/sqt/ - Stupid Question Thread: Homotopy Edition

A mechanical engineer designs a steel edger blade with a carbide tip for improved
wear resistance. You learn that the carbide tip is composed of WC with 10 wt. % Co.
a) Determine the molar ratio of Co to WC in the carbide tip.
b) If the density of WC is 15.77 g/cc, what is the volume % of cobalt in the carbide?

Please help

The LED is forward-biased if V2>Vr.

How much free time would I have if I were to get into physics (PhD and then research)?

Would I have time to do some programming on the side and contribute to free (as in freedom) software, like the GNU project?

And before you ask, I would never go for a programming career, I'm just a GNU/Linux and Unix enthusiast besides being passionable about physics and I want to learn more and give back to the community if I can.

Not a physicsfag, but couldn't you just pursue a career as an experimental physicist if you also enjoy programming? You'd kill two birds with one stone.

Theoretical and experimental are combined here.
There's computer physics, but I'm still more interested in the theoretical stuff.

whats the cheapest way to make an EMP proof storage container? I was thinking plastic box, lined with tinfoil, cardboard box inside that, electronics stored in anti static bags sealed with electrical tape - would this work? as you can probably tell im not very Veeky Forums

It depends upon the nature of the EMP you're trying to protect against. Protecting against a magnetic field is much harder than against an electric field.

Some dumb questions about group theory.

Can a word be of the form (x,y) or does it have to be concatenated to (xy)? Can a tuple be of the form (xy)?

What is the Kleene Star operation? Is it the set of all possible strings from some sequence or the set of all possible tuples or elements?

Does the set a Kleene Star is used on need to be a concatenated string or can it be used on a tuple?

How do I do this question? I've seen the example solution but I don't understand what they did

You've already got your answer in the last thread, m8.

Also is the length of a Kleene Star operation infinite or does it have some finite length? Or is the length arbitrary?

There's still some stuff that I wanted to clear up. I got a great bigger picture of what I'm dealing with but I want to be sure of the smaller things.
If you're that user then thanks a lot for your help before.

Anyone here writes scientific papers? I'm not a native english speaker, which of the following formatting is correct?

>It was demonstrated in 2015 (Luc and Wolf 2015).

or

>It was demonstrated in 2015. (Luc and Wolf 2015).

Should I place a dot after the first occurrence of 2015? This is the end of sentence, and the reference is only in relation to the sentence.

Reposting from previous thread (Not OP but I just can't seem to solve this):

"just looking for a hint, not a solution

given a continuous function f from the unit sphere embedded in R^3 to R, show there exists an orthonormal basis u1,u2,u3 of R^3 with f(u1)=f(u2)=f(u3)

i can do it when its a function f(theta):[0,2pi] to R from the unit circle in R^2 instead of the sphere in R^3 but i don't know if the proof is adaptable.

an orthonormal basis u1, u2 in R^2 has a pi/2 angle between them so we can consider the function f(theta)-f(theta+pi/2)

since the circle is compact f has a maximum u and a minimum v

these satisfy f(u)-f(u+pi/2)>0 and f(v)-f(v+pi/2)

I was the one who replied to you. What I don't understand is if you should prove the statement for ALL functions or just that there EXISTS one such function.

I'm not the user who originally posted that question. Proving that such a function exists is trivial (let f be constant), so I'm assuming the OP meant that it's supposed to be proved for all continuous functions

If a series converging to a function means it converges, is it also the way around (if it converges it also converges to a function)?
If we find a series from Taylor what can be said about the convergence radius?
Is the right (or left) derivative the same for an open interval and a closed one, for the same function?

Sorry for the triple questions

I have seen the notion of a character in multiple contexts, but in general what ís a character? Is it just a function that encodes properties of that which it is a function on? Or is there more to it?

It was demonstrated in 2015 (Luc & Wolf 2015).

thank you very much user

Is W/m/K same as W(m)^-1(K)^-1 or WK(m)^-1

this probably has been figured out before but only noticed it now

was making a list of square numbers eg (1^2=1, 2^2=4, 3^2=9 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100 ect..)

and noticed that 3rd and 4th square numbers add up to make the 5th square number, and got me thinking is there any other square number that is the sum of the two previous square numbers?

or another way to put it,

Shen is Sn + Sn+1 = Sn+2 True?? Sn=n^2

where Sn=n^2 and n is a positive interger

another another way to put is

when is a^2+(a+1)^2=(a+2)^2 True??

where a is a positive integer

>If a series converging to a function means it converges, is it also the way around (if it converges it also converges to a function)?
I'm not sure what you mean but probably yes

>If we find a series from Taylor what can be said about the convergence radius?
If a power series [math]\sum_{n \ge 0} a_nx^n [/math] converges absolutely at a point [math]x_0[/math], then it converges on the whole interval (-x_0,x_0) (and more generally the whole open disk D(0, |x_0|) in C) and the radius of convergence is at least |x_0|.
Also, you have the general formula for the radius of convergence [math] R = \frac{1}{\lim\sup |a_n|^{1/n}}[/math].

Not sure what you mean with your last question but again, probably yes

Any advice? Its been like 4 years since I took chemistry, I feel like I'm either over thinking it or there isn't enough information to solve it.

Well that's a quadratic equation, you just have to solve it to find out !
But no, there aren't any more because a^2 + (a+1)^2 = 2a^2 + 2a + 1 > (a+2)^2 for a > 2 (again, check it by hand).
Now, an interesting follow-up question could be whether there are other m < n < p such that S_m + S_n = S_p, and the answer is yes

Don't know if it fits here but

Book of Proof or How to Prove It?

Whoops was really sleep deprived when I responded. That works, but you could also write: It was demonstrated by Luc & Wolf (2015). The double dates are a little awkward and my PI would be kind of iffy about writing that way, but I don't really give a shit, English is not my native language either.

It's a reference so I have to keep the format like (Luc and Wolf 2015), I think I can live with a bit of that awkwardness.

Is carbon monoxide a meme? I sit in my bathroom with a heater on for several hours a day. Will I become stupid?

I was thinking that for fixed u1, there is a minimum of (f(u1)-f(u2))2 + (f(u2)-f(u3))2 attained for some U2 and U3. This is because the circle is compact and f is continuous. Thinking of U2 and U3 as functions of u1, we can create a vector field v(u1) =
(f(u1)-f(U2)) U2 + (f(u2)-f(U3)) U3
on the sphere. By the hairy ball theorem, this vector field vanishes at some U1. Then f(U1)=f(U2) and f(U2)=f(U3), which is what we wanted.

thinking a bit more about this, I think you would need to true this up a little. If U2 and U3 are not unique for some u1, you would need to choose one, and you would need to do that so that the whole vector field is continuous.

>you would need to do that so that the whole vector field is continuous.
I think you'll run into trouble if you try doing that. Assume that such U2 and U3 can be defined for each u1, then the field v(u1) = f(u1)(U2 + U3) would also be continuous on S2. By HBT that would imply f(u) = 0 for some u, but there's no reason why that should be true because you could just add some constant to f so that it's always positive.

I need a way, any way, that a horizontally launched projectile could travel upwards for at least a little bit of its path. Surely there is some force at work that could cause an amount of lift? If it was rotating on either axis when it launched or anything like that.

>Now, an interesting follow-up question could be whether there are other m < n < p such that S_m + S_n = S_p, and the answer is yes

do you mind explaining that in terms that the non mathemeaticans would understand?

Basically, does there exist positive integers [math]m, n, p[/math] with [math]m < n < p[/math] such that [math]m^2+n^2=p^2?[/math] The answer is obviously yes. Indeed, there are an infinite amount of these, and they are called Pythagorean triplets.

Read more: en.wikipedia.org/wiki/Pythagorean_triple

oh wait, are you saying that you there are square numbers that are the sum of two lower square numbers, just not directly before it as asked in my first question?

exactly

Incredibly stupid here, but bear with me. I'm not sure how this is lectured abroad, but depending on where you had a lecture, concave and convex functions varied. I know it sounds confusing, but in maths class, we were told that concave function is the one where function "fell" for a bit and then started to rise, and the opposite went for a convex function. But in physics class, it was the other way around.

And I'm still unsure of it today. So, what is the general consensus regarding these 2 functions? I'm going for the math explanation here and say the 1st is convex and the 2nd is concave, but I might as well be wrong.

Nevermind, I think it's the other way around.

How do I solve a right triangle if I'm only given the hypotenuse and the perimeter?

Really drawing a blank here. No problem specifically like it was gone over with me or in the textbook and I can't seem to find any advice online.

Specifically, it's asking to input all the values for the right triangle, and it's only giving me the information that the hypotenuse is 9 ft more than one of the sides, and that the perimeter is 418ft.

Have you had trigonometry yet?

That is a part of my memory that has been lost to time.

I realize it's probably extremely obvious, but it's been a while, and anything to do with shapes is not my strong suit, not that math itself is.

think of it like this: if you can pour water into the graph and it will stay, its concave

Alright, I've been out of the math loop for a long time, so let me give it a try. Do you have the solution though?

That's what I've been taught too, if you pour coffee (kava) and it stays, then it is concave (konkaven). But just googling for it shows the opposite

man this makes me miss topology

No, no solution. And the only information about the problem was what I posted already.

Taking pre-calc online, so most of this stuff I'm having to teach myself. Semester just started, so we're in the refresher portion. The chapters are going over everything at breakneck speeds, so it's kind of hard to take it all in.

I've done right triangle problems before, but it's been a while.

A shape is convex if the line connecting any two point in the shape is still all in the shape. When you're looking a graph use this same definition, but use the area below the curve to form the shape.

For a right triangle, if the side lengths are a, b, and c, where c is the hypotenuse, then a^2 + b^2 = c^2.

Let's call the sides [math]a, b, c.[/math] We use conventional notation and let [math]c[/math] be the hypotenuse. We know the following: [math]a^2+b^2=c^2[/math] (because it is a right triangle), [math]a+b+c=419,[/math] and [math]c=9+b.[/math] We can now use the Pythagorean theorem to arrive at [math]a^2+b^2=(9+b)^2 =81+18b+b^2.[/math] We can now remove the [math]b^2[/math] from both sides by simply subtracting by [math]b^2.[/math] When we do that, we get [math]a^2=81+18b \Leftrightarrow a^2-81=18b \Leftrightarrow \frac{a^2-81}{18} = b.[/math] We can now insert this and that [math]c=9+b[/math] into our equation regarding the perimeter and obtain [math]a+\frac{a^2-81}{18}+9+\frac{a^2-81}{18}=418.[/math] Now you simply solve that for [math]a[/math] and insert that in the previous equations to obtain the values of [math]a, b,[/math] and [math]c.[/math]

>Lecture easy
>Homework from professor are easy
>Exam questions fuck you over

What's the cause? How to do better?

t. Calc 2

>A shape is convex if the line connecting any two point in the shape is still all in the shape.

I know I should have gotten this, but that applies to concave shapes doesn't it?

Look for better resources. Maybe look online for practice exams or go look at some books.

Yeah, a shape is convex if and only if it's not concave.

suppose towards a contradiction that no such triple of unit vectors exists. then consider the map [math] g: SO_3(\mathbb{R}) \to \mathbb{R}^3\backslash \{ (x,x,x) \mid x\in \mathbb{R}\} [/math] defined by [math] g(\begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix})=(f(v_1), f(v_2), f(v_3)) [/math].

the fundamental group of [math] SO_3(\mathbb{R}) [/math] is [math] \mathbb{Z}/2\mathbb{Z} [/math] and the fundamental group of
[math] \mathbb{R}^3\backslash \{ (x,x,x) \mid x\in \mathbb{R}\} [/math] is [math] \mathbb{Z} [/math].

and so [math] g [/math] induces a homomorphism [math]g_*: \mathbb{Z}/2\mathbb{Z} \to \mathbb{Z} [/math] which must be trivial. Therefore [math] g [/math] must have been a constant map, contradicting there being no such triple.

en.wikipedia.org/wiki/Character_(mathematics)

Thanks, i solved that quadratic which proved that only that the only positive integer which could satisfy the equation could be 3.

went ahead and tried the same thing for cubed numbers, but no whole numbers satisfy the equation.
Got me thinking does it only work with 3 in squares or are there similar patterns using higher powers.

So: when is a^x+(a+1)^x=(a+2)^x True ,where a and x are integers

Given an infinite amount of numbers you'd think you'd think you might see this kind of pattern more then once, but maths is weird and says I've looked at infinity and all I found is 3 haha.

I'm far from an expert on this, but a projectile is defined as on object which has only force acting upon it- gravity. So I don't think you could find any upwards movement.

>similar patterns using higher powers.

en.wikipedia.org/wiki/Fermat's_Last_Theorem

Thanks, man. That really helped.

No problem! Remember, the solution to a problem is always just interpreting what the information you've been given means in mathematical terms and expressing it in equations.

I want a tip at how to start this :
what would be the average distance between two random points took inside a sphere with a given radius ?
I assume I'm gonna need integrals at some point, but I don't even now how to start :D

Inside a sphere ? Or on a sphere ?
In any case, assume your points are taken independently and in that case, the average distance is [math]\frac{1}{Vol(B^n)^2}\int_{B^n} \int_{B^n} ||x-y|| dx dy[/math]
It's probably not a pretty thing to compute

Very nice but maybe he needs something more basic? I don't know I'm if op knows or can use the fundamental group of SO(3)

i wrote both the original question (in the previous thread) and the answer you replied to

Yes I agree. It doesn't work. Thanks.

I came to that question when thinking about probabilty of an encounter while traveling into a 3D space, given the total size of the space and the total size of " things " you can encounter
Since I don't even understand what you mean by B^n, I think I'll just try to compute that in C++ with a finite number of random points :D
Main question now is : wouldn't i get something similar just by doing the same thing inside a sphere ?

Hey i'm double posting
by : the total size of " things " i meant the total number
and by same thing inside a sphere i meant a circle

Hey all, I'm reading about Bayesian probability right here: commonsenseatheism.com/?p=13156

He uses pearls in eggs as an example. See the pic related for the example I'm confused on. He says "If an egg is just as likely to be blue given that it contains a pearl as it is likely to be blue given that it doesn’t contain a pearl, then there are just as many eggs that are blue and contain a pearl as there are eggs that are blue and empty, and so the fact that the egg we picked is blue doesn’t give us any new information at all about whether or not it contains a pearl."

But that is wrong, isn't it? If 60% of eggs have no pearl, and 40% of eggs have a pearl, then wouldn't it mean that the proportion of eggs that are blue must be consistent with that proportion. Because if 20% of the pearled eggs are blue, and 20% of the nonpearled eggs are blue, then there would be more nonpearled blue eggs than pearled.

I agree that having a 20% probability for both wouldn't change the posterior probability. But I think his explanation is wrong.

Going to have a 3.75 by the time I apply to transfer to Georgia Tech or Emory. What can I do to help improve my chances?

>Ive completed all core classes
>Computer Science Major

Is there a certain semester that is usually easier to get accepted during?

So not only are there no powers greater than 2 that are the sum of the last two powers but there aren't even any powers that are the sum of any two lower powers and mathemeticians spent the good part of 400 years proving this was true and the proof is 150 pages long.

So that pattern I asked about here only occurs once, within the first ten whole numbers and using a power that's also within the first five numbers.

Just weird that it only shows up that early, and not with some higher numbers. But i guess that because of exponentional growth, and all the values for a^x, (a+1)^x, (a+2)^x gradually getting further and further away from each other.

>>Ive completed all core classes
>>Computer Science Major

Doubt it. Most graduates in CS have never completed the core classes.

>WK(m)^-1

What we have is a small flat rectangular object that is thrown horizontally. We have reason to believe that the object armed through the air instead of curving downwards, but we can't explain why.

3 questions would whole heartily appreciate responses

If one plans to major in cs, minor or double major in biology is it possible to get some sort of job related to the fields while still studying? Like literally even cleaning lab equipment
If so, what kinds?

What does Veeky Forums think of EPFL?

Bonus question for anyone in Switzerland:
Is it possible to self sustain yourself whilst studying there with the 15h/week limit even if it's the lowest of jobs?
I really want to study there and I'm willing to move early so I could work full time for some time just to be able to go to uni

Is there a continuous, analytic function which finds the nth term of the fibonacci sequence (i.e., not Binet's formula)?

"Find all values z1 and z2 such that (2, −1, 3), (−4, z1, z2) and (1, 2, 2) do not span R3 ."

I got z1 != 4.5 and z2 != -14.5, but how do I verify that it's correct?

Is there somewhere I can relearn grade high school maths online that's not shit?

I fucked up my maths education when I skipped year 9 but was never taught any year 9 maths so I had no idea where to start with the years after that.

I keep having problems where anything I try to learn is much harder to learn because of this missing knowledge. So I want to spend a few weeks catching up on everything.

Elements of Algebra by Euler
Algebra: An Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges by Chrystal

Can someone please explain what they did over those two steps?

Oh nevermind, I see that |q(2)|^2 is q(2) . q(2) and thats qi(2)^2

It is possible extract electric energy from photosynthesis process?

how do you optimally pay off two loans with 2 different interest rates and 2 different balances so that you accumulate the least amount of interest??

i tried to make a program that would make it so each loan would accrued the same amount of interest each month. but if you pay off the loan with the highest interest rate first, you accrued less interest over the same amount of time. this happened even when the higher interest loan had a lower balance to be paid off. is there a reason for this? some curve, or principle, to interest accumulating on debt??

It's more straightforward computing

[math] \dfrac {\partial} {\partial q_i} \left( \sum_{n=1} (q_n)^2 \right)^{ c/2 } [/math]

than juggle around the norm sign.

[eqn]\sum_{i=1}^{n}\frac{1}{(2i-1)(2i+1)}[/eqn]

How do I find this? I know the answer via WA, but I have no idea how to get there. Pretty sure you have to split it into partial fractions, but after that I have no idea where to go.

Looking at powers again and I noticed another neat pattern.

In the image for the first set i was finding squares, than the difference between one square and the previous one, and the difference between the differences and so on until there was no longer any difference.

Applied that for other powers and came up with the formula R*(P+1) = T

where T is the Remainder for current set.

Anyway just wondering is there anycould someone tell me the name and info for this pattern?

The optimal solution is to pay off the highest-interest loan entirely before starting to pay off the other.

Finite differences?

Difference equations are the discrete equivalent of derivatives.

The first derivative of a polynomial of degree N is a polynomial of degree N-1, the second derivative a polynomial of degree N-2, etc, and the Nth derivative is a constant.

Similarly, given a sequence whose terms are given by a polynomial of degree N in the index variable, the difference between consecutive terms is a polynomial of degree N-1, the second difference (difference between consecutive differences) of degree N-2, etc, with the Nth difference being a constant.

i guess the 'pattern' you have found is factorial, as a consequence of with polynomials (monomials in this case) of the form X^n

if you did another table to the left with power P=1, then your repeated number would be 1 = 1!
your first table finds 2! (=2x1)
then 3! = 6 = 3x2x1, 4! = 24 = 4x3x2x1, 5! = 120 = 5x4x3x2x1 and so on

why the heck would you use i for something that is not an imaginary number

>Is it possible to self sustain yourself whilst studying there with the 15h/week limit even if it's the lowest of jobs?
yes if you dont mind living in squalor

you're right about the partial fractions. after that notice that it's a telescoping series
[eqn]S=\sum_{i=1}^n\frac{1}{(2i-1)(2i+1)}=\frac{1}{2}\left(\sum_{i=1}^n\frac{1}{2i-1}-\sum_{i=1}^n\frac{1}{2i+1}\right)[/eqn]
Changing indexes
[eqn]S=\frac{1}{2}\left(1+\sum_{i=2}^n\frac{1}{2i-1}-\sum_{i=2}^{n+1}\frac{1}{2(i-1)+1}\right)=\frac{1}{2}\left(1+\left(\sum_{i=2}^n\frac{1}{2i-1}-\sum_{i=2}^{n}\frac{1}{2i-1}\right)-\frac{1}{2(n+1)-1}\right)[/eqn]

and so

[eqn]S=\frac{1}{2}\left(1-\frac{1}{2n+1}\right)=\frac{n}{2n+1}\, .[/eqn]