/sci/ - Science & Math

Why are most people too lazy to study constructive topology?

A function shouldn't have a right inverse just because it's surjective, that's just make-believe land. Make-believe lend can be fun, don't get me wrong, but there's only so far as to how seriously you should take it.

Unanswered questions from the previous thread:

Math questions:
>>11601405
>>11604494
>>11606836
>>11610836
>>11611824

Probability and statistics:
>>11604446
>>11607217
>>11610584
>>11611408

Physics questions:
>>11602109
>>11609996

Chemistry questions (a fucking recommendation request)
>>11612933

Biology and medicine questions:
>>11601472
>>11607597
>>11611827
>>11612933

/g/ related questions:
>>11602334
>>11602909
>>11603741
>>11613203

Advice requests:
>>11602650

Hard to categorize questions which I don't want to place in stupid:
>>11605344
>>11609245

Stupid questions:
>>11602603
>>11604453
>>11605774
>>11606747
>>11611859

>>11613906
Help, especially for solving the period without the v = (lambda)f formula

When the FUCK are they announcing whether classes are online or not for the fall? If they are, I can Google my way through the tough classes

Can someone help explain the thought process behind this question?
So I had completely guessed this questions answer by accident so I don't really understand it.
Looking at the answer, how did the person come to know that he should compare it to (1/2n)? Personally, I would've never thought of that or any of the other comparisons used in other sites such as (1/n - 1/2n) so I would definitely get this question wrong if I were to get it on an exam.

>>11613906
I am brainlet. Help me /sci/. We have 3 groups a,b and c. A has 7 elements, B has 9 and C has 12. We need to know how many outputs are possible. Note: Elements should be in order for instance abc or bca or cba etc. That implies that elements of a/b/c cannot be put it in others elements place. Using one of any of this order we must find the total numbers of outputs possible. Help.

what exactly is a moment of inertia?

When calculating the surface area of some solid around the x-axis, this is the formula given:
[math]\int^a_b A_{SURFACE}=2\pi f(x)\sqrt{1+f'(x)}dx[/math]

I get that if the shape we're trying to calculate the surface area of spans from [math]a[/math] to [math]b[/math], we integrate the circumferences of every point between a and b (2pi*r*f(x) at every point and add together) to get the surface. I don't understand why we need the curve path formula in there at all. Even more so, why is it in the integral. I'm so confused by this. It seems redundant.

>>11614540
Fucked up the formula, sorry.

[math]A_{SURFACE}=\int^a_b 2\pi f(x)\sqrt{1+f'(x)}dx[/math]

Holy fuck I am so stupid. What is this question even asking. Ya, I completed the square and found the normal solution for the quadratic equation. But the usual solutions for that aren't the roots for [math]x^2-\Delta[/math]. I feel so fucking dumb.

>>11613979
Scientifically speaking who is the best 2hu? If there is no scientific consensus what experiments can be done to determine who is best 2hu.

>>11614940
actually the best 2hu is jo'on and if you could post a high quality version of that picture that'd be great

>>11613906
Is this okey? Can i tend to infinity just with infinite repetition of any digit?
Consider the sequence of continued fractions:
[eqn]0.9 = \frac{1}{1+\frac{1}{9}}[/eqn]
[eqn]0.99 = \frac{1}{1+\frac{1}{99}}[/eqn]
[eqn]0.999 = \frac{1}{1+\frac{1}{999}}[/eqn]
[eqn]\cdots[/eqn]
[eqn]0.99... = \frac{1}{1+\frac{1}{99...}}[/eqn], this is, [eqn] 0.99... = \lim_{x\to\infty} \frac{1}{1+\frac{1}{x}} [/eqn]

Friendly reminder that math is for retards which is why it's the only subject this board ever discusses.

>>11615048
I math. I retard. Can confirm.

>>11614987
Yes this is fine. Look up the definition of a limit of a sequence :)

I need a physical book for calculus for reasons. Morris Kline has seems highly recommended and it's pretty cheap. Even used copies of Spivak are >2x more expensive. Any other quality calculus textbook recs?

>>11613998
Anons, I seriously can't figure out how to calculate wavelength. I only have the amplitude and velocity, right? How the hell do I figure out the frequency to then get the wavelength?

Retard here, would really help if one of you could answer or point me to the correct literature:

On many, many occasions back in High School I used to create "waterfall" bongs/pipes using Aluminum foil screens/bowls to smoke Marijuana. I've recently read that Aluminum exposure can cause early onset Alzheimers...

This was many years ago now, is any Aluminum I might have inhaled still in my brain?

And can the body naturally remove inhaled Aluminum? I've tried doing some googling but can't get any definitive answers.

I'm now kind of worried.

>>11615188
I wouldn't worry about it. I smoked a LOT of weed through aluminum foil and I turned out okay. Tbh it probably didn't do as much damage as the actual weed.

t. 30 year old former addict.

>>11615178
>>11613998
Is the wavelength just 0.9 meters? I don't see any specific reason why to assume this, but I don't know how to else proceed

recommend me some good books for learning circuits, from elementary resistor shit all the way up to ac analysis and beyond
please and ty

>>11613906
If I want to become Nikola Tesla and build his free energy generator and be a magnetic scientist monk, what academic path do I take?

>>11615188
Fast a bunch, then try dry fasting. I have pissed sediment once I rehydrated from dry fasting. It's invigorating to get shit out of your body. I haven't tried this (yet), but you could try a highly fruit based or all fruit diet. Drink the cleanest alkaline water you can. Your body wants to heal.

>>11615436
why dont you study the basics of electromagnetism before you commit to anything, tiger

>>11614476
/mass/ moment of inertia AKA moment of inertia is [math] \int r^2\text{ d}m [/math]. it measures how hard it is change angular momentum of an object. analogous to mass. units of slug-inches-squared. there's a scalar MoI associated with each axis of a reference coordinate system affixed the object you care about, you can write it as a tensor
/area/ moment of inertia AKA second moment of area is [math] \int r^2\text{ d}A [/math]. it measures out rigid a shape in the plane. this is a strictly geometric thing. units of inches-to-the-fourth. see parallel and perpendicular axis thms.
>>11614123
The very first term in the original sum should make you worried, because you should know off the top of your head that the harmonic series diverges; this is just a multiple of the harmonic series. so with that hint, maybe look at some multiple of the harmonic series to compare the whole sum to. every term in S is greater than the associated term in 1/2n
>>11614476
>>11614540
SA of a body of rotation is circumference times length, right? or the [math] 2\pi f(x)\Delta\ell [/math]. dL is not a change in x; it is small length of the arc. Realize [math] d\ell=\sqrt{dx^2+dy^2}=\sqrt{1+[f'(x)]^2}dx [/math] and take the integral in your posts to be the sum under the proper limit
>>11614905
>supposing x^2-D has a root, then D is positive and also p(x) has two roots as given by quadratic formula
>supposing p(x) has two roots you can isolate D from quadratic formula and realize the square of any number is positive
>>11615188
why are you shoving foil into your bong what in the fuck
>>11615298
sadiku
>>11613998
>>11615178
>>11615229
>a
given: L=1.5 meters
>b
90 cm is 9/15 wavelengths so T=0.60*15/9=1 second
>c
T
>d
f==1/T
>e
v==L/T=Lf; 1.5 m/s = (1.5 m)(1 s)^-1
>>11615158
>Morris Kline has seems highly recommended and it's pretty cheap
its probably fine

>>11614551
marking this one answered

>>11615563
I just need to know if the brain naturally eliminates Aluminum over time. And because I didn't have a bong..I was smoking out of gatorade bottles and shit

>>11615586
I don't know, bro. It doesn't sound good to have aluminum in the brain. Try smoking out of a nice apple.

>>11615591
I did that too lol. Just used Aluminum foil on some occasions,

>>11614940
Remilia.
>>11614954
Best I could find, reasonable improvement.

>>11615984
Was bored and tried to look for it again.
Remilia is still the best btw.

i'm having trouble understanding this pic related. i know that a set with a line above it indicates the complement, but i don't understand how that definition would fit into this definition, and why it appears over element names too. my textbook fails to explain what the line means in this context. thanks!

>>11616327
[math]\overline{n}[/math] is just the "n" inside the field anon.

>>11615563

You seem smart, maybe you can help me with this.

I've been reading about how computers work, and also reading their history. From what I've been reading, essentially, "classical" computers were only possible when we made the transition from electro-mechanical switches to solid-state switches via semi-conductors or "transistors." The key word their was "switch" however, as I understand it. Computation on a classical computer depends on a switch which depends on current/voltage.

Now, I've been reading about quantum computers too, because I want to know how they work in comparison to a "classical" computer. I am reading about ion traps, but I don't see how this relates to a "switch." Do quantum computers make use of the principle of a switching mechanism like classical ones, or is it a completely different principle?

>>11616459
> essentially, "classical" computers were only possible when we made the transition from electro-mechanical switches to solid-state switches via semi-conductors or "transistors."
We used valves (tubes) before transistors. A computer built from electromechanical relays would work fine, but it would be extremely slow.

> Do quantum computers make use of the principle of a switching mechanism like classical ones, or is it a completely different principle?
Completely different.

>>11616327
I already fucking explained this to you. Why did you post the question again? Did you forget?

A function is defined as a something that for every object returns only one image; so what about the trigonometric circle? you have a 2 points (up and down) for every x

>>11616533
A circle in the plane is not a function of x, you are correct

Why we do not get any diffraction signal from partially constructive interference, only full constructive interference?

>want to TA for a physics class
>requires an addition course, concurrent
>was already taking 18 hours next semester, would have to drop something
is it worth it bros?

>>11610836
That thing has a maximum, say [math]M[/math], so the real question is, how do you solve [math]\frac{x+1}{2^x}=a[/math] for [math]a<M[/math]?

>>11616830
Bisection method

>>11616704
Clarification: i'm reffering to X-ray crystallography. This is an exam question that physically makes no sense to me...

>>11616506

Hello, and thank you. Electromechanical relays were in fact used before transistors (and you're right they were slow), at least according to the book I'm reading written by herman goldstine, who was von neumann's assistant on developing the ENIAC and other early digital computers. He witnessed and was part of the transition from electro-mechanical to electrical/solid-state computing.

>completely different

Would you mind elaborating on what makes it different? I don't really know how to understand a model of computation without the concept of a switch. Are there any other examples of computation that don't rely on switches? Doesn't matter if they're slow just to help me understand. I watched a lecture Microsoft put out where they use finite state machines but I'm more interested in the actual physical implementation of it, what the physical concept/principle underlying it is (why I'm reading about ion traps).

Is part b supposed to be an iff?

>>11617048
yes

for each statement (a) through (g), if it is true, write the word "True." Otherwise, write the word "False." No explanation is necessary.

(a) The graph of a rational function can never cross its oblique asymptote.

(b) If the real number c is a zero of the denominator of a rational function, then the line x = c must be a vertical asymptote of the function's graph.

(c) A real number c is a zero of a polynomial function f(x) if and only if x-c is a factor of f ( x ).

(d) Every polynomial function of degree n(n ≥ 1) has n real zeros.

(e) Every graph of a polynomial function of degree n(n ≥ 1) has n − 1 turning points.

(f) Every real number is a complex number.

(g) \sqrt{-25}=\pm5i

>>11617120
>(a)
What's an oblique asymptote again?
>(b)
No, see [math]f(x) = \frac{x}{x}[/math]
>(c)
True.
>(d)
False, see [math]f(x)=x^2+1[/math]
>(e)
What's a turning point again? Either way, probably false, see [math]f(x)=x^4[/math]
>(f)
True.
>(g)
True.

>Explain why the set of nonzero squares is a subgroup of the multiplicative group of the field [math](F^x , \cdot)[/math].

Is this some coset nonsense?

need help wrapping this up, have to use comparison test. Is show
[math]lim_{n \to \infty} \frac{1}{n}\cdot \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = \lim_{n \to \infty} \frac{1}{n}[/math]


I'm not sure if demonstrating limit equality is, strictly speaking, a 'comparison test'. TIA

Give an example of a polynomial function of degree 5 with real coefficients, written in standard form, whose only real zeros are 0 (of multiplicity 1) and -5 (of multiplicity 2).

>>11617249
f(x) = x*(x+5)*(x+5)*(x-a)*(x-b) where a,b are not 0 or -5

>>11617249
[math] p(x)=x(x+5)^2(x+j)(x-j) [/math]

>>11617158
can someone check if this is correct?

>>11617259
>giving it 5 real roots when he asked for 3
>>11617249
x(x+5)^2(x^2+1) = x^5+10x^4+26x^3+10x^2+25x will work

>>11617239
bump to add that it should really look more like
[math]\lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = 1 [math], so this series approaches the series of 1/n as n approaches infinity, and is therefore D I V E R G E N T.

>>11617281
lmfao. the sand.

>>11617300
>giving it 5 real roots when he asked for 3
>x(x+5)^2(x^2+1)
Nigger, that's exactly what I wrote here >>11617259 j is the imaginary unit.

>>11617307
>j is the imaginary unit.
who the fuck calls [math]\sqrt{-1}[/math] j?

>>11617257
I missed the "only" part in " only real zeros are 0 (of multiplicity 1) and -5 (of multiplicity 2)"

f(x) = x*(x+5)*(x+5)*P(x)

where P(x) is any quadratic polynomial without real roots

>>11617226
wdym?

>>11617343
I just ended up using some homomorphism definitions.

>>11617305
>[math]\lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = 1 [math]
[math]\lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = 1 [/math]

Please lmk if this is a valid approach for the comparison test here!!!!!!: >>11617239

>>11617239
what are you trying to do ?

>>11617309
Engineers.
By the way, engineers are essentially children, so they find it funny when people get angry at them over this stuff.
The plan is, whenever an engineer uses [math]j[/math] for the complex unit, you act confused and ask them what's [math]j[/math], even if they explained it yesterday.
>hey dude, isn't there an extra variable in there?
>hey lad, what's that j?
>hey bro, what's that [math]j[/math] on the Fourier transform, and by the way, you forgot to add [math]i[/math]
If everyone who isn't an engineer cooperates, I have good hopes that they'll eventually get tired and quit it.
>>11617239
Weren't a whole bunch of solutions posted last thread?

>>11617368
trying to use the comparison test on the series here:>>11617239 (sum n=1 to infinity of the first term on the LHS). I try to compare it to the harmonic series, which diverges, but I'm unsure if taking the limit of second term on the last line and showing that it approaches 1/n * 1 as n approahces inifintiy is a valid form of the comparison test.

>>11617376
no, I got responses (thanks!) but they were to another problem. I think this one is pretty straightforward though since my question is a yes or no format

>>11616966
Not the guy you're responding to, and I'm by no means an expert in classical models of computation, but it seems to me that your hang up over switches is because you're stuck with the notion of classical information (0/1 bits). Of course a quantum computer is going to operate on fundamentally different principles because it's not working with classical information, it's working with quantum information (qubits).

I don't know how much more elaborate of a distinction you'd like. They're operating on completely different paradigms of information. Classical information can be derived as a special case of quantum information, but the reverse statement cannot be made. You can't derive universal quantum computation from the toolbox of classical computation (not in any sort of faithful sense, at least... I mean of course you can claim to write down exponentially large matrices and do linear algebra on them and so forth, but that's really just bruteforcing the theory of quantum mechanics; you're not physically accessing quantum information).

>>11617383
Ah, I see.
It isn't. *Any* sequence which converges to zero satisfies [math]\lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} \frac{1}{n}[/math]. Some of them are summable, some aren't.
You can just show that [eqn]\frac{1-\frac{2}{n}}{1+\frac{1}{n^2}} \geq \frac{1/3}{10/9}[/eqn] when [math]n \geq 3[/math] tho. Compute for [math]n=3[/math], compute both monotonicities on n.

>>11617407
I rewrote what I said to ask if this method was ok:
[math]\lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = 1[/math]
Because we have that term approaching 1 as n approaches inifnity, we have our series approaching the series of 1/n as n approaches infinity, thus it is divergent.

does that work? because that term goes to one, our series begins to look more and more like 1/n as n grows, so it's divergent. Or is that badmath?

>>11613906
Can the induced-fit mechanism of enzyme action be characterized as an isomerization reaction?

Could someone explain what the fundamental theorem of calculus is actually telling us? My understanding is, one of the conclusions we draw from it is that if a function is continuous on some interval (and of course differentiable, aka no sharp points or whatever), that such a function must have an antiderivative, ie there must exist such a function that when we take a derivative of it we end up with our original function. Why does it say that? I've only watched a video on it so I can't really draw a full conclusion. Also, this brings me to my next point, the FTOC allows us to find the integral of [math]\frac{1}{x}[/math] somehow. How we go about doing that is also not clear to me. If someone could clear these up in simple terms for someone who's studying this subject for the first time in depth, I'd reeally appreciate it!

>>11617573
>if a function is continuous on some interval (and of course differentiable, aka no sharp points or whatever), that such a function must have an antiderivative
is that true? i thought [math]\sin(x^2)[/math] didnt have an antiderivative

>>11617515
That does work, yes.
If [math]\lim_{n \rightarrow \infty} a_n =1[/math], then there's [math]N[/math] such that [math]n>N[/math] implies that [math]a_n>1/2[/math], and then, for a divergent series [math]b_n[/math], [eqn]\displaystyle \sum _{n=1}^{\infty} a_n b_n = \sum _{n=1}^{N} a_n b_n + \sum _{n=N+1}^{\infty} a_n b_n \geq \sum _{n=1}^{N} a_n b_n + \sum _{n=N+1}^{\infty} \frac{b_n}{2} = \sum _{n=1}^{N} a_n b_n +\frac{1}{2} \sum _{n=N+1}^{\infty}b_n [/eqn], so it diverges.

>>11617515
>we have our series approaching the series of 1/n as n approaches infinity, thus it is divergent
No. Your reasoning is that the terms approaching 1/n implies the divergence of the series, which is necessary but not sufficient. You need to show they get "really close".

>>11617612
Oh right, all the [math]b_n[/math] need to be positive, as is the case for 1/n.

>>11617573
fundamental theorem of calculus tells you that the total distance travelled can be computed from the knowledge of instataneous speed at each time

>>11617406

Hi Anon, I appreciate your attempt. I'm familiar with the terms you're using, and the manner in which you're using them.

What I'm looking here is for more of a concrete, physical distinction. Like I said, that's why I'm reading about ion traps, and josephson junctions. I just want to see how the actual physical implementations are different from each other. How are ion traps and josephson junctions different from mosfets? That's more along the lines of what I'm trying to get at.

>>11617573
It says that integration and differentiation are inverse processes. You're referring to the first part: if a function [math]f[/math] is continuous on an interval [math][a,b][/math], then it's integrable on that interval and the function [math]F(x)=\int_a^xf(t)dt[/math] is differentiable and [math]F'=f[/math] on [math](a,b)[/math]

>the FTOC allows us to find the integral
Kinda. It tells you that it if you can find an antiderivative, then that thing coincides with the integral. It doesn't explicitly give it to you.

>>11617591
It actually has one.

>>11617613
ok, it felt really loose and not proper to me to, like I had a big unjustified jump. In showing that they 'get really close', aren't I doing that when I show:
[math]
\lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = 1
[/math]
Because this implies that as n approaches infinity we have
[eqn]
\frac{1}{n}\cdot lim_{n \to \infty} \frac{(1 - \frac{2}{n})}{(1+\frac{1}{n^2})} = \frac{1}{n} \cdot 1 = \frac{1}{n}
[/eqn]

not sure how else to show they get 'really' close, since equality of limits doesn't imply equality of series (e.g lim 1/n and lim 1/n^2 both equal zero, but only one is convergent).

>>11617612
noice, thanks. that's simple and intuitively appealing

>>11617764
>It actually has one.
what is it?

>>11617809
>what is it?
it can't be expressed using elementary function, but it does exist

>>11617812
oh, i see

>>11613906
Is kim ded

>>11617812
so how do we know that it exists?

>>11613906
How to I calculate the Euler method increase of y vs time (h)
When Time (h) is a scale of 0 to 1 second in 0.01 increments?

>>11617821
[math]F(x) = \int_{0}^{x} \sin t^2 \, dt[/math]. of course one needs to show that this function is well-defined, differentiable, and that its derivative is sin(x^2). but all of this actually follows from (the precise mathematical statement of) TFOC.

If X is a random variable with a Poisson distribution with parameter 2
and Z=(0.5)^X what is the mean value of Z?
I've been stuck at it for a day

>>11617573
>what the fundamental theorem of calculus is actually telling us?
"The rate of change of the area under a curve is the height of the curve itself"
>>11617827
have you tried reading the wiki? first, you need an ODE to work with

How do I find the value of B?

If you had thousands of miles of space and a gearbox with thousands and thousands of gears hooked up to a normal combustion engine what's stopping you from getting up to extreme speeds at the higher gears? Can a regular Camry engine do 750 mph at 2k rpm in 50th gear? I retarded for even thinking about shit like this?

>>11617788
When you put it like that, you're only telling me the k-th term approaches 1/n for some n. By that reasoning 1/(n^2) diverges, since it also approaches 1/n as much as you want. Anyways, >>11617612 already did it for you.

>>11618070
2

>>11618115
Tell me how!

Ok, last answer check of the week. On this one we're asked to use the alternating series theorem to get an error estimate < 0.00001 for the series:
[eqn]
\sum_{n=0}^{\infty} (-1)^n \frac{n+1}{2^n}
[/eqn]

This is another one of those ones that felt suspiciously easy, so I wanted to post just in case.

>>11618117
do you know how to solve the integral [math]\int\frac{dx}{2x-4}[/math]?

>>11618105
I see, thanks. I agreed but was having trouble articulating why exactly it was a problem.

>>11618124
I'm having a hard time trying to understand the substitution method, but I think I do.

>>11618127
[eqn]\int\frac{dx}{2x-4}\\
\frac{1}{2}\int\frac{dx}{x-2}\\
u=x-2\\
du=dx\\
\frac{1}{2}\int\frac{du}{u}\\
\frac{1}{2}\left(\ln(u) + C\right)\\
\frac{1}{2}\left(\ln(x-2) + C\right)\\
\frac{1}{2}\ln(x-2) + C[/eqn]

>>11618086
Because with gear multiplication you trade angular speed for torque. So even ignoring the mass of the gears themselves and ignoring losses (which you can't do if you have this many fuckin gears), you could theoretically get whatever speed you desired, but that doesn't mean it would be able to turn a shaft.
>Can a regular Camry engine do 750 mph at 2k rpm in 50th gear
No. It doesn't have enough power.

>>11618070
You differentiate both sides.

>>11613906
how many numbers from 0 to 9999 contain at least one zero? plz hlp i cant do this shit

non math brainlet here
What's special about integers? If you look at all real numbers what makes 1 and 2 more special / useful than all the number that lie inbetween? Something like e or pi is clearly useful outside of just being a number but is there more to integers that make them different to say some random decimal value?

>>11618278
btw 0001 counts as if it has one zero cause the excersize was actually with 4 digits

>>11618278
10000 minus the number of digits that dont contain a zero, which is [math]9^4=6561[/math]
so answer is 3439

>>11613906
Career question. Say I want to go into either

-medical/cosmetic laser industry if that's what it's called. whatever helps make and build designs for health and cosmetic purposes
-Particularly skin research primarily into cosmetics and lazer treatments

Whats the path to do either of these 2 choices?

>>11615984
>>11616315
But Remilia has smelly unwashed vampire feet and fully loaded pichuuns. She can't possibly be best 2hu.

>>11617048
Can someone help me out with a and b? I'm about to blow my brains out and i'm just lost on time.

>>11618428
Lies and slander.
>>11617048
>>11618483
I mean, you did make it sound like you just wanted confirmation that b) is really an iff statement.
Checking that it's a homomorphism of monoids is trivial and left to the reader.
The image of a monoid homomorphism is a submonoid.
[math]a^2 - 10b^2 \mod 5 = a^2 \mod 5[/math]. We check that [math]0^2 \mod 5 = 0[/math], [math]1^2 \mod 5 = (-1)^2 \mod 5 =
4^2 \mod 5 = 1[/math], and [math]2^2 \mod 5 = (-2)^2 \mod 5 = 3^2 \mod 5 = 4[/math], so that's that.
It's easy to see that [math]D(a + b \sqrt{10}) = (a+b \sqrt{10})(a - b \sqrt{10})[/math]. The remainder follows from 0 times anything being zero and the real numbers forming an integral domain.

>>11618605
Small mistake: the image is a semigroup, but not necessarily a monoid.
Checking that it contains the identity is left as an exercise to the reader.

Why are electrolyses always shown with batteries? do they need to be floating voltages?
Can electrolysis be done with the +/GND of a wall charger?
What's the relation between amperage and reaction rate?

>>11618605
>I mean, you did make it sound like you just wanted confirmation that b) is really an iff statement.
Oh definitely. I thought that was the only question I had. Now my brain is mush. Thanks!

If diodes and op-amps can work at several GHz now, why aren't log and anti-log amps used in computing?

>>11618304
The primary importance of integers (IMO) is that integers are how you count things. Natural numbers (and only natural numbers) are the sizes of finite sets, and you tack on the negatives so you don't need a bunch of special rules about when you are and aren't allowed to subtract stuff. Counting is the most fundamental math you can do. It's how mathematics began in prehistory.

Also, the integers are substantially more basic objects than the reals in terms of complexity. In order to actually whip up a copy of the reals, you have to first
>build the natural numbers using set autism
>build the integers from the naturals
>build the rationals from the integers
>build the reals from the rationals
You can define all the properties of the real numbers with axioms, but in order to actually build an explicit copy, as far as I'm aware you can't escape climbing that ladder.

>>11618304
It depends on what you want to do. Feels like you're thinking about numbers just as, well, numbers in the colloquial sense. You can consider a shit ton of different structures on their sets, and each one of them will have interesting properties. As an example, the group structure of [math]\mathbb{Z}[/math] alone is so important in group theory that there is a fundamental theorem involving it.

idk what's the deal with WGS84/EGM are they only useful for inertial navigation?

I'm working on an alternating series problem, and I need to show that it is ultimately decreasing. I have a solution, but it's really bloated and I feel like there's a better one out there. So here's the starting inequality:

[eqn] \frac{(n+1)(n+2)}{2^{n+1} + 3} < \frac{n(n+1)}{2^{n} + 3}

[/eqn]
[eqn]
\frac{(n+2)}{2^{n+1} + 3} < \frac{n}{2^n + 3}
[/eqn]

My solution is pic related, it's super uggo tho.

>>11619045
Think I got it boys:

[eqn]
\frac{n+1}{2^{n+1} + 3} < \frac{n}{2^n + 3}
[/eqn][eqn]
\frac{2^n+ 3}{2^{n+1}+1} < \frac{n}{n+2}
[/eqn]
So we see the LHS has a limit of zero, while the RHS has a limit of 1. So it is a decreasing sequence

>>11618697
>>11618901
well I'd be lying if I said I completely understood all this but thank you for replying at least. I can at least comprehend that they're a kind of base that you build on because yeah that seems fairly intuitive. I dunno I've just suddenly become interested in this stuff despite being relatively shit at maths. Maybe I'll have a look into set theory and see if I can comprehend any of it.

>>11619045
How about

[math](n+2)(2^n+3) = \frac{n+2}{2} (2^{n+1}+6) < n(2^{n+1}+3)[/math]

>>11619129
do you like this one more or >>11619094 ?

Any IQ test pattern masters see anything going on in the coefficients here?
I'm already aware the columns sum to zero and the determinants are zero, but it kind of looks like there's something more.

>>11613906
G'day. I've solved this question though received the wrong answer on the part of my area calculation (I initially calculated it as 7.2 x 6 [using the length as the width measurement, which I assumed to be wrong though couldn't see any alternative]). Looking at the answer now it appears the area calculated was 30m^2 which leads me to assume that the box goes off of the diagram, would I be correct to visualize it as the related image instead of what I initially believed (that the box itself was filled with water and was the diagram)?

>>11619186
In the 3x3 and 5x5 ones the central entry is always zero. Also there's a symmetry [math]a_{i,j}=-a_{n+1-i,n+1-j} (n=3,4,5)[/math]. Not sure if there's some pattern to the sequence formed by the entries, but start by noticing that the largest denominator is 2 in 3x3, 6 in 4x4 and 12 in 5x5.

>>11613906
2nd from right is eyeballing rightmost's little notebook
I wonder what he sees.

>>11619186
Diaganols, horizontals, and verticals are mirrored and multiplied by -1.

>>11613906

brother i need help

>>11618141
Thank you!

>>11619829
Sides annihilated.

>>11613906
Why does it follows that 1/2a is in (0,1)?

I feel like a god damn buffoon.
How can I prove this is transitive?
R is defined on the set of natural numbers.

I feel like a god damn buffoon.
How can I prove this is transitive?
R is defined on the set of natural numbers.

>>11613906
How does pic related differentiate and what rule are we using here, product rule? It looks like it'd be 4uy/c - 4uy^2/c^2, why isn't it?

>>11618151
Thanks

>>11619981
x = x^2 mod 2 and therefore (a,b) in R actually means that a and b have the same parity. it follows

>>11619916
all in a days work, fren

>>11613529
i did try reading the textbooks but they make no sense and are too convoluted, going too much in detail and forgetting to make it simple

>>11620088
which book

>>11620089
well its a serbian book from some ex student now professor

>>11619930
>
>>11620097
>wtf this random serbian book is bad thus all books in the subject also are

>>11620157
no no, im not saying all the textbooks are bad but i would appreciate some other one since this one is clearly not helping me

Anyone recommend me some sci-fi books?

>>11620234
>>>/lit/sffg/

>>11613906
Whats the psychology term for taught disgust? like how we find some things disgusting even though we can't justify it it's just something taught by culture that we latch onto, anyone know what I'm on about?

>>11620232
Griffiths is recommended a lot.

>>11620242
>>>
Thanks anon

>>11620272
thanks

This is wrong right? Shouldn't it be 14 years?

>>11613906
Considering the following linel system (pic-related). In view of the step matrix obtained, the system is...(compatible, uncompatible, non sovable)..
Pls answer in less than 13 min

>>11620358
Use pert my man, as in P = Po*e^(rt)

>>11620415
[eqn]P=P_0e^{rt}\\
2P=Pe^{0.05t}\\
2=e^{0.05t}\\
\ln2=0.05t\\
t=\frac{\ln2}{0.05}\\
t\approx13.86[/eqn]

>>11620358
my calculator tells me that [math]\frac{\ln2}{0.05}=\ln(2^{20})[/math] but i dont see it

Forgive me for my poor English.

How can I find the forces and moments acting upon the truck and resolve the normal forces acting on the wheels?
>mass of the arm and the length of the truck are ignored

>>11620358
Oh fuck I didn't realize it was saying ln(2^20) I thought it was saying in 2^20

>>11620439
[math]0.05 = \frac{1}{20[/math]
[math]\frac{ \log 2 }{0.05} = 20 \log 2 = \log 2^{20}[/math]

>>11620515
ah is that how that works

>>11620560

>>11618634
Normal people do it with pic attached
No idea what floating voltage is, but works both AC and DC, depending what you want to do.
Don't know if there are any formulas, but the higher the amperage the faster the reacton goes, at least when I do them.

>>11619913
Just use funnel and paper ffs

>>11620603
>electrasyn
are these popular now? I'll have to check if they're easy to diy.
Floating voltage means "ground/-" is not referenced to earth. If you attach the + of a wall charger to the - of another, you get a short; but with batteries, you simply double the voltage.
I figured current=charge/sec, which could be converted to electrons/sec=moles/sec=reaction rate. But there might be some catch I'm missing. Am I wrong?

>>11619930
If 0 < a < 1, then dividing by 2 we get 0 < a/2 < 1/2. But 1/2 < 1. So 0 < a/2 < 1.
You can think of this proof as showing "homeomorphisms send things on the boundary to things on the boundary."

>>11620653
>diy
Well, you need pretty pure reactants and electrolytes to get anything close to decent yields, if you want to deposit metals, might as well just use a DC charger, separate the wires and put them into a solution.
The electrons=moles part seems sketchy and the speed would be of electrons added to the solution not the reaction itself, actually, there might not be any generic formula as it would differ based on the natures of solvent and reactants, conductivity and temperature, but if they are kept constant and only current is varied then higher results in a faster reaction.

>>11618395
EE is the usual path to optics and lasership specialization
>skin research
idk
>>11618634
because you need to power the reaction lmao
>do they need to be floating voltages?
no
>Can electrolysis be done with the +/GND of a wall charger?
sure
>What's the relation between amperage and reaction rate?
I'm not a chemist but with shit like this its usually
>proportional to the exponent of absolute temperature
>proportional to the square of current
>>11618658
I dunno how relevant analog amps are to computers these days but it looks like the practical issues are
>diodes saturate at higher temperatures and boy do computers like to get hot and then cold and then hot again
>depending on the junction in the feedback, only unipolar signals get thru
>>11619564
>7.2 x 6
Mate, I really do not understand where you got these numbers. Length AB is given as 5 and depth is explicitly stated to be 6. So the rectangular area is 30 m^2 with the centroid being obvious. This makes [math] h_\text{CG}=5.2+1.5=6.7\text{ m} [/math]. Pressure is [math] p_\text{CG}=\gamma h_\text{CG}=9.81\cdot1000\cdot6.7=65.727\text{ kPa} [/math]. You know [math] y_p=-\gamma\sin\theta I_{xx}/p_\text{CG}A=-9810\cdot(3/5)\cdot(6\cdot5^3/12)\cdot(65727\cdot30)^{-1}=-0.187\text{ m} [/math] which is consistent with the value given for center of pressure as measured from A, considering CG is 2.5 m from A. Finally, [math] F=\gamma h_\text{CG}A=9810\cdot6.7\cdot30=1.97\cdot10^6{ N} [/math].
>would I be correct to visualize it as the related image instead of what I initially believed (that the box itself was filled with water and was the diagram)?
frankly, I can't picture what you were originally imagining. The 5x6 rectangle in the pic is as if you are looking at the surface from above, looking straight down.
>>11619829
10/10
>>11619984
the equation under A doesn't look right at all. u is a multiple of u? that doesn't make sense. Also, evaluating at midpoint between plates usually means y=0.

Why is a high input impedance desirable? I thought the point of a MOSFET, for example, is current amplification?

Will science one day solve the paradox of having to post in a thread to tell people to stop fucking posting in it?

>>11620996
>Why is a high input impedance desirable?
Modularity. Ideally, the output of each module should depend only upon the design of that module and the inputs it receives from preceding modules, and be entirely unaffected by whatever is connected to the outputs.

Otherwise, you can't design modules in isolation but have to consider the entire system, where any change to any part can change the behaviour of the entire system.

>>11621150
Stop fucking posting it

>>11620779
Sorry, it'd probably make more sense with the image.

>>11621168
Right, but how does current travel through a MOSFET or ideal Op-amp then? Infinite input impedance means no current flow.

>>11620432
Your answer is the same as (1/.05)ln(2), which in turn equals 20ln(2) = ln(2^20)

>>11619984
>product rule?
Yes

>it'd be 4uy/c - 4uy^2/c^2
Think again.

>>11621194
Ah, okay. Sketch looks good.
>a
[math] u_\text{mid}=u(y=c/2)=(4U/2)(1-1/2)=U [/math]
>b
[math] \tau=\mu\cdot\partial u/\partial y=\mu\cdot(4U/c-8Uy/c^2), [/math] evaluate at 0, 15 and 30 mm.
>>11621277
Op-amps and MOSFETS aren't passive devices. Op-amps have an external power source usually not depicted in circuit diagrams. MOSFET have large, not infinite impedance (unlike op-amps).

If I have a function [math]f(x)[/math] that is the addition of a continuous function [math]g(x)[/math] and a fourier series of some other function, can I conclude that [math]f(x)[/math] is continuous?

Just starting community college, idk if my end goal is business or engineering or both. But my choices of majors that I like is math or physics. Which will be a better foundation? Thanks.

>>11621423
Nothing says that a fourier series has to constitute a continuous function, so no.

>>11621434
aren't fourier series always continuous though?

>>11621440
No. The infinite sum of a bunch of continuous functions doesn't have to converge everywhere.

>>11621448
So it deals with convergence of the fourier series then? I.e. if I show that the fourier series are absolutely convergent, then I can conclude [math]f(x)[/math] is a continuous function?

I need to generate a series of random numbers with a approximately fixed mean (+- 0.5 variation or so is fine)
I found this answer on SO https://stackoverflow.com/a/49856676
I have no idea what how that works. In the first example he picked two lists of random numbers and somehow the mean is 12.22, like he wanted!
This is complete wizardry to me, how did he do that?
And most importantly, how do I generalize to arbitrary sample size and means?

>>11621423
Fourier series or Fourier transform?

A Fourier transform may or may not be continuous; if a function is periodic, its Fourier transform isn't continuous but a sum of Dirac delta functions. A Fourier series is a list of coefficients describing a periodic function.

A periodic function is continuous if its Fourier series has a finite number of coefficients.

>>11621535
fourier series yeah. so would showing that the fourier series is finite (i.e. [math] \sum < \infty [/math]), then we can conclude [math]f(x)[/math] is continuous?

Anyone have Beauchamp and Childress' Principles of Biomedical Ethic? Any edition.

Does the math seem solid on this? My textbook does almost everything in stupid inches and foot pounds so hoping I didn't screw something up

>>11621646
[math] 1.4\cdot10^6\text{ Pa}=635\text{ N}/\big(\pi D^2/4\big). [/math] I got diameter to be about 24 millimeters. The part where you compute radius looks wrong.
>stupid inches and foot pounds
more like based inches and foot-pounds

wish me luck, bros

>>11621733
Thanks bro, I'll try to go back through it. Any idea where I screwed up on the radius? Can't imagine there's that many ways to fuck this up but apparently I found one lol.

>>11621845
You're welcome~ No idea, you probably bungled it when punching stuff into a calculator.

>>11621848
Nah I got it, I squared the value of the area not just the units. Thanks again.

>>11621550
yes

Man Richard Feynmen is so fucking funny. I just take one look at that guy's face and I just start howling with laughter. Is there something wrong with me?

>>11621506
are you looking for numpy.random.normal ?

Show that the squence of functions [math]f_{n}:[0,1]\to\mathbb{R}, f_{n}(x)=\frac{(1+x)^n}{e^{2nx}}[/math] converges uniformly on any interval [0,a] with 0<a<1

I know this can be solved with dinis theorem but desu im kinda running out of time

Show that the sequence of functions [math]f_{n}:[0,1]\to\mathbb{R}, f_{n}(x)=\frac{(1+x)^n}{e^{2nx}}[/math] converges uniformly on any interval [math] [0,a] [/math] with [math]0<a<1[/math]

I know this can be solved with dinis theorem but desu im kinda running out of time

>>11622429
Fuck

Converges uniformly on any interval [0,a] with 0<a<1

QUICK

what's the probability that out of 12 fair dice rolls, at least have a sum equalling 10? I tried by hand a few times, but I'm out of free tries now and have to get this one right. I plugged it into my calc as the binomial distrbution and got 3.375231134 * 10^-8, does that look right?

>>11622429
[eqn]\left ( \frac{(1+x)^n}{(e^{2x})^n} \right ) = \left ( \frac{1+x}{e^{2x}} \right )^n[/eqn]

>>11622472
>at least have a sum equalling 10?
*at least 9

>>11622472
>>11622216
I YOLO'd it and my answer was correct, but now I'm stuck on this.

>>11622620
For a group of ten people, there's a chance of [math]0.998^{10}[/math] that they'll do 1 test and a [math]1 - 0.998^{10}[/math] chance that they'll do 11.
The rest is multiplication and sheit.

>>11622634
>adds an extra nine like a retard
WTF past me.

>>11622634
I have this scrawled on paper too, but I'm stuck at the 'multiplication and sheeeit' step. I've marked it as something to come back to, this SE answer: https://math.stackexchange.com/questions/975824/expected-total-number referenced 'Linearirity of Expectation', something we haven't covered yet (this chapter is mostly about binomial distributions), so if I don't get spoonfed here I'll just go read about that stuff later, but if you wanna hold my hand through some multiplication that's fine too anon

>>11622429
>Converges uniformly
>on [0,a]
Nigga...

scientifically speaking how do i stop playing video games so much and spend more time studying/reading

>>11622654
It's easier to split the first test (which is always performed) from the subseqent 10 (which are performed with probability 1-0.98^10 = 0.1829). The expected number of first tests is 1, the expected number of subsequent tests is 0.1829*10 = 1.829, so the expected number of tests per group is 2.829.

>>11623343
smash your computer with a sledgehammer

Is there a way to express B in terms of A?

>>11623879
"It depends."
The answer you're probably searching for is "No".
Although
[math] B(x)=\sum_{n} \left( \dfrac{1}{n!} \dfrac{d^n}{dx^n} A(x) \right)_{x=0}^2 x^n [/math]

>>11623879
[eqn] B_n(x)=a_n\cdot A_n(x) \\
\text{or}\\
B(x)=\sum B_n(x)=\sum a_n\cdot A_n(x) [/eqn]

>>11623920
By this logic, I can "express"
[math] f(x):=1+x^3 [/math]
in terms of
[math] g(x):=-6+x^2+x^4 [/math]
because
[math] f(x):=1+x\cdot g_2(x) [/math]

>>11623879
btw. you generally have nice handwriting

>>11623918
thank you! yeah I guess I was trying to find a "closed form" answer that doesn't involve infinite sums.
i was trying to find a generating function for the logistic map recurrence relation using Wilf's method but i can't seem to find anything online about it so there's probably no nice way of writing it
>>11623930
i don't usually write this nice

>>11623920
tooker please
>>11623930
>nice handwriting
>that gay backwards parenthesis x that doesn't even cross in the middle
pick one

>>11623938
https://mathworld.wolfram.com/LogisticMap.html
generally not solvable. there's a handful of very special cases here

>>11622654
You compute the expected value for 10 people and multiply it by 16, because there are 16 groups of 10 people.

The percentage of titanium in an alloy used in aerospace castings is known to be normally distributed. If its standard deviation is σ = 0.3, what is the probability of obtaining a sample standard deviation equal to s = 0.37 or greater in a sample of n = 12 selected parts?

I'm supposed to get 0.116 but I don't even know how to start. I know how to create a confidence interval with 11 degrees of freedom in this case for σ but that's about it. How do I approach this?

Is there some site where I can pay someone to do my uni homework/labs? Please

>>11624243
weird i was way over thinking it

is there some kind of site where I can get paid to do people's homework? I'd like to just do more of the homework I'm already doing, for example.

>>11619981
a^2 + b = 0 mod 2
is equivalent to a=b mod 2

Baby chemistry student here. I have to do a project for my gen chem 3 class. I wanted to do a comparison of various chemicals used for sterilization in the healthcare setting: alcohol, hydrogen peroxide, chlorhexidine, iodine, and maybe bleach too or something. Then I thought this was too broad and wanted to look specifically at how alcohols interact with membranes of pathogens vs how hydrogen peroxide does it, because hydroxide/hydroxyl is involved in both cases. Like I didn't even know the difference between hydroxide ions and hydroxyl free radicals before yesterday. I had grand hopes of representing the mechanism by which they sterilize with chemical equations, characterizing the kind of reaction they do with cell membranes, figuring out why you would use one over the other, and so on.
Anyway the teacher bitch slapped that idea, said there really wasn't any chemistry there, and suggested I just do my project on how isopropyl alcohol is made. Was my original idea somehow unworthy of a novice chemistry student?

Is there some kind of site where I can pay someone to come up with homework questions I can give to my students?

>>11623950
>he writes x as a cross like an illiterate signing his name on a scam contract

>>11619981
>R is defined on the set of natural numbers.

>75% of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 10 employees.

What is the most likely number of computer science graduates among the 10 project team members? Your answer should be an integer. If there are two possible answers, please select the smaller of the two integers.

how THE FUCK is the answer not floor(0.75*10) = 7

>>11624964
Assume that the company has [math]100[/math] employees, [math]75[/math] of them being CS grads, [math]25[/math] not.
Then, the number of possible teams made up of [math]n[/math] CS graduates is choose [math]n[/math] out of [math]75[/math] times choose [math]10-n[/math] out of [math]25[/math].
Check what [math]n[/math] generates the most possibilities.
They might actually give the total number of employees somewhere btw.

>>11625006
Oh right, if they don't, you might be supposed to use a Bernoulli.
That is, they choose the first team member, he has a [math]75%[/math] chance of being a CS grad and a [math]25%[/math] chance of not being and so on.

>>11625006
>>11625011
There was another question on there: I meet 88 employees at random on a daily basis. What is the mean number of computer science graduates among the 88 that I meet?

The answer was 88*0.75 = 66. I don't see why the same math wouldn't apply to >>11624964, I'm just at a loss. Say there are 100 members in each team, with 75% CS majors. It is clear the most likely number in a team of 100 is 75, and I don't see why the answer differs when reduced by a factor of 10.

I think this online assignment is fucked up, in the previous question I was asked to find the 10th term of [math](1 - \frac{1}{n})^13[/math], so, unsure if the question was referrring to 10th + 0th or just the 10th, I tried 715/n^4 and -286/n^3, both of which were wrong. That didn't make any sense either.

>>11624964
>how THE FUCK is the answer not floor(0.75*10) = 7
There is no reason to assume that you would round down. Your reasoning is okay, but it only tells you that the most probable answer is either 7 or 8. You have to check to find out which (use a binomial distribution).
In fact P(8) ~ .28 while P(7) ~ .25

>>11625051
wow, what? check out the brains on the this one. are you serious? I would think P(8) = P(7)

>>11625049
>I don't see why the same math wouldn't apply to >>11624964
Because one of them is asking for a mode (most likely number of CS grads) and the other one is asking for the mean number of CS grads.
Different things.
> It is clear the most likely number in a team of 100 is 75
Low-key wouldn't surprise me if it wasn't.

OK, last one: I meet 20 employees at random. What is the probability that the third employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places.

For this I'm thinking 0.25 * 0.25 * 0.75, but that doesnn't seem to take into account that after meeting the first one, I can't meet him again, so the odds of meeting another non CS major are slightly lower the next time, say 0.2499.. (jk), but they don't give us a total number of employees that I can substract the first dork from, so initially I tried just assuming a perfect distribution, that 5/20 people were non CS, so I did 5/20 * 4/19 * 15/18, but unsuprisingly that was wrong. I have one shot left, so does 0.25 * 0.25 * 0.75 sound right? Kind of a shitty problem desu

>>11625059
I'd be surprised if they haven't shown you the binomial distribution in whatever class this is if they're asking you to solve this. Since the probability of of getting a CS major is .75, the probability of getting k CS majors in 10 rolls is [math]{10 \choose k}(.75)^k(.25)^{10-k}[/math].
>>11625061
No, it will be 75 there. IIRC (don't quote me on this) the max of the binomial occurs at floor( np ) (might be floor( (n+1)p), idk ). You can get that by looking at ratios of successive probabilities.

>>11625088
I would not have interpreted this question as "there are 20 employees, I line them up randomly and meet them". I would have taken it the way you did at first glance, where you simply pick the employees out of a big pool and each has a 75% chance of being CS.

>>11625088
If the binomial from before is valid, you're approximating the number of employees in the company as infinite, so the chance of meeting someone two times zeroes.
>>11625112
>does work
Ooo, neat.

>>11625088
>binomial
Interesting, I just assumed they would be equal (as you saw from my first post when I rounded down 7.5), but we have covered the binomial distribution and I should've double checked my feelings before tardposting.

Thanks though, the answer was simply 0.25*0.25*0.75 on the latter one.

Is this a complete question?:
>For EACH of the 16 relations over the set S = {a, b}, list whether the relation is reflexive, symmetric, and/or transitive.

No other context, there is no list of relations or way to derive them, that is the entirity of the info related to that question.

>>11620442
There's 400*g downwards, 7m*cos(35°) to the right of the centre, and 2000*g downwards, through the centre.

The downward forces from gravity sum to 2400*g, so the sum of the upward normal forces must equal that (no linear acceleration). The difference between the normal forces is determined from the fact that the net torque about any point is zero (no angular acceleration). Taking the net torque clockwise about any point on the centre-line (there are no horizontal forces involved), we have

F1*1.4-F2*1.4+7*cos(35°)*400*g = 0
=> F2-F1 = (7/1.4)*cos(35°)*400*g = 5*cos(35°)*400*g = 1638g

F2+F1=2400g, F2-F1=1638g
(F2+F1)+(F2-F1)=2400g+1638g => 2*F2=4038g => F2=2019g = 19808 N
(F2+F1)-(F2-F1)=2400g-1638g => 2*F1=762g => F1=381g = 3736 N

If it was tipping, F1 would be negative, i.e. you'd have to glue the left wheel to the road to obtain a negative normal force.

>>11625112
also I brainfarted here, we already proved by example in this thread that the max doesn't happen at floor(np), so I guess it must be floor( (n+1)p )

>>11625170
Do you recall the formal way a relation on a set is actually defined? A relation on S is a subset of S x S. S has cardinality 2, so S x S has cardinality 2x2 = 4, so there are 2^4 = 16 subsets of S x S. Although whoever wants you to actually sit down and check 16 examples of the same thing is a gigantic penis.

>>11625142
Yeah you probably technically actually want to use a hypergeometric distribution if you're trying to be precise because unless you're making clones of people you're sampling without replacement. You get the same answer here either way though.

>>11625198
>gigantic penis
lol, every time I post this guys questions he gets flamed.and yes thanks I remember now, ty!

how do I calculate cpi for a superscalar cpu (multiple alu, load/store etc.)?

retard check: [math]C-[(A-B)\cup(B-A)][/math] simplifies to [math](C-A+B)\cup(C-B+A)[/math], right?

Is it too late to take the SAT once you're out of high school? I have only taken the ACT a few times. I was homeschooled during the last three years of school so my diploma comes from an umbrella organization, not a real school.
I want to start taking education more seriously and eventually go to college, but is my academic record permanently fucked?

>>11625671
it doesn't; draw a venn diagram. Set union and difference aren't inverse operations nor do they commute

>>11625671
>A+B
what?

>>11625752
>>11625811
Yeah I was being retarded, thanks. I figured it out, but how is this proof of the symmetric difference being associative? It looks good to me, but I was also just posting nonsense so I just want to double check.

[math](A \Delta B) \Delta C = ((A \Delta B) - C) \cup (C-(A \Delta B)) \\
= ((A-B)\cup(B-A) - C) \cup (C - (A-B)\cup(B-A)) \\
= (A-B-C)\cup(B-A-C)\cup(C-A-B)\cup(C-B-A)\\
[/math]
Note: [math]A-B-C = A-C-B[/math]
[math]
= (A - (B-C)\cup(C - B)) \cup ((B-C)\cup(C - B) - A)\\
= (A - (B\Delta C)) \cup ((B\Delta C) - A
= A\Delta(B\Delta C)
[/math]

>>11625723
why not just go to community college? SAT only matters if you're trying to get into some ivy league place as a freshman, sounds like you're not trying to do that, so may as well just go to community college then transfer.

If Venus and Mars were both placed into the same orbit as Earth, all equal distance apart, would they have any affect on each other? Constrain this to the short term, which in this case is 1,000,000 years.

>>11625671
It's [math]A - (B \cup C) = (A -B) \cap (A-C)[/math], I think.
>>11625904
Legit can't read that.
I have two suggestions.
The first one that [math]x \in A \Delta B \Delta C[/math] if and only if [math]x[/math] is in one or three of [math]A, ~ B, ~ C[/math].
The second one is that your space is isomorphic to [math]Hom_{Set}(X, \mathbb{Z}_2)[/math] with pointwise addition, where [math]X[/math] is your base set thingy.

Also, what is this dea vu?

Ok, I need find the odds that a 3 randomly selected sets from a power set will have a symetric difference [math]A \Delta B \Delta C = \null[/math] (choosing the same element of the power set is ok).

I believe the only condition in which the symmetric difference above can be null is when [math] A \cup B =C, A \cup C = B, B\cup C=A [/math] or [math]A\cup B \cup C = A = B = C[/math], so that resultant symmetric difference is C-C for null. Being that is a power set it's quite likely that this will occur, but I'm not sure how to compute just /how/ likely it is. Alternitvely I could consider how likely it is that it won't happen, but still I'm not sure how to mathify this thinking.. I'll be thinking on it for awhile still but any hints would be great.
>>11626010
I know it's ugly, sorry. My eyes were bleeding when I wrote it. And yes you're right about the equality, I ended up just translating everything into proper set theory notation and applying deMorgan's to arrive at the ugly post above. I can reformat it with some big ass braces if you'd like. I think it's correct as it, after I figured out that equality it was all smooth sailing, but given that I fucked that up I'm a little paranoid now.

>>11626172
> [math]A = B = C[/math] implies that [math]A \Delta B \Delta C = \emptyset[/math]
It doesn't. Consider that [math](A \Delta A)\Delta A = \emptyset \Delta A = A[/math].
Same thing applies for the first condition you gave.
The obvious condition is [math]A \Delta B = C[/math], since [math]D \Delta C = \emptyset[/math] if and only if [math]D = C[/math].
>I can reformat it with some big ass braces if you'd like.
I'm willing to check through it if you do it.

>>11626172
>Being that is a power set it's quite likely that this will occur, but I'm not sure how to compute just /how/ likely it is.
It seems to me like this would be extremely _un_likely, no?
For any fixed A,B, there is exactly one C (C = A △ B) which kills the triple difference. So there's only a 1/2^n probability it's null.

>>11626204
Good point! Thanks. I realize I did mean symmetric difference, that's what I've been playing with not just unions.. Sorry :(

>>11626230
Yes it is unlikely, I see it is more unlikely than I originally thought too because I fudged up and was doing unions of A and B that equal C rather than symmetric differences, and in a power set you're likely (relative to random potentially disjoint sets) to find some union of two sets that equals another set.

But I don't think the probability is that simple. When I first looke at it that was my guess., you need that one set out of 1/2^n sets, but maybe it is right after all. I think it is right actually, just gotta think on this a little more now.

>>11626010
i like your picture

How long can a human being go without a shower? And do showers provide scientifically proven benefits?

How can I gain confidence in my maths, I changed my career paths from med to eng, so I had to re-learn all high school math to get to the college I want
The thing here is that because medicine isn't an "exact" science like math I always had think of various ways of solving something, but in Math there is only one way.
most of the times I'm right, but I feel like there is some simplification left that I don't see in my answer and I get stressed about it.

Do I need to include the \ in "\sqrt{a}"?

>>11626401
You practice.

[math]\sqrt{a}[/math]

[math] i^2 = -1 <=> i = \sqrt{-1}
\sqrt{a} * \sqrt{b} = \sqrt{ab}
\sqrt{-1} * \sqrt{-1} = \sqrt{1} = 1
[/math]
Does i not make any sense or am I retarded?

retard that teachs me stats is a programmer. This is the way she defined "random variables". She NEVER defined B btw... Literal retard tier. Do you have any easy abstratc or guide from your unis??
Can somebody explain wtf is "b"

>>11626401
>medicine isn't an "exact" science like math I always had think of various ways of solving something, but in Math there is only one way.
cringe and retarded normie thought. quite the opposite. your retarded non exact are all about memorizing aka one way only

[math] i^2 = -1 <=> i = \sqrt{-1} [/math]
[math] \sqrt{a} * \sqrt{b} = \sqrt{ab}[/math]
[math] \sqrt{-1} * \sqrt{-1} = \sqrt{1} = 1[/math]

Does i not make any sense or am I retarded?

>>11626500

pemdas friend

sqrt is exponent of 1/2

since base is the same, you add exponents
before multiplying their bases

1/2 + 1/2 = 1

>>11626518
So, is
[math] \sqrt{a} * \sqrt{b} = \sqrt{ab} [/math]
only true for real a & b?

>>11626500
[math]\sqrt{1} = -1[/math], anon.
Because square root is multivalued and sheit.
>>11626526
It's sort of not quite false for complex a and b.

>>11626538
Oh fuck, you're right. I've always struggled remembering that square roots are positive and negative. Thanks.

Trying to wrap up a proof that the number of odd subsets of a set equals the number of even (or that exactly half the subsets are even/odd). The number of subsets is of course given by 2^n, there are n+1 unique cardinalities (null to n inclusive), and the number of sets of each cardinality is given by n choose k (so 2^n = sum (n choose k)).

I feel I'm really close to proving it, i have all the pieces, but I could use a hint. To close the gap I need to prove that sum (n choose oddK) = sum (n choose even(k)), but I don't know how to prove that and I don't feel that sufficiently proves that there's the same number of odds and evens, even if it does so algebraically

>>11626526

is a = b? no.

you only add the exponents if the base are equal.

when the base are equal the exponents come first, ala pemdas.

>>11626561
so what i have currently is
[eqn]
\sum_{k=0}^{n} {n \choose k} = \sum_{k=0}^{\frac{n}{2}} {n \choose 2k} +\sum_{k=0}^{\frac{n}{2}} {n \choose 2k+1}
[/eqn]

but it feels hacky and bad

>>11626589
fuck nvm it doesn't play nice with odd n's, i don't want to split it into cases

>>11626494
In math you also have to memorize laws of exponents, fractions, logarithms, etc., but there is only one answer
In medicine you have to memorize some things too but there isn't JUST one answer, there are always more that are less rigth.
You can't say Throat pain will always mean bacterial infection, or that every Alergie manifests one way and one way only, you have to connect dots to see what happens and what's the treatment.
But you can say that 6+6 will always be 12.

Maybe I have to memorize the rules of math first tho.

>>11626616
>but there is only one answer
lololol I forgot about quadratic equations and inequalities.
Sorry f.a.m, this isn't my field of study.

any tips for proving
[eqn]
\sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k} =\sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k+1}
[/eqn]

I looked at pascal's identity/rule but it didn't seem directly helpful, but im going to go back now and try to manipulate

Why is this a valid homotopy? Probably it has to do with the fact that the intermediate point has in fact nothing to do with the origin and I'm reading the concept of continuity wrong. But still, why is this tearing apart at the origin allowed, what am I getting wrong here?

How can I make the function f(1)=1, f(n)=1+2×f(n-1) into a non-recursive function?

>>11626806
Do you mean Tn = 2T(n-1)+ 1? https://www.youtube.com/watch?v=JvcqtZk2mng

>>11626815
f is a function defined recursively.
f(n) = 2f(n-1) + 1

what is going on here?

>>11626825
generally recursive functions are expressed with subscript notation
[eqn]F_1 = 1\\
F_n=2F_{n-1}+1[/eqn]

>>11626856
why do .1 and .2 fail to make sense but .25 and .3 do?

>>11626561
We induct.
First of all, it's clearly true for [math]Z_1[/math], the set with [math]1[/math] element.
We assume it's true for the set with [math]n[/math] elements.
Define [math]f: P(Z_n) \times \{ 0, 1 \} \rightarrow P(Z_{n+1})[/math] by [math]f(A, 0)=A[/math] and [math]f(A, 1)= A \cup \{n+1 \}[/math]. Prove it's a bijection. Notice what does it does to odd sets and even sets.
Das it mane.
>>11626689
>why is this tearing at the origin allowed
Because a loop is a map [math]S^1 \rightarrow X[/math] and not simply it's image, and the maps are being continuously deformed while the base point stays at the base point.
>>11626806
It's probably gonna be [math]f(n)= \sum_{i=1}^n 2^{i-1}[/math] or something similar enough.

>>11626204
>I'm willing to check
tia any anons that are willing to check this symmetric difference proof

>>11626882
>>11626856
anyone? I know how modulo works (or apparently not) but this shit doesnt make any sense.

One cop out is that its integer only by definition but it wouldnt return a result right?

is the set (a, a) vacuously transitive and symmetric?

>>11627036
>this shit doesnt make any sense
Correct. One is congruent to zero modulo 0.1, 0.2 and 0.25, and congruent to 0.1 modulo 0.3.

>>11627066
so why is google wrong?

Can someone suggest a stat book that goes over the law of iterated logarithm from a theoretical viewpoint in painful detail?

Could someone explain how does an integral actually give out a function? Like, if you wanted to see what the derivative of x^2 was, you could put it through [math]f'(x)=lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/math] and get 2x. So is there a way that integrals do the same thing, but in reverse?

did oxford anon deliver on the bootleg

>>11627097
Isn't one of the endpoints of the area under the integral you're calculating is variable typically? E.g. \int_0^x y^2dy ?

>>11626856
>>11626882
0.1=0 mod 0.1 and 0.2=0 mod 0.2. There's nothing wrong

>>11627149
t. cant read

Is this correct? (I'm really just learning LaTeX, but I also want to know if what I just wrote is correct). ty.

>>11626526
>So, is
>√a*√b=√ab
>only true for real a & b?
It's not necessarily true for complex a & b, where √a*√b can be either √ab or -√ab.

For real, positive x, the two solutions to y^2=x both lie on the real line, one positive and one negative. √x denotes the principal root; for real solutions, that's the positive one.

In the general (complex) case, the two solutions are diametrically opposed. The principal root is the one whose argument is in the range (-π/2,π/2], i.e. the one closest to the real line (for the case of a negative real, this is the one with argument π/2, i.e. positive imaginary part).

Now, arg(x*y)=arg(x)+arg(y). Suppose that arg(√a) and arg(√b) are both in (0,π/2) but arg(√a*√b)=arg(√a)+arg(√b) is in (π/2,π), then arg(-(√a*√b)) is in (-π/2,0) and so -(√a*√b) is the principal square root of a*b.

>>11627097
> Could someone explain how does an integral actually give out a function?
An indefinite integral (antiderivative) is a function (or rather a family of functions which differ only in the constant of integration). A definite integral is a value. If F() is the antiderivative of f(), then
[eqn]
\int_a^b f(x)\,dx\,=\,F(b)-F(a)
[/eqn]
The constant of integration cancels.

Or conversely,
[eqn]
F(x)=\int_a^x f(t)\,dt \\
= \int_a^b f(t)\,dt\,+\,\int_b^x f(t)\,dt \\
= \int_b^x f(t)\,dt\,+\,C
[/eqn]
i.e. the antiderivative is the indefinite integral between some unspecified lower bound and x. The lower bound determines the constant of integration.

>>11613979
if my question is so stupid than why nobody can answer me?
duh dumb bitch

>>11627451
the fuck is this gibberish, mate. do you expect anyone but your teacher to read this shit? Nobody is ever going to write a Gauss pivot on latex a part for lecture examples' sake.
> looks correct still

>>11617845
The moment when young maths students realize not everything can be explicit, but that the theory still holds.

>>11613906
More /lit/ than /sci/, but which option is correct for a dissertation?

>The metal post has a uniform co and cross-polarised RCS signature...

>The metal post has a uniform co- and cross-polarised RCS signature...

>>11627097
[math]F(x) = \int_{a}^{x}f(t)\,dt = \sup\{ \sum_{i=1}^n f(t_i)(t_{i}-t_{i-1}) \}[/math] where the supremum is taken over all subdivisions [math](t_0,\dots,t_n)[/math] of [math][a,x][/math].

>>11627892
mistake, should be [math]\sup \{ \sum_{i=1}^n \inf_{t \in [t_i- t_{i-1}]} f(t)(t_i - t_{i-1}) \}[/math]

Could someone help me with this?

>>11628071
What have you tried?:

>>11619829
Its a food/beverage production facility dumbass

>>11628076
Some retard math and I got infinity but it's probably wrong

>>11628071
You could start by plugging in some large values of x and see what you get.

>>11627866
The second one.

>>11628076
>>11628112
Am I retarded?

>>11628132
No, that looks right to me.

>>11627847
Rude. I think it looks pretty

>>11626991
I might be retarded, but I still have absolutely no idea what it is you did after the note.

Is there any scientific basis for chakras? The idea the body has energy that can be channelled? Ive been meditating a lot recently and feel more aware of the world if I focus I can also feel energy travelling around my body - is it all just placebo?

how do I represent a position with two complex numbers? like both the x and y coordinates are complex numbers. can this even be drawn?

>>11628327
>like both the x and y coordinates are complex numbers. can this even be drawn?
not really. it would require 4 spatial dimensions to actually represent it as a single point in space, which obviously isn't really feasible
I guess if you're really desperate you could draw a pair of coordinate planes, one for the x and another for the y.

>>11628308
No

>>11628115
I told my brother the same, but he was told the 1st one by some other people. Is there an explanation for why the 2nd one is correct?