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Posts posted by Air


cos^2
in Mathematics
I've often seen in equations cos^2 then some angle so for example:cos^2 45deg. How does this work on a calculator or do you have to do something clever to work this out? Also what does cos^2 mean (other than cos x cos)?
Thanks
[math]\cos ^2 x = \left(\cos x\right)^2[/math]
Note that [math]\cos \left(45^{\circ}\right) = \frac{1}{\sqrt{2}} \therefore \cos ^2 \left(45^{\circ}\right) = \left(\frac{1}{\sqrt{2}}\right)^2 = ... [/math]
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The Sun is about 93 million miles from the earth. The star nearest to the Sun is Proxima Centauri. Proxima Centauri is 4.3 lightyears from the Sun. It is a dim red star in the constellation of Centaurus that lies at a distance of over 40 million million kilometers, some 270,000 times greater than the distance between the earth and the sun.
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The proof of [math]\pi[/math] being an irrational number is a beauty. There is a few proof, such as seen on wikipedia:
http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
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It's a good reference source although it is one which I visit less frequently. I tend to use Google (search engine) through which I can find all my resources so don't always feel the need to refer back to wikipedia.
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Hi Air  I think it's very possible that you hadn't yet read the past few pages of this thread before making your response.
It was aimed at the OP. I've added his quote to avoid confusion. Sorry for any confusion that it may have caused.
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There is a program called MathType but it isn't free, you have to purchase it. I think you can get trials so try it out before you purchase it. It allows you to type mathematical notations. You don't need to learn the codes.
Here's the link: http://www.dessci.com/en/products/mathtype/
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So if the universe has a finite size, which i had previously, previously meaning way in the past, heard it didnt, what is outside the universe? Is there any mathematical proof or such or just wild speculation? It seems very confusing that there is something outside the universe, i mean what would it be like and such? It must just be my tiny incompetent early 21st century mind........
This really depends on what you define as the "universe". If you are talking about the Observable Universe, then it simply expands into more of the same (more stars, more galaxies)  because it is defined by the distance of the most remote light we can see (imagine a sphere with a radious of some 13,7 billion years).
If you define the "universe" as everything that can possibly be, then there is nothing into which the Universe can expand. This would make the Universe infinite (but not necessarily occupying an infinite space  simply all the space that is available!).
Another way to view our Universe is to consider that it might be a part of a larger universe in which ours is only a small part (like an island in the ocean). This is actually just a modification of the first point above. However, depending on how each of the universes came into being, their physical laws and properties may be different.
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If your concentration is on:

Art subjects: Then go for Mac. It is better graphically and visually.

Science subject: Then go for PC. You may need to install many programs hence having a PC enables you to be sure that it can installed. At times, some programs cannot be installed on Mac.
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Art subjects: Then go for Mac. It is better graphically and visually.

The universe is beige
Cosmic Latte is the color of the universe, according to a team of astronomers from Johns Hopkins University. In 2001, Karl Glazebrook and Ivan Baldry determined that the color of the universe was a greenish white, but they soon corrected their analysis in "The 2dF Galaxy Redshift Survey: constraints on cosmic starformation history from the cosmic spectrum", published in 2002. In this paper, they reported that their survey of the color of all light in the universe added up to a slightly beige white. The survey included more than 200,000 galaxies, and measured the spectral range of the light from a large volume of the universe. The hexadecimal RGB value for Cosmic Latte is #FFF8E7.
In a Washington Post article, the color was displayed. Glazebrook jokingly said that he was looking for suggestions for a name for the new color. Several people who read the article sent in suggestions. "Cosmic Latte" was selected.
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I'm on many sites including Google so I believe it is a problem down your end.
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Completed. Link worked for me.
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[math]\displaystyle\int_0^{\infty} (Air) \ \mathrm{d}x[/math]
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Haha, Classic!
You know this didn't actually happen, right? It's a chain letter. It's hilarious regardless but I'm just making sure you're not one of the people who believes that this was an actual question on an exam and all that.Everyone know that noone would dare in reality unless they think otherwise.
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I looked throught this thread and realised that the icon to give rep isn't showed.
So, to add reputation to a user, click on this icon which is found on top of every post:
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Substitute Teacher's Day:
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I have read that Universe will go on expanding(Big Bang Theory).At one stage the expansion stops and the universe will shrink again(Big Crunch theory).Is it true ???
There are three alternative scenarios for the future fate of the Universe. If the expansion continues forever then the Universe is destined for the Big Freeze, gradually pulled apart into a cold desolate wasteland of dying stars and black holes. If space stops stretching and springs back on itself, it will shrink until galaxies start colliding in the Big Crunch  terminating in the mother of all black holes. However, there is a more peaceful option. The final scenario involves the Universe gradually slowing down to a halt. With the whole Universe balanced precisely, cosmic catastrophe would be averted and space would be saved. At least for a while. Eventually the Universe would succumb to the Big Freeze, it would just take a lot longer.
The fate of the Universe is basically a battle fought between the inward pull of gravity and the outward push of expansion. So astronomers are trying to calculate the strength of these forces. The amount of gravity the Universe has to wield against this expansive onslaught depends on how much stuff there is out there in space. Anything with a mass has its own gravity. Even you yourself have a gravitational force that attracts everything else around you, including other people. The bigger you are, the stronger this force is, and so, the Earth, being the most massive thing around, completely overwhelms the tiny forces that we personally possess. So to calculate the fate of the Universe, we must weigh it to find its density.
Antarctic IceIn astronomy, the density of the Universe goes under the symbol [math]\Omega[/math] (or Omega), the last letter of the Greek alphabet, meaning 'the end'. The precise amount of matter needed to gradually halt the expansion of the Universe is known as the critical density, where [math]\Omega=1[/math]. If [math]\Omega[/math] is [math]1[/math] then the future of the Universe is a gentle, serene stop. Smaller than [math]1[/math] and we're heading for the quick Big Freeze, a universal ice age. Larger than [math]1[/math] then it's Crunch time. So our destiny depends on our density. Recent results show that [math]\Omega[/math] is at least [math]0.3[/math]. That figure includes the mysterious dark matter that lurks invisibly in space and has yet to be fully understood.
It has also been proving difficult to measure the precise expansion rate of the Universe. Recently it's been discovered that this expansion is accelerating under the grip of a previously undetected force, called dark energy, that is helping to pull the Universe apart. Until both these dark questions are answered, the fate of the Universe still hangs in the balance.
An end for EarthHowever, although the end of the Universe may look pretty black, this impending cosmic catastrophe is not our most pressing concern. In about [math]4[/math] billion years the Sun will expand and engulf our planet Earth. Also around the same time, our nearest galactic neighbour, Andromeda, will start to crash into our own galaxy, the Milky Way. Life on Earth must escape into space if it is to survive.
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The standard SI unit for acceleration is [math]\mathrm{ms}^{2} = \frac{\mathrm{m}}{\mathrm{s}^2}[/math].
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Yes, that what I think too. Does anyone know exactly how many post are required?
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Some Common Logarithm Rules to note:
[math]\log_a(x)+\log_a(y) = \log_a(xy)[/math]
[math]\log_a(x)\log_a(y) = \log_a\left(\frac{x}{y}\right)[/math]
[math]\log_a(x^y) = y\log_a(x)[/math]
[math]\log_a(x) = \frac{\log_y(x)}{\log_y(a)}[/math]
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Nope, I only have the 'Search Groups' option.
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How are they made? Can we request to make one?
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Provided the initial coding is not changed in the process, all codes should be decryptable. For instance:
If '[math]D = T[/math]' then it would need to be kept as that. If changed in the process and unnotified, then you will not be able to decipher.
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Rearrangement?
in Mathematics
Posted
I don't see how you 'boiled' it down. I get:
[math]\frac{B}{W}=\sin x[/math]
[math]\frac{F}{T}=\cos x[/math]
[math]\frac{B}{W} \div \frac{F}{T} = \tan x[/math]
[math]\frac{B}{W} \times \frac{T}{F} = \tan x[/math]
[math]\frac{BT}{WF} = \tan x[/math]