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

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

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

","longDescription","

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

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

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

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

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

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

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a) Okres długości fali odczytujemy na osi czasu, ponieważ jest to czas jednego pełnego drgnięcia. Możemy przyjąć czas pomiędzy np. maksymalnymi wzniesieniami, ponieważ musi być to czas pomiędzy

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\"R\";\n}\n\n\n\n\n\nmjx-c.mjx-c2A7D.TEX-A::before {\n padding: 0.636em 0.778em 0.138em 0;\n content: \"\\2A7D\";\n}\n\nmjx-c.mjx-c2205::before {\n padding: 0.772em 0.5em 0.078em 0;\n content: \"\\2205\";\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-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\n\n\nmjx-c.mjx-c77::before {\n padding: 0.431em 0.722em 0.011em 0;\n content: \"w\";\n}\n\nmjx-c.mjx-c2E::before {\n padding: 0.12em 0.278em 0 0;\n content: \".\";\n}\n\nmjx-c.mjx-c3F::before {\n padding: 0.705em 0.472em 0 0;\n content: \"?\";\n}\n\nmjx-c.mjx-c2218::before {\n padding: 0.444em 0.5em 0 0;\n content: \"\\2218\";\n}\n\nmjx-c.mjx-c48::before {\n padding: 0.683em 0.75em 0 0;\n content: \"H\";\n}\n\nmjx-c.mjx-c2192::before {\n padding: 0.511em 1em 0.011em 0;\n content: \"\\2192\";\n}\n\nmjx-c.mjx-cF7::before {\n padding: 0.537em 0.778em 0.036em 0;\n content: \"\\F7\";\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-c1D70C.TEX-I::before {\n padding: 0.442em 0.517em 0.216em 0;\n content: \"\\3C1\";\n}\n\nmjx-c.mjx-c6B::before {\n padding: 0.694em 0.528em 0 0;\n content: \"k\";\n}\n\nmjx-c.mjx-c67::before {\n padding: 0.453em 0.5em 0.206em 0;\n content: \"g\";\n}\n\nmjx-c.mjx-c50::before {\n padding: 0.683em 0.681em 0 0;\n content: \"P\";\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-c2A::before {\n padding: 0.75em 0.5em 0 0;\n content: \"*\";\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\nmjx-c.mjx-c53::before {\n padding: 0.705em 0.556em 0.022em 0;\n content: \"S\";\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-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-c1D464.TEX-I::before {\n padding: 0.443em 0.716em 0.011em 0;\n content: \"w\";\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-c7B.TEX-S3::before {\n padding: 1.45em 0.75em 0.949em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c46::before {\n padding: 0.68em 0.653em 0 0;\n content: \"F\";\n}\n\n\n\n\n\nmjx-stretchy-v.mjx-c7C mjx-ext mjx-c::before {\n content: \"\\2223\";\n width: 0.333em;\n}\n\nmjx-stretchy-v.mjx-c28 mjx-beg mjx-c::before {\n content: \"\\239B\";\n padding: 1.154em 0.875em 0.655em 0;\n}\n\nmjx-stretchy-v.mjx-c28 mjx-ext mjx-c::before {\n content: \"\\239C\";\n width: 0.875em;\n}\n\nmjx-stretchy-v.mjx-c28 mjx-end mjx-c::before {\n content: \"\\239D\";\n padding: 1.165em 0.875em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c28 > mjx-end {\n margin-top: -1.809em;\n}\n\nmjx-stretchy-v.mjx-c28 > mjx-ext {\n border-top-width: 1.779em;\n border-bottom-width: 1.779em;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-beg mjx-c::before {\n content: \"\\239E\";\n padding: 1.154em 0.875em 0.655em 0;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-ext mjx-c::before {\n content: \"\\239F\";\n width: 0.875em;\n}\n\nmjx-stretchy-v.mjx-c29 mjx-end mjx-c::before {\n content: \"\\23A0\";\n padding: 1.165em 0.875em 0.644em 0;\n}\n\nmjx-stretchy-v.mjx-c29 > mjx-end {\n margin-top: -1.809em;\n}\n\nmjx-stretchy-v.mjx-c29 > mjx-ext {\n border-top-width: 1.779em;\n border-bottom-width: 1.779em;\n}\n\nmjx-c.mjx-c41::before {\n padding: 0.716em 0.75em 0 0;\n content: \"A\";\n}\n\nmjx-c.mjx-c44::before {\n padding: 0.683em 0.764em 0 0;\n content: \"D\";\n}\n\nmjx-c.mjx-c49::before {\n padding: 0.683em 0.361em 0 0;\n content: \"I\";\n}\n\nmjx-c.mjx-c2061::before {\n padding: 0 0 0 0;\n content: \"\";\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-c2223::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"\\2223\";\n}\n\n\n\nmjx-c.mjx-cB0::before {\n padding: 0.715em 0.5em 0 0;\n content: \"\\B0\";\n}\n\n\n\nmjx-c.mjx-c73::before {\n padding: 0.448em 0.394em 0.011em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-c65::before {\n padding: 0.448em 0.444em 0.011em 0;\n content: \"e\";\n}\n\nmjx-c.mjx-c69::before {\n padding: 0.669em 0.278em 0 0;\n content: \"i\";\n}\n\nmjx-c.mjx-c6E::before {\n padding: 0.442em 0.556em 0 0;\n content: \"n\";\n}\n\nmjx-c.mjx-c75::before {\n padding: 0.442em 0.556em 0.011em 0;\n content: \"u\";\n}\n\nmjx-c.mjx-c70::before {\n padding: 0.442em 0.556em 0.194em 0;\n content: \"p\";\n}\n\nmjx-c.mjx-c74::before {\n padding: 0.615em 0.389em 0.01em 0;\n content: \"t\";\n}\n\nmjx-c.mjx-c7A::before {\n padding: 0.431em 0.444em 0 0;\n content: \"z\";\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-c1D45C.TEX-I::before {\n padding: 0.441em 0.485em 0.011em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c1D452.TEX-I::before {\n padding: 0.442em 0.466em 0.011em 0;\n content: \"e\";\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-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-c1D460.TEX-I::before {\n padding: 0.442em 0.469em 0.01em 0;\n content: \"s\";\n}\n\nmjx-c.mjx-c25::before {\n padding: 0.75em 0.833em 0.056em 0;\n content: \"%\";\n}\n\nmjx-c.mjx-c43::before {\n padding: 0.705em 0.722em 0.021em 0;\n content: \"C\";\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-c4E::before {\n padding: 0.683em 0.75em 0 0;\n content: \"N\";\n}\n\nmjx-c.mjx-c42::before {\n padding: 0.683em 0.708em 0 0;\n content: \"B\";\n}\n\nmjx-c.mjx-c72::before {\n padding: 0.442em 0.392em 0 0;\n content: \"r\";\n}\n\nmjx-c.mjx-c6F::before {\n padding: 0.448em 0.5em 0.01em 0;\n content: \"o\";\n}\n\nmjx-c.mjx-c6C::before {\n padding: 0.694em 0.278em 0 0;\n content: \"l\";\n}\n\nmjx-c.mjx-c64::before {\n padding: 0.694em 0.556em 0.011em 0;\n content: \"d\";\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-c1D442.TEX-I::before {\n padding: 0.704em 0.763em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c7C::before {\n padding: 0.75em 0.278em 0.249em 0;\n content: \"|\";\n}\n\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-c2115.TEX-A::before {\n padding: 0.683em 0.722em 0.02em 0;\n content: \"N\";\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-c1D456.TEX-I::before {\n padding: 0.661em 0.345em 0.011em 0;\n content: \"i\";\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-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-c2209::before {\n padding: 0.716em 0.667em 0.215em 0;\n content: \"\\2209\";\n}\n\nmjx-c.mjx-c2227::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2227\";\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-TeXAtom {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c3E::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \">\";\n}\n\nmjx-c.mjx-c3C::before {\n padding: 0.54em 0.778em 0.04em 0;\n content: \"<\";\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-c.mjx-c1D436.TEX-I::before {\n padding: 0.705em 0.76em 0.022em 0;\n content: \"C\";\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-c2260::before {\n padding: 0.716em 0.778em 0.215em 0;\n content: \"\\2260\";\n}\n\nmjx-c.mjx-c2228::before {\n padding: 0.598em 0.667em 0.022em 0;\n content: \"\\2228\";\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-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-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-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-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-c2206::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-c7B.TEX-S2::before {\n padding: 1.15em 0.667em 0.649em 0;\n content: \"{\";\n}\n\nmjx-c.mjx-c7D.TEX-S2::before {\n padding: 1.15em 0.667em 0.649em 0;\n content: \"}\";\n}\n\nmjx-c.mjx-c61::before {\n padding: 0.448em 0.5em 0.011em 0;\n content: \"a\";\n}\n\nmjx-c.mjx-c78::before {\n padding: 0.431em 0.528em 0 0;\n content: \"x\";\n}\n\nmjx-c.mjx-c4F::before {\n padding: 0.705em 0.778em 0.022em 0;\n content: \"O\";\n}\n\nmjx-c.mjx-c59::before {\n padding: 0.683em 0.75em 0 0;\n content: \"Y\";\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-c1D453.TEX-I::before {\n padding: 0.705em 0.55em 0.205em 0;\n content: \"f\";\n}\n\nmjx-c.mjx-c3B::before {\n padding: 0.43em 0.278em 0.194em 0;\n content: \";\";\n}\n\nmjx-c.mjx-c58::before {\n padding: 0.683em 0.75em 0 0;\n content: \"X\";\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-c2F::before {\n padding: 0.75em 0.5em 0.25em 0;\n content: \"/\";\n}\n\nmjx-c.mjx-c37::before {\n padding: 0.676em 0.5em 0.022em 0;\n content: \"7\";\n}\n\nmjx-mfenced {\n display: inline-block;\n text-align: left;\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-c28::before {\n padding: 0.75em 0.389em 0.25em 0;\n content: \"(\";\n}\n\nmjx-c.mjx-c2C::before {\n padding: 0.121em 0.278em 0.194em 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-c1D43E.TEX-I::before {\n padding: 0.683em 0.889em 0 0;\n content: \"K\";\n}\n\nmjx-c.mjx-c3A::before {\n padding: 0.43em 0.278em 0 0;\n content: \":\";\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-c1D45F.TEX-I::before {\n padding: 0.442em 0.451em 0.011em 0;\n content: \"r\";\n}\n\nmjx-c.mjx-c2032::before {\n padding: 0.56em 0.275em 0 0;\n content: \"\\2032\";\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-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-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-msqrt {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c.mjx-c221A::before {\n padding: 0.8em 0.853em 0.2em 0;\n content: \"\\221A\";\n}\n\nmjx-c.mjx-c39::before {\n padding: 0.666em 0.5em 0.022em 0;\n content: \"9\";\n}\n\nmjx-c.mjx-cB7::before {\n padding: 0.31em 0.278em 0 0;\n content: \"\\22C5\";\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 text-align: left;\n}\n\nmjx-mstyle {\n display: inline-block;\n}\n\nmjx-merror {\n display: inline-block;\n color: red;\n background-color: yellow;\n}\n\nmjx-mphantom {\n visibility: hidden;\n}\n\n_::-webkit-full-page-media, _:future, :root mjx-container {\n will-change: opacity;\n}\n\nmjx-math {\n display: inline-block;\n text-align: left;\n line-height: 0;\n text-indent: 0;\n font-style: normal;\n font-weight: normal;\n font-size: 100%;\n font-size-adjust: none;\n letter-spacing: normal;\n border-collapse: collapse;\n word-wrap: normal;\n word-spacing: normal;\n white-space: nowrap;\n direction: ltr;\n padding: 1px 0;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"] {\n display: block;\n text-align: center;\n margin: 1em 0;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"][width=\"full\"] {\n display: flex;\n}\n\nmjx-container[jax=\"CHTML\"][display=\"true\"] mjx-math {\n padding: 0;\n}\n\nmjx-container[jax=\"CHTML\"][justify=\"left\"] {\n text-align: left;\n}\n\nmjx-container[jax=\"CHTML\"][justify=\"right\"] {\n text-align: right;\n}\n\nmjx-semantics {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mrow {\n display: inline-block;\n text-align: left;\n}\n\nmjx-mn {\n display: inline-block;\n text-align: left;\n}\n\nmjx-c {\n display: inline-block;\n}\n\nmjx-utext {\n display: inline-block;\n padding: .75em 0 .2em 0;\n}\n\nmjx-mo {\n display: inline-block;\n text-align: left;\n}\n\nmjx-stretchy-h {\n display: inline-table;\n width: 100%;\n}\n\nmjx-stretchy-h > * {\n display: table-cell;\n width: 0;\n}\n\nmjx-stretchy-h > * > mjx-c {\n display: inline-block;\n transform: scalex(1.0000001);\n}\n\nmjx-stretchy-h > * > mjx-c::before {\n display: inline-block;\n width: initial;\n}\n\nmjx-stretchy-h > mjx-ext {\n /* IE */ overflow: hidden;\n /* others */ overflow: clip visible;\n width: 100%;\n}\n\nmjx-stretchy-h > mjx-ext > mjx-c::before {\n transform: scalex(500);\n}\n\nmjx-stretchy-h > mjx-ext > mjx-c {\n width: 0;\n}\n\nmjx-stretchy-h > mjx-beg > mjx-c {\n margin-right: -.1em;\n}\n\nmjx-stretchy-h > mjx-end > mjx-c {\n margin-left: -.1em;\n}\n\nmjx-stretchy-v {\n display: inline-block;\n}\n\nmjx-stretchy-v > * {\n display: block;\n}\n\nmjx-stretchy-v > mjx-beg {\n height: 0;\n}\n\nmjx-stretchy-v > mjx-end > mjx-c {\n display: block;\n}\n\nmjx-stretchy-v > * > mjx-c {\n transform: scaley(1.0000001);\n transform-origin: left center;\n overflow: hidden;\n}\n\nmjx-stretchy-v > mjx-ext {\n display: block;\n height: 100%;\n box-sizing: border-box;\n border: 0px solid transparent;\n /* IE */ overflow: hidden;\n /* others */ overflow: visible clip;\n}\n\nmjx-stretchy-v > mjx-ext > mjx-c::before {\n width: initial;\n box-sizing: border-box;\n}\n\nmjx-stretchy-v > mjx-ext > mjx-c {\n transform: scaleY(500) translateY(.075em);\n overflow: visible;\n}\n\nmjx-mark {\n display: inline-block;\n height: 0px;\n}\n\nmjx-mi {\n display: inline-block;\n text-align: left;\n}\n\nmjx-msub {\n display: inline-block;\n text-align: left;\n}\n\nmjx-msup {\n display: inline-block;\n text-align: left;\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-mspace {\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: 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