This document provides an aim and review for fractional equations. It includes instructions to take out a cumulative review sheet and class notes sheet. It then provides example problems and answers for three stations of fractional equation questions. It concludes with a self-assessment for students to reflect on their strengths and weaknesses with fractional equations and notes there is no homework assigned.
The document provides steps to solve an inequality involving fractions: (1) determine values of x that make the fraction undefined by setting the denominator equal to 0; (2) turn the inequality sign into an equal sign to form an equation; (3) solve the equation and graph points on a number line; (4) test points to determine what values satisfy the inequality; (5) shade the number line to show the interval of values for which the inequality is true.
This document provides an example of using a genetic algorithm to fit a polynomial curve to data points. It describes representing the polynomial coefficients as arrays, calculating a fitness score based on error from actual data points, initializing a random population, and using crossover and mutation over generations to find coefficients that minimize the error. The example shows the process step-by-step on a simple dataset to find the linear formula y=2x+3 that best fits the points (1,5) and (3,9).
Alg II Unit 4-4 Factoring Quadratic Expressionsjtentinger
This document provides instruction on factoring quadratic expressions. It begins with the essential understanding that many quadratic trinomials can be factored into products of two binomials. It then discusses factoring methods like finding common factors, using the distributive property, and factoring special forms like perfect square trinomials and differences of two squares. Examples are provided to demonstrate each factoring technique. The document concludes with assigning homework practice in factoring quadratic expressions.
The document provides step-by-step instructions for factoring polynomials, finding inverse functions, simplifying rational expressions, and graphing rational functions. It includes examples of each type of problem worked out in detail from beginning to end. The examples range from relatively simple to more complex in order to demonstrate a variety of situations that may occur.
The document provides instructions for factoring quadratic trinomials using 4 examples. It explains that you write the trinomial as two parentheses, factor the constant term into the parentheses, then check that the factors give the middle term of the original expression when multiplied out. The process involves 4 steps and is demonstrated factoring expressions like x^2 + 10x + 24 and x^2 - 8x + 15.
This document discusses factoring trinomials using algebra tiles to represent the terms x^2 + 2x - 8. After plotting the tiles, it can be seen that the trinomial factors into the binomial (x+4)(x-2), with solutions of x = -4 or x = 2.
This document discusses finding the rational zeros of polynomials using the Rational Zeros Theorem. It provides examples of finding all rational zeros of polynomials by considering possible values of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. It also discusses using synthetic division and the Quadratic Formula to find the exact zeros of polynomials when not all zeros are rational.
This document provides an aim and review for fractional equations. It includes instructions to take out a cumulative review sheet and class notes sheet. It then provides example problems and answers for three stations of fractional equation questions. It concludes with a self-assessment for students to reflect on their strengths and weaknesses with fractional equations and notes there is no homework assigned.
The document provides steps to solve an inequality involving fractions: (1) determine values of x that make the fraction undefined by setting the denominator equal to 0; (2) turn the inequality sign into an equal sign to form an equation; (3) solve the equation and graph points on a number line; (4) test points to determine what values satisfy the inequality; (5) shade the number line to show the interval of values for which the inequality is true.
This document provides an example of using a genetic algorithm to fit a polynomial curve to data points. It describes representing the polynomial coefficients as arrays, calculating a fitness score based on error from actual data points, initializing a random population, and using crossover and mutation over generations to find coefficients that minimize the error. The example shows the process step-by-step on a simple dataset to find the linear formula y=2x+3 that best fits the points (1,5) and (3,9).
Alg II Unit 4-4 Factoring Quadratic Expressionsjtentinger
This document provides instruction on factoring quadratic expressions. It begins with the essential understanding that many quadratic trinomials can be factored into products of two binomials. It then discusses factoring methods like finding common factors, using the distributive property, and factoring special forms like perfect square trinomials and differences of two squares. Examples are provided to demonstrate each factoring technique. The document concludes with assigning homework practice in factoring quadratic expressions.
The document provides step-by-step instructions for factoring polynomials, finding inverse functions, simplifying rational expressions, and graphing rational functions. It includes examples of each type of problem worked out in detail from beginning to end. The examples range from relatively simple to more complex in order to demonstrate a variety of situations that may occur.
The document provides instructions for factoring quadratic trinomials using 4 examples. It explains that you write the trinomial as two parentheses, factor the constant term into the parentheses, then check that the factors give the middle term of the original expression when multiplied out. The process involves 4 steps and is demonstrated factoring expressions like x^2 + 10x + 24 and x^2 - 8x + 15.
This document discusses factoring trinomials using algebra tiles to represent the terms x^2 + 2x - 8. After plotting the tiles, it can be seen that the trinomial factors into the binomial (x+4)(x-2), with solutions of x = -4 or x = 2.
This document discusses finding the rational zeros of polynomials using the Rational Zeros Theorem. It provides examples of finding all rational zeros of polynomials by considering possible values of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. It also discusses using synthetic division and the Quadratic Formula to find the exact zeros of polynomials when not all zeros are rational.
Jacob's and Vlad's D.E.V. Project - 2012Jacob_Evenson
The document provides steps to simplify a rational function and find its domain. It factors the numerator and denominator, finds the x-intercepts where the numerator is 0, finds the vertical asymptotes where the denominator is 0, and determines the horizontal asymptote by comparing the powers of the numerator and denominator. It then uses this information to sketch the graph and identify the domain as the intervals where the function is defined.
The document discusses the distributive property in mathematics. It provides examples of applying the distributive property, such as:
3(4 + 7) = 3*4 + 3*7 = 12 + 21 = 33
It explains that the distributive property distributes multiplication over addition or subtraction. For any real numbers x, y, and z, the rules are:
x(y + z) = xy + xz
x(y - z) = xy - xz
The document provides additional examples of applying the distributive property and explains the concepts of exponents that arise when multiplying variables.
This document discusses limits of functions. It begins by defining the limit of a function f(x) as x approaches a number c as the value that f(x) approaches as x gets closer to c. It provides examples of limits, including one-sided limits and limits at infinity. Key theorems are presented for computing limits, including properties of limits and the sandwich theorem. The document focuses on conceptual understanding and applying techniques to evaluate a variety of limit examples.
The document discusses solving rational inequalities. It explains the steps to solve rational inequalities which are to simplify the expression so zero is on one side, factor any quadratics, place critical numbers on a number line, test points in intervals to determine if the expression is positive or negative, and state the solution intervals. It then works through examples of solving various rational inequalities graphically and algebraically, placing the critical numbers on a number line and determining the intervals where the expressions are positive or negative.
This document discusses solving polynomials using various numerical approximation methods and finding real roots. It provides examples of:
1) Finding the real roots of a cubic polynomial using numerical methods and comparing to the exact solution;
2) Approximating roots of a polynomial using the bisection method and comparing approximations to exact solutions;
3) Finding possible real roots of a quartic polynomial and approximating them using the bisection method.
The document provides a study plan and review for a test on systems of equations and inequalities. It lists that the student spent 1428 minutes each on Khan Academy on Saturday for review. It includes a quick 6 question review on various math topics. It asks if the student has any other questions before taking the test. It provides 2 sample word problems to solve systems of equations and notifies the student that a pencil and scratch paper will be provided for the test.
1) An antiderivative of a function f(x) is any function F(x) whose derivative is equal to f(x).
2) The general antiderivative of a function f(x) is written as F(x) + C, where F(x) is a particular antiderivative and C is an arbitrary constant.
3) The indefinite integral notation ∫f(x)dx represents the entire family of antiderivatives for a function f(x), since each value of C defines a different antiderivative.
6.4 factoring and solving polynomial equationshisema01
The document provides examples and instructions for factoring polynomials of various types, including:
- Trinomials like x^2 - 5x - 12
- Sum and difference of cubes like x^3 + 8 and 8x^3 - 1
- Polynomials with a common monomial factor like 6x^2 + 15x
- Quadratics in the form of au^2 + bu + c
It also discusses using the zero product property to solve polynomial equations by factoring and setting each factor equal to zero.
This document provides instruction on perfect square trinomials including defining them, identifying them, factoring them, and working practice problems. It begins by defining a perfect square trinomial as the result of squaring a binomial with the first and last terms being perfect squares and the middle term being twice the product of the square roots of the first and last terms. Examples are provided to illustrate. The document then provides guidance, activities, and an assessment to practice identifying, factoring, and working with perfect square trinomials.
1. This practice exam covers topics like complex numbers, functions, limits, and graphing.
2. It asks students to choose problems involving adding, multiplying, composing, and finding inverses of various functions like f(x)=9x^2+1 and g(x)=x-1.
3. Students also must graph and classify functions, evaluate limits, and perform operations on complex numbers, plotting them on a plane. The exam covers concepts in precalculus.
Solving polynomial equations in factored formListeningDaisy
The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x – 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x – 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
This document provides an overview of polynomials, including:
1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
1. The document contains examples of evaluating limits as the variable approaches certain values.
2. Several limits were found to be indeterminate forms that require further algebraic manipulation to find the limit.
3. Key observations were made about the behavior of functions as the variable approaches values like noticing a function approaches a certain value as the variable nears another value.
The document discusses factoring quadratic trinomials. It provides three examples of factoring expressions such as x^2 - 5x - 14, x^2 - 10x + 25, and x^2 + 2x - 35. Each example lists the steps to factor the expression which include finding factors of the constant term that sum to the coefficient of the middle term and then factoring the first term.
The document discusses perfect square trinomials and how to factor them. It provides examples of factoring various square trinomials using the properties that the first and last terms must be perfect squares, and the middle term must be twice the product of the square roots of the first and last terms. It then has students practice factoring several square trinomial examples on their own.
This document provides examples and explanations of using Pascal's triangle to expand binomial expressions. It shows how to:
1) Expand binomial expressions like (x + 1)5 and (x - y)8 using the appropriate row of Pascal's triangle as coefficients.
2) Determine missing coefficients in expansions like (x + y)7.
3) Compare directly multiplying factors to using the binomial theorem to expand expressions like (x - 5)4.
4) Expand various binomial expressions like (x + 2)6, (x2 - 3)5, and (-2 + 2x)4 by applying the binomial theorem.
1. The limit as x approaches 4 of x4-16 is 0. When factored, the expression becomes (x-4)(x+4)(x2+4) which equals 0 as x approaches 4.
2. The limit as x approaches infinity of x7-x2+1 is 1. When factored, the leading terms are x7 for both the top and bottom expressions, which equals 1 as x approaches infinity.
3. The limit as x approaches -1 of x2-1 is 0. When factored, the expression becomes (x+1)(x-1) which equals 0 as the factors are 0 when x is -1.
Amth250 octave matlab some solutions (2)asghar123456
This document contains the solutions to 5 questions regarding numerical analysis techniques. Question 1 finds the zeros of a function graphically and numerically. Question 2 finds the millionth zero of tan(x)-x. Question 3 examines the convergence rates of Newton's method for various functions. Question 4 applies Newton's method to find the inverse of a function. Question 5 finds the maximum of a function using golden section search and parabolic interpolation.
This document summarizes three innovative marketing campaigns for festivals in India:
Citi Bank's #WhatsYourDiwaliDelight campaign focused on people away from family for work and allowed digital gifting. It achieved over 4 million video views and 260 million impressions.
Sony LIV's #LIVThisDiwali campaign created an exclusive movie and Facebook app to send personalized greetings. The movie was widely viewed during Diwali week and the campaign increased followers by 1800.
Shaadi.com's #FastForHer encouraged husbands to fast for their wives on Karva Chauth through a microsite to track pledges. It received over 6.24 million pledges and celebrity
This document discusses cardiovascular syphilis, which can affect the heart, aorta and other blood vessels. It outlines the epidemiology, clinical features, investigations, treatment, prognosis and follow up for cardiovascular syphilis. While rare today due to penicillin treatment, syphilis can cause complications like aortic aneurysms in the heart, aorta and other large blood vessels up to 40 years after initial infection. Proper treatment and follow up is important as untreated syphilitic aneurysms have a high 2-year mortality rate.
Jacob's and Vlad's D.E.V. Project - 2012Jacob_Evenson
The document provides steps to simplify a rational function and find its domain. It factors the numerator and denominator, finds the x-intercepts where the numerator is 0, finds the vertical asymptotes where the denominator is 0, and determines the horizontal asymptote by comparing the powers of the numerator and denominator. It then uses this information to sketch the graph and identify the domain as the intervals where the function is defined.
The document discusses the distributive property in mathematics. It provides examples of applying the distributive property, such as:
3(4 + 7) = 3*4 + 3*7 = 12 + 21 = 33
It explains that the distributive property distributes multiplication over addition or subtraction. For any real numbers x, y, and z, the rules are:
x(y + z) = xy + xz
x(y - z) = xy - xz
The document provides additional examples of applying the distributive property and explains the concepts of exponents that arise when multiplying variables.
This document discusses limits of functions. It begins by defining the limit of a function f(x) as x approaches a number c as the value that f(x) approaches as x gets closer to c. It provides examples of limits, including one-sided limits and limits at infinity. Key theorems are presented for computing limits, including properties of limits and the sandwich theorem. The document focuses on conceptual understanding and applying techniques to evaluate a variety of limit examples.
The document discusses solving rational inequalities. It explains the steps to solve rational inequalities which are to simplify the expression so zero is on one side, factor any quadratics, place critical numbers on a number line, test points in intervals to determine if the expression is positive or negative, and state the solution intervals. It then works through examples of solving various rational inequalities graphically and algebraically, placing the critical numbers on a number line and determining the intervals where the expressions are positive or negative.
This document discusses solving polynomials using various numerical approximation methods and finding real roots. It provides examples of:
1) Finding the real roots of a cubic polynomial using numerical methods and comparing to the exact solution;
2) Approximating roots of a polynomial using the bisection method and comparing approximations to exact solutions;
3) Finding possible real roots of a quartic polynomial and approximating them using the bisection method.
The document provides a study plan and review for a test on systems of equations and inequalities. It lists that the student spent 1428 minutes each on Khan Academy on Saturday for review. It includes a quick 6 question review on various math topics. It asks if the student has any other questions before taking the test. It provides 2 sample word problems to solve systems of equations and notifies the student that a pencil and scratch paper will be provided for the test.
1) An antiderivative of a function f(x) is any function F(x) whose derivative is equal to f(x).
2) The general antiderivative of a function f(x) is written as F(x) + C, where F(x) is a particular antiderivative and C is an arbitrary constant.
3) The indefinite integral notation ∫f(x)dx represents the entire family of antiderivatives for a function f(x), since each value of C defines a different antiderivative.
6.4 factoring and solving polynomial equationshisema01
The document provides examples and instructions for factoring polynomials of various types, including:
- Trinomials like x^2 - 5x - 12
- Sum and difference of cubes like x^3 + 8 and 8x^3 - 1
- Polynomials with a common monomial factor like 6x^2 + 15x
- Quadratics in the form of au^2 + bu + c
It also discusses using the zero product property to solve polynomial equations by factoring and setting each factor equal to zero.
This document provides instruction on perfect square trinomials including defining them, identifying them, factoring them, and working practice problems. It begins by defining a perfect square trinomial as the result of squaring a binomial with the first and last terms being perfect squares and the middle term being twice the product of the square roots of the first and last terms. Examples are provided to illustrate. The document then provides guidance, activities, and an assessment to practice identifying, factoring, and working with perfect square trinomials.
1. This practice exam covers topics like complex numbers, functions, limits, and graphing.
2. It asks students to choose problems involving adding, multiplying, composing, and finding inverses of various functions like f(x)=9x^2+1 and g(x)=x-1.
3. Students also must graph and classify functions, evaluate limits, and perform operations on complex numbers, plotting them on a plane. The exam covers concepts in precalculus.
Solving polynomial equations in factored formListeningDaisy
The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x – 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x – 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
This document provides an overview of polynomials, including:
1. What a typical polynomial looks like, with a leading coefficient and terms in descending order of variables' exponents.
2. Polynomial basics, such as only adding or subtracting like terms. Methods for adding, subtracting, and multiplying polynomials are described.
3. The FOIL method for multiplying binomials is introduced, and the general rule that each term in one polynomial is multiplied by each term in the other. Exponents with like bases are added when multiplying terms. Examples of multiplying different types of polynomials are provided.
1. The document contains examples of evaluating limits as the variable approaches certain values.
2. Several limits were found to be indeterminate forms that require further algebraic manipulation to find the limit.
3. Key observations were made about the behavior of functions as the variable approaches values like noticing a function approaches a certain value as the variable nears another value.
The document discusses factoring quadratic trinomials. It provides three examples of factoring expressions such as x^2 - 5x - 14, x^2 - 10x + 25, and x^2 + 2x - 35. Each example lists the steps to factor the expression which include finding factors of the constant term that sum to the coefficient of the middle term and then factoring the first term.
The document discusses perfect square trinomials and how to factor them. It provides examples of factoring various square trinomials using the properties that the first and last terms must be perfect squares, and the middle term must be twice the product of the square roots of the first and last terms. It then has students practice factoring several square trinomial examples on their own.
This document provides examples and explanations of using Pascal's triangle to expand binomial expressions. It shows how to:
1) Expand binomial expressions like (x + 1)5 and (x - y)8 using the appropriate row of Pascal's triangle as coefficients.
2) Determine missing coefficients in expansions like (x + y)7.
3) Compare directly multiplying factors to using the binomial theorem to expand expressions like (x - 5)4.
4) Expand various binomial expressions like (x + 2)6, (x2 - 3)5, and (-2 + 2x)4 by applying the binomial theorem.
1. The limit as x approaches 4 of x4-16 is 0. When factored, the expression becomes (x-4)(x+4)(x2+4) which equals 0 as x approaches 4.
2. The limit as x approaches infinity of x7-x2+1 is 1. When factored, the leading terms are x7 for both the top and bottom expressions, which equals 1 as x approaches infinity.
3. The limit as x approaches -1 of x2-1 is 0. When factored, the expression becomes (x+1)(x-1) which equals 0 as the factors are 0 when x is -1.
Amth250 octave matlab some solutions (2)asghar123456
This document contains the solutions to 5 questions regarding numerical analysis techniques. Question 1 finds the zeros of a function graphically and numerically. Question 2 finds the millionth zero of tan(x)-x. Question 3 examines the convergence rates of Newton's method for various functions. Question 4 applies Newton's method to find the inverse of a function. Question 5 finds the maximum of a function using golden section search and parabolic interpolation.
This document summarizes three innovative marketing campaigns for festivals in India:
Citi Bank's #WhatsYourDiwaliDelight campaign focused on people away from family for work and allowed digital gifting. It achieved over 4 million video views and 260 million impressions.
Sony LIV's #LIVThisDiwali campaign created an exclusive movie and Facebook app to send personalized greetings. The movie was widely viewed during Diwali week and the campaign increased followers by 1800.
Shaadi.com's #FastForHer encouraged husbands to fast for their wives on Karva Chauth through a microsite to track pledges. It received over 6.24 million pledges and celebrity
This document discusses cardiovascular syphilis, which can affect the heart, aorta and other blood vessels. It outlines the epidemiology, clinical features, investigations, treatment, prognosis and follow up for cardiovascular syphilis. While rare today due to penicillin treatment, syphilis can cause complications like aortic aneurysms in the heart, aorta and other large blood vessels up to 40 years after initial infection. Proper treatment and follow up is important as untreated syphilitic aneurysms have a high 2-year mortality rate.
Las emociones llegan de golpe. Nacen con nuestro hijo. Al principio, como todo, es algo nuevo. ¿Por qué el bebé a veces llora desconsolado? ¿Por qué ríe? ¿Por qué rechaza determinado alimento? Las emociones comienzan a trabajar. Nuestro hijo tendrá que aprender a utilizarlas. No es fácil. De hecho, muchos adultos aún se sienten incapaces de dominar sus impulsos.
Disaster Management Empirical Study of 2009 Jeddah Floodnabaz4u
This document summarizes a study about disaster management during the 2009 floods in Jeddah, Saudi Arabia, which killed over 100 people. The study finds that due to a lack of disaster management policies, unplanned urban development, inadequate precautions and preparations, corruption, and poor organizational behavior, the effects of the flood were worse than expected. The study concludes that the Saudi government needs clearer policies and better technology to deal with natural disasters effectively.
Este documento habla sobre la utilidad de las herramientas web como recursos educativos para el trabajo didáctico. Explica que las estructuras y recursos web permiten el desarrollo de habilidades a través del pensamiento creativo o crítico de los estudiantes. También menciona que estas herramientas apoyan el trabajo cooperativo de los alumnos y su autonomía en el desarrollo básico de la tecnología educativa.
Het Programma Sociaal-Medische 1e lijn is een samenwerkingsprogramma tussen De Friesland Zorgverzekeraar, de 24 Friese gemeenten, de Provincie Fryslân en Zorgbelang Fryslân. Riverwise is als adviseur betrokken bij deze samenwerking en begeleidt de partijen in het realiseren van gezamenlijk resultaat.
The document discusses Aristotle's rhetorical modes of persuasion: ethos, logos, and pathos. Aristotle defined ethos as argument based on character and credibility, logos as reasoning and facts, and pathos as appealing to emotions. These three modes work together to help change others' views and motivate action. Ethos establishes the speaker's authority, logos provides evidence, and pathos influences emotions.
Este documento describe los diferentes tipos de antibióticos, sus mecanismos de acción, y la resistencia bacteriana. Explica que los antibióticos actúan contra bacterias sensibles inhibiendo su crecimiento o eliminándolas, y clasifica los antibióticos según su espectro de acción. También describe los mecanismos de resistencia bacteriana como los cambios genéticos y la transferencia de genes entre bacterias.
Git is a free and open source distributed version control system used to manage source code changes. The presentation discusses what git is, how it works using a distributed model, and common git commands like add, commit, push, pull and branch. It also provides resources for learning more about git's version control system and workflow.
Este documento describe los navegadores web más utilizados como Google Chrome, Mozilla Firefox, Internet Explorer y Opera. Explica las características clave de cada uno como su velocidad, facilidad de uso y seguridad. También define qué son los navegadores, su función de permitir ver páginas web y encontrar información de todo tipo en Internet de manera útil.
Este documento analiza el uso de redes sociales en la educación. Explora las redes más utilizadas como Facebook, LinkedIn y Twitter, describiendo brevemente sus propósitos y funcionalidades. Concluye que las redes sociales ayudan a mejorar la comunicación entre estudiantes, promocionar anuncios de trabajo y facilitar la realización de tareas.
A aula de ciências durou 2 horas com 15 alunos do 3o ano e incluiu atividades sobre formas, texturas e funções das folhas, exploração de sementes e uma atividade criativa sobre uma horta da imaginação.
David Buschauer has moved around frequently throughout his life but has found stability through his musical performances. He was introduced to violin at a young age by his father, who instilled a drive for success. This led him to pursue both law and the arts in high school, landing lead roles in plays. He was later invited to join the band The Radiomen, which has performed widely and reignited a passion for rock and roll. His experiences as a performer have shown him the emotional connection needed to engage an audience, and he aspires to one day be inducted into the Rock and Roll Hall of Fame.
Este documento parece ser uma atividade escolar sobre uma história envolvendo uma galinha e seus filhos diferentes. Ele contém perguntas sobre detalhes da história, como o conselho dado à galinha e como seus outros filhos salvaram o irmão pinto. Há também perguntas sobre lições aprendidas e atividades propostas, como discutir provérbios e com quem gostariam de se parecer.
The document provides a biography and obituary for John Ndungu Githinji in both English and Swahili. It summarizes that he was born in 1943 in Kairi, Kenya, attended local primary school, married in 1967 and had 10 children. He worked first as a carpenter then opened a successful shop before expanding into transportation, hardware and manufacturing. He retired to his farm before passing away on October 31, 2011 at a medical clinic after collapsing on his way home from Mtwapa. The funeral will be held on November 5th, 2011.
This module introduces exponential functions and covers:
- Finding the roots of exponential equations using the property of equality for exponential equations.
- Simplifying expressions using laws of exponents.
- Determining the zeros of exponential functions by setting the function equal to 0 and solving for x.
The document provides examples and practice problems for students to learn skills in solving exponential equations and finding zeros of exponential functions.
This module introduces polynomial functions of degree greater than 2. It covers identifying polynomial functions from relations, determining the degree of a polynomial, finding quotients of polynomials using division algorithm and synthetic division, and applying the remainder and factor theorems. The document provides examples and practice problems for each topic. It aims to teach students how to work with higher degree polynomial functions.
QUESTION 11. Select the graph of the quadratic function ƒ(x) = 4.docxIRESH3
A semiprofessional baseball team plays two home games per month for three months. It splits concession revenue 50/50 with the city and keeps all ticket revenue. The city charges $100 per month to use the field. The team pays players and manager $1,000 per month. Tickets are $10 each and average attendance is 30 people. Average concession spending per customer is $7. The team earns $300 revenue per game and $1800 total for the season. With total costs of $3000 for the season, the team finishes with a $1200 profit.
This document discusses the dynamic programming approach to solving the 0/1 knapsack problem. It covers the key concepts of dynamic programming including the sequence of decisions, problem state, principle of optimality, and dynamic programming recurrence equations. It provides the recurrence equations to solve the 0/1 knapsack problem using dynamic programming and discusses approaches to reduce the runtime from exponential to linear time complexity.
The document provides instructions on factorizing quadratic equations. It begins by explaining what quadratic equations are and provides examples. It then discusses factorizing quadratics where the coefficient of x^2 is 1 by finding two numbers whose product is the last term and sum is the middle term. The document continues explaining how to factorize when the coefficient of x^2 is not 1 and predicts the signs of the factors based on the signs of the terms in the quadratic equation. It provides examples of factorizing different quadratic equations.
1) The document introduces concepts of differential calculus including derivatives, limits, continuity, and fundamental rules of taking derivatives.
2) It provides examples of calculating derivatives using notations like delta f, limits, and various derivative rules including the power rule, product rule, and quotient rule.
3) Methods for finding local maxima and minima are discussed, including using the first derivative test and analyzing stationary points where the first derivative is zero based on whether the derivative is increasing or decreasing on both sides.
We develop a new method to optimize portfolios of options in a market where European calls and puts are available with many exercise prices for each of several potentially correlated underlying assets. We identify the combination of asset-specific option payoffs that maximizes the Sharpe ratio of the overall portfolio: such payoffs are the unique solution to a system of integral equations, which reduce to a linear matrix equation under suitable representations of the underlying probabilities. Even when implied volatilities are all higher than historical volatilities, it can be optimal to sell options on some assets while buying options on others, as hedging demand outweighs demand for asset-specific returns.
This document summarizes Chapter 9 from a textbook on introductory mathematical analysis. Section 9.1 discusses discrete random variables and expected value. Section 9.2 covers the binomial distribution and how it relates to the binomial theorem. Section 9.3 introduces Markov chains and their associated transition matrices. Examples are provided for each topic to illustrate key concepts like calculating expected values, applying the binomial distribution formula, and determining probabilities using Markov chains.
This document summarizes Chapter 9 from a textbook on introductory mathematical analysis. Section 9.1 discusses discrete random variables and expected value. Section 9.2 covers the binomial distribution and how it relates to the binomial theorem. Section 9.3 introduces Markov chains and their associated transition matrices. Examples are provided for each topic to illustrate key concepts such as calculating expected values, applying the binomial distribution formula, and determining probabilities using Markov chains.
This document summarizes Chapter 9 from a textbook on introductory mathematical analysis. Section 9.1 discusses discrete random variables and expected value. Section 9.2 covers the binomial distribution and how it relates to the binomial theorem. Section 9.3 introduces Markov chains and their associated transition matrices. Examples are provided for each topic to illustrate key concepts like calculating expected values, applying the binomial distribution formula, and determining probabilities using Markov chains.
This document discusses support vector machines (SVMs) for classification tasks. It describes how SVMs find the optimal separating hyperplane with the maximum margin between classes in the training data. This is formulated as a quadratic optimization problem that can be solved using algorithms that construct a dual problem. Non-linear SVMs are also discussed, using the "kernel trick" to implicitly map data into higher-dimensional feature spaces. Common kernel functions and the theoretical justification for maximum margin classifiers are provided.
support vector machine algorithm in machine learningSamGuy7
The objective of the support vector machine algorithm is to find a hyperplane in an N-dimensional space(N — the number of features) that distinctly classifies the
SVMs are known for their effectiveness in high-dimensional spaces and their ability to handle complex data patterns. data points
This document discusses support vector machines (SVMs) for classification tasks. It describes how SVMs find the optimal separating hyperplane with the maximum margin between classes in the training data. This is formulated as a quadratic optimization problem that can be solved using algorithms that construct a dual problem. Non-linear SVMs are also discussed, using the "kernel trick" to implicitly map data to higher dimensions where a linear separator can be found.
This document discusses solving quadratic inequalities. It provides examples of single-variable quadratic inequalities and explains how to find the solution set by first setting the inequality equal to an equation, solving for the roots, and then testing values within the intervals formed by the roots. The document also introduces quadratic inequalities with two variables and how to represent them. It defines a quadratic inequality and explains the process of solving them by relating it back to solving a quadratic equation.
Algebra lesson 4.2 zeroes of quadratic functionspipamutuc
This document provides information about quadratic functions and solving for their zeroes (x-intercepts). It discusses factoring quadratic expressions, using the zero product property to set each factor equal to zero. It also introduces the quadratic formula as a way to solve quadratic equations that are not factorable. There is an example of using the quadratic formula to find the zeroes of the function f(x)=x^2 - 3x - 1. The document concludes with practice problems for students to solve for the zeroes of various quadratic functions.
This document outlines 6 questions for a math assignment on various interpolation techniques:
1. Use a degree 3 polynomial to estimate life expectancies in 3 years for 2 countries.
2. Fit an exponential function to 5 data points to determine coefficients.
3. Compare accuracy of interpolating a function using cubic spline, pchip cubic, and degree 5 polynomial.
4. Generate and analyze cubic spline and pchip interpolants, with derivatives, for another data set.
5. Find the least squares solution to an overdetermined system of linear equations from altitude measurements.
6. Determine the best fitting function - quadratic, power, or exponential - for another data set. Instructions are provided for including
The document discusses derivative-free optimization methods for non-convex problems. It introduces direct-search methods that optimize a function using only function evaluations in different directions, without requiring derivatives. It then covers model-based approaches that fit a polynomial model to approximated points and minimize that instead of the original function. Trust-region methods are discussed that build local models within a region Δ around each point and iteratively improve the model and minimize within each region.
This document provides an overview of key concepts in probability and probability distributions. It introduces random variables and their probability distributions, and covers discrete and continuous random variables. Specific probability distributions discussed include the binomial, Poisson, and normal distributions. Expected value and variance are defined as measures of the central tendency and variability of random variables. Examples are provided to illustrate calculating probabilities and parameters for different probability distributions.
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1. University of Phoenix MAT 117 Week
7&8 Quiz
Get help for Universityof PhoenixMAT117 Week 7&8 Quiz. We provide assignment, homework,
discussions and case studies help for all subject Universityof Phoenixfor Session 2015-2016.
MAT 117 WEEK 7 QUIZ
1.
Whichof the followingconclusionsistrue aboutthe statementbelow?
2 x = x
•
The statementisnevertrue.
•
The statementistrue whenx is negative.
•
The statementisalwaystrue.
•
The statementistrue whenx=0.
2.
Solve forxx inthe equationx2- 8x - 9 = 0.