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| -rw-r--r-- | mat/domace_naloge/5/dokument.toc | 2 | ||||
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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}} 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\end{tabular}\par}% <------ + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +%opening +\newcommand{\stevilkadn}{5} +\newcommand{\snovdn}{Merjenje, trikotniška neenakost } +\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{16. 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 15. septembra 2020, in njihove + rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so + iz učnega lista. Kjer je bilo potrebno izbrati neke poljubne naloge, + sem jih vedno izbral naključno. +\end{abstract} +\tableofcontents + +\section{Učni list \textit{\snovdn}: Naloge 1 do 12} +\begin{enumerate}[label=\textbf{\arabic*.}] % 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Na premici $p$ leži točka $T$. Opiši množico vseh tistih točk na premici, ki so od $T$ oddaljene za 3 dolžinske enote. + $$m=(X; d(T,X) = 3 \wedge X \in p)$$ + \item Izmeri daljici $AB$ in $CD$ in načrtaj daljico $EF$, za katero velja: + \begin{enumerate}[label=\textbf{b\arabic*)}] + \begin{multicols}{2} + \item $|EF|=|AB|+|CD|$ + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} + \tkzDefPoint(1,0){B} + \tkzDefPoint(1,0){C} + \tkzDefPoint(2,0){D} + \tkzDefPoint(0,0){E} + \tkzDefPoint(2,0){F} + \tkzDrawPoints(A,B,C,D,E,F) + \tkzLabelPoints[above right](A,B,D) + \tkzLabelPoints[below left](E,F,C) + \tkzDrawLine(C,D) + \tkzDrawLine(A,B) + \end{tikzpicture} + \end{center} + \item $|EF|=2|AB|+|CD|$ + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} + \tkzDefPoint(1,0){B} + \tkzDefPoint(1,0){C} + \tkzDefPoint(2,0){D} + \tkzDefPoint(-1,0){E} + \tkzDefPoint(2,0){F} + \tkzDrawPoints(A,B,C,D,E,F) + \tkzLabelPoints[above right](A,B,D) + \tkzLabelPoints[below left](E,F,C) + \tkzDrawLine(E,F) + \tkzCompass(B,E) + \end{tikzpicture} + \end{center} + \end{multicols} + \end{enumerate} + + \end{enumerate} + + \item Naslednje kote zapiši s stopinjami, minutami in sekundami. + \begin{multicols}{2} + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $\alpha=\ang{23.58}=\ang{23}0,58\cdot60'=\ang{23}34'0,8\cdot60''= + \mathbf{\ang{23}34'48''}$ + \item $\beta=\ang{78.409}=\ang{78}0,409\cdot60'= + \ang{78}24'0,54\cdot60''=\mathbf{\ang{78}24'32,4''}$ + \end{enumerate} + \end{multicols} + \item Naslednjim kotom izračunaj komplementarne in suplementarne kote: + \begin{multicols}{2} + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $\alpha=\ang{23}$ + \begin{center} + $$\text{komplementarni: } \ang{90}-\ang{23}=\ang{67}$$ + $$\text{suplementarni/sokot: } \ang{180}-\ang{23}=\ang{157}$$ + \end{center} + \item $\beta=\ang{78.49}$ + \begin{center} + $$\text{komplementarni: } \ang{90}-\ang{78.49}=\ang{11.51}$$ + $$\text{suplementarni/sokot: } \ang{180}-\ang{78.49}=\ang{101.51}$$ + \end{center} + \end{enumerate} + \end{multicols} + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Razlika dveh sokotov je \ang{23,58}. Koliko merita oba kota? Rezultata naj bosta vsaj do kotne minute natančna. + $$\ang{23.58}=(\ang{180}-\alpha)-\alpha \rightarrow + 2\alpha=\ang{180}-\ang{23,58}\rightarrow\alpha=\frac{\ang{180}-\ang{23,58}}{2}=\ang{78.21}\rightarrow\beta=\ang{180}-\alpha=\ang{101.79}$$ + \item Razlika dveh komplementarnih kotov je $\ang{23}58'$. Koliko merita oba kota? Rezultata naj bosta vsaj do kotne minute natančna. + $$\alpha=\frac{\ang{180}-\ang[parse-numbers=false]{23,9\overline{6}}}{2}=\ang[parse-numbers=false]{78,01\overline{6}} \rightarrow \beta=\ang{180}-\alpha=\ang{180}-\ang[parse-numbers=false]{78,01\overline{6}}=\ang[parse-numbers=false]{101,98\overline{3}}$$ + \item Vsota dveh kotov je $\ang{146}15'$, njuna razlika pa $\ang{23}38'$. Koliko merita oba kota? Rezultata naj bosta do kotne minute natančna. + $$(\alpha-\ang[parse-numbers=false]{23,6\overline{3}})+\alpha=\ang{146,25}\rightarrow2\alpha=\ang{146,25}-\ang[parse-numbers=false]{23,6\overline{3}}\rightarrow\alpha=\frac{\ang{146,25}-\ang[parse-numbers=false]{23,6\overline{3}}}{2}=\ang[parse-numbers=false]{61,308\overline{3}}\rightarrow$$ + $$\beta=\ang{146,25}-\alpha=\ang[parse-numbers=false]{84,941\overline{6}}$$ + \end{enumerate} + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Koliko meri kot, če je petkratnik svojega komplementarnega kota? + $$\frac{5}{6}\ang{90}=\ang{75}$$ + \item Koliko meri kot, če je šestkratnik svojega suplementarnega kota? Rezultat naj bo vsaj do kotne minute natančen. + $$\frac{6}{7}\ang{180}=\ang[parse-numbers=false]{154.\overline{285714}}$$ + \item Od dveh sokotov je eden za $\frac{3}{7}$ pravega kota večji od drugega. Koliko meri eden in drugi? Rezultat naj bo vsaj do kotne minute natančen. + $$(\alpha+\frac{3}{7}\ang{90})+\alpha=\ang{180}\rightarrow + \alpha=\frac{\ang{180}-\frac{3}{7}\ang{90}}{2}=\ang[parse-numbers=false]{19,\overline{285714}}\rightarrow\beta=\ang{180}-\alpha=\ang{180}-\ang[parse-numbers=false]{19,\overline{285714}}=\ang[parse-numbers=false]{160,\overline{7142857}}$$ + \item Eden od dveh komplementarnih kotov je 4-kratnik drugega. Koliko meri eden in drugi? + \begin{multicols}{2} + $$\alpha=\frac{4}{5}\ang{90}=\ang{72}$$ + + $$\beta=\frac{1}{5}\ang{90}=\ang{18}$$ + \end{multicols} + \item Kolikšna je vsota sokotov dveh komplementarnih kotov? + $$\ang{90}$$ + \item Poišči tak par suplementarnih kotov, katerih razlika je pravi kot. + $$(\alpha+\ang{90})+\alpha=\ang{180}\rightarrow\alpha=\frac{\ang{180}-\ang{90}}{2}=\ang{45}\rightarrow\beta=\ang{180}-\alpha=\ang{180}-\ang{45}=\ang{135}$$ + \item Kota $\alpha=3x$ in $\beta=x+\ang{20}$ sta komplementarna. Poišči ju. + $$3x+x+\ang{20}=\ang{90}=4x+\ang{20}\rightarrow x=\frac{\ang{90}-\ang{20}}{4}=\ang{17.5}\rightarrow\alpha=3x=\ang{52.5}\wedge\beta=x+\ang{20}=\ang{37.5}$$ + \end{enumerate} + \iffalse % nedokončano ˇˇˇ + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Dve premici se sekata. Dokaži, da oba para nesosednjih kotov merita enako. + \begin{center} + trenutno mi ne kane na misel ... + \end{center} + \item Tri premice se sekajo v skupni točki. Dokaži, da je vsota treh nesosednjih kotov enaka \ang{180}. + \begin{center} + tudi tole ne ... + \end{center} + \item Skozi vrh pravega kota potegnem premico tako, da dobimo štiri kote. Pokaži, da je razlika dveh nesosednjih kotov enaka \ang{90}. + \begin{center} + jutri dalje, prepozno je, da bi moji možgani uporabno funkcionirali ... + \end{center} + \end{enumerate} + \item Konstruiraj, kjer je to mogoče, trikotnik s podatki: + \begin{multicols}{2} + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $a=\SI{7}{\centi\meter}, b=\SI{4}{\centi\meter}, c=\SI{5}{\centi\meter}$ + \item $a=\SI{7}{\centi\meter}, b=\SI{4}{\centi\meter}, c=\SI{8}{\centi\meter}$ + \item $a=\SI{7}{\centi\meter}, b=\SI{4}{\centi\meter}, c=\SI{13}{\centi\meter}$ + \item $a=\SI{7}{\centi\meter}, b=\SI{4}{\centi\meter}, c=\SI{2}{\centi\meter}$ + \item $a=\SI{15}{\centi\meter}, b=\SI{8}{\centi\meter}, c=\SI{23}{\centi\meter}$ + \item $a=\SI{14}{\centi\meter}, b=\SI{8}{\centi\meter}, c=\SI{23}{\centi\meter}$ + \end{enumerate} + \end{multicols} + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Točki $A$ in $B$ sta oddaljeni 5. Ali obstaja točka, ki je od $A$ oddaljena 12, od $B$ pa 6? + \item Točki $A$ in $B$ na ravnini sta oddaljeni za 5. Opiši, kje leži točka $C$, ki je od točke $A$ oddaljena 3, hkrati pa najbližja točki $B$. + \end{enumerate} + \item Ali obstajajo trikotniki z naslednjimi dolžinami stranic? + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $a=\SI{8}{\centi\meter}, b=\SI{5}{\centi\meter}, c=\SI{14}{\centi\meter}$ + \item $a=\SI{8}{\centi\meter}, b=\SI{15}{\centi\meter}, c=\SI{32}{\centi\meter}$ + \end{enumerate} + \item \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Palico prelomiš na tri dele tako, da je vsak naslednji del polovico krajši od prejšnjega. Ali lahko iz teh treh delov sestaviš trikotnik? + \item[\textbf{* b)}] Palico prelomiš na tri dele tako, da je vsak naslednji del za desetino dolžine celotne palice krajši od prejšnjega. Ali lahko iz teh treh delov sestaviš trikotnik? + \end{enumerate} + \item[\textbf{* 11.}] Naj bo $D$ poljubno izbrana točka na stranici $BC$ trikotnika $\bigtriangleup ABC$. Dokaži: + $$d(A,D)+d(D,B)\leq d(A,C) + d(C,B)$$ + \setcounter{enumi}{11} + \item Če se komu zdi, da je v matematiki odveč zahtevati komutativnost razdalje med točkama $(d(A,B)=d(B,A))$, ker da je to pač \textit{"samo po sebi umevno"}, naj pomisli: Dostikrat merimo ratdaljo dveh krajev A in B s časom, ki ga potrebujemo, da pridemo iz enega kraja v drugi kraj. In če je, denimo, kraj A v dolini, kraj B pa vrh gore, je zagotovo: + $$d(A,B)\not=d(B,A)$$ + \fi % ^^^ nedokončano +\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/5/dokument.toc b/mat/domace_naloge/5/dokument.toc new file mode 100644 index 0000000..d1d63e7 --- /dev/null +++ b/mat/domace_naloge/5/dokument.toc @@ -0,0 +1,2 @@ +\contentsline {section}{\numberline {1}Učni list \textit {Merjenje, trikotniška neenakost }: Naloge 1 do 12}{1}{section.1}% +\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}% diff --git a/mat/domace_naloge/5/stderr.log b/mat/domace_naloge/5/stderr.log new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/mat/domace_naloge/5/stderr.log diff --git a/mat/domace_naloge/5/stdout.log b/mat/domace_naloge/5/stdout.log new file mode 100644 index 0000000..965d157 --- /dev/null +++ b/mat/domace_naloge/5/stdout.log @@ -0,0 +1,465 @@ +This is pdfTeX, 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