[{"_1":2,"_370":-5,"_371":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/9bf5397e-6092-44bf-87d7-0dc77c50b22e?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_99":100,"_178":179,"_51":255,"_328":329,"_366":367,"_368":369},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":41,"_43":44,"_45":46,"_77":78,"_93":41,"_94":95,"_96":97,"_98":16},"correctOptionId","","difficulty","id","9bf5397e-6092-44bf-87d7-0dc77c50b22e","metadata",{"_47":48,"_73":74,"_75":76},"pd",{"_49":50,"_51":52,"_53":54,"_61":62,"_63":64,"_65":16,"_66":67,"_68":16,"_69":70,"_71":72},"area","Outros","tags",[],"subjects",[55],{"_43":56,"_57":58,"_59":60},669639,"name","Termodinâmica","alias","termodinamica","materialId","158821737","answerCount",1,"isIndexable","mainSubject",{"_43":56,"_57":58,"_59":60},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","158824866","options",[79,85,89],{"_43":80,"_81":82,"_83":84},"6b70ae89-d957-4a54-9f20-983872a20387","label","A","text","

Emissões de gases de efeito estufa

",{"_43":86,"_81":87,"_83":88},"076456f8-6697-4de3-a306-373711154630","B","

Consumo de água

",{"_43":90,"_81":91,"_83":92},"b762e63e-b244-44c2-bddc-1b1674542e30","C","

Desigualdade social

","solution_explanation","statement","

O que a geração de energia em pequenas comunidades contribui para reduzir?

","status","pending_classification","hasRelatedVideo","relatedVideos",[101],{"_102":103,"_121":122,"_51":137,"_156":157,"_174":175},"content",{"_43":104,"_57":105,"_106":-5,"_107":108,"_109":110,"_111":-5,"_45":112,"_115":116,"_117":116,"_118":-5,"_119":120},"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",{"_113":114},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_123":124,"_130":131,"_132":133,"_134":135,"_28":136},"provider",{"_43":125,"_126":127,"_128":129},"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",[138],{"_43":139,"_57":140,"_59":141,"_142":143,"_144":145,"_115":146,"_117":146,"_45":147,"_119":141,"_154":155},"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",{"_148":149,"_150":151,"_152":153},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":110,"_13":105,"_106":-5,"_158":159,"_160":161,"_28":-5,"_162":-5,"_123":161,"_163":164,"_134":-5,"_165":-5,"_166":-5,"_167":-5,"_168":-5,"_45":169,"_170":151,"_171":-5,"_96":172,"_115":173,"_117":173},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_113":114},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_43":139,"_57":140,"_59":141,"_142":143,"_144":145,"_115":146,"_117":146,"_45":176,"_119":141,"_154":177},{"_148":149,"_150":151,"_152":153},[],"similarQuestions",[180,212,232],{"_40":181,"_42":41,"_43":182,"_77":183,"_93":200,"_94":201,"_51":202},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[184,187,190,193,197],{"_43":185,"_81":82,"_83":186},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":188,"_81":87,"_83":189},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":191,"_81":91,"_83":192},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":194,"_81":195,"_83":196},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":181,"_81":198,"_83":199},"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

",[203],{"_43":204,"_57":205,"_59":206,"_142":143,"_144":207,"_115":208,"_117":208,"_45":209,"_119":206},"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",{"_148":210,"_150":151,"_152":211},4,12302,{"_40":213,"_42":41,"_43":214,"_77":215,"_93":227,"_94":228,"_51":229},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[216,219,222,224],{"_43":217,"_81":82,"_83":218},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":220,"_81":87,"_83":221},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":213,"_81":91,"_83":223},"

Verdadeiro, falso, verdadeiro

",{"_43":225,"_81":195,"_83":226},"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?

",[230],{"_43":204,"_57":205,"_59":206,"_142":143,"_144":207,"_115":208,"_117":208,"_45":231,"_119":206},{"_148":210,"_150":151,"_152":211},{"_40":233,"_42":41,"_43":234,"_77":235,"_93":250,"_94":251,"_51":252},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,244,247],{"_43":237,"_81":82,"_83":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":240,"_81":87,"_83":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":233,"_81":91,"_83":243},"Indeterminado",{"_43":245,"_81":195,"_83":246},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":248,"_81":198,"_83":249},"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????",[253],{"_43":204,"_57":205,"_59":206,"_142":143,"_144":207,"_115":208,"_117":208,"_45":254,"_119":206},{"_148":210,"_150":151,"_152":211},[256,258,265,275,282,289,291,299,305,310,316,323],{"_43":204,"_57":205,"_59":206,"_142":143,"_144":207,"_115":208,"_117":208,"_45":257,"_119":206},{"_148":210,"_150":151,"_152":211},{"_43":259,"_57":58,"_59":60,"_142":143,"_144":260,"_115":146,"_117":146,"_45":261,"_119":264},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_148":262,"_150":151,"_152":263},2,11846,"termodinamica-3",{"_43":266,"_57":267,"_59":268,"_142":143,"_144":269,"_115":270,"_117":270,"_45":271,"_119":274},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_148":272,"_150":151,"_152":273},5,30614,"engenharia-mecatronica-1",{"_43":276,"_57":277,"_59":278,"_142":143,"_144":266,"_115":208,"_117":208,"_45":279,"_119":281},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_148":272,"_150":151,"_152":280},25741,"mecanica-3",{"_43":260,"_57":283,"_59":284,"_142":143,"_144":269,"_115":270,"_117":270,"_45":285,"_119":288},"Engenharia Mecânica","engenharia-mecanica",{"_148":286,"_150":151,"_152":287},11,36318,"engenharia-mecanica-2",{"_43":139,"_57":140,"_59":141,"_142":143,"_144":145,"_115":146,"_117":146,"_45":290,"_119":141},{"_148":149,"_150":151,"_152":153},{"_43":292,"_57":293,"_59":294,"_142":143,"_144":-5,"_115":295,"_117":295,"_45":296,"_119":294},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_148":297,"_150":151,"_152":298},18,135489,{"_43":300,"_57":58,"_59":60,"_142":143,"_144":204,"_115":301,"_117":301,"_45":302,"_119":304},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_148":151,"_150":151,"_152":303},8597,"termodinamica-5",{"_43":207,"_57":306,"_59":307,"_142":143,"_144":269,"_115":270,"_117":270,"_45":308,"_119":309},"Engenharia de Petróleo","engenharia-de-petroleo",{"_148":272,"_150":151,"_152":211},"engenharia-de-petroleo-1",{"_43":145,"_57":311,"_59":312,"_142":143,"_144":292,"_115":270,"_117":270,"_45":313,"_119":315},"Física","fisica",{"_148":286,"_150":151,"_152":314},13777,"fisica-4",{"_43":269,"_57":317,"_59":318,"_142":143,"_144":-5,"_115":319,"_117":319,"_45":320,"_119":318},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_148":321,"_150":151,"_152":322},29,351586,{"_43":324,"_57":58,"_59":60,"_142":143,"_144":276,"_115":325,"_117":325,"_45":326,"_119":327},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_148":151,"_150":151,"_152":303},"termodinamica-4","tagsTree",[330,339],{"_43":292,"_57":293,"_59":294,"_142":143,"_144":-5,"_115":295,"_117":295,"_45":331,"_119":294,"_154":332},{"_148":297,"_150":151,"_152":298},[333],{"_43":145,"_57":311,"_59":312,"_142":143,"_144":292,"_115":270,"_117":270,"_45":334,"_119":315,"_154":335},{"_148":286,"_150":151,"_152":314},[336],{"_43":139,"_57":140,"_59":141,"_142":143,"_144":145,"_115":146,"_117":146,"_45":337,"_119":141,"_154":338},{"_148":149,"_150":151,"_152":153},[],{"_43":269,"_57":317,"_59":318,"_142":143,"_144":-5,"_115":319,"_117":319,"_45":340,"_119":318,"_154":341},{"_148":321,"_150":151,"_152":322},[342,351,357],{"_43":266,"_57":267,"_59":268,"_142":143,"_144":269,"_115":270,"_117":270,"_45":343,"_119":274,"_154":344},{"_148":272,"_150":151,"_152":273},[345],{"_43":276,"_57":277,"_59":278,"_142":143,"_144":266,"_115":208,"_117":208,"_45":346,"_119":281,"_154":347},{"_148":272,"_150":151,"_152":280},[348],{"_43":324,"_57":58,"_59":60,"_142":143,"_144":276,"_115":325,"_117":325,"_45":349,"_119":327,"_154":350},{"_148":151,"_150":151,"_152":303},[],{"_43":260,"_57":283,"_59":284,"_142":143,"_144":269,"_115":270,"_117":270,"_45":352,"_119":288,"_154":353},{"_148":286,"_150":151,"_152":287},[354],{"_43":259,"_57":58,"_59":60,"_142":143,"_144":260,"_115":146,"_117":146,"_45":355,"_119":264,"_154":356},{"_148":262,"_150":151,"_152":263},[],{"_43":207,"_57":306,"_59":307,"_142":143,"_144":269,"_115":270,"_117":270,"_45":358,"_119":309,"_154":359},{"_148":272,"_150":151,"_152":211},[360],{"_43":204,"_57":205,"_59":206,"_142":143,"_144":207,"_115":208,"_117":208,"_45":361,"_119":206,"_154":362},{"_148":210,"_150":151,"_152":211},[363],{"_43":300,"_57":58,"_59":60,"_142":143,"_144":204,"_115":301,"_117":301,"_45":364,"_119":304,"_154":365},{"_148":151,"_150":151,"_152":303},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários