miniaufgabe.js ==== 7. Februar 2022 bis 11. Februar 2022 ==== === Donnerstag 10. Februar 2022 === Beschreiben Sie, wie der Winkel $\alpha$ bestimmt werden kann. (Was wird gerechnet und warum):miniAufgabe("#exowinkel_an_parallelen","#solwinkel_an_parallelen", [["", ["$CD$ ist die Mittelsenkrechte von $A,B$. $C$ liegt auf $m_{AB}$, also ist $\\overline{AC}=\\overline{BC}$ und $\\Delta\\, ACB$ ist gleichschenklig.\n
\nAlso ist $\\sphericalangle CBA = \\sphericalangle BAC = 65^\\circ$ (Basiswinkel).\n
\n$\\alpha = 180^\\circ - 90^\\circ - 65^\\circ = 25^\\circ$ (Innenwinkelsumme im $\\Delta\\, BCM_{AB}$)"]], ["", ["Winkel $\\sphericalangle ACD = 180^\\circ-90^\\circ-62^\\circ = 28^\\circ$ (Innenwinkelsumme im Dreieck).\n
\nWinkel $\\alpha = \\sphericalangle ACD = 28^\\circ$ (Wechselwinkel an Parallelen)"]], ["", ["$w_{\\alpha}$ ist die Winkelhablierende und halbiert den Winkel $\\alpha$.\n
\n$\\sphericalangle CWA = 180^\\circ - 70^\\circ = 110^\\circ$ (Nebenwinkel)\n
\n$\\frac{\\alpha}{2} = 180^\\circ - 110^\\circ - 50^\\circ = 20^\\circ$ (Innenwinkelsumme im $\\Delta\\, AWC$).\n
\nAlso $\\alpha = 40^\\circ$."]]], "
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");
ruby geometrie-aufgaben-dokumentieren.rb 1
 === Freitag 11. Februar 2022 === Ausquadrieren, Resultat in NormalformminiAufgabe("#exobinomeausquadrieren","#solbinomeausquadrieren", [["$\\displaystyle \\left(-\\frac{12}{11}a^{2}e^{2}+\\frac{3}{4}a^{2}p^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{12}{11}a^{2}e^{2}+\\frac{3}{4}a^{2}p^{2}\\right)^2 = \\frac{144}{121}a^{4}e^{4}-\\frac{18}{11}a^{4}e^{2}p^{2}+\\frac{9}{16}a^{4}p^{4}$"], ["$\\displaystyle \\left(-\\frac{4}{3}ex+\\frac{7}{12}k^{2}x\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{3}ex+\\frac{7}{12}k^{2}x\\right)^2 = \\frac{16}{9}e^{2}x^{2}-\\frac{14}{9}ek^{2}x^{2}+\\frac{49}{144}k^{4}x^{2}$"], ["$\\displaystyle \\left(-\\frac{3}{7}f^{2}n-\\frac{5}{3}nu^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{7}f^{2}n-\\frac{5}{3}nu^{2}\\right)^2 = \\frac{9}{49}f^{4}n^{2}+\\frac{10}{7}f^{2}n^{2}u^{2}+\\frac{25}{9}n^{2}u^{4}$"], ["$\\displaystyle \\left(-\\frac{8}{5}k^{2}p-\\frac{5}{11}pw\\right)^2$", "$\\displaystyle \\left(-\\frac{8}{5}k^{2}p-\\frac{5}{11}pw\\right)^2 = \\frac{64}{25}k^{4}p^{2}+\\frac{16}{11}k^{2}p^{2}w+\\frac{25}{121}p^{2}w^{2}$"], ["$\\displaystyle \\left(\\frac{4}{11}a^{2}e^{2}-\\frac{11}{3}em\\right)^2$", "$\\displaystyle \\left(\\frac{4}{11}a^{2}e^{2}-\\frac{11}{3}em\\right)^2 = \\frac{16}{121}a^{4}e^{4}-\\frac{8}{3}a^{2}e^{3}m+\\frac{121}{9}e^{2}m^{2}$"], ["$\\displaystyle \\left(-\\frac{7}{5}cd^{2}-\\frac{5}{6}dx^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{7}{5}cd^{2}-\\frac{5}{6}dx^{2}\\right)^2 = \\frac{49}{25}c^{2}d^{4}+\\frac{7}{3}cd^{3}x^{2}+\\frac{25}{36}d^{2}x^{4}$"], ["$\\displaystyle \\left(-\\frac{7}{5}kw^{2}-\\frac{5}{11}pw\\right)^2$", "$\\displaystyle \\left(-\\frac{7}{5}kw^{2}-\\frac{5}{11}pw\\right)^2 = \\frac{49}{25}k^{2}w^{4}+\\frac{14}{11}kpw^{3}+\\frac{25}{121}p^{2}w^{2}$"], ["$\\displaystyle \\left(-\\frac{9}{5}mu+\\frac{5}{11}s^{2}u^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{9}{5}mu+\\frac{5}{11}s^{2}u^{2}\\right)^2 = \\frac{81}{25}m^{2}u^{2}-\\frac{18}{11}ms^{2}u^{3}+\\frac{25}{121}s^{4}u^{4}$"], ["$\\displaystyle \\left(\\frac{3}{4}d^{2}y^{2}+\\frac{5}{9}ny\\right)^2$", "$\\displaystyle \\left(\\frac{3}{4}d^{2}y^{2}+\\frac{5}{9}ny\\right)^2 = \\frac{9}{16}d^{4}y^{4}+\\frac{5}{6}d^{2}ny^{3}+\\frac{25}{81}n^{2}y^{2}$"], ["$\\displaystyle \\left(-\\frac{4}{5}dm^{2}-\\frac{7}{8}my^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{5}dm^{2}-\\frac{7}{8}my^{2}\\right)^2 = \\frac{16}{25}d^{2}m^{4}+\\frac{7}{5}dm^{3}y^{2}+\\frac{49}{64}m^{2}y^{4}$"]], "
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ruby ausquadrieren.rb 1