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V' = \\frac{V}{2}

",{"_22":65,"_60":66,"_62":67},"ef7de684-d2af-466c-9bb9-c34cb0833dd4","B","

V' = 2V

",{"_22":69,"_60":70,"_62":71},"24aa2839-9ce8-47d9-a553-f41f0fd170f7","C","

V' = V

",{"_22":73,"_60":74,"_62":75},"93183be6-d70e-4aaf-9693-506d7139764d","D","

V' = 4V

","solution_explanation","statement","

Em um gás ideal, a relação entre a pressão P, volume V e temperatura T é descrita pela equação de estado ideal. Se a pressão for duplicada e a temperatura mantida constante, qual será o novo volume V' do gás?

","status","pending_classification","hasRelatedVideo","relatedVideos",[84],{"_85":86,"_104":105,"_30":120,"_139":140,"_158":159},"content",{"_22":87,"_36":88,"_89":-5,"_90":91,"_92":93,"_94":-5,"_24":95,"_98":99,"_100":99,"_101":-5,"_102":103},"162087be-594f-460e-bbdd-a339ac2f10ad","Calor Latente - Parte 1","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","f2b62fc2-7079-40e7-a5b5-c4a9769b205d","user_id",{"_96":97},"external_id","3659","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","calor-latente-parte-1","prometheusData",{"_106":107,"_113":114,"_115":116,"_117":118,"_6":119},"provider",{"_22":108,"_109":110,"_111":112},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","bf8aacba-3de9-4b10-961c-47ada80dfe8c","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/bf8aacba-3de9-4b10-961c-47ada80dfe8c/levels.m3u8",[121],{"_22":122,"_36":123,"_38":124,"_125":126,"_127":128,"_98":129,"_100":129,"_24":130,"_102":124,"_137":138},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9","2025-04-29T03:44:27.560682+00:00",{"_131":132,"_133":134,"_135":136},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_22":93,"_141":88,"_89":-5,"_142":143,"_144":145,"_6":-5,"_146":-5,"_106":145,"_147":148,"_117":-5,"_149":-5,"_150":-5,"_151":-5,"_152":-5,"_24":153,"_154":134,"_155":-5,"_79":156,"_98":157,"_100":157},"title","duration",17,"source_type","prometheus","iframe_url","provider_video_id","748a4adb-ad8f-4c5f-88a9-bc522d3b4246","format","quality","file_path","file_size",{"_96":97},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_22":122,"_36":123,"_38":124,"_125":126,"_127":128,"_98":129,"_100":129,"_24":160,"_102":124,"_137":161},{"_131":132,"_133":134,"_135":136},[],"similarQuestions",[164,195,215],{"_18":165,"_20":21,"_22":166,"_57":167,"_76":183,"_77":184,"_30":185},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[168,171,174,177,180],{"_22":169,"_60":61,"_62":170},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_22":172,"_60":66,"_62":173},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_22":175,"_60":70,"_62":176},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_22":178,"_60":74,"_62":179},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_22":165,"_60":181,"_62":182},"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

",[186],{"_22":187,"_36":188,"_38":189,"_125":126,"_127":190,"_98":191,"_100":191,"_24":192,"_102":189},"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",{"_131":193,"_133":134,"_135":194},4,12302,{"_18":196,"_20":21,"_22":197,"_57":198,"_76":210,"_77":211,"_30":212},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[199,202,205,207],{"_22":200,"_60":61,"_62":201},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":203,"_60":66,"_62":204},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":196,"_60":70,"_62":206},"

Verdadeiro, falso, verdadeiro

",{"_22":208,"_60":74,"_62":209},"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????",[236],{"_22":187,"_36":188,"_38":189,"_125":126,"_127":190,"_98":191,"_100":191,"_24":237,"_102":189},{"_131":193,"_133":134,"_135":194},[239,241,248,258,265,272,274,282,288,293,299,306],{"_22":187,"_36":188,"_38":189,"_125":126,"_127":190,"_98":191,"_100":191,"_24":240,"_102":189},{"_131":193,"_133":134,"_135":194},{"_22":242,"_36":37,"_38":39,"_125":126,"_127":243,"_98":129,"_100":129,"_24":244,"_102":247},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":245,"_133":134,"_135":246},2,11846,"termodinamica-3",{"_22":249,"_36":250,"_38":251,"_125":126,"_127":252,"_98":253,"_100":253,"_24":254,"_102":257},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":255,"_133":134,"_135":256},5,30614,"engenharia-mecatronica-1",{"_22":259,"_36":260,"_38":261,"_125":126,"_127":249,"_98":191,"_100":191,"_24":262,"_102":264},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":255,"_133":134,"_135":263},25741,"mecanica-3",{"_22":243,"_36":266,"_38":267,"_125":126,"_127":252,"_98":253,"_100":253,"_24":268,"_102":271},"Engenharia Mecânica","engenharia-mecanica",{"_131":269,"_133":134,"_135":270},11,36318,"engenharia-mecanica-2",{"_22":122,"_36":123,"_38":124,"_125":126,"_127":128,"_98":129,"_100":129,"_24":273,"_102":124},{"_131":132,"_133":134,"_135":136},{"_22":275,"_36":276,"_38":277,"_125":126,"_127":-5,"_98":278,"_100":278,"_24":279,"_102":277},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":280,"_133":134,"_135":281},18,135489,{"_22":283,"_36":37,"_38":39,"_125":126,"_127":187,"_98":284,"_100":284,"_24":285,"_102":287},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":134,"_133":134,"_135":286},8597,"termodinamica-5",{"_22":190,"_36":289,"_38":290,"_125":126,"_127":252,"_98":253,"_100":253,"_24":291,"_102":292},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":255,"_133":134,"_135":194},"engenharia-de-petroleo-1",{"_22":128,"_36":294,"_38":295,"_125":126,"_127":275,"_98":253,"_100":253,"_24":296,"_102":298},"Física","fisica",{"_131":269,"_133":134,"_135":297},13777,"fisica-4",{"_22":252,"_36":300,"_38":301,"_125":126,"_127":-5,"_98":302,"_100":302,"_24":303,"_102":301},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":304,"_133":134,"_135":305},29,351586,{"_22":307,"_36":37,"_38":39,"_125":126,"_127":259,"_98":308,"_100":308,"_24":309,"_102":310},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":134,"_133":134,"_135":286},"termodinamica-4","tagsTree",[313,322],{"_22":275,"_36":276,"_38":277,"_125":126,"_127":-5,"_98":278,"_100":278,"_24":314,"_102":277,"_137":315},{"_131":280,"_133":134,"_135":281},[316],{"_22":128,"_36":294,"_38":295,"_125":126,"_127":275,"_98":253,"_100":253,"_24":317,"_102":298,"_137":318},{"_131":269,"_133":134,"_135":297},[319],{"_22":122,"_36":123,"_38":124,"_125":126,"_127":128,"_98":129,"_100":129,"_24":320,"_102":124,"_137":321},{"_131":132,"_133":134,"_135":136},[],{"_22":252,"_36":300,"_38":301,"_125":126,"_127":-5,"_98":302,"_100":302,"_24":323,"_102":301,"_137":324},{"_131":304,"_133":134,"_135":305},[325,334,340],{"_22":249,"_36":250,"_38":251,"_125":126,"_127":252,"_98":253,"_100":253,"_24":326,"_102":257,"_137":327},{"_131":255,"_133":134,"_135":256},[328],{"_22":259,"_36":260,"_38":261,"_125":126,"_127":249,"_98":191,"_100":191,"_24":329,"_102":264,"_137":330},{"_131":255,"_133":134,"_135":263},[331],{"_22":307,"_36":37,"_38":39,"_125":126,"_127":259,"_98":308,"_100":308,"_24":332,"_102":310,"_137":333},{"_131":134,"_133":134,"_135":286},[],{"_22":243,"_36":266,"_38":267,"_125":126,"_127":252,"_98":253,"_100":253,"_24":335,"_102":271,"_137":336},{"_131":269,"_133":134,"_135":270},[337],{"_22":242,"_36":37,"_38":39,"_125":126,"_127":243,"_98":129,"_100":129,"_24":338,"_102":247,"_137":339},{"_131":245,"_133":134,"_135":246},[],{"_22":190,"_36":289,"_38":290,"_125":126,"_127":252,"_98":253,"_100":253,"_24":341,"_102":292,"_137":342},{"_131":255,"_133":134,"_135":194},[343],{"_22":187,"_36":188,"_38":189,"_125":126,"_127":190,"_98":191,"_100":191,"_24":344,"_102":189,"_137":345},{"_131":193,"_133":134,"_135":194},[346],{"_22":283,"_36":37,"_38":39,"_125":126,"_127":187,"_98":284,"_100":284,"_24":347,"_102":287,"_137":348},{"_131":134,"_133":134,"_135":286},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários