[{"_1":2,"_536":-5,"_537":-5},"loaderData",{"_3":4,"_31":32},"root",{"_5":6,"_28":29,"_30":-5},"registerModalConfig",{"_7":8,"_15":16},"blockedConfig",{"_9":10,"_15":16,"_17":18,"_21":22,"_24":25},"answerQuestion",{"_11":12,"_13":14},"subtitle","Crie sua conta gratuita e utilize todos os nossos recursos de questões disponiveis","title","Para responder, cadastre-se gratuitamente","customBlockedUI",true,"defaultRegister",{"_11":19,"_13":20},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis","Cadastre-se gratuitamente","imageSearch",{"_11":19,"_13":23},"Para buscar por imagem, cadastre-se gratuitamente","questionAnswer",{"_11":26,"_13":27},"Crie sua conta gratuita e utilize todos os nossos recursos disponíveis para responder","Para ver a resposta, cadastre-se gratuitamente","url","https://prouniversitario.com/exercicios/67a732b4-d7a5-4414-8390-75f27edaf571?video=true","user","pages/questions/show/index",{"_33":34,"_35":36,"_37":36,"_38":39,"_251":252,"_352":353,"_52":428,"_491":492,"_532":533,"_534":535},"comments",[],"hasVideoHash",false,"isAiGenerated","question",{"_40":41,"_42":43,"_44":45,"_46":47,"_226":227,"_245":43,"_246":247,"_248":249,"_250":16},"correctOptionId","d59f7aa0-6e3d-4404-93ac-3586c7af9cc3","difficulty","","id","67a732b4-d7a5-4414-8390-75f27edaf571","metadata",{"_48":49,"_222":223,"_224":225},"pd",{"_50":51,"_52":53,"_190":191,"_210":211,"_212":213,"_214":16,"_215":216,"_217":16,"_218":219,"_220":221},"area","Outros","tags",[54,60,64,68,71,75,79,82,86,90,93,96,99,103,106,110,114,118,121,124,127,130,134,137,141,145,149,152,156,160,163,167,171,175,178,182,186],{"_44":55,"_56":57,"_58":59},55,"name","ARGAMASSA","alias","argamassa",{"_44":61,"_56":62,"_58":63},56,"CONCRETO","concreto",{"_44":65,"_56":66,"_58":67},64,"Apostila","apostila",{"_44":69,"_56":70,"_58":70},117,"calculo",{"_44":72,"_56":73,"_58":74},689,"Derivada","derivada",{"_44":76,"_56":77,"_58":78},690,"Integral","integral",{"_44":80,"_56":81,"_58":81},745,"civil",{"_44":83,"_56":84,"_58":85},845,"Engenharia","engenharia",{"_44":87,"_56":88,"_58":89},938,"Topografia","topografia",{"_44":91,"_56":92,"_58":92},1079,"arquitetura",{"_44":94,"_56":95,"_58":95},1340,"sondagem",{"_44":97,"_56":98,"_58":98},1725,"materiais",{"_44":100,"_56":101,"_58":102},1839,"edificações","edificacoes",{"_44":104,"_56":105,"_58":105},3318,"tijolo",{"_44":107,"_56":108,"_58":109},3452,"Caracteristicas","caracteristicas",{"_44":111,"_56":112,"_58":113},3974,"técnicas","tecnicas",{"_44":115,"_56":116,"_58":117},6774,"construção","construcao",{"_44":119,"_56":120,"_58":120},11489,"ensaios",{"_44":122,"_56":123,"_58":123},13272,"cimento",{"_44":125,"_56":126,"_58":126},16171,"areia",{"_44":128,"_56":129,"_58":129},17990,"agregados",{"_44":131,"_56":132,"_58":133},41206,"Fundação","fundacao",{"_44":135,"_56":136,"_58":136},50318,"agregado",{"_44":138,"_56":139,"_58":140},63263,"materiais-de-construção","materiais-de-construcao",{"_44":142,"_56":143,"_58":144},71332,"Materiais-de-Construção-Civil","materiais-de-construcao-civil",{"_44":146,"_56":147,"_58":148},85269,"Materiais-I","materiais-i",{"_44":150,"_56":151,"_58":151},85994,"compresao",{"_44":153,"_56":154,"_58":155},169307,"Apostila-materiais","apostila-materiais",{"_44":157,"_56":158,"_58":159},210644,"material-de-construção","material-de-construcao",{"_44":161,"_56":162,"_58":162},219524,"slump",{"_44":164,"_56":165,"_58":166},356322,"MATECO","mateco",{"_44":168,"_56":169,"_58":170},362099,"materiais-para-construção","materiais-para-construcao",{"_44":172,"_56":173,"_58":174},399629,"apostila-granulometria-","apostila-granulometria",{"_44":176,"_56":177,"_58":177},537173,"pesada",{"_44":179,"_56":180,"_58":181},694743,"#Arq","%23arq",{"_44":183,"_56":184,"_58":185},837837,"civil1 civil II civil III","civil-1-civil-ii-civil-iii",{"_44":187,"_56":188,"_58":189},1006294,"Apostila_Materiais_Construcao_Marcio_Varela","apostila-materiais-construcao-marcio-varela","subjects",[192,196,200,203,207],{"_44":193,"_56":194,"_58":195},681265,"Desenho Técnico","desenho-tecnico",{"_44":197,"_56":198,"_58":199},1481802,"Engenharia Civil","engenharia-civil",{"_44":201,"_56":202,"_58":140},1524904,"Materiais de Construção",{"_44":204,"_56":205,"_58":206},1663620,"Resistência dos Materiais","resistencia-dos-materiais",{"_44":208,"_56":209,"_58":63},1725643,"Concreto","materialId","24056928","answerCount",1,"isIndexable","mainSubject",{"_44":204,"_56":205,"_58":206},"isIndexableSEO","materialFormat","Text","studentDegreeLevel","Graduate","source","PD","externalId","132617424","options",[228,233,237,241],{"_44":41,"_229":230,"_231":232},"label","A","text","0.86 \\, m^3 de pasta de gesso para 1 \\, m^3 de pó de gesso",{"_44":234,"_229":235,"_231":236},"79e2d2af-0bc5-4272-a294-1b3c7dedbdb5","B","1.65 \\, m^3 de pasta de gesso para 1 \\, m^3 de pó de gesso",{"_44":238,"_229":239,"_231":240},"6840bcde-18e3-42eb-9a8b-6e7bbbaf449d","C","0.89 \\, m^3 de pasta de gesso para 1 \\, m^3 de pó de gesso",{"_44":242,"_229":243,"_231":244},"032f2c3b-8c59-4c43-b5ee-f4c802886bb0","D","1.22 \\, m^3 de pasta de gesso para 1 \\, m^3 de pó de gesso","solution_explanation","statement","

Qual é o coeficiente de rendimento para o pó de gesso?

","status","pending_classification","hasRelatedVideo","relatedVideos",[253],{"_254":255,"_273":274,"_52":289,"_324":325,"_342":343},"content",{"_44":256,"_56":257,"_258":-5,"_259":260,"_261":262,"_263":-5,"_46":264,"_267":268,"_269":268,"_270":-5,"_271":272},"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",{"_265":266},"external_id","4963","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","optica-geometrica-parte-1","prometheusData",{"_275":276,"_282":283,"_284":285,"_286":287,"_28":288},"provider",{"_44":277,"_278":279,"_280":281},"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",[290],{"_44":291,"_56":292,"_58":293,"_294":295,"_296":-5,"_267":297,"_269":297,"_46":298,"_271":293,"_305":306},"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",{"_299":300,"_301":302,"_303":304},"childrenCount",18,"content_count",0,"question_count",135489,"children",[307],{"_44":308,"_56":309,"_58":310,"_294":295,"_296":291,"_267":311,"_269":311,"_46":312,"_271":315,"_305":316},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_299":313,"_301":302,"_303":314},10,19948,"mecanica-2",[317],{"_44":318,"_56":205,"_58":206,"_294":295,"_296":308,"_267":319,"_269":319,"_46":320,"_271":322,"_305":323},"ac55bdba-154d-42e7-bc25-72dde822663d","2025-04-29T03:44:29.139762+00:00",{"_299":302,"_301":302,"_303":321},3376,"resistencia-dos-materiais-4",[],"video",{"_44":262,"_13":257,"_258":-5,"_326":327,"_328":329,"_28":-5,"_330":-5,"_275":329,"_331":332,"_286":-5,"_333":-5,"_334":-5,"_335":-5,"_336":-5,"_46":337,"_338":302,"_339":-5,"_248":340,"_267":341,"_269":341},"duration",20,"source_type","prometheus","iframe_url","provider_video_id","1cd3d633-d690-4f4b-9995-9b0e44994e35","format","quality","file_path","file_size",{"_265":266},"views_count","last_played_at","draft","2025-08-19T11:56:20.758718+00:00","tag",{"_44":291,"_56":292,"_58":293,"_294":295,"_296":-5,"_267":297,"_269":297,"_46":344,"_271":293,"_305":345},{"_299":300,"_301":302,"_303":304},[346],{"_44":308,"_56":309,"_58":310,"_294":295,"_296":291,"_267":311,"_269":311,"_46":347,"_271":315,"_305":348},{"_299":313,"_301":302,"_303":314},[349],{"_44":318,"_56":205,"_58":206,"_294":295,"_296":308,"_267":319,"_269":319,"_46":350,"_271":322,"_305":351},{"_299":302,"_301":302,"_303":321},[],"similarQuestions",[354,385,405],{"_40":355,"_42":43,"_44":356,"_226":357,"_245":373,"_246":374,"_52":375},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[358,361,364,367,370],{"_44":359,"_229":230,"_231":360},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_44":362,"_229":235,"_231":363},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":365,"_229":239,"_231":366},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":368,"_229":243,"_231":369},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":355,"_229":371,"_231":372},"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

",[376],{"_44":377,"_56":378,"_58":379,"_294":295,"_296":380,"_267":381,"_269":381,"_46":382,"_271":379},"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",{"_299":383,"_301":302,"_303":384},4,12302,{"_40":386,"_42":43,"_44":387,"_226":388,"_245":400,"_246":401,"_52":402},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[389,392,395,397],{"_44":390,"_229":230,"_231":391},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":393,"_229":235,"_231":394},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":386,"_229":239,"_231":396},"

Verdadeiro, falso, verdadeiro

",{"_44":398,"_229":243,"_231":399},"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?

",[403],{"_44":377,"_56":378,"_58":379,"_294":295,"_296":380,"_267":381,"_269":381,"_46":404,"_271":379},{"_299":383,"_301":302,"_303":384},{"_40":406,"_42":43,"_44":407,"_226":408,"_245":423,"_246":424,"_52":425},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[409,412,415,417,420],{"_44":410,"_229":230,"_231":411},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":413,"_229":235,"_231":414},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":406,"_229":239,"_231":416},"Indeterminado",{"_44":418,"_229":243,"_231":419},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":421,"_229":371,"_231":422},"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????",[426],{"_44":377,"_56":378,"_58":379,"_294":295,"_296":380,"_267":381,"_269":381,"_46":427,"_271":379},{"_299":383,"_301":302,"_303":384},[429,431,440,446,450,452,454,460,465,473,475,480,486],{"_44":377,"_56":378,"_58":379,"_294":295,"_296":380,"_267":381,"_269":381,"_46":430,"_271":379},{"_299":383,"_301":302,"_303":384},{"_44":432,"_56":433,"_58":434,"_294":295,"_296":435,"_267":311,"_269":311,"_46":436,"_271":439},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_299":437,"_301":302,"_303":438},5,30614,"engenharia-mecatronica-1",{"_44":441,"_56":205,"_58":206,"_294":295,"_296":442,"_267":443,"_269":443,"_46":444,"_271":445},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_299":302,"_301":302,"_303":321},"resistencia-dos-materiais-6",{"_44":442,"_56":309,"_58":310,"_294":295,"_296":432,"_267":381,"_269":381,"_46":447,"_271":449},{"_299":437,"_301":302,"_303":448},25741,"mecanica-3",{"_44":291,"_56":292,"_58":293,"_294":295,"_296":-5,"_267":297,"_269":297,"_46":451,"_271":293},{"_299":300,"_301":302,"_303":304},{"_44":318,"_56":205,"_58":206,"_294":295,"_296":308,"_267":319,"_269":319,"_46":453,"_271":322},{"_299":302,"_301":302,"_303":321},{"_44":455,"_56":198,"_58":199,"_294":295,"_296":435,"_267":311,"_269":311,"_46":456,"_271":459},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331",{"_299":457,"_301":302,"_303":458},21,45865,"engenharia-civil-3",{"_44":380,"_56":461,"_58":462,"_294":295,"_296":435,"_267":311,"_269":311,"_46":463,"_271":464},"Engenharia de Petróleo","engenharia-de-petroleo",{"_299":437,"_301":302,"_303":384},"engenharia-de-petroleo-1",{"_44":466,"_56":467,"_58":468,"_294":295,"_296":455,"_267":469,"_269":469,"_46":470,"_271":472},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_299":437,"_301":302,"_303":471},8852,"estruturas-1",{"_44":308,"_56":309,"_58":310,"_294":295,"_296":291,"_267":311,"_269":311,"_46":474,"_271":315},{"_299":313,"_301":302,"_303":314},{"_44":476,"_56":205,"_58":206,"_294":295,"_296":377,"_267":477,"_269":477,"_46":478,"_271":479},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_299":302,"_301":302,"_303":321},"resistencia-dos-materiais-7",{"_44":481,"_56":482,"_58":206,"_294":295,"_296":466,"_267":483,"_269":483,"_46":484,"_271":485},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_299":302,"_301":302,"_303":321},"resistencia-dos-materiais-5",{"_44":435,"_56":84,"_58":85,"_294":295,"_296":-5,"_267":487,"_269":487,"_46":488,"_271":85},"2025-04-29T01:55:38.635246+00:00",{"_299":489,"_301":302,"_303":490},29,351586,"tagsTree",[493,502],{"_44":291,"_56":292,"_58":293,"_294":295,"_296":-5,"_267":297,"_269":297,"_46":494,"_271":293,"_305":495},{"_299":300,"_301":302,"_303":304},[496],{"_44":308,"_56":309,"_58":310,"_294":295,"_296":291,"_267":311,"_269":311,"_46":497,"_271":315,"_305":498},{"_299":313,"_301":302,"_303":314},[499],{"_44":318,"_56":205,"_58":206,"_294":295,"_296":308,"_267":319,"_269":319,"_46":500,"_271":322,"_305":501},{"_299":302,"_301":302,"_303":321},[],{"_44":435,"_56":84,"_58":85,"_294":295,"_296":-5,"_267":487,"_269":487,"_46":503,"_271":85,"_305":504},{"_299":489,"_301":302,"_303":490},[505,514,523],{"_44":432,"_56":433,"_58":434,"_294":295,"_296":435,"_267":311,"_269":311,"_46":506,"_271":439,"_305":507},{"_299":437,"_301":302,"_303":438},[508],{"_44":442,"_56":309,"_58":310,"_294":295,"_296":432,"_267":381,"_269":381,"_46":509,"_271":449,"_305":510},{"_299":437,"_301":302,"_303":448},[511],{"_44":441,"_56":205,"_58":206,"_294":295,"_296":442,"_267":443,"_269":443,"_46":512,"_271":445,"_305":513},{"_299":302,"_301":302,"_303":321},[],{"_44":455,"_56":198,"_58":199,"_294":295,"_296":435,"_267":311,"_269":311,"_46":515,"_271":459,"_305":516},{"_299":457,"_301":302,"_303":458},[517],{"_44":466,"_56":467,"_58":468,"_294":295,"_296":455,"_267":469,"_269":469,"_46":518,"_271":472,"_305":519},{"_299":437,"_301":302,"_303":471},[520],{"_44":481,"_56":482,"_58":206,"_294":295,"_296":466,"_267":483,"_269":483,"_46":521,"_271":485,"_305":522},{"_299":302,"_301":302,"_303":321},[],{"_44":380,"_56":461,"_58":462,"_294":295,"_296":435,"_267":311,"_269":311,"_46":524,"_271":464,"_305":525},{"_299":437,"_301":302,"_303":384},[526],{"_44":377,"_56":378,"_58":379,"_294":295,"_296":380,"_267":381,"_269":381,"_46":527,"_271":379,"_305":528},{"_299":383,"_301":302,"_303":384},[529],{"_44":476,"_56":205,"_58":206,"_294":295,"_296":377,"_267":477,"_269":477,"_46":530,"_271":479,"_305":531},{"_299":302,"_301":302,"_303":321},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários