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http://www.chegg.com/homework-help/questions-and-answers/imagine-mike-lives-earth-rest-sara-traveling-past-theearth-velocity-8900m-s-meteor-moving--q144103 | math | Imagine Mike lives on the earth at rest. Sara is traveling past theearth with a velocity of 8900m/s. If a meteor moving in the samedirection passes Sara, Mike sees the meteor velocity to be13600m/s. Suppose that a photon of light is passing Sara instead ofa meteor. Mike measures the photon speed to be c, thespeed of light. What speed does Sara measure? | s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860124045.24/warc/CC-MAIN-20160428161524-00085-ip-10-239-7-51.ec2.internal.warc.gz | CC-MAIN-2016-18 | 354 | 1 |
https://www.hoferlife.at/de/ebook-download/wissenschaft/mathematik-naturwissenschaft-und-technik/naturwissenschaft-und-technik-allgemein/linearity%2C-symmetry%2C-and-prediction-in-the-hydrogen-atom/p/2013022201593 | math | Linearity, Symmetry, and Prediction in the Hydrogen Atom
The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, involving the mathematical area of representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra. Wide applications of this method occur in crystallography, atomic structure, classification of manifolds with symmetry, and other areas. The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. Then the reader is given just enough mathematical tools to make predictions about the numbers of each kind of electronic orbital based solely on the physical spherical symmetry of the hydrogen atom. The final chapters address the related ideas of quantum spin, measurement and entanglement. This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. Linearity, Symmetry, and Prediction in the Hydrogen Atom will benefit students in mathematics, physics and chemistry, as well as a literate general readership. A separate solutions manual is available to instructors.
Weiterlesen weniger lesen | s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670535.9/warc/CC-MAIN-20191120083921-20191120111921-00410.warc.gz | CC-MAIN-2019-47 | 1,679 | 3 |
https://mully.net/en/entropy_en/ | math | Where did the pendulum’s energy go?
A pendulum that vibrates in the air continues to collide with air molecules in the process of vibrating. Air molecules get their energy from the pendulum. In this process, Air molecules increase their speed. Conversely, the pendulum has lost its energy.
Eventually, the mechanical energy in the pendulum is converted into the air molecule’s heat energy.
Mechanical energy of the pendulum → heat energy of air molecules
A phenomenon that can return to its original state, such as electrons moving in a vacuum, is called a ‘reversible phenomenon.’
However, most natural phenomena are ‘irreversible phenomena’ that occur only in one direction.
Let’s take an example of a pendulum. Can the pendulum move itself using the heat energy of air molecules?
If many air molecules collide with the pendulum in one direction, the pendulum can move by itself. However, this doesn’t happen because each air molecule has a disorderly movement.
As such, most natural phenomena are irreversible, occurring only in one direction. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943809.76/warc/CC-MAIN-20230322114226-20230322144226-00625.warc.gz | CC-MAIN-2023-14 | 1,064 | 9 |
https://www.coursehero.com/file/6621155/02-P34InstructorSolution/ | math | 2.34. Solve:(a)The velocity is the integral of the acceleration. ()11102210000 m/s101010tttxxxtvvadttdtt t=+=+− = −= −∫∫The velocity is zero when ( )( )211110100 sor20 sxvtttt==−=−×⇒==The first solution is the initial condition. Thus the particle’s velocity is again 0 m/s at 120 s.t=(b)Position is the integral of the velocity. At
This is the end of the preview.
access the rest of the document. | s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948592202.83/warc/CC-MAIN-20171217000422-20171217022422-00163.warc.gz | CC-MAIN-2017-51 | 415 | 3 |
http://openstudy.com/updates/522a49fde4b0fbf34d628e78 | math | At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
?? What's the question
my net is working very slow that s y i m unable to post my answer and question
tan B goes up side down
my solution is incorrect
sinC is wrong
cos C, tan C are both wrong
what would be sinC
what is the definition of sin? sin = opposite/hypotenus, what are they for C?
hey, you ask for check, not for guiding, I am not good at teaching, please @surjithayer teach him.
IN tr. ABC , angle A = 90 degree (given)
I don't talk about A, I am talking about C
your questions are about B and C. Surely A is right angle. When considering B, ignore everything else. just B. The same with C, to C, consider which is its opposite, which is its adjacent, then, put them into formula, that's it. Redo, please, I can check. I don't do it for you. Wish you can do it by yourself.
plse any one tell me urgently needed
sin SOH cos CAH Tan TOA Sin is the Opposite side over the Hypotenuse side Cos is the Adjacent side over the Hypotenuse side Tan is the Opposite side over the Adjacent side
|dw:1378505159254:dw| i have not mentioned angle. I have written in general.
you misunderstanding many basic concept, 90 degree is a right angle. In a triangle, cannot have 2 right angles. In a triangle , total of 3 angles is 180 degree
now everybody is confusing me
sinC = opposite / hypotenuse
you need to check your answers .. all wrong i think
sinB = opposite / hypotenuse .. that's opposite side of the given angle over its hypotenuse ..
hope it helps a bit
sinB = AC/BC cosB = AB/BC tanB= sinB/cosB = AC/AB sinC = AC/BC cosC = AB/BC tanC = sinC/cosC = AC/AB
try to check again sinC, cosC and tanC ..
|dw:1378544651728:dw| use the figure below to answer sinC, cosC and tanC
adjacent side = AC
so sinC= AB/BC cosC=AC?BC
yes, you got it
where's your final answer? | s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806660.82/warc/CC-MAIN-20171122194844-20171122214844-00034.warc.gz | CC-MAIN-2017-47 | 2,451 | 29 |
http://kosiyaefirewalls.com/software/positional-notation-binary-options.php | math | Positional notation or place-value notation is a method of representing or encoding numbers. . The binary numeral system, base-2, is straightforwardly implemented in digital electronic circuitry and used by. . and this extends with few, if insignificant, variations on the choice of alphabetic digits for those bases above 10.
I'm using positional notation method convert binary to decimal and its different i guess nobody has tried it yet i guess, and in this I'm using for_each loop Here are some steps: store binary as.
Positional Notation What if 642 has the base of 13? 642 in base 13 is. 10 Power of 2 Number System Binary Octal Decimal 000 001 1 010 2 011 3 001 1 010 2.
Binary number - Wikipedia
Convert Erlang integer to positional notation binary. Ask Question. up vote 0 down vote favorite. I can convert an integer to a binary easily in Erlang: Binary options trade on the Nadex exchange, the first legal U.
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The trading platform provides real-time charts along with direct market access to current binary option prices. They are the Goldilocks choice among numbering systems: When base 2 is too.
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The general formula for a numeral in any positional notation goes something like. Base 2 dominates computing technology because binary devices are simple.
Binary options let traders profit from. What You Need To Know About Binary Options. the trader's account when the position is closed.
Other Types of Binary. A positional or place-value notation is a numeral system in which each position is related. The choice of base determines the set of numerals that will be used. | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202723.74/warc/CC-MAIN-20190323040640-20190323062640-00475.warc.gz | CC-MAIN-2019-13 | 1,857 | 12 |
https://socratic.org/questions/how-do-you-factor-3x-2-7x-6 | math | How do you factor #3x^2-7x-6#?
Ans: (3x + 2)(x - 3).
Use the new AC Method: y = 3(x - p)(x - q)
p' and q' have opposite signs. (Rule of signs)
Factor pairs of (-18)--> (-2, 9). This sum is 7 = -b.
Change this sum to the opposite. Then p' = 2 and q' = -9. | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540500637.40/warc/CC-MAIN-20191207160050-20191207184050-00463.warc.gz | CC-MAIN-2019-51 | 254 | 6 |
https://www.techvenge.net/jigsaw-puzzle-boxes/ | math | It all started with a 1 smart kid
A few weeks ago, Patrick Honner, who is an award-winning math teacher, posted a realization on Twitter. His 7-year-old had just realized discovered that their 300-piece jigsaw puzzle was made out of 324 pieces as it was in an 18 x 18 format.
Calculating number of pieces – DIY
What this means is that a puzzle number is regarded as valid if it is a y x z format. In this format, y is lesser than or equal to z and z is equal to or lesser than 4z. The constant 4 is a random choice and can be any number according to the specification of a certain puzzle. With that in mind, a puzzle number would be something that looks like this, 10x4 = 40, 20x4 = 80, and 30x4 = 120. In the OEIS puzzle, numbers can be found under A071562, where they are described as numbers whose middle divisor is not zero. A middle divisor is the divisor of a number that is between the square root of a number divided by 2 and the square root of a number x 2. This means your middle divisors will have to be 8.660254037844386 and 34.64101615137755 to make a puzzle that will have exactly 300 pieces. However, puzzle piece rows are rarely ever arranged in this manner as they usually get rounded over to the nearest natural number. That is why most manufacturers choose to divide their desired number of pieces with a middle divisor to determine how many pieces will be on one row.
truth vs. Practice
After determining how many rows one side will have using the middle divisor, the remaining number will be used to constitute the other side’s rows. Due to this, the number of pieces advertised on jigsaw puzzle boxes rarely ever represent what you will find inside and math enthusiasts on the internet have realized this.
One of those math enthusiasts is known as John D. Cook once said jigsaw puzzles that claim to have 1,000 pieces mean they approximately have 1,000 pieces. He said the term “1000-piece” is not meant in its literal form because puzzle pieces are normally arranged in a grid-like formation. Since the pieces are in a grid-like formation, this means the number of pieces on one side is a divisor of the total number of pieces. Cook said the grid formation found in many jigsaw puzzles makes it very hard for manufacturers to make a puzzle that has exactly 1,000 pieces. Cook’s assessment of 1,000-piece jigsaw puzzles makes it easier for us to understand why most puzzles have aspect ratios that produce numbers that are around the advertised sum.
Also, there is a puzzle blog that suggests that most 500-piece jigsaw puzzles have 513 pieces. The blog says this because most manufacturers use an aspect ratio of 27 x 19 to make 500-piece puzzles. They also said that most manufacturers also use 38 x 27 aspect ratios to make 1,000-piece puzzles. The 38 x 27 and 27 x19 aspect ratios can be translated as “2Y-piece” and “y-piece.” That makes it a better working model for manufacturers who want to produce both 500-piece and 1,000-piece puzzles. | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473598.4/warc/CC-MAIN-20240221234056-20240222024056-00693.warc.gz | CC-MAIN-2024-10 | 2,986 | 8 |
http://www.mathemafrica.org/?p=13259 | math | Why ? I assume this is the question on everyone’s mind. (Whether you’re a Math lover or not)
The simple answer would be that we all love pie, now don’t we?
Before I begin discussing any technicalities, I’d like to acknowledge that it is possible for some of us to find the concepts easy whilst others might struggle with them. This is the reason why I’m choosing to speak in a very simple and understandable manner. (I’m baby proofing my post!)
Firstly, let us have a look at the Maclaurin series of
Aside: A Maclaurin series is a polynomial which approximates a function around the point x = 0. The level of accuracy decreases as you move further away from x = 0. The only way to get an exact answer and not an approximate is to let the sum go to infinity.
Below is a table of the first few derivatives of . We will now use this to determine what the Maclaurin polynomial should look like.
It is now quite clear that the polynomial should look something like this:
The next step is quite clever. Since = (Some of you may know this as 45 degrees); we can let x = 1 to arrive at an expression for . It is now evident that if we multiply the series by 4 we will arrive at an expression for . This is shown as follows:
Now let us try out the result we’ve just arrived at and see just why it is the least preferred method of approximating . It is quite easy to see the pattern in the terms of the above sum. So let us see how our sum converges towards to the value of as we increase the number of terms. These calculations can be done using WolframAlpha if your calculator has insufficient memory.
The sum we will be using is as follows:
When the number of terms = 10, the sum equals 3.232315809505594
When the number of terms = 100, the sum equals 3.1514934010709914
This looks horrible, doesn’t it? Intuitively, we all know that = 3.14… So what’s going wrong? A good answer would be that this series converges towards at an extremely slow rate so even though it doesn’t seem to be accurate right now; it’ll most definitely be more accurate if we add more terms to the sum. Before we do this, let us try and understand why it converges so slowly. One reason is the fact that our sum provides accurate approximations around the point x = 0, but here we are approximating around the point x = 1. Secondly, we multiplied the sum for by 4 which added to the inaccuracy when approximating itself. Of course, there are a few other reasons as well.
Why don’t we sum ten million terms and see what we arrive at? This gives us a value of 3.1415927535897814. It is clear now that this value is equal to up to 7 decimal places.
I hope that the above paragraph proves why this is the least preferred method of approximating . The reason I chose to discuss it is because it is relatively simple to understand in comparison to other sums which do in fact arrive at much better approximations of in a much shorter time span. Lastly, I think we can all agree that this method is quite beautiful in its own way. | s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740343.48/warc/CC-MAIN-20200814215931-20200815005931-00039.warc.gz | CC-MAIN-2020-34 | 3,017 | 15 |
https://www.grandtermpapers.com/the-arrival-time-of-an-elevator-in-a-12-story-dormitory-is-equally-likely-at-any-time-range-during-the-next-3-6-minutes-a-calculate-the-expected-arrival-time-round-your-answer-to-2-decimal-places/ | math | The arrival time of an elevator in a 12-story dormitory is equally likely at any time range during the next 3.6 minutes. a. Calculate the expected arrival time. (Round your answer to 2 decimal places.) b. What is the probability that an elevator arrives in less than 2 minutes? (Do not round intermediate calculations. Round your answer to 4 decimal places.) c. What is the probability that the wait for an elevator is more than 2 minutes? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
Use this worksheet to strategize a plan for how you will conduct your study to best examine your hypothesis. Reviewing Chapters 6 and 15 and the chapter that corresponds to your particular design (one of the chapters from 7 through 14) is helpful for this assignment. Please write in complete sentences and please submit a completed worksheet.
TOPIC: How effective is ABA therapy for children with Autism?
Due by 9 pm on June 11th, 2023! | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100308.37/warc/CC-MAIN-20231201215122-20231202005122-00025.warc.gz | CC-MAIN-2023-50 | 958 | 4 |
http://pepaperunhg.gvu-edu.us/a-descriptive-explanation-of-the-physics-in-playing-golf.html | math | To understand the physics of a golf swing one must consider the mechanics of hit than if the golf club were held rigid (meaning the wrists are not allowed to.
Many people consider golf to be an art form - but if it is, it's one that's founded on physics: momentum, impulse, force and torque, all of which can be explained with and that's just the equation describing the “wrist joint torque necessary to.
And the torques that generate power in the golf swing robert d grober describing what can be learned by measuring the motion of the golf club using two a biomechanical explanation for the ratio was hypothesized. Modeling in golf, by briefly describing a few of the many ways mathematics can be used to understand or the physics of the golf club and ball • the impact of element analysis or via simplified 1- or 2-dimensional models 3 the ball's. But a golf ball when it leaves the club is only in rare cases devoid of spin, and it the ball moves off to the left, describing the path indicated by the dotted line this is before proceeding to the explanation of this effect of spin, i will show some.
The physics of a golf swing and the swing release angle hit than if the golf club were held rigid (meaning the wrists are not allowed to rotate during the swing. | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515539.93/warc/CC-MAIN-20181022201445-20181022222945-00005.warc.gz | CC-MAIN-2018-43 | 1,271 | 4 |
https://ifedugadokir.gq/generalized-network-design-problems-modeling-and-optimization.php | math | The principal objective of this book is to present a collection of challenging test problems arising in literature studies and a wide spectrum of applications. Due to the non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth optimization model is established. A generalized bundle subgradient projection is presented to effectively solve the network design problem.
Global convergence analysis for the proposed method is also delivered. Network design problems NDP consist of identifying an optimal subgraph of a graph, subject to side constraints. In generalized NDP, the vertex set is partitioned into clusters and the feasibility conditions are expressed in terms of the clusters.
Fuzzy generalized network approach for solving. Formulation and feasibility test of optimal road network design model with endogenously determined travel demand. Proceedings of the 5th World Conference on Transport.
Abstract: Many combinatorial optimization problems can be considered as nding a subgraph of a given graph with di erent requirements of graph properties e. They can be generalized for network design in di erent application areas, such as power. Solving the Transit Network Design problem with Constraint. Modeling and solving a distribution network design problem. Wiley Online Library. Several results Generalized network design problems : modeling. Chapter 11 Net w ork Optimization Net ork mo dels ha v e three main adv an tages o v er linear programming: 1.
They can b e solv ed v ery quic kly.
Approximating the Generalized Capacitated Tree-Routing Problem | SpringerLink
Problems whose linear program w ould ha v e ro ws and 30, columns can b e solv ed in a matter. Generalized Network Design Problems : Modeling. Network Optimization: Continuous and Discrete Models. The monograph describes in a unified manner a series of mathematical models, methods, propositions, and algorithms developed. The LLamasoft Digital Design and Decision Center provides end-to-end supply chain perspective to quickly pinpoint inefficiencies to offer solutions to create the network you want.
Create digital models to evaluate and compare trade-offs of potential supply chain network changes. By modeling in a no-risk environment, you can make high-stakes. General Optimization Methods for Network Design of different notational conventions for modeling and formulating network design problem and introduces the. A variety of practical network optimization problems arising in the context of models and the analysis of five such problems, and the subsequent design and new algorithm for solving the generalized lp distance location-allocation problem.
In what it follows we describe an application encountered in the design of regional network design.
Network models Network representation is widely used in:. Alggorithms and software are beingg used to solve hugge network problems on a routine basis. Many network problems are special cases of linear. Design network inserting links in order. This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method.
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Sustainable supply chain network design: An optimization. Transportation models play an important role in logistics and. The express purpose of this monograph is to describe a series of mathematical models, methods, propositions, algorithms developed in the last years on generalized network design problems in a unified. After separately studying these two pooling problem instantiations, we have unified our work by developing APOGEE Algorithms for Pooling-problem Optimization in GEneral and Extended classes , a generic computational tool that globally optimizes standard, generalized, and extended pooling problems.
Generalized network design problems : modeling and optimization
Generalized Network Design Problems Modeling and Optimization In combinatorial optimization, many network design problems can be generalized in a natural way by considering a related problem on a clustered graph, where the original problem s feasibility constraints are expressed in terms of the clusters, i. Decomposition Methods and Network Design Problems.
Network Optimization by Generalized Methodology - wseas. Introduction to Network Models Network models are applicable to an enormous variety of decision problems that can be modeled as networks optimization problems and solved efficiently and effectively. Some of these decision problems are really physical problems such as transportation or flow of commodities. Integer programming models and branch-and-cut approaches.
The generalized methodology for the electronic networks optimization was elaborated by means of the optimal control theory approach. In this case the problem of the electronic system design. Mathematical optimization alternatively spelled optimisation or mathematical programming is the selection of a best element with regard to some criterion from some set of available alternatives.
Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods Ordinary network flow models require flow conservation on all arcs: The amount of flow entering an arc equals the amount of flow leaving the arc.
Generalized network flow models, on the other hand, is a generalization of standard network flow models in which each arc of the underlying graph has an associated positive gain or loss factor. Generalized Network Design Problems by Petrica The Modeling and Optimization: Theory and Applications MOPTA conference is an annual event aiming to bring together a diverse group of people from both discrete and continuous optimization, working on both theoretical and applied aspects. Optimal solutions generated turn out to be integer if the relevant constraint data are integer.
A common. PAPER Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures There are various ways that network functionalities can be allocated to different layers and to different network elements, some being more desirable than others. The intellectual goal of the research surveyed by this article is to provide. Model and heuristic for a generalized access network.
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- Generalized Network Design Problems: Modeling and Optimization by Petrica C. Pop - ifedugadokir.gq;
Model predictive control MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models. Authors; In this paper the routing problem is formulated as a fuzzy multiobjective optimization model.
The fuzzy approach allows for the inclusion and evaluation of several criteria simultaneously. The express purpose of this monograph is to describe a series of mathematical models, methods, propositions, algorithms developed in the last years on generalized network design problems in a unified manner. The book consists of seven chapters, where in addition to an introductory chapter, the following generalized network design problems are formulated and examined: the generalized minimum spanning tree problem, the generalized traveling salesman problem, the railway traveling salesman problem, the generalized vehicle routing problem, the generalized fixed-charge network design problem and the generalized minimum vertex-biconnected network problem.
The book will be useful for researchers, practitioners, and graduate students in operations research, optimization, applied mathematics and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will find this book useful, too. Petrica C.
Related Generalized Network Design Problems: Modeling and Optimization
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https://studysolve.online/wbp-math-solution-bengali-pdf-download/ | math | WBP Math Solution Bengali PDF Download: Dear students, are you looking for WBP Math solutions Bengali PDF? If yes, then here is the right place for you. Because in this post you are going to download WBP Math Somadhan or Solution PDF.
This math solution will be very helpful for West Bengal Police Constable Preliminary Exam. So, if you are preparing for the upcoming WBP Preliminary, then you must download this Math Solution PDF or WBP Preliminary Maths Solved Paper pdf in Bengali.
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https://rd.springer.com/chapter/10.1007/978-1-349-02767-5_8 | math | There are practical situations where one would like to estimate some parameters of an underlying statistical distribution. For example, a toothpaste manufacturer would like to make a statement such as his new toothpaste would reduce cavities by 21 to 49%. Here the manufacturer is interested in two numbers such as 21% and 49% such that the true proportion of reduction in cavities is somewhere between 21% and 49%. A weather bureau may forecast the temperature variation in a forthcoming month as between a°F and b°F and it may claim that, the forecast will be correct in 95% of the cases. A design engineer would like to get an estimate of the average weight of the type of passengers who are likely to fly, when designing an aircraft. In all these problems one would like to get an estimate of an unknown quantity. In statistical estimation problems, one is interested in getting an estimate of either an unknown parameter or an unknown probability-statement. Two types of estimates for a parameter are usually sought for. They are the point estimates and the interval estimates.
KeywordsStatistical Estimation Interval Estimate Stomach Ulcer Central Interval True Proportion
Unable to display preview. Download preview PDF. | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592875.98/warc/CC-MAIN-20180722002753-20180722022753-00033.warc.gz | CC-MAIN-2018-30 | 1,229 | 3 |
https://techcommunity.microsoft.com/t5/Excel/Excel-Formula-for-Colored-cells/td-p/752956 | math | Hello see the attached screen shot is there a way to write a formula so that I can add up the colored cells per color?column F please advise me.
Perform any calculations based on color that's only with VBA programming, formulas work with values. But if you have some formal rules why this or that color is applied, such rules could be used for the calculations.
@Sergei Baklan well red equals dead jobs green equals sold jobs and peach equals jobs bid pending
Sorry, but that says me nothing. What it will be in Excel terms? For example, if cell in column C is equal to "Dead" then red, if equal to "Sold" then green, etc
@Sergei Baklan wsell it would be as follows then
if cell in column F is red then equakls dead
if cell in column f is green it equals sold
if cell in column f is peach then equals bid / pending
I meant opposite - if cell value is ... then ...
You may add one more column with the status which could be selected from drop-down menu: dead, sold, pending.
Base on values in this column you may color your table using conditional formatting and make some calculations taking status values as logical test. | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540521378.25/warc/CC-MAIN-20191209173528-20191209201528-00315.warc.gz | CC-MAIN-2019-51 | 1,122 | 11 |
https://collaborate.princeton.edu/en/publications/the-longest-cycle-of-a-graph-with-a-large-minimal-degree | math | We show that every graph G on n vertices with minimal degree at least n/k contains a cycle of length at least [n/(k − 1)]. This verifies a conjecture of Katchalski. When k = 2 our result reduces to the classical theorem of Dirac that asserts that if all degrees are at least 1/2n then G is Hamiltonian.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Geometry and Topology | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476137.72/warc/CC-MAIN-20240302215752-20240303005752-00585.warc.gz | CC-MAIN-2024-10 | 417 | 4 |
https://www.reference.com/web?q=find%20equation%20of%20line%20excel&qo=pagination&o=600605&l=dir&sga=1&qsrc=998&page=4 | math | To find the slope of a line, often written as m, take two points on the line, (x1,y1) and (x2,y2); the slope is equal to (y2 - y1)/(x2 - x1). Y-intercept (b): The y-intercept of a line, often written as b, is the value of y at the point where the line crosses the y-axis. The equation of a straight line is y = mx + b.
The Excel Linest Function uses the least squares method to calculate the line of best fit through a supplied set of y- and x- values. If there is a single range of x-values, the calculated line satisfies the simple straight line equation:
I've used goal seek to solve equations, but it is not very useful when there are several possible solutions and one needs them all. I also have used trendlines in charts to find the equation for the line of best fit. Not quite the same as solving equations, but easier than running linear regressions to find the same result.
How do i find the equation of the line and R2? I don't have Excel 2008 handy to test, but usually one way is to right-click (or Control-click) the trendline, choose Format Trendline from the pop-up menu, click Options, click "Display equation on chart" and "Display R-squared value on chart," and click OK.
Equations in excel are none other than our formulas which we type in cell, to write an equation we start with an equals to sign (=) which excel recognizes as to calculate and then we use variables which are connected with each other with some operators, depending upon the operators we get results, an equation can be both linear or non linear.
In this article, we will see how to solve it with Excel. To find intersection of two straight lines: First we need the equations of the two lines. Then, since at the point of intersection, the two equations will have the same values of x and y, we set the two equations equal to each other. This gives an equation that we can solve for x
Select "Linear," click the box for "Display Equation on chart" and click "Close." This trend line is an approximation for the actual tangent line. The equation for the trendline is displayed on the graph using the "y = mx + b" format. Using the previous example, this gives the approximate equation for the tangent line as "y = 0.5x + 2.5."
In Correlation we study the linear correlation between two random variables x and y. We now look at the line in the xy plane that best fits the data (x 1, y 1), …, (x n, y n).. Recall that the equation for a straight line is y = bx + a, where b = the slope of the line a = y-intercept, i.e. the value of y where the line intersects with the y-axis. For our purposes we write the equation of the ...
I want to show my college class how to create an XY scatter plot on Excel, and to show the trendline together with the equation of the line, and R squared value. Our institution recently bought top of the line ipads for all students. Yet I cannot figure out how to get the equation of the line to show on the ipad.
In scattered table,i draw linear trend line. my trendline equation is y=5.3864x+37.5. I use an formula to find angle of trend line.The formula is | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141182794.28/warc/CC-MAIN-20201125125427-20201125155427-00263.warc.gz | CC-MAIN-2020-50 | 3,076 | 10 |
https://library.exemplars.com/representations/difference | math | Rounding to the nearest 10, students determine how many insects are let go from glass jars.
Given the amount of cans of paint on two shelves, student determine how many cans of paint are on the third shelf.
Students determine how many balloons Betty has left after giving some to Ben.
Students determine how many pink shells Kim found on the beach.
Students determine how many plastic dinosaurs Danny has left after he gives some to a friend.
Students determine how many nuts Sam the squirrel hides under a rock.
Students find the total number of legs on 8 cows and 10 chickens.
Students determine possible movie seating arrangements for 30 students.
Just verify your email address, and we'll send it out. | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107919459.92/warc/CC-MAIN-20201031151830-20201031181830-00282.warc.gz | CC-MAIN-2020-45 | 705 | 9 |
https://solvedlib.com/n/eala-300n12013given-ue-amal23-19-13-gt-find-tho-rna6verify,6872026 | math | But were asked to prove that if B is equal to P. Inverse AP and X is an Eigen vector of a corresponding to an Eigen Value lambda, then PM Verse X is an Eigen vector of B corresponding also to Lambda. So we have that. Yes, A X is equal to Lambda X, where, of course, Lambda is not equal to zero or not. Lambda.
I mean, the Eigen Vector X is non zero by definition. Then we have that P inverse a X well, this is equal to Lambda P Inverse X now since be was PM verse AP It follows that be times p Inverse Times X is equal to p inverse ap times p inverse X which is equal to well, because PM's PM versus the identity. This is the same as P inverse times A. Which times the identity is still a Times X and here I'll group the A and the X together for emphasis. This is the same as P inverse times Lambda X, which is the same as land of times p in verse X.
So it follows that well, we have that X is non zero and we have that p is in vertebral, so it follows that P inverse of X Times X is also a non zero vector. This is actually because p and verses in vertical So we have that p inverse Times X is an Eigen vector of be corresponding to I can value of Lambda.. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511361.38/warc/CC-MAIN-20231004052258-20231004082258-00460.warc.gz | CC-MAIN-2023-40 | 1,157 | 3 |
https://www.knowpia.com/knowpedia/Deontic_logic | math | Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that A (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A, which is defined as .
Note that in natural language, the statement "You may go to the zoo OR the park" should be understood as instead of , as both options are permitted by the statement; See Hans Kamp's paradox of free choice for more details.
When there are multiple agents involved in the domain of discourse, the deontic modal operator can be specified to each agent to express their individual obligations and permissions. For example, by using a subscript for agent , means that "It is an obligation for agent (to bring it about/make it happen) that ". Note that could be stated as an action by another agent; One example is "It is an obligation for Adam that Bob doesn't crash the car", which would be represented as , where B="Bob doesn't crash the car".
In Georg Henrik von Wright's first system, obligatoriness and permissibility were treated as features of acts. Soon after this, it was found that a deontic logic of propositions could be given a simple and elegant Kripke-style semantics, and von Wright himself joined this movement. The deontic logic so specified came to be known as "standard deontic logic," often referred to as SDL, KD, or simply D. It can be axiomatized by adding the following axioms to a standard axiomatization of classical propositional logic:
In English, these axioms say, respectively:
FA, meaning it is forbidden that A, can be defined (equivalently) as or .
where . It is generally assumed that is at least a KT operator, but most commonly it is taken to be an S5 operator. In practical situations, obligations are usually assigned in anticipation of future events, in which case alethic possiblities can be hard to judge; Therefore, obligation assignments may be performed under the assumption of different conditions on different branches of timelines in the future, and past obligation assignments may be updated due to unforeseen developments that happened along the timeline.
The other main extension results by adding a "conditional obligation" operator O(A/B) read "It is obligatory that A given (or conditional on) B". Motivation for a conditional operator is given by considering the following ("Good Samaritan") case. It seems true that the starving and poor ought to be fed. But that the starving and poor are fed implies that there are starving and poor. By basic principles of SDL we can infer that there ought to be starving and poor! The argument is due to the basic K axiom of SDL together with the following principle valid in any normal modal logic:
If we introduce an intensional conditional operator then we can say that the starving ought to be fed only on the condition that there are in fact starving: in symbols O(A/B). But then the following argument fails on the usual (e.g. Lewis 73) semantics for conditionals: from O(A/B) and that A implies B, infer OB.
Indeed, one might define the unary operator O in terms of the binary conditional one O(A/B) as , where stands for an arbitrary tautology of the underlying logic (which, in the case of SDL, is classical).
The accessiblity relation between possible world is interpreted as acceptibility relations: is an acceptable world (viz. ) if and only if all the obligations in are fulfilled in (viz. ).
Alan R. Anderson (1959) shows how to define in terms of the alethic operator and a deontic constant (i.e. 0-ary modal operator) standing for some sanction (i.e. bad thing, prohibition, etc.): . Intuitively, the right side of the biconditional says that A's failing to hold necessarily (or strictly) implies a sanction.
In addition to the usual modal axioms (necessitation rule N and distribution axiom K) for the alethic operator , Anderson's deontic logic only requires one additional axiom for the deontic constant : , which means that there is alethically possible to fulfill all obligations and avoid the sanction. This version of the Anderson's deontic logic is equivalent to SDL.
However, when modal axiom T is included for the alethic operator ( ), it can be proved in Anderson's deontic logic that , which is not included in SDL. Anderson's deontic logic inevitably couples the deontic operator with the alethic operator , which can be problematic in certain cases.
An important problem of deontic logic is that of how to properly represent conditional obligations, e.g. If you smoke (s), then you ought to use an ashtray (a). It is not clear that either of the following representations is adequate:
Under the first representation it is vacuously true that if you commit a forbidden act, then you ought to commit any other act, regardless of whether that second act was obligatory, permitted or forbidden (Von Wright 1956, cited in Aqvist 1994). Under the second representation, we are vulnerable to the gentle murder paradox, where the plausible statements (1) if you murder, you ought to murder gently, (2) you do commit murder, and (3) to murder gently you must murder imply the less plausible statement: you ought to murder. Others argue that must in the phrase to murder gently you must murder is a mistranslation from the ambiguous English word (meaning either implies or ought). Interpreting must as implies does not allow one to conclude you ought to murder but only a repetition of the given you murder. Misinterpreting must as ought results in a perverse axiom, not a perverse logic. With use of negations one can easily check if the ambiguous word was mistranslated by considering which of the following two English statements is equivalent with the statement to murder gently you must murder: is it equivalent to if you murder gently it is forbidden not to murder or if you murder gently it is impossible not to murder ?
Some deontic logicians have responded to this problem by developing dyadic deontic logics, which contain binary deontic operators:
(The notation is modeled on that used to represent conditional probability.) Dyadic deontic logic escapes some of the problems of standard (unary) deontic logic, but it is subject to some problems of its own.[example needed]
Philosophers from the Indian Mimamsa school to those of Ancient Greece have remarked on the formal logical relations of deontic concepts and philosophers from the late Middle Ages compared deontic concepts with alethic ones.
In his Elementa juris naturalis (written between 1669 and 1671), Gottfried Wilhelm Leibniz notes the logical relations between the licitum (permitted), the illicitum (prohibited), the debitum (obligatory), the, and the indifferens (facultative) are equivalent to those between the possibile, the impossibile, the necessarium, and the contingens respectively.
Ernst Mally, a pupil of Alexius Meinong, was the first to propose a formal system of deontic logic in his Grundgesetze des Sollens (1926) and he founded it on the syntax of Whitehead's and Russell's propositional calculus. Mally's deontic vocabulary consisted of the logical constants U and ∩, unary connective !, and binary connectives f and ∞.
Mally defined f, ∞, and ∩ as follows:
Mally proposed five informal principles:
He formalized these principles and took them as his axioms:
From these axioms Mally deduced 35 theorems, many of which he rightly considered strange. Karl Menger showed that !A ↔ A is a theorem and thus that the introduction of the ! sign is irrelevant and that A ought to be the case if A is the case. After Menger, philosophers no longer considered Mally's system viable. Gert Lokhorst lists Mally's 35 theorems and gives a proof for Menger's theorem at the Stanford Encyclopedia of Philosophy under Mally's Deontic Logic.
The first plausible system of deontic logic was proposed by G. H. von Wright in his paper Deontic Logic in the philosophical journal Mind in 1951. (Von Wright was also the first to use the term "deontic" in English to refer to this kind of logic although Mally published the German paper Deontik in 1926.) Since the publication of von Wright's seminal paper, many philosophers and computer scientists have investigated and developed systems of deontic logic. Nevertheless, to this day deontic logic remains one of the most controversial and least agreed-upon areas of logic. G. H. von Wright did not base his 1951 deontic logic on the syntax of the propositional calculus as Mally had done, but was instead influenced by alethic modal logics, which Mally had not benefited from. In 1964, von Wright published A New System of Deontic Logic, which was a return to the syntax of the propositional calculus and thus a significant return to Mally's system. (For more on von Wright's departure from and return to the syntax of the propositional calculus, see Deontic Logic: A Personal View and A New System of Deontic Logic, both by Georg Henrik von Wright.) G. H. von Wright's adoption of the modal logic of possibility and necessity for the purposes of normative reasoning was a return to Leibniz.
Although von Wright's system represented a significant improvement over Mally's, it raised a number of problems of its own. For example, Ross's paradox applies to von Wright's deontic logic, allowing us to infer from "It is obligatory that the letter is mailed" to "It is obligatory that either the letter is mailed or the letter is burned", which seems to imply it is permissible that the letter is burned. The Good Samaritan paradox also applies to his system, allowing us to infer from "It is obligatory to nurse the man who has been robbed" that "It is obligatory that the man has been robbed". Another major source of puzzlement is Chisholm's paradox. There is no formalisation in von Wright's system of the following claims that allows them to be both jointly satisfiable and logically independent:
Responses to this problem involve rejecting one of the three premises. | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103037649.11/warc/CC-MAIN-20220626071255-20220626101255-00660.warc.gz | CC-MAIN-2022-27 | 10,223 | 28 |
https://math.answers.com/other-math/What_is_difference_between_mean_and_mode | math | The mean is the average. For example if you had the numbers 11, 10, 12, 11, 7, and 15. You would add them up and divide by how many numbers there are (which in this case is 6). The number you get is your mean (in this case the means in 11).
The mode is the number that occurs most often. Using the same set of numbers above (11, 10, 12, 11, 7, and 15), the mode would be 11 because that's the only number that occurs the most. In other words, there is more than one of the same number.
It doesn't actually mean difference, but it can be used to get the difference between values. 11 subtract 4 is 7, and 7 is the difference between 4 and 11.
They differ in formula.
Range means finding the difference between the highest number in a set of numbers and the lowest. Mean means dividing the total of a set of numbers by the number of numbers there are Mode means the most frequent number. Median is the number in the middle. To find the median you have to first order the numbers from lowest to highest.
Mean = 21.6 Median = 19.5 Mode = 20 and 21 ------------------------------------------------------------------------ If the "2 1" (between 18 and 20 at the end) is supposed to be "21" then Mean = 26 Median = 20 Mode = 20
3 popular questions about mean,median,mode is whats the mean? whats the mode? whats the median? hope this helps
= What is the difference between real mode and protected mode =
mode is the number that occurs the most and to find the mean/average, add all numbers, then divid that number by the number of numbers there were in your group of numbers.
There is no direct relationship between the mean and mode.
The mean, median, and mode are all measures of central tendency. For symmetrical distributions they all have the same value. For assymetrical distributions they have different values. The mean is the average and the mode is the most likely value.
The Related Link below explains the difference between enhancement mode and depletion mode N channel MOSFETs.
well a spreadsheet is what your making, spreadsheet mode is the view
by average we mean any measure of central tendency and mean is one of the averages. other measures of average are median ,mode, geomatric mean and harmonic mean.
single mode fiber have higher bandwidth than multimode
nothing they are both the same
you do it yourself
Yes they do. All graphs have a mean and a mode. The difference with a double bar graph is that you have to find the mean and mode separately with each different thing you are measuring
The 8251 is a USART (Universal Synchronous Asynchronous Receiver Transmitter). It does not have a minimum and maximum mode. | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00691.warc.gz | CC-MAIN-2022-27 | 2,629 | 19 |
http://gucquebec.ml/blog2879-sin2xdx.html | math | integrate sin 4x cos 6x dx. My WordPress Blog. Sample Page.4x dx- cos4x sin2x dx let us do one by one Math2.org Math Tables: Table of Integrals Power of x. x n dx x n1 (n1)-1 C (n -1) d/dx [-sin(x)] -cos(x). The thing is though, that all of these arent just the derivative of the trig functions, if you do it step by step you would get intermediated/dx [cos(x)] d/dx [x] . -sin(x) 1 . Type in any integral to get the solution, steps and graph int(sin2x )/(1cos2x)dx-ln(1cos2x)C At first glance, this one seems like a toughie Get the answer to Integral of sin(x)2 with the Cymath math problem solver - a free math equation solver and math solving app for calculus and algebra. Possible intermediate steps: integral sin(x) sin(2 x) dx Use the trigonometric identity sin(alpha) sin(x)-cos(3 x)) dx Integrate the sum term by term and factor out constants: 1/2 integral cos( x) dx-1/2 Повторите попытку позже. Опубликовано: 4 сент. 2013 г. This video is about integrate sin2 x dx. cos X sin X dx. so the original integral becomes.There are a LOT Of sin Xs. so lets say sinX u. it becomes. Lets use integration by parts: If we apply integration by parts to the rightmost expression again, we will get cos 2(x)dx cos2(x)dx, which is not very useful.
The solution of the differential equation cos x cos y dx sin x sin y dy 0 is. Question Posted / rajasekar. Yes, thats correct! Basically, usinx du/dxcos x. Put this back into the equation, you get integrate (u3). then the final answer is .25(sin4 x). int x2sin2x dx. I am given to evaluate: Please, the result is 1/4I cant get thisshould it be just normal multiplying rule for integrals or something else? (n-1)INTEGRAL sin(n-2)(x)(1-sin2(x))dxAnother approach is to use a trigonometric identity to express sin10(x) as a sum of terms of the form. integral of x sin 2 (x) dx. attempt: Let u sin2 (x) v x u 2sinxcosx v x2 / 2.For this one: Using the identity, [tex]sin2(x)frac1-cos(2x)2[/tex], rewrite as This video is about integrate sin2 x dx. The full question is 2xsin(3x2). sin x ] sin 3x dx [ 2 sin 2x. Write back if you need more help, Penny . Simple harmonic motion: the swing of the pendulum The Guardian The slope of the curve is the rate of change ( dx/dt).
When the wave is at its highest, the slope is changing quickest How to integrate sin6 x cos2 x dx. I do not know of an easy way to evaluate this integral. But heres one way that isnt too bad. Another method for integrating sec x dx, that is more tedious, but less dependent on a memorized trick, is to convert sec x dx into the integral of a rational function using the substitution y sin x int: x sin(2x) dx. This can be done using integration by parts-x/2 cos(2x) 1/2 int: cos(2x) dx. Again, by simple substitution this second integral is done and we get our final answer xsin(2x) dx (-1/2)xcos2x (1/4)sin2x You get this by using Integration by Parts. An integral in the form udv can be written as uv-vdu In.thus the given integral becomes: sinx cosx dx (1/4)sin(2x) dx (1/4) sin(2x) dx now you can reduce the order of the integrand using the half-angle identity: sinx (1/2) [1 - cos(2x) Compute sin4(x) cos2(x) dx. Solution. c2. We conclude that: sin4 x cos2 x dx. Write integrand as (sin x cos x)2 (frac12sin 2x)2 . Then use the following facts: sin2 2x 1-cos2 2x. cos2 2x frac12(cos 4x 1). Note: The original question asked for the A Reduction Formula Problem: Integrate I (sin x)n dx. Try integration by parts with. We get.du (n 1)(sin x)n2 cos x dx dv sin x dx. sin(x y) dx dy | sin(y) cos(y) dy | / /. 0 0 0. and this last integral is equal to int fracdxcos3x fracsin x2cdot cos2x frac12lnleft|tanleft(frac x2fracpi2right)right| . Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Type in any integral to get the solution, steps and graph sin x dx cos x C. 163. 164 Chapter 8 Techniques of Integration.2x cos(x2) dx. This is not a simple derivative, but a little thought reveals that it must have come from. It means we have to find the sin2x dx. As we know the trigonometry identity of sin( xy)sinxcosy cosxsiny. By putting xy we will get. Answer: d/dx(sinx) cosx, so use substitution.intu(-2) du which evaluates to -1/u C. Reverse the substitution to finish: int cosx/ sin2x dx -1/sinx -cscx. The integral int sin6 x dx has to be determined. (Some more advanced calculators can.) integral of (cos 2x cos x) dx How to integrate sin(2x) / cos3(x)? SOLUTION Simply substituting u cos x isnt helpful, since then du sin x dx. In order to integrate powers of cosine, we would need an extra sin x factor. To integrate sin2x cos2x, also written as cos2x sin2x dx, sin squared x cos squared x, sin2(x) cos2(x), and (sin x)2 (cos x)2, we start by using standard trig identities to to change the form. Z Z integral of sin 2x /8 - 1/16 cos 2x to integrate sin 2x cos 2 2x put cos 2x t then 2 sin 2x dx dt we get t2 dt/2 integrating we get t3/6 Free derivative calculator - differentiate functions with all the sin 3x cosx dx ( integrate sin x/cos3 x dx ) No. Though youre just a 10th grade student, you know how to solve integrals. 2. Relevant equations I know the integral of sin(x)dx -cos(x) C. 3. The attempt at a solution What I did was to say that the integral is -cos( 2x) C, which isnt the correct answer Rahul Pillai. how to integrate. f (log(sin x ))dx. Varun Nagarajan. what is integral of log( x)? cos(x)dx d(sin(x)).
giving 2sin(x)d(sin(x)), or 2zdz by replacing sin( x) by z. >>also is there a general pattern for integral like this ? Int dx/(sinxcosx) Int (cosx-Sinx)dx/(Cos2x-sin2x) Int cosx dx/ (1-2Sin 2x) - Int sinx dx/ (2cos2x-1) (.1).lets now plug-in the value of sin x and cosx in (1). sin x cos x. Integral. sin x dx - cos x C. Eulers formula. For each of these, we simply use the Fundamental of Calculus, because we know their corresponding derivatives. cos( x) sin(x), cos(x) dx sin(x) c. The good news is that your indefinite integral is correct, but off by 1/24, which can be absorbed in the integration constant. Depending on how you integrated, it could give equivalent results of: (3sin( x) There are Cinfty test functions in L1(0, infty) that make the integral value of int0infty(sin x/x) phi(x) dx range from 0 to infty. What does narrowing these test For each of these, we simply use the Fundamental of Calculus, because we know their corresponding derivatives. cos( x) sin(x), cos(x) dx sin(x) c. Find: (intergrate) 2sin3x sin 2x dx? Type in any integral to get the solution, steps and graph Find: (intergrate) 2sin3 x sin 2x dx? Related QuestionsMore Answers Below. How can I integrate sin(x) /sin(4x)?What is integral sin (cos x).dx? integrate 1/(sinx cosx) dx. For the second integral, use u sin(x), du cos(x)dx. and now the substitution u cos(x), so that du -sin(x)dx, makes that a polynomial integtration: Of course, if m is odd, you can do the same thing, switching "sine" and "cosine". Use the half angle formula, sin2(x) 1/2(1 - cos(2x)) and substitute into the integral so it becomes 1/2 times the integral of (1 - cos( 2x)) dx. Example: sin3(x) sin2(x) sin(x). Hence the given integral may be written as followsWe now let u cos(x), hence du/dx -sin(x) or -du sin(x)dx and substitute in the given intergral to obtain. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863684.0/warc/CC-MAIN-20180520190018-20180520210018-00293.warc.gz | CC-MAIN-2018-22 | 7,252 | 4 |
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This math-related data from Fineweb was specifically used in OpenCoder pre-training. We employ fastText in three iterative rounds to recall a final dataset of 55B code and math-related data. You can find code-related data at OpenCoder-LLM/fineweb-code-corpus.
Citation
@inproceedings{Huang2024OpenCoderTO,
title={OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models},
author={Siming Huang and Tianhao Cheng and Jason Klein Liu and Jiaran Hao and Liuyihan Song and Yang Xu and J. Yang and J. H. Liu and Chenchen Zhang and Linzheng Chai and Ruifeng Yuan and Zhaoxiang Zhang and Jie Fu and Qian Liu and Ge Zhang and Zili Wang and Yuan Qi and Yinghui Xu and Wei Chu},
year={2024},
url={https://arxiv.org/pdf/2411.04905}
}
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