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zw;dHYKqzME?wmh>4@qLDre-oN3iQiwX@Q}?xsdijHUFt!ysr;L#;g@rr(}5(+MDvU zO|8lzm%|-ETlY!xA&_Xa@j?ZP~Vq`3@nRD3;uVt}C!}7gZ{z+}!*#Tg|a|i@q91hkNA-YGcBJ z*Q#+1d&I(@3FF2rq(@rT74K1N*dfpVcPP8ML0sItTwca5514}+h(Sjur7Vr{KS59# A7ytkO literal 0 HcmV?d00001 diff --git a/5-1.tex b/5-1.tex new file mode 100644 index 0000000..1d180f8 --- /dev/null +++ b/5-1.tex @@ -0,0 +1,39 @@ +\documentclass[10pt,a4paper]{article} +\usepackage[utf8]{inputenc} +\usepackage[ngerman]{babel} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} +\usepackage{enumitem} +\author{Beat Jäckle (Jb)} +\begin{document} +Lösungen für: Mathematik fürs Gymnasium +%\setcounter{section}{4} +%\setcounter{subsection}{2} +\subsection*{Selber erklären 5.1} +\subsubsection*{Aufgabe 1} +Die Quadratwurzel von p ist der positive Wert, welcher mit sich selber multipliziert genau p ergibt. +\subsection*{Aufgabe 2} +Da $10^2=100<111$ ist, können wir sagen, dass die Wurzel von 111 grösser als 10 sein muss. Die selbe Idee nützen wir, um die Wurzel eine obere Schranke zu finden. +$11^2=121>111$. Somit muss die Wurzel von 111 im Intervall $(10,11)$ liegen. + +\subsection*{Aufgabe 3} +$\sqrt{0.04}=|0.2|=+0.2=0.2$\\ +Die Wurzel ist immer positiv. +\footnote{ +Die Wurzel ist eine Funktion. Dadurch muss es eine eindeutige Antwort geben. Der Betrag eignet sich perfekt dazu, dass man sich genau auf einen Wert einigt. +} +\subsection*{Aufgabe 4} +$\sqrt{1234}$ hat genau eine Lösung. $x^2=1234$ hat unter anderem $\sqrt{1234}$ als Lösung, aber auch die Gegenzahl der Wurzel. Denn auch $(-\sqrt{1234})^2=1234$. $\mathbb{L}=\{-\sqrt{1234},\sqrt{1234}\}$ + +\subsection*{Aufgabe 5} +Sei $a$ eine Ziffer. Dann ist $\overline{1a}$ die Zahl die aufgeschrieben wird mit einem 1 beginnend und nachher die Ziffer $a$, also $10+a$. Wenn man diese Zahl quadriert, bekommt man mit der Binomischen Formel $(10+a)^2=100+2\cdot10\cdot a+a^2$. Die ersten zwei Summanden tragen nichts zur letzten Ziffer bei, da sie mit Zehn multipliziert wurden. +Daher kommt es nur auf die hinterste Ziffer der Basis drauf an, wie die hinterste Ziffer der Quadratzahl lautet. + +Dadurch kommt für die Wurzel von 28\textbf{9} nur eine der gegebenen in Frage: 17\\ +$6^2=3\textbf{6}$, $7^2=4\textbf{9}$, $8^2=6\textbf{4}$ und $9^2=8\textbf{1}$. + + +\end{document} \ No newline at end of file