College Algebra 5.4
•Download as PPT, PDF•
1 like•603 views
This document discusses solving exponential and logarithmic equations. It notes that: 1) Logarithmic equations can be solved using the one-to-one property by setting log expressions equal. 2) Exponential equations can be transformed into logarithmic form by taking the log of both sides, then solved for the variable. 3) There are several steps to solve logarithmic equations - combining log terms, using one-to-one properties, or converting to exponential form.
Report
Share
Report
Share
![5.4 Exponential and Logarithmic Equations ,[object Object],[object Object],[object Object]](https://image.slidesharecdn.com/collegealgebra54-111110133704-phpapp02/85/College-Algebra-5-4-1-320.jpg)
![A. One-to-one and inverse properties ,[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Course syllabus college algebra
This document is a course syllabus for Math I - College Algebra taught at Bicol University Gubat Campus. The syllabus outlines the course details including the course title, number, prerequisites, credits, placement, term, description, learning outcomes, course outline, requirements, grading system, and references. The course outline lists 9 topics that will be covered throughout the semester, from the real number system to systems of linear equations, along with the specific learning outcomes, content, assessment tasks, and time allotment for each topic. The overall goals of the course are for students to develop mathematical skills and apply algebraic principles to problem solving.
College Algebra Chapters 1 and 2
This document contains exercises from a week 2 individual work assignment involving topics in algebra, geometry, and trigonometry. Some key exercises include:
- Exercise 22 lists the irrational numbers from a given set as -π, √2, √3
- Exercise 36 justifies the statement (-2.6) + 7 = 7 + (-2.6) using the cumulative property of addition
- Exercise 40 uses the triangle area formula to find the area of a triangle with base 12m and altitude 14m as 84m^2
Algebra difficulties among second year bachelor of secondary
This study examined the difficulties that second year Bachelor of Secondary Education students experienced with algebra. Questionnaires were used to understand what causes difficulties and specific algebraic topics that posed problems. The results showed that ineffective teaching strategies were the primary cause of difficulties. Special products/factoring and rationalizing denominators were the most challenging topics. The researchers concluded that teachers must find better ways to explain concepts and cater their lessons to students' needs.
Exponents
The document discusses exponents and exponential functions. It begins by defining key terms like base, exponent, and exponential form. It then provides examples of how to write numbers in exponential form and evaluate expressions with positive, negative, and zero exponents. The document also discusses exponential growth, logarithmic functions, and their inverse relationships. Exponential functions have a constant rate of growth, while logarithmic functions are the inverse of exponential functions. Graphs of exponential functions increase rapidly, while logarithmic functions slowly increase.
Log properties
Logs have many useful properties that allow them to be simplified. Logs with the same base can have their expressions combined by multiplying or dividing the expressions, depending on if they are added or subtracted. Additionally, if the expression inside a log is raised to a power, the exponent can be brought down as a coefficient to the outside of the log. However, exponents only apply to the expression inside the log, not the log as a whole.
Log properties
Logs have many useful properties that allow them to be simplified. Logs with the same base can have their expressions combined by multiplying or dividing the expressions, depending on if they are added or subtracted. Additionally, if the expression inside a log is raised to a power, the exponent can be brought down as a coefficient to the outside of the log. However, exponents only apply to the expression inside the log, not the log as a whole.
Logarithmic Functions
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
Logarithmic functions (2)
Logarithmic functions relate the exponent of a number to the logarithm of its base. They are inverse functions of exponentials, where the domain and range are flipped. Key properties include:
1) Logarithmic graphs have a domain of positive real numbers and range of all real numbers, while being always increasing with a vertical asymptote at y=0.
2) Logarithms can have various bases, with common bases being base 10 (common log), base e (natural log), and base 2 or 10.
3) Logarithmic equations can be solved by converting them to exponential form and then solving the exponential equation.
Recommended
Course syllabus college algebra
This document is a course syllabus for Math I - College Algebra taught at Bicol University Gubat Campus. The syllabus outlines the course details including the course title, number, prerequisites, credits, placement, term, description, learning outcomes, course outline, requirements, grading system, and references. The course outline lists 9 topics that will be covered throughout the semester, from the real number system to systems of linear equations, along with the specific learning outcomes, content, assessment tasks, and time allotment for each topic. The overall goals of the course are for students to develop mathematical skills and apply algebraic principles to problem solving.
College Algebra Chapters 1 and 2
This document contains exercises from a week 2 individual work assignment involving topics in algebra, geometry, and trigonometry. Some key exercises include:
- Exercise 22 lists the irrational numbers from a given set as -π, √2, √3
- Exercise 36 justifies the statement (-2.6) + 7 = 7 + (-2.6) using the cumulative property of addition
- Exercise 40 uses the triangle area formula to find the area of a triangle with base 12m and altitude 14m as 84m^2
Algebra difficulties among second year bachelor of secondary
This study examined the difficulties that second year Bachelor of Secondary Education students experienced with algebra. Questionnaires were used to understand what causes difficulties and specific algebraic topics that posed problems. The results showed that ineffective teaching strategies were the primary cause of difficulties. Special products/factoring and rationalizing denominators were the most challenging topics. The researchers concluded that teachers must find better ways to explain concepts and cater their lessons to students' needs.
Exponents
The document discusses exponents and exponential functions. It begins by defining key terms like base, exponent, and exponential form. It then provides examples of how to write numbers in exponential form and evaluate expressions with positive, negative, and zero exponents. The document also discusses exponential growth, logarithmic functions, and their inverse relationships. Exponential functions have a constant rate of growth, while logarithmic functions are the inverse of exponential functions. Graphs of exponential functions increase rapidly, while logarithmic functions slowly increase.
Log properties
Logs have many useful properties that allow them to be simplified. Logs with the same base can have their expressions combined by multiplying or dividing the expressions, depending on if they are added or subtracted. Additionally, if the expression inside a log is raised to a power, the exponent can be brought down as a coefficient to the outside of the log. However, exponents only apply to the expression inside the log, not the log as a whole.
Log properties
Logs have many useful properties that allow them to be simplified. Logs with the same base can have their expressions combined by multiplying or dividing the expressions, depending on if they are added or subtracted. Additionally, if the expression inside a log is raised to a power, the exponent can be brought down as a coefficient to the outside of the log. However, exponents only apply to the expression inside the log, not the log as a whole.
Logarithmic Functions
The document defines logarithmic functions and provides examples of converting between logarithmic and exponential forms. It discusses the properties of logarithmic equality and solving logarithmic equations by rewriting them in exponential form. Key points include: logarithmic and exponential forms are inverses; the exponent becomes the logarithm; logarithmic functions have a domain of positive real numbers; and solving logarithms involves setting arguments equal when bases are the same.
Logarithmic functions (2)
Logarithmic functions relate the exponent of a number to the logarithm of its base. They are inverse functions of exponentials, where the domain and range are flipped. Key properties include:
1) Logarithmic graphs have a domain of positive real numbers and range of all real numbers, while being always increasing with a vertical asymptote at y=0.
2) Logarithms can have various bases, with common bases being base 10 (common log), base e (natural log), and base 2 or 10.
3) Logarithmic equations can be solved by converting them to exponential form and then solving the exponential equation.
8.4 logarithmic functions
Logarithms were invented to solve exponential equations like 2x = 6, where x is between 2 and 3. A logarithm with base b is defined as logby = x if and only if bx = y. Common properties of logarithms include logb1 = 0 and logbb = 1. Logarithmic functions have inverse relationships with exponential functions and can be graphed by shifting and reflecting the standard logarithmic curve.
Exp log equations
This document discusses solving equations involving exponentials and logarithms. It provides examples of solving equations with:
1) Exponentials on both sides by taking the log of both sides.
2) Exponentials with different bases by taking the natural log of both sides.
3) Logarithms on both sides by exponentiating both sides.
4) Checking solutions for logarithmic equations to avoid extraneous solutions from properties of logs only being valid for positive inputs.
Exp log equations
This document discusses solving equations involving exponentials and logarithms. It provides examples of solving equations with:
1) Exponentials on both sides by taking the log of both sides.
2) Exponentials with different bases by taking the natural log of both sides.
3) Logarithms on both sides by exponentiating both sides.
4) Checking solutions for logarithmic equations to avoid extraneous solutions from properties of logs only being valid for positive inputs.
College Algebra 5.2
The document discusses logarithms and log functions. It defines what a logarithm is using the example "Log 10 100 = 2". It explains how to convert from logarithmic form to exponential form. It discusses the common log and natural log, and properties of logarithmic functions. It describes the graph of a basic log function, including that it has an asymptote at the y-axis and an x-intercept of (1,0). It asks the reader to graph and find features of shifted log functions, like asymptotes, domains and x-intercepts.
7.6 solving logarithmic equations
This document discusses different types of exponential and logarithmic equations and methods for solving them. It covers:
1) Exponential equations with like bases, which can be solved by setting exponents equal to each other.
2) Exponential equations with different bases, which require using logarithms and properties of logarithms to isolate the variable.
3) Logarithmic equations, where the variable can be inside or outside the logarithm. These also use logarithm properties and are rewritten as exponential equations to solve for the variable.
Rational, Irrational & Absolute Value Functions Review
The document discusses various topics related to graphing rational, irrational, and absolute value functions. It provides instructions on how to graph these functions by finding intercepts, asymptotes, points of discontinuity, and applying transformations. It also discusses how to simplify and solve rational expressions and inequalities.
Exponential_Functions.ppt
This document discusses exponential functions. It begins by stating the objectives of understanding properties of exponents, simplifying exponential expressions, solving exponential equations, and sketching graphs of exponential functions. It then defines exponential functions and discusses their general form. Several properties of exponents are listed and examples of simplifying expressions using these properties are shown. The document also demonstrates how to solve various exponential equations. Finally, it discusses graphing and properties of exponential functions, including the special number e and the exponential function with base e.
Common natural logarithms
The document discusses common logarithms and natural logarithms. It defines common logarithms as logarithms with base 10, which are often used in real-world problems. It shows how to use properties of logarithms to solve exponential equations and by graphing. The document then defines natural logarithms as logarithms with base e, which are the inverse of exponential functions with base e. It demonstrates using natural logarithms and exponential base e to solve equations and expressions.
161 course information spring 2016
This document provides information about the MATH 161 Introduction to Statistics course offered in Spring 2016. It outlines the course sections, times, locations, instructor contact information, course content and objectives, student responsibilities, evaluation criteria including assignments, projects, exams and grading scale, key dates, policies on academic integrity and students with disabilities. The goal of the course is to provide students with a general statistical background to understand probabilities and statistics reported in media and research.
Summer 2014 moseley 098 syllabus addendum
This document provides the syllabus addendum for an Elementary Algebra course. It outlines the course details including schedule, location, office hours, and instructor contact information. It describes the university mission statement, catalog description, purpose and objectives of the course. It outlines the student responsibilities and the evaluation criteria including exams, grading scale, attendance policy, and academic integrity policy. It also notes services available for students with disabilities.
2.1 homework
This document contains 10 multiple choice questions about finding the equation of lines given characteristics like two points on the line, a point and slope, or a point and being parallel or perpendicular to another line. The questions ask the learner to determine the equation for lines matching each given description.
2.6 homework
This document contains homework problems involving algebraic expressions and functions. Problem 1 asks to evaluate expressions involving square roots. Problem 2 asks to identify the meaning of an equality involving a function. Problems 3-5 ask to evaluate and simplify expressions involving square roots and composite functions. Problem 6 asks to find two functions whose composition is a given function.
2.2 homework b
This document contains 10 math and functions questions: questions 1-5 ask to find values of x for which certain equations are true, questions 6 asks to identify which sentence correctly describes functions, and questions 7-10 ask to find values of expressions given values of variables.
2.2 homework a
This document contains 10 multiple choice and short answer questions that assess understanding of functions and function notation. Questions 1 and 2 ask students to identify which charts and ordered pairs represent functions. Questions 3-7 require students to evaluate specific functions for given input values. Questions 8-10 deal with piecewise functions, asking students to evaluate expressions and find output values.
College algebra hw 1.4
This homework assignment contains 10 algebra problems to solve using different techniques: problems 1-4 involve factoring quadratic equations; problems 5-6 require extracting the square root of equations to find exact solutions; problems 7-8 involve finding the discriminant of equations to determine the number of real solutions; and problems 9-10 should be solved using the quadratic formula.
1.3 homework
This document contains 10 math homework problems from a College Algebra 1 class taught by Dr. Moseley. The problems include finding x-intercepts and y-intercepts of linear equations, writing expressions for distance and discounted prices, solving equations for unknown numbers, calculating original prices from sale prices, finding required test scores to get a grade average, calculating trip times with constant speed, and finding dimensions of a picture frame given its perimeter and a ratio of its width to height.
Math 111 College Algebra 1.2
Este documento contiene 10 problemas de álgebra de una tarea de matemáticas 111. Los problemas incluyen ecuaciones, funciones y expresiones algebraicas que deben resolverse.
P.5 homework a
El documento contiene la tarea de álgebra de la universidad con 19 problemas numéricos y una lista de letras mayúsculas como posibles respuestas. El profesor asignado es el Dr. Moseley para la clase de Matemáticas 111 de Álgebra Universitaria.
P.3 homework
This document contains a math homework assignment on polynomials and FOIL method. It includes definitions of polynomial terms, instructions to perform operations using FOIL, and word problems involving costs and revenues from producing MP3 players to calculate profit.
P 2 homework b
Este documento contiene un conjunto de ejercicios de álgebra sobre raíces cuadradas. Los estudiantes deben calcular valores de raíces cuadradas simples y compuestas, simplificar expresiones con raíces cuadradas, y convertir expresiones entre formas radical y exponencial. El documento proporciona valores numéricos y letras para ser usados en las respuestas de opción múltiple.
P.2 homework A
This document contains a math homework assignment with 38 problems involving exponents, radicals, and simplifying expressions. Students are asked to identify components of exponential and radical expressions, evaluate expressions, and simplify expressions using properties of exponents. They will rewrite expressions with positive exponents and find values of expressions for given variables.
More Related Content
Similar to College Algebra 5.4
8.4 logarithmic functions
Logarithms were invented to solve exponential equations like 2x = 6, where x is between 2 and 3. A logarithm with base b is defined as logby = x if and only if bx = y. Common properties of logarithms include logb1 = 0 and logbb = 1. Logarithmic functions have inverse relationships with exponential functions and can be graphed by shifting and reflecting the standard logarithmic curve.
Exp log equations
This document discusses solving equations involving exponentials and logarithms. It provides examples of solving equations with:
1) Exponentials on both sides by taking the log of both sides.
2) Exponentials with different bases by taking the natural log of both sides.
3) Logarithms on both sides by exponentiating both sides.
4) Checking solutions for logarithmic equations to avoid extraneous solutions from properties of logs only being valid for positive inputs.
Exp log equations
This document discusses solving equations involving exponentials and logarithms. It provides examples of solving equations with:
1) Exponentials on both sides by taking the log of both sides.
2) Exponentials with different bases by taking the natural log of both sides.
3) Logarithms on both sides by exponentiating both sides.
4) Checking solutions for logarithmic equations to avoid extraneous solutions from properties of logs only being valid for positive inputs.
College Algebra 5.2
The document discusses logarithms and log functions. It defines what a logarithm is using the example "Log 10 100 = 2". It explains how to convert from logarithmic form to exponential form. It discusses the common log and natural log, and properties of logarithmic functions. It describes the graph of a basic log function, including that it has an asymptote at the y-axis and an x-intercept of (1,0). It asks the reader to graph and find features of shifted log functions, like asymptotes, domains and x-intercepts.
7.6 solving logarithmic equations
This document discusses different types of exponential and logarithmic equations and methods for solving them. It covers:
1) Exponential equations with like bases, which can be solved by setting exponents equal to each other.
2) Exponential equations with different bases, which require using logarithms and properties of logarithms to isolate the variable.
3) Logarithmic equations, where the variable can be inside or outside the logarithm. These also use logarithm properties and are rewritten as exponential equations to solve for the variable.
Rational, Irrational & Absolute Value Functions Review
The document discusses various topics related to graphing rational, irrational, and absolute value functions. It provides instructions on how to graph these functions by finding intercepts, asymptotes, points of discontinuity, and applying transformations. It also discusses how to simplify and solve rational expressions and inequalities.
Exponential_Functions.ppt
This document discusses exponential functions. It begins by stating the objectives of understanding properties of exponents, simplifying exponential expressions, solving exponential equations, and sketching graphs of exponential functions. It then defines exponential functions and discusses their general form. Several properties of exponents are listed and examples of simplifying expressions using these properties are shown. The document also demonstrates how to solve various exponential equations. Finally, it discusses graphing and properties of exponential functions, including the special number e and the exponential function with base e.
Common natural logarithms
The document discusses common logarithms and natural logarithms. It defines common logarithms as logarithms with base 10, which are often used in real-world problems. It shows how to use properties of logarithms to solve exponential equations and by graphing. The document then defines natural logarithms as logarithms with base e, which are the inverse of exponential functions with base e. It demonstrates using natural logarithms and exponential base e to solve equations and expressions.
Similar to College Algebra 5.4 (8)
Rational, Irrational & Absolute Value Functions Review
Rational, Irrational & Absolute Value Functions Review
More from Jeneva Clark
161 course information spring 2016
This document provides information about the MATH 161 Introduction to Statistics course offered in Spring 2016. It outlines the course sections, times, locations, instructor contact information, course content and objectives, student responsibilities, evaluation criteria including assignments, projects, exams and grading scale, key dates, policies on academic integrity and students with disabilities. The goal of the course is to provide students with a general statistical background to understand probabilities and statistics reported in media and research.
Summer 2014 moseley 098 syllabus addendum
This document provides the syllabus addendum for an Elementary Algebra course. It outlines the course details including schedule, location, office hours, and instructor contact information. It describes the university mission statement, catalog description, purpose and objectives of the course. It outlines the student responsibilities and the evaluation criteria including exams, grading scale, attendance policy, and academic integrity policy. It also notes services available for students with disabilities.
2.1 homework
This document contains 10 multiple choice questions about finding the equation of lines given characteristics like two points on the line, a point and slope, or a point and being parallel or perpendicular to another line. The questions ask the learner to determine the equation for lines matching each given description.
2.6 homework
This document contains homework problems involving algebraic expressions and functions. Problem 1 asks to evaluate expressions involving square roots. Problem 2 asks to identify the meaning of an equality involving a function. Problems 3-5 ask to evaluate and simplify expressions involving square roots and composite functions. Problem 6 asks to find two functions whose composition is a given function.
2.2 homework b
This document contains 10 math and functions questions: questions 1-5 ask to find values of x for which certain equations are true, questions 6 asks to identify which sentence correctly describes functions, and questions 7-10 ask to find values of expressions given values of variables.
2.2 homework a
This document contains 10 multiple choice and short answer questions that assess understanding of functions and function notation. Questions 1 and 2 ask students to identify which charts and ordered pairs represent functions. Questions 3-7 require students to evaluate specific functions for given input values. Questions 8-10 deal with piecewise functions, asking students to evaluate expressions and find output values.
College algebra hw 1.4
This homework assignment contains 10 algebra problems to solve using different techniques: problems 1-4 involve factoring quadratic equations; problems 5-6 require extracting the square root of equations to find exact solutions; problems 7-8 involve finding the discriminant of equations to determine the number of real solutions; and problems 9-10 should be solved using the quadratic formula.
1.3 homework
This document contains 10 math homework problems from a College Algebra 1 class taught by Dr. Moseley. The problems include finding x-intercepts and y-intercepts of linear equations, writing expressions for distance and discounted prices, solving equations for unknown numbers, calculating original prices from sale prices, finding required test scores to get a grade average, calculating trip times with constant speed, and finding dimensions of a picture frame given its perimeter and a ratio of its width to height.
Math 111 College Algebra 1.2
Este documento contiene 10 problemas de álgebra de una tarea de matemáticas 111. Los problemas incluyen ecuaciones, funciones y expresiones algebraicas que deben resolverse.
P.5 homework a
El documento contiene la tarea de álgebra de la universidad con 19 problemas numéricos y una lista de letras mayúsculas como posibles respuestas. El profesor asignado es el Dr. Moseley para la clase de Matemáticas 111 de Álgebra Universitaria.
P.3 homework
This document contains a math homework assignment on polynomials and FOIL method. It includes definitions of polynomial terms, instructions to perform operations using FOIL, and word problems involving costs and revenues from producing MP3 players to calculate profit.
P 2 homework b
Este documento contiene un conjunto de ejercicios de álgebra sobre raíces cuadradas. Los estudiantes deben calcular valores de raíces cuadradas simples y compuestas, simplificar expresiones con raíces cuadradas, y convertir expresiones entre formas radical y exponencial. El documento proporciona valores numéricos y letras para ser usados en las respuestas de opción múltiple.
P.2 homework A
This document contains a math homework assignment with 38 problems involving exponents, radicals, and simplifying expressions. Students are asked to identify components of exponential and radical expressions, evaluate expressions, and simplify expressions using properties of exponents. They will rewrite expressions with positive exponents and find values of expressions for given variables.
P.1 hw
This document contains a list of 43 questions about concepts in college algebra including: 1) numbers with non-repeating decimal representations, 2) properties of real numbers and their representations on a number line, 3) classifying numbers as natural, whole, integer, rational, irrational or real, 4) evaluating algebraic expressions, and 5) finding distances between points on a number line. Students are instructed to submit their answers on Moodle by the specified due date.
Moseley schedule
Dr. Lauren "Jeneva" Moseley's fall 2013 schedule is available by viewing her Google calendar online at https://www.google.com/calendar/embed?src=jenevamoseley%40gmail.com&ctz=America/New_York. Her contact information includes her email address LMOSELEY@LeeUniversity.edu and phone number 423-614-8283.
Moseley m113 syllabus_summer2013
This document is a syllabus for a summer 2013 Math 113 course. It provides information about course details
such as meeting times and location, instructor contact information, course description and goals, required text,
grading scale, exam dates, attendance and make-up policies, academic honesty, and classroom expectations. The
course covers classical and modern topics in number theory, logic, geometry, and probability with an emphasis
on problem solving and real-world applications. Grades are based on 4 exams, projects, and a final exam.
Magic Money
Two friends had a meal that cost $25 total and each paid $15, but the cashier returned $5 in change to the waiter. The waiter kept $3 as a tip and returned $1 to each friend. While the friends paid $14 each, totaling $28, and the waiter received $3, this accounts for $31 of the original $25 bill, with $1 unaccounted for.
Which Road to Travel
A traveler comes to a fork in the road guarded by two figures, one who always lies and one who always tells the truth. The traveler can ask one guard one question to determine which path leads to paradise. By asking which path the other guard would claim leads to paradise, the traveler will be directed to the correct path regardless of whether they asked the truth-teller or liar.
We three sisters
Sarah always tells the truth, Sue always lies, and Sally sometimes lies and sometimes tells the truth. When Victor asked each sister a question to identify them, Sarah correctly identified herself as being on the left, Sally identified herself as being in the middle, and Sue identified the middle sister as herself, confusing Victor as to their identities.
More from Jeneva Clark (20)
Recently uploaded
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneChapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
skeleton System.pdf (skeleton system wow)
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...Nguyen Thanh Tu Collection
https://app.box.com/s/qhtvq32h4ybf9t49ku85x0n3xl4jhr15How to Predict Vendor Bill Product in Odoo 17
This slide will guide us through the process of predicting vendor bill products based on previous purchases from the vendor in Odoo 17.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Educational Technology in the Health Sciences
Plenary presentation at the NTTC Inter-university Workshop, 18 June 2024, Manila Prince Hotel.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Temple of Asclepius in Thrace. Excavation results
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Recently uploaded (20)
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...