Stupid Questions Thread

Thanks, user. 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)

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

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

Why just -2 in the numerator?

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'

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

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

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.

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

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

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?

>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.

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

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.

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) }

Anyone have any good references on gauge theories.

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.

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

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.

...I guess it isn't.

>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.

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

Holy shit dude.

You are amazing.

I think I understand it.

Thanks a lot!

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

don't ask to ask you brainlet

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

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.

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

Thank you.

How do I become a meme scientist?

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

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

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

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

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

I have a bunch of disodium inosinate.

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

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

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?

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

[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]).

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.

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

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?

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

> 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?

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?

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)

no brainlet shaming in SQT

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.

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

Thanks user.

> 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

> 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)

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.

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.

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

guys...
help ;_;

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

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

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) = )

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..

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?

> 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).

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

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

>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.

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

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.

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

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.

square both sides, work backwards

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

I'll try that tomorrow, thanks.

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.