[{"_1":2,"_275":-5,"_276":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/ecbe9e2c-e9a3-45e6-bd49-ee08faf2d5af","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_48":49,"_70":247,"_248":249},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_41":17,"_42":43,"_44":45},"correctOptionId","","difficulty","id","ecbe9e2c-e9a3-45e6-bd49-ee08faf2d5af","options",[23,29,33,37],{"_19":24,"_25":26,"_27":28},"4c92c937-5187-4fab-88f2-7907d2fd1a8d","label","A","text","13 moléculas",{"_19":30,"_25":31,"_27":32},"8cc41362-15f4-4e7f-84dd-945d4f438973","B","15 moléculas",{"_19":34,"_25":35,"_27":36},"4eb9ec36-b603-423b-801e-0dfec163ade9","C","17 moléculas",{"_19":38,"_25":39,"_27":40},"f49218aa-8717-4405-ba91-e9f3bd2b66f1","D","25 moléculas","solution_explanation","statement","

O melhor vácuo que pode ser obtido em um laboratório corresponde a pressão de 1,01 \\times 10^{-13} \\text{ Pa}.
Quantas moléculas existem por cm³ em tal vácuo, a 293 \\text{ K}? Assinale a alternativa correta:

","status","has_issues","relatedVideos",[],"similarQuestions",[50,173,190,207,227],{"_16":17,"_18":17,"_19":51,"_21":52,"_41":17,"_42":69,"_70":71},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[53,56,59,62,65],{"_19":54,"_25":26,"_27":55},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":57,"_25":31,"_27":58},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":60,"_25":35,"_27":61},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":63,"_25":39,"_27":64},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":66,"_25":67,"_27":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",[72,94,104,114,121,128,136,144,150,155,161,168],{"_19":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",{"_19":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","Termodinâmica","termodinamica","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0","2025-04-29T03:44:27.560682+00:00",{"_87":101,"_89":90,"_91":102},2,11846,"termodinamica-3",{"_19":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":113},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_87":111,"_89":90,"_91":112},5,30614,"engenharia-mecatronica-1",{"_19":115,"_74":116,"_76":117,"_78":79,"_80":105,"_82":83,"_84":83,"_85":118,"_93":120},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_87":111,"_89":90,"_91":119},25741,"mecanica-3",{"_19":98,"_74":122,"_76":123,"_78":79,"_80":108,"_82":109,"_84":109,"_85":124,"_93":127},"Engenharia Mecânica","engenharia-mecanica",{"_87":125,"_89":90,"_91":126},11,36318,"engenharia-mecanica-2",{"_19":129,"_74":130,"_76":131,"_78":79,"_80":132,"_82":99,"_84":99,"_85":133,"_93":131},"96193fa0-9495-45b2-81cc-b547604354af","Física Térmica - Termologia","fisica-termica-termologia","c8ab2a95-fd84-4d6f-ade0-835d34ba00f9",{"_87":134,"_89":90,"_91":135},10,8575,{"_19":137,"_74":138,"_76":139,"_78":79,"_80":-5,"_82":140,"_84":140,"_85":141,"_93":139},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_87":142,"_89":90,"_91":143},18,135489,{"_19":145,"_74":96,"_76":97,"_78":79,"_80":73,"_82":146,"_84":146,"_85":147,"_93":149},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_87":90,"_89":90,"_91":148},8597,"termodinamica-5",{"_19":81,"_74":151,"_76":152,"_78":79,"_80":108,"_82":109,"_84":109,"_85":153,"_93":154},"Engenharia de Petróleo","engenharia-de-petroleo",{"_87":111,"_89":90,"_91":92},"engenharia-de-petroleo-1",{"_19":132,"_74":156,"_76":157,"_78":79,"_80":137,"_82":109,"_84":109,"_85":158,"_93":160},"Física","fisica",{"_87":125,"_89":90,"_91":159},13777,"fisica-4",{"_19":108,"_74":162,"_76":163,"_78":79,"_80":-5,"_82":164,"_84":164,"_85":165,"_93":163},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_87":166,"_89":90,"_91":167},29,351586,{"_19":169,"_74":96,"_76":97,"_78":79,"_80":115,"_82":170,"_84":170,"_85":171,"_93":172},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_87":90,"_89":90,"_91":148},"termodinamica-4",{"_16":17,"_18":17,"_19":174,"_21":175,"_41":17,"_42":188,"_70":189},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[176,179,182,185],{"_19":177,"_25":26,"_27":178},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":180,"_25":31,"_27":181},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":183,"_25":35,"_27":184},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":186,"_25":39,"_27":187},"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.

",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":17,"_18":17,"_19":191,"_21":192,"_41":17,"_42":205,"_70":206},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[193,196,199,202],{"_19":194,"_25":26,"_27":195},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":197,"_25":31,"_27":198},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":200,"_25":35,"_27":201},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":203,"_25":39,"_27":204},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":17,"_18":17,"_19":208,"_21":209,"_41":17,"_42":225,"_70":226},"996628fc-4ac3-4821-86bd-839f86a97a6d",[210,213,216,219,222],{"_19":211,"_25":26,"_27":212},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":214,"_25":31,"_27":215},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":217,"_25":35,"_27":218},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":220,"_25":39,"_27":221},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":223,"_25":67,"_27":224},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[72,94,104,114,121,128,136,144,150,155,161,168],{"_16":17,"_18":17,"_19":228,"_21":229,"_41":17,"_42":245,"_70":246},"c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,239,242],{"_19":231,"_25":26,"_27":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":234,"_25":31,"_27":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":237,"_25":35,"_27":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":240,"_25":39,"_27":241},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":243,"_25":67,"_27":244},"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????",[72,94,104,114,121,128,136,144,150,155,161,168],[72,94,104,114,121,128,136,144,150,155,161,168],"tagsTree",[250,257],{"_19":137,"_74":138,"_76":139,"_78":79,"_80":-5,"_82":140,"_84":140,"_85":141,"_93":139,"_251":252},"children",[253],{"_19":132,"_74":156,"_76":157,"_78":79,"_80":137,"_82":109,"_84":109,"_85":158,"_93":160,"_251":254},[255],{"_19":129,"_74":130,"_76":131,"_78":79,"_80":132,"_82":99,"_84":99,"_85":133,"_93":131,"_251":256},[],{"_19":108,"_74":162,"_76":163,"_78":79,"_80":-5,"_82":164,"_84":164,"_85":165,"_93":163,"_251":258},[259,265,269],{"_19":105,"_74":106,"_76":107,"_78":79,"_80":108,"_82":109,"_84":109,"_85":110,"_93":113,"_251":260},[261],{"_19":115,"_74":116,"_76":117,"_78":79,"_80":105,"_82":83,"_84":83,"_85":118,"_93":120,"_251":262},[263],{"_19":169,"_74":96,"_76":97,"_78":79,"_80":115,"_82":170,"_84":170,"_85":171,"_93":172,"_251":264},[],{"_19":98,"_74":122,"_76":123,"_78":79,"_80":108,"_82":109,"_84":109,"_85":124,"_93":127,"_251":266},[267],{"_19":95,"_74":96,"_76":97,"_78":79,"_80":98,"_82":99,"_84":99,"_85":100,"_93":103,"_251":268},[],{"_19":81,"_74":151,"_76":152,"_78":79,"_80":108,"_82":109,"_84":109,"_85":153,"_93":154,"_251":270},[271],{"_19":73,"_74":75,"_76":77,"_78":79,"_80":81,"_82":83,"_84":83,"_85":86,"_93":77,"_251":272},[273],{"_19":145,"_74":96,"_76":97,"_78":79,"_80":73,"_82":146,"_84":146,"_85":147,"_93":149,"_251":274},[],"actionData","errors"]

Comentários