The document contains 20 multiple choice questions about logarithms. The questions cover topics such as logarithmic equations, properties of logarithms, and exponential growth models involving logarithms. They range in difficulty from straightforward calculations to modeling real-world scenarios using logarithmic functions.
Eratosthenes, an ancient Greek scholar, estimated one of the first measurements of Earth's radius by observing the sun from two different cities in Egypt on the summer solstice. Noting that a vertical rod cast no shadow in Syene but did cast a shadow in Alexandria, he calculated the angle between the sun's rays and used this angle and the known distance between the cities to estimate Earth's circumference as approximately 25,000 miles.
This document contains a test with 15 multiple choice questions covering various topics in mathematics including algebra, geometry, trigonometry, and calculus. The test is for Escola Naval 2020. The questions involve concepts like progressions, functions, limits, vectors, and factorials. No answer key is provided.
This document contains a 16 question multiple choice test covering topics in mathematics. The questions involve solving word problems related to ratios, percentages, geometry, algebra and other mathematical concepts. Correct answers are provided for each question at the end.
The document contains 20 multiple choice questions about mathematics topics such as functions, geometry, trigonometry, and algebra. The questions cover concepts like parabolas, areas, solid geometry, probability, combinatorics, and equations. The document provides a key with the correct answer for each question listed from A to E.
The document contains 20 math and science problems with multiple choice answers. The problems cover topics like virus spread over time, graphing functions, calculating distances using jumps, quadratic functions, data shown in graphs like temperature and sales over time, and calculating logarithms and function compositions.
This document contains a 12 question multiple choice exam covering topics in mathematics and geometry. The questions involve functions, graphs, probability, volumes, areas, and geometric relationships.
This document contains 20 multiple choice questions from an exam in Brazil (ITA 2011). The questions cover a range of mathematical topics including algebra, geometry, trigonometry, and complex numbers. For each question there are 5 possible answer choices labeled a-e. The document also includes the answer key at the end listing the correct choice for each question.
This document contains 25 math problems and their solutions. The problems cover a range of arithmetic topics like number properties, operations, sequences, and word problems. The correct answers to the problems are provided in a key at the end.
Eratosthenes, an ancient Greek scholar, estimated one of the first measurements of Earth's radius by observing the sun from two different cities in Egypt on the summer solstice. Noting that a vertical rod cast no shadow in Syene but did cast a shadow in Alexandria, he calculated the angle between the sun's rays and used this angle and the known distance between the cities to estimate Earth's circumference as approximately 25,000 miles.
This document contains a test with 15 multiple choice questions covering various topics in mathematics including algebra, geometry, trigonometry, and calculus. The test is for Escola Naval 2020. The questions involve concepts like progressions, functions, limits, vectors, and factorials. No answer key is provided.
This document contains a 16 question multiple choice test covering topics in mathematics. The questions involve solving word problems related to ratios, percentages, geometry, algebra and other mathematical concepts. Correct answers are provided for each question at the end.
The document contains 20 multiple choice questions about mathematics topics such as functions, geometry, trigonometry, and algebra. The questions cover concepts like parabolas, areas, solid geometry, probability, combinatorics, and equations. The document provides a key with the correct answer for each question listed from A to E.
The document contains 20 math and science problems with multiple choice answers. The problems cover topics like virus spread over time, graphing functions, calculating distances using jumps, quadratic functions, data shown in graphs like temperature and sales over time, and calculating logarithms and function compositions.
This document contains a 12 question multiple choice exam covering topics in mathematics and geometry. The questions involve functions, graphs, probability, volumes, areas, and geometric relationships.
This document contains 20 multiple choice questions from an exam in Brazil (ITA 2011). The questions cover a range of mathematical topics including algebra, geometry, trigonometry, and complex numbers. For each question there are 5 possible answer choices labeled a-e. The document also includes the answer key at the end listing the correct choice for each question.
This document contains 25 math problems and their solutions. The problems cover a range of arithmetic topics like number properties, operations, sequences, and word problems. The correct answers to the problems are provided in a key at the end.
ANÁLISIS SÍSMICO DE LOSA TRIANGULAR DE DOS PISOS.Rosbert Malpaso
ANÁLISIS SÍSMICO DE UNA EDIFICACIÓN DE LOSA TRIANGULAR DE DOS PISOS A NIVEL PREGRADO DESARROLLADO EN LA FACULTAD DE INGENIERÍA CIVIL DE LA UNASAM. (GRADOS DE LIBERTAD, MODOS DE VIBRAR, FRECUENCIAS, DESPLAZAMIENTOS, ETC).
This document contains a 16 question math exam covering topics such as functions, trigonometry, geometry, and linear systems. The questions involve solving equations, analyzing graphs, calculating areas and probabilities, and determining properties of functions and geometric shapes. The correct answers are provided at the end.
1) The document contains 10 math problems from a Brazilian entrance exam (Fuvest). The problems cover topics like functions, geometry, probability, and word problems.
2) Mafalda is frustrated that she cannot solve one of the math problems. The problem asks her to solve 291.
3) A transportation company received a request to make an additional delivery, which would require deviating from the most direct route. The question calculates the minimum price the company would need to charge for the extra time and fuel required.
This document contains 13 math problems related to geometry, algebra, and other topics. Some key details:
- Problem 1 involves finding parameters of linear functions relating shoe size and length for Brazil and the US.
- Problem 2 analyzes data from Felix Baumgartner's skydive record, calculating velocity at a given time and when he broke the sound barrier.
- Problem 3 involves matrix multiplication and finding the value of a parameter for a system of equations to have a solution.
- Problems 4-6 cover marketing discounts on course enrollments, volume calculations for a pool with dimensions in geometric progression, and nutrient content relationships in fertilizers.
- Later problems analyze triangles, polynomials,
This document contains 13 multiple choice questions from the Fuvest 2021 exam. The questions cover topics such as functions, graphs, probability, geometry, numbers, and word problems. Correct answer options are provided for each question.
1) The document contains 6 questions regarding matrices, geometry, trigonometry, and statistics.
2) The first question involves calculating the product of two matrices and solving a linear system.
3) The second question determines the number of vertices and edges of a polyhedron given its dimensions, and calculates its volume.
This document contains a 12 question multiple choice exam covering various topics in mathematics and physics. The questions involve concepts like geometry, trigonometry, probability, coordinate systems, and data analysis. For each question there are 5 possible answer choices labeled a-e. The last section provides the answer key showing the correct choice for each question.
This document contains 20 multiple choice questions from an exam in Brazil called ITA 2017. The questions cover a range of mathematical topics including sets, geometry, trigonometry, logarithms, and number theory. For each question there are 5 possible answer choices labeled a-e.
The document contains 20 multiple choice questions about functions. Each question provides context about a function or functions, such as their definitions, graphs, or properties. The questions then ask the examinee to determine properties of the functions or choose the best representation of a function based on the information provided.
The document contains 25 multiple choice questions about arithmetic progressions. The questions cover topics such as determining terms in an arithmetic sequence, calculating sums and differences of terms, and identifying patterns in sequences of numbers or geometric shapes that follow an arithmetic progression.
The document contains 15 multiple choice questions about binomial expansions. Some questions ask for coefficients of specific terms, the number of terms, or the sum of all coefficients when expanding expressions using the binomial theorem. The questions cover expanding binomials according to decreasing powers of variables like x and y, as well as applications involving compound interest rates and probability.
This document contains 18 math word problems involving inequalities. The problems cover a range of topics including: calculating heart rate ranges based on age; selecting bus sizes given passenger and cost constraints; determining investment amounts to meet return thresholds; and finding domains and ranges of functions. Readers are asked to determine interval solutions, identify valid parameter values, and select system of inequality representations.
This document contains a question asking for the number of factors of N3 given information about the number of factors of N. It also contains two statements, A and B, that could potentially be used to answer the question. The correct answer is c), as the question can be answered by using both statements together, but neither statement alone provides enough information to determine the number of factors of N3.
This document contains 19 multiple choice questions about functions. The questions cover topics such as function graphs, polynomial functions, logarithmic functions, and inequalities involving functions. For each question there are 5 possible answer choices labeled a-e. The answers given are: 1) B 2) C 3) D 4) D 5) D 6) A 7) C 8) E 9) B 10) C 11) A 12) C 13) B 14) C 15) D 16) D 17) A 18) B 19) C.
The document contains 20 multiple choice questions related to systems of linear equations. The questions cover topics such as determining the number of solutions to a system, properties of matrices, and using systems of equations to solve word problems. Sample questions ask the learner to determine the number of possible values for a variable that would make a given system possible and indeterminate, or to identify properties of matrices that would satisfy certain conditions.
This document presents a multi-part math problem involving a polygon with sides of decreasing length forming an arithmetic progression. It provides information about the polygon and asks the reader to analyze several propositions related to distances traveled by a formic along the polygon's path. It then asks the reader to identify which of the propositions are true.
The document contains 20 multiple choice questions about functions. The questions cover topics such as exponential functions, linear functions, quadratic functions, modular functions, and geometric progressions. They involve calculating function values, analyzing function graphs, finding maximums and minimums, and modeling real-world scenarios mathematically.
The document contains 12 math problems from a Brazilian university entrance exam (Unicamp 2014). Some key details:
- Problem 1 involves finding the 6th term of a harmonic progression and a property of harmonic progressions.
- Problem 2 concerns quadratic functions of the form f(x) = ax^2 + bx and their graphs.
- Problem 3 deals with modeling plant growth over time using logarithmic and composite functions.
- Problem 4 is about a water bill pricing scheme and sketching the associated cost function.
- The remaining problems cover topics like matrices, probability, geometry, polynomials, statistics, and consumer preferences for pizza types.
The document contains 14 multiple choice questions about mathematical concepts such as linear equations, graphs, coordinate planes, and word problems. The questions are drawn from past Brazilian National High School Exam (Enem) tests from 2007 to 2018 and cover topics like linear functions, coordinate geometry, rates of change, and proportional reasoning.
The document contains 20 multiple choice questions from an exam in Brazil (ITA 2018). The questions cover a range of math and geometry topics including: arithmetic and geometric progressions, matrices, polynomials, probability, triangles, circles, trigonometry and complex numbers.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document contains 6 questions regarding mathematics from a Brazilian university entrance exam (UNICAMP).
The questions cover topics such as: solving equations for real numbers; geometric and arithmetic sequences; matrix operations; properties of triangles; percentages and rates of change.
The summary provides the key results and solutions for each question in less than 3 sentences per question.
ANÁLISIS SÍSMICO DE LOSA TRIANGULAR DE DOS PISOS.Rosbert Malpaso
ANÁLISIS SÍSMICO DE UNA EDIFICACIÓN DE LOSA TRIANGULAR DE DOS PISOS A NIVEL PREGRADO DESARROLLADO EN LA FACULTAD DE INGENIERÍA CIVIL DE LA UNASAM. (GRADOS DE LIBERTAD, MODOS DE VIBRAR, FRECUENCIAS, DESPLAZAMIENTOS, ETC).
This document contains a 16 question math exam covering topics such as functions, trigonometry, geometry, and linear systems. The questions involve solving equations, analyzing graphs, calculating areas and probabilities, and determining properties of functions and geometric shapes. The correct answers are provided at the end.
1) The document contains 10 math problems from a Brazilian entrance exam (Fuvest). The problems cover topics like functions, geometry, probability, and word problems.
2) Mafalda is frustrated that she cannot solve one of the math problems. The problem asks her to solve 291.
3) A transportation company received a request to make an additional delivery, which would require deviating from the most direct route. The question calculates the minimum price the company would need to charge for the extra time and fuel required.
This document contains 13 math problems related to geometry, algebra, and other topics. Some key details:
- Problem 1 involves finding parameters of linear functions relating shoe size and length for Brazil and the US.
- Problem 2 analyzes data from Felix Baumgartner's skydive record, calculating velocity at a given time and when he broke the sound barrier.
- Problem 3 involves matrix multiplication and finding the value of a parameter for a system of equations to have a solution.
- Problems 4-6 cover marketing discounts on course enrollments, volume calculations for a pool with dimensions in geometric progression, and nutrient content relationships in fertilizers.
- Later problems analyze triangles, polynomials,
This document contains 13 multiple choice questions from the Fuvest 2021 exam. The questions cover topics such as functions, graphs, probability, geometry, numbers, and word problems. Correct answer options are provided for each question.
1) The document contains 6 questions regarding matrices, geometry, trigonometry, and statistics.
2) The first question involves calculating the product of two matrices and solving a linear system.
3) The second question determines the number of vertices and edges of a polyhedron given its dimensions, and calculates its volume.
This document contains a 12 question multiple choice exam covering various topics in mathematics and physics. The questions involve concepts like geometry, trigonometry, probability, coordinate systems, and data analysis. For each question there are 5 possible answer choices labeled a-e. The last section provides the answer key showing the correct choice for each question.
This document contains 20 multiple choice questions from an exam in Brazil called ITA 2017. The questions cover a range of mathematical topics including sets, geometry, trigonometry, logarithms, and number theory. For each question there are 5 possible answer choices labeled a-e.
The document contains 20 multiple choice questions about functions. Each question provides context about a function or functions, such as their definitions, graphs, or properties. The questions then ask the examinee to determine properties of the functions or choose the best representation of a function based on the information provided.
The document contains 25 multiple choice questions about arithmetic progressions. The questions cover topics such as determining terms in an arithmetic sequence, calculating sums and differences of terms, and identifying patterns in sequences of numbers or geometric shapes that follow an arithmetic progression.
The document contains 15 multiple choice questions about binomial expansions. Some questions ask for coefficients of specific terms, the number of terms, or the sum of all coefficients when expanding expressions using the binomial theorem. The questions cover expanding binomials according to decreasing powers of variables like x and y, as well as applications involving compound interest rates and probability.
This document contains 18 math word problems involving inequalities. The problems cover a range of topics including: calculating heart rate ranges based on age; selecting bus sizes given passenger and cost constraints; determining investment amounts to meet return thresholds; and finding domains and ranges of functions. Readers are asked to determine interval solutions, identify valid parameter values, and select system of inequality representations.
This document contains a question asking for the number of factors of N3 given information about the number of factors of N. It also contains two statements, A and B, that could potentially be used to answer the question. The correct answer is c), as the question can be answered by using both statements together, but neither statement alone provides enough information to determine the number of factors of N3.
This document contains 19 multiple choice questions about functions. The questions cover topics such as function graphs, polynomial functions, logarithmic functions, and inequalities involving functions. For each question there are 5 possible answer choices labeled a-e. The answers given are: 1) B 2) C 3) D 4) D 5) D 6) A 7) C 8) E 9) B 10) C 11) A 12) C 13) B 14) C 15) D 16) D 17) A 18) B 19) C.
The document contains 20 multiple choice questions related to systems of linear equations. The questions cover topics such as determining the number of solutions to a system, properties of matrices, and using systems of equations to solve word problems. Sample questions ask the learner to determine the number of possible values for a variable that would make a given system possible and indeterminate, or to identify properties of matrices that would satisfy certain conditions.
This document presents a multi-part math problem involving a polygon with sides of decreasing length forming an arithmetic progression. It provides information about the polygon and asks the reader to analyze several propositions related to distances traveled by a formic along the polygon's path. It then asks the reader to identify which of the propositions are true.
The document contains 20 multiple choice questions about functions. The questions cover topics such as exponential functions, linear functions, quadratic functions, modular functions, and geometric progressions. They involve calculating function values, analyzing function graphs, finding maximums and minimums, and modeling real-world scenarios mathematically.
The document contains 12 math problems from a Brazilian university entrance exam (Unicamp 2014). Some key details:
- Problem 1 involves finding the 6th term of a harmonic progression and a property of harmonic progressions.
- Problem 2 concerns quadratic functions of the form f(x) = ax^2 + bx and their graphs.
- Problem 3 deals with modeling plant growth over time using logarithmic and composite functions.
- Problem 4 is about a water bill pricing scheme and sketching the associated cost function.
- The remaining problems cover topics like matrices, probability, geometry, polynomials, statistics, and consumer preferences for pizza types.
The document contains 14 multiple choice questions about mathematical concepts such as linear equations, graphs, coordinate planes, and word problems. The questions are drawn from past Brazilian National High School Exam (Enem) tests from 2007 to 2018 and cover topics like linear functions, coordinate geometry, rates of change, and proportional reasoning.
The document contains 20 multiple choice questions from an exam in Brazil (ITA 2018). The questions cover a range of math and geometry topics including: arithmetic and geometric progressions, matrices, polynomials, probability, triangles, circles, trigonometry and complex numbers.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document contains 6 questions regarding mathematics from a Brazilian university entrance exam (UNICAMP).
The questions cover topics such as: solving equations for real numbers; geometric and arithmetic sequences; matrix operations; properties of triangles; percentages and rates of change.
The summary provides the key results and solutions for each question in less than 3 sentences per question.
This document contains 12 multiple choice questions from the 2010 FUVEST exam. The questions cover topics such as functions, progressions, probability, geometry, trigonometry, and data interpretation. For each question there are 5 possible answer choices labeled a-e. The questions range in difficulty and cover high school level math concepts.
The document contains a 20 question multiple choice exam covering various topics in mathematics and geometry. For each question, there are 5 potential answer choices labeled a-e. The questions cover topics such as functions, complex numbers, limits, integrals, geometry, and probability. At the end, a key is provided indicating the correct answer for each question.
Revisão ENEM - Matemática e suas tecnologiasThiago Coelho
The document defines the term "infodemic" as declared by the WHO regarding the COVID-19 pandemic and response. An infodemic refers to a large increase in the volume of information associated with a specific topic that can grow exponentially in a short time due to an event like the current pandemic. In this situation, rumors and misinformation arise along with manipulation of information for dubious intentions. In the information age, social media amplifies and spreads this phenomenon more rapidly like a virus.
This document contains 10 multi-part questions related to mathematics. The questions cover topics such as functions, probability, geometry, and trigonometry. For example, question 1 involves calculating values of functions, finding where two functions are equal, and sketching their graphs. Question 4 analyzes the distances traveled by two planes flying routes between cities.
This document contains a pie chart showing the sources of funds collected by the National Highways Authority of India for Phase II projects. It also includes 5 multiple choice questions about the pie chart. The total funds collected were Rs. 57,600 crores. The questions ask about the percentage of funds from different sources, the central angle corresponding to different sources on the pie chart, and calculations involving the data from the pie chart, such as determining amounts based on percentages.
This document contains a test for the Caribbean Examinations Council Secondary Education Certificate examination in Mathematics from January 2010. The test has two sections, with Section I containing 7 compulsory questions and Section II containing 2 questions to choose from. The questions cover topics such as algebra, geometry, trigonometry, vectors and matrices. The test instructions specify the time allowed, materials permitted, and that working must be clearly shown.
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O documento apresenta 17 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: corrida de regularidade, monitoramento de substâncias no sangue, crescimento populacional de médicos, modelos predador-presa, crescimento exponencial de bactérias, ativação de rádio automotivo por código secreto e frequências de transmissão de aparelhos sem fio. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio sobre probabilidades.
O documento apresenta três questões sobre um teste realizado com um novo modelo de carro. A primeira questão descreve que 50 litros de combustível foram colocados no tanque do carro e ele foi dirigido em uma pista de testes até o combustível acabar. A segunda questão fornece um gráfico que relaciona a quantidade de combustível no tanque com a distância percorrida. A terceira questão pede a expressão algébrica que relaciona essas duas grandezas.
O documento descreve um fabricante que decidiu contratar o plano B de uma empresa de entregas, ao invés do plano A que havia escolhido inicialmente. O plano B tem taxa fixa mensal menor, mas taxa variável maior por quilograma enviado. Com 650kg a serem enviados, o plano B terá custo total menor do que o plano A.
O documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: estatística, física, geometria e probabilidade. As questões envolvem interpretação e análise de gráficos, cálculos, resolução de problemas e relações entre grandezas geométricas.
Este documento apresenta 15 questões sobre diversos assuntos como: salário comissionado, interação predador-presa, doenças relacionadas ao saneamento, depreciação de veículos, probabilidades, geometria espacial e volumes de sólidos geométricos. As questões envolvem interpretação e análise de gráficos, cálculos, raciocínio lógico e resolução de problemas.
O documento apresenta 19 questões do ENEM PPL de 2014 sobre diversos assuntos como física, química e matemática. As questões abordam tópicos como emissão de poluentes em veículos, crescimento bacteriano, probabilidade, geometria espacial e outros.
1) O documento apresenta 15 questões do ENEM PPL de 2013 sobre diversos assuntos como matemática, probabilidade e estatística.
2) As questões envolvem cálculos, interpretação de gráficos e tabelas para analisar problemas relacionados a produção industrial, vendas, financiamentos, jogos de azar e outros.
3) As respostas variam entre letras que indicam o resultado correto de cada questão após realizar os procedimentos matemáticos necessários.
1) O documento apresenta 15 questões do ENEM PPL de 2012 sobre diversos assuntos como probabilidades, estatística, geometria e física.
2) As questões envolvem cálculos e análises de gráficos, tabelas e figuras para responder sobre tópicos como produção de resíduos, vendas de produtos, taxas de abandono escolar, capacidade de lixeiras e propriedades geométricas de figuras.
3) São abordados também conceitos como acomodação ocular, convergência de lentes, á
Este documento contém 18 questões do Exame Nacional do Ensino Médio (ENEM) de 2017 sobre diversos assuntos como geometria, funções, probabilidade e estatística. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio lógico.
O documento relata sobre o Exame Nacional do Ensino Médio (ENEM) de 2009 que foi cancelado e traz 15 questões objetivas sobre diversos assuntos como probabilidade, geometria, estatística e análise combinatória.
O documento apresenta 18 questões do ENEM 2010 sobre diversos assuntos como: planejamento de treinos, estimativa de quantidade de estrelas para um painel, volumes de leite em reservatórios, desperdício de água por torneiras, uso de bicicletas compartilhadas, consumo de sacolas plásticas, escolha de estacionamentos, conta de água, necessidade diária de ferro e zinco por meio de alimentos, escolha de museus a visitar, estatísticas de chutes a gol, probabilidade em teste para detecção de
O documento apresenta 16 questões do Enem 2016 sobre diversos assuntos como matemática, física, probabilidade e estatística. As questões abordam tópicos como cálculo de áreas, sistemas lineares, funções exponenciais e probabilidades.
O documento contém 15 questões do Exame Nacional do Ensino Médio (ENEM) da segunda aplicação de 2014. As questões abordam tópicos como matemática, física, biologia, história e língua portuguesa.
O documento descreve os tipos sanguíneos e os resultados de um teste em 200 pessoas. 100 pessoas tinham o antígeno A, 110 o antígeno B e 20 nenhum. Portanto, o número de pessoas com tipo sanguíneo A é igual a 100.
O documento discute um problema de trânsito no Brasil relacionado ao consumo de bebidas alcoólicas por motoristas. Dados mostram que após mudanças no código de trânsito em 2013, como redução do limite de álcool no sangue e aumento de multas, houve queda no número de acidentes entre 2013 e 2015.
The document provides information about 12 multiple choice questions that appeared on the 2018 Brazilian National High School Exam (ENEM). The questions cover topics such as mathematics, statistics, geometry, probability, and other subjects. Specifically, the document provides the questions, answer options, and sometimes additional context or information needed to solve each question.
O documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) de 2017, cobrindo diversos assuntos como geometria, física, probabilidade e estatística. As questões envolvem interpretação e análise de gráficos, cálculos e resolução de problemas.
O documento descreve um problema de engenharia sobre a construção de uma galeria subterrânea para transporte de água entre uma fonte e um reservatório em uma cidade. Dois projetos são apresentados: um segmento de reta ou uma semicircunferência. Após cálculos, o projeto da semicircunferência levaria menos tempo para ser concluído.
Este documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) de 2015 sobre diversos assuntos como física, matemática, probabilidade e estatística. As questões envolvem cálculos, interpretação de gráficos e tabelas para analisar situações problemas.
[1] Um professor alterou as notas de uma prova usando uma função polinomial para compensar questões difíceis. [2] Uma pessoa recebeu propostas de planos de telefonia e pretende gastar R$30,00. [3] A figura mostra a trajetória de um balanço e a equação que a descreve.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
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This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
2. LOGARITMOS
1
01. (Unesp 2019) Um banco estabelece os preços dos seguros de vida de seus clientes com base no índice de risco do
evento assegurado. A tabela mostra o cálculo do índice de risco de cinco eventos diferentes.
Evento (E)
Risco de morte
(1 em n mortes)
log n
Índice de risco de
E (10 log n)
−
Atingido por
relâmpago
1 em 2.000.000 6,3 3,7
Afogamento 1 em 30.000 4,5 5,5
Homicídio 1 em 15.000 4,2 5,8
Acidente de
motocicleta
1 em 8.000 3,9 6,1
Doenças provocadas
pelo cigarro
1 em 800 2,9 7,1
Sabe-se que, nesse banco, o índice de risco de morte pela prática do evento BASE jumping é igual a 8.
O risco de morte para praticantes desse esporte, segundo a avaliação do banco, é de
a) 2,5%.
b) 2%.
c) 1%.
d) 1,5%.
e) 0,5%.
02. (Mackenzie 2019) Se a e b, a b,
< são soluções da equação 5
4
log x x
x ,
125
= então o valor de
1
(b a)
2
− é
a) 125
b) 120
c) 60
d) 3
e) 1
3. LOGARITMOS
2
03. (Famerp 2019) A figura indica os gráficos das funções f e g, definidas de ℝ+
∗
em ℝ, cujas leis são, respectivamente,
f(x) 4logx
= e g(x) 3logx.
=
O valor de m, indicado na figura, é igual a
a) log12
b) 0,75
2
c) log7
d) 0,25
2
e) 1,25
2
04. (Fuvest 2019) Se 2 2
1 2
log y log x,
2 3
=
− + para x 0,
> então
a)
3 2
x
y
2
=
b)
3
x
y
2
=
c)
3 2
1
y x
2
=
− +
d)
3 2
y 2 x
= ⋅
e) 3
y 2x
=
05. (Mackenzie 2019) Se a, b e c são números reais positivos e diferentes de 1, e b
log c k,
= então b a
c
log a log c
log b
⋅
é
igual a
a) 1
b)
1
k
c) k
d) 2k
e) 2
k
4. LOGARITMOS
3
06. (Mackenzie 2018) O sistema
b
3b
log (9a 35) 6
,
log (27a 81) 3
− =
− =
com b 1,
> tem como solução (a, b) igual a
a) (2,11)
b) (11, 2)
c) (1,11)
d) (11,1)
e) (1
, 2)
07. (Mackenzie 2018) O valor do determinante
1
3
1
3
1
3 3
3
3 3
0 log 3 log
1 log 27 log 27
0 log 81 log 243
é
a) 0
b) 1
c) 1
−
d) 3
e)
1
3
08. (Mackenzie 2017) Considerando m e n raízes da equação
x x
2
2 2
2 8 0
log x log x 0 0,
1 2 3
= onde x 0,
> então m n
+ é
igual a
a)
2
3
b)
3
4
c)
3
2
d)
4
3
e)
4
5
09. (Fuvest 2017) Uma quantidade fixa de um gás ideal é mantida a temperatura constante, e seu volume varia com
o tempo de acordo com a seguinte fórmula: 2
V(t) log (5 2 sen( t)), 0 t 2,
π
= + ≤ ≤ em que t é medido em horas e V(t)
é medido em 3
m . A pressão máxima do gás no intervalo de tempo [0, 2] ocorre no instante
a) t 0,4
=
b) t 0,5
=
c) t 1
=
d) t 1,5
=
e) t 2
=
5. LOGARITMOS
4
10. (Fatec 2017) O relatório anual “Tendências Globais”, que registra o deslocamento forçado ao redor do mundo,
aponta um total de 65,3 milhões de pessoas deslocadas por guerras e conflitos até o final de 2015 – um aumento de
quase 10% se comparado com o total de 59,5 milhões registrado em 2014. Esta é a primeira vez que o deslocamento
forçado ultrapassa o marco de 60 milhões de pessoas. No final de 2005, o Alto Comissariado das Nações Unidas para
Refugiados (ACNUR) registrou uma média de 6 pessoas deslocadas a cada minuto. Hoje (2015), esse número é de 24
por minuto. O universo de 65,3 milhões inclui 21,3 milhões de refugiados ao redor do mundo, 3,2 milhões de
solicitantes de refúgio e 40,8 milhões de deslocados que continuam dentro de seus países.
Suponha um aumento exato de 10% no número de pessoas deslocadas no ano de 2015 em relação a 2014, e que esse
crescimento ocorrerá a essa mesma taxa anualmente. O número de pessoas deslocadas, em relação a 2014, dobrará
no ano
Adote:
log2 0,30
log1,1 0,04
=
=
a) 2018 b) 2020 c) 2022 d) 2024 e) 2026
11. (Insper 2016) A figura mostra os gráficos das funções f e g, que são simétricos em relação à reta de equação
y x.
=
Se a função f é dada pela lei
3
1 x
f(x) 1 3 ,
−
= + então a lei da função g é
a) 3
3
g(x) [1 log (x 1)]
=
− −
b) 3
3
g(x) [1 log (x 1)]
=
+ −
c) 3
3
g(x) 1 log (x 1)
=
− −
d) 3
3
g(x) 1 log (x 1)
=
+ −
e) 3
3
g(x) 1 log (x 1)
=
− −
6. LOGARITMOS
5
12. (Fac. Albert Einstein 2016) Uma pesquisa foi desenvolvida a partir de 250 bactérias de uma cultura. Estimou-se
então, de maneira aproximada, que, durante certo tempo, o aumento percentual do número de bactérias na cultura
poderia ser obtido pela expressão 3
B(t) 30 log (t 21) 150,
=
− ⋅ + + em que t é o tempo decorrido, em minutos, após o
início da pesquisa. Nessas condições, ao fim da primeira hora da pesquisa, quantas bactérias havia em tal cultura?
a) 325
b) 400
c) 450
d) 525
13. (Unesp 2016) Um torneio de futebol será disputado por 16 equipes que, ao final, serão classificadas do 1º ao 16º
lugar. Para efeitos da classificação final, as regras do torneio impedem qualquer tipo de empate. Considerando para
os cálculos log 15! 12
= e log 2 0,3,
= a ordem de grandeza do total de classificações possíveis das equipes nesse
torneio é de
a) bilhões
b) quatrilhões
c) quintilhões
d) milhões
e) trilhões
14. (Fuvest 2016) O valor
2 3 7
1 1 1
S
2 log 2016 5 log 2016 10 log 2016
= + +
⋅ ⋅ ⋅
é
a)
1
2
b)
1
3
c)
1
5
d)
1
7
e)
1
10
15. (Mackenzie 2016) A equação do 2º grau 2
x x logt 0,5 logt 0
+ ⋅ + ⋅ = tem duas raízes reais distintas, se
a) t 0
>
b) t 1
>
c) t 0
= ou t 2
=
d) 0 t 2
< <
e) 0 t 1
< < ou t 100
>
16. (Unicamp 2016) A solução da equação na variável real x, x
log (x 6) 2,
+ =é um número
a) primo
b) par
c) negativo
d) irracional
7. LOGARITMOS
6
17. (Unesp 2015) No artigo “Desmatamento na Amazônia Brasileira: com que intensidade vem ocorrendo?”, o
pesquisador Philip M. Fearnside, do INPA, sugere como modelo matemático para o cálculo da área de desmatamento
a função k t
D(t) D(0) e ,
⋅
= ⋅ em que D(t) representa a área de desmatamento no instante t, sendo t medido em anos
desde o instante inicial, D(0) a área de desmatamento no instante inicial t 0,
= e k a taxa média anual de
desmatamento da região. Admitindo que tal modelo seja representativo da realidade, que a taxa média anual de
desmatamento (k) da Amazônia seja 0,6% e usando a aproximação n 2 0,69,
≅
o número de anos necessários para
que a área de desmatamento da Amazônia dobre seu valor, a partir de um instante inicial prefixado, é
aproximadamente
a) 51.
b) 115.
c) 15.
d) 151.
e) 11.
18. (Insper 2014) Analisando o comportamento das vendas de determinado produto em diferentes cidades, durante
um ano, um economista estimou que a quantidade vendida desse produto em um mês (Q), em milhares de unidades,
depende do seu preço (P), em reais, de acordo com a relação 2P
Q 1 4 (0,8) .
= + ⋅ No entanto, em Economia, é mais
usual, nesse tipo de relação, escrever o preço P em função da quantidade Q. Dessa forma, isolando a variável P na
relação fornecida acima, o economista obteve
a) 0,8
Q 1
P log .
4
−
=
b) 0,8
Q 1
P log .
8
−
=
c) 0,8 Q 1
P 0,5 .
4
−
= ⋅
d) 0,8 Q 1
P .
8
−
=
e) 0,8
Q
P 0,5 log 1 .
4
=
⋅ −
19. (Unesp 2014) O que era impressão virou estatística: a cidade de São Paulo está cada dia mais lenta. Quem mostra
é a própria CET (Companhia de Engenharia de Tráfego), que concluiu um estudo anual sobre o trânsito paulistano. Os
dados de 2012 apontam que a velocidade média nos principais corredores viários da cidade foi de 22,1 km/h no pico
da manhã e de 18,5 km/h no pico da tarde. Uma piora de 5% e 10% em relação a 2008, respectivamente.
Caso a velocidade média do trânsito nos principais corredores viários paulistanos continue decaindo nos mesmos
percentuais pelos próximos anos e sabendo que 𝑙𝑙𝑙𝑙 2 ≈ 0,69, 𝑙𝑙𝑙𝑙 3 ≈ 1,10, 𝑙𝑙𝑙𝑙 5 ≃ 1,61 e ln 19 2,94,
≈ os anos
aproximados em que as velocidades médias nos picos da manhã e da tarde chegarão à metade daquelas observadas
em 2012 serão, respectivamente,
a) 2028 e 2019 b) 2068 e 2040 c) 2022 e 2017 d) 2025 e 2018 e) 2057 e 2029
8. LOGARITMOS
7
20. (Insper 2014) Uma pessoa irá escolher dois números reais positivos A e B. Para a maioria das possíveis escolhas, o
logaritmo decimal da soma dos dois números escolhidos não será igual à soma de seus logaritmos decimais. Porém,
se forem escolhidos os valores A = 4 e B = r, tal igualdade se verificará. Com essas informações, pode-se concluir que
o número r pertence ao intervalo
a) [1, 0; 1, 1]
b) ]1, 1; 1, 2]
c) ]1, 2; 1, 3]
d) ]1, 3; 1, 4]
e) ]1, 4; 1, 5]
GABARITO
1 - C 2 - C 3 - B 4 - A 5 - E
6 - B 7 - C 8 - C 9 - D 10 - C
11 - A 12 - A 13 - E 14 - E 15 - E
16 - A 17 - B 18 - A 19 - B 20 - D