[{"_1":2,"_347":-5,"_348":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/fabd3c7b-eb76-4ed6-8b27-ee956ffad752","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":16,"_17":18,"_101":102,"_178":179,"_31":249,"_319":320,"_343":344,"_345":346},"comments",[],"hasVideoHash",false,"isAiGenerated",true,"question",{"_19":20,"_21":22,"_23":24,"_25":26,"_71":72,"_94":95,"_96":97,"_98":99,"_100":16},"correctOptionId","deea7b45-5c9b-47fa-8b83-d09d9259e7e7","difficulty","","id","fabd3c7b-eb76-4ed6-8b27-ee956ffad752","metadata",{"_27":28,"_53":54,"_67":68,"_69":70},"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","68745103","answerCount",1,"isIndexable","mainSubject",{"_23":36,"_37":38,"_39":40},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","runic",{"_55":56,"_58":44,"_59":60},"issues",[57],"has_unencoded_character","issuesCount","issuesDetectionTokenUsage",{"_61":62,"_63":64,"_65":66},"total",536,"prompt",527,"completion",9,"source","PD","externalId","160903585","options",[73,79,83,87,90],{"_23":74,"_75":76,"_77":78},"5d60db26-bb03-4854-a5cd-2093285a8ab8","label","A","text","reouve",{"_23":80,"_75":81,"_77":82},"7218cccb-fd63-4eb6-87a4-8c4374d09b20","B","esteja",{"_23":84,"_75":85,"_77":86},"1dac476c-698e-4abd-be7f-9e6c81099156","C","punha",{"_23":20,"_75":88,"_77":89},"D","tiver",{"_23":91,"_75":92,"_77":93},"c92f20cb-ca96-4226-9d45-e1e852614268","E","propor","solution_explanation","Em “quando o caminho for…”, o verbo “for” está no futuro do subjuntivo (1ª/3ª pessoa singular de “ser”): usado em orações condicionais introduzidas por “quando”, “se”, “logo que” etc. Entre as opções, apenas “tiver” (futuro do subjuntivo de “ter”: “quando eu/ele tiver”) apresenta o mesmo tempo e modo. As demais estão em tempos ou modos diferentes ou nem estão conjugadas.","statement","O verbo que está conjugado no mesmo tempo e modo de for, como no trecho “quando o caminho for de mão dupla confessional” (�. 53-54) é","status","published","hasRelatedVideo","relatedVideos",[103],{"_104":105,"_123":124,"_31":139,"_158":159,"_177":140},"content",{"_23":106,"_37":107,"_108":-5,"_109":110,"_111":112,"_113":-5,"_25":114,"_117":118,"_119":118,"_120":-5,"_121":122},"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",{"_115":116},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_125":126,"_132":133,"_134":135,"_136":137,"_6":138},"provider",{"_23":127,"_128":129,"_130":131},"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",[140],{"_23":141,"_37":142,"_39":143,"_144":145,"_146":147,"_117":148,"_119":148,"_25":149,"_121":143,"_156":157},"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",{"_150":151,"_152":153,"_154":155},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_23":112,"_160":107,"_108":-5,"_161":162,"_163":164,"_6":-5,"_165":-5,"_125":164,"_166":167,"_136":-5,"_168":-5,"_169":-5,"_170":-5,"_171":-5,"_25":172,"_173":153,"_174":-5,"_98":175,"_117":176,"_119":176},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_115":116},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[180,210,228],{"_19":181,"_21":22,"_23":182,"_71":183,"_94":198,"_96":199,"_31":200},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[184,187,190,193,196],{"_23":185,"_75":76,"_77":186},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_23":188,"_75":81,"_77":189},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_23":191,"_75":85,"_77":192},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_23":194,"_75":88,"_77":195},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_23":181,"_75":92,"_77":197},"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

",[201],{"_23":202,"_37":203,"_39":204,"_144":145,"_146":205,"_117":206,"_119":206,"_25":207,"_121":204},"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",{"_150":208,"_152":153,"_154":209},4,12302,{"_19":211,"_21":22,"_23":212,"_71":213,"_94":225,"_96":226,"_31":227},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[214,217,220,222],{"_23":215,"_75":76,"_77":216},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_23":218,"_75":81,"_77":219},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_23":211,"_75":85,"_77":221},"

Verdadeiro, falso, verdadeiro

",{"_23":223,"_75":88,"_77":224},"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?

",[201],{"_19":229,"_21":22,"_23":230,"_71":231,"_94":246,"_96":247,"_31":248},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[232,235,238,240,243],{"_23":233,"_75":76,"_77":234},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_23":236,"_75":81,"_77":237},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_23":229,"_75":85,"_77":239},"Indeterminado",{"_23":241,"_75":88,"_77":242},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_23":244,"_75":92,"_77":245},"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????",[201],[201,250,257,267,274,281,282,290,296,301,307,314],{"_23":251,"_37":38,"_39":40,"_144":145,"_146":252,"_117":148,"_119":148,"_25":253,"_121":256},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_150":254,"_152":153,"_154":255},2,11846,"termodinamica-3",{"_23":258,"_37":259,"_39":260,"_144":145,"_146":261,"_117":262,"_119":262,"_25":263,"_121":266},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_150":264,"_152":153,"_154":265},5,30614,"engenharia-mecatronica-1",{"_23":268,"_37":269,"_39":270,"_144":145,"_146":258,"_117":206,"_119":206,"_25":271,"_121":273},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_150":264,"_152":153,"_154":272},25741,"mecanica-3",{"_23":252,"_37":275,"_39":276,"_144":145,"_146":261,"_117":262,"_119":262,"_25":277,"_121":280},"Engenharia Mecânica","engenharia-mecanica",{"_150":278,"_152":153,"_154":279},11,36318,"engenharia-mecanica-2",{"_23":141,"_37":142,"_39":143,"_144":145,"_146":147,"_117":148,"_119":148,"_25":149,"_121":143},{"_23":283,"_37":284,"_39":285,"_144":145,"_146":-5,"_117":286,"_119":286,"_25":287,"_121":285},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_150":288,"_152":153,"_154":289},18,135489,{"_23":291,"_37":38,"_39":40,"_144":145,"_146":202,"_117":292,"_119":292,"_25":293,"_121":295},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_150":153,"_152":153,"_154":294},8597,"termodinamica-5",{"_23":205,"_37":297,"_39":298,"_144":145,"_146":261,"_117":262,"_119":262,"_25":299,"_121":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_150":264,"_152":153,"_154":209},"engenharia-de-petroleo-1",{"_23":147,"_37":302,"_39":303,"_144":145,"_146":283,"_117":262,"_119":262,"_25":304,"_121":306},"Física","fisica",{"_150":278,"_152":153,"_154":305},13777,"fisica-4",{"_23":261,"_37":308,"_39":309,"_144":145,"_146":-5,"_117":310,"_119":310,"_25":311,"_121":309},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_150":312,"_152":153,"_154":313},29,351586,{"_23":315,"_37":38,"_39":40,"_144":145,"_146":268,"_117":316,"_119":316,"_25":317,"_121":318},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_150":153,"_152":153,"_154":294},"termodinamica-4","tagsTree",[321,325],{"_23":283,"_37":284,"_39":285,"_144":145,"_146":-5,"_117":286,"_119":286,"_25":287,"_121":285,"_156":322},[323],{"_23":147,"_37":302,"_39":303,"_144":145,"_146":283,"_117":262,"_119":262,"_25":304,"_121":306,"_156":324},[140],{"_23":261,"_37":308,"_39":309,"_144":145,"_146":-5,"_117":310,"_119":310,"_25":311,"_121":309,"_156":326},[327,333,337],{"_23":258,"_37":259,"_39":260,"_144":145,"_146":261,"_117":262,"_119":262,"_25":263,"_121":266,"_156":328},[329],{"_23":268,"_37":269,"_39":270,"_144":145,"_146":258,"_117":206,"_119":206,"_25":271,"_121":273,"_156":330},[331],{"_23":315,"_37":38,"_39":40,"_144":145,"_146":268,"_117":316,"_119":316,"_25":317,"_121":318,"_156":332},[],{"_23":252,"_37":275,"_39":276,"_144":145,"_146":261,"_117":262,"_119":262,"_25":277,"_121":280,"_156":334},[335],{"_23":251,"_37":38,"_39":40,"_144":145,"_146":252,"_117":148,"_119":148,"_25":253,"_121":256,"_156":336},[],{"_23":205,"_37":297,"_39":298,"_144":145,"_146":261,"_117":262,"_119":262,"_25":299,"_121":300,"_156":338},[339],{"_23":202,"_37":203,"_39":204,"_144":145,"_146":205,"_117":206,"_119":206,"_25":207,"_121":204,"_156":340},[341],{"_23":291,"_37":38,"_39":40,"_144":145,"_146":202,"_117":292,"_119":292,"_25":293,"_121":295,"_156":342},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários