/sci/ - Science & Math

I'm at a community college right now. (It's actually a really good one for the science lower divisions).
I'm going for a BS in a biochemistry so I mapped out my course plan. I've never taken a physics course before and I will need a year of it when I transfer to uni. Should I take a baby physics course over a summer as a way to prepare for the relatively more difficult physics later on? Or would I be better off taking a math course as a way to boost my math skills? Would you guys recommend I take extra chemistry/biology classes to fill up my upper divisions or take on a minor in like computer science? Goal is to go to grad school btw.

>>9559005
I am absolutely torn between going into academia (math or statistics) or going into industry, making a lot more money and fucking with a relationship and shit.

Fuck

>>9559288
>Goal is to go to grad school
This is a question for your advisor then, do not take recommendations from internet strangers on a 6 year academic plan.
Physics is super math heavy so depending on your current skill level, it may behoove you to take some of it before taking physics. Only if you can jump straight into calculus though.

>>9559288
>I'm going for a BS in a biochemistry
Why are you fussed about physics/math then?
I mean, if you can afford it and want to sure. But I don't think anyone will really care about your physics grades.

>Would you guys recommend I take extra chemistry/biology classes to fill up my upper divisions or take on a minor in like computer science?

What do you want to do with your degree? For biochem, I'd probably fill up on extra chem/bio classes if you want to do something in science with it. If you dont, then yeah cs would be a good minor

Ask yourself what you want to do with your degree???? Then the answer should be clear

>Let A be a real n-by-n matrix. Show A is conjugate to a diagonal matrix only if there exists a basis of R^n consisting of eigenvectors
I'm not asking for a direct answer to this, but where the hell do I even start looking? I've only barely figured out how to show two different bases of the same Vector space are conjugate.

>>9559403
Think about how A acts on its eigenvectors and prove that they form a basis.

>>9559428
So if I understand eigenvalues correctly, they're effectively the scalars applied to vectors in V in the linear map T:V->V to yield v' or what-have-you, right?
So the only logical way for these to remain linearly independent (as a linear map) is for the eigenvalues themselves to form a basis of the vector space they're applying to?
Or am I missing a part/skipping ahead
I've only done computational stuff and nobody ever told me what the hell any of it meant

I have asked this in another thread with no answers.

What does it mean when the amount of equations and unknowns are the same? Does it make any difference if there would be one more unknown than equation? Does it mean that if the amount of unknowns is equal or less than the equations, then the unknowns are completely determinate? (that's what I'm thinking) Does this always hold true?

>>9559488
iirc Fewer unknown than equations (or the same) does not guarantee solvability, but more unknowns than equations does

>>9559504
neither guarantee solvability

>>9559397
>>9559401
I'm able to jump right into calc, I've just been waiting until I start my calc/physics sequence to start because I don't want to be rusty.

Yeah, I just found out I can even take masters level chemistry/biology courses as a senior, so that's good.

BS in Chemistry (w/ Biotechnology certification)
MS in Chemistry (Bioorganic and Biomedical Chemistry)
PhD in Bioengineering

Are my goals, after I finish my biotech internship next summer hopefully I'll be able to start working at biotech companies.

>>9559504
MORE unknowns than equations guarantees solvability? You sure?

It seems like it's just a matter of which are the independent and which are the dependent variables, and how you determine or find the independent variables. Still, it seems like there is something good about having the amount of equations be equal to the unknowns, like it makes the equations definable.

>>9559488
look up Rouché Capelli theorem

>>9559448
>they're effectively the scalars applied to vectors in V in the linear map T:V->V to yield v' or what-have-you, right?
No. Read your textbook lmao.

>>9559547
Nigger I'm trying, it's all abstract and this problem is asking questions way ahead of the chapter we're in

What programming language would be most helpful to learn for a mechanical engineer? I've found I really like writing code in MATLAB and i want to branch out.

>>9559560
Prove: If [math]A=VDV^{-1}[/math], then eigenvectors of A form a basis.
Hint: Get [math]AV=VD[/math], where [math]V[/math] is invertible and so has [math]n[/math] independent column vectors. Take a big fat guess what the columns of V could be. Formalise.

I'm trying to do graphing in trig but I'm fucking retarded and don't understand what I'm doing wrong. Equation I'm given is

>Y = 2 - 3Cos((3/2)x-π)

My Y values seem to be right by themselves (5 at the top, -1 at the bottom), but my X values are all fucked. Five coordinates I'm getting

>(2π/3, 5)
>(π/3, 2)
>(0,-1)
>(-π/3, 2)
>(-2π/3, 5)

Yet when I plug the equation in on desmos the X values are completely different. What the hell am I doing wrong?

>>9559572
I can work with that. Vielen dank, i plan to meet with my prof but I need some kind of base to start off

>>9559524

Hmm. Learning some cs couldn't hurt. It would help to know if you are working with engineers and other programmers. Even if you don't minor, take maybe cs 1 and 2

>>9559567
>as a mech e
If you want to learn to program, it doesn't matter "for what."

It's most helpful to learn more than one language. I recommend C, racket/scheme, and haskell/ocaml. No programming language is very good, but if you learn enough of them then in a weird way they all become tolerable, except for python which is utter fucking shit.

Personally I would suggest staying away from C++ until you have two or three languages under your belt. Early in "learning to program" it's best to be able to separate the abstractions and their application from the peculiarities of an individual language and C++ is basically the most peculiar language in serious use. For that reason I think scheme or racket are the best beginner languages, but I don't feel extremely strong about it. A good language should have little syntax in my opinion so you can get to the meat of programming quickly. Forth and scheme are just about the most bare bones languages which nevertheless offer an extremely high ceiling.

Good languages: racket/scheme/lisp, forth, C
>why are these good to learn first
they have a very low surface profile, it's relatively easy to master the language in a short period of time, yet they are flexible enough to allow you to build powerful abstractions (C less than the other two, but it's still alright)
Bad languages: C++, Java
>why are these bad to learn first
They are too feature-rich and therefore difficult to start with when you are simultaneously trying to learn good ways to solve common problems in the first place. Arguably they get better when you are a better programmer but I think they are overrated even then.

>>9559600
>It's most helpful to learn more than one language. I recommend C, racket/scheme, and haskell/ocaml. No programming language is very good, but if you learn enough of them then in a weird way they all become tolerable, except for python which is utter fucking shit.
>Personally I would suggest staying away from C++

Fuck off /g/, you don't belong here.

>>9559567
C++. You can even include it into your Matlab code with MEX files. C++ is also what most everything is written in and you learn most of C at the same time.

Read: Programming: Principles and Practice Using C++ by Stroustrup
Then read: Data Structures and Algorithms in C++ by Drozdek

>>9559596
>take maybe cs 1 and 2

Why the fuck would you ever pay money to learn java?

>>9559615
>>9559622
here come the C++ apologists, they're like jehova's witnesses

>>9559403
Show that basis consisting of eigenvectors is linearly independent and spans your domain. Then you change to the eigenbasis using general change of bases and use the properties of c.o.b to get the conjugate relationship
>>9559403


>>9559403

>>9559288
>Should I take a baby physics course over a summer as a way to prepare for the relatively more difficult physics later on?

(Algebra based) Physics is just like theory in Gen Chem. If you could do one, you can do the other. University Physics assumes no background in physics so you're not going to be behind.

>Or would I be better off taking a math course as a way to boost my math skills?

Sure but your options are limited to linear algebra or proofs if you haven't finished calculus yet... (and even then you might need to get permission if they have calculus prerequisites)

>>9559524
>I'm able to jump right into calc, I've just been waiting until I start my calc/physics sequence to start because I don't want to be rusty.

You're not going to be rusty. The sooner you start calculus, the better.

>>9559627
Fuck off to /g/. You faggots have never even coded in C++.

>>9559600
>>9559622
Thanks boys

>>9559654
We have Introduction to Physics (101) -> General physics I & II -> University Physics I & II (Calculus Based)

Indians wipe their butts with their hands.

Might sounds retarded but how dirty is this, truly? What if you thoroughly wash your hands afterwards? Is there still a dangerous amount of poo-germs left?

Im trying to create a small scale rigid bosy simulation of an object rotating but im having a hard time think about how i can define the ibject computationally. Ive. Written my lagrangian out for the rigid body, but what would be the best way of defining the rigid body? Im using python and c++. I was thinking of drawing the part in blender, but idk how to export the data into something useful. Any thoughts?

>>9559579
Possibly because its interpreting the X input in something other than radians?

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

>>9560145
If g is a real-valued function, then the “largest” possible domain is [0,infinity) because any x<0 will mean that g(x) is not in R.
I really don’t understand what you mean by the third line. g(5) is equal to sqrt(2)

>>9560145
√2 is a real number, what's the issue

I am working on a mathematical model of a disease, and have to give a talk to an audience of physicians.
How much math do doctors know? Should I go into some details of the model, or just gloss over them and focus on the results?

my professor is fucking with me
i submitted a paper a month ago and he still hasn't graded it
how do i deal with professors who fuck with me

>>9559448
visual explanation
https://youtu.be/PFDu9oVAE-g?t=3m

>>9560040
Why dont you use a finite element software?

Why the fuck do all calculus books define the "≥" relation as a relation in the real numbers such that satisfy certain properties (total order, x≥y implies x+z≥y+z and xz≥yz for z>0)?

If we were to define the "≥" relation as the relation between two numbers x and y such that their difference x-y belongs to the non-negative numbers, then ALL of the above properties could be proven from this definition.

So instead of stating like 7 order axioms we could just state the existence of a subset of R (named the nonnegative numbers) and the existence of that relation, and then prove all of those other properties

>>9559524
Jump straight into calc and physics will be a trillion times easier, you end up doing a lot of integrations.
Learn some basic python and maybe mathmatica, but it's not necessarily worth spending time in a class for. It's really simple to learn and you'll end up needing it to do number crunching.
C++ may behoove you if you stick closer to engineering.

I don't understand the answers in this fucking question. Shouldn't it just be zero considering ethane requires C and this formula has none of it?

Any graduate TAs or professors here?

Whats your love life like? How much time do you have to spend with your partner?

>>9561690
wat? Isn't [math]C_2 H_6[/math] ethane?

>>9561725
Yeah nvm I'm fucking retarded, I have no idea what I thought the C was.

>>9560764
what do you mean by relation? what kind of relation?

Retard here

I'm trying to calculate the length of a vector (-1, sqrt(3))
It's 2. I can draw it on a piece of paper and measure out that it's 2, I type it into an online calculator and it says it's 2.

The problem now is that I try to calculate the length myself it won't say 2.
Typing sqrt(-1^2+sqrt(3)^2) into a calculator or wolfram alpha or whatever will say sqrt(2).
So now I thought I'm and idiot it must have to do with the square roots and shit
sqrt(-1^2+1.7320508...^2) will feed me 1.41421 which is the square root of fucking 2

Please help I know I'm literally a fucking retard having trouble with like 6th grade math, this isn't homework but I just don't comprehend
The solution is probably fucking obvious to anyone that's not me, I just need someone to tell me

>>9561858
You're typing [math]-(1^2) instead of (-1)^2

>>9561858
It's because you're typing in -1^2 = - (1^2) instead of (-1)^2

>>9561864
>>9561868
Thanks friends
Turns out I'm too dumb to use a fucking calculator, I must have typed this wrong like 20 times into different calculators and online tools

>>9561872
hey man we've all made this mistake once in our lives. Don't be too hard on yourself and keep doing maths

Is it correct to say that atoms with more electrons are larger than atoms with fewer electrons? Or heavier?

>>9561872
It's literally the most common calculator mistake. There are threads about it here weekly or so. Not a big deal.

>>9561884
>>9561899
Thank you for the encouragement
I'll take this as a lesson to be more careful with my brackets

This was part of me calculating the angle between two vectors, what I got was 15 degrees off what I knew the solution should be, with the whole thing being rather straight forward and the small numbers it was quite irritating for a bit
Vectors are pretty cool

What sort of group should I look for when being forced to do assignments with complete strangers? I know to avoid the international students but that's about it.

>>9561917
I feel kinda dumb saying this, but Linear Algebra changes the way you look at the world. It really is a beautiful field.

what do i do when my exponents have exponents

>>9561972
[math]a^{b^c} = a^{(b^c)}[/math]
[math](a^b)^c = a^{b*c}[/math]

>>9561983
alri that's fairly simple

>>9561891
Heavier is probably better. Or you could say the atoms with more electrons have more orbitals and so take up more space or something. Idk.

>>9561891
Electrons weigh next to nothing but atoms have the same number of electrons and protons so they would be heavier by implication
And they need more orbitals but I'm not sure how that would actually look in a 3D space

Say the orange car collided with the blue car, which both have the same mass.

If you know the initial speed and direction as well as the final speed and direction of the orange car, including the exact location where the collision took place, can you figure out the final direction and final speed of the blue car, or is there not enough information to solve for that?

>>9561891
Due to increasing electronegativity, moving from left to right along the periodic table generally results in smaller atomic radii.

>>9562209

You would need to also know the starting speed/direction of the blue car.

If that's what you meant they yes, you could figure it out using the conservation of momentum in the x and y axis'.

Work = q(change in kinetic energy)
So should this be (4.2x10^-9)*(2.2x10^-6)?
I read somewhere online that work is actually kinetic energy, or 2.2x10^-6 in this case. Why or why isn't this true?

>>9562327
work = change in kinetic energy = charge * field strength * displacement

You couldn't calculate work without the field strength, but since they give you the change in energy you don't need to.

how do i work these for tn= 2n-1 and n is greater than equal to 1.

on the first one i just do ti = (2(1)-1) + (2(2)-1) + (2(3)-1) right?

i have no idea how to do the second one or what that symbol is called

>>9562508
It's the same as the first, except you multiply every term instead of adding them.

>>9562508
14) the sum is equal to [math]t_1 + t_2 + t_3[/math]

16) the product is equal to [math]t_1 * t_2 * t_3[/math]

>>9562281
>>9562209
Provided you knew the initial momentum vectors for each car and supposinh any acceleration along the z axis (normal to Earth) is minimal, there is ALMOST enough information to deduce the final situation. We can apply conservation of momentum, but it would be even more useful to know HOW the cars interact with each other: elastically, plastically or other? Sometimes momentum goes to other stuff, like a bumper flying off. Energy is lost to friction and noise.

>>9559572
dude that hint is basically the whole theorem

Sonic the Hedgehog's mass is 34.9266125. When he's in a spinball, it takes him 3 seconds for him to fully charge up to go at the speed of light. How much force can Sonic exert?

>>9562603
When Sonic is charging up his spinball, he's spinning really really fast in place. I'm not sure if that might have something to do with the outcome. I also don't know if this is sufficient information to calculate his force. I'm not really a physics guy, so please explain if there is an answer to this question.

>>9562534
Yeah, sorry, I meant imply that there were no external forces like gravity, and the collision was completely elastic.

Okay so, what would you need to know in order to solve for the final momentum and direction of the blue car?

Would the initial momentum be enough? Or would you also need the initial direction? What if you had the initial direction but not the initial momentum?

>>9562603
(300000m/s)^2*~35kg = the energy necessary to reach the speed of light at that mass. To reach that speed at 3 seconds feom a standstill depends on the force of friction among other things.

>>9562603
What is the radius of his body in the form of a ball?

>>9562629
Uhh, no. It takes infinite energy to reach the speed of light.

>>9562638
I don't know actually. He's 100 centimeters tall, but in his ball form he's 50 centimeters if that helps. I don't think I have enough information.

>>9562603
>mass is 34.9266125
>go at the speed of light

Brainlet here, how the hell do I calculate two angles needed for equilibrium when I know 3 vector magnitudes and one angle? The numbers are:
Vector Magnitude (g) | Angle
168.6 g 0°
99.7 g ?
119.9 g ?

What is the best(fastest) way to reliably prep for the ACT and SAT considering I've been out of high school for nearly 8 years?

>>9562789
For the writing section, there is a set guideline that they look for. Look up how to pass the writing section and you'll be fine.

For the reading, you have to know a lot of vocab. They don't allow you to take advantage of suffix and prefix usage because they don't want you to be able to study for the exam, they want you to use you built-up vocabulary from many years of experience.

For math, it's mostly your innate logic combined with algebra and trig. At the very least, you can learn algebra and trigonometry before taking the exam.

Two questions concerning dentistry:
1. Is there any legitimacy to conspiracy theories about fluoride in the water?
2. Do fillings and dental fissures have health side effects?

Is ho3 2016 a second moon or a completely separate celestial body?

Why Mathematica keep using Log[e]? Isn't it just 1 ffs
Is there a way to change it?

>>9562994
Does Mathematica default log to base e, or is it like ti83/84 that defaults to base 10

Today I got my first Fluid Mechanics class and I noticed there won't be any conformal maps in the curriculum. Is there an introductory text or a book that focus on this application for conformal maps and maybe the underlying mathematical principles? I like mathematics and I was disappointed when I noticed it won't be covered in class. One with exercises will be much appreciated.

>>9562994
You probably just need to use a simplifying function around the results.

>>9562822
>1. Is there any legitimacy to conspiracy theories about fluoride in the water?
It is a fact that over-dosage of fluoride causes health problems. Wether the low dosage recommended to avoid cavities present long-term problems is a matter of debate. But there was a (anecdotal) case in my state where the water company put too little fluoride in the water. So, how much do you trust your company not to put too much in it?

>>9563169
Log to base e

>>9563244
Simplyify[] doesn't work

If you meet a random woman at the gym and she carries a negative recessive gene, isn't that just as dangerous as breeding with your sister that carries a negative recessive gene? Does the presence of similar negative recessive genes increase the likelihood of outcome? What if I carry a negative recessive gene that may cause Tonsillitis or something, and this woman I meet at the gym also carries a gene that may cause Tonsillitis, would breeding with her cause the same danger of Tonsillitis in our offspring as mating with my sister?

>>9563534
>If you meet a random woman at the gym and she carries a negative recessive gene, isn't that just as dangerous as breeding with your sister that carries a negative recessive gene?
yes

>>9563534
no your sister carries much much more recessive negative genes that you have too
the random lady shares only a few with you, but your sister a lot

>>9563695
But it's the same danger for Tonsillitis specifically, or the same "danger" for blue eyes specifically.

>>9563382
That's not the exponential e, dummy. <esc>ee<esc> for that.

Protip: Blue means undefined symbol.

How would you write the equations to solve for the seven currents in matrix form?

>>9563818
Oooh, I didn't knew that
Thank you kind anon

>>9563905
Connect ground and V+ through a 6V voltage source, then set up mesh currents and solve simultaneously.

>>9562621
>Okay so, what would you need to know in order to solve for the final momentum and direction of the blue car?
>Would the initial momentum be enough? Or would you also need the initial direction? What if you had the initial direction but not the initial momentum?
Momentum is a vector, so if you know the momentum you (by definition) know the direction. If no momentum is transferred to the earth, the final momentum of the car wreck will equal the total initial combined momentum of the cars. Remember, momentum is p=mv, where v is the velocity vector and m is mass ( a scalar). The direction is included in the vector.

so i just got my grade back for a 5000 word research paper on sustainability and it's an A+
i'm pretty happy. i had to wait 5 weeks to get a final grade

how do i keep my ego in check lads

Test

I've been thinking alot about future space travel and I'm stuck on a recuring thought. What if space travel inherently destroys civilisations?

Consider:

All objects influnce each other.
Orbits are inherently unstable
Energy is neither created nor destroyed only transformed

So with these 3 things in mind, would a species that depends and grows on spave travel, even just within a solar system, alter the orbits of their celestial bodies just by using gravity assists to get from place to place or going counter rotation using propulsion? The energy the object has is used by the space craft, and gravitational attraction, even if its very small, adds up in effect over time.

I cant stop concluding that a solution to the Fermi paradox, and an explanation to some of the missing matter in the universe is that civilsations do arise extremely quickly, but due to spave travel they destabilise their solar system and fling the planets out into space just by doing normal space travel.

Please point out the flaws in my thinking and explain why I have nothing to worry over

Pls send help

>>9564398
What have you tried?

>>9564393
Planets are absolutely fucking enormous, no civilisation stands any chance of significantly altering their orbits, unless that civilisation is already so advanced that it'd be unthinkable for them to be destroyed. Look it up, planets are fucking heavy heavy heavy

>>9564402
Expressing the each individual term as its sum, so exp(1/z) with factorials and so on....
but that gives me a form that seems completely different to what they're asking

So I’m considering taking Physics I next semester (Not general.) I’m a Math+CS double major, but I wanna get a basic understanding of electricity/magnetism so I can begin to self-study EE/CE. From what I understand it’s a calc-based course, but that doesn’t tell me much. I took regular physics and highschool and did okay.

Is this a bad idea?

>>9564403
I heard on curious droid that when voyager 1 used Jupiter for a gravity assist to saturn, jupiter lost about a foot of speed every trillion miles.

A small change but still a change. Add that up over a thousand years of inter solar travel and multiple by, say, 10,000 similar assists for industrial, economic and personal travel.

I'm thinking really long term.

>>9564446
Honestly a negligible change, Jupiter's travelling at 43,000 ft/s, and it's orbit takes it around ~3 billion miles, so its would take hundreds and hundreds and hundreds of orbits of Jupiter (11 years per orbit) for it to lose 1/43000 of it's orbital speed.

Maybe with one of Mars' shitty moons we could have a noticeable effect, but they're gravity is so weak we'd pretty much never use them for gravity assists anyway

My professor from last semester was in my class/lab today for a brief second. He patted my shoulder on his way out to say hi.

D-does that mean we are buddies now?

Can someone help me come up with a test to confirm whether or not I'm being MKUltra'd?

Thought I was for a few years, but not anymore. But then I got more of those weird brain aneurysms that made me smarter a few weeks ago and now I'm curious to know if they're back.

>>9564583
No, he was just being friendly.

>>9564440
Physics I is probably just mechanics. You won't get to electrodynamics until Physics II. If you want to learn circuits, you're better off taking an actual circuits class. Physics II is going to focus on the physical aspects of electromagnetism moreso than the applications in circuitry and beyond.

>>9564360
It's easier to get good grades on topics which are politically charged (and in agreement with the grader). Sustainability is very important to anyone interested in geosciences or other environmental sciences.

You asked.

lads send help

I think the answer for 4 is just the 3x3 matrix with 1 in all entries but i'm not confident in my reasoning

I basically have no idea how to approach 5

>>9564805
>I think the answer for 4 is just the 3x3 matrix with 1 in all entries but i'm not confident in my reasoning
What's your reasoning?

>>9564806
actually now i think its 1/3 times that matrix
i rearranged the orthogonal projection equation and solved it using (1,1,1)^T

The field is set up by four electrons forming a square, each separated by 10nm. Point A is in the middle of the square.
I'm having trouble starting problem 3. I've read my textbook many times and looked online, but it says nothing about eV or alpha particles.

>>9564806
I've been checking that result and it seems to be correct but but i'm still lost on 5

>>9564833
I've come up with
Voltage at point A = .7481
W = -q(Va - Vinfinity)
= -2e(.7481) = -1.4962eV
Then I just multiply 1.4962 by the charge of an electron. Does this seem correct? It sounds right, but I have nothing to verify.

If I randomly choose 4 lowercase letters and then 4 digits to create a sequence (repetition allowed, order important), would this have 26^4 * 10^4 possible outcomes?

To clarify, all results would be in the format:
>abcd1234
>xxyy9876
>ajex3484
>ubcs2983
etc.

>>9564891
26×26×26×26×10×10×10×10=26^4×10^
Yep.

>>9564907
Thanks Anon.

How would you explain the solution to this problem step-by-step to a brainlet?

>>9564805
There are several matrices that work for problem 4, most generally, matrices that have their i-th row(or column, depends which side you're multiplying) as the vector (a_i, a_i, a_i), where there's at least one j for which a_j!=0.

What EXACTLY does dP(w) here mean? Or even in other contexts I've seen dP or d(mu). I understand that P/mu are measures, but why do we write "dx" if we are just integrating over a variable "x".

My only knowledge of measure theory (that I learnt to learn probability theory): sigma-algebras, probability-measure, sigma-additivity, algebras, semi-algebras, measurable sets

Just got back the first test of my graduate career and didn't do as well as I hoped. Scored a 60%.

Average - 72.01%
Std Dev - 10.81%
Lowest Grade - 31%
Highest Grade - 94%
80 students in the class

My professor says he typically gives out B's and A's in the class and rarely any C's. How are graduate classes typically graded?

>>9565278
>What EXACTLY does dP(w) here mean?
Integration with respect to the measure P.
Look at the case where you can write the Integral as a sum.

>but why do we write "dx" if we are just integrating over a variable "x".
You can use both, although normally dx is used in the context of Riemann Integrals, while dP(x) or just dP is used for general measures, if you see a dx with a non-Riemann integrable function, which is Lebesgue integrable just pretend the you are Integrating over the Lebesgue measure.

>>9565278
It's just a notation (which is not completely uniform) to say that you integrate the function X wrt the measure P. If you want to mention the variable of integration w, then you want to write int(X(w)dP(w)), otherwise write int(X dP).
If you integrate over R^n with Lebesgue, the measure is usually implied (to conform to the previous notation).

What are some good exercises to "sharpen" the mind?

>>9562603
>be SONIC
>go at the speed of light

kill yourself

>>9565437
find a good boxing gym

>>9565437
Squats and deadlifts.

How do i stop wasting time? I keep playing vidya, and while i want to study, i also want to play vidya with friends. What do?

What is the correct [math]k[/math]-th derivative for: [math]\displaystyle f(x) = \sum_{n=0}^{\infty} (-1)^{n}\frac{x^{2n}}{(2n)!}[/math]?
I get
[eqn]f^{(k)}(x)= \sum_{n=k}^{\infty} (-1)^{n}\frac{x^{2n-k}}{(2n-k)!}[/eqn]
but this is wrong apparently.

>>9565737
Why is it wrong?

>>9565744
I get this for the second derivative.

>>9565737
The sum doesn't start from k

>>9565758
Isn't that what you wrote if you substitute k=2?

>>9565761
ah. what does it start from then? I tried n=1 and n=0 and it gave me the correct answer. any n less than k?

>>9565770
Check the kth derivative of the (k-1)th term of the original sum, probably starts something like floor(k/2) but I haven't thought much about it

What do you do to waste time while your simulation runs, /sci/?

>>9559005
>pic

Stupid chinks. That's not math. There's not even any numbers!

>inb4 lower case L is a 1

Hurrr

>>9565805
>implying 2 isn't a number
Put in some effort my man

>>9565822
That's a Zed not a 2, double brainlet.

>>9565839
look right below the z and you'll see a 2

>>9565805
>There's not even any numbers!
There are no ``numbers" in math.

>>9564398
Pls people, I'm stuck

>>9565594
Sonic is just his name, dipshit.

What's wrong with simply giving g as a function with domain the natural numbers here? I know I'm missing some idea..

>>9566205
Because Dom(f_i) could be N, and so you wouldn't have Dom(g) != Dom(f_i)

>>9566209
Oh. The question I have to actually answer is slightly different than that one. Sorry, yeah, my idea wouldn't work there, but this one seems to say that each f is actually undefined at some value and doesn't have domain N. I emailed the lecturer about it and was too to use a version of Cantor's diagonal method, but I really don't think that's even needed?

>>9566205
it should probably say "partial function g"

>>9566214
This version is trivial

>>9565908
I don't remember if the Laurent series only has to work locally, if so, remember that [math]\frac{1}{1+z}=\frac{1}{1-(-z)}[/math]

https://www.youtube.com/watch?v=d-o3eB9sfls
>8:40
>only applies in the limiting case for a tiny screen
omg lame

can you do anything like this but with a larger screen?

Honest question, would taking lsd help "free" your mind. Not talking taking it everyday, or week even, just once or twice a year. Can it do permanent damage? What other drugs can help free your mind?
Should I take drugs to be smarter, as in more perceptive to patterns and ideas? If so, which?

>>9566297
It WILL cause permanent damage but it's soooooo worth it. Normies are fucking stupid.

>>9566306
Looking for actual answers though.

>>9559005
In pic related, where the arrow is pointing shouldn't that be -sin^2 B? And would that not make the answer 1/-csc(B) or 1/csc(-B)?

For [math]a,b,c \in \mathbb{C} -\{0\}[/math], [math]a|bc|+b|ac|+c|ab|=0[/math] implies [math]\frac{a}{|a|}+\frac{b}{|b|}=-\frac{c}{|c|}[/math], which is impossible, right?

Are traps gay?

>>9566297
I did a bunch of LSD (among other psychedelics) when I was 15-16, and I think I continued using psychedelics occasionally up until maybe 18 or 19. I'd say that I have less of an "ego", and perhaps i'm a bit more open minded than I would've been otherwise. I wouldn't say LSD or any psychedelic had any perceivable impact on my intelligence. It's a powerful tool in altering your mental state, but I don't think you should take it with the hopes of increasing your intelligence. It might help you get over mental hang-ups you have (or make them much worse), and I think it may facilitate the process of making certain connections you hadn't noticed before, but to be honest I don't think LSD deserves the mythical aura it's assigned. I know plenty of dumb fucks who've taken boatloads of acid and they're still the same as always. Maybe slight personality changes, but ultimately they're pretty much the same as always, definitely not any smarter.

I believe LSD works only with what you already have there. I do have a theory that LSD could lead to some amazing results and insights if someone with a really high IQ were to use it, but I have no way to verify that.

>>9566371
Wait, sorry, I'm retarded, ignore this

what does this symbol mean

>>9566370
when you're subtracting (1-sin^2x) from something, you're subtracting 1 and adding sin^2x
1-(1-x) is the same thing as 1+(-1)(1-x), which is just 1+(x-1)=x

>>9566436
product my nigger
It means multiply

I've got to to my hw in recursive functions in LaTeX
What's the best TeX editor you can recommend me?

>>9566380
https://twitter.com/obamamalik/status/809796188782399488

>>9566437
Thanks anon, apparently I'm a retard and can't do basic arithmetic.

D.J. Griffith says
>"over small enough regions, any wave is essentially plane, as long as the wavelength is much less than the radius of the curvature of the wave front."
I can understand the part about the radius of curvature, so that the field vectors don't point in different directions in the region of interest, but I don't get why the wavelength needs to be small compared to the radius of curvature. It seems to me that, if anything, the plane wave approximation DOESN'T work if the wavelength is too small.

I've tried to sketch it, the blue line is the region of interest. The magnitude of the field peaks on the spherical wavefront touching the middle of the blue line. If the wavelength is small enough, there's a significant phase difference at the edges so the field magnitude is different too.

please respond

How would I accurately calculate how much fuel my car used on a single trip?

I can see information such as the average consumption rate in mpg, average speed, fuel tank range, and time traveled.

Pic related, how many gallons of gasoline would I have used on this trip?

>>9566456
>Obama Malik
If this isn't racist Jewish Irnic pol propaganda I'll kms
Jews are smarter than racist retards so they're yailef as heros in America, the dumbest country on the planet

I guess I should've posted this here instead of its own thread.

This is for a pest control solution. I bought a concentrate and need to know how much to measure to spread it properly. Pic related, I need to know how much of solution 36% X I shoudl put into a 32fl oz bottle to create a concentrate of 1.5%

>>9566496
I assume 47366 is the total miles traveled for all trips, and 780.7 is how many miles you traveled on this particular trip, right? If so, then 28 gallons per mile means that 780.7/28 = 27.9 gallons used for this trip.

Sci-fi weapon question: would a plasma beam weapon lose effectiveness in range in space because of inverse-square or would it be minimal?

>>9566392
So short answer no and maybe, alright.
Second part about drugs? I'm not talking about adderall.

>>9566489
Just look up the difference between near field and far field, once you're a few wavelengths away from the source it cleans up

>>9566529
ingredient = .015*32 = .48 fl oz
concentration = .36
y = .48/.36 = 1.33 fl oz

>>9566297
Na-selank-amidate from ceretroic. Selank or semax products all do good.

Cerebrolysin

NAC

Coq10


Social fluency phenibut and tianeptin sulfate

In order of effect i'd say: na-selank-amidate, tianeptin and phenibut, and nac

Haven't tried cerebrolysin but I'm guessing it would be synergetic with selanks.

If you do lsd take a lot of selank anecdotally it might help you focus more on what you want whilst tripping instead of overwhelming me you

I can't seem to get much intuition on continuous time Markov chains. The transition matrix, instead of describing the probability that in the next time block we will be at some state given the current state, is the rate at which state changes? How do you determine probabilities? I've seen quite a few explanations but none of it intuitively makes sense to me

>>9566618
Which part of my illustration is wrong then? That's supposed to be a huge number of wavelengths away from the source. If the wavelength was made smaller, the variation of the field magnitude across the blue line would be even more pronounced

Somebody help me clear this up:
Eigenvectors of a given map/operator are all linearly independent from each other, correct?
So if I have some T(a_1, a_2 ... a_n) = (2a, 3a_1, ... , n+1a_n) then my eigenvalues are equal to n+1 with repsect to each a_i for 1 to n, and because all a are linearly independent they have to be in some sort of form (i, 0, 0 ...) where i is in the respective nth position?
Or am I misreading this book entirely

>>9566449
>What's the best TeX editor you can recommend me?
overleaf.com

>>9566717
>So if I have some T(a_1, a_2 ... a_n) = (2a, 3a_1, ... , n+1a_n) then my eigenvalues are equal to n+1 with repsect to each a_i for 1 to n
No.

>>9566737
[math]$T(a_1, a_2, ... ,a_n) = (2a_2, 3a_2, ... , n+1 a_n) \\
Ta_1, Ta_2 ... = 2a_2, 3a_2 ... \\
\lambda_1 a_1, \lambda_2 a_2 ... = 2a_2, 3a_2 ... \\
\lambda_1, \lambda_2 = 2, 3, ...[/math]
???

I have about half an hour on the bus to classes, is there a recommended mini-lecture series, math focused?

>>9566744
The first two lines you wrote can not be simultaneously true.

>>9564861
look up what eV means. It's a unit of energy, not a unit of electric potential.

>>9566749
Is it a notation issue or a logic issue?
How is an operator from one set to another on the same field not possible?

>>9566761
The a_i are scalars, so T(a_1,a_2,...,a_n) implies the domain of T is n-dimensional, while Ta_1 implies the domain of T is one-dimensional

>>9566543
probably it's going to lose its effectiveness but you could start here
https://en.wikipedia.org/wiki/Astrophysical_jet

>>9566591
Hmmm, well I don't know about other drugs. You say you're not talking about adderall but in my experience that's the one drug I'd say genuinely did seem to improve my cognition. I wouldn't go so far as to claim it made me more intelligent, but when I use it for studying or whatever I certainly make a shit ton more progress, and a lot faster, too. It just gives me this massive boost in focus and productivity and motivation. When I use adderall, I will easily sit down and just study math for hours straight and not lose focus or get distracted for even a moment, it's god tier. I also get a lot of other stuff done: clean everything, organize everything, get errands done, whatever.

Only downsides I can think of are insomnia and loss of appetite, but I don't get either of those when I take a smaller dose. I still eat and sleep just fine. The come downs can kind of suck though, just feel "bad' at the end of the day when it's wearing off. Weed helps take the edge off, though. The other con is that the guy I buy adderall from charges me waaay more than they're actually worth, but that's got nothing to do with the substance.

You may also look into nootropics, i've heard good things about those but never tried them personally.

Alright so i've got this set of points that i'm trying to fit into a gamma distribution with matlab so i can estimate theta. The trick is that I want to use custom gamma since I know the k parameter (yes for the set in the picture , k= 1 so i can fit it into an exponential quite straightforward, but I've got other distributions with other integer k parameters to fit afterwards).

First i tried with 'mle' function and with a custom pdf but I've had 'not enough input parameter' or 'NaN' kind of error, i suppose it's because my data isn't normalized.

Then I tried to use nlinfit but it says :
"Warning: Some columns of the Jacobian are effectively zero at the solution, indicating that the model is insensitive to some of its
parameters. That may be because those parameters are not present in the model, or otherwise do not affect the predicted values. It may
also be due to numerical underflow in the model function, which can sometimes be avoided by choosing better initial parameter values, or
by rescaling or recentering. Parameter estimates may be unreliable. "
and the estimate of theta is my starting value.

Can someone detail me a method for finding theta in matlab when sample points of the distribution and k are known please ?

>>9566774
Okay that's fair.
So if I reworked it so some vectors 1 to n are linearly independent, then find the eigenvalues for each of those, that might work?
I mean it's pretty clear to me that the eigenvalues are index+1 for each a, I'm just trying to connect the dots

Does anyone happen to have a pdf of the answer book to Spivak's Calculus, 4th edition?

>>9566659
You can't write an interval as a discrete list. The best you can do is require your random variables transition continuously in your time parameter.

What areas of physics deal with probability and statistics?

I've never seen this shit before in my life guys. How do I start on this?

>>9567006
Use the hint.

>>9567029
But anon I don't even know what they are asking

>>9567000
quantum physics

>>9567033
What part do you not understand?

>>9567049
I don't understand what they want me to do. Do they want me to show that A(sub tau) is diagonalizable? Even so, I have no idea how to show that.

This shit seems easy af, but my solution seems off. Basically these rods constrain the masses and for them to have the same lenght and be riggid, the motion should be such that these rhombus shape is mantained. But if that is the case, my system just has 1 degree of freedom and everything is expressible by the angle one rod makes with any axis, but doing this I got to a Lagrangian that was [math]L=mL^2\dot{\theta}^2-kL^2[/math], i.e. the potencial energy is constant. So I don't know If I'm assuming something else, because that would mean that it's stationary.

>>9567063
They want you to show there exists invertible P with A_{tau}=PA_{sigma}P^{-1}, and they suggest using P=A_{tau sigma^{-1}}. So you should show P=A_{tau sigma^{-1}} satisfies A_{tau}=PA_{sigma}P^{-1}, and that P=A_{tau sigma^{-1}} is invertible.

>>9566659
You can have intuition similar to a discrete time Markov chain, except the time it's in any particular state isn't fixed and is instead described by an exponential RV

If I'm doing a line integral for Z(x,y) over a range A-B should I be taking the double integral of the function?

How do i determine how many orbitals an atom has at 4f?

currently a physics major. im really interested in the material but im average at it. i get mostly Bs with some As. should I change majors now?

what I dont want to happen is get rejected from grad schools and be left with a physics bs

>>9567236
Your question makes no sense.

Matlab/coding question:
I have two vectors X and V, if the nth element of X is negative I want the nth element of V to be multiplied by -1. Is there a more elegant way to do it than with a "for" loop and an "if"?

>>9567505
try abs(x)?

>>9567505
sign(x).*v?

>>9567505
I doubt it.

>>9567514
sgn(0)=0 will break his needs

>>9567517
>sgn(0)=0 will break his needs
sign(x+tiny epsilon).*v

>>9567531
no

>>9567514
Thanks, I feel dumb now. Right after posting I figured it out and was going to use x./abs(x), but that's even better

>>9567517
that shouldn't be a problem, x and v are filled with random values so none of them should be 0. if it is a problem maybe I'll replace sign(x) with the horror I was going to use initially: ones(1,length(x)) - 2*(x<0)

>>9567543
>x and v are filled with random values so none of them should be 0
wut

>>9567548
I filled the vectors using "rand" so one of the values being 0 is virtually impossible because of probabilities (and actually impossible since rand only produces values on the open interval ]0,1[ )

>>9559567
Python is good.

So I was studying algebra (well, fuck you gotta start somewhere) and I was at a place where you solve some problems relating to angles (acute, right, obtuse, straight,etc) and I gotta ask:
Is an angle falling on one of these categories matter at all in algebra?
It seems kind of arbitrary. When does it matter if an angle measures 2 degrees or 260 degrees that we need to differentiate from an obtuse or a straight angle?

>>9567617
>Is an angle falling on one of these categories matter at all in algebra?
it matters sometimes, yes, for instance if you're solving some system and get two solutions corresponding to two different triangles but only one of the triangles fits for reasons I'm not going to bother with

>>9567622
Okay, thanks. I was wondering whether it was going to be relevant to remember these concepts.

I'm trying to plot a hyperbolic parabaloid, which is a surface my differential geometry textbook defines as:
[math]
X(u_1, u_2) = (u_1 \cdot \cosh(u_2), u_1 \cdot \sinh(u_2), (u_1)^2)
[/math]

But when I try to plot it with matlab, I just get a weird, discontinuous surface. Am I doing something wrong?
(When I plot other surfaces, they tend to come out just fine... This is the only one I'm having trouble with)

Hey what's the most common nonsilicate mineral in the Earth's crust?

>>9567617
Hardly. It's useful for some practical problems but in general you're better off learning the equivalent of angles as fractions of π expressed in radians. This is way easier than it sounds. 360 degrees equals "2π" radians, 180 degrees equals π radians, 90 degress π/2 radians and so on. This is actually very important for more advanced stuff.

>>9567617
https://www.youtube.com/watch?v=p-0SOWbzUYI

Does pi look any different in base n numbering (where n = all natural numbers except 10)?

Is undergoing an actuarial course worth it? I would need to clear 15 papers on top of the entrance exam.

When I become an engineer, if I work for a company that makes consumer products and I fuck up. Would I be involved in the strict liability case?

Should I go to U of A or UC Davis for space meme degree

> https://web.archive.org/web/20140401081546/http://cosmologystatement.org/

is this 'objectively wrong' ?

>>9559394
I've heard Academia is absolutely terrible for math majors right now.

Too many PhDs and not enough job openings because tenure keeps peeps complacent

>>9567979
Typically no (if it was an honest mistake), They go through rounds of safety testing on well defined regulations. If its not a regulation and it kills someone... itll be a regulation.

Now, the company might not be too happy with you, but you shouldn't be directly involved. Thats what corporate lawyers are for.

>>9568007
Lmao, you're an idiot if you think tenure is what's keeping them complacent.

>>9567617
In trigonometry, there are often reasons to care about the "quadrant", which is roughly equivalent to acute/obtuse/reflex.

Brainlet here, I'm getting 41 and 1/6 while proper answer is 40 and 5/6

I've ended up with
200/4 - 121/6 + 11 = 61 - 121/6 = 41 and 1/6
where did I fuck up?

>>9567806
X appears to be a mapping from R2 to R3, how do you expect to plot this?

In all likelihood you wan to give matlabs surf function the X and Y coordinates you generated with meshgrid() and then the value of the function at that particular X,Y coordinates in the Z argument.

This works if you have a function from the R2 to R, but I really don't see what you are trying to accoplish here.

>>9568295
6*(1/4)*8-3*(2/3)*5*(1/2)+2*(2/5)*4*(7/12)
This is what you want to evaluate?

>>9568323
If he's having trouble with them, they're probably mixed numbers, so it would be 25/4, not 6*(1/4)

>>9559005
i know the hausdorff distance induces a metric on the set of all closed subsets of a metric space, but does it also induce a metric on the set of all subsets of a metric space?
english is not my first language so i apologize for any mistakes.
thanks

>>9568323
No, it is mixed numbers, not multiplication.

6(1/4) = 25/4

>>9567982
wtf is u of a? arizona? arkansas? alaska? alabama?

either way, the cali college system is only beaten by ivys so id go ucdavis

>>9568330
The Hausdorff distance induces a metric on the set of all compact subsets of the metric space, not necessarily on the set of all closed sets.
It's trivial to define closed sets on R whose H-distance is infinite, for example [math]d_H([0,1],[1,\infty])=\infty[/math].

>>9567286
Um. Its hard to know from this.

How much physics do you want your future to have? Most physics regretters or dropouts I know are because they didnt want physics to be their lives. They wanted hobbies, families, etc. They didnt want to constantly be pushing the forefronts of knowledge.

Its not for everyone. Physics takes dedication. So ask yourself where you want to be in 5 years. If its writing papers and researching, spending all day most days in labs and offices, stick with physics. If you want a different type of job, consider something else.

>>9568331
Oh, fuck.

anyways:
61 - 121/6 = 41
Is wrong.

it is 61- 120/6 -(!) 1/6=40 + 5/6

Has anyone else noticed that most professors and teaching staff use reddit spacing when they reply to a email you send them?
Is this because they actually use reddit, or is it because of the Latex thing where you have to make two spaces to make one space?

>>9568370
It's because it looks nice and makes things more readable.

>>9568376
sure, but if he only writes two sentences in response, is it really necessary to put two line breaks between the sentences? does he think that, as a university student, i don't have the attention span to read two sentences?

>>9568376
>more readable
Only if you're actually writing substantial paragraphs. It only becomes more cumbersome to read if you're separating single sentences.

>>9568307
>How do you expect to plot this
Same way I plot a parametric equation, which goes from R1 to R2.
The first two coordinates essentially give me the spacing of points on the XY plane, and the last coordinate gives me the height.

If you don't believe me that this works, here's a pic of a sphere and a parabaloid

>>9567806
Here's what Mathematica gets.

>>9568398
>Same way I plot a parametric equation, which goes from R1 to R2.
But your function clearly goes from the R2 to the R3, that can not work.
[math]X(u_1, u_2) = (u_1 \cdot \cosh(u_2), u_1 \cdot \sinh(u_2), (u_1)^2) [/math] this function clearly takes 2 values and outputs a vector in the R3.

>>9566730
Thanks breh

>>9559005

>>9568464
I am completely lost now.

>>9567000
Statistical physics

p,q distinct primes

x = 1 mod p
x = 1 mod q

How tf does it follow that x = 1 mod pq? I can't get the chinese remainder theorem to show that

>>9568519
x-1=pa=qb
since p,q distinct primes, q divides a, so x-1=pqc, so x=1 mod pq

>>9568525
Nice

how the fuck do i derivate square roots?

>>9568359
Why?
How come 5(1/2) != 11/2?

so
3(2/3) * 5()1/2 = 11/3 * 11/2, no?

Fellas am I doing something wrong here

[math]\int \frac{1}{\sqrt{-1+t^2}}dt [/math]
[math]=i\int \frac{1}{\sqrt{1-t^2}}dt [/math]
[math]=i(\arcsin{t})+C[/math]

>>9568555
Whoops meant for it to be
[math]\frac{1}{i}[/math]
But I didn't make that mistake on the problem I'm having so would it still be wrong?

>>9567625
It doesn't come up often but it does come up. Algebraically it can happen because some valid manipulations can introduce extra solutions, for instance "squaring both sides" can introduce spurious solutions that the original didn't have, since
you can see that both 2 and -2 square to 4. Since trig functions have symmetries in various ways you can end up with a similar issue that multiple solutions exist algebraically but non-algebraic constraints force one solution or another. So the acute/obtuse distinction is a specific case of this more general problem and it's good to have some small understanding of this that builds up over time.

If waters boiling point decreases with altitude why doesn't water boil in the vacuum of space?

>>9568555
>>9568557

putting in that -i changes the domain, right?

>>9568652

or rather, it's a change of variables?

How do I apply the Robin boundary conditions in polar when using separation of variables? Normally it's the partials with respect to the normal vector. After separation of variables u=T*R, do I get the BC T'(0)+T(0)=0 and T'(a)+T(a)=0, or is it more complicated than that?

>>9568716
Picture

>>9568430
So then how does a parametric equation work, then?
[math]
c(t) = (cos(t), sin(t), t)
[/math]
is the parametric equation, R1 to R3, of a helix. Its input is one variable, and outputs a 3-vector.... I'm having trouble understanding your argument.

>>9568425
Small update:
It appears the problem was that I had my axes way too large, so the hyperbolic nature of the cosh and sinh functions dominated...
Here's what the graph looks like for more reasonable values of u1 and u2

>>9568532
Treat them as exponents, not radicals. Work from there.

>>9568652
I'm using
[math]i=\sqrt{-1}[/math]

Having trouble with a chemistry question.

I am wondering what is keeping, stereochemically, molecule I from becoming molecule II.

I thought that trans-isomers were more stable than cis deu to less steric hindrance between the substituents.

Dunno where else to ask this, does anyone have that expanding brain meme with the different ways of converting AC to DC?

I started studying propositional logic.
Why is p→q equivalent to ¬p∨q? Is it just because they share the same truth table?

>>9568867

nah, i^2 = -1.

pretty tricky.

>>9568555
http://www.wolframalpha.com/input/?i=Integrate%5B1%2FSqrt%5B-1%2Bt%5E2%5D,t%5D

This might look like high school physics but it actually is med school physics

5 meters deep in a recipient full of a liquid of unknown density, there is an object of volume 8 mL and mass 2kg, tied with a rope to the bottom of the recipient. The buoyancy is 23.52 N
1. Determine the density of the liquid (R: 300kg/m3) -shouldn’t it be 300.000? (because 1 ml is 1e-6 m3, not 1e-3)
2. The rope is cut. Determine the depth of the object after 2.5 seconds. (R: 1.4m)  pretty sure it has already reached the surface and is floating at that point. After the rope is cut, there is only (no friction) buoyancy and weight, buoyancy going upwards and being 23.52 and weitght going downwards and being 19,6. Net force is 3,92, thus acceleration 1,96 m/s2 (positive), initial speed is 0. I used -5 m as the starting height
3. After an infinite amount of time, the object is floating in the recipient in a rest state. What is the percentage of the object (volume) that is submerged in the liquid? (R: 83,33%)  I don’t see the problem here

>>9569143
the object should have a volume of 8 l not 8 ml

>>9568960

actually, sqrt(-1) is equal to i by definition, at least in the book i have. but you can't can't say that sqrt(x) = i*sqrt(-x), since then you'd have 1=i*sqrt(-1) = i^2 = -1.

skimmed over complex square root. this question threw me for a loop. i'll have to think about it.

>>9568918
literally just that. logical equivalence between two sentences A and B is just the relationship that making A true (or false) 'forces' B to be true (or false). it's the same as a biconditional. that is, [math](p\rightarrow q)\equiv (\not p\lor q)[/math] is the same as [math](p\rightarrow q)\iff (\not p\lor q)[/math], which is exactly the same as the condition that the truth tables coincide.

>>9569227
i'm a dumbass -- should be [math]\neg p[/math] in both cases, not [math]\not p[/math]. but otherwise still correct.

>>9569185
I always thought about that, it made no sense to have a liquid that dense.
Any idea on how they got 1.4m in the second one?
>inb4 there was friction, but they forgot to tell you

>>9567934
there is no such base

>>9568879
Pi-bonds cannot rotate, only sigma bonds can.

Give me a second to draw a diagram and you will immediately see why pi-bonds cannot rotate.

>>9568635
It does.

>>9567934
>>9569314
Meant to write, n = any natural number other than 10, not all

>>9569215
>actually, sqrt(-1) is equal to i by definition, at least in the book i have.
[math]\sqrt{16} = \sqrt{-4 \cdot -4} = i\sqrt{4}\cdot i\sqrt{4}
= i^2\cdot 2\cdot 2 = -4[/math]

>>9568879
>>9569331
A sigma-bond only binds one lobe to another single lobe.

A pi-bond binds two lobes to another two lobes. Two bonds positioned parallel to each other cannot rotate without breaking. If the bond did rotate, not only would it have to overcome the binding energy of that pi-bond, but it would have to overcome the binding energy of forming a pi*-bond.

>>9568879
>I thought that trans-isomers were more stable than cis deu to less steric hindrance between the substituents.

They are, but you cannot convert a cis-isomer to a trans-isomer by a simple rotation. You would have to use other methods.

>>9569386
One more thing so that everything makes sense. There is also a concept called hybridization. The 3 p-orbitals and 1 s-orbital hybridize to form 3 sp-orbitals and 1-p orbital.

sp-orbitals don't have a locked direction and thus don't have to stick strictly in the x, y, or z axis. So if you show the same diagram put with the hybridized orbitals, you can see how the H and Cl atoms are 120 degrees from each other.

>>9569341

sqrt(x) = e^(1/2 log x)

log(x) = ln(|x|) + i Theta

-4*-4 = 16, so theta is zero in this case.

but by taking sqrt(-4) and sqrt(-4) separately, you're putting you're giving it an angle that it didn't have before.

Please halp

>>9569423
>>9569437

>>9569227
>>9569229
that makes sense.
do you have any book rec about logic? sounds like a fun math branch

I asked this in Mathematics General too but:

Brainlet here. I am wondering if it is possible to prove the following postulate:
"For every odd number |n|, there exists an even number |n| + 1 which has a number of factors equal to or greater than the number of factors of |n|."

(I'm not sure if I'm phrasing that properly, but essentially I'm trying to say that 2 has >= factors than 1, 4 has >= factors than 3, 126 has >= factors than 125, etc etc..)

>context
I'm trying to figure out a way to explain the fact that picking two arbitrary numbers is more likely to generate an even product when multiplied than an odd. I recognize that the ratio is 3:1 in favor of even (EE, EO, and OE all generate even products while only OO generates an odd product) but wanted to try and obtain a more rigorous proof than that.

>>9569497
Logic is not a branch of math.

>>9569440
nvm

>>9569504
yeah, i just remembered that.
sorry, i had a stroke while posting

>>9559005
how do you properly prepare for the putnam

>>9569503
>385

>>9569897
also
>105 (3*5*7)
>106 (2*53)

Given the alphabet {a, b}, I believe a deterministic FSA recognizing this language would only recognize the empty language - a*b* includes empty strings concatenated together, right?

>>9570189
forgot pic

>>9568543
Anyone?

>>9568543
If those are mixed fractions, then your last line is correct.

how do we know that time doesn't move in reverse?

>>9570334
So why then he got:
>>9568359
120/6 ?

If line:
3(2/3) * 5()1/2 = 11/3 * 11/2, no?
is correct then we can simplify it as improper fraction:
11*11/3*3 = 121/6

But the correct number is 120/6

So I'm fucking going crazy or what?

>>9570345
[math]\frac{121}{6}=\frac{120+1}{6}=\frac{120}{6}+\frac{1}{6}[/math], he was saying to calculate it as [math]61-(\frac{120}{6}+\frac{1}{6})=61-20-\frac{1}{6}=41-\frac{1}{6}=40+1-\frac{1}{6}=40+\frac{5}{6}[/math].

>>9570189
> Given the alphabet {a, b}, I believe a deterministic FSA recognizing this language would only recognize the empty language
No. The language includes e.g. ba, aba, etc.

Also, "deterministic FSA" is a red herring. The language is what it is, regardless of whether you're using a NFA, DFA or whatever. The language is regular, so there exists a FA which recognises it.

> - a*b* includes empty strings concatenated together, right?
Yes. "*" means any number of repetitions, including zero.

>>9569331
>>9569386
>>9569388
>>9569406

True, thank you all! Makes sense

>>9570387
>>9570387
new
>>9570387
>>9570387

>>9569530
This is the best /sci/ John I've ever heard