/sqt/ - Stupid Questions Thread

Is 1/2 spin always taking into account the magnetic dipole moment inherent to the electron? Is that why it takes 2 rotations for the electron to face the same direction?

>>8529535
You mean organic chemistry or molecular biology?

Molecular biology probably has greater application in future technology.
.

So when you're doing integration by substitution with a definite integral, the upper and lower limits have to be plugged into u, right? Because I keep getting answers that are completely wrong when I do this, but then the answer comes out fine when I keep the limits what they are.

>>8529567
Are you substituting back in for u AFTER you change the limits? Because that will fuck things up.

Consider [math]\int_0^\pi x \cos(x^2) \, dx[/math]. If we say u = x^2 and substitute, we need to change the limits because everything has to be in terms of u. So we have [math]\int_0^{\pi^2} \frac{1}{2} \cos(u) \, du[/math]. Then when we integrate we get [math][\frac{1}{2} \sin(u)]_0^{\pi^2}[/math]. We can do one of two things at this point. You can either just plug the limits in and get your answer, or you get change everything back in terms of x. If we do the latter, we have to change the limits back to what they were before, so we would have [math][\frac{1}{2} \sin{x^2}]_0^{\pi}[/math]. Notice that you'll get the same answer if you evaluate either of these.

>>8529546
funny, I am studying molecular biology atm, and was thinking of changing

>>8529592
Thanks for your help. I'll try it out.

Pedantic question about notation but my autism prevents me from leaving it unanswered.

Is [math]\mathbf{Set}[/math] the only category where [math]f \in \text{Hom}_{\mathbf{Set}}(X, Y) \rightarrow f: X \rightarrow Y[/math]?

Like if you're in [math]\mathbf{Top}[/math], is it still proper to say [math]f \in \text{Hom}_{\mathbf{Top}}((X,\mathcal{O}_X),(Y,\mathcal{O}_Y))[/math] even though [math]f: X \rightarrow Y[/math]? Or do I have this wrong and it is simply that [math]f \in \text{Hom}_{\mathbf{Top}}(X,Y)[/math]

What value is there in knowing whether the momentum operator^2 is hermitian for certain hydrogen states?

Why is learning math/science history important? Why do I need to know who discovered what by doing something in the year X?
When was the last time anyone referred to a historical event when they were solving a problem? Is learning the concepts not enough?

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IF the LD50 of caffeine anhydrous is 200mg/kg in humans, and I, a human, weigh 70kg, while the bioavailability of powdered caffeine anhydrous is 90%...

The highest likelihood of fatal caffeine toxicity would come from ingestion of 30800mg / 30.8g or greater, right? Is this math correct?

>>8529840

It gives you a deeper understanding of how the problem came about and how it was originally solved, while giving you proper context for its importance.

How to increase IQ?
Should I just spend an entire day studying advanced academics and then get into the habit of learning new things?

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Units for moment of inertia is distance^4 (mm^4, ft^4, m^4, etc.)

What is the physical representation of distance^4?

>>8529881
An IQ test measures your ability to detect patterns, and if you include verbal IQ, ability to infer text. So your best idea would to just get really good at pattern detection.

What's the best grad degree to get if I'm studying Mathematics in University right now and I want to be set for life?

Anyone in academia?

Does 'pubish or perish' get in the way of productive research?

Is there something like 'The Journal of Negative Results' where papers with no methodology section or results that cannot be reproduced are refuted?

Define a sequence of functions [math](f_{n})_{n \in \mathbb{N}}[/math] for [math] f_{n} : \mathbb{R} \rightarrow \mathbb{R}, \; f_{n}: x \mapsto \frac{x}{n} [/math]. Does [math] f_{n} [/math] converge uniformly to some [math] f [/math]?

I think it does not, but I am not doing well a proving it.

>>8529939
dude 4-dimensions lmao

>>8530022
Isn't the 4th dimension time? How does that relate to inertia?

>>8529803
this kind of depends on whether you abuse notation like most people do by disregarding the collection of sets

>>8530016
Well (fn) converges pointwise to the function which is zero everywhere. So if you suppose (fn)->f uniformly, you must have f=0; you can look for a contradiction from here.

I need help proving that [math](1-1/2^a)*...*(1-1/n^a)[/math] converges to [math]0[/math] if [math]a < 1, a = 1[/math] or to a positive real if [math]a > 1[/math]

My reasoning so far.
->If a < 1, let a = 1/b with b superior or equal to 1.
We have : [math](1 - 1/n^\frac{1}{b}) = (n - n^\frac{1}{b})/n[/math], so if you make the product, you've got [math]\frac{1}{n!}*(1-2^\frac{1}{b})*...*(1-n^\frac{1}{b})[/math], and of course, the factorial win this one.

For the second part, I have the reasoning, but I need it more rigorously.

Basically I transform the thing on [math](n^a - 1)/(n^a)[/math] and since all terms are positives, and the general term of the product converges to one, there's "no way" it can go to zero or diverges, but I don't feel like putting it like that. How can I explain it ?

>>8530016
Your series of functions can be factorised with respect to x : x (1 + 1/2 + 1/3 + ... + 1/n)

(1 + 1/2 + ... + 1/n) is a well-known divergent series.

>>8530016
>>8530083
Whoops, I've read series of functions instead of sequence of functions. My bad.

>>8530083
When a=1, you have (1-1/2)...(1-1/n)=(1/2)(2/3)...(n-1/n)=1/n, so this of course goes to zero

Now when a>1, the sequence converges since it is decreasing and bounded below by 0. Also we have (1-1/2^a)...(1-1/n^a)>=(1-1/n^a)^n, and this converges to e^(-1/n^(a-1)), hence the limit must be strictly positive.

>>8530110
My bad, that second bit is wrong

I was reading this
http://www.world-nuclear.org/information-library/nuclear-fuel-cycle/conversion-enrichment-and-fabrication/uranium-enrichment.aspx

to better understand the implications of 20% of the US Reserve of U3O8 being sold to a Russian company but I am an uneducated plebeian and I'm having trouble fully understanding the meaning of the sentence

>Natural uranium contains 0.7% of the U-235 isotope. The remaining 99.3% is mostly the U-238 isotope

so does this mean that 99.3% of all Natural Uranium is the U-238 isotope and 0.7% of all Natural Uranium is U-235, or that all Natural Uranium is made of 99.3% U-238 /and/ 0.7% U-235?

>>8530131
basically: Can two isotopes exist within the same unit of an element?

>>8530110
>since it is decreasing and bounded below by 0.
Yeah, but does the product of every member of the sequence converges ?

Also, is my reasoning with the exponential good or bad ?

>>8530137
In every mole of natural Uranium, there is 0.993 mole of U-238 and 0.007 mole of U-235.
It's like, natural uranium is a mix of both, but it's not an element as itself.

>>8530131
>all Natural Uranium is made of 99.3% U-238 /and/ 0.7% U-235?
I think it's this one. It's basically the reason Oxygen's molar mass is not 16 but 15,9994 +/- 0.0004 g/mole.

>>8530146
>>8530144
Thank you, I thought so but I wasn't sure and it was making me feel incredibly stupid.

>>8530140
you said - since all terms are positives, and the general term of the product converges to one, there's "no way" it can go to zero or diverges

this reasoning is not correct, take your example when a=1

now i've figured out what to do when a>1

we have log( (1-1/2^a) ... (1-1/n^a) ) = log(1-1/2^a) + ... + log(1-1/n^a)

now in the range [0,1/2] we have log(1-x)>=-x, so using this inequality we get

log( (1-1/2^a) ... (1-1/n^a) ) >= -1/2^a - ... -1/n^a > -1 * (sum from k=2 to inf 1/k^a), and since a>1 this sum converges, say to C

then (1-1/2^a) ... (1-1/n^a) >e^-C and you're done

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Does having a bigger brain actually make you smart?

>>8530176
a = 1 is excluded, I said that it goes to 0 for a < 1 and a = 1, but to a positive real if a > 1.

If a = 1, we have (2-1)/2 * (3-1)/3 * ... * (n-1)/n
Which is 1*2*3*(n-1) / 2*3*...*n = 1/n which converges to 0.

Thanks for the rest.

>>8530137
> Can two isotopes exist within the same unit of an element?
Define "unit".

Any given atom of uranium is of a specific isotope. If you mine uranium ore, 0.7% of the uranium atoms will be U-235, the other 99.3% U-238. These proportions will remain unchanged by chemical processes such as smelting.

The only viable process for changing the relative proportions of the isotopes is isotopic separation (enrichment) of UF6 using gas centrifuges. Because U238 is heavier than U235, gas drawn from the outside of the centrifuge will contain a slightly lower proportion of U235 while gas drawn from the centre will contain a slightly higher proportion.

The difference in concentrations is fairly slight, so practical enrichment requires a "cascade" consisting of a chain of centrifuges, with the outputs from each feeding the inputs of its neighbours. Thus, U235 concentration increases from one centrifuge to the next.

reposting from last thread, would really appreciate any help

I just failed an exam in a basic chemistry class. It's the only chemistry I need to take and I need to pass it this next exam or else I will need to re-do this whole year.
How do I best teach myself chemistry? I was pretty far away from the passing mark(I got 22 points, needed 40 for a passing grade).
Do I just keep on studying through the book or are there any simple tips for learning basic chemistry? This is some basic shit I just failed it, no excuses honestly.
The exam is in the end of Jan.

How do I know y if i have a system of this form:

y''+y=1+f(t)+g(t)+h(t)+...

y'+y=2+f(t)+g(t)+h(t)+...

Can it even be done?

>>8530207
You have two separate equations. Each can be solved individually, but there's no reason to suspect that they will have the same solution.

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just starting with derivatives, how did this guy get from the second step to the third one?

>>8530233
or rather: from the first step to the second

>>8530202
just fucking study holy shit

how can anyone be this helpless

>>8530076
I actually did find that the sequence converges to the constant zero function, I conveniently forgot uniform convergence implies pointwise convergence. I can take it from here, thanks!

>>8530083
>>8530095
Thats alright dude, thanks for replying anyway.

>>8530243
converges pointswise to the constant zero function *

>>8530233
rootX(x) = x^(1/x)

and using the definition of logarithms ( the fact that e^ln(n) = n )

x^(1/x) = (e^ln(x))^(1/x)

>>8530267
thanks, and the next part? after the =

>>8530227

This came from a DE system where I already solved for x. Then I used x in the original equations and that's where the functions of t come from. The y solution should be such that it works for both of those equations right? But I don't know how to solve them. I thought I could do:

y''=-y+1+f(t)+g(t)+h(t)+...

y'=-y+2+f(t)+g(t)+h(t)+...
y''=-y'+f'(t)+g'(t)+h'(t)+...

-y+1+f(t)+g(t)+h(t)+... = -y'+f'(t)+g'(t)+h'(t)+...
-y+y' = stuff

But I still have y and y' and I don't know how to solve mixed stuff like that. What do?

>>8530279
well then you differentiate (e^ln(x))^(1/x)

derivative of e^f(x) = e^f(x) * f`(x)

>>8530202
two months

just study

>>8529994
Polite bump

Help me /sci/, I am complete idiot. How can I prove that [math]sinh(x) -sin(x)\ge 0[/math]?

I tried to estimate that the derivative is positive so that the function is increasing and then show its zero when x = 0. And that proves it. But I'm having difficulties with showing that [math]f'(x) = 1/2(e^x + e^{-x}) - cos(x) \ge 0[/math]

>>8530284
oh okay, thanks, I kept looking at (e^x)' = e^x

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>>8530312
Keep in mind that sinh(x) = (e^x-e^-x)/2
Shouldn't be that hard to prove that this is always higher than 1, and therefore sin(x). (by the way, your equation is only true in R+.

>>8530207
>>8530283

Regarding these. Can I just assume the terms in common are y? For example:

y''+y=1+f(t)+g(t)+h(t)+...

y'+y=2+e(t)+g(t)+h(t)+...

Then y = g(t)+h(t), since those are the terms in common in both equations. Would this work?

>>8530283
You can solve each of those equations using the Laplace transform.

E.g.
y''=-y+1+x(t)
=> Y(s).s^2 - y(0).s - y'(0) = -Y(s) + 1/s + X(s)
=> Y(s).(s^2+1) = X(s) + y(0).s + y'(0) + 1/s
=> Y(s) = X(s)/(s^2+1) + y(0).s/(s^2+1) + y'(0)/(s^2+1) + 1/s(s^2+1)
=> y(t) = x(t)*sin(t) + (y(0)-1).cos(t) + y'(0).sin(t)
where * indicates convolution. The convolution x(t)*sin(w*t) is simply the frequency component of x(t) having angular frequency w, phase-shifted by 90 degrees.

IOW, it's a system which oscillates at a frequency of one radian per second, the phase and amplitude varying according to initial conditions and resonance with the driving signal x(t).

>>8529943
Thanks lad

>>8530338
I doubt it.

How exactly did you end up with a single parameter being described by multiple equations in the first place?

In particular, a system with y proportional to -y'' tends to be sinusoidal, whereas y proportional to -y' tends to be exponential, while a damped oscillator has y'' proportional to both -y and -y'.

>>8530324
But (e^x-e^-x)/2 isn't always bigger than 1, even for x => 0? You can even see that on your graph? Did you mean 1/2(e^x + e^-x) => 1? Thats excatly where I'm having trouble :D

Whats the integral of? Do I used trigonometic sub or what?

[eqn]\int_{0}^{2\pi}\sqrt(4cos^2\theta)d\theta[/eqn]

When finding zeros of a polynomial, how do you know what numbers to try next with the intermediate value theorem?
People keep saying how intuitive it is, but I still don't fucking get it.
I end up just trying a shit ton of different numbers and it takes me forever to factor out a polynomial of degree 4 or greater.
It's embarrassing.

Can science one day solve moral problems?

>>8530202
Learn conversions. Learn how stoicheometry works.
PV=NRT
M1V1=M2V2.
Work them examples dude.

>>8530489
That's just 2*abs(cos(theta)) under the integral m8...

>>8530503
Just keep trying with it. Usually it's pretty obvious. Also cheat and take the derivative to see where the function is increasing and decreasing. Try the obvious stuff, -1, 0, 1, 100 etc.

>>8530508
I actually completely forgot about that, damn.
Thanks

Is it possible to find closed form solutions to
[eqn]\zeta (x)=x[/eqn]

>>8530542
do you know that there are any?

If I have to solve a Laplace problem with initial conditions, there comes a time where y(0) appears and I plug the initial condition there. But what happens if there are no initial conditions? For example, I know that

L{y'} = sL{y} - y(0)

If my initial conditions said that y(0)=7, then I would write

L{y'} = sL{y} - 7

And proceed to do a bunch of algebra and finally the inverse Laplace to know y (Am I right?), but if I don't have any initial conditions, What should I do with the y(0) term? All I know is from watching videos and solving stuff with tables, so please don't mention any buzzwords about frequency and domainwhatever.

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how did he get to the last line?

>>8530566
cant solve a DE by laplace without initial conditions, that is its downside
different methods work for different cases

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>>8529479
Have most optimistic people experienced trauma in their lives, in which they rather feel happy all the time than not?

>>8530567
I guess z=sqrt{a(x-r_1)/(x-r_2)}

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>>8530566
>>8530570

>cant solve a DE by laplace without initial conditions

The funny thing is that I've got some excercises of Laplace without initial conditions. For example:

x' = x-2y

y' = 5x-y

And the alleged answers are:

x = -Cos(3t)-(5/3)Sen(3t)

y = 2Cos(3t)-(7/3)Sen(3t)

Did the book forget to print the initial conditions or is there something to be done?

>>8530179

Not necessarily. Its mainly about how wrinkled your brain is, which increases the surface area.

Would it be correct to say that tidal locking is the result of gravity neutralizing angular momentum? or matching angular momentum?

Are shadows two dimensional?

>>8530566
If you don't know the initial conditions then you just leave y(0), y'(0) etc as constants, which will end up as coefficients in the resulting time-domain equation.

E.g. given the DE
y''(t) = -w^2.y(t)

the solution is
y(t) = (y'(0)/w)*sin(w*t) + y(0)*cos(w*t)

This should be reasonably intuitive.

If y'(0)=0 (e.g. moving the mass in a spring-mass system to a fixed offset and releasing it at t=0, or charging a capacitor in an L-C circuit to a fixed voltage and connecting it to an inductor at t=0), then you get a cosine wave whose amplitude is equal to the initial value.

Conversely, if y(0)=0 (e.g. imparting an impulse at t=0 to a mass which is at the equilibrium point, or starting an L-C circuit with zero capacitor voltage but non-zero inductor current), then you get a sine wave whose derivative at the zero-crossing is its derivative at t=0.

And if both y(0)=0 and y'(0)=0, you get nothing; no energy = no motion/tension/voltage/current = zero amplitude.

>>8530656
The thing is, any time-varying system ... varies with time, duh. If you change your zero reference point, you change the equation describing the system.

So a system which is described by the equation y(t)=a*sin(w*t) is just as well described by y(t')=a*cos(w*t') where t'=t+pi/2w.

IOW, the only system whose behaviour is independent of its initial conditions is one which never changes.

this slow ass thread mang

yahoo answers is probably faster

>>8530813

Yahoo Answers! is unironically very fast.

Not really a science or math realted question but, I didn't want to make a thread about it.

Do schools charge more if you pick a dual degree program? I'm thinking about going for an MD/MPH program when I graduate soon.

>>8530987
why dont you look at your school's website brainlet?

>>8530588
> x' = x-2y
> y' = 5x-y
x = ((x(0)-2*y(0))/3)*sin(3t)+x(0)*cos(3t)
y = ((5*x(0)-y(0))/3)*sin(3t)+y(0)*cos(3t)

> x = -Cos(3t)-(5/3)Sen(3t)
> y = 2Cos(3t)-(7/3)Sen(3t)
=> x(0)=-1, y(0)=2

But suppose you had x(0)=y(0)=1, i.e.
x = (-1/3)*sin(3t)+cos(3t)
y = (4/3)*sin(3t)+cos(3t)
so:
x' = -cos(3t)-3*sin(3t)
y' = 4*cos(3t)-3*sin(3t)
x-2y = (-1/3)*sin(3t)+cos(3t) - (8/3)*sin(3t)-2*cos(3t)
= -3*sin(3t) - cos(3t)
= x'
5x-y = (-5/3)*sin(3t)+5*cos(3t) - (4/3)*sin(3t)-cos(3t)
= -3*sin(3t) + 4*cos(3t)
= y'

It should be self-evident that, while a system of differential equations can describe the nature of a system, the exact behaviour depends upon its inputs.

In particular, if a system of equations is linear and time-invariant (i.e. it consists only of the unknown functions and their derivatives), scaling all of the functions by the same factor scales all of their derivatives by the same factor, which (as there's nothing else in the equations) scales both sides of every equation by that factor. IOW, such a system always has an "amplitude" parameter.

Even more particularly, anything that models a physical system will have a "zero energy" state where it just sits there with nothing changing.

>>8531013
>Even more particularly, anything that models a physical system will have a "zero energy" state where it just sits there with nothing changing.

kind of like your life

>>8531012
I did but, no answer. That's why I asked here.

>>8529516

the two rotations thing is a consequence of being a spinor. the rotation operator ends up having factors of like, h/2 or something so that you need 4 pi to cancel with the 1/2 to make 2pi (a full rotation)

>>8530043

first of all, moment of inertia has units kg*m^2, not m^4. secondly, that guy above is trolling you

Is physics actually useful?

>>8531071
it's arguably the most useful field in existence

>>8531071

depends on your occupation, but in general, a familiarity with the essential concepts contributes immensely to general understanding of nature and the world

>>8531071

I rate physics among the noblest branches of human knowledge. I think it would be a scandal for anyone who considers themselves a philosopher to lack at least a rudimentary understanding of modern physics, including classical mechanics, quantum mechanics, general relativity and cosmology.

>>8531081
Speaking solely of tangible benefits I would say agriculture is more useful. Yeah you can do neat things with physics, but it's not gonna do you a lot of good if you can't eat.

Is there a minimum unit to empty space? Or can it be divided infinitely?

>>8531103

>implying there is a such thing as 'empty space'

that being side the limit of divisibility is probably close the planck length

>>8531110

being said*

>>8531110
If the universe is expanding then doesn't that imply that there is something for it to expand into? That space should be empty since the universe has not expanded into it yet.

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What would you do if you had

a) 10 minutes to live?
b) one week to live?
c) one year to live?

More importantly, what wouldn't you do in the shorter timespan that you would do in the longer span? How to prioritize?

>>8531115

that's a common fallacy, akin to arguing there must be a beginning to time. all beginnings are in time; in just the same way, all limits are in space. it is nonsensical to speak of a limit to space. material space is not expanding into an infinite void, any more than time is expanding into an infinite future

>>8531013

So you got the initial values based on the answers right? But it would've been impossible to solve without previously knowing the expected answer. Am I getting it right?

How long will it be before bacteria that decompose plastics become a common thing? I would think it would be a logical adaptation considering all the shit we dump out there on a daily basis.

Will this development have bad side effects for us, as our plastic gadgets suddenly start decaying around us? Or would it be slow enough to not be a big deal?

Can someone explain to me what a function is, I'm really not being able to grasp the concept with the whole input/output sausage factory analogy chickenshit bullshit.

>>8531254
a function from X to Y is a set S of ordered pairs (x,y) where x is in X and y is in Y

where if (x,y) and (x,z) are in S then y=z

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How do I express implication through conjuction and negation using composition (superposition)?

[math]f(x_1,\dots,x_n) = g(h_1(x_1,\dots,x_n),\dots,h_m(x_1,\dots,x_n))[/math]

So,
f is x -> y, g is x*y, h1 is not x, h2 is not y.
f(0,0) = g(h_1(0,0), h_2(0,0))
f(0,0) = g(1,1)
f(0,0) = 1; g(1,1) = 1
???

Barely makes sense to me. It is easy to to do that using shit like (x -> y) = (not(x)V(y)), etc, but I don't know how to do it using composition.

>>8531255
Does this explain it though?

Maybe I wasn't meant to math...

Would nuclear propulsion be an effective use of waste generated by nuclear power plants? Why?

>>8531255
Classic /sci/. I'm sure he'll understand that.
>The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.

>>8531410
What part of that definition is difficult?

>>8531132
Right. The coefficients of the cos(3t) terms are x(0) and y(0), so examining the answer you gave determines those, and plugging them into the coefficients of the sin(3t) terms confirms them.

Different values for x(0) and y(0) will give different amplitudes for the sin/cos terms, but the DEs will still hold.

>>8531424
Most of the functions you're likely to encounter in practice correspond to infinite sets (often uncountably infinite), which probably isn't a particularly intuitive concept to someone who isn't already fluent in math.

>>8531310
It defines it; I wouldn't call it an "explanation".

The key point about
> where if (x,y) and (x,z) are in S then y=z
is that if you look for the pair whose first element is x, you'll find at most one pair, meaning that the function has a specific output for any given input.

It may help to think of a function as a graph which can go up and down but never "doubles back" on itself, i.e. you can draw it on a plotter where the paper always scrolls one way. For any given x coordinate, there is a single y coordinate (or there might be a gap in the graph at that point).

Im taking the acs tomorrow for gen chem2 how can i not die

why are there so many stars and galaxy?

shouldnt they be rare??

>>8531144
Apparently they have already found some species that do this, so it's just a question of whether they spread.

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what's going on here, I was never taught this.

>>8531623
I don't see any problem. A negative second derivative means that the function "looks like a parabola with the shape of a bell" in that region and a positive second derivative means that it "looks like a parabola with the shape of a glass (or a tea cup)".

Positive first derivative is a increasing function and negative first derivative is decreasing function.

Therefore the answers are C, E and A.

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>>8531653
I see now, I've never seen that notation for higher order derivatives, so I had no idea what the question was asking. Thanks m8

How do I find the energy eigenvalues of a Hydrogen Atom?

All I find in places is it's given w/o any proof, how do I show it myself?

>>8531676
You can find it in any basic QM textbook (for eg, chapter 4 of Griffith)

>>8531688
checked
Also, Griffiths*

>>8531424
people are taught functions before sets.
most first semesters have trouble grasping relations, so you'd think that someone not able to understand what a function is (apparently not even heuristically) wouldn't be quite able to understand your definition

You use 53,56 GBq of fluorine-18 (t½ = 109,8 minutes) to synthesize something. The synthesis takes 40 minutes. The radiochemical yield (product's activity divided by original activity) was 2%, so the activity of your product is 1,07 GBq. The molar radioactivity (A/n) of your product is measured and it is 5 TBq/µmol. Can you calculate the molar radioactivity of the fluorine-18 (F-) used in the reaction from this?

I feel like I'm missing something here. This feels like it should be a simple arithmetic problem,. To calculate the original molar radioactivity, I need to somehow find the chemical amount of F-, and the just calculate the specific activity = A/n. But how do I do that using the information I have?

>>8531623
B,E,A.

Imagine a point following the curve.

Both derivatives having the same sign means the point is accelerating, i.e. the first derivative is changing in the same direction as its current value (positive getting more positive or negative getting more negative).

Opposing signs means that the point is decelerating, i.e. the first derivative changing in the opposite direction to its current value (positive getting less positive, negative getting less negative).

1/x = 0.9
How find the x ?

>>8532055
>1/x = 0.9
0.9=9/10 therefore x=10/9

>>8529479
What is this guy doing?

https://youtu.be/qCE5bmNlpi8?t=6m54s

How do I get the number of "stacks" in his picture of the vector field?

>>8532055
This is a 18+ website.

I'm hoping that /sci/ can help me, I'm trying to solve some problems of Systems of DE's, but they want us to solve them using eigenvalues and eigenvectors, I know it can also be done with LaPlace transformations but they're gonna cover that in another course. What I don't get is how you can find the eigenvectors for two equations that both equal zero.

So say that functions:

x'(t)=y(t)

and

y'(t)=4x(t)+5y(t)

I get that the eigenvalues are 1/2*(5+sqr(41)) and 1/2*(5-sqr(41)). And then you plug each into:

(M+λ*I)*V=0

Where M is the original Matrix for the system, λ is each of the eigenvalues, I is the Identity matrix in this case [{1,0},{0,1}] , V is the eigenvector matrix and 0 is just a zero matrix.

What I don't get is how you find the vectors themselves. Because if you're equating the whole thing to zero, then no matter what the value of (M+λ*I) isn't it only possible for the Vector to only be [{0,0}]? I really feel like there's some basic concept that I'm missing, because I've worked it out with all kind s of numbers and every time the only answer is just zero.

Thank you.

>>8532190
I don't understand your question very well, but I remember that you have to work in terms of determinants.
If you have the system: X' = A*X, the solution will be of the form:

X = c1*(e^(λ1*t))*U1 + c2*(e^(λ2*t))*U2+..

where λ1, λ2, ..., λn are the eigenvalues of A; U1, U2, ..., Un are the respective eigenvectors of A ; and c1, c2, ...., cn are constants.

To find the eigenvalues just apply:

det(A-λ*I)= 0

To find the eigenvectors:

A*X = λ*X

>>8532055
dude what

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studying for exam for retard physics monday
>pic related
an object of mass m, on a friction-less table, is connected to an object of mass m hanging from the edge of the table, over a pulley of mass m.
what is the acceleration?

I have:
>ma = mg - Ta
>ma = Tb
>Torque = 1/2 ma = Ta-Tb
>3/2 ma = Ta
> ma = 9.8m - 3/2ma
>a = 9.8 - 3/2a
>a = 2/5 9.8

>>8529828
If its not hermitian, then it's not a physical observable (lest you get non-real results of your measurement).

>>8529994
I'm in academia. If anything, publish or perish motivates productive research. I work in mathematical physics though, so it's not like we can just write any sort of nonsense down and submit it. I suppose for fields like experimental physics and (shudder) bio, there's more danger of people just publishing unverifiable bullshit for the sake of it.

>>8531623
https://www.youtube.com/watch?v=dIE22eL6q90

>>8531121
you would spend your time on what can give you the most pleasure or reward in return for the time you devote to it. 10 minutes would probably be apologizing to my loved ones and sex. one week would probably be travel as well as the former, one year i'm not sure.

>>8532263
Don't you need the radius of the pulley?
>Torque = 1/2 ma = Ta-Tb
Don't you have to work in terms of angular acceleration instead of linear acceleration?

>>8532303
Torque is 1/2 mr^2 * (angular a)
angular a = (linear a)/r
therefore torque is 1/2 mra
but torque is also T * r
so T = 1/2 ma
where T is Ta-Tb

>>8532220
That actually is my question. I'm not too familiar with matrices so I'm sure how you equate A*X = λ*X, I know you convert it into:

(A -λ)*X = 0

And then solve the equations to find X. But if all the equations equal zero, then isn't the only answer that X equals zero?

I mean, it's pretty much the same as regular systems of functions, right? If you have ax + by =0 and cx + dy =0 , then the only possible answer is that both x and y equal zero.

>>8532263
>>8532303

Oh, you just applied a = R * α
In that case your solution look correct

>>8532318
You are considering the vectors and matrices as scalars. That's the problem. Maybe this example can clarify the concepts.

https://en.wikipedia.org/wiki/Matrix_differential_equation#Solving_deconstructed_matrix_ordinary_differential_equations

can anyone give me an intuitive picture of the Riemann-Roch theorem, and how it would be useful in some simple examples?

>>8532318
Use det (A- λ*I) to find λ.
Now replace λ in A*X = λ*X.

Look the wikipedia link for understand the matrix treatment.

If earth pulls you down with 9,8 m/s^2, why is escape velocity so much higher?

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why do you multiply by cube root of 3b^2c? i understand you cant have roots in the denominator but why the fuck is 3b^2c multiplied and not cube root 9bc^2

>>8532433
9.8 m/s^2 is not a velocity anon

>>8532494
the entire thing is correct, in any form -- the "correct answer" on that problem is whatever specific form your teacher wants it, which is a relatively arbitrary choice (of course there are some that make more sense than others).
Your teacher chose to mulitply it by something that would give you a cube under a cube root, thus simplyfing the denominator, but you can do that in any way you want. Multiply it by what you were thinking about and figure out if what you get in the denominator is helpful.

When you go to apply this knowledge of algebraic manipulation (if you ever do) you surely won't be giving a damn about roots in the denominator.

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Does anyone have maple or mathematica that could tackle this and post the solution path? Trying to get to the bottom of this quantum problem but I keep shitting the bed trying to do the integration by parts.

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Hello guys I've got my math final in two days

I'm about to study for another class since that is tomorrow

But for the math one. He has thrown in proofs he put on the slides on the exam

My question is should I just memorize all the proofs I can get out knowing what it means or what or why they did a certain things on a step

When I was studying I would get caught up and itd take hours for me to finally see every little thing for it to make sense

Should I just memorize all the steps in the proofs even if it doesn't make sense to me yet?

how do you solve for x given x^x^a=a algebraically?

>>8532584
If every single step of every proof is difficult to you, there's a problem going on, likely the fact that you don't really grasp the basic definitions very well.

Most proofs you're going to encounter in undergrad have at most 2-3 tricky steps and the rest is extremely straightforward definition-pushing

What you should be doing to prepare for proof-based finals is "I know the step I need to get past the block in proof X and I can fill in the rest". You can try to memorize it all but if you actually succeed at it you have an incredible memory.

>>8532574
also of note g and f are functions of r

>>8532584
>Should I just memorize all the steps in the proofs even if it doesn't make sense to me yet?
My two cents: you only have two days to study for this final, so for the moment, do whatever you can to get a good grade in the course. If you had more time, I would say yes, take your time to make sure you fully understand everything. But in this case, thinking you'll be able to sit down and spend the hours to understand everything is a little optimistic...

>>8532613
I think I have autism or something. The reason it takes me so long for it to understand is they will skip a step or not fully state why they did a certain thing and as soon as that happens my mind won't let it go.

Like one I was working was basically g1=gcd(a,m). The step was just g1 divides a so it divides by b according to the notes. But it didn't make sense in their third step. After wasting time I found the reason for that which was simple like if g1 divides a that means it divides what its equal to which then means because b and some other stuff is equal to a just means g1 is also equal to b. Easy as heck now but when one little thing doesn't make sense to me the whole thing doesnt make sense

How do I tell a stupid person that gamma-ray emissions do not go faster than light?

>>8532678
"Gamma-ray emissions do not go faster than light."

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What would be the best method for teaching myself calculus. I'm in highschool and am currently taking calculus but my teacher sucka some pretty hefty ass. She is terrible at explaining, has skipped over basic things such as derivatives, and isn't very confident as she makes plenty of mistakes. She couldn't teach for 2 months for a health related reason which is why she skipped over alot of stuff. At this point, i'd much rather start all over and learn from some other source. Any recommendations as to where I can learn from, I'd like to know the why behind equations, not just how.

>>8532688
https://mrgilmartin.files.wordpress.com/2013/02/ib-hl-mathematics-textbook-3rd.pdf
go to the differentiation section, it introduces limits and riemann sums, then goes into first principles and the derivations of derivatives.

>>8532709
Thanks

How does one go about solving an equation like this
[math]x^x=y[/math]

>>8532761
solving? what is there to solve, it is a function.
if you wish to take the derivative, apply the exponential logarithm to both sides and differentiate implicitly.

>>8532767
He's asking to solve for x given y obviously

>>8532767
>>8532784
this
for example, how would I find the value of x, given
[math]x^x=5[/math]

>>8532796
generally speaking these equations are not solvable

you can express them in terms of a tool from complex analysis called the Lambert W function but it's going to spit out something transcendental

>>8532318
> But if all the equations equal zero, then isn't the only answer that X equals zero?
Not if the determinant of the matrix is zero.

Note that x=0 is considered a trivial solution (x=0 is *always* a solution to A.x=0 for any A) and usually ignored.

The eigenvectors are the non-zero vectors for which (A-λI).x=0, and those only exist when |(A-λI)|=0. For an NxN matrix, |(A-λI)| will be a degree-N polynomial in λ, of which the eigenvalues are the roots.

> If you have ax + by =0 and cx + dy =0 , then the only possible answer is that both x and y equal zero.
Not if ad=bc (=>d/c=b/a)

ax + by =0
cx + dy =0

cax + cby =0
acx + ady =0
(bc-ad)y=0
ad=bc => 0 = 0 (i.e. y could be anything)

dax + dby =0
bcx + bdy =0
(bc-ad)x=0
ad=bc => 0 = 0 (i.e. x could be anything)

But:
ax + by =0 => ax=-by => x=(-b/a)y <=> y=(-a/b)x
cx + dy =0 => cx=-dy => x=(-d/c)y <=> y=(-c/d)x
d/c=b/a => these all say the same thing, i.e. that any multiple of (b,-a) is a solution.

More generally, if an NxN matrix A only has M linearly-independent rows, then its rank is M and its nullity is N-M, i.e. the set of vectors for which Ax=0 forms an M-N dimensional "null space" (if M=N, then the null space is zero-dimensional, i.e. it consists only of the zero vector).

Hey, /sci/.

How would you determine the probability of two random variables being the same in an unknown set size. So not from negative to positive infinity but from one unknown to another unknown.

>>8532976
Well if they're continuous then 0...

>>8532999
Nice trips

Sorry, two random variables from two different identical sets being equal.

So X1 from set E1, and X2 from set E2, where E1 = E2 but X1 and X2 are random variables from the set and E1, E2 aren't defined in size but are continuous, and made up of positive integers.

>>8533009
>continuous
>positive integers

I don't follow the question. We have a finite set of positive integers and pick two random values (with replacement) from the set? Is that what you're saying?

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I have some data that suggests a certain variable is much much better at predicting an outcome than any other. It's a factor with 500 levels. And the data is about 100,000 datapoints.

How would I best represent this graphically?

If I wanted to calculate the surface integral of <x,y,z> over the sphere of radius 1 centered at the origin, I understand that can parameterize the sphere and get the appropriate answer. But WHY can't I just take the gradient of the sphere's equation and get <2x, 2y, 2z>? I end up getting 8pi instead of the appropriate answer 4pi obviously.

can someone find the mclaurin series of
e^(x^2)

>>8532574
And nevermind I was able to work it out

>>8533412
Even terms only, the coefficient is n!/(n/2)!.

So sum(x^n/(n/2)!) for even n.

>>8529479
I was talking to a guy about the speed of light in space (universe).
When I tell you that nothing can overcome the speed of light, he answers this: what i mean the speed of light did not fixed to a given speed, our local time flow can be different from here and there and space between, gravity mofify time flow so , Ex: at 8000 light / years light speed at our local zone can be diff from all the course let say at half of the cource time flux are half and other half same as our local time flow so 8000 light / years become 6000 for us This ra example is to undersand how speed of light can be faster than our local speed of light, it's one way to explain how we can go faster than speed of light but true not true ^^ .. gravity affect time flow, and this Are a gravitational wave. It's interfering with itself ... so who know

My knowledge of physics is only: Speed of light, emptiness, effects of matter and energy, but I have no idea about this. Is it true? Is he just an idiot saying bullshit?

>>8531598
Thanks, I'm getting there..

A question on my assignment is to describe the meaning of the term 'function' to someone who is unfamiliar with them; in my own words.

I'm thinking of saying something like "the term 'function' means to calculate the quantity of a dependent variable based on the independent variable"

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I have finished the chemistry exercises in khanacademy.
Is this book a good next step to pass my chem class or do I have to read something else?
My chem professor doesn't really care and another chemistry student from the chemistry faculty pointed out that his presentations are showing obsolete and wrong data.

>>8533450
Is this pasta?

>>8533571
What he said, yes.

Is definition of truth a tautology?

is there a reason why killer move heuristics is called a heuristic? it just orders more likely important moves first right, so why can it lead to error?

>>8533859
>it just orders more likely important moves first right
because there's no guarantee that the move that is more likely to be important is _always_ important

>>8533888
right, but there's no extra work done if it's not important. It would have still been a node of that tree right? as opposed to something like null moves which might give make a lost position seem won

>>8533902
In any non-trivial game, you don't get to evaluate every possible sequence of moves. So prioritising some moves causes others to be ignored, or examined in less detail.

>>8529994
>Journal of Negative Results
AKA PLoS

>>8533857
Yes

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How do I solve/evaluate this using series?

[math]\lim_{x \to 0}\frac {e^x - \sqrt{1+2x}}{\ln\cos x}[/math]

Is the Elysium Basis pill worth buying or is NAD just bullshit?

i just want to live forever

>>8534122
>Is NAD just bullshit
No, you need it to carry out every bit of your basic metabolism.
>Is the Elysium Basis pill worth buying
No, NAD is derived from Vitamin B3 or niacin (same thing). If you really want to try to accumulate NAD for whatever reason take the vitamin and don't fall for the pill meme.

But you also don't need to kickstart your NAD levels, if you were that low on NAD you would probably have a health problem and have contacted a doctor by now (the disease is called pallagra).

>>8529994
Publish or perish being oh so awful is a meme. It is real, but it doesn't ruin anyone's results, career, research plans, etc. And anyways, at some point, if you're publishing nothing at all, maybe you should perish.

>>8530202
Don't be intimidated by chemistry. It might not come easily to you, but it is not as scary as it probably sounds. Be sure you understand the basics before you work problems, and find someone on Youtube or similar that you understand well to explain it. Don't listen to the first videos you find if you don't like them, at the gen chem level there are plenty of different resources.

>>8529479
I'm trying to cultivate waterplants in agar jelly. They grow fine, but after a few weeks the agar starts to crack up when the plant grows in volume.

Does anyone know a trick to make agar jelly less prone to tear?
Now I'm just keeping the moisture constant and use thick layers of agar over each plant. I'm running out of lab space and want to optimize the size before I move into a greenhouse.

guys I need to write a chapter on my relativity essay about to what extend its possible to reach speed of light and why its impossible to reach it

Does anyone know some good sources. would really appreciate.

how to hypothesis test for a proportion of zero?

so far I've been doing a regular z-statistic test
H_0: p = .001 (or some other really small)
H_A: p < .001

but i need very large sample sizes for this.

can I do a confidence interval capturing zero and claim that we can conclude the proportion is zero?

Can someone give me answer >>8533952

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Is number 2 correct or false? When are we able to minus 1 from a conditional probabilty as seen with 1?

>>8530645
It can be considered three dimensional, as a shadow can be seen in say fog or dust.

>>8532164
>>8532227
There are often many posters here who have not had a formal math class and want to learn more.

>>8532605
Algebraically, it's not possible. You would have to use the lambert W function, and get [math]\displaystyle x = \left ( \frac {a \log(a)} {W(a \log(a)) } \right ) ^ {\frac {1} {a}}[/math]

And yes, I got that from wolfram alpha. I knew you'd have to use the W lambert function though. You always have to use that function for any x^x^... = n sort of function.

>>8534460
>When are we able to minus 1

opinion discarded

>>8532349
Not sure how intuitive it is but the way to think about it is that it gives you existence properties, which is what we always want.
It tells you that, the more poles you allow, the easier it is to find independent meromorphic sections of a line bundle on an algebraic curve.
A lot of information is encoded in the poles of a meromorphic function. In a sense, its divisor tells you almost everything there is to know, so you can encode many properties of meromorphic functions solely in terms of their divisors.
For example, the way you prove that any compact Riemann surface is projective is by proving that you can find an appropriate amount of non-simultaneously vanishing meromorphic functions (by using RR), then by justifying that these give you a morphism to a big projective space. Saying that this morphism is actually an embedding is actually another condition that can be phrased in terms of the zeroes and poles of the derivatives, and can also be seen to be satisfied for a sufficiently big divisor using Riemann-Roch.
That's the typical basic application of RR: computing dimension of spaces of sections and proving the existence of sections

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https://www.youtube.com/channel/UCgNAhHlBDOJ6hTkJVlf5gIw

wtf is this channel about - claims to solve a lot of shit and barely has any views - way above my head - anyone knows enough to comment?

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why isn't the derivative of x^x just x*x(x-1)

utilising pic related

I'm a Maths & CS student (50/50 split)

which courses would complement this?
What field or area of either side has a big future?
machine learning?

side Q, if anyone else is doing a Maths/CS course, what's your course content like? I've had no web development, databases, statistics etc

>>8534813
>x*x(x-1)
i meant x*x^(x-1)

>>8531121
heroin to all 3, maybe the year one I'd do something else for the first 9 months but then a big heroin binge.

I'm so fucking curious about heroin.

I'm currently simplifying rational expressions and I'm getting stumped on a couple of problems in my book.

y/(y-1) + 2/(1-y)

a/(a-b) + b/(b-a)

x/(2x-3y) - y/(3y-2x)

I keep fucking up and getting the wrong answers.

It has something to do with utilizing the inverses. Any help understanding how to work this problem would be very appreciated. I know the answers, but I just cannot figure out how to solve it myself.

>>8534813
Because that rule only applies when a is a constant.

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>>8534830
oh, makes sense.

I wonder why my prof only gave us these formulas and somehow expects us to know more shit

I may be missing something here.

>>8534721
>not being able to mentally rearrange to minus 1

Huh. Must suck to be a brainlet, right?

>>8534772
His videos are generally full of inaccuracies or just overall don't make sense, take https://www.youtube.com/watch?v=MmMfH_ZAxe4 for example.

He literally just came up with equations for the lines x+2 and x-2 and said "there's an infinite amount of numbers that are in this equation, therefore there must be an infinite amount of primes that follow this". He doesn't understand how induction works, and he's basically saying the equivalent of "3,5,7 are primes and there's 2 odd numbers below 10 that aren't, 11,13,17,19 are primes and there's 1 odd number between 10 and 20 that aren't, therefore by induction there must be 0 odd numbers between 20 and 30 that aren't primes".

>>8534838
the hyperbolic shit is unnecessary but the rest should be pretty easy to figure out no?

>>8534842
how would i just figure out that, say, e^(g(x)) derived is e^(g(x)) * g'(x) on my own

>>8534849

I mean understanding what it means, not figuring it out.

Also that part is just chain rule, that's pretty simple.

>>8534838
Geez, what a shit professor.

Just try to make do with what you have, I guess. I recommend the MIT OCW calculus course online if you want actual explanations of this stuff.

>>8534849
Wait I think I'm misunderstanding you.

I'm 23 the last school I was in was High School 5 years ago and I want to get into meteorology. How bad of an idea is this?

>>8534827
Multiply each one by the denominator of the other.

By that, I mean if you have something like (a/b) + (c/d), do (a*d/b*d) + (c*b/d*b), and then since the denominators are the same, you can do (a*d+c*b / d*b).

>>8534867
Not really, you'll probably do better because you've had some time to mature.

>>8534814
Curious about this as well

>>8534878
Thanks for the vote of confidence. I have never taken a college level course before, but math has always just been easy for me. I hope I still got it.

>>8534893
The freshmen math shouldn't go much further than college algebra or precalc, so if you brush up on trig and algebra, you'll do fine.

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REEEEEEEE WHAT THE FUCK DO I DO NOW?????????

>>8534957
Risk

>>8534957
roll the dice

>You can double both the pressure and the volume of an ideal gas if you change the temperature by?

I'm not sure why I'm second guessing myself on this one, I just was some reaffirmation. Would the answer be quadrupling it? At first I thought doubling because they're obviously proportional, but it says "both" pressure and volume, which is why I think quadruple.

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>>8534967
>>8534976
Sheeeeeeeit, I did it! Thanks, guys!

Learning JS, practicing on coderbyte.

function FirstReverse(str) {
var newString = "";
for (var i = str.length; i >= 0; i--) {
newString = newString + str.charAt(i);
}
return newString;
}


Var i within the loop should be defined as str.length - 1. Why does this code still run? Or alternatively, why do people insist on using -1 if it runs exactly the same? An example of how the code above could be a problem would be greatly appreciated. Or if the answer is simply "it shouldn't run, it's a problem with the coderbyte interface", that would be helpful to know as well. Thank you.

>>8535023
/sci/ isn't /g/.
The answer is because str.charAt(str.length) is "", so it's irrelevant. If you did str.charAt(str.length+100); you'd get the same.

>>8535035
Sorry, first time user and I somehow missed /g/ on the list. Thank you for the answer and correction.

Multivariable calc final on Wednesday (brainlet, I know), trying to understand this Divergence Theorem question that nobody even came close to getting correct on our last exam, professor is of no help in trying to help us understand it ("Graph it, you'll see"):
[math]\oint_{\partial E}F\cdot\,dS[/math] (F is a vector field), where the solid E is defined by r = 1, p (aka rho) = 2. I've looked through all 3 textbooks that this professor recommends, as well as Googling around, and can't really find anything similar to this problem. Sorry if the LaTeX is screwed up.

>>8535093
Screwed up the integral notation, but it's just supposed to be integral over the boundary of E, this professor is often wishy-washy with his integral notation so by all logic the dS implies surface integral.

>>8535093
>where the solid E is defined by r = 1, p (aka rho) = 2
By this I presume you mean the intersection between the cylinder of radius 1 and the sphere of radius 2?

If that's the case, then by the divergence theorem that integral is, of course, the same as the integral of the divergence of F throughout that volume of intersection.

We can integrate using cylindrical coordinates. The equation of that sphere is [math]r^2 + z^2 = 4[/math], so the limits on z are from [math]-\sqrt{4 - r^2}[/math] to [math]\sqrt{4 - r^2}[/math]. Then the limits on r are simply from 0 to 1 and the limits on theta are from 0 to 2pi.

>inb4 i fucked up

>>8535170
Thanks a lot Anon - my professor is the kind whose tests are completely different than what he teaches (thankfully, he publishes old exams and solutions online, though this type of question wasn't in any of his previous exams), and his coverage of the Divergence Theorem was weak at best.

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Is this herpes on my tongue ???

>>8535238
yes, you're already dead
cute mouth btw

>>8529479
What is a brainlet, exactly?

Does it refer to someone who thinks they're smart but aren't, or does it refer to someone who has the capacity for intelligence and instead wastes it on frivolous things?

>>8535238
does it sting like a motherfucker?
if so, looks like aphthous stomatitis

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Can /sci/ guess numbers from 1 to 60 for me?

Each anon gets one pick.

I will use the numbers of those who get trips or more to try to win the Lotery.

If win, will post back here.

>>8535259
7

>>8535266
>First post
>already dubs

Can't use your number coz not high enough (trips or higher only), but hell bro, that was a really goos start.

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is this correct?

>>8534827
In each of those three, one denominator is just the negative of the other: a-b = -(b-a). So you can just move the negation to the numerator:
x/-y = -x/y => x/(b-a) = -x/(a-b)

>>8534868 is unnecessary in this situation.

>>8529828
Hermitian operators have real eigenvalues and orthogonal eigenvectors. The eigenvalues correspond to the observed values and the eigenvectors correspond to the states of your system. The eigenvectors being orthogonal corresponds to the fact that every observed value corresponds to a single distinct state, since once you've made an observation you've collapsed the wave function.

>>8530237 >>8530288 >>8530507 >>8534267
thanks guys, appreciate it

>>8535294
You have 5 bonds to a carbon in the product, the structure drawn on the right of the arrow. Keep the double bond to the oxygen and make the other double bond a single bond.

An allylic alcohol, the structure drawn as the reactant - to the left of the arrow - is synonymous with a carbonyl, the structure you have on the right. You don't even need the oxidizing agent?

>>8535458

*** that is a vinyllic or vinyl alcohol, not allylic.

>>8535458
>You don't even need the oxidizing agent?
but that's the entire reaction that I have to do, tomorrow I have to add sulfochromic mixture to different alcohols but I'm not sure about the product on this one

>>8535242
Brainlet = someone who is unintelligent in general, e.g. not smart enough to pass a basic calculus course

>>8533857
a-anyone?

>>8535494
You're gonna have to expand on your question. What do you mean by "definition of truth"?

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URGENT QUESTION - Due by 12


Why does it not work when I do the same thing as the solutions mannual?

Can someone please help me find correct answer?

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>>8535546

QUICK HELP I HAVE A FINAL IN 2 HOURS AND I JUST FOUND OUT ABOUT THIS

HOW DO I PROVE THAT

[eqn]e^{i\theta}=-1[/eqn]

>>8535678
More like how do I find a solution, I already managed to prove that [math]e^{i\theta}=cos\theta + isin\theta[/math]

>>8535678
In general, that equation is false.
[math]
e^{i \theta} = \sum_{n=1}^{\infty} \frac {(i \theta)^n}{n!}
[/math]
Which you'll notice is the Taylor expansion for cos (theta)+i sin (theta)

>>8535686
Why does your series start from 1?

>>8535678
the real part = -1 and the imaginary part = 0

Even symmetry is one thing, but what is the Fourier transform just the even part of a signal?

That is, what is the Fourier transform of (s(t) + s(-t)) / 2?

Does a similar principle apply to finding the Fourier transform of a the odd component?

>>8535962
The Fourier transform of an even function will contain only a cosine component (real part), that of an odd function only a sine component (imaginary part).

The integral of an odd function over a symmetric interval [-a,a] is always zero. So if f(x) is even, then f(x)*sin(x) will be odd and the integral of f(x)*sin(x) over [-T/2,T/2] will be zero; if f(x) is odd, then f(x)*cos(x) will be odd and the integral of f(x)*cos(x) over [-T/2,T/2] will be zero.

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I'm absolutely retarded. I'm reviewing gradients of multivariate functions, and am having trouble understanding pic related.

Can anyone explain how the book got to the "chain rule" using paths? Or at least, why this is true.

>>8535680
The identity holds true when theta is 2*k*pi + pi;

Not really sure what aspect of this confuses you if you already expanded e^i(theta)

>>8534460
False. P (t|s)+P (t|~s)=P (t)

>>8536017
(7) is just the first equation re-written in vector notation.

∇f(r(t))=∇w=[∂w/∂x,∂w/∂y,∂w/∂z]
r'(t)=[dx/dt,dy/dt,dz/dt]
∇f(r(t)).r'(t)=[∂w/∂x,∂w/∂y,∂w/∂z].[dx/dt,dy/dt,dz/dt]
=∂w/∂x.dx/dt + ∂w/∂y.dy/dt + ∂w/∂z.dz/dt

>>8535999
So, the Fourier transform of any odd component of a function is zero? Than what is the point of odd symmetry? And about of the even component?

Also, my f(x) in this case is neither odd nor even, but the whole. I'm trying to find the transform of the even as it relates to the whole function.

As in to find for Feven(f) and Fodd(f), while not seeing f(t) as fully even or odd in the first place.

I'm helping someone understand basic trigonometry and geometry considering they've never been confident with math.

They asked me "why do all the angles in a triangle add up to 180 degrees?"
I answered "because all the angles in a square add up to 360 degrees"

Is that a decent answer?

>>8536025
Could you show me how that is derived?

And is it possible to show conditional probability on venn diagram?

>>8536042
> So, the Fourier transform of any odd component of a function is zero?
The result of a Fourier transform has cosine and sine parts for each frequency. An odd function has only sine parts, no cosine parts.

>>8536055

you could also visually show how those 4 angles of the square create a whole, then visually show how that relates to a right angle triangle, the isosceles, the other one, all creating a half a whole.

make sure to explain that degrees is an arbitrary number, the relation is the most important

Quantum uncertainty principle.

Unknown momentum? Does that mean it can go faster or slower? Isn't energy conserved?

[math]{3x^2+2x+\lambda \over x(1-3\lambda)}=\lambda[/math]

Why?

>>8536112
So sorry, it's actually

[math]{3x^2+2x+\lambda \over x(1-3\lambda)}=P(x) +\lambda[/math]

What I'm asking here is how do I do:

[math]{3x^2+2x+\lambda \over x(1-3\lambda)}[/math]

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I can't make sense of the solution provided.

Acording to the formula they got, they got
[eqn]
\mu = Ax + b \\
\Sigma = Q
[/eqn]
I can sort of deal with [math]\mu[/math] though I would feel more comfortable if they got [math]A\mu_x + b[/math], but [math]\Sigma = Q[/math]? How? I get [math]\Sigma = A^T\Sigma_xA + Q[/math] . x being independent of [math]\epsilon[/math] only means their covariance is 0, but how did they zero [math]A^T\Sigma_xA[/math]?

>>8536117
Oh I got it know lol. the mean is x and the "variance" of x is 0 because the values are already given lel. Basically my solution is for [math]p(y)[/math]

>>8536021
I needed to prove that part

>tfw did mediocre

Thanks anyways, /sci/

>>8536115
Polynomial division. You could also try factoring the numerator but I don't think that leads anywhere

>>8536084
Thanks friend!

Also, this same person is pretty much incompetent in maths considering their history of classmates, teachers and overall sub-par education and home conditions.

Like, linear functions with (y= mx + c) are their current "A-grade" at around 18 yrs.

Any efficient and quality material to teach them to boost them up to basics knowledge faster?
Key concern; they may inherit a farm, do agriculture.

>Pulling my hair out trying to write a proof
>Say fuck it and go to sleep
>Wake up the next morning and solve it instantly

Why the hell does this happen

Should I work through a book like Spivak or Apostol before trying to learn real analysis?

I already took calculus 1-3 "for engineers," and I could understand and easily do all the problems in those courses, but we didn't go over most of the proofs, so I only have an intuitive understanding. When I flip through the aforementioned books, I realize that I probably missed a lot of material. Should this be a concern? Is this a matter of "you'll learn that stuff more in-depth in real analysis, anyway, so just go ahead and learn real analysis" or is it a good idea to learn the babby version first?

I got a job offer for java web development at another company. They are an agile environment trying to implement the latest frameworks to build from.

I am currently a dba/dev at another company. They are old in their ways.

Should I make the jump?

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Does anyone know the name of the substance that the QUACK head transplant doc will supposedly be using to assist him. If i remember correctly it activates itself when it detects inflammation in the body.

>>8536392
ask /g/ a lot of them have similar stories im sure

>>8536308
what is being tired for 100?

Wtf am i doing wrong

use a double integral in polar coordinates to find the area of the region bounded by the graphs of the given polar equations

r = 2sin(theta) and r = 1

sin(theta) = 1/2

therefore theta = pi/6 and 5pi/6

1 <= r <= 2sin(theta)

double integral rdrd(theta)

The answer is wrong though. WTFFF!!@#!$!@#@!#@!#!@

>>8536511
Have you accounted for the fact that it's only defined between 0 and pi?

>>8536548
but pi/6 and 5pi/6 is between 0 and pi

>>8536511
there's a lot of work missing here man
it's difficult to troubleshoot

what is the wrong answer you're getting? How are you setting up the integral?

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>>8536617

>>8536511
You are integrating the area outside of r = 1 but inside r = 2sin(theta). But you really want the area bounded by both curves.

What you want is one integral from r = 0 to r = 2sin(theta) from theta = 0 to pi/6, and then another integral from r = 0 to r = 1 from theta = pi/6 to pi/2. Then multiply all that by 2.

>>8536385
what do you mean by real analysis? measure and integration, or metric space based analysis (introduction to analysis and so on)?

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>>8536635
Do you mind elaborating on what exactly I'm doing wrong and how you came up with your solution?

I have the solutions manual and the answer you gave is exactly the same as the manual but I don't really understand how you (or the manual) arrived at the solution.

What effect does a diluted hydrocodone solution as eye drop have on the eyes? Does it actually lighten them and get you blind?

I was thinking about monobenzone first but then I realized that it will enter the bloodstream and there will be white patches everywhere. Also the application of applying the drop itself, whitening the eyelashes and the skin underneath. Not worth it. But what about hydrocodone?

Just scientific curiosity.

>>8536674
>What effect does a diluted hydrocodone solution as eye drop have on the eyes? Does it actually lighten them and get you blind?
>I was thinking about monobenzone first but then I realized that it will enter the bloodstream and there will be white patches everywhere. Also the application of applying the drop itself, whitening the eyelashes and the skin underneath. Not worth it. But what about hydrocodone?
>Just scientific curiosity.

What effect does a diluted hydroquinone* solution as eye drop have on the eyes? Does it actually lighten them and get you blind?

I was thinking about monobenzone first but then I realized that it will enter the bloodstream and there will be white patches everywhere. Also the application of applying the drop itself, whitening the eyelashes and the skin underneath. Not worth it. But what about hydroquinone?

Just scientific curiosity.

Corrected.

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>>8536646
Apologies for the shitty picture.

On the right is what you're doing. First, I can tell immediately that the limits on r are incorrect because we're trying to find the area *between* these two curves. And even if the limits on r were correct, the limits on theta, while indeed being the intersection of the two curves, wouldn't account for that little extra sliver of area on the sides.

So instead, we go from r = 0 to r = 1, from theta = pi/6 to pi/2 (we could go all the way up to 5pi/6, but this is a symmetrical problem, so we'll just integrate half the area and then multiply it all by 2). That will give us the stippled area on the left, but that's not enough. There's also that little sliver of area bounded by r = 2sin(theta) that goes beyond theta = pi/6. So we use another integral to get that area. Multiply that sum by 2 and you'e done.

!!!!!!!!(sorry, the upper limits on r are switched in my picture... the first integral should be from r = 0 to 1 and the second should be from r = 0 to 2sin(theta). Also, it's all multiplied by 2 so we can get the total area)

>>8536644
>what do you mean by real analysis?
As in the introductory real analysis course an undergraduate math major would take, a la Baby Rudin (though I don't expect to jump into Rudin at first).

>>8536690
Thanks a lot!

That makes a lot of sense now!

>>8536017
Retarded notation. What is w a function of exactly?

If the atoms in an atomic bomb has a too slow of a chain reaction, will is just be a container with nuclear waste or will it explode just a little bit?

>>8536703
if you already took calc III then I say go ahead. just pick up an intro to analysis book. don't waste your time with intro to memeproofs books and shit like that.

I'm working on this question for my physics class and I feel like it should be easy but I'm struggling:

>An electron is released from rest at a distance of 9.00 cm from a proton. If the proton is held in place, how fast will the electron be moving when it is 3.00 cm from the proton?

I know I can use A=(K*q1q*2)/(m*r^2) to solve for acceleration at a given point but I don't know how to translate that into velocity at a point. I don't think kinematics are the answer because the acceleration isn't constant. Thanks for any help.

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hello i'm staying in the tropics for one year and my toilet is outside, if i open the door i always have 20+ moquitos in my face and it sucks getting them out just to take a shit.

is there something i can put in the toilet so they dont wait for me there anymore.

preferably natural but not at the cost of efficiency

thanks

>>8534814
bump

>>8537050
Citronella, if the climate there is right for growth (probably as long as there's a good bit of sun)

>>8529479
I can't seem to find a decent proof for this, that doesn't resort to differentials or ends up with primatives
[eqn] \int f[y(x)] \frac{dy}{dx} \, dx = \int f(y) \, d y [/eqn]

Anyone got a rigorous proof?

>>8536972
Bump

>>8537188
You can't find a proof that u-substitution works?

https://proofwiki.org/wiki/Integration_by_Substitution#Proof_for_Indefinite_Integrals
it's not very long, it's just chain rule

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>>8537182
thx alot!

>>8536927
Depends how slow. Could just get a bit warm, could just be a low yield boom.

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>>8536972

This may help you
(of course, sub in your own numbers)

Solution manual for Physics Volume 2, (Halliday et al)

>>8537206
Ah thanks.
I knew it was something simple like fundamental theorem of calculus, but couldn't quite think of u=substitution.

I should have a proof of u substitution in my analysis notes.

>>8537343
I can see how that work but in this problem there are 2 charges (the proton and the electron) while that formula only uses 1.

>>8537369
you better study up for that exam buddy, review those fundamentals lol...

I am seriously fucking dumb, there I admit it.
Now can some good anon help me understand (with substantive) interpretation how to recreate a multiple regression analysis?

I have all the relevant data I just can't formulate my null and alternative hypotheses correctly.
X1: Exercise

H0: X1 ≥ 0
Ha: X1 < 0


X2: Gender (as a binary/dummy variable)

H0: X2 = 0
Ha: X2 ≠ 0


X3: Age

H0: X3 ≥ 0
Ha: X3 < 0

dependent variable is depression.
Does this notation look correct? How do I fix it?

>>8530505
We'll be able to say what the human brain finds as the most pleasing outcome in a situation and why, but if you're talking about objective truth, then that would be impossible to know with certainty. We'll be able to refine our approximation of the truth to the point where our current notions will seem like those of a bug or something, though.

>>8534813
y = x^x

log(y) = xlog(x)

differentiate both sides with respect to x

(1/y)dy/dx = log(x) + 1

dy/dx = y(log(x) + 1)

dy/dx = x^x(log(x) + 1)

>>8537343
>>8537377
Ok I did some reading and I think I have a much better idea of what is going on. But when I try to solve for the velocity I end up with about 706 m/s while the review key my prof provided says the answer is 106 m/s. I've tried solving using both the formula you provided as well as through my own calculations and I get the same answer every time. I have a strong suspicion that there's a typo on the key but I'm not sure. If anyone could work though it and confirm it would be appreciated.

>>8537523
It's 106 m/s.

k=9e9
q1=q2=1.6e-19
m=9.1e-31

F(r)=k.q1.q2/r^2
= 2.304e-28/r^2
Potential energy E(r) = integral F(r) dr = -2.304e-28/r
E(0.09)-E(0.03) = -2.56e-27 - -7.68e-27 = 5.12e-27
Kinetic energy = (1/2).m.v^2 = 5.12e-27
=> v^2 = 2*5.12e-27/9.1e-31 = 11252.747
=> v = 106.08 m/s

>>8537685
Oh I see, I think I had the initial and final potential energies mixed up. I got it now, thank you.

If light is polarized horizontally, then at some diagonal, then vertically, does some light get through?

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Does this make sense what I did?

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Did I write proof right?
(1+ab)-(a+b) = 1+ab-a+b
ab+b+1=a
ab+b=a-1(as we know a>1, so a-1 bigger than 0)
ab+b>0
ab>b
a>1 and this is true from problem definition

>>8538266
no
>(1+ab)-(a+b) = 1+ab-a+b
this is wrong

>>8538266
>(1+ab)-(a+b) = 1+ab-a+b
should be 1 + ab - a - b
continuing with the correct equation
ab - b = a - 1
in this equation b = 1
I feel like you could still salvage a proof from this since ab - b + 1 = a, is only true if 1 + ab - a - b = 0, but as it stands, it is wrong
>ab+b>0
>ab>b
forgot to flip sign again

don't really know what the hint means but the way I'd prove it is

a = c+1
since a > 1, then c > 0
b + c + 1 < 1 + b + bc
c < bc
b > 1

Can someone help me here:
A parabola y = ax2 + bx + c is a set of points that has the same distance from the point (3,2) and the line y = -1. What is the sum: a+b+c?

So, the answer is 10/3.
But no matter what I do, every single equation(finding vertex, definition of parabola, formula of parabola, whatnot) always gives me 7/6.
Does someone knows how can I find the answer 10/3?