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Há materiais que podem ser submetidos a grandes deformações antes de sofrerem ruptura. Com base nesses materiais, assinale a alternativa:

","status","pending_classification","hasRelatedVideo","relatedVideos",[108],{"_109":110,"_128":129,"_50":144,"_179":180,"_197":198},"content",{"_43":111,"_54":112,"_113":-5,"_114":115,"_116":117,"_118":-5,"_45":119,"_122":123,"_124":123,"_125":-5,"_126":127},"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",{"_120":121},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-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","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",[145],{"_43":146,"_54":147,"_56":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":153,"_126":148,"_160":161},"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",{"_154":155,"_156":157,"_158":159},"childrenCount",18,"content_count",0,"question_count",135489,"children",[162],{"_43":163,"_54":164,"_56":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":167,"_126":170,"_160":171},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_154":168,"_156":157,"_158":169},10,19948,"mecanica-2",[172],{"_43":173,"_54":62,"_56":63,"_149":150,"_151":163,"_122":174,"_124":174,"_45":175,"_126":177,"_160":178},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_154":157,"_156":157,"_158":176},3376,"resistencia-dos-materiais-4",[],"video",{"_43":117,"_13":112,"_113":-5,"_181":182,"_183":184,"_28":-5,"_185":-5,"_130":184,"_186":187,"_141":-5,"_188":-5,"_189":-5,"_190":-5,"_191":-5,"_45":192,"_193":157,"_194":-5,"_103":195,"_122":196,"_124":196},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_120":121},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_43":146,"_54":147,"_56":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":199,"_126":148,"_160":200},{"_154":155,"_156":157,"_158":159},[201],{"_43":163,"_54":164,"_56":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":202,"_126":170,"_160":203},{"_154":168,"_156":157,"_158":169},[204],{"_43":173,"_54":62,"_56":63,"_149":150,"_151":163,"_122":174,"_124":174,"_45":205,"_126":177,"_160":206},{"_154":157,"_156":157,"_158":176},[],"similarQuestions",[209,240,260],{"_40":210,"_42":41,"_43":211,"_80":212,"_100":228,"_101":229,"_50":230},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[213,216,219,222,225],{"_43":214,"_84":85,"_86":215},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":217,"_84":90,"_86":218},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":220,"_84":94,"_86":221},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":223,"_84":98,"_86":224},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":210,"_84":226,"_86":227},"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

",[231],{"_43":232,"_54":233,"_56":234,"_149":150,"_151":235,"_122":236,"_124":236,"_45":237,"_126":234},"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",{"_154":238,"_156":157,"_158":239},4,12302,{"_40":241,"_42":41,"_43":242,"_80":243,"_100":255,"_101":256,"_50":257},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[244,247,250,252],{"_43":245,"_84":85,"_86":246},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":248,"_84":90,"_86":249},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":241,"_84":94,"_86":251},"

Verdadeiro, falso, verdadeiro

",{"_43":253,"_84":98,"_86":254},"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?

",[258],{"_43":232,"_54":233,"_56":234,"_149":150,"_151":235,"_122":236,"_124":236,"_45":259,"_126":234},{"_154":238,"_156":157,"_158":239},{"_40":261,"_42":41,"_43":262,"_80":263,"_100":278,"_101":279,"_50":280},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[264,267,270,272,275],{"_43":265,"_84":85,"_86":266},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":268,"_84":90,"_86":269},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":261,"_84":94,"_86":271},"Indeterminado",{"_43":273,"_84":98,"_86":274},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":276,"_84":226,"_86":277},"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????",[281],{"_43":232,"_54":233,"_56":234,"_149":150,"_151":235,"_122":236,"_124":236,"_45":282,"_126":234},{"_154":238,"_156":157,"_158":239},[284,286,295,301,305,307,309,317,322,330,332,337,343],{"_43":232,"_54":233,"_56":234,"_149":150,"_151":235,"_122":236,"_124":236,"_45":285,"_126":234},{"_154":238,"_156":157,"_158":239},{"_43":287,"_54":288,"_56":289,"_149":150,"_151":290,"_122":166,"_124":166,"_45":291,"_126":294},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_154":292,"_156":157,"_158":293},5,30614,"engenharia-mecatronica-1",{"_43":296,"_54":62,"_56":63,"_149":150,"_151":297,"_122":298,"_124":298,"_45":299,"_126":300},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-6",{"_43":297,"_54":164,"_56":165,"_149":150,"_151":287,"_122":236,"_124":236,"_45":302,"_126":304},{"_154":292,"_156":157,"_158":303},25741,"mecanica-3",{"_43":146,"_54":147,"_56":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":306,"_126":148},{"_154":155,"_156":157,"_158":159},{"_43":173,"_54":62,"_56":63,"_149":150,"_151":163,"_122":174,"_124":174,"_45":308,"_126":177},{"_154":157,"_156":157,"_158":176},{"_43":310,"_54":311,"_56":312,"_149":150,"_151":290,"_122":166,"_124":166,"_45":313,"_126":316},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_154":314,"_156":157,"_158":315},21,45865,"engenharia-civil-3",{"_43":235,"_54":318,"_56":319,"_149":150,"_151":290,"_122":166,"_124":166,"_45":320,"_126":321},"Engenharia de Petróleo","engenharia-de-petroleo",{"_154":292,"_156":157,"_158":239},"engenharia-de-petroleo-1",{"_43":323,"_54":324,"_56":325,"_149":150,"_151":310,"_122":326,"_124":326,"_45":327,"_126":329},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_154":292,"_156":157,"_158":328},8852,"estruturas-1",{"_43":163,"_54":164,"_56":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":331,"_126":170},{"_154":168,"_156":157,"_158":169},{"_43":333,"_54":62,"_56":63,"_149":150,"_151":232,"_122":334,"_124":334,"_45":335,"_126":336},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-7",{"_43":338,"_54":339,"_56":63,"_149":150,"_151":323,"_122":340,"_124":340,"_45":341,"_126":342},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_154":157,"_156":157,"_158":176},"resistencia-dos-materiais-5",{"_43":290,"_54":344,"_56":345,"_149":150,"_151":-5,"_122":346,"_124":346,"_45":347,"_126":345},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_154":348,"_156":157,"_158":349},29,351586,"tagsTree",[352,361],{"_43":146,"_54":147,"_56":148,"_149":150,"_151":-5,"_122":152,"_124":152,"_45":353,"_126":148,"_160":354},{"_154":155,"_156":157,"_158":159},[355],{"_43":163,"_54":164,"_56":165,"_149":150,"_151":146,"_122":166,"_124":166,"_45":356,"_126":170,"_160":357},{"_154":168,"_156":157,"_158":169},[358],{"_43":173,"_54":62,"_56":63,"_149":150,"_151":163,"_122":174,"_124":174,"_45":359,"_126":177,"_160":360},{"_154":157,"_156":157,"_158":176},[],{"_43":290,"_54":344,"_56":345,"_149":150,"_151":-5,"_122":346,"_124":346,"_45":362,"_126":345,"_160":363},{"_154":348,"_156":157,"_158":349},[364,373,382],{"_43":287,"_54":288,"_56":289,"_149":150,"_151":290,"_122":166,"_124":166,"_45":365,"_126":294,"_160":366},{"_154":292,"_156":157,"_158":293},[367],{"_43":297,"_54":164,"_56":165,"_149":150,"_151":287,"_122":236,"_124":236,"_45":368,"_126":304,"_160":369},{"_154":292,"_156":157,"_158":303},[370],{"_43":296,"_54":62,"_56":63,"_149":150,"_151":297,"_122":298,"_124":298,"_45":371,"_126":300,"_160":372},{"_154":157,"_156":157,"_158":176},[],{"_43":310,"_54":311,"_56":312,"_149":150,"_151":290,"_122":166,"_124":166,"_45":374,"_126":316,"_160":375},{"_154":314,"_156":157,"_158":315},[376],{"_43":323,"_54":324,"_56":325,"_149":150,"_151":310,"_122":326,"_124":326,"_45":377,"_126":329,"_160":378},{"_154":292,"_156":157,"_158":328},[379],{"_43":338,"_54":339,"_56":63,"_149":150,"_151":323,"_122":340,"_124":340,"_45":380,"_126":342,"_160":381},{"_154":157,"_156":157,"_158":176},[],{"_43":235,"_54":318,"_56":319,"_149":150,"_151":290,"_122":166,"_124":166,"_45":383,"_126":321,"_160":384},{"_154":292,"_156":157,"_158":239},[385],{"_43":232,"_54":233,"_56":234,"_149":150,"_151":235,"_122":236,"_124":236,"_45":386,"_126":234,"_160":387},{"_154":238,"_156":157,"_158":239},[388],{"_43":333,"_54":62,"_56":63,"_149":150,"_151":232,"_122":334,"_124":334,"_45":389,"_126":336,"_160":390},{"_154":157,"_156":157,"_158":176},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários