/sci/ - Science & Math

I might start posting homework questions that redditors have asked other redditors in the past, including the venerable
>How can the graph a value at zero when zero has no value?

http://openstax.org
If you never finished high school this has free textbooks, more topics than just math

Let [math]Z(G)[/math] denote the center of a group [math]G[/math]. My stupid conceptual question: How to make sense of [math]G / Z(G)[/math]? What is this object and how should I perceive it on an intuitive level?

I can make sense of [math]\mathbb{Z} / 5\mathbb{Z}[/math] like so: "We hereby declare all integers whose difference is a multiple of 5 to be identical". How should I apply the same logic apply for [math]G/Z(G)[/math]? "Declaring all elements [math]g,h \in G[/math] s.t. [math]gh^{-1}[/math] commutes with everything else in [math]G[/math] to be identical" sounds like abstract gibberish. Surely there is some simpler way to interpret this object that I'm not seeing

I was attacked by a swan as a child. And I used to think they were so pretty. Makes you realize they are actually pretty dinosaurs.

If there is a real number, is there a fake number?

In programming x=x+1 is a good thing but can it be rational is x is infinity?

If something is 3 times as big , does that mean it's exponential?

If "god created the integers and all else is the work of man", then what falsifiable experiment can be done to detect if integers exist or not?

If one nail costs $0.20, and 12 nails costs $0.40, how much do 112 nails cost?

Would $1^145 = $1?

DAE read factorials as if you were yelling?

Any one of these reddit bullshit would get 5-30 replies if posted as a separate thread on this boarf

>>12677096
>>12677222
>>12677226
>>12677251
>>12677257
>>12677263
>>12677264
>>12677268
>>12677273
>>12677279
YAMEROOOOOOOO

>>12677226
last week i realized that fishes are aquamarine dinosaurs

>>12677268
>If one nail costs $0.20, and 12 nails costs $0.40, how much do 112 nails cost?
it can be anything.

>>12677601
...no lad, are you touched in the head?
I'll rephrase it in a simple way:
You go to the supermarket. You can buy individual nails for twenty cents each, and a box with a dozen nails for forty cents. How much would you have to pay for a hundred and twelve nails?

>>12677268
$4.40 if you want the cheapest option
9*.40+4*.20=4.40

>>12677662
>not buying ten sets of twelve nails for two dollars and throwing eight nails in the trash

>>12677686
>two dollars
*four.

>>12677549
Is there a nigga samefagging the entite thread?

>>12677703
Yes considering there's only 8 posters and 20 posts in this thread now.

Why isn't it possible that the reason other galaxies appear to hold together at too high a speed is that time is actually moving faster for them than for us?

>>12677846
Because that is the complete opposite way that relativity works. Time slows down for an object the faster we see it move.

>>12677862
Not its speed, its time.

>>12677865
You have no idea what you are saying.

>>12677876
Say the milky way has a more profound gravity well than we think. We're somewhere in that gravity well. Just like satellites have to be built to account for time dilation due to its higher position in earths gravity well, why couldn't galaxies outside of the milky way have time literally be moving faster than inside the milky way from our perspective?

>>12677881
Because if we were in a gravity well that strong we would know. It would effect observations locally within our galaxy to start with.

Apart from around very close to massive objects space time is flat. Any region that isn't is obvious.

when I use a us kitchen appliance in the eu without a transformer and the wattage gets too high, it causes a blown fuse, but seemingly it works fine at low power. what's happening in the circuit when the fuse blows? how come it works fine at low power?

>>12677958
How would we know? Wouldn't everything in our galaxy appear to be moving the "right speed" for our mass? With the outer edges of the galaxy seemingly moving a little bit faster, and the inner parts a little bit slower?

>>12677984
Maybe I'm misunderstanding the question, but that's just how fuses are supposed to work. The appliance works fine when fed lower power, since the standard in the US is smaller than in the EU. However once the wattage exceeds a certain threshold, it's possible for components to start failing. To make it so that the failure will always occur in the same place to make repairs easier & less costly, fuses are included in circuits as an intentional weakpoint. When things get too hot, the fuse literally burns out (the filament inside melts or whatever), breaking the circuit and preventing any more power from flowing into the system to protect the more costly components.

>>12677060
How does one make their pee pee longer

>>12678065
steel wire and bricks.

>>12678062
I guess my question is what is happening in the circuit when an induction motor device is connected to a higher voltage than it was designed for? is a greater amount of work done rotating the motor, or is it just working less efficiently somehow thus drawing a higher current just to heat the device more than if it were connected to a 110v source? Im just too retarded to picture the electrodynamics of it.

Rerequesting from the previous thread:
Can anyone post the meme with the two pepes shaking hands while there's a tiny apu and a short crying wojak to the side?

The apu might not have actually been an apu, I'm not all that good at telling my frogs apart. But it was kinda apu-like.

>>12678144
not the same guy as above and I have very limited knowledge of ED, but just using the fact that V=IR and that if a system is designed with some voltage, and frequency, in mind then the internal resistance is designed to be a ccertain amount also. So connecting it to more voltage that it should would produce more current and in effect blow the fuse.

>>12678144
If a higher-than-expected voltage source is connected to a device, you would expect the motor to start overworking itself , since the applied voltage (and therefore applied current, just by modelling the motor as some resistive element & using V = iR) is higher than expected. This can lead to mechanical failure, if the parts are moving faster than they are rated to handle, or electrical component failure, such as shorting across capacitors if the voltage is too large, damaging resistors, etc.

>>12678206
>>12678204
so I can just think of the motor as a resistor giving off kinetic energy instead of heat, and an increase in voltage and thus current just means both the motor and the other resistance absorb more energy than they are designed for? thanks bros, this is much simpler than how I was trying to picture it

>>12678334
That's the basic idea, anon. Working with complicated electrical systems is difficult, which is why finding Thevenin equivalent circuits is so useful and so heavily emphasized in your introductory circuits courses, or in the case of electromechanical systems, figuring out how to model your motors in a simple way.

>>12677251
No real numbers is a classification used, other examples include complex and transcendental numbers.
>>12677257
No because computers can only store limited amounts of data. Assuming they could however then yes since that is how you would handle infinity.
>>12677263
Only when that something is zero. Otherwise no.
>>12677268
Theres many different options for this. You need to add some restrictions for this to have a definite answer.
>>12677273
1^2=1x1, 1^x=1 in the same way.
>>12677279
You could, but usually math isnt read aloud. you could add emphasis if you wanted too but it serves no purpose to the calculations.

sorry if this sounds esoteric
After learning a very, very surface level amount about groups, it's finally clicked that vectors really are completely distinct things from normal numbers/scalars.

My question is, why? What is it in a vector that necessitates that we use different operations and treat them much differently than regular scalar numbers?
The best answer I can come up with is that since vectors inherently have both magnitude and direction, and in order to preserve those quantities algebraically, we must necessarily operate on them using a fundamentally different set of rules than with scalar quantities.

But that doesn't feel satisfactory.

>>12678591
No, you're mislead. We don't treat vectors like numbers because, unless you get more specific, they are very abstract objects, which lack any inherent direction, distance and magnitude. Only when you start to 'add' these structures you get to do more, but they will remain abstract objects anyway and we can only operate with the rules induced by the additional structures.

>>12678162
Come on lads, I need it for a shitpost. There were like, five different versions of it floating around here.

>>12678825
0.02 seconds google search, you're a disappointment

Does anybody forgot how to do basic math operations every now and then? Taking this course in topics in partial differential equations and when we expand a function in terms t, slow timescale, super-slow timescale, and then I have to do partial derivatives with respect to hypothetical functions that are dependent on certain kinds of variables I just get lost

>>12678591
It's because arbitrary dimension vectors don't form a field the way real numbers do. They do form a group under addition, but you don't have a multiplication operation with nice properties (gives back a vector of the same dimension, has inverses for everything other than zero, distributive law, etc.)

>>12678839
Google gives different results for different people lad.
I ended up finding it on know your meme later.
https://knowyourmeme.com/photos/1946081-manlet

can anybody recommend a calculus book that has worked solutions for all exercises?

>>12679133
stewart or lang or courant or apostol or spivak or rudin

>>12679133
stewart or spivak or apostol

>>12679133
Spivak is famously good but also difficult. Only get it if you won't get discouraged by not being able to solve a large part of the exercises

>>12679133
Simmons' Calculus with Analytic Geometry has solutions

>>12677060
Does anyone know how to simplify this exponential function? I'm dying.

A(t) = [ 5(1.08)^t – 5 ] [ 2(1.08)^t ] 2

>>12679459
20[ (1.08)^t – 1 ][ (1.08)^t ]
20[ (1.08)^2t – (1.08)^t ]

This dialogue immediately reminded me of this thread.

I've got a TI89 and I've got the polar format set to degrees.
I plug in (36.7e-3<-23)*(190<23) and get (6.973<821.680474876e-15)
Pretty sure the degrees should come out to zero. What gives? Am I missing something ?

This is really on topic, STUPID god damn question.

So the problem is: Calculate the volume of a rectangular cuboid with the dimension of 2, 3 and 5 using triple and double integrals.

So of course, the volume is 30, and for the triple integral I go 3 integrals, 0 to 2, 0 to 3 and 0 to 5, dzdydx
But what about the double one?
I'm supposed to do z=f(x,y) inside the integral, but z isn't really a function of x and z is it? I mean I could write f(x,y)=5, and then that would represent a plane which I can then limit by setting the boundaries for x and y, right? I'm so confused.

>>12679734
That's exactly the right f(x,y). Because you've got a rectangular prism, the upper surface that you're trying to integrate in the double integral case is just a constant flat plane, 5 units above the xy plane. So to use double integrals, you'd have to integrate f(x,y) = 5 between x in [0, 2] and y in [0, 3].

>>12679745
Thanks a bunch anon!

>>12677060
I dont get a tiny detail about this proof.

>"Supose that [math]D \subset \mathbb{C}[/math] is an open and connected set, then suppose [math]f:D \rightarrow \mathbb{C}[/math] is complex differentiable but only takes real values, prove that [math]f[/math] is constant on [math]D[/math]"

Now the proof I wrote is that since the function is differentiable then the Cauchy-Riemann equations hold and by those then all the partial derivatives of the function are 0 and thus the function is constant.

But why must the domain be connected? I dont understand how that comes into play.

>>12679827
Partial derivatives being 0 means the function is locally constant on D. It's constant on D in the end because it's a connected set.

>>12679827
Consider a separated D with two distinct regions. Then f could be 1 on one region and 2 on the other, but still satisfy all the conditions in your proof.

doing some linear algebra work and im kinda stuck at the last hurdle. I need to prove [math]a^2 + b^2 +2c^2 +2d^2 + \frac{1}{\sqrt2}(2ac + 2aci +2bd +2bdi) \ge 0[/math] for real a,b,c,d

>>12680007
That's not a real number brozius.

>>12680017
uuuh im pretty sure you can get the stuff in brackets to cancel with the stuff not in brackets by looking at (a+bi) and (c+di) and their conjugates and the modulus of them. not sure how though. i think given enough time putting numbers together ill figure it out but ive been trying for a while and cant

>>12680027
>>12680017
>>12680007
nvm idek i may have done something wrong earlier in the work im gonna restart

I have a midterm tomorrow and can't figure this one out and don't understand the explanation. I'm shelfing it for now but have this thread set to notify me if I'm replied to (inb4 "(you)")

https://www.slader.com/discussion/question/a-transverse-sinusoidal-wave-is-moving-along-a-string-in-the-positive-direction-of-an-x-axis-with-a/#

TIA!

>>12679214
>>12679220
>>12679284
>>12679402
thank you all, I'll have a look at these!

Hi guys, I know that the further you get from earth's surface the more stored gravitational potential energy you have. Does hold true even for objects that in orbit? For example does the moon have gravitational potential energy?

We are choosing a pair of 2 numbers, one after another, from a set {1,2,...,50}.
How many ways are there to choose a pair such that the first number divided by the second would give us a number from the range (1,2]?

Whoever posted that FM formula a few days ago, thank you. I'm now using that knowledge accordingly.

>>12680753
>We are choosing a pair of 2 numbers, one after another
do you mean just picking two different numbers?

>>12680736
gravitational potential energy is not an inherent quantity, it is your potential energy relative to another celestial body.
you have gravitational potential energy relative to the Earth, the Moon, the Sun. every object that interacts with others via gravity has gravitational potential energy relative to them.

>>12680862
Yeah, but the original question was also quite wonky so you couldn't be 100% sure if it meant 2 different numbers or not.
I've solved it and the answer is 625. I can think of other ways to solve it but I think there's a specific way which I'm missing but I don't want to tell more to suggest a way of thinking.

>>12680893
i also got 625
1+1+2+2+3+3+...+24+24+25=625

>>12680912
can you explain your way of counting it?

>>12680912
one way to do it, but I'm looking for something else

>>12680917
iunno, i just counted the number of numbers smaller than n such that [math]\frac{n}{2}[/math] is in the range, starting from one, and noticed that it went up like that
I suppose it would be [math]\sum_{n=1}^{50}\lfloor\frac{n}{2}\rfloor=625[/math]

>>12677060
are there any good books on signaling theory within evolutionary biology?

I don't know how SSS similarity works, help.

>>12681124
wait no, i meant to say SAS

>>12681124
>>12681144
https://www.ck12.org/geometry/sas-similarity/lesson/SAS-Similarity-BSC-GEOM/#:~:text=The%20SAS%20Similarity%20Theorem%20states,the%20two%20triangles%20are%20similar.&text=A%20similarity%20transformation%20is%20one,transformations%20followed%20by%20a%20dilation.

>>12681124
Cosine theorem shows the angles are the same, thus giving an AAA similarity

Why do i keep waking up early at 4.30-4.45 am every single day? I read about it being stress related issues as the cortizol rises at that time. Is it true?

>>12677222
Tbh I can't imagine it well either, but Wikipedia says that [math]G/\text{Z}(G)[/math] is isomorphic to the inner automorphism group [math]\text{Inn}(G)[/math] which seems more intuitive.

>>12680736
Yes. Note that bodies in an elliptical orbit are constantly exchanging potential and kinetic energy. As the orbiting body gets closer to its parent, potential energy is converted to kinetic energy (akin to rolling downhill); as it gets farther, kinetic energy is converted to potential energy. Their sum remains constant.

>>12681324
Yes. Stress, anxiety, depression, or bad sleep hygiene can play a role in early awakening.
Also I'm assuming you're not elderly but it's normal for them

>>12681360
this is actually a very good intuition. there's the obvious epimorphism G -> inn(G), its kernel is exactly Z(G)

How long will it take me to self study a course in Qm? At the introductory level.

If a stick hits a rock exerting like twice the force needed to break the rock, what happens? does the rock break? does the stick get decimated and nothing happens to the rock?

>>12680753
Let the two numbers be x, y. The constraint y/x∈(1,2] => x<y<=2x. There's the additional constraint that y<=50. If x<=25 then the first constraint is binding, and |{y : x<y<=2x}| = x.
[eqn]\sum_{x=1}^{25} x = 25 \left( {1 + 25 \over 2} \right) = 325[/eqn]
If x>25 the second constraint is binding and |{y : x<y<=50}| = 50-x.
[eqn]\sum_{x=26}^{50} (50-x) = 25 \left( {24 + 0 \over 2} \right) = 300[/eqn]
325+300=625

>>12681604
>Stress, anxiety, depression
Oh yeah i have a lot of these but arent ssri's supposed to minimalize it?
>bad sleep hygiene
whats that?

Having trouble with line integrals
>Find the E field at a point 3 cm above a charged wire and 2 cm away from the end from the charged wire that is 4 cm long and has a charge of - 8 nC on it.

This would be
[math](9*10^9)*(2*10^{-7})*3 \displaystyle\int_{-2}^2 \frac{1}{(9+x^2)^{3/2}}\, dx[/math]
Which gives me -665N.
Is this right?

Is every every orthogonal basis complete? I'm trying to get an intuition as to what complete means. Does it just mean that I can describe any vector in a complete vector space with its orthogonal basis?

I see people on the internet say that the minimum speed at which a meteor can enter Earth's atmosphere is 11.2km/s. Why can't they enter it at slower speeds?

What would happen if we entangled two particles and then threw one into a black hole?

>>12681783
what is a "complete basis"?

>>12681751
I haven't done E&M in a few years, so apologies in advance if I'm wrong. The distance function you have seems to be a bit off - it should be [math] \sqrt{9+(2+x)^2}, x \in [0,4] [/math]. The way you have it right now suggests that the point of interest is 3cm above the wire, but located above the center of it, not 2cm off to the side. Also why the prefactor of 3 before the integral?

Thats exactly what I'm trying to find out. In my notes it says that the "Completeness of a basis means that" [eqn]\sum_n (v_i^n)* (v_j^n)=\delta_{ij}[/eqn] where [math] (v_i^n) [/math] means the ith component of the nth vector in that basis and [math](v_i^n)*[/math] is the complex conjugate.

>>12681994
Where I'm from that's called orthonormality.
Because [math]A^TA = I[/math] implies [math]AA^T = I[/math].

You think with medicine having a history of biases like removing the toes of black slaves or not washing their hands for surgery, that they even have any insight into the mistakes of today?

>>12682014
This is what makes it confusing because the very next line defined orthogonality as [eqn]\sum_i (v_i^n)* (v_i^m)=\delta_{ij}[/eqn]. WHich is the definition im also familair with.

>>12682032
[eqn]\sum_i (v_i^n)* (v_i^m)=\delta_{nm}[/eqn] sorry messed up the delta.

>>12677222
I'm in a similar boat atm, anon, but if this helps: always think in cosets. Z(G) forms a subgroup of G, hence its order divides G by Lagrange's Theorem - Z(G) and its cosets form a partition of G. So you've got a1 Z(G), a2 Z(G), etc, where each a1 could be chosen from that particular coset (and any element in Z(G), usually e, can be chosen for the trivial coset Z(G) itself).
So you can think of it as, just as with Z/5Z, saying "if all the elements that commute in G are '''equivalent''' in some sense, then G can be cut into some set of '''multiples''' of that set". That's not special to Z(G), that just how quotient groups work, but keeping that definition in mind can be helpful - maybe it's not intuitive (I don't know if there is an intuitive explanation desu), but at least it can make it seem less strange that a natural object like Z(G) could be used in that way.
And, of course, if G is abelian then Z(G) = G -- there's only the trivial coset -- whereas if G somehow lacks *any* commutating elements other than e, the cosets of Z(G) would be the sets containing every element of G. If more than just e commutes, that in some sense "collapses" the latter trivial partitioning by calling certain objects 'equal'.
Idk hope that sort of helps

>>12682032
Yes, that's the usual definition of orthonormality.
They're trivially equivalent by >>12682014

>>12678591
A vector space and a field are both commutative groups, with a relevant addition operator. However, they have additional further structure:
- A field is an integral domain is a ring, meaning it has a (I think necessarily?) commutative multiplication operator that works how you expect in Q or R: every element has a multiplicative inverse.
- Vector spaces don't really usually have a great corresponding "multiplication". Think in 3D: the inner (dot) product gives a scalar, not a vector; the cross product sort of fits the bill, but it's not distributive or commutative (ab = -ba) (note: differential calc is beyond me, but I've read how the cross product going 3D x 3D --> 3D is actually kind of coincidental in some weird way).
- Vector spaces, in general, are a collection of objects satisfying additive properties group properties (vectors), plus an additional set of objects you can use to scale and distribute over the vectors (scalars, hence the name). The scalars specifically have to be a field as defined above - you couldn't use Z, I think.

These definitions can give really wide variety of things the vector definition - sets of continuous functions, for instance, can be vector fields, usually using either R or C as the associated scalars. And I think that R itself is, technically, both a vector space and a field - it's a 1D column vector over R for the former, treated as usual for real numbers for the latter.

>>12678591
Also, to tack on a note: "magnitude and direction", technically, are only properties of "inner product spaces", a subset of vector spaces. You need an inner product, which is usually the dot product for what you'll be using. From the dot product, you can define an angle, since a • b = ||a|| ||b|| cos theta, the angle between a and b. You can also define a 'norm', since sqrt(x • x) is just the usual Euclidean distance (eg think Pythagorean Theorem in 2D).
You can have other norms: for instance, "taxicab distance" would be measuring distance between two points if you can only move vertically/horizontally, like on a city street grid. These correspond to different measurements of "distance" or "length" of vectors -- although you probably won't be able to get a sense of "angle" with such a norm.

>>12680892
>>12681572
Thanks. I have a follow up question.
How come we don't feel the acceleration of gravity during free fall? Based purely on our sensations, it would seem that we aren't accelerating at all during free fall. But we are always accelerating upward while stationary on the ground. What's really going on here?

>>12681967
My professor writes weird, I think he means the point is centered above the middle of the wire,
the integral is multiplied by k, lambda, and the distance (z).

>>12681967
shit it should be .03 outside of the integral, and 9*10^-4 in the denominator

>>12682149
Excellent, this implies then that every orthogonal basis is also complete under this definition.

When making substrate for bacteriological purpose, what kind of meat extract do i need? Does it matter weather i buy "meat extract" or "beef extract". If i'm working with yeast would "yeast extract" be better? Also, where do i buy C. elegans? I have found no sellers...

>>12682259
In that case this integral isn't quite right - right now, you're integrating the magnitudes of the E field from each point, but there's some cancellation since the directions aren't all uniform. You'd have to include some sin(theta) term or w/e to account for only the vertical components, since all horizontal forces end up cancelling out.

>>12681967
isn't 2cm away from the end of a 4cm wire the middle?

So I got a bit of a weird conundrum. Someone took the picture of their graded exam last year, and this one thing is really messing with my head.

So it's about line integrals of a vector field. The curve is an intersection of a cylinder y^2+z^2=4 and a plane, x=1, so, a circle.
So a) the student was supposed to parametrize the curve
and b) calculate the circulation of the vector field (z+x, 2x, y+z).

What happened is that the student parametrized the curve as such:
r(t)=(1, 2(cost)^2, 2(sint)^2) where t goes from 0 to 2pi. And the professor marked it as correct. To my understanding, this should be done using polar coordinates, so r(t)=(1, 2cost, 2sint), but nvm, I thought I might be missing something.

Then for b), the student did an integral (from 0 to 2pi) of r(t) (dot product) r'(t) dt, and got a result of 2pi, and professor marked it as incorrect. Now, the result is false, even if you use her parametrization, the result would be 0.
But the thing that bothers me is that, ignoring the result, the problem would still not be done correctly, because of the a), which was marked as correct. Shouldn't it be (1, 2cost, 2sint) and then for b), the correct result is 4pi? Or am I missing something?

>>12682337
>Does it matter weather i buy "meat extract" or "beef extract".
No.
>If i'm working with yeast would "yeast extract" be better?
Yes
>Also, where do i buy C. elegans? I have found no sellers...
I have no idea. My lab buys all that shit for me.

>>12681692
>whats that?
https://www.cdc.gov/sleep/about_sleep/sleep_hygiene.html
>Oh yeah i have a lot of these but arent ssri's supposed to minimalize it?
SSRIs are supposed to minimize it and make it more manageable (ie reduce symptoms so you can function day-to-day) but it's important to use therapy as well so you have a control over your emotional state and mood. Because there are still the basic biofeedback mechanisms you learned from before which led up to your anxiety and depressive response, which could stem from some sort of trauma, burnout, sensory overload, disturbances, genetic, etc.

What would the stability of the critical points of an equation that doesn't have critical points in real be like? For instance x^2+1

Is a free variable a variable where its column doesn't have a leading one? (Linear Algebra)

>>12682540
thank you, this is one of those situations where im way too deep into my studyes for me to ask this from my professors. i realy should have known this, but i just couldnt find anything in my notes or in the books,,,

>>12677060

16(2)^t – 6 = 100(0.5)^t

I know this is probably simple for some of you, but I'm dying, how do you solve this? I have to graph it with tables, and I've been reading my notes for 3 hours now ;.;

I've gotten 10=100? but I'm not sure how Id graph it??

>>12682581
if the domain of the function is only the reals and if the gradient has some imaginary roots then they cannot be critical points.

>>12682902
If you just need to graph it, plot the LHS and RHS separately (i.e. [math] y_1 = 16*2^t - 6, y_2 = 100*0.5^t [/math]) and look for where the curves intercept each other.
If you want to find an analytical solution, I'd look at the problem like so:
Let [math] x = 2^t [/math]. Then the equation becomes [eqn] 16x - 6 = 100x^{-1} \implies 16x^2 - 6x -100 = 0 [/eqn] Just solve for x, and then recalling that [math] x = 2^t [/math], you can find the corresponding [math] t [/math] just using logarithms.

Is there an ODE textbook you can recommend for beginners?

>>12682211
You don't feel gravity. Your senses only feel when things are touching you, because of how nerves work. If the gravity was really really strong, you would "feel" it, when in reality you're just feeling your body pulling on itself.
Since in free fall your body is accelerating as a unit and there are no forces on your nerves, you don't feel anything.
>we are always accelerating upward while stationary on the ground
this would be funny if true, but unfortunately we don't all get launched into the air randomly. the ground is pushing upward to match your feet pushing downward on it, due to gravity pulling you down.

>>12682559
thanks anon, i'll try to implement those tips.

>>12681783
No. Consider the vector space [math]\mathbb{R}^3[/math] and the vectors [1, 0, 0] and [0, 1, 0]. This is an orthogonal basis as the vectors are orthogonal to each other (their dot product equals 0). But it's not complete because there's no way of combining these two vectors that will get you [0, 0, 5], for example.

>>12683389
No problem. Hope it helps.

>>12683410
Oh sorry, I scrolled down and it looks like you're using some weird definition of completeness. Where I'm from, a basis being complete simply means that it generates the whole vector space.

>>12681649
How long will it take for you to study a course that you're interested in vs something you're not?

>>12682211
In freefall, the force exerted on every part of your body is equal, so there's no forces between parts of your body, which is how we sense acceleration. We're more used to acceleration involving forces applied to the outside of the body (skin) which are then transmitted to other parts, and it's the compression or tension that is sensed.

>>12683410
>This is an orthogonal basis as the vectors are orthogonal to each other (their dot product equals 0).
It's orthogonal but it isn't a basis.

https://www.youtube.com/watch?v=qTz7aKEJLV4
why does paper blow up like this?

>>12683549
Paper acts as a cushion until it can't deform any further, when this happens, all the sheets give in almost at the same time which converts all of the elastic potential energy into kinetic energy.

>>12683544
Sorry. Brain fart due to sleepiness.

>>12683031
Thank you anon!! life saver!

>>12677060
I'm (self-)studying the proof of the Chinese Remainder Theorem for a ring R not necessarily commutative, and not necessarily with unit. Specifically, the crucial bit as follows: for J a finite family of two-sided ideals, if they're pairwise comaximal (i.e, Ij + Ik = R for any two distinct members of J), then the natural embedding [math]R/\bigcap J \to \oplus_{I_j \in J} R/I_j[/math] is surjective, so that for any tuple (r_j) in the RHS, the system of congruences [math](x = r_j \mathrm{mod} I_j) [/math] has a (unique) solution mod [math]R/\bigcap J[/math].
But all the proofs I've seen require an induction on card(J) to "build up" the solution x, which in turn requires a separate proof of the tedious lemma [math]I_j + \bigcap_{ k\neq j }I_k = R[/math] for arbitrary j. Is this the only way to do this, or is there a more elegant proof that sidesteps either (or hopefully both) of these problems?

>>12682636
if youre talking in the context of eigenvectors, which is where I think you are. Then a free variable can have any value. Its customary to choose this value to make it easy to normalize the vector, at least it is in physics.

Hello, is there something like
"teachyourselfcs", or "theoreticalminimum", or "chicmath" for EE?

>>12684136
Thinking about it further, I'm not sure if the usual proof of the lemma [math]I_j + \bigcap_{k \neq j}I_k = R[/math] even goes through when [math]R^2 \neq R[/math], e.g R = 2Z. But I can't seem to come up with a counterexample either. Is there something I'm missing, or will I have to resort to nonelementary techniques?

Is Kelly criterion useless if you don't have a very precise knowledge on the win%?

>>12684826
utility maximization (kelly is just a special case) is always possible as long as the expected utility of the total wealth in the next period (if discrete) is a function that can reasonably be maximized either analytically or numerically, so you have to know at least numerically the probability measure of the events. If you have to guess, you're just gambling your money on horse races

>>12677645
Old post but no, >>12677601 is right. There's not enough information to interpolate this in any meaningful way. Does the price rise linearly, or quadratically, or logarithmically, or exponentially, or logistically, or is it an oscillating function? We don't know from the information given and we can't guess because we only have 2 points of interpolation. You can fit any type of growth model to 2 points and they will all fit exactly.

>>12685231
That's not how brainteasers work brainlet, a simple discount is applied. 112 nails cost 3.73 dollars

>>12685235
>a simple discount is applied
[citation needed]

any british lads have any recommendations for physic books for the GCSE level?

>>12677060
Can someone please post that slick proof that [math]e^{j2\pi}=1[/math] ? (Think it was that identity in particular but I'm not so sure, it was definitely an identity regarding e^z tho)

>>12685627
Use Euler's identity.

>>12685627
The simplest is using the Euler identity [math]e^{ix} = \cos{x} + i\sin{x}[/math]. So

[math]e^{i2\pi} = \cos{2\pi} + i\sin{2\pi} = 1[/math]

>>12685627
it depends on your exact definition of e^z

>>12685235
>there is only one transformation of points in the plane

>>12677645
brainlets don't understand that the price of 1 unit depends actually on the price in bulk. What matters is the price in bulk and the price is not even related linearly for one bulky qty to another bulky qty. It really can be anything.
Unit price is useless basically, as soon as you buy more than 1 unit.
In fact, unit price is not a price per se. It's just a number with a currency unit next to it, to make retards believe it's really a price, but it's not the actually price of the trade. unit price is a fantasy.

why is there nothing on wikipedia about Seitz symbols

Bros I know that for a m x n matrix, n - rank determines whether the system has equations. But how do I determine the number of basic solutions for Ax= 0? I'm just stuck like an idiot. Am I supposed to use m and n or something?

>>12686259
What youre saying doesnt make any sense. A mxn matrix, A, requires an additional n-rank vector,x , for the equation Ax=0 to make sense. In this case there will be n different equations that result. If x is known, i.e if all the components of x is known, then A might have nontrivial solutions, different from every component in A being zero. Similarly if A is known then x might have nontrivial solutions.
The way to go about calculating these non-trivial solutions would be to perform the matrix multiplication and solve the resulting equations or to diagonalize A.

>>12686259
Solutions to Ax=0 form the null space of A. It's dimension is the nullity of A, and is equal to the number of columns in A minus its rank, i.e. n-rank(A). If all rows are linearly independent, the nullity is n-m.

>>12686259
It has a single solution (x = 0) if [math]\text{det}(A) \neq 0[/math] (or alternatively if A's columns/rows are linearly independent vectors).
Otherwise, it has infinitely many solutions.

my old roommate shit on the floor every once in a while.
she had autism.

it's just her right?
not all autistic people do this right?
i cannot accept or cope with this reality if that's the case. (high functioning)

alternatively she was trolling me and spreading a rumor about autistics

>>12686657
Yes not everyone who has autism has fecal incontinence or is not toilet trained.
https://www.cdc.gov/ncbddd/autism/signs.html

I'm going to be reviewing the entirety of basic circuits analysis today, please wish me the best bros....... I'm super scared of this topic for some reason...

>>12686677
Sum of series resistors
Sum of parallel resistors
Ohm's law
Kirchoff's current law
Kirchoff's voltage law
Review over.

So I'm supposed to prove that a vector field is potential.

I know I'm supposed to prove that rotF is equal to zero, but the damn field is two dimensional. I always calculated rot as a 3x3 determinant, and that's not possible here. z part is not 0, it's non existent. Can I still take it as zero and then still go 3x3?

Is there a way to cheat a COVID test or almost guarentee a false positive?

>>12686768
Of course I've struggling for half an hour before I asked, and when I asked I immediately stumbled upon an answer. If you go with 3x3 and pick z=0, you'll get Py-Qx, which is in a fucking Green's theorem. And of course it is, Stoke's theorem is just a generalization of the Green's.

>>12686768
>>12686779
Good job anon! You figured it out on your own.

>>12686768
If a field is two-dimensional, then:
a) the Z component is zero everywhere, thus so is its partial derivative w.r.t. any variable, and
b) the value is independent of Z, so the partial derivative of any components w.r.t. Z is zero everywhere.
If you substitute those into the formula for curl, you end up with <0, 0, ∂f_y/∂x-∂f_x/∂y>.
For a planar field, the curl is always perpendicular to the plane. The vector produced by the curl operator is essentially the axis of rotation.

>>12686774
well since its a virus I think your best bet would be to infect yourself with some virus. The common cold might work. If theyre using the antigen test then you can only hope though.

>>12686860
homie here literally copy-pasted deltas instead of using Latex, what a fucking weirdo man, get a grip

Does anyone have the basedjak about wearing a bunch of masks that was posted here a while ago?

>>12687180
>>>/wsr/

>>12687186
I'm not killing a thread over this.
Also, it was posted here, so the lads here are more likely to have it.

Best Precalculus textbooks?
I haven't studied maths for 2 years and I want to relearn

>>12687277
Also, I'm looking into doing Comp Engineering
What are some things I should study to prepare myself? I've got time

If I microwave an agar solution in a glass bottle to make petri dishes and it boils, will that ruin anything? Also does the concentration have to be exact?

Bros how do I solve an equation that looks like this? [math] |x+y|=z[/math]

>>12687301
If it boils, your culture will probably not grow as well because of denatured proteins and burnt sugars.
>does the concentration have to be exact?
No not usually. But you should note any significant changes from protocol so others can reproduce your experiment

>>12677264
Butchered quote. He said naturals.

>>12687330
Okay thanks anon. I probably fucked it up a bit, but as long as it doesn't ruin it entirely, it should be fine. I'll take note of what happened differently.

Bros what the fuck is an LR circuit, I know what an RL circuit is but I know don't know what an LR is. Every time I search it, it shows RL on google.

Can you use Stokes' theorem on a line segment?

I understand that the formulation says that you need a surface with a boundary, and a line segment cannot act as such, but it also says "given the induced orientation" and you fix that by multiplying with -1 if it's oriented in the opposite direction.
My professor has a thing for trick questions on an exam, and one of the questions always seems to be "can you use Stokes' theorem for a [insert here]", and it's usually a line segment, that's why I'm asking. You can only use Gauss-Ostrogradsky for closed surfaces, but if you have an open one you can close it, and then subtract that from the result, that's what I mean.

>>12687491
They're the same thing: a circuit containing an inductor and a resistor, either in series or in parallel.

>>12687604
>Can you use Stokes' theorem on a line segment?
Yes. It's the fundamental theorem of calculus!

>>12687621
Should've specified that the line segment is given in 3D, and so is the vector field. My hunch is no, you need the surface, but I don't know why she keeps putting that as a question, students would've figured it out by now. Makes me thing it's possible and everyone gets it wrong.

How long does it generally take to get through a math text assuming that you're studying it everyday? For example, Shilov or Tenebraum dover books.

>>12685221
I was using it for gambling yes but so far not effective

can someone give me a clue how to start this? i'm not sure how to set the equation of motion up.

>Five cards are dealt off of a standard 52-card deck and lined up in a row. How many such lineups are there in which exactly one of the 5 cards is a queen?
For a queen in a given place there are [math]48*47*46*45=4\ 669\ 920[/math] ordered lineups. There are 4 different queens and each queen can be in five different places, so in total there are [math]5*4*4\ 669\ 920[/math] ordered lineups.
Is that right?

>>12688112
Looks correct to me.

Is it possible to sterilize myself without inflicting physical harm on myself? Is this question better suited for /med/?

What exactly is this epsilon less than 1 meme?

Is anyone here good at quantum? I'm learning about the Bloch sphere and was told that not all states on the sphere are unique. Is this true? What states are not unique, or how would I determine that?

>>12687277
What the fuck is a precalc textbook? Just basic math?

>>12687309
All that tells you is that z is always positive. It cant be solved any more than that.

Capacitor question.
Why is it that after a long time, t=infinity, the current through the circuit that has only a resistor, a voltage source, and a capacitor, is 0? Shouldn't current still be able to flow even if the capacitor is max'ed out? Or does it just completely stop the current from flowing.

>>12688483
If you think of capacitors as just two metal plates with a gap between them, after infinite time the charges will have fully settled on either side, and no more current will flow because there is nowhere for the charges to actually go.
Another way to see this is the equation for the voltage of a capacitor - it is directly proportional to the charge difference between the plates. Thus by KVL, if there is enough charge on the capacitor, there will be no voltage difference across the resistor which implies that the current is zero.
Lastly, you could solve the differential equation of an RC circuit (in terms of i), which produces a decaying exponential that of course goes to 0 as t goes to infinity.

>>12688679
Okay yea I think I get what you mean with the first one, everything's so filled up that current can't move or something. And aaaa I'm just starting to learn diff eq so I'm a bit fucked by my curriculum for this. Thank you though anon, I really mean it.

>>12688762
No problem. Diff eqs can be pretty weird and unintuitive when you start out, even more so when you're working with circuits instead of mechanical systems. Good luck with your studies!

>>12688384
what do you mean by unique?

>>12688479
Yes? Are you going to answer the question or not

About how large would a personal spacecraft vehicle need to be in order to hold enough fuel/food/water/tech to live off of for the amount of time it would take to be financially reasonable?

I want something like the Bebop, but I'm wondering how big it would need to be, in comparison to something else. Is this kind of travel even possible? I don't see why the fuck it wouldn't be, honestly.
About how much do you think it would all cost?

>>12689014
> to be financially reasonable
what does the even mean?

I don't think I know how to integrate, is this correct?

>>12689585
yes, maybe just simplify it as -ln(3)

Hello great /sci/ geniuses. I, a humble brainlet, beseech you for assistance. I need some advice/tips on how to do four bar mechanism synthesis on MATLAB and to also output it graphically.

why the FUCK do people say 'Jounal Science' or 'Journal Nature' instead of 'The Journal of Nature', explain right now scientists??

>>12689910
Because the journal is called "nature".
So correct phrasing would be the nature journal or nature journal.

>>12689914
Ye the Nature Journal or Journal of Nature, not the Journal Nature xDD what is this french?
still waiting scientists

>>12688879
You need to be more specific on what you want to learn. I'm going to guess you mean elementary algebra, absolute values, trig ect. If so then
https://tutorial.math.lamar.edu/
might be a good starting point. I cant recommend a textbook because highschool math isnt usually taught out of one. At least in my experience.

>>12689910
>>12690003
The dog Pluto is very tired.
The journal Nature is very prestigious

>>12689903
B-b-bump

how bad is finance desu? is it worth the slightly higher pay than software engineering?

>>12689910
The same reason as using "in the book 1984" or "in the play Hamlet". Using a title on its own is often confusing, as it's likely to be mistaken for the thing the title refers to. E.g. "in Nature" would be assumed to just refer to the concept of nature, so you clarify that you're referring to the journal named "Nature". Putting it the other way around would form a noun phrase; e.g. "in the Nature journal" would be interpreted as some non-specific journal about nature. Putting the common noun first makes it clear that what follows is a proper noun.

Any anons here studying or working with Maths that use Linux? What's your distro of choice?

>>12690492
Fucked up the wording, I mean that YOU use Linux to do Maths stuff.

>>12690492
I used Debian stable for a while. Comfy, would recommend.
I'm currently using Windows so I can play vidya i.e. Eiyuu Senki Gold: A New Conquest. Also 2hu.
Most professors just use vanilla Ubuntu.
This one professor used fucking ancient Ubuntu and never updated it because he was afraid it would break shit.

>>12690492
>>12690529
It feels relevant to mention that this professor researched numerical analysis and used his Ubuntu computer to implement the algorithms he was researching.

okay, this is divergent right? it's supposedly supposed to evaluate to something but I cannot figure it out for the life of me.

>>12690529
>>12690560
>Debian stable
>vanilla Ubuntu
Yeah that's basically what I imagined.
I want to get a Linux laptop and I was wondering what distros people in the industry use, thanks for the reply anon.

>>12690562
I can't see how that evaluates to anything. If you Taylor expand the bracket you get obviously divergent terms.

>>12690699
That's what I thought, I'm fairly certain somebody is fucking with me. Thanks.

why does the subgroup have to contain all powers of x? what part of the definition of a group does that fall under?

>>12690775
Operations on G take values in G

>>12690824
thanks

>Professor has a massive list of papers. mentorships, and background
>22 pages
> self-deprecating while teaching
y-you guys aren't like that right?

>>12691009
Oh no, I always make sure to stress to my students that I'm the best and they'll never even remotely measure up to me.

Should I go to office hours every week if I have actual computation/conceptual questions or would I just annoy the fuck out of the math professor?

>>12691147
Go to office hours, that's the entire point of their existence. So long as you aren't dominating the time to the detriment of other students, it's fine.

>>12691009
Not a professor yet but that's probably how I'd act in front of students.
>>12691147
Yes go to office hours. It doesn't annoy them. What annoys them is when you didn't use that opportunity to pick at their brain and ask for help, instead failed, and then whined to them about how the exam was unfair

>>12691176
>What annoys them is when you didn't use that opportunity to pick at their brain and ask for help
Wait does math professors actually like it when their brain gets picked? Now that I realized it, the most grumpy professors were older ones while the freshly graduated/closer to millennial professors is so much more energetic/passionate.

>>12691245
Old people get grumpier in general over time from my experience. But there are some old professors who are willing to spend their time to teach students.
Yes professors, regardless of subject, like revisiting old topics and helping students. It refreshes our memories, tries our conceptual understanding, and also it's nice to help someone.

>>12691256
Thanks bro. I'll make sure to visit more often then! I guess it can get pretty lonely in a zoom call just waiting for students to come too

>>12677060
Hey /sci?, brainlet here who is going back too highschool after three years. I'm struggleing with maths, is there a good channel that covers all of basic highschool math in a consistant way? My teachers are not very helpful.

>>12691336
khanacademy.com

Tex idiot here. I have a few .tex files that contain short abstracts, and each of them has its own bibliography. All of them are articles (in terms of document class).

I was trying to compile them into a short booklet, but because of the formatting I want I'd need to define it as a book, and just including the previous .tex files completely messes up the formatting (regardless of whether I do it with /input or /include) so that's not good. I'm now trying to create a new environment to contain the abstracts and some other information, and that was going reasonably well but I don't know how to handle the bibliography now. The only option I could think of is manually entering each reference into a global .bib file and then using keywords to print them below their respective articles. But that sounds like it could take forever, so I wanna know if there's a better workaround. Does anyone know how I can handle bibliography when I'm working with several files, so I can print the references right after the content of each .tex?

In general, is there a better way to just compile all these articles into a booklet while mostly preserving the formatting (that doesn't involve compiling them into pdfs and inserting the pdf files instead)?
pic unrelated

Many many years ago I had a lecture on civil defense. Lecturer claimed that there is a forbidden substance named strawberry gas developed to quell protests that paralyses sphincters (and makes protesters literally shit themselves.) Is that possible at all?

>design a circuit that evaluates to high only when the binary input is greater than binary 4
What the fuck does that mean? I know how to draw circuits and shit, I just don't know what the hell that's supposed to mean. What is a "binary 4"? Sounds to me like " x > 0010", but I still don't get it.

i know the roots of the characteristic polynomial, but don't know how to proceed in finding the general solution

>>12692145
i was getting the wrong roots before. so given that the roots are just 0 and 1, is the answer
[math] C_1 + C_2e^x [/math]?

>>12692145
[math]z = y''[/math].
Then that's [math]z'' - 2z' + z = 0[/math].
We split off the differential operator for explicitness.
[math](D^2 - 2D + I)z = 0[/math].
That operator factors as [math](D - I)^2 z = 0[/math].
Since [math](D-I)z = 0[/math] has sole solution [math]ae^x[/math], we have one solution. Assuming instead that [math](D - I)z = ae^x[/math], you find the other one.
Then you integrate whatever the fuck you find twice.

>>12692145
>>12692163
oops, thje root had multiplicity two, so now i think I've got it totally solved. my answer agrees with the computers and u can ignore this now

>>12677060
Please help with following proof.
Let [math]\varphi[/math] be a path from [math][a,b][/math] to some metrix space [math]X[/math] and let [math]\psi[/math] be a path from [math][c,d][/math] also to [math]X[/math]
Prove that [math]L(\varphi \cup \psi) = L(\varphi) + L(\psi)[/math]
it seems rather obvious but I cant prove it, yes L denotes the length

>>12691894
yw

>>12691894
>>12692370
slight revision

Why do drugs so often cause health problems?

If I have the subgroup 3+15[math] \mathbb{Z} [/math] of group [math] \mathbb{Z} [/math]/15[math] \mathbb{Z} [/math] then is the index of the subgroup 5 with the cosets being
0+15[math] \mathbb{Z} [/math]
3+15[math] \mathbb{Z} [/math]
6+15[math] \mathbb{Z} [/math]
9+15[math] \mathbb{Z} [/math]
12+15[math] \mathbb{Z} [/math]

Trying to get a handle on this stuff.

>>12690775
Why do math problems always say "let" like they are commanding me to allow something rather than wording itself as a matter of fact?

>>12692415
5 is the order of the subgroup (it has 5 elements). What you have listed there is just the subgroup generated by $3+\mathbb{Z}$. The index can be computed as $\frac{|G|}{|H|}$ where G is the group and H the subgroup (assuming these are finite of course). In your case it would be $\frac{15}{5} = 3$.

Indexes are basically the amount of equivalence classes (which are precisely the cosets) generated by the partition that results from the subgroup you pick. In your particular case, {0,3,6,9,12} are all in the same equivalence class because they are all in the subgroup H. Using the definition of the equivalence relation, the other cosets would be {1,4,7,10,13} and {2,5,8,11,14}, and the 3 of them (which is the index) combined form the whole group G.

>>12692428
Because of the somewhat fucked up helper verb system in English, "let" in this case is not an imperative verb meaning "allow," but rather part of the construction for the subjunctive mood. This indicates that the statement / condition is hypothetical or possibly contrary to fact. After all, x might not always be a rational number, but for the purposes of this problem suppose that it is.
If it still affronts you, an alternative interpretation is that "let" is a command, but that it is addressing an implied 3rd person that would have the ability to make the statement true. It's like an impersonal construction.

>>12692415
5 is the order of the subgroup (it has 5 elements). What you have listed there is just the subgroup generated by [math]3+15 \mathbb{Z}[/math]. The index can be computed as [math]\frac{|G|}{|H|}[/math] where G is the group and H the subgroup (assuming these are finite of course). In your case it would be [math]\frac{15}{5} = 3[/math].

Indexes are basically the amount of equivalence classes (which are precisely the cosets) generated by the partition that results from the subgroup you pick. In your particular case, {0,3,6,9,12} are all in the same equivalence class because they are all in the subgroup H. Using the definition of the equivalence relation, the other cosets would be {1,4,7,10,13} and {2,5,8,11,14}, and the 3 of them (which is the index) combined form the whole group G.
Also, reposting because I'm a dumbass and forgot where I was posting

I'm stuck on part d.) here. Any advice or tips?

>>12692464
Since you're asking about (d), I assume that you already have (a) done. Think about how the pmf of X is related to the pmf of Y. If X <= 3, what is the corresponding value of Y? What about when X > 3? Then, based on the probability for a given X, what can you say about the probability of the corresponding Y?

>>12692476
If X <= 3, then Y should just follow f(x); however, if X > 3, then Y will always be identically equal to 3, so the pmf is 0 for all k != 3. Though this seems kinda messy and I'm not sure how nice it will be in solving the last part.

>>12692457
Thanks that is so helpful.

/biz/ here. I have an unlimited supply of baked sweet potatoes. I would like to do something useful with them- specifically extracting the sugars and starch into something like syrup (to use and sell.) Sweet potato syrup, if you will. How should I try and separate the sugars from the fiber/cell material? I am thinking of blending the potatoes up and then mixing them in very high proof alcohol, then cooking them, straining out the plant matter, and then boiling the solution until the ethanol is gone. Would this work? Thanks.

>>12692481
Just because Y is piecewise doesn't mean that it's not nice. You should be able to calculate out the expected value manually - Y has a finite number of nonzero entries, and you can calculate the pmf at Y=3 by using the fact that the sum over the entire pmf of X must be 1.

>>12692481
>>12692481
Just because Y is piecewise doesn't mean that it's not nice. You should be able to calculate out the expected value manually - Y has a finite number of nonzero entries, and you can calculate the pmf at Y=3 by using the fact that the sum over the entire pmf of Y must be 1.

>>12692524
I see so my formulation is correct?
something like [math]P(Y=k)=\begin{cases}P(X=k) && X\leq 3 \\
1 && k=3 \text{ and }X>3 \\
0 && \text{o.w.}
\end{cases}[/math]

>>12692535
That's the right idea, but not quite there. With that formulation, you'd see that [eqn] \sum_{k=0}^{\infty} P(Y = k) = 1+P(X = 0)+P(X = 1)+P(X = 2) \neq 1 [/eqn], which violates the property that all pmfs should sum to 1. With the above expression written out though, is it clear how you need to modify the value of your [math] P(Y = 3) [/math]?

>>12692566
hmmm, so would it be [math]\tfrac{1}{N}[/math] where N is the total steps k takes?

>>12692599
Not quite - you don't even need to introduce a variable like [math] n [/math]. We know that [math] X [/math] is a Poisson random variable with [math] \lambda = 2 [/math], and so using the formula for its pmf you can directly calculate [math] P(X = 0), P(X = 1), [/math] and [math] P(X = 2) [/math]. So, since we know these values, and we know that [eqn]
\sum_{k=0}^{\infty}P(Y=k) = P(Y = 0)+P(Y = 1)+P(Y = 2)+P(Y = 3) = P(X = 0)+P(X = 1)+P(X = 2)+P(Y = 3) = 1, [/eqn]
we can solve for [math] P(Y = 3) [/math] directly.

>>12692640
Dankeschoen anon

Imagine I have a hollow neutral conductive sphere, and then I place 5 electrons on it. What are the positions of the electrons? Is there a simple general formula?

>>12692665
>bruteforce umlaut
Basiert.

>>12692508
Dont use rubbing alcohol, use edible kind. Rubbing has trace toxic shit .

>>12693319
> Is there a simple general formula?
In general, no. There are known optima for specific numbers of electrons, but the general case is a hard problem. See e.g.
https://arxiv.org/pdf/math/0611451.pdf
(that's the only relevant link I can find that's not paywalled).

>>12693363
>paywall
But we have https://scihub.tw

>>12693363
Ty btw been hankering

Given [math]a^0=1[/math] and [math]1/0= \pm \infty[/math]:
Doesn't that mean that [math]1^{\pm \infty} = a[/math], an unknown variable in the reals?

>"undefined" isn't an answer; use logic not feelings or heuristics

>>12693363
>the paper is about the classical problem instead of the quantum problem
big_disappointed.jpg

>>12693406
1/0 is defined to be undefined. There is no heuristics involved.

So 1^x = 1 for all x, even +/- infinity.

>>12692464

[math]X \sim Poisson(\lambda), E[X]=\lambda=2 \Rightarrow P(X=k)=\frac{\lambda^ke^{-\lambda}}{k!}=\frac{2^ke^{-2}}{k!} [/math]

MGF:

[math]M(\theta)=\sum_{n \in \mathbb{N}_0} e^{\theta k}\frac{\lambda^ke^{-\lambda}}{k!}=e^{-\lambda}\sum_{n \in \mathbb{N}_0}\frac{(e^{\theta}\lambda)^k}{k!}=e^{-\lambda}e^{e^{\theta}\lambda}=e^{\lambda(e^{\theta}-1)}[/math]

[math] E[X]=M'(0)=(\lambda e^{\theta} e^{\lambda(e^{\theta}-1)})_{\theta=0}=\lambda [/math]

[math] E[X^2] =M''(0)=((1+\lambda e^{\theta})\lambda e^{\theta} e^{\lambda(e^{\theta}-1)})_{\theta=0}=\lambda+\lambda^2 [/math]

[math] V[X]=E[X^2]-E[X]^2=\lambda+\lambda^2-\lambda^2= \lambda [/math]


[math]Y=\min(X,3) \Rightarrow P(Y=k)=P(X=k), k=0,1,2[/math]
[math]\Rightarrow P(Y=3)=\sum_{n=3}^{\infty}P(X=n)=1-\sum_{n=0}^2P(X=n)[/math]

[math]E[Y]=P(Y=1)+2P(X=2)+3(1-\sum_{n=0}^2P(X=n))=3-P(X=2)-2P(X=1)-3P(X=0)[/math]

>>12693684
Python script for numerical simulation:

import numpy
import scipy.stats

lam = 2

I = 1000000


Y = numpy.minimum(3,scipy.stats.poisson.rvs(size=I,mu=lam))

print(numpy.average(Y))
print(3-scipy.stats.poisson.pmf(k=2,mu=lam)-
2*scipy.stats.poisson.pmf(k=1,mu=lam)-
3*scipy.stats.poisson.pmf(k=0,mu=lam))

>>12689903
Bros..

>>/sci/thread/12694299
Can someone report this on warosu? The button is just not working for me.
If you're wondering, it seems to be dog pornography.

I'm a bit confused with Bra-Ket notation. If we have some vector [math] |v >[/math] and we take its scalar product then [math]a | v > = | a v >[/math]. Its corrosponding bra is then [math]< v |a^* [/math]. Then it should follow that [eqn]<v|(a|w>) = <(v|a^*)|w>[/eqn] but just by inspection this isnt true because changing taking the adjoint of a obviously changes the dot product from [math]a<v|w>[/math] to [math]a^*<v|w>[/math]. So what am I missing here?

>>12677060

Good day anons, do these calc make any sense? I'm sure its very basic for you I'm sure but I'm retarded

>>12694318
[math]\lambda \langle u | v \rangle = \langle u | v \rangle \lambda = \langle \overline{\lambda} u | v \rangle = \langle u | \lambda v \rangle[/math]

>>12694321
your result is nonsensical - a triangle with equal angles is by definition equilateral. Start by labelling your sides / angles. It's unclear which angle A refers to, and it looks like you're getting confused by that too.

>>12694339
I'm afraid I'm still in the dark here. Just taking some generic values as a test it shows that they arent equal. Are they not supposed to equal, am I taking the wrong conjugate somewhere, I dont understand how the two are equal under these rules.

>>12694318
It does not follow. A scalar can be applied to a bra or a ket in any order. [math]<v|(a|w>) = <(v|a)|w> = a<v|w>[/math]

To obtain the conjugate you would do this [math](a<v|w>)^{\dagger} = a^*(<v|w>)^* = a^*<w|v>[/math]

I'm asked to find the complementary solution to [math]y''+y = sec^2x[/math]. The characteristic polynomial is [math]r^2 + r = 0[/math], so the roots are [math]r = -1, r = 0[/math]. So because these are real, distinct roots I would think [math]y_c[/math] would be [math]y_c = C_1e^{0x} + C_2e^{-1x}[/math]. But the computer generated answers return an answer implying the roots are complex.

What am I missing here?

>>12694611
nevermind, i fucked up the characteristic equation. I should have [math]r^2 + r^0 = 0[/math]

>>12694586
>[math](a<v|w>)^{\dagger}[/math]
>taking the hermitian conjugate of a scalar

Could someone possibly check if I messed up somewhere?

Problem: Calculate flux of a vector field F=(0,x,0) through the part of the plane x+z=1, for which x>0, 0<y<1, and z>0.

I assumed a positive (counter clockwise) orientation from the perspective of the top of the z axis.
Then I said that (x,y) -> (x, y, 1-x)
Derivative with respect to x is (1,0,-1)
Derivative with respect to y is (0,1,0)
and (1,0,-1)x(0,1,0) is (-1,1,1) which is pointing outwards, so no correction.

Then double integral<(0,x,0),(-1,1,1)>dxdy, which is double integral of x. Let both x and y go from 0 to 1 and the final result is 1/2.

Sorry if I messed up the terminology or notations, it takes a long time to translate math terminology.

>>12694633
perfectly valid, the Hermitian conjugate of a scalar is simply its complex conjugate.

>>12694769
Okay I can immediately see that I messed up the cross product. Should be (1,1,1), but it doesn't change the result.

>>12694586
Excellent, so [math]a|v>=|w>[/math] then [math]<w| = <v|a^*[/math] but [math]a<v| = |u>[/math]. You can multiply a bra by any scalar but the adjoint of a specific ket is dependent on the conjugate of the scalar used to produce it. I understand it now thanks.

>>12694797
i mean [math]a<v| = <u|[/math]

>>12694309
the disgusting nature of humans never fails to amaze me, sometimes makes me think we are better off not existing

In a video lecture, my prof takes the equation [math]{y}' + \frac{1}{x}y = e^{x}[/math]

and then manipulates it by multiplying the whole thing by x, resulting in [math]{(xy)}'= xe^{x}[/math]

clearly I'm missing something because how did we go from what should be [math]x{y}' + y[/math] to [math]{(xy)}'[/math]

i've tried to do some algebraic manipulation to see why this is true but i just don't get it :(

>>12694586
Well, no, because then we can do
[math] u = \lambda v[/math]
and then
[math]\langle u, u \rangle = \langle \lambda v, \lambda v \rangle = \lambda ^2 \langle v, v \rangle[/math]
And by setting [math]\lambda = i[/math] we get negative norm.
Instead using >>12694339 you guarantee that your norms are positive real.

>>12694893
Product rule, anon. You're differentiating with respect to x, so [math] (xy)' = x'y + xy' = y + xy'. [/math]

>>12694902
Forgot to use bra-ket for a second.
[math]\langle u | u \rangle = \langle \lambda v | \lambda v \rangle = \lambda^2 \langle v | v \rangle[/math].

What good P&ID software are out there? I've been using autocad and it's fucking shit for this.

>>12694907
Thank you <3. It was staring me right in the face, been too long since I've thought about the product rule explicitly. I think I need to brush up on my methods of differentiation/integration.

This also makes the whole idea of an integrating factor much more obvious, my prof completely skipped over explaining it. You're just trying to set up the product rule.

>>12694769
Please help? ;_;

>>12694919
Exactly right, the method of integrating factors is just about setting up the product rule so that you can solve for y directly, without making an ansatz. Good luck with the rest of the class!

what would be an example of a non-distributive infinite lattice? can't think of one

>>12694769
Are you sure you copied the problem down correctly? The plane x + z = 1 runs parallel to the y axis, so the vector normal to the plane necessarily has a y-component of 0. Then the flux of F, a function whose only nonzero component is the in y direction, must necessarily be 0.

for part a.), isn't this zero? P(X=Y) = 1 - P(X<Y) - P(X>Y). I calculated this and got zero. However, this seems fishy as there are infinitely many solutions to Y=X.

>>12694996
Oh god you're right, of course y component should be 0. I messed up the cross product completely. The numbers are right but it's
(1,0,-1)x(0,1,0)=(-1,0,1)

Which means I'm getting zero result, since (0,x,0)*(-1,0,1) is 0. Damn that's a bit suspicious, but it might be. Supposed to be an easy problem.

>>12694902
Not true since we would never write [math]⟨u|u⟩=⟨\lambda v|\lambda v⟩[/math].

|bra> is the hermitian conjugate of <ket|, and vice versa, so [math](|\lambda v⟩)^{\dagger} = <\lambda^*v|[/math]. Hence [math]⟨u|u⟩ = <\lambda^*v|\lambda v⟩ = |\lambda|^2⟨u|u⟩[/math] and so always positive.

>>12694996
The exam is tomorrow, I'm stressed out so hard, I've been trying to get a degree for 8+ years and this is second to last course. Thank you so much for answering, I'll have to be more careful tomorrow.

>>12695048
>|bra> is the hermitian conjugate of <ket|, and vice versa, so [math](|\lambda v⟩)^{\dagger} = <\lambda^*v|[/math]
Do you feel no embarrassment posting this stuff with a straight face?

>>12695041
I had this intuition but it may be wrong what do you think
[math]P(X=Y)=\int_{Y}f_{X,Y}(t,t)f_Y(t)dt [/math]
[math]f_Y(t)=\int_{X}f_{X,Y}(s,t)ds=\int_{0}^{\infty}2e^{-2s-t}ds=2e^{-t}\int_{0}^{\infty}e^{-2s}ds=e^{-t}[/math]
[math]\int_{0}^{\infty}2e^{-2t-t-t}dt=1/2[/math]

>>12695041
Nice, you've happened upon on a type of event that occurs "almost never." These sorts of events have a 0 probability chance of occurring, but aren't empty - as you said, there are an infinite amount of solutions to X=Y. The weirdness comes from the fact that for a joint PDF, to calculate probabilities you need to integrate across some non-zero area (e.g. the square given by [math] 0 \leq x \leq a, 0 \leq y \leq b [/math]) in order to get a non-zero probability. But, since X=Y is just a line, it has area 0, and so probability zero. If you're curious, wikipedia has a couple other examples you might find helpful.

>>12695074
Why would they? He's right.

>>12695089
thanks, math is beautifully weird

>>12695090
>[math]u = \lambda v[/math] but [math]\langle u | \neq \langle \lambda v|[/math]
>implying this not only makes some distant semblance of sense, but that it's also correct

>>12695103
if you think that's right then you don't understand the notation. you can't directly substitute into a < | like that.

>>12695111
Then don't say he's right, say we're both wrong, dumbass.

>>12695067
Don't worry anon, you got this! Just take a deep breath, and exhale slowly. Simple numerical errors like the one you had come more easily if you're stressed, so just don't psyche yourself out. You're gonna make it!

>>12695114
I can't since he was right and you were wrong.

>>12695115
Oh man... Simple mistakes like this is what failed me the last time around. First time I expected close to a 90% on a math exam, and I got 60% because (rsin(theta))^2+(rcos(theta))^2 is 1 according to my calculations, and 2 or 3 other things like that. Awful shit.
Thanks for the kind words tho, I'll keep them in mind.

Today in lab we made Nitrogen Triiodide and set it off. For some reason the professor didn't want to do the reaction under a fume hood so the iodine gas went everywhere.
I used about .3 g of solid iodine for the reaction and once it was completed I walked over to clean up the area but realized I stepped right into the gas plume.
Am I going to die? I have a slight headache now and after class I looked up on my phone to find the I2 gas is highly toxic.
I did find something though. pic related.
I did the calculation and 0.3 g of solid iodine should produce around 232ppm per cubic meter. My exposure was very brief and limited so I think I'm going to survive. Any thoughts? Some shit scared me that days later your lungs could fuck up and go edemic.

I thought it would make an aldehyde and the O(minus) gets protonated but that is wrong

Hypothetically, would any good come from microneedling (aka dermarolling) my glans?

For ever [math] x \in G [/math] the left coset [math] xH \text{ of } H \text{ containing } x [/math] is defined to be the subset [math] \{g \in G \,|\, g=xh \text { for some } h \in H\} [/math].
Is there anything wrong with that definition?

Absolute chemistry retard here. I've got a small alcohol lamp at home that uses denatured alcohol and a cloth wick. It's nice for what I use it for because it burns cleanly and doesn't create any soot. I'm out of denatured alcohol. Can I use isopropyl alcohol in it instead? If not, can you explain why?

>>12695428
Me thinks the O- would get protonated by the sulfuric acid, HNO2 leaves. Potassium chromate reduces OH into carboxilic acid.
I could be totally wrong. Second semester of organic and we haven't covered any of this stuff yet.

>>12695891
Yeah, second semester here too, it wasn't covered but was on a hw.
I actually just missed the charge on the N. The bottom gets left alone and the OH gets oxidized just to the aldehyde (PCC).

>>12695941
based. We've only begun multistep synthesis at my school.

>>12677060
Sophomore with schizophrenia here. Should I try getting on antipsychotics if I plan for MS in mathematics? I already feel emotionally and socially retarded compared to 2-3 years ago. Thanks

>>12696407
are you high functioning? im impressed you are capable of keeping up with uni work with schizophrenia and being unmedicated. ive heard the primary issue with schizos is that many refuse to get medicated, but once they do get on meds, its much easier to function in society. id give it a shot anon, good luck, you are playing life on hardcore mode.

>>12696407
>>12696417
Zoomers making up mental sickness to feel quirky and special deserve bullying. A true schizo is absolutely unable to keep up with uni courses, let alone attend lectures without causing trouble. Fuck off

lets say I have the boxplots of two random variables side by side, can I even say something about their means? or compare anything besides their medians and standard deviations?

>>12696407
I heard that aripiprazole is less harmful than other antipsychs so maybe you could try that first?

>>12696908
I don't think you can compare standard deviations either

>>12696908
There are different variants of boxplot, see https://en.wikipedia.org/wiki/Box_plot . But for a typical boxplot, no. It only gives you the minimum, 25 percentile, median, 75 percentile, and maximum.

>>12697112
>>12697088
Figured as much, thank you bros