SQT - Stupid questions thread

Banach's fixed point theorem.

How did they use logarithms? I feel there is something I'm missing here though I'm not particularly sure how to use them in the case of hyperbolic functions. My guess is that it relates to the said functions being represented using exponential (I lack the knowledge to write it out on here using whatever tool you guys use, though its a fraction with multiple exponentials on top essentially). So how do you go from that to logs at once, it just seems like a bit of a step.

Do you know what arctanh is?

Do deserts affect global temperature? They're large areas of land where the sun rays hit the ground then just bounce back into space because of nearly no water vapor in the air to trap infrared.

suppose you are looking at some data over the last 100yrs(eg: height of people). collating everthing you find some distribution. how can you find out whether the distribution changes over time if the sample is on the small side? as the most recent data provide the best indicator but your samples could be victim to variance.

is there some sort of transform for the distribution based on average drift(in mean or something else)?

idk man, it seems about right
why do you say it's wrong, I get 3.2m/s as well
same goes for the power, I think you did right

[math] y:=\tanh(x) [/math]
You wanna solve for x which would be arctanh(y)
[math] y= \frac{\sinh(x)}{\cosh(x)} = \frac{e^x-e^{-x}}{e^x+e^{-x}} [/math]
Multiply numerator and demoninator by e^x
[math] y=\frac{ (e^x)^2-1 }{(e^x)^2+1} [/math]
Move the denominator.
[math] (e^x)^2-1 = y ( (e^x)^2+1 ) = y (e^x)^2 + y [/math]
And now you get
[math] (e^x)^2 (1-y) = y+1 [/math]
when y is not 1 (it never is so it's ok) you can write
[math] (e^x)^2 = \frac{y+1}{1-y} [/math]
therefore
[math] e^x = \sqrt{ \frac{y+1}{1-y}} \text{ or } e^x = \sqrt{ \frac{y+1}{1-y}} [/math]
Since e^x is always positive, the second solution is not accepted. You can easily see check that the first solution satisfies the original equation.
From the first solution you get
[math] x = \log \sqrt{ \frac{y+1}{1-y}} = \log (\frac{y+1}{1-y})^{\frac{1}{2}} = \frac{1}{2} \log (\frac{y+1}{1-y}) [/math]

is it normal that in this correctly bound structure, the global equilibrium equations (which are 3: vertical forces, lateral forces and momentum) have 4 unknown terms (lateral reactions in A and F, vertical reactions in A and E) resulting in the inability of calculating the binding reactions?

The logarithm is the inverse of the exponential, so if you can represent the hyperbolic trig functions as exponentials, you can represent their inverses using logs.

Humans came out of the universe, and what we know of as consciousness did as well. Isn't it weird that the universe created a being within itself to explain and discover itself?

Yep.

At risk of sounding stupid I feel like that was supposed to be way harder, when you put it like that its really strait forward. Thank you tons guys, hope you all have good days ahead.

let x be a fixed point of this recursion. Then
[math] x = \frac{\alpha +x }{1+x} \Leftrightarrow \alpha = x(1+x) -x = x^2 [/math]
The rest is

Best way to learn MATLAB? I got a summer '18 position recently and said I have experience with it, when really I just use it like a calculator. Specifically for optics in matlab does anyone know good books?

Can anyone help me understand what a force actually is? I know it results when there's an interaction between two objects, but is this interaction always physical? I can understand force when thinking in terms of idk. an object hitting another object and transfering its energy/momentum. But what exactly IS a force? Is it a term we use to describe the action/period of transfer? As soon as the transfer begins, there's a force, and as soon the force stops, the transfer ceases. What is acceleration describing? Is it describing the period in which the force acts? As soon as the acceleration stops, there's no more force acting on the body. So, is force simply a period of transfer of momenta/energy? Also, this doesn't make much sense when talking about force in terms of charge. How is there a force acting on a charge? What is transferring it physically? How is the force constant if the acceleration of the field isn't constant? Fuck my brain will explode someone just please explain.

Not really. It's just chemistry.

What are you getting for the time in part c?

idk man it's really easy, the acceleration is linear, so you take the space and divide it by average speed
for the second sentence I don't really know what it means

power = work/time, so time = work/power right? but its not giving me the same answer as the acceleration and velocity is the problem I am having or at least, I dont understand why it isnt.

So I need to find the thevenin equivalent of this circuit

I know I need to find the voltage drop and the current across those points, but how do I go about that?

forgot pic

How to get good at recurrence definitions?

pic related is the sort of stuff I need to be able to do.

Well. I think it is pretty simple. When doing this you only need to look at the prime example of a recursively defined set, the great natural numbers. The most beautiful set ever conceived. Let's follow their model.

First let's explicitly say that an element is inside the set. I think the simplest element of S would be 1, so let's start with [math] 1 \in S [/math].

Now we need a relation that yields all the other elements from the elements that are already inside. We can do this by including two axioms: Let's say that concatenation is [math] C [/math]. So that for example, [math] C(1,1) = 11 [/math] or [math] C(0110,011) = 0110011 [/math].

With that, let's say:
[math] s \in S \implies C(s,1) \in S [/math]

So because 1 is in S, we know that 11 is in S, and therefore 111 is in S, and on and on and on.

And our second axiom is
[math] s \in S \implies C(00,s) \in S [/math].

So because 1 is in S, so is 001, and 00001 and 000000111111111. etc.

And that's all. I think if Steve Jobs was alive today he'd say: Great jobs.

>Great jobs.

why do you have to fucking ruin everything

It's what Steve would say.

in response to

Trump is the new Jobs

I somewhat understand but I just can't grasp how this logically adds up and makes sense. thank you.

Well, I have this commutator:

[math][A, B] = B[/math]

How is this possible? Which are the values for [math]A[/math] and [math]B[/math]?

A=B=0 for example

Anybody?

There are more possible values? I thought about that case too, but I was wondering at first if there were more values.

Can somebody help me understand this?

i:=1 to n-1 basically means 1 through the second to last element?

What does j:=1 to n-i mean?

sure. you got a system of n^2 equations and 2n^2 variables to solve for nxn matrices.
Here's an example
[eqn] A = \begin{bmatrix}
1 & .5\\
.5 & 1
\end{bmatrix},
B=\begin{bmatrix}
.5 & -.5\\
.5 & -.5
\end{bmatrix} [/eqn]

if your first loop is at i = 2 for example, your second loop is going from 1 to n-2

>P=F⋅v
Can't do that. As the mass is accelerating during the period, the velocity isn't constant, so you'd have to integrate it:
[eqn]P = \int^{t}_{0} F \cdot dv = \int_0^t F \cdot \frac{dv}{dt}dt = \int_0^t F \cdot a \space dt [/eqn]
But since you don't know the final time, it's easier to just use the dislocation formula
[eqn]S = S_0 + v_0t + \frac{at^2}{2}[/eqn]
[eqn]4m = 0 + 0 + \frac{4t^2}{6}[/eqn]
So, the final time is [math] t = \sqrt{6} [/math], the average velocity during this period is [math]\bar v = \frac{\Delta S}{\Delta t} = \frac{4}{\sqrt{6}} \approx 1,6 \space m/s[/math]. Now you can use the Power formula [math] P = F \cdot v = 24 \cdot \frac{4}{\sqrt{6}} = 39,2 \space W[/math].

To be honest, it is either that or twice that. Hehehe, I got 78,4W by doing the integration for some reason. Hopefully someone will come along and explain to me why the integration is giving me the wrong result.

So my first loop would be 1-2, and my second loop would be 1-1? If the loop is from 1 to n-1, how can it evaluate the last element?

Well. Do you understand the natural numbers? They are defined as such:
[math] 1 \in \mathbb{N} \\ n \in \mathbb{N} \implies n+1 \in \mathbb{N} [/math]
(the formal definition uses the succesor function but you know what I mean).

And the idea is that you state that the set contains that element and then you find a rule that connects that element to every other element you want to put inside the set. In the simple case of the natural numbers we start with [math] 1 \in \mathbb{N} [/math]. And the second axiom tells us that [math] 1 \in \mathbb{N} \implies 2 \in \mathbb{N} [/math]. So 2 is in the natural numbers. But if 2 is in the natural numbers so is 3. And then so is 4. And to put it in simple terms, this goes on "forever".

In the case of your set you start with saying that 1 is in S. And then by the two rules I stated

If 1 is in S, so is 11. And so is 001. If 11 is in S so is 111, and 0011. And this goes on forever. Generating all the elements of S.

>So my first loop would be 1-2, and my second loop would be 1-1
if n=3, yes.

>If the loop is from 1 to n-1, how can it evaluate the last element?
a_n never gets compared to any other elements, but as you can see in the if loop, a_j can get interchanged with a_(j+1), so if j = n-1 and a_j > a_(j-1), a_n changes places with a_(n-1)

en.wikipedia.org/wiki/Bubble_sort
Also there's a typo in your pic. It should be "interchange a_j a_{j-1}".
Consider the boxes in pic related labeled from n to 1, instead of from 1 to n.

>Consider the boxes in pic related labeled from n to 1, instead of from 1 to n.
nvm

>so if j = n-1
Isn't i=n-1? How can j be equal to n-1 when it's n-i?

In this case, how will the 1st element interchange with the 2nd element, since it can only be evaluated against a previous element a_(j-1)?

Am I supposed to know what the hell professors are researching in depth when applying to a PhD from undergrad? All of their research is over my knowledge level but does the first few years get me caught up quick enough? It sounds interesting and the real applications of the research are neat, but I just dont know half the shit they talk about! In photonics and optics btw

1+1/2+1/3+1/4+1/5+1/6
does this series diverge or converge?

A force isn't a completely "naturalized" thing. The universe will behave in ways we don't fundamentally understand the causes behind, but we can map the behavior with math, and make models that predict that behavior. "Force" is then just a name we give to different behaviors in the models.

Whether or not there are literal forces as the word intuitively makes it seem, acting on other stuff, is a metaphysical question.

You can think of force as the rate of change of momentum with time.

in this problem once I convert to polar, and dV becomes rdzdrd(theta)

Would my theta bounds be from 0 to pi over 4 since it's held within the first octant?

>Can anyone help me understand what a force actually is?
In F = ma, force is a measurement of the amount of "push" or "pull" needed to change the velocity of a certain mass by a certain amount.

>What is acceleration describing?
An acceleration is a change in velocity. Mass can be thought of as resistance to change in velocity.

>Also, this doesn't make much sense when talking about force in terms of charge.
A charge is a type of force (electromagnetic). There are 3 others: gravity and the 2 nuclear forces, weak and string.
Note that a charge can create a change in velocity (acceleration) in some objects with mass, as descibed in F = ma.

All you're really asking is, "What is a push?" and the answer is that nobody knows, not even Yang or Mills.

Lol... Weak and strong*

Actually, if you look closely the picture says
>if a_j > a_(j+1) then interchange a_j and a(j+1)

holy shit you're right

Why is Kurisu Makise such a piece of shit whore who deserves to get punched in the face?

How do #17 lads?

Why are they called steps outside but stairs inside?

Yes.

do you think astronauts have sex in space

so this is what i've got

AC=x+y
AD=(x+y)+CD
BE=y+CD-x
AE=y+CD
BF=CD-x
DF=-y-x

is there anyway i can express CD with x and y?

how is min(C)-1-a concluded to be the smallest element of A here? for each c in C, c=a+1+b, where b

Does ionizing radiation actually cause a visual grain-like distortion phenomenon when near an intense enough source, or is this just the theatrical work of video games?

Been playing a few games with nuclear radiation sources, and I just now realized most of them have this effect in one way or another, basically looking like a film grain.

It feels like an obvious answer, however I've been rationalizing it by thinking that any particles that pass through the eye may distort what you see, or your brain would process it like a fuzzy grain image, kind of like how you can sometimes see the white cells passing through your eye's veins.

where can I read up on the various phenomena created by nuclear radiation?

pretty sure there's a typo and it should be min(C)-1-b

I'd also add that, contrary to my rationale for its presence in the games, I would assume realistically if particles were entering your body in that area in a sufficient amount to cause that distortion effect, you wouldn't be living anymore after a few hours, let alone seeing.

Seems like they shouldn't have a positive contribution, but then, my knowledge about climatology is literally from primary school.

Man, those are some sexy dunes.

Consciousness evolves out of a need for selfpreservation. It's not a mystery.

You do get bright blue flashes. Other than that no.

If you're looking for the answer of a.ii), You would use the Kf - Ki = W and 1/2 mv^2 = K

So, (1/2)(18)v^2 = 96 solving for v gives you 1.633 as the final velocity.

I would do c) before b) as you solve for time using d/v and then you can find average power from there then switch over to b) where you integrate and end up with the final power

There's a few things you could have done differently Δt = Δd/Δv so you could have found out t easily from that after finding v from the W = Kf - Ki equation. (the question said to thing of conservation of energy)

Next, you could have found P through W/t which is *average* power which is 39.2.

This is where you think you are making a mistake because that's only the average. When you integrate it, and apply the final time,(which is what you did) you are finding out the overall power that was given which turns out to be 78.4.

You did everything right, it seems as though you just didn't know exactly what you were looking for.

I think I get it. But then, average power is a pretty useless physical quantity, as, usually, when you want to know the power of the system, you want to know about all of it, not just most of it. So suppose this particle is a single geared car, the engine would have to be able to give all 80W to keep it accelerating, instead of just 40W? If so, then yeah, average power is pretty useless.

Why is tan so different from sin and cos (given the the graph is vertical, functions are far different related formulae e.g. addition formulae bears no resemblance)?

Because instead of tan being directly related to the circle (like sin and cos), we divide sin by cos to get our final tan function.

Can anyone explain to me in a few words why this is the case in Boolean algebra?
[math](a+\overline{a}b) = (a+b) [/math]

what is +?

Help
Is this true, and if so, for any frame?
[math]g^{ad}\Gamma^c_{dc} = 0[/math]

AND

That makes more sense, thank-you user!

Consider the tangent line at the unit circle at (1,0).
tan(x) is the the (signed) length shown in the graph.

...

If I have a cube with positive charges q lying on the center of each of its faces, what's the electric flux on each of its faces? I'm thinking the total flux of the cube is 6q because of Gauss's law which would mean the flux on each face is q but I'm not so sure.

Appreciate the responses.

draw a venn diagram and you'll see it

I see now, I'll download the images for reference. Thanks a ton guys, it all makes sense.

What does inductive mean in this context?

what it says below the blue line ?

you literally posted the definition

nigga how the FUCK i do this without a pdf for X

X is uniformly distributed, so you gotta use that.

It's badly phrased. Whoever retard wrote this meant X~U(-1,3).

you don't need it to be explicitly given to you
where is that stated?

let f be the density function of X, then for the density function g of Y you have the property
g(x) = f(x)+f(-x) for 0

This: It's not stated because picking a random number without any context always means uniformly distributed, be it discrete or continuous.

this is what I'm thinking. in the context of how this course has been in the past, I feel the prof would explicitly say 'assume f is the pdf of x' in the question if they wanted an answer as a function of it

So would you express it as:

p(y) = {1/2 for 0

it's a problem that can be solved without assuming anything about the random variable.
Assuming that the person phrasing the question is an idiot who can't do it properly is kind of presumptuous, don't you think?