[{"_1":2,"_354":-5,"_355":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/fd7f9033-c219-4efe-a641-8ea04f4e65f5","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":16,"_17":18,"_83":84,"_163":164,"_31":239,"_312":313,"_350":351,"_352":353},"comments",[],"hasVideoHash",false,"isAiGenerated",true,"question",{"_19":20,"_21":22,"_23":24,"_25":26,"_57":58,"_76":77,"_78":79,"_80":81,"_82":16},"correctOptionId","347d8afe-d107-49ab-9b32-c7f8f5b95738","difficulty","","id","fd7f9033-c219-4efe-a641-8ea04f4e65f5","metadata",{"_27":28,"_53":54,"_55":56},"pd",{"_29":30,"_31":32,"_33":34,"_41":42,"_43":44,"_45":16,"_46":47,"_48":16,"_49":50,"_51":52},"area","Outros","tags",[],"subjects",[35],{"_23":36,"_37":38,"_39":40},669639,"name","Termodinâmica","alias","termodinamica","materialId","159714678","answerCount",1,"isIndexable","mainSubject",{"_23":36,"_37":38,"_39":40},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","159715648","options",[59,65,69,72],{"_23":60,"_61":62,"_63":64},"557d7cc8-ae12-48df-adea-70ccd38c7c1f","label","A","text","A transferência da capital, do império de Ngungunhana, de Mossurize para Mandlakazi",{"_23":66,"_61":67,"_63":68},"f19ed7de-1333-43d6-b279-3f41c55b70dd","B","o Mfecane",{"_23":20,"_61":70,"_63":71},"C","a segunda metade do século XIX",{"_23":73,"_61":74,"_63":75},"3de22123-69ba-49d4-bc00-70926d6258e5","D","nenhuma das respostas é correcta","solution_explanation","Os termos “Chopi” e “Ndau” não são designações ancestrais usadas pelos próprios grupos; foram rótulos etno-linguísticos difundidos por viajantes, missionários e pela administração colonial portuguesa quando esta começou a sintetizar e mapear as populações do sul-centro de Moçambique. Este esforço classificatório intensificou-se depois de 1850, sobretudo nas décadas de 1870-1890, acompanhando a disputa imperial luso-britânica e o avanço sobre o Império de Gaza. Por isso, os nomes surgem na documentação na segunda metade do século XIX.","statement","Os nomes Chopi e Ndau surgiram durante","status","published","hasRelatedVideo","relatedVideos",[85],{"_86":87,"_105":106,"_31":121,"_140":141,"_159":160},"content",{"_23":88,"_37":89,"_90":-5,"_91":92,"_93":94,"_95":-5,"_25":96,"_99":100,"_101":100,"_102":-5,"_103":104},"162087be-594f-460e-bbdd-a339ac2f10ad","Calor Latente - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f2b62fc2-7079-40e7-a5b5-c4a9769b205d","user_id",{"_97":98},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_107":108,"_114":115,"_116":117,"_118":119,"_6":120},"provider",{"_23":109,"_110":111,"_112":113},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","bf8aacba-3de9-4b10-961c-47ada80dfe8c","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/levels.m3u8",[122],{"_23":123,"_37":124,"_39":125,"_126":127,"_128":129,"_99":130,"_101":130,"_25":131,"_103":125,"_138":139},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9","2025-04-29T03:44:27.560682+00:00",{"_132":133,"_134":135,"_136":137},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_23":94,"_142":89,"_90":-5,"_143":144,"_145":146,"_6":-5,"_147":-5,"_107":146,"_148":149,"_118":-5,"_150":-5,"_151":-5,"_152":-5,"_153":-5,"_25":154,"_155":135,"_156":-5,"_80":157,"_99":158,"_101":158},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_97":98},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_23":123,"_37":124,"_39":125,"_126":127,"_128":129,"_99":130,"_101":130,"_25":161,"_103":125,"_138":162},{"_132":133,"_134":135,"_136":137},[],"similarQuestions",[165,196,216],{"_19":166,"_21":22,"_23":167,"_57":168,"_76":184,"_78":185,"_31":186},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[169,172,175,178,181],{"_23":170,"_61":62,"_63":171},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_23":173,"_61":67,"_63":174},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_23":176,"_61":70,"_63":177},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_23":179,"_61":74,"_63":180},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_23":166,"_61":182,"_63":183},"E","y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[187],{"_23":188,"_37":189,"_39":190,"_126":127,"_128":191,"_99":192,"_101":192,"_25":193,"_103":190},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_132":194,"_134":135,"_136":195},4,12302,{"_19":197,"_21":22,"_23":198,"_57":199,"_76":211,"_78":212,"_31":213},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[200,203,206,208],{"_23":201,"_61":62,"_63":202},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_23":204,"_61":67,"_63":205},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_23":197,"_61":70,"_63":207},"

Verdadeiro, falso, verdadeiro

",{"_23":209,"_61":74,"_63":210},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[214],{"_23":188,"_37":189,"_39":190,"_126":127,"_128":191,"_99":192,"_101":192,"_25":215,"_103":190},{"_132":194,"_134":135,"_136":195},{"_19":217,"_21":22,"_23":218,"_57":219,"_76":234,"_78":235,"_31":236},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[220,223,226,228,231],{"_23":221,"_61":62,"_63":222},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_23":224,"_61":67,"_63":225},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_23":217,"_61":70,"_63":227},"Indeterminado",{"_23":229,"_61":74,"_63":230},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_23":232,"_61":182,"_63":233},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[237],{"_23":188,"_37":189,"_39":190,"_126":127,"_128":191,"_99":192,"_101":192,"_25":238,"_103":190},{"_132":194,"_134":135,"_136":195},[240,242,249,259,266,273,275,283,289,294,300,307],{"_23":188,"_37":189,"_39":190,"_126":127,"_128":191,"_99":192,"_101":192,"_25":241,"_103":190},{"_132":194,"_134":135,"_136":195},{"_23":243,"_37":38,"_39":40,"_126":127,"_128":244,"_99":130,"_101":130,"_25":245,"_103":248},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_132":246,"_134":135,"_136":247},2,11846,"termodinamica-3",{"_23":250,"_37":251,"_39":252,"_126":127,"_128":253,"_99":254,"_101":254,"_25":255,"_103":258},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_132":256,"_134":135,"_136":257},5,30614,"engenharia-mecatronica-1",{"_23":260,"_37":261,"_39":262,"_126":127,"_128":250,"_99":192,"_101":192,"_25":263,"_103":265},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_132":256,"_134":135,"_136":264},25741,"mecanica-3",{"_23":244,"_37":267,"_39":268,"_126":127,"_128":253,"_99":254,"_101":254,"_25":269,"_103":272},"Engenharia Mecânica","engenharia-mecanica",{"_132":270,"_134":135,"_136":271},11,36318,"engenharia-mecanica-2",{"_23":123,"_37":124,"_39":125,"_126":127,"_128":129,"_99":130,"_101":130,"_25":274,"_103":125},{"_132":133,"_134":135,"_136":137},{"_23":276,"_37":277,"_39":278,"_126":127,"_128":-5,"_99":279,"_101":279,"_25":280,"_103":278},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_132":281,"_134":135,"_136":282},18,135489,{"_23":284,"_37":38,"_39":40,"_126":127,"_128":188,"_99":285,"_101":285,"_25":286,"_103":288},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_132":135,"_134":135,"_136":287},8597,"termodinamica-5",{"_23":191,"_37":290,"_39":291,"_126":127,"_128":253,"_99":254,"_101":254,"_25":292,"_103":293},"Engenharia de Petróleo","engenharia-de-petroleo",{"_132":256,"_134":135,"_136":195},"engenharia-de-petroleo-1",{"_23":129,"_37":295,"_39":296,"_126":127,"_128":276,"_99":254,"_101":254,"_25":297,"_103":299},"Física","fisica",{"_132":270,"_134":135,"_136":298},13777,"fisica-4",{"_23":253,"_37":301,"_39":302,"_126":127,"_128":-5,"_99":303,"_101":303,"_25":304,"_103":302},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_132":305,"_134":135,"_136":306},29,351586,{"_23":308,"_37":38,"_39":40,"_126":127,"_128":260,"_99":309,"_101":309,"_25":310,"_103":311},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_132":135,"_134":135,"_136":287},"termodinamica-4","tagsTree",[314,323],{"_23":276,"_37":277,"_39":278,"_126":127,"_128":-5,"_99":279,"_101":279,"_25":315,"_103":278,"_138":316},{"_132":281,"_134":135,"_136":282},[317],{"_23":129,"_37":295,"_39":296,"_126":127,"_128":276,"_99":254,"_101":254,"_25":318,"_103":299,"_138":319},{"_132":270,"_134":135,"_136":298},[320],{"_23":123,"_37":124,"_39":125,"_126":127,"_128":129,"_99":130,"_101":130,"_25":321,"_103":125,"_138":322},{"_132":133,"_134":135,"_136":137},[],{"_23":253,"_37":301,"_39":302,"_126":127,"_128":-5,"_99":303,"_101":303,"_25":324,"_103":302,"_138":325},{"_132":305,"_134":135,"_136":306},[326,335,341],{"_23":250,"_37":251,"_39":252,"_126":127,"_128":253,"_99":254,"_101":254,"_25":327,"_103":258,"_138":328},{"_132":256,"_134":135,"_136":257},[329],{"_23":260,"_37":261,"_39":262,"_126":127,"_128":250,"_99":192,"_101":192,"_25":330,"_103":265,"_138":331},{"_132":256,"_134":135,"_136":264},[332],{"_23":308,"_37":38,"_39":40,"_126":127,"_128":260,"_99":309,"_101":309,"_25":333,"_103":311,"_138":334},{"_132":135,"_134":135,"_136":287},[],{"_23":244,"_37":267,"_39":268,"_126":127,"_128":253,"_99":254,"_101":254,"_25":336,"_103":272,"_138":337},{"_132":270,"_134":135,"_136":271},[338],{"_23":243,"_37":38,"_39":40,"_126":127,"_128":244,"_99":130,"_101":130,"_25":339,"_103":248,"_138":340},{"_132":246,"_134":135,"_136":247},[],{"_23":191,"_37":290,"_39":291,"_126":127,"_128":253,"_99":254,"_101":254,"_25":342,"_103":293,"_138":343},{"_132":256,"_134":135,"_136":195},[344],{"_23":188,"_37":189,"_39":190,"_126":127,"_128":191,"_99":192,"_101":192,"_25":345,"_103":190,"_138":346},{"_132":194,"_134":135,"_136":195},[347],{"_23":284,"_37":38,"_39":40,"_126":127,"_128":188,"_99":285,"_101":285,"_25":348,"_103":288,"_138":349},{"_132":135,"_134":135,"_136":287},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários