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Quais são eles?","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_163":164,"_181":145},"content",{"_43":111,"_54":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_130":131,"_137":138,"_139":140,"_141":142,"_28":143},"provider",{"_43":132,"_133":134,"_135":136},"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",[145],{"_43":146,"_54":147,"_56":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":154,"_126":148,"_161":162},"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",{"_155":156,"_157":158,"_159":160},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":117,"_13":112,"_113":-5,"_165":166,"_167":168,"_28":-5,"_169":-5,"_130":168,"_170":171,"_141":-5,"_172":-5,"_173":-5,"_174":-5,"_175":-5,"_45":176,"_177":158,"_178":-5,"_103":179,"_122":180,"_124":180},"duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag","similarQuestions",[184,215,233],{"_40":185,"_42":41,"_43":186,"_80":187,"_100":203,"_101":204,"_50":205},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[188,191,194,197,200],{"_43":189,"_84":85,"_86":190},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":192,"_84":90,"_86":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":195,"_84":94,"_86":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":198,"_84":98,"_86":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":185,"_84":201,"_86":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],{"_43":207,"_54":208,"_56":209,"_149":150,"_151":210,"_122":211,"_124":211,"_45":212,"_126":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",{"_155":213,"_157":158,"_159":214},4,12302,{"_40":216,"_42":41,"_43":217,"_80":218,"_100":230,"_101":231,"_50":232},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[219,222,225,227],{"_43":220,"_84":85,"_86":221},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":223,"_84":90,"_86":224},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":216,"_84":94,"_86":226},"

Verdadeiro, falso, verdadeiro

",{"_43":228,"_84":98,"_86":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?

",[206],{"_40":234,"_42":41,"_43":235,"_80":236,"_100":251,"_101":252,"_50":253},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[237,240,243,245,248],{"_43":238,"_84":85,"_86":239},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":241,"_84":90,"_86":242},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":234,"_84":94,"_86":244},"Indeterminado",{"_43":246,"_84":98,"_86":247},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":249,"_84":201,"_86":250},"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????",[206],[206,255,262,272,279,286,287,295,301,306,312,319],{"_43":256,"_54":62,"_56":63,"_149":150,"_151":257,"_122":153,"_124":153,"_45":258,"_126":261},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":259,"_157":158,"_159":260},2,11846,"termodinamica-3",{"_43":263,"_54":264,"_56":265,"_149":150,"_151":266,"_122":267,"_124":267,"_45":268,"_126":271},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":269,"_157":158,"_159":270},5,30614,"engenharia-mecatronica-1",{"_43":273,"_54":274,"_56":275,"_149":150,"_151":263,"_122":211,"_124":211,"_45":276,"_126":278},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":269,"_157":158,"_159":277},25741,"mecanica-3",{"_43":257,"_54":280,"_56":281,"_149":150,"_151":266,"_122":267,"_124":267,"_45":282,"_126":285},"Engenharia Mecânica","engenharia-mecanica",{"_155":283,"_157":158,"_159":284},11,36318,"engenharia-mecanica-2",{"_43":146,"_54":147,"_56":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":154,"_126":148},{"_43":288,"_54":289,"_56":290,"_149":150,"_151":-5,"_122":291,"_124":291,"_45":292,"_126":290},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":293,"_157":158,"_159":294},18,135489,{"_43":296,"_54":62,"_56":63,"_149":150,"_151":207,"_122":297,"_124":297,"_45":298,"_126":300},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":299},8597,"termodinamica-5",{"_43":210,"_54":302,"_56":303,"_149":150,"_151":266,"_122":267,"_124":267,"_45":304,"_126":305},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":269,"_157":158,"_159":214},"engenharia-de-petroleo-1",{"_43":152,"_54":307,"_56":308,"_149":150,"_151":288,"_122":267,"_124":267,"_45":309,"_126":311},"Física","fisica",{"_155":283,"_157":158,"_159":310},13777,"fisica-4",{"_43":266,"_54":313,"_56":314,"_149":150,"_151":-5,"_122":315,"_124":315,"_45":316,"_126":314},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":317,"_157":158,"_159":318},29,351586,{"_43":320,"_54":62,"_56":63,"_149":150,"_151":273,"_122":321,"_124":321,"_45":322,"_126":323},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":299},"termodinamica-4","tagsTree",[326,330],{"_43":288,"_54":289,"_56":290,"_149":150,"_151":-5,"_122":291,"_124":291,"_45":292,"_126":290,"_161":327},[328],{"_43":152,"_54":307,"_56":308,"_149":150,"_151":288,"_122":267,"_124":267,"_45":309,"_126":311,"_161":329},[145],{"_43":266,"_54":313,"_56":314,"_149":150,"_151":-5,"_122":315,"_124":315,"_45":316,"_126":314,"_161":331},[332,338,342],{"_43":263,"_54":264,"_56":265,"_149":150,"_151":266,"_122":267,"_124":267,"_45":268,"_126":271,"_161":333},[334],{"_43":273,"_54":274,"_56":275,"_149":150,"_151":263,"_122":211,"_124":211,"_45":276,"_126":278,"_161":335},[336],{"_43":320,"_54":62,"_56":63,"_149":150,"_151":273,"_122":321,"_124":321,"_45":322,"_126":323,"_161":337},[],{"_43":257,"_54":280,"_56":281,"_149":150,"_151":266,"_122":267,"_124":267,"_45":282,"_126":285,"_161":339},[340],{"_43":256,"_54":62,"_56":63,"_149":150,"_151":257,"_122":153,"_124":153,"_45":258,"_126":261,"_161":341},[],{"_43":210,"_54":302,"_56":303,"_149":150,"_151":266,"_122":267,"_124":267,"_45":304,"_126":305,"_161":343},[344],{"_43":207,"_54":208,"_56":209,"_149":150,"_151":210,"_122":211,"_124":211,"_45":212,"_126":209,"_161":345},[346],{"_43":296,"_54":62,"_56":63,"_149":150,"_151":207,"_122":297,"_124":297,"_45":298,"_126":300,"_161":347},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários