[{"_1":2,"_326":-5,"_327":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/e6be1b75-87c0-4453-bc55-0abd0e3a819e","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_78":79,"_155":156,"_29":228,"_298":299,"_322":323,"_324":325},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_56":57,"_72":19,"_73":74,"_75":76,"_77":44},"correctOptionId","","difficulty","id","e6be1b75-87c0-4453-bc55-0abd0e3a819e","metadata",{"_25":26,"_52":53,"_54":55},"pd",{"_27":28,"_29":30,"_31":32,"_39":40,"_41":42,"_43":44,"_45":46,"_47":14,"_48":49,"_50":51},"area","Outros","tags",[],"subjects",[33],{"_21":34,"_35":36,"_37":38},669639,"name","Termodinâmica","alias","termodinamica","materialId","145668086","answerCount",1,"isIndexable",true,"mainSubject",{"_21":34,"_35":36,"_37":38},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","137810404","options",[58,64,68],{"_21":59,"_60":61,"_62":63},"41e23171-f805-4dd8-aa56-4d48dbcdc5c6","label","A","text","Propiedades intensivas e propriedades extensivas.",{"_21":65,"_60":66,"_62":67},"b4402686-e411-4370-8d3e-fdc30ca5f66b","B","Propiedades internas e propriedades externas.",{"_21":69,"_60":70,"_62":71},"4ba14c53-5084-4908-9c33-6ee9255fc3cb","C","Propiedades observadas direta ou indiretamente e resposta a uma influência infinitesimal.","solution_explanation","statement","

¿Cuál es la clasificación general de las propiedades de un sistema según el texto proporcionado?

","status","pending_classification","hasRelatedVideo","relatedVideos",[80],{"_81":82,"_100":101,"_29":116,"_135":136,"_154":117},"content",{"_21":83,"_35":84,"_85":-5,"_86":87,"_88":89,"_90":-5,"_23":91,"_94":95,"_96":95,"_97":-5,"_98":99},"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",{"_92":93},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_102":103,"_109":110,"_111":112,"_113":114,"_6":115},"provider",{"_21":104,"_105":106,"_107":108},"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",[117],{"_21":118,"_35":119,"_37":120,"_121":122,"_123":124,"_94":125,"_96":125,"_23":126,"_98":120,"_133":134},"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",{"_127":128,"_129":130,"_131":132},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_21":89,"_137":84,"_85":-5,"_138":139,"_140":141,"_6":-5,"_142":-5,"_102":141,"_143":144,"_113":-5,"_145":-5,"_146":-5,"_147":-5,"_148":-5,"_23":149,"_150":130,"_151":-5,"_75":152,"_94":153,"_96":153},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_92":93},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[157,189,207],{"_18":158,"_20":19,"_21":159,"_56":160,"_72":177,"_73":178,"_29":179},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[161,164,167,170,174],{"_21":162,"_60":61,"_62":163},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":165,"_60":66,"_62":166},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":168,"_60":70,"_62":169},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":171,"_60":172,"_62":173},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":158,"_60":175,"_62":176},"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

",[180],{"_21":181,"_35":182,"_37":183,"_121":122,"_123":184,"_94":185,"_96":185,"_23":186,"_98":183},"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",{"_127":187,"_129":130,"_131":188},4,12302,{"_18":190,"_20":19,"_21":191,"_56":192,"_72":204,"_73":205,"_29":206},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,201],{"_21":194,"_60":61,"_62":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":197,"_60":66,"_62":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":190,"_60":70,"_62":200},"

Verdadeiro, falso, verdadeiro

",{"_21":202,"_60":172,"_62":203},"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?

",[180],{"_18":208,"_20":19,"_21":209,"_56":210,"_72":225,"_73":226,"_29":227},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[211,214,217,219,222],{"_21":212,"_60":61,"_62":213},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":215,"_60":66,"_62":216},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":208,"_60":70,"_62":218},"Indeterminado",{"_21":220,"_60":172,"_62":221},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":223,"_60":175,"_62":224},"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????",[180],[180,229,236,246,253,260,261,269,275,280,286,293],{"_21":230,"_35":36,"_37":38,"_121":122,"_123":231,"_94":125,"_96":125,"_23":232,"_98":235},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_127":233,"_129":130,"_131":234},2,11846,"termodinamica-3",{"_21":237,"_35":238,"_37":239,"_121":122,"_123":240,"_94":241,"_96":241,"_23":242,"_98":245},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_127":243,"_129":130,"_131":244},5,30614,"engenharia-mecatronica-1",{"_21":247,"_35":248,"_37":249,"_121":122,"_123":237,"_94":185,"_96":185,"_23":250,"_98":252},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_127":243,"_129":130,"_131":251},25741,"mecanica-3",{"_21":231,"_35":254,"_37":255,"_121":122,"_123":240,"_94":241,"_96":241,"_23":256,"_98":259},"Engenharia Mecânica","engenharia-mecanica",{"_127":257,"_129":130,"_131":258},11,36318,"engenharia-mecanica-2",{"_21":118,"_35":119,"_37":120,"_121":122,"_123":124,"_94":125,"_96":125,"_23":126,"_98":120},{"_21":262,"_35":263,"_37":264,"_121":122,"_123":-5,"_94":265,"_96":265,"_23":266,"_98":264},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_127":267,"_129":130,"_131":268},18,135489,{"_21":270,"_35":36,"_37":38,"_121":122,"_123":181,"_94":271,"_96":271,"_23":272,"_98":274},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_127":130,"_129":130,"_131":273},8597,"termodinamica-5",{"_21":184,"_35":276,"_37":277,"_121":122,"_123":240,"_94":241,"_96":241,"_23":278,"_98":279},"Engenharia de Petróleo","engenharia-de-petroleo",{"_127":243,"_129":130,"_131":188},"engenharia-de-petroleo-1",{"_21":124,"_35":281,"_37":282,"_121":122,"_123":262,"_94":241,"_96":241,"_23":283,"_98":285},"Física","fisica",{"_127":257,"_129":130,"_131":284},13777,"fisica-4",{"_21":240,"_35":287,"_37":288,"_121":122,"_123":-5,"_94":289,"_96":289,"_23":290,"_98":288},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_127":291,"_129":130,"_131":292},29,351586,{"_21":294,"_35":36,"_37":38,"_121":122,"_123":247,"_94":295,"_96":295,"_23":296,"_98":297},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_127":130,"_129":130,"_131":273},"termodinamica-4","tagsTree",[300,304],{"_21":262,"_35":263,"_37":264,"_121":122,"_123":-5,"_94":265,"_96":265,"_23":266,"_98":264,"_133":301},[302],{"_21":124,"_35":281,"_37":282,"_121":122,"_123":262,"_94":241,"_96":241,"_23":283,"_98":285,"_133":303},[117],{"_21":240,"_35":287,"_37":288,"_121":122,"_123":-5,"_94":289,"_96":289,"_23":290,"_98":288,"_133":305},[306,312,316],{"_21":237,"_35":238,"_37":239,"_121":122,"_123":240,"_94":241,"_96":241,"_23":242,"_98":245,"_133":307},[308],{"_21":247,"_35":248,"_37":249,"_121":122,"_123":237,"_94":185,"_96":185,"_23":250,"_98":252,"_133":309},[310],{"_21":294,"_35":36,"_37":38,"_121":122,"_123":247,"_94":295,"_96":295,"_23":296,"_98":297,"_133":311},[],{"_21":231,"_35":254,"_37":255,"_121":122,"_123":240,"_94":241,"_96":241,"_23":256,"_98":259,"_133":313},[314],{"_21":230,"_35":36,"_37":38,"_121":122,"_123":231,"_94":125,"_96":125,"_23":232,"_98":235,"_133":315},[],{"_21":184,"_35":276,"_37":277,"_121":122,"_123":240,"_94":241,"_96":241,"_23":278,"_98":279,"_133":317},[318],{"_21":181,"_35":182,"_37":183,"_121":122,"_123":184,"_94":185,"_96":185,"_23":186,"_98":183,"_133":319},[320],{"_21":270,"_35":36,"_37":38,"_121":122,"_123":181,"_94":271,"_96":271,"_23":272,"_98":274,"_133":321},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários