/sqt/ - Stupid Questions Thread

math hard! math make head hurt! brainlet want smash!! - edition

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arxiv.org/pdf/hep-th/0012092.pdf
www2.math.su.se/reports/2001/11/2001-11.pdf
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A force of 10 N stretches a spring 2 meters. A mass of 5 kilograms is attached to the end
of the spring and a damper which offers a damping coefficient of 0.6. The mass is
released from 1 meter above the equilibrium position with an upward velocity of 1 m/s.
Find the equation of motion.
5x'' + .6x' + 5x
5x'' because 5kg
.6x' because damping coefficient
5x because k = f/s = 10/2
Is this right? When I solve for the auxillary equation, I get something like -.6 + sqrt(99.64) i / 10
Then I would e^(-.6/10t)(c_1 cossqrt(99.64)t/10 + c_2 sinsqrt(99.64)t/10 which feels pretty wrong.

what do professors and teachers do when a student asks a question they don't know the answer to?

"I don't know the answer, I'll explain it tomorrow".

in my experience, most of the time the question is poorly phrased and built on a false understanding which confuses the lecturer. The lecturer would then offer to deal with it after class, or during office hours

-dismiss the question and insult the student
-ignore the question
-"That is a very interesting question user"
-"I'm not sure but I will look into it" - finds an answer after class. This is the best outcome.

Very rarely will they directly admit that they don't know.

Why do some university math classes grade attendance? Please answer in whole and complete English sentences.

only classes that ever did this was first year courses. usually, in my math courses your attendance meant the difference between rounding the grade up from a B+ to A, of course if it was close enough to warrant it.

>Why do some university math classes grade attendance?
because you're going to a daycare, not a real university

yes that's right, now find an expression for x' and solve for the initial conditions

note that
[math] A \sin ( \omega t) + B \cos ( \omega t ) = \sqrt{A^2+B^2} \cos (\omega t - \tan ^{-1} ( \frac{A}{B} )) [/math]
if you want to make the expression look pretty

How do magnets work?

arxiv.org/pdf/hep-th/0012092.pdf

Literally magic

>charged particles moving in circle create a magnetic moment
>magnetic moments create a magnetic field and tend to align themselves with and follow external magnetic fields
>electrons have a magnetic moment linked with their quantum spin
>take an atom with an unbalanced outer shell
>almost all its electrons have the same spin
>they all generate a magnetic moment in a direction that depends on their spin
>add them up to get the magnetic moment of the atom (non-negligible since all electrons on the outer shell have the same spin)
>build something out of these atoms while assembling the atoms so their magnetic moments all point in the same direction
>your material has a non-null magnetization

so archimedian property removes the need for 'infinitesimals', but it in itself is an infinite process. what is the subtly here?

>but it in itself is an infinite process
No, it's not.

explain

They're trying their best to get as many of the students to pass the courses so they can get their funds and that's one of the tricks they came up with.

Thank god we don't have retarded shit like that here.

[eqn]\forall x\,>\,0,\,\forall y\,\geqslant\,0,\,\exists n\,\mathbf N,\,n\,x\,>\,y[/eqn]
How is this "an infinite process"?

there's an infinite amount of selection for n.

So?

Brainlet here, I can't understand Trig Identities for the life of me, do any of you have shit that would make learning identities not as confusing?

Didn't learn in class because I have class once a week and 3 lab hours, failed the fuck outta that test and now I'm finals with my dick in my hand.

example -3cosθ+3=2sin^2θ,
MyMathLab has like 18 confusing ass steps to do it

what the FUCK is 0/0?

>what the FUCK is 0/0?
In which wheel?

use unit circle ID on sin^2

get: 2cos^2x - 3cosx +1 =0

proof: think

>Stupid question thread
>Brings up wheel theory

>In which wheel?
what the FUCK are you talking about?

>he doesn't know

Refer to

>tfw too much of a brainlet and don't know how to approach this problem

I don't understand. Goodbye, world.

Why was energy not uniformly spread across the universe at it's creation?

And DON'T say quantum fluctuations of the void.

sleep tight
*places paper on your grave*
www2.math.su.se/reports/2001/11/2001-11.pdf

you need the PHENOTYPE to tackle such questions, pea-brain. sorry.

Quick question. I'm at the point where I have a sum with the indices k=2. Do I have to set c_0 = 0 and c_1 = 1 for y_1 and c_0 = 1, c_1 = 0 for y_2?
Then I just get c_1*y_1 + c_2*y_2 ?
There are 2 examples in my book that does what I just mentioned, and then another where they just plug in values of k= 1,2,3...
It doesn't state why they do one or the other, they just do it.

All you need to know is:
[math] (\cos(x),\sin(x)) [/math] is the point at the circle of radius 1 and center (0,0) ( i.e. [math] \{(x,y) \in \mathbb{R}^2 : x^2+y^2=1 \} [/math] ) given that you travelled distance x on it starting at (1,0) and going counter-clockwise.
[math] \cos^2(x) + sin^2(x)=1 \\
e^{i x}=\cos(x) + i\sin(x) \\
\tan(x)=\frac{\sin(x)}{\cos(x)} [/math]

For example. What is the formula for [math] \cos(x+y) [/math] ?
[math] cos(x+y) + i\sin(x+y) = e^{i(x+y)} =e^{ix} e^{iy} = (\cos(x) + i\sin(x)) (\cos(y) + i\sin(y)) = (\cos(x) \cos(y) - \sin(x) \sin(y) ) + i (\cos(x) \sin(y) + \sin(x) \cos(y) ),
\\
\\ \text{therefore } \cos(x+y) = \cos(x) \cos(y) - \sin(x) \sin(y) \text{ and } \sin(x+y) = \cos(x) \sin(y) + \sin(x) \cos(y) [/math]
And this way you found the formula for Both cos(x+y) And sin(x+y).
From this, the identity for tan(x) easily follows.

Now, about your problem, all you need is to use [math] \cos^2(\theta) + \sin^2(\theta)=1 [/math] and solve the quadratic equation in [math] \cos(\theta) [/math] .

It is not.

test

what's the most efficient way to input
>1+2+(Veeky Forums isn't letting me put ellipses here)+999+1000
into a calculator

Ok, so I'm reading some Larry Niven books and tides keep coming up.
I usually think I'm top of the science, but tides are fucking me in the head.
Explain me this

You have a spaceship. It's a hollow cigar. Rounded cylinder, right?
So it's orbiting a neutron star. Heavy heavy gravity gradient. The star is only just a bit above Sol in mass now.
The spaceship is orbiting a few dozen km above the surface.
The big thing is the tide. How do the tides act in such a scenario?
In the story, the spaceship, that cigar shape, orbits around the neutron star, passing close at the perihelion. The crewman finds on his approach that there is a "gravity" down to nose of the ship. It's gaining and gaining. Soon he'll be crushed against the hull at the bottom most point of the ship during the orbit.
But then he finds that the outer most point is undergoing the same event.
So he take shelter in the exact middle, with each extremity being pulled in opposite directions.

What I don't get is WHY
I thought tides involved too similarly massed bodies, like the moon and Earth.
How does a spaceship orbiting a neutron star experience tides?

Just do 1000!
That's what it is.

Also, use Wolfram Alpha. It's your cheat system for math

That's a good question.
The answer is the same as "Why is there more matter than anti-matter?"

1+2+3+4+5+6+7+8+9+10
= 10+(1+9)+(2+8)+(3+7)+(4+6)+5
= 10*5+5
= 55

Now do the same thing but for 1 to 1000

that's what i did and it gives me "error"
and when i do 10! it gives me 3,628,800

????

and how would i input this into wolfram alpha?

wow neat trick

1000*500+500 then?

i'm not so good with math dude
how would I do it for 29 then

i dont get it bro, i did it on my phone and it gave me the results that i told you
it gives me the product instead of the sum.

>phoneposter
KYS

You said it yourself: gravity *gradiant*. Tidal force is the difference in the effect of gravity over distanc. E.g. the moon's gravity pulls much harder on the side of the earth nearest to it, and much weaker on the opposite side of the earth. You get a high tide on both sides. A neutron star's extreme gravity has an extreme gravity gradient. It causes a noticeable difference in 'pull' over even small distances, meaning you will be stretched in the direction of the gradiant, and squeezed perpendicular to it. Just like the tides on Earth.

n*n+1/2

wat
im posting from my laptop

gradient*

No I get that
In my mind, if you're in a extreme gravity gradient, say a neutron star, then the tide force should be "horizontal" right?
Like ok, let's take the Moon as an example.
The closest part of the Moon wants to orbit at X speed due to its orbit.
But the farthest part of the Moon wants to orbit at Y speed.
Since they're both connected due to the, you know, actual fucking body of the moon, the closer part wants to orbit faster and the farther part wants to do it slower.
So there's a torsion between the close and far.

What I'm not getting is that why is that gradient pulling DOWN and not perpendicular to the gravitational force.

[math] 1+2+ \cdots + n= \frac{n(n+1)}{2} \\ \frac{1000 \cdot 1001}{2} = 500 \cdot 1001 = 500 \cdot 1000 + 500 = 500500 [/math]

Fe2O3 + ZnO = ZnO*Fe2O3
all solids
I need standard enthalpy of reaction (delt H, 298)

If the moon was a black hole, with all of its mass compressed into one tiny point, it would still cause tides on Earth. It has to do only with the inverse square of the distance between the closest and farthest sides of the Earth. The fall-off of gravitational force between those two points is what causes the Earth's tidal force. It has nothing to do with the size of the moon, only its mass.

Yeah yeah yeah
I said I understood that. Keep up

I'm thinking that in an orbit a tidal force should be orthogonal to the regular gravitational force, yeah?

The gradient, and thus the tidal force, would be toward/away-from the center of the neutron star. Either Niven's cigar is pointed toward the star (I just assumed that since it's the only thing that makes sense) or he's full of the proverbial poop.

Niven is often full o "proverbial poop" and he has said that in this story, he is partly.
What I'm giving a grievance isn't about the gradient.

Ok, so, in my knowledge (maybe I need to edify you too) the gradient should give a torsion effect. The bottom wants to go faster than the top. So the ship wants to tear apart.
But the issue is that in this story (and another), it isn't about the ship tearing apart, it's about the bottom wanting to go more down and the top wanting to go more up.
It's those directions that I don't understand

If Niven was any other writer, I'd say he was just a dumb pencil man. But Niven was at the core of the 70s Sci-Fi movement and that meant he went to all the NASA events and had all his work edited by real scientists.
The problem in this story isn't Niven. It's my understanding of it.

>1000*500+500 then?
You got it

Tidal force has nothing to do with rotation or orbit. If the Earth didn't rotate and the moon didn't orbit the Earth, there would still be a permanent tide on the Earth. It would just be stationary. It has only to do with the moon's gravity and the diameter of the earth.

just realized the pic you posted is a product as well
factorials give you a product not a sum bro
you're making the same mistake i did lols

>If the Earth didn't rotate and the moon didn't orbit the Earth
How do you define this?
Whatever, that's some relativistic shit

I'm still talking about why the tidal force in this fictional fucking is vertical (i.e. towards the star) rather than horizontal (i.e. in the direction of the orbit) that I think it should be

I'm given the function y= 2/(3+x)
Using a geometric series, I need to find 2 power series centered at x = 0 and x= 1.
How do I start to solve this? Are geometric series the same as Maclaurin series?

I know that its not possible, but how would I formalize this into a mathematical proof?

Consider the matrix R(a) corresponding to a rotation by angle a:
[cos(a) -sin(a)]
[sin(a) cos(a)]

Note that rotation by a+b is equivalent to the composition of rotations by a and b: R(a+b)=R(a)*R(b)=R(b)*R(a).
=>
[cos(a+b) -sin(a+b)] = [cos(a)*cos(b)-sin(a)*sin(b) -(cos(a)*sin(b)+sin(a)*cos(b))]
[sin(a+b) cos(a+b)] [cos(a)*sin(b)+sin(a)*cos(b) cos(a)*cos(b)-sin(a)*sin(b)]
=>
sin(a+b) = cos(a)*sin(b)+sin(a)*cos(b)
cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)

Alternatively, use Euler's formulae and x^(a+b)=(x^a)*(x^b):
e^(ix)=cos(x)+i*sin(x) => e^(i*(a+b)) = (e^ia)*(e^ib)
=> cos(a+b)+i*sin(a+b) = (cos(a)+i*sin(a))*(cos(b)+i*sin(b))
= cos(a)*cos(b)+i*cos(a)*sin(b) + i*sin(a)*cos(b)+i*sin(a)*i*sin(b)
= cos(a)*cos(b)-sin(a)*sin(b) + i*(cos(a)*sin(b) + sin(a)*cos(b))

Put a=b to get the double-angle formulae:
sin(2*a) = 2*sin(a)*cos(a)
cos(2*a) = cos^2(a)-sin^2(a) = 2*cos^2(a)-1 (by substituting sin^2(a)=1-cos^2(a)).

To get the half-angle formulae, solve the latter for sin(a)/cos(a):
2*cos^2(a) = 1+cos(2*a)
=> cos^2(a) = (1+cos(2*a))/2
=> cos(a) = sqrt((1+cos(2*a))/2)
=> cos(a/2) = sqrt((1+cos(a))/2)

2*cos^2(a) = cos(2*a)+1
=> 2*(1-sin^2(a)) = cos(2*a)+1
=> 2-2*sin^2(a) = cos(2*a)+1
=> -2*sin^2(a) = cos(2*a)-1
=> sin^2(a) = (1-cos(2*a))/2
=> sin(a) = sqrt((1-cos(2*a))/2)
=> sin(a/2) = sqrt((1-cos(a))/2)

For anything involving tangents, just use tan(a)=sin(a)/cos(a). Where necessary, convert between sin(a) and cos(a) using sin^2(a)+cos^2(a)=1.

>I know that its not possible
Why?

can somebody quickly check if last row is same as other two?

i got the last row by adding log to each side and then migrated x from exponent to multiplier position and then divided it by log2
is this correct?

Yes.

You can check it with a calculator:
log(5)/log(2) = 2.321928094887362
2^2.321928094887362 = 5

thanks to the skies mate
teacher fucked me because she said when i wrote second step that i needed to do it further so i wrote third one instead and i thought i haven't done it correctly.
either way, both are correct lol

The junctions alternate between north-south and east-west in a chequerboard pattern. The one immediately north of the starting position is east-west. Each street is one-way; the junction at one end is north-south, the other east-west. It's only possible to enter a street from one end. The starting street can only be entered from the south.

Are the Feynman Lectures + Exercises good to learn physics?
I only studied physics in HS

Yes. Excellent, in fact. But then you'll want to study each area in more depth:
classical mechanics: Kleppner/Kolenkow
electrodynamics: Purcell
thermodynamics: Reif
quantum mechanics: Shankar
special relativity: Taylor/Wheeler

Then on to:
general relativity: d'Inverno
quantum field theory: Peskin/Schroeder

How do I study physics

I'm a brainlet and programmer. But I never went to uni. I've been working in software for 10+ years now.

I want to move abroad but most other countries do not welcome self-taught people as much as Germany does so I need a degree.

I signed up for computer science in October but the high amount of math is really difficult for me to learn since I can't quit my job.

Right now I am working 4 days a week, studying on 3.

What way can I find to memorize the amount of information more efficently? It's not that I don't understand the things, it's that I forgot most part of it after a day again

Is the answer to this not 0? Because if μ was 0 (and y was 0), it would satisfy the requirements of the equation.

Could someone please explain matrix puzzles to me?

Our professor was out on the day we were supposed to go over them. The substitute was an old Chinese man I could barely understand that wrote small on the far side of the whiteboard that seemed to assume we already knew most of the new stuff he went over.

I have no idea how to do these. I know the rows are numbered 0-4 and the, same with the columns (it's a computer class so we start counting at 0 instead of 1)

But after that, I have no idea. The homework is asking to give an assertion about the matrix. Pic related is what I'm talking about. It's not one from my homework, but it's a really similar one.

Really at the end of my rope here. I can't seem to find any videos or anything going over how to do these. I would really appreciate it if someone could go over making an assertion of these step by step, or if there is some youtube video to link that.

What pajeet wrote this problem?

Why the fuck do we even need this general?
The whole board is nothing but stupid questions.

My stats professor. I really don't know how to approach this problem. without just assuming y = 0, and μ = 0. Since X is normally distributed around μ i figure that would make it =0 the other 1/2)

>read book
>do problems
>get problems wrong
>think about it
>retry until right
pretty much it for anything undergrad

the fuck do you mean "matrix puzzle"? reducing to row-echelon form?

I have no idea. Like I said, I've tried searching how to solve these but nothing came up.
In the lecture notes, right under that one I posted it says
"Assertion:
Given an nXn matrix A, for row i from 0 to n-1, for column j from 0 to i, A[i,j] = 1" And there is a box on that same page which is this picture.

The substitute seemed to assume we already knew most of this stuff and how to do them so he didn't go into very much detail on anything. It's a beginner computer concepts course.

can you do this?

No. There were no variables of any kind involved in the lecture notes or with what the substitute did.

Here's another page from the lecture notes.

True/false: "Every nonempty, bounded subset [math]A\subseteq \mathbb{R}[/math] has a least upperbound"

Does bounded imply both an upper and lower bound? or just one?

Depends on the 0/0, some examples:
[math]\lim\limits_{n \to 0} \frac {n^2} n = 0[/math]

[math]\lim\limits_{n \to 0} \frac n n = 1[/math]

[math]\lim\limits_{n \to +0} \frac n {n^2} = \infty[/math]

[math]\lim\limits_{n \to -0} \frac n {n^2} = - \infty[/math]

0/0 = undefined

This is because of the axioms all the other rules are set up on. To divide a number strictly by 0 (and not a limit approaching 0), is not possible for the rules division is set up on

Yeah, it's 0. The only number with a single real root is 0 (I think?). Since a normal distribution is symmetric, p(0 < -X) = 0.5 is equivalent to saying the mean is 0

So you just want a formula expressing the elements of the matrix?
It is:
[math] a_{ij} = 1 \text{, if } i \geq j \\
a_{ij} = 0 \text{, if } i

No, that's not quite it.

What the homework is asking for is the assertion. Written like the example in What I don't understand is the process that you reach the assertion.

>0/0 = undefined
Wrong.

why isn't logic covered in high school? the usual "core" classes are algebra and trig. i would think that logic is arguably more relevant than trig, both for the layman and for someone who wants to move on to college or AP math classes.

>assertion
wtf is this choice of word your retarded professor picked... anyway it's literally what I posted, just rephrased:

For i from 0 to n-1
For j from 0 to i
A[i,j] = 1

And I assume that your proffesor assumes that the rest is filled with 0s.

>Does bounded imply both an upper and lower bound?
Yes.

What would the proper word for it be? I just want to know what to search to learn more about this type of problem.

I can't seem to learn very well unless I see a problem being worked out first.

Can anyone show me why the spectral radius of a Bounded Linear Operator is less than the norm of the operator?

False. Consider [math]A = \{0.9, 0.99, 0.999, \dots \}[/math] for example

What is frame dragging?

>A={0.9,0.99,0.999,…}
sup(A)=1.