[{"_1":2,"_322":-5,"_323":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/cf9f485c-71ac-4b19-b0a9-ea058f523138","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_74":75,"_151":152,"_29":225,"_294":295,"_318":319,"_320":321},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_56":57,"_68":19,"_69":70,"_71":72,"_73":44},"correctOptionId","","difficulty","id","cf9f485c-71ac-4b19-b0a9-ea058f523138","metadata",{"_25":26,"_52":53,"_54":55},"pd",{"_27":28,"_29":30,"_31":32,"_39":40,"_41":42,"_43":44,"_45":46,"_47":44,"_48":49,"_50":51},"area","Outros","tags",[],"subjects",[33],{"_21":34,"_35":36,"_37":38},669639,"name","Termodinâmica","alias","termodinamica","materialId","134800405","answerCount",2,"isIndexable",true,"mainSubject",{"_21":34,"_35":36,"_37":38},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","134817779","options",[58,64],{"_21":59,"_60":61,"_62":63},"f29406f9-b3cc-448a-a8e3-3d54c305f59c","label","A","text","Certo",{"_21":65,"_60":66,"_62":67},"3c67c45b-8253-45c8-8fa9-ed7f386c9331","B","Errado","solution_explanation","statement","

A energia mecânica vem da queima de carvão, gás e combustível nuclear, turbinas a gás ou, ocasionalmente, do motor de combustão interna.

","status","pending_classification","hasRelatedVideo","relatedVideos",[76],{"_77":78,"_96":97,"_29":112,"_131":132,"_150":113},"content",{"_21":79,"_35":80,"_81":-5,"_82":83,"_84":85,"_86":-5,"_23":87,"_90":91,"_92":91,"_93":-5,"_94":95},"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",{"_88":89},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_98":99,"_105":106,"_107":108,"_109":110,"_6":111},"provider",{"_21":100,"_101":102,"_103":104},"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",[113],{"_21":114,"_35":115,"_37":116,"_117":118,"_119":120,"_90":121,"_92":121,"_23":122,"_94":116,"_129":130},"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",{"_123":124,"_125":126,"_127":128},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_21":85,"_133":80,"_81":-5,"_134":135,"_136":137,"_6":-5,"_138":-5,"_98":137,"_139":140,"_109":-5,"_141":-5,"_142":-5,"_143":-5,"_144":-5,"_23":145,"_146":126,"_147":-5,"_71":148,"_90":149,"_92":149},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_88":89},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[153,186,204],{"_18":154,"_20":19,"_21":155,"_56":156,"_68":174,"_69":175,"_29":176},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[157,160,163,167,171],{"_21":158,"_60":61,"_62":159},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":161,"_60":66,"_62":162},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":164,"_60":165,"_62":166},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_21":168,"_60":169,"_62":170},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_21":154,"_60":172,"_62":173},"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

",[177],{"_21":178,"_35":179,"_37":180,"_117":118,"_119":181,"_90":182,"_92":182,"_23":183,"_94":180},"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",{"_123":184,"_125":126,"_127":185},4,12302,{"_18":187,"_20":19,"_21":188,"_56":189,"_68":201,"_69":202,"_29":203},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[190,193,196,198],{"_21":191,"_60":61,"_62":192},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":194,"_60":66,"_62":195},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":187,"_60":165,"_62":197},"

Verdadeiro, falso, verdadeiro

",{"_21":199,"_60":169,"_62":200},"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?

",[177],{"_18":205,"_20":19,"_21":206,"_56":207,"_68":222,"_69":223,"_29":224},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[208,211,214,216,219],{"_21":209,"_60":61,"_62":210},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":212,"_60":66,"_62":213},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":205,"_60":165,"_62":215},"Indeterminado",{"_21":217,"_60":169,"_62":218},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":220,"_60":172,"_62":221},"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????",[177],[177,226,232,242,249,256,257,265,271,276,282,289],{"_21":227,"_35":36,"_37":38,"_117":118,"_119":228,"_90":121,"_92":121,"_23":229,"_94":231},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_123":42,"_125":126,"_127":230},11846,"termodinamica-3",{"_21":233,"_35":234,"_37":235,"_117":118,"_119":236,"_90":237,"_92":237,"_23":238,"_94":241},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_123":239,"_125":126,"_127":240},5,30614,"engenharia-mecatronica-1",{"_21":243,"_35":244,"_37":245,"_117":118,"_119":233,"_90":182,"_92":182,"_23":246,"_94":248},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_123":239,"_125":126,"_127":247},25741,"mecanica-3",{"_21":228,"_35":250,"_37":251,"_117":118,"_119":236,"_90":237,"_92":237,"_23":252,"_94":255},"Engenharia Mecânica","engenharia-mecanica",{"_123":253,"_125":126,"_127":254},11,36318,"engenharia-mecanica-2",{"_21":114,"_35":115,"_37":116,"_117":118,"_119":120,"_90":121,"_92":121,"_23":122,"_94":116},{"_21":258,"_35":259,"_37":260,"_117":118,"_119":-5,"_90":261,"_92":261,"_23":262,"_94":260},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_123":263,"_125":126,"_127":264},18,135489,{"_21":266,"_35":36,"_37":38,"_117":118,"_119":178,"_90":267,"_92":267,"_23":268,"_94":270},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_123":126,"_125":126,"_127":269},8597,"termodinamica-5",{"_21":181,"_35":272,"_37":273,"_117":118,"_119":236,"_90":237,"_92":237,"_23":274,"_94":275},"Engenharia de Petróleo","engenharia-de-petroleo",{"_123":239,"_125":126,"_127":185},"engenharia-de-petroleo-1",{"_21":120,"_35":277,"_37":278,"_117":118,"_119":258,"_90":237,"_92":237,"_23":279,"_94":281},"Física","fisica",{"_123":253,"_125":126,"_127":280},13777,"fisica-4",{"_21":236,"_35":283,"_37":284,"_117":118,"_119":-5,"_90":285,"_92":285,"_23":286,"_94":284},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_123":287,"_125":126,"_127":288},29,351586,{"_21":290,"_35":36,"_37":38,"_117":118,"_119":243,"_90":291,"_92":291,"_23":292,"_94":293},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_123":126,"_125":126,"_127":269},"termodinamica-4","tagsTree",[296,300],{"_21":258,"_35":259,"_37":260,"_117":118,"_119":-5,"_90":261,"_92":261,"_23":262,"_94":260,"_129":297},[298],{"_21":120,"_35":277,"_37":278,"_117":118,"_119":258,"_90":237,"_92":237,"_23":279,"_94":281,"_129":299},[113],{"_21":236,"_35":283,"_37":284,"_117":118,"_119":-5,"_90":285,"_92":285,"_23":286,"_94":284,"_129":301},[302,308,312],{"_21":233,"_35":234,"_37":235,"_117":118,"_119":236,"_90":237,"_92":237,"_23":238,"_94":241,"_129":303},[304],{"_21":243,"_35":244,"_37":245,"_117":118,"_119":233,"_90":182,"_92":182,"_23":246,"_94":248,"_129":305},[306],{"_21":290,"_35":36,"_37":38,"_117":118,"_119":243,"_90":291,"_92":291,"_23":292,"_94":293,"_129":307},[],{"_21":228,"_35":250,"_37":251,"_117":118,"_119":236,"_90":237,"_92":237,"_23":252,"_94":255,"_129":309},[310],{"_21":227,"_35":36,"_37":38,"_117":118,"_119":228,"_90":121,"_92":121,"_23":229,"_94":231,"_129":311},[],{"_21":181,"_35":272,"_37":273,"_117":118,"_119":236,"_90":237,"_92":237,"_23":274,"_94":275,"_129":313},[314],{"_21":178,"_35":179,"_37":180,"_117":118,"_119":181,"_90":182,"_92":182,"_23":183,"_94":180,"_129":315},[316],{"_21":266,"_35":36,"_37":38,"_117":118,"_119":178,"_90":267,"_92":267,"_23":268,"_94":270,"_129":317},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários