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Existem 1.000 cadeiras escolares para serem

transportadas. Inicialmente, 30 pessoas, em 12

minutos, conseguiram se mobilizar a transportaram

400 cadeiras. Para o transporte das cadeiras restantes,

foram contratadas mais 6 pessoas. Em quanto tempo

todas elas conseguirão transportar e restante das

cadeiras?

","status","pending_classification","hasRelatedVideo","relatedVideos",[112],{"_113":114,"_132":133,"_50":148,"_183":184,"_201":202},"content",{"_43":115,"_54":116,"_117":-5,"_118":119,"_120":121,"_122":-5,"_45":123,"_126":127,"_128":127,"_129":-5,"_130":131},"468e3e62-35e0-47be-a15f-68dd43bb32bb","Óptica Geométrica - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","fa6aaf42-4cc4-4d76-8915-7a67081f7e9a","user_id",{"_124":125},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-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","d80487a0-0f98-42c8-99bb-551165ba3068","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/d80487a0-0f98-42c8-99bb-551165ba3068/levels.m3u8",[149],{"_43":150,"_54":151,"_56":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_45":157,"_130":152,"_164":165},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_158":159,"_160":161,"_162":163},"childrenCount",18,"content_count",0,"question_count",135489,"children",[166],{"_43":167,"_54":168,"_56":169,"_153":154,"_155":150,"_126":170,"_128":170,"_45":171,"_130":174,"_164":175},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_158":172,"_160":161,"_162":173},10,19948,"mecanica-2",[176],{"_43":177,"_54":62,"_56":63,"_153":154,"_155":167,"_126":178,"_128":178,"_45":179,"_130":181,"_164":182},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_158":161,"_160":161,"_162":180},3376,"resistencia-dos-materiais-4",[],"video",{"_43":121,"_13":116,"_117":-5,"_185":186,"_187":188,"_28":-5,"_189":-5,"_134":188,"_190":191,"_145":-5,"_192":-5,"_193":-5,"_194":-5,"_195":-5,"_45":196,"_197":161,"_198":-5,"_107":199,"_126":200,"_128":200},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_124":125},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_45":203,"_130":152,"_164":204},{"_158":159,"_160":161,"_162":163},[205],{"_43":167,"_54":168,"_56":169,"_153":154,"_155":150,"_126":170,"_128":170,"_45":206,"_130":174,"_164":207},{"_158":172,"_160":161,"_162":173},[208],{"_43":177,"_54":62,"_56":63,"_153":154,"_155":167,"_126":178,"_128":178,"_45":209,"_130":181,"_164":210},{"_158":161,"_160":161,"_162":180},[],"similarQuestions",[213,243,263],{"_40":214,"_42":41,"_43":215,"_80":216,"_104":231,"_105":232,"_50":233},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[217,220,223,226,229],{"_43":218,"_84":85,"_86":219},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":221,"_84":90,"_86":222},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":224,"_84":94,"_86":225},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":227,"_84":98,"_86":228},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":214,"_84":102,"_86":230},"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

",[234],{"_43":235,"_54":236,"_56":237,"_153":154,"_155":238,"_126":239,"_128":239,"_45":240,"_130":237},"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",{"_158":241,"_160":161,"_162":242},4,12302,{"_40":244,"_42":41,"_43":245,"_80":246,"_104":258,"_105":259,"_50":260},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[247,250,253,255],{"_43":248,"_84":85,"_86":249},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":251,"_84":90,"_86":252},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":244,"_84":94,"_86":254},"

Verdadeiro, falso, verdadeiro

",{"_43":256,"_84":98,"_86":257},"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?

",[261],{"_43":235,"_54":236,"_56":237,"_153":154,"_155":238,"_126":239,"_128":239,"_45":262,"_130":237},{"_158":241,"_160":161,"_162":242},{"_40":264,"_42":41,"_43":265,"_80":266,"_104":281,"_105":282,"_50":283},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[267,270,273,275,278],{"_43":268,"_84":85,"_86":269},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":271,"_84":90,"_86":272},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":264,"_84":94,"_86":274},"Indeterminado",{"_43":276,"_84":98,"_86":277},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":279,"_84":102,"_86":280},"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????",[284],{"_43":235,"_54":236,"_56":237,"_153":154,"_155":238,"_126":239,"_128":239,"_45":285,"_130":237},{"_158":241,"_160":161,"_162":242},[287,289,298,304,308,310,312,320,325,333,335,340,346],{"_43":235,"_54":236,"_56":237,"_153":154,"_155":238,"_126":239,"_128":239,"_45":288,"_130":237},{"_158":241,"_160":161,"_162":242},{"_43":290,"_54":291,"_56":292,"_153":154,"_155":293,"_126":170,"_128":170,"_45":294,"_130":297},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_158":295,"_160":161,"_162":296},5,30614,"engenharia-mecatronica-1",{"_43":299,"_54":62,"_56":63,"_153":154,"_155":300,"_126":301,"_128":301,"_45":302,"_130":303},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-6",{"_43":300,"_54":168,"_56":169,"_153":154,"_155":290,"_126":239,"_128":239,"_45":305,"_130":307},{"_158":295,"_160":161,"_162":306},25741,"mecanica-3",{"_43":150,"_54":151,"_56":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_45":309,"_130":152},{"_158":159,"_160":161,"_162":163},{"_43":177,"_54":62,"_56":63,"_153":154,"_155":167,"_126":178,"_128":178,"_45":311,"_130":181},{"_158":161,"_160":161,"_162":180},{"_43":313,"_54":314,"_56":315,"_153":154,"_155":293,"_126":170,"_128":170,"_45":316,"_130":319},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_158":317,"_160":161,"_162":318},21,45865,"engenharia-civil-3",{"_43":238,"_54":321,"_56":322,"_153":154,"_155":293,"_126":170,"_128":170,"_45":323,"_130":324},"Engenharia de Petróleo","engenharia-de-petroleo",{"_158":295,"_160":161,"_162":242},"engenharia-de-petroleo-1",{"_43":326,"_54":327,"_56":328,"_153":154,"_155":313,"_126":329,"_128":329,"_45":330,"_130":332},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_158":295,"_160":161,"_162":331},8852,"estruturas-1",{"_43":167,"_54":168,"_56":169,"_153":154,"_155":150,"_126":170,"_128":170,"_45":334,"_130":174},{"_158":172,"_160":161,"_162":173},{"_43":336,"_54":62,"_56":63,"_153":154,"_155":235,"_126":337,"_128":337,"_45":338,"_130":339},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-7",{"_43":341,"_54":342,"_56":63,"_153":154,"_155":326,"_126":343,"_128":343,"_45":344,"_130":345},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_158":161,"_160":161,"_162":180},"resistencia-dos-materiais-5",{"_43":293,"_54":347,"_56":348,"_153":154,"_155":-5,"_126":349,"_128":349,"_45":350,"_130":348},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_158":351,"_160":161,"_162":352},29,351586,"tagsTree",[355,364],{"_43":150,"_54":151,"_56":152,"_153":154,"_155":-5,"_126":156,"_128":156,"_45":356,"_130":152,"_164":357},{"_158":159,"_160":161,"_162":163},[358],{"_43":167,"_54":168,"_56":169,"_153":154,"_155":150,"_126":170,"_128":170,"_45":359,"_130":174,"_164":360},{"_158":172,"_160":161,"_162":173},[361],{"_43":177,"_54":62,"_56":63,"_153":154,"_155":167,"_126":178,"_128":178,"_45":362,"_130":181,"_164":363},{"_158":161,"_160":161,"_162":180},[],{"_43":293,"_54":347,"_56":348,"_153":154,"_155":-5,"_126":349,"_128":349,"_45":365,"_130":348,"_164":366},{"_158":351,"_160":161,"_162":352},[367,376,385],{"_43":290,"_54":291,"_56":292,"_153":154,"_155":293,"_126":170,"_128":170,"_45":368,"_130":297,"_164":369},{"_158":295,"_160":161,"_162":296},[370],{"_43":300,"_54":168,"_56":169,"_153":154,"_155":290,"_126":239,"_128":239,"_45":371,"_130":307,"_164":372},{"_158":295,"_160":161,"_162":306},[373],{"_43":299,"_54":62,"_56":63,"_153":154,"_155":300,"_126":301,"_128":301,"_45":374,"_130":303,"_164":375},{"_158":161,"_160":161,"_162":180},[],{"_43":313,"_54":314,"_56":315,"_153":154,"_155":293,"_126":170,"_128":170,"_45":377,"_130":319,"_164":378},{"_158":317,"_160":161,"_162":318},[379],{"_43":326,"_54":327,"_56":328,"_153":154,"_155":313,"_126":329,"_128":329,"_45":380,"_130":332,"_164":381},{"_158":295,"_160":161,"_162":331},[382],{"_43":341,"_54":342,"_56":63,"_153":154,"_155":326,"_126":343,"_128":343,"_45":383,"_130":345,"_164":384},{"_158":161,"_160":161,"_162":180},[],{"_43":238,"_54":321,"_56":322,"_153":154,"_155":293,"_126":170,"_128":170,"_45":386,"_130":324,"_164":387},{"_158":295,"_160":161,"_162":242},[388],{"_43":235,"_54":236,"_56":237,"_153":154,"_155":238,"_126":239,"_128":239,"_45":389,"_130":237,"_164":390},{"_158":241,"_160":161,"_162":242},[391],{"_43":336,"_54":62,"_56":63,"_153":154,"_155":235,"_126":337,"_128":337,"_45":392,"_130":339,"_164":393},{"_158":161,"_160":161,"_162":180},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários