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The advantages and disadvantages of diesel engines.

",{"_43":93,"_88":94,"_90":95},"94cdb70c-89e2-467d-af31-032975d77236","B","

The environmental impact of diesel engines.

",{"_43":97,"_88":98,"_90":99},"32d99b92-90f2-4f47-944b-b1bb12134dca","C","

The history of diesel engines.

",{"_43":101,"_88":102,"_90":103},"6c4cefe0-d9be-4322-845a-358ea7ef85d0","D","

The future of diesel engines.

","solution_explanation","statement","

What is the article about?

","status","pending_classification","hasRelatedVideo","relatedVideos",[112],{"_113":114,"_132":133,"_50":148,"_167":168,"_185":149},"content",{"_43":115,"_54":116,"_117":-5,"_118":119,"_120":121,"_122":-5,"_45":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",{"_43":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],{"_43":150,"_54":151,"_56":152,"_153":154,"_155":156,"_126":157,"_128":157,"_45":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",{"_43":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,"_45":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","similarQuestions",[188,219,237],{"_40":189,"_42":41,"_43":190,"_84":191,"_104":207,"_105":208,"_50":209},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[192,195,198,201,204],{"_43":193,"_88":89,"_90":194},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":196,"_88":94,"_90":197},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":199,"_88":98,"_90":200},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":202,"_88":102,"_90":203},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":189,"_88":205,"_90":206},"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

",[210],{"_43":211,"_54":212,"_56":213,"_153":154,"_155":214,"_126":215,"_128":215,"_45":216,"_130":213},"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":217,"_161":162,"_163":218},4,12302,{"_40":220,"_42":41,"_43":221,"_84":222,"_104":234,"_105":235,"_50":236},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[223,226,229,231],{"_43":224,"_88":89,"_90":225},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":227,"_88":94,"_90":228},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":220,"_88":98,"_90":230},"

Verdadeiro, falso, verdadeiro

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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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[210],[210,259,266,276,283,290,291,299,305,310,316,323],{"_43":260,"_54":66,"_56":67,"_153":154,"_155":261,"_126":157,"_128":157,"_45":262,"_130":265},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_159":263,"_161":162,"_163":264},2,11846,"termodinamica-3",{"_43":267,"_54":268,"_56":269,"_153":154,"_155":270,"_126":271,"_128":271,"_45":272,"_130":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_159":273,"_161":162,"_163":274},5,30614,"engenharia-mecatronica-1",{"_43":277,"_54":278,"_56":279,"_153":154,"_155":267,"_126":215,"_128":215,"_45":280,"_130":282},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_159":273,"_161":162,"_163":281},25741,"mecanica-3",{"_43":261,"_54":284,"_56":285,"_153":154,"_155":270,"_126":271,"_128":271,"_45":286,"_130":289},"Engenharia Mecânica","engenharia-mecanica",{"_159":287,"_161":162,"_163":288},11,36318,"engenharia-mecanica-2",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":156,"_126":157,"_128":157,"_45":158,"_130":152},{"_43":292,"_54":293,"_56":294,"_153":154,"_155":-5,"_126":295,"_128":295,"_45":296,"_130":294},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_159":297,"_161":162,"_163":298},18,135489,{"_43":300,"_54":66,"_56":67,"_153":154,"_155":211,"_126":301,"_128":301,"_45":302,"_130":304},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_159":162,"_161":162,"_163":303},8597,"termodinamica-5",{"_43":214,"_54":306,"_56":307,"_153":154,"_155":270,"_126":271,"_128":271,"_45":308,"_130":309},"Engenharia de Petróleo","engenharia-de-petroleo",{"_159":273,"_161":162,"_163":218},"engenharia-de-petroleo-1",{"_43":156,"_54":311,"_56":312,"_153":154,"_155":292,"_126":271,"_128":271,"_45":313,"_130":315},"Física","fisica",{"_159":287,"_161":162,"_163":314},13777,"fisica-4",{"_43":270,"_54":317,"_56":318,"_153":154,"_155":-5,"_126":319,"_128":319,"_45":320,"_130":318},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_159":321,"_161":162,"_163":322},29,351586,{"_43":324,"_54":66,"_56":67,"_153":154,"_155":277,"_126":325,"_128":325,"_45":326,"_130":327},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_159":162,"_161":162,"_163":303},"termodinamica-4","tagsTree",[330,334],{"_43":292,"_54":293,"_56":294,"_153":154,"_155":-5,"_126":295,"_128":295,"_45":296,"_130":294,"_165":331},[332],{"_43":156,"_54":311,"_56":312,"_153":154,"_155":292,"_126":271,"_128":271,"_45":313,"_130":315,"_165":333},[149],{"_43":270,"_54":317,"_56":318,"_153":154,"_155":-5,"_126":319,"_128":319,"_45":320,"_130":318,"_165":335},[336,342,346],{"_43":267,"_54":268,"_56":269,"_153":154,"_155":270,"_126":271,"_128":271,"_45":272,"_130":275,"_165":337},[338],{"_43":277,"_54":278,"_56":279,"_153":154,"_155":267,"_126":215,"_128":215,"_45":280,"_130":282,"_165":339},[340],{"_43":324,"_54":66,"_56":67,"_153":154,"_155":277,"_126":325,"_128":325,"_45":326,"_130":327,"_165":341},[],{"_43":261,"_54":284,"_56":285,"_153":154,"_155":270,"_126":271,"_128":271,"_45":286,"_130":289,"_165":343},[344],{"_43":260,"_54":66,"_56":67,"_153":154,"_155":261,"_126":157,"_128":157,"_45":262,"_130":265,"_165":345},[],{"_43":214,"_54":306,"_56":307,"_153":154,"_155":270,"_126":271,"_128":271,"_45":308,"_130":309,"_165":347},[348],{"_43":211,"_54":212,"_56":213,"_153":154,"_155":214,"_126":215,"_128":215,"_45":216,"_130":213,"_165":349},[350],{"_43":300,"_54":66,"_56":67,"_153":154,"_155":211,"_126":301,"_128":301,"_45":302,"_130":304,"_165":351},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários