/sci/ - Science & Math

The previous problem we used induction to show that the formula for a geometric series is true.

I'm sort of confused with this one.

I was thinking we could make our formula:
1/(1-x^a)

but then the two examples we want to expand aren't in the same form as what I came up with.

Any hints would be appreciated

>>9166299
That equation is the limit of thd geometric series for ratios that are less than 1.

>>9166307
So how do I expand something like 1/(x^3-1) ?

Like is it something like 1 + x^3 + x^6...? I I know it is not exactly that, but maybe something along those lines? I'm sorry if this is simple and I'm just being a brainlet.

>>9166299
>but then the two examples we want to expand aren't in the same form as what I came up with.
they're extremely close though... just do some basic algebraic manipulations

>>9166313
Oh could we rewrite

1/(x^3-1) ----> -1/(1-x^3)?? and then build the series from there?

so it would be -1 + x^3 - x^6+x^9...?

If so, I'm dumb and thanks for the help.

If not, I'm dumb and thanks for being patient haha.

>>9166312
negate the expression, then enclose in parentheses and negate again

>>9166317
>1/(x^3-1) ----> -1/(1-x^3)?? and then build the series from there?
>so it would be -1 + x^3 - x^6+x^9...?
yes

then for 1/(8-x^2) move the 8 outside

Can a college professor fulfill their research output requirements with articles like this?

>>9166330
wtf is this shit

>>9166317
>1/(x^3-1) ----> -1/(1-x^3)?? and then build the series from there?
this is the right way to start

>so it would be -1 + x^3 - x^6+x^9...?
this is wrong though, they should all be minuses

>>9166354
Yeah I caught that when I was writing it down. Thanks!

>>9166297
Here is a dumb one for you: can you recommend a calculator for math up to Calc 1, or an Android app that can replace a traditional calculator? The cheaper the better, I am a poor college student.

I just did an extensive big five personality test, turns out I'm high in neuroticism and agreeableness and very low in openess, creativity and extraversion.

Are there things that people like me can do and be good at or should i just off myself

Why does an Acetic acid + H2O <=> C2H3O2 + H3O

instead of

C2H5O2 + OH- . I know acetic acid is an acid and acts as a Lewis acid, but I dont understand why it couldn't also act like a base in this reaction.
Any insight is appreciated, thanks!

Suppose I have eight socks, two of each color: (e.g. red, white, blue, black). I randomly draw four socks. What is the probability that I have exactly one pair of socks with the same color?

If the exchange rate between euro and usd is 1/1.25 how do I find the reverse?

>>9166809
How many socks do you need to draw to ensure a match of at least one color?

>>9166819
Just set up a proportion.
1 (euro) x(euro)
---- =
1.25 (dollar) 1(dollar)

cross multiply and you are good.

lets say i have a regression
y = b1x + b2x + b3x + e
all it says is that a unit change in a given beta, say b1, changes output(y) assuming all other betas are held constant, correct?
what happens if two or more of the betas change at the same time?


>>9166819
1/(1/1.25)

>>9166809
I make it 24/35.
Sample space is 8!/4! = 1680 (all possible ways of taking 4 socks from a possible 8).
Then we need the number of ways of getting XXYZ (X,Y,Z are sock colours).
There are 4 possible ways of getting XX (4 pairs).
Then there are 6 possible values of Y.
That leaves 4 possible values for Z. (Any of the two colours not yet picked).
Which gives 4*6*4 = 96 ways of getting XXYZ.
Then there are 4!/2! = 12 ways of arranging XXYZ. Giving 12*96 = 1152 possible ways of getting exactly one pair from a set of 8 socks.
Thus the probability of getting exactly one pair is 1152/1680 = 24/35, or approximately 69%.

I then confirmed this experimentally using a Python script.

Find an example of subspaces [math]W_1,
W_2[/math] of [math]R^3[/math] with dimensions [math]m, n[/math] where [math]m \geq n[/math], such that both dim[math](W_1\cap W_2) < n[/math] and dim[math](W_1+W_2 < m + n[/math].

SOS

>>9166927

x-y plane and y-z plane

Getting a PhD in Physics

I graduated in May with a BS in phyiscs to start a job in the semiconductor industry (intel). After 3 months here, the job has gotten mundane, and granted I dont hate it yet but I can see myself growing to hate it very soon.

I'm thinking of going back for a PhD in physics. Should I re-apply immediately? Or should I wait a year to reapply with some industry experience on my resume. Would it look bad if I only stayed at a job for this little time? On the other hand, the job has an R&D title on it so it may look nice on a resume before aplying to grad school. But this also means I'd stay here for at least 2 full years before starting graduate school

>>9166568
Where the heck are the protons gonna go lad

How hard is vector calc compared to calc 2? Calc 2 was pretty easy.

>>9166513
tech support

What is the truth behind Scientology?
Everyone knows that it's a bogus religion that invites rich people to become members to take all their money. Ok yeah.
But most rich people aren't idiots. After all, they wouldn't have made is this far if they were. So there must be something they expect to get out of joining the Church of Scientology. And I'm wondering what that is.
Is it maybe a "muh secret club" thing, because all members are rich?

So this is for matlab.

I have a set of values, G

G=[68 83 61 70 75 82 57 5 76 85 62 71 96 78 76 68 72 75 83 93]

I'm trying to obtain the mode for this, which is 68,75,76, 83. However when I plug in mode(G) it just gives me 68. I have no idea what I am doing wrong here. Pic related.

>>9167281
Oh boy. So my uncle is a member sadly, has an entire bookcase full of L Ron Hubbard shit and various evils of psychology sort of nonsense. I actually have very strong opinions on the cult, but I can't say anything or he'd no longer be allowed to interact with the family.

Anyways the more money you throw at the church, the higher your rank is. Guess who has a lot of money? On top of that the celebrities and artists are basically pampered so these people fall in love with the church, and are more willing to buy their bullshit. Finally, don't overestimate the intelligence of successful people. Steve Jobs thought psychics and fruit smoothies would cure his cancer.

Can anyone recommend good books on biomechanics for a literal retard?

>>9167040
I'd wait desu

>>9166931
Fuck no coz you have n=2 and dim(w1+w2)=3

You must have w1=w2

>>9166839
Pls respond

>>9167334
dim(w1+w2)=3<4

obviously w1 != w2 because then the dimension of the intersection would not be greater less than the dimension of either

>>9167395

>dimension of the intersection would not be less than the dimension of either

*correction

>>9167301
Look at the documentation of mode (help mode or doc mode).

Can someone critique this proof of mine? I'm mainly just wondering about the "style" and if the procedure is correct.

Prove by induction that : [math]2^{n} \geq n+1 [/math]

Let [math]P(n)[/math] be the above mathematical statement.

Basis: [math]P(1):[/math] [math]2^{1} \geq 1+1 \implies 2 \geq 2[/math] , holds true.

Inductive Step: Assume [math]P(k)[/math], [math]2^{k} \geq k+1 [/math] holds true. Thus [math]P(k+1)[/math], [math]2^{k+1} \geq k+2[/math] will hold true as well. Proof:

Consider [math]2\cdot P(k)[/math], that is: [math]2^{k}\cdot 2 \geq 2\cdot \left( k+1\right) \implies 2^{k+1} \geq 2k+2 [/math]

Since [math]2k+2 \geq k+1 [/math]. [math]P(k+1)[/math] holds true.

So by PMI, [math]P(n)[/math] is true.

We landed a person on the moon with a computer as good as my apple watch 50 years ago.
https://www.instagram.com/p/BZA0s7EAmF1/?taken-by=elonmusk
now we have super computers and shit, why are we still having problems?

>>9167435

it's fine, just don't forget to specify you're in N or R+, or wherever, that last bit about (2k+2)>(k+1) does not hold for a real k

>>9167435
My hand-waving proof would go like this:

We have
[math]2^0 \geq 0 + 1[/math]
and
[math]\mathcal{O}(2^n) \geq \mathcal{O}(n)[/math]

Thus [math]2^n \geq n + 1[/math] for [math]n \geq 0[/math].

>>9167447
But there you are misusing big O notation, which makes you seem retarded

>>9167445
Ah yes, thank you for pointing that out.

>>9167437
>We landed a person on the moon

>>9167447
>Using big O's as variables

Compsci alert

>>9167508
>Retard alert
ftfy

>>9167435
>Basis is 1
???

>>9167550
[math]0 \not\in \mathbb{N}[/math] here

>>9167193
Always found vectors and matrices much easier than summations.

>>9167310
Bump

>>9166395
>android app
TI calculator emulator
your professor certainly won't let you use your phone in exams though

>>9167281
you seem to be under the false impression that
a.) 90% of humans aren't complete idiots
and
b.) being rich somehow requires personal merit rather than just inheriting parents' money or being a pretty face for the movie cameras

Have to show the conditional statement is a tautology without truth tables.

(p∧r)-->p

Would it be okay if I just say
>True except T-->F
>in which case the conditional statement would have to be (p∧r)-->¬p

Shouldn't white holes also be invisible/undetectable?
>The opposite of a black hole > something where nothing can enter > it can't reflect light

Why is assumed that if white holes existed they would spew out information if they can't hold any information in the first place?

How could you ever detect a tachyon if they were real?

>>9167437
It was worse than your Apple watch.

[math](a+bi)^n[/math]

=

[math][r(cos\theta+isin\theta)]^n[/math]

=

[math]r^n[cos(n\theta)+isin(n\theta)][/math]

Question: How and why does "n" get into the angle in the third step? I took a Trig/pre-Calc class and this was never really explained.

>tfw you try to organize your post and it ends up all fucked up anyways

[math](a+bi)^n

=

[r(cos\theta+isin\theta)]^n

=

r^n[cos(n\theta)+isin(n\theta)][/math]

Question: How and why does "n" get into the angle in the third step? I took a Trig/pre-Calc class and this was never really explained.

>>9168133
This is the De Moivre formula
Its proven by induction
for n=1 its a trivial statement
now assume its true for some n, and see if u can prove for n+1

>>9166568
Because it's a stronger acid than water

I just bought Michael Artin's 'Algebra' and I struggled through the first chapter, I am considering saving Michael Artin's book for later and studying linear algebra now. What would be a good textbook for linear algebra if I really want to learn Modern Algebra? I don't have much knowledge in matrices other than the first chapter of Artin's book. Thanks.

>>9168259
https://www.goodreads.com/book/show/554752.Algebra_I_for_Dummies?ac=1&from_search=true

>>9168397
>>9168259
Guess you want "Linear Algebra For Dummies"
The simplest explanation is usually the best.

>>9168259
Don't listen to >>9168397.
Get yourself a copy of Charles Pinter's "A book of Abstract Algebra." You can thank me later.

>>9168259

I think >>9168398
and >>9168401
would be a good combination. You don't need that much linear algebra to start studying modern algebra.

Help with babby analysis.

Let [math]A[/math] and [math]B[/math] be two nonempty sets of real numbers that are bounded above and below, respectively. Let [math]s = supA[/math] and t = [math]infB[/math]. We form the set [math]C={c=a+2b:a\in A, b\in B}[/math]. Prove or disprove: [math]supC = s+2t[/math].

What I have so far:

Let [math]s=supA[/math]. This means [math]\forall\epsilon >0, \exists a\in A, a>
s-\epsilon[/math].
Let [math]t = infB[/math]. This means [math]\forall \epsilon > 0, \exists b\in B, b < t +
\epsilon[/math].
Prove [math]supC=s-2t[/math]. Prove [math]\forall\epsilon > 0, \exists c_0\in C,
c_0 > s-2t+\epsilon[/math].
Fix arbitrary [math]\epsilon > 0[/math].
By first assumption, know [math]\exists a_0\in A, a_0 > s-\epsilon[/math].
Likewise, know [math]\exists b_0\in B, b_0 < t + \epsilon[/math].
Choose [math]c_0 = a_0 - 2b_0[/math].

I think this will work out, I'm just not sure how to connect the inequalities.

>>9168425
Fucked up the problem statement.

We form the set [math]C=\{a-2b:a\in A, b\in B\}[/math]. Prove or disprove: [math]supC = s - 2t[/math].

Bonus:

[math]A, B[/math] are bounded below and [math]B\subseteq A[/math]. Prove inf[math]B\geq[/math] inf[math]A[/math].

Gah, I perfectly understand why this is true, I just can't finangle with the epsilons to prove this. I want to say, assume for contradiction that infB < infA, this means there's some x sandwiched between which violates the subset property, but I can't formalize that...

>>9167437
because new things are new
we've never landed a booster before, so HOW to land one was unknown
Now we do know, and we're getting closer and closer to perfect landings

do remember that the Apollo missions had many very near failures, saved only by a hair for a few of em

>>9168425
dude this is obviously not true. counterexample is easy.

The only group homomorphism from [math]S^3[/math] to [math]\mathbb{Z}[/math] is trivial, right?

>>9168630
what group operation on [math] S^3 [/math]?

>>9168624
See
>>9168430

>>9168471
hint: [math]\inf B < \inf A[/math] means that [math]\inf A - \inf B > 0[/math]. Use this as your [math]\epsilon > 0[/math].

>>9168635
[math]a_0 - 2b_0 > s - 2t -3\epsilon[/math]

>>9168632
I'm retarded, I meant [math]S_3[/math] and not the 3-sphere.

>>9168670
then yes since for any homomorphism f, |S_3/ker(f)| = |im(f)| forces im f=0 and so ker(f)=S_3

I am but a humble layman and the explanations that I heard or looked up with regards to what generates lift were dense and confusing, is my pic wrong?

>>9166923
Thanks senpai. I admire your dedication

>>9168711
I don't know if your picture correct, but have you looked up 'Bernoulli's Principle'

I read about an algorithm in a paper on arxiv and I asked the author if he could send me an implementation of his work. It's been months without a reply. What should I do?

>>9168711
lift is an immensely complicated concept, even if we are only concerned with ideal fluids the two main explanations for lift are pretty incomplete.

If you just want to gain an intuition for lift focus on the Newtons's third law explanation and conservation of momentum. If you want to get a bit fancy you can then learn the Bernoulli's principle explanation and conservation of energy

your pic isn't "wrong" but it is really shitty, even for the basic explanations, and the block of text on the right is completely retarded.

>>9168636
Thanks!

>>9168653
Can you show how to get that? I'm just not seeing it.

>>9168774
>>9168766
Thanks for the info.

>>9168404
>>9168401
>>9168398
Thanks a ton guys.

>>9168773
Send him another letter. Send him one every week. The squeaky wheel gets the grease.

>>9168869
kek, dont do this

What does [math]2^A[/math] mean when A is a set?

>>9169221
https://en.wikipedia.org/wiki/Power_set

>>9169224
>>9169221
and more generally X^Y denotes the set of functions from Y to X

>>9169224
>>9169230
Thanks, friendo.

What can I do with a bachelor's in physics? Except kill myself

just came into /sci/ for the first time worried about finding a place to ask a dumb question, so thanks for having this thread exist. If a surgeon finds previously unknown problems/damage during surgery, how likely would it be that they 1) fix the problem and bill you after, or 2) tell you about it after to schedule a second operation. thanks.

Why can 1g of centrifugal force not replace 1g of gravity? With our current level of technology we could easily redirect a suitable asteroid to geosync orbit, use nukes to smash a habitation chamber along an axis, rotate and done.

I'm looking to do some scoring analysis for a design competition prompt where the prompt gives equations that define the scoring guidelines. Are there any tried and true methods for doing this?

>>9166297
i've graduated college and i don't think i understand electricity and magnetism well.

i also want to understand modern physics.

what online resources do you guys suggest for a comprehensive understanding of these topics?

>Educational advice.
>Be taking macroeconomics.
>Teacher is bro-tier.
>Can't stand his lecture style.
>I want to drop and take the class later because I'm in no rush to get this class out of the way. It's not important to get it done this semester.
>Should I drop and retake later? I get most of the money back. Pretend that's not an issue.

Guys, any good resources for Radiometry and Photometry? (Calculus-based)
Preferably videos, but, they I can't find any.

And some Thermodynamics and Fluid Mechanics resources as well..

THanks!

>>9167040
Most people on here don't have a PhD, and I wouldn't be surprised if most didn't have at least an associate's or bachelor's degree.
I don't have a PhD, but industry experience might help you get accepted, for whatever that is worth. Of course, you probably knew that.
If your grades for your B.S. didn't suck ass, you might wish to apply so you don't waste any time.

>>9167310
I'd be interested to know this as well.
Books that I can get a free PDF of would be most welcome, but the book name is really all I need.

>>9169275
Have a great fucking time studying more.
Relax, bud, it isn't the end of the world. If I were you, I would strive to learn more and eventually get a higher level degree, so to speak. You could always educate morons on 4chan in your spare time.

Ultimately, knowledge for the sake of knowledge isn't the worst thing in the world, you know?

Also: kek

>>9169732
If you wish to learn the subject, and the lecture style gets in the way of that, drop it.

Others might tell you to suck it up and study on your own time, which isn't terrible advice, but I'm practically retarded, so lectures help me greatly.

Only drop if you wish, and it won't fuck you over. Good luck, babe.

>>9169892
Thanks anon. You're alright.
I'm going to get a study group together, suck it up and take the first test and if that fails then I'll chuck it.
Happy studies.

>>9166299
[math]
x^{an} = (x^a)^n \\
\frac{1}{x^3-1} =-1\cdot \frac{1}{1-x^3} \\
\frac{1}{8-x^2} = \frac{1}{8} \cdot \frac{1}{1-\left(\frac{x}{\sqrt{8}} \right )^2}
[/math]

Why does differentiation from first principles only work only after you've found the derivative? I tried to use differentiation from first principles with concrete values (i.e by substituting in appropriate numbers into the variables). What is going wrong behind the scenes?

>>9166297
How can I print a Tactical Pilotage Chart so that it retains its scale, preferably on an A3 size sheet?

>>9169356
I don't think they're allowed to do anything to you without your consent, so probably 2.

>>9170103
unless, of course, it was immediately life threatening

Let's say I had two large steel drums that are fixed separately over a fire heat source, that can heat up the drums evenly and equally. The goal is to fill these drums completely with cold water and bring them to a boil as fast as possible.

For drum #1, I fill it completely with water all at once before lighting the flame.

For drum #2, I fill the drum incrementally, light the flame, and slowly watch as the until the water starts to bubble before pouring more water in, repeating until the drum is completely full.

Which method would be quicker?

>>9169873
bumb

>>9170238
Making a guess, probably #1 since it'll establish a constant convection current that'll heat the water, as opposed to a new current being set up with every addition of water for case #2.

>>9170238
The former.

I have an extremely ignorant question that I was reminded of by >>9170238
:
If I boil the same amount of water in two identically sized vessels, and then dilute vessel A with X amount of cold water, wait ten minutes, and then dilute vessel B with the same X amount of cold water, what will be the relative temperatures of water in the two vessels?
Will they be identical, or will vessel A be hotter?

>>9170269
I don't think the question can be answered without knowing how much hot water you have and how much cold water you'll pour.

>>9168869
I did this and he responded:

"Hi, I lost the implementation due to a computer problem. Thanks for your interest."

A literal one-liner.

Insane math fag here calling on you pharm/chemistry fags.

I got a urine drug panel for my psychiatrist. Everything came back negative except for MDMA. My prescriptions are as follows.

Bupropion - 100mg 1x daily
Lamotrigine- 200mg 1x daily
Alprazolam - 0.5mg up to 2x daily as needed
Methylphenidate- 10mg 1x daily ( was out of my system during the urine test since it had been 10 days since I took one )
Levothyroxine 88 Mcg 1x daily
Had some Diphendramine Citrate after the gym the night before cause I tweaked my neck.

1) Based on the skeletal structures I think it was the Bupropion that false positived it, but I have minimal chem knowledge I'm going off of.
2) I took Alprazolam for 3 consecutive nights before the urine test and Benzos came back negative?

Interested to hear why this might be the case from a chemical standpoint ( don't see my doctor for a few weeks to ask ). I wish I knew more about chemistry. Thanks bros.

Using the fact that e^3 ~ 20 and 2^10 ~ 1000, how do I approximate ln 2 ?

>>9170269
the intuitive answer is, since the heat equation is
[math] \frac{\partial }{\partial t}u(x,t)= a\frac{\partial^2 }{\partial x^2}u(x,t) [math]
we expect bigger change in heat, wherever the heat gradient is bigger, meaning the nondilluted vessel will lose heat faster than the dilluted one.

I illustrated it for you in a numerical solution for the 1D heat equation.
the blue dotted line is the initial nondilluted solution, the red dotted line is the initial dilluted solution (half as hot, twice the volume)
the drawn out lines are the heat distributions after a fixed amount of time.
As you can see, the red and blue lines are almost identical. Once you dillute the blue line though, you will get the green distribution which is way lower than the red one

>>9170290
Well if he's telling the truth, you got your problem fixed. If he wants you to fuck off, try to find someone else who might have it, a colleague of his or something.

>>9166297
var myMoney = 0;
var savingsPerYear = 6000;
var investingYears = 10;
var interestPercentPerYear = 12;

for(var i = 0; i < investingYears; i++){
myMoney = (myMoney + savingsPerYear) * (interestPercentPerYear / 100 + 1);
}

console.log(myMoney);

result: 117927.49966727578 money in 10 years.

how do i even math? trying to calculate earnings from compound interest with math but no chances, i'm a dumbass CS worker btw

TLDR: how to replicate for loops in a math formula

Biochem fags, pls help:

What is the difference between total activity of an enzyme and specific activity? Also what does Kcat describe? If you're purifying an enzyme, is it better to increase specific activity and decrease total activity? Does "activity" refer to a single enzyme that you're studying or multiple?

>>9170702
>interestPercentPerYear / 100
This has to be a joke...

Also, compound interest formula is pic related. You're missing an exponent as far as I can tell.

If i throw a dice n > 6 times, what is the probability of getting each face at least one time in my sequence?
Or at least how is this probability topic called?

>>9170702

>>9170727
doesn't work if you add money every year.

the formula you're looking for is
savings * (1-(1+interest/100)^(n+1)) / (1-(1+interest/100))
and is derived from the geometric series

>>9170727
it works, in my case n is always 1

in my calculations i was also adding 6k each year to the investment but i changed it just to match your formula (pic related)

thanks
also, what is wrong with: >interestPercentPerYear / 100

>>9170748
oops i messed up, forgot to subtract one because the series starts at 1 not 0.
[math]
Money = Savings *\left( \frac{1-(1+Interest/100)^{n+1}}{1-(1+Interest/100)} -1 \right )
[/math]

>>9170748
what the.. my brain can't compute that sorry, i just tried it and result was
-9999999.999999251

>>9170754
It would be easier to declare your variable as a value already divided by 100, e.g., 0.12 instead of 12. Saves a smidgen of memory for your machine at the very least and is stylistically easier to read.

>>9170759
that didn't work (maybe i messed up) pic related

>>9170771
ah yeah, is just direct scripting with the browser console so i was feeling lazy there

>>9170779
oops, typo there, savings was 6000 not 60000 but didn't work either (of course not)
result: -12086

>>9170779
you forgot a bracket

>>9170787
fuuuck and now i did it wrong again.
the bracket needs to be around the term
1 - (1 + interest/100)

>>9170779
Remember to remove the /100 since you've changed the interest value to 0.12

is there such a thing as a pulse in your brain? its something I feel all the time, it feels like theres a pulse inside my brain, like a heart beat. Ive asked some doctors and they say its no big deal, but Ive always found it kind of distracting and weird feeling.

>>9170779
just realised, there are even more brackets missing, than i had noticed in
>>9170787
just copy this:
money = savings * ((1 - Math.pow((1+interest),(years+1))) / (1-(1+interest)) -1);
and do this
>>9170797
depending on how you define your interest rate

>>9170797
oops yeah i fixed that now

>>9170787
uhm well i'm not sure.. i tried with and without the brackets and still doesn't match initial calculations


initial calculations from >>9170702

result: 117927.49966727578 money in 10 years.

>>9170812
Finally they matched
so this is called geometric series?
Thanks everyone btw

>>9170819
let
savings = s, money in year n = M_n, interest rate in decimals = i
then you have

[math]
M_1 = s(1+i)
[/math]

[math]

M_2 = (M_1+s)(1+i)
= (s(i+1)+s)(1+i)

= s(i+1)^2 + s(i+1)
[/math]

[math]
M_3 = (M_2+s)(1+i)
= (s(i+1)^2 + s(i+1)+s)(1+i)
= s(i+1)^3 + s(i+1)^2+s(i+1)
[/math]

and finally (if you are familiar with sum notation)

[math]
M_n = s \sum_{k=1}^{n}(i+1)^k = s \left( \frac{1-(1+i)^{n+1}}{1-(1+i)}-1\right )
[/math]

where I turned the sum into a fraction via geometric series

How does a positive displacement pump move fluid at the same speed regardless of the pressure on the inlet end and why does a centrifugal not?

I'm unable to visualize the way both pumps work and my best guess is that with the positive chamber only allows so much to be expelled with maximum force.

Where did lny(4) go?
Im trying to find an explicit solution

>>9170869
is there some initial condition on y(x)? like y(4)=1 so that ln(y(4))=0?

>>9170869
it looks like your initial condition is y(4) = 1, and therefore ln(y(4)) = 0

Is calculus just a form of algebra?

>>9169550
A lot of the MIT open course resources are very good for this kind of thing. Also, you should check out the Feynman Lectures (notes) on physics it will take you from undergrad to advanced undergrad but give you a good basis to go forward or to understand physics with more math involved

>>9170628
Wow, thanks.
It's along the lines that my intuition suggested, but the effect is more dramatic than I realized.

>>9170771
The memory saved is completely insignificant and irrelevant, but it is embarrassing to unnecessarily introduce percentages to the program when it's more elegant and aesthetically pleasing to just type 0.12.

>>9170729
Pls anyone

"Wrtie an expression in terms of p and q, so that this equation has no real roots"

can someone tell me how to re-arrange pic related into ax^2+bx+c=0

>>9171080

multiply both sides by a common denominator so the fractions go away. So multiply both sides by (x+q)(x-2q).(Your answer will be the same as just cross multiplying)

(x-p) * (x-2q) = (3x+p) * (x+q)

now just FOIL

x^2 - px - 2qx + 2pq = 3x^2 + px + 3qx + pq

combine like terms

-2x^2 -2px - 5qx + p = 0

multiply both sides by -1 to make it cleaner looking:

2x^2 + 2px + 5qx - p = 0

whala

>>9171103

oops last p should be a pq.

How often should one go to the doctor for a check up?

>>9171114
Yearly

>>9170884
No.

>>9171103
thanks

>>9171117
Thanks, hope you have a nice weekend.

what's an outcrop

>>9166297
Will man ever walk on the sun?

>>9170718
pls help for i am dumb

>>9171080
now i'm stuck again, i've got the discriminant but I can't solve it since it has another variable

(5q+2p)^2 - 4(2)(-pq) < 0

25q^2+28pq+4p^2 < 0

did i do it wrong

>>9171120
Why?

>>9171114
Sounds like you have AIDS anon.

Is this scenario possible?
1: a population splits into two equal groups, A and B that are completely physically separated and don't interbreed
2: after a few generations group B splits into a large group Ba and a much smaller group Bb
3: because of their lower gene pool, the Bb group eventually splits and becomes its own species, I can no longer in interbreed with Ba, Ba can still interbreed with A(if the physical barrier is removed) even though Bb is more closely related to Ba than Ba is to A

What would happen when I hit a fish when diving from a platform 27m high at 90km/60mph?

>>9171547

if Bb is closer related to Ba than Ba is to A then they would have to be the same species pretty much. By the time they've changed enough to be a new species they would pretty much have to be genetically too different from Ba for them to be closer than Ba is to A, it's just not going to happen any other way.

In theory I suppose you could have some weird mutation in population Bb that makes them technically unable to breed with Ba while still being genetically 99% similar, but in practice that never really happens.

Strictly speaking in theory it's possible, but in practice, no, not even in a lab designed for this to happen using the simplest bacteria.

>>9171579
What if the entirety of Bb became sterile? Ha, gotcha

>>9168778
i would start with s-2t-eps and play with the inequalities a0>= s-eps and b0<=t+eps on the side and then use them

>>9171369

the original question was

>"Write an expression in terms of p and q, so that this equation has no real roots"

looks like all it wants you to do is write the discriminant in a way which has no real roots, which you did.

25q^2+28pq+4p^2 < 0 is the answer. No further solving is required.

>>9166927
A plane and a line lying inside it.

I was in a foreign hospital once and the nurses did rounds at night time injecting something into everyone's butt cheek. I didn't speak the language and so didn't know what they were trying to inject me with so I refused it, what would it have probably been?

>>9171565
You would die or something

I know the smallest number of red would be four.

I'm having trouble figuring out the maximum number of red faces. I'm thinking it is eleven. You could place a minimum of four blue faces, (I could only get the minimum of five black faces to work after picking the four blue ones).

Am I right or can you really get 12 red faces?

>>9172420
Icosahedron for reference

Using the fact that e^3 ~ 20 and 2^10 ~ 1000, how do I approximate ln 2 ?

https://arxiv.org/pdf/1512.07208v1.pdf

Could someone give me some pointers as to how to implement this? I don't understand how he sets up the algorithm (more specifically, I don't understand his superscript/subscript notation).

>>9172448
Take the log of the first equation and get
3 = log(20) = log(2) + log10
log2 =3 - log10

Do the same for the second one and get
10 log(2) =3 log10


From these two equations you can easily get what you need.

Best template to use in sharelatex for lab reports? New year new me, wanna freshen up my lab reports. Want a really aesthetic template, think /fa/ mixed with /sci/

\marginpar{$u_{w}u$}

If [math]p \implies r[/math] and [math]q \implies r[/math], can I say that [math](p \lor q) \implies r[/math]?

>>9172510
You have that [math]p \land q \implies r[/math] so yes.

>>9172514
Thanks!

Consider the regression model y = a + bx + u where y is not directly observed, and instead Y is observed and Y = y + v where v is I correlated with x and u.

This model would give inefficient estimates, but not biased estimates, correct? Is v is simply a random measurement error with a mean close to zero, there would be no systematic inaccuracy, and just large standard errors, right?

>>9172524
*where v is UNcorrelated is x and u

Not sure about this one either.

My personal best is 7 red faces. I haven't been able to optimize it though so that every vertex has two red faces connected to it. I'm not sure if it is possible, but if it is I should be able to get 8 red faces then.

>>9166297
Does anyone know of a good chemistry youtuber akin to PatrickJMT the calculus shlub ?

>>9172629
or of a top tier into to chem textbook I can obtain for free?

Seven sticks with lengths 2, 3, 5, 7, 11, 13 and 17 inches are placed in a box. Three of the sticks are randomly selected. What is the probability that a triangle can be formed by joining the endpoints of the sticks?

>>9171714
What country?

My guess is it was an antimalarial drug , doxycycline or the suchlike. If it was Canada or Germany idk.

>>9172634
35 possible combinations, 9 cases where one stick is longer than the other two combined, so 26/35 = 0.7429

>>9172677
oops, it should be the other way round.
there are 9 cases where no stick is longer than the other two combined, so 9/35

Let [math]G[/math] be a non-trivial finite group. To prove that [math]\mathbb{Z} \times G \not \cong \mathbb{Z}[/math] is it enough to note that [math]G[/math] is the kernel of the first projection and that [math]\mathbb{Z}[/math] has no non-trivial finite subgroups?
I think I understand why that should be the case informally, but is there a theorem for this?

>>9172901
>and that ZZ has no non-trivial finite subgroups?

you mean no infinite subgroups?

Assumimg E, L, and R is constant, how do I integrate this?

>>9172980
nvm

>>9172667
>What country?
Russia

>>9172901
assume f: Z -> Z x G is an isomorphism. f is determined by f(1)=(n,g) for some n in Z and g in G. since f is a homomorphism you have f(k)=(k*n, g^k), so if h != g is any other element of G then there's no pre-image of (n,h) [since that would require f(c)=(c*n, g^c)=(n,h), forcing c=1, but then g^1 != h], so f isn't actually an isomorphism

>>9172901
>To prove that Z×G≆Z is it enough to note that G is the kernel of the first projection
tells you ZxG / G is isomorphic to Z

> and that Z has no non-trivial finite subgroups?
how does this help?

>>9172917
What do you mean?
>>9173068
It also tells me that [math]G[/math] is a non-trivial subgroup of [math]\mathbb{Z}[/math], since it's a subgroup of [math]\mathbb{Z} \times G[/math]. But [math]\mathbb{Z}[/math] has no non-trivial finite subgroups.
Or is isomorphism not enough to conclude that [math]\mathbb{Z}[/math] also has a subgroup isomorphic to [math]G[/math]?

>>9173154
>It also tells me that G is a non-trivial subgroup of Z, since it's a subgroup of Z×G. But Z has no non-trivial finite subgroups.
oh yeah, that's enough then

>Or is isomorphism not enough to conclude that Z also has a subgroup isomorphic to G?
isomorphism preserves everything except names of elements. same subgroups, same number of subgroups, same normal subgroups, etc.

I live in a neighborhood with lots of drug addicts and so used needles are everywhere on the ground. I assume the city has no sort of 'needle cleanup team', so is there any way for me to clean them up myself in a protected way? Firstly needing a a tool to safely pick them up with, secondly having a safe container to store them in, and then thirdly a safe place to bring the container to...

>>9173198
>isomorphism preserves everything except names of elements.
That's what I thought. But what is the formal way of expressing that? I haven't seen it mentioned in any text I was reading.

>>9173214
>But what is the formal way of expressing that?
most books should contain propositions that would give you the result, all you really need is that the homomorphic image of a subgroup is a subgroup, homomorphic image of normal subgroup is a normal subgroup, etc. then since isomorphisms are injective and surjective you know the subgroups in that case have the same number of elements

>>9173242
>surjective* homomorphic image of normal subgroup is a normal subgroup

uses for two year out of date fruit punch mix
it smells really good

>>9173279
i need to know

When is a differential equation exact?
For example:
(2x-1)dx + (3y+7)dy = 0
m = 2x - 1
n = 3y + 7
Now I'm stuck.

>>9166297

I don't understand how psychology is a science. How can any study actually account for all the variables of a human being, and everything that has happened in their life

>>9173307
>I don't understand how psychology is a science.
It's not, psychologists don't use the scientific method. It's a "soft science" or "social science", both of which are misnomers like jellyfish (not actually fish)

Suppose I have has 6 identical plants, and three different window sills I can put them on. How many ways are there for me to put the plants on the window sills?

How would I find the limit of this as lamba goes to 0? I can't use L'Hopital's rule...

Assume T = a constant

[math]
\frac{2 \pi c^{2} h}{ \lambda ^{5} } \ast \frac{1}{ e^{ \frac{hc}{ \lambda kT} } -1}
[/math]

Struggling to figure out a suitable isomorphism for part (c). Any advice would be appreciated.

>>9173676
Well then ideal in part b is just <x>. So an element of F[[x]]/<x> is just an element of F.

>>9173676
Just take the evaluation homomorphism at 0 and use the first isomorphism theorem. jk

>>9173734
actually not jk nvm
it works

my chem1 homework is unirnocally forcing me to label digesting a hot dog as either intensive or extensive . Like wtf is this question i know that digestion is chemical but i think we cant know if its intensive or extensive ? any suggestion ?

>>9173484
just say goes to 0 because the exponential grows faster than to the power of 5 (which is true btw)

>>9173746
anon who just posted this . I decided to go with extensive cause how we digest a hotdog could change from a raw hot dog to a well done hot dog

Currently working on b/c - the hint suggests using the fact that Q[x] is a UFD, but I'm not sure how this is useful (probably because I'm a brainlet). Any pointers to get me started?

>>9173934
Actually I think I figured it out (was originally over complicating it): the quadratic monic divisors of f should be: h=(x-1)(x+1), h=(x-7)(x+1), and h=(x-7)(x-1)

>>9173484
take a look at the denominators in both factors
[math]
\lambda^5 \left( e^{\frac{x}{\lambda}} \right ) = \lambda^5 \left(\sum_{k=0}^{\infty}{\frac{1}{k!}\frac{x^k}{\lambda^k}} -1\right ) = \lambda^5 \left(\sum_{k=1}^{\infty}{\frac{1}{k!}\frac{x^k}{\lambda^k}} \right ) =
\\
x\lambda^4+ \frac{x^2 \lambda^3}{2} + \frac{x^3\lambda^2}{6}+\frac{x^4\lambda}{24}+\sum_{k=5}^{\infty}{\frac{1}{k!}\frac{x^k}{\lambda^{k-5}}}
[/math]
the first part will go to 0 when lambda goes to 0, while the sum part goes to infinity. Thus the whole term goes towards infinity.
Since it's in the denominator, your whole thing will have it's limit at 0

I'm measuring the period of a pendulum with a photodiode monitored by a DAQ operating at 100Hz. The software I'm handling the DAQ with measures time registering a sequence of indexes when the photodiode is obscurated (the frequency I'm using makes it so that I'm getting 5-6 indexes every passage of the pendulum), and those indexes are later converted to time measurements simply by diving them for the DAQ acquisition rate.
The question is, how do I go about associating an error to the mean of the indexes relative to a single passage? You can't really say they follow a distribution as they're bound to be a sequential list of natural numbers, but strictly speaking they're all different measurements of the same physical quantitiy. Do I have to resort to (max index - min index)/2?

>Is the Wronskian of some scalar functions [math]f_1,...,f_n[/math] a scalar or a tensor? With [math]f_1,...,f_n \in C^\infty (R \leftarrow R)[/math].
1. What is [math]C^\infty[/math]?
2. Is not a scalar a tensor?

>>9174068
>[math]\leftarrow[/math]
Should point in other direction. Although it matters not in this case?

>>9174068
a determinant is a multilinear form on the rows of a matrix [(0,n) tensor].
the rows of the matrix that create the wronskian matrix are the result of differentiation operators acting on the f_i [(n,0) tensor].

in that sense you can think of the wronskian as a tensor, but i'm not sure how many results you can get from that insight.

C^\infty(R->R) is the space of functions from R to R, which are differentiable infinately often

\sum_ix_i

Is the following true? Both equations?

>>9173296
it's exact if you take the partial derivatives and they're equal to eachother

[math] (2x-1)dx + (3y+7)dy = 0 [/math]
taking derivatives
[math] \frac{\partial}{\partial y} (2x-1) = \frac{\partial}{\partial x} (3y+7) [/math]
[math] 0 = 0 [/math]
therefore the differential equation is exact and you don't need the integrating factor

>>9174087
yes, write it out for yourself if you aren't sure

>>9174083
Thanks. I don't know what multilinear form is. I know how the Wronskian looks like in this case. My teacher asks if it is a scalar or a tensor? It is a determinant so we only get a single number. My retard intuition tells me then scalar. But. If we interchange two functions we interchange two columns so we get a minus sign. So if [math]W(f_1,f_2,...,f_n) = D[/math] then [math]W(f_2,f_1,...,f_n) = -D[/math] correct? We can say that [math]T_{\vec{f}} = T_{f_1,f_2,...,f_n} = D[/math] and interchanging two [math]f_i[\math] will add a minus sign. So then it might be a tensor. But I don't understand if this is correct.

>>9174087
Does [math]\sum_{i,j} x_{ij} = \sum_{j,i} x_{ij}[/math]? If yes is there a difference between the two equations?

>>9174087
Write down the x_ij s in table form.
One summation does it by rows, the other one does it by columns; both are adding the exact same stuff.

>>9174124
>I don't know what multilinear form is
it just means, that it's linear in each argument, i.e.
[math]
W(\lambda f_1+g,f_2,...,f_n) = \lambda W( f_1,f_2,...,f_n) +W(g,f_2,...,f_n)
[/math]
the minus sign doesn't have much to do with anything.
since it is multilinear, it can be understood as a (0,n) tensor (mapping n-tuples of C^\infty functions onto a scalar)

>>9174142
Thanks!
So.
1. W is a determinant of some n-by-n matrix.
2. A determinant is a multilinear form on the rows of a matrix.
3. A determinant maps the rows of a matrix onto a scalar.
4. These rows are n-tuples, so it maps n-tuples onto a scalar.
5. This is also what a (0,n)-tensor does.
6. Because it is a multilinear form and because it maps n-tuples onto a scalar, a determinant can be understood as a (0,n)-tensor.
7. Therefore, W can be understood as a (0,n)-tensor.
Is that the reasoning?

By the way, do you happen to know a good introduction at introduction-level on this subject (tensors)? I have Frankel's Geometry of Physics (maybe you know it) but it doesn't look introduction-level to me...

>>9174260
>4. These rows are n-tuples, so it maps n-tuples onto a scalar.
although matrix rows can be understood to be n-tuples of scalars, I meant the collection of n matrix rows to be your n-tuple.

To be able to make the step from 6 to 7 you also have to argue, that the function mapping your f_i onto the rows of the wronsky matrix, is a linear one, so that it's composition with a tensor is still a tensor, i.e you got to show that
[math]
D: f \mapsto (f,\frac{\mathrm{d} }{\mathrm{d} x} f,\frac{\mathrm{d^2} }{\mathrm{d} x^2} f,...,\frac{\mathrm{d^{n-1}} }{\mathrm{d} x^{n-1}} f)^T
[/math]
is linear, then
[math]
W(f_1,...,f_n) = \det(D(f_1),...,D(f_n))
[/math]
is a (0,n) tensor

>By the way, do you happen to know a good introduction at introduction-level on this subject (tensors)? I have Frankel's Geometry of Physics (maybe you know it) but it doesn't look introduction-level to me...

If you want a non-handwavy introduction from a mathematical perspective, you should take a functional analysis class once you meet the prerequisites (it's a big help for quantum mechanics too)
I also know that physics students already start working with tensors in their first year, so that might not be the best tip.

Need a strategy to go about proving this, my guess is that I need to find one ideal which is not principal. Thoughts/tips/tricks/hints?

>>9174359
do it for [math] R = \mathbb{Z} [/math] first then generalize

>>9174359
https://math.stackexchange.com/questions/500254/is-mathbbzx-a-principal-ideal-domain

>>9173749
>>9174049

Thanks. I actually did fully prove it by applying L'Hopitals rule, but it was probably unnecessary.

>>9166297
shit i posted this in the wrong thread, this seems to be the right one for me.

can anyone help me understand this problem

Show that ¬ p → (q → r) and q → (p ∨ r) are logically equivalent.

im staring at a bunch of equivalences and the only one I can find thats applicable is

q → (p ∨ r) ≡ (q → p) ∨ (q → r)

What is this equation simplified?

(x^2+2xy-y^2)/(x+y)^2

I tried making the numerator into a factored form bu I can't.

I'm trying to solve a differential equation and that equation is supposed to be equal to (y^2+2xy-x^2)/(x+y)^2 after taking their partial derivatives.

>>9175201
you can get it to
[math]
1-2\left (\frac{y}{x+y} \right )^2
[/math]
by adding and subtracting 2y^2 in the numerator
>and that equation is supposed to be equal to (y^2+2xy-x^2)/(x+y)^2 after taking their partial derivatives.
which partial derivative?

>>9174873
use [math] A\rightarrow B \equiv \neg A \vee B [/math] with the equivalence you have: [eqn] Q\rightarrow (P \vee R) \\
(Q\rightarrow P) \vee (Q\rightarrow R) \\
\neg Q \vee P \vee ( Q\rightarrow R)\\
\neg Q \vee P \vee \neg Q \vee R \\
P \vee \neg Q \vee R \\
P \vee (Q\rightarrow R)\\
\neg\neg P \vee (Q\rightarrow R) \\
\neg P \rightarrow (Q\rightarrow R)
[/eqn]

>>9175201
Two words: Wolfram Alpha

>>9166297
I took the mensa iq test and got 128 the first time and 145 or more the next is the test just garbage?

>>9175356
>is the test just garbage?
yes

online IQ tests are not credible

Solve the given D.E. by using substitution.
(x - y)dx + xdy = 0
I let y = ux
I end up with (x - ux)dx + x dy.
I'm supposed to have (x - ux) dx + x(udx +xdu) = 0
How do you go from xdy to x(udx +xdu) ?

>>9175383
>I end up with (x - ux)dx + x dy.
why did you not substitute for every occurrence of y?

>>9175388
man im dumb

>>9175339
thank-you for your help

Are you sure about the 4th step when you go from

¬Q∨P∨(Q→R)

¬Q∨P∨¬Q∨R

i'm getting different truth tables and i can't find that law

>>9166297
How many seconds are in an hour how did you calculate 1t?

can anyone enlighten me on what device is this sean connery uses (aiming at the moon) in the name of the rose?

>>9175513
whoops i meant the 5th line when you are dropping the ~q is it redundant?

i might be beyond help

Can someone help me understand this?
How come the answers are different when I plug in the values?

>>9175568
>How come the answers are different when I plug in the values?
well what answer did you get...

This is probably really retarded but how does one travel in space? Like tell the direction they are going in and that they are not way off course? Also you always see space with light. Are there parts of space that are completely submerged in shadow? Pitch Black.

>>9175571
Its on the image. One is 2.3333, the other is 8.

God I suck at these analysis proofs. I just can't manipulate the absolute value inequalities.

Prove: (a_n) --> 2 and (b_n) --> 3. Prove, using the definition of convergence, that (3a_n - 2b_n) --> 0.

My attempt:
Assume for all epsilon > 0, exists N in Naturals s.t. |a_N - 2| < epsilon.
Assume for all epsilon > 0, exists N in Naturals s.t. |b_N - 3| < epsilon.
Must prove for all epsilon > 0, |exists N in Naturals s.t |3a_N - 2b_N - 0| < epsilon.
Fix arbitrary epsilon > 0.
We know exists N in Naturals s.t. |a_N - 2| < ep and |b_N - 3| < ep.

How do I connect the inequalities to show what I want?

>>9175568
>How come the answers are different when I plug in the values?
c and c_1 are different constants

>>9175582
>Assume for all epsilon > 0, exists N in Naturals s.t. |a_N - 2| < epsilon.
you should write things out properly, this isn't what convergence means

>>9175590
Assume for all epsilon > 0, exists N in Naturals s.t. for all n >= N, |a_n - 2| < epsilon

Fixed

>>9175589
Shouldn't I get the same answer though? Why bother going through that extra step?

>>9175582
A hint: The maximum function will be useful

>>9175608
>Shouldn't I get the same answer though?
no, do the algebra yourself from the line with c to the line with c_1 and you'll see how they relate

>>9175582
protip:
|3a_n-2b_n| = |3a_n-6+6-2b_n|

>>9172510
Yes

>>9172514
No
[math](p\land q \implies r) \nRightarrow(r \lor q \implies r)[/math]
[math](r \lor q \implies r) \implies (p\land q \implies r)[/math]

>>9175608
>You multiply 3*c, which became your new constant: c1

2.3333*3=8

Struggling to figure this question out

>>9175637
Ooo I'm pickin up what you're putting down. Now I have:

|3(a_n - 2) - 2(b_n - 3)| < epsilon

Now I know that:
a_n - 2 < epsilon
and
b_n - 3 < epsilon
And these can be leveraged. Now how do I "insert" them into the inequality above? Idk the algebraically correct way of doing that.

>>9175691
Triangle Inequality

Anyone know some counter-examples for this problem?

>>9166297
someone rec me a book on set theory that doesn't go over the same bullshit 50 times

Not really science but asking here since it's related to education: I'm a native English speaker but it's been a while since I was in school and I want to brush up on my my English/grammar skills from the ground up.

Is there any place I can find a good complete K-12 English curriculum (or books with the equivalent) online? My vocab and spelling is pretty good so that type of stuff is not what I'm after, I just want grammar/composition related stuff.

It's kinda tricky since everything "learn English" online is geared towards people learning it as a second language, not native speakers trying to re-learn all the proper grammar rules and stuff.

I failed out of uni because I didn't have the discipline to do big projects in my non stem classes which ended up with me not doing anything at all.

Is it possible to study advances maths by myself and still get a solid grasps on the subjects?

>>9176364
Possible? Sure!

Possible for you? That depends on you. Do you know OpenCourseWare from MIT? See ocw.mit.edu, there are a lot of courses you can follow for free.

How do i answer this?

>>9176878
Q3

>>9176878

A bipartite graph is a G=(V,E) graph which admits [math]V=V_{1}\cup V_{2}, V_{1}\neq \phi ,V_{2}\neq \phi,V_{1}\cap V_{2}\neq \phi[/math] and for any (a,b) in E, either [math]a\epsilon V_{1},b\epsilon V_{2}[/math] or [math]b\epsilon V_{1},a\epsilon V_{2}[/math].
If this is a valid definition for bipartite graph, then how is it true that "a graph is bipartite if and only if it contains no odd cycle"? A trivial graph would contain no odd cycle and it wouldn't be bipartite. What am I doing wrong?

I don't study EE but i have this problem for a complex analysis course. How do you solve this?

Really rusty on functions, if I do f(n)*f(n) does it come out to f(n^2)? I'm confused cause I thought anything you do to the variable you also do to the variable inside the function but only the variable I.e f(3n) = n + 1 would equal 3n + 1

>>9176890
>V1, V2 not empty
This part is not generally considered part of the definition of a bipartite graph.

>>9166330
This is a published "research article" in a journal called Qualitative Inquiry.
>Qualitative Inquiry is a peer-reviewed academic journal in the social sciences.
What the actual fuck?

>>9167447
You managed to write down a worse proof than what OP had. Good job.

>>9167445
That's already assumed you fucking idiot.

>>9176973
Thanks for the answer, if there are no restrictions of emptiness over V1 and V2 then the statement about odd cycles makes sense.
It bothers me though, since on the notes I've been given there's such a restriction in the definition.

Hey /sci/, dumbass here. What does this notation with the parenthesis around two terms on top of one another signify? I thought it might be a tuple or something but it doesn't make sense to me in the context.

>>9177137
https://en.wikipedia.org/wiki/Binomial_coefficient

>>9176878
Guise?

>>9177181
Are you serious? So how many ways are there to choose 0.5 students out of a class of cot(beta)/2?

Probably just meant to indicate a two dimensional vector. Why does that not make sense, OP?

>>9176878

C-A = p(B-A)

A=O+a
B=O+b
C=O+(ka-b)
=>
C-A = (k-1)a-b
B-A = b-a

C-A = p(B-A)
=> (k-1)a-b = p(b-a) = pb-pa
=> (k+p-1)a=(p+1)b

Given that a,b aren't colinear, this requires
k+p-1=0
p+1=0
=> p=-1
k+p-1=0
=> k-2=0
=> k=2

>>9177232
I've seen the binomial coefficient used like that before, so I suggested it even though it made no sense for me. But yeah, your answer seems more likely.

What's a good method to determine the active area of an induction cooktop without looking inside of it?

>>9177240
I'm not really getting your notation desu

>>9176951
It's not hard to come up with a counter example. Consider f(n) =1+n. Then f(n)*f(n)=(1+n)*(1+n)=1+2n+n^2 but f(n^2)=1+n^2. So they're not equal. Hence squaring the function is not always the same as squaring the argument. Note that they may be equal for some special cases.

I'm trying to find a (bachelor) thesis topic for my computer science degree, but I just can't think of any. I have decided that the easiest, most straight-forward way to find a topic, is to find papers published by researchers that have some "to-do" parts and help with that, or to find papers that have mistakes/bugs and fix them, or to find papers with software implementations that are written in archaic programming languages (like PHP, Lisp, etc.) and port them to a modern one.
Basically, how do i find papers like that? I tried a few research websites like dblp.org and researchgate, but they don't have any options to look for "incomplete" research

>>9177232
OP here. That's kind of what I meant by tuple, and in other equations in this text 2D vectors does make sense. So this equation would produce 2 outputs in a 2D vector? Again, I'm a dumbass but I'll see if I can Google it. Thanks a bunch

Help please I'm retarded.

I want to evaluate the complex contour integral
[math]\int_\Gamma (z^2+1)dz[/math] Where [math]\Gamma[/math] is the straight line from [math]z_1=-i[/math] to [math]z_2=1[/math]

I've found a working parameterization of this curve
[math]p = -i(1-t)+t \quad \quad t\in[0,1][/math]

What do I do now??

>>9178434
>What do I do now??
https://en.wikipedia.org/wiki/Contour_integration#For_continuous_functions

>>9177606
>Lisp
>archaic

You have learnt nothing in your computer science degree and do not deserve it. Saying this also discredits your institution, which now stands as a degree mill.

Your thesis should be "How to drop out of CS". Don't forget to empirically verify it.

>>9166297
Why is g also entire?

>>9178547
hmmsmt

How do I turn sin(x)^2 back to sin(x)?

If we have a continuous function [math]f[/math] s.t [math]|f(x) - f(y)| \leq c, \forall x,y\in[0,1][/math], [math]c[/math] some positive constant. Does this imply that [math]f[/math] is uniformly bounded at [math][0,1][/math]?

Can a fission-fragment rocket theoretically be used as a directed-energy weapon?

>>9178437
I'm not really sure here's what I've done
[math]z=-i(1-t)+t [/math]
so
[math]\frac{dz}{dt}=i+1[/math] or [math]dz=(i+1)dt [/math]
Insert into integral
[math]\int_0^1((-i(1-t)+t)^2+1)(i+1)dt [/math]

[math]=(i+1)\int_0^1-1+2t-t^2-2it+2it^2+t^2+1 dt [/math]

[math]=2(i+1)\int_0^1it^2-it+t dt [/math]

[math]=2(i+1)\left (\frac{i}{3}-\frac{i-1}{2} \right )[/math]

[math]=\frac{4+2i}{3}[/math]

>>9177286
Steel plate and a sensitive thermal camera suspended above it? Unless I'm misunderstanding you.

Is there a name for this differential equation x''=t^2x? Finding a solution seems easy enough, but my professor acted surprised that we didn't knew it's name or solution by heart.

>>9178730
It's correct.

>>9178762
http://www.wolframalpha.com/input/?i=Solve+x%27%27%3Dt%5E2x

I dunno wtf the parabolic cylinder function is.

>>9178776
Thank you

>>9170551
It was most definetley the Wellbutrin that caused the false positive. Some of the other drug in your system may have altered the metabolism of the drug to cause this. Just my two cents. Wellbutrin is a nasty drug in general and I would bet you wouldn't have to take Alprazolam if you weren't on Wellbutrin.

>>9178649
You don't. But you can use
sin^2(x)=(1-cos(2*x))/2

>>9175653
Bump for interest

How did coding even become a thing? Like, did someone just think "I'll type a load of stuff that looks like gibberish to everyone else into my computer and see what happens"?

I struggle with this problem anyone want to help me ?
Paul is in front of the parade, he run at the end and come back in 1m36s, Paul run at 10 Km/hours, the parade is 250m long, what is the speed of the parade ?

>>9179175
This question can't be serious.

Due to laziness, lm just gonna post ths >>9179314

Every news report about microbiology/ genetics/ cloning they show someone doing this. What are these tools called and what are they actually doing?

Category theory noob here, if exponentiation represents an isomorphic type of growth, then are complex numbers a violation of that rule? Or is the complex space just another separate isomorphic space? Also, what do complex numbers mean philosophically?

Having a bit of problem with electromagnetics.
I'm being asked the question in pic related.

Since I know that the E field can be given by
[eqn]\mathbf{E}={\frac{1}{4\pi\varepsilon}}\int_{V}\frac{\rho_v}{R^2}\:dV[/eqn]

And since [math]\mathbf{D}=\varepsilon\mathbf{E}[/math]

Then is this true?

[eqn]\mathbf{D}={\frac{1}{4\pi}}\int_{V}\frac{\rho_v}{R^2}\:dV[/eqn]

>>9179188
Something like this approach seems promising. I may have messed up somewhere though.

A bio cuck here, how do chromosomes adhere to each other in meiosis in such a way to exchange the same locus on the same chromosome number with a relatively low rate of error.

I was thinking some sort of protein markers, but would that not interfere with the other times that chromosomes need to condense such as meiosis?

How do I calculate the force necessary for a sharp edge to press straight through a material, without slicing or sawing?
Pic related, for example.

Would relativity be more digestable for the layman if we started calling "c" the space-time metric or something?

>>9168774
>If you just want to gain an intuition for lift focus on the Newtons's third law explanation and conservation of momentum
Oh shit, so the wing is shaped to direct air downward, forcing conservation of momentum to generate an upward thrust on the reaction mass? That's such a simple explanation it *has* to be wrong.

Are there any biologists here?
How do I go about identifying the species of this insect? A friend of mine found them in her room. She lives in Sweden.

>>9180030
"c" as in the speed of light? that would be confusing... also why care about it being digestible for the layperson?

>>9180377
I don't, I just have to keep reminding myself that light isn't the hot shit it thinks it is.

>>9178547
bumpO

>>9180232
Damn, Sweden really is being taken over by things that are big and black.

>>9180433
what's the problem? show g is holomorphic

>>9179175
programming languages are built upon older lower level languages.
Every command in say C corresponds to a command in a lower language like basic, at the lowest of which is simply binary commands, the high level languages are simply easier for people to read and write.