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Why are overdeterminate systems of linear equations always have no solutions?
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>>7806680
TM™
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>>7806680
you are wrong.
x+y=0
2x+2y=0
3x+3y=0
this overdeterminate system has an infinite number of solutions.
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>>7806687
It's not overderminate since the equations are linear dependent.
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>>7806696
>In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[1] An overdetermined system is almost always inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.
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>>7806696
>>7806680
I get what you mean, please use proper vocabulary though because it wasn't clear at first.

Anyway, a system of p linearily independent linear equations in a space of dimension n>=p defines a subspace of dimension n-p.
1 equation defines a hyperplane (subspace of dim n-1).
n-1 equations define a line.
when p=n, the set of equations defines one single point.
If you add more equations, the only chance they are consistent is if the define the same point exactly.
example in n=2 dimensions
2x-y = 2
x+y = 1

this yields x=1 and y=0

now imagine you add one more equation in the form ax+by = c.
IF a*1 + b*0 is not equal to c, then the point (1,0) is no longer a solution of the system of three equations.
the only possible way you could add more equations is if a*1+b*0 = c. Which makes it a linearily dependent equation on the other two anyway.
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If i had a pair of entangled particles and preformed measurements on one of them can you know instantly from the other particle that the measurement occurred (no information transmitted other than the timing of the measurement)
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>>7806788
know, because you would have to observe the other particle.

There is nothing travelling here.

Imagine I have a piece of black chocolate, and a piece of white chocolate and two boxes.
I put one in a box and give it to you and send you home.
I put the other one in the other box, give it to your friend and send him home.

If you don't open the box (observation), you don't know which one is inside, but there is only one inside.
If you open the box and your friend doesn't, he still won't know (unless you tell him). But you will know what your friend has, that's all.
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>>7806680
This isn't true. Looking for solutions to a system of [math]n[/math] linear equations in [math]m[/math] unknowns is the same thing as asking if the solution vector [math]b\in\mathbb R^n[/math] is in the image of the linear map [math]A:\mathbb R^m \to \mathbb R^n[/math] coming from the matrix of coefficients of the equations. The system is overdetermined when [math]n>m[/math], i.e. when [math]A[/math] is not surjective. This does not guarantee that there are no solutions for any [math]c[/math] (some will have infinitely many solutions), but it guarantees that there exists *some* [math]c[/math] such that the system will have no solutions.
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>>7806922
I think I switched c for b near the end. Also
>>7806687 is completely correct.
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How many chances do I have of getting into the MIT when I have no money and live in south america? How much would I have to sacrifice and study before even attempting to apply?

I want to apply to either the MIT or UTokyo.
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>>7806788
Not with out also measuring it. Let me explain, say you create an electron and a positron, we know that they can either be spin up or spin down. Before measurement they exist in an superposition of both spin states. Now if we separate them, you keep one (the electron) and give the positron to another research group. If you preform a measurement on your electron to determine its spin, then you collapse the state into a definite spin. Now by conservation laws, as soon as the electron collapses into a definite state then the positron too must also collapse.

However the other group would have to measure their positron in order to find out what state their positron has collapsed into.
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Am I supposed to know what field and specialty I want to go into after getting a BS in Mathematics, or will I figure that out with higher ed?

Alternatively, if I wanted to switch to CS, would I be better off doing post-bac to fill in the blanks, jumping right into Masters/PhD, or getting a second bachelor's?
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How hot is the element of my wall heater? Let's say it's 1500 watts 120 volts.
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I need to write an undergraduate project proposal for a scholarship. Do you know of any good resources to write a good proposal ?
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>>7806680
I'm struggling with a proof. I need to show that if A is defined so that s=sup A exists, then s is an element of the closure of A.

Proof: Let [math] A [/math] be bounded above and let [math] s= sup~A [/math]. Then for [math] \epsilon > 0 [/math] there exists an [math] a \in A ~~\text{such that} ~~ s-\epsilon < a [/math]. Hence [math] a [/math] falls in the [math] \epsilon [/math]-neighbourhood, [math] V_{ \epsilon} (s) [/math]. So [math] V_{ \epsilon} (s) [/math] intersects [math] A [/math] at some point other than s, and hence s is a limit point of [math] A ~~\text{so} ~~ s \in \bar{A} [/math]

The line I'm having difficulty with is:

Hence [math] a [/math] falls in the [math] \epsilon [/math]-neighbourhood, [math] V_{ \epsilon} (s) [/math]. So [math] V_{ \epsilon} (s) [/math] intersects [math] A [/math] at some point other than s

I don't get why [math] V_{ \epsilon} (s) [/math] should intersect at some point other than s just because a falls in the neighbourhood. I'm guessing I've missed something really basic, but I don't know what.
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How do I survive the fourth industrial revolution?
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>>7807196
It must intersect at some point other than s because otherwise s is not the *least* upper bound -- if the only intersection is s, then any point in ([math]s - \epsilon , s [/math]) is also an upper bound of A, but which is less than s.
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>>7806954
Cheers for clearing this up I originally thought I could transmit information using synchronised clocks, precoding and entanglement using the timing as a trigger.
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>>7807196
it intersects it at the point a.
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>>7807212
so my chocolate in the box image didn't work but this did?
dafuq
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>>7807210
Thanks

>>7807212
Anytime

>>7807219
Autism, man.
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how do i evaluate a line integral
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Why don't overdeterminate systems on linear equations have any solutions?**

FTFY
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>>7807219
My bad, forgot to quote. Thanks anyway.
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>>7806680
How to find purpose in life?

How to find happiness in life?

When should I quit?
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>>7807312
Hawking gave his children the following advice:

"One, remember to look up at the stars and not down at your feet. Two, never give up work. Work gives you meaning and purpose and life is empty without it. Three, if you are lucky enough to find love, remember it is there and don't throw it away."

For me, I live by two. My work gives me happiness and purpose in life.
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>>7806680
Since people are a random 50/50 split between their parents, does that mean someone's parent could be 12.5% Black and their child could be the same percentage too?
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>>7807321
yes yes, work for me, good goy
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>>7807336
>working means working as a wageslave
No, I'm furthering human progress you kike bitches
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>>7807419
>implying that isn't what the Jews want you to do
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>>7807126
Solve the Riemann Zeta Function Conjecture.
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>>7807126
bump
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>>7807702
I already have a topic, I need some good guide that explains what one should write/ how to write on background, purpose, objective etc.

>baby's first proposal
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>>7807126
Prove that the there infinitely many primes of the form [math]x^2 + 1[/math].
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>>7807695

If the Jews jew us, then who jews the Jews?
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what kind of fucking sphinx riddle is this? how do i input the answer? both fields have to have SOMETHING in them
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>>7807196
You could just take a sequence converging to the sup, then it's clear.
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>>7807730
For t going to 0, sin and t both converge to 0. Using l'Hospital, you get that t/sin(t) -> 1 as t to 0. Thus n!=0
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>>7807740
oh duh; thanks for the help
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>/sqt/
yes
So tell me why Rose, who is objectively the best female to to have (almost) ever existed, was born in the UK where the women look like inbred dogs?
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>>7807196
perfectly legitimate to have trouble with that line, since it's plain wrong. the claim that [math]V_{\epsilon}(s)[/math] intersects [math]A[/math] in some point that's not [math]s[/math] is both wrong and unnecessary. any point of intersection is enough, don't assume it to be different from [math]s[/math].

an example to prove that the proof's argumentation is wrong: take the set [math]A:=\{1,2,3\}[/math]. it's defined such that [math]\sup A =3[/math], but for [math]\epsilon = 0.5[/math] that one claim fails. this example also proves >>7807210 wrong.
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Can someone explain to me exactly how i is neither rational nor irrational? It makes sense in my head but I have no idea why in a technical sense this is true. Something about complex numbers not fitting into either category for some reason?
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>>7807957
>Something about complex numbers not fitting into either category for some reason?
Look:
[math] \mathbb Z \subset \mathbb Q \subset \mathbb R \subset \mathbb C [/math]

Rationality is a property of real numbers, and i is not a real number. Clearly an imaginary number can't possibly be a ratio of integers.
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>>7807957
for any real number [math]x[/math], it holds that [math]x^2>0[/math]. but since [math]i^2=-1[/math], [math]i[/math] can't be real (and therefor neither rational an irrational real number). it is however an element of [math]\mathbb{Q}[i] \subset \mathbb{C}[/math], so you could say it's a "complex rational" if you wanted to.
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>>7807978
meant to say [math]x^2 \ge 0[/math], obviously.
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>>7807968
>>7807978
Ah, I guess for some reason I just thought that if you could apply rationality to real numbers that since all real numbers are complex numbers then it still holds, but I see why that's wrong. Thanks guys.
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>>7807715
The Germans.
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I'm taking my second real analysis course, after having taken 5 calculus courses, complex analysis, 2 abstract algebra courses and a prior real analysis course.

We're STILL starting at square 1 (What is a Euclidean space? What is a norm?)

At what point do professors stop reviewing this shit. I get it, it's been years and literally every single undergraduate math course I take seems to go on and on about the same shit.

Does anyone else know this feeling?
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>>7808040
5 calculus courses? I've seen some people count DiffEQs as Calc IV but what's the fifth?

But I guess I can give you a bit of perspective from the other side. I'm actually taking Complex Analysis before Real Analysis whereas it's typical at least at my school to do Real first, but not everyone does that so they have to go over some basics in Complex that all the kids that took Real already know. Basically you just have to realize that not everyone has had the same level of preparation as you have, they might just be younger and haven't had the chance to learn the basics yet,
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About negative temperature:

I understand how you can get it in a system and so on, but why does it not break the second law of thermodynamics, as entropy is decreasing in the system? Obviously I did not fully understand the second law, but what is the explanation?
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>>7808040
Some people may not have completed the prereqs or come from a different uni for a semester and not be on the same page as everyone else.
Also, a quick reminder never hurt anyone. It serves as a warmup and helps you get used to the notations the prof uses, which might not have been the ones used in your former course (better to notice that while he is reviewing old material rather than when he's rushing through new stuff).
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>>7807968
What's C?
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>>7808182
Complex numbers.
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If c is perpendicular to both a and b why the fuck does the cross product if a and b give you c
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>>7808203
Cross product of
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>>7808203
I don't understand what you're asking, the cross product is defined to be a vector c that is perpendicular to both a and b.
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>>7808211
Well now I'm just more confused
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Statics question here. So you have the brace that is a two force member (pin connected at A and C). I know you will have one single T force at the A connection, but how do I handle the connection at C? I plan on breaking this into four parts for the analysis. Would I just use one T for that connection? Sorry if I don't make sense. Can't find an example like this in my textbook.
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If I want a revolver to fire one bullet into a tube that is coiled with many turns how many turns of coil and what curvature would I have to give my coiled tube so that if I put my hand at the end part of the tube the bullet will arrive at my palm at such a speed that I can simply let it fall into my hand?

Does my question even make sense sense
Is it impossible
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Is my textbook wrong this doesn't seem proof enough to me.
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>>7808079
I was counting PDEs as the last calculus and a high school calc. course as well, but yeah.

>>7808122
>>7808079
That's true I suppose.

At this point it just feels like there's this one same set of material that every class wants me to learn and they just put a new twist on it. Like if I take the essence of all my calculus and analysis books together, it's all essentially the same thing just shown in a slightly different way each time.

But I admit the first time I heard most of it, I struggled and didn't do so well. I thought "that's so much material, there's no way I'll ever be able to fully grasp it all. How the hell did my professor even memorize this up to this level anyway? How is he not relying on a book to do these proofs?!" Hearing it again several times later, I can see now how it's possible.
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>>7808299
Why not? They just check the definitions of what an even and an odd function is, and conclude that it's neither.
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Line integrals are just the area under a curve in 3d space right?
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>>7808299
Write them both out. It's clearly not even, that's done for you so lets just look if it's odd. [eqn] -h(x)= -(2x-x^2)= -2x+x^2 [/eqn] so then [math] h(-x) \neq -h(x) [/math] thus it's neither open nor closed.

>>7808203
That's literally how it's defined.

>>7808214
What's confusing you?
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>>7808307
>>7808320
Alright I get it thanks
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>>7808299
No..? Your textbook is correct. That's exactly how proofs are made.

If you're hung up on them not proving well enough that [math] 2x - x^2 \neq -2x - x^2[/math], simply plug in a value for [math] x \neq 0 [/math] to each function and conclude that results are not equal.

But your textbook doesn't look like it's presenting a proof. Just looks like an example, which is fine.
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>>7808314
Seriously guys I took complex analysis and everything and have used line integrals plenty of times without ever being really sure or certain of this.

I remember studying arc length and understood intuitively how the calculations of it work.

Why isn't a line integral just the arc length times the height of my function at each individual point?

Is a line integral just a calculation of the area underneath my curve in 3d space or not?
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>>7808333
Anyone?

What the fuck is a line integral?
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>>7808314
>>7808333
Line integrals of real functions and of complex functions are slightly different animals.

The line integral of a real function [math] \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R} [/math] is the area under the curve.

The line integral in complex analysis is the same idea -- we take the limit of the riemann sum of rectangles under the curve. But (!) the "area" of each "rectangle" is a complex number -- the "width" of the base is a complex number, and the "height" is a complex number. The area of the rectangle is the "width" times the "height", which is also a complex number. We take the limit of this riemann sum.
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>>7808460
I see. So it is just arc length times the function, for reals at least.
Thank you for the detailed explanation on the complex version as well.
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Best youtube channel to teach myself elementary linear algebra? diff. eq's?
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>>7808537
Honestly, I'd say to use Paul's Online Math Notes. It's not videos, but it is really clear and a good resource to use.
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>>7808553
didn't know he had a section for diff. eq's. Appreaciate the tip.

What about linear algebra?

forgot to ask, whats a good book for the first class of college physics with calc?
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I'm doing Gauss method to find inverse matrices and I keep getting the wrong answer, what's the best way to do Gauss method? preferably the most efficient one
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>>7808635
there's only one way to do it, sit down and do it right. really.
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>>7808403
it's the integral of a parametric equation.
It gives you the length of a line instead of area
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>>7806680
what the fuck is going on in that pick related?
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>>7806680
Taking my first statistics class, is E(X) the same thing as E(Xbar)?
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>>7809262
Yes
E(Xbar) = E(1/n * sum Xi) = 1/n sum E(Xi) = 1/n n E(X) = E(X)
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>>7807419
>I'm furthering human progress
how?
>>
could someone explain logarithm in a simple manner?
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>>7809469
[math]\log_b[/math] is the unique continuous grouphomomorphism from [math](\mathbb{R}_{>0}, \cdot) [/math] to [math](\mathbb{R}, +) [/math] with [math]\log_b(b) = 1[/math].
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>>7809483
>>
>>7809469
>take a graph of y = e^x
>interchange axes
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>>7809483
Hmph. I actually understood that when I figured out that you were using operator notation. Now all I need is a proper understanding of the base of all natural logarithms and my dominion will be complete.
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>>7809469
Result of log of a number for say base 10 is what you need to raise 10 to the power of to get back to that number

Natural log of a number is what you need to raise e to in order to arrive at original number

Useful in like chemistry where something say like something is pH7 and you're like what does that shit mean and it's 10^7 hydrogen atoms floating around in one litre of your solution
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>>7806680
That isn't a stupid question actually. It has to do with the fact that a base of a vector space of dimension N has exactly N vectors. Intuitively, it's because you're adding too many constraints to the set so that it can produce no solutions.
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What are the extra dimensions in string theory? Every reference I find cites them as compact dimensions, but what the fuck does that mean mathematically, what is the definition of?
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Need help in rearranging this equation:
[math]M = \frac{mol}{vol} [/math]
into this:
[math]mol = mol * M [/math]

And how do I strengthen this ability?
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>>7809756
sorry, it is
[math]mol = vol*M [/math]
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>>7806680
Would my skills transfer more from A levels to SAT or ACT?
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>>7809756
>>7809758
Is this low quality bait?
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What is the relationship between the domain of a function and its first derivative? Specifically, if a function isn't differentiable at some point, does it mean that the derivative function is undefined at that point?
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>>7809743
"Compact dimensions" was just a nice way for science to explain the concept of hyperdimension. Yes, it's freakishly retarded, but hey! Distributing irrelevant information to the population at large has never hurt anyone, amirite?
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>>7809770
it is a stupid question.
Answer me.
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>>7809814
algebra, look up how to solve for x.
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>>7809743
https://en.wikipedia.org/wiki/Compactification_(physics)
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>>7809743
They're compact in the sense that the manifold they consider is fibered over r^3 with compact manifolds as fibers.
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why is the two a minus and not a plus.
8^2+11^2-2×8×11 cos(150°)= 337.42
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>>7809822
Oh okay, that makes sense. Thanks.

>>7809820
Kind of what I meant when I cited the references.

>>7809783
It always annoys me how in physics they never bother to state clearly what the hell they're working with.
>>
Is that a fucking mouse or a giant cockroach in that gif?
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I was looking through the sticky, and I found exams with solutions in calculus 3.

Are there any good exams with solutions for electro magnetics?
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>>7808327
>plug in a value
I agree with this... doesn't seem complete without.
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hm while doing mohrs salts lab, why do you have to keep the iron sulfate solution warm while filtering?
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Please help, I'm not sure if the proton and the alpha particle would be stop at the same time, or if one of the particles would rebound before the other. Either way I don't know how to do this question.
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I have an assignment that I'm unsure how to solve. Maybe you can help me.

A particle with mass 6,03u is moving with 898 MeV of Kinetic energy. The particle then sends out a photon with frequency 128Zhz (zetta). How much Total Energy does the particle then have left?
>>
Should I study industrial chemistry, economics or computer engineering?
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>>7810408
Use the work function, energy of the ejected photon is equal to h*f, subtract that from the initial energy and there you go.
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>>7810412
whatever you like the most
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>>7810423

I was thinking E(particle) + E(particle mc2) - E(photon).

I'm getting 5.99GeV doing that.
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>>7806930
Being an international student gives you a huge advantage in terms of cost and acceptance if your grades and test scores are sufficiently high
>>
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When I sketch r(t) = (cos(t), sin^2(t)) in MATLAB, I get this sketch if I go for very large (10^6+) values of t. I get a similar version for smaller values of t, but the boomerang shape isn't as defined.

I have a feeling that this isn't possible and it's the sketch is the result of a limitation of MATLAB or whatever. I am right or is this curve actually correct?
>>
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>>7810528
I should add, the block is actually lots and lots of individual lines like so.
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