Stupid Questions Thread

>>8504277
search sqt, still 50 posts to go
>>8495521

>>8504283
Shit, hopefully this'll at least get used when that thread fills so that I'm not wasting space.

If something works under bad conditions, it will work under improved conditions.

E.g. if I can run at least 15 km/h, I can also run more than 10 km/h.

What's this principle (perhaps fallacy) called?

>>8504490
>What's this principle (perhaps fallacy) called?
Beats me, but my problem is that I don't understand why one method of solving the problem is the "improved" version. Though I do see why the second problem is more complicated of course. It reminds me of doing second order equations where you'd have a function y(t) ay''+by'+cy and write a quadratic equation with ar^2+br+c then solve for r, which was then used in an e^rt shaped solution, but I don't totally see the connection.

> if I can run at least 15 km/h, I can also run more than 10 km/h.

I think you got your example wrong if it was meant to be an example of a fallacy. If I can run at least 15 km/h, then I can run 15 km/h. 15 km/h is faster than 10 km/h. Since 15km/h is faster than 10km/h and I can run at 15 km/h, I can run faster than 10km/h. Saying you can run faster than 10km/h is just a less specific way of saying you can run at 15km/h, so that's valid, not fallacious.

>>8504277
Since I got another reply I'll just let this be the next SQT, sorry for not having the acronym in the title.

Also the solution to this problem is wrong, if you actually take the first equation they write with the r's and separate the variables, you get another lambda on the second term of your Xr equation. If you were to change the T' in the second term of the first equation to a T, then you'll actually get the same X equation. I'm pretty sure the original problem was supposed to be uxx+ux+ut=0.

>>8504548
Yes, but the principle, if it has a name, might be fallacious. For example if you get sick.
0mg dose of antibiotic will kill you.
1000mg dose will heal you.
100 000mg dose will kill you.

I just need a name for this principle or fallacy.

>>8504693
sounds like inproper use of the law of excluded middle

>>8504490
Engineering

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Why is the limit negative infinity, /sci/?
I've tried using 1+h to help me :
[math]\frac{(1+h)2-5(1+h)+2}{|1+h-1|}[/math]
[math]\frac{1+2h+h2-5-5h+2}{h}[/math]
[math]\frac{-3h+h2-2}{h}[/math]
[math]\frac{-3h}{h}+\frac{h2}{h}-\frac{2}{h}[/math]
[math]-3 + h - \frac{2}{h}[/math]
Now as h->0 so that (1+h) approaches 1, should not the 2/h approaches 0 [I believe there is something that says this] too and then the answer be -3? I fail to understand limits when it comes to this.

if h goes to 0 then 2/h is getting very large because it has a small denominator

>>8505162
Thanks, anon. I just saw that I mistook
1/x x-> infinity to 1/x x->0

Function round(x) round's off the number to some number of fractional digits.
Is the following true:

round(x) + round(y) = round(x + y)
round(x) - round(y) = round(x - y)

>>8505151
Lets do the limit from the left. Let e be an infinitesimal. The limit evaluates to:

-2/l1-e -1l = -2/l-el = -2/e = -infinity
from the right
-2/l1+e-1l = -2/lel = -2/e = -infinity

>>8505172
Counterexamples for rounding towards integers
>round(x) + round(y) = round(x + y)
x=y=0.5
>round(x) - round(y) = round(x - y)
x=1, y=0.5
counterexamples for every other number of fractional digits can be obtained by dividing x and y by powers of 10

>>8505180
Why just -2 in the numerator?

>>8504693
http://rationalwiki.org/wiki/Continuum_fallacy


This to me seems most like it. I generally don't think learning the individual names of different fallacies is relevant.

I would just call it 'nonlinear effect' or 'discontinuous function'

>>8505196
Okay thanks. How about with floor(x) or ceil(x)?
Function floor(x) always "rounds" downwards.
Function ceil(x) always "rounds" upwards.

>>8505307
I don't think it will help you much to give more examples. Try to think of some yourself. It shouldn't be too hard

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what do you actually use degrees for

how do jobs work

I almost finished getting my mechE degree but I don't feel like doing anything. I really only went for it because I figured it would be easier to take a harder route and drop down into a fingerpainting BA if nessecary than doing the reverse.

Question:
Suppose that A={1,2,3}, B={4,5,6}, R={(1,4),(1,5),(2,5),(3,6)}, and S={(4,5),(4,6),(5,4),(6,6)}. R is a relation from A to B, and S is a relation form B to B, find the following:
1) SoR
2)SoS^-1

The answer is in the back but it only has the answer and I have no idea why it is what it is; in this chapter it has not yet dealt with the specifics of relations such as them being reflexive and transitive and such.
The first one is {(1,4),(1,5),(1,6),(2,4),(3,6)}
I also don't know how to use the math typing function for this place so i apologize.

>>8505678
Your school has failed you if it didn't teach you some of the basics of starting off your career. Would've been a bonus if they also encouraged/required you to take an internship, but apparently you went to a shithole.

>but I don't feel like doing anything
You are a failure of a human life. Get off your ass and start learning how to make money. This information is a Google search away. You don't want to end up like the niggers, do you?

i need help finding the limits of integration for double and triple integrals? can anyone guide me to a good source? my textbook is cancer

>>8505711
I don't know of any resources, but what issues are you having? Do you have an example?

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>>8505730
Well I have solutions for it but I have a hard time visualizing and drawing functions.

For example pic related

I have no idea why its (c).

If its possible, I want an algebraic way to solve these problems :/

Double integrals are okay but triple integrals gets pretty confusing for me. It's even harder for me to draw.

I have some medical questions that I would like answered and i figure it's kind of science related
is this the board to ask them on?

>>8505744
>Well I have solutions for it but I have a hard time visualizing and drawing functions.
Practice. For all practical purposes, there are only so many functions you need to know how to draw. Practice drawing regions, especially the 3D ones. You will get the hang of it.

>I have no idea why its (c).
First, you should see that you indeed need a triple integral, but they just evaluated a little bit of it. The triple integral would be:
[eqn]2 \int_{y = -2}^{2} \int_{x = 0}^{\sqrt{4 - y^2}} \int_{z = 0}^{4 - y} dz\, dx\, dy.[/eqn]
So, first we're integrating in the z direction. Note that the limits of integration for the first variable should always be functions in terms of the other two variables!
Now that we've integrated in the z direction, we're done with the z-axis. Get rid of it. Project your region onto the xy-plane. In this case, the projected region is a circle. (It doesn't apply in this problem, but algebraically you want to set z equal to a constant (usually 0) such that you end up with the projected 2D region). The projected region is described by the function x^2 + y^2 = 4. We want the limits in the x direction, so rewrite this in the form [eqn]x = \pm \sqrt{4 - y^2}[/eqn].
So, x will go from that negative square root to the positive square root. But a circle is symmetrical, so we can just go from zero to the positive square root and multiply by 2 (this only works because we're finding the volume; if you're integrating some non-constant function, this may not always work). Notice, again, that the limits of integration for the second variable are functions in terms of the final variable.

>>8505744
Just imagine it's your usual triple integral and do the first one

Then realize it's symmetric over the y-axis so you can just cut the 2D region in half and multiply by 2

>>8505815
Finally, y. One way to think of this is to do the same thing we did previously. Project the 2D region onto the y-axis. You will get a 1D region that spans y = -2 to y = 2. Algebraically, this means setting x equal to some constant such that we get the correct projected region. In this case, we can just set x = 0. This gives us y^2 = 4, or y = plus or minus 2. The limits of integration of the final variable should always be constants.

>>8505679
looks like you want to find all pairs that look like
(b,c) (a,b)
which can be written
(a,c) as the composition

so for 1) you have
(4,5)(1,4)=(1,5)
(4,6)(1,4)=(1,6)
(5,4)(1,5)=(1,4)
(5,4)(2,5)=(2,4)
(6,6)(3,6)=(3,6)

and for
2)

(4,5)(4,5)^-1=(4,5)(5,4)=(5,5)
(4,5)(4,6)^-1=(4,5)(6,4)=(6,5)
(4,6)(4,6)^-1=(4,6)(6,4)=(4,4)
(4,6)(4,5)^-1=(4,6)(5,4)=(5,6)
(5,4)(5,4)^-1=(5,4)(4,5)=(4,4)
(6,6)(4,6)^-1=(6,6)(6,4)=(6,6)
(6,6)(6,6)^-1=(6,6)(6,6)=(6,6)

so SoS^-1={(4,4), (5,5), (5,6),(6,5) (6,6) }

>>8504277
Anyone have any good references on gauge theories.

>>8505845
This still doesn't really make sense to me, I can SEE where you got those, but for the first one why isn't the combination (4,5)(2,5)=(2,5) considered? There a few others but I'm just using that one for an example, it just seems random why some combinations are chosen and some aren't.

>>8505912
A relation just assigns one number in one set, with another number in another set. We're told that R maps A to B (so it takes a number in A and produces a number in B), in particular we're told that [math] R(1) \to 4 [/math] so applying R to the first element in A, produces the first element in B. When you have [math] S \circ R [/math] apply the relation [math] R [/math] first, so since R takes an element in A and produces and element in B we get [math] R( A_1 ) \to B_1 = (1,4) [/math] my notation here is non-standard (and I think most people would say abusive) but I'm hoping it'll help you understand. Now we have that we apply [math] S ~~ S ( R ( A_1 ) ) \to S( B_1 ) [/math] but [math] S ( B_1 ) \to 5 [/math] we can write this out in a chain [math] R ( 1 ) \to 4 ~~ S ( 4 ) \to 5 [/math] So we have our result [math] S \circ R = (4,5)(1,4) = (1,5) [/math] Now do the same for the rest.

Has that helped or made it worse?

How to ID sodium bicarbonate besides titration? Undergraduate chem student asking, apparently a new chem prof is suspected of making a meth lab with stolen lab equipmemt, recently there was a fire in his garage and possible baking soda was found there (for purification most likely), deadass. Crime lab is letting one of my classes test the stuff, need to confirm its baking soda

>>8505943
After reading this a few times and working with that chain process yes I finally see why this is so.
At first I was merely looking at it as (a,c) and cartesian crossing A and C, thus taking {1,2,3}X{4,5,6} and finding all ordered pairs. But the way you showed makes more sense since they seem to work the same as functions, as if it was S(R(x)). Thank you.

>>8505805
...I guess it isn't.

>>8505976
>they seem to work the same as functions

They're [math] like [/math] functions, in fact all functions are relations, but the converse is not true.

>>8505976
A function is a relation where
<a,b>∈f and <a,c>∈f => b=c
i.e. a function can only have a single value for any given argument.

>>8505818
Holy shit dude.

You are amazing.

I think I understand it.

Thanks a lot!

>>8505815
Actually but lets say you are given two functions of z?

Like this question z = 1-x^2, z=1-y^2 , x = 0 , y= 0 , z =0, first octant

>>8505805
>>8505981
don't ask to ask you brainlet

What does "inference" mean in a probability/stats context? Also what's variational inference / approximate inference?

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I've been doing trigonometry because I am 23 and I've been forgetting. Is the answer to this supposed to be 2? Please help I am a brainlet.

>>8506465
[math] 2\sqrt2 [/math]
good way to remember is if a = b, c = root(2) a
4 / root(2) = 2root(2)

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>>8506473
Thank you.

How do I become a meme scientist?

How can I generate square wave with DC supply (without a LM555 op-amp)?

>>8506510
do a phd in deep leanring

not sure if this is best place to ask this but I need to specialize soon for my EE major and was wondering which might be best if I wanted to get an aerospace or defense job and which might be best for a job at tech companies. I've narrowed down about 4 im interested in:
Communications/Signal processing
EM fields and optics
Electronic Design
And energy and power systems

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>>8505948
Sodium bicarbonate for purification? I dunno maybe just react with any acid and look for formation of CO2

>>8506465
>>>/b/

If you can't figure this out yourself, you are a brainlet. There's nothing here for you

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Question 74 to 77. Why not use a LU decomposition ?

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I have a bunch of disodium inosinate.

Is there a cheap way of converting it to free acid?

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How the fuck do you learn this? I don't understand how they got to this result

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Reading first Feynman book cos how hard can it be.

He mentions something off-hand and I just can't figure it out. "[math]\frac{v^2}{c^2}[/math] differs from 1 by in part in 4 million".

He then states offhand "or [math] c - v = \frac{1}{8000000[/math]" with no explanation. I just cannot show it algebraically.

[eqn]1 - \frac{v^2}{c^2} = a[/eqn]
[eqn]c^2 - v^2 = ac^2[/eqn]
[eqn](c - v)(c + v) = ac^2[/eqn]

Somehow gets to

[eqn]c - v = \frac{a}{2}[/eqn]

Is he using some unspoken approximation like a binomial expansion or something?

>>8506973
you can use whatever you want in practice, this textbook just asks you to use determinants

>>8507116
[math]c[/math] being the speed of light I'm guessing?

He may just be referring to a particular velocity (which in this case would have to be [math]v=2c^2-c[/math]).

>>8507116
c^2-v^2=ac^2
(c+v)(c-v)=ac^2
c-v=ac^2/(c+v)=a/2
Therefore:
c^2/(c+v)=1/2
2c^2=c+v
2c^2-c-v=0
c=1+sqrt(1+8v)/4
c=1-sqrt(1+8v)/4
c^2=[1+4v+sqrt(1+8v)]/8
c^2=[1+4v-sqrt(1+8v)]/8
1-8v^2/(1+4v+sqrt(1+8v))=1/4000000
1-8v^2/(1+4v+sqrt(1+8v))=1/4000000
4000000-8v^2/(1+4v+sqrt(1+8v))=1
4000000-8v^2/(1+4v-sqrt(1+8v))=1
3999999=8v^2/(1+4v+sqrt(1+8v))
3999999=8v^2/(1+4v-sqrt(1+8v))
3999999+15999996v+3999999sqrt(1+8v)=8v^2
3999999+15999996v-3999999sqrt(1+8v)=8v^2
You could go on to solve this for v, to verify the statements. I was just kinda bored and I have no context so I'm not sure if it's worth it.

>>8507143
>000
You can't add c^2 and c, they have different units. Also, no speed can exceed c.

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>>8507143
>>8507158

The context is that the relativistic momentum is related to the Newtonian by
[eqn]p = mv = \frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}[/eqn]
and that experimentally was found to be 2000x higher than expected by Newtonian mechanics
[eqn]m = 2000m_0[/eqn]
[eqn]1-\frac{v^2}{c^2} = \frac{1}{4000000}[/eqn]
Then, he simply states cryptically, "or"
[eqn]c - v = \frac{1}{8000000}[/eqn]

The next paragraph down he states an approx. expansion that may be related, it suggests where the 1/2 may come from:
[eqn]m \approx m_0 + \frac{1}{2}m_0v^2(\frac{1}{c^2})[/eqn]

I can't see the wood for the trees.

What sort of jobs can I get with a BSc in Math?

>>8507190
[eqn]m \approx m_0 + \frac{1}{2} m_0 \frac{v^2}{c^2}[/eqn]

>>8507116
> Is he using some unspoken approximation
Yup. If you evaluate v=c*sqrt(1-1/4000000) numerically, you'll find that (c-v)/c = ~1/7999999.5

If you have
1/b=(c-v)/c
1/a=1-v^2/c^2
and solve it algebraically, you end up with b=a+sqrt(a^2-a) which, for large a, approximates to b=2a.

Okay. This makes no sense. Why would you multiply propellant mass flow rate by time to find the final mass?

>>8507207

Thanks, I knew it had to be something simple cos I was going in circles and it was only an anecdotal aside in the text.

Stupid question: I'm running a logistic regression model with an interaction term. I have the main effects model and the interaction model. The Pseudo R square did not change. Is it supposed to change if the interaction was an improvement?

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>>8504277
I have "Fundamentals of Analytical Chemistry" (Skoog) and I'm retard, help

n is a natural number
f is a real number in range [0, 1] inclusive.

I need to know if any of the following can be nagative:
n - floor(n * f)
n - round(n * f)
n - ceil(n * f)

>>8506820
no brainlet shaming in SQT

>>8504277
Brainlet here. I'm reading in my algebra textbook about integer notation, and it states that the notation (a,b) include all real numbers in between, but does not include the endpoints; however, the notation (a,∞) includes all real numbers, not including a, to infinity.

If the notation is (a,∞), then wouldn't that mean some number would not be included in the infinite list of real numbers? I heard something about the 1/12 thing, and I know that infinite numbers have no end, but by the very definition that I was given for the notation, the ')' means that it includes every real number until that number.

>>8507560
> n is a natural number
> f is a real number in range [0, 1] inclusive.
=> n*f <= n
floor(n*f) can only be equal to n if f=1, otherwise it will be less than n.
round(n*f) will be equal to n if n*f>=n-1/2, otherwise it will be less than n.
round(n*f) will be equal to n if n*f>n-1, otherwise it will be less than n.

I.e. floor(n*f), round(n*f) and ceil(n*f) will always be less than or equal to n, and n minus those will always be greater than or equal to zero.

>>8507612
Thanks anon.

>>8507590
> If the notation is (a,∞), then wouldn't that mean some number would not be included in the infinite list of real numbers?
It excludes numbers less than or equal to a, and excludes infinity. It doesn't exclude any finite real number greater than a.

Basically, (a,b) means all x satisfying a<x<b, while (a,∞) means all x satisfying a<x. I.e. specifying the upper bound as infinity means that there isn't any upper bound. Similarly, (-∞,a) means all x satisfying x<a, i.e. there isn't any lower bound.

>>8507612
> round(n*f) will be equal to n if n*f>=n-1/2, otherwise it will be less than n.
> round(n*f) will be equal to n if n*f>n-1, otherwise it will be less than n.
That last one was meant to be ceil(n*f)

>>8507590
It's just a notational quirk. There is no real number called "infinity." Chances are, your textbook does not rigorously define infinity, and they explicitly the defined the notation (a,∞) as "all real numbers x such that x > a." Always follow how the notation is explicitly defined. Don't let your intuition fuck you over.

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>>8506108
The general strategy is to imagine an arbitrary ray going through your region parallel to one of the axes. The limits of integration for that dimension will be the surface the ray enters through and the surface it exits out of. In the problem you gave, I started with the y direction. Any given ray (in green) will enter the region through the plane [math]y=0[/math] (aka the xz plane) and exit through the surface [math]y=\sqrt{1-z}[/math]. So the innermost integral will be [math]\int _0^{\sqrt{1-z}}\:dy[/math]. Now that y is taken care of you project the region onto the xz plane (figure on the right). My professor called this the 2D "shadow" of the original 3D region. You said you're okay with double integrals so I'll just jump to the end and say the final integral will be [math]\int _0^1\int _0^{1-x^2}\:\int _0^{\sqrt{1-z}}\:dydzdx[/math].

Note that I didn't do [math]dz[/math] first because there is no ray that will work for the entire shape. For half it will enter through the xy plane and exit through one of the parabolas, and the other half it will exit through the other parabola. Which means if you really wanted to do z first you'd need to set up two separate integrals and add them together.

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I need help for this question
My system of Differential equations has its coefficient matrix as a 2x1 matrix instead of a square matrix.

How do I find the eigenvalues/vector for this question?

I don't get it

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>>8507555
guys...
help ;_;

>>8507670
That's a 2x2 matrix: [[-16,21],[-14,19]].

>>8507700
oh shit lmao. thanks senpai

What is the definition of a harmonic wave? I can't seem to find it on Google or my text book. Please respond

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Going fuckin full here
To solve the nullspace of the given matrix, first I rref it to solve [math] A\vec{x}=0 [/math]. Then the rref tells me [math] x_2, x_3, x_4 [/math] are all zero, but how the fuck do I get that [math] x_1=1[/math]?

(answer is NS(A) = <1,0,0,0>)

>>8507972
protip, nullspace is a subspace

it doesnt matter which x1 you pick

i read some research papers and implemented them into scripts and programs that i wrote as side projects

whats the best way for me to put that on my resume? so far i have:

>_____ Classifier/Clusterer

>Implemented semi-supervised algorithm (as explained by Franklin et al.) in order to find the ______
>Live demo available here: [link to live demo here]

i feel like i should have a link to the research paper as well..

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Why do law students all think they're going to make so much money? Like, more money than math majors?

Surely they have the IQ to recognize that the field is oversaturated with shit-kicking paralegals, and even attorneys.

Help me understand this.

I have Un and Vn sequences defined as the sum from k=1 to n of Vk is equal to the sum from k=1 to 2n of Uk.

I need to show that the series coming from Uk and Vk have the same limit.
Obviously it's because when n is infinite, then 2n is infinite too, so they are "equivalents" but I feel l miss something.

How much of the estimated energy content in the universe is EM radiation?
How much gravitational influence does EM radiation have on cosmological scales? Surely not negligible since it contributes to energy density?

>>8508418
> I have Un and Vn sequences defined as the sum from k=1 to n of Vk is equal to the sum from k=1 to 2n of Uk.
> I need to show that the series coming from Uk and Vk have the same limit.

Proof of a limit requires showing that
1. for any epsilon>0,
2. there exists an N such that
3. for all n>N, the sum to n terms differs from the limit by no more than epsilon.

Clearly if #3 holds for Uk for some N, it also holds for Uk for N/2 (the converse isn't true because the odd terms may be "worse" than the even terms).

>>8508573
Thanks. I knew it was true, but I wasn't very rigorous about it.

>>8508240
They are not as smart as you think. Law majoring is a meme created by a inefficient state. Occam favoring everything would end with the automatic judicial system

>>8504277
>How do you know to place these Rs into this problem?

You assume the harmonic solution because the product of transpose matrices equals 0.

Could someone draw a flowchart for doing Fourier series problems? Every time I look at explanations I'm never sure how much of the stuff used is considered pre-proven that you pull out from memory vs assumed due to form vs actually deduced.

>>8504490
Transitive relation
X > 15 & 15 > 10 -> x > 10

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>>8504277
Okay so this year I studied so fucking hard I got a scholarship to Japan, I'm starting uni in Japan april next year (actually prer year, year after that I apply to 7 unis, going for todai and TIT).
The thing is I haven't touched a book since june (After my exams, hardest exams of my life) and I feel fucking retarded, also I smoked a lot of weed this year, even while studying and I've got memory problems it seems.

How do I get back on track before april?
I kinda wanna review 90% math, phys and chem are easy. Any advice? Sorry for asking for handholding I just feel fucking retarded and lost right now even though last week my scholarship got confirmed.

>>8504277
Will someone explain the controversy surrounding the axiom of choice? I don't really see how it could be argued.

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I have a multiplication like this:

(a-(b-c))*tg(x)

How do I transform that to contain only addition? I know that I should use Taylor/Maclaurin series, but can't figure out how exactly

Simplify SQRT(11-4*SQRT(7)) to the form SQRT(n) - m, where n and m are natural numbers.

Sorry for formatting, I'm on phone.

>>8509319
square both sides, work backwards

>>8509247
what do you mean 'how it could be argued'?

>>8509325
I'll try that tomorrow, thanks.

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Can someone help me understand what exactly they're doing to the numerator to manipulate it? I can't follow it the way they have it written.

If Phi is an isomorphism from a group G under addition to a group G' under addition, prove that for any integer n, the mapping from G to G' defined by π(x) = nPhi(x) is a homomorphism.

>>8509400
it looks like you want to write the numerator s/2+5/3 in the form a(s+2)+b for some a,b

so you add 0:
s/2+5/3
=s/2+0+5/3
=s/2+(2/2-2/2)+5/3
=(1/2)(s+2)-2/2+5/3
=(1/2)(s+2)-6/6+10/6
=(1/2)(s+2)+4/6
=(1/2)(s+2)+2/3

>>8509408
pi(x+y)=nphi(x+y)=n(phi(x)+phi(y))=nphi(x)+nphi(y)=pi(x)+pi(y)

>>8509417
Thanks a bunch. I'm a big dummy.

>>8509408

Actually I think I got this.

Let a,b € G then π(a+b) = nPhi(a+b) = n(Phi(a) + Phi(b)) = nPhi(a) + nPhi(b) = π(a) + π(b) therefore π is a homomorphism.

Correct?

>>8509420

Yep thanks I just got it and answered below right after you. It looked harder then it was.

>>8509425
>n(Phi(a) + Phi(b)) = nPhi(a) + nPhi(b)
this is the only step that requires some justification

>>8509327
As far as I understand it, the axiom of choice is just the statement that the product of two non-empty sets is non-empty, which seems so obvious that it's not even worth stating, yet people argue back and forth about it.
It's like arguing against an integer plus an integer equaling an integer. Based on the way that the terms are defined, there's no other answer possible.
So why is there controversy around it?

>>8509537
>So why is there controversy around it?
because you can't prove it, which is why it's an axiom

and because a LOT of proofs rely on it, without any obvious way of getting around it

and because it leads to some results which seem 'non-intuitive' (i.e. banach-tarski)

can somebody please tell me why light is slower in a medium?

i know it's not actually because photons get absorbed and new ones emitted.

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Hey can someone help me with this problem my friend is telling me that it is a) but hes a fucking brainlet and would like some other input

>>8509606
The speed of light is a constant, so each photon is moving at the same speed.

Therefore, the photon following the shortest path length reaches the image first.

Therefore, the answer is b.

:^)

>>8509552
Banach tarski is not unintuitive. Only the oversimplified caricature which most people hear about is unintuitive.

>>8504277
← portion in red is incorrect, should be
[math] \frac{X_r''}{X_r'+X_r}[/math]
...why does TeX preview not work?

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>>8509625
...image-attach not working, either

If you had sex with a gender swapped clone of yourself and the ensuing child was carried to term, would the child be a clone as well?

>>8509613
But doesn't it go through the thickest part of the material or does that not matter

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How do I have sex?

>>8509645
You go boosh boosh pow until you skadoosh

>>8509537
The other anon is correct, in that some strange things happen when you accept the axiom of choice, but there are other issues too, and historically the other issues were what led people to deny it.

One of the common patterns of using the Axiom is that you assert something exists without specifying it. Not only do you never define a particular object, sometimes you CAN'T define the object, and in many cases these objects are hard to believe in, like a well-ordering of R for example.

The bone they pick is basically that you can pick things without being able to say how you did it.
The reason it seems "obvious" to you is that you're likely using either a finite analogue in your head, or at most a countably infinite analogue, and in these cases picking an arbitrary element is easy.

Let's look at your example: AxB is non-empty, and both sets are uncountable. What's inside? An ordered pair (a,b)? What is b? You can't pick the first element of B (there isn't one) or the largest or smallest. There's no way at all to say in general which element from B is in there; you need a choice function to do it's voodoo for you and remove the "how".

>>8509631
>gender swapped clone of yourself
Then it's not a clone.

So I need to prove that the series of general term :
[math]\sqrt{\frac{Log(n)}{n}}[/math]
converges by using comparison criteria.

Log n < n for any n >= 1
(Log n)/n < 1
Where do I go here ?

>>8509696
You're going to have a hard time proving it converges, because it doesn't.

ln(n)/n > 1/n for most numbers and you can probably show that sqrt(1/n) does not converge.

>>8508498
Please answer.

Let [math]a(x)=4x^4+2x^3+6x^2+4x+5[/math] and [math]b(x)=3x^3+5x^2+6x[/math] be polynomials in [math]\mathbb Z_7[x][/math]. Use irreducible factors to find the GCD of these two polynomials.

Any help is appreciated.

>>8509775
>Use irreducible factors to find the GCD of these two polynomials.
No.

>>8509537
You've got it wrong, the product of *two* non-empty sets is non-empty. That's provable without the axiom of choice. Stuff happens when you consider Infinite products, since a proof is a finitary object, you need a way to uniformly pick elements in each set. That's what the axiom of choice provides.

Also, nobody "argues" about it, except math undergrads. It's independent from ZF, meaning you can work with it, without it, or with its negation, and remain consistent. You get three mathematical settings which are all equally interesting, picking one is just a matter if what you wanna do, there's no personal opinion involved

>>8509695
You seem to be mixing up choice and excluded middle

>>8509775
theres hardly anything to check brainlet

look for roots and start factoring

>>8509844
Isn't there something special about this problem since the polynomials are in [math]\mathbb Z_7[/math]?

Why is this board so fucking dead?

I have like 20 goddamn tabs open and nobody posts anything for hours at a time. Talk, faggots!

>>8509855
what do you mean something special?

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can someone help me solve the last part?

>>8509775
Factoring gives:
4(x + 6) (x^3 + 5x^2 + 3x + 4)
3x(x + 5)(x + 6)
Thus their GCD is x+6

>>8509939
Conservation of energy:

- Kinetic energy
- Potential energy wrt earth's gravity
- Potential energy wrt moon's gravity

The sum of those three is the same at launch and impact.

>>8509632
They will all arrive at the same time. The refraction coefficient is governed by the path that will take the shortest time for the photon to travel. The speed of light through the material is less than the speed of light in a vacuum, so the path length changes but the travel time doesn't.

Look up Fermat's Principle if you want to know more.

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>>8504277
I work in a restaurant.
One of the prep cooks in the kitchen was microwaving a dessert for me to bring to a table.
This bitch...this bitch stuck her face directly against the front panel of the microwave.
How long would she have to do this (assuming a 1200 watt microwave) to get any real damage to her eyes, brain, etc?

>>8510194
Aren't microwaves encased in a Faraday cage specifically to prevent dumbasses like that from dying?

>>8510215
I thought so too, but I can't imagine it would be 100% effective at blocking retard-harming microwave radiation?

How much would it affect life on Earth if everything outside the solar system just stopped existing?

>>8510235
if it stopped existing now, nothing happens. if it would have stopped existing billions of years ago we wouldn't exist

anyone here gud at matlab?

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If there was no friction and you drop these two balls simultaneously, will they reach the ground at the same time?

How do I derive the partial sum for n(n+1)? Apparently is 1/3 * n(n+1)(n+2). Can I prove it without induction?

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Can someone explain me how to understand these results? Like I have no clue how they derived the second last one, so I just memorize it but I prefer to understand them if possible but can't find any explanations online

>>8510424
No, the ball on the right has to travel further to reach the ground

What would be the venn diagram of the set:
~AU(BUC)
I'm still trying to get my head around how they work and it's confusing as fuck.
I.E. sometimes universal will be included in the result, and sometimes it won't, but I can't see a pattern which denotes when it will and won't be included.

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>>8510628
pic related
what the fuck

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The Binary Star system is moving away correct? We can say this because the frequency is on the lower range, right?

>>8504277
ok lets say g is a primitive root mod p, an odd prime, and we wanna solve g^x = a(mod p). Let's say I use the following approach.

First, I find (a/p) [a LEGENDRE p], and by doing this I find the parity of x.
If x is even, rewrite x as 2x and take a square root on both sides, then go back to the first step
If x is odd, multiply both sides by g, and write x+1 as 2x, and take a square root of both sides and go back to the first step

What are the flaws, if any, with this method?

why does a partially ordered set have to be reflexive?

>>8510194
The mesh over the glass should completely block the microwaves. Even if it doesn't, it won't damage the brain. Microwaves aren't ionising radiation.

The main risk from microwaves is eye cataracts; the cornea is a fairly good insulator and doesn't have a blood supply, so heat generated internally can't easily escape.

>>8510781
It's defined like that

>>8510424
No. The impact with the slope will convert some of the ball's downward velocity into sideward velocity. Energy is (at best) conserved, so after the impact the ball on the right will have less downward velocity than the ball on the left, meaning it will take longer to reach the ground.

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>>8510628
see pic for ~AU(BUC). (it's from wolframalpha)

A and B doesn't include universal
not A and not B does because universal is not in either

>>8510631
universal is not in C or A or B so it is included

however if this was C and ~(A or B) it would not because C does not include universal and "C and ~(A or B)" only includes C

>>8510799
that's what I thought... thx

>>8510803
adding to this to mb make it simpler..
if you're not limiting to A or B or whatever, then universal does include

~A or ~B does not limit to either A or B but to whatever is outside A or B

>>8510560
Just expand it out.
(B.x)[r] = sum[i](B[r,i]*x[i])
x^T.B.x = sum[j](x[j]*(B.x)[j])
= sum[j](sum[i](x[j]*B[j,i]*x[i]))
If x[i] changes to x[i]+d, x^T.B.x changes by
sum[j](x[j]*B[j,i]*d) + sum[j](d*B[i,j]*x[j])
= sum[j](x[j]*B[j,i]*d) + sum[j](x[j]*B[i,j]*d)
= sum[j](x[j]*(B[j,i]+B^T[j,i])*d)
= sum[j](x[j]*(B+B^T)[j,i])*d)
= d*(x^T.(B+B^T))

>>8510631
Draw what you think each of
~C
A ∩ B
~(A ∩ B)
should look like.

>>8510628
>>8510631
The universal set is the whole thing, the part you seem to be calling "universal" is ~(A ∪ B ∪ C).

How much programming should you know before you apply for coding jobs?

I've taken a couple of classes in C and C++ on my way to becoming an EE. Wondering if that's marketable yet. Hoping to get a better paying job than dishwasher to help pay for school.

Can anyone help me with designing a p-n junction for a homemade betavoltaic cell? Or at the very least, point me to some good reading on the topic?

I can't find anything about construction in particular -- but I'm thinking about a simple silicon wafer stack (cheap online), you can buy both p and n doped wafers for a fair price. I understand that this style of cell has problems such as charge-carrier depletion over time, but I don't want it to power anything, just want to see if I can create a voltage using tritium beta-emissions.

>>8508498
>How much of the estimated energy content in the universe is EM radiation?
How much gravitational influence does EM radiation have on cosmological scales? Surely not negligible since it contributes to energy density?
Please answer this simplistic question, thank you.

>>8510902
There isn't much of a market for lightly-skilled C/C++ programmers.

If you need programming work soon, it would probably be faster to learn a Pajeet-tier language like PHP or JS than to improve your C/C++ skills to the point that you're employable.

Mediocre PHP/JS programmers are employable, although I wouldn't assume that it pays better than dish-washing.

>>8509325
It didn't work. I have an expression, not an equation, so I can't square it.
Anyone else have any ideas?

>>8511058
I figured it out, nevermind.

>>8511058
x = sqrt(11-4*sqrt(7))
=> x^2 = 11-4*sqrt(7)
=> 11-x^2 = 4*sqrt(7)
=> (11-x^2)^2 = 16*7 = 112
=> x^4-22*x^2+121 = 112
=> x^4-22*x^2+9 = 0
=> (x^2-4*x-3)*(x^2+4*x-3) = 0
x^2-4*x-3 = 0 => x = 2±sqrt(7)
x^2+4*x-3 = 0 => x = -2±sqrt(7)

i.e. sqrt(7)-2

Is calculus just the formula monkey version of real analysis?

>>8509729
Thanks. Didn't know why I thought it would converge.

>>8511005
Thanks!

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1,5 < I < 2,3,

Should I just work it out with the reduction formula, and hit everything under exponent of 3/2?

If you're in a weightless environment and you have two boxes filled with materials of different densities, how do you find which one is denser? Say you're on a spaceship or something.

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>>8511455
They both have a density of zero because they both have a weight of 0.

sqrt(11-4*sqrt(7)) = sqrt(n)-m
square both sides...
11-4*sqrt(7) = n-2*m*sqrt(n)+m^2
n+m^2=11
2*m*sqrt(n)=4*sqrt(7)
n=7
m=2

>>8511455
Density is mass over volume, not weight

>>8511506
Meant for>>8511474

If you want to prove that the series of general term Un converges, can you prove it by saying that something superior as -1*Un converges too ?
(Un > 0 for all n.)
Doesn't look right to me.

>>8511266
Have you tried Mr. Euler and/or changing variables ?

how do i split up the limits for this
[math]\int_{0}^{1} \int_{0}^{1} \int_{0}^{min(1,\frac{b^2}{4c})}da\,db\,dc[/math]

>>8510916
There's a book on semiconductors online for free in PDF form just search google. I think it's just called "semiconductors", can't remember the author. It's a legit textbook though.

Does the median have a continuous analogue?

This is something I've been wondering for a while. I know that visible light is spectrum of wavelengths of light and that violet light is around 400 nm in wavelength. However if you took red (700 nm) light and blue (475 nm) light and made what we perceive as purple is that a true 400 nm wavelength of light? Does the light energy mix together to make that 400 nm light?

If it isn't, then how do we know that any purple colored light is truly 400 nm or just very tiny amount of red and blue mixed to look purple? I already understand that red and blue make purple is sort of a trick our eyes do because of how the way the cones in our eyes perceive light.

>>8504277
Should I take a C programming intro courses or Data Structures in C++ (already experienced in C++) next term? I only get to fit one more class in

>>8511608
I'd do data structures, personally. Intro programming classes tend to start with the absolute basics- you'll spend the first half of the term bored.

>>8511639
good point

>>8511608
Absolutely take data structures. You don't need to take a programming course if you already know a language. Start learning actual computer science.

>>8511560
Light doesn´t mix like that, that is, when two photons of different wavelengths come close, they don´t mix to make a third with a middle wavelength. In general photons don´t interact with each other, save for QED loop corrections which result in nonlinear optical effects, but these are too rare to observe readily.

EE undergrad here. Can't decide between minoring in math, physics, or CS.

Any EE grownups have any insight?

>>8511550
Informally speaking, it would be the point you integrate to to get half the total integral.

>>8511769

An EE with a minor in CS tells employers that you likely:

1) substituted programming in C++/C in the EE department for one (or two) Java class(es) focused on making GUIs rather than solving problems
2) substituted vector calculus based probability and random processes course(s) with an 8th grade algebra based course on discrete probability that's barely better than "probability for business majors"
3) substituted the detailed EE/CpE computer architecture course for a CS computer organization class that spends 1/2 its time on C, 1/3 of its time on flipflops and logic gates, and only 1/6 on any computer architecture
4) took a watered down CS Discrete Math course rather than the more richer CpE's DM or Math Proof courses
5) took a weaker data structure class than CpEs do and again in Java rather than C/C++
6) took a superficial CS Numerical Methods class which doesn't require DEs over the thorougher and more useful math departments' Numerical Analysis course

Honestly, it's a minus rather than a plus on your resume.

>>8511836
Are there really schools where you can substitute classes out like that? At mine, your major degree track is fixed. If you want to minor in something, you're taking like six extra classes on top of the normal load.

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>tfw talking a class on [math] \mathbb{A}^1 [/math] homotopy theory next semester
am i gonna make it?

>>8511455
Spin each one in a circle about its center of gravity. For the box that has denser material, more mass will move away from the center, which will increase the moment of inertia.

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what are the pre requisites for this book

https://www.amazon.com/gp/product/0071226613

>>8504490
Your example is not a fallacy.
I can run >=15km/h
therefore i can run > 10km/h
run>=15>10 both are true

now if you were trying to say that you can run at any speed >10 that is where fallacy occurs
run>=15 >>known
since world is not continuous and is quantized
you do not know you can
15>run>10 >>unknown

Also, your statement is not a fallacy.
The definition of improve is to make better.
Improving conditions guarantees that an already working thought, principle, item, ect will continue to work.
It would be a fallacy to say that improving conditions would improve the work, because improving conditions could improve quality, cost, speed, ect meaning that the idea of improved work changes. Your idea of improved work may mean that the quality of your works increases, but your boss's idea of improved work might mean that you put out a greater number of works.
Number of works != Quality of works

Name of fallacy.... I forget
:p

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>>8511520
I have tried changing variables. But I cant get out of the square root.

>>8504277
This looks like a relatively straightforward SLP. U in this case is a function corresponding to either position of a vibrating string or the heat in a finite rod. They are using a standard separation of variables approach. What specifically is confusing you here?

>>8512237
As for the ri they are the roots to the SLP shown in the time independent variable separation. Were you not given boundary conditions?

>>8512145
>His classic book Probability, Random Variables, and Stochastic Processes[2] is used as a textbook in many graduate-level probability courses in electrical engineering departments all over the world
>Two classic texts aimed at [engineering] practitioners were [first] published in 1965... [One was] Athanasios Papoulis' Probability, Random Variables, and Stochastic Processes... These books popularized a pedagogy that balanced rigor and intuition.[3]
>https://en.wikipedia.org/wiki/Athanasios_Papoulis

Vector Calculus and being mature.

I'm starting a 6 week linear algebra course in a months time, what should I read up on?

>>8512255

What kind of linear algebra course is it

>>8512256
https://handbook.unimelb.edu.au/view/2015/MAST10007

>>8512257
It's the standard matrix algebra course. You don't need much more than pre-calculus for that.

Maybe read up on proofs and proofs by contradiction if that's new to you.

>>8512211
cos^2 + sin^2 = 1

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>>8512274
lol. And I stayed almost all night wondering out what I was missing out...

>>8512295
Not here though. We have cos^2(2t) + sin^2(t), so a few more transformations are needed

Basic statistics: I want to find a random variable WITH expected value, but WITHOUT variance.

I realized that reduces to finding a variable X with [math] EV(X) [/math], but no [math] EV(X^2) [/math]. I that reduces to finding [math]f(x)[/math] such [math] \int_{-\infty}^{infty} x * f(x) [\math] exists but [math] \int_{-\infty}^{infty} x * f^{2}(x) [\math] does not. Aaaaand I'm stuck. Any ideas?

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>>8512299

A "random" variable that always gives the same number (the expected value)

>>8511550
For a continuous distribution, the median is the point where the CDF is 1/2, i.e. the integral of the PDF on each side is 1/2.

>>8511560
1. Light doesn't mix like that.
2. Purple is an awkward case (it's on the opposite side of blue to red, not between them). It's simpler to consider the red+green=yellow case.
3. You can tell the difference with a prism.
4. Experiment: get a yellow LED and a tri-colour LED (red and green LEDs in one package). Adjust the currents until the light from the tri-colour LED matches that from the yellow LED. Use a prism to split the light into discrete wavelengths. The yellow LED will show a single wavelength, the light from the tri-colour LED will split into red and green.

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What's this supposed to mean? Lefthand side is a matrix and right side is a scalar. How are they equal?

>>8512447
Oh wait right side is not a scalar sorry

>>8504277
What is this probability actually saying ?

[math] P(X > x + y \, | \, X > x) [/math]

>>8512466
Looks like a conditional probability
"The probability that X>x+y given that X>x"

>>8512467
it is. thanks. just realized what i was being asked to solve

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Anyone knows how did they get to the determinant? Why is that the only solution?

>>8512519
Are you 12? It's an eigenvalue problem. That shit is common everywhere

>>8512519
M.x=0 iff either x=0 or |M|=0

>>8512519
if you want a nontrivial solution, then the columns/ vectors of the A-kI matrix need to be linearly dependent. thus their determinant is 0
aka Google eigenvalues
kisses

How to solve it?
My thoghts:
a(first factor)*b(second)=p(product)
lets add 10% for each:
(a+a*0.1)*(b+b*0.1)=p
we got: ab+0.2ab+0.01ab=p
at this point I am stack.

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>>8512629
forgot the pic

>>8512629
You done fucked up because you defined p = a*b, so p =/= (a + a*0.1)*(b + b*0.1).

Instead, define q as your new product, then substitute p wherever a*b appears.

By the way, a + a*0.1 = a * (1 + 0.1) = a*1.1.

>>8512631
21% bigger.
(a*1.1)*(b*1.1)=a*b*1.1*1.1=a*b*1.21

>>8512631
Curious, what book is that?

>>8512629
Oh, seems like I did it.
due to distributive property :
(1+0.2)ab+0.01ab=p
(1.2+0.01)ab=p
1.21ab=p
ab=p/1.21
so product will be smaller by 1.21

>>8512641
Gelfland, Algebra

>>8512642
oh, yeah, thanks guys
I have to use q(new product) instead of p
so q=1.21*p or p (old product) become 21% bigger

>>8512642
>so product will be smaller by 1.21
If each of the factors gets larger, how could the product get smaller?

Scrap it and redo.

>>8512615
>M.x=0 iff either x=0 or |M|=0
yeah but my question is how do you get there

>>8512619
>the columns/ vectors of the A-kI matrix need to be linearly dependent.
I understand now thanks

>>8512706
i meant how you get from (A-lambda.I).x=0 to |A-lambda.I|=0 but this explanation made sense "the columns/ vectors of the A-kI matrix need to be linearly dependent"

>>8512652
A.x=λ.x
=> A.x=λ.x
=> A.x=λ.I.x
=> A.x-λ.I.x=0
=> (A-λ.I).x=0
=> |A-λ.I|=0 or x=0
If you exclude x being the zero vector, you're left with the requirement that |A-λ.I|=0

What's the point of the QR decomposition?

I wanted to ask any astronomy fags about something I've seen clearly this evening

Why does unlit side of the moon look darker than post sunset sky?

I'm prety certain that ir wasnt opticak illusion created by lit side of the moon, unlit side was just black/very dark grey, while surrounding sky was deep dark blue.

couldnt find any anwser in google

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Sci, help.

>>8512744
Point 50

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what must I study to become a rare disease expert?

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>>8512744
Add the other two midpoints, P' and Q'. Join P to P' and Q to Q'. Let O be their intersection, the centre of the quadrilateral. Let X be the intersection of AQ with P'O.

Clearly, P'X=XO=(1/2)DQ.

DEQ is similar to OEX and twice its size. Thus DE=2EO. By symmetry, BF=2FO, FO=EO, FO+EO=DE=BF.

How come another human feels warm (e.g. when you're spooning a girl) when both have the same body temperature?

>>8512789
Because they're hotter than the ambient temperature which is what you're contrasting them with.

>>8512789
usualy you radiate heat out of your body to colder environment, wich feels cold/ comfortably cool depending on temperature difference
temperature of other person is higher than usual environment temperature and same as your body temperature so your body doesn't radiate as much heat out so you feel warm

also:
>>8512743
anyone?

>>8512743
Optical illusion. The unlit side of the moon is next to the lit side, which makes it look darker.

When a CRT TV is turned off, the screen is a not-particularly-dark grey colour. If you turn it on and display a chequerboard pattern, the black squares look completely black, much darker than the colour when off.

tl;dr: our vision is bad at gauging absolute intensity.

what are some useful books that will help me understand the basics of small molecules like ligands and small but essential antibiotics, things like that, like a sort of encyclopedia.

>>8512825
I dont believe illusions can be as clear and strong
I'm not saying I'm certain that you are wrong, but it looked prety clear to me, visible difference in brightnes and colour

I'll try to take photo tommorow if the sky is clear to see if I'm wrong

>>8506514
keep flicking the power switch on and off.

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What is a good formula for calculating tax rate in a hypothetical economy for a game?

A valid base formula is
y = x / (x + 1)
To add parameters min/max tax rate:
y = minTax + (maxTax - minTax) * x / (x + 1)
What about parameters for adjusting how much income is needed? Is there a better base formula?
It also needs to be integrated, so that if you transfer m money you pay the same tax as if you had transferred two times m/2 money.

The point of this tax is to discourage money hording.
Gathered tax is than used to inflate resource prices so players can profit from selling.

>>8512775
just watch house

>>8512588
no brainlet shaming in SQT

>>8512299
[math]f(x)=\delta(x-EV(X))[/math]

>>8513006
man that tax code is fucked, top end is not much higher than the us but the middle class pays out the ass

>>8512740
https://www.quora.com/Why-is-QR-factorization-useful-and-important

What are some good resources to learn about natural deduction/box proofing in logic? I'm confused about how disjunction and contradictions work, as well as the rules of boxes i.e. bringing stuff in.

This look feasible for randomization code?

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>>8513131
This.

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Alright guys, how do I solve this? L'Hosptial's Rule doesn't apply since its -infinity over 0, so I rewrote it as a product as (1/x)(lnx), which yields infinity times -infinity.

So for now I just have it written as the limit is equal to -infinity, but I don't think my method is right.

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Could someone help me with this proof? I think my bound for the |x-4| factor is sound, but no matter how I try I can't seem to get one for 1/|2x-3|.

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Are perfectly circular orbits a solution to newtonian gravity? How come I can't find it? Am I making some kind of fundamental mistake?

Is there any /sci/ approved way to making big cums?

if a number with units is raised to 0, would it still have units?

>>8513146
I just realized there is a sign error there, but that is not relevant to my question, the 1/R3 is.

How do I know if my wave function is an eigenstate of a particular operator?

like if my wave function is expressed in spherical harmonics and I want to know if it's an eigenstate of the hamiltonian

Do i just see if there are any eigenvalues?

>>8513143
Well, the difficulty in bounding 1/|2x-3| is that it flies off to infinity around 3/2.

You can fix that by tightening your delta enough that 3/2 is no longer inside; say |x-1| < 1/4 or something.

1/|2x-3| has an upper bound if you only consider the interval (3/4, 5/4)

>>8513150
Edging.

The size of your cum is directly proportional to the number of times you make it to the edge and deny yourself.

Trust me I've done several experiments.

>>8513142
You dummy dumb dumb. Infinity times infinity is not indeterminate. inf*inf=inf so you can figure it out.

>>8511848
>Are there really schools where you can substitute classes out like that? At mine, your major degree track is fixed. If you want to minor in something, you're taking like six extra classes on top of the normal load.

Usually, it's subbing out easier classes for harder ones like switch out Gen Physics for Premeds for the one physics and engineering majors take or swapping Calculus I/II/III for Honors Calculus and Analysis I/II/III.

>>8513177
Most appreciated anon

>>8513146
All solutions are of the form: [math]r=\frac{l}{1+e \cos(\theta)}[/math]. Let e=0.

so my logic is right when -infinity*infinity = -infinity? hmm thought that was too easy

>>8513226
I was thinking of a parametric solution. How would one be?

>>8513177
Wait, I must be a dummy or something, but how did you get that interval? When I try to manipulate |1-x| <1/4 i get -3/2 < 2x-3 < -1/2. Perhaps I don't fully understand the process of finding bounds?

Why do you always hear people talking about solving PDEs with Fourier Transforms, but not with Laplace Transforms? Is there something about Fourier Transforms that makes it better for solving PDEs?

Just curious.

>>8513265
The interval in the post you replied to is for x

I didn't fill in all the legwork of manipulating it into the function for you

>>8513383
Laplace Transforms are just Fourier Transforms offset a tad.

http://www.robots.ox.ac.uk/~jmb/lectures/pdelecture4.pdf
https://www.youtube.com/watch?v=kvEqw6tUtgM

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algebra Q:

hey /sci/, exams coming up and ive encountered same question from 2 separate years but i cant solve it, hoping you guys can show me how to crank out the algebra. I'm guessing find a way to factor out the 10^8 or 5*10^7 that differ under the line on the RHS and then it's nicer? Either way if someone could show me how to do it thatd be great, if it takes longer than a page dont worry about it i can find another method of getting Wp without this formula

>>8513451
I know it's possible but it seems like Fourier is much more popular for it.

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Damn, I'm stumped on this one too. Please help.

I know I need to manipulate |f(x) - L| into something involving |x+1| to find delta, but Idk if I'm even on the right track. I see I can get it in the numerator of third to last expression in my pic by distributing the (-1) into (x^2+1), then use (1-x^2) = (1-x)(1+x). But that seems to make the inequality even worse...

>>8513472
Wait, I'm an idiot. I guess I can get |x+1| in the numerator

>>8510706
bump, there has to be at least one number theory nerd in this board, critique this friggin thing

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how does wolfram alpha get the partial sum as pic related? i feel like i'm not seeing a simple trick or something

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Here's a dumb one, how do I find length of A?

How can you deduce that

v(t)*v'(t) = (1/2(v(t))^2)'

without first knowing that the right hand side equals the left hand side through implicit differentiation?

>>8513523
using the top triangle
tan(100/2)=(A/2)/12 (opposite/adjacent)
so A=24tan(50)

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>>8513550
Thank you anon, what about this one?

I graduated from my program in June, but the school recently dropped me from the VPN account rolls last month. How can I still get access to scientific journals? Even if I ask someone a year behind me to share their password, their account will still only last another year. How can I still get access to scientific journals in the long-term?

>>8513595
Contact your uni library and ask. My library has an alumni program, and if yours doesn't you can usually purchase public-access library cards, although I don't know if those work for the digital journals or not. Your librarian would know though.

>>8513547
Apply the chain rule or product rule to the RHS:

Chain rule:
u=v^2
du/dt=du/dv.dv/dt
=2v.v'

Product rule:
d(v.v)/dt = v.v'+v'.v
= 2.v.v'

>>8513628
I said without differentiating the RHS.
Context is I came across the LHS and the book simplified it to the RHS without explanation.
I take it the only way to accomplish this is by recognizing that the LHS is in the form of the expression obtained from

(1/2(v(t))^2)'

?

>>8513146
Can anybody tell me where the excess R3 comes from in my calculation?

>>8513595
http://sci-hub.bz/

>>8513657
Well, you could try integrating by parts, which would give you
integral v.v' dt = v.v - integral v'.v dt
=> 2 * integral v.v' dt = v^2
=> 2 * v.v' = (v^2)'

But then ... why would you integrate unless you've recognised that it's going to give you something simpler.

>>8513727
>But then ... why would you integrate unless you've recognised that it's going to give you something simpler.

Yeah. I guess the book just assumed the reader knew the relationship. I hadn't seen it in a while so it threw me off for a little bit.

>>8513519
It probably has rules for 1/polynomial.

In that particular case, if you set x(n)=1/((n-1/2)*(n+1/2)) = 4/((2n-1)*(2n+1)) and sum adjacent terms, you find that

x(n)+x(n+1)
= 4/((2n-1)*(2n+1)) + 4/((2n+1)*(2n+3))
= 4*(2n+3)/((2n-1)*(2n+1)*(2n+3)) + 4*(2n-1)/((2n-1)*(2n+1)*(2n+3))
= 4*((2n+3)+(2n-1))/((2n-1)*(2n+1)*(2n+3))
= 4*(4n+2)/((2n-1)*(2n+1)*(2n+3))
= 8*(2n+1)/((2n-1)*(2n+1)*(2n+3))
= 8/((2n-1)*(2n+3))

i.e. the numerator increases by 4 and the larger term in the denominator increases by 2. So the sum from m=a to m=b is

4(b-a+1)/((2a-1)*(2b+1))

Put a=1,b=m to get 4m/(2m+1)

>>8504277
Mathematically, how would I represent the following scenario:

At each step of the graph:

y = (x+1)^3

Such that, for example you'd have a set of coordinates like:

A(1, 8); B(2, 27); C(3, 125) and so on.

>>8513777
did you not just represent it with that function

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How am I supposed to git gud at integration by parts? Especially when integrating once yields another integral that requires integration by parts.

How do I know I'm not just running in circles when doing this? Especially when doing trigonometric integrals

>>8513688
You forgot the omega (angular velocity).
d(R*sin(w*t))/dt = w*R*cos(w*t)
d^2(R*sin(w*t))/dt^2 = -w^2*R*sin(w*t)

Thus you end up with
w^2=1/R^3 <=> (2pi/T)^2=1/R^3 <=> T^2=2pi.R^3

Kepler's third law:
> The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

>>8513805
>keep integrating until you arrive at the integral you originally started with.
>you know have an equation in terms of that integral
>solve for the integral as if it were a regular variable in an equation

>>8513805
By being able to do any integral in your mind and only start writing shit down once you have an entire path described in your brain.

I'm not even joking here. Anyone who is any good at integrals is able to do this, if you are not then you will at best be mediocre, wasting time and paper on trying out results

>>8513805
> How am I supposed to git gud at integration by parts?
Practice. And more practice.

> Especially when integrating once yields another integral that requires integration by parts.
Uh, it requires integration, although not necessarily by parts.

> How do I know I'm not just running in circles when doing this?
Well, you're supposed to choose the factors such that the second integral is simpler than the first. Otherwise, there's not much point using integration by parts.

Integration is basically the point in mathematics where shit gets real. Everything up to that point tends to be quite mechanistic: given an expression, it's fairly obvious which rules you should apply to it. Integration requires that you've differentiated every expression in under the sun and memorised the results, because it's basically a mental database search for "what do I have to differentiate to get this?". Or at least to get something close to it.

>>8513831
>Otherwise, there's not much point using integration by parts.

Wrong, sometimes you can get an algebraic expression involving your integral and the solution if the functions are kinda cyclic.

Like when you have (e^x)sinx

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>>8513831
>Integration is basically the point in mathematics where shit gets real

>>8513831
>Integration is basically the point in mathematics where shit gets real. Everything up to that point tends to be quite mechanistic: given an expression, it's fairly obvious which rules you should apply to it. Integration requires that you've differentiated every expression in under the sun and memorised the results, because it's basically a mental database search for "what do I have to differentiate to get this?". Or at least to get something close to it.

what...the fuck

>>8513831
>Integration is basically the point in mathematics where shit gets real
Not quite. I think TRIPLE integration is that point where we really start getting hardcore.

>>8513805
You know to use integration by parts if
a) you're integrating the product of two functions of x, and
b)differentiating one of the functions makes the integrand (what's inside the integral) simpler (to integrate), and integrating the second factor/function doesn't make it any more difficult or easy to integrate.

Typically, what you are differentiating will, eventually, either equal 1 or a constant, or be something you can use for u-substitution for integrating the other factor.

>>8506727
Com/signals, no question

t. Electron device guy

>>8513844
Well, it's not quite that bad, but ...
https://en.wikipedia.org/wiki/Lists_of_integrals
https://en.wikipedia.org/wiki/Lists_of_integrals#Lists_of_integrals

>>8513815
Thanks man. That was really bugging me out. Super interesting.

>>8513170
I suppose not. c^2 = c*c. c^-2 = 1/c * 1/c, c^0 = c*c^-1 = c* 1/c and thus the units cancel each other.

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where does the -1/2 come from in f`(x)^2 ?

>>8513982
(a+b)^2 = a^2 + 2ab + b^2

You dummy dumb dumb.

>>8513985
w-what


would't I just take the first term squared minus the second term squared ?

>>8513987
Look man, why are you dealing with derivatives when you clearly don't know even basic algebra.

Are you implying that (a-b)^2 = a^2 - b^2?

Because if so, literally kill yourself my man.

>>8513987
are you retarded?

>>8513987
No. Put the parenthesis two times next to itself and multiply term by term.

>>8513987
>>8513990

wait


like

(2+3)^2 = 25

2^2 + 3^2 = 13


what the fuck

I didn't know that, or it wasn't obvious.

So I'm working with wind turbines and it says it's rated at 4 MW, now how exactly can I turn this into MWh?

Is it 4 / 24 MWh or something?

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>>8513989
>>8513990
>>8513991
I'm sorry ;_;

>>8513998
Multiply it by the time it is in 100% operation. Ideally, you would integrate it 4*n(t)*dt where n is the efficiency at a specific time, which depends on the wind condition (how close to optimal rotation the blades are).

>>8514000
Time in hours right?

Also, do you mean ,

Efficiency = 2*Power / (air density*blade area*windspeed^3) ?

>>8513992
https://en.wikipedia.org/wiki/Freshman%27s_dream

>>8514002
I don't work with wind turbines, so I wouldn't know the exact formula for your case. But to turn power to power*h you usually do that, just make sure efficiency always yield a number between 0 and 1. And yes, time must be in hours.

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>>8513987
Thanks for the laugh, anon.
But yeah see
>>8513985

>>8514003
Literally was just about to post this, fuck.

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>>8504277
Can a based anon help me with #3 please.
Thanks :)

>Inb4 comic sans
Hippie prof

>>8514007
>tfw professor gives out homework
>it's in wingdings again

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>>8514005
I see, thanks!

I can't believe I'm on a course with advanced fluid mechanics and this stumped me

>>8514009
>Implying homework
More like take home exam REEEEEEEE

Can you solve a problem 3 university students are stumped with? Because I fucking can't.

A boat travels 25 miles per hour in still water. It takes 3 and 1/3 hours to travel 40 miles up a river and then to return by the same route. What is the speed of the current in the river?

I know the answer is 5 miles per hour, with guessing and checking, but how the fuck do I solve it showing work?

>>8514014
>tfw the takehome exam was in in hieroglyphics

>>8514018
>Tfw anon is more interested in exam's mechanics than the problem itself

>>8514017
Should be 3 and 1/3rd mph right?

u = 25mph, d = 80 miles

d/u = t = 3.2 hours

actual t = 3.333_ hours

dt = 8/60 hours

speed of river = 8/60 * 25 = 3 1/3 minutes?

>>8514024
if i knew how to solve it i would help but i am a retard in calc1 so i come to these threads for help and not to help


i probably won't every be able to help anyway because I'm a meme major [spoiler]environmental science[/spoiler] and won't go very far into math/physics

>>8514026
3 1/3 mph*

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>>8514007
I finished doing it and then saw he asks for a specific way. Well, fuck him. It is not conservative because it can't be displayed as a gradient of a scalar.

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>>8513982
>>8513987
>>8513992
>>8513999
There needs to be an algebra exam that you need to get 100% on to post on /sci/

>>8514026
No, because I set it up like (25 - current) * time1 = 40 and (25+current) * time2 = 40

If you plug in 5, you get 30 miles per hour one way, 20 miles the other way. That means you need 4/3 hr going the 30 miles per hour route, and 2 hours going the slower route against the current, which gives you 3 and 1/3 hours total journey.

>>8514032
>that handwriting

>>8514036
I just don't know how the fuck to get t1, t2, or current without guessing and checking. I set up another question, where t1 + t2 = 10/3 hr, but that didn't help either.

>>8514027
It's okay, you'll get to a better level eventually.

>>8514032
Thanks.
Kinda messy but I'll work it out.
Oh and hippie prof is a girl haha

>>8514038
It's pretty shitty writing in a glass screen desu. Beats doing it in TeX, though, that's for sure.

>>8514017
Nevermind, solved it. You need to set up the equation based on time, not distance.
Time total = 10/3 hr
s = d/t
st = d
t = d/s <- using this formula now

25 - c = speed 1
25 + c = speed 2

distance (one way) = 40 miles

40/(25 - c) + 40/(25 + c) = 10/3
Everything else is easy after that, since it is just one variable.

>>8514033
No bully in the brainlet thread.

>>8514036
So,
(25 - c) * t1 = 40
(25 + c) * t2 = 40
t1 + t2 = 3.333
t2 = 3.333 - t1 =>
(25 - c) * t1 = (25 + c) * (3.333 - t1)
(25 - c) * t1 = 83.333 + 25*t1 + 3.333*c + c*t1
25 - c = 83.333/t1 + 25 + 3.333*c/t1 + c
25 = 83.333/t1 + 25 + 3.333*c/t1 + 2c
t1 = 40 / (25 - c)
25 = 83.333/(40 / (25 - c)) + 25 + 3.333*c/(40/ (25 - c)) + 2c
solve for c