[{"_1":2,"_324":-5,"_325":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/d2cfd68a-b81d-4b96-9b8c-b18025f86525?video=true","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_77":78,"_153":154,"_29":226,"_296":297,"_320":321,"_322":323},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":21,"_22":23,"_24":25,"_56":57,"_71":21,"_72":73,"_74":75,"_76":44},"correctOptionId","a804f38a-3010-4b2b-8efc-ea60efa43808","difficulty","","id","d2cfd68a-b81d-4b96-9b8c-b18025f86525","metadata",{"_26":27,"_52":53,"_54":55},"pd",{"_28":-5,"_29":30,"_31":32,"_39":40,"_41":42,"_43":44,"_45":46,"_47":14,"_48":49,"_50":51},"area","tags",[],"subjects",[33],{"_22":34,"_35":36,"_37":38},669639,"name","Termodinâmica","alias","termodinamica","materialId","122612960","answerCount",1,"isIndexable",true,"mainSubject",{"_22":34,"_35":36,"_37":38},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122745867","options",[58,63,67],{"_22":19,"_59":60,"_61":62},"label","A","text","

The decomposition of organic matter in anaerobic conditions.

",{"_22":64,"_59":65,"_61":66},"72a736c8-3ff2-4c75-8bd8-670694ab3fe1","B","

The decomposition of metallic carbides by water.

",{"_22":68,"_59":69,"_61":70},"bb00b21b-4565-4877-a801-1c36b84ac376","C","

The combination of simple and compound substances in the deepest regions of the earth's crust.

","solution_explanation","statement","

What is the most accepted theory about the origin of petroleum?

","status","pending_classification","hasRelatedVideo","relatedVideos",[79],{"_80":81,"_99":100,"_29":115,"_134":135,"_152":116},"content",{"_22":82,"_35":83,"_84":-5,"_85":86,"_87":88,"_89":-5,"_24":90,"_93":94,"_95":94,"_96":-5,"_97":98},"17af1394-ae27-4d49-bad0-6dfbc097b00c","Termologia e Termometria","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","e0ab6092-71a6-4b78-8930-845a08dc3495","user_id",{"_91":92},"external_id","2594","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","termologia-e-termometria","prometheusData",{"_101":102,"_108":109,"_110":111,"_112":113,"_6":114},"provider",{"_22":103,"_104":105,"_106":107},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","b502b486-7b81-4345-a10c-e462c3043183","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/b502b486-7b81-4345-a10c-e462c3043183/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/b502b486-7b81-4345-a10c-e462c3043183/levels.m3u8",[116],{"_22":117,"_35":118,"_37":119,"_120":121,"_122":123,"_93":124,"_95":124,"_24":125,"_97":119,"_132":133},"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",{"_126":127,"_128":129,"_130":131},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_22":88,"_136":83,"_84":-5,"_137":129,"_138":139,"_6":-5,"_140":-5,"_101":139,"_141":142,"_112":-5,"_143":-5,"_144":-5,"_145":-5,"_146":-5,"_24":147,"_148":129,"_149":-5,"_74":150,"_93":151,"_95":151},"title","duration","source_type","prometheus","iframe_url","provider_video_id","a58dea8f-5fbf-4462-bf04-83e715504a2f","format","quality","file_path","file_size",{"_91":92},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[155,187,205],{"_18":156,"_20":21,"_22":157,"_56":158,"_71":175,"_72":176,"_29":177},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[159,162,165,168,172],{"_22":160,"_59":60,"_61":161},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":163,"_59":65,"_61":164},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":166,"_59":69,"_61":167},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":169,"_59":170,"_61":171},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_22":156,"_59":173,"_61":174},"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

",[178],{"_22":179,"_35":180,"_37":181,"_120":121,"_122":182,"_93":183,"_95":183,"_24":184,"_97":181},"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",{"_126":185,"_128":129,"_130":186},4,12302,{"_18":188,"_20":21,"_22":189,"_56":190,"_71":202,"_72":203,"_29":204},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[191,194,197,199],{"_22":192,"_59":60,"_61":193},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":195,"_59":65,"_61":196},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":188,"_59":69,"_61":198},"

Verdadeiro, falso, verdadeiro

",{"_22":200,"_59":170,"_61":201},"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?

",[178],{"_18":206,"_20":21,"_22":207,"_56":208,"_71":223,"_72":224,"_29":225},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[209,212,215,217,220],{"_22":210,"_59":60,"_61":211},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_22":213,"_59":65,"_61":214},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_22":206,"_59":69,"_61":216},"Indeterminado",{"_22":218,"_59":170,"_61":219},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_22":221,"_59":173,"_61":222},"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????",[178],[178,227,234,244,251,258,259,267,273,278,284,291],{"_22":228,"_35":36,"_37":38,"_120":121,"_122":229,"_93":124,"_95":124,"_24":230,"_97":233},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_126":231,"_128":129,"_130":232},2,11846,"termodinamica-3",{"_22":235,"_35":236,"_37":237,"_120":121,"_122":238,"_93":239,"_95":239,"_24":240,"_97":243},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_126":241,"_128":129,"_130":242},5,30614,"engenharia-mecatronica-1",{"_22":245,"_35":246,"_37":247,"_120":121,"_122":235,"_93":183,"_95":183,"_24":248,"_97":250},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_126":241,"_128":129,"_130":249},25741,"mecanica-3",{"_22":229,"_35":252,"_37":253,"_120":121,"_122":238,"_93":239,"_95":239,"_24":254,"_97":257},"Engenharia Mecânica","engenharia-mecanica",{"_126":255,"_128":129,"_130":256},11,36318,"engenharia-mecanica-2",{"_22":117,"_35":118,"_37":119,"_120":121,"_122":123,"_93":124,"_95":124,"_24":125,"_97":119},{"_22":260,"_35":261,"_37":262,"_120":121,"_122":-5,"_93":263,"_95":263,"_24":264,"_97":262},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_126":265,"_128":129,"_130":266},18,135489,{"_22":268,"_35":36,"_37":38,"_120":121,"_122":179,"_93":269,"_95":269,"_24":270,"_97":272},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_126":129,"_128":129,"_130":271},8597,"termodinamica-5",{"_22":182,"_35":274,"_37":275,"_120":121,"_122":238,"_93":239,"_95":239,"_24":276,"_97":277},"Engenharia de Petróleo","engenharia-de-petroleo",{"_126":241,"_128":129,"_130":186},"engenharia-de-petroleo-1",{"_22":123,"_35":279,"_37":280,"_120":121,"_122":260,"_93":239,"_95":239,"_24":281,"_97":283},"Física","fisica",{"_126":255,"_128":129,"_130":282},13777,"fisica-4",{"_22":238,"_35":285,"_37":286,"_120":121,"_122":-5,"_93":287,"_95":287,"_24":288,"_97":286},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_126":289,"_128":129,"_130":290},29,351586,{"_22":292,"_35":36,"_37":38,"_120":121,"_122":245,"_93":293,"_95":293,"_24":294,"_97":295},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_126":129,"_128":129,"_130":271},"termodinamica-4","tagsTree",[298,302],{"_22":260,"_35":261,"_37":262,"_120":121,"_122":-5,"_93":263,"_95":263,"_24":264,"_97":262,"_132":299},[300],{"_22":123,"_35":279,"_37":280,"_120":121,"_122":260,"_93":239,"_95":239,"_24":281,"_97":283,"_132":301},[116],{"_22":238,"_35":285,"_37":286,"_120":121,"_122":-5,"_93":287,"_95":287,"_24":288,"_97":286,"_132":303},[304,310,314],{"_22":235,"_35":236,"_37":237,"_120":121,"_122":238,"_93":239,"_95":239,"_24":240,"_97":243,"_132":305},[306],{"_22":245,"_35":246,"_37":247,"_120":121,"_122":235,"_93":183,"_95":183,"_24":248,"_97":250,"_132":307},[308],{"_22":292,"_35":36,"_37":38,"_120":121,"_122":245,"_93":293,"_95":293,"_24":294,"_97":295,"_132":309},[],{"_22":229,"_35":252,"_37":253,"_120":121,"_122":238,"_93":239,"_95":239,"_24":254,"_97":257,"_132":311},[312],{"_22":228,"_35":36,"_37":38,"_120":121,"_122":229,"_93":124,"_95":124,"_24":230,"_97":233,"_132":313},[],{"_22":182,"_35":274,"_37":275,"_120":121,"_122":238,"_93":239,"_95":239,"_24":276,"_97":277,"_132":315},[316],{"_22":179,"_35":180,"_37":181,"_120":121,"_122":182,"_93":183,"_95":183,"_24":184,"_97":181,"_132":317},[318],{"_22":268,"_35":36,"_37":38,"_120":121,"_122":179,"_93":269,"_95":269,"_24":270,"_97":272,"_132":319},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários