STUPID QUESTIONS THREAD

ln(2x)-ln(x) = ln2

the integral from 0 to 2 of ln 2 is 2ln2

>>8716769
aaaaaaaaaha, for some reason I was considering the area only above the x-axis

thanks a lot, anon

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Okay cool.
I'm having trouble getting the right answer for this. I'm taking cosine law, deriving it and putting it into the work energy equation but my answer is not what it should be. Am I doing it the right way.

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So, I've been given pic related as a task, but I'm confused since it seems that all I'm doing is squaring and summing elements of a white noise vector, which is independent of m. The question says to do it for 2 values of m, but they're (from how I'm reading it) both going to give the same answer anyway.

I don't know whether the question is so supposed to reduce to something stupid like this or whether I'm, well, being stupid instead.

How the FUCK does light have momentum but not mass

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how does this work? why are there 2 e states? why not just write a single e state then fork out with either a or b

aa* | bb* = {a,b,aa,bb,aa..., bb...} right?

>>8717473

>doesn't know about dark mass

>>8717494
are you memeing me or does it explain the problem

>>8716967
use the lagrangian

Can a molecule be a stereoisomer and enantiomer at the same time?

How did they find the value for pi

>>8717598
meme

>>8719314
they divided circumpherence by diameter

what should i do next

>>8718502
Yeah
Enantiomer is a type of stereoisomer. As are diastereomers, and meso compounds.

>>8719421
>and meso compounds
ehh actually probably not, since mesos are basically the same thing

>gief mesos plox

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Retard here, question is in pic related.

Im just not sure of the technique to pick to minimize all values, im sure its related to derivation but I dont remember how to minimize the ENTIRE graph, only how to find mins and maxes of that graph. Been 3.5 years since ive touched calculus so be gentle pls.

>>8719448
well first you find all values of p where the derivative is 0
(every min or max will have derivative = 0, but not every point where derivative is 0 will be a local min or max)
then just look at each point individually on the graph of the function. there won't be too many of them.

although in this case it looks like you're just trying to minimize [math]\frac{\frac{1}{p}}{ln\frac{1}{p}}[/math]
you can look at a graph of the function and see that it asymptotically approaches [math]-\infty[/math] as p approaches 1 from the positive direction

>>8716967

Interesting problem, anon. What answer are you supposed to get?

If the answer I have matches what is correct, then I'll take you through it, but I am not 100% convinced that my approach is correct.

Would love to hear /sci/'s opinion on this: How old is too old for grad school?

What's the difference between SEM and factor analysis?

Is the mount hood volcano in Oregon literally all basalt rock? Is there a history of the layers like say the grand canyon? I know that is a crazy comparison but one should get the point. Surely, there has to be something out there describing the history of the layers before it formed into what is it today or is volcano formation simply another situation entirely?

>>8719510
I think the oldest new student in our department is early thirties.

Really, never, if you just want to learn, but if your past forty, it's going to take you at least five years to get the degree, and it may be tough finding a job when you get out and are approaching/over fifty.

>>8719520
I'm 24, currently working full-time as an engineering tech and pursuing a bachelor's in Applied Math part time. I expect to graduate in about 3 years, but who knows what can happen in a lifetime? Really interested in studying CFDs and generally scientific computing. Thanks for your input, anyways.

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>>8717486
>why are there 2 e states?
It could be to make it more noticable that it's supposed to branch into a's and b's. So it's not actually necessary, but it's just like that to make it more visually stimulating.
It could also be to emphasize the difference between a deterministic and a non-deterministic finite automaton. In a deterministic one, you are only allowed to have one transition per symbol and state. So in this case, you would only be allowed one ε transition from state 0. (or maybe even none. it's not very normal to have a ε transition. we never did that in my automaton class). Then there are also deterministic complete automata, where you need to have one transition for every symbol from your alphabet, for every state. pic related
>why not just write a single e state then fork out with either a or b
You can do that. In fact, you can just leave out state 1 and 3 entirely, because nothing is gained from having them, because ε (greek e) is the empty word. pic related
>aa* | bb* = {a,b,aa,bb,aa..., bb...} right?
Yes. You can use brackets to make it more obvious. ( (a) ((a)*) ) || ( (b) ((b)*) )

>>8719520
I'm thirty in my Junior year. Admittedly, it does feel shitty but no one really bothers you about but I guess my looks help? My first year, someone thought I was a dual enrollment student in HS. kek. I see people older than me going for their first degree as well so that helped my confidence somewhat. 3.8 GPA at the moment.

>>8719488
Thank you! Ill mess with this a bit more, I knew this wasnt difficult I just had a bit of a brain fart I guess.

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When you pump a bike tire up, the pressure and volume of it changes, therefore temperature should remain constant, but the surface of the tire feels warmer after. What causes this?

>>8719510
a friend of my dad's went to med school in his late 40s and now works at NIH

>>8719607
>pressure and volume of it changes, therefore temperature should remain constant
where'd you get that idea from anon
P, V n, and T are all related to each other. Just because P and V are changing doesn't mean T can't change as well, as long as the math works out and the whole equation remains constant.

And in this case n is increasing as well. You're adding more air to the tire.

>>8716741
Real quick question. I haven't ever taken a combinatorics class, but I know that it exists, so I know a littler jargon.

So, I've got 4 slots, and each slot has the possibility of holding 1 of 3 balls. Two balls can't fit in one slot, and all the slots are filled with at least something. Assuming that reading the slots off in a row produces a sequence, how many different combinations are there EXCLUDING duplicates.

So, if the choice of balls were blue, red, and yellow, you could have R, Y, Y, B.

>>8716741
when using a steam table, you can just do h = h'' - h' to find out how much enthalpy was used to make steam out of water at a fixed temp/pressure, does this work backwards? like is the same enthalpy 'used'/created to condensate water as vaporizing water (at the same fixed temp/pressure) ?

>>8717486
There's no need for any epsilon moves; you could just fork from the start state.

But it's much easier to algorithmically construct a NFA from a RE if you allow epsilon moves.

E.g. to compile the | operator, you might construct the NFA for each branch with distinct start states, then add an epsilon move from the parent start state to the start state for each branch.

That way, the overall NFA will be correct even if the child NFAs loop back to their start states.

>>8719699
fuck im dumb

of course it is

>>8719696

Must all colours appear (at least once), or is YYYY allowed?

>>8719696

I count 15 (it's easiest just to generate them, rather than worry about an algorithm).

RRRR
BBBB
YYYY

RRRB
RRRY
BBBR
BBBY
YYYR
YYYB

RRBB
RRBY
RRYY
BBRY
BBYY
YYRB

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I am struggling with part B of exercise 3.3.6

Any ideas? My only coherent thought has been that because the cantor set is compact, there exist a convergent subsequence of both Xn and Yn that converges to a number inside the cantor set. But then I don't know how that helps me.

Is that something? Does it ring any bells?

>>8720042
Wait wait wait. My IQ just increases by 5 points.

As I can pick a convergent subsequence of Xn, I choose an arbitrary one. Call it XXn

Then I pick the subsequence of Yn such that it contains the same 'steps' as XXn and call that subsequence YYn

As these sequences have the property that
1) XXn converges to x
2) At every step n, xn + yn = s

I can prove that YYn converges to s - xn

Is this something?

>>8720061
This is the correct idea. The only thing left for you to do is to prove that x and y (the limits of xn and yn = s -xn) are both in C.

Hint: All C_n are closed.

>>8720042
>>8720061

NO NO wait. I have seen the light. My IQ is oficially unbounded.

I can pick a subsequence of Xn that converges all cait X2n and then construct a subsequence of Yn such that it contains the same steps, call it Y2n.

Them pick a subsequence of Y2n such that it converges and call it Y3n. Then construct the subsequence of X2n that contains the same steps, call it X3n

Then X3n converges too because it is the subsequence of a convergent sequence!

And then, as X3n and Y3n are sequences defined in a compact set, they converge to a point in the cantor set.

Now, say X3n converges to x and Y3n to y.

In each step, xn + yn = s so now

lim(X3n + Y3n) = s
but also
(lim X3n + Y3n) = lim(X3n) + lim(Y3n) = x + y

So then we conclude x + y = s

Thank you guys.

I think I am correct but if some topologists or Analysts can check my proof I'd appreciate it.

>>8720102
>And then, as X3n and Y3n are sequences defined in a compact set, they converge to a point in the cantor set.
This line seems very glossed over considering there's at least a couple of lines worth of reasoning you need to establish that the limit of xn is actually in C. Just saying "compactness" is not enough. What compact set are the sequences defined in? How does that allow you to claim the limit is in C? (compactness only talks about the set the sequence is in, and the entire sequence is quite likely not in C).

Everything else is correct but there's enough of a chunk missing there that you'd lose a mark or two at least on a test.

>>8720134
Fuck man I am a fucking brainlet after all.

>>8720134
My next idea would be to go even deeper with an X4n that contains only the points in X3n such that xn is in a boundary of the closet sets that make up C.

I know there are infinitely many of this, because of the way I defined my Xn for part 1.

Then this X4n converges to a point in C (as it is a sequence defined entirely in C)

But then as it is a subsequence of X3n, it converges to x! So x is in C

Then I can do the same to prove y is on C.

Is this it Papa? Do I get a Fields Medal now? I don't want to be a brainlet.

From my own understanding, information that is being transferred must exist in its entirety in the transmitter and again in total, or greater in the case of redundancies, in the combination of the transmission and the receiver.

In a similair vein, you cannot impart or glean information without gleaning or imparting it.

This draws strange parallels to energy conservation rules to me, is infirmation a conserved quantity?

>>8719537

is this stuff in a graph theory books? where do i read about this stuff

good books on compilers??

What does resection mean? How is it different from amputation? Any medfags who can answer because google isn't helping.

>>8719696
please elaborate on your definition of a duplicate

does anyone know the lecture series that outlines that there are repeating numerical results to equations in the universe?

it also talked about some geometry shapes, number theory and all that fun stuff.

it was a full lecture series and it was presented by an older gentleman

is there a way to describe a parabola using trygonometric or hyperbolic functions?

Is there a fundamental definition for length, area, and volume?

Let [math] m \in \mathbb { Z } ^{+} [/math]. Let [math] M [/math] be a smooth manifold with [math] p \in M [/math] and [math] \left ( U, \phi \right ) [/math] a smooth chart with [math] \phi ( p ) = 0 [/math]. Show that [math] X_i : C^{ \infty } (M) \to \mathbb { R } [/math] defined by: [eqn] \forall f \in C^{ \infty } ( M ): \hspace { 3 cm } X_i f = \left ( \frac { \partial } { \partial x^i } \left ( f \circ \phi ^{-1} |_{ \phi (U) } \right ) \right ) (0) [/eqn] Show that [math] X [/math] is a tangent vector at [math] p [/math]

The fact that it's a map from [math] C^{ \infty } (M) \to \mathbb { R } [/math] follows from it's definition, likewise the fact it's linear follows since derivatives are linear. So all that remains is to show it satisfies Leibniz rule, let [math] g [/math] be another function defined as above, then [eqn] X(fg) = \frac { \partial } { \partial x } \left [ \left ( f \circ \phi ^{-1} \right ) \cdot \left ( g \circ \phi ^{-1} \right) \right ] \text { but f,g,} \phi \text { are just smooth functions, so we can just employ the chain and product rules} \\ \hspace {1.3cm} = \left [ \left ( f' \circ \phi ^{-1} \right ) \phi ' ^{-1} \right ] \cdot \left [ f \circ \phi ^{-1} \right ] + \left [ f \circ \phi ^{-1} \right ] \cdot \left [ \left ( g' \circ \phi ^{-1} \right ) \phi ' ^{-1} \right ] \\ \hspace { 1.3 cm }= X(f)g + fX(g) [/eqn] Which is precisely Leibniz rule.

Does that look alright to everyone else?

>>8721131
what was the point of m in Z^+?

>>8721140
Just to show that M was m-dimensional, I didn't realize that I'd cut that out.

I cant figure out this question, and I cant find it anywhere!:
Solve sin(a) = sin(b), or cos(a) = cos(b) , where a and b are linear functions.

Any help would greatly be appreciated! :D

>>8721192
For example, solve:
sin(x+2) = sin(3x-5)

>>8720544
Amputation refers specifically to removal of a limb. Resection is more general; it refers to removal of some "part" (e.g. an organ, or a specific portion such as a lobe) in its entirety..

Basically, if the tissue to be removed is defined by an anatomical boundary (i.e. it's a part that has its own name), it's a resection. If it's "whatever tissue is infected / damaged / needs to be removed", it's an excision.

>>8720900
> is there a way to describe a parabola using trygonometric or hyperbolic functions?
Algebraically, a parabola is just y=x^2, or an affine transformation of that.

Geometrically, it's the set of points whose distance to a point (the focus) is equal to the distance to a line (the directrix).

>>8721204
sin(x)=sin(y) if x=y, or y=x+2nπ for integer n (periodicity), or y=π-x (symmetry about π/2), or y=(2n+1)π-x for integer n (corollary of periodicity and symmetry).

cos(x)=cos(y) if x=y, or y=x+2nπ for integer n (periodicity), or y=-x (symmetry about 0), or y=2nπ-x for integer n (corollary of periodicity and symmetry).

In each case, the first and third equations are just specialisations of the second and fourth. So sin(f(x))=sin(g(x)) gives you two equations involving f(x), g(x) and integer n, each of which has infinitely many solutions (one for each n).

E.g.
sin(x+2) = sin(3x-5)
=> x+2 = 2nπ + 3x-5 or x+2 = (2n+1)π-(3x-5)
x+2 = 2nπ + 3x-5 => 2x=2nπ+7 => x=nπ+7/2
x+2 = (2n+1)π-(3x-5) => 4x = (2n+1)π+3 => x=(n/2+1/4)π+3/4

More generally:
sin(ax+b) = sin(cx+d)
=> ax+b = 2nπ + cx+d or ax+b = (2n+1)π-(cx+d)
ax+b = 2nπ + cx+d => (a-c)x+(b-d) = 2nπ => x=(2nπ+d-b)/(a-c)
ax+b = (2n+1)π-(cx+d) => (a+c)x+(b+d)=(2n+1)π => x=((2n+1)π-b-d)/(a+c)

>>8721300
Thanks man!

Should I choose Electrical & Electronics Engineering or Computer Engineering?

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>>8716741
in pic related, how does the poster change the upper limit from a = pi/2?

>>8721517
it literally says the substitution right before they do it

>>8716741
How do I know if I'm too unintelligent to learn programming? I've made progress but I feel like I'm failing to grasp some
concepts at all. Nested loops and recursive functions in particular give me a headache. Im having so much trouble with Python, an easy language, I wonder how I can ever expect to move on to other languages.

>>8721524
Know your math.

>>8721523
I know it _says_ so right there, m8, what I wonder is how does he go from a to pi/2? the reasoning behind it?

is it because the ellipse equation itself is =1, subsequently -1<x<1, making a=1

or?

>>8721532
sin u = x/a

if x=0 then sin u = 0 => u= 0
if x=a then sin u=1 => u=pi/2

>>8721533
fuck I'm a moron, thanks guy

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I think my professor just gave me some bullshit that doesn't make any sense. Any Physics majors out there wanna tell me this shit makes sense. The answer is in bold. for the velocity to be constant the accel has to be 0 right.

>>8721634
>I think my professor just gave me some bullshit that doesn't make any sense.
>blaming your own stupidity on someone else
I hate your kind. This is high school physics.

>>8721675
then solve it, and prove that this problem isnt borked

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if evolution is real then how come monkeys still exist???

check mate atheists

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>>8721675
your right im blaming myself.

>>8721634
>for the velocity to be constant the accel has to be 0 right
Yes, which just means that the friction has to exactly balance out the force due to gravity.

Do you think having an acceleration of 0 means something can't be moving?
That's a surprisingly common misconception for how dumb it is.

>>8721727
>>8721727
>for the velocity to be constant the accel has to be 0 right
never said that have no acceleration would mean that something isn't moving. lrn to read

>>8721699
If adam and eve were real then why are there niggers?

>>8721699
That is one of the biggest mysteries of evolutionary science

>>8721730
Well then why do you think it's bullshit that doesn't make any sense?

>>8721765
look at the weight differences. there is no way a 10 kg block will slide down a slope connected to a another block 5 times in weight

>>8721770
oh yeah
that's likely a simple editing mistake. somebody was copy-pasting problems and changing numbers around and forgot to verify that the whole thing made sense

you can probably safely assume that it's moving up the slope instead

>>8721770
I posted this formula in your other thread:
u=(Msin(theta)-m)/(Mcos(theta)). Since as you pointed out the block moves up the slope rather than down it, the friction force points down the slope. The new formula should be:
u=(m-Msin(theta))/(Mcos(theta))

I was plugging in the values, and I accidentally put did (10-10sin(30))/54cos(30) and got .1 so your professor must have plugged in two numbers wrong and used the wrong formula. Sorry but your school sucks

>>8716741
My brain feels stuffed with wool today. I'm a Calc I student learning inverse function and logarithm differentiation blanking on why (d/dx)(xln(a))=ln(a). The full problem so far is (d/dx)(a^x)=(e^(xln(a)))*(d/dx)(xln(a)) and I get that, but I just keep thinking in circles that the right side is just (a^x)*(1/a^x)*(da/dx).

>>8721805
ty i really appreciate your post.
my proffesor has parkinsons and dementia but has tenor so this is probably why he can write shit.

>>8721805
>u=(Msin(theta)-m)/(Mcos(theta))

Shouldn't that be [eqn] \mu = \frac { M \sin \left ( \theta \right ) - m \cos \left ( \theta \right ) } { M \cos \left ( \theta \right ) } [/eqn]

Since the normal force is at an incline.

>>8721851
>why (d/dx)(xln(a))=ln(a)
ln(a) is just a real number. Or am I missing something?

>>8721866
No, I got the formula from setting the force on the small block equal to the force on the large block:
Mgsin(theta)-uMgcos(theta)=mg

>>8721895
if it's moving up the slope it's Mgsin(theta)+uMgcos(theta)=mg

>>8721895
Oh, I'd inserted an additional cos(x) for some reason.

>>8721881
No, you're absolutely right. It as trivial as I was sure it had to be, fuck this sleeping four hours a night for two weeks garbage, never again. Thank you anon.

>>8721939
No problem, I had worse fuck ups.

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>>8716741
Help a megabrainlet out:
What is BD and CD?

>>8721959
google law of cosins

>>8721959
Angles ABC and CBD are supplementary, so CBD=180-100=80, and BCD=180-80-90=10.

You know the length of BC, so use the Law of Sines for the others.

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helo how to solve this

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>>8722231

In a mechanics problem, a particle is accelerating with constant power [math]P[/math] from [math]v_0[/math] to [math]v[/math].
Trying to work out an expression for power, in order to find out time needed to accelerate:
[eqn]
W=Fx \implies \dot W = \dot F x + F \dot x
\implies P = \dot F x + Fv
[/eqn].
I don't know how to make sense of this, as F is a function of v (I think?) Is this a second-order ODE? Textbook explainations seem to ignore the possibility of varying F and just give P=Fv.

hey im going to keep this thread up in the background so people thing imr eally smart and stuff

ill go to the library later today and then ill reallly show those homeless twats whos what

Okay this is making me mad.
There is no way to find f completely from pic rel?
You find f from the second statement, but end up with an expression with 2 unknown constants.
Then you can use the first statement to find one constant in terms of the other.
So ultimately you get f, but with one unknown constant in?

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>>8723692
forgot pic

>>8719607
it's an adiabatic process

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html

>>8721092
bls respond

>>8723713
https://en.wikipedia.org/wiki/International_System_of_Units

>>8723713
also
https://en.wikipedia.org/wiki/Lebesgue_measure

>>8723694
>>8723692
you don't deserve to be in here.

>>8723732
Nice meme.
There are much more basic questions in here all the time.
Jesus, last week there was a question about fractions (as it's own thread) which got taken seriously and answered.

>>8723732
>Deserving to be on 4chan

What a depressing concept.

>>8723714
>>8723718
thank you

>>8723732
His question is legit you braindead prick.

>>8723694
Is that all the information you have ? Also you should be carefull with x and X. Don't you have any bound on the integrande ?

>>8723790
It's from another thread on here, that for some reason just got deleted (interesting choice btw mods considering the other things which float around this board).
The pic is not mine.
And yes that's all I have.

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>>8723771
>>8723772
>>8723790

But guys, it's so easy. pic related.

>>8723823
Yeah that's what I thougth, just a troll question where you're supposed to end up mixing f and f'.

>>8723823
But that's not f, that's f'.
Notice that the derivative of f is given by an indefinite integral, not f itself.

>>8723824
>>8723826

whoops, my bad. I'm not ashamed, still.

>>8722566
W is not Fx, it's [math] \displaystyle \int{F \cdot dx }[/math], or, more clearly, [math] \displaystyle \int{ F(r(t)) \cdot r'(t) dt } [/math], where r is the path over which you integrate. So P is indeed just [math] F \cdot v [/math].

>>8719504
I second this. This problem is dope and I want to see how it's done.

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how do I solve this?

>>8723886
factor out the n^2

split the rest into two sums

use the formula for the sum of the first 3n numbers

>>8723886
Which of the following sums can you calculate?

[eqn] \sum_{k=1}^N k [/eqn]
[eqn] \sum_{k=1}^{3n+1} k [/eqn]
[eqn] \sum_{k=0}^{3n} (k+1) [/eqn]
[eqn] \sum_{k=0}^{3n} \frac{k+1}{n^2} [/eqn]

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How the fuck can i guess hybridization and molecule symmetry only from the way the electrons are put

What coding languages/software/skills in general are the most valuable to learn as someone going for a pure math degree?

>>8716741
Can someone explain to me how numbers are expressed in binary if numbers also correspond to letters of the alphabet?
I know it's probably a trivial question, but I know I would have to read a lengthy article on binary just to find the answer.

>>8723937
you just restrict yourself to 0s and 1s
i.e.

0 -> 0
1 -> 1
2 -> 10
3 -> 11
4 -> 100
5 -> 101
6 -> 110
7 -> 111
8 -> 1000
9 -> 1001
10 -> 1010

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I'm really sorry because I know how autistic this sounds but what is the name of the jobs/positions "scientists" in epidemic disaster movies (like Contagion) hold, the ones that figure out how viruses work and make cures
Like the dudes that work in the CDC, WHO, and the like?
Cellular biologists? Microbiologists? Biochemists?
Lots of labwork and using your brain.

>>8723945
Then how do you represent the alphabet? I seem to remember that the letter A
is represented by the number 48 in binary or something?

Do differential equations classes go over all the different types? Trying to do an BMen MS but DE is a prerequisite I need. I took ODEs too but I'm not sure that counts.

>>8723931

Depends a little bit on what you intend to do afterwards and what your interests are.

For starters, many pure math degree courses involve introductory courses on programming/numerical analysis as standard (or at least as options). Hence, you don't necessarily need to worry. However, if you want a headstart, then just try to find a syllabus for your courses and see what they teach.

If you can't find materials, or if programming is not offered, then go with MATLAB. Most maths courses love MATLAB these days, so I'd say that was your best bet, particularly if you don't know what else you want to do. It's simple to learn.

If you want something a little more versatile (with a view to having more options when you graduate), then C/C++ or Python are good choices but also have plenty of relevance for mathematical tasks - lots of modern numerical simulations are written in C++/Python (well, Fortran was the standard, but it's far less popular these days).

To be honest, I advise avoiding niche languages like Mathematica and R unless you know that you'll be working in numerical analysis as a career. They're excellent for what they do, but people reading your CV might not even have heard of them.

>>8723903
that took me a while, thanks

>>8724072
I'm not too interested in tech jobs. I'm more interested in working in whatever university that's nearby as I feel I would have more time/opportunity to do math research.
I just see alot of people having experience in coding in some way or another to the point that it seems to be required to be able to do anything in my field.

>>8723993
those you mentioned, plus molecular biologists, virologists, epidemiologists, etc

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what did they mean by this?

>>8724130
To Rina with love for (her) support and sympathy

Not really a /sci/ question but has scientific knowledge made you happier/more content with your life? Life is pretty mediocre for me atm and I'm trying to regain some control by becoming smarter, hope someone can direct me. Sorry if it doesn't fit the thread.

>>8720900
In general, or hyperbolic/trigonometric functions in xy coordinates? I dunno about hyperbolic, but you get trig functions in polar coordinates by using the substitution [math]x = rcos(\theta), y = rsin(\theta)[/math] to get [math]r = \frac{tan(\theta)}{cos(\theta)}[/math].

>>8724152
the problem with scientific knowledge is that it offers no guidance of how to use that knowledge

take the jordanpill
https://www.youtube.com/user/JordanPetersonVideos/featured

So I'm supposed to calculate the Arrhenius Parameters of a reaction from values of the rate constant at various temperatures. That in itself is fairly easy (linear relation between [math]ln (k)[\math] and [math]1/T[\math]).
However, it also asks me to calculate the standard deviation of the parameters. I don't know how to proceed for that second part, neither what I'm supposed to look for nor how I split the deviation between the two parameters. Pls help me, /sci/

>>8724001
Anon, you're thinking about things in the wrong order. Binary numbers don't represent letters. Binary CODE represents letters OR numbers, depending on context. When your computer writes the letter 'A' to a memory address, it stores the bit pattern 00100001 at that memory address. If you ask your computer to look for a number stored there, it will say the number 65 is at that memory address, because 100001 is 65 in binary.

If you tell your computer to take 'A' as a character, add 1 to it as though it were a number, and then report the result as if it were a character, it will tell you 'B', because 'B' is the bit pattern corresponding to 66. If you ask your computer to do 2 + 2, it takes in each '2' as the bit pattern 00110010, and has to do some logic (specifically &= 0x0F, but don't worry about that) to wind up with the binary number 2, which is 10.

Bits aren't really numbers, letters, image data, logical statements, processor instructions, or anything else. They're just patterns -- they're not even stored the same way in RAM, storage, optical drives, or the processor. It's the context a program encounters those patterns in that determines how it's displayed. That's why you can open up a program or image or song in Notepad but you get a bunch of garbage -- Notepad's whole job is to look at bits and tell you what characters they are, but those other filetypes are bits that were never supposed to be characters. You've given the wrong data in the wrong context.

That's also what makes digital data and circuitry so cool -- ANYTHING that can store patterns in discrete chunks of yes/no, on/off, black/white, or whatever can store digital data. You could copy a whole movie on your hard drive onto graph paper, with a filled-in square for each 1 and a blank square for each 0, it would just take hundreds of millions of pages. Similarly, anything that can take digital input and produce digital output can build a processor (google "push logic").

>>8724003
That's a question about your school's curriculum and equivalencies that has little to do with differential equations and much to do with your school's particular bureaucracy. That said, if they're only expecting a one-semester undergrad course in differential equations, they're probably expecting that you only covered ODEs.

Are you required to have multivariate calculus? I'd be shocked if they wanted partial (multivariate) differential equations but not multivariate integrals and derivatives. ODEs cover everything that isn't a PDE, i.e. everything where the derivatives are only taken with respect to one variable in a given equation or system.

>>8724157
>[math]r = \frac{tan(\theta)}{cos(\theta)}[/math] renders in the preview but not my comment
What did Hiroshima mean by this?

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Given right triangle picrelated, where P and h are known (specifically, h = 12 cm and P is an independent variable), how do I find the hypotenuse c?

I can get big ugly substitutions, but it's in a section on clever problem-solving (specifically, the "Principles of Problem Solving" section in Stewart's _Calculus, Early Transcendentals_, 7th ed.), so I think there's an elegant approach I'm too dumb to see.

>>8724199
Nevermind, I'm clearly too retarded to read.

>>8724235
Oh, to be clear, h is the altitude or height. Also, I'm specifically supposed to find c = f(P), and I know
[math]c^2 = a^2 + b^2[/math]
[math]P = a + b + c[/math]
[math]ab = hc[/math] (by the formula for area)

>>8724219
Thanks, I was wondering what differential equations meant, but now I realize they're most likely not expecting PDEs but just ODEs. Multivariate calculus isn't a prerequisite.

>>8724290
It's pretty straightforward to get a formula for c in terms of P and h from those formulae. No "big, ugly substitutions"

>move c to the lhs in the second equation
>square both sides
>cancel c^2 = a^2 + b^2
>use ab = ch to get c = P^2/(2*(P+h))

>>8724235

[math]a^2+b^2=c^2, P=a+b+c, ab=hc[/math]
add ab to the left and hc to the right (since they are equal)
[math]a^2+(2ab)+b^2=c^2+(2hc)[/math]
[math](a+b)^2=c^2+(2hc)[/math]
replace a+b with P-c since P=a+b+c
[math](P-c)^2=c^2+(2hc)[/math]
expand
[math]P^2-2Pc+c^2=c^2+(2hc)[/math]
[math]P^2=(2hc)+2Pc[/math]
factor c and divide both sides by the remainding part
[math]c=\frac{P^2}{2h+2P}[/math]

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If you're shaking a spring back and forth to create a certain harmonic, with the other end fixed, is it an open or closed harmonic? It looks like it's closed, but if you're moving the end back and forth, is it sort of half-open?

>>8724159
I watch his video about changing the world. He says you need to change yourself to change the world. What if you don't want to change the world though? Do you still go through the same steps but with a different outlook?

is there some sort of "trick" to get the limits for a definite integral from a riemann sum?

I think I found an error in a study manual I'm using, but I would like someone to double check it for me
"11.7 Let X and Y be discrete random variables with joint probability function
f(x,y) = {y/24 for x = 1, 2, 4; y = 2, 4, 8; x<=y; 0, otherwise}
What is P[X + Y/2 <= 5]?"
The solution given to this problem on page 146 includes the following:
"11.7 For X + Y/2 to be no greater than 5, either X =1, or X = 2 and Y = 2, 4."
This ignores the case when X = 4 and Y = 2, as 4 + 2/2 = 4 + 1 <= 5. The resulting solution (given as follows) is therefore incorrect:
"The sum of these probabilities is
[ (2 + 4 + 8) / 24 (1) ] + [ ( 2 + 4) / 24 (2) ] = 17/24"
The correct answer should be
"The sum of these probabilities is
[ (2 + 4 + 8) / 24 (1) ] + [ ( 2 + 4) / 24 (2) ] + 2 / 96 = 35 / 48"
sorry i don't know LaTeX

>>8724235
probably something with similar triangles. remember dropping a perpendicular line from the right angle of a triangle splits it into 3 similar triangles

>>8724541
nvm, figured it out the hard way

>>8723692
>>8723694
Still haven't gotten a serious answer on this.
I'm right though?

>>8724310
>>8724311
Thanks anons! I don't know why I can't see shit like that sometimes.

>>8724683

If I am interpreting what you have written correctly, then yes, you need another constraint.

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math gods,

when a question asks what is the probabiltiy distribution of X.. what does it mean exactly? are they asking for a probability distribution model that is appropriate for the question? I don't quite understand that, since several models can be used for the same type of situation depending on what we want right?

sincerely,
brainlet

if love is the most poweful force in the world? why haven't we start harnessing it??

How the fuck do series work? What the fuck is a Riemann zeta function, and how the fuck does it converge to -1/12? Like I just can't wrap my mind around it. Can someone link me some resources. How the fuck does 1+2+3+4+5+6+...=-1/12. Shouldn't it be infinity??????????? I hate being a brainlet.

>>8724958
>How the fuck does 1+2+3+4+5+6+...=-1/12.
It doesn't. Let no one try and trick you into believing it is, what is true is that Z(-1) = -1/12, where Z is the zeta function.

[math]Z(s) \neq \sum_{n=1}^{\infty} \frac{1}{n^s} [/math]

Z is only defined for that FOR s where s's REAL part is greater than 1.

When Z is given values that are negative, it is defined by a process called ANALYTIC CONTINUATION, where the mathematician CONSTRUCTS an extension to the function in what is seen as the most natural way to do so.

e.g. why is [math]2^{\pi} \cdot 2^{e} = 2^{\pi + e} [/math] true? Think about what [math]2^{\pi} [/math], means. If you try to think about it like how: [math]2^{3} = 2 \times 2 \times 2[/math] then obviously it doesn't make sense, so what did mathematicians do? They EXTENDED the definition of exponentiation to allow all numbers to satisfy that property.

That is not exactly the idea of analytic continuation, but it illustrates the concept of EXTENDING mathematics

>>8724974
Oh ok. That makes a lot of sense. Thanks

>>8716741

How does crossing over affect gamete genetic makeup? In other words, with one pair of homologous chromosomes, what are the different gamete combinations possible with and without crossing over, assuming nondisjunction doesn't occur?

What is space-time?

I have a language L defined recursively as follows:
(i) the empty string and * are in L;
(ii) if A is in L, so is (A);
(iii) if A and B are in L, so is AB.

Is there a way to enumerate L (i.e., construct a bijection L->N) that doesn't involve wellordering the set of all strings on { *, (, ) } and skipping over the strings not in L?
I'd like to be able to compute the nth word of L without having to iterate through all numbers < n.

>>8725111
I've realized that the number of words with n *s and m pairs of brackets is the number of ways to distribute the stars among the 2m+1 slots of the corresponding Dyck word. Progress!

If a function is injective and the domain and codomain have the same cardinality then it's bijective too, correct? I have injectivity for this function but i'm having some trouble proving surjectivity

Why the fuck is e? I know it's about natural growth or whatever but why is it such a random number? And why is its derivative unique?

>>8725203
>If a function is injective and the domain and codomain have the same cardinality then it's bijective too, correct? I have injectivity for this function but i'm having some trouble proving surjectivity
no

consider the multiplication by 2 map from natural numbers to natural numbers

How do you read the line above letters in math?

Like on a line from A =>D there will be B and C, and AD will have the line above it and so will BC

>>8725253
damn okay, makes sense. thanks

i'm working with infinite sets but it looks like it works for finite sets?

>>8725268
Segment

>>8725207
https://en.wikipedia.org/wiki/E_(mathematical_constant)

everything you ever wanted to know

Do you guys think it's possible to attain a sufficient level of knowledge in physics/mathematics after getting a degree in an unrelated field?

Almost done my chemical engineering degree but the actual work is a real bore for me. Looking to pursue graduate school but would also love to study math and physics in my spare time in hopes of getting somewhere with those. My math skills are pretty pleb tier because >engineering.

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General job question:

How possible is it to actually get into space? Whether it'd be as a scientist, astronaut, engineer or all the above, what're the odds? I'm currently in my junior year of my engineering degree (low tier industrial engineering). I have a mid tier GPA, I'm not anything special and my resume is below average at best. How can I up my game to become an astronaut? What're some steps to take to help me get there?

If not, what do you think the best alternative with an industrial engineering degree is? Opinions on grad school?

>>8725465
Maybe. Depends entirely on what you think a "sufficient level of knowledge" is.

>>8725483
A high enough level to be able to contribute something meaningful to the field.

>>8725465
>chemical engineering
>unrelated
Surely that's enough groundwork to pursue math or physics on your own?

>>8725489
Not technically impossible, but you're not going to do it.

People who become successful researchers spend years in a very supportive environment studying nothing but their topic for full-time hours and then some to reach that level.

The amount of energy and obsessiveness you'd need to accomplish the same thing while working a completely unrelated day job is ridiculous.

You can absolutely learn a lot of math as a hobby but I think you're underestimating how much you need to know to really do something new.

>>8725498
I have a good grasp on ordinary differential equations and some basic linear algebra stuff in terms of mathematics. In terms of physics, it's mostly all phase equilibria. I can't tell you how many classes I've had that were glorified mass and energy balances.

Electrical engineering seems much more rigorous in the math department.

>>8725505
I see, thanks for the information. Maybe I can self-study enough to be able to get a bachelors degree in another over a number of years part-time and pursue something further if my financial situation allows for it.

Is there in psychology some explanation and term for giving everything gender?
What I mean is - when I'm thinking about cars then Tesla, Alfa Romeo, Dacia is for me always SHE. But Wolksvagen, Fiat, Renault is for me always HE.

And it is like that with every non living thing. Why our brains make everything about gender?

>>8725346
>i'm working with infinite sets but it looks like it works for finite sets?
correct

How can I get into graduate school with shitty grades in my first two years? I have over a 3.7 GPA now in my third year, but I can't find any professors willing to take me on into their labs. I need letters of reference but I have no idea how to get a hold of some with my awful track record.

Can't find an internship either, I have no connections and my GPA is an extremely limiting factor. I have a 2.1 GPA in my first two years, it is that bad. Is there any hope? Schools in Canada only really care about your most recent two years of study for graduate school but I'm worried I won't be able to attain the experience needed to get in.

What are my options for post-undergrad? Employment is a no-go since no internship and my family is poor so I can't just go do another degree.

What's the difference between technology and engineering in STEM?

>>8725536
It sounds like you've already done this to some extent, but the most likely way to get these sorts of things is to talk to your professors.
If you're doing very well in their classes and they know your name you should be able to find at least one or two that can help you out with something, either finding something you can do with them or pointing you somewhere else.

I don't know if this works for lab experience because I didn't study in a field that did that, but I had a very similar academic experience to you (pathetic grades in years 1-2 and then virtually perfect in 3-4) and I got grad school letters and an internship in an actuarial firm this way (I spoke to a prof who offered to send my name to the company the university does a program with because of my performance in his class).

There's an aspect of luck involved obviously but generally professors who know you will do what they can to help you out, provided you ask.

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assuming there was a cure for lung cancer, would it be ethical to say there's nothing wrong with smoking?

>>8725647
That's up to you, it's based on your morals.

>>8725647
there's nothing morally wrong with fucking up your own health in the first place, as long as you don't subjcet others to shit like secondhand smoke

>>8725523
All vehicles are referred to as female, so the correct term for you is fag

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This is a really easy question but I keep getting it wrong. The answer I'm getting is "e^(x-y) + c".

The first thing I did was factor the right hand side and rearrange it so all y-related terms are on one side and the x-related on the other. I then integrated both sides, took the exponential of both sides to get rid of the logs, and finally rearranged to get it in the desired form.

I would really appreciate it if someone helped me on this because it's so simple but I continue to get it wrong.

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Calling all mathematicians to answer this question I found in the textbook "Basic Category Theory"

>3.3.1 Choose a mathematician at random. Ask them whether they can accurately state any axiomatization of sets (without looking it up). If not, ask them what operating principles they actually use when handling sets in their day-to-day work.

>>8725857
(y-3)/(y+4) dy/dx = (x-1)/(x+6)
(1 - 7/(y+4)) dy/dx = (1 - 7/(x+6))
y - 7 log(|y+4|) = x - 7 log(|x+6|) + c
7 log(|x+6|/|y+4|) = x - y + c
(|x+6|/|y+4|)^7 = e^(x - y + c)

>>8724152
No one really gave me a concrete answer to this. Anyone care to share their opinion?

>>8716967

This is an energy problem.

Call the total energy at the start 0. Then kinetic energy and potential energy are 0.

When theta is 60 degrees, m2 has gone down some height and lost some potential energy. Body B has gone up some height (which is clearly 3b(1 - sin theta) ), and gains potential energy.

Whatever it is, the change in potential energy must be equal to the new kinetic energy in both m1 and m2.

Lastly, relating the speed of m2 to the speed of body B (body B clearly travels at 3 times the speed of m2), you can solve for the kinetic energy and speed of either body B or m2, and so theta'.

now i have to select all the images with a storefront

>>8724152

yes, but only because it has ever since i can remember. it may be different for you, no one knows

>>8725893
Thanks a heap mate, I can see where I went wrong. I should have been more careful with what I was doing with the constant. Funny, I did it a few times and made the same idiotic mistake each time.

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>>8716741

HOW THE FUCK IS IT DONE FFS?!

RETARDED FUCKING WOLFRAM
>CANNOT DETERMINE GENERAL FUCKING TERM
NO MATTER HOW MUCH I FUCKING SPOON FEED IT

Where are my socks?

>>8726312
I know the way but this corner of the board wouldnt fit my proof

>>8726131
So what about it makes you happy. The knowledge? The application of said knowledge?

>>8726552
Just write it on your own paint file. Or better yet use latex.

>>8726312
[eqn] \sum_{k=n+1}^m \frac{1}{2^k} [/eqn]
[eqn]= \frac{1}{1 - \frac{1}{2}} \sum_{k=n+1}^m \frac{1}{2^k} \left(1 - \frac{1}{2} \right) [/eqn]
[eqn] = \frac{1}{1 - \frac{1}{2}} \sum_{k=n+1}^m \left( \frac{1}{2^k} - \frac{1}{2^{k+1}} \right) [/eqn]
[eqn] = \frac{1}{1 - \frac{1}{2}} \left( \frac{1}{2^{n+1}} - \frac{1}{2^{m+1}} \right) [/eqn]

>>8726655
That's not how sigma fucking works. It would be a sum of [1/2^k - 1/2^(k+1)] of every k.

>>8726680
try writing out the first few terms of the summation on line 3

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>>8726680
>That's not how sigma fucking works.
kys brainlet

>>8726655
ur a truest heroe yet! thanks.

How to PIRATE fucking wolfram? I need a lot of the pay2play functionality but it only gives some fucking crumbs from the master's table.

ALSO: WHY THE FUCK CAN I NOT CREATE A FUCKING THREAD? IT KEEPS BULLSHITTING ABOUT WRONG FUCKING CAPTCHA, FFS!!?

>>8726765
>ALSO: WHY THE FUCK CAN I NOT CREATE A FUCKING THREAD? IT KEEPS BULLSHITTING ABOUT WRONG FUCKING CAPTCHA, FFS!!?
the captcha system is a brainlet filter

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this isn't a question and there's no math thread up but i'll just leave this book recommendation here, it's a good read

>>8726765
you are probably using an extension to replace the new image-picker captcha with the older one
but you need captcha v2 to post threads now

>>8726781
ffs

>>8726809
4chanX allows you to use legacy captcha for thread responses but nu-captcha for creating new threads, btw

>>8726765
>How to PIRATE fucking wolfram?
It is a web service ...
You can not pirate a web service.

You are probably looking for mathematica or even something similar like maple, but you really should get them from your university for free.

Pirating them has a 99% chance of infecting your PCs with a virus, so I would avoid that.

Stupid statistics question:

For some estimate of mu (mu-hat) described as a function of 2 independent variable, how do you compute mu-hat so that one may determine the bias, variance, etc.

Eg.

mu-hat = (X[1] + 2X[3]) / 3

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>>8728110
>don't pirate wolfram pirate mathmatica
are you talking about WOLFRAM mathmatica, anon?

I live in Cali. Should I be worried about sushi in the wake of Fukushima?

How do I do this?

sin(60+θ) = cosθ where -90°<θ<90°? It says to use the compund ange formulae, but I don't see how it can help here.

>>8725207

>why is it such a random number

If it was any other number you'd be asking the same thing.

what would it take to cause the entire internet to become inaccessible for an extended period of time?

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I can do every other question here but for some reason I get nowhere with these.
For the first two I understand I need to sub in the spherical coordinate values for [math]x=rsin(a)cos(b)[/math], etc but I can't get it into a decent form. All the other ones simplified nicely.

For the last one, I just get a big clusterfuck answer of like [math]\frac{ln|\frac{-5}{3e^{5x}}|}{3}[/math] which is wrong.

Would anyone be able to give me an idea of how to go about these questions?

>>8728439
your answer for the differential equation looks pretty right, at least essentially identical to what wolfram spits out modulo a constant

why do you think its wrong?

>>8728439
First one is ezpz. You have radial symmetry... this is it in polar coords:
[math]7z^2=6\rho^2[/math]
Now go to spherical
[math]7r^2\cos^2\theta=6r^2\sin^2\theta[/math]
[math]\tan^2\theta=\frac{7}{6}[/math]
[math]\theta=\arctan\sqrt{\frac{7}{6}}[/math]

>>8728439
Second - use polar first as well you dummy (hint: rotate it you spastic):
[math]x=r\cos\phi\\
z=r\sin\phi\\
r^2(\cos^2\phi+5\sin^2\phi)=2[/math]

>>8728476
It said it was wrong when I put it in. Maybe I messed up the constants. I'll have another go

>>8728523
Wow maybe I am retarded. I left the answer as [math]tan\theta=\sqrt{\frac{7}{6}}[/math]

>>8728531
I'll give it ago.

>>8728531
Doesn't [math]x=rsin(\phi) cos(\theta)[/math] though?
Making the whole thing [math]r^2(sin^2\phi cos^2\theta + 5cos^2\phi)[/math] ?
When I enter this it says it's wrong though..

Can anyone suggest a good linear algebra book?

>>8726655

neat

What is a good baseline of mathematics/science do I need to know if I want to study electrical engineering?

>>8728351

sin(60 + x)
= sin(60) cos(x) + cos(60) sin(x)
= √(3)/2 cos(x) + 1/2 sin(x)
= cos(30) cos(x) + sin(30) sin(x)
= cos(30 - x)
= cos(x - 30)

[ 2nd to last step since cos(a)cos(b) - sin(a)sin(b) = cos(a + b) ]
[ last step because cox(-x) = cos(x) ]

>>8724928

From what I can tell, it means to write the distribution exactly. Which you would use in part b to calculate P(3) exactly.

>>8724356

it's open on the end you shake it, and closed on the other?

How do I into autodidacticism?

How can i demonstrate the finiteness of the set of numbers which are egal to the sum of their digits + the products of its digits is finite ?

#{Number = Product + sum}

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Posting this from other thread since I need help
Can someone PLEASE show me actual math behind this as opposed to y is sin x is cos equation is 2y-3x=2

>>8728902
Divide both sides by r.
Use r*sin=y, r*cos=x,
1=2/(2y-3y)

>>8728912
holy shit I've been multiplying by r or substituting like crazy jesus christ am I really this much of a brainlet
thank you anon

>>8728738

Ah, thank you.

>>8728902
[eqn]r^2=x^2+y^2[/eqn]
[eqn]\cos \theta = \frac{x}{r}[/eqn]
[eqn]\sin \theta = \frac{y}{r}[/eqn]

Plug those in and do a little bit of algebra. You should get C.

>>8728882
Is there even anything in this set other than 0?

>>8728946
Found 19

>>8728946
Aaaand 99 (random guess)

>>8724108
It's hard to know which language you will end up needing. However, once you learn one, it's surprisingly easy to learn another. The differences are mostly superficial. I suggest just picking one and going with it until you have a reason to change. Java is amazing, and C++ is nice because it shows more of the underlying systems but it's more complex.

>>8728882
If N is a number n digits long:
sum+product <= 9n+9^n < 10^(n-1) <=N for n>=22

What's the benefit of knowing math if you don't want to learn anything that needs it like physics or mechanical engineering? Also what's the fun that some people see in it? Legit baffled by some people who think doing math problems is entertaining.

>>8724622
One of the conditions is x <= y

I have a question.
If I know that something is [math]3,84*10^4[/math] degrees pr 1 kg, and I know that that something has a density of 8,9 [math]g/cm^3 [/math] or a mass of 116g and has a length of 25 km, how do I connect these numbers?

>>8729525
>degrees per kilogram
what the heck are you talking about

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Find v for θ = π/4

θ'' =26⋅48 sinθ
θ(initial)=3π/4
v=4θ'

The answer given is 34.619 and I get 30ish. Don't know what im doing wrong I think even this is outwith my maths skills.

>>8729532
Sorry. I mean degrees celcius pr 1 kg. I think. Is that not possible? Oh shit.

Stuck between biomed, chemical, and environmental. Leaning environmental. I'm in Georgia but go to UGA. Have the opportunity to go to Georgia Tech for grad school. What's what arguments do you anons have for those three listed degrees

>>8729540
Of course it's possible. But degree's per kilogram could mean a million things.
how'd you measure it?

>>8729569
Okay, it's the last of a 9 parter. The question is "what is the rise in temperature in the kobber cable, when the energy is removed in a period of an hour".
So I figured out what the heat capacity is (385 J/kg*degree C) or c, and I knew the electric power which is [math]4,11*10^3[/math] W. The time is 1 hour or 3600 sec. Which equalled [math]1,48*10^7[/math] J, which is both the electric energy and the thermal energy.
Then I said [math]E/c[/math] and got [math]1,48*10^7/385 J/kg*degree C[/math] which is equal to [math]3,84*10^4[/math] degree C.

>>8729602
if you take a unit in J and divide it by a unit in (J/(kg*K)), your results units should be degress TIMES kg, not degrees PER kg

>>8729645
My apologies. And thank you.

>>8729651
to add on to this: with problems like this you should make sure to pay attention to the units of all your numbers. don't take shortcuts by not writing them down while you're doing your work, because the half a second it saves you in writing down your work on paper is not worth the possibility of getting the units wrong later

in this case, once you look at the units you can see that what you currently have is in degrees * kg and the answer you want should be in degrees, so the clear next step is just to divide by the mass of the cable (which you may need to solve for first)

Is it possible to be a scientist and be fit?

>>8729661
I see, thanks to you as well.

What is the relationship between math and autism??

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how do i do this?

Anyone good at discrete math? my prof is an ass hat and doesn't know how to teach the class

can someone help me out with this problem?

Compute E[X] and V[X]

X= x_1 when you pick a nonnegative integer solution of x_1 + x_2 + x_3 +...+ x_10 = 4 uniformly at random.

>>8719520
you'll also have the advantage of being mature

How come when I do [math]\displaystyle \int_{-1}^1 \int_{-\sqrt {1-x^2}}^{\sqrt {1-x^2}} \sqrt {1 + \frac {x^2+y^2} {1-x^2-y^2} }dy dx[/math]
I get 2pi instead of 4pi? (surface area of sphere)

What makes it so that I only get the positive portion of the sphere?

>>8730173
I-is that Calc 3?

why do torque's exist?

>>8730181
Because moments (of forces) exist?
And because shear forces get transferred through bodies

>>8730104
Virtual ground principle, i.e. the voltage at the inverting input is zero. Also, the current flowing into the inverting input is zero, so the current flowing into that node from the voltage source equals the current flowing out toward the output (clearly, Vo must have the opposite sign to Vin).

>>8730176
Yes. It's nothing too difficult.

I'll go over the basics of how surface integrals work without any actual proofs or derivations, since I'm bored and have nothing else to do while I wait for an answer.

Basically in calc I and II, when you take a derivative of a function, [math]\frac{df}{dx}[/math], f is only ever a function of x. That means the arclength integral you guys do in calc II works fine (if you haven't done it yet, it's [math]\int_a^b \sqrt{f'(x)^2+1}dx[/math] In Calc III, f is a function of multiple variables, so f'(x,y) makes little sense.

What you're actually (informally) adding up, or integrating, in 2D is a sum of small segment lengths or infinitely small lengths of tangent lines. In 3D, it's a sum of small tangent planes. Tangent planes in 3D are defined as the cross product of the partial derivatives.

Partial derivatives are the measure of the change in f as all other variables are held constant and x is subject to change. (so if f(x,y)=x^2+2xy+y^3, [math]\frac {\partial{f}} {\partial{x}}=2x+2y, \frac {\partial{f}} {\partial{y}}=2x+3y^2[/math]. Cross products always give you a normal vector to the two points, and you can describe a plane using that normal vector ([math]n_x(x-x_0)+n_y(y-y_0)-n_z(z-z_0)=0[/math] where x_0,y_0,z_0 is the point you want the equation of the tangent plane at). So the cross product of those two partials give you the area. The magnitude should be obvious just looking at the normal vector equation there, since each "n_" is the partial for each. The derivative of "z" with respect to "z" is obviously equal to 1, even if it looks "wrong". The magnitude of a vector is the root of the sum of the squares of the components, so in calc III the surface area looks like [math]\displaystyle {\int \int}_A \sqrt{(\frac {\partial{f}} {\partial{x}} )^2+(\frac {\partial{f}} {\partial{y}} )^2+1}dA[/math] where dA can equal dxdy or dydx. You can also convert this to other systems (cylindrical, etc).

>>8730237
That's pretty cool.

I am a math major taking Calc 3 next semester which coincidentally starts next monday.

I wanna be able to model problems using crazy integrals like that too my man. I was just making sure that shit wasn't measure theory or whatever because yesterday in a thread some gay came up with a really weird integral to solve a problem and he mentioned measure theory.

If you care, the problem was:

Say you have a square of side length 2. Consider the points inside this square that are closer to the center of the square, than to the sides of the square. Find the area of the shape formed.

What he did was define a double integral like yours but weirdly it had an inequality in there and he said he was integrating over half the square, whatever that means.

>>8730151

can you post the exact question or is that the question cuz i dont understand anything

or im just a brainlet

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>>8730259
>Consider the points inside this square that are closer to the center of the square, than to the sides of the square. Find the area of the shape formed.
I was in that thread. (https://warosu.org/sci/thread/S8726965 for reference) The guy was either an idiot or just too tired/lazy to write it correctly. The way he treated inequalities was the same way you should treat bounds, and I've never seen anyone write bounds the way he did. If you look at this picture, you can see easily where he got his bounds from.

I'll set up the integral and just solve it immediately to spare you the details. You basically just integrate the inner and then the outer, treating whatever isn't the current variable like a constant.

I drew a line on it to make it easier, you actually do have to use symmetry here or else it gets difficult real quick. I might forget to multiply by 8 because I'm too tired/lazy to get out a sheet of paper to think.

It's trivial to show that x^2=1-2y intersects y^2=1-2x where x=y=sqrt(2)-1 ~.414. (please don't try to do this by hand).

Basically, x goes from 0 to .414 and y goes from (1/2 - x) to ((1-x^2)/2 - x) where that "-x" comes in because I'm making a triangle-like shape to exploit the symmetry.
In calculus III terms, that's [math]\displaystyle 8\int_0^{\sqrt{2}-1} \int_0^{\frac{1-x^2}{2}-x} 1 dy dx[/math]
and in calculus II terms, it's a really really easy problem, it's basically the region y=(1-x^2)/2 minus y=x, or
[math]\displaystyle8\int_0^{\sqrt{2}-1}\frac{1-x^2}{2}-x dx[/math]

Yes he got the answer right, it is in fact 4/3(4sqrt(2)-5), but his setup was absolute trash. I think he just threw in the word "measure theory" to sound smart, since this is a very basic problem after you figure out the equations.

>>8730380
>y goes from (1/2 - x) to ((1-x^2)/2 - x)
Oops, I meant 0 to ((1-x^2)/2-x)

>>8724210
underrated post. Very good answer.

>>8728110
wxMaxima is basically the free version of Maple....

Is every isosmotic solution isotonic?

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If you add two Gauss curves, how does the resulting curve look like?

>>8730604
it depends on the membrane properties

>>8728110
> but you really should get them from your university for free.
Stop assuming irrelevant things you have no fucking basis for assuming.

Next time you answer a fucking question, ASSUME THERE'S A FUCKING REASON IT WAS ASKED you retarded autist.

> Pirating them has a 99% chance of infecting your PCs with a virus
That reminds me of beta virgins who say that having sex has a 99% chance of infecting your dick with STD.

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HOW DO YOU SOLVE THIS FFS? AM I RETARDED OR WHAT?!!

>>8730789
whats obchislit mean?

>>8730789
yes you're retarded

obviously square it, simplify, then take the square root

>>8730793
> SOLVE
What else ffs...

>>8730789
definitely retarded, i thought slavshits were supposed to be good at math

what did you even try? how do you even do this wrong? you see square roots, there's literally one thing that you should be thinking, you try it, and it works

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WHY THE FUCK is the bottom statement true? It implies that n + 1 = n when n -> infinity, but it wasn't proved in the book yet. So how do I know this is true?

>>8731049
In other words, would it really make sense if I wrote lim_[n -> inf]b = Z provided b is in {x_n}?

>>8731049
Assume that the sequence converges and use the definition of convernge to prove it

I don't want to latex so bear with me, I will write x(n) to mean the sequence

You want to prove that for all epsilon, there exists M such that whenever n > M,
| x(n+1) - x| < epsilon

First, let epsilon be arbitrary

But you have that x(n) converges so simply pick N such that whenever n > N
|x(n) - x| < epsilon

And now lets use this N to x(n+1).
We have that the above inequality holds whenever n is larger or equal than N, so you can pick N-1
And whenever n > N-1 in your new sequence, that means n+1 > N-1 in your old sequence, which means n > N

So you get |x(n+1) - x| < epsilon

Which then, by definition, means that the sequence x(n+1) converges to x

>>8731049
because it doesn't matter whether you start "counting" at n or n+1, you can even pick a random natural number c and still have lim(n->inf)(x_n+c)=x

>>8731059
I can't fucking assume that cause that's what I'm proving here. There must be something else.

Basically if the expression c -> x when n -> infinity given that c is in {x_n} makes sense there's no problem. But does it?

>>8731106
>I can't fucking assume that cause that's what I'm proving here.

What can't you assume?

>>8731113
I think he was refering to my post: >>8731061
which was not meant to be a proof but to give him the intuition for why it works

>>8730552
Thx senpaiino.

>>8730173
I'm too dumb to remember all my calc III skillz, but in the spirit of "did you check if it's plugged in?": are you sure the negative portion of the sphere hasn't disappeared because of the square root? (By analogy to [math]x^2 + y^2 = 1[/math] being the unit circle but [math]y = \sqrt{1 - x^2}[/math] being only the positive semicircle.)

>>8732660
[math]\displaystyle x^2+y^2+z^2=1, z^2=1-x^2-y^2, z=\pm\sqrt{1-x^2-y^2}[/math]. If I made that part 0, it'd give half of what I got (so pi)
It's probably the fact that I have to take the root of [math]||\vec{N}||[/math], since that number squared equals the sum of the squares of the elements squared. I was just hoping for a way to mathematically and reliably give the correct answer, without using other coordinate systems or graphs, since not every implicitly defined function has a good corresponding coordinate system.

>>8730380
>those y bounds
Wow I definitely wasn't thinking, I meant from x to ((1-x^2)/2). It's the same answer but the second integral was meant to give intuition.

>>8730782
see
>>8730573
for a possible solution

>>8730798
arent russians supposed to be really good at math? I work with a guy name Vlad - fucking genius at math. Be more like Vlad.

What are some current ethical issues in engineering? I need some topics for a paper and ASAP

Rules to determining if an integral is improper or proper?

Also rules to determining if an integral converges or diverges?

>>8721743

It is actually within the field of 'conservation biology' most people think its about muh zoo animals n shit but it says that they are still banana picking primates because of no genetic drift.

How would you simplify this equation to get x in terms of A, B, and C (which are constants)? I've tried some log properties but things aren't working out.

[math]1-A = e^{B/x} - Ae^{C/x} [/math]

>>8728734
google electrical engineering university of reno, nevada and follow their curriculum except the retard classes like eng101 and intro to engineering proffesionalism.

Stupid question.

Say I've got an asteroid, and it slams into the ocean as opposed to the ground -- does the asteroid stand a better chance of surviving the landing or is it just as pulverized as if it were to hit the ground?

I can't find anything on this question on the internet, every article autistically focuses in on how big the tsunami would be, or some other shit, and that isn't what I want to know.

What happens if you mix methyl alcohol and ammonia together?

>>8716741
>>8733664

why is intelligence correlated with mental illness?

>>8730813
>>8733168
since when are eastern europeans good at maths? i thought asians were good at maths and eastern europeans good at programming/hacking things together

>>8733779
there's high schools in moscow where they're already learning about manifolds and abstract algebra

>>8733783
no there aren't

>>8733785
why are you making claims about things you know nothing about? have you ever even studied in russia? i've studied in moscow, and here's one of the schools

http://sch57.ru

>>8733801
so where do i see evidence for your claims?

>>8719341
A woman, if you can.

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>>8733804
can you not even read the website?... here's some of the abstract algebra material they've put up

group theory:
http://sch57.ru/files/mathcamp/2016//seniors/3.GroupTheoryII/s1.pdf
http://sch57.ru/files/mathcamp/2016//seniors/3.GroupTheoryII/s2.pdf
http://sch57.ru/files/mathcamp/2016//seniors/3.GroupTheoryII/s3.pdf

field theory:
http://sch57.ru/mathcamp/2013/Bunina_Sr_1.pdf
http://sch57.ru/mathcamp/2013/Bunina_Sr_2.pdf

>>8716741
> x = 2
are you looking for the area to the left of x = 2, or to the right of x = 2?
If the former, then take the integral from epsilon to 2 of (ln(2x) - ln(x)) dx, where epsilon is a positive, real number less than 2. The integral simplifies to epsilon to 2 of (ln(x) + ln(2) - ln(x)) dx, which is epsilon to 2 of ln(2) dx. This becomes [(ln(2)*2) - (ln(2)*epsilon)]. Because you are trying to find the area to the left of x = 2, you want to take epsilon to 0, so lim epsilon -> 0^+ [(ln(2)*2) - (ln(2)*epsilon)] = [(ln(2)*2) - (ln(2)*0)] = ln(2)*2. This procedure is basically the process of computing the improper integral 0 to 2 of (ln(2x) - ln(x)) dx.

When teachers/tutors/society value people more who first failed and then succeeded rather than those who succeeded right away.
Is there a name for this phenomenon?

Example:
Math teacher assumes kid #1 will be able to solve a problem, therefor he doesn't get much praise when he does. When kid #2 solves it he gets more praise because the teacher had lower expectations of him.

>>8733829
Why are gorillaposters the most based posters?

>>8733733
it's not?
you just never see the autistic kids who aren't smart because they're stuck inside while their poor parents wipe their asses and try to manage their autistic temper tantrums all day
the smart ones are the only ones who actually go out and participate in society