text:
# Tag Info

As a simple example, consider the discrete-time signal $$x[n]=a^nu[n],\qquad |a|<1\tag{1}$$ where $u[n]$ is the unit step function. The discrete-time Fourier transform (DTFT) of $x[n]$ is given by $$X(e^{j\omega})=\frac{1}{1-ae^{-j\omega t}}\tag{2}$$ Note that $\omega$ is a normalized angular frequency: $$\omega=2\pi f/f_s\tag{3}$$ where $f_s$ is ...


text:
# Freeman Dyson

Jump to navigation Jump to search

{{ safesubst:#invoke:Unsubst||$N=Use dmy dates |date=__DATE__ |$B= }} Template:Infobox scientist Freeman John Dyson FRS (born December 15, 1923) is an English-born American[1][2] theoretical physicist and mathematician, famous for his work in quantum electrodynamics, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists.[3]

## Biography

Born at Crowthorne in Berkshire, Dyson is the son of the English composer George Dyson, who was later knighted. His mother had a law degree, but after Dyson was born she worked as a social worker.[4] Although not known to be related to the early 20th-century astronomer Frank Watson Dyson, as a small boy Dyson was aware of him and has credited the popularity of an astronomer sharing his surname as having helped to spark his own interest in science.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} At the age of five he calculated the number of atoms in the sun.[5] As a child, he showed an interest in large numbers and in the solar system, and was strongly influenced by the book Men of Mathematics by Eric Temple Bell.[6] From 1936 to 1941, Dyson was a Scholar at Winchester College, where his father was Director of Music. On July 25, 1943, he entered the Operational Research Section (ORS) of the Royal Air Force’s Bomber Command,[7] where he developed analytical methods to help the RAF bomb German targets during World War II.[8] After the war, Dyson enrolled in the University of Cambridge, where he obtained a Bachelor of Arts degree in mathematics.[9] From 1946 to 1949 he was a Fellow of Trinity College, Cambridge, occupying rooms just below those of the philosopher Ludwig Wittgenstein, who would resign his professorship in 1947.[10] ### Career in the United States In 1947 Dyson moved to the US, as Commonwealth Fellow at Cornell University (1947–1948) and the Institute for Advanced Study (1948–1949). Between 1949 and 1951, he was a teaching fellow at the University of Birmingham (UK).[11] In 1951 he joined the faculty at Cornell as a physics professor, although still lacking a doctorate, and in 1953 he received a permanent post at the Institute for Advanced Study in Princeton, New Jersey—where he has now lived for more than fifty years.[12] In 1957 he became a naturalized citizen of the United States and renounced his British nationality. One reason he gave decades later is that his children born in the US had not been recognized as British subjects.[1][2] Dyson is best known for demonstrating in 1949 the equivalence of two then-current formulations of quantum electrodynamicsRichard Feynman's diagrams and the operator method developed by Julian Schwinger and Sin-Itiro Tomonaga.[13] He was the first person (besides Feynman) to appreciate the power of Feynman diagrams, and his paper written in 1948 and published in 1949 was the first to make use of them. He said in that paper that Feynman diagrams were not just a computational tool, but a physical theory, and developed rules for the diagrams that completely solved the renormalization problem. Dyson's paper and also his lectures presented Feynman's theories of QED (quantum electrodynamics) in a form that other physicists could understand, facilitating the physics community's acceptance of Feynman's work. Robert Oppenheimer, in particular, was persuaded by Dyson that Feynman's new theory was as valid as Schwinger's and Tomonaga's. Oppenheimer rewarded Dyson with a lifetime appointment at the Institute for Advanced Study, "for proving me wrong", in Oppenheimer's words.[14] Also in 1949, in a related work, Dyson invented the Dyson series.[15] It was this paper that inspired John Ward to derive his celebrated Ward identity.[16] Dyson also did work in a variety of topics in mathematics, such as topology, analysis, number theory and random matrices.[17] There is an interesting story involving random matrices. In 1973 the number theorist Hugh Montgomery was visiting the Institute for Advanced Study and had just made his pair correlation conjecture concerning the distribution of the zeros of the Riemann zeta function. He showed his formula to the mathematician Atle Selberg who said it looked like something in mathematical physics and he should show it to Dyson, which he did. Dyson recognized the formula as the pair correlation function of the Gaussian unitary ensemble, which has been extensively studied by physicists. This suggested that there might be an unexpected connection between the distribution of primes 2,3,5,7,11, ... and the energy levels in the nuclei of heavy elements such as uranium.[18] From 1957 to 1961 he worked on the Orion Project, which proposed the possibility of space-flight using nuclear pulse propulsion. A prototype was demonstrated using conventional explosives, but the 1963 Partial Test Ban Treaty (which Dyson was involved in and supported) permitted only underground nuclear testing, so the project was abandoned. In 1958 he led the design team for the TRIGA, a small, inherently safe nuclear reactor used throughout the world in hospitals and universities for the production of medical isotopes. A seminal work by Dyson came in 1966 when, together with Andrew Lenard and independently of Elliott H. Lieb and Walter Thirring, he proved rigorously that the exclusion principle plays the main role in the stability of bulk matter.[19][20][21] Hence, it is not the electromagnetic repulsion between outer-shell orbital electrons which prevents two wood blocks that are left on top of each other from coalescing into a single piece, but rather it is the exclusion principle applied to electrons and protons that generates the classical macroscopic normal force. In condensed matter physics, Dyson also did studies in the phase transition of the Ising model in 1 dimension and spin waves.[17] Around 1979, Dyson worked with the Institute for Energy Analysis on climate studies. This group, under the direction of Alvin Weinberg, pioneered multidisciplinary climate studies, including a strong biology group. Also during the 1970s, he worked on climate studies conducted by the JASON defense advisory group.[12] Dyson retired from the Institute for Advanced Study in 1994.[22] In 1998, Dyson joined the board of the Solar Electric Light Fund. Template:As of he was president of the Space Studies Institute, the space research organization founded by Gerard K. O'Neill; Template:As of he is on its Board of Trustees.[23] Dyson is a long-time member of the JASON group. Dyson is a regular contributor to The New York Review of Books. Dyson has won numerous scientific awards but never a Nobel Prize. Nobel physics laureate Steven Weinberg has said that the Nobel committee has "fleeced" Dyson, but Dyson himself remarked in 2009, "I think it's almost true without exception if you want to win a Nobel Prize, you should have a long attention span, get hold of some deep and important problem and stay with it for ten years. That wasn't my style."[12] In 2012, he published (with William H. Press) a fundamental new result about the Prisoners Dilemma in PNAS.[24] ### Marriages and children With his first wife, the mathematician Verena Huber-Dyson, Dyson has two children, Esther and George. In 1958 he married Imme Jung, a masters runner, and they eventually had four more children, Dorothy, Mia, Rebecca, and Emily Dyson.[12] Dyson's eldest daughter, Esther, is a digital technology consultant and investor; she has been called "the most influential woman in all the computer world." [25] His son George is a historian of science,[26] one of whose books is Project Orion: The Atomic Spaceship 1957–1965. ### Character Friends and colleagues describe Dyson as shy and self-effacing, with a contrarian streak that his friends find refreshing but his intellectual opponents find exasperating. "I have the sense that when consensus is forming like ice hardening on a lake, Dyson will do his best to chip at the ice", Steven Weinberg said of him. His friend, the neurologist and author Oliver Sacks, said: "A favorite word of Freeman's about doing science and being creative is the word 'subversive'. He feels it's rather important not only to be not orthodox, but to be subversive, and he's done that all his life."[12] Template:Clarify In The God Delusion (2006), biologist Richard Dawkins criticized Dyson for accepting the religious Templeton Prize in 2000; "It would be taken as an endorsement of religion by one of the world's most distinguished physicists."[27] However, Dyson declared in 2000 that he is a (non-denominational) Christian,[28] and he has disagreed with Dawkins on several occasions, as when he criticized Dawkins' understanding of evolution.[29] ## Honors and awards In 1952 he was elected a Fellow of the Royal Society.[30] Dyson was awarded the Lorentz Medal in 1966, Max Planck Medal in 1969 and the Harvey Prize in 1977. In the 1984–85 academic year he gave the Gifford lectures at Aberdeen, which resulted in the book Infinite In All Directions. In 1989, Dyson taught at Duke University as a Fritz London Memorial Lecturer. In the same year, he was elected as an Honorary Fellow of Trinity College, University of Cambridge. Dyson has published a number of collections of speculations and observations about technology, science, and the future. In 1996 he was awarded the Lewis Thomas Prize for Writing about Science. In 1993, Dyson was given the Enrico Fermi Award. In 1995 he gave the Jerusalem-Harvard Lectures at the Hebrew University of Jerusalem, sponsored jointly by the Hebrew University and Harvard University Press that grew into the book Imagined Worlds.[31] In 2000, Dyson was awarded the Templeton Prize for Progress in Religion. In 2003, Dyson was awarded the Telluride Tech Festival Award of Technology in Telluride, Colorado. In 2011, Dyson was received as one of twenty distinguished Old Wykehamists at the Ad Portas celebration, the highest honour that Winchester College bestows. ## Concepts ### Biotechnology and genetic engineering My book The Sun, the Genome, and the Internet (1999) describes a vision of green technology enriching villages all over the world and halting the migration from villages to megacities. The three components of the vision are all essential: the sun to provide energy where it is needed, the genome to provide plants that can convert sunlight into chemical fuels cheaply and efficiently, the Internet to end the intellectual and economic isolation of rural populations. With all three components in place, every village in Africa could enjoy its fair share of the blessings of civilization.[32] Dyson cheerfully admits his record as a prophet is mixed, but "it is better to be wrong than to be vague."[33] "To answer the world's material needs, technology has to be not only beautiful but also cheap."[34] ### Dyson sphere Artist's concept of Dyson rings, forming a stable Dyson swarm, or "Dyson sphere". {{#invoke:main|main}} One should expect that, within a few thousand years of its entering the stage of industrial development, any intelligent species should be found occupying an artificial biosphere which completely surrounds its parent star.[35] In 1960 Dyson wrote a short paper for the journal Science, entitled "Search for Artificial Stellar Sources of Infrared Radiation".[36] In it, he theorized that a technologically advanced extraterrestrial civilization might completely surround its native star with artificial structures in order to maximize the capture of the star's available energy. Eventually, the civilization would completely enclose the star, intercepting electromagnetic radiation with wavelengths from visible light downwards and radiating waste heat outwards as infrared radiation. Therefore, one method of searching for extraterrestrial civilizations would be to look for large objects radiating in the infrared range of the electromagnetic spectrum. Dyson conceived that such structures would be clouds of asteroid-sized space habitats, though science fiction writers have preferred a solid structure: either way, such an artifact is often referred to as a Dyson sphere, although Dyson himself used the term "shell". Dyson says that he used the term "artificial biosphere" in the article meaning a habitat, not a shape.[37] The general concept of such an energy-transferring shell had been advanced decades earlier by author Olaf Stapledon in his 1937 novel Star Maker, a source that Dyson has credited publicly.[38][39] ### Dyson tree {{#invoke:main|main}} Dyson has also proposed the creation of a Dyson tree, a genetically-engineered plant capable of growing on a comet. He suggested that comets could be engineered to contain hollow spaces filled with a breathable atmosphere, thus providing self-sustaining habitats for humanity in the outer solar system. Plants could grow greenhouses…just as turtles grow shells and polar bears grow fur and polyps build coral reefs in tropical seas. These plants could keep warm by the light from a distant Sun and conserve the oxygen that they produce by photosynthesis. The greenhouse would consist of a thick skin providing thermal insulation, with small transparent windows to admit sunlight. Outside the skin would be an array of simple lenses, focusing sunlight through the windows into the interior… Groups of greenhouses could grow together to form extended habitats for other species of plants and animals.[40] ### Space colonies I've done some historical research on the costs of the Mayflower's voyage, and on the Mormons' emigration to Utah, and I think it's possible to go into space on a much smaller scale. A cost on the order of$40,000 per person [1978 dollars, \$143,254 in 2013 dollars] would be the target to shoot for; in terms of real wages, that would make it comparable to the colonization of America. Unless it's brought down to that level it's not really interesting to me, because otherwise it would be a luxury that only governments could afford.[35]

Dyson has been interested in space travel since he was a child, reading such science fiction classics as Olaf Stapledon's Star Maker. As a young man, he worked for General Atomics on the nuclear-powered Orion spacecraft. He hoped Project Orion would put men on Mars by 1965, Saturn by 1970. He's been unhappy for a quarter-century on how the government conducts space travel:

The problem is, of course, that they can't afford to fail. The rules of the game are that you don't take a chance, because if you fail, then probably your whole program gets wiped out.[35]

He still hopes for cheap space travel, but is resigned to waiting for private entrepreneurs to develop something new—and cheap.

No law of physics or biology forbids cheap travel and settlement all over the solar system and beyond. But it is impossible to predict how long this will take. Predictions of the dates of future achievements are notoriously fallible. My guess is that the era of cheap unmanned missions will be the next fifty years, and the era of cheap manned missions will start sometime late in the twenty-first century.

Any affordable program of manned exploration must be centered in biology, and its time frame tied to the time frame of biotechnology; a hundred years, roughly the time it will take us to learn to grow warm-blooded plants, is probably reasonable.[40]

Dyson also has proposed the use of bioengineered space colonies to colonize the Kuiper Belt on the outer edge of our Solar System. He proposed that habitats could be grown from space hardened spores. The colonies could then be warmed by large reflector plant leaves that could focus the dim, distant sunlight back on the growing colony. This was illustrated by Pat Rawlings on the cover of the National Space Society's Ad Astra magazine.

### Space exploration

A direct search for life in Europa's ocean would today be prohibitively expensive. Impacts on Europa give us an easier way to look for evidence of life there. Every time a major impact occurs on Europa, a vast quantity of water is splashed from the ocean into the space around Jupiter. Some of the water evaporates, and some condenses into snow. Creatures living in the water far enough from the impact have a chance of being splashed intact into space and quickly freeze-dried. Therefore, an easy way to look for evidence of life in Europa's ocean is to look for freeze-dried fish in the ring of space debris orbiting Jupiter.

Freeze-dried fish orbiting Jupiter is a fanciful notion, but nature in the biological realm has a tendency to be fanciful. Nature is usually more imaginative than we are. [...] To have the best chance of success, we should keep our eyes open for all possibilities.[40]

### Dyson's transform

{{#invoke:main|main}} Dyson also has some credits in pure mathematics. His concept "Dyson's transform" led to one of the most important lemmas of Olivier Ramaré's theorem that every even integer can be written as a sum of no more than six primes.

### Dyson series

The Dyson series, the formal solution of an explicitly time-dependent Schrödinger equation by iteration, and the corresponding Dyson time-ordering operator ${\displaystyle {\mathcal {T}}\,,}$ an entity of basic importance in the mathematical formulation of quantum mechanics, are also named after Dyson.

Freeman Dyson in 2007 at the Institute for Advanced Study

### Quantum Physics and the Primes 2, 3, 5, 7, 11, 13, 17, ...

Dyson and Hugh Montgomery discovered together an intriguing connection between quantum physics and Montgomery's pair correlation conjecture about the zeros of the Zeta function. The primes 2, 3, 5, 7, 11, 13, 17, 19, ... are described by the Riemann Zeta function, and Dyson had previously developed a description of quantum physics based on m by m arrays of totally random numbers. [41] What Montgomery and Dyson discovered is that the eigenvalues of these matrices bear an uncanny resemblance to the spacings between numbers where the Zeta function has the value zero. After this discovery, Andrew Odlyzko began verifying it on a computer, using his Odlyzko–Schönhage algorithm to calculate many zeros and verify this connection. Dyson recognized this connection because of a number theory question Montgomery asked him. Dyson had worked in number theory in his youth in England. If Montgomery had not been visiting the Institute for Advanced Study that week, this connection might not have been discovered.

## Views

### Metaphysics

Dyson has suggested a kind of cosmic metaphysics of mind. In his book Infinite in All Directions he writes about three levels of mind: "The universe shows evidence of the operations of mind on three levels. The first level is the level of elementary physical processes in quantum mechanics. Matter in quantum mechanics is [...] constantly making choices between alternative possibilities according to probabilistic laws. [...] The second level at which we detect the operations of mind is the level of direct human experience. [...] [I]t is reasonable to believe in the existence of a third level of mind, a mental component of the universe. If we believe in this mental component and call it God, then we can say that we are small pieces of God's mental apparatus" (p. 297).

### Global warming

Dyson agrees that anthropogenic global warming exists, and has written that "[one] of the main causes of warming is the increase of carbon dioxide in the atmosphere resulting from our burning of fossil fuels such as oil and coal and natural gas."[42] However, he believes that existing simulation models of climate fail to account for some important factors, and hence the results will contain too much error to reliably predict future trends:

The models solve the equations of fluid dynamics, and they do a very good job of describing the fluid motions of the atmosphere and the oceans. They do a very poor job of describing the clouds, the dust, the chemistry and the biology of fields and farms and forests. They do not begin to describe the real world we live in ...[42]

He is among signatories of a letter to the UN criticizing the IPCC[43][44] and has also argued against ostracizing scientists whose views depart from the acknowledged mainstream of scientific opinion on climate change, stating that "heretics" have historically been an important force in driving scientific progress. "[H]eretics who question the dogmas are needed ... I am proud to be a heretic. The world always needs heretics to challenge the prevailing orthodoxies."[42]

Dyson says his views on global warming have been strongly criticized. In reply, he notes that "[m]y objections to the global warming propaganda are not so much over the technical facts, about which I do not know much, but it’s rather against the way those people behave and the kind of intolerance to criticism that a lot of them have."[45]

More recently, he has endorsed the now common usage of "global warming" as synonymous with global anthropogenic climate change, referring to "measurements that transformed global warming from a vague theoretical speculation into a precise observational science."[46]

He has, however, argued that political efforts to reduce the causes of climate change distract from other global problems that should take priority:

I'm not saying the warming doesn't cause problems, obviously it does. Obviously we should be trying to understand it. I'm saying that the problems are being grossly exaggerated. They take away money and attention from other problems that are much more urgent and important. Poverty, infectious diseases, public education and public health. Not to mention the preservation of living creatures on land and in the oceans.[47]

Since originally taking interest in climate studies in the 1970s, Dyson has suggested that carbon dioxide levels in the atmosphere could be controlled by planting fast-growing trees. He calculates that it would take a trillion trees to remove all carbon from the atmosphere.[48][49]

In a 2014 interview, he said that "What I’m convinced of is that we don’t understand climate ... It will take a lot of very hard work before that question is settled." [6]

### Nuclear winter

From his 1988 book Infinite in All Directions, he offered some criticism of then current models predicting a devastating nuclear winter in the event of a large-scale nuclear war:

As a scientist I want to rip the theory of nuclear winter apart, but as a human being I want to believe it. This is one of the rare instances of a genuine conflict between the demands of science and the demands of humanity. As a scientist, I judge the nuclear winter theory to be a sloppy piece of work, full of gaps and unjustified assumptions. As a human being, I hope fervently that it is right. Here is a real and uncomfortable dilemma. What does a scientist do when science and humanity pull in opposite directions?[50]

### Warfare and weapons

On hearing the news of the bombing of Hiroshima:

I agreed emphatically with Henry Stimson. Once we had got ourselves into the business of bombing cities, we might as well do the job competently and get it over with. I felt better that morning than I had felt for years… Those fellows who had built the atomic bombs obviously knew their stuff… Later, much later, I would remember [the downside].[51]

I am convinced that to avoid nuclear war it is not sufficient to be afraid of it. It is necessary to be afraid, but it is equally necessary to understand. And the first step in understanding is to recognize that the problem of nuclear war is basically not technical but human and historical. If we are to avoid destruction we must first of all understand the human and historical context out of which destruction arises.[52]

In his capacity as a military adviser Dyson wrote an influential paper on the issue of possible US use of nuclear weapons in the Vietnam War. When a general said in a meeting "We should throw in a nuke once in a while to keep the other side guessing," Dyson became alarmed and obtained permission to write an objective report discussing the pros and cons of using such weapons from a purely military point of view. His report, declassified from SECRET in 2002, was sufficiently objective that both sides in the debate based their arguments on the report. Dyson says that the report showed that even from a narrow military point of view the US was better off not using nuclear weapons. Dyson stated on the Dick Cavett show that the use of nuclear weaponry was a bad idea for the US at the time because "our targets were large and theirs were small."

At the British Bomber Command, Dyson and colleagues proposed ripping out two gun turrets from the RAF Lancaster bombers, to cut the catastrophic losses due to German fighters in the Battle of Berlin. A Lancaster without turrets could fly Template:Convert faster and be much more maneuverable.

All our advice to the commander in chief [went] through the chief of our section, who was a career civil servant. His guiding principle was to tell the commander in chief things that the commander in chief liked to hear… To push the idea of ripping out gun turrets, against the official mythology of the gallant gunner defending his crew mates…was not the kind of suggestion the commander in chief liked to hear.[53]

Dyson opposed the Vietnam War, the Gulf War, and the invasion of Iraq. He supported Barack Obama in the 2008 US presidential election and The New York Times has described him as a political liberal.[12]

### The role of failure

You can't possibly get a good technology going without an enormous number of failures. It's a universal rule. If you look at bicycles, there were thousands of weird models built and tried before they found the one that really worked. You could never design a bicycle theoretically. Even now, after we've been building them for 100 years, it's very difficult to understand just why a bicycle works – it's even difficult to formulate it as a mathematical problem. But just by trial and error, we found out how to do it, and the error was essential.[54]

### On English academics

My view of the prevalence of doom-and-gloom in Cambridge is that it is a result of the English class system. In England there were always two sharply opposed middle classes, the academic middle class and the commercial middle class. In the nineteenth century, the academic middle class won the battle for power and status. As a child of the academic middle class, I learned to look on the commercial middle class with loathing and contempt. Then came the triumph of Margaret Thatcher, which was also the revenge of the commercial middle class. The academics lost their power and prestige and the business people took over. The academics never forgave Thatcher and have been gloomy ever since.[55]

### Science and religion

He is a non-denominational Christian and has attended various churches from Presbyterian to Roman Catholic. Regarding doctrinal or Christological issues, he has said, "I am neither a saint nor a theologian. To me, good works are more important than theology."[56]

Science and religion are two windows that people look through, trying to understand the big universe outside, trying to understand why we are here. The two windows give different views, but they look out at the same universe. Both views are one-sided, neither is complete. Both leave out essential features of the real world. And both are worthy of respect.

Trouble arises when either science or religion claims universal jurisdiction, when either religious or scientific dogma claims to be infallible. Religious creationists and scientific materialists are equally dogmatic and insensitive. By their arrogance they bring both science and religion into disrepute. The media exaggerate their numbers and importance. The media rarely mention the fact that the great majority of religious people belong to moderate denominations that treat science with respect, or the fact that the great majority of scientists treat religion with respect so long as religion does not claim jurisdiction over scientific questions.[56]

Dyson partially disagrees with the famous remark by his fellow physicist Steven Weinberg that "With or without religion, good people can behave well and bad people can do evil; but for good people to do evil—that takes religion."[57]

Weinberg's statement is true as far as it goes, but it is not the whole truth. To make it the whole truth, we must add an additional clause: "And for bad people to do good things—that [also] takes religion." The main point of Christianity is that it is a religion for sinners. Jesus made that very clear. When the Pharisees asked his disciples, "Why eateth your Master with publicans and sinners?" he said, "I come to call not the righteous but sinners to repentance." Only a small fraction of sinners repent and do good things but only a small fraction of good people are led by their religion to do bad things.[57]

While Dyson has labeled himself a Christian, he identifies himself as agnostic about some of the specifics of his faith.[58][59] For example, here is a passage from Dyson's review of The God of Hope and the End of the World from John Polkinghorne:

I am myself a Christian, a member of a community that preserves an ancient heritage of great literature and great music, provides help and counsel to young and old when they are in trouble, educates children in moral responsibility, and worships God in its own fashion. But I find Polkinghorne’s theology altogether too narrow for my taste. I have no use for a theology that claims to know the answers to deep questions but bases its arguments on the beliefs of a single tribe. I am a practicing Christian but not a believing Christian. To me, to worship God means to recognize that mind and intelligence are woven into the fabric of our universe in a way that altogether surpasses our comprehension.[60]

## References

1. Template:Cite news
2. Freeman Dyson: Disturbing the universe, pg 131, "I had finally become an American ... The decision to abjure my allegiance to Queen Elizabeth might have been a difficult one, but the Queen's ministers made it easy for me."
3. Board of Sponsors | Bulletin of the Atomic Scientists. Bulletin of the Atomic Scientists. Retrieved January 7, 2013.
4. The Scientist as Rebel at the Wayback Machine (archived September 27, 2007). Wild River Review Interview by Joy E. Stocke
5. Template:Cite web
6. Template:Cite web
7. "A Failure of Intelligence", Essay in Technology Review (November–December 2006)
8. Template:Cite web
9. Dyson, F., "What Can You Really Know", New York Review of Books (Nov 10, 2011)
10. Template:Cite web
11. Dawidoff, Nicholas. The Civil Heretic. The New York Times. March 25, 2009
12. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
13. Freeman J. Dyson, Disturbing the Universe, 1979
14. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
15. {{#invoke:Citation/CS1|citation |CitationClass=journal }}. [Note: this Ward letter opens with "It has been recently proven by Dyson ..."]
16. F. J. Dyson, E. H. Lieb, Selected papers by Freeman Dyson, AMS (1996).
17. John Derbyshire, Prime Obsession, 2004, ISBN 0309085497.
18. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
19. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
20. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
21. Template:Cite web
22. Template:Cite web
23. "Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent". William H. Press and Freeman Dyson. PNAS vol. 109 no. 26 pp 0409–10413
24. http://www.bbc.com/news/magazine-26858383
25. See excerpt from Digerati: Encounters with the Cyber Elite by John Brockman (HardWired Books, 1996)
26. {{#invoke:citation/CS1|citation |CitationClass=book }}
27. Progress In Religion, Edge.org (2000-05-16). Retrieved on 2014-11-18.
28. http://www.edge.org/discourse/dawkins_dyson.html
29. Template:Cite web
30. {{#invoke:citation/CS1|citation |CitationClass=book }}
31. Our Bio tech Future. Nybooks.com. Retrieved on 2011-10-07.
32. Dyson, 1999, The Sun, the Genome, and the Internet
33. Dyson, FJ, "The Greening of the Galaxy" in Disturbing the Universe, 1979
34. Interview by Monte Davis, October 1978 at the Wayback Machine (archived December 7, 1998). Retrieved on 2011-10-07.
35. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
36. 20 minutes into a video
37. Template:Cite speech
38. {{#invoke:citation/CS1|citation |CitationClass=book }}
39. Dyson, FJ, "Warm-blooded plants and freeze-dried fish: the future of space exploration. Played" The Atlantic Monthly, November 1997 Subscribers only
40. A Brownian‐Motion Model for the Eigenvalues of a Random Matrix, Freeman J. Dyson, J. Math. Phys. 3, 1191 (1962); http://dx.doi.org/10.1063/1.1703862
41. Template:Cite webdl
42. Don't fight, adapt at the Wayback Machine (archived January 10, 2009). Open Letter to the Secretary-General of the United Nations. National Post. December 13, 2007
43. Wiggles, Open Mind, 16 December 2007Template:Dead link
44. "Freeman Dyson Takes On The Climate Establishment", interview published June 2, 2009 by Yale University's Environment 360
45. Dyson in The New York Review of Book, 12 June 2008. Nybooks.com (2008-06-12). Retrieved on 2011-10-07.
46. Template:Cite web
47. Freeman J. Dyson, "Can we control the carbon dioxide in the atmosphere?", Energy, Volume 2, Issue 3, September 1977, Pages 287–291. Template:Hide in printTemplate:Only in print
48. Template:Cite news
49. {{#invoke:citation/CS1|citation |CitationClass=book }}
50. F.J. Dyson, "The Blood of a Poet" in Disturbing the Universe, 1979
51. F.J. Dyson, Weapons and Hope, 1984
52. F.J. Dyson, "The Children's Crusade" in Disturbing the Universe, 1979
53. Interview by Stewart Brand, February 1998. Wired.com (2009-01-04). Retrieved on January 07, 2013.
54. Template:Cite web
55. Templeton Prize Lecture. Edge.org (2000-05-16). Retrieved on 2011-10-07.
56. NYRB June 22, 2006. Nybooks.com. Retrieved on 2011-10-07.
57. {{#invoke:citation/CS1|citation |CitationClass=book }}
58. {{#invoke:citation/CS1|citation |CitationClass=book }}
59. Template:Cite web

## Further reading

### Famous articles by Freeman Dyson

• Birds and Frogs - American Mathematical Society[1]

format: plain


text:
# Vascular smooth muscle

Vascular smooth muscle refers to the particular type of smooth muscle found within, and composing the majority of the wall of blood vessels.

Vascular smooth muscle
Diagram showing the location of vascular smooth muscle cells.
Vascular smooth muscle cells, isolated from human aorta, growing and forming a monolayer in cell culture.
Details
Part ofsmooth muscle wall of blood vessels.
Identifiers
MeSHD009131
Anatomical terminology

## Structure

Vascular smooth muscle refers to the particular type of smooth muscle found within, and composing the majority of the wall of blood vessels.

### Nerve supply

Vascular smooth muscle is innervated primarily by the sympathetic nervous system through adrenergic receptors (adrenoceptors). The three types of adrenoceptors present are: ${\displaystyle \alpha _{1}}$ , ${\displaystyle \alpha _{2}}$  and ${\displaystyle \beta _{2}}$ . The main endogenous agonist of these cell receptors is norepinephrine (NE).

The adrenergic receptors exert opposite physiologic effects in the vascular smooth muscle under activation:

• ${\displaystyle \alpha _{1}}$  receptors. Under NE binding ${\displaystyle \alpha _{1}}$  receptors cause vasoconstriction (i.e. contraction of the vascular smooth muscle cells decreasing the diameter of the vessels). ${\displaystyle \alpha _{1}}$  receptors are activated in response to shock or low blood pressure as a defensive reaction trying to restore the normal blood pressure. Antagonists of ${\displaystyle \alpha _{1}}$  receptors (doxazosin, prazosin) cause vasodilation (i.e. decrease in vascular smooth muscle tone with increase of vessel diameter and decrease of the blood pressure). (See also receptor antagonist)
• ${\displaystyle \alpha _{2}}$  receptors. Agonists of ${\displaystyle \alpha _{2}}$  receptors in the vascular smooth muscle lead to vasoconstriction. However, in clinical practice drugs applied intravenously that are agonists of ${\displaystyle \alpha _{2}}$  receptors (clonidine) lead to powerful vasodilation, which causes a decrease in blood pressure by presynaptic activation of ${\displaystyle \alpha _{2}}$  receptors in the sympathetic ganglia. This presynaptic effect is predominant and completely overrides the vasoconstrictive effect of the ${\displaystyle \alpha _{2}}$  receptors in the vascular smooth muscle.[citation needed]
• ${\displaystyle \beta _{2}}$  receptors. Agonism of ${\displaystyle \beta _{2}}$  receptors causes vasodilation and low blood pressure (i.e. the effect is opposite of the one resulting from activation of ${\displaystyle \alpha _{1}}$  and ${\displaystyle \alpha _{2}}$  receptors in the vascular smooth muscle cells). Usage of ${\displaystyle \beta _{2}}$  receptor agonists as hypotensive agents is less widespread due to adverse effects such as unnecessary bronchodilation in lungs and increase in blood sugar levels.

## Function

Vascular smooth muscle contracts or relaxes to change both the volume of blood vessels and the local blood pressure, a mechanism that is responsible for the redistribution of the blood within the body to areas where it is needed (i.e. areas with temporarily enhanced oxygen consumption). Thus the main function of vascular smooth muscle tone is to regulate the caliber of the blood vessels in the body. Excessive vasoconstriction leads to high blood pressure, while excessive vasodilation as in shock leads to low blood pressure.

Arteries have a great deal more smooth muscle within their walls than veins, thus their greater wall thickness. This is because they have to carry pumped blood away from the heart to all the organs and tissues that need the oxygenated blood. The endothelial lining of each is similar.

Excessive proliferation of vascular smooth muscle cells contributes to the progression of pathological conditions, such as vascular inflammation, plaque formation, atherosclerosis, restenosis, and pulmonary hypertension.[1][2] Recent studies have shown that the majority of cells within atherosclerotic plaque, the predominant cause of heart attack and stroke, are vascular smooth muscle cell derived.[3]


text:
openvpn cannot resolve host address matlab bin matrix

# Desmos area between 3 curves

## rape my wife porn

forced haircut story

## razor e100 control module bypass

Use this calculator to learn more about the areas between two curves. Figure 2.3 (a)We can approximate the area between the graphs of two functions, f ( x) f ( x) and. g ( x), g ( x), with rectangles. (b) The area of a typical rectangle goes from one curve to the other. The height of each individual rectangle is.. Jun 12, 2021 · Q:- Find the area between curves: y=4x-x^2 and y=x Hit OK. You won't see any new curve 2. To change the color or style of an expression, long-hold the colored icon to the left of the expression. Integrals. 7. Use the Definite Integral tool to explore the area under a curve. Use Desmos to investigate the beautiful world of integral calculus. 2.. May 06, 2021 · I am trying to find the area between these three curves y=6/x, y=x+4 and y=x-4. Is there any good command to use in mathematica to make it simple?. Use this calculator to learn more about the areas between two curves. Figure 2.3 (a)We can approximate the area between the graphs of two functions, f ( x) f ( x) and. g ( x), g ( x), with rectangles. (b) The area of a typical rectangle goes from one curve to the other. The height of each individual rectangle is.. Get the free "Area Between Curves Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.. Area Between 2 Curves Murder Mystery February 03, 2019 I have posted a lot of murder mysteries already, but this one is a little different. Lines: Point Slope Form. May 3, 2020 #1 Hi Apologies if this is not in the correct forum. Idealy, I want to just shade the area between the curves f(y) = y+1 and g(y) = 3-y^ 2 . I don't care if I integrate in regards to dx or dy (depending on the integral) as long. Area between two curves desmos. Area Between Curves.Area Between 2 Curves Murder Mystery February 03, 2019 I have posted a lot of murder mysteries already, but this one is a little different. Lines: Point Slope Form. May 3, 2020 #1 Hi Apologies if this is not in the correct forum.The area is always the 'larger' function minus the 'smaller' function. Thanks! Enter f(x) 1. f. In our example, we are looking at speed (magnitude. Get the free "Area Between Curves Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.. 4 Answers. Sorted by: 2. Yes, as you guessed, a good way to do the integral is to find the intersection of the lines y = − x + 10 and y = 4 x (this occurs at x = 2 ), and divide the area into the portion to the left of the line x = 2 (bounded by y = 4 x above and y = 2 x below) and the portion to the right of the line x = 2 (bounded by y ....

## legendre differential equation calculator

An area between two curves can be calculated by integrating the difference of two curve expressions The cardioid is r = 1 + sinθ and the circle is r = 3sinθ The cardioid is r = 1 + sinθ and the circle is r = 3sinθ. ... (or "origin" in a rectangular grid) is the pole But when we graph the curves using the amazing Desmos calculator, there are.. You can play around with various Cubic Beziers shapes at desmos .com. When implementing a Cubic Bezier curve , the first oddity you will encounter is the fact that unlike polynomial When implementing a Cubic Bezier curve, the first oddity you will encounter is the fact that unlike polynomial equations, the Bezier does not give you y-coordinates as. Jul 02, 2022 · Tag: area between two curves desmos. Area Between Two Curves Calculator Online, Step by Step. Posted by mike — July 2, 2022 in EDUCATION ONLINE 0.. cheap boxing gym singapore New Desmos Statistics Package. Calculus Questions: (a) Find the area of one loop. Finding the correlation and lines and curves of best fit is pretty easy and works really well. Day 87: Curve-fitting with Desmos College-Prep Physics : Curve-fitting by hand can be tedious and linerization can be confusing. Area Between Curves Loading... Area Between Curves Loading... Untitled Graph Log InorSign Up 1 2 powered by powered by "x" x "y" y "a" squared a 2 "a" Superscript, "b" , Baseline a b 7 7 8.

## udmse datasheet

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and. Find the area A between the curves. y = 1 + x 2. y = 3 + x. Introduction. To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration.You can then divide the area into vertical or horizontal strips and integrate. Comment. Sketch the area and find points of intersection. Yes, if there exists the area between two curves, then it will always be a non-negative value. The area can be 0 or any positive value, but it can never be negative. The area between two curves is calculated by the formula: Area = ∫ b a [f (x) −g(x)] dx ∫ a b [ f ( x) − g ( x)] d x which is an absolute value of the area.

## private homemade amateur teen girlfriend

To use the area between the two curves calculator, follow these steps: Step 1: Enter the smaller function, the larger function, and the limit values in the given input fields. Step 2: To calculate the area, click the Calculate Area button. Step 3: Finally, in the new window, you will see the area between these two curves.. Free area under between curves calculator - find area between functions step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept.

## fantasy football cage punishment

We first calculate the area A of region A as being the area of a region between two curves y = 3 x - x 2 and y = 0.5 x, x= 0 and the point of intersection of the two curves. First find the point of intersection by solving the system of equations. y = 3x - x2 and y = 0.5 x. which gives. 3x - x2 = 0.5 x. 2.5x - x2 = 0.. Idealy, I want to just shade the area between the curves f(y) = y+1 and g(y) = 3-y^ 2 . I don't care if I integrate in regards to dx or dy (depending on the integral) as long. Area between two curves desmos. region should yield the area between the curves : Z 4 2 (2x+ 7) x2 1 dx= Z 4 2 2x+ 8 x2 dx = x2 + 8x x3 3 4 2 = 16 + 32 64 3 4 16 + 16 3 = 48 64 3 + 12 8 3 = 60 72 3 = 60 24 = 36: So the area between the curves is 100 3 . 2.What is the volume of the solid obtained by rotating the region bounded by the graphs of y= p x,.. Area Between Curves . Conic Sections: Parabola and Focus. example. ... how much does it cost to import a car from japan to california wellmont theater general admission cinestill film. Area Between 2 Curves Murder Mystery February 03, 2019 I have posted a lot of murder mysteries already, but this one is a little different. Lines: Point Slope Form. May 3, 2020 #1 Hi Apologies if this is not in the correct forum.

## astd trello discord

. Summing vertically to find area between 2 curves Likewise, we can sum vertically by re-expressing both functions so that they are functions of y and we find: A=int_c^d(x_2-x_1)dy Notice the c and d as the limits on the 1 2 3. An area between two curves can be calculated by integrating the difference of two curve expressions The cardioid is r = 1 + sinθ and the circle is r = 3sinθ The cardioid is r = 1 + sinθ and the circle is r = 3sinθ. ... (or "origin" in a rectangular grid) is the pole But when we graph the curves using the amazing Desmos calculator, there are.. I'm trying to graph the area between curves in Geogebra by using the "IntegralBetween" function, but when I download it and attach it to the Step, I. Feb 23, 2012 · Idealy, I want to just shade the area between the curves f(y) = y+1 and g(y) = 3-y^2. I don't care if I integrate in regards to dx or dy (depending on the integral) as long as I am able to shade, but seeing if I can shade in regards to dy would be good. Any ideas on how to do this would be appreciated. Thank you!.

## how to generate keystore file from certificate using keytool

In the coordinate plane, the total area is occupied between two curves and the area between curves calculator calculates the area by solving the definite integral between the two different functions. So, let’s begin to read how to find the area between two curves using definite integration, but first, some basics are the thing you need to consider right now!. Dec 27, 2021 · The area between two curves calculator desmos. The area between two curves calculator (polar) is also available online very easily. Actually, you do not have to remember the formula for calculating the area between two polar curves. So, this calculation becomes a lot easier. Firstly, plug in the outer curve’s equation in the f(θ) box.. Apologies if this is not in the correct forum. I have used Desmos to help visualise graphs in which areas are calculated using definite integrals. You can use the sliders to change the limits of the x values and find the area below the curve and the x-axis. In the question it says find the area of the curve. and the y axis, y=2 and y=4.Solution: Calculating area under curve for given function. Dec 27, 2021 · The area between two curves calculator desmos. The area between two curves calculator (polar) is also available online very easily. Actually, you do not have to remember the formula for calculating the area between two polar curves. So, this calculation becomes a lot easier. Firstly, plug in the outer curve’s equation in the f(θ) box..

## an error occurred while processing your request reference 30

The procedure to use the area under the curve calculator is as follows: Step 1: Enter the function and limits in the respective input field. Step 2: Now click the button "Calculate Area " to get the output. Step 3: Finally, the area under the curve function will be displayed in the new window.. The concept of finding the area under the curve is one that many students struggle with, so using a visual tool like Desmos will allow students to see the concept much better, and hopefully lead to a better understanding overall.. region should yield the area between the curves : Z 4 2 (2x+ 7) x2 1 dx= Z 4 2 2x+ 8 x2 dx = x2 + 8x x3 3 4 2 = 16 + 32 64 3 4 16 + 16 3 = 48 64 3 + 12 8 3 = 60 72 3 = 60 24 = 36: So the area between the curves is 100 3 . 2.What is the volume of the solid obtained by rotating the region bounded by the graphs of y= p x,. The concept of finding the area under the curve is one that many students struggle with, so using a visual tool like Desmos will allow students to see the concept much better, and hopefully lead to a better understanding overall.. Section 7-6 : Area and Volume Formulas. In this section we will derive the formulas used to get the area between two curves and the volume of a solid of revolution. Area Between Two Curves. Use this calculator to learn more about the areas between two curves. Figure 2.3 (a)We can approximate the area between the graphs of two functions, f ( x) f ( x) and. g ( x), g ( x), with rectangles. (b) The area of a typical rectangle goes from one curve to the other. The height of each individual rectangle is.

## mounjaro vs wegovy

Area Between 2 Curves Murder Mystery February 03, 2019 I have posted a lot of murder mysteries already, but this one is a little different. Lines: Point Slope Form. May 3, 2020 #1 Hi Apologies if this is not in the correct forum. We now care about the y-axis. So let's just rewrite our function here, and let's rewrite it in terms of x. So if y is equal to 15 over x, that means if we multiply both sides by x, xy is equal to 15. And if we divide both sides by y, we get x is equal to 15 over y.. The concept of finding the area under the curve is one that many students struggle with, so using a visual tool like Desmos will allow students to see the concept much better, and hopefully lead to a better understanding overall..

## hypno girl videos

If we add all these typical rectangles, starting from a and finishing at b, the area is approximately: sum_(x=a)^b(y_2-y_1)Delta x Now if we let Δx → 0, we can find the exact area by integration: A=int_a^b(y_2-y_1)dx Summing vertically to find area between 2 curves. The concept of finding the area under the curve is one that many students struggle with, so using a visual tool like Desmos will allow students to see the concept much better, and hopefully lead to a better understanding overall.. Calculating area for polar curves, means we're now under the Polar Coordinateto do integration. And instead of using rectangles to calculate the area, we are to use triangles to integrate the area. Jun 12, 2021 · Q:- Find the area between curves: y=4x-x^2 and y=x Hit OK. You won't see any new curve 2. To change the color or style of an expression, long-hold the colored icon to the left of the expression. Integrals. 7. Use the Definite Integral tool to explore the area under a curve. Use Desmos to investigate the beautiful world of integral calculus. 2.. Question: Inc 1. Please follow the steps below to find the area using an online area between two curves calculator: Step 1: Go to Cuemath's online area between two curves calculator. Step 2: Enter the larger function and smaller function in the given input box of the area between two curves calculator. Step 3: Enter the limits (Lower and upper. Yes, if there exists the area between two curves, then it will always be a non-negative value. The area can be 0 or any positive value, but it can never be negative. The area between two curves is calculated by the formula: Area = ∫ b a [f (x) −g(x)] dx ∫ a b [ f ( x) − g ( x)] d x which is an absolute value of the area. Question: Inc 1. Please follow the steps below to find the area using an online area between two curves calculator: Step 1: Go to Cuemath's online area between two curves calculator. Step 2: Enter the larger function and smaller function in the given input box of the area between two curves calculator. Step 3: Enter the limits (Lower and upper. The procedure to use the area under the curve calculator is as follows: Step 1: Enter the function and limits in the respective input field. Step 2: Now click the button "Calculate Area " to get the output. Step 3: Finally, the area under the curve function will be displayed in the new window.. Free area under between curves calculator - find area between functions step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept. Method 1 Use the equations of the curves as y as a function of x and integrate on x using the first formula above. Figure 4. Area between curves example 2. The region from x = -2 to x = 0 is under the curve y = √ (x + 2) andarea.

## a nurse is caring for a client who is postoperative following a craniotomy

Conic Sections: Parabola and Focus. example. Conic Sections: Ellipse with Foci. Jun 12, 2021 · Q:- Find the area between curves: y=4x-x^2 and y=x Hit OK. You won't see any new curve 2. To change the color or style of an expression, long-hold the colored icon to the left of the expression. Integrals. 7. Use the Definite Integral tool to explore the area under a curve. Use Desmos to investigate the beautiful world of integral calculus. 2.. The procedure to use the area under the curve calculator is as follows: Step 1: Enter the function and limits in the respective input field. Step 2: Now click the button "Calculate Area " to get the output. Step 3: Finally, the area under the curve function will be displayed in the new window.. To that end, we have provided a partial list of common symbols supported in Desmos — along with their associated commands: The Multiplication symbol can be obtained by typing * ( Shift + 8 on US keyboards). The Division line can be obtained by typing / (i.e., backslash). π can be obtained by typing pi, and θ by theta. We now care about the y-axis. So let's just rewrite our function here, and let's rewrite it in terms of x. So if y is equal to 15 over x, that means if we multiply both sides by x, xy is equal to 15. And if we divide both sides by y, we get x is equal to 15 over y.. Thanks to all of you who support me on Patreon. You da real mvps! \$1 per month helps!! :) https://www.patreon.com/patrickjmt !! Area of a Region Bounded b.... We first calculate the area A of region A as being the area of a region between two curves y = 3 x - x 2 and y = 0.5 x, x= 0 and the point of intersection of the two curves. First find the point of intersection by solving the system of equations. y = 3x - x2 and y = 0.5 x. which gives. 3x - x2 = 0.5 x. 2.5x - x2 = 0.. Dec 27, 2021 · The area between two curves calculator desmos. The area between two curves calculator (polar) is also available online very easily. Actually, you do not have to remember the formula for calculating the area between two polar curves. So, this calculation becomes a lot easier. Firstly, plug in the outer curve’s equation in the f(θ) box.. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators .... Use this calculator to learn more about the areas between two curves. Figure 2.3 (a)We can approximate the area between the graphs of two functions, f ( x) f ( x) and. g ( x), g ( x), with rectangles. (b) The area of a typical rectangle goes from one curve to the other. The height of each individual rectangle is. The procedure to use the area between the two curves calculator is as follows: Step 1: Enter the smaller function, larger function and the limit values in the given input fields. Step 2: Now click the button “Calculate Area” to get the output. Step 3: Finally, the area between the two curves will be displayed in the new window.

## jury duty alameda county covid

The Desmos Math Curriculum. Celebrate every student’s brilliance. Math 6–8 is available now. Algebra 1 will be available for the 2022–2023 school year. Learn More.. Area Between Two Curves Calculator: Definition. It is an online calculation tool that computes the area between curves (the enclosed shape). With this tool, you can save yourself the agonies of manually calculating extended functions, which may confuse you in the process.. If we add all these typical rectangles, starting from a and finishing at b, the area is approximately: sum_(x=a)^b(y_2-y_1)Delta x Now if we let Δx → 0, we can find the exact area by integration: A=int_a^b(y_2-y_1)dx Summing vertically to find area between 2 curves.

Area Between Curves.Area Between 2 Curves Murder Mystery February 03, 2019 I have posted a lot of murder mysteries already, but this one is a little different. Lines: Point Slope Form. May 3, 2020 #1 Hi Apologies if this is not in the correct forum.The area is always the 'larger' function minus the 'smaller' function. Thanks! Enter f(x) 1. f. In our example, we are looking at speed (magnitude. The Graph Setting Menu in Desmos . In addition, underneath the wrench icon, you should be able to see a. The value of the definite integral of the difference f (x)-g (x) from a to b is given in cell B10 for comparison with the area between the curves . Drag the slider "Select Interval" to see the area in each interval. Please follow the steps below to find the area using an online area between two curves calculator: Step 1: Go to Cuemath’s online area between two curves calculator. Step 2: Enter the larger function and smaller function in the given input box of the area between two curves calculator. Step 3: Enter the limits (Lower and upper bound) values .... As a fun little exercise, try adding in the ability to switch between LRAM, RRAM, and MRAM. Without giving away too much, a good first step is to make a slider -1 —> 1, with step one, where -1 is LRAM, 0 is MRAM, etc. I don’t know how much you’ve learned about calculus yet, but if you want some more cool calc and non calc projects to try. Jul 02, 2022 · Tag: area between two curves desmos. Area Between Two Curves Calculator Online, Step by Step. Posted by mike — July 2, 2022 in EDUCATION ONLINE 0..

## strange disappearances in the woods

Get the free "Area Between Curves Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. To add the widget to iGoogle, click here.On the next page click the. Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and. We now care about the y-axis. So let's just rewrite our function here, and let's rewrite it in terms of x. So if y is equal to 15 over x, that means if we multiply both sides by x, xy is equal to 15. And if we divide both sides by y, we get x is equal to 15 over y. These right over here are all going to be equivalent.. 4 Answers. Sorted by: 2. Yes, as you guessed, a good way to do the integral is to find the intersection of the lines y = − x + 10 and y = 4 x (this occurs at x = 2 ), and divide the area into the portion to the left of the line x = 2 (bounded by y = 4 x above and y = 2 x below) and the portion to the right of the line x = 2 (bounded by y .... May 06, 2021 · I am trying to find the area between these three curves y=6/x, y=x+4 and y=x-4. Is there any good command to use in mathematica to make it simple?. Find the area A between the curves. y = 1 + x 2. y = 3 + x. Introduction. To find the Introduction. To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration.You can then divide the area into vertical or horizontal strips and integrate. Area in Rectangular Coordinates. Recall that the area under the graph of a continuous function f (x) between the vertical lines x = a, x = b can be computed by the definite integral: where F (x) is any antiderivative of f (x). Figure 1. We can extend the notion of the area under a curve and consider the area > of the region between two curves. As far as the bounding curves can be easily expressed either as y = f ( x) or x = f ( y) , there are more options to calculate the area. For example, we can recognize that while y changes its values from 2 to 3, for every value of y , x changes accordingly from 3 − y to 1 4 y 2 . Hence.

## kpop idols who are twice fans

The area calculation is straightforward in blocks where the two curves don't intersect: thats the trapezium as has been pointed out above. If they intersect, then you create two triangles between x [i] and x [i+1], and you should add the area of the two. I am trying to find the area between these three curves y=6/x, y=x+4 and y=x-4. Is there any good command to use in mathematica to make it simple?. Find the area A between the curves. y = 1 + x 2. y = 3 + x. Introduction. To find the Introduction. To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration.You can then divide the area into vertical or horizontal strips and integrate.

## ikman lk house colombo

Find the area A between the curves. y = 1 + x 2. y = 3 + x. Introduction. To find the area between two curves you should first find out where the curves meet, which determines the endpoints of integration.You can then divide the area into vertical or horizontal strips and integrate. Comment. Sketch the area and find points of intersection. Example Calculate the shaded area between the curve and the $$x$$ -axis as shown below. how to win a rental application; how to convert lowercase to uppercase in c .... Find the area between the polar curves. r = 2 r=2 r = 2. r = 3 + 2 sin θ r= 3 +2\sin {\theta} r = 3 + 2 sin θ. Since the problem doesn't give us an interval over which to evaluate the area, we'll need to find the points of intersection of the curves. We'll set the polar curves equal to each other and solve for θ \theta θ. traffic simulator. Get the free "Area Between Curves Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. To add the widget to iGoogle, click here.On the next page click the.

## openwrt vs ubuntu

To work out the area below the $$x$$-axis uses the same technique as for above the $$x$$-axis. Example Calculate the shaded area between the curve and the $$x$$ -axis as shown below.. Method 1 Use the equations of the curves as y as a function of x and integrate on x using the first formula above. Figure 4. Area between curves example 2. The region from x = -2 to x = 0 is under the curve y = √ (x + 2) andarea. May 25, 2020 · Finding the area between two polar curves. Example. Find the area between the polar curves. r = 2 r=2 r = 2. r = 3 + 2 sin θ r=3+2\sin {\theta} r = 3 + 2 sin θ. Since the problem doesn’t give us an interval over which to evaluate the area, we’ll need to find the points of intersection of the curves.. Quadric surfaces are the graphs of equations that can be expressed in the form. When a quadric surface intersects a coordinate plane, the trace is a conic section. An ellipsoid is a surface described by an equation of the form Set to. I am trying to find the area between these three curves y=6/x, y=x+4 and y=x-4. Is there any good command to use in mathematica to make it simple?. We first calculate the area A of region A as being the area of a region between two curves y = 3 x - x 2 and y = 0.5 x, x= 0 and the point of intersection of the two curves. First find the point of intersection by solving the system of equations. y = 3x - x2 and y = 0.5 x. which gives. 3x -.

## look i am a man of very few words i am not playing with anyone

Area Between Curves Loading... Area Between Curves Loading... Untitled Graph Log InorSign Up 1 2 powered by powered by "x" x "y" y "a" squared a 2 "a" Superscript, "b" , Baseline a b 7 7 8. 4 Answers. Sorted by: 2. Yes, as you guessed, a good way to do the integral is to find the intersection of the lines y = − x + 10 and y = 4 x (this occurs at x = 2 ), and divide the area into the portion to the left of the line x = 2 (bounded by y = 4 x above and y = 2 x below) and the portion to the right of the line x = 2 (bounded by y. To that end, we have provided a partial list of common symbols supported in Desmos — along with their associated commands: The Multiplication symbol can be obtained by typing * ( Shift + 8 on US keyboards). The Division line can be obtained by typing / (i.e., backslash). π can be obtained by typing pi, and θ by theta. Apologies if this is not in the correct forum. I have used Desmos to help visualise graphs in which areas are calculated using definite integrals. You can use the sliders to change the limits of the x values and find the area below the curve and the x-axis. In the question it says find the area of the curve. and the y axis, y=2 and y=4.Solution: Calculating area under curve for given function. region should yield the area between the curves : Z 4 2 (2x+ 7) x2 1 dx= Z 4 2 2x+ 8 x2 dx = x2 + 8x x3 3 4 2 = 16 + 32 64 3 4 16 + 16 3 = 48 64 3 + 12 8 3 = 60 72 3 = 60 24 = 36: So the area between the curves is 100 3 . 2.What is the volume of the solid obtained by rotating the region bounded by the graphs of y= p x,.. Section 7-6 : Area and Volume Formulas. In this section we will derive the formulas used to get the area between two curves and the volume of a solid of revolution. Area Between Two Curves.

## peterbilt sleeper trucks for sale

Question 1: Calculate the total area of the region bounded between the curves y = 6x – x 2 and y = x 2. Answer : The intersection points of the curve can be solved by putting the value of y = x 2 into the other equation. We then get: x 2 = 6x – x 2. 2x 2 -6x = 0. 2x (x – 3) = 0. The radius of curvature of a curve at a point is called the inverse of the curvature of the curve at this point: Hence for plane curves given by the explicit equation the radius of curvature at a. The Wikimedia Endowment provides dedicated funding to realize the power and promise of Wikipedia and related Wikimedia projects for the long term. You will use the Desmos applet for a definite integral. Areas under both curves are shaded. Follow these steps to shade the area below the curved line: 1: Add Helper Column to Data- To add a shaded area to this line chart, we need a helping column that has the exact same value as the original series has.

### knn numerical example pdf

boothbay ymca pool schedule


text:
# numpy.random.vonmises¶

numpy.random.vonmises(mu, kappa, size=None)

Draw samples from a von Mises distribution.

Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi].

The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution.

Parameters: mu : float Mode (“center”) of the distribution. kappa : float Dispersion of the distribution, has to be >=0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned. samples : scalar or ndarray The returned samples, which are in the interval [-pi, pi].

scipy.stats.distributions.vonmises
probability density function, distribution, or cumulative density function, etc.

Notes

The probability density for the von Mises distribution is

p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)},

where \mu is the mode and \kappa the dispersion, and I_0(\kappa) is the modified Bessel function of order 0.

The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science.

References

Abramowitz, M. and Stegun, I. A. (ed.), Handbook of Mathematical Functions, New York: Dover, 1965.

von Mises, R., Mathematical Theory of Probability and Statistics, New York: Academic Press, 1964.

Examples

Draw samples from the distribution:

>>> mu, kappa = 0.0, 4.0 # mean and dispersion
>>> s = np.random.vonmises(mu, kappa, 1000)

Display the histogram of the samples, along with the probability density function:

>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
>>> count, bins, ignored = plt.hist(s, 50, normed=True)
>>> x = np.arange(-np.pi, np.pi, 2*np.pi/50.)
>>> y = -np.exp(kappa*np.cos(x-mu))/(2*np.pi*sps.jn(0,kappa))
>>> plt.plot(x, y/max(y), linewidth=2, color='r')
>>> plt.show()

#### Previous topic

numpy.random.uniform

#### Next topic

numpy.random.wald


text:
# Solve the Following Problem. When Two Resistors Are Connected in Series, Their Effective Resistance is 80 W. When They Are Connected in Parallel, Their Effective Resistance is 20 W. - Science and Technology

Short Note
Sum

Solve the following problem.
When two resistors are connected in series, their effective resistance is 80 W. When they are connected in parallel, their effective resistance is 20 W. What are the values of the two resistances?    (Answer : 40 W , 40 W)

#### Solution

Let the two resistances be R_1 and R_2 . Therefore,
R_1 + R_2 = 80 Ω
or , R_1 = 80 - R_2 ....(i)
and
1/R_1 + 1/R_2 = 1/20
⇒ R_1R_2 = 20(R_1+R_2)
As , R_1 = 80-R_2
⇒ (80 - R_2)R_2 = 20(80 - R_2 + R_2)
80R_2^2 - R_2 = 1600
R_2^2 - 80R_2 + 1600 = 0
(R_2 - 40) (R_2 - 40) = 0
⇒ R_2 = 40 Ω
From (i) , we get
R_1 = 80-40 =40 Ω

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Science and Technology 9th Standard Maharashtra State Board
Chapter 3 Current Electricity
Exercise | Q 9.2 | Page 45


text:
# Talk:Story telling

## The Code

Very good but where's the code ? -- Derek Ross | Talk 20:20, 13 October 2006 (PDT)

It will come, just be patient. I want to rewrite it before putting it here. Lehalle
Excellent ! -- Derek Ross | Talk 16:20, 27 October 2006 (PDT)

## Questions

Also there seems to be a lot of category confusion in the mathematics. In particular it's still very unclear to me whether E is supposed to be a set, or a natural number. In some places it's used as the former in other places as the latter. -- Derek Ross | Talk 20:35, 13 October 2006 (PDT)

E is into the set of of subsets of $\mathcal{E}$, so it's a subset of $\mathcal{E}$, where do you think it's used as a natural number? Lehalle
You show E being used as an indexing subscript of τ, which is fair enough. But then further on you show τ with subscripts 1, 2, 3, etc. This implies (to me at any rate) that τ can be indexed by natural numbers and thus that E can be a natural number. Of course this conflicts with the explicit definition of E as a member of the powerset of $\mathcal{E}$ which cannot include natural numbers. Hence my confusion. Can you clarify things ? I'd appreciate it as this looks interesting. -- Derek Ross | Talk 16:20, 27 October 2006 (PDT)

##  Scheme pieces of code

Here are some hints about a scheme implementation:

<<story_elements.sc>>=
;; typical element
(define an-element '((properties ((name "Alpha") (type "character") (age 28)))
(relations ((knows
(lambda (e) (if (prop-equal? e (quote name) "Beta") 3 0)))))))
(define element-2 '((properties ((name "Beta")))))
;; some simple functions
(define (prop-equal? e key value) (equal? (prop-e e key) value))


text:
Public Group

# design time

This topic is 5108 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I am currently trying to built the game "chicken invaders". It is a simple game where the user has to fire bullets and kill many chickens which are coming down on him. The user moves sideways and the chickens release eggs which can kill the user. The user fires bullets . If chickens get hit, they die and a bone falls down which if taken gives the user some points. There is a special packet which falls randomly in each level. If the user can collect that, then each firing releases 2 bullets instead of one (This goes on increasing till 7 bullets per shot)...blah blah.... I have already spent like 2 days on planning out the classes and still i have not been able to come up with something good. I was wondering if i am a fool :) so , please tell me what is the approx time that should be required for planning this kind of a game?? Thanx Mishal

##### Share on other sites
If you are new to programming (I guess) you will need much more time I think. Just try out your concept. If you feel you can't get far with it, just forgett the old one and think for a new way to do it. Give yourselfe some time and don't make haste...

##### Share on other sites
Hi,

Quote:
 Original post by mishal153I have already spent like 2 days on planning out the classes and still i have not been able to come up with something good. I was wondering if i am a fool :) so , please tell me what is the approx time that should be required for planning this kind of a game??

Well, tell us what you came up with, otherwise, how would we know if you are a fool or not? [smile]

Seriously though, designing is hard. If you've never done it, and if you've never been taught it, it is even so much harder. But practice makes perfect, so keep at it.

As far as "something good" is concerned, thing is, it's hard to say if something is good or not until you start coding, when you are just learning to design. And chances are, it's no good. Except you won't know untill you try implementing it. But the whole idea of design is to get an idea for good coding and then code it, but you are then doing something exactly opposite, so it doesn't make sense. But that's the way it is. [smile]

One bit of advice: don't overdesign. Countless are the times when I wanted to start a small little game, so that for once I would actually finish one, and then I would go on and design, and I would try to make say my rendering class so flexible that it could not only draw my game, but a whole family of related ones. And so I would get so bogged down in flexibility, that even this simple game would never see the light of day.

Any ways, post an outline of your idea here somewhere, and you are bound to get plenty of critique on it. [smile] (I mean, the design idea. The game idea we pretty much already got.)

Vovan

##### Share on other sites
I'm a relitivly new c++ programmer, but i have done aa lot of qbasic before this.

it usually takes me about 2 weeks to get to the point where i could finish the project, but i never do because i can't be bothered. usually i just start coding and then add and update stuff when i have a better idea, i don't like the planning part

##### Share on other sites
That sounds like a fun game!! I think I'll steal your idea! ha ha just kidding... but it does sound like a fun game and not too difficult to do.

Don't worry about figuring out how to implement every little detail up front. By the time your are done, your finished game will be very different from your original design anyway. Start with a basic framework, then work on a complete framework, then implement some basic (non-interactive) game logic and minimal rendering (enough to verify the game logic), then get the input working, then more game logic and a basic HUD, ...

##### Share on other sites
Quote:
 Original post by JohnBoltonThat sounds like a fun game!! I think I'll steal your idea! ha ha just kidding... but it does sound like a fun game and not too difficult to do.Don't worry about figuring out how to implement every little detail up front. By the time your are done, your finished game will be very different from your original design anyway. Start with a basic framework, then work on a complete framework, then implement some basic (non-interactive) game logic and minimal rendering (enough to verify the game logic), then get the input working, then more game logic and a basic HUD, ...

pretty sure the game already exists, so don't think he would mind if you did one too :)

Good points though, and try not to over plan.. Like I said before, if you guestimate the game will take say 2 weeks to make, don't sit there and plan everything out for a good 7 days..
Make a pretty decent plan but it should take you as long to plan a game as it takes you to make it or else you are going to spend all your time planning and none programming

##### Share on other sites
class Thing {  public:    virtual void update( DWORD delta ) = 0;    virtual void draw( DWORD curTime ) = 0;};class Cannon : public Thing {  ...};class Chicken : public Thing {  ...};class Egg : public Thing {  ...};...std::list< Thing * > gStuff;bool gRunning = true;Cannon * gCannon;void Initialize() {  gStuff.push_back( new Chicken );  gCannon = new Cannon;  gStuff.push_back( gCannon );}class Update {  public:    DWORD stepSize_;    Update( DWORD step ) : stepSize_( step ) {}    void operator()( Thing * t ) {      t->update( stepSize_ );    }};class Draw {  ...};void MainLoop() {  DWORD now = timeGetTime();  while( gRunning ) {    DWORD then = timeGetTime();    while( then > now + TIMESTEP_SIZE ) {      Commands cmds;      ReadInputAndConvertToCommands( &cmds );      gCannon->readCommands( &cmds );      DWORD dTime = then-now;      std::for_each( gStuff.begin(), gStuff.end(), Update( TIMESTEP_SIZE ) );      now += TIMESTEP_SIZE;    }    std::for_each( gStuff.begin(), gStuff.end(), Draw( then ) );  }}

Obviously, Chicken::step() moves the chicken, and checks whether any bullet has hit it, and checks whether it's time to drop an egg; if so, it creates a new Egg and adds it to the list of things. Similarly, each other object step() function updates the state of that specific concrete object.

1. 1
2. 2
frob
16
3. 3
4. 4
5. 5

• 18
• 13
• 14
• 76
• 22
• ### Forum Statistics

• Total Topics
632138
• Total Posts
3004356

×


text:
Exercise 16.2 Introduction to Graphs- NCERT Solutions Class 8

Chapter 16 Ex.16.2 Question 1

If $$21y5$$ is a multiple of $$9,$$ where $$y$$ is a digit, what is the value of $$y$$?

Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. $$y.$$

Reasoning:

If the sum of all digits of a number is equal to $$9,$$ then the number is a multiple of $$9.$$

Steps:

If a number is a multiple of $$9,$$ then the sum of its digits will be divisible by $$9.$$

Sum of digits of

$21y5 = 2 + 1 + y + 5 = 8 + y$

Hence, $$8 + y$$ should be a multiple of $$9.$$

This is possible when $$8 + y$$ is any one of these numbers $$0,\; 9, \;18, \;27,$$ and so on ...

However, since $$y$$ is a single digit number, this sum can be $$9$$ only.

\begin{align} 8 + y &= 9\\ y &= 9 - 8\\ y &= 1 \end{align}

Therefore, $$y$$ should be $$1$$ only.

Chapter 16 Ex.16.2 Question 2

If $$31z5$$ is a multiple of $$9,$$ where $$z$$ is a digit, what is the value of $$z$$?

You will find that there are two answers for the last problem. Why is this so?

Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. $$y.$$

Reasoning:

If the sum of all digits of a number is equal to $$9,$$ then the number is a multiple of $$9.$$

Steps:

If a number is a multiple of $$9,$$ then the sum of its digits will be divisible by $$9.$$

Sum of digits of

$31z\,5 = 3 + 1 + z + 5 = 9 + z$

Hence, $$9 + z$$ should be a multiple of $$9.$$

This is possible, when $$9 + z$$ is any one of these numbers $$0,\; 9,\; 18,\; 27,$$ and so on ...

However, since $$z$$  is a single digit number, this sum can be either $$9$$ or $$18.$$

$$9+z =9\\z=9-9\\z=0$$

Therefore, $$z$$ should be either $$0$$ or $$9.$$

Chapter 16 Ex.16.2 Question 3

If $$24x$$ is a multiple of $$3,$$ where $$x$$ is a digit, what is the value of $$x$$?

(Since $$24x$$ is a multiple of $$3,$$ its sum of digits $$6+x$$ is a multiple of $$3$$ ,so $$6+x$$ is one of these numbers: $$0, 3, 6, 9, 12, 15, 18...$$ But since $$x$$ is a digit, it can only be that $$6+x=\,6$$ or $$9$$ or $$12$$ or $$15.$$ Therefore, $$x=0$$ or $$3$$ or $$6$$ or $$9.$$ Thus, $$x$$ can have any of four different values)

Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. $$x.$$

Reasoning:

If the sum of the digits of a number is divisible by $$3,$$ then the given number is a multiple of $$3.$$

Steps:

Since $$24x$$ is a multiple of $$3,$$ the sum of its digits is a multiple of $$3.$$

Sum of digits of

$$24x = 2 + 4 + x = 6+ x$$

Hence, $$6+x$$ is a multiple of $$3.$$

This is possible when $$6+x$$ is any one of these numbers $$0, \;3,\; 6,\; 9,$$ and so on ...

\begin{align}\text{For},&\\&6 + x = 0 \Rightarrow x = 0 - 6 = - 6\\\text{For},&\\&6 + x = 3 \Rightarrow x = 3 - 6 = - 3\\\text{For},&\\&6 + x = 6 \Rightarrow x = 6 - 6 = 0\\\text{For},&\\&6 + x= 9 \Rightarrow x = 9 - 6 = 3\\\text{For},&\\&6+x =12 \Rightarrow x=12-6=6\\&\dots \text{so on} \end{align}

Since $$x$$ is a single digit number, the sum of the digits can be $$6$$ or $$9$$ or $$12$$ or $$15$$ and thus, the value of comes to $$0$$ or $$3$$ or $$6$$ or $$9$$ respectively.

Thus, $$x$$ can have its value as any of the four different values $$0,\; 3,\; 6,\;$$ or $$9.$$

Chapter 16 Ex.16.2 Question 4

If $$31z5$$ is a multiple of $$3,$$ where $$z$$ is a digit, what might be the values of $$z$$?

Solution

What is known?

A puzzled number

What is unknown?

Value of the alphabet i.e. $$z.$$

Reasoning:

If sum of the digits of a number is divisible by $$3,$$ then the given number is a multiple of $$3.$$

Steps:

Since $$31z5$$ is a multiple of $$3,$$ the sum of its digits will be a multiple of $$3.$$

That is, $$3 + 1 + z + 5 = 9 + z$$ is a multiple of $$3.$$

This is possible when $$9 + z$$ is any one of $$0,\;3,\; 6, \;9,\; 12,\; 15,\; 18,$$ and so on ...

\begin{align} \text{For},&\\&9 + z = 0 \Rightarrow z = 0 - 9 = - 9\\ \text{For},&\\&9 + z = 3 \Rightarrow z = 3 - 9 = - 6\\ \text{For},&\\&9 + z = 6 \Rightarrow z = 6 - 9 = - 3\\ \text{For},&\\&9 + z = 9 \Rightarrow z = 9 - 9 = 0\\ \text{For},&\\&9 + z = 12 \Rightarrow z = 12 - 9 = 3\\ \text{For},&\\&9 + z = 15 \Rightarrow z = 15 - 9 = 6\\ \text{For},&\\&9 + z = 18 \Rightarrow z = 18 - 9 = 9 \end{align}

Since $$z$$ is a single digit number, the value of $$9 + z$$ can only be $$9$$ or $$12$$ or $$15$$ or $$18$$ and thus, the value of $$z$$ comes to $$0$$ or $$3$$ or $$6$$ or $$9$$ respectively.

Thus, $$z$$ can have its value as any one of the four different values $$0, \;3,\; 6,\;$$ or $$9.$$

Instant doubt clearing with Cuemath Advanced Math Program