[{"_1":2,"_346":-5,"_347":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/d0860254-0e72-4cd8-8544-7124fdf617e3","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_73":74,"_153":154,"_28":231,"_304":305,"_342":343,"_344":345},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_55":56,"_67":19,"_68":69,"_70":71,"_72":43},"correctOptionId","","difficulty","id","d0860254-0e72-4cd8-8544-7124fdf617e3","metadata",{"_25":26,"_51":52,"_53":54},"pd",{"_27":-5,"_28":29,"_30":31,"_38":39,"_40":41,"_42":43,"_44":45,"_46":14,"_47":48,"_49":50},"area","tags",[],"subjects",[32],{"_21":33,"_34":35,"_36":37},669639,"name","Termodinâmica","alias","termodinamica","materialId","124607441","answerCount",1,"isIndexable",true,"mainSubject",{"_21":33,"_34":35,"_36":37},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","124607473","options",[57,63],{"_21":58,"_59":60,"_61":62},"375976d3-7143-4268-923a-1eff004abfd3","label","A","text","El flujo másico en \text{Kg/s}",{"_21":64,"_59":65,"_61":66},"7d7e5d61-fc63-486b-8eaa-3120e0d81751","B","La velocidad de la manguera en \text{m/s}","solution_explanation","statement","Por una manguera de jardín de 2.50 \\, \text{cm} de diámetro interior circula agua a 20^{\text{°C}} y 0.20 \\, \text{Mpa} y sale por una tobera de 0.60 \\, \text{cm} de dímetro de salida. La velocidad de salida es 6.0 \\, \text{m/s}, determínese:

","status","pending_classification","hasRelatedVideo","relatedVideos",[75],{"_76":77,"_95":96,"_28":111,"_130":131,"_149":150},"content",{"_21":78,"_34":79,"_80":-5,"_81":82,"_83":84,"_85":-5,"_23":86,"_89":90,"_91":90,"_92":-5,"_93":94},"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",{"_87":88},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_97":98,"_104":105,"_106":107,"_108":109,"_6":110},"provider",{"_21":99,"_100":101,"_102":103},"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",[112],{"_21":113,"_34":114,"_36":115,"_116":117,"_118":119,"_89":120,"_91":120,"_23":121,"_93":115,"_128":129},"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",{"_122":123,"_124":125,"_126":127},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_21":84,"_132":79,"_80":-5,"_133":134,"_135":136,"_6":-5,"_137":-5,"_97":136,"_138":139,"_108":-5,"_140":-5,"_141":-5,"_142":-5,"_143":-5,"_23":144,"_145":125,"_146":-5,"_70":147,"_89":148,"_91":148},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_87":88},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_21":113,"_34":114,"_36":115,"_116":117,"_118":119,"_89":120,"_91":120,"_23":151,"_93":115,"_128":152},{"_122":123,"_124":125,"_126":127},[],"similarQuestions",[155,188,208],{"_18":156,"_20":19,"_21":157,"_55":158,"_67":176,"_68":177,"_28":178},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[159,162,165,169,173],{"_21":160,"_59":60,"_61":161},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":163,"_59":65,"_61":164},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":166,"_59":167,"_61":168},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_21":170,"_59":171,"_61":172},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":156,"_59":174,"_61":175},"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

",[179],{"_21":180,"_34":181,"_36":182,"_116":117,"_118":183,"_89":184,"_91":184,"_23":185,"_93":182},"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",{"_122":186,"_124":125,"_126":187},4,12302,{"_18":189,"_20":19,"_21":190,"_55":191,"_67":203,"_68":204,"_28":205},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[192,195,198,200],{"_21":193,"_59":60,"_61":194},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":196,"_59":65,"_61":197},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":189,"_59":167,"_61":199},"

Verdadeiro, falso, verdadeiro

",{"_21":201,"_59":171,"_61":202},"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?

",[206],{"_21":180,"_34":181,"_36":182,"_116":117,"_118":183,"_89":184,"_91":184,"_23":207,"_93":182},{"_122":186,"_124":125,"_126":187},{"_18":209,"_20":19,"_21":210,"_55":211,"_67":226,"_68":227,"_28":228},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[212,215,218,220,223],{"_21":213,"_59":60,"_61":214},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":216,"_59":65,"_61":217},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":209,"_59":167,"_61":219},"Indeterminado",{"_21":221,"_59":171,"_61":222},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":224,"_59":174,"_61":225},"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????",[229],{"_21":180,"_34":181,"_36":182,"_116":117,"_118":183,"_89":184,"_91":184,"_23":230,"_93":182},{"_122":186,"_124":125,"_126":187},[232,234,241,251,258,265,267,275,281,286,292,299],{"_21":180,"_34":181,"_36":182,"_116":117,"_118":183,"_89":184,"_91":184,"_23":233,"_93":182},{"_122":186,"_124":125,"_126":187},{"_21":235,"_34":35,"_36":37,"_116":117,"_118":236,"_89":120,"_91":120,"_23":237,"_93":240},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_122":238,"_124":125,"_126":239},2,11846,"termodinamica-3",{"_21":242,"_34":243,"_36":244,"_116":117,"_118":245,"_89":246,"_91":246,"_23":247,"_93":250},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_122":248,"_124":125,"_126":249},5,30614,"engenharia-mecatronica-1",{"_21":252,"_34":253,"_36":254,"_116":117,"_118":242,"_89":184,"_91":184,"_23":255,"_93":257},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_122":248,"_124":125,"_126":256},25741,"mecanica-3",{"_21":236,"_34":259,"_36":260,"_116":117,"_118":245,"_89":246,"_91":246,"_23":261,"_93":264},"Engenharia Mecânica","engenharia-mecanica",{"_122":262,"_124":125,"_126":263},11,36318,"engenharia-mecanica-2",{"_21":113,"_34":114,"_36":115,"_116":117,"_118":119,"_89":120,"_91":120,"_23":266,"_93":115},{"_122":123,"_124":125,"_126":127},{"_21":268,"_34":269,"_36":270,"_116":117,"_118":-5,"_89":271,"_91":271,"_23":272,"_93":270},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_122":273,"_124":125,"_126":274},18,135489,{"_21":276,"_34":35,"_36":37,"_116":117,"_118":180,"_89":277,"_91":277,"_23":278,"_93":280},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_122":125,"_124":125,"_126":279},8597,"termodinamica-5",{"_21":183,"_34":282,"_36":283,"_116":117,"_118":245,"_89":246,"_91":246,"_23":284,"_93":285},"Engenharia de Petróleo","engenharia-de-petroleo",{"_122":248,"_124":125,"_126":187},"engenharia-de-petroleo-1",{"_21":119,"_34":287,"_36":288,"_116":117,"_118":268,"_89":246,"_91":246,"_23":289,"_93":291},"Física","fisica",{"_122":262,"_124":125,"_126":290},13777,"fisica-4",{"_21":245,"_34":293,"_36":294,"_116":117,"_118":-5,"_89":295,"_91":295,"_23":296,"_93":294},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_122":297,"_124":125,"_126":298},29,351586,{"_21":300,"_34":35,"_36":37,"_116":117,"_118":252,"_89":301,"_91":301,"_23":302,"_93":303},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_122":125,"_124":125,"_126":279},"termodinamica-4","tagsTree",[306,315],{"_21":268,"_34":269,"_36":270,"_116":117,"_118":-5,"_89":271,"_91":271,"_23":307,"_93":270,"_128":308},{"_122":273,"_124":125,"_126":274},[309],{"_21":119,"_34":287,"_36":288,"_116":117,"_118":268,"_89":246,"_91":246,"_23":310,"_93":291,"_128":311},{"_122":262,"_124":125,"_126":290},[312],{"_21":113,"_34":114,"_36":115,"_116":117,"_118":119,"_89":120,"_91":120,"_23":313,"_93":115,"_128":314},{"_122":123,"_124":125,"_126":127},[],{"_21":245,"_34":293,"_36":294,"_116":117,"_118":-5,"_89":295,"_91":295,"_23":316,"_93":294,"_128":317},{"_122":297,"_124":125,"_126":298},[318,327,333],{"_21":242,"_34":243,"_36":244,"_116":117,"_118":245,"_89":246,"_91":246,"_23":319,"_93":250,"_128":320},{"_122":248,"_124":125,"_126":249},[321],{"_21":252,"_34":253,"_36":254,"_116":117,"_118":242,"_89":184,"_91":184,"_23":322,"_93":257,"_128":323},{"_122":248,"_124":125,"_126":256},[324],{"_21":300,"_34":35,"_36":37,"_116":117,"_118":252,"_89":301,"_91":301,"_23":325,"_93":303,"_128":326},{"_122":125,"_124":125,"_126":279},[],{"_21":236,"_34":259,"_36":260,"_116":117,"_118":245,"_89":246,"_91":246,"_23":328,"_93":264,"_128":329},{"_122":262,"_124":125,"_126":263},[330],{"_21":235,"_34":35,"_36":37,"_116":117,"_118":236,"_89":120,"_91":120,"_23":331,"_93":240,"_128":332},{"_122":238,"_124":125,"_126":239},[],{"_21":183,"_34":282,"_36":283,"_116":117,"_118":245,"_89":246,"_91":246,"_23":334,"_93":285,"_128":335},{"_122":248,"_124":125,"_126":187},[336],{"_21":180,"_34":181,"_36":182,"_116":117,"_118":183,"_89":184,"_91":184,"_23":337,"_93":182,"_128":338},{"_122":186,"_124":125,"_126":187},[339],{"_21":276,"_34":35,"_36":37,"_116":117,"_118":180,"_89":277,"_91":277,"_23":340,"_93":280,"_128":341},{"_122":125,"_124":125,"_126":279},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários