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You are currently reading a thread in /sci/ - Science & Math

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The old one is over the bump limit


Mine: What's the easiest way to learn the LaTeX markup subset used on /sci/?
>>
Is this book a good starting point for someone studying proofs for the first time?
Can you guys recommend some other intro to proofs books?
>>
>>7833056
This is my favorite intro to proof book.

It's very short, very well-written, and covers some useful (and interesting, in my opinion) things as well rather than the contrived examples many how-to-prove-it books are filled with.
It's also cheap, which is nice.

Keep in mind that there's very little to actually _learn_ about doing proofs. Only a few pages.
The important part is to do a fuckton of them to get experience with writing and reading proof.
>>
How can I calculate the volume traced by a circle in R^3 that rotates x radians while translating a distance d along a line? (center of circle stays on the line)
At the start the circle is oriented along the xy plane and it's translated along a line in the xy plane while rotating "forwards". For example if r=1, x=2pi and d=0 it's obviously a unit sphere.
How to plot the resulting shape?
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>>7833071
draw something because I don't want to have to decipher that shitty description of the problem
>>
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>>7833112
Here's a shitty drawing.
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>>7832996
>>
>>7833071
>>7833204
Does anyone know how to plot such a shape in Maple?
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>>7833235
>convenient way
>>
>>7833328
>easiest way
>still bitching
fuck off.
>>
>>7833328
I don't know how much more I can spoonfeed you than an image containing as little information as possible. Why don't you fucking grow up and read the sticky or the LaTeX wikibook?
>>
>>7833334
>>7833335
I meant that in the image it says that /sci/ offers a convenient way to write equations, and latex syntax is not really convenient. chill
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>>7833339
>2+3
>a^b
>\frac{x}{y}
>inconvenient

It's hardly more than you would type in plaintext for even the most complicated parts. And honestly, what more are you using on /sci/?
>>
>>7833343
>\frac{x + z}{y - q}
i would just type (x + z)/(y- q) in plaintext
>>
>>7833353
[math](x+z)(y-q)[/math]

I can do that in LaTeX, too. It's a pain in the ass to read to savae 3 keystrokes.
>>
>>7833359
that's not a fraction tho?
>>
>>7833360
[math](x+z) / (y-q)[/math]

I missed a key.
>>
>>7833366
but it's not rendered as an actual fraction bro
>>
>>7833353
>>7833339
4chan lied to you.
Move on, nothing new here.
>>
How come I can't read this? >>7833366
Using appchan x btw.
>>
>>7833368
It's not rendered as an actual fraction when you use plaintext either; that was my point. It's not any harder to type math, and for an extra 3-5 keystrokes per post you can even make it readable.
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>>7833372
well your point is not really related. i was complaining about latex as a markup language that, like you highlighted in your example, it doesn't render plaintext-like formulas as expected and it uses more cumbersome syntax such as `\frac{}{}`. and it's not only about "extra keystrokes".. typing is also about where these keystrokes are, how convenient they are to reach, how common they are in one's typing patterns, etc.
>>
>>7833376
Plaintext formulas are ambiguous and don't resemble actual math. What would I want if I typed "rm/n?" Would I want [math]\frac{rm}{n}[/math] or [math]r\frac{m}{n}[/math] (there are times where the distinction is needed). This isn't a flaw; it's a feature. Plaintext formulas display exactly how you'd expect: as plaintext formulas. You get the ability to format it however you want with pretty minimal effort.

But honestly, anyone posting math on a math board should be more than comfortable with LaTeX considering its ubiquity in the field.
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>>7833385
>What would I want if I typed "rm/n?"
the latter cause no parenthesis around `rm`

>anyone posting math on a math board should be more than comfortable with LaTeX
that doesn't make typing latex inherently more convenient tho

obviously convenient is both subjective and relative, but i don't believe it's particularly convenient for the average /sci/ user.
>>
I can only really understand, and have fun with, math problems when I'm on painkillers.

The supply is going to run out.

Is it the more relaxed state of mind that is the key? Should I start meditating? Any other drugs would have to be OTC, can't go to the MD for anything psych-related.
>>
>>7833424
time for le adhd pills
>>
>>7833429

Anything OTC or "herbal."

Seriously I can't go for anything psych related because of a clearance.

But it's just amazing that I suddenly understand shit.

CBD oil? Should I ask /fit/? I think you're right though.
>>
>>7833405
I think most people who talk badly about it have never used it, and if more people took the time to get comfortable they'd see it's not inconvenient at all. But I agree, some people really just won't get anything out of it.
>>
at which point does the speed of sound become equal to the speed of light?
>>
LaTeX isn't a markup language. It's a Turing complete macro language.
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>>7833481
Furthermore LaTeX isn't designed for rendering math. It's designed for typesetting printed documents (the math mode stuff is just some of it's functionality).

MarhJax, what /sci/ uses is a web based version of much of LaTeX' math mode features. It does not implement all or even most of LaTeX.

For you it looks cumbersome because you only want to learn to do one simple thing. However for people (like the math people on /sci/) who use LaTeX on a daily basis it would be much more confusing and cumbersome to have to learn a different language just to post on the internet. Keep in mind that languages like MathJax were designed so that people who use LaTeX daily could talk to each other without much extra effort.
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>>7833503
>i can't follow a discussion, understand arguments, or logic
thanks for sharing
>>
When applying to Oxford, must I apply to a specific college within Oxford or do I simply apply to the course and choose colleges etc at a later date?
Applying from outside the UK and information here on the topic is sparse at best
>>
Why are real numbers defined as sets of all numbers smaller than themselves?
>>
>>7833512
The point was that if you're looking for a markup language for math, LaTeX isn't it. Your complaints about it will fall on deaf ears.
>>
>>7833574
Formally they're not (because then your using the term in the definition). This is also why wildberger complains about it. If you're only allowed to give rational numbers in the definition of a set then you can only produce countably many such sets.
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>>7833071
Shouldn't this problem be a fairly simplistic exercise in integration for you, /sci/?
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>>7833574
There's a bit of a caveat in your statement. It's the set of all _rational_ numbers smaller than itself. Not just numbers.

Think of it this way: you're defining r as the least upper bound of all rational numbers smaller than r. (Behind all the rigour this is pretty much what you're doing).

The least upper bound always exists and is unique (and this is a property of the reals the rationals don't have, so we really are constructing new numbers here) so this is a solid definition of what a real number is.

>>7833589
memester please go
>>
What is the value of
[eqn]\lim_{\:x\rightarrow 1^{+}}\left \lceil x \right \rceil[/eqn]
?
>>
>>7833618
https://www.wolframalpha.com/input/?i=lim+x-%3E1%2B+ceiling%28x%29
>>
>>7833625
Doesn't this contradict the whole philosophy that 0.999...=1?
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>>7833644
No. Why would it?
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>>7833481
I cann't believe this shit is actually true.
https://www.tug.org/TUGboat/Articles/tb11-3/tb29greene.pdf
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>>7832996
doubleclick LaTeX
look how it's done
>>
>>7833071
/sci/ please answer, surely this can't be all that challenging for you.
>>
Ok, so I have a directory and in it I got a bunch of files and a folder. How can I write an expression to grab all the files, but not the folder?
If it makes things easier, the folder has '.stat' at the end of its name.
>>
>>7833702
The number of files and their names are, say for this example, random. I want to use something like just '*', but that grabs the folder too, and it fucks my shit up.
>>
How do I get motivated to study for my exam which is on Monday?
I'm so demotivated. I don't remember the last time I way excited for anything. Are there maybe some kind of drugs I can take to raise my motivation?
>>
>>7833702
*!{.stat}

Or something like that. It involves ! for sure.
>>
>>7833618
2
>>
>>7833589
> If you're only allowed to give rational numbers in the definition of a set then you can only produce countably many such sets.
So the power set of the rationals is countable ?
>>
>>7833732
How much sunlight do you get? If little, are you supplementing with vitamin D? How much physical exercise? Do you have a stable, consistent sleep rhytm? Do you eat diversely? Etc.
>>
>>7833803
>How much sunlight do you get?
Not much because it's winter.
>If little, are you supplementing with vitamin D?
No
>How much physical exercise?
Not much, I try to work out once in a while, but most the time I spend sitting around.
Do you have a stable, consistent sleep rhytm?
No
>Do you eat diversely? Etc.
No.

I think you don't even need to respond to this, I can already figure what the issue is now.
I also don't have any friends so there's that too.
>>
>>7833807
Maybe you're just depressed. Do you cry or feel sad?
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Is this notation correct?

Specifically the park under "hence".

Thanks senpai.
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>>7833821
No, I don't really feel anything.
>>
>>7833864
Sounds like depression.
>>
>>7833859
>35^2=25^2 + 6^2
This isn't decimal. What base is this?
>>
Our lecturer showed us d'Alembert's solution to the wave equation, and we had a second order mixed partial derivative equal to 0. The solution just required integrating twice, which gave two 'constants' of the integration, which we functions of the other variable. My question is that when the second integration occurs, with respect to the other function (of which the constant of integration was a function), why does nothing happen to that constant? Surely it shouldn't just integrate to itself?
The solution was A(s) + B(r) for d^2f/dsdr=0
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>>7833872

Here's the full problem.
>>
Retarded question here, but I've never needed to do this before. Is it fine to write, for example,

5 + 3 × square root of 14 = 16 (to 2 s.f.)
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>>7833902
>pythagorean theorem
is this geometry?
but the approx symbol is well placed
>>7833964
which symbol should also be used there too
>>
>>7833972

The approx symbol instead of =
>>
>>7833976
yes that what I meant
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>>7833972

Yes geometry. I've rewrote it like this.
>>
how would I go on about drawing an orbital correlation diagram that shows how CO is stabilised by an alcohol?

ochem help?
>>
>>7833982

Thanks s-s-senpai
>>
Last autistic question of the night

Which would be the best way to write pic related, 1 or 2.
>>
Should i work or study?
>>
DIFFERENTIAL TOPOLOGY AND GEOMETRY

How do I embed an arbitrary smooth manifold M into some euclidean space? It's surprisingly easy for M compact, I don't know about the non-compact case, however. I think it has something to do with M being paracompact. I'm not looking for the Whitney embedding theorem - obviously, that's my next step but it assumes that M is already embedded in some (most likely very large) euclidean space.
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>>7834099
I think the compact space proof only relies on the existence of a partition of unity dominated by any open cover. This exists for any smooth manifold and indeed follows from paracompactness.
>>
>>7834108
Well suppose I have an open cover and the subordinate partition of unity. How do I proceed ?
>>
>>7833755
No, the set of finite length sentences over a finite alphabet is countable.

You can define the set containing all of them but when it comes to defining individual objects in your set you can only define finitely many.
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>>7833071
Please /sci/, answer this question that is without doubt trivially simplistic for you to answer.
>>
What are some really highly regarded MOOCs on Coursera besides Andrew Ng's Machine Learning course?

Something AI related (data science, computer vision, neural networks, etc) ideally, but also maths, neuroscience, or whatever you have that is actually good and STEM related

pls respond. if not coursera, then other MOOCs
>>
>>7834432
btw I ve done most of the maths courses on Khan Academy and I'm a final year undergraduate finishing CS and applying for machine learning master's this year
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>>7832996
To be honest, the easiest way is to take a math class way over your head so you're forced to cheat with Math Stack Exchange, then memorize every command as you need it while you communicate or be laughed out of MSE and fail your degree.

That's the ideal way to do it.
>>
Why are addition and multiplication described as related to each other (multiplication is literally just "quick addition" the same way taking exponents is quick multiplication and you could define any number of operations as being "quick" version of an operation below it) but this idea is completely lost in abstract algebra?

In abstract algebra, multiplication and addition are effectively just "laws of composition" which can be completely unrelated, but exponentiation is still defined like "quick multiplication."

What gives?
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>>7834415
Not certain of what you mean "forwards"
Nevertheless I'll give it a shot
Suppose [math]x=2\pi[/math]. Then you can use the volume by rotation formula on three solids half-sphere (0-r), cylinder (r,d-r) and another half-sphere (d-r,r). [see image.] By symmetry you can derive the volume for [math]x<2\pi[/math] as [math]V=V_{tot} x / 2\pi [/math].
Not certain though.
>>
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Can one of you faggots confirm that the notation in this problem is correct? I will forever be your grateful little bitch.
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>>7834528
You're giving too much attention to irrelevant details m8. If the solution is correct it doesn't matter if you used approx or equality.
Personally I would have just answered:
[eqn]A_{\Delta A B C '} = A_{tot} - A_{\Delta A B C} = \pi r^2 - (b+B)h/2 = \pi 35^2 - 25 (35+10 \sqrt{6} )[/eqn]
Hence, [math]A_{\Delta A B C '} \approx 2400 cm^2 = 0.24 m^2[/math]
where [math]A_{\Delta A B C '}[/math], [math]A_{\Delta A B C}[/math], [math]A_{tot'}[/math] the requested area, the are of the trapeze and area of circle respectively.
>>
>>7834522
By forwards I mean the circle rotates in the direction of translation. So if the circle is initially centered at the origin (lying in the xy-plane) and rotates pi rad during a translation of length d along the x-axis, then the point of the circle that's initially at (-r, 0, 0) will be at (d/2, 0, r) halfway through, and finally at (d+r, 0, 0).
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>>7834562

My tutor is very strict with notation. He takes marks with no remorse.
I haven't yet learned how to solve it in that way, but surprisingly, I can understand it. I know only basic algebra currently (pre-quadratics).
>>
>>7834579
is your problem defined exactly
that is you are given that the rotation is e.g. \pi rad or the rotation is a variable?
if it is a variable then I think the dependence of x to the distance d traveled is also needed, that is x=x(d) (or perhaps it can be found, not sure)
>>
>>7834596
of course you can understand it; it is what you wrote expressed with symbols
math is a consise language made so we don't have write wordy explanations
>>
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>>7833654
holy crap!
>>
>>7834601
For now the rotation is fixed, though of course it would be interesting to have it vary.
>>
What is the solution to [math]dx + x =dy[/math]?
>>
I'm 29 with nothing past high school diploma, just been working pretty generic jobs the last 10 years.

Suddenly want to be doctor - how fucked am I?
>>
>>7834704

>wants to do medicine
>posts on a science board

>>>/adv/
>>>/x/
>>
what was the name of that japanese guy who apparently had figured out some retarded math problem that would turn the whole discipline around and they had to convene a bunch of experts to figure out his work last year?

anyone know what this is?
>>
>>7834704
dont do it, you're 29, it would take you at least 6 years to even qualify for residency. you've also got a massive 10 year gap to explain for.
>>
>>7834710
Thanks, I'll keep that in mind while I think about it.

I also thought about doing it through the military (Canadian) which was my first goal anyway, since they provide all the school and training and that's where I wanted to end up. I just wonder if there's any conventional wisdom in the profession that people who started late just can't cut it, or anything like that?
>>
>>7834704

Go for it. You only live once.
>>
>>7834610
No it's not. It's a formal language made so that we have absolute precision. Natural languages are shit and let you say all sorts of ambiguous and unparsable shit.
>>
The Bolzano–Weierstrass_theorem is true for R^n. It's that theorem all bounded sequences have a convergent subsequence.

Is this true for R^inf? Asking because the proof that comes to my head is inductive which does not address R^inf.
>>
>>7834826
u fucking wot m8
>>
>>7834826
Consider the sequence in which the nth term has a 1 in the nth coordinate and 0 everywhere else.
>>
>>7834939
Fuck... Sorry...
It's that theorem that says that all bounded...

>>7834941
Good thinking. Thanks.
>>
I'm trying to brush up on chem for an exam and I haven't done chem in 4 years I think

so I'm trying to find the BP elevation of a mixture (0.1 mole of C2H6O2 and CH3OH respectively) in water.

Now what confuses me is the van't Hoff factor: is it safe to say that i in iFm would be 1, since neither particles in the mixture don't dissociate?
>>
>>7834680
Plz help
>>
>>7835067
You can see the vector Weight in the picture pointing straight down, and so since sin(theta) = ratio of lengths of opposite/hypotenuse, we see sin(theta) = |W_par|/|W|. So |W|sin(theta)=|W_par|
>>
>>7834444
>>7834432
Bump
>>
>>7834826
Note that it's not at all clear what converging means in the context of an infinite-dimensional space (contrary to the finite dimensional case where all norms are equivalent).
For example, if you only consider the space of bounded sequences and set the norm [math]||u||_{\infty} = \sup\{u_n, n \in \mathbb N\}[/math], then the sequence in >>7834941 doesn't converge. It does converge, however, if you set the norm [math]\displaystyle ||u|| = \sum_{n\in \mathbb N} \frac{u_n}{2^n}[/math]
>>
>>7835435
I forgot absolute values everywhere..
It should read [math]||u||_{\infty} = \sup\{|u_n|, n \in \mathbb N\}[/math] and [math]\displaystyle ||u|| = \sum_{n\in \mathbb N} \frac{|u_n|}{2^n}[/math]
>>
>>7832996

Should Critical Theory properly be called, "Theory"?
>>
What is a quotient set?
>>
>>7835594
A set of equivalence classes.
>>
Just wondering, can any of the images I post here (screenshots or camera phone pictures) of my work be detected by plagiarism software?
>>
>>7835607
thank
>>
Can someone explain to me the concept determinants? What are they used for and how did they come up with it?
>>
>>7835709
Also why are they called determinants? Determinant of what, the inverse of a matrix?
>>
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I have part a down, but part b is giving me trouble. Right now I'm using F = q*e (q being the answer to part a), then a = F/m to find acceleration. So I plug the acceleration into the formula vf^2 = vi^2 + 2ax, but I'm not getting the right answer. Am I on the right track?
>>
>>7834680
It is an exact differential.
[math]dy - dx = d(y-x)=x \Rightarrow y-x = x^2 /2 + c[/math]
>>
>>7835763
[math]d(x^2 /2 + c) = x dx \neq x [/math]
>>
>>7835777
are you retarded
>>
>>7835777
indeed--the solution I have given is probably wrong
>>
>>7833204
What's the axis of rotation for the circle?
>>
>>7834680
thats not possible
>>
>>7835390
pls
>>
>>7834680
That formula does not make sense, unless you are using differential forms (and I suppose you are not doing that)

>>7835763
What the fuck are you operating with. What you did has zero sense. You're doing the analysis equivalent of the pic.
>>
>>7835943
The axis of rotation for the circle is orthogonal to the direction of translation.
>>
I had an idea for a suberbowl commercial
>An equation is dancing to "Niggas in Paris"
>The Y variable steps out and raps a bit of JayZ's verse
>"Ball so hard mothafuckas want to fine me. First niggas gotta DEFINE me."
>Cut to an image telling us we have to keep an eye on inner city education
What do you think?
>>
>>7836528
I don't understand why you wouldn't use Z for this Jay-Z variable. Who's funding this multimillion dollar ad? They should put that money towards inner city education.
>>
are humans apex predators or can they not be considered part of the food chain?
>>
What are some cool hobbies I can engage in while watching videos?

All I have is playing music instruments and pen spinning.
>>
I'm getting my associate's degree in Math at this community college. It took me three years, but I did it. What can I do with it?
>>
>>7832996
I've got two, totally unrelated.

1) This is more of a 'not deserving of a thread' question than a stupid question, but can the reals be constructed from group theory?

2) This one really is stupid... please excuse the fact that of all the sciences, biology is the one where I'm by far the least educated. I was eating my morning Weetabix earlier, and noticed that per 100g it contains something like 170 microgrammes of folic acid, which is something like 80% of the recommended intake. This got me thinking, how does 170 fucking microgrammes have any effect? Why does my body give any shits about such a tiny amount?
>>
How can I know if I have what it takes to study mechanical engineering prior to studying it? I barely went to school, had a 20% attendance rate in high school, so I can't use that as an indication.
>>
>>7836759
possibly someone will correct me, but the reals are not that interesting from group theory/algebra standpoint. The integers give you a nice group structure. For a field structure you have to go to the rationals. The next step would be finding algebraic closures (spaces where every polynomial has all of its root on that same space), but the reals are not that space (we need the complex).

The reals are defined through topology: we take the rational, build all possible Cauchy series in that space and then add their limits to the space (in other, simpler, words, the topological closure of Q is R).
>>
Is there an introduction to transistors that I might actually understand (i.e. not some retarded “if current gos to de tranzistor then it allows bigger current to poo in de loo” bullcrap)?
>>
>>7836698
Why are you focusing on other things while you have videos on? Just turn off the videos and do whatever you want.
>>
>>7836786
Go to your local glory hole.
>>
>>7833071
Please answer.
>>
>>7834460
kek
>>
>>7832996
How many ways are there to place 10 distinct people within 3 distinct
rooms with exactly 5 people in the first room and 2 people in the second room?


It seems like an easy question from an earlier unit, but it's being asked in the context of inclusion/exclusion principle unit. My result seems to be too large. Any help or confirmation would be appreciated.
>>
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>>7832996
would like an explanation of what triple barnett-muhler theory is?
>>
>>7836805
>The integers give you a nice group structure. For a field structure you have to go to the rationals.
>what are finite fields
>>
>>7837068
The integers are not the prime subfield of any finite field.
>>
>>7835709
Determinants can be used for all sorts of applications. The determinant of an nxn matrix has a connection to the n dimentional analogue of volume (volume, area, length, etc.).
Determinants are also extremely important because they determine whether a matrix is invertable or not.
The determinant is non-zero if and only if the matrix has an inverse.
Depending on the physical objects a matrix is constructed upon, the determinant will have different implications (the determinant of the curvature tensor of a surface, curve, hypersurface, etc., which can be represented by a matrix, determines the gaussian curvature).
>>
What would the effect of a geomagnetic reversal have on electronic technology? Would power grids go down?
>>
The period of a carrier wave is T=0.01 seconds. Determine the frequency and wavelength of the carrier wave.

So, frequency = 1/T = 1/0.01 = 100, so f= 100. but, how do I find the wavelength? is it 3E6?
>>
How can I prove:
|cosh(z)|^2 = sinh(x)^2 + cos(y)^2 for z = x + iy?

I started my proof with the definition of the absolute square of a complex number being equal to it times its complex conjugate, but I can't seem to connect that to the second half?
>>
>>>>7836996
bump
>>
>>7836996
2520
>>
>>7837144
bump
>>
>>7837150
Bump
>>
Given the following AM signal, determine the carrier wave's amplitude (Ac) and frequency (fc), the message signals frequency (fm), and the modulation index (µ): s(t) = 10[1 + 0.5cos (2π1kHz*t)] cos (2π1MHz*t)

Ac=0.5, fc=1kHz, fm=MkHz, µ=1 is what i get.
>>
>>7833071
I want to know this answer badly senpai
>>
I do some calculations, I end up with 612 * 10^-4
I need to convert this to 6.12, but I cannot for the life of me figure if out when I do these, whether to go add the extra 10s to the -4 or subtract more, when I go and convert that 612 to 6.12.

I know the answer is going to be either:
6.12 * 10^-6
OR
6.12 * 10^-2

Does anyone ever have a way to remember this? Or to understand what I'm doing when I do this?
>>
>>7837230
10^-2

612E-4=6.12E-2

add the exponents on 10
>>
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>>7837233
Thank you

With your help, I think I figured out the logic of it so I can see what's happening to get the answer, pic related
>>
>>7837068
There are plenty of other fields than the rationals. Did you feel clever asserting that you know this in a situation where it's irrelevant?
>>
>>7836729

You can become a tutor. They usually pay 20-30 dollars an hour.
>>
>>7837189
can someone please help me with this?
>>
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n=k+1

Then 2n^2 becomes 2(k+1)^2 or (2(k+1))^2
?

thanks
>>
>>7837680
Exponentials before multiplication
>>
>>7837279
What are you talking about. He said that the integers have a group structure but for fields youd have to go to something like the rationals.
If you know anything about elementary field theory you know that there are an infinite number of finite fields constructable from the integers.
If I have misinterpreted what he was saying then I retract my comment.
I also didn't read the post he was responding to and if I have taken him very much out of context then again, I retract my statement.
>>
The archive is down so I can't check if this got answered so if this is a repost I'm sorry.
Why doesn't gravity eventually overcome the particulates in colloids? Futhermore, is there an equation to figure out the range of ratios of solute particle sizes vs solvent particle sizes at a fixed temperature that can and can't be colloided?
>>
How is my answer incorrect?
>>
>>7832996
Who is this semen demon?
>>
>>7837870
literally how new are you?
>>
>>7837870
lenna del rey
>>
can i ever surpass my genes

t. Solid Snake
>>
>>7836786

BUMP!!!
>>
My brain went full retard after going back to simple physics.

If a car does 80km/h, then decides to go 90km/h. How much time does he save per mile? I thought it was 47 seconds.
>>
>>7838489
that question is unsolveable without knowing the time period for each speed
>>
>>7836238
>Coursera

Do all these courses cost money? Jesus, this is terrible. Just google something.

Honestly if you are this bored just go create something like a rubik's cube solver that uses a camera in real life. You learn mechatronics which basically covers everything you need to be successful in 2016.,
>>
>>7838550
>Do all these courses cost money? Jesus, this is terrible.
What? no
>>
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So I applied to SDSU, CP Pomona, and CSU Long Beach. I just got an email today saying that I did not get accepted to CSU Long Beach. My major is Computer Engineering. What are the chances of getting into SDSU or Pomona if I can't get into Long Beach?
>>
>>7837745
Those fields aren't really constructed from the integers like the rationals are. The radicals are the fraction field of the integers and a field extension. Finite fields don't have any relationship with the integers other than being a Z-algebra, but all rings are Z-algebras.
>>
>>7838920
I was talking about common spaces, naturals, integers, rationals, reals, then complex numbers, because that was the context of the question. I know there are fields other than the rationals, but I didn't need them
>>
Coursera has courses that they offer for free and they have a fee if you want to get a certificate. However, the system only offers taking the course for free once to click on the enroll button. I thnk it's backwards too but they're really pushing the certificate thing in order to try and legitimize it in the eyes of industries.

They do also offer packs of courses aimed at covering a field as a whole, but as far as I can tell these courses are not free. This seems to be a newer feature though and I could just be mistaken.

Coursera actually started out at Stanford. Their first courses were Stanford courses taught by Stanford profs.
>>
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Has anyone read this? What did you think of it?
I'm really interested in picking it up but I want to know if at least is a well made theory
>>
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>>7839049
>deepak chopra quote on the cover
>>
>>7836759
It depends what you want to define exactly.
As a set, the reals are the same as any other set of the same cardinality, so you just need to find a group theoretical method for constructing a group with cardinality of the continuum.
If you want to construct the reals with their additive group structure, then you face problems. You could characterise them as a 1-dimensional non-compact Lie group, but that requires stepping out of pure group theory, either by defining a Lie group as a group with some manifold structure, or as a group object in the category of smooth manifolds.
>>
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>>7832996
I need a books recommendation for phase portraits. Which is the best textbooks for self-learning?
>>
>>7839049
It's basically a meme on sci.
>LE CONSCIOUSNESS LE CREATES LE UNIVERSE
>>
>>7836759
Also, a more formal way of phrasing you question might be "does the additive group of reals satisfy a universal property?".
That means it can be defined as the unique (up to a unique isomorphism), most general solution to a problem phrased entirely in terms of group homomorphisms. Products and coproducts (direct product and direct sum resp.) are examples of such.
Of course, if you mean something more general than "defined in terms of group morphisms", this won't work.
>>
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What humanities courses do the engineers on here take?
>>
>>7839182
Where on Earth are humanities modules required for STEM?
I'd go with philosophy if I had to choose.
>>
>>7839182
i took a language course, a contract law course, and a drawing class. all of which have been pretty helpful.
>>
>>7833071
bump
>>
>>7839193
It's probably part of undergrad requirements, but like in a weird way. Like you don't actually have to take a social science class, but you do have to take a class that fulfills a "qualitative writing" requirement, which most social science classes have. Thats how it is at my uni
>>
>tfw want a degree that focuses on computation
>not enough computation in cs courses
>loved calc 1, 2, 3, ordinary diff equations, discrete maths 1, 2, linear algebra, and numerical analysis

is there a degree for me
>>
>>7839182
At my uni economics courses count towards the humanities requirement so I have a minor in econ now

I guess because it's a social science or something
>>
>>7839284
Just major in math and fill up your math electives with applied courses instead of abstract stuff.
>>
>>7838489

>If a car does 80 furlongs/minute, then decides to go 90 furlongs/minute. How much time in months does he save per millimeter?
>>
I know this is something obvious, but I don't see it.

Let [math]F:M\to N[/math] is a continuous map between smooth manifolds. I want to show that if smooth real valued functions on all of [math]N[/math] pullback to smooth real valued functions on [math]M[/math], then [math]F[/math] is smooth. I get the idea -- given a smooth chart [math](V,\psi)[/math] in [math]N[/math], we want to say that [math]\pi_1 \circ \psi \circ F[/math] is smooth ([math]\pi_1[/math] is a coordinate projection), but we can only say that smooth functions on *all* of [math]N[/math] pullback to smooth functions, right? What's the way around this?
>>
>>7839403
kek
>>
>>7836316
>>7835952
Thanks mates I appreciate it.
>>
>>7838518
You can give a general answer per time period
>>
>>7837167
how did you get this anon?
>>
>>7839103
Good thing I didn't spend money of it.
Any good /sci/ related books? At least I know you guys would never recommend Dawkins, Hawking or deGrasse Tyson
>>
Can someone please explain to me one thing?

I have a cup of coffee that's been sitting on the table for around 4-5 hours. The room isn't cold, in fact it is a pretty nice temperature. Coffee was brewed around 1:50 PM. It's 6:16 PM at the moment of this post.

When I take a sip of my coffee, the coffee is colder than the air. Why is that? Why isn't the coffee the same temperature as the room? Heck, even if I stick my tongue out for a long time, my tongue doesn't feel as cold as the coffee. When I dip my pinky finger into the coffee, it feels colder than the room temperature. Why is this?
>>
>>7839741
Just a guess on this.
Coffee has a higher specific heat than air. This means it's relatively easier to bring the air around you to body temperature than it is the coffee. What you're perceiving as cold is the increased energy transfer of warming up the coffee with your own body heat.
>>
>>7839741
>doesn't feel as cold
>feels colder
>feels feels feels feels

fuck your shit retard this is SCIENCE AND MATH we don't talk about how things "feel", get a thermometer and MEASURE something or get the fuck out.
>>
>>7839741
use newton's law of cooling, I'll let a first-year calc student plug in the #s
>>
>>7839751
Yeah but a thermometer wouldn't tell me jack shit about why it FEELS colder. >>7839746 tells me why it feels colder (thanks for the response btw that explains a lot)

So sure, a thermometer would tell me that it's the same temperature, but it doesn't explain why it feels colder when I sip it. Like why do two things that are the same temperature feel like totally different temperatures? Thankfully, because of the other guy's response, I have the answer.

Love yourself, man.
>>
>>7839721
God tier: Journal paper
Top tier: Textbooks
OK tier: Histories and biographies
Shit tier: Everything else
>>
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When the fuck in your university education do you learn:

>Fourier transforms

>Applications of Laplace transforms
We were introduced to them in our calc III, which was a combination of simple linear algebra and differential equations.
I'm a MatSci major, and frankly, I feel that my math abilities are severely lacking. Like any third year student, if you give me the textbook or Wikipedia, I can read enough to solve the problem generally, but I can't help but feel that these things should be more intuitive from a math perspective.
>>
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[math]
f(x) = \sqrt{r^2-x^2} = \sqrt{4-x^2}
\newline
\vec{g} = \binom{cos(deg)}{sin(deg)} = \binom{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}
[/math]

How do I find the cross point p?
>>
Why do more stable bonds have lower bond dissociation energies? Wouldn't having to put in more energy to cleave the bond make it more stable?
>>
>>7832996
w-why is warosu down? is there any other service that archives /sci/?
>>
>>7832996
>mfw lenna pic is from a playboy magazine and searching for "lenna full image" shows her nudes
hahahahah oh wow this is ridiculous
>>
>>7832996
going over minimax for AI course, still not really clear why pruning works. couldn't the alg be tricked to prune a viable option node?
>>
>>7841576
4ch.be

It doesn't seem to archive pruned threads for some reason though.
>>
There's a piece of lab equipment that I'm desperately trying to remember.

It's a pump that sits on top of a bottle. You set the desired volume (1ml for example) and then raise the button. It automatically stops at 1ml at which point you press down again and it pours 1ml into your container.
>>
>>7841719

automatic pipette?
>>
>suddenly get extreme nosebleed from both of my nostrils
>blood is super thin and splatters everywhere
>tissue plugs get soaked through
what do i do? do i habe cancer?
>>
Prove that [math]6|n(n + 1)(n + 2) [/math] for any integer [math]n ≥ 1[/math]. (Or, prove [math]120|n(n + 1)(n + 2)(n + 3)(n + 4)[/math] for any integer[math] n ≥ 1.)[/math]

I don't know how to approach this. From what I can tell, it has something to do with a factorial and its factors.Any help/direction would be appreciated.
>>
>>7833204
the width is constant = 2r
find the highest/lowers points, it depens on the ratio of movement speed to rotation speed
now you have the upper and lower envelope, constant width, integrate over one period.
>>
>>7841979
note that n, n+1, n+2 are three consecutive numbers. therefore at least one is divisible by three, and at least one is divisible by two.

you can apply the same logic to show that n consecutive numbers must be divisible by n, n-1, n-2....2 and therefore by n!
>>
>>7836729
Work at McDonalds
>>
s1: x = 0
s2: x = x + 1

How do i represent this in a graph?
>>
>A solid sphere carries charge Q distributed uniformly throughout its volume
Does that mean the charge at every point is Q or that the sum of the charges at every point is Q? Or something else? I don't really get how charge works.
>>
>>7842428
the sum of the charges at every point is Q
>>
>>7842252
Well the first one is a spike at x=0 and the second one is an invalid equation, so maybe you should shed some light on what you're trying to say
>>
>>7842428
it means the volume charge density is a constant.
>>
>>7836996
you are first choosing 7 people out of 10 to be in a room
>> 10 choose 2
then choose 5 to be in one room and 2 to be in other
>> 7 choose 2 (7 choose 5 is the same)
2520
>>
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>>7837881
haueheau
>>
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>>7838489
the other posters are literally retarded

80km/h = 49.71mi/h = 49.71/60 mi/min =>

at 80km/h it takes 1.207 minutes to go a mile

by the same derivation it takes 1.073 minutes going 90km/h

(1.207-1.073 minutes) 60 seconds/minute = about 8 seconds

desu senpai
>>
What's an memorization guide to help remember the 14 Polyatomic ions

Im dying over here
>>
>>7840169
you arrive at fourier transforms in probability theory (albeit in a kind of contrived way, called 'characteristic functions') in order to find the distribution of a sum of independent random variables.

you arrive at fourier transforms in real analysis to be able to work with convolutions easily. convolutions are motivated because they show up in nature everywhere (e.g. when you flick a bell, the bell doesnt just move along with your finger, being displaced and then jumping back... instead there is a gradual impulse response which we perceive as a ringing noise that slowly fades..)

you arrive at fourier transforms in differential equations in order to more simply find . this is probably the worst introduction because all of entry level DE study is so hand-wavey

basically there is this (virtually) bijective function transformation that turns ugly things like derivatives and convolutions into nice things like multiplications
>>
>>7842501
Never mind I just made flash cards and I'm starting to remember them better.
>>
>>7833983
Doesn't work like that, just leave it as 600.
>>
What joke always accompanied this picture
>>
How do I write a good labb report?
>>
>>7832996
What the fuck does this mean

>In mathematics, a manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
>>
>>7832996
How do I solve this? (Not homework - returned math exam)
>>
>>7837144
Assuming you know the medium through which the wave is travelling through, you could simply use v = lambda . f
--> lambda = v/f
where v is the speed of the wave in the medium : IE; 343ms^-1 for sound in air
>>
>>7842455
I'm referring to the graphs in graph theory...
>>
how do I learn to learn
you know what I mean
the third semester ends and next month I'm writing tons of exams (6 or 7 I think), until now I passed most of the stuff pretty easily, but I don't think I will be able to pass everything without learning this time

my problem is (and always was), I NEVER learn stuff on my own
in my entire life, there wasn't one time I sat down at home and learned
that's why I only got mediocre grades at school

it's really hard for me to sit down and focus on learning, it feels impossible
>>
>>7842882
Have you taken a topology course? If not, the theory is not going to make sense to you.
>>
NEET here. Interested in mathematics. Is there anything meaningful I could actually accomplish in this field on my own? That is to say, does it require massive teams and financial backing to actually do anything with mathematical knowledge?
>>
>>7832996
Do you take notes while studying from khan academy or other internet resources? Like do you write what they say on the video on your notebook or something like that?
>>
>>7842882

Let's split it up.

>a topological space
Basically, it's a fancy word mathematicians use for "thing". Your coffee mug is a manifold. The earth is a manifold. Any object with shape can be considered as a manifold. The "topological" part can be ignored if you don't know topology.

>resembles Euclidean space near each point.
Euclidean space is a "straight space". E.g., If you're in a 2-dimensional manifold (a surface), if you look at each point closely enough it just looks like a plane.

> More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.

Replace "Euclidean space" by "n-dimensional ball" (1-dimensional ball: a circle; 2-dimensional ball: a disc, 3-dim: sphere). Now, what this part says is that, for every point in your manifold, you can take a set of points close to it and bend and stretch that part of the manifold so it is transformed into a n-dimensional ball.

For example. if you take a torus (2-dimensional manifold), for each point you can cut a part of it and bend it so it looks like a disc.
>>
>>7843214

Mathematics doesn't require much backing. However, if by "on my own" you mean outside of academia, it's difficult to do anything. It's hard to do research just by yourself. However, you can learn math to apply to other jobs.
>>
Why do electrophilic aromatic nitration reactions give only one isomer of product? Is it because the nitro group deactivates the ring, or something else?
>>
Can someone convert this into matlab code?

plot bessely(0,x) plot besselj(0,x), x from 0 to 10pi

I'm tired and matlab syntax makes me butthurt.
You can use that i defined bessely/j as Y0 and J0 respectively. I need them to overlay and only display on that domain ( 0 <= x <= 10pi)

I've only used matlab a few hours so far
>>
>>7844040
nvm, got it
>>
Given that both √ 2 and √ 7 are irrational, prove or disprove that √ 7 − √ 2 is irrational.
I think I'm retarded. I have no idea what to do.
>>
>>7844314
The rationals are closed under addition (this is easy to prove). That's all you need.
>>
>>7844314
what if it was rational? then it would be equal to p/q

set it equal to that and then try to manipulate it into a contradiction
>>
>>7844314

Proof by contradiction. Assume [math]\sqrt{7} - \sqrt{2} = p / q[/math], [math]p, q \in \mathbb{Z}[/math], [math]q \neq 0[/math] (in this case we know from the property of squaring that [math]\sqrt{7} - \sqrt{2} > 0[/math] so we can restrict ourselves to [math]p, q \in \mathbb{N}[/math] (clearly they can also both be negative, and equally clearly it's the exact same problem)).

Now just square the equation and move [math]q[/math] out of the denominator.

[math](7 - 2\sqrt{14} + 2) q^2 = p^2 \\
9 q^2 - p^2 = 2\sqrt{14} q^2[/math]

The left side must be a (positive) integer. The right side is irrational (if you need to, use a similar argument to demonstrate that [math]\sqrt{14}[/math] is indeed irrational and that [math]r\sqrt{14}[/math] is irrational for any [math]r \in \mathbb{Z}[/math] (true in fact for any [math]r \in \mathbb{Q} multiplied by any irrational[/math]).
>>
>>7844364
??
1+sqrt(2) and sqrt(2) are irrational but 1 is rational
maybe you're thinking of something else?
>>
>>7844380
Think about why what you typed doesn't disprove what I said. A set is closed under addition whenever the sum of two elements of the set is again in the set. The rationals are a field; I promise I'm right. I've done things like this more than a few times.
>>
>>7844388
I know rationals are closed under addition, I'm not a fucking middle-schooler.
But how does that apply to his problem?
>>
when do you start to understand differential equations
started taking diffeq this semester and so far we've only gone over algorithms and tricks for solving them
it's easy enough to memorize but i have no fucking clue why any of this shit works and it's making me mad
>>
>>7844755
When you take an upper-division course titled "theory of differential equations".
>>
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>>7844761
you mean to tell me that this entire class is just nifty party tricks? if i wanted to memorize a fuckload of shit without understanding that shit i would have taken computer science
>>
>>7844755
if you understood calculus, i don't see how diff eq is hard to grasp.
>>
>>7844768
Yes. Your lower-division class is intended primarily for engineers who will need to solve differential equations in practice without understanding the rigorous theory behind it.
>>
>>7834710
>you've also got a massive 10 year gap to explain for.
That's not how it works, not over here at least. You get extra points when applying to medical doctor education if you have worked a few other jobs before. As a medical doctor you are supposed to work with people so any experience learning about and dealing with people outside of school bench is very useful.
>>
>>7844755
you need linear algebra nigga
it will explain so many things
>>
>>7839741
Many liquids transport heat more efficiently than air. That's why water cooling is more efficient than air cooling for computers, just that in this case your lips are the CPU and the coffee is the cooling liquid. It is more efficient at removing heat from you than the air is.
>>
>>7839741
it's like how metal feels colder than plastic or wood. the coffee (mainly the water in the coffee) conducts heat much more efficiently than the air, so heat transfers from your body into the coffee faster than into the air, so the coffee feels colder.
>>
>>7839741
if you're looking for the specific science behind it :

https://en.wikipedia.org/wiki/Thermal_effusivity

this is why cardboard feels warmer than steel
>>
>>7839751
if you were a true scientist, you'd find a way to physically quantify a "feel".
But hey, I guess some of us are only average, right?

as I said, the scientific description is here
>>7845072
>>
How do I prove a certain object is a tensor?
>>
>>7845159
see if it stresses you
>>
>>7845168
It's not enough if it stresses someone, it should be able to stress the same not depending on switching coordinate systems too ;)
>>
>>7845159
>>7845186
This. See if it stresses you the same if you lie down or stand on your head or do the "Hitler's dogs" et.c.
>>
>>7845159
this is trivial
>>
>>7845201
epic
>>
I am very tired and try to learn about limits before I have my shift again.
Now I am unsure about this:
[latex]\sqrt{n+2} - \sqrt{n-1}[/latex]
What am I allowed to do in order to find out if this converges?
I know that i could just raise them by the power of 2 to cancel out the roots, but I think this is illegal.
And I do know that n^(1/2) = sqrt(n) and this means it diverges.
What is the right step to take?
>>
Is my interpretation of these terms correct?

- Likelihood is the probabilty of a model given the data without using information outside the given data
- Prior is the probability of the models happening in the first place -- it is usually guessed/subjective info
- Posterior is just the final probability of the model given all the data i.e. prior x likelihood
>>
>>7845745
multiply and divide by [math]\sqrt{n+2} + \sqrt{n-1}[/math], simplify and see what happens.
>>
Now THIS is a dumb one.

When a question is to do with numbers that do not share a common factor, is the factor 1 ignored, and is the number itself ignored? Is zero counted as a factor? Do prime factors count?

So, to illustrate my point, some examples:
Does 9 and 19 have a common factor?
Does 0 and 15 have a common factor?
Does 13 and 26 have a common factor?

Sorry for the amateur question, I am not a mathematician by trade.
>>
What formula is that on the 2nd line of the solution?

[eqn] p(H = 50, T = 50) = \sum_{i=1}^{n} p(H = 50, T = 50|\theta _{i})p(\theta_{i})[/eqn]

i know joint probability is [math]p(H = 50, T = 50) = p(H = 50, T = 50|\theta)p(\theta)[/math] but how do you generalise it to that sum?
>>
>>7846004
No, wait, the joint probability I know is [math] p(H=50, T=50) = p(H=50|T=50)p(T=50)[/math]
>>
>>7845986
usually it says "prime factor", but I guess "factor" means "prime factor" as well.
9 and 19 don't have a common one.
0 and 15 do (3,5 and 15)
13 and 26 have one : 13
>>
>>7846006
I believe it has something to do with the posterior probability, but I don't know what formula is that where it sums over all producs
>>
>>7846014

Right. So 1 doesnt count as a factor?

thanks man.
>>
>>7846023
it's a factor, but not a prime factor, and no one cares about 1 really because 1 divides everything. Your book (or whatever) should say prime factor, they just abuse the nomenclature
>>
>>7846032

Okay, I get it. This question was handwritten, so I guess he just didn't quite write it down rigorously. 'Preciate it!
>>
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Question about maths. Maybe you can help me.
a + log2 (2d/w) - 2 = a + log2 (2d/w) - log2 4.

That is what I have but I have no idea how to get from "- 2" to the "- log2 4". (The 2 is supposed to be small on the bottom, but don't know how to do that with the keyboard).
>>
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>>7846061
pic related how to actually write it.
Anyone?
>>
>>7846061
>>7846091
They just write 2 as a base 2 log. We have 2^2 = 4, so log_2 (4) = 2. Just like you could write 3 as log_2(8), because 2^3 = 8.
>>
>>7846131
thanks anon
>>
>>7844388
Just because two numbers are irrational doesn't mean their sum is irrationnal ([math]\sqrt 2 - \sqrt 2 = 0[/math], after all)
>>
>>7845745
The following identity is quite helpful whenever you're working on these sorts of problems [math]\sqrt b - \sqrt a = \frac{b-a}{\sqrt b + \sqrt a[/math]
It's dumb but people tend to forget it
>>
How can you tell if a paper is important/influential? Do I just check on Google Scholar how many cited it? Are there better measurements?
>>
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How important is sleep before writing an exam? Have my test tomorrow but still a shit-ton to learn and memorize. Already 1 at night.
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>>7846256
>How can you tell if a paper is important/influential?

If you're familiar with the field, it will be obvious. If you're not familiar with the field, why do you care?
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>>7846790
>How important is sleep before writing an exam?

Extremely.
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>>7846790
Learning the material is way way more important than sleep. Lack of sleep takes about a day to hit you anyway. So unless you're doing this days in a row, you should study.
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>>7846795
Thats what I wanna hear. Thanks, friend.
More motivated now. Last night I had lots of sleep, so it should be fine.
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>>7846795

This is very bad advice.
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>>7846790
Important, but it depends on how badly behind you are.

Thought process should look something like this; would I rather write the exam sober right now or a little drunk but I'm allowed to study eight hours?
That's about what your mental state will be like.

It's better to cram all night and not sleep if you're severely behind on the material but sleeping will prevent you from losing a bunch of marks on dumbass mistakes you made because you were tired and unfocused.
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is it possible to move in space if your only source of energy is a solar panel? i can't think of any ways, since you have nothing to use as a propellant

alternatively, what are some neat resource-efficient methods of travelling around in space?
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>>7846814
Thanks a lot. I'm going to take that as an advice for the next exam and start learning earlier to have enough sleep.
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>>7846820
I've told myself this at least 100 times in my life.
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>>7846827
kek this
engineers are efficient because we optimize for the last second
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>>7846815
shoot electrons
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>>7847384
forgive me if this is a dumb question (or if im replying to bait), but where are you getting the electrons from? you aren't implying they're coming from the sun are you?
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>>7847384
wouldn't this is just be a really bad version of ion propulsion?
ion propulsion engines use really heavy ions (xenon), which might as well be shooting suns out of your ass compared to the mass of an electron.
Besides, ion propulsion engines have the issue that they build up charge and thus have to shoot out a trail of electrons for the sole purpose of keeping a neutral electric charge. Any positively charged thing you want to use for this purpose on an electron propulsion device would of course weigh many many many times more than the electron which would raise the point that you should be using those ions for propulsion instead of the electrons.

I mean I'm no expert but doesn't this just seem like a really bad way of creating impulse?
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Could pi eventually lead to a repeating pattern? Why not?
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>>7847451
No. You can convert every repeating decimal into a rational number, and pi is irrational. It can't start repeating.

Now, that's not to say there might not be _some_ sort of pattern in pi (it's highly unlikely that there is, but nobody has proved it). It just can't repeat the same finite string over and over.
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>>7834050
1. -> ALWAYS include units.
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>>7846793
Fuck off
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When does /sci/ autosage?
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I'm trying to understand polynomials and everything that makes them.
I've used Purplemath and random articles from Google as my guide, but there are some things that don't make sense.

>1. A polynomial has terms, for example 4x +x has two terms. But if you look at the 4x, it's technically 4 times x. So shouldn't it be trinomial? Because then the polynomial has 3 terms in total. 4 * x + x

>2. Does the term polynomial only apply to algebraic formulas with a variant/unknown?

>3. Are unknowns and variants even the same name for the same thing?
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>>7847658
in 1 or 2 posts

new thread at >>7847660
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>>7847659
4x is a term
https://simple.wikipedia.org/wiki/Term_(mathematics)
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>>7833071
(Diameter of circle times length of movement) plus area of circle
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>>7847659
if two things are multiplied together they almost always count as one term
addition separates terms (i think it might be something to do with the fact that you can't factor out of a sum, but you can factor out of a product)
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>>7847659
Terms are separated by addition and subtraction. Multiplication and division are interior operations that happen within terms.
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How can I construct a functions with an integral of exactly 1?

f(x) = 1/360 from 0 to 360 integrates to 1. I want to construct a sin function with the exact same integral.
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>>7848696
Get a random function, integrate it over the interval. Divide your function by that integration result, this new function integrates one.
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>>7848838
I am so horribly stupid. I cannot believe I didn't thought of doing it this way. Thanks anon. You helped me a lot!
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