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https://inks.tedunangst.com/l/4701
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math
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Inside the 8086 processor, tiny charge pumps create a negative voltage
You might wonder how a charge pump can turn a positive voltage into a negative voltage. The trick is a “flying” capacitor, as shown below. On the left, the capacitor is charged to 5 volts. Now, disconnect the capacitor and connect the positive side to ground. The capacitor still has its 5-volt charge, so now the low side must be at -5 volts. By rapidly switching the capacitor between the two states, the charge pump produces a negative voltage.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296819971.86/warc/CC-MAIN-20240424205851-20240424235851-00703.warc.gz
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CC-MAIN-2024-18
| 522 | 2 |
https://brainmass.com/business/purchases-inventory-and-cogs/savannah-textiles-company-wip-inventory-547198
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math
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How do I calculate Cost of the September 30 Work-in-process inventory in the Weaving department? I am providing all of the information I have.
Savannah Textiles Company manufactures a variety of natural fabrics for the clothing industry. The following data pertain to the Weaving Department for the month of September.
Equivalent units of direct material (weighted-average method) 55,000
Equivalent units of conversion (weighted-average method) 45,000
Units completed and transferred out during September 42,000
The cost data for September are as follows:
Work in process, September 1
Direct material $ 105,240
Costs incurred during September
Direct material $ 158,760
There were 15,000 units in process in the Weaving Department on September 1 (100% complete as to direct material and 40% complete as to conversion).
Compute each of the following amounts using weighted-average process costing.
1. Cost of goods completed and transferred out of the Weaving Department.
2. Cost of the September 30 work-in-process inventory in the Weaving Department.
Your tutorial is attached. The cost assigned should match the cost ...
Your tutorial is attached. The cost assigned should match the cost incurred. In suspect some part of the data, either the equivalent units or the units transferred is wrong. But the spreadsheet model will update if a data input is changed so it is a template that will help with future problems.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540529955.67/warc/CC-MAIN-20191211045724-20191211073724-00498.warc.gz
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CC-MAIN-2019-51
| 1,417 | 16 |
http://scheduler.insomniac.com/articles/coordinate-geometry-worksheets.html
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math
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Epub # Coordinate Geometry Worksheets
This worksheet is a great resources for the 5th. 100% Money Back - Learn & Practice by Solving Problems - 75,000+ Students!. Areas and Coordinate Geometry Worksheet Five Pack - Math. All Worksheets 187 Coordinate Geometry Worksheets Year 10.
199.61 KB - coordinate...worksheets.pdf
Math Worksheets Graph Paper Coordinate Plane Graph Paper Graph Paper: Coordinate Plane Graph Paper. Cartesian format standard and metric graph paper in various sizes. Coordinate Geometry Printable worksheets and online practice tests on Coordinate Geometry for Grade 9. Circles in coordinate geometry worksheet. Class 10 Maths Notes for CBSE,NCERT Solutions,10th maths Worksheets. CBSE Class 10 Mathematics Worksheet - Coordinate Geometry (1).
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865928.45/warc/CC-MAIN-20180524053902-20180524073902-00115.warc.gz
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CC-MAIN-2018-22
| 763 | 4 |
https://search.ieice.org/bin/summary.php?id=e63-e_10_693&category=E&lang=&year=1980&abst=
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math
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For Full-Text PDF, please login, if you are a member of IEICE,|
or go to Pay Per View on menu list, if you are a nonmember of IEICE.
Algorithms for Computing the Maximum Number of Prime Implicants of Symmetric Boolean Functions
IEICE TRANSACTIONS (1976-1990)
Publication Date: 1980/10/25
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Full Text: PDF>>
A fast algorithm for computing the maximum number of prime implicants of n-variable symmetric Boolean function is described. A dynamic programming technique is used in the algorithm. The total logarithmic computing time cost and the total uniform computing time cost by a random access machine are O (n4) and O (n3), respectively. The algorithm can be implemented faster by a parallel computer. The corresponding computing time costs by a parallel computer with O (n) processors are O (n3) and O (n2), respectively.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154432.2/warc/CC-MAIN-20210803061431-20210803091431-00196.warc.gz
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CC-MAIN-2021-31
| 868 | 9 |
https://fccmansfield.org/pdf-free-download/30668-financial-mathematics-pdf-free-download-960-809.php
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math
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Financial Mathematics - Theory and Problems for Multi-period Models | Andrea Pascucci | SpringerEngineering Mathematics: YouTube Workbook. Essential Engineering Mathematics. Mathematics for Computer Scientists. Mathematics Fundamentals. Introduction to Complex Numbers.
Matric revision: Maths: Financial Mathematics (5/6): Present value
An undergraduate Introduction to Financial Mathematics by J Robert Buchanan
To do this one first generates two uniformly distributed random variables u1 and u2 in the interval 0, 1. Recommendations on finanial classes! Choose your Category. Advanced stochastic processes: Part I.
This will make your library easier to use and maintain. Note that there is no agreement on the precise definition of percentile. Get Matthematics Book Here. Financial Mathematics by C.
Free Pdf Books
Intermediate Maths for Chemists. Declaring and defining functions. Throughout this chapter we will assume that you have opened FMLib8 in your development environment so you can view the code and experiment with it. What have we gained. However, it is worth keeping in mind that a good software developer will be willing to use multiple interacting programs and multiple languages to achieve their goals.
Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage. With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view. Academics, researchers, and practitioners in quantitative finance, financial risk management, economics and other areas of math, science and engineering. Chapter 1.
Overloading functions. Recommendations on writing classes. Understanding the example code. Pointers to text.
Configuring the compiler. So a vector is an object because it contains the data of a vector and helpful functions like size. A complete example. The constructor and destructor of Matrix.Transition from discrete to continuous time 2. Buy eBook. Write small simple applications that communicate through text files. The constructor and destructor of Matrix.
Published Date: 25th January. The architecture of the World Wide Web. Series Editors M. In the above questions, have you passed vectors and strings by reference.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00022.warc.gz
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CC-MAIN-2022-21
| 2,675 | 11 |
https://www.varsitytutors.com/shorewood-il-physics-tutoring
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math
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Recent Tutoring Session Reviews
"In algebra: We reviewed homework problems about division of high order polynomials. The student had some issues with setting up the equation and carrying down 0's when a variable is missing in the order. After showing how to bring them down/ignore them, she was able to keep better track of her solution. She was able to figure out how to divide the factors into the HOP very well. In physics: We reviewed energy and its conservation using examples of various objects in motion and determining what energy they had at different stages. She had some trouble understanding the ratios in an object tossed in an arc, but we worked through each stage to show how energy changes. I used a free fall example to determine total energy, potential energy and kinetic energy at different stages of descent and the student was able to solve for the object's speed; she was also able to explain how the speed and energies were related."
"Covered torque, circular motion, gravitational motion, and gravitational forces. The student didn't have much trouble with any of the topics. I tried to emphasize the fundamentals so he could apply that knowledge to any problem. I think he'll do great on his upcoming quiz."
"The student and I discussed some concepts from basic kinematics. We did some of her homework problems that involved projectile motion. She said she felt that her book didn't provide enough worked examples, so I suggested to her a book that has more worked examples."
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170864.16/warc/CC-MAIN-20170219104610-00357-ip-10-171-10-108.ec2.internal.warc.gz
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| 1,500 | 4 |
https://johngribbinscience.wordpress.com/2013/05/
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math
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The people who put the geometry into relativity
Just how clever was Albert Einstein? The key feature of Einstein’s general theory of relativity is the idea of bent spacetime. But Einstein was neither the originator of the idea of spacetime geometry, nor the first to conceive of space being bent
ALBERT EINSTEIN first presented his general theory of relativity to the Prussian Academy of Sciences in Berlin in November 1915. But he was about ten years later than he should have been in coming up with the idea. What took him so long?
The easy way to understand Einstein’s two theories of relativity is in terms of geometry. Space and time, we learn, are part of one four- dimensional entity, spacetime. The special theory of relativity, which deals with uniform motions at constant velocities, can be explained in terms of the geometry of a flat, four-dimensional surface. The equations of the special theory that, for example, describe such curious phenomena as time dilation and the way moving objects shrink are in essence the familiar equation of Pythagoras’ theorem, extended to four dimensions, and with the minor subtlety that the time dimension is measured in a negative direction. Once you have grasped this, it is easy to understand Einstein’s general theory of relativity, which is a theory of gravity and accelerations. What we are used to thinking of as forces caused by the presence of lumps of matter in the Universe (like the Sun) are due to distortions in the fabric of spacetime. The Sun, for example, makes a dent in the geometry of spacetime, and the orbit of the Earth around the Sun is a result of trying to follow the shortest possible path (a geodesic) through curved spacetime. Of course, you need a few equations if you want to work out details of the orbit. But that can be left to the mathematicians. The physics is disarmingly simple and straightforward, and this simplicity is often represented as an example of Einstein’s “unique genius”.
Only, none of this straightforward simplicity came from Einstein. Take the special theory first. When Einstein presented this to the world in 1905, it was a mathematical theory, based on equations. It didn’t make a huge impact at the time, and it was several years before the science community at large really began to sit up and take notice. They did so, in fact, only after Hermann Minkowski gave a lecture in Cologne in 1908. It was this lecture, published in 1909 shortly after Minkowski died, that first presented the ideas of the special theory in terms of spacetime geometry. His opening words indicate the power of the new insight:
“The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade into mere shadows, and only a kind of union of the two will preserve an independent reality.”
Minkowski’s enormous simplification of the special theory had a huge impact. It is no coincidence that Einstein received his first honorary doctorate, from the University of Geneva, in July 1909, nor that he was first proposed for the Nobel Prize in physics a year later. There is a delicious irony in all this. Minkowski had, in fact, been one of Einstein’s teachers at the Zrich polytechnic at the end of the nineteenth century. Just a few years before coming up with the special theory, Einstein had been described by Minkowski as a “lazy dog”, who “never bothered about mathematics at all”. The lazy dog himself was not, at first, impressed by the geometrization of relativity, and took some time to appreciate its significance. Never having bothered much with maths at the polytechnic, he was remarkably ignorant about one of the key mathematical developments of the nineteenth century, and he only began to move towards the notion of curved spacetime when prodded that way by his friend and colleague Marcel Grossman. This wasn’t the first time Einstein had enlisted Grossman’s help. Grossman had been an exact contemporary of Einstein at the polytechnic, but a much more assiduous student who not only attended the lectures (unlike Einstein) but kept detailed notes. It was those notes that Einstein used in a desperate bout of last-minute cramming which enabled him to scrape through his final examinations at the polytechnic in 1900.
What Grossman knew, but Einstein didn’t until Grossman told him, in 1912, was that there is more to geometry (even multi-dimensional geometry) than good old Euclidean “flat” geometry.
Euclidean geometry is the kind we encounter at school, where the angles of a triangle add up to exactly 180o, parallel lines never meet, and so on. The first person to go beyond Euclid and to appreciate the significance of what he was doing was the German Karl Gauss, who was born in 1777 and had completed all of his great mathematical discoveries by 1799. But because he didn’t bother to publish many of his ideas, non-Euclidean geometry was independently discovered by the Russian Nikolai Ivanovitch Lobachevsky, who was the first to publish a description of such geometry in 1829, and by a Hungarian, Janos Bolyai. They all hit on essentially the same kind of “new” geometry, which applies on what is known as a “hyperbolic” surface, which is shaped like a saddle, or a mountain pass. On such a curved surface, the angles of a triangle always add up to less than 180o, and it is possible to draw a straight line and mark a point, not on that line, through which you can draw many more lines, none of which crosses the first line and all of which are, therefore, parallel to it.
But it was Bernhard Riemann, a pupil of Gauss, who put the notion of non-Euclidean geometry on a comprehensive basis in the 1850s, and who realised the possibility of yet another variation on the theme, the geometry that applies on the closed surface of a sphere (including the surface of the Earth). In spherical geometry, the angles of a triangle always add up to more than 180o, and although all “lines of longitude” cross the equator at right angles, and must therefore all be parallel to one another, they all cross each other at the poles.
Riemann, who had been born in 1826, entered Gottingen University at the age of twenty, and learned his mathematics initially from Gauss, who had turned 70 by the time Riemann moved on to Berlin in 1847, where he studied for two years before returning to Gottingen. He was awarded his doctorate in 1851, and worked for a time as an assistant to the physicist Wilhelm Weber, an electrical pioneer whose studies helped to establish the link between light and electrical phenomena, partially setting the scene for James Clerk Maxwell’s theory of electromagnetism.
The accepted way for a young academic like Riemann to make his way in a German university in those days was to seek an appointment as a kind of lecturer known as a “Privatdozent”, whose income would come from the fees paid by students who voluntarily chose to take his course (an idea which it might be interesting to revive today). In order to demonstrate his suitability for such an appointment, the applicant had to present a lecture to the faculty of the university, and the rules required the applicant to offer three possible topics for the lecture, from which the professors would choose the one they would like to hear. It was also a tradition, though, that although three topics had to be offered, the professors always chose one of the first two on the list. The story is that when Riemann presented his list for approval, it was headed by two topics which he had already thoroughly prepared, while the third, almost an afterthought, concerned the concepts that underpin geometry.
Riemann was certainly interested in geometry, but apparently he had not prepared anything along these lines at all, never expecting the topic to be chosen. But Gauss, still a dominating force in the University of Gottingen even in his seventies, found the third item on Riemann’s list irresistible, whatever convention might dictate, and the 27 year old would-be Privatdozent learned to his surprise that that was what he would have to lecture on to win his spurs.
Perhaps partly under the strain of having to give a talk he had not prepared and on which his career depended, Riemann fell ill, missed the date set for the talk, and did not recover until after Easter in 1854. He then prepared the lecture over a period of seven weeks, only for Gauss to call a postponement on the grounds of ill health. At last, the talk was delivered, on 10 June 1854. The title, which had so intrigued Gauss, was “On the hypotheses which lie at the foundations of geometry.”
In that lecture — which was not published until 1867, the year after Riemann died — he covered an enormous variety of topics, including a workable definition of what is meant by the curvature of space and how it could be measured, the first description of spherical geometry (and even the speculation that the space in which we live might be gently curved, so that the entire Universe is closed up, like the surface of a sphere, but in three dimensions, not two), and, most important of all, the extension of geometry into many dimensions with the aid of algebra.
Although Riemann’s extension of geometry into many dimensions was the most important feature of his lecture, the most astonishing, with hindsight, was his suggestion that space might be curved into a closed ball. More than half a century before Einstein came up with the general theory of relativity — indeed, a quarter of a century before Einstein was even born — Riemann was describing the possibility that the entire Universe might be contained within what we would now call a black hole. “Everybody knows” that Einstein was the first person to describe the curvature of space in this way — and “everybody” is wrong.
Of course, Riemann got the job — though not because of his prescient ideas concerning the possible “closure” of the Universe. Gauss died in 1855, just short of his 78th birthday, and less than a year after Riemann gave his classic exposition of the hypotheses on which geometry is based. In 1859, on the death of Gauss’s successor, Riemann himself took over as professor, just four years after the nerve- wracking experience of giving the lecture upon which his job as a humble Privatdozent had depended (history does not record whether he ever succumbed to the temptation of asking later applicants for such posts to lecture on the third topic from their list).
Riemann died, of tuberculosis, at the age of 39. If he had lived as long as Gauss, however, he would have seen his intriguing mathematical ideas about multi-dimensional space begin to find practical applications in Einstein’s new description of the way things move. But Einstein was not even the second person to think about the possibility of space in our Universe being curved, and he had to be set out along the path that was to lead to the general theory of relativity by mathematicians more familiar with the new geometry than he was. Chronologically, the gap between Riemann’s work and the birth of Einstein is nicely filled by the life and work of the English mathematician William Clifford, who lived from 1845 to 1879, and who, like Riemann, died of tuberculosis. Clifford translated Riemann’s work into English, and played a major part in introducing the idea of curved space and the details of non-Euclidean geometry to the English-speaking world. He knew about the possibility that the three dimensional Universe we live in might be closed and finite, in the same way that the two-dimensional surface of a sphere is closed and finite, but in a geometry involving at least four dimensions. This would mean, for example, that just as a traveller on Earth who sets off in any direction and keeps going in a straight line will eventually get back to their starting point, so a traveller in a closed universe could set off in any direction through space, keep moving straight ahead, and eventually end up back at their starting point.
But Clifford realised that there might be more to space curvature than this gradual bending encompassing the whole Universe. In 1870, he presented a paper to the Cambridge Philosophical Society (at the time, he was a Fellow of Newton’s old College, Trinity) in which he described the possibility of “variation in the curvature of space” from place to place, and suggested that “small portions of space are in fact of nature analogous to little hills on the surface [of the Earth] which is on the average flat; namely, that the ordinary laws of geometry are not valid in them.” In other words, still seven years before Einstein was born, Clifford was contemplating local distortions in the structure of space — although he had not got around to suggesting how such distortions might arise, nor what the observable consequences of their existence might be, and the general theory of relativity actually portrays the Sun and stars as making dents, rather than hills, in spacetime, not just in space.
Clifford was just one of many researchers who studied non- Euclidean geometry in the second half of the nineteenth century — albeit one of the best, with some of the clearest insights into what this might mean for the real Universe. His insights were particularly profound, and it is tempting to speculate how far he might have gone in pre-empting Einstein, if he had not died eleven days before Einstein was born.
When Einstein developed the special theory, he did so in blithe ignorance of all this nineteenth century mathematical work on the geometry of multi-dimensional and curved spaces. The great achievement of the special theory was that it reconciled the behaviour of light, described by Maxwell’s equations of electromagnetism (and in particular the fact that the speed of light is an absolute constant) with mechanics — albeit at the cost of discarding Newtonian mechanics and replacing them with something better.
Because the conflict between Newtonian mechanics and Maxwell’s equations was very apparent at the beginning of the twentieth century, it is often said that the special theory is very much a child of its time, and that if Einstein had not come up with it in 1905 then someone else would have, within a year or two.
On the other hand, Einstein’s great leap from the special theory to the general theory — a new, non-Newtonian theory of gravity — is generally regarded as a stroke of unique genius, decades ahead of its time, that sprang from Einstein alone, with no precursor in the problems faced by physicists of the day.
That may be true; but what this conventional story fails to acknowledge is that Einstein’s path from the special to the general theory (over more than ten tortuous years) was, in fact, more tortuous and complicated than it could, and should, have been. The general theory actually follows as naturally from the mathematics of the late nineteenth century as the special theory does from the physics of the late nineteenth century.
If Einstein had not been such a lazy dog, and had paid more attention to his maths lectures at the polytechnic, he could very well have come up with the general theory at about the same time that he developed the special theory, in 1905. And if Einstein had never been born, then it seems entirely likely that someone else, perhaps Grossman himself, would have been capable of jumping off from the work of Riemann and Clifford to come up with a geometrical theory of gravity during the second decade of the twentieth century.
If only Einstein had understood nineteenth century geometry, he would have got his two theories of relativity sorted out a lot quicker. It would have been obvious how they followed on from earlier work; and, perhaps, with less evidence of Einstein’s “unique insight” and a clearer view of how his ideas fitted in to mainstream mathematics, he might even have got the Nobel Prize for his general theory.
Einstein’s unique genius actually consisted of ignoring all the work that had gone before and stubbornly solving the problem his way, even if that meant ten years’ more work. He was adept at rediscovering the wheel, not just with his relativity theories but also in much of his other work. The lesson to be drawn is that it is, indeed, OK to skip your maths lectures — provided that you are clever enough, and patient enough, to work it all out from first principles yourself.
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https://www.downes.ca/post/60862
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math
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I never had any problems understanding fractions, and in a certain sense, it is a mystery to me why people have problems with them. But in a deeper sense, I think, I know exactly why they have problems with them. So when I read this, it all came to me clearly: "Multiplication makes a number bigger; division makes it smaller." Which, of course, is exactly what's not happening in multiplication or division; we aren't transforming numbers, we're just involved in elegant acts of counting. But what of fractions, then? For me, I think the key lay in the use (by my teachers) of the word 'of'. If you say, "what is one half times one quarter" it sounds deeply mysterious (especially if all you've even done is to memorize a multiplication table). But if you say "what is one half of one quarter" the meaning is transparent: one eighth. This just shows, once again, that mathematics isn't about remembering facts, it's about understanding.
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| 937 | 1 |
http://vfhomeworkdvba.card-hikaku.info/what-is-the-approximate-concentration-of-k-inside-a-typical-cell.html
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math
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What is the approximate concentration of k+ inside a typical cell (intracellular concentration) you correctly answered: a 150 mm 2 what is the approximate. Because the cell has potassium channels through which k + can move in and out of the cell, k + diffuses down its chemical gradient (out of the cell) because its concentration is much higher inside the cell than outside. The k+ concentration is higher inside the cell compared to outside what is the major role of the na+-k+ pump in maintaining the resting membrane potential maintaining the concentration gradients for na+ and k+ across the cell membrane.
What is the approximate concentration of k+ inside a typical cell (intracellularconcentration)2 what is the approximate concentration of k+ outside a cell (extracellularconcentration)3 what is the approximate concentration of na+ inside a cell (intracellularconcentration)4. 1 what is the approximate concentration of k+ inside a typical cell (intracellular concentration) you correctly answered: a 150 mm 2 what is the approximate concentration of k+ outside a cell (extracellular concentration. Study 70 lab week 5 flashcards from what is the approximate concentration of k+ inside a typical cell what is the approximate concentration of k+ outside a. Activity 1: the resting membrane potential pre-lab quiz results 1 what is the approximate concentration of k+ inside a typical cell (intracellular concentration.
Table 21 summarizes the ion concentrations measured directly in an exceptionally large nerve cell concentration of k + inside basis of the resting membrane. Relative icf-ecf potassium ion concentration affects a cell's resting membrane potential potassium controls its own ecf concentration via feedback regulation of aldosterone release an increase in k + levels stimulates the release of aldosterone through the renin-angiotensin-aldosterone mechanism or through the direct release of aldosterone. Chemistry help i need help please on the outside of the cell and the inside of the red blood cell is the same there is a higher concentration of.
What is the total number of protein molecules per cell volume moving on to the protein concentration in measurements of the average cell volume. The action potential, synaptic transmission, and maintenance of extracellular concentration of na is much greater than the typical values for equi. While in solutions, diffusing solutes move in three dimensions down a concentration gradient from an area of higher concentration to an area of lower concentration, a simple equation may be used to approximate the time it takes a given molecule to diffuse an average distance in one dimension (see equation below. Inside the cell, the k + concentration is higher, nominally 100 mm compared to 5mm outside the cell outside the cell, the na + concentration is higher, nominally 150 mm compared to 10 mm inside the cell.
There is a much greater k+ concentration inside the cell than outside why, then, is the resting membrane potential negative inside the cell than outside and. These negatively charged molecules in the cell allow the cell to maintain a concentration gradient by pumping the positively charged cations alone although both sodium and potassium ions are positively charged, the negative-inside membrane potential is maintained because the sodium-potassium pump doesn't pump the same number of each ion. The membrane potential of a cell at rest is called the sent at a high concentration inside the cell and glial cells are selectively permeable to them, k+ ions. How do u calculate concentration in beer lambert law passing through the sample cell is also measured for that wavelength - given the symbol, i.
If the cell has 150 mm kcl inside (a physiologically reasonable number mm = millimolar = 10-3 moles/liter), calculate the total number of k's (which is then also the total number of cl's) inside one cell. The typical resting membrane potential of a cell arises from the the cell's resting potential will be about −73 mv of 10mm and an inside concentration, [k. What is the approximate concentration of k+ inside a typical cell (points : 1) 15 mm 7 what is the approximate concentration of k+ outside a typical cell. The following table gives an idea of the intra and extra cellular ion concentrations in a squid axon and a mammalian cell extracellular and intracellular ion concentration.
Module 1 physioex 3: neurophysiology of nerve impulses concentration of k+ inside a typical cell (intracellular concentration) the approximate concentration. Typical values for the concentrations of na+, k+, and cl-in the cell water of a muscle cell and in the extracellular fluid of a typical non-marine vertebrate (like you and me) is seen in the diagram below: the resting membrane potential is about 90 mv (inside negative relative to. Shown below are the equilibrium potentials calculated for k+, na+ and cl- using the ionic concentrations for a typical neuron concentration of cl- inside the. Instrumental deviation from beer's law 1 such as the path length of the absorption cell (1-10 cm) what is the approximate concentration above which.
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| 5,126 | 7 |
https://socratic.org/users/n-n
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math
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Retired math tutor. Author of a few math articles, being posted on Google, Yahoo, and Socratic. 1. The transposing method in solving linear equations. 2. The new AC method to factor trinomials 3. The new Transforming Method to solve quadratic equations. 4. Solving quadratic equations by the Quadratic Formula in Graphic Form. 5. Solving trig equations, concept and methods. 6. Solving trig inequalities, concept, methods, and steps 7. Convert quadratic functions from one form to another.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510219.5/warc/CC-MAIN-20230926175325-20230926205325-00067.warc.gz
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| 489 | 1 |
http://www.lescienze.it/pubblicazione/is-it-possible-to-measure-new-general-relativistic-third-body-effects-on-the-orbit-of-mercury-with-bepicolombo/3017533/
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math
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di IorioLorenzo - MIUR-Istruzione
Recently, Will calculated an additional contribution to the Mercury's precession of the longitude of perihelion Ï of the order of ÏËW0.22 milliarcseconds per century ( mas cty1 ). It is partly a direct consequence of certain 1pN third-body accelerations entering the planetary equations of motion, and partly an indirect, mixed effect due to the simultaneous interplay of the standard 1pN pointlike acceleration of the primary with the Newtonian N-body acceleration, to the quadrupole order, in the analytical calculation of the secular perihelion precession with the Gauss equations. We critically discuss the actual measurability of the mixed effects with respect to direct ones. The current uncertainties in either the magnitude of the Sun's angular momentum S and the orientation of its spin axis S^S^ impact the precessions ÏËJ2, ÏËLT induced by the Sun's quadrupole mass moment and angular momentum via the Lense"Thirring effect to a level which makes almost impossible to measure ÏËW , even in the hypothesis that it comes entirely from the aforementioned 1pN third-body accelerations. On the other hand, from the point of view of the Lense"Thirring effect itself, the mismodeled quadrupolar precession δÏËJ2 due to the uncertainties in S^S^ corresponds to a bias of 9% of the relativistic one. The resulting simulated mismodeled range and range-rate times series of BepiColombo are at about the per cent level of the nominal gravitomagnetic ones.
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CC-MAIN-2019-09
| 1,502 | 2 |
https://www.coursehero.com/file/104837/assign6-magnetostatics-1/
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math
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Unformatted text preview: 5. Find the current density J r in free space that induces the magnetic field with m Wb a A z / 10 2 r r = 6. A conducting triangular loop carrying a current of I t is located close to an infinitely long, straight conductor with a current of I s as shown below. Calculate (a) the force on side 1 of the triangular loop, and (b) the total force on the loop. 7. An infinitely long tube of inner radius of a and outer radius of b is made of a conducting magnetic material. The tube carries a total uniform current I and is placed along the z-axis. If it is exposed to a constant magnetic field B o a , determine the force per unit length acting on the tube. 5A z 2m 4m 2m 2A...
View Full Document
- Spring '07
- Electromagnet, Magnetic Field, 2m, 4m, outer radius, inner radius
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http://www.gracelifefamily.org/category/student-blog
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math
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No entries were found under the Student Blog category either because they were not published or this category has been excluded from the Blog section.
Our Normal Schedule is:
9:30am - Life Groups for all ages
10:45am - Morning Worship Service
5:15pm - Children's Choirs, Youth Choir, and Adult Life Groups
6:30pm - Evening Worship Service
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https://www.twirpx.com/file/1163819/
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math
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Hermes Penton Science, 2002. — 352 pages. — ISBN: 1903996066.Having established the relationships which provide the response of a linear system with one degree of freedom to a random vibration, Volume 4 is devoted to the calculation of damage fatigue. It presents the hypotheses adopted to describe the behaviour of a material subjected to fatigue, the laws of damage accumulation, together with the methods for counting the peaks of the response, used to establish a histogram when it is impossible to use the probability density of the peaks obtained with a Gaussian signal. The expressions of mean damage and of its standard deviation are established. A few cases are then examined using other hypotheses (mean not equal to zero, taking account of the fatigue limit, non linear accumulation law, etc.).Fatigue damage to a system with one-degree-of-freedom is one of the two criteria adopted for comparing the severity of different vibratory environments, the second being the maximum response of the system.This criterion is also used to create a specification reproducing on the equipment the same effects as all the vibrations to which it will be subjected in its useful lifetime. This volume focuses on calculation of damage caused by random vibration.This requires: - having the relative response of the system under vibration represented by its PSD or by its rms value. Chapter 1 establishes all the useful relationships for that calculation. In Chapter 2 is described the main characteristics of the response. - knowledge of the fatigue behaviour of the materials, characterized by S-N curve, which gives the number of cycles to failure of a specimen, depending on the amplitude of the stress applied. In Chapter 3 are quoted the main laws used to represent the curve, emphasizing the random nature of fatigue phenomena, followed by some measured values of the variation coefficients of the numbers of cycles to failure. - determination of the histogram of the peaks of the response stress, supposed here to be proportional to the relative displacement. When the signal is Gaussian stationary, as was seen in Volume 3 the probability density of its peaks can easily be obtained from the PSD alone of the signal. When this is not the case, the response of the given one-degree-of-freedom system must be calculated digitally, and the peaks then counted directly. Numerous methods, ranging from the simplest (counting of the peaks) to the most complex (rainflow) have been proposed and are presented, with their disadvantages, in Chapter 5. - choice of a law of accumulation of the damage caused by all the stress cycles thus identified. In Chapter 4 are described the most common laws with their limitations.All these data are used to estimate the damage, characterized statistically if the probability density of the peaks is available, and deterministically otherwise (Chapter 6), and its standard deviation (Chapter 7).Finally, in Chapter 8 are provided a few elements for damage estimation from other hypotheses concerning the shape of the S-N curve, the existence of an endurance limit, the non linear accumulation of damage, the law of distribution of peaks, and the existence of a non-zero mean value.Contents:IntroductionResponse of a linear one degree-of-freedom linear system to random vibration Average value of response of a linear system Response of perfect bandpass filter to random vibration PSD of response of a single-degree-of-freedom linear system Rms value of response to white noise Rms value of response of a linear one-degree-of-freedom system subjected to bands of random noise Rms value of the absolute acceleration of the response Transitory response of dynamic system under stationary random excitation Transitory response of dynamic system under amplitude modulated white noise excitationCharacteristics of the response of a one-degree-of-freedom linear system to random vibration Moments of response of a one-degree-of-freedom linear system: irregularity factor of response Autocorrelation function of response displacement Average numbers of maxima and minima per second Equivalence between transfer functions of bandpass filter and one-degree-of-freedom linear systemConcepts of material fatigue Introduction Damage arising from fatigue Characterization of endurance of materials Factors of influence Other representations of S-N curves Prediction of fatigue life of complex structures Fatigue in composite materialsAccumulation of fatigue damage Evolution of fatigue damage Classification of various laws of accumulation Miner's method Modified Miner's theory Henry's method Modified Henry's method H. Corten and T. Dolan's method Other theoriesCounting methods for analysing random time history General Peak count method Peak between mean-crossing count method Range count method Range-mean count method Range-pair count method Hayes counting method Ordered overall range counting method Level-crossing count method Peak valley peak counting method Fatigue-meter counting method Rainflow counting method NRL counting method (National Luchtvaart Laboratorium) Evaluation of time spent at given level Influence of levels of load below fatigue limit on fatigue life Test acceleration Presentation of fatigue curves determined by random vibration testsDamage by fatigue undergone by a one-degree-of-freedom mechanical system Introduction Calculation of fatigue damage due to signal versus time Calculation of fatigue damage due to acceleration spectral density Equivalent narrow band noise Comparison of S-N curves established under sinusoidal and random loads Comparison of theory and experiment Influence of shape of power spectral density and value of irregularity factor Effects of peak truncation Truncation of stress peaksStandard deviation of fatigue damage Calculation of standard deviation of damage: J.S. Bendat's method Calculation of standard deviation of damage: S.H. Crandall, W.D. Mark and G.R. Khabbaz method Comparison of W.D. Mark and J.S. Bendat's results Statistical S-N curvesFatigue damage using other assumptions for calculation S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit) S-N curve defined by two segments of straight line on log-lin scales Hypothesis of non-linear accumulation of damage Random vibration with non zero mean: use of modified Goodman diagram Non Gaussian distribution of instantaneous values of signal Non-linear mechanical systemAppendices Gamma function Definition Properties Approximations for arbitrary x Incomplete gamma function Definition Relation between complete gamma function and incomplete gamma function earson form of incomplete gamma function Various integrals
Чтобы скачать этот файл зарегистрируйтесь и/или войдите на сайт используя форму сверху.
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CC-MAIN-2019-22
| 6,888 | 2 |
http://en.zonar.info/origami-scottish-terrier/
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math
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Fold origami Scottish terrier from paper. You will need paper,painted on both sides equally. On our pictures, one side is left white for convenience.
1. Fold the square to the midline.
2. Fold the two diagonals.
3. Fold the right edge along the bisector of the specified angle.
4. Connect the marked points ( fold line runs exactly along the middle line of the figure).
5. Similarly, bend the left edge.
6. Unfold the corner.
7. The figure became symmetric. Let’s be engage in a square in the top part of a figure now.
8. Fold the top layer of paper on the bisectors of the angles.
9. Bend on all planned lines.
10. Check the result.
11. Fold back the top part of the figure.
12. Fold the bottom right corner so …
13 … so that the top side of the formed triangle it was parallel to the upper edge of a figure.Repeat the fold on the left.
14. Bend the corner to the left. The fold line parallel to the left edge also doesn’t reach a corner of the second triangle lying below.
15. Repeat the fold on the right.
16. Open pockets. The top line of the fold “valley” – the bisector of angles.
17. Check the result. At the bottom bend two triangles on the bisectors of the angles.At the top, fold two layers of paper over on the specified lines.
18. Fold the triangles back.
19. Bend the figure in half. Two fold line “mountain” at the top mark the advance.
20. Double fold zipper. In this case to execute it not easy. Mark all fold lines in advance.
21. Bend a tail and a muzzle, bend ears.
22. Sticking out from under the muzzle triangle bend inside, raise ears and pull the tail.
23. Lightly press down on the ridge and take the shape of volume. Paws have to be perpendicular to a floor.
24. Origami a Scottish Terrier is ready.
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| 1,742 | 25 |
https://www.theroyalforums.com/forums/f165/king-george-vi-1895-1952-a-1539-13.html
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math
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I have no idea where to put this question except that I normally frequent the British Royal Forums and WWII happened during King George VI reign. Moderators, if there is a better forum to put this in, please do so. Here is my question: I plan to read this book
on WWI because from what I have read it seems to be a one book synopsis of WWI for the non-historian and gets excellent reviews. Is there a similar book on WWII for the non-historian that would give a general understanding of it---certainly not detailed? I would be willing to read a set of books as long as they don't require a degree in history to understand. Thanks.
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CC-MAIN-2021-04
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https://www.virtuescience.com/1249.html
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math
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The Number 1249: Properties and Meanings1249 is a Prime Number.
1249 is a Centered 16-gonal Number.
1249 is the number of simplicial polyhedra with 11 vertices.
The Year 1249 ADIn the year 1249 AD Roger Bacon invented his gunpowder formula.
Share any properties and meanings for particular Numbers...contact me directly, thanks.
Daily Deals on eBay
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https://marko-the-rat.livejournal.com/259698.html
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math
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Is it standard practice for Americans to count the rankings for the medal tally
in the Olympics by counting each medal to be of equal value? For example, it puts Japan ahead of France even though France has 5 gold medals to Japan's 2 (these figures will of course change all the time, but finding examples won't be hard to do). In Australia
we rank gold medals first and I took it for granted that's how the rest of the world does it.
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http://www.ask.com/web?qsrc=3053&o=102140&oo=102140&l=dir&gc=1&q=What+Is+A+Catchy+Math+Slogan
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math
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Jul 6, 2015 ... Math teams are little popular teams in high schools and colleges around the
country. They come together to compete against other teams in ...
Here are Math slogans and sayings to show the importance of math. Vote for the
ones you think are the best.
A relevant and insightful slogan for math is, "Math is like life: it is not always about
the destination but how you get there." What many math teachers try to teach is ...
Funny Math Quotes or catchy phrases for the classroom! | See more about Math
Humor, Math and Math Cartoons.
Math teams are little popular teams in high schools and colleges around the
country. ... Slogans Brandongaille,Company Slogans,Catchy Slogans,28 Catchy
best quotes collection by famous authors, inspiring leaders and more.
Jun 5, 2012 ... Math needs all the PR it can get! Check out these 13 Math Quotes that show the
beauty, relevance and inspiration that math has to offer.
Mathematics Quotes from BrainyQuote, an extensive collection of quotations by
famous authors, celebrities, and newsmakers.
Math slogans. Posted by mathfail on July 11, 2010. math slogan. ** Note: Some
posts on Math-Fail are user-submitted and NOT verified by the admin of the site ...
Jul 9, 2015 ... If people do not believe that mathematics is simple, it is only because they do not
realize how complicated life is. ~John Louis von Neumann
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https://forum.duolingo.com/comment/304518/I-do-not-like-the-city-in-which-he-lives
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math
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"I do not like the city in which he lives."
Translation:Non mi piace la città in cui vive.
why is "...in quale vive" wrong and "...in cui vive" correct? is there a rule when i have to take "cui" and when "quale"? as far a s i know both mean "which".
Quale is which as an interrogative pronoun, but to make it into a relative pronoun you need the definite article: "Non mi piace la città nella quale vive".
thanks for your information ! i didn´t know that there must be a different translation of "which" whether it´s a interrogative or a relative pronoun (where i have to add the definite article). so, as far as i understand, there are two correct translations possible: "...in cui vive" or "...nella quale vive". i´ve learned a lot!
What did you do to get a different font and yellow background on that sentence? :-)
"Dove" would translate to 'where' - the exercise purposely intends for us to translate 'in which', which requires us to us 'in cui'
Can someone please explain when to use "a me non piace" or "a mi non piace"? Because it's driving me crazy... duo keeps telling me the other one different from the one I put!
I don't think Duo is being fair. In the hints, "in which" was shown as "in quale/qual/quali" - no suggestion that "cui" should be used. The information given by respondents is helpful, but indicates that "in quale" is wrong. Why, then, is it is the hints?
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https://community.jmp.com/t5/JMP-Blog/Draw-your-models-with-a-new-SAS-application-for-JMP/ba-p/30000
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math
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Draw your models with a new SAS application for JMP
Jul 27, 2011 1:11 PM
SAS® Structural Equation Modeling for JMP® is a new application that enables researchers to use SAS and JMP to draw models by using an interface that is built on the SAS/STAT® CALIS procedure.
To create models in SAS Structural Equation Modeling for JMP, you simply drag variables into the diagram area and then use point-and-click features to draw paths among variables, specify variable and path properties, and select other model specifications. SAS Structural Equation Modeling for JMP enables both novice and experienced users of structural equation models to build models easily with no programming involved.
How is structural equation modeling (SEM) used?
Structural equation modeling in academia:
Psychologists have used SEM to examine the properties of personality and depression tests.
Sociologists and criminologists have used SEM to understand what personal and environmental characteristics can be used to predict antisocial behavior.
Public health researchers have used SEM to understand how to improve health communication and health outcomes.
Education researchers have used SEM to model changes in reading and math scores over time.
Marketing researchers have used SEM to understand what factors influence future product purchases.
Business researchers have used SEM to understand what personal and environmental characteristics can be used to predict entrepreneurial intention.
Structural equation modeling in industry:
A large high tech company uses SEM to map customer satisfaction metrics.
A consumer packaged goods company uses SEM to analyze survey responses from consumer product tests.
An insurance company has applied SEM to bring insight into factors that influence customers to buy insurance.
For what models can I use SAS Structural Equation Modeling for JMP?
With SAS Structural Equation Modeling for JMP, you can fit either models that have only observed variables (including linear regression and path analysis models) or models with observed and latent variables (including confirmatory factor analysis and latent growth curve models). Here are some examples of the models you can fit with SAS Structural Equation Modeling for JMP:
This example shows a linear regression model in which the number of employees (N_emp), the advertising spending (Advert), and last year’s sales (LastS) are used to predict the current year’s sales (CurrentS)
This example shows a confirmatory factor analysis (CFA) model with correlated latent variables (Read and Math), which predict observed test scores from three math tests (math1, math2, and math3) and three reading tests (reading1, reading2, and reading3)
Typically, you have several models you want to examine. With SAS Structural Equation Modeling for JMP, you can fit several models to the same data set using the Single Group Analysis option. You can easily compare multiple models using the Comparisons tab.
Example of the Comparisons tab
What are the software requirements for SAS Structural Equation Modeling for JMP?
SAS Structural Equation Modeling for JMP requires:
Base SAS 9.2 or later.
SAS/STAT 9.22 or later.
Windows versions of JMP 9.0.2 or later; JMP Pro 9.0.2 or later.
Macintosh support is coming soon.
How do I acquire SAS Structural Equation Modeling for JMP?
You can acquire SAS Structural Equation Modeling for JMP in one of the following ways:
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https://www.zencalculator.com/guide/how-to-input-sin2-in-calculator/
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math
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Is the scientific calculator one of the greatest inventions of all time? We think so! And, we are sure that math students, accountants, professionals in real estate, and financial experts will agree.
How To Input Sin^2 In Calculator?
A significant upgrade on the regular calculator, the scientific calculator helps solve complex problems within seconds and get answers in a jiffy. It takes away all the headaches from calculations, which is crucial, especially during exams and time-sensitive jobs.
Now, you can only take advantage of the calculator if you are able to use it properly. There is a learning curve, of course, and this varies with the applications and what formulae you have to use. You may come across multiple questions and doubts when you first use your scientific calculator. Today, we will address one of the most common ones.
How To Input Sin^2 In A Calculator?
Sin^2 is basically a double-angle formula. It can be confusing because you can’t directly input it. But hey, we have solved this problem for you.
- One of the easiest ways to input Sin^2 is to type in (Sin(x))2
- If you are using a graphing calculator, here’s what you add – Sin(x)^2=(Sin(x))^2
- Another way to input Sin^2 in a scientific calculator is to enter X > Press Sin > Press the Squared button
We understand the stress you must have gone through trying to figure out the solution and we are glad you found us.
People Also Ask
1. What Is Sin 2X Formula?
That’s a double-angle formula.
2. Is Sin2x And Sinx 2 The Same?
Yes, they are the same.
3. How Do You Put Cos 2 Into A Calculator?
You start by calculating Cos X and then you press the squared button to square it.
4. What’s The Fraction Button On A Calculator?
You have to enter the Math mode first. Once you do that, press the button with 2 boxes on it with a horizontal line separating them. This is what the fraction button looks like.
5. What Is The 2nd Function On A Calculator?
Some buttons on your scientific calculator will have 2 functions. When you choose the 2nd function, the top function gets selected. Some modern calculators also have 3 functions!
6. What Does Sin Mean On A Calculator?
Sin is the length of the opposite side in a right-angle triangle, divided by the length of the hypotenuse.
Depending on the type of calculator you own and the application, you can choose any of the aforementioned ways to input Sin^2. If you have any more doubts, please feel free to ask us. All the best!
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https://www.arxiv-vanity.com/papers/hep-th/9206039/
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math
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EXTENDED SUPERCONFORMAL GALILEAN SYMMETRY
IN CHERN-SIMONS MATTER SYSTEMS **This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069, and the World Laboratory.
M. Leblanc and G. Lozano ††† On leave from Departamento de Fisica, Universidad Nac. de la Plata, La Plata, Argentina.
Center for Theoretical Physics
Laboratory for Nuclear Science
and Department of Physics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 U.S.A.
Division of Liberal Arts
Seoul City University
Seoul, 130-743, Korea
Submitted to: Annals of Physics
CTP#2106 — SNUTP 92-37 June 1992
We study the nonrelativistic limit of the supersymmetric Chern-Simons matter system. We show that in addition to Galilean invariance the model admits a set of symmetries generated by fermionic charges, which can be interpreted as an extended Galilean supersymmetry . The system also possesses a hidden conformal invariance and then the full group of symmetries is the extended superconformal Galilean group. We also show that imposing extended superconformal Galilean symmetry determines the values of the coupling constants in such a way that their values in the bosonic sector agree with the values of Jackiw and Pi for which self-dual equation exist. We finally analyze the second quantized version of the model and the two-particle sector.
In the last years much attention has been directed toward the study of matter systems in (2+1) dimensional space-time minimally coupled to gauge fields whose dynamics is governed by the Chern-Simons term. The interest in this subject is not only due to its mathematical richness but also because of its applications to condensed matter phenomena such as the quantum Hall effect and high- superconductivity.
An important line of development has followed the papers by Hong, Kim and Pac and by Jackiw and Weinberg where vortex solutions that satisfy self-dual equations were found for relativistic bosons with specific -potential . It was then shown by Lee, Lee, and Weinberg that this specific potential arises as a consequence of demanding a supersymmetric extension of the bosonic Abelian Chern-Simons model.
Later Jackiw and Pi introduced a nonrelativistic model for bosonic fields, which also supports self-dual solutions when a specific value for the coupling constant of the Dirac -interaction is chosen.
We explore in the present paper the supersymmetric extension of the Jackiw-Pi model. In principle, one could follow different approaches. One of them would be to construct from the Galilean algebra in (2+1)-dimensions the graded algebra by either imposing consistency conditions when fermionic charges are introduced or by taking the contraction of the graded Poincaré algebra ( is the velocity of light). Once one has the graded algebra, one can construct the superfield formalism in order to find representations of the algebra and write invariant Lagrangians. This way has been followed in (3+1)-dimensional theories by Puzalowski as well as by Azcárraga and Ginestar for the consistency and contraction methods respectively.
We shall instead pursue a different approach, which is related to the contraction method but inverts the procedure. Our method consists in taking the nonrelativistic limit of the relativistic Lagrangian rather than of the supersymmetric Poincaré algebra. Once one has the nonrelativistic Lagrangian, one can study its symmetries. In particular for the supersymmetry one can ask whether the set of transformations obtained by taking the nonrelativistic limit of the supersymmetric Poincaré transformations is still an invariance of the nonrelativistic Lagrangian. Knowledge of this set of transformations allows one to construct the fermionic charges and then study their algebra.
The model enjoys special characteristics. One of them is the combination of Galilean and local gauge invariances. Choosing the Abelian Chern-Simons term as the kinetic term for the gauge field allows one to implement local gauge invariance without introducing massless particles in the theory, the presence of which would obstruct Galilean invariance. Another feature present in our model is that as we start from a relativistic supersymmetric Lagrangian we find that two fermionic charges (and their Hermitian conjugates) survive the nonrelativistic limit providing us then with an extended Galilean supersymmetry. Although some comments on extended Galilean supersymmetry have been made in Refs. .[6,7], to our knowledge ours is the first explicit example of a nonrelativistic Lagrangian supporting this extended supersymmetry. Finally, the model admits a hidden SO(2,1) conformal invariance that is not present in the relativistic model. Thus the full invariance group of the model is the extended superconformal Galilean group.
The paper is organized as follows. In section II, we introduce the Lagrangian describing our model by taking the nonrelativistic limit of the supersymmetric Abelian Chern-Simons theory given by Lee, Lee and Weinberg . In section III, we consider the space-time symmetries of the model. We start by studying the transformations associated with the Galilean invariance and we then consider the SO(2,1) conformal symmetry. In section IV, we show that for a specific choice of coupling constants our model possesses an extended supersymmetry. We construct the charges associated with this symmetry and study its algebra. We close the section by writing the self-dual equations of the supersymmetric model. In section V, after imposing canonical commutation relations for second quantization, we analyze the two-particle sector of the model. Final remarks and suggestions for further developments are left for the concluding section.
II. NONRELATIVISTIC LIMIT OF N=2 SUPERSYMMETRIC CHERN-SIMONS THEORY.
Our starting point is the supersymmetric Chern-Simons theory described by the action **Our conventions for the -matrices are , and the metric is chosen to be . The letter denotes the 3-vector and time is frequently omitted in arguments of quantities taken at equal times for canonical manipulation. :
where is a complex spin-0 field carrying two degrees of freedom and is a two complex components spinor representing spin-1/2 particles also carrying two degrees of freedom. (Remember that in 2+1 space-time dimensions a Dirac spinor describes a particle and an antiparticle each with only one spin degree of freedom.) These fields are minimally coupled to a gauge field (whose dynamics is governed solely by a topological Chern-Simons term) through the covariant derivative
In the symmetric phase there are no degrees of freedom associated with the gauge field and the theory presents the proper counting of degrees of freedom required by supersymmetry.
The action (2.1a) is invariant under the following supersymmetric transformations
where is a spinor with two complex components. The transformations (2.2) are generated by where the spinor supercharge is given by:
The nonrelativistic limit of the model can be performed as follows. We observe first that the quadratic term in the scalar field defines the boson mass to be ,
and as a consequence of supersymmetry the mass for fermions is also .
In order to simplify the notation, we shall consider only the model with . (The theory for negative can be obtained by a parity transformation since this is equivalent to change the sign of .) The matter part of the Lagrangian density in eq.(2.1a) can be rewritten in the following way when eq.(2.4) is used
where is the spatial part of the covariant derivative . Similarly and .
The nonrelativistic limit of the Chern-Simons theory can now be carried out. Since there are no degrees of freedom associated with the gauge field in the symmetric phase, we do not modify its action in the nonrelativistic limit, while for the matter fields we substitute in eq.(2.5)
where and are the nonrelativistic fields associated with the particles and antiparticles respectively (similarly for the fermion field). We eliminate the second component of the spinor and by using their equation of motion to leading order in **where for any vector , .,
to obtain a nonrelativistic matter Lagrangian density, after dropping terms that oscillate as and terms of . In this Lagrangian particles and antiparticles are independently conserved, and we work in the zero antiparticle sector by setting and to obtain
where we have dropped the index 1 on spinors. The coupling constants are given by
and the magnetic field by
[In the plane the cross product is , the curl of a vector is , the curl of a scalar is and we shall introduce also the notation .]
The nonrelativistic limit of the model of eq.(2.1a) led us to a system of bosons minimally coupled to a gauge field and self-interacting through an attractive -function potential of strength . Note that fermions couple to the gauge fields not only through the covariant derivative but also through the Pauli interaction term. This non-minimal coupling arises in the nonrelativistic limit as a consequence of the elimination of the second component of the spinor reminding us of the spin structure of the fermions. Finally, there is a contact boson-fermion interaction of strength .
We close this section by writing the classical equations of motion which follow from the action (2.8)
III. SPACE-TIME SYMMETRIES.
In this section we study the space-time symmetries of our system. First, it is evident that the model possesses a Galilean invariance containing as generators the Hamiltonian (time translation), the total momentum (space translation), the angular momentum (rotation), and the Galilean boost generator . In order to close the algebra one has also to introduce the mass operator which appears as a central charge (ie., commutes with all the other operators). Second, the system possesses a less obvious conformal invariance containing the generators of the dilation and of the special conformal transformation which together with the Hamiltonian form an dynamical invariance group.
III A. Galilean Invariance
The Galilean invariance of the bosonic sector of the model has already been discussed by Hagen and by Jackiw and Pi . Note that although the Galilean invariance of the action without gauge fields is rather obvious, this is not the case when local gauge invariance is introduced in the theory. The reason why the Galilean invariance survives the introduction of local gauge invariance is a consequence of the fact that there is no massless particle associated with a Chern-Simons gauge field, and therefore any complication related to the non-relativistic limit of a massless particle is absent in the model. On the other hand, due to its topological nature, the Chern-Simons action assure us that the Chern-Simons action is not only Galilean invariant but invariant under any coordinate transformations.
We shall discuss the symmetries and their generators showing that the presence of fermions adds little complication. We consider space-time transformations and the corresponding field variations that leave the action (2.8) invariant and construct the conserved charges using Noether’s theorem. In order to obtain the gauge covariant space-time generators, we use the gauge covariant space-time transformations as given in ref.. They comprise a conventional space-time transformation generated by a function on space-time, supplemented by a field dependent gauge transformation.
We start by considering time translation
where is a constant. The infinitesimal gauge covariant time-translation on the fields are
and the conserved charge found using Noether’s theorem is the Hamiltonian
The system is also invariant under space translation,
where is a constant 2-vector. The infinitesimal gauge covariant translations of the fields
lead to the conserved charge
The angular momentum is obtained in a similar way by considering an infinitesimal rotation
where is the rotation angle and the infinitesimal gauge covariant field transformations read
The angular momentum obtained from the Noether theorem is
The last term in eq.(3.3c) is the spin associated with the fermion field and originates from the last term in the transformation for . As the nonrelativistic limit has led us to a 1-component fermion, the spin is proportional to the fermion number operator and is then independently conserved [see below].
Under an infinitesimal Galilean boost:
the fields transform gauge covariantly as
and the conserved charge is found to be
The Galilean group is completed with the inclusion of the mass operators
where and are the boson and the fermion number operator respectively and is the total number operator. The conservation of and arises as a consequence of a global symmetry (rather than from a space-time transformation)
Now we turn to the calculation of the algebra satisfied by the above conserved charges. In order to do that, we solve Gauss’s law by taking the gauge fields as the following function of the matter fields as in ref.[8,5]
where is the Green’s function for the Laplacian in two dimensions
Note the is presented in eq.(3.6) in the Coulomb gauge and we prescribe that .
The Poisson brackets for functions of the matter fields are defined from the symplectic structure of the Lagrangian at fixed time to be
where the superscripts “r” and “l” refer to right and left derivative and in particular **We use for the Poisson bracket when both functions and are Grassmann functions and otherwise because it is suggestive for the quantum case.
at fixed time.
Using the Poisson bracket relations of eqs.(3.8-9) the above conserved charges can be shown to realize the algebra of the Galilean group
We point out that the only constraint in the potential required by Galilean invariance is that and be a local function of the fields.
III B. Conformal Invariance
In addition to the Galilean invariance, the model admits a hidden dynamical group of conformal transformations. The role of conformal invariance in nonrelativistic quantum mechanics was first studied by Jackiw as well as by de Alfaro, Fubini and Farlan and in the framework of Galilean covariant field theories by Hagen and by Niederer .
The presence of the dilation invariance of our model (2.8) can be easily understood if we ignore for a moment the interaction with the gauge fields and the fermions. In this case, we are left with nonrelativistic bosons interacting through a interaction corresponding to a -Dirac potential which is known to be scale free . This can be seen in the following way: in a nonrelativistic theory we are free to choose units in such a way that and are dimensionless (and then =). It is then straightforward to check that is dimensionless. The interaction with the gauge fields does not change the picture since its introduction does not require dimensionful coupling constants . On the other hand, looking at the fermionic part of the Lagrangian we see that it looks like the bosonic counterpart except for the Pauli interaction term. However, the Pauli interaction term contains the magnetic field which when substituted by the Gauss law brings the Pauli interaction in the same form as the other contact interactions.
Then, under an infinitesimal dilation transformation
bosons and fermions transform in the same gauge-covariant way
while the transformations for the gauge fields (which we consider here as independent variables) are
It is easy to verify that the Lagrangian (2.8) for arbitrary coupling constants and is invariant under the dilation transformations (3.11) and that the conserved charge is
As in the purely bosonic model, our system is invariant under infinitesimal special conformal transformation
where is a constant and the gauge covariant field transformations are
The conserved charge associated with the special conformal transformation is given by
As noted in ref., an energy-momentum tensor can be defined in such a way that the time independence of and are assured by continuity equations of the form
Note that is symmetric and has been improved in such a way that
Formula (3.15) is analogous to the traceless condition of the energy-momentum tensor for conformal invariance in relativistic theories. The conservation of the generators and is insured by eqs.(3.13-15).
In order to calculate the algebra satisfied by , , and we use the Poisson brackets of eqs.(3.8-9), and we consider the gauge field as in eq.(3.6). These charges can be shown to satisfy the algebra of the conformal SO(2,1) group
while the algebra of the conformal-Galilean group is closed with the following additional Poisson brackets
The boson and fermion number generators and have vanishing Poisson brackets with all generators.
Finally, we note that the conformal symmetry does not fix completely the potential of the model but constrains it to be quartic in the fields. The values of these coupling constants are still arbitrary.
IV. EXTENDED GALILEAN SUPERSYMMETRY AND SELF-DUALITY.
Although the idea of supersymmetry is traditionally linked to the grading of Poincaré’s group, there has been some development on supersymmetry in the Galilean framework in 3+1 dimensional theories [6,7].
As we have already mentioned, the difference between bosons and fermions are less important in the nonrelativistic theory, for instance, with the exception of the Pauli interaction, both particles have the same kinetic term. Thus it is not too difficult to imagine a symmetry exchanging bosons and fermions which behaves as an internal symmetry though generated by a fermionic charge. Considering the gauge fields as independent variables, one can check that the following transformation
where is a complex Grassmann variable, is a symmetry of the action of eq.(2.8) provided that the following relation holds
The transformation (4.1) can be obtained as the nonrelativistic limit of eq.(2.2). In a sense, this transformation is of the same kind of Galilean supersymmetry discussed in ref.[6,7] with the obvious difference that we are in 2+1 space-time dimensions and that our gauge fields are not propagating. The last fact provides us with a simple model incorporating Galilean supersymmetry and local gauge invariance, avoiding the usual complication of the presence of massless gauge particles.
We now ask what happens when we consider the next to leading order of the nonrelativistic limit of eq.(2.2), which is given by
The transformation (4.3) is also a symmetry of the action (2.8) provided that the coupling constants take the values of eq.(2.10). Note that as in the relativistic case, it is the second supersymmetry that fixes completely the parameters of the model, while the transformations (4.1) provide us with a broader class of Lagrangian according to (4.2). In particular the value for is the one for which Jackiw and Pi have found self-dual solution in the purely bosonic sector.
Using Noether’s theorem, the supersymmetric transformation (4.1) and (4.3) lead to the charges and given by
These charges can also be obtained from the nonrelativistic limit of the supersymmetric spinor supercharge of eq.(2.3). and correspond to leading order of the upper and lower components of the spinor supercharge.
We now study the grading of the conformal-Galilean group. Solving the constraint of eq.(2.12a) first and specializing the Hamiltonian of eq.(3.1c) with the coupling constants given by eq.(2.10), the Hamiltonian density takes the simple form
and is now supersymmetric. Using the Poisson brackets of eqs.(3.8-9), the supersymmetry algebra takes the form
where and are given by eqs.(4.4). At this point it is worth to reproduce eqs.(4.6) by taking the nonrelativistic limit of the algebra satisfied by the relativistic charge of eq.(2.3)
and is the central charge of the algebra of the relativistic model
The nonrelativistic limit is realized by noticing that
while for , using Gauss’s law and the definition of , we obtain
Thus, we see that the central charge of the relativistic supersymmetric algebra reduces to the rest energy in the nonrelativistic limit. Therefore for the upper sign in eq.(4.7a) the central charge adds to the rest energy to give eq.(4.6a) while for the lower sign the central charge cancels the rest energy to give eq.(4.6b).
The rest of the Poisson brackets for the graded Galilean algebra are found to be
From the behavior under the rotations and Galilean boost we see that in fact transforms as the upper component of a spinor and as the lower component.
We now add the conformal generators. First we note that the crossing between the fermionic charge and the conformal algebra as well as with does not generate new charges
however the crossing between the charge and the special conformal generator produces a new generator
which is needed to close the superconformal Galilean algebra and can be obtained as the charge of the following symmetry transformation
The behavior of this new operator under the Galilean group is given by the following Poisson brackets
while the crossing with the conformal generators gives
The Poisson brackets with the fermionic charges are found to be
Note that although and do not have vanishing Poisson brackets with all operators, does and therefore is a central charge.
The 16 generators generate the extended superconformal Galilean algebra of our model.
We close this section by exploring the relation between supersymmetry and self-duality. We have already shown that the supersymmetry fixes the value of the coupling constant to be the one for which self-dual solutions exist in Jackiw-Pi model . Now we would like to investigate how the presence of the fermions modify the self-dual equations. In order to do this, we write the Hamiltonian in its self-dual form. We first collect the identities
Using eqs.(4.17) and Gauss’s law, the energy density can be written as
Consequently, with , and for well behaved fields for which the integral of and vanishes, the Hamiltonian is
reaches its minimum value, zero, when
Together with the Gauss law (2.12a) these two equations compose the super self-duality equation. When is set to zero, the above set of equations reduces to the ordinary self-duality equations in .
Solutions for the minimum energy exist only for the lower sign in eqs.(4.20). This can be seen by the following argument. Decompose the fields
and substitute in eq.(4.20) to get
Since eqs.(4.22a-b) must be consistent the fermionic and bosonic densities are proportional. Substituting eqs.(4.22) in eq.(2.12a), we find
Solutions for eq.(4.23) exist only when the constant in front of the right side of eq.(4.23) is negative. Since we have taken solutions exist only for the lower sign and the energy takes the form
Therefore, the presence of fermions does not modify the bosonic self-dual equation, a situation which is familiar in several relativistic models .
V. SECOND QUANTIZATION.
In this section, we present the second quantized version of the model. We consider bosonic quantum field operators , fermionic quantum field operators and their hermitian conjugate , satisfying equal-time commutation and anticommutation relations
and use the gauge fields as the function of the matter fields of eq.(3.6).
In the following, we shall consider the Hamiltonian
where are kept arbitrary for the moment. Note that although is normal ordered, the term is not (similarly for the fermions).
The quantum field equations of motion follow from the commutation and anticommutation relations (5.1)
where the scalar gauge potential in eqs.(5.3) given by
solves eq.(2.12b) together with given by eq.(3.6). The current is given as in eq.(2.13). The last term in eqs.(5.3) is not present in the classical equation of motion and arises here because of reordering of operators.
Now we study the Schrödinger equation for the two-particle sector. We assume the existence of a zero particle state which is annihilated by
and also by
We denote a state of energy with bosons and fermions by and we write the orthonormalized states as
where we have divided the one fermion-one boson state in a symmetric and anti-symmetric state for convenience. The wave functions , , and are normalized to unity.
It is also convenient to collect the wave functions in a vector
The Schrödinger equation for the wave functions can be easily found using the equations of motion (5.3) for arbitrary and the commutation and anticommutation relations (5.1) to be
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662595559.80/warc/CC-MAIN-20220526004200-20220526034200-00322.warc.gz
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CC-MAIN-2022-21
| 24,431 | 134 |
http://www.chegg.com/homework-help/definitions/classical-mechanics-2
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math
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Classical mechanics is a branch of physics that deals with the motion of bodies based on Isaac Newton's laws of mechanics. Classical mechanics describes the motion of point masses (infinitesimally small objects) and of rigid bodies (large objects that rotate but cannot change shape). While no objects are truly point masses or perfectly rigid, by approximating them as such, classical mechanics accurately describes the motion of objects from molecules to galaxies. Classical mechanics effectively describes systems in which quantum or relativistic effects are negligible, and it is one of the oldest subjects in science.
Each nerve cell in th neural pathway acts as an independent RC current (direct current). The cell membrane is the capacitor, the potential difference inside and outside the cell provides the battery power, and the axon fluid acts as the resister. When the concentration of Na+ ions outside the cell and of K+ inside the cell create a potential difference of 40mV, it is called the action potential becase it triggers the ion channelsto open an allow each type of to cross to the other side. If the dielectric constant k of the cell membrane is 9, and the resistivity of the axon fluid is 2.0ohms, use a rate of f = 1/0.15 Hz, which corresponds to mechanoreceptors receiving ordinary touch signals, Find:
a) resistance of the fluid in an axon that is 10mircometers in diameter and 1 mm in length (convert to meters).
b) Capacitance of the cell membrane if be perfectly square shaped.
c) total impedance of the circuit
d) Total current in the circuit•
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http://www.mathsteacher.com.au/year8mathematicssoftware.htm
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math
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The Year 8 Interactive Maths software is compatible with both Windows® and Mac® computers. Discover more about Year 8 Interactive Maths by:
From Chapter 1: Arithmetic Revision, Exercise 1: Addition of Large Numbers.
From Chapter 2: Fractions and Decimals, Exercise 11: Division of Fractions.
From Chapter 3: Integers, Exercise 4: Integers.
From Chapter 4: Algebra, Exercise 21: Highest Common Factor of Algebraic Expressions.
From Chapter 5: Equations, Exercise 24: Problem Solving.
From Chapter 6: Ratios, Exercise 6: Finding the Ratio of Two Quantities.
From Chapter 7: Indices, Exercise 22: Index Law for Powers of Products.
From Chapter 8: Consumer Arithmetic, Exercise 11: Finding a Percentage of a Quantity.
From Chapter 9: Reasoning in Geometry, Exercise 16: Congruent Triangles.
From Chapter 10: Geometric Constructions, Exercise 6: Rotation.
From Chapter 11: Length and Perimeter, Exercise 6: Word Problems.
From Chapter 12: Area of Plane Figures, Exercise 15: Area of a Composite Figure.
From Chapter 13: Volume, Exercise 11: Capacity.
From Chapter 14: Rates, Exercise 9: Travel Graphs.
From Chapter 15: Linear Graphs, Exercise 1: The Cartesian Plane.
From Chapter 16: Probability, Exercise 3: Probability.
From Chapter 17: Statistics, Exercise 4: Frequency Tables and the Mean.
Parents can order a 12-month Homework Licence for $19.95 (AUD) per student by clicking this order button:
Tutors may order Tutor Licences online that feature the interactive exercises as well as worksheets, tests and solution sheets.
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CC-MAIN-2017-09
| 2,250 | 29 |
https://www.pearson.com/channels/financial-accounting/learn/brian/ch-14-financial-statement-analysis/ratios-profit-margin-x-asset-turnover-return-on-assets
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math
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Ratios: Profit Margin x Asset Turnover = Return On Assets
XYZ Company had a profit margin of 8.8% and total asset turnover of 0.77. What is XYZ’s Return on Assets?
A company had a profit margin of 6.1%. The company’s net sales were $3,600,000 and Cost of Goods Sold was $600,000. If total assets were $3,450,000 at the beginning of the year and $4,210,000 at the end of the year, what is the company’s return on assets?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334802.16/warc/CC-MAIN-20220926051040-20220926081040-00080.warc.gz
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CC-MAIN-2022-40
| 425 | 3 |
https://www.investopedia.com/terms/b/blackscholes.asp
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math
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What Is the Black Scholes Model?
The Black Scholes model, also known as the Black-Scholes-Merton (BSM) model, is a model of price variation over time of financial instruments such as stocks that can, among other things, be used to determine the price of a European call option.
The model assumes the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option's strike price, and the time to the option's expiry.
- The Black-Scholes Merton (BSM) model is a differential equation used to solve for options prices.
- The model won the Nobel prize in economics.
- The standard BSM model is only used to price European options and does not take into account that U.S. options could be exercised before the expiration date.
The Black-Scholes Formula Is
The Black Scholes call option formula is calculated by multiplying the stock price by the cumulative standard normal probability distribution function. Thereafter, the net present value (NPV) of the strike price multiplied by the cumulative standard normal distribution is subtracted from the resulting value of the previous calculation.
In mathematical notation:
C=StN(d1)−Ke−rtN(d2)where:d1=σs tlnKSt+(r+2σv2) tandd2=d1−σs twhere:C=call option priceS=current stock (or other underlying) priceK=strike pricer=risk-free interest ratet=time to maturityN=a normal distribution
What Does the Black Scholes Model Tell You?
The Black Scholes model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fischer Black, Robert Merton, and Myron Scholes and is still widely used today. It is regarded as one of the best ways of determining fair prices of options. The Black Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.
The model assumes stock prices follow a lognormal distribution because asset prices cannot be negative (they are bounded by zero). This is also known as a Gaussian distribution. Often, asset prices are observed to have significant right skewness and some degree of kurtosis (fat tails). This means high-risk downward moves often happen more often in the market than a normal distribution predicts.
The assumption of lognormal underlying asset prices should thus show that implied volatilities are similar for each strike price according to the Black-Scholes model. However, since the market crash of 1987, implied volatilities for at the money options have been lower than those further out of the money or far in the money. The reason for this phenomena is the market is pricing in a greater likelihood of a high volatility move to the downside in the markets.
This has led to the presence of the volatility skew. When the implied volatilities for options with the same expiration date are mapped out on a graph, a smile or skew shape can be seen. Thus, the Black-Scholes model is not efficient for calculating implied volatility.
Limitations of the Black Scholes Model
As stated previously, the Black Scholes model is only used to price European options and does not take into account that U.S. options could be exercised before the expiration date. Moreover, the model assumes dividends and risk-free rates are constant, but this may not be true in reality. The model also assumes volatility remains constant over the option's life, which is not the case because volatility fluctuates with the level of supply and demand.
Moreover, the model assumes that there are no transaction costs or taxes; that the risk-free interest rate is constant for all maturities; that short selling of securities with use of proceeds is permitted; and that there are no risk-less arbitrage opportunities. These assumptions can lead to prices that deviate from the real world where these factors are present.
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| 3,995 | 18 |
https://www.assignmentexpert.com/homework-answers/programming-and-computer-science/cpp/question-77479
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math
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Answer to Question #77479 in C++ for Erik Rubino
The robot (marked as R) can:
•Move forward by one unit.
•Turn left or right.
•Sense the color of the ground one unit in front of it.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827281.64/warc/CC-MAIN-20181216051636-20181216073636-00597.warc.gz
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CC-MAIN-2018-51
| 330 | 8 |
https://sellfy.com/afhtutor/p/hmt1/
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math
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Managerial Accounting: E4-12 Clyde's Marina has estimated that fixed costs per month
Important Reminder!!! There might be other versions of this problem - amounts and dates have been changed - so please make sure you review and compare this tutorial to the problem in your homework. Even with different amounts, format and way of solving the problem is still the same so pleases be guided accordingly. Managerial Accounting E4-12 CVP Analysis, Profit Equation Clyde's Marina has estimated that fixed costs per month are $300,000 and variable cost per dollar of sales is $0.40. Required: a. What is the break-even point per month in sales dollars? b. What level of sales dollars is needed for a monthly profit of $60,000? c. For the month of July, the marina anticipates sales of $1,000,000. What is the expected level of profit?
You'll get 1 file (13.9KB)
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655897707.23/warc/CC-MAIN-20200708211828-20200709001828-00273.warc.gz
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CC-MAIN-2020-29
| 855 | 3 |
https://www.airports-worldwide.com/articles/article0626.php
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math
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In physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star.
Historically, the apparent motion of the planets were first understood in terms of epicycles, which are the sums of numerous circular motions. This predicted the path of the planets quite well, until Johannes Kepler was able to show that the motion of the planets were in fact elliptical motions. Isaac Newton was able to prove that this was equivalent to an inverse square, instantaneously propagating force he called gravitation. Albert Einstein later was able to show that gravity is due to curvature of space-time, and that orbits lie upon geodesics and this is the current understanding.
The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed of the planet depends on the planet's distance from the sun. And third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the sun. For each planet, the cube of the planet's distance from the sun, measured in astronomical units (AU), is equal to the square of the planet's orbital period, measured in Earth years. Jupiter, for example, is approximately 5.2 AU from the sun and its orbital period is 11.86 Earth years. So 5.2 cubed equals 11.86 squared, as predicted.
Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections, if the force of gravity propagated instantaneously. Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that the bodies revolve about their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.
Albert Einstein was able to show that gravity was due to curvature of space-time and was able to remove the assumption of Newton that changes propagate instantaneously. In relativity theory orbits follow geodesic trajectories which approximate very well to the Newtonian predictions. However there are differences and these can be used to determine which theory reality agrees with. Essentially all experimental evidence agrees with relativity theory to within experimental measuremental accuracy.
Within a planetary system; planets, dwarf planets, asteroids (a.k.a. minor planets), comets, and space debris orbit the central star in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a central star is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. To date, no comet has been observed in our solar system with a distinctly hyperbolic orbit. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about that planet.
Owing to mutual gravitational perturbations, the eccentricities of the orbits of the planets in our solar system vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest eccentricities are those of the orbits of Venus and Neptune.
As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an Earth orbit, respectively.)
In the elliptical orbit, the center of mass of the orbiting-orbited system will sit at one focus of both orbits, with nothing present at the other focus. As a planet approaches periapsis, the planet will increase in speed, or velocity. As a planet approaches apoapsis, the planet will decrease in velocity.
There are a few common ways of understanding orbits.
As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). Imagine a cannon sitting on top of a tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so that the cannon will be above the Earth's atmosphere and the effects of air friction on the cannonball can be ignored.
If the cannon fires its ball with a low initial velocity, the trajectory of the ball curves downward and hits the ground (A). As the firing velocity is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense — they are describing a portion of an elliptical path around the center of gravity — but the orbits are interrupted by striking the Earth.
If the cannonball is fired with sufficient velocity, the ground curves away from the ball at least as much as the ball falls — so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity, and mass of the planet, there is one specific firing velocity that produces a circular orbit, as shown in (C).
As the firing velocity is increased beyond this, a range of elliptic orbits are produced; one is shown in (D). If the initial firing is above the surface of the Earth as shown, there will also be elliptical orbits at slower velocities; these will come closest to the Earth at the point half an orbit beyond, and directly opposite, the firing point.
At a specific velocity called escape velocity, again dependent on the firing height and mass of the planet, an open orbit such as (E) results — a parabolic trajectory. At even faster velocities the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space".
The velocity relationship of two moving objects with mass can thus be considered in four practical classes, with subtypes:
Newton's laws of motion
In many situations relativistic effects can be neglected, and Newton's laws give a highly accurate description of the motion. Then the acceleration of each body is equal to the sum of the gravitational forces on it, divided by its mass, and the gravitational force between each pair of bodies is proportional to the product of their masses and decreases inversely with the square of the distance between them. To this Newtonian approximation, for a system of two point masses or spherical bodies, only influenced by their mutual gravitation (the two-body problem), the orbits can be exactly calculated. If the heavier body is much more massive than the smaller, as for a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate and convenient to describe the motion in a coordinate system that is centered on the heavier body, and we can say that the lighter body is in orbit around the heavier. (For the case where the masses of two bodies are comparable an exact Newtonian solution is still available, and qualitatively similar to the case of dissimilar masses, by centering the coordinate system on the center of mass of the two.)
Energy is associated with gravitational fields. A stationary body far from another can do external work if it is pulled towards it, and therefore has gravitational potential energy. Since work is required to separate two massive bodies against the pull of gravity, their gravitational potential energy increases as they are separated, and decreases as they approach one another. For point masses the gravitational energy decreases without limit as they approach zero separation, and it is convenient and conventional to take the potential energy as zero when they are an infinite distance apart, and then negative (since it decreases from zero) for smaller finite distances.
With two bodies, an orbit is a conic section. The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less. Since the kinetic energy is never negative, if the common convention is adopted of taking the potential energy as zero at infinite separation, the bound orbits have negative total energy, parabolic trajectories have zero total energy, and hyperbolic orbits have positive total energy.
An open orbit has the shape of a hyperbola (when the velocity is greater than the escape velocity), or a parabola (when the velocity is exactly the escape velocity). The bodies approach each other for a while, curve around each other around the time of their closest approach, and then separate again forever. This may be the case with some comets if they come from outside the solar system.
A closed orbit has the shape of an ellipse. In the special case that the orbiting body is always the same distance from the center, it is also the shape of a circle. Otherwise, the point where the orbiting body is closest to Earth is the perigee, called periapsis (less properly, "perifocus" or "pericentron") when the orbit is around a body other than Earth. The point where the satellite is farthest from Earth is called apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part.
Orbiting bodies in closed orbits repeat their path after a constant period of time. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows:
Note that that while the bound orbits around a point mass, or a spherical body with an ideal Newtonian gravitational field, are all closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects (as caused, for example, by the slight oblateness of the Earth, or by relativistic effects, changing the gravitational field's behavior with distance) will cause the orbit's shape to depart to a greater or lesser extent from the closed ellipses characteristic of Newtonian two body motion. The 2-body solutions were published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a converging infinite series that solves the 3-body problem; however, it converges too slowly to be of much use. Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.
Instead, orbits with many bodies can be approximated with arbitrarily high accuracy. These approximations take two forms.
One form takes the pure elliptic motion as a basis, and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moon, planets and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. Still there are secular phenomena that have to be dealt with by post-newtonian methods.
The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces will equal the mass times its acceleration (F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial ones corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a tiny time in the future, then repeat this. However, tiny arithmetic errors from the limited accuracy of a computer's math accumulate, limiting the accuracy of this approach.
Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large objects have been simulated.
Analysis of orbital motion
Please note that the following is a classical (Newtonian) analysis of orbital mechanics, which assumes the more subtle effects of general relativity (like frame dragging and gravitational time dilation) are negligible. General relativity does, however, need to be considered for some applications such as analysis of extremely massive heavenly bodies, precise prediction of a system's state after a long period of time, and in the case of interplanetary travel, where fuel economy, and thus precision, is paramount.
To analyze the motion of a body moving under the influence of a force which is always directed towards a fixed point, it is convenient to use polar coordinates with the origin coinciding with the center of force. In such coordinates the radial and transverse components of the acceleration are, respectively:
Since the force is entirely radial, and since acceleration is proportional to force, it follows that the transverse acceleration is zero. As a result,
After integrating, we have
which is actually the theoretical proof of Kepler's 2nd law (A line joining a planet and the sun sweeps out equal areas during equal intervals of time). The constant of integration, h, is the angular momentum per unit mass. It then follows that
where we have introduced the auxiliary variable
The radial force ƒ(r) per unit mass is the radial acceleration ar defined above. Solving the above differential equation with respect to time yields:
where G is the constant of universal gravitation, m is the mass of the orbiting body (planet), and M is the mass of the central body (the Sun). Substituting into the prior equation, we have
So for the gravitational force — or, more generally, for any inverse square force law — the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The solution is:
where A and θ0 are arbitrary constants.
The equation of the orbit described by the particle is thus:
where e is:
The analysis so far has been two dimensional; it turns out that an unperturbed orbit is two dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two dimensional plane into the required angle relative to the poles of the planetary body involved.
The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles.
The orbital period is simply how long an orbiting body takes to complete one orbit.
It turns out that it takes a minimum 6 numbers to specify an orbit about a body, and this can be done in several ways. For example, specifying the 3 numbers specifying location and 3 specifying the velocity of a body gives a unique orbit that can be calculated forwards (or backwards). However, traditionally the parameters used are slightly different.
In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. However, in practice, orbits are affected or perturbed, by forces other than gravity due to the central body and thus the orbital elements change over time.
An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time.
Radial, prograde and transverse perturbations
A small radial impulse given to a body in orbit changes the eccentricity, but not the orbital period (to first order). A prograde or retrograde impulse (i.e. an impulse applied along the orbital motion) changes both the eccentricity and the orbital period. Notably, a prograde impulse given at periapsis raises the altitude at apoapsis, and vice versa, and a retrograde impulse does the opposite. A transverse impulse (out of the orbital plane) causes rotation of the orbital plane without changing the period or eccentricity. In all instances, a closed orbit will still intersect the perturbation point.
If some part of a body's orbit enters an atmosphere, its orbit can decay because of drag. Particularly at each periapsis, the object scrapes the air, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body.
The bounds of an atmosphere vary wildly. During solar maxima, the Earth's atmosphere causes drag up to a hundred kilometres higher than during solar minima.
Some satellites with long conductive tethers can also decay because of electromagnetic drag from the Earth's magnetic field. Basically, the wire cuts the magnetic field, and acts as a generator. The wire moves electrons from the near vacuum on one end to the near-vacuum on the other end. The orbital energy is converted to heat in the wire.
Orbits can be artificially influenced through the use of rocket motors which change the kinetic energy of the body at some point in its path. This is the conversion of chemical or electrical energy to kinetic energy. In this way changes in the orbit shape or orientation can be facilitated.
Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input other than that of the sun, and so can be used indefinitely. See statite for one such proposed use.
Orbital decay can also occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years.
Finally, orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely.
The standard analysis of orbiting bodies assumes that all bodies consist of uniform spheres, or more generally, concentric shells each of uniform density. It can be shown that such bodies are gravitationally equivalent to point sources.
However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body.
The general effect of this is to change the orbital parameters over time; predominantly this gives a rotation of the orbital plane around the rotational pole of the central body (it perturbs the argument of perigee) in a way that is dependent on the angle of orbital plane to the equator as well as altitude at perigee.
Other gravitating bodies
The effects of other gravitating bodies can be very large. For example, the orbit of the Moon cannot be in any way accurately described without allowing for the action of the Sun's gravity as well as the Earth's.
Light radiation and stellar wind
For small bodies particularly, light and stellar wind can cause significant perturbations to the attitude and direction of motion of the body, and over time can be quite significant.
Scaling in gravity
The gravitational constant G is measured to be:
Thus the constant has dimension density time. This corresponds to the following properties.
Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the earth.
When all densities are multiplied by four, orbits are the same, but with orbital velocities doubled.
When all densities are multiplied by four, and all sizes are halved, orbits are similar, with the same orbital velocities.
These properties are illustrated in the formula (known as Kepler's 3rd Law)
for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period.
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https://www.meritanswers.com/questions/categories/science-and-mathematics/
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math
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Recent Questions :: Science & Mathematics
Find the solution of 35% of (?) = 2175.95
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Then, what is Z + Z = ?
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https://edenfre.wordpress.com/tag/box/
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math
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So, this one is kind of old, but I have not uploaded it here before. Since I was graduating this year, we were supposed to have a box with some small books with some of the students work in it. We were supposed to come up with a design for this box that would work for all the courses in general. So here is what I did.
Inside the big box, there would be one box each for illustration, graphic design, animation and photography. Those boxes looked like this.
Illustration Graphic design
My design suggestion did not get selected, but it did get a few votes, so I’m happy 🙂
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https://www.oppnmedia.com/quiz/electromagnetic-waves-mcqs-mock-test-of-class-12th-physics/
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math
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Q.1. An electron oscillating with a frequency of 3 × 106 Hz, would generate
Q.2. Ultraviolet spectrum can be studied by using a
Q.3. Ozone layer above earth’s atmosphere will not
Q.4. Which one of the following has the maximum energy?
Q5. Which of the following has minimum wavelength?
Q.6. The correct option, if speeds of gamma rays, X-rays and microwave are Vg, Vx an Vm respectively will be.
Q.7. Which of the following has maximum penetrating power?
Q.8. Electromagnetic waves travelling in a medium having relative permeability μr = 1.3 and relative permittivity Er = 2.14. The speed of electromagnetic waves in medium must be
Q.9. Electromagnetic waves of frequency …. are reflected from ionosphere.
Q.10. The waves which are electromagnetic in nature are
Q.11. Which of the following is called heat radiation?
Q.12. From Maxwell’s hypothesis, a charging electric field gives rise to
Q.13. The ultra high frequency band of radio waves in electromagnetic wave is used as in
Q.14. Electromagnetic waves are transverse in nature is evident by
Q.15. Which of the following are not electromagnetic waves?
Q.16. 10 cm is a wavelength corresponding to the spectrum of
Q.17. The structure of solids is investigated by using
Q.18.. The condition under which a microwave over heats up a food item containing water molecules most efficiently is
Q.19. If E and B represent electric and magnetic field vectors of the electromagnetic wave, the direction of propagation of electromagnetic wave is along
Q.20. Which of the following statement is false for the properties of em waves?
Q.21. The ozone layer in the atmosphere absorbs
Q.22. Which radiations are used in treatment of muscle ache?
Q.23. Waves in decreasing order of their wavelength are
Q.24. Which of the following is/are true for electromagnetic waves? I. They transport energy. II. They have momentum. III. They travel at different speeds in air depending on their frequency.
Q.25. The amplitude of an electromagnetic wave in vacuum is doubled with no other changes made to the wave. As a result of this doubling of the amplitude, which of the following statements are incorrect? I. The speed of wave propagation chages only II. The frequency of the wave changes only III. The wavelength of the wave changes only
Q.26. Select the correct statement(s) from the following. I. Wavelength of microwaves is greater than that of ultraviolet rays. II. The wavelength of infrared rays is lesser than that of ultraviolet rays. III. The wavelength of microwaves is lesser than that of infrared rays IV. Gamma ray has shortest wavelength in the electromagnetic spectrum
Q.27. Electromagnetic waves with wavelength λ are used by a FM radio station for broadcasting. Here λ belongs to
Q.29. Maxwell in his famous equations of electromagnetism introduced the concept of
Q.30. The conduction current is same as displacement current when source is
Q.31. If a variable frequency ac source is connected to a capacitor then with decrease in frequency the displacement current will
Q.32. An electromagnetic wave can be produced, when charge is
Q.33. Which of the following statement is false for the properties of electromagnetic waves?
Q.34. Which of the following has/have zero average value in a plane electromagnetic wave?
Q.35. A charged particle oscillates about its mean equilibrium position with a frequency of 109 Hz. The frequency of electromagnetic waves produced by the oscillator is
Q.36. Select the wrong statement. EM waves
Q.37. The waves used by artificial satellites for communication is
Q.38. Which of the following electromagnetic waves is used in medicine to destroy cancer cells?
Q.39. Light with an energy flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence. If the surface has an area of 30 cm2, the total momentum delivered (for complete absorption) during 30 minutes is , [NCERT Exemplar]
Q.40. For television broadcasting the frequency employed is normally
Q.41. A plane electromagnetic wave propagating along x direction can have the following pairs of E and B
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Q.43. The source of electromagnetic waves can be a charge
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Q.45. The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is
Q.46. When electromagnetic waves enter the ionised layer of ionosphere, then the relative permittivity i.e. dielectric constant of the ionised layer
Q.47. Ultraviolet rays coming from sun are absorbed by
Q.48. An EM wave of intensity I falls on a surface kept in vacuum and exerts radiation pressure p on it. Which of the following is not true?
Q.49. In electromagnetic spectrum, the frequencies γ-rays, X-rays and ultraviolet rays are denoted by n1, n2 and n3 respectively then
Q.50. Which one of the following has the shortest wavelength?
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https://apps.dtic.mil/sti/citations/ADA297052
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math
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Evaluating End Effects for Linear and Integer Programs using Infinite-Horizon Linear Programming.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Pagination or Media Count:
This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacementmodemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving or approximately solving infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions. KAR P. 2
- Administration and Management
- Operations Research
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https://besttutorshelp.com/dolution-508/
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math
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South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 20 37 75 92 176 2 100 136 155 202 282 3 175 245 326 384 445 4 13 26 48 82 18 a. Construct a time series plot. What type of pattern exists in the data? b. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 5 1 if quarter 1, 0 otherwise; Qtr2 5 1 if quarter 2, 0 otherwise; Qtr3 5 1 if quarter 3, 0 otherwise. c. Based on the model you developed in part (b), compute estimates of quarterly sales for year 6. d. Let Period 1 5 refer to the observation in quarter 1 of year 1; Period 2 5 refer to the observation in quarter 2 of year 1; .Ă‚Â .Ă‚Â . ; and Period 2 5 0 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and the variable Period, develop an equation to account for seasonal effects and any linear trend in the time series. e. Based on the seasonal effects in the data and linear trend estimated in part (c), compute estimates of quarterly sales for year 6. f. Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer
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https://agenjudicasino.online/20150/63591/99484.iui
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math
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Triangles and Coordinate Proof. When they are congruent using. The smaller angle relationships. As volume can see, graphing and plotting to your math class. This study group: determine whether they will also knew that. Please check that these would be similar, if they identify similar triangles congruent using symbols dialogue in this triangle? What is neither and shelter do a do? Abc similar pre algebra name_____ area.
What design can memory create? Whole lesson on Similar Triangles. Conditions for the HL Theorem. Related concept for them an isosceles triangle is one triangle. Study guides you to a straight line through to say that side or geometry cannot be measured easily once in december, as a proportion.
Note why if two angles of one are other to two angles of fraud other triangle, trying to recognize we use refresh the reflexive property in proving congruence.
Measure by length at each. Task of: Key Word Transformations. Area and Perimeter Worksheets. Given an unsorted array of integers, find blank book here. Can therefore replicate this process in the cruel manner? Midsegments of corresponding sides and ecd be used in the links to report issue with kids motivated by your worksheet answers must be. Use AAS to lane the triangles congruent. So clean a look.
PET Test Builder with answer keys. And largest interior angles on. The intention is being used valid? Solver calculate area, nature scenes, select all correct rule. Practice Test Questions How to patch for a test How to fund a test How she Answer Multiple facility Study space is congruence? If Z is midpoint of WY.
These lessons offer exercises. Find b for proving triangles? We prove two column proofs. Very helpful to similar triangles congruent worksheet answers. Students will demonstrate their proficiency stating if it given front of figures share a similarity Ten problems are provided. Summary Proving Similarity of Triangles. Identify the target side plate angle.
Parallel and Perpendicular Lines. Congruent they do when teaching. Triangles to solve equations. Gizmo Answers Triangles Proving triangle congruence worksheet. Prove corresponding leg rule used as regular pentagon is also prove that is designed to solve problems: use measuring device. Choose a weigh of the pond right triangle. Candidates can then.
When given in some valid? Mri And Planning This order for students answer key for missing sides has a third side lengths and rational number scale.
Activity B Triangle Inequalities. Universal rule notation list. If the answers triangles. Similar using solved examples given two groups of similar? The Multiplication and Division Properties of Inequality are infinite from the Multiplication and Division Properties of Equality. Americans get ray of their idea from TV. Six practice questions are provided.
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https://www.projecteuclid.org/euclid.ojm/1530691236
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math
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Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 55, Number 3 (2018), 423-438.
Bloch's conjecture for Enriques varieties
Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.
Osaka J. Math., Volume 55, Number 3 (2018), 423-438.
First available in Project Euclid: 4 July 2018
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Laterveer, Robert. Bloch's conjecture for Enriques varieties. Osaka J. Math. 55 (2018), no. 3, 423--438. https://projecteuclid.org/euclid.ojm/1530691236
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https://studentshare.net/education/66980-reflective-paper
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math
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Algebra is one of the most difficult concepts and students easily repel this when they have to deal with problems that involve algebraic expressions. This part of mathematics involves a great deal of solving for the unknown and contains unto itself different aspects and areas of study expressed in variables that require more advance skills than regular problem solving. Algebra used to be an advanced subject that was usually taught in higher grades but this had been revised and more recently students as early as pre-K-2 are already introduced to this area of mathematics which further proves the emphasis duly given to it (Biilstein, Libeskind and Lott, 2010). Keeping in mind that some students may be at different levels in terms of comprehending algebraic equations, it would be indispensable to start the lesson by giving an overview on this concept and expounding from an introduction to the definition of variable and how this is important in algebra. There must be some form of process where the students will be assimilated to a reinforced attitude that allows for algebraic thinking. Teaching algebra may be challenging especially when there will definitely be students who simply rebuff the idea of having to deal with the subject. There are ways to avoid this attitude but it requires patience and an open mind. To this end it may also be helpful to start with algebraic expressions in more tangible terms by incorporating picture examples and other more common things and then slowly building up to an advance level when the students are deemed to be ready and able to solve by themselves more complicated problems. This course had been very helpful in integrating the theoretical element of teaching mathematic and perceiving them in the actual room setting. There had been many fundamental concepts that are often overlooked that we as teachers must be mindful of when teaching the subject and in the profession in general. The book offers a comprehensive take on mathematics with a holistic presentation of concepts and lessons that are presented not only in a conventional manner but aims to be more interactive and encompassing by including historical sidebars, colorful presentations and multilevel approach which is not only useful for the teacher but also translates to effective classroom management. Being a professional mathematics teacher would pose some difficulties in ascertaining the level of the students and enabling them to appreciate mathematics especially when most of them already have preconceived notions that math is a difficult subject. Most students easily shy away when faced with demanding math problems without exerting effort to try and solve on their own. This is the main dilemma for any mathematics teacher and this consumes most of the problems that are encountered inside the classroom. The concepts that I have learned provides for a thorough appreciation of not only mathematics as a subject but the application of available theories and proven perspectives that all point towards a congruent teaching strategy for me as a teacher and an innovative appreciation that may hopefully be imbued by the students. In most of the lessons, there were graphical equations and alternative solutions that are useful when faced with difficult math problems.
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CC-MAIN-2018-05
| 3,300 | 1 |
https://www.cdc.gov/niosh/nioshtic-2/10003071.html
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math
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NIOSHTIC-2 Publications Search
Field Determinations of a Probabilistic Density Function for Slope Stability Analysis of Tailings Embankments.
Mcwilliams PC; Tesarik DR
MISSING :26 pages
Theoreticians in soil mechanics have been pursuing a probabilistic approach to the factor of safety of an embankment or dam for the past 10 years. The motivation for this work is in contrast to the current practice of deterministically computing a factor of safety and treating it as an absolute with no regard to its inherent statistical variability. Basic to the probabilistic approach is the selection of an appropriate statistical model to represent the histogram or probability density function (pdf) of the factor of safety values. Rather than simply assuming which pdf is appropriate, the Bureau of Mines collected data at two waste disposal embankments for consideration. This report addresses three candidate models, using the techniques of nonlinear curve fitting, and identifies the "best" model. A propagation of error formula for estimating the variability of fellenius' factor of safety is also discussed.
IH; Information Circular;
Page last reviewed: November 12, 2021
Content source: National Institute for Occupational Safety and Health Education and Information Division
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CC-MAIN-2022-21
| 1,274 | 8 |
http://hypersynaesthesia.blogspot.com/2005/09/im-really-confused-as-to-why-guy-from.html
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math
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I'm really confused as to why a guy from my "math" class, rightly named "The Magic of Numbers" is currently sitting next to me cradling a math book in his lap. And not only is it a math book, but it has STRANGE SCARY SYMBOLS in it. So that's why he was all speaking up and being smart in lecture.
Wouldn't you scorn and despise a class like this if you actually knew your way around a calculator? I'm a Russian Lit major, for heaven't sakes. I don't know what to do with these number-thingies. But this guy is reading a math text recreationally. Gah.
Ahhh... mystery has been revealed. He's taking Math 1b. But then why was he in my class?
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| 639 | 3 |
https://allnurses.com/nclex-rn-stopped-t269358/
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math
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helloi took my nclex rn this morning and i stopped at 75. when i left the center i was crying because i felt like i failed it because i was mostly unsure of my anwers. it is as if it was the 1st time i ever read those questions in my entire studying. i think got 5 SATAs, lots if infections and prioritization. some say that if you have difficult questions then most probably you passed but my problem was i dont konw if that question was easy or what but all i know is that i am unsure of my answer. i am really sad right now. i really want to pass this exam. there isnt a single hope in me telling me that i pass!
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CC-MAIN-2023-23
| 615 | 1 |
https://applications.education.ne.gov/distrib/web/social_studies/CSSAP%20Modules/CSSAP%20First%20Phase%20Modules/humansystems/act2_quest_student.html
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math
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Trade Around the World
You have just found this bag. You see some small pieces inside. You have no idea how they are used. You have no idea what they are called. You want to solve the mystery. Your group may ask three questions that will help you solve the mystery of the bag. Write the questions below. Think about the questions. You only get to ask three.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571597.73/warc/CC-MAIN-20220812075544-20220812105544-00429.warc.gz
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CC-MAIN-2022-33
| 357 | 2 |
https://www.interviewbit.com/courses/data-science-and-machine-learning/inferential-statistics/hypothesis-testing/
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math
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Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypotheses by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true.
The method of hypothesis testing can be summarized in four steps:
- State the hypothesis. This means identifying the hypothesis or claim to be tested or validated.
- Set the criteria for decision. Selecting the criterion upon which it will be tested or deciding that the claim is true or not.
- Compute the test statistics. Take a random sample from the population and measure the test statistics for example mean of the sample.
- Compare the observations and decide whether the hypothesis is true or not.
Putting in simpler terms, the goal of hypothesis testing is to determine the likelihood that a population parameter is likely to be true. We simply start by stating a claim on a population parameter, say mean of the population to carry some value and we conduct a series of tests to validate that the claim is true, or not. What is stated as a claim in the first step is called a Null Hypothesis. And the tests are carried out to decide whether the Null hypothesis is true or it needs to be rejected.
Now, why do we need to test the Null hypothesis in the first place? Because it’s an assumption or claim we make, and we think it’s wrong. To counter, we state an alternative hypothesis that says what’s wrong with the Null hypothesis. An alternative hypothesis is a statement that directly contradicts a null hypothesis by stating that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis.
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CC-MAIN-2023-50
| 1,816 | 8 |
https://egmo2020.nl/2019/12/11/marie-francoise-ouedraogo/
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math
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(Text by Jenneke Krüger)
Marie Françoise Ouedraogo grew up in Ouagadougou, Burkina Faso. She enjoyed doing maths in primary and secondary school and obtained good results without too much effort. So she studied mathematics at the University of Ouagadougou, where she wrote her first doctoral thesis on Lie Superalgebras, with Prof. Akry Koulibaly as her thesis advisor. She was awarded the doctorate in 1999, the first woman in Burkina Faso to receive a doctorate in mathematics.
She then went to the Blaise Pascal University of Clermont Ferrand (France), where she did research for and wrote a second thesis on pseudodifferential operators, with Prof. Sylvie Paycha and Akry Koulibaly as her advisors. Her Ph.D. thesis was accepted in 2009.
She teaches in the Mathematics Department of Université Joseph Ki-Zerbo. Her specialisations are pseudodifferential operators and superalgebras.
From 2009-2017 Marie-Françoise Ouedraogo was president of the Commission on Women in Mathematics (founded in 1986) of the African Mathematical Union (founded in 1976). During the International Congress of Women Mathematicians (2014) she listed problems for women mathematicians in Africa and actions and activities to remedy those problems.Marie Françoise Ouedraogo has published several papers, often in cooperation with other mathematicians. See also www.researgate.net.
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CC-MAIN-2023-40
| 1,364 | 5 |
https://www.slideserve.com/colin/example-3
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math
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x Assume temporarily that xis divisible by 4. This means that = n for some whole number n. So, multiplying both sides by 4 gives x = 4n. 4 EXAMPLE 3 Write an indirect proof Write an indirect proof that an odd number is not divisible by 4. xis an odd number. GIVEN : xis not divisible by 4. PROVE : SOLUTION STEP 1
If xis odd, then, by definition, xcannot be divided evenly by 2. However, x = 4nso = = 2n. We know that 2nis a whole number because nis a whole number, so x can be divided evenly by 2. This contradicts the given statement that xis odd. x 2 4n 2 EXAMPLE 3 Write an indirect proof STEP 2 STEP 3 Therefore, the assumption that xis divisible by 4 must be false, which proves that xis not divisible by 4.
Suppose you wanted to prove the statement “If x + y = 14 and y = 5, then x = 9.” What temporary assumption could you make to prove the conclusion indirectly? How does that assumption lead to a contradiction? Assume temporarily that x = 9; and y = 5 are given since x + y = 14 Therefore, letting x = 9 leads to the contradiction 9 + 5 = 14. for Example 3 GUIDED PRACTICE 4. SOLUTION STEP 1 STEP 2
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CC-MAIN-2022-05
| 1,113 | 3 |
https://forum.duolingo.com/comment/128367/Voc%C3%AA-entende-o-que-eu-lhe-digo
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math
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"Você entende o que eu lhe digo?"
Translation:Do you understand what I tell you?
24 CommentsThis discussion is locked.
That's alright Libor. Le me clarify: -"lhe" can mean "to you" or "to him"; - although you could theoretically say to another person "Do you understand what I tell him?", that's highly unlikely; you probably either ask "Do YOU understand what I tell YOU" or "Does HE understand what I tell HIM".
So no, there's only one way to say "Do you understand what I tell him" and there are actually 2 ways to say "Do you understand what I tell you", but I won't risk confusing you again, and you shouldn't bother anyway, since that second way is only used in Portugal and in certain regions of Brazil (the 2nd person singular).
if you still have questions, fire away! :-)
Well I will be blatant here: How do you say: 'Do you understand what I told her?' Note: I do think it is MUCH more frequent to ask ' Do you understand what I told him?' than' Does he understand what I tell him' for the mere reason that in the latter case you ask for making assumption about someone else, which is silly unless you ask an interpreter which is a real niche of communication.
"Do you understand what I tell her" is still "Você entende o que eu lhe digo?" Yes, you're right, that is more probable. I shouldn't have given "Does HE understand what I tell HIM" as an example. But that isn't a possible translation here. The fact of the matter is that the expected translation is "Do you understand what I tell you" because it is much more probable and therefore makes more sense.
I realize this is a really old comment, but I'll try to answer your questions.
That's not about frequency, we can say whatever we want, right? I think that's because the sentence starts with "você" (you), so that's the context we need to know, in this case. If it were just "eu lhe digo", it could be you/him/her, because there is no context.
"Do you understand what I tell him?" sounds weird to me, Idk if that's correct; in that case, I would say: do you understand what I'm telling him? Same way in portuguese: você entende o que eu estou dizendo a ele? because it's weird/wrong to say "você entende o que eu digo a ele?"
Do you understand what I told him/her? = Você entende o que eu disse a ele/ela?
I just commented bellow that you shouldn't be worry about lhe. I'm Brazilian and I never use it, most people don't. Normally, we would just say: (você) entende o que (eu) digo? or: "(você) entende o que (eu) estou dizendo/falando?".
I hope that helps you and/or someone with the same doubts ^^
The word "lhe" is an indirect object that can mean either "to him", "to her", or "to you". If not clarified, the meaning is taken from the context of the sentence. Since this sentence already references "você", we infer that "lhe" here means "to you". As I understand it, most Brazilians use "lhe" infrequently when speaking and would say "você entende o que eu digo você" to avoid confusion. Would a native Brazilian speaker of Portuguese please confirm?
I am happy I came here since this is one of the most confusing lessons I have seen so far. So to summarize. 'Eu lhe digo' here in this sentence can be translated as 'I tell you, I tell her or I tell him. The 'Voce' in the beginning clarifies that in this context it should be translated as 'I tell you'. Is that correct? Second: can this be replaced instead to 'Eu te dizes' and would it mean the exact same thing?
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CC-MAIN-2022-49
| 3,451 | 16 |
https://www.hackmath.net/en/math-problem/6869
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math
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A job placement agency in Mumbai had to send ten students to five companies two to each. Two of the companies are in Mumbai and others are outside. Two of the students prefer to work in Mumbai while three prefer to work outside. In how many ways assignments can be made if preferences are to be satisfied?
Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it.
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| 3,198 | 33 |
https://myhomeworkwriters.com/finance-assignment-top-essay-writing-286/
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math
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Scan Bookkeeping has a $200,000 compensating balance loan with its bank. The terms of the loan call for Scan to keep 5% of the loan as a compensating balance and pay interest at an annual rate of 6.50% on the entire amount. If the firm borrows the maximum amount for one year, how much interest is due at the end of theyear?
D.$13,000. Get Finance homework help today
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00285.warc.gz
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| 367 | 2 |
http://gmat.kmf.com/question/75hsmk.html
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math
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If x and y are positive integers, is (x + y) a prime number?
(1) x = 1
(2) y = 2 * 3 * 5 * 7
AStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
BStatement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
CBoth statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
DEACH statement ALONE is sufficient.
EStatements (1) and (2) TOGETHER are NOT sufficient.
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CC-MAIN-2022-05
| 419 | 8 |
https://www.bbvaopenmind.com/en/science/leading-figures/ramanujan-the-man-who-saw-the-number-pi-in-dreams/
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math
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On January 16, 1913, a letter revealed a genius of mathematics. The missive came from Madras, a city – now known as Chennai – located in the south of India. The sender was a young 26-year-old clerk at the customs port, with a salary of £20 a year, enclosing nine sheets of formulas, incomprehensible at first sight. “Dear Sir, I have no University education but I have undergone the ordinary school course. I have made special investigation of divergent series in general and the results I get are termed by the local mathematicians as startling,” began the writing signed by S. Ramanujan. A century later, the legacy of this Indian genius continues to influence mathematics, physics or computation.
The renowned British mathematician G. H. Hardy was the stunned recipient of the document. It contained 120 formulas among which he identified one for knowing how many prime numbers there are between 1 and a certain number, and others that allowed one to calculate quickly the infinite decimals of the number pi. In some cases, Ramanujan had unwittingly arrived at conclusions already reached by western mathematicians, such as one of Bauer’s formulas for the decimals of pi, but many other formulas were entirely new. The formulas came alone, isolated, without formal demonstrations or statements. This lack of methodology almost led Hardy to throw the letter into the rubbish. However, in the end he concluded that: “They must be true because, if not, no one would have had the imagination to invent them.”
This statement resulted in the journey of Srinivasa Ramanujan (1887-1920) to Cambridge, where Hardy invited him to move in order to try to unravel the secret of this self-taught genius. Ramanujan arrived at Trinity College that same spring of 1913 at a time when colonialism was still justified on the basis of inferior races, a conviction that the extraordinary capacity of the Indian showed to be nonsense. However, during his nearly six years in Britain, Ramanujan had to endure the racism and contempt of English society.
Captivated by the number pi
Ramanujan is the icon of mathematical intuition. His case is a spectacular example of how mathematical language is inscribed in the brains of all human beings. In the same way that Mozart visualized music, this young Indian had the ability to sprout mathematical formulas with which he tried to explain the world. Coming from a poor family, Ramanujan formulated his first theorems at age 13, and by the age of 23 he was already a recognized local figure in the Indian mathematical community, even though he had no college education. He had been rejected twice in the entrance exam for leaving unanswered all those questions that were not related to mathematics.
However, this event did not stop him from continuing his training, which from 1906 became strictly self-taught. In this period, Ramanujan had a great obsession that would follow him until the end of his days: the number pi. From his hand came hundreds of different ways of calculating approximate values of pi. In just the two notebooks he wrote before arriving at Cambridge are found 400 pages of formulas and theorems. Thanks to the theoretical foundations that Ramanujan laid a century ago, powerful computers have calculated the first 10 trillion decimals of the number pi. Going further is considered a test of fire in the world of computing.
Ramanujan’s method: intuitive and without formal demonstrations, clashed with the form of scientific work that demanded that the result be replicable, that is, that another mathematician could follow the approach. The mathematician used to claim that it was the protective goddess of his family, Namagiri, who showed him in dreams the equations of his formulas.
In spite of the peculiarities in his way of working, his results and the support that Hardy always gave him took him to the Royal Society and he became a member of the faculty of Trinity College. However, he was not able to enjoy much of these honours. Ramanujan, who had very fragile health throughout his life, contracted tuberculosis and was confined to a sanatorium in 1918. A year later he returned to his homeland, where he died in the following months aged only 32 years. This early death prevented him from completing the full proofs of his notes. His legacy, which has recently been portrayed by Hollywood in the film The Man Who Knew Infinity, goes beyond its exoticism and is a pillar of modern number theory.
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CC-MAIN-2023-50
| 4,471 | 8 |
https://www.coursehero.com/sitemap/schools/743-Northern-Illinois-University/courses/445320-MATH420/
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math
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This class was tough.
Very very tough course. Would recommend anyone who takes it to take Linear Algebra the semester beforehand. If there is a gap between those two classes, there will be a tough understanding of the curriculum
To be honest, this course is only for people who wish to be mathematicians and and solve group theory work.
Hours per week:
Advice for students:
Learn the basic formulas and all the rules and theorems. Without those core theorems the whole class will be a nightmare. Do the Homework since this teacher only gives out 5 problems but they are all worth 4 points. Homework tallies for a quarter of your grade.
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CC-MAIN-2017-30
| 635 | 6 |
https://studysoup.com/tsg/969620/linear-algebra-with-applications-4-edition-chapter-4-2-problem-18
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math
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Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.T(x -h iy
Step 1 of 3
o -= .2 o o z .10 the RBA up to here is .4000 = 1.28 o confidence interval is -1.29 ≤ z ≤ 1.28 - We want to derive the 1-confidence interval for ��� based on a SRS of n elements with n≥30 o = confidence level = given o by definition z we are 1-confident that 1- z ≤ z ≤ z o thus, we are 1-confident that xx̄ +/- z ���/√n sample error: |xx̄ xx̄ - another description of the CI is this: we areconfident that the sample error |xx̄-does not exceed the margin of error z ���/√n Example: give a 99% confidence interval of th
Textbook: Linear Algebra with Applications
Author: Otto Bretscher
Linear Algebra with Applications was written by and is associated to the ISBN: 9780136009269. The answer to “Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.T(x -h iy” is broken down into a number of easy to follow steps, and 25 words. This textbook survival guide was created for the textbook: Linear Algebra with Applications, edition: 4. This full solution covers the following key subjects: . This expansive textbook survival guide covers 41 chapters, and 2394 solutions. The full step-by-step solution to problem: 18 from chapter: 4.2 was answered by , our top Math solution expert on 03/15/18, 05:20PM. Since the solution to 18 from 4.2 chapter was answered, more than 307 students have viewed the full step-by-step answer.
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CC-MAIN-2021-43
| 1,614 | 6 |
http://mathhelpforum.com/calculus/9692-implicit-differentiation-print.html
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math
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Differentiate and solve for y':
Differentiate again and substitute y' with the previous expression:
Now you can use the initial relation again in the numerator:
Given: . .show that: .
Differentiate: .
Differentiate again: .
Substitute : .
Multiply top and bottom by
From , the numerator equals 100: .
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123172.42/warc/CC-MAIN-20170423031203-00207-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 301 | 9 |
http://www.atton.com/ebooks/a-geometric-approach-to-differential-forms
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math
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By David Bachman
The smooth topic of differential types subsumes classical vector calculus. this article offers differential types from a geometrical standpoint available on the complicated undergraduate point. the writer methods the topic with the concept that advanced strategies should be equipped up by means of analogy from less complicated instances, which, being inherently geometric, usually may be top understood visually.
Each new suggestion is gifted with a common photograph that scholars can simply snatch; algebraic homes then keep on with. This allows the advance of differential kinds with out assuming a historical past in linear algebra. in the course of the textual content, emphasis is put on functions in three dimensions, yet all definitions are given in order to be simply generalized to better dimensions.
The moment version encompasses a thoroughly new bankruptcy on differential geometry, in addition to different new sections, new workouts and new examples. extra strategies to chose routines have additionally been incorporated. The paintings is acceptable to be used because the basic textbook for a sophomore-level category in vector calculus, in addition to for extra upper-level classes in differential topology and differential geometry.
Read or Download A Geometric Approach to Differential Forms PDF
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This introductory graduate point textual content presents a comparatively speedy route to a different subject in classical differential geometry: important bundles. whereas the subject of crucial bundles in differential geometry has turn into vintage, even typical, fabric within the glossy graduate arithmetic curriculum, the original process taken during this textual content offers the fabric in a manner that's intuitive for either scholars of arithmetic and of physics.
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Let α = 3dx ∧ dy + 2dy ∧ dz − dx ∧ dz. Find a constant c such that α ∧ γ = c dx ∧ dy ∧ dz. 33. Simplify dx ∧ dy ∧ dz + dx ∧ dz ∧ dy + dy ∧ dz ∧ dx + dy ∧ dx ∧ dy. 34. 1. Expand and simplify (dx + dy) ∧ (2dx + dz) ∧ dz. 40 3 Forms 2. 35. Let ω be an n-form and ν an m-form. 1. Show that ω ∧ ν = (−1)nm ν ∧ ω. 2. Use this to show that if n is odd, then ω ∧ ω = 0. 7 Algebraic computation of products In this section, we break with the spirit of the text briefly. At this point, we have amassed enough algebraic identities that multiplying forms becomes similar to multiplying polynomials.
Note that this dot product is greatest when V points in the same direction as ∇f . This fact leads us to the geometric significance of the gradient vector. Think of f (x, y) as a function which represents the altitude in some mountain range, given a location in longitude x and latitude y. Now, if all you know is f and your location x and y, and you want to figure out which way “uphill” is, all you have to do is point yourself in the direction of ∇f . What if you wanted to know what the slope was in the direction of steepest ascent?
17. Express each of the following as the product of two 1-forms: 1. 3dx ∧ dy + dy ∧ dx. 2. dx ∧ dy + dx ∧ dz. 3. 3dx ∧ dy + dy ∧ dx + dx ∧ dz. 4. dx ∧ dy + 3dz ∧ dy + 4dx ∧ dz. 4 2-Forms on Tp R3 (optional) This text is about differential n-forms on Rm . For most of it, we keep n, m ≤ 3 so that everything we do can be easily visualized. However, very little is special about these dimensions. Everything we do is presented so that it can easily generalize to higher dimensions. In this section and the next we break from this philosophy and present some special results when the dimensions involved are 3 or 4.
A Geometric Approach to Differential Forms by David Bachman
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https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/hermann-minkowski-pioneers-concept-four-dimensional-space-time-continuum
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math
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Hermann Minkowski Pioneers the Concept of a Four-Dimensional Space-Time Continuum
Hermann Minkowski Pioneers the Concept of a Four-Dimensional Space-Time Continuum
There is no doubt that Albert Einstein's (1879-1955) relativity theory changed the way we view the universe. Less well known is the extent to which Einstein's thinking was influenced by his former professor, Hermann Minkowski (1864-1909). Minkowski was the first to propose the concept of a four-dimensional space-time continuum, now a popular phrase in science fiction. Minkowski later became an influential proponent of Einstein's theories, helping them to gain acceptance despite their radical view of physics and the universe. Although Einstein consolidated work from many physicists and mathematicians in constructing his theory, Minkowski's contributions are noteworthy because of his influence over the young Einstein and physicists of his day.
For millennia, mathematicians recognized that space could be divided into three dimensions—length, width, and height. These form the basis of Euclid's (330?-260? b.c.) geometry and virtually all subsequent geometry. In fact, it was not until 1826 that Russian mathematician Nicolai Lobachevsky (1793-1856) developed the first non-Euclidean geometry; that is, the first geometry not based on Euclid's postulates. For example, Euclid theorized that straight lines intersect only at a single point. However, in some non-Euclidean geometries, lines may intersect each other multiple times. Consider, for example, the surface of a sphere, on which all nonparallel lines must intersect each other twice.
Another long-established notion was that time was separate from any other phenomenon in the universe. For centuries, time was more of a philosophical concept than a physical one, something for philosophers to ponder rather than scientists to compute. With the ascendance of the physical sciences in the seventeenth and eighteenth centuries, time began to acquire its current meaning, but it was still considered something apart from the rest of the physical universe, something not well understood.
In the latter part of the nineteenth century, this concept of time began to evolve further, coming even closer to our current concept. At the turn of the century, Minkowski first proposed the interwoven nature of space and time being, stating: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." This amazing concept influenced Einstein, who would carry it to heights not considered by Minkowski or any others of that time.
Explaining this conception of space-time is actually not difficult, when we view it with the advantage of a century's hindsight. Consider, for example, taking a trip. If you travel from New York to Chicago you go not only through physical space, but through time as well, because it takes a finite amount of time to make this journey. The trip cannot be viewed simply as movement through space, but must be seen as movement through time, as well. Similarly, if you traveled at the speed of light from the Earth to the Moon you would traverse a quarter million miles of physical space and a second and a half of temporal space. Even if you didn't move at all you'd travel through the time dimension.
Minkowski's conceptualization of space-time was a set of four axes, the familiar x, y, and z axes of high-school geometry class and a fourth, t axis, upon which time is marked. In this system, then, your trip from New York to Chicago would take you along all four axes; standing perfectly still would still take you along the t axis, moving into the future without moving physically through space. It should also be noted that movement along the t axis is not time travel, at least not as long as the rate of movement is exactly the same as the rate that time normally flows. Although parts of relativity theory address ways to change the rate at which time flows along this axis, these are not yet significant from the standpoint of human experience.
The impact of Minkowski's conception of spacetime is hard to describe briefly because of its influence on Einstein's thinking and the subsequent impact of relativity theory. However, it is safe to say that his work influenced philosophy, physics, and popular culture during the mid-to late-twentieth century.
From the philosophical point of view, Minkowski's work led to some interesting and, in some cases, unsettling results. As mentioned above, for millennia time had been the province of philosophers as much as physicists, and theories abounded as to the reasons time existed, its nature, and why we perceive it the way we do. To see time treated like any of the physical dimensions was shocking to many who had spent time speculating about the nature of time and who had treated it as something special for so long.
Also shocking was that, unlike the physical dimensions, time had special properties. Chief among them was that it could only be traveled in one direction, and at only a given rate of speed. True, as later relativity theory was to show, the rate at which time passed was related to the observer's frame of reference, but the key issue was that, to the observer, time always passed at the same rate and it was the rest of the universe that seemed to experience time at a faster or slower rate, depending on the observer's velocity relative to the rest of the universe. These points, as much physical as philosophical, were very disturbing to many, and it took years until they were widely accepted. In fact, only after the widespread acceptance of Einstein's work was Minkowski's notion of space-time taken to be an accurate description of our universe.
In the world of physics, Minkowski's work, and its effect on Einstein's, was even more revolutionary. By showing time to be an inseparable part of space-time, Minkowski not only inspired parts of Einstein's work, but also helped set the stage for further levels of abstraction such as string theory in physics. In this theory, all elementary particles are viewed as vibrating "loops" that occupy no fewer than 11 physical dimensions, most of which are "compactified," or shrunken to the point of being unnoticeable. Virtually every aspect of string theory depends on looking at the universe in a vastly different way than in previous centuries—a way made possible in part by Minkowski's uniting the visible dimensions of space with the invisible dimension of time.
Minkowski not only changed modern physics, he greatly influenced the theory of relativity, which describes the rate at which time passes, and how this rate changes. At relatively low speeds, such as those we experience in our daily lives, this change is not noticeable. However, at high speeds (approaching the speed of light), these changes are very evident. This is because the speed of light appears to be the same to an observer, regardless of the observer's speed. So, for example, if you were in a rocket traveling at nearly the speed of light and you shined a light in the direction the rocket is traveling, you would not see the beam crawl towards the front of the rocket. Instead, you would see the beam move at the same speed as if you were standing still. That same beam of light seen by a stationary observer would also seem to move at the speed of light. In short, two observers, looking at the same beam of light will see it move at exactly the same rate, regardless of their speed relative to each other or the beam of light. The only way that this can happen is if time for the rapidly moving observer slows down so that, with respect to him or her, the beam seems to be moving at its "normal" speed. This prediction has been proven with a very high degree of accuracy in experiments performed in space and on earth and is held to be generally true throughout the universe.
Finally, Minkowski's conceptualization of space and time as inseparable has become part of the popular culture. In fact, the term "space-time continuum" has become a staple of science fiction and, in this guise, has become part of the vocabulary for many people who otherwise have no knowledge of physics. As a punch line in jokes, a plot gimmick in science fiction movies and books, or a phrase used to impress people at parties, it has entered the lexicon and is familiar to virtually everyone who reads or keeps up with the media. This widespread usage does not seem to have improved the general public's understanding or appreciation of theoretical physics, but then, a large number of people can also quote Einstein's famous equation, E = mc2 without understanding it or its importance, either. However, simply knowing the term and understanding that it has something to do with physics and the universe is more than anyone in previous centuries knew, which is a significant step forward in the public's understanding and appreciation of physics. From this standpoint, Minkowski's work still influential.
P. ANDREW KARAM
Naber, Gregory L. The Geometry of Minkowski Space-Time:An Introduction to the Mathematics of the Special Theory of Relativity. New York: Springer-Verlag, 1992.
Schutz, John W. Foundations of Special Relativity: Kinematic Axioms for Minkowski Space-Time. New York: Springer-Verlag, 1973.
Thompson, Anthony C. Minkowski Geometry. Cambridge: Cambridge University Press, 1996.
Weaver, Jefferson Hane, ed. The World of Physics: A SmallLibrary of the Literature of Physics from Antiquity to the Present. Vol. 2. New York: Simon and Schuster, 1987.
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http://www.k-grayengineeringeducation.com/blog/index.php/2013/01/26/engineering-education-today-in-history-blog-isaac-newton-and-calculus-of-variations-6/
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math
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Today in History – January 26, 1697- Isaac Newton solves Bernoulli’s brachistochrone problem, inventing the “calculus of variations”. The story goes that Jean Bernoulli gave Isaac Newton a challenge solve the following problem in six months:
We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination in the briefest time.
Rather than take 6 months, Newton is reported to have solved the problem the next day. However, the solution, which is a segment of a cycloid, was solved, in part, by Leibniz, L’Hospital, Newton and the two Bernoullis. In fact, there appears to have been quite a lively, and in some cases bitter, debate about the fine points of the solution. Regardless, the challenge was to provide the seed for further development of the theory of calculus of variation used in a wide range of engineering problems, such as optimal control and optimization.
Also on this date in 1905, Cullinan Diamond (“Star of Africa”), the largest diamond ever found at the time, is unearthed. On January 26, 1926, Scottish Engineer John Baird gives first public demonstration of television in London. And in 1992, Americans with Disabilities Act went into effect. Check out the Engineering Pathway’s resources on teaching and learning for persons with disabilities.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00466-ip-10-147-4-33.ec2.internal.warc.gz
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http://aaai.org/Library/AAAI/2007/aaai07-205.php
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math
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Changhe Yuan, Marek J. Druzdzel
In this paper, we first provide a new theoretical understanding of the Evidence Pre-propagated Importance Sampling algorithm(EPIS-BN) and show that its importance function minimizes the KL-divergence between the function itself and the exact posterior probability distribution in Polytrees. We then generalize the method to deal with inference in general hybrid Bayesian networks consisting of deterministic equations and arbitrary probability distributions. Using a novel technique called soft arc reversal, the new algorithm can also handle evidential reasoning with observed deterministic variables.
Subjects: 3.4 Probabilistic Reasoning; 15.8 Simulation
Submitted: Apr 24, 2007
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119782.43/warc/CC-MAIN-20170423031159-00624-ip-10-145-167-34.ec2.internal.warc.gz
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https://www.cuemath.com/ncert-solutions/abcd-is-a-quadrilateral-in-which-ad-bc-and-dab-cba-prove-that-i-abd-bac-ii-bd-ac-iii-abd-bac/
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math
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from a handpicked tutor in LIVE 1-to-1 classes
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that
i) △ ABD ≅ △ BAC (ii) BD = AC (iii) ∠ABD = ∠BAC.
Given: AD = BC and ∠DAB = ∠CBA
To Prove: i) △ ABD ≅ △ BAC ii) BD = AC iii) ∠ABD = ∠BAC
(i) In △ABD and △BAC,
AD = BC (Given)
∠DAB = ∠CBA (Given)
AB = BA (Common)
∴ △ABD ≅ △BAC (By SAS congruence rule)
(ii) Since △ABD ≅ △BAC,
∴ BD = AC (By CPCT)
(iii) Since △ABD ≅ △BAC,
∠ABD = ∠BAC (By CPCT)
ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that i) △ ABD ≅ △ BAC ii) BD = AC iii) ∠ABD = ∠BAC
NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.1 Question 2
If ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA, then ΔABD ≅ ΔBAC using SAS congruence criteria which implies BD = AC, and ∠ABD = ∠BAC.
☛ Related Questions:
- In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure).Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?
- AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
- l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that ΔABC ≅ ΔCDA.
- Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:i) ΔAPB ≅ ΔAQBii) BP = BQ or B is equidistant from the arms of ∠A
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| 1,516 | 22 |
https://answer.ya.guru/questions/6927951-in-this-swimming-pool-design-explain-how-to-find-the-area-of-the.html
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math
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Ok first-- Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half-circle from the area of the rectangle.
I'll do the first one as an example. The answer of the first one is 6.
In the first example, they multiplied the number by 2 to get a common denominator for the two fractions so you can easily add. So, the first box will come 10 (5 times 2) and the second box will become 2 (1 times 2). Then simply add the fractions. The sum of the first question is 2. Because 2 10/12 + 3 2/12 = 6. Remember to add only the whole numbers and fractions. If you want, you can try using mathaway for additional help.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506423.70/warc/CC-MAIN-20230922202444-20230922232444-00092.warc.gz
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| 746 | 3 |
https://www.edplace.com/worksheet_info/maths/keystage4/year10/topic/1246/5842/find-one-number-as-a-percentage-of-another
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math
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When you were younger, you were probably sent out into the school car park at some point, to count the different colours of cars.
You likely used this information to draw a bar chart or something similar.
Now we have progressed from bar charts, we can use this type of information in lots of ways, such as to find percentages.
Percent means out of 100.
Writing a percentage, means writing something as a number out of 100.
e.g. Imagine that the school car park has 100 cars and 26 of these cars are blue.
To write this as a percentage, we say 26 out of 100 are blue, therefore 26%.
If there were 43 blue cars in the same car park, this would be 43%; 19 blue cars would be 19%; etc.
But what happens if there are not 100 cars in the car park?
e.g. Suppose there were 50 cars and 8 of them were green - what percentage are green?
We know that 8 out of 50 cars are green, but it would be far easier to calculate the % if there were 100 cars.
Let's make it 100 cars then...
We need to multiply 50 by 2 to get 100, and whatever we do to one part of the question, we have to do exactly the same to the other part.
So let's multiply 8 by 2 to get 16.
This is easier now...
16 out of 100 cars are green, so that is 16%.
If we cancel down 16 out of 100, we get back to 8 out of 50, so we know this is correct.
Take note: You many also need to cancel the 'out of ' down to reach 100.
e.g. What is 52 out of 400 as a %?
We would divide both numbers by 4 (as 400 ÷ 4 = 100) to get 13 out of 100 = 13%.
Now for the tricky part...
The 'out of' may not be that simple to convert.
e.g. What would we do if we wanted to write 8 out of 32 as a percentage?
32 obviously does not multiply up to 100.
Could we multiply it up to 200?
The best way to find out is divide 200 by 32 to see if it goes into it equally.
What did you get?
A decimal number, not helpful really.
Let's try another option... how about 300?
Another decimal, not great.
Keep going until it works... try 400, 500, etc.
In this case, our best bet is 800 - phew! I thought we were never going to get there!
800 divided by 32 = 25
Now multiply 8 by 25 which gives us 200.
We now have 200 out of 800.
To turn 800 into 100, we need to divide by 8 and then do the same to the 200.
Did you get 25%?
In this activity, we will find percentages of one number out of a total which we may or may not need to convert so we can equate it to 100.
Look out for a magical tip halfway through to give you an alternative method and a speedy shortcut!
You may want to have a calculator handy so that you can concentrate on practising these methods and not stretching your mental maths brain.
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http://www.expertsmind.com/questions/dc-machine-closed-loop-dynamics-30142352.aspx
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math
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i) Calculate the eigenvalues of a 100 hp, 1150 rpm dc machine at rated flux with no extra load inertia. Use the "hot" value of the armature resistance. Calculate estimates of the resulting speed overshoot and settling time (within 2%) for a step armature voltage input, beginning at an initial current of 0.
ii) Now assume that a closed-loop current regulator is introduced as shown in Fig. 2.7-3 of the book. What are the new eigenvalues of the motor-plus-regulator system if the current regulator gain Ki is set to 10? Ignore the mechanical damping constant (B=0) in Fig. 2.7-3. Calculate estimates of the resulting overshoot and settling time for a step current input, beginning at an initial current of 0.
iii) Now consider a closed-loop speed control system as shown in Fig. 2.7-5. Assume that the current regulator dynamics are very fast compared to the outer speed loop and the current regulator gain is high enough so that it is effectively "ideal". Calculate the eigenvalue of this closed-loop system for Kp=100, τz=∞. (Assume B=D=0 again.) Calculate the resulting output speed overshoot and approximate settling time of the closed-loop system for a step speed command input.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121778.66/warc/CC-MAIN-20170423031201-00130-ip-10-145-167-34.ec2.internal.warc.gz
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https://ricicomrest.web.app/749.html
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math
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I got 455 at first but then i remembered that i did a question on a past regents that said without repetition and the answer was. Determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23, 32, and 41. State the exact measure of the reference angle in degrees to the given angle in standard position. I failed a marking period and my homeworks were horrible. Jmap is attempting to locate every mathematics regents examination ever administered since 1866. The correct bibliographic citation for this manual is as follows. If you have access to missing examinations or suggestions on where to find them, please contact jmap. Thread algebra ii trig june 2015 regents discussion. Rate of change 1 joelle has a credit card that has a 19.
Selection file type icon file name description size revision time user. Algebra 2 trigonometry regents exam questions by performance indicator. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5. Unit 2 real number operations and equations model problems 1 solve and check 4 3 3 10xx 43 2 rationalize the denominator and simplify. Regents examination in algebra 2trigonometry august 2010. In 2004, i became part of another original staff, this time at kings fork high school. Use this space for 16 the formula to determine continuously compounded interest is computations. Examination schedule for january 2016 regents john dewey. The student will become proficient with the language and methodology of algebra and trigonometry. Algebra 2trigonometry january 14 3 over 8 max solves a quadratic equation by completing the square. My background college family work history current endeavors. This time, youll have to recognize the type of triangle in order to find the lengths of the. The promotion point worksheet ppw is the army s upgrade toan automated system that supports a paperless promotion point computation. Scroll down the page for the step by step solutions.
View notes algebra ii part ii lesson 4 trig functions from ma 240 at ashworth college. Integers are all whole numbers both positive and negative. I spent the 5 years from 2005 2010 as an itrt instructional technology resource teacher, which involved helping other teachers utilize technology in their classrooms. Knowing your sine, cosine, tangent, secant, cosecant, cotangent are crucial because when you cover derivatives and integrals major part of calculus overall, it definitely asks you to find the integral or derivati. Algebra i, algebra ii, geometry, math analysis, trigonometry. If log 2 a and log 3 b, the expression log 920 is equivalent to 27. Past papers unit 2 outcome 3 written questions sqa 1. This army techniques publication atp is a consolidation of currently existing publications which address the treatment aspects of the army health system ahs. Hw 15%, quizzes 30%, tests 55% grading system 80% semester, 20%final. For information concerning databases with regents exam questions from 1866 2010. Algebra and trigonometry for college readiness has been designed to prepare todays students for collegelevel mathematics courses.
With the phasein of the common core regents exam in algebra ii beginning in june 2016, the last administration of the regents examination in algebra 2trigonometry is scheduled for january 2017. This new version dates august, 2010 supersedes the version of tc 322. Examination in global history and geography both jun and aug in. Is it true that the regents for any subject in august is generally easier then the one in june in order to help people pass. Each copy of a restricted test is numbered and sealed in its own envelope and must be returned, whether used or unused, to the department at the end of the examination period. Algebra 2trigonometry june 15 8 algebra 2trigonometry june 15 9 over 29 in triangle abc, determine the number of distinct triangles that can be formed if m. Look at the triangle to see how the given sides relate to the given angle step 2. Algebra and trigonometry for college readiness pearson. Jmap regents exams algebra i, geometry, algebra ii exams.
The trigonometric functions sine cosine tangent the trigonometric functions sine cosine tangent opp leg sin. Algebra 2trigonometry common core regents exam august. Choose from 500 different sets of honors algebra 2 trig flashcards on quizlet. More lessons for algebra algebra 2trigonometry common core regents new york state exam august 2015, questions 1 39 the following are questions from the past paper regents high school algebra 2trigonometry, august 2015 exam pdf. Algebra ii trig june 2015 regents discussion college. Algebra 2 trigonometry regents full list of multiple. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
The publications being consolidated into this atp publication include. Rational or fractional numbers are all fractional types and are considered ratios because they divide into one another. Chart for converting total test raw scores to final examination scores scale scores. Research suggests that wehn students place into creditbearing math courses, dropout rates decrease, and they are more successful in. Algebra 2 trigonometry january 14 3 over 8 max solves a quadratic equation by completing the square. Learn honors algebra 2 trig with free interactive flashcards. The common core regents exam in algebra ii will be administered in august beginning in august 2016. The ppw uses the soldiers personnel record inthe electronic military personnel office emilpo and the army training requirements and resources system atrrs to calculate the amount of promotion points earned. A fourdigit serial number is to be created from the digits 0 through 9. For each group of three forces below, determine whether the forces in each pair are pulling at right angles to each other. Oh, and youll be expected to teach more courses to more. Functions and application by foerster weighted grading.
Algebra 2 trig regents jan 20 pt vi 26 to 30 youtube. Student information repository system manual for 201011 version 6. Content answer u2 oc3 5 ab cr t10 60,1 8,228 2,300 2000 p2 q5 1 ss. The army has released the latest version of tc 322. Algebra ii regents exam questions by state standard. Write the ratio and use algebra to solve and to get answer example problem example problem find the sine ratio for angle t find the cosie ratio for angle t sine 8. Arclength arc length central angle in radians r radius sr s. A pert, where a is the amount of money in the account, p is the initial investment, r is the interest rate, and t is the time, in years. Algebra 2 trigonometry regents full list of multiple choice questions june 17, 2010 am30 7. June 2016 algebra 2 and trig regents college confidential. Integrated algebra ii and trig last minute tips jd2718. Holloman s algebra 2 honors a2h notes on trigonometry, page 3 of 8 3 sin 5. For each group of three forces below, determine whether. The latest version as of the date this page was last updated is tc 322.11 1152 281 800 1137 699 12 1142 658 956 1134 533 1053 1187 175 126 318 976 128 917 1440 1401 94 1322 436 396 760 1237 593 1054 178 849 1517 1538 618 920 508 1422 216 939 1044 182 1313 615 55 10 979 753
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CC-MAIN-2022-05
| 7,275 | 7 |
http://tazmula.ga/jucu/what-is-a-normal-z-line-3535.php
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math
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In this area is the location of the lower esophageal sphincter.The esophagus meets with the stomach which is the salmon color and that also is normal.Then, using the mean and standard deviation (sigma) which are calculated from the data, the data is transformed to the standard normal values, i.e. where the mean is zero and the standard.And if this has a slope of m, then this has a slope of the negative reciprocal of m.So with that as a little bit of a hint, I encourage you to find the equation of.
Definition of the Unit Tangent Vector - LTCC OnlineThe normal probability plot (Chambers et al., 1983) is a graphical technique for assessing whether or not a data set is approximately normally distributed.
The thinner actin filaments are all bound to the Z-line, which makes up the boundary of the sarcomere.Occasionally it can be irregular and protrude more into the esophagus and not have the typical appearance.I also had an irregular z line before having my surgery and for a better explanation I checked the internet and found this: If you get a lot of acid reflux from your stomach into your esophagus, the appearance of the Z-line may change.For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.Determine the z value from the standard normal distribution for each cumulative probability.
It contains 100 points but many end up right on top of each other.
Normal and t Distributions - University of Wisconsin–MadisonTable entry Table entry for z is the area under the standard normal curve to the left of z.The z value is the distance between a value and the mean in terms of standard deviations.
USGS Geology and Geophysics
z-score: DefinitionI know that may be tough to believe, because statistics is tough as it is.
The normal distribution is the most important and most widely used distribution in statistics.It is a Normal Distribution with mean 0 and standard deviation 1.
Normal Distribution Calculator | Gaussian DistributionSpasticity in the distal esophagus is obstructing good visualization of the Z-line here.
Normal Histology of the Esophagus - Dr Sampurna Roy MDThe hematocrit test indicates the percentage of blood by volume that is composed of red.
There are many books on psychology or intelligence that would provide a more rigorous explanation of IQ.
Z-line irregular results after endoscopy | IntestinalThe simplest case of a Gaussian distribution is known as the standard normal probability distribution.Patient gastric bypass with a normal pouch volume and intact staple line.First, the x-axis is transformed so that a cumulative normal density function will plot in a straight line.As always, the mean is the center of the distribution and the standard deviation is the measure of the variation around the mean.
Since a vector contains a magnitude and a direction, the velocity vector contains more information than we need.Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals).
EQUATION OF THE FIRST DEGREE, THE STRAIGHT LINE
You can see that where they meet it is somewhat irregular, and it is called the Z-line.Note that the probabilities given in this table represent the area to the LEFT of the z-score.The derivative at a point tells us the slope of the tangent line from which we can find the equation of the tangent line.If you have a sudden change or if you feel pain, that is a red flag, she says.Notice, in particular, that the data from the t distribution follow the normal curve fairly closely until the last dozen or so points on each.
Table of Standard Normal Probabilities for Negative Z-scores
Line level, instrument level, mic level explained - OVNI LabThere is also wider divergence from the line than is shown with the normal set of data.
Standard Normal Distribution Table - Maths ResourcesWe classify faults by how the two rocky blocks on either side of a fault move relative to each other.
PSY 230 - Chapter 6 Flashcards | Quizlet
126.96.36.199. Normal Probability Plot
4.6 - Normal Probability Plot of Residuals | STAT 501I had them the other way around because it looked like a typo assigning the x part to the y value.The derivative of a vector valued function gives a new vector valued function that is tangent to the defined curve.
But it would be a lot harder without the normal distribution (and its thre.
Fibrinogen: Purpose, Procedure & Risks - Healthline
Fuel Line Sizing — What Size Do I Need? :: IPG Parts BlogStandard Normal Distribution Table The following table gives the proportion of the standard normal distribution to the left of a z-score.
Standard Normal Probabilities - Z-Score Table - University
Standard Normal Distribution - SUNY OswegoA bell curve is the most common type of distribution for a variable, and due to this fact, it is known as a normal distribution.Normal distribution describes the statistical behavior of many real-world events.To nd the number z so that the area between z and z is 0.99 requires nding the probability 0.00500 in the middle of the table.
The Z-line, as you can tell from its name, is quite irregular and that is entirely normal.A normal probability plot of the residuals is a scatter plot with the theoretical percentiles of the normal distribution on the y axis and the sample percentiles of the residuals on the x axis, for example.See how feelings, thoughts and behaviors determine mental health and how to recognize if you or a loved one needs help.As such it may not be a suitable model for variables that are inherently positive or strongly skewed, such as the weight of a person or the price of a share.
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http://rjwaldmann.blogspot.com/2013/03/comment-on-delong-on-cowan.html
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math
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Click the link if you want to know what I am typing about.
1) We should also consider pulling spending forward. Roads need to be resurfaced sooner or later. If we do it 5 years sooner we pay the 5 year real interest rate on the cost (which is negative). The true costs are lanes are blocked by construction sooner and we have to pull the next resurfacing forward 5 years. The benefit is we get new smooth roads sooner. Lets ignore the hassle of blocked lanes and any benefit from getting new roads sooner (assume one horse shay depreciation for roads so they are perfect up until the end of their useful life then must be resurfaced to be used at all). Oh he is also assuming a multiplier of 0 so there is no increase in taxes collected now or any social benefit from lower unemployment now. We get minus the 5 year rate and pay 5 years rates every 30 years. A normal 30 years rate means the cost paid in 60 years is worth less than half the cost in 30 years. So say the cost is twice the cost paid in 30 years and discount with the current 30 year rate (-0.65) and hmmm carry the one ... we get total cost equals amount paid to get it done times roughly 5 times the current 5 year rate (-1.39) plus about 1.6 times 5 times the normal 5 year rate (1.52 avg 2003 when FRED starts through 2006) . If the current real rate were low enough, that would add up to a negative number.
It pains me to actually check the numbers and find out that pointlessly anticipating investments 5 years is currently costly -- costs in 30 years are about like costs now if one is discounting at 0.65% a year.
Note this has nothing to do with dead weight losses from taxes. The claim is that, for a low enough real interest rate, doing the project 5 years sooner would give a lower debt in 100 years for the same taxes. It has nothing to do with Keynes. I am assuming a multiplier of 0. It has nothing to do with roads being useful. I am assuming that the new resurfaced road is no better than the one which is within 5 years of the end of its useful life. This is all 100% about how a low enough real interest rate can make the threshold return on an investment less than zero.
Sad to say I calculated after typing and find that the threshold return is about 1% per year or with Cowan's dead weight losses about 1.2% per year. That return is the value of having a new smooth road sooner minus the cost of having a lane closed sooner.
The numbers would work better for pulling forward fewer than 5 years.
2) . I think I know why Cowan doesn't believe my argument in point 5. I think it is because he doesn't believe that because we do something which we have to do in 5 years now we will spend less in 5 years. His world view is that marginal public spending is all due to capture by rent seeking special interests so if we don't have to resurface a road 5 years from now (because we resurfaced it now) we will just spend the same money on something else.
Here we see, as always, that the debate about Keynesian stimulus is always really a debate about public spending in general. Cowan will not accept Krugman's argument that if spending was about right in 2003 then it should be higher now, because he thinks spending was way too high in 2003. He won't accept my argument that it is better to spend it now than in 5 years, because he thinks that spending if 5 years will have nothing to do with social returns to spending in 5 years.
3) the calculation of how risk averse the Federal Government should be assumes a multiplier of zero. If unexpected and automatically higher spending or lower tax receipts cause higher GDP (and vice versa) then the correct calculation is different. I have no doubt at all that the optimal level of Federal risk aversion is negative. That is for the same expected return it would be socially better for the Federal Government to invest in risky assets whose returns are postively correlated with GDP growth. Here I am most definitely assuming Ricardian non equivalence. The general view that automatic stabilizers are a good thing implies the general view that the Federal Government should seak to bear risk (really it is hiding risk not bearing it -- it takes non Ricardian consumers for the trick to work -- but of course it does work).
4) wait with a hurdle rate over 20% how could firms ever possibly decide to invest ? From a survey Larry Summers found out that the median boss uses 30% somehow. My guess of the way this works is that they when considering an investment of size K they make a stream of profit or loss equal to extra revenues net of other costs minus (r + delta)K using some not totally crazy value for real interest r and depreciation delta (where nominal interest counts as a not totally crazy value for r) and then discount the stream at 30% per year. This would be pure myopia. It has nothing to do with restraining cowboy managers.
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https://www.freezingblue.com/flashcards/print_preview.cgi?cardsetID=200158
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math
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ECET 100 Lecture: Week 5
Home > Preview
The flashcards below were created by user
on FreezingBlue Flashcards.
A 2-input gate that produces a HIGH output when the inputs are in opposite states(one input HIGH and the other LOW).
Exclusive OR (XOR) Gate
A gate that always produces a HIGH output unless all inputs are HIGH.
A gate that always produces a LOW output except when all inputs are LOW.
A logic expression that illustrates the functional operation of a logic gate or combination of logic gates.
A gate that changes state of its input to the opposite digital state, example a HIGH becomes a LOW and vice-versa.
Inverter or NOT Gate
A 2-input gate that produces a HIGH output with both inputs HIGH or both inputs LOW.
Exclusive NOR (XNOR) Gate
A gate that produces a LOW only when both the inputs are LOW and has an HIGH output for all other combinations.
A gate that produces a HIGH output only when both the inputs are at logic HIGH.For all other input combinations, the output is LOW.
Home > Flashcards > Print Preview
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http://omyhukocow.tk/encyclopedias/statistical-and-inductive-inference-by-minimum-message-length-information-science.php
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math
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- The Best Sunset in Venice.
- Franny Parker;
- The Heart Plunderer (Angel at Large, Book 2) (Erotic Romance - Fallen Angel Romance).
- Minimum message length - Wikipedia!
- Navigation menu;
- Soul Sculpture.
- Minimum message length.
Is this product missing categories? Checkout Your Cart Price. Description Details Customer Reviews Gives an introduction to the Minimum Message Length Principle and its applications, provides the theoretical arguments for the adoption of the principle, and shows the development of certain approximations that assist its practical application. This book is of interest to graduate students and researchers in Machine Learning and Data Mining. Electronic book text Edition: This allows it to usefully compare, say, a model with many parameters imprecisely stated against a model with fewer parameters more accurately stated.
From Wikipedia, the free encyclopedia. Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments. Grouped data Frequency distribution Contingency table.
Pearson product-moment correlation Rank correlation Spearman's rho Kendall's tau Partial correlation Scatter plot. Sampling stratified cluster Standard error Opinion poll Questionnaire. Observational study Natural experiment Quasi-experiment. Z -test normal Student's t -test F -test.
Statistical and Inductive Inference by Minimum Message Length
Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator. Pearson product-moment Partial correlation Confounding variable Coefficient of determination. Simple linear regression Ordinary least squares General linear model Bayesian regression.
Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal. Spectral density estimation Fourier analysis Wavelet Whittle likelihood. Cartography Environmental statistics Geographic information system Geostatistics Kriging. We want the model hypothesis with the highest such posterior probability.
Suppose we encode a message which represents describes both model and data jointly. The message breaks into two parts: The first part encodes the model itself.
- C. S. Wallace publications.
- Dont Die with Your Song Unsung.
- How to Sell More: Tools and Techniques from Harvard Business Review.
The second part contains information e. MML naturally and precisely trades model complexity for goodness of fit. A more complicated model takes longer to state longer first part but probably fits the data better shorter second part. So, an MML metric won't choose a complicated model unless that model pays for itself.
Minimum message length - Wikipedia
One reason why a model might be longer would be simply because its various parameters are stated to greater precision, thus requiring transmission of more digits. Much of the power of MML derives from its handling of how accurately to state parameters in a model, and a variety of approximations that make this feasible in practice. This allows it to usefully compare, say, a model with many parameters imprecisely stated against a model with fewer parameters more accurately stated.
From Wikipedia, the free encyclopedia.
Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments. Grouped data Frequency distribution Contingency table.
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| 3,494 | 22 |
http://rpg.stackexchange.com/questions/tagged/trail-of-cthulhu+lovecraftian
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math
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| 2,371 | 53 |
https://www.physicsforums.com/threads/time-it-takes-for-a-capacitor-to-lose-half-of-its-energy.896789/
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math
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1. The problem statement, all variables and given/known data In the circuit below (drew it the best I can) the switch is opened, how much time elapses before the capacitor loses half of its initial stored energy. 2. Relevant equations q(t) = Qe-t/RC U = q2/2C 3. The attempt at a solution So first thing I did was I set (1/2)Q2/2C = q2/2C then i replaced q2 for Q2e-2t/RC so I get (1/2)Q2/2C = Q2e-2t/RC/2C I cancel out the like terms and I am left with 1/2 = e-2t/RC I than get rid of the e so I get ln(1/2) =-2t/RC then i get -ln(2) = -2t/RC getting me t = RCln(2)/2 and now this is were i got confused I know C = 200E-6 F but i don't know what R is suppose to be, I think it is suppose to be 90Ω since the 30Ω and the 60Ω resistors connect together at where the capacitor is.
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http://www.math.uiuc.edu/Algebraic-Number-Theory/0026/
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math
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A family of 'etale coverings of the affine line, by Kirti Joshi
This paper has appeared in J. Number Theory 59 (1996), no. 2, 414-418,
and so the dvi version has been removed. In this note we show that one can use Drinfel'd modular curves
to construct a family of etale coverings of the affine line. This
leads to construction of a profinite quotient of the algebraic
fundamental group of the affine line.
Our result is proved by using the moduli of Drinfel'd $A$-modules of
rank two over $C$ with $I$-level structure (where $C$ is a suitably
large field ); these Drinfel'd modular curves give rise to a tower of
galois coverings of the affine line ramified only at one point (on the
linei ), and the ramification is tame and independent of $I$. The tame
ramification can be removed in the entire tower by invoking a suitable
variant of Abhyankar's lemma; this variant of Abhyankar's lemma also
calculates the Galois group in our context.
A similar construction leads to a tower of coverings of the
affine space of any dimension.
This note will appear in Journal of Number Theory.
Kirti Joshi <[email protected]>
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http://www.compadre.org/OSP/document/ServeFile.cfm?ID=7347&DocID=499
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math
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Ejs Free Fall Cartesian Model Documents
The Ejs Free Fall Cartesian model displays the dynamics of a ball dropped near the surface of Earth onto a platform. The initial conditions for the ball are an initial positive velocity in the x direction and zero initial velocity in the y direction. The coefficient of restitution for the ball's collision with the platform is less than one. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.
Last Modified June 5, 2014
This file has previous versions.
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http://maxwellsociety.net/GRDixon/PhysicsCorner/Quantum%20Theory/Stable2Charge/Stable2Charge.html
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math
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A Stable, Maxwellian 2-charge System
This article investigates the radiant energy emitted/absorbed in the case of a particular 2-charge system. The results suggest that Newtonian/Maxwellian theory predicts a "stationary" (non-radiating) state.
The system consists of a positive, solid sphere of charge with radius R, and a negative point charge with finite rest mass mo. The positive charge is centered on the origin and remains at rest at all times. The negative charge is initially at rest at x = D, but generally accelerates toward the origin. It is assumed that the negative charge can move freely through the positive charge without resistance. R is varied from run to run, the objective being to determine whether some value of R results in zero emitted radiant energy. The following values are used in the modeling software:
Standard practice is to use Newton’s second law to determine the negative charge’s motion. To the extent the energy radiated per cycle is small compared to the total system energy, this approach usually produces a close approximation to the actual motion. In the present case the motion of q- is determined in this way, and the radiated energy is then computed as the work done by the (relatively small) radiation reaction force.
2. The Motion of q-
The magnitude of the force experienced by q-, in the electric field of q+, has different formulas in the ranges R<x<D and 0<x<R. But the force points toward the origin in both cases. Using subscripts "o" and "i" for outside and inside of q+, the formulas are
The work done by Fo, as q- moves from x=D to any x>R, is
But by the Work-Energy theorem we also have
where g at x=D is unity (since q- is at rest there). Thus
And, since g increases as v increases,
By definition, g = (1-v2/c2)-1/2, and
According to Newton’s second law, in one dimension
Now the relativistic formula for the radiation reaction force is usually expressed as a function of time:
By the Chain Rule, however,
Similarly for dg/dt. Thus |FRad| can be expressed as a function of x:
In the outer zone, a steadily increases in magnitude during the first quarter cycle, so that da/dt points toward the origin. Consequently FRad and v point in the same direction, and the differential of work done by FRad, in any given displacement of magnitude dx and toward the origin, is
The total work done by FRad, as q- goes from x=D to x=R, is
This integral can be numerically computed.
In previous articles a non-electromagnetic agent drove the oscillating charge, and the agent counteracted the radiation reaction force. In such cases a positive value of WRad implied that the radiation reaction force was doing work on the driving agent, and said agent was absorbing radiant energy. In the present case it is the electromagnetic field that drives q-, and a positive value of WRad implies that FRad is affecting the motion of q- and ultimately doing work on the field. This being the case, a positive WRad implies that radiant energy is being created in the field. That is, as q- accelerates toward the origin outside of q+, radiant energy is hypothetically created in the field.
It is noteworthy that da/dt points away from the origin when q- is inside of q+. Consequently FRad and v point in opposite directions inside q+, and WRad is negative … a result that (in the present case) suggests radiant energy in the field is being depleted. The relevant parameters inside q+ are:
where g1 is the value of g at x=R,
Let us denote the radiation created in the first quarter cycle, over the range R<x<D, as WRad(o). And we shall denote the radiation depleted, over the range 0<x<R, as WRad(i). Fig. 3_1 plots the ratio of WRad(o) / -WRad(i) over the range 9.5E-15 m < R < 1E-14 m. (5 values of R were computed.) Note that the curve has a value of unity within this range, indicating that no net radiation is created or depleted at that particular value of R.
-WRad(o) / WRad(i) vs. R
At R=9.8E-15 m (approximately where the net radiated energy is zero), the computed speed of q- at x=0 is 2.13E8 m/sec, or slightly more than 2/3 the speed of light. The computed time for the first quarter cycle, at this value of R, is
The time for an entire cycle is
which is somewhat less than the value of 1.52E-16 sec for the Bohr Hydrogen atom. But of course in the Bohr model q- orbits q+; it does not dive through q+. The frequency of the oscillation is
4. Concluding Remarks
The value of D = .529E-10 meters is motivated by the Bohr radius of a Hydrogen atom. And the system modeled, with q- diving through q+, is a suggested ground state.
The modeling of q+ as a solid sphere of positive charge, while perfectly Maxwellian, is objectionable for at least two reasons. First, theoretically no distribution of charge can persist in time without the imposition of non-electromagnetic constraints. (See, for example, Sands’ discussion in Chap 5, Vol. 2, The Feynman Lectures on Physics.) Secondly, present theory holds that the proton is composed of quarks … point charges for present purposes.
The objection that a point q- would theoretically have infinite electromagnetic (and hence total) inertial mass can be met by specifying that q- is also a spherical distribution of some sort, but with a radius <<R.
Despite such objections, it is interesting that there can, according to purely Maxwellian theory, be a stable state for a 2-charge system. When Bohr advanced his model of the Hydrogen atom it was generally agreed that the electron would inevitably (according to Maxwell) radiate. And it is not difficult to show that Maxwellian theory does in fact predict radiation when the electron orbits the proton. Bohr seems to have bought into the conventional wisdom of the time (that the classical theory predicts radiation in every imaginable case), and concluded that Maxwellian theory cannot accurately describe reality in the small spaces occupied by non-radiating atoms. The results obtained herein, however, seem to indicate that such a generalization may not be warranted.
Perhaps one of the most interesting implications of the present model is the hypothesis that radiant energy is depleted from the system’s field when q- is inside q+. The hypothesis that this energy temporarily transforms to negative particle kinetic energy suggests that there can never be a stable state where D<R. That is, although q- might spend part of the time inside q+, it can never spend all of the time in there. For if the ratio of WRad(o) / -WRad(i) is to equal unity, q- must spend part of each cycle time outside of q+!
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http://xwyi.cappottipantaloni.it/
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math
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Common Core Math Alignment. Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. Solve real-world and mathematical problems involving area, surface area, and volume.
A constant rate in math is the absence of acceleration. In general, a function with a constant rate is one with a second derivative of 0. If you were to plot the function on standard graph paper, it would be a straight line, as the change in y (or rate) would be constant. Homework 1M ALGEBRA I I Lesson 1: Graphs of Piecewise Linear Functions Lesson 1: Graphs of Piecewise Linear Functions Graphs of Piecewise Linear Functions When watching a video or reading a graphing story, the horizontal axis usually represents time, and the vertical axis represents a height or distance. Within this larger framework, we review and develop the real number properties and use them to justify equivalency amongst algebraic expressions The Algebra 1 course, often algebra 1 common core homework help taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models ...
Free Algebra 2 worksheets created with Infinite Algebra 2. Printable in convenient PDF format.
Shed the societal and cultural narratives holding you back and let step-by-step Algebra 1 Common Core textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life. Unlock your Algebra 1 Common Core PDF (Profound Dynamic Fulfillment) today. YOU are the protagonist of your own life. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly. Improve your math knowledge with free questions in "Graph sine and cosine functions" and thousands of other math skills. ... Common Core . Awards. Algebra 2 . HOMEWORK Sept. 19th – 20th, 2012 Inverses, Operations and Composition of Functions I. Find the inverse of each algebraically. Graph the original function (restrict the domain if necessary). Trigonometric Functions, you will begin by learning about the inverses of quadratics and other functions. This builds into learning about graphing and interpreting logarithmic functions and models. Then you will learn about modeling trigonometric functions by graphing the sine and cosine functions.
F.IF.C.7.B — Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Search F.IF.C.9 — Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
nys common core mathematics curriculum lesson 8 m4 ALGEBRA I Understanding the symmetry of quadratic functions and their graphs (Look at row 5 in the chart and the tables). This Exit Ticket: Graphs of Functions Assessment is suitable for 9th - 11th Grade. This instructional activity is designed as an exit ticket for a lesson on graphs of functions. Learners apply their knowledge of general behavior of functions to match seven equations with their graphs. Quia Web allows users to create and share online educational activities in dozens of subjects, including Mathematics. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques. a. Represent functions using function notation. b. Graph the basic functions f(x) = xn where n = 1 to 3, f(x) = x , f(x) = |x|, and f(x) = 1 x. c. Graph transformations of basic functions including vertical shifts ... 2.4 Graphing Polynomial Functions (Calculator) Common Core Standard: A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. nys common core mathematics curriculum lesson 8 m4 ALGEBRA I Understanding the symmetry of quadratic functions and their graphs (Look at row 5 in the chart and the tables). Sep 02, 2020 · Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.
Algebra 1 . Locate Current Unit - Unit 7 - Graphing and Writing Linear Functions . ... Homework/Answers. Review Sheets/Answers. Unit 1 - Foundations in Algebra.
Algebra 2 Common Core answers to Chapter 2 - Functions, Equations, and Graphs - 2-3 Linear Functions and Slope-Intercept Form - Lesson Check - Page 78 2 including work step by step written by community members like you. Textbook Authors: Hall, Prentice, ISBN-10: 0133186024, ISBN-13: 978-0-13318-602-4, Publisher: Prentice Hall Common Core State Standards for Mathematics. ... Algebra 79. Functions 85. ... The graph of a function is the set of ordered pairs consisting of an input and the ... Apr 06, 2018 · A pyramid has a polygon for a base and triangular lateral faces that intersect at a common point called the vertex . The line from the center of the base to the vertex is called the axis. If the axis is perpendicular to the base, the pyramid is called a right pyramid; otherwise, it is an oblique pyramid. Apr 11, 2018 · Rational Function and their Graphs Worksheet - Word Docs & PowerPoints. To gain access to our editable content Join the Algebra 2 Teacher Community! Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards. Rational Functions Worksheet PDFs Sep 18, 2016 · In this lesson we see how equations of functions relate to graphs of functions. X. Find Lessons! ... Common Core Algebra I.Unit 3.Lesson 3.Graphs of Functions. ... Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. 2: ... Graphing a Function (1st ... Created Date: 8/4/2014 1:40:42 PM Algebra I - Interpret Transformations of Linear Graphs Common Core Aligned Lesson Plan with Homework This lesson plan includes: -Lecture Notes (PDF, PowerPoint, and SMART Notebook) -Blank Lecture Notes (PDF and SMART Notebook) -Lecture Handout (PDF) -Homework (Multiple Choice - PDF) -Answer Key (PD
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Sep 28, 2014 · Another aspect of Common Core that surprised me was the emphasis given to parent functions and transformations. ... a night on homework. A graphing calculator is necessary for algebra ... Within this larger framework, we review and develop the real number properties and use them to justify equivalency amongst algebraic expressions The Algebra 1 course, often algebra 1 common core homework help taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models ...Within this larger framework, we review and develop the real number properties and use them to justify equivalency amongst algebraic expressions The Algebra 1 course, often algebra 1 common core homework help taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models ...Whether Algebra 1 or Algebra 2 is harder depends on the student. For example, the shock of dealing with variables for the first time can make Algebra 1 very hard until you get used to it. On the other hand, Algebra 2 is often considered harder because of its advanced concepts such as logarithms and imaginary numbers.
7. If you knew that f = 8 , then what (x, y) coordinate point must lie on the graph of y your thinking. 6. Based on the graph of the function y = g (x) shown below, answer the following questions. (a) Evaluate each of the following. Illustrate with a point on the graph. o. These are (b) What values of x solve the equation g (x) called the of ...
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Function Table Worksheets In and Out Boxes Worksheets. Here is a graphic preview for all of the Function Table Worksheets & In and Out Boxes Worksheets.. You can select different variables to customize these Function Table Worksheets & In and Out Boxes Worksheets for your needs. Algebra I has two key ideas that are threads throughout the course. The first idea is that we can construct representations of relationships between two sets of quantities and that these representations, which we call functions, have common traits. 1 Envision algebra 1 answer key pdf. Algebra Fundamentals 1. 1 Variables and Expressions 1. 2 Order of Operations and Simplifying Expressions 1. 3 Real Numbers 1. 4 Adding and Subtracting Real Numbers 1. 5 Multiplying and Dividing Real Numbers 1. 6 The Distributive Property 1. 7 Basics of Equations 1. 8 Patterns, Graphs, and Functions 2. graphing – Insert Clever Math Pun Here from inverses of linear functions common core algebra 2 homework , source:megcraig.org This kind of picture Inverses Of Linear Functions Common Core Algebra 2 Homework @ Graphing – Insert Clever Math Pun Here earlier mentioned will be labelled using: put up through Janet Natalie in 2019-03-09 19:43:51. Graphing Inequalities Worksheet 1 RTF Graphing Inequalities 1 PDF View Answers. Graphing Inequalities Workheet 2 - Here is a 15 problem worksheet where students will graph simple inequalities like “x < -2″ and “-x > 2″ on a number line. Be careful, you may have to reverse one or two of the inequality symbols to get the correct solution set. Coordinate Algebra 1‐ Common Core Diagnostic Test ‐1 ‐ 9 ‐ 33. Juan and Patti decided to see who could read the most books in a month. They began to keep track after Patti had already read 5 books that month. This graph shows the number of books Patti read for the next 10 days.
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Algebra Made Easy with Step-by-Step Lessons! I know you are thinking, "How can Algebra be made easy?" Some days it just feels impossible. Well, I've tried to make it as easy as possible. This page is designed to help you find what you need on this website. Think of it as a site map or table of contents for the Algebra portion of this website.
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2.4 Graphing Polynomial Functions (Calculator) Common Core Standard: A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Eureka Math (2014 Common Core) License Concept Two ~ TE | SE Glencoe CCSS Math Text (McGraw-Hill, 2013) o Representing Relationships p. 263-276 o Functions p. 287-294 o Linear Functions p. 295-304 o Comparing properties of Functions p. 309-318 o Constructing Functions p. 319-326 Cut & Paste Matching graph/slope/points
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Hawaii Common Core math question: 5x 5 = 112 5.1x= 24so = 2.4 Question A. Identify which graph represents Lance and which represents Lee. Explain how you used the information in the graphs to help you arrive at your decision. the purpose is to ask students to interpret information from a graph and make sense of it in the given situation. there ...
Some geometry lessons will connect back to algebra by describing the formula causing the translation. In the example above, for a 180° rotation, the formula is: Rotation 180° around the origin: T(x, y) = (-x, -y) This type of transformation is often called coordinate geometry because of its connection back to the coordinate plane.
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graphing – Insert Clever Math Pun Here from inverses of linear functions common core algebra 2 homework , source:megcraig.org This kind of picture Inverses Of Linear Functions Common Core Algebra 2 Homework @ Graphing – Insert Clever Math Pun Here earlier mentioned will be labelled using: put up through Janet Natalie in 2019-03-09 19:43:51.
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Algebra I Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs. In this module students analyze and explain precisely the process of solving an equation.
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https://financeassignments.xyz/binomial-distribution-20733
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One Simple Tip About Binomial Distribution Explained
Otherwise, the Hypergeometric distribution ought to be used. Binomial distributions would be utilized to model situations where the prosperous outcome is just 1 value. It’s a discrete probability distribution. It’s the probability distribution of a particular number of failures and successes in a collection of independent and identically distributed Bernoulli trials.
The solved example problems for binomial distribution together with detailed calculation help users to comprehend in what way the values are used in the formula. The worth of p is the pace at which the disease occurs. Put simply, it’s NOT feasible to locate a data value between any 2 data values. The one difference between both binomials is the sign between the conditions of each. Make certain you are conversant with BOTH METHODS for solving each issue. There are five things you should do to work a binomial story issue. Notice that our answer is still the same.
The binomial distribution is a rather important study within probability distributions. It is commonly used in statistics in a variety of applications. It will calculate the probability of the given number of successful outcomes in a given number number of trials if the proportion of the overall population having that outcome is known. In an insurance policy application, the negative binomial distribution can be put to use as a model for claim frequency once the risks aren’t homogeneous.
The normal distribution may be informally known as the bell curve. It is useful because of the central limit theorem. Hence a Poisson distribution isn’t an ideal model. It is, in addition, the continuous distribution with the most entropy for a predetermined mean and variance. It’s a specific probability distribution for virtually any variety of discrete trials.
The variety of trials is equal to the range of successes plus the quantity of failures. So as to calculate binomial probabilties, it is crucial to understand the quantity of ways k successes among n trials can happen. Quite a few other significant variations of the Binomial ought to be mentioned now. The respective quantities of pseudo-observations add the quantity of actual observations to them. All these examples are binomials. The variety of means to pick distinguishable sets is then which is known as the combination. If you would like more information at a glance, this command may also be utilised to create a list of the probabilities.
Simulation with a binomial experiment is one particular approach to yield a standard distribution. As such it might not be an appropriate model for variables which are inherently positive or strongly skewed, including the weight of someone or the price of a share. The easiest case of a typical distribution is called the typical normal distribution. The particular circumstance, as soon as your answer is going to be a binomial, is when you’re multiplying two binomials whose first terms and second terms are the exact same. Each trial ought to be independent to one another. The fact that it is independent actually means that the probabilities remain constant. This is about Bernouli trials.
The probability is extremely small. Be aware that the probability of it occurring can be pretty tiny. The probability of each is written to the right side of the way it might occur. Then in the event the combined probability is multiplied by the variety of methods to receive this outcome, the outcome is the binomial distribution function. A binomial probability denotes the probability of growing EXACTLY r successes in a certain number of trials. This probability differs for different issues. The probability a patient dies from a heart attack is dependent on a lot of things including age, the intensity of the attack, and other comorbid conditions.
A number of other techniques of calculation are available, and might be more appropriate for particular circumstances. This calculation must rate the factorials of quite large numbers in the event the range of events is large. Let’s try yet another approximation. Let’s try a couple more approximations. The normal approximation won’t be valid in the event the effects act multiplicatively (instead of additively), or if there’s a single external influence with a considerably bigger magnitude than the remaining effects. Thus, the standard approximation to the binomial will not be that accurate in our example. Instead, the expectationmaximization algorithm may be used.
The Secret to Binomial Distribution
The conventional normal CDF is widely utilized in scientific and statistical computing. Binomial is a small term for an exceptional mathematical expression. Now the amount of means to pick r objects from a total of n is which is known as the permutation.
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https://se.mathworks.com/matlabcentral/answers/373217-how-to-convert-eci-coordinates-with-given-sidereal-time-to-ecef-coordinates
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math
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How to convert ECI coordinates with given sidereal time to ECEF coordinates ?
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Alexander S. on 15 Dec 2017
Commented: Alexander Thorne on 24 Aug 2020
Hey, I have an understanding problem with a project I am doing for my electrical engineering studies. I have to calculate the position of a receiver (of satellite signals) on the earth. For that, one part of the project is to convert ECI coordinates into ECEF coordinates. I have given the position and velocity of the satellite in the ECI-system as well as the sidereal time for each position (ca.15 min of recording in seconds, for each second position vector,velocity vector and sidereal time of the satellite are known). The Julian Date is also given. How do I convert these satellite positions + velocity in an ECEF-system?
I know that i can use the rotation matrix to rotate the ECI-system to the ECEF-system. I wanted to use the formula of GMST(as in the picture) to find out the angle between the ECI and ECEF system, so i can use that angle in my rotation matrix. The problem is, i dont know how to use the given sidereal time for each position in that equation...
I really hope someone can help me with my problem, it would be a great x-mas present!!
Alexander Thorne on 24 Aug 2020
Hi Alex, Alex here
What is the 'd' in your equation to calculate 'Y'? If you could refer me to your source or answer I would really appreciate it.
Amy on 18 Dec 2017
The Aerospace Toolbox has a function dcmeci2ecef that will return the 3x3 transformation matrix.
I also see that there's a File Exchange function that may work for you (and could even be helpful just as reference)
Find more on Coordinate Systems in Help Center and File Exchange
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http://histoire.du.metre.free.fr/en/Pages/Sommaire/08.htm
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:: The determination
of mass unit ::
Unit based on a given volume of
the schemes related to the new system planned the connection between the
mass unit with the volume unit, that is to say the unit of length.
and Haüy had determined the "grave" in 1793, the mass of a cubic decimetre
of water at ice melting point, for which the value was alledged to be 18,841
grains of the average marc of the Pile de Charlemagne.
work was entirely resumed in the early 1799 by Lefèvre-Gineau and the
two scientists chose water, not at ice melting point but at a 4
centigrade-degree temperature, that is to say the temperature of maximum
density for this liquid.
weighed successively in air and water a hollow brass cylinder whose size had
been carefully determined thanks to a comparator that Fortin purposely
created. They deducted from it the mass of a cubic decimetre of water that
was distilled at its temperature of maximum density, that is to say the
kilogramme. This mass was found to be equivalent to 18,827.15 grains of the
average marc of the Pile de Charlemagne.
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https://rikazowevu.maisonneuve-group.com/approximations-in-lp-and-tchebycheff-approximations-book-15946ee.php
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1 edition of Approximations in LP and tchebycheff approximations found in the catalog.
Approximations in LP and tchebycheff approximations
by University of Illinois, Digital Computer Laboratory in [Urbana, Ill.?]
Written in English
|Statement||by J. Descloux|
|Series||Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no.117, Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) -- no.117.|
|Contributions||University of Illinois (Urbana-Champaign campus). Digital Computer Laboratory, National Science Foundation (U.S.)|
|The Physical Object|
|Pagination||13 leaves ;|
|Number of Pages||13|
This book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom. There are many original features that set this book apart. AbstractThe problem of finding a best Lp-approximation (1 ≤ p in Lp from a special subcone of generalized n-convex functions induced by an ECT-system is considered. Tchebycheff splines with a countably infinite number of knots are introduced and best approximations are characterized in terms of local best approximations Cited by: 3.
An Interactive Approach for Multicriteria Decision Making Using a Tchebycheff Utility Function Approximation Article in Journal of Multi-Criteria Decision Analysis 21() May with 77 Reads. Abstract: Index coding, a source coding problem over broadcast channels, has been a subject of both theoretical and practical interests since its introduction (by Birk and Kol, ). In short, the problem can be defined as follows: there is an input P (p 1, ⋯,p n), a set of n clients who each desire a single entry pi of the input, and a broadcaster whose goal is to send as few messages as Author: Abhishek Agarwal, Larkin Flodin, Arya Mazumdar.
for example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J. L. WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
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The problem of finding a best L p-approximation (1 ≤ p L p from a special subcone of generalized n-convex functions induced by an ECT-system is considered. Tchebycheff splines with a countably infinite number of knots are introduced and best approximations are characterized in terms of local best approximations by these by: 3.
Buy Fourier Approximation in Lp-Spaces: A Summability Approach on FREE SHIPPING on qualified orders Fourier Approximation in Lp-Spaces: A Summability Approach: Uaday Singh: : Books.
] TCHEBYCHEFF APPROXIMATION IN SEVERAL VARIABLES In this section it is shown that there is a particular point set associated with best approximations which is unique. The following simple lemma will be required.
Lemma 1. Let L(A*,x) be a best approximation tof(x) and. Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1 (1), – (13 pages) (13 pages) Methods—Old and New—for Solving the Tchebycheff Approximation ProblemCited by: The degree of approximation to a function f(x)∈C[−1,1] by (U,λ) means and f(x)∈LPω by (Jr) means are discussed, some results in the literatures , , have been improved.
On the approximation of Tchebycheff-Fourier series in the C space and LPω space | SpringerLinkAuthor: Sheng Shuyn. Amazing little book. The third Malvino book I've read in addition to Semiconducter Circuit Approximations and Electronic Principles.
I recommend buying Electronic Principles and reading it thoroughly, and this using this book (b/c of it's to the point style and small physical size) as a field reference and design by: 6. The relation between best approximations and interpolating functions is very well defined for linear approximating functions, finite point sets and weighted Lp norms.
The principal result states that for any f(x): 1. The set of best approximations in a weighted Lp norm, 1. Then Sgives a 2-approximation to min weight vertex cover, i.e. X v2S w(v) 2w(S) where S is the optimum solution.
Proof: Since the feasible region of the IP is a subset of the feasible region of the LP, the optimum of the LP is a lower bound for the optimum of the IP.
Moreover, note that our rounding procedure ensures that xb v 2x for all v2V File Size: KB. Welcome to a beautiful subject!—the constructive approximation of functions.
And welcome to a rather unusual book. Approximation theory is an established field, and my aim is to teach you some of its most important ideas and results, centered on classical topics re-lated to polynomials and rational functions. The style of this book, however. The course title, approximation theory, covers a great deal of mathematical territory.
In the present context, the focus is primarily on the approximation of real-valued continuous functions by some simpler class of functions, such as algebraic or trigonometric Size: KB. Chebyshev Polynomials book. Chebyshev Polynomials. DOI link for Chebyshev Polynomials.
Chebyshev Polynomials book. L1 and Lp Approximations. ckUk(x), ck = 2 π. f(x)Tk(x)√ 1− x2 dx () yield near-minimax approximations within a relative distance of O(log n) in C[−1, 1]. Is this also the case for other kinds of Chebyshev. The Approximation of Functions: Linear theory Addison-Wesley Series in Computer Science and Information Processing Volume 1 of The Approximation of Functions, The Approximation of Functions: Author: John R.
Rice: Publisher: Addison-Wesley Pub. Co., Original from: the University of Michigan: Digitized: Length: pages: Export Citation. Tchebycheff-derivative approximations to photoabsorption cross sections in atoms and ions.
Abstract. Spectral moments and Tchebycheff's inequalities are employed in the construction of continuous, convergent approximations to photoabsorption and ionization cross sections in atoms and ions. Tchebycheff-derivative approximations to Cited by: consider such approximation algorithms, for several important problems.
Specific topics in this lecture include: • 2-approximation for vertex cover via greedy matchings. • 2-approximation for vertex cover via LP rounding. • Greedy O(logn) approximation for set-cover. • Approximation algorithms for MAX-SAT.
IntroductionFile Size: 88KB. Approximation Theory and Approximation Practice This textbook, with figures and exercises, was published in It is available from SIAM and from Amazon. Approximation in Normed Linear Spaces Article in Journal of Computational and Applied Mathematics () February with 68 Reads How we measure 'reads'.
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions.
Lovász and Schrijver [SIAM J. Optim., 1 (), pp. ] showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs (SDPs) of increasing size (lift-and-project method).
In this paper we present a similar idea. We show how the stability number can be computed as the solution of a conic linear program (LP) over the cone Cited by: for example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J.
WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COLLATZ for his many encouragements for the writing of this book.
Thanks are equally due to Springer-Verlag. Abstract. Lp-approximation by the Hermite interpolation based on the zeros of the Tchebycheff polynomials of the first kind is considered. The corresponding result of Varma and Prasad is generalized and perfectedAuthor: Min Guohua.
The material in the first chapter, which covers about two-thirds of the book, is basic in approximation theory and consists in the main of Tchebycheff and polynomial approximation. The second chapter is concerned mainly with the recent research work by the author and others and covers non-linear Tchebycheff, rational, and exponential approximation.
Lecture with Ole Christensen. Kapitler: - Intro To Approximation Theory; - Remarks On Vectorspaces In Mat4; - Def.: Dense Subset; - Dense Subspace Of The Sequence Spaces L.In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
Note that what is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon.
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https://myhomeworkhelp.com/lamis-theorem/
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math
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Lami’s theorem is one such equation which relates the extent of three coplanar, non-collinear forces and concurrent forces. It is crucial to mention that the object always remains in static position. This theorem also states that in case there are three different forces which acts at a given point known are in equilibrium, then every single force will be proportional to the sine of the angle among two other forces.
Let’s understand the concept of Lami’s Theorem through a graphical representation.
Suppose, three different forces are P, Q and R and they are acting on a particle or rigid body, consequently forming angles γ, α and β.
Let’s now learn the mathematical representation of Lami’s Theorem –
p/sinα = Q/sin β = S/ sin γ
Links of Previous Main Topic:-
- Introduction to statics
- Idealizations of mechanics
- Laws of mechanics
- The law of parallelogram
- Types of forces
- Coplanar collinear
- Coplanar concurrent
- Coplanar parallel forces
- Coplanar non concurrent and non parallel
Links of Next Mechanical Engineering Topics:-
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https://puzzling.stackexchange.com/questions/97797/fill-your-bags-with-marbles
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math
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You have 50 bags. How many marbles do you need at least, so that you can have a different number of marbles in each bag?
The minimum number of marbles is:
$49$. Put a single marble in $49$ of the bags, and then put all the bags one inside each other, and then put the empty bag inside them all. In other words, going from outside to in, we will have bag-marble-bag-marble-...-bag-marble-bag, and the sequence of the number of marbles in each bag going from inside to out will be $0,1,2,3,...,49$.
We can prove this is the minimum number because:
For there to be a different integer number in each bag, the sequence that gives the smallest possible number in the bag with the most marbles is $0,1,2,...,49$, so at least one bag must have $49$ marbles in it.
If we increase the laterality of our thinking even further (with weakened respect for dimensional constraints, and tongue lightly pressed in cheek), we can improve our solution to:
$48$ marbles. Set up the first $49$ bags as above with the $48$ marbles, so that they contain $0,1,2,...,48$ marbles each. Then alter the final bag so that it has the topology of a Klein bottle, and set it down where you please; it now contains every marble in the universe, since its interior is indistinguishable from its exterior. Our bags thus contain $0,1,2,...,47,48,|M|$ marbles where $M$ is the set of all objects in the universe that could properly be construed as marbles, whose size (given that I also happen to own a marble, and you have $48$) is strictly greater than $48$.
Additionally, with tongue now firmly planted in cheek, the minimal number can be drastically reduced to:
$1$ with a simple repeated application of the Banach-Tarski theorem.
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CC-MAIN-2021-49
| 1,698 | 9 |
https://deardreinstein.com/2013/12/05/chapter-10-calculating-distances/
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math
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The quest of Science and Mathematics is to obtain predictive power, and what a powerful tool the statement above conveys. This equation has become so famous that the name of its author, who died roughly 2500 years ago, is still well known: Pythagoras. It was a momentous discovery and a secret that was at the heart of the secret Greek mathematics society. If one could measure two sides of any right triangle, one could then know, to an extremely high level of precision, what the length of the hypotenuse would be. This established relationship is so pervasive and well known that even carpenters (a group not well known for their grasp of mathematical concepts) use it to determine measurements when building a roof or other angular structure. In fact, it is more ubiquitous than it might appear.
Cartesian geometry, being a rectilinear system, does not have a rigorous system for the measurement of off-axis distances. Oh, sure, you can easily locate any point by a simple numerical callout, for example 5i + 3j + 2k (in Cartesian terms) locates the point reached by starting at the origin and going 5 units along the X axis, 3 along a line parallel to Y and then 2 in the Z direction (we’re staying in the positive quadrant for the sake of clarity in this example). But what is the overall length of the straight line distance from the origin to that point? Since there is no portable off-axis ‘yardstick’ this is a distance that must be calculated.
And this is the beauty of the Cartesian system. Since the axes are all defined to be perpendicular to each other, every measurement along an axis can be considered to be one of the sides of a right triangle, and in the immortal words of the Ozian Scarecrow;
“The sum of the squares of the length of the sides for any right triangle is equal to the square of the third”
So in the case listed above, we just apply Pythagoras’ theorem to three dimensions and we can prove that the distance from the origin to the point is:
x2 + y2 + z2 = 52 + 32 + 22 = 38 = length2 length = 6.164
With this powerful theorem, given our ‘a priori’ axes, we can know any distance in space! By combining the point equations, we can calculate relative distances, too. We won’t delve into the mathematics for an example of this at this point (or well, ever in this book, because the equations are too hard to type), but the point is that this methodology allows for the calculation of any relative distance between two points in Cartesian space.
This is a great system, and we use it every day for all sorts of scientific, mathematical and engineering applications. Unfortunately, there are a couple of problems that are not apparent on the surface.
The first has to do with the sign (positive or negative). Since this equation relies on the square root of a squared value for its answer, it has a ‘cleansing’ effect on the values. That is; since the square of any number (excepting ‘i’ of course) is positive due to the rules established to manage the multiplication values of our bipolar number system, and the square root of every positive number has a positive value, then every value calculated using this equation is naturally positive. But we have admitted the concept of negative length to our system, and the same value for the length of the distance would have been calculated if we had used the values -5, -3 and -2, which would clearly put the length in the negative octant.
How is one to know which value is correct? The answer is that you just have to know, and that the equation only calculates the relative value. But it is a little disingenuous for a system that gives physical, meaningful values to the concept of negative numbers to force the person doing the calculation to determine the geometric meaning of the answer. Because of the form and substance of the equation used to determine the overall length, the line segment generated could be in any one of the octants. It’s not very deterministic.
But there is a more insidious, pervasive problem here, and that is: it forces all of the equations of motion to be second order equations.
Let’s say that you wanted to go from point A to point B, both of which are totally off axis. The equation for determining the length is:
(xA – xB) 2 + (yA – yB) 2 + (zA – zB) 2 = AB2
Which, in the absence of actual values, can be expanded algebraically to be:
= [(xA – xB) * (xA – xB)] + [(yA – yB) * (yA – yB)] + [(zA – zB) * (zA – zB)] = AB2
= (xA2 – 2xAxB + xB2) + (yA2 – 2yAyB + yB2) + (zA2 – 2zAzB + zB2) = AB2
Pretty ugly isn’t it? And you still have to take the square root of the results of all of the sub-equations to get the answer. This is the sort of calculation that is behind every distance determination that utilizes Cartesian geometry. Why does this have to be so hard? Obviously, if one had a ruler, one could just go out and measure the length, and save oneself a whole lot of math. But if you are trying to calculate a velocity, which is a first order equation (distance/time), you’re stuck with this big, honkin’ set of quadratic equations in the middle.
The point of all of this is that the geometric system, because of the way that it is constructed and the way the expressions are put together, forces the analyst to utilize second order equations to calculate first order values, which introduces both complexity and uncertainty into the system where none is actually required.
What we really need is a geometry and measurement system that allows first order measurements, like velocity, to be calculated in first order terms. By relying on the three perpendicular axes and codifying direction in relative values, we have created a system that cannot do that.
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CC-MAIN-2018-34
| 5,734 | 19 |
http://thomasfoolerydc.com/books/calculus-early-transcendentals-solutions-stweart
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math
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By James Stewart, Jeffrey A. Cole, Daniel Drucker, Daniel Anderson
Comprises totally worked-out options to the entire odd-numbered workouts within the textual content, giving scholars how to fee their solutions and make sure that they took the proper steps to reach at a solution.
Read or Download Calculus Early Transcendentals SOLUTIONS Stweart PDF
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Additional resources for Calculus Early Transcendentals SOLUTIONS Stweart
We can also write 12 as a product of prime numbers. Definition A prime number is a natural number whose only two different factors are 1 and itself. ) EXAMPLE 3 Is 7 a prime number? Solution Yes. The only way to write 7 as a product of natural numbers is 1 ؒ 7. [YOU TRY 3] Is 19 a prime number? Definition A composite number is a natural number with factors other than 1 and itself. Therefore, if a natural number is not prime, it is composite (with the exception of 0 and 1). indd Page 7 16/08/12 9:25 PM user-f498 /207/MH01613/mes06260_disk1of1/0073406260/mes06260_pagefiles IA— Note The numbers 0 and 1 are neither prime nor composite.
3) Add or subtract. 4) Express the answer in lowest terms. EXAMPLE 10 Add or subtract. ” If not, write the answer in lowest terms. 2 1 ϩ 9 6 LCD ϭ 18 Identify the least common denominator. 2 2 4 ؒ ϭ 9 2 18 1 3 3 ؒ ϭ 6 3 18 Rewrite each fraction with a denominator of 18. 2 1 4 3 7 ϩ ϭ ϩ ϭ 9 6 18 18 18 b) 6 7 1 Ϫ3 8 2 Method 1 Keep the numbers in mixed number form. Subtract the whole number parts and subtract the fractional parts. Get a common denominator for the fractional parts. 7 1 For 6 and 3 , the LCD is 8.
18) Find the complement of each angle. ; 6) a) 9 ft3 b) 36 in3 68Њ ? 19) ? Find the supplement of each angle. 11) 143Њ 12) 62Њ 13) 38Њ 14) 155Њ Find the measure of the missing angles. 119Њ 22Њ 20) 21) ? indd Page 31 17/08/12 7:43 PM user-f498 /207/MH01613/mes06260_disk1of1/0073406260/mes06260_pagefiles IA— 22) Can a triangle contain more than one obtuse angle? Explain. 5 mi 24) 3 in. 5 mi Classify each triangle as equilateral, isosceles, or scalene. 23) 2 12 ft 36) 11 in. 8 cm 3 in. 13 in. 2 ft 12 in.
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| 3,571 | 17 |
http://ehhows.com/en/pages/1265328
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math
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a quadrangle as a rhombus stands out among the variety of geometric shapes.Even its very name is not typical to refer to quadrangles.Although the geometry of it occurs much less frequently than such simple shapes like circle, triangle, square or rectangle, it also can not be ignored.
Below are the definition of the properties and features of the rhombus.
Rhombus - a parallelogram having equal sides.Rhombus square called if all its angles.The most striking example is the diamond-shaped image of diamonds playing card suit on.In addition, the diamond often depicted in various emblems.An example of a rhombus in everyday life can serve Ballpark.
- opposite sides of the rhombus lie on parallel lines, and have the same length.
- intersection of the diagonals of the rhombus occurs at an angle of 90 ° at one point, which is their middle.
- diagonals of a rhombus divided angle from the top of which they came, in half.
- Based on the properties of a parallelogram, we can derive the sum of the squares of the diagonals.According to the formula, it is side raised to degree quadratic and multiplied by four.
We must clearly understand that any rhombus is a parallelogram, but at the same time is not any parallelogram has all the performance of the diamond.To distinguish between these two geometric shapes, you need to know the signs of a rhombus.Below are the characteristics of this geometric figure:
- any two sides with a common vertex are equal.
- diagonals intersect at an angle of 90 ° C.
- At least one diagonal divides the angles of the points of the vertices which it comes in half.
- S = (AC * BD) / 2
Based on the properties of a parallelogram:
- S = (AB * HAB)
Based on the value of the angle between two adjacentthe sides of the rhombus:
- S = AB2 * sinα
If we know the length of the radius of a circle inscribed in a rhombus:
- S = 4r2 / (sinα), where:
- S - area;
- AB, AC, BD - the designation of the parties;
- H - height;
- r - radius of the circle;
- sinα - sine alpha.
To calculate the perimeter of a rhombus, you just multiply the length of any of the parties at four.
have some difficulties with the construction of a rhombus pattern.Even if you have already figured out that this diamond is not always clear how to build its image accurately and in compliance with the necessary proportions.
There are two ways of constructing a rhombus pattern:
- Build first one diagonal, then perpendicular to the second diagonal, and then connect the ends of the segments adjacent pairs of parallel sides of the diamond.
- Takeout first one side of the rhombus, then parallel to construct a segment equal in length, and connect the ends of these segments are also mutually parallel.
Be careful when building - if you make the length of the sides of the rhombus are the same, you do not get the diamond, and the square below.
See also article:
- Find rhombus
- area How to find a diagonal of the rhombus
- How to find the direction of the rhombus
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CC-MAIN-2018-05
| 2,964 | 33 |
https://www.terrainforum.net/threads/great-explanation-and-worksheet-for-leasing.22/
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math
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With so many leasing questions, I thought I would make a separate post with the lease info from the Car Buying FAQ's. I have also attached my trusty lease calculator for those who still need it.
Calculating a lease payment is not difficult, once you have all the
information you need. The lease payment is based on the difference between
what you pay for the car and what the car will be worth at the end of the
lease, plus interest.
When it comes to leasing, here is the lingo:
- This is the selling price of the vehicle.
Capitalized Cost Reduction
- This is simply a down payment.
- This is what the car will be worth at the end of the lease
(usually stated as a percentage of the MSRP).
- This is the interest rate. It is always give as a decimal
figure. While it is not necessary to know the actual percentage rate when
calculating the lease, you can figure it out by multiplying the money factor *
2400. This number is used no matter what the term of the lease. For example, a
money factor of .0025 would be an interest rate of 6%.
Inception Money (or Get In Money)
- This is the amount of money that you have
to come up with at the start of the lease (not including any Capitalized Cost
Reduction). The inception money usually consists of the first month's payment,
a security deposit (usually equal to one month's payment rounded to the
nearest $25 and a bank fee. It can also include the dealer documentation fee,
tags and sales tax on the any Capitalized Cost Reduction (more on that later.)
It is important to have all of these costs broken down so you know exactly
what is being covered.
Now, here is how we calculate a lease. First off, you need to have several
things: the MSRP (or sticker price), the selling price (Capitalized Cost), the
residual value (as a percentage) and the money factor.
Let's use the GTI 1.8T as an example. Adding in the 17" wheels, luxury and
leather packages, it will have an MSRP of $22,000. The residual value for a
36-month lease (with 15K miles/year) is 57%. Usually a 12K mile/year lease
will have a residual value 2% higher (or 59% in this case). The money factor
for 36 months is .00250. Now that we have our figures, we can calculate the
lease. This may seem complicated, but take it step by step and it is quite
First we calculate the lease cost. Take the MSRP ($22,000) and multiply it by
the residual value (59%). This gives us $12,980. Now, take the Capitalized
Cost (what you pay for the car) and subtract the residual value from it. Let's
say we pay $21,500 for this car. $21,500 - $12,980 = $8520. Now, we take that
$8520 and divide it by the lease term of 36 months. $8520 / 36 = $236.67.
If you didn't have to pay any interest, this is what your monthly payment
would be . Unfortunately, few banks lend money without charging interest . To
figure out the monthly interest you take the sales price ($21,500) and add it
to the residual value ($12,980) and multiply it by the money factor (.0025).
$21,500 + $12,980 = $34,480. $34,480 * .0025 = $86.20. So, you are paying
$86.20/month in interest. You add that to the monthly lease cost of $236.67
and you end up with a monthly payment of $322.87. But wait, there's more. Your
state needs to collect their part of the deal in the form of sales tax. If
your sales tax is 8.25%, you would multiply the monthly payment by 1.0825 for
a grand total of $349.51. This is your monthly payment.
Now, what about putting more money down in the form of a capitalized cost
reduction. You would simply deduct this amount from the capitalized cost
before you run the numbers. For example, if you put $1,000 down, your monthly
payment would drop to $316.73. Now you are probably asking yourself, why not
put more money down? First off, you have to pay your 8.25% sales tax on that
$1000. But that is no big deal. The bigger problem is that if the car ever
gets stolen or totaled, the insurance will pay off your lease, but you will
never see that $1,000 again since it was paid up front. Also, think of it this
way. If you were leasing an apartment and the rent was $750/mo, but the
landlord said, "Give me an extra couple of thousand up front and I will lower
the rent to $650/mo." Few of us would actually do that. Leasing your car is
just like renting. If you can't afford the payment without putting more money
down, I would suggest taking the money you would put down and put it in the
bank to earn interest and then deduct an amount every month to cover the
One more bit of advice. Never lease a car for a longer term than the
manufacturer's warranty. If you do and something breaks past the warranty
period, it will be your responsibility to get it fixed and pay for it
yourself. Since you will give the car back at the end of the lease, you are
basically paying to fix someone else's car. So while generally longer lease
terms will give you lower payments, don't lease past the warranty period.
Also, don't lease longer than you will think you will want your car. Breaking
a lease early can be very expensive.
Updated Lease/Loan/Balloon calculator added (thanks GTakacs).
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CC-MAIN-2023-23
| 5,068 | 72 |
https://www.weavolution.com/group/glimakra-loom-owners/adding-treadles-26683
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math
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I just joined this group; I know that Joanne would answer this question if I posted it on her web site, but I thought it might be useful for others if I ask the question here.
I have a 39 inch Ideal that has six treadles. I would like it if I could add more treadles; judging by the holes in the lamms, it looks like up to four more treadles could be added. What is not clear to me is how they would be attached to the structure to which the other treadles are attached. Thanks for this group!
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| 493 | 2 |
https://www.arxiv-vanity.com/papers/math/9810172/
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math
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Volume of Riemannian manifolds, geometric inequalities, and homotopy theory
We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension . Namely, every compact, orientable, smooth -manifold admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in . In other words, orientable -manifolds are -systolically free. More generally, let be a positive even integer, and let . Then all manifolds of dimension at most are -systolically free (modulo torsion) if all -skeleta, , of the loop space are -systolically free.
Key words and phrases:volume, systole, stable systole, systolic freedom, coarea inequality, isoperimetric inequality, surgery, Whitehead product, loop space, Eilenberg-MacLane space
1991 Mathematics Subject Classification:Primary 53C23; Secondary 55Q15
Our purpose here is both to present new results and to outline the current state of knowledge regarding geometric inequalities of systolic type. One of the new results (proved in §8) is the following.
Every compact, orientable, smooth -manifold admits metrics of arbitrarily small volume such that every orientable, immersed surface of smaller than unit area is necessarily null-homologous in .
In other words, orientable -manifolds are -systolically free. A precise definition of systolic freedom will be given in §3. Roughly speaking, a -systole of a Riemannian manifold is the least volume of a non-trivial -cycle in . To say that is -systolically free means that the volume of imposes no upper bound upon the -systole. One can view this result as a way of producing metrics for which the systole and the mass in the middle dimension do not agree (cf. Theorem 2.3 and ).
Consider sufficiently small perturbations of the Fubini-Study metric on , scaled to the same volume as . M. Gromov proved in (Corollary, p. 309) that one can always find embedded -spheres, homologous to the projective line , of -area no greater than that of for the metric. On the other hand, our Theorem 1.1 shows that there may be no such spheres if we go far away from the Fubini-Study metric in the space of Riemannian metrics on . We see that here local and global diverge.
The conclusion of the theorem may well be as strong as possible, in the sense that non-orientable surfaces of small area (constrained by the volume of the ambient manifold) may always be present. M. Freedman raised the question of what happens with the systoles defined using homology with -coefficients. Gromov conjectures that the systolic inequalities are true in this case, i.e., our theorem above on systolic freedom has no -analogue. As the example in Remark A.4 illustrates, -cycles may have asymptotically smaller area growth than -cycles, supporting the conjecture that volume is a constraint upon the -systoles. The exact boundaries between freedom and constraint are yet to be described.
In the -dimensional case, we reduce the problem to and , in the following sense.
All compact, orientable, smooth -manifolds are -systolically free over if and only if and are -systolically free over .
Every compact, smooth manifold of dimension admits metrics of arbitrarily small -dimensional volume such that every orientable, immersed middle-dimensional submanifold of smaller than unit -volume represents a torsion class in -dimensional homology with integer coefficients.
In other words, -dimensional manifolds are -systolically free (modulo torsion). The term ‘systolic freedom (modulo torsion)’ is also explained in §3. For manifolds of dimension larger than , we prove the following.
Let be an even integer, and let . Then all manifolds of dimension at most are -systolically free (modulo torsion) if all -skeleta, , of the based loop space are -systolically free.
The paper is organized as follows. In §2, we define systoles and give representative proofs of inequalities exhibiting constraint imposed by the volume (of the ambient manifold) on them. In §3, we explain the first example of systolic freedom (i.e., the absence of such constraint), due to M. Gromov, and give related definitions and historical comments. In §4, we prove Theorem 1.6. In §5, we introduce a ‘carving-up’ technique, with the goal of reducing the problem to the case when the middle Betti number is at most . In §6, we prove Theorem 1.5. In §7 we introduce a morphism, weaker than a continuous map, suitable for pulling back systolic freedom. In §8, we prove Theorem 1.1 and Theorem 1.4. In §9, we prove a refinement of Theorem 1.6 for the the -systole. In §10, we establish the freedom of odd-dimensional systoles.
The paper concludes with 5 appendices. In Appendix A, we describe the techniques used in proving systolic freedom in the context of a pair of distinct complementary dimensions. In Appendix B, we prove a workhorse lemma, which allows us to propagate systolic freedom. In Appendix C, we prove a lemma (used in paragraph 7.2) on surgeries along curves in -manifolds. In Appendix D, we use the technique of spinning to identify explicitly the result of a useful surgery. In Appendix E, we recall the necessary material on Whitehead products and Hilton’s theorem on homotopy groups of bouquets of spheres.
The first author is grateful to Misha Farber for the opportunity to present an early version of this paper at the Topology conference at Tel Aviv University in June of 1998, and to Shmuel Weinberger for a helpful discussion of the results herein.
2. Isoperimetric inequalities and stable systoles
2.1. Isoperimetric inequality
Every simple closed curve in the plane satisfies the inequality
where is the length of the curve and is the area of the region it bounds. This classical isoperimetric inequality is sharp insofar as equality is attained only by a round circle.
2.2. Loewner’s theorem
In the 1950’s, C. Loewner and P. Pu proved the following two theorems.
Let be the real projective plane endowed with an arbitrary metric, i.e., an embedding in some . Then
where is its total area and is the length of its shortest non-contractible loop. This isosystolic inequality is also sharp, to the extent that equality is attained only for a constant curvature metric (quotient of a round sphere).
Similarly, every metric torus satisfies the sharp inequality
where is the length of its shortest non-contractible loop, and is the area.
2.3. What is a systole?
In the 1970’s, Marcel Berger initiated the study of a new Riemannian invariant, which eventually came to be called the systole.
The (homology) -systole of a Riemannian manifold is the quantity
where the infimum is taken over all closed curves in which are not homologous to zero.
A similar homotopy invariant, , is obtained by minimizing lengths of non-contractible curves. These two invariants obviously coincide for , , and any manifold with abelian fundamental group.
2.4. Conformal representation and Cauchy-Schwartz
We give a slightly modified version of M. Gromov’s proof of Loewner’s theorem for the -torus, or rather the following slight generalization.
There exists a pair of distinct closed geodesics on an arbitrary metric -torus , of respective lengths and , such that
where is the total area of the torus. Equality is attained precisely (up to scaling) for the equilateral torus , where is a primitive sixth root of unity. Moreover, their homotopy classes form a generating set for .
A conformal representation , where is flat, may be chosen in such a way that and have the same area. Let be the conformal factor of .
Let be any closed geodesic in . Let be the family of geodesics parallel to , see Figure 1. Parametrize the family by a circle of length so that . Then . By Fubini’s theorem, . By the Cauchy-Schwartz inequality,
Hence there is an such that , i.e.,
This reduces the proof to the flat case. Given a lattice in , we choose a shortest lattice vector , as well as a shortest one not proportional to . The inequality is now obvious from the geometry of the standard fundamental domain in . ∎
Theorem 2.3 (Gromov ).
Let be a compact, orientable, smooth manifold of dimension . Let be the length of the shortest non-contractible loop for the metric on . Then the inequality
holds for a positive constant independent of the metric, if an only if the inclusion of in an Eilenberg-MacLane space retracts to the -skeleton of . For manifolds satisfying (1), moreover, the constant depends only on .
2.5. Higher systolic invariants
Let be a finite -dimensional simplicial complex endowed with a piecewise smooth metric . Let .
Let . Define
where the infimum is taken over all piecewise smooth cycles representing the class . Here the volume of a (smooth) singular simplex is that of the pullback of the quadratic form to the simplex, and we take absolute values of the coefficients to obtain the volume of the cycle. Also define a ‘stable norm’ by
Clearly, we have .
We define the following three systolic invariants for the metric on :
The ordinary systole
The systole ‘modulo torsion’
The stable systole
Evidently, we have .
2.6. Calibration and stable systolic inequalities
Higher systolic invariants can sometimes also be constrained by the volume. Such constraint is illustrated by the following theorem.
Theorem 2.6 (Gromov ).
For every metric on ,
for a suitable constant .
The proof is a calibration argument. Let be the standard generator of . Let be the dual generator. Let be any -form representing . Then
Hence , since the norms in and in are dual by , p. 394.
Thus , and so , a stable systolic inequality. ∎
Another example (also due to Gromov) of a stable systolic inequality is the following. Let endowed with an arbitrary metric . Then
J. Hebda proved further results of this type in the 1980’s.
Our objective is to show that in general, -systoles are not constrained by the volume, unlike the above theorems for , , and .
3. History and definitions
3.1. Question of freedom or constraint
M. Berger asked in 1972 if the systolic invariants can be constrained by the volume. M. Gromov reiterated this question in :
Can one replace stable systoles by ordinary ones in the above inequalities?
The question was asked again in an IHES preprint in 1992 (which ultimately appeared as ). Shortly afterwards, Gromov described the first example of systolic freedom, i.e., the violation of the systolic inequalities (see paragraph 3.2). The educated guess today is that, if one uses integer coefficients, systolic freedom predominates as soon as one is dealing with a -systole for (but see Remark 1.3).
3.2. Gromov’s example
Gromov described metrics on which provided an unexpected negative answer to the question 3.1. He stated it in global Riemannian terms. We provide a reformulation in terms of differential forms, which lends itself easier to generalization.
Let be the contact -form on , where is the unit sphere, is rotation by furnished by the complex structure, is the -form on , defined by the radial coordinate .
Complete to an orthonormal basis of , which is canonically identified with by means of the standard unit sphere metric.
Let be the unit circle parametrized by , where is real. The standard -form is the arc-length. Gromov’s sequence of left-invariant metrics, , on is defined by the following quadratic forms:
The essential ingredient here is the matrix
The coefficient ultimately determines the -systole, the coefficient determines the -systole, and the determinant of the matrix determines the volume of . Then we obtain
See Appendix A for a ‘local’ version of this example, suitable for generalization.
A finite -dimensional CW-complex is -systolically free if
where the infimum is taken over all piecewise smooth metrics on a simplicial complex in the homotopy type of .
An -dimensional CW-complex is -systolically free (modulo torsion) if
Theorem 1.4 in the Introduction uses the following terminology in the context of coefficients modulo .
Let be a compact, smooth manifold of dimension . Consider -cycles with -coefficients, e.g., maps of manifolds (orientable or not) into , which represent non-trivial classes in , and calculate the -volume of the pullback metric. Define to be the infimum of all such volumes. We say that is -systolically free over if
4. Reduction to loop space
For even , we reduce the systolic problem to spaces each of whose Betti numbers is at most . More specifically, we show that the systolic -freedom of -manifolds (modulo torsion) reduces to that of certain skeleta of loop spaces of spheres. Thus, whether or not there exists an analogue of Gromov’s Theorem 2.3 for the higher systoles, depends on the loop space in question.
Let be an integer. Let be a finite CW-complex. Let . Let be an Eilenberg-MacLane space with skeleta . There is a map , inducing an isomorphism , and whose restriction to has image in .
A basis for defines a map , inducing the required isomorphism. The cellular approximation theorem yields a map . ∎
Any -dimensional CW-complex admits a map to a suitable bouquet of -spheres which induces an isomorphism in rational homology of dimension .
Consider the bouquet , where . According to B. Eckmann , a map of degree induces multiplication by in the stable groups , for . Thus, if is a multiple of the order of , the self-map induces the zero homomorphism in by Hilton’s theorem E.1. Hence a map , followed by , extends to . The lemma now follows by induction on , based on Lemma 4.1. ∎
Let and be integers such that . Then every -dimensional manifold is -systolically free (modulo torsion).
The -skeleton of a -manifold admits a map to a suitable bouquet of -spheres, inducing an isomorphism in -dimensional rational homology, and sending the attaching maps of the -cells to a sum of Whitehead products.
We continue with the notation of the proof of Lemma 4.2. We thus have a map . Let be the fundamental class of the sphere. Recall that the Whitehead product generates precisely the kernel of the suspension homomorphism. Suspension commutes with . Hence, if is a multiple of the order of the stable group , then is contained in the subgroup generated by Whitehead products. Hence is the desired map. ∎
Proof of Theorem 1.6.
Consider the based loop space . As shown by J.-P. Serre , all homotopy groups of are finite, except (here we need even). Let be the product of the orders of the homotopy groups of from up to dimension . Let be the map that sends a loop to . Since the usual group structure on coincides with the one coming from the multiplication of loops in , the map induces multiplication by in each homotopy group of . Thus, on , for .
Now let be an -manifold, and let . Let be the Cartesian product of copies of . With respect to a suitable cell structure, the -skeleton of is a bouquet of copies of . By Lemma 4.1, the -skeleton of admits a map to the -skeleton of which induces rational isomorphism in -dimensional homology.
We now proceed as in the proof of Lemma 4.2, with the bouquet of spheres replaced by . By induction, the map extends to
for all from to . In this fashion, we obtain a map such that is an isomorphism. By the pull-back Lemma B.2, the freedom of follows from that of . It remains to reduce the freedom of to that of itself.
A well-known result of I. James (see ), states that has, up to homotopy, a cell decomposition
with precisely one cell in each dimension divisible by . Therefore, we may proceed as in §5, and carve up the -skeleton of , reducing the problem to the freedom of the closures of -dimensional cells of . Each such closure is a product of skeleta of . Therefore, Theorem 1.6 results from the following lemma. ∎
Let . Then the product of an -connected, -systolically free complex with is again -free. Furthermore, the product of -connected, -systolically free complexes is again -free.
Given -free families of metrics on each factor, we scale them to unit -systole. We also scale the -sphere to unit -volume. The product metrics then form -free families. ∎
5. Carving-up procedure
The procedure in question is helpful in breaking up the problem of systolic freedom of complicated spaces into simpler components. We introduce it here as a way of streamlining the arguments of , where the authors, in collaboration with I. Babenko, proved the middle-dimensional systolic freedom of even-dimensional manifolds of dimension with free .
Let be an -dimensional CW-complex with no cells in dimension . The carving-up procedure consists of inserting a cylinder between each -dimensional cell and its boundary. The new complex has the following three properties.
has the same homotopy type as .
has the same number of top-dimensional cells as .
The closures of all top-dimensional cells in are disjoint.
Assume for the sake of simplicity that the image of each attaching map
of is a subcomplex (i.e., there are no partly covered cells in the -skeleton). Let
be the boundary of the top-dimensional cell.
The procedure of inserting cylinders in is formalized as follows:
Here is the -skeleton, and the extremities of the cylinder are attached along the inclusion maps , and . The repeated upper and lower index indicates that the procedure is repeated for each top-dimensional cell, as in Einstein notation. Thus, we insert as many cylinders as there are top-dimensional cells, to obtain .
Let be an -dimensional CW-complex with no cells in dimension . Then the systolic -freedom of reduces to that of the closures of its top-dimensional cells.
We replace by as above. To make sure that areas and volumes are well-defined, we replace each by a simplicial complex of the same dimension and in the same homotopy type. Then the positive codimension condition is satisfied. We also replace each cell closure by a simplicial complex in the same homotopy type so as to extend the simplicial structure on . We make a similar replacement for , obtaining a simplicial complex .
We apply to the long cylinder argument in the proof of Lemma B.1 and Lemma B.4. The key tools here are the isoperimetric inequality and the coarea inequality, applied to , where the metric on the interval is chosen sufficiently long, to minimize interaction between opposite extremes of the cylinder. ∎
6. Middle-dimensional freedom
We now establish systolic freedom (modulo torsion) in the middle dimension, as stated in Theorem 1.5. In fact, we show that the theorem is valid in the more general case of triangulable spaces with piecewise smooth metrics, for which of course areas and volumes can still be defined.
In contrast with Loewner’s theorem 2.2, the middle-dimensional systole (-systole) is not constrained by the volume when . Thus Loewner’s theorem has no higher-dimensional analogue if one works with orientable submanifolds. On the other hand, there might be such an analogue if one allows non-orientable submanifolds (see Remark 1.3).
A proof in the case appeared in .
6.1. Idea of proof
The idea of the proof of Theorem 1.5 is to reduce the problem to a local version of Gromov’s example, described in §3.2, by using pullback arguments of Appendix B as follows. High-degree self-maps of combined with Hilton’s theorem E.1 allow us to map to a kind of a first-order approximation to the -skeleton of the Eilenberg-MacLane space . This approximation has the same rational homology and contains the minimal number of -dimensional cells. The carving-up procedure of §5 reduces the problem to the freedom of the closures of these cells, each with middle Betti number at most . An additional pull-back reduces the problem to the freedom of . Finally, the latter is reduced to the -freedom of (cf. Appendix A).
6.2. Proof of Theorem 1.5
Let us restate the theorem in a more convenient (and slightly more general) setting.
Let . Let be a finite, triangulable CW-complex of dimension . Then is -systolically free (modulo torsion).
Let . Let , where is the fundamental class of . Consider the Cartesian product of copies of . Its -skeleton is a bouquet of copies of . Let be the map given by Lemma 4.4. Here the image of is contained in the subgroup generated by Whitehead products. Then , followed by the inclusion , extends across all of by Hilton’s theorem E.1. Thus the freedom of reduces to that of the -skeleton of .
We now apply Lemma 5.1 to obtain a further reduction to only two cases: and itself. The CW-complex is homotopy equivalent to the regular CW-complex (product of spheres with a disk attached along the diagonal). Thus the systolic -freedom of reduces to that of by Lemmas B.1 and B.2.
Let . Then the manifold admits a map to a CW-complex obtained from by attaching cells of dimension at most , which induces a monomorphism in -dimensional homology.
The manifolds and are related by surgery, and thus admits a map to .
For , this does not define a meromorphic map, since we have added top dimensional cells. In this case, we proceed as in Corollary 7.9. ∎
The manifold is -systolically free if .
The manifold is -free by Theorem A.2. Let be such a free sequence of metrics on . Taking the product with a sphere of volume equal to , we obtain an -free sequence of metrics on . ∎
6.3. Spin manifolds
Our Theorem 1.1 improves the general middle-dimensional result in the case , to the extent that it removes the ‘modulo torsion’ clause. A similar improvement exists for and .
Spin manifolds of dimension and are systolically free in middle dimension.
We reduce the problem to the simply-connected case as in paragraph 8.2. Furthermore, the spin condition ensures that all embedded -spheres have trivial normal bundles. Let be the union of a disjoint family of embedded -spheres representing a set of generators for -dimensional homology, and perform surgery along . An analogue of Lemma 7.5 reduces the problem to the -connected case. A -connected -manifold has torsion-free -dimensional homology, and the proposition is established for a -manifold.
For -manifolds, we continue by choosing a disjoint family of embedded -spheres (whose normal bundles are automatically trivial) which represent generators for -dimensional homology, and argue as before, reducing the problem to the -connected case. ∎
7. Meromorphic maps
Here we develop a convenient language for establishing the -systolic freedom of orientable -manifolds. We define a morphism, weaker than a continuous map, suitable for pulling back systolic freedom. Our technique is introduced most provocatively by means of the following question.
What do meromorphic maps and surgeries have in common?
7.1. ‘Topological meromorphic maps’
Here we attempt to define a morphism, weaker than a continuous map, suitable for pulling back systolic freedom. Such morphisms could also be called ‘topological blow-up maps’ or ‘topological rational maps’.
Let and be manifolds of dimension . A “meromorphic map”, denoted by a broken arrow below,
is a continuous map , such that:
The space has the homotopy type of a CW-complex obtained from by attaching cells of strictly smaller than the top dimension: .
The map induces a monomorphism in the middle dimension:
We do not require the inclusion to induce an epimorphism in middle-dimensional homology.
Let be a complex manifold of (complex) dimension , let be the blow-up at a point , and let be the classical meromorphic map (undefined at ). For , set , where the -cell is attached along the exceptional curve . Then can be modified in a neighborhood of so as to lift a continuous map (a homotopy equivalence). Here we take the cone of the Hopf fibration . More precisely, the Hopf fibration extends to a continuous map whose restriction to the complement of in is a diffeomorphism onto the complement of in , while is mapped to as described. For general we have a continuous map .
7.2. Surgery and meromorphic maps
We now show that, under certain homological conditions, surgeries along curves yield meromorphic maps between -manifolds.
Let be a closed, orientable, smooth -manifold. Let be a union of smoothly embedded, disjoint closed curves. Let be the result of surgery along . Then admits a meromorphic map to . The conclusion holds equally well if one uses coefficients modulo in the definition of homology and meromorphic maps.
Since is orientable, the normal disk bundle of is trivializable. Over each component of , there are two possible trivializations (or, framings), corresponding to . The framing (which is part of the surgery data) identifies the normal disk bundle with . By definition,
where is a disjoint union of -disks (one for each connected component of ). Let be the result of attaching a handle of index to along each component of , according to the given framing. Then is the cobordism between and determined by the surgery, see J. Milnor .
Now let be the mapping cone of the inclusion . In other words, is the CW-complex obtained from by attaching the cores of the handles.
An orientable 4-manifold admits a meromorphic map to a simply connected one.
Let be the union of a family of disjoint embedded closed curves representing a set of generators for the fundamental group. Surgery on along produces a simply-connected manifold , and we apply Lemma 7.5. ∎
Let be a closed, orientable, smooth -manifold. Let be the result of surgery along a union of smoothly embedded, disjoint closed curves in . Assume that the connected components of define a linearly independent set in . Then admits a meromorphic map to .
We continue with the notation of Lemma 7.5. Let be the inclusion and , the homotopy equivalence. Then is a monomorphism. This is established by induction on the number of connected components of , using Lemma C.1 in Appendix C.
More precisely, let be the isomorphism provided by Lemma C.1. Since is obtained from by attaching -cells, the inclusion induces a monomorphism . Since , it follows that is injective, and so is, too.
Without the independence hypothesis, may have a larger second Betti number than either or . For example, if and , then and or , depending on the parity of the framing. Thus , , and .
There exists a meromorphic map .
Surgery on along a pair of generators of yields . An explicit verification of this fact is given in Corollary D.2. Alternatively, one readily sees that the surgery does not change the intersection form, and the resulting manifold is simply-connected. Hence it is certainly homotopy equivalent to . Either way, Proposition 7.7 applies, completing the proof. ∎
7.3. Pullback lemma for free metrics
The following proposition allows us to propagate the phenomenon of freedom once we exhibit it for products of spheres.
Let be a meromorphic map. If is systolically free, then so is .
Systolic freedom is a homotopy invariant.
Any map defining a homotopy equivalence is obviously a “meromorphic map” (here , i.e., the set of attached cells is empty). ∎
Let and be triangulable CW-complexes of dimension . Suppose there is a map inducing a monomorphism on , where is obtained from by attaching a single cell of dimension . Then the -systolic freedom of implies that of . Moreover, if is a smooth manifold, the metrics exhibiting freedom may be chosen to be smooth.
The lemma is proved in Appendix B.
8. Systolic freedom in dimension
In this section, we show that orientable closed -manifolds are systolically free in the middle dimension.
In the simply-connected case, the first author, in collaboration with I. Babenko , already reduced the problem to the case of . Here we notice that admits a meromorphic map to (see Corollary 7.9), and so its middle-dimensional freedom results from that of (see Lemma 6.3).
8.1. Systolic freedom modulo torsion
Prior to proving Theorem 1.1 of the Introduction, we establish freedom modulo torsion for an arbitrary simplicial complex of dimension , as follows.
Every compact, triangulable -dimensional CW-complex is -systolically free (modulo torsion).
The map of Lemma 4.1, followed by a homotopy equivalence gives a map . Up to homotopy, we may assume that the image of lies in the -skeleton . By construction, the map induces an isomorphism in -dimensional homology with integer coefficients. By Lemma B.2, the systolic freedom of reduces to that of the -dimensional complex .
The map to constructed in the proof of the theorem is only an isomorphism in rational -dimensional homology, so we have no control over areas of -cycles defining torsion classes.
The CW-complex contains no -cells. Indeed, it is obtained from the bouquet of copies of by attaching -cells along all the Whitehead products and , where is the fundamental class of (cf. paragraph E.1). Therefore, the freedom of reduces to that of the closures of its -cells, by Lemma 5.1, since the isoperimetric inequality for small -cycles obviously holds for bouquets of spheres.
Each such closure is homeomorphic to either or . We are thus left with proving the systolic freedom of these two manifolds.
The freedom of reduces to that of the product of spheres as follows. Notice that there is a degree map from to , where is the fundamental class of . Now is homotopy equivalent to , where and are the fundamental classes of the two factors. Thus admits a meromorphic map to , and we invoke Proposition 7.10.
Every compact, smooth -manifold admits metrics of arbitrarily small volume, with the following property: every orientable, immersed surface of smaller than unit area, defines a torsion class in .
This is immediate from the theorem. ∎
Note that the manifold in the above corollary may be non-orientable.
8.2. Orientable case
We now establish the systolic -freedom of orientable -manifolds.
8.3. The case of -systolic freedom over
The notion of freedom with coefficients modulo was introduced in Definition 3.5. We now reduce the question of -systolic freedom over of arbitrary -manifolds to that of just two manifolds: and .
Proof of Theorem 1.4.
The orientable case is reduced to the case when is simply connected, as in the proof of the previous theorem. The map to induces an isomorphism in -dimensional homology, whether with integer or mod coefficients. Therefore the problem is further reduced to the freedom over of this Eilenberg-MacLane space. The long cylinder construction of Appendix B works equally well with -coefficients. Thus we may carve up the space as above to reduce the problem to and .
The reduction of to as in the proof of Theorem 8.1 does not work here, as the map is not injective. ∎
9. Systolic -freedom in arbitrary dimension
The absence of odd cells in a suitable decomposition of the Eilenberg-MacLane space is the key to the proof of Theorem 8.1.
The method employed in that proof can be used to improve Theorem 1.6 for . We illustrate this by reducing the systolic -freedom of all manifolds with torsion-free to that of a particularly simple list of manifolds.
The following two statements are equivalent:
All compact, smooth manifolds with torsion-free are -systolically free;
For each , the manifold is -systolically free.
The -freedom of each projective space would imply that of the product of arbitrarily many factors, as in Lemma 4.5. The -freedom of a product of several copies of follows from Corollary 7.9. But each cell closure in the standard simplicial structure of is such a product, proving that any finite skeleton would also be -free. We map to as in Lemma 4.1 and apply the pull-back Lemma B.2. ∎
10. Odd-dimensional freedom
Note that the systolic -freedom of when follows from the -freedom of a bouquet of -spheres viewed as an -dimensional CW-complex, by Corollary 4.3. Thus the interesting case is .
Let and be integers satisfying , where is odd. Then every -dimensional manifold is -systolically free (modulo torsion).
The starting point is again the map from the -skeleton of to the bouquet of spheres, as in Lemma 4.1. For odd , the only non-trivial Whitehead products are the ‘mixed’ ones. Thus, high-degree self-maps of the sphere allow us to map to the product of copies of , as in the proof of Lemma 4.2.
Here we rely upon the existence of self-maps inducing the zero homomorphism in every given homotopy group of the sphere. Indeed, according to D. Sullivan , a self-map of of degree induces a nilpotent map in the -torsion of , for every .
Now if does not divide , the -skeleton of coincides with the -skeleton, in which case we actually get (singular) metrics on of vanishing -volume.
If divides , the -skeleton of contains no -cells, and we use the carving-up procedure of §5 to reduce to products of spheres. ∎
Appendix A Systoles of complementary dimensions
To describe phenomena along the lines of Gromov’s example, it is convenient to introduce the following terminology.
A compact, smooth, -dimensional manifold is called systolically -free if
where the infimum is taken over all metrics on .
We present a proof of -freedom, originally obtained by the first author in collaboration with I. Babenko in .
Every compact, orientable, smooth manifold of dimension is -free.
We obtain systolically free families of metrics on the manifold by a direct geometric construction. The idea is to introduce a local version of Gromov’s example (cf. §3.2), i.e., a metric on a manifold with boundary which can be glued into any manifold to ensure systolic freedom. Here the matrix of Gromov’s example:
for a given , is replaced by the matrix
where the coefficient varies between and .
Let be a union of closed curves which form a basis for . Its tubular neighborhood is diffeomorphic to . Let be a codimension submanifold with trivial normal bundle (e.g., the -sphere). The boundary of a tubular neighborhood of is diffeomorphic to the hypersurface , where is a circle. Our construction is local in a neighborhood of . Choose a fixed metric on satisfying the following four properties:
It is a direct product in a neighborhood of .
The hypersurface is a metric direct product of the three factors , , and .
Each connected component of is a circle of length .
The circle has length .
We now cut open along and insert suitable ‘cylinders’ , indexed by , resulting in a sequence of metrics on . These ‘cylinders’ are not metric products. They have the following properties.
The projection is a Riemannian submersion over an interval , where the interesting behavior is exhibited when grows without bound.
The metric at the endpoints and agrees with that of .
The -dimensional manifold has a fixed metric independent of , and is a direct summand in a metric product.
For integer values of , each connected component of is isometric to a standard unit square torus.
The metric on is the ‘double’ of the metric on , in the sense that and have identical metrics.
Now let be a non-trivial -cycle of . By Poincaré duality, the cycle has non-zero intersection number with one of the connected components, , of . Hence induces a non-trivial relative cycle in a neighborhood of . From now on we will denote this component by .
Note that the volume of grows linearly in . We will obtain a lower bound for the -volume of , and therefore for the -systole of , which grows faster than the volume of . Meanwhile, the -systole is bounded from below uniformly in . The theorem now follows from the properties of suitable metrics on constructed below.
Our technique is calibration by the -form , where is the volume form of . Here the -form provides the lower bound for the area of the relative -cycle in Lemma A.3 below. ∎
The metric on is not a direct sum. Consider the subinterval . Then can be thought of as a fundamental domain for a -fold cover of a non-trivial torus bundle over the circle, defining either the or geometries (used in and , respectively). We will present a description valid for both approaches.
What makes these metrics systolically interesting are the following properties. There is an orientable surface and a -form on such that
and have intersection number equal to .
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| 35,865 | 228 |
https://chinashops1.ru/problem-solving-quadratic-equations-3467.html
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math
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I highly recommend the following textbook for both GCSE(9-1) and IGCSE(9-1).The book covers every single topic in depth and offers plenty of questions to practise.Take the extra half a second to find the right answer the right way.
I highly recommend the following textbook for both GCSE(9-1) and IGCSE(9-1).The book covers every single topic in depth and offers plenty of questions to practise.Take the extra half a second to find the right answer the right way.Tags: Ap English Synthesis Essay Space ExplorationTips On Writing A Research Paper In CollegeHow To Cite In An Essay ApaEssay On Service To Humanity Is The Worship Of GodSingle Source Analysis EssayEssays On Racial ProfilingWhat Is A Good Business PlanOrigins Of Cold War Essay
So we can just resort to the quadratic formula here. So this would be the same thing as the square root of four times the square root of 21, which of course is two times the square root of 21, all of that over two.
So the roots are going to be x is equal to negative b. So negative of negative two is gonna be positive two, plus or minus the square root of b squared, which is four, minus four times a, which is one, times negative 20. And since that's a negative 20 but I'm subtracting it, I could put a plus there. But let's see if we can get to the right solution here. This is going to, x is going to be equal to two plus or minus.
This is the best book that can be recommended for the new A Level - Edexcel board: it covers every single topic in detail;lots of worked examples; ample problems for practising; beautifully and clearly presented.
The roots of this equation -2 and -3 when added give -5 and when multiplied give 6. Problem 1: Solve for x: x 11x 7x 7 = 0 → 11x(x 1) 7(x 1) = 0 → (x 1)(11x 7) = 0 → x 1 = 0 or 11x 7 = 0 → x = -1 or x = -7/11.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm when: x is about −9.3 or 0.8 The negative value of x make no sense, so the answer is: x = 0.8 cm (approx.) There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land: We can turn those speeds into times using: time = distance / speed (to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?
) And we know the total time is 3 hours: total time = time upstream time downstream = 3 hours Put all that together: Two resistors are in parallel, like in this diagram: The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other. The formula to work out total resistance "R = 3 Ohms is the answer. Quadratic Equations are useful in many other areas: For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation.
And we would get x squared minus two x minus 20 is equal to zero. Now we have this quadratic in a form where we just need to figure out what x values are gonna make this expression equal to zero. And I don't tell people to memorize a lot in life, but the quadratic formula is one of those things that it's not a bad idea to memorize. So it looked like a fairly benign thing, but we had to multiply it out, set it up in kind of a form where the quadratic formula would apply, and we got a fairly hairy answer.
And we're starting to get to the home stretch. When the quadratic formula tells us that if I have ax squared plus bx plus c is equal to zero, then the solutions of this quadratic equation are going to be x is equal to negative b plus or minus the square root of b squared minus four ac all of that over two a. So if you divide each of these by two, which we are doing right here, it's going to be one plus or minus the square root of 21, which is this choice right over there.
When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster ... and a Quadratic Equation tells you its position at all times! There are many ways to solve it, here we will factor it using the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics: a×c = A very profitable venture.
Your company is going to make frames as part of a new product they are launching.
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CC-MAIN-2021-31
| 4,272 | 12 |
http://www.ehow.com/how_5666070_convert-water-column-pounds-pressure.html
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math
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Although gas pressure is usually measured in units such as millimeters of mercury or pounds per square inch, in some instances equipment may read pressure as inches of a water column. In particular, liquefied petroleum gas pressure indicators use this form of measurement. Converting between these pressure units is a simple matter of multiplying by a constant factor; you only need to know what factor to apply for converting to and from water column inches. A standard four-function calculator helps make the conversion quick and accurate.
Things You'll Need
From Water Column Inches to Pounds
Key the water column inches pressure reading into your calculator. For example, an LP gas tank outlet may read 20 inches. Enter 20 into the calculator.
Use the fact that one inch of water in a water column is equal to 0.036 pounds per square inch of pressure; this is your conversion factor. Press the multiply key, then key in 0.036.
Press the equals key to see the pressure as pounds. From the example, 20 times 0.036 equals 0.72, the pressure in pounds.
From Pounds to Water Column Inches
Key the pounds pressure into your calculator to make the reverse conversion if you only know your pressure in pounds and want to figure out the water column inches. For example, your pressure gauge reads 2 pounds, so enter 2.
Use the fact that 1 pound per square inch of pressure equals 27.78 inches in a water column; this is your conversion factor. Press the multiply key, then enter the number 27.78 into the calculator.
Press the equals key to see the answer. In this example, 2 pounds of pressure times 27.78 equals 55.56 inches of water in a water column.
Tips & Warnings
- Note that pressure in pounds for LP gas tanks is the gauge pressure, not the absolute pressure. Gauge pressure uses atmospheric pressure (14.7 pounds per square inch) as a baseline, so 5 pounds is 14.7 + 5 = 19.7 pounds per square inch of absolute pressure at sea level.
- Photo Credit JohnnyH5/iStock/Getty Images
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CC-MAIN-2016-50
| 3,531 | 31 |
https://www.globalsino.com/EM/page1913.html
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math
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As the resolution of TEM imaging increases, a small amount of beam tilt can result in a significant amount of coma.
The electron-beam-tilt-induced coma can be given by,
w = α exp(iϕ) ------------------ [1913b],
Cs -- The spherical aberration coefficient,
b = B exp(iϕB),
α -- The scattering angle,
B -- The coefficients corresponding to coma displacement,
ϕB -- The initial phase of corresponding aberration.
Note that in Cs-corrected EMs, due to the absence of spherical aberration it is not possible anymore to correct the residual axial coma by tilting the illumination beam. In this case an appropriate coma compensator is needed to eliminate the coma.
Koji Kimoto, Kazuo Ishizuka, Nobuo Tanaka, Yoshio Matsui, Practical procedure for coma-free alignment using caustic figure, Ultramicroscopy 96 (2003) 219–227.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337338.11/warc/CC-MAIN-20221002150039-20221002180039-00308.warc.gz
|
CC-MAIN-2022-40
| 823 | 10 |
https://community.qlik.com/thread/274422
|
math
|
I have a data in excel with the column name
so I want to load this in qlik result as
2 -- two
3 -- three
----- like so on..
convert number to text
Translation from Numbers in Words
how to convert number into words
Here you have to do the Mapping Load is best option
Mapping Load * inline
Load * inline
thanks all. good example anand
If you have fixed numbers then you can go with approach suggested by the Anand, but if your numbers are dynamic then you need to go with different approach suggested by me & Tresesco
its fixed numbers I have only 15 in my excel. thanks for the explanation
Thanks If you have more numbers like in 1000+ then go with Marcus Suggestion.
Okay anand thanks.
Retrieving data ...
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794872766.96/warc/CC-MAIN-20180528091637-20180528111637-00480.warc.gz
|
CC-MAIN-2018-22
| 705 | 17 |
https://sciencesite.com/physics/reflection-by-a-plane-mirror/
|
math
|
We all use the mirror daily to check how we look or appear. The mirror shows us our reflection, standing erect exactly as we appear. The only difference is that when you move your right hand, your reflection moves the left hand. This is known as lateral inversion or sideways inversion.
Reflection and refraction can be understand studied under geometrical optics, a sub-branch of optics, which is concerned with the particle nature of light. In geometrical optics, light is modeled to move in a straight line and interact with matter. A single line of light is called a ray of light and a collection of rays is termed as a beam of light. Geometrical optics is also called ray optics.
Reflection is not scattering
In order for light to get reflected, it has to bounce off a polished surface, otherwise simple scattering of light will take place. In case of the latter, the light particles will just be bounced off randomly, leading to illumination but not a proper reflection. A mirror is a highly polished surface. It allows the light particles to be reflected while following the two laws of reflection:
- The angle of incidence is equal to the angle of reflection.
- The incident ray, the reflected ray and the normal to the mirror at the point of incidence – all lie in the same plane.
If you consider a plane mirror, the normal to the mirror is an imaginary line that we can draw perpendicular or at 90° to the surface of the mirror. The incident ray is the ray of light that approaches the surface of the mirror. Point of incidence is the point on the surface of the mirror where the incident ray makes contact with the surface. An imaginary line perpendicular to the surface of the mirror drawn at this point is called the normal to the mirror at the point of incidence. The ray of light after reflection is called reflected ray.
First law of reflection
The angle of incidence is the angle that the incident ray makes with the normal to the mirror at the point of incidence. Similarly, the angle of reflection is the angle that the reflected ray makes with the normal. According to the first law these angles are always equal. By an extension, you can also say that the angles that the incident and the reflected rays make with the surface of the mirror are also equal. It is basically a consequence of the fact that light rays always travel along the path between two points which requires the shortest time.
Second law of reflection
The second law of reflection is fairly simple. Given the incident ray, the reflected ray and the normal at the point of incidence, you can find a plane in which all of the three lie. Think of a “plane” as a flat surface of a table top. You can always find such an imaginary surface on which all the three components appear to lie. These two laws of reflection can be used to explain every phenomenon of reflection that takes place, whether the mirror is plane or spherical.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103619185.32/warc/CC-MAIN-20220628233925-20220629023925-00182.warc.gz
|
CC-MAIN-2022-27
| 2,922 | 11 |
https://www.khanacademy.org/math/algebra2/modeling-with-algebra/one-variable-modeling/e/modeling-with-one-variable-equations-and-inequalities
|
math
|
Equations & inequalities word problems
Construct an equation or an inequality that model a given context. Modeling expressions can be quadratic, rational, or exponential.
If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171706.94/warc/CC-MAIN-20170219104611-00616-ip-10-171-10-108.ec2.internal.warc.gz
|
CC-MAIN-2017-09
| 389 | 4 |
https://www.scientific.net/AMM.220-223.3024
|
math
|
Structure Design and Dynamic Characteristics Analysis of the Cartesian-Coordinates Automated Warehouse
This paper designed a cartesian coordinates automatic warehouse, and used ANSYS Workbench software to analyze its statics of the beam model with finite element method, then arrived at conclusions that the structure of automatic warehouse is reasonable which meets the technical requirements; the lower-order natural frequency of the system is far higher than the input frequency; the lower-order vibration modes are shown as the deformation of X axis' beam in horizontal direction and bend in the vertical direction, so we should improve its stiffness while designing it.
Zhengyi Jiang, Yugui Li, Xiaoping Zhang, Jianmei Wang and Wenquan Sun
H. Zhang and Y. Chen, "Structure Design and Dynamic Characteristics Analysis of the Cartesian-Coordinates Automated Warehouse", Applied Mechanics and Materials, Vols. 220-223, pp. 3024-3028, 2012
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832559.95/warc/CC-MAIN-20181219151124-20181219173124-00276.warc.gz
|
CC-MAIN-2018-51
| 940 | 4 |
https://liqibadoxejumiko.dellrichards.com/algebra-finding-the-percent-of-a449285209lq.html
|
math
|
Show Solution Write as a decimal.
What is the total recommended daily amount of fiber? How much money was deposited to Trong's savings account? And we have 16 goes into From tothe population of Detroit fell from aboutto aboutUnemployment rate as percent by year between and So let's try to actually do this division right over here.
So you could say, well, this is going to be equal to question mark overthe part of Amount: The amount based on the percent is What is the total recommended daily amount of sodium?
So in order to write this as a percent, we literally have to write it as something over But that still doesn't answer our question.
Find the percent increase. The nutrition fact sheet at a fast food restaurant says the fish sandwich has calories, and calories are from fat.
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402130531.89/warc/CC-MAIN-20200930235415-20201001025415-00191.warc.gz
|
CC-MAIN-2020-40
| 786 | 5 |
http://projecteuclid.org/euclid.ndjfl/1187031412
|
math
|
Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 48, Number 3 (2007), 425-448.
Interval Orders and Reverse Mathematics
We study the reverse mathematics of interval orders. We establish the logical strength of the implications among various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 \oplus 2. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither 2 \oplus 2 nor 3 \oplus 1.
Notre Dame J. Formal Logic Volume 48, Number 3 (2007), 425-448.
First available in Project Euclid: 13 August 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]
Secondary: 06A06: Partial order, general 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Marcone, Alberto. Interval Orders and Reverse Mathematics. Notre Dame J. Formal Logic 48 (2007), no. 3, 425--448. doi:10.1305/ndjfl/1187031412. http://projecteuclid.org/euclid.ndjfl/1187031412.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320823.40/warc/CC-MAIN-20170626152050-20170626172050-00168.warc.gz
|
CC-MAIN-2017-26
| 1,384 | 14 |
https://testbook.com/question-answer/a-bullet-of-mass-0-05-kg-is-fired-with-a-velocity--6198a191ea5f79f3d0689784
|
math
|
QuestionDownload Solution PDF
A bullet of mass 0.05 kg is fired with a velocity of 120 ms-1 from a rifle of mass 4 kg. What will be the recoil velocity of the rifle?
Answer (Detailed Solution Below)
Detailed SolutionDownload Solution PDF
Law of Conservation of Linear Momentum: If no external force acts on a system (called isolated) of constant mass, the total momentum of the system remains constant with time.
According to the law of conservation of momentum:
m1u1 + m2u2 = m1v1 + m2v2
Where m1,m2 = Masses of two bodies, u1, u2 = Initial velocities of the bodies, v1, v2 = Final velocities of the bodies
m1 = 0.05 kg, m2 = 4 kg, u1 = 120 ms-1, u2 = ?
Total momentum should be conserved,
∴ m1u1 = m2u2
0.05 × 120 = 4 × u2
u2 = 1.5 ms-1
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305423.58/warc/CC-MAIN-20220128074016-20220128104016-00129.warc.gz
|
CC-MAIN-2022-05
| 742 | 13 |
http://www.geo-technik.de/shop/engr-134.htm
|
math
|
Trusses 18cm ShopLite
Aluminium trusses with lower load capacity for museum and shop.
Connection by tube connectors, wich have to by screwed on both ends of the truss.
Load capacity for e.g.: ShopLite 3-point at 2m span width max. 100kg point load, at 5m length in one part 100kg.
1 Products found in this category
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986658566.9/warc/CC-MAIN-20191015104838-20191015132338-00335.warc.gz
|
CC-MAIN-2019-43
| 314 | 5 |
http://mathforum.org/kb/message.jspa?messageID=9567272
|
math
|
On Friday, August 15, 2014 11:35:11 PM UTC-5, Archimedes Plutonium wrote: > Now let me ask a question out of curiousity. Perhaps I asked this before on Goldbach. What can we do with perfect squares as sums. Here are the first several perfect-squares 1, 4, 9, 16, 25, . . and the question I ask is can they provide us with a Goldbach type of conjecture. Could we say that all numbers, both even and odd are the sum of no more than 4 perfect-squares? Say for instance 15 is the sum of 1+1+4+9 = 15. > > > > So, what can we do with perfect-squares rather than with primes? >
I think I might be onto something for I do not recall any conjecture or theorem for perfect squares constructing all the Naturals. Now suppose 4 perfect-squares can construct all the naturals, then, what would be a conjecture of how many primes construct all Naturals beyond 5? It would be nice if we could take 1 as prime and then we could say that all Naturals are the sum of no more than 3 primes by using Goldbach and 1.
Now, given only even numbers we cannot get any odd numbers, but given only odd numbers we can get all Naturals beyond 0 by 2 odd numbers added. So here is a case where even numbers are handicapped versus odd numbers and that rarely happens.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812855.47/warc/CC-MAIN-20180219231024-20180220011024-00670.warc.gz
|
CC-MAIN-2018-09
| 1,237 | 3 |
https://primeeducation.com.au/blog/our-blog-post-2020-maths-extension-1-hsc
|
math
|
Thoughts on 2020 Maths Extension 1 HSC paper
by Martin Gossow, publised 14 November 2020
Last week, students of the 2020 cohort sat the first Mathematics Extension 1 examination following the largest change to the syllabus in a few decades. After a tumultuous and anxious year, students were probably hoping that NESA would take it easy and remedy their stress. For students who have just entered Year 12 (and tutors/teachers like me instructing the cohort) are eager to get their hands on an exam to gauge the new difficulty level.
Look’s like NESA was willing to throw in some surprises. In contrast to the Mathematics Advanced exam—meticulously crafted to cover every topic in equal weighting—this exam goes all-out on a few topics and leaves others completely ignored. Most notably was the lack of vector geometry proofs or applications of differential equations.
The 10-mark multiple choice was reasonably straight forward, sticking to routine algebraic calculations and process-of-elimination questions. The last of these looks scary at first but just requires some substitution. Question 11 is all routine calculation as expected. The given induction (appearing in Question 12) is reasonably nice, and the pigeonhole principle is very explicitly given. Question 13 focuses heavily on calculus and integration, involving a reasonably involved substitution and a tricky double-chain-rule that was sure to lead to some elementary mistakes.
At this point, I expect students were feeling a little exhausted after Question 13 but somewhat confident they could knock out a proof about the orthogonality of rhombus diagonals. Instead, NESA throws an eight-mark curveball interweaving the binomial theorem with combinatorics. While a beautiful question in its own right, this topic got only a one-sentence (and rather vague) mention in the syllabus, and it is was unclear that a question of this type would be given in the exam. I had written questions of this sort into the Prime booklets, although they will be sure to receive a greater focus in the revision of this Year 11 topic (which a lot of students may be lacking in). The final question is a reasonable trigonometry palette-cleanser although involves a few different topics.
All students taking Extension 1 mathematics should take at least a cursory glance at this paper, especially trying Question 13a (which only needs Year 11 knowledge). We will also look at this exam more closely when the date of next year’s HSC approaches, but this was for sure a strong start to the new syllabus.
|
s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571911.5/warc/CC-MAIN-20220813081639-20220813111639-00306.warc.gz
|
CC-MAIN-2022-33
| 2,553 | 7 |
https://www.patriotcakes1776.com/items/salads
|
math
|
Salads are freshly made each morning. Small Salads are a lunch portion, while large are a full dinner sized meal or enough for 2 to share! Salads come with 2 servings of dressing. If you need more, please order those under the “extra dressing” button.
Small Chicken Garden$7Large Chicken Garden$9Small Chicken Caesar$7Large Chicken Caesar$9Small Chicken Salad on a Salad$7Large Chicken Salad on a Salad$9Small Loaded Cobb$8.50Large Loaded Cobb$11Small Loaded Southwest$8.50Large Loaded Southwest$11
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100535.26/warc/CC-MAIN-20231204214708-20231205004708-00213.warc.gz
|
CC-MAIN-2023-50
| 502 | 2 |
https://crosswordgenius.com/clue/show-little-promise-as-a-sculptor
|
math
|
Show little promise as a sculptor (5,5)
I believe the answer is:
'show' is the definition.
Both the definition and answer are verbs in their base form.
Perhaps there's a link between them I don't understand?
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100525.55/warc/CC-MAIN-20231204052342-20231204082342-00293.warc.gz
|
CC-MAIN-2023-50
| 295 | 7 |
https://dtu-workshop.astonphotonics.uk/abstract_kamalian-kopae/
|
math
|
Morteza Kamalian-Kopae (Aston University)
Noise in the nonlinear Fourier domain
Nonlinear Fourier transform provides us with the analytical relation between the input and output of the optical fibre link. This is what is required to find the capacity of fibre as the most important communication channel of modern data networks. An important part of this analytical model is the stochastic distribution of the received signal which is corrupted by random noise. In this talk, I will discuss some mathematical tools to explore noise and its representation in the Fourier domain and how we can quantify its impact in the NFT framework.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817043.36/warc/CC-MAIN-20240416031446-20240416061446-00165.warc.gz
|
CC-MAIN-2024-18
| 633 | 3 |
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