[{"_1":2,"_337":-5,"_338":-5},"loaderData",{"_3":4,"_8":9},"root",{"_5":6,"_7":-5},"url","https://prouniversitario.com/exercicios/b645fcf6-5514-49f3-be29-ef341c72e2f9","user","pages/questions/show/index",{"_10":11,"_12":13,"_14":15,"_46":47,"_144":145,"_84":310,"_311":312,"_333":334,"_335":336},"comments",[],"isAiGenerated",false,"question",{"_16":17,"_18":17,"_19":20,"_21":22,"_41":17,"_42":43,"_44":45},"correctOptionId","","difficulty","id","b645fcf6-5514-49f3-be29-ef341c72e2f9","options",[23,29,33,37],{"_19":24,"_25":26,"_27":28},"90e49bb1-129a-4012-942c-d8b7938b1384","label","A","text","23.",{"_19":30,"_25":31,"_27":32},"2c2098f6-a069-4abb-8877-a2cacea333ea","B","34.",{"_19":34,"_25":35,"_27":36},"befc85a8-3c71-4958-bbcd-ef4a13ce9d6e","C","28.",{"_19":38,"_25":39,"_27":40},"01d6f7b8-8095-4fd4-9ead-8be3210e36f5","D","13.","solution_explanation","statement","

5 – Uma peça de concreto cilíndrica, de 10 \text{ cm} de raio e 30 \text{ cm} de altura, foi ensaiada por compressão axial. Como resultado deste ensaio, foi possível observar uma carga de ruptura de 42,05 \text{ toneladas}. Com base na resistência à compressão do concreto, em \text{MPa}, assinale a alternativa:

","status","has_issues","relatedVideos",[48],{"_49":50,"_68":69,"_84":85,"_86":87,"_106":107},"content",{"_19":51,"_52":53,"_54":-5,"_55":56,"_57":58,"_59":-5,"_60":61,"_64":65,"_66":65,"_67":-5},"fea1149f-ed42-488e-b8d0-46e5016f329f","name","Relações Trigonométricas no Triângulo Retângulo, Leis dos Senos e Cossenos - 06 - Revisando e Praticando - Parte 06","description","content_type_id","1051eee7-c62e-4b2c-9900-77a29fcec080","resource_id","d7fcad9c-530e-4eec-824f-930373662cdc","user_id","metadata",{"_62":63},"external_id","12593","created_at","2025-08-20T12:27:41.608438+00:00","updated_at","content_group_id","prometheusData",{"_70":71,"_77":78,"_79":80,"_81":82,"_5":83},"provider",{"_19":72,"_73":74,"_75":76},"d6d15d4b-87f1-4181-b20a-19190395ac14","key","grupo_q_cloudflare_stream","kind","cloudflare_stream","reference","788b0a69895b7d4d00f0f7c468c32531","state","completed","thumbnail_url","https://videodelivery.net/eyJraWQiOiIzNDIwNjA3YjJiNTVjMjc2ZTVhNmE1NzYzMGRkNDlhYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTM0MjAyfQ.AZuvjF3chqKhwGKv7hR9fW5KQOdgAlArcHPYo1FZKUsibnU4lQg1epPaNrWqMIsD3oPlZwt5IqgYFRqVqQIMmW4fE1upiKDI5XwmUkDW_0z4Z3-O6YFVGMWqXq8kOCGK1S3H-FIhiD077hQYmVe-PWx4-d5Zf1DqyNU9YXh2KzFGLFnTYKkK_ibOMNw1VQTW4zyAhfJR73K8HQaQGQaT-IULCdzZ4zmVdV9oUt_b9vktFHhfIaVtPRr2sg1QpKoHmKnBqgN0W-vPf9Qcg6hgtSbDikDYTlGeSWmwzIVn_9YfgbrIBD77RAUIxPc3pUiQduhsz3EAMm31IJ7SOiz6rQ/thumbnails/thumbnail.jpg?time=10s&height=360","https://customer-356s6wt60g79gz5u.cloudflarestream.com/eyJraWQiOiIzNDIwNjA3YjJiNTVjMjc2ZTVhNmE1NzYzMGRkNDlhYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiI3ODhiMGE2OTg5NWI3ZDRkMDBmMGY3YzQ2OGMzMjUzMSIsImtpZCI6IjM0MjA2MDdiMmI1NWMyNzZlNWE2YTU3NjMwZGQ0OWFjIiwiZXhwIjoxNzU1OTM0MjAyfQ.AZuvjF3chqKhwGKv7hR9fW5KQOdgAlArcHPYo1FZKUsibnU4lQg1epPaNrWqMIsD3oPlZwt5IqgYFRqVqQIMmW4fE1upiKDI5XwmUkDW_0z4Z3-O6YFVGMWqXq8kOCGK1S3H-FIhiD077hQYmVe-PWx4-d5Zf1DqyNU9YXh2KzFGLFnTYKkK_ibOMNw1VQTW4zyAhfJR73K8HQaQGQaT-IULCdzZ4zmVdV9oUt_b9vktFHhfIaVtPRr2sg1QpKoHmKnBqgN0W-vPf9Qcg6hgtSbDikDYTlGeSWmwzIVn_9YfgbrIBD77RAUIxPc3pUiQduhsz3EAMm31IJ7SOiz6rQ/manifest/video.m3u8","tags",[],"video",{"_19":58,"_88":53,"_54":-5,"_89":90,"_91":92,"_5":-5,"_93":-5,"_70":92,"_94":95,"_81":-5,"_96":-5,"_97":-5,"_98":-5,"_99":-5,"_60":100,"_101":102,"_103":-5,"_44":104,"_64":105,"_66":105},"title","duration",21,"source_type","prometheus","iframe_url","provider_video_id","8335867d-4f35-401e-a9c3-13c4a0db8c56","format","quality","file_path","file_size",{"_62":63},"views_count",0,"last_played_at","draft","2025-08-19T11:56:14.613229+00:00","tag",{"_19":108,"_52":109,"_110":111,"_112":113,"_114":-5,"_64":115,"_66":115,"_60":116,"_122":111,"_123":124},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","alias","exatas","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","2025-04-29T01:56:45.284172+00:00",{"_117":118,"_119":102,"_120":121},"childrenCount",18,"content_count","question_count",135489,"slug","children",[125],{"_19":126,"_52":127,"_110":128,"_112":113,"_114":108,"_64":129,"_66":129,"_60":130,"_122":133,"_123":134},"ca6fee0e-79c6-4f1c-b500-ee081a071949","Mecânica","mecanica","2025-04-29T02:19:12.828432+00:00",{"_117":131,"_119":102,"_120":132},10,19948,"mecanica-2",[135],{"_19":136,"_52":137,"_110":138,"_112":113,"_114":126,"_64":139,"_66":139,"_60":140,"_122":142,"_123":143},"ac55bdba-154d-42e7-bc25-72dde822663d","Resistência dos Materiais","resistencia-dos-materiais","2025-04-29T03:44:29.139762+00:00",{"_117":102,"_119":102,"_120":141},3376,"resistencia-dos-materiais-4",[],"similarQuestions",[146,236,253,270,290],{"_16":17,"_18":17,"_19":147,"_21":148,"_41":17,"_42":165,"_84":166},"3c0b9441-b878-4896-8bac-fa4ca61e3f13",[149,152,155,158,161],{"_19":150,"_25":26,"_27":151},"265bd71a-6749-41f5-b291-67efd646ca64","y'' + 2y' - 3y = 0",{"_19":153,"_25":31,"_27":154},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_19":156,"_25":35,"_27":157},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_19":159,"_25":39,"_27":160},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_19":162,"_25":163,"_27":164},"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

",[167,176,185,191,195,196,197,204,209,217,218,223,229],{"_19":168,"_52":169,"_110":170,"_112":113,"_114":171,"_64":172,"_66":172,"_60":173,"_122":170},"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",{"_117":174,"_119":102,"_120":175},4,12302,{"_19":177,"_52":178,"_110":179,"_112":113,"_114":180,"_64":129,"_66":129,"_60":181,"_122":184},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_117":182,"_119":102,"_120":183},5,30614,"engenharia-mecatronica-1",{"_19":186,"_52":137,"_110":138,"_112":113,"_114":187,"_64":188,"_66":188,"_60":189,"_122":190},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_117":102,"_119":102,"_120":141},"resistencia-dos-materiais-6",{"_19":187,"_52":127,"_110":128,"_112":113,"_114":177,"_64":172,"_66":172,"_60":192,"_122":194},{"_117":182,"_119":102,"_120":193},25741,"mecanica-3",{"_19":108,"_52":109,"_110":111,"_112":113,"_114":-5,"_64":115,"_66":115,"_60":116,"_122":111},{"_19":136,"_52":137,"_110":138,"_112":113,"_114":126,"_64":139,"_66":139,"_60":140,"_122":142},{"_19":198,"_52":199,"_110":200,"_112":113,"_114":180,"_64":129,"_66":129,"_60":201,"_122":203},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_117":90,"_119":102,"_120":202},45865,"engenharia-civil-3",{"_19":171,"_52":205,"_110":206,"_112":113,"_114":180,"_64":129,"_66":129,"_60":207,"_122":208},"Engenharia de Petróleo","engenharia-de-petroleo",{"_117":182,"_119":102,"_120":175},"engenharia-de-petroleo-1",{"_19":210,"_52":211,"_110":212,"_112":113,"_114":198,"_64":213,"_66":213,"_60":214,"_122":216},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_117":182,"_119":102,"_120":215},8852,"estruturas-1",{"_19":126,"_52":127,"_110":128,"_112":113,"_114":108,"_64":129,"_66":129,"_60":130,"_122":133},{"_19":219,"_52":137,"_110":138,"_112":113,"_114":168,"_64":220,"_66":220,"_60":221,"_122":222},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_117":102,"_119":102,"_120":141},"resistencia-dos-materiais-7",{"_19":224,"_52":225,"_110":138,"_112":113,"_114":210,"_64":226,"_66":226,"_60":227,"_122":228},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_117":102,"_119":102,"_120":141},"resistencia-dos-materiais-5",{"_19":180,"_52":230,"_110":231,"_112":113,"_114":-5,"_64":232,"_66":232,"_60":233,"_122":231},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_117":234,"_119":102,"_120":235},29,351586,{"_16":17,"_18":17,"_19":237,"_21":238,"_41":17,"_42":251,"_84":252},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[239,242,245,248],{"_19":240,"_25":26,"_27":241},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":243,"_25":31,"_27":244},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":246,"_25":35,"_27":247},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":249,"_25":39,"_27":250},"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.

",[167,176,185,191,195,196,197,204,209,217,218,223,229],{"_16":17,"_18":17,"_19":254,"_21":255,"_41":17,"_42":268,"_84":269},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[256,259,262,265],{"_19":257,"_25":26,"_27":258},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":260,"_25":31,"_27":261},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":263,"_25":35,"_27":264},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":266,"_25":39,"_27":267},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

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

",[167,176,185,191,195,196,197,204,209,217,218,223,229],{"_16":17,"_18":17,"_19":271,"_21":272,"_41":17,"_42":288,"_84":289},"996628fc-4ac3-4821-86bd-839f86a97a6d",[273,276,279,282,285],{"_19":274,"_25":26,"_27":275},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":277,"_25":31,"_27":278},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":280,"_25":35,"_27":281},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":283,"_25":39,"_27":284},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":286,"_25":163,"_27":287},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[167,176,185,191,195,196,197,204,209,217,218,223,229],{"_16":17,"_18":17,"_19":291,"_21":292,"_41":17,"_42":308,"_84":309},"c478a46c-46a8-4942-ae14-2e79def3dda2",[293,296,299,302,305],{"_19":294,"_25":26,"_27":295},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":297,"_25":31,"_27":298},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":300,"_25":35,"_27":301},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":303,"_25":39,"_27":304},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":306,"_25":163,"_27":307},"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????",[167,176,185,191,195,196,197,204,209,217,218,223,229],[167,176,185,191,195,196,197,204,209,217,218,223,229],"tagsTree",[107,313],{"_19":180,"_52":230,"_110":231,"_112":113,"_114":-5,"_64":232,"_66":232,"_60":233,"_122":231,"_123":314},[315,321,327],{"_19":177,"_52":178,"_110":179,"_112":113,"_114":180,"_64":129,"_66":129,"_60":181,"_122":184,"_123":316},[317],{"_19":187,"_52":127,"_110":128,"_112":113,"_114":177,"_64":172,"_66":172,"_60":192,"_122":194,"_123":318},[319],{"_19":186,"_52":137,"_110":138,"_112":113,"_114":187,"_64":188,"_66":188,"_60":189,"_122":190,"_123":320},[],{"_19":198,"_52":199,"_110":200,"_112":113,"_114":180,"_64":129,"_66":129,"_60":201,"_122":203,"_123":322},[323],{"_19":210,"_52":211,"_110":212,"_112":113,"_114":198,"_64":213,"_66":213,"_60":214,"_122":216,"_123":324},[325],{"_19":224,"_52":225,"_110":138,"_112":113,"_114":210,"_64":226,"_66":226,"_60":227,"_122":228,"_123":326},[],{"_19":171,"_52":205,"_110":206,"_112":113,"_114":180,"_64":129,"_66":129,"_60":207,"_122":208,"_123":328},[329],{"_19":168,"_52":169,"_110":170,"_112":113,"_114":171,"_64":172,"_66":172,"_60":173,"_122":170,"_123":330},[331],{"_19":219,"_52":137,"_110":138,"_112":113,"_114":168,"_64":220,"_66":220,"_60":221,"_122":222,"_123":332},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários