/sci/ - Science & Math

WAT IS DIS INTEGRAAL

>>10006543
PS this is me

[math] \sup [ \frac{1}{4},\frac{1}{2}] = 2 [/math] where [math]f(\frac{1}{2}) = 1[/math], right?

>my school's introductory linear algebra course for math majors (&non math majors) is a applied course
Should I transfer? I've been considering it anyway. I have a 3.85 and some extracurriculars.

>>10006770
intro lin alg is almost always skewed towards the applied side of things to give you an intuition.

>>10000000
just checking

>>10006810
>intro lin alg is almost always skewed towards the applied side
Which school for brainlets do you go to?

>>10006543
Find out how the terms you wrote are defined and that will easily answer your question

>>10006818
anyone?

>>10006909
Sure, assume the definition with closed intervals holds. You are given epsilon. Take a closed covering such that the total length of the covering is less than epsilon/2. Then substitute each closed interval with an open interval which contains the original closed interval and whose length is bigger by epsilon/2n. You obtain an open covering with length less than epsilon. The other direction is trivial.

literal brainlet here with babby-tier question

>Bob is installing a phone line and has to choose a 5-digit phone number, but the phone number can't be divisible by 7. How many possible phone numbers can he choose from?
I think the answer is 85715 because I just found the last number divisible by 7 (99995) and subtracted the number of 7 multiplies from permutations like 10^5-(99995/7) to get 85715. But that's probably wrong and/or there's a better way. How would I work it out?

>>10006927
5 digit number. Hence numbers with less than 5 digits won't do.

>>10006932
I just assumed that there could be a leading 0 for a phone number.

>>10006932
nevermind didnt think this through lol. 0 can be a leading digit

>>10006927
yeah this is right and the easiest way to do it. Like nigga it just takes 2 arithmetic steps, how can you be looking for an easier solution lmao

>>10006901
i checked wikipedia, it didn't help :(
>t. >>10006548

For [math]1\leq p\leq q<\infty[/math] we have that [math]L^p(\Omega,\mu)\cap L^q(\Omega,\mu)[/math] (arbitrary measure space) is a Banach space when equipped with the norm [math]\max\{\|\cdot\|_{L^p},\|\cdot\|_{L^q}\}[/math].

My whole problem with this is that a Cauchy sequence might have a different limits in the other norm, say [math]f[/math] for [math]\|\cdot\|_{L^p}[/math] and [math]g[/math] for [math]\|\cdot\|_{L^q}[/math] in their corresponding spaces.
I also see no possibility to connect these norms in any way (like estimates).

Please help. Any hint is helpful for me.

>>10006919
Thanks

>>10006941
Because I had to use a calculator to check each number backwards to see if it was div by 7 before finding 99995. I'm a brainlet and don't know if there's an easier way to do it without one.

Also the answer seems to be 85714. Where did I miss the 1?

brainlet btw

This isnt a question but FUCK STATISTICS

>>10006972
when counting numbers divisible by 7 you need to add 1 bc 0 is divisible by 7 too ( e.g. from 0 to 7, 7/7 = 1 but theres 2 of them)

After I refill a bottle with tap water, what causes those little bubbles to form after a few hours?
I can't remember where I read or heard this but someone said it was from chlorine in the water slowly breaking down.
I live in the south of the UK if it matters, (tap water is hard here)

>>10007009
my friend in pre-med told me that it was because of bacteria
just googled and found out that isn't true

>>10007009
i don't know but i would guess it has something to do with change in vapor pressure as it settles, as tap water is a solution and not a pure substance?

>>10007009
stop using bottles for water you utter idiot.

>>10007093
how is using a bottle dumb? they're convenient, and if I use a glass my cat drinks out of it

>>10006972
>10^5-(99995/7)
You are considering all naturals from 10^5 downwards. 10^5 isn't a five digit number.

>>10007200
00000 is.
t.brainlet

>>10007213
Yes I just thought about that case, if 00000 is valid then it's just because of >>10006978

meant to post this >>10007369 here.

So I have the following tri-variable function:

f(x,y,z) = x^2 + 3y^2 + z^2 - xy - xz

All I want to do is determine if it's convex or concave. The Hessian is as follows:


2 -1 -1
-1 6 0
-1 0 2

How do i determine whether it is convex or concave from that?

>>10007586
is it positive definite or negative definite?

>>10007604

I'm not sure how to check that. Doesn't negative definite imply that the signs are alternating? That isn't the case, it seems.

>>10007622
https://www.youtube.com/watch?v=tccVVUnLdbc

>>10007093
What do you recommend?

>>10007634

So which one (positive definite, etc.) implies concave and which implies convex?

>>10007692
glass + water filter.

Say I throw a nuke at the moon. Since there's no atmosphere, what would the blast look like?

>>10007703
like your mom at a bukkae session

>>10007708
>bukkae
Try again, nigger.

>>10007703
There's enough atmosphere on the moon to get you a similar reaction, just more spread out and somewhat less destructive.

Exploding one in a vacuum (or say the surface of a small asteroid), isn't particularly destructive (bright flash, heats up one side of the asteroid), but the gamma rays travel a *lot* farther with nothing to absorb them, thus while the material destruction and blast isn't as impressive (most of which is caused by the atmospheric heat up and subsequent displacement), the deadly radiation effect extends a lot further.

4X + 3O2 -> 2X2O3.... where X = {As, Sb, Bi}
For oxidative roasting, above 850 ° C, As, Sb and Bi are transformed into 2As2O3, 2Sb2O3 and 2Bi2O3.
If then through "cyclonic separation" (heat recovery boilers) and electrostatic precipitators. They recover as dust and add to the calcine.
What happens to these oxides at low temperatures?
Are they recovered as dust?
And if they recover, do they remain as oxides? "2As2O3" for example, or return to "As"?

>>10006948
>>10006948
>>10006948

What the fuck am I looking at and what it means?

>>10007586
By Sylvester's criterion, the matrix is positive definite, so the function is convex.

Hey, guys, I'm literally retarded and need help with this linear algebra problem.

I don't even know where to start.

Anything is appreciated

Am i retarded? i can’t figure out this problem.

A car travels 40m in 8.5s and slows to vf of 2.8m/s. I need to find Vi and a. I did 40m/8.5 to get vi but that gives me 4.7 which is not right. What am i doing wrong here?

>>10008057
First, note that the determinant of that matrix is equal to 5 times the determinant of
[c+2a d+2b]
[-7a -7b]
by the recursive formula for a determinant.

Second, note that the above matrix can be factored as:
[ 2 1]*[a b]
[-7 0] [c d]
And the left-hand matrix has a determinant of (2*0)-(1*-7)=0-(-7)=7.

As det(A.B)=det(A).det(B), the overall result is 5*7*4=140.

>>10008076
> A car travels 40m in 8.5s
=> average speed = 40/8.5 = 4.7 m/s
> and slows to vf of 2.8m/s
> I need to find Vi and a
(Vi+2.8)/2 = 4.7
=> Vi+2.8 = 9.4
=> Vi = 6.6 m/s
a = (vf-vi)/8.5
= (2.8-6.6)/8.5
= -3.8/8.5
= -0.45 m/s^2.

>>10006948
They may not have different limits. If it's limit exists in both spaces then it's equal. This follows from basic inequalities.

>>10007720
>There's enough atmosphere on the moon
Son you just blew my mind right there, I'm gonna have to read some more. Thanks.

>>10007945
bumping

Help!

Is from a freud book on the masses and group psycology

I'm studying RC circuits atm and I'm stuck on a very tricky question. I have these equations:
[math]i_{6}+i_{3}=i_{2}[/math]
[math]i_{4}+i_{6}=i_{5}[/math]
[math]i_{2}+i_{4}=i_{1}[/math]
[math]\epsilon - i_{4}R_{s}-i_{5}R_{x}=0[/math]
[math]-i_{2}R-i_{6}r+i_{4}R_{s}=0[/math]
[math]i_{6}r -i_{3}R+i_{5}R_{x}=0[/math]
and I have to find expressions for [math]i_{1}[/math] to [math]i_{6}[/math] using epsilon, r, R, Rs and Rx.
Is this even possible to solve by hand? I just used Mathematica to solve the problem but I feel like I'm just being dumb at algebra

I'm studying RC circuits atm and I'm stuck on a very tricky question. I have these equations:
[math]i_{6}+i_{3}=i_{2}[/math]
[math]i_{4}+i_{6}=i_{5}[/math]
[math]i_{2}+i_{4}=i_{1}[/math]
[math]\epsilon - i_{4}R_{s}-i_{5}R_{x}=0[/math]
[math]-i_{2}R-i_{6}r+i_{4}R_{s}=0[/math]
[math]i_{6}r -i_{3}R+i_{5}R_{x}=0[/math]
and I have to find expressions for i1 to i6 using epsilon, r, R, Rs and Rx.
Is this even possible to solve by hand? I just used Mathematica to solve the problem but I feel like I'm just being dumb at algebra

>>10008266
6 equations in 6 unknowns. It's entirely possible to solve by hand, and fairly simple as the equations are sparse (2 or 3 unknowns per equation). Use Gaussian elimination.

>>10008209
>freud
that's your problem

>>10008209
>freud
not science or math

why does wolfram say the series diverges when using variables? because negative values for x?
also, why is the result always the denominator with positive integers if x.999999... is not x+1

>>10006539
What sorcery is this? Why does the amperage stay the same after you transition between wire sizes? Why don't the smaller wire's electrons displace the larger wire's electrons at a lower amperage rate?

It's like blowing a leaf blower toward an entire hallway and expecting all the air in the hall to move at the same rate as it's moving out of the leaf blower. What am I missing?

>>10008403
An ampere is charge per second. If you point a leafblower down a large hall instead of a small hall, it doesn't change how much energy is acting on the air in question, only how it's distributed. Imagine adding the same amount of food coloring to two different water containers. It doesn't actually change how much food coloring there is, just how much water it discolors. The amount of charge does not change.

>>10008403
I don't think you understand well what current intensity means. 1 Amp just tells us that 1 C (which is equivalent to the charge of a constant amount of protons/electrons) is flowing through a surface in one second. Regardless of how big or small that surface is (picture it as a "slice" of wire at a particular point), the amount of electrons that are flowing because of the potential difference will remain the same. That's of course considering that you don't change the potential difference.
>It's like blowing a leaf blower toward an entire hallway and expecting all the air in the hall to move at the same rate as it's moving out of the leaf blower
The analogy doesn't work because it's not a correct interpretation of what current represents for electricity. If you blow a leaf blower toward a hallway, if you measure the amount of air particles that flow through a "slice" of the hallway before and after you turn on the blower, the difference will be that of the air particles that actually get pushed by the blower (assuming ideal conditions of course, in reality if you measure the difference at point that's far away from the blower you will probably not see a change because of friction and what not). Think about it like this, if you have x amount of people walking through a narrow hallway, and later on the hallway leads into a broader hallway, even if the new hallway has more space to fit more people walking through a slice of it at a given time, the amount of people walking through it will still be x. Assuming they all walk at the same speed and the system's closed (so no people leave/enter), the amount of people who walk through a slice of hallway in a time t will be the same as before.

I feel like a retard for not being able to figure this out

any help lads?

>>10008105
Thanks, man.

I get what you did but have no idea how to even decompose the matrix in your last step. Like I said, literally retarded.

Thanks for the help though.

>>10008455
multiply the last inequation so that:
|sqrt(a)-sqrt(5)|*|sqrt(a)+sqrt(5)| < c*ε*|sqrt(a)+sqrt(5)|
we can do that because |sqrt(a)+sqrt(5)|>0, of course
then you have
|sqrt(a)^2-sqrt(5)^2| < c*ε*|sqrt(a)+sqrt(5)|
which is of course
|a-5| < c*ε*|sqrt(a)+sqrt(5)|
then, you can choose c such that ε = c*ε*|sqrt(a)+sqrt(5)|:
ε = c*ε*|sqrt(a)+sqrt(5)|
1 = c*|sqrt(a)+sqrt(5)|
c = 1/|sqrt(a)+sqrt(5)|
which fits your first inequation for c perfectly for any value of a

>>10006539
give me some compelling evidence that education has even the smallest effect on iq after pre-pubescence and that there is any reason why we should put more money into public edu

>>10006543
Unit impulse function, aka dirac delta function.
>https://www.youtube.com/watch?v=msEeaAlfPcs

>>10007009
Tap water has tiny air bubbles in it. They get caught in the surface friction of the bottle and coalesce as you leave the water sitting.
>https://water.usgs.gov/edu/qa-chemical-cloudy.html

>>10007750
Those materials are metal oxides, which are generally stable. In fact, your common solid metals develop surface layers of metal oxide under atmospheric conditions. Aluminum, tin, iron, copper, they all have oxidation layers on their surfaces. They're typically salt-like, crusty materials, technically ceramics, as they're held together by non-chaining covalent bonds. If you got a thick enough layer of it, you might be able to get a little plate of it, like you could with rust, which is an iron oxide.

>>10008267
You're just being dumb at algebra. Two of your KCL equations give you expressions for i6, and two of your KVL equations give you two more expressions for i6, so start by replacing i6 with shit. Then, replace another current value in terms of the remaining variables. Keep going until you're left with only one current value, such that the resistance and voltage variables are all in one equation. From that first expression, you can suss out the other 5 by just replacing them with KCL equation equivalents.

>>10008486
Public education is a manufacturing process where the product is employees. Its goal is not to influence IQ, because IQ is the rate at which one learns, not the amount of information one can access. Public education eases use of the information that employers require their product to access. However, when your process is not producing a quality product but there is still a clear demand for that product, do you scrap the process entirely or do you look for ways to improve it? Albeit, the investment shouldn't be in the teachers so much as it should be in better, more open educational research.

What is the equation to find the maximum degree a vehicle can turn while stilling remaining in circle using the speed of the vehicle?

If that didn't make sense... If there is a plane moving at 100km/ph what is the maximum degree it can turn while still maintaining a circle.

>>10008646
>What is the equation to find the maximum degree a vehicle can turn while stilling remaining in circle using the speed of the vehicle?
Ops I meant what is the equation to find the maximum degree a vehicle can turn while still remaining in a circle using it's current speed...

I asked a friend of mine who's a mechanical engineer and he laughed at me :/ I'm not sure if I've missed something or what..

>>10007945
It's a chart where Freud attempts to describe how a group of individuals can collectively have their perception of reality changed when they have substituted one and the same object for their ego ideal and have consequently identified themselves with one another in their ego.

In short, Pope says thing is red, many Catholics agree thing is red, even if it is blue. (Though this example is more geared towards a micro-group. Gramps say X is Y, the kids who love him all identify X as Y, as they trust his judgement as the ideal to aspire to. Thus, in their eyes, all rocks are dinosaur turds.)

>>10008358
>Psycology
>not a science
>inb4 thousands of Dunning-Krugers replies

>>10008646
>>10008667
if a vehicle can turn at all then it can turn in a circle, also what do you mean by degree? do you mean the angle around the circle, or are you using it for slope or what. Neither of those make any sense anyway.

When thinking about turning usually we think about it in terms of tangential speed, centripetal acceleration, and radius.

>>10008164
You need to consider the Cauchy sequence in each space individually with their corresponding norm.
You are just asserting that the limit exists in both spaces, but I don't see how that must be true, unless one can prove that the intersection of the two spaces is complete (considering only one of the two norms). I could probably try to prove that this intersection is a closed subspace, but to prove this, I need the other norm too, which will cannot be estimated.

If you have a hint on how to prove this completeness/closedness, I would appreciate it.

>>10008646
The centripetal acceleration required to turn in a circle is v^2/r, where v is the speed and r is the radius.

For a car, the centripetal acceleration is limited by the coefficient of friction (k) between the tyres and the road, so you have v^2/r<k => r>v^2/k => v<sqrt(r*k). I.e. as speed increases, minimum turning radius increases, as turning radius decreases maximum speed decreases.

For a plane, it's determined by the lift/mass ratio and gravity. You need lift*cos(a)>=weight => cos(a)>=weight/lift (where a is the bank angle) in order to maintain height, the centripetal acceleration is equal to (lift/mass)*sin(a) = (lift/mass)*sqrt(1-cos^2(a)) <= (lift/mass)*sqrt(1-weight^2/lift^2) = (lift/mass)*sqrt((lift^2-weight^2)/lift^2) = sqrt((lift/mass)^2-(weight/mass)^2) = sqrt((lift/mass)^2-g^2) (where g is gravitational acceleration = 9.81 m/s^2).

>>10006539
what is /sci/s opinion on modafinil?

>>10006948
>>10006948
>>10006948
???

Is there a general rule or sth to know when you're supposed to split a statics problem into two parts?

>pic rel

>>10006539
Is racism correlated with high IQ?

\color{red}{\text{(USER WAS BANNED FOR THIS POST)}}

In 1.2.5, the a' that replaces the operator A on the left isn't the same as the a' inside the ket, right? If so, is this notation common? It seems unnecessarily confusing.

I don't understand this. For a sphere, da = 4πr2, right? It doesn't look like he actually integrated.

is two's complement magic? I see that it works but how do I understand why inverting bits and adding one works as a negative number in addition

>>10009382
When one isn't or won't get you the information you need

>>10009403
Constant magnitude electric field at radius, hence the chosen (spherical) Gaussian surface.

>>10009616
The so called 2's complement is just modular arithmetic. If you add an 8-bit number to its 1's complement, you get 11111111 which is just 2^8 - 1 = - 1 mod 2^8. Now you add a 1 to get 0 mod 2^8.

>>10006927
99999/7= how many numbers you cant have

Or am I dumb?

>>10009648
Thanks, makes sense

>>10009693
The latter. That isn't even an integer.

>>10006948
Banach spaces

factorise a3-a2+2a+2
I'm fucking stupid pls

>>10009735
the 3 and 2 next to the a are a to the third and a to the second not actual a3

>>10009616
Consider 10's complement. Suppose we use 6 digits, so -123456 is represented as:
1000000-123456
= 999999-123456+1
= 876543+1
= 876544
Check:
876544+123456 = 1000000
= 0 (mod 1000000)

2's complement is just 2^k-n rather than 10^k-n. 2^k-n = (2^k-1)-n+1, and 2^k-1 is just k 1s, and subtracting from 2^k-1 is just inverting all the bits.

>>10009616
you start with unsigned numbers then you get a signed number
It's stupid

>>10009720
What. Maybe answer my question?

I dont understand statistics and probability

My homework asks me to check if I can divide a polynomial by x - 1 without actually doing the division.
How would I do this?

>>10010006
Evaluating the polynomial for x=1. If it equals 0, it means that it can be factorized such that (x-1) is a factor (and thus if you replace x with 1 the whole expression cancels out), so it means you can divide by (x-1)

Can someone help me to understand convolution?

>>10010384
Weighted moving average.

>>10009382

haha ur filename says ass

does base matter in set equivalence?

How much energy would it take to create a wormhole, and how far could we place the other end?

Why does water boil at 100c rather than the hydrogen or oxygen boiling first? How come is it that I cannot boil some wood?

I have a ba in ecology but need a bs to get most jobs. I have taken supplementary classes to suffice the requirements for a bs in ecology. I do not however have a official bs, but classes added on to my ba. (Already graduated and moved away from uni. Took supplemental classes at local college.) what harm is there in saying i have a bs on my resume to get past the applicant tracking systems?

Maple or Mathematica? for symbolic shit ofc

>>10010595
Rather than lie to your prospective employer why don’t you explain why you have a BA and not a BS. You might say something like “my university doesn’t offer a BA in ecology” or “ I studied in the college of arts and letters rather than the college of science because…” I bet that a last hr rep wrote the posting and just wrote BS rather than BA/BS or if they really care explain that you’ve supplemented your education to the desired level.

>>10010589
Because the hydrogen and oxygen atoms are bonded to each other very strongly.

You can "boil" wood, as long as you don't have oxygen present. This is called pyrolysis.

>>10010589
>Why does water boil at 100c rather than the hydrogen or oxygen boiling first?
What? Hydrogen and Oxygen ARE both gaseous way before the 100C mark gets reached. That's how they are gaseous even at room temperature, so you can breathe them from air. The only intramolecular bonds in a water molecule are between Hydrogen and oxygen atoms. Hydrogen and Oxygen can't boil earlier because there are no O-O or H-H bonds to break to begin with. However, the reason the difference of boiling points between water and H2/O2 molecules is so big is because unlike the latter, the bonds found in water molecules are also polar, which result in a particularly strong union between the atoms.
>How come is it that I cannot boil some wood?
Wood combusts before it can even get to a hypothetical melting point. Combustion is an irreversible reaction so it's not like you can undo it afterwards to get back your liquid wood. Maybe it would work under under very specific pressure/temperature conditions, but considering the oxygen found in the molecules in wood I don't think it could be pratically doable.

>>10010614
Yes im just worried about the software which idk what the parameters are set for

>>10010790
Submit it as it is. I bet the requirements for BA vs BS vary by school. Also I understand and appreciate the anxiety that comes with applying for a job. Just don’t beat yourself up by finding reasons for feeling “unqualified”

are there any REALLY good books on mental illness? the crazy ones like psychosis and mass hysteria

For [math]1\leq p\leq q<\infty[/math] we have that [math]L^p(\Omega,\mu)\cap L^q(\Omega,\mu)[/math] (arbitrary measure space) is a Banach space when equipped with the norm [math]\max\{\|\cdot\|_{L^p},\|\cdot\|_{L^q}\}[/math].

My whole problem with this is that a Cauchy sequence might have a different limit in the other norm, say [math]f[/math] for [math]\|\cdot\|_{L^p}[/math] and [math]g[/math] for [math]\|\cdot\|_{L^q}[/math] in their corresponding spaces.
I also see no possibility to connect these norms in any way (like estimates).

I tried to prove that this intersection is a closed subspace, but to prove this, I need the other norm too, which cannot be estimated.

Please help. Any hint is helpful for me.

How often do you guys have internal monologues? i've been trying to avoid them together with meditation sessions because i think it might make me less autistic

Are compounds "perfect"?
For example, common salt, NaCl.

If I pick any amount of salt, is the proportion exact? Half the atoms are sodium and half the atoms are chlorine?
I understand that it at least approximates that, but is it perfect?

>>10012151
Benzene is perfect

>>10012008
Think that'd have the opposite effect... Don't fall for that NPC polarizing effort meme article that's going around, almost everyone has internal monologue (which, if you read the stupid study in the stupid article, is what it actually says.) Indeed, part of the *challenge* of meditation is to get it to STFU - most people can't do that for very long, even though it may be idle more often than they realize.

But that monologue acts as "practice communication", so if you want to seem less autistic, shutting it down is kind of the opposite direction you wanna go. If anything, you wanna try to create and practice an internal dialogue while juggling multiple viewpoints.

>>10012161
my theory is i don't have enough brain power to think and speak at the same time so if i stop thinking altogether it will make me speak more fluidly
just a theory though

>>10012196
"Think before you speak" is a saying for a reason. You need to practice predicting how the other person might react to what you're going to say, and change your response accordingly, to the point where you can do it faster than real time, as you've developed an intuition for it.

>>10012007
Use the fact that a sequence that converges in L^p has a subsequence that converges almost everywhere

>>10012288
I tried this but then I'm just stuck with two (possibly [partly] disjoint) subsequences where one limit is in L^p and the other in L^q. The most I can conclude from this that (assuming by contradiction that the limits are different) the sequence doesn't have a limit almost everywhere, but this is not really useful in the context of L^p spaces.

But maybe you had another application in mind. Do you have a further hint?

why is the outdoor air so fucking gross
if i walk outside for 5 mins there's this nasty earthy smell that gets stuck on my clothes
i can't get the air in my room to be fresh even if i open the window and let the fucking spiders in

>>10012744
Moleman detected. You're not "outside" unless you can see the sky Anon.

>>10012008
i'm autistic and i don't mainly rely on internal speech as if that's the only way to think which some anons seem to believe, i have an internal monologue mainly when thinking about things that are directly related to speech/writing, if i'm thinking about other things i might conduct inner speech but it's not my primary mode of thinking so it's like some keywords, not full sentences, not like the narration in the stanley parable, at other times i might just play some music in my head and not do much talking

>>10006770
Yes, transfer immediately! Even as a comp sci major, I had a theoretical lin alg class.

>>10010183
thanks, friend

What is the main difference between an Ordinary Differential Equation and a Partial Differential Equation?

>>10012928
how hard it is

>>10012928
PDE involves partial derivatives (i.e. derivatives w.r.t. multiple variables), ODE is all w.r.t. a single variable (usually time).

>>10013124
Thanks.
Are PDEs related to n-body problems? If so, I assume many of them don't have analytical solutions, right?
(Yes I am very ignorant)

I am really confusing myself. If the guy in this diagram weighed slightly more than 50 lbs, wouldn't the potential energy of the system increase as he lifts up the 150 lbs weight?

Okay, I'm going through MIT's 18.01 and started after watching like 4 lectures, the exercises.
This one is more like precalculus but I don't remember seeing this in HS, 3rd world country yadda yadda.

So, I have to express in the form A sin (x+c) the following:

sin x + (sqrt(3)cos x).

How do I deal with that? The rule itself is easy to understand but maybe I'm lacking some info on trig properties?

>>10012765
On a side note i imagine quite a portion of /sci/ is composed by autists
Surely some of you guys figured something out to improve it?

Computer Enginnering Junior. I haven't done any internships or have any job experience other than working for Subway. Am I fucked and if not what should I do?

>>10013251
it's not incredibly apparent, but the guy has to pull three units in length of rope to lift the load 1 unit, you could think of it that he has to pull one length for each of the three supporting ropes. With this in mind if we look at the system at equilibrium no matter the height of the load, the potential energy is the same. If we look at a snapshot of the potential energy when the weight of the guy is greater than 50 lbs, then the potential energy of the system is decreasing as we would expect.

>>10013334
>am I fucked
yes
>what should I do
get work experience next summer
it's not rocket science desu

>>10013307
Nevermind guys, I'm a fucking retard.
solved.

>>10013307
you have to use maths
A sin(x + c)
= A [sin(x)cos(c) + cos(x)sin(c)]
if we want this to be F sin x + G cos x for all x, then
A cos(c) = F, and
A sin(c) = G.
Squaring and adding the equations, we get A^2 = F^2 + G^2,
and to get c, we can solve for sin(c), cos(c), and also tan(c) by dividing the equations

For sin x + sqrt(3) cos x, F = 1 and G = sqrt(3), so A^2 = 1 + 3 -> A = 2, and with F and G positive, sin(c) and cos(c) are positive, so c is in the 1st quadrant. cos(c), for example, is F/A = 1/2, so c = pi/3.
2 sin(x + pi/3)

I'm confused about the doppler effect (thanks to my shitty grad. student lecturer with black and white slides and handouts)
Electromagnetic spectrum has red connected to radio waves and long waves. Violet-ish has gamma rays and short fast waves.
The doppler effect says blue away and red towards with blue being the long waves and red being the short waves?

Why are red long slow waves in one but short fast waves in another? Was it just a poorly structured handout? Are the two ideas not related?

>>10013348
Ah of course! Thank you.

Need some help with calc.
I need to find u x v and show the vector is orthogonal to u and v
U = < 2, -3, 1>
V = < 1, -2, 1>
I found the vector to be <-1,-1,-1>
My question is how do I prove it’s orthogonal?
I tried u x v / || u x v ||
But I just get -3/sqrt(3)
Shouldnt it be orthogonal if it’s equal to 1?

If [math] x_0 [/math] is irrational, how can I construct a sequence of rational numbers that has [math] x_0 [/math] as its limit?

>>10013442
>u x v / || u x v ||
What is this supposed to be? Do you mean uv/||u||||v||? By definition, 2 vectors are orthogonal when their dot product is 0

>>10013466
The n-th term has n digits of x_0. For example: 3, 3.1, 3.14, 3.141, 3.1415, ... approaches pi

>>10013373
Thanks for the information mate

>>10013466
If you believe in the axiom of choice, and don't care that the sequence is totally non constructive:

Create a sequence [math]\{a_n\}[/math] by picking as the nth term a random element [math]a_n\in (x_0-\frac1n,x_0+\frac1n)[/math].

If you want an inefficient but constructive sequence then the first anon to respond to you gives a valid answer.

The best constructive sequence is created through partial fraction approximations.

Is showing a map: [math]f: A\to B[/math] to be well defined equivalent to showing [math]\forall[/math] [math]x,y\in A[/math], [math]x=y \implies f(x)=f(y)[/math] ?

>>10013133
> Are PDEs related to n-body problems?
An n-body problem is just a non-linear second-order ODE. It relates accelerations (second derivative of position w.r.t. time) to positions.

> If so, I assume many of them don't have analytical solutions, right?
There are no analytical solutions for n-body problems with more than two non-negligible masses. Ignoring relativity, the 2-body problem results in Kepler's laws. It's possible to predict motion of additional bodies with negligible mass (i.e. the additional bodies are affected by the gravity of the first two, but their own gravities are too weak to affect anything).

>>10013383
red has less energy, while blue has more, owing due to its higher frequency (thinner waves). the doppler effect actually says the opposite. it should be red away and blue towards.

your handout probably was poorly constructed.

Does every function f(x,y) = f(sqrt(x^2+y^2)) have circular level curves?

>>10013613
No

>>10013617
Counterexample?

>>10013617
Can you give a counterexample?

>>10013632
If he can, it's going to either be some weird corner case or sheer pedantry (e.g. f(x)=k, which doesn't have level curves). Given that x^2+y^2 is independent of the angle, so is any function of it.

>>10013626
>>10013632
>f(x,y) = g(sqrt(x^2+y^2))
g(x) = 0
g(x) = 1 if x is rational, 0 otherwise

So linear algebra is a widely studied and used and has its own field. What about nonlinear algebra?

Under what conditions on the matrix is pivoting unnecessary to compute an LU factorization?
-The diagonal entries of the matrix are nonzero
-The matrix is invertible
-A singular value decomposition of the matrix exists
-The matrix is symmetric positive definite
-The matrix is banded
-The matrix is diagonally dominant

>>10013677

It exists but is not as popular precisely because it's easier to deal and reduce most things down to linear systems.

Why is he multiplying it by its complex conjugate? abs(psi)^2 is just equal to psi^2.

>>10013703
What's the modulus of a complex number?

>>10013734

>>10013528
Yes. Issues where this might come up are when equivalence relations are introduced, such as in quotients, where maps might actually depend on the element

>>10013677
nonlinear algebra is called algebra, and its geometry called algebraic geometry

>>10006539
what are the chances of mutational load causing serious problems for dysgenically breeding populations not subject to purging selection in the next 100-200 years?

>>10013654
Right, pedantry.

If f(sqrt(x^2+y^2)) actually has level curves, they're circular.

>>10000000

>>10013475
Ah. I was reading an example and it said that the formula I used is for a unit vector orthogonal to u and v. It should be 1 still, which i’m not getting. Guess I’ll use the dot product.

>>10013703
> abs(psi)^2 is just equal to psi^2.
Not when psi is complex.

(a+bi)(a-bi) = a^2-b^2i^2 = a^2+b^2 = |(a+bi)|^2
(a+bi)^2 = a^2+2abi+b^2i^2 = (a^2-b^2)+2abi

Also note that in polar form, (r*(cos(a)+i.sin(a)))^2 = r^2*(cos(2a)+i.sin(2a)), i.e. square the magnitude, double the angle.

>>10013924
How can a function not have level curves?

>>10013944
> it said that the formula I used is for a unit vector orthogonal to u and v. It should be 1 still
It can't be 1. The result of a cross product is a vector, not a scalar.

If u and v are orthogonal, then ||u×v||=||u||*||v|| (and u.v=0, which is a somewhat simpler calculation).

>>10013944
>u x v / || u x v ||
This an expression to get a unit vector that's orthogonal to both u and v. It doesn't help you check if 2 vectors are orthogonal or not

>>10013968
Consider g(x)=0. The level set for g(hypot(x,y))=0 will be a 2D area, not a curve (or set of curves). Similarly for any function which is constant over a non-zero interval.

I think the rational/irrational example is wrong though. Both the rationals and irrationals are totally-disconnected sets, so the level sets of g(hypot(x,y)) will consist of disjoint circles.

>>10013373
I already solved it but thanks a lot for the throughout explanation, it was really useful.

Have a good week.

>>10014106
Oh crap, I sound too serious, forgot to place some exclamations marks here and there!

I think my prob and stats prof is full of shit. An exam asked me to find the probability of being dealt three queens in a five-card poker hand..
Disregarding order, the sample space had C(52,5) points. Then, there were C(4,3) ways to choose the kings, and C(48,2) ways to choose the remaining two cards. Thus, there were C(4,3)*C(48,2) favorable outcomes.
The professor said this was wrong, and claimed that there were C(13,1)*C(4,3)*C(48,2) favorable outcomes because "we would need to choose the face value." This seems like the number of favorable outcomes for any three of a kind, but I didn't ask him. Which of us has the right idea here?

What is the inverse of two in Residue number system mod 12? I'm sure I'm saying it incorrectly I don't how to say it properly.

>>10014410
Under which operation? It doesn't exist under multiplication. Under addition it would just be 10.

>>10014427
multiplication. That's what I came to as well but I was unsure of my answer. I'm trying to find x in 2 * x = 3. But since the inverse of 2 doesn't exist does this mean that there is no answer?

>>10014430
Yes, x can only have a multiplicative inverse mod(a) iff gcd(x,a)=1.
Also that's correct, there's no solution for that equation. You can prove it using the definition of modulo n equivalence and gcd(2,12)=/=1 , or maybe more easily if you already know about the group structure of the integers modulo n.

>>10014455
Think I'll do the former thanks anon.

Is there a good and not so lengthy book about fluids and thermodynamics?
I searched the wiki but the books are goddamn big, more than 500 pages each

Why is memorization called education these days?

I'm guessing I should use the property that cT(v) = T(cv).

So lost on how to do this one.

>>10014676
If you're doing engineering, then I'd recommend Understand Thermodynamics. It's less than 200 pages.

>>10014680
Because it provides the illusion of intelligence without the practice of practical application.
In effect "How to create a slave class without anyone realizing it"

>>10014682
Use the fact that T can be represented by a 2x3 matrix. Then solve the simultaneous equations to find out what the matrix is. Then multiply it out with the last vector.

>mfw 2 digit IQ humanities brainlet struggling with high school math
Should I even bother asking?

>>10013383
>The doppler effect says blue away and red towards with blue being the long waves and red being the short waves?
that seems wrong to me. if a galaxy/object approaches us, it is blue-shifted. if it moves away, it is red-shifted. red waves are ALWAYS lower energy, lower frequency, and longer wavelength than blue waves.

How do you demonstrate this equality? I know how using logic to make the definitions equal but is there an easier way?

>>10014888
LS = RS

why is d(e^x)/dlog(x) = e^x

>>10014925
cause of definition kinda idk, that's my favorite definition

>>10014925
It's not

>>10014925
>>10014929
>>10014933
oh yeah, why dlog(x)
that's just wrong then

>>10014925
d(e^x)/d(log(x)) = x*e^x.
Put x=e^y => y=log(x)
d(e^x)/dy = d(e^x)/dx * dx/dy
= e^x * e^y
= e^x * e^log(x)
= x*e^x

>>10014888
>posts stupid ass question thinking anyone can or will attempt to guess what any of the notation means, as if there weren't 100s of different-meaning bars, or objects with cartesian products

>>10014971
|x|*e^x

>>10014975
It probably means complement in X

>>10014987
here i was thinking it was the closure of a topological space

>>10014975
A and B are subsets of X

>>10015028
still doesnt explain what the bar is, and what X is

>>10015035
X is a set. The bar means the complementary set of whatever's below it

How the fuck is condensed water not distilled?
Do the water molecules keep the salt and minerals when they evaporate?

Need recommendation for website / book on applied statistics geared towards social work / therapy. Want to write up a paper, have data in hand showing improvement based on therapy, but want to be able to analyze data appropriately. Most of what I'm seeing is t-test and ANOVA work; it's been years since I covered stats in college and need a refresher.

>>10014888
>I know how using logic to make the definitions equal but is there an easier way?
Are you asking if there's a way to prove it without using logic?

>>10014683
Thanks! Do you have a recommendation for fluids?

>>10013684
pls respond

>>10013684
perhaps writing LU instead of what it stands for in the most important part of the question would make someone care enough to answer the question?

>>10014888
>>10015056
well in fact that identity is wrong. It should be an intersection, not a union, because the right hand side is [math]X\times X [/math]

>>10015356
No it's not
No it shouldn't
No it's not

For [math]1\leq p\leq q<\infty[/math] we have that [math]L^p(\Omega,\mu)\cap L^q(\Omega,\mu)[/math] (arbitrary measure space) is a Banach space when equipped with the norm [math]\max\{\|\cdot\|_{L^p},\|\cdot\|_{L^q}\}[/math].

My whole problem with this is that a Cauchy sequence might have a different limit in the other norm, say [math]f[/math] for [math]\|\cdot\|_{L^p}[/math] and [math]g[/math] for [math]\|\cdot\|_{L^q}[/math] in their corresponding spaces.
I also see no possibility to connect these norms in any way (like estimates).

I tried to prove that this intersection is a closed subspace, but to prove this, I need the other norm too, which cannot be estimated.
I also tried using the a.e. converging subsequence, but even this doesn't yield anything useful about the intersection of the spaces (as far as I found).

Please help. Any hint is helpful for me.

I'm seeing a bit of quantum mechanics for my Analogic circuits course, and I don't understand what should it represent Schrödinger's equation. I understand that the square of it represents a density function of the position of a particle in a volume, but I can't understand what it is the equation alone. Also, what does it mean that a particle travelling is represented as a pack of waves?

>>10009401
when a number is written inside of a ket, it is just acting as a label. Typically when dealing with an operator the eigenfunctions of that operator are labeled with their corresponding eigenvalues.

Why do I always read about scientists raving about thingamajigs about time distortions 3d vectors and shit, when everybody fucking knows that the cause that time *seems* to go slower when higher density masses or forces are involved, is only because it simply takes more fucking energy for those poor peer-pressured particles to move?

What am I missing? I get the concept of time dilation, but those fuckers make it sound like time, the actual clock ticking time of the universe, is actually running at different speed in some instances, which seems complete bullshit to me. Am I wrong?

>>10015739
>am I wrong
yeah.
GR can be pretty counterintuitive, and the opinion of the masses doesn't determine how the universe works

I'm looking for a way to reduce water's surface tension without making it foamy using common household items
any suggestions?

>>10015739
>the actual clock ticking time of the universe
There is no universal clock. Time is relative.

Might help:
https://www.youtube.com/watch?v=msVuCEs8Ydo

>>10015522
>what does it mean that a particle travelling is represented as a pack of waves?
It means the particle hasn't resolved yet, so it's exact position hasn't been determined, only its potential.

>>10015777
Measured time is relative but what make us sure the universe isn't running on a fixed tick?

I mean, the space and time we experience are just byproducts of whatever calculations the universe is making to run, aren't they?

I don't get why that should preclude the possibility that the dilations in time are just because the molecules are moving slower.

I mean kicking the air is faster than kicking inside water, but I don't see anyone suddenly claiming that time inside water is slower. Because that's metaphorically what the electrons and other particles have to go through under greater pressures.

>>10015739
Again the idiot that doesn't believe in SR and thinks everything is due to differences in pressure...

>>10015847
>I don't get why that should preclude the possibility that the dilations in time are just because the molecules are moving slower.
Because they aren't. Each frame runs at the same speed as ever, from its own perspective.

But if this another relativity denial attempt: We can't help you if you insist your broken theory is better because you don't like the one that works. Don't clutter up /sqt/ (or /sci/) with flat earther "questions", that are just science denial birthed from refusal to accept evidence and deliberate lack of understanding.

Anybody here get their undergraduate degree only to go back to the same school years later to fulfill prerequisites for a master's degree? How do you register for classes if you've graduated already? Do you have to wait until everybody else has registered and hope there's a seat still open for you?

>>10006539
How would one go about graphing something like [math] f(x,y) = x^2y^3 [/math] ?
I know how to graph quadratic surfaces and things of the sort but nothing like this.
Do I just take random contour lines?

>>10006539

Why do worms freak the fuck out whe nyou pour lemon on the ground? Specifically lemon jucie that has been mixed with soda ash or sodium bicarbonate.

It's a game of "4chan picks my undergrad electives for a Data Mining phd application"

Pick 10 from the following:

CS
>Object oriented programming
>Parallel Processing

Math
>Real Analysis 1&2
>Algebra 1&2
>Topology 1&2
>Numerical methods 1&2
>PDEs
>Math Models
>Intro to Stochastics

>>10015985
Email your advisor immediately. He/she should let you register immediately

>>10016307
Alright. That's kind of what I was thinking of doing, anyway.

paid math classes vs free math classes(government subsidized)?

i was lazy at school but want to actually re-learn math from scratch(starting from grade 10 level) now in my mid 20’s.
my goal is to get very good at it because i’m noticing i could have used more advanced levels in my job and hobbies.

>>10016304
>pick 10
>9 things listed
kek, some one is retaking a class

Is this a valid solution? Its just scrap work so wondering if I had the right idea

>>10016369
1 and 2 are separate courses

I'm being asked to find to covariance cov(x,y) but I'm only given y=6x+z and that var(x) =2 , var(y)=172. Don't I need the means to calculate covariance though?

Can someone tell me how to do this

>>10016643
Nvm I figured it out

What's his(Nassim Taleb) setup?
Programming language+extension+software?

https://youtu.be/hRwimmE2wEk

>>10016056
First find special points, such as critical points, local extremas, saddle points, then you can either:

>Try to draw the general shape of the surface (difficult if it's not a special surface)
>Draw level sets
>Draw a cross-section through some symmetry axes (no point if the graph is not symmetric)

>>10016304
in order of unimportance for data mining
>algebra 1&2
>topology 2
Assuming topology 2 is more algebraic-topological like intro to homology/fundamental group, topology 1 could be quite useful as a complement to real analysis, and you can always learn algebraic topology later when you've learnt about groups, etc

>>10016996
Wouldnt I need to find like 20 points or more just to get a vague idea of how the graph looks like?
How do computers graph surfaces?
Just brute force and plot like 10 thousand points in a given place in space?

>>10007009
>>10008517
Those "tiny airbubbles" are in solution of the water. It has also to do with the pressure lowering when you open the bottle.

>>10008267
can you post the circuit also?

>>10017025
> How do computers graph surfaces?
They'll typically just sample the domain on a regular grid, i.e. brute force. This isn't a viable approach for graphing by hand.

For a bivariate function you'd typically draw contour lines. For x^2y^3, each quadrant is going to look a lot like y=k/x, except there'll be non-linear (but monotonic) transformations applied to the x and y. Note that f(x,y)=0 => x=0 or y=0, i.e. the axes are asymptotes. It's symmetric about x=0 and antisymmetric about y=0 (i.e. contour lines for f>0 will appear in the y>0 half-plane and vice versa).

Thefuck is L(V, W)? Pic related.

Can someone tell me how to quickly simplify a something like this
9√42 without having to divide 3402 until i find the best awnser

>>10017134
Simplifying roots boils down to factorisation then moving repeated factors outside (duplicate factors for a square root, triplicate for a cube root, etc). Clearly 3402 is a multiple of 9 (digits sum to 9). 3402/9=378, which is also a multiple of 9 (digits sum to 18, a multiple of 9). 378/9 = 42 = 2*21=2*3*7. 3402=9*9*42 => sqrt(3402)=sqrt(9*9*42)=9*sqrt(42).

>>10017208
>Clearly 3402 is a multiple of 9
How is that clear to you?

>>10017212
Oh sorry saw the explaination after i replied.
Buf what if you have something like
6√36
I have to use my calculator to divide 1296 until i find the right awnser,
is there a trick where i am not dividing until i find what i am looking for?

>>10017091
Set of linear maps from V to W

>>10017212
>he doesn't know
Get ready to get your mind blown
3+4+0+2=9 therefore 3402 is multiple of 9
The proof is about modulo and whatnot so yeah

>>10017219
What the fuck

>>10017223
https://www.mathsisfun.com/divisibility-rules.html

>>10017216
> I have to use my calculator to divide 1296 until i find the right awnser,
You don't have to use a calculator. Mental arithmetic or pen-and-paper also work.
> is there a trick where i am not dividing until i find what i am looking for?
No. You have to factor it, although you can optimise the general case by only considering squares of primes (4, 9, 25, 49, 121, ...).

There are various tricks for spotting divisibility by specific integers: multiples of 3 have a digital sum (sum of the digits) which is a multiple of 3, multiples of 9 have a digital sum which is a multiple of 9, multiples of 2 have an even last digit, multiples of 5 end in 5, multiples of 11 have a base-100 digital sum which is a multiple of 11.

Do American universities accept undergrads from Europe for PhD positions? I am doing a bachelor's in Europe which is three years and I'm wondering if it's possible to continue with a PhD in the US or if I need a masters to compensate for the short bachelor's compared to the US.

>>10006948
What’s q when p=1? It’s been years since I studied this.

>>10006973
I’m pretty sure it’s already fucked itself.

>>10017240
where has this information been all my life

>>10017240
So if i ask you to simplify the 4th root of 625, how do you aproach this?

I know the awnser is 5 because 5^4 is 625 but thats because i am using a calculator.

Do you just memorize these kinds of numbers or what is the best way to learn these problems?

>>10015870
Why shouldn't i believe in SR? Nothing I said goes against that.
What if it's another kind of pressure?

I don't recall anyone finding out yet how exactly time happen or if time is scalar or not.

What can I do with a Bachelor of Science and a Bachelor of Music?

>>10017323
Procedurally generated music

>>10006539
Could someone please explain why the coefficient for j is omitted in the answer here? Been trying to get back into mathematics after a long time and every-time I get to stuff like this the fatigue starts to near in and I can't fathom how basic-looking material functions.

>>10017363
Antiderivative to cos is sin which is zero at t=0 and t=pi. So the coefficient of j is zero, so it doesn't end up in the answer.

>>10017376
Ah, thank-you for clearing that up. If you don't mind further clarifying, I kept obtaining 0.054... which threw me off somewhat due to using degree mode as opposed to radian mode. Completely forgot to make the switch though are there any other cases where I may need to switch to the latter? Just as a heads up.

>>10017391
Do you mean when you need to switch between radians and degrees? If so, then it's often just what the question uses, in your example it is an integral to pi so it's obviously radians, but had it been degrees then use that instead. When I question doesn't provide with either you can use whatever you want, radians are better since they mathematically allow for a lot of relationships concerning a circle but since degrees are taught so early and used more in daily life they are often more intuitive.

>>10017323
what is a bachelor of science?

>>10017091
hory shet, greek letters in math and greek letters in actual sentences
my life is now complete, thanks L(V,W) anon

>>10017412
Thanks for the help, I get it all now.

>>10017091
No idea, its all Greek to me.

Let [math]A: \mathbb{Q}^{+} \to \mathbb{Q}[/math] be defined as [math]A(\frac{n}{m})=m+n[/math] This function isn't well defined, right? Since A(1/1) = 2, but A(2/2) = 4.

>>10017259
Allahu akbar is the answer. Also for all other (real) p.

I need to calculate how much stress the ropes are enduring. How the fuck do I go about calculating this? Where do I even start? Make it two triangles and calculate sin/cos/tan or something?

I can't find anything similar to this in my textbook and I can't find similar problems online. Can you guys help?

>>10017543
You'll need a length

>>10017543

>>10017543
Just draw them nigger

Is CRISPR actually as revolutionary as people say?

>>10017577
I love crispr bacon

I would like to improve my general STEM, science-ish knowledge. For fun and possible future profit.
Is it possible at an older age? How do I even get started? I am not asking for a premade path to walk on, I just want to get started and get into the momentum. I could use a hobby anyway.

>give context
I am basically the 30 year old boomer meme. I had a rough period in life due to reasons I don't wish to talk about. I used to be interested in general STEM stuff in high school but I was a lazy bum when I used to attend. This means I don't know shit, and pretty much forgot how I could get back to learning.
>describe your thought process if you're stuck
I am having 3 main problems here.
1) I am not living in an environment that can help me with these subjects
2) I feel directionless, I at least need to learn the high school (in an European sense) curriculum and understand it -- I can specialize later when I have the fundamentals and I also know what is the more interesting angle to take
3) I basically have no money for nor access to formal education
>try wolframalpha.com and stackexchange.com
I was looking around the general subject for a while. I mostly found the usual positive attitude one is expect with less cynical parts of the internet, but there are things I trust 4chan a lot more than other sites.

>>10017611
>is it possible at an older age
yes
>how do I get started
start reading, question things, do problems to practice your knowledge.
for physics, I HIGHLY recommend the Lewin lectures (you can find on Youtube for free).

>>10017624
>yes
That's reassuring to hear.
>start reading, question things, do problems to practice your knowledge. for physics, I HIGHLY recommend the Lewin lectures (you can find on Youtube for free).
That is a start and thank you for the recommendation. I will check it out.

>>10017471
The range is actually the integers, and it's not well-defined, since (-1)/(-1)=1=1/1 is mapped to both -2 and 2.

Let [math]P(A) \to Q(A)[/math] be a proposition that must be proved by induction, and where [math]A[/math] has [math]n[/math] cases. Is it valid a proof by induction where you use the induction hypothesis only in one of these cases?

>>10017247
unless you're super good, there's a slim chance the university is gonna want someone without a visa studying there, since it is a major hassle. Bachelor's in Europe are much better than American's anyways, so that isn't much of a problem. You might benefit from asking someone at the university you'll be applying for, specifically who you want to be under.

>>10017471
obviously not, the map depends directly on what equivalence class in Q that you're using.

>>10017547
it has been a while since I've done any sort of physics, but here's my attempt:

This problem is better done in polar coordinates, so transform to [math]x=r\cos\theta, y=r\sin\theta[/math]. Then temperature function becomes [math]T(r,\theta)=r\cos\theta\sin(3r\sin\theta))[/math]. Note that both [math]r,\theta[/math] are also functions of time [math]t[/math]. The conditions of the problem state that [math]r=1[/math] is constant, and that [math]\frac{d\theta}{dt}=-\frac{v}{r}=-\frac{2}{1}=-2[/math] is also constant. Note the minus sign comes from the convention that rotations are considered anticlockwise.

The first question asks you to find [math]r\frac{\partial T}{\partial\theta}=\frac{\partial T}{\partial\theta}[/math] (since [math]r=1[/math]) at the given point, which you can easily do once you figure out the polar coordinates of the point.

The second question asks you to find [math]\frac{\partial T}{\partial t}[/math], where you must use the chain rule and the given fact that [math]\frac{d\theta}{dt}=-2[/math].

>>10017683
man, the math font not working makes that really hard to read. Thanks for helping though.

>>10017684
turn off adblock

>>10017692
oh wow.

>>10017652
If I understand you're question right, then no is it not a valid proof technique.

You can't assume A is only one of its n cases, unless you intend to prove that for all A, it is in that particular case.

Think about our proof in the context of k from the naturals where k is either odd or even.

If you just assumed k is always odd, clearly your proof would be invalid because, in the cases where k is even, your argument would not be applicable

Is there are an online tool which is designed for kids, playing around with gears, transmission and the like?
You put stuff together, the software will simulate how it works in RL.
Also usable for people with limited minds, who cannot into conventional CAD.

>>10014111
Pretty sure you are right. The choosing the face value thing makes no sense. What face value needs to be chosen?

any takers?
>>10017835

Why is this false?

Trying to prove [math]\displaystyle \sum_{p=0}^{n}(-1)^{p}\binom{n}{p}=0[/math] for all [math]n>0[/math] by induction.
Base: trivial.
Step: Assume for all integers [math]k>0[/math] that [math]\displaystyle \sum_{p=0}^{k}(-1)^{p}\binom{k}{p}=0[/math] holds.
So I notice that [math]\displaystyle \sum_{p=0}^{k+1}(-1)^{p}\binom{k+1}{p}= \binom{k+1}{k+1}+ \sum_{p=0}^{k}(-1)^{p}\binom{k}{p}+ \sum_{p=1}^{k+1}(-1)^{p+1}\binom{k}{p-1} = 1 + \sum_{p=1}^{k+1}(-1)^{p+1}\binom{k}{p} [/math] . The next step would seem to be to massage out a [math]-1[/math] from the remaining summation, but I can't seem to see how to do this.

>>10018156
should be [math]\displaystyle 1 + \sum_{p=1}^{k+1}(-1)^{p+1}\binom{k}{p-1}[/math] on the end there.

>>10018271
meant for
>>10018270

I once searched out of curiosity for a geometrical way to divide a given segment into n equal parts but all I could find was that one method where they draw another line on an angle and divide the segment trial-and-error style with a drawing compass. Are there any more exact ways to do that kind of dividing, considering one was given a very big length and had to divide this segment in odd/prime subsegments ?

>>10018270
'cause I think on the one hand I could go [math]\displaystyle 1 + \sum_{p=1}^{k+1}(-1)^{p+1}\binom{k}{p-1} = \binom{k}{k} + \sum_{p=1}^{k}(-1)^{p+1}\binom{k}{p-1}[/math], but then I'm left with 2 and not 0.

Why do you call it "Hydrofluoric acid" " Hydrochloric acid" etc. if the acid implies that it has a hydrogen atom anywys? Isn't that redundant?

Brainlet here.

I have this problem about flux with a wire loop.

Am I supposed to use F = Blv ?

>>10017847
No

[eqn]\begin{bmatrix}
1 & 1 \\
1 & 1
\end{bmatrix}
\mapsto
\begin{bmatrix}
1 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 1
\end{bmatrix} [/eqn]

>>10018304
the original question was expanded upon in the thread.

>>10018302
use Faraday's law
[eqn] \textrm{EMF}= - \frac{d \Phi_m}{dt} [/eqn]
if you don't know how to calculate magnetic flux, you need to review

Basic discrete structures question:

List the subsets (ie the power set) of the following set:

{R,Q,N} where R is the real numbers, Q is the irrational numbers, and N is the natural numbers

If I am asked to write the power set of a set that includes as its elements, the rational numbers, the irrational numbers, and the natural numbers, can i write this explicitly (eg like { {}, {R}, {Q}, {N}, ... etc etc } through all combinations of the elements? Or does the fact that each of these symbols represent an infinite set mean that this new set is uncountably infinite and therefore cannot be written explicitly? I thought I was being clever by including in the power set of P(R,Q,N) other power sets like P(R) which would obviously have to be in there, but i don't know if that's enough to make it defined.

The question seems easy either way, but I feel like it's trying to trick me conceptually.

>>10018338
>If I am asked to write the power set of a set that includes as its elements, the rational numbers, the irrational numbers, and the natural numbers, can i write this explicitly (eg like { {}, {R}, {Q}, {N}, ... etc etc } through all combinations of the elements?
Yes.

A simple check is to remember that a set of n elements has a power set with 2^n elements.

What is the answer?

>>10018420
Is this correct? I can't find out if I'm right.

How psychologically unhealthy is it to recreationally use opiates occasionally? Aka "no physical withdrawals"

>>10006539
how do homo sapiens sapiens get carbon

Why are chem teachers so strict when it comes to significant figures?

>>10017683
Thanks anon, I'll contact the university for more information.

>>10018327
The electromotive force induced over the boundary of the contour in his problem setup vanishes along the two lines that make up the width.

VXB=VB is constant over the contour, so:

E=B*V*L.

This is identical to the equation he gave.

I have an IQ of 50 and I've never understood this.
If i'm trying to find the mass of a certain compound do I include the coefficient in my calculation?

>>10018156
Let A = [1 0; 0 0] b = [1 0]. Ax = b is consistent only means that b is in the column space of A.

>>10018425
>>10018420
[eqn]\forall x\in\mathbb R-\{2\}:3\neq \frac{kx-5}{2-x}\iff 6-3x\neq kx-5\iff 11\neq (k+3)x\iff k=-3[/eqn]

>>10006539
Good-day /sgt/, been studying polar coordinates and while I easily remember the formula's I can't seem to apply them well in this question. Tried caculating r using the formula then using it to find the x + y coordinates to convert to Cartesian form and display the answer graphically though it doesn't appear to have been successful. Apologies for the stupid mistake I must have made.

>>10019187
>Tried caculating r using the formula

What's your question? The first element of a point in polar coordinates *is* the radius. There's no need to calculate anything.

>>10019224
Holy shit I'm fucking retarded, just had another look and yeah it makes sense. Sorry for the waste of time. I'll admit I'm rather tired but that's a mistake that really shouldn't be made.

So i am watching "the human calculator"
https://www.youtube.com/watch?v=NgIICQvhqMc

Is it possible to learn how to do this?
not to break his record but to understand how he does this so fast and being able to do this yourself

How do I get TeX to display properly on 4chan?

>>10019547
See the little [math]\TeX[/math] link in the upper left corner of the reply window? Click it.

How is the answer to 1b. not .325? How the fuck do you do these problems.

1a. is .87 for reference

I stumbled upon trying to find the curvature for a given shape.
How would you simplify sqrt(4 + 4t + 18t^2)?
Also, is there a better way of finding curvature other than taking using K = T’(t)/||r’(t)|| ? Taking these derivatives takes way too long and I can’t bother to simplify these shitty equations, thus leading me to leave a mess on my exam.

>>10019690
[math]\displaystyle \kappa(t) = \frac{\mathbf{r}^{\prime}(t) \times \mathbf{r}^{\prime\prime}(t)}{||{r^{\prime}(t)}||^{3}}[/math]
Proof: think.

bümping to limit +1

+2

+3

>>10019775
new
>>10019775

Is there a better way of doing this

=(D3*40)/IF(COUNTIF(F3:3;TRUE)=1;2;IF(COUNTIF(F3:3;TRUE)=2;4;IF(COUNTIF(F3:3;TRUE)=3;8;IF(COUNTIF(F3:3;TRUE)=4;16;1))))

>>10019654
none of the given values have any digits in the thousandths place, how could you possibly get 0.325?

the easiest way to solve these is to draw a venn diagram and fill in all of the values for the exclusive regions as in the regions that cannot be subdivided further. then draw out the region for which you are trying to find the probability of, and sum all of the values that are within that region. Also notice that since [math] P(A \cup B \cup C) < 1 [/math] then [math] A^c [/math] includes values that are not in the venn diagram

>>10019547
adblock off

>>10019690
first rule of differential geometry is that everything is a pain to write out. if you think computing curvature is a pain in the ass, wait till you get to christoffel symbols and first/second fundamental form computations

do electromagnetic waves that travel through space use virtual particles to accomplish this? If not how do they? Also can all of the electromagnetic frequency act as both a wave and a particle or only some of it?