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http://www.thescienceforum.com/physics/16772-future-changeable.html	1,674,886,905,000,000,000	text/html	crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00451.warc.gz	78,628,845	38,115	# Thread: Is the future changeable? 1. I'm in a dilemma here. I don't know what to believe. If you consider the uncertainty principles in physics the the future is changeable and can't be predicted. But this uncertainty principles only says that we can't measure some thing at the same time to an arbitrary precision. For example is we measure speed and place at the same time we can only know 1 very precise. But I for example we know every single property of every single thing that exists. And we know all the formulas. Then theoretical we should be able to calculate exactly what will happen. At a single moment everything has a place and velocity and a lot of other things. And the rules are always the same. So I should be possible to predict everything is we know everything. This got me confused. I believe that the uncertainty principle is true but that only applies to measuring things. That doesn't say the future is changeable. What is wrong in my thinking? 2. 3. thats why i hate newtonian relativistic phyiscs: deterministic and love quantum physics indeterministic they contradict each other in their philososphy my opinion is the future cant be changed though you have free will, just as with the past 4. hmm you believe things can't be changed and yet you believe in free will? isn't our will, our thoughts, determined by a bunch of particles and physic laws? the things you say that aren't changeable? if future is unchangeable free will doesn't exist 5. Originally Posted by jan-pieterv I'm in a dilemma here. I don't know what to believe. If you consider the uncertainty principles in physics the the future is changeable and can't be predicted. But this uncertainty principles only says that we can't measure some thing at the same time to an arbitrary precision. For example is we measure speed and place at the same time we can only know 1 very precise. But I for example we know every single property of every single thing that exists. And we know all the formulas. Then theoretical we should be able to calculate exactly what will happen. At a single moment everything has a place and velocity and a lot of other things. And the rules are always the same. So I should be possible to predict everything is we know everything. This got me confused. I believe that the uncertainty principle is true but that only applies to measuring things. That doesn't say the future is changeable. What is wrong in my thinking? "Changing the future" is an oxymoron. Change it from what ? The deterministic nature of Newtonian mechanics was observed long ago, by LaPlace if I recall correctly. Nobody knows if physics is really deterministic or not. General relativity is completely deterministic. Quantum mechanics is not. Some think that Bell's inequality rules out a deterministic explanation for QM. Gerard 'tHoof is not convinced. 6. can we determine or atleast influence what the future will be or has the future already been determined? 7. they mention this issue on how future is fixed but at the same time you have free will in the matrix movie they explain you chose and then you live it to know why you chose that so the free will would transcend time 8. This is a philosophy question, not a physics question. The uncertainty principle, the deterministic nature of relativity and the random nature of quantum mechanics are all points to be addressed, but that doesn't mean the question or the answer has anything to do with physics. 9. Originally Posted by jan-pieterv can we determine or atleast influence what the future will be or has the future already been determined? Of course you can iinfluence the future. That is what choices are all about. If you don't believe that, try telling the judge that "the devil made you do it". 10. It comes together in the laws of probability. Specifically the law of large numbers which states that, over a sufficiently large number of die rolls, the outcomes become increasingly uniform with greater numbers of rolls. For example, it would be astronomically rare to roll a million dice, and get 200,000 one's. You could roll 10 dice, and get 2 one's, or maybe even 100 dice, and get 20 one's, but you couldn't roll 6.023 * 10^23 dice (the number of atoms in a mole of matter) and get 1.24 * 10^23 one's. That just doesn't happen. So, the fact that physics is governed by probability on the smallest scale does nothing to prevent it from being deterministic on the large scale. 11. in an infinite trow of dices actually that must happen in an infinite row even a trillion of six in a row can happen is there something that can be divided in halves infinitally exists? 12. Originally Posted by luxtpm in an infinite trow of dices actually that must happen in an infinite row even a trillion of six in a row can happen is there something that can be divided in halves infinitally exists? This is true, but you will only encounter an infinite number of die rolls after you've observed an infinite amount of matter. The fact it can happen, and that it would happen in an infinitely sized universe, doesn't mean that humanity will ever experience it to happen. 13. three words: unfalsifiable 14. Originally Posted by DrRocket Of course you can iinfluence the future. That is what choices are all about. If you don't believe that, try telling the judge that "the devil made you do it". Well choices are made by the brain. The brain works by processing a stream of electrons, molecules, ... These things all obey the laws of physics so if you were able to "back-up" the universe. And then let it run a few times. Wouldn't you're choice be the same all the time? Or would there be some weird uncertainty principle that would alter the outcome every time? I think because the laws of physics are the exact same thing everywhere and every time everything is determined beforehand. Even the choices we make because the are the result of what physical laws do with particles. Originally Posted by MagiMaster This is a philosophy question, not a physics question. The uncertainty principle, the deterministic nature of relativity and the random nature of quantum mechanics are all points to be addressed, but that doesn't mean the question or the answer has anything to do with physics. I don't think so. Maybe because I used humans and free will it seems as if this is a philosophy question. But there are other things that can be used to pose the same problem. I just can't find a good one for the moment Originally Posted by kojax It comes together in the laws of probability. Specifically the law of large numbers which states that, over a sufficiently large number of die rolls, the outcomes become increasingly uniform with greater numbers of rolls. For example, it would be astronomically rare to roll a million dice, and get 200,000 one's. You could roll 10 dice, and get 2 one's, or maybe even 100 dice, and get 20 one's, but you couldn't roll 6.023 * 10^23 dice (the number of atoms in a mole of matter) and get 1.24 * 10^23 one's. That just doesn't happen. So, the fact that physics is governed by probability on the smallest scale does nothing to prevent it from being deterministic on the large scale. But that doesn't mean there can't be tiny differences. What we calculate in quantum dynamics and thing like that is based on probability. But is there really a chance that thing will be different? The probability is only introduced because we can't measure certain quantity simultaneously. So we have to be satisfied with approximate values. Here we get our probabilities because the chance that it is a specific quantity is normally distributed. But certainly the particle in question must have an exact value for that quantity so in my opinion if we would know everything we wouldn't be able to change anything because everything is determined. Originally Posted by marcusclayman three words: unfalsifiable what exact thing here is unfalsifiable? I know what unfalsifiable is after looking at wikipedia but can't understand what you mean 15. Originally Posted by jan-pieterv Originally Posted by MagiMaster This is a philosophy question, not a physics question. The uncertainty principle, the deterministic nature of relativity and the random nature of quantum mechanics are all points to be addressed, but that doesn't mean the question or the answer has anything to do with physics. I don't think so. Maybe because I used humans and free will it seems as if this is a philosophy question. But there are other things that can be used to pose the same problem. I just can't find a good one for the moment The human ego doesn't like the idea of accepting that we are just another object in the universe. Everything you will do in the future is determined by a combination of external events and "who you are". The thing is, you can't change who you are. At the most fundamental level, you are what you desire to choose. You can change what you actually choose, but you can't change what you desire to choose. If you are an alcoholic, and you reform, it will be because you desire to reform. But certainly the particle in question must have an exact value for that quantity so in my opinion if we would know everything we wouldn't be able to change anything because everything is determined. In situations like Schrodinger's Cat, a given object may have no exact state for a very long time, while it waits for someone to observe it. http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat This might even suggest backwards time causality, if you interpret it certain ways. (It's not a very popular, or widely accepted interpretation, however) Perhaps future and past are just matters of perspective? Maybe there might exist a unifying perspective from which they are all "now"? 16. Originally Posted by DrRocket Of course you can iinfluence the future. That is what choices are all about. If you don't believe that, try telling the judge that "the devil made you do it". This is where, in my opinion, materialism fails completely. Unless you accept a non-material component in the human being, you have to conclude that all our choices are determined by the makeup of our bodies (including the brain of course) plus the surrounding world, and the only non-deterministic factor is any quantum effects involved in the synnapses or wherever. In brief, whatever isn't determined is purely random. No room for a free will (Kojax says just about the same in other words) that might be held morally accountable for its choices. So, in the eyes of a materialist judge, any offender, however wicked and ruthless, should be morally as innocent as the baby who was thrown out of a window and fell on passing nonagenarian, killing her. 17. Originally Posted by luxtpm in an infinite trow of dices actually that must happen false Originally Posted by luxtpm in an infinite row even a trillion of six in a row can happen true Originally Posted by luxtpm is there something that can be divided in halves infinitally exists? gibberish 18. Originally Posted by jan-pieterv Originally Posted by DrRocket Of course you can iinfluence the future. That is what choices are all about. If you don't believe that, try telling the judge that "the devil made you do it". Well choices are made by the brain. The brain works by processing a stream of electrons, molecules, ... These things all obey the laws of physics so if you were able to "back-up" the universe. And then let it run a few times. Wouldn't you're choice be the same all the time? Or would there be some weird uncertainty principle that would alter the outcome every time? I think because the laws of physics are the exact same thing everywhere and every time everything is determined beforehand. Even the choices we make because the are the result of what physical laws do with particles. But so far as we know physics is not deterministic. Yoiu can still try telling that to the judge. I predict stripes. There is no physical theory that explains consciousness. Originally Posted by jan-pieterv But that doesn't mean there can't be tiny differences. What we calculate in quantum dynamics and thing like that is based on probability. But is there really a chance that thing will be different? The probability is only introduced because we can't measure certain quantity simultaneously. So we have to be satisfied with approximate values. Here we get our probabilities because the chance that it is a specific quantity is normally distributed. But certainly the particle in question must have an exact value for that quantity so in my opinion if we would know everything we wouldn't be able to change anything because everything is determined. The law of large numbers does not guarantee a specific outcome or distribution of outcomes. It only guarantees a high probability is assigned to that outcome. There is nothing whatever that guarantees the normal probability distribution in all situations. The usual justification for the assumption of a normal distribution is the central limit theorem. That applies to an infinite sum of independent normally distributed random variables, and only to a sum. The world is not normally distributed. If it were there would be bolts breaking in tension under a compressive load. Usually the normal distribution is a good approximation near the mean of a random variable. It is not a good approximation for the analysis of low probability events. That comes along with the central limit theorem. 19. Originally Posted by kojax Originally Posted by jan-pieterv Originally Posted by MagiMaster This is a philosophy question, not a physics question. The uncertainty principle, the deterministic nature of relativity and the random nature of quantum mechanics are all points to be addressed, but that doesn't mean the question or the answer has anything to do with physics. I don't think so. Maybe because I used humans and free will it seems as if this is a philosophy question. But there are other things that can be used to pose the same problem. I just can't find a good one for the moment The human ego doesn't like the idea of accepting that we are just another object in the universe. Everything you will do in the future is determined by a combination of external events and "who you are". The thing is, you can't change who you are. At the most fundamental level, you are what you desire to choose. You can change what you actually choose, but you can't change what you desire to choose. If you are an alcoholic, and you reform, it will be because you desire to reform. But certainly the particle in question must have an exact value for that quantity so in my opinion if we would know everything we wouldn't be able to change anything because everything is determined. In situations like Schrodinger's Cat, a given object may have no exact state for a very long time, while it waits for someone to observe it. http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat This might even suggest backwards time causality, if you interpret it certain ways. (It's not a very popular, or widely accepted interpretation, however) Perhaps future and past are just matters of perspective? Maybe there might exist a unifying perspective from which they are all "now"? That particular interpretation of that particular experiment has long been debunked. Observation is not something done by somebody. It's done by any particle not part of the system being observed. Unless the box can be completely isolated from the rest of the universe (it can't), this doesn't apply the way most people think it does. Also, the millions of dice are still random. No matter how many dice you add, it never becomes deterministic. It's just that you can predict the outcome very accurately by assuming the system is deterministic. BTW, this is definitely a philosophy question, no matter what terms you put it in. (Not Schrodinger's cat; the discussion on free will and determinism.) 20. Originally Posted by MagiMaster Also, the millions of dice are still random. No matter how many dice you add, it never becomes deterministic. It's just that you can predict the outcome very accurately by assuming the system is deterministic. Yeah. It approaches determinism, but never reaches it. The odds are never infinity to one for any outcome, but they can reach the point where they are 10^1,000,000 to one (or some other absurd number) very easily. So from the perspective of theory, it's not true determinism, but from the perspective of practice, it so near to it that you can't measure a difference. Originally Posted by Leszek Luchowski Originally Posted by DrRocket Of course you can iinfluence the future. That is what choices are all about. If you don't believe that, try telling the judge that "the devil made you do it". This is where, in my opinion, materialism fails completely. Unless you accept a non-material component in the human being, you have to conclude that all our choices are determined by the makeup of our bodies (including the brain of course) plus the surrounding world, and the only non-deterministic factor is any quantum effects involved in the synnapses or wherever. In brief, whatever isn't determined is purely random. No room for a free will (Kojax says just about the same in other words) that might be held morally accountable for its choices. So, in the eyes of a materialist judge, any offender, however wicked and ruthless, should be morally as innocent as the baby who was thrown out of a window and fell on passing nonagenarian, killing her. Maybe the makeup of your body is still a good reason to put you in prison. Suppose you contracted a form of AIDS that was transmittable through the air, instead of just by sex. We'd want to quarantine you. A chronic criminal who continually violates the law might be isolated for a similar reason: to protect the rest of us. Also, if your chemical makeup responds to penalties, then penalizing your makeup does some good. It's unfortunate that doing so has the side effect of penalizing you, the person, along with you, the person's makeup, but maybe it's still morally acceptable if it's necessary in order to bring about a good result. 21. Most scientific evidence at this point in time suggests that the future is entirely fixed. And to those who think this is a philosophical debate, your wrong, its a perfectly legitament scientiffic question to ask if events that will happen in the future are fixed. This is all about Causality. The next event that happens is entirely dependant on the events that occurred before it, nothing else can happen. There is only one final frontier to find out for sure whether or not humans have free will, and that is when we discover what "conciousness" is and how it works. Admittedly, there is absolutely no scientiffic explaination for conciousness whatsoever at present, its easily the most profound mystery of the universe. But sadly, my opinion is that the future is fixed and there is nothing that can be done to change the way things are happening. We are like the watchers of a movie, we get to observe the events happening in the movie, but the future of that movie has obviously already been decided, its future is fixed and cannot be changed. 22. Originally Posted by Waveman28 Most scientific evidence at this point in time suggests that the future is entirely fixed. . Baloney. There are two major physical theories. Quantum theory and general relativity. Quantum theory is stochastic. General relativity is deterministic. Nobody really knows if an ultimate theory will be stochastic or deterministic, but most researchers have thrown their hat into the stochastic ring. That is why there is such emphasis on developlment of a theory of quantum gravity. The counter-point is that some pretty smart people, like Roger Penrose and Gerard 'tHooft, seriously consider the possibility of an encompassing deterministic theory. But the statement that "Most scientific evidence at this point in time suggests that the future is entirely fixed" has no basis whatever. 23. i didslike einstein for mistreating psicologically his wife i think he tried to elude his faults by blaming them on determinism man i know in the past i took choices with my free will the past is unmovable and yet i had free will as so can happen with the future unmovable yet with free will in fact theres only one future a precognition of something that wont happens cause has beeen changed is wrong 24. uncertainty appliess as well to the past you cant determine spin and momentum neither in the present future or past 25. Originally Posted by kojax Maybe the makeup of your body is still a good reason to put you in prison. Suppose you contracted a form of AIDS that was transmittable through the air, instead of just by sex. We'd want to quarantine you. A chronic criminal who continually violates the law might be isolated for a similar reason: to protect the rest of us. Also, if your chemical makeup responds to penalties, then penalizing your makeup does some good. It's unfortunate that doing so has the side effect of penalizing you, the person, along with you, the person's makeup, but maybe it's still morally acceptable if it's necessary in order to bring about a good result. These are all plausible propositions, but they have some disturbing consequences: - Prisons would no longer be what we understand them to be: places of well-deserved and just punishment. Instead, their role would be indistinguishable from psychiatric hospitals and quarantine centers (known as leprosaria in the good old days). This opens the way to locking people up because they might do something terrible in the future - given that they are morally just as innocent after as before the deed. - "Me, the person" would still suffer the effects of decisions made by "me, the makeup", while having no say in what "I, the makeup" decide. In fact, there is not much left of "me, the person" other than the undeniable ability to suffer or enjoy (the latter is, of course, less disturbing). Cheers, L. 26. Originally Posted by luxtpm i didslike einstein for mistreating psicologically his wife i think he tried to elude his faults by blaming them on determinism man i know in the past i took choices with my free will the past is unmovable and yet i had free will as so can happen with the future unmovable yet with free will in fact theres only one future a precognition of something that wont happens cause has beeen changed is wrong I think you used free will to skip english classes....... 27. oh synchronicity in 45 minutes i start to give class to an erasmus student ill get paid 12 euro per hour just to converstae amazingly i have a degree in english philology 28. Originally Posted by luxtpm amazingly i have a degree in english philology That is amazing. How much did you pay the diploma mill? 29. Originally Posted by Leszek Luchowski [ These are all plausible propositions, but they have some disturbing consequences: - Prisons would no longer be what we understand them to be: places of well-deserved and just punishment. Instead, their role would be indistinguishable from psychiatric hospitals and quarantine centers (known as leprosaria in the good old days). This opens the way to locking people up because they might do something terrible in the future - given that they are morally just as innocent after as before the deed. Cheers, L. In this perfectly deterministic, clockwork, universe, the actions of society in establishing prisons, apprehending people and incarcerating them are also not acts of any free will, but simply the inevitable consequences of initial conditions. There is no need for morals and moral judgments at all, everything is pre-ordained, and I do mean everything. It is a pretty bleak prospect. If your are disturbed it s because initial conditions cause you to be disturbed. This position is sufficiently at odds with the everyday experience of nearly everyone to be rejected. 30. Originally Posted by DrRocket In this perfectly deterministic, clockwork, universe, the actions of society in establishing prisons, apprehending people and incarcerating them are also not acts of any free will, but simply the inevitable consequences of initial conditions. There is no need for morals and moral judgments at all, everything is pre-ordained, and I do mean everything. It is a pretty bleak prospect. If your are disturbed it s because initial conditions cause you to be disturbed. Damn, you beat me to it, and what youve said there is exactly right. Originally Posted by DrRocket This position is sufficiently at odds with the everyday experience of nearly everyone to be rejected. Why'd you have to throw that in at the end!? You were on a roll. As I was saying before, its all about cause and effect: the same cause will always result in the same effect, provided that all other factors are identical. And because at any instant in time, the factors that exist are the same as itself, there can only be one outcome. I had a really freaky dream once that involved this kind of thing. I was in a perfectly symmetrical room with an identical version of my exact self on the other side of the room (which was circular). Whenever I went to say something, the other me said the exact same thing. I knew that the other me knew about determinism just like I did (because we were identical) so I tried to think of a way to break the symmetry somehow. But this proved to be completely futile, everything i tried to do, the other me tried aswell so when I went to ask him to help, he asked me too. The dream seemed to go forever, i tried everything. And then we both said "holy s**t", and put our hands over our mouths and started crying. It was such a wierd dream, i was so glad to wake up, worst nightmare ever. 31. Originally Posted by DrRocket gibberish My favourite word. 32. cause my image in the mirror does as me that doesnt nullify my free will as i see it idiots blame deterministic fate whos gonna accept to be an idiot is it so difficult to understand that either with free will or not theres only one future as theres only one past in fact the only way to not have free will is that if both outcomes of a choice become real as long as there are two choices as happens in quantum level in the quantic computer that is the brain and only one becomes real free will has been exerted by taking a choice your determinism is obsolote and not anymore valid as quantum physics has proved since the microworld affetcs the marcowolrd 33. Originally Posted by luxtpm cause my image in the mirror does as me that doesnt nullify my free will as i see it idiots blame deterministic fate whos gonna accept to be an idiot is it so difficult to understand that either with free will or not theres only one future as theres only one past in fact the only way to not have free will is that if both outcomes of a choice become real as long as there are two choices as happens in quantum level in the quantic computer that is the brain and only one becomes real free will has been exerted by taking a choice your determinism is obsolote and not anymore valid as quantum physics has proved since the microworld affetcs the marcowolrd 34. Originally Posted by DrRocket Originally Posted by Waveman28 Most scientific evidence at this point in time suggests that the future is entirely fixed. . Baloney. There are two major physical theories. Quantum theory and general relativity. Quantum theory is stochastic. General relativity is deterministic. Nobody really knows if an ultimate theory will be stochastic or deterministic, but most researchers have thrown their hat into the stochastic ring. That is why there is such emphasis on developlment of a theory of quantum gravity. The counter-point is that some pretty smart people, like Roger Penrose and Gerard 'tHooft, seriously consider the possibility of an encompassing deterministic theory. But the statement that "Most scientific evidence at this point in time suggests that the future is entirely fixed" has no basis whatever. Quantum theory is stochastic because we cant measure everything to an arbitrary precision. Because of this there is a chance that it will be a different value. Because can only work with the chance that a value it this or that the outcome of the calculations are also expressed in chances But is we would know everything: all the laws to exact precision and all the properties to exact precision then these stochastic thing would become deterministic because the chances would become 100% 35. The future doesn't exist, thus, its not changeable. 36. 1) The universe is either stochastic or deterministic. We don't know which and nobody can claim either 2) The theory that there would be only one future is unfalsifyable, and thus such claim cannot be made. Similarly, the fact whether Schrödinger's cat is both dead and alive simultaneously or not is unfalsifyable. The multiverse interpretation is just as valid as any other interpretation. 3) Whether the universe is stochastic or deterministic doesn't affect free will. This is a philosophical point that requires an exact definition of free will. As long as we can't affect the way in which quantum waves collapse, any indeterminism might as well be for the purpose of determining our actions, a kind of "soft" determinism. Determinism does not oppose free will. 4) The only reason a "lack" of free will would influence our justice system is for punishment as revenge or retribution, which is completely pointless anyway. 5) luxtpm: if you have a degree in english philology, you have probably heard about capitalisation, punctuation and spelling checkers. If you want others to take the time to read what you have to say you could show them some respect by using those. (hereby I excuse any spelling errors in this post: I don't have the privilege to install firefox on this PC, am not an native speaker and have no degree in English whatsoever.) 37. however good my writting was still would have to listen spell nazis and those who PRETEND not to understand 38. Originally Posted by luxtpm however good my writting was still would have to listen spell nazis and those who PRETEND not to understand It's about respect for your readers. If you don't think what you write is worth the effort of pressing a shift key once in a while, why would we think it's worth reading. 39. plz point me to the mistakes here not caused by dixlesia which makes this not understandable as someone pointed out: cause my image in the mirror does as me that doesnt nullify my free will as i see it idiots blame deterministic fate whos gonna accept to be an idiot is it so difficult to understand that either with free will or not theres only one future as theres only one past in fact the only way to not have free will is that if both outcomes of a choice become real as long as there are two choices as happens in quantum level in the quantic computer that is the brain and only one becomes real free will has been exerted by taking a choice your determinism is obsolote and not anymore valid as quantum physics has proved since the microworld affetcs the marcowolrd as for using capital letters thats a rule i refuse to follow not for disrespect but to be consecuent with my lazy personality if you dont agree- like what i say but cant refute it i see childish counterattack on the grammar this is a serious discussion in the end i think is about wether we have a soul- free will or not and that my grammar is bad doesnt change the fact we are responsible for our actions what is worse that i dont use capital letters for being lazy or pretend not to understand with a mean will 40. We understand, but it takes longer, especially if you are gluing sentences head to tail and omit words: your laziness requires more effort by those who read it, which is a sign of arrogance. And yes it affects a serious discussion: if you don't even bother about punctuation, do you even think about the content? PS: my apologies to everyone else for hijacking this thread. I'm easily annoyed if posters show lack of respect/interest by ignoring basic posting courtesy. 41. i understand nobody here belives in free will right? 42. Originally Posted by luxtpm i understand nobody here belives in free will right? I do 43. thats nice i dislike people who think theyre not responsible for their acts thats the very same reason i dislike not neccesarily disbelieve newtonian and relativistic physics but find amazing quantum physics thousands of years of determinism to be brought down by the atom i dont think well ever prove god exists but sometime in the future i think the soul existance might be proved edit: back on topic nobodys adressing the issue on whatever it is theres only one present one past and one future was the past random? yes it was, yet theres only one, the same can be applied for the future the only theory my ethics makes me refuse to admit is the one that kills the posibility of free will: that for every choice the universe divides in two making both real this is a theory explained in the crap gubernamental propaganda of the made up story of time traveller john titor 44. I have never known an English major who could stand a complete lack of any punctuation. Are you sure you're not an English literature major? I know there are some poets who write like that (and I'm pretty sure they weren't English majors). 45. But I for example we know every single property of every single thing that exists. And we know all the formulas. Then theoretical we should be able to calculate exactly what will happen. Yes, you can indeed predict the future with 100% certainty across any span of time. In fact, its done all the time :wink: 46. Not yet, but most things are better than chance. 47. Originally Posted by Bender Originally Posted by luxtpm i understand nobody here belives in free will right? I do And so do I. 48. i believe to the future can be predicted, i know by experience i have many precognitions most people has had dreams that later happened, this is common but imo though the future can be predicted still we have free will, just as we know the past and we still know we had free will the matrix movie is in favour of this theory also free will in a fixed future, choices seem to be taken transcending time 49. Originally Posted by jan-pieterv Quantum theory is stochastic because we cant measure everything to an arbitrary precision. Because of this there is a chance that it will be a different value. Because can only work with the chance that a value it this or that the outcome of the calculations are also expressed in chances But is we would know everything: all the laws to exact precision and all the properties to exact precision then these stochastic thing would become deterministic because the chances would become 100% Originally Posted by luxtpm uncertainty appliess as well to the past you cant determine spin and momentum neither in the present future or past Taken together, these two points seem to make the future and the past identical. We can only be certain of the past up to a certain level of precision, and we can only be certain of the future up to a certain level of precision. So: if we use uncertainty as the basis for our decision, then either we must conclude that both the past and future are changeable, or we must accept that neither are changeable. Originally Posted by luxtpm however good my writting was still would have to listen spell nazis and those who PRETEND not to understand If English is not your first language, why don't you just say so, and people will have more sympathy for you? If English is your first language, then you need to understand that, on a forum like this your ideas will be complicated, which means they're hard to understand even if they are properly punctuated. Add further complications, like spelling and grammar mistakes, and it might honestly become too difficult to understand you. 50. oh yes im from spain and my english degree was mostly centered in feminist literature 51. If you were to take into consideration all that has been said; Yes, you do have a free will but it's already been determined what your free will will decide. Logically speaking, that would mean the future is unchangable, as all the factors put into the "present" would have decided what your free will will decide. Whether deterministic or stochastic makes no difference, as the choice you make is always the same. The question is, will those factors put into the decision ever change? Will the uncertainty principle cause a truck that SHOULD be there diverge somehow, thus avoiding an early death? Would the same principle cause a neuron in your brain that was supposed to be fired, not be fired, thus causing a change in your thought process? Either way, your free will, will have decided that way due to the circumstances. Whether the circumstances will be the same every time is up in the air. One atom or electron gone missing can change everything? That's a question science has to answer. 52. Originally Posted by Burnedalive If you were to take into consideration all that has been said; Yes, you do have a free will but it's already been determined what your free will will decide. Logically speaking, that would mean the future is unchangable, as all the factors put into the "present" would have decided what your free will will decide. Whether deterministic or stochastic makes no difference, as the choice you make is always the same. The question is, will those factors put into the decision ever change? Will the uncertainty principle cause a truck that SHOULD be there diverge somehow, thus avoiding an early death? Would the same principle cause a neuron in your brain that was supposed to be fired, not be fired, thus causing a change in your thought process? Either way, your free will, will have decided that way due to the circumstances. Whether the circumstances will be the same every time is up in the air. One atom or electron gone missing can change everything? That's a question science has to answer. The answer won't make a difference to the current discussion. Even if these quantum effects affect our choices, it has no bearing on the determined nature of our choices, since we cannot affect the quantum effects. In that case they're just not pre-determined. 53. that we cannot affect the quantum effects in an assumption. that everything follows distinct unchanging laws is also an assumption. these assumptions seem to be obvious because the world around us behaves rather newtonianly. we assume them because we're so used to things working that way. Conway and Kochen say they can essentially prove that our universe is not deterministic under the prevailing theories. http://www.sciencenews.org/view/gene...e_free_will%3F interesting stuff. 54. Originally Posted by Leszek Luchowski Originally Posted by kojax Maybe the makeup of your body is still a good reason to put you in prison. Suppose you contracted a form of AIDS that was transmittable through the air, instead of just by sex. We'd want to quarantine you. A chronic criminal who continually violates the law might be isolated for a similar reason: to protect the rest of us. Also, if your chemical makeup responds to penalties, then penalizing your makeup does some good. It's unfortunate that doing so has the side effect of penalizing you, the person, along with you, the person's makeup, but maybe it's still morally acceptable if it's necessary in order to bring about a good result. These are all plausible propositions, but they have some disturbing consequences: - Prisons would no longer be what we understand them to be: places of well-deserved and just punishment. Instead, their role would be indistinguishable from psychiatric hospitals and quarantine centers (known as leprosaria in the good old days). This opens the way to locking people up because they might do something terrible in the future - given that they are morally just as innocent after as before the deed. - "Me, the person" would still suffer the effects of decisions made by "me, the makeup", while having no say in what "I, the makeup" decide. In fact, there is not much left of "me, the person" other than the undeniable ability to suffer or enjoy (the latter is, of course, less disturbing). Cheers, L. I've been thinking about this some more. Whether you believe in time travel or not, the human mind allows for a limited form of backwards time causality. I mean that your present actions are often determined on the basis of what you perceive to be the probable future. The prediction that someone will be jailed if they attempt to rob a bank honestly does stop bank robberies before they ever happen in the first place. How do you create that perception, unless you make a few examples? Prisons are not about punishing past events. They're about preventing future events. So: to say a person has no free will is not the same as saying that perception of the likely future has no effect on their behavior. People who are in psych hospitals instead of prison are placed there because the expectation of future punishment has no effect on their behavior (or the wrong effect), not because they lack "free will" in a general sense. I think this whole concept of "moral accountability" is just an illusion. 55. i dont know if you will find this helpful but i remember a post about determinism a while back where we had the discussion about whether Quantum indeterminism can have an effect on determinism on the macro scale, I.E. Suggesting that indeterminism 'smoothes out' into determinism on the macro scale. http://www.thescienceforum.com/viewtopic.php?t=17769 From reading my posts on this, it looks like im wrestling with the concepts im my own mind, with the same dilemma as the orignal poster in this thread. in the end i dont think it matters. If the future has not occured then what is it deviating from? like Dr rocket said the question is not entirely sound. there is the fallacy of human constructions hiding behind questions like these. butI think im just making an excuse so that my brain does not have get bogged down in it ever again! :-D 56. We cannot change something that did not yet happen. We cannot change the past, for then it did not pass. Conclusion: Time exists only in the sense of our records of past events. 57. the future is infinite potential. how can potential be changed? we must wait until the potential is encoded to our reality as a choice (metaphor lol) before we change it. by that time it isn't the future it's the present. but tomorrow, you could still do anything. Bookmarks ##### Bookmarks Posting Permissions You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement	9,121	43,102	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.59375	3	CC-MAIN-2023-06	latest	en	0.953627
https://studysoup.com/tsg/953150/investigating-astronomy-a-conceptual-view-of-the-universe-1-edition-chapter-2-problem-3	1,660,664,181,000,000,000	text/html	crawl-data/CC-MAIN-2022-33/segments/1659882572408.31/warc/CC-MAIN-20220816151008-20220816181008-00561.warc.gz	498,869,783	14,860	× Log in to StudySoup Get Full Access to Thousands of Study Materials at Your School Join StudySoup for FREE Get Full Access to Thousands of Study Materials at Your School Already have an account? Login here × Reset your password # The hottest stars have a blackbody curve with an intensity that a. peaks at longest ISBN: 9781429210638 427 ## Solution for problem 3 Chapter 2 Investigating Astronomy: A Conceptual View of the Universe \| 1st Edition • Textbook Solutions • 2901 Step-by-step solutions solved by professors and subject experts • Get 24/7 help from StudySoup virtual teaching assistants Investigating Astronomy: A Conceptual View of the Universe \| 1st Edition 4 5 1 301 Reviews 22 0 Problem 3 The hottest stars have a blackbody curve with an intensity that a. peaks at longest wavelengths. b. peaks at shortest wavelengths. c. is nearly identical to cooler stars. d. peaks in the blue-green region. Step-by-Step Solution: Step 1 of 3 L4 %f is usually 6 decimal places Type, help then a word to get an explanation form MATLAB rd Law of cosines: given two sides and an angle, find 3 side a^2 =b^2 + c^2 -2bccos(A) HW1: If statements -> flow control-> changes the order of execution -conditional logic-> run certain code snippets depending on an answer to a question Syntax: if(Keyword) condition statement (just a question, if the answer is true then do this code) end(keyword) If condition statementA (if question is true) else (if question was false) statementB How to ask questions: Syntax: If variable/equation operator variable/equation Operator: < > <= >= ~= (not equal) == (both are the same) *(= vs. ==, = assigns (change the left hand side), == equality (checks if these things are the same)) -Compound conditions: and=&& or =\|\| -Possible to put if statements inside of if statements 3) if conditionA (statementA) elseif condition(statementB) elseif conditonC (statementC) … Else last statement end Step 2 of 3 Step 3 of 3 ##### ISBN: 9781429210638 The answer to “The hottest stars have a blackbody curve with an intensity that a. peaks at longest wavelengths. b. peaks at shortest wavelengths. c. is nearly identical to cooler stars. d. peaks in the blue-green region.” is broken down into a number of easy to follow steps, and 34 words. Since the solution to 3 from 2 chapter was answered, more than 234 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Investigating Astronomy: A Conceptual View of the Universe, edition: 1. The full step-by-step solution to problem: 3 from chapter: 2 was answered by , our top Science solution expert on 03/14/18, 08:06PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 15 chapters, and 213 solutions. Investigating Astronomy: A Conceptual View of the Universe was written by and is associated to the ISBN: 9781429210638. ## Discover and learn what students are asking Calculus: Early Transcendental Functions : Directional Derivatives and Gradients ?In Exercises 13 - 18, find the gradient of the function at the given point. $$w=3 x^{2}-5 y^{2}+2 z^{2}, \quad(1,1,-2)$$ Calculus: Early Transcendental Functions : Conservative Vector Fields and Independence of Path ?In Exercises 1 - 4, show that the value of $$\int_{C} F \cdot d r$$ is the same for each parametric representation of C. \(\mathbf{F}(x, y)=\ Statistics: Informed Decisions Using Data : Data Collection ?In Problems 1–5, provide a definition using your own words. 5. Designed experiment Statistics: Informed Decisions Using Data : Data Collection ?List and describe the three major types of observational studies. Statistics: Informed Decisions Using Data : Testing the Significance of the Least-Squares Regression Model ?Why don’t we conduct inference on the linear correlation coefficient? #### Related chapters Unlock Textbook Solution Enter your email below to unlock your verified solution to: The hottest stars have a blackbody curve with an intensity that a. peaks at longest	987	4,047	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.5	4	CC-MAIN-2022-33	latest	en	0.792817
https://ti.inf.ethz.ch/ew/mise/mittagssem.html?action=show&what=abstract&id=5aca0757326be1ab11ff9f918acf6ca1ad74695e	1,726,671,767,000,000,000	text/html	crawl-data/CC-MAIN-2024-38/segments/1725700651899.75/warc/CC-MAIN-20240918133146-20240918163146-00862.warc.gz	512,058,337	4,287	## Theory of Combinatorial Algorithms Prof. Emo Welzl and Prof. Bernd Gärtner # Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer) Mittagsseminar Talk Information Date and Time: Thursday, March 08, 2018, 12:15 pm Duration: 30 minutes Location: OAT S15/S16/S17 Speaker: Florian Meier ## Even flying cops should think ahead We study the following version of cops and robbers, called the entanglement game, on sparse directed and undirected graphs. First, the robber chooses a starting position and the k cops are outside the graph. In every turn, the cops can either stay where they are, or they can fly one of them to the current position of the robber. Regardless of whether the cops stayed or one of them flew to the location of the robber, the robber then has to move to a neighbor of his current position that is not occupied by a cop. If there is no such neighbor, the cops win. The robber wins if he can run away from the cops indefinitely. While the minimum degree of a graph G is a trivial lower bound for the number of cops needed to catch a robber in G, we show that the required number of cops can be much larger, even for graphs with small maximum degree. In particular, we show that there are 3-regular graphs where a linear number of cops are needed. The presented results are joint work with Anders, Patrick and Angelika. Information for students and suggested topics for student talks	336	1,434	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.921875	3	CC-MAIN-2024-38	latest	en	0.932126
http://www.homeworkrank.com/ecet-210	1,601,153,255,000,000,000	text/html	crawl-data/CC-MAIN-2020-40/segments/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00713.warc.gz	173,859,678	5,604	Shopping Cart # ECET 210 ECET 210 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 1 Homework NEW Chapter 13 2. For the sinusoidal signal in Fig. 13.82: a.. \$11.99 \$5.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 1 iLab AC Fundamentals, Sinusoidal and Other Waveform Characteristics NEW Lab.. \$0.00 \$5.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 2 Homework NEW Chapter 15, 2, 4a-4c, 16a-16g, 18 Find the current i&n.. \$11.99 \$5.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 2 iLab NEW Objectives: To analyze a series AC circuit is containing an .. \$11.99 \$5.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 3 iLab Analysis of AC Parallel RLC Circuit using Simulation and Construction NEW.. \$11.99 \$5.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 4 Homework NEW Problem 2 page 735 Problem 8 page 739 Problem 2 page 908.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 4 iLab Analysis of AC Series and Parallel RLC Resonance Circuits using Simulatio.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 5 Homework NEW Chapter 17: 2, 4 & 6 2. Convert the voltage source in F.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 5 iLab Verification of Network Theorems by Simulation NEW iLab: Verifica.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 6 Homework NEW Chapter 21: Problem 10: A power level of 100 W is 6 dB abov.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 6 iLab 6 NEW .. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 6 iLab Frequency Response of Low Pass, High Pass, and Band Pass Filters NEW O.. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 7 Homework Part 1 NEW .. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 7 Homework Part 2 NEW .. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 7 Homework NEW Homework Week 7 Chapter 22 # 6, 8, 10, 12 Homework Sheet 6... \$11.99 \$6.99 This Tutorial was Purchased: 6 Times Rated:A+ by student like you. ECET 210 Week 7 iLab 7 NEW .. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 7 iLab Voltage Rectifier and Voltage Regulation Circuits NEW Objectives: .. \$11.99 \$6.99 This Tutorial was Purchased: 3 Times Rated:A+ by student like you. ECET 210 Week 3 Homework NEW Find the total admittance for the networks of Fig. 15.142. Identify .. \$11.99 \$5.99	940	2,947	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.765625	3	CC-MAIN-2020-40	latest	en	0.884876
https://ask.libreoffice.org/en/question/133104/add-to-total-if-there-is-data-in-another-field/	1,571,226,979,000,000,000	text/html	crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00047.warc.gz	385,056,416	14,359	Add to total if there is data in another field? Hi all, first post so please excuse the long winded version that ensues! ... I sell books and have a spreadsheet with the data I need, such as title, ISBN, cost price, sell price, P&P, profit, etc. I have a column with the "potential profit" based on making a sale, then another column with "actual profit" which I populate when I actually make the sale. I originally totalled the column for "sell price" but this obviously gives me the total potential sale value of all the books, not the actual sale value and I could potentially create another column and populate this with the sale value when I sell a book like I do for potential profit and actual profit but would there be a way to have a running total of the sales column based on an entry in the "actual profit" column. So, for example, I have my "sell price" column, my "potential profit" column and "actual profit" column. When I make a sale, I enter the amount I made in profit in the "actual profit" column and a formula recognised I've entered something in that column and then add's the "sell price" to a total at the top of the sheet. Another sale, another entry in another "actual profit" column and another addition to the sell total. All the data concerning the individual books are on one line of course, such as title A1, ISBN B1, Sell Price C1, Potential Profit D1, Actual Profit E1, etc. Hope this all makes sense :) Mark edit retag close merge delete Sort by » oldest newest most voted The function you're looking for is called SUMIF. In the example below, the formula for F2 is =SUMIF(E2:E5,">0",C2:C5). title ISBN Sell Price Potential Profit Actual Profit Sell Total ~~~~~~ ~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~ ~~~~~~~~~~ Book A 123456789 $5.00$2.00 $25.00 Book B 123456788$10.00 $3.00$2.50 Book C 123456787 $15.00$4.00 $3.50 Book D 123456786$20.00 \$5.00 more	500	1,992	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2019-43	latest	en	0.863215
https://wordnik.com/words/secant	1,524,686,936,000,000,000	text/html	crawl-data/CC-MAIN-2018-17/segments/1524125947957.81/warc/CC-MAIN-20180425193720-20180425213720-00354.warc.gz	705,999,237	10,941	secant love # secant ## Definitions ### from The American Heritage® Dictionary of the English Language, 4th Edition • n. A straight line intersecting a curve at two or more points. • n. The straight line drawn from the center through one end of a circular arc and intersecting the tangent to the other end of the arc. • n. The ratio of the length of this line to the length of the radius of the circle. • n. The reciprocal of the cosine of an angle in a right triangle. • n. A straight line that intersects a curve at two or more points. • n. In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec ### from the GNU version of the Collaborative International Dictionary of English • adj. Cutting; dividing into two parts. • n. A line that cuts another; especially, a straight line cutting a curve in two or more points. • n. A right line drawn from the center of a circle through one end of a circular arc, and terminated by a tangent drawn from the other end; the number expressing the ratio of this line to the radius of the circle. See Trigonometrical function, under Function. ### from The Century Dictionary and Cyclopedia • Cutting; dividing into two parts. • n. A line which cuts a figure in any way. • n. Specifically, in trigonometry, a line from the center of a circle through one extremity of an are (whose secant it is said to be) to the tangent from the other extremity of the same are; or the ratio of this line to the radius; the reciprocal of the cosine. • Specifically, noting a stream which cuts across folded strata. • n. ratio of the hypotenuse to the adjacent side of a right-angled triangle • n. a straight line that intersects a curve at two or more points ## Etymologies ### from The American Heritage® Dictionary of the English Language, 4th Edition From Latin secāns, secant-, present participle of secāre, to cut. From Latin secans, present participle of secare ("to cut")	454	1,932	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.140625	3	CC-MAIN-2018-17	latest	en	0.846008
http://mathworkorange.com/division-of-mathematics.html	1,521,663,398,000,000,000	text/html	crawl-data/CC-MAIN-2018-13/segments/1521257647692.51/warc/CC-MAIN-20180321195830-20180321215830-00541.warc.gz	189,992,036	11,404	# Your Math Help is on the Way! ### More Math Help Try the Free Math Solver or Scroll down to Tutorials! Depdendent Variable Number of equations to solve: 23456789 Equ. #1: Equ. #2: Equ. #3: Equ. #4: Equ. #5: Equ. #6: Equ. #7: Equ. #8: Equ. #9: Solve for: Dependent Variable Number of inequalities to solve: 23456789 Ineq. #1: Ineq. #2: Ineq. #3: Ineq. #4: Ineq. #5: Ineq. #6: Ineq. #7: Ineq. #8: Ineq. #9: Solve for: Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg: # Division of Mathematics algebraically whenever possible. You have at most 80 minutes to take this 100 point exam. No cellular phones allowed. The exam questions are 100 points. Don't forget to sign your exam! 1. Given answer each of the following questions. (a) Rewrite this logarithmic equation in exponential form. That is, solve for x. Work: So, we finally have (b) Create a simple table, or list, of at least five ordered pairs (x, y) that are solutions to Work: Using and using easy values for y, I get: (c) Graph f (x) and be sure to clearly indicate at least one point and all asymptotes. Work: 2. Given answer each of the following questions. (a) What is the y-intercept? Work: Set x = 0, and evaluate to find y. (0, 2) (b) What are the x-intercepts? Work: Set y = 0, and evaluate to find x. (-4, 0) and (1/2, 0) (c) What is the equation of the horizontal asymptote? Work: This is found by taking a look at two limits, one where and the other . If you do this you will see that both limits equal 2. So the horizontal asymptote is y = 2 . and (d) What are the equations of the two vertical asymptotes? Work: Four limits required. So the vertical asymptotes are: x = 1 and x = -2 . (e) What is the domain of f (x)? Work: (f) Graph f (x) and be sure to clearly indicate at least one point and all asymptotes. Work: (g) What is the range of f (x)? Work: R 3. Given and its graph. Answer each of the following questions. (a) What is the y-intercept? Work: Just set x = 0 and you'll get (0, 36) . (b) Using the Rational Root Theorem, what are the candidate rational roots? Work: Writing the ratios out. Then you'll need to figure out the set. (c) Using the graph, and your answers from (b), what are reasonable candidates for rational roots. Test them to see if they actually are. Work: You should be able to roughly determine the values of the candidate rational roots by looking at the graph, and -3, 2, -3/2 and 3/2 are good candidates if they're rational. Testing them shows that only three of these are. (d) Using (c), factor f (x) completely. Work: Now we know that x+3, 2x+3, x-2 are factors of f. Just use long division to find the missing quadratic factor. (e) List all roots, real and imaginary. Work: From above. Here's a close-up of the region between -2 and -1. You should notice the two roots, what are they? You should also look back at the original graph on page one.	842	3,028	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.96875	4	CC-MAIN-2018-13	latest	en	0.897928
http://www.java-gaming.org/topics/id/28991/msg/264958/rev/1/view.html	1,550,528,679,000,000,000	text/html	crawl-data/CC-MAIN-2019-09/segments/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00553.warc.gz	373,119,387	25,830	Java-Gaming.org Hi ! Featured games (90) games approved by the League of Dukes Games in Showcase (780) Games in Android Showcase (233) games submitted by our members Games in WIP (857) games currently in development News: Read the Java Gaming Resources, or peek at the official Java tutorials Pages: [1] ignore \| Print Complex number cookbook (Read 25099 times) 0 Members and 1 Guest are viewing this topic. Wiki Duke ? « Posted 2013-03-14 16:44:34 » Note: you are watching revision 1 of this wiki entry. ( view plain diff ) By representing an orientation (or rotation) by a complex number instead of an explicit angle we can drop a fair number of expensive operations. So instead of storing angle 'a', we store complex number (cos(a), sin(a)). Another potential advantage is the algebra framework (just manipulating algebra) and reasoning. Algebra's like complex number, vectors, quaternions, etc allow thinking in terms of relative information which can greatly simplify the process. We will assume that standard mathematical convention of the X axis pointing the to right and the Y axis pointing up. Additionally we will assume that the reference orientation of objects is pointing straight right. Combining these together when thinking about some specific entity, we can think in terms of its center being at the origin and its facing straight down the X axis. NOTE: Although angles are talked about, this is for understanding and thinking purposes and not computation. Common definitions Capital letter are complex number and small are scalars. X=(a,b) Y=(c,d) P=(x,y) R=(cos(a), sin(a)) S=(cos(b), sin(b)) ## Complex number basics Complex numbers are represented by two numbers, which we will denote as a pair (a,b). The first number we will call 'x' and the second 'y'. Conjugate X* = (a,b)* = (a,-b) R* = (cos(a),sin(a))* = (cos(a),-sin(a)) = (cos(-a),sin(-a)) So the conjugate reflects (wikipedia) about the X axis, which is the same as negating the angular information. (SEE: Trig identities: Symmetry) X+Y = (a,b)+(c,d) = (a+c,b+d) X-Y = (a,b)-(c,d) = (a-c,b-d) Operation is component-wise. Can represent translation. Product XY = (a,b)(c,d) RP = (cos(a), sin(a))(x,y) = (x cos(a) - y sin(a), y cos(a) + x sin(a)) RS = (cos(a), sin(a))(cos(b), sin(b)) = (cos(a)cos(b) - sin(a)sin(b), cos(b)sin(a) + cos(a)sin(b)) = (cos(a+b), sin(a+b)) So the product sums the angular information of the two inputs. (SEE: Trig identities: angle sum) Product combined with conjugate XY = (a,b)(c,d) = (a,-b)(c,d) = (ac+bd, ad-bc) RS = (cos(a),sin(a))(cos(b),sin(b)) = (cos(-a),sin(-a))(cos(b),sin(b)) = (cos(a)cos(b)+sin(a)sin(b), -cos(b)sin(a)+cos(a)sin(b)) = (cos(b-a),sin(b-a)) Since we can add angles with the product and can negate an angle with the conjugate, the two together allow us to subtract angles. (AKA get relative angular information) Magnitude (L2 norm) \|X\| = \|XX\| = \|(a,b)(a,-b)\| = sqrt(a2+b2) Notice that we're not calling this length. Complex numbers, vectors, etc do not have lengths (nor positions). What they represent in a give instance might have a length equal to its magnitude. Unit complex and trig form Unit complex numbers have a magnitude of one and can be written in 'trig form': (cos(t),sin(t)). Since scale factors can be pulled out (see scalar product) all complex numbers can also be written in 'trig form': m(cos(t),sin(t)). Scalar product sX = s(a,b) = (s,0)(a,b) = (sa, sb) This can be reversed, so all scale factors can be pulled out. Inverse 1/X = X/(XX) = (a,-b)/(a2+b2) 1/R = (cos(-a),sin(-a))/(cos(a)2+sin(a)2) = (cos(-a),sin(-a)) = R The multiplicative inverse of a unit complex is the same as its conjugate. Counterclockwise rotation of point about the origin Falls directly out of the product. Given rotation (R) and point (P), the point after rotation (P'): P' = RP = (cos(a), sin(a))(x,y) = (x cos(a) - y sin(a), y cos(a) + x sin(a)) Example: P = (3,3) R = (cos(pi/4), sin(pi/4)) = (.707107, .707107) P' = (3,3)(.707107, .707107) = (0, 4.24264) How do I find rotation of A into B Solve the above. Assuming A & B are unit vectors: RA = B R = B(1/A) R = BA Example: A = (0.809017, 0.587785) B = (0.5, -0.866025) R = BA* = (0.5, -0.866025)(0.809017, 0.587785)* = (0.5, -0.866025)(0.809017, -0.587785) = (-0.104528, -0.994522) Counterclockwise rotation of point about arbitrary point We can rotate about the origin, to rotate about an arbitrary point (C) translate the system to the origin, perform the rotation and then undo the translation. P' = R(P-C)+C = RP-RC+C = RP+C-RC = RP+C(1-R) = RP+T where T = C(1-R). Look at the last line. It is telling you that the rotation R about point C is equivalent to a rotation about the origin R followed by a translation T. And C is recoverable from T & R: C = T/(1-R) (assuming R isn't 1...or no rotation). Composition of rotations Falls directly out of the product. Given rotation (R) followed by rotation (S): RS = (cos(a+b), sin(a+b)) Relation to dot and cross products Falls directly from the product where one is conjugated: XY = (a,b)(c,d) = (a,-b)(c,d) = (ac+bd, ad-bc) dot(X,Y) = ac+bd The dot product is the parallel projection and the cross is the orthogonal projection. ## Basic examples At the top we say we can represent an entity by its position and orientation and think about it as being at the origin and facing straight down the X axis (the reason for this is because that's the entity's local coordinate frame). Let's call it's position E and orientation F and we have some test point P. We can translate the system to the origin (P-E) and then we can undo the rotation of the system by multiplying by F, which gives us: (P-E)F. So P in the reference frame of our entity is: P' = (P-E)F* Example: P = (100,100) E = (200,200) F = (.92388, .382683) <- Pi/8 or 22.5 degrees P' = ((200,200)-(100,100))(.92388, -.382683) = (130.656, 54.1196) If you've ever worked with vectors, this should seem similar: find the delta distance and perform the dot and/or cross product. The above equation is finding the delta distance and then effectively computing both. (Obviously you only compute one if only need one). So the dot product is simply the 'x' coordinate in the local coordinate frame (parallel projection) and the cross is the 'y' coordinate (orthogonal projection). What's my unit direction vector? It's pretending the unit complex number of the orientation is a unit vector. It has the same numeric values for 'x' & 'y'. Is it behind me? As noted above the dot product is 'x' in the local coordinate frame, so the sign of the dot product. If negative it's behind the center point with respect to facing and positive if forward. Turn clockwise or counterclockwise? As noted above the cross product is 'y' in the local coordinate frame, so the sign of the cross product. If positive the shortest turn is counter clockwise, if negative it's clockwise and if zero it's straight ahead. Turn toward point with constant angular velocity Again, the sign of cross product tells the minimum direction. Take a constant angular velocity, store as a unit complex number 'A'. If the sign of the cross product is negative, we need to conjugate A (negate it's 'y' component). Multiply the current facing 'F' by the potentially modified 'A'. Take our new 'F' and cross again. If the sign has changed, we've overshot the target. delt0r JGO Wizard Medals: 145 Exp: 18 years Computers can do that? « Reply #1 - Posted 2013-03-14 17:04:55 » That is a pretty complicated intro/explanation. Really for representing angles you can keep it much simpler. Forget useless definitions like complex numbers don't have length. Who cares? You can interpret them as a vector, in which case they do. They are just a vector pointing in the direction they represent. By some fluke of math, complex multiplication is the same as adding angles. Division is subtracting angles. Pure interpolation with normalization works well enough for interpolation. The real part is the same as cos, the imaginary part the same as sin. tan=sin/cos. To compare to angles we use the fact that atan2(x,y) >=< tan2(x',y') is the same as comparing y/x to y'/x'. Just take care of the degen you get with x tending to 0 and really compare yx' to y'x and you get the same result. Now you can check to see if something is withing a bracketed set of angles. Perhaps i should expand a little. But really i don't even follow the why of what is the previous post. I have no special talents. I am only passionately curious.--Albert Einstein Roquen JGO Kernel Medals: 518 « Reply #2 - Posted 2013-03-15 15:34:53 » Some suggesting on how to make it easier to understand would be helpful. This is a wiki page and I certainly won't cry if you modify it. To address some of your points. Why mention length != mag? Because un-learning stuff you've learned wrong is hard and lots of text say vectors have lengths and/or are centered at the 'origin' and make it sound like direction and position vectors are somehow different things. And I've seen people struggle to unlearn stuff they've mis-learned. Personally I had a heck of of time unlearning that the cross product of vectors in 3-space isn't a vector and wish someone would has said something like: "the cross product of two vectors is a bi-vector. What's a bi-vector? Something we're going to pretend is a vector for the moment. Don't worry about it for now, just keep this is the back of your head.". But having said that, I don't have any strong opinion about keeping that sentence...it's simply my reasoning for having there in the first place.zZ Quote By some fluke of math, complex multiplication is the same as adding angles. Division is subtracting angles. I don't like black boxes. You give people black-boxes they're stuck with what you've spoon feed them. As examples, consider the three reflection implementations from my toy complex class: here. Or the rectangle vs. point and circles intersection tests. Quote Pure interpolation with normalization works well enough for interpolation. Here I assume you mean for angle parametrization: lerp instead of slerp. While true for probably most cases, I'm of the opinion that it's better to understand how slerp works and want you get if you straight lerp instead. As an example, a many entity game could have a simulation rate as low as 10 Hz, with smoothing on the rendering side. Straight lerp is highly likely to cause noticeable defects. Of course this is easy to fix, but you only can if you understand how the parts work. Quote The real part is the same as cos, the imaginary part the same as sin. I like to avoid using "real" and "imaginary" as I find terminology is a source of confusion. Forget "i". Quote To compare to angles we use the fact that atan2(x,y) >=< tan2(x',y') is the same as comparing y/x to y'/x'. Just take care of the degen you get with x tending to 0 and really compare yx' to y'x and you get the same result. I'm slow today and am not understanding what you're saying here. Roquen JGO Kernel Medals: 518 « Reply #3 - Posted 2013-03-19 16:24:09 » Added a couple of examples: field-of-view and point/line test with supporting stuff. matheus23 JGO Kernel Medals: 138 Projects: 3 You think about my Avatar right now! « Reply #4 - Posted 2014-04-15 08:49:26 » I think it's really hard to understand without any pictures describing what is going on. I have to do this in my mind and that only works if I have already understood it. It's the Bret-Victor-Syndrom I'm talking about Someone made a really nice intro to Complex numbers and why they can be used to represent sqrt(-1) and how we should picture them: http://acko.net/blog/how-to-fold-a-julia-fractal/ See the first Presentation on that page (Initially shows the number line). You might like other things from him as well, so check his blog out, he does exactly what Bret Victor initially encouraged to do See my: My development Blog: \| Or look at my RPG \| Or simply my coding http://matheusdev.tumblr.comRuins of Revenge \| On Github Roquen JGO Kernel Medals: 518 « Reply #5 - Posted 2014-04-15 13:22:08 » Yeah I've seen that site. Diagrams are great and very helpful...interactive is even better. And I can't motivate myself to do either. matheus23 JGO Kernel Medals: 138 Projects: 3 You think about my Avatar right now! « Reply #6 - Posted 2014-04-15 13:32:19 » Yeah I've seen that site. Diagrams are great and very helpful...interactive is even better. And I can't motivate myself to do either. See my: My development Blog: \| Or look at my RPG \| Or simply my coding http://matheusdev.tumblr.comRuins of Revenge \| On Github Roquen JGO Kernel Medals: 518 « Reply #7 - Posted 2014-04-17 14:05:43 » Think about integers for a second. We start with 0 (or 1 depending on who to talk to) and they're formed by repeatedly adding 1. Each time giving you the next number in the sequence. Then you get wild-and-crazy and extend the concept to extend in the negative direction. Negative numbers! What? You can't say have a negative number of cows!! Madness! At least to the ancient greek math-heads it was...they didn't have the concept. Now jump to complex numbers. Constructed by using two instead of one number where the 'second' has a magic basis that squares to -1. Placing special "meaning" to the sqrt(-1) in complex numbers is the same as placing special meaning to subtracting 1 in integers. Neither are interesting as operations. The sqrt(-1) is meaningless in reals just as you can't give away a cow you don't have. Riven « JGO Overlord » Medals: 1357 Projects: 4 Exp: 16 years « Reply #8 - Posted 2014-04-17 14:33:36 » <offtopic> Unless you are among the federal farmers, which can accumulate cow-depth by loaning imaginary cows to peasants, skimming off the milk for profits. </offtopic> In other news: blasting newbies with a 'succinct specification' is a sure way to turn them off. It doesn't really matter whether you are correct, if your audience can't follow your step by step reasoning. A few visualisations will help enlighten them, but given the amount of work required, and the already available resources on the internet, I doubt anybody here would be willing to make the effort. Hi, appreciate more people! Σ ♥ = ¾ Learn how to award medals... and work your way up the social rankings! Roquen JGO Kernel Medals: 518 « Reply #9 - Posted 2014-04-17 14:42:10 » Yeah: I know. My main barrier is I doubt that enough people would bother to understand even with "aids" to make the effort worthwhile. Pages: [1] ignore \| Print hadezbladez (1139 views) 2018-11-16 13:46:03 hadezbladez (509 views) 2018-11-16 13:41:33 hadezbladez (1144 views) 2018-11-16 13:35:35 hadezbladez (258 views) 2018-11-16 13:32:03 EgonOlsen (2552 views) 2018-06-10 19:43:48 EgonOlsen (2754 views) 2018-06-10 19:43:44 EgonOlsen (1552 views) 2018-06-10 19:43:20 DesertCoockie (2256 views) 2018-05-13 18:23:11 nelsongames (2091 views) 2018-04-24 18:15:36 nelsongames (2787 views) 2018-04-24 18:14:32 Deployment and Packagingby philfrei2019-02-17 20:25:53Deployment and Packagingby mudlee2018-08-22 18:09:50Java Gaming Resourcesby gouessej2018-08-22 08:19:41Deployment and Packagingby gouessej2018-08-22 08:04:08Deployment and Packagingby gouessej2018-08-22 08:03:45Deployment and Packagingby philfrei2018-08-20 02:33:38Deployment and Packagingby philfrei2018-08-20 02:29:55Deployment and Packagingby philfrei2018-08-19 23:56:20 java-gaming.org is not responsible for the content posted by its members, including references to external websites, and other references that may or may not have a relation with our primarily gaming and game production oriented community. inquiries and complaints can be sent via email to the info‑account of the company managing the website of java‑gaming.org	4,386	15,913	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.3125	3	CC-MAIN-2019-09	latest	en	0.885057
https://riddles360.com/riddle/find-the-number-6194	1,695,608,715,000,000,000	text/html	crawl-data/CC-MAIN-2023-40/segments/1695233506676.95/warc/CC-MAIN-20230925015430-20230925045430-00795.warc.gz	546,315,131	7,703	# Find The Number I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number: First digits is divisible by 1. First two digits are divisible by 2. First three digits are divisible by 3. First four digits are divisible by 4. First five digits are divisible by 5. First six digits are divisible by 6. First seven digits are divisible by 7. First eight digits are divisible by 8. First nine digits are divisible by 9. The number is divisible by 10. Can you find out the number ? # Similar Riddles ##### Prisoner to be freed The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another. "In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything. "After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell. "No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead. "Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.' "If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you" What is the strategy they come up with so that they can be free? Asked by Neha on 10 May 2021 ##### Analytical Riddle John buys rice at Rs.60/kg from Britain and then sells them at Rs.5/kg in India. As a result of this, he becomes a millionaire. How come? Asked by Neha on 22 Jun 2023 ##### Biased Coin Puzzle A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result. Can you find how bias is the floor in this case? Asked by Neha on 15 Feb 2023 ##### Judge the Age How old is your son? asked a man to his neighbour. My son is five times as old as my daughter and my wife is five times as old as my son. I am twice as old as my wife whereas my grandmother, who is celebrating her eighty-first birthday is as old as all of us put together. How old is the man's son ? Asked by Neha on 17 May 2021 ##### Label the Boses There are three boxes which are labeled as Rs100, Rs150, and Rs200. One box contains two notes of Rs. 50. The second box contains one note of Rs50 and one note of Rs100 The third box contains two Rs. 100 notes. All boxes are labeled incorrectly. What is the minimum number of boxes you must check in order to label all boxes correctly? Asked by Neha on 02 Feb 2021 ##### Next Child Name Problem A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly? Asked by Neha on 29 Mar 2023 ##### Thief in Akbar Emperor One day, all the courtiers from Akbar's court were gathered in the assembly hall when one of them told the Emperor that all his valuables had been stolen by a thief the previous night. This shocked the Emperor to his core as the place where that courter stayed was the most secured in the kingdom. The Emperor thought that it is not at all possible for an outsider to enter into the courtier's house and steal the valuables. Only another courtier could commit this crime. He quickly called Birbal to identify the thief. Birbal thought for a while and successfully solved the mystery by identifying the thief in just one statement. What did Birbal say? Asked by Neha on 17 May 2021 Which is the correct shadow of the bird? Asked by Neha on 23 Aug 2021 ##### The sum of the Numbers Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal? Note: 9 cannot be turned over to make it 6. Asked by Neha on 19 Jul 2023 ##### Magic Math A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396. What is the sum of the three digits? Asked by Neha on 13 Dec 2020 ### Amazing Facts ###### Gamers In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.	1,251	5,198	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.515625	4	CC-MAIN-2023-40	longest	en	0.958027
https://www.daniweb.com/programming/software-development/threads/446681/double-precision	1,548,161,439,000,000,000	text/html	crawl-data/CC-MAIN-2019-04/segments/1547583850393.61/warc/CC-MAIN-20190122120040-20190122142040-00277.warc.gz	774,699,046	14,925	i want to print a 'double' variable upto 8 decimal places without trailing zeroes. for eg: if a= 10.1234 then print 10.1234 if a= 10.00 then print 10 if a= 10.11111111111 then print 10.11111111 (max of 8 decimal places). how to do it? i searched for it and found this: printf("%g",a); this work fine but print upto 6 decimal places. Off the top of my head, I'm going to say that it's not possible to mix and match %f (which supports a precision) and %g (which has a zero removal rule). You'd need to use a less direct solution, such as sprintf() followed by a right trim of zeros. From the Linux fprintf() man page: `````` The flag characters The character % is followed by zero or more of the following flags: # The value should be converted to an "alternate form". For o conversions, the first character of the output string is made zero (by prefixing a 0 if it was not zero already). For x and X conversions, a non-zero result has the string "0x" (or "0X" for X conversions) prepended to it. For a, A, e, E, f, F, g, and G conversions, the result will always contain a decimal point, even if no digits follow it (nor- mally, a decimal point appears in the results of those conversions only if a digit follows). For g and G conversions, trailing zeros are not removed from the result as they would otherwise be. For other conversions, the result is undefined. 0 The value should be zero padded. For d, i, o, u, x, X, a, A, e, E, f, F, g, and G conversions, the con- verted value is padded on the left with zeros rather than blanks. If the 0 and - flags both appear, the 0 flag is ignored. If a precision is given with a numeric conversion (d, i, o, u, x, and X), the 0 flag is ignored. For other conversions, the behavior is undefined. - The converted value is to be left adjusted on the field boundary. (The default is right justification.) Except for n conversions, the converted value is padded on the right with blanks, rather than on the left with blanks or zeros. A - overrides a 0 if both are given. ' ' (a space) A blank should be left before a positive number (or empty string) produced by a signed conver- sion. + A sign (+ or -) should always be placed before a number produced by a signed conversion. By default a sign is used only for negative numbers. A + overrides a space if both are used. The five flag characters above are defined in the C standard. The SUSv2 specifies one further flag character. ' For decimal conversion (i, d, u, f, F, g, G) the output is to be grouped with thousands’ grouping char- acters if the locale information indicates any. Note that many versions of gcc(1) cannot parse this option and will issue a warning. SUSv2 does not include %'F. glibc 2.2 adds one further flag character. I For decimal integer conversion (i, d, u) the output uses the locale’s alternative output digits, if any. For example, since glibc 2.2.3 this will give Arabic-Indic digits in the Persian ("fa_IR") locale. The field width An optional decimal digit string (with non-zero first digit) specifying a minimum field width. If the con- verted value has fewer characters than the field width, it will be padded with spaces on the left (or right, if the left-adjustment flag has been given). Instead of a decimal digit string one may write "" or "m\$" (for some decimal integer m) to specify that the field width is given in the next argument, or in the m-th argument, respectively, which must be of type int. A negative field width is taken as a '-' flag followed by a positive field width. In no case does a nonexistent or small field width cause truncation of a field; if the result of a conversion is wider than the field width, the field is expanded to contain the conversion result. The precision An optional precision, in the form of a period ('.') followed by an optional decimal digit string. Instead of a decimal digit string one may write "" or "m\$" (for some decimal integer m) to specify that the precision is given in the next argument, or in the m-th argument, respectively, which must be of type int. If the precision is given as just '.', or the precision is negative, the precision is taken to be zero. This gives the minimum number of digits to appear for d, i, o, u, x, and X conversions, the number of digits to appear after the radix character for a, A, e, E, f, and F conversions, the maximum number of significant digits for g and G conver- sions, or the maximum number of characters to be printed from a string for s and S conversions. The length modifier Here, "integer conversion" stands for d, i, o, u, x, or X conversion. hh A following integer conversion corresponds to a signed char or unsigned char argument, or a following n conversion corresponds to a pointer to a signed char argument. h A following integer conversion corresponds to a short int or unsigned short int argument, or a following n conversion corresponds to a pointer to a short int argument. l (ell) A following integer conversion corresponds to a long int or unsigned long int argument, or a fol- lowing n conversion corresponds to a pointer to a long int argument, or a following c conversion corre- sponds to a wint_t argument, or a following s conversion corresponds to a pointer to wchar_t argument. ll (ell-ell). A following integer conversion corresponds to a long long int or unsigned long long int argument, or a following n conversion corresponds to a pointer to a long long int argument. L A following a, A, e, E, f, F, g, or G conversion corresponds to a long double argument. (C99 allows %LF, but SUSv2 does not.) q ("quad". 4.4BSD and Linux libc5 only. Don’t use.) This is a synonym for ll. j A following integer conversion corresponds to an intmax_t or uintmax_t argument. z A following integer conversion corresponds to a size_t or ssize_t argument. (Linux libc5 has Z with this meaning. Don’t use it.) t A following integer conversion corresponds to a ptrdiff_t argument. `````` Pay special attention to the "precision" and "field width" specs above. Pay special attention to the "precision" and "field width" specs above. No disrespect, but unless I'm misreading your post (in which case I apologise) you should follow your own advice. ;) The %f specifier doesn't remove trailing zeros when the precision exceeds the value, and the precision on the %g specifier affects significant digits rather than digits after the radix. So while %g can be used to get the correct behavior, that's only after doing introspection on the value to determine how many whole digits are present: ``````#include <stdio.h> #include <math.h> int main(void) { double a = 1234.567891234; // Quick and dirty digit count int digits = log10((double)(int)a) + 1; printf("%.g\n", 8 + digits, a); return 0; } `````` commented: Good point - haven't had to deal with this cruft in 20 years! :-) +11 @deceptikon can you please explain the printf statement? @deceptikon can you please explain the printf statement? This is the point where I'll suggest that you RTFM, because format strings are clearly and completely described. But, I'll also explain it. The %g specifier selects the behavior of either the %f or %e specifier (that's fixed or scientific format, respectively), depending on the actual value being printed. By default, if the exponent in your value exceeds 6 or -4, %g uses scientific format rather than fixed format. Trailing zeros are omitted, which is behavior you want (%f doesn't provide this). When you provide a precision to the specifier (a dot followed by a numeric value), %g treats that as a maximum number of significant digits, which means both whole number digits and precision digits. For example, the value 123.456 has six significant digits. IF you try to print it with `printf("%.4g", 123.456)`, you'll get 123.4 as output. The numeric value in the precision can be a placeholder for an argument rather than a literal value in the string, that's what the asterisk does. It says "take the next argument to printf() and use that value as the precision". Another way of writing the example above using a placeholder would be `printf("%.g", 4, 123.456)`. All in all, what my example does is calculate the number of digits in the whole value, then adds 8 to this (where 8 corresponds to the number of precision digits you want), then uses that value as the significant digits for the %g specifier. It simulates through value introspection the behavior of the precision for the %f specifier.	2,123	8,632	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2019-04	latest	en	0.857331
https://mathematica.stackexchange.com/questions/278013/how-to-plot-contour-plots-of-r0-against-two-parameters	1,718,771,208,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861797.58/warc/CC-MAIN-20240619025415-20240619055415-00784.warc.gz	345,574,149	38,871	# How to plot contour plots of R0 against two parameters? I am working on an epidemiological model and I would like to know how to plot contour plots of R0 (basic reproduction number) against two given parameters using Mathematica. An example contour plot is given below. The values of the parameters (except beta and gamma) of my model and the formula for R0 are given below. c = 0.01 theta = 0.2778 p = 0.05 phi = 0.95 epsilon = 0.084 delta = 0.011 mu = 0.000027 R0 = (epsiloncbetatheta(mu+(1-phi)p))/(mu(mu+p)(mu+epsilon)(mu+gamma+delta)) I wish to draw the contour plot of R0 against the two parameters beta and gamma which could both vary between 0 and 1. Any help would be greatly appreciated. Thanks a lot in advance! • Try: ContourPlot[R0, {gamma, 0, 1}, {beta, 0, 1}] Commented Dec 31, 2022 at 17:05 Clear["Global"] c = 0.01; theta = 0.2778; p = 0.05; phi = 0.95; epsilon = 0.084; delta = 0.011; mu = 0.000027; R0 = (epsiloncbeta theta(mu + (1 - phi)p))/(mu(mu + p)(mu + epsilon)*(mu + gamma + delta)); ContourPlot[R0, {beta, 0, 1}, {gamma, 0, 1}, FrameLabel -> (Style[#, 14] & /@ {β, γ}), PlotLegends -> BarLegend[Automatic, LegendLabel -> Placed[HoldForm[R0], Bottom]]] ` Compared with the example shown in the question, R0 has much larger values.	424	1,286	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.046875	3	CC-MAIN-2024-26	latest	en	0.79572
https://calculatorshub.net/mechanical-calculators/balance-bead-calculator/	1,718,905,437,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861989.79/warc/CC-MAIN-20240620172726-20240620202726-00599.warc.gz	132,700,340	28,335	Home » Simplify your calculations with ease. » Mechanical Calculators » Balance Bead Calculator: Solution to Accurate Tire Balancing # Balance Bead Calculator: Solution to Accurate Tire Balancing ## Introduction Maintaining well-balanced tires is essential for your vehicle's performance, safety, and longevity. In this blog post, we introduce the Balance Bead Calculator, a handy tool designed to simplify the process of calculating the right amount of balance beads required for tire balancing. Balance beads are small, round beads made from materials like ceramic or glass, which serve as an internal tire balancing system. They sit inside the tire cavity and, as the wheel rotates, the beads distribute themselves evenly within the tire, counterbalancing any heavy spots and providing a smoother ride. ### Benefits of using balance beads 1. Improved tire balance and performance 2. Reduced vibration and road noise 3. Longer tire life due to reduced uneven wear 4. Environmentally friendly, as they are reusable and lead-free ### When to use balance beads Balance beads are suitable for various applications, including: 1. Trucks, SUVs, and RVs 2. Motorcycles and scooters 4. Industrial equipment and trailers ## Using the Balance Bead Calculator Our Balance Bead Calculator uses the following formula to determine the correct amount of balance beads needed for a tire: `BB = TW / 13` Where: • BB: Balance bead weight in ounces • TW: Tire weight in pounds ### Input: Tire weight Enter the tire weight in pounds. You can typically find this information on the tire's sidewall or the manufacturer's website. The calculator will provide the balance bead weight in ounces, based on the tire weight entered. ## Step-by-Step Guide to Using the Calculator 1. Enter the tire weight (in pounds) in the "Tire Weight" input field. 2. Click the "Calculate" button. 3. The "Balance Bead" output field will display the required balance bead weight in ounces. 4. To reset the calculator, click the "Reset" button. This will clear the input and output fields. ## Tips for Properly Installing Balance Beads ### Precautions to take before installation 1. Inspect the tire for damage or wear, as balance beads cannot correct problems caused by structural issues. 2. Remove any existing wheel weights or other balancing materials from the tire. ### Installation process 1. Deflate the tire and break the bead from the rim. 2. Pour the calculated amount of balance beads into the tire using a bead applicator or a DIY funnel. 3. Re-seat the bead and inflate the tire to the manufacturer's recommended pressure. 4. Mount the tire back on the vehicle and enjoy a smoother, more balanced ride. ## Alternative Methods for Tire Balancing 1. Traditional wheel weights: Small weights that attach to the rim, balancing the tire externally. 2. Liquid tire balancing: A liquid compound poured into the tire that distributes itself as the tire rotates, providing balance. ## FAQs Are balance beads safe for all types of tires? Balance beads are generally safe for most tires, but it is always recommended to consult the tire manufacturer or a professional mechanic before using them. How long do balance beads last? Balance beads are designed to last the lifetime of the tire. They can be reused when replacing the tire. Yes, balance beads can be collected and reused in a new tire. What are the possible drawbacks of using balance beads? Some potential drawbacks include possible tire damage if beads clump together, or ineffective balancing if an incorrect amount of beads is used. Additionally, certain tire types, like high-performance or low-profile tires, may not be suitable for balance bead use.	758	3,709	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.171875	3	CC-MAIN-2024-26	latest	en	0.882792
http://math.stackexchange.com/questions/tagged/gauss-sums?sort=votes&pagesize=15	1,469,415,226,000,000,000	text/html	crawl-data/CC-MAIN-2016-30/segments/1469257824201.56/warc/CC-MAIN-20160723071024-00193-ip-10-185-27-174.ec2.internal.warc.gz	149,981,937	26,952	# Tagged Questions For questions on Gauss sums, a particular kind of finite sum of roots of unity. 135 views ### What is the Gauss sum equivalent of $\Gamma(s+1) = s\Gamma(s)$? Gauss sums are analogous to the Gamma function: fix a complex number $s$ with real part $>0$. Then we have a multiplicative character $\chi_s :\mathbf R^{\times}_{>0} \to \mathbf C^\times$ given ... 260 views ### Prime power Gauss sums are zero Fix an odd prime $p$. Then for a positive integer $a$, I can look at the quadratic Legendre symbol Gauss sum $$G_p(a) = \sum_{n \,\bmod\, p} \left( \frac{n}{p} \right) e^{2 \pi i a n / p}$$ where ... 290 views ### Relation that holds for the Legendre symbol of an integer but not for the Jacobi symbol? Let $p$ be a prime number and $\big(\frac{a}{p} \big)$ the Legendre symbol. Then we have the equality $$\sum_{a=1}^{p-1} \big(\frac{a}{p} \big) \zeta^a =\sum_{t=0}^{p-1} \zeta^{t^2},$$ where $\zeta$ ... 140 views ### Gauss Sum of a Field with Four Elements I need to calculate a couple of Gauss sums to solve a problem I'm working on, but I keep getting the wrong answer because the absolute value of what I calculate is impossible for such a sum. Can ... 238 views 61 views 93 views ### Dirichlet character modulo p How can I prove that if $\chi$ is a non-principal character modulo $p$ prime, then $\chi (-1) = \overline{\chi} (-1)= \pm 1$ and $\sum_{x=1}^p \chi (x) e^{2\pi i x}=0$? For the first question, I just ... 379 views 55 views ### Multi-dimensional MLE Guassian I wonder that what is the mu and sigma formula MLE(maximum likelihood estimates) for a 3 dimension guassian ? It is the same form as 1 and 2 dimension (+ 1 mu and sigma for the new vector) ? 40 views 36 views ### Reversing the $T(n) = \frac{n(n+1)}{2}$ formula Can someone reverse this formula? Sorry if it's too basic, i'm an old guy and my math is rusty :-D $s =\frac{n(n+1)}{2}$ If it ain't clear, by reverse I mean obtaining the value of ... 39 views 23 views ### Product of Gauss sums $\tau_p,\tau_q$ Let $p,q$ be different odd primes, and let $\tau_p = \sum\limits_{a=1}^{p}\left(\frac{a}{p}\right)e^{\frac{2\pi ia}{p}}$, $\tau_p = \sum\limits_{b=1}^{q}\left(\frac{b}{q}\right)e^{\frac{2\pi ib}{q}}$. ... 112 views ### Gamma function and Gauss sums In this Wikipedia article appears this : "Gauss sums are the analogues for finite fields of the Gamma function." What was the relation between gamma functions and non-finite fields? 110 views ### Definition: Gauss Sum - Where is the error? In my algebraic number theory lecture we defined Gauss sums as follows. However, I am quite unsure whether this definition is correct. My intuition says "there is a mistake somewhere". I tried double-... 212 views ### Fractions in limits of a summation What if on the sum there is a fraction in the limit? $\sum_{m=k/12}^{k}$ or $\sum_{m=0}^{k/12+1}$ thank you very much! what type of sequence is used for summing this type of interval? 92 views 34 views ### Upper bound for $\frac{\\|x\\|_1}{\\|x\\|_2}$ if each entry of $x\in R^d$ is i.i.d. sampled from Gaussian distribution $N(0,1)$ In the question, $\\|x\\|_1=\sum_{i=1}^d\|x_i\|$ with $\|\cdot\|$ being the absolute value, and $\\|x\\|_2=\sqrt{\sum_{i=1}^d x_i^2}$. In general, $\frac{\\|x\\|_1}{\\|x\\|_2}\leq \sqrt{d}$ always holds for ... 75 views ### Cross-correlation of Gaussian and Jacobian sums I recently came upon the following kind of sum and I'm wondering if anyone has seen it before, or could point out something interesting about them. Let $F$ be a finite field with $q > 2$ elements ... 56 views 12 views ### Summation of gaussians Suppose we have given constants $A_i, x_i (i=1..N)$ Is it possible to approximately calculate the sum of N gaussians in less than N iterations for any x? (may be with some preprocessing) \sum_{i=1}... I have a problem which goes as follows. I am trying to predict the value of a variable $x$. I also have a set of measurements (the actual context is an image) $x^i$. I know from some training ...	1,193	4,016	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.5	4	CC-MAIN-2016-30	latest	en	0.761316
http://www.absoluteastronomy.com/topics/Counting_measure	1,548,315,931,000,000,000	text/html	crawl-data/CC-MAIN-2019-04/segments/1547584519382.88/warc/CC-MAIN-20190124055924-20190124081924-00174.warc.gz	249,800,322	3,612	Counting measure Counting measure Discussion Encyclopedia In mathematics Mathematics Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity... , the counting measure is an intuitive way to put a measure Measure (mathematics) In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume... on any set: the "size" of a subset Subset In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment... is taken to be the number of elements in the subset, if the subset is finite, and ∞ if the subset is infinite. Formally, start with a set Ω and consider the sigma algebra Σ on Ω consisting of all subsets of Ω. Define a measure μ on this sigma algebra by setting μ(A) = \|A\| if A is a finite subset of Ω and μ(A) = ∞ if A is an infinite subset of Ω, where \|A\| denotes the cardinality of set A. Then (Ω, Σ, μ) is a measure space.	328	1,421	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.859375	4	CC-MAIN-2019-04	latest	en	0.898467
http://www.gaussianwaves.com/2011/04/correlative-coding-modified-duobinary-signaling-2/	1,438,503,312,000,000,000	text/html	crawl-data/CC-MAIN-2015-32/segments/1438042989018.48/warc/CC-MAIN-20150728002309-00066-ip-10-236-191-2.ec2.internal.warc.gz	453,079,735	25,004	(1 votes, average: 1.00 out of 5) Modified Duobinary Signaling is an extension of duobinary signaling. Modified Duobinary signaling has the advantage of zero PSD at low frequencies (especially at DC ) which is suitable for channels with poor DC response. It correlates two symbols that are 2T time instants apart, whereas in duobinary signaling, symbols that are 1T apart are correlated. The general condition to achieve zero ISI is given by $$p(nT)=\left\{\begin{matrix} 1,\; n=0\\ 0,\; n\neq 0 \end{matrix}\right.$$ As discussed in a previous article, in correlative coding , the requirement of zero ISI condition is relaxed as a controlled amount of ISI is introduced in the transmitted signal and is counteracted in the receiver side In the case of modified duobinary signaling, the above equation is modified as $$p(nT)=\left\{\begin{matrix} 1,\; n=0,2\\ 0,\; otherwise \end{matrix}\right.$$ which states that the ISI is limited to two alternate samples. Here a controlled or “deterministic” amount of ISI is introduced and hence its effect can be removed upon signal detection at the receiver. ### Modified Duobinary Signaling: The following figure shows the modified duobinary signaling scheme (click to enlarge). Modified DuoBinary Signaling ### Encoding Process: 1) an = binary input bit; an ∈ {0,1}. 2) bn = NRZ polar output of Level converter in the precoder and is given by, $$b_{n}=\left\{\begin{matrix} -d,\; if\;a_{k}=0\\ +d,\; if\; a_{k}=1 \end{matrix}\right.$$ where ak is the precoded output (before level converter). 3) yn can be represented as $$y_{n}=b_{n}+b_{n-2}=\left\{\begin{matrix} 2d , \; \; \; \; if \;a_{k}=a_{k-2}=1\\ 0 , \; \; if \; a_{k}\neq a_{k-2}\\ -2d , \; if \; a_{k}=a_{k-2}=0 \end{matrix}\right.$$ Note that the samples bn are uncorrelated ( i.e either +d for “1″ or -d for “0″ input). On the other-hand,the samples yn are correlated ( i.e. there are three possible values +2d,0,-2d depending on ak and ak-2). Meaning that the modified duobinary encoding correlates present sample ak and the previous input sample ak-2. 4) From the diagram,impulse response of the modified duobinary encoder is computed as $$h(t)=sinc \left( \frac{t}{T} \right )-sinc \left( \frac{t-2T}{T} \right)$$ ### Decoding Process: 5) The receiver consists of a modified duobinary decoder and a postcoder (inverse of precoder).The modified duobinary decoder implements the following equation (which can be deduced from the equation given under step 3 (see above)) $$\hat{b}_{n}=y_{n}-\hat{b}_{n-2}$$ This equation indicates that the decoding process is prone to error propagation as the estimate of present sample relies on the estimate of previous sample. This error propagation is avoided by using a precoder before modified-duobinary encoder at the transmitter and a postcoder after the modified-duobinary decoder. The precoder ties the present sample and the sample that precedes the previous sample ( correlates these two samples) and the postcoder does the reverse process. 6) The entire process of modified-duobinary decoding and the postcoding can be combined together as one algorithm. The following decision rule is used for detecting the original modified-duobinary signal samples {an} from {yn} $$\begin{matrix} if \; y_{n} < d , \;\; then \; \hat{a}_{n}=0\\ if \; y_{n} > d , \;\; then \; \hat{a}_{n}=1\\ if \; y_{n}=0 , \;\; randomly \; guess \; \hat{a}_{n} \end{matrix}$$ ### Matlab code: Check this book for full Matlab code. Simulation of Digital Communication Systems Using Matlab – by Mathuranathan Viswanathan ### Simulation Results: Impulse Response of Modified DuoBinary Signaling Modified DuoBinary Signaling	1,001	3,673	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.171875	3	CC-MAIN-2015-32	longest	en	0.804938
https://kseebsolutions.in/2nd-puc-statistics-model-question-paper-2/	1,670,191,376,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00439.warc.gz	394,242,139	27,706	# 2nd PUC Statistics Model Question Paper 2 with Answers Students can Download 2nd PUC Statistics Model Question Paper 2 with Answers, Karnataka 2nd PUC Statistics Model Question Papers with Answers helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams. ## Karnataka 2nd PUC Statistics Model Question Paper 2 with Answers Time: 3 Hours 15 Minutes Max. Marks: 100 Section – A I. Answer any Ten of the following questions: (10 × 1=10) Question 1. Mention a source of vital statistics. Registration or census method Question 2. What is price relative ? Price relative is the price in the current year expressed as the percentage of the price in the base year. ie„ p = $$\frac{p_{1}}{p_{0}}$$ × 100 Question 3. State the relation between Lapeyere’s, Paasche’s and Fishers index nunbers. Ansewr: p01 (F) = $$\sqrt{\mathrm{p}_{01}(\mathrm{L}) \times \mathrm{p}_{01}(\mathrm{p})}$$ ie., Fisher’s index number is the geometric mean of Laspeyre’s and Passche’s price index numbers. Question 4. Define seasonal variation. Seasonal variations are the variations occurring annually due to the seasons of the year. But also includes the variations of any kind which are periodic in nature and whose period is shorter than one year (t <) year). Question 5. Write down the probability mass function of a Bernoulli distribution. The p.m.f is: p(x) = px q1 – x ; x = 0,1 ,0 < p < 1 and x is a bernoulli variate. Question 6. If mean of a poisson distribution is 4, find its S.D. If Mean = λ = 4 variance; SD (x) = $$\sqrt{\text { variance }}=\sqrt{\lambda}=\sqrt{4}=2$$ Question 7. What is parameter space ? The set of all admissible values of the population parameters is called parameters space. Question 8. Define Acceptance Region? The set of all admissible values of the test statistic, which leads to the acceptance of the null hypothesis is called acceptance region (A.R.) Question 9. If P = 0.5 and n = 100 then find S.E (P) Question 10. Mention one advantage of statistical Quality control. SQC improves the quality of goods and decreases the proportion of defectives. Question 11. Define Optimal Solution of an L.P.P. If a feasible solution which optimises the objectives function Z = CX is called optimal solution. Question 12. What is meant by a fair game? If the value of the game V = 0 the game is called fair. Section – B II. Answer’any Ten of the following questions: (10 × 2 = 20) Question 13. Write two uses of life table. 1. Life tables are used in computation of acturials such as bonus, premium, etc., of insurance policies by insurance agencies. 2. They are used to study the population growth and forecast the size and sex distribution of the population. Question 14. If ΣP1qo = 375 and ΣP0qo = 300, calculate suitable index number. Question 15. Mention the steps involved in the constrction of cost of living index number. • Object and the scope. • Conducting a family budget survey • Obtaining the price Quatation • Methods of construction. Question 16. What is irregular variation ? Give an example. Irregular variations are those changes of time series, which are irregular in nature and do not show any pattern. The causes of irregular variations are due to accidental happenings such as wars, earth quacks, floods, famine, fire accidents, strikes etc., are the examples. Question 17. Expand the Binomial expansion (y – 1)5 (y – 1)5 = y5 – 5y4 + 10y3 – 10y2 + 5y1 – y0 = 0. Question 18. Under what conditions binomial distribution tends to normal distribution? When (i) ‘n’ is large ie., n → ∞ (ii) Neither p nor q are very small ie., p = q with Mean = np = µ and S.D : σ = $$\sqrt{\mathrm{npq}}$$ Question 19. The first two frequency terms of a poisson distribution are 150 and 180 respectively, find the next frequency term. Given : Frequency term : Tx = p(x). N, ie.,T0 =150 and T1 = 180. Usmg recurrence relation: Tx = $$\frac{\lambda}{x}$$Tx-1; T1 = $$\frac{\lambda}{1}$$T0; 180 = λ × 150 ∴ λ = $$\frac{180}{150}$$ = 1.2; The next frequency term : T2 = $$\frac{1.2}{2}$$ × 180 = 180. Question 20. What are type I error and type II error ? Type I error is taking a wrong decision to reject the null hypothesis when it is actually true. Type II error is taking a wrong decision to accept the null hypothesis when it is actually true. Question 21. What are the mean and variance of a chi – square distribution with n degrees of freedom ? Mean = n; Variance = 2n. Question 22. Mention any two types of causes of variation in a manufacturing process. 1. Chance causes and 2. Assignable causes. Question 23. In a T.P define feasible solution. A set of values xij where i = 1,2,… .m and j = 1,2 …n which satisfies the following conditions Question 24. The following is the pay – off matrix of player – A. write the payoff matrix of player – B. The pay – off matrix of player B is: Section – C III. Answer any Eight of the following questions: (8 × 5 = 40) Question 25. For the following data find TFR. Total fertility rate: T.F.R = 5 Σ Quinquennial ASFRs ASFR (15 – 49) = $$\frac{200}{5,000}$$ × 1000 = 40; similarity compute for other age groups. T.F.R = 5 × 466.5 = 2332.5 children bom per 1000 women of (15 – 49) years. Question 26. Mention three uses and two limitations of Index number. Uses : 1. Index numbers are useful to governments in formulating Economic policies such as Taxation, Imports, Exports, fixation of bank rates. 2. Fixation of salary and grant of dearess allowances to employees. 3. Comparing variations in prices, production, shares etc. Limitations: 1. Many formulae are used and gives different answers for the index. 2. As the customs and habits change from time to time, the uses of commodities also vary. Question 27. Compute consumer price Index number from the following data. Weights-’w are given, use Family budget Method: C.P.I : = I01 = $$\frac{\Sigma P w}{\Sigma w}$$ = $$\frac{p_{1}}{p_{0}}$$ × 100 I01 = $$\frac{27633.1}{200}$$ = 138.165 The cost of living has increased by 38.165% in the current year as compared to base year. Question 28. For the following data find three yearly moving averages and indicate the trend. Let X and Y be the year and profit in the table 3Y MT : 3 yearly moving total From the ŷ – trend values, the profit shows upward trend. Question 29. Use Newton’s method to find the number of employees whose wages is Rs. 400 day. Solution : Let x and y be the wages and number of employees. The number of known values of ‘y’ n = 5, so prepare the leading differences (Δs) upto Δ4. (x – 1) = (1.5 – 1) = 0.5; (x – 2) = (1.5 – 2) = -0.5 ; (x – 3) = (1.5 – 3) = -1.5 The Newton’s formula of interpolation is y400 = 72 – 15 – 1.5 – 0.875 – 0.6562 = 54.84 = 55 ∴ Number of employees whose wages is Rs. 400/-day = 55 Question 30. The probability of an arrow hitting a tree is $$\frac { 1 }{ 2 }$$ . If 5 arrows atfe aimed at the tree find the probability that i) 3 arrows hit the tree ii) at least 4 arrows hit the tree Given: Let x be the number of arrows hitting a tree is k Binomial variate with the parameters n = 5; p = $$\frac { 1 }{ 2 }$$ = 0. 5 and q = 1 – p = 0.5. Then the p.m.f is p(x) = ncx px qn – x; x = 0,1,2 …… n = 5cx (0.5)x (0.5)5 – x; x = 0,1,2….5 (i) p ( 3 arrows hit) = p (x = 3) = 3c3(0.5)3 (0.5)5-3 = 1 × 0.125 × 0.25 = 0.03125 (ii) p (atleast 4 arrows hit) = p (x > 4) = p(x = 4) + p (x = 5) = 5c4 (0.5)4 (0.5)5-4 + 5c5 (0.5)5 (0.55-5 = 5 × 0.0625 × 0.5 + 1 × 0.03125 × 1 = 0.15625 + 0.03125 = 0.1875 Question 31. Write down five features of normal distribution. Features of Normal distribution are 1. The normal curve is bell – shaped, symmetrical ie., Non – skew (Pj = 0) and so, Mean = Median = mode. 2. The parameters are : Mean = µ, S.D = σ and variance = σ2 3. The curve is mesokurtic (β2 = 3) 4. Area under the Normal curve = 1 5. For the distribution : Q.D = $$\frac { 2 }{ 3 }$$ σ; M.D = $$\frac { 4 }{ 5 }$$σ Question 32. The average monthly income of 50 families is found to be Rs. 44,950 can we Conclude that the average monthly income of the population is 45,000 with S.D Rs. 50? Test at 5% level of significance. Given : n = 50; x̄ = 44,950, µ = 45,000, σ = 50, α = 5% H0 : Mean monthly income is Rs 45,000 (ie., µ = 45,000) H1 : Mean monthly income differs from Rs. Rs. 45,000 (ie., µ ≠ 45,000) (Two tailed test} At α = 5% the two tail critical values are ±k = ±1.96 ∴ Here Zcal is rejected and H1 is accepted. Conclusion : Mean monthly income differs from Rs. 45,000 (µ ≠ 45,000) Question 33. From the following 2 × 2 contingency table, test whether result and areas of the students are independent ? [use 1% L.O.S]. H0 : Attributes result and areas of the students are independent. H1 : Attributes result and areas of the students are dependent, [upper tail test] under H0, the χ2 – test statistic is The given data can be written under 2 × 2 – contingency table as below: χ2cal = $$\frac{200(62 \times 61-28 \times 49)^{2}}{90 \times 110 \times 111 \times 89}=\frac{200(2410)^{2}}{97802100}$$ = 11.88 At α = 1% for 1.d.f. the upper tail critical region K2 = 6.65 Here χ2cal > k2 / χ2cal lies in rejection region (R.R) ∴ H0 is rejected and H1 is accepted. Conclusion : Result and areas of the students are dependent. Question 34. The following table gives the number of defectives found during the inspection of 8 samples of size 50 each. Calculate control limits for np chart. Given : No. of defectives ae given, so use ‘d’ or np – chart. Standard is not known. So, we need p̄ = $$\frac{\Sigma \mathrm{d}}{\mathrm{nk}}$$ n – sample size = 50 ; k – Sample no. = 8. ∴ p̄ = $$\frac{12}{50 \times 8}$$ = 0.03. ∴ q̄ = 1 – p̄ = 1 – 0.03 = 0.97 The control limits are: C.L = np = 50 × 0.03 = 1.5 Question 35. Solve the foUowing L.P.P graphically: Maximize z = 5x + 4y Subject to 3x + 2y ≥ 30 2x + 3y ≤ 60 and x, y ≥ 0 Consider the constraints as equalities and obtain the co – ordinates to get a straight line on x,y – plane as below Consider, 3x + 2y ≥ 30 as 3x + 2y = 30; put x = 0 ; we get y = 15; (0,15) as co – ordinate put y = 0, weget x = 10; (10,0) and from 2x + 3y = 60 ; put x = 0; we get y = 20 ; (0,20) put y = 0; we get x = 30 ; (30,0) Also : the non – negative restrictions as x = 0 ; y = 0. Now plot the points on an x,y – plane. From the graph the feasible region / common shaded region exists at the comer points A(0,15) B(0,20), C(30,0) and D( 10,0) Determination of optimum value of ‘z’- objective function at the comer points: From the above table the objectivity Maximises at the comer point C(30,0). The suggested solution is : x = 30, y = 0. The optimum value of Zc = 150. For visually challenged students Following are the steps involved in graphical method of solving an L.P.P:- • Consider the constraints as equalities • Find the co – ordinates for each constraints as (x, y) • Draw a graph and represent by straight line for each constraints • Identify the feasible region – Which satisfies the constraints and Non – negative restrictions simultaneaasly (The common shaded region) • Locate the corner points of the feasible region • Find the value of the objective function for each of the comer points of the feasible region • Suggest the solution to the L.P.P with its optimum value. Question 36. A firm is considering the replacement of machine whose cost price is Rs. 12,800 and scrap value is Rs. 300. The‘maintenance costs are as followes. Determine the optimal period for replacement of the machine. Given : p = 12, 800, Sn = 300, ∴ the depreciation cost (P – Sn) = (12,800 – 300) = 12, 500 is fixed for all the years. The given data is represented in the following table: From the above table Annual average maintenance cost A(n) is minimum for n = 6th year. So the optimum period for the replacement of the machine is 6th year. The optimum cost: Section – D IV. Answer any Two of the following questions: (2 × 10 = 20) Question 37. Calculate standardardized Death Rates from the following data and write your conclusion Let Ps – the standards population, A, B – be A.S.D.R.S of city A and city B. For cityA: ASDR (Below 10) = $$\frac{32}{4,000}$$ × 1000 = 8 For city B: ASDR (Below 10) = $$\frac{120}{12,000}$$ × 1000 = 10, Similarlly ASDRs can be calculate for other age groups. S.D.R (A) = $$\frac{\Sigma p_{s} A}{\Sigma p_{s}}=\frac{226,000}{26,000}$$ = 8.6,923 S.D.R (B) = $$\frac{\Sigma p_{s} B}{\Sigma p_{s}}=\frac{247,000}{26,000}$$ = 9.5 deaths/1000 population in a year. Conclusion : Here SDR(A) < SDR (B) City A is more healthier than city B. Question 38. Construct Marshall- Edgeworth’s, Fisher, and Dorbish Bowley’s price index numbers from the following data. Question 39. Fit a quadratic trend for the following time series by the method least squares and estimate the sales in 2008. Given : Let x and y be the year and sales. From the normal equations obtain the values of a, b and c as below : Here n = 7 years, na + bΣx + cΣx2 = Σy; 7a + b.0 + c.28 = 64 ie., 7a + 28c = 64 → (1) a Σx + b Σx2 + c Σx3 = Σxy; a.0 + b. 28 + c.0 = 46 28b = 46; b = $$\frac{46}{28}$$ = 1.6429 28 a Σx2 + b Σx3 + c Σx4 = Σx2y; a.28 + b.0 + c.196 = 262, we get, 28a + 196 c = 262 → (2) from (1) & (2) ∴ c = $$\frac{6}{84}$$ = 0.0714; put c = 0.0714 in (1) 7a + 28(0.0714) = 64 7a + 1.9992 = 64; a = $$\frac{64-1.9992}{2}$$ = 31 The fitted quadratic trend equation is : y = a + bx + cx2; ŷ = 31 + 1.6429 x + 0.0714 x2 Estimation for the year 2008; x = 5; x2 = 25 ŷ(2008) = 31 + 1.6429 (5) + 0.0714(25) = 40.9995 = 41(000’s) Question 40. Fit a binomial distribution to the following data and test at 5% level of significance that whether the distribution is good fit. The parameters are n = 5, and p is obtained as: Mean = np = x̄ = $$\frac{\Sigma \mathrm{fx}}{\mathrm{N}}$$ from the given distribution ∴ 5p = $$\frac{0 \times 10+1 \times 29+2 \times 55+3 \times 71+4 \times 28+5 \times 7}{10+29+55+71+28+7}$$ 5p = $$\frac{499}{200}$$ ∴ p = $$\frac{2.495}{5}$$ = 0.499 = 0.5 and q = 1 – p = 0.5 and N = 200 The p.m.f is ; p(x) = ncx px qn – x, x = 0,1,2 …… n; 5(x 0.5x 0.5 5-x; x = 0,1,2 …….. 5) ∴ T0 = 0(x = 0) × 200 = 5c0 0.50 0.55 – 0 × 200 = 0.03125 × 200 = 6.25 The successive theoretical frequencies are obtained using the recurrence : The observed and theoretical frequency distribution is: – (approximated) CHI – SQUARE TEST; H0 : Binomial distribution is good fit (ie., Oi = Ei) H1 : Binomial distribution is not good fit (ie., Oi ≠ Ei){upper tail test}. ∴ χ2cal = 5.629 At α = 5% for (n – 2) = (6 – 2) = 4 d.f the upper tail critical value k2 = 9.49 Here χ2cal < k2 / χ2cal lies in Acceptance region (A.R.) ∴ Ho is accepted Conclusion : Binomial distributon is good gift Section – E V. Answer any Two of the following questions: (2 × 5 = 10) Question 41. The heights of a group of soldiers are Normally distributed with mean 170 cms and S.D. of 4 cms. Then Rnd the probability that a randomly selected soldier has height (i) More than 180 cms (ii) between 162cms and 172cms. Let x be the height is a Normal variate with the parameters µ = 110 and σ = 4, then the S.N.V is: z = $$\frac{x-\mu}{\sigma}$$ ~ N(0,1) : z = $$\frac{x-170}{4}$$ (i) p (more than 180) = p(x >180) = p$$\left(z>\frac{180-170}{4}\right)$$ = p(Z > 2.5) = Area from 2. 5 to ∞ p(z > 2.5) = 0.0062 (From the table) (ii) p(between 162 and 172) p (162 < × < 172) = p$$\left(\frac{162-170}{4}<z<\frac{172-170}{4}\right)$$ = P(-2 < Z < 0.5) = Area from (-2) to 0.5 = Area from (-2) to ∞ – Area from 0.5 to ∞ = 0.9772 – 0.3085 = 0.6687 Question 42. For the following data test whether there is any significant difference between the proportions of two populations? (use – k = -196, k = 1.96) Given : p1 = 0. 26, p2 = 0.2; n1 = 1000, n2 = 500. H0 : There is no significant different between the proportions the two populations (ie., P01 = P02) H1: There is a significant difference between the proportions of the two populations (ie., P01 ≠ P02) { Two tail test} Q0 = 1 – p0 = 1 – 0.24 = 0.76 Given : k = -1.96, k= 1.96 Here Zcal lies in rejection region (R.R) ie., Zcal > 1.96 (k). ∴ H0 is rejected and H1 is accepted Conclusion: There is a significant difference between the proportions of the two populations. (ie., P01 ≠ P02). Question 43. A sample of 15 values shows that S.D to be 6.4 Does this agree with the hypothesis that the population S.D is more than 5 (α = 0.01) Given: n = 15; s = 6.4, σ = 5, α = 0.01 (1%) H0 : population S.D is 5 (ie., σ = 5) H1 : population S.D is more than 5 (ie., σ > 5) { upper tail tfest} under H0, the χ2 – test statistic is: χ2 = $$\frac{\mathrm{ns}^{2}}{\sigma^{2}}$$ ~ χ2 (n – 1) d.f χ2cal = $$\frac{15 \times 6.4^{2}}{5^{2}}$$ = 24.576 At α = 1% for (n – 1) = (15 – 1) = 14 df The upper tail critical value k2 = 29. 14 Here χ2cal lies in acceptance region / χ2cal < k2 ∴ H0 is accepted. Conclusion : population S.D is (ie., σ = 5). Question 44. There is a demand for 10,000 items per year. The setup cost is Rs.1600 and Maintanance cost is Rs. 4 per item per year. Shortages are not allowed. Find (i) E.O.Q (ii) Number of orders per year (iii) Minimum average cost. (ii) No. of orders : n° = $$\frac{1}{t^{0}}=\frac{R}{Q^{0}}=\frac{10,000}{2828.4271}$$ = 3.535 orders / year (iii) Min. Average cost: C (Q°) = $$\sqrt{2 \mathrm{C}_{3} \mathrm{RC}_{1}}=\sqrt{2 \times 1600 \times 10,000 \times 4}$$ = Rs. 11313.71	5,714	17,320	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4	4	CC-MAIN-2022-49	latest	en	0.833538
http://toomai.wordpress.com/category/geometry/	1,369,325,547,000,000,000	text/html	crawl-data/CC-MAIN-2013-20/segments/1368703532372/warc/CC-MAIN-20130516112532-00059-ip-10-60-113-184.ec2.internal.warc.gz	275,995,614	9,238	# MATH with my KIDS ## Latin Squares, Squared Squares, and Legoed Squares I introduced my kids to Latin Squares the other day. If you know Sudoku then you have seen examples of Latin squares. The idea is to fill in a grid of squares with colors or numbers or some other symbols, such that each symbol appears exactly once in each row and each column. (see also the Wikipedia Latin square entry). I handed them graph paper and let them loose. This is what my eight-year-old produced: Note that she produced some Latin squares, but also explored other ideas. I wasn’t sure initially how long my kids would be content to explore Latin squares, so I also planned to tell them about squared squares. A squared square is just a square made up of smaller squares (this is easy to accomplish). A perfect squared square is much more difficult, consisting of squares each of different sizes. For a long time it was thought that perfect squared squares didn’t exist, but they do! Here is the smallest (in some sense) one: We got excited about it and decided to make one for our wall: Next, the ten-year-old wanted to produce some squared squares of his own, but found the perfect ones difficult (they were thought to be completely non-existent for a long time after all). He settled for producing imperfect ones. After making an imperfect squared square on graph paper, he decided to reproduce it with Legos. Here is the result: This led us to considered perfect Legoed squares. That is to say, squares made up of some number of Lego pieces, each piece having a unique size. Here is one of our first examples: It’s a 3×3 made up of a 1×1, a 1×2, and a 2×3. Here’s another, somewhat larger: We found a bunch more (maybe ten or so total). I’m not sure that we got all of them. How many can you find? Look for up-coming posts on: 1) further progress in building our marble computer, and 2) teaching my five-year-old to count (which required some deep thought about just what counting is). ## Rep-tiles It’s been a while since I’ve done an evening of math with my two older kids (6 years and 8 years), so this week I decided I would teach them about rep-tiles. (If you don’t know what rep-tiles are, don’t worry. I’ll be explaining that shortly, or check out this excellent article on rep-tiles) First we pulled out our copy of the board game Blokus (a great game involving placing polyominoes). I laid out the four monominoes on the board and asked them if they could make a square of the four. “Of course!” I had told them previously that we would be working with rep-tiles, not the animals, but something to do with mathematics. They had been dying to know what a mathematical rep-tile was. I asked them if now they understood. “It’s a shape that you can make a bigger one out of a bunch of them.” I was surprised that they caught on so quick, expecting something more along the lines of “a shape that you can make a square from several copies of it.” I had told them previously that Utah was a rep-tile (The pentomino that most people call “P”, I call “Utah”, me being from Utah originally). So we did that one next. It took them several minutes to piece four copies of Utah together into a bigger one and they passed the pieces back and forth several times. Here is what they came up with: I had them select several other polyominoes and decide whether they were rep-tiles. The domino, for instance, was easy. The tetromino Zstumped them. With the aid of paper and a pen I gave them an argument that Z is not a rep-tile. They were convinced and later gave me a similar argument that the pentomino Xis not a rep-tile (how could you fill in a corner with a smaller copy?). I told them that of course not only polyominoes can be rep-tiles. For instance what about circles? “No,” they said. Packing circles together always leaves gaps, after all. I had previously cut out some polyiamonds (also see: another polyiamond article) printed on card stock. We proceeded to determine which of these were rep-tiles. We spent quite some time on this, but I’ll skip the details and give you the end result. Namely, we pasted our rep-tiles to construction paper. The kids and I were pretty pleased with the results.	994	4,222	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.1875	4	CC-MAIN-2013-20	latest	en	0.963625
http://bankersdaily.in/coding-and-decoding-for-sbi-po-set-14/	1,600,995,133,000,000,000	text/html	crawl-data/CC-MAIN-2020-40/segments/1600400221382.33/warc/CC-MAIN-20200924230319-20200925020319-00687.warc.gz	13,765,144	21,884	## Coding and Decoding For SBI PO : Set – 14 1) If GARDEN is coded as 325764 and WATER as 92165, how can we code the word WARDEN in the same way? a) 925764 b) 295764 c) 952764 d) 957264 a) G A R D E N 3 2 5 7 6 4 W A T E R 9 2 1 6 5 W A R D E N 9 2 5 7 6 4 2. In a certain language A. PIC VIC NIC means winter is cold B. TO NIC RE means summer is hot C. RE THO PA means nights are hot Which of the following is the code for summer? a) TO b) NIC c) PIC d) VIC a) Summer – TO is – NIC Hot – RE 3. If P denotes multiplied by, T denotes subtracted from;, M denotes added to and B denotes divided by, then 28 B 7 P8 T 6 M 4 = ? a) -3/2 b) 30 c) 32 d) 34 b) Put the proper sign in the given equation we get = 30 4) In Certain code, ‘253’ means ‘books are old’; ‘546’ means ‘man is old’ and ‘378’ means ‘buy good books’. What stands for “are” in that code? a) 2 b) 4 c) 5 d) 6 a) From above coding we know that 5 means old 3 means book 2 means are 5. In a certain code “MOUSE” is written as “PRUQC”. How is “SHIFT” written in that code ? a) VJIDR b) VIKRD c) RKIVD d) VKIDR d) M+3=P ;O+3=R; U+0=U; S-2=Q; E-2=C like that S+3=V ;H+3=K; I+0=I; F-2=D;T-2=R 6. BHARATHI is written as 2811812089 in a certain code. How would SAMRAT is written as a) 1911311820 b) 1911318120 c) 1913118120 d) 1911320118 b) Alphabetical letter with series number B H A R A T H I 2 8 1 18 1 20 8 9 S A M R A T 19 1 13 18 1 20 7. If ‘+’ means ‘÷’ , ‘÷’ means ‘-’ , ‘-’ means ‘x’ and ‘x’ means ‘+’ then, which of the following equation equal a) 12×7 – 363 +121=39 /4+6-9 b) 12+7 +363 x121=40/4-6-9 c) 12+7×363 +121=39+4÷6-9 d) 12+7 +363 x121+4+6-9=40 a) Put the proper sign in the given expression, we get 12+7 x 363/121=39-4/6 x 9 33=33 8. IF E=10, PRT=108, then find HWF=? a) 33 b) 74 c) 88 d) 64 b) The position of alphabet E is 5, 52= 10, then similarly PRT= 16+18+20=542=108, then HWF=8+23+6=37*2=74. 9. in certain code GLITER is written as TERGLI, in that code TAILOR is written as a) TAIROL b) IATLOR c) LORIAT d) LORTAI d) G L I T E R T E R G L I The pattern is 1st three characters are placed at the last part and the last three characters are placed at the first part T A I L O R L O R T A I 10. if E is A, A is R, R is X M is S, T is W, P is D, W is E and D is T. Then what is “WATERED”? a) XERSWTA b) ERSXIAW c) ERWAXAT d) ETRXWXD	1,059	2,550	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.484375	3	CC-MAIN-2020-40	latest	en	0.835297
https://www.physicsforums.com/threads/light-optics-need-help-please.408935/	1,521,495,018,000,000,000	text/html	crawl-data/CC-MAIN-2018-13/segments/1521257647146.41/warc/CC-MAIN-20180319194922-20180319214922-00193.warc.gz	841,653,252	14,199	# Light Optics Need help please 1. Jun 8, 2010 ### SprintsMcgee When a blue light from a certain filtered light source is passed through a deffraction grid with 1000 slits per cm, it produces a pattern of fringes on a screen. If the screen is placed .25 meters form the grid, find the wavelength of the blue light. I have no idea how to even start this problem let alone solve. My teacher's philosophy is too make us do the hw for sections we havent done first then talk about and the book is of no help either. Any help would be great!!! 2. Jun 9, 2010 ### cartonn30gel Re: Light Optics!!! Need help please!!! You need more information to be able to solve this problem. Is anything given about how where the first (or nth) fringe appears on the screen? You can verify the fact that some information is missing by doing this: Change one of the given data and see if you can construct the same system without any flaws: 1) When red light from a certain filtered light source is passed through a diffraction grid with 1000 slits per cm, it would produce a pattern of fringes on a screen placed .25 meters away. Nothing wrong with that.. 2) When blue light from a certain filtered light source is passed through a diffraction grid with 2000 slits per cm, it would produce a pattern of fringes on a screen placed .25 meters away. Nothing wrong with that either.. 3) When blue light from a certain filtered light source is passed through a diffraction grid with 1000 slits per cm, it would produce a pattern of fringes on a screen placed .5 meters away. That's OK as well.. Therefore, the problem is unbound. You have one relationship between the variables in the problem; however there is more than one unknown. You can forget about this last part if it was confusing. The point is that you need to be given something else.	422	1,832	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.390625	3	CC-MAIN-2018-13	longest	en	0.932719
https://courseoutline.auckland.ac.nz/dco/course/MATHS/320/1215	1,701,639,177,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00121.warc.gz	218,777,538	16,716	# MATHS 320 : Algebraic Structures ## Science ### Course Prescription This is a framework for a unified treatment of many different mathematical structures. It concentrates on the fundamental notions of groups, rings and fields. The abstract descriptions are accompanied by numerous concrete examples. Applications abound: symmetries, geometry, coding theory, cryptography and many more. This course is recommended for those planning graduate study in pure mathematics. ### Course Overview This course is intended for students who have enjoyed the examples of algebraic structures presented in MATHS 254/255, 253 and/or MATHS 328, and who are interested in a unified treatment of many different mathematical structures. The main focus of the course is on the fundamental algebraic structures of groups, rings and fields. The abstract descriptions are accompanied by numerous concrete examples. Emphasis is placed on the contexts in which basic structures occur, methods by which they can be modelled and analysed, and their diverse applications. This course is recommended for those planning graduate study in pure mathematics. A student completing this course will have a basic knowledge of the fundamental of algebraic systems, and be able to construct simple proofs in an algebraic setting and appreciate the strength the strength of abstract algebraic methods. ### Course Requirements Prerequisite: MATHS 250, and MATHS 254 or 255 ### Capabilities Developed in this Course Capability 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 4: Communication and Engagement Capability 5: Independence and Integrity ### Learning Outcomes By the end of this course, students will be able to: 1. Display basic knowledge of fundamental algebraic systems: groups, rings and fields and their properties by solving relevant questions and examples (Capability 1 and 2) 2. Display ability to analyse and answer questions, through examples and methods (Capability 1, 2 and 3) 3. Demonstrate understanding of connections with other disciplines and real world applications by the use of relevant examples (Capability 1, 2, 3 and 4) 4. Demonstrate understanding of the nature of proof and precision in mathematics, and the ability to present arguments both formally and informally in written form (Capability 2, 4 and 5) ### Assessments Assessment Type Percentage Classification Tutorials 10% Individual Coursework Assignments 20% Individual Coursework Test 25% Individual Test Final Exam 45% Individual Examination 1 2 3 4 Tutorials Assignments Test Final Exam A minimum mark of 35% must be obtained in the final exam to pass the course ### Key Topics Week 1: Symmetric operations and groups Week 2: Subgroups (including cyclic subgroups) Week 3: Cyclic groups; Permutation groups; Week 4: Group isomorphisms; Direct products; Inner products; Cosets; Week 5: Lagrange’s Theorem; Orbite-Stabiliser Theorem; Burnside's Theorem; Normal subgroups and factor groups Week 6: Group homomorphisms; Finite abelian groups; The Cauchy theorem; Week 7: Rings and integral domains Week 8: Ideals, factor rings and ring homomorphisms Week 9: Polynomial rings and factorisation Week 10: Vector spaces (including extension fields) Week 11: Field extensions (including algebraic extensions) Week 12: Finite fields. ### Special Requirements This course has no special requirements. This course is a standard [15] point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in. For this course, you can expect [36] hours of lectures, a [11] hour tutorial, [36] hours of reading and thinking about the content and [67] hours of work on assignments and/or test preparation. ### Delivery Mode #### Campus Experience Attendance is [expected] at scheduled activities including [tutorials] to [receive credit for] components of the course. However it will be available for remote students with special circumstances (for example those outside New Zealand). Lectures will be available as recordings, however students should be aware that it is not always possible to record material written on the whiteboards. Other learning activities including tutorials will not be available as recordings. Attendance on campus is [required] for the [test] at the COVID alert level 1 and the test is online at levels 2, 3, 4. The exam in 2021 is online. The activities for the course are scheduled as a weekly timetable delivery. ### Learning Resources The recommended textbook is "Contemporary Abstract Algebra", by J. A. Gallian (published by D.C. Heath & Company), 8th edition or later, but also detailed course notes will be provided, and these will include definitions, examples, properties and applications of the key concepts developed in the course. ### Student Feedback During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees. At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback. Your feedback helps to improve the course and its delivery for all students. ### Digital Resources Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available). Please remember that the recording of any class on a personal device requires the permission of the instructor. Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available). Please remember that the recording of any class on a personal device requires the permission of the instructor. The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms. The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license. You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person. ### Inclusive Learning All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor. Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website ### Special Circumstances If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due. If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page . This should be done as soon as possible and no later than seven days after the affected test or exam date. ### Learning Continuity In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed. With respect to the COVID alert levels this course will be delivered in the following fashion. Level 1: Delivered normally as specified in delivery mode Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option. Level 3 / 4: All teaching activities and assessments are delivered remotely ### Student Charter and Responsibilities The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter . ### Disclaimer Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas. In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published. Published on 27/05/2021 02:58 p.m.	1,973	10,128	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.65625	3	CC-MAIN-2023-50	latest	en	0.904881
https://www.montgomeryschoolsmd.org/curriculum/math-support/middle/math6-unit2.aspx	1,601,285,284,000,000,000	text/html	crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00457.warc.gz	918,171,679	14,163	# Mathematics Support Math 6 \| Unit 1 2 3 4 5 6 7 8 9 ### Introducing Ratios What are Ratios? Representing Equivalent Ratios Solving Ratios and Rate Problems ## What are Ratios? A ratio is an association between two or more quantities. For example, say we have a drink recipe made with cups of juice and cups of soda water. Ratios can be represented with diagrams like those below. Here are some correct ways to describe this diagram: • The ratio of cups of juice to cups of soda water is 6:4. • The ratio of cups of soda water to cups of juice is 4 to 6. • There are 3 cups of juice for every 2 cups of soda water. The ratios 6:43:2, and 12:8 are equivalent because each ratio of juice to soda water would make a drink that tastes the same. There are 4 horses in a stall. Each horse has 4 legs, 1 tail, and 2 ears. 1. Draw a diagram that shows the ratio of legs, tails, and ears in the stall. 2. Complete each statement. • The ratio of ________ to ________ to ________ is ________ : ________ : ________. • There are ________ ears for every tail. There are ________ legs for every ear. Solution: 2. Answers vary. Sample response: The ratio of legs to tails to ears is 16:4:8. There are 2 ears for every tail. There are 2 legs for every ear. ## Representing Equivalent Ratios There are different ways to represent ratios. Let’s say the 6th grade class is selling raffle tickets at a price of $6 for 5 tickets. Some students may use diagrams with shapes to represent the situation. For example, here is a diagram representing 10 tickets for$12. Drawing so many shapes becomes impractical. Double number line diagrams are easier to work with. The one below represents the price in dollars for different numbers of raffle tickets all sold at the same rate of $12 for 10 tickets. Here is a task to try with your student: Raffle tickets cost$6 for 5 tickets. 1. How many tickets can you get for $90? 2. What is the price of 1 ticket? Solution: 1. 75 tickets. Possible strategies: Extend the double number line shown and observe that$90 is lined up with 75 tickets. Or, since 90 is 6 times 15, compute 5 times 15. 2. $1.20. Possible strategies: Divide the number line into 5 equal intervals, as shown. Reason that the price in dollars of 1 ticket must be 6÷5. ## Solving Ratio and Rate Problems Over the course of this unit, your student has learned to use the language of ratios and to work with ratios using representations like diagrams and double number lines. In the final sections of the unit, they use tables to organize equivalent ratios. Double number lines are hard to use in problems with large amounts. Let’s think about an example we saw before: the 6th grade class is selling raffle tickets at a price of$6 for 5 tickets. If we tried to extend the double number line below to represent the price of 300 raffle tickets, it would take 5 times more paper! A table is a better choice to represent this situation. Tables of equivalent ratios are useful because you can arrange the rows in any order. For example, a student may find the price for 300 raffle tickets by making the table shown. Although students can choose any representation that helps them solve a problem, it is important that they get comfortable with tables because they are used for a variety of purposes throughout high school and college mathematics courses. At a constant speed, a train travels 45 miles in 60 minutes. At this rate, how far does the train travel in 12 minutes? If you get stuck, consider creating a table. Solution: 9 miles. Possible strategy: time in minutes distance in miles 60 45 1 0.75 12 9 IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/. Disclaimer: This site provides external links and videos as a convenience and for informational purposes only. The appearance of external hyperlinks on the MCPS Family Mathematics Support Center website does not constitute an endorsement by the Montgomery County Public School System of any of the products or opinions contained therein.	1,011	4,283	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.84375	5	CC-MAIN-2020-40	latest	en	0.90632
https://stats.stackexchange.com/questions/108471/the-distribution-of-a-sufficient-statistic	1,702,182,538,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679101195.85/warc/CC-MAIN-20231210025335-20231210055335-00778.warc.gz	438,742,438	40,617	# The distribution of a sufficient statistic If I understand correctly, a distribution in the exponential family... $$\underline X\sim f_{\underline\theta}(\underline x) = exp\{\sum\limits_{i}\eta_i(\underline\theta)T_i(\underline x)-B(\underline\theta)\}~h(\underline x)$$ ...where $\underline\eta(\centerdot)$ is a (possibly vector valued) parameter, $\underline T(\centerdot)$ is a corresponding vector of sufficient statistics, $B(\theta)$ is the log partition, and $h(\underline x)$ is the base measure and $\underline T(\underline x)$ itself has the following distribution: $$\underline T(\underline x) =\underline t\sim g_{\underline\theta}(\underline t) = exp\{\sum\limits_{i}\eta_i(\underline\theta)t_i-B(\underline\theta)\}~h^(\underline t)$$ ...where $h^(\centerdot)$ is not necessarily the same function as the one from $f_{\underline\theta}(\underline x)$ above. My questions are: • Are the other two functions ($B(\underline\theta)$ and $\underline\eta(\underline\theta)$) identical to the ones from $f_{\underline\theta}(\underline x)$? • What is the general strategy for finding $h^*(\centerdot)$?	301	1,120	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.109375	3	CC-MAIN-2023-50	longest	en	0.613593
https://www.6miu.com/read-18.html	1,702,311,684,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679515260.97/warc/CC-MAIN-20231211143258-20231211173258-00097.warc.gz	669,899,458	5,946	# 递归（Recursion） xiaoxiao2021-02-27 1.0K+ ## 实例： e.g.1 阶乘 #include <iostream> using namespace std; int main() { int fact(int a); int num; cout<<"input the order the item"<<endl; cin>>num; cout<<fact(num); return 0; } int fact(int a) { int f; if (a==1) f=1; //基础项 else f=fact(a-1)a;//通项 return f; } e.g.2 阶乘求和 #include <iostream> using namespace std; int main() { int fact(int a); int num,s=0; cout<<"input the order the item"<<endl; cin>>num; for (int i=1;i<=num;i++) s=s+fact(i); cout<<s; return 0; } int fact(int a) { int f; if (a==1) f=1;//基础项 else f=fact(a-1)a;//通项 return f; } e.g.3 Fibonacci Sequence #include <iostream> using namespace std; int main() { int fibonacci(int a); int num,s=0; cout<<"input the order the item"<<endl; cin>>num; cout<<fibonacci(num); return 0; } int fibonacci(int a) { int f; if (a==1) f=1; else if (a==2) f=1; //基础项 else f=fibonacci(a-1)+fibonacci(a-2);//通项 return f; }	338	914	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.1875	3	CC-MAIN-2023-50	latest	en	0.108852
https://activegaliano.org/62500-a-year-is-how-much-an-hour-update-new/	1,701,458,644,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100304.52/warc/CC-MAIN-20231201183432-20231201213432-00390.warc.gz	113,558,771	33,671	Home » 62500 A Year Is How Much An Hour? Update New # 62500 A Year Is How Much An Hour? Update New Let’s discuss the question: 62500 a year is how much an hour. We summarize all relevant answers in section Q&A of website Activegaliano.org in category: Blog Marketing. See more related questions in the comments below. ## Is \$62500 a good salary? San Jose, CA beats the national average by \$12,062 (19.3%), and San Francisco, CA furthers that trend with another \$17,502 (28.0%) above the \$62,500 average. What are Top 10 Highest Paying Cities for Class A Jobs. City San Francisco, CA \$80,003 \$6,667 \$1,539 \$38.46 ## How much is \$35 hourly annually? 40 hours multiplied by 52 weeks is 2,080 working hours in a year. \$35 per hour multiplied by 2,080 working hours per year is an annual income of \$72,800 per year. ### 525,600 minutes lyrics 525,600 minutes lyrics 525,600 minutes lyrics ## How much is 44.00 an hour annually? \$44 per hour multiplied by 2,080 working hours per year is an annual income of \$91,520 per year. ## How much is \$33.75 an hour annually? 33.75/hour = \$67,500/year \$33.75 an hour is how much a year? Convert between annual and hourly salaries. ## How much per hour is 55000 a year? That means, if you work the standard 40 hour work week, 52 weeks per year, you’d need to divide \$55,000 by 2,080 hours (40 * 52). If this is your measure, \$55,000 per year is \$26.44 an hour. ## How much is 30 dollars and hour a year? \$30 an hour is \$62,400 a year before taxes. Check our math: 40 hours of work per week multiplied by 52 (the number of weeks in a year) equals 2,080 hours worked per year (on average). ## How much is 80k a year hourly? If you make \$80,000 per year, your hourly salary would be \$41.03. This result is obtained by multiplying your base salary by the amount of hours, week, and months you work in a year, assuming you work 37.5 hours a week. ## Is 35\$ an hour good? Is \$35 an Hour a Good Salary? Making \$35 an hour will put you in one of the higher tiers of income among Americans. Only ~30% of household incomes make more than the \$66,560 salary that \$35 an hour provides. ## Is making 60000 a year good? According to the Bureau of Labor Statistics, a 60k annual income is the median US income. This means that half of all workers in the US make more than 60k per year, and half make less. However, 60k per year is generally considered to be a good salary. ## What is \$45 an hour annually? If you make \$45 per hour, your Yearly salary would be \$87,750. This result is obtained by multiplying your base salary by the amount of hours, week, and months you work in a year, assuming you work 37.5 hours a week. ## What is 47 an hour annually? \$47 per hour multiplied by 2,080 working hours per year is an annual income of \$97,760 per year. ### How Much An Hour Is 65000 A Year? How Much An Hour Is 65000 A Year? How Much An Hour Is 65000 A Year? ## What is \$48 an hour annually? \$48 per hour multiplied by 2,080 working hours per year is an annual income of \$99,840 per year. ## How much is \$34 dollars an hour annually? If you are working a full-time job, you will be working 40 hours per week on average. 40 hours multiplied by 52 weeks is 2,080 working hours in a year. \$34 per hour multiplied by 2,080 working hours per year is an annual income of \$70,720 per year. ## Is 55k a year good 2021? What kind of lifestyle can you have on a \$55k salary? In 2021, the national average person in the United States earned approximately \$51,480. Earning 55,000 a year will allow you to live comfortably and even save money if you budget. ## Is 55k a year middle class? Those whose incomes fall in the bottom 20% are considered poor. Everyone else (the middle 60%) is middle class. Income Range: There are some economists who say that anyone who makes between \$25,000 and \$100,000 a year is middle class. ## Is a 55 ka year good? As we stated earlier if you are able to make \$55,000 a year, that is a decent salary. You are making more money than the minimum wage and almost double in many cities. What is this? While 55000 is a good salary starting out in your working years. ## How much is \$60 000 a year per hour? To calculate the hourly rate, you divided the total pay—\$60,000—by the number of hours worked— 1,920. The answer to this calculation comes out as \$31.25 per hour. ## What is \$28 hour annually? 40 hours multiplied by 52 weeks is 2,080 working hours in a year. \$28 per hour multiplied by 2,080 working hours per year is an annual income of \$58,240 per year. ## Is \$31 an hour good pay? \$31 per hour multiplied by 2,000 working hours per year is an annual income of \$62,000 per year. ## What is 120k a year hourly? If you make \$120,000 per year, your hourly salary would be \$61.54. This result is obtained by multiplying your base salary by the amount of hours, week, and months you work in a year, assuming you work 37.5 hours a week. ### Seasons of Love – Rent (Music Video) Seasons of Love – Rent (Music Video) Seasons of Love – Rent (Music Video) ## What is 90000 a year hourly? Results. A salary of \$90,000 equates to a monthly pay of \$7,500, weekly pay of \$1,731, and an hourly wage of \$43.27. ## Is 80000 a year middle class? With the median U.S. income being about \$80,000 a year, a household of four earning between roughly \$52,000 and \$175,000 a year is considered middle class. Related searches • how much is \$18.82 an hour annually • 65000 a year is how much an hour • 62500 a year is how much per month • \$62,500 a year is how much an hour after taxes • how much is 84k a year hourly • 62500 a year is how much an hour after taxes • if i make 62500 a year how much is that an hour • how much is \$23 an hour a year • \$62,500 a year is how much per month • 62500 a year is how much an hour 40 hours a week • \$65,000 a year is how much an hour • 62500 a year is how much biweekly • how much is 24.00 an hour annually • is \$62,500 a good salary • is 62500 a good salary • 62500 a year is how much a month after taxes • 62 000 a year is how much an hour • how much is \$22.66 an hour annually • \$62,500 a year is how much biweekly ## Information related to the topic 62500 a year is how much an hour Here are the search results of the thread 62500 a year is how much an hour from Bing. You can read more if you want. You have just come across an article on the topic 62500 a year is how much an hour. If you found this article useful, please share it. Thank you very much.	1,768	6,546	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.046875	3	CC-MAIN-2023-50	latest	en	0.922177
https://notebook.community/ijstokes/wakari_tutorial/Introduction%20to%20Data%20Analysis%20with%20IPython%20and%20Wakari	1,708,515,804,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947473472.21/warc/CC-MAIN-20240221102433-20240221132433-00770.warc.gz	435,879,861	11,868	# Introduction to Data Analysis with IPython and Wakari Introduction to Data Analysis with IPython and Wakari Based on a work at https://github.com/ijstokes/wakari_tutorial. ## Outline • Freemium web-based data analytics service • Platform for collaborative data intensive analytics, visualization, and publishing • Combines Continuum's Anaconda Python distribution and IPython Notebook • This tutorial will focus on "hosted" IPython Notebook service • Just like IPython makes Python easier to use interactively on your computer, Wakari makes Python-centric analytics easier to do through your browser ## First Steps 1. Create a Wakari account at http://wakari.io (will need to confirm email within 24 hours) 2. Start a bash terminal in Wakari 3. git clone https://github.com/ijstokes/wakari_tutorial.git 4. Refresh file manager (left window) 5. Double click on wakari_tutorial directory 6. Click on IPython Notebook file Introduction to Data Analysis with IPython and Wakari.ipynb 1. Follow along and execute commands with SHIFT-ENTER in each cell. 2. If you are in a classroom setting, introduce yourself to the person on either side. Tell them your name and your favorite Monty Python movie. These two people will be your Python programming buddies for the next hour, so be prepared to help each other out. ## Python Statements and Notebook Cells Each cell can contain one or more Python statements In [ ]: print "This is a cell" In [ ]: x = 4 y = 7 result = x + y print result ## Practice: Cells and Kernels In [ ]: import time time.asctime() In [ ]: print "Seconds since the epoch:", time.time() print "Years since the epoch (approx): %.2f" % (time.time()/(365 * 24 * 60 * 60)) print "Previously computed value result: ", result 1. And cells can be evaluated multiple times -- try re-executing the above time cells and watch the time change ` 2. A running notebook (like this one, if you've opened it in IPython Notebook") has a Python kernel associated with it, and executing a cell is like running the statements in that cell inside an interactive IPython interpreter. 3. You can re-order cells and then re-execute them, but re-ordering does not re-run all other cells. For example, try moving the above "seconds since the epoch" cell up near the First Steps section using the ⬆ button in the toolbar, then re-run it. 4. Notice that the time module and the result variable are still in scope. 1. When you save your Notebook (with the 💾 button in the toobar) all your input and output cells are saved as well. Try it now, then select File→Close and Halt -- you will get a warning message that the kernel has stopped. 2. Close the notebook by clicking the ⊗ in the tab. 3. Re-open the notebook by double clicking on it in the left sidebar menu. 4. Notice the output has been saved -- this hasn't re-executed. Clear the output by selecting Cell→All Output→Clear. 5. Now try re-executing all the cells in the notebook by selecting Cell→Run All. 6. If you moved the time cell up before saving, then you'll get an exception when this runs, since import time hasn't been called yet. In [ ]: wont_work = 73 + 'some string' 1. Notice that Run All will stop if it hits a code cell that throws an exception. Fix 'some string' by making it a number, then select Cell→Run All Below. 2. You can also delete and insert cells. Select the cell above and then cut it out with the ✂ menu bar button. Add a new cell above this one using the ⤒ button. Try adding some code and executing it. 3. You can also copy cells with the copy button (right of the scissors), and paste them with the paste button (clipboard two-right of the scissors). Try copying the "time since epoch" cell. ## Non-Code Cells • You can use the tool bar drop-down menu to change a particular cell from code to something that will allow you to enter plain text, HTML, or Markdown. • This can even include mathematical notation via LaTeX $$c = \sqrt{a^2 + b^2}$$ • Click on any text cell in this notebook to see examples of this. • Markdown is a great way to quickly write readable text that can also render to HTML for the web. Here is a short tutorial 1. The loop below will take a long time to run. In IPython Notebook we can interrupt the kernel similar to a CTRL-C signal by clicking on the stop button "■" in the menu bar. Selecting Kernel→Interrupt will do the same thing. Start the loop running, then after a few seconds stop it with this method. 2. It is often necessary to "start fresh", and that is done by resetting the Notebook kernel with Kernel→Reset. After you've done this, you'll need to re-execute cells from the Cells menu or by selectively using SHIFT-ENTER in cells of interest. In [ ]: for i in xrange(1000): print i time.sleep(0.5) ## IPython and IPython Notebook IPython extends the functionality of the standard python interactive interpreter. ⁇ Should you ever use IPython to run Python programs? ⁇ What are some features of IPython? • IPython should only be used interactively, never ipython myprog.py. • Extended commands and syntax are only meant for interactive use, not to be added to Python modules. • Many great features: • tab-completion • logging of commands (and output) • file system interaction (cd ls cp etc.) • extensions • "magics" • QT console (inline graphics) • Notebook In [ ]: pwd In [ ]: ls data In [ ]: # tab completion on attributes and functions with code-insight time. In [ ]: # Help text time? In [ ]: # tab completion on file names fh = open('data/cla In [ ]: ls data/eur In [ ]: %%bash for f in data/.dat; do echo -n $f " " cat$f \| wc -l done In [ ]: %autosave 300 In [ ]: time? In [ ]: %run power ## Explore IPython and IPython Notebook • you can run ipython yourself: • Install it (if you don't have it already): $pip install ipython • Run it from the command line:$ ipython • And if you have ipython then you can start your own ipython notebook: $ipython notebook --pylab=inline • But for now, stick with Wakari 1. In a new cell, import math and execute it. 2. In a new cell, type the following: • math.<TAB> • math.cos(<TAB> 3. In a new cell, execute: • math.atan? 4. In a new cell, execute: • %run weather.py 5. Double click on weather.py in the left menubar file browser to open it in a file editor. Take a look at what it is doing. 6. In this notebook, write a small script that opens data/europe-cities-temp.dat and prints out each line. • If that is easy for you, convert the data into a list of tuples, each tuple containing the data on each row, with fields converted to ints or floats if possible. • If you still have time, change this into a dictionary, with city names as keys, and Lat/Lon converted to floats. ## Publishing Your Work • IPython Notebooks are simply JSON files • Any code and all output (including generated graphics) are embedded in the JSON file • This means you can share your published notebook by email or post it to the web • Does not include and custom code, data files, or other dependencies • Wakari facilitates publishing notebooks • Wakari can also publish bundles that include all files in a directory • And via conda environments, Wakari can automatically describe any package dependencies • If you know virtualenv, imagine this as a manifest of all special packages required for the bundle to work ## Create Your Own Shared Notebook 1. Click on New Notebook 2. This will create a notebook with the name "Untitled X". Change the notebook name to "Weather Analysis" and save it. 3. Make the first cell Markdown and enter a title similar to the one used for this notebook, including a title and your name. 4. Add in a code cell with the autosave extension loaded and activated. 5. Add the following code block and execute it: 6. If you get an error regarding basemap then go to the Terminals tab in Wakari and start a Shell terminal then execute (don't inculde the dollar sign):$ conda install basemap In [ ]: from mpl_toolkits.basemap import Basemap import matplotlib.pyplot as plt import numpy as np fig = plt.figure(figsize=(12,12)) map = Basemap(projection='merc', lat_0 = 50, lon_0 = 5, resolution = 'i', llcrnrlon=-15, llcrnrlat=35, urcrnrlon=20, urcrnrlat=62) map.drawcoastlines() map.drawcountries() map.fillcontinents(color = 'coral') map.drawmapboundary() plt.show() 1. Share your notebook by clicking on the [Share] button beside it in the left menubar file manager. Provide a short description. Do not check "Share Environment" or set a password. 3. Click on the code link near the top to hide the code in the notebook. Depending on the notebook content, this is sometimes a more useful and readable view. 4. This published notebook view is a static, read-only snapshot of your notebook. Others can clone your notebook into their own Wakari environment, or they can download the notebook to load in their own IPython Notebook environment. 5. Return to your "live" notebook and enter the code below after your import statements, but before the figure is generated into the existing code cell: In [ ]: 'Reykjavik 61 (64,45,"N") (21,56,"W") 0.9 6.2 3.7 9.8 7.1 12.4 8.8 13.9' regexp = "".join(['([^\t]+)\t([^\t]+)\t$$(\d+),(\d+),"(\w)"$$\s+$$(\d+),(\d+),', '"(\w)"$$\t([^\t]+)\t([^\t]+)\t([^\t]+)\t([^\t]+)\t([^\t]+)\t([^\t]+)', '\t([^\t]+)\t([^\t]+)\n']) ndtype=[('city',str), ('elev', float), ('lat', float), ('lats', float), ('latns', '\|S1'), ('lon', float), ('lons', float), ('lonew', '\|S1'), ('apr_min', float), ('apr_max', float), ('may_min', float), ('may_max', float), ('jun_min', float), ('jun_max', float), ('jul_min', float), ('jul_max', float), ] with open('data/europe-cities-temp-mod.dat') as fh: cities = np.fromregex(fh, regexp, ndtype) print cities.size print cities['jul_max'] This should print out 17 and a list of values which are the July maximum temperatures for 17 European cities. If it does not, and you can't see what the problem is, ask your tutorial buddy for debugging help. Finally, add the code below into the code cell just before the plt.show() statement. In [ ]: lat = cities['lat'] + cities['lats']/60 lon = cities['lon'] + cities['lons']/60 lon = lonnp.where(cities['lonew'] == 'E', 1, -1) x,y = map(lon, lat) map.plot(x, y, 'bo', markersize=30, alpha=0.5) The last few steps are to save the figure as a file in PDF and PNG formats, save your work, and then share the notebook again. This time we will also share a bundle of all the work, for comparison. 1. Add the code below as a new cell at the end of your notebook, and execute it: In [ ]: plt.savefig('weather.pdf') plt.savefig('weather.png')	2,732	10,577	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.828125	3	CC-MAIN-2024-10	latest	en	0.809384
http://www.gurufocus.com/term/Accts%20Rec./CNBKA/Accounts%252BReceivable/Century%2BBancorp%252C%2BInc	1,490,835,232,000,000,000	text/html	crawl-data/CC-MAIN-2017-13/segments/1490218191444.45/warc/CC-MAIN-20170322212951-00486-ip-10-233-31-227.ec2.internal.warc.gz	537,709,601	28,262	Switch to: GuruFocus has detected 6 Warning Signs with Century Bancorp Inc \$CNBKA. More than 500,000 people have already joined GuruFocus to track the stocks they follow and exchange investment ideas. Century Bancorp Inc (NAS:CNBKA) Accounts Receivable \$9.65 Mil (As of Dec. 2016) Accounts Receivable are created when a customer has received a product but has not yet paid for that product. Century Bancorp Inc's accounts receivables for the quarter that ended in Dec. 2016 was \$9.65 Mil. Accounts receivable can be measured by Days Sales Outstanding. Century Bancorp Inc's Days Sales Outstanding for the quarter that ended in Dec. 2016 was 39.18. In Ben Grahams calculation of liquidation value, accounts receivable are only considered to be worth 75% of book value. Century Bancorp Inc's Liquidation Value for the quarter that ended in Dec. 2016 was \$-4,149.75 Mil. Definition Accounts Receivable is money owed to a business by customers and shown on its Balance Sheet as an asset. Explanation 1. Accounts Receivable are created when a customer has received a product but has not yet paid for that product. Days sales outstanding measures of the average number of days that a company takes to collect revenue after a sale has been made. It is a financial ratio that illustrates how well a company's accounts receivables are being managed. Century Bancorp Inc's Days Sales Outstanding for the quarter that ended in Dec. 2016 is calculated as: Days Sales Outstanding = Account Receivable / Revenue * Days in Period = 9.645 / 22.462 * 91 = 39.18 2. In Ben Grahams calculation of liquidation value, Century Bancorp Inc's accounts receivable are only considered to be worth 75% of book value: Century Bancorp Inc's liquidation value for the quarter that ended in Dec. 2016 is calculated as: Liquidation value = Cash and Cash Equivalents - Total Liabilities + (0.75 * Account Receivable) + (0.5 * Inventory) = 65.583 - 4222.567 + 0.75 * 9.645 + 0.5 * 0 = -4,149.75 * All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency. Be Aware Net receivables tells us a great deal about the different competitors in the same industry. In competitive industries, some attempt to gain advantage by offering better credit terms, causing increase in sales and receivables. If company consistently shows lower % Net receivables to gross sales than competitors, then it usually has some kind of competitive advantage which requires further digging. Average Days Sales Outstanding is a good indicator for measuring a companys sales channel and customers. A company may book great revenue and earnings growth but never receive payment from their customers. This may force a write-off in the future and depress future earnings. Related Terms Historical Data * All numbers are in millions except for per share data and ratio. All numbers are in their local exchange's currency. Century Bancorp Inc Annual Data Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Dec13 Dec14 Dec15 Dec16 Accts Rec. 6.59 6.72 5.81 6.60 6.02 5.81 6.54 6.24 8.00 9.65 Century Bancorp Inc Quarterly Data Sep14 Dec14 Mar15 Jun15 Sep15 Dec15 Mar16 Jun16 Sep16 Dec16 Accts Rec. 6.32 6.24 6.91 7.28 7.31 8.00 7.52 8.71 7.60 9.65 Get WordPress Plugins for easy affiliate links on Stock Tickers and Guru Names \| Earn affiliate commissions by embedding GuruFocus Charts GuruFocus Affiliate Program: Earn up to \$400 per referral. ( Learn More)	854	3,469	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.765625	3	CC-MAIN-2017-13	latest	en	0.952
https://www.coursehero.com/file/34362744/Brewer-MAT-275-ONLINE-B-Spring-2018digambleMAT-275-TEST-1v1pdf/	1,642,850,720,000,000,000	text/html	crawl-data/CC-MAIN-2022-05/segments/1642320303845.33/warc/CC-MAIN-20220122103819-20220122133819-00122.warc.gz	764,517,975	54,737	# Brewer_MAT_275_ONLINE_B_Spring_2018.digamble.MAT_275_TEST_1,v1.pdf • Test Prep • 2 • 95% (21) 20 out of 21 people found this document helpful This preview shows page 1 - 2 out of 2 pages. David Gamble Brewer MAT 275 ONLINE B Spring 2018 Assignment MAT 275 TEST 1 due 03/30/2018 at 11:39pm MST Problem 1. 1. (1 point) A function y ( t ) satisfies the differ- ential equation dy dt = - y 4 - 3 y 3 + 40 y 2 . (a) What are the constant solutions of this equation? (b) For what values of y is y increasing? Answer(s) submitted: 0,-8,5 -8 5 (correct) Problem 2. 2. (1 point) It can be helpful to classify a differ- ential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two clas- sifications are the order of the equation – (what is the highest number of derivatives involved) and whether or not the equation is linear . Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: ? 1. d 2 y dt 2 + sin ( t + y ) = sin t ? 2. y 00 - y + t 2 = 0	343	1,180	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.703125	4	CC-MAIN-2022-05	latest	en	0.819999
https://handwiki.org/wiki/Philosophy:Syllogism	1,675,616,856,000,000,000	text/html	crawl-data/CC-MAIN-2023-06/segments/1674764500273.30/warc/CC-MAIN-20230205161658-20230205191658-00193.warc.gz	308,695,187	31,915	Philosophy:Syllogism Short description: Type of logical argument that applies deductive reasoning A syllogism (Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. "Socrates" at the Louvre In its earliest form (defined by Aristotle in his 350 BCE book Prior Analytics), a syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across.[1] For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.[2] In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism.[3] From the Middle Ages onwards, categorical syllogism and syllogism were usually used interchangeably. This article is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to inductive reasoning in which facts are determined by repeated observations. Within an academic context, the syllogism was superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift (Concept Script; 1879). However, syllogisms remain useful in some circumstances, and for general-audience introductions to logic.[4][5] Early history Main page: Philosophy:History of logic In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism.[3] Aristotle Main page: Philosophy:Term logic Aristotle defines the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so."[6] Despite this very general definition, in Prior Analytics, Aristotle limits himself to categorical syllogisms that consist of three categorical propositions, including categorical modal syllogisms.[7] The use of syllogisms as a tool for understanding can be dated back to the logical reasoning discussions of Aristotle. Before the mid-12th century, medieval logicians were only familiar with a portion of Aristotle's works, including such titles as Categories and On Interpretation, works that contributed heavily to the prevailing Old Logic, or logica vetus. The onset of a New Logic, or logica nova, arose alongside the reappearance of Prior Analytics, the work in which Aristotle developed his theory of the syllogism. Prior Analytics, upon rediscovery, was instantly regarded by logicians as "a closed and complete body of doctrine," leaving very little for thinkers of the day to debate and reorganize. Aristotle's theory on the syllogism for assertoric sentences was considered especially remarkable, with only small systematic changes occurring to the concept over time. This theory of the syllogism would not enter the context of the more comprehensive logic of consequence until logic began to be reworked in general in the mid-14th century by the likes of John Buridan. Aristotle's Prior Analytics did not, however, incorporate such a comprehensive theory on the modal syllogism—a syllogism that has at least one modalized premise, that is, a premise containing the modal words 'necessarily', 'possibly', or 'contingently'. Aristotle's terminology, in this aspect of his theory, was deemed vague and in many cases unclear, even contradicting some of his statements from On Interpretation. His original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of the day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use and would be replaced by new distinctions and new theories altogether. Medieval syllogism Boethius Boethius (c. 475–526) contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of Prior Analytics went primarily unused before the 12th century, his textbooks on the categorical syllogism were central to expanding the syllogistic discussion. Rather than in any additions that he personally made to the field, Boethius's logical legacy lies in his effective transmission of prior theories to later logicians, as well as his clear and primarily accurate presentations of Aristotle's contributions. Peter Abelard Another of medieval logic's first contributors from the Latin West, Peter Abelard (1079–1142), gave his own thorough evaluation of the syllogism concept and accompanying theory in the Dialectica—a discussion of logic based on Boethius's commentaries and monographs. His perspective on syllogisms can be found in other works as well, such as Logica Ingredientibus. With the help of Abelard's distinction between de dicto modal sentences and de re modal sentences, medieval logicians began to shape a more coherent concept of Aristotle's modal syllogism model. Jean Buridan The French philosopher Jean Buridan (c. 1300 – 1361), whom some consider the foremost logician of the later Middle Ages, contributed two significant works: Treatise on Consequence and Summulae de Dialectica, in which he discussed the concept of the syllogism, its components and distinctions, and ways to use the tool to expand its logical capability. For 200 years after Buridan's discussions, little was said about syllogistic logic. Historians of logic have assessed that the primary changes in the post-Middle Age era were changes in respect to the public's awareness of original sources, a lessening of appreciation for the logic's sophistication and complexity, and an increase in logical ignorance—so that logicians of the early 20th century came to view the whole system as ridiculous.[8] Modern history The Aristotelian syllogism dominated Western philosophical thought for many centuries. Syllogism itself is about drawing valid conclusions from assumptions (axioms), rather than about verifying the assumptions. However, people over time focused on the logic aspect, forgetting the importance of verifying the assumptions. In the 17th century, Francis Bacon emphasized that experimental verification of axioms must be carried out rigorously, and cannot take syllogism itself as the best way to draw conclusions in nature.[9] Bacon proposed a more inductive approach to the observation of nature, which involves experimentation and leads to discovering and building on axioms to create a more general conclusion.[9] Yet, a full method of drawing conclusions in nature is not the scope of logic or syllogism, and the inductive method was covered in Aristotle's subsequent treatise, the Posterior Analytics. In the 19th century, modifications to syllogism were incorporated to deal with disjunctive ("A or B") and conditional ("if A then B") statements. Immanuel Kant famously claimed, in Logic (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know. (This work is not necessarily representative of Kant's mature philosophy, which is often regarded as an innovation to logic itself.) Although there were alternative systems of logic elsewhere, such as Avicennian logic or Indian logic, Kant's opinion stood unchallenged in the West until 1879, when Gottlob Frege published his Begriffsschrift (Concept Script). This introduced a calculus, a method of representing categorical statements (and statements that are not provided for in syllogism as well) by the use of quantifiers and variables. A noteworthy exception is the logic developed in Bernard Bolzano's work Wissenschaftslehre (Theory of Science, 1837), the principles of which were applied as a direct critique of Kant, in the posthumously published work New Anti-Kant (1850). The work of Bolzano had been largely overlooked until the late 20th century, among other reasons, because of the intellectual environment at the time in Bohemia, which was then part of the Austrian Empire. In the last 20 years, Bolzano's work has resurfaced and become subject of both translation and contemporary study. This led to the rapid development of sentential logic and first-order predicate logic, subsuming syllogistic reasoning, which was, therefore, after 2000 years, suddenly considered obsolete by many. The Aristotelian system is explicated in modern fora of academia primarily in introductory material and historical study. One notable exception to this modern relegation is the continued application of Aristotelian logic by officials of the Congregation for the Doctrine of the Faith, and the Apostolic Tribunal of the Roman Rota, which still requires that any arguments crafted by Advocates be presented in syllogistic format. Boole's acceptance of Aristotle George Boole's unwavering acceptance of Aristotle's logic is emphasized by the historian of logic John Corcoran in an accessible introduction to Laws of Thought.[10][11] Corcoran also wrote a point-by-point comparison of Prior Analytics and Laws of Thought.[12] According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by:[12] 1. providing it with mathematical foundations involving equations; 2. extending the class of problems it could treat, as solving equations was added to assessing validity; and 3. expanding the range of applications it could handle, such as expanding propositions of only two terms to those having arbitrarily many. More specifically, Boole agreed with what Aristotle said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced Aristotle's four propositional forms to one form, the form of equations, which by itself was a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle." Basic structure A categorical syllogism consists of three parts: 1. Major premise 2. Minor premise 3. Conclusion Each part is a categorical proposition, and each categorical proposition contains two categorical terms.[13] In Aristotle, each of the premises is in the form "All A are B," "Some A are B", "No A are B" or "Some A are not B", where "A" is one term and "B" is another: • "All A are B," and "No A are B" are termed universal propositions; • "Some A are B" and "Some A are not B" are termed particular propositions. More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion). For example: Major premise: All humans are mortal. Minor premise: All Greeks are humans. Conclusion: All Greeks are mortal. Each of the three distinct terms represents a category. From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises are universal, as is the conclusion. Major premise: All mortals die. Minor premise: All men are mortals. Conclusion: All men die. Here, the major term is die, the minor term is men, and the middle term is mortals. Again, both premises are universal, hence so is the conclusion. Polysyllogism Main page: Philosophy:Polysyllogism A polysyllogism, or a sorites, is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, one might argue that all lions are big cats, all big cats are predators, and all predators are carnivores. To conclude that therefore all lions are carnivores is to construct a sorites argument. Types Relationships between the four types of propositions in the square of opposition (Black areas are empty, red areas are nonempty.) There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): Major premise: All M are P. Minor premise: All S are M. Conclusion: All S are P. The premises and conclusion of a syllogism can be any of four types, which are labeled by letters[14] as follows. The meaning of the letters is given by the table: code quantifier subject copula predicate type example A All S are P universal affirmative All humans are mortal. E No S are P universal negative No humans are perfect. I Some S are P particular affirmative Some humans are healthy. O Some S are not P particular negative Some humans are not clever. In Prior Analytics, Aristotle uses mostly the letters A, B, and C (Greek letters alpha, beta, and gamma) as term place holders, rather than giving concrete examples. It is traditional to use is rather than are as the copula, hence All A is B rather than All As are Bs. It is traditional and convenient practice to use a, e, i, o as infix operators so the categorical statements can be written succinctly. The following table shows the longer form, the succinct shorthand, and equivalent expressions in predicate logic: Form Shorthand Predicate logic All A is B AaB $\displaystyle{ \forall x (A(x) \rightarrow B(x)) }$ or $\displaystyle{ \neg \exist x (A(x) \land \neg B(x)) }$ No A is B AeB $\displaystyle{ \neg \exist x (A(x) \land B(x)) }$ or $\displaystyle{ \forall x (A(x) \rightarrow \neg B(x)) }$ Some A is B AiB $\displaystyle{ \exist x (A(x) \land B(x)) }$ Some A is not B AoB $\displaystyle{ \exist x (A(x) \land \neg B(x)) }$ The convention here is that the letter S is the subject of the conclusion, P is the predicate of the conclusion, and M is the middle term. The major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise where it appears. The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the figure. Given that in each case the conclusion is S-P, the four figures are: Figure 1 Figure 2 Figure 3 Figure 4 M–P P–M M–P P–M S–M S–M M–S M–S (Note, however, that, following Aristotle's treatment of the figures, some logicians—e.g., Peter Abelard and Jean Buridan—reject the fourth figure as a figure distinct from the first.) Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure". The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). The table below shows the valid forms. Even some of these are sometimes considered to commit the existential fallacy, meaning they are invalid if they mention an empty category. These controversial patterns are marked in italics. All but four of the patterns in italics (felapton, darapti, fesapo and bamalip) are weakened moods, i.e. it is possible to draw a stronger conclusion from the premises. Figure 1 Figure 2 Figure 3 Figure 4 Barbara Cesare Datisi Calemes Celarent Camestres Disamis Dimatis Darii Festino Ferison Fresison Ferio Baroco Bocardo Calemos Barbari Cesaro Felapton Fesapo Celaront Camestros Darapti Bamalip <score lang="lilypond">e</score> Fig. 1, treble clef. "A syllogism's letters can be best represented in music— take E, for example." -Marilyn Damord The letters A, E, I, and O have been used since the medieval Schools to form mnemonic names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE, etc. Next to each premise and conclusion is a shorthand description of the sentence. So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term, the second term ("rectangle") is the predicate of the conclusion, and the relationship between the two terms is labeled "a" (All M are P). The following table shows all syllogisms that are essentially different. The similar syllogisms share the same premises, just written in a different way. For example "Some pets are kittens" (SiM in Darii) could also be written as "Some kittens are pets" (MiS in Datisi). In the Venn diagrams, the black areas indicate no elements, and the red areas indicate at least one element. In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression. It is also possible to use graphs (consisting of vertices and edges) to evaluate syllogisms.[15] Examples Celarent (EAE-1) Similar: Cesare (EAE-2) Darii (AII-1) Similar: Datisi (AII-3) Ferio (EIO-1) Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4) Celaront (EAO-1) Similar: Cesaro (EAO-2) Template:SyllogismSentences Camestros (AEO-2) Similar: Calemos (AEO-4) Template:SyllogismSentences Felapton (EAO-3) Similar: Fesapo (EAO-4) Template:SyllogismSentences Table of all syllogisms This table shows all 24 valid syllogisms, represented by Venn diagrams. Columns indicate similarity, and are grouped by combinations of premises. Borders correspond to conclusions. Those with an existential assumption are dashed. figure A ∧ A A ∧ E A ∧ I A ∧ O E ∧ I 1 Barbara Barbari Celarent Celaront Darii Ferio 2 Camestres Camestros Cesare Cesaro Baroco Festino 3 Darapti Felapton Datisi Disamis Bocardo Ferison 4 Bamalip Calemes Calemos Fesapo Dimatis Fresison Terms in syllogism With Aristotle, we may distinguish singular terms, such as Socrates, and general terms, such as Greeks. Aristotle further distinguished types (a) and (b): 1. terms that could be the subject of predication; and 2. terms that could be predicated of others by the use of the copula ("is a"). Such a predication is known as a distributive, as opposed to non-distributive as in Greeks are numerous. It is clear that Aristotle's syllogism works only for distributive predication, since we cannot reason All Greeks are animals, animals are numerous, therefore all Greeks are numerous. In Aristotle's view singular terms were of type (a), and general terms of type (b). Thus, Men can be predicated of Socrates but Socrates cannot be predicated of anything. Therefore, for a term to be interchangeable—to be either in the subject or predicate position of a proposition in a syllogism—the terms must be general terms, or categorical terms as they came to be called. Consequently, the propositions of a syllogism should be categorical propositions (both terms general) and syllogisms that employ only categorical terms came to be called categorical syllogisms. It is clear that nothing would prevent a singular term occurring in a syllogism—so long as it was always in the subject position—however, such a syllogism, even if valid, is not a categorical syllogism. An example is Socrates is a man, all men are mortal, therefore Socrates is mortal. Intuitively this is as valid as All Greeks are men, all men are mortal therefore all Greeks are mortals. To argue that its validity can be explained by the theory of syllogism would require that we show that Socrates is a man is the equivalent of a categorical proposition. It can be argued Socrates is a man is equivalent to All that are identical to Socrates are men, so our non-categorical syllogism can be justified by use of the equivalence above and then citing BARBARA. Existential import If a statement includes a term such that the statement is false if the term has no instances, then the statement is said to have existential import with respect to that term. It is ambiguous whether or not a universal statement of the form All A is B is to be considered as true, false, or even meaningless if there are no As. If it is considered as false in such cases, then the statement All A is B has existential import with respect to A. It is claimed Aristotle's logic system does not cover cases where there are no instances. Aristotle's goal was to develop "a companion-logic for science. He relegates fictions, such as mermaids and unicorns, to the realms of poetry and literature. In his mind, they exist outside the ambit of science, which is why he leaves no room for such non-existent entities in his logic. This is a thoughtful choice, not an inadvertent omission. Technically, Aristotelian science is a search for definitions, where a definition is 'a phrase signifying a thing's essence.'... Because non-existent entities cannot be anything, they do not, in Aristotle's mind, possess an essence... This is why he leaves no place for fictional entities like goat-stags (or unicorns)." [16] However, many logic systems developed since do consider the case where there may be no instances. Medieval logicians were aware of the problem of existential import and maintained that negative propositions do not carry existential import, and that positive propositions with subjects that do not supposit are false. The following problems arise: 1. (a) In natural language and normal use, which statements of the forms, All A is B, No A is B, Some A is B, and Some A is not B, have existential import and with respect to which terms? 2. In the four forms of categorical statements used in syllogism, which statements of the form AaB, AeB, AiB and AoB have existential import and with respect to which terms? 3. What existential imports must the forms AaB, AeB, AiB and AoB have for the square of opposition to be valid? 4. What existential imports must the forms AaB, AeB, AiB and AoB have to preserve the validity of the traditionally valid forms of syllogisms? 5. Are the existential imports required to satisfy (d) above such that the normal uses in natural languages of the forms All A is B, No A is B, Some A is B and Some A is not B are intuitively and fairly reflected by the categorical statements of forms AaB, AeB, AiB and AoB? For example, if it is accepted that AiB is false if there are no As and AaB entails AiB, then AiB has existential import with respect to A, and so does AaB. Further, if it is accepted that AiB entails BiA, then AiB and AaB have existential import with respect to B as well. Similarly, if AoB is false if there are no As, and AeB entails AoB, and AeB entails BeA (which in turn entails BoA) then both AeB and AoB have existential import with respect to both A and B. It follows immediately that all universal categorical statements have existential import with respect to both terms. If AaB and AeB is a fair representation of the use of statements in normal natural language of All A is B and No A is B respectively, then the following example consequences arise: "All flying horses are mythical" is false if there are no flying horses. If "No men are fire-eating rabbits" is true, then "There are fire-eating rabbits" is true; and so on. If it is ruled that no universal statement has existential import then the square of opposition fails in several respects (e.g. AaB does not entail AiB) and a number of syllogisms are no longer valid (e.g. BaC,AaB->AiC). These problems and paradoxes arise in both natural language statements and statements in syllogism form because of ambiguity, in particular ambiguity with respect to All. If "Fred claims all his books were Pulitzer Prize winners", is Fred claiming that he wrote any books? If not, then is what he claims true? Suppose Jane says none of her friends are poor; is that true if she has no friends? The first-order predicate calculus avoids such ambiguity by using formulae that carry no existential import with respect to universal statements. Existential claims must be explicitly stated. Thus, natural language statements—of the forms All A is B, No A is B, Some A is B, and Some A is not B—can be represented in first order predicate calculus in which any existential import with respect to terms A and/or B is either explicit or not made at all. Consequently, the four forms AaB, AeB, AiB, and AoB can be represented in first order predicate in every combination of existential import—so it can establish which construal, if any, preserves the square of opposition and the validity of the traditionally valid syllogism. Strawson claims such a construal is possible, but the results are such that, in his view, the answer to question (e) above is no. On the other hand, in modern mathematical logic, however, statements containing words "all", "some" and "no", can be stated in terms of set theory. If the set of all A's is labeled as $\displaystyle{ s(A) }$ and the set of all B's as $\displaystyle{ s(B) }$, then: • "All A is B" (AaB) is equivalent to "$\displaystyle{ s(A) }$ is a subset of $\displaystyle{ s(B) }$", or $\displaystyle{ s(A) \subseteq s(B) }$. • "No A is B" (AeB) is equivalent to "The intersection of $\displaystyle{ s(A) }$ and $\displaystyle{ s(B) }$ is empty", or $\displaystyle{ s(A) \cap s(B) = \empty }$. • "Some A is B" (AiB) is equivalent to "The intersection of $\displaystyle{ s(A) }$ and $\displaystyle{ s(B) }$ is not empty", or $\displaystyle{ s(A) \cap s(B) \neq \empty }$. • "Some A is not B" (AoB) is equivalent to "$\displaystyle{ s(A) }$ is not a subset of $\displaystyle{ s(B) }$", or $\displaystyle{ s(A) \nsubseteq s(B) }$. By definition, the empty set $\displaystyle{ \empty }$ is a subset of all sets. From this fact it follows that, according to this mathematical convention, if there are no A's, then the statements "All A is B" and "No A is B" are always true whereas the statements "Some A is B" and "Some A is not B" are always false. This also implies that AaB does not entail AiB, and some of the syllogisms mentioned above are not valid when there are no A's ($\displaystyle{ s(A) = \empty }$). Syllogistic fallacies People often make mistakes when reasoning syllogistically.[17] For instance, from the premises some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C.[18][19] However, this does not follow according to the rules of classical logic. For instance, while some cats (A) are black things (B), and some black things (B) are televisions (C), it does not follow from the parameters that some cats (A) are televisions (C). This is because in the structure of the syllogism invoked (i.e. III-1) the middle term is not distributed in either the major premise or in the minor premise, a pattern called the "fallacy of the undistributed middle". Because of this, it can be hard to follow formal logic, and a closer eye is needed in order to ensure that an argument is, in fact, valid.[20] Determining the validity of a syllogism involves determining the distribution of each term in each statement, meaning whether all members of that term are accounted for. In simple syllogistic patterns, the fallacies of invalid patterns are: References 1. Lundberg, Christian (2018). The Essential Guide to Rhetoric. Bedford/St.Martin's. pp. 38. 2. John Stuart Mill, A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation, 3rd ed., vol. 1, chap. 2 (London: John W. Parker, 1851), 190. 3. Frede, Michael. 1975. "Stoic vs. Peripatetic Syllogistic." Archive for the History of Philosophy 56:99–124. 4. Hurley, Patrick J. 2011. A Concise Introduction to Logic. Cengage Learning. ISBN:9780840034175 5. Zegarelli, Mark. 2010. Logic for Dummies. John Wiley & Sons. ISBN:9781118053072. 6. Aristotle, Prior Analytics, 24b18–20 7. Bobzien, Susanne. [2006] 2020. "Ancient Logic." Stanford Encyclopedia of Philosophy. § Aristotle. 8. Lagerlund, Henrik (2 February 2004). "Medieval Theories of the Syllogism". The Stanford Encyclopedia of Philosophy. Edward N. Zalta. Retrieved 17 February 2014. 9. Bacon, Francis. [1620] 2001. The Great Instauration. – via Constitution Society. Archived from the original on 13 April 2019. 10. Boole, George. [1854] 2003. The Laws of Thought, with an introduction by J. Corcoran. Buffalo: Prometheus Books. 11. van Evra, James. 2004. "'The Laws of Thought' by George Boole" (review). Philosophy in Review 24:167–69. 12. Corcoran, John. 2003. "Aristotle's 'Prior Analytics' and Boole's 'Laws of Thought'." History and Philosophy of Logic 24:261–88. 13. "Philosophical Dictionary: Caird-Catharsis". Philosophypages.com. 2002-08-08. 14. According to Copi, p. 127: 'The letter names are presumed to come from the Latin words "AffIrmo" and "nEgO," which mean "I affirm" and "I deny," respectively; the first capitalized letter of each word is for universal, the second for particular' 15. See, e.g., Evans, J. St. B. T (1989). Bias in human reasoning. London: LEA. 16. Khemlani, S., and P. N. Johnson-Laird. 2012. "Theories of the syllogism: A meta-analysis." Psychological Bulletin 138:427–57. 17. Chater, N., and M. Oaksford. 1999. "The Probability Heuristics Model of Syllogistic Reasoning." Cognitive Psychology 38:191–258. 18. Lundberg, Christian (2018). The Essential Guide to Rhetoric. Bedford/St. Martin's. pp. 39. Sources • Aristotle, [c. 350 BCE] 1989. Prior Analytics, translated by R. Smith. Hackett. ISBN:0-87220-064-7 • Blackburn, Simon. [1994] 1996. "Syllogism." In The Oxford Dictionary of Philosophy. Oxford University Press. ISBN:0-19-283134-8. • Broadie, Alexander. 1993. Introduction to Medieval Logic. Oxford University Press. ISBN:0-19-824026-0. • Copi, Irving. 1969. Introduction to Logic (3rd ed.). Macmillan Company. • Corcoran, John. 1972. "Completeness of an ancient logic." Journal of Symbolic Logic 37:696–702. • — 1994. "The founding of logic: Modern interpretations of Aristotle's logic." Ancient Philosophy 14:9–24. • Corcoran, John, and Hassan Masoud. 2015. "Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions." History and Philosophy of Logic 36(1):39–61. • Englebretsen, George. 1987. The New Syllogistic. Bern: Peter Lang. • Hamblin, Charles Leonard. 1970. Fallacies. London: Methuen. ISBN:0-416-70070-5. • Cf. on validity of syllogisms: "A simple set of rules of validity was finally produced in the later Middle Ages, based on the concept of Distribution." • Łukasiewicz, Jan. [1957] 1987. Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. New York: Garland Publishers. ISBN:0-8240-6924-2. OCLC 15015545. • Malink, Marko. 2013. Aristotle's Modal Syllogistic. Cambridge, MA: Harvard University Press. • Patzig, Günter. 1968. Aristotle's theory of the syllogism: a logico-philological study of Book A of the Prior Analytics. Dordrecht: Reidel. • Rescher, Nicholas. 1966. Galen and the Syllogism. University of Pittsburgh Press. ISBN:978-0822983958. • Smiley, Timothy. 1973. "What is a syllogism?" Journal of Philosophical Logic 2:136–54. • Smith, Robin. 1986. "Immediate propositions and Aristotle's proof theory." Ancient Philosophy 6:47–68. • Thom, Paul. 1981. "The Syllogism." Philosophia. München. ISBN:3-88405-002-8.	7,880	32,379	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.65625	3	CC-MAIN-2023-06	longest	en	0.934525
http://sciencehq.com/chemistry/ostwalds-dilution-law.html	1,542,632,708,000,000,000	text/html	crawl-data/CC-MAIN-2018-47/segments/1542039745762.76/warc/CC-MAIN-20181119130208-20181119152208-00545.warc.gz	297,343,762	4,409	# Ostwald’s Dilution Law Ostwald’s dilution law is the application of the law of mass action to weak electrolytes in solution. Suppose an acid HA is dissolved in water, it will ionise as under: $\underset{\underset{C(1- \alpha)} C}{HA} \leftrightharpoons \underset{\underset{C \alpha} 0}{H^+} + \underset{\underset{C \alpha} 0}{a^-} \underset{\underset{(\text{Eq. conc.}} (\text{Initial conc.)}}{}$ Applying law of mass action, $K_a = \dfrac{[H^+][A^-]}{[H A]} \\[3mm] \therefore K_a = \dfrac{(C \alpha)(C \alpha)}{C(1- \alpha)} = \dfrac{C \alpha^2}{1- \alpha}$ Where $K_a$ is the dissociation (or ionisation) constant of the acid HA and $\alpha$ is its degree of dissociation. This equation is known as Ostwald’s dilution law equation. If $\alpha <<1$ then the above equation may be written as: $K_a = C \alpha^2 or \alpha = \sqrt{\dfrac{K_a}{C}} \\ \text{As} C \propto \dfrac{1}{V} \\ \text{So} K_a = \dfrac{\alpha^2}{(1- \alpha)V} = \dfrac{\alpha^2}{V} \\[3mm] K_a.V = \alpha \\[3mm] \alpha = \sqrt{KV} \\[3mm] \alpha \propto \sqrt{V} \hspace{3mm} \text{At constant temperature}$ Thus at constant temperature degree of dissociation of weak electrolyte is directly proportional to square root of its dilution. The value of $\alpha$ can be calculated by measuring conductance of the solution as: $\alpha = \dfrac{\lambda_v}{\lambda_{infty}}$ Where $\lambda_v$is the equivalent conductance at a particular dilution and $\lambda_{\infty}$ is equivalent conductance at infinite dilution. With the help of this equation; $[H+ ]$ or $p^H$of the acid solution may be calculated. If we know the value of $\alpha$and C for any acid then $K_a$ may be calculated. For example, the value of $\alpha$for 0.05 N acetic acid is 0.03. Therefore the value of $K_a$ for acetic acid will be, $K_a = \dfrac{0.05 \times 0.03 \times 0.03}{1- 0.02} \\[3mm] 4.64 \times 10^{-5}$ Weak electrolytes obey Ostwa1d’s dilution law fairly well, but strong electrolytes do not obey this law; because these electrolytes almost completely ionise at every concentration i. e. , $\alpha =1 \hspace{2mm}\text{or} \hspace{2mm}\lambda_v = \lambda_{\infty}$ , but in practice it is not so. thus $\alpha = \lambda_v/\lambda_{\infty}$ is not applicable for strong electrolytes. It is observed that $\lambda_v < \lambda_{\infty}$even though $\alpha =1$. This is due to the following two main effects: 1. The relaxation effect: According to this effect, each cation is surrounded by a number of anions and vice versa in solution; which is called ionic atmosphere of the oppositely charged ions. On applying e.m.f., the ion moves towards oppositely charged electrode leaving behind the ionic atmosphere. To form a new ionic atmosphere some time is taken which is called relaxation time and this effect of the ionic atmosphere is called relaxation effect. Due to this effect the value of $\lambda_v$, is not limiting. 2. The electrophoretic effect: Since solvent molecules attached to the ionic atmosphere moving in the opposite direction produce friction hence reduce the motion of central ion. Related posts: 1. Group Displacement Law Group displacement law Fajan, Russel and Soddy (1913) gave group... 2. Gay-Laussac’s law Gay-Laussac’s law (1809): according to this law, “when gases react,... 3. Formulas of Gaseous State Boyle’s law, (At constant temperature) Charle’s law; Gas... 4. Pressure Temperature Law Pressure Temperature Law (Amonton’s Law): According to this Law at... 5. Dalton’s Law of Partial Pressure Dalton’s Law of Partial Pressure (1807): This law states that,...	1,032	3,568	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.71875	4	CC-MAIN-2018-47	latest	en	0.723207
http://love2learn2day.blogspot.com/2013/04/multiplying-fractions-on-geoboard-w.html	1,488,119,817,000,000,000	text/html	crawl-data/CC-MAIN-2017-09/segments/1487501172017.60/warc/CC-MAIN-20170219104612-00500-ip-10-171-10-108.ec2.internal.warc.gz	156,707,377	39,016	## Tuesday, April 30, 2013 ### Multiplying Fractions on a Geoboard (w/ free app!) It might be an understatement to say that my life changed the day I realized that you can visually represent fractions. I had a rather tortured early fraction experience. (Tummy ache every day of fourth grade if that tells you anything!) What I wouldn't have given for someone to tell me that "fractions" doesn't equate "memorizing steps that mean absolutely nothing to the average fourth grade brain!" In this little video I show you one thing that I wish someone--anyone--had shown me as a fourth grader. The Geoboard App I use is from The Math Learning Center and is free, both online and as a mobile app. 1. Thanks for sharing this! I cant wait to try it out! :) 1. Thanks for commenting, Jenny! I hope you report back. :) 2. Thanks so much for the great video! We just got this app on our student ipads and have explored it a little but I Love the idea of using it for fractions. Also love that you can use a website version. I linked that to my classroom blog so students can use it at home even if they don't have an ipad! Great idea! 1. Lesa, that's awesome! I'd love to hear more about how your use it. Thanks for your comment. :) 3. I love this! It is so clear and visual. Your students are in good hands! 1. That's so kind of you to say. Thank you! Thank you for leaving me a message. I love comments almost as much as I love chocolate! And I do LOVE chocolate. :) Blogging tips	356	1,482	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.515625	3	CC-MAIN-2017-09	longest	en	0.957648
https://www.eng-tips.com/viewthread.cfm?qid=502831	1,695,692,763,000,000,000	text/html	crawl-data/CC-MAIN-2023-40/segments/1695233510130.53/warc/CC-MAIN-20230926011608-20230926041608-00162.warc.gz	806,538,951	12,816	× INTELLIGENT WORK FORUMS FOR ENGINEERING PROFESSIONALS Are you an Engineering professional? Join Eng-Tips Forums! • Talk With Other Members • Be Notified Of Responses • Keyword Search Favorite Forums • Automated Signatures • Best Of All, It's Free! *Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail. #### Posting Guidelines Promoting, selling, recruiting, coursework and thesis posting is forbidden. # How to create a system curve for recirculation system in Epanet ## How to create a system curve for recirculation system in Epanet (OP) I'm trying to use Epanet for calculating headloss. But I'm not getting the idea of the software clearly. I'm using a pump for recirculating water through the filter for cleaning the pool. Its just a simple system having pool, pump and filter. Water comes from 2 seperate lines and entering the pump. Then pump pushes the water to the filter and through the filter to the pool again. Also how can I consider the minor losses ( elbows, tee, losses in filter,etc.) in Epanet? I just need 10m3/hr flow rate and I'm using 2" pipes. How to put the nodes and base demands? ### RE: How to create a system curve for recirculation system in Epanet Simulation of fitting and other minor losses can be easily done by just adding the total equivalent length of pipe loss to your real pipe. If you have a variable pressure loss with flow, most simulators will allow you define a flow element with a resistance coefficient proportional to flow squared. Sorry, I don't use EPANET. --Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed." ### RE: How to create a system curve for recirculation system in Epanet For such a small simple system you should just be able to use standard head loss tables. But any piping head loss will be small compared to what the max head loss is across your filter. These types of small pool pumps are pretty robust so don't mind going from high flow low head to lower flow higher head. Usually only 1-2 hp Remember - More details = better answers Also: If you get a response it's polite to respond to it. #### Red Flag This Post Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework. #### Red Flag Submitted Thank you for helping keep Eng-Tips Forums free from inappropriate posts. The Eng-Tips staff will check this out and take appropriate action. #### Resources Low-Volume Rapid Injection Molding With 3D Printed Molds Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a partâ€™s function at the center of their design considerations. Download Now Taking Control of Engineering Documents This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now Close Box # Join Eng-Tips® Today! Join your peers on the Internet's largest technical engineering professional community. It's easy to join and it's free. Here's Why Members Love Eng-Tips Forums: • Talk To Other Members • Notification Of Responses To Questions • Favorite Forums One Click Access • Keyword Search Of All Posts, And More... Register now while it's still free!	824	3,800	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.84375	3	CC-MAIN-2023-40	longest	en	0.919124
https://www.coursehero.com/file/5647279/The-density-of-the-column-of-liquid-Force-N-Area-m2-CHM/	1,495,941,023,000,000,000	text/html	crawl-data/CC-MAIN-2017-22/segments/1495463609409.62/warc/CC-MAIN-20170528024152-20170528044152-00355.warc.gz	1,097,017,259	23,701	chapter_6_Student_Sp07_6perpage # The density of the column of liquid force n area m2 This preview shows page 1. Sign up to view the full content. This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: . The density of the column of liquid. Force (N) Area (m2) CHM 25 SP07 LU P = g ·h ·d CHM 25 SP07 LU Slide 8 of 23 Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Pressure Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). P of Hg pushing down related to Hg density column height CHM 25 SP07 LU Slide 10 of 23 CHM 25 SP07 LU Slide 9 of 23 Pressure Column height measures P of atmosphere 1 standard atm = 760 mm Hg = 760 torr = 29.9 inches Hg = about 34 feet of water SI unit is PASCAL, Pa, where 1 atm = 101.325 kPa Slide 11 of 23 CHM 25 SP07 LU Simple Gas Laws Boyle 1662 P 1 V PV = constant Slide 12 of 23 CHM 25 SP07 LU CHM 25 SP07 LU 2 Boyle’ Law s A bicycle pump is a good example of Boyle’ s law. As... View Full Document ## This note was uploaded on 10/24/2009 for the course CHEM 025 taught by Professor X during the Spring '06 term at Lehigh University . Ask a homework question - tutors are online	369	1,240	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.65625	3	CC-MAIN-2017-22	longest	en	0.866233
https://proofwiki.org/wiki/Definition:Point_at_Infinity/Homogeneous_Cartesian_Coordinates/Point_on_Line	1,701,374,273,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100232.63/warc/CC-MAIN-20231130193829-20231130223829-00591.warc.gz	542,671,028	10,740	# Definition:Point at Infinity/Homogeneous Cartesian Coordinates/Point on Line ## Definition Let $\LL$ be a straight line embedded in a cartesian plane $\CC$. Let $\LL$ be given in homogeneous Cartesian coordinates by the equations: $l X + m Y + n Z = 0$ The point at infinity is expressed in homogeneous Cartesian coordinates by an ordered triple in the form: $\tuple {-m, l, n}$	90	386	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.78125	3	CC-MAIN-2023-50	latest	en	0.748963
https://www.bloodraynebetrayal.com/suzanna-escobar/articles/how-do-you-translate-logarithmic-functions/	1,722,781,775,000,000,000	text/html	crawl-data/CC-MAIN-2024-33/segments/1722640404969.12/warc/CC-MAIN-20240804133418-20240804163418-00643.warc.gz	536,988,974	30,725	## How do you translate logarithmic functions? The logarithmic function, y=logb(x) , can be shifted k units vertically and h units horizontally with the equation y=logb(x+h)+k . If k>0 , the graph would be shifted upwards. If k<0 , the graph would be shifted downwards. If h>0 , the graph would be shifted left. ## What is the domain of a transformed logarithmic function? The domain of a transformed logarithmic function is always {x ∈ R}. What are the transformations of exponential functions? Transformations of exponential graphs behave similarly to those of other functions. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f(x)=bx f ( x ) = b x without loss of shape. ### What are logarithmic functions? Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. This unknown exponent, y, equals logax. ### How do you tell if a logarithmic function is increasing or decreasing? State the domain, range, and asymptote. Before graphing, identify the behavior and key points for the graph. Since b = 5 is greater than one, we know the function is increasing. The left tail of the graph will approach the vertical asymptote x = 0, and the right tail will increase slowly without bound. How to solve logarithmic functions? Simplify the logarithmic equations by applying the appropriate laws of logarithms. • Rewrite the logarithmic equation in exponential form. • Now simplify the exponent and solve for the variable. • Verify your answer by substituting it back in the logarithmic equation. • ## How to graph logarithmic functions? Since all logarithmic functions pass through the point (1, 0), we locate and place a dot at the point. • To prevent the curve from touching the y-axis, we draw an asymptote at x = 0. • If the base of the function is greater than 1, increase your curve from left to right. Similarly, if the base is less… • ## Why are logarithmic functions used? Logarithmic functions are used to simplify complex calculations in many fields, including statistics, engineering, chemistry, physics, and music. For example, and are logarithmic functions that essentially simplify multiplication to addition and division to subtraction.	517	2,434	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.46875	4	CC-MAIN-2024-33	latest	en	0.874453
https://writeessaysformoney.net/questions/avd-economics-game-theory-there-are-6-tokens-on/	1,656,294,537,000,000,000	text/html	crawl-data/CC-MAIN-2022-27/segments/1656103324665.17/warc/CC-MAIN-20220627012807-20220627042807-00790.warc.gz	682,847,642	12,944	Avd Economics-Game Theory: There are 6 tokens on the table. Two players alternate removing some… 22. There are 6 tokens on the table. Two players alternate removing some of the tokens. In each move any player can either remove exactly one or exactly two tokens. Whoever removes the last token is the winner (tokens are worthless per se – it does not matter who removed how many of them). a) Represent this game as a game tree b) Which player is going to win? Find the subgame perfect Nash equilib- rium using backward induction. Precisely describe full strategies.	127	565	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.59375	3	CC-MAIN-2022-27	latest	en	0.914684
http://www.chegg.com/homework-help/questions-and-answers/consider-slab-copper-thickness-25-cm-area-of90-cm2-separates-environments-different-temper-q968495	1,394,547,559,000,000,000	text/html	crawl-data/CC-MAIN-2014-10/segments/1394011208420/warc/CC-MAIN-20140305092008-00056-ip-10-183-142-35.ec2.internal.warc.gz	271,827,149	6,414	# simple thermal physics 0 pts ended Consider a slab of copper which has a thickness of 25 cm and an area of 90 cm2 which separates two environments with different temperatures. Initially environment A has a temperature of 125oC and environment B has a temperature of 10oC. (Thermal conductivity of Copper = 400 W/m K) a. Determine the initial rate of energy transfer through the slab? b. Sketch the temperature of environment A as a function of time. Only changes due to heat transfer through the slab should be considered. c. On the same sketch draw the temperature of environment B as a function of time. d. Explain the form of the sketches.	146	645	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.65625	3	CC-MAIN-2014-10	latest	en	0.921073
https://www.docsity.com/en/answers/economics/statistics-and-economics/	1,508,240,554,000,000,000	text/html	crawl-data/CC-MAIN-2017-43/segments/1508187821088.8/warc/CC-MAIN-20171017110249-20171017130249-00040.warc.gz	932,689,900	10,931	# Recent questions in Statistics and Economics - Economics ## 1 #### What we study in the inferential statistics? What is the meaning of inferential statistics and what are the major concepts associated with it? 27/12/2012 ## 6 #### What type of variable is the independent variable? Can some one out in the Docsity world provide the details of the independent variable. 27/12/2012 ## 1 #### What kind of sample is the independent sample? Hey guys! One more question stuck, anyone know about the independent samples. 27/12/2012 ## 1 #### "Any one frome you please tell me the details of the these two terms. (a)group (sample) mean: (b)hypothesis" Hi all, need help!!!!!! any one please tell me about the group (sample) mean. 27/12/2012 ## 1 #### What type of mean is the grand (overall) mean? Hello everyone! My assignment is due next monday and I haven't got a clue how to solve it. The question is about the grand (overall) mean. 27/12/2012 27/12/2012 ## 1 #### What you know about the family of t distributions. I have an important test next week. I need the information for the family of t distributions. 27/12/2012 ## 1 #### What is the F ratio and what are the uses of the F ratio? I'm preparing for my exams, any one know about the F ratio. 27/12/2012 ## 6 #### Provide me the definition of the term expected frequency ? Hello to everyone on this website. Can any one know about the expected frequency. 27/12/2012	372	1,445	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.59375	3	CC-MAIN-2017-43	latest	en	0.910412
https://answerbun.com/artificial-intelligence/should-i-use-the-discounted-average-reward-as-objective-in-a-finite-horizon-problem/	1,696,389,752,000,000,000	text/html	crawl-data/CC-MAIN-2023-40/segments/1695233511351.18/warc/CC-MAIN-20231004020329-20231004050329-00770.warc.gz	110,335,322	15,646	# Should I use the discounted average reward as objective in a finite-horizon problem? Artificial Intelligence Asked by lll on December 18, 2020 I am new to reinforcement learning, but, for a finite horizon application problem, I am considering using the average reward instead of the sum of rewards as the objective. Specifically, there are a total of $$T$$ maximally possible time steps (e.g., the usage rate of an app in each time-step), in each time-step, the reward may be 0 or 1. The goal is to maximize the daily average usage rate. Episode length ($$T$$) is maximally 10. $$T$$ is the maximum time window the product can observe about a user’s behavior of the chosen data. There is an indicator value in the data indicating whether an episode terminates. From the data, it is offline learning, so in each episode, $$T$$ is given in the data. As long as an episode doesn’t terminate, there is a reward of $${0, 1}$$ in each time-step. I heard if I use an average reward for the finite horizon, the optimal policy is no longer a stationary policy, and optimal $$Q$$ function depends on time. I am wondering why this is the case. I see normally, the objective is defined maximizing $$sum_t^T gamma^t r_t$$ And I am considering two types of average reward definition. 1. $$1/T(sum^?_{t=0}gamma^t r_t)$$, $$T$$ varies is in each episode. 2. $$1/(T-t)sum^T_{i=t-1}gamma^i r_i$$ ## Related Questions ### Can GANs be used to generate something other than images? 1 Asked on November 24, 2021 ### What should the output of a neural network that needs to classify in an unsupervised fashion XOR data be? 1 Asked on November 20, 2021 ### Choosing a policy improvement algorithm for a continuing problem with continuous action and state-space 1 Asked on November 20, 2021 ### Why is the policy loss the mean of $-Q(s, mu(s))$ in the DDPG algorithm? 1 Asked on November 17, 2021 by dhanush-giriyan ### Are tabular reinforcement learning methods obsolete (or getting obsolete)? 1 Asked on November 12, 2021 ### How do I test an LSTM-based reinforcement learning model using any Atari games in OpenAI gym? 1 Asked on November 10, 2021 ### How does the target network in double DQNs find the maximum Q value for each action? 1 Asked on November 7, 2021 ### Understanding the loss function in deep Q-learning 2 Asked on November 4, 2021 ### Is a reward given at every step or only given when the RL agent fails or succeeds? 1 Asked on November 4, 2021 ### Ways to keep up with the latest developments in Machine Learning and AI? 0 Asked on November 4, 2021 by tinu ### What is the expectation of an empirical model in model based RL? 1 Asked on November 4, 2021 by ijuneja ### How can I change observation states’ values in OpenAI gym’s cartpole environment? 1 Asked on August 24, 2021 by kashan ### What does the term $\|mathcal{A}(s)\|$ mean in the $epsilon$-greedy policy? 1 Asked on August 24, 2021 by metrician ### Do the order of the features ie channel matter for a 1d convolutional network? 1 Asked on August 24, 2021 by user289602 ### What is convergence analysis, and why is it needed in reinforcement learning? 1 Asked on August 24, 2021 by daniel-koh ### Correct dimensionality of parameter vector for solving an MRP with linear function approximation? 0 Asked on August 24, 2021 by soitgoes ### How can I convert a simple CLI RPG to a compatible environment for training an RL agent via stable-baselines? 0 Asked on August 24, 2021 by seunosiko ### What is the amount of test data needed to evaluate a CNN? 0 Asked on August 24, 2021 by user38639 ### What is the Turing test? 2 Asked on August 24, 2021	974	3,671	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2023-40	latest	en	0.899254
http://www.thegasgame.com/2012/11/18/how-i-do-my-calculations-these-days/	1,466,947,683,000,000,000	text/html	crawl-data/CC-MAIN-2016-26/segments/1466783395346.6/warc/CC-MAIN-20160624154955-00044-ip-10-164-35-72.ec2.internal.warc.gz	915,262,021	31,666	# How I Do My Calculations These Days Comment on the November 4 prediction: The hike I predicted for November 8 came two days early, up to \$3.55. Then, we got another hike last week, to \$3.69. Feels like the best call here is WRONG. Sunday, November 18, 2012, 7:00PM: Here is how I have been doing my calculations lately. I have been estimating the cost to retailers in this way: start with the Chicago Spot Price from Bloomberg, (\$2.645 at the close on Friday), add in an estimated 10-cent profit for the wholesaler, 18.4 cents Federal gas tax, and 3 cents for miscellaneous costs such as transportation and storage (\$2.959). Then, add in the Michigan taxes (6% sales tax plus 19 cents per gallon), and we get a base cost to retailers of \$3.33 right now. When we get a hike, the new retail price is on average about 15 cents higher, so if there were going to be a hike on Monday, the new price would be around \$3.49. Currently, retail prices in the Grand Rapids area are in the \$3.42-\$3.59 range, so I’m not worried about any price hike coming up, and maybe we’ll make it through Thanksgiving week OK. That hike last Monday to \$3.69 was due in part to an mysterious two-day spike of 16 cents in the Chicago Spot Price, a spike that has settled down. Go figure. — Ed Aboufadel Updated: November 18, 2012 — 7:00 pm 1. Ed, Cost today 3.39 Friday was 3.34 2. Channel 8 is doing a news story about gas prices going down. Whenever they do a news story about gas, it seems there is a spike within the next 2 days. So, i’m going to predict a spike on Tuesday. 3. Hell, I’ve seen the spike hit BEFORE the news story even hits the air. The best is when they have someone standing in front of the sign as it changes(goes up). 4. Chicago unleaded is up 11.77¢ just after 12:00 noon. Brace yourself for a good spike before Thanksgiving, betcha. 5. Figured we’d get a spike tomorrow, regardless of what wholesale did. I bet Ohio sees either \$3.659 or \$3.699 tomorrow. Looks like it’s time to cash in my 2000 Kroger points and get \$2/gallon off. 6. It IS a holiday week, we WILL have a spike – LOL! 7. At the risk of stating the obvious, why is it that other products, including commodities, are not as sensitive to the daily ups and downs of commodity exchange prices? You don’t see Burger King rushing to update menus every time beef goes up in the Globex… 8. A barrel of oil is conveniently up on the middle east unrest which I’m sure will reflect in the Chicago Spot price. Greedway states can expect another 20-30 cent spike by week’s end….just watch. 9. One can only imagine the hilarity of the Speedway effect if it applied to, say, beef… “Hundreds of Burger Emperor restaurants raised prices by 20 cents a burger after a herd of cows broke thru a fence and escaped without a trace. In response, the Chicago Board of Trade raised its prices on beef futures by 10.23 cents a pound” Seriously, now, what is the point of having commodities future trading if it is used by a specific company towards a goal (wild retail price fluctuations) that is exactly the opposite of what commodities futures trading was established to prevent (i.e. wild retail price fluctuations)? 10. Ohio has begun jumping to \$3.599. Visual confirmation. 11. The price is \$3.659 for Michigan. Glad I got my E30 for \$3.339 this morning. 12. 3.659 in Grand Rapids (East side). So much for no spike. 13. Using your formula above, I calculated \$3.59 today based on the jump in the Chicago SPOT. Using that, I was able to fill up this morning for \$3.35 before it jumped to \$3.65. Thanks again! 14. This was a quick settling spike to boot. I got the Meijer notification around 11:00 AM and it was well on its way. I did fill up for \$3.28 but this time it ‘felt’ different. 15. Another concern is diesel and other distillate fuels. Diesel in many areas went up to \$4.19, and even \$4.39 at the Meijer on Tittabawassee in Saginaw, for example. I know this is the time of year that diesel and other distillate fuels are more expensive, but a 30 cent hike like that for diesel is too much. 16. David, you are welcome. I filled up yesterday morning, too, at \$3.49, because I needed gas, but my prediction was WRONG. Sorry to all! We got a one-day spike in the wholesale price on Monday, which gave them the excuse to raise prices, but that wholesale spike started subsiding on Tuesday. I am starting to work back in my data and it does appear that Speedway and friends have been pushing margins higher, at least since April. That has been throwing off my calculations and leading to more WRONGs. 17. I have been giving this increase in profits some thought. I have no empirical evidence, just anecdotal: The quick marts, such as Speedway, used to depend heavily on the inside traffic to drive profits. The daughter of an independent quickie mart here in Fort Wayne told me that the inside traffic/sales have fallen by about 10%. Thus taking the profit on chips, pop, pretzels, etc have dropped by about 33%. So the profit has to be made up someplace. Makes sense to me. But it is only an anecdotal explanation. People, myself included, have a lot less free \$\$ to spend anywhere. 18. Maybe people are getting smart, and not buying anything inside. Their prices are outrageous to begin with. Now, if only people would stop getting gas at Greed/Speedway. 19. There were some stations in the northern part of town that were \$3.059 before the jump yesterday. They went up TWICE yesterday, first to \$3.219 and then to the memo/collusuion price of \$3.599. 20. Went to 3.65 and I noticed the Speedway at leonard and 131 was one of the first. NEXT day even the prices in Rockford hadn’t changed YET so I filled up at 3.54..oh boy I have three extra dollars in my pocket! On the way home from work last nite everyone uip here fell on the bandwagon of 3.65. “There is money to be made from these travelers of the holiday, lets take them!” Whatever. At least we don’t live in the Middle East…and that I am truly thankful for. And Turbo, great analogy! 21. Ya know it baffles me that so many people (or maybe they don’t) know that Speedway controls a lot of how the gas prices rise and fall, yet in Charlotte on any given day, the parking lot of Speedway is jam packed and the QD across the road is empty. Also, can anyone explain to me why the independents and other stations find it necessary to follow Speedway and hike prices. It seems to me that if Speedway were to hike to \$3.65 and QD were to stay at \$3.35 (the price yesterday) or hike to maybe \$3.50 that Speedway either would follow suit or QD and others would gain more business. I understand the margins and making more money, but if QD is making a profit of 5 cents a gallon and Speedway is making a profit of 20 cents a gallon, yet QD is getting 10 cars buying 10 gallons each to Speedway’s 1 car, QD is still making a larger profit. Not to mention that if I buy gas at QD, I generally go in and buy a water or donut or pop and spend more money there. I guess I just don’t understand this theory that Speedway controls the Midwest market. It seems more like all stations equally are just itching to hike prices. 22. Steve, I’ve asked myself the same question for years. Why is it on one day, the competitions competes and on another day, it doesn’t? 23. Excellent analogy, Turbo! 24. There are some additional strange analogies I could come up with that defy explanation when used in our context. For example, we’re told that if prices at the terminal rise, the gas in the underground tank of a gas station all of a sudden becomes more expensive because of ‘replacement cost’. At the same time, if the prices at the terminal drop, ‘replacement cost’ goes out the window and now it’s ‘I bought expensive’. I remember reading about this from businesses selling PC processors. Say, a mail order or bricks and mortar retailer would have a few Intel P4 2.4’s sitting on the shelf for \$200 and Intel would have their regular scheduled model introductions and price cuts dropping the 2.4 to \$160. Hard as it may sound to believe, consumers actually expected to see the updated prices on retail stock never mind what the retailer paid and eventually we saw retail follow Intel price cuts pretty quickly. On a couple of occasions where Intel raised prices for one reason or another retail prices rose also. But hey, it’s not like anyone is watching. I just finished reading a book on tape about energy in general (The Quest: Energy, Security, and the Remaking of the Modern World by Daniel Yergin). Waste of time actually but one point he made was that during the major mergers of the late 90’s the Feds were concerned that no company ends up owning more than a certain percentage of the market… Of course, we all know how seriously this was taken, but it is interesting to notice that in our 5-6 state area of concern, the market share attributed to our favorite company is considerably higher than the percentages the FTC was concerned about during the mergers… Not, of course, that the FTC did anything about any of the mergers… 25. With Kroger stores doing their 4x fuel points on gift cards, I was able to cash in 2000 points yesterday. Filled up both cars for \$1.419/gallon. Take that, Speedway!! 26. I can’t say how accurate it is, but here in Fort Wayne, there is a Marathon on the South Side that is selling gas for \$3.11, and on the the near NW side, there is Kroger, Shell, and Speedway selling gas for \$3.35. Most stations are in the mid \$3.40s. Some are above \$3.50. This is a very wide range which may lead to a local reset? The zero margin, I calculate to be in the low \$3.40s, and it looks like the local average may be getting close. 27. It’s been a few months since I’ve posted here. Since I last posted, Speedway redesigned their website and finally got around to creating a Twitter account. Their first tweet was posted on October 8, but they created the account on September 28. Followers: 83 Klout Score: 40.31, True Reach: 0 28. Chicago spot holding steady, WTI Crude nearing \$90 and an Indiana Spike Line deviation of about 16 cents. Sounds like the perfect excuse for Greedway to run it up once again this week. 29. I was gonna say – gas has dropped quite a bit this last week – hence, yeah, I would imagine so. Hopefully not until tomorrow, but, my tank is full as I got it over the weekend. TheGasGame.com (c) 2015 Frontier Theme	2,526	10,444	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.671875	3	CC-MAIN-2016-26	longest	en	0.94187
https://segmentfault.com/q/1010000004517596	1,656,565,475,000,000,000	text/html	crawl-data/CC-MAIN-2022-27/segments/1656103661137.41/warc/CC-MAIN-20220630031950-20220630061950-00788.warc.gz	562,645,886	12,397	# 用kNN算法识别手写数字，归一化对准确率的影响？ PenguinGoHack • 227 ``````# 归一化，把所有不为1的值化为1 def nomalizing(array): m,n=shape(array) for i in xrange(m): for j in xrange(n): if array[i,j]!=0: array[i,j]=1 return array`````` ``````# -- coding: utf-8 -- import numpy as np import _csv as csv import operator # path 文件路径 # rowNum 可指定取数据集中特定数量向量 # 将图片转换为向量矩阵，返回数据集、类别 def loadTrainingData(path, rowNum = -1): rawData = [] with open(path) as file: for line in lines: rawData.append(line) # 去除pixel行 rawData.remove(rawData[0]) dataSet = rawData[0:rowNum] # dataSet = map(int, dataSet) dataSet = np.array(dataSet) labels = dataSet[:,0] dataSet = dataSet[:,1:] dataSet = dataSet.astype(int) # print np.shape(dataSet) resultSet = dataSet return resultSet, labels rawData = [] with open(path) as file: for line in lines: rawData.append(line) # 去除pixel行 rawData.remove(rawData[0]) dataSet = np.array(rawData) dataSet = dataSet.astype(int) resultSet = dataSet return resultSet # knn算法分类器 # inX 所要测试的向量 # dataSet 训练样本集 # labels 标签向量 # k 所选的最邻近数目 def knnClassifier(inX, dataSet, labels, k): # 矩阵化 inX = np.mat(inX) dataSet = np.mat(dataSet) labels = np.mat(labels) dataSetSize = dataSet.shape[0] # 计算与每个样本的差值 diffMat = np.tile(inX, (dataSetSize, 1)) - dataSet # 求欧式距离 sqDiffMat = np.array(diffMat)2 sqDistances = sqDiffMat.sum(axis=1) distances = sqDistances0.5 # 得到以距离排序的索引列表，距离由近到远 sortedDistIndicies = distances.argsort() #得到类别:个数的字典 classCount={} for i in range(k): voteIlabel = labels[0,sortedDistIndicies[i]] classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1 sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True) return sortedClassCount[0][0]`````` 1 个回答 `array`里面存储的是什么？像素值么？ `kNN`不是一种很有竞争力的算法，它利用的还是裸的像素值来做图像表示。 ###### 你尚未登录，登录后可以 • 和开发者交流问题的细节 • 关注并接收问题和回答的更新提醒 • 参与内容的编辑和改进，让解决方法与时俱进	703	1,824	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.015625	3	CC-MAIN-2022-27	latest	en	0.226865
https://www.mydigitalchalkboard.org/portal/default/Resources/Browser/ResourceBrowser?matchedOnly=true&sortby=view&standard=6241&action=2&page=116	1,597,207,356,000,000,000	text/html	crawl-data/CC-MAIN-2020-34/segments/1596439738864.9/warc/CC-MAIN-20200812024530-20200812054530-00264.warc.gz	761,908,688	18,542	## Resource Options • ##### Free/Non-commercial Resources: Displaying 2301-2308 of 2308 resources • Resource Type: Website / HyperLink ## Symmetry and Pattern - The Art of Oriental Rugs Subjects: Mathematics, Visual Arts & Performing Arts, Visual Arts, Geometry and 2 additional.. This Math Forum resource, reviewed for grades 6-8 by Illuminations, features information about symmetry and patterns. Oriental r... Contributor: Thinkfinity Views: 0Favorites: 0 • Resource Type: Website / HyperLink ## Line Jumper Subjects: Mathematics, Addition & Subtraction, Number Sense This interactive activity from FunBrain.com, reviewed for grades 6-8 by Illuminations, challenges students to solve addition and... Contributor: Thinkfinity Views: 0Favorites: 0 • Resource Type: Website / HyperLink ## Algebraic Problem Solving Subjects: Mathematics, Variables & Expressions, Algebra & Functions Using a spreadsheet moving from numerical to symbolic representation. This unit takes four days: formulas on a spreadsheet, set... Contributor: CTAP Region 4 Views: 0Favorites: 0 • Resource Type: Website / HyperLink ## Golden Ratio, Fibonacci Sequence Subjects: Mathematics, Geometry, Data Analysis, Statistics, and Probability, Measurement & Geometry This resource from the Math Forum s Frequently Asked Questions page explains the Golden Ratio, the Golden Rectangle, and the rel... Contributor: Thinkfinity Views: 0Favorites: 0 • Resource Type: Website / HyperLink ## Tessellations: Geometry and Symmetry Subjects: Mathematics, Geometry, Data Analysis, Statistics, and Probability, Measurement & Geometry This lesson, from the Shodor Education Foundation, Inc., allows students to examine tessellations and their geometric properties... Contributor: Thinkfinity Views: 0Favorites: 0 • Resource Type: Website / HyperLink ## Slope and Y Intercept Subjects: Mathematics, Equations and Inequalities, Coordinate Systems & Graphing, Algebra & Functions Tutorial on graphing equations and inequalities, followed by examples and practice problems. Student gets immediate feedback if ... Contributor: CTAP Region 4 Views: 0Favorites: 0 • Resource Type: Document	476	2,150	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.84375	3	CC-MAIN-2020-34	latest	en	0.751969
https://practicaldev-herokuapp-com.global.ssl.fastly.net/clearlythuydoan/big-o-notation-as-a-mid-level-developer-who-has-been-avoiding-it-since-bootcamp-arrays-and-time-complexity-np8	1,716,006,140,000,000,000	text/html	crawl-data/CC-MAIN-2024-22/segments/1715971057260.44/warc/CC-MAIN-20240518023912-20240518053912-00017.warc.gz	436,363,508	33,023	Thuy Doan Posted on # Big O Notation as a Mid-Level Developer Who Has Been Avoiding It Since Bootcamp: Arrays and Time Complexity At the beginning of this year, I was promoted to intermediate developer 🎊 At your company, that might be an IC2 - or whichever level is after your entry level developer, but right before the senior developer. In any case, I was now at a place in my career where computer science fundamentals needed to be stronger compared to the beginning when I could just throw myself into building things with what I learned in full-stack Javascript bootcamp. I decided I needed to better understand data structures and be more comfortable with algorithms. Not because I wanted to leetcode more. I really don't want to leetcode more. But I couldn't shake the feeling that I would be better off if I understood more why data structure A over data structure B. So I reached out to a friend for help and this is what I've learned 🤓 ## What did I know about Big O notation? My mental model of Big O has always been this: 1) A unit of measurement 2) Related to computer science that 3) Describes the complexity of things From here, I needed to understand why? 💭 ## Why must we measure the complexity of things? As developers, we deal with data. Sometimes not very much of it, like on a static website. Sometimes a whole lot of it. The multi-millions of users kind. And most of the time, that data is not in a format that we need and we need to manipulate it. Sort it, filter it, or find something. Sometimes we even need to change it into an entirely different format! And how efficiently we do that matters at scale. What's also true is that there are many ways to solve a problem. This is especially true in programming. You can then think of Big O notation as a way to describe how efficient a solution is relative to another one. ## What types of Big O notation are there? In this post, we'll focus just on the types that apply to arrays but know there are a number of them that you can see below: Source: Big O Cheatsheet For arrays, you can have 2 types of time complexities (or Big O): 1) Constant time or O(1) 2) Linear time or O(n) Source: Big O Notation for Arrays by KodinKevin on YouTube With Big O, the n refers to the amount of data you are working with. ## Practical Examples ### Example A. Kanto Starter Pokemon Let's say you're building a Pokemon app and you have an array of Pokemon. ``````const kantoStarters = ['Charmander', 'Bulbasaur', 'Squirtle'] `````` If you know the index of Squirtle in the array, you can access it by simply doing `kantoStarters[index]`. If this was instead an array of all 151 Kanto Pokemon, the number of steps it takes to access a Pokemon at a known index will be the same as when there were only 3 starter Pokemon because you can go directly to the index of the Pokemon. Hence, access in an array is considered constant time - also known as O(1). Because constant time takes the least number of steps to complete an operation, it is considered the most efficient. Check that first graph out again! ### Example B. All Kanto Pokemon Let's say instead of knowing where exactly to look for a Pokemon in an array, we have to flip through it like a clothing rack at the mall or files in a filing cabinet. In this case, it would take at worst as many steps as there are Pokemon. Remember that n in Big O notation stands for the amount of data we are working with. So should we have to look through an unordered array of all 151 Pokemon to find a Psyduck it would take us O(n) steps. This is called linear time because given more data we take proportionately more steps. At this point, since constant time - or O(1) - takes a constant amount of steps, no matter the amount of data versus linear time - or O(n) - which takes proportionately more steps when given more data, we can say that constant time is faster or more efficient than linear time 💨 ### Example C. It Depends Once we move into insertion or removal of data into an array, it gets a little nuanced. Let's say we create a new type of Pikachu that wears a coloured party hat (think Nintendo 64 Super Smash Bros) and we wanted to officially recognize it as a Kanto Pokemon: Party Pikachu. If we add Party Pikachu to the end of the list of Pokemon, that would only take one step. Hence, insertion at the end of arrays is constant time - or O(1). The same goes for removal. It's different, however, if we're trying to insert or remove an item from any other place in the array. Why? If we added Party Pikachu to the beginning, all the indices of the Pokemon after it would have to change because the order of Pokemon is now different. This also applies if Party Pikachu were to be added in the middle of the list. We would have to take as many steps as the number of Pokemon that come after it to change the indices to the new ones. Hence, insertion or removal anywhere but the end is linear time - or O(n). ``````const originalKantoPokemon = ['Bulbasaur', 'Ivysaur', 'Venusaur'] // and so on // Where Bulbasaur is index 0 const newKantoPokemon = ['Party Pikachu', 'Bulbasaur', 'Ivysaur'] // and so on // Where Bulbasaur is now index 1 `````` ## Career Value You might be thinking, "That's great and all but why do I need to know this?" That's fair. I've been able to have a successful last 4-5 years as a developer without it. Heck, I even got promoted. But there's two possible reasons: 1) You want to get hired at a company that does leetcode. FAANG companies - also known as Facebook, Amazon, Apple, Netflix, and Google - or similar, are infamous for testing leetcode, algorithms, and data structures in their interview process. If you want to get hired by them, you need to be able to reference Big O when you write an algorithmic solution. 2) You need to come up with efficient solutions. Even if you avoid interviewing for companies that do leetcode, you will still have to work with data. And unless you can always work with a small amount of data, how performant the solutions you write to handle data will be important. Especially as you become a more senior engineer. (This will become more apparent as I continue this series by moving into showing actual algorithms. Follow me and stay tuned!) I'm personally in the second boat but I've since been opening myself up to the idea of the first one. Let's get better first then we'll see 🤡 ## Onward I was the kind of kid who was, for all intents and purposes, intelligent but didn't identify with being good at STEM subjects despite being an honour roll student throughout my education. Heck, my favourite subject was music. But at some point, you hit a wall that makes you realize your work could go much more smoothly if you deepened your knowledge in a particular area 🚀 My goal is to be able to confidently answer why we should store data a certain way (i.e. dictionary vs. list) or traverse large amounts of data in a certain way, no matter if I'm being asked in an interview or if I simply have to complete a task for a job I'm currently employed for 💃🏻 You can think of what we discussed so far as the building blocks for choosing between multiple ways of handling data. If we know that searching through an array is linear time and we later find out that there's an alternate solution for searching through data that is constant time, which is faster, we might want to use the latter solution. However, there's other things to weigh, like readability and maintainability. More on that another time. I'll keep learning and be sure to share more 😬 Keep it candid, Thuy 🙋🏻‍♀️ Note: This post focuses more on practical examples than it does on mathematical visuals. This is because not everyone will understand Big O with mathematical graphs. But if you are someone that will, I recommend this. hidden_dude We don't always need things to be super duper fast. Often times one may prefer an O(N log N) algorithm over an O(N) one because the code will be simpler. For example, in some cases you can avoid sorting things, but doing so will make your code 5x longer and more complex. However, in general we want to avoid O(N^2) type stuff such as this Java code: ``````String s = ""; for (int i = 0; i< N; i++) { s += "something"; } `````` This sort of thing can appear in our code by mistake and can really create a lot of slow downs. And sometimes we say: "ah.. no big deal.. I'll just make it search through the list every time.. how long can that list really be?" And bad things can happen. For example: ``````while (... ) : for x in list: if x in otherList : // something `````` Adding a line to convert otherList into a set would make this algorithm linear instead of quadratic. Rarely, it really really does make sense to optimize it to as fast as possible. But that is generally when we're optimizing some process that takes minutes or hours, and we really want to bring that down as much as possible. Or if we're doing something realtime. Fortunately, often you can solve things by just using a dictionary (or hash map) or a set (or hash set) to speed up your code a lot just using the datastructures your library provides. So as a rule of thumb: 1. don't do obviously slow things (like I showed above) 2. keep your code simple (you don't have to use a heap each time or some fancy tree that will make your code too complex) 3. Use built in tools like hash maps to speed up your code 4. When it really really really matters, get super fancy but make sure you really need to go there hidden_dude Leetcode can be expensive to build and expensive to maintain. So make sure it's worth it. Also, in the real world if you're dealing with tons of data, often you delegate that hard work to the database. So writing a super fast SQL query can be more important that importing it all in RAM and running some fancy binomial queue based super treap solution. ;) Thuy Doan We don't always need things to be super duper fast. I had mentioned that there are other factors to consider like readability and maintainability so definitely agree with this! "It depends" hehe. Anthony D. Mays Well done! This is a great intro to Big O! One thing I noticed is that you said adding to an array is constant time. Not quite correct since arrays in JavaScript really work like vectors. A true array is immutable, so if you want a bigger array than what you've got, you have to create a new, larger array and copy the old elements over to it, making the resize cost O(n). Vectors hide this from you to make it easier to work with them. Thuy Doan Interesting! I don't know too much about vectors. If you have any intro resources, let me know. Thanks :) Anthony D. Mays Note that adding to a vector is amortized constant time, meaning that it essentials averages out to constant time in normal situations. You'll also notice that retrieval from a Map or Dictionary is also linear time, but is amortized constant time. Looking forward to your next article! PerezContrerasLuis Wow, excellent introduction, I'm just picking up the data structure and I have identified with your article because I think we share the same reasons ^_^ Thuy Doan Awesome! Just the tip of the ice berg for me. Many more data structures and Big O notation types to go haha. We can do it :)	2,591	11,298	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.3125	3	CC-MAIN-2024-22	latest	en	0.967567
https://m.hindlish.com/rate	1,718,514,413,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198861643.92/warc/CC-MAIN-20240616043719-20240616073719-00530.warc.gz	325,331,418	8,865	× # rate meaning in Hindi [ reit ] sound: rate sentence in Hindi ### Examples More: Next 1. So we could show the firing rate of that neuron तो हम इस न्यूरोन के तरंग भेजने की दर को दिखा सकते है 2. Check whether the loan has a variable rate of interest . पता कर लीजिए कि क्या ऋण के सूद की दर बदल सकती है । 3. Check whether the loan has a variable rate of interest . पता कर लीजिए कि क्या ऋण के सूद की दर बदल सकती है . 4. However in 1979 the growth rate slumped to 1.3 per cent . लेकिन सन् 1979 में विकास दर घटकर 1.3 प्रतिशत रह गयी . 5. Calls are charged at your local call rate. इस फोन का पैसा आपके स्थानीय फोन की दर से लिया जायेगा \| 6. The pulse rate varies from 40 to 45 per minute . नाड़ी की गति 40 से 45 प्रति मिनट के बीच बदलती रहती है . 7. Calls are charged at your local call rate . इस फोन का पैसा आपके स्थानीय फोन की दर से लिया जायेगा 8. Cannot export MP2 with this sample rate and bit rate इस नमूना दर और बिट दर के साथ MP2 निर्यात नहीं कर सकते 9. Cannot export MP2 with this sample rate and bit rate इस नमूना दर और बिट दर के साथ MP2 निर्यात नहीं कर सकते 10. The rate of growth of this industry was 3.44 per cent per year . इस उद्योग की विकास दर 3.44 प्रतिशत वार्षिक थी . ### Meaning noun. 1. the relative speed of progress or change; "he lived at a fast pace"; "he works at a great rate"; "the pace of events accelerated" synonyms： 2. amount of a charge or payment relative to some basis; "a 10-minute phone call at that rate would cost \$5" synonyms： 3. a quantity or amount or measure considered as a proportion of another quantity or amount or measure; "the literacy rate"; "the retention rate"; "the dropout rate" 4. a magnitude or frequency relative to a time unit; "they traveled at a rate of 55 miles per hour"; "the rate of change was faster than expected" verb. 1. assign a rank or rating to; "how would you rank these students?"; "The restaurant is rated highly in the food guide" synonyms：, , , , 2. estimate the value of; "How would you rate his chances to become President?"; "Gold was rated highly among the Romans" synonyms： 3. be worthy of or have a certain rating; "This bond rates highly" PC Version हिंदी संस्करण	679	2,145	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.8125	3	CC-MAIN-2024-26	latest	en	0.507416
https://forum.solidworks.com/message/418147	1,555,806,649,000,000,000	text/html	crawl-data/CC-MAIN-2019-18/segments/1555578530100.28/warc/CC-MAIN-20190421000555-20190421021618-00025.warc.gz	420,521,513	25,309	8 Replies Latest reply on Mar 24, 2014 12:48 PM by Todd Bennett # Reorder numbers function Does anyone have a function (or snippet) for reordering three variables highest to lowest? I have three variables: dimA, dimB, and dimC (all as Double). I need them reordered so that dimC is always the smallest number and dimA is always the largest. dimA and dimB may be equal as long as they are larger than dimC. dimB and dim C may be equal as long as they are smaller than dimA. If dimA, dimB, and dimC are all equal, nothing needs to change. I made some If, Then, Else statements but there is a bug I couldn't figure out (it has been deleted). Thanks, Todd • ###### Re: Reorder numbers function This works but it seems clunky. I wouldn't want to use it with many more variables. dim dblA as double dim dblB as double dim dblC as double dim tempA as double dim tempB as double tempA = dblA tempB = dblB If dblC > dblB Then dblB = dblC dblC = tempB End If If dblB > dblA Then dblA = dblB dim = tempA End If If dblC > dblB Then dblC = dblB dblB = tempB End If • ###### Re: Reorder numbers function Which language? .Net (so, c#, VB or even VSTA macros) have access to System.Collections which all have Sort facilities • ###### Re: Reorder numbers function VBA • ###### Re: Reorder numbers function I looked up "bubble sort" and the improved "selection sort". There are a few problems. 1) I haven't finished my coffee. 2) I don't know C++ (or how to convert it to VBA) 3) I'm not working with integers. 4) I haven't finished my coffee. • ###### Re: Reorder numbers function In VBA, you can use a Collection. http://stackoverflow.com/questions/3587662/how-do-i-sort-a-collection • ###### Re: Reorder numbers function Here's my fix: Function GnomeSort(ByRef pvarArray As Variant) Dim i As Long Dim j As Long Dim iMin As Long Dim iMax As Long Dim varSwap As Variant iMin = LBound(pvarArray) + 1 iMax = UBound(pvarArray) i = iMin j = i + 1 Do While i <= iMax If pvarArray(i) < pvarArray(i - 1) Then varSwap = pvarArray(i) pvarArray(i) = pvarArray(i - 1) pvarArray(i - 1) = varSwap If i > iMin Then i = i - 1 Else i = j j = j + 1 End If Loop End Function '--------------------------------------------------------------------------------- Private Sub XYZ() Dim tempVar As Variant Dim XYZvar(3) As Variant Set swApp = CreateObject("SldWorks.Application") Set Part = swApp.ActiveDoc If bPartIsReady = False Or bAssembly = False Then Corners = Part.GetPartBox(False) XYZvar(1) = Abs(Corners(3) - Corners(0)) XYZvar(2) = Abs(Corners(5) - Corners(2)) XYZvar(3) = Abs(Corners(4) - Corners(1)) tempVar = GnomeSort(XYZvar) txtX.Value = Format\$(XYZvar(3), "####.000") ' Length is always the longest side txtY.Value = Format\$(XYZvar(2), "####.000") ' Width/height/depth is whatever is not length or thickness txtZ.Value = Format\$(XYZvar(1), "####.000") ' Thickness is always the shortest side End If End Sub • ###### Re: Reorder numbers function Best way to do this is to assign your values to an array like so: Option Explicit Dim dblA, dblB, dblC, dblTemp As Double Dim dblArray(0 To 2) As Double Dim i, j As Integer Sub main() dblA = 3 dblB = 4 dblC = 1 dblArray(0) = dblA dblArray(1) = dblB dblArray(2) = dblC For i = 0 To UBound(dblArray) For j = i + 1 To UBound(dblArray) If dblArray(i) < dblArray(j) Then dblTemp = dblArray(i) dblArray(i) = dblArray(j) dblArray(j) = dblTemp End If Next j Next i dblA = dblArray(0) dblB = dblArray(1) dblC = dblArray(2) End Sub If you want to use more values just change the length of the array	1,093	3,626	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.921875	3	CC-MAIN-2019-18	longest	en	0.872525
http://supportingphysicsteaching.net/Ee03PNnugget07.html	1,544,455,930,000,000,000	text/html	crawl-data/CC-MAIN-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00139.warc.gz	275,636,317	3,839	# Mechanisms of accelerating(Exposition) ### Loudspeakers deflashing to do Loudspeakers reproduce sounds by turning the to-and-fro movements of electrical currents, which encode the sound, into the to-and-fro movements of air. Power is switched from an electrical working pathway at the loudspeaker, and again to the electrical working pathway at the ear(this may not be so helpful a way of thinking about it—so not worth emphasising,but it is defensible). What happens over here affect what happens over there, so it is a kind of remote working, and it is mechanical: pressure differences and forces on the ear and the loudspeaker are connected by the mechanical working pathway. Place a wire in a magnetic field and alter the current in it. There is a force acting on the wire that changes as the current alters, even reversing in direction as the current reverses. Force changes motion, so the wire's movements change in response to the changing current. Now you need some careful engineering so that the moving wire sets enough air in motion for people to hear, and to ensure that the movement of the wire follows the changes in the electric current exactly. Attach the wire to a cone of paper. As the wire moves, so the paper will move, in turn shifting the air. ### Improving loudspeakers The first improvement is rather easier than the second. Rather than making the current travel once through the magnetic field, make it travel through the field many times by winding the wire into a coil. An extra force, equal in magnitude and direction to the original, is acting on each transit of the wire. Add these contributing forces (one acting on each transit of the wire) to get the resultant force on the coil. This resultant force can be increased further by altering the shape of the magnetic field so that a greater length of the wire is in the field–in fact the whole of the coil. This resultant force can now drive a large surface area to-and-fro, causing significant changes in density of the air over a large enough volume for people to hear. The prices that some are willing to pay for their speakers in search of fidelity is evidence that the second improvement is not an easy quest, and that complete success is likely to be both elusive and controversial. There's much debate about the quality of sound produced by speakers, and refining this quality is a subtle art, linking together physics with psycho-acoustics. ### Simple direct current motors deflashing to do Simple electric motors spin, but arranging magnets and currents in wires to obtain this motion is not straightforward. Place a wire carefully in a magnetic field, connect a battery to drive current through the wire, and a force is acting on the wire, catapulting it out of the magnetic field at right angles to both the field and the current. This is a one-time effect and only the start of arranging for the motor to spin. As with the loudspeaker, arranging for the wire to make multiple transits of the field increases the resultant force. To achieve this, wind the wire into a coil. The charge travels up one side of the coil and back down the other–two significant transits for each turn of the coil. This time, don't reshape the magnetic field–a near-uniform field works well for simple motors. As the current reverses in direction on the return journey down the second side of the coil, so the force on the current in the wire is reversed. The wires on one side of the coil get thrown upwards; those on the other side get thrown downwards. ### How the turning happens deflashing to do The first quarter turn is achieved by adding an axis to the middle of the coil for it to spin round. With the coil now at right-angles to the magnetic field, the forces on the wires simply stretch the coil–they no longer act so as to spin it. But neither do they slow it down. That happens as soon as the coil, which is already moving, spins so that the out and back wires swap sides. The forces now act so as to return the coil to its position after the first quarter turn, at right angles to the field. To continue the spin, simply reverse the direction of the current in the wires as the coil reaches this quarter-turn position. Now, as the wires swap sides, the force acting on the current also reverses by 180 degrees. The result is that whichever wire is on one side will always be pulled down, while the wire on the other side will always be pulled up. The wire coil is kept spinning. To reverse the direction of the current, use a split-ring commutator–a simple position-dependent reversing switch made of two brushes and a sliced ring that encases the axle of the coil. ### Further improvements You can, of course, switch the magnetic field rather than the current to alter the direction of the force, but this is rather harder to do quickly. Reshaping the magnetic field by curving the poles makes the field near radial and so keeps the out and back transits of the wire at right angles to the field for longer. You can add more coils, cutting the split-ring commutator once for each coil that you add. This makes the motor smoother, just as adding more cylinders to a car motor produces a smoother torque to drive the car.	1,088	5,225	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.78125	3	CC-MAIN-2018-51	latest	en	0.929383
https://matrixmarketinggroup.com/glossary/distance/	1,721,473,106,000,000,000	text/html	crawl-data/CC-MAIN-2024-30/segments/1720763515079.90/warc/CC-MAIN-20240720083242-20240720113242-00239.warc.gz	335,798,657	56,572	# Distance Introduction Distance is a term used to describe the amount of space between two objects or points. It is a crucial concept in the fields of science, mathematics, engineering, and everyday life. From measuring the distance between planets in our solar system to calculating the distance between two cities, distance plays a vital role in understanding the world around us. What is Distance? Distance is a physical quantity that is defined as the shortest path between two points. It is commonly measured in units such as meters, kilometers, miles, or even astronomical units. The distance between two points is typically represented by the symbol d and is calculated using the Pythagorean theorem, which is a mathematical formula that uses the lengths of the sides of a right-angled triangle. Why is Distance Important? Distance is an essential concept in many areas of study and everyday life. It allows us to understand the physical world and our surroundings accurately. Measuring distance also helps us to make informed decisions, whether it is planning a trip, constructing a building, or conducting scientific experiments. In Science and Mathematics In the fields of science and mathematics, distance is a fundamental concept used to describe the space between objects or points. It is crucial in understanding the laws of physics, such as motion and gravity. For example, the distance between a planet and its moon plays a significant role in determining the gravitational force between them. In Engineering and Construction In engineering and construction, accurate measurements of distance are crucial for designing and building structures. Engineers use distance to determine the dimensions of structures, plan routes for roads and highways, and ensure the safety of buildings. In Everyday Life In everyday life, distance is used to measure the distance between two locations for navigation, determine the length of a trip, or estimate the amount of fuel needed for a journey. It is also used for measuring the sizes of objects, such as the distance between two adjacent buildings, the height of a tree, or the length of a swimming pool. Use Cases and Applicability Distance has numerous use cases in various fields, including: 1. Astronomy: In astronomy, distance is used to measure the vast distances between celestial bodies, such as planets, stars, and galaxies. 2. Surveying: Distance is essential in surveying to measure land boundaries, plot maps, and create topographic maps. 3. Sports: In sports, distance is used to measure the length of a course in races such as marathons and cycling events. 4. Navigation: Distance is crucial in navigation, whether it is for air, sea, or land travel. It helps determine the location of a person or object and plot routes for travel. 5. Medicine: In medicine, distance is used to measure the size of a tumor, the distance between bones, and the length of blood vessels. 6. Education: In education, distance is used to teach students about geometry, physics, and other subjects that involve measuring distances. Synonyms for Distance There are several synonyms for distance, such as: 1. Space 2. Gap 3. Span 4. Interval 5. Extent HTML Format: Introduction Distance is a term used to describe the amount of space between two objects or points. It is a crucial concept in the fields of science, mathematics, engineering, and everyday life. From measuring the distance between planets in our solar system to calculating the distance between two cities, distance plays a vital role in understanding the world around us. What is Distance? Distance is a physical quantity that is defined as the shortest path between two points. It is commonly measured in units such as meters, kilometers, miles, or even astronomical units. The distance between two points is typically represented by the symbol d and is calculated using the Pythagorean theorem, which is a mathematical formula that uses the lengths of the sides of a right-angled triangle. Why is Distance Important? Distance is an essential concept in many areas of study and everyday life. It allows us to understand the physical world and our surroundings accurately. Measuring distance also helps us to make informed decisions, whether it is planning a trip, constructing a building, or conducting scientific experiments. In Science and Mathematics In the fields of science and mathematics, distance is a fundamental concept used to describe the space between objects or points. It is crucial in understanding the laws of physics, such as motion and gravity. For example, the distance between a planet and its moon plays a significant role in determining the gravitational force between them. In Engineering and Construction In engineering and construction, accurate measurements of distance are crucial for designing and building structures. Engineers use distance to determine the dimensions of structures, plan routes for roads and highways, and ensure the safety of buildings. In Everyday Life In everyday life, distance is used to measure the distance between two locations for navigation, determine the length of a trip, or estimate the amount of fuel needed for a journey. It is also used for measuring the sizes of objects, such as the distance between two adjacent buildings, the height of a tree, or the length of a swimming pool. Use Cases and Applicability Distance has numerous use cases in various fields, including: Astronomy: In astronomy, distance is used to measure the vast distances between celestial bodies, such as planets, stars, and galaxies. Surveying: Distance is essential in surveying to measure land boundaries, plot maps, and create topographic maps. Sports: In sports, distance is used to measure the length of a course in races such as marathons and cycling Scroll to Top	1,119	5,843	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.859375	4	CC-MAIN-2024-30	latest	en	0.95656
http://poj.org/problem?id=1219	1,590,702,234,000,000,000	text/html	crawl-data/CC-MAIN-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00156.warc.gz	100,194,194	4,045	Online JudgeProblem SetAuthorsOnline ContestsUser Web Board F.A.Qs Statistical Charts Problems Submit Problem Online Status Prob.ID: Register Authors ranklist Current Contest Past Contests Scheduled Contests Award Contest Register Language: L-I-N-G-O: LINGO Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 1167 Accepted: 247 Description A new TV game show requires contestants to deduce a five letter word based on hints obtained by guessing other five letter words. The way the game is played is as follows: a secret five letter word is selected by the production staff of the game show. The object of the game is for the contestant to guess the secret word. The first letter of the secret word is revealed. The contestant will then guess a five letter word that may match the secret word. A computer then provides feedback to the contestant on the accuracy of the guess. Feedback consists of a report indicating if any letters in the guessed word are correct and in the same position in the secret word, if any letters in the guessed word are correct but not in the correct position in the secret word, and any letters in the guessed word that do not appear in the secret word. As an example, the production staff chooses the secret word: "HELLO". The contestant is told the first letter of the word is "H". The contestant then guesses what the word could be, knowing it begins with the letter "H". Let's say the contestant guesses the word: "HOLES". The game show computer would report that the "H" and "L" are in the secret word and in the correct position. In addition, the "O" and "E" are in the secret word, but in the incorrect position, and the "S" is not in the secret word. This is conveyed to the contestant by a single line report: HoLe. The upper case letters ("H" and "L") indicate correct letter and position. The lower case letters ("o" and "e") indicate correct letter, wrong position. The period (".") indicates a wrong letter (not in the secret word). You will write a program that evaluates the contestant guesses, and prints out the single line report for each guess.If the contestant guesses the secret word exactly, then the five capital letters of the secret word will be displayed in the report. Input The input data file consists of datasets for one or more games. A blank line marks the beginning of the next dataset (game). The line after the blank line contains the secret word. The remaining lines in the dataset represent the contestant's guesses; there may be too few or too many guesses than are necessary to guess the secret word. The secret word will contain exactly five upper case letters. The contestant抯 guesses, however, have to be checked for validity: valid guesses consist of exactly five upper case letters. Input is terminated by a dataset with the secret word: "LINGO" (that is, game play is stopped at that point, the program terminates, and no further guessing occurs). Output Each game's output should be preceded by a single blank line (except for the terminating case). The first single line status report should be printed, which consists of the first letter of the secret word, followed by four periods. For each guess, print the single line status report for that guess. For an invalid guess, repeat the previous single line status report. If the guess exactly matches the secret word, that game ends and you should move on to the next one.The contestant may guess a maximum of six times; after the sixth guess, if the contestant did not guess the secret word, or you run out of guesses (the contestant gives up) print out the secret word in lower case letters and move on to the next game. Sample Input ```HELLO HOLES HAPPY HELMS HELLO HELPS PARTY PARKS PARES PARIS PONDER PATTY PUNTS PARTY HELIX HeLIX HELIX LINGO``` Sample Output ```H.... HoLe. H.... HEL.. HELLO P.... PAR.. PAR.. PAR.. PAR.. PA.TY party H.... H.... HELIX``` Source [Submit] [Go Back] [Status] [Discuss]	915	3,967	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.859375	3	CC-MAIN-2020-24	longest	en	0.900241
https://www.padeepz.net/ce8395-question-paper-strength-of-materials-for-mechanical-engineers-regulation-2017-anna-university/	1,581,884,515,000,000,000	text/html	crawl-data/CC-MAIN-2020-10/segments/1581875141396.22/warc/CC-MAIN-20200216182139-20200216212139-00420.warc.gz	874,971,798	15,105	# CE8395 Question paper Strength of Materials for Mechanical Engineers CE8395 Question Paper Strength of Materials for Mechanical Engineers Regulation 2017 Anna University free download. Strength of Materials for Mechanical Engineers Question Paper CE8395 pdf free download. ## Sample Questions from CE8395 Question Paper Strength of Materials for Mechanical Engineers: 1. State the condition for the use of Macaulay’s method. 2. What is the maximum deflection in a simply supported beam subjected to uniformly distributed load over the entire span? 3. What is crippling load? Give the effective length of columns when both ends hinged and when both ends fixed. CE8395 Question Paper Strength of Materials for Mechanical Engineers 4. Find the critical load of an Euler’s column having 4 m length, 50 mm x 100 mm cross section and hinged at both the ends E = 200 kn/mm2. 5. Calculate the maximum deflection of a simply supported beam carrying a point load of 100 CE8395 Question Paper Strength of Materials for Mechanical Engineers CE8395 Question Paper Strength of Materials for Mechanical Engineers KN at mid span. Span = 6 m, E= 20000 kn/m2. 6. A cantilever beam of spring 2 m is carrying a point load of 20 kn at its free end. Calculate the CE8395 Question Paper Strength of Materials for Mechanical Engineers slope at the free end. Assume EI = 12 x 103 KNm2. 7. Calculate the effective length of a long column, whose actual length is 4 m when : a. Both CE8395 Question Paper Strength of Materials for Mechanical Engineers ends are fixed b. One end fixed while the other end is free. 8. A cantilever is subjected to a point load W at the free end. What is the slope and deflection at the free end? 9. What are the methods for finding out the slope and deflection at a section? 10. Why moment area method is more useful, when compared with double integration? CE8395 Question Paper Strength of Materials for Mechanical Engineers 11. Explain the Theorem for conjugate beam method? 12. What are the points to be worth for conjugate beam method? 13. What are the different modes of failures of a column? 14. Write down the Rankine formula for columns. 15. What is effective or equivalent length of column? 16. Define Slenderness Ratio. 17. Define the terms column and strut. 18. What are the advantages of Macaulay method over the double integration method, for finding the slope and deflections of beams? 19. State the limitations of Euler’s formula 20. A cantilever beam of spring 4 m is carrying a point load of 2x103Nat its free end. Calculate CE8395 Question Paper Strength of Materials for Mechanical Engineers the slope at the free end. Assume EI = 2X105N/mm2 Subject name STRENGTH OF MATERIALS FOR MECHANICAL ENGINEERS Short Name SMM Semester 4 Subject Code CE8395 Regulation 2017 regulation CE8395 Strength of Materials for Mechanical Engineers Syllabus CE8395 Strength of Materials for Mechanical Engineers Notes CE8395 Strength of Materials for Mechanical Engineers Important Questions CE8395 Strength of Materials for Mechanical Engineers Question Bank	695	3,073	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.40625	3	CC-MAIN-2020-10	latest	en	0.821654
https://www.gradesaver.com/textbooks/math/other-math/basic-college-mathematics-9th-edition/chapter-8-geometry-8-6-circles-8-6-exercises-page-577/26	1,527,239,141,000,000,000	text/html	crawl-data/CC-MAIN-2018-22/segments/1526794867055.20/warc/CC-MAIN-20180525082822-20180525102822-00395.warc.gz	756,252,477	12,652	## Basic College Mathematics (9th Edition) Total area effected by the earthquake: 2,543,400 km$^{2}$ We will treat the distance that the earthquake was felt as the radius since it was in all directions. Area of a Circle: $A$ = $\pi$$r$$^{2}$ Therefore: $A$ = (3.14)(900 km)$^{2}$ $A$ = 2,543,400 km$^{2}$	98	305	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.0625	4	CC-MAIN-2018-22	longest	en	0.963937
https://www.ademcetinkaya.com/2022/11/when-to-sell-and-when-to-hold-nse.html	1,686,066,346,000,000,000	text/html	crawl-data/CC-MAIN-2023-23/segments/1685224652959.43/warc/CC-MAIN-20230606150510-20230606180510-00173.warc.gz	669,352,534	61,043	Recurrent Neural Networks (RNNs) is a sub type of neural networks that use feedback connections. Several types of RNN models are used in predicting financial time series. This study was conducted to develop models to predict daily stock prices based on Recurrent Neural Network (RNN) Approach and to measure the accuracy of the models developed and identify the shortcomings of the models if present. We evaluate Bombay Dyeing & Mfg Company Limited prediction models with Supervised Machine Learning (ML) and Logistic Regression1,2,3,4 and conclude that the NSE BOMDYEING stock is predictable in the short/long term. According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Hold NSE BOMDYEING stock. Keywords: NSE BOMDYEING, Bombay Dyeing & Mfg Company Limited, stock forecast, machine learning based prediction, risk rating, buy-sell behaviour, stock analysis, target price analysis, options and futures. ## Key Points 1. What are main components of Markov decision process? 2. Market Signals 3. What are buy sell or hold recommendations? ## NSE BOMDYEING Target Price Prediction Modeling Methodology The stock market is an interesting industry to study. There are various variations present in it. Many experts have been studying and researching on the various trends that the stock market goes through. One of the major studies has been the attempt to predict the stock prices of various companies based on historical data. Prediction of stock prices will greatly help people to understand where and how to invest so that the risk of losing money is minimized. We consider Bombay Dyeing & Mfg Company Limited Stock Decision Process with Logistic Regression where A is the set of discrete actions of NSE BOMDYEING stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4 F(Logistic Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Supervised Machine Learning (ML)) X S(n):→ (n+1 year) $∑ i = 1 n s i$ n:Time series to forecast p:Price signals of NSE BOMDYEING stock j:Nash equilibria k:Dominated move a:Best response for target price For further technical information as per how our model work we invite you to visit the article below: How do AC Investment Research machine learning (predictive) algorithms actually work? ## NSE BOMDYEING Stock Forecast (Buy or Sell) for (n+1 year) Sample Set: Neural Network Stock/Index: NSE BOMDYEING Bombay Dyeing & Mfg Company Limited Time series to forecast n: 02 Nov 2022 for (n+1 year) According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Hold NSE BOMDYEING stock. X axis: Likelihood% (The higher the percentage value, the more likely the event will occur.) Y axis: Potential Impact% (The higher the percentage value, the more likely the price will deviate.) Z axis (Yellow to Green): Technical Analysis% ## Adjusted IFRS Prediction Methods for Bombay Dyeing & Mfg Company Limited 1. When rebalancing a hedging relationship, an entity shall update its analysis of the sources of hedge ineffectiveness that are expected to affect the hedging relationship during its (remaining) term (see paragraph B6.4.2). The documentation of the hedging relationship shall be updated accordingly. 2. Paragraph 5.7.5 permits an entity to make an irrevocable election to present in other comprehensive income changes in the fair value of an investment in an equity instrument that is not held for trading. This election is made on an instrument-by-instrument (ie share-by-share) basis. Amounts presented in other comprehensive income shall not be subsequently transferred to profit or loss. However, the entity may transfer the cumulative gain or loss within equity. Dividends on such investments are recognised in profit or loss in accordance with paragraph 5.7.6 unless the dividend clearly represents a recovery of part of the cost of the investment. 3. Credit risk analysis is a multifactor and holistic analysis; whether a specific factor is relevant, and its weight compared to other factors, will depend on the type of product, characteristics of the financial instruments and the borrower as well as the geographical region. An entity shall consider reasonable and supportable information that is available without undue cost or effort and that is relevant for the particular financial instrument being assessed. However, some factors or indicators may not be identifiable on an individual financial instrument level. In such a case, the factors or indicators should be assessed for appropriate portfolios, groups of portfolios or portions of a portfolio of financial instruments to determine whether the requirement in paragraph 5.5.3 for the recognition of lifetime expected credit losses has been met. 4. An entity is not required to restate prior periods to reflect the application of these amendments. The entity may restate prior periods if, and only if, it is possible without the use of hindsight and the restated financial statements reflect all the requirements in this Standard. If an entity does not restate prior periods, the entity shall recognise any difference between the previous carrying amount and the carrying amount at the beginning of the annual reporting period that includes the date of initial application of these amendments in the opening retained earnings (or other component of equity, as appropriate) of the annual reporting period that includes the date of initial application of these amendments. International Financial Reporting Standards (IFRS) are a set of accounting rules for the financial statements of public companies that are intended to make them consistent, transparent, and easily comparable around the world. ## Conclusions Bombay Dyeing & Mfg Company Limited assigned short-term B3 & long-term B1 forecasted stock rating. We evaluate the prediction models Supervised Machine Learning (ML) with Logistic Regression1,2,3,4 and conclude that the NSE BOMDYEING stock is predictable in the short/long term. According to price forecasts for (n+1 year) period: The dominant strategy among neural network is to Hold NSE BOMDYEING stock. ### Financial State Forecast for NSE BOMDYEING Bombay Dyeing & Mfg Company Limited Stock Options & Futures Rating Short-Term Long-Term Senior OutlookB3B1 Operational Risk 3283 Market Risk3631 Technical Analysis4365 Fundamental Analysis6642 Risk Unsystematic7259 ### Prediction Confidence Score Trust metric by Neural Network: 79 out of 100 with 850 signals. ## References 1. G. Shani, R. Brafman, and D. Heckerman. An MDP-based recommender system. In Proceedings of the Eigh- teenth conference on Uncertainty in artificial intelligence, pages 453–460. Morgan Kaufmann Publishers Inc., 2002 2. Abadie A, Diamond A, Hainmueller J. 2015. Comparative politics and the synthetic control method. Am. J. Political Sci. 59:495–510 3. L. Prashanth and M. Ghavamzadeh. Actor-critic algorithms for risk-sensitive MDPs. In Proceedings of Advances in Neural Information Processing Systems 26, pages 252–260, 2013. 4. Chernozhukov V, Newey W, Robins J. 2018c. Double/de-biased machine learning using regularized Riesz representers. arXiv:1802.08667 [stat.ML] 5. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, et al. 2018a. Double/debiased machine learning for treatment and structural parameters. Econom. J. 21:C1–68 6. Hastie T, Tibshirani R, Friedman J. 2009. The Elements of Statistical Learning. Berlin: Springer 7. Semenova V, Goldman M, Chernozhukov V, Taddy M. 2018. Orthogonal ML for demand estimation: high dimensional causal inference in dynamic panels. arXiv:1712.09988 [stat.ML] Frequently Asked QuestionsQ: What is the prediction methodology for NSE BOMDYEING stock? A: NSE BOMDYEING stock prediction methodology: We evaluate the prediction models Supervised Machine Learning (ML) and Logistic Regression Q: Is NSE BOMDYEING stock a buy or sell? A: The dominant strategy among neural network is to Hold NSE BOMDYEING Stock. Q: Is Bombay Dyeing & Mfg Company Limited stock a good investment? A: The consensus rating for Bombay Dyeing & Mfg Company Limited is Hold and assigned short-term B3 & long-term B1 forecasted stock rating. Q: What is the consensus rating of NSE BOMDYEING stock? A: The consensus rating for NSE BOMDYEING is Hold. Q: What is the prediction period for NSE BOMDYEING stock? A: The prediction period for NSE BOMDYEING is (n+1 year) ## People also ask What are the top stocks to invest in right now?	2,107	8,798	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.703125	3	CC-MAIN-2023-23	latest	en	0.932237
https://darkhavenbookreviews.com/slide/powerpoint-presentation-qzk6vk	1,610,821,210,000,000,000	text/html	crawl-data/CC-MAIN-2021-04/segments/1610703506832.21/warc/CC-MAIN-20210116165621-20210116195621-00610.warc.gz	288,993,168	55,313	# 1 Pragmatic Functional and Parallel Programming in Dyalog 1 Pragmatic Functional and Parallel Programming in Dyalog APL Morten Kromberg, CXO Dyalog Ltd Chuo University, Tokyo July 6th, 2016 Functional Parallel Programming in Dyalog APL 2 Agenda 50-Year-Old Constructs for Parallel Programing: a Brief Introduction to APL Some recent additions of parallel and asynchronous extensions to the Dyalog APL dialect of APL A very short demo - if I don't talk too much Functional Parallel Programming in Dyalog APL 3 A Programming Language (for Math) ab Problems: Mat1 +. Mat2 x f g x - Wide variety of syntactical forms - Strange and inconsistent precedence rules xy when you deal with matrices - Things get worse See http://www.jsoftware.com/papers/EvalOrder.htm ba (3x)2 +/46 an /46 Functional Parallel Programming in Dyalog APL 4 Comments The lamp symbol () indicates the beginning of a comment: 23 two times three 6 Functional Parallel Programming in Dyalog APL 5 Scalar Functions 1 2 3 + 4 5 6 addition 10 20 30 > 25 greater than 1 2 3 3 2 1 maximum 5 7 9 0 0 1 3 2 3 ? 6 6 6 6 4 3 5 4 "roll" Below: 10 times a 2x3 matrix containing the integers from 1 to 6 10 2 3 6 10 20 30 40 50 60 Functional Parallel Programming in Dyalog APL 6 Order of Execution No "precedence", only one rule: as f g x in mathematics f g x f(g(x)) Each function takes as its right argument the result of the entire expression to its right. Good APL can be read from left to right by an experienced programmer, but as a beginner you may need to break it down. 10 2 3 6 Let's experiment at https://tryapl.org: https://tryapl.org/?a=10%20%D7%202%203%20%u2374%20%u2373%206&run Functional Parallel Programming in Dyalog APL 7 Functional Parallel Programming in Dyalog APL 8 Reduction (f/ or f or f/[n]) mat 3 4 12 /mat mat 1 2 3 4 24 5 6 7 8 1680 9 10 11 12 11880 45 120 231 384 Functional Parallel Programming in Dyalog APL 9 Scan (f\ or f or f\[n]) mat 3 4 12 +\mat +mat 1 2 3 4 1 3 6 10 5 6 7 8 5 11 18 26 9 10 11 12 9 19 30 42 1 2 3 4 6 8 10 12 15 18 21 12 Functional Parallel Programming in Dyalog APL 10 Outer Product (.f) f for all combinations of items from left & right 1 2 10 vec1 .x vec2 Functional Parallel Programming in Dyalog APL 100 1000 11 Inner Product (f.g) f/ row g col for all combinations of rows left, cols right. m1 m2 1 2 0 1 1 1 0 3 0 2 1 0 m1 +. m2 1 5 2 1 +/ 1 2 0 1 2 0 (+. is the regular dot product) Functional Parallel Programming in Dyalog APL 12 Inner Product (f.g) m1 m2 1 2 0 1 1 1 0 3 0 2 1 0 m1 +.= m2 +/ 1 2 0 = 1 2 0 0 3 2 0 (+.= is count of matches) Functional Parallel Programming in Dyalog APL 13 Selected "Mixed" Functions 1/4 Rotate: and [n] mat 3 4 12 0 1 0 1mat 2 0 1mat 1 2 3 4 3 4 1 2 5 6 7 8 5 6 7 8 9 10 11 12 12 9 10 11 1 6 3 12 5 10 7 4 9 2 11 8 Functional Parallel Programming in Dyalog APL 14 Selected Mixed Functions 2/4 Take and Drop 2 2mat mat 3 4 12 1 2 3 4 5 6 7 8 5 6 9 10 11 12 9 10 5 6 7 8 9 10 11 12 1mat Functional Parallel Programming in Dyalog APL 15 Selected Mixed Functions 3/4 Transpose mat 3 4 12 1 1mat mat 1 2 3 4 1 5 9 5 6 7 8 2 6 10 9 10 11 12 3 7 11 4 8 12 1 6 11 Functional Parallel Programming in Dyalog APL 16 Selected Mixed Functions 4/4 IndexOf 3 1 4 1 5 9 1 2 3 2 7 1 Grade (Up) 3 1 4 1 5 9 2 4 1 3 5 6 {[]}3 1 4 1 5 9 index by grade 1 1 3 4 5 9 Membership 'HELLO WORLD''AEIOU' 0 1 0 0 1 0 0 1 0 0 0 Functional Parallel Programming in Dyalog APL 17 Look Ma, No Loops! The fact that map is implicit, and indexing can be done using arrays, encourages switch free logic. Your data structure acts as a control structure: Example data2 7 15 60 data 5 5 7 15 60 data + data 3 7 15 2 8 16 60 (x mask) + y ~mask ages'child' 'young' '20s' 'old' ages[14 data10] child child young old Comments if data[i]>5 then data[i] else 5 Increment where data[i] is in [3,7,15]. If mask[i] then x else y bucketing NB: This stuff is really* easy for a compiler to parallelise Functional Parallel Programming in Dyalog APL 18 Summary: Basic [Parallel] Forms The following forms have existed since the beginning: Scalar functions: +-\| * <=> ~ ! ?(roll) Reduction: / and Scan: \ Outer Product: .f Inner Product (rows-left vs cols-right): f.g and Mixed: , ?(deal) Functional Parallel Programming in Dyalog APL 19 User-defined Functions Lambdas, aka dfns provide a lexically scoped, functional form of functions in APL. Alternative to procedural style of coding from 1966 APL. plusdouble{+2} left arg + two times right fibonacci{ Tail-recursive Fibonacci. 0 1 Default left argument =0: If =0, return 1st item of (1,+/) -1 Tail recursion } Functional Parallel Programming in Dyalog APL 20 Summary: Syntax of APL Syntactical Form Example array 1 3.1415 1.2E18 function argument 6 1 2 3 4 5 6 left-arg function right-arg 1 2 3 1 10 100 1 plusdouble 2 3 1 20 300 5 7 operand operator / 1 2 3 4 5 6 2 +/ 1 2 3 4 5 6 plusdouble/1 2 3 720 3 5 7 9 11 17 left-opnd operator right-opnd 1 0 2 +. 1 2 3 7 array[indices] 'ABCDEF'[2 5 5 6] BEEF Functional Parallel Programming in Dyalog APL Result 21 1982: Nested Arrays APL2: Any item of an array can be another array Scalar functions pervade: (1 2 3) 10 (4 5 6) (7 (8 9)) 4 10 18 7080 90 Functional Parallel Programming in Dyalog APL 22 Each Operator () The Each operator maps non-scalar functions. For example, +/ reduces vectors so: +/ (4 5 6) (7 8 9) (4 5 6)+(7 8 9) 11 13 15 +/ (plus reduce each) will sum each top-level item: +/ (4 5 6) (7 8 9) (4+5+6) (7+8+9) 15 24 Functional Parallel Programming in Dyalog APL 23 Recent Extensions Modern APL has introduced additional high-order functions and combinators: Function trains (f + g) Power () applies a function repeatedly Rank () breaks arguments into sub-arrays of specified ranks Key () uses values found in one argument to partition another Stencil () applies a function to neighborhoods of each item of an array Function application using such operators can be highly optimised and parallelised by compilers (AND interpreters). Functional Parallel Programming in Dyalog APL 24 Function Trains Atop: (f g) (f g) f ( g ) 10000 (? ) 6 Roll 10000 dice w/out 10000 element temp array Fork: (f g h) (f g h) (f ) g (h ) (f + h) (f ) + (h ) (+ ) (+) ( ) mean is sum count (f g h) (f) g (h) 1 (+ , -) 0.1 (1+0.1),(1-0.1) 1.1 0.9 or 1 0.1 Tines of a fork can be computed in parallel, and Trains allow creation of more efficiently parallelisable units Functional Parallel Programming in Dyalog APL 25 Power Operator Apply a function a fixed number of times, or until the right operand function tells you to stop. 2 (+ 3) 3 Add 2 three times 9 twice2 2 +twice 3 Bind one operand; twice is a monadic opr 7 ({1+})1 until fn fn-1 1.618033989 Functional Parallel Programming in Dyalog APL 26 Rank Operator (1 of 2) mat (x1 0) vec Multiplication with left rank 1 (vectors), right rank 0 (scalars) 1 2 3 4 5 6 10 10 20 30 400 500 600 Functional Parallel Programming in Dyalog APL 100 27 Rank Operator (2 of 2) mat 2 2 4 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ((+ )2) mat avg cols 3 11 4 5 6 12 13 14 (+ ) mat average along 1 st dimension 5 9 6 7 8 10 11 12 ((+ )1) mat avg rows 2.5 6.5 10.5 14.5 Functional Parallel Programming in Dyalog APL 28 Key () Apply operand function to items corresponding to unique keys. keys 'red' 'blue' 'red' 'red' 'blue' values 10 20 30 40 50 keys { } values Group by key red 10 30 40 blue20 50 keys {,+/} values Sum items by key red 80 blue70 Functional Parallel Programming in Dyalog APL 29 Stencil () Stencil applies function operand to each item of an array and selected neighbours: 1 2 0 1 1 2 2 3 1 2 3 is same: identity function 3 ( 3) 1 2 3 Window Size = 3 2 3 0 Neighbors Items A classical blur stencil can be expressed as: ({ .25 .5 .25 +. } 3) 0 10 0 0 10 0 2.5 5 2.5 2.5 5 2.5 Functional Parallel Programming in Dyalog APL 30 John Conways Game of Life Computing the next generation: Any live cell with fewer than two live neighbours dies, as if caused by underpopulation. Any live cell with two or three live neighbours lives on to the next generation. Any live cell with more than three live neighbours dies, as if by over-population. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction. life{1 .3 4=+/,1 0 1.1 0 1.} life{1 .3 4={+/,} 3 3} Functional Parallel Programming in Dyalog APL 31 Life is a Convolution life{1 .3 4={+/,} 3 3} Stencil Life edges.2 1 2 Neighbors weighted 2, centre = 1 2 2 2 2 1 2 2 2 2 If there are two or three neighbours for a live cell, the edge-weighted sum of the 3x3 tile around the cell will be (1+2+2) or (1+2+2+2). If there are three neighbours for an empty cell (birth), the sum will be (2+2+2). So: good5 6 718 Index Origin Zero 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 And now life is a super-optimisable parallel stencil calculation: life{good[{+/,edges} 3 3]} Functional Parallel Programming in Dyalog APL 32 Neural Networks APL is a direct notation for expressing the math at the core of artificial neural networks. For example, the following function applies a sigmoid function to the output of a collection of sigmoid neurons: sn{1+-+.} contains neuron weights (rows are neurons, one col per input) is an array of input stimuli (row are inputs, one col per case). This applies the computation as a stencil of size 7 7, to an input matrix: img{1+-weights+.,} 7 7} Functional Parallel Programming in Dyalog APL 33 Parallel Functional Forms in APL Parallel Forms Sometimes Parallelizable ... f (map often implicit) f (each: explicit map) f.g (inner product) fn (rank: map sub-arrays) f (key: group by) fsz (stencil: map to neighborhoods) f/ (reduction) f\ (scan) fn (apply n times or until fixpoint) Functional Parallel Programming in Dyalog APL 34 Objects in APL: Dot is Parallel APL Namespaces are dynamic objects: lifeNS '' Create an empty namespace life.meaning42 Create variable within it (altlifeNS '').meaning321 Another one universeslife,altlife Array of namespaces universes How many items? 2 universes.meaning Parallel universes 42 321 Functional Parallel Programming in Dyalog APL 35 Class-based Objects FNEW'Form' (('Caption' 'Hello World') ('Coord' 'Pixel')('Size'(100 400))) F.(B1 B2 B3)F.NEW{'Button' (('Caption'('Button ',))('Posn'(5+500 )))}1 2 3 F.(B1 B2 B3).(Caption Posn) Button 15 55Button 25 105Button 35 155 F.(B1 B2 B3).(Posn[1]50) Functional Parallel Programming in Dyalog APL 36 More Arrays of Objects XLNEW 'OleClient' ('ClassName' 'Excel.Application') citiesXL.Workbooks.Open 'c:\...\cities.xls' sheetscities.Sheets Sheets collection as an array sheets.Name DDKUK sheets.UsedRange.Value2 Germany 82.4 Denmark 5.4 United Kingdom60.2 Berlin 3.4 Copenhagen2 London 7 Mnchen 1.2 Helsingr 0.03 Birmingham 1 Stuttgart0.5 Basingstoke 0.1 Functional Parallel Programming in Dyalog APL 37 Parallel Execution of APL Use vector instructions (SSE etc) Multithread primitives Done some scalar dyadic functions Need to look at operators and trains Compile to Parallel Hardware Aaron Hsu at Indiana University: co-dfns compiler HyperFit / University of Copenhagen: APL to Futhark Bernecky / Scholz @ Herriot Watt: Single Assignment C Introduce Asynchronous Features into Language Futures and Isolates Functional Parallel Programming in Dyalog APL 38 Compilers Compiler projects are very exciting and will make APL competitive in new areas Image manipulation Fluid dynamics-style applications But not all applications are data parallel And compilers sometimes put unpleasant constraints on the users Functional Parallel Programming in Dyalog APL 39 Interpreter Needs Help... APL is SIMD at the core But parallelising sequences of SIMD instructions is hard We have parallel cores, but they dont have parallel access to memory The user has the knowledge which is hard to deduce throught static analysis of APL: Array size vs number of parallel threads Side effects (or lack thereof) (S)he can help make decisions on when to fork and collect Conclusion: We need new language features to allow the user to express optionally asynchronous parts of algorithms Functional Parallel Programming in Dyalog APL 40 Futures and Isolates Goal: Allow the APL user to explicitly express parallelism / asynchronicty in a natural way In the interpreter, futures and isolates enable coarsegrained task parallelism Tasks with a duration of at least 100ms In a compiler, futures can be used to express finegrained data parallelism Functional Parallel Programming in Dyalog APL 41 Isolates An Isolate tastes, smells, looks like a Dyalog namespace, except that... Expressions executed in the isolate run in a separate process from the main interpreter thread (in parallel) Functional Parallel Programming in Dyalog APL 42 Isolate Example I3isolate.New3'' I3.X(1 2 3)(4 5)6 I3.({(+)}X) 2 4.5 6 X6 X1 2 3 X4 5 Functional Parallel Programming in Dyalog APL 43 Futures The result of an expression executed in an Isolate is a Future Futures can be passed as arguments to functions without blocking Structural functions can work on arrays containing futures without blocking Primitives which need to reference the value will block Functional Parallel Programming in Dyalog APL 44 The Parallel Operator Monadic operator parallel () derives a function which: - creates an empty isolate - executes the operand inside the isolate - returns a future (and discards the isolate when no longer needed) sums{+/}100 returns 100 futures - IMMEDIATELY sums structural functions do not realize futures 100 partitions(100251)sums Partitioned Enclose 4 partitions 4 groups, each containing 25 futures 25 25 25 25 +/ +/partitions 4 parallel +/es 171700 (We used 1+4+100 parallel threads to compute the end result) Functional Parallel Programming in Dyalog APL 45 Deterministic Parallelism Inserting or removing Parallel operators does not change the meaning of the code. Thus, parallelism does not interfere with the notation. sums{+/}100 sums{+/} 100 partitions(100251)sums +/+/partitions +/+/ partitions 171700 (as long as your functions have no side effects) ( and there are no errors) Functional Parallel Programming in Dyalog APL 46 The Model Implementation Futures are fully implemented in the Dyalog interpreters from v14.0 (2014) onwards The creation and management of isolates is still modelled using APL code, most importantly: Proposed Name in Primitive Construct Current Model Comment New Isolate II Parallel I Parallel Each Functional Parallel Programming in Dyalog APL 47 Demo Functional Parallel Programming in Dyalog APL 48 Fun with Isolates ! Example: Start an isolate server on each of two Raspberry Picontrolled robots, then under Windows/Linux/Mac: {isolate.AddServer '192.168.0.',}100 101 bots bot bot clone bot driver API 500 bots.Drive (45 0)(0 45) This means: call the Drive function on each bot in parallel, - With a left argument of 500ms - With right arg of (45 0) for first and (0 45) for 2nd bot (power settings for right and left wheels) Functional Parallel Programming in Dyalog APL 49 Dancing Robots Functional Parallel Programming in Dyalog APL 50 Selected Customers KCI Corp (US) Budgeting and Planning Carlisle Group (US) Collateral and Securitization for Global Capital Markets CompuGroupMedical (Sweden) Worlds Largest Patient Record system: 40,000 users and 2.5 million patients records at largest hospital in Scandinavia ExxonMobil (US) Optimizes the Cracking of Petroluem Products using APL SimCorp (DK), APL Italiana (I), Fiserv Investment Services (US), Infostroy Ltd (Russia) Leaders in various markets for Asset Management Systems A Finnish game company Functional Parallel Programming in Dyalog APL 51 Infostroy Functional Parallel Programming in Dyalog APL 52 SimCorp Functional Parallel Programming in Dyalog APL 53 APLIT Functional Parallel Programming in Dyalog APL 54 CGM TakeCare Patient Journal System Functional Parallel Programming in Dyalog APL 55 Any Questions Prefix: Roll (scalar) - Integer in range 1 to : ? 6 6 6 6 4 3 4 2 ? Infix: Deal deal items from range 1 to : 5 ? 6 2 5 1 4 6 Selfie: Permutation: ? 6 3 1 4 2 6 5 Functional Parallel Programming in Dyalog APL 56 Resources Supporting documentation and materials online: Interactive APL Session on line: http://tryapl.org (see the "resources" tab) Online Help and Manuals http://help.dyalog.com http://docs.dyalog.com Introduction to Dyalog APL by Bernard Legrand http://http://www.dyalog.com/mastering-dyalog-apl.htm Google: Try for example https://www.google.com/?q=dyalog+apl+power+operator Functional Parallel Programming in Dyalog APL ## Recently Viewed Presentations • This is an optional feature but allows you to control access to email, leverage AD groups for policies, and authenticate again corporate credentials. ... User-based authentication for access. Alert users on new or updated content. ... Set policies on a... • We are also very interested in keeping costs down for our customers and a great way of doing that is thru automation. 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Some have similar...	5,483	18,527	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.9375	3	CC-MAIN-2021-04	latest	en	0.73917
https://11011110.github.io/blog/2017/09/29/images-graph-drawing.html	1,675,198,049,000,000,000	text/html	crawl-data/CC-MAIN-2023-06/segments/1674764499890.39/warc/CC-MAIN-20230131190543-20230131220543-00659.warc.gz	85,103,796	4,472	Rather than make a traditional I-went-to-this-conference-and-saw-these-talks post, I thought it might be more interesting to put up a gallery of a few of the prettier images from the graph drawing proceedings, with explanations. This first one looks like the kabbalah, but it’s actually $$K_{4,6}$$, with the four vertices of one side of the bipartition in the center and the other six above and below them. It’s from “On Vertex- and Empty-Ply Proximity Drawings” by Angelini et al. (arXiv:1708.09233) and depicts a drawing with empty ply: if you cover each edge by two circles, centered at the edge endpoints with radius equal to half the edge length, then none of these circles contains any other vertices. This one depicts Lombardi drawings of knots (all crossings are at right angles and all curves between crossings are circular arcs) for all the knots with eight or fewer crossings that have such drawings. It’s from “Lombardi drawings of knots and links” by Kindermann et al. (arXiv:1708.09819). Maarten Löffler’s talk on this was the runner-up for the best presentation award. This is a friendship graph (a collection of triangles joined at a vertex), drawn as a quasi-thrackle. That means that, as in a thrackle, every two edges that don’t share an endpoint cross each other, but they can cross any odd number of times rather than only once. The central vertex $$v$$ appears twice in this drawing but it would be easy to stretch one of its copies around the drawing so that it only appears once. It’s from “Thrackles: An improved upper bound” by Fulek and Pach (arXiv:1708.08037), which proves that $$n$$-vertex thrackles have at most $$1.3984n$$ edges and quasi-thrackles have at most $$1.5n$$ edges. The drawing shows that the quasi-thrackle bound has the best possible constant factor. This shows two evolutionary trees, of pelicans (the light blue thick shaded tree) and their lice (the black node-link tree). Each louse has one host species that it infects, and typically those host-parasite relations are inherited (the ancestors of the parasites are ancestors of their hosts), but sometimes lice will jump sideways across the host tree from one species to another. This new visualization style is from “Visualizing co-phylogenetic reconciliations” by Calamoneri et al. (arXiv:1708.09691). This shows another complete bipartite graph, $$K_{4,8}$$, with a casing (over-under relation at each crossing) that gives only one gap per edge, from “Gap-planar Graphs” by Bae et al. (arXiv:1708.07653). An older paper of mine shows how to minimize the number of gaps per edge for a fixed drawing, but this one is about finding good drawings given only the graph. It’s also closely related to my recent paper on road crossings, which showed that crossings can be assigned to road segment in real-world road networks so that there are few assigned crossings per road segment. The difference is that this paper allows cycles of gaps (see e.g. the 4-cycles above and below the central diamond of this image) while the road network paper uses an acyclic assignment. There were plenty of other interesting papers and results, if perhaps not with quite as eye-catching graphics, so check out the full open-access proceedings for more.	759	3,239	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.890625	3	CC-MAIN-2023-06	latest	en	0.949826
https://www.jiskha.com/display.cgi?id=1399166172	1,526,941,519,000,000,000	text/html	crawl-data/CC-MAIN-2018-22/segments/1526794864558.8/warc/CC-MAIN-20180521220041-20180522000041-00340.warc.gz	771,324,313	3,744	# calculus help posted by Christine Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 4(square root of (3y)), x = 0, y = 3; V=????? 1. Steve x=4√(3y) x^2 = 48y To use discs, note that the radius of each disc is x, and the thickness is dy, so v = ∫[0,3] πx^2 dy = 48π∫[0,3] y dy = 216π To use shells, each shell has radius x, and height 3-y, so v = ∫[0,12] 2πx(3-y) dx = 2π∫[0,12] x(3-x^2/48) dx = 216π ## Similar Questions 1. ### calculus edit 1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the … 2. ### calculus Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^4, y=0, x=2, x=9; about y=–5 3. ### Calculus [rotation of region bounded by curves] Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=3x^2, x=1, y=0 about the x-axis 4. ### calculus find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region and a typical disk or washer. y^2=x, x=2y; about the y-axis i am confused because i do not know how … 5. ### Calculus I don't understand Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x … 6. ### calculus help Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis V = ? 7. ### Calculus Help Please Urgent!!! Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x^2, y = 5x, x ≥ 0; about the x-axis V = ? 8. ### calculus 2 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3x^4, y = 3x, x ≥ 0; about the x-axis 9. ### calculus Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. x+y = 3, x = 4−(y−1)^2; about the y-axis. 10. ### Calculus Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,y=1; about y=7 More Similar Questions	765	2,585	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.9375	4	CC-MAIN-2018-22	latest	en	0.856464
http://www.armoredpenguin.com/crossword/Data/best/math/vocabulary.11.html	1,444,427,489,000,000,000	text/html	crawl-data/CC-MAIN-2015-40/segments/1443737935954.77/warc/CC-MAIN-20151001221855-00003-ip-10-137-6-227.ec2.internal.warc.gz	400,365,315	8,761	### math vocabulary Mr. Bourque 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Across 1.step by step instructions 4.180 degrees 7.compares to 100% 10.fraction with an equal value 11.rectangle made up of equal rows and or equal columns 12.distance around a circle / sphere 13.triangle with two sides the same length 15.bottom number of a fraction 16.difference between the maximum and minimum 17.chart usings ones and tens 21.number expressed at the product of prime factors 22.number that divides another number 23.number subtracted 26.has two or more factors 27.polygon whose sides and angles are all equal 30.middle number in a set of numbers 32.number being divided 33.nothing evenly divisible into numerator and denominator 35.whole numbers and whole negative numbers Down 2.polygon - sides or angles are not equa; 3.distance around a shape 4.number written with the power of 10 5.numerator greater than the denominator 6.please excuse my dear Aunt Sally 14.the average of a set of numbers 18.occurs most frequently in a set of numbers 19.triangle with a right angle 20.factor found in two or more numbers 25.same size and shape on either other side of a line 28.quadrilateral with all the sides the same length 29.lines where two faces meet The look has changed! Some of the puzzles that people list for the public get indexed by the search engines (like Google). Some people find those puzzles and cannot figure out how to make a puzzle of their own. So this page now has the navigation sidebar. Use the "Printable HTML" button to get a clean page, in either HTML or PDF, that you can use your browser's print button to print. This page won't have buttons or ads, just your puzzle. The PDF format allows the web site to know how large a printer page is, and the fonts are scaled to fill the page. The PDF takes awhile to generate. Don't panic! Web armoredpenguin.com	492	1,929	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.609375	4	CC-MAIN-2015-40	longest	en	0.818082
https://www.html5gamedevs.com/topic/30494-aligning-a-set-of-planes-to-another-objects-pathsides/	1,679,590,010,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296945182.12/warc/CC-MAIN-20230323163125-20230323193125-00714.warc.gz	853,651,123	32,196	# Aligning a set of planes to another objects path/sides ## Recommended Posts So, making a card game. Im trying to spread the cards in the players hand out, essentially along an upside down, elongated U pattern (basically, the reverse of how you would hold playing cards in real life. - But reverse or not, the task is pretty much the same, fanning the cards and rotating, evenly distributing amongst a finite amount of space. - originally I tried solving it via a super janky function. Then I realized: if I draw the shape I am trying to align the objects around, in theory I could get the coordinates of various points of the shape and then essentially assign each card in hand the distributed coordinates. - So I guess I'm wondering, is there an easy way to do this? I've finally set up a playground to replicate the basic structure of my scene. Sidenote: I am trying to replicate as close as I can to what I actually have, because what I actually have is less than ideal (im having various issues with text rendering, positioning, and other things, that I think may be a scene structure type of issue. (So if you see something stupid that I am doing or that could be improved I'm all ears.) - Anyways here's scene 1, with what I am currently doing with the hand (the rotation is causing the middle cards to appear higher than the cards on the ends, which is the opposite of what I want). Instead I would rather align the bottoms of the cards to the bottom of the half ovalish shape seen here (the player hand shape object) But I have been struggling to figure out how to do so. Is there a technique to do this easily? Or anyone have any suggestions? Any help much appreciated as always. P.S. I read https://doc.babylonjs.com/overviews/how_rotations_and_translations_work which sounded like it might lead me to what I am trying to do, but it's still a little advanced for me, and ultimately, the starting point would be knowing how to split up the path of the oval shape into positions, which I am failing to figure out. (and IDK if there is a built in, easier way to align the planes to the bottom of the oval). ##### Share on other sites You could get a range of curves using curve3. Then use curve3.getPoints() and use these to create a path3D object and then not only can you get positions but also normals, tangents and binormals to the curve. You could then align the cards to the normals using RotationFromAxis to get the rotation values. ##### Share on other sites That extension seems pretty awesome. Although I couldn't get it to work with my use case. (cards were always standing up no matter how I rotated the cylinder, and doesn't handle the direction of the rotation as far as I can tell) ##### Share on other sites 2 hours ago, JohnK said: You could get a range of curves using curve3. Then use curve3.getPoints() and use these to create a path3D object and then not only can you get positions but also normals, tangents and binormals to the curve. You could then align the cards to the normals using RotationFromAxis to get the rotation values. Cool, I will take a stab at that, thanks ##### Share on other sites @thrice check this out, click on the plane to make paths where you want the card to be positioned, you can make a "U" path by clicking at different point, wait for sometime the card will appear: http://www.babylonjs-playground.com/#Z7YI2T#2 ##### Share on other sites This will be a good place to start off: ##### Share on other sites I didn't follow this thread until now, but to answer your question : yes, the code of RotationFromAxis() changed in an improved way (I hope) https://github.com/BabylonJS/Babylon.js/blob/master/dist/preview release/what's new.md it's weird that the behavior changes though Actually the former algo was more tolerant to not well designed 3 axis system (left handed) passed as a parameter (in other terms, it could compute something even with not a real LH orthogonal system and the result often looked like it were right) Does this one run a bit better ? http://www.babylonjs-playground.com/index.html#D3UFQ2#1 I just shift the parameters or this one (+ addRotation) : http://www.babylonjs-playground.com/index.html#D3UFQ2#2 Maybe did I do something wrong with the quaternion and matrices used in this new version .?I need to check this with @adam ##### Share on other sites 1 hour ago, JohnK said: Couldn't give a suggestion without trying it out to check it works It does in version 2.5 http://www.babylonjs-playground.com/index2_5.html#D3UFQ2 Exactly what I was trying to do, thanks so much! ##### Share on other sites @jerome It works if you flip the x axis: ##### Share on other sites but it used to behave differently in 2.5 http://www.babylonjs-playground.com/index2_5.html#D3UFQ2#4 I'm showing here the default axes (nothing flipped) That's what I don't really get. ##### Share on other sites The functions that RotationFromAxis is now using expects the axes to be left handed. There probably needs to be some code to check for that if we want to maintain the behavior of 2.5. ##### Share on other sites Actually the old behavior tolerance was just a side-effect ... It MUST be passed a LH orthogonal system like it's written in the API doc. ##### Share on other sites On 5/18/2017 at 2:20 PM, jerome said: I didn't follow this thread until now, but to answer your question : yes, the code of RotationFromAxis() changed in an improved way (I hope) https://github.com/BabylonJS/Babylon.js/blob/master/dist/preview release/what's new.md it's weird that the behavior changes though Actually the former algo was more tolerant to not well designed 3 axis system (left handed) passed as a parameter (in other terms, it could compute something even with not a real LH orthogonal system and the result often looked like it were right) Does this one run a bit better ? http://www.babylonjs-playground.com/index.html#D3UFQ2#1 I just shift the parameters or this one (+ addRotation) : http://www.babylonjs-playground.com/index.html#D3UFQ2#2 Maybe did I do something wrong with the quaternion and matrices used in this new version .?I need to check this with @adam So I am close to getting this working in my project, but realized there is still one more issue, which may or may not be related to what you guys were talking about the axis system (I am stuck on 2.5 version as I am using Canvas2d text library in project), but, once I got it implemented in my project, I realize that the cards were facing the wrong direction (like they were flipped over facing away), and rotated 180 degrees (flat), from where I expected them to be. - I can reproduce if I use FRONTSIDE instead of DOUBLESIDE in the playground. The only playground where I can get FRONTSIDE working as expected, is in a 3.0 playground, using the addRotation method as shown in I believe one of Jeromes examples. When I try to replicate the behavior in 2.5 by manually adding, it falls apart Any idea what's going on, or what I am doing wrong, or if this is related to issue mentioned above? ##### Share on other sites 2 hours ago, thrice said: So I am close to getting this working in my project, but realized there is still one more issue, which may or may not be related to what you guys were talking about the axis system (I am stuck on 2.5 version as I am using Canvas2d text library in project), but, once I got it implemented in my project, I realize that the cards were facing the wrong direction (like they were flipped over facing away), and rotated 180 degrees (flat), from where I expected them to be. - I can reproduce if I use FRONTSIDE instead of DOUBLESIDE in the playground. The only playground where I can get FRONTSIDE working as expected, is in a 3.0 playground, using the addRotation method as shown in I believe one of Jeromes examples. When I try to replicate the behavior in 2.5 by manually adding, it falls apart Any idea what's going on, or what I am doing wrong, or if this is related to issue mentioned above? I THINK, I may have finally figured out a working solution by backporting the addRotation method in master. Still, I had to rotate Y by -Math.PI (not -Math.PI /2 as in master version), so the discrepancy seems a bit strange ##### Share on other sites Looks like that did it, except still suffering from upside down behavior (which ended up being easy fixed after backporting addRotation, as just needed to rotate z by Math.PI) https://playground.babylonjs.com/index2_5.html#KGPGAV#2 - coolio ## Join the conversation You can post now and register later. If you have an account, sign in now to post with your account. Note: Your post will require moderator approval before it will be visible. × Pasted as rich text. Paste as plain text instead Only 75 emoji are allowed.	2,102	8,816	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.84375	3	CC-MAIN-2023-14	longest	en	0.967978
http://experiment-ufa.ru/1020-is-what-percent-of-2220	1,513,163,928,000,000,000	text/html	crawl-data/CC-MAIN-2017-51/segments/1512948522999.27/warc/CC-MAIN-20171213104259-20171213124259-00165.warc.gz	106,821,941	6,952	# 1020 is what percent of 2220 - step by step solution ## Simple and best practice solution for 1020 is what percent of 2220. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework. If it's not what You are looking for type in the calculator fields your own values, and You will get the solution. To get the solution, we are looking for, we need to point out what we know. 1. We assume, that the number 2220 is 100% - because it's the output value of the task. 2. We assume, that x is the value we are looking for. 3. If 100% equals 2220, so we can write it down as 100%=2220. 4. We know, that x% equals 1020 of the output value, so we can write it down as x%=1020. 5. Now we have two simple equations: 1) 100%=2220 2) x%=1020 where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that: 100%/x%=2220/1020 6. Now we just have to solve the simple equation, and we will get the solution we are looking for. 7. Solution for 1020 is what percent of 2220 100%/x%=2220/1020 (100/x)x=(2220/1020)x - we multiply both sides of the equation by x 100=2.3*x - we divide both sides of the equation by (2.3) to get x 100/2.3=x 45.=x x=45. now we have: 1020 is 45.% of 2220 ## Related pages finding least common denominator calculatorprime factorization 147gcf monomials calculator40-6-71sin 4x graphadd improper fractions calculatorprime factorization 49math solution finder144-640.625 as a fraction in simplest form8x squaredsolve tanx 1derivative calculator stepshow do you write 0.8 as a fraction2log5factor 25x 2-16derivative of cos3xgreatest common multiple finderrtd rtprime factorization 252mdt solution4y x 149.99 to eurofractions addition calculatordividing mixed numbers and fractions calculatorppqrstgcf of 42 and 66how to graph y 5xderivative of e xsinxx 5y graphconvert 0.85 to a fraction726.5solve cos 2x65-307x 3y 29x 7i 3 3x 7uwhat is the prime factorization of 59determine the prime factorization of 90factor x2 6x 8what is the square root of 196 simplifiedroman numeral conversionshow to graph y 4xcosh2xwhat is 0.11111 as a fraction2sinx-1 0y 2cosxfind the prime factorization of 140square root of 2401820-100.6 percent as a decimalsinh 2x5x 2 10xthe prime factorization of 200hgfvfactorization tableadding fractions with variables calculatorderivative of cosxy 2 sinx2020 in roman numeralsprime factorization of 528derivative of x cosx220-45sin 2x derivative64rprime factorization of 4412997924581965 in roman numeralssimplify the square root of 320bodmas theory1982 roman numeralsinequalities calculator with stepslcm of two numbers calculatorgcf of 150graph of 2x 25h 5tx 3y 9 graphsolve 3x 2y 8simplify x 2 3x 2	838	2,803	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.15625	4	CC-MAIN-2017-51	longest	en	0.876086
https://p2p.wrox.com/visual-c/87289-i-need-help.html	1,701,450,664,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100290.24/warc/CC-MAIN-20231201151933-20231201181933-00643.warc.gz	529,293,268	10,223	Wrox Programmer Forums I need a help. \| Visual C++ Questions specific to Microsoft's Visual C++. For questions not specific to this Microsoft version, use the C++ Programming forum instead. Welcome to the p2p.wrox.com Forums. You are currently viewing the Visual C++ section of the Wrox Programmer to Programmer discussions. This is a community of software programmers and website developers including Wrox book authors and readers. New member registration was closed in 2019. New posts were shut off and the site was archived into this static format as of October 1, 2020. If you require technical support for a Wrox book please contact http://hub.wiley.com April 17th, 2012, 09:33 AM undead Registered User Join Date: Apr 2012 Posts: 1 Thanks: 0 Thanked 0 Times in 0 Posts I need a help. Quote: how to be a problem here, my code does not calculate the complex roots, the code only calculates the real roots Code: ```//horner's polynomial soln, synthetic division #include <iostream> #include <conio.h> #include <stdio.h> #include <math.h> using namespace std; int main() { int it, n, i; double a,b,c,x=-1000; cout<<"Enter the degree of the polynomial:"; cin>>n; a=new double [n]; b=new double [n]; c=new double [n]; cout<<"Enter the coefficients of the polynomial"<<endl; for ( i = 0; i < n; i++ ) cin >> a[i]; do { it = 0; c[0] = a[0]; b[0] = a[0]; do { for ( i = 1; i < n; i++ ) b[i] = a[i] + xb[i-1]; for ( i = 1; i < n; i++ ) c[i] = b[i] + x*c[i-1]; x = x - b[n]/c[n-1]; it++; } while (abs( b[n]) > 1e-5 && it<100 ); cout << "The root is:" << x << endl; n--; for ( i = 0; i < n; i++ ) a[i] = b[i]; } while( n >= 1 ); getch(); return 0; }``` my code can't calculated a complex root, imaginare numbers. i don't know how can i used this library #include <complex.h> Last edited by undead; April 17th, 2012 at 10:36 AM.. Contact Us - Wrox - Privacy Statement - Top Powered by vBulletin® Copyright ©2000 - 2020, Jelsoft Enterprises Ltd. Copyright (c) 2020 John Wiley & Sons, Inc.	600	2,007	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.03125	3	CC-MAIN-2023-50	latest	en	0.825672
http://www.gregthatcher.com/Stocks/StockFourierAnalysisDetails.aspx?ticker=SRTI	1,524,708,982,000,000,000	text/html	crawl-data/CC-MAIN-2018-17/segments/1524125948047.85/warc/CC-MAIN-20180426012045-20180426032045-00072.warc.gz	426,500,279	102,638	Back to list of Stocks See Also: Seasonal Analysis of SRTIGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks # Fourier Analysis of SRTI (SRTI Blockchain Generation Incorporated) SRTI (SRTI Blockchain Generation Incorporated) appears to have interesting cyclic behaviour every 93 weeks (.2459cosine), 84 weeks (.2217cosine), and 77 weeks (.2066cosine). SRTI (SRTI Blockchain Generation Incorporated) has an average price of .55 (topmost row, frequency = 0). Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest. ## Fourier Analysis Using data from 7/13/2000 to 4/23/2018 for SRTI (SRTI Blockchain Generation Incorporated), this program was able to calculate the following Fourier Series: Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod 0.55236 0 1.49295 .40529 (12π)/929929 weeks 2.39387 .16183 (22π)/929465 weeks 3.41907 .20525 (32π)/929310 weeks 4.362 .20596 (42π)/929232 weeks 5.39767 .23039 (52π)/929186 weeks 6.27465 .28888 (62π)/929155 weeks 7.22825 .20472 (72π)/929133 weeks 8.23917 .21235 (82π)/929116 weeks 9.21377 .17364 (92π)/929103 weeks 10.24591 .18805 (102π)/92993 weeks 11.22165 .19186 (112π)/92984 weeks 12.2066 .20157 (122π)/92977 weeks 13.19427 .19025 (132π)/92971 weeks 14.18593 .18838 (142π)/92966 weeks 15.19515 .18318 (152π)/92962 weeks 16.1927 .21333 (162π)/92958 weeks 17.1413 .21268 (172π)/92955 weeks 18.15248 .19201 (182π)/92952 weeks 19.13859 .19205 (192π)/92949 weeks 20.15758 .19072 (202π)/92946 weeks 21.13586 .22007 (212π)/92944 weeks 22.10632 .21689 (222π)/92942 weeks 23.09818 .19767 (232π)/92940 weeks 24.10073 .20428 (242π)/92939 weeks 25.07701 .20678 (252π)/92937 weeks 26.06714 .1898 (262π)/92936 weeks 27.06177 .19066 (272π)/92934 weeks 28.05498 .18486 (282π)/92933 weeks 29.0423 .1812 (292π)/92932 weeks 30.03671 .16368 (302π)/92931 weeks 31.04444 .16634 (312π)/92930 weeks 32.02093 .16836 (322π)/92929 weeks 33.02234 .14983 (332π)/92928 weeks 34.01853 .14795 (342π)/92927 weeks 35.00887 .1393 (352π)/92927 weeks 36.00964 .12572 (362π)/92926 weeks 37.01305 .1153 (372π)/92925 weeks 38.02517 .11791 (382π)/92924 weeks 39.01567 .12309 (392π)/92924 weeks 40.00966 .1177 (402π)/92923 weeks 41.0017 .10652 (412π)/92923 weeks 42.01279 .09366 (422π)/92922 weeks 43.02106 .09733 (432π)/92922 weeks 44.02034 .10047 (442π)/92921 weeks 45.01282 .10027 (452π)/92921 weeks 46.01558 .09488 (462π)/92920 weeks 47.01324 .09651 (472π)/92920 weeks 48.0151 .09264 (482π)/92919 weeks 49.01104 .09468 (492π)/92919 weeks 50.00877 .08981 (502π)/92919 weeks 51.00617 .09224 (512π)/92918 weeks 52.0011 .08257 (522π)/92918 weeks 53.00585 .0811 (532π)/92918 weeks 54.00119 .07922 (542π)/92917 weeks 55.00047 .07156 (552π)/92917 weeks 56.0036 .06727 (562π)/92917 weeks 57.00427 .0628 (572π)/92916 weeks 58.01102 .05711 (582π)/92916 weeks 59.02002 .05904 (592π)/92916 weeks 60.02139 .06384 (602π)/92915 weeks 61.0226 .07028 (612π)/92915 weeks 62.01794 .07171 (622π)/92915 weeks 63.01896 .0709 (632π)/92915 weeks 64.0174 .07589 (642π)/92915 weeks 65.01169 .07687 (652π)/92914 weeks 66.00898 .07486 (662π)/92914 weeks 67.00636 .07446 (672π)/92914 weeks 68.00373 .07373 (682π)/92914 weeks 69.00059 .07361 (692π)/92913 weeks 70-.00249 .06762 (702π)/92913 weeks 71.00032 .07139 (712π)/92913 weeks 72-.01101 .07371 (722π)/92913 weeks 73-.01911 .06552 (732π)/92913 weeks 74-.01797 .05412 (742π)/92913 weeks 75-.01616 .05075 (752π)/92912 weeks 76-.01464 .04908 (762π)/92912 weeks 77-.01978 .04613 (772π)/92912 weeks 78-.02144 .03481 (782π)/92912 weeks 79-.01179 .03148 (792π)/92912 weeks 80-.01432 .0302 (802π)/92912 weeks 81-.00739 .02404 (812π)/92911 weeks 82-.0083 .02815 (822π)/92911 weeks 83-.01037 .01937 (832π)/92911 weeks 84-.00086 .01591 (842π)/92911 weeks 85-.00074 .01638 (852π)/92911 weeks 86.00354 .01418 (862π)/92911 weeks 87.00658 .01569 (872π)/92911 weeks 88.00268 .01145 (882π)/92911 weeks 89.01079 .00488 (892π)/92910 weeks 90.01784 .00531 (902π)/92910 weeks 91.02324 .00906 (912π)/92910 weeks 92.022 .0108 (922π)/92910 weeks 93.02751 .00919 (932π)/92910 weeks 94.03037 .01323 (942π)/92910 weeks 95.03247 .01199 (952π)/92910 weeks 96.03695 .01492 (962π)/92910 weeks 97.03996 .01905 (972π)/92910 weeks 98.04033 .02324 (982π)/9299 weeks 99.04085 .02626 (992π)/9299 weeks 100.04055 .02862 (1002π)/9299 weeks 101.04249 .03179 (1012π)/9299 weeks 102.03863 .03728 (1022π)/9299 weeks 103.03582 .0362 (1032π)/9299 weeks 104.03407 .03882 (1042π)/9299 weeks 105.03365 .03589 (1052π)/9299 weeks 106.03656 .03731 (1062π)/9299 weeks 107.03516 .04233 (1072π)/9299 weeks 108.03046 .04435 (1082π)/9299 weeks 109.02676 .0421 (1092π)/9299 weeks 110.02744 .04071 (1102π)/9298 weeks 111.02789 .03985 (1112π)/9298 weeks 112.02726 .04374 (1122π)/9298 weeks 113.02234 .04142 (1132π)/9298 weeks 114.0256 .04082 (1142π)/9298 weeks 115.02238 .04314 (1152π)/9298 weeks 116.02318 .03997 (1162π)/9298 weeks 117.02402 .04058 (1172π)/9298 weeks 118.02246 .04374 (1182π)/9298 weeks 119.0181 .0436 (1192π)/9298 weeks 120.01694 .04079 (1202π)/9298 weeks 121.01576 .0395 (1212π)/9298 weeks 122.01668 .03595 (1222π)/9298 weeks 123.01639 .0353 (1232π)/9298 weeks 124.01814 .03334 (1242π)/9297 weeks 125.01993 .03288 (1252π)/9297 weeks 126.02281 .03386 (1262π)/9297 weeks 127.02382 .0373 (1272π)/9297 weeks 128.02165 .03872 (1282π)/9297 weeks 129.0213 .03874 (1292π)/9297 weeks 130.0202 .04078 (1302π)/9297 weeks 131.01762 .04027 (1312π)/9297 weeks 132.01605 .03893 (1322π)/9297 weeks 133.01723 .03744 (1332π)/9297 weeks 134.01835 .03799 (1342π)/9297 weeks 135.01739 .03931 (1352π)/9297 weeks 136.01684 .03959 (1362π)/9297 weeks 137.01645 .0393 (1372π)/9297 weeks 138.01749 .04063 (1382π)/9297 weeks 139.0151 .04273 (1392π)/9297 weeks 140.01271 .04247 (1402π)/9297 weeks 141.01098 .04137 (1412π)/9297 weeks 142.0108 .04212 (1422π)/9297 weeks 143.00767 .04224 (1432π)/9296 weeks 144.00596 .04159 (1442π)/9296 weeks 145.00153 .03993 (1452π)/9296 weeks 146.0024 .03457 (1462π)/9296 weeks 147.00359 .03865 (1472π)/9296 weeks 148-.00203 .03417 (1482π)/9296 weeks 149.00213 .03107 (1492π)/9296 weeks 150-.00061 .03297 (1502π)/9296 weeks 151-.00245 .02767 (1512π)/9296 weeks 152.00028 .02705 (1522π)/9296 weeks 153-.00217 .02616 (1532π)/9296 weeks 154-.0011 .01987 (1542π)/9296 weeks 155.0021 .02036 (1552π)/9296 weeks 156.00122 .01759 (1562π)/9296 weeks 157.00716 .01546 (1572π)/9296 weeks 158.00809 .01923 (1582π)/9296 weeks 159.00753 .01885 (1592π)/9296 weeks 160.00682 .01855 (1602π)/9296 weeks 161.00661 .01362 (1612π)/9296 weeks 162.01476 .01398 (1622π)/9296 weeks 163.0127 .0202 (1632π)/9296 weeks 164.01106 .01495 (1642π)/9296 weeks 165.01532 .01531 (1652π)/9296 weeks 166.01742 .01671 (1662π)/9296 weeks 167.01873 .02028 (1672π)/9296 weeks 168.01739 .0206 (1682π)/9296 weeks 169.0171 .02151 (1692π)/9295 weeks 170.0183 .02129 (1702π)/9295 weeks 171.01933 .02297 (1712π)/9295 weeks 172.01975 .02651 (1722π)/9295 weeks 173.01509 .02824 (1732π)/9295 weeks 174.01417 .02423 (1742π)/9295 weeks 175.0158 .02531 (1752π)/9295 weeks 176.0147 .02695 (1762π)/9295 weeks 177.01374 .02637 (1772π)/9295 weeks 178.01513 .02572 (1782π)/9295 weeks 179.01471 .02968 (1792π)/9295 weeks 180.00928 .02974 (1802π)/9295 weeks 181.01049 .02602 (1812π)/9295 weeks 182.01082 .02835 (1822π)/9295 weeks 183.00887 .02745 (1832π)/9295 weeks 184.00992 .02679 (1842π)/9295 weeks 185.00764 .02918 (1852π)/9295 weeks 186.00383 .02732 (1862π)/9295 weeks 187.00493 .025 (1872π)/9295 weeks 188.0027 .02471 (1882π)/9295 weeks 189.00311 .02095 (1892π)/9295 weeks 190.00348 .02125 (1902π)/9295 weeks 191.00377 .019 (1912π)/9295 weeks 192.00439 .02026 (1922π)/9295 weeks 193.00174 .0164 (1932π)/9295 weeks 194.00646 .0134 (1942π)/9295 weeks 195.00752 .0181 (1952π)/9295 weeks 196.00478 .01494 (1962π)/9295 weeks 197.0092 .01419 (1972π)/9295 weeks 198.00815 .01614 (1982π)/9295 weeks 199.00721 .01331 (1992π)/9295 weeks 200.01072 .01244 (2002π)/9295 weeks 201.01247 .01476 (2012π)/9295 weeks 202.01232 .0169 (2022π)/9295 weeks 203.01124 .01636 (2032π)/9295 weeks 204.01321 .01461 (2042π)/9295 weeks 205.01391 .01853 (2052π)/9295 weeks 206.01083 .01917 (2062π)/9295 weeks 207.01086 .01708 (2072π)/9294 weeks 208.01124 .01804 (2082π)/9294 weeks 209.01124 .01653 (2092π)/9294 weeks 210.01268 .0184 (2102π)/9294 weeks 211.0109 .01894 (2112π)/9294 weeks 212.01068 .01867 (2122π)/9294 weeks 213.01015 .01918 (2132π)/9294 weeks 214.00938 .01919 (2142π)/9294 weeks 215.00884 .0173 (2152π)/9294 weeks 216.00995 .01807 (2162π)/9294 weeks 217.00968 .01785 (2172π)/9294 weeks 218.01012 .01958 (2182π)/9294 weeks 219.00655 .01927 (2192π)/9294 weeks 220.00701 .01662 (2202π)/9294 weeks 221.00826 .01725 (2212π)/9294 weeks 222.00734 .01701 (2222π)/9294 weeks 223.00796 .01819 (2232π)/9294 weeks 224.00548 .01888 (2242π)/9294 weeks 225.00377 .01478 (2252π)/9294 weeks 226.0057 .01395 (2262π)/9294 weeks 227.00604 .01386 (2272π)/9294 weeks 228.0065 .01375 (2282π)/9294 weeks 229.00685 .01391 (2292π)/9294 weeks 230.00697 .01329 (2302π)/9294 weeks 231.00635 .01366 (2312π)/9294 weeks 232.00647 .01264 (2322π)/9294 weeks 233.00721 .01211 (2332π)/9294 weeks 234.0079 .01579 (2342π)/9294 weeks 235.00312 .01354 (2352π)/9294 weeks 236.00498 .0099 (2362π)/9294 weeks 237.00664 .01067 (2372π)/9294 weeks 238.00656 .01194 (2382π)/9294 weeks 239.00422 .01249 (2392π)/9294 weeks 240.00368 .0097 (2402π)/9294 weeks 241.00273 .0078 (2412π)/9294 weeks 242.0039 .00606 (2422π)/9294 weeks 243.00537 .00545 (2432π)/9294 weeks 244.00609 .00467 (2442π)/9294 weeks 245.0064 .00433 (2452π)/9294 weeks 246.00784 .00311 (2462π)/9294 weeks 247.00853 .00289 (2472π)/9294 weeks 248.00918 .00264 (2482π)/9294 weeks 249.00988 .0033 (2492π)/9294 weeks 250.01091 .00158 (2502π)/9294 weeks 251.01178 .00271 (2512π)/9294 weeks 252.01063 .00159 (2522π)/9294 weeks 253.01226 .00121 (2532π)/9294 weeks 254.01355 -.00048 (2542π)/9294 weeks 255.01599 .0003 (2552π)/9294 weeks 256.01689 .00043 (2562π)/9294 weeks 257.01953 .00242 (2572π)/9294 weeks 258.01831 .00404 (2582π)/9294 weeks 259.01762 .00391 (2592π)/9294 weeks 260.01762 .00306 (2602π)/9294 weeks 261.01967 .00227 (2612π)/9294 weeks 262.0195 .00372 (2622π)/9294 weeks 263.02105 .0038 (2632π)/9294 weeks 264.02144 .00486 (2642π)/9294 weeks 265.02048 .00421 (2652π)/9294 weeks 266.02288 .00497 (2662π)/9293 weeks 267.02179 .00546 (2672π)/9293 weeks 268.02384 .00598 (2682π)/9293 weeks 269.02382 .00597 (2692π)/9293 weeks 270.02564 .00744 (2702π)/9293 weeks 271.02436 .00903 (2712π)/9293 weeks 272.02507 .00867 (2722π)/9293 weeks 273.0248 .01021 (2732π)/9293 weeks 274.02587 .00912 (2742π)/9293 weeks 275.02668 .01243 (2752π)/9293 weeks 276.02624 .01268 (2762π)/9293 weeks 277.0257 .01557 (2772π)/9293 weeks 278.02448 .01558 (2782π)/9293 weeks 279.02412 .01644 (2792π)/9293 weeks 280.02161 .01642 (2802π)/9293 weeks 281.02264 .01562 (2812π)/9293 weeks 282.02104 .01605 (2822π)/9293 weeks 283.02186 .01549 (2832π)/9293 weeks 284.02191 .01451 (2842π)/9293 weeks 285.02286 .01651 (2852π)/9293 weeks 286.02115 .01668 (2862π)/9293 weeks 287.02264 .01542 (2872π)/9293 weeks 288.02169 .01686 (2882π)/9293 weeks 289.02364 .01686 (2892π)/9293 weeks 290.02255 .01926 (2902π)/9293 weeks 291.02196 .0192 (2912π)/9293 weeks 292.02115 .01941 (2922π)/9293 weeks 293.02109 .01833 (2932π)/9293 weeks 294.02292 .01985 (2942π)/9293 weeks 295.02118 .0212 (2952π)/9293 weeks 296.0214 .02138 (2962π)/9293 weeks 297.02104 .02347 (2972π)/9293 weeks 298.01947 .02255 (2982π)/9293 weeks 299.02121 .02311 (2992π)/9293 weeks 300.0194 .02662 (3002π)/9293 weeks 301.01823 .02551 (3012π)/9293 weeks 302.01715 .02784 (3022π)/9293 weeks 303.01388 .02591 (3032π)/9293 weeks 304.01678 .02593 (3042π)/9293 weeks 305.01469 .029 (3052π)/9293 weeks 306.012 .02829 (3062π)/9293 weeks 307.01035 .02811 (3072π)/9293 weeks 308.00996 .02757 (3082π)/9293 weeks 309.00874 .02848 (3092π)/9293 weeks 310.00626 .02838 (3102π)/9293 weeks 311.00382 .0274 (3112π)/9293 weeks 312.00237 .02469 (3122π)/9293 weeks 313.00256 .02341 (3132π)/9293 weeks 314.00148 .02239 (3142π)/9293 weeks 315.00201 .02106 (3152π)/9293 weeks 316.00098 .02099 (3162π)/9293 weeks 317-.00006 .01945 (3172π)/9293 weeks 318-.00048 .01843 (3182π)/9293 weeks 319-.00152 .01617 (3192π)/9293 weeks 320.00049 .01367 (3202π)/9293 weeks 321.00146 .01452 (3212π)/9293 weeks 322.00073 .01371 (3222π)/9293 weeks 323.00189 .01324 (3232π)/9293 weeks 324.00125 .0129 (3242π)/9293 weeks 325.0017 .01139 (3252π)/9293 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weeks 788.01098 -.04137 (7882π)/9291 weeks 789.01271 -.04247 (7892π)/9291 weeks 790.0151 -.04273 (7902π)/9291 weeks 791.01749 -.04063 (7912π)/9291 weeks 792.01645 -.0393 (7922π)/9291 weeks 793.01684 -.03959 (7932π)/9291 weeks 794.01739 -.03931 (7942π)/9291 weeks 795.01835 -.03799 (7952π)/9291 weeks 796.01723 -.03744 (7962π)/9291 weeks 797.01605 -.03893 (7972π)/9291 weeks 798.01762 -.04027 (7982π)/9291 weeks 799.0202 -.04078 (7992π)/9291 weeks 800.0213 -.03874 (8002π)/9291 weeks 801.02165 -.03872 (8012π)/9291 weeks 802.02382 -.0373 (8022π)/9291 weeks 803.02281 -.03386 (8032π)/9291 weeks 804.01993 -.03288 (8042π)/9291 weeks 805.01814 -.03334 (8052π)/9291 weeks 806.01639 -.0353 (8062π)/9291 weeks 807.01668 -.03595 (8072π)/9291 weeks 808.01576 -.0395 (8082π)/9291 weeks 809.01694 -.04079 (8092π)/9291 weeks 810.0181 -.0436 (8102π)/9291 weeks 811.02246 -.04374 (8112π)/9291 weeks 812.02402 -.04058 (8122π)/9291 weeks 813.02318 -.03997 (8132π)/9291 weeks 814.02238 -.04314 (8142π)/9291 weeks 815.0256 -.04082 (8152π)/9291 weeks 816.02234 -.04142 (8162π)/9291 weeks 817.02726 -.04374 (8172π)/9291 weeks 818.02789 -.03985 (8182π)/9291 weeks 819.02744 -.04071 (8192π)/9291 weeks 820.02676 -.0421 (8202π)/9291 weeks 821.03046 -.04435 (8212π)/9291 weeks 822.03516 -.04233 (8222π)/9291 weeks 823.03656 -.03731 (8232π)/9291 weeks 824.03365 -.03589 (8242π)/9291 weeks 825.03407 -.03882 (8252π)/9291 weeks 826.03582 -.0362 (8262π)/9291 weeks 827.03863 -.03728 (8272π)/9291 weeks 828.04249 -.03179 (8282π)/9291 weeks 829.04055 -.02862 (8292π)/9291 weeks 830.04085 -.02626 (8302π)/9291 weeks 831.04033 -.02324 (8312π)/9291 weeks 832.03996 -.01905 (8322π)/9291 weeks 833.03695 -.01492 (8332π)/9291 weeks 834.03247 -.01199 (8342π)/9291 weeks 835.03037 -.01323 (8352π)/9291 weeks 836.02751 -.00919 (8362π)/9291 weeks 837.022 -.0108 (8372π)/9291 weeks 838.02324 -.00906 (8382π)/9291 weeks 839.01784 -.00531 (8392π)/9291 weeks 840.01079 -.00488 (8402π)/9291 weeks 841.00268 -.01145 (8412π)/9291 weeks 842.00658 -.01569 (8422π)/9291 weeks 843.00354 -.01418 (8432π)/9291 weeks 844-.00074 -.01638 (8442π)/9291 weeks 845-.00086 -.01591 (8452π)/9291 weeks 846-.01037 -.01937 (8462π)/9291 weeks 847-.0083 -.02815 (8472π)/9291 weeks 848-.00739 -.02404 (8482π)/9291 weeks 849-.01432 -.0302 (8492π)/9291 weeks 850-.01179 -.03148 (8502π)/9291 weeks 851-.02144 -.03481 (8512π)/9291 weeks 852-.01978 -.04613 (8522π)/9291 weeks 853-.01464 -.04908 (8532π)/9291 weeks 854-.01616 -.05075 (8542π)/9291 weeks 855-.01797 -.05412 (8552π)/9291 weeks 856-.01911 -.06552 (8562π)/9291 weeks 857-.01101 -.07371 (8572π)/9291 weeks 858.00032 -.07139 (8582π)/9291 weeks 859-.00249 -.06762 (8592π)/9291 weeks 860.00059 -.07361 (8602π)/9291 weeks 861.00373 -.07373 (8612π)/9291 weeks 862.00636 -.07446 (8622π)/9291 weeks 863.00898 -.07486 (8632π)/9291 weeks 864.01169 -.07687 (8642π)/9291 weeks 865.0174 -.07589 (8652π)/9291 weeks 866.01896 -.0709 (8662π)/9291 weeks 867.01794 -.07171 (8672π)/9291 weeks 868.0226 -.07028 (8682π)/9291 weeks 869.02139 -.06384 (8692π)/9291 weeks 870.02002 -.05904 (8702π)/9291 weeks 871.01102 -.05711 (8712π)/9291 weeks 872.00427 -.0628 (8722π)/9291 weeks 873.0036 -.06727 (8732π)/9291 weeks 874.00047 -.07156 (8742π)/9291 weeks 875.00119 -.07922 (8752π)/9291 weeks 876.00585 -.0811 (8762π)/9291 weeks 877.0011 -.08257 (8772π)/9291 weeks 878.00617 -.09224 (8782π)/9291 weeks 879.00877 -.08981 (8792π)/9291 weeks 880.01104 -.09468 (8802π)/9291 weeks 881.0151 -.09264 (8812π)/9291 weeks 882.01324 -.09651 (8822π)/9291 weeks 883.01558 -.09488 (8832π)/9291 weeks 884.01282 -.10027 (8842π)/9291 weeks 885.02034 -.10047 (8852π)/9291 weeks 886.02106 -.09733 (8862π)/9291 weeks 887.01279 -.09366 (8872π)/9291 weeks 888.0017 -.10652 (8882π)/9291 weeks 889.00966 -.1177 (8892π)/9291 weeks 890.01567 -.12309 (8902π)/9291 weeks 891.02517 -.11791 (8912π)/9291 weeks 892.01305 -.1153 (8922π)/9291 weeks 893.00964 -.12572 (8932π)/9291 weeks 894.00887 -.1393 (8942π)/9291 weeks 895.01853 -.14795 (8952π)/9291 weeks 896.02234 -.14983 (8962π)/9291 weeks 897.02093 -.16836 (8972π)/9291 weeks 898.04444 -.16634 (8982π)/9291 weeks 899.03671 -.16368 (8992π)/9291 weeks 900.0423 -.1812 (9002π)/9291 weeks 901.05498 -.18486 (9012π)/9291 weeks 902.06177 -.19066 (9022π)/9291 weeks 903.06714 -.1898 (9032π)/9291 weeks 904.07701 -.20678 (9042π)/9291 weeks 905.10073 -.20428 (9052π)/9291 weeks 906.09818 -.19767 (9062π)/9291 weeks 907.10632 -.21689 (9072π)/9291 weeks 908.13586 -.22007 (9082π)/9291 weeks 909.15758 -.19072 (9092π)/9291 weeks 910.13859 -.19205 (9102π)/9291 weeks 911.15248 -.19201 (9112π)/9291 weeks 912.1413 -.21268 (9122π)/9291 weeks 913.1927 -.21333 (9132π)/9291 weeks 914.19515 -.18318 (9142π)/9291 weeks 915.18593 -.18838 (9152π)/9291 weeks 916.19427 -.19025 (9162π)/9291 weeks 917.2066 -.20157 (9172π)/9291 weeks 918.22165 -.19186 (9182π)/9291 weeks 919.24591 -.18805 (9192π)/9291 weeks 920.21377 -.17364 (9202π)/9291 weeks 921.23917 -.21235 (9212π)/9291 weeks 922.22825 -.20472 (9222π)/9291 weeks 923.27465 -.28888 (9232π)/9291 weeks 924.39767 -.23039 (9242π)/9291 weeks 925.362 -.20596 (9252π)/9291 weeks 926.41907 -.20525 (9262π)/9291 weeks 927.39387 -.16183 (9272π)/9291 weeks	16,016	35,723	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.703125	3	CC-MAIN-2018-17	latest	en	0.758926
http://nag.com/numeric/MB/manual64_24_1/html/S/s15abf.html	1,501,181,386,000,000,000	text/html	crawl-data/CC-MAIN-2017-30/segments/1500549429417.40/warc/CC-MAIN-20170727182552-20170727202552-00298.warc.gz	221,431,617	3,902	Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int Chapter Contents Chapter Introduction NAG Toolbox # NAG Toolbox: nag_specfun_cdf_normal (s15ab) ## Purpose nag_specfun_cdf_normal (s15ab) returns the value of the cumulative Normal distribution function, P(x)$P\left(x\right)$, via the function name. ## Syntax [result, ifail] = s15ab(x) [result, ifail] = nag_specfun_cdf_normal(x) ## Description nag_specfun_cdf_normal (s15ab) evaluates an approximate value for the cumulative Normal distribution function x P(x) = 1/(sqrt(2π)) ∫ e − u2 / 2du. − ∞ $P(x)=12π∫-∞xe-u2/2du.$ The function is based on the fact that P(x) = (1/2)erfc(( − x)/(sqrt(2))) $P(x)=12erfc(-x2)$ and it calls nag_specfun_erfc_real (s15ad) to obtain a value of erfc$\mathit{erfc}$ for the appropriate argument. ## References Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications ## Parameters ### Compulsory Input Parameters 1: x – double scalar The argument x$x$ of the function. None. None. ### Output Parameters 1: result – double scalar The result of the function. 2: ifail – int64int32nag_int scalar ${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]). ## Error Indicators and Warnings There are no failure exits from this function. The parameter ifail is included for consistency with other functions in this chapter. ## Accuracy Because of its close relationship with erfc$\mathit{erfc}$, the accuracy of this function is very similar to that in nag_specfun_erfc_real (s15ad). If ε$\epsilon$ and δ$\delta$ are the relative errors in result and argument, respectively, they are in principle related by \|ε\| ≃ \|( x e − (1/2) x2 )/(sqrt(2π)P(x))δ\| $\|ε\|≃ \| x e -12 x2 2πP(x) δ \|$ so that the relative error in the argument, x$x$, is amplified by a factor, (xe(1/2)x2)/(sqrt(2π)P(x)) $\frac{x{e}^{-\frac{1}{2}{x}^{2}}}{\sqrt{2\pi }P\left(x\right)}$, in the result. For x$x$ small and for x$x$ positive this factor is always less than one and accuracy is mainly limited by machine precision. For large negative x$x$ the factor behaves like x2$\text{}\sim {x}^{2}$ and hence to a certain extent relative accuracy is unavoidably lost. However the absolute error in the result, E$E$, is given by \|E\| ≃ \|( x e − (1/2) x2 )/(sqrt(2π))δ\| $\|E\|≃ \| x e -12 x2 2π δ \|$ so absolute accuracy can be guaranteed for all x$x$. None. ## Example ```function nag_specfun_cdf_normal_example x = -20; [result, ifail] = nag_specfun_cdf_normal(x) ``` ``` result = 2.7536e-89 ifail = 0 ``` ```function s15ab_example x = -20; [result, ifail] = s15ab(x) ``` ``` result = 2.7536e-89 ifail = 0 ```	882	2,755	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 19, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.046875	3	CC-MAIN-2017-30	latest	en	0.541099
https://codeforces.com/problemset/problem/536/B	1,719,209,979,000,000,000	text/html	crawl-data/CC-MAIN-2024-26/segments/1718198865074.62/warc/CC-MAIN-20240624052615-20240624082615-00318.warc.gz	152,828,092	14,890	B. Tavas and Malekas time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output Tavas is a strange creature. Usually "zzz" comes out of people's mouth while sleeping, but string s of length n comes out from Tavas' mouth instead. Today Tavas fell asleep in Malekas' place. While he was sleeping, Malekas did a little process on s. Malekas has a favorite string p. He determined all positions x1 < x2 < ... < xk where p matches s. More formally, for each xi (1 ≤ i ≤ k) he condition sxisxi + 1... sxi + \|p\| - 1 = p is fullfilled. Then Malekas wrote down one of subsequences of x1, x2, ... xk (possibly, he didn't write anything) on a piece of paper. Here a sequence b is a subsequence of sequence a if and only if we can turn a into b by removing some of its elements (maybe no one of them or all). After Tavas woke up, Malekas told him everything. He couldn't remember string s, but he knew that both p and s only contains lowercase English letters and also he had the subsequence he had written on that piece of paper. Tavas wonders, what is the number of possible values of s? He asked SaDDas, but he wasn't smart enough to solve this. So, Tavas asked you to calculate this number for him. Answer can be very large, so Tavas wants you to print the answer modulo 109 + 7. Input The first line contains two integers n and m, the length of s and the length of the subsequence Malekas wrote down (1 ≤ n ≤ 106 and 0 ≤ m ≤ n - \|p\| + 1). The second line contains string p (1 ≤ \|p\| ≤ n). The next line contains m space separated integers y1, y2, ..., ym, Malekas' subsequence (1 ≤ y1 < y2 < ... < ym ≤ n - \|p\| + 1). Output In a single line print the answer modulo 1000 000 007. Examples Input 6 2ioi1 3 Output 26 Input 5 2ioi1 2 Output 0 Note In the first sample test all strings of form "ioioi?" where the question mark replaces arbitrary English letter satisfy. Here \|x\| denotes the length of string x. Please note that it's possible that there is no such string (answer is 0).	614	2,039	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2024-26	latest	en	0.904849
http://www.spoj.com/problems/MOVIFAN/	1,527,287,602,000,000,000	text/html	crawl-data/CC-MAIN-2018-22/segments/1526794867220.74/warc/CC-MAIN-20180525215613-20180525235613-00336.warc.gz	460,826,191	8,446	## MOVIFAN - Movie Fan no tags Alice is a cinephile. He wanted to watch a recently released movie. There are many movie shows whose start time and length are given.Your task is to help Alice count the number of ways he can watch the movie. Since he is a cinephile, he can watch many shows as long as they do not overlap. ### Input First line contains an integer t denotine number of test cases. Each test case contains n,l denoting number of shows and length of the shows. n integer follows denoting start time of show. 1<=t<=10 1<=n,l<=300000 ### Output Print the number of ways Alice can watch shows if he want to watch atleast one show modulo 1000000007. ### Example ```Input: 3``` `3 4` `3 8 12` `3 1` `1 2 3` `3 3` ```3 5 9 Output: 7``` `7` `5` `For testcase1 ,Alice can watch 1 show in 3 ways,2 shows in 3 ways and 3 show in 1 way total ways=7` `For test case3 Alice can watch 1 show in 3 ways, 2 shows in 2 ways ,total ways=5` hide comments hodobox: 2017-04-18 21:45:42 start times seem to be given in sorted order, and are smaller than 10^6 Chinmay Kousik: 2016-11-22 11:33:20 Solve ACTIV after this Vipul Srivastava: 2016-11-16 16:42:34 Constraints on start times?? Added by: Umesh Malhotra Date: 2016-11-12 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 GOSU	425	1,351	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.859375	3	CC-MAIN-2018-22	latest	en	0.810502
https://layton.fandom.com/wiki/Puzzle:How_Old_Am_I%3F	1,627,998,231,000,000,000	text/html	crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00336.warc.gz	347,132,329	155,847	2,508 pages ← 092 - Precious Metals 093 - How Old Am I? 094 - The Mystery Cube → How Old Am I? is a puzzle in Professor Layton and the Diabolical Box. ## Puzzle US Version "Hi there! Yeah, I know I'm all cute and stuff, but I'm ALSO really good at puzzles. What's that? You wanna know my age? Well...OK. The difference between Mama's age and Papa's age is the same as my age. Oh, and my big sister is twice my age, which happens to be one-third my mom's age. And one more thing: in five years, I'll be my sister's age. OK, enough hints! How old am I?" UK Version "The difference between Mum's age and Dad's age is the same as my age. Oh, and my big sister's twice my age, which happens to be one third my mum's age. And one more thing: In five years, I'll be my sister's age. How old am I?" ## Hints Click a Tab to reveal the Hint. US Version "When you've got a puzzle like this one, what you wanna do is go over all the info you've got and find the stuff you can use. The difference between my parents' ages probably won't help you. But...my sister's age could be kinda useful." UK Version When you've got a puzzle like this one, what you should do is go over all the information you've got and find the stuff you can use. The difference between her parents' ages probably won't help you. But her sister's age might be more useful... US Version "Five years ago, my sis was the same age as I am now, and she's now twice my age." UK Version The girl's sister is twice her age, and in five years' time, the girl will be the age her sister is now. US Version "Read Hint Two REALLY CAREFULLY, OK? "Five years ago, my sis was the same age as I am now, and she's now twice my age." UK Version Five years ago, her sister was the same age she is now, and her sister is now twice her age. ## Solution ### Incorrect US Version "Nope!" "You know, I'd bet you're older than me. A grown-up like you should be able to figure this one out!" UK Version Nope! A grown-up like you should be able to work this one out! ### Correct US Version Papa's 35 and Mama's 30, meaning the difference in their ages is the same as my age, like I said. As for my big sis, she's 10. That's twice my age and a third of Mama's. In five years, I'll be 10 and my sister will be 15. Can you believe it? I'll practically be a grown-up by then!" UK Version	621	2,354	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.0625	3	CC-MAIN-2021-31	latest	en	0.970985
https://www.weegy.com/Home.aspx?ConversationId=8AD57BF3	1,534,848,106,000,000,000	text/html	crawl-data/CC-MAIN-2018-34/segments/1534221218101.95/warc/CC-MAIN-20180821092915-20180821112915-00497.warc.gz	1,019,398,700	8,800	(-5) - 11 Question Updated 3/3/2014 9:56:03 AM Original conversation User: (-5) - 11 Weegy: 11/15 - 9/15 = 2/15. Thanks for asking Weegy. inspirations\|Points 725\| User: (-6)(-3) Weegy: The answer is -9 .Thanks! User: 2(x - y) + 3(2y - 3x) Weegy: The answer is B=3/2. To find the slope of this line, first rearrange the equation to slope intercept form which is y=mx+b where m is the slope. [ After rearranging it, we get 2y=3x- 4.......divide by 2 to get y by itself......which in turn leaves us with y=1.5x- 2........therefore the slope is 1.5, or 3/2. ] groove_jhune\|Points 232\| User: 20% of \$90? Weegy: 80 yestfl\|Points 1444\| User: ow much money is 20% of \$90? Question Updated 3/3/2014 9:56:03 AM Rating 0 (-5) - 11 = -16 Confirmed by alfred123 [3/3/2014 9:56:02 AM] 0 (-6)(-3) = 18 Confirmed by alfred123 [3/3/2014 9:56:07 AM] 0 2(x - y) + 3(2y - 3x) = -7x + 4y Confirmed by alfred123 [3/3/2014 9:57:06 AM] 27,211,263 * Get answers from Weegy and a team of really smart live experts. Popular Conversations What is Amendments III? Weegy: The First Amendment prohibits the making of any law respecting an establishment of religion, impeding the free ... 15. What is 26% as a fraction in simplest form? Weegy: 22% as a fraction in the simplest form is 11/50. What is 5.25% of 200 Weegy: 2003/5 = 120. User: A certain alloy contains 5.25% copper. How much copper is there in a piece weighing 200 ... Only a _______ technician may wear the ASE insignia on his or her ... Weegy: Only a certified technician may wear the ASE insignia on his or her uniform. User: Which of these engine ... S L Points 181 [Total 181] Ratings 0 Comments 141 Invitations 4 Offline S L R P R P R Points 150 [Total 610] Ratings 0 Comments 30 Invitations 12 Offline S L P P Points 131 [Total 585] Ratings 0 Comments 131 Invitations 0 Offline S Points 59 [Total 59] Ratings 0 Comments 49 Invitations 1 Offline S R L R P R P R R R Points 55 [Total 877] Ratings 0 Comments 5 Invitations 5 Offline S Points 16 [Total 33] Ratings 0 Comments 16 Invitations 0 Offline S Points 12 [Total 12] Ratings 0 Comments 12 Invitations 0 Offline S Points 10 [Total 40] Ratings 1 Comments 0 Invitations 0 Online S Points 2 [Total 2] Ratings 0 Comments 2 Invitations 0 Offline S Points 1 [Total 1] Ratings 0 Comments 1 Invitations 0 Offline Excludes moderators and previous winners (Include) Home \| Contact \| Blog \| About \| Terms \| Privacy \| © Purple Inc.	861	2,425	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.203125	3	CC-MAIN-2018-34	latest	en	0.88269
https://mileiq.com/blog/actual-expense-method-tax-law/	1,601,058,804,000,000,000	text/html	crawl-data/CC-MAIN-2020-40/segments/1600400228707.44/warc/CC-MAIN-20200925182046-20200925212046-00389.warc.gz	498,077,691	11,769	Updated February 28, 2019 When you use your car for business there are two ways to calculate your deduction: using the standard mileage rate or the actual expense method. The standard mileage rate method has remained the same and your miles are worth more in 2019. But, let’s go over how the actual expense method has changed. ## Standard mileage rate vs. actual expense method Most people use the standard mileage rate because it’s easier and simpler. All you do is keep track of your business mileage and deduct a set amount for each business mile. The actual expense method is more complicated and time consuming. In addition to tracking your mileage, you must also keep track of what you spend on gas and other car expenses. You then get to deduct your business use percentage of your actual car expenses. In addition, you may deduct an amount each year for depreciation. The Tax Cuts and Jobs Act which took effect January 1, 2018. It greatly increased the amount you may deduct for passenger automobile depreciation each year. ## How does depreciation work for vehicles? Depreciation works differently for vehicles than for other types of property. The annual depreciation deduction for automobiles is limited to a maximum dollar amount each year no matter how much the vehicle cost. The annual limit applies to all vehicles that qualify as “passenger automobiles.” A passenger automobile is any four-wheeled vehicle made primarily for use on public streets and highways that has an unloaded gross weight of 6,000 pounds or less. Vehicles heavier than 6,000 pounds fall under Section 179 deduction rules. The chart below shows the maximum annual depreciation deduction allowed for passenger automobiles placed in service in 2017 and 2018. ## What’s the depreciation limits for passenger automobiles? Year Place Into Service2017 & Previous Tax Law AmountsAfter 2018 & New Tax Law First Year\$3,160\$10,000 (plus \$8,000 bonus depreciation) Second Year\$5,100\$16,000 Third Year\$3,050\$9,600 Fourth Year\$1,875\$5,760 Remember, these numbers assume 100 percent business usage. If you use your personal vehicle for business purposes X amount of the time, you can only take the percentage that’s equal to your business usage. ## Has the new tax law increased the amount of depreciation? You can see that the new tax law has vastly increased the amount of depreciation that may be claimed each year for passenger automobiles for 2018 and later. If you qualify for bonus depreciation, you can deduct up to a whopping \$18,000 the first year. Of course, this assumes 100 percent business use of the vehicle. Bonus depreciation may be claimed only if you use a vehicle over 50 percent of the time for business. And you must continue to do so for the first six years you own the vehicle or be required to give back part of your deduction. You must use an automobile 100 percent for business to qualify for the full deduction listed in the above chart. The limits are reduced by the percentage of personal use. For example, if you use the vehicle 40 percent of the time for personal use, your annual deduction limits are reduced by 40 percent. These are by far the highest depreciation limits we’ve ever had for passenger automobiles. Yet, your actual depreciation deduction, up to the annual limit, depends on the cost of your car and your depreciation method. ## How to depreciate your business vehicle There are two basic methods to depreciate a vehicle: the straight-line method and the accelerated depreciation method. You must use your vehicle for business more than 50 percent of the time to use accelerated depreciation. Your deduction is subject to the annual limits set forth above no matter the method used. The following table shows how much of the basis of an automobile may be depreciated each year using the different depreciation methods. ## What are the different depreciation methods? YearStraight-Line MethodAccelerated Depreciation 110%20% 220%32% 320%19.2% 420%11.5% 520%11.5% 610%5.76% ## A depreciation example Let’s say you buy a new car for \$50,000 in 2018 and use it 75 percent for business driving during the year. Here’s how to determine your deduction: • Your depreciable basis is \$37,500 (\$50,000 cost x 75 percent business use = \$37,500 basis) • Using accelerated depreciation, your depreciation deduction for 2018 would be 20 percent x \$37,500 = \$7,500 • You also qualify for 75 percent of the maximum \$8,000 bonus depreciation deduction, which is \$6,000 • Your total deduction for 2018 is \$13,500 In 2019, your deduction will be .32 x \$37,500 = \$12,000, well under the \$16,000 limit for the year. In two years, you’ve deducted \$25,500. You also get to deduct 75 percent of your actual costs of driving your car each year, including gas and repairs. ## Other things to know about the actual expense method Keep in mind that once you use the actual expense method, you’re stuck using that method for as long as you own the vehicle. It’s basically impossible to switch to the standard mileage rate after you’ve used the actual expense method. Also, if you want to use the actual expense method, you must do so the first year you use a vehicle for business. Yet, it may be worth it based on the size of your deduction. ## Tracking mileage for the actual expense method If you use the actual expense method, you can still benefit from a mileage tracker app like MileIQ. If you ever face an audit, you’ll need documentation of your business use of your personal vehicle. Keeping proper mileage logs is the best way to keep yourself covered. ### Stephen Fishman Stephen Fishman is a self-employed tax expert and regular contributor to MileIQ. He has dedicated his career as an attorney and author to writing useful, authoritative and recognized guides on taxes and business law for entrepreneurs, independent contractors, freelancers and other self-employed people. He is the author of over 20 books and hundreds of articles, and has been quoted in The New York Times, Wall Street Journal, Chicago Tribune, and many other publications. Visit Fishman Law and Tax Files for more information on his work.	1,320	6,172	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.796875	3	CC-MAIN-2020-40	latest	en	0.919605
http://www.mathskey.com/homework-help/algebra-1-2008/book/43/page/195	1,537,326,926,000,000,000	text/html	crawl-data/CC-MAIN-2018-39/segments/1537267155817.29/warc/CC-MAIN-20180919024323-20180919044323-00190.warc.gz	368,118,099	12,933	Algebra 1, 2008 66 PAGE: 195 SET: Exercises PROBLEM: 66 The given table of ordered pairs. x 1 2 3 4 5 y 5 10 15 20 25 The difference of the x values is 1, and the difference of the y values is 5. The difference in y values is five times the difference of x values. Then the equation of the function f (x) = y = 5x. The solution of the equation is y = 5x. TESTIMONIALS "I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett "Your site is amazing! It helped me get through Algebra." Charles "My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease Tweets by @mathskeydotcom QUESTIONS? LET US HELP.	221	813	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2018-39	latest	en	0.935104
https://www.physicsforums.com/threads/applicaton-of-taylor-series.399406/	1,511,483,391,000,000,000	text/html	crawl-data/CC-MAIN-2017-47/segments/1510934807044.45/warc/CC-MAIN-20171123233821-20171124013821-00779.warc.gz	862,407,143	15,526	# Applicaton of taylor series 1. Apr 28, 2010 ### apiwowar so F = mgR2/(R+h)2 where R is the radius of the earth. consider the situation where h is much smaller than R. a) show that F is approximately equal to mg b)express F as mg multiplied by a series in h/R so i need help on getting started. would showing that F is approximately equal to mg be the same as expressing F as mg multiplied by a series in h/R since taylor series are used as approximations? i can pull an R2 out of the denominator and get rid of the R2 on the top and be left with mg(1+h/R2)-2 and in that case i could use the binomial expansion of a taylor series. would that solve a or b? any other help would be appreciated 2. Apr 28, 2010 ### Dick Yes, expanding F as a taylor series around h=0 is exactly what they are asking for. 3. Apr 28, 2010 ### apiwowar therefore a and b would be the same answer? just an expansion of the taylor series around h=0? 4. Apr 28, 2010 ### Dick You consider h to be small, so, yes, when h is near zero F is near mg. You don't need taylor series for the first one, if h is small compared with R you can just just put h=0 into the expression to find approximately what F is when h is small. You would use the taylor series to find out how good the approximation is. I'm not really sure what your question is. What they want in b is pretty clear, isn't it? 5. Apr 28, 2010 ### apiwowar there is a part c to this question asking how far above the surface of the earth you can go before the first order correction changes the estimate f ~ mg by more than 10% (and assume that R=6400km) so for that i just plug in .10 for h and 6400km for R into the first order approximation, i did so and got .9996875mg. is that saying that you can go 99.99% away from the surface before the first order estimate is changed by more than 10%? 6. Apr 28, 2010 ### Dick No. You want to calculate h from the series. If F changes by 10%, then mg changes to 0.9mg. Figure out the value of the first order correction that will change mg (at h=0) to 0.9mg. 7. Apr 28, 2010 ### Dick BTW mg(1+h/R^2)^(-2) should be mg(1+h/R)^(-2). Check the algebra.	611	2,158	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.671875	4	CC-MAIN-2017-47	longest	en	0.967842
https://celestrak.com/columns/v02n02/	1,643,293,111,000,000,000	text/html	crawl-data/CC-MAIN-2022-05/segments/1642320305266.34/warc/CC-MAIN-20220127133107-20220127163107-00649.warc.gz	222,865,207	7,352	## Orbital Coordinate Systems, Part II By Dr. T.S. Kelso November/December 1995 November/December 1995 ## Orbital Coordinate Systems, Part II By Dr. T.S. Kelso In our last column, we were working our way through the process of calculating the position and velocity of an observer on the Earth's surface in the Earth-Centered Inertial (ECI) reference frame. The goal, of course, was to be able to determine the position of the observer relative to an orbiting satellite to aid the process of visually acquiring or otherwise tracking the satellite from the ground. At the end of the last column, we had seen that it would be impossible to determine an observer's position in the ECI reference frame without knowing that observer's local sidereal time, that is, the angle between the observer's meridian (longitude) and the vernal equinox. But because this time is measured relative to the stars and not the Sun, the equations to do the calculations are a bit complicated. Let's start of this column with a brief review of the equation for the local sidereal time and then explore, bit by bit, how to develop a computer routine to calculate this value for us. We will then continue the process by calculating the remaining information needed to determine an observer's position in the ECI reference frame. As we saw last time, the local sidereal time, θ(τ), can be calculated by adding the observer's east longitude, λE, to the Greenwich sidereal time (GST), θg(τ). Using an equation from Page 50 of the Explanatory Supplement to the Astronomical Almanac, we can first determine θg(0h), the Greenwich sidereal time at 0h (midnight) UTC, from which θg(τ) = θg(0h) + ωe·Δτ where Δτ is the UTC time of interest and ωe = 7.29211510 × 10-5 radians/second is the Earth's rotation rate. Recalling that θg(0h) is given as θg(0h) = 24110s.54841 + 8640184s.812866 Tu + 0s.093104 Tu2 - 6.2 × 10-6 Tu3 where Tu = du/36525 and du is the number of days of Universal Time elapsed since JD 2451545.0 (2000 January 1, 12h UT1), we can now set about determing what we know and what we need to calculate. Let's develop a top-down algorithm to see what we need to do. Our goal in this portion of the algorithm is to determine the value of θg at a particular time, τ. To do this, we need values of θg(0h), ωe, and Δτ. The value of ωe is fixed and Δτ is the fraction of the day since 0h UTC or Δτ = fraction(τ) in days. Therefore, we still need to know Tu, which depends upon du. But du depends upon knowing the number of days of Universal Time elapsed since JD 2451545.0. So, if we know the Julian Date (JD) of τ, we have everything we need. Our top-down algorithm then looks something like this: Calculate: θg which depends on (θg(0h), ωe, Δτ); ωe constant; Δτ = fraction(τ) Calculate: θg(0h) which depends on (Tu); Tu = du/36525 Calculate: du which depends on (JD(τ)) Calculate: JD(τ) Therefore, our most basic calculation is the determination of the Julian Date. The Julian Date can be calculated from the equation in Section 12.95 (Page 606) [actually, this should be Section 12.92 (Page 604)] of the Explanatory Supplement to the Astronomical Almanac, or using the approach on Page 61 of Astronomical Algorithms by Jean Meeus. This latter text is an excellent reference source for many relevant calculations in orbital mechanics and is highly recommended. Using Meeus' approach, the Pascal code for calculating the Julian Date of January 0.0 of any year would be: ```Function Julian_Date_of_Year(year : double) : double; { Calculate Julian Date of 0.0 Jan year } var A,B : longint; begin year := year - 1; A := Trunc(year/100); B := 2 - A + Trunc(A/4); Julian_Date_of_Year := Trunc(365.25 * year) + Trunc(30.6001 * 14) + 1720994.5 + B; end; {Function Julian_Date_of_Year} ``` To calculate the Julian Date of any calendar date, we simply combine the Julian Date of that year with the day of the year, where the day of the year can be calculated as: ```Function DOY(yr,mo,dy : word) : word; const days : array [1..12] of word = (31,28,31,30,31,30,31,31,30,31,30,31); var i,day : word; begin day := 0; for i := 1 to mo-1 do day := day + days[i]; day := day + dy; if ((yr mod 4) = 0) and (((yr mod 100) <> 0) or ((yr mod 400) = 0)) and (mo > 2) then day := day + 1; DOY := day; end; {Function DOY} ``` As an example, the Julian Date of 0h UTC on 1995 October 01 would be written as: ```JD := Julian_Date_of_Year(1995) + DOY(1995,10,1); ``` with a result of 2449991.5 = 2449717.5 + 274. Therefore, du equals -1553.5 days and Tu equals -1553.5/36525. From this value of Tu, θg(0h) can now be calculated to be -343378.2154 seconds. Since there are 86,400 seconds in a day, this is the same time (angle) as 2221.7846 seconds, so the equivalent GMST is 0h 37m 01s.7846 or an angle of 9.257 degrees. Now, if the time of interest on 1995 October 01 was 9h UTC, we would have to add ωe·Δτ to the value of θg(0h), where Δτ = 32,400 seconds (9 hours). Being careful to use the proper units, our new GMST is 9h 38m 30s.4928 or 144.627 degrees. We can consolidate our calculation of the Greenwich Mean Sidereal Time into the following simple Pascal function where the input is the Julian Date of the time of interest (in our example of 9h UTC on 1995 October 01, JD is 2449991.875) and the output is the GMST in radians. For our test case, this should be 2.524218 radians. ```Function ThetaG_JD(jd : double) : double; { Reference: The 1992 Astronomical Almanac, page B6. } var UT,TU,GMST : double; begin UT := Frac(jd + 0.5); jd := jd - UT; TU := (jd - 2451545.0)/36525; GMST := 24110.54841 + TU * (8640184.812866 + TU * (0.093104 - TU * 6.2E-6)); GMST := Modulus(GMST + 86400.01.00273790934UT,86400.0); ThetaG_JD := twopi * GMST/86400.0; end; {Function ThetaG_JD} ``` Now, we can complete our calculation of the ECI position of our observer. We'll start by assuming a spherical Earth and then go back and rework our solution, in our next column, using an oblate Earth. If our observer is located at 40° North latitude and 75° West longitude (near Philadelphia), we can easily calculate the z coordinate according to z = Re sin φ where Re = 6378.135 km and φ = 40°. To calculate x and y, we use x = R cos θ y = R sin θ where θ = θg + λE R = Re cos φ. Using our example, λE = -75° and θg = 144°.627, so θ = 69°.627 (remember, this is the local sidereal time—the angle between the observer's meridian and the vernal equinox) and R = 4885.935 km. Therefore, the ECI position of our observer at the time of interest is: x = 1700.938 km, y = 4580.302 km, z = 4099.786 km. After all that work calculating the local sidereal time, the rest of the calculation was relatively easy! We can encapsulate this calculation using the following simple Pascal procedure: ```Procedure Calculate_User_Pos(lat,lon,alt,time : double; var x,y,z : double); { Reference: The 1992 Astronomical Almanac, page K11. } const re = 6378.135; var theta : double; begin theta := Modulus(ThetaG_JD(time) + lon,twopi); r := (re + alt)Cos(lat); x := rCos(theta); y := rSin(theta); z := (re + alt)Sin(lat); end; {Procedure Calculate_User_Pos} ``` In the inputs for this routine, lat and lon are in radians, alt is in kilometers, and time is the Julian Date of interest. The outputs (x, y, and z) are in kilometers. So, how do we now calculate the look angle to a satellite? If the satellite's position in the ECI coordinate system is defined as [xs, ys, zs] and the observer is [xo, yo, zo], then the range vector is simply [rx, ry, rz] = [xs - xo, ys - yo, zs - zo]. This vector, however, is in the ECI system and to generate look angles, we need it to be in the topocentric-horizon system shown in Figure 1. That system has its z axis pointing toward the zenith, the x axis pointing South, and the y axis pointing East. Figure 1. Topocentric-Horizon Coordinate System To transform to the topocentric-horizon system, we must first rotate through an angle θ (the local sidereal time) about the z axis (Earth rotation axis) and then through an angle φ (the observer's latitude) about the y axis. The coordinates (rS, rE, rZ) become: rS = sin φ cos θ rx + sin φ sin θ ry - cos φ rz rE = -sin θ rx + cos θ ry rZ = cos φ cos θ rx + cos φ sin θ ry + sin φ rz The range to the satellite is r = √ [rS2 + rE2 + rZ2], the elevation is El = sin-1(rZ / r), and the azimuth is Az = tan-1(-rE / rS). The minus sign is necessary because azimuth is measured clockwise from North instead of counter-clockwise from South (which would be standard for a right-handed orthogonal coordinate system). Care must be taken with the azimuth to ensure the proper quadrant is selected for the arctangent. We can calculate the look angles using the procedure described with the Pascal procedure Calculate_Look, shown below. The inputs are the satellite's ECI coordinates (xs, ys, and zs) in kilometers, the observer's latitude and longitude (lat and lon) in radians and altitude (alt) in kilometers, along with the time of interest (time) as a Julian Date. The outputs are the azimuth and elevation (az and el) in radians and the range (rg) in kilometers. ```Procedure Calculate_Look(xs,ys,zs,lat,lon,alt,time : double; var az,el,rg : double); var xo,yo,zo, rx,ry,rz, theta, top_s,top_e,top_z : double; begin Calculate_User_Pos(lat,lon,alt,time,xo,yo,zo); theta := Modulus(ThetaG_JD(time) + lon,twopi); rx := xs - xo; ry := ys - yo; rz := zs - zo; top_s := Sin(lat)* Cos(theta)rx + Sin(lat) Sin(theta)ry - Cos(lat)rz top_e := - Sin(theta)rx + Cos(theta)ry; top_z := Cos(lat)* Cos(theta)rx + Cos(lat) Sin(theta)ry + Sin(lat)rz; az := ArcTan(-top_e/top_s); if top_s > 0 then az := az + pi; if az < 0 then az := az + twopi; rg := Sqrt(rxrx + ryry + rz*rz); el := ArcSin(top_z/rg); end; {Procedure Calculate_Look} ``` To sum things up, in order to calculate the look angles for a satellite relative to an observer on the ground, we must first calculate the satellite's position in the ECI coordinate system, then calculate the observer's ECI position, take the difference of the two vectors, and then transform (rotate) the vector from the ECI coordinate frame to the topocentric-horizon frame. The most difficult part of this process is in calculating the Earth's rotation angle when determining the observer's position. As always, if you have questions or comments on this column, feel free to send me e-mail at TS.Kelso@celestrak.com or write care of Satellite Times. Until next time, keep looking up!	3,022	10,485	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.5	4	CC-MAIN-2022-05	latest	en	0.893267
https://www.luogu.org/problemnew/show/P2909	1,553,308,003,000,000,000	text/html	crawl-data/CC-MAIN-2019-13/segments/1552912202711.3/warc/CC-MAIN-20190323020538-20190323042538-00112.warc.gz	834,952,341	6,072	# P2909 [USACO08OPEN]牛的车Cow Cars • 528通过 • 1.1K提交 • 题目提供者 FarmerJohn2 • 评测方式云端评测 • 标签排序贪心 USACO 2008 • 难度普及- • 时空限制 1000ms / 128MB • 提示：收藏到任务计划后，可在首页查看。 ## 题目描述 N (1 <= N <= 50,000) cows conveniently numbered 1..N are driving in separate cars along a highway in Cowtopia. Cow i can drive in any of M different high lanes (1 <= M <= N) and can travel at a maximum speed of S_i (1 <= S_i <= 1,000,000) km/hour. After their other bad driving experience, the cows hate collisions and take extraordinary measures to avoid them. On this highway, cow i reduces its speed by D (0 <= D <= 5,000) km/hour for each cow in front of it on the highway (though never below 0 km/hour). Thus, if there are K cows in front of cow i, the cow will travel at a speed of max[S_i - D * K, 0]. While a cow might actually travel faster than a cow directly in front of it, the cows are spaced far enough apart so crashes will not occur once cows slow down as described, Cowtopia has a minimum speed law which requires everyone on the highway to travel at a a minimum speed of L (1 <= L <= 1,000,000) km/hour so sometimes some of the cows will be unable to take the highway if they follow the rules above. Write a program that will find the maximum number of cows that can drive on the highway while obeying the minimum speed limit law. 编号为1到N的N只奶牛正各自驾着车打算在牛德比亚的高速公路上飞驰．高速公路有M(1≤M≤N)条车道．奶牛i有一个自己的车速上限Si(l≤Si≤1,000,000)．在经历过糟糕的驾驶事故之后，奶牛们变得十分小心，避免碰撞的发生．每条车道上，如果某一只奶牛i的前面有南只奶牛驾车行驶，那奶牛i的速度上限就会下降kD个单位，也就是说，她的速度不会超过Si – kD(O≤D≤5000)，当然如果这个数是负的，那她的速度将是0．牛德比亚的高速会路法规定，在高速公路上行驶的车辆时速不得低于/(1≤L≤1,000,000)．那么，请你计算有多少奶牛可以在高速公路上行驶呢？ ## 输入输出格式输入格式： * Line 1: Four space-separated integers: N, M, D, and L * Lines 2..N+1: Line i+1 describes cow i's initial speed with a single integer: S_i 输出格式： * Line 1: A single integer representing the maximum number of cows that can use the highway ## 输入输出样例输入样例#1：复制 3 1 1 5 5 7 5 输出样例#1：复制 2 ## 说明 There are three cows with one lane to drive on, a speed decrease of 1, and a minimum speed limit of 5. Two cows are possible, by putting either cow with speed 5 first and the cow with speed 7 second. 提示标程仅供做题后或实在无思路时参考。请自觉、自律地使用该功能并请对自己的学习负责。如果发现恶意抄袭标程，将按照I类违反进行处理。	850	2,196	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.015625	3	CC-MAIN-2019-13	latest	en	0.709786
https://metanumbers.com/33515	1,669,721,265,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446710691.77/warc/CC-MAIN-20221129100233-20221129130233-00274.warc.gz	438,050,186	7,348	# 33515 (number) 33,515 (thirty-three thousand five hundred fifteen) is an odd five-digits composite number following 33514 and preceding 33516. In scientific notation, it is written as 3.3515 × 104. The sum of its digits is 17. It has a total of 2 prime factors and 4 positive divisors. There are 26,808 positive integers (up to 33515) that are relatively prime to 33515. ## Basic properties • Is Prime? No • Number parity Odd • Number length 5 • Sum of Digits 17 • Digital Root 8 ## Name Short name 33 thousand 515 thirty-three thousand five hundred fifteen ## Notation Scientific notation 3.3515 × 104 33.515 × 103 ## Prime Factorization of 33515 Prime Factorization 5 × 6703 Composite number Distinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 2 Total number of prime factors rad(n) 33515 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0 The prime factorization of 33,515 is 5 × 6703. Since it has a total of 2 prime factors, 33,515 is a composite number. ## Divisors of 33515 1, 5, 6703, 33515 4 divisors Even divisors 0 4 2 2 Total Divisors Sum of Divisors Aliquot Sum τ(n) 4 Total number of the positive divisors of n σ(n) 40224 Sum of all the positive divisors of n s(n) 6709 Sum of the proper positive divisors of n A(n) 10056 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 183.071 Returns the nth root of the product of n divisors H(n) 3.33284 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors The number 33,515 can be divided by 4 positive divisors (out of which 0 are even, and 4 are odd). The sum of these divisors (counting 33,515) is 40,224, the average is 10,056. ## Other Arithmetic Functions (n = 33515) 1 φ(n) n Euler Totient Carmichael Lambda Prime Pi φ(n) 26808 Total number of positive integers not greater than n that are coprime to n λ(n) 13404 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3586 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares There are 26,808 positive integers (less than 33,515) that are coprime with 33,515. And there are approximately 3,586 prime numbers less than or equal to 33,515. ## Divisibility of 33515 m n mod m 2 3 4 5 6 7 8 9 1 2 3 0 5 6 3 8 The number 33,515 is divisible by 5. ## Classification of 33515 • Arithmetic • Semiprime • Deficient • Polite • Square Free ### Other numbers • LucasCarmichael ## Base conversion (33515) Base System Value 2 Binary 1000001011101011 3 Ternary 1200222022 4 Quaternary 20023223 5 Quinary 2033030 6 Senary 415055 8 Octal 101353 10 Decimal 33515 12 Duodecimal 1748b 20 Vigesimal 43ff 36 Base36 puz ## Basic calculations (n = 33515) ### Multiplication n×y n×2 67030 100545 134060 167575 ### Division n÷y n÷2 16757.5 11171.7 8378.75 6703 ### Exponentiation ny n2 1123255225 37645898865875 1261702300489800625 42285952600915667946875 ### Nth Root y√n 2√n 183.071 32.2413 13.5304 8.03615 ## 33515 as geometric shapes ### Circle Diameter 67030 210581 3.52881e+09 ### Sphere Volume 1.57691e+14 1.41152e+10 210581 ### Square Length = n Perimeter 134060 1.12326e+09 47397.4 ### Cube Length = n Surface area 6.73953e+09 3.76459e+13 58049.7 ### Equilateral Triangle Length = n Perimeter 100545 4.86384e+08 29024.8 ### Triangular Pyramid Length = n Surface area 1.94554e+09 4.43661e+12 27364.9 ## Cryptographic Hash Functions md5 b2c2fc5ac884cfbbf3f384adbacf2195 4a687acd0f367b3fa7a825bbd8cbc221d703e953 29bb4975696252af21763644cdcca5da755653a7a4d983d7503d2681b96b110c 248f5c7a876a010bd2a5e3b20a9aa879fe63cbfdfa2d9924105198131600c0b376e42b53b319de58f3040e972193ed10f80ba70a317b73c0ba5543cb41a985b4 cbf4f0d27411b548ffc795c711b6e69d69e53276	1,446	4,138	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.78125	4	CC-MAIN-2022-49	latest	en	0.816876
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2014.19.2145	1,653,057,795,000,000,000	text/html	crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00770.warc.gz	722,277,943	16,238	# American Institute of Mathematical Sciences September 2014, 19(7): 2145-2157. doi: 10.3934/dcdsb.2014.19.2145 ## Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids 1 Dipartimento di Matematica e Fisica "N. Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy, Italy, Italy Received May 2013 Revised March 2014 Published August 2014 We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit. Citation: Giulio G. Giusteri, Alfredo Marzocchi, Alessandro Musesti. Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2145-2157. doi: 10.3934/dcdsb.2014.19.2145 ##### References: [1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623-727. doi: 10.1002/cpa.3160120405. [2] G. K. Batchelor, Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech., 44 (1970), 419-440. doi: 10.1017/S002211207000191X. [3] A. T. Chwang and T. Y.-T. Wu, Hydromechanics of low-Reynolds-number flow. II. Singularity method for Stokes flows, J. Fluid Mech., 67 (1975), 787-815. doi: 10.1017/S0022112075000614. [4] E. Fried and M. E. Gurtin, Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales, Arch. Ration. Mech. Anal., 182 (2006), 513-554. doi: 10.1007/s00205-006-0015-7. [5] G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in Handbook of mathematical fluid dynamics, North-Holland, Amsterdam, 1 (2002), 653-791. [6] G. G. Giusteri, The multiple nature of concentrated interactions in second-gradient dissipative liquids, Z. Angew. Math. Phys., 64 (2013), 371-380. doi: 10.1007/s00033-012-0229-5. [7] G. G. Giusteri and E. Fried, Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, Meccanica, 49 (2014), 2153-2167. doi: 10.1007/s11012-014-9890-4. [8] G. G. Giusteri, A. Marzocchi and A. Musesti, Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies, Mech. Res. Commun., 37 (2010), 642-646. doi: 10.1016/j.mechrescom.2010.09.001. [9] G. G. Giusteri, A. Marzocchi and A. Musesti, Nonsimple isotropic incompressible linear fluids surrounding one-dimensional structures, Acta Mech., 217 (2011), 191-204. doi: 10.1007/s00707-010-0387-5. [10] G. G. Giusteri, A. Marzocchi and A. Musesti, Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number,, to appear in Evol. Equ. Control Theory (, (). [11] J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media, Martinus Nijhoff Publishers, The Hague, 1983. [12] R. E. Johnson, An improved slender-body theory for Stokes flow, J. Fluid Mech., 99 (1980), 411-431. doi: 10.1017/S0022112080000687. [13] J. B. Keller and S. I. Rubinow, Slender-body theory for slow viscous flow, J. Fluid Mech., 75 (1976), 705-714. doi: 10.1017/S0022112076000475. [14] J. Lighthill, Mathematical Biofluiddynamics, SIAM, Philadelphia, 1975. [15] ________, Flagellar hydrodynamics, SIAM Rev., 18 (1976), 161-230. doi: 10.1137/1018040. [16] J.-L. Lions, Quelques Méthodes de Résolution Des Problèmes Aux Limites Non Linéaires, Dunod, Paris, 1969. [17] A. Musesti, Isotropic linear constitutive relations for nonsimple fluids, Acta Mech., 204 (2009), 81-88. doi: 10.1007/s00707-008-0050-6. [18] D. Serre, Chute libre d'un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., 4 (1987), 99-110. doi: 10.1007/BF03167757. show all references ##### References: [1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623-727. doi: 10.1002/cpa.3160120405. [2] G. K. Batchelor, Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech., 44 (1970), 419-440. doi: 10.1017/S002211207000191X. [3] A. T. Chwang and T. Y.-T. Wu, Hydromechanics of low-Reynolds-number flow. II. Singularity method for Stokes flows, J. Fluid Mech., 67 (1975), 787-815. doi: 10.1017/S0022112075000614. [4] E. Fried and M. E. Gurtin, Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales, Arch. Ration. Mech. Anal., 182 (2006), 513-554. doi: 10.1007/s00205-006-0015-7. [5] G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in Handbook of mathematical fluid dynamics, North-Holland, Amsterdam, 1 (2002), 653-791. [6] G. G. Giusteri, The multiple nature of concentrated interactions in second-gradient dissipative liquids, Z. Angew. Math. Phys., 64 (2013), 371-380. doi: 10.1007/s00033-012-0229-5. [7] G. G. Giusteri and E. Fried, Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, Meccanica, 49 (2014), 2153-2167. doi: 10.1007/s11012-014-9890-4. [8] G. G. Giusteri, A. Marzocchi and A. Musesti, Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies, Mech. Res. Commun., 37 (2010), 642-646. doi: 10.1016/j.mechrescom.2010.09.001. [9] G. G. Giusteri, A. Marzocchi and A. Musesti, Nonsimple isotropic incompressible linear fluids surrounding one-dimensional structures, Acta Mech., 217 (2011), 191-204. doi: 10.1007/s00707-010-0387-5. [10] G. G. Giusteri, A. Marzocchi and A. Musesti, Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number,, to appear in Evol. Equ. Control Theory (, (). [11] J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media, Martinus Nijhoff Publishers, The Hague, 1983. [12] R. E. Johnson, An improved slender-body theory for Stokes flow, J. Fluid Mech., 99 (1980), 411-431. doi: 10.1017/S0022112080000687. [13] J. B. Keller and S. I. Rubinow, Slender-body theory for slow viscous flow, J. Fluid Mech., 75 (1976), 705-714. doi: 10.1017/S0022112076000475. [14] J. Lighthill, Mathematical Biofluiddynamics, SIAM, Philadelphia, 1975. [15] ________, Flagellar hydrodynamics, SIAM Rev., 18 (1976), 161-230. doi: 10.1137/1018040. [16] J.-L. Lions, Quelques Méthodes de Résolution Des Problèmes Aux Limites Non Linéaires, Dunod, Paris, 1969. [17] A. Musesti, Isotropic linear constitutive relations for nonsimple fluids, Acta Mech., 204 (2009), 81-88. doi: 10.1007/s00707-008-0050-6. [18] D. Serre, Chute libre d'un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., 4 (1987), 99-110. doi: 10.1007/BF03167757. [1] Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633 [2] Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199 [3] Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluid-structure interaction. Networks and Heterogeneous Media, 2008, 3 (4) : 787-813. doi: 10.3934/nhm.2008.3.787 [4] Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355 [5] George Avalos, Roberto Triggiani. Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations and Control Theory, 2013, 2 (4) : 563-598. doi: 10.3934/eect.2013.2.563 [6] Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012 [7] Daniele Boffi, Lucia Gastaldi, Sebastian Wolf. Higher-order time-stepping schemes for fluid-structure interaction problems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3807-3830. doi: 10.3934/dcdsb.2020229 [8] Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić. Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks and Heterogeneous Media, 2007, 2 (3) : 397-423. doi: 10.3934/nhm.2007.2.397 [9] George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817 [10] Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349 [11] Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 269-287. doi: 10.3934/dcdss.2016.9.269 [12] Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295 [13] George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3-D fluid-structure interaction. Evolution Equations and Control Theory, 2014, 3 (4) : 557-578. doi: 10.3934/eect.2014.3.557 [14] Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102 [15] Henry Jacobs, Joris Vankerschaver. Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes. 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A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424 [20] Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam. Conference Publications, 2011, 2011 (Special) : 813-823. doi: 10.3934/proc.2011.2011.813 2020 Impact Factor: 1.327	3,955	12,378	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.546875	3	CC-MAIN-2022-21	longest	en	0.700238
https://krunalkanojiya.com/data-structure-and-algorithms/dsa/Arrays-prefix-sum/equilibrium-index-of-an-array	1,721,414,784,000,000,000	text/html	crawl-data/CC-MAIN-2024-30/segments/1720763514917.3/warc/CC-MAIN-20240719170235-20240719200235-00291.warc.gz	323,034,798	11,568	Data Structure & Algorithms DSA Arrays prefix sum Equilibrium Index of an Array # Equilibrium index of an array ## Problem Description You are given an array A of integers of size N. Your task is to find the equilibrium index of the given array The equilibrium index of an array is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. If there are no elements that are at lower indexes or at higher indexes, then the corresponding sum of elements is considered as 0. Notes : - • Array indexing starts from 0. • If there is no equilibrium index then return -1. • If there are more than one equilibrium indexes then return the minimum index. ### Problem Constraints ``````1 <= N <= 10^5 -105 <= A[i] <= 10^5`````` ### Input Format ``First arugment is an array A.`` ### Output Format ``Return the equilibrium index of the given array. If no such index is found then return -1.`` ### Example Input ``````Input 1: A = [-7, 1, 5, 2, -4, 3, 0] Input 2: A = [1, 2, 3]`````` ### Example Output ``````Output 1: 3 Output 2: -1`````` ### Example Explanation ``````Explanation 1: i Sum of elements at lower indexes Sum of elements at higher indexes 0 0 7 1 -7 6 2 -6 1 3 -1 -1 4 1 3 5 -3 0 6 0 0 3 is an equilibrium index, because: A[0] + A[1] + A[2] = A[4] + A[5] + A[6] Explanation 2: i Sum of elements at lower indexes Sum of elements at higher indexes 0 0 5 1 1 3 2 3 0 Thus, there is no such index.`````` ### Output Java ``````public int equilibriumIndex(int[] A) { int n = A.length; long totalSum = 0; long leftSum = 0; for (int i = 0; i < n; i++) { totalSum += A[i]; } for (int i = 0; i < n; i++) { totalSum -= A[i]; if (leftSum == totalSum) { return i; } leftSum += A[i]; } return -1; }`````` Python ``````def equilibrium_index(A): n = len(A) total_sum = sum(A) left_sum = 0 for i in range(n): total_sum -= A[i] if left_sum == total_sum: return i left_sum += A[i] return -1`````` JavaScript ``````function equilibriumIndex(A) { const n = A.length; let totalSum = 0; let leftSum = 0; for (let i = 0; i < n; i++) { totalSum += A[i]; } for (let i = 0; i < n; i++) { totalSum -= A[i]; if (leftSum === totalSum) { return i; } leftSum += A[i]; } return -1; }``````	746	2,769	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.78125	4	CC-MAIN-2024-30	latest	en	0.703101
https://sourceforge.net/p/libmesh/mailman/message/20208688/	1,498,254,794,000,000,000	text/html	crawl-data/CC-MAIN-2017-26/segments/1498128320174.58/warc/CC-MAIN-20170623202724-20170623222724-00113.warc.gz	815,035,561	11,160	Re: [Libmesh-users] how to give variables non-zero initial values? Re: [Libmesh-users] how to give variables non-zero initial values? From: Roy Stogner - 2008-09-03 20:53:03 ```On Wed, 3 Sep 2008, yunfei zhu wrote: > I am following example 13 and trying to solve a set of nonlinear PDEs using > the solver of libmesh. > I have noted that: >> From previous Newton iterate, the variable values of "u" and "v" can be > assigned by > u += phi[l][qp]navier_stokes_system.current_solution (dof_indices_u[l]); > v += phi[l][qp]navier_stokes_system.current_solution (dof_indices_v[l]); > For the first nonlinear loop, > "current_solution (dof_indices_u[l])" is zero, so all the initial values of > "u" and "v" are assigned 0. But I would like to give the variables non-zero > initial values, could you guys please tell me how should I do that? what > function should be used? Thanks in advance. It depends how your initial values are defined. If they're a known function of (x,y,z), then try System::project_solution. --- Roy ``` [Libmesh-users] how to give variables non-zero initial values? From: yunfei zhu - 2008-09-03 20:48:21 ```Hi all, I am following example 13 and trying to solve a set of nonlinear PDEs using the solver of libmesh. I have noted that: >From previous Newton iterate, the variable values of "u" and "v" can be assigned by u += phi[l][qp]navier_stokes_system.current_solution (dof_indices_u[l]); v += phi[l][qp]navier_stokes_system.current_solution (dof_indices_v[l]); For the first nonlinear loop, "current_solution (dof_indices_u[l])" is zero, so all the initial values of "u" and "v" are assigned 0. But I would like to give the variables non-zero initial values, could you guys please tell me how should I do that? what function should be used? Thanks in advance. Best wishes, yunfei ``` Re: [Libmesh-users] how to give variables non-zero initial values? From: Roy Stogner - 2008-09-03 20:53:03 ```On Wed, 3 Sep 2008, yunfei zhu wrote: > I am following example 13 and trying to solve a set of nonlinear PDEs using > the solver of libmesh. > I have noted that: >> From previous Newton iterate, the variable values of "u" and "v" can be > assigned by > u += phi[l][qp]navier_stokes_system.current_solution (dof_indices_u[l]); > v += phi[l][qp]navier_stokes_system.current_solution (dof_indices_v[l]); > For the first nonlinear loop, > "current_solution (dof_indices_u[l])" is zero, so all the initial values of > "u" and "v" are assigned 0. But I would like to give the variables non-zero > initial values, could you guys please tell me how should I do that? what > function should be used? Thanks in advance. It depends how your initial values are defined. If they're a known function of (x,y,z), then try System::project_solution. --- Roy ```	755	2,772	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.5625	3	CC-MAIN-2017-26	latest	en	0.857086
https://gmatclub.com/forum/if-a-taxicab-charges-x-cents-for-the-first-1-9-mile-and-x-97525.html?sort_by_oldest=true	1,496,112,117,000,000,000	text/html	crawl-data/CC-MAIN-2017-22/segments/1495463613738.67/warc/CC-MAIN-20170530011338-20170530031338-00030.warc.gz	891,359,209	63,531	Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack It is currently 29 May 2017, 19:41 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # If a taxicab charges x cents for the first 1/9 mile and x/5 Author Message TAGS: ### Hide Tags Intern Joined: 06 Aug 2007 Posts: 31 Location: Montreal Followers: 0 Kudos [?]: 39 [1] , given: 19 If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 19 Jul 2010, 16:17 1 KUDOS 14 This post was BOOKMARKED 00:00 Difficulty: (N/A) Question Stats: 62% (03:24) correct 38% (02:05) wrong based on 308 sessions ### HideShow timer Statistics If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x + (xy-x)/45 (B) x - (xy-x)/45 (C) 2x+9y/5 (D) x + (9x-y)/5 (E) x + (9xy-x)/5 Last edited by Safiya on 20 Jul 2010, 15:16, edited 2 times in total. Manager Joined: 20 Mar 2010 Posts: 84 Followers: 2 Kudos [?]: 96 [1] , given: 1 ### Show Tags 19 Jul 2010, 19:07 1 KUDOS Safiya wrote: Hi All, I hope someone can explain me the solution of the below problem; If a taxicab charges x cents for the first 1/9 mile and x/9 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ xy-x /45 (B) x- xy-x /45 (C) 2x+9y / 5 (D) x+ 9x-y / 5 (E) x+ 9xy-x / 5 Total cost for y miles = cost for first 1/9 mile + cost for the additional (y-1/9) miles = x + (y-1/9)* x (Since each additional 1/9 th mile costs x/9 cents , each additional mile costs x cents and (y-1/9) additional miles cost (y-1/9)x cents) = x + xy -x/9 which i don't see in the answers Are you sure the answer choices are accurate? Thanks Harsha _________________ ___________________________________ Please give me kudos if you like my post Intern Joined: 06 Aug 2007 Posts: 31 Location: Montreal Followers: 0 Kudos [?]: 39 [0], given: 19 ### Show Tags 19 Jul 2010, 19:57 Total cost for y miles = cost for first 1/9 mile + cost for the additional (y-1/9) miles = x + (y-1/9) x (Since each additional 1/9 th mile costs x/9 cents , each additional mile costs x cents and (y-1/9) additional miles cost (y-1/9)x cents) = x + xy -x/9 which i don't see in the answers Are you sure the answer choices are accurate? Thanks Harsha[/quote] Hi Harsha, I double checked - the answer choices are correct Math Expert Joined: 02 Sep 2009 Posts: 39062 Followers: 7756 Kudos [?]: 106578 [2] , given: 11628 ### Show Tags 20 Jul 2010, 02:13 2 KUDOS Expert's post 3 This post was BOOKMARKED Safiya wrote: Hi All, I hope someone can explain me the solution of the below problem; If a taxicab charges x cents for the first 1/9 mile and x/9 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ xy-x /45 (B) x- xy-x /45 (C) 2x+9y / 5 (D) x+ 9x-y / 5 (E) x+ 9xy-x / 5 Charge will be the sum of the following: $$x$$ cents for for the first $$\frac{1}{9}$$ mile; In 1 mile there are 9 parts of $$\frac{1}{9}$$, hence in $$y$$ miles (where $$y$$ is a whole number) there are $$9y$$ parts of $$\frac{1}{9}$$ miles minus one part (first $$\frac{1}{9}$$ mile) = $$9y-1$$ parts of $$\frac{1}{9}$$ miles to be charged additionally. $$\frac{x}{9}$$ cents per part = $$(9y-1)\frac{x}{9}$$ cents; $$x+(9y-1)\frac{x}{9}=x+\frac{9xy-x}{9}$$. If you say that OA is E, then charge for each additional 1/9 mile should be x/5 cents instead of x/9. Hope it helps. _________________ Intern Joined: 06 Aug 2007 Posts: 31 Location: Montreal Followers: 0 Kudos [?]: 39 [0], given: 19 ### Show Tags 20 Jul 2010, 15:18 Crack 700 and Bunuel ; I am so sorry it was written x/9 instead of x/5 , I've just edited the question. Many thanks for the answer! Math Expert Joined: 02 Sep 2009 Posts: 39062 Followers: 7756 Kudos [?]: 106578 [0], given: 11628 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 24 Jun 2013, 04:03 Bumping for review and further discussion. Get a kudos point for an alternative solution! New project from GMAT Club!!! Check HERE All DS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=36 All PS Fractions/Ratios/Decimals questions: search.php?search_id=tag&tag_id=57 _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2292 Kudos [?]: 15168 [4] , given: 224 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 18 Jul 2013, 22:28 4 KUDOS Expert's post 3 This post was BOOKMARKED Safiya wrote: If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ (xy-x) /45 (B) x- (xy-x) /45 (C) 2x+9y / 5 (D) x+ (9x-y) / 5 (E) x+ (9xy-x) / 5 Responding to a pm: You can assume values for x and y to get the answer. Charges for first 1/9 mile = x = 5 cents (assume) Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents) So say, we need to cover a total distance of y = 1 mile. How much would be the charge? 5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents. So total charge = 5 + 8 = 13 cents Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 22 Nov 2013 Posts: 40 Followers: 1 Kudos [?]: 95 [0], given: 3 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 30 Nov 2013, 03:18 VeritasPrepKarishma wrote: Safiya wrote: If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ (xy-x) /45 (B) x- (xy-x) /45 (C) 2x+9y / 5 (D) x+ (9x-y) / 5 (E) x+ (9xy-x) / 5 Responding to a pm: You can assume values for x and y to get the answer. Charges for first 1/9 mile = x = 5 cents (assume) Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents) So say, we need to cover a total distance of y = 1 mile. How much would be the charge? 5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents. So total charge = 5 + 8 = 13 cents Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13. Answer (E) I tried solving it this way, however failed. What am I doing wrong? Many thanks. I did the following: x=5 y=9 Charges for the first 1/9 mile: 1/9 9 * 5 = 5 Charges for the remaining 1/9 miles: 8/9 * 9 * 5/5 = 8 The sum of both is indeed: 5+8 = 13 Putting this into answer E: x+(9xy-x) / 5 yields the following: 5 + (959 - 5)/5 = 5 + (405 - 5)/5 = 5 + 80 = 85 ...thus, not 13. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2292 Kudos [?]: 15168 [1] , given: 224 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 01 Dec 2013, 23:37 1 This post received KUDOS Expert's post BabySmurf wrote: VeritasPrepKarishma wrote: Safiya wrote: If a taxicab charges x cents for the first 1/9 mile and x/5 cents for each additional 1/9 mile or fraction thereof, what is the charge, in cents, for a ride of y miles, where y is a whole number? (A) x+ (xy-x) /45 (B) x- (xy-x) /45 (C) 2x+9y / 5 (D) x+ (9x-y) / 5 (E) x+ (9xy-x) / 5 Responding to a pm: You can assume values for x and y to get the answer. Charges for first 1/9 mile = x = 5 cents (assume) Charges for each subsequent 1/9 mile = x/5 = 1 cent (if x = 5 cents) So say, we need to cover a total distance of y = 1 mile. How much would be the charge? 5 cents for the first 1/9 mile. Now we are left with 8/9 mile distance. 1 cent for every subsequent 1/9 mile i.e. 8 cents. So total charge = 5 + 8 = 13 cents Now put x = 5 and y = 1 in the options. The moment you put y = 1, you see that options (A), (B) and (C) are out of the picture since they give very small values. In option (D), 9x - y will be 1 less than a multiple of 5 so it will not be divisible by 5. Only (E) gives you 13. Answer (E) I tried solving it this way, however failed. What am I doing wrong? Many thanks. I did the following: x=5 y=9 Charges for the first 1/9 mile: 1/9 * 9 * 5 = 5 Charges for the remaining 1/9 miles: 8/9 * 9 * 5/5 = 8 The sum of both is indeed: 5+8 = 13 Putting this into answer E: x+(9xy-x) / 5 yields the following: 5 + (959 - 5)/5 = 5 + (405 - 5)/5 = 5 + 80 = 85 ...thus, not 13. The first 1/9 mile is charged at 5 cents (as per the numbers assumed) Now every remaining 1/9th of a mile will be charged at 1 cent. If you have to cover a distance of total 9 miles, the first 1/9th of a mile will be charged ta 5 cents. Now remaining distance is 8 miles and 8/9th of a mile. For every 1 mile now the fare will be 9 cents (1 cent per 1/9th of a mile) and for the 8/9th of a mile, the fare will be 8 cents. So total fare of the remaining distance will be 98 + 8 = 80 Total fare of first 1/9th of a mile + additional 8/9th of a mile and 8 more miles = 5 + 80 = 85 Note that I had assumed y = 1. You assumed y = 9. Hence total fare for both cannot be 13 cents. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 15524 Followers: 651 Kudos [?]: 211 [0], given: 0 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 07 Apr 2015, 20:36 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 17 Jul 2015 Posts: 5 Followers: 1 Kudos [?]: 1 [0], given: 1 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 03 Aug 2015, 16:29 First 1/9 mile: x 1/9 additional miles past the first 1/9: x/5 * (y - 1/9) x/9 + x/5(y - 1/9) = x/9 + xy/5 - x/45 Now remember that E is: x + (9xy-x)/5 so if we multiple our equation by 9, we get: x + 9/5 * xy - x/5 factor out the 1/5 in second part of the equation: x + 1/5 ( 9xy - x) GMAT Club Legend Joined: 09 Sep 2013 Posts: 15524 Followers: 651 Kudos [?]: 211 [0], given: 0 Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] ### Show Tags 21 Dec 2016, 09:52 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: If a taxicab charges x cents for the first 1/9 mile and x/5 [#permalink] 21 Dec 2016, 09:52 Similar topics Replies Last post Similar Topics: 1 The mall charges 50 cents for the first hour of parking and \$3 for eac 2 27 Jun 2016, 12:24 1 A taxicab fare costs x dollars for the first quarter of a mile and 1/4 3 09 Jun 2016, 03:38 7 A taxi charges d dollars for the first two miles and c cents per quart 7 20 Apr 2015, 04:57 1 If a taxi driver charges x cents for the first quarter-mile of a trip 7 11 Jun 2016, 02:32 8 The rental charge for a car is 34 cents for the first 1/4 mi 10 18 Oct 2016, 10:14 Display posts from previous: Sort by	4,379	13,052	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.03125	4	CC-MAIN-2017-22	latest	en	0.842291
https://www.exceldemy.com/tag/sum/page/3/	1,679,891,111,000,000,000	text/html	crawl-data/CC-MAIN-2023-14/segments/1679296946637.95/warc/CC-MAIN-20230327025922-20230327055922-00676.warc.gz	842,728,446	52,914	SUM Function ### How to Apply Vector Formula in Excel (5 Suitable Examples) If you are looking for a vector formula in Excel, you have come to the right place. Here, we will walk you through 5 easy examples of doing the task ... ### How to Calculate Mean Squared Error in Excel (3 Easy Methods) In this article, I will show how to calculate Mean Squared Error in Microsoft Excel with quick steps and clear illustrations. In practical life, ... ### How to Do Analysis Sales Pipeline in Excel (with Easy Steps) Microsoft Excel is a handy software. We use Excel functions for our educational, business, and sales management. Further in sales management, sales ... ### How to Do Kernel Density Estimation in Excel (with Detailed Steps) Kernel Density Estimation is a form of probability distribution function used in statistics. This method is used for nonparametric statistical data. ... ### How to Create Progress Thermometer in Excel (with Easy Steps) If you are looking for some special tricks to know how to create a Progress Thermometer in Excel, you've come to the right place. There is one way to ... ### How to Create Fundraising Thermometer in Excel (with Easy Steps) Microsoft Excel is one of the most beneficial programs you can use. Using Excel's features and tools, you can do an almost infinite number of things ... ### How to Create Project Pipeline in Excel (2 Suitable Methods) Sometimes for business or institute purposes, you may need to create a project pipeline in Excel to track all your projects easily. So, if you are ... ### How to Optimize Multiple Variables in Excel (with Detailed Steps) Optimization of variables is needed to solve any equation in mathematics. Excel has some tricks for solving equations with less time consumption. The ... ### How to Create a Workflow Tracker in Excel (with Easy Steps) If you want to create a workflow tracker in Excel, you have come to the right place. Here, we will walk you through 10 easy and suitable steps to do ... ### How to Count Words in Excel (6 Easy Methods) In this article, I will show you how to count words in Excel. While working in Excel, we may want to calculate the total number of words in a cell or ... ### How to Create Pipeline Report in Excel (With Easy Steps) In this article, we will learn how to create a pipeline report in Excel. A pipeline report is very important for any company. The company can track ... ### How to Create Sprint Burndown Chart in Excel (with Easy Steps) Creating a sprint burndown chart is now an essential part of the inventory management system. Sprint burndown chart aids the team in determining how ... ### Project Cost Estimation Example in Excel (with Easy Steps) Cost estimation is the basis of project management. In our day-to-day life, we have to design several types of estimation lists or tools. Using ... ### How to Create Debt Thermometer in Excel (with Easy Steps) This tutorial will demonstrate how to create a debt thermometer chart in Excel. A debt thermometer chart is very useful when you want to represent ... 5 Excel Hacks You Never Knew	635	3,101	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.171875	3	CC-MAIN-2023-14	latest	en	0.906023
https://nz.education.com/lesson-plans/second-grade/multiplication/	1,600,854,232,000,000,000	text/html	crawl-data/CC-MAIN-2020-40/segments/1600400210616.36/warc/CC-MAIN-20200923081833-20200923111833-00396.warc.gz	535,476,878	23,327	# 2nd grade Multiplication Lesson Plans 6 filtered results 6 filtered results Multiplication Sort by Animal Spots: Multiplication Practice Lesson Plan Animal Spots: Multiplication Practice Animals and spots are used to make multiplication interesting! In this lesson, students will practice multiplying one digit numbers. Math Lesson Plan Domino Multiplication Lesson Plan Domino Multiplication Don't knock the dominoes over! In this lesson, your students will practice multiplying by 2's with dominoes. Math Lesson Plan Multiplication Cups Competition Lesson Plan Multiplication Cups Competition Motivate your students by engaging them in a competition! In this lesson, your students will review and practice multiplication strategies. Math Lesson Plan Come "Array" With Us Lesson Plan Come "Array" With Us In this scavenger hunt lesson, students will look for rectangular arrays within their school environment. Whether it is a set of cubbies or windows, students will see that arrays are all around us. Math Lesson Plan What Are Arrays? Lesson Plan What Are Arrays? In this lesson, students will explore the characteristics of arrays and find out why they are important. Use this lesson independently or alongside Come Array With Us! Math Lesson Plan How Many Are There? Lesson Plan How Many Are There? Lay the foundation for multiplication by introducing your second graders to the concepts of skip counting and repeated addition. This lesson can be used alongside Up, Up, and Array, or separately to reinforce these important skills.	322	1,539	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.9375	3	CC-MAIN-2020-40	latest	en	0.886763
https://adsy.me/home_questions/what-size-heater-do-i-need-for-a-10x10-room/	1,709,412,264,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947475897.53/warc/CC-MAIN-20240302184020-20240302214020-00333.warc.gz	73,163,008	24,851	# What size heater do I need for a 10×10 room? ### Understanding the Importance of Sizing Your Heater Correctly When it comes to heating a room, especially a small one like a 10×10 room, it’s important to choose the right size heater to ensure optimal comfort and efficiency. Selecting the correct heater size will not only help you maintain the desired temperature but also prevent wasting energy and money. Here’s a breakdown of how to determine the ideal size heater for your 10×10 room. ### Calculating the Heating Capacity Needed The first step in finding the right size heater is to calculate the heating capacity needed for your 10×10 room. This calculation is typically based on the room’s square footage, insulation level, and desired temperature. The general rule of thumb is to allow about 10 watts of heating power per square foot of a well-isolated room. Thus, for a 100 square foot (10×10) room, you would require approximately 1000 watts (10×100 = 1000) of heating capacity. ### Consider Additional Factors While calculating the heating capacity based on square footage gives you a starting point, there are additional factors to consider to ensure your heater provides adequate warmth for a 10×10 room. One crucial aspect is insulation. If your room lacks proper insulation or has drafty windows and doors, it may require more heating capacity to compensate for the heat loss. Keep in mind that rooms with high ceilings or large windows may also require additional heating power to counteract the increased heat loss. ### Types of Heaters Suitable for a 10×10 Room Once you determine the required heating capacity, you can select from different types of heaters available on the market. Here are a few options that are suitable for a 10×10 room: 1. Electric Space Heaters: These heaters are popular due to their affordability, ease of use, and efficiency. Electric space heaters are available in various sizes and styles, including fan-forced models that distribute heat evenly throughout the room. If safety is a concern, look for models with tip-over and overheat protection features. 2. Infrared Heaters: Infrared heaters use electromagnetic radiation to produce heat, which is then absorbed by objects and people in the room, making them feel warm. They are energy-efficient and can quickly heat up a small space like a 10×10 room. Infrared heaters are often compact and portable, allowing you to move them around the room as needed. 3. Baseboard Heaters: Baseboard heaters are a popular choice for small rooms due to their slim profile and silent operation. These heaters are typically installed along the baseboard of a wall and use convection to circulate warm air. They can be an excellent option for rooms with limited floor space. ### Finding the Right Size Heater for Your 10×10 Room To determine the right size heater for your 10×10 room, consider the heating capacity needed and match it to the available options. Keep in mind that heater sizing is not an exact science, and there may be variability based on factors such as insulation and individual comfort preferences. If you’re unsure about the exact sizing, it’s always a good idea to seek advice from a professional heating installer or consult the manufacturer’s guidelines for the specific heater you are considering.	675	3,317	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.640625	3	CC-MAIN-2024-10	latest	en	0.917187
https://www.quizzes.cc/metric/percentof.php?percent=61.5&of=518	1,591,209,073,000,000,000	text/html	crawl-data/CC-MAIN-2020-24/segments/1590347435987.85/warc/CC-MAIN-20200603175139-20200603205139-00423.warc.gz	850,451,340	4,373	#### What is 61.5 percent of 518? How much is 61.5 percent of 518? Use the calculator below to calculate a percentage, either as a percentage of a number, such as 61.5% of 518 or the percentage of 2 numbers. Change the numbers to calculate different amounts. Simply type into the input boxes and the answer will update. ## 61.5% of 518 = 318.57 Calculate another percentage below. Type into inputs Find number based on percentage percent of Find percentage based on 2 numbers divided by Calculating sixty-one point five of five hundred and eighteen How to calculate 61.5% of 518? Simply divide the percent by 100 and multiply by the number. For example, 61.5 /100 x 518 = 318.57 or 0.615 x 518 = 318.57 #### How much is 61.5 percent of the following numbers? 61.5% of 518.01 = 31857.615 61.5% of 518.02 = 31858.23 61.5% of 518.03 = 31858.845 61.5% of 518.04 = 31859.46 61.5% of 518.05 = 31860.075 61.5% of 518.06 = 31860.69 61.5% of 518.07 = 31861.305 61.5% of 518.08 = 31861.92 61.5% of 518.09 = 31862.535 61.5% of 518.1 = 31863.15 61.5% of 518.11 = 31863.765 61.5% of 518.12 = 31864.38 61.5% of 518.13 = 31864.995 61.5% of 518.14 = 31865.61 61.5% of 518.15 = 31866.225 61.5% of 518.16 = 31866.84 61.5% of 518.17 = 31867.455 61.5% of 518.18 = 31868.07 61.5% of 518.19 = 31868.685 61.5% of 518.2 = 31869.3 61.5% of 518.21 = 31869.915 61.5% of 518.22 = 31870.53 61.5% of 518.23 = 31871.145 61.5% of 518.24 = 31871.76 61.5% of 518.25 = 31872.375 61.5% of 518.26 = 31872.99 61.5% of 518.27 = 31873.605 61.5% of 518.28 = 31874.22 61.5% of 518.29 = 31874.835 61.5% of 518.3 = 31875.45 61.5% of 518.31 = 31876.065 61.5% of 518.32 = 31876.68 61.5% of 518.33 = 31877.295 61.5% of 518.34 = 31877.91 61.5% of 518.35 = 31878.525 61.5% of 518.36 = 31879.14 61.5% of 518.37 = 31879.755 61.5% of 518.38 = 31880.37 61.5% of 518.39 = 31880.985 61.5% of 518.4 = 31881.6 61.5% of 518.41 = 31882.215 61.5% of 518.42 = 31882.83 61.5% of 518.43 = 31883.445 61.5% of 518.44 = 31884.06 61.5% of 518.45 = 31884.675 61.5% of 518.46 = 31885.29 61.5% of 518.47 = 31885.905 61.5% of 518.48 = 31886.52 61.5% of 518.49 = 31887.135 61.5% of 518.5 = 31887.75 61.5% of 518.51 = 31888.365 61.5% of 518.52 = 31888.98 61.5% of 518.53 = 31889.595 61.5% of 518.54 = 31890.21 61.5% of 518.55 = 31890.825 61.5% of 518.56 = 31891.44 61.5% of 518.57 = 31892.055 61.5% of 518.58 = 31892.67 61.5% of 518.59 = 31893.285 61.5% of 518.6 = 31893.9 61.5% of 518.61 = 31894.515 61.5% of 518.62 = 31895.13 61.5% of 518.63 = 31895.745 61.5% of 518.64 = 31896.36 61.5% of 518.65 = 31896.975 61.5% of 518.66 = 31897.59 61.5% of 518.67 = 31898.205 61.5% of 518.68 = 31898.82 61.5% of 518.69 = 31899.435 61.5% of 518.7 = 31900.05 61.5% of 518.71 = 31900.665 61.5% of 518.72 = 31901.28 61.5% of 518.73 = 31901.895 61.5% of 518.74 = 31902.51 61.5% of 518.75 = 31903.125 61.5% of 518.76 = 31903.74 61.5% of 518.77 = 31904.355 61.5% of 518.78 = 31904.97 61.5% of 518.79 = 31905.585 61.5% of 518.8 = 31906.2 61.5% of 518.81 = 31906.815 61.5% of 518.82 = 31907.43 61.5% of 518.83 = 31908.045 61.5% of 518.84 = 31908.66 61.5% of 518.85 = 31909.275 61.5% of 518.86 = 31909.89 61.5% of 518.87 = 31910.505 61.5% of 518.88 = 31911.12 61.5% of 518.89 = 31911.735 61.5% of 518.9 = 31912.35 61.5% of 518.91 = 31912.965 61.5% of 518.92 = 31913.58 61.5% of 518.93 = 31914.195 61.5% of 518.94 = 31914.81 61.5% of 518.95 = 31915.425 61.5% of 518.96 = 31916.04 61.5% of 518.97 = 31916.655 61.5% of 518.98 = 31917.27 61.5% of 518.99 = 31917.885 61.5% of 519 = 31918.5 1% of 518 = 5.18 2% of 518 = 10.36 3% of 518 = 15.54 4% of 518 = 20.72 5% of 518 = 25.9 6% of 518 = 31.08 7% of 518 = 36.26 8% of 518 = 41.44 9% of 518 = 46.62 10% of 518 = 51.8 11% of 518 = 56.98 12% of 518 = 62.16 13% of 518 = 67.34 14% of 518 = 72.52 15% of 518 = 77.7 16% of 518 = 82.88 17% of 518 = 88.06 18% of 518 = 93.24 19% of 518 = 98.42 20% of 518 = 103.6 21% of 518 = 108.78 22% of 518 = 113.96 23% of 518 = 119.14 24% of 518 = 124.32 25% of 518 = 129.5 26% of 518 = 134.68 27% of 518 = 139.86 28% of 518 = 145.04 29% of 518 = 150.22 30% of 518 = 155.4 31% of 518 = 160.58 32% of 518 = 165.76 33% of 518 = 170.94 34% of 518 = 176.12 35% of 518 = 181.3 36% of 518 = 186.48 37% of 518 = 191.66 38% of 518 = 196.84 39% of 518 = 202.02 40% of 518 = 207.2 41% of 518 = 212.38 42% of 518 = 217.56 43% of 518 = 222.74 44% of 518 = 227.92 45% of 518 = 233.1 46% of 518 = 238.28 47% of 518 = 243.46 48% of 518 = 248.64 49% of 518 = 253.82 50% of 518 = 259 51% of 518 = 264.18 52% of 518 = 269.36 53% of 518 = 274.54 54% of 518 = 279.72 55% of 518 = 284.9 56% of 518 = 290.08 57% of 518 = 295.26 58% of 518 = 300.44 59% of 518 = 305.62 60% of 518 = 310.8 61% of 518 = 315.98 62% of 518 = 321.16 63% of 518 = 326.34 64% of 518 = 331.52 65% of 518 = 336.7 66% of 518 = 341.88 67% of 518 = 347.06 68% of 518 = 352.24 69% of 518 = 357.42 70% of 518 = 362.6 71% of 518 = 367.78 72% of 518 = 372.96 73% of 518 = 378.14 74% of 518 = 383.32 75% of 518 = 388.5 76% of 518 = 393.68 77% of 518 = 398.86 78% of 518 = 404.04 79% of 518 = 409.22 80% of 518 = 414.4 81% of 518 = 419.58 82% of 518 = 424.76 83% of 518 = 429.94 84% of 518 = 435.12 85% of 518 = 440.3 86% of 518 = 445.48 87% of 518 = 450.66 88% of 518 = 455.84 89% of 518 = 461.02 90% of 518 = 466.2 91% of 518 = 471.38 92% of 518 = 476.56 93% of 518 = 481.74 94% of 518 = 486.92 95% of 518 = 492.1 96% of 518 = 497.28 97% of 518 = 502.46 98% of 518 = 507.64 99% of 518 = 512.82 100% of 518 = 518	2,907	5,452	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.96875	4	CC-MAIN-2020-24	latest	en	0.873851
https://ch.mathworks.com/matlabcentral/profile/authors/21339204	1,623,922,004,000,000,000	text/html	crawl-data/CC-MAIN-2021-25/segments/1623487629632.54/warc/CC-MAIN-20210617072023-20210617102023-00299.warc.gz	167,979,102	20,818	Community Profile # Nguyen Duong ##### Last seen: 17 days ago 89 total contributions since 2021 #### Nguyen Duong's Badges View details... Contributions in View by Solved Vector creation Create a vector using square brackets going from 1 to the given value x in steps on 1. Hint: use increment. 2 months ago Solved Doubling elements in a vector Given the vector A, return B in which all numbers in A are doubling. So for: A = [ 1 5 8 ] then B = [ 1 1 5 ... 2 months ago Solved Whether the input is vector? Given the input x, return 1 if x is vector or else 0. 2 months ago Solved Flip the vector from right to left Flip the vector from right to left. Examples x=[1:5], then y=[5 4 3 2 1] x=[1 4 6], then y=[6 4 1]; Request not ... 2 months ago Solved Inner product of two vectors Find the inner product of two vectors. 2 months ago Solved Arrange Vector in descending order If x=[0,3,4,2,1] then y=[4,3,2,1,0] 2 months ago Solved Find the maximum number of decimal places in a set of numbers Given a vector or matrix of values, calculate the maximum number of decimal places within the input. Trailing zeros do not coun... 2 months ago Solved Find the Best Hotels Given three input variables: * \|hotels\| - a list of hotel names * \|ratings\| - their ratings in a city * \|cutoff\| - the rat... 2 months ago Solved Find the Oldest Person in a Room Given two input vectors: * \|name\| - user last names * \|age\| - corresponding age of the person Return the name of the ol... 2 months ago Solved Convert from Fahrenheit to Celsius Given an input vector \|F\| containing temperature values in Fahrenheit, return an output vector \|C\| that contains the values in C... 2 months ago Solved Calculate Amount of Cake Frosting Given two input variables \|r\| and \|h\|, which stand for the radius and height of a cake, calculate the surface area of the cake y... 2 months ago Solved Calculate BMI Given a matrix \|hw\| (height and weight) with two columns, calculate BMI using these formulas: * 1 kilogram = 2.2 pounds * 1 ... 2 months ago Solved Draw a 'X'! Given n as input Draw a 'X' in a n-by-n matrix. example: n=3 y=[1 0 1 0 1 0 1 0 1] n=4 y=[1 0 0... 2 months ago Solved Draw a 'N'! Given n as input, generate a n-by-n matrix 'N' using 0 and 1 . Example: n=5 ans= [1 0 0 0 1 1 1 0 0 1 1 0 ... 2 months ago Solved Draw 'I' Given n as input, draw a n-by-n matrix 'I' using 0 and 1. example: n=3 ans= [0 1 0 0 1 0 0 1 0] n=... 2 months ago Solved Draw 'F' Draw a x-by-x matrix 'F' using 1 and 0. (x is odd and bigger than 4) Example: x=5 ans= [1 1 1 1 1 1 0 0 0 0 ... 2 months ago Solved Draw 'H' Draw a x-by-x matrix 'H' using 1 and 0. (x is odd and bigger than 2) Example: x=5 ans= [1 0 0 0 1 1 0 0 0 1 ... 2 months ago Solved Get the length of a given vector Given a vector x, the output y should equal the length of x. 2 months ago Solved Create a vector Create a vector from 0 to n by intervals of 2. 2 months ago Solved Pascal's Triangle Given an integer n >= 0, generate the length n+1 row vector representing the n-th row of <http://en.wikipedia.org/wiki/Pascals_t... 2 months ago Solved Which values occur exactly three times? Return a list of all values (sorted smallest to largest) that appear exactly three times in the input vector x. So if x = [1 2... 2 months ago Solved The Goldbach Conjecture The <http://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach conjecture> asserts that every even integer greater than 2 can ... 2 months ago Solved Find the two most distant points Given a collection of points, return the indices of the rows that contain the two points most distant from one another. The inpu... 2 months ago Solved Indexed Probability Table This question was inspired by a Stack Overflow question forwarded to me by Matt Simoneau. Given a vector x, make an indexed pro... 2 months ago Solved Target sorting Sort the given list of numbers \|a\| according to how far away each element is from the target value \|t\|. The result should return... 2 months ago Solved Most nonzero elements in row Given the matrix a, return the index r of the row with the most nonzero elements. Assume there will always be exactly one row th... 2 months ago Solved Find all elements less than 0 or greater than 10 and replace them with NaN Given an input vector x, find all elements of x less than 0 or greater than 10 and replace them with NaN. Example: Input ... 2 months ago Solved Return the largest number that is adjacent to a zero This example comes from Steve Eddins' blog: <http://blogs.mathworks.com/steve/2009/05/27/learning-lessons-from-a-one-liner/ Lear... 2 months ago Solved Sort a list of complex numbers based on far they are from the origin. Given a list of complex numbers z, return a list zSorted such that the numbers that are farthest from the origin (0+0i) appear f... 2 months ago Solved Making change Given an amount of currency, return a vector of this form: [100 50 20 10 5 2 1 0.5 0.25 0.1 0.05 0.01] Example: Input a = ... 2 months ago	1,462	5,044	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.359375	3	CC-MAIN-2021-25	latest	en	0.744739
http://brkmnd.com/pages/math/Default.aspx?id=2	1,575,574,895,000,000,000	text/html	crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00335.warc.gz	23,554,324	5,513	# Linear regression using python and matrix alg ## statistics/python :: 18-12-2017 Continuing from the last math article. Instead of finding $$\hat{w_0} = \bar{y} - w_1 \bar{x}$$ and $$\hat{w_1} = \frac{\bar{yx} - \bar{y} \bar{x}}{\bar{x^2} - \bar{x}^2}$$ in $$f(x) = w_0 + w_{1}x$$ we can combine variables into vectors and matrixes. This eases the work when we are calculating regression with more than a couple of variables. So again, lets delve. First off lets rewrite our individual variables into vectors $$\textbf{w} = \begin{bmatrix} w_0 \\ w_1 \end{bmatrix}$$ and $$\textbf{x}_n = \begin{bmatrix} 1 \\ x_n \end{bmatrix}$$ where the first element of the vector x is so to avoid cancelling out the first element of w when multiplying. Thus our model can be expressed as $$f(x) = w_0 + w_{1}x = \textbf{w}^\top \textbf{x}_n$$ given normal vector multiplication. Following this idea we can describe the squarred error as: $$sqrErr = (y_n - \textbf{w}^\top \textbf{x}_n)^2$$ and the mean of sqrErr as $$meanErr = \frac{1}{N}(\textbf{y} - \textbf{X} \textbf{w})^\top (\textbf{y} - \textbf{X} \textbf{w})$$ where $$\textbf{X} = \begin{bmatrix}1 & x_1\\1 & x_2\\. & . \\. & . \\1 & x_N\end{bmatrix}$$ and $$\textbf{y} = \begin{bmatrix} y_1 \\ y_2 \\ . \\ . \\ y_N \end{bmatrix}$$ and where any given matrix and/or vector operation is given as that of linear algebra. What is remarkable is that given the vector $$\textbf{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$$ we can calculate $\textbf{x}^\top \textbf{x}$ as the sum $$x_{1}^2 + x_{2}^2$$ which fits the squarring of the squarred error. By differentiating the vectorized exspression we get $$\frac{\partial meanErr}{\partial \textbf{w}} = \frac{2}{N} \textbf{X}^\top \textbf{X} \textbf{w} - \frac{2}{N} \textbf{X}^\top \textbf{t}$$ (that is partial differentiate the whole vector w) and equating 0 and rewriting we get $$\textbf{X}^\top \textbf{X} \textbf{w} = \textbf{X}^\top \textbf{t}$$ and lastly multiplying both sides by $(\textbf{X}^\top \textbf{X})^{-1}$ we get $$\textbf{w} = (\textbf{X}^\top \textbf{X})^{-1} \textbf{X}^\top \textbf{t}$$ the key expression to do linear regression in matrix form. Matrix multiplication can be quite exhaustive for us humans. Fortunately python has numpy. By adding import numpy as np in the top of the python script matrix algebra suddently becomes as easy as anything. So lets redo the regression from the last article. We are given the observations, and we get: import numpy as np #aux-functions def initA(f,l): retval = [] for i in range(0,l): retval.append(f(i)) return retval; #obtain observations x = [1.2,2.0,3.3,4.0,4.9] y = [2.5,3.5,4.0,4.5,5.0] X = np.array(initA(lambda i : [1,x[i]],len(x))) #calculate w using formula w = np.dot(X.transpose(),X) w = np.linalg.inv(w) w = np.dot(w,X.transpose()) w = np.dot(w,y) print w the cool thing is that this method scales. Thus we can add as many different w-parameters as we want.	984	2,943	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.15625	4	CC-MAIN-2019-51	latest	en	0.647565
https://www.coursehero.com/file/6664383/hw3/	1,490,640,563,000,000,000	text/html	crawl-data/CC-MAIN-2017-13/segments/1490218189495.77/warc/CC-MAIN-20170322212949-00132-ip-10-233-31-227.ec2.internal.warc.gz	868,581,518	74,734	# hw3 - ECE 594D Robot Locomotion Homework 3 Winter 2010 (due... This preview shows pages 1–3. Sign up to view the full content. ECE 594D Robot Locomotion Winter 2010 Homework 3 (due 5pm 2/5, in HFH 5115) 3.1 Non-collocated Partial Feedback Linearization (PFL) control for the acrobot. In class, we looked at MATLAB simulation results for collocated PFL control of the acrobot (Figure 1), as outlined in Spong [3]. Download two m-ﬁles from the course homework website: ac- robot_collocated_linearization.m , which solves the equations of motion (EOMs) for the system with collocated PFL control , and acrobot_animate.m , which will allow you to ani- mate the motion. You can then run a simulation using the following MATLAB commands: X0 = [-pi/2+.1;0;0;0]; % set an initial condition [t,y] = ode45(@acrobot_collocated_linearization,[0 20],X0); % to simulate gure(1) acrobot_animate(t,y) % to animate a) Modify acrobot_collocated_linearization.m to implement non-collocated PFL control, as outlined in [3]. (It is probably best to begin by copying this m-ﬁle to a new ﬁle called ac- robot_noncollocated_linearization.m , so you have the old code to look at if you need to debug anything as you edit. In addition to [3], you may wish to reference the PFL class notes, handed out in class and also available for download from the class handouts website.) (i) Include a print-out of your code in your homework. (ii) Include a print-out of a plot of the states over time, e.g., from: plot(t,y) Figure 1: The acrobot (image taken from [2]; torque input τ at elbow not shown). (Last revised January 30, 2010) 1 Homework 3 This preview has intentionally blurred sections. Sign up to view the full version. View Full Document ECE 594D Robot Locomotion Winter 2010 3.2 Underpowered actuators. The torque required to achieve PFL control was not an issue ad- dressed in [3] nor in class so far. Separate from the issue of being “underactuated” (where we cannot independently control every degree of freedom), the system dynamics may be notice- ably “underpowered”. Motors, for example, generally provide much lower torque and higher velocity than desired (which is why they are often geared down). However, gearing down a motor changes the actuator dynamics, making it challenging (if not impossible) to provide a pure “torque” output. So, we wish to use either a “direct drive” motor or very low transmission ratio (e.g., a belt drive increasing torque by a factor of 2-3 or so). All of which is to say: it is This is the end of the preview. Sign up to access the rest of the document. ## This note was uploaded on 12/29/2011 for the course ECE 594d taught by Professor Teel,a during the Fall '08 term at UCSB. ### Page1 / 4 hw3 - ECE 594D Robot Locomotion Homework 3 Winter 2010 (due... This preview shows document pages 1 - 3. Sign up to view the full document. View Full Document Ask a homework question - tutors are online	767	2,924	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.75	3	CC-MAIN-2017-13	longest	en	0.900446
https://au.mathworks.com/matlabcentral/cody/problems/750-accumulate-cells/solutions/746720	1,582,305,462,000,000,000	text/html	crawl-data/CC-MAIN-2020-10/segments/1581875145533.1/warc/CC-MAIN-20200221142006-20200221172006-00511.warc.gz	279,354,941	15,593	Cody Problem 750. Accumulate Cells Solution 746720 Submitted on 26 Sep 2015 by Mehmet OZC This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. Test Suite Test Status Code Input and Output 1 Pass %% assert(isequal(accumcell(@plus,{1,2,3,4},0),10)) assert(isequal(accumcell(@times,{1,2,3,4},1),24)) assert(isequal(accumcell(@times,{1,2,3,4},0),0)) M = rand(3,4,5); C = num2cell(M,1:2); assert(isequal(accumcell(@plus,C,0),sum(M,3))) assert(isequal(accumcell(@times,C,1),prod(M,3)))	192	541	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.625	3	CC-MAIN-2020-10	latest	en	0.674361
https://www.geeksforgeeks.org/javascript-program-to-illustrate-different-set-operations/?ref=ml_lbp	1,716,404,353,000,000,000	text/html	crawl-data/CC-MAIN-2024-22/segments/1715971058560.36/warc/CC-MAIN-20240522163251-20240522193251-00307.warc.gz	689,906,471	45,290	# JavaScript Program to Illustrate Different Set Operations Last Updated : 18 Sep, 2023 This article illustrates the various operations that can be applied in a set. There are various operations that can be applied on a set that are listed below: • Union of sets • Intersection of sets • Set difference • Set Subset Operation ## Union of sets A union set is the combination of two elements. In mathematical terms, the union of two sets is shown by A âˆª B. It means all the elements in set A and set B should occur in a single array. In JavaScript, a union set means adding one set element to the other set. Example: ## Javascript `function` `showUnion(sA, sB) { ` ` ``const union = ``new` `Set(sA); ` ` ``for` `(const num of sB) { ` ` ``union.add(num); ` ` ``} ` ` ``return` `union; ` `} ` `const s1 = ``new` `Set([``'1'``, ``'6'``, ``'8'``]); ` `const s2 = ``new` `Set([``'2'``, ``'3'``, ``'4'``]); ` `console.log(showUnion(s1, s2));` Output ```Set(6) { '1', '6', '8', '2', '3', '4' } ``` ## Intersection of sets An intersection of two sets means the element that occurs in both sets. In mathematical terms, the intersection of two sets is shown by A âˆ© B. It means all the elements which is common in set A and set B should occur in a single array. Example: ## Javascript `function` `getIntersection(set1, set2) { ` ` ``const ans = ``new` `Set(); ` ` ``for` `(let i of set2) { ` ` ``if` `(set1.has(i)) { ` ` ``ans.add(i); ` ` ``} ` ` ``} ` ` ``return` `ans; ` `} ` `const set1 = ``new` `Set([1, 2, 3, 8, 11]); ` `const set2 = ``new` `Set([1, 2, 5, 8]); ` ` ` `const result = getIntersection(set1, set2); ` `console.log(result);` Output ```Set(3) { 1, 2, 8 } ``` ## Set difference Set difference means that the array we subtract should contain all the unique element which is not present in the second array. Example: ## Javascript `let A = [7, 2, 6, 4, 5]; ` `let B = [1, 6, 4, 9]; ` `const set1 = ``new` `Set(A); ` `const set2 = ``new` `Set(B); ` ` ` `const difference = ``new` `Set(); ` `set1.forEach(element => { ` ` ``if` `(!set2.has(element)) { ` ` ``difference.add(element); ` ` ``} ` `}); ` `console.log([...difference]);` Output ```[ 7, 2, 5 ] ``` ## Set Subset Operation The set subset operation returns true if all the elements of setB are in setA. Example: ## Javascript `function` `subSet(val1, val2) { ` ` ``// Get an iterator for val2 ` ` ``const iterator = val2.values(); ` ` ` ` ``let nextVal = iterator.next(); ` ` ` ` ``while` `(!nextVal.done) { ` ` ``if` `(!val1.has(nextVal.value)) { ` ` ``return` `false``; ` ` ``} ` ` ``nextVal = iterator.next(); ` ` ``} ` ` ` ` ``return` `true``; ` `} ` ` ` `// Two sets ` `const val1 = ``new` `Set([``'HTML'``, ``'CSS'``, ``'Javascript'``]); ` `const val2 = ``new` `Set([``'HTML'``, ``'CSS'``]); ` ` ` `const result = subSet(val1, val2); ` ` ` `console.log(result);` Output ```true ```	993	3,009	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.53125	4	CC-MAIN-2024-22	latest	en	0.683497
https://www.teacherspayteachers.com/Product/Solving-a-Quadratic-by-Completing-the-Square-Intro-6-Assignments-for-SMART-2179646	1,500,717,454,000,000,000	text/html	crawl-data/CC-MAIN-2017-30/segments/1500549423927.54/warc/CC-MAIN-20170722082709-20170722102709-00122.warc.gz	848,132,155	21,871	# Main Categories Total: \$0.00 Whoops! Something went wrong. # Solving a Quadratic by Completing the Square, Intro + 6 Assignments for SMART Product Description Included in this zip folder are 7 SMART Notebook files. 1 is a introductory lesson and 6 are assignments. A brief description of each: The Lesson is a 65 slide presentation that introduces the completing the square method of solving a quadratic equation. Many short answer and complete problems are embedded in the file as formative assessment. Assignment E is a 24 question short answer and multiple choice assignment. The emphasis is recognizing what is needed to "complete the square" in an expression and an equation. It is on 1 page for easy printing and coded for SMART Response. Assignment F is a 24 question and short answer assignment. It is a continuation of assignment E. Equations are emphasized over expressions. The student must recognize reasons in a proof table as well as equivalent equations. It is on 1 page for easy printing and coded for SMART Response. Assignment #5 is 8 problems where the student must complete the square to solve quadratic equations. it is 2 pages, 4 problems per page. Assignment #6 is like #5 Degree 2 Proof Assignment #9 is a 12 question assignment. The student must choose from the following as a missing reason in the proof: 1. Subtraction property of equality 3. Division property of equality 4. Symmetric property 5. Simplify by like terms 6. Distributive property 7. Extracting roots 8. Simplify by factoring 9. Definition of +- 10. Zero product property 11. Completing the square It is on 1 page for easy printing and coded for SMART Response. This assignment is also on socrative.com. The socrative share number is included in the file. Degree proof Assignment #10 is 2 proofs. The student must fill in the reasons column. The statements column is already filled in. It is on 1 page for easy printing and coded for SMART Response. Thank you for looking Total Pages 65+ Included Teaching Duration 3 days Report this Resource • Product Q & A \$1.75 \$1.75	469	2,079	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.890625	3	CC-MAIN-2017-30	latest	en	0.936894
https://tslearn.readthedocs.io/en/latest/user_guide/shapelets.html	1,713,617,368,000,000,000	text/html	crawl-data/CC-MAIN-2024-18/segments/1712296817650.14/warc/CC-MAIN-20240420122043-20240420152043-00221.warc.gz	533,592,029	6,099	# Shapelets¶ Shapelets are defined in [1] as “subsequences that are in some sense maximally representative of a class”. Informally, if we assume a binary classification setting, a shapelet is discriminant if it is present in most series of one class and absent from series of the other class. To assess the level of presence, one uses shapelet matches: $d(\mathbf{x}, \mathbf{s}) = \min_t \\| \mathbf{x}_{t\rightarrow t+L} - \mathbf{s} \\|_2$ where $$L$$ is the length (number of timestamps) of shapelet $$\mathbf{s}$$ and $$\mathbf{x}_{t\rightarrow t+L}$$ is the subsequence extracted from time series $$\mathbf{x}$$ that starts at time index $$t$$ and stops at $$t+L$$. If the above-defined distance is small enough, then shapelet $$\textbf{s}$$ is supposed to be present in time series $$\mathbf{x}$$. In a classification setting, the goal is then to find the most discriminant shapelets given some labeled time series data. Shapelets can be mined from the training set [1] or learned using gradient-descent. ## Learning Time-series Shapelets¶ tslearn provides an implementation of “Learning Time-series Shapelets”, introduced in [2], that is an instance of the latter category. In Learning Shapelets, shapelets are learned such that time series represented in their shapelet-transform space (i.e. their distances to each of the shapelets) are linearly separable. A shapelet-transform representation of a time series $$\mathbf{x}$$ given a set of shapelets $$\{\mathbf{s}_i\}_{i \leq k}$$ is the feature vector: $$[d(\mathbf{x}, \mathbf{s}_1), \cdots, d(\mathbf{x}, \mathbf{s}_k)]$$. This is illustrated below with a two-dimensional example. In tslearn, in order to learn shapelets and transform timeseries to their corresponding shapelet-transform space, the following code can be used: from tslearn.shapelets import LearningShapelets model = LearningShapelets(n_shapelets_per_size={3: 2}) model.fit(X_train, y_train) train_distances = model.transform(X_train) test_distances = model.transform(X_test) shapelets = model.shapelets_as_time_series_ A tslearn.shapelets.LearningShapelets model has several hyper-parameters, such as the maximum number of iterations and the batch size. One important hyper-parameters is the n_shapelets_per_size which is a dictionary where the keys correspond to the desired lengths of the shapelets and the values to the desired number of shapelets per length. When set to None, this dictionary will be determined by a heuristic. After creating the model, we can fit the optimal shapelets using our training data. After a fitting phase, the distances can be calculated using the transform function. Moreover, you can easily access the learned shapelets by using the shapelets_as_time_series_ attribute. It is important to note that due to the fact that a technique based on gradient-descent is used to learn the shapelets, our model can be prone to numerical issues (e.g. exploding and vanishing gradients). For that reason, it is important to normalize your data. This can be done before passing the data to the fit and transform methods, by using our tslearn.preprocessing module but this can be done internally by the algorithm itself by setting the scale parameter. ## Examples Involving Shapelet-based Estimators¶ Learning Shapelets Learning Shapelets Aligning discovered shapelets with timeseries Aligning discovered shapelets with timeseries Learning Shapelets: decision boundaries in 2D distance space Learning Shapelets: decision boundaries in 2D distance space	809	3,520	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.9375	3	CC-MAIN-2024-18	latest	en	0.849622
https://study.com/academy/lesson/principal-quantum-number-definition-example-quiz.html	1,568,738,221,000,000,000	text/html	crawl-data/CC-MAIN-2019-39/segments/1568514573098.0/warc/CC-MAIN-20190917161045-20190917183045-00265.warc.gz	630,547,148	45,019	# Principal Quantum Number: Definition & Example Coming up next: Strong Force: Definition, Equation & Examples ### You're on a roll. Keep up the good work! Replay Your next lesson will play in 10 seconds • 0:25 What is the Principal… • 1:11 Visualization • 3:00 Subshells and Electrons • 3:50 Lesson Summary Save Save Want to watch this again later? Timeline Autoplay Autoplay Speed #### Recommended Lessons and Courses for You Lesson Transcript Instructor: Nissa Garcia Nissa has a masters degree in chemistry and has taught high school science and college level chemistry. Quantum numbers were developed to characterize electrons - its electron configuration, movement and position in an atom. Each electron has a unique set of quantum numbers. Of the four quantum numbers, our focus in this lesson is the principal quantum number. ## What is the Principal Quantum Number? Let us imagine an apartment building with multiple floors - the more floors there are, the more people can reside in the building, and each person's address is different, based on the room and floor they occupy. Just like each person or family occupies different floors in the apartment building, for electrons, they occupy different principal electron shells. How do we know which principal electron shell these electrons occupy? The principal quantum number tells us which principal electron shells the electrons occupy. For example, the electron configuration of helium (He), is 1s^2 - the principal quantum number is the number '1'. This means the two electrons of helium occupy the first principal electron shell. Just like the apartment building, we have a first floor, second floor, third floor and so on. To assign the principal quantum numbers, we use the symbol n, where you can assign values to n, and these values are: If you occupy a higher floor, and if there is no elevator, you need to spend more energy going to where you need to be. In the same way, as n increases, this means that the energy of the electron also increases. ## Visualization When there are more floors in an apartment building that means more people can occupy the building and spread out more on each floor. If there are not as many floors, the people occupying the building are more concentrated in a smaller space. The same can be said about the principal quantum number and electron density. The principal quantum number tells us not only the energy of an electron, but also gives us an idea about the electron density around the nucleus of an atom. In the illustration below, it shows on the left that when the principal quantum number is smaller the electron density is more concentrated closer to the atom, which means the electron cloud is smaller. On the right, the electron density is more spread out when the principal quantum number is larger, and the electron cloud is larger. Based on the previous illustration, we can conclude that higher values of n have a larger atomic radius, and a greater distance between the nucleus and the electron. The attraction between electrons and the nucleus is not as strong for an atom with a larger atomic radius. This means that the energy needed to remove an electron, the ionization energy, is smaller when the atomic radius is larger due to the lower attraction between the nucleus and the electron. To unlock this lesson you must be a Study.com Member. ### Register to view this lesson Are you a student or a teacher? #### See for yourself why 30 million people use Study.com ##### Become a Study.com member and start learning now. Back What teachers are saying about Study.com ### Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.	802	3,944	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.296875	3	CC-MAIN-2019-39	longest	en	0.903797
https://www.coursehero.com/file/26749/HW8/	1,521,923,042,000,000,000	text/html	crawl-data/CC-MAIN-2018-13/segments/1521257650993.91/warc/CC-MAIN-20180324190917-20180324210917-00240.warc.gz	805,965,259	92,512	{[ promptMessage ]} Bookmark it {[ promptMessage ]} HW8 - homework 08 GAUTHIER JOSEPH Due 1:00 am Question 1... This preview shows pages 1–3. Sign up to view the full content. homework 08 – GAUTHIER, JOSEPH – Due: Oct 26 2007, 1:00 am 1 Question 1, chap 11, sect 4. part 1 of 1 10 points An open cart on a level surface rolls without frictional loss through a downpour of rain. The rain falls vertically downward as shown below. As the cart rolls, an appreciable amount of rain water accumulates in the cart. v rain rain water cart The speed of the cart will 1. increase because of conservation of mo- mentum. 2. decrease because of conservation of me- chanic energy. 3. increase because of conservation of me- chanic energy. 4. remain the same because the raindrops are falling perpendicular to the direction of cart’s motion. 5. decrease because of conservation of mo- mentum. correct Explanation: This is an inelastic collision in the direction along which the cart is rolling. Only mo- mentum vectorp along that direction is conserved. Because the raindrops fall vertically, they do not carry momentum horizontally. Assume Δ m of rain water accumulates on the cart: p i = p f m v = ( m + Δ m ) v . Therefore v = m m + Δ m v v < v . The speed of the cart will decrease because of conservation of momentum. Question 2, chap 11, sect 1. part 1 of 2 10 points A 52 kg pole vaulter falls from rest from a height of 4.9 m onto a foam rubber pad. The pole vaulter comes to rest 0.27 s after landing on the pad. a) Calculate the athlete’s velocity just be- fore reaching the pad. Correct answer: 9 . 805 m / s (tolerance ± 1 %). Explanation: Let : m = 52 kg , Δ y = 4 . 9 m , t = 0 . 27 s , and a = 9 . 81 m / s 2 . Since v i = 0 m/s, v 2 f = 2 a Δ y v f = ± radicalbig 2 a Δ y = ± radicalBig 2 ( 9 . 81 m / s 2 ) ( 4 . 9 m) = 9 . 805 m / s , which is 9 . 805 m / s directed downward. Question 3, chap 11, sect 1. part 2 of 2 10 points b) Calculate the constant force exerted on the pole vaulter due to the collision. Correct answer: 1888 . 37 N (tolerance ± 1 %). Explanation: Since v f = 0 m/s, vector F Δ t = m Δ vectorv = mvectorv f mvectorv i = mvectorv i F = m v i Δ t = (52 kg) ( 9 . 805 m / s) 0 . 27 s = 1888 . 37 N This preview has intentionally blurred sections. Sign up to view the full version. View Full Document homework 08 – GAUTHIER, JOSEPH – Due: Oct 26 2007, 1:00 am 2 directed upward. Question 4, chap 11, sect 1. part 1 of 1 10 points A 1 kg steel ball strikes a wall with a speed of 4 . 05 m / s at an angle of 51 . 1 with the normal to the wall. It bounces off with the same speed and angle, as shown in the figure. x y 4 . 05 m / s 1 kg 4 . 05 m / s 1 kg 51 . 1 51 . 1 If the ball is in contact with the wall for 0 . 156 s, what is the magnitude of the average force exerted on the ball by the wall? Correct answer: 32 . 6058 N (tolerance ± 1 %). Explanation: Let : M = 1 kg , v = 4 . 05 m / s , and θ = 51 . 1 . The y component of the momentum is un- changed. The x component of the momentum is changed by Δ P x = 2 M v cos θ . Therefore, using impulse formula, F = Δ P Δ t = 2 M v cos θ Δ t = 2 (1 kg) (4 . 05 m / s) cos 51 . 1 0 . 156 s bardbl vector F bardbl = 32 . 6058 N . Note: The direction of the force is in negative x direction, as indicated by the minus sign. This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]} Page1 / 11 HW8 - homework 08 GAUTHIER JOSEPH Due 1:00 am Question 1... This preview shows document pages 1 - 3. Sign up to view the full document. View Full Document Ask a homework question - tutors are online	1,133	3,611	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.9375	4	CC-MAIN-2018-13	latest	en	0.802455
https://math.stackexchange.com/questions/tagged/constraints	1,708,767,506,000,000,000	text/html	crawl-data/CC-MAIN-2024-10/segments/1707947474526.76/warc/CC-MAIN-20240224080616-20240224110616-00300.warc.gz	390,588,834	50,928	# Questions tagged [constraints] In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. 979 questions Filter by Sorted by Tagged with 16 views • 6,087 41 views ### How do I determine the maximum subgraph that avoids certain edges? I have a graph where I want to select a subset of the nodes subject to a particular constraint: An edge between nodes A and B indicates that I cannot select BOTH A and B to belong to the subset. I ... • 113 1 vote 57 views 11 views ### Proof of solvable constrained optimization with a subset of a larger set of constraints Way out of my comfort zone here so apologies if I'm not providing enough or correct information. I work with an application of constrained optimization to assemble test forms (automated test assembly).... • 101 17 views ### Deriving correct integral constraint equation for calculus of variations problem I have the following calculus of variations problem: $$\mathcal{L}=-2X'(t)\ln{x'(t)}-2Y'(t)\ln{y'(t)}$$ where $x(t)$ and $y(t)$ are the functions I'm interested in, and $X(t)$ and $Y(t)$ are given as ... • 101 40 views ### How to add discrete function constraints to a calculus of variations problem Suppose that $L$ is the Lagrangian of a system and $f$ is a function of $x$. The objective is to find a function $f$ that optimises: $J[f] = \int{L(x, f, f')}dx$ How do you fix the value of $f(x)$ at ... • 1 63 views I'm trying to explain how to use Lagrangian multipliers, through an example. I start in this way: Understanding how Lagrangian multipliers work can be done through a simple example. Consider the ... • 45 1 vote 36 views 1 vote 42 views ### Can we assume for free the upper bound for a variable in the minimization problem $\min_{(x,t) \in \mathbb{R}^n\times \mathbb{R}} t$? Problem: Let us consider the following minimization problem \begin{align*} &\min_{(x,t) \in \mathbb{R}^n\times \mathbb{R}} t\\ \text{s.t }& \Vert x-q_i\Vert^2 \le r_i^2 + t,\ \forall i = \... • 1,218 1 vote 88 views • 14.9k 171 views • 135 33 views ### Optimization constraint I'm learning optimization and I came across equality constraints. Lets say we have an objective function J defined over $V$ with values in $\mathbb{R}$, where $V$ is the normed vector space in which ... 68 views ### Optimisation Problem Setup and KKT conditions I am trying to setup an optimization problem with equality and inequality constraints. I want to estimate a specific variable call $\chi$ subject to a minimisation problem -- guidance on the setup and ... 1 vote 84 views ### Point isolation through linear constraints I consider a set of $n$ points in $\mathbb R^d$: $X=${$x_i$}$_{i=1}^n$. I would like to know for each point $\tilde x\in X$ if there exists a dimension $j\in${$1, ..., d$} and $k$ linear constraints (... • 61 63 views ### Discrete point inside a polygon formed by set of vertices I am working on a problem where I have a set of 2D vertices and a test point. I want to check whether the test point lies inside the polygon formed by the set of given vertices. I am trying to model ... 67 views ### Same sign constraint in linear optimization problem I'm trying to find a way to force a group of variables to take the same sign. Either positive or negative. Clearly, the fact that an OR statement is required implies that the problem becomes non-... • 195 17 views • 920	893	3,402	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.328125	3	CC-MAIN-2024-10	latest	en	0.831168
https://brainmass.com/business/inventory/fifo-lifo-and-average-cost-methods-62809	1,550,532,885,000,000,000	text/html	crawl-data/CC-MAIN-2019-09/segments/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00214.warc.gz	514,755,107	18,595	Explore BrainMass Share # Fifo, Lifo and Average cost methods This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here! E4-16 In June, Naperville Company reports the following for the month of June. Units Unit Cost Total Cost June 1 Inventory 200 \$5 \$1,000 12 Purchases 300 6 1,800 23 Purchases 500 7 3,500 30 Inventory 150 8 1,200 1,150 7,500 Instructions (a) Compute the cost of the ending inventory and the cost of goods sold under (1) FIFO: and (2) LIFO. (b) Which costing method gives the higher ending inventory? Why? (c) Which method results in the higher cost of goods sold? Why? E4-17 Inventory data for Naperville Company are presented in E4-16. Instructions (a) Compute the cost of the ending inventory and the cost of goods sold using the average cost method. (b) Will the results in (a) be higher or lower than the results under (1) FIFO and (2) LIFO? (c) Why is the average unit cost not \$6?	265	967	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.578125	3	CC-MAIN-2019-09	longest	en	0.885753
https://forums.adobe.com/thread/963731	1,521,769,833,000,000,000	text/html	crawl-data/CC-MAIN-2018-13/segments/1521257648113.87/warc/CC-MAIN-20180323004957-20180323024957-00203.warc.gz	599,288,347	32,422	7 Replies Latest reply on Jun 23, 2014 5:36 PM by guyofgod # Deleting every nth frame (again) Hey all, I have a video where every single 5th frame is a duplicate. So I need frames 0,1,2,3 - 5,6,7,8 - 10,11,12,13 - etc... I've seen this post but I myself am not familiar with expressions enough to write it just by what the person is suggesting. I found a few suggestions such as: f = timeToFrames(); n = Math.floor(f/5); framesToTime(n+f); Also this from a random YouTube video I can't find: f = timeToFrames(); p = Math.floor(f/1); framesToTime(p1.5); Neither work. The frames start jumping erratically. 2 frames at a time, then 150 frames, etc etc. In general programming to iterate and skip every nth number I'd just do a modulos check and skip any 0 sum. Something like: f = timeToFrames(); n = f % 5; if (n == 0) { f++; } framesToTime(f); This also produces some really odd frame counts although it doesn't jump to the hundreds eratically. It just doesn't work. How would I skip every 5th frame? Thanks for tips! • ###### 1. Re: Deleting every nth frame (again) Neither work. The frames start jumping erratically. 2 frames at a time, then 150 frames, etc etc. That would only be true, if the framerate is a fractional one like 23.96 or whtever. Of course this messes with the logic of discrete frames as integer values, if you don't have any precautions built into your code. Just the same happens when multiplying back with fractional values like in the second example or adding back the normal time as per the first example. Time in AE is a "real" time, not an arbitrary multipication of frames with a fixed factor. What you are seeing is perfectly normal. And your own code doesn't work, because you are not running a loop - AE does not store persistent variables, it can only accumulate values over time. Therefore your code only increments by one frame every 5 frames and returns a much smaller value. Additionally, of course you are missing the else statement, so your code doesn't know what to do when the condition is not met and the whole expression breaks. It's simply sloppy syntax (no offense). Mylenium • ###### 2. Re: Deleting every nth frame (again) Here's a 5 second example of PHP iterating over the same logic perfectly. Regardless, my code didn't have an 'else' because it never needed one. What my code attempt did, that do I do NOT claim should work, just an attempt, is ONLY add +1 to the value of the current frame IF the modulos returned 0 (it was a nth frame to remove). The next line of code is run regardless if I'm skipping or not, so I don't need an else. Thanks for reminding me to include details. The footage is 1920x1080p 30fps ap1.0 video from a stock video site. They repeat every 5th frame for some reason. I'm simply trying to remove it. Now that we know we're working with 30 and not 23.976 or 29.97, does this make a difference in the script? edit: Regarding the persistence, this is just me making an assumption with the already previously addmittedly lack of expression knowledge. I would assume that this script is run every single frame. I would then assume f = timeToFrames(); is my iterating value. That's what I'm depending on. Here's what I don't understand. Is this able to actually skip the playhead +1 frames? That is my intention on export. To skip the playhead over that frame. re-edit: In the expression manual: Though the expression language is based on a scripting language, a subtle but important difference exists between a script and an expression: Whereas a script tells an application to do something, an expression says that a property is something. I think I'm beginning to understand a bit about what you're saying. I can't skip the playhead because I can't do that. I have to somehow come up with a way to calculate what frame I should be showing regardles of the current time. The current time will always progress from start to finish but my calculation needs to do the work of re-adjusting what the actual time should be, controlling what is showed. If I have no persistence, yes, I'm a bit lost on how I'm supposed to figure out what frame I showed last. I'm going to need to use the current time to figure out how many times I've cut a frame out by then and add that to where I am, no? And that's the logic that looks like what the very first bit of code I posted seems to do. • ###### 3. Re: Deleting every nth frame (again) You could jump through all those hoops in AE, but if it's at all possible, I heartily recommend the following: Apply a vigorous Dope Slap to the back of the head of the genius who thought creating 3:2 pulldown was as simple as putting 23.976 footage into a 27.97 timeline. Insist that Einstein give you 23.976 files. If Einstein needs 29.97 video for ultimate delivery, you can do it easily and CORRECTLY in AE from a 23.976 comp. I hope for your sake and sanity that it's possible. • ###### 4. Re: Deleting every nth frame (again) Here's a 5 second example of PHP iterating over the same logic perfectly. Sure, but PHP automatically stores every valid last value of a function and fetches it in the next cycle. So unless it is an invalid data type or an invalid result (division by zero etc.), it will always return true and evaluate. AE dimply doesn't have any such thing. Therefore f++ does nothing but increment any value assigned to that variable until either the internal limit is reached and the engine runs out of iterations or the counter overflows for other reasons. Without any further logic this is useless. And that's the logic that looks like what the very first bit of code I posted seems to do. No, it doesn't. It merely returns the current time quantized to the next possible value fullfilling the equation, so at 5 frames it will skip the 5th frame and at 10frames the 10th only, but not the 5th. If you will, it doesn't tighten the gap as in fact at frame 10 you actually want it to skip frame 9 after frame 5 has been excised. Again, your only chance is to count all frames, which could be doen with an if()else() statement inside a loop (pseudo code): for(f < x,f=0,f++) { if (n%5 == 0) {f-1} else {f} } f is your frame, x the comp duration in frames. The rest should fall in place, if you have programming experience. Mylenium • ###### 5. Re: Deleting every nth frame (again) We paid \$500 for a short clip of this HD car driving by. Amazingly, no, they don't have the correct fps source (we already asked). I'm taking the cop-out.. Exporting a sequence of images, rm 5].png, rm 0].png, reimport, done.. Thanks anyhow edit: Mylenium~ Mylenium wrote: for(f < x,f=0,f++) { if (n%5 == 0) {f-1} else {f} } In the spirit of understand anyhow I'd like to determine what you mean. I've never seen a for(condition, evaluation, iterator) constructed like that so I'll reconstruct it to my knowledge as AE is said to use ECMAScript 1.2 so I should be familiar.. Nope... Nope I tried but I cannot see the logic in the script at all. There are magical things going on here. I see no assignment, just an iterator that will actually cause an infinite loop as you're iterating f at the same time you seem to want to subtract 1 from it every time modulos is 0. e.g. as soon as f = 5, modulos returns 0 thus f is 4, script runs again and iterates to 5, rinse repeat infinitely. I know that the last 'value' is automagically applied to the current property so that's how I assume f is being applied to the time. I just don't see why you want to subtract from f and not add to it. • ###### 6. Re: Deleting every nth frame (again) try this as your Time remapping expression: framesToTime(Math.floor(timeToFrames()1.25)+0); IMPORTANT: you must replace the "+0" at the end of the expression with an integer between 0 and 4 WHO SUITS YOUR NEEDS. "+1" worked for me, but your video surce determines this number, so you 'll have to try all 5 integers. Not an elegant solution at all, but it worked for me. • ###### 7. Re: Deleting every nth frame (again) wiclies wrote: try this as your Time remapping expression: framesToTime(Math.floor(timeToFrames()*1.25)+0); IMPORTANT: you must replace the "+0" at the end of the expression with an integer between 0 and 4 WHO SUITS YOUR NEEDS. "+1" worked for me, but your video surce determines this number, so you 'll have to try all 5 integers. Not an elegant solution at all, but it worked for me. I know this is old, but logged in to thank you willies! Your script did exactly what I needed. In my case, for search engine benefits, the render farm we used for rendering out 3D mograph from C4D threw a garbage duplicate of frame 1 in our render every 5th frame (sequence images). I didn't want to delete every 5th frame, even though I had it in a sequence, because then I would get errors from After Effects thinking I was missing those frames. I was ripping my hair out - thanks for this again - an admin or mod should definitely set this as the "correct answer".	2,218	9,000	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.90625	3	CC-MAIN-2018-13	latest	en	0.904048
https://dsp.stackexchange.com/questions/37731/differential-equations-and-lti-systems	1,716,217,971,000,000,000	text/html	crawl-data/CC-MAIN-2024-22/segments/1715971058291.13/warc/CC-MAIN-20240520142329-20240520172329-00004.warc.gz	200,946,363	36,603	# Differential equations and LTI systems [duplicate] I've seen in many textbooks on Signals and Systems that an LTI (Linear Time-Invatiant) system can be described as a constant-coefficient linear differential equation, such as $$\sum_{k=1}^N a_k \frac{d^k}{dt^k}y(t) = \sum_{l=1}^M b_l \frac{d^l}{dt^l}x(t)$$ Later on, it is stated that the response of any LTI system can be decomposed into two terms: a zero-input response, and a zero-state response: $y(t) = y_{zi}(t) + y_{zs}(t)$ (among other decompositions) which are independent. Zero-input (ZI) response $y_{zi}(t)$ is the output of the system when the input is zero, that is, the output to the initial conditions of the system. This means that ZI-response is the same as long as the initial conditions are the same and no matter what the input is. Zero-state (ZS) response $y_{zs}(t)$ is the output of the system when the input in nonzero and the initial condition are zero. Thus, ZS-response depends only on the input (via convolution integral etc.) Now, the question: if the system is LTI, it means it satisfies the linearity and the time-invariance property. That is: Linearity: for input-output pairs $x_1(t) \to y_1(t)$, $x_2(t) \to y_2(t)$, we must have $$ax_1(t) + bx_2(t) \to ay_1(t) + by_2(t)$$ However, this is not true for nonzero ZI-response $y_{zi}(t)$. If $y_{zi}(t) = e^{-t}u(t)$, for example, then this response is not scaled by $a$ or $b$ when an input is applied, because it does not depend on the input! Thus, any system with nonzero ZI-response cannot be linear! Time-invariance: if the input-output pairs are $x(t) \to y(t)$, and $x(t-t_0) \to y(t-t_0)$, then the system is time-invariant. However, since again the ZI-response is the same as long as the initial conditions do not change, there is no shifting of the ZI-response when the input is shifted! Thus, a system cannot be time-invariant! This makes me assume that a system described by a constant-coefficient differential equation is LTI only when the zi-response is zero, that is, when the initial conditions are zero! The last one makes the system causal as well. Where do I make the mistake??? It seems to me that linearity and time-invariance (and causality) is only valid when initial conditions are zero but this is rarely noted in textbooks... • You're right: non-zero initial conditions make the system non-linear and time-varying, simply because part of the output does not depend on the input signal. For the system to be LTI you need a linear constant coefficients differential equation AND require the initial conditions to be zero. Feb 19, 2017 at 18:10 Your "mistake" if it can be called that is to assume that your input signal was zero for $t\le0$.	729	2,715	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.84375	4	CC-MAIN-2024-22	latest	en	0.886138
https://www.coursehero.com/file/6721467/L15/	1,516,788,662,000,000,000	text/html	crawl-data/CC-MAIN-2018-05/segments/1516084893629.85/warc/CC-MAIN-20180124090112-20180124110112-00204.warc.gz	903,367,285	24,453	# L15 - 6.889 — Lecture 15 Traveling Salesman(TSP Christian... This preview shows pages 1–3. Sign up to view the full content. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: 6.889 — Lecture 15: Traveling Salesman (TSP) Christian Sommer [email protected] (figures by Philip Klein) November 2, 2011 Traveling Salesman Problem (TSP) given G = ( V,E ) find a tour visiting each 1 node v ∈ V . NP –hard optimization problem, hard even for planar graphs Polynomial-time approximation for general graphs: Christofides’ algorithm achieves 3 / 2 approximation Assumption (all of Lecture 15) undirected planar G , ‘ : E → R + 2 –approximation simple algorithm, bound approximation ratio in terms of minimum spanning tree • compute minimum spanning tree T . let ‘ ( T ) := ∑ e ∈ T ‘ ( e ) • duplicate all edges Eulerian graph • find Eulerian cycle, length at most 2 ‘ ( T ) • (if G is the complete graph K n , Eulerian cycle can be converted into Hamiltonian cycle by skipping already visited nodes) any tour needs to visit all nodes, total length at least ‘ ( T ) , hence 2 –approximation Recall: Linear-Time Approximation Schemes for Planar Graphs (L. 8) Example min VERTEXCOVER Algorithm given G and approximation parameter ∈ (0 , 1) , let k = 1 / 1. BFS in G 2. G ij ← graph induced by k + 1 BFS levels jk + i to ( j + 1) k + i ( shift i , 6 i < k , and slice j ) 3. S ij ← min VERTEXCOVER of G ij (dynamic programming on graph with tree-width O ( k ) ) 4. S i ← S j S ij 5. RETURN best S i (best shift i , 6 i < k , smallest \| S i \| ) Running Time dynamic program runs in time 2 O ( k ) \| V ( G ij ) \| , overall 2 O ( k ) n Correctness and Approximation Ratio two properties used 3. part of OPT in G ij is a feasible solution for G ij . consequence: \| OPT ∩ V ( G ij ) \| > \| S ij \| optimum solution OPT induces solution on subgraph G ij for at least one shift i overlap \| OPT i \| is small 2 ( 6 \| OPT \| /k = \| OPT \| ) 4. solutions in G ij together form a feasible solution for G , S j S ij is a solution for G (for any i ) 1 visiting only a subset U ⊆ V to be discussed in Lectures 16 and 17 2 define OPT i = OPT ∩ { all nodes on BFS level i mod k } 1 Figure 1: Consecutive slices (subgraphs) overlap by one single level (boundary).... View Full Document {[ snackBarMessage ]} ### Page1 / 5 L15 - 6.889 — Lecture 15 Traveling Salesman(TSP Christian... This preview shows document pages 1 - 3. Sign up to view the full document. View Full Document Ask a homework question - tutors are online	730	2,650	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3	3	CC-MAIN-2018-05	latest	en	0.791219
https://community.jmp.com/t5/Discussions/Nonlinear-Script/m-p/33509/highlight/true	1,582,777,488,000,000,000	text/html	crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00212.warc.gz	314,701,367	70,462	Choose Language Hide Translation Bar Highlighted Community Trekker Nonlinear Script Performing NLR via the Platform on a data table generates the expected results (see Croucher http://... [didnt see how to attach table but I can send as needed.] I have used similar scripts [change data and equation] with no issue. Any thoughts? The equation section of the script is: Parameter( {b0 = 1, b1 = 0.2}, b0 * Cosine( b1 * :X ) + b1 * Sine( b0 * :X )) ``````Clear Log(); Clear Globals(); xv = [ -2, -1.64, -1.33, -.07, 0, 0.45, 1.2, 1.64, 2.32, 2.9]; yv = [.699369,.700462,.695354,1.030905,1.97389,2.411430,1.910910,0.919576,-0.770975,-1.42001]; dt = New Table( "Croucher Data", New Column( "x", SetValues( xv ) ), New Column( "y", SetValues( yv ) ), ); //close New Table dt << Nonlinear( Y( :y ), X( :x ), Model( Parameter( {b0 = 1., b1 = 0.2}, b0 * Cosine( b1 * :x ) + b1 * Sine( b0 * :x ) ) ), QuasiNewton SR1,Finish,plot(1), Confidence Limits );//close NonLinear`````` 1 ACCEPTED SOLUTION Accepted Solutions Super User Re: Nonlinear Script Your script works well. There a slight difference in the input data if compared with the linked example (cf. xv[4] & yv[9]). It is also possible to do this nonlinear fit without using the platform: ``````Model = Expr( b0 * Cosine(b1 * xv) + b1 * Sine(b0 * xv) ); xv = [-2, -1.64, -1.33, -0.7, 0, 0.45, 1.2, 1.64, 2.32, 2.9]; yv = [0.699369, 0.700462, 0.695354, 1.03905, 1.97389, 2.41143, 1.91091, 0.919576, -0.730975, -1.42001]; b0 = 1; b1 = 0.2; SSE = Minimize(Sum((Model - yv) ^ 2), {b0, b1}); Eval List({b0, b1, SSE});`````` 4 REPLIES 4 Super User Re: Nonlinear Script Your script works well. There a slight difference in the input data if compared with the linked example (cf. xv[4] & yv[9]). It is also possible to do this nonlinear fit without using the platform: ``````Model = Expr( b0 * Cosine(b1 * xv) + b1 * Sine(b0 * xv) ); xv = [-2, -1.64, -1.33, -0.7, 0, 0.45, 1.2, 1.64, 2.32, 2.9]; yv = [0.699369, 0.700462, 0.695354, 1.03905, 1.97389, 2.41143, 1.91091, 0.919576, -0.730975, -1.42001]; b0 = 1; b1 = 0.2; SSE = Minimize(Sum((Model - yv) ^ 2), {b0, b1}); Eval List({b0, b1, SSE});`````` Highlighted Community Trekker Re: Nonlinear Script Thanks much for the script. It works fine for me. I've not used that function much but it obviously is ideal for many models. Highlighted Staff Re: Nonlinear Script Looks like one of your x values should be -0.7, not -0.07, Highlighted Community Trekker Re: Nonlinear Script Thanks, typing issue! I fixed them for my file.	980	2,574	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.84375	3	CC-MAIN-2020-10	latest	en	0.582746
https://math.stackexchange.com/questions/4605302/largest-known-positive-integer-n-such-that-binomnk-has-k-prime-factors-c	1,701,854,096,000,000,000	text/html	crawl-data/CC-MAIN-2023-50/segments/1700679100583.31/warc/CC-MAIN-20231206063543-20231206093543-00219.warc.gz	427,172,112	37,978	# Largest known positive integer n such that $\binom{n}{k}$ has k prime factors (counted with multiplicity) for each $k\le32$ The numbers n such that $$\binom{n}{1}$$ have $$1$$ prime factor (counted with multiplicity) are simply the primes. Therefore, for $$k=1$$ this gives the largest known prime, $$n=2^{82589933}-1$$. For $$k=2$$, the numbers n such that $$\binom{n}{2}$$ have $$2$$ prime factors (counted with multiplicity) are $$2p$$ such that $$p$$ and $$2p-1$$ are primes and the safe primes, primes $$p$$ such that $$(p-1)/2$$ is also prime. Since $$2618163402417\cdot2^{1290001}-1$$, the largest known prime $$p$$ such that $$(p-1)/2$$ is also prime, is greater than $$7775705415\cdot2^{175116}+2=2p$$, where $$p$$ is the largest known prime such that $$2p-1$$ is also prime, $$2618163402417\cdot2^{1290001}-1$$ is the largest known such $$n$$ for $$k=2$$. This will change from time to time. What about $$3\le k \le 32$$? For $$3\le k\le 14$$, I found in OEIS that $$\binom{2918756139031688155200+k}{k}$$, where $$n=2918756139031688155200+k$$, $$k\le 14$$, and $$\binom{7272877497848202239}{k}$$, where $$n=7272877497848202239$$, $$k\le 14$$, have k prime factors (counted with multiplicity). These are just the lower bounds for such $$n$$'s. Definitely these aren't the largest known $$n$$'s such that $$\binom{n}{k}$$ has $$k$$ prime factors (counted with multiplicity) for $$3\le k \le6$$. Main problem: Find at least one positive integer $$n\gt10^4$$ such that $$\binom{n}{k}$$ has exactly $$k$$ prime factors (counting multiplicity) for each $$15\le k\le 32$$. • Not sure why this is down- and closevoted. It is surely interesting (+1). However, I am not sure whether the actual records can be found with the sources as the cases you mentioned. Are you content with huge examples to begin with ? Or do you actually want to have the current world records ? Dec 25, 2022 at 10:42 • For $k=32$ , the largest $n$ I found so far is $4793$ Dec 25, 2022 at 10:56 • For $k=12$, the only further example up to $10^{12}+11$ is $n=1676641693$. The next example in the case $k=12$ is $n=1852069955839$. For $k=2$, a large example is $n=3^{541}-1$ ($n/2$ and $n-1$ are both prime). – user1115547 Dec 27, 2022 at 7:59 • What did you find in OEiS? Can you post a link to your findings? Dec 29, 2022 at 17:39 • related Jan 2 at 14:52 This is a partial answer. As above mentioned, those values are probably much too small. The table (created with the free calculator PARI/GP) lists the largest solution $$n\le 3\cdot 10^5$$ for $$k=3,\cdots ,32$$ : gp > for(k=3,32,maxi=0;for(m=k,3*10^5,s=binomial(m,k);if(bigomega(s)==k,maxi=m));print(k," ",maxi)) 3 299723 4 298204 5 280223 6 280223 7 280223 8 280223 9 2089 10 362 11 319 12 797 13 797 14 719 15 799 16 1241 17 593 18 2099 19 2399 20 1052 21 2103 22 2974 23 2399 24 1403 25 2239 26 2106 27 5179 28 3548 29 3229 30 5182 31 5183 32 4793 gp > For small $$k$$ , we can find at least lower bounds for the desired values. Define $$n(k)$$ to be the largest known $$n$$ for the corresponding $$k$$ , we can say $$n(3)\ge 10^{1000}+1401064021050844540399$$ $$n(4)\ge 10^{200}+6985786741233199$$ $$n(5)\ge lcm([1..200])\cdot 5012200-1$$ $$n(6)\ge lcm([1..200])\cdot 5012200-1$$ $$n(7)\ge lcm([1..80])\cdot 15688070-1$$ $$n(8)\ge lcm([1..80])\cdot 15688070-1$$ $$n(9)\ge lcm([1..35])\cdot 160479169-1$$ $$n(10)\ge 101114034374873519$$ With increasing $$k$$ , it will become more and more difficult to find huge examples. Everyone finding larger examples can edit the question accordingly. • The largest solutions appeared as close to $300000$ for small $k$, but for larger $k$, they became small for $k\gt9$, approximately $c(k)\cdot k^e$ for some function $c(k)=k^{o(1)}$. Why did this happen? – user1115547 Dec 26, 2022 at 10:43 • Exaclty that is what I wondered as well. Can we reformulate the requirement in terms of prime tuples ? Would that explain the break ? Dec 26, 2022 at 10:45 • Yes, it would. Use the conjecture that the sum of the prime factors (counted with multiplicity) of $\binom{n}{k}$ is at least $k\cdot log(log(n)-log(k))-(2+o(1))(log(n))$ as the positive integers $n$ and $k\ge n$ both vary. – user1115547 Dec 26, 2022 at 11:13 • It is difficult to find large examples from about $k=10$ on. As I said , everyone is invited to edit my answer who found a (significantly) larger example than the given one. An example for $k=8$ (and all smaller $k$) is the $42$ digit number $k=lcm([1..80])\cdot 15688070-1$ Jan 2 at 8:55 • Although I tried various approaches , I did not find a solution for $15\le k\le 32$ larger than those in the table. There are no larger solutions upto $n=10^8$ , for $k=15$ and $k=16$ even upto $10^9$. Jan 10 at 17:05	1,685	4,743	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 53, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.625	4	CC-MAIN-2023-50	latest	en	0.912392
https://boards.straightdope.com/t/whats-a-kagome-lattice-a-quantum-spin-liquid-and-how-are-they-related/645143	1,674,832,791,000,000,000	text/html	crawl-data/CC-MAIN-2023-06/segments/1674764494986.94/warc/CC-MAIN-20230127132641-20230127162641-00810.warc.gz	149,643,782	6,778	# What's a kagome lattice, a quantum spin liquid and how are they related? Oh, and when you’re done, if you could send me my PhD, that could be really cool. Thanks. I understand that there are probably a few conceptual layers one needs to penetrate before you even get to ask a question like this, so if you try reach for my throat I’ll understand - it’s probably just short of asking for a mind meld. But hey, there’s always a chance. Anyway, a little background. Physorg has literally been abuzz over this the past week so I’ll just cite this one article which seems like the best I’ve sampled thus far. kagome lattice sounds like something I’d make a green salad out of. With quantum spin juice on it of course. That’s a nice article. Can you elucidate what you didn’t understand about its explanation of the Kagome lattice and spin liquids, and what you already know about, say, electron spins? Well, when you read this, it seems pretty straight forward. Some of the electrons are spin up, some spin down and then the rest are sort of caught in the middle and that’s what makes it “antiferromagnetic.” The thing is, that when I THINK I understand something in quantum mechanics, that’s a pretty good indication that I don’t. Just take a look at the wiki entry for example. Well, there are some additional complexities, but I think you got the gist – kagome lattice is just another name for a tiling using hexagons and triangles, and not in any way intrinsically related to quantum spin liquids. As for those QSLs, well, basically, two adjacent electron spins ‘want’ to align thenselves opposite to one another, in order to minimize total energy. However, in certain configurations, this isn’t possible: take a triangle, with spins situated at its vertices. If the spin at A is up, the spin at B is down, then what should the spin at C be? It wants to be upposite to A, so down; but it also wants to be opposite to B, so up. This is an example of what’s known as ‘frustration’; in a quantum spin liquid, now, this phenomenon occurs on a ‘large scale’ basis, i.e. all throughout the crystal lattice (it is not hard to see that a kagome lattice is a good candidate for such a situation). Because of the resulting ‘disorderedness’, the whole thing is called a liquid. Ah, I was really getting hung up on that use of the word “liquid.” Thanks. While wearing a schoolgirl uniform. Wot, no Inuyasha jokes yet?	559	2,420	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.640625	3	CC-MAIN-2023-06	latest	en	0.952134
https://www.esaral.com/q/prove-the-following-19158	1,675,709,706,000,000,000	text/html	crawl-data/CC-MAIN-2023-06/segments/1674764500357.3/warc/CC-MAIN-20230206181343-20230206211343-00474.warc.gz	734,348,811	37,560	# Prove the following Question: Two charges $2.0 \times 10^{-6} \mathrm{C}$ and $1.0^{\times 10^{-6}} \mathrm{C}$ are placed at a separation of $10 \mathrm{~cm}$. Where a third charge should be placed such that it experiences no net force due to these charges? Solution:	81	273	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.734375	3	CC-MAIN-2023-06	longest	en	0.858611
http://www.cde.state.co.us/scripts/allstandards/COStandards.asp?stid=4&glid=0&pgcid=191	1,371,678,278,000,000,000	text/html	crawl-data/CC-MAIN-2013-20/segments/1368709224828/warc/CC-MAIN-20130516130024-00017-ip-10-60-113-184.ec2.internal.warc.gz	372,273,372	8,136	Current Display Filter: Mathematics - All - by Specific Prepared Graduate Competency - (Remove PGC Filter) ## Content Area: MathematicsGrade Level Expectations: High SchoolStandard: 3. Data Analysis, Statistics, and Probability Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter) Concepts and skills students master: 3. Probability models outcomes for situations in which there is inherent randomness Evidence Outcomes 21st Century Skill and Readiness Competencies Students Can: Understand independence and conditional probability and use them to interpret data. (CCSS: S-CP)Describe events as subsets of a sample space5 using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events.6 (CCSS: S-CP.1)Explain that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (CCSS: S-CP.2)Using the conditional probability of A given B as P(A and B)/P(B), interpret the independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. (CCSS: S-CP.3)Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.7 (CCSS: S-CP.4)Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.8 (CCSS: S-CP.5) Use the rules of probability to compute probabilities of compound events in a uniform probability model. (CCSS: S-CP)Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. (CCSS: S-CP.6)Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (CCSS: S-CP.7) Analyze the cost of insurance as a method to offset the risk of a situation. (PFL) Inquiry Questions: Can probability be used to model all types of uncertain situations? For example, can the probability that the 50th president of the United States will be female be determined? How and why are simulations used to determine probability when the theoretical probability is unknown? How does probability relate to obtaining insurance? (PFL) Relevance & Application: Comprehension of probability allows informed decision-making, such as whether the cost of insurance is less than the expected cost of illness, when the deductible on car insurance is optimal, whether gambling pays in the long run, or whether an extended warranty justifies the cost. (PFL) Probability is used in a wide variety of disciplines including physics, biology, engineering, finance, and law. For example, employment discrimination cases often present probability calculations to support a claim. Nature Of: Some work in mathematics is much like a game. Mathematicians choose an interesting set of rules and then play according to those rules to see what can happen. Mathematicians explore randomness and chance through probability. Mathematicians construct viable arguments and critique the reasoning of others. (MP) Mathematicians model with mathematics. (MP) 5 the set of outcomes. (CCSS: S-CP.1) 6 "or," "and," "not". (CCSS: S-CP.1) 7 For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. (CCSS: S-CP.4) 8 For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. (CCSS: S-CP.5) ## Content Area: MathematicsGrade Level Expectations: Seventh GradeStandard: 3. Data Analysis, Statistics, and Probability Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter) Concepts and skills students master: 2. Mathematical models are used to determine probability Evidence Outcomes 21st Century Skill and Readiness Competencies Students Can: Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.4 (CCSS: 7.SP.5) Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.5 (CCSS: 7.SP.6) Develop a probability model and use it to find probabilities of events. (CCSS: 7.SP.7)Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (CCSS: 7.SP.7)Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.6 (CCSS: 7.SP.7a)Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.7 (CCSS: 7.SP.7b) Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (CCSS: 7.SP.8)Explain that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. (CCSS: 7.SP.8a)Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. (CCSS: 7.SP.8b)For an event8 described in everyday language identify the outcomes in the sample space which compose the event. (CCSS: 7.SP.8b)Design and use a simulation to generate frequencies for compound events.9 (CCSS: 7.SP.8c) Inquiry Questions: Why is it important to consider all of the possible outcomes of an event? Is it possible to predict the future? How? What are situations in which probability cannot be used? Relevance & Application: The ability to efficiently and accurately count outcomes allows systemic analysis of such situations as trying all possible combinations when you forgot the combination to your lock or deciding to find a different approach when there are too many combinations to try; or counting how many lottery tickets you would have to buy to play every possible combination of numbers. The knowledge of theoretical probability allows the development of winning strategies in games involving chance such as knowing if your hand is likely to be the best hand or is likely to improve in a game of cards. Nature Of: Mathematicians approach problems systematically. When the number of possible outcomes is small, each outcome can be considered individually. When the number of outcomes is large, a mathematician will develop a strategy to consider the most important outcomes such as the most likely outcomes, or the most dangerous outcomes. Mathematicians construct viable arguments and critique the reasoning of others. (MP) Mathematicians model with mathematics. (MP) 4 Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (CCSS: 7.SP.5) 5 For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. (CCSS: 7.SP.6) 6 For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. (CCSS: 7.SP.7a) 7 For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? (CCSS: 7.SP.7b) 8 e.g., "rolling double sixes" (CCSS: 7.SP.8b) 9 For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? (CCSS: 7.SP.8c)	1,818	8,384	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.40625	4	CC-MAIN-2013-20	latest	en	0.910799
https://puretables.com/angstroms-to-chains	1,653,386,252,000,000,000	text/html	crawl-data/CC-MAIN-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00326.warc.gz	521,369,719	4,160	# Angstroms to Chains Online converter A ch -> Chains to Angstroms ## How to convert Angstroms to Chains 1 Angstrom is equal to 4.9709695378987E-12 Chains. 1 A = 4.9709695378987E-12 ch. Formula x(A) / 201168000000 = x(ch) To get the result in chains divide the number of angstroms by 201168000000. Example Convert 5 Angstroms to Chains: 5 A / 201168000000 = 2.4854847689493E-11 ch ## Angstroms to Chains Conversion Table Angstroms [A] Chains [ch] 0.01 A4.9709695378987E-14 ch 0.1 A4.9709695378987E-13 ch 1 A4.9709695378987E-12 ch 2 A9.9419390757973E-12 ch 3 A1.4912908613696E-11 ch 5 A2.4854847689493E-11 ch 10 A4.9709695378987E-11 ch 20 A9.9419390757973E-11 ch 30 A1.4912908613696E-10 ch 50 A2.4854847689493E-10 ch 100 A4.9709695378987E-10 ch 500 A2.4854847689493E-9 ch 1000 A4.9709695378987E-9 ch	340	808	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	2.65625	3	CC-MAIN-2022-21	latest	en	0.555591
https://tutorme.com/tutors/114669/interview/	1,670,530,342,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446711360.27/warc/CC-MAIN-20221208183130-20221208213130-00564.warc.gz	597,345,945	50,507	Enable contrast version # Tutor profile: Ryan G. Ryan G. University Math Tutor ## Questions ### Subject:Linear Algebra TutorMe Question: Find a basis for the row space and a basis for the column space of the matrix $(A=\begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ -1 & \phantom{-} 1 & -1\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix}.$) Ryan G. Begin by applying elementary row operations in order to reduce $$A$$ to echelon form. Designate the rows of $$A$$ by $$r_i$$, $$i\in\{1,2,3\}$$. First, row replace the second row by adding the first row to the second row, $$r_1+r_2$$, obtaining $(A=\begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ -1 & \phantom{-} 1 & -1\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix} \rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix}.$) Next, row replace the third row by adding $$-2$$ times the first row to the third row, $$-2r_1+r_3$$, obtaining $(A=\begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ -1 & \phantom{-} 1 & -1\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix} \rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-}0 & -2 & \phantom{-} 0 \end{bmatrix}.$) Finally, row replace the third row by adding the second row to the third row, $$r_2+r_3$$, obtaining $(A=\begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ -1 & \phantom{-} 1 & -1\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix} \rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-} 2 & \phantom{-} 0 & \phantom{-} 2 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-}0 & -2 & \phantom{-} 0 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & \phantom{-} 1 & \phantom{-} 1\\ \phantom{-}0 & \phantom{-} 2 & \phantom{-}0\\ \phantom{-}0 & \phantom{-}0 & \phantom{-} 0 \end{bmatrix}.$) The last matrix listed above is the echelon form of $$A$$, and its nonzero rows form a basis for the row space of $$A$$. We can conclude that a basis for the row space of $$A$$ is the set $(\{(1,1,1),(0,2,0)\}.$) To find a basis for the column space, we will apply the same method on the transpose of the given matrix, $$A^T$$. The matrix $$A^T$$ is produced by listing the columns of $$A$$ as rows (or by listing the rows as columns). The result is $(A^T=\begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}1 & \phantom{-} 1 & \phantom{-}0\\ \phantom{-} 1 & -1 & \phantom{-} 2 \end{bmatrix}.$) Again applying elementary row operations, we row replace the second row by adding $$-1$$ times the first row to the second row, obtaining $(A^T=\begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}1 & \phantom{-} 1 & \phantom{-}0\\ \phantom{-} 1 & -1 & \phantom{-} 2 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}0 & \phantom{-} 2 & -2\\ \phantom{-} 1 & -1 & \phantom{-} 2 \end{bmatrix}.$) Next, row replace the third row by adding $$-1$$ times the first row to the third row, obtaining $(A^T=\begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}1 & \phantom{-} 1 & \phantom{-}0\\ \phantom{-} 1 & -1 & \phantom{-} 2 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}0 & \phantom{-} 2 & -2\\ \phantom{-} 1 & -1 & \phantom{-} 2 \end{bmatrix}\rightarrow \begin{bmatrix}\phantom{-} 1 & -1 & \phantom{-} 2\\ \phantom{-}0 & \phantom{-} 2 & -2\\ \phantom{-} 0 & \phantom{-}0 & \phantom{-} 0 \end{bmatrix}.$) This last matrix is the echelon form of $$A^T$$, and its nonzero rows form a basis for the row space of $$A^T$$, which is also the column space of $$A$$. We conclude that a basis for the column space of $$A$$ is the set $(\{(1,-1,2)^T,(0,2,-2)^T\}.$) ### Subject:Pre-Calculus TutorMe Question: As an application of logarithms, solve the following equation for $$x$$, $(4^x=2^x+3.$) Ryan G. By the properties of exponents, express the left side of the equation as $$4^x=(2^2)^x=(2^x)^2$$. The equation becomes $((2^x)^2=2^x+3,$) or $((2^x)^2-2^x-3=0,$) where the latter is a quadratic equation in $$2^x$$. By the quadratic formula, the solution of this equation is $(2^x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-3)}}{2(1)}=\frac{1\pm\sqrt{13}}{2}.$) Recognizing that $$(1-\sqrt{13})/2$$ is negative but $$2^x$$ is positive for all $$x$$, we disregard the negative solution so that $(2^x=\frac{1+\sqrt{13}}{2}.$) Take the base $$2$$ logarithm of both sides to obtain $(x=\log_2\left(\frac{1+\sqrt{13}}{2}\right).$) Using the properties of logarithms this simplifies to $(x=\log_2(1+\sqrt{13})-\log_22=\log_2(1+\sqrt{13})-1.$) ### Subject:Calculus TutorMe Question: Evaluate the indefinite integral $(\int \sin^3x\cos^2x\ dx.$) Ryan G. This problem demonstrates the simplifying power of an appropriate substitution. Since I have no trigonometric identities for $$\sin^3x$$, I'll begin by factoring that term $(\int \sin^3x\cos^2x\ dx=\int \sin x\sin^2x\cos^2x\ dx.$) The trigonometric identity $$\sin^2x+\cos^2x=1$$ allows us to write $$\sin^2x=1-\cos^2x$$. Making this replacement, the integral becomes $(\int \sin^3x\cos^2x\ dx=\int \sin x(1-\cos^2x)\cos^2x\ dx.$) Now consolidate the cosine terms by multiplying $$(1-\cos^2x)$$ and $$\cos^2x$$. It follows that $(\int \sin^3x\cos^2x\ dx=\int \sin x(\cos^2x-\cos^4x)\ dx.$) The cosine makes for a natural substitution, since it is related to sine by differentiation. We substitute $$u=\cos x$$ and $$du=-\sin x\ dx$$ so that, after some manipulation, the integral becomes $(\int \sin^3x\cos^2x\ dx=\int u^4-u^2\ du.$) From here we can evaluate the integral, remembering the constant of integration, $(\int \sin^3x\cos^2x\ dx=\frac{1}{5}u^5-\frac{1}{3}u^3+C.$) As a final step, we resubstitute $$\cos x=u$$, giving the solution $(\int \sin^3x\cos^2x\ dx=\frac{1}{5}\cos^5x-\frac{1}{3}\cos^3x+C.$). ## FAQs What is a lesson? A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard. How do I begin a lesson? If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson. Who are TutorMe tutors? Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you. BEST IN CLASS SINCE 2015 TutorMe homepage	2,570	7,061	{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4.375	4	CC-MAIN-2022-49	latest	en	0.276845
https://aspirantszone.com/quantitative-aptitude-number-series-set-66/?_page=2	1,670,143,408,000,000,000	text/html	crawl-data/CC-MAIN-2022-49/segments/1669446710968.29/warc/CC-MAIN-20221204072040-20221204102040-00584.warc.gz	145,498,114	24,992	# Quantitative Aptitude: Number Series Set 66 1. 8, ? , 8 , 14, 30, 77 7 5 6 4 None Option C Solution: 80.5+2=6 61+2=8 81.5+2=14 142+2=30 302.5+2=77 2. 120, 112 , ?, 92, 76, 58 110 98 104 100 None Option C Solution: 120……….112……….104………..92……..76………58 …….6………….8……………12…….16……..18 Difference alternate multiples of 6 and 8. 3. 1, 3, ?, 48 ,400, 6432 21 16 14 10 None Option D Solution: 11+2 1= 3 32+22= 10 104+23= 48 488+24= 400 40016+25= 6432. 4. 150, 162, 186, 222, 270, ? 292 310 330 316 None Option C Solution: 150+112=162 162+212=186 186+312=222 222+412=270 270+512=330. 5. 2 , 11 , 38, 197, ?, 8227 1650 1174 1341 1422 None Option B Solution: 2 3 + 5=11 11 * 4 – 6=38 38 * 5 + 7=197 197* 6-8=1174 11747+9=8227. 6. 24, 12, 18, 45, ? , 708.75 175.3 160 157.5 220 None Option C Solution: 240.5=12 121.5=18 182.5=45 453.5=157.5 157.54.5=708.75. 7. 2, 3, 12, 65, 462, ? 4167 3555 4321 5482 None Option A Solution: 21+1=3 33+3=12 125+5=65 657+7=462 4629+9=4167. 8. 6, 6, 16, ?, 108, 228 40 46 62 54 None Option A Solution: 6+13-1=6 6+23+2=16 16+33-3=40 40+43+4=108 108+53-5=228. 9. 9 4.5 ? 6.75 13.5 33.75 5 4.8 4.5 5.4 None Option C Solution: 905=4.5 4.51=4.5 4.51.5=6.75 6.752=13.5 13.52.5=33.75. 10. 8, 19, 29, ?, 46, 53 40 42 35 38 None Option D Solution: 8+11=19 19+10=29 29+9=38 38+8=46 46+7=53. ## 2 Thoughts to “Quantitative Aptitude: Number Series Set 66” 1. jaga Thank u mam 2. pulkit thank you mam	840	1,447	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	3.34375	3	CC-MAIN-2022-49	latest	en	0.259432
https://gmatclub.com/forum/an-insurance-company-sells-only-one-type-of-health-and-one-type-of-208004.html	1,547,613,071,000,000,000	text/html	crawl-data/CC-MAIN-2019-04/segments/1547583656665.34/warc/CC-MAIN-20190116031807-20190116053807-00469.warc.gz	519,555,700	58,710	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 15 Jan 2019, 20:31 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History ## Events & Promotions ###### Events & Promotions in January PrevNext SuMoTuWeThFrSa 303112345 6789101112 13141516171819 20212223242526 272829303112 Open Detailed Calendar • ### \$450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth \$100 with the 3 Month Pack (\$299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # An insurance company sells only one type of health and one type of Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 52108 An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 01 Nov 2015, 08:23 1 3 00:00 Difficulty: 45% (medium) Question Stats: 69% (02:14) correct 31% (01:52) wrong based on 207 sessions ### HideShow timer Statistics An insurance company sells only one type of health and one type of life insurance policy. The monthly premium for a health insurance policy is \$80. If the insurance company took in a total \$5000 in premiums, what was the monthly premium of a life insurance policy? (1) The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums. (2) The insurance company sold 2.5 times as many health insurance policies as life insurance policies. Kudos for a correct solution. _________________ CEO Joined: 11 Sep 2015 Posts: 3318 Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 01 Nov 2015, 08:26 Bunuel wrote: An insurance company sells only one type of health and one type of life insurance policy. The monthly premium for a health insurance policy is \$80. If the insurance company took in a total \$5000 in premiums, what was the monthly premium of a life insurance policy? (1) The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums. (2) The insurance company sold 2.5 times as many health insurance policies as life insurance policies. Kudos for a correct solution. Let H = the number of health insurance policies Let L = the number of life insurance policies Let p = the monthly premium on a life insurance policy So, 80H + pL = 5000 Target question: What is the value of p? Statement 1: The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums. Total revenue = \$5000 (4/5)(\$5000) = \$4000 So, 80H = \$4000. Take 80H + pL = 5000 and replace 80H with \$4000 to get 4000 + pL = 5000, which simplifies to pL = 1000 Since there are many possible values for p that satisfy this equation, statement 1 is NOT SUFFICIENT Statement 2: The insurance company sold 2.5 times as many health insurance policies as life insurance policies. In other words, H = 2.5L Take 80H + pL = 5000 and replace H with 2.5L to get 80(2.5L) + pL = 5000, which simplifies to be 200L + pL = 5000 Since there are many possible values for p that satisfy this equation, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined From the two statements we get two equations: 200L + pL = 5000 pL = 1000 Subtract the bottom equation from the top equation to get: 200L = 4000, which means L = 20 Now that we know L = 20 and pL = 1000, we can see that p = 50 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Cheers, Brent _________________ Test confidently with gmatprepnow.com Verbal Forum Moderator Status: Greatness begins beyond your comfort zone Joined: 08 Dec 2013 Posts: 2165 Location: India Concentration: General Management, Strategy Schools: Kelley '20, ISB '19 GPA: 3.2 WE: Information Technology (Consulting) Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 01 Nov 2015, 10:32 Let h= number of health insurance policies l= number of life insurance policies L= monthly premium on a life insurance policies 80 h + Ll = 5000 We need to find the value of L 1. 80h = 4000 Ll = 1000 Not sufficient 2. h=2.5l 802.5l +Ll = 5000 => 200l +Ll = 5000 Not sufficient Combining 1 and 2, we get 200l=4000 =>l=20 L= 50 Sufficient. _________________ When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful Board of Directors Joined: 17 Jul 2014 Posts: 2601 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 01 Nov 2015, 11:43 1 -> 80H = 4/5 5000 or 80H = 4000. H = 50. Can't Find L. 2 -> H = 2.5L write 2.5L80 +xL = 5000 20L+xL = 5000 L(20+x) = 5000 don't have X. both -> L(20+x) = 5000 H = 50. 2.5L = 50, and L = 20. now we have 40L = 5000. we can solve for L. Manager Joined: 10 Apr 2015 Posts: 70 Location: India Concentration: Healthcare, Strategy GMAT 1: 680 Q49 V34 GPA: 2.4 WE: Marketing (Health Care) Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 01 Nov 2015, 21:57 Hi, Statement 1: We arrive at H = 5000/180 - Not sufficient Statement 2: Only relation is provided. - Not sufficient Now using 1 and 2, we arrive at the Value of L. Option C. Regards Manager Status: One Last Shot !!! Joined: 04 May 2014 Posts: 239 Location: India Concentration: Marketing, Social Entrepreneurship GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 03 Nov 2015, 21:28 GMATPrepNow wrote: Bunuel wrote: An insurance company sells only one type of health and one type of life insurance policy. The monthly premium for a health insurance policy is \$80. If the insurance company took in a total \$5000 in premiums, what was the monthly premium of a life insurance policy? (1) The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums. (2) The insurance company sold 2.5 times as many health insurance policies as life insurance policies. Kudos for a correct solution. Let H = the number of health insurance policies Let L = the number of life insurance policies Let p = the monthly premium on a life insurance policy So, 80H + pL = 5000 Target question: What is the value of p? Statement 1: The total revenue from health insurance premiums was 4/5 of the total revenue the company received from premiums. Total revenue = \$5000 (4/5)(\$5000) = \$4000 So, 80H = \$4000. Take 80H + pL = 5000 and replace 80H with \$4000 to get 4000 + pL = 5000, which simplifies to pL = 1000 Since there are many possible values for p that satisfy this equation, statement 1 is NOT SUFFICIENT Statement 2: The insurance company sold 2.5 times as many health insurance policies as life insurance policies. In other words, H = 2.5L Take 80H + pL = 5000 and replace H with 2.5L to get 80(2.5L) + pL = 5000, which simplifies to be 200L + pL = 5000 Since there are many possible values for p that satisfy this equation, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined From the two statements we get two equations: 200L + pL = 5000 pL = 1000 Subtract the bottom equation from the top equation to get: 200L = 4000, which means L = 20 Now that we know L = 20 and pL = 1000, we can see that p = 50 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Cheers, Brent Hi, I have a doubt in the explanations provided. I see all have arrived at C with only taking these three variables into account Let H = the number of health insurance policies Let L = the number of life insurance policies Let p = the monthly premium on a life insurance policy But what about the number of months? Should that not be considered? The question says that "If the insurance company took in a total \$5000 in premiums". But in how many months?? (How can we assume that this total is for one month?) Therefore, 80H will represent premium collected from H policies for 1 month and not for all the months. Similarly Lp. IMO, the equation should be something like this- 80HM1 + Lp*M2 = 5000 where, M1=number of months for which premium was collected for health insurance policies M2=number of months for which premium was collected for life insurance policies Thanks! _________________ One Kudos for an everlasting piece of knowledge is not a bad deal at all... ------------------------------------------------------------------------------------------------------------------------ Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. -Mark Twain Non-Human User Joined: 09 Sep 2013 Posts: 9406 Re: An insurance company sells only one type of health and one type of [#permalink] ### Show Tags 31 Mar 2017, 03:53 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: An insurance company sells only one type of health and one type of &nbs [#permalink] 31 Mar 2017, 03:53 Display posts from previous: Sort by	2,896	10,625	{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}	4	4	CC-MAIN-2019-04	latest	en	0.885895

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