Time in Classical and Relativistic Physics
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Analytic Geometry
Guide Study Georgia End-Of-Course Tests Georgia ANALYTIC GEOMETRY TABLE OF CONTENTS INTRODUCTION ...........................................................................................................5 HOW TO USE THE STUDY GUIDE ................................................................................6 OVERVIEW OF THE EOCT .........................................................................................8 PREPARING FOR THE EOCT ......................................................................................9 Study Skills ........................................................................................................9 Time Management .....................................................................................10 Organization ...............................................................................................10 Active Participation ...................................................................................11 Test-Taking Strategies .....................................................................................11 Suggested Strategies to Prepare for the EOCT ..........................................12 Suggested Strategies the Day before the EOCT ........................................13 Suggested Strategies the Morning of the EOCT ........................................13 Top 10 Suggested Strategies during the EOCT .........................................14 TEST CONTENT ........................................................................................................15 -
Chapter 11. Three Dimensional Analytic Geometry and Vectors
Chapter 11. Three dimensional analytic geometry and vectors. Section 11.5 Quadric surfaces. Curves in R2 : x2 y2 ellipse + =1 a2 b2 x2 y2 hyperbola − =1 a2 b2 parabola y = ax2 or x = by2 A quadric surface is the graph of a second degree equation in three variables. The most general such equation is Ax2 + By2 + Cz2 + Dxy + Exz + F yz + Gx + Hy + Iz + J =0, where A, B, C, ..., J are constants. By translation and rotation the equation can be brought into one of two standard forms Ax2 + By2 + Cz2 + J =0 or Ax2 + By2 + Iz =0 In order to sketch the graph of a quadric surface, it is useful to determine the curves of intersection of the surface with planes parallel to the coordinate planes. These curves are called traces of the surface. Ellipsoids The quadric surface with equation x2 y2 z2 + + =1 a2 b2 c2 is called an ellipsoid because all of its traces are ellipses. 2 1 x y 3 2 1 z ±1 ±2 ±3 ±1 ±2 The six intercepts of the ellipsoid are (±a, 0, 0), (0, ±b, 0), and (0, 0, ±c) and the ellipsoid lies in the box |x| ≤ a, |y| ≤ b, |z| ≤ c Since the ellipsoid involves only even powers of x, y, and z, the ellipsoid is symmetric with respect to each coordinate plane. Example 1. Find the traces of the surface 4x2 +9y2 + 36z2 = 36 1 in the planes x = k, y = k, and z = k. Identify the surface and sketch it. Hyperboloids Hyperboloid of one sheet. The quadric surface with equations x2 y2 z2 1. -
ANALYTIC GEOMETRY Revision Log
Guide Study Georgia End-Of-Course Tests Georgia ANALYTIC GEOMETRYJanuary 2014 Revision Log August 2013: Unit 7 (Applications of Probability) page 200; Key Idea #7 – text and equation were updated to denote intersection rather than union page 203; Review Example #2 Solution – union symbol has been corrected to intersection symbol in lines 3 and 4 of the solution text January 2014: Unit 1 (Similarity, Congruence, and Proofs) page 33; Review Example #2 – “Segment Addition Property” has been updated to “Segment Addition Postulate” in step 13 of the solution page 46; Practice Item #2 – text has been specified to indicate that point V lies on segment SU page 59; Practice Item #1 – art has been updated to show points on YX and YZ Unit 3 (Circles and Volume) page 74; Key Idea #17 – the reference to Key Idea #15 has been updated to Key Idea #16 page 84; Key Idea #3 – the degree symbol (°) has been removed from 360, and central angle is noted by θ instead of x in the formula and the graphic page 84; Important Tip – the word “formulas” has been corrected to “formula”, and x has been replaced by θ in the formula for arc length page 85; Key Idea #4 – the degree symbol (°) has been added to the conversion factor page 85; Key Idea #5 – text has been specified to indicate a central angle, and central angle is noted by θ instead of x page 85; Key Idea #6 – the degree symbol (°) has been removed from 360, and central angle is noted by θ instead of x in the formula and the graphic page 87; Solution Step i – the degree symbol (°) has been added to the conversion -
Pioneers in Optics: Christiaan Huygens
Downloaded from Microscopy Pioneers https://www.cambridge.org/core Pioneers in Optics: Christiaan Huygens Eric Clark From the website Molecular Expressions created by the late Michael Davidson and now maintained by Eric Clark, National Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 . IP address: [email protected] 170.106.33.22 Christiaan Huygens reliability and accuracy. The first watch using this principle (1629–1695) was finished in 1675, whereupon it was promptly presented , on Christiaan Huygens was a to his sponsor, King Louis XIV. 29 Sep 2021 at 16:11:10 brilliant Dutch mathematician, In 1681, Huygens returned to Holland where he began physicist, and astronomer who lived to construct optical lenses with extremely large focal lengths, during the seventeenth century, a which were eventually presented to the Royal Society of period sometimes referred to as the London, where they remain today. Continuing along this line Scientific Revolution. Huygens, a of work, Huygens perfected his skills in lens grinding and highly gifted theoretical and experi- subsequently invented the achromatic eyepiece that bears his , subject to the Cambridge Core terms of use, available at mental scientist, is best known name and is still in widespread use today. for his work on the theories of Huygens left Holland in 1689, and ventured to London centrifugal force, the wave theory of where he became acquainted with Sir Isaac Newton and began light, and the pendulum clock. to study Newton’s theories on classical physics. Although it At an early age, Huygens began seems Huygens was duly impressed with Newton’s work, he work in advanced mathematics was still very skeptical about any theory that did not explain by attempting to disprove several theories established by gravitation by mechanical means. -
Analytic Geometry
STATISTIC ANALYTIC GEOMETRY SESSION 3 STATISTIC SESSION 3 Session 3 Analytic Geometry Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into: Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres Point, Line, Plane and Solid A Point has no dimensions, only position A Line is one-dimensional A Plane is two dimensional (2D) A Solid is three-dimensional (3D) Plane Geometry Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper). 2D Shapes Activity: Sorting Shapes Triangles Right Angled Triangles Interactive Triangles Quadrilaterals (Rhombus, Parallelogram, etc) Rectangle, Rhombus, Square, Parallelogram, Trapezoid and Kite Interactive Quadrilaterals Shapes Freeplay Perimeter Area Area of Plane Shapes Area Calculation Tool Area of Polygon by Drawing Activity: Garden Area General Drawing Tool Polygons A Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons. Here are some more: Pentagon Pentagra m Hexagon Properties of Regular Polygons Diagonals of Polygons Interactive Polygons The Circle Circle Pi Circle Sector and Segment Circle Area by Sectors Annulus Activity: Dropping a Coin onto a Grid Circle Theorems (Advanced Topic) Symbols There are many special symbols used in Geometry. Here is a short reference for you: -
Topics in Complex Analytic Geometry
version: February 24, 2012 (revised and corrected) Topics in Complex Analytic Geometry by Janusz Adamus Lecture Notes PART II Department of Mathematics The University of Western Ontario c Copyright by Janusz Adamus (2007-2012) 2 Janusz Adamus Contents 1 Analytic tensor product and fibre product of analytic spaces 5 2 Rank and fibre dimension of analytic mappings 8 3 Vertical components and effective openness criterion 17 4 Flatness in complex analytic geometry 24 5 Auslander-type effective flatness criterion 31 This document was typeset using AMS-LATEX. Topics in Complex Analytic Geometry - Math 9607/9608 3 References [I] J. Adamus, Complex analytic geometry, Lecture notes Part I (2008). [A1] J. Adamus, Natural bound in Kwieci´nski'scriterion for flatness, Proc. Amer. Math. Soc. 130, No.11 (2002), 3165{3170. [A2] J. Adamus, Vertical components in fibre powers of analytic spaces, J. Algebra 272 (2004), no. 1, 394{403. [A3] J. Adamus, Vertical components and flatness of Nash mappings, J. Pure Appl. Algebra 193 (2004), 1{9. [A4] J. Adamus, Flatness testing and torsion freeness of analytic tensor powers, J. Algebra 289 (2005), no. 1, 148{160. [ABM1] J. Adamus, E. Bierstone, P. D. Milman, Uniform linear bound in Chevalley's lemma, Canad. J. Math. 60 (2008), no.4, 721{733. [ABM2] J. Adamus, E. Bierstone, P. D. Milman, Geometric Auslander criterion for flatness, to appear in Amer. J. Math. [ABM3] J. Adamus, E. Bierstone, P. D. Milman, Geometric Auslander criterion for openness of an algebraic morphism, preprint (arXiv:1006.1872v1). [Au] M. Auslander, Modules over unramified regular local rings, Illinois J. -
Chapter 1: Analytic Geometry
1 Analytic Geometry Much of the mathematics in this chapter will be review for you. However, the examples will be oriented toward applications and so will take some thought. In the (x,y) coordinate system we normally write the x-axis horizontally, with positive numbers to the right of the origin, and the y-axis vertically, with positive numbers above the origin. That is, unless stated otherwise, we take “rightward” to be the positive x- direction and “upward” to be the positive y-direction. In a purely mathematical situation, we normally choose the same scale for the x- and y-axes. For example, the line joining the origin to the point (a,a) makes an angle of 45◦ with the x-axis (and also with the y-axis). In applications, often letters other than x and y are used, and often different scales are chosen in the horizontal and vertical directions. For example, suppose you drop something from a window, and you want to study how its height above the ground changes from second to second. It is natural to let the letter t denote the time (the number of seconds since the object was released) and to let the letter h denote the height. For each t (say, at one-second intervals) you have a corresponding height h. This information can be tabulated, and then plotted on the (t, h) coordinate plane, as shown in figure 1.0.1. We use the word “quadrant” for each of the four regions into which the plane is divided by the axes: the first quadrant is where points have both coordinates positive, or the “northeast” portion of the plot, and the second, third, and fourth quadrants are counted off counterclockwise, so the second quadrant is the northwest, the third is the southwest, and the fourth is the southeast. -
A New Earth Study Guide.Pdf
A New Earth Study Guide Week 1 The consciousness that says ‘I am’ is not the consciousness that thinks. —Jean-Paul Sartre Affi rmation: "Through the guidance and wisdom of Spirit, I am being transformed by the renewing of my mind. All obstacles and emotions are stepping stones to the realization and appreciation of my sacred humanness." Study Questions – A New Earth (Review chapters 1 & 2, pp 1-58) Chapter 1: The Flowering of Human Consciousness Refl ect: Eckhart Tolle uses the image of the fi rst fl ower to begin his discussion of the transformation of consciousness. In your transformation, is this symbolism important to you? Describe. The two core insights of early religion are: 1) the normal state of human consciousness is dysfunctional (the Hindu call it maya – the veil of delusion) and 2) the opportunity for transformation is also in human consciousness (the Hindu call this enlightenment) (p. 8-9). What in your recent experience points to each of these insights? “To recognize one’s own insanity is, of course, the arising of sanity, the beginning of healing and transcendence” (p. 14). To what extent and in what circumstances (that you’re willing to discuss) does this statement apply to you? Religion is derived from the Latin word religare, meaning “to bind.” What, in your religious experience, have you been bound to? Stretching your imagination a bit, what could the word have pointed to in its original context? Spirit is derived from the Latin word spiritus, breath, and spirare, to blow. Aside from the allusion to hot air, how does this word pertain to your transformation? Do you consider yourself to be “spiritual” or “religious”? What examples of practices or beliefs can you give to illustrate? How does this passage from Revelation 21:1-4 relate to your transformation? Tease out as much of the symbolism as you can. -
Global History and the Present Time
Global History and the Present Time Wolf Schäfer There are three times: a present time of past things; a present time of present things; and a present time of future things. St. Augustine1 It makes sense to think that the present time is the container of past, present, and future things. Of course, the three branches of the present time are heavily inter- twined. Let me illustrate this with the following story. A few journalists, their minds wrapped around present things, report the clash of some politicians who are taking opposite sides in a struggle about future things. The politicians argue from histori- cal precedent, which was provided by historians. The historians have written about past things in a number of different ways. This gets out into the evening news and thus into the minds of people who are now beginning to discuss past, present, and future things. The people’s discussion returns as feedback to the journalists, politi- cians, and historians, which starts the next round and adds more twists to the en- tangled branches of the present time. I conclude that our (hi)story has no real exit doors into “the past” or “the future” but a great many mirror windows in each hu- man mind reflecting spectra of actual pasts and potential futures, all imagined in the present time. The complexity of the present (any given present) is such that no- body can hope to set the historical present straight for everybody. Yet this does not mean that a scientific exploration of history is impossible. History has a proven and robust scientific method. -
Outlook Calendar and Time Management Tips
Outlook Calendar and Time Management Tips: Setting up and maintaining your Outlook calendar is an easy way to manage your busy schedule and daily activities. Outlook calendar is great because you can sync it to your mobile and other devices, which you can access no matter where you are. You can also set up reminders to appear on your phone to remind you when and where you need to be. When setting up your Outlook calendar initially, it is recommented to do so on a computer so you can have access to more options (like color-coding, repeating appointments, etc.). You will start with a blank template, as shown below: Start with the basics – put in your formation, and your meal breaks (remember, your brain and body need fuel!). Then you can start putting in your class schedule with the class name, times and location. Be sure when scheduling events that you select the “Recurrence” option and specify what days you want the event to repeat, so it is on your calendar every week! After inputting your class schedule, take the opportunity to schedule your homework and study schedule into your week! Be sure to use the study time ratio: For each 1 unit, you should be studying 2-3 hours per week. (That means for a 3 unit class, you should be allocating 6-9 hours of study time per week. For a more difficult class, such as Calc I, start with 3 hours per unit. Study time includes homework, tutoring, paper writing and subject review.) If you’d like to add more to your calendar, feel free! Adding activites you like to do routinely, like working out, or Friday dinner with friends, helps motivate you to complete other tasks in the day so that you are free to go to these activities. -
Analytic Geometry
INTRODUCTION TO ANALYTIC GEOMETRY BY PEECEY R SMITH, PH.D. N PROFESSOR OF MATHEMATICS IN THE SHEFFIELD SCIENTIFIC SCHOOL YALE UNIVERSITY AND AKTHUB SULLIVAN GALE, PH.D. ASSISTANT PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF ROCHESTER GINN & COMPANY BOSTON NEW YORK CHICAGO LONDON COPYRIGHT, 1904, 1905, BY ARTHUR SULLIVAN GALE ALL BIGHTS RESERVED 65.8 GINN & COMPANY PRO- PRIETORS BOSTON U.S.A. PEE FACE In preparing this volume the authors have endeavored to write a drill book for beginners which presents, in a manner conform- ing with modern ideas, the fundamental concepts of the subject. The subject-matter is slightly more than the minimum required for the calculus, but only as much more as is necessary to permit of some choice on the part of the teacher. It is believed that the text is complete for students finishing their study of mathematics with a course in Analytic Geometry. The authors have intentionally avoided giving the book the form of a treatise on conic sections. Conic sections naturally appear, but chiefly as illustrative of general analytic methods. Attention is called to the method of treatment. The subject is developed after the Euclidean method of definition and theorem, without, however, adhering to formal presentation. The advan- tage is obvious, for the student is made sure of the exact nature of each acquisition. Again, each method is summarized in a rule stated in consecutive steps. This is a gain in clearness. Many illustrative examples are worked out in the text. Emphasis has everywhere been put upon the analytic side, that is, the student is taught to start from the equation. -
The Best Time to Market Sheep and Goats by Anthony Carver, Extension Agent – Grainger County UT Extension
The Best Time to Market Sheep and Goats By Anthony Carver, Extension Agent – Grainger County UT Extension Any producer of any product always wants the best price they can get. Sheep and goat producers are the exact same way. To really understand the demand and supply economics of sheep and goats, one must first understand the large groups purchasing them. The main purchasers for sheep and goats are ethnic groups. The purchasers recognize different holidays and feast days than most Tennessee producers. This is the most important factor to understand in marketing sheep and goats. Just like all holidays, the demand for certain foods go up. An example would be Thanksgiving. Thanksgiving usually means having a turkey on the table. The same can be said for the Eid-al-Fitr or Eid-al-Adha only with goat and sheep. It’s not only important to know the different holidays that the ethnic groups recognize, but to understand when they are held. Now, it gets complicated. Most of the holidays are not on our calendar year, but follow the lunar calendar. This means the holiday is not the same days year after year. It will be critical to look up the dates each year for the ethnic holidays. Here are some search words and websites to help: Interfaith Calendar - http://www.interfaithcalendar.org/index.htm Cornell University Sheep and Goat Marketing - http://sheepgoatmarketing.info/calendar.php North Carolina State University MEAT GOAT NOTES - https://rowan.ces.ncsu.edu/wp-content/uploads/2014/04/Ethnic-Holidays-2014-2018.pdf?fwd=no Some sheep and goat producers have heard of Ramadan (a Muslim and Somalis holiday).