/sci/ - Science & Math

here's a gif to get you startd

~UNANSWERED~

Math:
>>11360201
>>11360930 (pretty much already answered. only spoonfeed if you like)
>>11362913 (hold off tho)

Physics:
>>11348498 (they mostly help them spread and grow rapidly, I think)
>>11350750
>>11352674
>>11353046
>>11360787

Biology and Physiology:
>>11353423
>>11354924

/g/:
>>11359763

Stupid:
>>11348339 (I just wrote a very brief paper on woodpeckers if ur interested lol)
>>11350018
>>11353161
>>11355436
>>11357024
>>11360772
>>11362114

>>11363088
yw~
>>11363095
Thank you, gif anon.

>>11363090
can someone help me understand this game theory homework?

>>11362187
>so I can't add you
Nice try hun but I'm already taken.

Do you need a flyback diode on a simulated inductor?

>>11363090
Why doesn't donated blood cause agglutination (f.eg giving type 0 blood to A, B, AB even tho 0 has anti-A and anti-B bodies)? Is it because donated blood is mostly plasma?

>>11360201
yes, +90°

How was this video shot?
https://www.youtube.com/watch?v=LWGJA9i18Co

165 seconds are spent in zero-G, meaning the plane is accelerating downwards at 9.8m/s^2.
The formula d = (a*t^2)/2 tells me the plane would have had to plummet 133km to do that, meaning it'd be starting a good way into space; and it'd have achieved a final speed of 1.6km/s by the end which I'm doubtful that kind of plane could achieve even in a nosedive.

Did they do all this stuff really fast and speed the footage up or something? Every second less spent in freefall makes the numbers make a lot more sense. Even just getting it down to 100 seconds would take that 133km plummet down to a 49km plummet, which is far more realistic.

>>11363844
They don't start from level flight, so it starts with a rise, not a drop. And parabolic flights only last like 30 seconds, not 165. You can see in the video when the weightlessness stops, it's edited to cut to the next parabolic flight pretty quickly.

Hello can anybody help me with exercise 2? I have nothing to solve it with in my folder and dont find anything online... my intuition says the displacement has to be the half of the first one but i have no clue about the tension...
--------------------------------------------------------------
A 2m long steel rod with a 0,0005m radius hangs on the roof. A 100kg body is later hanged on the rod.
Steel density: 7800kg/m^3. Young module: 2*10^11. Volumetric module (K): 1,13*10^11. Rigidity module (G): 8*10^10

1. Find the length variation of the rod. (¿aprox 12mm?)
2. Find the displacement and the draft towards the ground in the middle length point of the rod.

>>11364156
Is the rod cantilevered or is it hung? It sounds a little unclear. Draw a picture if you can.

>>11364173
hung. i think i wrote it twice lmao

>>11364180
I ask because the problem is really easy if it is hung. You know the original length of the rod [math] L_0 [/math]. You know the tension on the rod [math] P [/math]. You know the shape and of the rod [math] R [/math]. You know the density of the rod [math] \rho [/math]. It's simple then that the average stress in the middle rod is [eqn]
\sigma=\frac{P+\pi R^2L_0\rho}{\pi R^2} [/eqn] You are given Young's modulus [math] E [/math]. The strain at the middle is thus [math]\epsilon=\sigma/E=\delta/(L_0/2) [/math]. So the displacement at the middle is
[eqn] \delta=\epsilon L_0/2=\frac{PL_0+\pi R^2L_0^2\rho}{2E\pi R^2} [/eqn].
It's the exact same process for the whole rod. If you need a formula to remember, remember [math] \delta=\Delta L=PL_0/EA [/math].

>>11364207
>>11364180
YIKES. I forgot gravity. The correct expressions for stress and displacement are
[eqn] \sigma=\frac{P+\pi R^2L_0\rho g}{\pi R^2} [/eqn]
[eqn] \delta=\epsilon L_0/2=\frac{PL_0+\pi R^2L_0^2\rho g}{2E\pi R^2} [/eqn]

...what does <v> (v is supposed to be a vector) mean? It came up in what I was reading from my physics stuff but it's kinda hard to search/find results for what it means.

>>11364225
Oh wait never mind, it's the average isn't it?

>>11364225
Depends on context. In quantum [math]\langle u|[/math] is a row vector and [math] |v\rangle [/math] is a column vector. So [math] \langle u|v\rangle [/math] is an inner product (look up bra-ket notation.
In material science [math]\langle x_1x_2x_3\rangle[/math] is the set of all direction vectors that are crystallographically equivalent [math](x_1 x_2 x_3)[/math] by symmetry

>>11364245
Yup. Time average would be a usage of <v>, like in this article https://en.wikipedia.org/wiki/Virial_theorem

>>11363090
>/qtddtot/
questions too damn dumb to osk them?

Given two groups S and T, both being all the natural numbers with addition as the binary operator.
Is there an isomorphism with f(n) =n+1?

I concluded with no because of no homomorphism, is that correct?
I feel as if I came to the wrong answer

Hey guys.
How do I calculate the dynamic viscosity of air traveling through a flow measurement device?
I want to use it to find the kinematic viscosity, which I will then use to calculate the Reynold's number. I know the diameter of the flow measurement device at different points, I know the velocity, density, and mass flow rate. I have a pitot-tube, venturi, and orifice plate in the device.

>>11364496
I mean, you could just look up the viscosity in a table. To actually measure viscosity is more complicated and you will need some method of measuring the (tiny) shear force between the air and the duct.

Can I eat anything a squirrel can eat?

>>11364496
I flow air all the time and don't know what you want. What units? Like centistokes? Anyhoo, I don't know but, maybe if I call you a faggot, someone will help

>>11364207
thank you bronie. are you a neet or why are you allways online?
>The strain at the middle is thus ϵ
wait isnt that the change in lenght divided original lenght?? is that what we call strain? i thought i would have to do something with σ. Can you tell me what it really means?
also the excersize said you can ignore the weight of the rod itself (forgot that).

>>11364496
To actually measure viscosity of a gas is quite difficult and you will need some method of measuring the (tiny) shear force between the air and the duct. An alternative is to use the Sutherland equation of state http://jullio.pe.kr/fluent6.1/help/html/ug/node294.htm (bottom formula) which treats air as an ideal gas. Or, you can always just look it up in a table.

>>11364207
>>11364522
i think i translated it wrong. it meant to say traction rather than strain probably. still i dont get it

>>11364524
I'm being autistic and want to impress my proff by calculuating it myself instead of using a table. Maybe I should just get a table and reference it..

>>11364520
>>11364524
>>11364540
While we are on the topic, any advice as to how best to determine which device is the most accurate at measuring the mass flow rate out of the three?

>>11364540
get the result and make up a formula with the data you have to match it. B&R

>>11364522
Strain (or what engineers call strain, true strain is different) is defined as
[eqn] \epsilon\equiv\frac{\Delta L}{L_0} [/eqn]
When we say a material is elastic, what we mean is that its strain is proportional to its stress. Remember stress-strain curves? The elastic portion is the part at the very beginning where it looks like a straight line. Young's modulus is the slope of this portion. So for very small deformations,
[eqn] \sigma=E\epsilon [/eqn]
The equation above is the definition for Young's modulus. Combine both the equations in this post with the average normal stress in a member to get
[eqn] \Delta L=\frac{PL_0}{EA} [/eqn]
>neet
No. I work weekends and I don't have lab on Thursdays until late. Other than that I phonepost. I take answering stupid questions very seriously, plus reviewing the basics is good for me.
>>11364514
Why don't you try and find out?

>>11364524
>http://jullio.pe.kr/fluent6.1/help/html/ug/node294.htm
Who's the author for that article, any ideas?

>>11364540
>instead of table
Use Sutherland equation.
>which is most accurate
For air, pitot-tubes are very good if you want to know the dynamic pressure at a point. As long as you know the density, you can find the airspeed, and from there the volumetric flux and mass flowrate. The problem with this method is that there will be a boundary layer along the sides of the duct and the velocity will be slower, so you have to measure at different locations throughout the x-section. Venturis are good except for the fact that air is compressible. I dunno about the orifice plate.
>>11364537
I don't understand your question.
>>11364570
Dunno. Here's a source from NASA with the same equation if it makes you feel better. https://www.grc.nasa.gov/WWW/BGH/viscosity.html
Just use a table, sweetheart. Empirical tables are literally, unironically more accurate than some hamfisted equation of state.

>>11364582
>so you have to measure at different locations throughout the x-section.
The cross-sectional area is split into 16 smaller squares, we've measured each square, then derived an average.
>>11364582
>Dunno. Here's a source from NASA with the same equation if it makes you feel better. https://www.grc.nasa.gov/WWW/BGH/viscosity.html
>Just use a table, sweetheart. Empirical tables are literally, unironically more accurate than some hamfisted equation of state.
I just used the two co-efficient equation and got a value very close to a table. Think I'll use both.

>>11364582
>degrees rankine

>>11364594
>The cross-sectional area is split into 16 smaller squares, we've measured each square, then derived an average.
Perfect. The average of all those velocities is the average airspeed in the duct. Then you have it that (mass flow rate) = (average airspeed)*(area of cross section)*(density). This is the most accurate method, I'd say.
>I just used the two co-efficient equation and got a value very close to a table
wonderful~

>>11364594
>The cross-sectional area is split into 16 smaller squares, we've measured each square, then derived an average.
Perfect. The average of all those velocities is the average airspeed in the duct. Then you have it that (mass flow rate) = (average airspeed)*(area of cross section)*(density). This is the most accurate method, I'd say.
>I just used the two co-efficient equation and got a value very close to a table
wonderful~
>>11364599
better than (((Kelvin)))

>>11363128
>not listing my question
Are you pícking a fight lad?
>>11363285
Basically, you solve it bottom upwards by making the optimal choice in the bottom and using that result to simplify the above choice, and so on.
There should be a good explanation of the process on your book.
>>11363384
My heart is broken.
>>11364451
The natural numbers aren't a group.
But, to answer your question, the only automorphisms of the group of integers are the identity and multiplication by -1.

what does this question even mean

How do you make DNA?

I'm trying to calculate Reynold's number for air, with the right diameter, kinematic viscosity, and air density, but I'm getting absurdly high numbers. Over hundred thousand. I'm using Re = d*v/kinematic viscosity. The fuck is going on? Diameter has been converted to meters.

>>11364436
Questions that don't deserve their own thread.
>>11364770
I'll split the question up into subsets. You can then agglutinate the solutions and deliver the result to your professor.
a) Give explicitly the set of elements related to (0, 0)
b) Draw (0, 0)'s equivalence class
c) Repeat a) and b) for a random element of the plane.
d) Find and draw a subset of the plane which contains exactly one representative of each equivalence class.

>>11364822
Anime fag, how do you get time to do anything when you're always helping fags ITT?

>>11364770
>>11364822
i'm not an anime poster but i don't think it's as complicated as that, i think the answer is just that it's all lines with a gradient of 1

>>11364795
Never mind, I used the wrong diameter

>>11364795
>Re~10^5
For air flowing through a duct? Sounds about right.
>>11364681
>Are you pícking a fight lad?
I must have missed it, lover. I'm sorry ;_;
>í

>>11364871
Oh goodie

>>11363090

I killed a spider and now I feel bad, what do?

>>11364881
>For air flowing through a duct? Sounds about right
No anon, I got over a hundred thousand. Numbers after the decimal place, lol.

>>11364947
before**

>>11364947
Like I said, Reynolds numbers between a hundred thousand and a million are fairly normal for air conditioning systems.
>>11364906
Don't eat meat for a week, pay for your sins.

>>11364971
>Like I said, Reynolds numbers between a hundred thousand and a million are fairly normal for air conditioning systems.
But that would mean it's turbulent flow? The graph I've plotted with my data is parabolic. I just did it with the right numbers and I got 12980.

>>11364994
>The graph I've plotted with my data is parabolic
Yes, Re~100000 would indicate turbulent flow. Are you sure the velocity profile is truly parabolic? It is likely just fully developed turbulent flow. In FDTF, you are going to have a rounded velocity profile and a thin boundary layer where the velocity is much less. Do you recall the concept of "entrance length" from fluid mechanics?

>>11365011
Wait, so is this table wrong or do I need to go to sleep.

>>11364843
I don't actually spend that much time here.
I usually shitpost in between studying.
>>11364858
>i'm not an anime poster
Please don't say "anime poster" like you'd say "licensed professional."

What do you mean complicated?
(0, 0)'s equivalence class is the (t, t) line, which we'll call l.
Drawing it is trivial.
For any point x, its equivalence class is the line parallel to l passing through x.
Any line which isn't parallel to l solves d. The one you'd usually thing of is (t, -t). Solving d) is important because it fully characterizes the quotient.
A full geometric characterization of the relation in terms of basic euclidean geometry. It might be overkill, but it is what the question asked for.

>>11365017
No, it isnt.
>approx. rectangular
Pic rel. is what is meant by "approx. rectangular." Check out the velocity profile for full developed Re=1000000 flow. Fluid mechanics is fake and gay though, so it's normal to be confused~

>>11365028
Now that I look at my graphs again, it looks more square than parabolic. Thanks anon.

>>11365026
Do you find that helping fags in here is conducive for your own learning?

>>11365039
You're so welcome, anon. Let me know if you need more help.

>>11365028
>Fluid mechanics is fake and gay though
What makes you say that?

>>11365039
You're so welcome, anon. Let me know if you need more help.
>>11365051
I do. Feynman method and all that.

May as well ask another question while we are at it. The geometry where I used the pitot-static tube is a square, which then connects to a regular pipe, where the venturi and orifice plate are. The readings at the bottom of the square box show a much higher velocity and mass flow rate. Shouldn't that be in the middle, rather than at the bottom, where a boundary layer can form?

>>11365088
Drawing for what I mean. Highest mfr and vel in the bottom section I colored red.

>>11365088
>>11365091
It's possible that your flow isn't fully developed. What is the ductwork like before this section with the pitot tubes? I bet there is a sharp corner or turn or something.
Also, stop saying mfr. Mfr and vfr are only defined for the entire cross section. Just say velocity.

>>11365122
Yeah there is a sharp corner. The duct that sucks in the air through an inlet cone is 90 degrees to the rest of the device and the pitot static is the first measuring device and close to the inlet cone.

>>11364560
>Why don't you try
Fucker. Now my question is answered. I don't try because I don't want to die. You owe me now Anon. You can help me math some shit some time. I wll just eat it.

>>11365129
Well there ya go, you are probably taking measurements from within the entrance length (there are multiple empirical formulas out there to calculate just how long the entrance length is). Trust your velocity measurements from the pitot tubes and do whatever you need to do for the write up.
>>11365057
D'Almbert's paradox.

What's keeping me from making ketamine with simple cross-coupling reactions? Amination and arylation of ketones, creation of alpha-tertiary carbons, many possibilities for allylic reactions involcing a cyclohexenyl, there are a million reactions of those types but no one puts them together. What factor am I missing?

>>11348498
It doesn't start them, it just makes it more easy for the proverbial sparks to survive and catch on. It's a probabilistic model. It's like your immune system, you're healthy not because you never come in contact wih foreign bodies -- you might have more microbes on you than cells in you -- but because it's permanently fighting all sorts of threats.

>>11350018
Dopamine, most likely.

>>11352674
Good question. I confess I got curious enough and just googled it: https://quantumcomputing.stackexchange.com/questions/2595/if-quantum-speed-up-is-due-to-the-wave-like-nature-of-quantum-mechanics-why-not/2598

>>11350750
Keep in mind this answer is my deduction. Altho neutrons have a charge which adds up to zero, it has an uneven charge distribution. It's positive inside, but negative closer to the surface, so it can reach an equilibrium with protons. It's important to note that lone neutrons by themselves are unstable, so this union is "mutually beneficial", so to speak.

>>11365161
is it weird that I know exactly where that is from?
https://www.youtube.com/watch?v=-PKNuZovuSw

>>11365219
Why would it be weird? Especially now that the artist is becoming popular.

>>11365051
No way. Not in the slightest.
I do feel like I gained enough skill explaining basic maths to become a good middle/high school math teacher, tho.
>>11365058
>Feynman method and all that.
This does make me wonder if Yukariposter forcefully shoving unrelated maths into problem solutions is his way of applying Feynman's method.

Can someone help me prove that if for all x:
[math]
ax^2 + bx + c > 0 [/math\]

Then the discriminant of this quadratic is
[math]b^2 - 4ac < 0 [/math]

??

>>11365269
This was me, BTW.
>>11365272
Use Bhaskara.

>>11365272
>latex
huuuemygod ok let me retry that with preview this time
[math]
ax^2 + bx + c > 0 [/math]
then the discriminant of the quadratic is
[math]
b^2 - 4ac < 0
[/math]

??

>>11365276
>Bhaskara
i'd prefer algebra, pls

trying to prove
when x-->∞, ax^(n+1) > bx^(n) for all positive a and b
just to formalize it for myself

is it valid to say
as x --> ∞, ax^(n+1) --> ∞^n * ∞
as x --> ∞, bx^(n) --> ∞^n
and from this use
∞^n * ∞ > ∞^n
or is it not correct to use infinity like this, that is to say, to assert there are "larger" infinities.

alternatively, could we divide both terms by ∞^n so we have
a(∞) and b
and we see a(∞) --> ∞
and obviously ∞ > b

apologies for the ugly typesetting

Who's retarded, me or the author? Why would an annual increase of $200 only amount to an increase $100 for every two 6 month periods?

>>11365283
Let [math]x = - \frac{b}{2a}[/math], expand, simplify and use the given inequality.
>why x assuming specifically that value
x-value of the parabola's critical point.
The proof is fully algebraic, tho, and doesn't actually rely on x being that.

>>11365292
ok so I did it slightly differently, please let me know if this is valid

consider ax and b
as x --> ∞ , ax --> ∞
∞ > b

∴ as x --> ∞, ax > b

now multiplying both sides of the equality

ax > b when x --> ∞
ax^(n+1) > bx^(n) when x --> ∞

which is what was to be proven

>>11365314
this is what I did originally, but on #math irc was told it wasn't that good of a proof. Someone offered something I didn't understand, doing something like
[math]
a(x + \frac{b}{2sqrt{a}})^2 + c - \frac{b^2}{4a} > 0
- a(x + \frac{b}{2sqrt{a}})^2 + c - \frac{b^2}{4a} < 0
[/math]
and using something like that to lead to the conclusion. The fella said there was a typo in it though, but I can't figure out how to prove it using
[math]
- a(x + \frac{b}{2{a}})^2 + c - \frac{b^2}{4a} < 0
[/math]

and I have no idea where the square roots in the denominator of his idea came from.

>>11365377
there was supposed to be a line break between inequalities there

fuck i hate captchas, it really hurts those of us with shitty internet the most

>>11365314
>>11365276
Can you please link me to whatever relevant proof this Bhaskara guy has? I can't find anything, it just seems like it's synonymous with 'quadratic equation'.

>>11365295
>Why would an annual increase of $200 only amount to an increase $100 for every two 6 month periods?
Because there are 12 months in a year. 1/2 of a year will have 1/2 of your $200 raise in it.

>>11365377
That's really not better by any margin, tho.
>>11365395
No, no. The Bhaskara equation gives you the roots of a quadratic (the one from middle school, minus b plus or minus etc.). The proof is just "the quadratic has no roots, but if the discriminant were larger than zero we could swap it into Bhaskara to get a real zero." It's the slickest, most piece of shit proof you can give.

>>11365295
Looks like he fucked up, his numbers show a $100 annual increase for the first job instead of $200. Maybe something was lost in translation?

Are there any in-depth descriptions of what happens when you have something like an empty universe that contains nothing but a single proton and an electron, separated by 1 light year?

>>11365415
But it only shows a $200 raise after four 6 month periods

How long will it take me to learn calculus, if I start at algebra 1 and study for an hour a day?
tired of being a math brainlet

>>11365418
>not really better
Can you help me flesh it out anyway, pal? :-)

Isn't 'minus b plus or minus etc' literally the quadratic equation?:
[math]
\frac {-b \pm \sqrt{b^2 - 4ac}}{2a} [/math]

Thanks btw

>>11365465
Start by opening Jame's Stewart's Calculus and just back-fill the algebra as you go. The intro/first couple chapters are all algebra review.

At an hour a day, if you start with Stewart's book, probably like 6 months for single variable calc. It will be slow at first, but in the latter half you'll be zoomin'

>>11365422
>Maybe something was lost in translation
No, he's actually trying to show that a $200 annual raise is inferior to a $50 semi annual raise. Plus he started the book trash talking pure math saying that scientific application is math's TRUE purpose. Starting to think that this book belongs in the trash

>>11365295
>900, 900, 1000
wtf lol, who's the author? what book?

>>11365487
Possibly a typo then. If the upper paragraph said $100 annually instead of $200, his point would stand.

>>11365468
If I had to guess what he did, he set [math]z= x - \frac{b}{2a}[/math], so that the polynomial becomes centered around zero, and then he did some manipulation with that.
>isn't it literally the quadratic equation
I'm used to calling it Bhaskara.

>>11365499
Well the mistake is repeated on the next page

>>11365499
Forgot pic

>>11365497
Mathematics and physical world by Morris Kline. Nearly 5 stars on Amazon.

What is the simplest device that can produce truly random numbers?

>>11365269
Not unrelated, just unnecessarily general and abstract. And yes, this is how I make sure I truly understand what I've learned, aside from actually talking to colleagues/professors and making memes and edits.
>>11365430
Yes. Shift into proton's reference frame and the theory becomes 1-body.
>>11365523
Quantum dots.

>>11365295
>>11365487
>>11365497
>No, he's actually trying to show that a $200 annual raise is inferior to a $50 semi annual raise.
Watch out! You are comparing different units there.
The $200 are in relation to the full year wage.
The $50 are in relation to a 6 month wage.
In the end both mean the 6 month wage rises by $100 each year.
But since the first $50 come in earlier for the latter case, you get more each year.

>>11365566
I'm trying very hard to understand how this makes sense.
>In the end both mean the 6 month wage rises by $100 each year.
There is no actual 6 month raise in the first job, only a 12 month raise of $200. So you can pretend that there's an immediate $100 6 month raise and another IOU $100 6 month raise which is paid when the immediate 6 month raise is paid out, equalling an immediate raise of $200 every 12 months. This is double the amount of the second job which is two immediate raises of $50 every 6 months equalling $100 every 12 months.

>>11365598
Had written up a reply, but it gets deemed "spam" by the board software.

>>11365628
Can you screen cap it?

>>11365638
Cutting away the math:

Look at his numbers.
Those are the respective 6 month wages.
Whatever you are thinking you understood is not written in that book.
Let's look at the raise vs. raise interval quotient.
It's exactly the same "acceleration", but the latter one happens more frequently resulting in a surplus.

>>11365643
I'd appreciate a screencap that includes the math

>>11365663
The bottom line is you get

[math]\frac{\frac{\$200}{12 month}}{12 month} = \frac{\frac{\$50}{6 month}}{6 month} = 1.3888... \frac{\$}{month^2}[/math]

>>11365695
Thank you

>>11365516
That seems even more wrong than before.

It's not possible that such crass errors made it to publication. Now you got me doubting myself as well.

>>11365643
>It's exactly the same "acceleration"
The thing is, it's not supposed to be the same acceleration in the first place, as he said the first job would increase $200 a year, yet the progression shown increases only $100 a year.

>>11365295
I think I'm getting it. 1800 per year is 900 every 6 months for both jobs before raises. So
>900, 900, 1000
Is option a's pay for the first 18 months. In the next six he gets another 1000 (900 base pay + 100 for other half of his raise). It increments by 100 from 900 to 1000 because that's half his raise. Etc.

Option b now might make more sense.

>>11365763
So in essence if we were to do 900, 900, 1100, 1100.. we would be 'double counting' option a's raise since we're looking at 6 month intervals.

Explain, nerds

When an object falls within a gravitational field, does the conversion of gravitational potential energy into kinetic energy cause the object to cool down?

>>11365377
>The fella said there was a typo in it though
the typo is the 'sqrt'. he's just completing the square and rearranging. to finish just substitute x=-b/(2a) and rearrange
am i not reading this right?

>>11365292
>>11365338
not sure what your asking but i think it's one of the following:

>let [math] a,b>0 [/math] and [math] n\in\mathbf{N} [/math]. then for all [math] x>0 [/math] it holds that [math] ax^{n+1} > bx^{n} [/math]
not true. take [math] a=1 [/math], [math] b=500 [/math], then [math] 1\cdot x^{n+1}\not> 500 x^n [/math] when [math] x=1 [/math].

>for all [math] a, b>0 [/math] and [math] n\in\mathbf{N} [/math], where the limits exist, [math] \lim_{x\to\infty} ax^{n+1} > \lim_{x\to\infty} bx^{n} [/math]
true, but trivially

>let [math] a,b>0 [/math] and [math] n\in\mathbf{N} [/math]. then there exists an [math] x'>0 [/math] such that [math] ax^{n+1}>bx^{n} [/math] whenever [math] x\geq x' [/math]
i think true, but maybe another anon can prove it

>>11365880
on second thoughts, just take x'>b/a for the last one

>>11365822
ugh, I explictly asked where the sqrt(a) came from too but it was never answered. My issue stems from the fact that the proof i proposed did exactly that, sub'd x with that value -b/2a, but he proposed a proof that seemed to use the fact that -[a(x+b/2a)^2 +c - b^2/4a] < 0 and I was interested in how to prove it like that, but I'm not sure if the proof was valid and I couldn't figure it out.

I tend to doubt my math abilities, so when I was told it insufficient I ate it right up and immediately thought this other proof I've yet to figure out was 'better', but if just setting x=-b^2/a works well enough, then that's even better cuz that's how i instinctively interpreted the problem.

>>11364906
I always feel like the other spiders know what I did. Gotta watch your back for a few days.

>>11365880
it was the second case (and I guess the third as well), I wanted to more formally state that the absolute value of a higher degree monomial will always become greater than that of a lower degree monomial regardless of coefficients.

>>11365908
like this?

[math] ax^2+bx+c>0 [/math] so, completing the square, [math] a\left((x+\frac{b}{2a})^2-\frac{b^2}{4a^2}+\frac{c}{a}\right)>0 [/math].
now rearranging [math] -\left(a(x+\frac{b}{2a})^2 - \frac{b^2}{4a}+c\right) < 0 [/math].
so [math] -a(x+\frac{b}{2a})^2 <-\frac{b^2}{4a}+c[/math].
substituting [math] x=-b/2a [/math], because the inequality holds for all [math] x [/math], gives [math] 0<-\frac{b^2}{4a}+c [/math].
rearranging once again, [math] b^2-4ac<0 [/math]

If you have a very tiny cylinder with one end closed off, will the casmir effect cause it to experience a force facing in the direction of the open end? Since the base of the cylinder has a higher energy density on one side than the other, it should be pushed, shouldn't it?

>>11365930
I appreciate the effort. It's possible the proof I had in mind isn't feasible. What was typed on #math irc was something more like (in psuedo-math, cuz I don't know the proof):

[math]-a(x+\frac{b}{2a})^2 - \frac{b^2}{4a}+c < 0[/math]
[math]\frac{b^2}{4a} - c < -a(x+\frac{b}{2a})^2 < -c + \frac{b^2}{2a} - c[/math]
But [math] -a(x+\frac{b}{2a})^2 < 0[/math], so [math]\frac{b^2}{4a} - c < 0[/math]

The only thing I'm certain of is that the proof didn't involve sub'ing x for any value.

>>11365985
i thnk the proofs basically there, i got frustrated trying to solve captchas on my shitty wifi but here we go for real now:
[math]-a(x+\frac{b}{2a})^2 + \frac{b^2}{4a}-c < 0[/math]
[math]-a(x+\frac{b}{2a})^2 < -\frac{b^2}{4a}+c [/math]
So, times the RHS by -1 and it's by def'n less than the square, right? then:
[math]\frac{b^2}{4a} - c< -a(x+\frac{b}{2a})^2 < -\frac{b^2}{4a}+c [/math]
And [math]-a(x+\frac{b}{2a})^2 < 0 [/math], so [math]\frac{b^2}{4a} - c < 0[/math]

QED?

>>11365998
>times
i need to stop

So P = Vi, and if P > 0, then the element is absorbing power, right? But the current is leaving the element rather than entering into it so I don't know what my i is. Is it -0.25A entering the element from the other side as well? Yes I am fucking retarded.

>>11365742
Despite the explanations above this is what I'm still stuck on

>>11366068
Generating. P = Vi = -12.5 W. It is removing -12.5 W from the circuit, or it is adding +12.5 W. Look at the orientation of the battery. The battery is trying to push current clockwise but whatever that element is is reacting against it.
>Is it -0.25A entering the element from the other side as well
Yes. If charge is not accumulating in an element, then current in=current out.

>>11366083
>>11366068
Then again, I just saw the arrow, so it's a double-negative type situation. This is a really stupid question.

>>11366083
>>11366085
So then if the arrow is pointing to the + side rather than the - side, does that mean I would flip the sign on the voltage (50V to -50V) and end up with a positive P after V * i instead? Meaning the element is actually absorbing? I'm sorry if I'm being extra retarded and completely misunderstood what you were getting at, I don't get this stuff at all.

>>11366095
I dont actually know. If negative current is flowing in the direction indicated by the arrow, that means positive current is flowing in the opposite direction. That means the element has a positive impedance and the power it dissipates/absorbs is positive and it doesn't generate anything. I meant the question in the pic you posted is stupid, not you. Whatever your answer is, just justify it.

>>11365742
The salary increases $200 a year, so the salary per 6 month period increases by $100 each.

>>11363090
>This book is primarily a practical guide to how to solve a certain class of problems, specifically, what I call formal problems ... do not include probems of defining "mathematically interesting axiom systems"
are there any textbooks that DO make this a goal at all?

Why is mechatronics a meme degree?

Where can I read in some depth about eigenfunctions of laplacian? Specifically in QM.

Physicslet here, what the fuck is work done by a vector field meant to model?

Seems to me that in one dimension the work done by a force on an object in some interval of time tells you the difference between starting and ending velocity, if this is true does it generalise to R^n?

I am guessing the scalar product is there to measure how responsible a force is for an objects change in position? Is there a better or correct explanation?

>>11366528
Search for math books ending in stein and berg.

>>11366654
Your job would be working at a shop where boomers bring their sexbot in for maintenance.

>>11366687
Into to QM, Griffiths, Chapter 3.
>>11366694
The work done on a particle on a path [math] C [/math] is [math] W=\int_C\mathbf{F}\cdot\text{d}\mathbf{r} [/math]. This integral represents the sum of all the forces on an particle, times the distance parallel to the trajectory. That's why there is a dot product. Physically, there is something called the work-energy theorem that shows that the work done on a particle along a path is exactly equal to its change in kinetic energy. If all forces on a particle are conservative, the work on the particle is only dependent on the endpoints of the path and not on the path itself. In a conservative system, [math] W=-\Delta U [/math] where [math] U [/math] is potential energy. That book looks like absolute shit, btw.
>>11366654
Is that even a degree offered to undergrads?

>>11366744
Chapter 3 doesn't have shit on spectral equation for laplacian and neither does chapter 4.

>>11366737
do you have an actual example of such a book?

>>11366853
http://people.math.harvard.edu/~shlomo/

>>11365998
is this a good proof fags?

>>11366528
Try something like Gromov's Great Circle of Mysteries, random non-fiction books written by mathematicians, and autobiographies of mathematicians who came up with interesting concepts.
>>11366694
The intuition I got in high school was that the part of the vector field tangent to the object's velocity was the "effective" part of the force, i.e. the part of the force that "worked".
So for example, if you have a large, heavy box, and you try to push it frontwards and upwards, the box will more frontwards, so that the upwards component of the force didn't do anything.
It actually makes perfect sense if you hold it up against Torricelli's equation.
>>11366744
>Is that even a degree offered to undergrads?
Not that anon, but it is here.

>>11366909
Fuck, I forgot the most important part of the explanation.
The component of the force that's orthogonal to the velocity doesn't actually change the velocity's intensity (the amount of kinectic energy), it only rotates it. For example, in a circular orbit, everywhere the force is perpendicular to the velocity, and it has no effect on the velocity's intensity, only on the direction.
In contrast, if the entire force points in the same direction at the velocity, it affects the velocity's norm the most.

>>11363090
I have a humidifier that needs the filter changed every 3 weeks. IF I add table salt to the water tank, would that extend the life of the filter by softening the water?

What happens when you add salt to hard water? Does the mineral drop to the bottom? Picture is the minerals left behind after evaopration.

is vinegar really turned into a base inside the body? I just want convientant way to keep acidity levels down

>>11367315
Im not sure if that makes sense. You are just adding one more mineral to be deposited, left behind to be cleaned up later.

what's a good source to learn basic conditional probability?

Given the average distance between two water molecules, the energy required to break their bond, the density of water and the acceleration of gravity how does one find the maximum size of a water droplet?

>>11367411
By considering the strength of the hydrogen bond between molecules and the shape of the water molecule itself you can determine surface tension. From there, knowing gravity and density, you can find the maximum size of a bead of water on a flat surface on earth.

Is string theory science?

>>11367315
You'll have better luck in >>>/diy/sqt/
>>11367564
While no string theory predictions can be verified as of now, it does produce predictions that can "technically" be verified in extreme cases, plus it has good potential of eventually producing practically testable predictions.
So I'd say it is.

Why would a chemical spray "go away" slower if there was a door with cold air going inside the room?

>>11363090
How would I go about proving this?

>Prove that every open subset of [math]\mathbb{R}[/math] is at most a numerable quantity of disjoint open intervals

>>11367673
>Is an union of at most a numerable quantity of disjoint open intervals

Forgot to add the union part

>>11367681
[math]\mathbb{R}[/math] is homeomorphic to [math](0, 1)[/math]. There, every connected component has nonzero measure, so there can only be a countable amount of them. Pass the intervals back and forth, yada yada yada.

For an extremely explicit proof, call U the open set, and take some a in U. There is at least one b such that (b, a) is in U, take the smallest one, and do the same for (a, c), to get the largest interval containing a (also known as a's connected component). Then, take the suprema of d in U such that d<b, and, for some e, we have (e, d) is in U. You get the idea, show that the process eventually gives a countable decomposition.

>>11366474
The first progression clearly shows the salary going up $100 every 2 semesters.

>>11367731
Oh, one thing.
If you just iterate that, you might hit a wall like (1/2^(n+1), 1/2^n), so you'll need to modify it a bit.

Is there any connection between linear subspaces and subrings? They give me the same sort of vibe.

>>11367731
Can you explain this in a bit more detail please, I think I get the main idea behind what you're trying to say but I dont see how I can construct a proof from that and desu its not really clear what you're trying to do.

It may help to know that this is from a problem set dealing with basic topology on metric spaces so its about things like limit points, neighborhoods, etc.

>>11367732
The salary for each 6 month period goes up by $100 every year, which is an annual $200 raise.
Raising the salary for a 6 month period twice by $50 each year does the same thing (a $200 raise over the year), except partially earlier, which makes it the better option.

can someone explaining to me linear independence and span? I'm confused.

lets say a set of vectors are linearly independent, how do I produce another set of vector that has the same span? How do I conclude they are in the span R^n??

>>11368088
Linear independence means that the only linear combination of said vectors equal to the zero vector is the one where all coefficients are equal to zero. This is the same as saying that none of said vectors are equal to a linear combination of the others. Basically when vectors are linearly independent they are not redundant in defining the span.

The Span of said vectors is the set of all vectors that are equal to a linear combination of said vectors.

If you want to produce another set of vectors that have the same span, you can apply the Gram Schmidt algorithm to the original set to get vectors that orthogonal between each other.

If you want to see if said span is included in R^n you put each of the n standard vectors (i.e (1, 0, .....), (0, 1, .....)) and then each of the vectors of the set in the rows of a matrix. You then apply Gauss's algorithm. If you you have some vector that you are unable to eliminate then the span is not included in R^n.

Would anything interesting happen to the water in this apparatus? Say I had a conductive sphere filled with water and some small hydrophillic mass. Then, that sphere is coated in some thin dielectric (or simply air) and another conductive sphere is enclosed about it, and those spheres are charged; basically a capacitor, such that the inside sphere was positively charged.

>>11363090
Holy fuck I hate tutoring these arrogant fucking comp sci students. Why do we even make these losers take calculus, discrete math, and linear algebra.
At least a shitty gen ed student who comes in for stats help doesn't think they know everything.

how do you deal with mediocrity and salieri syndrome regarding career and education path?

>>11367893
[math]\mathbb{R}[/math] has a homeomorphism to [math](0, 1)[/math] which sends open intervals to open intervals, doesn't it? And since it's a homeomorphism, it sends open sets in [math]\mathbb{R}[/math] to open sets in [math](0, 1)[/math], doesn't it? So we really just have to prove the same statement for [math](0, 1)[/math].
Now, in either case, open intervals are precisely the only open, connected sets.
Proof: left to the reader.
So, we have an open set [math]V[/math] in [math](0, 1)[/math]. By taking the map which sends each [math]x \in V[/math] to its connected component, we decompose [math]V[/math] into a union of disjoint connected components, which are all open
intervals.
This decomposition is unique, so we need to show that it's countable. But any of the connected components has nonzero measure, and since they're all inside [math](0, 1)[/math] and are disjoint, they need to be countable, since otherwise they'd sum an infinite measure.

Another proof is as follows: we decompose [math]V[/math] into connected components as earlier. Each connected component contains at least one rational number, and they're all disjoint, so there can only be countably many of them.

But you can also follow some route like this >>11367731 , which would be a "direct, brute, trickless proof."
>>11368088
n vectors aren't linearly independent if they all embed into an n-1 dimensional subspace.
So three vectors aren't linearly independent if they fit into a plane, and two vectors aren't linearly independent if they ambed in a line.
>how do I produce another set of vector that has the same span?
Order up the vectors, and remove 0 if it's in. Take the first one into a set [math]S[/math]. If [math]S[/math] and the second vector are linearly indepent, add in the second vector to S. If it isn't, discard the second vector. Either way, iterate for the third vector, and so on.

>>11368947
Learn to have some humility.

>>11365784
what book?

>>11368976
> they need to be countable, since otherwise they'd sum an infinite measure.
That sounds like begging the question, since if they are uncountable, their measures do not add up using sigma-additivity.

>>11369054
Spivak's calc, it's the supplied answer to 2-21c, which itself is a variant of a simpler cauchy-schwarz proof in 1-19.

I just don't get the algebra / index magic from line 1 to 3. I do see why i < j, but not i != j.

>>11369082
You're being anal about things you shouldn't worry about.
Since the sets all have positive measure, and they're uncountable, there needs to be at least a countable amount of them with measure larger than [math]\epsilon \geq 0[/math]. Just taking this subset of V already gives a set with measure larger than one and completes the contradiction.

>>11369100
>countable amount
Countably infinite amount, to be specific.

>>11369087
>>11365784
BUMPEROONI

Is risperidone safe? My doctor prescribed it to me (even though i don't have schizophrenia) but i'm scared of taking anti-psychotics.

how do i view a .localstorage in safari on 10.8.5 as a web document or whatever?

Can anyone here help me with writing my systematic review - do I need to use PRISMA guidelines? What are the alternatives to PRISMA?

>>11368336
>>11368976
thank you anons, appreciate it

>>11369306
>>11369087
>>11365784
ok, i just need the last equality proven, pic related PLEASE help

>>11369714
Literally just count?

How come humans require a bunch of built items to live? stuff like toothbrushes, shoes, clothes? have we always needed them or have we just devolved to be less capable of endurance?

>>11369422
ya, i took double dose b4 sleep 1ce

>>11363090
169 is coprime to 210. Let a(x) be the sequence of coprimes to 210:
a(1) = 1
a(2) = 11
a(3) = 13
etc.

If a(x) = 169, how do I determine x? Is there a better way than just counting?

>>11370229
>210=2*3*5*7
There is, but in this case, it's garbage, because 210 has a bunch of prime divisors and they're all small.
Essentially, consider something like 104=8*13=2^3 * 13
If a number is coprime to 104, it's not divided by 2 or 13. So for a random number like 85, we know there are 84/2=42 multiples of two which are smaller than it, and 6 multiples of 13 smaller than it (divide 85 by 13 and take the integral part). Out of those, 3 are divided by 26, so we remove the double count and get that there are 45 numbers smaller than 85 which aren't coprime to 104, thus there are 40 numbers smaller than 85 which are, and 85 has position 41.
Someone probably has a better idea, tho.

Is quantum chromodynamics actually used for engineering any practical technologies?

>>11370019
Probably evolution. Our teeth probably didn't decay at all or not as bad (think processed foods).

Our feet can adapt to rough and tough surfaces.

And we probably didn't need clothes in Africa( the continent of human origins)

>>11370334
>>11370334
Social conditioning

>>11368976
Dude I dont know anything about measure theory.
A direct trickless proof is what I need

>>11370363
>direct, trickless
Doing one of those usually takes ~half an hour, so you'll have to do it on your own. Basically, take the construction, study the cases where it fails, adapt and readapt it until it works. Really no two ways about it.
But what's wrong with the proof with rational numbers, tho? I'd still classify it as a trick proof, but it is pretty simple.
>the open set admits a decomposition into disjoint intervals
>the decomposition is countable because each interval contains at least one rational number, and this rational is in no other component

>>11370282
Do you have a link where I could read about this method? And/or do you have an example with three or more prime factors? I'm having trouble keeping track of all the double-countings and I don't think I'm doing it right.

>>11370432
>do you have a link
No.
> I'm having trouble keeping track of all the double-countings and I don't think I'm doing it right.
Use this: https://proofwiki.org/wiki/Cardinality_of_Set_Union/General_Case

Ok -- I habe a spreadsheet that has daily sales data, and total number of inputs. I need to create an item level forecast. Any ideas as to wat do?

>>11370363
You know what, I feel like it, so I'll type out a full direct, trickless proof.

First, we start with an open set [math]U[/math]. We want to decompose it as an union of disjoint open intervals.
The basic, obvious idea we start with is as follows: we take a point in the set, and we find the open, disjoint subset is in. This is trivial, and we can just take the largest open interval which contains the point and is a subset of the original set.
Now that we've gotten the first interval, we'll search for the rest from it, by going to the right and to the left.
So there should be a closest interval to the right of our original interval, and we try to find it by messing around with suprema and minima. We quickly find that it's not there. This is because, if our original interval is (a, b), then there fit a whole bunch of open intervals in (b, b+ epsilon).
So our next idea is simple: we pick one of those intervals, and we try to meet up again with our original interval by moving left.
We hit again the same problem from before, but we think a bit more and we conclude that, even if we could just keep moving from interval to interval, there might be an infinite amount of intervals between our new set and our original set.
So starting the iteration process from one point doesn't work, and starting from two points doesn't work, even when it kind of works.
Our next thought is as follows: we start from an infinite amount of points. Now, from basic set theory, we know that a countable union of countables is countable, so we just need to choose a countable infinite set and start the iteration from there.
The first one that comes to mind are the rationals.
If you just take the largest open interval that contains the rational in the original open set, you'll cover the entire thing, but you'll get a bunch of duplicates, which aren't really a problem.

>>11370447
Okay then, I'll apply that theorem and the method you described here: >>11370282
First I'll give a formula for your example, to show that it gets the same answer, and then I will try it on my example.

>your example
>85 is a coprime of 104. Determine its position x among the coprimes of 104.
x = 85 -floor[85/2] -floor[85/13]
+floor[85/26]
+1

x = 85 -42 -6
+3
+1
= 41

>my example
>169 is a coprime of 210. Determine its position x among the coprimes of 210.
x = 169 -floor[169/2] -floor[169/3] -floor[169/5] -floor[169/7]
+floor[169/6] +floor[169/10] +floor[169/14] +floor[169/15] +floor[169/21] +floor[169/35]
-floor[169/30] -floor[169/42] -floor[169/70] -floor[169/105]
+1

x = 169 -84 -56 -33 -24
+28 +16 +12 +11 +8 +4
-5 -4 -2 -1
+1
= 40

But I counted it out, and I think I should be getting x = 46. What am I missing?

>>11370524
I've just spent five minutes in Excel.
I think you counted wrong desu, I got 39.

>>11370561
By the way, I also got 40 for the 85 ~ 104 one.
I think I added in the +1 on accident, my bad.

>>11370423
>>11370514
Thanks for all the help, really appreciate it you guys taking the time to help me.

>>11370561
>>11370569
Oh, yeah, I did count wrong. I was using the sequence of coprimes to 30 instead of 210. Thanks!

>>11370504
Pls respond

>>11370322
naw

Hello sqt, can anyone tell me how did they derive the formula for n possible number of combinations to be 2^n-1?

>>11370229
The predicate "is coprime to 210" is periodic with period 210. In any range of 210 consecutive integers, 48 are coprime to 210. So for all n, a(n+48)=a(n)+210. So if a(x)=y, find x' s.t. a(x')=(y mod 210), then x=x'+48*floor(y/210). The first part can be done with a lookup table.

The other option is to note that a(x)=x*210/48+f(x) where f(x) is periodic with period 48. So given the values of f(x)=a(x)-x*210/48 for 1<=x<=48, you can use the DFT to get f(x) as a sum of 48 c_i*cos(2*pi*n*x/48+phi_i) terms.

If A[math]\subseteq[/math]B and B[math]\subseteq[/math]A then A=B.

Is there a situation where that isn't true?

Is my university a meme? Our sched is fixed, and we have 5 subjects per semester. Two of those are 5 hours nonstop lectures.

Not sure where else to ask this.

What is a good free Mac OS alternative to Solidworks for 3D modelling with similar features?
Any of these able to convert output file to a SW prt file?

I don’t need any analysis built in as I’ll use ANSYS.

>>11370855
Look up the axiom of extensionality.

IS THERE IS SUCH A THING AS OVEREXERCISING? I'M ADDICTED TO 4 HOUR OF RUNNING EVERYDAY AND I DON'T FEEL PAIN
AM I GOING TO DIE? IS IT OKAY?

>>11371441
>humans literally evolved to be marathon runners
>this nigga asks if doing what is he supposed to be doing will kill him

>>11371447
THAT'S RACIST YOU PIGSKIN

>>11365465
Getting a handle on calc 1(single variable) won't be too bad. Calc 2 is tougher but calc 3 is a breeze if you have a good understanding of 1. At an hour a day, 7 days a week, you could get there in like a year or a little less.

What am I doing wrong?

>>11371555
[math]\sqrt{x} \sqrt[3]{x} = x^{1/2} x^{1/3} = x^{5/6}[/math]

>>11371577
I am trying to find the derivative of f(x)

>>11371580
And that's the first step of doing so.
It's trivial to avoid using the product rule by doing that simplification first.
Using the product rule there in the first place is what you are doing wrong.

>>11371555
what exactly did you do in your last step in the addition?

>>11371617
I fucked it up that's what I did, kek. Fixed.

>>11371609
not that anon but I like that the product and quotient rule can be used even for trivial bullshit like [math]{1\cdot x}[/math] or [math]{x \over 1}[/math]

Is there any quick way to find the inverse of a 3x3 matrix? Because this shit is boring as fuck

Are partial derivatives calc 2?

can someone help me finish this?

[math]
\sum_{i>j}(x_i^2y_j^2 - x_iy_ix_jy_j) + \sum_{i<j}(x_j^2y_i^2 - x_iy_ix_jy_j)
[/math]

How do I combine the two sums?

I've got an answer key

if x = 2 sec theta, how do I solve for theta?
I have an answer key telling me theta equals sec^-1 of x/2, I'm just trying to understand how to know that the 2 goes in the denominator of the inverse secant

>>11371807
>divide both sides by two
>apply inverse secant
>>11371682
Gauss-Jordan

>>11371816
How exactly does gauss elimination help here?

>>11371871
Nevermind

>>11371871
>set up an n×2n articulated matrix
>matrix you want to invert on left, identity on right
>RREF
>you get the identity matrix on the left, inverse of original matrix on right

Any1 here with any experience doing 6 hours of lectures and 6 hours of labs back 2 back on a friday? Is it gonna kill me?

In Young-Freedmanland, there's a swing that consists of:
- An axial rotating shaft (fixed rotational speed)
- A radial bar connected to that shaft (red here)
- A cable lying in the axial-radial plane connecting that that bar to a mass (blue here)
Does the tension in the bar act on the mass? I know they're not connected, but the problem just seems to easy if there are only two forces acting on the mass. The last one I was assigned involved four.

>>11372057
The bar is not connected so no, the cat does not act on the person. The bar does act on the cable so those two diagrams are connected, but can be treated and analyzed individually remembering that the tension in the cable is equal to the tension in the cable

>>11372065
If the linkages are assumed massless I can just ignore the forces acting on the nodes, right?

Would one be able to store an aqueous solution of 12% sodium hypochlorite in a latex bladder for prolonged periods of time?

>>11372057
The force of the cable in the red FBD is pointing the wrong direction. Also, there shouldnt be a mass/gravity force there.
>>11372071
No. There is still tension on the nodes.

>>11372086
Both diagrams are for the mass at the end of the cable. The red was for if the bar acted on the mass. Sorry that wasn't clear.
If I need to solve for the rotation rate, I use the blue diagram:
- Equate vertical component of tension to weight
- Equate centripetal force to horizontal component of tension
- Solve for rotation rate using (centripetal acceleration) = (mass) (angular velocity)^2 (radius)
Right?

>>11372108
> Solve for rotation rate using (centripetal FORCE) = ...

>>11372071
You can always treat the object as one object or break into multiple parts. It may not answer the question you're wanting if you choose to treat them differently, but yes, the links are irrelevant for the overall motion under standard assumptions that apply here. Treating as one object would be blind to which link would break first or have most strain, but that's a separate question.

>tfw a bunch of 4chan autists have helped me understand physics and mathematics better than my lecturers over the past 2 years
Thanks, lads. I'm not exaggerating when I say that you've increased my grades by at least 20-30%.

>>11372108
>>11372117
>Right?
Use the blue FBD and you've got it right.
>>11372151
<3

>>11370755
We have a set S.
Choosing some of them means that you have a function [math]f : S \rightarrow \{0, 1 \} [/math] , where we'll say that if [math]f(x)=1[/math] then x was chosen, and otherwise it wasn't.
There are 2^n of these functions, and we subtract the case of no element being chosen.
>>11371253
Sounds normal.
>>11371743
Depends.
>>11371798
[math]x_i y_i x_j y_j = x_j y_j x_i y_i[/math].
>>11372151
Please don't post such depressing things.

I want to work with radiation. I'm in the medical field, with medical qualifications. I don't want to be a radiographer, I want to actually measure radiation and monitor the health of people in contact with radiation.
What type of jobs, qualifications should I look at?

>>11372323
>in the medical field
Too vague. Are you a nurse? Medical student? Tech? Housekeeper?

I dont understand greens theorem. Integral of pdx + integral of qdy. Hows that supposed to be a line integral around a loop? Wtf are P and Q?

Why does center of mass work regardless of this:

i open my laptop wide vs closed and the center of mass varies. But all the weight of the upper half of the laptop rests on one point, so why should the COM vary?

>>11372700
Green's Theorem: "The line integral of a vector field along a closed path is equal to the surface integral of the curl of the vector field on the area that the path encloses"
the Pdx+Qdy thing is just a way of expressing [math] \mathbf{v}\cdot\mathbf{r} [/math] in Cartesian coordinates

>>11372740
v*dr, whoops.
>>11372708
Because the geometry changes, obviously. I dont know why you think it wouldn't change

>>11372740
can you explain the pdx again? I took multivariable last year and it was not taught well

>>11372748
why does a geometry change cause a change in the forces? theres one insertion point on the laptop holding the weight, why does the weights angle then transfer force thru ? what occurs on a infinitesimal/continuum level

>>11370577
>>11370561
>>11370569
Okay, I actually have a followup question.

The coprimes to 6 are given by the formula
a[x] = (6*x+cos[pi*x]-3)/2

I used the method you showed me to get a formula b(x) which gave me the numbers corresponding to the coprimes of 6 which are multiples of 5:
b[x] = floor[5*a[x]] -floor[5*a[x]/2] -floor[5*a[x]/3]
+floor[5*a[x]/6]
So
b[1] = 2 (since 5 is the 2nd coprime of 30)
b[2] = 9 (since 25 is the 9th coprime of 30)
b[3] = 12 (since 35 is the 12th coprime of 30)
etc.

Now I would like a formula which "inverts" this function, so that
c[2] = 1
c[9] = 2
c[12] = 3
etc.

Now I know it is impossible to literally invert b[x], because it fails the horizontal line test with all those flat steps. However, maybe there is a way to get a formula which still has the desired property of the inverse, namely that if you compose the two functions together it returns the original argument? I have also thought about changing b[x] so that the "steps" in it are slanted and joined together, so that it passes the horizontal line test. I'm not sure how to do that mathematically though, or how I would invert it if I even managed to get that far. Can anyone help?

Why should I keep paying rent if I'm just going to shrivel up and die like some old lonely farmer?

Why don't squirrels have to pay rent if I do?

>>11372811
you dont gotta pay rent. just go live in the forest wiht the squirels

>>11372700
We'll consider [math]P = 0[/math] for the sake of intuition.
You want to compute [math]\int _C Q ~ dy [/math], where [math]C=C1+C2[/math] where sum means you glue both paths, so it starts in A and finishes in A.
Immediately, you know that [math]\int _C Q ~ dy = \int _{C_1} Q ~ dy - \int _{C_2} Q ~ dy[/math] , which means that the integral along the closed curve identifies how much the path integral changes when we swap from one curve to another. If you look at the ideal representation, you'll notice that dy vanishes while we move horizontally, so we're really just comparing the two vertical strips.
So if we string two points in either curve together (with the green line in the picture), we can use the fundamental theorem of line integrals to compute how the function changed from one point in one curve to a point in the other curve. By gluing together these line integrals along the entire path from A to B, we get a double integral (one along dx, one along dy) and this gives an area integral, which complete's Green's theorem.

Im trying to figure out how large the radius of those cylinder shaped sci fi space stations would have to be before you would stop noticing that you are walking on a constant slope.

So after some research a 3% (34:1) slope, is a decent breakpoint, where its gets obvious that you are on a slope, so i wanted to take that as my goal, or as the number to hit. But i cannot figure out what the radius of a circle would be that would give me a 34:1 ratio slope on the inside.

>>11372218
>Please don't post such depressing things.
Such is life, anon. I get more robust responses to my questions on /sci/ than I do when asking my professors.

>>11372768
>can you explain the pdx again
[math] P\text{ d}x+Q\text{ dy}=\mathbf{v}\cdot\text{d}\mathbf{r} [/mah]
You know about the dot product, right? This quantity is the change in v times the change in the path parallel to v. This anon explained very well. >>11372852
>CoM
Center of mass is all about the geometry of an object. Has nothing to do with forces. If you change the geometry, you are going to change the CoM.

>>11372768 #
>can you explain the pdx again
[math] P\text{ d}x+Q\text{ dy}=\mathbf{v}\cdot\text{d}\mathbf{r} [/math]
You know about the dot product, right? This quantity is the change in v times the an increment in the path parallel to v. This anon explained very well. >>11372852 #
>CoM
Center of mass is all about the geometry of an object. Has nothing to do with forces. If you change the geometry, you are going to change the CoM. Read your textbook for an explicit definition.

>>11370322
actually if qcd is neutrinos then u can turn chlorine to argon

>>11372918
like this, anon

>>11373056
I don't understand what you're saying here. Does QCD predict that you can turn chlorine into argon with neutrinos? Because that's not a very practical technology.

>>11372918
all circles will have a gradient of 1/34 at some point

>>11373015
>nothing to do with forces
:| thats not how physics works

yes i know about dot product its starting to make sense now i just didnt realise it was a vector function lel

>>11373124
>fundamentally misunderstands what COM is
>tells me I don't know how physics works

>>11373140
youre the one who didnt answer my stupid question, stupid

>>11373075
>>11373097

Yikes, damn i should have known /sci/ was useless. At least reddit managed to help me find the way how to calculate it. And it ended up being a circle with a radius of 578,5 calculated by using a 3 coordinate system, since the slope is a 34:1 that means 3 coordinates could be (0,0)(34,1)(-34,1). Next time if you have no clue about it, just don't anwser.

>>11363090
please explain; there's a followup that I'll reply with

>>11373224

>>11373212
I'm not advanced but I'm a little confused. As the other dude said, won't all circles somewhere have that ratio as its slope?

>>11373159
>pic
Never call me stupid again, slut.
>>11373212
>578,5
578.5 what? Millimeters? The question doesnt make sense unless you know the size of a human foot, how large their gait is, etc.
>>11373224
>>11373226
It looks like there is already an explaination for each example. Specifically what part don't you understand?

>>11373212
>spacing after quotes
>yikes
>calling /sci/ useless
>reddit helped
>some ilegible stuff about coordinate systems and measurements with no units
Is this some sort of bait to get me to decipher your post, calculate it and then correct you or did you actually post the question in two places simultaneously?

What qualities do the four fundamental forces share with each other that make them all "forces"? If you were to imagine a simple, hypothetical force for the purpose of conveying what a force is, how would you describe it?

so when you square both sides of an equation you can introduce an extraneous solution, since the process of squaring ignores the sign of the original values, or to put it differently. f(x) = g(x) ==> [f(x)]^2 = [g(x)]^2 but, [f(x)]^2 = [g(x)]^2 does not imply f(x) = g(x) since it could also be f(x) = -g(x). I understand why this creates extraneous solutions. However, in the case when squaring does not create extraneous solutions, that is, all solutions obtained from squaring both sides are valid for the original equation, how do we rationalize this case? An example of this is

sqrt(2[x^2]-1) = -x+2

which when solved by squaring both sides, then collecting all terms and solving via the quadratic formula or otherwise leads us to: x=1 or x=-5, which are both valid for the original equation.

>>11373243
okay for the first one, if the force applied simply causes the object to spin, won't the center of mass velocity be 0?
by this logic, for the second one, we don't have any guarantee the cm velocity will be the same?

>>11373305
>if the force applied simply causes the object to spin, won't the center of mass velocity be 0?
No. It has translational and rotational motion. The net force on a rigid body is the mass of the body*acceleration of the center of mass, always.

>>11373243
you are really stupid. you just solved a simple equation based on the COM rules. thats NOT what im asking. im asking WHY COM works how it does, not how to work the equations typically existing - why do those equations exist to begin with?

laptop i stage 1, half open, vs slightly ajar. all the weight of the upper portion rests on the bottom at one point. so why does the weight distribute how it does according to com rules?

>>11371816
thanks lol

as I was driving to work I was like "maybe I should've attempted a little algebra before asking".. sure enough

I took calculus in high school in like 2004 and now I'm taking calc 2 in college and my professor tells me I need to study "a minimum" of 2 hours per day but I work 13 hour days so I'm feeling a little bit challenged..

well, I'm doing better than I was a month ago, but this next test will make or break my whole semester and right now I really need to grasp all of this trigonometry review at the same time as conquering what my professor is saying is the hardest section of calc 1, 2, or 3

i imagine u guys have seen this before, but just wanted to know if this had a real solution.

>>11373320
>prove the definition lol
Say you have a 2D plate of arbitrary shape and you want to balance it on your finger. From statics, the only place this is possible is the point where it requires no external net moment or torque to support the body (see Newton's second law). But, for each little piece of mass of that object, you know that it will be pulled downward by gravity in proportion to the mass of that little piece. Say the body has a varying density [math] \sigma[/math] (mass/area). So if [math] r [/math] is the distance of an element of the plate to your finger, we need it that [eqn] M_{net}=\int r\sigma g\text{ d}A=0\qquad(1) [/eqn].
Notice, however, that for a 2D body like a plat it is ***defined*** that [eqn] \mathbf{r}_{cm}\equiv\frac{\int\mathbf{r}\sigma \text{ d}A}{\int\sigma\text{ d}A}=\frac{1}{m_{tot}}\int\mathbf{r}\sigma\text{ d}A\qquad (2) [/eqn]
Now, use your little brain and think, darling. If the relative location of the center of mass (defined above, you don't yet know its properties), is zero, then what happens when you plug (2) into (1)? You get [math] M_{net}=0 [/math] and the plate is balanced because the first moment of mass is zero and the sum of all torques is zero. This is the """proof""" that center of mass is the balance point and it can easily be generalized to higher dimensions. You absolute faggot.

Use cylinder shell method to find volume of region bounded by y = sqrt(25-x^2) x=4 and x=5 about the y-axis. What is the radius of this cylinder? Is it just x?

brainlet undergrad here, what the fuck is this overline notation? sketch the sets of the bounding of a ball and ??????? the prof uses one notation during lecture and another on the graded homework and neither of them match the textbook so half of the time I spend on the homeworks is just trying to figure out what the fuck is being asked. /rant, if anyone could answer I'd appreciate it deeply.

I have testosterone gel. Will it improve, reduce, or worsen baldness if i put it in my hair? Or will I just get jizzy hair? I have plenty.

>>11372218
>x_i...y_j=x_i...y_j
I know, but I don’t get how to add everything together under one index as one combined sum.

pls halp

hey there, hard question..
will masturbation make me age faster by deleting the stem cells in my testicles?

>>11366875
Damn.

Non /pol/ related question:
So Eugenics was obviously based on some bullshit like some races being inherently superior which is nonsense.
But if you actually decided to create a worldwide program where only people who don't have any genetically inherited diseases and maybe reach a certain IQ (assuming in that world that IQ is reliable measure for intelligence which it isn't really, and inconsistencies due to upbringing and schooling wouldn't exist which is impossible) Would it actually improve humanity? (except for maybe in the field of ethics as not letting certain people procreate is extremely unethical) Or would it go down the shitter and not work?

tl;dr was eugenics doomed because of wrong parameters, or was it doomed no matter what.

>>11373701
Protip: Don't get medical advice from /sci/. Simply don't.
Go to a doctor that knows his shit on this.

I can only tell you that I used testosterone once (for a different reason), and nothing about my hair changed.

>>11373651
Isn't overline a common notation for the inverse?
I can't guarantee you it means that there, though.

>>11373701
Testosterone is generally assumed to be a cause of hairloss, which is ironic because apparently a lot of those "receeding hairline beta male" type characters have really high testosterone levels. (not that that says anything really, just something Idiots like Paul Joseph Watson and other retard like to use as a fake 'manliness measure' to sell their onions pills)

>>11374289
>So Eugenics was obviously based on some bullshit like some races being inherently superior which is nonsense
Niggers have statistically significant longer calf muscles than Caucasians, thus have improved running abilities. They are inherently superior in that regard alone. Caucasians have statistically significant lower crime rates than Niggers, thus have improved civilizations. They are inherently superior in that regard alone.
>assuming in that world that IQ is reliable measure for intelligence which it isn't really
You're correct in that IQ is not a reliable, quantifiable measure. Hence, your question isn't really asking anything. Go be a nigger somewhere else.

>>11374333
Dht not test

>>11374338
DHT *basically* comes from test. Having high testo levels will usually result in having high levels of DHT as well, so there's no real reason to clarify DHT as the "actual" culprit.

>>11374301
Yeah, I have it for other reasons. Just thought I may get two birds with one stone. I haven't the same faith in doctors as you but, these opinions come from personal experience. We all have our own.
>>11374333
I have theorized as much. Almost paradoxical. I guess the flame that burns twice as bright and all.
>>11374338
Interesting. I got pretty thin on top but not quite bald. It has remained stable for about 8 years. After going sterile from radiation treatment. I wonder if getting snipped would help some people.

Anyone knows where I can download the Feynman lectures I/II/III in ebook format?

I can't fucking bear reading that on a computer screen.

>>11374455
>where can I download an ebook
>but i dont want it on a computer
???

>>11374457
Reading tablet. Much nicer to the eyes.

>>11374345
>so there's no real reason to clarify DHT as the "actual" culprit.
It's a ratio, and it increases with age in favor of DHT.
While it does technically increase along with test, the ratio stays low if you're young

>>11374289
I think you could even have a more libertarian eugenics regime than that and still benefit humanity after a couple centuries. You could let most people procreate as they wish, and only exert selection effects on the margins. Because people on the margins mix with the general population every generation, this could still have a eugenic effect. For example, if I sterilized every violent criminal (like murder, rape, theft, assault, etc) the entire population would become less aggressive in subsequent generations, since under normal circumstances criminals sometimes reproduce after their crime. And even for the criminals, you wouldn't necessarily have to force sterilization on them- you could just offer it as an option in exchange for reducing their prison sentence by a couple years. Most of them would gladly take such an option.

>>11374289
It would change humanity, that's for sure.
It would also striate humanity, depending on the reach and severity of the program. Lower classes (think indian slums) would be ignored, high ranking politicians would pay to get through. The people in charge would use it as an outlet for their own biases. Much like the university system, it will become less about intelligence/genetic superiority, and more about who can afford to get in.
Basically, it would have the same major shortcomings as communism. Failure to account for abuses in power, centralization of power, and the necessity of world-wide acceptance (i.e. domination, repression of objectors) to succeed.

>>11374305
meant closure apparently so the question was asking for a closed ball, thanks for trying to help though.

>>11374639
Thanks for coming back to tell us what it meant.
May also help others down the line.

>>11372775
Someone asked that a while ago.
The best method we could come up with was solving by hand for enough values and doing trigonometric interpolation.
>>11373277
The set of the reals have a relation [math]x ~ R_a ~ y [/math] given by [math]x^2 = y^2[/math].
We can add in another relation [math]a ~ R_b
~ y [/math] given by [math]xy \geq 0[/math], from which we can conclude that, if [math]x ~ R_a ~ y[/math] and [math]x ~ R_b ~ y[/math], then [math]x=y[/math], so that, in a sense, the set of relations is capable of distinguishing between elements.
So if we have always have that [math]f(x) ~ R_b ~ g(x)[/math], then whenever [math]f(x) R_a g(x)[/math] we get [math]f(x) = g(x)[/math].
>>11373441
IIRC it did, but I'm not solving homological algebra problems without being paid for it.
>>11373533
I think y is supposed to be the radius.
>>11374455
libgen.is
And what do you mean ebook format, .epub? You might need to convert in Calibre.
>>11374639
Were you using [math]Cl(A)[/math] for the closure? Overline is genuinely the most common notation.

So this might be a pretty stupid question, but why don't we actually have flying cars? Is lifting a mass and keeping it suspended a few feet off the ground really that difficult? I'd presume you don't even have to overcome gravity most of the time, just match it in equal magnitude to stay hovering. Is the energy requirement for something like this just simply beyond us?

I guess bonus question: How would I calculate the needed energy to keep a mass suspended at a certain height for a certain amount of time in a gravity field? For this toy example, don't presume I'm burning fuel and losing mass or anything like that. I just want to know the energy required to oppose a gravitational field.

Why do electron shells have a tendency towards being either full, or empty? Why does a fluorine atom prefer to be in a covalent bonded pair rather than an individual atom? Why can't neutrinos form similar shells?

>>11373317
that was a simple explanation, thanks

>>11375226
>flying cars
Helicopters
>gravity
No energy is needed at all to keep a mass at a fixed height above the ground.
>>11375586
yw~

>>11374466
I'd love it if Apple came out with a phone that allowed you to switch it into this mode. Don't think they will, but eh

>>11363090
Pls help with proof.

Let [math]\mathbb{X} = \mathbb{R}^2[/math] and [math]d:\mathbb{X} \times \mathbb{X} \rightarrow \mathbb{R}[/math] such that:

[eqn]d(\boldsymbol{x} , \boldsymbol{y} ) = max \{ | x_1 - y_1 | , | x_2 - y_2 | \}[/eqn]

Prove that [math]d[/math] is a metric and the prove that [math]d[/math] is also a metric if [math]\mathbb{X} = \mathbb{R}^k[/math]

The first 2 conditions are easy, but the triangle inequality part is killing me.

Is there a general trick/mindset/intuition that helps with proving things are metrics? I dont struggle with shit that's supposed to be harder but proving metrics are in fact metrics eludes me.

>>11375270
Radicals are unstable, because radicals are magnets and magnets don't like to exist

>>11376186
Why though? Why does a smooth electron shell represent a state of lower potential energy compared to a bumpy one?

>>11373710
BUMP GODFUCKINGDAMMIT

>>11376095
It's extremely tedious but I can do it via casework. It's like the frog from Naruto says - "sorry it is so inelegant" haha

Consider the case d(x,z) = |x_1 - z_1|:

If d(x,y) = |x_1 - y_1| and d(y,z) = |y_1 - z_1| the result follows by the triangle inequality on the real line.

If d(x,y) = |x_1 - y_1| and d(y,z) = |y_2 - z_2|

then by definition of d(y,z): |y_2 - z_2| >= |y_1 -z_1| so that

d(x,y) + d(y,z) = |x_1 - y_1| + |y_2 - z_2| >= |x_1 - y_1| + |y_1 - z_1| >= |x_1 - z_1| = d(x,z).

The other cases use exactly the same method. The trick is to use the max property.

>>11376227
Because the kinetic part [math]\int_\Omega |\nabla \phi|^2 [/math] of the action [math]S[\phi][/math] describes the surface tension of a material defined by the scalar [math]\phi:\Omega \rightarrow \mathbb{R}[/math]; semiclassically we can treat [math]\phi[/math] as a "density" of the "electron probability material" over the shells [math]\Omega \cong S^2[/math] so that the strong EL [math]\Delta \phi = \hat{p}^2\phi = 0[/math] minimizes the surface tension by the maximum principle.
>>11376186
Unfilled shells have a non-zero spin [math]S_z \neq 0[/math], yes, but terms proportional to it do not enter the Hamiltonian unless something couples to it, such as spin-orbit coupling [math]S\cdot L[/math] or some external magnetic field [math]h \cdot S[/math], and these terms can actually reduce the energy when the ions are put on a lattice next to each other. So magnets defined as a collection of tightly-bound electrons [math]do[/math], in fact, like to exist.
>>11376095
Write [math]\max\{f,g\} = \frac{1}{2}(f+g+|f-g|)[/math].

>>11376333
Does this "surface" tension only apply to electrons, or does it also work on other fermions?

>>11376360
The scalar [math]\phi[/math] is only a semiclassical description of the coordinate sector [math]\phi(x) = \langle \phi|x\rangle[/math] of the electron state [math]|\phi\rangle[/math], so the surface tension analogy is strictly speaking independent of the statistics of the state. Fermions are in general sections of a spin bundle, so locally they consist of a spatial part [math]\phi \in C^\infty[/math] and a spinor part [math]\chi\in \operatorname{Cliff}[/math].

>>11376333
>So magnets defined as a collection of tightly-bound electrons do, in fact, like to exist.
You have to tighly bound them first, you dummy. If I press two north poles together really hard, to they attract?

>>11376377
It seems that you don't understand at all what tight-binding means, sweetie. Please read Ashcroft-Mermin before posting next time.

>>11374563
I guess any system gets upended by the rich. Communism, Capitalism, Socialism in the end you get the best life from being filthy rich and cheating the system, and in the end the poor range from sentenced to death to shitty lives depending on the system that then does apply to them.

>>11376375
If 10 neutrinos are pushed together, can they from something similar to a neon atom's electron shell and thus stay together? Or does the shell require the nucleus-electron attraction to form?

>>11376383
Crystals are not exactly simple structures, my dude. They can force all kinds of things to "minimize energy"

What is the intuition behind ring homomorphisms? For isomorphism it's easy, they're essentially the same ring, with different labels, but I don't really know what a homomorphism "means".

>>11376476
homomorphism is just an isomorphism without the "bijective" restriction - so i gues the only difference is the objects under question don't need to have the same size?

like you could represent the group of all invariant rotations of the triangle using the hexagonal rotation group ... but the two groups aren't isomorphic but one can be homomorphic to the other. is that the idea? algebra not really my strong suit sorry.

>>11363285

There should be a hyphen between "subgame" and "perfect," if that helps. I'm trying to lay off of wiki-holes for a while, though...

It looks tantalizingly interesting, and I'm pretty sure I'd spend the rest of my night reading about Nash-equilibria, and what differentiates pure-strategy from whatever alternative there is to it, and pretending there was such a thing as subgame-perfect equilbiria for as long as the narrator in my head could explain it before I had a question that could not be answered within the article, and thus began to search related articles, and eventually conclude that game theory itself is basically a thought-experiment where you have limited resources and a goal to accomplish, and the entire enterprise is based on the concept that competition is inherent in such a situation, which I've concluded every time I've delved into the subject.

All I need to know is that the Nash-equilibrium is a concept where "the optimal outcome of a game is where there is no incentive to deviate from their initial strategy" (https://www.investopedia.com/terms/n/nash-equilibrium.asp).).

That means it has no application in the world in which I live. I have no idea whether the people I know will stand by their claimed strategy, or whether they have an alternative one of which I am ignorant.

This is why game theory is a waste of time. Motives are subjective, and every player in every game has one.

>>11363799

I'm no biologist, but I'm pretty sure that they keep track of blood types for exactly that reason, so you don't wind up trying to infuse an incompatible one.

I think plasma is different, and you can donate that too, but you have to have really wide veins, so it seems more selective than just donating blood.

>>11364790

DNA = dioxyribose nucleic acid.

So you take a ribose (it's a carbon-based sugar, so one of the most common elements in the universe) and attach a couple of oxygen atoms (whose atomic number is 8, even though it needs a couple more electrons to become neutral with a full outer shell of 8 electrons, so its charge is -2).

Smash 'em together awhile and you'll inevitably get some form of DNA.

What it amounts to can wildly vary, though, so you should probably have some sort of kill-switch before you begin this experiment.

>>11364906

You've already done it. If your life was ended by a giant, incomprehensible being who was capable of things you essentially couldn't even imagine, you'd feel better knowing that even if it weren't able to tell you, it felt bad having to end your life like that, for whatever incomprehensible reason it had, right?

That's the best you can really hope for, now that the act has been done.

I mean, spiders are fucking creepy. It's not anymore your fault than it is theirs, and you're the one who has brooms and sticks and sprays and torches and whatnot, and the fact is that some of them have poison sacs that they inject into your skin with tiny fangs, so like what are you gonna do, interview the fucking thing?

Until better spider-human communication is established, I'd say that you are absolved.

Like, that whole "they're more scared of you than you are of them" line is sort of bullshit - I mean, that's sort of the problem, isn't it?

But you're a good human to feel bad about it, and I commend you. I feel bad about every spider or other arthropod I kill... but until I can communicate with them, you best believe I do not hesitate in eliminating their existence except in controlled environments.

>>11365026
>A full geometric characterization of the relation in terms of basic euclidean geometry

I'm not sure why people are calling you a fag-helper, nor why there's anything wrong with helping fags.

Like, who cares who's a fag unless you want to find out who else is a fag?

I'll help a fag any day, because I simply don't care. This is fucking science.

Helping a fag doesn't make you a fag, Chad. Wanting dick when you already have one makes you that.

Basic euclidean geometry exists in an ideal plane, though, and parallel lines don't exist outside of an imagined space in which two vectors of energy never intersect.

>>11365272

So, you seem to be making some claim - there are three terms: something multiplied by the square of another variable added to the product of a different thing multiplied by the square root of whatever second variable was squared in the first place, then added to a third and completely different variable, will produce a value which is greater than nothing [insert indiscriminate and nonsensical notation that implies some sort of multiplicand] and then you imply that based on whatever you said , the square of the first multiplicand of the second term in the original proposition subtracted from four times the product of the first multiplicand and the third (some call it a constant) variable would be greater than nothing.

If we could prove this for all x, then we would be able to prove that literally anything that exists, be it imaginary or not, is greater than nothing.

>>11376679

>the square of the first multiplicand of the second term in the original proposition subtracted from four times the product of the first multiplicand and the third (some call it a constant) variable would be greater than nothing.

> Less than

I don't know how anything is less than nothing, lol...

How much math does the average normie know? My knowledge stops at limits and derivatives.

>>11376331
This works, thanks.

>>11376333
>Write [math]max \{ f , g \} = \frac{1}{2} ( f + g + | f - g| )[/math]

Tried this and got nowhere :/

>>11366878
NOOOOO
what did you do...
this should be an easy proof by contraposition
First consider the discriminant to be zero or gfreater, then you can plug this into the Quadratic equation and you get an Solution where ax^2+bx+c=0 and you got your contradiction

>>11376701
about that much, maybe a little linear algebra and elementary analysis too depending on location

>>11376240
nvm

>>11376701
You expect absolutely nothing from normies, and they still manage to disappoint you.

>>11376701
>>11377262
>>11377769
now how much knowledge is enough for you to say about a person they aren't a normie? If it needs to be specialized, please give an example on topic you understand

How much may the Feynman Lectures books teach me?
If I read all three as an applied math student, what will I be missing from a physics BS at a decent uni?

>>11377941
Doesn't need to be specialized.
Frankly said, if a guy is able to differentiate [math]f(x)=x^2[/math] without an accident, he is already not normal anymore.
Most people don't ever see it in school, and those that do mostly forget about it after the exams.
I'm not suggesting there is anything wrong with that, mind you.

>>11377955
well, >>11377262 put the bar much higher

>>11377959
He is wrong.

I can only speak for Germany, but 50% of our adult population have never seen any analysis or algebra.
And another 40% never meet it again after high school (and are largely happy about that).