/sqt/ Stupid Questions Thread

[Anonymous No.9547881]

This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way http://www.catb.org/~esr/faqs/smart-questions.html

Previous thread >>9537723

[Anonymous No.9548385]

>>9547881
What if we flung a black hole into another black hole?
Who wins?

[Anonymous No.9548387]

Is this a stupid question?

[Anonymous No.9548388]

>>9548385
The even larger Black Cock of course

[Anonymous No.9548393]

If you have a thin plate with δ(x,y) being its density at (x,y), and you integrate that function twice with respect to x and y, shouldn’t the units of δ be mass/area? I asked my teacher and he said the units are mass/volume but you’re looking at it at a specific point in time or something. I don’t think that really makes sense, if you have a density function in one dimension whose units are mass/distance it should give you mass. Shouldn’t integrating a function of mass/volume once or twice yield units of mass/area of mass/distance, respectively?

[Anonymous No.9548398]

>>9548393
If you're expecting a unit of mass at the end of two integrations (one w/ resp. to x, one w/ resp. to you), the unit of delta should be mass/area.

[Anonymous No.9548401]

>>9548385
They just sort of merge, I think.

[Anonymous No.9548409]

>>9548401
How?

[Anonymous No.9548412]

I want to do a Taylor series of f(x) = cotan^2(x) around 0. The first term of the series is f(0), which is infinity (and so are others), but WolframAlpha tells me it's 1/x^2. What am I doing wrong? Am I not supposed to just plug 0 in the equation to find the first term?

[Anonymous No.9548423]

>>9548412
https://math.stackexchange.com/questions/637169/taylor-series-for-cot-x

[Anonymous No.9548428]

>>9548423
yeah, I failed to realize I can't make a series around 0 since cotan is not continuous there

I'm such a brainlet

[Anonymous No.9548430]

>>9547881
How do you know that Tree(3) is so big that it's impossible to even think about it? How do you know it has an end? Why can't anyone describe Tree(3) completely?

[Anonymous No.9548509]

>>9548409
by falling into each other, how else

[Anonymous No.9548522]

>>9547881
My prof derived EM waves from Maxwell's equations and I had a hard time following it. Anyone got a brainlet way to derive it or a really thorough explanation?

[Anonymous No.9548741]

>>9547881
Is there a way to draw a circle through 3 of its points without introducing a coordinate system?
Sorry if the question is too dumb, I've just always been bad at Euclidean geometry.

[Anonymous No.9548746]

>>9547881
Let [math]G[/math] be the group of matrices of the form [math]\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}[/math] for [math]a \in \mathbb{C}[/math].

I'm supposed to show that there are finite-dimensional [math]\C G[/math]-modules which are not completely reducible. My hunch is that [math]\C G[/math] as a module over itself is not completely reducible, but I have no idea how to prove this. What does it mean for a module to be finite dimensional anyway? I thought not all modules had invariant basis number.

[Anonymous No.9548771]

>>9548746
If one considers (Lie) group representations, "finite-dimensional" usually means "finite-dimensional over the ground field" - this is [math] \mathbb{C} [/math] here.
Do you know a somehow "natural" finite-dimensional vector space over [math] \mathbb{C} [/math] on which [math] G [/math] acts linearly (you'll probably guess the one which is not completely irreducible)? Then you immediately get a [math] \mathbb{C}G [/math]-module which fulfills the desired condition.

[Anonymous No.9548779]

>>9548522
This derivation is pretty brainlet-friendly.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxsup.html#c2

[Anonymous No.9548964]

I'm stuck on this problem. (For some context, the text being used is Royden - roughly 6.1-6.2)

For part a) is it sufficient to say that since the terms are nonnegative, f(x) is increasing?

For part b) is the argument a standard continuity argument with |s_i - x_i|?

For part c) do we have to start by using Lebesgue's Theorem to state f(x) is differentiable almost everywhere?

Mainly, I'm trying to find where Lebesgue's and Vitali's follows in the grand scheme of this.

Sorry for the long question and I'm not looking for a full proof but rather an approach that might be useful. I appreciate any help I may recieve.

[Anonymous No.9548970]

>>9548964
*Vitali's covering lemma by the way

In case there are other vitali theorems around

[Anonymous No.9548997]

>>9548779
Thanks.

[Anonymous No.9549006]

Really stuck on this one.

>Find a sequence of functions, [math](f_{n})[/math], on the closed interval [math][0,1][/math] such that each [math]f_{n}[/math] is differentiable, and the derivatives, [math](f^{\prime}_{n})[/math], converge uniformly to some function [math]g[/math], but the functions, [math](f_{n})[/math] do not converge to a differentiable function, [math]f[/math].

It'll probably be piece wise and I wouldn't doubt if the absolute value shows up.

[Anonymous No.9549010]

Why can I use Cauchy'S integral theorem to say the line integral on the curve c=unit circle of (z^3 * cotz) is equal to zero? I am unfamiliar with Laurent series so my only tool to assess applicability is determining where it's analytic. I can see it's not analytic for z=n*pi, n=0,1,2,3... since cotz = cosz/sinz

However, my book says it's diffferentiable and therefore analytic in the neighborhood of n= 0. Please explain. How can it be discontinuous at z=0*pi and still differentialable?

[Anonymous No.9549028]

>>9549010
It IS continuous at [math] z = 0 [/math]:
You can use l'Hospital (legit for fractions of holomorphic functions!) to determine [math] \lim_{z \to 0} \frac{z^3}{\cot z} [/math].
That this limit indeed gives a holomorphic function follows now from the fact that your function is bounded and holomorphic in an open neighborhood of [math] z = 0 [/math] (else there couldn't be a limit).

[Anonymous No.9549037]

>>9549006
what about [math]f_n(x) = x+n[/math]

[Anonymous No.9549038]

>>9549006
I don't have Rudin next to me but there is an example of this in the beginning of chapter 7. Something to do with trig functions if I remember correctly.

[Anonymous No.9549042]

>>9549037
fuck it's so simple, i think it works too
>>9549038
i'll take a look

[Anonymous No.9549059]

>>9549037
so this isn't differentiable since its derivative isn't defined on the end points right?

[Anonymous No.9549061]

>>9549028
Hmm, I see. Stupid question, but why is it sufficient say, e.g., 1/z-3 has a discontinuity when z=3 since rational numbers can't have zero in the denominator, but not here?

[Anonymous No.9549062]

>>9549061
Sorry, brainlet's first complex analysis course

[Anonymous No.9549067]

>>9549059
It might not work because the functions don't converge, period, and so definitely can't converge to a differentiable function. That's kind of a degenerate solution to the problem and probably not what is asked for.

[Anonymous No.9549069]

>>9549067
suppose it was [math]f_{n}(x)= x+ \frac{1}{n}[/math], which converges to [math]x[/math]. Then this was be non-degenerate, correct?

[Anonymous No.9549073]

>>9549069
But f(x) = x is differentiable.

[Anonymous No.9549076]

>>9549061
Actually, your function isn't defined in zero, either. But you can find a continuation which is holomorphic in this point.
Your integral doesn't go through zero, so one might use the continued function as well in order to be able to use Cauchy's theorem. So, you're indeed right - actually the function isn't defined in this point - but one can define it there in a nice way.

[Anonymous No.9549079]

>>9549073
but not everywhere on [math][0,1][/math] though

[Anonymous No.9549080]

>>9548964
a) is pretty self explanatory, arguing about adding terms should be sufficient
b) for a rational s_i, f(s_i)-f(s_i-∆)≥1/2^i for all ∆>0
Can't help you with c) right now, going to sleep, good luck anon.

[Anonymous No.9549097]

>>9549079
where isn't it differentiable

[Anonymous No.9549381]

>>9549097
o-on the endpoints ?

[Anonymous No.9549401]

when using power series to solve differential equations, why is it ok to split the sums? in general is it always ok or are there instances where it doesn't work?
i ask because i thought for certain series rearranging resulted in a different limit (https://en.wikipedia.org/wiki/Riemann_series_theorem))

[Anonymous No.9549404]

>>9549381
>the function locally extends to a differentiable function defined on some open set
this is the usual definition of differentiability at a point which is not an interior point. clearly it holds in this case.

[Anonymous No.9549424]

>>9549404
shieeet

[Anonymous No.9549452]

I know the answer but don't know how to get it from the information...

[Anonymous No.9549487]

Any good lecture about gravitation (with lots of examples too, if possible)? I'm studying undergrad physics and this topic is specially difficult for me.

I have trouble with free body diagrams (I fuck up with gravitational forces sometimes), Kepler laws and conservation of energy.

[Anonymous No.9549499]

>[math] x^2 - 2x + 2 > 0 [/math]

My solution
>[math] (x-1)^2 > -1 [/math]
Because the exponent is odd, the left hand side of the equation will always be positive, and so any value in the set of reals will work for x.

But the solution here, https://etoix.wordpress.com/category/calculus-by-spivak/page/2/ , has a different answer. How did they arrive at that? Pic related. Ultimately we both had the same final answers, all reals, but I'm curious as to how I may have arrived at the same answer differently. My method for arriving at this answer was a straightforward completion of the square. It looks as though this person used a similar method, but I don't understand how they could've done anything differently.

>pic related
Can't post duplicate image until 2019, but it's right here: >>9549493

[Anonymous No.9549531]

>>9549401
It depends on the particular form of the recursion relation you get when you substitute the series solution into the differential equation.
If you get an [math]a_{n+2} = f(n) a_n [math], as you often get for a second order ODE, then clearly the odd and even [math]a_n[/math] terms are independent and can be split in this way.

[Anonymous No.9549541]

>>9549531
>>9549401
fug, I mean
If you get an
[math]a{_n+2}=f(n)a_n[/math],as you often get for a second order ODE,then clearly the odd and even [math]a_n[/math] terms are independent and can be split in this way.

[Anonymous No.9549611]

I'm so fucking bad at programming I'm seriously considering switching out of EE into MechE just because I know I wouldn't have to deal with this shit any longer. Fuck me even harder knowing that most of the jobs available for EE are in embedded systems.

[Anonymous No.9549739]

Someone put me out of my misery

[Anonymous No.9549754]

>>9549739
Actually I think I have a solution, would image = (2 + (-1))^n = 1^n = 1 work?

[Anonymous No.9549755]

>>9549754
>>9549754
yeah that's right, the binomial theorem gives that as an alternate form for (2 + (-1))^n.

[Anonymous No.9549758]

>>9549611
>I'm so fucking bad at programming

You just have to practice. Programming isn't hard, just a bit alien at first. Just remember that the computer is retarded and you have to be stupidly explicit when telling it what to do.

[Anonymous No.9549759]

>>9549401
it works for power series, you don't have to worry about the details in undergrad ODE

[Anonymous No.9549760]

>>9549754
da

[Anonymous No.9549764]

>>9549755
>>9549760

Thanks! It took me way too long to figure that out.

[Anonymous No.9549772]

>>9547881
Why hasn't /sci/ figured out women?

[Anonymous No.9549790]

>>9549758
How do i practice?

[Anonymous No.9549928]

sin(x) and cos(x) are linearly independent. I know that's true.

However, when trying to prove it, I can show it for every (x) EXCEPT For pi/4
Everything else there is no such a/b so that asin(x) + bcos(x) = 0 except a=b=0
But if x = pi/4 then
sin(x) = sqrt(2) / 2
cos(x) = sqrt(2) / 2
so
a = 1
b = -1
1 * (sqrt(2) / 2) + (-1) * (sqrt(2) / 2) = 0
Where both a and b are not equal 0
How does this not show them linearly dependent?

[Anonymous No.9549932]

>>9549928
>How does this not show them linearly dependent?
Because you showed sin(pi/4) and cos(pi/4) are linearly dependent, not sin(x) and cos(x).

[Anonymous No.9549939]

>>9549932
But that makes them linearly dependent on the periodic set {0 ... 2pi} for (x = {pi/4, 3pi/4, 5pi/4, 7pi/4})
Am I skipping over a property of the definition?

[Anonymous No.9549947]

>>9549939
>But that makes them linearly dependent on the periodic set {0 ... 2pi} for (x = {pi/4, 3pi/4, 5pi/4, 7pi/4})
This doesn't mean anything.

>Am I skipping over a property of the definition?
If sin(x) and cos(x) were linearly dependent then there are scalars a,b with a*sin(x)+b*cos(x)=0. This is an equality of functions, so if this equality is true then for every x you must have a*sin(x)+b*cos(x)=0.

[Anonymous No.9549955]

>>9549947
See that's where I'm getting lost.
For every x. x = pi/4.
a = 1
b = -1
The equality now holds true when both a,b != 0
Which, from what I understand, means these are not linearly independent

[Anonymous No.9549956]

>>9549955
>For every x. some x = pi/4.
forgot a word

[Anonymous No.9549957]

>>9549955
>For every x. x = pi/4.
Not every x is equal to pi/4.

[Anonymous No.9549959]

>>9549955
>Which, from what I understand, means these are not linearly independent
Is 1*sin(x)-1*cos(x)=0 for all x?

[Anonymous No.9549960]

>>9549957
>>9549956
I've had a few beers, bear with me

>>9549959
No, but it is for some x (7pi/8)

[Anonymous No.9549961]

>>9549960
>No, but it is for some x (7pi/8)
Then you haven't shown linear dependence.

[Anonymous No.9549965]

>>9549961
I'm missing a step somewhere.
Am I meant to be treating sin(x) and cos(x) as separate sets?

[Anonymous No.9549966]

>>9549965
>Am I meant to be treating sin(x) and cos(x) as separate sets?
I don't know what you mean by this.

Your a,b need to satisfy a*sin(x)+b*cos(x)=0 for every x.

[Anonymous No.9549969]

>>9549966
So even though there exists an a,b for x = pi/4, because this a,b does not apply to all x this shows them linearly independent?
I'm trying to work through all of this in an abstract linear alg class without having taking the computational version beforehand so I'm a little in over my head

[Anonymous No.9549970]

>>9549969
>So even though there exists an a,b for x = pi/4, because this a,b does not apply to all x this shows them linearly independent?
No, it just shows that the a,b you've chosen doesn't prove linear dependence. To show linear independence you need to prove the only solution is a=b=0.

[Anonymous No.9549981]

>>9547881
How do make learning mathematics interesting?

[Anonymous No.9549983]

>>9548430
Wasn't there a numberphile video on this? They usually do an okay job describing things.
From what I remember, the amount of variables you need to "solve" tree(3) is some 2 to the power of 2 to the power of 2.... Like a thousand times. Which is obviously some finite number, but fuck doing that kind of math.
Also he kept saying shit like "your brain will turn into a black hole!" rather than we simply can't fathom it.

[Anonymous No.9549986]

>>9548385
Black holes don't exist

[Anonymous No.9549989]

>>9548741
Something about triangles and bisection

[Anonymous No.9549997]

>>9549989
>>9548741
https://www.mathopenref.com/const3pointcircle.html

[Anonymous No.9550005]

>>9549989
perpendicular bisectors

[Anonymous No.9550009]

>>9549970
>you need to prove the only solution is a=b=0.
Right but a solution of a,b != 0 exists for odd multiples of pi/4. This is what's tripping me up, I can show it independent for everything else but this confuses me

[Anonymous No.9550020]

>>9550009
anon you're overthinking this in ways that are difficult to understand

1) do you agree 1 and x are linearly independent
2) does it matter that the line y=x and the line y=1 intersect
3) do you agree that x and x^2 are linearly independent
4) does it matter that y=x and y=x^2 intersect
5) do you agree that 1, x, x^2, ... form a basis for polynomials

[Anonymous No.9550025]

>>9550020
Like I said I've only had purely abstract definitions to work with, I've never seen actual representations of what I'm working with so I never really considered the fact that an intersection existing doesnt matter for linear independence
I think I got messed up with linear maps having direct sums that don't intersect with linear independent sets possibly intersecting

[Anonymous No.9550031]

>>9550009
>Right but a solution of a,b != 0 exists for odd multiples of pi/4.
It needs to hold for all x.

[Anonymous No.9550035]

>>9550031
Right, that's starting to finally sink into my brain. It's about the a,b being consistent for all x, not for some a,b working for some x.
This has been helpful, a lot of this shit has me working at 60% understanding and just kind of getting by without really knowing why. I actually feel like I kind of understand what makes linear independence work more

[Anonymous No.9550222]

Did you guys need to use hyperbolic trig functions in Calc II? I'm retaking the class and it wasn't in the curriculum the first 2 times. This bitch made a third of the questions based on hyperbolic trig functions and now I got a 40 on it and I feel like a retard because I didn't study that crap. At least give us the formula

[Anonymous No.9550278]

Why is the "aligned" environment messing up the equations? They're supposed to be aligned horizontally, with the equal signs being right above one-another, but somehow they're just slightly off center...

Here's the LaTeX:
https://pastebin.com/gbWtEJwE

[Anonymous No.9550299]

Can someone explain where I'm going wrong? Book says answer is zero (actually chegg does). #30 in chapter 14.2 of advanced engineering mathematics by kerzwig

[Anonymous No.9550301]

>>9550299
I think my decomposition is wrong, but I'm not sure why

[Anonymous No.9550303]

>>9550299
What's the question asking?

[Anonymous No.9550312]

>>9550303
evaluate the contour integral over that curve

[Anonymous No.9550374]

>>9549983
>, the amount of variables you need to "solve" tree(3) is some 2 to the power of 2 to the power of 2.... Like a thousand times.
But how do they know that's the amount of variables?

[Anonymous No.9550383]

>>9550299
>residue of (2z^3+z^2+4)/(z^4+4z^2)
>limit z->0 of z(2z^3+z^2+4)/(z^4+4z^2)
>limit (2z^3+z^2+4)/(z^3+4z)
>limit (6z^2+2z^1)/(3z^2+4)
> 0 / 4 = 0

Therefore it's 0

[Anonymous No.9550384]

>>9550383
Idk residues yet, but at least i know my answer is wrong, i guess.

I see now i dont know how to deal with complex numbers and fraction decomposition at all, so yeah, that's where the error is.

[Anonymous No.9550410]

Whats the difference between log and ln?

[Anonymous No.9550418]

>>9550410
ln always means log base e
log is most commonly base e in the context or mathematics (on rare occasions it'll mean base 10), and base 2 in the context of computer science

[Anonymous No.9550433]

>>9550299
what you need to is split it so that
[math]\frac{2z^3+z^2+4}{z^2(z^2+4)} = \frac{2z^3}{z^2(z^2+4)} + \frac{z^2+4}{z^2(z^2+4)} = \frac{2z}{z^2+4} + \frac{1}{z^2}[/math] and then you can apply residue theorem to each separate fraction

[Anonymous No.9550451]

>>9550418
thanks anon!

[Anonymous No.9550470]

Is anyone able to help with a proof of this? I've been fiddling for a while and can't seem to crack it.
I've tried expressing g(x) as a generic polynomial of degree n, taking the p-th derivative and playing with the coefficients but nothing seems to work. Any help would be appreciated

[Gaylord No.9550475]

Why bother graduating high school If I can't go to Ivy League?

[Anonymous No.9550476]

>>9550470
>Any help would be appreciated
Write down the ith derivative of h.

[Anonymous No.9550479]

>>9550476
Well as far as I can tell, the essence of it is seeing how the coefficients of g turn out and then showing that each can then be divided by (p-1)!. Then in addition to that showing each of those then has factor p. I feel like I need to crack what's happening with g before I look at h.

[Anonymous No.9550482]

>>9550470
the coefficients are binomial coefficients times other integers.

[Anonymous No.9550487]

>>9550479
>seeing how the coefficients of g turn out and then showing that each can then be divided by (p-1)!
This isn't necessarily true, re-read the question, and then write down the ith derivative of h.

[Anonymous No.9550489]

>>9550482
Damn I didn't see that at all. I think it's correct saying each term gives its degree multiplied by a factor p (for the p-th derivative of h(x)).
i.e. x^n gives nCp * p
x^{n-1} gives (n-1)Cp * p
etc.
Thanks anon

[Anonymous No.9550490]

>>9550487
>>9550487
n*(n-1)*....*(n-i-1)/p-1! = n*(n-1)*....*(n-p-2)*(n-p-1)*....*(n-i-1)/p-1! = nCp-1 * (n-p-1)....(n-i-1)

[Anonymous No.9550502]

Let [math]\mathbb{C}[x]_n\subseteq\mathbb{C}[x][/math] be the Subspace of all [math]\mathbb{C}[/math]-Polynomials so that the Degree of the Polynomials is maximal [math]n[/math].

Let [math]\mathcal{C}_n=\{i,ix,...,ix^n\}[/math] be the Basis of [math]\mathbb{C}[x]_n[/math] and[math]\varphi:\mathbb{C}[x]_3\to\mathbb{C}[x]_2[/math] be the [math]\mathbb{C}[/math]-linear mapping with [math]\varphi(\sum_{j=0}^{3}a_jx^j)=-2ia_0-4ia_1+ia_2+(-3ia_0-3ia_1+3ia_2-ia_3)x+(-ia_0-5ia_1-ia_2-ia_3)x^2.[/math]
Find a Basis [math]\mathcal{B}:=\{b_1,b_2,b_3,b_4\}[/math] of [math]\mathbb{C}[x]_3[/math], a Basis [math]\mathcal{B'}:=\{b_1',b_2',b_3'\}[/math] of [math]\mathbb{C}[x]_2[/math] and [math]l\in\{1,2,3\}[/math] such that [math]\varphi(b_j)=b_j'[/math] for [math]1\leq\:j\leq\:l[/math] and [math]\varphi(b_j)=0[/math] for [math]l\leq\:j\leq\:4[/math]

Can someone give me a start, a hint on how to solve this problem?

[Anonymous No.9550515]

Hello /sci/, any economists here?
I am having a problem trying to solve this last exercise. Indeed, I can't even start.

[Anonymous No.9550518]

>>9550515
What have you tried?

[Anonymous No.9550520]

>>9547881
Didn't think this was worth a thread so I'm asking here. I've gotta choose between business intelligence and service oriented architecture for my CS degree. Any advice on which is most useful?

[Anonymous No.9550548]

>>9550515
I am trying to write in latex but since I am not very used to it I need a second.

[Anonymous No.9550556]

What are the mathematical prerequisites for Introductory Quantum Mechanics? I'm guessing Linear Algebra and Probability will be main ones. Anyone know a good probability text that is helpful or geared towards quantum mechanics?

[Anonymous No.9550559]

>>9550518
Ok, I will not use latex as I am too slow with it... This will be terrible.
What I tried is using the definitions of EE, RC, TC and tried to apply them to the problem but I have no idea on how to utilize that utility function to form the conditions (EE and TC).
As regards RC,

ct + kt+1 = f(kt) + (1-d)kt

should be the condition for what concerns this problem.

[Anonymous No.9550583]

>>9550470
>>9550482
From you giving me that small comment I was able to write up an entire proof. I'd been stuck on this for a while. Thanks based anon!

[Anonymous No.9550620]

I just got a 50 on my STS quiz that's worth 10% of my final grade. I spent countless hours reading the course material, and I thought I knew everything. I feel like fucking killing myself right now.

[Anonymous No.9550679]

>>9550374
http://googology.wikia.com/wiki/TREE_sequence

[Anonymous No.9550686]

>>9550679
what the actual fuck
TREE(1)=1
TREE(2)=2
TREE(3)=????????????

[Anonymous No.9550695]

>>9550686
TREE(2)=3*

[Anonymous No.9550710]

>>9549928
Nigga use the Wronskian.

[Anonymous No.9550810]

Best book/course/lectures to learn matlab?
From the basics like arithmetics to complex and advanced stuff

I've never programmed in my life, so I'm quite lost

[Anonymous No.9550915]

Can someone explain what the fuck a radius of convergence is? Like i get that a series can converge to a value but how does it converge to a range of values?

[Anonymous No.9550970]

>>9550915
It doesn't converge to a range of values. Take for example a series a(n) = c ^ n. c is a real number. Now you are interested for which values of this real number c does your series a(n) converge (to anything - generally different values for different values of c) as n --> inf. That set of values of parameter c is a range of convergence of this series a(n).

[Anonymous No.9551027]

Consider a rod with a mass attached to it by a string (like child's toy or maybe something similar to a flail). The mass is moving tangentially so that we have circular motion. Angular momentum is conserved here but I want someone to help clear up something for me. In order for angular momentum to be conserved, there needs to be a net external torque of zero. In the plane of rotation, the only external force on the mass is the tension of the string which is radial and thus it creates no torque. However, why is it that I don't have to consider the torque created by gravity? Do I only need to consider external torques in the plane of rotation?

[Anonymous No.9551082]

How do you find the pressure inside a single effect evaporator if no information about the steam being used to heat it is stated?

[Anonymous No.9551122]

i'm doing power series solutions of 2nd order ODES and have an equation like
[math]\sum\limits_{n=0}^{\infty}[a_{n+2}(n+1)(n+2)+a_n(2-n)]x^n=e^x[/math].
Have i gone wrong somewhere? I ask because the (2-n) term, which means the solution ends up with only one constant a_1 instead of two.

[Anonymous No.9551172]

>>9551122
nvm. i was basically wondering why some terms didn't have constants, but it's because the series involves the particular solution..

[Anonymous No.9551330]

>>9551027
You do need to consider it, if you want to consider it. Basically the mass no longer is at the same height as the the tip of the rod where the string is atrached. The tension rises because now you have the vector sum of the fictitious centripetal force and the force of gravity. You could also find the height at which the ball moves relative to the tip of the rod as a function of its tangential momentum. Could be a nice exercise.

[Anonymous No.9551335]

>>9550556
Linear Algebra, basic complex analysis. You beed to know how to evaluate improper integrals. Some DiffEq's obviously. Probability not really. Any probability, at least for introductory quantum mechanics, is so basic you probably already know it.

[Anonymous No.9551339]

>>9550915
The radius of convergence of f(x) is the range of values x may take for f to converge. It's not a radius on the limit of the series, it is a radius on what you can plug into the series for the series to have a limit.

[Anonymous No.9551366]

>>9550556
Differential Equations and Fourier Analysis.

[Anonymous No.9551368]

For an assignment I had to explain why water doesn't flow out of a hole in a bottle when the cap is on and there's air at the top. I said it's because if the water level sinks then the pressure outside becomes greater than inside, so the pressure on both sides of the hole must be in equilibrium. My teacher (who has a PhD) marked it wrong and said it's because when you screw through cap on, the air pressure inside decreases since there's less air above it. Wtf? Either I'm really missing something or it was a cheap degree.

[Anonymous No.9551374]

>>9550810
http://4chan-science.wikia.com/wiki/Programming_Textbook_Recommendations#Matlab

[Anonymous No.9551390]

>>9551368
I'm wondering this too. How would the pressure decrease if there's less volume occupying the fluid?

[Anonymous No.9551449]

what's a good IDE to use for python? I want to learn it.

[Anonymous No.9551499]

>>9550502
Hint: write the map as a matrix.

[Anonymous No.9551507]

>>9551449
Your IDE choice doesn't really matter. I use VSCode because it's very sleek, but for learning python it might have extra gadgets that might be overwhelming to a newcomer. The default python interpreter works fine.

[Anonymous No.9551521]

>>9551368
if you have a think glass pipette or clear straw you can test his hypothesis directly

>fill glass with water
>put pipette in
>observe fluid height (may be a little above the water due to capillary etc forces
>put your finger over the top of the pipette
>see if the water rises inside the pipette

His statement is that when the system is open you have the entire column of air pushing down, but when you screw on the cap you have disconnected this and now the pressure should be greater outside than inside.

To be honest this would surprise me if true and I'm more inclined to side with you but since this can be fairly trivially solved by an experiment there's really no point in arguing about it.

[Anonymous No.9551576]

>>9551521
Yeah I'm pretty sure he's wrong, if the air pressure outside was greater than inside you'd see air bubbles rising in the bottle. Also, by the ideal gas law, since volume, temperature, and amount of gas don't change, pressure can't change.

[Anonymous No.9551581]

>>9551507
what's the default interpreter, where do I download this stuff?

[Anonymous No.9551677]

Right, say you've got a burner. You want to increase efficiency of said burner, which directly increases Carbon Monoxide levels of the exhaust. The law dictates you can't go above a level, so you think of ways to remove this carbon monoxide (around 500'c, 1bar)

My solution is either to use a Water-Gas Shift Reaction or just simply putting the exhaust gas through an oxidizer (think catalytic converter in a car, but without the reduction)

I want to model this within some type of CFD program (ANSYS?), do any of you guys know of software which would be good for me?
Thanks

[Anonymous No.9551680]

>>9551581
>what's the default interpreter,
python
>where do I download this
python.org
Take like half a second to google anything

[Anonymous No.9551944]

>>9547881
What is a good website where I can pay someone to tutor me in math? KhanAcademy is great, but some of the shit I just hit a brick wall on. I would rather pay someone to teach me even if it's all online.

[Anonymous No.9551948]

How the fuck did that woman clone her dog for 50k?

[Anonymous No.9552069]

>>9551944
We call that "college"

[Anonymous No.9552111]

Good introductory texts to pharmacology? Preferably with copious chemistry explanations for a chembrainlet.

[Anonymous No.9552125]

are bodily fluid CONTACT or VEHICLE transmission in microbiology? And why the fuck are "fomites" contact transmission but air, water, and food vehicle transmission? Was it fucking special needs day at the office when they came up with these distinctions?

[Anonymous No.9552140]

for e. and f. I'm trying to prove if it's linear independent or not. For 2. I'm completely clueless.

[Anonymous No.9552242]

>>9551581
Just download winpython and use Sypder.

[Anonymous No.9552285]

>>9552140
>For 2. I'm completely clueless.

A matrix is nonsingular iff it has an inverse
They provide a potential inverse
See if it works

[Anonymous No.9552308]

Anyone got any of those infographics on good books for daft freshmen engineers like me
Or just some recommendations for any specific topic I'll see in first year

Thanks in advance

[Anonymous No.9552332]

TRUE/FALSE

There exists a finite group with >50 elements where every element is its inverse.

[Anonymous No.9552335]

>>9552308
http://4chan-science.wikia.com/wiki/Universal_Material#Engineering_Philosophy

[Anonymous No.9552353]

>>9548412
>the first term is infinity
brainlet detected

>>9548741
ofc, read Euclid's elements and git gud

>>9549487
check theoretical limits lectures maybe, I dont know tho

>>9549611
just git gud anon, as the other anon said

>>9549790
solve hard problems and program more, ofc

>>9549981
read "Elements of Mathematics: Euclid to Godel" and "What is Mathematics?" or "Discrete Mathematics: Elementary and Beyond" if you just want some fun.

>>9550475
don't, one of my biggest regrets is not being based enough to drop out at 16 to work and study for 2 years and save up a $$30k+ scholarship then just go to community college

>>9550810
there's a few edx and coursera courses on it if you want someone else to take care of gathering and organizing the material. Also plenty of YouTube tutorials

>>9551944
Just read books, watch lectures/videos, use some software help and shitpost here, I will help you anon

>>9552111
>introductory
As always, start with the Greeks

>>9552308
>engineers
Do you suck at math? Look up your schools cirriculum and see if you need to be doing rigorous calculus first. If you're just using Stewart and that's all your ever gonna use, don't listen to the meme recommendations here like Spivak and Apostol unless you want to master the material out of interest.

And if your school just uses a computational non-proof like Stewart, Thomas etc just work through it and use Professor Leonard's lectures. If you really suck at math work through something like Axler's precalc or "What is Mathematics?"

[Anonymous No.9552359]

>>9552332
What have you tried?

[Anonymous No.9552361]

>>9552359
Zmod 51 where the group operation is subtraction

identity axiom fails

[Anonymous No.9552385]

>>9552353
I don't suck at it but I might be shaky on some parts. Trig, probably.

Yeah we're using Stewart and maybe Spivak, guess the engie memes are true. I'll look into those lectures I guess, but I'm interested in a more rigurous approach as well

[Anonymous No.9552389]

>>9552361
>identity axiom fails
This is a meaningless notion.

[Anonymous No.9552395]

Supposed there's a negative and positive particle that moves from 1m to 6m.
Is Delta V the particles experience positive or negative?
I think it's both negative because you move farther from the source?

[Anonymous No.9552401]

>>9552389
What?

1 - 0 = 1 gucci
0 - 1 = 50 NOT 1, not gucci

[Anonymous No.9552403]

>>9552401
>What?
You seem very confused.

[Anonymous No.9552411]

>>9552403
As do you, considering you have yet to provide insightful input

[Anonymous No.9552414]

>>9552385
In industry, engineers don't need to 'prove' their maths (in the mathematician's sense), so their efforts a best spent on courses that reflect this by having more of a computational nature to gain the computational tools of their trade and not 'waste' time like a pure mathematician would. If you wanna cover precalc (trig) and calc, plenty of options exist. I'd recommend Axler's precalc cuz half the answers are fully worked out (not merely provided) and for calc id familiarize yourself with your colleges text and perhaps pair it with professor Leonard's lectures.

If you're going into Spivak, grab a proofs book like Book of Proofs and cntrl + f this page for 'Spivak' for some relevant lectures notes and resources: https://functionalcs.github.io/curriculum/

[Anonymous No.9552426]

>>9552411
>As do you, considering you have yet to provide insightful input
Actually we understand the problem, which is why it's unclear why you would try doing calculations in something that is not a group for a question regarding groups.

[Anonymous No.9552435]

I've been self-studying math since I finished my EE degree, but I'm toying with the idea of going for a masters in math in a few years. Beyond the specific requisite knowledge for whatever classes I end up taking, what topics to I need to know before starting?

[Anonymous No.9552437]

>>9552435
>masters in math
literally why

[Anonymous No.9552439]

>>9552332
try XOR

[Anonymous No.9552621]

kind of a weird question but how much force does it take to completely rip a head off from a body?
pulling straight up, of course

[Anonymous No.9552630]

>>9552435
Proofs, Vector Spaces, Abstract Algebra, Real Analysis, Topology

[Anonymous No.9552855]

Hey, I have a quick question. When you use the sum/difference rule, or any rule on a derivative number, lets say d/dx(sin x + y)*(cos x - 1) is the whole result multiplied as a quantity? In other words, is it:

(cos x) + dy/dx*(cos x - 1) ?

Or:

(cos x + dy/dx)(cos x - 1) ?

[Anonymous No.9553023]

>>9552414
Gotcha. I'll look into Axler's then. Been watching a few of professor Leonard's lectures, they seem pretty good. Only problem is I'm not a native English speaker so I might run into some problem down the line.
But I'll cross that bridge when I get to it. Thanks for the help anon.

[Anonymous No.9553047]

>>9552414
Is Axler's Precalculus significantly different from his Algebra and Trigonometry book?

[Anonymous No.9553058]

>>9552395
Yes theyre both losing electric potential.

[Anonymous No.9553083]

>>9553047
No, they're very similar.

[Anonymous No.9553122]

>>9549499
no solutions so it doesn't intersect the x-axis, so it must be above or below

[Anonymous No.9553126]

>>9553122
no real solutions, that is.

[Anonymous No.9553233]

Is it possible to train a machine learning program to figure out whether a woman has done Porn?
Input: photo of woman
Output: has done porn, yes/no
The training and test data would include tens of thousands of photos of women wearing normal clothes in normal situations (i.e. not nude, not at a porn shoot). Half of them did porn before, half of them didn't.

Is it possible to train a machine learning algorithm to recognize sluts?
These are the questions that Computer Science was developed for and i need to know the answer

[Anonymous No.9553256]

Most efficient way to learn Calc II in a week.
I haven't been paying attention at all. I do all the homework but i'm slower than a snail, i'm talking > 1 hour / problem
Spring break is next weekend I gotta learn this. What's your favorite online course or something

[Anonymous No.9553364]

[math]\gamma\ \rightarrow\ e^-+e^+[/math]
[math]e^-+e^+\rightarrow\ 2\gamma[/math]
why is this the case?

[Anonymous No.9553369]

>>9553256
lmao good luck. As long as you're doing literally nothing else during break I bet you can do it.

[Anonymous No.9553444]

>>9553364
A photon doesn't go into two elections. A photon and something it can recoil against (say, a proton) turns into that same something (proton) with more energy, an election, and a positron. The something is required to conserve 4-momentum. The shorthand is leaving out that something and assuming it exists. To conserve 4 momentum in pair annihilation, one (say the election) radiates a photon, leaving the one (election) with precise 4-momentum that can annihilate the other (positron) with only 1 photon in the annihilation. The end result is initial election and positron and two final photos. The immeasurable time between radiating one photon and annihilating is practically insignificant. But overall you get 2 photos to account for the degrees of freedom the two massive particles have turning into two massless particles.

tl;ddo to conserve both energy and momentum. In creation, assumed something to recoil off of. In annihilation, need two massless particles to conserve.

[Anonymous No.9553453]

how did they come up with the second to last step?

[Anonymous No.9553504]

>>9553453
cos(e)=-cos(p)
think about the unit circle

[Anonymous No.9553517]

>>9553453
the coefficient of the ab term in the e^2+f^2 expression is zero, so it's just solving for the coefficient basically

[Anonymous No.9553726]

Can anyone recommend an introductory linear algebra text with a heavy emphasis on the applications of matrices to statistics? Preferably on the cheap side

heres a reaction pic as thanks

[Anonymous No.9553771]

does anyone know a good place to practice for the ACT online? preferably some place that gives me a score

[Anonymous No.9553984]

If G is a graph, which is not an odd cycle or a complete graph, then [math]\chi(G)\leq \Delta(G)[/math].
But what is the worst case? By that i mean graphs or families of graphs that maximise [math]\Delta(G)-\chi(G)[/math].
My first thought was a star on n>1 vertices, which gives [math]\Delta(G)-\chi(G)=n-1-2=n-3[/math] though i cant think of much else.

[Anonymous No.9554069]

>>9553984
That already gives you an arbitrarily high value, what else did you want?

[Anonymous No.9554170]

how are physicists able to tell that galaxies farther away from us are moving away from us faster than close galaxies because space is expanding rather than because those galaxies are moving through space?

if space is expanding everywhere then does that everything is getting bigger? like atoms are getting bigger?
if not, why not?

[Anonymous No.9554178]

>>9554170
>how are physicists able to tell that galaxies farther away from us are moving away from us faster than close galaxies because space is expanding rather than because those galaxies are moving through space?
They can't tell. But there's an overwhelming relationship in general to the measured speed of the galaxy and its distance. One explanation is that galaxies fucking hate us, but the other is that space is expanding and galaxies are just riding the wave.

>if space is expanding everywhere then does that [mean] everything is getting bigger
No. Atoms aren't getting bigger because the forces that hold an atom together are stronger than dark energy. Same for the earth, the solar system, the galaxy, some clusters, etc.

[Anonymous No.9554180]

>>9554170
because there are a lot of different theories such as the theory of relativity that only make sense if the universe is expanding. of course all those theories could just be wrong. we don't know anything for sure. but it's the best explanation we have right now

[Anonymous No.9554220]

thank you for responding.
>>9554178
is dark energy a force or energy?

>>9554178
>>9554180
what actually is it that physicists are measuring when they say that galaxies further away from us are moving away from us faster than galaxies closer to us?
are they measuring the velocity of those galaxies?
If the velocity of those further way galaxies is higher, doesn;t that mean that they are moving through space (as opposed to staying still in an expanding space)
and if they aren't moving through space at a faster velocity but just staying still in an expanding space then wouldn't their velocity be equal to those of closer galaxies?

what does "moving faster" mean when you're talking about space expanding?

[Anonymous No.9554237]

>>9554220
>what actually is it that physicists are measuring when they say that galaxies further away from us are moving away from us faster than galaxies closer to us?
They are measuring the wavelengths of light they receive versus what they expect to receive, if galaxies are basically the same everywhere (red/blue shift)

>If the velocity of those further way galaxies is higher, doesn;t that mean that they are moving through space (as opposed to staying still in an expanding space)
They are moving, and space is expanding. For instance you can imagine one moving left across the sky, while also receding away from us.

>what does moving faster mean when you're talking about space expanding
The apparent velocity of the galaxy is larger the farther away from us it is. We don't believe galaxies would have a distribution of velocities that depend on their distance from earth because we don't believe we occupy any special region of the universe. So we explain this by saying that galaxies have galaxy-like velocities, nothing crazy, but space everywhere is expanding, causing things very far from us to move away from us a lot more than things that are closer.

[Anonymous No.9554256]

how do i solve this?

[Anonymous No.9554258]

>>9554256
its literally a parallel plate on top of each other with a distance d

[Anonymous No.9554411]

I'm getting the right numerical answer for the second part, but in this form there isn't really anything I can do with it

I tried d=b[0,1] and stuff, what do?

[Anonymous No.9554430]

>>9554411
how do I select only the 0.3397..?

[Anonymous No.9554439]

>>9554430
use b(2) as your variable

[Anonymous No.9554455]

What's the latex to do the following:
[math]
\section*{ \textbf{Section Number Five} }
[/math]

I want to make the above latex be what happens when I do
\section{ Section Number Five}
essentially every time I make a new section, remove the number and bold it.

I know I might have to use "\renewcommand" but I'm not sure

[Anonymous No.9554491]

>>9554439
thanks

[Anonymous No.9554493]

>>9550515
I have made some progress I believe.
I managed to do the first point. I will in parenthesis the subscript.

EE) c(t+1) / c(t) = b

TC) lim(t->infinity) b^t * 1 / c(t) * k(t+1) = 0

RC) c(t) + k(t+1) = k(t)

Now, I have a problem in the second point. When I do the following substitutions:

c(t) = c(t+1) = c*
k(t) = k(t+1) = k*

I encounter some problems.

From the RC, I obtain:

c* + k* = k* <--> c* = 0

Substituting in the EE:

0 / 0 = b

Substituting in the TC:

lim(t->infinity) b^t * 1 / 0 * k*

So i get two results with by-0 divisions. Should I interpret this as inexistence of a steady state? Then why does the exercise specify that it is unique and solves the planner's problem?

Thanks in advance.

[Anonymous No.9554517]

>>9547881
I don't know if I'm an idiot or if this question is poorly worded. I'm trying to learn hydrometallurgy on my own so I don't have a prof to bug about this.

>Determine the equilibrium concentration of Ag+ and the equilibrium pH when when 0.05 mol of AgNO3 are added to 1000 g of water with an initial pH of 12.3,
I think I could figure this out. I have silver ions, I have nitrate ions, I can use Gibb's free energy to determine the activity ratio of my ions in solution. I'm not sure how the pH got to be 12.3 (maybe NaOH is in there?) but I can accept that.

>Assume I = 0.1.
Okay, so I can use the Debye-Huckel equation to figure out what my activity coefficient ought to be. This isn't too bad.

>assuming the only product is Ag(OH).
Wait, what? What happened to the Nitrate? Is the nitrate just not a part of this equation? The fact that the only product is Ag(OH) makes me want to think the equilibrium I want to worry about is Ag+ + OH- <-> AgOH, but then why was I told about the nitrate?

Can anybody help me out with this?

[Anonymous No.9554592]

>Why are equipotentials parallel to the electrode at their surface?
(electric fields)

brainlet here, can someone explain this for me?

[Anonymous No.9554601]

I don't need you to do my homework, but this is my first year at uni and I don't even know what kind of equation this is. Can you lead to resources helping out with this shit?

[Anonymous No.9554624]

>>9554601
What's so hard about this one? They give you r and m. Plug and chug

[Anonymous No.9554629]

>>9554624
What does the little e next to the r mean? what function is it?

[Anonymous No.9554640]

>>9554629
It tells you something about the variable. In this case it means interest rate (effective).

[Anonymous No.9554643]

>>9554629
It's not a function it's just a subtext used to distinguish between two different types of rates. Consider it as if it were a completely different variable.

[Anonymous No.9554770]

>>9554592
>>Why are equipotentials parallel to the electrode at their surface?
You agree that if you have a line of charge, going further away from the line lowers your electric potential. However, the way you lower your electric potential the *most* is by going directly perpendicular to the surface.

The reason this is the case is that, going parallel to the surface doesn't change your electric potential, just as walking left/right on a floor doesn't change your gravitational potential energy.

I did my best. Sorry for shitty approximation.

[Anonymous No.9554781]

If there was a guy shooting at you with a rifle, would it be possible to run at him and atrack him or would the bullets' momentum grind you to a halt? (Presuming you build up speed before he noticed and started shooting you, and adreneline means that the pain is irrelevant)

[Anonymous No.9554819]

I'm thinking it's infinitely many since there is a free variable right?

[Anonymous No.9554827]

>>9554819
Correct

[Anonymous No.9554829]

>>9554781
Assuming you mean that jrotc kid situation, no he never stood a chance. You need a gun to take down a gunman, or a corner turn.
If you mean the bullet force vs your force, typically a rifle isn't gonna push you over.

[Anonymous No.9554830]

Anyone who is familiar with this proof for Fermat's Last Theorem for n=3, please help. Here's a rough sketch leading up to what I'm having trouble with.

You end up with [math] p= 1-\zeta_3 [/math]
[math]pr=(x+y), ps=(x+\zeta_3 y)\zeta_3, pt=(x+\zeta_3^2 y)\zeta_3^2 [/math], r,s,t are coprime and r+s+t=0.
So
[math]p^3rst = z^3 [/math]
Since r,s,t are coprime
[math] r=ux_0^3, s=vy_0^3, t=wz_0^3[/math]

I'm wondering where the units u,v,w come from, and why they are not cubes (or maybe they are idk) and why is [math] uvw\in \{ 1, -1 \} [/math]

[Anonymous No.9554833]

>>9554819
x=3-y-2z
x=y-z

3-y-2z=y-z
There's a whole line of solutions for you buddy

[Anonymous No.9554834]

Is it possible to multiply a permutation on seven letters with a permutation on eight letters?

Say we have a permutation [math] \rho [\math] on [math] \{1,2,3,4,5,6,7,8\} [\math] and a permutation [math] x [\math] on [math] \{1,2,3,4,5,6,7\} [\math]. Is [math] \rho x [\math] defined?

My modern algebra book (Fraleigh) did not talk about this and google has not helped.

[Anonymous No.9554838]

>>9554834
Fucked up my TeX, here is the fixed version:

Is it possible to multiply a permutation on seven letters with a permutation on eight letters?

Say we have a permutation [math] \rho [/math] on [math] \{1,2,3,4,5,6,7,8\} [/math] and a permutation [math] x [/math] on [math] \{1,2,3,4,5,6,7\} [/math]. Is [math] \rho x [/math] defined?

My modern algebra book (Fraleigh) did not talk about this and google has not helped.\

[Anonymous No.9554840]

>>9554834
If you consider the eighth letter as a fixed point of the seven letter permutation then it can be well-defined, but technically these are elements of different groups

[Anonymous No.9554880]

>>9553364
Because minimal coupling couples [math]A[/math] to [math]\bar{\psi}[/math] and [math]\psi[/math]. In general suppose you have a [math]G[/math]-principal bundle [math]E \rightarrow M[/math] as well as a linear representation [math]E \rightarrow V[/math], then the pullback of the connection 1-form [math]A_\alpha \equiv s_\alpha^* A \in \Omega^1(M) \otimes \operatorname{Lie}G[/math] on the de Rham complex of Lie algebra-valued graded differential algebra is the gauge field, with connection [math]\nabla = d + \omega = d +
[A,\cdotp][/math], where the second equality comes from the linear representation on the associated vector bundle [math]V[/math]. For Abelian Yang-Mills theory, [math]\operatorname{Lie}G[/math] is central and hence no terms in [math]A[/math] higher order than 1 in the action can couple to the fields, which are treated as elements of the sheaf of operator-valued distributions living in the local operator algebra [math]\bigcup_{U\subset \mathbb{M}}\mathcal{A}(U)[/math], otherwise the action would not be gauge invariant under gauge transformations [math]u \in \operatorname{End}V[/math].
>>9554592
Because in electrostatics the electric potential satisfy Dirichlet boundary conditions on conductors. In general the electromagnetic action [math]S = \int_M F^2 = \int_M dA \wedge \ast dA = \int_{\partial M}A\wedge dA[/math] by Stokes's theorem. For a conductor [math]S \subset \mathbb{R}^d[/math] is open and hence [math]M = \mathbb{R} \setminus S[/math] is closed. Therefore the trace map [math]\operatorname{tr}:H^1(M) \rightarrow L^p(\partial M)[/math] must vanish on the minimizer. The space of variations for the principle of least action is then [math]\mathcal{A}_0 = \{\lambda \in \Omega^1(M) \otimes \mathbb{R}\cong \Omega^1(M)\mid A|_{\partial M} = 0\}[/math] and hence the solution of the Euler-Lagrange equation [math]dF = 0 \iff \nabla \phi = 0[/math] satisfies Dirichlet boundary conditions.
I hope this clears up any confusion.

[Anonymous No.9555076]

Help a brainlet out. I keep fucking up K_{sp} calculations. Can somebody tell me where I'm going wrong?

I'm working with the equation [math] AgOH \leftrightarrow Ag^{+} + OH^{-} [\math].

\Delta G_{r}^{^{\circ}} = \Delta G_{products}^{^{\circ}} - \Delta G_{reactants}^{^{\circ}}

Solving for \Delta G_{r}^{^{\circ}}:

(77,100)+(-157,328) - (-91,970) = 11,742\: J/mol

Next, I solve for K_{sp}:

\Delta G_{r}^{^{\circ}} = -RTln(K_{sp})

K_{sp} = e^{\frac{-\Delta G_{r}^{^{\circ}}}{R*T}}

Assuming a standard temperature of 298 degrees Kelvin:

K_{sp} = e^{\frac{-11742}{8.314*298}} = 8.74*10^{-3}

Googling the K_{sp} of AgOH shows that it has been measured as 2.0*10^{-8}. I've obviously gone wrong somewhere.

[Anonymous No.9555087]

Help a brainlet out. I keep fucking up K_{sp} calculations. Can somebody tell me where I'm going wrong?

I'm working with the equation [eqn] AgOH \leftrightarrow Ag^{+} + OH^{-} [/eqn].

[eqn]\Delta G_{r}^{^{\circ}} = \Delta G_{products}^{^{\circ}} - \Delta G_{reactants}^{^{\circ}}[/eqn]

Solving for [math]\Delta G_{r}^{^{\circ}}[/math]:

[eqn](77,100)+(-157,328) - (-91,970) = 11,742\: J/mol[/eqn]

Next, I solve for [math]K_{sp}[/math]:

[eqn]\Delta G_{r}^{^{\circ}} = -RTln(K_{sp})[/eqn]

[eqn]K_{sp} = e^{\frac{-\Delta G_{r}^{^{\circ}}}{R*T}}[/eqn]

Assuming a standard temperature of 298 degrees Kelvin:

[eqn]K_{sp} = e^{\frac{-11742}{8.314*298}} = 8.74*10^{-3}[/eqn]

Googling the [math]K_{sp}[/math] of AgOH shows that it has been measured as [math]2.0*10^{-8}[/math]. I've obviously gone wrong somewhere.

[Anonymous No.9555089]

>>9555087
btw, sorry for the formatting - I'm new at LaTeX.

[Anonymous No.9555097]

>>9555087
What is your reference for the standard Gibbs free energy for AgOH? I can't find it anywhere.

[Anonymous No.9555102]

>>9555097
My textbook states that the value is -91,970 J/mol.

It says that it got this value from "Reference 2", which is listed as
"R. M. Garrels and C. L. Christ, “Solutions, Minerals, and Equilibria,” Jones and Bartlett Publishers, Boston (MA), , 1990."

[Anonymous No.9555110]

>>9555102
It looks like there are hard copies out there but no digital copies that I can access - it'll be a while until I can access the UBC Library to double-check that value.

[Anonymous No.9555113]

>>9555110
I found it: sci-hub () tw/http://onlinelibrary.wiley.com/doi/10.1002/9781118732465.app4/summary

I don't see anything wrong with what you did, but I took analytical a year ago so I may not be the best resource. Can you definitely relate Ksp with Gibbs free energy?

[Anonymous No.9555120]

>>9555113
Oh never mind I'm dumb, I probably just found your book.

[Anonymous No.9555122]

>>9555113
That's a copy of the textbook I'm using, not the original text by Garrels & Christ. Thanks for looking though!

I'm assuming that the questions in the textbook can be answered using information derived from the text - seems like a valid assumption.

Pic attached states that the final equilibrium speciation in the system can be derived using the formula I used.

[Anonymous No.9555129]

>>9555120
Here's an example from the text where [math]K_{sp}[/math] was derived using the same method I did - note that I calculate [math]K_{sp}[/math] directly because I'm using a dissociation reaction rather than a formation reaction.

I feel like I must be missing something though - I must not be taking something into account if the measured [math]K_{sp}[/math] for AgOH differs from my theoretical value.

[Anonymous No.9555135]

>>9555122
Maybe try using delta H and delta S to calculate delta G? That's the only thing that I can think of.

[Anonymous No.9555136]

>>9555135
That's a great idea. Thanks man!

[Anonymous No.9555204]

I'm a NEET trying to relearn the things from way back in highschool. How is that top equation equal to the bottom? My goal for the year is to at least make it to calculus, I don't think I have a chance if I can't solve a dumbass algebra problem.

[Anonymous No.9555217]

>>9555204
(a+b)/c = a/c + b/c

[Anonymous No.9555226]

>>9555204
Division is distributive on addition/substraction. Then instead of writing x/5 you can write 1/5 * x which is cleaner when doing other stuff

[Anonymous No.9555233]

>>9555217
>>9555226

Ayy I finally get it now, thanks

[Anonymous No.9555243]

>>9555233
But only on the top.
a/(b+c) =/= a/b + a/c

ex
1=2/2 = 2/(1+1) =/= 2/1 + 2/1 = 4

[Anonymous No.9555245]

>>9553726
http://joshua.smcvt.edu/linearalgebra/
http://www.ulaff.net

[Anonymous No.9555247]

how can I perform lasso analysis without R autism

[Anonymous No.9555359]

electromagnetism midterm in 3 HOURS WTF LADSL :dddddddddd Do me a GAuss, do me A LAPLASS, do me a P O T E N T I A L
O
T
E N T I A L

[Anonymous No.9555748]

[Anonymous No.9555779]

Can someone explain how one is supposed to answer these questions on partial sums. This book has been completely useless in explaining it.

[Anonymous No.9555795]

>>9555779
sum the formulas from k to n to find the partial sums

apply convergence test. should be a list of them in the chapter

[Anonymous No.9555830]

>>9555779
Use induction to figure them out or apply arithmetic/geometric partial sum formulas.

[Anonymous No.9555837]

>>9549928
show that evaluating sin and cos at 2 different x leads to a matrix that has a nonzero determinant.

Ie

c1sin(x1) + c2cos(x1) = 0
c1sin(x2) + c2cos(x2) = 0

If we row reduce the matrix above or just take the determinant since it's a lot easier

sin(x1)cos(x2) - cos(x1)sin(x2) != 0 therefore the two functions are linearly independent. Because if they were linearly dependent then there would be a combo of c1 and c2 that satisfy the equation for ANY x. And we have shown that there is no c1 and c2 that satisfy the system at two different x values.

[Anonymous No.9555856]

f(x,y) is homogeneous of degree P
g(x,y) is homogeneous of degree Q

Is f*g homogeneous, and if so of what order, when the operation * is

>addition
>multiplication
>subtraction
>division

Somebody give me a pointer, this should be easy but I don't know where to start.

[Anonymous No.9555862]

>>9555856
What have you tried?

[Anonymous No.9555887]

https://en.m.wikipedia.org/wiki/Doping_(semiconductor)

If people do this to make a SEMIconductor more CONDUCTIVE then why use a SEMIconductor in the first place instead of a CONDUCTOR?

[Anonymous No.9555893]

>>9550025
tell me what does it mean for two functions f(x) and g(x) to be equal

[Anonymous No.9555894]

>>9555887
Because we sometimes want current to flow in just one direction.

[Anonymous No.9555906]

>>9555894
i dont get it
im a dumbass
why wouldnt it always go in one direction? I mean like as far as i know, "current flows from high to low voltage" (is what people say) so if you have one wire connected to 5v and one to gnd it will go from 5v to gnd no matter what

[Anonymous No.9555908]

>>9555906
or i mean if you have one end of the wire to 5v and the other end to gnd not two separate wires obviously

[Anonymous No.9555914]

>>9555906
But what if we use AC????

[Anonymous No.9555918]

>>9555914
how do you decide what to use, i mean like how do you physically decide that, is it a switch on a battery? what controls that?

[Anonymous No.9555920]

i'm an engineering science major, 1st year, and i don't know how to dress. some of my classmates wear flannels and fluffy hats. is that in style? i tried on a flannel but it doesn't fit me. i'm a chisel-faced athletic guy. i've always worn jeans and a tshirt. i'd like to snag a qt engineering student gf so i need to be fashionable

[Anonymous No.9555928]

>>9555920
wear brony shirts from 2012 that are 2 sizes too small

[Anonymous No.9555929]

>>9555918
https://www.quora.com/Which-is-more-efficient-AC-or-DC-power

[Anonymous No.9555941]

>>9555359
are you feeling it mr crabs

[Anonymous No.9555942]

>>9555779
they give you the formula lil nigga

first one is the sum of 1/3^n from 0 to n
i imagine you take the limit and see what happens

[Anonymous No.9555943]

>>9555928
might do this

[Anonymous No.9555945]

>>9555887
Semiconductors allow us to
1) control the conductivity (transistors)
2) remove symmetry (current flows better one way than the other)

>>9555906
>why wouldnt it always go in one direction?
Here is an example. Suppose we apply current to a coil, like a motor. If the motor is always spinning in one direction, we only apply one direction of current. The energy goes into building up the magnetic field in the coil, and this moves the motor a little bit. But now we need to release this energy. It's going to want to come back opposite of the way it went in when the field collapses. This could damage all kinds of things, so we want a special path for reverse current.

[Anonymous No.9555961]

>>9555887
you fucking donut

an n-type semicondcutor is still a semiconductor. no matter how much you dope the semiconductor the bandgap stays the same size, plus you're not dramatically altering the conductivity so that it's tantamount to a conductor

also there's a difference between p-type and n-type, and the junction of the two is a big deal. even if n-type was the same, how do you get p-type properties from a single element? also the most common n-type dopants arent even good conductors like boron

the point is to take something with a decent bandgap, that doesn't dramatically resist the flow of electrons (so there isnt crazy amounts of heat), that you can precisely alter the conductivity of because the most common diodes are just a junction of these two types of semiconductors as well as transistors.. pure silicon is the best thing to do it with

[Anonymous No.9555971]

>>9555945
>>9555961
you know im gonna be honest i only understood about 30% of your posts
my professor was talking about this stuff the other day is the thing, im probably going to drop out. i got through the initial weed-out classes but now there's like a second level of weed-out and thats where im getting stuck at

[Anonymous No.9555976]

>>9555971
>he thinks he's gone through the first wave of weed-out at all
This is high school level shit lmfao how fucking stupid are you?

[Anonymous No.9555977]

>>9552332
Z/2Z ^ 50, you dink.

[Anonymous No.9555979]

>>9555976
i literally did go through the first wave, all my class numbers used to start with 1 and now they start with 2 and a few of them are even 3

[Anonymous No.9555986]

>i literally did go through the first wave, all my class numbers used to start with 1 and now they start with 2 and a few of them are even 3

[Anonymous No.9555991]

@9555986
well what the fuck is a "second wave" if not the 2 or 300 level classes?

[Anonymous No.9555998]

##9555991
>well what the fuck is a "second wave" if not the 2 or 300 level classes?

[Anonymous No.9556007]

dear 9555998,
do yo not even BELIEVE im IN any 300 level classes smugboy?

[Anonymous No.9556020]

>>9556007
His point is that you went through the first round of classes, not the weed-out round. EE doesn't weed out that early, unless you can't handle the basic physics classes.

[Anonymous No.9556033]

>>9556020
it's CE
but thats quite worrying to hear still

i dont know what the hostility is about from him anyway, i straight up said "i'll probably have to drop out"; i made an immediate admission to inferiority and humility and concession that i am shit and nothing, and he's STILL mean to me and posting smug anime pictures

[Anonymous No.9556040]

>>9556033
Don't worry about him he's just super insecure. Are you planning to drop out entirely or switch majors? What majors are you looking at?

[Anonymous No.9556052]

>>9556040
CE where i'm at requires a math minor, i think it would be hilarious if someone like me had a fucking degree of any sort in math since I suck at it and am struggling in linear algebra right now. CS doesn't require a math minor so maybe I could switch to that and take a little load off, I dont know. the issue is i have to decide this soon because like, what if im in too deep already? if i drop out there is absolutely zero return on the time i've spent here

[Anonymous No.9556153]

>>9549452
90/6 = x /20

Multiply by 6 and divide by x and you get (2)

[Anonymous No.9556222]

>>9555247
somebody please help

[Anonymous No.9556264]

>>9556222
python

[Anonymous No.9556266]

>>9556264
>trading r autism for python autism

[Anonymous No.9556279]

>>9556264
If I had a time machine I would go back in time and kill guido before he had a chance to make python.

[Anonymous No.9556298]

>>9556266
Well, I don't think you can realistically do it without a computer, and doing it with a computer will involve programming autism

>>9556279
Why though?

[Anonymous No.9556317]

>>9556298
welp isn't there a software where you just put your data in and get results out like biostat, excel, prism and so on?

[Anonymous No.9556328]

>>9556317
Apparently it is possible in Excel

http://www.real-statistics.com/multiple-regression/ridge-and-lasso-regression/lasso-regression/

[Anonymous No.9556332]

Let [math] \alpha: I\!R^2 \rightarrow I\!R[/math] be a curve that's 2 times differentiable, [math] v [/math] its first derivative, [math] a [/math] its second derivative and [math] v_{s} = || v || [/math] the scalar velocity.
Then it holds that
[eqn] v_{s}' = \frac{v.a}{v_{s}} [/eqn] where the . is the scalar product. My question is what's the physical intuition behind this formula.
Now, I have demonstrated that statement and I can understand that, since the acceleration is divided into two components, the tangential one (the one that "controls" velocity) and the normal one (the one that "controls" curvature). it's easy to understand that [math] v_{s}' [/math] is related to [math] v.a [/math] given that that is the size of the projection of the acceleration on the velocity, right? However, what is the [math] \frac{1}{v_{s}} [/math] doing there?
Thanks

[Anonymous No.9556337]

>>9556332
>α:IR2→IR
shit
[math] \alpha : I\!R \rightarrow I\!R^2 [/math]

[Anonymous No.9556422]

I don't think i ever took a single class whose course number started with a 2

[Anonymous No.9556425]

∞

[Anonymous No.9556459]

>>9556422
what a special boy
im sure mommy is very proud

[Anonymous No.9556464]

Why can't we use nitrogen as a power source? That shit is literally everywhere.

[Anonymous No.9556513]

>>9556332
>>9556337
homie, use \mathbb{R}, not this disgusting IR

[Anonymous No.9556628]

Alright, tell me where the wrong part is in my thought experiment please.
You have two perfect mirrors facing each other and photons bouncing between the two. You move the group of mirrors while the photons are bouncing, redshifting them; then you stop the mirrors to come back to a "resting" state like at the begining of the experiment, except your photons are a little more red.
Given that the energy of a photon is h*c/λ, it seems to me like some energy disappeared.

[Anonymous No.9556637]

So apparently my university offers a master's in stats for free if you're domestic. Only it's a certain company that technically pays for your tuition and on top of that they hire and pay you to work for them.
I know it's not uncommon for companies to do that. But for whatever reason it sounds too good to be true. Does anyone have experience with this sort of stuff? What's the catch?

[Anonymous No.9556640]

>>9556637
the catch is if the company were worth working for they wouldn't have to hide behind bullshit like this, therefore this faustian bargain is not worth it, but there's a sucker born every minute and they can exploit this continuous source of idiots

[Anonymous No.9556782]

>>9556328
wow nice
I hope it's legit

thank you my nigga

[Anonymous No.9556788]

>>9556637
enjoy becoming a slave to that company

[Anonymous No.9556852]

>>9556628
Photons have momentum, so you have to take into account the change in the mirrors' velocity when calculating system energy.

[Anonymous No.9556909]

I'm doing a degree with a major in Biology and Materials Chemistry. How fucked am I?
I stress out constantly about my degree being useless and whether I should transfer or not.

[Anonymous No.9557016]

Once like half a dozen years ago I saw a documentary where a lab rat who lived his entire life in a cage without toys, just eating and drinking to stay alive grew to consider headbutting the cage's walls a fun activity, I can't remember the name of the experiment, does anyone remember anything about this?
The aim was to show how an animal's perception of "enjoyment" can change when forced to live in a certain environment and circumstances or something like that, I need to find informations on that project for a research.

[Anonymous No.9557040]

How to now get sleepy on lectures? Even after a good night of sleep I still get sleepy, my productivity is affected by this
Pls help

[Anonymous No.9557280]

>>9552855
the second. think of them as numbers.
clearly for any numbers c*(a+b)=ca+cb. now if c=(d+e), what is c*(a+b)? is it

d+e*(a+b)

or

(d+e)*(a+b)

[Anonymous No.9557304]

I've completely forgotten all my log/exponential laws because my brain doesn't retain mathematics.

If we have 1/8 = e^(-9x), why am I able to rearrange it as -ln (1/8) = 9x ?

[Anonymous No.9557437]

If i'm running a statistical test comparing the diameters of two sets of trees, is it enough to run a t-test showing that the means are significantly different, then literally looking at the means to see which is significantly larger than the other? Or do i need to run a separate test to see which set has larger diameters?

[Anonymous No.9557440]

>>9557016

Pretty sure the rat was just trying to kill itself

[Anonymous No.9557448]

Is it normal to see light beams off of almost all light sources?

[Anonymous No.9557459]

>>9547881
http://www.wolframalpha.com/input/?i=Euler%27s+identity

What is this shit? Why is this relation defined in terms of sine and cosine instead of sine and cosine being defined as the imaginary and real parts of this function? Is there even a point to limiting a function to the domain of the complex roots of 1?

[Anonymous No.9557482]

>>9557448
like rays of god?

I think as long as you're not seeing rainbows around all light sources its ok, rainbows can be a sign of high pressure in your eye

[Anonymous No.9557555]

>>9556637
How long are you forced to work for them?

[Anonymous No.9557560]

>>9557304
[math]ln(e^x) = e^{ln(x)} = x[/math]
so you take the log of both sides then multiply by -1.

[Anonymous No.9557624]

>>9555856
use the definition

[Anonymous No.9557652]

>>9557440
lmao no really, they had sensors that detected his brain was feeling something akin to enjoyment/euphoria.

[Anonymous No.9557859]

I'm working through a mathematics book list recommended to me on /g/. So far I have gone through Lial's Basic College Mathematics. I was shocked at how much I had forgotten from school but it is pretty much basic I know but I'm glad I did it. However my next book is Axler's Precalculus which I'm getting through slowly. However after flicking through it I don't see much about Cos, Sin, and Tan. I have really hit a brick wall since I remember NOTHING about what this is and I want a full concrete knowledge of these before going further. All I remember from school was that we had a small copy book which you had to use to get these cos, sin, tan values. I'd like to be able to do it like this again before relying on my calculator.
So really my question is where (book recommendation please) to get a bullet proof understanding of this before I go further. My goal for this year is to master Calculus and maintain that knowledge which I'm hoping to do by afterwards continuing on with that reading list.

[Anonymous No.9557890]

Riemann Geometry
Am I correct to conclude that the following is wrong/mistranslated?
>The number of parallel lines that can be drawn through a given point to a given line is one in Euclid's geometry, none in Riemann's, and an infinite number in the geometry of Lobachevsky. Let. us add that Riemann's space is finite, although unbounded in the sense which we have above attached to these words.
http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_non-Euclidean.html

You can't have a parallel line to a line/loop connecting polar opposite coordinates, but you can any other sets of points. Right?

[Anonymous No.9557894]

>>9552140
just verify it. this is called sherman woodbury matrix inverse

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

https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula

[Anonymous No.9557899]

>>9557890
nm

[Anonymous No.9557908]

>The number of parallel lines that can be drawn through a given point to a given line is one in Euclid's geometry, none in Riemann's, and an infinite number in the geometry of Lobachevsky.
http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_non-Euclidean.html

OK, I made a mistake, but I am still confused. Once a line is given--I was thinking about two points without a settled on line--why can't you draw a parallel line/loop from a given point in Riemann geometry? Given a line and a point, you can draw exactly a single line/loop that never intersects the first line. Right? What am I missing?

[Anonymous No.9558123]

How do I verify my knowledge with self-study? Now, I do go to university, but because one written exam is 100% of our grade and we get no homework assignments, I need to find better ways to test myself so that, come exam day, it doesn't feel like a risky dice roll like it has for the past year and a half.

[Anonymous No.9558146]

>>9547881
2+2 can both be 4 and 5, depending on the scope.

2.4+2.4=4.8
Round to one number.

2+2=5.

Can you disprove this?

[Anonymous No.9558157]

>>9558146
2 != 2.4
4 != 4.8 != 5

There, disproved

[Anonymous No.9558160]

>>9558157
in english Einstein.

[Anonymous No.9558162]

>>9558160
Two is not equal to two point four.

[Anonymous No.9558163]

With an IQ of 107 AT MOST based on an online verbal score (pic related - contrary to your intuitions verbal tests are the most predictive of any IQ subtest) how do I make sure I intuitively understand what I'm learning and doing in algebra, trig, and calc instead of just blindly memorizing the process.

[Anonymous No.9558165]

>>9558163
Pic

[Anonymous No.9558166]

>>9558162
2.4 rounded down is 2.

By not rounding down initially this is true, 2.4 is not equal to 2, however by rounding up and down post solution, we have the result of 2+2=5.

It's a gag trick that can be used to screw with observers.

[Anonymous No.9558255]

I'm doing a data analysis course, I'm not required to get any book but the reference texts are "All of Statistics" by Wasserman and "Introduction to Statistics and Data Analysis" by Heumann and Schomaker. Should I get them both, if not, which one is better after a basic probability course?

[Anonymous No.9558431]

Could someone help me with Q2. Ive used triangle equality but dont know what to do from there

[Anonymous No.9558564]

I'm finally going to go for it, I'm going to study physics.
What math should I be going over to prepare for the first year?

[Anonymous No.9558575]

[math] T \left( \begin{bmatrix}
1 \\
0
\end{bmatrix} \right) =
\begin{bmatrix}
1 \\
2 \\
0
\end{bmatrix}, T \left( \begin{bmatrix}
0 \\
1
\end{bmatrix} \right) =
\begin{bmatrix}
1 \\
0 \\
-1
\end{bmatrix}[/math]

What's
[math]T\left( \begin{bmatrix}
3 \\
0
\end{bmatrix} \right) \text{ and }
T\begin{bmatrix}
2 \\
-1
\end{bmatrix}[/math]?

[Anonymous No.9558717]

>>9558575
use linearity

[Anonymous No.9558790]

I'm trying to find a ≤ x ≤ b, where f(x) = 0.00625 and the mean being 136. I know that 0.00625 = 1/160 but what formula do I use to find a and b?

[Anonymous No.9558832]

>>9558717
Is the first one the same as 3T([1,0])?

[Anonymous No.9558837]

>>9558832
yeah

[Anonymous No.9558851]

>>9558837
Fuck yeah.

[Anonymous No.9559131]

Besides studying previous exams, are there any other good ways to study for the math GRE?

[Anonymous No.9559562]

>>9557555
It's pretty weird actually. You only work for them as long as you study. So if you study in fall and spring you work for them then. However if you study in the summer you have the option of working for them or somewhere else. Part of the degree requirement is to get an internship so that completes it. I'm not actually sure if you have to continue working for them after graduation though.

[Anonymous No.9559881]

g(x) = √x-3 (square root sign extends over the minus 3)
The domain is assumed to be |3,infinity|
Why is this true since the domain is also assumed to be the set of real numbers and x=5 will result in √2. Or is there some other assumption that I'm missing?

[Anonymous No.9560075]

>>9559881
You can't assume two different domains for the same function.