4 7 Notes A
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Day 2 Opener: - Review problem solving linear equations from the previous day - Introduce different forms of writing linear equations: point-slope form, slope-intercept form, standard form - Students work with a partner to practice identifying properties of lines from their equations Section 4.7 Jiffy Graphs: - Explain how to quickly write an equation of a line given certain information using the different forms - Demonstrate graphing lines using point-slope and slope-intercept form by plotting points - Ask students to consider how to graph a line in standard form for the exit slip
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4 7 Notes B
This document provides instruction on writing and graphing linear equations in different forms. It begins with a review of equivalent forms of linear equations, including point-slope, slope-intercept, and standard form. Students are then given examples of writing equations of lines given a point and slope, or two points. The document concludes with examples of graphing lines by using the point-slope and slope-intercept forms to easily find points and draw the line. Students are challenged to graph a line given in standard form and explain their process.
4.6 Notes B
This document provides instructions and examples for a skills competition involving solving equations for the variable y. Students have 5 minutes to solve 5 equations, showing their work, and circle their final answers. Correctly solving at least 4 equations earns a prize. Examples are given for finding the slope and equation of a line passing through two points, and for determining the slope from a linear equation. An exit slip assignment involves applying these skills.
Writing linear equations
1) The document provides steps for writing linear equations given the slope and a point or two points that the line passes through.
2) Examples are worked through of finding the equation of a line given its slope and one point, or given two points that the line passes through.
3) Practice problems are provided and worked through, along with a review of the process and a short quiz to assess understanding.
Complex Number's Applications
Complex numbers were first conceived by Cardano to solve cubic equations and ultimately led to the fundamental theorem of algebra. Complex numbers form an algebraically closed field where any polynomial equation has a root. Rules for addition, subtraction, and multiplication of complex numbers were developed by Bombelli. Complex numbers can be expressed as a + bi and are used throughout fields like signal processing, image processing, and more. Fractals generated from complex numbers produce beautiful patterns through iteration.
3.12 3.13 Notes A
1) The document discusses graphing equations and finding intersection points of graphs. It includes examples of graphing equations like y = x2 - 4x + 3 and finding the intersection points of the graphs y = x and y = 1000 - x.
2) Tony and Sasha's method for graphing y = x2 - 4x + 3 involved choosing x-values of 0 and -1 to plot points and draw a curve between them.
3) The document provides homework problems from pages 263 and 267 involving graphing equations and finding intersection points.
3.12 3.13 Notes B
This document contains a lesson plan on graphing equations. It includes instructions for students to graph equations like y=x^2 - 4x + 3 by plotting points, determine intersection points between two graphs, and identify the region each quadrant represents on a coordinate plane. It provides guidance for students to practice graphing, identifies key ideas to remember, and assigns homework problems for students to complete.
coordinate_geometry
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This document provides a learning guide about binary relations. It includes definitions of key concepts like ordered pairs, Cartesian products, and binary relations. It presents examples and problems for students to practice these concepts. The guide aims to help students understand binary relations and how they can be used to model real-world situations and solve problems in various disciplines like mathematics, engineering, and science. Students are asked to analyze information, apply definitions, properties, and find Cartesian products. They also self-evaluate their understanding through an assessment scale.
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4 7 Notes B
This document provides instruction on writing and graphing linear equations in different forms. It begins with a review of equivalent forms of linear equations, including point-slope, slope-intercept, and standard form. Students are then given examples of writing equations of lines given a point and slope, or two points. The document concludes with examples of graphing lines by using the point-slope and slope-intercept forms to easily find points and draw the line. Students are challenged to graph a line given in standard form and explain their process.
4.6 Notes B
This document provides instructions and examples for a skills competition involving solving equations for the variable y. Students have 5 minutes to solve 5 equations, showing their work, and circle their final answers. Correctly solving at least 4 equations earns a prize. Examples are given for finding the slope and equation of a line passing through two points, and for determining the slope from a linear equation. An exit slip assignment involves applying these skills.
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2) Examples are worked through of finding the equation of a line given its slope and one point, or given two points that the line passes through.
3) Practice problems are provided and worked through, along with a review of the process and a short quiz to assess understanding.
Complex Number's Applications
Complex numbers were first conceived by Cardano to solve cubic equations and ultimately led to the fundamental theorem of algebra. Complex numbers form an algebraically closed field where any polynomial equation has a root. Rules for addition, subtraction, and multiplication of complex numbers were developed by Bombelli. Complex numbers can be expressed as a + bi and are used throughout fields like signal processing, image processing, and more. Fractals generated from complex numbers produce beautiful patterns through iteration.
3.12 3.13 Notes A
1) The document discusses graphing equations and finding intersection points of graphs. It includes examples of graphing equations like y = x2 - 4x + 3 and finding the intersection points of the graphs y = x and y = 1000 - x.
2) Tony and Sasha's method for graphing y = x2 - 4x + 3 involved choosing x-values of 0 and -1 to plot points and draw a curve between them.
3) The document provides homework problems from pages 263 and 267 involving graphing equations and finding intersection points.
3.12 3.13 Notes B
This document contains a lesson plan on graphing equations. It includes instructions for students to graph equations like y=x^2 - 4x + 3 by plotting points, determine intersection points between two graphs, and identify the region each quadrant represents on a coordinate plane. It provides guidance for students to practice graphing, identifies key ideas to remember, and assigns homework problems for students to complete.
coordinate_geometry
This document contains exercises from a math textbook on coordinate geometry. It includes questions about describing the position of an object using coordinates, drawing a city street map using coordinates, defining key terms of the Cartesian plane like quadrants and axes, finding coordinates of points on a graph, and plotting points from a table on the Cartesian plane. The answers provide step-by-step workings and explanations for finding coordinates and interpreting points in the different quadrants and axes.
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American public university math 110 complete course
Get help for American Public University MGT 656 New for all week assignments and discussions. We provide assignment, homework, discussions and case studies help for all subject American Public University for Session 2015-2016.
C452023.pdf
1) The study develops a symmetric encryption algorithm based on finding a third point from two points on a line. This rule, typically used for elliptic curves, is also found to apply to lines intersecting both axes.
2) When applying the rule sequentially, the line is found to wrap around at three points - the third point from points A and B is C, and the third point from B and C is A. This feature enables key generation.
3) ASCII character codes are represented as the sum of 10 random numbers for encryption. Keys are also 10 random numbers selected such that no numbers are the same as the character code. Encryption finds the third point of the key numbers relative to the character code numbers.
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This document provides 10 complex exercises involving:
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2) Multiplying and taking the inverse of complex numbers.
3) Finding the cube roots of -1 and 1 and plotting them.
4) Drawing complex numbers and their multiples as vectors.
5) Deriving trigonometric identity formulas from the complex exponential.
6) Analyzing the motion of a point moving in the complex plane as a function of time.
7) Calculating velocity and acceleration vectors from position functions.
8) Analyzing the behavior of a complex function with varying real and imaginary parts.
9) Plotting the
คาบ2 2
The document provides instructions for writing and graphing linear equations in slope-intercept form (y = mx + b). It defines key terms like slope (m), y-intercept (b), and parallel lines. Examples are given for writing equations from slope and y-intercept, graphing lines on a coordinate plane, and determining if two lines are parallel based on having the same slope. Key steps are outlined for graphing a line passing through a given point with a given slope.
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This video models solving linear equations of the form x + a = b using algebra tiles. It shows three examples of equations solved concretely with tiles: x + 3 = 7, r + 5 = -2, and 3x - 4 = 5. The tiles represent integers and unknowns, with an equals sign separating the left and right sides. Solving involves using the zero property to isolate the unknown, requiring adding the same amount to both sides to maintain balance.
Chpt 3 Rev Notes A
The document contains information about triathlon-style teams competition with three legs:
1. The first two legs have 15 possible points each but are graded out of 12, with extra credit for speed and accuracy.
2. The third leg is a 25-minute group mini quiz.
3. Teams and team members are listed, and homework assignments are given.
8 2 Notes A
1. The geometric mean between 2 and 10 is 5.
2. A right triangle problem is presented with missing side lengths for QS, QT, and RT given side lengths of 8, 32, and an unknown side R.
3. A homework problem asks to write trigonometric ratios as fractions and decimals and use special right triangles to write ratios in terms of degrees. It also asks which ratio would be used to find missing side lengths in sample right triangles.
5 3 5 3 Notes B
The document provides instructions for students to complete an opener assignment. It instructs students to draw two identical acute triangles, each filling half of the provided box. Students are then asked to sketch the perpendicular bisector of each side and the angle bisector of each angle of the triangles. The document asks students to notice anything interesting about their drawings. It then provides a radicals worksheet for students to check over and mark any incorrect problems on.
Alg2.4 A Notes
The document provides examples and explanations of key concepts related to rates, expressions, and order of operations in mathematics:
1) It gives an example of calculating rate using the equation r = d/t, showing how to find the rate of a person running 100 meters in 40 seconds.
2) It lists two "number tricks" involving multiple steps of operations on a chosen number, but notes that only one trick allows determining the original number.
3) It discusses combining like terms in expressions and the rules of arithmetic for expressions.
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American public university math 110 complete course
Get help for American Public University MGT 656 New for all week assignments and discussions. We provide assignment, homework, discussions and case studies help for all subject American Public University for Session 2015-2016.
C452023.pdf
1) The study develops a symmetric encryption algorithm based on finding a third point from two points on a line. This rule, typically used for elliptic curves, is also found to apply to lines intersecting both axes.
2) When applying the rule sequentially, the line is found to wrap around at three points - the third point from points A and B is C, and the third point from B and C is A. This feature enables key generation.
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1) Representing complex numbers in the form reiq and plotting them on the complex plane.
2) Multiplying and taking the inverse of complex numbers.
3) Finding the cube roots of -1 and 1 and plotting them.
4) Drawing complex numbers and their multiples as vectors.
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Chpt 3 Rev Notes A
The document contains information about triathlon-style teams competition with three legs:
1. The first two legs have 15 possible points each but are graded out of 12, with extra credit for speed and accuracy.
2. The third leg is a 25-minute group mini quiz.
3. Teams and team members are listed, and homework assignments are given.
8 2 Notes A
1. The geometric mean between 2 and 10 is 5.
2. A right triangle problem is presented with missing side lengths for QS, QT, and RT given side lengths of 8, 32, and an unknown side R.
3. A homework problem asks to write trigonometric ratios as fractions and decimals and use special right triangles to write ratios in terms of degrees. It also asks which ratio would be used to find missing side lengths in sample right triangles.
5 3 5 3 Notes B
The document provides instructions for students to complete an opener assignment. It instructs students to draw two identical acute triangles, each filling half of the provided box. Students are then asked to sketch the perpendicular bisector of each side and the angle bisector of each angle of the triangles. The document asks students to notice anything interesting about their drawings. It then provides a radicals worksheet for students to check over and mark any incorrect problems on.
Alg2.4 A Notes
The document provides examples and explanations of key concepts related to rates, expressions, and order of operations in mathematics:
1) It gives an example of calculating rate using the equation r = d/t, showing how to find the rate of a person running 100 meters in 40 seconds.
2) It lists two "number tricks" involving multiple steps of operations on a chosen number, but notes that only one trick allows determining the original number.
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3.10 3.11 Notes A
This document provides homework questions on solving equations and graphing equations. It includes:
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3) Graphing equations like y = x^2 - 3x + 2 on a graphing calculator and determining features of the graph like where it crosses the x-axis.
4) Applying a transformation like (x,y) -> (x + 5, y) to the points on a graph.
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The document provides instruction and examples for graphing related quantities qualitatively. It discusses using graphs to represent how a bouncing basketball or Curious George's skydiving experience might change over time. Students are asked to come up with stories about money growing or shrinking and graph them, including an important feature from the lesson. The homework assigned is to complete practice problems and a writing assignment.
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4.3 4.4 Notes B
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7 3 Zero Product Property A
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3.4 Notes B
The document provides instructions and examples for graphing related quantities qualitatively. It discusses using graphs to represent a bouncing basketball with varying speeds and prices of Nike shoes over time. Students are asked to identify independent and dependent variables, construct their own qualitative graphs representing scenarios, and interpret other qualitative graphs. The homework assignment is to complete practice problems and a writing assignment by a due date.
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1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. It includes examples of using the midpoint formula to find the midpoint of a segment and using given midpoints and endpoints to find missing endpoints.
3. There are also examples of using the Pythagorean theorem and distance formula to find the length of a segment between two points.
8.7 notes
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
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W200
This document discusses different forms of linear equations and methods for graphing linear equations. It covers slope-intercept form, general/standard form, using a t-chart to graph, and using the slope and y-intercept. Examples and practice problems are provided for each topic. The document is intended to teach students how to solve, write in different forms, and graph linear equations.
Algebreviewer
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
Algebreviewer
This document provides a review for algebra sections on various topics including:
1) Solving word problems involving equations with one unknown variable.
2) Finding sums, differences, and ratios of numbers.
3) Representing word problems using tables and equations.
4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described.
5) Graphing linear equations and finding slopes of lines from equations or two points.
6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.
1.1a
The document provides examples for translating words into algebraic expressions and equations. It gives several word problems describing real-world situations and shows how to represent each with variables and equations. The problems are solved by graphing the lines represented by the equations on a coordinate plane and finding their point of intersection. This identifies the solution that satisfies both equations simultaneously. The document demonstrates how to set up and solve systems of linear equations to find unknown values described in word problems.
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
Lesson 3-7 Equations of Lines in the Coordinate Plane 189
3-7
Objective To graph and write linear equations
Ski resorts often use steepness to rate the difficulty
of their hills. The steeper the hill, the higher the
difficulty rating. Below are sketches of three new hills
at a particular resort. Use each rating level only once.
Which hill gets which rating? Explain.
Difficulty Ratings
Easiest
Intermediate
Difficult
3300 ft 3000 ft 3500 ft
1190 ft 1180 ft 1150 ft
A B C
Th e Solve It involves using vertical and horizontal distances to determine steepness.
Th e steepest hill has the greatest slope. In this lesson you will explore the concept of
slope and how it relates to both the graph and the equation of a line.
Essential Understanding You can graph a line and write its equation when you
know certain facts about the line, such as its slope and a point on the line.
Equations of Lines in the
Coordinate Plane
Think back!
What did you
learn in algebra
that relates to
steepness?
Key Concept Slope
Defi nition
Th e slope m of a line is the
ratio of the vertical change
(rise) to the horizontal change
(run) between any two points.
Symbols
A line contains the
points (x1, y1) and
(x2, y2) .
m 5
rise
run 5
y2 2 y1
x2 2 x1
Diagram
(x2, y2)
(x1, y1)
O
x
y run
rise
Lesson
Vocabulary
• slope
• slope-intercept
form
• point-slope form
L
V
L
V
• s
LL
VVV
• s
hsm11gmse_NA_0307.indd 189 2/24/09 6:49:09 AM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
190 Chapter 3 Parallel and Perpendicular Lines
Finding Slopes of Lines
A What is the slope of line b?
m 5
2 2 (22)
21 2 4
5 4
25
5 245
B What is the slope of line d?
m 5
0 2 (22)
4 2 4
5 20 Undefi ned
1. Use the graph in Problem 1.
a. What is the slope of line a?
b. What is the slope of line c?
As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative,
zero, or undefi ned. Th e sign of the slope tells you whether the line rises or falls
to the right. A slope of zero tells you that the line is horizontal. An undefi ned slope
tells you that the line is vertical.
You can graph a line when you know its equation. Th e equation of a line has diff erent
forms. Two forms are shown below. Recall that the y-intercept of a line is the
y-coordinate of the point where the line crosses the y-axis.
O
y
c
b
d a
x
2
2 86
4
6
( 1, 2)
(4, 2)
(4, 0)
(5, 7)(1, 7)
(2, 3)
Positive slope
O
x
y
Negative slope
O
x
y
Zero slope
O
x
y
Undefined slope
O
x
y
Key Concept Forms of Linear Equations
Defi nition
Th e slope-intercept form of an equation of
a nonvertical line is y 5 mx 1 b, where m
is the slope and b is the y-intercept.
Symbols
Th e point-slope form of an equation of a
nonvertical line is y 2 y1 5 m(x 2 x1),
where m is the slope and (x1, y1) is a point
on the line.
y mx b
slope y-intercept
y y1 m(x x1)
slope x-coordinatey-coordinate
A
...
New approaches in linear inequalities
This lesson teaches students how to graph and solve systems of linear inequalities on a coordinate plane. It begins by reviewing how to graph single linear inequalities and shade the correct region. Students then learn that a system involves graphing two or more inequalities on the same plane. The solution region is where the shading overlaps - where all inequalities are simultaneously satisfied. Students practice graphing systems with two, three and four inequalities, and interpreting the solution region where shading coincides. The lesson concludes by challenging students to locate treasure using coordinates satisfying a given system of inequalities.
January 21, 2015
1. The document provides information on linear functions and how to determine if an equation represents a linear function. It discusses using standard form (Ax + By = C) to identify linear equations and determine intercepts.
2. The document contains examples of writing equations of lines given points and slopes in various forms. It discusses using point-slope form and converting between slope-intercept and standard form.
3. The document provides practice problems determining if graphs are functions, whether equations represent lines, finding rates of change, intercepts, and writing equations in different forms. It aims to help students work with linear functions and equations.
local_media5416891530663583326.ppt
This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.
FindingSlope.ppt
This document provides instruction on calculating and understanding slope. It defines slope as the steepness of a line and discusses how to calculate slope given two points on a line using the rise over run formula or the slope formula. It provides examples of finding the slope of lines from their graphs or given two points and discusses the slopes of horizontal and vertical lines.
Notes Day 6
1. The document provides instructions and examples for solving problems involving midpoint and distance formulas, as well as transformations in the coordinate plane. Practice problems are given for finding midpoints and distances between points, as well as homework instructions.
2. Key terms related to transformations are defined, including reflection, rotation, translation, arrow notation, and the rule for describing translations.
3. Examples are given of transformations, including reflections across lines and rotations about points. Formulas and notation for describing translations are also provided.
Math Algebra
The document provides an overview of key algebra concepts covered on the ACT exam, including expressions, equations, inequalities, functions, and quadratic equations. It discusses how to simplify and combine like terms in expressions, solve different types of equations (linear, quadratic, absolute value), factor expressions using techniques like greatest common factor and difference of squares, work with fractions and systems of equations. Example problems and step-by-step explanations are provided for many of the concepts. The document is intended as a review of essential algebra skills and strategies for tackling related questions that may appear on the ACT.
Alg II 2-3 and 2-4 Linear Functions
This document provides an overview of key concepts in Algebra II Chapter 2 on functions, equations, and graphs. It introduces the concept of slope as the ratio of vertical to horizontal change between points on a line. Students will learn to graph linear equations, write equations of lines given slope and a point, and identify parallel and perpendicular lines based on their slopes. The objectives are to graph and write equations of lines in different forms including slope-intercept, point-slope, and standard form.
April 13, 2015
This document contains information about a math class that is reviewing quadratic functions. It includes:
1. An outline of the class agenda which focuses on reviewing key concepts like how the b-value affects the parabola and completing classwork.
2. Details about grading which includes assignments, homework, tests, the final exam, and notebook checks.
3. Sample problems and class notes focused on quadratic functions, including the axis of symmetry, vertex, graphing techniques, and how changing a, b, and c values impacts the parabola.
4. Examples of completing the steps to graph quadratic functions like plotting points and reflecting over the axis of symmetry.
4 10 Notes B
This document contains homework questions and examples about solving systems of equations using substitution. It includes:
1) A race between Demitri and Yakov with distance-time graphs and questions about their speeds and when Yakov overtakes Demitri.
2) Three examples walking through the substitution method to solve systems of equations step-by-step. The examples find the intersection point of lines and solve systems algebraically.
3) Questions checking understanding of what it means for something to be a solution to a system of equations and what the solution represents.
Linear Functions Presentation
My final project that was to be a PowerPoint that could be worked on by individual students. This PowerPoint goes over linear functions.
Writing linear equations KG Math Middle School
The document provides information about graphing and writing linear equations in slope-intercept form (y=mx+b). It defines slope and y-intercept, and explains how to graph lines by using the slope and y-intercept. It also demonstrates how to write an equation of a line when given the slope and y-intercept, a point and the slope, or two points. Key steps include finding the slope using the formula (m=(y2-y1)/(x2-x1)), setting up and solving equations to find the y-intercept, and plugging the slope and y-intercept into the slope-intercept form to write the equation.
3.3 Notes B
This document provides instruction and examples for calculating distance and absolute value. It begins by asking the reader to calculate the distance between several pairs of points on a coordinate plane. It then defines absolute value as the distance between two numbers and provides examples of calculating absolute values. The document continues with more practice problems calculating absolute values and rewriting expressions using absolute value notation. It concludes by explaining how to solve equations involving absolute values and providing an example of using the Pythagorean theorem to calculate the distance between two points.
3.3 Notes B
This document provides instruction and examples for calculating distance and absolute value. It begins by asking the reader to calculate the distance between several pairs of points on a coordinate plane. It then defines absolute value as the distance between two numbers and provides examples of calculating absolute values. The document continues with more practice problems calculating absolute values and rewriting expressions using absolute value notation. It concludes by explaining how to solve equations involving absolute values and providing an example of using the Pythagorean theorem to calculate the distance between two points.
Finding slope
The document discusses slope and how to calculate it given points on a line or its graph. It provides examples of finding the slope between two points using the rise over run formula or slope formula. It explains that horizontal lines have a slope of 0 and vertical lines have undefined slope. It also gives an example of solving for an unknown value in one of the points when given the other point and slope.
Essay On Linear Function
1. The research question investigates the relationship between the force applied to one side of a cantilever beam and the maximum acceleration reached by the free end.
2. Materials used include an acrylic plastic cantilever beam, accelerometer, string, and force meter.
3. Experiments are conducted to pull the cantilever with varying forces and measure the corresponding maximum accelerations using the accelerometer.
4. Results are analyzed to understand the elastic properties of the cantilever beam based on the relationship between applied force and acceleration. Potential and kinetic energy concepts are also explored.
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Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
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Unit 1 test 2.9 notes b
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
2.8 notes a
1. The document discusses solving equations by backtracking. It begins by defining an equation and identifying true and false equations. It then discusses the concept of solutions - the values that make the equation true.
2. Examples are provided to illustrate finding solutions to equations by reversing the steps of number tricks. Backtracking involves working backwards through the operations to determine the starting value.
3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations (translations, reflections, rotations, and dilations) and provides examples of identifying each type using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.6 2.7 notes a
1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations.
2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined.
3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages. Finally, it addresses solving an equation like x^3 + 5x = 7x^2 - 5 by graphing and reflects on graphing techniques from prior lessons.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
8.7 d2 a
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
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zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex Proofs
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Paper: https://eprint.iacr.org/2023/1886
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Climate Impact of Software Testing at Nordic Testing Days
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
4 7 Notes A
- 1. Day 2: Opener Think back: Complete the following problem on a math raffle ticket. Good Luck! 1. Write the equation of the line that is parallel to x = ‐6 and passes through the point (3,10). 1
- 2. Homework Questions: 2
- 3. 3
- 4. 4
- 5. Section 4.7 Jiffy Graphs TOPIC ONE (cont.) Solve your given equation for y. Information from Equations Think back: Are these equations equivalent? How do you know? Since they are equivalent then they should all be the same line! This means they should all have the same __________, ________________, and ___________. It's Your Turn! 1. What is the slope of line l ? Complete the following 4 questions with your partner.(5 minutes) 2. Where does l cross the y‐axis? 3. Where does l cross the x‐axis? 4. Which equation for l makes it easiest to see that the point (5,3) is on the line? Explain. 5
- 6. Linear Equation Forms Point‐Slope Form (IYT # 1 & 4): • • Slope‐Intercept Form (IYT # 1 & 2): • • Standard Form (IYT # 3): • • 6
- 7. TOPIC TWO We can use the different forms of linear equations that we Writing equations of learned today to write the equation of a line in a jiffy! lines using the different forms. Given slope and through (10, ‐3) with slope 7 the given point: (Ex. #1) Step 1: Substitute the given information into point‐slope form. Step 2: Simplify to slope‐intercept form (solve for y). Given 2 points: (Ex. # 2) (0,7) and (‐4,9) Step 1: Find the slope between these 2 points. Step 2: Substitute one of the points and the slope into point‐ slope form. Step 3: Simplify to slope‐intercept form (solve for y). 7
- 8. TOPIC THREE Think back: How did we graph equations last chapter? Jiffy Graphing We are going to use the forms of linear equations to help us graph in a jiffy! Using Point‐Slope Graph y+2 = ‐3(x+1). Form: (Ex. # 3) Step 1: Plot the given point. Step 2: Use the slope to plot two more points. Step 3: Connect all three points with a line. Using Slope‐Intercept Graph y = 1.75x ‐1. Form: (Ex.#4) Step 1: Plot your y‐intercept. Step 2: Use the slope to plot two more points. Step 3: Connect all three points with a line. 8
- 9. Exit Slip: 1.) Think about how you might graph the equation of a line given to you in standard form. Write down what your method would be on a half‐sheet of paper and turn it in before you leave. Think back: What information can you easily get from standard form? OR Can you change it to an equivalent form? 2.) Graph 3x+4y = 12 using your method. 9
- 10. 10