3002 a more with parrallel lines and anglesupdated 10 22-13
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1. If x = 1 and y = 2008, the value of 1/x + 1/y is 105.85. 2. The document provides instructions for homework to be placed on the corner of a desk. It also contains objectives and a two-column proof regarding parallel lines cut by a transversal.
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사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
Maths activity
The document provides the 100m race times for two classes and asks five questions about analyzing and comparing the results between the classes. It lists the individual times for each student in each class, and gives the answers to the five questions, including: the average time for each class, which class was slower/faster, the range of times for each class, and the mode time for each class.
Proving quads are parralelograms
The document contains notes from a geometry drill on identifying parallelograms and determining values of x and y in parallelogram figures. It lists homework answers and a classwork assignment to identify parallelograms from figures and state the relevant definition or theorem, as well as an assignment to complete 15 problems showing work.
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
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사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
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사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
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사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
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사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
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사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
사설토토 사설토토 ＜＆＆＞∃‰∩kid85⊇∬△ ＜＆＆＞사설토토 사설토토
Linear approximations and_differentials
The document discusses linear approximations and differentials. It explains that a linear approximation uses the tangent line at a point to approximate nearby values of a function. The linearization of a function f at a point a is the linear function L(x) = f(a) + f'(a)(x - a). Several examples are provided of finding the linearization of functions and using it to approximate values. Differentials are also introduced, where dy represents the change along the tangent line and ∆y represents the actual change in the function.
2d 3d animation and Digital services from Vinformax and Creantt
This document summarizes the services of a creative company called Aviformax. It has production hubs in Stockholm, the US, UK and India. The company provides creative and visual design, pre-production, production and post-production services. It helps clients with 2D and 3D motion graphics, product visualization, visual branding and digital signage solutions. The document highlights the advantages of digital signage for branding, finance, operations and technical aspects. It also describes the company's content management system and data analytics dashboard tools.
Math project
1) The document provides steps to find the coordinates of the circumcenter of a triangle with vertices A(-4,0), B(2,6), and C(8,-4).
2) It finds the equations of the perpendicular bisectors of each side by calculating the midpoints and slopes to get the equations.
3) The intersections of the three perpendicular bisectors are calculated to find the circumcenter, which is determined to be (2.5,-0.5).
Minkowski Sum on 2D geometry
The document discusses the Minkowski sum, which is an operation that combines two sets in 2D geometry by translating one set along the border of the other. It provides examples of applying the Minkowski sum to polygons and discs. The Minkowski sum has applications in motion planning to determine if a moving object will collide with obstacles. It can be computed for convex polygons by taking every vertex combination, and for general polygons by decomposition or convolution methods.
Congruent figures 2013
The document provides information about congruent triangles:
- Two triangles are congruent if their corresponding sides are congruent and they have the same shape and size.
- Examples are provided to demonstrate using properties of congruent triangles to find missing angle measures and prove triangles are congruent by showing corresponding parts are equal.
- One example proves two triangles are congruent by showing bisectors of angles bisect the opposite sides, making corresponding parts congruent.
114333628 irisan-kerucut
The document discusses properties of parabolas, including their definition as the set of points equidistant from a focus point and directrix line. It presents the standard equation for a par
Power series
A power series is an infinite series of the form Σcixi or Σci(x-a)i, where the cis are constants. It represents a "polynomial" with infinitely many terms that can be used to expand functions. Common power series include the Taylor series expansions of exponential, logarithmic, and other important functions. Power series are very useful for certain mathematical calculations.
Deductivereasoning and bicond and algebraic proofs
1. The document discusses biconditional statements, conditional statements, and using deductive reasoning in geometry. It provides examples of identifying conditionals within biconditionals, writing definitions as biconditionals, and solving equations with justification in both algebra and geometry.
2. Key concepts covered include using properties of equality to write algebraic proofs, properties of congruence corresponding to properties of equality, and identifying properties of equality and congruence that justify statements.
3. Examples are provided of solving equations algebraically and geometrically with justification for each step, identifying conditionals within biconditionals, and writing definitions as biconditionals.
Symmetry,rotation, reflection,translation
The document discusses different types of symmetry including lines of symmetry, reflection, rotation, and translation. It provides examples of these symmetries using shapes like hearts, flags, polygons and math symbols. Regular polygons are noted to have multiple lines of symmetry and there is a pattern to how many lines different regular polygons will have.
Local linear approximation
The document discusses local linear approximations, which provide a linear function that closely approximates a given non-linear function near a specific point. It defines the local linear approximation at a point x0 as f(x0) + f'(x0)(x - x0). Graphs and examples are provided to illustrate how the local linear approximation can be used to estimate function values close to x0. The concept of differentials is also introduced to estimate small changes in a function using its derivative. Examples demonstrate using differentials to approximate changes and estimate errors in computations involving measured values.
Transformations of functions
The document discusses transformations in geometry. It defines a geometric transformation as a bijective mapping between two geometries that maps points to points and lines to lines. Reflections, rotations, and translations are provided as examples of geometric transformations in Euclidean plane geometry. It is shown that reflections, rotations, and translations are isometries that preserve distance, angle measure, and area. The composition of transformations is also discussed, and it is shown that the composition of isometries is again an isometry.
2002 more with transformations
The document discusses reflections, translations, and rotations of geometric figures. It provides examples of reflecting a triangle across the x-axis, y-axis, and line y=x. It then discusses identifying reflections and translations from diagrams. Examples are given of translating a figure along a vector in the coordinate plane and rotating a triangle 180 degrees about the origin.
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2d 3d animation and Digital services from Vinformax and Creantt
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Deductivereasoning and bicond and algebraic proofs
Deductivereasoning and bicond and algebraic proofs
Similar to 3002 a more with parrallel lines and anglesupdated 10 22-13
8.1 angles 2
This document contains lesson materials on lines and angles including:
- Solving two equations involving variables w and v
- Vocabulary terms related to lines and angles
- Identifying different angle relationships (corresponding angles, interior angles, etc.) when lines are cut by a transversal
- Worked examples of finding missing angle measures using properties of parallel lines
Obj. 8 Classifying Angles and Pairs of Angles
The student will be able to (I can):
Correctly name an angle
Classify angles as acute, right, or obtuse
Identify
linear pairs
vertical angles
complementary angles
supplementary angles
and set up and solve equations.
angles formed when two parallel lines are cut by a transversal.ppt
When two parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are equal, as are alternate interior angles and alternate exterior angles. If corresponding angles are equal when two lines are cut by a transversal, then the lines are parallel. Similarly, if alternate interior angles are equal, then the lines must be parallel. Understanding the angle relationships that result when parallel lines are cut by a transversal allows one to prove whether lines are parallel or determine missing angle measures.
Module 3 geometric relations
This module discusses geometric relationships involving angles formed when parallel lines are cut by a transversal. It covers identifying corresponding angles, alternate interior angles, alternate exterior angles, and angles on the same side of the transversal. Relationships between these angles are that corresponding angles and alternate interior angles are congruent, and angles on the same side of the transversal are supplementary. Examples are provided to demonstrate solving for unknown angle measures using these relationships.
LINES AND ANGLES.pptx
Alternate interior angles are congruent
3. 1 5
4.l m
1. Given
2. Vertical Angles Thm
3. Transitive Property of Congruence
4. Converse of Alternate Interior Angles Theorem
Angles formed by parallel lines cut by transversal
If parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent. Interior angles and exterior angles on the same side of the transversal are supplementary. The document provides examples of angle measurements that illustrate these properties and includes practice problems asking to determine angle measures using these relationships.
UCSD NANO106 - 08 - Principal Directions and Representation Quadrics
UCSD NANO106 - 08 - Principal Directions and Representation QuadricsUniversity of California, San Diego
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.Torsion_2.pdf
The document discusses torsion and torsional deformation of circular shafts. It defines torsion as a moment that twists a member about its longitudinal axis. For a circular shaft under pure torsion, the angle of twist is linearly proportional to the distance along the shaft. The maximum shear stress occurs at the outer surface of the shaft and is calculated using the torsion formula. Non-uniform torsion is analyzed by dividing the shaft into segments or using differential elements and integrating along the length. The document also provides examples of solving for shear stress and required shaft diameter given applied torques.
Geometry 201 unit 3.4
This document discusses parallel and perpendicular lines. It begins with examples of finding distances from points to lines and using properties of perpendicular lines to prove statements. It explains that the perpendicular bisector of a segment is a line perpendicular to the segment at its midpoint. It also explains that the shortest distance from a point to a line is the perpendicular segment from the point to the line. Several examples are provided of using properties of parallel and perpendicular lines to solve problems and write two-column proofs. Key terms like perpendicular bisector are defined.
TEMP COEFF OF RESISTANCE 01.pptx
This document describes how to determine the temperature coefficient of resistance using a Carey Foster bridge. Key steps include:
1. Calibrating the bridge to determine the resistance per unit length of the bridge wire by measuring balancing lengths with known resistors.
2. Measuring the resistance of an unknown resistor at different temperatures by determining balancing lengths and calculating resistance using the resistance per unit length.
3. Plotting resistance versus temperature and determining the slope, which is equal to the temperature coefficient of resistance.
Precautions like using keys and gently contacting the jockey are described to minimize errors.
Chapter 5 unit f 001
This document provides definitions, examples, and practice problems related to perpendicular bisectors and angle bisectors. It begins by defining perpendicular bisectors as the locus of points equidistant from the endpoints of a segment. Angle bisectors are defined as the locus of points equidistant from the sides of an angle. Examples show applying theorems about perpendicular and angle bisectors to find missing measures. The document concludes with an example writing an equation for a perpendicular bisector in point-slope form.
Chapter 5 unit f 001
This document contains a geometry lesson on perpendicular bisectors and angle bisectors. It begins with definitions of perpendicular bisectors and angle bisectors. It then provides examples of using theorems about perpendicular bisectors and angle bisectors to find unknown measures in geometric figures. It also gives examples of writing equations of perpendicular bisectors and angle bisectors in the coordinate plane. The document aims to prove and apply theorems about perpendicular bisectors and angle bisectors.
Chapter 5 unit f 001
This document contains a geometry lesson on perpendicular bisectors and angle bisectors. It begins with definitions of perpendicular bisectors and angle bisectors. It then provides examples of using theorems about perpendicular bisectors and angle bisectors to find unknown measures in geometric figures. It also gives examples of writing equations of perpendicular bisectors and angle bisectors in the coordinate plane. The document aims to prove and apply theorems about perpendicular bisectors and angle bisectors.
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
This document covers phasors, complex numbers, and their application to representing alternating current (AC) signals. It defines phasors as rotating vectors used to represent sinusoids, and complex numbers as numbers with real and imaginary parts that allow representing phasors. The document explains how to convert between polar and rectangular complex number forms, and how to perform operations like addition, subtraction, multiplication and division on complex numbers. It then discusses using phasors to model AC voltages and currents by transforming them into the frequency domain using complex numbers. Finally, it covers topics like phase difference between waveforms and using phasors to understand phase relationships between AC signals.
Q1Perform the two basic operations of multiplication and divisio.docx
Q1
Perform the two basic operations of multiplication and division to a complex number in both rectangular and polar form, to demonstrate the different techniques.
· Dividing complex numbers in rectangular and polar forms.
· Converting complex numbers between polar and rectangular forms and vice versa.
Q2
Calculate the mean, standard deviation and variance for a set of ungrouped data
· Completing a tabular approach to processing ungrouped data.
Q3
Calculate the mean, standard deviation and variance for a set of grouped data
· Completing a tabular approach to processing grouped data having selected an appropriate group size.
Q4
Sketch the graph of a sinusoidal trig function and use it to explain and describe amplitude, period and frequency.
· Calculate various features and coordinates of a waveform and sketch a plot accordingly.
· Explain basic elements of a waveform.
Q5
Use two of the compound angle formulae and verify their results.
· Simplify trigonometric terms and calculate complete values using compound formulae.
Q6
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules
· Use the chain, product and quotient rule to solve given differentiation tasks.
Q7
Use integral calculus to solve two simple engineering problems involving the definite and indefinite integral.
· Complete 3 tasks; one to practise integration with no definite integrals, the second to use definite integrals, the third to plot a graph and identify the area that relates to the definite integrals with a calculated answer for the area within such.
Q8
Use the laws of logarithms to reduce an engineering law of the type y = axn to a straight line form, then using logarithmic graph paper, plot the graph and obtain the values for the constants a and n.
· See Task.
Q9
Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form
· See Task.
Q10
Use differential calculus to find the maximum/minimum for an engineering problem.
· See Task.
Q11
Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.
· See Task.
Q12
Use numerical integration and integral calculus to analyse the results of a complex engineering problem
· See Task.
Level of Detail in
Solution
s: Need to show work leading to final answer
Need
Question 1
(a) Find:
(4 + i2)
(1 + i3)
Use the rules for multiplication and division of complex numbers in rectangular form.
(b) Convert the answer in rectangular form to polar form
(c) Repeat Q1a by first converting the complex numbers to polar form and then using the rules for multiplication and division of complex numbers in polar form.
(d) Convert the answer in polar form to rectangular form.
Question 2
The following data within the working area consists of measurements of resistor values from a producti ...
RESISTENCIA DE MATERIALES
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2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
3) The procedure for drawing shear force and bending moment diagrams involves first calculating support reactions, then plotting the shear diagram with slope equal to loading, and finally the moment diagram with slope equal to shear.
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1) Shear force and bending moment diagrams show the variation of shear force V and bending moment M over the length of a beam, which is necessary for design analysis.
2) The maximum bending moment is the primary consideration in design, and its value and position must be determined.
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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...
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3002 a more with parrallel lines and anglesupdated 10 22-13
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- 7. Proof Statement Reason 1. Transversal t cuts l & n; l t; l // n 2. m 1 90 1. Given 2. Def of perpendicular lines 3. Corresponding Angle postulate 4. Substitution prop. Of = 5. Def of perpendicular lines 3. m 1 m 2 4. m 2 90 5. t n