From 65e37185f75d38734e245d6864ec1bbf3797a342 Mon Sep 17 00:00:00 2001 From: sijanec Date: Sun, 13 Dec 2020 16:14:42 +0100 Subject: =?UTF-8?q?doma=C4=8Da=20naloga=2020=20za=20matematiokop?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- mat/domace_naloge/20/dokument.aux | 2 +- mat/domace_naloge/20/dokument.log | 139 +++++++++++++++------ mat/domace_naloge/20/dokument.pdf | Bin 64521 -> 75040 bytes mat/domace_naloge/20/dokument.synctex.gz | Bin 20994 -> 21311 bytes mat/domace_naloge/20/dokument.tex | 150 +++++++++++++++++++---- mat/domace_naloge/20/dokument.toc | 2 +- mat/domace_naloge/20/stderr.log | 2 +- mat/domace_naloge/20/stdout.log | 203 ++++++++++++++++++------------- 8 files changed, 345 insertions(+), 153 deletions(-) diff --git a/mat/domace_naloge/20/dokument.aux b/mat/domace_naloge/20/dokument.aux index 3a80296..2bf999a 100644 --- a/mat/domace_naloge/20/dokument.aux +++ b/mat/domace_naloge/20/dokument.aux @@ -27,7 +27,7 @@ \babel@aux{slovene}{} \babel@aux{slovene}{} \@writefile{toc}{\contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 50, dve sodi in dve lihi nalogi 317-336}{1}{section.1}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Zaključek}{1}{section.2}\protected@file@percent } \exsheets@sum@of@points {0} \exsheets@sum@of@bonus {0} \gdef \numberofquestions {0} +\@writefile{toc}{\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}\protected@file@percent } diff --git a/mat/domace_naloge/20/dokument.log b/mat/domace_naloge/20/dokument.log index 87a219e..4e113df 100644 --- a/mat/domace_naloge/20/dokument.log +++ b/mat/domace_naloge/20/dokument.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2020.11.12) 12 DEC 2020 18:52 +This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2020.11.12) 13 DEC 2020 16:14 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -1680,67 +1680,127 @@ File: umsb.fd 2013/01/14 v3.01 AMS symbols B \openout6 = `dokument.toc'. +! 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Nariši še vektorje: - \footnote{Za sezname ne uporabljam več \texttt{enumerate}, ampak \texttt{tasks} (Deutsche Kvalität)} - \begin{primerTasks}(8) - \task $\displaystyle\frac{1}{3}\vektor{a}$ % a - \task $\displaystyle\frac{4}{5}\vektor{a}$ % b - \task $\displaystyle-\frac{3}{7}\vektor{a}$ % c - \task $\displaystyle-\frac{3}{4}\vektor{a}$ % č - \task $\displaystyle\frac{5}{4}\vektor{a}$ % d - \task $\displaystyle\frac{7}{5}\vektor{a}$ % e - \task $\displaystyle-\frac{3}{2}\vektor{a}$ % f - \task $\displaystyle-\frac{8}{5}\vektor{a}$ % g - \task $\displaystyle\sqrt{2}\vektor{a}$ % h - \task $\displaystyle\sqrt{5}\vektor{a}$ % i - \task $\displaystyle-\sqrt{7}\vektor{a}$ % j - \task $\displaystyle-\sqrt{10}\vektor{a}$ % k - \task $\displaystyle\frac{\sqrt{3}}{4}\vektor{a}$ % l - \task $\displaystyle\frac{\sqrt{6}}{7}\vektor{a}$ % m - \task $\displaystyle-\frac{\sqrt{12}}{3}\vektor{a}$ % n - \task $\displaystyle-\frac{\sqrt{15}}{8}\vektor{a}$ % o - \end{primerTasks} + \if\false1 + \setcounter{enumi}{317} + \item Nariši vektor $\vektor{a}$, dolg \cm{3}. Nariši še vektorje: + \footnote{Za sezname ne uporabljam več \texttt{enumerate}, ampak \texttt{tasks} (Deutsche Kvalität)} + \begin{primerTasks}(8) + \task $\displaystyle\frac{1}{3}\Vec{a}$ % a + \task $\displaystyle\frac{4}{5}\Vec{a}$ % b + \task $\displaystyle-\frac{3}{7}\Vec{a}$ % c + \task $\displaystyle-\frac{3}{4}\Vec{a}$ % č + \task $\displaystyle\frac{5}{4}\Vec{a}$ % d + \task $\displaystyle\frac{7}{5}\Vec{a}$ % e + \task $\displaystyle-\frac{3}{2}\Vec{a}$ % f + \task $\displaystyle-\frac{8}{5}\Vec{a}$ % g + \task $\displaystyle\sqrt{2}\Vec{a}$ % h + \task $\displaystyle\sqrt{5}\Vec{a}$ % i + \task $\displaystyle-\sqrt{7}\Vec{a}$ % j + \task $\displaystyle-\sqrt{10}\Vec{a}$ % k + \task $\displaystyle\frac{\sqrt{3}}{4}\Vec{a}$ % l + \task $\displaystyle\frac{\sqrt{6}}{7}\Vec{a}$ % m + \task $\displaystyle-\frac{\sqrt{12}}{3}\Vec{a}$ % n + \task $\displaystyle-\frac{\sqrt{15}}{8}\Vec{a}$ % o + \end{primerTasks} + \begin{center} + \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}] + % 0 + \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B} + \tkzDrawPoints[red](A,B) \tkzDrawSegments[vect](A,B) + \tkzLabelLine[above](A,B){$\Vec{a}$} + % a + \tkzDefPoint(30:3){aA} + \tkzDrawLine(A,aA) \tkzDrawLine(aA,B) + \tkzDefPoint(1,0){a1} \tkzDefPoint(30:1){a2} \tkzDefPoint(30:2){a3} + \tkzDefPoint(2,0){a4} + \tkzCompass(A,a2) \tkzCompass(a2,a3) \tkzDrawLine(a3,a4) + \tkzDrawLine(a1,a2) \tkzDrawPoints[red](a1) \tkzDrawSegment[vect](A,a1) + \tkzLabelLine[below](A,a1){$\frac{1}{3}\Vec{a}$} + % b + \tkzDefPoint(30:(3/5)){b1} \tkzDefPoint(30:(3/5)*2){b2} + \tkzDefPoint(30:(3/5)*3){b3} \tkzDefPoint(30:(3/5)*4){b4} + \tkzCompass(A,b1) \tkzCompass(b1,b2) \tkzCompass(b2,b3) + \tkzCompass(b3,b4) \tkzCompass(b4,aA) + \tkzDefPoint((3/5)*4,0){b5} \tkzDrawLine(b4,b5) \tkzDrawPoints[red](b5) + \tkzDrawSegments[vect](A,b5) + \tkzLabelLine[below](A,b5){$\frac{4}{5}\Vec{a}$} + \end{tikzpicture} + \end{center} + \fi + \setcounter{enumi}{318} + \item Nariši trikotnik $ABC$ s podatki $a=\cm{4}$, $b=\cm{6}$, $c=\cm{7}$. Nariši še $\displaystyle\frac{1}{3}\vektor{AC}+\sqrt{2}\vektor{AB}$. % 319 \begin{center} - \begin{tikzpicture} - \tkzDefPoint(0,0){A} \tkzDefPoint(0,3){B} - \tkzDrawPoints(A,B) + \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}] + \tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B} + \tkzDefPoint(6,0){bh} \tkzDefPoint(7-4,0){ah} + \tkzDefPoint(0,6){3h} \tkzDefPoint(0,4){2h} \tkzDefPoint(0,2){1h} + \tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$c$} + \tkzInterCC(A,bh)(B,ah) \tkzGetPoints{C}{CX} + \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C) + \tkzLabelLine[below right](A,C){$\vektor{AC}$} + \tkzDrawLine(A,3h) \tkzCompass(A,1h) \tkzCompass(1h,2h) + \tkzCompass(2h,3h) \tkzDrawLine(3h,C) + \tkzDefPointWith[colinear=at 1h](3h,C) \tkzGetPoint{Z} + \tkzInterLL(A,C)(1h,Z) \tkzGetPoint{T} + \tkzLabelLine[above](A,T){$\frac{1}{3}\vektor{AC}$} + % sedaj pa sqrt(2)AB + \tkzDefPoint(0,7){P} \tkzCompass(A,P) + \tkzDefPoint(7,7){K} \tkzDrawLine(B,K) \tkzDrawLine(P,K) + \tkzInterLC(A,B)(A,K) \tkzGetPoints{K2X}{K2} \tkzCompass(A,K2) + \tkzLabelLine[below](A,K2){$\sqrt{2}\vektor{AB}$} + % sedaj pa seštevek + \tkzDefPointWith[colinear=at B](A,C) \tkzGetPoint{S} + \tkzLabelLine[above left](A,S){$\frac{1}{3}\vektor{AC}+\sqrt{AB}$} + \tkzDrawSegments[vect](A,C A,T, A,K A,K2) + \tkzDrawSegments[red, vect](A,S) + \tkzMarkRightAngles(A,P,K P,K,B K,B,A B,A,P) + \tkzDrawPoints[red](A,B,C,T,K,K2,S) \tkzLabelPoints(A,B,C) \end{tikzpicture} \end{center} - \setcounter{enumi}{319} + \newpage \item Nariši pravokotnik $ABCD$ s podatki: $a=\cm{6}$, $b=\cm{2}$. Nariši še $\displaystyle-\frac{3}{2}\vektor{AC}+\frac{\sqrt{2}}{2}\vektor{BC}$. + \begin{center} + \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}] + \tkzDefPoint(0,0){A} \tkzDefPoint(6,2){C} \tkzDefPoint(6,0){B} + \tkzDefPoint(0,2){D} + \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D) + \tkzDefPoint(0,(2/3)){a1} \tkzDefPoint(0,(2/3)*2){a2} + \tkzCompass(A,a1) \tkzCompass(a1,a2) \tkzCompass(a2,D) + \tkzDefPointWith[colinear=at a1](D,C) \tkzGetPoint{Z} + \tkzInterLL(A,C)(a1,Z) \tkzGetPoint{V} + \tkzDrawLine(a1,V) \tkzLabelLine[above left](A,C){$\vektor{AC}$} + \tkzLabelLine[below](V,C){$-\frac{2}{3}\vektor{AC}$} + % zdaj pa še koren iz dve polovic vektorja BC + \tkzDefPoint(6-2,0){K} \tkzDefPoint(6-2,2){P} + \tkzCompass(B,K) \tkzCompass(C,P) + \tkzInterLC(C,B)(C,K) \tkzGetPoints{K2X}{K2} + \tkzDefMidPoint(C,K2) \tkzGetPoint{K22} + \tkzLabelLine[left](C,K22){$\frac{\sqrt{2}}{2}\vektor{CB}$} + \tkzDefPointWith[colinear=at K22](C,V) \tkzGetPoint{S} + \tkzDrawPoints[red](A,B,C,D,V,K2,K22,S) \tkzLabelPoints[](A,B,C,D) + \tkzDrawSegments[vect](A,C C,V C,K2 C,K22) + \tkzDrawSegments[vect, red](C,S) + \tkzMarkRightAngles(C,P,K P,K,B K,B,C B,C,P) + \end{tikzpicture} + \end{center} \setcounter{enumi}{324} - \item Naj bo $\vektor{m}=2\vektor{a}+3\vektor{b}$ in $\vektor{n}=\vektor{a}-2\vektor{b}$. Izrazi vektor $2\vektor{m}-\frac{1}{2}\vektor{n}$ z vektorjema $\vektor{a}$ in $\vektor{b}$. + \item Naj bo $\Vec{m}=2\Vec{a}+3\Vec{b}$ in $\Vec{n}=\Vec{a}-2\Vec{b}$. Izrazi vektor $2\Vec{m}-\frac{1}{2}\Vec{n}$ z vektorjema $\Vec{a}$ in $\Vec{b}$. + $$ + 2\Vec{a}+3\Vec{b}-(\frac{1}{2}(\Vec{a}-2\Vec{b})) = + 2\Vec{a} + 3\Vec{b} - \frac{1}{2}\Vec{a} + \frac{1}{2} \cdot 2\Vec{b} = + 1\frac{1}{2}\Vec{a}+4\Vec{b} + $$ \setcounter{enumi}{328} \item Nariši daljico $AB$, dolgo \cm{6}. Na njen nariši tako točno $M$, da velja $|AM|:|MB|=1:2$, in tako točno $N$, da velja $|AN|:|AB|=1:2$. Vektorja $\vektor{AM}$ in $\vektor{AN}$ izrazi z vektorjem $\vektor{AB}$. + \begin{center} + \begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}] + \tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B} + \tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$AB$} + \tkzDefPoint(30:6){3h} \tkzDefPoint(30:4){2h} \tkzDefPoint(30:2){1h} + \tkzDrawLine(A,3h) \tkzDrawLine(3h,B) + \tkzCompass(A,1h) \tkzCompass(1h,2h) \tkzCompass(2h,3h) + \tkzDefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M) + \tkzDefMidPoint(A,B) \tkzGetPoint{N} + \tkzDrawPoints[red](A,B,M,N) \tkzLabelPoints[below left](A,B,M,N) + \tkzDrawSegments[vect](A,M A,N) + \end{tikzpicture} + \end{center} + $$ + \vektor{AM} = \frac{1}{3}\vektor{AB} + $$ + $$ + \vektor{AN} = \frac{1}{2}\vektor{AB} + $$ \end{enumerate} diff --git a/mat/domace_naloge/20/dokument.toc b/mat/domace_naloge/20/dokument.toc index 37ec10b..58c131a 100644 --- a/mat/domace_naloge/20/dokument.toc +++ b/mat/domace_naloge/20/dokument.toc @@ -1,4 +1,4 @@ \babel@toc {slovene}{} \babel@toc {slovene}{} \contentsline {section}{\numberline {1}Vaje \textit {Matematika 2}: stran 50, dve sodi in dve lihi nalogi 317-336}{1}{section.1}% -\contentsline {section}{\numberline {2}Zaključek}{1}{section.2}% +\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}% diff --git a/mat/domace_naloge/20/stderr.log b/mat/domace_naloge/20/stderr.log index 09bb3f0..feb56f3 100644 --- a/mat/domace_naloge/20/stderr.log +++ b/mat/domace_naloge/20/stderr.log @@ -1 +1 @@ -<]/Index[ 0 161]/Info 159 0 R/Length 415/Root 158 0 R/Size 161/W[ 1 3 1]>> +<<0E6437A0780AE3AF08A9727F1B146732>]/Index[ 0 145]/Info 143 0 R/Length 377/Root 142 0 R/Size 145/W[ 1 3 1]>> diff --git a/mat/domace_naloge/20/stdout.log b/mat/domace_naloge/20/stdout.log index ba30731..ed1fc7d 100644 --- a/mat/domace_naloge/20/stdout.log +++ b/mat/domace_naloge/20/stdout.log @@ -476,39 +476,84 @@ your preamble. 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Package PGF Math Error: Unknown function `T' (in 'T'). -Package tasks Warning: The width of `label-width' is too small on line 157. -(tasks) Please set it at least to 14.05548pt. +See the PGF Math package documentation for explanation. +Type H for immediate help. + ... + +l.208 ...\tkzDrawSegments[vect](A,C A,T, A,K A,K2) + +! Package PGF Math Error: Unknown function `T' (in 'T'). -Overfull \hbox (3.05548pt too wide) in paragraph at lines 157--157 -\OT1/cmr/bx/n/10 m) +See the PGF Math package documentation for explanation. +Type H for immediate help. + ... + +l.208 ...\tkzDrawSegments[vect](A,C A,T, A,K A,K2) + -Overfull \hbox (3.4002pt too wide) in paragraph at lines 157--157 -|$\OMS/cmsy/m/n/10 ^^@[][]$| +! Package PGF Math Error: Unknown function `T' (in 'T'). -Overfull \hbox (3.4002pt too wide) in paragraph at lines 157--157 -|$\OMS/cmsy/m/n/10 ^^@[][]$| +See the PGF Math package documentation for explanation. +Type H for immediate help. + ... + +l.208 ...\tkzDrawSegments[vect](A,C A,T, A,K A,K2) + +[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] + +! Package pgf Error: No shape named `h1' is known. + +See the pgf package documentation for explanation. +Type H for immediate help. + ... + +l.256 ...DefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M) + + +! Package pgf Error: No shape named `h1' is known. + +See the pgf package documentation for explanation. +Type H for immediate help. + ... + +l.256 ...DefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M) + + +! Package pgf Error: No shape named `h1' is known. + +See the pgf package documentation for explanation. +Type H for immediate help. + ... + +l.256 ...DefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M) + Package hyperref Warning: Composite letter `\textasciicaron+c' (hyperref) not defined in PD1 encoding, -(hyperref) removing `\textasciicaron' on input line 173. +(hyperref) removing `\textasciicaron' on input line 271. -Overfull \hbox (16.93909pt too wide) in paragraph at lines 174--179 +Overfull \hbox (16.93909pt too wide) in paragraph at lines 272--277 \OT1/cmtt/m/n/10 pdf$[] \OT1/cmr/m/n/10 in/ali []$\OT1/cmtt/m/n/10 https : / / git . sijanec . eu / sijanec / sola-[]gimb-[]2 / raw / branch / master / mat / domace _ naloge / 20 / dokument . -[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] (./dokument.aux) ) +[2] (./dokument.aux) ) (see the transcript file for additional information) -Output written on dokument.pdf (2 pages, 189212 bytes). +/type1/public/amsfonts/cm/cmsy7.pfb> +Output written on dokument.pdf (2 pages, 197099 bytes). SyncTeX written on dokument.synctex.gz. Transcript written on dokument.log. 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This may have been caused -- cgit v1.2.3