SQT - Stupid Questions

How does one go about doing this?
[math]\mathbf{A}[/math] is a 3x3 matrix and [math]\mathbf{b}[/math] is a 3x1 column vector. Show that all solutions of the equation
[eqn]\mathbf{Ar=d}[/eqn]
can be expressed in the form [math]\mathbf{r=p+k}[/math], where [math]\mathbf{p}[/math] is any particular solution of [math]\mathbf{Ar=d}[/math] and [math]\mathbf{k}[/math] is any solution of the related equation
[eqn]\mathbf{Ar=0}[/eqn].

hint: k is r-p

how can the sum of all the natural numbers be negative?
is there any case where positive plus positive can give a negative result?

Just think a bit about what you asked.

>being this stupid

Kys brainlet

>being stupid in /sqt/
going to kill myself anyway

tell me with reason if my working is correct?

The
Question

E=hf is only true for electromagnetic waves. The rest is wrong, since photons do not have mass and you can not write down their momentum like that. It's p=E/c.

What's the Laplace transform of this function?

(t^2)(U(t-3))

U(t-3) would be a function expressed in terms of a unit step function, and I'm always stuck with these because I don't understand how to convert between this notation and the other one. If it wasn't expressed in the U thing notation I probably could solve this easily.

The limit as x -> 0 of x / (x^2 + 0^2) is not 1 / x, it's infinity. Then say 0 =/= infinity.

Then, for the conclusion, just say that since when we let y=0, the limit as x -> 0 =/= f(0), f is discontinuous at (0,0).

Convolution.

Each output value is a weighted average of a region of the input. If the window function (in this case, Gaussian) is some kind of "hump", this acts as a low-pass filter (i.e. higher frequencies will be attenuated more than lower frequencies).

This concept is the basis of digital signal processing. It's simplest form is referred to as a "rolling average".

> "s=numpy.r_[x[window_len-1:0:-1],x,x[-1:-window_len:-1]]
r_[] is just a short-hand for the hstack() function, i.e. it concatenates 1D arrays.

x[window_len-1:0:-1] is the first window_len elements of x but in reverse. x[-1:-window_len:-1] is the last window_len elements of x but in reverse.

The overall expression takes x and adds reflected copies of the start and end regions. This allows convolution to find the average at the ends without trying to access elements outside the array.

Copying ensures that the values of the added elements have "reasonable" magnitudes (i.e. comparable to what you'd expect to find if x was a portion of a larger array). Using a reflected copy ensures that there isn't a discontinuity at the ends (which doesn't really matter in this case, but does for other types of convolution).

Note that scipy.ndimage.convolve can do this automatically via mode='reflect'.

If P=F/A, why does a nozzle decrease Pressure? Wouldn't a smaller area equate to larger pressure?

When trying to find characteristic equation of a recurrence relation, like the following:

2^n - a(sub)n + 2a(sub)n-1 = 0

I follow that the a(sub)n's would convert as follows:

... -r + 2r^-1 = 0

However, I'm not sure what to do to 2^n when trying to find the characteristic equation.

t^2*U(t-3)=(q+3)^2*U(q) for q=t-3
I.e. it's (t+3)^2*U(t), time-shifted by 3.

Tables of common Laplace transforms often take the U(t) for granted, because the Laplace transform is an integral over [0,infinity], and U(t)=1 over that range.

Time-shifting by a scales the Laplace transform by e^(-a*s), i.e.
L(f(t-a)*U(t-a)) = e^(-a*s)*L(f(t)*U(t)).

L((t+3)^2*U(t))
= L((t+3)^2)
= L(t^2+6*t+9)
= 2/s^3 + 6/s^2 + 9/s
= (9*s^2 + 6*s + 2)/s^3

L(t^2*U(t-3))
= e^(-3*s)*L((t+3)^2.U(t))
= e^(-3*s)*(9*s^2 + 6*s + 2)/s^3

Alternatively, you could just evaluate the integral directly over [3,infinity], but that's more involved than using L(t^n) and time-shifting.

The characteristic equation is only meaningful for a linear recurrence relation.

FWIW, the solution to that is a[n]=(a[0]+n)*2^n.

It doesn't . A smaller nozzle with the same force behind it has a bigger force per metre exerted on it

I want to relearn every math from class six on until calculus.
Maybe add some mathematical "maturirty" preparation.
Sadly, I do not ALWAYS have Internet to just access khanacademy and I seem to be db as I can't use KA Lite as well.
Where do I start?
I am spending 32h a week just to close all my gaps and I am most of the times in places where I have to use my phone as a Hotspot.
And I am almost out of data.

I mean, what books do I need from libgen?
Any recommendations?
Please be honest.

>Babby Probability Problem

What is the probability that you win at least one prize given there are "n" tickets, 5 prizes are to be given, and you hold 3 tickets?

So I thought it was just one minus C(n-5, 3)/C(n,3), but the answer is supposedly one minus C(n-3, 5)/C(n,5) which is really bothering the crap out of me.

I thought the probability of no prizes is the number of distinct sets of cardinality 3 (three tickets) built from the set of tickets that contain no winning tickets (a set of cardinality n-5) all over the possible selections of "n" tickets and "k = 3 bought tickets", or just C(n-5, 3)/C(n, 3). How is this wrong?>

>forgive me I can't latex but please help

>rewording question

If you hold 3 tickets for which n tickets were sold and 5 prizes are to be given, what is the probability that you will win at least 1 prize?

Absolutely based, thank you

> What is the probability that you win at least one prize
It's one minus the probability that you don't win any prizes.

So there is no need for the working of x=0? Because y=0 is enough to prove discontinuous?

also, why is 1/x infinity?

Also why can you set either y=0 and x=0 if the question states that it (x,y) =/= 0

Are cohort crushes common?

How calculate sin(pi/12) and cos(pi/12) without a calculator ?

You just imagine sin(x) and make x = pi/12

sin(3x)=sin(pi/4)
Expand using angle-sum identity.
Solve cubic.
cos(x)=sqrt(1-sin(x)^2);

isn't just like pi/6 = 30 (remarkable value) so pi/6/2 = 30 / 2 = 15

it doens't help me in fact lol

Help please

top kek

Ok, this is my solution.
F^3=F*F^2=I
let's multiply both sides by squared inverse
F^-2*F^2*F=I*F^-2
F^2*F^-2 equal to identity (or I)
thus F=I*F^-1*F^-1
lets think about F^2=I(identity)
as we know from isometries inverses, if F*G=I then G-inverse of F
F^2=F*F=I
thus F=F^-1
lets recall our previous equality:
F=I*F^-1*F^-1
and as we know F=F^-1 thus F^-1*F^-1=F^2=I
thus F=I*I=I
and this finally proves that F=I
Did I prove it right?

How do I find a parametrization [math] X: \mathbb{R} ^2 \rightarrow \mathbb{R} ^3 [/math] of the regular surface [math] M = \{ (x,y,z) \in \mathbb{R} ^3 ; xsinz=ycosz \} [/math] ?

Oh Jeez, even easier.
F^3=I
this means that
F^2*F=I
and as we know F^2=I
thus I*F=I
therfore F=I
proofs for b,c are the same

Well,
F=F*I=F*F^2=F^3=I
I=I^2=F^4*F^4=F^8=F^7*F=I*F=F
I=I^2=F^8*F^8=F^16=F*F^15=F*(F^5)^3=F*I^3=F
I'm sure yours is fine too, but I'd rather not use inverses if I can help it.

thank you

Thanks

z = t
x = r cos(t)
y = r sin(t)

Aw, makes sense. Thank you

What's the name of those functions?

mathworld.wolfram.com/LipschitzFunction.html

Thank you sir

is a de broglie wavelength just an uncertainty-type thing?
Like it's not an actual physical wave-like motion right?

I'm aware of that, I actually made mention to that. Can anyone actually give me a solid answer to my concern regarding the combinations?

If you let x=0 and then take the limit as y->0, as you did, you see that it's equal to 0. This does not prove discontinuity, in fact it is perfectly consistent with what a continuous function would do. It's not necessary to include that calculation.

I meant to say that the limit as x->0 of 1/x doesn't exist.

In your work, you took the limit as x->0 of x / (x^2 + 0^2), and said it's equal to 1/x. If you take the limit of something with respect to x, you can't have x in the answer. You need to continue by taking the lim x->0 of 1/x, which doesn't exist because the denominator is shrinking, and it goes to positive or negative infinity depending on which side you approach from.

You hold 3 tickets out of n. Initially, there are n-3 tickets which you don't hold. The probability that you don't win the first prize is (n-3)/n.

After that prize has been awarded, you hold 3 tickets out of n-1; there are n-4 tickets which you don't hold. So the probability that you don't win the second prize is (n-4)/(n-1).

The probability that you don't win any of the 5 prizes is:
(n-3)/n * (n-4)/(n-1) * (n-5)/(n-2) * (n-6)/(n-3) * (n-7)/(n-4)
= ((n-3)!/(n-8)!) / (n!/(n-5)!)
= ((n-3)!*(n-5)!) / (n!*(n-8)!)

C(n-3, 5)/C(n,5)
= ((n-3)!/(5!*(n-8)!)) / (n!/(5!*(n-5)!))
= ((n-3)!*5!*(n-5)!) / (n!*5!*(n-8)!)
= ((n-3)!*(n-5)!) / (n!*(n-8)!)

i'm doing basic thermochem and can't figure out what i'm doing wrong

i have an 80.0-gram sample of a gas
it heated from 25 °C to 225 °C.
346 J of work was done by the system and its internal energy increased by 7075 J. What is the specific heat of the gas?

here's what i did:
7075J-346J (because work was done by the system)= c(what i'm looking for) (80.0g)(225C-25C)
what i go was 0.42056J/(gC) but it says i'm wrong

You say if I take limit wrtx which I presume you mean x-->0 lim and x remains in the limit instead of a constant after subbing y=0 in

But. If you were to set (x,y) = (1/n,1/n) where n--> infinity then n would still exist simplifying to n/2. I have "n" in my answer and I presume you would say I can't. Why?

First law of thermodynamics: [math]\Delta U \,=\, W \,+\, Q[/math] then [math]Q \,=\, \Delta U \,-\, W[/math].
Always take the [math]\Delta U \,=\, W \,+\, Q[/math] convention where [math]W[/math] is the work *received* by the system, cause the other one makes no sense. It should be 7075 J + 346 J.

What does delta and epsilon mean in terms of limits?

Linear Algebra.

----------------------------------------------------------------------------
Let A be an n × n matrix such that A2 = A. Show that (AB − ABA)2 = 0 for all
n × n matrices B.
----------------------------------------------------------------------------

I can't figure this out guys. First I tried some fuckery with the fact that you can substitute B for A (since B can be ANY nxn matrix) and it works out to 0, but it only works when B = A. Then I tried shifting ABA around, but then I remembered that matrix multiplication is not communicative.

Stuck at the moment.

There are no tricks involved in this problem user
(AB - ABA)^2 = (AB(1 - A))^2 = AB(1 - A)AB(1 - A)
Now notice the term (1 - A)A and draw your conclusion

sigh...why didn't I think to factor out the AB?

thanks user!

In isoparametric coordinate mapping (4 nodes), let's say I have an initial configuration and a final configuration, Bo and Bt. Instead of just mapping a single configuration to a parent with coordinates (1,1) (-1,1) (-1,-1) (1,-1), what would I do to find the displacement tensor between the two? Do I map both to the parent or do I map the final config to the initial config?

thank you so much I appreciate it!

I'm in a beginner proof course and I'm trying to do practice problems from my book. For some reason the autists who wrote this don't give answers for every question and only some of them

I'm stuck on this and there's no solution given. Trying to do it through induction

Anyone pls. I feel like this should be so simple but there are literally no examples online where it isn't just mapping a configuration to some form of the unit square.

just say obviously true by triangle inequality

Well yeah I've done the triangle inequality before but I can't leave it like that, I'm doing these to prepare for an exam

It's by induction, it's true for n = 2

suppose that it is true for n in N

then abs(a_1+...+a_n+1)

I actually managed to solve it another way, its one minus the number of ways that you can have five winning tickets out of a set of n-3 tickets, and the three tickets left out in the set are the ones that are bought.

Also could you recommend me a good text on probability? Thanks

I don't think you're taking limits correctly.

Here's a different function as an example:

The limit as x-> inf of ( x / x^2 )

= the limit as x -> inf of ( 1 / x )

'note, here I've just simplified the part inside the limit. Next, i will actually evaluate the limit.

= 0

'this is because the denominator gets arbitrarily large, shrinking the value completely.

After you evaluate the limit of something with respect to a variable, the variable is eliminated. Otherwise you're not doing it completely.

Also, with regards to the function at (0,0), the piece-wise definition of the function tells you that f(0,0) = 0.

Why is a circle the most efficient way to bound an area (uses the least perimeter while covering the most area)?

Try a proof by contradiction. Assume that some other shape is more efficient than a circle and, and show how that property would lead to a contradiction unless that shape is in fact a circle after all.

how is this a proof of uncountability? isn't the basic argument being used here the same as in most common "no largest prime" proofs? by that logic isn't there an uncountable number of primes?

It's similar, but not the same.

In a infinite prime proof, you assume there are FINITE primes and then get a contradiction. That means you're assuming a bijection with some numbers 1...n, not with all of N like you are here.

The "no largest prime" proof shows that for any finite set of primes, there must be another prime outside of that set, and so the primes as a whole must be infinite.

The diagonalization argument does not assume finity, just countability. It shows that for any countable set of reals, there must be some real outside that set, and so the reals as a whole must be uncountable.

Every shape that is not a circle will have an arc somewhere that you can replace with a "more circular" arc that encompasses the same area in less perimeter.

What is the force pulling, say, earth outwards from sun? If the gravity of sun is pulling earth towards itself and that's why we're circling around it, then what's keeping us from getting closer?

It's easy to confuse yourself with this shit but it's quite simple.

All that the ramanujan summation stuff, cutoff and zeta regularization does, is look at the smoothed curve at x = 0.
What sums usually do is look at the value as x->inf.

It's just a unique value you can assign to a sum, really they have many such values.

en.wikipedia.org/wiki/File:Sum1234Summary.svg

> What is the force pulling, say, earth outwards from sun?
There isn't one.

> If the gravity of sun is pulling earth towards itself and that's why we're circling around it, then what's keeping us from getting closer?
Momentum.

If an object A is subjected to a force which is always in the direction of object B, it doesn't follow that A will get closer to B.

For an object to move in a circle (i.e. remaining at a constant distance from some point), an inward force is required. In the absence of such a force, the object would move in a straight line.

Even though the speed may not be changing much the velocity is constantly changing, which is a result of the force. You don't need a "counter-force" to keep things in orbit, you'd need a counter force to keep things moving at a constant velocity in a straight line.

333pi/7 = x -pi =< x < pi

how we do ? i don't remember

Thanks for the clarification. I have done it correctly if you consider subbing (x,y) as (1/n,1/n) as x->inf because you end up with n/2 which is inf hence inf =/= 0 so not continous.

(I believe it also works the same if you put y->inf insread of x-> correct me if I'm wrong)

As with my first example it's wrong because 1/x as x-> 0 is 0 and the question states 0 elsewhere, hence 0=0 does not disprove continuous.

Is this correct?

what are some good books of first order logic suited suited for a grad level comp.sci course?

i need something full of formal proofs. i can learn the concepts in class but i'm bored as fuck when it comes to copy formal proofs, so my notebook lacks those parts.

I dare you to express this series in terms of n :

Un : { U0=2/3 , U(n+1)=3(Un)^2 }

How come covariance of 2 vectors is a matrix? This seems to be like it returns a scalar

Let's assume that an incredibly sharp instrument clearly severs my leg at the hip. Could I beat myself to death with it before losing consciousness from blood loss/control from shock?

The covariance of two variables is a scalar.

The covariance matrix of a vector variable X is a matrix M where M[i,j] = Cov(X[i], X[j]), i.e. the covariance between two elements of the vector.

An element on the main diagonal M[i,i] is Cov(X[i],X[i])=Var(X[i]), i.e. the variance of a specific element of the vector.

Let X be a random variable with Poisson(λ) distribution, with 0 < λ < 1. Find E[X!]

What did they mean by this? Does this mean that I have to find the "Factorial Moment"?

en.wikipedia.org/wiki/Factorial_moment

I have not been attending classes so I don't know whether this subject has been covered or what kind of notation is the professor using.

Please help!

why dont you ask the professor?

self bump

let's say I have a function
f(x)=(x+1)/(x-1) but when x=1 f(x)=1

is that function onto/one-to-one then?

shitty picture attached

Why do people in computational optimizations say that sometimes is difficult to calculate the Hessian/2nd derivatives?

Can't you do something like
[eqn]
f'(x) = \frac{f(x + 0.00000001) - f(x)}{0.00000001}
[eqn]
twice, and generalised to multivariate case?

Yes, you dumb dumb. Now prove it yourself. Set f(a)=f(b) and show a=b

what the HELL is going on

What are you confused about?
I can help. All of it made sense to me.

Let X be a set with an associative binary operation * and identity e. Suppose every element of X satifsies x*x=e. Prove that * is commutative.

Holy shit please help me