint(\c+10,0){HisaJV} \tkzDefPoint(\c,20){HisaSZ} \tkzDefPoint(\c+10,20){HisaSV} + \tkzDefPoint(\c,0){StolpJZ} \tkzDefPoint(\c+10,0){StolpJV} \tkzDefPoint(\c,40){StolpSZ} \tkzDefPoint(\c+10,40){StolpSV} + \tkzDrawPolygon[fill=red!30, opacity=.3](HisaJZ,HisaJV,HisaSV,HisaSZ) + \tkzDrawPolygon[fill=blue!30, opacity=.3](StolpJZ,StolpJV,StolpSV,StolpSZ) + \tkzDrawLine(Jaz,HisaSZ) \tkzDrawLine(Jaz,StolpSZ) \tkzDrawLine(Jaz,StolpJZ) + \tkzDrawPoints(Jaz) \tkzLabelPoints(Jaz) + \end{tikzpicture} + \vfill\null\columnbreak + Predpostavljam, da ne govorimo o \href{https://sl.wikipedia.org/wiki/Po\%C5\%A1evni\_stolp\_v\_Pisi}{stolpu v Pisi}. + $$\displaystyle\arctan{\left(\SI{40}{\meter}:\frac{\SI{20}{\meter}}{\tan{\ang{30}}}\right)}\Tilde=\ang{49,1}$$ + \end{multicols} + \setcounter{enumi}{7} + \newpage + \item Plavalec v morjo opazuje ladjo, ki pravkar izginja za obzorjem. Ve, da je njen jambor visok 10 metrov. Kako daleč od plavalca je ta ladja? + \small + + Zemljo v računu poenostavi v kroglo s polmerom \SI{6368}{\kilo\meter}. Računaj razdaljo po morju. Zatem poišči še razdaljo po zraku. Presenečenje ne bo izostalo. + \normalsize + \begin{multicols}{2} + \def\r{6368} + \def\a{1132.96} + \begin{tikzpicture}[scale=.005] + \tkzDefPoint(0,0){Zemlja} \tkzDefPoint(90:\r){Plavalec} \tkzDefPoint(\a,\r){Vrh} + \tkzDrawCircle(Zemlja,Plavalec) + \tkzDrawLine[add=0 and 0](Zemlja,Plavalec) \tkzLabelLine[left](Zemlja,Plavalec){$r$} + \tkzDrawLine[add=0 and 0](Plavalec,Vrh) \tkzLabelLine[above](Plavalec,Vrh){Pogled} + \tkzDrawLine[add=0 and 0](Zemlja,Vrh) \tkzLabelLine[below](Zemlja,Vrh){$r+jambor$} + \tkzDrawPoints(Zemlja,Plavalec,Vrh) \tkzLabelPoints(Plavalec,Zemlja,Vrh) + \end{tikzpicture} + \vfill\null\columnbreak + Po zraku: + $$\sqrt{(r+\SI{10}{\meter})^2-r^2}\Tilde=\SI{11,285393}{\kilo\meter}$$ + Po morju: + $$r\pi\arccos{\left(\frac{r}{r+\SI{10}{\meter}}\right)}:\ang{180}\Tilde=\SI{11,285380}{\kilo\meter}$$ + \paragraph{Presenečenje?} po zraku $<$ po morju + \vfill + \small + * skica nima pravih razmerij, jambor je dolg \SI{100}{\kilo\meter} + \normalsize + \end{multicols} + \setcounter{enumi}{12} + \item Izračunaj ploščino pravilnega 12-kotnika, ki ima stranico dolgo \SI{1}{\centi\meter}. + $$\left(\left(\frac{\sin{\frac{\ang{360}}{12}:2}}{\SI{1}{\centi\meter}:2}\right)^2\cdot12\cdot\sin{\frac{\ang{360}}{12}}\right):2\Tilde=\SI{2700}{\centi\meter}$$ + \item Izračunaj dolžino diagonale pravilnega petkotnika s stranico dolžine \cm{4}. + $$\sin{\left((5-2)\ang{180}:5:2\right)}\cdot4\cdot2\Tilde=\cm{6,472135955}$$ +\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. 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