[{"_1":2,"_272":-5,"_273":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/d8845a51-58e9-4fa6-a1f1-7253376e6ac9","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_34":35,"_36":37,"_61":242,"_243":244},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_29":17,"_30":31,"_32":33},"correctOptionId","","difficulty","id","d8845a51-58e9-4fa6-a1f1-7253376e6ac9","options",[23],{"_19":24,"_25":26,"_27":28},"e9c51352-7401-436d-ad35-690f745a2158","label","A","text","506 \times 10^3 \text{ mm}^3 e 758 \times 10^3 \text{ mm}^3.","solution_explanation","statement","

1 - Determine o momento estático em relação aos eixos x e y da superfície a seguir e responda quais são os momentos estáticos Qx e Qy, respectivamente:

Os momentos estáticos Qx e Qy, respectivamente, são 506 \times 10^3 \text{ mm}^3 e 758 \times 10^3 \text{ mm}^3.

","status","has_issues","relatedVideos",[],"similarQuestions",[38,168,185,202,222],{"_16":17,"_18":17,"_19":39,"_21":40,"_29":17,"_30":60,"_61":62},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[41,44,48,52,56],{"_19":42,"_25":26,"_27":43},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":45,"_25":46,"_27":47},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","B","6y'' - y' - y = 0",{"_19":49,"_25":50,"_27":51},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_19":53,"_25":54,"_27":55},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_19":57,"_25":58,"_27":59},"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",[63,85,95,104,110,118,124,132,137,145,150,155,161],{"_19":64,"_65":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":74,"_76":77,"_84":68},"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",{"_78":79,"_80":81,"_82":83},"childrenCount",4,"content_count",0,"question_count",12302,"slug",{"_19":86,"_65":87,"_67":88,"_69":70,"_71":89,"_73":90,"_75":90,"_76":91,"_84":94},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_78":92,"_80":81,"_82":93},5,30614,"engenharia-mecatronica-1",{"_19":96,"_65":97,"_67":98,"_69":70,"_71":99,"_73":100,"_75":100,"_76":101,"_84":103},"8850e507-a691-4d45-a7c7-16221e9c5af2","Resistência dos Materiais","resistencia-dos-materiais","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_78":81,"_80":81,"_82":102},3376,"resistencia-dos-materiais-6",{"_19":99,"_65":105,"_67":106,"_69":70,"_71":86,"_73":74,"_75":74,"_76":107,"_84":109},"Mecânica","mecanica",{"_78":92,"_80":81,"_82":108},25741,"mecanica-3",{"_19":111,"_65":112,"_67":113,"_69":70,"_71":-5,"_73":114,"_75":114,"_76":115,"_84":113},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_78":116,"_80":81,"_82":117},18,135489,{"_19":119,"_65":97,"_67":98,"_69":70,"_71":120,"_73":121,"_75":121,"_76":122,"_84":123},"ac55bdba-154d-42e7-bc25-72dde822663d","ca6fee0e-79c6-4f1c-b500-ee081a071949","2025-04-29T03:44:29.139762+00:00",{"_78":81,"_80":81,"_82":102},"resistencia-dos-materiais-4",{"_19":125,"_65":126,"_67":127,"_69":70,"_71":89,"_73":90,"_75":90,"_76":128,"_84":131},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_78":129,"_80":81,"_82":130},21,45865,"engenharia-civil-3",{"_19":72,"_65":133,"_67":134,"_69":70,"_71":89,"_73":90,"_75":90,"_76":135,"_84":136},"Engenharia de Petróleo","engenharia-de-petroleo",{"_78":92,"_80":81,"_82":83},"engenharia-de-petroleo-1",{"_19":138,"_65":139,"_67":140,"_69":70,"_71":125,"_73":141,"_75":141,"_76":142,"_84":144},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_78":92,"_80":81,"_82":143},8852,"estruturas-1",{"_19":120,"_65":105,"_67":106,"_69":70,"_71":111,"_73":90,"_75":90,"_76":146,"_84":149},{"_78":147,"_80":81,"_82":148},10,19948,"mecanica-2",{"_19":151,"_65":97,"_67":98,"_69":70,"_71":64,"_73":152,"_75":152,"_76":153,"_84":154},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_78":81,"_80":81,"_82":102},"resistencia-dos-materiais-7",{"_19":156,"_65":157,"_67":98,"_69":70,"_71":138,"_73":158,"_75":158,"_76":159,"_84":160},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_78":81,"_80":81,"_82":102},"resistencia-dos-materiais-5",{"_19":89,"_65":162,"_67":163,"_69":70,"_71":-5,"_73":164,"_75":164,"_76":165,"_84":163},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_78":166,"_80":81,"_82":167},29,351586,{"_16":17,"_18":17,"_19":169,"_21":170,"_29":17,"_30":183,"_61":184},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[171,174,177,180],{"_19":172,"_25":26,"_27":173},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":175,"_25":46,"_27":176},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":178,"_25":50,"_27":179},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":181,"_25":54,"_27":182},"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.

",[63,85,95,104,110,118,124,132,137,145,150,155,161],{"_16":17,"_18":17,"_19":186,"_21":187,"_29":17,"_30":200,"_61":201},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[188,191,194,197],{"_19":189,"_25":26,"_27":190},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":192,"_25":46,"_27":193},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":195,"_25":50,"_27":196},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":198,"_25":54,"_27":199},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[63,85,95,104,110,118,124,132,137,145,150,155,161],{"_16":17,"_18":17,"_19":203,"_21":204,"_29":17,"_30":220,"_61":221},"996628fc-4ac3-4821-86bd-839f86a97a6d",[205,208,211,214,217],{"_19":206,"_25":26,"_27":207},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":209,"_25":46,"_27":210},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":212,"_25":50,"_27":213},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":215,"_25":54,"_27":216},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":218,"_25":58,"_27":219},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[63,85,95,104,110,118,124,132,137,145,150,155,161],{"_16":17,"_18":17,"_19":223,"_21":224,"_29":17,"_30":240,"_61":241},"c478a46c-46a8-4942-ae14-2e79def3dda2",[225,228,231,234,237],{"_19":226,"_25":26,"_27":227},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":229,"_25":46,"_27":230},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":232,"_25":50,"_27":233},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":235,"_25":54,"_27":236},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":238,"_25":58,"_27":239},"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????",[63,85,95,104,110,118,124,132,137,145,150,155,161],[63,85,95,104,110,118,124,132,137,145,150,155,161],"tagsTree",[245,252],{"_19":111,"_65":112,"_67":113,"_69":70,"_71":-5,"_73":114,"_75":114,"_76":115,"_84":113,"_246":247},"children",[248],{"_19":120,"_65":105,"_67":106,"_69":70,"_71":111,"_73":90,"_75":90,"_76":146,"_84":149,"_246":249},[250],{"_19":119,"_65":97,"_67":98,"_69":70,"_71":120,"_73":121,"_75":121,"_76":122,"_84":123,"_246":251},[],{"_19":89,"_65":162,"_67":163,"_69":70,"_71":-5,"_73":164,"_75":164,"_76":165,"_84":163,"_246":253},[254,260,266],{"_19":86,"_65":87,"_67":88,"_69":70,"_71":89,"_73":90,"_75":90,"_76":91,"_84":94,"_246":255},[256],{"_19":99,"_65":105,"_67":106,"_69":70,"_71":86,"_73":74,"_75":74,"_76":107,"_84":109,"_246":257},[258],{"_19":96,"_65":97,"_67":98,"_69":70,"_71":99,"_73":100,"_75":100,"_76":101,"_84":103,"_246":259},[],{"_19":125,"_65":126,"_67":127,"_69":70,"_71":89,"_73":90,"_75":90,"_76":128,"_84":131,"_246":261},[262],{"_19":138,"_65":139,"_67":140,"_69":70,"_71":125,"_73":141,"_75":141,"_76":142,"_84":144,"_246":263},[264],{"_19":156,"_65":157,"_67":98,"_69":70,"_71":138,"_73":158,"_75":158,"_76":159,"_84":160,"_246":265},[],{"_19":72,"_65":133,"_67":134,"_69":70,"_71":89,"_73":90,"_75":90,"_76":135,"_84":136,"_246":267},[268],{"_19":64,"_65":66,"_67":68,"_69":70,"_71":72,"_73":74,"_75":74,"_76":77,"_84":68,"_246":269},[270],{"_19":151,"_65":97,"_67":98,"_69":70,"_71":64,"_73":152,"_75":152,"_76":153,"_84":154,"_246":271},[],"actionData","errors"]

Comentários