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-rw-r--r--mat/domace_naloge/22/dokument.aux38
-rw-r--r--mat/domace_naloge/22/dokument.log1822
-rw-r--r--mat/domace_naloge/22/dokument.out1
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-rw-r--r--mat/domace_naloge/22/dokument.tex239
-rw-r--r--mat/domace_naloge/22/dokument.toc9
-rw-r--r--mat/domace_naloge/22/stderr.log1
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+\newcommand{\snovdn}{Računanje s komponentami }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{22}
+\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.
+\end{abstract}
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \setcounter{enumi}{12}
+ \item Določi koordinate točke $M$, tako da bo točka $Z(-7, 8, -10)$ razpolovišče daljice $LM$, če je $L(-4, 2, -8)$.
+ \begin{center}
+ skica:
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){L} \tkzDefPoint(2,0){Z} \tkzDefPoint(4,0){M}
+ \tkzDrawLine(L,M)
+ \tkzDrawPoints(L,Z,M)
+ \tkzLabelPoints(L,Z,M)
+ \end{tikzpicture}
+ \end{center}
+ $$
+ Z\left(-7, 8, -10\right) = Z\left(\frac{-4+M_1}{2}, \frac{2+M_2}{2}, \frac{-8+M_3}{2}\right)
+ $$
+ $$
+ \frac{-4+M_1}{2} = -7 \wedge
+ \frac{2+M_2}{2} = 8 \wedge
+ \frac{-8+M_3}{2} = -10
+ \rightarrow M\left(M_1, M_2, M_3\right) = M\left(-10, 14, -12\right)
+ $$
+ \paragraph{Rešitev} $M\left(-10, 14, -12\right)$
+ \item Dani sta točki $A\left(4, -7, -1\right)$ in $B\left(-4, -3, -8\right)$. Določi točko $C$, tako da bo točka $T\left(1, -1, 3\right)$ težišče trikotnika $ABC$.
+ \begin{center}
+ skica:
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B} \tkzDefPoint(3,3){C}
+ \tkzDefMidPoint(A,B) \tkzGetPoint{M} \tkzDefMidPoint(B,C) \tkzGetPoint{N} \tkzDefMidPoint(C,A) \tkzGetPoint{O}
+ \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C)
+ \tkzDrawLine(M,C) \tkzDrawLine(N,A) \tkzDrawLine(O,B)
+ \tkzInterLL(N,A)(O,B) \tkzGetPoint{T}
+ \tkzDrawPoints(A,B,C,T,M) \tkzLabelPoints(A,B,C,T,M)
+ \end{tikzpicture}
+ \end{center}
+ $$
+ M = M\left(\frac{4+\left(-4\right)}{2}, \frac{-7+\left(-3\right)}{2}, \frac{-1+\left(-8\right)}{2}\right) = M\left(0, -5, 4,5\right)
+ $$
+ Vemo, da težišče razpolovi težiščnico na tri enake dele. Naredimo vektor $\vektor{MT}$ in ga pomnožimo s skalarjem tri, da dobimo vektor $\vektor{MC}$.
+ $$
+ \vektor{MT} = \Vec{T} - \Vec{M} = \left(1-0, -1-\left(-5\right), 3-4,5\right) = \left(1, 4, -1,5\right) \rightarrow \vektor{MC} = 3\vektor{MT} = \left(3, 12, -4,5\right)
+ $$
+ $$
+ \rightarrow r_C = r_M + \vektor{DC} = \left(0+3, -5+12, 4,5+\left(-4,5\right)\right) = C\left(3, 7, 0\right)
+ $$
+ \parahraph{Rešitev} $C\left(3, 7, 0\right)$
+ \item Točka $P$ leži na daljici $AB$ tako, da je $|AP|:|PB|=1:1$. Zapiši koordinate točke $P$, če je $A\left(-6, -13, 2\right)$ in $B\left(-13, 5, 4\right)$. Koordinate zaokroži na dve decimalni mesti.
+ \begin{center}
+ skica:
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){A} \tkzDefPoint(2,0){P} \tkzDefPoint(4,0){B}
+ \tkzDrawLine(A,B)
+ \tkzDrawPoints(A,P,B)
+ \tkzLabelPoints(A,P,B)
+ \end{tikzpicture}
+ \end{center}
+ $$
+ P = \left(\frac{-6+\left(-13\right)}{2}, \frac{-13+5}{2}, \frac{2+4}{2}\right) = \left(-9,5, -4, 3\right)
+ $$
+ \paragraph{Rešitev} Točka $P$ ima koordinate $P \left(-9,5, -4, 3\right)$
+ \item Dane so točke $A\left(6, 5, 2\right)$, $B\left(6, 2, -5\right)$, $C\left(-7, -2, -6\right)$. Določi koordinate točke $D$, tako da bo štirikotnik $ABCD$ paralelogram.
+ \begin{center}
+ skica:
+ \begin{tikzpicture}
+ \tkzDefPoint(0,0){A} \tkzDefPoint(2,0){B} \tkzDefPoint(3,2){C} \tkzDefPoint(1,2){D}
+ \tkzDrawPolygon[fill=red!30, opacity=0.3](A,B,C,D)
+ \tkzDrawPoints(A,B,C,D) \tkzLabelPoints(A,B,C,D)
+ \end{tikzpicture}
+ $$
+ \vektor{AD} = \vektor{BC} = \Vec{C}-\Vec{B} = \left(-7-6, -2-2, -6-\left(-5\right)\right) = \left(-13, -4, -1\right)
+ $$
+ $$
+ \rightarrow r_D = r_A + \vektor{AD} = (-13+6, -4+5, -1+2) = (-7, 1, 1)
+ $$
+ \end{center}
+ \paragraph{Rešitev} $D\left(-7, 1, 1\right)$
+ \item Zapiši prvo komponento vektorja $\Vec{b}=\left(x, -4\right)$, da bo vzporeden z vektorjem $\Vec{a}=\left(6, -2\right)$.
+ $$
+ \Vec{b} = k\cdot\Vec{a} = (6k, -2k) \wedge -2 \cdot 2 = -4 \rightarrow k = -4 \rightarrow \Vec{b} = (12, -4)
+ $$
+ \paragraph{Rešitev} $x = 12$
+\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. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+% \item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}
diff --git a/mat/domace_naloge/22/dokument.toc b/mat/domace_naloge/22/dokument.toc
new file mode 100644
index 0000000..7b05b7b
--- /dev/null
+++ b/mat/domace_naloge/22/dokument.toc
@@ -0,0 +1,9 @@
+\babel@toc {slovene}{}
+\babel@toc {slovene}{}
+\contentsline {section}{\numberline {1}Opazovalni poskus, ki vodi do odkritja plinske enačbe}{1}{section.1}%
+\contentsline {paragraph}{NALOGA:}{1}{section*.2}%
+\contentsline {paragraph}{Nekaj nasvetov}{1}{section*.3}%
+\contentsline {paragraph}{Navodila:}{1}{section*.4}%
+\contentsline {section}{\numberline {2}Uporaba znanja --- plinska enačba}{2}{section.2}%
+\contentsline {paragraph}{NALOGA:}{2}{section*.5}%
+\contentsline {section}{\numberline {3}Zaključek}{2}{section.3}%
diff --git a/mat/domace_naloge/22/stderr.log b/mat/domace_naloge/22/stderr.log
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