[{"_1":2,"_328":-5,"_329":-5},"loaderData",{"_3":4,"_9":10},"root",{"_5":-5,"_6":7,"_8":-5},"registerModalConfig","url","https://prouniversitario.com/exercicios/dc553e21-acf7-46a4-ab1d-8597770a13ee","user","pages/questions/show/index",{"_11":12,"_13":14,"_15":14,"_16":17,"_81":82,"_158":159,"_28":230,"_300":301,"_324":325,"_326":327},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_18":19,"_20":19,"_21":22,"_23":24,"_55":56,"_75":19,"_76":77,"_78":79,"_80":43},"correctOptionId","","difficulty","id","dc553e21-acf7-46a4-ab1d-8597770a13ee","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","122957239","answerCount",1,"isIndexable",true,"mainSubject",{"_21":33,"_34":35,"_36":37},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","123595734","options",[57,63,67,71],{"_21":58,"_59":60,"_61":62},"159b38a6-218b-48a1-92d2-a7e148e8b85f","label","A","text","elevação dos leitos dos rios.",{"_21":64,"_59":65,"_61":66},"3f431790-14c8-493c-b650-92dead0b9297","B","impermeabilização dos solos.",{"_21":68,"_59":69,"_61":70},"74b4091e-9eb9-495e-a423-2ab25f172ab1","C","intensificação do efeito estufa.",{"_21":72,"_59":73,"_61":74},"40e759c5-6adc-41b3-b7a7-ea9bff5199e9","D","liberação de clorofluorcarbonos.","solution_explanation","statement","

O problema descrito nesse texto é uma consequência direta da acidificação dos oceanos.

","status","pending_classification","hasRelatedVideo","relatedVideos",[83],{"_84":85,"_103":104,"_28":119,"_138":139,"_157":120},"content",{"_21":86,"_34":87,"_88":-5,"_89":90,"_91":92,"_93":-5,"_23":94,"_97":98,"_99":98,"_100":-5,"_101":102},"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",{"_95":96},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_105":106,"_112":113,"_114":115,"_116":117,"_6":118},"provider",{"_21":107,"_108":109,"_110":111},"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",[120],{"_21":121,"_34":122,"_36":123,"_124":125,"_126":127,"_97":128,"_99":128,"_23":129,"_101":123,"_136":137},"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",{"_130":131,"_132":133,"_134":135},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_21":92,"_140":87,"_88":-5,"_141":142,"_143":144,"_6":-5,"_145":-5,"_105":144,"_146":147,"_116":-5,"_148":-5,"_149":-5,"_150":-5,"_151":-5,"_23":152,"_153":133,"_154":-5,"_78":155,"_97":156,"_99":156},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_95":96},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[160,191,209],{"_18":161,"_20":19,"_21":162,"_55":163,"_75":179,"_76":180,"_28":181},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[164,167,170,173,176],{"_21":165,"_59":60,"_61":166},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":168,"_59":65,"_61":169},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":171,"_59":69,"_61":172},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":174,"_59":73,"_61":175},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_21":161,"_59":177,"_61":178},"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

",[182],{"_21":183,"_34":184,"_36":185,"_124":125,"_126":186,"_97":187,"_99":187,"_23":188,"_101":185},"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",{"_130":189,"_132":133,"_134":190},4,12302,{"_18":192,"_20":19,"_21":193,"_55":194,"_75":206,"_76":207,"_28":208},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[195,198,201,203],{"_21":196,"_59":60,"_61":197},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":199,"_59":65,"_61":200},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":192,"_59":69,"_61":202},"

Verdadeiro, falso, verdadeiro

",{"_21":204,"_59":73,"_61":205},"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?

",[182],{"_18":210,"_20":19,"_21":211,"_55":212,"_75":227,"_76":228,"_28":229},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[213,216,219,221,224],{"_21":214,"_59":60,"_61":215},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":217,"_59":65,"_61":218},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":210,"_59":69,"_61":220},"Indeterminado",{"_21":222,"_59":73,"_61":223},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":225,"_59":177,"_61":226},"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????",[182],[182,231,238,248,255,262,263,271,277,282,288,295],{"_21":232,"_34":35,"_36":37,"_124":125,"_126":233,"_97":128,"_99":128,"_23":234,"_101":237},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_130":235,"_132":133,"_134":236},2,11846,"termodinamica-3",{"_21":239,"_34":240,"_36":241,"_124":125,"_126":242,"_97":243,"_99":243,"_23":244,"_101":247},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_130":245,"_132":133,"_134":246},5,30614,"engenharia-mecatronica-1",{"_21":249,"_34":250,"_36":251,"_124":125,"_126":239,"_97":187,"_99":187,"_23":252,"_101":254},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_130":245,"_132":133,"_134":253},25741,"mecanica-3",{"_21":233,"_34":256,"_36":257,"_124":125,"_126":242,"_97":243,"_99":243,"_23":258,"_101":261},"Engenharia Mecânica","engenharia-mecanica",{"_130":259,"_132":133,"_134":260},11,36318,"engenharia-mecanica-2",{"_21":121,"_34":122,"_36":123,"_124":125,"_126":127,"_97":128,"_99":128,"_23":129,"_101":123},{"_21":264,"_34":265,"_36":266,"_124":125,"_126":-5,"_97":267,"_99":267,"_23":268,"_101":266},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_130":269,"_132":133,"_134":270},18,135489,{"_21":272,"_34":35,"_36":37,"_124":125,"_126":183,"_97":273,"_99":273,"_23":274,"_101":276},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":275},8597,"termodinamica-5",{"_21":186,"_34":278,"_36":279,"_124":125,"_126":242,"_97":243,"_99":243,"_23":280,"_101":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":245,"_132":133,"_134":190},"engenharia-de-petroleo-1",{"_21":127,"_34":283,"_36":284,"_124":125,"_126":264,"_97":243,"_99":243,"_23":285,"_101":287},"Física","fisica",{"_130":259,"_132":133,"_134":286},13777,"fisica-4",{"_21":242,"_34":289,"_36":290,"_124":125,"_126":-5,"_97":291,"_99":291,"_23":292,"_101":290},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":293,"_132":133,"_134":294},29,351586,{"_21":296,"_34":35,"_36":37,"_124":125,"_126":249,"_97":297,"_99":297,"_23":298,"_101":299},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":275},"termodinamica-4","tagsTree",[302,306],{"_21":264,"_34":265,"_36":266,"_124":125,"_126":-5,"_97":267,"_99":267,"_23":268,"_101":266,"_136":303},[304],{"_21":127,"_34":283,"_36":284,"_124":125,"_126":264,"_97":243,"_99":243,"_23":285,"_101":287,"_136":305},[120],{"_21":242,"_34":289,"_36":290,"_124":125,"_126":-5,"_97":291,"_99":291,"_23":292,"_101":290,"_136":307},[308,314,318],{"_21":239,"_34":240,"_36":241,"_124":125,"_126":242,"_97":243,"_99":243,"_23":244,"_101":247,"_136":309},[310],{"_21":249,"_34":250,"_36":251,"_124":125,"_126":239,"_97":187,"_99":187,"_23":252,"_101":254,"_136":311},[312],{"_21":296,"_34":35,"_36":37,"_124":125,"_126":249,"_97":297,"_99":297,"_23":298,"_101":299,"_136":313},[],{"_21":233,"_34":256,"_36":257,"_124":125,"_126":242,"_97":243,"_99":243,"_23":258,"_101":261,"_136":315},[316],{"_21":232,"_34":35,"_36":37,"_124":125,"_126":233,"_97":128,"_99":128,"_23":234,"_101":237,"_136":317},[],{"_21":186,"_34":278,"_36":279,"_124":125,"_126":242,"_97":243,"_99":243,"_23":280,"_101":281,"_136":319},[320],{"_21":183,"_34":184,"_36":185,"_124":125,"_126":186,"_97":187,"_99":187,"_23":188,"_101":185,"_136":321},[322],{"_21":272,"_34":35,"_36":37,"_124":125,"_126":183,"_97":273,"_99":273,"_23":274,"_101":276,"_136":323},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários