[{"_1":2,"_379":-5,"_380":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/ab4147a4-52a6-4cee-b3e2-7559a69f4f05?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_110":111,"_189":190,"_51":264,"_337":338,"_375":376,"_377":378},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_81":82,"_104":43,"_105":106,"_107":108,"_109":16},"correctOptionId","61d07ab3-3247-4db4-9cbd-f0448d5beac3","difficulty","","id","ab4147a4-52a6-4cee-b3e2-7559a69f4f05","metadata",{"_48":49,"_77":78,"_79":80},"pd",{"_50":-5,"_51":52,"_59":60,"_65":66,"_67":68,"_69":16,"_70":71,"_72":16,"_73":74,"_75":76},"area","tags",[53],{"_44":54,"_55":56,"_57":58},98,"name","Exercício","alias","exercicio","subjects",[61],{"_44":62,"_55":63,"_57":64},669639,"Termodinâmica","termodinamica","materialId","122218636","answerCount",1,"isIndexable","mainSubject",{"_44":62,"_55":63,"_57":64},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","High School","source","PD","externalId","122221689","options",[83,89,92,96,100],{"_44":84,"_85":86,"_87":88},"86b6bbd2-9b4f-4ee0-8f9e-c2ca2bcfc12d","label","A","text","Fluido.",{"_44":41,"_85":90,"_87":91},"B","Energia.",{"_44":93,"_85":94,"_87":95},"be0b77f0-82ba-4617-aed9-4e6cd13a9d40","C","Aceleração.",{"_44":97,"_85":98,"_87":99},"e2b537d6-2524-43a8-98af-6984b3ee0daa","D","Massa.",{"_44":101,"_85":102,"_87":103},"4219708d-5bbe-49c7-9819-6302ac6ef91c","E","Trabalho Mecânico.","solution_explanation","statement","

Essa afirmação refere-se ao conceito de:

“É a capacidade de se realizar um trabalho”.

","status","pending_classification","hasRelatedVideo","relatedVideos",[112],{"_113":114,"_132":133,"_51":148,"_167":168,"_185":186},"content",{"_44":115,"_55":116,"_117":-5,"_118":119,"_120":121,"_122":-5,"_46":123,"_126":127,"_128":127,"_129":-5,"_130":131},"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",{"_124":125},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_134":135,"_141":142,"_143":144,"_145":146,"_28":147},"provider",{"_44":136,"_137":138,"_139":140},"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",[149],{"_44":150,"_55":151,"_57":152,"_153":154,"_155":156,"_126":157,"_128":157,"_46":158,"_130":152,"_165":166},"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",{"_159":160,"_161":162,"_163":164},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":121,"_13":116,"_117":-5,"_169":170,"_171":172,"_28":-5,"_173":-5,"_134":172,"_174":175,"_145":-5,"_176":-5,"_177":-5,"_178":-5,"_179":-5,"_46":180,"_181":162,"_182":-5,"_107":183,"_126":184,"_128":184},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_124":125},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_44":150,"_55":151,"_57":152,"_153":154,"_155":156,"_126":157,"_128":157,"_46":187,"_130":152,"_165":188},{"_159":160,"_161":162,"_163":164},[],"similarQuestions",[191,221,241],{"_40":192,"_42":43,"_44":193,"_81":194,"_104":209,"_105":210,"_51":211},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[195,198,201,204,207],{"_44":196,"_85":86,"_87":197},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":199,"_85":90,"_87":200},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":202,"_85":94,"_87":203},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":205,"_85":98,"_87":206},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":192,"_85":102,"_87":208},"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

",[212],{"_44":213,"_55":214,"_57":215,"_153":154,"_155":216,"_126":217,"_128":217,"_46":218,"_130":215},"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",{"_159":219,"_161":162,"_163":220},4,12302,{"_40":222,"_42":43,"_44":223,"_81":224,"_104":236,"_105":237,"_51":238},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[225,228,231,233],{"_44":226,"_85":86,"_87":227},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":229,"_85":90,"_87":230},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":222,"_85":94,"_87":232},"

Verdadeiro, falso, verdadeiro

",{"_44":234,"_85":98,"_87":235},"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?

",[239],{"_44":213,"_55":214,"_57":215,"_153":154,"_155":216,"_126":217,"_128":217,"_46":240,"_130":215},{"_159":219,"_161":162,"_163":220},{"_40":242,"_42":43,"_44":243,"_81":244,"_104":259,"_105":260,"_51":261},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[245,248,251,253,256],{"_44":246,"_85":86,"_87":247},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":249,"_85":90,"_87":250},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":242,"_85":94,"_87":252},"Indeterminado",{"_44":254,"_85":98,"_87":255},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":257,"_85":102,"_87":258},"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????",[262],{"_44":213,"_55":214,"_57":215,"_153":154,"_155":216,"_126":217,"_128":217,"_46":263,"_130":215},{"_159":219,"_161":162,"_163":220},[265,267,274,284,291,298,300,308,314,319,325,332],{"_44":213,"_55":214,"_57":215,"_153":154,"_155":216,"_126":217,"_128":217,"_46":266,"_130":215},{"_159":219,"_161":162,"_163":220},{"_44":268,"_55":63,"_57":64,"_153":154,"_155":269,"_126":157,"_128":157,"_46":270,"_130":273},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_159":271,"_161":162,"_163":272},2,11846,"termodinamica-3",{"_44":275,"_55":276,"_57":277,"_153":154,"_155":278,"_126":279,"_128":279,"_46":280,"_130":283},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_159":281,"_161":162,"_163":282},5,30614,"engenharia-mecatronica-1",{"_44":285,"_55":286,"_57":287,"_153":154,"_155":275,"_126":217,"_128":217,"_46":288,"_130":290},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_159":281,"_161":162,"_163":289},25741,"mecanica-3",{"_44":269,"_55":292,"_57":293,"_153":154,"_155":278,"_126":279,"_128":279,"_46":294,"_130":297},"Engenharia Mecânica","engenharia-mecanica",{"_159":295,"_161":162,"_163":296},11,36318,"engenharia-mecanica-2",{"_44":150,"_55":151,"_57":152,"_153":154,"_155":156,"_126":157,"_128":157,"_46":299,"_130":152},{"_159":160,"_161":162,"_163":164},{"_44":301,"_55":302,"_57":303,"_153":154,"_155":-5,"_126":304,"_128":304,"_46":305,"_130":303},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_159":306,"_161":162,"_163":307},18,135489,{"_44":309,"_55":63,"_57":64,"_153":154,"_155":213,"_126":310,"_128":310,"_46":311,"_130":313},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_159":162,"_161":162,"_163":312},8597,"termodinamica-5",{"_44":216,"_55":315,"_57":316,"_153":154,"_155":278,"_126":279,"_128":279,"_46":317,"_130":318},"Engenharia de Petróleo","engenharia-de-petroleo",{"_159":281,"_161":162,"_163":220},"engenharia-de-petroleo-1",{"_44":156,"_55":320,"_57":321,"_153":154,"_155":301,"_126":279,"_128":279,"_46":322,"_130":324},"Física","fisica",{"_159":295,"_161":162,"_163":323},13777,"fisica-4",{"_44":278,"_55":326,"_57":327,"_153":154,"_155":-5,"_126":328,"_128":328,"_46":329,"_130":327},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_159":330,"_161":162,"_163":331},29,351586,{"_44":333,"_55":63,"_57":64,"_153":154,"_155":285,"_126":334,"_128":334,"_46":335,"_130":336},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_159":162,"_161":162,"_163":312},"termodinamica-4","tagsTree",[339,348],{"_44":301,"_55":302,"_57":303,"_153":154,"_155":-5,"_126":304,"_128":304,"_46":340,"_130":303,"_165":341},{"_159":306,"_161":162,"_163":307},[342],{"_44":156,"_55":320,"_57":321,"_153":154,"_155":301,"_126":279,"_128":279,"_46":343,"_130":324,"_165":344},{"_159":295,"_161":162,"_163":323},[345],{"_44":150,"_55":151,"_57":152,"_153":154,"_155":156,"_126":157,"_128":157,"_46":346,"_130":152,"_165":347},{"_159":160,"_161":162,"_163":164},[],{"_44":278,"_55":326,"_57":327,"_153":154,"_155":-5,"_126":328,"_128":328,"_46":349,"_130":327,"_165":350},{"_159":330,"_161":162,"_163":331},[351,360,366],{"_44":275,"_55":276,"_57":277,"_153":154,"_155":278,"_126":279,"_128":279,"_46":352,"_130":283,"_165":353},{"_159":281,"_161":162,"_163":282},[354],{"_44":285,"_55":286,"_57":287,"_153":154,"_155":275,"_126":217,"_128":217,"_46":355,"_130":290,"_165":356},{"_159":281,"_161":162,"_163":289},[357],{"_44":333,"_55":63,"_57":64,"_153":154,"_155":285,"_126":334,"_128":334,"_46":358,"_130":336,"_165":359},{"_159":162,"_161":162,"_163":312},[],{"_44":269,"_55":292,"_57":293,"_153":154,"_155":278,"_126":279,"_128":279,"_46":361,"_130":297,"_165":362},{"_159":295,"_161":162,"_163":296},[363],{"_44":268,"_55":63,"_57":64,"_153":154,"_155":269,"_126":157,"_128":157,"_46":364,"_130":273,"_165":365},{"_159":271,"_161":162,"_163":272},[],{"_44":216,"_55":315,"_57":316,"_153":154,"_155":278,"_126":279,"_128":279,"_46":367,"_130":318,"_165":368},{"_159":281,"_161":162,"_163":220},[369],{"_44":213,"_55":214,"_57":215,"_153":154,"_155":216,"_126":217,"_128":217,"_46":370,"_130":215,"_165":371},{"_159":219,"_161":162,"_163":220},[372],{"_44":309,"_55":63,"_57":64,"_153":154,"_155":213,"_126":310,"_128":310,"_46":373,"_130":313,"_165":374},{"_159":162,"_161":162,"_163":312},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários