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\"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" to niezastąpiony zeszyt ćwiczeń wydawany przez Nową Erę dedykowany uczniom pierwszych klas liceum i technikum. Stanowi on doskonałe uzupełnienie dla podręcznika, oferując praktyczne zadania i eksperymenty, które pomagają w lepszym zrozumieniu chemicznych zagadnień. Na kilku pierwszych stronach znajdziemy informacje o układzie okresowym pierwiastków chemicznych. Uczniowie nauczą się odczytywania informacji z układu, co ułatwi im rozwiązywanie zadań oraz opanują pełny i skrócony zapis konfiguracji elektronowej atomów. Dodatkowo, książka zawiera regulamin pracowni chemicznej oraz liczne przykłady reakcji chemicznych i zadań z ich opisem.

Dzięki naszym materiałom oferujemy odpowiedzi do zeszyt ćwiczeń, które pozwalają na szybsze opanowanie materiału i przygotowanie się do lekcji. Możesz skorzystać z naszej oferty, aby pobrać PDF z odpowiedziami do książki \"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" i ułatwić sobie naukę. Nasze gotowe rozwiązania pomogą każdemu uczniowi!

","longDescription","

\"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" to wyjątkowy zeszyt ćwiczeń, stworzony z myślą o uczniach pierwszej klasy liceum i technikum, który wspiera nauczanie chemii na poziomie ponadpodstawowym. Ta publikacja wydawnictwa Nowa Era zawiera nie tylko rozwinięte wyjaśnienia i przykłady praktyczne, ale także ćwiczenia laboratoryjne, które pozwalają uczniom na samodzielne eksperymentowanie i lepsze zrozumienie zagadnień chemicznych.

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Na pierwszych stronach znajdziemy szczegółowy spis treści, który wprowadza nas w świat chemii poprzez układ okresowy pierwiastków chemicznych. Uczniowie mogą łatwo odczytywać dane potrzebne do rozwiązywania zadań i sprawdzać swoją znajomość nazw oraz symboli chemicznych pierwiastków. Ważna część tego działu poświęcona jest nauce odczytywania informacji z układu okresowego, co jest kluczowym elementem w dalszej nauce chemii.

\n\n

W kolejnych rozdziałach prezentowane są zagadnienia związane z zapisem konfiguracji elektronowej atomów. Podpowłokowe zapisy konfiguracji elektronowej, zarówno pełne jak i skrócone, pozwalają na lepsze zrozumienie struktury atomowej dla różnych pierwiastków chemicznych. W praktyce, często preferowany jest zapis skrócony, który ułatwia pracę chemików w codziennych obliczeniach i analizach. Autorzy zeszytu ćwiczeń zachęcają również do korzystania z zasobów online dostępnych na platformie edukacyjnej ukladokresowy.edu.pl, co ułatwia zrozumienie funkcjonowania układu okresowego w życiu codziennym.

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Warto podkreślić, że zeszyt ćwiczeń \"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" oferuje również karty laboratoryjne, które są cennym dodatkiem do nauki chemii. Uczniowie mogą wykonywać doświadczenia chemiczne, ściśle według instrukcji, co pomaga im odkrywać tajniki chemicznych reakcji i rozwiązywać praktyczne problemy. Dla tych, którzy potrzebują dodatkowego wsparcia, istnieje możliwość skorzystania z gotowych odpowiedzi do książki i PDF-ów z odpowiedziami, dostępnych na popularnych platformach edukacyjnych.

\n\n

W ramach szczegółowych zadań zawartych w tej publikacji, uczniowie mają okazję zmierzyć się z zagadnieniami takimi jak: charakterystyka wodorotlenków, właściwości chemiczne związków nieorganicznych czy praktyczne korzystanie z zasad stechiometrii. Te ćwiczenia nie tylko pomagają zrozumieć teoretyczne aspekty chemii, ale także sprawdzają umiejętność ich zastosowania w praktyce. \"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" to nieoceniona pomoc w przygotowaniu do egzaminów i sprawdzianów, umożliwiająca uczniom zdobycie pewności siebie w codziennej nauce.

\n\n

Jednocześnie zeszyt ćwiczeń zwraca uwagę na bezpieczeństwo w laboratorium. Zawiera szczegółowy regulamin pracowni chemicznej, który jest niezbędny do bezpiecznego wykonywania eksperymentów. Uczniowie są zobowiązani do przestrzegania zasad, co podkreśla odpowiedzialne podejście do nauki chemii i rozwija świadomość w zakresie pracy z substancjami chemicznymi.

\n\n

Dzięki przemyślanemu układowi treści oraz możliwości skorzystania z odrobionych zadań do podręcznika, uczniowie mogą efektywnie przyswajać materiał i w pełni rozumieć omawiane zagadnienia. Wszystkie te elementy sprawiają, że \"To jest chemia 1. Karty pracy ucznia. Zakres podstawowy\" jest niezastąpionym narzędziem w nauczaniu chemii na poziomie licealnym i technicznym.

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Szkło laboratoryjne: kolby stożkowe o pojemności 500cm^(3). Obserwacje: W 1. kolbie pojawiają się pojedyncze pęcherzyki","answers",[1351,1355,1357],{"_225":1352,"_1353":1354},1,"access","premium",{"_225":226,"_1353":1356},"all",{"_225":1358,"_1353":1359},3,"logged_in","routes/$subjectSlug.$bookSlug.$pageNumber",{},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug",{"_1343":1364},{"_1345":1346,"_55":1313,"_209":1314,"_1347":1348,"_1349":1365},[1366,1367,1368],{"_225":1352,"_1353":1354},{"_225":226,"_1353":1356},{"_225":1358,"_1353":1359},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug.$answerPosition",{"_1371":1372,"_1373":1374,"_1378":1379},"comments",[],"visit",{"_13":1375,"_15":1376,"_1377":39},"2b3e7315-60e9-4fd2-85ac-4af53619bcc1","ZzYoYTJNWOQPMklvKh8BHQ","visibleReCaptcha","excerpt",{"_1380":1381,"_1382":1383},"content","

Odpowiedź:

\r\n\r\n

Dodanie tlenku manganu(IV) zwiększa szybkość reakcji chemicznej. MnO₂pełni funkcję katalizatora tej reakcji chemicznej.

\r\n\r\n

Objaśnienie:

\r\n\r\n

W naszym doświadczeniu sprawdzano wpływ tlenku manganu(IV)

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0.201em 0;\n content: \"g\";\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-c1D425.TEX-B::before {\n padding: 0.694em 0.319em 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-c.mjx-c1D40A.TEX-B::before {\n padding: 0.686em 0.901em 0 0;\n content: \"K\";\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-c2D::before {\n padding: 0.252em 0.333em 0 0;\n content: \"-\";\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-c1D7D3.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"5\";\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.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\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2A7E.TEX-A::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2A7E\";\n}\n\n\n\nmjx-c.mjx-c1D41A.TEX-B::before {\n padding: 0.453em 0.559em 0.006em 0;\n content: \"a\";\n}\n\nmjx-c.mjx-c2212.TEX-B::before {\n padding: 0.281em 0.894em 0 0;\n content: \"\\2212\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c27F6::before {\n padding: 0.511em 1.638em 0.011em 0;\n content: \"\\27F6\";\n}\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c1D6FF.TEX-I::before {\n padding: 0.717em 0.444em 0.01em 0;\n content: \"\\3B4\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c1D468.TEX-BI::before {\n padding: 0.711em 0.869em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c1D469.TEX-BI::before {\n padding: 0.686em 0.866em 0 0;\n content: \"B\";\n}\n\nmjx-c.mjx-c1D46A.TEX-BI::before {\n padding: 0.703em 0.855em 0.017em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-cB0.TEX-B::before {\n padding: 0.702em 0.575em 0 0;\n content: \"\\B0\";\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-c2221.TEX-A::before {\n padding: 0.714em 0.722em 0.02em 0;\n content: \"\\2221\";\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-stretchy-v.mjx-c2191 mjx-beg mjx-c::before {\n content: \"\\2191\";\n padding: 0.6em 0.667em 0 0;\n}\n\nmjx-stretchy-v.mjx-c2191 mjx-ext mjx-c::before {\n content: \"\\23D0\";\n width: 0.667em;\n}\n\nmjx-stretchy-v.mjx-c2191 > mjx-ext {\n border-top-width: 0.57em;\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c1D411.TEX-B::before {\n padding: 0.686em 0.862em 0.011em 0;\n content: \"R\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2282::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \"\\2282\";\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\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-c1D70C.TEX-I::before {\n padding: 0.442em 0.517em 0.216em 0;\n content: \"\\3C1\";\n}\n\n\n\n\n\n\n\n\n\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\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c25.TEX-MI::before {\n padding: 0.75em 0.847em 0.056em 0;\n content: \"%\";\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-c3A9::before {\n padding: 0.704em 0.722em 0 0;\n content: \"\\3A9\";\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-c3F::before {\n padding: 0.705em 0.472em 0 0;\n content: \"?\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2124.TEX-A::before {\n padding: 0.683em 0.667em 0 0;\n content: \"Z\";\n}\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2A::before {\n padding: 0.75em 0.5em 0 0;\n content: \"*\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c2191::before {\n padding: 0.694em 0.5em 0.193em 0;\n content: \"\\2191\";\n}\n\n\n\nmjx-stretchy-h.mjx-c23DF mjx-beg mjx-c::before {\n content: \"\\E152\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DF mjx-ext mjx-c::before {\n content: \"\\E154\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DF mjx-end mjx-c::before {\n content: \"\\E153\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DF mjx-mid mjx-c::before {\n content: \"\\E151\\E150\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DF > mjx-ext {\n width: 50%;\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c25A1.TEX-A::before {\n padding: 0.689em 0.778em 0 0;\n content: \"\\25A1\";\n}\n\nmjx-c.mjx-c2207::before {\n padding: 0.683em 0.833em 0.033em 0;\n content: \"\\2207\";\n}\n\n\n\nmjx-stretchy-v.mjx-c2193 mjx-ext mjx-c::before {\n content: \"\\23D0\";\n width: 0.667em;\n}\n\nmjx-stretchy-v.mjx-c2193 mjx-end mjx-c::before {\n content: \"\\2193\";\n padding: 0.6em 0.667em 0 0;\n}\n\nmjx-stretchy-v.mjx-c2193 > mjx-end {\n margin-top: -0.6em;\n}\n\nmjx-stretchy-v.mjx-c2193 > mjx-ext {\n border-bottom-width: 0.57em;\n}\n\nmjx-c.mjx-c2193::before {\n padding: 0.694em 0.5em 0.194em 0;\n content: \"\\2193\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D440.TEX-I::before {\n padding: 0.683em 1.051em 0 0;\n content: \"M\";\n}\n\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\nmjx-c.mjx-c1D44D.TEX-I::before {\n padding: 0.683em 0.723em 0 0;\n content: \"Z\";\n}\n\n\n\nmjx-c.mjx-c4C::before {\n padding: 0.683em 0.625em 0 0;\n content: \"L\";\n}\n\n\n\n\n\n\n\n\n\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-c.mjx-c2005::before {\n padding: 0 0.25em 0 0;\n content: \"\";\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\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-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\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-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\n\n\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-c2264::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2264\";\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-c.mjx-c1D45C.TEX-I::before {\n padding: 0.441em 0.485em 0.011em 0;\n content: \"o\";\n}\n\n\n\n\n\n\n\n\n\n\n\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-c2216::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\2216\";\n}\n\nmjx-c.mjx-c221E::before {\n padding: 0.442em 1em 0.011em 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-c27E8::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"\\27E8\";\n}\n\n\n\n\n\nmjx-c.mjx-c5A::before {\n padding: 0.683em 0.611em 0 0;\n content: \"Z\";\n}\n\nmjx-c.mjx-c70::before {\n padding: 0.442em 0.556em 0.194em 0;\n content: \"p\";\n}\n\nmjx-c.mjx-c56::before {\n padding: 0.683em 0.75em 0.022em 0;\n content: \"V\";\n}\n\nmjx-c.mjx-c22A5::before {\n padding: 0.668em 0.778em 0 0;\n content: \"\\22A5\";\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\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c1D412.TEX-B::before {\n padding: 0.697em 0.639em 0.011em 0;\n content: \"S\";\n}\n\nmjx-c.mjx-c1D427.TEX-B::before {\n padding: 0.45em 0.639em 0 0;\n content: \"n\";\n}\n\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-c1D6FE.TEX-I::before {\n padding: 0.441em 0.543em 0.216em 0;\n content: \"\\3B3\";\n}\n\nmjx-c.mjx-c1D700.TEX-I::before {\n padding: 0.452em 0.466em 0.022em 0;\n content: \"\\3B5\";\n}\n\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-c66::before {\n padding: 0.705em 0.372em 0 0;\n content: \"f\";\n}\n\nmjx-c.mjx-c68::before {\n padding: 0.694em 0.556em 0 0;\n content: \"h\";\n}\n\nmjx-c.mjx-c221E::before {\n padding: 0.442em 1em 0.011em 0;\n content: \"\\221E\";\n}\n\nmjx-c.mjx-c222A::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\222A\";\n}\n\nmjx-c.mjx-c2225::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\2225\";\n}\n\n\n\nmjx-c.mjx-c6A::before {\n padding: 0.669em 0.306em 0.205em 0;\n content: \"j\";\n}\n\nmjx-c.mjx-c65::before {\n padding: 0.448em 0.444em 0.011em 0;\n content: \"e\";\n}\n\nmjx-c.mjx-c25::before {\n padding: 0.75em 0.833em 0.056em 0;\n content: \"%\";\n}\n\n\n\nmjx-c.mjx-c79::before {\n padding: 0.431em 0.528em 0.204em 0;\n content: \"y\";\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-c221A.TEX-S3::before {\n padding: 1.45em 1.02em 0.95em 0;\n content: \"\\221A\";\n}\n\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-c2061::before {\n padding: 0 0 0 0;\n content: \"\";\n}\n\nmjx-c.mjx-c2265::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2265\";\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-c1D437.TEX-I::before {\n padding: 0.683em 0.828em 0 0;\n content: \"D\";\n}\n\nmjx-c.mjx-c49::before {\n padding: 0.683em 0.361em 0 0;\n content: \"I\";\n}\n\nmjx-c.mjx-c4A::before {\n padding: 0.683em 0.514em 0.022em 0;\n content: \"J\";\n}\n\nmjx-c.mjx-c54::before {\n padding: 0.677em 0.722em 0 0;\n content: \"T\";\n}\n\nmjx-c.mjx-c50::before {\n padding: 0.683em 0.681em 0 0;\n content: \"P\";\n}\n\nmjx-c.mjx-c52::before {\n padding: 0.683em 0.736em 0.022em 0;\n content: \"R\";\n}\n\nmjx-c.mjx-c58::before {\n padding: 0.683em 0.75em 0 0;\n content: \"X\";\n}\n\nmjx-c.mjx-c59::before {\n padding: 0.683em 0.75em 0 0;\n content: \"Y\";\n}\n\nmjx-c.mjx-c2228::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2228\";\n}\n\n\n\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\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-c1D456.TEX-I::before {\n padding: 0.661em 0.345em 0.011em 0;\n content: \"i\";\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-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\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-c1D7CE.TEX-B::before {\n padding: 0.654em 0.575em 0.01em 0;\n content: \"0\";\n}\n\nmjx-c.mjx-c1D41D.TEX-B::before {\n padding: 0.694em 0.639em 0.006em 0;\n content: \"d\";\n}\n\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-c78::before {\n padding: 0.431em 0.528em 0 0;\n content: \"x\";\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-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-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-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\nmjx-c.mjx-c3B::before {\n padding: 0.43em 0.278em 0.194em 0;\n content: \";\";\n}\n\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-c2260::before {\n padding: 0.716em 0.778em 0.215em 0;\n content: \"\\2260\";\n}\n\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-c.mjx-c1D452.TEX-I::before {\n padding: 0.442em 0.466em 0.011em 0;\n content: \"e\";\n}\n\nmjx-TeXAtom {\n display: inline-block;\n text-align: left;\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-c2208::before {\n padding: 0.54em 0.667em 0.04em 0;\n content: \"\\2208\";\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-c2216::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\2216\";\n}\n\nmjx-c.mjx-c2206::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\nmjx-c.mjx-c394::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\nmjx-c.mjx-c2223::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"\\2223\";\n}\n\nmjx-c.mjx-c3E::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \">\";\n}\n\nmjx-c.mjx-c2227::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2227\";\n}\n\nmjx-c.mjx-c57::before {\n padding: 0.683em 1.028em 0.022em 0;\n content: \"W\";\n}\n\nmjx-c.mjx-c2209::before {\n padding: 0.716em 0.667em 0.215em 0;\n content: \"\\2209\";\n}\n\nmjx-c.mjx-c1D447.TEX-I::before {\n padding: 0.677em 0.704em 0 0;\n content: \"T\";\n}\n\nmjx-c.mjx-c1D461.TEX-I::before {\n padding: 0.626em 0.361em 0.011em 0;\n content: \"t\";\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-c1D464.TEX-I::before {\n padding: 0.443em 0.716em 0.011em 0;\n content: \"w\";\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-c1D714.TEX-I::before {\n padding: 0.443em 0.622em 0.011em 0;\n content: \"\\3C9\";\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-c1D44A.TEX-I::before {\n padding: 0.683em 1.048em 0.022em 0;\n content: \"W\";\n}\n\nmjx-c.mjx-c2248::before {\n padding: 0.483em 0.778em 0 0;\n content: \"\\2248\";\n}\n\nmjx-c.mjx-c2220::before {\n padding: 0.694em 0.722em 0 0;\n content: \"\\2220\";\n}\n\nmjx-c.mjx-c25B3::before {\n padding: 0.716em 0.889em 0 0;\n content: \"\\25B3\";\n}\n\nmjx-c.mjx-c21D2::before {\n padding: 0.525em 1em 0.024em 0;\n content: \"\\21D2\";\n}\n\nmjx-c.mjx-c62::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"b\";\n}\n\nmjx-c.mjx-c77::before {\n padding: 0.431em 0.722em 0.011em 0;\n content: \"w\";\n}\n\nmjx-c.mjx-c1D451.TEX-I::before {\n padding: 0.694em 0.52em 0.01em 0;\n content: \"d\";\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-c.mjx-c4D::before {\n padding: 0.683em 0.917em 0 0;\n content: \"M\";\n}\n\nmjx-c.mjx-cF7::before {\n padding: 0.537em 0.778em 0.036em 0;\n content: \"\\F7\";\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-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-c6F::before {\n padding: 0.448em 0.5em 0.01em 0;\n content: \"o\";\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-c221A.TEX-S2::before {\n padding: 1.15em 1.02em 0.65em 0;\n content: \"\\221A\";\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-c1D450.TEX-I::before {\n padding: 0.442em 0.433em 0.011em 0;\n content: \"c\";\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-c1D442.TEX-I::before {\n padding: 0.704em 0.763em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c2192::before {\n padding: 0.511em 1em 0.011em 0;\n content: \"\\2192\";\n}\n\nmjx-c.mjx-c53::before {\n padding: 0.705em 0.556em 0.022em 0;\n content: \"S\";\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-c4E::before {\n padding: 0.683em 0.75em 0 0;\n content: \"N\";\n}\n\nmjx-c.mjx-c6C::before {\n padding: 0.694em 0.278em 0 0;\n content: \"l\";\n}\n\nmjx-c.mjx-c61::before {\n padding: 0.448em 0.5em 0.011em 0;\n content: \"a\";\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-mspace {\n display: inline-block;\n text-align: left;\n}\n\nmjx-stretchy-v.mjx-c7C mjx-ext mjx-c::before {\n content: \"\\2223\";\n width: 0.333em;\n}\n\nmjx-c.mjx-c221A::before {\n padding: 0.8em 0.853em 0.2em 0;\n content: \"\\221A\";\n}\n\nmjx-c.mjx-c3C::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \"<\";\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-c1D434.TEX-I::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c41::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c42::before {\n padding: 0.683em 0.708em 0 0;\n content: \"B\";\n}\n\nmjx-c.mjx-c44::before {\n padding: 0.683em 0.764em 0 0;\n content: \"D\";\n}\n\nmjx-c.mjx-c46::before {\n padding: 0.68em 0.653em 0 0;\n content: \"F\";\n}\n\nmjx-c.mjx-c47::before {\n padding: 0.705em 0.785em 0.022em 0;\n content: \"G\";\n}\n\nmjx-c.mjx-c45::before {\n padding: 0.68em 0.681em 0 0;\n content: \"E\";\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-c2032::before {\n padding: 0.56em 0.275em 0 0;\n content: \"\\2032\";\n}\n\nmjx-c.mjx-c21D4::before {\n padding: 0.526em 1em 0.025em 0;\n content: \"\\21D4\";\n}\n\nmjx-c.mjx-c2E::before {\n padding: 0.12em 0.278em 0 0;\n content: \".\";\n}\n\nmjx-c.mjx-cD7::before {\n padding: 0.491em 0.778em 0 0;\n content: \"\\D7\";\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-c1D449.TEX-I::before {\n padding: 0.683em 0.769em 0.022em 0;\n content: \"V\";\n}\n\nmjx-c.mjx-c1D441.TEX-I::before {\n padding: 0.683em 0.888em 0 0;\n content: \"N\";\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-c1D444.TEX-I::before {\n padding: 0.704em 0.791em 0.194em 0;\n content: \"Q\";\n}\n\nmjx-c.mjx-c1D45F.TEX-I::before {\n padding: 0.442em 0.451em 0.011em 0;\n content: \"r\";\n}\n\nmjx-c.mjx-c2F::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"/\";\n}\n\nmjx-c.mjx-c6E::before {\n padding: 0.442em 0.556em 0 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c1D460.TEX-I::before {\n padding: 0.442em 0.469em 0.01em 0;\n content: \"s\";\n}\n\nmjx-mfenced {\n display: inline-block;\n text-align: left;\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-c.mjx-c7C::before {\n padding: 0.75em 0.278em 0.249em 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-c1D465.TEX-I::before {\n padding: 0.442em 0.572em 0.011em 0;\n content: \"x\";\n}\n\nmjx-c.mjx-c1D462.TEX-I::before {\n padding: 0.442em 0.572em 0.011em 0;\n content: \"u\";\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-c1D467.TEX-I::before {\n padding: 0.442em 0.465em 0.011em 0;\n content: \"z\";\n}\n\nmjx-c.mjx-c43::before {\n padding: 0.705em 0.722em 0.021em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c48::before {\n padding: 0.683em 0.75em 0 0;\n content: \"H\";\n}\n\nmjx-c.mjx-c4F::before {\n padding: 0.705em 0.778em 0.022em 0;\n content: \"O\";\n}\n\nmjx-mtext {\n display: inline-block;\n text-align: left;\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\nmjx-c.mjx-c64::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"d\";\n}\n\nmjx-c.mjx-c6B::before {\n padding: 0.694em 0.528em 0 0;\n content: \"k\";\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-c1D41C.TEX-B::before {\n padding: 0.453em 0.511em 0.006em 0;\n content: \"c\";\n}\n\nmjx-c.mjx-c1D426.TEX-B::before {\n padding: 0.45em 0.958em 0 0;\n content: \"m\";\n}\n\nmjx-c.mjx-c1D7D0.TEX-B::before {\n padding: 0.654em 0.575em 0 0;\n content: \"2\";\n}\n\nmjx-c.mjx-c3D.TEX-B::before {\n padding: 0.393em 0.894em 0 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-c1D7D4.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"6\";\n}\n\nmjx-c.mjx-c2218.TEX-B::before {\n padding: 0.474em 0.575em 0 0;\n content: \"\\2218\";\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-c1D7CF.TEX-B::before {\n padding: 0.655em 0.575em 0 0;\n content: \"1\";\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-c2218::before {\n padding: 0.444em 0.5em 0 0;\n content: \"\\2218\";\n}\n\nmjx-c.mjx-c22C5::before {\n padding: 0.31em 0.278em 0 0;\n content: \"\\22C5\";\n}\n\nmjx-c.mjx-c28::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"(\";\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::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"\\2212\";\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-c.mjx-cB0::before {\n padding: 0.715em 0.5em 0 0;\n content: \"\\B0\";\n}\n\nmjx-msub {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mi {\n display: inline-block;\n text-align: left;\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-msup {\n display: inline-block;\n text-align: left;\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-c1D45D.TEX-I::before {\n padding: 0.442em 0.503em 0.194em 0;\n content: \"p\";\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-c1D454.TEX-I::before {\n padding: 0.442em 0.477em 0.205em 0;\n content: \"g\";\n}\n\nmjx-c.mjx-c210E.TEX-I::before {\n padding: 0.694em 0.576em 0.011em 0;\n content: \"h\";\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-c1D463.TEX-I::before {\n padding: 0.443em 0.485em 0.011em 0;\n content: \"v\";\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-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 {\n display: inline-block;\n}\n\nmjx-utext {\n display: inline-block;\n padding: .75em 0 .2em 0;\n}\n\nmjx-mn {\n display: inline-block;\n text-align: left;\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: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_AMS-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 11 */ {\n font-family: MJXTEX-C;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Calligraphic-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 12 */ {\n font-family: MJXTEX-CB;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Calligraphic-Bold.woff\") format(\"woff\");\n}\n\n@font-face /* 13 */ {\n font-family: MJXTEX-FR;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Fraktur-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 14 */ {\n font-family: MJXTEX-FRB;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Fraktur-Bold.woff\") format(\"woff\");\n}\n\n@font-face /* 15 */ {\n font-family: MJXTEX-SS;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 16 */ {\n font-family: MJXTEX-SSB;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Bold.woff\") format(\"woff\");\n}\n\n@font-face /* 17 */ {\n font-family: MJXTEX-SSI;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_SansSerif-Italic.woff\") format(\"woff\");\n}\n\n@font-face /* 18 */ {\n font-family: MJXTEX-SC;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Script-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 19 */ {\n font-family: MJXTEX-T;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Typewriter-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 20 */ {\n font-family: MJXTEX-V;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Regular.woff\") format(\"woff\");\n}\n\n@font-face /* 21 */ {\n font-family: MJXTEX-VB;\n src: url(\"https://cdn.jsdelivr.net/npm/mathjax@3/es5/output/chtml/fonts/woff-v2/MathJax_Vector-Bold.woff\") format(\"woff\");\n}\n\nmjx-c.mjx-c7B::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c30::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"0\";\n}\n\nmjx-c.mjx-c2C::before {\n padding: 0.121em 0.278em 0.194em 0;\n content: \",\";\n}\n\nmjx-c.mjx-c31::before {\n padding: 0.666em 0.5em 0 0;\n content: \"1\";\n}\n\nmjx-c.mjx-c32::before {\n padding: 0.666em 0.5em 0 0;\n content: \"2\";\n}\n\nmjx-c.mjx-c33::before {\n padding: 0.665em 0.5em 0.022em 0;\n content: \"3\";\n}\n\nmjx-c.mjx-c34::before {\n padding: 0.677em 0.5em 0 0;\n content: \"4\";\n}\n\nmjx-c.mjx-c35::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"5\";\n}\n\nmjx-c.mjx-c36::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"6\";\n}\n\nmjx-c.mjx-c37::before {\n padding: 0.676em 0.5em 0.022em 0;\n content: \"7\";\n}\n\nmjx-c.mjx-c38::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"8\";\n}\n\nmjx-c.mjx-c39::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"9\";\n}\n\nmjx-c.mjx-c7D::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"}\";\n}\n\nmjx-c.mjx-cB7::before {\n padding: 0.31em 0.278em 0 0;\n content: \"\\22C5\";\n}\n\nmjx-c.mjx-c3D::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"=\";\n}\n\nmjx-c.mjx-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\n}\n","actionData","errors"]

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