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Odkryć fizykę 3. Karty pracy ucznia zakres podstawowy to zeszyt ćwiczeń wydany przez Nowa Era, przeznaczony dla uczniów klas 3 liceum i technikum. Publikacja doskonale uzupełnia podręcznik pod tytułem Odkryć fizykę, dostarczając szeregu zadań praktycznych i teoretycznych z dziedziny fizyki.

Spis treści obejmuje szeroki zakres tematów, rozpoczynając od zagadnień dotyczących termodynamiki, takich jak cząsteczki i energia, rozszerzalność cieplna, ciepło właściwe, przemiany fazowe, ciepło topnienia i parowania, bilans cieplny, a kończąc na wartości energetycznej. Następnie, książka przechodzi do drgań i fal, omawiając prawa Hooke’a, opis ruchu drgającego, wahadło sprężynowe, fale mechaniczne i dźwiękowe oraz fale elektromagnetyczne. Kolejna część skupia się na zjawiskach falowych i fizyce atomowej, przedstawiając między innymi powierzchnie falowe, odbicie fali, rozpraszanie, oraz zjawiska takie jak dyfrakcja czy interferencja światła. Rozdział kończy się omówieniem fizyki jądrowej, gwiazd i Wszechświata, w tym budowy jądra atomowego i promieniowania jądrowego.

Zapewniamy gotowe odpowiedzi do książki 'Odkryć fizykę 3. Karty pracy ucznia zakres podstawowy', aby ułatwić uczniom przygotowania do sprawdzianów i egzaminów. Dostępne są w formie PDF, które szczegółowo omawiają każde zadanie, pomagając w lepszym zrozumieniu tematu i skutecznym przyswajaniu wiedzy.

","longDescription","

Podręcznik Odkryć fizykę 3. Karty pracy ucznia zakres podstawowy od wydawnictwa Nowa Era, dedykowany dla uczniów trzecich klas liceum oraz technikum, jest kluczowym zasobem dla młodych naukowców pragnących zgłębić tajniki fizyki na poziomie podstawowym. W skład tej publikacji wchodzą nie tylko szczegółowe wyjaśnienia teoretyczne, ale również bogaty zestaw zadań praktycznych, które pomagają zrozumieć i przyswoić materiał na głębszym poziomie.

Rozpoczynając od Rozdziału 7. Termodynamika, książka oferuje czytelnikowi możliwość nauki o cząsteczkach i energii, rozszerzalności cieplnej i cieple właściwym aż po zjawiska takie jak przemiany fazowe czy ciepło topnienia i parowania. Każdy z tych działów zawiera zadania, które ułatwiają utrwalenie wiedzy i są niezwykle pomocne do zadawania pytania, przygotowania na egzaminy, a także rozwijania umiejętności analitycznych i eksperymentalnych uczniów.

Kolejny niezbędny rozdział, Rozdział 8. Drgania i fale, porusza zagadnienia od Prawa Hooke’a, przez różne rodzaje drgań jak drgania wymuszone i rezonans, aż po fale mechaniczne, dźwiękowe, i elektromagnetyczne. Tutaj również znaleźć można wiele zadań aplikacyjnych wspierających naukę oraz dzienniki laboratoryjne, które są integralną częścią nauki praktycznej.

W Rozdziale 9. Zjawiska falowe, uczniowie zaznajamiają się z podstawami rozchodzenia fal, takimi jak odbicie, rozpraszanie, czy załamanie oraz inne zjawiska takie jak dyfrakcja czy interferencja. Rozdział ten, podobnie jak poprzednie, jest wypełniony praktycznymi zadaniami i kartami powtórzeniowymi, które pomagają zrozumieć omawiane koncepcje na praktycznym poziomie.

Przechodząc do bardziej zaawansowanych zagadnień, Rozdział 10. Fizyka atomowa oraz Rozdział 11. Fizyka jądrowa, uczniowie mogą zgłębić wiedzę na temat natury światła, promieniowania termicznego, budowy jądra atomowego oraz zasad rządzących gwiazdami i wszechświatem. Te rozdziały są szczególnie przydatne dla tych, którzy chcą rozwinąć swoją wiedzę w sposób krytyczny i analityczny.

Dla tych, którzy szukają odrobionych zadań do podręcznika Odkryć fizykę 3. Karty pracy ucznia zakres podstawowy albo PDF z odpowiedziami do książki, gotowiec.pl oferuje bogaty zbiór rozwiązań, które są doskonale dostosowane do treści oraz wymogów edukacyjnych. Pozwala to na błyskawiczne sprawdzenie zrozumienia materiału i jest nieocenione podczas przygotowań do egzaminów lub przyswajania nowej wiedzy.

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Jeżeli dany obiekt astronomiczny hipotetycznie udałoby się ścisnąć do kuli pewnych rozmiarów, to stałby się on czarną dziurą. Promień tej kuli (tzw. promień Schwarzschilda) wyrażamy wzorem: R=(2GM)/(c^(2)), gdzie: c - prędkość światła w próżni, G - stała grawitacji, M - masa ciała. Jaki promień musiałaby mieć kula, do","answers",[1471,1474,1475],{"_263":771,"_1472":1473},"access","premium",{"_263":264,"_1472":1473},{"_263":1476,"_1472":1477},3,"logged_in","routes/$subjectSlug.$bookSlug.$pageNumber",{},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug",{"_1463":1482},{"_1465":1466,"_55":305,"_247":305,"_1467":1468,"_1469":1483},[1484,1485,1486],{"_263":771,"_1472":1473},{"_263":264,"_1472":1473},{"_263":1476,"_1472":1477},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug.$answerPosition",{"_1489":1490,"_1491":1492,"_1496":1497},"comments",[],"visit",{"_13":1493,"_15":1494,"_1495":39},"78b3c5e1-9b1d-41ab-8068-58072383548b","98zwWEld3z1nWYU6I90_Jg","visibleReCaptcha","excerpt",{"_1498":1499,"_1500":1501},"content","

Wykorzystując wcześniej podany przykład, można rozpatrzeć promień Schwarzschilda dla Ziemi.

\r\n\r\n

Dane:

\r\n\r\n

- stała grawitacji

\r\n\r\n

- szacunkowa masa Ziemi (źródło: Jaka jest waga Ziemi?

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padding: 1.45em 1.02em 0.95em 0;\n content: \"\\221A\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c27E8.TEX-B::before {\n padding: 0.75em 0.447em 0.249em 0;\n content: \"\\27E8\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c21CC::before {\n padding: 0.671em 1em 0.011em 0;\n content: \"\\21CC\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-stretchy-v.mjx-c28 mjx-beg mjx-c::before {\n content: \"\\239B\";\n padding: 1.154em 0.875em 0.655em 0;\n}\n\nmjx-stretchy-v.mjx-c28 mjx-ext mjx-c::before {\n content: \"\\239C\";\n width: 0.875em;\n}\n\nmjx-stretchy-v.mjx-c28 mjx-end mjx-c::before {\n content: \"\\239D\";\n padding: 1.165em 0.875em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c28 > mjx-end {\n margin-top: -1.809em;\n}\n\nmjx-stretchy-v.mjx-c28 > mjx-ext {\n border-top-width: 1.779em;\n border-bottom-width: 1.779em;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-beg mjx-c::before {\n content: \"\\239E\";\n padding: 1.154em 0.875em 0.655em 0;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-ext mjx-c::before {\n content: \"\\239F\";\n width: 0.875em;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-end mjx-c::before {\n content: \"\\23A0\";\n padding: 1.165em 0.875em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c29 > mjx-end {\n margin-top: -1.809em;\n}\n\nmjx-stretchy-v.mjx-c29 > mjx-ext {\n border-top-width: 1.779em;\n border-bottom-width: 1.779em;\n}\n\nmjx-c.mjx-c21D4::before {\n padding: 0.526em 1em 0.025em 0;\n content: \"\\21D4\";\n}\n\nmjx-c.mjx-c221E::before {\n padding: 0.442em 1em 0.011em 0;\n content: \"\\221E\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2032::before {\n padding: 0.56em 0.275em 0 0;\n content: \"\\2032\";\n}\n\n\n\n\n\nmjx-c.mjx-c2009::before {\n padding: 0 0.167em 0 0;\n content: \"\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c5B.TEX-S4::before {\n padding: 1.75em 0.583em 1.249em 0;\n content: \"[\";\n}\n\nmjx-c.mjx-c5D.TEX-S4::before {\n padding: 1.75em 0.583em 1.249em 0;\n content: \"]\";\n}\n\nmjx-c.mjx-c5B.TEX-S2::before {\n padding: 1.15em 0.472em 0.649em 0;\n content: \"[\";\n}\n\nmjx-c.mjx-c5D.TEX-S2::before {\n padding: 1.15em 0.472em 0.649em 0;\n content: \"]\";\n}\n\n\n\n\n\n\n\n\n\n\n\nmjx-stretchy-h.mjx-cAF mjx-ext mjx-c::before {\n content: \"\\AF\";\n padding: 0.59em 0 0 0;\n}\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c56::before {\n padding: 0.683em 0.75em 0.022em 0;\n content: \"V\";\n}\n\nmjx-c.mjx-c4A::before {\n padding: 0.683em 0.514em 0.022em 0;\n content: \"J\";\n}\n\nmjx-c.mjx-c1D702.TEX-I::before {\n padding: 0.442em 0.497em 0.216em 0;\n content: \"\\3B7\";\n}\n\nmjx-c.mjx-c1D452.TEX-I::before {\n padding: 0.442em 0.466em 0.011em 0;\n content: \"e\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-cF7::before {\n padding: 0.537em 0.778em 0.036em 0;\n content: \"\\F7\";\n}\n\nmjx-c.mjx-c2221.TEX-A::before {\n padding: 0.714em 0.722em 0.02em 0;\n content: \"\\2221\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\n}\n\nmjx-c.mjx-c1D420.TEX-B::before {\n padding: 0.455em 0.575em 0.201em 0;\n content: \"g\";\n}\n\nmjx-c.mjx-c1D424.TEX-B::before {\n padding: 0.694em 0.607em 0 0;\n content: \"k\";\n}\n\nmjx-c.mjx-c1D433.TEX-B::before {\n padding: 0.444em 0.511em 0 0;\n content: \"z\";\n}\n\nmjx-c.mjx-c1D7D7.TEX-B::before {\n padding: 0.654em 0.575em 0.011em 0;\n content: \"9\";\n}\n\nmjx-c.mjx-c1D425.TEX-B::before {\n padding: 0.694em 0.319em 0 0;\n content: \"l\";\n}\n\n\n\n\n\n.mjx-stretched mjx-c.mjx-c2013::before {\n content: \"\\2013\";\n}\n\nmjx-stretchy-h.mjx-c2013 mjx-ext mjx-c::before {\n content: \"\\2013\";\n padding: 0.285em 0 0 0;\n}\n\nmjx-c.mjx-c7B.TEX-S1::before {\n padding: 0.85em 0.583em 0.349em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c7D.TEX-S1::before {\n padding: 0.85em 0.583em 0.349em 0;\n content: \"}\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2026::before {\n padding: 0.12em 1.172em 0 0;\n content: \"\\2026\";\n}\n\nmjx-c.mjx-c2032::before {\n padding: 0.56em 0.275em 0 0;\n content: \"\\2032\";\n}\n\n\n\nmjx-c.mjx-c1D444.TEX-I::before {\n padding: 0.704em 0.791em 0.194em 0;\n content: \"Q\";\n}\n\nmjx-c.mjx-c200B::before {\n padding: 0 0 0 0;\n content: \"\";\n}\n\nmjx-c.mjx-c66::before {\n padding: 0.705em 0.372em 0 0;\n content: \"f\";\n}\n\nmjx-c.mjx-c1D466.TEX-I::before {\n padding: 0.442em 0.49em 0.205em 0;\n content: \"y\";\n}\n\nmjx-c.mjx-c1D465.TEX-I::before {\n padding: 0.442em 0.572em 0.011em 0;\n content: \"x\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2219::before {\n padding: 0.444em 0.5em 0 0;\n content: \"\\2219\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c5B.TEX-S1::before {\n padding: 0.85em 0.417em 0.349em 0;\n content: \"[\";\n}\n\nmjx-c.mjx-c5D.TEX-S1::before {\n padding: 0.85em 0.417em 0.349em 0;\n content: \"]\";\n}\n\nmjx-c.mjx-c1D42B.TEX-B::before {\n padding: 0.45em 0.474em 0 0;\n content: \"r\";\n}\n\nmjx-c.mjx-c1D426.TEX-B::before {\n padding: 0.45em 0.958em 0 0;\n content: \"m\";\n}\n\nmjx-mmultiscripts {\n display: inline-block;\n text-align: left;\n}\n\nmjx-prescripts {\n display: inline-table;\n padding-left: .05em;\n}\n\nmjx-scripts {\n display: inline-table;\n padding-right: .05em;\n}\n\nmjx-prescripts > mjx-row > mjx-cell {\n text-align: right;\n}\n\n[script-align=\"left\"] > mjx-row > mjx-cell {\n text-align: left;\n}\n\n[script-align=\"center\"] > mjx-row > mjx-cell {\n text-align: center;\n}\n\n[script-align=\"right\"] > mjx-row > mjx-cell {\n text-align: right;\n}\n\n\n\nmjx-c.mjx-c21::before {\n padding: 0.716em 0.278em 0 0;\n content: \"!\";\n}\n\nmjx-c.mjx-c3F::before {\n padding: 0.705em 0.472em 0 0;\n content: \"?\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2061::before {\n padding: 0 0 0 0;\n content: \"\";\n}\n\n\n\nmjx-c.mjx-c1D44D.TEX-I::before {\n padding: 0.683em 0.723em 0 0;\n content: \"Z\";\n}\n\n\n\n\n\nmjx-c.mjx-c68::before {\n padding: 0.694em 0.556em 0 0;\n content: \"h\";\n}\n\nmjx-c.mjx-c76::before {\n padding: 0.431em 0.528em 0.011em 0;\n content: \"v\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c2205::before {\n padding: 0.772em 0.5em 0.078em 0;\n content: \"\\2205\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D462.TEX-I::before {\n padding: 0.442em 0.572em 0.011em 0;\n content: \"u\";\n}\n\n\n\nmjx-c.mjx-c75::before {\n padding: 0.442em 0.556em 0.011em 0;\n content: \"u\";\n}\n\n\n\n\n\n\n\n\n\nmjx-maction {\n display: inline-block;\n text-align: left;\n position: relative;\n}\n\nmjx-maction > mjx-tool {\n display: none;\n position: absolute;\n bottom: 0;\n right: 0;\n width: 0;\n height: 0;\n z-index: 500;\n}\n\nmjx-tool > mjx-tip {\n display: inline-block;\n padding: .2em;\n border: 1px solid #888;\n font-size: 70%;\n background-color: #F8F8F8;\n color: black;\n box-shadow: 2px 2px 5px #AAAAAA;\n}\n\nmjx-maction[toggle] {\n cursor: pointer;\n}\n\nmjx-status {\n display: block;\n position: fixed;\n left: 1em;\n bottom: 1em;\n min-width: 25%;\n padding: .2em .4em;\n border: 1px solid #888;\n font-size: 90%;\n background-color: #F8F8F8;\n color: black;\n}\n\nmjx-munderover {\n display: inline-block;\n text-align: left;\n}\n\nmjx-munderover:not([limits=\"false\"]) {\n padding-top: .1em;\n}\n\nmjx-munderover:not([limits=\"false\"]) > * {\n display: block;\n}\n\nmjx-msubsup {\n display: inline-block;\n text-align: left;\n}\n\nmjx-script {\n display: inline-block;\n padding-right: .05em;\n padding-left: .033em;\n}\n\nmjx-script > mjx-spacer {\n display: block;\n}\n\nmjx-c.mjx-c1D448.TEX-I::before {\n padding: 0.683em 0.767em 0.022em 0;\n content: \"U\";\n}\n\nmjx-c.mjx-c1D6FA.TEX-I::before {\n padding: 0.704em 0.786em 0 0;\n content: \"\\3A9\";\n}\n\nmjx-c.mjx-c2211.TEX-S1::before {\n padding: 0.75em 1.056em 0.25em 0;\n content: \"\\2211\";\n}\n\nmjx-c.mjx-c1D456.TEX-I::before {\n padding: 0.661em 0.345em 0.011em 0;\n content: \"i\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c5C::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\5C\";\n}\n\nmjx-c.mjx-c2229::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2229\";\n}\n\n\n\nmjx-c.mjx-c7B.TEX-S4::before {\n padding: 1.75em 0.806em 1.249em 0;\n content: \"{\";\n}\n\n\n\n\n\nmjx-c.mjx-c4E::before {\n padding: 0.683em 0.75em 0 0;\n content: \"N\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c59::before {\n padding: 0.683em 0.75em 0 0;\n content: \"Y\";\n}\n\nmjx-c.mjx-c21D2::before {\n padding: 0.525em 1em 0.024em 0;\n content: \"\\21D2\";\n}\n\nmjx-c.mjx-c2217::before {\n padding: 0.465em 0.5em 0 0;\n content: \"\\2217\";\n}\n\nmjx-c.mjx-c2A::before {\n padding: 0.75em 0.5em 0 0;\n content: \"*\";\n}\n\n\n\nmjx-c.mjx-c2013::before {\n padding: 0.285em 0.5em 0 0;\n content: \"\\2013\";\n}\n\nmjx-c.mjx-c1D7D6.TEX-B::before {\n padding: 0.654em 0.575em 0.011em 0;\n content: \"8\";\n}\n\nmjx-c.mjx-c20::before {\n padding: 0 0.25em 0 0;\n content: \" \";\n}\n\nmjx-c.mjx-c1D6FE.TEX-I::before {\n padding: 0.441em 0.543em 0.216em 0;\n content: \"\\3B3\";\n}\n\nmjx-c.mjx-c1D6FF.TEX-I::before {\n padding: 0.717em 0.444em 0.01em 0;\n content: \"\\3B4\";\n}\n\nmjx-c.mjx-c1D44C.TEX-I::before {\n padding: 0.683em 0.763em 0 0;\n content: \"Y\";\n}\n\nmjx-c.mjx-c1D441.TEX-I::before {\n padding: 0.683em 0.888em 0 0;\n content: \"N\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D43D.TEX-I::before {\n padding: 0.683em 0.633em 0.022em 0;\n content: \"J\";\n}\n\nmjx-c.mjx-c1D444.TEX-I::before {\n padding: 0.704em 0.791em 0.194em 0;\n content: \"Q\";\n}\n\nmjx-c.mjx-c6A::before {\n padding: 0.669em 0.306em 0.205em 0;\n content: \"j\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D467.TEX-I::before {\n padding: 0.442em 0.465em 0.011em 0;\n content: \"z\";\n}\n\nmjx-c.mjx-c51::before {\n padding: 0.705em 0.778em 0.193em 0;\n content: \"Q\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c1D445.TEX-I::before {\n padding: 0.683em 0.759em 0.021em 0;\n content: \"R\";\n}\n\nmjx-c.mjx-c1D45E.TEX-I::before {\n padding: 0.442em 0.46em 0.194em 0;\n content: \"q\";\n}\n\n\n\nmjx-munder {\n display: inline-block;\n text-align: left;\n}\n\nmjx-over {\n text-align: left;\n}\n\nmjx-munder:not([limits=\"false\"]) {\n display: inline-table;\n}\n\nmjx-munder > mjx-row {\n text-align: left;\n}\n\nmjx-under {\n padding-bottom: .1em;\n}\n\nmjx-c.mjx-c2228::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2228\";\n}\n\nmjx-c.mjx-c32.TEX-MI::before {\n padding: 0.666em 0.551em 0.022em 0;\n content: \"2\";\n}\n\n\n\n\n\nmjx-c.mjx-c28.TEX-S4::before {\n padding: 1.75em 0.792em 1.249em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c29.TEX-S4::before {\n padding: 1.75em 0.792em 1.249em 0;\n content: \")\";\n}\n\nmjx-c.mjx-c1D7D5.TEX-B::before {\n padding: 0.676em 0.575em 0.011em 0;\n content: \"7\";\n}\n\nmjx-c.mjx-c47::before {\n padding: 0.705em 0.785em 0.022em 0;\n content: \"G\";\n}\n\nmjx-c.mjx-c2206::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\nmjx-c.mjx-c1D463.TEX-I::before {\n padding: 0.443em 0.485em 0.011em 0;\n content: \"v\";\n}\n\nmjx-c.mjx-c1D461.TEX-I::before {\n padding: 0.626em 0.361em 0.011em 0;\n content: \"t\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c57::before {\n padding: 0.683em 1.028em 0.022em 0;\n content: \"W\";\n}\n\nmjx-c.mjx-c54::before {\n padding: 0.677em 0.722em 0 0;\n content: \"T\";\n}\n\nmjx-c.mjx-c2225::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\2225\";\n}\n\nmjx-c.mjx-c1D44B.TEX-I::before {\n padding: 0.683em 0.852em 0 0;\n content: \"X\";\n}\n\nmjx-c.mjx-c58::before {\n padding: 0.683em 0.75em 0 0;\n content: \"X\";\n}\n\nmjx-c.mjx-c1D431.TEX-B::before {\n padding: 0.444em 0.607em 0 0;\n content: \"x\";\n}\n\nmjx-c.mjx-c2208.TEX-B::before {\n padding: 0.587em 0.767em 0.086em 0;\n content: \"\\2208\";\n}\n\nmjx-c.mjx-c2C.TEX-B::before {\n padding: 0.171em 0.319em 0.194em 0;\n content: \",\";\n}\n\nmjx-c.mjx-c221E.TEX-B::before {\n padding: 0.452em 1.15em 0.008em 0;\n content: \"\\221E\";\n}\n\nmjx-c.mjx-c27E9::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"\\27E9\";\n}\n\nmjx-c.mjx-c2265::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2265\";\n}\n\nmjx-c.mjx-c27E8::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"\\27E8\";\n}\n\nmjx-c.mjx-c222A.TEX-B::before {\n padding: 0.604em 0.767em 0.016em 0;\n content: \"\\222A\";\n}\n\nmjx-c.mjx-c222A::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\222A\";\n}\n\nmjx-c.mjx-c7B.TEX-S2::before {\n padding: 1.15em 0.667em 0.649em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c7D.TEX-S2::before {\n padding: 1.15em 0.667em 0.649em 0;\n content: \"}\";\n}\n\nmjx-c.mjx-c2115.TEX-A::before {\n padding: 0.683em 0.722em 0.02em 0;\n content: \"N\";\n}\n\nmjx-c.mjx-c2E::before {\n padding: 0.12em 0.278em 0 0;\n content: \".\";\n}\n\nmjx-c.mjx-c5B.TEX-S3::before {\n padding: 1.45em 0.528em 0.949em 0;\n content: \"[\";\n}\n\nmjx-c.mjx-c5D.TEX-S3::before {\n padding: 1.45em 0.528em 0.949em 0;\n content: \"]\";\n}\n\nmjx-c.mjx-c1D43E.TEX-I::before {\n padding: 0.683em 0.889em 0 0;\n content: \"K\";\n}\n\nmjx-c.mjx-c2221.TEX-A::before {\n padding: 0.714em 0.722em 0.02em 0;\n content: \"\\2221\";\n}\n\nmjx-c.mjx-c4F::before {\n padding: 0.705em 0.778em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c4C::before {\n padding: 0.683em 0.625em 0 0;\n content: \"L\";\n}\n\nmjx-c.mjx-c4B::before {\n padding: 0.683em 0.778em 0 0;\n content: \"K\";\n}\n\nmjx-TeXAtom {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c1D45C.TEX-I::before {\n padding: 0.441em 0.485em 0.011em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c1D446.TEX-I::before {\n padding: 0.705em 0.645em 0.022em 0;\n content: \"S\";\n}\n\nmjx-c.mjx-c53::before {\n padding: 0.705em 0.556em 0.022em 0;\n content: \"S\";\n}\n\nmjx-c.mjx-c2227::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2227\";\n}\n\nmjx-c.mjx-c52::before {\n padding: 0.683em 0.736em 0.022em 0;\n content: \"R\";\n}\n\nmjx-c.mjx-c4D::before {\n padding: 0.683em 0.917em 0 0;\n content: \"M\";\n}\n\nmjx-c.mjx-c50::before {\n padding: 0.683em 0.681em 0 0;\n content: \"P\";\n}\n\nmjx-c.mjx-c1D6E5.TEX-I::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\nmjx-c.mjx-c2A7E.TEX-A::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2A7E\";\n}\n\nmjx-c.mjx-c2A7D.TEX-A::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2A7D\";\n}\n\nmjx-c.mjx-c1D451.TEX-I::before {\n padding: 0.694em 0.52em 0.01em 0;\n content: \"d\";\n}\n\nmjx-c.mjx-c1D45F.TEX-I::before {\n padding: 0.442em 0.451em 0.011em 0;\n content: \"r\";\n}\n\nmjx-mover {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mover:not([limits=\"false\"]) {\n padding-top: .1em;\n}\n\nmjx-mover:not([limits=\"false\"]) > * {\n display: block;\n text-align: left;\n}\n\nmjx-stretchy-h.mjx-c2192 mjx-ext mjx-c::before {\n content: \"\\2212\";\n padding: 0.583em 0 0.082em 0;\n}\n\nmjx-stretchy-h.mjx-c2192 mjx-end mjx-c::before {\n content: \"\\2192\";\n padding: 0.583em 0 0.082em 0;\n}\n\nmjx-c.mjx-c1D453.TEX-I::before {\n padding: 0.705em 0.55em 0.205em 0;\n content: \"f\";\n}\n\nmjx-c.mjx-c28.TEX-S3::before {\n padding: 1.45em 0.736em 0.949em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c29.TEX-S3::before {\n padding: 1.45em 0.736em 0.949em 0;\n content: \")\";\n}\n\nmjx-c.mjx-c5B::before {\n padding: 0.75em 0.278em 0.25em 0;\n content: \"[\";\n}\n\nmjx-c.mjx-c5D::before {\n padding: 0.75em 0.278em 0.25em 0;\n content: \"]\";\n}\n\nmjx-c.mjx-c221E::before {\n padding: 0.442em 1em 0.011em 0;\n content: \"\\221E\";\n}\n\n\n\n\n\nmjx-c.mjx-c2208::before {\n padding: 0.54em 0.667em 0.04em 0;\n content: \"\\2208\";\n}\n\nmjx-c.mjx-c2124.TEX-A::before {\n padding: 0.683em 0.667em 0 0;\n content: \"Z\";\n}\n\nmjx-c.mjx-c1D447.TEX-I::before {\n padding: 0.677em 0.704em 0 0;\n content: \"T\";\n}\n\n\n\n\n\nmjx-c.mjx-c64::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"d\";\n}\n\nmjx-c.mjx-c1D440.TEX-I::before {\n padding: 0.683em 1.051em 0 0;\n content: \"M\";\n}\n\nmjx-c.mjx-c1D43B.TEX-I::before {\n padding: 0.683em 0.888em 0 0;\n content: \"H\";\n}\n\nmjx-c.mjx-c1D454.TEX-I::before {\n padding: 0.442em 0.477em 0.205em 0;\n content: \"g\";\n}\n\n\n\nmjx-c.mjx-c72::before {\n padding: 0.442em 0.392em 0 0;\n content: \"r\";\n}\n\nmjx-c.mjx-c7A::before {\n padding: 0.431em 0.444em 0 0;\n content: \"z\";\n}\n\nmjx-c.mjx-c1D464.TEX-I::before {\n padding: 0.443em 0.716em 0.011em 0;\n content: \"w\";\n}\n\nmjx-c.mjx-c2260::before {\n padding: 0.716em 0.778em 0.215em 0;\n content: \"\\2260\";\n}\n\n\n\nmjx-c.mjx-c210E.TEX-I::before {\n padding: 0.694em 0.576em 0.011em 0;\n content: \"h\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D70B.TEX-I::before {\n padding: 0.431em 0.57em 0.011em 0;\n content: \"\\3C0\";\n}\n\nmjx-c.mjx-c211D.TEX-A::before {\n padding: 0.683em 0.722em 0 0;\n content: \"R\";\n}\n\nmjx-c.mjx-c7B::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c7D::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"}\";\n}\n\nmjx-c.mjx-c6C::before {\n padding: 0.694em 0.278em 0 0;\n content: \"l\";\n}\n\nmjx-c.mjx-c2248::before {\n padding: 0.483em 0.778em 0 0;\n content: \"\\2248\";\n}\n\nmjx-c.mjx-c1D45B.TEX-I::before {\n padding: 0.442em 0.6em 0.011em 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c2212.TEX-B::before {\n padding: 0.281em 0.894em 0 0;\n content: \"\\2212\";\n}\n\nmjx-c.mjx-c1D7D3.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"5\";\n}\n\nmjx-c.mjx-c2264.TEX-B::before {\n padding: 0.697em 0.894em 0.199em 0;\n content: \"\\2264\";\n}\n\nmjx-c.mjx-c1D422.TEX-B::before {\n padding: 0.695em 0.319em 0 0;\n content: \"i\";\n}\n\nmjx-c.mjx-c1D427.TEX-B::before {\n padding: 0.45em 0.639em 0 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c2B.TEX-B::before {\n padding: 0.633em 0.894em 0.131em 0;\n content: \"+\";\n}\n\nmjx-c.mjx-c1D7D1.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"3\";\n}\n\nmjx-c.mjx-c2264::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2264\";\n}\n\nmjx-stretchy-v.mjx-c7B mjx-beg mjx-c::before {\n content: \"\\23A7\";\n padding: 0.899em 0.889em 0.01em 0;\n}\n\nmjx-stretchy-v.mjx-c7B mjx-ext mjx-c::before {\n content: \"\\23AA\";\n width: 0.889em;\n}\n\nmjx-stretchy-v.mjx-c7B mjx-end mjx-c::before {\n content: \"\\23A9\";\n padding: 0.01em 0.889em 0.899em 0;\n}\n\nmjx-stretchy-v.mjx-c7B mjx-mid mjx-c::before {\n content: \"\\23A8\";\n padding: 1.16em 0.889em 0.66em 0;\n}\n\nmjx-stretchy-v.mjx-c7B > mjx-mid {\n margin-top: -0.91em;\n margin-bottom: -0.91em;\n}\n\nmjx-stretchy-v.mjx-c7B > mjx-end {\n margin-top: -0.909em;\n}\n\nmjx-stretchy-v.mjx-c7B > mjx-ext {\n height: 50%;\n border-top-width: 0.879em;\n border-bottom-width: 0.879em;\n}\n\nmjx-c.mjx-c394::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\nmjx-c.mjx-c1D450.TEX-I::before {\n padding: 0.442em 0.433em 0.011em 0;\n content: \"c\";\n}\n\nmjx-c.mjx-c3E::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \">\";\n}\n\nmjx-c.mjx-c1D43C.TEX-I::before {\n padding: 0.683em 0.504em 0 0;\n content: \"I\";\n}\n\nmjx-c.mjx-c2192::before {\n padding: 0.511em 1em 0.011em 0;\n content: \"\\2192\";\n}\n\nmjx-c.mjx-c49::before {\n padding: 0.683em 0.361em 0 0;\n content: \"I\";\n}\n\nmjx-c.mjx-c1D44A.TEX-I::before {\n padding: 0.683em 1.048em 0.022em 0;\n content: \"W\";\n}\n\nmjx-c.mjx-c1D460.TEX-I::before {\n padding: 0.442em 0.469em 0.01em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-c1D41C.TEX-B::before {\n padding: 0.453em 0.511em 0.006em 0;\n content: \"c\";\n}\n\nmjx-c.mjx-c1D428.TEX-B::before {\n padding: 0.452em 0.575em 0.005em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c1D42C.TEX-B::before {\n padding: 0.453em 0.454em 0.006em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-cB7.TEX-B::before {\n padding: 0.336em 0.319em 0 0;\n content: \"\\22C5\";\n}\n\nmjx-c.mjx-c1D416.TEX-B::before {\n padding: 0.686em 1.189em 0.007em 0;\n content: \"W\";\n}\n\nmjx-c.mjx-c1D408.TEX-B::before {\n padding: 0.686em 0.436em 0 0;\n content: \"I\";\n}\n\nmjx-c.mjx-c3C.TEX-B::before {\n padding: 0.587em 0.894em 0.085em 0;\n content: \"<\";\n}\n\nmjx-stretchy-v.mjx-c7C mjx-ext mjx-c::before {\n content: \"\\2223\";\n width: 0.333em;\n}\n\nmjx-c.mjx-c2220::before {\n padding: 0.694em 0.722em 0 0;\n content: \"\\2220\";\n}\n\nmjx-c.mjx-c1D458.TEX-I::before {\n padding: 0.694em 0.521em 0.011em 0;\n content: \"k\";\n}\n\nmjx-c.mjx-c1D442.TEX-I::before {\n padding: 0.704em 0.763em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c61::before {\n padding: 0.448em 0.5em 0.011em 0;\n content: \"a\";\n}\n\nmjx-c.mjx-c62::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"b\";\n}\n\nmjx-c.mjx-c78::before {\n padding: 0.431em 0.528em 0 0;\n content: \"x\";\n}\n\nmjx-c.mjx-c79::before {\n padding: 0.431em 0.528em 0.204em 0;\n content: \"y\";\n}\n\nmjx-c.mjx-c3C::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \"<\";\n}\n\nmjx-c.mjx-c25::before {\n padding: 0.75em 0.833em 0.056em 0;\n content: \"%\";\n}\n\nmjx-c.mjx-c2F::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"/\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D438.TEX-I::before {\n padding: 0.68em 0.764em 0 0;\n content: \"E\";\n}\n\nmjx-c.mjx-c1D439.TEX-I::before {\n padding: 0.68em 0.749em 0 0;\n content: \"F\";\n}\n\nmjx-c.mjx-c1D402.TEX-B::before {\n padding: 0.697em 0.831em 0.011em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c1D403.TEX-B::before {\n padding: 0.686em 0.882em 0 0;\n content: \"D\";\n}\n\nmjx-c.mjx-c1D7D4.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"6\";\n}\n\nmjx-c.mjx-c1D404.TEX-B::before {\n padding: 0.68em 0.756em 0 0;\n content: \"E\";\n}\n\nmjx-c.mjx-c1D405.TEX-B::before {\n padding: 0.68em 0.724em 0 0;\n content: \"F\";\n}\n\nmjx-c.mjx-c3D.TEX-B::before {\n padding: 0.393em 0.894em 0 0;\n content: \"=\";\n}\n\nmjx-c.mjx-c1D7D2.TEX-B::before {\n padding: 0.656em 0.575em 0 0;\n content: \"4\";\n}\n\nmjx-c.mjx-c73::before {\n padding: 0.448em 0.394em 0.011em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-c69::before {\n padding: 0.669em 0.278em 0 0;\n content: \"i\";\n}\n\nmjx-c.mjx-c6E::before {\n padding: 0.442em 0.556em 0 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c6F::before {\n padding: 0.448em 0.5em 0.01em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c1D6FD.TEX-I::before {\n padding: 0.705em 0.566em 0.194em 0;\n content: \"\\3B2\";\n}\n\nmjx-c.mjx-c74::before {\n padding: 0.615em 0.389em 0.01em 0;\n content: \"t\";\n}\n\nmjx-c.mjx-c67::before {\n padding: 0.453em 0.5em 0.206em 0;\n content: \"g\";\n}\n\nmjx-c.mjx-cB0::before {\n padding: 0.715em 0.5em 0 0;\n content: \"\\B0\";\n}\n\nmjx-c.mjx-c1D6FC.TEX-I::before {\n padding: 0.442em 0.64em 0.011em 0;\n content: \"\\3B1\";\n}\n\nmjx-c.mjx-c2218::before {\n padding: 0.444em 0.5em 0 0;\n content: \"\\2218\";\n}\n\nmjx-c.mjx-c2223::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"\\2223\";\n}\n\nmjx-c.mjx-c7C::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"|\";\n}\n\nmjx-c.mjx-c2222.TEX-A::before {\n padding: 0.551em 0.722em 0.051em 0;\n content: \"\\2222\";\n}\n\nmjx-c.mjx-c1D436.TEX-I::before {\n padding: 0.705em 0.76em 0.022em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c1D437.TEX-I::before {\n padding: 0.683em 0.828em 0 0;\n content: \"D\";\n}\n\nmjx-msqrt {\n display: inline-block;\n text-align: left;\n}\n\nmjx-root {\n display: inline-block;\n white-space: nowrap;\n}\n\nmjx-surd {\n display: inline-block;\n vertical-align: top;\n}\n\nmjx-sqrt {\n display: inline-block;\n padding-top: .07em;\n}\n\nmjx-sqrt > mjx-box {\n border-top: .07em solid;\n}\n\nmjx-sqrt.mjx-tall > mjx-box {\n padding-left: .3em;\n margin-left: -.3em;\n}\n\nmjx-c.mjx-c221A.TEX-S1::before {\n padding: 0.85em 1.02em 0.35em 0;\n content: \"\\221A\";\n}\n\nmjx-c.mjx-c1D43F.TEX-I::before {\n padding: 0.683em 0.681em 0 0;\n content: \"L\";\n}\n\nmjx-c.mjx-c77::before {\n padding: 0.431em 0.722em 0.011em 0;\n content: \"w\";\n}\n\nmjx-c.mjx-c70::before {\n padding: 0.442em 0.556em 0.194em 0;\n content: \"p\";\n}\n\nmjx-c.mjx-c65::before {\n padding: 0.448em 0.444em 0.011em 0;\n content: \"e\";\n}\n\nmjx-c.mjx-cB1::before {\n padding: 0.666em 0.778em 0 0;\n content: \"\\B1\";\n}\n\nmjx-c.mjx-c1D449.TEX-I::before {\n padding: 0.683em 0.769em 0.022em 0;\n content: \"V\";\n}\n\nmjx-c.mjx-c1D45D.TEX-I::before {\n padding: 0.442em 0.503em 0.194em 0;\n content: \"p\";\n}\n\nmjx-c.mjx-cD7::before {\n padding: 0.491em 0.778em 0 0;\n content: \"\\D7\";\n}\n\nmjx-c.mjx-c48::before {\n padding: 0.683em 0.75em 0 0;\n content: \"H\";\n}\n\n\n\n\n\nmjx-mfenced {\n display: inline-block;\n text-align: left;\n}\n\nmjx-msub {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c1D434.TEX-I::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c1D435.TEX-I::before {\n padding: 0.683em 0.759em 0 0;\n content: \"B\";\n}\n\nmjx-c.mjx-c7B.TEX-S3::before {\n padding: 1.45em 0.75em 0.949em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c1D44E.TEX-I::before {\n padding: 0.441em 0.529em 0.01em 0;\n content: \"a\";\n}\n\nmjx-c.mjx-c1D44F.TEX-I::before {\n padding: 0.694em 0.429em 0.011em 0;\n content: \"b\";\n}\n\nmjx-c.mjx-c1D466.TEX-I::before {\n padding: 0.442em 0.49em 0.205em 0;\n content: \"y\";\n}\n\nmjx-c.mjx-c1D465.TEX-I::before {\n padding: 0.442em 0.572em 0.011em 0;\n content: \"x\";\n}\n\nmjx-c.mjx-c28.TEX-S2::before {\n padding: 1.15em 0.597em 0.649em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c29.TEX-S2::before {\n padding: 1.15em 0.597em 0.649em 0;\n content: \")\";\n}\n\nmjx-c.mjx-c28.TEX-S1::before {\n padding: 0.85em 0.458em 0.349em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c29.TEX-S1::before {\n padding: 0.85em 0.458em 0.349em 0;\n content: \")\";\n}\n\nmjx-mtable {\n display: inline-block;\n text-align: center;\n vertical-align: .25em;\n position: relative;\n box-sizing: border-box;\n border-spacing: 0;\n border-collapse: collapse;\n}\n\nmjx-mstyle[size=\"s\"] mjx-mtable {\n vertical-align: .354em;\n}\n\nmjx-labels {\n position: absolute;\n left: 0;\n top: 0;\n}\n\nmjx-table {\n display: inline-block;\n vertical-align: -.5ex;\n box-sizing: border-box;\n}\n\nmjx-table > mjx-itable {\n vertical-align: middle;\n text-align: left;\n box-sizing: border-box;\n}\n\nmjx-labels > mjx-itable {\n position: absolute;\n top: 0;\n}\n\nmjx-mtable[justify=\"left\"] {\n text-align: left;\n}\n\nmjx-mtable[justify=\"right\"] {\n text-align: right;\n}\n\nmjx-mtable[justify=\"left\"][side=\"left\"] {\n padding-right: 0 ! important;\n}\n\nmjx-mtable[justify=\"left\"][side=\"right\"] {\n padding-left: 0 ! important;\n}\n\nmjx-mtable[justify=\"right\"][side=\"left\"] {\n padding-right: 0 ! important;\n}\n\nmjx-mtable[justify=\"right\"][side=\"right\"] {\n padding-left: 0 ! important;\n}\n\nmjx-mtable[align] {\n vertical-align: baseline;\n}\n\nmjx-mtable[align=\"top\"] > mjx-table {\n vertical-align: top;\n}\n\nmjx-mtable[align=\"bottom\"] > mjx-table {\n vertical-align: bottom;\n}\n\nmjx-mtable[side=\"right\"] mjx-labels {\n min-width: 100%;\n}\n\nmjx-mtr {\n display: table-row;\n text-align: left;\n}\n\nmjx-mtr[rowalign=\"top\"] > mjx-mtd {\n vertical-align: top;\n}\n\nmjx-mtr[rowalign=\"center\"] > mjx-mtd {\n vertical-align: middle;\n}\n\nmjx-mtr[rowalign=\"bottom\"] > mjx-mtd {\n vertical-align: bottom;\n}\n\nmjx-mtr[rowalign=\"baseline\"] > mjx-mtd {\n vertical-align: baseline;\n}\n\nmjx-mtr[rowalign=\"axis\"] > mjx-mtd {\n vertical-align: .25em;\n}\n\nmjx-mtd {\n display: table-cell;\n text-align: center;\n padding: .215em .4em;\n}\n\nmjx-mtd:first-child {\n padding-left: 0;\n}\n\nmjx-mtd:last-child {\n padding-right: 0;\n}\n\nmjx-mtable > * > mjx-itable > *:first-child > mjx-mtd {\n padding-top: 0;\n}\n\nmjx-mtable > * > mjx-itable > *:last-child > mjx-mtd {\n padding-bottom: 0;\n}\n\nmjx-tstrut {\n display: inline-block;\n height: 1em;\n vertical-align: -.25em;\n}\n\nmjx-labels[align=\"left\"] > mjx-mtr > mjx-mtd {\n text-align: left;\n}\n\nmjx-labels[align=\"right\"] > mjx-mtr > mjx-mtd {\n text-align: right;\n}\n\nmjx-mtd[extra] {\n padding: 0;\n}\n\nmjx-mtd[rowalign=\"top\"] {\n vertical-align: top;\n}\n\nmjx-mtd[rowalign=\"center\"] {\n vertical-align: middle;\n}\n\nmjx-mtd[rowalign=\"bottom\"] {\n vertical-align: bottom;\n}\n\nmjx-mtd[rowalign=\"baseline\"] {\n vertical-align: baseline;\n}\n\nmjx-mtd[rowalign=\"axis\"] {\n vertical-align: .25em;\n}\n\nmjx-mpadded {\n display: inline-block;\n text-align: left;\n}\n\nmjx-rbox {\n display: inline-block;\n position: relative;\n}\n\nmjx-menclose {\n display: inline-block;\n text-align: left;\n position: relative;\n}\n\nmjx-menclose > mjx-dstrike {\n display: inline-block;\n left: 0;\n top: 0;\n position: absolute;\n border-top: 0.067em solid;\n transform-origin: top left;\n}\n\nmjx-menclose > mjx-ustrike {\n display: inline-block;\n left: 0;\n bottom: 0;\n position: absolute;\n border-top: 0.067em solid;\n transform-origin: bottom left;\n}\n\nmjx-menclose > mjx-hstrike {\n border-top: 0.067em solid;\n position: absolute;\n left: 0;\n right: 0;\n bottom: 50%;\n transform: translateY(0.034em);\n}\n\nmjx-menclose > mjx-vstrike {\n border-left: 0.067em solid;\n position: absolute;\n top: 0;\n bottom: 0;\n right: 50%;\n transform: translateX(0.034em);\n}\n\nmjx-menclose > mjx-rbox {\n position: absolute;\n top: 0;\n bottom: 0;\n right: 0;\n left: 0;\n border: 0.067em solid;\n border-radius: 0.267em;\n}\n\nmjx-menclose > mjx-cbox {\n position: absolute;\n top: 0;\n bottom: 0;\n right: 0;\n left: 0;\n border: 0.067em solid;\n border-radius: 50%;\n}\n\nmjx-menclose > mjx-arrow {\n position: absolute;\n left: 0;\n bottom: 50%;\n height: 0;\n width: 0;\n}\n\nmjx-menclose > mjx-arrow > * {\n display: block;\n position: absolute;\n transform-origin: bottom;\n border-left: 0.268em solid;\n border-right: 0;\n box-sizing: border-box;\n}\n\nmjx-menclose > mjx-arrow > mjx-aline {\n left: 0;\n top: -0.034em;\n right: 0.201em;\n height: 0;\n border-top: 0.067em solid;\n border-left: 0;\n}\n\nmjx-menclose > mjx-arrow[double] > mjx-aline {\n left: 0.201em;\n height: 0;\n}\n\nmjx-menclose > mjx-arrow > mjx-rthead {\n transform: skewX(0.464rad);\n right: 0;\n bottom: -1px;\n border-bottom: 1px solid transparent;\n border-top: 0.134em solid transparent;\n}\n\nmjx-menclose > mjx-arrow > mjx-rbhead {\n transform: skewX(-0.464rad);\n transform-origin: top;\n right: 0;\n top: -1px;\n border-top: 1px solid transparent;\n border-bottom: 0.134em solid transparent;\n}\n\nmjx-menclose > mjx-arrow > mjx-lthead {\n transform: skewX(-0.464rad);\n left: 0;\n bottom: -1px;\n border-left: 0;\n border-right: 0.268em solid;\n border-bottom: 1px solid transparent;\n border-top: 0.134em solid transparent;\n}\n\nmjx-menclose > mjx-arrow > mjx-lbhead {\n transform: skewX(0.464rad);\n transform-origin: top;\n left: 0;\n top: -1px;\n border-left: 0;\n border-right: 0.268em solid;\n border-top: 1px solid transparent;\n border-bottom: 0.134em solid transparent;\n}\n\nmjx-menclose > dbox {\n position: absolute;\n top: 0;\n bottom: 0;\n left: -0.3em;\n width: 0.6em;\n border: 0.067em solid;\n border-radius: 50%;\n clip-path: inset(0 0 0 0.3em);\n box-sizing: border-box;\n}\n\nmjx-mspace {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c6B::before {\n padding: 0.694em 0.528em 0 0;\n content: \"k\";\n}\n\nmjx-c.mjx-c1D7CF.TEX-B::before {\n padding: 0.655em 0.575em 0 0;\n content: \"1\";\n}\n\nmjx-c.mjx-c1D7CE.TEX-B::before {\n padding: 0.654em 0.575em 0.01em 0;\n content: \"0\";\n}\n\nmjx-c.mjx-c1D7D0.TEX-B::before {\n padding: 0.654em 0.575em 0 0;\n content: \"2\";\n}\n\nmjx-mroot {\n display: inline-block;\n text-align: left;\n}\n\nmjx-root {\n display: inline-block;\n white-space: nowrap;\n}\n\nmjx-surd {\n display: inline-block;\n vertical-align: top;\n}\n\nmjx-sqrt {\n display: inline-block;\n padding-top: .07em;\n}\n\nmjx-sqrt > mjx-box {\n border-top: .07em solid;\n}\n\nmjx-sqrt.mjx-tall > mjx-box {\n padding-left: .3em;\n margin-left: -.3em;\n}\n\nmjx-c.mjx-c221A::before {\n padding: 0.8em 0.853em 0.2em 0;\n content: \"\\221A\";\n}\n\nmjx-c.mjx-c3B::before {\n padding: 0.43em 0.278em 0.194em 0;\n content: \";\";\n}\n\nmjx-c.mjx-c221A.TEX-S2::before {\n padding: 1.15em 1.02em 0.65em 0;\n content: \"\\221A\";\n}\n\nmjx-mfrac {\n display: inline-block;\n text-align: left;\n}\n\nmjx-frac {\n display: inline-block;\n vertical-align: 0.17em;\n padding: 0 .22em;\n}\n\nmjx-frac[type=\"d\"] {\n vertical-align: .04em;\n}\n\nmjx-frac[delims] {\n padding: 0 .1em;\n}\n\nmjx-frac[atop] {\n padding: 0 .12em;\n}\n\nmjx-frac[atop][delims] {\n padding: 0;\n}\n\nmjx-dtable {\n display: inline-table;\n width: 100%;\n}\n\nmjx-dtable > * {\n font-size: 2000%;\n}\n\nmjx-dbox {\n display: block;\n font-size: 5%;\n}\n\nmjx-num {\n display: block;\n text-align: center;\n}\n\nmjx-den {\n display: block;\n text-align: center;\n}\n\nmjx-mfrac[bevelled] > mjx-num {\n display: inline-block;\n}\n\nmjx-mfrac[bevelled] > mjx-den {\n display: inline-block;\n}\n\nmjx-den[align=\"right\"], mjx-num[align=\"right\"] {\n text-align: right;\n}\n\nmjx-den[align=\"left\"], mjx-num[align=\"left\"] {\n text-align: left;\n}\n\nmjx-nstrut {\n display: inline-block;\n height: .054em;\n width: 0;\n vertical-align: -.054em;\n}\n\nmjx-nstrut[type=\"d\"] {\n height: .217em;\n vertical-align: -.217em;\n}\n\nmjx-dstrut {\n display: inline-block;\n height: .505em;\n width: 0;\n}\n\nmjx-dstrut[type=\"d\"] {\n height: .726em;\n}\n\nmjx-line {\n display: block;\n box-sizing: border-box;\n min-height: 1px;\n height: .06em;\n border-top: .06em solid;\n margin: .06em -.1em;\n overflow: hidden;\n}\n\nmjx-line[type=\"d\"] {\n margin: .18em -.1em;\n}\n\nmjx-mtext {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c1D45A.TEX-I::before {\n padding: 0.442em 0.878em 0.011em 0;\n content: \"m\";\n}\n\nmjx-c.mjx-c1D443.TEX-I::before {\n padding: 0.683em 0.751em 0 0;\n content: \"P\";\n}\n\nmjx-c.mjx-c41::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c44::before {\n padding: 0.683em 0.764em 0 0;\n content: \"D\";\n}\n\nmjx-c.mjx-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\n}\n\nmjx-c.mjx-c1D457.TEX-I::before {\n padding: 0.661em 0.412em 0.204em 0;\n content: \"j\";\n}\n\nmjx-c.mjx-c46::before {\n padding: 0.68em 0.653em 0 0;\n content: \"F\";\n}\n\nmjx-c.mjx-c43::before {\n padding: 0.705em 0.722em 0.021em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c42::before {\n padding: 0.683em 0.708em 0 0;\n content: \"B\";\n}\n\nmjx-c.mjx-c45::before {\n padding: 0.68em 0.681em 0 0;\n content: \"E\";\n}\n\nmjx-c.mjx-c2212::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"\\2212\";\n}\n\nmjx-c.mjx-c28::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c2B::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"+\";\n}\n\nmjx-c.mjx-c29::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \")\";\n}\n\nmjx-c.mjx-c3A::before {\n padding: 0.43em 0.278em 0 0;\n content: \":\";\n}\n\nmjx-mi {\n display: inline-block;\n text-align: left;\n}\n\nmjx-msup {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c2C::before {\n padding: 0.121em 0.278em 0.194em 0;\n content: \",\";\n}\n\nmjx-c.mjx-c22C5::before {\n padding: 0.31em 0.278em 0 0;\n content: \"\\22C5\";\n}\n\nmjx-c.mjx-c1D459.TEX-I::before {\n padding: 0.694em 0.298em 0.011em 0;\n content: \"l\";\n}\n\nmjx-c.mjx-c63::before {\n padding: 0.448em 0.444em 0.011em 0;\n content: \"c\";\n}\n\nmjx-c.mjx-c6D::before {\n padding: 0.442em 0.833em 0 0;\n content: \"m\";\n}\n\n\nmjx-container[jax=\"CHTML\"] {\n line-height: 0;\n}\n\nmjx-container [space=\"1\"] {\n margin-left: .111em;\n}\n\nmjx-container [space=\"2\"] {\n margin-left: .167em;\n}\n\nmjx-container [space=\"3\"] {\n margin-left: .222em;\n}\n\nmjx-container [space=\"4\"] {\n margin-left: .278em;\n}\n\nmjx-container [space=\"5\"] {\n margin-left: .333em;\n}\n\nmjx-container [rspace=\"1\"] {\n margin-right: .111em;\n}\n\nmjx-container [rspace=\"2\"] {\n margin-right: .167em;\n}\n\nmjx-container [rspace=\"3\"] {\n margin-right: .222em;\n}\n\nmjx-container [rspace=\"4\"] {\n margin-right: .278em;\n}\n\nmjx-container [rspace=\"5\"] {\n margin-right: .333em;\n}\n\nmjx-container [size=\"s\"] {\n font-size: 70.7%;\n}\n\nmjx-container [size=\"ss\"] {\n font-size: 50%;\n}\n\nmjx-container [size=\"Tn\"] {\n font-size: 60%;\n}\n\nmjx-container [size=\"sm\"] {\n font-size: 85%;\n}\n\nmjx-container [size=\"lg\"] {\n font-size: 120%;\n}\n\nmjx-container [size=\"Lg\"] {\n font-size: 144%;\n}\n\nmjx-container [size=\"LG\"] {\n font-size: 173%;\n}\n\nmjx-container [size=\"hg\"] {\n font-size: 207%;\n}\n\nmjx-container [size=\"HG\"] {\n font-size: 249%;\n}\n\nmjx-container [width=\"full\"] {\n width: 100%;\n}\n\nmjx-box {\n display: inline-block;\n}\n\nmjx-block {\n display: block;\n}\n\nmjx-itable {\n display: inline-table;\n}\n\nmjx-row {\n display: table-row;\n}\n\nmjx-row > * {\n display: table-cell;\n}\n\nmjx-mtext {\n display: inline-block;\n}\n\nmjx-mstyle {\n display: inline-block;\n}\n\nmjx-merror {\n display: inline-block;\n color: red;\n background-color: yellow;\n}\n\nmjx-mphantom {\n visibility: hidden;\n}\n\n_::-webkit-full-page-media, _:future, :root mjx-container {\n will-change: opacity;\n}\n\nmjx-math {\n display: inline-block;\n text-align: left;\n line-height: 0;\n text-indent: 0;\n font-style: normal;\n font-weight: normal;\n font-size: 100%;\n font-size-adjust: none;\n letter-spacing: normal;\n border-collapse: collapse;\n word-wrap: normal;\n word-spacing: normal;\n white-space: nowrap;\n direction: ltr;\n padding: 1px 0;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"] {\n display: block;\n text-align: center;\n margin: 1em 0;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"][width=\"full\"] {\n display: flex;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"] mjx-math {\n padding: 0;\n}\n\nmjx-container[jax=\"CHTML\"][justify=\"left\"] {\n text-align: left;\n}\n\nmjx-container[jax=\"CHTML\"][justify=\"right\"] {\n text-align: right;\n}\n\nmjx-semantics {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mrow {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mn {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c {\n display: inline-block;\n}\n\nmjx-utext {\n display: inline-block;\n padding: .75em 0 .2em 0;\n}\n\nmjx-mo {\n display: inline-block;\n text-align: left;\n}\n\nmjx-stretchy-h {\n display: inline-table;\n width: 100%;\n}\n\nmjx-stretchy-h > * {\n display: table-cell;\n width: 0;\n}\n\nmjx-stretchy-h > * > mjx-c {\n display: inline-block;\n transform: scalex(1.0000001);\n}\n\nmjx-stretchy-h > * > mjx-c::before {\n display: inline-block;\n width: initial;\n}\n\nmjx-stretchy-h > mjx-ext {\n /* IE */ overflow: hidden;\n /* others */ overflow: clip visible;\n width: 100%;\n}\n\nmjx-stretchy-h > mjx-ext > mjx-c::before {\n transform: scalex(500);\n}\n\nmjx-stretchy-h > mjx-ext > mjx-c {\n width: 0;\n}\n\nmjx-stretchy-h > mjx-beg > mjx-c {\n margin-right: -.1em;\n}\n\nmjx-stretchy-h > mjx-end > mjx-c {\n margin-left: -.1em;\n}\n\nmjx-stretchy-v {\n display: inline-block;\n}\n\nmjx-stretchy-v > * {\n display: block;\n}\n\nmjx-stretchy-v > mjx-beg {\n height: 0;\n}\n\nmjx-stretchy-v > mjx-end > mjx-c {\n display: block;\n}\n\nmjx-stretchy-v > * > mjx-c {\n transform: scaley(1.0000001);\n transform-origin: left center;\n overflow: hidden;\n}\n\nmjx-stretchy-v > mjx-ext {\n display: block;\n height: 100%;\n box-sizing: border-box;\n border: 0px solid transparent;\n /* IE */ overflow: hidden;\n /* others */ overflow: visible clip;\n}\n\nmjx-stretchy-v > mjx-ext > mjx-c::before {\n width: initial;\n box-sizing: border-box;\n}\n\nmjx-stretchy-v > mjx-ext > mjx-c {\n transform: scaleY(500) translateY(.075em);\n overflow: visible;\n}\n\nmjx-mark {\n display: inline-block;\n height: 0px;\n}\n\nmjx-c::before {\n display: block;\n width: 0;\n}\n\n.MJX-TEX {\n font-family: MJXZERO, MJXTEX;\n}\n\n.TEX-B {\n font-family: MJXZERO, MJXTEX-B;\n}\n\n.TEX-I {\n font-family: MJXZERO, MJXTEX-I;\n}\n\n.TEX-MI {\n font-family: MJXZERO, MJXTEX-MI;\n}\n\n.TEX-BI {\n font-family: MJXZERO, MJXTEX-BI;\n}\n\n.TEX-S1 {\n font-family: MJXZERO, MJXTEX-S1;\n}\n\n.TEX-S2 {\n font-family: MJXZERO, MJXTEX-S2;\n}\n\n.TEX-S3 {\n font-family: MJXZERO, MJXTEX-S3;\n}\n\n.TEX-S4 {\n font-family: MJXZERO, MJXTEX-S4;\n}\n\n.TEX-A {\n font-family: MJXZERO, MJXTEX-A;\n}\n\n.TEX-C {\n font-family: MJXZERO, MJXTEX-C;\n}\n\n.TEX-CB {\n font-family: MJXZERO, MJXTEX-CB;\n}\n\n.TEX-FR {\n font-family: MJXZERO, MJXTEX-FR;\n}\n\n.TEX-FRB {\n font-family: MJXZERO, MJXTEX-FRB;\n}\n\n.TEX-SS {\n font-family: MJXZERO, MJXTEX-SS;\n}\n\n.TEX-SSB {\n font-family: MJXZERO, MJXTEX-SSB;\n}\n\n.TEX-SSI {\n font-family: MJXZERO, MJXTEX-SSI;\n}\n\n.TEX-SC {\n font-family: MJXZERO, MJXTEX-SC;\n}\n\n.TEX-T {\n font-family: MJXZERO, MJXTEX-T;\n}\n\n.TEX-V {\n font-family: MJXZERO, MJXTEX-V;\n}\n\n.TEX-VB {\n font-family: MJXZERO, MJXTEX-VB;\n}\n\nmjx-stretchy-v mjx-c, mjx-stretchy-h mjx-c {\n font-family: MJXZERO, MJXTEX-S1, MJXTEX-S4, MJXTEX, MJXTEX-A ! important;\n}\n\n@font-face /* 0 */ {\n font-family: MJXZERO;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Zero.woff\") format(\"woff\");\n}\n\n@font-face /* 1 */ {\n font-family: MJXTEX;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 2 */ {\n font-family: MJXTEX-B;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Bold.woff\") format(\"woff\");\n}\n\n@font-face /* 3 */ {\n font-family: MJXTEX-I;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Math-Italic.woff\") format(\"woff\");\n}\n\n@font-face /* 4 */ {\n font-family: MJXTEX-MI;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Main-Italic.woff\") format(\"woff\");\n}\n\n@font-face /* 5 */ {\n font-family: MJXTEX-BI;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Math-BoldItalic.woff\") format(\"woff\");\n}\n\n@font-face /* 6 */ {\n font-family: MJXTEX-S1;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size1-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 7 */ {\n font-family: MJXTEX-S2;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size2-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 8 */ {\n font-family: MJXTEX-S3;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size3-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 9 */ {\n font-family: MJXTEX-S4;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Size4-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 10 */ {\n font-family: MJXTEX-A;\n src: 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