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Biologia na czasie 3. Maturalne karty pracy zakres rozszerzony to nieodzowny zeszyt ćwiczeń wydawnictwa Nowa Era, przeznaczony dla uczniów szkół ponadpodstawowych, a mianowicie liceum klasy 3 oraz technikum klasy 3. Ta publikacja wspiera naukę biologii na poziomie rozszerzonym, przynosząc wiele korzyści w przygotowaniach do matury. Na początku książki znajdziemy spis treści, który obejmuje m.in. tematy dotyczące organizmu człowieka jako funkcjonalnej całości, układu powłokowego, ruchu, układu pokarmowego, oddechowego, krążenia, nerwowego, hormonalnego, oraz wielu innych. Maturalne karty pracy zawierają zadania praktyczne oraz wskazówki do ich rozwiązywania, co stanowi znakomite uzupełnienie wiedzy zdobywanej podczas lekcji. Dodatkowo, część \"To było na maturze!\" pozwala uczniom prześledzić przykłady pytań maturalnych, co znacząco ułatwia przygotowanie do egzaminu. Jeśli potrzebujesz wsparcia, skorzystaj z odpowiedzi do zeszyt ćwiczeń oraz materiałów: odpowiedzi do podręcznika Biologia na czasie 3. Maturalne karty pracy zakres rozszerzony i \"PDF z odpowiedziami\". Pamiętajmy, że poszanowanie praw autorskich to klucz do legalnego użytkowania materiałów edukacyjnych.

","longDescription","

Biologia na czasie 3. Maturalne karty pracy zakres rozszerzony, zeszyt ćwiczeń opracowany przez wydawnictwo Nowa Era, stanowi nieodzowne narzędzie dla uczniów trzeciej klasy liceum i technikum, którzy realizują rozszerzony zakres biologii. Ta publikacja została stworzona z myślą o efektywnym przygotowaniu do matury oraz zrozumieniu złożonych biologicznych zagadnień.

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Już od pierwszych stron Biologia na czasie 3 wprowadza uczniów w fascynujący świat ludzkiego organizmu. Pierwsze rozdziały podręcznika koncentrują się na zrozumieniu człowieka jako skomplikowanej całości biologicznej. Tematy takie jak 'Miejsce człowieka w systemie klasyfikacji organizmów' czy 'Hierarchiczna budowa organizmu człowieka' stanowią solidną podstawę wiedzy, pomagając wyjaśnić zawiłości homeostazy oraz jej znaczenia w codziennym funkcjonowaniu.

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W dalszych częściach książki pojawia się szczegółowy opis układów ciała ludzkiego, począwszy od układu powłokowego, gdzie omówione są aspekty takie jak budowa i funkcje skóry. Publikacja szczegółowo wyjaśnia również zasady higieny oraz najczęstsze choroby skórne, co jest niezwykle istotne nie tylko w kontekście teoretycznym, ale i praktycznym. Kolejne rozdziały zagłębiają się w układ ruchu, omawiając jego budowę, funkcje oraz higienę, a także choroby, które mogą go dotknąć.

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Układ pokarmowy to kolejny istotny temat omawiany w książce. Zawarte w nim informacje odnośnie odżywiania, roli witamin i procesów trawienia pozwalają uczniom nie tylko zrozumieć zasady racjonalnego odżywiania, ale również dostrzec konsekwencje jego zaburzeń. Autorzy nie pomijają również chorób układu pokarmowego, co umożliwia kompleksowe spojrzenie na ten temat.

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Książka jest również nieocenioną pomocą dla tych, którzy chcieliby pogłębić swoją wiedzę o układzie krwionośnym i odpornościowym. Omawia szczegółowo skład i funkcje krwi, mechanizmy krążenia oraz funkcjonowanie układu limfatycznego, analizując jednocześnie choroby, które mogą dotykać tych mechanizmów. Wspomniane są także typy odporności i potencjalne dysfunkcje układu odpornościowego.

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Dzięki PDF z odpowiedziami do książki Biologia na czasie 3, uczniowie mają możliwość bieżącego sprawdzania swoich odpowiedzi i analizowania błędów, co znacznie przyspiesza proces nauki i przyswajania materiału. Zestaw maturalnych zadań oraz zamieszczone odpowiedzi są nieocenionym narzędziem w przygotowaniach do egzaminów końcowych. Serwis gotowiec.pl oferuje odpowiedzi do zeszytu ćwiczeń, co jest ogromnym wsparciem dla tych, którzy chcą mieć pewność, że poprawnie rozwiązali każde zadanie.

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Dzięki tej książce, uczniowie będą mogli nie tylko zdać maturę z biologii, ale przede wszystkim zrozumieć i polubić ten przedmiot, co zaowocuje lepszymi wynikami i głębszym zainteresowaniem naukami przyrodniczymi. Odrobione zadania do podręcznika Biologia na czasie 3 i gotowe odpowiedzi dostępne na gotowiec.pl to gwarancja sukcesu i pewność, że nauka jest nie tylko skuteczna, ale i przyjemna.

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3. Temat 7.2. Wykres przedstawia zależność między resorpcją jonów Na' w kanalikach nerkowych a zużyciem tlenu przez nerki. [601] nung anz 0,750 A. 0,600 mikroelementów, 0,500 B. makroelementów, 0375 0,250 0,125 Zadanie 3.1. (0-1) Odczytaj z wykresu, jakie jest przybliżone zużycie tlenu przez nerki przy resorpcji jonów Na w kanalikach nerkowych na poziomie 5 mmol/min. 100g. 0 Zadanie 3.2. (0-1) Korzystając z informacji zawartych na wykresie, uzasadnij, że resorpcja jonów Na' w kanalikach nerkowych odbywa się na drodze transportu czynnego. 15 20 10 resorpcja Na Immol/min 100 gl Zadanie 3.3. (0-1) Zaznacz poprawne dokończenie zdania. W kanalikach nerkowych, oprócz jonów","answers",[1299,1303,1304],{"_280":1300,"_1301":1302},1,"access","premium",{"_280":281,"_1301":1302},{"_280":1305,"_1301":1306},3,"logged_in","routes/$subjectSlug.$bookSlug.$pageNumber",{},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug",{"_1291":1311},{"_1293":1294,"_55":322,"_263":322,"_1295":1296,"_1297":1312},[1313,1314,1315],{"_280":1300,"_1301":1302},{"_280":281,"_1301":1302},{"_280":1305,"_1301":1306},"routes/$subjectSlug.$bookSlug.$pageNumber.$solutionSlug.$answerPosition",{"_1318":1319,"_1320":1321,"_1325":1326},"comments",[],"visit",{"_13":1322,"_15":1323,"_1324":39},"c74b5470-43c3-40d6-8157-390a9ad05a09","rUIEBB6W70uhxr7hNe6PIQ","visibleReCaptcha","excerpt",{"_1327":1328,"_1329":1330},"content","

3.1.

\r\n\r\n

Aby poprawnie odczytać wartość z wykresu należy na osi poziomej odnaleźć wartość 5, a następnie sprawdzić jakiej wartości na osi pionowej ona odpowiada.

\r\n\r\n

Przybliżone zużycie tlenu przez nerki przy

","stylesheet","mjx-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\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-c27E8.TEX-S1::before {\n padding: 0.85em 0.472em 0.35em 0;\n content: \"\\27E8\";\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\nmjx-c.mjx-c1D412.TEX-B::before {\n padding: 0.697em 0.639em 0.011em 0;\n content: \"S\";\n}\n\nmjx-c.mjx-c3D.TEX-B::before {\n padding: 0.393em 0.894em 0 0;\n content: \"=\";\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-c1D42A.TEX-B::before {\n padding: 0.45em 0.607em 0.194em 0;\n content: \"q\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c25B3::before {\n padding: 0.716em 0.889em 0 0;\n content: \"\\25B3\";\n}\n\nmjx-c.mjx-c1D706.TEX-I::before {\n padding: 0.694em 0.583em 0.012em 0;\n content: \"\\3BB\";\n}\n\n\n\nmjx-c.mjx-c2013::before {\n padding: 0.285em 0.5em 0 0;\n content: \"\\2013\";\n}\n\n\n\n\n\n\n\nmjx-c.mjx-c2197::before {\n padding: 0.72em 1em 0.195em 0;\n content: \"\\2197\";\n}\n\nmjx-c.mjx-c27E9.TEX-S2::before {\n padding: 1.15em 0.611em 0.649em 0;\n content: \"\\27E9\";\n}\n\nmjx-c.mjx-c2198::before {\n padding: 0.695em 1em 0.22em 0;\n content: \"\\2198\";\n}\n\nmjx-c.mjx-c1D402.TEX-B::before {\n padding: 0.697em 0.831em 0.011em 0;\n content: \"C\";\n}\n\n\n\n\n\n\n\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\nmjx-stretchy-h.mjx-c23DE mjx-beg mjx-c::before {\n content: \"\\E150\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DE mjx-ext mjx-c::before {\n content: \"\\E154\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DE mjx-end mjx-c::before {\n content: \"\\E151\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DE mjx-mid mjx-c::before {\n content: \"\\E153\\E152\";\n padding: 0.32em 0 0.2em 0;\n}\n\nmjx-stretchy-h.mjx-c23DE > mjx-ext {\n width: 50%;\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-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-c27E8::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"\\27E8\";\n}\n\nmjx-c.mjx-c27E9::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"\\27E9\";\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\n\n\n\n\n\n\n\n\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\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c21::before {\n padding: 0.716em 0.278em 0 0;\n content: \"!\";\n}\n\n\n\nmjx-c.mjx-c1D6FA.TEX-I::before {\n padding: 0.704em 0.786em 0 0;\n content: \"\\3A9\";\n}\n\n\n\n\n\n\n\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\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-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-c1D457.TEX-I::before {\n padding: 0.661em 0.412em 0.204em 0;\n content: \"j\";\n}\n\nmjx-c.mjx-c394::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\n}\n\n\n\n\n\nmjx-c.mjx-c3B::before {\n padding: 0.43em 0.278em 0.194em 0;\n content: \";\";\n}\n\nmjx-c.mjx-cB1::before {\n padding: 0.666em 0.778em 0 0;\n content: \"\\B1\";\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-c1D7D5.TEX-B::before {\n padding: 0.676em 0.575em 0.011em 0;\n content: \"7\";\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-c2212.TEX-B::before {\n padding: 0.281em 0.894em 0 0;\n content: \"\\2212\";\n}\n\nmjx-c.mjx-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\n}\n\nmjx-c.mjx-c1D409.TEX-B::before {\n padding: 0.686em 0.594em 0.011em 0;\n content: \"J\";\n}\n\n\n\nmjx-c.mjx-c1D41B.TEX-B::before {\n padding: 0.694em 0.639em 0.006em 0;\n content: \"b\";\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-c2115.TEX-A::before {\n padding: 0.683em 0.722em 0.02em 0;\n content: \"N\";\n}\n\nmjx-c.mjx-c1D438.TEX-I::before {\n padding: 0.68em 0.764em 0 0;\n content: \"E\";\n}\n\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-c54::before {\n padding: 0.677em 0.722em 0 0;\n content: \"T\";\n}\n\nmjx-c.mjx-cB0::before {\n padding: 0.715em 0.5em 0 0;\n content: \"\\B0\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c55::before {\n padding: 0.683em 0.75em 0.022em 0;\n content: \"U\";\n}\n\n\n\n\n\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-c2228::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2228\";\n}\n\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-c1D7D3.TEX-B::before {\n padding: 0.655em 0.575em 0.011em 0;\n content: \"5\";\n}\n\nmjx-c.mjx-c1D7D0.TEX-B::before {\n padding: 0.654em 0.575em 0 0;\n content: \"2\";\n}\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c1D447.TEX-I::before {\n padding: 0.677em 0.704em 0 0;\n content: \"T\";\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-stretchy-v.mjx-c5B mjx-beg mjx-c::before {\n content: \"\\23A1\";\n padding: 1.154em 0.667em 0.645em 0;\n}\n\nmjx-stretchy-v.mjx-c5B mjx-ext mjx-c::before {\n content: \"\\23A2\";\n width: 0.667em;\n}\n\nmjx-stretchy-v.mjx-c5B mjx-end mjx-c::before {\n content: \"\\23A3\";\n padding: 1.155em 0.667em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c5B > mjx-end {\n margin-top: -1.799em;\n}\n\nmjx-stretchy-v.mjx-c5B > mjx-ext {\n border-top-width: 1.769em;\n border-bottom-width: 1.769em;\n}\n\nmjx-stretchy-v.mjx-c5D mjx-beg mjx-c::before {\n content: \"\\23A4\";\n padding: 1.154em 0.667em 0.645em 0;\n}\n\nmjx-stretchy-v.mjx-c5D mjx-ext mjx-c::before {\n content: \"\\23A5\";\n width: 0.667em;\n}\n\nmjx-stretchy-v.mjx-c5D mjx-end mjx-c::before {\n content: \"\\23A6\";\n padding: 1.155em 0.667em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c5D > mjx-end {\n margin-top: -1.799em;\n}\n\nmjx-stretchy-v.mjx-c5D > mjx-ext {\n border-top-width: 1.769em;\n border-bottom-width: 1.769em;\n}\n\n\n\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\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\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\n\n\n\n\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-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-c21D4::before {\n padding: 0.526em 1em 0.025em 0;\n content: \"\\21D4\";\n}\n\n\n\n\n\nmjx-c.mjx-c1D44A.TEX-I::before {\n padding: 0.683em 1.048em 0.022em 0;\n content: \"W\";\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-c2A::before {\n padding: 0.75em 0.5em 0 0;\n content: \"*\";\n}\n\n\n\nmjx-c.mjx-c1D70E.TEX-I::before {\n padding: 0.431em 0.571em 0.011em 0;\n content: \"\\3C3\";\n}\n\nmjx-c.mjx-cAF::before {\n padding: 0.59em 0.5em 0 0;\n content: \"\\AF\";\n}\n\nmjx-c.mjx-c2026::before {\n padding: 0.12em 1.172em 0 0;\n content: \"\\2026\";\n}\n\nmjx-c.mjx-c1D459.TEX-I::before {\n padding: 0.694em 0.298em 0.011em 0;\n content: \"l\";\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-c2124.TEX-A::before {\n padding: 0.683em 0.667em 0 0;\n content: \"Z\";\n}\n\n\n\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-c1D7CE.TEX-B::before {\n padding: 0.654em 0.575em 0.01em 0;\n content: \"0\";\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-c1D420.TEX-B::before {\n padding: 0.455em 0.575em 0.201em 0;\n content: \"g\";\n}\n\n\n\n\n\n\n\n\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-c21D2::before {\n padding: 0.525em 1em 0.024em 0;\n content: \"\\21D2\";\n}\n\n\n\n\n\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-c1D444.TEX-I::before {\n padding: 0.704em 0.791em 0.194em 0;\n content: \"Q\";\n}\n\nmjx-c.mjx-c51::before {\n padding: 0.705em 0.778em 0.193em 0;\n content: \"Q\";\n}\n\nmjx-c.mjx-c2222.TEX-A::before {\n padding: 0.551em 0.722em 0.051em 0;\n content: \"\\2222\";\n}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nmjx-c.mjx-c68::before {\n padding: 0.694em 0.556em 0 0;\n content: \"h\";\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\n\n\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\n\n\n\n\nmjx-c.mjx-c50::before {\n padding: 0.683em 0.681em 0 0;\n content: \"P\";\n}\n\n\n\n\n\n\n\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-c1D45E.TEX-I::before {\n padding: 0.442em 0.46em 0.194em 0;\n content: \"q\";\n}\n\nmjx-c.mjx-c71::before {\n padding: 0.442em 0.528em 0.194em 0;\n content: \"q\";\n}\n\n\n\n\n\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-c2032::before {\n padding: 0.56em 0.275em 0 0;\n content: \"\\2032\";\n}\n\nmjx-c.mjx-c3E::before {\n padding: 0.54em 0.778em 0.04em 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-c2227::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2227\";\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-c5C::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"\\5C\";\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-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-c2205::before {\n padding: 0.772em 0.5em 0.078em 0;\n content: \"\\2205\";\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\nmjx-mtext {\n display: inline-block;\n text-align: left;\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-c2223::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"\\2223\";\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-c4D::before {\n padding: 0.683em 0.917em 0 0;\n content: \"M\";\n}\n\nmjx-c.mjx-c52::before {\n padding: 0.683em 0.736em 0.022em 0;\n content: \"R\";\n}\n\nmjx-c.mjx-c53::before {\n padding: 0.705em 0.556em 0.022em 0;\n content: \"S\";\n}\n\nmjx-c.mjx-c45::before {\n padding: 0.68em 0.681em 0 0;\n content: \"E\";\n}\n\nmjx-c.mjx-c5A::before {\n padding: 0.683em 0.611em 0 0;\n content: \"Z\";\n}\n\nmjx-c.mjx-c4A::before {\n padding: 0.683em 0.514em 0.022em 0;\n content: \"J\";\n}\n\nmjx-c.mjx-c57::before {\n padding: 0.683em 1.028em 0.022em 0;\n content: \"W\";\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-c3F::before {\n padding: 0.705em 0.472em 0 0;\n content: \"?\";\n}\n\nmjx-c.mjx-c1D43A.TEX-I::before {\n padding: 0.705em 0.786em 0.022em 0;\n content: \"G\";\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-c1D44D.TEX-I::before {\n padding: 0.683em 0.723em 0 0;\n content: \"Z\";\n}\n\nmjx-TeXAtom {\n display: inline-block;\n text-align: left;\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-c7C::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"|\";\n}\n\nmjx-c.mjx-c1D446.TEX-I::before {\n padding: 0.705em 0.645em 0.022em 0;\n content: \"S\";\n}\n\n\n\n\n\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-c70::before {\n padding: 0.442em 0.556em 0.194em 0;\n content: \"p\";\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-c2192::before {\n padding: 0.511em 1em 0.011em 0;\n content: \"\\2192\";\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-c1D436.TEX-I::before {\n padding: 0.705em 0.76em 0.022em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c21CC::before {\n padding: 0.671em 1em 0.011em 0;\n content: \"\\21CC\";\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-c2264::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2264\";\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-c4C::before {\n padding: 0.683em 0.625em 0 0;\n content: \"L\";\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-c73::before {\n padding: 0.448em 0.394em 0.011em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-c2061::before {\n padding: 0 0 0 0;\n content: \"\";\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\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-cF7::before {\n padding: 0.537em 0.778em 0.036em 0;\n content: \"\\F7\";\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-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\n\n\n\n\nmjx-c.mjx-cD7::before {\n padding: 0.491em 0.778em 0 0;\n content: \"\\D7\";\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-c1D463.TEX-I::before {\n padding: 0.443em 0.485em 0.011em 0;\n content: \"v\";\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-c1D439.TEX-I::before {\n padding: 0.68em 0.749em 0 0;\n content: \"F\";\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-c1D458.TEX-I::before {\n padding: 0.694em 0.521em 0.011em 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-c2248::before {\n padding: 0.483em 0.778em 0 0;\n content: \"\\2248\";\n}\n\nmjx-c.mjx-c2F::before {\n padding: 0.75em 0.5em 0.25em 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-c.mjx-c221A.TEX-S3::before {\n padding: 1.45em 1.02em 0.95em 0;\n content: \"\\221A\";\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-c1D45B.TEX-I::before {\n padding: 0.442em 0.6em 0.011em 0;\n content: \"n\";\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-c74::before {\n padding: 0.615em 0.389em 0.01em 0;\n content: \"t\";\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-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\nmjx-c.mjx-c72::before {\n padding: 0.442em 0.392em 0 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-c.mjx-c4E::before {\n padding: 0.683em 0.75em 0 0;\n content: \"N\";\n}\n\nmjx-c.mjx-c48::before {\n padding: 0.683em 0.75em 0 0;\n content: \"H\";\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-c4B::before {\n padding: 0.683em 0.778em 0 0;\n content: \"K\";\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-c43::before {\n padding: 0.705em 0.722em 0.021em 0;\n content: \"C\";\n}\n\nmjx-c.mjx-c49::before {\n padding: 0.683em 0.361em 0 0;\n content: \"I\";\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-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-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-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-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-c3A::before {\n padding: 0.43em 0.278em 0 0;\n content: \":\";\n}\n\nmjx-c.mjx-c2206::before {\n padding: 0.716em 0.833em 0 0;\n content: \"\\394\";\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-c7B.TEX-S4::before {\n padding: 1.75em 0.806em 1.249em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c2260::before {\n padding: 0.716em 0.778em 0.215em 0;\n content: \"\\2260\";\n}\n\nmjx-c.mjx-c3C::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \"<\";\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-c28::before {\n padding: 0.75em 0.389em 0.25em 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-c78::before {\n padding: 0.431em 0.528em 0 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\n\n\nmjx-c.mjx-c6C::before {\n padding: 0.694em 0.278em 0 0;\n content: \"l\";\n}\n\nmjx-c.mjx-c75::before {\n padding: 0.442em 0.556em 0.011em 0;\n content: \"u\";\n}\n\nmjx-c.mjx-c62::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"b\";\n}\n\nmjx-mspace {\n display: inline-block;\n text-align: left;\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-mfenced {\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-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-c1D450.TEX-I::before {\n padding: 0.442em 0.433em 0.011em 0;\n content: \"c\";\n}\n\nmjx-c.mjx-c221A::before {\n padding: 0.8em 0.853em 0.2em 0;\n content: \"\\221A\";\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-cB7::before {\n padding: 0.31em 0.278em 0 0;\n content: \"\\22C5\";\n}\n\nmjx-c.mjx-c37::before {\n padding: 0.676em 0.5em 0.022em 0;\n content: \"7\";\n}\n\nmjx-c.mjx-c67::before {\n padding: 0.453em 0.5em 0.206em 0;\n content: \"g\";\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-c38::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"8\";\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-cB0::before {\n padding: 0.715em 0.5em 0 0;\n content: \"\\B0\";\n}\n\nmjx-c.mjx-c2220::before {\n padding: 0.694em 0.722em 0 0;\n content: \"\\2220\";\n}\n\nmjx-c.mjx-c41::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c4F::before {\n padding: 0.705em 0.778em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c42::before {\n padding: 0.683em 0.708em 0 0;\n content: \"B\";\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-c1D434.TEX-I::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\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-c1D435.TEX-I::before {\n padding: 0.683em 0.759em 0 0;\n content: \"B\";\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-c25::before {\n padding: 0.75em 0.833em 0.056em 0;\n content: \"%\";\n}\n\nmjx-c.mjx-c39::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"9\";\n}\n\nmjx-c.mjx-c7A::before {\n padding: 0.431em 0.444em 0 0;\n content: \"z\";\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-c2E::before {\n padding: 0.12em 0.278em 0 0;\n content: \".\";\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-msub {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mi {\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-mn {\n display: inline-block;\n text-align: left;\n}\n\nmjx-msup {\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-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-c1D449.TEX-I::before {\n padding: 0.683em 0.769em 0.022em 0;\n content: \"V\";\n}\n\nmjx-c.mjx-c77::before {\n padding: 0.431em 0.722em 0.011em 0;\n content: \"w\";\n}\n\nmjx-c.mjx-c6F::before {\n padding: 0.448em 0.5em 0.01em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c64::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"d\";\n}\n\nmjx-c.mjx-c79::before {\n padding: 0.431em 0.528em 0.204em 0;\n content: \"y\";\n}\n\nmjx-c.mjx-c3D::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"=\";\n}\n\nmjx-c.mjx-c33::before {\n padding: 0.665em 0.5em 0.022em 0;\n content: \"3\";\n}\n\nmjx-c.mjx-c30::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"0\";\n}\n\nmjx-c.mjx-cA0::before {\n padding: 0 0.25em 0 0;\n content: \"\\A0\";\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-c2B::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"+\";\n}\n\nmjx-c.mjx-c6B::before {\n padding: 0.694em 0.528em 0 0;\n content: \"k\";\n}\n\nmjx-c.mjx-c61::before {\n padding: 0.448em 0.5em 0.011em 0;\n content: \"a\";\n}\n\nmjx-c.mjx-c69::before {\n padding: 0.669em 0.278em 0 0;\n content: \"i\";\n}\n\nmjx-c.mjx-c65::before {\n padding: 0.448em 0.444em 0.011em 0;\n content: \"e\";\n}\n\nmjx-c.mjx-c6E::before {\n padding: 0.442em 0.556em 0 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c35::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"5\";\n}\n\nmjx-c.mjx-c2212::before {\n padding: 0.583em 0.778em 0.082em 0;\n content: \"\\2212\";\n}\n\nmjx-c.mjx-c1D45A.TEX-I::before {\n padding: 0.442em 0.878em 0.011em 0;\n 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