/SQT/ AKA /QTDDTOT/

10 years

Why is the entropy of the universe increasing? Are we gonna die when we reach thermodynamic equilibrium?

>>8677716

we're more than likely going to die off way before then, but I reckon the universe will have a cold death, yes.


Entropy is increasing because of the rate of expansion. Eventually all the stars will burn out, there won't be any hydrogen or helium gas left to burn, black holes will probably dominate until they also "burn out" and then we will just be left with a vacuum. Entropy will have reached its highest and final point, given there is no more matter remaining.

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>>8677722
I don't like this one bit, why can't magic be real.

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AAAAAAAA WHY IS LIBGEN DOWN NOW

>>8677743
its not

http://gen.lib.rus.ec/

>>8677745
have you tried searching for anything? The homepage itself is of no use

>>8677737

maybe it is and we just don't know how yet!

1000 years ago, flying through the air was magic.
100 years ago, having a playing card sized object that can recall any piece of information ever created while also being able to speak to someone on the other side of the planet with a similar playing card object was also considered magic


What kind of magic u lookin for buddy?

>>8677747
true it is down, but libgen doesn't host anything anyway, just look at the sites its indexes instead...
http://bookzz.org
http://libgen.io

>>8677754
Thanks anon

>>8677748
A way to reverse this process to be honest. The thought of not only humanity going extinct, but all of life isn't comforting.

>>8677778
Sad!

>>8677769

maybe we will figure out, 10,000 years in the future, how and why gravity works, how to create artificial gravity, and keep stuff "static" kinda.


won't solve the hydrogen problem, but maybe we will figure that out, too.

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How do I learn proofs?

>>8677870
memorize them
that's what I do.
I ask what proofs are gonna be on the test and just memorize those

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Should I use that Velleman's book?

is there any sensible notion of the image of a functor

does this extend to "higher" morphisms, like natural transformations?

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>missed the first two weeks of my precakc course
Is the material easy enough to recover from this?

>>8678033
>precalc courses
I never understood this meme. What kind of third world shithole allows kids to graduate high school without knowledge of precalc

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>>8678046
Good ol' burgerland.

Many people left highschool knowing no math beyond algebra or trig.

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I'm studying for a statistics midterm tomorrow, and I have a quick question: How the hell would you even begin to do Part b?

There was a similar problem I did a bit ago, where what you had to do was P(X > Y) = P(X - Y > 0), and because X and Y were normally distributed, you could integrate to find that probability. Here, though, it's a discrete probabiilty, so I'm not exactly sure what to do (What would X - Y even mean in this case? I'm thinking it's something like this: for f(X =1 , Y = 2), you would subtract the sum of all values for X = 1 by the sum of all values for Y = 2? )

I'm very lost

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On my homework we had this question on it, and I had to look up how to solve it because we just learned how to work with resistors yesterday and I really didn't know how to approach it. The answer seemed reliant on all nodes getting equal current or relied on symmetry. My question is what if the resistors all have different resistance, or if it isn't symmetrical?

Suppose V and W are subsets of a normed vector spaces, with [math]V \cap W = \{0\}[/math], and there are sequences [math]\{v_n\} \in V[/math], [math]\{w_n\} \in W[/math], such that [math]|v_n| \to \infty[/math] and [math]|w_n| \to \infty[/math]. Show [math] |v_n + w_n| \to \infty[/math].

>>8678316
Just add up all the probabilities where x>y. when x=1, the only situation is y=0, so .14
when x=2, the only situations are y=1 and y=0, so .04 and .02
for x=3, we have .03, .02, and .01
Adding them all together, and we have .26, which is less than .5
Intuitively you could explain that P(X>Y) and P(X<Y) cannot both be .5 because there is a probability that X=Y.

>>8678404
Math
https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

>>8678490
Doesnt seem true in general. Take your normed vector space to be the reals, V={n : n is natural including 0} W={-n: n is natural and 0} and v_n=n, w_n=-n

you have to learn the rules of the matrix.

ODE A+
Linear A+
Calc 3 A+

that's as far as I'm going to go because I'm an engineer.

>>8678490
>>8678590
I'm going to assume the problem is intended to be in terms of sub_spaces_ instead of subsets.

It seems like a more reasonable question and it would mean the sequences can't cancel each other entirely because they have some components going off in different directions.

If suddenly the Earth will be vanished from space, is there a case, then the Moon will fly right into the Sun?

What is R* in algebra?

>>8678654
space of rational numbers

>>8677706
Depends on your skill level. My teacher recommended a minimum of 10-20 hours a week not including class, but including homework. I spent roughly 8 hours and skimmed by with a B. If i spent 15 hours a week it would have been a cake walk.

>>8678657
Real numbers, surely. So you mean it's the same as R^3?

>>8678663
>When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol R3

https://en.wikipedia.org/wiki/Three-dimensional_space

How does one study Discrete Mathematics?

what the fuck is sleeping
like why do we have to be comatose and have vivid hallucinations for 8 hours a day

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Woah! Look at this math trick /sci/! Literally made my life 100x easier!

What kind of GENIUS could EVER think of that?

https://www.reddit.com/r/AskReddit/comments/5u9y0a/what_are_the_most_useful_mental_math_tricks/ddsg6x5/

>>8678654
Depends on the context.
Could be the extended reals.
The real complex numbers etc.

>>8678805
Which part

Prove 11^(n+1)+12^(2n−1) is divisible by 19 for n being an integer equal or larger than 1... This is via induction I'm stuck with trying to figure out how to factor P(n+1) in terms of P(n) + some multiple of 19

>>8678889
Hey I think I did something, but I'm not yet educated in the subject so pls don't bash me

x(n+1)=11[x(n)-12^(2n-1)]+12(2n+1)
if x(n) = 19k
x(n+1)=11[19k-12^(2n-1)]+12(2n+1)
x(n+1)=11.19k-12^(2n-1).11+12(2n+1)
-12^(2n-1).11+12(2n+1) = 12^(2n-1)[-11+144]
12^(2n-1)[-11+144]=19.7.12^(2n-1)

x(n+1)=11.19k+19.7.12^(2n-1)
Therefore X(n+1) is divisible by 19 if X(n) is divisible by 19

>>8678869
Basic proving, set theory, number theory

>>8678900
the first line (although not exactly correct for my question) put me on the right track! Thanks for it!

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If suddenly the Earth will be vanished from space, is there a case, then the Moon will fly right into the Sun?

>>8678962

gravity is not instantaneous, just like the speed of light. however, the moon would probably not fly right into the sun, it would more than likely move in an ellipses

So I'm trying to prove whether
[math]\int{0}^{\infty} \frac{x}{x^3 + 1}dx[/math] converges or diverges. I've tried splitting this up into
[math]\int{0}^{1} \frac{x}{x^3 + 1}dx + \int{1}^{\infty} \frac{x}{x^3 + 1}dx[/math]
and then evaluating the second integral.
[math]\frac{x}{x^2 + 1} \geq \frac{x}{x^3 + 1}[/math] for [math]x \geq 1[/math]
Using u-sub, [math]\int{1}^{\infty} \frac{x}{x^2 + 1} = \frac{1}{2} \int{1}^{\infty} \frac{1}{u}du = \frac{1}{2} = \frac{1}{2} \ln \left x^2 + 1 \right = \frac{1}{2} \left \ln \infty - \ln 2 \right = \infty[/math]
Therefore, by the Comparison Theorem, since this diverges, the original function should diverge too. But the book says it converges. What exactly am I doing wrong?

So I got this ODE:

[eqn] t^2y^{\prime} + 2ty - y^{3} = 0 [/eqn]

So I divide by [math]y^{n}[/math] and make the substituion:
[eqn]v = \frac{1}{y^{2}} \implies v^{\prime} = -\frac{2y^{\prime}}{y^{3}} [/eqn]

to get:

[eqn]-\frac{1}{2}t^{2}v^{\prime} +2tv = 1[/eqn]

I try to write this in: [math] y^{\prime} + p(t)y(t) = q(t) [/math] to get

[eqn] v^{\prime} - \frac{4}{t}v = \frac{2}{t^{2}} [/eqn]

But my solution is not correct after applying integrating factor. Where did I go wrong?

>>8680044
No, th

Are there any /sci/ approved guides for error propagation/analysis? I've think I've been told a ton of retarded ways by different lecturers throughout uni. Whats the standard?

>>8679284
>Therefore, by the Comparison Theorem, since this diverges, the original function should diverge too.
wrong

>>8680056
Why?

>>8680073
go read what the comparison theorem says

>>8680075
For a continuous function f(x), if a function g(x) >= f(x) for x >= a, if
[math]\int_{a}^{\infty} g(x) dx[/math]
is converging/diverging, then
[math]\int_{a}^{\infty} f(x) dx[/math]
is converging/diverging, respectively

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>>8677706
How did this author go from the component values, to the substitution on the next step?

>>8680115
you wrote it down wrong

read the correct statement of the theorem here
http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegralsCompTest.aspx

>>8680115
You need to do a sanity check here. That's not what the comparison theorem says.

Saying f <= g when g diverges doesn't mean anything. You're just saying the integral of f is less than or equal to infinity.

>>8680117
>Solving the first of these equations for |T_2| and substituting into the second

>>8680131
ty all I needed was someone else to greentext it to me, got it now

don't know why I'm like this

>>8678033
Do the assigned homework, whenever you get stuck watch a video on it ( not khan academy though fuck that pajeet.) if still doesn't come naturally to you work even more problems. If you can't focus do your work in the library.

>>8677858
>won't solve the hydrogen problem, but maybe we will figure that out, too
easy; we'll break some alpha particles to free the protons
of course, one day protons might start decaying; then we'll be fucked

>>8680160

yeah we'll just fix that too. in 10,000 years, we actually create atoms better than the atoms we have now. Protons, neutrons, and electrons all become obsolete for the Omnitron, which will do anything.

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>>8680166
>jumbonium will one day be real
god bless

>>8680171

When you think about it, there really is no reason that this isn't possible for the future. We cannot predict what insane discoveries we will have, and when. Like I mentioned earlier, flying was IMPOSSIBLE for all of humanity until just a few years ago. Putting a person on the fucking MOON would blow the mind of Newton, much less the philosophers and physicists of 2000 years prior.


Imagine what, in 5 times the span between Aristotle and now, we can discover. We [humanity] are going to consider ourselves [current day you and me shitposting] pure brainlet retards who know fuck about nothing.

>>8678006

You can define image of a functor F in the same way as you would in Set or any other category: as the universal arrow factoring through F. This gives a monic arrow that can be identified with the subcategory that is its image.

>>8677706
Are subtraction, multiplication, and division just snobby forms of addition?

>>8680265
>as the universal arrow factoring through F
(if it exists)

>>8678654

The multiplicative subgroup of R, i.e. R \ {0}.

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What's the proper method to solve this problem?

>>8680328
a line can be specified by a point and a direction

so (1,0,6) is the point and the direction should be perpendicular to the plane, i.e. given by the normal vector of the plane which is (1,3,1)

so the line is (1,0,6)+t(1,3,1)

Define a sequence by:
[math]a_1=2; a_n=2^{a_n}-1[/math]
Is it possible that the sequence is only primes?

>>8680347
do you mean a_n= 2^(a_{n-1}) - 1?

>>8680356
I do indeed. Turns out its an open problem, I didn't realise.

https://en.wikipedia.org/wiki/Double_Mersenne_number#Catalan.E2.80.93Mersenne_number_conjecture

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G-g-guys can you please help a brainlet with this differential calculus question. Have I d-d-done it right?

P1 of 5.

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P2 of 5

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P3 of 5

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P4 of 5

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P5 of 5.

I could have fitted it all onto 1 page, but I thought it would be easier for you guys to follow with some working out.

Please help.

>>8680444
>>8680446
I'm gonna simplify S a bit to make it easier, because using the quotient rule when there is only a constant on the bottom is not just a waste of time, but its absolutely unnecessary and annoying especially when asking someone to check your work.
S=9*(100-20L+L^2)/4pi+sqrt(3)L^2/4
S=(900-180L+9L^2+sqrt(3)piL^2)/4pi
dS/dL=(-180+2(9+sqrt(3)pi)L)/4pi=0
-180+2(9+sqrt(3)pi)L=0
2(9+sqrt(3)pi)L=180
(9+sqrt(3)pi)L=90
L=90/(9+sqrt(3)pi)
So you're good.

>>8680466
I'm sorry for that, it's how I was taught to do it.

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>>8680466
And thank you!!!
>mfw I got it right

>>8680477
I never use quotient rule, it's a waste of time memorizing it. Instead, if I have a fraction, I convert it to negative exponents and use the product rule. Alternatively, you could just put a 1/(4pi) on the top to replace the 4pi on the bottom. It's just a constant, so when you take the derivative you can forget about it until the end. It may seem like nitpicking, but when you're taking an exam and using the quotient rule in this manner you are wasting energy and time. Keep practicing, and strive for efficiency.

>>8680283
Yes

>>8677722
matter can't be destroyed. dummy

>>8680265
my bad, it's actually the universe monic (or regular monic etc.) factoring through F:

https://ncatlab.org/nlab/show/image

>>8680285
fite me

>>8681214

who said matter was being destroyed? space will be so spread out that there will be a cold death. no one said anything about matter being destroyed, the energy will be dissipated.


try to read what i said first, doofus. in fact, the "cold death via entropy" theory is the least controversial idea in this thread

bump because the other one hit the bump limit

Best way to correctly teach myself Algebra in a few months?

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>>8681419
baby high school algebra?

http://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/algebra_gelfand.pdf

>>8681419
skip everything and just go straight to spivak out of the womb

thats how u separate the brainlets from the real ogs

>>8681419
>https://archive.org/details/ElementsOfAlgebraLeonhardEuler2015

>"Read Euler, read Euler! He is the master of us all!" ~ Laplace
>"The study of Euler's works remains the best instruction in the various areas of mathematics and can be replaced by no other." ~ Gauss

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How do I calculate the required portion of x if I'm given a percentage of what it needs to be?

For example, let's say I'm mixing colors together, and can only mix them in 20/80 portions. Let's say I want to mix 20% of Red with 80% of Blue, and that I have 30ml of Red. How do I calculate how much Blue I need such that the total ml (when both colors are dumped into a container) reflects a ratio of 20 Red:80 Blue?

>>8677716
Equilibrium is not an end point. It is when the forward and reverse reactions product amounts are equal

Can you not plot an ellipse in polar coordinates? When I try in cartesian, it turns out fine, but in polar it becomes a weird peanut shape. How do I do it?

>>8677706
How is that cat alive with only 2 legs?

>>8681694
I only have 2 legs and I've been doing just fine.

How does a commutator reverse the direction of the current in a DC motor? I know what the commutator does, I just can't seem to get my head around how it actually does it.

>>8681448

Euler had no taste. He just messed around with stuff until he stumbled across something.

I need help understanding this statement:

"All groups of prime order are cyclic"

We just learned Lagrange's theorem, which I understand. Does this mean every single non-identity element is the generator? Also, why does <a> have to be a group? Can't an element generate a sequence that isn't a group?

>>8682350
>Does this mean every single non-identity element is the generator?
Obviously you only need one at a time, but yes.

>Also, why does <a> have to be a group? Can't an element generate a sequence that isn't a group?
<a> is not the set of all things you get by applying the group operation to a over and over.
The subgroup generated by a is defined the smallest subgroup of G that contains a.

This is where Lagrange's theorem comes in, since |G| has no divisors this subgroup has to have order |G| (provided you don't be a goober and pick a to be the identity, but |G|>=2 so you aren't forced to do that)

>>8682410
>The subgroup generated by a is defined the smallest subgroup of G that contains a.

Yes and it will be isomorphic to Z/kZ for some k via exponentiation (a^(x + y) = a^x a^y).

>>8678654
usually >>8680288
or the R+{+- infinity}

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>>8682410
><a> is not the set of all things you get by applying the group operation to a over and over.

See pic related from my book... it's exactly that. It also says it is what you say it is--The subgroup generated by a is defined the smallest subgroup of G that contains a.

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>>8677706
The Bogdanoffs are rumored to have mastered linear algebra in minutes.

>>8678490
Maybe look at v_n/|v_n| and similar for w. Two Sequences on unit ball and in distinct sub spaces. Show lim inf of pairwise elements is positive? Otherwise they wouldn't be closed subspaces? Then just rescale.

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I'm shitting the bed in my probability class sci. I don't know how to set up equations for permutations and combinations and I'm struggling with the hard conditional probability questions. Does anyone have good online resources that can help me?

Is it possible to drown a tectonic plate into the magma layer by putting enough weight onto it? If so how much would it take.

>>8683314
>applying the group operation to a over and over

be careful, in a finite group, yes this is <a>

how would you get a^-1 (= -a) in Z by doing this? a+a+a+...+a =/= -a

>>8683824
>If so how much would it take.
A little bit more than the weight of the pleight.

Anybody know anything about Freudian slips that are lies?

>be me
>having group conversation about sex
>not really paying attention
>someone asks me a question
>"I've never had sex with a girl before"
>they think I slipped and that I've never actually had sex or I'm gay

I've had sex with 3 girls previously at the time I said that. Can't find anything on Google anymore. Anybody know anything about this?

Can anyone help me with this intro OChem problem?

Complete the following reaction:
1,2-dibromobutane + zinc --> ...

Thanks in advance!

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how do these two exercies differ?

why is one yes and the other no

description is: determine which sets are bases for r^2 or r^3.

>>8684171
So is it safe to say a^k is always a subgroup in finite groups?

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I'm going to self-taught some math before I go back to college and I'll be following this guide list from the /sci/ wiki. Any recommendations for a intro to proof book?

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Is the notation acceptable here, or should I show more working out?

>>8684842
either a typo or you're not telling us the right questions

>>8684883
a^k is a single group element, not a subgroup (unless k=0 and the subgroup is trivial)

>>8684973
intro to proof books are a meme

study an actual subject instead and learn your proofs by reading and doing real proofs

>>8681488
30/x = 20/100
x = 150

y/150 = 80/100 or 150/150 - 30/150 = y
y = 120

>>8685214
should probably include the integral before you've actually integrated, otherwise you've made it seem like your integral is equal to your differential.

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>>8685347
Is pic related better?

>>8685464
ur 'x' 's are fucking cancer

>>8678939
try reading rosens discrete math book, its not the best but it gets the job done, the proofs are a bit lacking

>>8685464
You changed nothing. Look at your second and third lines.
sin(x)+3/x=-cos(x)+3ln(x)
Is this true? No. You need to put an integral in front of the sin(x)+3/x in order for that statement to be true. Also, you don't add c until after integrating.
sin(x)+3/x+c integrates to -cos(x)+3ln(x)+cx+d.

>>8677706
I oopsidentalied myself into taking the red pill.

>>8685533

it's how the british do x's, it is markedly inferior to the american convention.

>>8685574
I'm not sure what you mean. We are currently denoting an integral of a function by the capital version of the function since we haven't covered integral notation yet. For example an integral of a function g has to be denoted by G.
>>8685533
They are usually neater, I wrote this stuff down as fast as possible.

>>8677722
>>8677737
>the expansion of the universe slows as the momentum of the Big Bang dies down
>then stops entirely
>then all the matter in the universe begins to drift back towards each other
>then accelerates until everything is condensed into one gargantuan mass again
>this mass is unstable and a new Big Bang happens
>this has already happened an infinite number of times
find a flaw

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How do I do, sci?

>>8686034
the only way you could not get this after seeing this picture is by being a massive brainlet

>>8685636
>We are currently denoting an integral of a function by the capital version of the function
Alright, then why did you put capital F(x)=sin(x)+3/x+c? You already denoted this to be lowercase f(x).

>>8686072
Oh my mistake, did I ask my question in the "math phd question thread" or the "stupid question thread"? Yes I know it's an easy question and I'm aware that I'm a retard, that's why I'm asking in the stupid question thread you fucking faggot

>>8677777

>>8666666

>>8686034
>>8686072

I don't know what that is, haven't come across it yet. Just finished with differentiation.

>>8686074
I want to show some of the working out. I will lose marks if I don't show some intermediate steps.

[math] (P \Rightarrow Q) \Rightarrow ( \neg P \vee Q) [/math]

Is there a name for this?

>>8686527
https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)

>>8686543
thank you

Why don't we have something equivalent to like, soylent green?

Nutrient paste, or the like. It seems like humanity at this point in time would be really receptive to something like that.

>>8686570
people like eating
either way:
http://lmgtfy.com/?q=soylent

>>8686034
15?

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>>8677876
Velleman's book is an excellent primer. Then diving into technical texts (eg something like rudin or munkres) will fill in the rest.

It's just another mathematical method that you get better at with practice. Just keep pushing.

I am reading an introductory textbook on analysis and I was just presented Cantor's diagonal argument and then was asked to show counter arguments to some complaints people had about this proof.

1) Every rational number has a decimal expansion so we could apply this
same argument to show that the set of rational numbers between 0 and 1 is uncountable.
However, because we know that any subset of Q must be countable,
the proof of Theorem 1.5.1 must be flawed.

Here my counter argument is that by the way x is defined (x being the number taking 2's and 3's based on the digits in the diagonal of the list), x is an irrational number and therefore need not be in a list of rational numbers.

And

2) A few numbers have two different decimal representations. Specifically,
any decimal expansion that terminates can also be written with repeating 9’s.
For instance, 1/2 can be written as .5 or as .4999 ... . Doesn’t this cause some
problems?

My counter argument is that we could restrict ourselves to using only one decimal representation and the argument would still work.

Am I right in both? Or what?

Also, where mathematicians really these fucking retarded back in the day? Like holy shit. If I am correct, then the mathematicians who originally created these complaints are some top brainlets.

>>8686725
1.decimal expansions of rationals either terminate or repeat
2.there are many decimal expansions without the digit 9/without the digit 0

use these facts to make counterarguments

>>8685968
How do you know it has happened an infinite number of times?

>>8686345
Oh my god. You're fucking stupid mate

if a function takes 2 values a,b and outputs 3 value xy is this how you express it mathematically?

[eqn]f(a,b) = (x,y)[/eqn]

or maybe

[eqn]f(a,b) = [x,y]^T[/eqn]

>>8687006
It depends what the image of the function is.
If it is the R^n the transponent of your first example is pretty common.

Although it is mostly irrelevant because after you stated the domain and image of your function it should be obvious what you mean.

This is how I commonly see it used:
[math]f:R^n\rightarrow R^m [/math]
[math]f((x_1,...,x_n)^T)=(y_1,...,y_m)^T[/math]

>>8687016
the function is [math] f:\mathcal{R}^2 \to \mathcal{R}^2 [/math].

Is it not alright to use [math]f(a,b) = (x,y)[/math] without transposing? It looks a bit cumbersome with all the superscript T

>>8677706
is it unethical to upload extra cheat sheet-esque programs onto your calculator for exams?

>>8687022
You can leave the ^T, it really doesnt matter.
Unless you are doing something where the meaning isnt obvious.

Although I think that you should rather use:
[math]f:R^2\rightarrow R^2 [/math]
[math]f((a,b))=(x,y)[/math]

f maps one vector to another so it only gets one input parameter which is the vector (a,b).

This would be diffent if you instead defined the function. (Although RxR is R^2 here you make clear that both input parameters are really seperate)
[math]f:R\times R\rightarrow R^2 [/math]
[math]f(a,b)=(x,y)[/math]

>>8687034
> you make clear that both input parameters are really seperate

Hmmm, what do you mean the parameters are separate? Like semantically independent? Or probabilistically independent? Separated in any mathematical way?

>>8687036
I just meant that the function really gets 2 parameters from potentially different sets and not 1 parameter which is a 2 dimensional vector.


You can look at this:
[math]f:R\times C^1\rightarrow R^2 [/math] (C^1 is the set of coniunous functions)
[math]f(a,b)=(x,y)[/math]
here it is neccesarry to a make clear that f gets 2 different parameters from 2 different sets.

This:
[math]f((a,b))=(x,y)[/math]
doesnt make sense because the parameter of the function is not a vector but it really takes 2 parameters which are from different sets.

>>8687059
I see what you mean thanks m8

>>8687063
no problem

so electric flux density [math] \phi = \int D.da [/math]

I don't understand the integral. Is this a surface integral? Or is it an integral with respect the rate of change of the surface or what? This is explained very poorly by my textbook

>>8687203
sorry, flux, not flux density. D is flux density

What's more important, money or love?
I have the chance to move to America and be with my honey, or stay here and do my master's degree. I don't know what to do. I cannot combine them because students fees are too high in America, and if i stay here, it would be the end of the relationship

>>8687388
Either get a scholarship and study in America or finish your Master's and find someone else later. Also, in UK Master's are only one year and if your girl can't wait one year (or even 2) then she's obviously not in it for the long run so there's no point in making sacrifices rn

>>8685225
Forgot angle brackets. Is <a^k> always a subgroup in finite groups?

>>8687492
yes, and even in infinite groups

>>8687029
>is it unethical to upload extra cheat sheet-esque programs onto your calculator for exams?
only if you get caught

>>8687203
>>8687224
p-please /sci/

>>8687388
If shes going to leave you for furthering your education, bettering yourself and your future, she can fuck off. Leave her, focus on yourself, and eventually you will be in the position to settle down.

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I have been trying to figure this out for like 40 minutes and I can't

How do you get the approximations ? I can't find any formula or explanation

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>>8686796
we don't

but it's impossible to know

you just have to believe in the metaphysics

>>8678046
As of right now, I'm going to graduate high school with only knowledge of basic Geometry.

t. burgerland

>>8687618
you're just supposed to pretend dx is 0.3, 0.15, 0.075, 0.0375 and work your way up to 0.3 and 0.6

>>8687834
to elaborate I think you're supposed to do this

>y0 = 1
>y1 = y0 + y(t1-t0)
>y2 = y0 + y(t2-t1)
>...

for delta t = 0.3 the approximation at 0.3 would then be y1 and the approximation at 0.6 would be y2

for t = 0.15 you'd have to go up to y4, for t = 0.075 to y8 and for 0.0375 you'd have to go up to y16, step by step

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Can anyone give me a little push?

I'm pretty sure it has something to do with the fact that a selection of 3 students can have at most 246 people marked as a no, but I'm not sure how it connects.

>>8686796
well, if time stops and restarts, is it really even possible to count one thing happening after the other? It's not happened 3 times in a row or whatever, given that each one resets time itself. So logically it has happened infinitely

>>8687994
https://en.wikipedia.org/wiki/Tur%C3%A1n%27s_theorem

>>8687994
btw what class is this?

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i need saving. the problem i'm trying to solve goes like this.

an object is thrown from the surface of a celestial body with no atmosphere.
the trajectory is suborbital, and will collide again with the celestial body.
the trajectory is an elliptical orbit.
all classic orbital parameters are provided.
solutions in any coordinate system are valid.

find the general equation for the first derivative of the vector angle between the object's position vector and the object's velocity vector with respect to time.

[spoiler]i'm using it for a game.[/spoiler]

What is the point of QR factorization?

What is the point of linear algebra anyway? (Brainlet chemistry student, have to take intro to lin-alg, unsure why)

>>8688182
>>8688184
I appreciate this answer, but we haven't discussed graph theory in class yet, so I'm gonna keep looking for a method of solving this without Turan's.

This is for a Discrete Math course.

>>8688234
>what is the point of linear algebra
Literally everything has linear algebra applications. Economics, engineering, physics, graph theory, cryptography (lattices), many cs algorithms, the list goes on and on. Besides like women's studies or some bullshit.

Applications to chem: http://aix1.uottawa.ca/~jkhoury/chemistry.htm

Admittedly this is kind of a weak application since it's just solving a system of linear equations, but I'm sure there are others. I don't know shit about chem though.

Physics question:

"At what point does a skier on a frictionless (circular) snowball skiing down the side lose contact and fly off at a tangent?"

I got 90° because you lose contact with something, your normal force is zero, and the normal force's magnitude is equal to |F_g| cos(theta), where theta is the angle between the center of the snowball and the person skiing, and |F_n| == 0 when cos(theta) == 0, so theta == 90°, right? Or am I just not understanding this?

>>8688527
>I got 90°
The answer would only be 90° if the skier had zero speed.

>>8688553
They say the skiier starts of with "very small initial speed"

>>8688566
Yes, but they'll accelerate as they slide down the side.

>>8688594
Alright... I figured the problem wouldn't be this easy... Would I need to find the point at which the instantaneous velocity is greater than (V^2/R), the centripetal acceleration?

I'm kind of lost, so I might just go to office hours tomorrow

Why, geometrically, is the dot product of perpendicular vectors 0?


If I have two vectors, b and a, let's say a is parallel to the x axis, b is at a 45 degree angle to it. I'm safe to understand the Dot Product as the sum of the magnitudes in the x direction, correct? It is not only the projection of b onto a.


Why then, is it zero in the case where it's cos90? I understand cos90=0, but there could still be magnitude in the x direction.

>>8688636
The projection explanation is the more correct way for understanding this case, as when two vectors are perpendicular, neither vector has components in the direction of the other vector.

If
\vec{v} = i\\
\vec{u} = j

There's no component of v in u's direction and vice-versa, so the projection of one vector onto another is zero, so the dot product is zero (you could also think of it this way, if two 2-D vectors are perpendicular, you could rotate both of them in such a way that they're aligned with the x-y axes, which have no component in the other axis' direction)

Is there a way I can pull an all nighter without feeling tired or breaking out in acne?

When I sleep it seems to heal my skin, pimples just disappear overnight as if sleep deprivation is the cause, I may need to do an all nighter or 2 with an exam being tomorrow and another the next day, I need to at least last until 2 PM tomorrow, any tips?

Will coffee really work? Just drink a shipload?

>>8688691
>shipload

lol no but if you're pulling an allnighter, you irreversibly have fucked up already. One way or another you're going to have to tough it out, either your body and mind or your GPA..

just use your time wisely and learn form your mistakes, whatever they may have been, young grasshopper

>>8688723
plus 5 hour energies and music like IDM Future Sounds of London or something usually do the trick for me :)

I have an urn with 8 black and 10 white balls in it. I reach in and take one ball to check its colour before putting it back in the urn, I do this seven times total.
What's the probability of me getting 4 black balls in total?
I get it to 0.223 but the key says 0.23.
Am I doing something wrong or is it a rounding error in the key?

>>8688763
howd you get 0.223?

>>8688527
I will give you a hint. Use the potential energy to solve the speed for y. Then look for the angle where the normal force is equal to the centripetal force.

>>8688784
How'd you not get 0.223?
(nCr(20,7))/(nCr(24,7))

>>8688763
7nCr4 * P(b)^4 * P(w)^3 = 0.234

>>8688805
That just describes the chance of getting 4 black in a row, followed by 3 white.
The order doesn't matter as long as there's 4 black balls.
>>8688806
Could you describe it more in depth?

>>8688810
Binomial expansion:
[math](x+y)^n=\sum _{r=0}^n\begin{pmatrix}n\\ r\end{pmatrix}x^{n-r}y^r\:[/math]
Where the coloumn vector is the nCr. Then you let x = probability of getting black and y = probability of getting white.

For a specific combination of black or white like b = 4 after 7 attempts you just look at the term of r = 4 and n = 7

>>8688813
Thanks.

>>8688203
There isn't a closed-form expression for the eccentric anomaly E as a function of time; you have to solve Kepler's equation, M=E-e*sin(E) numerically. M is the mean anomaly which is just (2*pi/period)*t, i.e. the angle which you'd get from a circular orbit of the same period, and e is the eccentricity

Once you have E, the position in Cartesian coordinates is just x=a*(cos(E)-e), y=b*sin(E) where x and y are the semi-major and semi-minor axes. You can differentiate that using the chain rule and dE/dt = (dM/dt) / (1-cos(E)) to get the velocity.

The angle between them can then be found from the cross product: |UxV|=|U|*|V|*sin(theta) => sin(theta)=|UxV|/(|U|*|V|)

There are other approaches, but they all start with a numerical (e.g. Netwon-Raphson) solution of Kepler's equation to find E from M.

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What is up my dudes

Organic chemist here, I've just finished my fourth year doing an honours in med. chem and my PhD APA application was rejected. One of the more jaded post-docs in my lab reckons that they did me a favour.

Should I make the jump to pharmacy. all I need are three more 1st year units and i'll be able to enrol in an M.Pharm. which would hopefully lead to a job.

I love my current field but the thought of having my dick in a test tube 70 hours a week for the next four years to graduate with next to no job prospects is getting me down.

Any advice from someone who's been there/done that

>sorry for my diary desu

>>8684680
http://pubs.acs.org/doi/abs/10.1021/jo01265a091

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>>8688905
yep this solved it thanks boss!
it was for an algorithm that steps through time ascents and curves through an atmosphere. i made a drag table and so at any given time i know position and velocity and the forces acting on the vessel. and with your help now i can estimate the rate of change of flight angles at each step so i know where the next position will be and its flight angle (ish)!

i've yet to implement it, but i believe this is the best programmatic solution to the atmospheric gravity turn problem i can think of for keplerian mechanics.

>>8688929
>getting rejected from PhD programs

justbrainletthings

>>8685968
entropy wouldn't be reset on each cycle

>>8677706

Can you represent a 3d line defined by 2 points as

[math]
point = (p1-p2)t + p1
[/math]

>>8689541
You mean a line segment between two points? [math]S=(p1-p2)t+p1(1-t)[/math] is what you want.

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What's this question asking?

I'm guessing that for the denominator,
[math]
\frac{\partial}{\partial\theta}
[/math]
We would be differentiating f_x(X) with respect to X (Because X is the parameter?)

Or is this just completely wrong?

>>8677743
Also check out bookzz

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>>8689685
My bad... forgot to upload a picture

Is it a good idea to take Matrix Algebra and Intro to Differential Equations in the same quarter?

>>8690439
Is there anything more to this problem? I don't think it's asking anything, just making statements.
>We would be differentiating f_x(X) with respect to X (Because X is the parameter?)
I'm not sure, I'm not very familiar with any of this. But if x is a function of theta, then the derivative reduces to (1/f)*(df/dx)*(dx/dtheta). Good luck.

>>8689435
ur right 2bh

Does anybody know of any good resources for population genetics? Not intro stuff. I need fourth year material. I have an assignment due next week and my professor is probably going to be fucking his wife for this entire week (university holiday).

>>8680115

no its not always, lets say you have 1/(x - e^-x ) with 3 to inf integral. you are trying to find if it converges or diverges. consider 1/x from 3 to inf. it diverges (because as u increase the x in 1/x and add it continuously it becomes larger, very slowly (Diverging). you compare 1/(x-e^-x) to 1/x. 1/x - e^-x becomes larger at equal values of x than 1/x. therefore since the current function is greater than the function you compared to (1/x) youcan say it diverges.

Anyone have a book recommendation for combinatorics? I don't need anything too advanced - undergrad level would be good.

Some topics we covered in class (we don't have a book and I'd like one for studying): combinations, permutations, stars and bars, burnside's lemma, stirling numbers, catalan numbers, isomorphisms, partitions, 12fold way.

Thanks in advance!

>>8690705
harris, hirst and mossinghoff - combinatorics and graph theory

When constructing regular expressions for automatons, how would a non-deterministic transition be represented?

E.G. {q0, 0, q0}, {q0, 1, q0} and {q0, 0, q1},
Would this be represented as (0+1)0?
I'm not sure if q0 could take (0+1)* because 0 also goes to q1?

>>8689541
The segment can be represented as
(p1-p2)*t + p1
or alternatively as
p1*(1-t) + p2*t
Or using barycentric coordinates
p1*s + p2*t where s+t=1

3D lines (rather than segments) are often represented using Plücker coordinates, which represents the line as <p2-p1,p2xp1> (difference and cross-product, 2 vectors, 6 scalars).

>>8691344
cba to give a long explanation, but you can do as many 0s and 1s as you want before being forced to go through a 0 to q1

so (0+1)*0

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Can anybody give me an idea on how to do the second part of this question? I don't really have any idea what I'm supposed to do with the majority of the hint given.

>>8691517
Oh, and the bit that is cut off just says 'the conjugacy classes'.

When removing epsilon transitions from an FSA, it records (e*w) where e* are any number of epsilons and w is an element from the alphabet.
Do you record what state the FSA is in AFTER taking w, or before?
So for example if q0 takes an e and goes to q1, and then q1 can take an a and go to q2. Would you record q0 (before taking a, but showing that it CAN take an a) or q2 (showing the state it's in AFTER taking an a)?

>>8691478
Also thanks.

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If converting hexadecimal numbers to decimal numbers is giving me a headache, should I give up on going for computer science ?

What, exactly, is an integral?

>>8691517
what are you confused by?

>>8691907
you literally just multiply the digits by powers of 16

I'm sure these are common/easy questions, but just for safety:

x±y*0=x
x±y=x/0

Does this work? Is this another reason why x/0 is undefined?

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>>8677716
maybe

science doesn't offer a solution to the problem eitherway

test

>>8693193
ok why does [math]\frac{2\ \cdot \tfrac{d}{dx}[x]}{2x}[/math] no simplify to [math]\frac{2}{2x} = > x[/math]

>>8693201
because 2/(2x)=1/x

Russell's paradox tells us some things we might hope are sets aren't actually sets

This is because we get a very straightforward logical contradiction by asking whether the set of all sets contain itself.

But what about other collections we might hope are sets that don't have such immediately reachable contradictions? How does one formally check that a given description of elements actually gives a set? Might it be very difficult to show something isn't a set?

is near future AI singularity a meme?

Is this ranking correct?

Eutocius > Apollonius > Pythagoras > Euclid > Archimedes > Eudoxus >>>>>>>>>>>>>>>>>>>>>>>>>> Eratosthenes

>>8693328
this is not a stupid question at all. i think it is safe to say that most working mathematicians with the exception of logicians will routinely ignore this question and happily treat all such collections as though they were sets. i'm not sure whether there is some algorithm to check whether a class (this is the formal term for "something that may or may not be a set") is actually a set (if it's not a set, it's called a "proper class"). also, while the collection of all groups (say) may not be a set, it turns out that the set of all homomorphisms Func(G,H) from one group G to another H actually IS a set (this also holds for many other structures like sets, rings, etc.). said another way, groups form a "locally small category", and category theorists claim that this property allows one to bypass most of the problems associated with russell's paradox in practice (i'm not entirely clear on the details here).

>>8691932
It is basically a better sum.
While derivivatives are about giving 0/0 a sense Inegrals are about giving 0*infinity a sense.

But there are many, many differnet integrals, from Rieman to lebsgue, even integrals on manifolds or paths over a k-form.

>>8677706
Wat happen to ket?

Okey /sci/ tell me. Should I do double major in math and physics, or apply fpr an intenational exchange program?

>>8693559
Also
>Why not both?
My uni doesn't allow it

I have R^2 vector space and two vectors A: (1, 2) and B: (3, 4). I need to define a scalar product so the vectors (1, 2) and (3, 4) are perpendicular to each other.

So far I've tried shifting B to (2, -1) which is perpendicular to A by defining the dot product as <(x1, x2), (y1, y2)> = x1*2/3*y1 + x2*-1/4*y2 but that violates the <x, x> >= rule.

Any ideas? I feel this is either completely trivial or it's almost impossible to solve and the prof is just fucking with me.

>>8693625
I havent thought this through, but have you tried just finding a gramian matrix such that the 2 vectors are orthogonal?

You need to find a symetric positiv definite matrix such that (1,2)^t*G*(3,4)=0.

This would (I believe) give you a fitting skalar product.

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What are those equations called?

What is a polynomial ring?

>>8693701
a ring of polynomials

Can you define "red pill" in this context please?

>>8693625
I don't remember the rules required for scalar product but can't you just let a*b=8*a_1*b_1 - a_2*b_2

>>8693720
That doesnt work, <x,x>>=0 is neccesarry for all x. (choose a=b=(0,1))

>>8693704
What is a ring?

>>8693680
I'm not sure, we still haven't studied gramian matrixes. I'm starting to belive the prof is just fucking with me, given it's the first week of 2nd semester of 1st year at compsci.

>>8693755
The rundown is, that a scalar product is defind by a symetric matrix with only positive eigenvalues (which is depended on the basis).

Without the knowledge of that I cant think of more then guessing.

What can you do, to make note taking on a computer more efficient for learning? A study says, that you perform better in shorttime memory tests if you used handwritten notes. But I really want to organize my informations on a computer.

>>8693747
a set equipped with a nice addition and multiplication

https://en.wikipedia.org/wiki/Ring_(mathematics)

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I'm starting to learn about steady flow systems but the thing that's confusing me here is what the fuck is Ac? He hasn't indicated anywhere on the slides, is this a common equation? if so do you know what it is?

>>8694389
I would guess that A stands for Area.

You are basically dividing the flowing speed per unite area (that is the integral, which means that you integrate the velocity over an area) and then you divide this by the total area.

Imagine a cube where water flows though at a constant speed, then the integral is just the volume of the cube multiplied by the speed and that divided through the total area. which is just the constant speed again.
I personally have no idea about fluid dynamics but in my EE class there were similar integrals.

Although this is probably a very informal way to write it down.
Because it implies that Ac is not only a real number but also a set and a measure, but I think you can ignore that.

>>8693848
Use a tablet

>>8694465
thank you man, I thought it was something like that but I didn't want to be making a dumb mistake

>>8693694
standard model lagrangian

What is the relationship between gorillas and topology?

>>8693732
do you have to explicitly define it

can't you just use the fancy { thing and say it's just the plain old regular scalar product for all vectors except A, B and 0 for A and B

that's as mathematical as it gets

>>8694499
Both are memes and both are used by brainlets to seems smart.

>>8694499
gorillas have trivial fundamental group

>>8694512
>{
No.

You can not split it in case,s look up the conditions for a scalar product. (especially its bilinearity)

Most importantly you need to define a scalar products only for the combinations of the vectors of the basis (the gramianmatrix), everything else folows from that.

You can not just change it for 1 vector unless you change it for a whole base vector.

>>8694516
but are they related in some way?

>>8694537
They are brothers.

>>8693625
let <(a,b),(c,d)> = 0

>>8694557
That violates the <a,a> = 0 only when a = 0 rule.

>>8694538
could you give me a quick rundown on them?

>>8694570
-Mathematicians bow to the hairy topologist brothers
-In contact with 15 dimensional manifolds
-Possess smooth compacta-like properties
-Control Mathematics with an linear fist
-Direct descendants of Gauß
-Will proof the next millenium problems (moneky-topoligy theorem will be the first theorem)
-Own 99% of Math research facilities on Earth
-both brothers said to have [math]lim_{n\rightarrow \infty}{n}[/math] IQ, such intelligence on Earth has only existed deep in Tibetan monasteries & Area 51
-Ancient Indian scriptures tell of one hairy angle and a mathamatical theory who will descend upon Earth and will bring an era of enlightenment and unprecedented mathemtical progress with them
-You likely are a topological structure
-In regular communication with the Archangel Riemann , forwarding the word of Gauß to various universties.
-They understood teichmuller thoery in under a week
-The twins are about 7 decades old, from the space-time reference point of the base human currently accepted by our society
-In reality, they are timeless beings existing in all points of time and space from the big bang to the end of the universe. We don’t understand their ultimate plans yet. We hope they’re benevolent beings.

>>8694570
here is a paper one of my old lecturers wrote about them
https://en.wikipedia.org/wiki/Brother_Bear

>>8694606
>>8694607
Thanks

Can someone help me apply this boundary condition? I already solved for the general solution: u(x,y) = f((x^2 + y^2 +1)/x)

I have the condition u(x,0) = x(1-x) where 0 < x < 1

From there I go to f((x^2 +1)/x) = x(1-x), but after that I'm not sure what to do. I tried a substitution where w = (x^2 +1)/x then solve for x to give me f(w). But when I substitute my f(w) into the boundary condition, I don't get the right answer.

>>8677706

How old is too old to be on /sci/?

Reason I ask is that just a little bit ago, like completely out of nowhere, I suddenly realized that the people who post Pepes and feelsbro brain memes and start flat earth threads and overuse the word "brainlet"? They probably giggle when they do those things. And while that might be obvious to the giggleposters, I've been assuming it was some kind of ironic hipster move. Like it was sophisticated satire that was going over my head. So I just pretended to get it and started a few flat earth threads to be polite and blend in. But then I realized that people actually invested time and effort in making all of the shitty memes that keep getting reposted, and now I'm worried that I've been bathing in the figurative childrens' tub, when all this time I thought I was lathering up with grown men. Please advise.

>>8695279
The level of the homework that gets posted didn't give it away ? Most people here are in their first or second year, so around 18/19. Just check the board every once in a while to see if interesting stuff has been posted (shouldn't take more than 5 minutes) and move along

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Would I be stupid to take a full time class load in the summer? I'm finishing my "second" year of college (chose mechanical engineering this year) and I'm pretty behind course-wise

The classes would last for 2 months, each one 5 days a week.

The courses I may take are
Calculus III
Mechanics of materials
Thermofluids
Electromechanical systems


How feasible would it be to take all of these and pass with good grades? I won't be working if I do it

Any tips?

Any recommendations for a differential geometry text? I know undegrad analysis and grad-level algebra.

>>8695921
brush up on your linear algebra, john lee's intro to smooth manifolds is a great read

>>8677706
i didn't really "get" linear algebra (fuck off with your red pill crap) until i took some upper division physics courses. Literally every problem in quantum is a linear algebra problem. It either becomes a part of your brain or you fail.

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>>8677706
>the 'red pill'
gtfo pill-popping /pol/esmoker

>>8696165
>>>/re**it/

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We have this rod which has a wheel at each end. The wheels are individually controlled: one moves backward and one moves forward. Each wheel will spin with the same RPM and has the same radius. How can I calculate the rate of change of the angle of the rod? In this case it would begin rotating to the left

>>8696381
Shouldn't it just be 2x-15, not 2f(x)-15? It's just asking for g(x), not g(f(x))

>>8696376
Tangential velocity is angular velocity times radius

How can I hold a 3.9 - 4.0 GPA?
It's important.

>>8696504
just be smart.

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in an asymmetric cryptography scheme, how does someone verify a digital signature with a public key?

As I understand it, I can use a private key to generate a string "SIG". Then anyone with a public key can verify "SIG" was generated with the private key. If they don't have the private key, how the hell can they confirm it?

>>8696656
Okay, found another explanation. Am I to understand that the encrption goes both ways?

encrypted by public key, can only be un-encrypted by private key

And


encrypted by private key, can only be un-encrypted by public key?

>>8693824
>>8693625

I finally managed to solve it. (3x1y1-8x2y2)^2 seems to do the trick.

>>8696728
I dont think so.
x=y=(sqrt(1/3),sqrt(1/8)) is zero although x,y=/=0

So I'm in a biochem class right now and there was a question on the minimum number of tRNA's there would have to be for translation of all of the essential amino acids to occur. I chose 20 because I thought well no shit there's 20 essential aminos.

However, someone argued in class that it was 21 because of the unique initiator-tRNA that's charged with Methionine, and convinced the Prof. it was 21. Am I autistic? In the hypothetical scenario, would there need to be two methionine specific tRNA's, and thus, 21 tRNA's minimum? Thanks /sci/

How large is an electron?

>>8696919
He might be correct, but also you're missing selenocysteine, so 22 is 'more right'.

If an event has a 1 in 25,000,000 chance of occurring, and you have 80,000,000 attempts, how many successes can you get before the probability of that outcome drops below 1%?

Alternately, is there a site that lets you quickly and easily calculate such things?

>>8695921

Are you a physicist or a mathematician? I find that both learn this subject, but approach it quite differently. Indeed, every textbook on the subject seems to set things out differently/cover different aspects.

Anyway, I am agreed on Lee (as this anon >>8696075 says) as agood starting point. His book has problems but no solutions; there's a nice appendix that covers some preliminaries too. I'll say that it's quite dense.

I also like 'An Introduction To Manifolds' by Loring Tu. It has solutions to some of its problems which is nice.

Also 'Introduction to Differentiable Manifolds' by Serge Lang.

>>8696994
Well shit. Thanks for info

>>8697014

Pretty standard binomial problem.

P(X=x) = nCx * p^x * q^(n-x)

where P(X=x) is the probability that we have a certain number of successes (x)
n is the number of trials (80,000,000)
nCx is the relevant binomial coefficient
p is the probability of success (=1/25,000,000)
q = (1-p)

Theoretically, you can plug stuff into the formula. However, the numbers are so large that you need to cancel a couple of bits with a bit of ingenuity. Calculators exist: http://stattrek.com/online-calculator/binomial.aspx

Like I said, you need to cancel some bits, so calculators like this aren't always the smartest choice. However, once the cancelling is done, you can start computing (with a calculator!). I got these answers:

P(0) = 0.041
P(1) = 0.130
P(2) = 0.209
P(3) = 0.222
P(4) = 0.178
P(5) = 0.114
P(6) = 0.061
P(7) = 0.028
P(8) = 0.011
P(9) = 0.004

Hence, 8 is your answer, because there's a 1.1% chance of getting 8 (and a 0.4% chance of getting 9). I have to step out for an hour, but if you come back and want more info on how I got this answer, then let me know.

am I correct in thinking that [math] P2 = \rho_{clear water}*g*0.6 - \rho_{mercury}*g*0.1 + \rho_{air}*g*70 + \rho_{salt water}*g*40 [/math]
?
The bit that is confusing me most is the air. I can't tell whether that'd be a + or a -

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>>8697265
forgot to upload the picture for fucks sake

>>8696165
Redpill is not a /pol/-exclusive meme.

>>8697265

The air is a negative contribution also, I think.

>>8697265

You also need not include the mercury term:

[math]P_2 = \rho_{water}*g * 0.5 - \rho_{air}*g * 0.7 + \rho_{salt water}*g * 0.4[/math]

>>8697385
why not, doesn't the mercury have a negative contribution to P2? Also should P1 and P2 be equal?

>>8697389

Horizontally aligned -> equal pressure i.e. things at the same height are at the same pressure (right?). Hence P1 and P2 are not the same.

I just tried to simplify by leaving the mercury out by using the above idea (by changing the coefficient for the water term). But your formula is perfectly fine if you make the sign change - sorry if I have confused you.

>>8697400
nah you've not confused me, you've helped me out actually. I used the formula and P2 came out as very low (around 3kPa) and P1 came out as -3kPa. So i'm fucking up somewhere i just dunno where

>>8697410

I think I was wrong to try to simplify by leaving out mercury, so your formula is right. Ignore my comments about that part.

For P1, I get:

[math]P_1 = -0.2*g*\rho_{air} + 0.2*g*\rho_{sea water}[/math]

That should be positive, given how low the density of air is!

Is it correct to say that in a case where the volume and mass are constant, the ideal gas law can be written as
[math] p = RT [/math]

>>8697930

No

The Ideal Gas Law is unchanged - it is what it is. What it means is that some of the variables in the equation are constant.

Hence, you could write the law as [math]P = R'T[/math] where R' is some new constant built from rearranging the constant terms into one new single constant. Hence, you would deduce that temperature is proportional to pressure (or vice-versa) in this case.

Can I ask homework questions here?

If so, how would I rationalize sin(9x)/8x

I'm learning L'Hopital's rule. Should I tackle every indeterminate problem rationalizing the number first and see if I can simplify easily or would most problems be faster by applying said rule?

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Anybody want to help? I have no clue what to do

How does one write a taylor series for three variables? I'm in a numerical ODEs class and I need to solve a system of the following:

x' = x - y + 2t -t^2 -t^3
y'= x + y - 4 t^2 + t^3
x(0)=1
y(0)=0

>>8695239
if f((x^2 +1)/x) = x(1-x),
and w = 1/2 (x - sqrt(x^2 - 4)) , then
f( (w^2+1)/ w ) = w(1-w), so
f(x) = 1/2 (x - sqrt(x^2 - 4)) *
(1-(1/2 (x - sqrt(x^2 - 4))))
so f( (x^2+y^2+1)/x ) =

1/2 (X - sqrt(X^2 - 4)) *
(1-(1/2 (X - sqrt(X^2 - 4))))


huge mess
where X = (x^2+y^2+1)/x

can you multiply trig functions with different angles? for example (sinx)(-sinx^-1)? is that the simplest form?

>>8698943

That's probably the simplest form you're going to get, and there's nothing wrong with it.

>>8698542

Do you need to? There's nothing wrong with what you have written - it can't be made any simpler.

>>8698553

That depends. If you have a textbook with a section on a specific topic, usually the problems require you to use it. And applying the rule blindly instead of messing around is faster. But trying other methods as well will make you a better mathematician.

>>8698943
sin(x)=x
sin(1/x)=1/x
sin(x)*sin(1/x) = x*1/x = 1

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/sci/ I wanna be a fuckin astronaut, which school should I go to to accomplish this? Is aerospace engineering the best major to take for helping this pipe dream? I'm also open to joining the Air Force.