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Questão 02: Uma força axial e um torque são aplicados ao eixo de diâmetro 40 \text{ mm}. As tensões principais, em kPa, são, respectivamente:

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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

",[174],{"_20":175,"_59":176,"_98":177,"_100":101,"_102":178,"_71":179,"_73":179,"_67":180,"_75":177},"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",{"_105":181,"_107":108,"_109":182},4,12302,{"_17":18,"_19":18,"_20":184,"_22":185,"_46":18,"_47":198,"_93":199},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[186,189,192,195],{"_20":187,"_26":27,"_28":188},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_20":190,"_26":32,"_28":191},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_20":193,"_26":36,"_28":194},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_20":196,"_26":40,"_28":197},"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.

",[174],{"_17":18,"_19":18,"_20":201,"_22":202,"_46":18,"_47":215,"_93":216},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[203,206,209,212],{"_20":204,"_26":27,"_28":205},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_20":207,"_26":32,"_28":208},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_20":210,"_26":36,"_28":211},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_20":213,"_26":40,"_28":214},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[174],{"_17":18,"_19":18,"_20":218,"_22":219,"_46":18,"_47":235,"_93":236},"996628fc-4ac3-4821-86bd-839f86a97a6d",[220,223,226,229,232],{"_20":221,"_26":27,"_28":222},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_20":224,"_26":32,"_28":225},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_20":227,"_26":36,"_28":228},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_20":230,"_26":40,"_28":231},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_20":233,"_26":44,"_28":234},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[174],{"_17":18,"_19":18,"_20":238,"_22":239,"_46":18,"_47":255,"_93":256},"c478a46c-46a8-4942-ae14-2e79def3dda2",[240,243,246,249,252],{"_20":241,"_26":27,"_28":242},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_20":244,"_26":32,"_28":245},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_20":247,"_26":36,"_28":248},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_20":250,"_26":40,"_28":251},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_20":253,"_26":44,"_28":254},"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????",[174],[174,258,267,273,277,278,279,287,292,300,301,306,312],{"_20":259,"_59":260,"_98":261,"_100":101,"_102":262,"_71":117,"_73":117,"_67":263,"_75":266},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_105":264,"_107":108,"_109":265},5,30614,"engenharia-mecatronica-1",{"_20":268,"_59":125,"_98":126,"_100":101,"_102":269,"_71":270,"_73":270,"_67":271,"_75":272},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_105":108,"_107":108,"_109":129},"resistencia-dos-materiais-6",{"_20":269,"_59":115,"_98":116,"_100":101,"_102":259,"_71":179,"_73":179,"_67":274,"_75":276},{"_105":264,"_107":108,"_109":275},25741,"mecanica-3",{"_20":96,"_59":97,"_98":99,"_100":101,"_102":-5,"_71":103,"_73":103,"_67":104,"_75":99},{"_20":124,"_59":125,"_98":126,"_100":101,"_102":114,"_71":127,"_73":127,"_67":128,"_75":130},{"_20":280,"_59":281,"_98":282,"_100":101,"_102":262,"_71":117,"_73":117,"_67":283,"_75":286},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_105":284,"_107":108,"_109":285},21,45865,"engenharia-civil-3",{"_20":178,"_59":288,"_98":289,"_100":101,"_102":262,"_71":117,"_73":117,"_67":290,"_75":291},"Engenharia de Petróleo","engenharia-de-petroleo",{"_105":264,"_107":108,"_109":182},"engenharia-de-petroleo-1",{"_20":293,"_59":294,"_98":295,"_100":101,"_102":280,"_71":296,"_73":296,"_67":297,"_75":299},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_105":264,"_107":108,"_109":298},8852,"estruturas-1",{"_20":114,"_59":115,"_98":116,"_100":101,"_102":96,"_71":117,"_73":117,"_67":118,"_75":121},{"_20":302,"_59":125,"_98":126,"_100":101,"_102":175,"_71":303,"_73":303,"_67":304,"_75":305},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_105":108,"_107":108,"_109":129},"resistencia-dos-materiais-7",{"_20":307,"_59":308,"_98":126,"_100":101,"_102":293,"_71":309,"_73":309,"_67":310,"_75":311},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_105":108,"_107":108,"_109":129},"resistencia-dos-materiais-5",{"_20":262,"_59":313,"_98":314,"_100":101,"_102":-5,"_71":315,"_73":315,"_67":316,"_75":314},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_105":317,"_107":108,"_109":318},29,351586,"tagsTree",[95,321],{"_20":262,"_59":313,"_98":314,"_100":101,"_102":-5,"_71":315,"_73":315,"_67":316,"_75":314,"_111":322},[323,329,335],{"_20":259,"_59":260,"_98":261,"_100":101,"_102":262,"_71":117,"_73":117,"_67":263,"_75":266,"_111":324},[325],{"_20":269,"_59":115,"_98":116,"_100":101,"_102":259,"_71":179,"_73":179,"_67":274,"_75":276,"_111":326},[327],{"_20":268,"_59":125,"_98":126,"_100":101,"_102":269,"_71":270,"_73":270,"_67":271,"_75":272,"_111":328},[],{"_20":280,"_59":281,"_98":282,"_100":101,"_102":262,"_71":117,"_73":117,"_67":283,"_75":286,"_111":330},[331],{"_20":293,"_59":294,"_98":295,"_100":101,"_102":280,"_71":296,"_73":296,"_67":297,"_75":299,"_111":332},[333],{"_20":307,"_59":308,"_98":126,"_100":101,"_102":293,"_71":309,"_73":309,"_67":310,"_75":311,"_111":334},[],{"_20":178,"_59":288,"_98":289,"_100":101,"_102":262,"_71":117,"_73":117,"_67":290,"_75":291,"_111":336},[337],{"_20":175,"_59":176,"_98":177,"_100":101,"_102":178,"_71":179,"_73":179,"_67":180,"_75":177,"_111":338},[339],{"_20":302,"_59":125,"_98":126,"_100":101,"_102":175,"_71":303,"_73":303,"_67":304,"_75":305,"_111":340},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários