[{"_1":2,"_346":-5,"_347":-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","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_99":100,"_175":176,"_51":248,"_318":319,"_342":343,"_344":345},"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":138},"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","similarQuestions",[177,209,227],{"_40":178,"_42":41,"_43":179,"_77":180,"_93":197,"_94":198,"_51":199},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[181,184,187,190,194],{"_43":182,"_81":82,"_83":183},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":185,"_81":87,"_83":186},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":188,"_81":91,"_83":189},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":191,"_81":192,"_83":193},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":178,"_81":195,"_83":196},"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

",[200],{"_43":201,"_57":202,"_59":203,"_142":143,"_144":204,"_115":205,"_117":205,"_45":206,"_119":203},"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":207,"_150":151,"_152":208},4,12302,{"_40":210,"_42":41,"_43":211,"_77":212,"_93":224,"_94":225,"_51":226},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[213,216,219,221],{"_43":214,"_81":82,"_83":215},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":217,"_81":87,"_83":218},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":210,"_81":91,"_83":220},"

Verdadeiro, falso, verdadeiro

",{"_43":222,"_81":192,"_83":223},"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?

",[200],{"_40":228,"_42":41,"_43":229,"_77":230,"_93":245,"_94":246,"_51":247},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[231,234,237,239,242],{"_43":232,"_81":82,"_83":233},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":235,"_81":87,"_83":236},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":228,"_81":91,"_83":238},"Indeterminado",{"_43":240,"_81":192,"_83":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":243,"_81":195,"_83":244},"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????",[200],[200,249,256,266,273,280,281,289,295,300,306,313],{"_43":250,"_57":58,"_59":60,"_142":143,"_144":251,"_115":146,"_117":146,"_45":252,"_119":255},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_148":253,"_150":151,"_152":254},2,11846,"termodinamica-3",{"_43":257,"_57":258,"_59":259,"_142":143,"_144":260,"_115":261,"_117":261,"_45":262,"_119":265},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_148":263,"_150":151,"_152":264},5,30614,"engenharia-mecatronica-1",{"_43":267,"_57":268,"_59":269,"_142":143,"_144":257,"_115":205,"_117":205,"_45":270,"_119":272},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_148":263,"_150":151,"_152":271},25741,"mecanica-3",{"_43":251,"_57":274,"_59":275,"_142":143,"_144":260,"_115":261,"_117":261,"_45":276,"_119":279},"Engenharia Mecânica","engenharia-mecanica",{"_148":277,"_150":151,"_152":278},11,36318,"engenharia-mecanica-2",{"_43":139,"_57":140,"_59":141,"_142":143,"_144":145,"_115":146,"_117":146,"_45":147,"_119":141},{"_43":282,"_57":283,"_59":284,"_142":143,"_144":-5,"_115":285,"_117":285,"_45":286,"_119":284},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_148":287,"_150":151,"_152":288},18,135489,{"_43":290,"_57":58,"_59":60,"_142":143,"_144":201,"_115":291,"_117":291,"_45":292,"_119":294},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_148":151,"_150":151,"_152":293},8597,"termodinamica-5",{"_43":204,"_57":296,"_59":297,"_142":143,"_144":260,"_115":261,"_117":261,"_45":298,"_119":299},"Engenharia de Petróleo","engenharia-de-petroleo",{"_148":263,"_150":151,"_152":208},"engenharia-de-petroleo-1",{"_43":145,"_57":301,"_59":302,"_142":143,"_144":282,"_115":261,"_117":261,"_45":303,"_119":305},"Física","fisica",{"_148":277,"_150":151,"_152":304},13777,"fisica-4",{"_43":260,"_57":307,"_59":308,"_142":143,"_144":-5,"_115":309,"_117":309,"_45":310,"_119":308},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_148":311,"_150":151,"_152":312},29,351586,{"_43":314,"_57":58,"_59":60,"_142":143,"_144":267,"_115":315,"_117":315,"_45":316,"_119":317},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_148":151,"_150":151,"_152":293},"termodinamica-4","tagsTree",[320,324],{"_43":282,"_57":283,"_59":284,"_142":143,"_144":-5,"_115":285,"_117":285,"_45":286,"_119":284,"_154":321},[322],{"_43":145,"_57":301,"_59":302,"_142":143,"_144":282,"_115":261,"_117":261,"_45":303,"_119":305,"_154":323},[138],{"_43":260,"_57":307,"_59":308,"_142":143,"_144":-5,"_115":309,"_117":309,"_45":310,"_119":308,"_154":325},[326,332,336],{"_43":257,"_57":258,"_59":259,"_142":143,"_144":260,"_115":261,"_117":261,"_45":262,"_119":265,"_154":327},[328],{"_43":267,"_57":268,"_59":269,"_142":143,"_144":257,"_115":205,"_117":205,"_45":270,"_119":272,"_154":329},[330],{"_43":314,"_57":58,"_59":60,"_142":143,"_144":267,"_115":315,"_117":315,"_45":316,"_119":317,"_154":331},[],{"_43":251,"_57":274,"_59":275,"_142":143,"_144":260,"_115":261,"_117":261,"_45":276,"_119":279,"_154":333},[334],{"_43":250,"_57":58,"_59":60,"_142":143,"_144":251,"_115":146,"_117":146,"_45":252,"_119":255,"_154":335},[],{"_43":204,"_57":296,"_59":297,"_142":143,"_144":260,"_115":261,"_117":261,"_45":298,"_119":299,"_154":337},[338],{"_43":201,"_57":202,"_59":203,"_142":143,"_144":204,"_115":205,"_117":205,"_45":206,"_119":203,"_154":339},[340],{"_43":290,"_57":58,"_59":60,"_142":143,"_144":201,"_115":291,"_117":291,"_45":292,"_119":294,"_154":341},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários