/sqt/ - Stupid Questions Thread

I don't understand u-substitution for integrals.
Why do we treat the [math]\frac{du}{dx}[/math] as an arithmetic fraction and perform algebra on it?
I don't even really understand what the [math]\frac{d}{dx}[/math] or the [math]dx[/math] at the end of an integral _really_ means, no one ever explained it.

It's just a rule of thumb to make the computation easy, but it's in no way something you should take as a rigorous mathematical statement. If you want a proof, try googling it.

>Why do we treat the dudx as an arithmetic fraction and perform algebra on it?
i have really struggled with whether and how to respond to this. The execution of this message was very nice and respectful, and I genuinely appreciate that. The premise, however, is problematic. Maybe not inherently, but within the context of the sexist society we live in. Men are allowed, and often feel compelled, to think out loud at women, to share unsolicited not necessarily informed thoughts at women. (And usually these men, unlike you, don’t even seem to recognize that their thoughts may not be useful.) Women on the other hand aren’t allowed to be as open. So, if you want to not just be respectful, but actually be anti-oppression, it is better (IMO) not to respond to a woman’s work with the types of thoughts that other men pawn off as insights, if you know what i mean. again, i appreciate your honesty, but i feel obligated to point these things out.

>tfw too fucking dumb to understand trig substitution

Does anyone have a resource, video, etc that breaks this down in absolute brainlet terms? When I look at examples I literally have no clue where the substitution function comes from or how you determine it. I dropped Calc II last semester after getting lost in it and have to pass it this summer.

Another calc 2 brainlet here.

I've gotten as far as converting this equation into the integral of cos^2x.

What is the integral of cos^2x?

Okay google helped me.
How are you supposed to remember every trig identity?

>How are you supposed to remember every trig identity?
you're not

Wolfram it. It's ugly.

I second this question.

My calc II proof expects us to. He has shitty problems where you trig sub using double/half angle formulas including obscure af ones for cofunctions.

Wolfram engine must have fucked up because once you convert it to 1/2*(1+cos(2x)) it's pretty simple.

Seriously I don't trust any ugly answer that comes out of wolfram, chances are the algorithm just failed for what you gave it.

Why are the rationals countable? I know there's a proof using Cantor, but I don't know enough math to understand Cantor's stuff yet. According to Wikipedia, a set is uncountable if it's cardinality exceeds the set of natural numbers, but doesn't the cardinality of rationals exceed the set of N?

I mean you can go 1/1, 1/2, 1/3, etc all the way to infinity, and do that with every integer as the numerator as well. It looks uncountable to me.

...

So why can't you draw diagrams like that with irrationals? Even if they go on forever, some are larger than others, and can, in theory, be ordered.

...

because given any list of irrationals you can construct a new one not on that list

Can anyone recommend a textbook for quantum physics? Something suitable for self-teaching, preferably.

First, do you know the math? Second, shankar.

Linearize it first with double angle identity.
cos^2x=(cos2x+1)/2

Damn, posted this in the old thread without noticing there was a new one:

Thinking about majoring in chemical engineering but heard its incredibly hard to find work.

Are the job prospects really that bad? Any chemical engineer here struggle to find work? I live in California so it feels like my options for employment are heavily limited.

\frac{d}{dx} [e^{\int p(x) \, dx}]

How this works

kek
[math]\frac{d}{dx} [e^{\int p(x) \, dx}][/math]

Dw I figured it out

p(x)e^int(p(x))dx
Derivative of e^f(x) is f'(x)e^f(x), derivative of int(p(x))dx is p(x).

I think I'm missing something regarding complexity theory. Can someone answer the following (preferably with examples):

>Are there problems that are in NP that aren't NP-complete and aren't in P?
>Why aren't all problems in EXPTIME NP-hard if NP is in EXPTIME?
>Why is the halting problem NP-hard? Surely since NP refers to all decision problems then that implies that anything that's NP-hard is decidable?
>How do we know that NP-hard problems like SAT are the hardest problems in NP? Could we potentially find a harder problem than SAT that's still in NP?

Looking to major in applied math in college and minor in Chem. Am I wasting my time? Should I just do actuarial maths and make the big bucks? Or do I have a shot at moolah with my current choice of degree? Save the "do what you want" lecture, I'm fucking broke and strictly just looking for the math based major that will gimme the best payout. Comp sci is not an option. Applied math vs. actuary maths. Go!!!

>had anyone used NetLogo
>does anyone use NetLogo

Economics is pretty math based.

Are you familiar with one-to-one and onto functions?

I feel like this is something really obvious but I'm an algebralet and I'm not sure specifically what terms to search for. How does he get x^2 −2x−2=0 from x^2 −2x−2=0 / (x^2 +2)^2 ?

What am I supposed to do in cases like that?

Multiply both sides of the equation by the denominator

If I multiply the left side by zero, it stays zero, right?

Yes, anything multiplied by 0 is 0. Think about it like this, you want to find when that equation equals 0 you know that 0 divided by anything is 0 like 0/6 = 0 so you just need to find out when the numerator is 0, thats when the entire left side of that equation is 0.

>I'm fucking broke and strictly just looking for the math based major that will gimme the best payout.

Look at entry level job posting and see what courses they want to see.

Ok, but could you show how multiplying by the denominator yields x^2 -2x -2 = 0?

I'm getting something wildly different.

How can you get something wildly different? What are you getting?

major in applied math and minor in comp sci faggot

Well (x^2 + 2)^2 is x^4 + 4x^2 + 4, so multiplying that against the numerator is going to give a polynomial starting with X^5. Nothing close to the answer.

x^6 rather

But isn't (x^2 + 2)^2 also in the denominator? So it would cancel out on that side.

I don't see it in the numerator

>But isn't (x^2 + 2)^2 also in the denominator?
>I don't see it in the numerator

>also

...

Hey, you're the one who doesn't get that a/b = 0 implies a = 0.

Ok, but how does x^2 become positive and 2x become negative?

and +2 become -2 as well

You can multiply both side by -1

(-x^2 + 2x + 2)*(-1) = ?

That makes sense, but why would I do that specifically? Does it make factoring the polynomial easier?

x^2 - 2x -2

Yes and its also a convention to not have leading terms be negative

Ok, thank you.

I need a biologyfag to help me out here.
Every time I wake up from sleep, no matter if it was a one hour nap or a ten hour rest, no matter if I fell asleep tired or not, no matter any variables at all, I always awake in a state of delirium and what I'd describe as temporary amnesia. This didn't start happening until a couple weeks ago. I'll try to describe to the best of my ability; I wake up confused about where I am, thinking nonsensical thoughts (i.e, today I woke up terrified of my pillow, thinking something about green crystals, and the day before about stuffed animal tulpas.) I know how 'xd random' that sounds, I am not making a joke- these 'episodes' can last for well over ten minutes and I had the cops called to my apartment before because I was literally screaming at the top of my lungs for a solid five to ten minutes. Is this a documented thing? I realize this sounds like a retarded joke but it's not and I am legitimately worried that I might have some degenerative brain disease or something. Other sleep related problems include that I usually wake up feeling like blood is rushing to my head (I sleep with my head on a pillow, not leaning down or anything though) and sometimes I can't see anything besides solid white for up to thirty seconds after waking up. I should probably mention that I can remember these fits clearly, it's not a muddled memory or anything. No changes in my lifestyle either that could trigger this either.

...

It may have something to do with your blood pressure affecting your brain's oxygenation while you sleep, giving you mild hypoxia when you awake, which would absolutely throw you into a delirium. I'm not a biologyfag, but I've suffered from blood-pressure related hypoxia before and sometimes get very mild versions of what you describe.

It sounds quite serious, user. I think you should see a doctor. If what I'm saying has any truth to it though, you can at least rest assured that your brain is not degenerating, just starved for oxygen.

Why are the Fraunhofer lines of heavy elements (Calcium, Sodium...) more prominent than those of Hydrogen and Helium in the solar spectrum? There are way more lighter elements so why don't they have a greater effect on the spectrum?

do terrorist attacks follow a poisson process?

so i get

delta enthalpy of reaction = -21 kj/mol
delta gibbs e of reaction = -8.2 kj/mol

both i calculated correctly

for delta entropy of reaction i get = -35 j/(k*mol)

which was correct, until the prof changed the sign on the grounds of "entropy cant ever be negative", so she just changed it to +35 j/(k*mol)

is her reasoning correct? actually it was a classmate who told her

delta G = delta H - T delta S

can you just switch signs on delta S like that?

try sleeping with a pillow under your feet, elevating them

In what way? By location or time?
Either way I doubt it, since terrorist organisations probably want to spread them out to make them as unpredictable as possible.

I assume as a time process.

Run the data, see what the MLE gives you as a parameter and evaluate the fit with an F-test

>that data would not be terribley hard to find
>it'd probably neEd to be transformed

>If you have 2n points arbitrarily placed in [math]\Re^3[/math], what is the maximum number of connections between the points an arbitrarily placed plane can 'cut'?
I have no fucking clue how to do this, i've tried all the geometry I can, do I need to use multi-variable calculus? Am I a brainlet?

Good question, you should be able to formulate the situation that maximizes possible edges, now think about graphs.

So, I took a [math]^{1}\text{H}[/math] NMR spectrum of pic related and I seem to get a weird [math]^{3,4}\text{J}[/math] coupling in both the ortho and the meta proton with the same coupling constant of 1.1 Hz. I know that this might be from a coupling with [math]^{15}\text{N}[/math] or [math]^{17}\text{O}[/math], but I'm not sure which one. Judging from the MS, the product does not have any impurities. Can anyone help me? I'd really appreciate it.

Nvm, got it. They couple with each other. Should've realised that earlier...

n^2

>you should be able to formulate the situation that maximizes possible edges
thats literally the question

how?

The answer given in the last thread is still there:

>posts the wrong image
Oops. Again,

How would I attempt to prove this? I can understand how there's elements of order 2 and 7, but not sure on the last identity. I haven't done a course on group presentations, so can't use any possible theorems that make this rather simple.

i dont know what theorems you know but the group has to be D4

Heh, that's the next part of the question. I know the required isomorphism to show that but I guess I can't use it here since it's the answer to ii)

what did you use to show the existence of a,b with order 7 and 2?

I was going for using Lagrange's theorem, but now you mention it that doesn't mean that the group can't be a load of elements with order 2 and none of order 7..

yeah lagrange won't do it

do you know sylow theorems?

Oh. They were in this module last year but were moved to a different one this year. I assumed that this question didn't require them. Damn

...

A quantity is measured by two different methods and the values and standard deviations are

x1 +σ 1 = 1.5 ±0.6 and x2 + σ2 = 2.9 ±1.5

The value of the test is : ?

What do I calculate with?

t= (|x1−x2|)/
(√(𝜎x1)^2 +(𝜎x2)^2)

It's a consequence of them.

Is the formula for triangle numbers used outside of discrete mathematics?

If I give my hormone therapy hormones to my cat will it turn into a cat girl

cant you just get a cat thats a girl and have sex with it?

Currently learning about Laplace Transforms, and I'm a bit puzzled by an example...

Why would [math]\lim_{t \to \inf} \frac{-t}{s} e^{-st}[/math]
be zero?

try using the taylor series for the exponential function

Thank you very much!

I just got a bit confused because when I used L'Hopital's Rule, I got the derivative to be equal to:

[math]
-\frac{1}{s}e^{-st} + -t^2 e^{-st}
[/math]
Which I don't think brings me closer to the answer.

Might have dropped a negative somewhere accidentally

Is (A^-1)A necessarily equal to the identity matrix?

Because (e^-st) is equal to 1/(e^st), and if t is approaching infinity, the denominator will increase at a fuckhuge rate so the function will equal zero. If you don't believe me, do a l'hopital.