SQT - Stupid Questions Frog

Fish gills evolved into insect wings, so yes.

You'd learn more from getting fucked by one.

It doesn't say because that's common sense.
If you have a billion boxes containing ten balls each, you can be pretty sure you have ten billion balls.

Unless you count the balls in pairs if they're still in the scrotal sac.

Given a square or circle (whichever makes the maths simpler) of known area facing towards the viewer, how to I calculate the size it appears for the viewer?

If all body cells are replaced every 5 years or so, then why do scars last a lifetime?

For a circle, the "size" basically means the solid area of the cone formed by the circle and the viewpoint.

en.wikipedia.org/wiki/Solid_angle#Cone.2C_spherical_cap.2C_hemisphere

The cells forming the scar tissue are replaced by more of the same, not by whatever was there before the scar.

Trying to get the residue of [math]\frac{e^z}{1-cos(z)}[/math] , but by following the formula for simple poles it doesn't work. I managed to get it from its Laurent series expansion, but I don't understand why would such a function be problematic. Thanks in advance anons, if you see any problems with the process feel free to instruct me.

>What's a decent approximation for how much of an explosion's force a prism would be exposed to?

I'd imagine that it would be roughly proportional to it's projected area.

I'm not looking to find the volume of a cone though.
I'm trying to find the size of the object in like, square degrees.

That's the hard part though, getting the projected area.

do you not know what simple pole means?

Are there limits on what kind of major/minors combinations one might take?

How bad of an idea is doing a bachelor's in microbiology, like virology?

got a question for you: we all know that the fundamental group of a torus is ZxZ, what does it became if you join two of its points(by a curve, or just identify them)? can you find its universal covering space? (rem. for the torus is just a plane, with deck composed of integer translations in two directions)

Sorry for the stupid question but... What if something's mass is zero?

By zero, I mean m = 0, not something close to zero like photon. I tried Google-ing it, but could not get the good answer.

>not something close to zero like photon.

Photons have 0 mass, not near 0, but actually 0.

It has zero rest mass, not zero mass, right?

It's a double pole at zero. You can see that from your series expansion.

No, there is no frame where the photon is at rest, that would violate the principle of relativity. Moreover there is only one kind of mass and that's the invariant mass, ie the square of the energy-momentum 4-vector.

The idea of a "rest mass" and "relativistic mass" leads to lots of problems, and can be removed by suitable definition, for a simple example look at [eqn] \vec { p } = \gamma m \vec { v } [/eqn] You could put the [math] \gamma [/math] on the mass, or on the velocity. Putting it on the velocity is perfectly fine.

What function or symbol captures this behaviour? Like an anti-kronecker delta

[math]\delta ^{ij}=\left\{1\:if\:i=j,\:0\:otherwise\right\}\:???=\left\{0\:if\:i=j,\:1\:Otherwise\right\}[/math]

1 - \delta_{ij}

A hurr durr thank you for curing my retardation

What did he mean by this?

lol jk I was only trolling

so I decided to learn maths on my own, starting from basic shit, I'm trying to prove why pic related has "no solution" I only got halfway. I checked it on wolfram alpha and it gave me a longass non solution

where do you stop?

x - root(x-2) will always be less than x + root(x-2), so it'll never be greater than 1.
Are you trying to do a formal proof?

Help me understand this pls Veeky Forums

Aren't those highlighted sentences contradictory?
Am I missing something?

Nvm I get it now
Fucking brainfarted

A lot of people get tripped up on the second property you posted at first.

Probably you understand the first one; if I claim something exists in the empty set that satisfies P, obviously it's false. Nothing exists in it at all so clearly you can't find an example.

The second one is something like this; I claim every element of { } is an elephant. Which objects am I claiming are elephants? None at all.
This is why it's vacuously true; when you say something about "all elements" of the empty set you aren't actually describing anything so you can say whatever the fuck you want.

Thanks user
It's also nice to hear that other people get that brainfart too kek

Also it sort of helped me thinking [math]\exists[/math] means that there is at least one, so when you negate it it fits the context

What the fuck is a digital motor?

A buzzword.

How do i get good in Math in general? Is it possible to self-teach by starting below?

These days there are pretty good online resources that will walk you through it from easy stuff to hard stuff. And they're free.

nah, just trying to "solve it" have something that can say that is has no solution, like what you said

how you put it it makes PERFECT sense, thank you

this might be a bit unrelated, but how do you just train your mind to "see" those (mathematical) things that make you understand maths better? like it took me some time to understand inequalities and absolute values, but then I just saw it and it was so stupid easy

So, the black dot IS part of the red set (the result of a cartesian product) but not part of the blue set (a line which intercepts with the interior of an open circle so the boundary is not included).

My question is, can the separating hyperplane theorem be applied? Both sets look disjoint, convex and non-empty, but I can't imagine a hyperplane separating them.

Imma different dude but I would say practice practice practice. Maths is a skill and the more you do it the more familiar you become with how it works until you don't even have to 'think' to recognise things like that, you just instantly know because you've seen it before.

It's like a dude speedsolving a Rubiks cube, he doesn't really think much about what he's doing, he's just practiced so much he can quickly recognise some pattern of colours and then his muscle memory does the work from there without him thinking about it

thanks, my man

TI NSPIRE/laplace transfer functions

I am given the following open loop transfer function:
[eqn]G(p) = \frac{3}{(p+1)(2p+1)(4p+0.5)}[/eqn]
And am ask for which additional constant [math]K[math] the closed loop system becomes an oscillator and at which frequency [math]\omega_0[math]

----------------------
My reasoning:

The closed loop system oscillates when the open loop system becomes -1 for \omega_0[math].

So
[eqn]\angle{K \cdot G(\omega_0 \cdot j)} = \angle{G(\omega_0 \cdot j)} = 180\degree[\eqn]
which gives you [math]\omega_0[math]
[eqn]|{K \cdot G(\omega_0 \cdot j)}| = 1[\eqn]
which gives you [math]K[math]

I want to be able to solve these equation quickly with a TI nspire CAS machine (without additional software). So basically just solve system of complex equations. But when I try to solve the first equation it already gives me this apparent nonsense:

1=-2/(sign(G)-1)

(with G := G(w*j) )
---------------------------

So, is my reasoning wrong, or is my is my use of the calculator wrong?

The LaTex gods don't favour you today

They never seem to favor me..

anyone willing to help me with any?
need to prove with epsilon delta and completly lost.

Use [ / math ] instead

I am given the following open loop transfer function:

[eqn]G(p) = \frac{3}{(p+1)(2p+1)(4p+0.5)}[/eqn]

And am ask for which additional constant [math]K[/math] the closed loop system becomes an oscillator and at which frequency [math]\omega_0[/math]

----------------------
My reasoning:

The closed loop system oscillates when the open loop system becomes -1 for [math]\omega_0[/math].

So

[eqn]\angle{K \cdot G(\omega_0 \cdot j)} = \angle{G(\omega_0 \cdot j)} = 180\degree[/eqn]

which gives you [math]\omega_0[/math]

[eqn]|{K \cdot G(\omega_0 \cdot j)}| = 1[/eqn]

which gives you [math]K[/math]

I want to be able to solve these equation quickly with a TI nspire CAS machine (without additional software). So basically just solve system of complex equations. But when I try to solve the first equation it already gives me this apparent nonsense:

1=-2/(sign(G)-1)

(with G := G(w*j) )
---------------------------

So, is my reasoning wrong, or is my is my use of the calculator wrong?

[math]\textrm{text}[/math]

> I'm trying to find the size of the object in like, square degrees.
Solid angle is measured in steradians. Which is what that formula gives you.

can't u just take the inverse to solve the problem

anything in biology in its name is probably a bad idea unless you 100% know this is your passion

is there anyway 1/3 can be a natural number, is it not a rational number?

>How bad of an idea is doing a bachelor's in microbiology, like virology?

can you really do a bachelors in something so specialized? aren't those more like masters? or is that how it works in us of a

You can multiply it by 3

I am such an imbecile, I was checking at the wrong answers

R3posted from other thread, hoping for a response.

Help me Veeky Forums

Math brainlet here, but trying to get better.

What does 1 minus a ratio represent? For instance, we have 3 Blue Balls and 4 Red Balls. That means we have 3/7 chance of drawing Blue and 4/7 chance of drawing red. But there are 3:4 Blue : Red balls. So 1-(3/4)= 1/4. What does one quarter mean in the context of the balls? A ratio? A likelihood? Plz help.

relavance: the equation on the screen at youtu.be/-q7EvLhOK08?t=322

I don't think it represents anything in particular, it just happens to appear in that equation.
Maybe some mega nerd will know that the 1/4 in that context represents the oggooly-boogly stationary torus state in quaternion meme space as part of Discrete hyper-dank theory but there's nothing obviously meaningful about it

I'm a math major but I haven't taken probability since high school, so I'm just asking this question for my own curiosity. If we start at 0, and we flip a coin, and if we get heads, get +1 point, and tails, -1 point, what's the expected number of flips to get to 5 points, given that we can't go below 0 points? I've found a bunch of papers on random walks but none of them seem to talk about what happens if you have a lower bound you can't go past.

What are those balls under my mouth skin, like at the bottom? Why is there are pair of bollocks under my tongue?

Related, why are there two little slit-like holes on the roof of my mouth?

first, use the substitution x = 2cos^2(t)
then, 2cos^2(t)+3sqrt[2]isin(t)=0
this has solution
t=2(npi-itanh^-1(sqrt[2]-sqrt[3])) for all integer values of n
so choose n=0 to get
t=-2itanh^-1(sqrt[2]-sqrt[3]))
because x=2cos^2(t), plug t back in to get

x = 2cos^2(-2itanh^-1(sqrt[2]-sqrt[3]))

and by the wolfram alpha black magic theorem, we get
x = 3 (seriously, how the hell does it do that?)
but clearly, if x=3, then 1/2 = 2
therefore there are no solutions over the numbers

How can I stop being a brainlet?

Can we mathematically describe a scenario where you're rotated along the x-t plane but staying in the same location?

What's a good way of generating stars of random size and temperature?
The problem is that the two are interrelated in a non-linear way; small stars are cold, absurdly huge stars are cold, medium stars are warm, and giant stars seem to be whatever they want.

(You)
nevermind, i figured out how. it's just

[math]
x' = x \cosh \zeta\\
t' = t \cosh \zeta + x \sinh \zeta[/math]

I hope I did't fuck up the latex

Quick stats question, if you have a constant, b, does
Expectation(b^2) == Expectation^2 (b)?

Also, any tips to get better at writing LaTeX?

Read! If I remember correctly, the Veeky Forums sticky has a ilnk to a ton of textbooks

There was a FiveThirtyEight "Riddler" problem similar to what you're asking (see pic related)

I'm not entirely sure about why you would need a "recurrence relation" (or even what that is), but hopefully the link may help you:
fivethirtyeight.com/features/solve-the-puzzle-stop-the-alien-invasion/

What's a function that produces 0 from 0 and 1 from infinity?

{(0,0), (infinity, 1)}

Is a double major a good idea or are they generally looked down upon?

I was thinking about double majoring in computer science & engineering and electrical engineering but the uni I plan on going to doesn't allow any double major combination between CS, CE, and EE. So I was opting for a CS and mechanical engineering double major. My plan was to go to school for CS work a bit then go back to get a BS in ME. I'd like the ability to both design and program the machine I'll work with. I'm interested in robotics and A.I. and I want the ability to be able to do work in both but I do lean toward AI.

Would a double major be a good idea? Is it unlikely to work on a project where one person works with both hardware and software on a machine so am I better of focusing on one? Would CE be better even though I prefer software?

And does what in between?

f(t)=e^-t-e^-kt for k>1 is 0 at t=0 and ->0 as t->inf, peaking at t=log(k)/(k-1).

It depends why you can't go below zero. I.e. whether you just ignore any tails if the current score is zero, whether you count the tail as a flip but don't adjust the score, or whether you discard the entire sequence (i.e. calculate the expected value for sequences where the score never goes negative).

In either case, it's easy enough to write a simulation to produce an empirical result so that you can check whether a theoretical result is likely to be correct.

If we know [math] \sum_{i=1}^{n} a_i [/math], then what do we know about [math] \sum_{i=1}^{n} \frac{1}{a_i} [/math]?

You guys are smart

I wish I could understand you

not difficult to understand if you go through each term or concept 1 by 1, it is just daunting at first

A couple months ago I went through a summer calc class since I failed calc back at my regular university. When I was there, the professor recommended some course he liked that aimed to solve normally calculus problems using algebra. I can't for the life of me remember what the class was but I don't think it was differential equations.
Does anyone happen to know what the hell I'm talking about? It sounded like an interesting thing to study or read about so I'm searching everywhere I can.

Can someone help me here?
Why is this function's graph defined in x = 1 if x = 1 is not in its domain(neither is x = -1 and x = 2, which clearly are not defined in this graph).

can't seem to understand this simple one-line proof that a field of rational functions isn't an archimedian ordered field.

archimedian fields require this condition to be met
>for all x,y belonging to P there exists a natural number n such that n*x > y

the proof:
>let x = 1/t (belonging to P) and y = 1 (belonging to P). Then for every natural n: n*x < y

I get that 1/t has to be less than 1, but plugging in actual numbers quickly leads to a contradiction, unless 1/t is infinitesimal. I can't just assume that, though, right?

it doesn't work for any t < n

i have this non-homogenous 2nd order differential eq. of oscillating motion
[math]y''(t) + y(t) = sin(t)[/math]

and i want to transform this into a first order system of the form

[math]x' = f(t,v)[/math]
[math]v' = g(t,x)[/math]

to apply a semi-implicit euler-scheme

how to transform this?

forgot IVP:

[math]y(0) = 0[/math]
[math]y'(0) = 1[/math]

Read up on the ordering used between rational functions. It's not what you would expect.

It isn't. There's a hole there. But Wolfram Alpha doesn't render that hole explicitly.

Can someone help me out on the following:
Let [math] X_1,...,X_n [/math] be an iid sample, uniformly distributed on [math](0,\theta)[/math] and [math]M:=max(X_1,...,X_n)[/math].
For [math]0

Thank you, user.

okay I rechecked the ordering criteria

a rational function W + U/V belongs to P if lc(W) > 0 or W = 0 AND lc(U) > 0

it follows that 1 - (anything/t) belongs to P and therefore anything positive/t is less than 1

I think that makes sense now, is my reasoning correct? anyway thanks

how about
u =y' and x = y

then

u'= sint - x
x'= u

??

How do you do trig in 3d

I'm adding refraction to a ray tracer and I need to do this

thank you very much!

>23 years old
I'm looking to get a bs in EE, I'm studied in math up to Calc I, but aside from further calc, what could I self study with to prep for electronics courses when I can eventually transfer?

The only thing I remember is that the squares of the cosines in each plane should add up to one

i am supposed to find the supremum of the following set
[math]A=\{\frac{n+1}{n}\mid n\in\mathbb{N}\}[/math]
i know the answer is 2 but i don't understand the set notation. I gather A the set of values of [math]\frac{n+1}{n}[/math] where n is a natural number, but why?
shouldn't it be a subset of natural numbers where the property n+1/n is true, or even a set of boolean values depending on whether n+1/n is true for n.
sorry if this doesn't come off clearly, i'm really not sure how else to put it

>shouldn't it be a subset of natural numbers where the property n+1/n is true
What does "(n+1)/n is true" even mean to you?
It's a number. It doesn't make any sense to say "5/4 is true".

The first half of set builder notation tells you what to do with the number, and the second half tells you what numbers to use.

So in this case what you do with the number is take (n+1)/n, and the numbers you use are those that satisfy n in N.

>this whole post
smdh

The incident and refracted rays lie in the same plane, so it's only 2D.

Given the incident ray I and the normal N, construct a basis Z=N, X=I×N, Y= Z×X. Then you can convert I to 2D, find R, convert back to 3D.