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This document discusses how to graph linear equations in a coordinate plane. It defines a linear equation as one whose graph is a line and provides the standard form of a linear equation as ax+by=c. It explains that solutions to linear equations are ordered pairs that make statements true when substituted into the equation. To graph a linear equation, you create a domain of at least three convenient values, solve the equation for those values, and plot the points. Examples are given of graphing the equations y=b, x=a, y=3x-2, y=2.5, and x=-4. The vertical line test is introduced to determine if an equation represents a function.
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This upload is actually experimental, so sorry for the lost animations. This is my first post on SlideShare. Future presentations will take into account the loss of animation.
Also, I saw that the titles of all my slides got covered by something, so I'll never use this theme again. The titles of the slides are:
Slide 1: Vectors and Scalars
Slide 2: In this lecture, you will learn
Slide 3: What are vectors?
Slide 4: What are scalars?
Slide 5: A joke
Slide 6: A joke
Slide 7: What was that for?
Slide 8: What was that for?
Slide 9: Vectors
Slide 10: Geometric Representation
Slide 11: Vector Addition
Slide 12: Scalar Multiplication
Slide 13: The Zero Vector
Slide 14: The Negative of a Vector
Slide 15: Vector Subtraction
Slide 16: More Properties of Vector Algebra
Slide 17: Magnitude of a Vector
Slide 18: Vectors in a Coordinate System
Slide 19: Unit Vectors
Slide 20: Algebraic Representation of Vectors
Slide 21: Algebraic Addition of Vectors
Slide 22: Algebraic Multiplication of a Vector by a Scalar
Slide 23: Example 1
Slide 24: Example 2
Slide 25: A few words of caution
Slide 26: Problems
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4 scalarsvectors-161127184703
1. A scalar is a physical quantity that has only magnitude, such as mass, length, and time. A vector is a physical quantity that has both magnitude and direction, such as displacement, velocity, and force.
2. Vectors can be classified based on their orientation as parallel, anti-parallel, or perpendicular. They can also be added using geometric methods like the triangle law or analytical methods using components.
3. Multiplying a vector by a scalar multiplies the magnitude by the scalar value. Vector multiplication can produce a scalar using the dot product or a vector using the cross product. The dot product returns the magnitudes of the vectors and their cosine angle.
Lesson 1: Vectors and Scalars
This upload is actually experimental, so sorry for the lost animations. This is my first post on SlideShare. Future presentations will take into account the loss of animation.
Also, I saw that the titles of all my slides got covered by something, so I'll never use this theme again. The titles of the slides are:
Slide 1: Vectors and Scalars
Slide 2: In this lecture, you will learn
Slide 3: What are vectors?
Slide 4: What are scalars?
Slide 5: A joke
Slide 6: A joke
Slide 7: What was that for?
Slide 8: What was that for?
Slide 9: Vectors
Slide 10: Geometric Representation
Slide 11: Vector Addition
Slide 12: Scalar Multiplication
Slide 13: The Zero Vector
Slide 14: The Negative of a Vector
Slide 15: Vector Subtraction
Slide 16: More Properties of Vector Algebra
Slide 17: Magnitude of a Vector
Slide 18: Vectors in a Coordinate System
Slide 19: Unit Vectors
Slide 20: Algebraic Representation of Vectors
Slide 21: Algebraic Addition of Vectors
Slide 22: Algebraic Multiplication of a Vector by a Scalar
Slide 23: Example 1
Slide 24: Example 2
Slide 25: A few words of caution
Slide 26: Problems
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This document discusses key concepts related to vector quantities in physics:
1. A vector is represented by an arrow that shows both magnitude and direction, such as the velocity of an object.
2. Vector addition and subtraction can be done graphically by drawing vectors head-to-tail to find the resultant vector.
3. The Pythagorean theorem can be used to add perpendicular vectors numerically by treating them as components of the overall resultant vector.
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The document provides information about an introductory physics module including the topics, instructors, and meeting times. It then summarizes various core concepts in physics measurements and quantities including: physical quantities and their magnitude and units; base and derived quantities and units; supplementary quantities of plane angle and solid angle; and significant figures in measurements. Dimensional analysis and the benefits of checking for dimensional homogeneity in equations is also outlined. Vectors, scalar and vector products, and torque are defined.
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- Matrices can only be added or subtracted if they are the same size. The sum or difference of matrices A and B yields a matrix C of the same size.
- Matrices can be multiplied by a scalar. Multiplying a matrix A by a scalar k results in a new matrix kA where each element is multiplied by k.
- Matrix multiplication allows combining information from two matrices but has specific rules regarding the dimensions of the matrices.
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This document contains information about sets and set operations. It defines what a set is, provides examples of standard sets like natural numbers and real numbers, and discusses concepts like subsets, power sets, Cartesian products, unions, intersections, differences and complements of sets. It also presents methods to prove equations involving set operations.
Singular and non singular matrix
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- A particle starts from the point with position vector (3i + 7j) m and then moves with constant velocity (2i – j) ms-1. The question asks to find the position vector of the particle 4 seconds later.
- Substituting the values into the displacement equation gives the final position vector as (12i + 3j) m.
- A second particle is given a position vector of (2i + 4j) m at time t = 0 and a position vector of (12i + 16j) m five seconds later. Using the displacement equation gives the velocity of the particle as (2i + 4j) ms-1.
- For a third particle
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Today's lesson reviews graphing quadratic functions by examining how the b value changes the parabola's position. The teacher discusses important concepts from the previous day like the axis of symmetry and vertex. Students learn that a positive b value results in a shift of the parabola to the left. For class work, students will practice graphing quadratic functions by finding the axis of symmetry and vertex, then plotting additional points to complete the parabola.
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The document discusses key concepts regarding vector quantities including:
1) Vectors can be represented graphically with arrows to indicate both magnitude and direction.
2) A vector can be described by its components in different directions or bases.
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4) Important vector relationships include the direction cosines that specify a vector's direction, and calculating the angle between two vectors.
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This document provides instructions for graphing rational functions without making a table. It explains that the graph is a hyperbola made of two symmetrical branches. It outlines steps to sketch the asymptotes and plot points to draw the branches, being careful not to cross the asymptotes. The steps are to sketch the asymptotes, choose x-values on each side to plug into the function, plot the points, and draw the branches without crossing the asymptotes.
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This document provides an overview of vectors and their applications in physics. It defines vectors and differentiates them from scalars, discusses vector notation and representation, and covers key concepts like addition, subtraction, and multiplication of vectors. Examples are given of vector quantities like displacement, velocity and force. The document also explains vector operators like gradient, divergence and curl, which allow converting between scalar and vector quantities, and outlines how calculus is important in physics for studying change.
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This document discusses physical quantities and vectors. It defines two types of physical quantities: scalar quantities which have only magnitude, and vector quantities which have both magnitude and direction. Examples of each are given. Vector quantities are represented by magnitude and direction. The document then discusses methods for adding and subtracting vectors graphically using head-to-tail and parallelogram methods. It also covers resolving vectors into rectangular components, finding the magnitude and direction of vectors, dot products of vectors which yield scalar quantities, and cross products of vectors which yield vector quantities. Examples of applying these vector concepts are provided.
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The document discusses quadrants and points on a Cartesian plane. It asks where common objects like a ball, table, bag, and laptop would lie in the four quadrants, and explains that any two points on the plane will form a straight line. It was prepared by Ms. Ma. Antonette P. de Castro.
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The document discusses how to draw and interpret line graphs from data. It provides instructions on properly labeling the axes, plotting data points, and drawing a best-fit line through the points. It also defines slope as the constant in the linear equation y=kx and explains how to calculate slope using the rise over run formula.
Linear equations lesson 8 day 2 graphing linear equations
The document is from a pre-algebra lesson on graphing linear equations. It discusses re-arranging equations into slope-intercept form (y=mx+b) and explains the procedure for graphing a line when given an equation in this format. Specifically, it describes using the slope (m) to rise/run and the y-intercept (b) to locate the point where the line crosses the y-axis. The document provides examples and questions to reinforce understanding of graphing linear equations from their slope-intercept form.
Line Graph Presentation
This document provides information about line graphs and bar graphs, including:
- Line graphs show changes over time, with time measured along the x-axis. They can be used to show things like rainfall or temperature changes monthly or yearly.
- Bar graphs are used to compare categorical data rather than changes over time.
- When making a line graph, labels should be included on the x and y axes to identify what each represents, such as time or values. Data points are plotted by reading the x-axis value first.
- Intervals on the axes should be chosen appropriately based on the scale of data, for example not plotting every single day or temperature value.
K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Quarter 3)
This document provides a lesson plan on solving linear equations and inequalities in one variable algebraically. It begins with reviewing translating between verbal and mathematical phrases and evaluating expressions. The main focus is on introducing and applying the properties of equality, including reflexive, symmetric, transitive, and substitution properties, to solve equations algebraically. Word problems involving equations in one variable are also discussed. The objectives are to identify and apply the properties of equality to find solutions to equations and solve word problems involving one variable equations.
Grade 7 Learning Module in MATH
Here are the answers:
(a) A B is shown in Set 2. It contains all elements that belong to A or B or both.
(b) A B is shown in Set 3. It contains elements that belong to both A and B.
2. Given sets P = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8}, find P Q and P Q.
3. Draw a Venn diagram to represent the following sets:
A = {x | x is a prime number less than 10}
B = {x | x is an even number less than 10}
Designing Teams for Emerging Challenges
The document discusses designing teams and processes to adapt to changing needs. It recommends structuring teams so members can work within their competencies and across projects fluidly with clear roles and expectations. The design process should support the team and their work, and be flexible enough to change with team, organization, and project needs. An effective team culture builds an environment where members feel free to be themselves, voice opinions, and feel supported.
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Linear equations lesson 8 day 2 graphing linear equations
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K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Quarter 3)
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4.7 notes
Functions can be written in function notation such as f(x)=mx+b, where f(x) represents the linear equation mx+b with x as the variable. The parentheses indicate that the variable x in the equation will be replaced by the number written inside the parentheses. For example, if evaluating f(2), x would be replaced with 2. Other letters besides f can also be used to represent functions. The domain of a function is the x-values, while the range is the y-values or f(x)-values produced by inputting x-values into the function.
4.6 notes
Two variables show direct variation if their relationship can be written in the form y=ax, where a is the constant of variation. Direct variation equations represent relationships where one variable varies directly as the other changes. To determine if an equation represents direct variation, substitute coordinates to solve for the constant a and rewrite the equation in the form y=ax. The constant of variation and the graphs of direct variation equations can then be used to find output values for given input values.
4.4 notes
The document discusses slope and how it represents the rate of change of a line. It defines slope as the rise over the run between two points on a line. Positive slope lines rise from left to right, negative slope lines rise from right to left, horizontal lines have zero slope, and vertical lines have undefined slope. The slope formula is defined as the change in y over the change in x between two points.
4.5 notes
This document discusses how to graph linear equations using slope-intercept form. It identifies the slope and y-intercept of several equations in slope-intercept form, such as y=3x+4 and 3x-3y=12. It then shows how to graph these equations by plotting the y-intercept and running the line with the given slope. As an example, it graphs the equation y=5x-3 on an xy-plane. It also demonstrates graphing parallel lines, such as y=3x+4 and y=3x+6, which have the same slope but different y-intercepts.
4.4 notes
Slope represents the rate of change of a line and is calculated by rise over run. A positive slope indicates the line rises from left to right, while a negative slope rises from right to left. Horizontal lines have a slope of zero as there is no rise, and vertical lines have an undefined slope as the run is zero.
4.3 notes
This document discusses how to graph linear equations by finding the x-intercept and y-intercept. It explains that the x-intercept is where the line crosses the x-axis and the y-intercept is where it crosses the y-axis. It provides an example of an equation with an x-intercept of -3 and a y-intercept of 5. It then explains how to find the intercepts by setting either x or y to 0 and solving for the other variable.
4.3 notes
This document discusses how to graph linear equations by finding the x-intercept and y-intercept. It explains that the x-intercept is where the line crosses the x-axis and the y-intercept is where it crosses the y-axis. It provides an example of an equation with an x-intercept of -3 and a y-intercept of 5. It then explains how to find the intercepts by setting either x or y to 0 and solving for the other variable.
4.2 notes
Graph linear equations in a coordinate plane by following these steps:
1) Choose a domain of at least three convenient values for the variable.
2) Solve the linear equation for those values to obtain ordered pairs.
3) Plot the ordered pairs on a coordinate plane to graph the line represented by the linear equation. Vertical lines must pass through only one point for the graph to represent a function.
4.1 notes
The document describes plotting points and graphs on a coordinate plane. It defines an x-axis, y-axis, and four quadrants. Examples of ordered pairs are given with points labeled on the plane. Two linear equations, y=2x-1 and y=-1/3x+2, are shown graphed on the plane with their domains.
Simple factoring
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Amendment 27
The 27th Amendment regulates congressional pay increases by preventing any increase in pay from taking effect until after the next set of elections, allowing voters to retaliate against increases they view as unjust. It was originally proposed in 1789 as part of the Bill of Rights but was not ratified for over 200 years until 1992. Gregory Watson, a university student, researched the amendment and began a campaign that led to its ratification by 38 states, the final being Michigan.
What Are The Components Of A Well Planned
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4.2 notes
- 1. 4.2 Graph linear equations in a coordinate plane
- 2. Linear Equation • An equation whose graph is a line.
- 3. Standard form of a linear equation • ax+by=c
- 4. Solutions to linear equations • Ordered pairs that result in true statements when substituted into a linear equation.
- 6. Graphing linear equations • Create a domain of at least three values. • Choose values that are convenient. • Solve the equation for those values.
- 7. Graph a linear equation • -2x + y = -3
- 8. y=b and x=a
- 9. Vertical Line Test • A function is represented by a graph in which a vertical line will not pass through more than one point. • Is y=b a function? • Is x=a a function?
- 10. Graph the Equation: • y = 3x - 2
- 11. Graph the Equation • y = 2.5
- 12. Graph the Equation • x = -4