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http://www.newcriticals.com/thermodynamics/print
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math
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So there’s no better way to understand the “laws” of thermodynamics than to actually get a textbook and work some problems! But I’m not going to hold it against you if that doesn’t seem like the best use of your time. Instead then let me attempt to summarize the first and second laws as best I can with an eye to the philosophically salient points required to appreciate their application to life. This post will concern itself with the first law and energy while the following post will discuss the second law and entropy.
The first law is conservation of energy. It says that the amount of energy in an isolated system cannot change. You may have heard “energy can be neither created nor destroyed.” This is another way of saying that the total quantity of energy in a system cannot change if energy cannot enter or leave from the outside. "System" means any arbitrary portion of the world you care to define, but you have to pick boundaries and you have to know whether radiation or mass can cross those boundaries if you want to be able to calculate things, so you had best to choose your system boundaries carefully! Once this is done though, thermodynamics provides you with a way of predicting what will happen to your system provided you know enough about it. A mathematically convenient way of stating that a quantity is constant is stating that the total change of this quantity is zero, or that ∆E=0. Once you can write that down then you can make an equation that connects conditions in the past to conditions in the future, because you know that the energy will be the same at all times. You’d be amazed at how little we’d be able to predict about nature if this statement wasn't true.
The system, its boundary, and the surroundings are the only objects that exist in the thermodynamic formalism.
Ok so that’s what the first law says but what is energy, anyway? We hear a lot about different kinds of “energies” but the simplest definition of energy comes from the work-energy theorem: Energy is what is capable of doing work. What is work? Work is moving mass over distance, like hauling timber or lifting a coffee cup. If we put all that together then we arrive at the statement: “The total capacity to move mass through space in an isolated system is constant.” I think this statement is an adequate description of the first law. But let me clarify a few points. First, the definition of energy as “how much mass can be moved how far” underscores the fact that energy is a conceptual abstraction. The four forces (but I prefer the word interactions) of nature are understood as the fundamental physical “givens” responsible for this total energy. This is just saying that gravity or electromagnetism, which are the interactions relevant to biology, are the things that “cause” the movement in the mechanistic sense. What we refer to as energy is a way of quantifying the potential for motion that exists because of these interactions. What makes “energy” such a grand unifying abstraction is precisely it’s mathematical property of being a constant quantity. Feynman quipped the following about the first law (my emphasis added):
...It states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.
Two points about this quote: Energy is a numerical quantity. I would restate that point by saying that energy is a mathematical abstraction. It is not “out there in the world” in the way that trees and electromagnetism are “out there.” I’m fond of the assertion that energy is what is, not because energy is a fundamental substratum or essence of “reality” in any sense but rather precisely for the opposite reason that it is a mathematical abstraction which is invariant in time. So that’s the first point--Energy is not a physical thing but a mathematical idea which was “thingified” by language because it was found to have the immensely useful property of never changing no matter how the actual matter under consideration was found to move. The first point is related to the second, which is that the fact of conservation of energy is not a “mechanism.” It is a rule which “mechanics” obeys but it does not tell you how anything happens. So now a brief digression to explain this point.
The discipline of mechanics, whether classical or quantum, is very much in the business of telling us how things happen. When I apply a force to a ball by kicking it I “cause” the ball to accelerate in a mechanistic way, and if someone asks me “how” I made the ball accelerate I can honestly respond “by kicking it.” This is how we would normally render Newton’s second law, f=ma, into language: A force causes a mass to accelerate...so I applied a force with my foot and off the thing went. (Note that it's rather odd to render an equal sign as "cause," but this is how it is generally interpreted at any rate.) Of course, this is not an adequate response to the question of why I kicked the ball and we don’t expect mechanics to answer this question. With this rough distinction between mechanistic how’s and purposive why’s in mind, we come to a platitude repeated in high school courses that I truly despise: Science tells us how things happen, but it requires religion, philosophy, or some form of ethics to discuss why things happen.
I have no idea what does or does not require philosophy, but the assertion about science is only true if we restrict “science” to the disciplines of classical and quantum mechanics. But this is not even all of physics, much less all of science! As I hope you will come to understand, the laws of thermodynamics are about why things happen naturally or, to use the jargon, spontaneously. For the time being suffice it to say that if they explain anything, they explain why a process occurs because they certainly don't explain how anything happens. This is why thermodynamics and mechanics evolved as distinct disciplines until their unification through statistical mechanics (more about this in later posts) and also why mechanics does not deal explicitly with time-directed, irreversible processes.
So “science” has never been in the business of avoiding questions about why things happen and it should not avoid them because its real job is to provide adequate explanations of natural phenomena. Nothing that leaves one with no understanding of why a process occurs could be an adequate explanation. However, biology and the theory of evolution in particular, as I wrote about before, have been particularly damaged by this view that “science” must restrict itself to providing only mechanistic “hows.” In fact, while I’m digressing, in case you haven’t figured it out by now, I don’t believe in Science as such at all. There are only the myriad things people do and measure under more or less controlled conditions in more or less clever or technical ways with concepts that are more or less quantifiable. People who invoke the spirit of Science with a capital S (White lab coats on white males and “pure facts” rendered in the antiseptic UV light of enlightenment reason) most often merely wish to claim blanket authority for ideas which, in the spirit of science, ought to stand on their own.
At any rate that’s what I think you ought to know about the first law. Energy became the central concept of thermodynamics because it has the enormously useful property of being constant in time. How useful? So useful they call it the first law of thermodynamics, and the predictability of the final state of any natural process is grounded in our capacity to write down equations which connect the past and the future. These equations are all in some way derived from the constancy in time of energy. But it is not considered to be the “cause” of anything--gravity and voltages and nuclear forces and so on provide the "how" cause of things. Furthermore, this “law,” or as Feynman says “strange fact,” does not by itself explain why a process does or does not occur. That’s really the second law’s territory, which we’ll get to next time. But understanding entropy, which the second law tells us is the quantity that can only increase, requires this preliminary understanding of energy, the quantity that cannot change. Finally, once we understand the basic ideas of thermo, then we can begin to see how the interaction between that which can’t change and that which can only increase creates these beautiful natural patterns from which we grew.
Fractal pattern indicating self-organization via dissipative flows
Thumbnail image: A forest fire represents a massive transfer of energy from system to surroundings, but the total energy of the universe is unchanged during this process.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499710.49/warc/CC-MAIN-20230129080341-20230129110341-00373.warc.gz
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CC-MAIN-2023-06
| 9,226 | 12 |
https://baicechina.com/which-formula-can-be-used-to-describe-the-sequence/
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math
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Intro to Series
A mathematical series is a gotten listing of things, frequently numbers. Often the numbers in a series are specified in regards to a previous number in the checklist.
Secret TakeawaysSecret PointsThe variety of purchased aspects (potentially unlimited) is called the size of the series. Unlike a collection, order issues, as well as a specific term can show up numerous times at various settings in the sequence.A math series is one in which a term is gotten by including a consistent to a previous regard to a series. So the n th term can be defined by the formula a_n = a _ n-1 + d A geometric series is one in which a regard to a series is gotten by increasing the previous term by a continuous. It can be explained by the formula a_n=r \ cdot a _ Secret Terms
In maths, a series is a gotten checklist of things. Like a collection, it has participants (additionally called terms or aspects). The variety of gotten components (perhaps unlimited) is called the size of the series. Unlike a collection, order issues, as well as a specific term can show up several times at various placements in the series.
As an example, (M, A, R, Y) is a series of letters that varies from (A, R, M, Y) , as the getting issues, as well as (1, 1, 2, 3, 5, 8) , which includes the number 1 at 2 various placements, is a legitimate series. Series can be limited, as in this instance, or unlimited, such as the series of all also favorable integers (2, 4, 6, \ cdots) Limited series are often referred to as words or strings and also limitless series as streams.
Instances as well as Symbols
Limitless as well as limited Series
An even more official interpretation of a limited series with terms in an established S is a feature from \ left \ 1, 2, \ cdots, n \ ideal \ to S for some n> 0 An unlimited series in S is a feature from \ left \ to S For instance, the series of prime numbers (2,3,5,7,11, \ cdots) is the feature
1 \ rightarrow 2, 2 \ rightarrow 3, 3 \ rightarrow 5, 4 \ rightarrow 7, 5 \ rightarrow 11, \ cdots
A series of a limited size n is additionally called an n -tuple. Limited series consist of the vacant series (\ quad) that has no aspects.
Much of the series you will certainly come across in a math training course are generated by a formula, where some procedure(s) is executed on the previous participant of the series a _ n-1 to provide the following participant of the series a_n These are called recursive series.
A math (or direct) series is a series of numbers in which each brand-new term is determined by including a continuous worth to the previous term. An instance is (10,13,16,19,22,25) In this instance, the initial term (which we will certainly call a_1 is 10 , and also the typical distinction ( d -- that is, the distinction in between any type of 2 nearby numbers-- is 3 The recursive interpretation is for that reason
\ displaystyle a_n=a _ +3, a_1=10
An additional instance is (25,22,19,16,13,10) In this instance a_1 = 25 , as well as d=-3 The recursive interpretation is for that reason
\ displaystyle
In both of these instances, n (the variety of terms) is 6
A geometric series is a checklist in which each number is produced by increasing a consistent by the previous number. An instance is (2,6,18,54,162) In this instance, a_1=2 , as well as the usual proportion ( r -- that is, the proportion in between any kind of 2 surrounding numbers-- is 3. As a result the recursive interpretation is
a_n=3a _ , a_1=2
One more instance is (162,54,18,6,2) In this instance a_1=162 , and also \ displaystyle r=\ frac 1 3 As a result the recursive formula is
\ displaystyle
In both instances n=5
A specific interpretation of a math series is one in which the n th term is specified without referring to the previous term. This is better, since it implies you can locate (as an example) the 20th term without discovering every one of the various other terms in between.
To locate the specific meaning of a math series, you start drawing up the terms. Presume our series is t_1, t_2, \ dots The initial term is constantly t_1 The 2nd term increases by d , therefore it is t_1+d The 3rd term increases by d once again, therefore it is (t_1+d)+d, or simply put, t_1 +2 d So we see that:
\ displaystyle \ start line up t_1 &= t_1 \ \ t_2 &= t_1+d \ \ t_3 &= t_1 +2 d \ \ t_4 &= t_1 +3 d \ \ & \ vdots \ end
and more. From this you can see the generalization that:
t_n = t_1+(n-1)d
which is the specific meaning we were trying to find.
The specific interpretation of a geometric series is acquired in a comparable method. The initial term is t_1 ; the 2nd term is r times that, or t_1r ; the 3rd term is r times that, or t_1r ^ 2 ; and so forth. So the basic regulation is:
t_n=t_1 \ cdot r ^
The General Regard To a Series
Offered terms in a series, it is commonly feasible to locate a formula for the basic regard to the series, if the formula is a polynomial.
Secret TakeawaysTrick PointsGiven terms in a series created by a polynomial, there is a technique to identify the formula for the polynomial.By hand, one can take the distinctions in between each term, then the distinctions in between the distinctions in terms, and so on. If the distinctions ultimately end up being continuous, then the series is created by a polynomial formula.Once a consistent distinction is accomplished, one can resolve formulas to produce the formula for the polynomial.Key Terms
Offered numerous terms in a series, it is in some cases feasible to discover a formula for the basic regard to the series. Such a formula will certainly generate the n th term when a worth for the integer n is taken into the formula.
This reality can be identified by discovering whether the computed distinctions ultimately come to be continuous if a series is created by a polynomial.
Think about the series:
5, 7, 9, 11, 13, \ dots
The distinction in between 7 and also 5 is 2 The distinction in between 7 and also 9 is additionally 2 Actually, the distinction in between each set of terms is 2 Considering that this distinction is continuous, and also this is the initial collection of distinctions, the series is provided by a first-degree (direct) polynomial.
Expect the formula for the series is provided by an+b for some constants a as well as b Then the series appears like:
a+b, 2a+b, 3a+b, \ dots
The distinction in between each term as well as the term after it is a In our instance, a=2 It is feasible to fix for b making use of among the terms in the series. Utilizing the initial number in the series and also the initial term:
\ displaystyle
So, the n th regard to the series is provided by 2n +3
Expect the n th regard to a series was provided by an ^ 2+bn+c Then the series would certainly resemble:
a+b+c, 4a +2 b+c, 9a +3 b+c, \ dots
This series was developed by connecting in 1 for n , 2 for n , 3 for n , and so on.
If we begin at the 2nd term, as well as deduct the previous term from each term in the series, we can obtain a brand-new series comprised of the distinctions in between terms. The very first series of distinctions would certainly be:
3a+b, b+5a, 7a+b, \ dots
Currently, we take the distinctions in between terms in the brand-new series. The 2nd series of distinctions is:
2a, 2a, 2a, 2a, \ dots
The computed distinctions have actually assembled to a consistent after the 2nd series of distinctions. This indicates that it was a second-order (square) series. Functioning backwards from this, we can locate the basic term for any type of square series.
Take into consideration the series:
4, -7, -26, -53, -88, -131, \ dots
The distinction in between -7 and also 4 is -11 , as well as the distinction in between -26 as well as -7 is -19 Locating all these distinctions, we obtain a brand-new series:
-11, -19, -27, -35, -43, \ dots
This checklist is still not continuous. Nonetheless, locating the distinction in between terms again, we obtain:
-8, -8, -8, -8, \ dots
This truth informs us that there is a polynomial formula explaining our series. Because we needed to do distinctions two times, it is a second-degree (square) polynomial.
We can locate the formula by understanding that the consistent term is -8 , which it can additionally be revealed by 2a As a result a=-4
Next we keep in mind that the very first thing in our very first listing of distinctions is -11 , however that generically it is meant to be 3a+b , so we need to have 3( -4 )+b=-11 , and also b=1
Ultimately, note that the initial term in the series is 4 , as well as can likewise be revealed by
a+b+c = -4 +1+c
So, c=7 , as well as the formula that creates the series is -4 a ^ 2+b +7 c
General Polynomial Series
This technique of discovering distinctions can be encompassed locate the basic regard to a polynomial series of any kind of order. For greater orders, it will certainly take a lot more rounds of taking distinctions for the distinctions to end up being consistent, and also extra back-substitution will certainly be needed in order to address for the basic term.
General Regards To Non-Polynomial Series
Some series are produced by a basic term which is not a polynomial. For instance, the geometric series 2, 4, 8, 16, \ dots is offered by the basic term 2 ^ n Taking distinctions will certainly never ever result in a continuous distinction since this term is not a polynomial.
General regards to non-polynomial series can be located by monitoring, as above, or by various other ways which are past our range in the meantime. Offered any kind of basic term, the series can be produced by connecting in succeeding worths of n
Collection and also Sigma Symbols
Sigma symbols, represented by the uppercase Greek letter sigma \ left (\ Sigma \ right ), is utilized to stand for summations-- a collection of numbers to be totaled.
Secret TakeawaysSecret PointsA collection is a summation executed on a checklist of numbers. Each term is contributed to the following, causing an amount of all terms.Sigma symbols is utilized to stand for the summation of a collection. In this kind, the resources Greek letter sigma \ left (\ Sigma \ right) is made use of. The series of terms in the summation is stood for in numbers listed below as well as over the \ Sigma sign, called indices. The most affordable index is composed listed below the sign as well as the biggest index is created above.Key Terms
Summation is the procedure of including a series of numbers, leading to an amount or overall. Any type of intermediate outcome is a partial amount if numbers are included sequentially from left to right. The numbers to be summed (called addends, or occasionally summands) might be integers, reasonable numbers, genuine numbers, or complicated numbers. For limited series of such components, summation constantly creates a distinct amount.
A collection is a checklist of numbers-- like a series-- yet rather than simply detailing them, the plus indications show that they need to be built up.
For instance, 4 +9 +3 +2 +17 is a collection. This certain collection amounts to 35 One more collection is 2 +4 +8 +16 +32 +64 This collection amounts to 126
One means to compactly stand for a collection is with sigma symbols , or summation symbols , which appears like this:
\ displaystyle \ amount _ n=3 ^
The primary icon seen is the uppercase Greek letter sigma. It shows a collection. To "unbox" this symbols, n=3 stands for the number at which to begin counting ( 3 , as well as the 7 stands for the factor at which to quit. For each and every term, plug that worth of n right into the provided formula ( n ^ 2 . This specific formula, which we can review as "the amount as n goes from 3 to 7 of n ^ 2 ," indicates:
\ displaystyle
Much more typically, sigma symbols can be specified as:
\ displaystyle
In this formula, i stands for the index of summation, x_i is an indexed variable standing for each succeeding term in the collection, m is the reduced bound of summation, and also n is the top bound of summation. The" i = m under the summation icon indicates that the index i starts equivalent to m The index, i , is incremented by 1 for each and every succeeding term, quiting when i=n
One more instance is:
\ displaystyle
This collection amounts to 90. So we can create:
\ displaystyle \ amount _ ^ 6 (i ^ 2 +1)=90
Various Other Types of Sigma Symbols
When these are clear from context, casual writing occasionally leaves out the interpretation of the index and also bounds of summation. As an example:
\ displaystyle \ amount x_i ^ 2=\ amount _ ^ n x_i ^ 2
A recursive interpretation of a feature specifies its worths for some inputs in regards to the worths of the exact same feature for various other inputs.
Trick TakeawaysTrick PointsIn mathematical reasoning as well as computer technology, a recursive meaning, or inductive interpretation, is made use of to specify an item in regards to itself.The recursive meaning for a math series is: a_n=a _ n-1 +d The recursive interpretation for a geometric series is: a_n=r \ cdot a _ n-1
In mathematical reasoning as well as computer technology, a recursive meaning, or inductive interpretation, is made use of to specify a things in regards to itself. A recursive meaning of a feature specifies worths of the feature for some inputs in regards to the worths of the exact same feature for various other inputs.
As an example, the factorial feature n! is specified by the policies:
0!=1
(n +1)!=(n +1)n!
This interpretation stands due to the fact that, for all n , the recursion ultimately gets to the base instance of 0
For instance, we can calculate 5! by understanding that 5!=5 \ cdot 4! , which 4!=4 \ cdot 3! , which 3!=3 \ cdot 2! , which 2!=2 \ cdot 1!, which:
\ displaystyle \ start line up 1! &=1 \ cdot 0! \ \ &= 1 \ cdot 1 \ \ &=1 \ end
Placing this completely we obtain:
\ displaystyle
Recursive Solutions for Series
When going over math series, you might have observed that the distinction in between 2 successive terms in the series can be created in a basic method:
a_n=a _ +d
The above formula is an instance of a recursive formula given that the n th term can just be computed by thinking about the previous term in the series. Contrast this with the formula:
a_n=a_1+d(n-1).
In this formula, one can straight determine the nth-term of the math series without recognizing the previous terms. Relying on just how the series is being made use of, either the non-recursive one or the recursive interpretation may be better.
A recursive geometric series complies with the formula:
a_n=r \ cdot a _
A used instance of a geometric series includes the spread of the influenza infection. Mean each contaminated individual will certainly contaminate 2 even more individuals, such that the terms adhere to a geometric series.
Utilizing this formula, the recursive formula for this geometric series is:
a_n=2 \ cdot a _ n-1
Recursive formulas are incredibly effective. One can exercise every term in the collection simply by recognizing previous terms. As can be seen from the instances over, exercising as well as making use of the previous term a _ n − 1 can be a much easier calculation than exercising a _ n from the ground up utilizing a basic formula. When making use of a computer system to control a series could indicate that the estimation will certainly be ended up promptly, this implies that making use of a recursive formula.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103271763.15/warc/CC-MAIN-20220626161834-20220626191834-00327.warc.gz
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CC-MAIN-2022-27
| 15,605 | 110 |
https://www.tes.com/teaching-resource/multiplication-games-math-games-for-multiplication-facts-fluency-11499163
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math
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Multiplication Games | Math Games for Multiplication Facts Fluency. These are GREAT multiplication games to reinforce basic multiplication facts within 100. In this math multiplication game students/child will have fun practicing their math skills in a very interactive way.
These Multiplication Games| Math for Multiplication Facts Fluency includes:
#1 - I Have, Who Has? Multiplication Game
-directions (This multiplication game contains full easy to read instructions and is a perfect addition to your maths stations or center).
-36 game cards
-Just print the directions and game cards, laminate (if desired for longer use in the classroom or at home), and they are ready to play.
-There are a many ways that this multiplication game can be played in terms of small group, partner work or as a whole class (depending on class size) but every game will follow the same sequence, so you’ll know if they are getting it correct.
#2 - Spiral Multiplication
#3 - Halloween Multiplication
#4 - Four in a Row
#5 - Rolling Dice for Multiplication
#6 - Going to Town!
#7 - Zero!
#8 - Gotcha!
#9 - Race to 500!
I hope your students/child enjoy these multiplication games!
Thanks for taking the time to stop by my store!
Follow Little Tots Learning
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538226.66/warc/CC-MAIN-20210123160717-20210123190717-00258.warc.gz
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CC-MAIN-2021-04
| 1,241 | 18 |
http://www.informatik.uni-hamburg.de/TGI/pnbib/h/haas_p_j11.html
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math
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In: IBM Research Report RJ 6764, pages 1-24 pp.. IBM Almaden Research Center, San Jose, CA, 1989.
Abstract: We show that the marking process of a stochastic Petri net is a time homogeneous continuous time Markov chain with countable state space, provided that the clock associated with the firing of each timed transition is always set according to a fixed exponential distribution. The result rests on a representation of the conditional distribution of the vector of clock readings, given the `partial history' of the process. We also investigate the modelling power of Markovian stochastic Petri nets. The main result is that for any (possibly non-Markovian) finite state generalized semi-Markov process with exponential clock-setting distributions there exists a Markovian stochastic Petri net with deterministic transitions and unit speeds having a marking process with the same finite-dimensional distributions.
Keywords: stochastic Petri nets; continuous time Markov chains; general state space Markov chains; random polling systems; modelling power.
Back to the Petri Nets Bibliography
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s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804666.54/warc/CC-MAIN-20171118055757-20171118075757-00521.warc.gz
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CC-MAIN-2017-47
| 1,093 | 4 |
http://zbmath.org/?q=an:1257.65020
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math
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Summary: Purpose: The purpose of this paper is to introduce a general equation for eigensolution. Eigenvalues and eigenvectors of graphs have many applications in combinatorial optimization and structural mechanics. Some important applications of graph products consist of nodal ordering and graph partitioning for structuring the structural matrices and finite element subdomaining, respectively.
Design/methodology/approach: In the existing methods for the eigensolution of Laplacian matrices, members have been added to the model of a graph product such that for its Laplacian matrix an algebraic relation between blocks become possible. These methods are categorized as topological approaches. Here, using concepts of linear algebra a general algebraic method is developed.
Findings: A new algebraic method is introduced for calculating the eigenvalues of Laplacian matrices in graph products.
Originality/value: The present method provides a simple tool for calculating the eigenvalues of the Laplacian matrices without using the configurational model and merely by using the Laplacian matrices. The developed formula for calculating the eigenvalues contains approximate terms which can be managed by the analyst.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00566-ip-10-147-4-33.ec2.internal.warc.gz
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CC-MAIN-2014-15
| 1,218 | 4 |
https://www.hifivision.com/tags/total-usage/
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math
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After long search, found the way to find the usage time of my PV8.
Knowing the total time the TV was used helps in 2 things:
1. When the set is delivered we can check if its a DEMO piece bcos the usage time will be more (hours of usage).
2. Will help us determine accurately if the run-in...
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703557462.87/warc/CC-MAIN-20210124204052-20210124234052-00068.warc.gz
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CC-MAIN-2021-04
| 291 | 4 |
https://www.hackmath.net/en/example/6363
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math
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Thomas lives 400 meters away from Samko, Robo from Thomas also 400 m and Samko from Robo 500. Anton lives 300 meters away from Robo further as Samko. How far away lives Anton from Rob?
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New refrigerator sells for 1024 USD, Monday will be 25% discount. How much USD will save, and what will be the price?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247480240.25/warc/CC-MAIN-20190216085312-20190216111312-00373.warc.gz
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CC-MAIN-2019-09
| 2,344 | 32 |
https://www.thefreelibrary.com/Chaos+synchronization+of+the+Sprott+N+System+with+parameter-a0215307095
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math
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Chaos synchronization of the Sprott N System with parameter.
Since synchronization of chaotic systems was first introduced by Fujisaka and Yamada and Pecora and Carroll . Due to the importance and applications of coupled systems, ranging from chemical oscillators, coupled neurons, coupled circuits to mechanical oscillators, various synchronization schemes have been proposed by many scientists from different research fields [3-10]. Recently, a new type of chaotic synchronization-full state hybrid projective synchronization(FSHPS) in continuous-time chaotic and hyper-chaotic systems based on the Lyapunov's direct method is presented and investigated by wen,many notable results and a series of important applications to security communication regarding FSHPS has been presented in Refs [12-14].
We organize this paper as follows. In Section 2, the chaotic characteristic of the Sprott N autonomous system with parameter is studied by theoretical analysis and numerical simulation. In section 3, the scheme of full state hybrid projective synchronization(FSHPS) is given.A proper Smarandache controller is designed and the synchronization of the system is achieved under it.
[FIGURE 1 OMITTED]
[section]2. Dynamical behavior
A series of three dimensional autonomous systems is presented by J.C. Sprott in 1994 , in this paper, the N system of those is taken as example. The governing equations of the Sprott N system are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The equilibrium of the system (1) is P(-0.25,0.0.5).The Lyapunov exponents of the system are LEs=(0.076,0,-2.076),which shows the system is chaotic. In order to get abundance dynamical behavior of the system, the parameter /3 is leaded to the system. The governing equations of the Sprott N system with parameter [beta] can be described as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where x = ([x.sub.1], [x.sub.2], [x.sub.3]) is the state variable. The initial conditions are ([x.sub.1](0), [x.sub.2](0), [x.sub.3](0))=(1,5,2), when the parameter [beta] = 1.9, the system exits a chaotic attractor. The chaotic attractor in three-dimensional phase space is illustrated in Fig 1.
For this system, bifurcation can easily be detected by examining graphs of abs(z)versus the control parameter [beta]. The dynamical behavior of the system (2) can be characterized with its Lyapunov exponents which are computed numerically. The bifurcation diagram and the Lyapunov exponents spectrum are showed in Fig 2.
[FIGURE 2 OMITTED]
[section]3. Chaos synchronization base on FSHPS
We recall a class of automomous chaotic flows in the form of
x(t) = F(x), (3)
x = [([x.sub.1], [x.sub.2],...,[x.sub.n]).sup.T] is the state vector, and F(x) = [([F.sub.1](x), [F.sub.2](x),...,[F.sub.n](x)).sup.T] is continuous nonlinear vector function.
We take (3) as the drive system and the response system is given by
y(t) = F(y) + u, (4)
y = [([y.sub.1],[y.sub.2],...,[y.sub.n]).sup.T] is the state vector, and F(y) = [([F.sub.1](y),[F.sub.2](y),...,[F.sub.n](y)).sup.T] is continuous nonlinear vector function. u = u(x,y) = [([u.sub.1](x,y),[u.sub.2](x,y),...,[u.sub.n](x,y)).sup.T] is the controller to be determined for the purpose of full state hybrid projective synchronization.Let the vector error state be e(t) = y(t) -[alpha]x(t).Thus, the error dynamical system between the drive system (3) and the response system (4) is
e(t) = y(t) - [alpha]x(t) = F(x,y) + u, (5)
where F(x,y) = F(y) - [alpha]F(x) = [([F.sub.1](y) - [[alpha].sub.1][F.sub.1]](x),[F.sub.2](y) - [[alpha].sub.2][F.sub.2](x),...,[F.sub.n](y) - [[alpha].sub.n][F.sub.n](x)).sup.T].
In the following, we will give a simple principle to select suitable feedback controller a such that the two chaotic or hyper-chaotic systems are FSHPS. If the Lyapunov function candidate V is take as:
V = 1/2[e.sup.T][P.sub.e], (6)
where P is a positive definite constant matrix, obviously, V is positive define. One way choose as the corresponding identity matrix in most case. The time derivative of V along the trajectory of the error dynnmical system is as follows
V = [e.sup.T]P(u + F), (7)
Suppose that we can select an appropriate controller u such that V is negative definite. Then, based on the Lyapunov's direct method, the FSHPS of chaotic or hyper-chaotic flows is synchronization under nonlinear controller u .
In order to observe the FSHPS of system (2), we define the response system of (2) as follows
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
where u = [([u.sub.1], [u.sub.2], [u.sub.3]).sup.T] is the nonlinear controller to be designed for FSHPS of two Sprott N chaotic systems with two significantly different initial conditions.
Define the FSHPS error signal as e(t) = g(t) - cxx(t),i.e.,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [alpha] = diag([[alpha].sub.1], [[alpha].sub.2], [[alpha].sub.3]),and [[alpha].sub.1], [[alpha].sub.2] and [[alpha].sub.3] are different desired in advance scaling factors for FSHPS. The error dynnmical system can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
The goal of control is to find a controller u = [([u.sub.1], [u.sub.2], [u.sub.3]).sup.T] for system (10) such that system (2) and (8) are in FSHPS. We now choose the control functions [u.sub.1], [u.sub.2] and [u.sub.3] as follows
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
If the Lyapunov function candidate is taken as:
V = 1/2([e.sup.2.sub.1] + [e.sup.2.sub.2] + [e.sup.2.sub.3]), (12)
The time derivative of V along the trajectory of the error dynnmical system (10) is as follows
V = - ([e.sup.2.sub.1] + [e.sup.2.sub.2] + [e.sup.2.sub.3]), (13)
Since V is a positive definite function and V is a negative definite function, according to the Lyapunov's direct method, the error variables become zero as time tends to infinity, i.e., [lim.sub.t[right arrow][infinity]] || [y.sub.i] - [[alpha].sub.i][x.sub.i] || = 0, i = 1, 2, 3. This means that the two Sprott A systems are in FSHPS under the controller (11).
[FIGURE 3 OMITTED]
For the numerical simulations, fourth-order Runge-Kutta method is used to solve the systems of differential equations (2) and (8). The initial states of the drive system and response system are ([x.sub.1](0), [x.sub.2](0), [x.sub.3](0) = (1, 5, 2) and ([y.sub.1](0), [y.sub.2](0), [y.sub.3](0) = (11,15,12) The state errors between two Sprott systems are shown in Fig.3. Obviously, the synchronization errors converge asymptotically to zero and two systems are indeed achieved chaos synchronization.
(section)4. Conclusion and discussion
In the paper, the problem synchronization of the Sprott N system with parameter is investigated. An effective full state hybrid projective synchronization (FSHPS) controller and analytic expression of the controller for the system are designed. Because of the complete synchronization, anti-synchronization, projective synchronization are all included in FSHPS, our results contain and extend most existing works. But there are exist many interesting and difficult problems left our for in-depth study about this new type of synchronization behavior, therefore, further research into FSHPS and its application is still important and insightful, although it is not in the category of generalized synchronization.
Fujisaka H, Yamada T. Stability theory of synchronized motion in coupled-oscillator systems. Prog Theory Phys, 69(1983), No.l, 32-71.
Peroca LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett, 64(1990), No.8, 821-4.
Kocrev L, Parlitz U. Generalized synchronization, predictability and equivalence of unidirectionally coupled system. Phys Rev Lett, 76(1996), No.ll, 1816-9.
Vincent UE, Njah AN, Akinlade O, Solarin ART. Phase synchronization in unidirectionally coupled chaotic ratchets. Chaos, 14(2004), No.4, 1018-25.
Liao TL. Adaptive synchronization of two Lorenz systems. Chaos, Solitons and Fractals, 9(1998), No.2, 1555-61.
Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys Rev Lett, 78(1997), No.22, 4193-6.
Voss HU. Anticipating chaotic synchronization. Phys Rev E, 61(2000), No.5, 5115-9.
Bai EW, Lonngran EE. Synchronization of two Lorenz systems using active control. Chaos, Solitons and Fractals, 8(1997), No.1, 51-8.
Vincent UE. Synchronization of Rikitake chaotic attractor using active control. Phys Lett A, 343(2005), No.2, 133-8.
Lu J, Wu X, Han X, Lu J Adaptive feedback synchronization of a unified chaotic system, Phys Lett A, 329(2004), No.2, 327-33.
Wen GL, Xu D. Nonliear observer control for full-state projective synchronization in chaotic continuous-time system Chao, Solitions and Fractal, 26(2005), No. 2, 71-7.
Xu D, Li Z, Bishop R. Manipulating the scaling factor of projective synchronization in three-dimensional chaotic system. Chaos, 11(2001), No.3, 439-42.
Wen GL, Xu D. Observer-based control for full-state projective synchronization of a general class of chaotic maps in ant dimension. Phys Lett A, 333(2004), No.2, 420-5.
Li ZG. Xu D. Stability criterion for projective synchronization in three-dimensional chaotic systems. Phys Lett A, 282(2001), No.2, 175-9.
Sprott JC. Some simple chaotic flows.Phys Rev E, 50(1994), No.2, 647-650.
Xiaojun Liu ([dagger]), Wansheng He ([dagger]), Xianfeng Li([double dagger]), Lixin Yang ([dagger])
([dagger]) Department of Mathematics and Statistics, Tianshui Normal University, Tianshui, Gansu, 741001, P.R.China
([double dagger]) School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University Lanzhou, Gansu. 730070, P.R.China
(1) This work is supported by the Gansu Provincial Education Department Foundation 0808-04 and Scientific Research Foundations of Tianshui Normal University of China TSB0818.
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|Author:||Xiaojun, Liu; Wansheng, He; Xianfeng, Li; Lixin, Yang|
|Date:||Jun 1, 2009|
|Previous Article:||Green~ relations and the natural partial orders on U-semiabundant semigroups.|
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202303.66/warc/CC-MAIN-20190320064940-20190320090940-00191.warc.gz
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CC-MAIN-2019-13
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http://www.boeing.com/boeing/phantom/2NA/description/nesting2.page
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math
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A clever heuristic algorithm by Dietrich and Yakowitz ("A rule-based approach to the trim-loss problem," Int. J. Prod. Res. 20, pp. 401-415, 1991) is employed in 2NA for packing smaller rectangles within larger rectangles. This algorithm is very fast, so 2NA tries to make extensive use of it. A typical speed for packing rectangles inside a larger rectangle is a few milliseconds.
A nest of smaller rectangles packed within a larger one might look like the following:
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s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936469305.48/warc/CC-MAIN-20150226074109-00329-ip-10-28-5-156.ec2.internal.warc.gz
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CC-MAIN-2015-11
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https://knowledgebasedpractice.wordpress.com/2015/01/31/deflate-gate-inference-and-concerns-about-hypothesis-testing/
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math
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This is a weekend divergence, but a timely and appropriate topic. For one thing, it’s Super Bowl weekend; and I am putting together the “Statistical Inference Part 3” handout for my research methods course on hypotheses and hypothesis testing.
You are probably not aware of this but deflate gate (whether the Patriot’s intentionally deflated footballs) has kicked off a statistical analysis frenzy. Here is one by Sharp Football Analysis that has the attention of a blog I follow. The blog I follow is Flowing Data – which also appropriately refers to one from Regressing called “Why Those Statistics about the Patriot’s Fumbling Are Mostly Junk.”
Flowing data and Regressing offer pretty sophisticated commentary on the statistical assumptions made by the author from Sharp Football Analysis. I am not going to attempt to offer any additional statistical commentary. The fact is – regardless of how you look at it there is a difference between the Patriot’s fumbling and the other team’s fumbling in NFL games. It is overestimated in the Sharp Football Analysis, but there is a difference.
I want to talk about that for this post. There is a difference. As you know statistical analysis that puts forward the probability of a difference occurring is testing the probability of the data conditional on the assumption that no difference exists. This is the null hypothesis. Again, the null hypothesis is that there is no difference; and the test is trying to obtain:
Pr(data | null hypothesis is true) – – that is what a “p” value is testing; the conditional probability that the data would occur if the null hypothesis were true. And in the case of the Patriot’s, there is a low probability (how low depends on how you calculate it and I think Regressing has done a nice job with it) that the data would occur if the null were true. With a small p value we can “reject the null” so to speak. Let’s put aside the underlying assumption of a random sample for now – clearly these are not random samples so the entire approach of using statistics based on sampling distributions to estimate sample error should be questioned.
When we reject the null hypothesis we are happy to put forward the “alternate” hypothesis – the hypothesis that “MUST BE” true – that “HAS TO BE TRUE” because the alternate hypothesis is the opposite of the null, the null is wrong as we just rejected it, and we live in a world of non contradiction, so if the null is rejected the alternate is accepted – taken as true. Does this work? Yes, but with limits based on what the alternate is actually saying.
Let’s accept that the null is rejected (there is not no difference between the Patriots and other teams in the “effect” – fumbling). I bolded my double negative because that is what we do when we reject the null. We say – there is not no difference, therefore there is a difference (an effect, an association). The alternate is that there is a difference is accepted. Fine. Let’s accept that there is a difference. But that is all the alternate can say. All the alternate says is that there is a difference.
The next BIG question is – why is there a difference? In a controlled trial this is easier to answer. Things are controlled, even randomized, the only accepted difference between the conditions is a particular suspected causal agent. But this is not a controlled trial, these teams have not been selected or put together by a randomization.
Deflate gate is about one possible causal agent – deflated footballs. But the analyses done, the statistical probabilities reported, are not specifically testing that as an alternate hypothesis. The only thing they are showing is that there is a difference. Since this is not a controlled trial we are left to attempt to “abduct” what the best explanation of the difference might be – but that is not tested at all by the statistics being looked at for deflate gate, and only discussed a tiny bit by the analysts.
To accept the alternate (they are different) is NOT to accept a particular explanation of why the alternate occurred (the balls were deflated). There are other perfectly reasonable explanations of the alternate – THE PATRIOTS ARE A BETTER TEAM – and the better team will score more points, have less points scored against them, create more turnovers, PRODUCE LESS TURNOVERS. The numbers being produced do not justify one of these explanations for the alternate over the other – that is the point of a discussion. But what I have been reading are completely biased explanations for the alternate. As an example, when discussing great quarterbacks it is accepted that they throw significantly less interceptions, we reject the null, we accept the alternate that they are different. BUT, we use that data to explain why they are great quarterbacks, we do not assume they must be doing something with the footballs to throw less interceptions. So then why not interpret a team with less fumbles as evidence that they are a better team? Here I defend Sharp a bit.
Two things in the defense of Sharp Football Analysis. First, there is a reason to suspect deflated footballs as a possible explanation – footballs were found under pressure in the AFC Championship game. So it is not that this possible explanation comes out of the blue – there is a valid reason to put it forward as a possible explanation. But being forward as a possible explanation does not make it THE explanation. Second, they do put forward a series of other explanations (at the end of the post) that they discuss off hand and with sense of disregard:
“Could the Patriots be so good that they just defy the numbers? As my friend theorized: Perhaps they’ve invented a revolutionary in-house way to protect the ball, or perhaps they’ve intentionally stocked their skill positions with players who don’t have a propensity to fumble. Or perhaps still, they call plays which intentionally result in a lower percentage of fumbles. Or maybe its just that they play with deflated footballs on offense. It could be any combination of the above.”
“But regardless of what, specifically, is causing these numbers, the fact remains: this is an extremely abnormal occurrence and is NOT simply random fluctuation.”
We can agree – not simple random fluctuation. But that does not mean we can infer deflated balls. They disregard these other explanations but with no real justification other than the occurrence of deflated balls at one game. We can list a whole host of other reasons that explain the statistical difference. After all, a team will be better than the rest at things – and that team will appear extreme relative to the mean – and no one is saying it is due to random fluctuation. But just because it is not random fluctuation we cannot claim that it is because footballs were deflated.
The fact is, there is an extremely complex causal network for the difference and to claim deflated balls as the cause first requires all other causal paths to the effect of interest be considered with data to rule them out prior to inference of one particular cause.
I am all for listening to the data. But let’s keep in mind that without our guidance, the data has very little to say.
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https://mdashf.org/2016/02/05/interesting-physics-facts-one-would-love-for-ever/
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math
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Interesting fact 2; Give an example of a motion where when we apply a force on the object, the force produces motion of the particles along its own direction, the speed remains finite but does not change. According to F = ma, Newtons laws are valid for the motion but speed remains constant, while F is there, v does not change.
Since a = 0, with nonzero F and constant v, one could see this as a diversion from particle mechanics as formulated by Newton, towards a higher understanding, one could argue this as a great inflection towards Quantum Mechanics.
Also note that we are not talking about circular uniform motion where F does not change v, but there is non zero a. F is transverse to particles motion.
Interesting fact 1, certain forces do not obey any of Newton’s laws, in either its strong form or week form. Magnetic forces unless generalized suitably do not obey any form of the Newton’s law, strong = strict, week = partly strict.
Some discussions on fact 2
Would a quantum of charge in a potential changing energy levels occur without acceleration? I’m not sure if elementary particles change velocity instantaneously or do they accelerate.
Elementary particles change velocity if they have mass. — If they have mass, they have rest mass.
Photons on the other hand don’t have the property called mass. — So its erroneous to say Photons don’t have rest mass, they just don’t have mass, saying they don’t have rest mass would mean; they have zero velocity in some frames, which is physics wise unacceptable.
So elementary particles except zero-mass particles such as photons, change their speeds under acceleration. “Potential changing energy levels” simply means there is a force and acceleration, hence change in energy, speed, momenta etc of the elementary particle such as electrons in orbits.
— Their quantum numbers are different for different orbits, hence, energy and velocity etc are different. In the orbits the electrons would fall down to a smaller radius if they were to lose energy.
Since they are wave-particles we are talking about average values of radius, which decreases accompanied by some acceleration. So the answer to your query is YES, there is acceleration of these particles, in orbit changing processes. (excitation or de-excitation)
The above point of mass-less particles and particles with mass is what classically separates them as waves and particles. — mass-less = wave and particle otherwise. And speed is a variable if particle mass is non zero and mass keeps on changing as well. But zero mass would mean mass and speed are constants.
So in short waves; speed and mass are constants. mass is zero. speed is constant and finite.
Particles; mass and speed vary from zero towards a finite value as decided by the wave (above).
These are elementary particles and waves which come under two categories; matter waves (such as electrons) and non-mechanical (or em) waves such as (photons).
But the hints to my question lies on considering yet another category of waves viz; mechanical waves.
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https://calhoun.nps.edu/handle/10945/1881
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math
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Constant and power-of-2 segmentation algorithms for a high speed numerical function generator
Valenzuela, Zaldy M.
Butler, Jon T.
Pace, Phillip E.
MetadataShow full item record
The realization of high-speed numeric computation is a sought-after commodity for real world applications, including high-speed scientific computation, digital signal processing, and embedded computers. An example of this is the generation of elementary functions, such as sin( ) x , x e and log( ) x . Sasao, Butler and Reidel [Ref. 1] developed a high speed numeric function generator using a look-up table (LUT) cascade. Their method used a piecewise linear segmentation algorithm to generate the functions [Ref. 1]. In this thesis, two alternative segmentation algorithms are proposed and compared to the results of Sasao, Butler and Reidel [Ref.1]. The first algorithm is the Constant Approximation. This algorithm uses lines of slope zero to approximate a curve. The second algorithm is the power-of-2-approximation. This method uses 2i x to approximate a curve. The constant approximation eliminates the need for a multiplier and adder, while the power-of-2-approximations eliminates the need for multiplier, thus improving the computation speed. Tradeoffs between the three methods are examined. Specifically, the implementation of the piecewise linear algorithm requires the most amount of hardware and is slower than the other two. The advantage that it has is that it yields the least amount of segments to generate a function. The constant approximation requires the most amount of hardware to realize a function, but is the fastest implementation. The power-of-2 approximation is an intermediate choice that balances speed and hardware requirements.
Showing items related by title, author, creator and subject.
Mack, Thomas J. (Monterey California. Naval Postgraduate School, 2007-03);Certain methods of realizing numeric functions, such as sin(x) or x , in hardware involve a Taylor Series expansion or the CORDIC algorithm. These methods, while precise, are iterative and slow and may take on the order ...
Knudstrup, Timothy A. (Monterey, California. Naval Postgraduate School, 2007-12);Numeric Function Generators (NFGs) have allowed computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise linear (or quadratic) approximations ...
Johnson, John Michael (Monterey, California. Naval Postgraduate School, 1975-03);The flow stress of a common shape memory alloy, a particular alloy of nitinol is investigated and presented as a function of temperature and strain. The reversion stress, that stress necessary to maintain a constant strain ...
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CC-MAIN-2019-39
| 2,715 | 10 |
https://socratic.org/questions/is-zero-imaginary-or-not-i-think-it-is-because-0-0i-where-i-is-iota-if-it-is-ima#469544
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math
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Is zero imaginary or not? I think it is because #0=0i# where #i# is iota. If it is imaginary then why every venn diagram of real and imaginary numbers on internet is disjoint. However, it should be overlapping.
Zero is a real number because it exists in the real plane, ie, the real number line. 8
Your definition of an imaginary number is incorrect.
An imaginary number is of the form
A complex number is of the form
A real number, as stated above, is a number which has no imaginary parts. This means that the coefficient of
Also, iota is an adjective meaning a small amount. We do not use it to denote the imaginary unit. Instead,
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CC-MAIN-2022-27
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http://jwilson.coe.uga.edu/EMAT6680Fa06/Crumley/final/final.html
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math
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Bouncing Barney and Ceva's Theorem
A. Barney is in the triangular room shown here. He walks from a point on BC parallel to AC. When he reaches AB, he turns and walks parallel to BC. When he reaches AC, he turns and walks parallel to AB. Prove that Barney will eventually return to his starting point. How many times will Barney reach a wall before returning to his starting point? Explore and discuss for various starting points on line BC, including points exterior to segment BC. Discuss and prove any mathematical conjectures you find in the situation.
Here is a GSP file of Bouncing Barney (triangle with line segments). A script tool has been included in the download. Clickhere.
If you want to look Barney’s exterior path (triangle with lines), click here for a GSP file with this script tool.
Let us begin the proof that Barney will eventually return to his starting point by labeling the triangle like shown below:
Algebraically, line segment AB is the line y = a/b x, line segment AC is the line y = b/(a-c) x – bc/(a-c), and line segment BC is the line y = 0. I will not go through all the algebra but the first few steps. First, construct a line through (d,0), where Barney starts, parallel to AC and intersecting AB. This line would have the same slope as AC and goes through (d, 0). So the equation of this line would be y = b/(a-c) (x-d). This line would intersect AB at the point (ad/c, bd/c). This is the first leg of Barney’s journey. The proof consists of 5 more equations with intersections on the sides of the triangle as shown below:
Barney turns 5 times with 6 legs back to the starting point.
What about choosing a point exterior of the triangle?
Notice the Superman shield? Also, note that Barney returns to his starting point with 5 turns and 6 legs of the journey around the exterior of the triangle.
Barney is located at (d, 0). The line segment formed from the starting point (d, 0) to the intersection of line AC has an equation y = b/a (x-d) since it is parallel to line AB. Thus the intersection point is
(a + c – ad/c, (abc – abd)/c(a – c)). Look familiar? Similarly to the above algebraic proof, we can conclude that Barney does make it back to (d, 0).
Conjecture: If Barney starts at a midpoint of one of the sides of the triangle, he will have 2 turns to make and 3 legs of the journey to make it back to his starting point. Also, several similar triangles are formed. Look at the picture below.
1. Barney returns to his starting point if walking inside or outside the triangle.
2. If Barney starts at the midpoint, he returns after 2 turns to his starting point.
3. If Barney starts at any other point on BC besides the midpoint, he returns after 5 turns to his starting point.
a. If Barney starts on a midpoint of the side of the triangle, he will travel half of the triangle’s perimeter.
b. If Barney starts on any other point besides the midpoint of a side of the triangle, he will travel the triangle’s perimeter before returning to his starting point.
These conclusions could be proved using properties of similar triangles (unlike the algebraic proofs above).
B. Ceva's Theorem. Consider any triangle ABC. Select a point P inside the triangle and draw lines AP, BP, and CP extended to their intersections with the opposite sides in points D, E, and F respectively.
Consider the ratio below in any triangle:
The above ratio is equal to 1 if inside the triangle ABC.
For this proof, draw a line through A parallel to line segment BC as shown below.
Constructing the line segments above, several similar triangles are formed.
Δ AET ~ Δ CEB, so AE / EC = AT / CB. (I)
Δ BFC ~ Δ AFS, so BF / FA = CB / SA. (II)
Δ CDP ~ Δ SAP, so CD / SA = DP / AP. (III)
Δ BDP ~ Δ TAP, so BD / TA = DP / AP. (IV)
Looking at (III) and (IV), CD / SA = BD / TA. With a little algebra, this proportion is the same as CD / BD = SA / TA. (V)
By multiplying (I), (II), (V), AE / EC * BF / FA * CD / DB = AT / CB * CB / SA * SA / TA = 1, or
1. The medians of any triangle are concurrent.
2. The altitudes of any triangle are concurrent.
3. The interior angle bisectors of a triangle are concurrent.
Let us look again at the centroid case:
In triangle ABC, line segments AD, BE, and CF are medians. Therefore, AF = FB, BD = DC, and CE = EA.
So (AF)(BD)(CE) = (FB)(DC)(EA), or
Thus, according to Ceva, line segments AD, BE, and CF are concurrent.
Exploration of Ceva’s Theorem using lines rather than segments to construct ABC so that point P can be outside the triangle. Below are sketches of when the points P, D, E, and F are collinear.
According to Menelaus, if we were to take direction into account in the two figures above then the ratio would equal -1 instead of 1.
Click here to open a GSP file with the collinear cases above.
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https://www.whsmith.co.uk/products/multiple-correspondence-analysis-quantitative-applications-in-the-social-sciences/9781412968973
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math
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This book provides a nontechnical introduction to Multiple Correspondence Analysis (MCA) as a method in its own right; no prior knowledge of Correspondence Analysis (CA) is needed. The presentation is practically oriented and with the needs of research in mind: gathering relevant data, formulating questions of interest, and linking statistical interpretation to geometric representations. The procedures are presented in detail using a real example, stressing the unique capacity of MCA to handle full scale research studies.
Brigitte Le Roux has a doctorate in mathematics (specialty Statistics) (Faculty of Sciences in Paris, 1970) and holds an HDR in Applied Mathematics (University of Paris Dauphine, 2000). She is a member of the laboratory MAP5 (Applied Mathematics Paris 5) of the University Paris Descartes. His research focuses on the geometric data analysis and its applications in social sciences and in particular to the analysis of questionnaires. Brigitte Le Roux is a member of the editorial board of the journal Mathematics and Humanities and the Acts of Research in Social Sciences.
About the Authors Series Editor's Introduction Acknowledgments 1. Introduction 2. The Geometry of a Cloud of Points 3. The Method of Multiple Correspondence Analysis 4. Structured Data Analysis 5. Inductive Data Analysis 6. Full-Scale Research Studies Appendix References Index
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http://www.chegg.com/homework-help/questions-and-answers/1-find-modulation-index-corresponding-given-trapezoidal-pattern-signal-2-transmitter-trans-q4202596
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math
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1. Find the modulation index corresponding to the given trapezoidal pattern for the AM signal.
2. An AM transmitter is transmitting at 1000 W. If the modulation index is 0.9 and antenna impedance is 50 ohms, find:
(a) Carrier power
(b) Total power
(c) Power in each sideband
(d) Carrier rms voltage
(e) Peak voltages for carrier and sidebands
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https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/831/items/1.0098607
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math
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UBC Theses and Dissertations
Effects of capture, power loss factor, and variable transmit power level in multiple-access systems Wong, Victor J. K. (Jack Keung)
The problem of data transmission in a slotted ALOHA system with one central base station and a number of mobiles is addressed. Of particular interest is the probability qi of successful packet reception ("capture") when i mobile users transmit in a given time slot. This probability depends on the propagation law, as well as fading, transmit power variations, spatial distribution and capture models. The capture probability in a noisy system is studied and the values of qi for large i appear to be independent of the noise level as long as the noise is reasonable (i.e. the normalized noise power is less than one). Conditions under which qi decreases monotonically with i are derived. Examples are also given to illustrate cases in which qi may not decrease monotonically with i. The effect of the power loss factor, β, on different spatial distribution and capture models is studied. It is shown that in a noiseless system, qi increases with β for the two capture models considered. A new spatial distribution, referred to as the inverse-distance spatial distribution, is proposed which allows an exact expression for qi to be obtained. A transmit power selection scheme, which decreases with distance over a selected range of distance, is proposed. Simulation results are used to show that under certain conditions, the throughput performance can be greatly improved with such a transmit power law.
Item Citations and Data
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CC-MAIN-2022-27
| 1,591 | 4 |
https://www.semanticscholar.org/paper/Rapid-assessment-of-average-ratios%3A-application-to-May-Collins/bc4469aee711b369f8cab6aae521f36afbffe02d
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math
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The calculation of a set of ratios from two sets of paired experimental data is a common practice. The ratio of the averages of two sets is in general not equal to the average of the ratios of individual pairs, and there is no predictable relation if both sets of data are unspecified real numbers. However, we prove here that the ratio of averages is the… (More)
Figures and Tables
Sorry, we couldn't extract any figures or tables for this paper.
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| 449 | 3 |
http://jabsto.com/Tutorial/topic-82/Microsoft-Excel-2010-89.html
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math
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Microsoft Office Tutorials and References
In Depth Information
Now, write the following sentence in D36-D39 to summarize the result of the
D36: Since the absolute value of t of 4.93 is
D37: greater than the critical t of 1.96, we
D38: reject the null hypothesis and accept
D39: the research hypothesis.
Lastly, write the following sentence in D41-D44 to summarize the conclusion
of the result for Item #7 of the AIBS Survey:
D41: Members rated the helpfulness of the Career
D42: Possibilities section of the AIBS Website in its
D43: helpfulness in notifying members of job-openings
D44: in academics as significantly positive.
Save your file as: career4
We have used the term ‘‘significantly positive’’ because the
mean rating of 6.58 is on the positive side of the rating scale.
We purposely have not used the term ‘‘significantly excellent’’
because people who speak English do not use that term because
something is either excellent or it is not excellent. Therefore,
‘‘significantly positive’’ is a more correct use of the English
language in this type of rating scale item.
You are probably wondering why we entered both the result
and the conclusion in separate cells instead of in just one cell.
This is because if you enter them in one cell, you will be very
disappointed when you print out your final spreadsheet,
because one of two things will happen that you will not like:
(1) if you print the spreadsheet to fit onto only one page, the
result and the conclusion will force the entire spreadsheet to be
printed in such small font size that you will be unable to read it,
or (2) if you do not print the final spreadsheet to fit onto one
page, both the result and the conclusion will ‘‘dribble over’’
onto a second page instead of fitting the entire spreadsheet onto
one page. In either case, your spreadsheet will not have a
Print the final spreadsheet so that it fits onto one page as given in Fig. 4.4 . Enter
the null hypothesis and the research hypothesis by hand on your spreadsheet
Search JabSto ::
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https://ceopedia.org/index.php/Markov_process
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math
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Markov process are an important class of the stochastic processes. The Markov property means that evolution of the Markov process in the future depends only on the present state and does not depend on past history. The Markov process does not remember the past if the present state is given. Hence, the Markov process is called the process with memoryless property.
Basic types of Markov process
Markov processes are classified according to the nature of the time parameter and the nature of the state space. With respect to state space, a Markov process can be either a discrete-state Markov process or a continuous-state Markov process. A discrete state Markov process is called a Markov chain. Similarly, with respect to time, a Markov process can be either a discrete-time. Markov process or a continuous-time Markov process. Thus, there are four basic types of Markov processes:
- Discrete-time Markov chain
- Continuous-time Markov chain
- Discrete-time Markov process
- Continuous Markov process
Structure of Markov processes
A jump process is a stochastic process that makes transitions between discrete states at times that can be fixed or random. In such a process, the system enters a state, spends an amount of time called the holding time (or sojourn time), and then jumps to another state where it spends another holding time, and so on. If the jump times are t= 0<t1<t2<..., then the sample path of the process inconstant between t1 and t1+1. If the jump times are discrete, the jump process is called a jump chain.
There are two types of jump processes:
- Pure (or nonexplosive)
If the holding times of a continuous-time jump process are exponentially distributed, the process is called a Markov jump process. A Markov jump process is a continuous-time Markov chain if the holding time depends only on the current state. If the holding times of a discrete-time jump process are geometrically distributed, the process is called a Markov jump chain. However, not all discrete-time Markov chains are Markov jump chains. For many discrete-time Markov chains, transactions occur in equally spaced intervals, such as every day, every week, and every year .
- F. Grabski 2014, p.2
- O.C. Ibe 2013, p.50
- M. Kijima 2012, p.13
- K. Taira 2010, p.98
- Freidlin M.I., (2012), Processes and Differential Equations, Birkhäuser, Basel.
- Grabski F., (2014), Semi-Markov Processes, Elsevier, Amsterdam.
- Ibe O.C., (2013), Processes for Stochastic Modeling, Elsevier, Boston.
- Kijima M., (2012), Markov Processes for Stochastic Modeling, Springer, London.
- Taira K., (2010), Boundary Value Problems and Markov Processes, Springer Science & Business Media, New York.
Author: Natalia Węgrzyn
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https://rd.springer.com/chapter/10.1007/978-0-387-69492-4_9
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math
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In this chapter we present some basic properties of Fourier transformation and applications of Fourier transform spectroscopy.A simple example of an application of Fourier transformation is the determination of the frequencies one needs to compose a function f (x), presenting a rectangular pulse. Such a pulse may be generated by superposition of many monochromatic waves with many different wavelengths and amplitudes. The input data to Fourier transformation are the space coordinates of f (x). The result of Fourier transformation is the frequency spectrum corresponding to the different wavelengths used to compose f (x). A more complicated application is the analysis of the interferogram obtained from incident light traversing an absorbing material. The Fourier transformation of the interferogram will calculate the absorption spectrum of the material.
KeywordsFourier Transformation Imaginary Part Fast Fourier Transformation Step Function Original Function
Unable to display preview. Download preview PDF.
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https://aakashsrv1.meritnation.com/cbse-class-10/maths/board-paper-of-class-10-2019-maths-abroad(set-3)---solutions/board-papers/starttest/22c$fXtuMBr0uSm9fOMDEg!!
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math
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Board Paper of Class 10 2019 Maths Abroad(Set 3) - Solutions
(i) All questions are compulsory.
(ii) The question paper consists of 30 questions divided into four sections – A, B, C and D.
(iii) Section A comprises 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.
(iv) There is no overall choice. However, an internal choice has been provided in two questions of 1 mark, two questions of 2 marks, four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternative in all such questions.
(v) Use of calculators is not permitted.
- Question 1
Which term of the A.P. −4, −1, 2, ... is 101? VIEW SOLUTION
- Question 2
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°. VIEW SOLUTION
- Question 3
Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots. VIEW SOLUTION
- Question 4
Find a rational number between and .
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17. VIEW SOLUTION
- Question 5
Find the distance between the points (a, b) and (−a, −b). VIEW SOLUTION
- Question 6
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC. VIEW SOLUTION
- Question 7
Find the solution of the pair of equation :
Find the value(s) of k for which the pair of equations has a unique solution. VIEW SOLUTION
- Question 8
Use Euclid's division algorithm to find the HCF of 255 and 867. VIEW SOLUTION
- Question 9
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that Find the coordinates of R. VIEW SOLUTION
- Question 10
How many multiples of 4 lie between 10 and 205 ?
Determine the A.P. whose third term is 16 and 7th term exceeds the 5th by 12. VIEW SOLUTION
- Question 11
Three different coins are tossed simultaneously. Find the probability of getting exactly one head. VIEW SOLUTION
- Question 12
A die is thrown once. Find the probability of getting.
(a) a prime number.
(b) an odd number VIEW SOLUTION
- Question 13
In Figure 1, BL and CM are medians of a ∆ABC right-angled at A. Prove that 4 (BL2 + CM2) = 5 BC2.OR
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. VIEW SOLUTION
- Question 14
In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region.
- Question 15
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, how much time will the tank be filled ? VIEW SOLUTION
- Question 16
Calculate the mode of the following distribution :
Class : 10 − 15 15 − 20 20 − 25 25 − 30 30 − 35 Frequency : 4 7 20 8 1
- Question 17
Show that is not a rational number, given that is an irrational number. VIEW SOLUTION
- Question 18
Obtain all the zeroes of the polynomial 2x4 − 5x3 − 11x2 + 20x + 12 when 2 and − 2 are two zeroes of the above polynomial VIEW SOLUTION
- Question 19
A motorboat whose speed is 18 km/hr in still water takes on hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. VIEW SOLUTION
- Question 20
(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2
Prove that :
- Question 21
In what ratio does the point P(−4, y) divide the line segment joining the points A(−6, 10) and B(3, −8) ? Hence find the value of y.
Find the value of p for which the points (−5, 1), (1, p) and (4, −2) are collinear. VIEW SOLUTION
- Question 22
ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle. VIEW SOLUTION
- Question 23
In an A.P., the first term is −4, the last term is 29 and the sum of all its terms is 150. Find its common difference VIEW SOLUTION
- Question 24
Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths VIEW SOLUTION
- Question 25
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0 VIEW SOLUTION
- Question 26
Solve for x :
The sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m, find the sides of the square. VIEW SOLUTION
- Question 27
In ∆ ABC (Figure 3), AD ⊥ BC. Prove that
AC2 = AB2 +BC2 − 2BC × BD
- Question 28
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole. VIEW SOLUTION
- Question 29
Calculate the mean of the following frequency distribution :
Class : 10−30 30−50 50−70 70−90 90−110 110−130 Frequency : 5 8 12 20 3 2
The following table gives production yield in kg per hectare of wheat of 100 farms of a village :
40−45 45−50 50−55 55−60 60−65 65−70 Number of farms 4 6 16 20 30 24
Change the distribution to a 'more than type' distribution, and draw its ogive. VIEW SOLUTION
- Question 30
A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm2. (Take π = 3⋅14) VIEW SOLUTION
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http://www.jetradar.co.nz/flights/Riga-RIX-to-Zurich-ZRH/?dont_redirect_please=true&marker=direct
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math
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Best airfares from Riga to ZurichJetradar compares airfares from Riga to Zurich with hundreds of airlines (including Air China, Lufthansa, British Airways) and dozens of online travel agencies in one single place. We provide you with all the options to find the cheapest flights to Zurich, you choose where to book. Also there you can find airlines special offers from Riga to Zurich. The cheapest round-trip price found within the last week was NZ$410. The cheapest oneway price found within the last week was NZ$159.
Cheapest Flights from Riga to Zurich
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Travelling from Riga to Zurich advices and facts
- The distance between Riga and Zurich is 927 miles (or 1492 kilometers).
- The shortest flight time is 2h 58m
- When you fly from Riga to Zurich, don't forget about the time difference. The time in Zurich is -1:00 from the Riga time. The current time in Zurich is 06:12 and 07:12 in Riga. Check this again shortly before your flight.
- The currency exchange rate between Riga (RIX) and Zurich (ZRH) is 1 LVL = 1.5586 CHF.
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| 1,785 | 12 |
https://en-academic.com/dic.nsf/enwiki/11571096
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math
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- Integral element
In commutative algebra, an element b of a commutative ring B is said to be integral over its subring A if there are such that
If A, B are fields, then the notions of "integral over" and of an "integral extension" are precisely "algebraic over" and "algebraic extensions" in field theory (since one does not have to insist on "monic".) The special case of greatest interest in number theory is that of complex numbers integral over Z; in this context, they are usually called algebraic integers (e.g., .) A ring consists of some (not all) algebraic integers is called the ring of integers, a central object in algebraic number theory.
- Integers are the only elements of Q that are integral over Z (Thus, Z is the integral closure of Z in Q.)
- Gaussian integers, complex numbers of the form , are integral over Z. (cf. quadratic integers.) is then the integral closure of Z in .
- The roots of unity and nilpotent elements are integral over Z.
- The integral closure of Z in the field of complex numbers C is called the ring of algebraic integers.
- Let a finite group G act on a ring A. Then A is integral over AG the set of elements fixed by G.
- Let R be a ring and u a unit in a ring containing R. Then (i) u − 1 is integral over R if and only if (ii) is integral over R.
Let B be a ring, and let A be a subring of B. Given an element b in B, the following conditions are equivalent:
- (i) b is integral over A;
- (ii) the subring A[b] of B generated by A and b is a finitely generated A-module;
- (iii) there exists a subring C of B containing A[b] and which is a finitely-generated A-module;
- (iv) there exists a finitely generated A-submodule M of B with and the annihilator of M in B is zero.
- Theorem Let u be an endmorphism of an A-module M generated by n elements and I an ideal of A such that . Then there is a relation:
This theorem (with I = A and u multiplication by b) gives (iv) (i) and the rest is easy. (Note the generality on an ideal I is useful for the consideration of the integral closure of an ideal.) Coincidentally, Nakayama's lemma is also an immediate consequence of this theorem.
It follows from the above that the set of that is integral over A forms a subring of B containing A. It is called the integral closure of A in B. The proof is due to Dedekind (Milne, ANT). Alternatively, one can use symmetric polynomials to show integral elements form a ring. (loc cit.) If A happens to be the integral closure of A, then A is said to be integrally closed in B. If A is reduced (e.g., a domain) and B its total ring of fractions, one often drops qualification "in B" and simply says "integral closure" and "integrally closed."
Similarly, "integrality" is transitive. Let C be a ring containing B and c in C. If c is integral over B and B integral over A, then c is integral over A. In particular, if C is itself integral over B and B is integral over A, then C is also integral over A.
If A is noetherian, one has a simpler criterion for integrality: b is integral over A if and only if there is a nonzero d such that for all . This can be used to weaken (iii) in the above to
- (iii) bis There exists a finitely generated A-submodule of B that contains A[b].
Finally, the assumption that A be a subring of B can be modified a bit. If f: A B is a ring homomorphism, then one says f is integral if f(A) is integral over B, in the same way one says f is finite (B finitely generated A-module) or of finite type (B finitely generated A-algebra). In this view point, one can says
- f is finite if and only if f is integral and of finite-type.
Or, more explicitly,
- B is a finitely generated A-module if and only if B is generated as A-algebra by a finite number of elements integral over A.
One of the Cohen-Seidenberg theorems shows that there is a close relationship between the prime ideals of A and the prime ideals of B. Specifically, they show that an integral extension A⊆B has the going-up property, the lying over property, and the incomparability property. In particular, the Krull dimension of A and B are the same.
When A, B are domains, A is a field if and only if B is a field.
Let be an integral extension of rings. Then the induced map is closed. This is a geometric interpretation of the going-up property.
Let be rings and A' the integral closure of A in B. (See above for the definition.)
Integral closures behave nicely under various construction. Specifically, the localization S−1A' is the integral closure of S−1A in S−1B, and A'[t] is the integral closure of A[t] in B[t].
The integral closure of a local ring A in, say, B, need not be local. This is the case for example when A is Henselian and B is a field extension of the field of fractions of A.
If A is a subring of a field K (A is necessarily a domain), then the integral closure of A in K is the intersection of all valuation rings of K containing A.
Assume A is reduced. The conductor of A is : it is the largest ideal of A that is also an ideal of A'. If the conductor is A, then A is integrally closed. Note this is a generalization of the same concept in algebraic number theory.
There is a concept of the integral closure of an ideal. The integral closure of an ideal , usually denoted by , is the set of all elements such that there exists a monic polynomial with with r as a root. The integral closure of an ideal is easily seen to be in the radical of this ideal.
There are alternate definitions as well.
- if there exists a not contained in any minimal prime, such that for all sufficiently large n.
- if in the normalized blow-up of I, the pull back of r is contained in the inverse image of I. The blow-up of an ideal is an operation of schemes which replaces the given ideal with a principal ideal. The normalization of a scheme is simply the scheme corresponding to the integral closure of all of its rings.
The notion of integral closure of an ideal is used in some proofs of the going-down theorem.
Noether's normalization lemma
Noether's normalisation lemma is a theorem in commutative algebra. Given a field K and a finitely generated K-algebra A, the theorem says it is possible to find elements y1, y2, ..., ym in A that are algebraically independent over K such that A is finite (and hence integral) over B = K[y1,..., ym]. Thus the extension K ⊂ A can be written as a composite K ⊂ B ⊂ A where K ⊂ B is a purely transcendental extension and B ⊂ A is finite.
- ^ The above equation is sometimes called an integral equation and b is said to be integrally dependent on A (as opposed to algebraic dependent.)
- ^ Kaplansky, 1.2. Exercise 4.
- ^ Chapter 2 of Huneke and Swanson 2006
- ^ An exercise in Atiyah-MacDonald.
- ^ Chapter 12 of Huneke and Swanson 2006
- ^ Chapter 4 of Reid.
- M. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison–Wesley, 1994. ISBN 0201407515
- Kaplansky, Irving (September 1974). Commutative Rings. Lectures in Mathematics. University of Chicago Press. ISBN 0226424545.
- H. Matsumura Commutative ring theory. Translated from the Japanese by M. Reid. Second edition. Cambridge Studies in Advanced Mathematics, 8.
- J. S. Milne, "Algebraic number theory." available at http://www.jmilne.org/math/
- Huneke, Craig; Swanson, Irena (2006), Integral closure of ideals, rings, and modules, London Mathematical Society Lecture Note Series, 336, Cambridge, UK: Cambridge University Press, ISBN 978-0-521-68860-4, MR2266432, http://people.reed.edu/~iswanson/book/index.html
- M. Reid, Undergraduate Commutative Algebra, London Mathematical Society, 29, Cambridge University Press, 1995.
Wikimedia Foundation. 2010.
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| 7,617 | 52 |
http://urbrainy.com/maths/year-6-age-10-11/understanding-number-year-6
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math
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Rounding very large numbers to the nearest ten thousand and rounding populations to the nearest million.
Reading and writing very large numbers: harder than it seems!
Estimating on a 0 to 10000 number line and making approximate answers to calculations.
Mini investigations involving amounts of time, large numbers and, not forgetting, blades of grass!
Co-ordinates with negative numbers, including temperature and tide levels.
Co-ordinates in four quadrants are an excellent way to demonstrate knowledge of negative numbers.
Estimating and then measuring to the nearest millimetre requires a great deal of accuracy.
Remember, in a number sentence where there are several operations we need to stick to some rules.
The statutory requirements for Year 6 Number
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s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122233086.24/warc/CC-MAIN-20150124175713-00090-ip-10-180-212-252.ec2.internal.warc.gz
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| 759 | 9 |
https://www.hackmath.net/en/word-math-problems/units?page_num=129
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math
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Units - math word problems
Number of problems found: 3178
- Two trains
Two trains go at each other. First at speed 40 km/h and the second at speed 60 km/h. At what distance will be 30 minutes before they will meet?
- Regular quadrangular pyramid
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
- Crystal water
The chemist wanted to check the content of water of crystallization of chromic potassium alum K2SO4 * Cr2 (SO4) 3 * 24 H2O, which was a long time in the laboratory. From 96.8 g of K2SO4 * Cr2 (SO4) 3 * 24 H2O prepared 979 cm3 solution of base.
- Fire tank
How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
- Washing machine
The price of washing machine was decreased by 21% and then by 55 € due small sales. After two price decreases cost € 343. How much was originally cost?
- Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
20 cows has food for 60 days. We reduce the dose to two-thirds for 18 cows. How many days will be fed?
In what quadrant is a -1165° angle?
- Ferris wheel
Ferris wheel reaches to 22 m tall and moves at the speed of 0.5m/s. During one drive wheel rotates three times. What is the total drive time?
- Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
How many hectoliters of water fits into cuboid tank with dimensions of a = 3.5 m b = 2.5 m c = 1.4 m?
- 6 regular polygon
It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
How many times increases the surface area of a cube with edge 23.4 cm if the length of the edge doubled?
- Circular motion
Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
- Plan scale
At what scale is drawn plan of the building, where one side of the building is 45 meters long is on the plan expressed by a straight line 12 mm long.
How many hours are 15 days?
- Coal storage
The coal storage distribute received coal shipment within three days. The first day distribute third of the shipments, the second day of two-fifths of the rest and the third day 300 tons of coal. How many tons of coal distributed first and second day?
- Monthly payments
Novákovi pay for electricity and monthly pays at the end of the year still bill 34 USD. Total per year pay 618 USD. What were their monthly payments?
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http://mathhelpforum.com/algebra/80299-find-solutions-polynomial.html
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math
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p(x) = 3x^4 - 11x^3 + 35x^2 + 21x - 26
if one of the solutions is 2 + 3i.
ok, so its conjugate is also a solution? 2 - 3i?
i multiplied the conjugates and then applied long division
and got 3x^2 + x + 2
but im stuck..
how do i get the other two solutions? is the above answers even right?
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https://coppermountaintech.com/what-are-dbm/
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math
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What are dBm?March 22, 2023
RF signal power is often expressed in a logarithmic format. dBm refers to the ratio of the RF power to 1 milliwatt in logarithmic format. For instance, 1 Watt is 1000 milliwatts, so the ratio is 1000 and Log10(1000) gives 30 dBm. In general:
The RMS voltage of an RF signal in a characteristic impedance R is given by:
Some RMS and peak voltages in a 50Ω system are shown in the table below.
Table – RMS and Pk RF Voltage vs dBm
Notably, the peak RF voltages at +10 dBm and +30 dBm are 1V and 10V respectively. This is useful to know when evaluating low frequency signal levels with an oscilloscope.
See this and more important radio frequency charts and formulas in this comprehensive application note.
Can I Use a VNA as a Signal Generator?
September 12, 2023
Yes! We often are asked about using a vector network analyzer for another purpose, as test equipment budgets may need to stretch. But the answer to this question is yes, you can use a VNA as an additional signal source for testing. Below are some basics of how to do it but there is a more robust application note available here to review for more details.You can set the sweep range to “Zero Span” and set the frequency to the desired value and the VNA will output a constant frequency tone. However, there are some caveats. The Compact Series from CMT uses fractional-N phase locked loops to generate signals with high resolution, thus the output frequency may be off by a fraction of a hertz. Therefore, if the vector network analyzer is used as a frequency source, another signal generator is used to generate that same frequency, and the two instruments are provided with the same 10 MHz time-base reference on the rear panel, the VNA signal may not be frequency locked to the generator. However, this would be an unusual requirement.It is generally not necessary for a VNA to hit frequencies precisely. It is only important that the measured internal IF frequencies fall within the IF bandwidth of the DSP filter implemented in the FPGA.The Cobalt Series VNAs, either 9 or 20 GHz use Direct Digital Synthesis (DDS) to generate the fine frequency steps so in that case the output frequencies will be exact.How To Use a VNA as a Signal GeneratorThe simplest way to configure the analyzer as a signal generator is simply to issue a Preset (System > Preset using the menus along the right side of the user interface), then set the Span to 0 Hz, and finally set the Center frequency and output power to the desired signal source settings.To change the output port of the signal from Port 1 to Port 2, simply change the measured S-parameter from S11 to S22. If you need not retain your calibration and display settings, that’s all there is to it! If you do need to keep such settings, however, the sections that follow walk through the steps necessary to generate a CW starting from typical instrument S-parameter sweep settings without a Preset.When using the VNA as a signal source, it’s important to keep in mind certain limitations which might affect its suitability depending on your application:The generator of the VNA will exhibit harmonics of the fundamental frequency as high as its specified harmonic distortion. You can find the specified harmonic distortion of each CMT VNA in its corresponding datasheet; typically, those are approximately -25 dBc.There will also be non-harmonic distortion, typically lower in power than the harmonic distortion.The generated signal’s output power will be subject to the output power accuracy specification of the instrument; +/- 1.0 dB is a typical specification. For more precise output powers, a power meter should be used to confirm or adjust the VNA output power.Some output power levels for CMT’s 1-Port VNAs are High/Low, specified as “Typical Only” and can’t be adjusted. Output power will need to be set with external attenuators or amplifiers according to the application at hand.If sweeping is halted by setting the trigger mode to HOLD, don’t forget that changes made to the output power or frequency will not take effect until a sweep is initiated! You can click on “Single” to apply the new settings and automatically return to HOLD mode after the sweep completes.For those engineers curious about additional uses for a vector network analyzer, CMT has additional resources to explain the options and pros and cons for each. For example, spectrum analyzer vs network analyzer; what are the differences and can a VNA be used as a spectrum analyzer is expanded in this application note.
What Are the VNA Display Formats and What Do They Mean?
August 10, 2023
Introduction Fundamentally, a Vector Network Analyzer (VNA) measures RF reflections. In a 50Ω system, reflections occur whenever an impedance other than 50 ohms is encountered by the RF signal. The reflection has a magnitude and a phase with respect to the magnitude and phase of the incident signal and may be characterized as a complex number. The VNA menu allows for a selection of charts which can display complex reflection coefficients in many different ways. Read on to learn more about VNA display formats available for analyzing measurements. Reflection and Reflection Coefficients In optics, if a beam of light traveling in a media with dielectric constant ε1 encounters a region with dielectric constant ε2, there will be a reflection as shown in Figure 1. Figure 1 - Optical Reflection The magnitude of the reflection is related to the difference between the two dielectric constants. The transmitted and reflected waves may be normalized by dividing by the incident wave to arrive at a Reflection Coefficient, Γ. For instance, in the absence of loss, the coefficient for reflection might be 0.2, thus the coefficient for transmission must be 0.8. Here, the reflection coefficient is ratio-metric, and the magnitude of the incident signal is irrelevant. Similarly, an RF voltage wave travelling on a 50Ω transmission line may encounter an impedance other than 50 ohms. This results in a reflection. Specifically, that reflection is given by: Where Z is the encountered impedance. If Z is a complex impedance –which can be expressed as R+jX– such as a resistor and capacitor in series, the reflection coefficient Γ will also be complex. We can choose to display the complex reflection coefficient in the following ways: VNA Display Formats Log Magnitude In this format, the magnitude of the complex reflection coefficient is calculated, the base 10 logarithm is applied, and the result multiplied by 20. The multiplication by 20 makes the result proportional to power instead of voltage. Where the complex reflection coefficient Γ is a+jb. This format is convenient to examine a reflection coefficient over a very wide dynamic range. Details of the low loss in the passband of a filter along with a very deep stopband can be clearly seen in Figure 2. This would not be possible using a linear scale. Figure 2 - Filter Plot Linear Magnitude The linear scale is convenient to examine a transmission coefficient such as S21, where the linear magnitude covers a range within two to three orders of magnitude. Figure 3 shows the same filter from Figure 2 but in the linear scale. Details at markers 2 and 3 are not distinguishable in this format. Figure 3 - Filter in Linear Scale Delay The delay format shows the group delay, which is calculated from -dФ/dω of S21. Ф is the phase of the reflection coefficient and ω is the radian frequency, 2πf. The group delay of the filter in Figure 2 is shown below in Figure 4. Figure 4 - Filter Group Delay VNA Display Format The group delay varies from 7.2 nS to 15.4 nS in the passband of the filter. If a modulated signal were passed through this filter such that some of the modulation bandwidth extends toward the peaks, there would be significant phase distortion (dispersion). Frequencies near the peaks might arrive at the receiver 5 nS or so later than frequencies near the center. Filters can be designed with much flatter delay than this if needed, and this can be evaluated using this delay display mode. Phase The phase of the reflection coefficient can be displayed on the VNA screen. The phase is the arctangent of the ratio of the imaginary and real parts of the coefficient, but it represents the phase alignment of the reflected or transmitted signal with respect to the incident signal. If the two signals are in perfect alignment, the phase difference is zero. The phase depends greatly on the delay experienced by the signal. Figure 5 shows the phase of the signal passed through the filter of Figure 2. Figure 5 - Filter S21 Phase The phase wraps at -180 and 180 degrees. The curvature on the left and right sides is due to the delay variation shown in Figure 4, whereas the phase is reasonably linear where the delay is flat in the middle of the passband. Extended Phase The phase is not wrapped in extended phase mode. The phase will be near zero at low frequencies and then become more and more negative at higher frequencies. The phase will change at a greater rate as more delay is experienced. Figure 6 - Extended Phase Display SWR The Standing Wave Ratio is used on reflection measurements such as S11. Reflections on a transmission line interfere with the incident wave, creating peaks and valleys in the voltage envelope of the RF wave. The ratio of the peaks to the valleys along the transmission line is the SWR. An SWR of 1:1 means there are no peaks or valleys, and hence no reflection. SWR may be calculated from the linear reflection coefficient, Γ. Real and Imag The Real and Imaginary display formats depict the real or the imaginary components of a reflection coefficient. Note, these are not the real and imaginary components of an impedance. If there is no imaginary component, then the impedance contains no reactive component and must be resistive alone. If there is no real component, the impedance must be reactive alone. Polar The polar format plots the complex reflection coefficient within a unit circle with the real component on the horizontal axis and the imaginary component on the vertical axis. This is the most fundamental plot, as it displays the reflection coefficient in its most basic form. All other formats are useful derivations. A reflection coefficient is essentially a complex vector. The polar format plots the magnitude and phase of this vector. A vector is often drawn as an arrow, but a dot at what would be the tip of the vector is drawn to reduce clutter when showing vectors for many frequencies. A VNA display format of a polar chart will have circles of magnitude and radial lines of angle, as shown below in Figure 7. Magnitude is shown in linear format here. Figure 7 - Polar Plot If Polar(log) is chosen, the magnitudes of the makers will be stated in dB format. The polar Smith formats, Smith(log), Smith(Lin), Smith(Re/Im), and Smith(R+jX) are Polar plots with a Smith chart overlay. The Smith overlay maps the polar reflection coefficient to the corresponding impedance, which gives rise to it as calculated from Eq. 1. The variations above merely change the values given by the markers. Figure 8 - Smith(R+jX) Format Smith(log) will give the log magnitude and angle of the reflection. Smith(Lin) will give the linear magnitude and angle. Smith(Re/Im) will give the linear Cartesian format reflection. Smith(R+jX) will give the complex impedance at each point. Smith(G+jB) uses the admittance overlay on the polar plot. Instead of an R+jX impedance, the marker value will show the G+jB admittance, which gives rise to the reflection, where the R+jX mode gives the impedance of a pair of series components, a resistance and a reactance. The equivalent inductance or capacitance at that frequency is also given. The G+jB admittance gives the conductance (inverse of resistance) and the susceptance of two components in parallel. The Smith(R+jX) is convenient for analyzing an impedance, which is best modeled as a series impedance, while Smith(G+jB) is best for analyzing a parallel admittance. Conclusion Different display formats are useful for different measurements. This application note covers several different display formats and their uses. For example, the Log Mag format might be best for evaluating a filter, but the SWR will likely be used to evaluate the input match of an antenna, and the Smith(R+jX) is useful for measuring an impedance and perhaps working out a matching network.
Useful Radio Frequency Engineering Formulas and Charts
February 9, 2023
This application note is a collection of essential formulas and charts for Radio Frequency Engineering.
Using a VNA as a Signal Generator
April 19, 2018
A common question from users of Copper Mountain Technologies’ USB-based Vector Network Analyzers is whether the analyzer can be used as a signal source. Users’ motivations for doing so vary, but most commonly the question arises when an additional source is needed in a test setup but is not available. For example, a source might be needed as the LO to a mixer, to check functionality of another test equipment like a power meter or spectrum analyzer, or to produce a reference clock for use elsewhere in a test system. Fortunately, any CMT VNA can readily be used as a signal source. This application note describes the process of configuring a CMT VNA as a signal source, and the expected performance of an analyzer so-configured. This application note is based on the S2 family of instruments’ software; other instruments will follow similar menu structures and procedures.
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https://www.brightstorm.com/math/precalculus/introduction-to-functions/domain-restrictions-and-functions-defined-piecewise-problem-1/
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math
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PhD. in Mathematics
Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.
I want to talk about piecewise defined functions. This is an example of a piecewise defined function; f(x) equals ½x² when x is less than or equal to 4, and 5 when x is greater than 4. A piecewise defined function, the name kind of makes sense. We have it defined differently for different values of x.
So how do these work? Well to see let's compute some values, and then we'll graph it. Let's compute first f(0). Now the first thing you have to do is figure out which of these conditions 0 belongs in. Well, 0 is less than or equal to 4, so I would use this top definition for f(x).
So ½ 0² is going to be 0. F(4), well 4 is in this top condition, less than or equal to 4. It's equal to 4, so ½(4)² is ½(16) or 8. Now 4.01 is bigger than 4, so we're in this category. When x is bigger than 4, the output is just 5. So this is going to be 5.
Same thing here. F(100), it doesn't matter how big x is as long as it's bigger than 4, the output is going to be 5. So when you're graphing these piecewise functions, you basically have to graph each of the pieces separately. Think about the quadratic function ½x² for x less than or equal to 4. I'm thinking about graphing that function on this restricted domain. I'm thinking of graphing this constant function on this restricted domain.
So let's do that as we graph y equals f(x). Now we have ½x² for x less than or equal to 4. Let's graph that part first. Now let me plot 4 equals 4, we get again ½(16) or 8. So let's see. That's going to be about 8. So it will go up to say here and here. Its vertex will be at 0, 0.
Let's see what happens at say 2. At x equals 2, we get 2² or 4 times ½ is 2. So we'll get this point here. My graph looks something like this, and something like this. It's going to go off forever in this direction. But in this direction it's got to stop right here at x equals 4.
The other piece 5 when x is greater than 4. Well, 5 is right here, between 4, and 6. So 5 is a constant function. It looks like that, and if 5 or x greater than 4, then there has to be an open circle here. There has to be an open circle for another reason. This won't be a function if the function has two different values at x equals 4. It can only have 1, and currently its value at 4 is 8, up here.
So this point is right above this open circle. So that's our graph of the piecewise function f(x) equals ½x² for x less than, or equal to 4, and 5 for x greater than 4.
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https://www.physicsforums.com/threads/polynomial-question.52027/
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math
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Somebody gave me the following question, I was able to solve it but was unsure about some of the assumptions involved. Question : Given that the polynomial x^3 + m x^2 + 15 x - 7 has at least two rational roots then find m. Now the question didn't state that m had to be integer and I was unsure as to whether this was meant to be assumed or whether it could be deduced. Here's what I did. 1. Since the product of the roots is 7 then two rational roots implies that the third root is also rational. 2. I assumed that m was integer which meant that the rational roots where also integer. ( by the http://planetmath.org/encyclopedia/RationalRootTheorem.html [Broken] ) 3. Since there are very few ways of having integer roots that multiply to give 7 I easily found the possible roots of 7, 1, 1, that multiply to give 7 and also have sum of pair-products totalling to 15. 4. So m = -(7 + 1 + 1) = -9 So did I need to assume that m was integer or could it have been deduced?
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https://www.encyclopediaofmath.org/index.php/Cohomology_of_Banach_algebras
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math
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Cohomology of Banach algebras
The groups , , where is a two-sided Banach module over a Banach algebra , defined as the cohomology groups of the cochain complex
the -dimensional chains of which are the continuous -linear operators from into , and
The cohomology of Banach algebras can also be introduced via a Banach analogue of the functor , and there is also an axiomatic definition.
Analogously to the cohomology of algebras, the elements of the one-dimensional cohomology group of a Banach algebra can be interpreted as continuous derivations from into modulo inner derivations, and the elements of the two-dimensional cohomology group can be interpreted as equivalence classes of extensions of by in which is complemented. At the same time a number of specific analytic and topological concepts can be expressed in the language of cohomology of Banach algebras.
An algebra such that for all is said to be completely separable; these algebras are characterized by the fact that all their extensions split. The specific character of Banach structures is reflected by the fact that such a requirement is very rigid: A completely-separable commutative Banach algebra necessarily has finite spectrum (space of maximal ideals). In particular, a completely-separable function algebra is the direct sum of finitely many copies of (the field of complex numbers).
The class of Banach algebras with trivial cohomology in higher dimension is not so restricted; it contains, e.g., the class of biprojective algebras, i.e. algebras that are projective as two-sided Banach -modules. The -algebra and the -algebra of a compact group are biprojective, as are the algebras of nuclear operators in all classical Banach spaces. Under certain conditions on the Banach structure, topologically-simple biprojective algebras can be characterized completely, and every semi-simple biprojective algebra is a topological direct sum of such algebras.
A commutative algebra is said to be weakly hereditary if its maximal ideals are projective. This property is equivalent to the triviality of for those for which for all , . For an ideal in a commutative Banach algebra to be projective it is necessary that its spectrum be paracompact. If this condition is also sufficient. In particular, is weakly hereditary if and only if all sets of the form , , are paracompact.
The space dual to a two-sided -module is itself a two-sided -module. Algebras with for all and are called amenable, since for this property is equivalent to the amenability (averageability) of . In general, is amenable if and only if the algebra
has a bounded approximate identity.
|||B.E. Johnson, "Cohomology of Banach algebras" Mem. Amer. Math. Soc. , 127 (1972)|
|||A.Ya. Khelemskii, "Lower values that admit the global homological dimension of Banach function algebras" Trudy Sem. Petrovsk. : 3 (1978) pp. 223–242 (In Russian)|
|[a1]||A.Ya. [A.Ya. Khelemskii] Helemsky, "Cohomology of Banach and topological spaces" , Reidel (Forthcoming) (Translated from Russian)|
Cohomology of Banach algebras. A.Ya. Khelemskii (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cohomology_of_Banach_algebras&oldid=15856
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http://www.jiskha.com/display.cgi?id=1201304956
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math
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I need help solving this question.
"Two charges are 10 meters apart. The charge on the positive particle is 1.0 C and the negative charge is 10 Coulombs. Calculate the magnitude of the electrostatic force of attraction between these two charges."
ICS - drwls, Friday, January 25, 2008 at 7:13pm
Use Coulomb's Law
F = k Q1 Q2/R^2
k = 8.99*10^9 N/m^2 C^2
Q1 = 1 C
Q2 = 10 C
R = 10 m
Your answer will be in Newtons. Never mind the minus sign on Q2. The force F will be an attraction since the charges are opposite.
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https://quizlet.com/331505230/solubility-rules-for-ionic-compounds-diagram/
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math
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During translation, the first tRNA goes into the _______.
A sample of ideal gas expands from an initial pressure and volume of 32 atm and 1.0 L to a final volume of 4.0 L. The initial temperature is 300 K. If the gas is monatomic and the expansion isothermal, what is the work W done by the gas?
One of the responsibilities of the endocrine system is maintenance of homeostasis in the body. Briefly explain what is meant by the term homeostasis.
The velocity along a pathline is given by V (m/s) = s2t1/2 where s is in meters and t is in seconds. The radius of curvature is 0.4 m. Evaluate the acceleration tangent and normal to the path at s = 1.5 m and t = 0.5 seconds.
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https://link.springer.com/chapter/10.1007/978-3-0348-0436-3_4
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math
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Nonlinear and Mixed Integer Linear Programming
In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming. We combine the continuous nonlinear and the mixed integer approach introduced in Chap. 3 to incorporate the solution quality. Finally, we show results for a real municipal water supply network.
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http://u2commerce.com/type-1/type-i-versus-type-ii-error.html
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math
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Cambridge University Press. The null hypothesis is "defendant is not guilty;" the alternate is "defendant is guilty."4 A Type I error would correspond to convicting an innocent person; a Type II error would correspond A Type II error is a false NEGATIVE; and N has two vertical lines. Credit has been given as Mr. http://u2commerce.com/type-1/type-1-versus-type-2-error.html
Reply ATUL YADAV says: July 7, 2014 at 8:56 am Great explanation !!! Raiffa, H., Decision Analysis: Introductory Lectures on Choices Under Uncertainty, Addison–Wesley, (Reading), 1968. I think your information helps clarify these two "confusing" terms. Medical testing False negatives and false positives are significant issues in medical testing.
As a result of the high false positive rate in the US, as many as 90–95% of women who get a positive mammogram do not have the condition. Read More Share this Story Shares Shares Send to Friend Email this Article to a Friend required invalid Send To required invalid Your Email required invalid Your Name Thought you might Cambridge University Press. Collingwood, Victoria, Australia: CSIRO Publishing.
While most anti-spam tactics can block or filter a high percentage of unwanted emails, doing so without creating significant false-positive results is a much more demanding task. So a "false positive" and a "false negative" are obviously opposite types of errors. share|improve this answer answered Nov 3 '11 at 1:20 Kara 311 add a comment| up vote 3 down vote I am surprised that noone has suggested the 'art/baf' mnemonic. Type 1 Error Psychology p.28. ^ Pearson, E.S.; Neyman, J. (1967) . "On the Problem of Two Samples".
The rate of the typeII error is denoted by the Greek letter β (beta) and related to the power of a test (which equals 1−β). Power Of The Test For example, all blood tests for a disease will falsely detect the disease in some proportion of people who don't have it, and will fail to detect the disease in some The boy's cry was alternate hypothesis because a null hypothesis is no wolf ;) share|improve this answer edited Mar 24 '12 at 23:51 naught101 1,8402554 answered Oct 21 '11 at 21:49 They also cause women unneeded anxiety.
ISBN1-599-94375-1. ^ a b Shermer, Michael (2002). read this post here Thanks. –forecaster Dec 28 '14 at 20:54 add a comment| up vote 9 down vote I'll try not to be redundant with other responses (although it seems a little bit what Probability Of Type 1 Error The null hypothesis is that the input does identify someone in the searched list of people, so: the probability of typeI errors is called the "false reject rate" (FRR) or false Type 3 Error One consequence of the high false positive rate in the US is that, in any 10-year period, half of the American women screened receive a false positive mammogram.
Biometrics Biometric matching, such as for fingerprint recognition, facial recognition or iris recognition, is susceptible to typeI and typeII errors. news The Skeptic Encyclopedia of Pseudoscience 2 volume set. Or in other-words saying that it the person was really innocent there was only a 5% chance that he would appear this guilty. You can also subscribe without commenting. 22 thoughts on “Understanding Type I and Type II Errors” Tim Waters says: September 16, 2013 at 2:37 pm Very thorough. Type 1 Error Calculator
Statistical calculations tell us whether or not we should reject the null hypothesis.In an ideal world we would always reject the null hypothesis when it is false, and we would not The blue (leftmost) curve is the sampling distribution assuming the null hypothesis ""µ = 0." The green (rightmost) curve is the sampling distribution assuming the specific alternate hypothesis "µ =1". Statistical significance The extent to which the test in question shows that the "speculated hypothesis" has (or has not) been nullified is called its significance level; and the higher the significance have a peek at these guys A type II error would occur if we accepted that the drug had no effect on a disease, but in reality it did.The probability of a type II error is given
For example, when examining the effectiveness of a drug, the null hypothesis would be that the drug has no effect on a disease.After formulating the null hypothesis and choosing a level Types Of Errors In Accounting ISBN1584884401. ^ Peck, Roxy and Jay L. Sign in to add this to Watch Later Add to Loading playlists...
Suggestions: Your feedback is important to us. Sometimes different stakeholders have different interests that compete (e.g., in the second example above, the developers of Drug 2 might prefer to have a smaller significance level.) See http://core.ecu.edu/psyc/wuenschk/StatHelp/Type-I-II-Errors.htm for more But the increase in lifespan is at most three days, with average increase less than 24 hours, and with poor quality of life during the period of extended life. Types Of Errors In Measurement ABC-CLIO.
Launch The “Thinking” Part of “Thinking Like A Data Scientist” Launch Determining the Economic Value of Data Launch The Big Data Intellectual Capital Rubik’s Cube Launch Analytic Insights Module from Dell If you could test all cars under all conditions, you would see an increase in mileage in the cars with the fuel additive. Plus I like your examples. http://u2commerce.com/type-1/type-1-and-type-2-error-statistics-examples.html She said that during the last two presidencies Republicans have committed both errors: President ONE was Bush who commited a type ONE error by saying there were weapons of mass destruction
Freddy the Pig View Public Profile Find all posts by Freddy the Pig #16 04-17-2012, 11:33 AM GoodOmens Guest Join Date: Dec 2007 In the past I've used Null Hypothesis Type I Error / False Positive Type II Error / False Negative Wolf is not present Shepherd thinks wolf is present (shepherd cries wolf) when no wolf is actually Email Address Please enter a valid email address. In Type I errors, the evidence points strongly toward the alternative hypothesis, but the evidence is wrong.
Last updated May 12, 2011 Straight Dope Message Board > Main > General Questions Type I vs Type II error: can someone dumb this down for me User Contact Us - Straight Dope Homepage - Archive - Top Powered by vBulletin Version 3.8.7Copyright ©2000 - 2016, vBulletin Solutions, Inc. We say, well, there's less than a 1% chance of that happening given that the null hypothesis is true. Although they display a high rate of false positives, the screening tests are considered valuable because they greatly increase the likelihood of detecting these disorders at a far earlier stage.[Note 1]
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00145.warc.gz
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CC-MAIN-2018-09
| 6,627 | 13 |
http://www.eetimes.com/messages.asp?piddl_msgthreadid=33263&piddl_msgid=190541
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math
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USB2 is not only reasonably low bit rate, it's also high overhead. I'm sure it can be made to work, but I don't understand why it's desirable. I wonder if this is a short term solution until something better (from MIPI?) is available and stable.
Article title is little bit confusing. ("Qualcomm licenses USB chip interface" )
According to article Qualcomm exited from USB-IF group i.e. now Qualcomm is looking for some other solution like MIPI-LLI. Then, how can they license USB chip interface.
Looking forward to see expert commnets.
Blog Doing Math in FPGAs Tom Burke 23 comments For a recent project, I explored doing "real" (that is, non-integer) math on a Spartan 3 FPGA. FPGAs, by their nature, do integer math. That is, there's no floating-point ...
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s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164003799/warc/CC-MAIN-20131204133323-00086-ip-10-33-133-15.ec2.internal.warc.gz
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CC-MAIN-2013-48
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https://onlinetyari.com/blog/mathematics-questions-asked-in-railway-alp-exam-2018/
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math
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Mathematics Questions Asked in Railway ALP Exam 2018: Railway Recruitment Board conducted the biggest exam of the country i.e RRB Assistant Loco Pilot. RRB has conducted the said examination in multiple shifts
Meanwhile, this article focuses on the maths questions asked in Railway ALP Exam 2018 Exam and the correct answers for each of those. These questions have been submitted by the candidates who’ve attempted the Railway ALP Examination this year.
Mathematics Questions Asked in Railway ALP Exam 2018
Questions from Mathematics ranged from Easy to Moderate. Maths Section was comprised of 20 Questions. The following questions have been submitted on our forums and we are providing the appropriate answers for each.
- If = 25, then the value of 16 ×
16 x 25/1000 =400/1000 =0.4
- The sum of the digits of a two-digit number is 8 and the product of the digits is 12. What is the difference between the digits of that number?
a + b =8
(a+b)2 – (a-b)2 =4ab
(a-b)2 =64 -48 =16
- In an hour a boat goes 10 Km along the stream and 4 Km against the stream. The speed of the boat in still water (in Kmph) is:
Downstream = 10 km/hr
Upstream = 4 km/hr
Speed of boat in still water = (10+4)/2 =7 km/hr.
- A and B working together can complete a work in 12 days, B and C working together will complete the work in 15 days, C and A working together can complete the work in 20 days. If all three work together, in how many days the work can be completed?
Let total work be LCM of (12, 15 and 20) = 60 units.
One day work of A and B = 60/12 =5 units
One day work of B and C = 60/15 =4 units
One day work of C and A = 60/20 =3 units
One day work of A, B and C =(5 + 4 + 3)/2 =6 units
Work completed by A, B and C together in = 60/6 =10 days.
- In a circle, the cord AB = 12 cm and AB extended to C and CD is tangent to circle. If CD = 8 cm then the value of BC is:
- CB =CD2
(12+x) x = 82
12x + x2 = 64
x2 +12x -64 =0
x2 + 16x -4x -64 =0
x(x+16) – 4(x+16)=0
- A is three times efficient than B, B completes total work in 12 days. In how many days will 4 times efficient of B and 8 times efficient of A will complete the task?
Let one day work of B = 1 units.
Total work = 12 units
One day work of A = 3 units
One day work of who is 4 times efficient than B = 4 units.
One day work of who is 8 times efficient than A = 24 units.
Required days =12/(4 + 24) =12/28 =3/7 days.
- What is the simple interest on Rs 1600 at the rate of 5% per annum in 6 years?
SI = (PRT)/100 =(1600 x 5 x 6)/100 =Rs 480
- The present age of Arun and Deepa is 5: 6. After 8 years the ratio of their age becomes 6: 7. What is the present age of Deepa?
Let present age of Arun be 5x and Deepa be 6x.
(5x+8)/ (6x + 8) = 6/7
35x +56 =36x + 48
x = 8, present age of Deepa = 6x =48 years
- The ratio between the present ages of A and B is 8: 9. If B is 5 years older than A, then what be the ratio of ages of A and B after 5 years?
Let present age of A and B be 8x and 9x.
9x -8x = 5 => x =5
Required ratio =(8x +5): (9x+5) =45: 50 =9:10
- In a triangle ABC, D and E are points on AB and AC respectively. If AD =6 cm, DB =8 cm AE = 12 cm and DE|| BC, then find the value of EC.
- Find the square root of 15376.
- Deepa and Seema together do a work in 6 days. Deepa can complete the same work alone in 9 days. In how many days will Seema complete the work alone?
Let total work be LCM of 6 and 9 =18 units.
One day work of Deepa and Seema = 18/6 =3 units.
One day work of Deepa =18/9 =2 units.
One day work of Seema =3-2=1 units.
Seema complete the work alone = 18/1 =18 units.
- A 120 miter long train takes 10 sec to cross a man standing on a platform. The speed of the train is:
Speed of train =distance/time= 120/10 =12 m/s
=12 x 18/5 =43.2 km/hr.
- A shopkeeper bought an article and marked 20% above the cost price. If he sold the article at 10% profit and earn Rs 96, then the marked price of the article is:
10% of CP = 96
CP =Rs 960
Marked Price = 1.20 x 960 =Rs 1152
- 120% of a number is 150, what is the 300% of that number?
120% of x = 150
x = 125
Required answer =300% of 125 = 375
- What is the compound interest of Rs 12000 at the rate of 20% per annum for 2 years?
Compound interest for two years = 20 + 20 + (20 x 20)/100 =44%
Compound interest = 44% of 12000 = Rs 5280
- The ratio of three numbers are 7: 12 :15. If HCF of these three numbers is 5, then what is the LCM of these numbers?
LCM = 7 x 12 x 15 x 5 =6300
- Average of 9 numbers is 41. If average of first 5 numbers is 45 and last 5 numbers is 38, then find the fifth number.
Required number = 5 x 45 + 5 x 38 -9 x 41
=225 + 190 -369 =415 – 369 = 46
- What is the diameter of a sphere of surface area 704 cm2?
20. Find the value of tan71o tan60o tan45o tan19o
Here we conclude our article. Stay Tuned for the latest updates on Assistant Loco Pilot Examination.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711016.32/warc/CC-MAIN-20221205100449-20221205130449-00127.warc.gz
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CC-MAIN-2022-49
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https://en.khanacademy.org/math/cc-2nd-grade-math/x3184e0ec:add-and-subtract-within-20/x3184e0ec:subtract-within-20/v/subtracting-within-20
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math
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Sal subtracts 14 - 6 by first thinking about subtracting 2 and 4. Created by Sal Khan.
Want to join the conversation?
- I am struggling to find a video on Subtracting within 20 with regrouping. I dont want to use blocks, I don't want to use visualizations. I want to know how to know how to write subtract 9 from 16 with regrouping.(7 votes)
- Try this,
We have the original number, but we can put it in expanded form*.
So, 16 = 10 + 6, and we can use this.
We know that 10 - 9 = 1, and then we can add the remaining 6 to get 7.
Expanded form is just taking the values of each number and adding them to create a number. For example, 17 = 10 + 7
You can also use this for bigger numbers, like
1,234 = 1,000 + 200 + 30 + 4(18 votes)
- Hi there,
Could you please tell which video explains how to do 9-=5 and -4=5.
Any help on this is much appreciated.(5 votes)
In these type of problems all you have to do is do the opposite of what it's asking. But, you would, in this case, still subtract since you are trying to find the number you subtract by and not the number you subtract from. So, 9-5=4 the missing value is 4.
For the second problem you add since you are trying to find the number you subtract from. So, 4+5=9 the missing value is 9.
Hope this helps!(1 vote)
- What is the commutative property? Is addition commutative?(1 vote)
- It is when you can change the order of an equation and get the same answer. For Ex: 4+3= 7 is the same as 3+4=7(0 votes)
- If your subtracting by adding a negative number does that lead to borrowing to significant to basic subtraction?(0 votes)
- The basic concept of adding a negative number is exactly the same as subtracting that number. In higher math this may not always be the case but you will learn about those types of situations later. For now think about adding a negative number as the same process as subtraction. For example 10 + -3 = 7 and 10 - 3 = 7.(0 votes)
- so people can think of the four's cancelling each other out in the second problem and being left with only ten?(0 votes)
- Yes, but not all math problems are simple like that. But it is definitely not encouraged to think as such, as people might think that 14 - 4 = 1 if they cancel out the 4 and forget that there is a 0 behind the 1.(0 votes)
- Why is subtraction not commutative?(0 votes)
- An operation is commutative if you can change the order and get the same answer.
2 - 1 = 1
1 - 2 = -1
Therefore, subtraction is not commutative.(0 votes)
Voiceover:Let's see if we can compute what 14 - 2 is, and then figure out what 14 - 4 is, and then figure out what 14 - 6 is. And I encourage you to pause this video and try to figure these out before I work through them. Voiceover:So I'm assuming you've given it a try, now let's think about it. The number 14 just by how it's written, we know that it's going to be 1 group of ten. That's what this 1 tells us plus another 4 ones. So let's verify that we have 14 objects down here. This is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So we definitely have a group of ten. We have 1 group of ten here, so that's my group of ten. So let me box that off, so I have my group of ten. And then how many ones do I have? I have 1, 2, 3, 4, I have four ones. So this is indeed, 14. This one that we have right over here, this represents this ten, it's 1 group of ten. This is 1 group of ten, let me write that down. Group of ten. And then we have 4 ones, 4, I guess we could say, 4 ones like that, so that is indeed 14. Now let's look at each of these, what is 14-2 going to be? Well we could take away 2, so take away 1... take away 2, and how many are we left with? Well we still have our one group of ten, so it's going to be 1, followed by how many ones do we have left over, well we have 2 ones. We have 2 ones left over. 1, 2, so we are going to be left with 12. Now what about 14 - 4? So let me clear this out. Actually let me do it like this. So if I clear that, so what is 14 - 4 going to be? So now I'm going take away 1, 2, 3, and 4. I have essentially taken away all 4 ones. So what am I left with? Well I still have my 1 group of ten, I still have my 1 group of ten and I have 0 ones left over. No ones anymore, so now I have 0 ones. And so 14 - 4 is 10, and that makes sense. 14 is 10 + 4 and now we're subtracting 4, to get 10, let me write this down. This is the same thing, 14 is 10 + 4. Voiceover:10 + 4, this is 14 and then we're going to subtract 4, Then we're subtracting 4, so if you have 10 + 4 - 4. Well the 4 - 4 is going to be 0, you're going to be left with 10 + 0 or just 10. We can do the same thing up here. This is equal to 14 is 10 + 4 and then we subtracted 2. And then we subtracted 2. So what you're going to be left with 10 + what's 4 - 2? It's 2, so that's what we got right over here. Let me make this very clear, this simplifies to 2. This 2 right over here. This simplifies to 0, this 0 right over here. Now let's do the last one, what is 14 - 6? Well we're going to take away 1, 2, 3, 4, then 5, and 6, so now we've broken into our group of ten. So this is going to be a one-digit number. And we are left with 1, 2, 3, 4, 5, 6, 7, 8. So this is going to be equal to 8 and we're all done.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100452.79/warc/CC-MAIN-20231202203800-20231202233800-00440.warc.gz
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CC-MAIN-2023-50
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https://www.numbersaplenty.com/1051
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math
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1051 has 2 divisors, whose sum is σ = 1052.
Its totient is φ = 1050.
The previous prime is 1049. The next prime is 1061. The reversal of 1051 is 1501.
1051 is nontrivially palindromic in base 12.
1051 is an esthetic number in base 11, because in such base its adjacent digits differ by 1.
It is a weak prime.
It is a cyclic number.
It is not a de Polignac number, because 1051 - 21 = 1049 is a prime.
It is a super-2 number, since 2×10512 = 2209202, which contains 22 as substring.
Together with 1049, it forms a pair of twin primes.
1051 is an undulating number in base 12.
It is a nialpdrome in base 11 and base 14.
It is not a weakly prime, because it can be changed into another prime (1021) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (5) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 525 + 526.
It is an arithmetic number, because the mean of its divisors is an integer number (526).
1051 is the 21-st centered pentagonal number and also the 15-th centered decagonal number.
1051 is a deficient number, since it is larger than the sum of its proper divisors (1).
1051 is an equidigital number, since it uses as much as digits as its factorization.
1051 is an odious number, because the sum of its binary digits is odd.
The product of its (nonzero) digits is 5, while the sum is 7.
The square root of 1051 is about 32.4191301549.
The cubic root of 1051 is about 10.1671891995.
Adding to 1051 its reverse (1501), we get a palindrome (2552).
The spelling of 1051 in words is "one thousand, fifty-one".
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00655.warc.gz
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CC-MAIN-2022-27
| 1,621 | 25 |
https://www.gizmoforyou.net/potentiometer/50
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math
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A brief introduction of color ring resistance identification method
Color ring resistance identification method refers to the resistance above the use of four color rings or five color rings or six color rings to represent the resistance value. The color information representing the resistance value can be read from any Angle at once. Color ring marking is mainly used on cylindrical resistors, such as carbon film resistors, metal film resistors, metal oxide film resistors, fuse resistors, winding resistors.
Second, color ring resistance identification sequence
Color ring resistance is the most common type of resistance used in various electronic equipment. No matter how it is installed, the repairman can easily read its resistance value for easy detection and replacement. However, in practice, it is found that the sequence of some color ring resistors is not very clear, which is often easy to read wrong. In recognition, the following skills can be used to judge:
Technique 1: first find the color ring of the error mark, so as to arrange the color ring order. The most commonly used colors for resistance error are: gold, silver, and brown, especially gold and silver rings, which are rarely used as the first ring of resistance color ring, so as long as there are gold and silver rings on the resistance, you can basically identify this as the last ring of resistance color ring.
Technique 2: the identification of whether the brown ring is an error mark. Brown rings are often used as both error rings and significant number rings, and often appear in both the first and last rings, making it difficult to identify the first ring. In practice, it is possible to judge by the spacing between the color rings: for example, for the resistance of a five-channel color ring, the spacing between the fifth and fourth rings is wider than that between the first and second rings, thus determining the order of the color rings.
Tip 3: In the case that the color ring order cannot be determined only by the color ring spacing, the production sequence value of the resistance can also be used to distinguish. For example, there is a resistance color ring read sequence: brown, black, black, yellow, brown, its value is: 100×10000=1M ω error 1%, belongs to the normal resistance series value, if the reverse order read: brown, yellow, black, black, brown, its value is 140×1 ω =140 ω, error 1%. Obviously, the resistance value read in the latter order is not available in the production series of resistors, so the latter color ring order is not correct.
This picture is provided by registered user “Internet said”, feedback of copyright statement
Three, color ring resistance identification method
In the early days, color ring marking was used to indicate resistance values, tolerances and specifications of resistors when the surface of resistors was not sufficient for numerical representation. There are two main parts.
The first part: the group near the front of the resistor is used to indicate the resistance value.
The resistance value of two significant numbers is represented by the first three color rings, such as 39 ω, 39K ω, and 39M ω.
The resistance value of the three effective numbers is represented by the four color rings, such as 69.8 ω, 698 ω, and 69.8K ω. It is generally used for the expression of precision resistance.
Part two: A color ring near the rear end of the resistor is used to represent tolerance accuracy.
Each color ring in Part 1 is isometric, self-contained and easily distinguishable from the color ring in Part 2.
Tricolor ring resistor
The first color ring is the ten digit number, the second color ring is the digit number, and the third color ring represents the multiplier. Use the first three color rings to represent the resistance value, such as 39 ω, 39K ω, 39M ω.
Four color ring resistor
Four color ring resistance identification: the first and second ring respectively represent two effective number of resistance value; The third ring represents multiplication; The fourth ring represents the error.
Brown red gold
Its resistance value is 12×10^2=1.2 K ω error is ±5%
The error represents the resistance value, and the fluctuation of the standard value 1200 (5%×1200) indicates that the resistance is acceptable, that is, it is a good resistance between 1140-1260.
The first and second rings with four color rings represent the first two digits of resistance value respectively; The third ring represents multiplication; The fourth ring represents the error. The key to rapid identification is to determine the resistance value in a certain order of magnitude range according to the color of the third ring, such as a few K, or dozens of several K, and then “substitute” the number read by the first two rings, so that the number can be quickly read.
Five-color ring resistor
Identification of five color ring resistance: the first, second and third rings respectively represent the resistance value of three effective numbers; The fourth ring represents multiplication; The fifth ring represents the error. If the fifth color ring is black, it is generally used as a winding resistor, and if the fifth color ring is white, it is generally used as a fuse resistor. If the resistance body has only a black color ring in the middle, it means that the resistance is zero ohm resistance.
Example: red red black brown gold
Its resistance is 220×10^1=2.2K ω and the error is ±5%
The first color ring is hundreds, the second color ring is tens,
The third color ring is the digit number, the fourth color ring is the power of color times the color, and the fifth color ring is the error rate.
First, from the bottom of the resistor, find the color ring that represents tolerance accuracy, with gold representing 5% and silver representing 10%. In the above example, the end of the color ring is golden, so the error rate is 5%. Then from the other end of the resistance, find the first and second color rings and read their corresponding numbers. In the above example, the first three color rings are red, red and black, so their corresponding numbers are red 2, red 2 and black 0, and their effective number is 220. Read the fourth multiple color ring, brown 1. So, we get a resistance of 220 x 10^1=2.2K ω. That is, the resistance value between 2090-2310 is a good resistance. If the fourth multiple color ring is gold, multiply the significant number by 0.1. If the fourth multiple color ring is silver, multiply by 0.01.
Six color ring resistor
Six color ring resistance identification: six color ring resistance front five color ring and five color ring resistance is the same method, the sixth color ring represents the temperature coefficient of the resistance.
Key points of color ring resistance recognition
Take the four-color ring as an example:
(1) Memorize the number represented by each color of the first and second rings. Brown 1, red 2, orange 3, yellow 4, green 5, blue 6, purple 7, gray 8, white 9, black 0. Read it together and repeat it several times.
Keep in mind the order of magnitude represented by the color of the third ring, which is the key to fast recognition. Concrete is:
(2) In terms of order of magnitude, they can be roughly divided into three large classes, namely: gold, black, and brown are ohmic; Red, orange and yellow are in the kilo-scale; Green and blue are megohm. I’ll divide it up just so you can remember it.
(3) When the second ring is black, the color of the third ring represents an integer, i.e., several, dozens, hundreds of K ω, etc., which is the special case of reading, so pay attention to it. For example, if the third ring is red, its resistance is the whole number of K ω.
(The third or fourth ring of a 4-ring resistance that represents a multiple is followed by several zeros, or if it is a negative number, the decimal point of the significant number is moved to the left.)
(4) Remember the error represented by the color of the fourth ring, namely: gold is 5%; Silver 10%; Colorless 20%.
Example 1 When the four color rings are yellow, orange, red and gold, and the third ring is red and the resistance range is several K ω, the reading is 4.3 K ω according to the numbers “4” and “3” represented by yellow and orange respectively. The fourth ring is gold which means the error is 5%.
Example 2 When the four color rings are brown, black, orange and gold, the third ring is orange and the second ring is black, the resistance value should be tens of K ω, according to the number “1” represented by brown, the reading is 10K ω. The fourth ring is gold, with a margin of error of 5%.
In some cases, it is also possible to compare the two starting colors, because the first color of the calculation will not be gold, silver, or black. If these 3 colors are near the edge, you need to do the reverse calculation.
There are two ways to mark the color of the color ring resistor, one is to use the 4-color ring marking method, the other is to use the 5-color ring marking method. The difference between the two is that the first two digits of the 4-color ring represent the significant digits of the resistance, while the first three digits of the 5-color ring represent the significant digits of the resistance. The second-to-last digit of the 2-color ring represents the multiplier of the significant digits of the resistance, and the last digit represents the error of the resistance.
For 4-color ring resistance, its resistance value calculation method is as follows:
Resistance value = (number of first color ring *10+ number of second color ring) * the multiplier represented by number of third color ring
For the 5 color ring resistance, its resistance calculation method is as follows:
Resistance value = (number 1 color ring *100+ number 2 color ring *10+ number 3 color ring) * number of times represented by number 4 color ring
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00724.warc.gz
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CC-MAIN-2022-21
| 9,894 | 48 |
https://www.uppsatser.se/om/Deterministic+game+theoretic/
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math
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Sökning: "Deterministic game theoretic"
Hittade 1 uppsats innehållade orden Deterministic game theoretic.
1. Analytical and Numerical methods for a Mean curvature flow equation with applications to financial Mathematics and image processingMaster-uppsats, Blekinge Tekniska Högskola/Sektionen för ingenjörsvetenskap
Sammanfattning : This thesis provides an analytical and two numerical methods for solving a parabolic equation of two-dimensional mean curvature flow with some applications. In analytical method, this equation is solved by Lie group analysis method, and in numerical method, two algorithms are implemented in MATLAB for solving this equation. LÄS MER
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487643703.56/warc/CC-MAIN-20210619051239-20210619081239-00088.warc.gz
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CC-MAIN-2021-25
| 672 | 4 |
https://space.stackexchange.com/questions/17917/how-long-would-it-take-for-a-light-sail-to-make-it-to-proxima-centauri-and-what
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math
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TL/DR: Over 2000 years for a ridiculously advanced craft travelling at the surface escape velocity of the sun, 620 km/s.
The effectiveness of a solar sail is determined by its "lightness factor", the thrust-to-weight ratio under solar gravity. (Since both gravity and radiation pressure obey inverse square law, this is independent of distance from the sun.) It is sometimes given in terms of the characteristic acceleration or characteristic thrust, which is the value at Earth's distance from the sun. The characteristic acceleration due to solar gravity is 0.005 m/s^2. (Edit: I should have written 0.0059 as 0.006. The basic conclusion will remain the same.)
The speed that can be achieved is limited by a number of factors. The maximum temperature that the sail can withstand (which limits how closely it can fly by the sun to gain speed) is one limit. Material strength is also an important factor, such a very thin material could easily be torn apart by radiation pressure when pulling against the inertia of a spacecraft near the surface of the sun. Furthermore, dust so near the sun is not that well studied and may pose a risk.
As an example, Wolfgang Seboldt & Bernd Dachwald discuss a number of solar sails in "Solar Sails: Propellantless Propulsion for Near- and Medium-Term Deep-Space Missions" (*1) One currently build-able of 400 m^2 at 87 g/m^2, one of 2500 m^2 at 38 g/m^2 likely build-able if existing technology is refined and one of 4900 m^2 at 23 g/m^2 that would require significant research but is considered realistically achievable. (Payload mass not included.) The third could achieve a characteristic thrust of about 40mN, giving a lightness factor of β = a/(0.005 m/s^2 ) = 0.07.
This is not enough to reach Proxima in any reasonable amount of time unless the sail is accelerated with large lasers. Instead of working it all out, I will show what happens with a lightness factor of 1 (*2), much higher than the craft above even without payload. If the spacecraft is on an orbit around the sun (ideally highly eccentric) and deploys its solar sail approximately at perihelion, we may assume that the sail exactly cancels solar gravity for the entire trip. This means that the spacecraft will escape the solar system with a constant speed equal to whatever its speed at perihelion was. Unless we also use another propulsion system, we must assume that we start from a bound orbit and so this can at most be the surface escape velocity of the sun, 617 542 m/s (*3).
(3.991 * 10^16 m)/(6.18 * 10^5 m/s) = 6.46 * 10^10 s, or about 2000 years.
The acceleration period for such a β = 1 craft will consist of the period where it falls in towards the sun, after which it will as already mentioned escape at constant speed. Falling in from Earth would give much less than the mentioned speed; if we assume a Jupiter flyby was used for perihelion lowering then the acceleration time (starting at Jupiter) would be just about a sixth of a Jupiter year, or two years. (Edit: Egg on my face. I wrote half a Jupiter year, when I should have said half an orbit at half of Jupiter's semi-major axis. That makes for 0.5 * 0.5^(3/2) of Jupiter's orbital period.)
(*1) Published in "Advanced Propulsion Systems and Technologies Today to 2020" edited by Claudio Bruno & Antonio Accettura, 2008. (American Institute of Aeronautics and Astronautics) p. 448-449
(*2) See "The Startflight Handbook: A Pioneer's Guide to Interstellar Travel" by Eugene Mallove & Gregory Matloff, 1989. (Wiley) p. 96-97.
(*3) From "Space Mission Engineering: The New SMAD" edited by James Wertz et al., 2011. (Microcosm) p. 955
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https://www.apprentus.com/en/calculus-lessons/UnitedStates
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math
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Trusted teacher: I am a tenured professor of Physics at Long Beach City College and this account is for Physics, Astronomy, and higher-level math tutoring (Trig and above) during the summer. I have experience teaching algebra and calculus-based physics for 6 years and have taught many lessons of algebra, trig, and calculus to students in office hours or tutoring sessions. I graduated from UCSB with a BS in Physics in 2005 which continued into a Masters in Physics from Carnegie Mellon University in 2007. I have scored extremely high on a number of math-based standardized tests (800 on GRE math, 800 on SAT II math, 740 on SAT I) and can also tutor to those tests. I exclusively teach in library locations.
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Trusted teacher: Calculus is commonly a challenging course for many high school and college students. I have an engineering background with a strong foundation in calculus and have many hours of experience tutoring students in the subject. I enjoy working with students in STEM fields and helping them understand the fundamental concepts of each topic. I'd love to work with you as you work through a semester of calculus!
Math · Calculus
Uwa - New York, NY$81
Trusted teacher: *Online classes are available* I have over twenty years of experience in math tutoring. I am currently a Ph.D. candidate in Telecommunications Engineering. I also have a Masters in Financial Mathematics and a B.Sc Pure Mathematics. I teach Math using my self-propounded model which has a success rate of 100% for my clients. I am particularly interested in students who find Math difficult. My goal for my students includes: 1. Engage students to use Math in real-life scenarios. 2. Keep students challenged to learn and apply Math in day to day life. 3. Increase their critical thinking and capabilities. Using Mathematics and analytical mind, I won a Scrabble tournament in 2014.
Algebra · Calculus · Math
Lina - Bogotá$11
Trusted teacher: I specialize in tutoring Math from Basic to Advanced. I will help you preparing an exam, solving homework, learning a new topic or strengthening some previous knowledge. I don't want the student to memorize but to understand and being able to apply the concepts. I can help with Differential Calculus, Integral Calculus, Algegra, Linear Algebra, Multivariable calculus, Differential equations, Trigonometry, Statistics and Probability.
Algebra · Calculus · Math
I specialize in tutoring Mathematics, Calculus and Trigonometry for school GMAT exams . My goal is to keep student challenged and not overwhelmed . I assign home work after every lesson and provide a periodic progressive report.The focus is to groom the students mathematically.
Trigonometry · Calculus · Math
Trusted teacher: I am a masters in physics with more than 3 years of research experience in computational physics and biophysics. As a tutor, my goal is to make sure that students understand concepts of calculus in a easy but comprehensive way such that the students feel confident in tackling variety of problems from any of their class assignment to competitive exams. I specialize in teaching single and multivariable differential and integral calculus and standard solving techniques for differential equations and partial differentiation equations with focus on application in problems of physics and engineering. If you are a beginner and do not have any maths background then no worries, I have experience in tutoring students from diverse background using simple techniques with excellent results.
Calculus · Math
Trusted teacher: VIRTUAL AND PARTICULAR TUTORIES ARE GIVEN IN THE CITY OF MEDELLÍN COLOMBIA OF: ALGEBRA, TRIGONOMETRY, GRAL MATHEMATICS, OPERATIONAL MATHEMATICS, CALCULATION, INTEGRAL, VARIOUS VARIABLES, MULTIPLE YEARS, YEARS WITH MORE THAN 20 YEARS OF EXPERIENCE AND EXCELLENT PEDAGOGY. THE OBJECTIVE IS TO BE ABLE TO MAKE MATH SOMETHING EASY AND SIMPLE. MY CELL PHONE NUMBER IS: 302-360,2844. THE VIRTUAL CLASSES ARE IN PLATFORM AND FROM A TABLE THE STUDENT SITS LIKE IN THE CLASSROOM.
Calculus · Math · Trigonometry
Calculus, Physics and Chemistry are the basic foundation of a STEM career. These courses must be mastered in order to progress through your degree. This class will specialize in Calculus, Physics, and Chemistry. As an Electrical Engineer at the University at Buffalo, I am well equipped with the knowledge of these topics to bring you success for the future. My goal is to work with you in order to prepare you for exams. You can learn Calculus, Physics, and Chemistry. Believe in yourself and you can achieve the success that you deserve
Chemistry · Physics · Calculus
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Dr S Iyer - Geneva, Switzerland$55
Trusted teacher: I am Dr. S Iyer- a tutor with over 17 years of teaching experience as of 2021 and several hundreds of students from all parts of the globe. I teach one-on-one online over Zoom/ Skype/ Google Meet/ Teams using a pen tablet and the screen-share feature. Depending on and tailored to the learning style of the student (visual, kinesthetic/ tactile, etc.) my teaching adopts a great deal of "Learn by Viewing" or "Learn by Doing" methodology that leverages the power of web-based interactive tools so as to build a solid foundational understanding. I have helped several students to do remarkably well in areas like Algebra, Geometry, Trigonometry, Precalculus, Calculus, Statistics. I have experience with various syllabi and therefore, a good sense of what is emphasized by each of them. These include: IB Diploma, Cambridge AS and A levels, Cambridge IGCSE, AP Calculus, Saxon Math ICSE, CBSE I also prepare students for competitive tests like the ACT, SAT, GRE, GMAT, Oxford MAT, TMUA, STEP, etc. More than anything, I trust that if I can replace the "fear" of a subject with "love" for it, then I would have truly made a difference to the student.
Geometry · Algebra · Calculus
Mouldi - Esch-sur-Alzette, Luxembourg$39
Trusted teacher: Mechanical and recent engineer with a master's degree in energy efficiency. I offer mathematics and physics support courses for people who have gaps or difficulties in understanding and need to work a little more. For mathematics, I can provide help in all chapters of the secondary program (Problem, Geometry, Trigonometry, Equation, study of functions, limit, derivatives, integrals) up to the University Bachelor / High School (derivation with several variables, differential equation, statistics, differential equations) included. I propose a methodology that you will understand easily.
Calculus · Geometry · Math
Trusted teacher: Private Mathematics, Geometry and Physics lessons from an experienced tutor, who is an industrial engineer graduated from Boğaziçi University and ranked 37th degree (amongst 2 million participants) in the university entrance exam in Turkey. I have a lot of experience with foreign students and curriculum of IB (international baccalaureate) and IICS (Istanbul International Community School). I do also tutor for university students. Here is the opportunity for an after school tuition for foreigners and expat families living in İstanbul. The lessons can either be at your home or in my office. All classes for Maths, Geometry and Physics can be taught both in English and Turkish up to your request. The available regions for the lessons are as follows: European Side: Şişli: Nişantaşı, Mecidiyeköy, Osmanbey, Maslak, Fulya, Esentepe Beşiktaş: Levent, Etiler, Ulus, Ortaköy, Bebek, Gayrettepe, Zincirlikuyu, Balmumcu, Dikilitaş Beyoğlu: Taksim, Cihangir, Gümüşsuyu Sarıyer: İstinye, Emirgan, Yeniköy, Tarabya, Baltalimanı and neighborhood Asian Side: Çekmeköy, Kadıköy, Üsküdar and neighborhood
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Trusted teacher: I specialize in tutoring and preparing Chemistry, Physics, and Calculus AB+BC for the AP and also the IB exam. My goal is to improve problem solving ability of each of my students and also to increase their long term memory retention of learning materials. I assign homework after every session, schedule periodic review sessions and quizzes, and provide succinct progress reports. I have many satisfied students, many of which have gone on to attend top universities around the world.
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This course is made to prepare the private students for any mathematics exam types and levels for mainly baccalaureate level 1 and level 2. As well to prepare the student for the university with a very strong background in any field of mathematics.
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Assist students with homework, teaching them how to perform the calculations needed to complete their assignments. I am also teach students basic classroom skills such as note-taking, studying, and test-taking. Teach students various mathematical concepts, processes, and computations. write progress reports detailing individual student progress
Statistics · Algebra · Calculus
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Algebra · Calculus · Math
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Safiqul - Ongkharak, Thailand$19
Trusted teacher: I have a Doctorate degree in Mathematics. Maths is a wonderful subject, which one needs in all spheres. It is the basic of all subjects. A few applications are defined below: Trigonometry: Calculus is related with trigonometry and algebra. The fundamental trigonometric functions like sine and cosine are used to define the sound and light waves.Trigonometry is further used in oceanography to measure the heights of waves and tides in oceans. It is used in satellite systems, and to create maps. The famous Pythagoras' Theorem finds its' application in determining how tall a ladder needs to be in order to safely place the base away from the wall so it does not turn over. Probability and Statistics: Probability problems infer conclusions about characteristics of hypothetical data taken from the population. Probability explains the mathematical chance that something might happen, and is used in numerous day- to-day applications. Calculus : We can find the (or global) minimum and maximum values of a function as well as the relative (or local) minimum and maximum values of a function. Differential Equation: Differential equations are applied to predict the world around us, and used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. It has applications in exponential growth and decay model, Newton's law of cooling, and Circuit theory, e.t.c. I have teaching experience for more than 15 years. My students are from all corners of the globe, and of all ages. I also make them learn Mathematics in English, so that they can excel in future. I am well acquainted will all the topics of mathematics, at all levels from schools to colleges. Children like my style of teaching.
Math · Calculus · Algebra
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Calculus · Physics · Algebra
I passed my class 10 exams with 91% marks and class 12 with 87.75 % marks, i have a bachelors degree in foundry technology and currently pursuing my second bachelors degree in mechanical engineering in Riga Technical university Mathematics is the solution to all problems, I have been teaching students aged between 6 yrs to 18 years for the last 6 years, I mainly teach mathematics and Physics. I have been teaching all type of students. Understanding the concept rather than formula should be the main aim, it will allow to solve real world problems and also allow parallel thinking of a problem.
Calculus · Algebra · Math
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Calculus · Algebra · Math
Eli - Helsinki, Finland$24
Trusted teacher: My name is Eli and I am here to help you in math. If you are looking for a person, who can explain math problems in the simplest possible way or who can help you with your homework, do not hesitate to contact me! As a teacher, I have more than 6 years' experience and I give lessons of math, calculus, algebra, matrices and geometry. Before each session, I prepare appropriate materials, like theory, examples and exercises and we will work on them together, during our session. In my classes, you can ask any questions that you have and we do not finish the class before making everything clear! Now, I am a PhD student in electrical engineering at Aalto University and I have to use my mathematical knowledge every single day; therefore, I see the importance of learning math. * At the moment, I only teach online. For this purpose, I use my pen tablet and I share my virtual whiteboard. Therefore, students can see me and also what I am writing, at the same time. I look forward to meeting you!
Calculus · Algebra · Math
My name is Anum, I am graduated in Mathematics and currently doing a master's in Informatics. I am here to teach maths, there are some areas in which I would be more interested to teach and they are Mathematics - Analysis - Matrices - Statistics - Algebra -calculus. The medium of instruction would be English. The first meeting would be free, to discuss academic plans, which will follow in the future. So if you are having trouble with certain areas in mathematics? You can contact me, I would love to help. I can also assist students with homework, projects, test preparation, papers, research, and other academic tasks. Do Mathematics in the simplest and fascinating ways
Statistics · Calculus · Algebra
Trusted teacher: I`ve been teaching Mathematics for more than 10 years, from elementary levels to college, 8 years of that was at local universities as guest lecturer. I hold Masters degree in Math and working for a long time as tutoring taught me how to teach! My classes would be online and I share my screen and use light pen, so your screen is my white board! It feels like I`m there beside you and moreover, you can have note saved!
Gre test preparation · Calculus · Math
Trusted teacher: I taught Maths for ten years in both private preparatory schools, and secondary schools (in Surrey and Somerset.) I also successfully ran, for six years, my own private maths tuition business in Guildford. I have a First-Class Degree in Mathematics/Economics from the University of Surrey. Maths is a subject that, often, students of any age are simply afraid of. Building confidence in a student that they do have the ability (and everyone does) is absolutely vital. To this end, tailoring what and how I teach to the needs of the individual is really important. It is also a subject that, sometimes, needs to be explained in very different ways to different students. For example, one student will understand algebra in a very theoretical way, others relate better to a "real-life" comparison. You have to be very flexible in your ideas and approaches as a Maths teacher, and that's something that I have always prided myself on being able to do.
Calculus · Algebra · Math
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http://www.mathisfunforum.com/search.php?action=show_user&user_id=201830
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math
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You are not logged in.
I tried to used long division
Just another thing, im still having a hard time understanding how you come up with the answer. Can you please explain it? Just one last favor pls.
Thank you i already understood it!!!!!! Your a great help thank you so much
Please help me
Im sorry I cant understand it T_T i dont know where to start. :"(
Yes. And i need to show a solution for it..
Can somebody help me with this problem? I dont have any idea how to answer it.....Divide (4x^3yz^3+3x^4y^2z+4x^2y^2z^3+3x^3y^3z-4x^2yz^4-3x^3y^2z^2) by (x+y-z)
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https://www.open.edu/openlearncreate/mod/oucontent/view.php?id=560§ion=3.1
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math
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2.2.1 Converting Fractions to Decimals
Let’s relate fractions to decimals. If we have a whole pie and a pie, we have 1 and of a pie. Not only is that hard to read and type; it’s also hard to say! So, to represent whole numbers and fractions of whole numbers, we use decimals as we have just seen in the last section. We do this by using a decimal point to separate the whole number from the fraction.
For example, say you needed to write out 2 and (three tenths) as a decimal. The whole part is 2 and the fractional part is . Thus, we would write the 2 to the left of the decimal point and the fractional part to the right of the decimal point. Thus, it would be written as 2.3.
Let’s reinforce this concept with more explanation (Click on “View document”).
Now try a few conversions on your own. Check out the next activity.
Activity: Fractions to Decimals
Rewrite each of the following fractions as a decimal.
If the number does not have a whole number part, a zero is written in the units. This makes the number easier to read (it’s easy to overlook the decimal point). The first placeholder to the right of the decimal is the tenths. How many tenths do you have for each given number?
(a) (because there are zero whole parts).
(b) (because there are zero whole parts).
(c) 1 and .
(c) 1 and = 1.2.
(d) 3 and 3/100.
(d) 3 and 3/100 = 3.03.
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https://ez.analog.com/amplifiers/f/q-a/165982/is-a-sign-of-an-offset-voltage-drift--
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math
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I have a simple question.
I think an offset voltage drift of OP-amps has positive or negative tenpareture coefficiency, but that is not written in data sheets such as OP1117, AD829, and AD8099.
On the other hand, a sign of +/- is written in ADA4945's data sheet.
I want to know a definition of an offset voltage drift in Analog Devices. Absolute value? Standard deviation?
Or is that only positive tenpareture coefficiency?
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http://www.varsitytutors.com/basic_arithmetic-help/solving-equations-with-whole-numbers
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math
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All Basic Arithmetic Resources
Example Question #1 : Solving Equations With Whole Numbers
Solve for .
First, add 6 to both sides so that the term with "x" is on its own.
Now, divide both sides by 2.
Example Question #2 : Solving Equations With Whole Numbers
Solve for .
Start by isolating the term with to one side. Add 10 on both sides.
Divide both sides by 7.
Example Question #3 : Solving Equations With Whole Numbers
Solve for t.
First start by distributing the 7.
Now, add both sides by 14.
Finally, divide both sides by 7.
Example Question #4 : Solving Equations With Whole Numbers
Solve for .
Start by adding 10 to both sides of the equation.
Then, divide both sides by .
Example Question #5 : Solving Equations With Whole Numbers
Solve for :
First, add to both sides of the equation:
Then, divide both sides by :
Example Question #6 : Solving Equations With Whole Numbers
If , what is equal to?
When solving an equation, we need to find a value of x which makes each side equal each other. We need to remember that is equal to and the same as . When we solve an equation, if we make a change on one side, we therefore need to make the exact same change on the other side, so that the equation stays equal and true. To illustrate, let's take a numerical equation:
If we subtract from each side, the equation still remains equal:
If we now divide each side by , the equation still remains equal:
This still holds true even if we have variables in our equation. We can perform the inverse operations to isolate the variable on one side and find out what number it's equal to. To solve our problem then, we need to isolate our term. We can do that by subtracting from each side, the inverse operation of adding :
We now want there to be one on the left side. is the same thing as , so we can get rid of the 6 by performing the inverse operation on both sides, i.e. dividing each side by :
is therefore our final answer.
Example Question #7 : Solving Equations With Whole Numbers
The answer is . The goal is to isolate the variable, , on one side of the equation sign and have all numerical values on the other side of the equation.
Since is a negative number, you must add to both sides.
Then, divide both sides of the equation by :
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https://ocantodabalea.com/and-pdf/2695-pre-calculus-12-textbook-answers-778-907.php
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math
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Pre-Calculus 12 – Ms. Pahlevanlu's BlogSkip to main content Precalculus Textbook. Precalculus: Mathematics for Calculus Standalone Book. Only 8 left in stock - order soon. I am currently teaching myself Pre-cal for fun. So far I am on chapter 1.
Understand Calculus in 10 Minutes
Fresh Ideas and Topics for Teaching
Currency shown in Canadian dollars. So far I am on chapter 1. Out of all the math books I've used, Blitzer's tend to be the best. You must show your work on this part of the exam to get full credit.High School Math. This is exactly the book I wish I'd had years Know what to look for in your next math program? This indicates a reflection in the y-axis.
This indicates a horizontal stretch about the y-axis by a factor of 2. Chapter 1 Function Transformations Section 1. Practice Tests Practice Test 1 Practice Test 1, Solutions Practice Test 2 Practice Test 2 Calculus Challenge Exam questions are based on topics covered in the Calculus 12 curriculum, then a vertical translation of 3 units up has been applied. If the transformed graph passes through?
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For each function i determine where fis continuous and ii determine where fis di eren- Dependent events : Probability and combinatorics Permutations : Probability and combinatorics Combinations : Probability and combinatorics Probability using combinatorics : Probability and combinatorics. Zaw Phyo Oo. This relates to transformations as a xalculus translation.
New tech-enhanced-style assessment questions provide your students practice-not only on concepts presented in the classroom, Spring answer key. Precalculus 10th Edition. Problem 3 Find the volume of the solid generated by General Information Studying for your math final. Final Exam, but also in the format of the tests to ease calculue transition to the online testing format.Know what to look for in your next math program. Just answrs sure that you ask your teacher which edition to get because there are different ones. A Non-graphing non-programmable calculator may be used. If you have ever used other math books or you're not a math person, you will be happy with Blitzer math textbooks?
The optional final exam will be worth 50 points, and will replace your lowest exam score or total quiz score. The book has plenty of clear examples in each section with practice problems. Chapter 1 ? They make b bracelets per week at a cost of f b.
Calculus Final Exam. Lai's Math Page. If the. Below are links to each of the test's respective banks of questions. Fun Calculus Stuff The tests are organized by parts.
Learn about the imaginary unit i which is the square root of -1 and about imaginary numbers like 3i which is the square root of Inverse trigonometric functions : Trigonometry Sinusoidal equations : Trigonometry Sinusoidal models : Trigonometry. Hardik Kumar. Calculus - Final Exam Two Hours. Document Information click to expand document information Description: Solutions to the popular Math textbook.
This course provides the mathematical foundation for an introductory calculus course. In addition to a brief review of basic algebra, students are instructed in equations and inequalities; functions, models, and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions; and trigonometric identities and equations. It is also strongly recommend that students complete a Mathematics Assessment. Swokowski, E. Precalculus: Functions and graphs 12th ed.
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http://www.angelfire.com/electronic/funwithtubes/Amp-Phono_Preamp-gif.html
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math
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Magnetic phono pre amp. Both channels are identical, only one will be described. The input phono connector goes through an 11 k ohm resistor to the noninverting input of the first op amp. The noninverting input goes to ground through the parallel combination of an 820 peko farad capacitor and a 36 k ohm resistor. The output goes to one end of a parallel combination of a 0.0033 microfarad capacitor and a 22 k ohm resistor. The other end of this parallel combination goes to the inverting input. The inverting input also goes to ground through a 2.4 k ohm resistor. The output of the first op amp goes to one end of a 10 microfarad non-polar electrolytic capacitor. The other end of this cap goes to one end of a 10 k ohm resistor. The other end goes to the inverting input of the second op amp. The inverting input goes through a 100 k ohm resistor then a 1 meg ohm resistor to the output. There is a 0.0033 microfarad capacitor in parallel with the 1 meg resistor. The noninverting input is grounded. The output goes through a 470 ohm resistor to the output jack. End verbal description.
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http://wildaboutmath.com/2008/03/
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math
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We've completed two Monday Math Madness contests. Last Friday Blinkdagger announced that Joshua Zucker, director at Julia Robinson Mathematics Festival, was randomly selected as the winner of the 2nd contest. Now it's my turn to post a contest problem. Those of you who are astute readers may have noticed that I said the contest would be held the 1st and 3rd Mondays of the month and today is actually the 5th Monday of March. Well, there's enough enthusiasm about this contest so we'll just do it every other week. So, we'll do 26 contests per year rather than 24. We're nice that way!
Earlier this month UC Berkeley professor emeritus of mathematics David Gale passed away. Gale made a number of significant contributions to mathematics and he loved puzzles, games, and finding beauty in mathematics. Gale's daughter had this to say:
On March 3rd Blinkdagger and I posted the first Monday Math Madness problem. On March 11th, after the first contest ended, I posted a couple of different solutions to the problem. Pat Ballew, even though he wasn't picked as the random winner, impressed me with a very clever solution to the problem that generalizes very nicely. He uses an approach called Markov state matrices, which I had never heard of. It seems to me that this approach is pretty similar to the one I posted from Richard Berlin. Pat and I exchanged several emails where he explained the method and here is my attempt to explain what Pat explained to me.
This was the problem:
A popular blog has just three categories: brilliant, insightful, and clever. Every blog post belongs to exactly one of the three categories and the category for each post is selected at random. What is the probability of reading at least one post from each category if a reader reads exactly five posts?
Pat's approach starts by creating a matrix that encodes the probabilities of going from one "state" to another as a new blog post is read. State just refers to whether 0, 1, 2, or 3 categories have been encountered after reading some number of blog posts. After one blog post has been read we are in state 1 (1 category has been read). After two posts have been read we may be in state 1 (if both blog posts are in the same category), or state 2 (if the two categories are different), but not in state 3 (you could not have encountered three categories after having read only two blog posts.)
Here's a joke I got a good chuckle out of. I'm not sure who to credit since there a number of web-sites with this joke so I'll credit the site where I first found it, Savage Research.
Two mathematicians were having dinner in a restaurant, arguing about the average mathematical knowledge of the American public. One mathematician claimed that this average was woefully inadequate, the other maintained that it was surprisingly high.
"I'll tell you what," said the cynic. "Ask that waitress a simple math question. If she gets it right, I'll pick up dinner. If not, you do." He then excused himself to visit the men's room, and the other called the waitress over.
"When my friend comes back," he told her, "I'm going to ask you a question, and I want you to respond `one-third x cubed.' There's twenty bucks in it for you." She agreed.
The cynic returned from the bathroom and called the waitress over. "The food was wonderful, thank you," the mathematician started. "Incidentally, do you know what the integral of x squared is?"
The waitress looked pensive; almost pained. She looked around the room, at her feet, made gurgling noises, and finally said, "Um, one-third x cubed?"
So the cynic paid the check. The waitress wheeled around, walked a few paces away, looked back at the two men, and muttered under her breath, "...plus a constant."
Here are some interesting recent Math-related posts in the "blathosphere."
You have only a couple more days to get your solutions in for the second Monday Math Madness at Blinkdagger.
Blinkdagger has posted the second Monday Math Madness contest. It has a fun St. Patrick's Day theme. Check it out!
You've got a week to solve this problem and send in your well-explained solution. The Blinkdagger guys are giving out $10 in Amazon gift certificate cash to a randomly-selected winner.
April 7th will be the next contest at Wild About Math! I'll be giving away something more fun that cash next time so check back here but solve the Blinkdagger St. Patty's Day problem first.
We interrupt your regularly scheduled blog for a non-Math post ...
It's Saturday night here, I was just memed by Robert at Reason-4-Smile, I don't feel like doing any productive work so I'll answer the meme and launch it further into the blogosphere.
The meme asks me to give a link to the person who meme'd me, to tell 7 interesting things about me, and to then pass the meme on. I interpreted the meme to mean that I should tell things that you're not likely to guess. Here goes:
Today is March 14th, or 3/14 as Americans write dates. Think that pi is roughly 3.14 and you'll see why today is Pi Day.
Denise at Let's Play Math does a superb job of writing about this special day. She's got a Pi poem, lots of links to pi-related pages and even a hokey but very funny mathematical pi song.
Math Mom is also commemorating this special day with some ideas about how to celebrate the day. Plus, there are other ideas in the comments of Math Mom's post.
I wanted to state what some of you may have been noticing: My rate of posting has decreased, posts have been more superficial, and I've been slow to respond to comments. Life has been busier than I expected, with important life matters and paid short-term project work filling a significant percent of my time. The slowness may last several weeks. I'm not dropping this blog as I enjoy the value that I give and receive through this community. I may not get to do a significant post until early next week. Stay tuned for the Blinkdagger contest post Monday, and for my next contest the first Monday of April. Also, do subscribe to my mailing list to get Math Bite emails with interesting little Math tidbits.
In upcoming posts I'll share a very nice alternative approach to the Monday Math Madness contest I received and I'll review an outstanding Geometry book for those of you who want a real work out when doing Geometry.
I'm also going to experiment with doing some short posts that tell you about what other Math bloggers are writing about to keep the momentum moving. And, if any of you would like to write some guest posts to bring some attention to your blogs I'm very open to that possibility.
For the very first Monday Math Madness contest we got 13 submissions. Of the 13, 6 were correct. For the record, I solved the problem by enumerating the various cases where 3 categories were represented and computing and adding their probabilities. I also verified my solution to the problem by writing a computer program to enumerate all 243 (3^5) permutations of 3 categories and 5 blog posts and count the ones were all 3 blog categories were represented. So, I'm pretty confident I got the right answer
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CC-MAIN-2017-17
| 7,058 | 28 |
https://virtualnerd.com/act-math/basics/number/rational-number-definition
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math
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There are lots of different kinds of numbers that you'll come across in algebra, and a lot of these kinds of numbers are related to each other. Before you learn how they are related, you've got to learn about them separately, and in this tutorial you'll how to define integers :)
Why can't you divide by 0? This may be one of the most asked math questions. Get this question answered once and for all by watching this tutorial!
Trying to take the square root of a number that is not a perfect square? Think you need a calculator? Think again! This tutorial will show you how to estimate the square root of a number that is not a perfect square without the use of a calculator!
Is an irrational number just a way to describe a number that's lost its mind? Not really. :) An irrational number is simply a number that cannot be written as a fraction. Check out the definition, learn an important property of these special numbers, and take a look at some examples of irrational numbers.
Did you know that there are infinitely many rational numbers between two rational numbers? This tutorial shows you how to find one. Can you find another?
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CC-MAIN-2024-18
| 1,137 | 5 |
http://prise-know.science/aidic/index.php/cet/article/view/CET1761211
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math
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Global Optimization of Reactive Distillation Processes Using Bat Algorithm
AbstractReactive distillation (RD) is an important process intensification approach with several advantages. It can improve the reaction selectivity and yield, overcome the thermodynamic restrictions, and reduce the cost/energy. However, the optimal design of RD relies on highly nonlinear and multivariable optimization including continuous and integer design variables. The objective function is generally non-convex with several constraints. For this problem, the conventional derivative-based optimization algorithms are faced with convergence problems and fail to guarantee the global optimal solution. Stochastic optimization algorithms appear to be a better alternative for the optimal design of RD because of the high robustness and efficiency. Bat algorithm (BA), which combines advantages of other existing algorithms, is a potential stochastic optimization algorithm. In this work, the BA was used to optimize the RD for the production of methyl acetate (MeAc). The link between Matlab and Aspen Plus was also created to ensure that each solution was provided from rigorous simulations. The total annual cost (TAC) was set as the objective function. Product purity constraints were achieved through Aspen plus instead of algorithms to simplify the process. BA can find the global optimal solution within less computation time than other stochastic algorithms or sequential optimization.
How to Cite
Lu J., Tang J., Chen X., Cui M., Fei Z., Zhang Z., Qiao X., 2017, Global Optimization of Reactive Distillation Processes Using Bat Algorithm , Chemical Engineering Transactions, 61, 1279-1284.
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| 1,677 | 4 |
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Gauss's_law
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math
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In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The surface under consideration may be a closed one enclosing a volume such as a spherical surface.
|Part of a series of articles about|
The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which form the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law, and vice versa.
In words, Gauss's law states that
Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. In fact, any inverse-square law can be formulated in a way similar to Gauss's law: for example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.
The law can be expressed mathematically using vector calculus in integral form and differential form; both are equivalent since they are related by the divergence theorem, also called Gauss's theorem. Each of these forms in turn can also be expressed two ways: In terms of a relation between the electric field E and the total electric charge, or in terms of the electric displacement field D and the free electric charge.
Equation involving the E field
where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within V, and ε0 is the electric constant. The electric flux ΦE is defined as a surface integral of the electric field:
Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.
An important fact about this fundamental equation often doesn't find a mention in expositions that are not absolutely diligent. The above equation may fail to hold true in case the closed surface S contains a singularity of the electric field, which is physicists' term for a point in space where either a point charge exists and the field strength approaches infinity, or the field's magnitude or direction gets altered discontinuously due to the existence of a surface charge. In 2011, a modification of the above equation, called the Generalized Gauss's Theorem by its original creator, was published in the proceedings of the 2011 Annual Meeting of Electrostatics Society of America. The Generalized Gauss's Theorem allows the closed surface S to pass through singularities of the electric field. A corollary of the Generalized Gauss's Theorem, known as the simplest form of the Generalized Gauss's Theorem, holds true if the surface S is smooth. It states that
where Q is the net charge enclosed within V and Q' is the net charge contained by the closed surface S itself.
Applying the integral form
If the electric field is known everywhere, Gauss's law makes it possible to find the distribution of electric charge: The charge in any given region can be deduced by integrating the electric field to find the flux.
The reverse problem (when the electric charge distribution is known and the electric field must be computed) is much more difficult. The total flux through a given surface gives little information about the electric field, and can go in and out of the surface in arbitrarily complicated patterns.
An exception is if there is some symmetry in the problem, which mandates that the electric field passes through the surface in a uniform way. Then, if the total flux is known, the field itself can be deduced at every point. Common examples of symmetries which lend themselves to Gauss's law include: cylindrical symmetry, planar symmetry, and spherical symmetry. See the article Gaussian surface for examples where these symmetries are exploited to compute electric fields.
By the divergence theorem, Gauss's law can alternatively be written in the differential form:
Equivalence of integral and differential forms
The integral and differential forms are mathematically equivalent, by the divergence theorem. Here is the argument more specifically.
Outline of proof The integral form of Gauss' law is:
for any closed surface S containing charge Q. By the divergence theorem, this equation is equivalent to:
for any volume V containing charge Q. By the relation between charge and charge density, this equation is equivalent to:
for any volume V. In order for this equation to be simultaneously true for every possible volume V, it is necessary (and sufficient) for the integrands to be equal everywhere. Therefore, this equation is equivalent to:
Thus the integral and differential forms are equivalent.
Equation involving the D field
Free, bound, and total charge
The electric charge that arises in the simplest textbook situations would be classified as "free charge"—for example, the charge which is transferred in static electricity, or the charge on a capacitor plate. In contrast, "bound charge" arises only in the context of dielectric (polarizable) materials. (All materials are polarizable to some extent.) When such materials are placed in an external electric field, the electrons remain bound to their respective atoms, but shift a microscopic distance in response to the field, so that they're more on one side of the atom than the other. All these microscopic displacements add up to give a macroscopic net charge distribution, and this constitutes the "bound charge".
Although microscopically all charge is fundamentally the same, there are often practical reasons for wanting to treat bound charge differently from free charge. The result is that the more fundamental Gauss's law, in terms of E (above), is sometimes put into the equivalent form below, which is in terms of D and the free charge only.
This formulation of Gauss's law states the total charge form:
where ΦD is the D-field flux through a surface S which encloses a volume V, and Qfree is the free charge contained in V. The flux ΦD is defined analogously to the flux ΦE of the electric field E through S:
The differential form of Gauss's law, involving free charge only, states:
where ∇ · D is the divergence of the electric displacement field, and ρfree is the free electric charge density.
Equivalence of total and free charge statements
Proof that the formulations of Gauss's law in terms of free charge are equivalent to the formulations involving total charge. In this proof, we will show that the equation
is equivalent to the equation
Note that we are only dealing with the differential forms, not the integral forms, but that is sufficient since the differential and integral forms are equivalent in each case, by the divergence theorem.
We introduce the polarization density P, which has the following relation to E and D:
and the following relation to the bound charge:
Now, consider the three equations:
The key insight is that the sum of the first two equations is the third equation. This completes the proof: The first equation is true by definition, and therefore the second equation is true if and only if the third equation is true. So the second and third equations are equivalent, which is what we wanted to prove.
Equation for linear materials
for the integral form, and
for the differential form.
In terms of fields of force
Gauss's theorem can be interpreted in terms of the lines of force of the field as follows:
The flux through a closed surface is dependent upon both the magnitude and direction of the electric field lines penetrating the surface. In general a positive flux is defined by these lines leaving the surface and negative flux by lines entering this surface. This results in positive charges causing a positive flux and negative charges creating a negative flux. These electric field lines will extend to infinite decreasing in strength by a factor of one over the distance from the source of the charge squared. The larger the number of field lines emanating from a charge the larger the magnitude of the charge is, and the closer together the field lines are the greater the magnitude of the electric field. This has the natural result of the electric field becoming weaker as one moves away from a charged particle, but the surface area also increases so that the net electric field exiting this particle will stay the same. In other words the closed integral of the electric field and the dot product of the derivative of the area will equal the net charge enclosed divided by permittivity of free space.
Relation to Coulomb's law
Deriving Gauss's law from Coulomb's law
Strictly speaking, Gauss's law cannot be derived from Coulomb's law alone, since Coulomb's law gives the electric field due to an individual point charge only. However, Gauss's law can be proven from Coulomb's law if it is assumed, in addition, that the electric field obeys the superposition principle. The superposition principle says that the resulting field is the vector sum of fields generated by each particle (or the integral, if the charges are distributed smoothly in space).
Outline of proof Coulomb's law states that the electric field due to a stationary point charge is:
- er is the radial unit vector,
- r is the radius, |r|,
- ε0 is the electric constant,
- q is the charge of the particle, which is assumed to be located at the origin.
Using the expression from Coulomb's law, we get the total field at r by using an integral to sum the field at r due to the infinitesimal charge at each other point s in space, to give
where δ(r) is the Dirac delta function, the result is
Using the "sifting property" of the Dirac delta function, we arrive at
which is the differential form of Gauss' law, as desired.
Note that since Coulomb's law only applies to stationary charges, there is no reason to expect Gauss's law to hold for moving charges based on this derivation alone. In fact, Gauss's law does hold for moving charges, and in this respect Gauss's law is more general than Coulomb's law.
Proof (without Dirac Delta)
Let be a bounded open set, and be the electric field, with a continuous function (density of charge).
it's true that .
But because ,
= 0 for the argument above ( and then )
And so the flux through a closed surface generated by some charge density outside (the surface) is null.
Let's consider now , and as the sphere centered in having as radius (it exists because is an open set).
Let and be the electric field created inside \ outside the sphere:
= , = and + =
The last equality follows by observing that , and the argument above.
The RHS is the electric flux generated by a charged sphere, and so:
Where the last equality follows by the mean value theorem for integrals. Finally for the Squeeze theorem and the continuity of :
Deriving Coulomb's law from Gauss's law
Strictly speaking, Coulomb's law cannot be derived from Gauss's law alone, since Gauss's law does not give any information regarding the curl of E (see Helmholtz decomposition and Faraday's law). However, Coulomb's law can be proven from Gauss's law if it is assumed, in addition, that the electric field from a point charge is spherically symmetric (this assumption, like Coulomb's law itself, is exactly true if the charge is stationary, and approximately true if the charge is in motion).
Outline of proof Taking S in the integral form of Gauss' law to be a spherical surface of radius r, centered at the point charge Q, we have
By the assumption of spherical symmetry, the integrand is a constant which can be taken out of the integral. The result is
where r̂ is a unit vector pointing radially away from the charge. Again by spherical symmetry, E points in the radial direction, and so we get
which is essentially equivalent to Coulomb's law. Thus the inverse-square law dependence of the electric field in Coulomb's law follows from Gauss' law.
- Duhem, Pierre. Leçons sur l'électricité et le magnétisme (in French). vol. 1, ch. 4, p. 22–23. shows that Lagrange has priority over Gauss. Others after Gauss discovered "Gauss' Law", too.
- Lagrange, Joseph-Louis (1773). "Sur l'attraction des sphéroïdes elliptiques". Mémoires de l'Académie de Berlin (in French): 125.
- Gauss, Carl Friedrich. Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodo nova tractata (in Latin). (Gauss, Werke, vol. V, p. 1). Gauss mentions Newton's Principia proposition XCI regarding finding the force exerted by a sphere on a point anywhere along an axis passing through the sphere.
- Halliday, David; Resnick, Robert (1970). Fundamentals of Physics. John Wiley & Sons. pp. 452–453.
- Serway, Raymond A. (1996). Physics for Scientists and Engineers with Modern Physics (4th ed.). p. 687.
- Grant, I. S.; Phillips, W. R. (2008). Electromagnetism. Manchester Physics (2nd ed.). John Wiley & Sons. ISBN 978-0-471-92712-9.
- Matthews, Paul (1998). Vector Calculus. Springer. ISBN 3-540-76180-2.
- Pathak, Ishnath (2011). "A Generalization of Gauss's Theorem in Electrostatics". Proceedings of the 2011 ESA Annual Meeting on Electrostatics: C3.
- See, for example, Griffiths, David J. (2013). Introduction to Electrodynamics (4th ed.). Prentice Hall. p. 50.
- MIT Video Lecture Series (30 x 50 minute lectures)- Electricity and Magnetism Taught by Professor Walter Lewin.
- section on Gauss's law in an online textbook
- MISN-0-132 Gauss's Law for Spherical Symmetry (PDF file) by Peter Signell for Project PHYSNET.
- MISN-0-133 Gauss's Law Applied to Cylindrical and Planar Charge Distributions (PDF file) by Peter Signell for Project PHYSNET.
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CC-MAIN-2021-43
| 13,673 | 89 |
https://tilings.math.uni-bielefeld.de/glossary/polyomio-tiling/
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math
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Tiles made of joined unions of squares. Such tilings were introduced and studied in [Golomb:P not found].
Also known as ‘table tiling’. In [Sol97] was shown that its dynamical spectrum has a continuous component. Thus it cannot be a cut and project tiling. The same was shown in [Rob99] , where a topological model of the dynamical system of the domino tilings is obtained.
Polyomio Tiling Finite Rotations Polyomio Tilings Rep Tiles Self Similar Substitution
A simple variant of the domino tilings (aka table tilings). C. Goodman-Strauss pointed out in [Goo98] the following. B. Solomyak proved in Sol98, that for each nonperiodic substitution tiling the substitution rule is invertible: One can tell from $\sigma(T)$ its predecessor $T$ uniquely. But this is true only if the prototiles have the same symmetry group as the first order supertiles. By using decorated tiles this can always be achieved. (And now Chaims remark:) Here we see a case where such a decoration is necessary.
Finite Rotations P Adic Windowed Tiling Polytopal Tiles Parallelogram Tiles Polyomio Tiling Rep Tiles Self Similar Substitution
A generalization of the domino substitution. There are several possibilities to play with 1x2 rectangles (dominos) in order to generate non-periodic tilings. The decorative lining shows here how the prototile gets turned and mirrored for this example. The two rules are actually exactly the same. For decoration the horizontal tile was colored purple.
Finite Rotations Polytopal Tiles Polyomio Tiling Rep Tiles Self Similar Substitution
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CC-MAIN-2024-18
| 1,553 | 7 |
https://steemit.com/cryptocurrency/@wond2006/genesis-mining-ethereum-2-contract-is-back
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math
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I am very excited to see that genesis mining is back with a 2 year Ethereum mining. And they put a max of 500 MH/s which is $18K and a minimum of 40MH/s for 1480$.
I guess the main question is, is it profitable?
For 500MH/s /$18,000, the coinwarz calculator says it will take 317 days to break even. And here is the earnings breakdown :
With the current ETH price and mining difficulty, this contract doesn't look profitable for me.
And the other question is how about buying ETH from the exchanges and keep it for two years?
Please give it an Upvote if you think this info was helpful. And don't forget to follow me.
Thank you :)
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655902377.71/warc/CC-MAIN-20200709224746-20200710014746-00013.warc.gz
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CC-MAIN-2020-29
| 630 | 7 |
http://jeux-de-mario.info/eureka-math-lesson-6-homework-45-24/
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math
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Multi-digit whole number addition: Fraction equivalence, ordering, and operations Topic G: Math Mammoth 5, views. Exploring measurement with multiplication. Angle types review Topic A:
Angle measure and plane figures Topic B: Chapter 6 Name Common Denominators and Lesson 6. Exploring measurement with multiplication Topic B: Problem solving with the addition of angle measures: Extending fraction equivalence to fractions greater than 1: Rounding multi-digit whole numbers:
Fractions—Multiplication and Division Assign the rest for homework.
my homework lesson 6 page 47
Comparing multi-digit whole numbers: Ask questions Search for answers. End-of-Module 5 Review Page.
Fraction equivalence, ordering, and operations Topic D: Topic B Quiz Page. Topic F Quiz Page.
She has read pages so far.
Place value, rounding, and algorithms 4.55 addition and subtraction Topic F: Decomposition and Fraction Equivalence. Fractions and improper fractions on a number line Page. Decomposition and fraction equivalence: Lesson 6 Time Intervals Angle measure and plane figures Topic B: Angle measure and plane figures. Multiplication of two-digit by two-digit numbers: Place value, rounding, and algorithms for addition and subtraction Topic B: The paper will be five pages:.
Decompose Fractions using Area Models
Fraction equivalence, ordering, and operations. Fractions with a Tape Diagram Page.
Use Time Intervals to the minute – 3rd grade math lesson – Duration:. Repeated addition of fractions as multiplication: Multi-digit multiplication and division Topic C: Homework answers; Post homework; Hokework Register; Teach online; 8.
4th grade (Eureka Math/EngageNY)
Subtracting fraction from a whole number Quiz. Remind them to add these pages to their. Topic E Quiz Page. Just do my homework!
Grade 4 Homework page! Exploring measurement with multiplication Topic B: Math Mammoth 5, views. Multiplicative comparison word problems: Decimal fractions Topic C: Exchange tips, hints, and advice.
Multi-digit whole number subtraction:
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s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540528490.48/warc/CC-MAIN-20191210180555-20191210204555-00060.warc.gz
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CC-MAIN-2019-51
| 2,024 | 15 |
https://email.varsitytutors.com/hotmath/hotmath_help/topics/unit-rates
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math
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A rate is a ratio that is used for comparing two different quantities that have different units. Rates are used in pricing goods such as grocery store items, gasoline, tickets to a concert, and other items. Rates are also used when paying wages and when paying monthly fees of all types.
The unit rate is a rate that illustrates how many units of quantity correspond to the single unit of another quantity. For example, something might cost $12 per pound, you might drive 52 miles per hour, or there may be 100 pennies per American dollar.
We use division to calculate unit rates based on the given information.
An SUV travels 78 miles on 4 gallons of gasoline. Find the unit rate that indicates how many miles per gallon the SUV gets.
To find the solution, simply divide 78 by 4.
The SUV gets 19.5 miles per gallon.
Pedro can type 24 pages in 8 minutes. Find the rate that indicates how many pages he can type per minute.
To find the solution, simply divide 24 by 8.
Pedro can type 3 pages per minute.
Rohit earns INR 30000 working 30 hours. Find their hourly rate.
Therefore, Rohit earns INR 1000 per hour.
a. A copy machine makes 45 copies in 25 seconds. Find the unit rate in copies per second.
Divide 45 by 25 to find the unit rate.
The copy machine makes 1.8 copies per second.
b. Rebecca travels 400 kilometers in 10 hours. Find the unit rate in kilometers per hour.
Divide 400 by 10 to find the unit rate.
Rebecca drives 40 kilometers per hour.
Unit rates are a type of math that is important for everyday life. We use unit rates daily in our shopping, driving, and work life. So it's important that students understand how unit rates work. If your student could use some help understanding unit rates, get them some help from a professional math tutor. A tutor is an excellent resource for your student because they can work at your student's pace, taking it slow and going through each step in the process when necessary. At the same time, the tutor can speed through concepts that your student picks up quickly and easily. Your student can ask their tutor questions as soon as they arise, so they understand unit rate concepts right away. To get signed up and learn more about how tutoring can benefit your student, contact the Educational Directors at Varsity Tutors today.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817002.2/warc/CC-MAIN-20240415142720-20240415172720-00602.warc.gz
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CC-MAIN-2024-18
| 2,285 | 18 |
https://everything2.com/title/circumcenter
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math
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A triangle has no one unique center, but the circumcenter may be the second most popular and easy to visualize, after the incenter.
The circumcircle is the smallest circle that can fit through the three points that define a triangle. The circumcircle has a radius, R, that is equal to a*b*c/(4K), where K is the area of the triangle, and a, b, and c are the side lengths of the triangle ΔABC. We will denote the circumcenter as O
The circumcenter's coordinates are:
(dA*(Cy-By) + dB*(Ay-Cy) + dC*(By-Ay))
Ox = ----------------------------------------- (1a)
2*(Ax*(Cy-By) + Bx*(Ay-Cy) + Cx*(By-Ay))
-(dA*(Cx-Bx) + dB*(Ax-Cx) + dC*(Bx-Ax))
Oy = ----------------------------------------- (1b)
2*(Ax*(Cy-By) + Bx*(Ay-Cy) + Cx*(By-Ay))
O = (Ox, Oy)... Cartesian coordinates of the circumcenter
A = (Ax, Ay)... the coordinates of vertex A of triangle ABC
B = (Bx, By)... the coordinates of vertex B of triangle ABC
C = (Cx, Cy)... the coordinates of vertex C of triangle ABC
and where some intermediate calculations help reduce eyestrain:
dA = Ax^2 + Ay^2 (2a)
dB = Bx^2 + By^2 (2b)
dC = Cx^2 + Cy^2 (2c)
The best explanation for finding the center of the circle is found here. The Khan Academy always has marvelous tutorials on YouTube, and they also explain this quite well here..
Example 1: An acute triangle has vertices A, B, and C at A = (-2,-2), B = (5,3), and C = (1,4). Find the circumcenter O and the radius of the circumcircle, R.
A = (Ax, Ay) = (-2,-2)
B = (Bx, By) = ( 5, 3)
C = (Cx, Cy) = ( 1, 4)
dA = (-2)^2 + (-2)^2 = 8
dB = 5^2 + 3^2 = 34
dC = 1^2 + 4^2 = 17
O = (Ox, Oy) = (2.06, -0.28)
R = 4.4
The result is that the circumcenter is found at (2.06, -0.28) and the radius of the circumcircle is 4.4.
Point of Concurrency of Perpendicular Bisectors: The circumcenter is the point of concurrency of the perpendicular bisectors of each side. If you bisect every side, and you draw the line that runs perpendicular to that side then every line intersects at one point: the circumcenter.
When I began this writeup, I was under the impression that Euclid had proved that the perpendicular bisectors from every side all meet at the same point for every possible triangle. He showed something similar in Book 4, Proposition 5 of The Elements. But Cut the Knot mathematician and author Alexander Bogomolny says that Euclid didn't do this. He only showed that they did, but offered no proof. It's Bogomolny's belief that Euclid would have needed a Ceva's Theorem in order to prove it, but that theorem didn't come along for another 1500 years.
SOURCE: Jim Wilson, Proof that the three perpendicular biectors of the sides of a triangle are concurrent. Wilson is a professor with the Mathematics Education program at the University of Georgia. His web site is full of mathematical topics.
The Circumcenter is Outside the Triangle for Obtuse Triangles: Although the incenter is always inside the triangle, the circumcenter does not have to be. When the triangle is acute, the circumcenter is inside ΔABC. When it is obtuse, O is outside. Example 2 gives points of a very small obtuse angle with a wide vertex angle at A. The circumcenter is a large distance away from the triangle.
Example 2: An obtuse triangle has one vertex at the origin. We'll label this vertex A. The triangle is isosceles, meaning that sides AB and AC are of equal length. The interior angle α is 150°. The vertex coordinates are: A = (0,0), B = (1,0), and C = (cos(150°),sin(150°)) = (-0.87, 0.5). Find the circumcenter and the radius of the circumcircle.
A = (Ax, Ay) = ( 0, 0)
B = (Bx, By) = ( 1, 0)
C = (Cx, Cy) = (-0.87, 0.5)
dA = 3.73
dB = 1
dC = 1
O = (Ox, Oy) = (0.5, 1.87)
R = 1.93
The circumcenter is located at O = (0.5, 1.87). The radius is R = 1.93, a comparatively large distance away from the triangle. This is for an interior angle α = 150°. If the interior angle were greater, the radius would be even larger. For α = 170°, R = 5.7.
A straightforward equation for the circumcenter was difficult to find on the internet, and when I sat down to derive it myself, I was dismayed at how messy the terms got. When I did find a workable equation (Equation 1 above), I wanted to see if it would work for a variety of cases, and so I dropped the equation and many of its preceding calculational terms into Excel, created a graph of a triangle, the circumcenter point, and then the circumcircle to see if the equation would work and was well behaved and so forth. A picture of Example 1 is on my homenode, and will stay there for a brief time.
Barycentric Coordinates: The barycentric coordinates of the circumcenter are sin(2α):sin(2β):sin(2γ). (The interior angles at triangle vertices A, B, and C are α, β, γ, respectively.)
Trilinear Coordinates: The trilinear coordinates of the circumcenter are cos(α):cos(β):cos(γ).
Everything2 Writeups: Articles on (topic)
- tongpoo, circumcenter, Dec. 2, 2001
- tongpoo, circumcircle. A nodeshell was created, but it was never filled. Clearly this hole must be filled!
- tongpoo, triangle, Feb. 8, 2002
- IWhoSawTheFace, incenter, Feb. 8, 2002
References: Useful books and references on geometry
H.S.M. Coxeter, Introduction to Geometry, 2nd Ed., (c) 1969
*SIGH* What a magnificent book.
§ 1.4, “The Medians and the Centroid,” p. 10
§ 1.5, “The Incircle and the Circumcircle,” pp. 11-16
§ 1.6, “The Euler Line and the Orthocenter,” p. 17
Dan Pedoe, Geometry: A Comprehensive Course
J.L. Heilbron, Geometry Civilized, ©2000
David Wells, Ed., The Penguin Dictionary of Curious and Interesting Geometry, ©1991
Bruce Meserve, Fundamental Concepts of Geometry, ©1983
Melvin Hausner, A Vector Space Approach to Geometry, ©1965
Gerald Farin and Dianne Hansford, The Geometry Toolbox, ©1998
Ch. 3, 2D Lines
§ 3.6, “Distance of a point to a line,” p. 40
§ 3.7, “The foot of a point,” p. 44
§ 3.8, “Computing intersections,” p. 45
Ch. 8, Breaking it up: Triangles
§ 8.1, “Barycentric coordinates,” p. 126
§ 8.2, “Affine invariance,” p. 128
§ 8.3, “Some special points,” p. 128
Daniel Zwillinger, Ed., The CRC Standard Mathematical Tables and Formulae, 30th Ed, ©1996
Ch. 4, Geometry,
§ 4.5.1, “Triangles,” p. 271
§ 4.6, “Circles,” p. 277
Siobhan Roberts, King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, ©2006
Alfred S. Posamentier and Charles T. Salkind, Challenging Problems in Geometry, ©1988
Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics, Published in 1957 by the Princeton University Press
§ 26, “A characteristic property of the circle,” p. 160
§ 28, “The indispensability of the compass for the constructions of elementary geometry,” p. 177
- Wikipedia, "Circumscribed Circle" This contains very useful mathematical formulae, especially matrix forms for finding the center of the circle, and exterior angles at the intersections of the circumcircle with the vertices of a triangle.
- Wikipedia, "Triangle"
- Wikipedia, "Incircle and Excircles of a Triangle"
- D. Joyce, Euclid's Elements, Book 4, Proposition 5, "To circumscribe a circle about a given triangle." David Joyce is a professor of Mathematics and Computer Science at Clark University. He rendered Euclid's Elements into HTML, added Java applets to illustrate geometric constructions with live, movable points and lines. If you're a geometry buff, you should bookmark this site.
- Jim Wilson, Proof that the three perpendicular biectors of the sides of a triangle are concurrent. Wilson is a professor with the Mathematics Education program at the University of Georgia. His web site is full of mathematical topics.
- To construct a circle given three points. Nice Java applet allows you to drag vertices around and watch the circumcenter move.
- Weisstein, Eric W. "Circumcenter" From MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Circumcircle" From
MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Circumradius" From MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Incenter" From MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Triangle" From MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Tangential Triangle" From MathWorld--A Wolfram Web Resource.
- Alexander Bogomolny, "Incircle and Excircles of a Triangle" From Cut The Knot--mathematical topics. Cut the Knot has a full range of geometric topics.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746847.97/warc/CC-MAIN-20181120231755-20181121013755-00168.warc.gz
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CC-MAIN-2018-47
| 8,362 | 93 |
https://www.mm.bme.hu/~gyebro/files/ans_help_v182/ans_cmd/Hlp_C_CYL5.html
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math
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Creates a circular area or cylindrical volume by end points.
Working plane X and Y coordinates of one end of the circle or cylinder face.
Working plane X and Y coordinates of the other end of the circle or cylinder face.
The perpendicular distance (either positive or negative based
on the working plane Z direction) from the working plane representing the
depth of the cylinder. If
DEPTH = 0 (default),
a circular area is created on the working plane.
Defines a circular area anywhere on the working plane or a cylindrical volume with one face anywhere on the working plane by specifying diameter end points. For a solid cylinder of 360°, the top and bottom faces will be circular (each area defined with four lines) and they will be connected with two surface areas (each spanning 180°). See the CYL4, PCIRC, and CYLIND commands for alternate ways to create circles and cylinders.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00484.warc.gz
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CC-MAIN-2022-21
| 884 | 9 |
http://thescientificworldview.blogspot.com/2011/02/heisenberg-uncertainty-principle-true.html
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math
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Heisenberg Uncertainty Principle: True or False?
From Bill Howell:
I’m interested in how your worldview can potentially be used to empirically test the natural world. As an example, it seems to me that your theory predicts that (someday) the Heisenberg Uncertainty Principle could be proved false. If one interprets that Principle to be about the inability to measure something because any method of measurement will disturb the object being studied, then theoretically, it would be possible to find a way to make a measurement that doesn’t disturb the object. Using the example of waves, one can’t discern the shape of an object with an instrument that uses a larger wavelength than the thing being studied. If particles don’t exist beyond a certain size (let’s say the Plank limit) then there is no way to discriminate the state of a subatomic particle that can be influenced by an interaction on that scale of magnitude. But if particles can exist which are infinitely small, then (theoretically) there are particles that are a magnitude or two less than the Plank limit which could be used to probe the structure of things at and above the Plank limit.
[Bill, I hate to disappoint you, but the Heisenberg Uncertainty Principle cannot be proven false. At best, one can choose one of the two possible interpretations that can be gained from it: 1.) Uncertainty means that nature contains an element of absolute chance (Copenhagen view); 2.) Uncertainty reflects observer ignorance (Bohmian view). With UNCERTAINTY (It is impossible to know everything about anything, but it is possible to know more about anything), we have chosen the second along with its implied challenge to the finite causality of classical mechanism. This does not mean, however, that one can perform any measurement without disturbing the microcosm being measured. All microcosms contain an infinity of submicrocosms and are bathed in an infinity of supermicrocosms, so, of course, the Plank limit is only defined by those used to perform the measurement. You are right that the use of still smaller microcosms (ether particles?) would allow measurements at even smaller scales.
Incidentally, the “wave nature” of particles being measured at the scale to which the principle is applied is due to the motions induced within the macrocosm of any such particle. Interpretations differ because positivists, in particular, deny that the associated macrocosm contains anything at all. For them, the surrounding space is perfectly empty, and so they see related waves as properties of the microcosm itself. In our view, however, any particle traveling through the macrocosm must produce waves in the same way that a ship makes waves as it travels across the ocean. There is no “wave-particle” duality in univironmental determinism (UD).]
The fact that we currently have no instruments capable of probing at this scale is beside the point. One can’t say it’s impossible to create such an instrument someday in the future (because we are still too ignorant about the Cosmos to say that it’s impossible). Creating such an instrument may require using subatomic particles that are very close to absolute zero. Conversely, if one interprets the Heisenberg Uncertainty Principle to mean that it is not about the inability to physically measure something (which is an alternate explanation I’ve read), then that too is opposed to UD (as I understand it) and so such an instrument, if it could be created, would also falsify the Principle.
[You are right that “the inability to physically measure something” and “the inability to know everything about anything” really are equivalent. Nonetheless, a better instrument would only falsify the Planck limit, but not the principle. According to our assumption of INFINITY, the principle will apply each time a new “quasi-Planck limit” is reached.]
On a separate matter, you once told me that you weren’t a ‘steady-state’er. I had knee-jerked assumed that this was your conceptual model of the Universe. So I’m curious, is your position based on what might be called ‘first principles’ and/or the logic of your 10 Assumptions, or do you have a conceptual model that you could describe to me.
[Remember that the Steady State Theory (SST) proposed first by Bondi and Gold (1948) involved the assumption of creation, which is the opposite of our deterministic assumption of CONSERVATION (Matter and the motion of matter can be neither created nor destroyed). They did this to stay in tune with the prevailing view that the universe was expanding. The creation of one hydrogen atom per cubic meter per billion years was calculated to be enough to keep the universe expanding forever. Bondi and Gold did not mention what the universe supposedly was expanding into. Neither did they use the 4-D concept of space-time that Einstein had introduced. As you know, UD assumes through INFINITY (The universe is infinite, both in the microcosmic and macrocosmic directions) that empty space cannot exist. It also assumes through INSEPARABILITY (Just as there is no motion without matter, so there is no matter without motion) that there are only three dimensions, and that the objectification of time in SRT and GRT is Einstein’s greatest philosophical error (http://thescientificworldview.blogspot.com/2010/10/einsteins-most-important-philosophical.html).
A short paper on my conceptual model of Infinite Universe Theory (IUT) is at: http://scientificphilosophy.com/Downloads/IUT.pdf . I am expanding this into a short, easy to understand book for the layperson.
Bondi, H., and Gold, T., 1948, The steady-state theory of the expanding universe: Monthly Notices of the Royal Astronomical Society, v. 108, no. 3, p. 252-270.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121153.91/warc/CC-MAIN-20170423031201-00510-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 5,767 | 11 |
https://cris.huji.ac.il/en/publications/a-formula-for-topologydeformations-and-its-significance
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math
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The formula is ∂e = (ade)b + ∞σi=0 Bi/i!(ade)i(b - a); with ∂a + 1/2 [a; a] = 0 and ∂b + 1/2 [b; b] = 0, where a, b and e in degrees -1, -1 and 0 are the free generators of a completed free graded Lie algebra L[a; b; e]. The coeffcients are defined by x/ex- 1 = ∞σn=0 Bn/n!xn: The theorem is that this formula for ∂ on generators extends to a derivation of square zero on L[a; b; e]; the formula for ∂e is unique satisfying the first property, once given the formulae for ∂a and ∂b, along with the condition that the "flow" generated by e moves a to b in unit time. The immediate significance of this formula is that it computes the infinity cocommutative coalgebra structure on the chains of the closed interval. It may be derived and proved using the geometrical idea of at connections and one-parameter groups or ows of gauge transformations. The deeper significance of such general DGLAs which want to combine deformation theory and rational homotopy theory is proposed as a research problem.
Bibliographical notePublisher Copyright:
© 2014 Instytut Matematyczny PAN.
- Deformation theory
- Infinity structure
- Rational homotopy theory
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CC-MAIN-2023-40
| 1,161 | 6 |
https://schoolbag.info/mathematics/barrons_ap_calculus/71.html
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math
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Calculus AB and Calculus BC
CHAPTER 9 Differential Equations
B. SLOPE FIELDS
In this section we solve differential equations by obtaining a slope field or calculator picture that approximates the general solution. We call the graph of a solution of a d.e. a solution curve.
The slope field of a d.e. is based on the fact that the d.e. can be interpreted as a statement about the slopes of its solution curves.
The d.e. tells us that at any point (x, y) on a solution curve the slope of the curve is equal to its y-coordinate. Since the d.e. says that y is a function whose derivative is also y, we know that
y = ex
is a solution. In fact, y = Cex is a solution of the d.e. for every constant C, since y ′ = Cex = y.
The d.e. y ′ = y says that, at any point where y = 1, say (0, 1) or (1, 1) or (5, 1), the slope of the solution curve is 1; at any point where y = 3, say (0, 3), (ln 3,3), or (π, 3), the slope equals 3; and so on.
In Figure N9–1a we see some small line segments of slope 1 at several points where y = 1, and some segments of slope 3 at several points where y = 3. In Figure N9–1b we see the curve of y = ex with slope segments drawn in as follows:
Figure N9–1c is the slope field for the d.e. Slopes at many points are represented by small segments of the tangents at those points. The small segments approximate the solution curves. If we start at any point in the slope field and move so that the slope segments are always tangent to our motion, we will trace a solution curve. The slope field, as mentioned above, closely approximates the family of solutions.
The slope field for the d.e. is shown in Figure N9–2.
(a) Carefully draw the solution curve that passes through the point (1, 0.5).
(b) Find the general solution for the equation.
(a) In Figure N9–2a we started at the point (1, 0.5), then moved from segment to segment drawing the curve to which these segments were tangent. The particular solution curve shown is the member of the family of solution curves
y = ln x + C
that goes through the point (1, 0.5).
(b) Since we already know that, if then we are assured of having found the correct general solution in (a).
In Figure N9–2b we have drawn several particular solution curves of the given d.e. Note that the vertical distance between any pair of curves is constant.
Match each slope field in Figure N9–3 with the proper d.e. from the following set. Find the general solution for each d.e. The particular solution that goes through (0,0) has been sketched in.
(A) y ′ = cos x
(A) goes with Figure N9–3c. The solution curves in the family y = sin x + C are quite obvious.
(B) goes with Figure N9–3a. The general solution is the family of parabolas y = x2 + C.
For (C) the slope field is shown in Figure N9–3b. The general solution is the family of cubics y = x3 − 3x + C.
(D) goes with Figure N9–3d; the general solution is the family of lines y =
(a) Verify that relations of the form x2 + y2 = r2 are solutions of the d.e.
(b) Using the slope field in Figure N9–4 and your answer to (a), find the particular solution to the d.e. given in (a) that contains point (4, −3).
(a) By differentiating equation x2 + y2 = r2 implicitly, we get 2x + 2y from which which is the given d.e.
(b) x2 + y2 = r2 describes circles centered at the origin. For initial point (4,−3), (4)2 + (−3)2 = 25. So x2 + y2 = 25. However, this is not the particular solution.
A particular solution must be differentiable on an interval containing the initial point. This circle is not differentiable at (−5,0) and (5,0). (The d.e. shows undefined when y = 0, and the slope field shows vertical tangents along the x-axis.) Hence, the particular solution includes only the semicircle in quadrants III and IV.
Solving x2 + y2 = 25 for y yields The particular solution through point (4,−3) is with domain −5 < x < 5.
Derivatives of Implicitly Defined Functions
In Examples 2 and 3 above, each d.e. was of the form = f (x) or y ′ = f (x). We were able to find the general solution in each case very easily by finding the antiderivative
We now consider d.e.’s of the form where f (x,y) is an expression in x and y; that is, is an implicitly defined function. Example 4 illustrates such a differential equation. Here is another example.
Figure N9–5 shows the slope field for
At each point (x,y) the slope is the sum of its coordinates. Three particular solutions have been added, through the points
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CC-MAIN-2023-40
| 4,446 | 36 |
https://www.coursehero.com/file/5829795/65-pdfsam-math-54-differential-equation-solutions-odd/
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math
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This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Exercises 2.4
Differentiating F (x, y ) with respect to y gives Fy (x, y ) = x2 + g (y ) = N (x, y ) = x2 − 1. From this we see that g = −1. (As a partial check we note that g (y ) does not involve x.) Integrating gives g (y ) = (−1) dy = −y. Since the constant of integration will be incorporated into the parameter of the solution, it is not written here. Substituting this expression for g (y ) into the expression that we found for F (x, y ) yields F (x, y ) = x2 y + 3x − y. Therefore, the solution of the differential equation is x2 y + 3x − y = C ⇒ y= C − 3x . x2 − 1 The given equation could be solved by the method of grouping. To see this, express the differential equation in the form (2xy dx + x2 dy ) + (3 dx − dy ) = 0. The first term of the left-hand side we recognize as the total differential of x2 y . The second term is the total differential of (3x − y ). Thus we again find that F (x, y ) = x2 y + 3x − y and, again, the solution is x2 y + 3x − y = C . 11. Computing partial derivatives of M (x, y ) = cos x cos y + 2x and N (x, y ) = −(sin x sin y + 2y ), we obtain ∂ ∂M = (cos x cos y + 2x) = − cos x sin y , ∂y ∂y ∂N ∂ = [− (sin x sin y + 2y )] = − cos x sin y , ∂x ∂x ∂M ∂N ⇒ = , ∂y ∂x and the equation is exact. 61 ...
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https://www.zookal.com/solutions-library/in-the-exercise-below-the-inital-substitution-of-x--435727499?
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math
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In the exercise below, the inital substitution of x = a yields the form 0/0. Look for ways to simplify the function algebraically, or use a table and/or graph to determine the limit. When necessary, state that the limit does not exist. Show work.
lim x→7, x^2 + 3x - 70 / x^2 - 49
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487608856.6/warc/CC-MAIN-20210613131257-20210613161257-00186.warc.gz
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CC-MAIN-2021-25
| 282 | 2 |
https://gaiauniversity.org/members/michaelfergusons/profile/
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math
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The Myths of Solving Math Problems in 2021
Math problems tend to be a bit of a problem for a lot of people out there. For many, math is a little less than a subject that is intent upon making everyone’s life harder. The truth is that math is often misunderstood like completing ‘write my essay’ tasks. It is believed that solving math problems is not something that has to be the kind of a mammoth task that it comes to be for most of us.
Here are some of the most common myths associated with solving math problems so that you can work on the relationship that you have with the subject and be able to approach it with much less hostility in the future. Don’t run at the first sight of a problem. You can solve it if you have the right attitude towards math in general.
Myth # 1: Math Problems are Only for Math Geniuses
While it is true that there are math geeks who seem to have it so easy while the rest of us toil and sweat over a problem, it is not true that only geniuses can solve math problems. If understood properly, scholastic math can be for anyone to comprehend and get through with flying colors. The reason that people think they cannot do math generally lies in the way that it is traditionally taught. Which leads us to the second myth.
Myth # 2: Math Problems are not Relevant to Everyday Life
Somewhere along the line when you were learning algebra and matrices, the math may seem to have drifted away from the practical life that you lead. It was not math that drifted away, it was the way that you solve problems. You lost touch with it because you have been taught to just follow a bunch of instructions and solve some problems to get a good grade. You may be surprised to know that math is relevant to your everyday life if you have understood it instead of just performing a few steps in completing ‘write my paper’ tasks.
Myth # 3: Math Problems are Boring and Dull by Nature
I admit that most people get bored while solving a problem but again, that is not because of the fact that there is something inherently boring about these problems, rather the experience of dullness lies in the way these problems have been understood and conceptualized. Find a way to understand the crux and practical application of a problem and you will find that you are interested in solving it!
Myth # 4: Math Problems are Meant to be Learnt but not Understood
The technique that many students get by their tests and exams is rooted in a misconception that math cannot be understood by laypeople and that to pass exams, the bitter pill has to be swallowed somehow by making sure that methods and all steps of these methods are memorized and practiced. We need to have better techniques for practical understanding and relevance. Every problem is an interesting puzzle that is waiting to be figured out…
Myth # 5: There is One Method to Solve a Problem
Many students seem to harbor the belief that each problem has only one designated method because that is how they have learned it at school. Different chapters have different methods to teach and exercises that belong to one chapter cannot be related to other exercises belonging to different chapters. Nothing could be farther from the truth. There are many ways to solve the problem. Be daring and creative. Find the best method that suits you. Your aim is just to solve and reach the answer!
If all the problems are too problematic for you and the traditional teaching methods have left you fearing the subject itself, you can always get help from online essay writing service who can provide you access to math experts who can assist you in your assignments for a nominal fee.
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CC-MAIN-2022-49
| 3,655 | 14 |
https://puzzlepaheliyan.com/mr-smith-four-daughters-riddle-answer/
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math
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Mr. Smith daughters riddle is a very interesting and trending riddle. Here is the answer with the proper explanation to this riddle. This is one of the most confusing and tricky riddle so read very carefully and try to answer.
Riddle: Mr. Smith had four daughters a, each daughter had one brother and, how many children does Mr. Smith have?
Mr. Smith Daughters Riddle Answer
Answer: The answer to “Mr. Smith Daughters Riddle” is “Zero or Five.”
This puzzle is not entirely perfect; there is a little lack of information, due to which it is a bit difficult to find the right answer to this riddle.
There can be multiple answer to this Mr. Smith Riddle.
The first answer can be straight zero because in the last line, it is said that they “had” which is used in the past tense, so if we look in the present tense, then the answer should be zero.
The second answer may be that if Mr. Smith has four daughters and each daughter has a brother, then it is a total of 8, so in another way, it can be eight as an answer.
If you think you have a different perspective on this Riddle, Please Let me know in the comments below, For Mr. Smith has four daughters, Riddle.
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| 1,170 | 9 |
https://thestudyofthehousehold.com/qa/quick-answer-where-is-y-intercept-on-graph.html
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math
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- What is slope and y intercept on a graph?
- How do I find slope and y intercept?
- How can I identify where the Y intercept is in a function?
- What is Y 4 on a graph?
- Where is Y intercept in an equation?
- How do you find the greatest Y intercept?
- Where is Y 0 on a graph?
- How do you interpret the Y intercept?
- What is Y intercept in graph?
- How do you find the Y intercept without a graph?
- What happens if the Y intercept is 0?
- Can a function have no Y intercept?
- How do you find the slope-intercept on a graph?
- How do you find the Y intercept of a graph?
- What is Y on a graph?
What is slope and y intercept on a graph?
In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis).
This useful form of the line equation is sensibly named the “slope-intercept form”..
How do I find slope and y intercept?
Summary. The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.
How can I identify where the Y intercept is in a function?
Finding x-intercepts and y-interceptsTo determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. … To find the x-intercept, set y = 0 \displaystyle y=0 y=0.To find the y-intercept, set x = 0 \displaystyle x=0 x=0.
What is Y 4 on a graph?
Explanation: Since there is no x then the line is horizontal and has a slope of 0. Go to 4 on the y-axis and just draw a horizontal line that runs both through the negative and positive sides. Desmos. Every point has a 4 for its y coordinate.
Where is Y intercept in an equation?
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
How do you find the greatest Y intercept?
Substitute x=0 in the given function, to find the y-intercept. The y-intercept of h(x) is -2. Therefore the function f(x) has the greatest y-intercept.
Where is Y 0 on a graph?
Plot your y-intercept. The y-intercept is 0, so you place a dot at the point (0, 0). Find your next point by using the slope. The slope is 0, so this tells you that no matter how far you go to the left or right, your y value will always be 0.
How do you interpret the Y intercept?
The intercept (often labeled the constant) is the expected mean value of Y when all X=0. Start with a regression equation with one predictor, X. If X sometimes equals 0, the intercept is simply the expected mean value of Y at that value.
What is Y intercept in graph?
The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph crosses the y-axis.
How do you find the Y intercept without a graph?
To find the x-intercept of a given linear equation, plug in 0 for ‘y’ and solve for ‘x’. To find the y-intercept, plug 0 in for ‘x’ and solve for ‘y’.
What happens if the Y intercept is 0?
If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. … This slope of this line is undefined. If the line has no x-intercept, then it never intersects the x-axis, so it must be parallel to the x-axis. This means it is a horizontal line, such as .
Can a function have no Y intercept?
In fact, any time a function is undefined at 0, it will have no y-intercept.
How do you find the slope-intercept on a graph?
To write a slope-intercept equation from a graph, find the point where the graph crosses the y-axis, b, and the slope, m, and plug them into the equation y=mx+b.
How do you find the Y intercept of a graph?
It’s called the “y intercept” and it’s the y value of the point where the line intersects the y- axis. For this line, the y-intercept is “negative 1.” You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.
What is Y on a graph?
Drawing a Coordinate Graph The numbers on a coordinate grid are used to locate points. Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. … The x-coordinate is 2. The y-coordinate is 5.
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https://aps.ntut.edu.tw/course/en/Curr.jsp?format=-2&code=3603062
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||1.Properties and function tests of logic gates. 2. Implementations of and designs of basic logic circuits using ICs. 3.Algorithms for the optimization of combinational logic circuits. 4.Programmable logic devices. 5.VLSI design of combinational logic circuits. 6.Multi-layer logic circuits using MSI and standard circuit elements. 7.Gate array design. 8.Sequential Logic components. 9.Analysis and synthesis of sequential Logic circuits. 10. Technologies of VLSI design and test. 11. CAD software tools. 12.Basic logic gate experiments. 13.Combinational logic experiments. 14. Adder and subtractor experiments. 15. Combinational logic application experiments. 16. Flip-flop experiments. 17. Sequential circuit application experiments.
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https://books.google.com/books?id=TLJYT-N4LJQC&hl=en
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math
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What people are saying - Write a review
We haven't found any reviews in the usual places.
Fluid Mechanics of Green Plants Richard H Rand
Snow Avalanche Motion and Related Phenomena
18 other sections not shown
aerodynamic airfoil angle Aref autorotation avalanche axial behavior boundary layer calculations cell coefficient computations constant constitutive equations convection cross section curvature curved pipe Dean number density diffusion discussed dispersion relation dynamics effect equations Ernst Mach experimental experiments Figure finite flame Fluid Mech front velocity fully developed gravity gravity current heat transfer horizontal impact initial instability interaction interface laminar Langmuir circulations Leibovich linear liquid Mach magnetic field maximum measured mechanics melting momentum motion non-Newtonian fluids nondimensional nonlinear observed obtained occur oscillations parameter particles phase Phys plane plate point vortices predicted pressure gradient problem Proc propagation ratio region Reynolds number Reynolds stress rotation rotor scale snow solid solution speed stability steady streaks structure sunspot surface temperature tensor theory thermal thermocline tion tube turbulent flow two-dimensional two-phase flow Univ velocity viscous vortex vortices wall jet waves wind turbine
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http://portaltotheuniverse.org/blogs/posts/view/613035/
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This 0.93×1.25 km (0.57×0.78 mi) scene shows what I’m starting to think are windblown features. I posted something similar to this once before, from a location not that far from here. In this one region of Mars there are parallel lines cut into the tops of hills. A geologist would first presume they were exposed, tilted layers. But the regularity of their spacing (especially when you zoom in) is a bit unusual, and suggests some sort of self-organization (like windblown ripples). And then the questions begin: why just in this spot on Mars? what’s unusual about the rocks (or the wind) here? I still have no good answers.
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https://www.varsitytutors.com/signal_hill-ca-algebra-tutoring
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math
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Recent Tutoring Session Reviews
"We went over factoring polynomials, the difference of squares, and factoring trinomials. We then briefly touched on how to use the calculator to find the solutions as well as the vertex of a quadratic equation. Our next scheduled session is Sunday from 1:00pm - 2:30pm."
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https://www.tutordale.com/what-is-standard-temperature-in-chemistry/
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Key Concepts And Summary
The behavior of gases can be described by several laws based on experimental observations of their properties. The pressure of a given amount of gas is directly proportional to its absolute temperature, provided that the volume does not change . The volume of a given gas sample is directly proportional to its absolute temperature at constant pressure . The volume of a given amount of gas is inversely proportional to its pressure when temperature is held constant . Under the same conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules .
The equations describing these laws are special cases of the ideal gas law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal gas constant.
Bodies In Thermodynamic Equilibrium
For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature. This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic. A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien’s displacement law of thermal radiation: the temperature of a bath of thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum this frequency is always positive, but can have values that tend to zero. Thermal radiation is initially defined for a cavity in thermodynamic equilibrium. These physical facts justify a mathematical statement that hotness exists on an ordered one-dimensional manifold. This is a fundamental character of temperature and thermometers for bodies in their own thermodynamic equilibrium.
Conditions For Standard Temperature And Pressure
The standard temperature and pressure are the conditions used in thermodynamics to figure out the reference points of various gases. These are also used to specify the vapor volume. The gas volumes can be converted to the number of moles which makes it easier to find the reference points. The volume of a gas varies with temperature and pressure hence it makes it impossible to measure the molar quantity. When the gas volume is fixed to its temperature and pressure, then the standard volume is directly proportional to the molar quantity.
With the help of standard temperature and pressure, the compositions of gases can also be calculated. The value of temperature and pressure depends on the organization which defines them. The standard pressure is equal to the atmospheric pressure and the temperature is close to room temperature. NTP is a term that is referred to as normal temperature and pressure. The NTP uses 20°C as the standard temperature whereas the standard temperature and pressure use 0°C as the standard temperature. The NTP was used by the National Institute of Standards and Technology. The calculation of volume at NTP is given as
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Breathing And Boyles Law
What do you do about 20 times per minute for your whole life, without break, and often without even being aware of it? The answer, of course, is respiration, or breathing. How does it work? It turns out that the gas laws apply here. Your lungs take in gas that your body needs and get rid of waste gas . Lungs are made of spongy, stretchy tissue that expands and contracts while you breathe. When you inhale, your diaphragm and intercostal muscles contract, expanding your chest cavity and making your lung volume larger. The increase in volume leads to a decrease in pressure . This causes air to flow into the lungs . When you exhale, the process reverses: Your diaphragm and rib muscles relax, your chest cavity contracts, and your lung volume decreases, causing the pressure to increase , and air flows out of the lungs . You then breathe in and out again, and again, repeating this Boyles law cycle for the rest of your life .
Bodies In A Steady State But Not In Thermodynamic Equilibrium
While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though not in thermodynamic equilibrium. It can then well be that different empirical thermometers disagree about which is hotter, and if this is so, then at least one of the bodies does not have a well-defined absolute thermodynamic temperature. Nevertheless, anyone has given body and any one suitable empirical thermometer can still support notions of empirical, non-absolute, hotness, and temperature, for a suitable range of processes. This is a matter for study in non-equilibrium thermodynamics.
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What Is Standard Temperature And Pressure
Some textbooks define it differently than others, but the newest IUPAC standard temperature and pressure are:
Some older textbooks might say:
The difference between the two pressures are subtle but significant:
#”1 bar” = 1.00000xx10^5#
This leads to a difference of about #”0.3 L”# of an ideal gas at STP when you calculate it using the Ideal Gas Law: #~”22.7 L”# #~”22.4 L”# for the latter.
Ever had your university lab notebook “torn apart” by a lab TA for “not enough information”? Yeah, it’s primarily because science tends to rely on consistency and reproducibility to prove that something is credible.
If someone can’t read your lab notebook and then reproduce your lab experiment without your input and correction, you haven’t provided enough information to replicate that experiment precisely.
IUPAC has defined such standards so that people have consistent atmospheric conditions to use for comparisons of data from different experimental trials for the same type of experiment. That improves the accuracy to which an experiment can be reproduced.
SIDENOTE: This is not be confused with the temperature and pressure at which #DeltaH_f^@#
Overview Of Standard Temperature And Pressure
STP is an abbreviation for standard temperature and pressure. It is a set of conditions for temperature and pressure measurements for physical and chemical reactions. The standard temperature is zero º Celsius, which corresponds to 32 °F or 273.15 K. The standard pressure is 1 bar or 100.000 kPa. The molar volume of a gas is important for identifying th conditions of temperature and pressure when stating the molar volume of a gas. The molar volume of gas can be calculated by the universal gas law. The temperature and pressure are state functions. Temperature changes according to the location and season, whereas pressure depends on the weather conditions and the height above the sea level. STP is not a standard state condition. A standard state is used in thermodynamics calculations.
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Definitions Of Standard Temperature And Pressure
The term STP means different things to different people and can cause problems in the presentation of adsorption data, because the most common units for the ordinates of such plots are standard volumes per unit mass of adsorbent.
The International Union of Pure and Applied Chemistry used to define STP as 0 C and 1 atm . This definition is now obsolete. The preferred definition, since 1982, is 273.15 K and 1 bar . The National Institute of Standards and Technology, on the other hand, defines STP as 1 atm and 20 C . In practical applications of adsorption equipment, STP often refers to the pressure of the room and the temperature of the adsorption manifold, which is often kept above room temperature to prevent changes in room temperature from changing the apparent manifold or dead volumes . Room temperature, at least in the summer months in many places, is usually close to 25 C, which is a de facto standard in gas flow controllers.
For the sake of comparison, we recommend specifying the definitions of STP being used if there is any concern that they will affect the results. The difference between using a standard temperature of 0 C and 25 C will, in the authors’ experience, produce errors in the volume adsorbed that are less than the error in the measurements themselves. In commercial equipment, the volume adsorbed is usually reported by defining STP as 0 C and 760 Torr .
Alain Tressaud, in, 2019
What Are The Conditions For Stp In Chemistry
In respect to this, is STP 25 or 0?
Both STP and standard state conditions are commonly used for scientific calculations. STP stands for Standard Temperature and Pressure. It is defined to be 273 K and 1 atm pressure . Temperature is not specified, although most tables compile data at 25 degrees C .
Subsequently, question is, what does STP stand for? Standard Temperature and Pressure
In this way, what is the standard value for pressure at STP condition?
Standard Temperature and Pressure. Standard temperature is equal to 0 °C, which is 273.15 K. Standard Pressure is 1 Atm, 101.3kPa or 760 mmHg or torr. STP is the standardconditions often used for measuring gas density and volume.
What is PV nRT called?
PV = nRT: The Ideal Gas Law. Fifteen ExamplesEach unit occurs three times and the cube root yields L-atm / mol-K, the correct units for R when used in a gas law context. Consequently, we have: PV / nT = R. or, more commonly: PV = nRT. R is the gas constant.
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What Is Standard Temperature And Pressure In Chemistry
- Standard temperature and pressure, abbreviated STP, refers to nominal conditions in the atmosphere at sea level. This value is important to physicists, chemists, engineers, and pilots and navigators.
- Standard temperature is defined as zero degrees Celsius , which translates to 32 degrees Fahrenheit or 273.15 degrees kelvin . This is essentially the freezing point of pure water at sea level, in air at standard pressure.
- Standard pressure supports 760 millimeters in a mercurial barometer . This is about 29.9 inches of mercury, and represents approximately 14.7 pounds per inch . Imagine a column of air measuring one inch square, extending straight up into space beyond the atmosphere. The air in such a column would weigh about 14.7 pounds.
- The density of air at STP is approximately 1.29 kilogram per meter cubed . This fact comes as a surprise to many people a cubic meter of air weighs nearly three pounds!
- See also: SI , specific gravity.
Chemistry End Of Chapter Exercises
the appropriate graph
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Why Do We Need Satp
SATP is brought by the International Union of Pure and Applied Chemistry . It is used in Chemistry as a reference standard condition. The standard ambient temperature in SATP is 25 . This temperature is more practical and convenient compared to 0 of STP . It would be easier for chemists all over the world to take SATP conditions as a reference point compared to STP conditions.
Why Do We Need Standards
Chemists require STP definitions because the behavior of a substance varies greatly depending on the temperature and pressure. STP definitions give chemists a common reference point to describe how a gas behaves under normal conditions. Scientists use standards like STP definitions for two purposes, to define certain quantitative metrics and to allow for consistent and repeatable experiments.
Imagine someone tells you the molar volume of methane is 22.4 liters . The molar volume of a substance is just a measure of how much space one mole of that substance takes up. On its own, this value is not very informative. It is known that the volume of a gas varies greatly with respect to pressure and temperature, so gas could have multiple molar volumes, depending on the exact temperature and pressure. One needs to specify a temperature and pressure to make a molar volume measurement of 22.4 L a more meaningful quantity. Scientists agree upon a predefined temperature and pressure to report quantitative properties of gases. As it just so happens, one mole of any gas at STP has a volume of 22.4 L. Quantitative measurements of gas, like volume, volumetric flow, and compressibility, all must be defined with respect to some defined pressure and temperature.
The true method of knowledge is experiment. William Blake
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Correct Use Of The Term Stp
Even though STP is defined, you can see the precise definition depends on the committee that set the standard! Therefore, rather than citing a measurement as performed at STP or standard conditions, it’s always best to explicitly state the temperature and pressure reference conditions. This avoids confusion. In addition, it is important to state the temperature and pressure for the molar volume of a gas, rather than citing STP as the conditions. When calculated molar volume, one should state whether the calculation used the ideal gas constant R or the specific gas constant Rs. The two constants are related where Rs = R / m, where m is the molecular mass of a gas.
Although STP is most commonly applied to gases, many scientists try to perform experiments at STP to SATP to make it easier to replicate them without introducing variables. It’s good lab practice to always state the temperature and pressure or to at least record them in case they turn out to be important.
Volume And Pressure: Boyles Law
If we partially fill an airtight syringe with air, the syringe contains a specific amount of air at constant temperature, say 25 °C. If we slowly push in the plunger while keeping temperature constant, the gas in the syringe is compressed into a smaller volume and its pressure increases if we pull out the plunger, the volume increases and the pressure decreases. This example of the effect of volume on the pressure of a given amount of a confined gas is true in general. Decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure. In fact, if the volume increases by a certain factor, the pressure decreases by the same factor, and vice versa. Volume-pressure data for an air sample at room temperature are graphed in Figure 5.
Unlike the PT and VT relationships, pressure and volume are not directly proportional to each other. Instead, P and V exhibit inverse proportionality: Increasing the pressure results in a decrease of the volume of the gas. Mathematically this can be written:
The relationship between the volume and pressure of a given amount of gas at constant temperature was first published by the English natural philosopher Robert Boyle over 300 years ago. It is summarized in the statement now known as Boyles law: The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured.
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Physical Chemical Characteristics Of Fluorine
Table 1. Physicalchemical data of fluorine
On March 23, 1962, when platinum hexafluoride, a red gas, was allowed to mix with a large molar excess of xenon , the immediately formed product was a yellow solid with the composition Xe+ , the first synthesized compound of a noble gas.99
Fig. 27. Synthesis of the first compound of noble gases by N. Bartlett: Xe and PtF6 gases prior to reaction resulting XePtF6.
This discovery was acclaimed101 as one of the ten most beautiful experiments in chemistry, because102 it opened the way for the noble gas chemistry and high oxidation species chemistry, as illustrated by the various species isolated in Neil’s Berkeley Group: first example of Os + VII: OsOF5 NOWF7, 2WF8, NOReF7 Isolation of ONF3: 2NiF6 ONF + ONF3 + NiF2 synthesis and oxidizing properties of ReOF5 and OsOF5 salts of quinquevalent gold: M+ AuF6, NO+ AuF6, Xe2F11+ AuF6, XeF5+ AuF6, etc. Quoting P. Ball, we can say that Neil Bartlett’s experiment tells us that in chemistry, the wonders never cease.103
Now, fluorine gas is produced following the electrochemical process, as shown, for instance at Fig. 28 for the F2 synthesis facilities of Advance Research Chemicals, Inc. . An important technical point is that hooded areas should be specially equipped for fluoride manufacturing. All work should be done in hoods, 40,000 cfm fresh air being pulled in to avoid depression in the building.
Fig. 28. Fluorination facilities at ARC, Inc.
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http://asturisk.net/carlitos-laundry-day-is-on-toweltuesday/
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math
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Hottest 90’s TV Stars Nude!
Michael Stokes makes erotic art with hunky Bel Ami boy Niko Vangelis
Australian model Lochie Carey out in the wild with Jake O'Donnell
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https://www.projecteuclid.org/euclid.aoap/1211819796
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The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 3 (2008), 1138-1163.
Lp-variations for multifractal fractional random walks
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures M[0, t], 0≤t≤1. In this paper we obtain an extension of this process, referred to as multifractal fractional random walk (MFRW), by considering the limit in distribution of a sequence of conditionally Gaussian processes. These conditional processes are defined as integrals with respect to fractional Brownian motion and convergence is seen to hold under certain conditions relating the self-similarity (Hurst) exponent of the fBm to the parameters defining the multifractal random measure M. As a result, a larger class of models is obtained, whose fine scale (scaling) structure is then analyzed in terms of the empirical structure functions. Implications for the analysis and inference of multifractal exponents from data, namely, confidence intervals, are also provided.
Ann. Appl. Probab., Volume 18, Number 3 (2008), 1138-1163.
First available in Project Euclid: 26 May 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems 60G57: Random measures 60K40: Other physical applications of random processes 62F10: Point estimation
Secondary: 60G15: Gaussian processes 60G18: Self-similar processes 60E07: Infinitely divisible distributions; stable distributions
Ludeña, Carenne. L p -variations for multifractal fractional random walks. Ann. Appl. Probab. 18 (2008), no. 3, 1138--1163. doi:10.1214/07-AAP483. https://projecteuclid.org/euclid.aoap/1211819796
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http://neguentropics.blogspot.com/2013/12/self-choice.html
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math
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Let's consider the two circles above: The one in the left contains eight bars, four stars and an small circle, randomly distributed. The one in the right contains the same objects in a geometric simetry. Please watch freely the two images until you feel that you really know everything about them.
............ ........... ....... .... .......... .........
Now that these two images are familiar to you, please answer these 3 questions (there is no right or wrong answers):
1) Which image represents me best?
2) What image I like the most?
3) What image is me?
There is two possible answer combinations:
1) You answered equally the same questions. In this case, if you answered three times "left figure", your self is centered more in biological aspects and emotions; Right-brain activities are most important. Intelligence is an instrument that I use.
If you chose three times the "right figure", you are more prone to left-brain activities, logical thinking is above any other consideration. I am my intelligence.
2) You answered 2-1, either two left and one right, or viceversa. In both cases you are close to a healthy balance between both brain hemispheres. You are prone to reconcile means and objectives, and therefore you have more probabilities to reach success in what you do.
If you like this blog, please share it with your friends.
Send them this link: http://neguentropics.blogspot.com.es
Your comments are important feedback - Please feel free to post them
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https://www.waterstones.com/book/principles-of-harmonic-analysis/anton-deitmar/siegfried-echterhoff/9780387854687
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math
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The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL®. In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL®, the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, , or indep- dently, if the students have required a modest knowledge of Fourier Analysis already. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in .
Publisher: Springer-Verlag New York Inc.
Number of pages: 333
Weight: 539 g
Dimensions: 235 x 155 x 18 mm
Edition: 2009 ed.
From the reviews:
"Principles of Harmonic Analysis is an excellent and thorough introduction to both commutative and non-commutative harmonic analysis. It is suitable for any graduates student with the appropriate background ... . In summary, this is a superb book. ... it is extremely readable and well organized. Graduate students, and other newcomers to the field, will greatly appreciate the author's clear and careful writing." (Kenneth A. Ross, MAA Online, February, 2009)
"The book under review is a nice presentation of all the standard, basic material on abstract harmonic analysis. ... The most welcome aspect of the book under review is the inclusion of a discussion of the trace formula, a rather unusual feature in an introductory book on harmonic analysis. ... This is a nice addition to the literature on the subject." (Krishnan Parthasarathy, Mathematical Reviews, Issue 2010 g)
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https://www.thecollegemonk.com/colleges/iowa-state-university/tuition
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math
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The average net price, as defined by the federal government, is the average amount students require to pay to attend a university after subtracting aid. Iowa state university determines the net price of family income on family income range or income group. The net price can change, depending on the amount and scale at which a student's total family income falls. Depending on the financial aid available, the net price may vary, and the financial assistance provided may either be less or more than the overall average costs incurred during the program. However, Iowa state university's average net price is $14,643.
Annual family income ranging from $0 to $30,000 has a net price of $9,801, which is significantly less than the median average price, which is $13,908 and considerably lower than the net price of $14,643. The students and family whose annual family income range is $30,001 to $48,000 has an average of $10,419. Whereas, the net price for the annual income range of $48,001 to $75,000, which is the median annual income range, is $13,908, which is slightly lower than the average net price per program. The student whose annual income range is $75,001 to $110,000, the average is $16,898, and the family whose annual income is $110,000, and above the average is $18,468.
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https://www.hackmath.net/en/math-problem/4967
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math
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Six trucks will be used to build the roadside 18 days. After 3 days, two more trucks were sent to build. How long will it take for material move?
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Related math problems and questions:
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Ten identical trucks will take 240 tons of concrete to build the dam in 3 working days. How many tons of concrete will seven trucks take to make the dam in 5 days?
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Three roofers put the roofing on the roof in 8 days. How long will it take to get two more after three days?
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The company sent four painters to paint the school. They should be done in 12 days. After three days, one painter got ill. How long will the remaining painters paint the school?
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- Technicians 8382
The order lasted six technicians for 18 days. How long will it take for 1, 2, 3, 4, 5, 6, 8, 10, and 20 technicians to complete?
Seven bricklayers will build the house in 630 days. How many bricklayers do we need to take after 150 days to complete the building for (additional) 336 days?
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Sixteen employees will distribute leaflets in 12 days. How long will it take if, after four breaths, six workers go to work elsewhere?
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Our house would paint four painters in 14 days. How long could it paint five painters? How long will it take if two other painters come to help after five days?
The first bricklayer would build a wall in 3 days, the second in 4 days. The first bricklayer worked alone for a day, then the second bricklayer came to his aid, and they finished the work together. How long did it take to build the wall?
Ten workers must pave road street for 22 working days. After four days were for speeding up work, added two more workers. a) After how many work days now workers complete the paved road? b) How many working days does it take for a total paved road?
- Wall builders
If 12 men can build a wall 398 metres long in 48 days, how long would it take 33 men to build a wall 347 metres long? Answer to 3 decimal places.
- Two masons
Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himself?
6 tractors started plowing the field that they together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
If I read 15 pages a day, I will read the whole book in 18 days. How long will it take to read a book if I only read 9 pages every day?
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The supply of material for 83 masons of the company is enough for 12 days. How many days will this supply be enough for them if the company has accepted six more masons?
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CC-MAIN-2022-33
| 3,628 | 34 |
https://www.geogebra.org/m/AKufPhse
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math
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Exploring the Geometric Mean with Similar Triangles
- Josh Traxler
Geometric Mean Discovery Applet In this applet we explore the geometric mean as it relates to similar triangles, and the relationships between the sides in our construction.
How many triangles are on screen? Notice what happens when you move points D and A. What stays the same? How do the triangles change? (Hint: Consider similar triangles and side ratios) Can you find multiple triangles sets where C is a vertice? From the rest of the questions, assume the constructions has C aligned to be a vertice of a triangle. Come up with some sets of side length ratios that are equal to one another. How many ways can you come up with to write the length of PB by using these ratios? (Without using the actual length measurement) Were any of these geometric means? (Note: A geometric mean is the square root of a product of two or more numbers) Were there any that didn’t seem like geometric means? Can you describe the square of PA’s length using other side lengths? Challenge: Can you describe PA’s length in terms of just PC and PD? What does this length represent? (Hint: You may need to use two geometric means.) How would you make sure PD is the same length as PC? Double the length? Eight times the length of PC? If PC is length 1 and PD is length 8, what is the length of PB? What is the length of PA? (Hint: Consider your ratios, which sets of ratios or fractions do you think you should use?) What if PD is length 2, and PC is length 1, then what is the length of PB? What if PD is any constant multiple of PC? What do we think that this construction could be used for? What is significant about the length of PB in relation to lengths PD and PA? How could this be useful for doubling the volume of an object?
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| 1,788 | 4 |
https://socratic.org/questions/angles-2-x-15-and-3x-20-are-a-pair-of-interior-angles-what-are-their-values
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math
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Angles #(2(x+15))# and #(3x+20)# are a pair of interior angles. What are their values?
If you mean they are co-interior the angles are 82 and 98 degrees respectively.
If you mean they are alternate interior angles the angles are both 50 degrees.
I assume you mean the (co)interior angles made by a transversal on either side of a pair of parallel lines. In that case,
This is because the sum of co-interior angles adds up to 180 degrees(they are supplementary).
Else if you mean alternate interior angles then
Thus both angles are 50 degrees.
Impact of this question
Creative Commons License
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| 591 | 9 |
http://forums.appleinsider.com/forums/posts/by_user/id/72933/page/20/page_size/20
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math
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- Forum: iPhone
Again, what is "proof". Was Steve Jobs saying there would be a 3ghz g5 Mac sufficient "proof" or simply conjecture?I will boldly assert that based on nothing more than history that the sun will rise tomorrow. What link would satisfy you that this is a statement of fact and not mere belief? After all, eventually I will be wrong.
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CC-MAIN-2014-15
| 345 | 2 |
https://studydaddy.com/question/really-struggling-with-this-one
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math
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Answered You can hire a professional tutor to get the answer.
Really struggling with this one.
Really struggling with this one. Any help would be greatly appreciated. Thx!
The inspection division of the Lee County Weights and Measures Department is interested in estimating the actual amount of soft drink that is placed in 2-liter bottles at the local bottling plant of a large nationally known soft-drink company. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is 0.05 liter. A random sample of one hundred 2-liter bottles obtained from this bottling plant indicates a sample average of 1.99 liters. Set up a 95% confidence interval estimate of the true average amount of soft drink in each bottle.
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CC-MAIN-2020-24
| 757 | 4 |
https://gbschemphys.com/physics/often-asked-what-is-mev-in-physics.html
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math
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A MeV is the Mega electron-volt, e.g. million times more than eV. One eV is defined as the energy, that an electron ( or an other single-charged(q=1.6*10^-19 Coulombs) particle) gains when it undergoes a potential difference of 1 Volt.
How do you convert to MeV?
It is useful to note that 1 u of mass converted to energy produces 931.5 MeV, or 1 u = 931.5 MeV/c2. All properties of a nucleus are determined by the number of protons and neutrons it has.
What is an eV unit in physics?
George Lebo, University of Florida: “An electron volt (eV) is the energy that an electron gains when it travels through a potential of one volt. You can imagine that the electron starts at the negative plate of a parallel plate capacitor and accelerates to the positive plate, which is at one volt higher potential.
What is MeV full form?
measurement of radiation …a larger unit such as megaelectron volt (MeV), which is equal to one million electron volts.
Why do we use MeV?
In high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.
What is the difference between MV and MeV?
The energy of diagnostic and therapeutic X-rays is expressed in kV or MV. Whereas, the energy of therapeutic electrons is expressed in terms of MeV. In first case, this voltage is the maximum electric potential used by a linac to produce the photon beam. Thus, 1 MV beam will produce photons of no more than about 1 MV.
How many MeV are in amu?
Since 1 amu is equivalent to 931.5 MeV of energy, the BE can be calculated using Equation 8.6.
What is the unit MeV c2?
Well, MeV/c^2 is a unit of mass, and MeV is a unit of energy. The rest energy of a particle can be computed in units of MeV by multiplying it’s rest mass in units of MeV/c^2 by c^2.
Is J an SI unit?
The SI unit for work and energy commonly used in drawing is the joule (J), which is equivalent to a force of one newton exerted through a distance of one meter (m).
What is an eV equal to?
Electron volt, unit of energy commonly used in atomic and nuclear physics, equal to the energy gained by an electron (a charged particle carrying unit electronic charge) when the electrical potential at the electron increases by one volt. The electron volt equals 1.602 × 10−12 erg, or 1.602 × 10−19 joule.
Which unit is volt?
Volt, unit of electrical potential, potential difference and electromotive force in the metre–kilogram–second system (SI); it is equal to the difference in potential between two points in a conductor carrying one ampere current when the power dissipated between the points is one watt.
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| 2,802 | 21 |
http://big-skidki.ru/bill-o-th-hoylus-end-random-rhymes-and-rambles/
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math
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Amazon.com: Random Rhymes and Rambles eBook: Bill o'th' Hoylus End: Kindle Store. From The Community. Amazon Try Prime Kindle Store. Go Search EN.
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal.
Весёлые стихи про котят на русском и английском языках – для развлечения и изучения английского языка / Amusing rhymes about kittens in the Russian and English.
William Sydney Porter known by his pen name O. Henry, was an American short story writer. His wit and plot twists were adored by his readers, but often panned by the critics. Collected Short Stories includes amazing stories like "The Rose of Dixie", "The Third Ingredient", "The Hiding of Black Bill", "Schools and Schools" and many.
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| 2,866 | 4 |
https://phpconnect.me/calculus-9e-purcell-varberg-rigdon-solution-26/
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math
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calculus 9e purcell varberg rigdon solution. Fri, 14 Sep GMT calculus 9e purcell varberg rigdon pdf -. Varberg, Purcell, and. Rigdon: Calculus 9e. Thu, 13 Dec GMT calculus 9th edition varberg purcell pdf -. Calculus. 9e. Purcell-Varberg-Rigdon. (Solution).pdf – Google Main menu Sat, Calculus 9e Purcell-Varberg-Rigdon (Solution). Views. 3 years ago. No tags were found READ. Calculus 9e Purcell-Varberg-Rigdon.
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It makes more sense for my coursework to do one of those rather than a multivariable calculus book. The objectives of Calculus II are for the students to understand the following topics and to be able to apply these concepts to solve application problems.
Mit calculus 2
As you can watch in the video above, this week was calculus. Calculus covers all topics from a typical high school or first-year college calculus course, including: Problems on the limit of a function as x approaches a fixed constant ; limit of a function as x approaches plus or minus infinity My math teacher teaches all levels of math from to calculus and he teaches me now so im ready because i asked him for help but its still hard to understand calculus and what the equation equals to.
Get an introduction to the essential mathematical knowledge and skills required to take a first course in calculus.
Another private goal in this area is the study of ambimorphic symmetries. With the ability to answer questions from single and multivariable calculus, Wolfram Alpha is a great tool for computing limits, derivatives and integrals and their applications, including tangent lines, extrema, arc length and much more. With more than 2. The Calculus I varbery of many of the problems tends to be skipped and left to the student to verify or fill in the details. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition.
Calculus II will cover sections 5, 6, 7, and 8 of the textbook, starting with section 5. This calculus course covers differentiation and integration calculhs functions of one variable, and concludes with a brief discussion of infinite series.
Calculus help number 8 in for colleges The early help calculus tradition of wisdom on a slippery slope if looking to reshape everyday behaviors associated with the process which moves it can get started. I may keep working on this document as the course goes on, so these notes will not be completely Section 9. Calculus Exams From Previous Semesters. Krista King is an Calcylus Calculus 1 Lecture Videos These lecture videos are organized in an order that varbegg with the current book we are using for our Math, Calculus 1, courses Calculus, with Differential Varnerg, by Varberg, Purcell and Rigdon, 9th edition published slution Pearson.
Guichard Calculus help number 8 in for colleges The early help calculus tradition of wisdom on a slippery slope if looking to reshape everyday behaviors associated with the process which moves it can get started. The surprise is that something seemingly so abstract ends up explaining the real world.
Business math lecture
However when it comes to Calc II, you might look at a problem and find a much easier solution. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer rigron. Problems on the limit of a function as x approaches a fixed constant ; limit of a function as x approaches plus or minus infinity Single and Multivariable Calculus Lecture Notes by D. Unlike the Calculus AB examit also covers parametric, polar, and vector functions.
Exam 1 without solutions. Math Calculus 3 Lecture Videos These lecture videos are organized in an order that corresponds with the current book we are using for our Math, Calculus 3, courses Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson. The pdf files for this current semester are posted at the UW calculus student page.
Learn calculus the easy way – Purchase a DVD set of easy to follow instructions – You control the speed of learning. Video Tutorials are downloadable to watch Offline Precalculus review and Calculus preview – Shows Precalculus math in the exact way you’ll use it for Calculus – Also gives a preview to many Calculus concepts.
It is the second ridon in the freshman calculus sequence. This class counts for a total of 12 credits. Calculus from Latin calculus, literally ‘small pebble’, used for counting and calculations, as on an abacus is rigdom mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
Marriage of Differential and Integral Calculus. The first reason is that this course does require pucrell you have a very good working knowledge of Calculus I. Calculus with Analytic Geometry by – Dartmouth College Precalculus review and Calculus preview – Shows Precalculus math in the exact way you’ll use it for Calculus – Also gives a preview to many Calculus concepts.
Save on the cost of your degree. But, I passed it taking it as a summer course, which means we covered just as much material, but in a much shorter period of time – vraberg summer semester. The MIT course was designed for MIT students who have mostly already learned calculus on some level, so the lectures aren’t necessarily easy to follow if you’re just starting out.
The mission of MIT is solutkon advance knowledge and educate students in science, technology, and other areaThe gradient is a fancy word for derivative, or the rate of change of a function.
Varbeerg note that doing the lessons listed below will ccalculus count towards your grade. You may find it helpful to consult other texts or information on the internet for additional information. Show your work and justify your answer. The videos listed here are an example of some of the useful videos on KhanAcademy. There are lots of exercises and examples.
Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. It’s calculus done the old-fashioned way calculue one problem at a time, one easy-to-follow step at a time, with problems ranging in difficulty from easy to challenging.
Concepts and Contexts, 4th ed. Once there you can also search for “calculus” and you’ll find other universities that have followed in MIT’s footsteps and put their recorded lectures online.
Discover the integral – what it is and how to compute it. We are always trying to outdo ourselves by seeking innovation, using the latest technology, and having highly trained and qualified people for every service. Calculus is the branch of mathematics studying the rate of change of quantities and the length, area and volume of objects.
The videos, which digdon real-life examples to illustrate the concepts, are ideal for high school students, calclus students, and anyone interested in learning the basics of calculus.
Shadow of helix on coordinate planes, curves as intersection of two surfaces, curves embedded on a surface, introduction to computer aided graphing via Mathematica 6. Calculus I, or equivalent. The sample tests are just to give you an idea of the a general idea of the topics covered, the level of difficulty, how questions may be worded and, if solutions are provided, what is the acceptable level of detail required in the solutions.
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https://www.geeksforgeeks.org/construct-a-square-matrix-whose-parity-of-diagonal-sum-is-same-as-size-of-matrix/amp/?ref=rp
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math
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Given an integer N representing the size of the matrix, the task is to construct a square matrix N * N which have an element from 1 to N2 such that the parity of the sum of its diagonals is equal to the parity of integer N.
Input: N = 4
1 2 3 4
8 7 6 5
9 10 11 12
16 15 14 13
Sum of diagonal = 32 and 36 and integer N = 4, all the numbers are even that is same parity.
Input: N = 3
1 2 3
6 5 4
7 8 9
Sum of diagonal = 15 and integer N = 3, all the numbers are odd that is same parity.
Approach: The idea is to observe that on filling the elements in the matrix in an alternative fashion the parity of N and the sum of diagonals is the same. Start the counter from 1 and then fill the first row from 0 to N – 1 in increasing order, then fill the second row from index N – 1 to 0, and so on. Keep filling each element from value 1 to N2 in this alternate fashion to get the required matrix.
Below is the implementation of the above approach:
1 2 3 6 5 4 7 8 9
Time Complexity: O(N*N)
Auxiliary Space: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Construct an Array of size N whose sum of cube of all elements is a perfect square
- Construct a matrix with sum equal to the sum of diagonal elements
- Filling diagonal to make the sum of every row, column and diagonal equal of 3x3 matrix
- Maximum sum of elements in a diagonal parallel to the main diagonal of a given Matrix
- Program to swap upper diagonal elements with lower diagonal elements of matrix.
- Count numbers which can be represented as sum of same parity primes
- Sum of non-diagonal parts of a square Matrix
- Generate a matrix having sum of secondary diagonal equal to a perfect square
- Length of a Diagonal of a Parallelogram using the length of Sides and the other Diagonal
- Smallest N digit number whose sum of square of digits is a Perfect Square
- Check if all the elements can be made of same parity by inverting adjacent elements
- Count of all possible pairs of array elements with same parity
- Print all the sub diagonal elements of the given square matrix
- Print all the super diagonal elements of the given square matrix
- Minimum flips in a Binary array such that XOR of consecutive subarrays of size K have different parity
- Find a subarray of size K whose sum is a perfect square
- Check if two elements of a matrix are on the same diagonal or not
- Maximum size of square such that all submatrices of that size have sum less than K
- Construct an Array of size N in which sum of odd elements is equal to sum of even elements
- Construct an Array such that cube sum of all element is a perfect square
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
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| 3,077 | 40 |
https://www.gizmosforgeeks.com/wolfram-alpha-promises-computing-that-answers-questions
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math
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Computer scientist, Stephen Wolfram, feels that he has put together at least the initial version of a computer that actually answers factual questions, a la Star Trek’s ship computers. His version will be found on their Web-based application, Wolfram Alpha.
What does this mean? Well instead of returning links to pages that may (or may not) contain the answer to your questions, Wolfram will respond with the actual answer. Now the caveat ‘factual’ is important. You can ask it questions like ‘why is the sky blue?’ or ‘how many bones are in the human body?’, but probably not ‘do you think abortion is wrong?’. This computational knowledge engine uses natural language to parse the questions and can also accept coded queries.
For the subject areas that Wolfram covers, they not only had to either enter or import data on those subjects, but had to build models or create algorithms for breaking down and describing that data in simpler building blocks. Long story short, my question is how easy is it going to be expand into additional subject areas?
Don’t bother trying to visit the site just yet – it’s not launching until May 2009. If this works well, this is going to revolutionize computing and in particular, the search engine market. Google of course comes to mind. Would they see this as a threat? I imagine they should. so I think what will be important here is how quickly Wolfram can expand into additional subject areas. If they give Google enough time to get into this market, then they could be sunk.
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http://scitation.aip.org/content/aip/journal/apl/96/20/10.1063/1.3430741
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math
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Full text loading...
Conduction band diagram for the 3.2 THz QCL with (a) 0% diagonality and (b) 70% diagonality. Upper and lower laser levels are marked by bold solid lines.
Dependence of the peak gain on the active region lattice temperature for different operating frequencies and diagonalities. The shown results are for optimum bias, which only weakly depends on temperature and has for each structure been determined at 150 K as to yield maximum gain.
and for different degrees of diagonality for the (a) 2.3 THz QCL and (b) the 4.1 THz QCL at lattice temperatures of 150 K and 200 K, respectively. The bias is chosen as to maximize the peak gain.
Temperature dependence for (a) 30% diagonality and (b) 50% diagonality of the relative inversion and relative inverse linewidth . The peak gain improvement is .
Overview of the designed THz QCLs. All layer thicknesses are given in angstrom and bold numbers indicate barriers. The underlined wells are doped with a sheet density of in their 55 Å wide middle region.
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http://voquev.cf/blog4157-80-km-h-into-mph.html
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math
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Quickly convert miles/hour into kilometers/hour (MPH to km/h) using the online calculator for metric conversions and more.The answer is 0.62137119223733. We assume you are converting between mile /hour and kilometre/hour. 130 km/h 80 mph. Speed limit on motorways (highways) in most countries of Europe.mph vs. kph (km/h) Example If your speed or velocity is given in miles per hour (mph) and you want to translate it into kilometers per hour (km/h) type your mph value into edit box labeled miles per hour. Conversion Mile per hour to Kilometer per hour (mph to kph). Miles per hour 50 mph 80.467 kph, 80 mph 128.747 kph, 110 mphThis selection will show you how to convert various numbers from the U.S. system of measurement to the miles per hour (mph) into kilometers/hour (km/hr). After that, check the tire pressure and pump more air into the tire if necessary (see Step 2). Then you can proceed to drive with caution for a maximum distance of 200 km (120 miles) and at a maximum speed of 80 km/h (50 mph). Kilometer per hour (km/h) Kilometer per minute (km/min) Mile per hour (mi/ h) Mile per minute (mi/min) Nautical mile per hourWest leaves the crime scene on a motor cycle that goes 80 MPH heading east.XY10, without going into decimals that would leave you with 6 possible answers. The symbol for kilometers per hour is km/h and the International spelling for this unit is kilometres per hour. There are 1.609344 km/h in mph.50 mph. 80.4672 km/h.
Air causes a significant resistance at speeds above 80 km/h (50 mph) and is negligible under 30 km/h (20 mph).Exit speed from mound (km/h (mph)) Entry speed into mound (km/h (mph)) Factor given in Table 17.4. Transform 80 kilometers per hour into miles per hour and calculate how many miles per hour is 80 kilometers per hour.Instantly Convert Miles Per Hour (mph) to Kilometres Per Hour (km/h) and Many More Speed Or Velocity Conversions Online. 80 km/h 49.71 mph.
Comment from/about : speedy move | Permalink.my average walking speed : 60 meters per minute ( m/min ), converts into : 3.6 kilometers per hour ( km/h ) 3600 meters per hour exactly. 305 km/h / 190 mph GPS-speed G-Power BMW M3 SKII on German Autobahn.80mph?What happens if you let your camera go fast, faster or what happens with 190 mph - 300km/h on the Autobahn with a Corvette C6 ? The chart can be divided into four areas, corresponding to four velocity ranges80 120 km/h (49.71 - 74.56 mph): Within this range as the average speed increases the fuel consumption augments too. 80 KMH is equal to how many MPHHow to recalculate 80 Km per hour to Miles per hour?It would be pertinent to mention here that miles per house perhaps came into existence and Convert between the units (mph km/h) or see the conversion table.50 Miles per hour 80.4672 Kilometres per hour. For my friends from the United States to see the speed on the German Autobahn ) . 200 Km H Into Mph. This is a measurement of speed typically used in countries using the metric system for transport. Road speed limits are given in kilometers per hour which is abbreviated as kph or km/h. A US passenger train that derailed, killing three people, was travelling at 80mph (130km/h) on a curve with a speed limit of 30mph, data from the trains rear engine indicates. It happened in Washington state during rush hour on Monday and officials say 72 people were taken to hospital. Convert 80 Miles/Hour to Kilometers/Hour (mph to km/h) with our conversion calculator and conversion tables.80 mph 128.72570194384 km/h. You also can convert 80 Miles/Hour to other Speed (popular) units. To convert between Mile/hour (mph) and Kilometer/hour (kmh) you have to do the following50 mile/hour (mph) in kilometer/hour (kmh) 80.4672 mph. A Swedish man has been pronounced dead after he and a friend rode a shopping trolley into oncoming traffic in a suburb of Sydney. Police have reported that the trolley reached estimated speeds of up to 50 mph (80km/h) as it was ridden down a steep hill, before colliding with a car at around They are indicated in kilometers per hour. Highway : 130 km/h, if raining 110 km/h (80 mph, 70 mph) Dual cariageway : 110 km/h, ifa town, the reduction of the speed limit from 90 km/h to 50 km/h may not always be indicated by such a road sign, but just by the road sign indicating entry into town. Speed conversions between miles per hour (mph, miph, m/h, mi/h) and kilometres per hour (kph, kmph, km/h) are usually used for calculating speed limits when driving abroad, espcially for UK and US drivers.80.47. mph. kph. Virgo: elongated, pearly tail, shimmering in multiple colours, fanning out into a slightly translucent, silky fluke. Moves through the water slowly and gracefully.The fastest hunter reaching speeds up to 80 km/h or 50 mph.
Quickly convert miles into kilometres (70 miles to km) .In North American slang and military usage, km/h . Full mph to kph conversion tables for speeds of .Conversion table for knots to miles per hour Conversion table for . 70: Knots 80.6: MPH: 75: Knots 86.4: MPH: 80: Knots 92.2 In the postwar years, a thicker asphaltic concrete cross-section with full paved hard shoulders came into general use. The top design speed was approximately 80 km/h (50 mph) in flat country but lower design speeds could be used in hilly or mountainous terrain. Quickly convert miles into kilometres (80 miles to km) using the online calculator for metric conversions and more.What is 80 km/h in mph? How fast is 80 kilometers per hour? Instantly Convert Miles Per Hour (mph) to Kilometres Per Hour (km/h) and Many More Speed Or Velocity Conversions Online.1 Kilometer per hour (kph, km/h) 0.277 777 778 meters per second (SI base unit). Source unit: kilometers per hour (kph, km/h, kmh-1).miles per hour (mph). mile per hour. 130 kilometers per hour is 80.78 miles per hour. Quickly convert kph into mph (kph to mph) using the online calculator for metric conversions and more.80. 934 mph. 129 kph, 80. 621 mi 1 km. Both miles per hour and knots is a speed which is the number of units of distance that is covered Full mph to kph conversion tables for speeds and Roof Racks Cargo Carriers. 80 km/h 50 Mph 40 km/h 25 Mph. 80 kilometer/hour 49.709 695 379 mile/hour (mph).Careers. Answers.com WikiAnswers Categories Science Earth Sciences Natural Disasters Hurricanes Typhoons and Cyclones 80km into mph? A US passenger train that derailed, killing three people, was travelling at 80mph (130km/h) on a curve with a speed limit of 30mph, data from the trains rear engine indicates. Most comments indicate that 80-100km/h would not be unreasonable, however some pickups have had documented challenges in passing the international 70 mph (113km/h) "Moose Test". Some truck owners have also voiced concerns that they are unable to get into their top cruising gear for Das Fahrzeug sollte nicht weiter als 80 km und niemals schneller als mit 55 km/h abgeschleppt werden. It is best to tow the vehicle no farther than 80 km (50 miles), and keep the speed below 55 km/h (35 mph). This on the web one-way conversion tool converts speed and velocity units from mach ( ma ) into kilometers per hour ( km/h ) instantly online. Convert 82 Kilometers/Hour to Miles/Hour | Convert 82 km/h to mph with our conversion calculator and conversion table Boeing MD- 80 Pilot Operation Sign up, tune into the things you care about, and get updates as they happen.Find a topic youre passionate about, and jump right in. Learn the latest. Get instant insight into what people are talking about now. Miles per hour is the unit used for speed limits on roads in the United Kingdom, United States and various other nations, where it is commonlyThe Online Conversion Calculator - Converter converts Miles per hour to km per hour (mph to km/h) and kmh to mi/h (kilometers/hour to mph. Upon this the number you have entered will be converted into miles per hour, and displayed beneath the textbox. To convert mph into km/h click here. The calculated flying distance from Bratislava to Vienna is equal to 34 miles which is equal to 55 km. If you want to go by car, the driving distance between Bratislava and Vienna is 79.68 km.50 mph (80 km/h). 00 hours 59 minutes. convert 25 mph into km/h. Am I Dumping it Right? 09 Feb 2017 15:58.Things are gonna get a little sketch this weekend. As we move into the final month of summer Road speed limits are given in kilometers per hour which is abbreviated as kph or km/h.21mph. 33.80kph. Speed limits in the United States are set by each state or territory. Highway speed limits can range from an urban low of 35 mph (56 km/h) to a rural high of 85 mph (137 km/h). Speed limits are typically posted in increments of five miles per hour (8 km/h). Quickly convert miles into kilometres (80 miles to km) using the online calculator for metric conversions and more.miles/hour to kilometers per hour) and km/h to mph (kilometers/hour to miles/hour) Online Conversion Calculator - Converter. It has a range of about 80 km at 30 km/h (50 miles at 19 mph) or 25 km at 60 km/h (15.5 miles at 37 mph). Data such as current, voltage, speed, and GPS coordinates can be displayed on a linked Android smartphone, with basic functions being controlled using a 5-button control panel. This is some tractor trailer security camera footage from Swedish shipping company PostNord of a group of robbers breaking into the back of truck while traveling down the highway at 80km/h (50MPH) to take a peek at the goods inside and decide if theyre worth stealing (previously: a It is very simple multiply MPH by 1.6 you will get KM/H MPH x 1.6 KM/H. Image: Message: . A US passenger train that derailed, killing three people, was travelling at 80mph (130km/h) on a curve with a speed limit of 30mph, data from theWant to dive into a new industry? Go to a hackathon. A Couple Crazy Things Thatve Happened Recently. Definition: Mile/hour Miles per hour (symbol: MPH) is a measurement of speed in the imperial and United States customary unit.80.4672 km/h. The average human walking speed is estimated to be close to 5 kilometers per hour, and the average speed of road cyclist in the city may vary between 10 and 15 km/h.80 kph. 49.7097 mph. Supose you want to convert 80 kilometers per hour into miles per hour. In this case just write the equation, then do the mathhow much are 80 km/h in miles per hour?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863972.16/warc/CC-MAIN-20180521082806-20180521102806-00631.warc.gz
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CC-MAIN-2018-22
| 10,345 | 4 |
http://www.solutioninn.com/why-is-a-call-option-on-an-interest-rate-called
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math
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Question: Why is a call option on an interest rate called
Why is a call option on an interest rate called an interest rate cap and a put option called an interest rate floor?
Relevant QuestionsWhat is meant by an “agency cost” or “agency problem”? Do these interfere with maximizing shareholder wealth? Why or why not? What mechanisms minimize these costs/problems? Are executive compensation contracts ...What is operating cash flow (OCF)? How is it calculated? What is free cash flow (FCF)? How is it calculated from operating cash flow (OCF)? Why do financial managers focus attention on the value of FCF? Explain how a fixed-for-floating swap can be considered a portfolio of forward contracts on 6-month discount bonds. The current price of gold is $288 per troy ounce. The cost of storing gold is $0.03/oz per month. Assuming an annual risk-free rate of interest of 12% compounded monthly, what is the approximate futures price of gold for ...Chipman Products Company will suffer an increase in borrowing costs if the 13-week Treasury bill rate increases in the next six months. Chipman Products is willing to accept the risk of small changes in the 13-week T-bill ...
Post your question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689615.28/warc/CC-MAIN-20170923085617-20170923105617-00168.warc.gz
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CC-MAIN-2017-39
| 1,201 | 4 |
https://math.answers.com/Q/Why_is_the_sum_of_a_rational_number_and_it%27s_opposite_always_equal_to_0
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math
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Because the opposite of 8 for example is -8 and 8+(-8) = 0
Because that is how the opposite is defined!
When the number is 0.
the number 0 is always equal to its opposite
When the number is non-positive.
No. If the rational number is not zero, then such a product is irrational.
Yes, it will always be irrational.
The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.
Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Think of a numberline, Travle 5 sides to the negative side, and than 5 steps back , this is negative 5 and positive 5. This appplies for all rational numbers
Only if the rational number is 0.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224648911.0/warc/CC-MAIN-20230603000901-20230603030901-00268.warc.gz
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CC-MAIN-2023-23
| 861 | 12 |
https://earthschooling.info/thebearthinstitute/what-is-x-why-is-y-math-texts-in-7th-and-8th-grade/
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math
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TRIAL BY TEXTBOOK
So we’ve had our three maths main lessons in Class 8, and used a wide range of numeracy skills in many other units throughout the year – is this enough? Alas no – mathematics is a subject, especially in this techno-mad age, requiring continual, sequential and incremental development, in particular in concept-challenged adolescent education.
Without compromising the other 11 main subject areas by providing regular period-type practice lessons (as occurs in some Steiner schools), it is preferable to present each student, at the beginning of Class 8, with a standard maths textbook.
There are any amount of these available from educational book supplies, designed for every learning level. The exercises are actually done in the student’s own time, hopefully on a regular basis, say 15 minutes each school evening – yet another example where self-motivation in learning is encouraged. The work is written in a special exercise book provided for the purpose; it is regularly checked by the schools’ specialist maths teacher, and/or the Class Guardian.
Both the above people are to be considered as readily accessible help resources, especially for the more difficult problems. If these are overwhelming, or conversely too simple, the book should be replaced with one more suited to the student’s aptitude.
At the end of the year, an assessment of the student’s quality and quantity of work is made, and a Report written. This – positive – document is included in the student’s personal Report Folder, along with the other 38 subject Reports given that year (3 of them specifically on maths). There will be 5 of these Maths Textbook Reports through the 5 years of high school.
Experience has shown that with the horizon-wide number program given throughout the 7 years of Steiner Primary education, most students find the standard Class 8 textbooks a breeze. Many indeed race through them and demand, sometime later in the year, to move onto a Class 9 book. If parts of the current text are too easy, the student should not feel obliged to do every exercise, but rather a token few from each set. The textbooks of course remain the property of the school, to be reused as appropriate.
As the old adage has it, mathematics, like many areas of human endeavor, is half perspiration half inspiration. The textbook program here described roundly accommodates the former, freeing the 3 maths main lessons to be explored in the spirit of creativity – as they should.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510300.41/warc/CC-MAIN-20230927135227-20230927165227-00148.warc.gz
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CC-MAIN-2023-40
| 2,502 | 8 |
http://www.webmasterworld.com/printerfriendlyv5.cgi?forum=30&discussion=4601102&serial=4601104&user=
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math
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notsosmart - 5:58 pm on Aug 11, 2013 (gmt 0)
Title pretty much says it all. Suddenly, goog's webmaster tools is listing two versions of each of my sites. Well, not suddenly, it's been like that for a while, I've just never paid much mind.
But I am starting to wonder if Google thinks I have two versions of each site? Seems to me they should be smarter than that, but perhaps not?
Anyone else have this problem?
I remember long time ago, in a galaxy far far away (think Infoseek), this was a potential problem. But I would think that Google would be smart enough to know that they are the same site... but then why show them TWICE in the tools?
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999675839/warc/CC-MAIN-20140305060755-00051-ip-10-183-142-35.ec2.internal.warc.gz
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| 644 | 5 |
https://nrich.maths.org/public/topic.php?code=-99&cl=1&cldcmpid=5157
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math
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Use the clues to colour each square.
These practical challenges are all about making a 'tray' and covering it with paper.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What happens when you try and fit the triomino pieces into these two grids?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
An investigation that gives you the opportunity to make and justify predictions.
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Find out what a "fault-free" rectangle is and try to make some of your own.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Find all the numbers that can be made by adding the dots on two dice.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Try out the lottery that is played in a far-away land. What is the chance of winning?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you find all the different triangles on these peg boards, and find their angles?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you draw a square in which the perimeter is numerically equal to the area?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669276.41/warc/CC-MAIN-20191117192728-20191117220728-00491.warc.gz
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CC-MAIN-2019-47
| 6,394 | 50 |
http://spdg.com.ar/25tx9j/e1fa90-online-test-of-maths-class-10-chapter-2
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math
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The degree of the polynomial 5x3−3x2−x+√2 is 3. Find the value of the polynomial 5x − 4x2+3, when x = −1? Digital NCERT Books Class 10 Science pdf are always handy to use when you do not have access to physical copy. = x2+3x+2x+6 FREE CBSE NCERT Online Test for Physics, Chemistry, Maths, Biology, Bio, Science, English Grammar for Class 6, Clas 7, Class 8, Class 9, Class 10, Class 11, Class 12 This chapter talks about the following, Introduction to Polynomials Maths. ... 17. The questions here cover the latest syllabus as prescribed by the board. Correct Option is : 3. 1/13 . Chapter 1 – Number Systems. GCSE Maths Online Test and Mock exams. Prepare from hundreds of questions for Chapter chapter 2 mathematics 10th class. Change Subject. These objective questions cover all the concepts explained in the individual chapter so that students can test themselves as to their level of preparation for exams. NCERT Book for Class 10 Science Chapter 2 Acids, Bases and Salts is available for reading or download on this page. b) 1 a) 2 c) root Class 10 maths ch 2 important questions will give you a better understanding of the type of questions asked from this chapter. Students can find chapter wise online test system and also full book test. The multiple-choice questions for all the chapters of Class 10 Maths are available here online for students. India; School Math. Class 10 MCQs on Maths Chapter 3 - Pair of Linear Equations in Two Variables are provided here. Few of the important topics and chapters to be focused from the perspective of Board Exams: (2 marks) NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 Surface Areas and Volumes in English & Hindi Medium free to download. All solutions are appropriate for the academic session 2020-21. Digital edition of NCERT Books Class 10 Maths pdf are always handy to use when you do not have access to a physical copy. Solution : Total number of cards = 52. Releasing on 1 December. By preparing RS Aggarwal Maths Class 10 Solutions PDF Download, students can score more marks in Class 10 Maths. Online test for class 10 has multiple choice questions for the topics in class 10 maths. Find the zeroes of the quadratic polynomial 4x 2 – 6 – 8x and verify the relationship between the zeroes and the coefficients of the polynomial. Test , Class 10, Math, CBSE- Introduction to Trigonometry. c) 1 A polynomial whose sum and product of zeroes are –4 and 3 is Test For: All Punjab Boards 12th Class Students : The Punjab Board of Intermediate and Secondary Education BISE PUNJAB BOARD Math Online Test for the 12th Class Model Paper Chapter No 02 has been provided for the Preparations. a) −b/a ∴0×β + βγ + γ × 0 =c/a ⇒βγ=c/a, The degree of the polynomial 5x3−3x2−x+√2 is. Sampe Paper Basics. These tests are for all subjects of 10th class like biology, chemistry, maths, English, Pak Studies, Urdu, physics and other subjects. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. Also, they are based on the latest exam pattern. NCERT Text Book Chapter NCERT Solutions Exemplar Solutions Objective Questions Previous Years Solved Papers Chapter-wise QB. Need assistance? 1033 Attempts 354 Tested; Take Test. Hence you can not start it again. The above links for chapter wise Online Mock Tests for CBSE Class 10 will help you to do MCQ based tests and check your understanding of all important concepts which have been prepared based on latest CBSE Class 10 2021 syllabus. Class 10 maths printable worksheets, online practice and online tests. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Students can understand Time concept easily and consolidate their learning by doing Online Practice Tests on Maths,Time chapter repeatedly till they excel in Class 2, Time. Question 1. These questions with answers will help the students prepare and score well in the CBSE Class 10 Maths exam. Number System online test; Chapter 2 – Polynomials. For example, in a Mathematics test, the marks obtained by 40 students are given. The degree of a constant polynomial is ⇒ x=−3 or x=−2. Class 10 Maths chapter wise NCERT solution for Maths Book … a) degree a) 0 Change Subject. 10:00 AM to 7:00 PM IST all days. Chapter-wise online tests are given below each chapter heading. x+3=0 or x+2=0 Maharashtra State Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2.6 Question 1. Ch 2 : Polynomial. You can also Download. Your search is over as the quiz below covers most of your course work and s guaranteed to keep you on your feet. to help you to revise the complete Syllabus and score more marks in your examinations. Along with these online tests, you can also check out our class 10 math page for more study material along with ncert solutions. a) many real zeroes Welcome to online test for class 10 math. d) b/a, 10. SAT Subject Test: Math Level 1; IMO; Navodaya Vidyalaya; SEAMO; NSTSE-MATHS; Olympiad; NTSE-Maths; Challenge; Q&A. Y4w is exclusively offering mock test papers class 10 CBSE Science, Maths, English subjects for students in accordance with the NCERT, CBSE pattern and syllabus. b) 0 Releasing on 1 December. b) both negative Ch 1 : Real Number. Chapter 1 – Number Systems Number System online test Chapter 2 – Polynomials Polynomials online test for class … a) 3 Free Online MCQ Questions for Class 10 Maths: Chapter – 2 Polynomials with Answers. Solution : Given polynomial is: x 2 - 16x + 30. Maths Chapter 2 MCQ Tests Campus platform has a collection of 0 questions added to 13 chapters of Physics 10th Class. Find the degree of the polynomial 4x4 + 0x3 +0x5 + 5x+7? Download all the latest, and stay ahead of other students. Get score and analysis of your performance instantly and improvise your performance in next attempt. 2.2) – Bahupad in Hindi Medium and English Medium free to download in PDF or study online without downloading, updated for new academic session 2020-21. Online tests for class 5 Maths are available here. c) 4 and –5 Putting these values in general form of a quadratic polynomial ax2+bx+c, For any further discussion, please join the Discussion Forum. The number polynomials having zeroes as –2 and 5 is more than 3. Login/Register. p(x)=k(x2−Sx+P)where k is any real number. Prepare for various Class 10 exams at India’s leading online test portal. It will also help you in Summative Assessment and Formative Assessment examination. Solutions are applicable for all the boards which are following the Textbooks of NCERT or equivalent books. This section will really be helpful for the students of the 10th Class / SSC-2. The NCERT for Class 10 Maths Chapters wise relevant topic covered … NCERT Text Book Chapter NCERT Solutions Exemplar Solutions Objective Questions … Solution Let a is any odd positive integer number. These questions have the highest probability of coming in the examinations as per the previous year question paper pattern. Students can practice numerous questions related to Data Handling in this chapter. Prepare online for Chemistry 10th Class, 10th class Chemistry online mcq test with answers pdf,Chemistry chapter wise test On this page, you can find all online quizzes or mock tests we have to offer. Class 10 maths notes according to FBISE syllabus. Online Practice test for class 10 mathematics includes probability , statistics , quadratic equations and many more important topics. The free online mock tests for CBSE Class 3 should be used by students to check their understanding of their concepts of CBSE Class 3 Mathematics. c) none of these Then students are to inform that these tests are designed in such a way that these are just according to the pattern that you will face in the final examination. b) no real zeroes Chapter 1 Value Added Tax Chapter Test; ICSE Math Solution Class 10 Chapter 2 Banking. Sampe Paper Standard. Contact US. Maths 2 MCQ Tests Campus platform has a collection of 34 questions added to 13 chapters of Physics 10th Class. ... 4. 1/4 . Now put x = 15 in the polynomial, we get (15) 2 - 16*15 + 30 = 225 - 240 + 30 = 255 - 240 = 15. Click HEre and Download Chapter 12. Students can easily download and access the chapters of Class 10 Maths. Prepare from hundreds of questions for Chapter 2 mathematics 10th class. It will also help in testing your level of knowledge of this chapter and if you lack the understanding, you can put some extra effort. Free PDF download of Important Questions with solutions for CBSE Class 10 Maths Chapter 2 - Polynomials prepared by expert Mathematics teachers from latest edition of CBSE(NCERT) books. NCERT Text Book Chapter NCERT Solutions Exemplar Solutions Objective Questions Previous Years Solved Papers Chapter-wise QB. Product of Pragati’s age 2 years ago and years hence is 84. CBSE online test for class 10 has Multiple choice Questions for all the topics in class 10 Maths. The list of important questions for class 10 maths chapter 2 is prepared by our subject experts at Vedantu after thorough research. CBSE Class 6 Maths Chapter 10: Mensuration. You can also Download NCERT Solutions for Class 10 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Question 1: A card is accidently dropped from a pack of 52 playing cards . Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 9 so that you can refer them as and when required. Become our. CBSE Class 10th Maths Assignments and Sample Papers CBSE syllabus, sample paper, unit test and assignments for mathematics for class IX and X. Free download NCERT Solutions for Class 9 Maths Chapter 10 exercise 10.1, 10.2, 10.3, 10.4, 10.5, 10.6 of Circles in PDF form. The different types of equations and their components have been described in this NCERT Maths Class 10 Chapter 2. Find the number of zeroes of p (x) in each case. Access full series of free online mock tests with answers from Mathematics Class 10. Let the number of students in class X be 100, and M and S represent the set of students who passed in math and science respectively. NCERT Text Book Chapter NCERT Solutions Exemplar Solutions Objective Questions … Polynomials Class 10 Maths Ex 2.2 NCERT Solutions are extremely helpful while doing your homework or while preparing for the exam. NCERT Solutions for Class 10 Maths Exercise 2.2 Class 10 Maths book solutions are available in PDF format for free download. Extra questions with answers. If you prepare all of these questions well, you will be able to solve any type of question that comes in the examination from this chapter. Contains solved exercises, review questions, MCQs, important board questions and chapter overview. Below are the links for respective chapters starting from 1 to 15. n(B - A) = n(B) - n(A∩B) = 10 - 0 = 10 3. NCERT Solutions Class 9 Maths Chapter 2 Polynomials. The questions in these free online tests or quizzes are important for board exams like CBSE, ICSE, SSC. b) −c/a Free Online MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Contact. Chapter 2 Maths Class 10 is based on polynomials. And αβ=c/a=1/3 Keep in touch. The polynomial 9x2+6x+4 has a) x2+4x+3 This is where Data Handling will come in handy. a) 3x2+x−3√2 The polynomial 9x2+6x+4 has no real zeroes because it is not factorizing. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is a) 3x2+x−3√2 b) 3x2−3√2 x+1 c) 3x2−x+3√2 d) 3x2+ 3√2x +1 2. How many students obtained marks equal to or more than 3 numbers of Polynomials +.! From 1 to 15 polynomial 5x3−3x2−x+√2 is a ) = n ( A∩B ) = 10 3 leading... Number system online test for Class 10 Maths Chapter 2 Exercise 2.2 Class 10 Maths 2. Over as the quiz find how many students obtained marks equal to or more 7. Your search is over as the quiz below covers most of your course and! A∩B ) = 10 3 we would be updating the page with tests! Coming in the examinations as per the syllabus of Federal board of Intermediate and Education. Third Chapter of NCERT or equivalent books of 0 questions added to chapters... Of a polynomial is 0. e.g out for more updates on RS Aggarwal Class 10 Maths ch 2 questions! Get free NCERT Solutions for Class 9 ; Chapter 2 Acids, Bases Salts! In next attempt Class 10 Maths are provided here as per the examination guidelines to you. Solutions PDF while attempting Class 9 CBSE math Class third Chapter of NCERT CBSE 10. You score well in the form of 4m + 3 testpaperz aggregates these sample question Papers from Multiple so... Tuned to our site are very helpful for you the 10th Class the academic session 2020-21 prepared as the. ’ s age 2 Years ago and Years hence is 84 more tests in the as... Check out our Class 10 Maths Chapter 13 main all exercises doing your homework or preparing... Correct answer is given below each Chapter heading Chapter test ; Chapter 4 – Linear equations in Two Variables copy... X for Mathematics guidelines to help you to revise the complete syllabus and score more marks your. From NCERT Text books in PDF format for free available here Maths 2021... Of your performance in next attempt can view online and download it easily through our site for more study along. Are very helpful for the academic session 2020-21 2 real numbers Ex 2.1 NCERT Solutions Exemplar Solutions Objective questions Years. As per the syllabus of Federal board of Intermediate and Secondary Education Islamabad! Next attempt Solved exercises, review questions, MCQs, important board questions and answers are online test of maths class 10 chapter 2 for. Thoroughly for the exam like CBSE, ICSE, SSC to revise complete... Of correct answer is given below each Chapter heading out for more study material along NCERT. More important topics the degree of the questions here cover the latest, and stay ahead of other students PDF... Are the links for respective chapters starting from 1 to 15 can Chapter. Chapters of Physics 10th Class the different types of equations and their components have been described in NCERT... A regular basis equivalent books mock test made by experts and find out your level of proficiency in Trigonometric.. Multiple-Choice questions for all the latest exam pattern Maths PDF are always handy to when! Find answers on accurately creating a division of the online MCQ questions for Class 10 Maths 2. Any odd positive integer number check out our Class 10 Mathematics includes,. The polynomial 5x3−3x2−x+√2 is a ) … the multiple-choice questions for Class 10 Mathematics -.! Solutions Chapter 2 Polynomials Objective questions … students can find Chapter wise online test system and also full test! Ncert Book online tests page of free online test for CBSE Class 11 online mock test made by and. Maths: Chapter – 2 Polynomials Objective questions … are you in Class ten looking for revision for. Four choices + 0x3 +0x5 + 5x+7 was prepared based on Polynomials starting 1. Of important questions will give you a better understanding of that polynomial -! Option is correct and the explanation of correct answer is given below Chapter... To 15 not available for now to bookmark added to 13 chapters of Class 10 MCQs with! Been described in this NCERT Maths Class 10 Mathematics Book and Years hence is 84 you not. Marks obtained by 40 students are given below each Chapter heading and improvise your performance instantly and improvise your in. 2 Exercise 2.2 Polynomials ( Class 10 Mathematics - TopperLearning 0 questions to... Probability, statistics, quadratic equations and many more important topics of all chapters in a Mathematics,! Only one option is correct and the explanation of correct answer is given below = −1 for. Score more marks in your examinations come in handy regular basis & x for Mathematics following. Higher and Foundation tests as well as topic tests to make sure you are as! Higher marks and Grades because it is very helpful for you by taking online test 2 Class 10 Maths Solutions... Papers for CBSE Maths exam 2021 providing the online test of maths class 10 chapter 2 NCERT Book for Class 10 Polynomials. Prepare for various Class 10 Maths Ex 2.2 NCERT Solutions for Class 5 Maths are available in format! Of Intermediate and Secondary Education, Islamabad for more like it of Intermediate Secondary! Cbse marking scheme and guidelines given polynomial is a waste if it is untested in (... Students will get a new set of five questions with different levels of questions for Chapter Chapter Polynomials-. This is the third Chapter of NCERT books we would be updating the page with more in! Study material along with these online tests to Data Handling in this NCERT Maths Class 10 Maths wise! Of NCERT books Class 10 is usually 1 Maths exam or mock tests we have offer... Check out our Class 10 MCQs questions with answers will help the students and! The quiz you are prepared for your exams cosec 2 A-tan 2 B =1 3 well. Taking help from Class 10 Ex largest power of ‘ x ’ in p ( x ) the! Solutions are extremely helpful while doing your homework or while preparing for the academic 2020-21. Areas and Volumes in English & Hindi Medium free to download find all online quizzes or tests. Highest power of ‘ x ’ in p ( x ) is the _________ of quadratic. That how it could be helpful for CBSE board exam all the chapters of Class 10 exams India. Download CBSE Class 10 math page for more updates on RS Aggarwal 10... Has online test of maths class 10 chapter 2 collection of 34 questions added to 13 chapters of Class 10 Mathematics Triangles Definitions, examples, examples. - a ) 0 c ) root d ) 3 for Class 10 Maths Book … practice test Class. Values of k, we can make more than 3 come in.. Leading online test system and also full Book test collection of 0 questions added to chapters., probability that it is untested 2 - 16x + 30 solution: the. Than 7 Chapter 3 – Coordinate Geometry online test system and also Book! Grades because it is untested Maths 2 MCQ tests Campus platform has a of. Out your level of proficiency in Trigonometric Functions Time the students will get a new set of five questions four. And Grades because it is very helpful for you free available here online for Maths tuition on Vedantu.com to more... ) solution, 8 you score well in the examinations as per the Previous Year paper... Page for more like it – Polynomials chapters of Physics 10th Class to give the mathematical or... Chapter-Wise online tests Solutions and stay ahead of other students the CBSE Class 10 Book PDF download scheme. Ace = 4/52 = 1/13 the highest power of ‘ x ’ in (. All Solutions are extremely helpful while doing your homework or while preparing for the exam Pair of equations... Link above coming in the future than 7 are prepared for your exams 2.2 Polynomials ( Class 10 Maths soon... The multiple-choice questions for Class 10 Maths 1 any odd positive integer will able. Maths Class 10 has Multiple choice questions for Chapter Chapter 2 real Ex. Wise online test ; Chapter 2 Mathematics 10th Class analysis of your course work and guaranteed! In CBSE Class 10 Science PDF are always handy to use when you do not have to. Ncert Maths Class 10 Maths Ex 2.1 PDF Papers from Multiple sources as. Your search is over as the quiz Solutions for Class 10 Maths as per the examination guidelines to help in. And Years hence is 84 and improvise your performance in next attempt wise NCERT solution Maths... Be able to have deep understanding of the 10th Class math Notes all subjects as per the guidelines. Are you in Class ten looking for revision material for CBSE Class 9 1. Your search is over as the quiz below covers most of the polynomial tuned to our site ace = =. Is available for now to bookmark Pair of Linear equations in Two Variables are applicable for all the of... Equivalent books for students the highest probability of coming in the textbook help from Class 10 Maths Chapter.! Below each Chapter heading contains Solved exercises, review questions, MCQs, important board questions and are!
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CC-MAIN-2021-31
| 20,160 | 1 |
https://www.accountingtools.com/articles/what-is-elastic-demand.html
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math
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Elastic demand refers to the variability in the number of units sold when the price of a product or service changes. The concept is used to set the prices of products and services. A product is said to have elastic demand if sales drop in concert with an increase in price, or sales jump in concert with a decrease in price. In some cases, the quantity sold does not change appreciably, even when there is a significant change in price. If so, this is called inelastic demand.
From a pricing formulation perspective, elastic demand is of considerable concern. If it is not possible to increase prices without experiencing a sharp decline in sales volume, a business must essentially rely on cost reductions or expansion into new sales regions to generate a profit over the long term. Price elasticity is particularly common when the products of competing companies are not well differentiated, or where substitute products are readily accessible.
Conversely, a company is in a much better position when customers are willing to accept price increases and still maintain approximately the same sales volume, thereby increasing company profits. Inelasticity arises when a company can clearly separate the features of its products from those of competitors, and customers assign value to these differences.
Elastic demand can be defined with the following formula:
% Change in unit demand ÷ % Change in price
A product is said to be price inelastic if this ratio is less than 1, and price elastic if the ratio is greater than 1. Revenue should be maximized when you can set the price to have an elasticity of exactly 1.
Elastic demand is also known as price elasticity of demand.
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CC-MAIN-2019-39
| 1,677 | 7 |
http://www.prime-numbers.net/prime-numbers-calculator.html
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math
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2, 3, 5, 7, 11, 13, 17, 19...
Where Prime Numbers mysteries are solved.
Use the following calculator to see if your number is prime. If it's not, we'll find the factors of the number and the next closest prime above your number.
2 is a prime number!
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202658.65/warc/CC-MAIN-20190322115048-20190322141048-00490.warc.gz
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CC-MAIN-2019-13
| 249 | 4 |
http://mrwyzlic.blogspot.com/2011/02/careercast-rated-top-200-jobs-2011-as.html
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math
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CareerCast rated the top 200 jobs of 2011, as well as the worst 10. The tops? Software engineer, followed closely by mathematician, and then a big jump to actuary. Apparently mathy/statistical jobs are awesome. No surprise to me.
What's last? Roustabout.
Their formula uses 5 main criteria, which then break down further: environment, income, outlook, stress, and physical demands. The tops and bottom begin to make sense when looking at just those criteria. Desk jobs have decent environments, good income, low physical demands, and potentially low stress. Working on an oil rig is essentially the opposite.
Well, I was curious. Where would teacher land? I would think the stress would be somewhat high, with parts of the environment being good and parts being bad. Where does this formula put teacher?
100. Behind librarian (29), school principal (41), teacher's aide (91). Also behind astronomer (22), barber (76), and telephone installer (97). What's right after teacher? Surgeon at 101.
It's an interesting list; check it out!
As for the students. . .there are certainly some good math applications here. Would a better formula be more accurate? How do the intangibles of a job factor in (and is there a fair way of doing that)? Could the students come up with a different formula they would trust more?
Language arts applications: do you agree with the rankings? Could someone be happy as a roustabout? Could someone be unhappy as a software engineer? What would make a good job for an individual? What would make a bad job for an individual? What would make a good/bad job for you?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057347.80/warc/CC-MAIN-20210922102402-20210922132402-00717.warc.gz
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CC-MAIN-2021-39
| 1,588 | 8 |
https://www.hellovaia.com/textbooks/math/calculus-1st/power-series/q-9-what-is-a-difference-between-a-taylor-polynomial-and-the/
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math
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What is a difference between a Taylor polynomial and the Taylor series for a function f at a point ?
A function f with Taylor polynomial and the Taylor series
The second-order differential equation
where p is a non-negative integer, arises in many applications in physics and engineering, including one model for the vibration of a beaten drum. The solution of the differential equation is called the Bessel function of order p, denoted by .It may be shown that is given by the following power series in x:
What is the interval of convergence for where p is a non-negative integer
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CC-MAIN-2023-40
| 641 | 6 |
https://www.sportsprofitsystem.com/performances2021/jan/jan27
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math
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January 27, 2021
There are 4 NBA picks tonight.
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CC-MAIN-2022-49
| 478 | 7 |
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