/sci/ - Science & Math

The /g/ questions are in the stupid pile, because the first one I came across was stupid and I didn't want to make the category later.

Unanswered questions:

Math questions:
>>11937810
>>11943986
>>11951061
>>11951102
>>11951104
>>11951743
>>11951767
>>11957276

Physics questions:
>>11939380
>>11942699
>>11946891
>>11948942
>>11950986
>>11956855
>>11958739

Engineering questions:
>>11948969
>>11951704
>>11951983
>>11959176

Biology questions:
>>11942901
>>11943714
>>11943959

Stupid questions:
>>11938030
>>11942059
>>11942993
>>11943314
>>11944332
>>11949668
>>11949704
>>11955276
>>11955293
>>11956639
>>11957398
>>11958584
>>11960783
>>11961732
>>11962444

I am attempting to grasp the basics of moving load problems (beam vibration), but am atm failing to follow eq 18 and 19, how are they manipulating the formula in exact to derive the seperate equations?
Ex. wht is q_0 inside the 19 instead of q_1 on the left side?

Even when deviding both sides on 19 by epsilon, it previously came in a second power ... kind of stuck there.

Was I right? (the timing of an event = information)

can someone walk me through this one? I just do'nt get how to find the basis

>>11965073
nevermind, got it.

>>11965073
>>11965851
this one however, has got me stuck. the RREF is
[math]\begin{pmatrix} 1 & 0. & 0.333333334638 \\ 0 & 1. & 0.666666658969 \end{pmatrix}
[/math]

>>11965969
Pretty sure those two equations are low-key multiples of each other.
Evidence for it: I divided the first two entries and got 1.41 for both.

>>11966111
Nope, not multiples by very little, actually.

>>11966111
>>11966155
ok, but how would I enter the solution? it complains if the vector doesn't have three components.

>>11966194
Oh, right.
Well, it says that you can rescale it, so they probably expect you to give it with integer coordinates.

>>11966310
can you give me an example of an answer? I've exhausted a lot of options

how is b) wrong? rref is
[math]\begin{pmatrix} 1 & 0. &
0.272727272727 \\ 0 & 1. & -0.0909090909091 \\ 0 & 0. & 0. \\ 0 & 0. & 0. \end{pmatrix}
[/math]

two pivot columns, therefore col(A) = 2

>>11966355
furdged the rref there, here it is corrected:
[math]

\begin{pmatrix} 1 & 0. & 0. \\ 0 & 1. & 0. \\ 0 & 0. & 1. \end{pmatrix}

[/math]

i'm building an RC airplane the problem is xflr5 and Solidworks give me different lift results for my wing.

any idea ?

>>11966329
[math](1546, 3092, -4638)[/math]
>inb4 did you compute it by hand with a calculator
Yes.

>>11966456
what the hell? how did you get this answer? it's correct btw

>>11966504
>>11966504
I used substitution and a calculator like a middle schooler.
That is, I isolated c in the first equation, and then I isolated b on the second one. Then I chose a value of a which made everything integers.
I honestly don't remmber the linear algebra method of solving that.

>>11966568
thanks anon, I shoulda tried the middle schooler approach before posting..

anyone know the answers off the top of their high IQ dome?

>>11967328
>pic related

>>11967337
Mark C, unmark E.

>>11966355
>>11966398
still not understanding this. Corrected rref (again) is below.
[math]
\begin{pmatrix} 1 & 0. &
4. \\ 0 & 1. & -3. \\ 0 & 0. & 0. \end{pmatrix}
[/math]

There is clearly 2 pivot columns there, so the answer should be 2.

>>11967443
no bueno here unfortunately

>>11967607
>should be 2
https://www.wolframalpha.com/input/?i=what%27s+the+dimension+of+the+span+%7B%288%2C+2%2C+2%29%2C+%287%2C+-1%2C+2%29%2C+%2811%2C+11%2C+2%29%7D
Maybe they mean literally the number of vectors, in which case it's uncountable infinity.

>>11967623
Or the number of collumns, in which case it's 3 again.

>>11967628
inf was correct, dag nabbit thanks anon

>>11967636
>inf was correct
You can't make this shit up, Jesus Christ.

Why do I enjoy seeking out popsci trash with the purpose of getting upset at it? Is it just pic related?

>>11967702
can you explain why I'm so stupid

>>11967702
i thought col(a) was the number of pivot columns in the rref, why is it inf?

>>11963300
What is the most useless piece of information you know?

>>11967951
that im going to die one day

>>11967897
The dimension of the column space is 2. But as a space itself, it contains infinitely many vectors. Just take any vector and multiply it by any number. Then you have another vector in the column space.

>>11967891
Perhaps you have trained yourself to click on articles that you know you will hate, and now its a forced habit.

>>11967951
My entire phd thesis, probably

Is control theory useful for a physicist?
I am currently pursuing a bachelor in physics and I got interested in control theory.

>>11967891
It's either that, an undying subconscious hope that it will miraculously be good, or a habit like the other anon pointed out.
>>11967895
This one isn't on you.
>>11967951
How to program in Haskell.

>>11968697
If you are somewhat advanced in your studies, many of the mathematical tools needed to solve problems in control theory (e.g. differential eqs & integral transforms) should already be part of your knowledge, which is a good thing. As for the applications of control theory, you could work/research in robotics-related areas or in aerospace technology.

>>11967891
because it makes you feel superior / smart

Hypothetically, if I want to culture phages, can I do so by simply culturing the bacteria group that they should target, and then adding some sea water to find a suitable phage?
What are the chances of contaminants ruining the culture?

still stuck here

>>11969486
I hope you fail your class and are kicked out of your program you pathetic brainlet faggot

>>11969501
I'm averaging 96% right now but thx

>>11969512
Then you are still a massive retard for not being able to solve these problems you’ve been posting without help and I would be extremely embarrassed to have you attending my institution. Brainlet.

>>11969486
Oh.
A, C, F.

>>11969517
It's not that I'm horribly retarded, it's that I just haven't fully read the relevant material yet. I always end up doing really well on the exams as I find the time to fill in the gaps in my knowledge.

Just busy mang and 90% of the time skimming the theorems then doing the homework works just fine.

>>11969525
Fucking faggot

>>11969530
I don't care what you think angryboi

Test.

How do I find what values r and theta should be within in this problem?

>>11970047
Draw a picture of the region.

>>11970047
>bounds of integration include same variables as the integrand
unsolvable

I tried contacting NASA to ask this, but they just sent me a copypasta of their astronaut requirements page and completely ignored my question. Does anyone know if a PharmD Doctorate satisfies the requirements to be an astronaut considering it's the degree that allows you to work professionally as a pharmacist and not do research? I want to be a pharmacist someday, but I also want to be an astronaut if possible so I'm trying to get an idea of what I need to do.

>>11970074
The reason I wanted clarification is because they specifically say nursing doesn't apply so I wasn't sure how far into the medical field that applies.

>>11969537
You’re too stupid to do your own homework without help, I sincerely hope you understand you are worthlessx

>>11970051
I have trouble drawing it because the bounds of integration are variable

>>11970103
why are you in /sqt/ complaining about stupid questions, oh wise one?

>>11970155
he has a superiority complex

>>11970150
>>11970051
I've got the bounds for theta just by blind guessing, but I still don't know bounds for the radius, and I don't really see how this problem is supposed to be solved.

So I got the answer, but I basically just guessed. I don't know why bounds on the integrand are what they are, or how to draw the area.

Shouldn't [math]h(x)=x^4+2x^3-13x^2-14x+24[/math] have the evident root of [math]x+1[/math] ? because [math]a_4 + a_3 + a_2 + a_1 + C.T. = 0[/math] ?

>>11970155
>>11970179
Help is for people that are willing to improve.

>>11970150
The [math]\sqrt{9-y^2}[/math] should be a dead give-away for a semicircle (you figure out which one). As for the lower bound, that's just the line [math]x=y[/math].
That should be enough to get you started.

I have [math]h(x)=x^4+2x^3-13x^2-14x+24[/math]

and i suppouse that [math]x+1[/math] is an evident root because the sum of all coeficients is equal to 0, but, when i try to confirm this with Ruffini the rest is not 0, how is this possible?

i have [math]h(x)=x^4+2x^3-13x^2-14x+24[/math]

and i suppouse that [eqn](x+1)[/eqn] is an evident root, right? because the sum of all coeficients is equal to 0, but, when i try to confirm this with Ruffini the rest is not 0, how is this possible?

What the fuck is happening to the LaTeX interpreter in this fucking day? it's like the third time in a row i try to write a function and it's all fucked up

are complex numbers bi-dimensional?

>>11970306
Too many symbols, no spaces.
I think the second one is breaking because the first one is breaking.
See https://imgur.com/a/LpgxGsz

On slashdot, in the context of a discussion on dark matter, I stumbled over a poster saying there were "Galaxy-sized masses causing gravitational lensing where there's no galaxy".

Never heard about that one before. The replies don't question it, but is there any source for that?
(Slashdot has made "Anonymous coward" postings a pain in the ass, so I won't ask there.)

>>11970322
[math]\mathbb{C}[/math] is a two-dimensional vector space over [math]\mathbb{R}[/math], if that answers your question.

i have [math] h(x) = x^4 + 2x^3 -13x^2 -14x +24 [/math]

and this polynomial should have as an evident root [math] x+1 [/math] right? because the sum of all coeficients is equal to 0, but, when i try to confirm this with Ruffini the rest is not 0, how is this possible?

>>11970334
thanks man

>>11970387
>>11970391
By the by, if the coefficients sum to zero, [math]1[/math] is a root, not [math]-1[/math].
So it's divided by [math](x-1)[/math].

>>11970360
I see. I guess it doesn't make much sense to ask if a number has dimensions, now that I think about it (or does it?). but how does that work for any vector of more than two dimensions in C? I know that quaternions exist (which is as much as I can say about my knowledge on them), but I'm not sure if I understand why they're 4 dimensional and not, for instance 3 dimensional

>>11970415
A quick way to see the four-dimensional aspect of the quaternions is that to fully describe a quaternion [math]q\in\mathbb{H}[/math], you need four real numbers:
[eqn]q = a + bi + cj + dk,[/eqn]
where [eqn]a,b,c,d[/eqn] are real numbers.
This isn't enough, though, to show that the quaternions are a four-dimensional real vector space you still have to verify the vector space axioms, but that's pretty quick from how arithmetic in [math]\mathbb{H}[/math] is defined.

>>11970411
You're right, but wasn't [math](x-1)[/math] when [math]a_3 + a_1 = a_4 + a_2[/math] ?

>>11970297
I see, thanks!

>>11970437
No, that's for [math](x + 1)[/math], when [math]-1[/math] is a root.
You have a polynomial [math]p(x)[/math]. Direct two seconds computation tells you that [math]p(1)[/math] is the sum of the coefficients.
The linear polynomial (I don't remember if this was the correct name) [math](x - a)[/math] has a single root at [math]a[/math] (again, direct computation), so it divides every polynomial with a root at [math]a[/math].
Summing up, if [math]p(a) = 0[/math] then [math](x - a)[/math] divides [math]p(x)[/math].

>>11970430
I see, looking up the properties I kind of understood why. thanks a lot!

I've been stuck trying to prove some exercises from Apostol for a day.
Any tip about proving that, for arbitrary [math]x,y\in \mathbb{R}[/math] with [math]x<y[/math] there exists at least a [math]z \in \mathbb{R}[/math] so that [math] x<z<y[/math]? I know that you can construct a number that fulfills that condition but that sounds like a cheap way to prove it.
Also, any tips about proving stuff using the least-upper-bound axiom and related theorems in general? I don't know where to begin, proving stuff with the field and order axioms was way more easy than this.

Why is physics so pozzed with christfags? Can't take a single step without stumbling on some physicist muttering that you can't understand physics if you don't believe in a higher power.

>>11970808
Do you have enough things to show that [math]\dfrac{x+y}{2}[/math] is a real number and between the two?

Might sound too retarded but why do i have headaches everytime i let my hair grow?

if i have my hair too large my head starts to hurt, but if i cut my hair it that type of pain would decrease

>>11971040
I already proved it by constructing [math]\frac{x+y}{2}[/math] but it feels cheap.

>>11970155
It's tradition.
>>11970808
I'll prove it from the Dedekind cut construction:
[math]y[/math] and [math]x[/math] are Dedekind cuts. If there actually is a rational number in [math]y[/math] that isn't in [math]x[/math] (at most one of those, as is stated in the problem), it would be [math]y[/math]'s largest element, except it can't have one of those by definition.
Abstract nonsense tier proof, ten out of ten would recommend just using (x+y)/2.
>>11971023
Take the breadpill.

Ok, here i go.
>Definition: nothing is any bladeless knife with missing handle.
>Definition: a symbol is something, instead of nothing. It is only understood by it's using.
>Definition: A sign is also a symbol.
>Let:
>A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y and Z, the main upper case characters of the latin script.
>Let:
>a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y and z, the main lower case characters of the latin script.
>Together, lower and upper case lead to the next definition:
>Definition: the system of both upper and lower case latins scripts is called the Latin alphabet.
>Note: Is unavoidable the circularity when declaring the latin alphablet? The sigs L, D, e, t, f, i, n, t, o found in "Let" and "Definition" were used in beforehand.
>Note: Can any declaration of the natural numbers using signs be circular, because of the notion of sign already presupponing that of number?
>Definition: concatanation of latin scripts is any juxtaposition of signs in the latin alphabet system.
>Note: Isn't the last definition circular as it consists of words?
>Definition: a word is any concatanation of latin scripts.
>Note: definition of single words leads to the dictionary paradox.
How can one be any formal at all? How can one have systemic understanding of anything? I don't know answers to the notes.

>>11971145
Don't worry, I proved it by archimedean property.
Dedekind cuts sound interesting.

>>11969512
> 96% and shit at linear algebra

Ur institution is a joke, ur 96% is worthless if you’re having difficulty on a 100 level course

>>11971232
That proof where you reduce it to proving that there's no smallest positive real?
>Dedekind cuts sound interesting.
Dedekind cuts are the best geometric construction of the reals. Refuse the alternatives, they are homosexual bullshit made up by analysts and algebraists.

>>11971272
[math]x<y[/math] so there exists a [math]n\in\mathbb{Z}^+[/math] so that [math]n(y-x)>w[/math] for some [math]w\in\mathbb{R}[/math], and [math]y>x+\frac{w}{n}[/math].
if i pick [math]w\in\mathbb{R}^+[/math] then [math]x<x+\frac{w}{n}[/math] and i get [math]x<x+\frac{w}{n}<y[/math]
dunno if it's correct or not, i started studying math seriously two day ago

>>11971304
It's not really correct or incorrect, it's mostly just ilegible.
Am I supposed to choosd w? Can I choose w = (y-x), n = 2 and then recover the original (x+y)/2 proof?

>>11971265
the thing is, i dont have difficulty once the exams roll around. I have difficulty when ive been too slammed all week to catch up on the terminology required for the weeks homework.

>>11971322
Sorry if it's illegible, I don't know how to make it more readable. I basically used the archimedean property to make a number [math]z=x+\frac{w}{n}[/math] that is lesser than y and bigger than x.
You could choose w if you want to return to the original proof, but I guess that the inequality holds as long as w is positive.

Obviously if I move a magnet through a conducting loop it will induce a current. What if I break the loop at one place? Will it induce eddy current or nothing at all?

What am I looking at?

Let's say I'm breaking a symmetry group in two steps, something like [math]\mathfrak{g}_1 \rightarrow \mathfrak{g}_2 \rightarrow \mathfrak{g}_3 [/math]

What is the correct way of getting the vacuum equations?

I was thinking that first I only use the first vacuum, the one that breaks [math] \mathfrak{g}_1[/math], plug it back into my potential. I now have a new potential, and then get the other vacuum equation from it.

>>11971351
Yet you don’t have the capacity to solve extremely basic freshman lin alg exercises with absolutely no formal mathematical content. Literally too stupid to understand systems of equations or basic vector space structure. His point then stands, your institution or class is shit. You would have been failed out of my Lin Alg class by the midterm.

Why does 'quantum leap' mean something big? Quantum means small/breaking things down into smaller bits. Quantum leap literally means the opposite of how the phrase is uses colloquially. Am I missing something here?

>>11972139
Do you not understand the notation? Each of the large ∧ symbols on the left is performing a conjunction ('and') on multiple terms, analogous to how sigma notion performs addition of multiple terms.

If you construct a matrix where m[i,j]=(¬p[i]∨¬p[j]), the overall expression is the conjunction of all terms on one side of the main diagonal (not including the diagonal itself). As the matrix is symmetric (¬p[i]∨¬p[j] = ¬p[j]∨¬p[i]), it wouldn't matter if it included the opposite side, so long as it doesn't include the main diagonal i=j. IOW, it's the conjunction of every distinct term of the form ¬p[i]∨¬p[j] where i≠j.

¬p[i]∨¬p[j] = ¬(p[i]∧p[j]) is true if at most one of p[i] and p[j] are true. If both p[i] and p[j] are true then the expression is false. The outer conjunction is only true if all terms are true. As the conjunction involves every possible pair of p[i],p[j] for i≠j, it's only true if there exists no pair for which both are true,. If there were two or more true propositions, one of the pairs p[i],p[j] would have ¬p[i]∨¬p[j] false and thus the conjunction overall would be false.

>>11972317
A quantum is a discrete, indivisible unit. The phrase "quantum leap" implies a qualitative difference rather than merely a quantitative difference, that something has moved to the "next level".

Is it normal to think that most people aren't stupid, but they live in a constant state of groginess/brain fog that prevents them from mechanically applying algorithms?

I've heard that multitasking is bad for my brain but is it really that bad? will watching youtube videos while playing games make me retarded?

>>11972649
I mean listening

>>11972317
Are you seriously asking why a phrase used in the colloquial sense is inconsistent with its scientific usage?
People are stupid, man. That's all there is to it.

>>11963300
My question is:
Anime feet?
>inb4 2hu isn't anime

>>11972794
what have you tried?

Can somebody give me a hint on how to solve this? Intuitively I kind of understand why this is false(for each object in the domain for x we iterate through each object in the domain for y, thus there will inevitably be [math]x\rightarrow y[/math] such that x is true and y is false), but how do I formally prove it with models that assign new referents to new names and shit? Like the book wants me to. I am reading this book by N.J. Smith "Logic: The Laws of Truth" in case it helps.

>>11973108
Shouldn't you just let [math]y=r[/math]?

>>11963300
Opinions on Chemical Engineering? I read is more focused on theory than application (the degree, not the actual work). How true is this? I'm clumsy and don't really care for hands on work. Is it a good choice if I'm mostly interested in the science behind the different processes than in how to physically design them?

>>11972248
You have a very limited view of my understanding. I don't blame you at all for thinking what you think, but just because I'm behind in the present week's material doesn't mean I'm retarded. I always catch up.

>>11973018
An inordinate amount of masturbation

so the whiskers are 1.5*IQR in each direction from the outer border.
Why then, is the lower whisker further away from the box than the upper whisker?

How on earth is [math]f(x) = e^x[/math] surjective? the graph literally doesn't go below 0

When talking about a "strictly increasing" function, does this mean only exponential functions?

>>11973630
No. It just means that if [math]x<y,[/math] then [math]f(x) < f(y)[/math]. Easiest example is [math]f(x)=x.[/math]

>>11973644
I'm reading an exercise that says:

be [math]g : \mathbb{R} \to \mathbb{R}[/math] surjective, then [math]g[/math] is strictly increasing

i thought about [math]g(x)=x[/math] but apparently it's wrong

Bros, what is the differential of arch if the curve is a line going on top and against the x axis??
My physichit book says it is dl=dx but it makes no sense to me why it isn't dl=-dx. I actually never was actually thought what to do when the curves weren't "regular" i.e. they weren't differentiable.
pic rel is the excersize. I dont understand what values should the limits take either....
the work i should calculate is of a force agaist the electrostatic force aka -1*the work of the electric force

>>11973700
That's not a true statement. Try [math]f(x) = x(x+1)(x-1) = x^3 - x.[/math] It is surjective, but not strictly increasing.

>>11963300
Can anyone help me prove optimal page replacement Algorithm?
belady's optimal algorithm

if a pregnant woman sucks dick and swallows cum does babby eat cum?

>>11971023
I tend to see more of the militant atheist type instead of the christfag in physics, though I figure your average physicist would fall somewhere in between.

How to learn the same things from the school but from scratch as an adult? Not only math and science, i just mean complete education

>>11970216
y is between 0 and 3/sqrt(2)
x is between the line x=y and the circle of radius 3 around the origin
This example was very convenient to evaluate in polar coordinates because you can see immediately that the limits on x are a line through the origin and a quarter circle

>>11973536
There are no outliers greater than the upper fence value, so the whiskers do not extend that far.

>>11973737
Your book probably defines dl as a vector.
[math] d\vec{\ell} = d\ell\hat{\ell} = d\ell(-\hat{x}) = -d\vec{x} [/math]

>>11974116
how is its shortened length decided?

>>11974181
The fences are never going to enclose data that aren't in the set. If the set maximum is less than the upper fence value, or if the set minimum value is greater than the lower fence value, the whiskers only extend as far as the extremum.

>>11974197
>The whiskers are never going to enclose

>>11974197
ohhh ok
thanks

>>11973644
Is it enough to prove it only one time?

>>11963300
Please help. why does second equality (derivative 0) hold based on the above facts? I think i forgot something basic.

>>11974434
Because the limit of the constant zero sequence is zero.
In other words, in case you somehow didn't get it, [math]y (x_0) = y(x_n) = 0[/math], so [math]y(x_n) - y (x_0) = 0[/math].

Is it correct to say that all exponential functions cut through [math]y = 1[/math]

>>11974513
Thanks, I tried to get my head around 0/0 without actually considering individual terms.

>>11974658
An exponential function of the form [math] y = Ab^{x} + c [/math] equals one when [math] x = \log_b \left( \frac{1-c}{A} \right[/math]; if [math] \frac{1-c}{A} [/math] is not positive, the function won't intersect [math] y=1 [/math]. Try
[math] y_1 = 2^x + 2 [/math] or
[math] y_2 = (-4) 2^x [/math]

>>11975143
> [math] x = \log_b \left( \frac{1-c}{A} \right) [/math]

Anyone having trouble logging into Mendeley?

Do the real numbers have an uncountable proper subfield? Complex numbers (aside from the reals of course)?

>>11974658
Another counter-example: [math]f(x) = 0^x[/math]

Chemistry question - whats a quick and easy way to check if a gas is hydrogen or methane? according to google images the color and shape of their flames is near identical

>>11976465
Smell it nerd

>>11976467
>a yes, distinguish gasses that don't smell like anything by smell

>>11976474
Cabron dioxide is not odorless

>>11974133
yes it's a vector, but you are wrong tho.
I already solved this. dl=(dx,0) if you use the definition. (x,y)=(x,0) then dl=(x'dx,y'dx)=(dx,0)

>>11976465
CO detector
>>11976506
>Cabron
puta madre

>>11975951
Pretty sure it does by a classical Zorn's lemma argument.

I'm signing up to university right now and I could really use the opinion of someone that already experienced this shit, I'm planning on studying CS but I can't decide between the advanced course, or taking CS + math/physics, how useful would a math degree be when trying to get a job in software dev?

Any paleomagnetists here?
How do I plot someting like this?
It shows the polarity of samples and compares the depth with the age, determined through matching the polarity.

Why would soap kill 99.9% of bacteria, but not 100%?
Can that 0.1% somehow survive being coated in a lipid-destroying substance despite being made out of lipids?

>>11978783
there's bacteria in the soap, couldve evolved a protective capsid layer

Does a 1:10 ratio describe:
>1 part IN 10
>1 part EVERY 10(total solution of 11)

>>11977174
My advice is from somebody in England, so make of this what you will. I'd have to look at the specific syllabus for this advanced course but if your goal is just getting hired you're actually better off taking a pure math degree and teaching yourself to program in your own time.

It may be nonsensical but programming is one of the smaller aspects to a development job, or rather the coding practices one picks up in a typical university are used less than the standards you pick up post being hired. Mathematics comparatively can't really be taught on the fly, furthermore all math degrees should include elements of programming and afford you many opportunities to develop a more technical portfolio by the time you graduate. If you take a very comprehensive CS course they may include enough applied math but it'd still pale in comparison to what even a general math degree would teach you.

The exceptions to the above advice are if you want to work in hardware as an engineer, I can imagine a math degree would still be very helpful but I'm not speaking from experience on that point, my guess is that you'd be best served taking a good CS degree were that your inclination; nor can I speak on physics, I've not studied it nor are my immediate colleagues trained in it.

Best of luck. Were I you I'd take a math degree and spend my first year trying as many different things in the field as I could, decide on a specific job and specialty and then work backwards to fill in my competencies. Any good institute will allow you to change course after the first year and possibly transfer credits as well.

>>11971624
>eddy current
yeah that. and/or voltage spikes+sparks

>>11979187
It's the latter. That's how people usually use it, and that's what a ratio is.

How do i calculate enzyme activity (ug product/ min / uL) enzyme?
Isn't that a function of substrate concentration? which substrate concentration do i choose?

>>11979454
uL enzyme)*

Is this the correct inductance of a coil inside a larger, coplanar, coaxial, current-carrying coil?

say you had a glass fulla peanut butter, right
an yknow how peanut butter is real thick
could you heat the glass and the shit inside it till the peanut butter has the same consistency as water?
its gotta be way too hot, but could someone enjoy a toasty warm glass of peanut butter?

an electric stovetop works by turning on full blast for a bit and then turning off, so you never have a constant temperature. why don't stovetops use a variable transformer to get constant smooth heating?

I don't get how
[math]z^0(y)=arg min \underset{z} h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable? How is the optimal value a function of the fixed value?

I don't get how
[math]z^0(y)=arg \underset{z} min h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable? How is the optimal value a function of the fixed value?

We have
[math]\min \underset{y} [g(x,y)+\min \underset{z} h(x,y)][/math] and

[math]h^0(y)=\min \underset{z} h(y,z)[/math]
I don't get how
[math]z^0(y)=\arg \min \underset{z} h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable y? How is the optimal variable z then a function of the fixed variable?

We have
[math]\underset{y}\min [g(x,y)+\underset{z}\min h(x,y)][/math] and

[math]h^0(y)= \underset{z} \min h(y,z)[/math]
I don't get how
[math]z^0(y)=\arg\underset{z}\min h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable y? How is the optimal variable z then a function of the fixed variable?

We have
[math]\underset{y}\min [g(x,y)+\underset{z}\min h(y,z)][/math] and

[math]h^0(y)= \underset{z} \min h(y,z)[/math]
I don't get how
[math]z^0(y)=\arg\underset{z}\min h(y,z)[/math] isn't the derivative wrt z of the function h supposed to have zero values for the fixed variable y? How is the optimal variable z then a function of the fixed variable?

>>11980454
Would sure be nice if I recalled how does that notation work.
Hit me up with a link.
>How is the optimal variable z then a function of the fixed variable?
Probably something like this: You want to minimize [math]f(x, y)[/math]. If you fix [math]x[/math], you can solve the problem of minimization for just y. This one-variable minimization induces a function [math]g(x) = \min _{y} f(x, y)[/math]. Then, [math]\min _{x, y} f(x, y) = \min _{x} g(x)[/math], naturally.

If A is a 2x2 matrix how do I go about finding it exactly? Is it to do with matrix exponentials?

>>11980477
Less thinky thinky more computy computy.

>>11980477
[math](x'_1,x'_2) = A\cdot (x_1,x_2)[/math]

>>11980488
This was my thinking but to clarify Im on the right track [math] (x_1,x_2) [/math] is a 2x2 matrix with [math](e^t)sint and -(e^t)cost [/math] in the top left and bottom left corner, and for [math] (x'_1,x'_2) [/math] the derivative of [math](e^t)sint[/math] will be in the top left and the derivative of [math]-(e^t)cost [/math] will be the bottom left.

Then once each of the [math](x'_1,x'_2)[/math] matrix I can just look at it and find A?

>>11980488
>>11980487
I got
[math] A = \begin{bmatrix}
1 & -1 \\
1 & 1 \\
\end{bmatrix} [/math]

Does that seem right or did I fuck it up somehow?

>>11980517
not gonna check, but it looks ok

>>11980517
That's correct.

>>11980505
[x1' x2'] = A [x1 x2]
=> A = [x1' x2'] . [x1 x2]^-1

Is this book any good? are there better methods of reading? I have a friend who can talk and read at the same time or watch tv and read and he retains both pretty well, can talk about what's going on in the book or explain what the books about etc and keep up with everything else how does one get this ability?

>>11980551
I used to read a lot but since they shut down all the libraries and universities it's hard.

>>11980553
I got an ereader, don't have to pay for books or anything

>>11980554
Pleberoni pizza do you want a slice! Pleberoni pizza! It's very nice!

>>11980544
>>11980547
This is going to sound like a really dumb question, but is [math] (x_1,x_2)= x_1=\begin{bmatrix} x_1\\
y_1 \\
\end{bmatrix}+x_2=\begin{bmatrix}
x_2 \\
y_2 \\
\end{bmatrix}=
\begin{bmatrix}
x_1,1+x_2 \\
y_1,2+y_2 \\
\end{bmatrix}[Math]
Or is it a 2x2 matrix? was result in the same A

>>11980544
>>11980547
>>11980544
>>11980547
This is going to sound like a really dumb question, but is [math] (x_1,x_2)= x_1=\begin{bmatrix} x_1\\
y_1 \\
\end{bmatrix}+x_2=\begin{bmatrix}
x_2 \\
y_2 \\
\end{bmatrix}=
\begin{bmatrix}
x_1,1+x_2 \\
y_1,2+y_2 \\
\end{bmatrix}[/Math]
Or is it a 2x2 matrix? was result in the same A. I'm just a bit confused about notation.

>>11970337
To answer myself, it's probably https://doi.org/10.1086/508162 .

How do I fill the hole in my heart that Yukarifag left behind?

>>11980472
I think I understood, I deleted the question because I had not generalized the function well enough. If you differentiate [math]h(y,z) = yz^2 + z [/math] wrt z then equate to zero then the solution for z will be a function of y.

>>11980712
Yeah, but remember that the gradient zeroes if and only if all of its components zero.

>>11980718
No, this was the original question

We have
[math]\underset{y}\min [g(x,y)+\underset{z}\min h(x,y)][/math] and

[math]h^0(y)= \underset{z} \min h(y,z)[/math]
I don't get how
[math]z^0(y)=\arg\underset{z}\min h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable y? How is the optimal variable z then a function of the fixed variable?

I only wanted min z, so only z matters here.

>>11980718
This was the original question

We have
[math]\underset{y}\min [g(x,y)+\underset{z}\min h(y,z)][/math] and

[math]h^0(y)= \underset{z} \min h(y,z)[/math]
I don't get how
[math]z^0(y)=\arg\underset{z}\min h(y,z)[/math] isn't the derivative of the function supposed to have zero values for the fixed variable y? How is the optimal variable z then a function of the fixed variable?

I only wanted min z, so only z matters here

>>11966428
try the diy board fren

>>11971213
I thought the whole idea that made Baudrillard relevant was the idea of language being exclusionary. At least that's what they teach at the undergraduate level. We understand signs from what they are not, the same way we understand lexical items from what they are not. Simulacra comes up when you have an abundance of signs which cease being exclusionary, and fall into meaninglessness. A sign becomes simulated or false, and then you get into his whole depressive flimflam. He was influential (and still usable for the kost part), but we've been moving away from his ideas with postmodernism being practically dead.
t. Linguistics student

Hi, brushing my spectroscopy right now
I was waching this video by the Organic Chemistry tutor about diamagnetic anisotropy. https://www.youtube.com/watch?v=w8ew5bvdrqg
I get that since pi electrons move freely they generate a magnetic field opposite to the one induced by the NMR device. But I don't understand why he represented the benzene and the ethylene as perpendicular to the magnetic field whereas the acetylene is parallel. Do the molecules adopt a certain position relative to the magnetic field?

How do I learn to solve math problems? I'm currently working through a probability theory book and often have no idea how to convert words to equations. I get that this is the hard part, so do I get better at it? Just solve more problems? Are there any books with focus on this?

Wtf is a limit? Everyone tell me I have to know what a limit is before I learn calculus and I'm starting calc 1 in like 2 weeks.
>a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value
I don't know calculus, this tells me very little. So what is the limit of the function y = f(x) = x^2
or is there none? Is the limit of 9 here, 16? Since that's what comes next if we only count integers or whatever. Or is the limit of x^2 just infinity because it's always just nearing a bigger number?
If that's the case when is a limit not infinity?

>>11981300
When you talk about limits, you need to talk about the value that [math]x[/math] approaches. The notation [eqn]\lim_{x\to a} f(x)[/eqn] is read as "the limit as [math]x[/math] goes to [math]a[/math] of [math]f(x)[/math]". So an easy example is that [eqn]\lim_{x\to3} x^2 = 9.[/eqn] Now you may be wondering why you care about limits since in this example, [math]\lim_{x\to3} x^2 = 3^2,[/math] and you can just plug in the value directly. Let's instead have a piecewise function
[eqn]f(x) = \begin{cases}x^2 & \text{when }x\ne 3\\ 0 &\text{when }x = 3.\end{cases}[/eqn] In this case, [math]f(3) = 0[/math], but [math]\lim_{x\to3} f(x) = 9[/math].

>>11981321
thanks that makes some sense, to be sure if I really get the last example though.
lim x^2 = 9
x -> 3
in regards to the piecewise function, it's not 0 because you're never actually saying that x is 3 or y is 9, but just that when x is approaching 3, y is also approaching 9. Do I understand that correctly.
How about when we use infinity.
lim x^2 = ∞
x -> ∞
since when x approaches infinity it's just approaching ∞^2 which is still infinity (in regards to limits).
One thing I found while playing around with some website just now is
lim 2x+1/x = 2
x->∞
kinda simple but is it 2 because we can see that the larger x becomes the closer it gets to 2?
Just so I'm sure I got it. Thanks.

>>11970430
>you still have to verify the vector space axioms,
Seriously? Who would bother?
Proof: Obvious.

Does there exist a closed form for the product
[math]y = \prod_{n=1}^{\infty} n^{1/n!}[/math]
It can be rewritten as the sum
[math]e^y = \sum_{n=1}^{\infty} \frac{ln(n)}{n!}[/math]
But i can't get much further than that.

>>11967951
is there any information that is utterly useless in the end?

>>11980694
yukarianon stopped posting?

In the red box, shouldn't the concentration of silver ions be doubled? It's 2 silver ions for every one sulfate ion, doesn't that concentration need to be doubled?

>>11981627
All of it obviously

Why do we calculate area under the curve until the the x? I don't understand. We have a function, and it makes a certain curve, but did someone just choose this area? Why not above the curve, or to the side, or whatever?

>>11981764
Because f(x) is the length from the x-axis to the curve, so it's natural to talk about the area from the x-axis to the curve, within some interval.

>>11981764
>Why not above the curve
Yes I sure do have lots of uses for all those values in the infinite set that doesn't contain the exact integral

>>11981641
He's been gone for a while now.
He had left for a while a couple times before that, but this one has been dragging, so I'm assuming he's just gone.

>>11981722
Ag+ is just Ag+, no sulfate involved. That concentration is before it precipitates.
/after/ you precipitate it with sulfate, then yes two equivs will be needed for each equiv of sulfate.

>>11981016
not sure. I know that the pi orbitals of acetylene are degenerate, and thus would be better described as a circular sheath around the axis of the molecule, but I'm not sure how that would affect their magnetic susceptance

>>11981804
>>11981828
I guess I'm more confused with why it just werks, and how did someone come up with that idea. So we have numbers, easy enough. Then we have the variable for numbers say an x. Then we have functions say x^2 and we map out every number to get a graph. But then how did someone see that you can gain something from calculating the area under the curve?

>>11981845
Pretty sure it was just "hey, the angle of the curve is the rate at which it is changing. Therefore the other way around must be true as well"
The first statement there is pretty obvious so it should be easy enough to understand how someone figured it out.

>>11981300
For a function, a limit is defined for the argument approaching either a specific value, or positive or negative infinity.

E.g. the limit of 1/x as x approaches infinity is zero, written
[eqn]\lim \limits_{x \to \infty} {1 \over x} = 0[/eqn]

Formally, if
[eqn]\forall \varepsilon > 0 \; \exists c \; \forall x > c :\; |f(x) - L| < \varepsilon[/eqn]
then
[eqn]\lim \limits_{x \to \infty} f(x) = L[/eqn]
In plain English, a limit at (positive) infinity of a function f is a value such that for any positive value ε, there exists some value c such that for all x greater than c, the difference between f(x) and the limit is less than ε. IOW, you can choose some maximum deviation as small as you like, and the entire "tail" of the graph after that point is within that deviation.

Limits at a specific point are useful when a function is defined almost everywhere but not at that specific point. E.g. the unnormalised sinc function given by sinc(x)=sin(x)/x is defined for all x≠0. When x=0 sin(x) is also 0 and so sin(x)/x = 0/0 which isn't defined. However, it can be shown that the limit of sin(x)/x as x approaches 0 (from either above or below) is 1 (note that sin(x)~=x for small x).

>>11981641
>>11981834
Decided to look up the time frame for no particular reason.
Around here:
>>/sci/thread/S11553666
>>/sci/thread/S11556287

what should my term paper be about? civil engineering

>>11981513
For limits to infinity, [math]\lim_{x\to\infty}x^2 = \infty.[/math]

For the last example, you probably mean [math]\frac{2x+1}{x}[/math] and not [math]2x+\frac{1}{x}[/math]. In the first case, we can do
[eqn]\lim_{x\to\infty}\frac{2x+1}{x} = \lim_{x\to\infty}2 +\frac{1}{x}.[/eqn]
And then the [math]\frac{1}{x}[/math] goes to 0.

>>11982180
oh I see, that's cool

math is about games, right?

Say you had a flexible concave curved surface (blue), and at certain points anchored stretched rubber bands (yellow). As the rubber bands contract, the blue material curls inward/to the right.
If the surface was both convex and concave, when the rubber bands contract, some material would curve inward/right and some would curve outward/left, as shown in the middle graphic.
But if you draw a line tangent to the curved surface each point (red), you now have a choice; either contract the yellow rubber bands, or contract the red tangent lines. If you only choose whichever is furthest to the right, the material will always curve inward.

Is there a name for these kinds of problems? I've similar idea mentioned in finite element/fluid dynamics papers

>>11981607
try posting this on stackexchange, I feel like they would enjoy it.

>>11982236
You lost me on that last example with the tangent lines.

>>11982526
if you contract along the yellow dotted line, the lower half will just bend convex/leftward (like ex.2).
If you contract the red lines, first it'll straighten, then it'll bend concave/rightways (like ex.1)
You'll always have a choice between contracting the straight yellow lines or the red tangent lines. One of these choices will always be left of the blue curve, the other will always be right. If you only contract the yellow/red lines on the right of the curve, you will always get a convex/rightways result.
The catch is, the red tangent lines behave fundamentally differently than the yellow ones. AFAIK, most finite element analyses only use straight line segments like the yellow ones.

Has anyone else explored something like this?

I was reading "fundamentals of geometry" by Hilbert which, given my current level of study, may have been a bit ambitious. Here it gives a definition of the distance between two points of a line, which I thought would be different (everything being the same but omitting the y2-y1 in the first parentheses). Is Hilbert talking about a different geomety that would have that be a truth (at least that is what it sounds like based on the text)? What would such a geometry look like?

>>11963300
Hey guys, I'm interested in learning Gauge Theory and about the Yang-Mills equations (not the physics formulation of Yang-Mills, but the abstract formulation in terms of the minima of the Yang-Mills functional on connections on a fixed principal bundle). I know that the subject involves principal bundles, connections on principal bundles, and some other type of stuff like that. I've already taken grad courses in algebraic topology (Hatcher up to homology, some singular cohomology) and differential topology (up to de Rham cohomology and some stuff about characteristic classes). Which books would you guys recommend for someone with my background? I was thinking of getting Loring Tu's Differential Geometry book but it doesn't mention anything about the Yang-Mills functional, and it only has a short section on principal bundles. Any help would be greatly appreciated!

>>11963300
why is probability so hard? need help with b)

I have been staring at this question for an hour now but to no avail. Logically speaking, I really don't get how the fox can be found if it moves 281918290485 or something steps a day in x,y axis. I know that I am supposed to prove it mathematically how the fox can be found but I need help please.

Where can I learn more from this inequality ?

[math] |aq + b \dot{q}| \leq c [/math]

Showed up in a stability proof.

>>11982909
Am I missing something here, or is the following a trivial winning strategy?
>Choose your favorite enumeration of [math]\mathbb{Z} \times \mathbb{Z}[/math]
>At day n, guess that the fox had chosen the nth pair -- call it (x,y) -- by searching at point (nx,ny)

Is meteorite more likely to hit Earth around equator or one of poles?

>>11982613
>Is Hilbert talking about a different geomety that would have that be a truth (at least that is what it sounds like based on the text)?
Apparently.
>What would such a geometry look like?
Consider the map [math](x, y, z) \rightarrow (x + y, y, z)[/math]. The new norm of the point on the left is [math]\sqrt{(x+y)^2 + y^2 +z^2 }[/math]. The usual euclidean norm of the point on the right is [math]\sqrt{(x+y)^2 + y^2 + z^2}[/math].
In other words, the two geometries should just be isometric.
>>11982742
Tu is good for bundle stuff and characteristic classes.
All of my meager knowledge of Yang-Mills comes from Jost's Nonlinear Methods in Riemannian and Kählerian Geometry, so I'll also have to recommend that.

>>11980758
I'm not interested in Baudrillard but in the linguistics behind math, any recs? By the way, i think is not an actual quote of him, is just a meme i feel identified with.

>>11981641
I (and a few others) unironically bullied him off the board. Good riddance.

Why can't you just solve the Laplace equation in spherical coordinates by solving it in Cartesian coordinates and then doing a coordinate transform to spherical? I'm serious, I cannot see the difference.

Some people have theorized that we might be living in a computer simulation left to run. There is nothing truly physical about our universe. Well, there's a problem. Let's say someone from the real physical universe wants to create a simulation. They would need to use physical material from their universe to run the computations. The material would have to configured in such a way as to have variations that represent data whether its gears in a mechanical computer or a on-off switch representing 0's and 1's in an electronic computer. Since the computer would have to be made from material from the real universe, the simulation can not have the same level of variability/complexity as the real universe that it occupies. If anything, it would be a simplified dumb down version of it. This is more of an issue if there are sapient programs in the simulated universe the programmer is trying to fool. The way around this is to give the illusion of a whole, complex universe.

An example is the night sky in a video game. The white dots in the black background are just that-white dots against a black background. The programmers did not program the video game to simulate convection currents of the plasma, which composes a star, as it interacts with gravity, magnetic fields, and fusion reactions So each time someone looks through a telescope and sees something that is not visible to the naked eye, they offer evidence that we are not living in a simulation.

Okay, so the programmer is hiding the cheats deeper in the software. That he has a telescope.foolsims subroutine that gives a false image in every telescope. But then they have to have another one for microscopes and another one for Geiger counters and another one for X-ray machines and another one for space probe instruments and...you get the point.

(continue on next post)

>>11982967
Looks sound to me. Probably the point of the question is that the set of pairs of integers is countable.

>>11983219
Beyond the fact that more of the Earth's surface is near the equator than near the poles?

could [math]f(x) = -e^{x+1}[/math] be considered an exponential function? because an exponential function needs a base > 0 and =/= 1, right?

>>11984409
I don't think there is any problem with this. Besides, the base is positive—it's e. The negative prefactor doesn't matter.

>>11984409
[math]-e^{x+1} = -[e^1 e^x] = [-e]e^x[/math].
So if you set [math]a = - e[/math], it has the form [math]ae^x[/math].

>>11982967
Thank you very much for your help, I was over thinking it I guess.

>>11984150
Quick rundown?

>>11984150
Why would you do such a thing?

How do I get started with calculus?

>>11984770
Do you have pre-calc/good algebra skills? If so, I would try Khan Academy. If you benefit from a course-like structure, try https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/

>>11984897
Thanks anon

>>11982900
This would be the [math] \binom{8}{5} [/math] possibilities of the first round, multiplied by [math] \binom{5}{4} [/math], [math] \binom{4}{3} [/math], [math] \binom{3}{2} [/math], and [math] \binom{2}{1} [/math]. These last few combinations are each the result of every subsequent round - for instance, in round two, there are five people remaining and four chairs/"slots" to fill, so we look for the ways we can pick four out of the five people. This is simply [math] \binom{5}{4} [/math], and the next few rounds follow similar logic.

Let's say i have [math]\frac{2x \sqrt{3}}{8x}[/math]

would it be technically possible to do

[math]\frac{2 * x * \sqrt{3}}{8 * x} \to \frac{2 \sqrt{3}}{8}[/math] ?

because [math]x[/math] is multiplying in both parts of the fraction, so it can be eliminated, right?

>>11984948
you can do that if [math] x \neq 0 [/math]

Occasional reminder that this is, in fact, a containment thread.

did you guys started to see your everyday life more analytically when you started to get deeper into math/science in general?

i've been studying math for 5 months now and i see dumb things that i would have ignored in the past but now i look at them and i try to solve something in those actions or spot an error

for example i would see a person running from the bus for a short period of time and i wouldn't give a fuck, but now i see a person running and i try to calculate the velocity of their run

>>11963300
How do i get smart?

>>11985418
>i wouldn't give a fuck
Harsh

>>11985418
>try to
laugh at this brainlet and his wojak

Very easy question but fuck me I'm struggling here
h(t + 2) = −(t + 2)2 + 3(t + 2) + 4
= -(t^2 + 4t +4) + (3t + 6) + 4

Where the hell did that 4t come from?

>>11985625
h(t + 2) = −(t + 2)^2 + 3(t + 2) + 4
Made a mistake it's not -(t + 2)2 it's -(t+2)^2, fucking whops

>>11985633
[math](a+b)(c+d) = a(c+d) + b(c+d) = ac+ad + bc+bd[/math]

https://en.wikipedia.org/wiki/Freshman%27s_dream

>>11985638
Bless you anon.

How long does it take to master abstract algebra and will learning it help with elementary algebra?

>>11985862
Abstract algebra is such a broad field, do you have anything specific in mind?

>will learning it help with elementary algebra?
No.

>>11985862
> will learning it help with elementary algebra?
This is kind of like asking if learning how to scuba dive will help you learn how to swim.

Would UV light work to disinfect stuff of COVID? Yes it would but what are the protective measures one must abide by and what would be reasons not to use this in comparison with other disinfection methods?

>>11986037
hey buddy i think you got the wrong door
this thread is about monster girls

Who created this image and how can I get into contact with them?

>>11963300
The maximum doesn't exist right?
I'm not going crazy; the test writer just doesn't know analysis?

>>11986351
Also question 2. I think the answer is reversed (Quantity A is greater), but it's also 5:30am

>>11986351
No idea what he's talking about with the whole B part, but -5 the supremum, not the maximum

>>11986356
k=-3: 1/2^(-4)=1/16 < 1/8
So B is greater

>>11986362
They're saying given that funky equation, max(x-5) is greater than max(2x), because for any x that satisfies that equation: x-5 > 2x. But I think neither maximum exist

>>11986372
holy shit I'm an idiot!

>>11963300
I started physics a few days ago and have a bunch of motion questions, so far so good but I get a bit stumped when questions barely give any information.

A toy rocket is launched with an initial velocity of 34.0m/s, upward. Ignoring air resistance, calculate the maximum height.
a = -9.81
u = 34.0
v = Has to be 0 at maximum height
s = What I need to find

I chose u^2 = v^2 + 2as, rearranged and discarded v^2 as it equals 0 (Which I think is allowed?)
s = -u^2 / 2a which gave me a displacement of 59.92m

Is this right? I feel like I'm doing something horribly wrong.

Looking to get in to chemistry, anyone know of a good book I can buy that is well respected and covers a lot of info?

>>11986515
I don't know anything about physics anymore, but I used phywiz in highschool to check answers like this (app on Google Play)

>>11986667
Oh nice, that should help with study. My answer on paper was 58.9194 so I'm not sure why I wrote 59.92 here, thanks man.

>>11986515
>u^2 = v^2 + 2as

You've mixed up u and v here, but your working is otherwise correct. To double-check your answer, you could find the time it takes to reach its maximum height by doing 34÷9.81 and plug this value for t into the other displacement equations. This is the same calculation (just with extra steps), but it may help you to better understand what's going on.

>>11986683
By mixed up do you mean I misread the formula as being u^2 = v^2 rather than the other way around?
If that's the case then I guess I didn't even need to worry about discarding it for being 0 (That's allowed whether it's initial or final velocity, right?)
I've been getting fooled by that v^0 way of writing it but I'll try your division step with a few of the ones I've succeeded at to see what happens.

>>11986515
> which gave me a displacement of 59.92m
It's 58.92

>>11986704
Yeah, typed another number on my page instead of 58.9194

>>11986703

Pic related is the correct formula

>>11986709
Ah yeah, I see the problem now

v^2 = u^2+2as
Rearranged into
s = -u^2/2a

>>11986709
don't listen to him, you were correct the first time.
the equation is
inital velocity^2 = final velocity^2 + 2 * acceleration * distance

>>11986858
>inital velocity^2 = final velocity^2 + 2 * acceleration * distance

You're wrong bud. That "+" should be a "-"

>>11986862
correct. my bad

Have not done math in a long time. Am not getting this.
>(x+dx)^2
=x^2 + 2x * dx + (dx)^2
=x^2 +2x * dx
...
wtf? It's (x + dx)(x+dx) right?
So shouldn't it be
x^2 + xdx * xdx + (dx)^2
= x^2 + 2xdx + (dx)^2
What is happening when you're multiplying x with dx? why does (dx)^2 just randomly go away. Shouldn't it just still pretty much be dx since it's a really small number? I don't get where 2x*dx comes from. Considering you're multiplying x with dx and then dx with x right?

>>11987175
is it some kind of rule?
x * dx = 2x
dx * x = dx
???

>>11987175
> x^2 + xdx * xdx + (dx)^2
= x^2 + x*dx + x*dx + (dx)^2
= x^2 + 2*x*dx + (dx)^2
If you're calculating lim[dx->0] ((x+dx)^2-x^2)/dx, then subtracting x^2 =>
x^2 + 2*x*dx + (dx)^2 - x^2 = 2*x*dx + (dx)^2
dividing by dx =>
(2*x*dx + (dx)^2) / dx = 2*x + dx
The limit as dx->0 is just 2*x

Basically, any term with dx^1 will lose the dx when you divide by dx, any term with dx^n for n>=2 will have dx^(n-1) after division and will vanish when you take the limit.

>>11987175
Infinitesimal manipulation is an extremely non-intuitive meme forced by braindead engineers, stop doing it.
Unless you're actually manipulating n-forms, then it's easy to recall that the product is graded-anticommutative, so [math]dx \wedge dx = - dx \wedge dx = 0[/math].

>>11987193
My book just says that (dx)^2 means a little bit of a little bit of x^2. So it may be discarded because of it.

Does potential energy actually exist or is it an abstraction?
please use small words i have a humanities degree

>>11963300
What if gravity is a macro quanta and that's why there is no graviton?

Is this question too stupid for this thread or valid?

>>11987193
thank you though, makes a bit more sense to be.

>>11987228
That's the even handwavier explanation

>>11987232
it's an abstraction, but so is energy in general

>>11987232
>Does potential energy actually exist or is it an abstraction?
Depends on what you mean by exist
If I lift a rock it will fall down again. I exerted a force over a distance to lift it. That means I converted energy. Where is it? In its potential

>>11987392
how would you define energy ?

>>11987457
capacity to do work

>>11987175
This is why I don't understand why intro calc is taught this way. Who is responsible for this bullshit, confusing approach to derivatives? None of it is formally correct, even if we somehow assumed the hyperreals by default, one still needs more machinery to make these statements make sense.
>abloo bloo high schoolers and freshmen don't need rigor
Fine but clearly this way of teaching calculus, with "infinitesimals" that behave however you want so that you get the answer that the textbook says, is obviously doing more harm than good. This shit is not math, it's fucking voodoo witchcraft that replaces logical, sensible reasoning with "lol it's just a little bit of x, bro."

When considering bijectivity, should i only look at the range that the function is defined in or the whole y axis?

I have asked this a couple of times in these threads already but, considering a function

if [math]f : \mathbb{R} \to \mathbb{R}[/math] is a strictly increasing function, then [math]f[/math] is surjective

and i know that the counter-example is [math]f(x) = e^x[/math] but isn't this true for any function with the form [math]f(x) = a^x[/math] ? because all these functions will never go below [math]x = 0[/math] because their range is not defined for anything below 0, therefore, this is by definition, not surjective... is my reasoning correct?

>>11988696
Yeah, for [math]a > 1[/math].
But giving abstract "up to a choice of a" whatever the fuck counterexamples is a stupid habit, so anon just mentioned the usual exponential.

>>11988707
thanks anon

If you diff in 2D, you'll get the angle of the tangent line, the line as in "an infinite line", not a segment of line.
But if you diff in 3D, you'll find a vector, which has the direction of the tangent line(like in 2D), and where you can extract the module.

What the module geometrically means? Is it just, how "aggressive" the rate of change is?

Exercise says the following:

be a function [math]f : \mathbb{R} \to \mathbb{R} = 5^x[/math] explain how to obtain [math]g(x) = -5^{x+3}+2[/math]

?
i have the graph but i don't know how to obtain [math]g[/math] what is this supposed to be?

Is there a book specifically for drawing better graphs or should I just take a semester in art?

>>11988683

If your codomain is [math]\mathbb{R}[/math] then you have to consider the whole y-axis.

>>11988773
yeah i know, but if my function is [math]f : \mathbb{R} \to [0, \infty)[/math] then i should only conider [math]y = [0, \infty)[/math] and not the whole y-axis, right?

>>11988683
You should consider the codomain to be nontrivial. This is because every function is surjective onto its image.

>>11988756
Maybe the question wanted something like
[math]g(x) = -f(x+3)+2.[/math]

>>11988768
Lots of drawing practice. You can take an art class if you want, but there's a saying that you can learn everything in art class by yourself.

>>11988813

Yeah, you only have to consider the codomain when determining surjectivity

>>11988768
Tufte's The Visual Display of Quantitative Information is the standard answer here but I'm not going to pretend to have read it myself. There are a lot of these books about though, especially since the """data science revolution""" but I'm almost certain all the recent ones are going to be medium post tier cash in jobs.

If the derivative of an odd function is even, and the derivative of ln(x) is 1/x:

assuming 1/x is an odd function, doesn't that mean ln(x) should be an even function?

>>11988839
ln(x) is not a polynomial so it can't be even or odd

>>11988839
Domain of [math]\ln(x)[/math] is the positive reals, so the domain of the derivative is also only the positive reals. That means that you need to consider [math]\frac{1}{x}[/math] for positive real numbers only, and on that domain, it's not an odd function.

>>11988857
sound like a copout.
Also, the domain of ln(x) absolutely extends to the negative reals. do you even basic math?

>>11988853
then what is 1/x? does the even/odd derivatives rule only apply to polynomials?

>>11988868
Domain of [math]\ln|x|[/math] is all reals but zero, and this is an even function. Domain of [math]\ln(x)[/math] is positive reals. Do you basic math?

>>11988868
>the domain of ln(x) absolutely extends to the negative reals

bruh wat

>>11988875
>|x|
oh look it's this gorilla function for niggers. don't @ me.
[math]ln(-1) = i\pi[/math], deal with it.

>>11988888
what a waste

so. i have until the end of 2020 to learn enough calculus to prepare me for calculus two in spring 2021, does anyone have a good study plan on hand/tips/etc. i have "introduction to calculus" by that serge (?) guy, but i want to use other sources in tandem.

i'm not some mega genius (far from it, really) so please keep that in mind...thanks a bunch.

>>11988730
If you have a parametric curve defined by f : R->R^n, then differentiating gives you the tangent vector f' : R->R^n. The magnitude of which is ||f'|| and the direction (a unit vector) is f'/||f'||.

In 2D, there may be an implicit form y=g(x) which defines the same curve (i.e. the same set of points <x,y>) as a parametric definition <x,y>=f(t). From an implicit form you can get the direction of the tangent vector but the magnitude isn't meaningful.

For any implicit form g(x) you can derive infinitely many parametric forms: f(t)=<h(t),g(h(t))>. The direction of the tangent vector at any point is the same, but its magnitude depends upon h.

This doesn't apply if you have more than 3 dimensions as in N dimensions an implicit form defines a (N-1)-dimensional structure. In 2D this is a curve but in 3D it's a surface. Also, the converse isn't true: a parametric curve <x,y>=f(t) can only be expressed as y=g(x) if the x component of f is monotonic. If the curve "doubles back" you can have multiple y for the same x, which can't be expressed as y=f(x).

Have not touched maths in many years and am revising for a calculus course
What the fuck is the part I highlighted talking about and where can I read or watch something to learn it?

>>11989675
You have to remember te value of e.g. [math]\sin({\frac{\pi}{6}})[/math] without plugging it into your calculator.

>>11989682
em is that like this stuff? What do I search to learn it?

>>11989731
Yes. "unit circle". Really, there's only three things to remember: sin(π/6)=1/2, sin(π/4)=1/√2 and sin(π/3)=√3/2. The rest are just symmetries. Also note that sin^2(π/6)=1/4, sin^2(π/4)=1/2 and sin^2(π/3)=3/4. By symmetry (cos(θ)=sin(π/2-θ)) and Pythagoras' theorem (sin^2(θ)+cos^2(θ)=1), sin^2(π/6)+sin^2(π/3)=1 and 2*sin^2(π/4)=1.

>>11967951
my name, probably. if i could un-know it at-will, someone would just remind me when it became relevant again.

trying to get derivatives.
x is 100
y is 10,000
when x is raised to 101 y grows to 10,200
200 / 1 => 0.2/0.001 = 200. No matter how small it's always 200.
So do I understand it correctly that in this particular function the dy and dx are always these 0.2/0.001 numbers but infinitesimal, no matter how small the growth between them is it's always 200.
101 * 101 = 10,200
dy/dx = x^2
Is that an understandable way of thinking about it or will it bite me when I get to more complex functions?

>>11989988
> when x is raised to 101 y grows to 10,200
101^2 = 10201. (x+1)^2 = x^2+2x+1
> dy/dx = x^2
y = x^2 => dy/dx = 2x

If f(x)=x^2
=> f(x+δx) = (x+δx)^2 = x^2+2xδx+δx^2
=> f(x+δx)-f(x) = (x+δx)^2-x^2 = 2xδx+δx^2
=> (f(x+δx)-f(x))/δx = (2xδx+δx^2)/δx = 2x+δx
As δx -> 0, (f(x+δx)-f(x))/δx -> 2x

Draw the graph of y=x^2, then draw a chord through <x,x^2> and <x+δx,(x+δx)^2>. As δx->0, the chord approaches the tangent.

>>11989731

You basically just need to understand these two triangles. If you know Pythagoras' Theorem and SOH-CAH-TOA, they're pretty easy to remember.

How do I prove that the definition of a continuous function [math]f:X \to Y[/math] at a point [math]x \in X[/math], in terms of convergent filters/filterbases ([math]B\to x[/math] implies [math]f(B)\to f(x)[/math]), implies the usual definition in terms of inverse images (preimage of any [math]f(x)[/math]-neighborhood is a [math]x[/math]-neighborhood)?
I've already managed to do it the other way around.

Can somebody list all of the undergrad branches of physics?

>>11990104
sorry I'm just not getting this, I just asked my roommate who has passed calculus with a 9/10 and what I was told is that y is 10201 even though my book says it's 10201 => 10200 because "if we agree that we may ignore small quantities of the second order, 1 may be rejected". Is the book just simplifying it or something as a numerical example and not actually doing it correctly?
I also asked what dy/dx = (2(x)) = 200 was actually showing me but got no actual answer. Like I feel like I can get a bit closer to understanding what's happening when I understand what this number 200 is showing me when x is 100 and y is 10,000. Where does the number 200 fit into the function, what is it showing me?

What's representation theory in a nutshell? What makes the subject interesting?

Assume undergrad-tier knowledge in group theory. (Also, I've studied some Fourier analysis on LCA groups, and I've been told that it's closely related to representation theory. I'd love to see how)

Is 3+3 the same as 2+4?

>>11990298
Remember the boomer definition of continuity, "For every neighborhood [math]V[/math] of [math]f(x)[/math] there is a neighborhood [math]U[/math] of [math]x[/math] such that [math]x' \in U[/math] implies that [math]f(x) \in V[/math]"?
Use it as a connection. That is, show that it's equivalent to both definitions.

>>11990445
w.. what's the zoomer definition?

I'm going to start tutoring math at a community college soon. Any tips on how to be a better tutor?

>>11990629
The preimage one.

how do you even graph [math]f(x)=min(4,x) [/math] ?

>>11990643
Students are idiots and don't ask questions
Think for yourself where misunderstandings could happen and explain it
If it's online you're out of luck, because you'll spend two hours talking to yourself without any visual feedback

How to not procastinate?

>>11990682

>>11990710
thank anon.. i was doing it but doubted about [math]f(4) = 4[/math]

>>11990345
So I just think of the derivative as the slope or instant growth of the tangent on the specific x,y point?
so in regards to when
y = x^2, x = 3, derivative = 6, and y = 9 I still don't get where 6 comes into all of this. 6 would be the instant growth of y when x=3? Meaning what? First I thought x=3, derivative = 6 so y = 3+6 but that doesn't make sense when you go one higher to 4 where
x^2 = 16, derivative = 8. And 8+4 is not 16 but 8+4+4 is.

I've asked two people I know irl now that have passed calculus with a good grade what the number that the derivative is showing you and neither really know it. How can neither of them know and pass? Am I completely misunderstanding the point of a derivative?

Do I need to use trigonometry to solve this?

>>11990755
> So I just think of the derivative as the slope or instant growth of the tangent on the specific x,y point?
Yes.
> y = x^2, x = 3, derivative = 6, and y = 9 I still don't get where 6 comes into all of this.
3^2 = 9, 3.001^2 = 9.006001 ~= 9.006 = 9+6*0.001, 3.01^2 = 9.0601 ~= 9.06 = 9+6*0.01.

If you "zoom in" enough at x=3, y=x^2 "looks like" the tangent line y=3^2+6*(x-3). IOW, for a minuscule change x, the change in y will be approximately 6 times the change in x. The smaller the change, the more accurate the approximation.

I got [math]f(x)={2x-2 if x<0 , x^2-2 if x \geq 0[/math] and [math]g(x) = min(4,x)[/math]

and i have to do [math]f \circ g[/math], this is what i did:

[math](f \circ g) = {2(min(4,x))-2 if x<0 , (min(4,x))^2 - 2 if \geq 0[/math]

and made a table that looks like this (i'll call [math]f \circ g[/math] like [math]h(x)[/math]):

[math]h(-3) = -8, h(-2) = -6, h(-1) = -4, h(0) = -2, h(1) = -1, h(2) = 2, h(3) = 7, h(4) = 14, h(5) = 14, h(6) = 14[/math]

is this correct?

>>11990788
>Do I need to use trigonometry to solve this?
No. Conservation of energy (kinetic+potential) lets you convert speed at zero to height at zero speed. Any collision preserves total momentum; an elastic collision also conserves total kinetic energy.

>>11990927
thank you, that is awesome

i got:

[math]
f(x)=
\begin{cases}
2x-2 if x < 0
\\
x^2-2 if x \geq 0
\end{cases}
[/math]

and [math]g(x) = min(4,x)[/math]

and i have to make the composition [math](f \circ g) = h[/math]

so this is what i've done:
[math]
(f \circ g) = h(x) =
\begin{cases}
2 (min(4,x)) - 2, \text {if x < 0}
\\
(min(4,x))^2 -2, \text {if x \geq 0}
\end{cases}
[/math]

and i have a table that looks like this:

[math]h(-3) = -8, h(-2) = -6, h(-1) = -4, h(0) = -2, h(1) = -1, h(2) = 2, h(3) = 7, h(4) = 14, h(5) = 14, h(6) = 14[/math]

is this correct?

Very dumb question but where is the optimized area to place and aim a fan for this room? For optimizing cooling of the room is it better to cool the person down to produce less heat or to cool the room instead with different?

say i have [math]10 * 9^{ \frac{t}{2} +2 } * 5^{ 3t}[/math]

is the transofmation to [math]10 * 10125^t[/math] valid?

>>11990942
Okay, I've been working on this for two hours and am struggling.
I got speed of the first ball at zero to be v=sqrt(2gh). That is equal to the PE of the second ball? I don't know when conservation of momentum comes into play (Pi=Pf).

>>11990942
thanks!

>>11980517
1+i