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Determine os momentos de primeira ordem da superfície plana mostrada, em relação aos eixos baricentros.

","status","pending_classification","hasRelatedVideo","relatedVideos",[115],{"_116":117,"_135":136,"_50":151,"_186":187,"_204":152},"content",{"_43":118,"_54":119,"_120":-5,"_121":122,"_123":124,"_125":-5,"_45":126,"_129":130,"_131":130,"_132":-5,"_133":134},"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",{"_127":128},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_137":138,"_144":145,"_146":147,"_148":149,"_28":150},"provider",{"_43":139,"_140":141,"_142":143},"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",[152],{"_43":153,"_54":154,"_56":155,"_156":157,"_158":-5,"_129":159,"_131":159,"_45":160,"_133":155,"_167":168},"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",{"_161":162,"_163":164,"_165":166},"childrenCount",18,"content_count",0,"question_count",135489,"children",[169],{"_43":170,"_54":171,"_56":172,"_156":157,"_158":153,"_129":173,"_131":173,"_45":174,"_133":177,"_167":178},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_161":175,"_163":164,"_165":176},10,19948,"mecanica-2",[179],{"_43":180,"_54":66,"_56":61,"_156":157,"_158":170,"_129":181,"_131":181,"_45":182,"_133":184,"_167":185},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_161":164,"_163":164,"_165":183},3376,"resistencia-dos-materiais-4",[],"video",{"_43":124,"_13":119,"_120":-5,"_188":189,"_190":191,"_28":-5,"_192":-5,"_137":191,"_193":194,"_148":-5,"_195":-5,"_196":-5,"_197":-5,"_198":-5,"_45":199,"_200":164,"_201":-5,"_110":202,"_129":203,"_131":203},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_127":128},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[207,237,255],{"_40":208,"_42":41,"_43":209,"_83":210,"_107":225,"_108":226,"_50":227},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[211,214,217,220,223],{"_43":212,"_87":88,"_89":213},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":215,"_87":93,"_89":216},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":218,"_87":97,"_89":219},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":221,"_87":101,"_89":222},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":208,"_87":105,"_89":224},"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

",[228],{"_43":229,"_54":230,"_56":231,"_156":157,"_158":232,"_129":233,"_131":233,"_45":234,"_133":231},"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",{"_161":235,"_163":164,"_165":236},4,12302,{"_40":238,"_42":41,"_43":239,"_83":240,"_107":252,"_108":253,"_50":254},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[241,244,247,249],{"_43":242,"_87":88,"_89":243},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":245,"_87":93,"_89":246},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":238,"_87":97,"_89":248},"

Verdadeiro, falso, verdadeiro

",{"_43":250,"_87":101,"_89":251},"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?

",[228],{"_40":256,"_42":41,"_43":257,"_83":258,"_107":273,"_108":274,"_50":275},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[259,262,265,267,270],{"_43":260,"_87":88,"_89":261},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":263,"_87":93,"_89":264},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":256,"_87":97,"_89":266},"Indeterminado",{"_43":268,"_87":101,"_89":269},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":271,"_87":105,"_89":272},"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????",[228],[228,277,286,292,296,297,298,306,311,319,320,325,331],{"_43":278,"_54":279,"_56":280,"_156":157,"_158":281,"_129":173,"_131":173,"_45":282,"_133":285},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_161":283,"_163":164,"_165":284},5,30614,"engenharia-mecatronica-1",{"_43":287,"_54":66,"_56":61,"_156":157,"_158":288,"_129":289,"_131":289,"_45":290,"_133":291},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_161":164,"_163":164,"_165":183},"resistencia-dos-materiais-6",{"_43":288,"_54":171,"_56":172,"_156":157,"_158":278,"_129":233,"_131":233,"_45":293,"_133":295},{"_161":283,"_163":164,"_165":294},25741,"mecanica-3",{"_43":153,"_54":154,"_56":155,"_156":157,"_158":-5,"_129":159,"_131":159,"_45":160,"_133":155},{"_43":180,"_54":66,"_56":61,"_156":157,"_158":170,"_129":181,"_131":181,"_45":182,"_133":184},{"_43":299,"_54":300,"_56":301,"_156":157,"_158":281,"_129":173,"_131":173,"_45":302,"_133":305},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_161":303,"_163":164,"_165":304},21,45865,"engenharia-civil-3",{"_43":232,"_54":307,"_56":308,"_156":157,"_158":281,"_129":173,"_131":173,"_45":309,"_133":310},"Engenharia de Petróleo","engenharia-de-petroleo",{"_161":283,"_163":164,"_165":236},"engenharia-de-petroleo-1",{"_43":312,"_54":313,"_56":314,"_156":157,"_158":299,"_129":315,"_131":315,"_45":316,"_133":318},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_161":283,"_163":164,"_165":317},8852,"estruturas-1",{"_43":170,"_54":171,"_56":172,"_156":157,"_158":153,"_129":173,"_131":173,"_45":174,"_133":177},{"_43":321,"_54":66,"_56":61,"_156":157,"_158":229,"_129":322,"_131":322,"_45":323,"_133":324},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_161":164,"_163":164,"_165":183},"resistencia-dos-materiais-7",{"_43":326,"_54":327,"_56":61,"_156":157,"_158":312,"_129":328,"_131":328,"_45":329,"_133":330},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_161":164,"_163":164,"_165":183},"resistencia-dos-materiais-5",{"_43":281,"_54":332,"_56":333,"_156":157,"_158":-5,"_129":334,"_131":334,"_45":335,"_133":333},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_161":336,"_163":164,"_165":337},29,351586,"tagsTree",[152,340],{"_43":281,"_54":332,"_56":333,"_156":157,"_158":-5,"_129":334,"_131":334,"_45":335,"_133":333,"_167":341},[342,348,354],{"_43":278,"_54":279,"_56":280,"_156":157,"_158":281,"_129":173,"_131":173,"_45":282,"_133":285,"_167":343},[344],{"_43":288,"_54":171,"_56":172,"_156":157,"_158":278,"_129":233,"_131":233,"_45":293,"_133":295,"_167":345},[346],{"_43":287,"_54":66,"_56":61,"_156":157,"_158":288,"_129":289,"_131":289,"_45":290,"_133":291,"_167":347},[],{"_43":299,"_54":300,"_56":301,"_156":157,"_158":281,"_129":173,"_131":173,"_45":302,"_133":305,"_167":349},[350],{"_43":312,"_54":313,"_56":314,"_156":157,"_158":299,"_129":315,"_131":315,"_45":316,"_133":318,"_167":351},[352],{"_43":326,"_54":327,"_56":61,"_156":157,"_158":312,"_129":328,"_131":328,"_45":329,"_133":330,"_167":353},[],{"_43":232,"_54":307,"_56":308,"_156":157,"_158":281,"_129":173,"_131":173,"_45":309,"_133":310,"_167":355},[356],{"_43":229,"_54":230,"_56":231,"_156":157,"_158":232,"_129":233,"_131":233,"_45":234,"_133":231,"_167":357},[358],{"_43":321,"_54":66,"_56":61,"_156":157,"_158":229,"_129":322,"_131":322,"_45":323,"_133":324,"_167":359},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários