[{"_1":2,"_373":-5,"_374":-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/ac6a78d3-0530-4067-bad0-ca06252291c0?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_103":104,"_182":183,"_52":258,"_331":332,"_369":370,"_371":372},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_78":79,"_97":43,"_98":99,"_100":101,"_102":16},"correctOptionId","e3e05c72-ff30-4af9-91c8-f087076f0253","difficulty","","id","ac6a78d3-0530-4067-bad0-ca06252291c0","metadata",{"_48":49,"_74":75,"_76":77},"pd",{"_50":51,"_52":53,"_54":55,"_62":63,"_64":65,"_66":16,"_67":68,"_69":16,"_70":71,"_72":73},"area","Outros","tags",[],"subjects",[56],{"_44":57,"_58":59,"_60":61},669639,"name","Termodinâmica","alias","termodinamica","materialId","164696705","answerCount",1,"isIndexable","mainSubject",{"_44":57,"_58":59,"_60":61},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","164809848","options",[80,86,90,93],{"_44":81,"_82":83,"_84":85},"b377d1d3-fe4f-4119-af42-1ca99a6d47ca","label","A","text","

1200 J

",{"_44":87,"_82":88,"_84":89},"3c7a7043-ea21-48c9-b654-8a6f32b11d29","B","

1400 J

",{"_44":41,"_82":91,"_84":92},"C","

1600 J

",{"_44":94,"_82":95,"_84":96},"070f5d5b-dd69-479a-a4b4-851e42ba9fb2","D","

1800 J

","solution_explanation","statement","

Um sistema termodinâmico opera em um ciclo de Carnot entre duas fontes térmicas a 600 \\, K e 400 \\, K. Se o sistema realiza um trabalho de 800 \\, J, qual é a quantidade de calor absorvida da fonte quente?

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_52":141,"_160":161,"_178":179},"content",{"_44":108,"_58":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_46":116,"_119":120,"_121":120,"_122":-5,"_123":124},"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",{"_117":118},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_127":128,"_134":135,"_136":137,"_138":139,"_28":140},"provider",{"_44":129,"_130":131,"_132":133},"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",[142],{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":151,"_123":145,"_158":159},"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",{"_152":153,"_154":155,"_156":157},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_44":114,"_13":109,"_110":-5,"_162":163,"_164":165,"_28":-5,"_166":-5,"_127":165,"_167":168,"_138":-5,"_169":-5,"_170":-5,"_171":-5,"_172":-5,"_46":173,"_174":155,"_175":-5,"_100":176,"_119":177,"_121":177},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_117":118},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":180,"_123":145,"_158":181},{"_152":153,"_154":155,"_156":157},[],"similarQuestions",[184,215,235],{"_40":185,"_42":43,"_44":186,"_78":187,"_97":203,"_98":204,"_52":205},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[188,191,194,197,200],{"_44":189,"_82":83,"_84":190},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":192,"_82":88,"_84":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":195,"_82":91,"_84":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":198,"_82":95,"_84":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":185,"_82":201,"_84":202},"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

",[206],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":212,"_123":209},"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",{"_152":213,"_154":155,"_156":214},4,12302,{"_40":216,"_42":43,"_44":217,"_78":218,"_97":230,"_98":231,"_52":232},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[219,222,225,227],{"_44":220,"_82":83,"_84":221},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":223,"_82":88,"_84":224},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":216,"_82":91,"_84":226},"

Verdadeiro, falso, verdadeiro

",{"_44":228,"_82":95,"_84":229},"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?

",[233],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":234,"_123":209},{"_152":213,"_154":155,"_156":214},{"_40":236,"_42":43,"_44":237,"_78":238,"_97":253,"_98":254,"_52":255},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[239,242,245,247,250],{"_44":240,"_82":83,"_84":241},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":243,"_82":88,"_84":244},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":236,"_82":91,"_84":246},"Indeterminado",{"_44":248,"_82":95,"_84":249},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":251,"_82":201,"_84":252},"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????",[256],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":257,"_123":209},{"_152":213,"_154":155,"_156":214},[259,261,268,278,285,292,294,302,308,313,319,326],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":260,"_123":209},{"_152":213,"_154":155,"_156":214},{"_44":262,"_58":59,"_60":61,"_146":147,"_148":263,"_119":150,"_121":150,"_46":264,"_123":267},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":265,"_154":155,"_156":266},2,11846,"termodinamica-3",{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":273,"_121":273,"_46":274,"_123":277},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_152":275,"_154":155,"_156":276},5,30614,"engenharia-mecatronica-1",{"_44":279,"_58":280,"_60":281,"_146":147,"_148":269,"_119":211,"_121":211,"_46":282,"_123":284},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":275,"_154":155,"_156":283},25741,"mecanica-3",{"_44":263,"_58":286,"_60":287,"_146":147,"_148":272,"_119":273,"_121":273,"_46":288,"_123":291},"Engenharia Mecânica","engenharia-mecanica",{"_152":289,"_154":155,"_156":290},11,36318,"engenharia-mecanica-2",{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":293,"_123":145},{"_152":153,"_154":155,"_156":157},{"_44":295,"_58":296,"_60":297,"_146":147,"_148":-5,"_119":298,"_121":298,"_46":299,"_123":297},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_152":300,"_154":155,"_156":301},18,135489,{"_44":303,"_58":59,"_60":61,"_146":147,"_148":207,"_119":304,"_121":304,"_46":305,"_123":307},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_152":155,"_154":155,"_156":306},8597,"termodinamica-5",{"_44":210,"_58":309,"_60":310,"_146":147,"_148":272,"_119":273,"_121":273,"_46":311,"_123":312},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":275,"_154":155,"_156":214},"engenharia-de-petroleo-1",{"_44":149,"_58":314,"_60":315,"_146":147,"_148":295,"_119":273,"_121":273,"_46":316,"_123":318},"Física","fisica",{"_152":289,"_154":155,"_156":317},13777,"fisica-4",{"_44":272,"_58":320,"_60":321,"_146":147,"_148":-5,"_119":322,"_121":322,"_46":323,"_123":321},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":324,"_154":155,"_156":325},29,351586,{"_44":327,"_58":59,"_60":61,"_146":147,"_148":279,"_119":328,"_121":328,"_46":329,"_123":330},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_152":155,"_154":155,"_156":306},"termodinamica-4","tagsTree",[333,342],{"_44":295,"_58":296,"_60":297,"_146":147,"_148":-5,"_119":298,"_121":298,"_46":334,"_123":297,"_158":335},{"_152":300,"_154":155,"_156":301},[336],{"_44":149,"_58":314,"_60":315,"_146":147,"_148":295,"_119":273,"_121":273,"_46":337,"_123":318,"_158":338},{"_152":289,"_154":155,"_156":317},[339],{"_44":143,"_58":144,"_60":145,"_146":147,"_148":149,"_119":150,"_121":150,"_46":340,"_123":145,"_158":341},{"_152":153,"_154":155,"_156":157},[],{"_44":272,"_58":320,"_60":321,"_146":147,"_148":-5,"_119":322,"_121":322,"_46":343,"_123":321,"_158":344},{"_152":324,"_154":155,"_156":325},[345,354,360],{"_44":269,"_58":270,"_60":271,"_146":147,"_148":272,"_119":273,"_121":273,"_46":346,"_123":277,"_158":347},{"_152":275,"_154":155,"_156":276},[348],{"_44":279,"_58":280,"_60":281,"_146":147,"_148":269,"_119":211,"_121":211,"_46":349,"_123":284,"_158":350},{"_152":275,"_154":155,"_156":283},[351],{"_44":327,"_58":59,"_60":61,"_146":147,"_148":279,"_119":328,"_121":328,"_46":352,"_123":330,"_158":353},{"_152":155,"_154":155,"_156":306},[],{"_44":263,"_58":286,"_60":287,"_146":147,"_148":272,"_119":273,"_121":273,"_46":355,"_123":291,"_158":356},{"_152":289,"_154":155,"_156":290},[357],{"_44":262,"_58":59,"_60":61,"_146":147,"_148":263,"_119":150,"_121":150,"_46":358,"_123":267,"_158":359},{"_152":265,"_154":155,"_156":266},[],{"_44":210,"_58":309,"_60":310,"_146":147,"_148":272,"_119":273,"_121":273,"_46":361,"_123":312,"_158":362},{"_152":275,"_154":155,"_156":214},[363],{"_44":207,"_58":208,"_60":209,"_146":147,"_148":210,"_119":211,"_121":211,"_46":364,"_123":209,"_158":365},{"_152":213,"_154":155,"_156":214},[366],{"_44":303,"_58":59,"_60":61,"_146":147,"_148":207,"_119":304,"_121":304,"_46":367,"_123":307,"_158":368},{"_152":155,"_154":155,"_156":306},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários