[{"_1":2,"_281":-5,"_282":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/dae040f1-7773-4b27-b155-2eb90ea25d9b","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":251,"_252":253},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":19,"_20":21,"_22":23,"_41":19,"_42":43,"_44":45},"correctOptionId","4a4a3feb-da74-4307-8038-1c50ed911a95","difficulty","","id","dae040f1-7773-4b27-b155-2eb90ea25d9b","options",[24,30,33,37],{"_20":25,"_26":27,"_28":29},"79c32b6c-db1f-4449-bab2-f0715a02dbc1","label","A","text","0,5 A",{"_20":17,"_26":31,"_28":32},"B","1 A",{"_20":34,"_26":35,"_28":36},"32363b42-11b3-48d8-82f0-8063b1e486a0","C","2 A",{"_20":38,"_26":39,"_28":40},"45d41813-3550-4e79-b30a-71a9624be1cc","D","3 A","solution_explanation","statement","

Um capacitor de 2 \\, \text{µF} está conectado em série com um resistor de 4 \\, \text{Ω}. Se uma tensão de 12 \\, \text{V} é aplicada, qual é a corrente que flui após um longo tempo?

","status","has_issues","relatedVideos",[],"similarQuestions",[50,177,194,211,231],{"_16":19,"_18":19,"_20":51,"_22":52,"_41":19,"_42":69,"_70":71},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_20":54,"_26":27,"_28":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_20":57,"_26":31,"_28":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_20":60,"_26":35,"_28":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_20":63,"_26":39,"_28":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_20":66,"_26":67,"_28":68},"112831da-be9c-458e-94cb-e8292d0dba12","E","y'' - 2y' + 6y = 0","

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

","tags",[72,94,104,113,119,127,133,141,146,154,159,164,170],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":77},"6516bbbd-f2a3-4710-8382-702240b17836","name","Mecânica na Engenharia de Petróleo","alias","mecanica-na-engenharia-de-petroleo","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","b787e438-0ab3-454c-ab43-5d3d14c2720d","created_at","2025-04-29T03:44:35.328997+00:00","updated_at","metadata",{"_87":88,"_89":90,"_91":92},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_20":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_87":101,"_89":90,"_91":102},5,30614,"engenharia-mecatronica-1",{"_20":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":112},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_87":90,"_89":90,"_91":111},3376,"resistencia-dos-materiais-6",{"_20":108,"_74":114,"_76":115,"_78":79,"_80":95,"_82":83,"_84":83,"_85":116,"_93":118},"Mecânica","mecanica",{"_87":101,"_89":90,"_91":117},25741,"mecanica-3",{"_20":120,"_74":121,"_76":122,"_78":79,"_80":-5,"_82":123,"_84":123,"_85":124,"_93":122},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_87":125,"_89":90,"_91":126},18,135489,{"_20":128,"_74":106,"_76":107,"_78":79,"_80":129,"_82":130,"_84":130,"_85":131,"_93":132},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_87":90,"_89":90,"_91":111},"resistencia-dos-materiais-4",{"_20":134,"_74":135,"_76":136,"_78":79,"_80":98,"_82":99,"_84":99,"_85":137,"_93":140},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_87":138,"_89":90,"_91":139},21,45865,"engenharia-civil-3",{"_20":81,"_74":142,"_76":143,"_78":79,"_80":98,"_82":99,"_84":99,"_85":144,"_93":145},"Engenharia de Petróleo","engenharia-de-petroleo",{"_87":101,"_89":90,"_91":92},"engenharia-de-petroleo-1",{"_20":147,"_74":148,"_76":149,"_78":79,"_80":134,"_82":150,"_84":150,"_85":151,"_93":153},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_87":101,"_89":90,"_91":152},8852,"estruturas-1",{"_20":129,"_74":114,"_76":115,"_78":79,"_80":120,"_82":99,"_84":99,"_85":155,"_93":158},{"_87":156,"_89":90,"_91":157},10,19948,"mecanica-2",{"_20":160,"_74":106,"_76":107,"_78":79,"_80":73,"_82":161,"_84":161,"_85":162,"_93":163},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_87":90,"_89":90,"_91":111},"resistencia-dos-materiais-7",{"_20":165,"_74":166,"_76":107,"_78":79,"_80":147,"_82":167,"_84":167,"_85":168,"_93":169},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_87":90,"_89":90,"_91":111},"resistencia-dos-materiais-5",{"_20":98,"_74":171,"_76":172,"_78":79,"_80":-5,"_82":173,"_84":173,"_85":174,"_93":172},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":175,"_89":90,"_91":176},29,351586,{"_16":19,"_18":19,"_20":178,"_22":179,"_41":19,"_42":192,"_70":193},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[180,183,186,189],{"_20":181,"_26":27,"_28":182},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":184,"_26":31,"_28":185},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":187,"_26":35,"_28":188},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":190,"_26":39,"_28":191},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[72,94,104,113,119,127,133,141,146,154,159,164,170],{"_16":19,"_18":19,"_20":195,"_22":196,"_41":19,"_42":209,"_70":210},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[197,200,203,206],{"_20":198,"_26":27,"_28":199},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":201,"_26":31,"_28":202},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":204,"_26":35,"_28":205},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":207,"_26":39,"_28":208},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[72,94,104,113,119,127,133,141,146,154,159,164,170],{"_16":19,"_18":19,"_20":212,"_22":213,"_41":19,"_42":229,"_70":230},"996628fc-4ac3-4821-86bd-839f86a97a6d",[214,217,220,223,226],{"_20":215,"_26":27,"_28":216},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":218,"_26":31,"_28":219},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":221,"_26":35,"_28":222},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":224,"_26":39,"_28":225},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":227,"_26":67,"_28":228},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,94,104,113,119,127,133,141,146,154,159,164,170],{"_16":19,"_18":19,"_20":232,"_22":233,"_41":19,"_42":249,"_70":250},"c478a46c-46a8-4942-ae14-2e79def3dda2",[234,237,240,243,246],{"_20":235,"_26":27,"_28":236},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":238,"_26":31,"_28":239},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":241,"_26":35,"_28":242},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":244,"_26":39,"_28":245},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":247,"_26":67,"_28":248},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[72,94,104,113,119,127,133,141,146,154,159,164,170],[72,94,104,113,119,127,133,141,146,154,159,164,170],"tagsTree",[254,261],{"_20":120,"_74":121,"_76":122,"_78":79,"_80":-5,"_82":123,"_84":123,"_85":124,"_93":122,"_255":256},"children",[257],{"_20":129,"_74":114,"_76":115,"_78":79,"_80":120,"_82":99,"_84":99,"_85":155,"_93":158,"_255":258},[259],{"_20":128,"_74":106,"_76":107,"_78":79,"_80":129,"_82":130,"_84":130,"_85":131,"_93":132,"_255":260},[],{"_20":98,"_74":171,"_76":172,"_78":79,"_80":-5,"_82":173,"_84":173,"_85":174,"_93":172,"_255":262},[263,269,275],{"_20":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103,"_255":264},[265],{"_20":108,"_74":114,"_76":115,"_78":79,"_80":95,"_82":83,"_84":83,"_85":116,"_93":118,"_255":266},[267],{"_20":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":112,"_255":268},[],{"_20":134,"_74":135,"_76":136,"_78":79,"_80":98,"_82":99,"_84":99,"_85":137,"_93":140,"_255":270},[271],{"_20":147,"_74":148,"_76":149,"_78":79,"_80":134,"_82":150,"_84":150,"_85":151,"_93":153,"_255":272},[273],{"_20":165,"_74":166,"_76":107,"_78":79,"_80":147,"_82":167,"_84":167,"_85":168,"_93":169,"_255":274},[],{"_20":81,"_74":142,"_76":143,"_78":79,"_80":98,"_82":99,"_84":99,"_85":144,"_93":145,"_255":276},[277],{"_20":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":77,"_255":278},[279],{"_20":160,"_74":106,"_76":107,"_78":79,"_80":73,"_82":161,"_84":161,"_85":162,"_93":163,"_255":280},[],"actionData","errors"]

Comentários