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Um bloco de metal com densidade de 500 \\, \text{kg/m}^3 e volume de 0,5 \\, \text{m}^3 é colocado em um recipiente cheio de água. Qual será a fração do bloco que ficará submersa?

","status","pending_classification","hasRelatedVideo","relatedVideos",[105],{"_106":107,"_125":126,"_51":141,"_160":161,"_177":178},"content",{"_43":108,"_57":109,"_110":-5,"_111":112,"_113":114,"_115":-5,"_45":116,"_119":120,"_121":120,"_122":-5,"_123":124},"17af1394-ae27-4d49-bad0-6dfbc097b00c","Termologia e Termometria","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","e0ab6092-71a6-4b78-8930-845a08dc3495","user_id",{"_117":118},"external_id","2594","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","slug","termologia-e-termometria","prometheusData",{"_127":128,"_134":135,"_136":137,"_138":139,"_28":140},"provider",{"_43":129,"_130":131,"_132":133},"06f120be-2194-4548-8336-7ba44ffbae14","key","grupo_q_proteus","kind","proteus","reference","b502b486-7b81-4345-a10c-e462c3043183","state","completed","thumbnail_url","https://proteus.grupoq.io/videos/b502b486-7b81-4345-a10c-e462c3043183/thumbnailsthumb.0000000.jpg","https://proteus.grupoq.io/videos/b502b486-7b81-4345-a10c-e462c3043183/levels.m3u8",[142],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":151,"_123":145,"_158":159},"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",{"_152":153,"_154":155,"_156":157},"childrenCount",10,"content_count",0,"question_count",8575,"children",[],"video",{"_43":114,"_13":109,"_110":-5,"_162":155,"_163":164,"_28":-5,"_165":-5,"_127":164,"_166":167,"_138":-5,"_168":-5,"_169":-5,"_170":-5,"_171":-5,"_45":172,"_173":155,"_174":-5,"_100":175,"_119":176,"_121":176},"duration","source_type","prometheus","iframe_url","provider_video_id","a58dea8f-5fbf-4462-bf04-83e715504a2f","format","quality","file_path","file_size",{"_117":118},"views_count","last_played_at","draft","2025-08-19T11:56:22.11908+00:00","tag",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":179,"_123":145,"_158":180},{"_152":153,"_154":155,"_156":157},[],"similarQuestions",[183,214,234],{"_40":184,"_42":41,"_43":185,"_77":186,"_97":202,"_98":203,"_51":204},"112831da-be9c-458e-94cb-e8292d0dba12","3c0b9441-b878-4896-8bac-fa4ca61e3f13",[187,190,193,196,199],{"_43":188,"_81":82,"_83":189},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_43":191,"_81":87,"_83":192},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":194,"_81":91,"_83":195},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":197,"_81":95,"_83":198},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":184,"_81":200,"_83":201},"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

",[205],{"_43":206,"_57":207,"_59":208,"_146":147,"_148":209,"_119":210,"_121":210,"_45":211,"_123":208},"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",{"_152":212,"_154":155,"_156":213},4,12302,{"_40":215,"_42":41,"_43":216,"_77":217,"_97":229,"_98":230,"_51":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_43":219,"_81":82,"_83":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":222,"_81":87,"_83":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":215,"_81":91,"_83":225},"

Verdadeiro, falso, verdadeiro

",{"_43":227,"_81":95,"_83":228},"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????",[255],{"_43":206,"_57":207,"_59":208,"_146":147,"_148":209,"_119":210,"_121":210,"_45":256,"_123":208},{"_152":212,"_154":155,"_156":213},[258,260,267,277,284,291,293,301,307,312,318,325],{"_43":206,"_57":207,"_59":208,"_146":147,"_148":209,"_119":210,"_121":210,"_45":259,"_123":208},{"_152":212,"_154":155,"_156":213},{"_43":261,"_57":58,"_59":60,"_146":147,"_148":262,"_119":150,"_121":150,"_45":263,"_123":266},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":264,"_154":155,"_156":265},2,11846,"termodinamica-3",{"_43":268,"_57":269,"_59":270,"_146":147,"_148":271,"_119":272,"_121":272,"_45":273,"_123":276},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_152":274,"_154":155,"_156":275},5,30614,"engenharia-mecatronica-1",{"_43":278,"_57":279,"_59":280,"_146":147,"_148":268,"_119":210,"_121":210,"_45":281,"_123":283},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":274,"_154":155,"_156":282},25741,"mecanica-3",{"_43":262,"_57":285,"_59":286,"_146":147,"_148":271,"_119":272,"_121":272,"_45":287,"_123":290},"Engenharia Mecânica","engenharia-mecanica",{"_152":288,"_154":155,"_156":289},11,36318,"engenharia-mecanica-2",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":292,"_123":145},{"_152":153,"_154":155,"_156":157},{"_43":294,"_57":295,"_59":296,"_146":147,"_148":-5,"_119":297,"_121":297,"_45":298,"_123":296},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_152":299,"_154":155,"_156":300},18,135489,{"_43":302,"_57":58,"_59":60,"_146":147,"_148":206,"_119":303,"_121":303,"_45":304,"_123":306},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_152":155,"_154":155,"_156":305},8597,"termodinamica-5",{"_43":209,"_57":308,"_59":309,"_146":147,"_148":271,"_119":272,"_121":272,"_45":310,"_123":311},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":274,"_154":155,"_156":213},"engenharia-de-petroleo-1",{"_43":149,"_57":313,"_59":314,"_146":147,"_148":294,"_119":272,"_121":272,"_45":315,"_123":317},"Física","fisica",{"_152":288,"_154":155,"_156":316},13777,"fisica-4",{"_43":271,"_57":319,"_59":320,"_146":147,"_148":-5,"_119":321,"_121":321,"_45":322,"_123":320},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":323,"_154":155,"_156":324},29,351586,{"_43":326,"_57":58,"_59":60,"_146":147,"_148":278,"_119":327,"_121":327,"_45":328,"_123":329},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_152":155,"_154":155,"_156":305},"termodinamica-4","tagsTree",[332,341],{"_43":294,"_57":295,"_59":296,"_146":147,"_148":-5,"_119":297,"_121":297,"_45":333,"_123":296,"_158":334},{"_152":299,"_154":155,"_156":300},[335],{"_43":149,"_57":313,"_59":314,"_146":147,"_148":294,"_119":272,"_121":272,"_45":336,"_123":317,"_158":337},{"_152":288,"_154":155,"_156":316},[338],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":339,"_123":145,"_158":340},{"_152":153,"_154":155,"_156":157},[],{"_43":271,"_57":319,"_59":320,"_146":147,"_148":-5,"_119":321,"_121":321,"_45":342,"_123":320,"_158":343},{"_152":323,"_154":155,"_156":324},[344,353,359],{"_43":268,"_57":269,"_59":270,"_146":147,"_148":271,"_119":272,"_121":272,"_45":345,"_123":276,"_158":346},{"_152":274,"_154":155,"_156":275},[347],{"_43":278,"_57":279,"_59":280,"_146":147,"_148":268,"_119":210,"_121":210,"_45":348,"_123":283,"_158":349},{"_152":274,"_154":155,"_156":282},[350],{"_43":326,"_57":58,"_59":60,"_146":147,"_148":278,"_119":327,"_121":327,"_45":351,"_123":329,"_158":352},{"_152":155,"_154":155,"_156":305},[],{"_43":262,"_57":285,"_59":286,"_146":147,"_148":271,"_119":272,"_121":272,"_45":354,"_123":290,"_158":355},{"_152":288,"_154":155,"_156":289},[356],{"_43":261,"_57":58,"_59":60,"_146":147,"_148":262,"_119":150,"_121":150,"_45":357,"_123":266,"_158":358},{"_152":264,"_154":155,"_156":265},[],{"_43":209,"_57":308,"_59":309,"_146":147,"_148":271,"_119":272,"_121":272,"_45":360,"_123":311,"_158":361},{"_152":274,"_154":155,"_156":213},[362],{"_43":206,"_57":207,"_59":208,"_146":147,"_148":209,"_119":210,"_121":210,"_45":363,"_123":208,"_158":364},{"_152":212,"_154":155,"_156":213},[365],{"_43":302,"_57":58,"_59":60,"_146":147,"_148":206,"_119":303,"_121":303,"_45":366,"_123":306,"_158":367},{"_152":155,"_154":155,"_156":305},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários