/sqt/ - Stupid Question Thread: Homotopy Edition

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I'm currently reading a book and wtaching math lectures online but I feel like I'm learning way too slow. I feel like I learned way faster way back in school.

How can I speed up the learning process in STEM related subjects? Any tips and ideas?
It feels pretty bad desu

>>8605094
pretty sure RP2 minus a point is S1, because it's like the sphere without a point+antipode

so maybe uhh RP2#RP2 and a torus? when removing a point from each of them this should give a bouquet of 2 circles in each case, and I don't think they're homotopy equivalent

>>8605120
just keep working hard

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>>8605120
"there is no Royal Road" - Euclid

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I'm having some trouble formatting a chart in Excel:

I have 12 rows of data (2-D Array with 12 rows). Each entry in the row represents the power at a certain wire gauge, and I want to graph Wire Gauge vs. Power. The only problem is, when I select and graph, it plots ten lines (plotting the data downwards).

When I plot the data (separately) going from left to right it does it correctly... How can I make it so Excel plots it correctly?

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>>8605259
Yeah I'm a dumbass... There's a button in Excel's "Chart Design" tab that says "Switch Row/Column"

I need to learn Excel better

>>8605259
On a related note, how do I make a rule that highlights the lowest value in a row?

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Any tips for part iii of this question?

I've calculated V2 as 2.51 V and Vr as 0.99 V.

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Anyone here know how to use Maxima? I'm trying to make an online exercise that uses Maxima functions to check if a given answer is right, but my problem is that if the correct answer is 0, the function "equal(x, 0)" considers an empty argument to be a correct answer as well because apparently it interprets no argument as zero. From what I've understood, the function "numberp(x)" could be used to check if the argument is an actual integer, but I can't seem to combine these into one function that actually works. I tried to use "(numberp(x) and equal(x, 0)" but it still considers an empty argument to be correct. Any help? In case it wasn't evident, I have no idea what I'm doing. This is my first time working with Maxima.

>>8605259
Please, please, for your own sake, drop Excel and use something more appropriate (like python + numpy). Excel is such a terrible piece of software.

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

>>8605324
The LED is forward-biased if V2>Vr.

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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.

>>8606473
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.

>>8606479
Theoretical and experimental are combined here.
There's computer physics, but I'm still more interested in the theoretical stuff.

>>8605115
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 /sci/

>>8606624
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?

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

>>8606757
You've already got your answer in the last thread, m8.

>>8606757
Also is the length of a Kleene Star operation infinite or does it have some finite length? Or is the length arbitrary?

>>8606764
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 anon 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):

>>8596114
"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)<0, so by continuity there exists w with f(w)-f(w+pi/2)=0 and so the vectors corresponding to w and w+pi/4 are an orthonormal basis of R^2"

>>8607087
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.

>>8607096
I'm not the anon 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?

>>8606863
It was demonstrated in 2015 (Luc & Wolf 2015).

>>8607231
thank you very much anon <3

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

>>8607127
>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

>>8605895

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.

>>8607386
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?

>>8607243
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.

>>8607460
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?

>>8607087
>>8607096
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.

>>8607541
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.

>>8607558
>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.

>>8607406
>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?

>>8607621
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: https://en.wikipedia.org/wiki/Pythagorean_triple

>>8607621
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?

>>8607634
exactly

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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.

>>8607650
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.

>>8607752
Have you had trigonometry yet?

>>8607765
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.

>>8607650
think of it like this: if you can pour water into the graph and it will stay, its concave

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>>8607776
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?

>>8607787
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

>>8605115
man this makes me miss topology

>>8607792
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.

>>8607792
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.

>>8607752
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.

>>8607752
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

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>>8607827
>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?

>>8607849
Look for better resources. Maybe look online for practice exams or go look at some books.

>>8607862
Yeah, a shape is convex if and only if it's not concave.

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>>8607087
>>8607558
>>8607615
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.

>>8607147
https://en.wikipedia.org/wiki/Character_(mathematics)

>>8607639
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.

>>8607616
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.

>>8607970
>similar patterns using higher powers.

en.wikipedia.org/wiki/Fermat's_Last_Theorem

>>8607845
Thanks, man. That really helped.

>>8607995
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

>>8608021
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

>>8607945
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)

>>8608168
i wrote both the original question (in the previous thread) and the answer you replied to

>>8607615
Yes I agree. It doesn't work. Thanks.

>>8608051
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 ?

>>8608219
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

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Hey all, I'm reading about Bayesian probability right here: http://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?

>>8607987
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 >>8607386 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.

>>8608372
>>Ive completed all core classes
>>Computer Science Major

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

>>8607328
>WK(m)^-1

>>8607978
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.

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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 /sci/ 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?

>>8605115
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.

>>8608851

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

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

>>8609180
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??

>>8609180
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.

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>>8608376
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?

>>8609209
The optimal solution is to pay off the highest-interest loan entirely before starting to pay off the other.

>>8609322
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.

>>8609322
i guess the 'pattern' you have found is factorial, as a consequence of >>8609398 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

>>8609244
why the heck would you use i for something that is not an imaginary number

>>8608554
>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

>>8609244
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]

>>8609209
You pay off the higher rate loan entirely first. In fact, it would be more beneficial to draw upon the lower line of credit in order to pay of the higher loan.

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>>8605115
what's the square root of an imaginary number? a doubly-imaginary number?

>>8608831
>(2, −1, 3), (−4, z1, z2) and (1, 2, 2)

wolfram alpha says...

determinant{ {2, −1, 3}, {−4, x, y} ,{1, 2, 2} }
= x - 5 y - 32

So the line x-5y=32 is the answer.

>>8608804
Binet's formula is analytic in n. It's the difference of two exponentials.

>>8608219
if you are just playing around, you might consider using a cube rather than a sphere. could give an explicit result.

>>8609527
The square root of a purely imaginary number is a complex number whose argument is [math]\pi/4,[/math] assuming that we are taking the principal square root.

>>8607945
why does g have to be a constant map? why can't it map to a simply connected region of R^3?

Why is 3(2^k)+2^k = 2^k+2? Please, I just don't fucking understand

[math]|3(ix)^{2} + 3ix + 3| = \sqrt{9x^{4} + 9x^{2} + 9}[/math]
Just tell me if this is true or false.

>>8605115
It is a circle. You may construct a RP^2 by mapping the boundary of D^2 twice onto a circle, therefore once, you'll remove a point you may shrink whole 2-cell and get the circle you started with.

>>8609611
3(2^k)+2^k=4(2^k)=(2^2)(2^k)=2^(k+2)

>>8609613
It is false. The magnitude of a complex number is the square root of the real part squared and the imaginary part squared. Assuming x is real group the real terms and the imaginary ones and continue on from there

>>8609626
The 4(2^k) is what I don't understand. Please explain how you got to that?

>>8609635
if you have 3 (2^k)'s and add one more 2^k you now have 4 (2^k)'s

>>8609635
3(2^k) + 1(2^k)
3+1=4

>>8609645
>>8609643
Ohhh, thank you so much. I am so retarded

>>8609630
Oh I see... Is this better or is something bad happening somewhere in the steps? Absolute values combined with comblex numbers makes my brain melt.
[math]|3(ix)^{2} + 3ix + 3| = |3ix + (3 - 3x^{2})| = \sqrt{9x^{4} - 9x^{2} + 9}[/math]

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>>8609557
good point

How do you prove through induction that 5^n (bigger or equal to) 1+4n

>>8609652
You're right here

>>8609664
check n=1 then assume inductive hypothesis

then
1+4(n+1)
=1+4n+4
<=5^n+4 (by inductive hypothesis)
<5^n+5
<=5^(n+1)

What is a formal language? What do they do and why are they known as 'formal'?
Going through formal languages and automata and I have no clue what's going on.

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>>8609419
Working as what? Have you went through this or know someone that did?

What does 'enumerate' and 'enumeration' mean?
Is it essentially listing something?
I don't understand how it is used. For instance the definition of a grammar is "A device which enumerates the sentences of a language". What does that mean?

>>8605115
When two or more variables are grouped together, for example 2xy/x. Does that mean 2 * x * y / x ?

Or can xy be grouped together to mean one variable?

Why do people claim that Calc II is so hard? What's the best way to prepare? I got an A in Calc I but it's Calc I so...

>>8610014
>Does that mean 2 * x * y / x ?
Yes. When two variables are written next to each other, it means we take the product.

>>8609837
>What is a formal language?
As far as I know, it's a set of "words", ie. finite sequences of symbols taken in a fixed set called the "alphabet".

>>8609988
In this context, I think it designates the set of rules of formation for the sentences of your language

>>8610049
>As far as I know, it's a set of "words", ie. finite sequences of symbols taken in a fixed set called the "alphabet".
What makes it formal though? What other languages are there? As opposed to things like context-sensitive language, context-free language and regular languages?

>>8610071
>context-sensitive language, context-free language and regular languages
All of these are formal I think. I guess it's only to differentiate them from natural languages

How do you know you learned something without exams?

>had linear algebra + geometry in college
>passed thanks to linear algebra
>barely understood any geometry
>now want to know more
>started Springer's Geometry

But the book just throws concept after concept at you and there's just a few exercises per section.

How do I test my knowledge without an actual test?

>>8605895
>>8607405

If we suppose that the ratio W:C is 1:1 (I'm not an expert in carbide composition), then it's molar mass is 196 g/mol. If we take 1g as arbitrary quantity, we can do 0.9/196=mol WC, 0.1/59=mol Co, and then molWC/molCo to obtain the ratio.

Again, in 1g of material, 0.9g are WC and occupy 0.9/15.77=0.057cc. 0.1g of Co occupy 0.1/8.9(Co density)=0.011cc.
Which lead to the 16.1% of volume being Co.

Should be correct, but it's late here, so just double check it to be sure.

In finite state automaton, is a language "recognised" when the machine ends on an accept when it receives a specific word?

For instance a diagram where there is one accept state, and three other states. The automaton ends on an accept state when it receives the strings (ab) or (ba).
Does this mean that the language of this automaton is {ab, ba}?
Is an automaton's language defined by the strings it uses that results in it ending in an accept state?

Would really appreciate some clarification on this. Yes or where I'm going wrong.

>>8605115

for the problem:
[math]
-y^2 dx + x(x+y)dy = 0, y(1) = 1
[/math]

the first step suggested by my text book is to substitute [math]y=vx[/math], giving

[math]-x^2v^2dx+(x^2+x^2v)(vdx+xdv)[/math]

which makes sense to me, but I don't follow the next step:
[math]\int\frac{1+v}{v}=-\int\frac{dx}{x}[/math]

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A formal language is a subset for the kleene star of a alphabet A language being accepted - the easiest way possible - is just all words/strings/symbols which end up in an accepted state.

>The automaton ends on an accept state when it receives the strings (ab) or (ba).
Does this mean that the language of this automaton is {ab, ba}?

Depends on your finitie state automaton. Normally an automaton is defined to have a complete delta function thus you have on each state transitions. But if you automaton is f.e. like pic related, then yes.

>Is an automaton's language defined by the strings it uses that results in it ending in an accept state?

Yes.

>>8610230
>>8610162

>>8610230
Thanks

[math]x^2v^2dx=x^2vdx+x^3dv+x^2v^2dx+x^3vdv[/math]
Cancel out the left side, rearrange the equation
[math]-x^3dv-x^3vdv=x^2vdx[/math]
Simplify
[math](-x^3(1+v))dv=(x^2v)dx[/math]
Take out constants
[math](1+v)dv\cdot-x^3=(x^2)dx\cdot v[/math]
More rearranging
[math]\frac {1+v} {v} dv = - \frac {1} {x} dx[/math]

>>8610285
Is for >>8610183

>>8609512
>>8609366
I see that but where would I look to find the formulas that prove this

>>8608831
"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 = 2, z2 = 6
z1 = -8, z2 = -8

any smart person want to check this?

Is water a strong acid? Not like by-the-book definition of "strong acid" but relatively speaking?

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can someone help me figure out how to measure these readings? i honestly don't understand what i'm looking at here

>>8605115
I don't understand how Stewart got his solution to one of the factoring problems for the algebra diagnostic test at the beginning of the book.

Pic related, it's the problem.

He states the solution is: 3x^(-1/2) (x-1)(x-2)

However, I don't know what in the fuck to do with the exponents. Should I just convert them into radicals and attempt to factor that way?

My algebra textbook never went over how to factor when rational exponents are present in the problem. KhanAcademy doesn't really go over the topic to this degree much either. I've answered all of the factoring problems correctly, except this one, and it's bugging me.

Mainly because I've heard that it's common to be presented calculus problems dealing with factoring with rational exponents.

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Sorry, here's the pic related. ^^^^

>>8610538
3x^(3/2)-9x^(1/2)+6x^(-1/2)
=x^(-1/2)(3x^2-9x+6)
=3x^(-1/2)(x^2-3x+2)
=3x^(-1/2)(x-1)(x-2)

>>8610523
The first one is 25mA and the second one isn't 45mA. See if you get it now.

>>8610469

Relatively speaking to...what?

Pure water is ~6.5-7.0 (very slightly Acidic to pH Neutral)

Salt Water is ~7.5-8.5 (Basic)

By textbook definitions, water is not acidic unless it is contaminated.

>>8610548
Is b) 90?

I still can't understand a)

>>8610089
Practice problems. Since the book doesn't give many, look some up. If those problems are (too) difficult, you don't understand it. If you got a problem wrong but you see clearly where you were wrong, you still need to do more problems.

Or you can try to keep pushing until you get to the point where the exercises are much more difficult. I wouldn't recommend this testing strategy, though.

>>8610560

http://www.wikihow.com/Read-a-Multimeter

You can understand A) by matching the 50 mA setting to the scale of numbers that end on '50'.

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https://en.wikipedia.org/wiki/Induced_homomorphism_(fundamental_group)#Applications_of_the_theorem

>(If we delete a line lying in R^3, the space wouldn’t be simply connected any more. In fact this generalizes to R^n whereby deleting a (n-2)-dimensional parallelepiped from R^n leaves a non-simply connected space)

how does one prove this? trying to use it to think about R^4 in particular (theorem implies cutting any plane out of R^4 makes it non-simply connected)

>>8610162
A word (string) is "recognised" by a FA if it results in the FA ending in an accepting state.

A language is simply a set of words. The language defined or recognised by a FA is simply the set of words which are recognised by the FA.

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First semester of physics, first problem our teacher has given out for homework. I need to figure out what the exponents a, b, and c should be to make the equation dimensionally consistent.
The teacher sent out the answers and told us to work backwards if it helps, but that's not really helping me either. How the hell do I even start doing this?

Any cali residents here? I'm planning on transferring from a community college for computer science/engineering. How accurate is my ranking in terms of CS/CE for SoCal unis:

UCLA > UCSD > UCI > UCR > CPP > SDSU > CSULB > CSUF > CSUSB
I think UCR and CPP are equal but not too sure.

Most likely I'll be attending UCR/CPP/SDSU/CSUF/CSUSB so trying to see where my best option is. UCI/UCSD are small possibilities cause they're kinda far.

>>8610968
I did that in high school many years ago, but if I remember correctly, you have to write everything using only fundamental units (lenght, mass, temperature and time), use exponent properties to have "a", "b",... on every unit and then write a system where you put every exponent of the same unit obtained before equal to the exponent of that unit on the right. Then it's basic mathematic and solve the system for a, b, ecc...

The explanation might be a little complicated, but in reality it's very simple. As long as I'm right, but it sounds right to me.

>>8610579
isnt R^n minus (n-2)-dim affine space homotopy equivalent to R^2 minus a point?

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Non math major here, just been seeing the nabula operator a lot recently and want to know what the operator does with a simple explanation

Thanks

So I got through most of Calc in high school without really knowing how to integrate in any timely manner, but now it's come back to bite me in the ass. Does anyone know any fast way of knowing which method to use to integrate a function between U-substitution and rapid integration by parts?

>>8610579
R^n minus an (n-2)-plane P deformation retracts to a plane minus a point (consider the orthogonal projection on [math]P^{\perp}[/math] ), hence it has the same homotopy type

>>8610968
assuming r = position (m), E = energy (kg*m^2/s^2), p = momentum (kg*m/s), t = time (s)
Then you have 3 linear equations matching kg, m, s
1 m = 2*a + b
0 kg = a + b
0 s = -2*a + -1*b + c

solve for a, b, and c:
a=1
b=-1
c=1

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How do you do these?

>>8611204
help

>>8611204
What are you solving for? Would be nice to include that in the picture.

>>8611282
It's at the top of each figure

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Uhh I don't remember Sin coming into play when doing cross products, what's the geometry where this comes into play?

>>8611297
Oh Theta is the angle between r and n-hat

>>8611204
How the fuck do i do 3? I feel like the 2 triangles should be congruent, but I only have a SSA case which is not a congruency case

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What field of study/major should someone pursue if they love:
1. lots of time spending in labs
2. anything dealing with biology on a smaller scale (specifically viruses, bacteria, etc)
2. programming/computer literacy in general (not as important)
3. doing stuff that wasn't done before
as a bonus I speak 4 languages fluently (english, polish, russian and french) if it's of any significance.

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Could somebody rephrase this definition and explain the following excercise?

>>8611411
I mean the definition of topological graph. Some illustration would really help...

>>8611204
HJ = KJ
GJ is common.

GHJ is congruent to GKJ.
RHS congruency.

5x-4 = 4x+3
x = 7

Angle JGK = 4x+3 = 4*7+3 = 31 degrees.

31+90+ang.GJK = 180
ang.GJK = 180 - 90 - 31 = 59 degrees.

>>8611450
It is basically a graph drawing. Segments (=edges) connected at common vertices.

>>8611474
thank u genius anon

If the binding energy per nucleon increases towards iron, why does fission/fusion release energy? Yes, I know that it iron is proportionally lightest but why is energy released as more energy is in bonds?

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>>8611563
It's because the binding energy is a kind of potential energy which like gravitational energy is negative (GPE = -GMm/r).

When they form into a higher binding energy nucleus it's like 2 balls rolling into a hill and gaining kinetic energy as the magnitude of their GPE energy increases but energy is released as kinetic energy.

>>8611411
"explain the exercise" like give you the answer, or like clarify what it's asking?

>>8611585
Thanks

How would you show that any whole number can be wrtten as the sum of 4 squares or less?

>>8611629
https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem#The_classical_proof

Have one week to learn
resonance structure drawing
polarization
oxidation
intermolecular forces
acid- basic theory

is it possible?

>>8611669
Can't find khan academy videos for oxidation number, polarity.
Any places i could look into?

>>8611669
That's very basic stuff, if you have the entire day to study, one week should be enough

What would be the condition of the following iterative function eventually returning equivalent results?
[math]f(x, y) = {|x-y|;
2*min(x, y)}[/math] while x != y
For example [math]f(1, 47)[/math] eventually returns [math]{32, 16}[/math] and just locks up in that cycle, while [math]f(3, 13)[/math] eventually returns [math]{8, 8}[/math].
I figured that it would have something to do with the sum of parameters being equal to a power of 2 but that does not seem to be always the case as a combination like 3, 45 results in 24, 24

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I graduated with a bachelor of science major in medical science and a minor in statistics. My initial plan was to do an MSc in epidemiology but I don't really like study, student loan debt and having to compete for jobs that I wouldn't even be good at. So my plan is to learn a trade. Would having a degree be looked upon favourably by employers who are looking for an electrical apprentice? Is the sexism against women in trades really that bad?

Guess this might be a place to ask..

I had to sit on a workshop today at work. When we returned from a break we began chatting about random facts and I brought up the Birthday Problem/Paradox and we decided we'd test it on our group. (Only 10 of us including the tutor).

The first person said their birthday was the 17th October and got a match in the room. The second was 27th June and also got a match in the room.

We were all really amazed and it got me wondering about what the probably might be of that occurring?

I'm terrible at math, but would someone be kind of enough to calculate the probability that in a group of 10 people, if the first two people shared their birthdays they would both find one matching birthday in the group? What about if there was a third match?

I hope this is a simple calculation (sorry if not), but I don't have the faintest idea where to start!

>>8611772
I'm certainly not great at this kinda of combination questions but I found that to occur at a rate of 10 every billion times you get 10 people in a room. Probs worth finding out from someone else as well though since I'm really not certain

>>8605115

I'm dumb please help

How do I solve this step by step?
40=80-20·ln(x+1)

>>8611894
Actually I'm near 100% that's wrong

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>>8611907
I'm too lazy to type it out, so check pic.

>>8611936
Lol thank you, I think I tried something close to this solution but I obviously forgot something.

>>8610542
What I don't understand is why you distribute out a negative 1/2 exponent.

>>8612103
because it turns whats left into a quadratic

>>8610037
Read ahead in your book

>>8605115
this is more of an advice thing..I've been working since i left highschool but now im going to school late at 23. i need 30 more credits (largely critical tracking courses) before i can transfer to an engineering program. I work alot now and my job inst flexible. How do you swing being a full time student without working at all???

>>8611763
Can anyone help me please?

Taking 5 STEM classes and a Composition class this semester and I need a way to stay organized via phone reminders and keep up with class notes. Is there a good scheduling app that I can use to enter all of my assignment deadlines into for the semester?

Thinking about using MyHomework because it has a mobile app and desktop program that is linked together, but was wondering if you guys had any other ideas.

wich undergraduate physics books should I use?
University Physics or Halliday's Fundamentals?

please note that I am a brainlet

Two questions about Gödel's incompleteness theorem:
>It says arithmetic is incomplete i.e. there are truths we cannot prove. What is a (self-evident?) example of this?
>This may be way too ambitious but could we possibly create an algorithm that gives axioms in such a way that we structurally and arbitrarily make arithmetic more complete?

>>8612499
Use the best and smartest scheduling tool of them all: your brain (the ultimate organizer that runs on food).

or google calendar

>>8612514
Halliday and Resnick and Krane >>> Halliday and Resnick and Walker

>>8612603
>>It says arithmetic is incomplete i.e. there are truths we cannot prove. What is a (self-evident?) example of this?

Not quite. It says there are statements that we cannot prove or disprove from within the system. Something like "this sentence is false." Godel's proof (if you skim through it) is really just using sleight of hand to encode that quote in arithmetic. Not really but it's close enough.

My grandfather gave me some greek religious books that are 2500 years old or something like that

is that worth anything
or do I just keep it another 2000 years

I'm a brainlet with only average IQ. I've always had trouble with math, but that's also because I was very lazy and not interested in that during my high school years.

is it possible to become good at math and logical thinking, or am I fucked? I'd like to study engineering, but I looked over some old admissions tests and could barely understand let alone solve anything there. am I doomed to work some menial job for the rest of my life?

>>8612603
"truths we can't prove" was gödel's preferred interpretation of the result because he was a platonist

it does say that any first-order theory which can interpret Peano arithmetic has some sentence G such that neither G nor ~G are provable, but this only means that there are unprovable truths for the system if you believe:
1. each sentence in the system's language has an intrinsic, "real", truth or falsehood;
2. for any sentence S, at least one of S or ~S *must* be true

>>8612771
>I was very lazy and not interested in that during my high school years

you're fucked because you're lying while trying to get help. Every incompetent brainlet will make the excuse "i wuz lazy" to make them feel better.

>>8612603
>>8612798
correction: there are more conditions besides just "can interpret Peano arith"

also probably worth noting that the result is specifically about first-order theories

>>8611125

it's the sum of the partial spatial derivatives. e.g. in 3D rectangular coordinates:

nabla(F) = dF/dx + dF/dy + dF/dz

(the d's are meant to be curly partial derivatives)

What should I get a Master's Degree in if I'm majoring in Electrical Engineering with a minor in CS?

I am majoring in math and computer science, should I take a wide variety of courses or should I star getting specialized? Take into account that I am planning to go for a PhD in the near future.
If I start to get specialized it is, most likely, going to be in Algebraic Topology (A prof of mine is an active researcher in this topic) and I am able to do a shitton of algebra like representation theory, algebraic topology, commutative algebra , homological algebra and computational algebraic geometry

>>8613192
How would anyone else be able to tell you?

What do you like/what kind of career do you want to pursue? Does a master's degree in a particular field/emphasis help meet that goal or put you in a better position? Then do that.

>>8613306
Priority number one: Get involved in research. REUs, working on projects during the summer, finding a kind of undergrad research advisor for during the school year, etc. Present at some undergrad-friendly event (I PROMISE they will have these, just look and ask around or suggest you give a talk at one of the colloquiums in your department).

Then take what you like. Take what will help you. Don't feel restricted by classes/professors, look into stuff on your own if it interests you. Maybe look into a reading course directed by a professor familiar with the topic who can give suggestions/offer meetings to discuss material. Look at grad schools. What kinds of background do they expect? If you can't meet this with standard coursework, then supplement it with the additional readings. And by read I mean working through exercises, problems--don't *just* read the theorems.

Publish if you can. If nothing else, have a working pdf of progress and be ready to discuss what prevented publication and how your research efforts were personally fruitful.

>>8611763
Why not just learn a graduate diploma in teaching or something? It would be a waste of science degree (especially considering the time and money that goes into school) if you went back to start a qualification which isn't even degree level. If you really want that sort of thing then go for it and forget about the STEM meme degree you did and don't mention you did it.

>>8605115
are there number theory fags here?
find all n that satisfy phi(n) = 110. phi function is phi(n) = count of all numbers i up to n such that gcd(i,n)=1

>>8613316
>How would anyone else be able to tell you?
Quite simple. Tell me if it makes more money. If it does, I'll do it. If not, fuck that shit.

>>8613388
if n has prime factorization n=product p_i^(a^i) then
phi(n)
=phi(product p_i^(a_i))
=product phi(p_i^(a_i))
= product (p_i^(a_i)-p_i^(a_i-1))
=product p_i^(a_i-1)(p-1)

so since 110=2*55=2*5*11, if phi(n)=110 then 11 divides product p_i^(a_i-1)(p-1). so one case is n=11^2 since phi(11^2)=11^(2-1)(10)=110 and the only other possibility is if a single power of 2 divides n since that contributes 2^(1-1)(2-1)=1 to the product above

i.e. n=11^2=121 or n=2*(11^2)=242

How do you solve this cubic equation? Without applying fancy stuff like Newton-Raphson.. There must be a trick right?
[eqn]
\frac{x^3-5x+2}{x-10} = 4 \\

[/eqn]

Someone prove to me that if ignoring air resistance, that the ratio of the times for a pebble thrown upwards at [math]4ms^{-1}[/math] and another thrown upwards at the same time which eventually manages to reach twice the height of the first pebble at some arbitrary point in time is [math]\frac{1}{\sqrt{2}}[/math].

>>8613915
to be specific for any autists, by 'ratio of times' I mean the the ratio of the amount of time in motion for both objects.

>>8613815
[math] x^3 - 5x + 2 = 4x - 40 [/math]
[math] x^3 - 9x = -42 [/math]
[math] x(x^2 - 9) = -42 [/math]
[math] x(x - 3)^2 = -42 [/math]

i dont fucken know from there

where would i find such things as

easy problems solved hard?

i often see here rigorous solutions to trivial problems which somehow shows connection to other or more general solutions..

Is this a thing? Is there a book or a homepage or something which deals with that matter?

>>8613939
shouldn't [math](x^2-9)[/math] become [math](x+3)(x-3)[/math] not [math](x-3)^2[/math]...

Intro to Chemistry exam in 1 month. What's the best general chemistry book I can get my hands on?

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>>8613915
>>8613922
Here you go breh.

v1=v2=0
s2=2s1
u2=u, u1=4
t1=kt2

then use newon's equations.

>>8613975
Chemistry, The Central Science, Brown, Lemay is often suggested, but I've personally done little with it.
If it's just Intro to Chemistry and you have a month, use Khan Academy or something similar.

>>8613939
My next guess from here would be to solve
[eqn]x^3-9x+42=0[/eqn]
Looking at a graph there is only one real solution thus we can express it as
[eqn](x-a)(x^2-b)[/eqn].
This gives [math]ab=42[/math] and [math]-(a+b)=-9[/math] i.e. [math]a+b=9[/math]. But going futher to find [math]a[math] and [math]b[/math] doesn't seem to be a trivial matter because it seems to just result in solving a further quadratic equation.

>>8613996
*which seems to be giving complex solutions

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Do any of you smart guy know how much is the repelling force of two protons?

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For marginal density, g (x), do I integrate f(x,y) with the limits of y?

Please confirm to a brainlet

>>8614106

can't you just use the coulomb formula?

>>8614158
I could do that but I was hoping there would be some kind of constant value for it cited throughout the internet which doesn't seem to be the case.

>>8613955
yea hes right, its not (x-3)^2, cuz that binomial is (x^2 - 6x + 9)

>>8613946
https://en.wikipedia.org/wiki/Mathematics_Made_Difficult

>>8614147
>>8614147
>do I integrate f(x,y) with the limits of y?
thats literally what it says

>>8614163

Well there won't be a constant value for it by definition, since it depends inversely on the square of the distance, and protons are at different distances from each other in the nucleus (I assume you're talking about the nucleus).

So CVs.... I have to make one
I'm an undergrad though and I haven't done much, it would only be like half a page long with

-contact information
-education
-employment

employment consists of a TA position I had and two semesters where I was a grader

what else do I put? classes I've taken? research interests? i'm compsci so maybe languages? I know it's not supposed to be a resume so i don't think i'd include languages

Do I dare include things from high school? i've found a few websites that have things for undergraduate cvs but almost everything is for masters/phd+

>>8614201
It looks like it's using the limits from -inf to inf of x

>>8614374
it says dy you fucking brainlet

In Computer Science, more specifically in formal languages and automata theory, there is something called the Pumping Lemma.
There are two varities (at least two that i know about), one for regular languages, and one for context free languages.
For the regular languages, there is a weak pumping lemma, and a strong pumping lemma. Since i skip lectures a lot and study out of a textbook, i mistakenly thought there was only one (the strong one) and used that in a homework assignment, but it turned out our professor only taught the weak one.
Now i have a new homework assignment that's about the pumping lemma for context free languages. So far, it seems there exists only one version of it (no weak/strong difference). Am i right? Is there only the one? I'm already fucked because there's two versions of pushdown automata, i don't want to screw this one up too

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Can someone explain what these lecture notes mean? I can't understand how it gets these numbers.

It says experiment suggests 2s+1 = 2, so s = 1/2. Fine.

But before that it says "m_s takes (2s+1) values in integer steps from -s to s"

So by my reckoning, m_s can take on the values -2, -1, 0, 1, 2.

But then it says m_s is +/- 1/2, and I can't see how the fuck that was arrived at. It contradicts what was said above.

>>8614462
dumb brainlet, where are you getting -2,-1,0,1,2 from

if s=1/2 then

"m_s takes (2s+1) values in integer steps from -s to s" = "m_{1/2} takes (2) values in integer steps from -1/2 to 1/2"

so m_{1/2} takes value of -1/2 or 1/2

>>8614501
>where are you getting -2,-1,0,1,2 from

my bad, i meant 0, 1, 2

"m_s can take the (2s+1) values in integer steps from -s to +s"

s = 1/2
-s = -1/2

2*(1/2) + 1 = 2
2*(-1/2) + 1 = 0

so m_s = 0, 1, 2

>>8614505
youre really confused

(2s+1) refers to the number of possible values of m_s

so if s=1/2 then m_s takes 2 values

those 2 values are the integer steps from -s=-1/2 to s=1/2 which is just -1/2 and 1/2

>>8614432
never mind i just finished it
Just included research interests and some classes taken, wrote a little bit about my employment but thats it. Was only slightly longer than 1/2 page but that's okay

>>8614511

>(2s+1) refers to the number of possible values of m_s

Ohhh I see, I thought it meant it was the actual value of m_s

>>8614432
>Since i skip lectures a lot

Fucking children. Do you buy movie tickets and skip out watching them?

What's the difference between turnover number and total turnover number? Can't find a single difference anywhere.

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How many AA-batteries would you need to connect to the stuff inside a shock-pen before it gets spoopily dangerous?

As far as I understand, it is an inductor and a capacitor+some stuff

let's assume no swallowing or penetrating the skin.

What am I doing wrong when I can figure this out?

3x^2-12

Need a solution step by step...

>>8614536

did you mean

3x^2 - 12 = 0

?

>>8614539
Whoops, yeah that's what I meant

>>8614524
>hurr i need professors to hold my hands for everything
Automata theory is easy as fuck. I'm not going to sit in a lecture hall for 90 minutes and be bored just so i can have an answer to the question "does a weak pumping lemma exist".
If you grow up and become an adult, you will see that you have to decide for yourself what you consider important and necessary to spend your time on, and sometimes that means not going to a lecture. My university doesn't even check attendance because they are aware of this. University is not a kindergarten where professors have to watch you because your parents are at work.

>>8613192
>a minor in CS

That looks terrible.

>>8614542

3x^2 - 12 = 0
3x^2 = 12
x^2 = 12/3 = 4
x = +/- 2

>>8614536
https://en.wikipedia.org/wiki/Quadratic_formula

>>8614543
If it's should easy, they why are you paying money for someone to teach it to you? Why didn't you just register for a graduate ToC class instead?

>>8614548
Oh... I thought I had to find the discriminant.
Is that even possible in this equation?

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>>8614551
I need a bachelor's degree, and there's more classes than just automata. I'm not saying the whole degree is easy, but certain classes are.

>>8614562

That chick has cocaine all over her lips.

>>8614555

Quadratics are in the form

ax^2 + bx + c = 0

If b = 0 then you don't need to fiddle with discriminants, just solve it directly.

Hell you could solve with the quadratic formula if you wanted:

x = [ -b +/- sqrt(b^2 - 4ac ] / 2a

b = 0 so you have

x = [-b +/- sqrt(-4*a*c) ]/2a

Substitute in a = 3 and c = -12 and you'll get +/- 2.

Note that a*c has to be negative for this to have a solution, since otherwise you'll get a square root of a negative number.

>>8614543
then just ask your professor instead of asking here you lemon

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Is 0.215 correct?


Also is the following true?

P (SnG')/P (G')=P (S|G')

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I'm taking calc and I haven't had official trig, had a bit in algebra II, and I'm lost. I don't even know how to approach half these problems. When I do the calculation on a calculator, I get a different result than I should. How am I supposed to know when to change from sine to cosine and any other conversions? Pic related

>>8614730
make sure your calculator is in radians not degrees. calculus only works nicely if you use radians, otherwise you get pi/180 factors everywhere

>>8614738
>>8614730

also it isn't

f(3*sin(2pi/3))

it's

f(2pi/3) = 3*sin(2pi/3)

you just replace the x in the expression with 2pi/3

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>>8614738
>>8614743

that certainly helped, thanks. I kept seeing the steps in pic related, is that not necessary if you just solve using algebra? Or is there something else that's supposed to signal switching?

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>>8614757

that's a needlessly complicated way of doing it. if you have a calculator just put it straight in .. decent ones will give the answer as a multiple of sqrt(3) instead of a decimal.

you'd only do it that way if you didn't have a calculator and had to use the results you knew for special angles, pic related.

>>8614773

Thanks a ton, that puts me at ease. Guess I have a new calculator to purchase

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>>8614778

yeah get yourself one of these. you can get fancier graphing ones but they're probably overkill for your course.

again make sure you're in radians instead of degrees unless it tells you otherwise, loads of people make that mistake when doing calc for the first time.

I'm having a brain fart

I have a boolean function (X+Y)(X'+Y+Z)

what do I do next for simplification?

[math]9^{2x+1}-28.3^x+3=0 [/math]. I am looking at this problem which asks for the sum of the roots of that equation in for[math]\frac{a}{b}, a,b \in Z [/math] Anyone got any ideas?

>>8614803
Distribute the variables in (i.e. "expand):

(X+Y)(X' + Y + Z) = XX' + XY + XZ + X'Y + YY + YZ

Then use what you know to try and eliminate some of those terms, and then manipulate further by factorising

>>8615110
Not sure what you mean by a, b, I'll just show how to find sum of roots. What you have there if you notice is a quartic equation in [math]3^x[/math]. That is, the equation can be transformed to:

[math]9 \cdot 3^{4x} - 28 \cdot 3^x + 3 = 0 [/math]

Now, that means our roots in [math]3^x[/math], if we call them [math]a,b,c,d[/math] . But we are interested in the roots in [math]x[/math], which we can call [math]\alpha, \beta, \gamma, \delta[/math]. They are related to each other in that:

[math]3^\alpha = a [/math]
[math]3^\beta = b [/math]
[math]3^\gamma = c [/math]
[math]3^\delta = d [/math]

What we are interested in is [math]\alpha + \beta + \gamma + \delta [/math]. But thuis turns out to simply be:

[math]\log_3 a + \log_3b + \log_3c + \log_3d [/math]

Using our logarithm laws we have:

[math]\log_3 abcd [/math].

To get abcd, we find the product of the roots of that quartic equation in [math]3^x[/math], but this is simply the constant coefficient divided by the leading coefficient which is [math]\frac{3}{9} = \frac{1}{3} [/math]

Which means we find [math]log_3 \frac{1}{3} = -1[/math]

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Need help, if someone could explain these questions to me as I am confused how to solve them.

t. faggot who hasn't done math in 4 years.

>>8615171
First 3 anyways. Even I can do the last one. I just don't understand the symbols / what Im looking for in the first few.

>>8615171
a) This states that the open interval for all real numbers greater than 1 and "less than infinity" (really just means all numbers greater than 1) ([math](1, \infty [/math]), that this collection is the same ([math]=[/math]) as the collection of real numbers ([math]x \in \mathbb{R} [/math]) such that they are less than 1 ([math] x < 1 [/math]). Obviously this is false as they are the opposite of one another.

b) The left hand side is speaking about the real numbers such that they are "between" negative infinity and 3 (not including 3), ([math](-\infty, 3) [/math]), and the real numbers "between" -2 and infinity (not including -2) ([math](-2, \infty) [/math]). Now, of these two collections, it is asking if the UNION ([math] \cup [/math]), between those two collections is equal to the collection of real numbers between -2 and 3. The UNION of two collections is the new collection where it contains elements that occur in EITHER of the two collections.

e.g. [math]\{1, 2\} \cup \{2, 3 \} = \{1, 2, 3 \} [/math]

I'll let you think about then whether it is true or false

c) This is saying that the SET (collection) (denoted by [math] \{ \} [/math]) of numbers 1, [math]\sqrt{2}[/math], 5, form a PROPER SUBSET OF ([math] \subset [/math]), the set of RATIONAL numbers ([math] \mathbb{Q} [/math]).

A proper subset of something is basically a part of that set, that is not the whole set, e.g. [math]\{1, 2\} \subset \{1,2,3\} [/math].

The RATIONAL numbers are those numbers that can be expressed as a fraction, e.g. [math]2 = \frac{2}{1}, \frac{5}{3}[/math] etc.

I'll let you decide whether that statement is true or not

>>8615166
Thanks man you're a god <3

>>8615171
a) no, should be >
b) no, should be ∩
c) no, should be ⊂A
d) no, should be log(4^5/4^2)=5/2 * log(4)/log(4)=5/2

How do you use sci-hub.bz? Do you have to know what to search for? Can you browse through categories somehow?

>>8615402
find the journal on an external site then plug in the url to scihub

how can a bounded set be infinite?

>>8615554
[0,1] has infinitely many real numbers

Help me /sci/

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 https://youtu.be/-q7EvLhOK08?t=322

>>8615554
consider the set of 1/n, n being a positive integer

>>8612771
What reason is there for you to suddenly start thinking logically? If you weren't doing that before, why would you now? Are you trying to be something you aren't? That's probably not good for you, if so.

>>8612771
you don't need logic to study engineering

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If two people are on both sides of a cord (an ideal cord) and each one of them pulls it in an opposite direction, what is the tension on the cord? The sum of both tensions?

>>8616169
yeah basically.
depends how they pull

>>8616169

I don't think that is right. I am super rusty at physics, but I think it depends on mass unless they pull with equal force.

http://physics.stackexchange.com/questions/144407/tension-of-rope-different-answers

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Hello nigger,
now look at this figure (that I just found),
The bits circled in red,
are locked in my head,
but I am dead if this thread can't help me,
The bits circled in blue can be found through,
some maths on the formula for dV,
oh can someone show,
where to go,
to get to the blue,
Thank you!

(How to derive the scalar factors in various bits of the formulas for div/grad/curl in curvlinear coords?)

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Some data follows an inverse bell curve pattern.

What descriptive statistic would you use to report results on such a distribution?

Doesn't seem like the mean would be representitive of the data if it has the smallest frequency in the histogram.

Or do I need to transform this shit?

As an aside:
Fuck non-normal data. I just want report the fucking mean and finish my goddamned thesis.

LAPLACE TRANSFORM (Time domain vs. Frequency domain)
----------------------

Ok, if we look at a basic Linear Time-Invariant Open Loop transfert function H(s) in the frequency domain. Then the poles are the values for s for which H(s) is infinite, right?

So if H(s) is infinite than the time domain output for t->infinity is also infinite too right? (If not, why not?)

But how is that possible? If f.e. s = -3+2i. Then the the output should die out!


In other words, what is the meaning in the time domain of a pole in the frequency domain??

Can someone explain why this is true?

[math]\frac{d}{dt}\left(\frac{\partial L}{\partial x^.}\right)=\frac{\partial L}{\partial x}[/math]

Where [math]x^.[/math] is the time derivative of x

What's a simple definition of formal languages and the Chomsky Hierarchy in relation to set/group theory?

>>8616314
> Ok, if we look at a basic Linear Time-Invariant Open Loop transfert function H(s) in the frequency domain. Then the poles are the values for s for which H(s) is infinite, right?
Right.

> So if H(s) is infinite than the time domain output for t->infinity is also infinite too right? (If not, why not?)
It means that Y(s)/X(s) is infinite. That can mean that Y(s) is infinite or that Y(s) is finite while X(s) is zero.

> But how is that possible? If f.e. s = -3+2i. Then the the output should die out!
If s is complex (rather than imaginary), then it represents an exponentially-changing sine wave (a pure sine/cosine wave has s imaginary, with no real component). If the real part is positive, then it's exponentially increasing, i.e. the amplitude tends to infinity. It should be no surprise that you can get an exponentially-increasing output from an exponentially-increasing input.

If the real part is negative, then s represents an exponentially-decaying input, and an infinite H(s) typically means that Y(s) remains non-zero even as X(s) decays to nothing (e.g. an integrator will converge to a stable value if its input converges to zero).

> In other words, what is the meaning in the time domain of a pole in the frequency domain??
A system with an s-domain pole with a positive real component ("right half-plane", i.e. Re(s)>0) is unstable. That's one of the basics-of-the-basics of signal processing.

A physical LTI system can never have such a pole: any quantity increasing without bound is going to run into some kind of saturation condition, at which point the system ceases to be linear.

>>8616401
It's usually take as a postulate, or the action integral being extremal is taken as a postualte.

You may read it as generalizing

[math] \dfrac{d}{dt} p = - \dfrac{d}{dx} V [/math]

which you get for

[math] L(p,x) := T(p) -V(x) [/math]

for some "potential function" V and "kinetic energy" [math] T(p) := \int_0^p P\,dP=\frac{1}{2}p^2 [/math]

>>8616413
A language is just a set of words, and a word is just a string (Kleene star) of symbols from some finite set.

A formal language is one where the set of words is obtained from some formal process (e.g. a partial recursive function).

Typically, a formal language is defined by a grammar (a set of production rules). The language itself is the set obtained by applying the transitive closure of the production rules to the grammar's starting symbol then taking the strings which consist only of terminal symbols.

The Chomsky hierarchy classifies grammars via a set of restrictions on the production rules.

If you wanted a rigorous mathematical definition, it boils down to defining each production rule as a function which takes a string and returns a (possibly-modified) string: F1:Sym*->Sym*, F2:Sym*->Sym*, etc. From there, you combine the individual functions into a single function which returns a set of strings: F:Sym*->{Sym*} : F(x) = {F1(x), F2(x), ...}, then extend that to a function which operates on a set of strings: F':{Sym*}->{Sym*} : F'({})={}, F'({x}∪xs) = F(x)∪F'(xs).

Then you apply that to the set containing only the starting symbol, F'({S}), and extract the strings consisting only of non-terminals. The resulting set is the language.

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How do I isolate for v?

>>8616678
Square everything -> multiply through by the denominator -> Rearrange to get the v term on its own

>>8616683
ok, where do I go from multiplying through the denomenator because now I have T^2(1-(v^2/c^2) = T0^2

>>8616687
Multiply out the bracket -> Add T^2*v^2/c^2 to both sides -> Subtract T0^2 from both sides

As if it wasn't already obvious, you should defo know what to do from there, if you don't then dabbling in special relativity is pretty ambitious

I'm trying to show that [math]X = \mathcal{F} ( \{ 0 , 1 \} , \mathbb{N} )[/math] is equipotent to [math] \mathbb{N} [/math], [math]X[/math] being the set of all functions from [math] \{ 0 , 1 \} [/math] to [math] \mathbb{N} [/math].

Define [math] \varphi : X \rightarrow \mathbb{N} \times \mathbb{N} [/math] by having [math] \varphi ( f ) = ( f ( 0 ) , f ( 1 ) ) [/math].

Then if [math] \varphi ( f ) = \varphi ( g ) [/math], we have [math] ( f ( 0 ) , f ( 1 ) ) = ( g ( 0 ) , g ( 1 ) ) [/math], only if [math] f ( 0 ) = g ( 0 ) [/math] and [math] f ( 1 ) = g ( 1 ) [/math]. Then we have [math] f = g [/math], thus [math]\varphi[/math] being an injection.

For surjectivity, choose [math] ( a , b ) \in \mathbb{N} \times \mathbb{N} [/math]. So we define [math] f \in X [/math] such as [math] f ( 0 ) = a [/math] and [math] f ( 1 ) = b [/math].

We then have that [math]X[/math] is equipotent to [math] \mathbb{N} [/math], UNLESS I'm doing a mistake somewhere, and it's bothering me because the prof said that [math]X[/math] is equipotent to [math] \mathbb{R} [/math]. So could someone proof read this? Ty Ty in advance

Hi, can anyone tell me how to solve this step by step?

7 = 2/3 log (x/10^4,8 )

>>8615566
>DONT FORGET ABOUT ME YOU CUNTS

>>8616734
your proof is correct
http://math.stackexchange.com/questions/51059/what-is-the-set-of-all-functions-from-0-1-to-mathbbn-equinumerous-to

but if you change X to being functions from N to {0,1} then you get equipotence with R
http://math.stackexchange.com/questions/129851/show-that-the-set-of-functions-mathbbn-to-0-1-is-not-countable

>>8614528
Try to keep it lower than 1mA, since that can be fatal to some people. Tasers are made to be non lethal, but they still kill a couple people a year anyway. Here's an article: http://www.highvoltageconnection.com/articles/ElectricShockQuestions.htm

>>8614106
depends on their distance apart using Coulombs Law

>>8616233
If it were me, I'd just flip the y axis to make all calculations easy. So rather than have the y scale be "loudness", have it be "quietness".

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Pic related is an example from Concrete Design textbook. Can someone explain to me what is going on with that moment of inertia equation, specifically the second part.

>>8616991
yeah, that was the mixup in the prof's notes

How do I prove limits with epsilon delta? I just don't get it.

>>8617385
>fix an epsilon
>find a suitable delta
>???
>profit

>>8617048
The pic is just an example of an inverse bell curve... But is flipping the Y axis really an acceptable way to achieve data normality or is this a troll post? I'm very new to statistical methods

>>8617530
I'm not trolling, but I also haven't studied statistics much so I don't know if it's really acceptable. I was just proposing something as an option.

Quick question:

What's the use of a piviot element in gaussian elimination?

In the lecture, the professor introduced the pivot element and how to calculate systems of equations with it while in online videos and books the people are just working with all rows without a pivot element at all.

What's the reason for the choosing pivot element in the gaussian elimination?

>>8617547
The pivot method (ie. choose a pivot element in the column, eliminate all other coefficients, proceed to next column) gives you a systematic (understand algorithmic) way to solve linear systems of equations. You can implement it on a computer the exact way you would do it by hand, and it works (although it's not the fastest solution).

>>8617749
>>8617749
>>8617749

>>8608051
I suppose there is also a factor of two, since you will compute the same vector twice?