3.5 Notes A
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This document is a lesson on slopes of lines. It defines slope as rise over run and includes examples of finding the slope of different lines using the slope formula. It discusses how to identify if lines are parallel, perpendicular, or neither based on their slopes. Specifically, parallel lines have the same slope and perpendicular lines have slopes that multiply to -1. There are also examples of graphing lines and determining if they are parallel, perpendicular, or neither based on their slopes. The document concludes with assigning homework problems on finding slopes and classifying lines.
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Engineering-drawing and power point s.ppsx
This document provides a complete solution guide for engineering drawings and technical graphics. It covers topics such as scales, engineering curves, orthographic projections, sections and developments of solids, isometric projections, and more. Specific chapters describe different types of scales like plain, diagonal, and vernier scales. Others cover technical topics like projections of points and lines, intersections of surfaces, and conversions of pictorial views. Each chapter includes definitions, explanations, examples, and practice problems with step-by-step solutions. The document aims to equip readers with the essential skills and knowledge for technical drawing applications.
Engineering graphics
This document provides a complete solution guide for engineering drawings and technical graphics. It covers topics such as scales, engineering curves, orthographic projections, sections and developments of solids, isometric projections, and more. Specific chapters describe different types of scales like plain, diagonal, and vernier scales. Others cover technical topics like projections of points and lines, intersections of surfaces, and conversions of pictorial views. Each chapter includes definitions, explanations, example problems and their solutions. The document aims to be a comprehensive reference for learning technical drawing concepts and skills.
Engineering Graphics
This document provides a complete solution guide for engineering drawings and technical graphics. It covers topics such as scales, engineering curves, orthographic projections, sections and developments of solids, isometric projections, and more. Specific chapters describe different types of scales like plain, diagonal, and vernier scales. Others cover technical topics like projections of points and lines, intersections of surfaces, and conversions of pictorial views. Each chapter includes definitions, explanations, example problems and their solutions. The document aims to be a comprehensive reference for learning technical drawing concepts and skills.
Miller indecies
- Crystallographic points, directions and planes are specified using indexing schemes like Miller indices.
- Materials can be single crystals or polycrystalline aggregates of randomly oriented grains, leading to anisotropic or isotropic properties respectively.
- A crystal's diffraction pattern in reciprocal space is determined by its real space lattice and atomic structure. The reciprocal lattice is constructed geometrically from the real lattice and maps planes in real space to points in reciprocal space.
COMPLETE-engineering-graphics PPT.ppt
This document provides an overview of various topics related to engineering graphics including scales, engineering curves, loci of points, orthographic projections, projections of points/lines/planes/solids, sections and developments, intersections of surfaces, and isometric projections. It describes the key concepts, methods, and example problems for each topic. Plain scales, diagonal scales, vernier scales, and comparative scales are introduced for measuring distances with different levels of precision. Engineering curves like ellipses, parabolas, hyperbolas, involutes, and spirals are defined along with methods for drawing tangents and normals. Orthographic projections convert between pictorial and multi-view drawings. Projections determine how points, lines, planes and
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This document provides information on various types of engineering scales and their construction and applications. It discusses plain scales, which can measure dimensions up to a single decimal place, and provides examples of their construction and use. It also covers diagonal scales, which can measure up to two decimal places, and vernier scales, which also measure up to two decimal places. Comparative scales are described for comparing different units, and scales of cords are introduced for measuring and constructing angles. Construction techniques and example problems are provided for different scale types. The document serves as a reference for understanding and applying various engineering scales.
Structural engineering ii
Structural engineering ii Dr. Iftekhar Anam
Deflection of Grids due to Combined Flexural and Torsional Deformations
http://www.uap-bd.edu/ce/anam/
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Surface modeling represents the surfaces of 3D objects and can be used to model complex shapes like vehicles, ships, and aircraft wings. There are two main types of surface modeling: parametric surfaces and implicit surfaces. Parametric surfaces use a set of equations to define the x, y, and z coordinates as functions of parameters u and v. Common parametric surface types include planes, ruled surfaces, surfaces of revolution, and tabulated cylinders. Implicit surfaces use a single polynomial equation to define the surface. Surface modeling provides more realistic representations than wireframe models and can be used for applications like finite element analysis, machining tool paths, and rendering models.
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2.2 2.3 notes a
The document describes a numeric pattern where each row contains consecutive odd integers centered around 1. It asks students to conjecture the pattern and sum of terms in each row. It also provides homework questions on conditional statements, deductive reasoning, and analyzing the truth value of related conditional statements.
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. 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.
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.
2.4 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.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
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.
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.
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3.5 Notes A
- 1. 3.5 Slopes of Lines 10.20.09 Homework Questions: 1
- 2. 3.5 Slopes of Lines 10.20.09 3.5 Slopes of Lines 2
- 3. 3.5 Slopes of Lines 10.20.09 Slope of a Line: Quick Check: Find the value of m. 1.) m= 2.)m= 3
- 4. 3.5 Slopes of Lines 10.20.09 Use the slope formula to determine the slope of each line. 3.) EF 4.)GH 4
- 5. 3.5 Slopes of Lines 10.20.09 Slope of a Line Positive Slope Undefined Slope Negative Zero Slope Slope 5
- 6. 3.5 Slopes of Lines 10.20.09 Slopes of Parallel and Perpendicular Lines: • In a coordinate plane, two nonvertical lines are parallel if and only if they have the _________ slope. Any two vertical lines are ___________. • In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is ______. Vertical and horizontal lines are ___________. 6
- 7. 3.5 Slopes of Lines 10.20.09 Determining whether lines are Parallel, Perpendicular or Neither... Graph each pair of lines. Use their slopes to determine whether they are parallel, perpendicular, or neither. 5.) UV and XY for U (0,2), V (-1,-1), X (3,1), and Y (-3,3) 6.) CD and EF for C (-1,-3), D(1,1), E (-1, 1), and F (0,3). 7
- 8. 3.5 Slopes of Lines 10.20.09 Homework: *Pg. 186 # 11-23 odd, 26-33 all (As is on Assignment Sheet) *Writing Assignment # 2 (Due Monday, 10/26) 8
- 9. 3.5 Slopes of Lines 10.20.09 *NaMmMe ThAaAtT sLoOoPpE* 9