lehrkraefte:blc:miniaufgaben:kw06-2022 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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==== 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):<JS>miniAufgabe("#exowinkel_an_parallelen","#solwinkel_an_parallelen",
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stroke-linejoin=\"round\"/><path d=\"m87.03125 748.48594h64.60937\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m549.96094 393.25156v64.57031\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m517.65625 425.51719h64.60937\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m307.73437 102.54844 484.45313 645.9375\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m119.33594 748.48594h672.85156\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m307.73437 102.54844h672.85157\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m119.33594 748.48594 861.25-645.9375\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m792.1875 748.48594 188.39844-645.9375\" stroke-linecap=\"round\" stroke-linejoin=\"round\"/><path d=\"m619.96094 373.01719 52.53906 70-70.03906 52.53906\"/><path d=\"m477.77344 102.54844c0 55.625-26.71875 105.03906-68.00782 136.05468\" stroke-linejoin=\"round\"/><path d=\"m932.96875 265.86875c-35.74219-10.42969-66.64063-32.22656-88.4375-61.28906\" stroke-linejoin=\"round\"/></g><use height=\"100%\" width=\"100%\" x=\"21.239799\" xlink:href=\"#a0\" y=\"83.67984\"/><use height=\"100%\" width=\"100%\" x=\"81.3601\" xlink:href=\"#b0\" y=\"8.07984\"/><use height=\"100%\" width=\"100%\" x=\"100.1999\" xlink:href=\"#c0\" y=\"83.67984\"/><use height=\"100%\" width=\"100%\" x=\"1.3198\" xlink:href=\"#d0\" y=\"8.07984\"/><use height=\"100%\" width=\"100%\" x=\"29.5198\" xlink:href=\"#e0\" y=\"45.159939\"/><use height=\"100%\" width=\"100%\" x=\"39.239719\" xlink:href=\"#g0\" y=\"46.60017\"/><use height=\"100%\" width=\"100%\" x=\"45.239723\" xlink:href=\"#h0\" y=\"46.60017\"/><use height=\"100%\" width=\"100%\" x=\"48.719799\" xlink:href=\"#i0\" y=\"67.600166\"/><use height=\"100%\" width=\"100%\" x=\"53.759804\" xlink:href=\"#j0\" y=\"67.600166\"/><use height=\"100%\" width=\"100%\" x=\"58.7999\" xlink:href=\"#k0\" y=\"64.000168\"/><use height=\"100%\" width=\"100%\" x=\"81.3601\" xlink:href=\"#f0\" y=\"58.35994\"/></g></svg>", ["$CD$ ist die Mittelsenkrechte von $A,B$. $C$ liegt auf $m_{AB}$, also ist $\\overline{AC}=\\overline{BC}$ und $\\Delta\\, ACB$ ist gleichschenklig.\n<br>\nAlso ist $\\sphericalangle CBA = \\sphericalangle BAC = 65^\\circ$ (Basiswinkel).\n<br>\n$\\alpha = 180^\\circ - 90^\\circ - 65^\\circ = 25^\\circ$ (Innenwinkelsumme im $\\Delta\\, BCM_{AB}$)"]], ["<svg height=\"82.631248pt\" viewBox=\"0 0 106.05197 82.631248\" width=\"106.05197pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><symbol id=\"a1\" overflow=\"visible\"><path d=\"m1.78125-1.140625c-.390625.65625-.78125.796875-1.21875.828125-.125.015625-.21875.015625-.21875.203125 0 .0625.0625.109375.140625.109375.265625 0 .578125-.03125.84375-.03125.34375 0 .6875.03125 1 .03125.0625 0 .1875 0 .1875-.1875 0-.109375-.078125-.125-.15625-.125-.21875-.015625-.46875-.09375-.46875-.34375 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d=\"m657.22656 748.01719h64.57031\" stroke-linecap=\"round\"/><path d=\"m108.51563 102.50938h645.54687\" stroke-linecap=\"round\"/><path d=\"m108.51563 102.50938 581.01562 645.50781\" stroke-linecap=\"round\"/><path d=\"m754.0625 102.50938-64.53125 645.50781\" stroke-linecap=\"round\"/><path d=\"m477.22656 266.68906-474.921872-211.523435\" stroke-linecap=\"round\"/><path d=\"m477.22656 266.68906 474.96094 211.52344\" stroke-linecap=\"round\"/><path d=\"m881.83594 446.88437c-26.48438 59.41407-86.05469 100.78125-155.27344 100.78125-5.74219 0-11.36719-.27343-16.91406-.82031\"/><path d=\"m575.82031 621.72812c30.11719-27.14843 70-43.63281 113.71094-43.63281 5.70312 0 11.32812.27344 16.91406.82031\"/><path d=\"m278.47656 102.50938c0 50.11718-21.71875 95.19531-56.25 126.28906\"/></g><use height=\"100%\" width=\"100%\" x=\"1.3\" xlink:href=\"#a2\" y=\"83.67984\"/><use height=\"100%\" width=\"100%\" x=\"77.619904\" xlink:href=\"#b2\" y=\"83.67984\"/><use height=\"100%\" width=\"100%\" x=\"71.139801\" xlink:href=\"#c2\" y=\"8.07984\"/><use height=\"100%\" width=\"100%\" x=\"83.5\" xlink:href=\"#d2\" y=\"48.520039\"/><use height=\"100%\" width=\"100%\" x=\"90.580078\" xlink:href=\"#f2\" y=\"49.959881\"/><use height=\"100%\" width=\"100%\" x=\"79.780083\" xlink:href=\"#g2\" y=\"30.03998\"/><use height=\"100%\" width=\"100%\" x=\"84.820084\" xlink:href=\"#h2\" y=\"30.03998\"/><use height=\"100%\" width=\"100%\" x=\"89.860184\" xlink:href=\"#j2\" y=\"26.43998\"/><use height=\"100%\" width=\"100%\" x=\"53.139881\" xlink:href=\"#i2\" y=\"36.159901\"/><use height=\"100%\" width=\"100%\" x=\"58.179886\" xlink:href=\"#h2\" y=\"36.159901\"/><use height=\"100%\" width=\"100%\" x=\"63.219978\" xlink:href=\"#j2\" y=\"32.43998\"/><use height=\"100%\" width=\"100%\" x=\"29.139879\" xlink:href=\"#e2\" y=\"67.839981\"/></g></svg>", ["$w_{\\alpha}$ ist die Winkelhablierende und halbiert den Winkel $\\alpha$.\n<br>\n$\\sphericalangle CWA = 180^\\circ - 70^\\circ = 110^\\circ$ (Nebenwinkel)\n<br>\n$\\frac{\\alpha}{2} = 180^\\circ - 110^\\circ - 50^\\circ = 20^\\circ$ (Innenwinkelsumme im $\\Delta\\, AWC$).\n<br>\nAlso $\\alpha = 40^\\circ$."]]],
" <hr> ", " <hr> ");
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<div id="exowinkel_an_parallelen"></div>

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<hidden Lösungen>
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<div id="solwinkel_an_parallelen"></div>
<div style='font-size:12px;color:gray;'>ruby geometrie-aufgaben-dokumentieren.rb 1</div>
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=== Freitag 11. Februar 2022 ===

Ausquadrieren, Resultat in Normalform<JS>miniAufgabe("#exobinomeausquadrieren","#solbinomeausquadrieren",
[["$\\displaystyle \\left(-\\frac{12}{11}a^{2}e^{2}+\\frac{3}{4}a^{2}p^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{12}{11}a^{2}e^{2}+\\frac{3}{4}a^{2}p^{2}\\right)^2 = \\frac{144}{121}a^{4}e^{4}-\\frac{18}{11}a^{4}e^{2}p^{2}+\\frac{9}{16}a^{4}p^{4}$"], ["$\\displaystyle \\left(-\\frac{4}{3}ex+\\frac{7}{12}k^{2}x\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{3}ex+\\frac{7}{12}k^{2}x\\right)^2 = \\frac{16}{9}e^{2}x^{2}-\\frac{14}{9}ek^{2}x^{2}+\\frac{49}{144}k^{4}x^{2}$"], ["$\\displaystyle \\left(-\\frac{3}{7}f^{2}n-\\frac{5}{3}nu^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{7}f^{2}n-\\frac{5}{3}nu^{2}\\right)^2 = \\frac{9}{49}f^{4}n^{2}+\\frac{10}{7}f^{2}n^{2}u^{2}+\\frac{25}{9}n^{2}u^{4}$"], ["$\\displaystyle \\left(-\\frac{8}{5}k^{2}p-\\frac{5}{11}pw\\right)^2$", "$\\displaystyle \\left(-\\frac{8}{5}k^{2}p-\\frac{5}{11}pw\\right)^2 = \\frac{64}{25}k^{4}p^{2}+\\frac{16}{11}k^{2}p^{2}w+\\frac{25}{121}p^{2}w^{2}$"], ["$\\displaystyle \\left(\\frac{4}{11}a^{2}e^{2}-\\frac{11}{3}em\\right)^2$", "$\\displaystyle \\left(\\frac{4}{11}a^{2}e^{2}-\\frac{11}{3}em\\right)^2 = \\frac{16}{121}a^{4}e^{4}-\\frac{8}{3}a^{2}e^{3}m+\\frac{121}{9}e^{2}m^{2}$"], ["$\\displaystyle \\left(-\\frac{7}{5}cd^{2}-\\frac{5}{6}dx^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{7}{5}cd^{2}-\\frac{5}{6}dx^{2}\\right)^2 = \\frac{49}{25}c^{2}d^{4}+\\frac{7}{3}cd^{3}x^{2}+\\frac{25}{36}d^{2}x^{4}$"], ["$\\displaystyle \\left(-\\frac{7}{5}kw^{2}-\\frac{5}{11}pw\\right)^2$", "$\\displaystyle \\left(-\\frac{7}{5}kw^{2}-\\frac{5}{11}pw\\right)^2 = \\frac{49}{25}k^{2}w^{4}+\\frac{14}{11}kpw^{3}+\\frac{25}{121}p^{2}w^{2}$"], ["$\\displaystyle \\left(-\\frac{9}{5}mu+\\frac{5}{11}s^{2}u^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{9}{5}mu+\\frac{5}{11}s^{2}u^{2}\\right)^2 = \\frac{81}{25}m^{2}u^{2}-\\frac{18}{11}ms^{2}u^{3}+\\frac{25}{121}s^{4}u^{4}$"], ["$\\displaystyle \\left(\\frac{3}{4}d^{2}y^{2}+\\frac{5}{9}ny\\right)^2$", "$\\displaystyle \\left(\\frac{3}{4}d^{2}y^{2}+\\frac{5}{9}ny\\right)^2 = \\frac{9}{16}d^{4}y^{4}+\\frac{5}{6}d^{2}ny^{3}+\\frac{25}{81}n^{2}y^{2}$"], ["$\\displaystyle \\left(-\\frac{4}{5}dm^{2}-\\frac{7}{8}my^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{5}dm^{2}-\\frac{7}{8}my^{2}\\right)^2 = \\frac{16}{25}d^{2}m^{4}+\\frac{7}{5}dm^{3}y^{2}+\\frac{49}{64}m^{2}y^{4}$"]],
" <hr> ", " <hr> ");
</JS>
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<div id="exobinomeausquadrieren"></div>

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<div id="solbinomeausquadrieren"></div>
<div style='font-size:12px;color:gray;'>ruby ausquadrieren.rb 1</div>
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