Yoaniker morles1
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This document contains solutions to exercises from a mathematics applied course. It provides solutions to problems involving classifying differential equations by order, degree, linearity and identifying the unknown function and independent variable. It also involves finding the differential equation that a given solution satisfies and verifying if a given solution satisfies a differential equation.
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Johelbys campos1
This document contains exercises to classify different types of differential equations based on their order, degree, linearity, and to determine the independent and unknown functions. It also contains exercises to find the differential equation that a given function satisfies, and to verify if a given function satisfies a given differential equation. The exercises provide the step-by-step workings and solutions.
October 3
The document contains class notes and practice problems on solving various types of equations, including:
1) One-step and two-step equations with integers.
2) Equations with decimals, including combining like terms and solving.
3) Absolute value equations, which require writing two equations to account for the absolute value being positive or negative and then solving each equation.
4) Examples are provided of solving absolute value equations and identifying the solution set by graphing.
5) Homework assignments are listed for students to complete problems from specific pages and problems in their textbooks.
October. 27, 2014
The document provides information about an upcoming math exam and homework assignments. It includes a schedule for the week which focuses on absolute value, inequalities, and beginning a review for the final exam. Topics to study this week include absolute value equations, linear equation word problems, and solving rational equations. The document also provides practice problems and examples for the final exam review involving order of operations, simplifying expressions, integers, and solving absolute value equations.
November 14, 2014 compound
This document contains notes from a math class on November 14, 2014 including:
- Topics covered were set-builder notation, compound inequalities, and solving multi-step inequalities.
- Announcements about 1st quarter grades being posted, Khan Academy assignments due, and showing work for class work submissions.
- Examples of solving conjunction and disjunction compound inequalities by graphing the solutions and writing them in set-builder notation.
- Practice problems for students to complete involving compound inequalities.
Multiplication and Division of Integers
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
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https://tinyurl.com/ycjp8r7u
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
Systems of Equations by Elimination
This document provides instructions for solving systems of equations using elimination. It demonstrates eliminating variables by adding or subtracting equations. Sample systems are worked through, showing the steps of identifying which variable to eliminate, combining the equations accordingly, solving for one variable, then substituting back into the original equations to solve for the other. The solutions are checked in both equations to verify they satisfy the system.
Paso 2 profundizar y contextualizar el conocimiento de
This document contains 7 math tasks involving algebraic expressions and polynomials:
1) Simplifying an algebraic expression by distributing terms
2) Dividing two polynomials
3) Dividing a polynomial by a binomial using synthetic division
4) Solving two rational expressions for x and checking with Geogebra
5) Determining domains of functions
6) Factoring trinomials and a difference of squares
7) Simplifying a fraction involving algebraic expressions
Feb. 4, 2014
The document provides information about an upcoming math test on inequalities and systems of equations. It includes:
- A review of topics to be covered on the test like inequalities, parallel and perpendicular lines, and solving systems of equations by graphing, substitution, and elimination.
- Sample problems and step-by-step explanations for solving systems of equations using different methods.
- A word problem about determining the price of gloves and hats by setting up and solving a system of two equations.
The document reviews key concepts and provides practice problems to help students prepare for an upcoming test on inequalities and systems of equations.
Recommended
Johelbys campos1
This document contains exercises to classify different types of differential equations based on their order, degree, linearity, and to determine the independent and unknown functions. It also contains exercises to find the differential equation that a given function satisfies, and to verify if a given function satisfies a given differential equation. The exercises provide the step-by-step workings and solutions.
October 3
The document contains class notes and practice problems on solving various types of equations, including:
1) One-step and two-step equations with integers.
2) Equations with decimals, including combining like terms and solving.
3) Absolute value equations, which require writing two equations to account for the absolute value being positive or negative and then solving each equation.
4) Examples are provided of solving absolute value equations and identifying the solution set by graphing.
5) Homework assignments are listed for students to complete problems from specific pages and problems in their textbooks.
October. 27, 2014
The document provides information about an upcoming math exam and homework assignments. It includes a schedule for the week which focuses on absolute value, inequalities, and beginning a review for the final exam. Topics to study this week include absolute value equations, linear equation word problems, and solving rational equations. The document also provides practice problems and examples for the final exam review involving order of operations, simplifying expressions, integers, and solving absolute value equations.
November 14, 2014 compound
This document contains notes from a math class on November 14, 2014 including:
- Topics covered were set-builder notation, compound inequalities, and solving multi-step inequalities.
- Announcements about 1st quarter grades being posted, Khan Academy assignments due, and showing work for class work submissions.
- Examples of solving conjunction and disjunction compound inequalities by graphing the solutions and writing them in set-builder notation.
- Practice problems for students to complete involving compound inequalities.
Multiplication and Division of Integers
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
Systems of Equations by Elimination
This document provides instructions for solving systems of equations using elimination. It demonstrates eliminating variables by adding or subtracting equations. Sample systems are worked through, showing the steps of identifying which variable to eliminate, combining the equations accordingly, solving for one variable, then substituting back into the original equations to solve for the other. The solutions are checked in both equations to verify they satisfy the system.
Paso 2 profundizar y contextualizar el conocimiento de
This document contains 7 math tasks involving algebraic expressions and polynomials:
1) Simplifying an algebraic expression by distributing terms
2) Dividing two polynomials
3) Dividing a polynomial by a binomial using synthetic division
4) Solving two rational expressions for x and checking with Geogebra
5) Determining domains of functions
6) Factoring trinomials and a difference of squares
7) Simplifying a fraction involving algebraic expressions
Feb. 4, 2014
The document provides information about an upcoming math test on inequalities and systems of equations. It includes:
- A review of topics to be covered on the test like inequalities, parallel and perpendicular lines, and solving systems of equations by graphing, substitution, and elimination.
- Sample problems and step-by-step explanations for solving systems of equations using different methods.
- A word problem about determining the price of gloves and hats by setting up and solving a system of two equations.
The document reviews key concepts and provides practice problems to help students prepare for an upcoming test on inequalities and systems of equations.
Solving systems with elimination
The document provides steps for solving systems of equations using the elimination method with addition and subtraction:
1. Put both equations in standard form.
2. Determine which variable to eliminate by finding terms with the same coefficients.
3. Add or subtract the equations to eliminate the chosen variable.
4. Substitute and solve for the remaining variable and plug back into one equation to solve for the other.
5. Check the solution by substituting the values back into both original equations.
Subtraction of Integers
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document appears to be notes from a math class that includes the following:
1. Warm-up problems involving equations with variables, operations, and decimals.
2. Class notes on solving equations with decimals, including steps to combine constants and solve.
3. Practice problems for equations with decimals.
4. Class notes on solving absolute value equations, including rules for writing two equations and examples worked out.
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The document is a presentation on ordinary and partial differential equations. It summarizes solving a second order linear differential equation with constant coefficients. The equation is 4 d^2y/dx^2 - 2 dy/dx + 5y = 0. Letting y = e^mx, the auxiliary equation is derived as 4m^2 - 2m + 5 = 0. The general solution is found to be y = e^(1/4x) [A cos(76x/8) + B sin(76x/8)].
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For the example of 5y - 2 = 8, solving the equation determines that the solution is y = 2.
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2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
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An identity matrix is a square matrix with ones along its main diagonal and zeros elsewhere. When a matrix is multiplied by its corresponding identity matrix, the original matrix is returned. The identity matrix for an n×n matrix is denoted In×n. Some key properties of identity matrices are that AI = IA = A for any square matrix A of the same dimensions.
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Yoaniker morles2
1) The differential equation dy/dx = xy + 3x - y - 3 / xy - 2x + 4y - 8 is separable.
2) The differential equation y' = 2y + x^2 + 5 is linear.
3) The differential equation (y^2 + yx)dx - x^2 dy = 0 is homogeneous.
INVERSE DIFFERENTIAL OPERATOR
How do you calculate the particular integral of linear differential equations?
Learn this and much more by watching this video. Here, we learn how the inverse differential operator is used to find the particular integral of trigonometric, exponential, polynomial and inverse hyperbolic functions. Problems are explained with the relevant formulae.
This is useful for graduate students and engineering students learning Mathematics. For more videos, visit my page
https://www.mathmadeeasy.co/about-4
Subscribe to my channel for more videos.
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The document provides steps for solving systems of equations using the elimination method with addition and subtraction:
1. Put both equations in standard form.
2. Determine which variable to eliminate by finding terms with the same coefficients.
3. Add or subtract the equations to eliminate the chosen variable.
4. Substitute and solve for the remaining variable and plug back into one equation to solve for the other.
5. Check the solution by substituting the values back into both original equations.
Subtraction of Integers
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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The document appears to be notes from a math class that includes the following:
1. Warm-up problems involving equations with variables, operations, and decimals.
2. Class notes on solving equations with decimals, including steps to combine constants and solve.
3. Practice problems for equations with decimals.
4. Class notes on solving absolute value equations, including rules for writing two equations and examples worked out.
Second order linear diffrential equation with constant coeffecient
The document is a presentation on ordinary and partial differential equations. It summarizes solving a second order linear differential equation with constant coefficients. The equation is 4 d^2y/dx^2 - 2 dy/dx + 5y = 0. Letting y = e^mx, the auxiliary equation is derived as 4m^2 - 2m + 5 = 0. The general solution is found to be y = e^(1/4x) [A cos(76x/8) + B sin(76x/8)].
Chapter 4
7x + 3 = 9
The value of x that satisfies the equation is called the solution or root of the equation.
For the example of 5y - 2 = 8, solving the equation determines that the solution is y = 2.
Given the perimeter of a figure is 46 cm, the equation 46= 2(3a+4) + 2(2a-1) can be solved to determine the value of a is 4.
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1) The document discusses various algebraic expressions operations such as addition, subtraction, multiplication, division, and factorization using factoring by grouping. Examples of each operation are shown step-by-step.
2) Formulas for multiplying expressions with exponents are provided. Examples of multiplying and factoring quadratic expressions are worked out.
3) References for further reading on algebraic expression topics are listed.
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This document provides an overview of teaching addition of integers in the 7th grade mathematics curriculum for the first quarter. It introduces three methods for adding integers: using colored counters, a number line, and rules for same and different signs. Examples are provided for adding integers with these different methods. Students are then given practice problems to solve on their own and check their work against an answer key.
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This document provides examples for solving quadratic equations by factoring. It explains how to solve equations of the form ax^2 + bx = 0 and ax^2 + bx + c = 0 by factoring and setting each factor equal to zero. Some example problems are worked out step-by-step, including solving 11x^2 - 13x = 8x - 3x^2 and 7x^2 + 18x = 10x^2 + 12x. The document also discusses using the fact that the roots of ax^2 + bx = 0 are x = 0 and x = -b/a to solve equations without factoring. It concludes by explaining how to use the zero product property to solve a quadratic
Assure Method
This document outlines a lesson plan on quadratic equations for junior students. The objectives are for students to define quadratic equations, state their form, solve problems involving them, identify their use in everyday life, and evaluate their own performance. Concepts covered include the definition and forms of quadratic equations. The procedure involves grouping students, identifying quadratic equations, solving example equations using square roots, factoring, completing the square, and the quadratic formula. Students are then assigned additional equations to solve using these methods and evaluate their experience working in groups.
Derivatives of inverse trig functions
This document discusses derivatives of inverse trigonometric functions and provides examples of taking their derivatives. It contains the following key points:
1. The derivatives of the main inverse trigonometric functions are given as fractions involving the term 1/(1-x^2).
2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
3. The last example proves that if y = sin^(-1)(2x/(1+x^2)), then (1+x^2)dy/dx = 2 by making a u-substitution of x = tanθ.
Identity matrix
An identity matrix is a square matrix with ones along its main diagonal and zeros elsewhere. When a matrix is multiplied by its corresponding identity matrix, the original matrix is returned. The identity matrix for an n×n matrix is denoted In×n. Some key properties of identity matrices are that AI = IA = A for any square matrix A of the same dimensions.
Derivation and Application of Six-Point Linear Multistep Numerical Method for...
A six-step Continuous Block method of order (5, 5, 5, 5, 5, 5) T is proposed for direct solution of the second (2nd) order initial value problems. The main method and additional ones are obtained from the same continuous interpolant derived through interpolation and collocation procedures. The methods are derived by interpolating the continuous interpolant at 𝑥 = 𝑥𝑛+𝑗 , 𝑗 = 6 and collocating the first and second derivative of the
continuous interpolant at 𝑥𝑛+𝑗 , 𝑗 = 0 and 𝑗 = 2, 3, … 5 respectively. The stability properties of the methods are discussed and the stability region shown. The methods are then applied in block form as simultaneous numerical integrators. Two numerical experiments are given to illustrate the efficiency of the new methods.
Algebra paso2
1) The document presents solutions to exercises involving algebraic expressions and polynomials.
2) The exercises include factorizing expressions, performing operations on polynomials, dividing polynomials, solving rational expressions, and determining function domains.
3) The solutions show the step-by-step work and use GeoGebra to verify graphical solutions.
Implicit differentiation
This document discusses implicit differentiation, which is a technique for finding the gradient function of implicit equations where x and y are not explicitly defined. It provides examples of implicit equations and their derivatives using implicit differentiation. The key steps are to take the derivative of every term with respect to x and apply the chain rule to terms containing y. Practice questions are provided to find the equations of the tangent and normal to implicit curves at given points.
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Second order linear diffrential equation with constant coeffecient
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https://www.mathmadeeasy.co/about-4
Subscribe to my channel for more videos.
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Yoaniker morles1
- 1. PROGRAMA NACIONAL DE FORMACIÓN EN SISTEMA DE CALIDAD Y AMBIENTE. Matemática Aplicada. Ejercicios Unidad I. Integrante: Yonaiker Morles C.I.: 25.814.152 Trayecto 3 Fase 2 Grupo-A Febrero de 2021
- 2. Ejercicios propuestos 1.1: En los siguientes problemas, clasifique cada ecuación diferencial, según su orden, grado (si es posible) y si es lineal o no. Determine la función desconocida y la variable independiente. 𝟐) 𝒚 𝒅𝟐 𝒙 𝒅𝒚𝟐 = 𝒚𝟐 + 𝟏 Solución: Orden: E.D.O orden 2 Grado: 1 Linealidad: no lineal Variable independiente: 𝑦 Función desconocida: 𝑦 𝑑2𝑥 𝑑𝑦2 𝟔) 𝒕𝟓 𝒚(𝟒) − 𝒕𝟑 𝒚´´ + 𝟔𝒚 = 𝟎 Solución: Orden: E.D.O orden 4 Grado: 1 Linealidad: no lineal Función desconocida: 𝑡5 𝑦(4) − 𝑡3 𝑦´´ + 6𝑦 𝟏𝟎) 𝒕𝟐 𝒔̈ − 𝒕𝒔̇ = 𝟏 − 𝒔𝒆𝒏 𝒕 Solución: Orden: E.D.O orden 2 Grado: 1 Linealidad: no lineal Variable independiente: 𝑡 Función desconocida: 𝑡2 𝑠̈ − 𝑡𝑠̇
- 3. Ejercicios propuestos 1.2: Encontrar la ecuación diferencial de la cual es solución. 𝟐) 𝒚𝟐 = 𝑪𝟏 (𝑿 + 𝟏 𝟒 𝑪𝟏) Solución: 𝑦 = ±√𝐶1 (𝑥 + 𝐶1 4 ) ; trabajamos con la raíz positiva Derivamos: 𝑦´ = 𝐶1 2√𝐶1 (𝑋 + 𝐶1 4 ) Elevamos al cuadrado a ambos lados. 𝑦´2 = 𝐶1 2 4 (𝐶1𝑋 + 𝐶1 4 ) 𝑦´2 = 𝐶1 2 4𝐶1 (𝑋 + 1 4) 𝑦´2 = 𝐶1 4 (𝑋 + 1 4) 𝑦´2 = 𝐶1 4𝑥 + 1 Despejamos 𝐶1; 𝐶1 = 𝑦´2(4𝑥 + 1) Ahora sustituimos 𝐶1 en 𝑦2 = 𝐶1 (𝑋 + 1 4 𝐶1) 𝑦2 = (4𝑥 + 1)𝑦´2 . (𝑥 + (4𝑥 + 1)𝑦´2 4 ) 𝑦2 = 4𝑥𝑦´2 + 𝑦´2 . (𝑥 + 4𝑥𝑦´2 + 𝑦´2 4 ) 𝑦2 = 4𝑥𝑦´2 + 𝑦´2 . ( 4𝑥 + 4𝑥𝑦´2 + 𝑦´2 4 )
- 4. 𝑦2 = 4𝑥𝑦´2 + 𝑦´2 . (𝑥 + 𝑥𝑦´2 + 𝑦´2 4 ) 𝑦2 = 4𝑥2 𝑦´2 + 4𝑥2 𝑦´4 + 4𝑥𝑦´4 4 + 𝑥𝑦´2 + 𝑥𝑦´4 + 𝑦´4 4 𝑦2 = 4𝑥2 𝑦´2 + 4𝑥2 𝑦´4 + 2𝑥𝑦´4 + 𝑥𝑦´2 + 𝑦´4 4 𝑦2 = 𝑦´2 (4𝑥2 + 4𝑥2 𝑦´2 + 2𝑥𝑦´2 + 𝑥 + 𝑦´2 4 ) Es la ecuación diferencial buscada 𝟔) 𝒚 = 𝑪𝒙 + 𝑪 − 𝑪𝟐 Solución: Como 𝑦 = 𝐶𝑥 + 𝐶 − 𝐶2 entonces 𝑦´ = 𝐶 Sustituimos C en 𝑦 = 𝐶𝑥 + 𝐶 − 𝐶2 𝑦 = 𝑦´𝑥 + 𝑦´ + 𝑦´2 La ecuación diferencial es 𝑦 = 𝑦´𝑥 + 𝑦´ + 𝑦´2 Verifique que la función indicada es una solución de la E.D dada. Donde sea apropiado 𝐶1 y 𝐶2 son constantes. 𝟒) 𝒅𝒚 𝒅𝒕 + 𝟐𝟎𝒚 = 𝟐𝟒 ; 𝒚 = 𝟔 𝟓 − 𝟔 𝟓 𝒆−𝟐𝟎𝒕 Solución: 1𝑒𝑟𝑎 𝐷𝑒𝑟𝑖𝑣𝑎𝑑𝑎: 𝑦´ = 50 3 𝑒−20𝑡 Sustituimos 𝑦, 𝑦´´ en la ecuación diferencial. 50 3 𝑒−20𝑡 + 20 ( 5 6 − 5 6 𝑒−20𝑡 ) = 24 50 3 𝑒−20𝑡 + 50 3 − 50 3 𝑒−20𝑡 = 24 50 3 = 24 La ecuación no satisface la ecuación diferencial.