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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":186},"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",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":156,"_126":157,"_128":157,"_45":187,"_130":152,"_165":188},{"_159":160,"_161":162,"_163":164},[],"similarQuestions",[191,222,242],{"_40":192,"_42":41,"_43":193,"_84":194,"_104":210,"_105":211,"_50":212},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[195,198,201,204,207],{"_43":196,"_88":89,"_90":197},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":199,"_88":94,"_90":200},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":202,"_88":98,"_90":203},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":205,"_88":102,"_90":206},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":192,"_88":208,"_90":209},"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

",[213],{"_43":214,"_54":215,"_56":216,"_153":154,"_155":217,"_126":218,"_128":218,"_45":219,"_130":216},"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":220,"_161":162,"_163":221},4,12302,{"_40":223,"_42":41,"_43":224,"_84":225,"_104":237,"_105":238,"_50":239},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[226,229,232,234],{"_43":227,"_88":89,"_90":228},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":230,"_88":94,"_90":231},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":223,"_88":98,"_90":233},"

Verdadeiro, falso, verdadeiro

",{"_43":235,"_88":102,"_90":236},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[263],{"_43":214,"_54":215,"_56":216,"_153":154,"_155":217,"_126":218,"_128":218,"_45":264,"_130":216},{"_159":220,"_161":162,"_163":221},[266,268,275,285,292,299,301,309,315,320,326,333],{"_43":214,"_54":215,"_56":216,"_153":154,"_155":217,"_126":218,"_128":218,"_45":267,"_130":216},{"_159":220,"_161":162,"_163":221},{"_43":269,"_54":66,"_56":67,"_153":154,"_155":270,"_126":157,"_128":157,"_45":271,"_130":274},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_159":272,"_161":162,"_163":273},2,11846,"termodinamica-3",{"_43":276,"_54":277,"_56":278,"_153":154,"_155":279,"_126":280,"_128":280,"_45":281,"_130":284},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_159":282,"_161":162,"_163":283},5,30614,"engenharia-mecatronica-1",{"_43":286,"_54":287,"_56":288,"_153":154,"_155":276,"_126":218,"_128":218,"_45":289,"_130":291},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_159":282,"_161":162,"_163":290},25741,"mecanica-3",{"_43":270,"_54":293,"_56":294,"_153":154,"_155":279,"_126":280,"_128":280,"_45":295,"_130":298},"Engenharia Mecânica","engenharia-mecanica",{"_159":296,"_161":162,"_163":297},11,36318,"engenharia-mecanica-2",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":156,"_126":157,"_128":157,"_45":300,"_130":152},{"_159":160,"_161":162,"_163":164},{"_43":302,"_54":303,"_56":304,"_153":154,"_155":-5,"_126":305,"_128":305,"_45":306,"_130":304},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_159":307,"_161":162,"_163":308},18,135489,{"_43":310,"_54":66,"_56":67,"_153":154,"_155":214,"_126":311,"_128":311,"_45":312,"_130":314},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_159":162,"_161":162,"_163":313},8597,"termodinamica-5",{"_43":217,"_54":316,"_56":317,"_153":154,"_155":279,"_126":280,"_128":280,"_45":318,"_130":319},"Engenharia de Petróleo","engenharia-de-petroleo",{"_159":282,"_161":162,"_163":221},"engenharia-de-petroleo-1",{"_43":156,"_54":321,"_56":322,"_153":154,"_155":302,"_126":280,"_128":280,"_45":323,"_130":325},"Física","fisica",{"_159":296,"_161":162,"_163":324},13777,"fisica-4",{"_43":279,"_54":327,"_56":328,"_153":154,"_155":-5,"_126":329,"_128":329,"_45":330,"_130":328},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_159":331,"_161":162,"_163":332},29,351586,{"_43":334,"_54":66,"_56":67,"_153":154,"_155":286,"_126":335,"_128":335,"_45":336,"_130":337},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_159":162,"_161":162,"_163":313},"termodinamica-4","tagsTree",[340,349],{"_43":302,"_54":303,"_56":304,"_153":154,"_155":-5,"_126":305,"_128":305,"_45":341,"_130":304,"_165":342},{"_159":307,"_161":162,"_163":308},[343],{"_43":156,"_54":321,"_56":322,"_153":154,"_155":302,"_126":280,"_128":280,"_45":344,"_130":325,"_165":345},{"_159":296,"_161":162,"_163":324},[346],{"_43":150,"_54":151,"_56":152,"_153":154,"_155":156,"_126":157,"_128":157,"_45":347,"_130":152,"_165":348},{"_159":160,"_161":162,"_163":164},[],{"_43":279,"_54":327,"_56":328,"_153":154,"_155":-5,"_126":329,"_128":329,"_45":350,"_130":328,"_165":351},{"_159":331,"_161":162,"_163":332},[352,361,367],{"_43":276,"_54":277,"_56":278,"_153":154,"_155":279,"_126":280,"_128":280,"_45":353,"_130":284,"_165":354},{"_159":282,"_161":162,"_163":283},[355],{"_43":286,"_54":287,"_56":288,"_153":154,"_155":276,"_126":218,"_128":218,"_45":356,"_130":291,"_165":357},{"_159":282,"_161":162,"_163":290},[358],{"_43":334,"_54":66,"_56":67,"_153":154,"_155":286,"_126":335,"_128":335,"_45":359,"_130":337,"_165":360},{"_159":162,"_161":162,"_163":313},[],{"_43":270,"_54":293,"_56":294,"_153":154,"_155":279,"_126":280,"_128":280,"_45":362,"_130":298,"_165":363},{"_159":296,"_161":162,"_163":297},[364],{"_43":269,"_54":66,"_56":67,"_153":154,"_155":270,"_126":157,"_128":157,"_45":365,"_130":274,"_165":366},{"_159":272,"_161":162,"_163":273},[],{"_43":217,"_54":316,"_56":317,"_153":154,"_155":279,"_126":280,"_128":280,"_45":368,"_130":319,"_165":369},{"_159":282,"_161":162,"_163":221},[370],{"_43":214,"_54":215,"_56":216,"_153":154,"_155":217,"_126":218,"_128":218,"_45":371,"_130":216,"_165":372},{"_159":220,"_161":162,"_163":221},[373],{"_43":310,"_54":66,"_56":67,"_153":154,"_155":214,"_126":311,"_128":311,"_45":374,"_130":314,"_165":375},{"_159":162,"_161":162,"_163":313},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários