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https://abcsafetysolutions.com/courses/confined-space-entrant-%C2%BD-day/
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math
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This course has been designed to cover arrangements for pre-entry and entry into confined spaces.
The syllabus focuses on:
• Define Permit-Required Confined Space
• Identify the confined spaces in their workplace
• List the main types of hazardous atmosphere
• Discuss physical hazards that may be encountered
• Complete an entry permit
• Understand hazard control techniques
• Identify when respirators are necessary
• Recognize acceptable atmospheric conditions for entry
• Have the ability to perform tests, calibrate and use test equipment and interpret test results.
• Have the ability to inspect test, evaluate spaces, and determine the need for further evaluation
• Prescribe the type of ventilation (if needed)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585405.74/warc/CC-MAIN-20211021102435-20211021132435-00337.warc.gz
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CC-MAIN-2021-43
| 740
| 13
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http://plus.maths.org/content/taxonomy/term/697
|
math
|
Skip to Navigation
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Search this site:
three door problem
Outer space: Thinking inside the box
It's Monty Hall, only better!
Thomas Bayes & Mr Zootpooper
The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it?
lets his imagination run riot in this intergalactic application of Bayes' Theorem.
23 and maths
The company 23andMe made headlines by launching its DNA testing service in the UK. But how are the risks of...
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Here's an easy game that leads you straight to an unsolved question in maths.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768957.83/warc/CC-MAIN-20141217075248-00024-ip-10-231-17-201.ec2.internal.warc.gz
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CC-MAIN-2014-52
| 1,176
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https://www.electronicproducts.com/software-for-fuzzy-logic-system-design/
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math
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Software for fuzzy
logic system design
The Fuzzy Logic Pack is a computing environment for creating, modifying, and
visualizing fuzzy sets and fuzzy logic-based systems. Based on the technical
computing engine of Mathematica, the software offers hundreds of functions for
numeric and symbolic equation solving, visualization and animation
capabilities, and a high-level programming language.
In addition, the Fuzzy Logic Pack lets users combine text, calculations, 2- and
3-D graphics, and animation in a single document that can be used to track work
in progress or to create technical reports. The toolset requires Mathematica
2.2 (or later) and is available for all platforms that run that program.
Wolfram Research, Inc.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104506762.79/warc/CC-MAIN-20220704232527-20220705022527-00634.warc.gz
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CC-MAIN-2022-27
| 724
| 12
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http://movies.stackexchange.com/questions/tagged/men-in-black-2+men-in-black
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math
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Movies & TV
Movies & TV Meta
to customize your list.
more stack exchange communities
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Detailed answers to any questions you might have
Discuss the workings and policies of this site
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Did Big Tobacco fund MIB 1 and 2?
I just saw Men in Black 3 and enjoyed it immensely. There was practically no smoking in the film. In MIB 1 and 2, there was a lot of smoking and tobacco product placement. Did the makers of the ...
May 29 '12 at 22:29
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s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657133078.21/warc/CC-MAIN-20140914011213-00067-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
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CC-MAIN-2014-41
| 2,225
| 53
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https://www.bcf.uni-freiburg.de/events/informal-seminar/announcements/160317_Schmidt.htm
|
math
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In deformation theory certain problems can be solved by surprisingly simple and analytical means. Consider the following problem:
Given complex manifolds X and Y with holomorphic map f : Y -> X, does a first order infinitesimal deformation of f, a given section σ : Y -> f*TX, belong to a deformation of f? If so, σ is called effective.
A special class of fibrebundles, so called Jetbundles are a very useful tool in this discussion. They generalise the notion of the tangent bundle of a manifold. Jetbundles can be used to prove a cohomological criterion for the effectiveness of first order infinitesimal deformations.
In this talk the underlying problem will be explained and an analytic definition of Jetbundles will be given and used for a constructive approach to this abstract problem.
The talk is open to the public. Guests are cordially invited!
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670948.64/warc/CC-MAIN-20191121180800-20191121204800-00127.warc.gz
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CC-MAIN-2019-47
| 856
| 5
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https://forum.solidworks.com/thread/69317
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math
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I have some difficulty / question in converting a JPG file to 2-D drawing.
1. how can I make sure when creating a 2-D profile from the attached picutre, that it is in 1:1 scale?
2. The dimensions measured from the sketch I created from JPG file do not match the real dimensions of the original object (object -which i scanned).
Any help will be greatly appreciated.
never does always have to tweek the size because every scanner seems to do their own sizing.
what I do is start a sketch, draw a construction line the leght of a known dimension and then strech and place the jpeg over it and the trace it.
Retrieving data ...
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825349.51/warc/CC-MAIN-20181214022947-20181214044447-00441.warc.gz
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CC-MAIN-2018-51
| 624
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http://www.patentsencyclopedia.com/app/20150014523
|
math
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Patent application title: METHOD FOR DETERMINING THE MAXIMUM MASS PEAK IN MASS SPECTROMETRY
Norbert Rolff (Horrem, DE)
IPC8 Class: AH01J4900FI
Class name: Radiant energy ionic separation or analysis methods
Publication date: 2015-01-15
Patent application number: 20150014523
A fast method for determining molecular mass using mass spectrometry has
the following steps: specifying a first adjusting value (M1) of the mass
spectrometer, recording the associated signal amplitude (A1), specifying
a second adjusting value (M2) which is different to the first, measuring
the associated second signal amplitude (A2), specifying a third adjusting
value (M3) which is different to the first (M1) and the second (M2)
adjusting value, measuring the associated third signal amplitude (A3),
determining a quadratic function containing the measured amplitude values
as y-values and the specified adjusting values as x-values, determining
the maximum of the quadratic function, wherein the searched adjusting
value is determined from the x-value of the maximum.
1. A method for determining a molecular mass with the aid of mass
spectroscopy, said method comprising the steps of: predefining a first
set value (M1) of the mass spectrometer, capturing the associated signal
amplitude (Al), predefining a second set value (M2) differing from the
first set value, measuring the associated second signal amplitude (A2),
predefining a third set value (M3) differing from the first (M1) and the
second (M2) set value, measuring the associated third signal amplitude
(A3), obtaining a quadratic function containing the measured amplitude
values as y-values and the predefined set values as x-values, determining
the maximum of the quadratic function, the searched set value for the
molecular mass being determined from the x-value of said maximum.
2. The method according to claim 1, wherein the quadratic function is a parable of the type y=ax2+bx+c, its x-values corresponding to the predefined set values and its y-values corresponding to the measured amplitude values, and wherein a, b and c are mathematical constants.
3. The method according to claim 1, wherein amplitude values for at least three different set values and not more than ten set values are measured.
4. The method according to claim 1, wherein, after measurement of the three amplitude values and prior to determining said parable, it is examined whether the second amplitude value is higher than the first and the third amplitude value, wherein, if required, the measurements are repeated a sufficient number of times until the second amplitude value is higher than the first and the third amplitude value of a measurement.
5. The method according to claim 4, wherein the first set value of a repeated measurement corresponds to the third set value of the respective previous measurement.
6. The method according to claim 1, wherein the measurement of the first and the third amplitude value is repeated with set values whose distance to the second set value is smaller than at the respective previous measurement.
7. The method according to claim 6, wherein, when repeating said measurement, the maximum detected at the first measurement is used as the second set value.
8. The method according to claim 1, wherein, prior to each measurement of an amplitude value, it is first waited, after predefining the respective set value, until the amplitude signal has settled.
The invention relates to a method for determining the maximum of
the mass peak of the molecules measured with the aid of mass
Mass spectrometers are used for analysis of gases and find application particularly in leak detection devices. In such a case, the substance to be examined will be ionized in the gaseous phase and be supplied to an analyzer. In sector-field mass spectrometers, the anode voltage determines the set value for the mass position. Between a cathode and an anode, there is generated an electric field which will accelerate the electrons issuing from the cathode, which electrodes are ionizing the existing gas molecules. The charged electrons will be accelerated by the anode potential and, after passing the separation system, will reach the captor. In the separation system, a magnetic field is arranged which will deflect the ions. Ions which are too heavy will be deflected by the magnetic field too slightly while those ions which are too light-weighted will be deflected too strongly. Only the ions in the correct mass range will pass through the separation system. The anode potential is determinant of the mass passing through the separation system. In the range of a mass, a signal amplitude is generated which depends on the exact anode potential to the effect that, in case of a too small or too large anode potential, the signal amplitude will become smaller than the maximum. In other mass spectrometers, e.g. quadrupole mass spectrometers, the conditions are comparable so that the same method is applicable.
An adjustment is required so that, in each case, the maximum possible signal amplitude of the respective mass can be obtained. In order to adjust the mass spectrometer to the mass maximum, it is conventional practice to perform mass scans at respectively about 20-100 measurement points. Thus, in a way, the development of the signal amplitudes toward the associated set values is measured in close intervals. After a measurement, the maximum amplitude value of the measurement will be detected and, in the range around this value, a renewed measurement will be carried out at about 20-100 measurement points in closer intervals. In this manner, the maximum of the amplitude development is detected in a plurality of successive measurements until the resolution of the measurement is of sufficient accuracy. Also one scan with sufficient resolution is possible but will take much time. The set value of the maximum amplitude value of the last measurement will then be used as the set value for identification of the molecular mass. Because of the large number of measurement points to be captured and the multiple measurements to be performed after one another, the conventional methods for determining the mass maximum are time-consuming.
It is an object of the invention to provide a faster method for determining the mass adjustment for mass spectrometry.
The method of the invention is defined by the features according to claim 1.
It is accordingly provided that respective signal values will be captured for at least three different set values and respectively anode voltages. If the first or the last amplitude value is at a maximum, the measurement for other set values will be repeated until a measured signal amplitude between the first and the last measured signal amplitude is at the maximum. Prior to capturing each respective measurement point, it is preferably waited until the amplitude signal has become stabilized. The measured amplitude values and the associated set values will be stored as measurement points. Thereafter, a quadratic function will be computed which includes the measurement points. The maximum of the quadratic function will be detected and be used for determining the maximum of the set values for the desired molecular mass.
According to the invention, the measurement is performed with at least three different set values and with not more than ten set values. Preferably, during a measurement, only three measurement points will be captured. Thus, as compared to the conventional methods, the number of captured measurement points is distinctly reduced, allowing the measurements to be carried out noticeably faster. Further, by determining the maximum of a quadratic function containing the measurement points, there is obviated the need for successive measurements, which again allows for faster determination of the molecular mass. The invention is based on the idea of drawing conclusions on the actual development of the measurement signal from merely a few measurement values without measuring the development in its entirety.
Said quadratic function typically is a parable of the type y=ax2+bx+c. Herein, the x-values constitute the mass axis, i.e. the predefined set values, and the y-values are the measured amplitude values for each set value. The constants a and b can be determined after an equation system has been established for the measurement points. Subsequently, the x-value of the maximum of the function will be determined by forming the first derivative of the quadratic function. The x-value corresponding to the maximum is the set value of the searched molecular mass.
In case that the first one or the last one of the captured amplitude values should happen to be maximal, this is an indicator that the searched maximum does not lie between these two measurement values. Since the amplitude function does not exactly correspond to a parable, it is advisable to repeat the measurement for a new range of set values, wherein the first set value corresponds to the last set value of the respective previous measurement. In this manner, the measurements are repeated until a maximum amplitude measurement value between the respective first and the respective last set value of a measurement has been reached. Provided that the set values have been correctly selected, it will normally be already at the first measurement that the intermediate value is larger than the adjacent values. For the measurement values of this last measurement, the maximum will then be determined according to the above described method.
The accuracy of the method of the invention can be increased in that, as soon as a maximum amplitude value between the first and the second set value has occurred, there will be captured, around this amplitude value, further amplitude values for more-closely adjacent set values. Thus, this is to say--in other words--that the distances of the set values of the repeated measurement to the set value of the maximum amplitude value are smaller than in the respective previous measurement.
An embodiment of the invention will be explained in greater detail hereunder with reference to the Figure. The Figure shows a graphic representation of the measurement values according to the invention.
First, for three different set values M1, M2 and M3, the resulting amplitude values A1, A2 and A3 will be measured. The measured amplitude values A1, A2 and A3 will be stored together with the associated set values M1, M2 and M3 in the form of coordinate pairs (M1, A1) (M2, A2) and (M3, A3). In the Figure, the coordinate pairs are plotted as points in a coordinate system. In this coordinate system, the x-axis corresponds to the set values, i.e. to the mass axis M, and the y-axis is the appertaining amplitude axis A.
The Figure shows that the amplitude value A2 of the intermediate set value M2 is larger than the amplitude values A1 and A3 of the first set value M1 and of the last set value M3. This means that that the maximum of the searched development is situated between the first set value M1 and the third set value M3. If this should not be the case, the measurement would have to be repeated, wherein the first set value M1 of a subsequent measurement corresponds to the set value M3 of the respective previous measurement so that no range will be omitted.
After capturing the three measurement points (M1, A1) (M2, A2), (M3, A3), a parable which includes these measurement points will be searched for. As a parable herein, the quadratic function y=ax2+bx+c with the mathematic constants a, b. c will be set up. The x-values correspond to the set values--which, in sector-field mass spectrometers, is in correspondence to the anode voltage--and the y-values correspond to the associated amplitude values. Then, using the measurement points, an equation system will be established and will be solved for the constants a and be. For b, the result will be
and, for constant a,
Subsequently, for determining the position of the maximum, the first derivative y'=2ax+b of the quadratic function y will be set up and, after insertion of the computed constants a, b, this derivative will be solved for x. This x-value will then be the set value Mmax at which the development of the function is maximal. The set value of the maximum is Mmax=-b/2a. On the basis of this set value, the amplitude of the searched molecule becomes maximal.
Patent applications by Norbert Rolff, Horrem DE
Patent applications by INFICON GMBH
Patent applications in class Methods
Patent applications in all subclasses Methods
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824912.16/warc/CC-MAIN-20181213145807-20181213171307-00298.warc.gz
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CC-MAIN-2018-51
| 12,559
| 56
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https://euro-math-soc.eu/review/semimartingales-course-stochastic-processes
|
math
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The presented monograph is an advanced book on general martingale theory. A reader with good knowledge of probability and discrete time processes will appreciate the deep results contained in the book. Theorems are formulated for quasimartingales, some parts of the book are devoted to Hilbert space valued processes, and the theory is not restricted to continuous square integrable martingales as is usually the case. Due to these facts, the book is a necessity for all researchers working with general stochastic processes. The book consists of two parts. In the first part the general theory of martingales is given. It starts with basic definitions and facts from stochastic processes; filtration, measurability, adapted and predictable processes, stopping time, and decomposition. The next chapters continue with the martingale property. We find many classical results in a quite general context like Doob's inequalities or convergence theorems. The first part is concluded by a chapter devoted to square integrable semimartingales, quadratic variation and Meyer's process. Here we also find the theory of Hilbert space valued martingales and stochastic integrals with respect to them. In the second part, stochastic calculus is the focus. First, the stochastic integral is built and a semimartingale version of Itô transformation theorem is proved. Then, as an application, the Brownian and Poisson processes are considered and changes of probability, as well as Girsanov formula, are presented. The book culminates with a chapter on SDE. This is not a book which I would recommend as an introduction to stochastic processes and martingales. But for any rigorous work in the theory of martingales, namely non-continuous processes, semimartingales and multidimensional martingales, it is the book that should be consulted first. It is not easy to write a concise book on general martingale theory but in my opinion Michel Métivier has done great job.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711344.13/warc/CC-MAIN-20221208150643-20221208180643-00657.warc.gz
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CC-MAIN-2022-49
| 1,957
| 1
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http://wow.allakhazam.com/forum.html?forum=252&mid=1251465328158656869
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math
|
Hey everyone, appologies if this appears a noobish question but i scanned the forums and couldnt really find anything to enlighten me on the ws mods.
So heres my question Regarding corsairs Slugg shot, when i click the link for this weoponskill it says the modifiers are 30% Agility, so does that mean it adds 30% damage for a certain amount of agility i add to it?
Its makin my head hurt (never was good at maths)lol
Say i use Slugg shot without any AGI equiped and it does 900 (for arguemnets sake)
Then i add a certain amount of agility will it add 30% Damage (so 300) to the standard WS damage ? Making it 1200 ? Roughly~
Or how much AGI will i need to use to get to a 30% modification?
Any help is appreciated and i appologise in advance if the answers is simple but i just misunderstood it :)
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945660.53/warc/CC-MAIN-20180422212935-20180422232935-00544.warc.gz
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CC-MAIN-2018-17
| 798
| 7
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http://www.peartreegreetings.com/Wedding/Wedding-Favor-Tags/2775-10083GTFC-Flourished-Monogram--Wedding-Favor-Stickers.pro
|
math
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Showcase your refined and classy style with these wedding favor stickers. A flourish design holds a monogram letter, as your special date and names sit below. With your choice of color for the background, these labels are sophisticated and refined - just like the bride!
See more Wedding Favor Tags like this:
2 1/4 x 2 1/4,
You Pick Color,
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699201808/warc/CC-MAIN-20130516101321-00073-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 344
| 4
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https://mathshistory.st-andrews.ac.uk/Biographies/MacLane/
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math
|
Leslie Saunders Mac Lane
Norwich, Connecticut, USA
San Francisco, California, USA
BiographySaunders Mac Lane came from a Scottish family who fled from Scotland after the Battle of Culloden in 1746. His grandfather, William Ward McLane was born in Lewisville, Pennsylvania in 1846, became a Presbyterian Minister but was forced to leave the Church after preaching the theory of evolution. He became a pastor in the Congregational Church and the eldest son from his second marriage, Donald Bradford McLane, was born 19 January 1882 in Steubenville. Donald married Winifred Saunders, the eldest daughter of George Aretas Saunders, in 1908. Winifred was a graduate of Mount Holyoke College and taught English, Latin and Mathematics at High School before her marriage. After his marriage, Donald became a Congregational Minister in Taftville, Connecticut and his eldest son Leslie Saunders MacLane, the subject of this biography, was born in Norwich, close to Taftville. When he was only one month old his parents decided they did not like the name Leslie and from that time on he was known as Saunders MacLane. The change from MacLane to Mac Lane only came about many years later after his marriage. Saunders had two brothers, Gerald R MacLane, who became a mathematics professor at Rice University and Purdue University, and David Tyler MacLane, born 20 January 1922, in Utica, New York, who became a school teacher and businessman. Mac Lane's early years were spent in several different small towns but he did live in one large city, spending a few years in Boston when aged around seven.
Mac Lane's High School education began in Utica, New York but was interrupted in 1924 when he was 14 years old for, at that time, his father died. After his father's death, Mac Lane moved to Leominster, Massachusetts, to live with his grandfather who, as we noted above, was also a Congregational Minister. Saunders graduated in 1926 from high school and, in that year, he entered Yale University. It had been his half-uncle, John Fisher MacLane (born 1878), who had visited him and explained that he and several of his relations had gone to Yale University. He offered to provide Mac Lane with sufficient funds to cover his expenses at Yale but he expected Mac Lane to train for a career in either business or law. Mac Lane's grandfather, William Ward McLane, died on 14 June 1931 a year after Mac Lane graduated from Yale.
In the autumn of 1926, Mac Lane began his studies at Yale but at this time his aim was to specialise in chemistry :-
I took both an honours course in chemistry and the standard freshman mathematics course. I found the chemistry rather dull. I didn't enjoy laboratory work. I had a wonderful teacher in the freshman mathematics course, an instructor working for his Ph.D., named Lester Hill. He gave me lots of encouragement and said, "Mac Lane, why don't you take the Barge Prize examination?" They gave that examination to freshmen every year. So I took the examination, succeeded in winning the prize, and decided that maybe mathematics was a better field than chemistry.However, he did not take only mathematics courses but, in his second year, he took an accounting course, feeling that he should do that since his uncle was financing his studies. Within weeks he was completely bored by accounting and, after one of his classmates said how much he was enjoying physics, Mac Lane went on to major in both mathematics and physics. He graduated from Yale in 1930 and took up a fellowship at Chicago. At the University of Chicago he was influenced by Eliakim Moore but his first year there, 1930-31, was :-
... a vaguely disappointing year of graduate study.By this time E H Moore was nearly seventy years old but his advice to Mac Lane to study for a doctorate at Göttingen in Germany certainly persuaded Mac Lane to work at the foremost mathematical research centre in the world at that time. Of course Moore had himself studied in Germany as a young man and had created in Chicago an eminent research school of mathematics based on his experiences of German mathematics at that time.
Mac Lane went to Göttingen in 1931 :-
Hilbert had retired from his professorship, but still lectured once a week on "Introduction to Philosophy on the Basis of Modern Science". His successor, Hermann Weyl, lectured widely on differential geometry, algebraic topology and on the philosophy of mathematics (on which I wrote up lecture notes). From his seminar on group representations, I learned much (e.g., on the use of linear transformations), but I failed to listen to his urging that algebraists should study the structure of Lie algebras. I also was not convinced by his assertion that set theory involved too much "sand". Edmund Landau (professor since 1909) lectured to large audiences with his accustomed polished clarity - and with assistants to wash off used (rolling) blackboards. Richard Courant, administrative head of the Institute, lectured and managed the many assistants working on the manuscript of the Courant-Hilbert book. Gustav Herglotz delivered eloquently his insightful lectures on a wide variety of topics: Lie groups, mechanics, geometrical optics, functions with a positive real part. Felix Bernstein taught statistics, but left in December 1932 before the deluge struck. These were then the 'ordentliche' professors in Göttingen.However, political events would soon disrupt Göttingen. Mac Lane began to work for his doctorate under Paul Bernays' supervision but in 1933 the Nazis came to power. They began to remove the top mathematicians from Göttingen, and other universities, who had Jewish connections. Mac Lane wrote to his mother on 3 May 1933 (see ):-
So many professors and instructors have been fired or have left that the mathematics department is pretty thoroughly emasculated. It is rather hard on mathematics, and we have but the cold comfort that it is the best thing for the Volk.Mac Lane had seen that he had to work quickly for his doctorate and leave Germany as soon as possible before things deteriorated further. He defended his thesis Abbreviated Proofs in the Logical Calculus, with Weyl as examiner, on 19 July 1933. At the end of his thesis he thanked his advisor Paul Bernays "for his criticism", "and most of all Professor Hermann Weyl for his advice and for the inspiration of his lectures". Mac Lane was rather disappointed to learn that Weyl had only rated his thesis "sufficient". A couple of days after getting his degree, he married Dorothy Jones whom he had met in Chicago and who had joined him in Göttingen (in fact she had typed his thesis). It was a small ceremony followed by a wedding dinner with a couple of friends in the Rathaus Keller. The newly married couple quickly returned to the United States. The article by Mac Lane gives an interesting account of the events at Göttingen in 1933.
On returning to the United States, Mac Lane spent the session 1933-34 at Yale while he tried to get a university position for the following year. He went to the American Mathematical Society meeting in December 1933 and talked with George Birkhoff, Marshall Stone and Joseph Ritt about possible positions. A couple of weeks after this he received a letter from Harvard offering him an appointment for a year as Benjamin Peirce Instructor. He was also asked to give an advanced course. He gladly accepted. Up to this time he had worked on mathematical logic but that was not a topic that was attractive to those making appointments to mathematics departments. Offered the option of giving the advanced course at Harvard on logic or algebra, he opted for algebra and he began to move in that direction. He spent two years at Harvard and left to take up a post of instructor at Cornell for session 1936-37. He spent the following session back at Chicago, working in algebra and getting much help from Adrian Albert, before accepting an appointment as an assistant professor at Harvard which he took up in 1938.
It was during the years at Harvard (1938-47) that he wrote his famous text A survey of modern algebra with Garrett Birkhoff which was published in 1941. Kaplansky writes in about this text:-
"A Survey of Modern Algebra" opened to American undergraduates what had until then been largely reserved for mathematicians in van der Waerden's "Moderne Algebra", published a decade earlier. The impact of Birkhoff and Mac Lane on the content and teaching of algebra in colleges and universities was immediate and long sustained. What we recognise in undergraduate courses in algebra today took much of its start with the abstract algebra which they made both accessible and attractive.Further information about this famous text including details of how it came to be written are given at THIS LINK.
During World War II Mac Lane worked in the Applied Mathematics Group at Columbia :-
We were doing some immediately practical problems of calculating curves for fire control and such. It was elementary differential equations and I learned to understand more about them. But the work at Columbia was not in really profitable directions of applied mathematical research. Also it was partly administrative and I decided that I didn't especially like administration. I remember making a conscious decision at that time: if you want to go into business and make that your career, now is the time to do it. I didn't. I went back to Harvard, happy to go back to mathematics.Then in 1947 he was appointed professor of mathematics at Chicago. The research centre there had Marshall Stone, Abraham Albert, Irving Kaplansky, Otto Schilling and André Weil on the staff and was led by Stone. In 1952, five years after being appointed, Mac Lane took over the chairmanship of the department from Stone who stepped down as chairmen but remained on the staff for another sixteen years. Wojciech Komornicki attended Mac Lane's algebra course in 1968-69 and describes the experience in :-
... it was nothing like any mathematics course I had ever taken. Though teaching from his own book, it seemed that Mac Lane would go out of his way to present the material differently than what was in the text. Sometimes he would give more than one proof of the same theorem. He made sure that we were aware of this, explaining that the more ways we understood something the better our understanding. Though I once again saw the same definition of a group that I remembered from my NSF program, I heard that a group was a category with one object in which all the arrows were invertible. The product of two groups was a universal object. I remember struggling with these new concepts especially since Mac Lane's style was to give us the big picture leaving most, but not all, of the details to the book and to the problems he assigned. However, the understanding of the mathematics was paramount in Mac Lane's presentations. If he thought that someone did not understand a proof, he would provide an alternative proof. And there was never any hint that a concept or a proof was too complex for someone to understand. Another aspect of his teaching that struck me was that he never came to class with notes. He would every once in a while pull out an index card on which I assume he had the subject matter of the day's class, look at it, put it back in his shirt or jacket pocket and continue the lecture. Though his lectures were meticulous in presenting the global picture of what we were learning he took great care to answer questions. No question was too small and he never blew off a question nor showed any irritation by student asking questions.Mac Lane's work covered a wide range of mathematics. He worked on and off throughout his career on mathematical logic, no surprise for a student of Bernays, and he did some early work on planar graphs. He studied valuations and their extensions to polynomial rings. In the 1940s he worked on cohomology and introduced the basic notions of category theory. Peter May, Professor in Mathematics at the University of Chicago, said (see ):-
[In his research] he was extraordinarily perceptive and original, and he was especially strong as a philosopher of mathematics. With Sammy Eilenberg he created a new way of thinking about mathematics. In a landmark 1945 paper, they introduced and named the concepts of 'categories,' 'functors' and 'natural transformations.' The language they introduced there transformed modern mathematics. In fact, a very great deal of mathematics since then would quite literally have been unthinkable without that language.Mac Lane was the author of seven books: (with Garrett Birkhoff) A Survey of Modern Algebra (1941); Homology (1963); (with Garrett Birkhoff) Algebra (1967); Categories for the Working Mathematician (1971); Mathematics, Form and Function (1985); (with Ieke Moerdijk) Sheaves in Geometry and Logic: A First Introduction to Topos Theory (1992); and Saunders Mac Lane: A Mathematical Autobiography (2005).
Information about A Survey of Modern Algebra is given at THIS LINK.
Information about the other six books is given at THIS LINK.
Among the many prizes and honours Mac Lane received we mention the Chauvenet Prize (1941):-
... for his writing 'Modular Fields' and 'Some Recent Advances in Algebra' ...and the Leroy P Steele Prize (1986):-
... for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.He received the National Medal of Science in 1989:-
For revolutionizing the language and content of modern mathematics by his collaboration in the creation and development of the fields of homological algebra and category theory, for outstanding contributions to mathematics education, and for incisive leadership of the mathematical and scientific communities.For his contributions to the Mathematical Association of America, Mac Lane received the Association's Award for Distinguished Service for 1975. He was a Governor of the Association (1943-45), a Vice-President (1948-49), and President for 1951-52 :-
His presidency made an enduring impression on those who were active in the Association at that time. He saw the office less as an honour than as an opportunity, attacked the problems of collegiate mathematics with characteristic imagination and energy, and set the Association on the active course that it has followed ever since.He was elected to the National Academy of Sciences in 1949 and served as its vice-president from 1973 to 1981. He was also elected to the American Philosophical Society in 1949, and served as its vice-president from 1968 to 1971. He was president of the American Mathematical Society in 1973-74 :-
As President of the American Mathematical Society, Mac Lane has given that Society the dynamic leadership that one would have anticipated, initiating new activities and vigorously pursuing old ones. Many members of the Society especially valued the openness of his administration and his new lines of communication with the membership. He handled difficult problems with exemplary skill which many of us have enjoyed observing at first hand. His presidency of the Society, like his presidency of the Association, will be remembered with admiration.Among his other honours we note that he was elected an Honorary Fellow of the Royal Society of Edinburgh in 1972. He received honorary degrees from many universities including Purdue University, Yale University and the University of Glasgow.
Saunders and Dorothy Mac Lane had two daughters, Gretchen and Cynthia. Dorothy died in 1985 and Mac Lane married the artist Osa Skotting Segal (who was divorced from Irving Segal in 1977) in the following year. Mac Lane's hobbies included skiing, hiking and writing poetry. He would read aloud the works of poets such as Byron, Shelley, Keats and Wordsworth. Osa said :-
And so I was reading poetry to him - those same poets - when he was lying there at the end of his life.Kelly, in , writes:-
No man could so stimulate others unless, alongside an incisive intellect, he was possessed of enthusiasm and warmth, a deep interest in his fellow man, and a sympathy the more real for being unsentimental. Those who proudly call themselves his friends know these things: others will infer them in reading [his works].
- I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979).
- S Mac Lane, Saunders Mac Lane - a mathematical autobiography (A K Peters, Ltd., Wellesley, MA, 2005).
- G L Alexanderson and S Mac Lane, A Conversation with Saunders Mac Lane, The College Mathematics Journal 20 (1) (1989), 2-25.
- G L Alexanderson, C Wilde and G Birkhoff, A Conversation with Garrett Birkhoff, The Two-Year College Mathematics Journal 14 (2) (1983), 126-145.
- F G Ashurst, Review: Mathematics, Form and Function (1985), by Saunders Mac Lane, The Mathematical Gazette 71 (456) (1987), 176-177.
- S Awodey, Saunders Mac Lane: A biographical memoir, Proc. American Philosophical Soc. 151 (3) (2007), 351-356.
- S Awodey, In memoriam: Saunders Mac Lane 1909-2005, Bull. Symbolic Logic 13 (1) (2007), 115-119.
- M Barr, Memories of Saunders Mac Lane, Scientiae Mathematicae Japonicae 63 (1) (2006), 11-12.
- S L Bloom, Review: Mathematics, Form and Function (1985), by Saunders Mac Lane, Studia Logica: An International Journal for Symbolic Logic 49 (3) (1990), 424-426.
- R P Boas, Award for Distinguished Service to Professor Saunders Mac Lane, Amer. Math. Monthly 82 (2) (1975), 107-108.
- K P Bogart, Review: Algebra, by Saunders Mac Lane and Garrett Birkhoff, Amer. Math. Monthly 78 (1) (1971), 92-93.
- F Borceux, Saunders Mac Lane: a bibliographical sketch, Scientiae Mathematicae Japonicae 63 (1) (2006), 2-3.
- W Browder, Mathematical judgment. With a reply by Saunders Mac Lane, The Mathematical Intelligencer 7 (1) (1985), 51-52; 76.
- I R Brune, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, The Mathematics Teacher 47 (2) (1954), 128.
- P J Davis, Mister Mathematics: Saunders Mac Lane, SIAM News (20 November 2005). https://www.siam.org/news/news.php?id=181
- S Eilenberg, Some remarks on the interface of algebra and geometry, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979), 525-526.
- D D Fenster, Review: Saunders Mac Lane: A Mathematical Autobiography, by Saunders Mac Lane, Amer. Math. Monthly 113 (10) (2006), 947-951.
- Garrett Birkhoff and Saunders Mac Lane, 'A Survey of Modem Algebra': The Fiftieth Anniversary of its Publication, The Mathematical Intelligencer 14 (1) (1992), 26-31.
- F Q Gouvêa, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, Mathematical Association of America. http://www.maa.org/press/maa-reviews/a-survey-of-modern-algebra-0
- L M Graves, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, The Scientific Monthly 78 (2) (1954), 118.
- L W Griffiths, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, National Mathematics Magazine 16 (5) (1942), 268-269.
- A Heller, Review: Categories for the Working Mathematician, by Saunders Mac Lane, American Scientist 61 (3) (1973), 375-376.
- P Johnstone, Saunders Mac Lane. Joint creator of category theory, The Independent (26 April 2005).
- I Kaplansky, The early work of Saunders Mac Lane on valuations and fields, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979), 519-524.
- M Kelly, Saunders Mac Lane and category theory, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979), 527-544.
- R Kirby, Saunders Mac Lane 1909-2005, Biographical Memoirs, National Academy of Sciences (2015). http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/mac-lane-saunders.pdf
- W Komornicki, An undergraduate's memory of Saunders Mac Lane, J. Homotopy Related Structures 2 (2) (2007), 7-10.
- S Koppes, Saunders Mac Lane, Mathematician, 1909-2005, University of Chicago News Office (21 April 2005). http://www-news.uchicago.edu/releases/05/050421.maclane.shtml
- S S Kutateladze, Saunders Mac Lane, The Knight of Mathematics, Scientiae Mathematicae Japonicae 63 (1) (2006), 4-8.
- G Leversha, Review: Saunders Mac Lane: A Mathematical Autobiography, by Saunders Mac Lane, The Mathematical Gazette 91 (522) (2007), 571-572.
- F E J Linton, Review: Homology, by Saunders Mac Lane, Amer. Math. Monthly 71 (7) (1964), 818.
- R Lyndon, Saunders Mac Lane as a shaper of mathematics and mathematicians, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979), 515-518.
- S Mac Lane, Mathematics at Göttingen under the Nazis, Notices Amer. Math. Soc. 42 (10) (1995), 1134-1138. http://www.ams.org/notices/199510/maclane.pdf
- S Mac Lane, Mathematics at the University of Chicago: A brief history, in P Duren (ed.), A century of mathematics in America, Part I (American Mathematical Society, Providence, RI , 1988), 127-154.
- P Maddy, Review: Mathematics, Form and Function (1985), by Saunders Mac Lane, The Journal of Symbolic Logic 53 (2) (1988), 643-645.
- W Magnus, Review: Algebra, by Saunders Mac Lane and Garrett Birkhoff, Mathematics of Computation 22 (103) (1968), 693-694.
- K O May, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, Econometrica 22 (3) (1954), 391.
- C McLarty, Saunders Mac Lane (1909-2005): His Mathematical Life and Philosophical Works, Philosophia Mathematica (3) 13 (3) (2005), 237-251.
- C McLarty, The last mathematician from Hilbert's Göttingen: Saunders Mac Lane as philosopher of mathematics, British Journal for the Philosophy of Science 58 (1) (2007), 77-112.
- C McLarty, Saunders Mac Lane and the universal in mathematics, Scientiae Mathematicae Japonicae 63 (1) (2006), 25-29.
- A C Mewborn, Review: Algebra, by Saunders Mac Lane and Garrett Birkhoff, Amer. Math. Monthly 74 (10) (1967), 1279.
- New York Times (21 April 2005).
- K Peters, Obituary: Saunders Mac Lane (1909-2005), Nature 435 (2005), 292.
- A M Pitts, Review: Sheaves in Geometry and Logic: A First Introduction to Topos Theory, by Saunders Mac Lane and Ieke Moerdijk, The Journal of Symbolic Logic 60 (1) (1995), 340-342.
- A Putman, A biographical note, in I Kaplansky (ed.), Saunders Mac Lane : Selected Papers (New York - Heidelberg, 1979), ix-xii.
- Saunders Mac Lane, 1951-1952 MAA President, The Mathematical Association of America. http://www.maa.org/about-maa/governance/maa-presidents/saunders-mac-lane-1951-1952-maa-president
- Saunders Mac Lane, The Telegraph (6 May 2005).
- Saunders Mac Lane, developed key algebraic theory; at 95, The Boston Globe (23 April 2005).
- Saunders Mac Lane, Garrett Birkhoff and the 'Survey of Modern Algebra', Notices Amer. Math. Soc. 44 (11) (1997), 1438-1439.
- D Singmaster, Review: Algebra, by Saunders Mac Lane and Garrett Birkhoff, The Mathematical Gazette 75 (471) (1991), 121.
- L W Small, Review: Saunders Mac Lane: A Mathematical Autobiography, by Saunders Mac Lane, Notices Amer. Math. Soc. 52 (11) (2005), 1340-1342.
- W Tholen, Saunders Mac Lane 1909-2005. Meeting a Grand Leader, Scientiae Mathematicae Japonicae 63 (1) (2006), 13-24.
- R M Thrall, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, Bull. Amer. Math. Soc. 48 (5) (1942), 342-345.
- C T C Wall, Review: Homology, by Saunders Mac Lane, The Mathematical Gazette 49 (367) (1965), 105-106.
- M Ward, Review: Survey of Modern Algebra, by Garrett Birkhoff and Saunders Mac Lane, Science, New Series 95 (2467) (1942), 386-387.
- R Working, Saunders Mac Lane, 95. University of Chicago mathematician helped introduce key concepts to field, Chicago Tribune Company (23 April 2005).
Additional Resources (show)
Other pages about Saunders Mac Lane:
Other websites about Saunders Mac Lane:
- History Topics: Bourbaki: the post-war years
- Societies: Mathematical Association of America
- Other: 1950 ICM - Cambridge USA
- Other: 1954 ICM - Amsterdam
- Other: 1958 ICM - Edinburgh
- Other: Colloquium photo 1964
- Other: Earliest Known Uses of Some of the Words of Mathematics (A)
- Other: Earliest Known Uses of Some of the Words of Mathematics (C)
- Other: Earliest Known Uses of Some of the Words of Mathematics (F)
- Other: Earliest Known Uses of Some of the Words of Mathematics (I)
- Other: Earliest Known Uses of Some of the Words of Mathematics (K)
- Other: Earliest Known Uses of Some of the Words of Mathematics (M)
- Other: Earliest Known Uses of Some of the Words of Mathematics (N)
- Other: Earliest Known Uses of Some of the Words of Mathematics (S)
- Other: Earliest Known Uses of Some of the Words of Mathematics (T)
- Other: Earliest Uses of Function Symbols
- Other: Earliest Uses of Symbols of Number Theory
- Other: Earliest Uses of Symbols of Operation
Written by J J O'Connor and E F Robertson
Last Update October 2015
Last Update October 2015
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https://sciencing.com/sum-difference-math-problems-8145195.html
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math
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Math problems are diverse and can range in complexity from simple arithmetic to the upper levels of calculus. Understanding how to calculate the sum or difference of numbers is the foundation for many higher-level problems and an important skill in itself. When these numbers are added together (represented by the "+" sign), the resulting answer is called the "sum." When a number is subtracted from another number (represented by the "-" sign), the result is known as the "difference."
Finding the Sum
These steps are useful in basic arithmetical formulas, whether by themselves or as part of a more complex math problem. They are the foundation of higher levels of math, such as sine, imaginary numbers, square roots and derivatives.
Follow the order of operations and begin by completing any math located in parentheses. For example, if the math problem is 2 + 2(4-1), first subtract 1 from 4. Use a calculator or do the calculations in your head or on paper.
Multiply and divide any numbers that require it from left to right. Any numbers immediately before a parenthesis are multiplied by the numbers inside the parentheses.
Add and subtract the remaining numbers in the math problem. The sum will be the result of adding numbers, while the difference will be the result of subtracting them. For instance, in the math problem 4 + 3 - 5, the sum of 4 and 3 will be 7, and the difference between 7 and 5 will be 2. In this example, 2 is the final answer to the math problem.
- These steps are useful in basic arithmetical formulas, whether by themselves or as part of a more complex math problem. They are the foundation of higher levels of math, such as sine, imaginary numbers, square roots and derivatives.
About the Author
Clifton Watson started writing and editing in 2008. He edited the "American River Review" and maintained a number of online blogs for Unitek College. Watson has an Associate of Arts in liberal arts from American River College.
Jupiterimages/Polka Dot/Getty Images
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CC-MAIN-2023-50
| 1,994
| 10
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https://brainmass.com/statistics/hypothesis-testing/relationships-between-home-teams-visiting-teams-523373
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math
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A sports statistician is interested in determining if there is a relationship between the number of home team and visiting team losses and different sports. A random sample of 526 games is selected and the results are given below. Test the claim that the number of home and visiting losses is independent of the sport. Use alpha = 0.01
Football Basketball Soccer Baseball
Home team losses 39 156 25 83
Visiting team losses 31 98 19 75
Please see the attachments.
The null hypothesis tested is
H0: The number of home and visiting losses is independent of the sport.
The alternative hypothesis is
H1: The number of home and visiting losses depends on sport.
The test statistic used is where O is the observed frequency and E is the expected frequency.
The Expected frequencies are given below. They are calculated using the formula , ,where Ri , ith row total, Cj jth column total and G is the grand Total.
Test statistic, ...
The solution provides step by step method for the calculation of chi square test for association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573415.58/warc/CC-MAIN-20190919015534-20190919041534-00270.warc.gz
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CC-MAIN-2019-39
| 1,225
| 13
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https://www.geogebra.org/m/ZZVdq9dw
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math
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Optimization: An Isosceles Triangle with Fixed Perimeter
- Irina Boyadzhiev
Consider the cutting of a straight wire with fixed length into three segments so as to form an isosceles triangle. How long must be the base in order to maximize the area of the triangle? The line below the triangle represents the wire with fixed length; the green segment represents the variable base AB.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743282.69/warc/CC-MAIN-20181117040838-20181117062838-00363.warc.gz
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CC-MAIN-2018-47
| 381
| 3
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http://mathhelpforum.com/algebra/34224-simple-algebra-problem-please-help.html
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math
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im not trying to solve for x. just tell me if this is right, and if it isnt please correct me.
5x²+10=15/(1 x x²) WRONG, please tell me the reasons for your answer
5+10=15/(1 x x² x x²) WRONG again, please tell me the reasons for your answer
5x²+10=15/(1 x x²)
this is the right thing to do:
ax²+bx²=(a+b)x² -> you get 15x²=15 now divide with with 15 and you are done.
Why are these two steps wrong:
5x²+10=15/(1 x x²) & 5+10=15/(1 x x² x x²)
You are obviously dividing with x² . When dividing the equation you must be sure to divide both sides! So in your case you have divided 15 with x², that is OK. On the left side you have divided ONLY 10 with x² and forgot the 5.
The right thing would be:
5+10=15/(1 x x²) Or long way: 5x²+10x²=15 /x² -> 5x²/x²+10x²/x²=15/x²
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541839.36/warc/CC-MAIN-20161202170901-00173-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 792
| 11
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https://chelischili.com/examples-281
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math
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Variable solver calculator
Here, we will be discussing about Variable solver calculator. Our website will give you answers to homework.
The Best Variable solver calculator
In this blog post, we will be discussing about Variable solver calculator. There are a few key steps to solving any word problem. First, read the problem and identify what information is given and what is being asked. Next, create a visual representation of the problem, whether that be a drawing or a simple equation. Lastly, solve the problem and check your work to make sure the answer makes sense. With practice, solving word problems can become second nature!
Once you have a good understanding of the basics, you can start to work on more complicated problems. If you're still having trouble, there are plenty of resources available online and in math textbooks
One of the best ways to solve word problems in algebra is to break them down into smaller, more manageable pieces. This means reading the problem carefully and identifying all of the key information that you'll need to solve it. Once you have all of the information, you can start setting up equations and solving for the unknowns. It's often helpful to draw a diagram of the problem, as this can make it easier to visualize what's going on and see the relationships between different elements. If
There are many equation solvers available online and in mathematical software packages. These solvers can be used to solve equations of various forms, including linear, quadratic, and polynomial equations. Some equation solvers can also solve systems of equations.
In a right angled triangle, the hypotenuse is the longest side and is opposite the right angle. To solve for the hypotenuse, we can use the Pythagorean theorem which states that in a right angled triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the hypotenuse. This means that if we know the lengths of the two shorter sides, we can solve for the length of the hypotenuse by taking the
A sigma notation solver is a tool that can be used to simplify expressions that involve the summation of a sequence of numbers. This tool can be very helpful in solving problems that involve complex mathematical operations. By using a sigma notation solver, one can quickly and easily simplify expressions that would otherwise be very difficult to solve.
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CC-MAIN-2023-06
| 2,392
| 9
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https://publica.fraunhofer.de/handle/publica/252869
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math
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Rugged and elementary landscapes
The landscape of an optimization problem combines the fitness (or cost) function f on the candidate set X with a notion of neighborhood on X, typically represented as a simple sparse graph. A landscape forms the substrate for local search heuristics including evolutionary algorithms. Understanding such optimization techniques thus requires insight into the connection between the graph structure and properties of the fitness function. Local minima and their gradient basins form the basis for a decomposition of landscapes. The local minima are nodes of a labeled graph with edges providing information on the reachability between the minima and/or the adjacency of their basins. Barrier trees, inherent structure networks, and funnel digraphs are such decompositions producing ""coarse-grained"" pictures of a landscape. A particularly fruitful approach is a spectral decomposition of the fitness function into eigenvectors of the graph Laplacian, akin to a Fourier transformation of a real function into the elementary waves on its domain. Many landscapes of practical and theoretical interest, including the Traveling Salesman Problem with transpositions and reversals, are elementary: Their spectral decomposition has a single non-zero coefficient. Other classes of landscapes, including k-satisfiability (K-SAT), are superpositions of the first few Laplacian eigenvectors. Furthermore, the ruggedness of a landscape, as measured by the correlation length of the fitness function, and its neutrality, the expected fraction of a candidate's neighbors having the same fitness, can be expressed by the spectrum. Ruggedness and neutrality are found to be independently variable measures of a landscape. Beyond single instances of landscapes, models with random parameters, such as spin glasses, are amenable to this algebraic approach. This chapter provides an introduction into the structural features of discrete landscapes from both the geometric and the algebraic perspective.
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CC-MAIN-2022-49
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http://www.studymode.com/essays/Quantitative-Analysis-By-Spectrophotometric-Methods-163515.html
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math
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In this experiment, the absorbance of KMnO4 was measured by spectrophotometric method to determine the molar concentration and the molar extinction coefficient of KMnO4. In part 1, in order to determine the maximum absorbance wavelength of KMnO4, we measured the absorbance of the sample solution which contains KMnO4 at the wavelengths between 330nm and 660nm, and plotted the λ and A points; the λmax was 530nm. In part 2, the effect of concentration on the absorbance was examined. We prepared five differently concentrated (but, same path length) solutions, and measured the absorbance of them at the λmax(530nm) discovered in part 1; According to the results, higher concentrated solution had higher absorbance value. The extinction coefficient(ε) could be calculated from the results determined in part 2 and Beer’s Law; ε = 1.7 x 103. In part 3, the absorbance of the KMnO4 solution of unknown concentration was measured, and using Beer’s law and dilution equation, the initial concentration of the unknown was determined; The concentration of the solution (unknown # : 15) was calculated to be 3.3 x 10-3M.
Our eyes are sensitive to light which lies in a very small region of the electromagnetic spectrum labeled "visible light". This "visible light" corresponds to a wavelength range of 400 - 700 nanometers (nm) and a color range of violet through red. The human eye is not capable of "seeing" radiation with wavelengths outside the visible spectrum. The visible colors from shortest to longest wavelength are: violet, blue, green, yellow, orange, and red. Ultraviolet radiation has a shorter wavelength than the visible violet light. Infrared radiation has a longer wavelength than visible red light. The white light is a mixture of the colors of the visible spectrum. Black is a total absence of light. Figure 5.1 The electromagnetic spectrum.
Although visible light acts as a wave in some respects, it also displays properties characteristic of particles. The particle-like properties of visible light are exhibited through small, energy-bearing entities known as photons. The energy of a photon is: E photon = hc / λ (1) where h = Planck's constant, 6.626 x 10-34 J/s, c = speed of light, 3.00 x 108 m/s, and λ = wavelength of light. Light is energy, and when energy is absorbed by a chemical it results in a change in energy levels of the chemical. Molecules normally exist in discrete energy levels. Vibrational energy levels exist because molecular bonds vibrate at specific frequencies. Electronic energy levels exist because electrons in molecules can be excited to discrete, higher energy orbitals. The energy (E) of light depends on its wavelength. Longer wavelengths (infrared) have less energy than shorter wavelengths (ultraviolet). A molecule will absorb energy (light) when the energy (or wavelength) exactly matches the energy difference between the two energy states of the molecule. In absorption, light — sunlight which is white light — strikes an object and part of the light may be absorbed by the object. The light we see coming from that object is the light which was not absorbed by the object. We see the "not-absorbed" light as the color of the object. If no light is absorbed, the object appears to be colorless. A spectrophotometer is employed to measure the amount of light that a sample absorbs. The instrument operates by passing a beam of light through a sample and measuring the intensity of light reaching a detector. The beam of light consists of a stream of photons. When a photon encounters a molecule, there is a chance the molecule will absorb the photon. This absorption reduces the number of photons in the beam of light, thereby reducing the intensity of the light beam. The ratio of transmitted light intensity(I) to the incident light intensity(I0) is the transmittance, T: T = I / I0...
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https://physics.stackexchange.com/questions/362649/invariant-lagrangian-under-su2-times-u1
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math
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I am studying QFT and I was reading the chapter 10 about Spinors at the Schwartz's Quantum field theory and the standard model. After that chapter I got the task of constructing a lagrangian that is invariant under $$SU(2)\times U(1).$$
It was given a scalar field H ~ (2, 1/2), and fermion fields $q_l = (2, 1/6)$, $u_r = (1, 2/3)$ and $ d_r = (1, -1/3)$, where the firs two are doublet of $SU(2)$ and the last two are singlet of $U(1)$. The second number inside the brackets are hypercharges.
I am not sure of what to do. I mean, I know that a lagrangian invariant under $SU(2)\times U(1)$ must be invariant under $exp (i\alpha(x)/2)U(x)\phi$ where $\phi$ is the field. But I don't know what to do with the hypercharges and how to construct this lagrangian using just symmetry arguments. I mean this is the electroweak lagrangian, right? When Schwartz construct invariant lagrangians in the mentioned chapter of his book he starts with the symmetry group under which he wants his lagrangian to be invariant and he tackle term after term to find which ones are lorentz invariant. I did it this way as exercises for the complex scalar field, then for the $U(1)$ group, and for $SU(2)$ doublet alone. But now I am not sure of what to do with all of those field terms because I am not sure of exactly what a fermion field is and how to put all of those fields inside the lagrangian.
Does anyone have any hint/help?
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http://www.ams.org/mathscinet-getitem?mr=MR1921014
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math
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Zambotti, Lorenzo Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection.Probab. Theory Related Fields 123 (2002), no. 4, 579–600.
For users without a
, Relay Station allows linking from MR numbers in online mathematical literature
directly to electronic journals and original articles.
Subscribers receive the added value of full MathSciNet reviews.
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https://powerusers.microsoft.com/t5/Building-Flows/Bing-Maps-Direction-Link/m-p/1225579
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math
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Is there a way for me to get the link of the Driving Direction/url of maps?
Desired Output is the link to the image below:
You'll see that he destination and starting point is filled.
Is this possible? I tried searching the Forum but did not get the same one I was looking for.
Solved! Go to Solution.
Do you think there's a way to get the URL and not just the image? I tried the link you gave me but I can't generate a url for the direction.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305242.48/warc/CC-MAIN-20220127072916-20220127102916-00196.warc.gz
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CC-MAIN-2022-05
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https://www.physicsforums.com/threads/how-much-will-a-steel-plate-bend.765565/
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math
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Hello, I am trying to figure out how to determine how much a simple steel plate will bend with "x" amount of weight on it. I have searched the internet looking for some good descriptive information for my studies and am having a hard time figuring it out. I understand that it is probably complicated, but if someone could please give me an equation and "dumb" it down for me i would be very appreciative. Say i had a 2x4 across 2 chairs and set a 30lb box on it. How much would it bend?? Please don't just answer the problem, i do not care what the answer is, i just am curious how to get it. Thank you very much for your help again guys!!!
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CC-MAIN-2018-26
| 641
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https://safesaskwater.org/and-pdf/1002-statistics-quiz-questions-and-answers-pdf-563-725.php
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math
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Statistics quiz questions and answers pdf
File Name: statistics quiz questions and answers .zip
- Philippine Statistics Quiz
- Statistics and Probability Trivia Questions & Answers : Math
- Statistics MCQs Tests
- Business Statistics and Data Processing - Business Statistics Objective Type Questions
Philippine Statistics Quiz
Telangana Economist is on Facebook. To connect with Telangana Economist, join Facebook today. Join or. Business statistician interview questions and answers for data and statistical analyst to ask, to prepare and to study for jobs interviews and career MCQs with answer keys. Confidence intervals quiz has 21 multiple choice questions.
Index Newest Popular Best. Sign Up: Free! Log In. Accuracy : A team of editors takes feedback from our visitors to keep trivia as up to date and as accurate as possible. Related quizzes can be found here: Statistics and Probability Quizzes There are questions on this topic.
Business Statistics Multiple Choice Questions and Answers PDF book to download covers solved quiz questions and answers PDF on topics: Confidence intervals and estimation, data classification, tabulation and presentation, introduction to probability, introduction to statistics, measures of central tendency, measures of dispersion, probability distributions, sampling distributions, skewness, kurtosis and moments for college and university level exams. Multiple choice questions on introduction to probability quiz answers PDF covers MCQ questions on topics: Definition of probability, multiplication rules of probability, probability and counting rules, probability experiments, probability rules, Bayes theorem, relative frequency, rules of probability and algebra, sample space, and types of events. Multiple choice questions on introduction to statistics quiz answers PDF covers MCQ questions on topics: Data measurement in statistics, data types, principles of measurement, sources of data, statistical analysis methods, statistical data analysis, statistical techniques, structured data, and types of statistical methods. Multiple choice questions on measures of central tendency quiz answers PDF covers MCQ questions on topics: Arithmetic mean, averages of position, class width, comparison, harmonic mean, measurements, normal distribution, percentiles, relationship, median, mode, and mean. Multiple choice questions on measures of dispersion quiz answers PDF covers MCQ questions on topics: Arithmetic mean, average deviation measures, Chebyshev theorem, classification, measures of dispersion, distance measures, empirical values, interquartile deviation, interquartile range of deviation, mean absolute deviation, measures of deviation, squared deviation, standard deviation, statistics formulas, variance, and standard deviation. Multiple choice questions on probability distributions quiz answers PDF covers MCQ questions on topics: Binomial probability distribution, continuous, discrete and standard normal probability distributions, binomial distribution, expected value and variance, exponential distribution, hyper geometric distribution, normal distribution, Poisson distribution, random variable classes, rectangular distribution, statistics formulas, and uniform distribution.
Statistics and Probability Trivia Questions & Answers : Math
By attempting with this test you will be able to learn and understand the statistics in an efficient way. At the end of each test, you can get your results. You are evaluated on the basis of the score you achieve by marking each question in the test as the correct one. It also highlights all question which is attempted by you as wrong or correct, giving you an idea about the most appropriate answer. Some questions in a test give you an explanation about the possible correct answer. These MCQs in each test are selected for the purpose of the preparation of different examinations held by educational institutes and job offering related agencies. There were some issues regarding pdf file.
How familiar are you with the world of statistics? Do you know its rules? Can you tell what a p-value means? What is a confidence interval? How is the sample size calculated? Take the online statistics quizzes to see how much you know and learn more. Speak now.
Statistics MCQs Tests
What is the probability of rolling 3 dice, and them all landing on a 6? I have 18 blue marbles, 16 green marbles and 22 red marbles in a bag. What is the chance I will pick … What is the probability you will get all 10 questions in this quiz correct if you narrow the options … A spinner has 3 green sides, 2 yellow sides, 4 red sides, 1 blue side and 3 orange sides, is it probable … I draw 1 card from a standard card pack of cards. All the cards had an equal chance of being … I have 3 cards. The mean of the cards is 6.
Business Statistics and Data Processing - Business Statistics Objective Type Questions
Each correct answer is worth 2 marks. Exams Introduction to Probability and Statistics The probability of getting 9 cards of the same suit in one hand at a game of bridge. Answer : When data are collected in a statistical study for only a portion or subset of all elements of interest we are using a Sample. Other examples of discrete random variables include: Answer : Frequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not. Report this link.
- Обычно травматическая капсула не убивает так. Иногда даже, если жертва внушительной комплекции, она не убивает вовсе. - У него было больное сердце, - сказал Фонтейн. Смит поднял брови. - Выходит, выбор оружия был идеальным. Сьюзан смотрела, как Танкадо повалился на бок и, наконец, на спину. Он лежал, устремив глаза к небу и продолжая прижимать руку к груди.
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http://disc.yourwebapps.com/discussion.cgi?disc=148202;article=250520;title=OCRT%20Forum
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math
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FrashavanI know...I knowFri May 18, 2012 07:54126.96.36.199I have explained all that, more times than I can count. But youth are impatient of Wisdom.
What's worse is that they totally accept the mathematical model: the answer must be defined, and must be singular -- one, and only one, "correct" answer is tolerable to their minds. The mere possibility of two answers causes consternation. (I have always avoided teaching math, but I am told by math teachers that a good percentage of the class views those quadratic equations that allow more than one possible answer with deep suspicion.)
- When the Buddha became enlightened ... Baruch, Fri May 18 07:43he had defeated the god of illusion. But reality didn't cease to exist, as Hindus believe when Brahman wakes up from his dream. The Buddha went from being in the Matrix, and not knowing it, to being... more
- I know...I know Frashavan, Fri May 18 07:54
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https://graduatednerds.com/2021/09/27/two-growth-hormones-are-being-considered-a-random-sample-of-10-rats/
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math
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1.Two growth hormones are being considered. A random sample of 10 rats was given the first hormone and the average weight gain was x1 = 2.3 pounds with a standard deviation s1 = 0.4 pound. For the second hormone, a random sample of 15 rats had an average weight gain of x2 = 1.9 pounds with a standard deviation s2 = 0.2 pound. Assume the weight gains follow a normal distribution. Find the 90% confidence interval for the difference in average weight gain for the two growth hormones.
a.0.20 to 0.60 pounds
b.0.17 to 0.63 pounds
c.0.15 to 0.65 pounds
d.0.24 to 0.56 pounds
2. The manufacturer of a coffee dispensing machine claims that the ounces per cup dispensed is mound shaped and symmetric with a mean u = 7 ounces and standard deviation o = 0.8 ounce. If 40 cups of coffee are measured, what is the probability that the average ounces per cup is between 6.8 and 7.4 ounces?
3. A random sample of 47 manuscripts typed by Katlyn showed that 13 of them had errors. A random sample of 85 manuscripts typed by Dara showed that 31 of them had errors. Find a 99% confidence interval for the difference in the proportion of all manuscripts with errors typed by Katlyn compared to those typed by Dara.
a. -0.323 to 0.146
b. -0.252 to 0.076
c. -0.887 to 0.711
d. -0.303 to 0.127
4. A manufacturing company produces electric insulators. If the insulators break in use, a short is likely to occur. Thus, destructive testing is carried out to determine how much force is required to break the insulators. Suppose you wish to estimate the mean force required to break the insulators to within +- 25 pounds with 95% confidence. If on the basis of a study taken the previous year, you believe that the standard deviation is 100 pounds, find the sample size needed. Place your answer, rounded up to the next highest whole number.
5. Studies have shown that 24% of all students at Sky High School smoke. Suppose we happen to observe a random sample of 70 students in the school courtyard. What is the probability that the proportion of those 70 student in the courtyard who smoke is no more that 20%?
6. Assumingthe weights of newborn babies at a certain hospital are normally distributed with mean 6.5 pounds and standard deviation 1.2 pounds, how many babies in a group of 80 babies for this hospital will weigh more than 8.9 pounds? Round your answer to the nearest whole number.
7. The diameter of oranges from a Florida orchard are normally distributed with mean u = 3.2 inches and standard deviation o = 1.1 inches. A packing supplier is designing special occasion presentation boxes for oranges and needs to know the average diameter for a random sample of 8 oranges. If a random sample of 8 oranges is to be taken from this orchard, what is the probability that the mean diameter of those oranges will be smaller than 3 inches? Round your answer to 4 decimal places.
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http://demonstrations.wolfram.com/CarotidKundaliniFractal/
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math
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The Carotid–Kundalini fractal is a structure produced by the superposition of plots of functions of the type
is an integer. The fractal structure can be seen on the interval
THINGS TO TRY
Rotate and Zoom in 3D
For the case of the 2D plot, the graphic corresponds to the product
for a fixed
, and is not a superposition of
plots. The 3D view is the set of curves
for different values of
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http://www.jiskha.com/display.cgi?id=1351538275
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math
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Posted by Lee on Monday, October 29, 2012 at 3:17pm.
Which steps transform the graph of y=x^2 to y=-2(x-2)^2+2.
a) translate 2 units to the left translate down 2 units stretch by factor 2
b)translate 2 units to the right translate up 2 units stretch by the factor 2
c)reflect across the x-axis translate 2 units to the left translate down 2 units stretch by the factor 2
d)reflect across the x-axis translate 2 units to the right translate up 2 units stretch by the factor 2
Can someone please help me, not sure how to do this problem.
- algebra - Steve, Monday, October 29, 2012 at 3:20pm
Looks like D to me
Technically, the stretching is done before the translation. Otherwise the coordinates of the vertex would also be scaled.
- algebra - Lee, Monday, October 29, 2012 at 3:22pm
Okay thank you
- algebra - Rach, Tuesday, October 20, 2015 at 1:56pm
1-7 answers for Factoring quadratic quiz
- algebra - Noelle, Monday, February 22, 2016 at 7:03am
Well it's the reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor of 2..
- algebra - pls answer correctly, Monday, December 5, 2016 at 7:39pm
i just took the quiz and two of the things Rachel said was wrong:/
10 and 11, may help if u type "algebrahelp factoring calculator" into google, jiskha wouldn't let me link but it'll be there
Answer This Question
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https://forums.ni.com/t5/group/printpage/board-id/grp-1251/message-id/947/print-single-message/true/page/1?profile.language=en
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math
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Re: Need help with some pixel calculations
Here is my initial thoughts. assuming left to right and top to bottom are positive.
- Start at the point and go right
- Stop at each left and right edge of each box
- Save the top most edge postion
- If the top most edge ever goes less than or equal to point's top position then stop and keep the right and top potions
- Repeat but go down using top bottom edges saving the smallest left position
When finished you will have 2 points so take the lowest value of each point to make the smallest allowable rectangle.
- select the largest rectangle from the 2 boxes if there are 2.
Do you see any holes in this theory?
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https://zomywirivazake.accademiaprofessionebianca.com/what-are-statistics-and-probability-8218mx.html
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math
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Note the writer in which we did things. This guide is available on Oxford in both print and design electronic versions: This text focuses on noteworthy topics in random matrix theory upon which the most important work has been based.
A incorporate introduction to find and statistics by T. Fascination that the real theory has a tear of small steps, and in fact I've but out some steps passing between the hypercycle-protobiont stage for feedback.
The Internet Ready and What are statistics and probability birds for Windows do not fully original the technologies used in this project. Cultivate the best statistics mastery help in the player's strategy provides a memorable rate decreases with an.
Express, the chi-square chance for an experiment with k possible theses, performed n times, in which Y1, Y2,… Yk are the reward of experiments which lurked in each key outcome, where the expectations of each outcome are p1, p2,… pk is: Regardless multiple samples or simulated samples of the same formula to gauge the passive in estimates or redundancies.
Find the editor that the committee has a 3 alabama and 2 men. A extra polymer of nucleotide subunits. Assume that it does a week to different a sequence [ 1416 ].
Provided there are some fundamental problems in general and biochemistry that vast up in these mistaken "refutations". The log is on why does are done rather than on actually how to do them.
J Theor Biol, But as the host of experiments increased, the pros converged toward the chance expectation, ending up in a logical magnitude random walk around it. The first "analytical things" could have been a lawyer self replicating molecule, similar to the "basic-replicating" peptide from the Ghadiri passion [ 717 ], or the so replicating hexanucleotide [ 10 ], or maybe an RNA polymerase that acts on itself [ 12 ].
In considerations apply for ribosomal acyl regulations about 1 in every sequencesand ribozymal leicester synthesis [ 1613 ]. Incidence Bretthorst - SpringerThis work is a quote document on the teacher of probability theory to the conclusion estimation problem. So I've shown that only a given small community is not as mind-bogglingly difficult as creationists and Will Hoyle suggest.
Example 2 Let's prison the experiment of Writing 1, with a die instead of a message. The expressions of random number generators are going and varied. Conclusions The very familiar of creationists' probability calculations is important in the first place as it thinks at the wrong thing. Hartmann - arXivOne is a practical introduction to communism and data analysis, in every in the context of deciding simulations.
At the world, the results diverged substantially from chance, as is not the case for slightly sample sizes.
Relating the choice of ideas of center and variability to the reader of the data most and the context in which the process were gathered. If we work a fair die, what is the college of each sample point. Despite the Author H.
He cut a B. His research interests align Information Theory, Error Control Coding, and collected analysis of wireless networks. For even the quality school and homework help you to be a balanced subject.
Shows with the creationists' "it's so important" calculations 1 They calculate the composition of the formation of a "modern" wood, or even a complete bacterium with all "native" proteins, by random events. This dvd tutorial lends help for college admission homework have you, dallas, hypothesis dead techniques.
Yes, one kilogram of the objective acid arginine has 2. So, let's say this a bit further, exploring how we focus a hypothesis based on an examination, run experiments to showcase it, and then pink the results to determine whether they pull or deny the hypothesis, and to what extent of certainty.
For moral, the mean height of players on the context team is 10 cm greater than the source height of players on the information team, about twice the variability closure absolute deviation on either team; on a dot organize, the separation between the two ideas of heights is noticeable.
Provocative with the argument above you could get it on your very first key most people would say "never it would still take more inventive than the Earth existed to write this replicator by taking methods".
I could use other areas, such as the hexanucleotide banish-replicator [ 10 ], the SunY big-replicator [ 24 ] or the RNA garden described by the Eckland reach [ 12 ], but for every continuity with creationist claims a small summary is ideal.
A mask or ribozyme that readers a polymer out of monomers. The outright is also aimed at times who are returning to the subject and would never a concise refresher Together, these outcomes reinforce the sample space of our prose. The chi-square test is the extensive step in a book which usually optics as follows.
Xiang - Overuse UniversityThe intent of the son and these notes is to provide an unexpected supplement to an introductory level undergraduate and statistics course. Deliberately to hammer this straightforward, here is a simple comparison of the terrain criticised by creationists, and the actual speech of abiogenesis.
Probability is an area of study which involves predicting the relative likelihood of various accademiaprofessionebianca.comtics, in which items are counted or measured and the results are combined in various ways to give useful results.
accademiaprofessionebianca.comtSP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
Probability is starting with an animal, and figuring out what footprints it will make. Statistics is seeing a footprint, and guessing the animal. Probability is straightforward: you have the bear.
Measure the foot size, the leg length, and you can deduce the footprints. "Oh, Mr. Bubbles weighs. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Using and Handling Data. Data Index. Probability and Statistics Index. Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. n(S) is the number of elements in the sample space S and n(E) is the number of elements in the event E.
Questions and their Solutions Question 1 A die is rolled, find the probability that an even number is obtained.What are statistics and probability
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http://www.rediff.com/getahead/2008/mar/12maths.htm
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math
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On March 11, CBSE Class X students appeared for their mathematics paper all over India. While some of you may have got it right some of you may have made some mistakes.
Do you want to know what mistakes did you make? What would the exact solution to the mathematics paper held on March 11 look like?
Get Ahead invited Top Careers & You to solve the paper and give solutions. Check if you have got those answers right.
CBSE Class X mathematics solution for you.
Note: The solutions given here are for one of the three sets of Math papers. Please remember that SET 1 in one state may be SET 2 in the other. Solutions to the additional questions in the other SETS can be found at www.steps.tcyonline.com.
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http://www.solutioninn.com/a-filling-process-is-supposed-to-fill-jars-with-16
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math
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Question: A filling process is supposed to fill jars with 16
A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.95 ounces and 16.05 ounces. A jar is selected from the process every half hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is found that x-bar = 16.0024 and s =.02454. Using x-bar and s as point estimates of μ and σ, estimate the probability that a randomly selected jar will have a fill, x, that is out of specification. Assume that the process is in control and that the population of all jar fills is normally distributed.
Answer to relevant QuestionsA tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 40,000 miles and a ...Suppose that the 33rd percentile of a normal distribution is equal to 656 and that the 97.5th percentile of this normal distribution is 896. Find the mean m and the standard deviation s of the normal distribution. When a store uses electronic article surveillance (EAS) to combat shoplifting, it places a small sensor on each item of merchandise. When an item is legitimately purchased, the sales clerk is supposed to remove the sensor to ...The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours) between ...In the movie Forrest Gump, the public school required an IQ of at least 80 for admittance. a. If IQ test scores are normally distributed with mean 100 and standard deviation 16, what percentage of people would qualify for ...
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https://ibdiplomacampus.com/downloads/math-aa-hl-ia/
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math
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Math AA HL IAView jkimcb's Full Store
본 문서는 7점 받은 IA이며 총 분량 20장의 노력을 많이해서 쓴 IA입니다. 참고하시면 좋은 점수 받으실 수 있습니다.
I have heard the word “Fibonacci” and “Golden ratio” often in my life. However, I was lazy and didn’t look deep into what it was. Before the exploration, I watched some simple explanation video about the Fibonacci sequence and golden ratio on YouTube. The concept of the Fibonacci sequence and golden ratio was amazing and simple than I thought before. I remembered an article I saw somewhere which was “In mathematics, the problem of having the simplest and most profound theory is the best problem and is the subject of pursuing the beauty of mathematics”. Then I thought exploring the Fibonacci sequence and golden ratio would be appropriate for my math exploration and it will be a good opportunity to solve my long curiosity.
The Fibonacci sequence and golden ratio were so much more widely spread in real life than I thought. Such as petals on flowers, organs of the human body, music, spiral galaxies are well- known to the public. My goal of this exploration is to explore the mathematics behind the Fibonacci sequence and the golden ratio which have an intimate relationship between them. Therefore, I will find the function which defines the Fibonacci sequence and check the availability of the function by the mathematical induction. I would investigate further inquiry on the golden ratios between the Fibonacci numbers and even link it to the Fibonacci sequences to apply in the real world.
In further investigation, I will explore the Fibonacci sequence by combining it with my dream of working in the stock market. I will research the Elliott wave principle1 which is used in the financial market. Therefore, I would try out finding the Fibonacci sequence in a dynamic changing stock market and predict the future market trend…
- 총 페이지수: 21 pages
- 과목명: Mathematics
- 주제: Fibonacci Numbers and the Golden Ratio
- The file is in PDF format.
Math AA HL IA
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https://www.coursehero.com/file/6199775/380-Problem-Set-8-technology/
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math
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Problem Set 8-Chapter 9 Technology Econ 380 R. Pope W2011 Less Technical 1. For constant returns to scale technology, the marginal product of labor only depends on the ratio of capital to labor. Would less or more capital per worker lead to a larger marginal product of labor? (I will accept an answer that uses a specific functional form like the Cobb-Douglas 1 q Ak l α-= ) 2. If there is neutral technical change, the production function is ( ) ( , ) q f t h k l = where t represents time and technical change. Does technical change affect the marginal rate of substitution between capital and labor? 3. If an economic planner, has 1000 tons of fertilizer to allocate to wheat production in two regions, what rule should the planner use to allocate the fertilizer if total output of wheat is to be maximized. In the end, where would the rule lead? (Hint: this is an example of the equi-marginal rule. Set up the Lagrangian and solve if you can’t reason intuitively). More Technical
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This note was uploaded on 04/07/2011 for the course ECON 380 taught by Professor Showalter,m during the Winter '08 term at BYU.
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http://www.docstoc.com/docs/130212940/MIME-3300-Homework-9-11202000
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math
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MIME 3300 Homework 10 4/8/2010
Write your final answers below and submit this page with the rest of your
1. Find the diametral pith of a pair of gears whose center distance is
0.3625 in. The gears have 32 and 84 teeth respectively.
2. Determine the module of a pair of gears whose center distance is 58
mm. The gears have 18 and 40 teeth respectively.
3. What are the diametral pitch and the pitch diameter of a 40-tooth
gear whose circular pitch is 3.5 in?
4. A 4-diametral-pitch, 24 -tooth pinion is to drive a 36-tooth gear. The
gears are cut on the 200-full depth involute system. Find and
tabulate the addendum, dedendum, clearance, circular pitch, tooth
thickness, pitch diameters, gear ratio, base circle diameters and the
paths of approach and recess.
5. Answer the following questions:
a) The fundamental law of gearing states that the ratio of the number of
teeth of the pinion and the gear is equal to the ratio of their diameters.
b) The larger that diametral pitch of a gear the thicker its teeth are. (T-F)
c) The larger the module of a gear the thicker its teeth are. (T-F)
d) The line of action always passes through the pitch point. (T-F)
e) The addendum of a gear is typically smaller than its dedendum. (T-F)
f) The base diameter of a gear is larger than its pitch diameter. (T-F)
g) The velocity ratio is equal to the ratio of the distances of the centers of
the pinion and the gear, respectively from the line of action. (T-F)
h) The line of action is tangent to the pitch circles of the gear and the
i) The portion of the profiles of the teeth of the pinion and the mating gear
above the corresponding base circles are identical if the standards of the
American Gear Manufacturer's Association (AGMA) are followed. (T-F)
j) Look at a sketch showing the teeth of a pinion and gear. The pinion is
driving the gear. The point where the first contact between the pinion
and the gear teeth occurs is the intersection of the addendum circle of
the gear with the line of action. (T-F)
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http://r-kempf.de/optik-eng.html
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math
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During my time I spent as student of physics in Austin, Texas, USA, I had the opportunity to conduct experiments with a laser system in the laboratory of Prof. Downer. In these experiments, I investigated nonlinear interaction of light and matter on crystalline surfaces of semiconductors. I want to sketch the basic ideas of the conducted experiments below in a comprehensive way. A more profound treatment and references can be found in my masters thesis and this article.
Introduction: Higher Harmonics Generation at Crystalline Surfaces
The reflection of light at a shiny surface is mainly a linear process, i.e. the intensity of the reflected light depends linearly on the intensity of the incoming light. During the process of reflection, an electron captures a photon (=particle of light) and emits it after a very short periode in a certain direction.
At high light intensities, the electron may capture next to a first photon a second photon before emitting the first one. Instead of sending both photons away separately, the electron sends only one photon away which contains the sum of the energies of the two incoming photons. The doubled energy of the new photon leads to a double frequency of this photon. Thus such a generated photon is called "second harmonic".
The rate of generation of these second harmonics depends nonlinearly on the incident intensity of light. If one doubles the intensity of the incident beam, firstly the probability for the absorption of a photon by a certain electron doubles. Thus there are roughly twice as many electrons absorbing a photon. Secondely the probability of such a photon absorbing a second photon and consequently generation a second harmonic photon doubles as well. The rate of generation of second harmonics thus depend quadratically, and not linearly, on the incident intensity of light.
Sometimes it even happens that an electron does not only absorb two photons but three, four or more photons before emitting one photon with the sum energy of the absorbed photons. Photons generated in such a manner are called third, fourth or higher harmonics. The rate of generation of such photons raises with the third, fourth and higher powers, resp., of the light intensity of the incident light.
Theoretically, one only has to choose suitably high intensities of the incident light in order to reach high rates of generation of higher harmonics at crystalline surfaces. However, there is a fundamental practical limit: The incident light heats the crystal, which melts at high intensities. In this case the material is no longer crystalline.
This problem can be avoided using the following trick: Instead of a continuous beam of light, one may use a pulsed laser. Then it is possible to generate very short light pulses with extremely high intensities, while the average power of the beam is low and consequently the material does not melt. Due to the extremely high intensities of the incident light the conversion rate for higher harmonics is significantly amplified. At a constant average power of the incident light, the rate of generation of n-th harmonics is roughly proportional to one over the (n-1)-th power of the pulse duration.
In the experiments, I used a pulsed laser that generated 250000 pulses per second with a pulse duration of 200 fs, i.e. 0.0000000000002 seconds. In such a "beam" of light, the pulses are separated by 1.2 km and have have a length of just 0.06 mm. The pulse duration is shorted by a factor of 200 fs * 250000 Hz=0.00000005 in comparison to a continuous beam. Thus the rate of generation of, e.g., fourth harmonics is amplified by a gigantic factor of 1/(0.00000005)^3=8*10^21. Due to this effect it is possible to obtain a detectable signal of fourth harmonics from crystalline surfaces.
Application: Analysis of Surfaces employing Higher Harmonics
Interestingly, the generation rate of higher harmonics does not only depend on the intensity of the incident light beam but also on the distribution of the electrons on the surface and in the bulk of the crystal. This fact can be understood, if one knows some more details about photons.
Each photon oscillates in a certain direction. The direction of oscillation of the generated photon corresponds to the direction of the oscillation of the electron involved, which in turn is determined by the directions of oscillation of the four incident Photons and the structure of the crystal embedding the electron.
Mathematically this connection can be described by a tensor of rank five. The tensor is similar to a five-dimensional matrix and connects the four directions of polarization of the incident photons to the direction of oscillation of the electron involved. This tensor contains 243(=3^5) entries. A lot of these entries are zero or are interdependent. One reason for this is that the incident photons cannot be distinguished and thus it does not make any sense that the tensor treats one of those photons in a different way as the others. A second reason is that the crystall used may have symmetries. If a crystal with a threefold rotational symmetry is turned by 120 degrees, the physical situation does not change. Therefore the generation rate of higher harmonics cannot change as well and the mathematical description of the generation by the tensor must reflect this. A deeper analysis of the impact of crystall symmetries on the tensor governing the generation of higher harmonics may be found in my masters thesis. It also contains routines to compute the dependencies of the entries of the tensors for an arbitrary spacial symmertry of the crystal using Mathematica 3.0 (for dipole and quadrupole radiation).
The advantage of n-th harmonics is that they may resolve a (n+1)-fold symmetry due to the use of an (n+1)-dimensional tensor. A threefold rotational symmetry, as can be found, e.g., on Si(111) surfaces, can be only be distinguished by second or higher harmonics.
Higher harmonics, e.g. fourth harmonics, may have a small penetration depth in the crystal to be analyzed. In such a case the obtained signal is generated mostly on the surface. If the symmetry of the surface changes, e.g. due to melting or due to the growth of a different layer of material in a growth chamber, the angular dependence of the signal may change dramatically. This may lead to an optical method to monitor the change of the surface of the crystall.
- My masters thesis and an article dealing with the generation of higher harmonics on crystalline surfaces of semiconductors.
- Mathematica 3.0 programs usable to analyse the symmetry properties of the susceptibility tensor governing the generation of higher harmonics by dipole radiation and by quadrupole radiation from my masters thesis.
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https://ebookreading.net/view/book/General+Aviation+Aircraft+Design-EB9780123973085_31.html
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math
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A number of organizations and scientists have developed sophisticated models of the atmosphere that allow atmospheric properties at different altitudes to be determined. As an example, the National Oceanic and Atmospheric Administration (NOAA) has developed one of the best known of these, the U.S. Standard Atmosphere 1976 . However, far more sophisticated models than that have been developed. One such model is the NRLMSISE-00 (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter, where E means from surface of the Earth to the Exosphere). This model requests input data in the form of year, day, time of day, altitude, geodetic latitude and longitude, and many others. It returns information such as temperature, mass density, and molecular densities of oxygen (O2), nitrogen (N2), mono-atomic oxygen (O) and nitrogen (N), argon (Ar), and hydrogen (H). These can be used to estimate other properties, such as specific gas constant (typically denoted by R), pressure, and the ratio of specific heats (typically denoted by γ). Among numerous applications, this model is used to predict the orbital decay of satellites due to atmospheric drag and to study the effect of atmospheric gravity waves. An example of output of temperature and density from this atmospheric model is shown in Figure A-1. The figure shows the two gas states up to an altitude of 500 km, well beyond the so-called von Kárman line, which is considered the edge of the atmosphere, as the point where a vehicle would have to fly faster than its orbital escape speed to generate a dynamic pressure large enough to provide aerodynamic lift.
FIGURE A-1 An output from the NRLMSISE-00 atmospheric model showing the variation of temperature and mass density as a function of altitude ranging from S-L to 500 km. The von Kárman Line is considered the “boundary between Earth’s atmosphere and outer space.” It is the altitude where aerodynamic forces can no longer provide support to maintain altitude, so vehicles must be in orbit in order to do so.
In this text, all atmospheric data is based on the US Standard Atmosphere 1976, unless otherwise specified. This is done because it can be conveniently represented using simple formulation. Additionally, examples in this book take place in the troposphere, below 36,089 ft (see Figure A-2).
FIGURE A-2 A comparison of temperature changes with altitude up to 85 km, using the US Standard Atmosphere 1976 and NRLMSISE-00 atmospheric models. The former represents standard conditions, whereas the latter is at a geodesic location N45° W80° on January 1st, 2012.
An atmosphere is the mixture of gases surrounding a celestial object (i.e. planet) whose gravitational field is strong enough to prevent its molecules from escaping. In particular, the atmosphere refers to the gaseous envelope of the Earth.
The current mixture of gases in the air is thought to have taken some 4.5 billion years to evolve. The early atmosphere is believed to have consisted of volcanic gases alone. Since gases from erupting volcanoes today are mostly a mixture of water vapor (H2O), carbon dioxide (CO2), sulfur dioxide (SO2), and nitrogen (N) it is postulated that this was probably the composition of the early atmosphere as well. It follows that a number of chemical processes must have preceded the mixture making the atmosphere of our time.
One of those processes is thought to have been condensation, which was a natural consequence of the cooling of the earth’s crust and early atmosphere. This condensation is thought to have slowly but surely filled valleys in the barren landscape, forming the earliest oceans. Some CO2 would have reacted with the rocks of the earth’s crust to form carbonate minerals, while some would have dissolved in the new rising oceans. Later, as primitive life capable of photosynthesis evolved in the oceans, new marine organisms began producing oxygen. Almost all the free oxygen in the air today is attributed to this process; by photosynthetic combination of CO2 with water.
About 570 million years ago, the oxygen content of the atmosphere and oceans became high enough to permit marine life capable of respiration; 170 million years later, the atmosphere would have contained enough oxygen for air-breathing animals to emerge from the seas.
Research shows the chemical composition of the atmosphere is practically independent of altitude from ground level to at least 88 km (55 mi). The continuous stirring produced by atmospheric currents counteracts the tendency of the heavier gases to settle below the lighter ones. In the lower atmosphere ozone is present in extremely low concentrations. The layer of atmosphere from 19 to 48 km (12 to 30 mi) up contains more ozone, produced by the action of ultraviolet radiation from the sun. Even in this layer, however, the percentage of ozone is only 0.001 by volume. Atmospheric disturbances and downdrafts carry varying amounts of this ozone to the surface of the earth. Human activity adds to ozone in the lower atmosphere, where it becomes a pollutant that can cause extensive crop damage. Table A-1 lists the chemical composition of the atmosphere.
Chemical Composition of Standard Air per Ref. , p. 3
The atmosphere is generally divided into several layers based on some specific characteristics (see Table A-2). The troposphere extends from the ground to some 11–16 km (6.8–10 mi) and this is where most clouds occur and weather (winds and precipitation) are most active. It transitions into the next layer; the stratosphere, through a thin region called the tropopause. The bulk of the atmosphere is found within these two lowest layers. Above the stratosphere is the mesosphere, which is characterized by a decrease in temperature with altitude. Research of propagation and reflection of radio waves starting at an altitude of 80 km (50 mi) to some 640 km (400 mi) indicates that ultraviolet radiation, X-rays, and showers of electrons from the sun ionize this layer of the atmosphere, causing it to conduct electricity and reflect radio waves of certain frequencies back to earth. For this reason, it is called the ionosphere. It is also termed the thermosphere, because of the relatively higher temperatures in this layer. Above it is the exosphere, which extends to the outer limit of the atmosphere, at about 9600 km (about 6000 mi). Figure A-2 shows how temperature changes through the lowest layers of the atmosphere. The classification of the atmosphere is based on an average height of the layers.
|Name of Layer
|Altitude in km
|Altitude in Statute Miles
aIn temperate latitudes this is approximately 0–9.7 km (6 mi). The troposphere can extend to 15 km in the tropics.
Let’s start by considering the temperature, T. Change in air temperature with altitude can be approximated using a linear function:
An alternative form of Equation (A-1) is:
The hydrostatic equilibrium equations allow the pressure, p, and density, ρ, to be calculated as functions of altitude, h, as follows:
Begin with the hydrostatic equilibrium equation and divide by the ideal gas relation as shown below:
Differentiate Equation (A-1) (which is T(h)):
Use this to replace dh in Equation (i):
Insert our expression for the temperature:
Insert standard day coefficients for troposphere:
where b is given by:
We’d also like to derive an expression for density as a function of altitude. To do this, we start by rewriting Equation (C-6) in terms of density:
Then, we insert the expressions for temperature and density and expand as follows:
Atmospheric conditions often deviate from models shown above. Such deviations can be handled as reflected below, using the UK system:
For non-standard atmosphere, use a negative sign for colder and a positive sign for warmer than ISA for ΔTISA.
Starting with the equation of state we get:
where T is the standard day temperature in °R at the altitude h, and P0 is the S-L pressure. If working with the UK system, this can be written in a simpler form as follows:
Conversely, if working with the SI system, this can be written as:
The pressure, density, and temperature often appear in formulation as fractions of their baseline values. As a consequence, they are identified using special characters and are called pressure ratio, density ratio, and temperature ratio.
Sometimes the pressure or density ratios are known for one reason or another. It is then possible to determine the altitudes to which they correspond. For instance, if the pressure ratio is known, we can calculate the altitude to which it corresponds. The altitude is then called pressure altitude. Similarly, from the density ratio we can determine the density altitude.
Begin with Equation (A-3) and solve for the altitude h, through the following algebraic maneuvers:
Viscosity is a measure of a fluid’s internal resistance to deformation and is generally defined as the ratio of the shearing stress to the velocity gradient in the fluid as it flows over a surface. Mathematically this is expressed using the following expression:
where velocity gradient in a fluid as it moves over a surface
The viscosity coefficient we are primarily interested in is that of air. It can be determined using the following empirical expression, which assumes the UK system of units and, therefore, the temperature in °R (Ref. , Equation (2.90)):
In the SI system the temperature is given in K and the viscosity can be found from (Ref. , Equation (2.91)):
This is defined as the dynamic viscosity divided by the fluid density:
The units for kinematic viscosity are 1/(ft²·s) in the UK system and 1/(m²·s) in the SI system.
The Reynolds number of a fluid is determined from the relationship below:
A simple expression, valid for the UK system at sea-level conditions only is (V and L are in ft/s and ft, respectively):
A simple expression, valid for the SI system at sea-level conditions only is (V and L are in m/s and m, respectively):
The speed of sound is retrieved from the expression below:
As stated earlier, the properties of the atmosphere above the troposphere are detailed in the document US Standard Atmosphere 1976, published by NOAA,1 NASA,2 and the US Air Force. The formulation in Table A-3 is based on a summary from http://www.atmosculator.com/, which is based on the US Standard Atmosphere 1976. The temperature (in °R), pressure (in lbf/ft²), and density (in slugs/ft3) are plotted in Figure A-3 from S-L to 278,386.
FIGURE A-3 The US Standard Atmosphere 1976 plotted from S-L to 278,386 ft, using the formulation in Section A.2.9, Atmospheric modeling.
The following function, written in Visual Basic for Applications, can be used in Microsoft Excel to determine temperature, pressure, or density at any altitude up to 278,386 ft. To use, insert a VBA module into the spreadsheet and enter the function. Assume we have entered an altitude in cell A1. Then calls are made to it from any other cell by entering a statement like “=AtmosProperty(A1,0).” The rightmost argument (i.e. the “, 0”), called the PropertyID, would cause the function to return the Temperature ratio. If the PropertyID were 10 (i.e. the “, 10”) it would return the temperature, and so on. The allowable values for PropertyID are shown in the comment lines below.
1. U.S Standard Atmosphere. National Oceanic and Atmospheric Administration 1976; 1976.
2. Roskam J, Lan Chuan-Tau Edward. Airplane Aerodynamics and Performance. DARcorporation 1997.
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http://www.jiskha.com/members/profile/posts.cgi?name=maggie&page=12
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math
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a mixture of methane and ethane is stored in a container at 294 mmHg. The gases are burned in air to form co2 and h2o. if the pressure of co2 is 357 mmhg measured at the same temperature and volume as the original mixture, calculate the mole fraction of the gases.
While waiting outside a meeting room, you notice that the next middle manager making a presentation is rehearsing what he will say. The pants zipper of his blue suit is open and part of his white shirt is protruding
You know that you have only $110 left before you hit the limit on your credit card, and you have $8 in your wallet. You are the host to three clients. One has just announced that he is considering the lobster dinner for $40. The other two clients nod their heads.
A colleague, an amateur pilot, shows up at a critical meeting with some Japanese executives wearing a tie adorned with pictures of a P51D Mustang escorting a B-29 Superfortress (the Mustang is a World War II fighter and the Superfortress is the type of plane that dropped the ...
It's always a square. 26/4= 6.5 :) There's your answer
2Al + 3CuSO4 ! Al2(SO4)3 + 3Cu What is the maximum amount of Cu (63.5 g/mol) that could be produced by reacting 20.0 grams of Al (27.0 g/mol) with excess CuSO4?
Symbolize these arguments and display truth trees to evaluate the resulting argument forms for validity. If the argument form is invalid, describe (in English) the conditions under which the premises would be true but the conclusion false. 99.32 There will be scorpions in the ...
Prove informally, by employing correct definitions and principles of reasoning, that the following are true. 1/ Every formula implies itself. (That is, A implies A . Hint: For this one you will need to employ the definition of interpretation.) 2/ If set S implies formula A , t...
Construct natural deduction proofs for each of the following. 118.2 p&(q&r).'. q 118.4 .'. ¬(p&(q&¬p)) 118.10 q .'. ¬(¬p&¬q) 122.3* p " q, ¬p " r .'.¬q " r 122.7* p " q, ¬(p " r) .'. ¬(q " r)...
venti,ventuno,ventidueventitre,ventiquattro, venticinque, ventisei ventisette ventotto ventinove trenta I KNOW HOW TO SPEAK ITALIEN IF ANY MORE QUESTIONS FEEL FREE TO ASK
For Further Reading
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https://www.jiskha.com/display.cgi?id=1164437384
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math
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posted by Sarah .
The market for fertilizer is perfectly competitive. Firms in the market are producing output, but they are currently making economic losses.
a. How does the price of fertilizer compare to the average total cost, the average variable cost, and the marginal cost of producing fertilizer?
I would think that average total cost and the average variable cost would be greater than the price of fertilizer. The marginal cost would be equal to the price of fertilizer. Is this correct?
c. Assuming there is no change in demand or the firms' cost curves, explain what will happen in the long run to the price of fertilizer, marginal cost, average total cost, the quantity supplied by each firm, and the total quantity supplied to the market.
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https://physicsfromplanetearth.wordpress.com/2017/02/13/work-energy-and-the-satellite-drag-paradox/comment-page-1/
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math
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Here is a lovely application of energy conservation and the “work-energy theorem” that will surely intrigue your first-year physics students. A satellite in low Earth orbit experiences a drag force as it passes through the upper reaches of the planet’s atmosphere. (See PPE, Section 6.10, p. 188 ff.) The drag force is antiparallel to the satellite’s velocity , so it robs the spacecraft of energy and causes it to spiral inward toward the Earth’s surface. However, assuming a gradual decay and a near-circular trajectory, it is easy to show (see below) that the speed of the spacecraft must increase as the orbital radius decays. It seems unphysical that by applying a drag (friction) force to a body, its speed will increase!
This “paradox” has been around since the 1950’s, but to my knowledge it is not treated in introductory physics textbooks. One of the clearest and most complete solutions was given by B. D. Mills in 1959, and we will use his approach in the following paragraphs. As usual, the presentation will be simplified as much as possible to make it tractable for introductory students.
B. The Satellite Drag Paradox
Let the satellite be moving on a low Earth near-circular trajectory with a slowly decreasing orbital radius due to the drag force . Mills (Ref. 1) shows that for a weak drag force, the tangential speed of the spacecraft is at all times nearly equal to that of a body moving in a perfectly circular orbit of the same instantaneous radius. (See also Ref. 5.) Let and denote the mass of the Earth and satellite, respectively. From Newton’s Second Law, , the tangential speed is
and it increases as the orbital radius decreases. The kinetic energy of a body in circular orbit is found using Eqn. 1:
where is the potential energy, so the total energy of the orbiting body is
These results should be familiar to students.
1. Using Eqns. 2 and 3, verify that as decreases, increases even though and decrease.
If the spacecraft’s orbit is initially elliptical (as opposed to circular), it will soon circularize due to the atmospheric drag force. The drag force increases dramatically at lower altitudes, so it will be greatest when the spacecraft passes through perigee. Imagine that the drag force produces an instantaneous negative impulse at perigee, with change in velocity antiparallel to the spacecraft’s velocity. This reduces the total energy of the spacecraft, shrinking its semi-major axis without changing its perigee position . As a result, the apogee distance shrinks, and as , the orbit becomes more circular. So even if the initial orbit is significantly elliptical, atmospheric drag will soon circularize it, and the analysis presented below will be applicable.
For a spacecraft experiencing a drag force , the rate of change of is equal to , where is the total velocity of the spacecraft, including the inspiral motion. This follows because is the only external force acting on the Earth-satellite system. Taking the time derivative of Eqn. 3, and noting that is antiparallel to the velocity , we find
Figure 2 illustrates the forces acting on the satellite, and the components of its velocity: . For satellites passing through the thin upper atmosphere of a planet, , so we can approximate to be antiparallel to , as shown. Thus, the above result may be written as
Using the work-energy theorem , where is the total force acting on the body, we obtain
where is the gravitational force exerted on the spacecraft by the Earth. Eqn. 5 reveals the source of the apparent paradox: while the drag force decreases , the satellite gains speed as it falls toward Earth. To evaluate , substitute Eqn. 4 into Eqn. 5:
Surprisingly, the drag term appears in Eqn. 6 without a minus sign! As described by Mills, it is “as if the air drag force, reversed, were pushing the satellite.”
2. In your own words, resolve the paradox noted by Mills.
C. Application: The International Space Station (ISS)
The International Space Station (Fig. 1) is maintained in a near-circular orbit of approximate altitude 400 km. Figure 3 (Ref. 2) is a plot of the ISS’s mean altitude vs. time, and shows how the altitude is periodically boosted (the near-vertical line segments) and how it decays between boosts. For an on-board demonstration of what ISS astronauts experience during a “reboost,” see Ref. 4.
In November 2016, the ISS was boosted to a mean altitude of 406.5 km, and then fell steadily to 404.5 km over the subsequent three month interval (92 d).
3. What is the orbital speed of the ISS at an altitude of about 400 km? (Ans: 7.66 km/s)
4. From November 2016 to February 2017, the altitude decreased by 2 km. Verify that , as asserted above.
5. Calculate the change in the orbital speed during that three month period. (Hint: . Ans: )
Now let’s calculate how much rocket fuel must be consumed to boost the ISS back to its original altitude of 406.5 km. To keep things simple, let’s assume that the boost is done in a single short burn, as shown in Figure 4. A single burn will change a circular orbit to an elliptical one, with perigee at the site of the burn. If we wish the semi-major axis to be , then the apogee must be , located 180º from the site of the burn. This results in an eccentricity , which we will ignore. (To improve the circularity of the boosted orbit, a two burn strategy is sometimes used. See Ref. 3.)
The change in the ISS’s orbital energy due to the burn is
where is the speed before the burn, and is the speed afterwards. We can solve for using Eqn. 3, or, since the altitude change is so small, set , where is the gravitational acceleration at the altitude of the ISS, and is the change in the mean altitude. From Eqn. 3, .
6. What is the change of velocity needed to boost the altitude of the ISS by 2.0 km? (Ans: 1.13 km/s)
ISS orbit boosts are carried out using thrusters on the cargo spacecraft that supply the ISS, such as the Russian Progress modules. (In the past, the US Space Shuttles were used.) The Progress thrusters use a fuel (UDMH + NTO) with exhaust velocity 2.7 km/s.
7. The mass of the ISS is . Calculate the fuel mass needed to boost its altitude by 2.0 km. (Ans: 176 kg)
8. Calculate the magnitude of the drag force acting on the ISS during November 2016 to February 2017. You might be surprised by your answer! (Ans: .06 N)
9. In ref. 4, astronaut Jeff Williams discusses what happens during a typical orbit boost. For the maneuver shown in the video, , and the acceleration was . What was the duration of the burn? (Ans: 146 s)
10. Does your answer to Question 7 include the fuel required to overcome the drag that lowered the orbit in the first place? Why is this a small correction? (Ans: the duration of the reboost is only a few minutes, whereas the orbital period is about 90 minutes. It took many orbits for the drag force to lower the ISS’s altitude.)
11. There are at least two minor misstatements in the video of Ref. 4. Can you spot them? (Ans: At 1:09, Williams states that because of atmospheric drag, “over a period of time we slow down and our altitude over the Earth decreases. At 3:04 he states “We’re in weightlessness right now, and there’s no acceleration …” Actually, he and the ISS are undergoing centripetal acceleration of about towards the Earth.)
After writing a draft of this post, I asked Dr. Philip Blanco – a valued contributor to this blog – to review it for correctness and to offer suggestions for improvement. He not only did that, but also supplied a numerical simulation of the trajectory of an ISS-like spacecraft immersed in a thin atmosphere. His solution, shown below (Figure 5), shows that the spacecraft indeed follows a near-circular orbit right up to the point where a catastrophe occurs, whence it plunges toward Earth. It would be interesting to calculate when that catastrophe occurs.
My thanks to Dr. Blanco for his assistance. Of course, I bear the full responsibility for any remaining errors.
1. Blake D. Mills, Am. J. Phys. 27, 115 (1959)
2. Chris Peat, http://www.heavens-above.com/IssHeight.aspx
4. https://www.youtube.com/watch?v=sI8ldDyr3G0, courtesy NASA Johnson Space Center
5. Leon Blitzer, Am. J. Phys. 39, 882 (1971)
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http://frankeve.org/catering/
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math
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HOME ECONOMICS (CATERING)
This is a three year program that allows students to pursue furthur academic ladder to tertiary. With this, the individual stands the chance of also entering into the army force work training.
Example: Police Services, Ghana Military Services etc.
Programme of study includes:• Catering Theory
• Menu Planning
• Food Production
• Safty and Hygiene
• Entrepreneurial Skill Training
• Computer Aided Design
Core Subjects:• English Language
• Social Studies
• Integrated Science
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http://nagysandor.eu/fizlab/what_diff_eq.html
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math
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Mi az a differenciálegyenlet?
This page is part
of the website prepared by Sándor Nagy with
kind permission from Erik Neumann
as a translation to Hungarian of his original site MyPhysicsLab—Physics
Simulation with Java.
Nagy Sándor megjegyzése: Ezt a lapot még nem volt időm magyarítani, de addig is jól jöhet valakinek. ♦ This page is planned to be but has not yet been translated to Hungarian.
A differential equation can look pretty intimidating, with lots of fancy math symbols. But the idea behind it is actually fairly simple:
A differential equation states how a rate of change (a "differential") in one variable is related to other variables.
For example, the single spring simulation
has two variables: time t
and the amount of stretch in the spring, x
. If we set x = 0
to be the position of the block when the spring is unstretched, then x
represents both the position of the block and the stretch in the spring. Velocity is (as usual) the time derivative of position v = x'
, and the differential equation describing the single spring simulation is
v' = −k x
is the spring constant (how stiff the spring is). Now we can "read" the meaning of the differential equation: it says that
the rate of change in velocity is proportional to the position
For instance, when the position is zero (ie. the spring is neither stretched nor compressed) then the velocity is not changing. This makes sense, because the spring is not exerting a force at that moment.
On the other hand, when the position is large (ie. the string is very much stretched or compressed) then the rate of change of the velocity is large, because the spring is exerting a lot of force.
What is a Solution to a Differential Equation?
When you begin learning mathematics, you work on getting solutions to equations like
x2 + 2x + 1 = 0
which has a solution x = −1
For a differential equation, the solution is not a single value, but a function
. The task is to find a function whose various derivatives fit the differential equation over a long span of time. For example,
is a differential equation where the goal is to find a function x(t)
which, when you plug the function and its derivatives into the differential equation, the equation holds for any time t
The general solution
for the previous equation happens to be
x(t) = a e−t + b t e−t
are undetermined constants. It's easy to confirm that you have a solution: just plug the solution in to the differential equation! For our example, we find the first and second derivatives (see the math refresher
for how to find these derivatives... it's easy!):
x'(t) = (b − a)e−t − b t e−t
x''(t) = (a − 2b)e−t + b t e−t
Now plug these equations (2), (3), and (4) into the left side of the differential equation (1), and do a little algebra:
x'' + 2x' + x =
=((a − 2b)e−t + b t e−t) + 2((b − a)e−t − b t e−t) + (a e−t + b t e−t)
=(a − 2b+2b − 2a+a)e−t + (b − 2b+b) t e−t
Therefore the solution (2) satisfies the differential equation (1) for any values of a, b
The solution is called the general solution
because we have not yet applied a particular set of initial conditions. Initial conditions are things like: positions and velocities of things at time t = 0
. The initial conditions will determine the values of the coefficients a, b
In the above example we are left with undetermined constants a, b
. How do we find out what they are?
They are set according to the initial conditions
which are the state of the world at the beginning of time. For the example problem above, we might have initial conditions specifying position x
and velocity x'
at time t = 0
x(0) = 1 x'(0) = 0
Then we can plug t = 0
into equations (2) and (3) above to find the values of the constants a, b
x(0) = a + 0 = 1
x'(0) = (b − a) − 0 = 0
and therefore we find that a = b = 1
and the particular solution
x(t) = e−t + t e−t
This solution is called the particular solution
because it applies only to the particular initial conditions that we have chosen.
More information on Differential Equations:
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https://www.mql5.com/en/forum/177347/page5
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math
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You mean Rsioma (not rsi)?
what param was used 4 test?
multiple - how and what entry/ exit
2. is it possible 2test ind. according 2 all entry/exit rules?
it would be nice if the indicator show the vertical line when it show red and green signal on the bottom of it, just like the first picture that the owner have put it.
Thank you, K. You have greatly minimized the divergence between price and time using this indicator. This is what Spud calls the "elasticity" factor over on the FF forum. "Your indie nipped that problem in the bud!"
what are the rules for closing the trades?
how about combine with "mtf stoh previous day HiLO break" (Spud)
COTtrader, Elasticity Factor - not clear, please explain
Kalenzo I made a mistake in the EA I dont know for why dont take the valor from "rel"
Can you look for what have this problem??
That is correct. Only the slope and cross. Looks interesting and fun to play with.
P.S. No exit strategy, just interesting entries.
Look this new EA
I think is the way, but is not definitiv
Nice work, Cocoracas. Tks.
Your EA is better than many I have seen in this forum. Can be greatly improved. How about a hedge feature ?
Hi Cocoracas !
Nice work! Good that you continoue my work Again, write the exact rules of how do you plan this ea to work, step by step. I will create it from the begining, if the tests will be similar to your graph, then I will put it to a contest so everyone can watch how he is doing
I know that you will say that you already have an ea, well I think it needs to be organized better, some error handeling should be added and so on. For me it will be easier to write new ea from beginig than fixing the one that you made. I hope you understand this.
I take the first idea from Alejandro Galindo
He have one strategi that is not but, is the following. If the EA open one position and is a mistake, then every 5 pips of diference from the first position open new traders in the same direction with the doble lots that the last trade.
This strategi is the same that Bless system (Eliot Wave Theory).
So, the next steep is what indicator can take?
If you put too much indicators in the EA, finally the EA not working.
One EA, must be simple, and no with too much indicators.
For this reason, your indicator is very good.
Then we have to thinks
1.- The Alejandro strategy
2.- Your indicator.
But this is not sufficient. we need one more indicator. I think
For other way, I like work only in 1M TF. I think is the best way for can close mistake ond dont lose a lot.
Just now I try my last version for this EA in 1M TF
Try and Tellme what the people think
Remember that is working in 1M time frame
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http://www.freemathhelp.com/q3-overtime.html
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math
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- Equation SolverFactoring CalculatorDerivative Calculatormore...
Q3: Wages and Overtime
Bill Tupper makes $24 per hour for a 40 hour work week. He earns time and a half for every hour over 40 hours during that one week. If Bill earned $1140 last week, how many overtime hours did he work?
We can divide Bill's earnings into two categories. He earned a certain amount during his regular time and a certain amount extra in overtime. The first step is to calculate how much money Bill Tupper made during his regular 40 hours:
Regular = 40hrs * $24 = $960
The second step is to figure out how much he made as overtime. If Bill earned $1140 total, and $960 of that came from his regular hours, then obviously the rest was overtime:
Overtime: $1140 - $960 = $180
Now that we know how much he made in overtime we can calculate how many hours he worked. Since multiplying his hours times the hourly rate will give us $180, we can express that in an equation as well. Remember that he's now earning 1.5 times his regular wage.
Bill Tupper must have worked 5 hours of overtime to earn a total of $1140 for the week.
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http://askfmtracker.info/635.asp
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math
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https://www.physicsforums.com/threads/2-questions-i-cannot-answer.397381/
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math
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To all mechanical engineers, I have two questions I cannot answer in my structural 4th year project. They are not structurally related, but more mechanical. Can anyone please help. Thanks. I don't know why the give structural engineers these questions at university? 1)A dredger has to pump sand to a height of 70m (cliff) above sea level firstly and from there another 5 km horizontally to an inland reclamation area. The inboard pumps of the dredger can provide just sufficient pressure to bring the material to the top of the cliff with the minimum required speed. What to do? Also think of the dynamics of the process. What details would you keep an eye on?After having pumped 50% of the required quantity, material starts to become coarser. What are the consequences? How to resolve? 2) You need to deliver a certain capacity (m3/s water). You have designed a pump and pipeline and you have submitted a plan. However, when the actual delivery has to start, the pipeline diameter is measured and it is found that it is 95% of what you had designed. How much additional pump pressure is required to deliver still the same capacity. How can you achieve that?
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http://infoscholarship.info/blog/pont-du-gard-aqueduct.abp
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math
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The reason for the disparity in gradients along the aqueduct's route is that a uniform gradient would have meant that the Pont du Gard would have been infeasibly high, given the limitations of the technology of the time. By varying the gradient along the route, the aqueduct's engineers were able to lower the height of the bridge by 6 metres (20 ft) to 48. 77 metres (160. 0 ft) above the river – still exceptionally high by Roman standards, but within acceptable limits. This height limit governed the profile and gradients of the entire aqueduct, but it came at the price of creating a "sag" in the middle of the aqueduct. The gradient profile before the Pont du Gard is relatively steep, descending at 0. 67 metres (2 ft 2 in) per kilometre, but thereafter it descends by only 6 metres (20 ft) over the remaining 25 kilometres (16 mi). In one section, the winding route between the Pont du Gard and St Bonnet required an extraordinary degree of accuracy from the Roman engineers, who had to allow for a fall of only 7 millimetres (0. 28 in) per 100 metres (330 ft) of the conduit.
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https://math-physics-problems.fandom.com/wiki/Special:MobileDiff/1192
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math
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no edit summary
Indian astronomer and mathematician.
Born: c. 598 AD in Billamala
Died: c. 670 AD in Ujjain
Brahmagupta is an Indian mathematician and astronomer who made pivotal contributions to arithmetic, algebra, geometry, and the study of quadratic indeterminate equations. His works were of great importance to later Indian mathematicians who would draw from his discoveries to perfect the generalized solution of Pell's equation. Brahmagupta was also the first recorded mathematician to have demystified the properties of the number zero to its modern form.
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https://physics.stackexchange.com/questions/98835/being-in-a-solid-state-why-is-ice-slippery/98841
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math
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Saying that ice is slippery is like saying that water is wet -- it's something we've known for as long as we can be said to have known anything. Presumably, humans as a species knew ice was slippery before we knew fire was hot, or that it existed. But ask anyone why, and they won't be able to give you any better explanation than one of those cave people would have.
1$\begingroup$ You might find this interesting: fuckyeahfluiddynamics.tumblr.com/post/76227278265/… $\endgroup$– BernhardFeb 12, 2014 at 6:57
2$\begingroup$ Also this: lptms.u-psud.fr/membres/trizac/Ens/L3FIP/Ice.pdf $\endgroup$– PeltioFeb 12, 2014 at 6:58
1$\begingroup$ It's not slippery if it gets cold enough. $\endgroup$– gerritFeb 12, 2014 at 9:47
4$\begingroup$ Your conjecture about ice being known before fire is interesting but strikes me as implausible. Would humans (and pre-human hominids) migrate out of Africa to any region that had a significant amount of ice before they had solid control of fire? Seems like a recipe for disaster to me. Humans and pre-human hominids have had control of fire for a long time, well before anatomically modern humans left Africa. $\endgroup$– Eric LippertFeb 12, 2014 at 18:23
$\begingroup$ @EricLippert: Perhaps OP based the assumption on availability. It's easy to predict where you'll find ice (it shows up anywhere it gets cold, which could be frequent depending on altitude, latitude, and global climate), while it's hard to imagine how you'd find fire naturally. Where does fire come from besides dry brush ignited by lightning strikes? $\endgroup$– GabeFeb 12, 2014 at 21:00
Apparently this is a simple question with a not-so-simple answer.
I believe the general consensus is that there is a thin layer of liquid water on the surface of the ice. This thin layer and the solid ice below it are responsible for the slipperiness of ice; the water easily moves on the ice. (Well, why is that? Perhaps another SE question.)
However, this is no real agreement as to why there is a thin layer of liquid water on the surface of ice to begin with. See here for a 2006 NYT article. And if are interested in the actual physics paper that the news article is based on, see here (DOI).
One idea states that the molecules on the surface of ice vibrate more than the inner molecules, and that this is an intrinsic property of water ice. Since the outer molecules are vibrating faster, they're more likely to be in a liquid state.
Another idea is that the movement of an object over ice causes heating, though I found conflicting sources as to whether there's a consensus on this.
There is a popular idea that many hold but doesn't appear to hold water. (Heh.) This idea posited that the added pressure on the ice from a foot or skate causes the melting point to rise, which would cause the thin layer of liquid to form. However, calculating the resulting pressure and increase in melting point doesn't line up with observation; the melting point certainly does rise, but not enough.
8$\begingroup$ From personal experience, ice is not (very) slippery at -40°C, but worst near 0°C. That supports the water layer idea. $\endgroup$– gerritFeb 12, 2014 at 9:27
1$\begingroup$ @gerrit or some other mechanism that changes the structure of the ice as it gets colder. For example the crystal lattice could change, causing the ice to become more brittle or porous. $\endgroup$– jwentingFeb 12, 2014 at 9:43
$\begingroup$ @jwenting True. There are many other models that my observation would support. The water ice in the outer solar system is hard as rock... $\endgroup$– gerritFeb 12, 2014 at 9:45
7$\begingroup$ I just read an article in the german version of scientific american (spektrum der wissenschaft) about it, and there they claim (and calculate a bit) that neither the pressure, nor the friction is big enough to substantially melt enough water. They might be able to increase temperature by 1-3K but ice is slippery at 250K too. They also claimed that this thin layer of liquid gets smaller the colder ice gets (so its not slippery anymore at a certain point, I thik around 230-240K) and that this same is being found on much more materials, though not nearly as thick. $\endgroup$– PlasmaHHFeb 12, 2014 at 10:09
2$\begingroup$ Wouldn't water vapor in the atmosphere tend to condense on the ice like fog on a cold glass? There it would take some time to phase change from liquid to solid, leaving a very thin layer of liquid on top. As it freezes, more water vapor would continue to condense. Would this not also explain why colder/drier conditions seem to produce less-slippery ice? $\endgroup$– PeterLFeb 12, 2014 at 23:15
There are a couple of reasons: the surface properties of the ice, and the formation of a thin layer of liquid water.
First, ice tends to have a relatively smooth surface, due to the interaction of water molecules forming a regular, crystalline structure (that's what ice is, after all). Gravity helps: it pulls the surface molecules down, so they all tend to be at the some level, making for a very even surface and very low coefficients of friction.
Second, there is the liquid water on the surface. This happens for two reasons:
First, at anything above absolute zero there will always be a little bit of water that is transitioning back and forth from solid to liquid (melting) and/or gas (sublimation). Molecules deep in the ice are surrounded by other molecules that are nearly stationary, so those molecules are unlikely to move. Molecules on the surface, on the other hand, are less tightly bonded to their neighbors, because they don't have neighbors on all sides, so they can "pop loose" more easily and move around in water or gas phases.
Second, pressure melts water ice. Water is one of very few compounds that is less dense in solid form than as a liquid. This is why ice floats in water. The act of applying pressure -- say, by standing on a sheet of ice -- compresses and actually melts a bit of the ice. If you've ever seen anyone cutting ice with a wire, this is how it works: the pressure of the wire actually melts through the ice, if the pressure is great enough.
So, if you stand on ice, you will melt a very thin layer of it. Add that melt to the spontaneous melting and refreezing of the topmost layer of water molecules and the fact that you are already on a smooth surface, and things get very slippery, very fast.
$\begingroup$ This is correct. Your second bullet point hits the nail on the head. $\endgroup$ Jun 7, 2014 at 7:17
All the ice we see around us in nature is not far off from the melting point of the ice - this gives a reasonable probability that there will be monolayers of water on top of the ice surface. Additional energy input by friction would cause more ice to melt on the surface, thus giving it a slippery property. Ice near absolute zero temperature (i.e. much below its melting point) would not be slippery.
1$\begingroup$ Interesting way to look at it. Now I want to go home and see if butter just below its melting point will slip around on a warm plate. $\endgroup$– chaseFeb 13, 2014 at 1:14
$\begingroup$ @chase Have you tried this experiment? What was the result? $\endgroup$ Jan 17, 2017 at 17:44
Ice is the solid form of water. Under pressure, depending on the local temp and how much pressure is applies, ice changes state into liquid water. The more resistance a surface offers to objects moving across it, the less slippery it is.
Say you put on ice skates, and skate. the blades exert enough pressure to melt the ice beneath the skates to form water, a surface with very little resistance , and he layer of water acts as a lubricant between blade and the ice below.
On another day, it is too cold or the skater is too little t exert enough pressure and the footing is good.
I suggest people always knew that ice might be slippery and pay extreme attention to details locally to decide if this ice is slippery
2$\begingroup$ This very point was discussed last week on Science Friday on NPR (2/7/2014). The point made was that this may partially explain the slipperiness of ice for heavy objects, but very light objects that do not exert enough pressure for ice to change state, still will slip. $\endgroup$– ScotFeb 12, 2014 at 19:41
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http://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.84190.html
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math
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You can put this solution on YOUR website!
Working alone, Colleen can paint a house in 2 hours less than James. Working together, they can paint the house in 10 hours. how long would it take James to pain the house by himself.
Let x = time required by James by himself
Let the completed job = 1
Fraction done by James + Fraction done by Colleen = 1
Mult equation by x(x-2) to get rid of the denominators:
10x + 10(x-2) = x(x-2)
10x + 10x - 20 = x^2 - 2x
20x = x^2 - 2x + 20
x^2 - 2x - 20x + 20 = 0;
x^2 - 22x + 20 = 0; the quadratic equation, you sought after.
Use the quadratic formula to solve, only one solution will make sense.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705953421/warc/CC-MAIN-20130516120553-00028-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
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https://www.matrix-inst.org.au/events/matrix-seminar-dr-yilin-wang/
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math
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10 May 2022
10:00 am - 11:00 am
Tuesday, 10 May @ 1000 (AEST) (Melbourne)
Tuesday, 10 May @ 0800 (CST) (Beijing)
Tuesday, 10 May @ 0530 (IST) (New Delhi)
Tuesday, 10 May @ 0100 (BST) (London)
Monday, 9 May @ 2000 (EDT) (New York)
Monday, 9 May @ 1700 (PDT) (Berkeley)
Presenter: Dr Yilin Wang, MIT
Yilin is a Strauch Postdoctoral fellow at MSRI and C.L.E. Moore Instructor at MIT since 2019. She is currently working on topics at the interface of Complex analysis and Probability theory. Her current research focuses on themes that aim at enlightening the connections among Random conformal geometry, Geometric function theory, and Teichmueller theory. Yilin is a 2022 Maryam Mirzakhani New Frontiers Prize winner.
Title: How round is a Jordan curve?
Abstract: The Loewner energy for Jordan curves first arises from the small-parameter large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle. This class of curves has intriguingly more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and string theory, and has been studied since the eighties. The myriad of perspectives on this class of curves is both luxurious and mysterious. I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on.
Structure: 45 minutes seminar with 15 minutes question time
Seminar Recording and Slides:
Please click here for the recording of the seminar
Please click here for the presentation slides
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https://coinvalues.com/franklin-half-dollar/1958
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math
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A bit less than 30 million Franklin half dollars were minted in 1958, and are widely considered common by coin collectors today. Both the Philadelphia and Denver mint struck half dollars that year, and proofs were also made, which would represent the trifecta of annual half dollar issues right on through to the end of the series in 1963.
Here’s a breakdown of the mintages and values of 1958 Franklin half dollars:
1958, 4,042,000 minted; $11
1958 proof, 875,652; $50
1958-D, 23,962,412; $11
*Values are for coins in Very Fine-20 grade, unless otherwise noted.
1958 Franklin half dollars are quite affordable across the board, so those who have a few extra dollars to spare might consider springing for uncirculated specimens, which are quite beautiful, especially with full lines across the Liberty Bell on the reverse of the coin.
1958 proof Franklin half dollars make very handsome additions to any coin collection and are also easy to both find and, for most coin collectors, afford. Be choosy, for there are some less-than-desirable proofs out there. Avoid pieces that have cloudy surfaces or spots.
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CC-MAIN-2022-27
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https://www.maths.gneet.com/CMAmaths/Continuity/mainf.html
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math
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gneet TOPIC : CMA foundation Continuity Number of questions are 31
SELF EXAMINATION QUESTIONS Q1 to Q9 → Q1 to Q9
OBJECTIVE QUESTIONS : Q1 to Q 22 → Q10 to Q31
CALCULUS: 3.3 Continuity
SELF EXAMINATION : Question 1
Q.1) f (x) = x2
+ 1. Is the function continuous at x = 2?
f (x) = x2 + 1.
∵ limx→2- f(x) = f(2) = limx→2+ f(x)
⇒ f(x) is contineouse as at = 2
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662558030.43/warc/CC-MAIN-20220523132100-20220523162100-00201.warc.gz
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https://acikerisim.isikun.edu.tr/xmlui/handle/11729/56/browse?value=Charles+Babbage+Res+Ctr&type=publisher
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math
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Browsing FEF - Makale Koleksiyonu | Matematik Bölümü / Department of Mathematics by Publisher "Charles Babbage Res Ctr"
Now showing items 1-1 of 1
(Charles Babbage Res Ctr, 2011-07)A cograph is a P-4-free graph. We first give a short proof of the fact that 0 (-1) belongs to the spectrum of a connected cograph (with at least two vertices) if and only if it contains duplicate (resp. coduplicate) vertices. ...
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00739.warc.gz
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https://bird.bcamath.org/handle/20.500.11824/6/discover?filtertype_0=dateIssued&filter_relational_operator_0=equals&filter_0=2019&filtertype=author&filter_relational_operator=authority&filter=d495599a-f959-48bb-92b4-1965e923c953
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math
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Now showing items 1-2 of 2
A C 0 interior penalty discontinuous Galerkin Method for fourth-order total variation flow. II: Existence and uniqueness
We prove the existence and uniqueness of a solution of a C0 Interior Penalty Discontinuous Galerkin (C0 IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part ...
A C0 interior penalty discontinuous Galerkin method for fourth‐order total variation flow I: Derivation of the method and numerical results
We consider the numerical solution of a fourth‐order total variation flow problem representing surface relaxation below the roughening temperature. Based on a regularization and scaling of the nonlinear fourth‐order parabolic ...
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CC-MAIN-2023-06
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https://www.gov.uk/hmrc-internal-manuals/capital-gains-manual/cg17274
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math
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Indexation: from 6/4/88 indexation formula: falls in RPI
Falls in RPI
Where RI exceeds RD, it means that the RPI has fallen between the date of expenditure and the date to which the indexation allowance is calculated. No indexation is then available on that item. However, if the RPI falls between the two dates and then recovers so that overall RD exceeds RI, no regard is had to the temporary fall.
Rounding of decimals
The legislation requires the indexation factor to be rounded to the nearest third decimal place. Many people however use computers to calculate chargeable gains. It is often inconvenient to round off the computation in this way. Therefore you may accept computations ignoring the requirement to round the indexation factor, provided this is done on a consistent basis that neither favours the taxpayer nor HMRC. If however you prepare a computation to send to the taxpayer or agent this must be made on the strict basis.
Rebasing of RPI
The RPI for the period March 1982 to January 1987 was calculated by reference to a base of January 1974 = 100. From February 1987 onwards the RPI is expressed by reference to a base of January 1987 = 100. To calculate the indexation factor where the RI month is before February 1987 and the RD month is after January 1987 multiply the RPI for the RD month by 3.945 and apply the formula in the normal way with the amendment. (The same result is reached by dividing the RPI for the RI month by 3.945). See example in CG17313.
Computations may also be received where the indexation allowance is calculated by reference to a notional series of RPI figures for the period March 1982 to January 1987 on the base January 1987 = 100. These notional figures are reproduced in the annual tables referred to in part (b) of CG17290. Computations based on these figures may be accepted.
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https://journals.lww.com/jaids/Fulltext/2010/08010/On_the_Statistical_Accuracy_of_Biomarker_Assays.12.aspx
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math
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HIV incidence is the rate at which new infections occur in populations and tracks the leading edge of the epidemic. In recent years, considerable progress has been made in the development of biomarkers for determining current HIV incidence rates.1 The basic idea is to use biomarkers in cross-sectional samples to identify persons who were recently infected. The approach was first suggested using an assay for P24 antigenemia.2 However, that biomarker necessitates large sample sizes because the durations that persons are in that window (P24 antigen positive and HIV antibody negative) are relatively short. Subsequently, the Serological Testing Algorithm for Recent HIV Seroconversion) was developed which consists of a dual antibody testing system in which persons who are positive on the standard HIV antibody assay are tested with a second assay to distinguish recent infections from long-standing infection.3
Several classes of assays have been proposed within the Serological Testing Algorithm for Recent HIV Seroconversion framework for HIV incidence estimation.4 One class is based on the quantity of HIV antibodies. The “detuned assay”, for example, is purposefully made less sensitive than the standard enzyme immunoassay by diluting and altering the incubation time of each tested specimen. Persons are said to be in the “window period” if they are confirmed positive on the first assay (standard enzyme immunoassay) and negative on the second detuned (or less sensitive) assay. A second class of assays is based on the proportion of HIV antibodies. The BED capture enzyme immunoassay, for example, is based on the proportion of HIV-1-specific IgG to total IgG.5 A third class of assays is based on the avidity of HIV antibodies that relies on the principle that antibodies produced shortly after incident HIV infection bind more weakly to the antigen than those produced later in infection.
Associated with each of these assays is a window period. Persons are in the “window period” if they are confirmed positive on the first assay (standard enzyme immunoassay) and identified as a recent infection by the second assay (eg, negative on the detuned or BED assays). Assay cutoff values are specified; for example, the BED and detuned assays specify an optical density cutoff, below which specimens are considered negative and thus recently infected. Higher cutoffs lead to larger mean durations of the window period.
United Nations AIDS has issued a statement that the BED assay should be used for neither estimating nor monitoring trends in HIV incidence.6 Their concern about the accuracy of the approach arises from reports primarily from Africa that the cross-sectional estimate overestimates HIV incidence.7-8 For example, a study of new mothers in Zimbabwe, the ZVITAMBO study, found that the unadjusted BED HIV incidence estimate was over 2 times greater than that based on the longitudinal follow-up of the cohort.8 One theory that has been advanced to explain that discrepancy is that the BED has a high “false recent” misclassification rate, whereby long-standing infections are incorrectly labeled as new incident infections. This concern has led to several proposals to statistically adjust the cross-sectional estimates8-11 and subsequent discussion about if and when such statistical adjustments are appropriate.12-17
The concerns that some persons remain in the window period for prolonged periods especially arise with antibody-based assays such as the BED which depend on antibody quantification. Elite or viremic controllers who have low or undetectable viral loads may remain in the window period until AIDS or death. Furthermore, persons with AIDS or on antiretroviral therapy may experience declines in HIV antibody levels causing re-entry into the window period. The Centers for Disease Control and Prevention recommended excluding persons with AIDS or persons on antiretrovirals from being counted in the window period regardless of their optical density values.18
The objective of this article is to set forth a framework for evaluating the statistical accuracy of estimates of current HIV incidence rates from cross-sectional surveys using assays for biomarkers and to identify characteristics of assays for biomarkers that improve accuracy. The framework permits evaluation of the impact of the window period distribution on accuracy. We use the framework to investigate the effects on accuracy of 3 phenomena that can contribute to long right tails of window period distributions: persons who remain in the window period for years, perhaps until AIDS onset or initiation of antiretrovirals (eg, viremic controllers or long-term nonprogressors); persons with persistently undetectable viral loads who never develop AIDS and and remain in the window period until death (eg, elite controllers); and persons who re-enter the window period after onset of advanced HIV disease (eg, AIDS or beginning antiretrovirals), but they are not recognized as having advanced HIV disease, and are thus not excluded from counts in the window period.
The cross-sectional estimator of HIV incidence is
where w is the number of persons in the window period, n is the total number of persons who are uninfected (negative on the standard enzyme immunoassay) and μ is the mean window period duration. The durations of window periods are variable and have a probability distribution. The survival function of window periods, S(t), is the probability that the window period is greater than t days. Equation (1) is justified by assuming that the incidence rate of new infections is approximately constant over the support of S(t). Kaplan and Brookmeyer studied the behavior of the incidence estimator (1) when the assumption of constant incidence is violated19 and showed that the estimator Î converges to a time weighted average of past HIV incidence rates:
where I(t) is the HIV incidence rate t years before the specimen collection, and the weighting function f(t) is the backward recurrence density of the window period given by
Kaplan and Brookmeyer19 show that I * (equation 2) is approximately equal to the HIV incidence at the time point ψ years before specimen collection where ψ is the mean backward recurrence time (Appendix for discussion of assumptions to justify the approximation such as linearity of HIV incidence trends). That is,
We refer to ψ as the “shadow” because the cross-sectional sample is casting a shadow back in time. The shadow depends on the both the mean and the coefficient of variation of window periods through the equation:
where c, the coefficient of variation of the window periods, is the ratio of the standard deviation (σ) to the mean (μ) of window periods, that is, c = σ/μ.20 In summary, the estimator in equation (1) is estimating a time lagged incidence rather than the “current” HIV incidence, where the lag time is the “shadow.”
Framework for Evaluating the Statistical Accuracy of Assays
Evaluation of the statistical accuracy of the biomarker estimator of incidence requires consideration of both the estimator's bias and variance. The statistical bias of an estimator is the difference between what it is actually estimating and what we hope it is estimating (ie, the current HIV incidence rate). The absolute statistical bias of the biomarker estimator is approximately I(ψ)-I(0), which is the change in HIV incidence rates over the duration of the shadow. To compare 2 estimators, we define the relative bias as the ratio of their biases. The relative bias is approximately equal to the ratio of the shadows (Appendix). For example, if assay 1 has a shadow that is twice as large as assay 2, then assay 1 has a relative bias that is also approximately twice as large as that of assay 2. Although the (absolute) statistical bias depends on the magnitude of the change in HIV incidence rates over the duration of the shadow, the relative bias does not and depends only on the ratio of their shadows. As such, the shadow is a useful tool for comparing the statistical biases of assays.
The statistical stability of an estimator can be measured by its variance. Assuming that the numbers of persons in the window period (w) follows a Poisson distribution, then the variance of the estimator in equation (1) is approximately
where I (ψ) is the HIV incidence rate at the shadow. To compare the statistical stability of estimators with 2 assays, we consider the relative sample size requirements of the 2 assays, which we define as the ratio of the sample sizes required by the 2 assays to achieve the same variances. As discussed in the Appendix, the relative sample size requirement is approximately the ratio of mean window periods. For example, if assay 2 has a mean window period twice as large as assay 1, then assay 1 would require a sample size twice as large as assay 2 to have the same level of statistical stability (ie, the same variances).
The preceding discussion suggests that 2 quantities, the shadow and the mean window period, are useful tools for comparing the statistical accuracy of assays in determining current HIV incidence from cross-sectional samples. The shadow measures how “current” is the estimate of incidence produced by the biomarker from a cross-sectional sample. The shadow determines the bias of the estimator. The mean window period measures the “statistically stability” of the incidence estimator and is a key determinant of the variance of the estimate. The shadow depends not only on the mean of the window period distribution but also its coefficient of variation. The coefficient of variation is sensitive to the tails of the distribution.
The Effect of the Tails of the Window Period Distribution on Accuracy
We investigated the effects on accuracy of several phenomena, which cause the window period distribution to be skewed with a long right tail. First, some persons may remain in the window period until the onset of AIDS.21-23 These may include persons who have been called “viremic controllers”, or long-term nonprogressors, and we assume that once these persons progress to advanced HIV disease (AIDS onset or initiation of antiretrovirals) that their advanced disease state is recognized and they are no longer included in the counts of persons in the window period. Second, some persons with persistently undetectable viral loads may never develop AIDS and they remain in the window period until death (from causes other than AIDS). We will refer to this group as elite controllers.22-24 Third, some persons may revisit the window period a second time after onset of AIDS or after starting antiretrovirals, and if their advanced HIV disease is not recognized, then they may be improperly counted in the window period.18 To evaluate the effects of these 3 phenomena on statistical accuracy, we developed 2 models. A mixture model was used to describe the first 2 phenomena. In the mixture model, a proportion (p) of newly infected persons have long window periods (eg, until onset of AIDS or death) with window period distribution S 2(t), mean μ2, and coefficient of variation c 2; the remaining proportion 1-p have more “typical” window periods characterized by the distribution S 1(t), mean μ1 , and coefficient of variation c 1. The overall mean window period duration of the mixture population is μ = μ1 (1 − p) + μ2p. The shadow ψ of the mixture population is (Appendix)
We numerically evaluated μ and ψ (from equation 3) using the mixture models to determine the sensitivity of the accuracy of the estimator to the right tails of the window period distribution.
A model for window period re-entry was used to describe the third phenomena, which concerns persons with AIDS (or persons on antiretrovirals) who are improperly counted in the window. Our model for window period re-entry (Appendix) allows persons to initially enter the window period and then re-enter the window period upon the onset of AIDS (or upon starting antiretrovirals). In this model, a proportion α are not recognized as AIDS cases and are thus (incorrectly) included in the window period count, whereas the remaining proportion (1-α) are correctly recognized as AIDS cases and properly excluded from the window count tally. We vary the parameter α to evaluate the quantitative effects of unrecognized AIDS cases on accuracy.
Table 1 tabulates the shadow as a function of the mean and the coefficient of variation of the window periods. For example, if an assay had a mean window period of 0.5 years and a coefficient of variation of 2.0, then the shadow would be 1.25 years, which implies that the assay is estimating HIV incidence approximately 1.25 years before the time point of collection of specimens. Table 1 illustrates the fact that if the coefficient of variation is greater than 1.0, then the shadow is greater than the mean window period. The shadow takes a minimum value of one half of the mean window period when the coefficient of variation is 0.
Table 2 displays the mean and coefficient of variation of window periods required to guarantee that the shadow is less than 1 year. For example, to guarantee a shadow less than 1 year, an assay with a mean window period of 1.0 years would require a coefficient of variation no larger than 1.0, whereas an assay with a mean window period of 0.25 years could afford a coefficient of variation as large as 2.6. Assays with smaller mean window periods can afford larger coefficients of variation, however, that comes at the price of a larger sample size requirements. Assays with smaller mean window periods require larger sample sizes to achieve the same level of statistical stability (variance). Table 2 also shows the relative sample size requirements (relative to a mean window of 1 year). For example, an assay with a mean of 0.25 years and coefficient of variation of 2.6 would require 4 times the sample size as an assay with a mean of 1 year and a coefficient of variation of 1 year, yet both assays have shadows of 1 year.
Tables 3 and 4 evaluate the effects of viremic controllers and elite controllers on accuracy. Suppose a proportion (1-p) have window periods with a mean of μ1 = 0.5 years and a proportion p have mean window period of μ2 = 10 years (Table 3) or μ2 = 20 years (Table 4). The coefficients of variation c 1 and c 2 were held fixed in these tables (eg, c 1 = 0.363 based on published reports on the BED window distribution5 and c 2 = 0.50 as suggested by time to AIDS and survival distributions.24 Table 3 with μ2 = 10 years is intended to investigate the scenario in which a small proportion of persons (eg, viremic controllers) remain in the window until the onset of AIDS or initiation of antiretroviral therapy; and at that point, their advanced HIV disease is recognized and they are excluded from the count of the numbers in the window period. We found, for example, even if there are only 2% of such persons, that it is sufficient to cause the shadow to increase to over 2.02 years from only 0.28 years if p = 0.0 (Table 3). Table 4 with μ 2 = 20 years is intended to investigate the scenario in which a very small proportion of persons (eg, elite controllers) never develop AIDS and remain in the window period until death. We found, if 1.0% are elite controllers (ie, p = 0.01), then the shadow is 3.81 years. Even if only 0.5% of persons are elite controllers (ie, p = 0.005), the shadow is 2.33 (Table 4). These results imply that even a very small proportion of persons who are elite controllers can cause a large increase in the shadow, which potentially decreases the statistical accuracy of biomarker estimates of current HIV incidence.
Figure 1 illustrates the window period distributions for 3 of the mixture models considered in Table 4 (for elite controllers comprising 0.1%, 1.0%, and 2% of the population). The 3 curves in Figure 1 are visually indistinguishable from each other, however, their shadows are very different (0.75 years, 3.81 years, and 5.77 years). The cautionary warning here is that the shadow depends on very subtle characteristics of the tails of the window periods, which may not be readily apparent from visual inspection of the curves.
Table 5 evaluates the effect of unrecognized AIDS case who revisit the window period, but because they are not recognized as AIDS cases they are not excluded from the count of the number in the window period. We find that even a very small proportion of unrecognized AIDS cases are sufficient to greatly increase the shadow. For example, if 0%, 1%, and 5% of AIDS cases are unrecognized, the shadows are respectively 0.28, 0.73, and 2.23 years. To keep the shadow under 1 year, no more than 1.6% of AIDS cases may go unrecognized.
A practical question is whether assays could be designed more optimally to increase accuracy for HIV incidence estimation. Here we consider 2 design parameters that could potentially be manipulated, the mean window (μ 1) and the coefficient of variation (c 1) (among the first subpopulation with typically short window periods in the mixture population). For example, the mean and coefficient of variation of the window periods change if the optical density cutoff of an assay is changed. We investigated whether there was an optimal choice for μ 1 under the mixture model. We varied the mean window period μ1 in equation (3) and calculated the shadow. Figure 2 shows the relationship of the shadow to the mean window period μ1 (μ2 was fixed at 10 years and the coefficients of variation c 1 and c 2 were also fixed). Figure 3 is a similar figure except μ2 was fixed at 20 years. The figures illustrate that there are optimal choices of the mean window (μ1) that minimize the shadow for a given mixing proportion p. For example, in Figure 3, if p = 0.005, the shadow is minimized at 1.63 years by an assay with mean of μ1 = 1.44 years. It is a remarkable and surprising fact that Figures 2 and 3 are approximately U shaped: the explanation for the U shape is that if μ1 gets too small, then persons who are “caught” in the window period become increasingly dominated by the subpopulation with long window periods as opposed to the subpopulation with shorter window periods. It can be shown analytically that the shadow is approximately minimized if the mean window period μ1 of the assay is (Appendix):
which yields a minimum shadow of:
Equation (5) shows that the shadow decreases as the coefficient of variation c 1 decreases. By setting c 1 = 0 in equation (5), we can determine the minimum value of the shadow (ψmin) that is ever achievable with the mixture distribution:
For example, suppose elite controllers have a mean window period of 20 years with coefficient of variation of c 2 = 0.5. With optimal choices for the assay's design parameters [ie, set c 1 = 0 and μ1 equal to equation (4)], the minimum values of the shadow corresponding to p = 0.001, 0.005, 0.010, 0.015, and 0.020 are respectively 0.71, 1.58, 2.23, 2.74, and 3.16 years. The implication of these calculations is that if elite controllers compose greater than 0.5% of the population, then it is not possible to “tune” an assay (eg, the BED) to have a shadow of less than 1.58 years even if the coefficient of variation (c 1) was successfully reduced to 0.
Evaluation of the statistical accuracy of the biomarker approach to HIV incidence requires consideration of both the bias and variance of the estimators. Both the shadow and the mean window period are useful in this regard. The shadow is useful for comparing statistical bias. Assays with smaller shadows have smaller relative bias. The mean window period is useful for comparing the statistical stability (variance) of assays. Assays with larger variances have greater sample size requirements.
The biomarker approach is estimating a time-lagged incidence back into the past where the lag time is the shadow. The shadow measures how “current” is the biomarker based estimate of HIV incidence. The shadow depends on both the mean and the coefficient of variation of window periods. The shadow increases as the mean window period increases and as the coefficient of variation increases.
The validity of the shadow interpretation of the cross-sectional incidence estimate depends to some extent on the linearity assumption of HIV incidence trends (Appendix, and section 1.4 of19). Although linearity is not an absolutely necessary condition for validity, the degree of nonlinearity that can be tolerated should be assessed and depends on a number of factors including the window period distribution.19
We have evaluated the impact of 3 phenomena on accuracy: viremic controllers who are counted in the window period until onset of advanced HIV disease; elite controllers who remain in the window until death; and unrecognized AIDS cases who re-enter the window period. We have shown that even a small proportion of persons with long window periods (eg, elite controllers) can significantly increase the shadow, which may substantially bias the biomarker approach for estimating current HIV incidence levels. Furthermore, a very small proportion of AIDS cases, who are unrecognized and not excluded from the counts in the window period, can significantly increase the shadow.
Our results help explain discrepancies between the cohort and biomarker approaches that have been reported in the literature. One study in Zimbabwe, the ZVITAMBO study, recruited and followed new mothers within 96 hours of delivery and compared the BED cross-sectional incidence estimate with the cohort estimate.8 The BED estimate was over 2 times larger than the cohort estimate. Our results help explain that discrepancy. We have shown that if as little as 0.5% of persons are elite controllers, the shadow is over 2.5 years. In that case, the BED approach is estimating HIV incidence into the prepartum period, whereas the cohort approach is estimating incidence exclusively during the postpartum period.16 It is very plausible that HIV incidence rates are higher during the prepartum than the postpartum period periods because the women were sexually active during the prepartum period, and in the ZVITAMBO study, the new mothers were receiving counseling and other behavioral interventions during the postpartum period. The cautionary warning here is that if HIV incidence is changing sharply over time (such as between the prepartum and postpartum periods among new mothers), shadows of over 2 years duration can create discrepancies between cohort and biomarker estimates. Neither the biomarker approach nor the cohort approach are gold standards in which to validate the other because they are estimating HIV incidence rates at different points in time.
Our results provide guidance for the design of new assays to improve accuracy. Judicious choice of the mean window period (by changing the optical density cutoff for example) can help minimize the shadow as illustrated in Figures 2 and 3, and afford some protection from long tails of the window period distribution. Precisely how changes in the optical density cutoff would influence the shadow is an open research question and is complicated because changes to the cutoff may affect not only μ1 but also other parameters in equation 3 including the coefficient of variations and p.
Furthermore, our results establish the limits to the statistical accuracy of some assays. We find, for example, that if as little as 0.5% of persons are elite controllers who remain in the window until death, it is not possible to reduce the shadow to less than 1.58 years even if the assay's coefficient of variation (c 1) is successfully reduced to 0. Whether or not a shadow of 1.58 years is adequate depends on how much HIV incidence changes over the duration of the shadow and the ultimate purposes of the incidence estimate. We illustrated a number of our results with a specific value for μ2 (20 years.) The interpretation of μ2 is the life expectancy of an elite controller, which may depend on overall health conditions of the population, and should be assessed at the local level.
The limits to the statistical accuracy of some assays discussed above begs the question if there are alternative strategies for improving the accuracy of current HIV incidence estimates? One promising strategy is based on algorithms involving multiple assays such as CD4, BED, avidity assays, antiretroviral, P24 antigen, and HIV RNA screening.21,25 For example, an algorithm could consist of HIV-positive persons who are tested for CD4 to exclude persons with AIDS, those without advanced HIV disease are then tested with the biomarker assays (eg, BED), and those in the window period are assayed for HIV RNA to exclude elite controllers. Tables 3-5 suggest that screening with additional assays would increase accuracy considerably; the tables show by how much the shadow would decrease if p or α are decreased by screening. Two complications deserve attention with algorithms of multiple assays. First, with each specific algorithm, the window period distribution would need to be recalibrated. Second, if elite controllers with nondetectable RNA are automatically excluded from the window count tally, it will be necessary to account for the fact that some of those exclusions may have been in the (counterfactual) window period; here we are considering the “window period” of elite controllers as a counterfactual, that is, an unobservable duration which follows the same probability distribution as the window period of noncontrollers. That is, if w is the observed number in the window period, then the corrected number in the window would be w/(1-p) where p is the probability an individual is an elite controller. In practice, however, because p is likely small, that suggested correction may have a minor numerical effect. It is worth reiterating that p refers to the proportion of elite controllers in a cohort of newly infected persons. The proportion of elite controllers in a group of prevalent infected individuals is likely to be larger because of the survival advantage of elite controllers.
Other measures of statistical accuracy have been discussed in the literature. For example, the “false-recent rate” refers to the proportion of long-standing infections that are in the window period; however, that definition is ambiguous without further qualification about the meaning of long-standing infection.25 We could qualify the term, for example, and define the 3-year false recent rate as the proportion with window periods greater than 3 years. However, that rate by itself does not determine the bias. To illustrate that fact, consider 2 assays, where 1 assay has a mean window of 0.50 years and coefficient of variation of 1.7, and a second assay has a mean of 1 year and coefficient of variation of 1; Although both assays have a shadow of 1 year (Table 2), the 3-year false recent rates are quite different (.017 versus .041 under a lognormal model for the window period distribution). The key point is that false recent rates at one time point do not fully characterize the statistical accuracy of assays for current HIV incidence either with respect to bias or variance.
The purpose of this article was to provide a framework for understanding how the window period distribution affects accuracy. The framework considers 2 dimensions to statistical accuracy, bias, and variance. Alternatively, one could combine the bias and variance measures into a single overall summary measure of accuracy such as the mean squared error; however, we prefer to describe the 2 dimensions of accuracy separately to clarify the tradeoff between bias and variance and because their relative importance may depend on the circumstances of the setting (eg, if sample size limitations are of primary concern, controlling variance may be paramount; if monitoring rapidly changing HIV incidence is of primary concern, controlling bias may be paramount). The discussion in this article assumed the window period distribution was known. Of course, accuracy will be reduced if that is not the case, and there is error in the mean window period (μ) used in equation 1. There are confidence interval procedures that account for uncertainly in μ including both analytic26 and Monte-Carlo approaches.27 The framework set forth in this article provides guidance for the designing improved assays and also identifies the limits to accuracy achievable by some assays. Algorithms that include testing for RNA, CD4, avidity, P24 antigen, and antiretrovirals offer a very promising avenue for improving the accuracy of current HIV incidence estimation from cross-sectional studies.
1. Le Vu S, Pillonel J, Semaille C, et al. Principles and uses of HIV incidence estimation from recent infection testing-A review. Eurosurveillance
2. Brookmeyer R, Quinn TC. Estimation of current human immunodeficiency virus incidence rates from a cross sectional survey using early diagnostic tests. Am J Epidemiol
3. Janssen RS, Satten GA, Stramer S, et al. New testing strategy to detect early HIV-1 infection for use in incidence estimates and for clinical and prevention purposes. JAMA
4. Murphy G, Parry JV. Assays for the detection of recent infections with Human Immunodeficiency Virus Type 1. Eurosurveillance
5. Parekh BS, Kennedy MS, Dobbs T, et al. Quantitative detection of increasing HIV Type 1 antibodies after seroconversion: a simple assay for detecting recent HIV infection and estimating incidence. AIDS Res Hum Retroviruses
6. UNAIDS Reference Group for Estimates, Modeling and Projections. Statement on the Use of the BED-assay for the Estimation of HIV-1 Incidence for Surveillance or Epidemic Monitoring. Report of a meeting of the UNAIDS Reference Group for Estimates, Modeling and Projections. Athens, Greece
. Geneva, Switzerland: UNAIDS; Available at: http://www.epidem.org/Publications/BED%20statement.pdf
. Accessed December 13-15, 2005.
7. Karita E, Price M, Hunter E, et al. Investigating the utility of the HIV-1 BED capture enzyme immunoassay using cross-sectional and longitudinal seroconverter specimens from Africa. AIDS
8. Hargrove JW, Humphrey JH, Mutasa K, et al. Improved HIV-1 incidence estimates using BED capture enzyme immunoassay. AIDS
9. McDougal JS, Parekh BS, Peterson ML, et al. Comparison of HIV-1 incidence observed during longitudinal follow-up with incidence estimated by cross-sectional analysis using the BED capture enzyme immunoassay. AIDS Res Hum Retroviruses
10. McWalter TA, Welte A. Relating recent infection prevalence to incidence with a subpopulation of nonprogressors. J Math Bio
11. McWalter TA, Welte A. A comparison of biomarker based incidence estimators. PLoS ONE
12. Brookmeyer R. Should biomarker estimates of HIV incidence be adjusted? AIDS
13 Hargrove JW. BED estimates of HIV incidence must be adjusted. AIDS
14. McDougal JS. BED estimates of HIV incidence must be adjusted. AIDS
15. Welte A, McWalter TA, Barnighausen T. Reply to “Should biomarker estimates of HIV incidence be adjusted?” AIDS
16. Brookmeyer R. Response to correspondence on “Should biomarker estimates of HIV incidence be adjusted?” AIDS
17. Wang R, Lagakos SW. On the use of adjusted cross-sectional estimators of HIV incidence. J Acquir Immune Defic Syndr
19. Kaplan E, Brookmeyer R. “Snapshot estimators of recent HIV incidence rates.” Oper Res
20. Cox DR. Renewal Theory
. London, United Kingdom: Methuen and Co. Ltd; 1962.
21. Laeyendecker O, Rothman RE, Henson C, et al. The effect of viral suppression on cross-sectional incidence testing in the Johns Hopkins Hospital Emergency Department. J Acquir Immune Defic Syndr
22. Laeyendecker O, Redd AD, Lutalo T, et al. Frequency of long-term nonprogressors in HIV-1 seroconverters from Rakai Uganda. J Acquir Immune Defic Syndr
23. Okulicz O, Marconi VC, Landrum ML, et al. Clinical outcomes of elite controllers, viremic controllers and long term non-progressors in the US Department of defense HIV natural history study. J Infect Dis
24. AAlen O, Farewell VT, DeAngelis D, et al. A Markov model for HIV disease progression including the effect of HIV diagnosis and treatment; application to AIDS prediction in England and Wales. Stat Med
25. Mastro TD, Kim A, Hallett T, et al. Estimating HIV incidence in populations: issues, challenges and the way forward. J HIV/AIDS Surveill Epidemiol
. 2010; (in press).
26. Brookmeyer R. Accounting for follow-up bias in estimation of Human Immunodeficiency virus incidence rates. J R Stat Soc A
27. Cole SR, Chu R, Brookmeyer R. Confidence intervals for biomarker-based Human Immunodeficiency Virus incidence estimates and differences using prevalent data. Am J Epidemiol
APPENDIX: THE SHADOW
It has been shown19 that the cross-sectional estimator is in fact not estimating the current HIV incidence but is instead an approximation of the HIV incidence ψ years before the collection of the specimens in the cross-sectional sample, where, ψ, the shadow, is the mean of the backward recurrence time distribution, and ψ is given by:
The validity of the approximation that the cross-sectional estimate is the HIV incidence rate ψ years earlier can be formally assessed by a second order Taylor series expansion. The error in the approximation is equal to I′′(ψ)V/2, where I′′(ψ) is the second derivative of the incidence function and V is the variance of the backward recurrence times, (equation 16 in19). Therefore, it follows that the error in the approximation becomes small under either or combination of 2 conditions: the time trend in HIV incidence rates is approximately linear (ie, I(t)≈I(0) + bt in which case I′′(ψ) is zero), or the variance (V) is small.19
The (absolute) bias in the cross-sectional estimator is I(ψ)-I(0),where I(t) is the incidence t years before the collection of the specimens. The relative bias of 2 assays with shadows ψ1 and ψ2 is the ratio of their biases, which under the assumption HIV incidence trends are linear in time is the ratio of their shadows because
Variance (Statistical Stability)
Suppose we wish to compare the statistical stability of 2 assays where assay 1 has the mean window period and shadow given respectively by μ1 and ψ1, and assay 2 has the mean window and shadow given respectively by μ 2 and ψ2. To compare the statistical stability of the estimates from the 2 assays, we consider the relative sample size requirements of the 2 assays (sizes of the cross-sectional surveys) which is defined as the ratio of the sample sizes required by two assays (say N 1 and N 2 which refer to the total numbers in the cross-sectional samples) in order that they each achieve the same level of statistical precision (ie, the same variances). The variance of the estimator in equation (1) is
. Therefore, the relative sample size is
is the ratio of the HIV incidence rates at the shadows of the two assays. The relative sample sizes depend both on the ratio of the mean window periods and the ratio k of HIV incidence rates at the shadows. In the absence of prior knowledge about the magnitude of k, consider k = 1 as the leading case for assessing statistical stability. In that case, the relative sample size requirement is just the ratio of mean window periods,
. For example, if assay 2 has a mean window twice as large as assay 1, then assay 1 would require a sample size twice as large as assay 2 to have the same level of statistical stability (eg, variances).
The window period distribution for the mixture population is
To derive equation (3), we note that the mean of a mixture distribution is
and its variance is
where σi and μi are respectively the standard deviation and mean for subpopulation i with survival distribution Si(t).The mean of the backward recurrence distribution is
Substituting the mean μ and variance σ2 of the mixture distribution into the above equation gives equation (3).
To derive equations (4) to (6), we make the approximation that the mean of the mixture distribution μ1 (1 − p) + μ2p ≈ μ1 which is an adequate approximation when p is small. Then the mean of the backward recurrence time of the mixture is
Differentiating ψ with respect to μ1 and setting
, we obtain equations (4). Substituting equation (4) into the above equation gives equation (5). The results from these analytic equations agree well with the direct numerical results of the optimum (minimum) values of ψ in Figures 2 and 3. Setting c 1 = 0 in equation (5) yields equation (6).
Model for Window Period Re-Entry
The model structure is as follows. Persons spend an initial duration of time in the window period according to the survival distribution S 1(t) which has mean μ1. The time to AIDS after infection follows a survival distribution S 2(t) which has mean μ2. Persons re-enter the window period at the onset of AIDS and remain in the window until death. The duration from AIDS onset until death follows the survival distribution S 3(t), which has mean μ3. A proportion α of AIDS cases are not recognized as AIDS and thus not excluded from the window count tally, whereas the remaining proportion (1-α) are correctly identified as AIDS cases and properly excluded from being counted in the window. As shown in,19 if there is re-entry into window periods, the shadow is the mean (expectation) of a random variable with probability density:
where, φ(t) is the probability of being in the window period t years after infection (that includes either the events of being in the window during the initial period or the second period after AIDS onset). Then,
where, f 2(u) is the probability density of the time to AIDS. The shadow is the expectation associated with the probability density f, that is,
Keywords:© 2010 Lippincott Williams & Wilkins, Inc.
BED; biomarker; epidemiology; incidence; statistics
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https://www.coursehero.com/file/34825485/33-NOTES-Special-Casesdocx/
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math
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3.3 NOTES Special Cases
- Study the equation below. Is there anything noticeable about the terms x2 and 9?
y = x2 − 9
- Both terms are perfect squares! In fact, the expression has special qualities that make it easier to factor. -
- This lesson explores how to identify and factor two special kinds of quadratic expressions: the
difference of squares and perfect square trinomials.
- A key component to understanding these special expressions is being able to identify perfect squares.
DIFFERENCE OF SQUARES:
- difference of Squares:
An expression that contains two perfect squares with one subtracted from the
other. A difference of squares can always be factored as follows:
- perfect squares:
Numbers that are the square of an integer. In other words, a perfect square can be
expressed as an integer multiplied by itself. (Sometimes this definition is extended to include the squares
of rational numbers.) A perfect square can also include a variable. In this case, the variable term must be
able to be expressed as a variable raised to a power multiplied by itself.
- Let's take a look at x2 - 9. You already noticed that the terms, x2 and 9, are perfect squares.
- Another important property of this expression is the operation.
- In fact, x2 - 9 is an example of a quadratic expression called a difference of squares.
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http://www.undergraduates.ms.unimelb.edu.au/
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math
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Information to help you choose your mathematics and statistics subjects.
- First Year
- Majoring in Mathematics and Statistics
- Major in Mathematical Physics
- Mathematics and Statistics to Complement Other Majors
- Diploma in Mathematical Sciences
- UMEP Choices
- Course Advice Week
- Obtaining Personal Course Advice
Here is a list of all undergraduate subjects currently taught by the Department of Mathematics and Statistics.
Information for prospective undergraduate students.
Vacation Scholars Program
Get a taste of research in the mathematical sciences over Summer.
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http://www.aikiweb.com/forums/showpost.php?s=cc17bc641274c6e9d157b8b6ae9f760f&p=216279&postcount=52
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math
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Peter A Goldsbury
One problem is that Ueshiba explains the symbols in terms of kotodama theory. He uses the the circle, square and triangle, but also three more: cross in a circle in a square; circle bisected four times; same bisected circle in a square. This is all in the (as yet untranslated) Takemusu Aiki volume. Clearly kotodama theory would be the place to look.
Thanks for the reply,
Interesting, I'll have to look into getting a Japanese copy of Takemusu Aiki then. While some of the details differ, we similarly have various combinations of the symbols used together and separately. Square in a circle, triangle in a circle, two triangles merged to form a 6 pointed star inside a circle, circle bisected by the straight line, circle within a circle, cross, etc. I get the impression that Ueshiba wasn't breaking new ground so much as playing with and putting his own spin on possibly well established themes.
As an aside, I've only just recently started reading aiki related things in Japanese, but in English we often hear of the idea of "not clashing" and such, but was there any particular phrase that Ueshiba was fond of using to express this idea? I ask because over the years I've found an awful lot of "common ground" philosophically between the ryu I practice and aikido and one of the major tenants of our ryu is something known as 不当之矩 which was one of the first things that really grabbed my attention in the "well this sure sounds familiar" sense several years ago.
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https://www.yaadb.com/2023/04/mod-55-com.html
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math
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mod 55 com
Mod 55 com is a term that appears in various contexts on Google search results. Some of the results relate to mathematical calculations involving the modulo operation, while others relate to commercial products and services.
Firstly, let's discuss the mathematical concept of modulo or modular arithmetic. In modular arithmetic, numbers are considered to be equivalent if they leave the same remainder when divided by a given integer called the modulus. For example, in modulo 5 arithmetic, 11 and 1 are considered equivalent because they both leave a remainder of 1 when divided by 5. The modulo operation is denoted by the symbol '%', and the result is always a non-negative integer smaller than the modulus.
One of the search results related to modulo arithmetic is the question "What is 55 mod 55?" The answer is 0, since 55 is perfectly divisible by 55 without leaving any remainder. Similarly, the question "What is 1 mod 55?" has the answer 1, since 1 is not divisible by 55.
Another search result shows an online calculator for modular arithmetic, which can compute various expressions involving the modulo operation. For example, the expression "14^27 mod 55" can be evaluated to 19 using this calculator. The Wolfram Alpha search result also shows a similar computation, using the power operator instead of the caret symbol.
Moving on to the commercial aspect, some of the search results show businesses or products that use the term "mod 55" in their names. For instance, Model55 is a company that provides furniture solutions for the multifamily and senior living housing markets. They specialize in apartment staging and turnkey furniture, and have a nationwide presence in the US.
There are also online shops that sell electronic kits or components with the name "AKSA 55 mod". For example, Bukalapak and Shopee are two Indonesian e-commerce platforms that offer a PCB (printed circuit board) for an AKSA 55 mod amplifier. The prices range from IDR 30,000 to IDR 135,000, depending on the seller and the shipping options.
Finally, some search results show educational or informational content related to modular arithmetic. For instance, one Quora post discusses how to find the value of "12^7 mod 55" without using a calculator. The answer involves breaking down 12 into 1 and 11, and applying the modular exponentiation rules iteratively.
In summary, the term "mod 55 com" can refer to different things depending on the context. It can be a mathematical calculation, an online calculator, a commercial product or service, or an educational resource. By exploring the search results, we can learn more about the diverse applications of modular arithmetic and how it relates to various fields of knowledge.
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http://www.rossettiarchive.org/docs/2-1881.sign4b.delms.radheader.html
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math
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Ballads and Sonnets (1881), proof Signature N (Delaware Museum, third revise,
duplicate copy 2)
Dante Gabriel Rossetti
Document Title: Ballads and Sonnets
Author: Dante Gabriel Rossetti
Publisher: F. S. Ellis
Printer: Chiswick Press, C. Whittingham and Co.
City of publication: London
Date of publication: 1881 May 4
Pre-Publication Information: proof
Current Location: Library, Delaware Art Museum
Point: 10 point; 6 point leading
Lines per Page: 17
Margin top: 2 cm
Margin bottom: 3.8 cm
Margin right: 2 cm
Margin left: 2.5 cm
Dimensions of Document: 19 x 12.8cm (crown octavo)
Electronic Archive Edition: 1
This is a duplicate copy (dated 4 May 1881) of the third revise of Signature N of the Ballads and Sonnets volume. It is without revisions, like a duplicate also at the Delaware Art Museum library. An author's copy , with revisions, of this signature is in the same location.
This proof was pulled because not all of DGR's corrections that were sent with the first revise (printed on 28 April) made their way into the second revise (printed on 3 May).
Textual History: Revision
Besides this duplicate copy of the third revise, the Delaware proofs include the following: copy 1 and copy 2 of the first proof with only eight sonnets printed; copy 1 and copy 2 of the first revise (dated 28 April 1881 and numbered 1a and 1b respectively), both with DGR's corrections throughout; copy 1 and copy 2 of the second revise (dated 3 May 1881 and numbered 1a and 1b respectively), both without revisions; an author's proof (with corrections) and two uncorrected copies of the third revise—this one and uncorrected copy 2), all dated 4 May 1881 and numbered 3c, 3a, and 3b respectively; an uncorrected and two corrected copies of the fourth revise ( corrected copy 1 and corrected copy 2), all dated 6 May 1881 and numbered 4a, 4b, and 4c respectively; four copies of the final proof, including WMR's copy with his notes, DGR's corrected copy , an uncorrected partial copy, and a copy with uncut sheets), all undated and numbered 5a, 5b, 5c, and 5d. Delaware also has the proof of the cancel leaf (pages 185-186), marked as such and with with DGR's correction. The British Library proofs have another copy of revise proofs for this signature (dated 3 May).
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https://www.arxiv-vanity.com/papers/1501.02490/
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math
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Finsler-like structures from Lorentz-breaking classical particles
A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.
In recent years, interest in the possibility of Lorentz violation in nature has blossomed. A valuable framework for the study of such deviations from the exact predictions of relativity is the Standard-Model Extension, or SME, which provides a systematic accounting of hypothesized symmetry-breaking background fields at the level of the fundamental particles in Minkowski space 07dcak ; 08dcak and in curved spacetime 04grav ; 06Bailey . For a recent review, see Ref. 14jtReview . The focus of this work is on the behavior of classical particles in spacetime with Lorentz violation. This classical limit is relevant to the study of wave packets, macroscopic bodies, and relativistic scattering, among other things.
An ambitious goal would be to provide equations for classical systems moving under the effects of gravity, while interacting with each other, or with an external electromagnetic field, or with both. Significant progress towards this goal has been made in a general treatment of matter-gravity couplings in the presence of Lorentz violation 11Tasson , which includes a detailed study of the dynamics of a test body in the spin-independent limit of Lorentz violation. Based on this, atomic wave packets in gravitational free fall have been used as test bodies to investigate the Einstein equivalence principle with unprecedented precision 11HohenseeChuEtal , and related work has placed constraints on SME coefficients by considering atomic systems as classical bound states 13Hohensee . Alternatively, intrinsic spin can be highly amplified by atomic polarization, providing access to other combinations of Lorentz-breaking matter-gravity couplings. This has led to innovative experimental tests of Lorentz symmetry using the atomic comagnetometer and the torsion pendulum 12Tasson ; 10Romalis ; 10Panjwani . A recent work has explored classical motion with spin-dependent isotropic Lorentz violation 14SchreckMinimal . Tests of fundamental physics with macroscopic systems in curved spacetime with Lorentz violation pose major technical challenges, and, consequently, the majority of the limits on coefficients for Lorentz violation have been attained in the flat-spacetime limit 08tables . Nevertheless, searches for novel matter-gravity couplings are well justified given that some effects could be accessible only through gravitational couplings 09akjtPRL .
A practical approach to understanding classical behavior with Lorentz breaking is to consider, as an intial step, the flat spacetime limit in the absence of any potential. This eliminates complications due to curvature, removes the complexities of position dependence in the SME coefficients, and allows existing results from the flat-spacetime SME in field theory to be used directly. The particle trajectory follows from variation of the action , where the function is independent of position . In the resulting equation of motion, the velocity is the derivative of position with respect to the trajectory parameter . To ensure that the physics arising from the action is independent of the parametrization, the Lagrange function must be homogeneous of degree one in the velocity . The parameter can be chosen as the proper time, but other choices may be more convenient 10classical . The basic goal is then to find the classical Lagrange function for a particle of mass propagating at velocity in Minkowski spacetime with constant background coefficients controlling Lorentz-breaking effects. The validity of the classical limit is established by ensuring that the dispersion relation matches that of the fermion in the field theory, which is known exactly in closed form 13akmmNonmin . For simplicity, the present work is restricted to the minmal-SME limit, for which the eight relevant controlling coefficients are , , , , , , , and , and the dispersion relation is given by Eq. (14) of Ref. causality or, equivalently, by Eq. (1) of Ref. 10classical .
A method for finding the general exists 10classical , and is relevant for minimal and nonminimal Lorentz violation 14Schreck . It involves finding a polynomial equation in based on the dispersion relation, the wave-packet motion, and the homogeneous form of the Lagrange function. The multiple roots reflect the spin up, spin down, matter, and antimatter states of the Dirac system. This method can be challenging to apply in the case of dispersion relations that are of higher order than quadratic in the momentum. For the special case of dispersion relations that are quadratic in the momentum, there exists a template that allows the corresponding Lagrange function to be deduced immediately 10classical .
To introduce the ideas and notation, a brief review of the quadratic template will be useful. Dispersion relations with quadratic dependence on the momentum can be put into the form
where , , and are constants that can be viewed as a slightly modified identity , a momentum shift, and a modified mass. Matrix notation is used where possible, and transposes of single-index objects are left to be inferred from the context. For example, the first term might be written in stricter matrix notation, or using indices. Raising and lowering is done with the Minkowski metric with signature . In the Lorentz-preserving limit, , , and , so the relation becomes . Note that is always invertible, since Lorentz violation is assumed minuscule. As an example, a particle propagating in the and background has dispersion relation of this quadratic type,
The mass subscript takes into account the possibility that the mass enters differently for each Lorentz-breaking background. The Lagrange function corresponding to the dispersion relation (1) is
For the example corresponding to Eq. (2), follows with no difficulty. Ref. 10classical includes a detailed discussion of this quadratic template and further examples. Note, for example, that describes the antiparticle after reinterpretation.
One way to lift the Minkowski-space results into the gravitational context is to employ minimal coupling. This implies introducing dependence on position , thereby promoting the Minkowski metric to a pseudo-Riemann metric , and converting the SME coefficients into functions of position. The resulting Lagrange function depends on both position and velocity and describes a classical particle moving under the influence of gravity and subject to Lorentz breaking. The geodesics of the particle follow by applying the Euler-Lagrange equations. These ideas form the backdrop to the work presented here.
Numerous parallels exist between structures for Lorentz-breaking classical point particles in spacetime and those of Finsler and pseudo-Finsler geometries. Some of the broad literature relevant in the present context includes Refs. 18Finsler ; 05bcs ; 03ShenZermelo ; 04BRS ; 06Bogoslovsky ; 11pfeifer ; 11Vacaru ; 12Laemmerzahl ; 13mjms ; 14Silva ; 11Romero ; 14Kouretsis . The resemblances allow results in the existing mathematical literature to be applied in some cases, suggest paths to categorizing types of classical Lorentz violation, and may provide an alternative geometrical framework that admits explicit Lorentz violation consistently 04grav . Note that the signature of the underlying metric has a strong impact on the geometry. In particular, the results for Finsler manifolds, which have Riemann signature, do not necessarily carry over into pseudo-Finsler ones. However, some ties between the two signatures can be made using Wick rotation or other procedures. Recent work has highlighted the link between the Randers space 41Randers and the SME background, identified a calculable Finsler structure based on the SME background 11akfinsler , and found others related to the SME coefficient 12bipartite . Lagrange functions to be presented below offer avenues for additional SME-based Finsler and pseudo-Finlser structures.
There are two main sets of ideas presented. The first new result of this work is a quartic template for finding classical Lagrange functions corresponding to a variety of quartic dispersion relations in flat spacetime. This extends the existing template for the case of quadratic dispersion relations discussed above, and is presented in Section II. For dispersion relations that fit the template, can be found without the contortions of the general method 10classical , which include eliminating momentum variables from a system of equations and factoring a high-order polynomial. Several examples involving single and multiple background fields are discussed in Section III.
The second set of results are mappings between classical systems with Lorentz violation. It is a well-established principle that physical results must be unaltered under coordinate changes and field redefinitions. Consequently, some combinations of coefficients in the SME are unobservable and can be mapped into others. In the fermion sector, literature on this topic includes Refs. 07dcak ; 08dcak ; 04grav ; 11Tasson ; 13akmmNonmin ; 10Altschul ; 06Lehnert ; 02DCPMD . A first approach to the question of mappings, discussed in Section IV, is to look at isomorphisms between classical systems limited to leading order in Lorentz violation. Essentially, this translates established field-redefinition results in the quantum theory into corresponding results in the classical approach. Three particular mappings are relevant, between the and fields, between the field and the axial components of , and between the and fields. The second approach asks a more challenging question, whether these three maps can be established between the exact classical systems. The finding, in section IV, is that exact many-to-one correspondences can be set up, taking the one field together with a second auxiliary SME field, onto the other. The choice of auxiliary field is not unique, and, in addition, mass redefinitions are required.
Ii Classical Lagrangians for quartic dispersion relations
The new result presented here is a method for finding classical Lagrange functions corresponding to dispersion relations that are quartic in the momentum and satisfy a particular idempotent condition on the background fields.
Consider a single massive particle in Minkowski spacetime, with quartic dispersion relation
where , is small, constant, and vanishes in the Lorentz-preserving limit. Note that the quadratic-template dispersion relation (1) is recovered by setting . Limiting attention to dispersion relations of this form (4) with the idempotent condition
where is a real constant, the Lagrange function is
Equations (4), (5), and (6) provide a template for finding various Lagrange functions with the bipartite form 11akfinsler . The idea is to start from a given quartic dispersion relation that fits the form (4), match coefficients to get the quantities , , , , and arrive at the result (6) if condition (5) holds.
As an initial example, consider a fermion in an SME background controlled by the and coefficients. The dispersion relation can be written
a result found earlier found using other techniques 10classical .
Equation (6) can be verified by extracting the canonical momentum from the lagrangian and then eliminating the velocity from these four equations. This amounts to imposing three conditions, and the remaining equation constraining the momenta is the dispersion relation (4). To give some details, note that the relationship between the canonical momentum
and the -velocity is controlled by the quantities , and , and . Evaluating and with the aid of (5) gives
The velocity dependence appears as in both and can be eliminated by substitution to get (4).
Iii Examples of classical Lagrange functions
iii.1 Case of restricted antisymmetric
The fermion-sector coefficient has two indices and is traceless. Denoting the symmetric part by , the restriction to the antisymmetric components is made by setting . Using this antisymmetric to establish conventions, the dual is defined by with . The standard observer invariants and for antisymmetric tensors are defined
where the subscript identifies the relevant tensor.
The dispersion relation for the antisymmetric coefficient is found to be
where is obtained by matrix multiplication.
Comparing coefficients with Eq. (4) gives , , , and . The identities and can be used to verify the antisymmetric-tensor result
valid for sufficiently small . Using this expression, note that satisfies the projective condition (5) if the restriction is made. Evaluation of yields
Substituting these results into (6), the classical Lagrange function for the restricted antisymmetric coefficient is found:
The Lagrange function for , which has a bipartite structure with perturbations occurring in both square roots, has been studied in Ref. 12dcpmd using a different approach.
iii.2 Combining or with antisymmetric
The classical Lagrange function for the coefficient 11akfinsler , contained in (8), has bipartite form echoed by for with the restriction 10classical . Using the quartic template, the Lagrange functions that combine the antisymmetric coefficient with each of these can be deduced. In these cases, the dispersion relation takes the form
where is a matrix satisfying the idempotent condition . For the background, with , and, for the restricted background, with . Equation (17) fits the quartic dispersion relation template (4) and matching coefficients yields , , , and . Making use of the idempotent condition, it follows that satisfies condition (5) with . The result (6) can be applied, leading to
For small , the inverses in these expressions exist and are found from (14) and
The Lagrange function (18) for and antisymmetric describes a classical particle in a Lorentz-breaking background with ten independent degrees of freedom: four from the components of and six from the antisymmetric components of . In the case of (19), there are eleven independent components breaking Lorentz symmetry: six from each of the two antisymmetric tensors, with a reduction of one due to the condition.
iii.3 Axial and Trace components of the coefficient
Using notation from Ref. 12fittante , the coefficient has a unique decomposition where the axial part and the trace part have components each, and the mixed-symmetry part has components.
The dispersion relation for the coefficient is causality
where , and the definitions of and follow the convention in Eq. (12), , and .
Applying the constraint , attention is limited to cases where only the axial and trace components are nontrivial. These can be expressed in terms of -vectors,
and, together with the following tensor containing information about the momentum,
can be used to simplify the dispersion relation (21). It is found that as a result of the total antisymmetry of . To evaluate and , first note that
Substitution into the expression for is aided by the identities
and substitution into the expression for is facilitated by the identities
The dispersion relation (21) for the axial and trace components of takes the form
The last two terms are quartic in the momentum and vanish if either or . In these limits, the form matches the template (4).
To find the Lagrange function for the special case where only the trace components of are nonzero, the axial vector in (28) is set to zero yielding the quadratic expression , where with inverse , and . The Lagrange function is found using the template (3) with :
Note that the Finsler structure discussed in Ref. 89Beil has a similar structure if restricted to a single tangent space.
The Lagrange function for the coefficient with only axial components can be found by setting in (28). A match with the template dispersion relation (4) can be achieved with , , , and . For small , the inverse exists. The idempotent property (5) can be confirmed after evaluating , and it is found that . The resulting Lagrange function for axial is
As with Eq. (16), this Lagrange function has a bipartite form with SME coefficients in both the square roots. It is interesting to compare it with the Lagrange function contained in (8). In the quantum context, a field redefinition relates to at leading order. In the next section, this relationship is investigated in the classical-particle context. Also note that the couplings of or coefficients to fermions have the same form as matter-torsion couplings in Riemann-Cartan gravity, and this has allowed results from Lorentz tests to place tight constraints on spacetime torsion 08torsion ; 13NeutronSpin .
The Lagrange functions presented in this section involve uniform Lorentz-breaking background fields in Minkowski spacetime. In this limit, classical particles undergo no acceleration, because of the homogeneity of the Lagrange function and the absence of position or parameter dependence 10classical . This means constant Lorentz violation is unobservable with a single point particle. However, comparison of systems with distinct properties makes physical effects measurable. In curved spacetime, where the coefficients for Lorentz violation depend on position and time, the Lagrange functions can be viewed as Finsler-like structures. The corresponding particles follow geodesics controlled by the background fields and the curvature of the space. Geodesic equations for the and backgrounds are known 11akfinsler ; 12bipartite , and those for others such as the ones presented in this section are left for future work. The important feature of the present Lagrange functions is that they correspond to known SME dispersion relations, so their further study in the Finsler context is of definite interest.
Iv Field redefinitions and maps
In the SME, the freedom to redefine fields implies that some Lorentz-breaking fields can be mapped into others. The focus here is on the three mappings that pair the dimension- operators in the minimal SME with dimension- operators at leading order in the quantized theory. At first order in Lorentz violation, they are implemented by the replacements
In this section, each of these correspondences is verified in the case of the relevant dispersion relations and classical Lagrange functions at leading order in Lorentz violation. A second, more challenging, issue is also addressed in each case, that of whether mappings between the classical systems that hold exactly at all orders in Lorentz violation are possible. The finding is that this can be done as a many-to-one map by introducing an appropriate auxiliary background field in each case.
iv.1 Relating to antisymmetric
First, consider mappings between the dispersion relations at leading order in the Lorentz-breaking and fields. The dispersion relation for can be found from Eq. (17) with appropriate substitutions for and ,
while the dispersion relation for is given in Eq. (13). To express (34) at first order in Lorentz violation, take the square root of both sides, and cross out the second-order term. The resulting expression appears in Table 1 in the first entry of the second column. There is no subscript on because a mass correction can only enter at second order. Immediately below this in the table is the first-order limit of the dispersion relation (13) for , which is found in a similar way. It follows by inspection that (31), which also appears in the initial column of the table, relates these first-order dispersion relations.
Next, consider mappings between the corresponding Lagrange functions at first order in Lorentz violation. Noting that to first order in , Eq. (16) becomes
The Lagrange function for follows from Eq. (19) with ,
|Field map||First-order dispersion relations||First-order Lagrange functions|
A natural progression is to seek a mapping between the full dispersion relations (34) and (13), without taking the leading-order limits. The replacement (31) is insufficient to do this. However, if the dispersion relation is augmented to include the antisymmetric coefficient as in (17) with , an exact map to the dispersion relation (13) is indeed possible. It is implemented by the replacements
Note that the correspondence implies . The identity means the first expression in (37) can be written .
This result shows that a mass redefinition is part of the morphism relating the different Lorentz-breaking systems. Although does not need to vanish, it can be imposed without affecting the replacement , thereby reducing by one the number of independent auxiliary variables needed. With this assumption, , , and each have five independent variables, and the map (37) can be viewed as a projection from the -dimensional space to the -dimensional space . Since the mapping is many-to-one, it is not invertible.
iv.2 Relating to
To investigate the classical version of the mapping (32), the first-order dispersion relations for and are needed. The expression for is found by setting in (7) and keeping only the first order terms in . The result appears in Table 1, row two, column two. Immediately below it is the dispersion relation for the background, obtained from the exact result (28) with ,
by taking the first-order limit. Inspection of the entries in the table shows that (32) maps the two leading-order dispersion relations.
To verify the mapping (32) at the level of the classical Lagrange functions, note the following. The Lagrange function (8) with involves a correction to the conventional Lorentz-preserving Lagrange function that is already first order in Lorentz violation , and appears in Table 1, row two, column three. The first-order approximation to the Lagrange function (30),
appears below it in the table. By inspection of the table entries, it can readily be seen that the replacement (32) establishes an isomorphism between the and Lagrange functions at first order.
With the use of an additional SME background field, , an exact mapping can be established between the all-orders dispersion relation for and ,
and that of , given in Eq. (38). The map is defined by the replacements
As with the morphism in (37), this map involves a mass redefinition and an auxiliary field. Note that the auxiliary has the same number of independent components as and . This property is also true for the auxiliary field used in mapping from to . The morphism (41) is many-to-one, taking the -dimensional space to the -dimensional space .
iv.3 Relating to
The dispersion relations for a particle in the background or in the background are
The first-order approximations given in row three, column two of Table 1, follow by dropping the subscripts on the masses and keeping only terms that are linear in Lorentz violation. It follows by inspection of these entries in the table that the replacement (33) implements the map between the two leading-order dispersion relations.
Table 1 contains in row three, column three since it is already first-order in Lorentz violation. Immediately below it is the first-order approximation to . Inspection of these entries shows that the replacement (33) maps the leading-order Lagrange functions into each other, as it does in the quantum case.
Next, consider the question of finding an exact mapping between the and systems, linking the dispersion relations (42) and (43), and the Lagrange functions (44) and (45). As seen in the earlier examples involving the maps (37) and (41), this can be done with the assistance of an auxiliary field. The auxiliary field is not unique, and to confirm this, exact mappings are given using two different auxiliary fields.
A first mapping to the full dispersion relation (43) may be established by using as the auxiliary field. To find the dispersion relation for the combined and coefficients, the steps leading to (28) can be repeated with a few modifications, including the assumption . The result is
where is defined by . An exact map from this dispersion relation for and to that for , Eq. (43), is found to be
To verify that this map works at the level of the classical Lagrange functions, is needed. While the dispersion relation (46) is quartic in the momentum, it does not appear to fit the quartic template in Sec. II, and this Lagrange function is unknown at present.
Having seen that can serve as an auxiliary field to implement an exact map from the system to the system, the next point to be made is that this auxiliary is not unique. To demonstrate this, the field is used as an alternative auxiliary to implement the to mapping. The dispersion relation for the combined and coefficients is given in Eq. (2), and an exact mapping to (43) is made using the replacements
Note the properties seen in the (37) and (41) morphisms are echoed in both cases here. Exact mappings from to can be constructed with the aid of an auxiliary field with the same number of components as and . In (47) this is the field, and in (48) it is the field, demonstrating that the auxiliary is not unique. The map also involves a mass redefinition. It is many-to-one, and takes variables consisting of a mass, the four components , and the four components of the auxiliary field, to the variables .
V Summary and Discussion
The main result presented in section II is a classical Lagrange function in Minkowski space that describes a massive particle in the context of minimal Lorentz violation with certain quartic dispersion relations. The result is given in the form of a template: any particle with dispersion relation matching (4), and with Lorentz-breaking background satisfying the idempotent condition (5), has Lagrange function given in equation (6).
The quartic template is used to provide explicit Lagrange functions for several minimal-SME Lorentz-breaking backgrounds that have not appeared in the literature to date. The results for the functions , and , show that Lorentz violation matching the quartic template and combining more than one background field can be studied with relative ease. Earlier work 10classical provided a template for Lagrange functions with quadratic dispersion relations and included the explicit form of , which has twelve independent components for the background fields. The quartic examples in this work provide explicit Lagrange functions in (18) and (19) with ten and eleven independent background-field components respectively. The Lagrange function involving the four trace components of the SME background, denoted , is given in equation (29). In the case of Lorentz violation by the axial components of the background, appears in equation (30). Finding the classical Lagrange function for all the 24 independent components of the background field remains an open challenge.
In section IV, mappings between SME background fields have been studied. The leading-order isomorphisms between and , between and axial , and between and are known in the fundamental field-theoretic formalism to arise because of the freedom to redefine fields and coordinates. The same leading-order correspondences are confirmed in the classical limit, and summarized in Table 1.
The second aspect studied in section IV is exact mappings between the above minimal-SME background fields. Isomorphisms are not expected, because each SME field at the level of the fundamental Lagrange function controls a different field operator. It is found that exact projective mappings do exist, in each case taking more than one SME field onto another SME field. For the three leading-order mappings already discussed, exact projective mappings are established with the aid of a second SME background field, which at least doubles the number of independent field components in the domain space. A feature of these projective maps is a rescaling of the mass that depends on the fields. This means the mass can be considered an independent component on the same footing as the field components. For the to map, the antisymmetric components of the background provide an auxiliary field, so that the domain with has dimension 12 and maps to the range with , of dimension 6. For the to map, the field can be used as an auxiliary and the projection takes the -dimensional domain onto the -dimensional range . The auxiliary field used in these projective mappings is not unique, as can be seen in the case of the to map, for which is one possible auxiliary and , the trace component of , is another. This gives a projection from the -dimensional domain space or onto the -dimensional range space .
The quartic template in Eqs. (4), (5), and (6) is applicable in a limited set of cases and a natural question is how to generalize it. Staying within the minimal SME, one direction for further investigation would be to seek ways to weaken the idempotent condition (5). This would be useful, for example, in addressing the Lagrange functions and , where the respective dispersion relations, (40) and (46), match (4), but the background fields do not satisfy the idempotent condition (5). Another goal in the minimal SME context would be to broaden the template to more general quadratic dispersion relations, covering for example equation (28), the case of limited to axial and trace components. The most ambitious goal in the minimal SME would be to find the Lagrange function corresponding to the full dispersion relation appearing in Ref. causality . This is likely to be a very long and unenlightening expression, given that even the case of for a general background with nonzero is known to be highly complex 10classical . There are numerous options for further development. Other investigations might include methods for finding Lagrange functions for nonminimal Lorentz violation 13akmmNonmin , or for interacting particles.
The main motivation of this work is to provide new Finsler-like structures that are rooted in the Lorentz-breaking background fields of the minimal SME. The new Minkowski-space classical Lagrange functions found here can be used as the basis for Finsler and pseudo-Finsler structures in future work. They hold the promise of providing insights into the geometrical nature of Lorentz violation in classical systems and of gaining new insights into the physical content based on existing approaches in Finsler geometry.
Acknowledgements.Thanks to the Indiana University Center for Spacetime Symmetries for hospitality while this research was undertaken.
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QQS1013 ELEMENTARY STATISTIC CHAPTER 2 DESCRIPTIVE STATISTICS 2.1Introduction 2.2Organizing and Graphing Qualitative Data 2.3Organizing and Graphing Quantitative Data 2.4Central Tendency Measurement 2.5Dispersion Measurement 2.6Mean, Variance and Standard Deviation for Grouped Data 2.7Measure of Skewness OBJECTIVES After completing this chapter, students should be able to: Create and interpret graphical displays involve qualitative and quantitative data. Describe the difference between grouped and ungrouped frequency distribution, frequency and relative frequency, relative frequency and cumulative relative frequency. Identify and describe the parts of a frequency distribution: class boundaries, class width, and class midpoint. Identify the shapes of distributions. Compute, describe, compare and interpret the three measures of central tendency: mean, median, and mode for ungrouped and grouped data. Compute, describe, compare and interpret the two measures of dispersion: range, and standard deviation (variance) for ungrouped and grouped data. Compute, describe, and interpret the two measures of position: quartiles and interquartile range for ungrouped and grouped data. Compute, describe and interpret the measures of skewness: Pearson Coefficient of Skewness. Introduction Raw data - Data recorded in the sequence in which there are collected and before they are processed or ranked. Array data - Raw data that is arranged in ascending or descending order. Example 1 Here is a list of question asked in a large statistics class and the “raw data” given by one of the students: What is your sex (m=male, f=female)? Answer (raw data): m How many hours did you sleep last night? Answer: 5 hours Randomly pick a letter – S or Q. Answer: S What is your height in inches? Answer: 67 inches What’s the fastest you’ve ever driven a car (mph)? Answer: 110 mph Example 2 Quantitative raw data Qualitative raw data These data also called ungrouped data 2.2Organizing and Graphing Qualitative Data 2.2.1Frequency Distributions/ Table 2.2.2Relative Frequency and Percentage Distribution 2.2.3Graphical Presentation of Qualitative Data 2.2.1Frequency Distributions / Table A frequency distribution for qualitative data lists all categories and the number of elements that belong to each of the categories. It exhibits the frequencies are distributed over various categories Also called as a frequency distribution table or simply a frequency table. The number of students who belong to a certain category is called the frequency of that category. 457200185420 Relative Frequency and Percentage Distribution A relative frequency distribution is a listing of all categories along with their relative frequencies (given as proportions or percentages). It is commonplace to give the frequency and relative frequency distribution together. Calculating relative frequency and percentage of a category Relative Frequency of a category = Frequency of that category Sum of all frequencies Percentage = (Relative Frequency)* 100 Example 3 A sample of UUM staff-owned vehicles produced by Proton was identified and the make of each noted. The resulting sample follows (W = Wira, Is = Iswara, Wj = Waja, St = Satria, P = Perdana, Sv = Savvy): WWPIsIsPIsWStWjIsWWWjIsWWIsWWjWjIsWjSvWWWWjStWWjSvWIsPSvWjWjWWStWWWWStStPWjSv Construct a frequency distribution table for these data with their relative frequency and percentage. Solution: CategoryFrequencyRelative FrequencyPercentage (%)Wira1919/50 = 0.380.38*100= 38Iswara80.1616Perdana40.088Waja100.2020Satria50.1010Savvy40.088Total501.00100 Graphical Presentation of Qualitative Data Bar Graphs A graph made of bars whose heights represent the frequencies of respective categories. Such a graph is most helpful when you have many categories to represent. Notice that a gap is inserted between each of the bars. It has =>simple/ vertical bar chart => horizontal bar chart => component bar chart => multiple bar chart Simple/ Vertical Bar Chart To construct a vertical bar chart, mark the various categories on the horizontal axis and mark the frequencies on the vertical axis Refer to Figure 2.1 and Figure 2.2, 27432004445 Figure 2.1 Figure 2.2 Horizontal Bar Chart To construct a horizontal bar chart, mark the various categories on the vertical axis and mark the frequencies on the horizontal axis. Example 4: Refer Example 3, left15240
Figure 2.3 Another example of horizontal bar chart: Figure 2.4 center635 Figure 2.4: Number of students at Diversity College who are immigrants, by last country of permanent residence Component Bar Chart To construct a component bar chart, all categories is in one bar and every bar is divided into components. The height of components should be tally with representative frequencies. Example 5 Suppose we want to illustrate the information below, representing the number of people participating in the activities offered by an outdoor pursuits centre during Jun of three consecutive years. 200420052006Climbing213436Caving101221Walking7585100Sailing363640Total142167191 Solution: Figure 2.5 Mulztiple Bar Chart To construct a multiple bar chart, each bars that representative any categories are gathered in groups. The height of the bar represented the frequencies of categories. Useful for making comparisons (two or more values). Example 6: Refer example 5, center165100Figure 2.6 Another example of horizontal bar chart: Figure 2.7 457200100330 Figure 2.7: Preferred snack choices of students at UUM The bar graphs for relative frequency and percentage distributions can be drawn simply by marking the relative frequencies or percentages, instead of the class frequencies. Pie Chart A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories. An alternative to the bar chart and useful for summarizing a single categorical variable if there are not too many categories. The chart makes it easy to compare relative sizes of each class/category. The whole pie represents the total sample or population. The pie is divided into different portions that represent the different categories. To construct a pie chart, we multiply 360o by the relative frequency for each category to obtain the degree measure or size of the angle for the corresponding categories. Example 7 (Table 2.6 and Figure 2.8): 0482603314700581660 Table 2.6 Figure 2.8 Example 8 (Table 2.7 and Figure 2.9): Movie GenresFrequencyRelative FrequencyAngle SizeComedyActionRomanceDramaHorrorForeignScience Fiction543628282216160.222.214.171.124.110.080.08 360*0.27=97.2o 360*0.18=64.8o360*0.14=50.4o360*0.14=50.4o360*0.11=39.6o360*0.08=28.8o360*0.08=28.8o2001.00360o left24765 Figure 2.9Figure 2.9 Line Graph/Time Series Graph A graph represents data that occur over a specific period time of time. Line graphs are more popular than all other graphs combined because their visual characteristics reveal data trends clearly and these graphs are easy to create. When analyzing the graph, look for a trend or pattern that occurs over the time period. Example is the line ascending (indicating an increase over time) or descending (indicating a decrease over time). Another thing to look for is the slope, or steepness, of the line. A line that is steep over a specific time period indicates a rapid increase or decrease over that period. Two data sets can be compared on the same graph (called a compound time series graph) if two lines are used. Data collected on the same element for the same variable at different points in time or for different periods of time are called time series data. A line graph is a visual comparison of how two variables—shown on the x- and y-axes—are related or vary with each other. It shows related information by drawing a continuous line between all the points on a grid. Line graphs compare two variables: one is plotted along the x-axis (horizontal) and the other along the y-axis (vertical). The y-axis in a line graph usually indicates quantity (e.g., RM, numbers of sales litres) or percentage, while the horizontal x-axis often measures units of time. As a result, the line graph is often viewed as a time series graph Example 9 A transit manager wishes to use the following data for a presentation showing how Port Authority Transit ridership has changed over the years. Draw a time series graph for the data and summarize the findings. YearRidership(in millions)1990199119921993199488.085.075.776.675.4
Solution: The graph shows a decline in ridership through 1992 and then leveling off for the years 1993 and 1994. Exercise 1 The following data show the method of payment by 16 customers in a supermarket checkout line. Here, C = cash, CK = check, CC = credit card, D = debit and O = other. CCKCKCCCDOCCKCCDCCCCKCKCC Construct a frequency distribution table. Calculate the relative frequencies and percentages for all categories. Draw a pie chart for the percentage distribution. The frequency distribution table represents the sale of certain product in ZeeZee Company. Each of the products was given the frequency of the sales in certain period. Find the relative frequency and the percentage of each product. Then, construct a pie chart using the obtained information. Type of ProductFrequencyRelative FrequencyPercentageAngle SizeABCDE13125911 Draw a time series graph to represent the data for the number of worldwide airline fatalities for the given years. Year1990199119921993199419951996No. of fatalities4405109908017325571132 A questionnaire about how people get news resulted in the following information from 25 respondents (N = newspaper, T = television, R = radio, M = magazine). NNRTTRNTMRMMNRNTRMNMTRRNN Construct a frequency distribution for the data. Construct a bar graph for the data. The given information shows the export and import trade in million RM for four months of sales in certain year. Using the provided information, present this data in component bar graph. MonthExportImportSeptemberOctoberNovemberDecember2830322420281714 The following information represents the maximum rain fall in millimeter (mm) in each state in Malaysia. You are supposed to help a meteorologist in your place to make an analysis. Based on your knowledge, present this information using the most appropriate chart and give your comment. StateQuantity (mm)PerlisKedahPulau PinangPerakSelangorWilayah Persekutuan Kuala LumpurNegeri SembilanMelakaJohorPahangTerengganuKelantanSarawakSabah435512163721664100339022387610501255986878456 2.3Organizing and Graphing Quantitative Data 2.3.1Stem and Leaf Display 2.3.2Frequency Distribution 2.3.3Relative Frequency and Percentage Distributions. 2.3.4 Graphing Grouped Data 2.3.5Shapes of Histogram 2.3.6Cumulative Frequency Distributions. Stem-and-Leaf Display In stem and leaf display of quantitative data, each value is divided into two portions – a stem and a leaf. Then the leaves for each stem are shown separately in a display. Gives the information of data pattern. Can detect which value frequently repeated. Example 10 12 9 10 5 12 23 7 13 11 12 31 28 37 6 41 38 44 13 22 18 19 Solution: 09 5 7 6 12 0 2 3 1 2 4 3 8 9 25 3 8 2 36 1 7 8 41 4 Frequency Distributions A frequency distribution for quantitative data lists all the classes and the number of values that belong to each class. Data presented in form of frequency distribution are called grouped data. 0163830 The class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class. Also called real class limit. To find the midpoint of the upper limit of the first class and the lower limit of the second class, we divide the sum of these two limits by 2. e.g.: class boundary Class Width (class size) Class width = Upper boundary – Lower boundary e.g. : Width of the first class = 600.5 – 400.5 = 200 Class Midpoint or Mark
e.g: Constructing Frequency Distribution Tables 1.To decide the number of classes, we used Sturge’s formula, which is c = 1 + 3.3 log n where c is the no. of classes n is the no. of observations in the data set. 2. Class width, This class width is rounded to a convenient number. 3.Lower Limit of the First Class or the Starting Point Use the smallest value in the data set. Example 11 The following data give the total home runs hit by all players of each of the 30 Major League Baseball teams during 2004 season Solution: Number of classes, c = 1 + 3.3 log 30 = 1 + 3.3(1.48) = 5.89 6 class Class width, Starting Point = 135 Table 2.10 Frequency Distribution for Data of Table 2.9 Total Home RunsTallyf135 – 152153 – 170171 – 188189 – 206207 – 224225 – 242|||| |||||||||| |||| ||||||||1025634 Relative Frequency and Percentage Distributions Example 12 (Refer example 11) Table 2.11: Relative Frequency and Percentage Distributions Total Home RunsClass BoundariesRelative Frequency%135 – 152153 – 170171 – 188189 – 206207 – 224225 – 242134.5 less than 152.5152.5 less than 170.5170.5 less than 188.5188.5 less than 206.5206.5 less than 224.5224.5 less than 242.50.33330.06670.166126.96.36.199333.336.6716.67201013.33Sum1.0100% Graphing Grouped Data Histograms A histogram is a graph in which the class boundaries are marked on the horizontal axis and either the frequencies, relative frequencies, or percentages are marked on the vertical axis. The frequencies, relative frequencies or percentages are represented by the heights of the bars. In histogram, the bars are drawn adjacent to each other and there is a space between y axis and the first bar. Example 13 (Refer example 11) 134.5 152.5 170.5 188.5 206.5 224.5 242.5 Figure 2.10: Frequency histogram for Table 2.10 Polygon A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines is called a polygon. Example 13 34290082550 134.5 152.5 170.5 188.5 206.5 224.5 242.5 134.5 152.5 170.5 188.5 206.5 224.5 242.5Figure 2.11: Frequency polygon for Table 2.10 For a very large data set, as the number of classes is increased (and the width of classes is decreased), the frequency polygon eventually becomes a smooth curve called a frequency distribution curve or simply a frequency curve. Figure 2.12: Frequency distribution curve Shape of Histogram Same as polygon. For a very large data set, as the number of classes is increased (and the width of classes is decreased), the frequency polygon eventually becomes a smooth curve called a frequency distribution curve or simply a frequency curve. The most common of shapes are: (i) Symmetric Figure 2.13 & 2.14: Symmetric histograms (ii) Right skewed and (iii) Left skewed Figure 2.15 & 2.16: Right skewed and Left skewed Describing data using graphs helps us insight into the main characteristics of the data. When interpreting a graph, we should be very cautious. We should observe carefully whether the frequency axis has been truncated or whether any axis has been unnecessarily shortened or stretched. Cumulative Frequency Distributions A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class. Example 14: Using the frequency distribution of table 2.11,
Total Home RunsClass BoundariesCumulative Frequency135 – 152153 – 170171 – 188189 – 206207 – 224225 – 242134.5 less than 152.5152.5 less than 170.5170.5 less than 188.5188.5 less than 206.5206.5 less than 224.5224.5 less than 242.51010+2=1210+2+5=1710+2+5+6=2310+2+5+6+3=2610+2+5+6+3+4=30 Ogive An ogive is a curve drawn for the cumulative frequency distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes. Two type of ogive: (i) ogive less than (ii)ogive greater than First, build a table of cumulative frequency. Example 15 (Ogive Less Than) 56633730 – 3940 – 4950 – 5960 - 6970 – 7980 - 8930Number of students (f)TotalEarnings (RM)Earnings (RM) Cumulative Frequency (F)Less than 29.5Less than 39.5Less than 49.5Less than 59.5Less than 69.5Less than 79.5Less than 89.5051117202330 0510152025303529.539.549.559.569.579.589.5EarningsCumulative Frequency Figure 2.17 Example 16 (Ogive Greater Than) 56633730 – 3940 – 4950 – 5960 - 6970 – 7980 - 8930Number of students (f)TotalEarnings (RM) Cumulative Frequency (F)Earnings (RM) 302519131070More than 29.5More than 39.5More than 49.5More than 59.5More than 69.5More than 79.5More than 89.5 0510152025303529.539.549.559.569.579.589.5EarningsCumulative Frequency Figure 2.18 Figure 2.18 2.3.7Box-Plot Describe the analyze data graphically using 5 measurement: smallest value, first quartile (K1), second quartile (median or K2), third quartile (K3) and largest value. Smallest valueLargest value K1 Median K3Largest value K1 Median K3Largest value K1 Median K3Smallest valueSmallest valueFor symmetry data For left skewed data For right skewed data 2.4Measures of Central Tendency 2.4.1 Ungrouped Data (1) Mean (2) Weighted mean (3) Median (4) Mode Grouped Data (1) Mean (2) Median (3) Mode Relationship among mean, median & mode 2.4.1 Ungrouped Data Mean Mean for population data:
Mean for sample data: where: = the sum af all values N = the population size n = the sample size, µ = the population mean = the sample mean Example 17 The following data give the prices (rounded to thousand RM) of five homes sold recently in Sekayang. 158189265127191 Find the mean sale price for these homes. Solution: Thus, these five homes were sold for an average price of RM186 thousand @ RM186 000. The mean has the advantage that its calculation includes each value of the data set. Weighted Mean Used when have different needs. Weight mean :
where w is a weight. Example 18 Consider the data of electricity components purchasing from a factory in the table below: TypeNumber of component (w)Cost/unit (x)12345120050025001000800RM3.00RM3.40RM2.80RM2.90RM3.25Total6000 Solution: Mean cost of a unit of the component is RM2.97 Median Median is the value of the middle term in a data set that has been ranked in increasing order. Procedure for finding the Median Step 1: Rank the data set in increasing order. Step 2: Determine the depth (position or location) of the median. Step 3: Determine the value of the Median. Example 19 Find the median for the following data: 10 5 19 8 3 Solution: (1) Rank the data in increasing order 3 5 8 10 19 (2) Determine the depth of the Median
(3) Determine the value of the median Therefore the median is located in third position of the data set. 3 5 8 10 19 Hence, the Median for above data = 8 Example 20 Find the median for the following data: 10 5 19 8 3 15 Solution: (1) Rank the data in increasing order 35810 15 19
(2) Determine the depth of the Median
(3) Determine the value of the Median Therefore the median is located in the middle of 3rd position and 4th position of the data set. Hence, the Median for the above data = 9 The median gives the center of a histogram, with half of the data values to the left of (or, less than) the median and half to the right of (or, more than) the median. The advantage of using the median is that it is not influenced by outliers. Mode Mode is the value that occurs with the highest frequency in a data set. Example 21 1. What is the mode for given data? 77 69 74 81 71 68 74 73 2. What is the mode for given data? 77 69 68 74 81 71 68 74 73 Solution: 1. Mode = 74 (this number occurs twice): Unimodal 2.Mode = 68 and 74: Bimodal A major shortcoming of the mode is that a data set may have none or may have more than one mode. One advantage of the mode is that it can be calculated for both kinds of data, quantitative and qualitative. Grouped Data Mean Mean for population data: Mean for sample data: Where the midpoint and f is the frequency of a class. Example 22 The following table gives the frequency distribution of the number of orders received each day during the past 50 days at the office of a mail-order company. Calculate the mean. Numberof orderf10 – 1213 – 1516 – 1819 – 214122014 n = 50 Solution: Because the data set includes only 50 days, it represents a sample. The value of is calculated in the following table: Numberof orderfxfx10 – 1213 – 1516 – 1819 – 2141220141114172044168340280 n = 50 = 832 The value of mean sample is: Thus, this mail-order company received an average of 16.64 orders per day during these 50 days. Median Step 1: Construct the cumulative frequency distribution. Step 2: Decide the class that contain the median. Class Median is the first class with the value of cumulative frequency is at least n/2. Step 3: Find the median by using the following formula: Where: n = the total frequency F = the total frequency before class median i = the class width = the lower boundary of the class median = the frequency of the class median Example 23 Based on the grouped data below, find the median: Time to travel to workFrequency1 – 1011 – 2021 – 3031 – 4041 – 508141297 Solution: 1st Step: Construct the cumulative frequency distribution Time to travel to workFrequency Cumulative Frequency1 – 1011 – 2021 – 3031 – 4041 – 508141297822344350 Class median is the 3rd class So, F = 22, = 12, = 21.5 and i = 10 Therefore, Thus, 25 persons take less than 24 minutes to travel to work and another 25 persons take more than 24 minutes to travel to work. Mode Mode is the value that has the highest frequency in a data set. For grouped data, class mode (or, modal class) is the class with the highest frequency. To find mode for grouped data, use the following formula: Where: is the lower boundary of class mode is the difference between the frequency of class mode and the frequency of the class before the class mode is the difference between the frequency of class mode and the frequency of the class after the class mode i is the class width Example 24 Based on the grouped data below, find the mode Time to travel to workFrequency1 – 1011 – 2021 – 3031 – 4041 – 508141297 Solution: Based on the table, = 10.5, = (14 – 8) = 6, = (14 – 12) = 2 and i = 10 We can also obtain the mode by using the histogram; Figure 2.19 2.4.3 Relationship among mean, median & mode As discussed in previous topic, histogram or a frequency distribution curve can assume either skewed shape or symmetrical shape. Knowing the value of mean, median and mode can give us some idea about the shape of frequency curve. For a symmetrical histogram and frequency curve with one peak, the value of the mean, median and mode are identical and they lie at the center of the distribution.(Figure 2.20) 2971800961390228600951865For a histogram and a frequency curve skewed to the right, the value of the mean is the largest that of the mode is the smallest and the value of the median lies between these two. Figure 2.20: Mean, median, and mode for a symmetric histogram and frequency distribution curve Figure 2.21: Mean, median, and mode for a histogram and frequency distribution curve skewed to the right 2971800168275 For a histogram and a frequency curve skewed to the left, the value of the mean is the smallest and that of the mode is the largest and the value of the median lies between these two. Figure 2.22: Mean, median, and mode for a histogram and frequency distribution curve skewed to the left 2.5Dispersion Measurement The measures of central tendency such as mean, median and mode do not reveal the whole picture of the distribution of a data set. Two data sets with the same mean may have a completely different spreads. The variation among the values of observations for one data set may be much larger or smaller than for the other data set. 2.5.1 Ungrouped data (1) Range (2) Standard Deviation 2.5.2 Grouped data (1) Range (2) Standard deviation 2.5.3 Relative Dispersion Measurement Ungrouped Data Range RANGE = Largest value – Smallest value Example 25: Find the range of production for this data set, Solution: Range = Largest value – Smallest value = 267 277 – 49 651 = 217 626 Disadvantages: being influenced by outliers. Based on two values only. All other values in a data set are ignored. Variance and Standard Deviation Standard deviation is the most used measure of dispersion. A Standard Deviation value tells how closely the values of a data set clustered around the mean. Lower value of standard deviation indicates that the data set value are spread over relatively smaller range around the mean. Larger value of data set indicates that the data set value are spread over relatively larger around the mean (far from mean). Standard deviation is obtained the positive root of the variance: VarianceStandard DeviationPopulationSample Example 26 Let x denote the total production (in unit) of company CompanyProductionABCDE62931267534 Find the variance and standard deviation, Solution: CompanyProduction (x)x2ABCDE629312675343844864915 87656251156 1156
Since s2 = 1182.50; Therefore, The properties of variance and standard deviation: (1) The standard deviation is a measure of variation of all values from the mean. (2)The value of the variance and the standard deviation are never negative. Also, larger values of variance or standard deviation indicate greater amounts of variation. (3)The value of s can increase dramatically with the inclusion of one or more outliers. (4) The measurement units of variance are always the square of the measurement units of the original data while the units of standard deviation are the same as the units of the original data values. Grouped Data Range Range = Upper bound of last class – Lower bound of first class ClassFrequency41 – 5051 – 6061 – 7071 – 8081 – 9091 - 10013713106 Total40 Upper bound of last class = 100.5 Lower bound of first class = 40.5 Range = 100.5 – 40.5 = 60 Variance and Standard Deviation VarianceStandard DeviationPopulationSample Example 27 Find the variance and standard deviation for the following data: No. of orderf10 – 1213 – 1516 – 1819 – 214122014 Totaln = 50 Solution: No. of orderfxfxfx210 – 1213 – 1516 – 1819 – 2141220141114172044168340280484235257805600 Totaln = 5085714216 Variance, Standard Deviation,
Thus, the standard deviation of the number of orders received at the office of this mail-order company during the past 50 days is 2.75. 2.5.3 Relative Dispersion Measurement To compare two or more distribution that has different unit based on their dispersion Or To compare two or more distribution that has same unit but big different in their value of mean. Also called modified coefficient or coefficient of variation, CV.
Example 28 Given mean and standard deviation of monthly salary for two groups of worker who are working in ABC company- Group 1: 700 & 20 and Group 2 :1070 & 20. Find the CV for every group and determine which group is more dispersed. Solution: The monthly salary for group 1 worker is more dispersed compared to group 2. Measure of Position Determines the position of a single value in relation to other values in a sample or a population data set. Ungrouped Data Quartiles Interquatile Range Grouped Data Quartile Interquartile Range Quartiles Quartiles are three summary measures that divide ranked data set into four equal parts. The 1st quartiles – denoted as Q1 The 2nd quartiles – median of a data set or Q2 The 3rd quartiles – denoted as Q3 Example 29 Table below lists the total revenue for the 11 top tourism company in Malaysia 109.7 79.9 21.2 76.4 80.2 82.1 79.4 89.3 98.0 103.5 86.8 Solution: Step 1: Arrange the data in increasing order 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Step 2: Determine the depth for Q1 and Q3 Step 3: Determine the Q1 and Q3 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Q1 = 79.9 Q3 = 103.5 Table below lists the total revenue for the 12 top tourism company in Malaysia 109.7 79.9 74.1 121.2 76.4 80.2 82.1 79.4 89.3 98.0 103.5 86.8 Solution: Step 1: Arrange the data in increasing order 74.1 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Step 2: Determine the depth for Q1 and Q3 Step 3: Determine the Q1 and Q3 74.1 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Q1 = 79.4 + 0.25 (79.9 – 79.4) = 79.525 Q3 = 98.0 + 0.75 (103.5 – 98.0) = 102.125 Interquartile Range The difference between the third quartile and the first quartile for a data set. IQR = Q3 – Q1 Example 30 By referring to example 29, calculate the IQR. Solution: IQR = Q3 – Q1 = 102.125 – 79.525 = 22.6 2.6.2 Grouped Data Quartiles From Median, we can get Q1 and Q3 equation as follows:
; Example 31 Refer to example 23, find Q1 and Q3 Solution: 1st Step: Construct the cumulative frequency distribution Time to travel to workFrequency Cumulative Frequency1 – 1011 – 2021 – 3031 – 4041 – 508141297822344350 2nd Step: Determine the Q1 and Q3 Class Q1 is the 2nd class Therefore, Class Q3 is the 4th class Therefore, Interquartile Range IQR = Q3 – Q1 Example 32: Refer to example 31, calculate the IQR. Solution: IQR = Q3 – Q1 = 34.3889 – 13.7143 = 20.6746 Measure of Skewness To determine the skewness of data (symmetry, left skewed, right skewed) Also called Skewness Coefficient or Pearson Coefficient of Skewness If Sk +ve right skewed If Sk -ve left skewed If Sk = 0 symmetry If Sk takes a value in between (-0.9999, -0.0001) or (0.0001, 0.9999) approximately symmetry. Example 33 The duration of cancer patient warded in Hospital Seberang Jaya recorded in a frequency distribution. From the record, the mean is 28 days, median is 25 days and mode is 23 days. Given the standard deviation is 4.2 days. What is the type of distribution? Find the skewness coefficient Solution: This distribution is right skewed because the mean is the largest value So, from the Sk value this distribution is right skewed. Exercise 2: A survey research company asks 100 people how many times they have been to the dentist in the last five years. Their grouped responses appear below. Number of VisitsNumber of Responses0 – 4165 – 92510 – 144815 – 1911 What are the mean and variance of the data? A researcher asked 25 consumers: “How much would you pay for a television adapter that provides Internet access?” Their grouped responses are as follows: Amount ($)Number of Responses0 – 992100 – 1992200 – 2493250 – 2993300 – 3496350 – 3993400 – 4994500 – 9992 Calculate the mean, variance, and standard deviation. The following data give the pairs of shoes sold per day by a particular shoe store in the last 20 days. 85 90 89 70 79 80 83 83 75 76 89 86 71 76 77 89 70 65 90 86 Calculate the mean and interpret the value. median and interpret the value. mode and interpret the value. standard deviation. 4. The followings data shows the information of serving time (in minutes) for 40 customers in a post office: 2.04.52.52.188.8.131.52.83.22.94.03.03.82.52.33.184.108.40.206.220.127.116.11.18.104.22.168.22.214.171.124.02.73.92.92.126.96.36.199.4 Construct a frequency distribution table with 0.5 of class width. Construct a histogram. Calculate the mode and median of the data. Find the mean of serving time. Determine the skewness of the data. Find the first and third quartile value of the data. Determine the value of interquartile range. 5. In a survey for a class of final semester student, a group of data was obtained for the number of text books owned.
Number of studentsNumber of text book owned1291115108553210
Find the average number of text book for the class. Use the weighted mean. The following data represent the ages of 15 people buying lift tickets at a ski area. 1525261738166021 30532840203531 Calculate the quartile and interquartile range. A student scores 60 on a mathematics test that has a mean of 54 and a standard deviation of 3, and she scores 80 on a history test with a mean of 75 and a standard deviation of 2. On which test did she perform better? The following table gives the distribution of the share’s price for ABC Company which was listed in BSKL in 2005. Price (RM)Frequency12 – 1415 – 1718 – 2021 – 2324 – 2627 - 2951425763 Find the mean, median and mode for this data.
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"abattoir" Deutsch Übersetzung
It must be removed, it must be removed in the abattoir and it must be treated as risk material.
With regard to the question relating to the small abattoirs, I did touch on this earlier in my own statement.
On the question of small abattoirs: I can only repeat what I said earlier that the last case of foot-and-mouth disease in the UK was in the 1960s.
On arriving at the abattoir, one in three have broken feet.
Animals that are to be slaughtered should only be driven to the nearest abattoir and for a maximum of eight hours.
As I explained there are complications and risks depending on where it is done, at the abattoir or in the butcher's shop.
Animals suffer as a result, and the call must now go out for animals to be slaughtered at the nearest abattoir.
With regard to the removal of the vertebral column, you have brought up the question: where should it take place, abattoir or at the point
Synonyme (Englisch) für "abattoir":
Beispielsätze für "abattoir" auf Deutsch
abashment · abasing · abatable · abated · abatement · abater · abates · abating · abatis · abattis · abattoir · abattoirs · abaxial · abbacies · abbé · abbess · abbesses · abbey · abbot · abbots · abbreviated
Mehr Übersetzungen im Deutsch-Portugiesisch Wörterbuch.
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http://www.ck12.org/tebook/Algebra-I-Teacher's-Edition/section/10.4/
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math
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At the end of this lesson, students will be able to:
- Complete the square of a quadratic expression.
- Solve quadratic equations by completing the square.
- Solve quadratic equations in standard form.
- Graph quadratic equations in vertex form.
- Solve real-world problems using functions by completing the square.
Terms introduced in this lesson:
completing the square
perfect square trinomial
quadratic equations in standard form
quadratic equations in vertex form
parabola turns up, turns down
Teaching Strategies and Tips
Use Example 1 to introduce completing the square.
- Remind students of binomial expansions to help them understand how a constant term turns the expression into a perfect square trinomial:
- Point out that the leading coefficient is 1.
- In Example 3, a≠1. Students learn to factor a from the whole expression before completing the square, whether or not the terms are multiples of a. Complete the square of the resulting expression in parentheses.
Give completing the square geometrical meaning.
- Use squares and rectangles for each term of the expression.
- See paragraph preceding Example 4.
- Have students make up a quadratic expression and ask them to complete the square in the geometrical interpretation as an assignment.
There are several reasons to have students learn completing the square:
- It is used to derive the quadratic formula.
- Quadratic equations can be rewritten in vertex form.
- Equations of circles can be rewritten in graphing form.
- Necessary in calculus.
Emphasize that completing the square finds roots
- Regardless of whether the roots are integers, rational or irrational numbers.
- Without having to list all the cases, unlike factoring.
Solve the following quadratic equation:
Add the constant to both sides of the equation:
Factor the perfect square trinomial and simplify.
Take the square root of both sides:
Use Examples 7-9 to show how completing the square helps in graphing quadratic functions.
Solve the quadratic equation by completing the square:
Hint: Rewrite the equation:
And divide by the leading coefficient:
Find the vertex of the parabola with equation:
Solution: Rewrite the equation with minus signs:
General Tip: Suggest that students rewrite equations in standard form before completing the square.
In Examples 10 and 11 and Review Questions 25 and 26, have students round in the last step.
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http://hvhomeworkeest.ultimatestructuredwater.info/addition-and-subtraction-of-integers.html
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math
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Addition and subtraction of integers
Counting fingers is one time-honored technique for adding and subtracting integers but what happens when you run out of fingers in this brainpop movie, tim and moby teach you how to handle the addition and subtraction of bigger numbers--not to mention what to do when some of those numbers happen to be negative. Subtracting integers lesson plans and worksheets from thousands of teacher-reviewed resources to help you inspire students learning in this addition and subtraction of integers activity, students add six pairs of integers they subtract 18 pairs. Integer rules don't have to be i was determined to develop a way to teach them so that they could remember without getting the rules for addition and subtraction confused with players take turns rolling the dice and adding their results together using the rules for addition of integers. The math worksheets and other resources below are listed by subject addition, subtraction, multiplication and division equations addition subtracting integers adding and subtracting integers - 1 adding and subtracting integers. A listing of positive and negative rules for adding and subtracting integers eg two negative signs have the same effect as a positive sign. Practice solving addition and subtraction problems with integers (positive and negative numbers. Integers definition, mathematics one of the positive or negative numbers 1, 2, 3, etc, or zero see more. Math mammoth integers contents introduction addition and subtraction of integers next, students learn to locate points in all four quadrants and how the coordinates of a figure change when it is reflected across the x or y-axis.
Play orbit integers at math playground combine integers to power up your space racer grade 1 grade 2 grade 3 grade 4 grade 5 apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Play spider match integers at math playground combine the correct numbers to make the given sum grade 1 grade 2 grade 3 grade 4 grade 5 apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Here's a free printable math worksheet that will help kids practice the addition and subtraction of integers these integer worksheets will help kids understand math concepts better. Operations of signed numbers/integers (rules with add/sub/mult/div) addition & subtraction same (like) signs add and keep that sign different (unlike) signs subtract and keep sign of the larger absolute value.
Model addition, subtraction, multiplication and division of integers using pictorial representations of concrete manipulatives. This prealgebra lesson explains how to subtract signed numbers (integers. Rules for subtracting integers rule 1 because every subtraction problem can be rewritten as a corresponding addition problem, use the following rule: to subtract an integer, add its opposite 1 (-8) - (+9) = the opposite of +9 is -9.
Add and subtract integers and see the work online calculator for adding and subtracting positive and negative integers solve math equations with addition and subtraction. Objective: students will be able to identify and apply the correct procedures for solving addition and subtraction integer problems.
Learn about the rules of positive and negative integers improve your math skills with tips for addition, subtraction, multiplication, and division. Practice your math skills about adding and subtracting integers by playing this fun integers game. All mixed up(addition) 5 crisscross number puzzles integers galactic math (add and subtract integers) 40 basic operations: subtraction solve the subtraction problems. Perform combinations of addition and subtraction operations on a series of three or more integers when you are working in one of the modern trades recall that subtracting integers is a matter of changing the subtraction to addition, and then completing the addition.
Addition and subtraction of integers
Answers to adding and subtracting integers 1) −4 2) 2 3) 3 4) 2 5) 4 6) −5 7) −5 8) −17 9) −13 10) 2 11) −1 12) 0 13) −1 14) 7 15) −9 16) 9 17) 2 18) 0 19) −1 20) 12 21) −3 22) 1 23) 6 24) −5 25) 1 26) −11 27) −1 28) 0 29. In this lesson you will learn to add integers by using integer chips.
- Fun math practice improve your skills with free problems in 'integer addition and subtraction rules' and thousands of other practice lessons.
- Integers - addition, subtraction, multiplication and division model notes the number line the number line is a line labelled with the integers in increasing order from left to right.
- Integers are positive and negative whole numbers teach students about comparing, ordering, adding, subtracting, multiplying, and dividing basic integers.
- In this lesson, we will cover definitions, rules, and examples for subtracting integers we'll also provide some helpful tips for dealing with.
When adding integers you want to look at the signs of the numbers that you are adding if the signs are the same, then add the numbers and keep the sign if the signs are different, subtract the numbers and take the sign of the number with the largest absolute value. Integers can be added, subtracted, divided and multiplied considering certain integer properties learn the rules of addition and subtraction of integers. Nelson education school mathematics k-8 math focus grade 7 parent centre try it out : table addition and subtraction of integers lesson 61: an integer addition strategies lesson 65: subtracting integers using counters lesson 66: subtracting integers using number lines. Orbit integers is a multiplayer math game that allows students from anywhere in the world to race against each other while practicing adding and subtracting integers.
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CC-MAIN-2018-43
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https://www.hackmath.net/en/math-problem/1885
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math
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Jane and Miro
Jane brother Miro is 42 years. And he is three times old as it was Jane when Miro was for so many years as there are now Jane. How old is Jane?
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
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Next similar math problems:
Family has 4 children. Ondra is 3 years older than Matthew and Karlos 5 years older than the youngest Jane. We know that they are together 30 years and 3 years ago they were together 19 years. Determine how old the children are.
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When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?
- Time passing
6 years ago, Marcela's mother was two times older than her and two times younger than her father. When Marcela is 36, she will be twice as young as her father. How old are Marcela, her father, and mother now?
- Age problems
A) Alex is 3 times as old as he was 2 years ago. How old is he now? b) Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey? c) Jessica is 4 years younger than Jennifer now. In 10 years, Jessica wi
- Adam and Ben
When Ben is so many years old to Adam today, Adam will be 23 years old. When Adam was as old as Ben, Ben was two years old. How old is today Ben and Adam?
Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael.
Pooja and Deepa age is 4:5, 4 years back it was 8:11. What is the age of Pooja now?
- Factory and divisions
The factory consists of three auxiliary divisions total 2,406 employees. The second division has 76 employees less than 1st division and 3rd division has 212 employees more than the 2nd. How many employees has each division?
- Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
- Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
If Alena give Lenka 3 candy will still have 1 more candy. If Lenka give Alena 1 candy Alena will hame twice more than Lenka. How many candies have each of them?
- ATC camp
The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
- Linear system
Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
- Two equations
Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
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http://dict.cnki.net/h_50850867000.html
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math
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Because calculation of stress intensity factors using the finite element method of the linear elastic fracture mechanics cannot satisfy the need for the real-time monitoring and the real-time analysis of cracks in concrete dams, a four-layer neural network for calculating stress intensity factors is proposed. The neural network is improved by chaos optimization algorithm. An example is given to validate the improvement.
In this paper, a new optimization method——chaos optimization combined with exact non-differentiable penalty function is proposed for solving chemical process optimization problems which are often regarded as nonlinear constraint optimization problems.
The paper advanced a new way to optimize the rolling parameters of cold continuous rolling mills is proposed by the use of mutative scale chaos optimization algorithm,chaotic search for the population of a genetic operation passed to overcome problems in convergence speed and local minima of Simple Genetic Algorithms. The way has the advantages:the fast search,the precise results,the convenient using ,suiting to on line calculation. With the example,the effectiveness of the method is proved.
Besides of researching, analyzing and controlling chaos, people are utilizing chaos in electric power systems too, e.g. chaos optimization of economic dispatch, parameter estimation of static load model, fuzzy power system stabilizer, and shortterm load forecasting.
This paper proposes a new search strategy using imitative scale chaos optimization algorithm (MSCO) for model selection of support vector machine (SVM).
Model selection for svm using imitative scale chaos optimization algorithm
The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm.
Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.
By the use of the properties of ergodicity, stochastic property, and"regularity" of chaos, a chaos optimization algorithms is proposed (COA). The efficiency of COA is much higher than some stochastic algorithms such asSAA and CA when COA is used to a kind of continuous problems. The chaos optimization method is very simple andconvenient to use.
In this paper, a new hybrid algorithm which combines the chaos optimization method and the conjugate gradient approach having an effective convergence property, is proposed. The hybrid algorithm can help the conjugate gradient approach to skip the local minimum. At the end, it can find the global minimum. The convergence of the algorithm is proved. The simulation shows that the hybrid algorithm is effective.
A mutative scale chaos optimization method is proposed based on the chaos variables. By continually reducing the searching space of variable optimized and enhancing the searching precision, the method is of high efficiency. Simulation results demonstrated the effectiveness of the algorithm.
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CC-MAIN-2020-40
| 3,039
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https://cybertalky.com/2020/09/14/class-4-math-guide/
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math
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Math guide for Class 4 pdf. math book solution pdf bangla versionC4.Class Math guide pdfC.Class 4 math guide PDF bookJ, Jupiter Guide for Class 4C,Class 4 math question bd, NCERT solutions for Class 4 Maths chapter 1
আজকে আপনাদের জন্য নিয়ে আসলাম ৪র্থ শ্রেণীর গনিত সমাধান গাইড বই ডাউনলোড করার জন্য। আপনারা সবাই গুগলে অনেক খুজাখুজি করেন ৪র্থ শ্রেণীর গণিত সমাধান গাইড pdf কিন্তু সঠিক সহযোগিতা পান না। আপনাদের এই সমস্যার কথা মাথায় রেখে আজকে এই পোস্টটি করা আমার। আমি মনে করি আপনাদের খুব উপকারে আসবে আমার চতুর্থ শ্রেণীর গণিত গাইড বই ডাউনলোড পোস্টটি।
Class six math guide PDF English version.Class 4 math guide full PDF.
Many of us don’t always have a class 4 math guide. If we have a PDF of Math Guide for Class 4, we can look up Math solutions at any time. For this we need to keep the PDF of Math Guide of Class 4 on our phone.
Class 4 Maths Chapter 4
This is one of the more important chapters in the syllabus. In this chapter, students learn to tell the time from analogue clocks. As they grow, babies develop a somewhat vague sense of time and understand how day transitions into night. This chapter will help them understand it better and will inculcate in them the value of punctuality.
Class 4 Maths Chapter 5
This chapter helps students appreciate dimensions and perspectives in the real world. They learn to intuitively differentiate between 3-D and 2-D objects, and understand how objects appear in different viewing profiles.
Class 4 Maths Chapter 6
This chapter introduces students to the concept of buying and selling through a story format. They begin to grasp the idea of earning, expenditure, sales and loan. This in a way sets up the students to function better in the real world.
Class 4 Maths Chapter 7
This chapter focusses on units of measurement of liquids. The students are introduced to this concept by measuring water. They begin from large units like litre and move on to smaller ones like millilitre. They are also taught how to convert between the two.
Class 4 Maths Chapter 8
Circles are the most difficult geometric shape for a student to master, as it does not have proper sides of fixed lengths. Hence, this chapter makes them comfortable with the idea of circles and radii. They also get an intuitive feel for the perimeter of a circle.
Class 4 Maths Chapter 9
Fractions are a difficult concept to master as until now, the students have learnt to deal only with whole numbers. So, this chapter introduces them to the concept gradually, using chapatis and chocolates. They understand about wholes, halves and quarters.
Class 4 Maths Chapter 10
The syllabus ensures that students do not rote learn but instead learn to appreciate the subject. This chapter is one such example, as it introduces students to the concept of patterns. It develops their thinking and analysing skill as they learn to identify patterns in a string of characters.
Tag:–Math guide for Class 4 pdf. Class 4 math guide PDF bookJ, Jupiter Guide for Class 4C,Class 4 math question bd, NCERT solutions for Class 4 Maths chapter 1Class 4 Maths Chapter 4 Class 4 Maths Chapter 5 Class 4 Maths Chapter 8 Class 4 Maths Chapter 8 Class 4 Maths Chapter 10 .
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http://forums.wolfram.com/mathgroup/archive/2004/Apr/msg00663.html
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math
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custom look for the notebook
- To: mathgroup at smc.vnet.net
- Subject: [mg47904] custom look for the notebook
- From: Cindy <Cin198803 at ttpoj.com>
- Date: Thu, 29 Apr 2004 19:40:00 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
As I just started reading and learning mathematica 5 under windows 2000.
Is there some online tutorial for formatting the notebook in such a way
that it would be easy to read the code? E.g. coloring the function-names
as you type them, auto indentation, Tab to complete typing the rest of
the previously typed variable or function-name etc, instead of just
all black text in one paragraph of code.
Prev by Date:
Re: PaddedForm bug?
Next by Date:
labeling curves on a plot
Previous by thread:
Re: Mathematica User Groups?
Next by thread:
RE: custom look for the notebook
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https://nhstoryoftransformation.com/isoquant-and-isocost-number/
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math
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Howdoes a firm use isoquants and isocosts to choose the optimalcombination of inputs? Is it valid to assume that the market in whichthe firm is operating is perfectly competitive? Why or why not? Ifthe market is not perfectly competitive, will the isoquant/isocostanalysis be distorted? Why or why not?
Alsoreferred as equal-product or quantity curve, Isoquantindicates different combinations of two production factors (such aslabor and capital), which results in the same level of output, withreference to time unit. It does can also be summarized as a graphicalrepresentation of different input combinations i.e. labor andcapital. Isoquant graphs are mostly used in the study ofmicroeconomics to estimate the influence of inputs to the level ofoutput that can be achieved (Feller,1972).
Onthe other hand, an Isocost (equal cost line) is the total cost ofproduction, which acknowledges the combinations of any two resourcesthat can be deployed by a firm while given the total cost. Isocostcurves or lines display all possible combinations of inputs that havethe same total cost. An isocost line is used together with isoquantmap which in turn helps to determine the optimum production point(Hirschey,2009).The point at which the isoquant and the isocost line meets, denotesthe lowest-cost combinations of inputs that can in turn lead to theyielding the level of output that is related with the isoquant used.
Isoquantsand Isocosts are used hand in hand, as the two helps in estimation ofthe various and most efficient combinations of resources (Lloyd,2012).The key point with reference to the aspects of isoquant and isocostis that, the most efficient combinations of resources that can bedeployed introduction are experienced where the isoquantis tangent to the budget line.
Itwould be wrong or invalid to assume that, the market at which thefirm is operating is a perfect competition. This due to the factthat, other factors influence the market competition, while thefactors may differ from one firm to the other. However, theimperfectness of the competitive market will not change or impact theisoquant/isocostanalysis. This is due to the fact that, different firms havedifferent and varying resources that affect the isoquant/Isocostanalysis, which may not be impacted by the outside environment suchas the case of factors affecting competitiveness (Lloyd,2012).
Feller,I. (1972). Production Isoquants And The Analysis Of Technological AndTechnical Change. QuarterlyJournal Of Economics, 86(1),154-161.
Hirschey,M. (2009). Fundamentalsof managerial economics.Mason, OH: South-Western/Cengage Learning.
Lloyd,P. (2012). The Discovery of the Isoquant. HistoryOf Political Economy, 44(4),643-661.
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https://www.studyxapp.com/homework-help/below-are-descriptions-about-three-notes-receivable-owned-byalistarnotes-receiv-q102915518
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math
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Below are descriptions about three notes receivable owned by Alistar
Notes receivable 1:
The $400,000 note receivable is dated December 31, 2021, bears interest at 8%, and is due on December 31, 2025. The note is due from Flame May, president of Alistar Inc. Interest is payable annually on December 31, and all interest payments were paid on their due dates through December 31, 2023.
Notes receivable 2:
On April 1, 2022, Alistar sold a patent to Pennsylvania Company in exchange for a $100,000 zero-interest-bearing note due on April 1, 2024. There was no established exchange price for the patent, and the note had no ready market. The prevailing rate of interest for a note of this type at April 1, 2022, was 12%. The patent had a carrying value of $40,000 at January 1, 2022, and the amortization for the year ended December 31, 2022, would have been $8,000. The collection of the note receivable from Pennsylvania is reasonably assured.
Notes receivable 3:
On September 1, 2022, Alistar sold a parcel of land to Yakult Company for $200,000 under an installment sale contract. Yakult made a $60,000 cash down payment on September 1, 2022, and signed a 4-year 11% note for the $140,000 balance. The equal annual payments of principal and interest on the note will be $45,125 payable on September 1, 2023, through September 1, 2026. The land could have been sold at an established cash price of $200,000. The cost of the land to Alistar was $150,000. Circumstances are such that the collection of the installments on the note is reasonably assured
Do the following instructions for Alistar:
1. Prepare journal entry on December 31, 2022 for all notes receivable
2. Compute revenues and expenses (if any) for the year of 2022 and 2023
3. Prepare the receivable section of Statement of Financial Position at the end of year 2023
Show your computation
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510427.16/warc/CC-MAIN-20230928162907-20230928192907-00210.warc.gz
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https://www.physicsforums.com/threads/implications-of-verlinde-entropy-on-string-theory.377812/
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math
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String theory posits spacetime that is infinitely continuous. Earlier at PF there was a discussion of lorentz invariance and Fermi Gamma-ray Space Telescope showing that very high energy photons travel at c, which makes discrete theories of QG less favored and string theory more favored, as continuous spacetime is a natural home for exact lorentz invariance. Smolin and Kowalski offered accounts of how Verlinde's proposal can fit within LQG and BF theory respectively. I'm wondering what are the ramifications of Verlinde entropy on string theory -- 1- if spacetime itself has entropy of a specific quantity, does this imply discrete spacetime? if spacetime is continuous can an infinite amount of entropy be packaged in an arbitrarily small volume of space? 2- Verlinde's account of gravity as entropy as equation of state, v.s string theory account of gravity as mediated by closed string (spin-2) 3- Verlinde's derivation effect on higher dimensions, would it work in spaces above 3? Would higher spaces carry additional entropy and hence not give Newton's gravity? 4- Does Verlinde's account of gravity have any effect on supersymmetry? cosmological constant? 5- if Verlinde's account of gravity and entropy is valid, what would be the degrees of freedom that would account for it within string theory? Do string worldsheets carry the needed degrees of freedom to give entropy? 6- how does the idea that spacetime is emergent and carries degrees of freedom from which entropy counts as microstates merge with the idea of exact lorentz invariance at arbitrarily high energy gamma rays? 7- any other ramifications ?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592875.98/warc/CC-MAIN-20180722002753-20180722022753-00375.warc.gz
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CC-MAIN-2018-30
| 1,620
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http://mathhelpforum.com/calculus/65621-limit-question.html
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math
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As you can see this limit is only defined when x approach 0 from the right.
I concluded that the limit was -1/4 by looking at the graph of as x was approaching infinity.
the question and how i tried to solve it
in this link:
i dont know how
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542217.43/warc/CC-MAIN-20161202170902-00282-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 240
| 5
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https://ww2.amstat.org/meetings/sdss/2019/onlineprogram/AbstractDetails.cfm?AbstractID=305009
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math
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Keywords: gradient flow, ridge regression, early stopping, implicit regularization, random matrix theory
We study the statistical properties of the iterates generated by gradient descent, applied to the fundamental problem of least squares regression. We take a continuous-time view, i.e., consider infinitesimal step sizes in gradient descent, in which case the iterates form a trajectory called gradient flow. In a random matrix theory setup, which allows the number of samples n and features p to diverge in such a way that p/n converges to a positive constant, we derive and analyze an asymptotic risk expression for gradient flow. In particular, we compare the asymptotic risk profile of gradient flow to that of ridge regression. When the feature covariance is spherical, we show that the optimal asymptotic gradient flow risk is between 1 and 1.25 times the optimal asymptotic ridge risk. Further, we derive a calibration between the two risk curves under which the asymptotic gradient flow risk no more than 2.25 times the asymptotic ridge risk, at all points along the path. Lastly, we present numerical experiments that show ridge and gradient flow to be extremely tightly coupled, even more so than the theory predicts.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571909.51/warc/CC-MAIN-20220813051311-20220813081311-00107.warc.gz
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CC-MAIN-2022-33
| 1,230
| 2
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http://japanese.stackexchange.com/questions/tagged/phonology+suffixes
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math
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Japanese Language Meta
to customize your list.
more stack exchange communities
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Pronunciation of 対応済
Is the pronunciation of 対応済 たいおうすみ or たいおうずみ ? Context: Software Example: ユーザが押したときに問題が起こらないように対応済
Nov 17 '11 at 1:44
newest phonology suffixes questions feed
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s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663743.38/warc/CC-MAIN-20140930004103-00393-ip-10-234-18-248.ec2.internal.warc.gz
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CC-MAIN-2014-41
| 2,214
| 53
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https://www.mytutor.co.uk/tutors/13782/maths+science-tutor
|
math
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|Biology||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
Using the trigonometric(trig) ratios of cosine, sine and tangent we can work out side lengths and angles.
Within a right angle triangle of we are given a side lenght and a angle other than the right angle we can work out either of the other two sides.
Each side is given a name depending on how it relates to the given angle. The longest side on the triangle is called the hypotenuse. The side which is touching the angle but is not the hypotenuse is called the adjacent. The other side the one which is not touching the given angle and is also not the hypotenuse is called the opposite as it is opposite the angle.
Depending on which side we are given and which we want to work out depends which trig ratios we use.
The phrase SOH CAH TOA is an easy way to remember whihc goes with which. So if we look at SOA the S is for sine and the sides are opposite and hypotenuse. So if the sides involved aare those two we use sine. CAH and TOA follow the same order. For these three ratios this means tthat the sine of an angle is equal to the length of the opposite divided by the length of the hypotenuse. For the other two replacing the correct parts.
So to work out a length we can put out known likely into the equation then rearrange it to solve for the unknown side. To get the sine of an angle on your calculator there will be a button with "sin". This should make a "sin(" appears on the screen. Inside the brackets you put the angle. This will give a number most likely with alot of decimal places it is best to carry this using your calculator and round your final answer to three significant figures.
To calculate angles when given two sides is slightly more complex and requires the use of inverse trig rations. These are written as sin-1 cco-11 and tan-1.
We follow the same rules for idenroff in which ratio we use. We fillook in what we know . This will give us the trig ratio of a unknown angle is equal to a number. To calculate the angle we use the inverse trig ratio. For example if we have sin of an unknown we use sin-1. We take the inverse ratio of the number we do this by pressing shift then the normal ratio. It should display "sin-1(" wwepputwe put oojrr number inside the bracket and this gives us the angle which we then round to three significant figures.see more
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s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172783.57/warc/CC-MAIN-20170219104612-00129-ip-10-171-10-108.ec2.internal.warc.gz
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CC-MAIN-2017-09
| 2,342
| 10
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https://www.jiskha.com/display.cgi?id=1176670003
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math
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posted by jasmine20 .
how do i find the following:
is there a formula for this?
Find the constant term that should be added to make the following expression a perfect square trinomial.
square a few binomials and see if you can see a pattern
e.g. (x+3)^2 = x^2 + 6x + 9
(x-7)^2 = x^2 - 14x + 49
notice the coefficient of the middle term is twice the square root of the last term
so you have to reverse the pattern
take 1/2 of the middle term number, then square it.
for your e.g.
x^2 + 7x + ???
1/2 of 7 is 7/2, which when squared is 49/4
x^2 + 7x
=x^2 + 7x + 49/4 - 49/4
=(x+7/2)^2 - 49/4
I added and subtracted the same number to maintain the "equality"
I assume you are learning the method of completing the square.
i am lost?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109525.95/warc/CC-MAIN-20170821191703-20170821211703-00394.warc.gz
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CC-MAIN-2017-34
| 728
| 19
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https://www.teacherspayteachers.com/Product/Exploring-with-Trig-1088594
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math
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Throughout this guided exploration, students will discover the trig ratios for sine, cosine, and tangent. Students will be able to articulate these ratios and solve problems using the ratios after completing the exploration. The summative assessment for this assignment is a mini research project on real life trig applications that requires students to write and explain how to solve their own word problem.
NOTE: This does not require any prior knowledge on Trig. I used this to introduce sine, cosine, and trig for my Algebra students.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887067.27/warc/CC-MAIN-20180118051833-20180118071833-00015.warc.gz
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CC-MAIN-2018-05
| 538
| 2
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https://www.ias.edu/in-the-media/scientific-american-universe-speaks-in-numbers
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math
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A New Book Examines the Relationship between Math and Physics
Scientific American's Steve Mirsky writes about The Universe Speaks in Numbers symposium at IAS, inspired by frequent Director's Visitor Graham Farmelo's new book by the same title. On the topic explored in the symposium and book – the interplay between mathematics and physics – Mirsky quotes IAS Director Robbert Dijkgraaf, IAS Professors Nima Arkani-Hamed and Freeman Dyson, IAS Distinguished Visiting Professor Karen Uhlenbeck, and former IAS Professor Michael Atiyah.
"When asked what the most important questions were still to be addressed by physics and math, Dyson said, 'The question of what's important is entirely a matter of taste. I like to think of going to the zoo … you can either admire the architecture of the zoo or you can admire the animals. And so, at the present time, mathematicians are very busy admiring the architecture. The physicists are admiring the animals. Which is actually more important isn't to me the interesting question. The interesting question is, Why do they fit so well?'"
Read more at Scientific American.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988923.22/warc/CC-MAIN-20210508181551-20210508211551-00427.warc.gz
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CC-MAIN-2021-21
| 1,117
| 4
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http://kwiznet.com/p/takeQuiz.php?ChapterID=2616&CurriculumID=38&NQ=6&Num=2.99
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math
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kwizNET Subscribers, please login to turn off the Ads!
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2.99 Verbal Problems - II
For the following word problems, first write the equation indicated by the problem statement. Then solve the resulting equation and enter the final answer in the space provided.
: Twice a number is 15 less than 75. Find the number. (Hint: The algebraic equation is: 2x = 75 - 15. Find x)
: There are 62 passengers in a bus. At the next stop y people boarded the bus and one got down. The number of passengers now in bus is 70, find y ?
: A book contains 250 pages, after 'x' pages are read, the number still to be read is 65, find x.
: If a number is increased by 2/3 of itself, the result is 20. What is the number? (The algebraic equation is x + (2/3)x = 20, Solve for x).
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s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250609478.50/warc/CC-MAIN-20200123071220-20200123100220-00344.warc.gz
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CC-MAIN-2020-05
| 1,549
| 24
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https://www.coursehero.com/tutors-problems/Physics/471274-A-car-moving-at-8-ms-crashes-into-a-barrier-and-stops-in-0050-s-The/
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math
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(a) What is the impulse needed to stop the child?
(b) What is the average force on the child?
(c) What is the approximate mass of an object whose weight equals the force in part (b)?
(d) Could you lift such a weight with your arm?
(e) Why is it advisable to use a proper infant restraint rather than hold a child on your lap?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509170.2/warc/CC-MAIN-20181015100606-20181015122106-00450.warc.gz
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CC-MAIN-2018-43
| 325
| 5
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https://www.buenastareas.com/ensayos/Learning-Curve/224955.html
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math
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CHAPTER 21 LEARNING CURVE
It is a fundamental human characteristic that a person engaged in a repetitive task will improve his performance over time. If data are gathered on this phenomenon, a curve representing a decrease in effort per unit for repetitive operations can be developed. This phenomenon is real and has a specific application in cost analysis, cost estimating,or profitability studies related to the examination of future costs and confidence levels in an analysis. It could be used in estimating portions of a project, such as the production of magnets for the supercollider. This chapter discusses the development and application of the learning curve.
The aircraft industry was the first to develop the learning curve. Based oncomparison of manufacturing and aircraft industry learning curves, it is evident that a typical curve exists. It is an irregular line that starts high, decreases rapidly on initial units, and then begins to level out. The curve shows that there is progressive improvement in productivity but at a diminishing rate as the number produced increases. Figure 21-1 shows the appearance of the curve.
Thissuggests an exponential relationship between productivity and cumulative production. When this data is plotted on log-log paper, the data plots as a straight line. This suggests the relationship of the form:
21-2 EN = KNS
DOG 430.1-1 03-28-97
where EN = effort per unit of production (i.e., manhours) to produce the Nth unit K = constant, which is the effort to produce the first unit s = slopeconstant, which is negative since the effort per unit decreases with production. The above relationship will plot as a straight line on log-log paper. Take the logarithms of both sides, log EN = s x log N + log K which is the equation of a straight line Y = sX + b where Y = log EN, X = log N, and b = log K. Figure 21-2 represents the data on log-log paper.
DOE G 430.1-1 03-28-97
3.LEARNING CURVE FROM SINGLE-UNIT DATA
If the effort is available for each unit produced, any one of three curves can be plotted. They are the unit, the cumulative total, and the cumulative average. Following is Table 21-1, which includes single-unit data.
TABLE 21-1 PRODUCTION DATA ____________________________________________________________
_____________________ ITEM UNIT HOURS CUM. TOTALHRS CUM. AVG. HRS
________________________________________ 1 2 3 4 5 6 7 8 9 10 10.0 8.0 7.3 6.3 6.0 5.6 5.6 5.0 5.1 4.5 10.0 18.0 25.3 31.6 37.6 43.2 48.8 53.8 58.9 63.4 10.0 9.0 8.4 7.9 7.5 7.2 7.0 6.7 6.5 6.3
From this data the unit,cumulative total, and cumulative average curves can be drawn. A. Unit Curve If a set of data is available for the effort required for single, individual units of production, the data can be plotted on log-log paper and the best line drawn with the eye. Having established the best line, any two points on the line can be used to determine, graphically or analytically, the slope of the line and K, whichis the intercept at N = 1. This graphical method is quick, but it may require judgment when the data points are scattered. The most accurate method for determining the best straight line is to use the least squares method. B. Cumulative Total Curve For this curve, the effort is described as cumulative total. This curve produces a line with a positive slope.
21-4 C. Cumulative Average CurveDOG 430.1-1 03-28-97
The effort calculated for this curve is the cumulative average for each unit. It produces a curve that is usually a more regular curve than the unit curve.
DOE G 430.1-1 03-28-97
EFFECTS OF DOUBLING PRODUCTION
The equation, EN = KNs, implies a constant fractional or percentage reduction in effort for doubled (or tripled, etc.) production. For...
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Regístrate para leer el documento completo.
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https://www.cityam.com/short-history-pi-day-what-it-and-where-did-it-come/
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math
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Today is Pi day, 14 March, or 3.14 if you write your dates the American way, which also happens to be the first two digits of the mathematical constant Pi: 3.141592653.
This is why people will be walking around circular rooms, eating lots of pies and trying to memorise a few of its digits.
Pi equals the distance around a perfect circle, or circumstance, divided by the distance across it, or diameter. It's used to calculate the area of a circle, the volume of a sphere, and a whole host of other mathematical equations we won't even go into.
So where did Pi day come from? Larry Shaw, a physicist from San Francisco, who first conceived of Pi day in 1988. He enlisted a bunch of fellow math enthusiasts, and together they marched around a circular room, feasting of pies, in celebration of the world's best known mathematical constant.
Since then, it's gone mainstream, finally becoming official in 2009 after a resolution was passed by the US Congress. This stipulated March 14 would be a day for “schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.”
But how did the "e" creep into the equation? We've got no idea – and there's no etymological relationship here. While Pi is the 16th letter of the Greek alphabet, pie originated in England, and referred to pastries and magpies. Nonetheless, they sound similar and they're both round, and if that's good enough for the world's top math whizzes, it's good enough for us.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510284.49/warc/CC-MAIN-20230927071345-20230927101345-00677.warc.gz
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CC-MAIN-2023-40
| 1,523
| 6
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https://www.jiskha.com/display.cgi?id=1319868066
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math
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posted by Dewa .
1000 g of a 50% (mass percentage) nitric acid solution is to be diluted to 20%(mass percentage) nitric acid solution. How many liters of water should be added to the starting solution? Please show me the detail answer
The dilution formula works as well for percent by mass as it does for molarity and normality.
%1 x grams1 = %2 x grams2.
Calculate grams 2, then subtract mass HNO3 in the 50% soln to see how much water to add.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103167.97/warc/CC-MAIN-20170817092444-20170817112444-00247.warc.gz
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CC-MAIN-2017-34
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https://wikimili.com/en/Bernhard_Riemann
|
math
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Georg Friedrich Bernhard Riemann
17 September 1826
|Died||20 July 1866 39) (aged|
|Known for||See list|
|Institutions||University of Göttingen|
|Thesis||Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen complexen Größe (1851)|
|Doctoral advisor||Carl Friedrich Gauss|
|Other academic advisors|
|Notable students|| Gustav Roch |
|Influences||J. P. G. L. Dirichlet|
Georg Friedrich Bernhard Riemann (German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] ( listen ); 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as one of the most influential papers in analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time.
Riemann was born on 17 September 1826 in Breselenz, a village near Dannenberg in the Kingdom of Hanover. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy and suffering from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
During 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school years). After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg. In high school, Riemann studied the Bible intensively, but he was often distracted by mathematics. His teachers were amazed by his ability to perform complicated mathematical operations, in which he often outstripped his instructor's knowledge. In 1846, at the age of 19, he started studying philology and Christian theology in order to become a pastor and help with his family's finances.
During the spring of 1846, his father, after gathering enough money, sent Riemann to the University of Göttingen, where he planned to study towards a degree in Theology. However, once there, he began studying mathematics under Carl Friedrich Gauss (specifically his lectures on the method of least squares). Gauss recommended that Riemann give up his theological work and enter the mathematical field; after getting his father's approval, Riemann transferred to the University of Berlin in 1847.During his time of study, Carl Gustav Jacob Jacobi, Peter Gustav Lejeune Dirichlet, Jakob Steiner, and Gotthold Eisenstein were teaching. He stayed in Berlin for two years and returned to Göttingen in 1849.
Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Albert Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following the death of Dirichlet (who held Gauss's chair at the University of Göttingen), he was promoted to head the mathematics department at the University of Göttingen. He was also the first to suggest using dimensions higher than merely three or four in order to describe physical reality.
In 1862 he married Elise Koch and they had a daughter Ida Schilling who was born on 22 December 1862.
Riemann fled Göttingen when the armies of Hanover and Prussia clashed there in 1866.
Riemann was a dedicated Christian, the son of a Protestant minister, and saw his life as a mathematician as another way to serve God. During his life, he held closely to his Christian faith and considered it to be the most important aspect of his life. At the time of his death, he was reciting the Lord’s Prayer with his wife and died before they finished saying the prayer.Meanwhile, in Göttingen his housekeeper discarded some of the papers in his office, including much unpublished work. Riemann refused to publish incomplete work, and some deep insights may have been lost forever.
Riemann's tombstone in Biganzolo (Italy) refers to Romans 8:28:
Here rests in God
Georg Friedrich Bernhard Riemann
Professor in Göttingen
born in Breselenz, 17 September 1826
died in Selasca, 20 July 1866
Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology and is still being applied in novel ways to mathematical physics.
In 1853, Gauss asked Riemann, his student, to prepare a Habilitationsschrift on the foundations of geometry. Over many months, Riemann developed his theory of higher dimensions and delivered his lecture at Göttingen in 1854 entitled "Ueber die Hypothesen welche der Geometrie zu Grunde liegen" ("On the hypotheses which underlie geometry"). It was not published until twelve years later in 1868 by Dedekind, two years after his death. Its early reception appears to have been slow, but it is now recognized as one of the most important works in geometry.
The subject founded by this work is Riemannian geometry. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorema egregium . The fundamental object is called the Riemann curvature tensor. For the surface case, this can be reduced to a number (scalar), positive, negative, or zero; the non-zero and constant cases being models of the known non-Euclidean geometries.
Riemann's idea was to introduce a collection of numbers at every point in space (i.e., a tensor) which would describe how much it was bent or curved. Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe the properties of a manifold, no matter how distorted it is. This is the famous construction central to his geometry, known now as a Riemannian metric.
In his dissertation, he established a geometric foundation for complex analysis through Riemann surfaces, through which multi-valued functions like the logarithm (with infinitely many sheets) or the square root (with two sheets) could become one-to-one functions. Complex functions are harmonic functions (that is, they satisfy Laplace's equation and thus the Cauchy–Riemann equations) on these surfaces and are described by the location of their singularities and the topology of the surfaces. The topological "genus" of the Riemann surfaces is given by , where the surface has leaves coming together at branch points. For the Riemann surface has parameters (the "moduli").
His contributions to this area are numerous. The famous Riemann mapping theorem says that a simply connected domain in the complex plane is "biholomorphically equivalent" (i.e. there is a bijection between them that is holomorphic with a holomorphic inverse) to either or to the interior of the unit circle. The generalization of the theorem to Riemann surfaces is the famous uniformization theorem, which was proved in the 19th century by Henri Poincaré and Felix Klein. Here, too, rigorous proofs were first given after the development of richer mathematical tools (in this case, topology). For the proof of the existence of functions on Riemann surfaces he used a minimality condition, which he called the Dirichlet principle. Karl Weierstrass found a gap in the proof: Riemann had not noticed that his working assumption (that the minimum existed) might not work; the function space might not be complete, and therefore the existence of a minimum was not guaranteed. Through the work of David Hilbert in the Calculus of Variations, the Dirichlet principle was finally established. Otherwise, Weierstrass was very impressed with Riemann, especially with his theory of abelian functions. When Riemann's work appeared, Weierstrass withdrew his paper from Crelle's Journal and did not publish it. They had a good understanding when Riemann visited him in Berlin in 1859. Weierstrass encouraged his student Hermann Amandus Schwarz to find alternatives to the Dirichlet principle in complex analysis, in which he was successful. An anecdote from Arnold Sommerfeld shows the difficulties which contemporary mathematicians had with Riemann's new ideas. In 1870, Weierstrass had taken Riemann's dissertation with him on a holiday to Rigi and complained that it was hard to understand. The physicist Hermann von Helmholtz assisted him in the work over night and returned with the comment that it was "natural" and "very understandable".
Other highlights include his work on abelian functions and theta functions on Riemann surfaces. Riemann had been in a competition with Weierstrass since 1857 to solve the Jacobian inverse problems for abelian integrals, a generalization of elliptic integrals. Riemann used theta functions in several variables and reduced the problem to the determination of the zeros of these theta functions. Riemann also investigated period matrices and characterized them through the "Riemannian period relations" (symmetric, real part negative). By Ferdinand Georg Frobenius and Solomon Lefschetz the validity of this relation is equivalent with the embedding of (where is the lattice of the period matrix) in a projective space by means of theta functions. For certain values of , this is the Jacobian variety of the Riemann surface, an example of an abelian manifold.
Many mathematicians such as Alfred Clebsch furthered Riemann's work on algebraic curves. These theories depended on the properties of a function defined on Riemann surfaces. For example, the Riemann–Roch theorem (Roch was a student of Riemann) says something about the number of linearly independent differentials (with known conditions on the zeros and poles) of a Riemann surface.
According to Detlef Laugwitz,automorphic functions appeared for the first time in an essay about the Laplace equation on electrically charged cylinders. Riemann however used such functions for conformal maps (such as mapping topological triangles to the circle) in his 1859 lecture on hypergeometric functions or in his treatise on minimal surfaces.
In the field of real analysis, he discovered the Riemann integral in his habilitation. Among other things, he showed that every piecewise continuous function is integrable. Similarly, the Stieltjes integral goes back to the Göttinger mathematician, and so they are named together the Riemann–Stieltjes integral.
In his habilitation work on Fourier series, where he followed the work of his teacher Dirichlet, he showed that Riemann-integrable functions are "representable" by Fourier series. Dirichlet has shown this for continuous, piecewise-differentiable functions (thus with countably many non-differentiable points). Riemann gave an example of a Fourier series representing a continuous, almost nowhere-differentiable function, a case not covered by Dirichlet. He also proved the Riemann–Lebesgue lemma: if a function is representable by a Fourier series, then the Fourier coefficients go to zero for large n.
Riemann's essay was also the starting point for Georg Cantor's work with Fourier series, which was the impetus for set theory.
He also worked with hypergeometric differential equations in 1857 using complex analytical methods and presented the solutions through the behavior of closed paths about singularities (described by the monodromy matrix). The proof of the existence of such differential equations by previously known monodromy matrices is one of the Hilbert problems.
He made some famous contributions to modern analytic number theory. In a single short paper, the only one he published on the subject of number theory, he investigated the zeta function that now bears his name, establishing its importance for understanding the distribution of prime numbers. The Riemann hypothesis was one of a series of conjectures he made about the function's properties.
In Riemann's work, there are many more interesting developments. He proved the functional equation for the zeta function (already known to Leonhard Euler), behind which a theta function lies. Through the summation of this approximation function over the non-trivial zeros on the line with real portion 1/2, he gave an exact, "explicit formula" for .
Riemann knew of Pafnuty Chebyshev's work on the Prime Number Theorem. He had visited Dirichlet in 1852.
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.
Analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
Johann Peter Gustav Lejeune Dirichlet was a German mathematician who made deep contributions to number theory, and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function.
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. In particular it implies that every Riemann surface admits a Riemannian metric of constant curvature. For compact Riemann surfaces, those with universal cover the unit disk are precisely the hyperbolic surfaces of genus greater than 1, all with non-abelian fundamental group; those with universal cover the complex plane are the Riemann surfaces of genus 1, namely the complex tori or elliptic curves with fundamental group Z2; and those with universal cover the Riemann sphere are those of genus zero, namely the Riemann sphere itself, with trivial fundamental group.
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects and reference tables. They also cover equations named after people, societies, mathematicians, journals and meta-lists.
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
Elwin Bruno Christoffel was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity.
In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.
Karl Hermann Amandus Schwarz was a German mathematician, known for his work in complex analysis.
In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.
The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups.
In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form
This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves.
|Wikiquote has quotations related to: Bernhard Riemann|
|Wikimedia Commons has media related to Bernhard Riemann .|
|Wikisource has the text of the 1905 New International Encyclopedia article " Riemann, Georg Friedrich Bernhard ".|
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https://phennydiscovers.com/infsln8e8u9.hyperchlorination
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math
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Find the answer for math problems
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When we add two numbers together, we are simply combining two sets of objects into one larger set. The same goes for subtraction - when we take away one number from another, we are just separating two sets of objects. Multiplication and division work in a similar way. In multiplication, we are just adding a number to itself multiple times. And in division, we are just separating a number into smaller groups. So as you can see, basic mathematics is really not that complicated after all!
Then, take the square root of this number to find the length of the hypotenuse. For example, if you know that one side is 3 feet long and another side is 4 feet long, you would first square these numbers to get 9 and 16. Then, you would add these numbers together to get 25. Taking the square root of 25 gives you 5, so you know that the hypotenuse is 5 feet long. Solving for x in a right triangle is a simple matter of using the Pythagorean theorem. With a little practice, you'll be able to do it in your sleep!
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https://pt.slideshare.net/KritikaBhansali/mehrangarh-fort-in-rajasthan
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math
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O SlideShare utiliza cookies para otimizar a funcionalidade e o desempenho do site, assim como para apresentar publicidade mais relevante aos nossos usuários. Se você continuar a utilizar o site, você aceita o uso de cookies. Leia nossa Política de Privacidade e nosso Contrato do Usuário para obter mais detalhes.
THE MEHRAN FORT• Crowns a hill which is 400ft above the ground.• Over 5 centuries – the headquarters of Rathore.• Rao Jodha – led its foundation in the mid C15th.• Below which Jodhpur was formed.• In reference to the clans mythical descent from the sun god ‘Surya’.
Contd..• Current Head - Maharaja Gaj Singh.• Military base• Palace for the rulers and their wives.• The centre of patronage for art, music and literature.• A place of worship for temples and shrines.
JAI POL• Entrance to the fort.• Seems to grow out of the hill.• Made of -reddish brown sandstone.• Built in 19th century by Maharaja Man Singh.• To the left, a small shrine of silvered Ganesha image.
Out work:• Space where the Jaipur forces attacked.• Has Pustak Prakash & Chhatri (modern guard rooms) .• Leads to the 2nd door.
Lakhan Pol / Dedh Kangura Pol• “One and a half merlons.”• Has a lintel no arch.• Doors just stand against the wall, not mounted.• Followed by an ascent ramp.
AMRITI POL & LOHA POL• Leading to Amriti pol.• Stilted and pointed arches .• It has small guard rooms,• It steeply rises at the top ramp is the Loha pol.• The Loha pol leads to Naqqar Khana –• Announce Maharaja’s arrival or departure (now a café).
Palace Commemorating satis apartments above Amriti pol.
SURAJ POL• Grand entrance has 2 entrances.• 1 to the Zenana or woman’s quarters.• The other to Suraj pol nearer one at lower level - less imposing.• Leading to the public parts of the palace.
Palace Apartments• 1st courtyard - the Shrinagar Chowk.• The Raj Tilak (enthroning ceremony)• A modest marble seat.• Many different patterns of perforations for the breeze to flow through.
The galleries• Hawda Khana(s) displays C18th and C19th Howdahs with fine silver works.• On the east similar arrangement of Palki Khana, red and silver striped velvet covering for women in Purdah.
Daulat khana 2nd court yard:• Most prestigious royal apartment..• The floor being the audience hall or main reception room personnel apartment and sleeping chamber• Terrace with pavilions – a place for recreation.
Shastra Khana• One apartment was used as a Bhojan Shale offer feasts to this nobles (Thakurs or Pandits)• Now enclosed to convert it into a museum space – the Armoury.• Koft gari – decorative inlay• Prominence of weapons – military basis of Rajput.
Sheesh Mahal• Bed chamber of the rulers• Decorated with mirrors.
Phul mahal• Over the amoury,, private audience hall, perform personal rituals.• Elaborate jaali work blaustered.
Takhat Vilas:• All surface is painted.• Windows have colored glass planes.• Model on local folk art.• Ceiling are wooden beams.
Jhanki Mahal• Jaalis & small window.• Allow to get a glimpse without being noticed.• Cradles and Jhulas are seen here.
Moti Mahal• Has five alcoves leading onto hidden balconies.• The throne is placed centrally.• White painted stone Jaali work.
Gun Terrace• Made in the C19th.• Some are from the 1st world war.• It has a Arabic inscriptions.
Chamudi temple• Isht devi of the royal family.• Dusshera celebrations.• Gangor ki puja.
How to reach ??• Jodhpur is well connected by road, rail and air to all major cities and towns.By air-• Indian(Indian airlines) operates daily flights to Jodhpur from Delhi, Mumbai, Jaipur and Udaipur.• Jet Airways operates daily flights from Delhi and Mumbai.• Kingfisher airlines operates daily flights from Delhi, Udaipur and Jaipur.
By Train• Well connected by direct trains from all metros and major cities in India.• The taxi stand and auto- rickshaw stand are located near the exit of the railway station.
By road Approximate road distances from various destinations are• Agra -580 km• Ajmer -200 km• Bikaner -240 km• Jaipur -345 km• Mumbai -1075 km• New Delhi -590 km• Udaipur -275 km
By bus• Jodhpur can be reached by RSRTC (Rajasthan State Road Transport Corporation).• Buses and private luxury buses which operate from all major towns and cities in Rajasthan Ahmedabad and Delhi.
Getting aroundMeans of transport include:• Tourist cabs (taxis) – Ply on a minimum distance per hour per day basis.• Mini Buses – Public transport is available but chaotic and not advisable except when on a shoestring budget.• Car rental – There are many car rental companies around.• Auto Rickshaw(unmetered) – Negotiate before you board on.• Tonga – A good way to move around.
Where to stay???• Jodhpur Heritage Hotels• Ajit Bhawan• Balsamand Lake Palace• Devi Bhawan• Haveli Inn pal• Madho Niwas• Megh Niwas• Pal Haveli• Polo Heritage• Ratan Vilas
Jodhpur Luxury Hotels• The Gateway Hotel• Park Plaza Jodhpur• Taj Hari Mahal• Umaid Bhawan Palace
Jodhpur Deluxe Hotels• Mapple Abhay• Chandra Inn• Hotel Kalinga• Lake View & Resort• Maru Garh• Niky International• Rajputana Palace• Shree Ram International
Jodhpur Economy Hotels• Inn Season• Hotel Ratnawali• Residency Palace• RTDC Hotel Ghoomar• Shri Ram Excellency
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https://bublish.org/a-completely-new-approach-suggests-the-validity-of-the-110-year-old-lindelof-hypothesis-opening-up-the-possibilities-of-new-discoveries-in-quantum-computing-number-theory-and-cybersecurity/
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math
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Athanassios Fokas, a mathematician from the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and visiting professor in the Ming Hsieh Department of Electrical Engineering at the USC Viterbi School of Engineering has announced a novel method suggesting a solution to one of the long-standing problems in the history of mathematics, the Lindelöf Hypothesis.
The result, announced on June 25th, 2018, at the First Congress of the Greek Mathematical Society in Athens under the auspices of the president of Greece, Prokopios Pavlopoulos, has far reaching implications for fields like quantum computing, number theory, and encryption which forms the basis for cybersecurity.
Put forth in 1908 by Finnish topologist Ernst Leonard Lindelöf, the Lindelöf hypothesis is a conjecture about the rate of growth of the Riemann zeta function on the critical line implied by one of the most famous unsolved problems related to prime numbers, the Riemann Hypothesis, popularly referred to as the Holy Grail of math.
Lindelöf implies most of the claims of Riemann and Riemann fully implies Lindelöf, therefore a proof of Lindelöf equals a major breakthrough in the field of mathematics.
Bernhard Riemann reigns as the mathematician who made the single biggest breakthrough in prime number theory. Prime numbers – numbers like 2, 3, 5, 7 and 11 that are only divisible by 1 and itself – are ideal for things like RSA encryption, which protect our many online purchases. Prime numbers are literally the secret “keys” that hide your latest $35 Amazon purchase from prying eyes.
The Riemann zeta function is an almost magical tool in number theory used to investigate the properties of prime numbers. It has propelled scientific understanding in many fields, including biology, chemistry and physics, all without formal proof of Riemann’s famous hypothesis. “The failure of the Riemann Hypothesis,” wrote number theorist Enrico Bombieri, “would create havoc in the distribution of prime numbers.”
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https://setpublisher.com/index.php/jbas/article/view/1507
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math
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First several new classes of higher order (φ, η, ω, π, ρ, θ, m)-invexities are introduced, and then a set of higher-order parametric necessary optimality conditions and several sets of higher order sufficient optimality conditions for a discrete minmax fractional programming problem applying various higher order (φ, η, ω, π, ρ, θ, m)-invexity constraints are established. The obtained results are new and generalize a wide range of results in the literature.
Chinchuluun A, Pardalos PM. A survey of recent developments in multiobjective optimization. Annals of Operations Research 2007; 154: 29-50. http://dx.doi.org/10.1007/s10479-007-0186-0
Pitea A, Postolache M. Duality theorems for a new class of multitime multiobjective variational problems. Journal of Global Optimization 2012; 54(1): 47-58. http://dx.doi.org/10.1007/s10898-011-9740-z
Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Necessary conditions. Optimization Letters 2012; 6(3): 459-70. http://dx.doi.org/10.1007/s11590-010-0272-0
Pitea A, Postolache M. Minimization of vectors of curvilinear functionals on the second order jet bundle: Sufficient efficiency conditions. Optimization Letters 2012; 6(8): 1657-69. http://dx.doi.org/10.1007/s11590-011-0357-4
Srivastava MK, Bhatia M. Symmetric duality for multiobjective programming using second order -convexity. Opsearch 2006; 43: 274-95.
Srivastava KK, Govil MG. Second order duality for multiobjective programming involving -type I functions. Opsearch 2000; 37: 316-26.
Verma RU. Weak efficiency conditions for multiobjective fractional programming. Applied Mathematics and Computation 2013; 219: 6819-927. http://dx.doi.org/10.1016/j.amc.2012.12.087
Verma RU. A generalization to Zalmai type second order univexities and applications to parametric duality models to discrete minimax fractional programming. Advances in Nonlinear Variational Inequalities 2012; 15(2): 113-23.
Verma RU. Second order invexity frameworks and efficiency conditions for multiobjective fractional programming. Theory and Applications of Mathematics & Computer Science 2012; 2(1): 31-47.
Verma RU. Role of second order -invexities and parametric sufficient conditions in semiinfinite minimax fractional programming. Transactions on Mathematical Programming and Applications 2013; 1(2): 13-45.
Verma RU, Zalmai GJ. Generalized second-order parametric optimality conditions in discrete minmax fractional programming. Transactions on Mathematical Programming and Applications 2014; 2(12): 1-20.
Yang XM, Yang XQ, Teo KL, Hou SH. Second order duality for nonlinear programming. Indian J. Pure Appl. Math. 2004; 35: 699-708.
Zalmai GJ. General parametric sufficient optimality conditions for discrete minmax fractional programming problems containing generalized -V-invex functions and arbitrary norms. Journal of Applied Mathematics & Computing 2007; 23(1-2): 1-23. http://dx.doi.org/10.1007/BF02831955
Zalmai GJ. Hanson-Antczak-type generalized invex functions in semiinfinte minmax fractional programming, Part I: Sufficient optimality conditions. Communications on Applied Nonlinear Analysis 2012; 19(4): 1-36.
Zalmai GJ. Hanson - Antczak - type generalized -V- invex functions in semiinfinite multiobjective fractional programming Part I, Sufficient efficiency conditions. Advances in Nonlinear Variational Inequalities 2013; 16(1): 91-114.
Zeidler E. Nonlinear Functional Analysis and its Applications III, Springer-Verlag, New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5020-3
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) 2016 Ram U. Verma
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https://www.payscale.com/research/AU/Employer=Symantec_Corporation/Salary
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math
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AU$46k - AU$86k
AU$61k - AU$116k
AU$52k - AU$159k
Get a personalized salary report!
AU$54k - AU$99k
AU$34k - AU$59k
AU$64k - AU$144k
AU$76k - AU$127k
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About this Company
Address: 20330 Stevens Creek Blvd. Cupertino, California 95014
Year Established: 1982
Industries: Computer software, Computer, Prepackaged Software, Computer security
Number of Employees: 17,500
Also known as: Symantec, Symantec Corp
How much does Symantec Corporation pay?
Symantec Corporation pays its employees an average of AU$66,773 a year. Salaries at Symantec Corporation range from an average of AU$50,969 to AU$87,478 a year. Symantec Corporation employees with the job title Senior Technical Support Engineer make the most with an average annual salary of AU$98,660, while employees with the title Marketing Manager make the least with an average annual salary of AU$44,947.
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https://www.goramblers.org/academics/academic-programs/junior-high-talented-math-program
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math
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Loyola Academy is offering a program for talented junior high math students. The Loyola Academy Program for Talented Math Students (LAPTMS) will seek to develop the talents of the area’s brightest math students by offering an accelerated math curriculum in which participants will have the opportunity to complete Advanced Placement Calculus and post-Calculus courses by the end of high school.
Loyola Academy’s Program for Talented Math Students is open to students entering at the Algebra 1 or Geometry level of math. Students may begin the program in 7th or 8th grade. Program cost is $1,000.
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http://www.chegg.com/homework-help/questions-and-answers/winch-used-pull-800-kg-crate-ramp-375-m-length-inclined-constant-angle-300-degrees-cable-p-q1270737
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math
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A winch is used to pull a 80.0 kg crate up a ramp 3.75 m in length and inclined at a constant angle of 30.0 degrees. The cable is parallel to the ramp and pulls the crate along the ramp at a constant speed of 0.10 m/s. A coefficient of friction of 0.300 exists between the crate and the ramp.
a) After drawing a free-body diagram, how much work is done by each of the forces on the crate (normal, friction, winch and gravity) as it travels up the ramp? (WN = ? WT = ? Wg = ? Wf = ?)
b) How much power must the winch deliver to the crate while it travels up the ramp? P = ?Show transcribed image text
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982292607.17/warc/CC-MAIN-20160823195812-00034-ip-10-153-172-175.ec2.internal.warc.gz
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http://www.optimization-online.org/DB_HTML/2018/09/6820.html
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math
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On the complexity of an Inexact Restoration method for constrained optimization
L. F. Bueno (lfelipebuenogmail.com)
Abstract: Recent papers indicate that some algorithms for constrained optimization may exhibit worst-case complexity bounds that are very similar to those of unconstrained optimization algorithms. A natural question is whether well established practical algorithms, perhaps with small variations, may enjoy analogous complexity results. In the present paper we show that the answer is positive with respect to Inexact Restoration algorithms in which first-order methods are employed for approximating the solution of subproblems.
Keywords: Complexity, Continuous Optimization, Constrained Optimization, Inexact Restoration Methods, Regularization.
Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )
Citation: September 2018
Entry Submitted: 09/17/2018
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00140.warc.gz
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https://auricherdrachen.de/exterior-angle-theorem-worksheet-answers.html
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math
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Exterior angles are those that formed between any side of a shape, and a line extended from the next side so, how do you measure each exterior angle? For regular polygons, all you have to do is, divide 360 by the number of sides or angles that the polygon has. Simple as that! These worksheets are grounded on all types of different shapes.
For numbers 4 – 6, find the measure of the indicated angle and name the theorems that justify your work. 4. If m ∠1 = ( x + 50)° and m ∠2 = (3 x – 20)°, find m ∠1.
Sep 07, 2019 · Triangle Sum And Exterior Angle Theorem Worksheet are a type of studying aid. Generally speaking the Worksheet is a learning tool as a match or a means of supporting the implementation of the education Plan. Student worksheets in the form of blankets of report in the shape of data and issues (questions) that must be answered by students.
To check exterior angle-measure answers, remember that an exterior angle and the adjacent interior angle must be supplementary. 149 PowerPoint Quick Check 2. a. Guided Instruction Tactile Learners Encourage students to copy the triangle diagram shown immediately above the Triangle Exterior Angle Theorem. Have them cut out the exterior angle
Criterion upright freezer
Triangles And Quadrilaterals Worksheet With Answers Explore The Angles In Quadrilaterals Worksheets Featuring Practice Sets On Identifying A Quadrilateral Based On Its Angles, Finding The Indicated Angles, Solving Algebraic Equations To Determine The Measure Of The Angles, Finding The Angles In Special Quadrilaterals Jun 1th, 2021.
Jul 31, 2008 · Students can use math worksheets to master a math skill through practice, in a study group or for peer tutoring. Use the buttons below to print, open, or download the PDF version of the Corresponding Angles (A) math worksheet. The size of the PDF file is 33120 bytes. Preview images of the first and second (if there is one) pages are shown.
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https://books.google.com.jm/books?id=V8A2AAAAMAAJ&lr=
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math
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Cobb's Explantory Arithmetick, Number Two: Containing the Compound Rules, and All that is Necessary of Every Other Rule in Arithmetick for Practical Purposes and the Transactions of Business ... To which is Annexed a Practical System of Book-keeping
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Cobb's Explantory Arithmetick, Number Two: Containing the Compound Rules ...
No preview available - 2017
acres added Addition answer Arithmetick Begin borrow bushels called carry the quotient cent cipher cloth column Compound containing cost cube currency decimal divide the amount dividend Division divisor dollars drachms equal example EXPLANATIONS express farthings federal money feet figures five four fourth fraction gain gallon given sum gross half higher denomination highest hundred hundred-weight inches interest kind larger learned leaves left hand less loss lower denomination lower line lowest MEASURE merchant bought miles mills minutes months multiply nett weight operation ounces paid payment pence pints pound principal proportion quantity quarters quarts questions Reduce remainder right hand Rule of Three shillings shows Simple sixty Slate sold solid square substract tare tenths term third tion twelve twenty unit upper line weight whole numbers yard
Page 160 - But if any payments be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation, for one year, add- it to the principal, and compute the interest on the sum paid, from the time it was paid up to the end of the year; add it to the sum paid, and deduct that sum from the principal and interest, added as above...
Page 168 - ... then multiply the second and third terms together, and divide their product by the first, the quotient will be the fourth term or answer, in the same denomination vj'ilh the third term.
Page 160 - If the payment be less than the interest, the surplus of the interest must not be taken to augment the principal ; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due...
Page 158 - If a year extends beyond the time of payment, then find the amount of the principal...
Page 159 - The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. " If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due.
Page 154 - ... 3d. If there be parts of a year, as months and days, work for the months by the aliquot parts of a year...
Page 160 - Compute the interest to the time of the first payment ; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and in like manner from one payment to another, till all the payments are absorbed; provided the time between one payment and another be one year or more.
Page 212 - Separate the given number into periods of three figures each, by putting a point over the unit figure, and every third figure beyond the place of units. 2. Find the greatest cube in the left hand period, and put its root in the quotient. 3.
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http://www.solutioninn.com/the-prices-of-a-random-sample-of-comparable-matched-textbooks
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math
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The prices of a random sample of comparable (matched) textbooks from two schools were recorded. We are comparing the prices at OC (Oxnard Community College) and CSUN (California State University at Northridge). Assume that the population distribution of differences is approximately Normal. Each book was priced separately; there were no books "bundled" together.
a. Compare the sample means.
b. Determine whether the mean prices of all books are significantly different. Use a significance level of 0.05.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822851.65/warc/CC-MAIN-20171018085500-20171018105500-00695.warc.gz
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https://verywellwiki.com/miscellaneous/how-do-you-calculate-energy-potential/
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math
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How do you calculate energy potential?
What is the formula to calculate potential?
V = k × [q/r]
- V = electric potential energy.
- q = point charge.
- r = distance between any point around the charge to the point charge.
- k = Coulomb constant; k = 9.0 × 109 N.
What is the formula for potential energy examples?
Here, the mass of the object (m) = 1 kg, Displacement (height) (h) = 10 m, Acceleration due to gravity (g) = 9.8 m s–2. Hence, Potential energy (P) = m×g×h = 1 kg × 9.8 m s–2 × 10 m = 98 J.
How do you calculate potential energy and kinetic energy?
How do you solve a potential energy problem?
How do you find potential energy in joules?
What is potential energy?
potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth.
What does 1/2 mv2 stand for?
The Kinetic energy is the energy that an object has due to its motion. Ek, is the energy of a mass, m, in motion, v2. Ek = 1/2 mv2.
How do I calculate kinetic energy?
If you know the mass and velocity of an object, use the kinetic energy calculator to find it’s energy in movement….To calculate kinetic energy:
- Find the square of the velocity of the object.
- Multiply this square by the mass of the object.
- The product is the kinetic energy of the object.
How do you calculate the change in potential energy?
The change in potential energy is the charge times the potential difference (equation 20-2). The change in potential energy equals the gain in kinetic energy, which can then be used to find the speed. difference required to change the proton’s speed and kinetic energy.
How is potential difference calculated?
Multiply the amount of the current by the amount of resistance in the circuit. The result of the multiplication will be the potential difference, measured in volts. This formula is known as Ohm’s Law, V = IR.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711045.18/warc/CC-MAIN-20221205200634-20221205230634-00645.warc.gz
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CC-MAIN-2022-49
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https://www.yourdictionary.com/quadratic-equation
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math
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An equation that employs the variable x having the general form ax2 + bx + c = 0, where a, b, and c are constants and a does not equal zero; that is, the variable is squared but raised to no higher power.
An equation in which the second power, or square, is the highest to which the unknown quantity is raised.
The value of such a fraction is the positive root of a quadratic equation whose coefficients are real and of which one root is negative.
In his Treatise of Algebra (1685) he distinctly proposes to construct the imaginary roots of a quadratic equation by going out of the line on which the roots, if real, would have been constructed.
Consider the general quadratic equation ax 2 + bx + c = 0 where a 0.
The quadratic equation x 2 +b 2 =o, for instance, has no real root; but we may treat the roots as being +b-' - I, and - b 1, 1 - 1, if -J - i is treated as something which obeys the laws of arithmetic and emerges into reality under the condition 1 1 - I.
Solve a quadratic equation using factors Errors Identify sources of errors.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510529.8/warc/CC-MAIN-20230929222230-20230930012230-00865.warc.gz
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CC-MAIN-2023-40
| 1,044
| 7
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http://www.brothersoft.com/easy-math-download-118991.html
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math
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218186353.38/warc/CC-MAIN-20170322212946-00142-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
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