SQT thread

How does knowing whether a series/sequence/function diverges or converges help us at anything in math? Like what is it's purpose?

>>8341266
>2sin θ + 3cos θ= 1
When you square that you get crossed terms: 6sintcost.

>>8341303
oh shit im retarded thanks

I need to find the speed of a human moving east on the surface of the earth as it rotates on its axis (ignoring orbital velocity) and all i'm given is the radius of the earth. how do I do this?

>>8341275
It helps you discern the nature of the series/sequence/function at large values, it can be used to help solve complicated integrals, and more. Keep going to class, you'll see!

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N-no bully

>>8341711
law of cosines

>>8341619
i figured it out im good

>>8341717
I'm retarded, could you walk me through it?

If I jump inside a moving bullet train, will I get thrown back, get slammed in to a little asian train attendee, and potentially die?

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>>8341756
Breathe!
Draw a line which connects the tips of your two vectors. Follow the chart. Do you see how you have exactly one angle and exactly two sides to work with, just like the formula implies?

>>8341844
Oh, now I see what you mean! I feel so stupid now. Thanks for the help!

>>8341711
what are you trying to find?

What is the chance of humanity acquiring some form of immortality in 60 years?

>>8341903
I was trying to find the resultant vector ,which the kind anon >>8341844 showed me. Should have mentioned that...

How would you prove the following about combinations?

[math]\displaystyle \sum_{r=0}^{n} \dbinom{n}{r} = 2^{n}[/math]

??

can i just use induction, prove its true for 0 and 1, then more to induc hyp?

>>8341997
Is trivial

>>8342003
of course

>>8341997
>induction

Yup

>>8341997
if you're allowed, its just a case of the binomial expansion.

>>8341915
50%.

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>making a new thread when there's already one in the catalog >>8319889
>not even linking the old thread

check the catalog, brainlets

Self study cuck here

[math] \text{Show that } \pi i + \int_{-1}^{z} d\zeta/\zeta \text{ defines an analytic branch of} \log z \text{in the plane slit along the non-negative axis with} \\ 0<\mathrm{Im} \log z = \mathrm{Arg} z < 2\pi. \\ [/math]
I understand how they get [math]\pi i[/math] since they define [math]\log(-1)=\pi i[/math] but I don't see how you can show the range of that argument, although it is intuitively obvious, you are literally just ignoring the positive real axis which on the unit circle is 0 and [math] 2\pi [/math]. Do I just define
[math] \mathrm{f} (z) = \log z = u(z)+iv(z) = \log|z|+i\text{Arg }z [/math]
and just say it obviously goes from 0 to [math] 2\pi [/math] in polar coordindates? Once you take the exponential it can become the all familiar [math] Re^{i\theta}. [/math]

>>8341997
n choose r is just the number of subsets of {1,..,n} which have size r. So your sum is equal to the total number of subsets of {1,...,n}, i.e. 2^n

>>8341997
take (1+x)^n, apply binomial theorem, plug in 1 for x.

>>8342430
Depends on what they mean by "show". I would say that the integral expression gives a well-defined function because of path independence. (The integrand is holomorphic on the slit plane, and the slit plane is simply connected. ) Take the derivative of the expression and get 1/z. That's the same derivative you get from log(z). So log(z) and integral expression differ by a constant. They agree at a point too though, so they are equal.

Typically that's how the argument goes.

>>8341997
>what is power set?

>>8342475
I think I understand the approach now. You are using a theorem in the chapter that gives a condition under which your function is a branch of the logarithm and you are arguing for equality so that theorem is satisfied. That makes way more sense. Although I don't understand their solution . Probably read more Needham so I know wtf is going in visually .

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Speaking in number of people, is the modern Kuk/KEK/Keku cult already larger than the one in ancient Egypt?

>>8342926
>Kuk

Oh believe, the kuk cult is fucking huge nowadays.

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Yes, that too. but seriously. Wikipedians call it active "worship"
https://en.wikipedia.org/wiki/Talk:Kuk_(mythology)#Request_Lock

You have like 10 threads like this
>>>/pol/88704311
>>>/pol/88701649
and then the more extremist "Bureau of memetic warfare" on 8ch who actually plot what they do. And even the Democrats are commenting on it, pic related

But I mostly want to know the rough size of population that worshiped such gods in Egypt in the past. Was is a fling and all those many gods had their time, or did it have substance.

>>8341821
No you're moving at the same speed as the train

Where and how the do physicists get the individual electrons that are used when performing quantum experiments?

>>8343302
You don't necessarily do single electrons for quantum experiments, or electrons at all. E.g. any condensed matter low temperature (millikelvins over absolute zero) system does the trick.
And look up e.g. electrodes+ion traps.
https://en.wikipedia.org/wiki/Ion_trap

Question about Simplex method/algorithm. Is it done the same way no matter if the objective is maximize or minimize? I have only seen examples of maximizing, what changes if you do it for minimizing?

>>8341844
That will give you the difference not the resultant vector. You need some coordinate axis, but that is arbitrary.

Another question about Simplex. In all the examples I've seen the constraints are variables <= number, thus the slack is + something. But what if it was >= instead? Would it mean that the slack has to be negative and then I should input -1 in the identity matrix? And if it was just = instead of <=, then it means that I don't need a slack?

How would I begin this?

Prove that {a_n} converges, with a_n = 3*5*7*...*(2n-1) / 2*4*6*...*(2n), converges to A, where 0 <= A <= 1/2.

Since this section covers monotone sequences, I imagine I first need to find out whether the sequence is increasing or decreasing (it isn't obvious to me as it is) (is it possible using soley the definition?). I thought multiplying by 2*4*6*...*(2n)/2*4*6*...*(2n) would help, which gives 2n!/(2*4*6*...*(2n))^2, but I'm still not sure. Any help getting started would be fantastic.

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I can calculate the capacitance series and parallel capacitors but I'm too dumb for whatever else you do.

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Also, is it right that even though this isn't showing a circuit I get 25W of total power dissipation if 25W of power is supplied?

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>>8343749
It's okay. Physics isn't important.

Is it possible for humanity to have mastered everything in this universe in under one million years?

>>8343812
There's a bunch of things that could remain as seemingly impossible as they are now.
For example, creating atoms with many hundreds of protons.

>>8343431
How is that implemented with projects like the double slit experiment?

>>8343749
No one?
This is very basic I assume, although I still can't do it because I can't find out how to calculate the voltage across multiple capacitors when you do not know the charge.

>>8343749
capacitance in parallel combines like resistors in series, and capacitance in series combines like resistors in parallel.

literally all you need to solve this problem

>>8343761
>maximum in any ONE resistor is 25W
pick the series resistor
P = RI^2
25 = 100*I^2
I = 500mA
etc.

>>8343968
I said I could calculate capacitance.

And I have no idea what you're saying about the resistors, though it's the same calculation that I did to get to where I am.

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>go to community college A, stop attending this place after one semester because im a dumbass
>go to community college B without disclosing that I went to college A so no academic records were forwarded/transferred
>im getting good marks
>get into university based on my grades from college B, forward academic records from community college B. university has no academic records of courses taken at college A
>several semesters of good marks and internships pass by

I just realized how bad it is to hide academic records.

This is my second last semester of my undergraduate degree. How fucked am I if they find out that I spent a semester at college A? Not sure if I should bring it up with admissions before they find out (if they do), or if I should just continue without bringing it up with admissions and hope that consequences aren't bad if they do find out.

can machines be intelligent?

if yes, does an intelligent have morals?

is an intelligent machine responsible for its actions or is it the responsibility of its programmers?

>>8344345
>can machines be intelligent?
they COULD theoretically

>if yes, does an intelligent have morals?
sure

>is an intelligent machine responsible for its actions or is it the responsibility of its programmers?
a mix of both, not much different from
>who's responsible? the kid of the parents?

>>8344351
>who's responsible? the kid of the parents?
so you're saying that if the AI is 'old enough' (i.e. has learned about the consequences of its actions) it should be held accountable for mistakes? this makes sense, but now we would need to find out how old is old enough. what if the AI is retarded?

>>8344061
Nobody is going to witch hunt you like that. You are being paranoid.

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>>8341266
Help me understand this equation please.

Does the min/max at the beginning mean that it's trying to minimise/maximise the value returned by the function subscripted? so [math]min_{G}[/math] means that it tries to minimise [math]G(z)[/math]?

Also how did the second term get expanded into that form?

>>8343564
> Another question about Simplex. In all the examples I've seen the constraints are variables <= number, thus the slack is + something. But what if it was >= instead? Would it mean that the slack has to be negative and then I should input -1 in the identity matrix?
No, it means that you'd negate both sides and change >= to <=. Simplex assumes that all variables are non-negative.

> And if it was just = instead of <=, then it means that I don't need a slack?
No, you'd turn it into an inequality. with the sign chosen so that the dot product with the objective is negative (so that the constraint is guaranteed to be limiting for any optimal solution).

Simplex relies upon the existence of a basis, i.e. for a system with N equations, some subset of N columns forms an NxN identity matrix. Pivoting just changes which variables (columns) are part of the basis.

>>8343549
> what changes if you do it for minimizing?
You negate the coefficients of the objective function, then maximise it.

>>8341266
You're probably not here anymore, but I'll still post this response for the benefit of others who may be asking themselves the same thing.

As >>8341303 said, you got the algebra wrong.
But even if you get the algebra right, you should not square both sides of equations. The only exception at pre-calculus level are irrational equations.

Why is that? Imagine you have a equation in x "f(x) = g(x)". Compare it to the equation "[f(x)]^2 = [g(x)]^2". If you manipulate the second equation:

[f(x)]^2 = [g(x)]^2
[f(x)]^2 - [g(x)]^2 = 0
( f(x) - g(x) )( f(x) + g(x) ) = 0
f(x) = g(x) or f(x) = -g(x)

As you can see, you incur the risk of inserting external solutions to the equation (although you can be sure that all the solutions of the original equation are still present in the second). Therefore you'd have to check each solution of the second equation to see if they are also solutions of the original one.

>>8343749
Clearly there's 9V across the 5uF, and so 9*5=45uC charge.

For the 4uF and 6uF in series:
1. The voltages must add up to 9V
2. The charges must be equal (whatever flows out of one must flow into the other).
3. Q=C*V.

V1+V2=9
Q1=Q2
Q1=4u*V1
Q2=6u*V2

4u*V1=6u*V2
V1+V2=9
=> V1=5.4, V2=3.6

=>Q1=Q2=21.6uC

Why is turning point for y=2x/sqrt(4x-3) be 6/7 (should literally take you less than a minute using quotient rule, if you're not a brainlet :^) )
My book says 3/2, from a 4x-6 quotient, but I keep getting a 7x-6 quotient

Pls halp

>>8345244
Ignore the pajeet-tier english

>>8341266
do arts majors get impostor syndrome?

Does this converge?

f(x)=| infinity SIGMA n=1 | 3*sin(2^n*pi*x)/ 2^(n+1)

>>8345244
y=2*x/sqrt(4*x-3)
=2*x*(4*x-3)^(-1/2)
dy/dx = 2*(4*x-3)^(-1/2) + 2*x*(-1/2)*(4*x-3)^(-3/2)*4
= 2*(4*x-3)^(-1/2) - 4*x*(4*x-3)^(-3/2)
= 2*(4*x-3)/(4*x-3)^(3/2) - 4*x/(4*x-3)^(3/2)
= (2*(4*x-3) - 4*x) / (4*x-3)^(3/2)
= (8*x-6 - 4*x) / (4*x-3)^(3/2)
= (4*x-6) / (4*x-3)^(3/2)

dy/dx=0 when the numerator is zero, i.e. 4*x-6=0 => x=3/2.

No idea where you're getting a 7 from.

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>>8345575
>>8345267
>>8345262
Can one of you please help me with this question?

Really dumb question, but I am unsure how to enter in the direction here?

The angle has to be below the x-axis, so I will put 36 degrees correct? Or -36?

So I have Thyroid Cancer and I'm getting my Thyroid removed Friday. If we are capable of regrowing organs and what no 10 years from now, is it possible for me to regrow my Thyroids, would they be functioning, and would they re-obtain cancer like last time?

I'm being for real with this question.

>>8345267
> Does this converge?
If x is real, then clearly. The numerator is bounded, the denominator is exponential. The sum of the first k terms must be within 1/2^(k+1) of the limit.

If x is complex, it may not be, as sin(i*x)=i*sinh(x), and sinh(x)->(e^|x|)/2 for large x.

>>8345615
> If we are capable of regrowing organs and what no 10 years from now
If your head turned into an airplane, would the landing gear be down?

There's no way to answer a question based on a premise which is theoretically impossible and for which there's no empirical evidence available.

If the acceleration of a particle in a magnetic field is proportional to speed, how is it that the turning circle of a faster particle is larger rather than identical to that of a slower particle?

>>8345646
Answering questions you don't know the answer to is pointless.
Honestly, /sci/ and /g/ would be a lot better if it was against the rules.

>>8345679
For circular motion, the acceleration is proportional to the square of the speed and inversely proportional to the radius. But the acceleration on a charged particle in a magnetic field is only proportional to the speed. So the radius must also be proportional to the speed.

> Answering questions you don't know the answer to
Um, no. It's a case of pointing out that some questions don't have an answer. That tends to include most questions which start with " if <impossible thing> was possible ...".

If anything warrants a ban, it's asking that sort of question in the first place. It tends to start shitstorms between people who assume the poster is trolling and people who think they might just be retarded.

>>8346169
That's a terrible explanation.
None of what you said is founded by actual physics, you're telling the person believe your maths on faith.
Which I won't, because:
>acceleration is inversely proportional to the radius
Radius of the turning circle is not a factor of instantaneous acceleration, because the particle is travelling straight at any given instant.
Obviously you can use that radius to work out instantaneous acceleration, but that's because acceleration determines the turning radius.

Also, unless someone asks something like "Does P = NP?" which is proven to be unprovable with our current knowledge, you can be sure that even for the toughest question there's someone out there who could provide a very good guess with reasoning.

If you think it's acceptable to call questions dumb because you lack the intellect to entertain them, and give garbage answers that show you clearly don't understand the answers, you're the science equivalent of a Pajeet in IT.

>>8346206
> Radius of the turning circle is not a factor of instantaneous acceleration
> acceleration determines the turning radius.
Math doesn't have causality. For circular motion, the two are related. It doesn't matter whether you write a=s^2/r or r=s^2/a or s^2=a*r or s=sqrt(a*r) or s^2/(a*r)=1 or any other variation. They're all stating the same fact.

>>8346259
It doesn't, but this is physics.

>>8346206
> unless someone asks something like "Does P = NP?" which is proven to be unprovable with our current knowledge,
It would be more accurate (and rather less verbose) to simply state that the answer is unknown.

Certainly, it hasn't been proven to be unprovable. It's not even unprovable "with current knowledge". There's no evidence that a proof would first require knowing something we don't already know (although clearly such a proof would itself /be/ something we don't already know).

But at least that question actually has an answer, even if it's obvious (to anyone who knows what the question means) that no-one yet knows what that answer is (and maybe no-one ever will).

>>8346271
The moment you start talking about speed, acceleration, proportionality and circles, it's a math question.

Unless you replace "how" with "why", at which point it's a philosophy question.

>>8341275
dem taylor polynomials