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Um construtor deixou um espaço entre uma parede e uma viga de aço cujo coeficiente de dilatação linear é de 11 \\times 10^{-6} \\; /ºC. Ele sabe que a viga dilatará 2 \\; mm. Qual será a variação de temperatura necessária para que esta dilatação ocorra, se a viga inicialmente possui 2,1 \\; m?

","status","pending_classification","hasRelatedVideo","relatedVideos",[88],{"_89":90,"_108":109,"_29":124,"_159":160,"_178":125},"content",{"_21":91,"_35":92,"_93":-5,"_94":95,"_96":97,"_98":-5,"_23":99,"_102":103,"_104":103,"_105":-5,"_106":107},"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",{"_100":101},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_110":111,"_117":118,"_119":120,"_121":122,"_6":123},"provider",{"_21":112,"_113":114,"_115":116},"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",[125],{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":133,"_106":128,"_140":141},"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",{"_134":135,"_136":137,"_138":139},"childrenCount",18,"content_count",0,"question_count",135489,"children",[142],{"_21":143,"_35":144,"_37":145,"_129":130,"_131":126,"_102":146,"_104":146,"_23":147,"_106":150,"_140":151},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_134":148,"_136":137,"_138":149},10,19948,"mecanica-2",[152],{"_21":153,"_35":36,"_37":38,"_129":130,"_131":143,"_102":154,"_104":154,"_23":155,"_106":157,"_140":158},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_134":137,"_136":137,"_138":156},3376,"resistencia-dos-materiais-4",[],"video",{"_21":97,"_161":92,"_93":-5,"_162":163,"_164":165,"_6":-5,"_166":-5,"_110":165,"_167":168,"_121":-5,"_169":-5,"_170":-5,"_171":-5,"_172":-5,"_23":173,"_174":137,"_175":-5,"_83":176,"_102":177,"_104":177},"title","duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_100":101},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag","similarQuestions",[181,211,229],{"_18":182,"_20":19,"_21":183,"_56":184,"_80":199,"_81":200,"_29":201},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[185,188,191,194,197],{"_21":186,"_60":61,"_62":187},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_21":189,"_60":66,"_62":190},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_21":192,"_60":70,"_62":193},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_21":195,"_60":74,"_62":196},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_21":182,"_60":78,"_62":198},"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

",[202],{"_21":203,"_35":204,"_37":205,"_129":130,"_131":206,"_102":207,"_104":207,"_23":208,"_106":205},"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",{"_134":209,"_136":137,"_138":210},4,12302,{"_18":212,"_20":19,"_21":213,"_56":214,"_80":226,"_81":227,"_29":228},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[215,218,221,223],{"_21":216,"_60":61,"_62":217},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":219,"_60":66,"_62":220},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":212,"_60":70,"_62":222},"

Verdadeiro, falso, verdadeiro

",{"_21":224,"_60":74,"_62":225},"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????",[202],[202,251,260,266,270,271,272,280,285,293,294,299,305],{"_21":252,"_35":253,"_37":254,"_129":130,"_131":255,"_102":146,"_104":146,"_23":256,"_106":259},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_134":257,"_136":137,"_138":258},5,30614,"engenharia-mecatronica-1",{"_21":261,"_35":36,"_37":38,"_129":130,"_131":262,"_102":263,"_104":263,"_23":264,"_106":265},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-6",{"_21":262,"_35":144,"_37":145,"_129":130,"_131":252,"_102":207,"_104":207,"_23":267,"_106":269},{"_134":257,"_136":137,"_138":268},25741,"mecanica-3",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":-5,"_102":132,"_104":132,"_23":133,"_106":128},{"_21":153,"_35":36,"_37":38,"_129":130,"_131":143,"_102":154,"_104":154,"_23":155,"_106":157},{"_21":273,"_35":274,"_37":275,"_129":130,"_131":255,"_102":146,"_104":146,"_23":276,"_106":279},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_134":277,"_136":137,"_138":278},21,45865,"engenharia-civil-3",{"_21":206,"_35":281,"_37":282,"_129":130,"_131":255,"_102":146,"_104":146,"_23":283,"_106":284},"Engenharia de Petróleo","engenharia-de-petroleo",{"_134":257,"_136":137,"_138":210},"engenharia-de-petroleo-1",{"_21":286,"_35":287,"_37":288,"_129":130,"_131":273,"_102":289,"_104":289,"_23":290,"_106":292},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_134":257,"_136":137,"_138":291},8852,"estruturas-1",{"_21":143,"_35":144,"_37":145,"_129":130,"_131":126,"_102":146,"_104":146,"_23":147,"_106":150},{"_21":295,"_35":36,"_37":38,"_129":130,"_131":203,"_102":296,"_104":296,"_23":297,"_106":298},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-7",{"_21":300,"_35":301,"_37":38,"_129":130,"_131":286,"_102":302,"_104":302,"_23":303,"_106":304},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_134":137,"_136":137,"_138":156},"resistencia-dos-materiais-5",{"_21":255,"_35":306,"_37":307,"_129":130,"_131":-5,"_102":308,"_104":308,"_23":309,"_106":307},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_134":310,"_136":137,"_138":311},29,351586,"tagsTree",[125,314],{"_21":255,"_35":306,"_37":307,"_129":130,"_131":-5,"_102":308,"_104":308,"_23":309,"_106":307,"_140":315},[316,322,328],{"_21":252,"_35":253,"_37":254,"_129":130,"_131":255,"_102":146,"_104":146,"_23":256,"_106":259,"_140":317},[318],{"_21":262,"_35":144,"_37":145,"_129":130,"_131":252,"_102":207,"_104":207,"_23":267,"_106":269,"_140":319},[320],{"_21":261,"_35":36,"_37":38,"_129":130,"_131":262,"_102":263,"_104":263,"_23":264,"_106":265,"_140":321},[],{"_21":273,"_35":274,"_37":275,"_129":130,"_131":255,"_102":146,"_104":146,"_23":276,"_106":279,"_140":323},[324],{"_21":286,"_35":287,"_37":288,"_129":130,"_131":273,"_102":289,"_104":289,"_23":290,"_106":292,"_140":325},[326],{"_21":300,"_35":301,"_37":38,"_129":130,"_131":286,"_102":302,"_104":302,"_23":303,"_106":304,"_140":327},[],{"_21":206,"_35":281,"_37":282,"_129":130,"_131":255,"_102":146,"_104":146,"_23":283,"_106":284,"_140":329},[330],{"_21":203,"_35":204,"_37":205,"_129":130,"_131":206,"_102":207,"_104":207,"_23":208,"_106":205,"_140":331},[332],{"_21":295,"_35":36,"_37":38,"_129":130,"_131":203,"_102":296,"_104":296,"_23":297,"_106":298,"_140":333},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários