A thread for questions too stupid to have their own thread.
I'll start: pic related, where the fuck does the 2/3 come from?
>>8040874
Context? What are the brackets?
>study math
>take differential equations
>it's fucking physics with a little bit of biology
Why is this allowed? Why should I give le fug about omg so exciting predator prey relation in nature!! XDD!!kjhbnsadfghjkasd
>>8040894
>Go to community college
>Bitch about classes being bad
Fuck off
>>8040907
MIT, but nice try, monkeyboy.
>>8040894
Your class must have been taught very strangely for you to complain in that way. I know what type of examples you're talking about as far as physics bio stuff... But for me the class as a whole was dominated by learning new math concepts
Is it true that sugar is an immunosuppressant? If it is, then does eating a decent amount every day have a significant impact or is it just a meme?
>>8040912
Ahahahaha fucking /sci/ where 40% of the board goes to MIT. Its a meme kid
>>8040887
expectation value. its QM, S is the area of a circle
(particle in circular motion, well its semi classical)
Do you round up or round down experimental errors?
Me and my friends were debating this,
Say your calculated error is 1.2 cm
do you state the error as +/-1cm or +/-2cm?
>>8040966
+/- 1
What reason could you have for rounding up?
>>8040962
what is its wave funktion then?
fucking faggot how are we supposed to help you when you give no context asshole
>>8040978
chill your beans. pic related is all i have to go by. the lecture notes are utterly shit im afraid
Is this an adequate definition?
[math]
\emptyset := \{x \ | \ \text{False} \}
[/math]
>>8040997
you need to know what x and y are. I mean what distribution they have.
Is it just a decreasing exponential?
>>8040874
when you use biot-savart law, you almost always get a denominator with a (x^2+something^2)^(3/2)
>>8041037
Why?
>>8040969
Because if the minimum error is 1.2cm, you can't just round down (essentially saying the experiment is more precise than it actually is), instead you should round up so that there is 1 sig fig, but there is a 100% certainty that the value is within that range.
What do ya think?
>>8041063
How to fix?
[math]
\emptyset := \{ x \in S \ | \ \text{False} \}
[/math]
where S is an unspecified set.
Is it fix?
>>8041179
>I'm leaning towards Berkeley because they seem better for algebra, geometry, mathematical physics where UCLA seems better for analysis, number theory, and logic.
Nigga it's undergrad; the exact research strengths down to the subfield don't matter. Go to Berkeley since it's cheaper.
>>8041242
I'm looking to do as much (quality) research as I can in the next 2 years and so to me, I felt if I could connect with professors who have similar interests, it'd be much easier.
>>8041352
Both departments are huge, e.g. Berkeley has a shit ton of analysts. You'll find someone working on something you like at either school, and you will probably only work seriously with one prof. Honestly, most incoming grad students aren't even that sure of their specific research interests, and I bet yours will change a lot as you take upper level classes. I'm kind of amazed you're so set on certain subfields this early on. I just think there are better things to consider as an undergrad than research fit.
But yes, Berkeley is very good at algebra and geometry. Good luck, anon.
>Suppose we toss a fair coin until we get exactly two heads. Describe the sample space [math]S[/math]. What is the probability that exactly [math]k[/math] tosses are required?
Second part is [math](k - 1)\frac{1}{2}^{k}[/math], right?
If I have an equation f(x), and an equation g(x, y), how do I find the value for g(x, y) that would give me a function that is as close as possible to f(x)?
I mean I have this 3d plot of the function g(x, y) and somewhere I could take a cut that would give me the closest thing to f(x) that exists in g(x, y). Anyone who can help? Ideas are very appreciated too.
What I thought about is getting the integral of |f(x)-g(x, y)| and the global minima should be what I search for, but it doesn't seem to work very well.
>>8041549
More specifically,
f(x)=cos(x)-((12pi-48)/pi^3)*x^2-((72-24pi)/(3pi^2))x-1
g(x, y)=(x^3)y-((3pi)/4)(x^2)y+((pi^2)/8)xy
This is the result of "Oh how hard can it be to approximate cos(x) over an intervall with polynomials, let's try it out".
>>8041579
take the middle of the interval
write taylor series at that point
>>8040997
just use the last line where it says/x^2=y^2=z^2.
THe expected value is linear and r^2=x2+y2+z2 thats all you need
>>8041587
No, go away with your taylor series, it sucks. There's a reason it's not actually used for calculating cos, like ever.
Does a natural number divided by an aleph number mean anything?
Why does raising a number by the 1/2 power square it? I know it does, but what's the mechanics behind it?
Surely 64^1/2 = 32? But it doesn't, it equals 8. Why is that?
>>8041690
>Why does raising a number by the 1/2 power square it
Square root it I should say.
>>8041694
Because you're multiplying it with itself half a time, not multiplying it with a half
>>8041549
You want a function, or a point close to f(x)? A function seems sort of vague, but a point is easy enough. You set up a relation using the square of the distance between the two functions, and you find any critical points.
>>8041722
Yeah but I just don't get it. I understand what you're saying in principle, but I understand why. I can't visualize it.
How do you find the base element in a series?
I've just discovered that hiccups is because of carbon doxide content in the blood. I had the hiccups and I covered my mouth with a blacket and breathed through it and the hiccups went away. How do I get financial backing for a scinece experiemnt?
>>8041515
The reason I'm reasonably certain about my interests is because I self study a lot and have found my interests tend to lean in the direction of algebra topology and geometry.
Thanks for the advice my friend.
>>8041596
>I want the best approximation for a function like cos
>but pls no taylor series, it sucks
how retarded can one person get
>>8040894
? I took the DiffEq for Scientists and Engineers and we hardly talked about applications unless they were some hw/exam questions to give context.
>>8041596
Calculators use https://en.wikipedia.org/wiki/CORDIC
But Taylor series work and is how the majority of approximations are done in physics (analytically), so stop being a little bitch, acting like you know how things are done.
Can anyone explain how the bounds of integration are computed in the projection of the xz plane?
Is there a drug capable of distorting the brain's perception of time while maintaining consciousness and bodily functions, i.e. the drug makes it feel like a longer amount of time has passed than it actually has but doesn't impair the senses beyond that?
>>8041901
Try low doses of DALT
>>8041892
he wants polynomials
and he wants approximations over an interval.
CORDIC only gives the value at one point
that guy is retarded, he doesn't even deserve any help.
>>8040874
This text contains a hidden message:
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Hint: the hidden message is Huffman coded.
>>8041758
What number is halfway between 1 and 9? If you take an additive approach, it's 5. If you take a multiplicative approach, it's 3. The square root function is the latter.
>>8042056
So 9/2= (rounded up) 5, but 9^1/2= 1*9*1/3?
I just dont get it. I feel like I understand what you saying, but I can't write it mathematically.
>>8042071
First, you should really write square root as x^0.5 or x^(1/2) or [math]\sqrt{x}[/math].
Anyway, I'll try to be a bit clearer about what I was saying before. There's a slight difference between finding the additive half and the multiplicative half (bullshit terms I just came up with now). For the additive, you should start with zero:
[math]0+c+c=9[/math]
[math]2c=9[/math]
[math]c=\frac{9}{2}[/math]
For the multiplicative, start with one:
[math]1\cdot c \cdot c=9[/math]
[math]c^2=9[/math]
[math]c=3[/math] (ignore the negative root for now)
Now go back and check them:
[math]0+\frac{9}{2}+\frac{9}{2}=9[/math]
[math]1\cdot 3 \cdot 3 =9[/math]
>>8042056
one is called an arithmetic average, the other is a geometric average
>>8042115
Fuck, that was it, thank you.
>>8040874
For a prime p and integer b, if b^2 = -4 mod 4p, does that imply that b^2 = -1 mod p?
>>8042129
What integer are you squaring to get a negative result from modulo with a prime? Do you have a weird definition of prime that includes negative numbers somehow? Are your integers complex?
>>8042129
No, it would imply [math]\frac{b^2}{4}[/math] is congruent to -1 mod p, if [math]\frac{b^2}{4}[/math] is an integer.
>>8042137
4^2=17-1
>>8042137
Well, as an example, if p was 5, then b^2 = -1 mod 5 could have b = 2. They're all real integers.
>>8042141
Wouldn't that mean that b^2 = -4 mod p?
>>8042129
YES.
USE THE DEFINITION
B^2 = -4 + 4P*K FOR A CERTAIN K
DOES IT IMPLY B^2 = -1 + P*M FOR A CERTAIN M?
IN THAT CASE, BOTH B^2+1 AND B^2+4 ARE IN THE SAME CLASS MODULO P
WHICH MEANS 3 DIVIDES P
SO P=3 OR THE IMPLICATION IS INVALID
18) Consider V = IR4 of usual internal product, determine a non-0 vector v Є IR4 that is orthogonal to v1 = (1, 1, 1, −1),v2 = (1, 2, 0, 1) and
v3 = (−4,1,5,2).
Help
>>8042199
>>8042214
v= (a,b,c,d)
v.v1=0
v.v2=0
v.v3=0
three equations.
If you want to add one equation, you can fix one of the coordinates of v.
Does it make sense?
Don't be lazy, this is how you fail or succeed.
>>8042222
thank you, quads
i love you
What's a good reference text for learning discrete maths?
How do I do the convolution of two complex exponentials?
[eqn]h_1=1-e^{-j*\omega}[/eqn]
[eqn]h_2=1+e^{-j*\omega}[/eqn]
Calculate [eqn]h_1*h_2[/eqn]
>>8042328
The omage is supposed to be the normalized frequency but I couldn't be bothered putting in the hat.
What does compact support mean anyway?
I got a dumb one.
when squaring an infinite series, i vaguely remember seeing something about making a grid, and summing diagonal cells. i can't for the life of me remember what that's called so i can google it.
I think it's possible to keep a body alive without brain activity, but is it possible to sustain a brain's functions without the original body, i.e. by using a "mechanical" heart/lung machine?
How is the concept of "self" quantified in science; based on how the brain responds to stimuli, or something else?
>>8042383
FOIL
If I wanted to show that a set of vectors have the same angle between them, is it sufficient to just show that their dot products are equal? Or will I need to calculate the angle of all of them?
>>8042383
I believe something like "cauchy summation" might bring it up.
>>8042507
I'd normalize before taking the dot product, and then cite a theorem or definition.
>>8040874
Ha, nobody's actually told you yet.
[math]\displaystyle \pi\langle x^2+y^2\rangle=\pi \langle x^2\rangle + \pi \langle y^2 \rangle[/math]
From distribution of expectation values.
You also have:
[math]\displaystyle\pi\langle r^2\rangle=\pi\langle x^2+y^2+z^2\rangle=\pi\langle x^2\rangle + \pi \langle y^2 \rangle + \pi \langle z^2 \rangle[/math]
Assuming the situation is isotropic, you have:
[math]\displaystyle \langle x^2\rangle=\langle y^2\rangle= \langle z^2\rangle[/math]
This means:
[math]\displaystyle\pi\langle x^2\rangle+\pi\langle y^2 \rangle = 2\pi\langle x^2\rangle=\frac{2}{3}\pi\langle r^2\rangle[/math]
>>8041895
It's easy - you just need to integrate up to the point z=1-x for each point of x you're using.
What happened between
[math](5+2)*7^k-2*2^k[/math]
and
[math]5*7^k+2(7^k-2^k)[/math]
see pic for full solution.
I feel like this is a lot easier then i think it is
>>8042321
[math]j[/math] as complex number. Disgusting engineer.
Just take the fourier transform of each, into time space and then multiply and transform back. Convolutions in frequency space become multiplications in time space, and vice-versa.
>>8042542
both have a common factor of 2
>>8040926
>>8040912
Did someone mention /MIT/?
>>8042545
So, it'll be a basis for a 2D space. Every vector in [math]\mathbf V[/math]can be written in the form:
[math]\displaystyle\mathbf v=\mathbf x - \frac{\mathbf x\cdot\mathbf n}{\sqrt {\mathbf n \cdot \mathbf n}}\mathbf x[/math]
where
[math]\displaystyle\mathbf x \in \mathbf R^3,\ \mathbf n = (2, 3, -1)^T[/math]
Now, just show that [math]\mathbf v_1+\mathbf v_2[/math] and [math]c\mathbf v_3[/math] all can be written as some vector [math]\mathbf v_4\in \mathbf V[/math]
The other axioms of a vector space are already proved, because [math]\mathbf V[/math] inherits from [math]\mathbf R^3[/math]
A basis for [math]\mathbf V[/math] is easy to find. Just pick any 2 vectors orthogonal to [math]\mathbf n[/math], that are also orthogonal to themselves. Normalise them, and you have a basis. The dimension of [math]\mathbf V[/math] is 2 because you've put a constraint on the vectors allowed, which gives you 1 less dimension to play around with.
>>8042555
That feel when you get deferred then ultimately rejected. MIT broke my heart.
>>8042534
I forgot to say that all the vectors have the same magnitude, but I guess I should normalize anyway. But yeah, that's sort of what I was thinking rather than calculating the angle for every one. Though I don't think a definition or anything like that has been taught in my course so far so I'm not really sure.
>>8042635
Cal Tech masterrace here
Is this dictionary actually fruitful to make use of? I've only seen it for the first time in Etingof's "Introduction to Representation Theory" notes and not sure how common it is
>>8041549
Are you trying to find a y' such that g (x,y') is closest to f(x)?
If so, I don't think there is a unique solution, it all depend on what norm you want to minimize ||f(x) - g(x,y)|| under.
I suggest minimizing it under the L2 norm, so you integrate (f-g)dx and them minimize this w.r.t. y (i.e. find the critical points etc.)
>>8042694
I'm trying to find a g(x, y) that would give me the closest thing to f(x), with which I mean have the smallest area between g(x, y) and f(x).
Here's a shitty mspaint picture, I want to find a value g(x, y), that if plugged into the function would give me a new function g(x) with the smallest possible gray area between it and f(x).
>>8042807
And of course I forgot the picture.
![2016-05-01 22_21_29-ChemDraw Professional - [Untitled Document-1 _].jpg](https://i.imgur.com/zwFDKQB.jpg "2016-05-01 22_21_29-ChemDraw Professional - [Untitled Document-1 _].jpg")
would this ever happen?
>>8042816
Yes, however, f(x) includes a trigonometric function, while g(x, y) is a polynomial, so that is not the case. So I need to find the function that is closest to f(x).
>>8042832
Perform a taylor expansion of the f(x) function, and use that as g(x, y) to whatever accuracy you require.
>>8042839
No, I want to find a polynomial of third degree that gives me an accurate approximation of cos(x). I found the coefficients of a parabola that closely traces cos(x), with a maximum error of 0.02. If you substract the parabola from cos(x), you get a function that looks very close to 0.02*sin(4x).
Now I want to find the third degree polynomial that traces this function as close as possible. The taylor series is not good because if you take the third degree taylor series for cos(x), you get a maximum error of about 0.2. Which is horrible.
>>8042856
Ok, so you're going to need to fit a function [math]y=ax^3+bx^2+cx+d[/math], with the aim of reducing [math]\int_a^b\{y-f(x)\}dx[/math].
You can fit this on a computer, which is trivial, but maybe time consuming cause of the 4 variables.
Do you want me to explain the process of fitting these variables in a program?
>>8042876
Yes, however, I assumed I need to take the absolute value of f(x)-y, to really get the function closest to f(x). And at that point wolfram alpha tells me I exceeded computational time and I'm at a loss. What should I do?
>>8042888
This is probably easiest to do in python with the SciPy package.
Here's a basic form for the program:
Create a function f(a, b, c, d) that returns:
[math]\int_m^n|ax^3+bx^2+cx+d-cos(x)|dx[/math]
You'll need to do this integration numerically.
Scipy has an optimize function, in which you'll input this function, and some limits for a, b, c, d then it finds the values of them that give the lowest value for the integral.
If you tell me what the range you're integrating [math]f_{a,b,c,d}(x)-cos(x)[/math] over is, I can write a simple example for you?
>>8042893
The function f(x) I want to trace is
f(x)=cos(x)-((12pi-48)/pi^3)*x^2-((72-24pi)/(3pi^2))x-1
and the function g(x, y)
g(x, y)=(x^3)y-((3pi)/4)(x^2)y+((pi^2)/8)xy
the limits are 0 and pi/2
Thank you a lot if you can give me an example.
>>8042902
Ok, gimme a minute
>>8042902
Ok, here's a paste of the program: http://pastebin.com/8ag4GtN8
I minimised according to the function g(x, y) you gave, and received y=0.1136
If you minimise for a general polynomial you get:
a=0.1152
b=-0.2792
c=0.1551
d=-0.0039
for the equation y=ax^3+bx^2+cx+d
Let me know if you need anything else
>>8042929
Wow thank you very much, I will play around with it to get a better result, because ideally the result for d should be 0. What does lambda x do exactly?
>>8042940
That's alright :). Lambda x is an anonymous function - it's basically a function without a name that you can create and use as an argument. There's a lot more to them than just that though.
I doubt you'll get a value for d to be 0, cause of the cos(x) term. Here's a plot of the values found for [a,b,c,d] against the polynomial you're fitting to.
What's this for, by the way?
>>8042940
Ok these do seem to be good estimates, and as expected the error could be traced by a 5th degree polynomial, so everything worked fine. How could I get a more exact result? Does pysci already use double precision? If yes, can it use higher precision?
>>8042945
I think it would be as easy as keeping d out of the function, maybe the other results will get better then? That's what I did for the second degree polynomial anyways, usually it would have been ax^2+bx+c, but since I already knew what c is supposed to be, I set it to 1.
I want to get a function that I can use to aproximate cos(x) as fast as possible. A precision to 4 digits with a third degree polynomial would be pretty good, I don't know if there's anything better than that right now. A third degree polynomial would only take the time of 3 multiplications and one addition to calculate.
>>8042946
I'd expect it uses double precision, but I'm not sure - you should check the manual.
I don't think numerical precision would help improving the precision of results though, as that's probably not the bottleneck.
You can increase the number of iterations that the minimize algorithm goes through by adding the maxint=100000 argument into the options dictionary. This is what's cutting it out at the moment. You get vanishing returns on increasing max iterations though.
Minimize lets you specify which algorithm to use for this, so it might be worth researching an algorithm that'd be more useful for this specific case.
Can a trimatrix that doesn't have any 0s in its main diagonal ever be singular? Putting some code together to find the LU decomp of a any trimatrix where it exists, but not too sure if I need to account for it being singular anywhere.
>>8043067
A tri-diagonal matrix?
>>8043067
Any 2*2 matrix is vacuously tridiagonal so there's a counterexample right there.
The simplest 3*3 counterexample I can think of is:
[ 1 1 0 ]
[ 1 2 1 ]
[ 0 1 1 ]
>>8043093
Thought so. Ta
I'm interested in math textbooks with a heavy focus on motivation/narrative/fun. Something like Understanding Analysis fits this description perfectly. I am even interested in "softer" books like Godel, Escher, Bach, that have a heavy focus on mathematics in order to explore other topics. Any recommendations?
>>8043362
Jänich's Topology
It goes all over the place in terms of topics and tries to make everything very intuitive.
>>8043369
Cool, definitely looks like what i'm after. Does this book cover what you might traditionally learn in an undergrad topology course? My shitty school doesn't have a proper topology course at all (only offered as independent study), so it would be great for me if it did.
>>8043388
It does, but it is not a formal textbook. i.e. there are no exercises. Also it jumps around in terms of difficulty.
i.e.
Chapter 1 is your typical intro to Top. Spaces, but then Chapter 2 starts talking about Topological Banach&Hilbert Spaces.
or
In chapter 3 on Quotient Spaces it will at some point just casually bring up Grassmann Manifolds.
or
In chapter 5 on Homotopy it feels the need to teach you Category Theory in the middle of the chapter.
Also I don't remember where, but at some point it starts talking about Homology as if it assumes you already know what it is. (only briefly)
If you fire two arrows from a bow simultaneously does the power of the bow split?
It should right? Basic conservation of energy. Potential energy stored in the bow arms transfers to kinetic energy in the arrows. Since you have 2 arrows you have double the mass (assuming the arrows are identical) so each arrow gets half of the energy.
I might have answered my own question but i'm just checking i'm not missing anything out
>>8043478
as a rough first approximation, you're right.
How can I not solve this???
/sci/ help its driving me insane
second order nonlinear homogeneous differential equation ._.
[math]y'' + \frac{D}{m}y'^2 = -k[/math]
What if STS 27 lost another tile from its heat shield
Is the following proof correct? Working with the left side and praying my latex comes out properly.
[math]\frac{(sec x)(csc x)}{cot x} = sec^{2}x
=(\frac{1}{cos x}(\frac{1}{sin x}))\frac{cos x}{sin x}
=\frac{1}{cos x sin x}(\frac{sin x}{cos x}
=\frac{sin x}{cos^{2}x sin x}
=sec^{2}x[/math]
>>8044351
fuck, how do I make equations on new lines with latex?
>brb checking sticky
>>8042576
You can't actually assume that all the vector space axioms are inherited simply because V is a subset of R^3.
In order to show that V is a vector space, you have to show that it is non-empty, closed under addition, and closed under scalar multiplication. This should be fairly straightforward.
>>8044351
>>8044354
Ok, some mistakes in the formatting. Retrying here.
[math]\frac{sec x(csc x)}{cot x} = sec^2x[/math]
I will be attacking the left side.
[math]=\frac{\frac{1}{cosx}\frac{1}{sin x}}{\frac{cos}{sin}}[/math]
[math]=\frac{1}{cosxsinx}(\frac{sinx}{cosx})[/math]
[math]=\frac{sinx}{cos^2xsinx}[/math]
[math]=sec^2x[/math]
pls god proper latex
what's a site better than /sci/ for asking questions like the above?
Another trig question. More about just fractions. Can I cancel out 1-sinx in the following?:
[math]\frac{1-sinx}{(1-sinx)(cosx)}[/math]
And if so, I would correctly yield 1/cosx, or secx?
>>8044318
this is a riccati equation with unknown y'.
why is
[math]\frac{(\frac{1-cos^2x}{cosx}}{3tanxsinx}[/math]
equal to 1/3?
>>8044429
1-cos^2 = sin^2
(1-cos^2)/cos = sin^2/cos = sin*tan
if you divide by 3*tan*sin, you're left with 1/3
Anyone know how they found that CCDE? Usually I can go from block diagram to equation no problem but this is confusing me. I keep ending up in a loop
>>8044469
You're saying if I divide:
[math]\frac{\frac{sin^2x}{cos}}{3tanxsinx}[/math
by 3*tan*sin, I'll get 1/3?
>>8044559
*
[math]\frac{\frac{sin^2x}{cos}}{3tanxsinx}[/math]
>>8044564
That's not what he's saying
sin^2(x) / cos(x) = sin(x) / cos(x) * sin(x) = tan(x)*sin(x)
Cancel the tan and sin with those on the denominator and you're left with 1/3
>>8044568
ah! Thank you!!
Is there a better website for posting shitty questions like this over and over? With help as soon as possible?
And I'm a trig retard who feels like I'm lacking in some basic concepts. What's the best way to fix those? Review them as they appear (realistically, due to time constraints, I'd probably write down the problem (e.i: factoring), and come back to when I have time)? I just wanna have a SUPER solid base for calculus, I think I'm sort of ironing out my wrinkles as I go though.
thanks in advance. I think math is fun, but sometimes In gert frustrated at myself for overlooking elementary things and I want that to stop
I'm taking my Linear Algebra final tomorrow, I don't even browse /sci/ :^)
>>8044362
>closed under addition, and closed under scalar multiplication
I did say to do that... Read my post properly.
I said after showing it's closed under those, then it inherits the rest of the axioms from [math]\mathbf R^3[/math]
I have a bottle of vitamin supplements that expired in March, are they no good now?
When rounding sig figs do you include the sig figs of the samples you used to make a calibration curve?
I made a calibration curve then compared an unknown sample to it. The lowest sig figs in the creation of the calibration curve is 2 but the unknown sample prep did not go below 3.
Not sure if my final result for concentration should be 2 or 3.
>>8044389
I see no reason why you couldnt do that.
>>8041690
You can get a proof for exponentials by using the fact that
[eqn]exp(a*ln(x))= x^a[/eqn]
(im hoping im doing the latex right)
a simple proof: lets look at [eqn]exp(\frac{p}{q}*ln(x))^q[/eqn]
this equals (laws of exponents)
[eqn]exp(p*ln(a))=a^p[/eqn]
If you now take the q-th root of that you will see
[eqn]exp(\frac{p}{q}*ln(a))=\sqrt[q]{a^p}[/eqn]
Apparently, the equations of motion of this system should result in SHM if the small-angle approximation is used. However, I get an angular velocity term in the theta equation.. what am I not seeing?
>>8045590
Clearly the dimensions don't fit in your last equation.
Do a dimension analysis in each line to check where you went wrong.
>>8041063
What is the original set then?
I understand completely the law of conservation of energy in the context of mechanic energy. I can see the correlation of a moving particle in state A with potential energy equal to the total energy and the particle in state B with Kinetic energy equal to the total amount of energy.
But I just can't see it in the first law of thermodynamics. If a gas transitions from one state to antother state of energy, how am I getting that the total energy is constant? I don't get it.
Trigtard here again double checking my work.
Need to find exact value of cos285 using sum and difference formula.
Using a reference angle of 270, cos285=cos15
cos15=45-30
applying difference formula:
cos45cos30+sin45sin30
convert to exact values:
[math]\frac{\sqrt2}{2}(\frac{\sqrt3}{2}+\frac{\sqrt2}{2}\frac{1}{2}[/math]
>>8045755
[math]\frac{\sqrt2}{2}(\frac{\sqrt3}{2})+\frac{\sqrt2}{2}(\frac{1}{2})[/math]
And I end up with 1/4(sqrt6+sqrt2)
is that wrong?
Is it possible for a planet to have a moon larger than it? What if the planet was really dense and the moon was nearly entirely gaseous?
>>8045642
Do statistical mechanics. Makes much more sense from that perspective.
>>8045755
>cos285=cos15
you mean cos285 = sin15
I'm really having difficulty with 1 through 4. Can you direct me to a resource on how to do these?
Here's my stupid question: I have a 50 year probability of an event of 13%. How do I reduce this to a single year probability in the simplest, most elegant way possible? Assume that the probability of the event is the same in any given year of this period.
>>8046114
let p be the probability for each year.
the probability that, over 50 years, the event never happens is (1-p)^50
so the probability that it happens at least once is 1-(1-p)^50
equate this with 13% as you said.
0.13=1-(1-p)^50 which means (1-p)^50 = 0.87
so p = 1-(0.87^(1/50)) = 0.00278
the probability for each year is 0.278%
>>8046101
http://math2.org/math/trig/identities.htm
>>8046182
Thanks, same answer I got but my method was way absolutely disgusting. At least I know my mathematical gore worked though.
>>8046199
Curious as to how you did it
√-1 * √-1 = i^2 = -1
or
√-1*-1 = √1 = 1
What the fuck should I do?
>>8046308
sqrt(x*y) != sqrt(x)*sqrt(y)
>>8046334
if x,y < 0
>be me
>never really studied math, always had bad grades and lived in the edge of failing math every year
Now I want to make up for that but don't know where to start, I tried some teaching sites like khan academy but if I start from the beginning it is way too simple, if I start a little bit ahead I feel like I am skipping something important that will be missed later on.
My question is: what are the topics (for example algebra as a topic), in order, that I need to learn? Also, any books recommendations on those topics will be much appreciated. Thanks
Why does Pi show up in so many equations that seemingly have nothing to do with circles?
For example, pic related is a formula for approximating the amount of partitions of a number. How the hell does Pi come into this? Is it just a randomly chosen constant?
>>8046590
I was doing algebra II and getting a C when I started self-teaching calculus.
Basically, if I got stuck on something, I would look it up. So if I was doing integrals and an integral required trigonometry, then I would look up the trigonometry topic.
I tried learning math from the bottom up but it's not efficient, you learn a lot of shit you're going to forget anyway, and learning calculus, trig, geometry at the same time is a better learning experience.
>>8046640
https://en.wikipedia.org/wiki/Wallis_product
it appears here, which appears in a lot of asymptotic formulas.
Im stuck on this problem. I am suppose to find all answers on the interval 0<2pi. Can someone help out a lowly trig student :(
>>8046979
nigga, expanding the expression was your first reflex? Damn
what happens if a product of two things is equal to zero? One of them at least is equal to zero
>>8046984
omg..... What the hell was i thinking
I just need to set both products equal to zero...
sec-1=0
tan-1=0 So the answers for both of those on this interval are.
0, pi/4 5pi/4
Wow for some reason i made that way more complex than it needed to be.
How did the he go from the first row to the second row? The sum of combinations to that new combination
>>8047091
It's just a well known identity that someone derived a few centuries ago
>>8047114
What is it called like?
>>8047117
Vandermonde's identity
https://en.m.wikipedia.org/wiki/Vandermonde%27s_identity
>>8047091
just think about it
how many ways can you choose k things from n1+n2 things if you pick i of the first n1 things and k-i of the other n2 things? this number is (n1 choose i)(n2 choose k-i)
i can be anything from 0 to k so you get that sum
How do you approach this
> At a party N men throw their hats into the centre of a room. The hats are mixed up and each man randomly selects one. Find the expected number of men who select their own ha
Could someone please explain this notation to me?
[math]X \cap \left (\bigcap_{n<\omega} W_n \right ) \neq \emptyset.[/math]
>>8047251
To the best of my understanding, the intersection of X with the intersection all groups Wn (that satisfy the condition n < ω) does not equal the empty set.
Does that help any?
>>8047256
thanks
>>8047251
different anon, here a visual
>>8047256
Did you mean the intersection of X with the intersection OF all groups Wn?
>>8041901
I too have often wondered this. sort of like a neuroaccelerant if you will. It does work with DALT as >>8041913
suggested (at VERY low doses), but the best time dilation I ever had was with 4-HO-MiPT; what I thought was about 4 hours of walking with my friends was closer to 26 minutes. I mean, I had all the hallucinations and perspective warps, but it was basically what you're describing aside from that.
>>8042321
ah, Signals. Yeah, move those into the frequency domain so you can just multiply them (keep in mind they will transform as you move them), then move them back to the time domain after you've multiplied them (using the reverse of the process for getting them to the frequency domain.
Should be relatively easy to do by hand if I recall
>>8042545
>space that is orthogonal to a line
Think about that. What do they mean by orthogonal to a line?
>>8042662
>ass = pussy
If you say so
>>8047310
The inner product is 0.
>>8047296
Yes, sorry for the typo.
What are the differences between those 3: cumulative density, cumulative probability, cumulative distribution?
Guess I'll try here
>>8047432
Can anyone explain me what happens after the 2nd "="
>>8047609
Never mind I remembered how integrals are solved
>>8047578
Cumulative means that you sum something up so cumulative distribution is the integral or sum of a density. It is a sum if the density is discrete and integral if it is continuous.
https://en.wikipedia.org/wiki/Probability_density_function
>>8047621
Thanks, but what about cumulative probability and cumulative distribution?
>>8047625
Those are confusing things you should avoid saying or writing. Density is a momentary or differential probability and cumulative is a sum or integral probability.
I've got one that's been bugging me.
Why, in our solar system, do the orbit of our planets mostly fall on the same plane? Is this a coincidence or does that tend to happen around most stars?
>>8047638
I haven't thought so much about it, you should ask my space nerd friend, but I doubt he's on 4chan.
>>8047609
the x is the primitive function of 1 and the numbers to the right of the vertical line mean plugging in for x, upper minus lower.
>>8047638
https://www.youtube.com/watch?v=tmNXKqeUtJM
Some time ago i started reading about particle physics. Quarks, electrons, protons, etc and the four fundamental interactions. What i wasn't able to find were the formula for calculating the forces these interactions produce. Do they exist? Or have they yet to be discovered?
>tfw there's no way i pass this exam with questions like this
How can group elements be a basis for a vector space over F in the definition of a group algebra?
>>8047950
uhhh your image says exactly how
that's an F-vector space
>>8047956
I dont understand. Say for instance F = R, and G is the dihedral group of order n. If we take [math]s[/math] in G as the reflection of the n-gon, then how is 5[math]s[/math] defined?
>>8047970
Nevermind. Same as a FG-module. I was thinking of [math]V = F^{n}[/math].
>>8047949
Its just probability. That may appear complicated, but you will soon realize that it can get so much worse.
>>8047977
How bad does it get?
>>8047981
You are letting yourself be misled by things that look complicated because the calculation is long.
>>8047985
Is there a resource where I can practice this kind of stuff? The slides just explain the concepts, but I don't have a lot of practical exercises to go from
>>8047992
Like a course textbook?
>>8047998
I guess you're right. You gave me hope anon
Can anyone tell where the minus between the terms came from after differentiating?
>>8048113
What's the derivative of [math]-\theta[/math]?
>>8048117
Oh... I missed the chain rule bit. Thanks anon
Something in an exercise from the early sections of Hartshorne is bothering me. Let [math]X,Y[/math] be varieties (in the quasi-projective sense). For any point [math]P\in X[/math], we can define the local ring of regular functions at P, denoted [math]\mathscr O_{P,X}[/math]to be germs [math]\langle U, f \rangle[/math] where U is a nbd of P and f is regular on U. A morphism [math]\varphi: X \to Y[/math] gives rise to a homomorphism [math]\varphi_P^* : \mathscr O_{\varphi(P),Y} \to \mathscr O_{P,X}[/math] which just pulls back functions by [math]\varphi[/math]. I want to show that if [math]\varphi[/math] is a homeomorphism and [math]\varphi_P^*[/math] is an isomorphism for all [math]P \in X[/math], then [math]\varphi[/math] is an isomorphism of varieties.
The only thing to do is show that [math]\phi^{-1}[/math] is itself a morphism. For any [math]U \subset X[/math] open and [math]f[/math] regular on U, I can use surjectivity of the local maps to find some germ [math]\langle V, g \rangle \in \mathscr O_{\varphi(P), Y}[/math] so that [math]\langle \varphi^{-1}(V), g\circ\varphi \rangle = \langle U, f \rangle[/math]. Then [math]f \circ \varphi^{-1}=g[/math] on [math]\varphi(U) \cap V[/math], and so is regular on this set. Why is it then regular on all of [math]\varphi(U)[/math]? I feel that it should have something to do with agreeing on a dense subset of some open set, but g is only even defined on V.
Anyone here go to Cal Poly Pomona? Does the orientation really last from 8am to 5:30pm? Can we leave early?
>>8048234
>going to orientation days
What is the most streamlined path to studying C* Algebras? In terms of Analysis I am through babby's first Lesbegue integral.
>>8048164
Does the pullback functor not naturally reflect isomorphisms?
>>8048254
It does on global functions, yes, but these need only be regular near P. Since these are technically stalks of the global section sheaf, what you pointed out is probably (maybe?) enough, but I'm trying to go back through some basic AG in more concrete terms.
>>8048242
Says I have to or I won't be able to enroll.
if a set A is an element (not subset) of another set B, is an element of set A necessarily an element of set B? I'm fairly certain that the answer is no but I'd like to make sure.
>>8048642
why not try to come up with an example anon?
let's say A={1}, B={{1},2}
then A is an element of B, but 1 is not an element of B.
When there is a direct collision between two objects in space, where is the acceleration involved when one object instantaneously changes from one velocity to another without any gradual transition like that which seems to be implied in F = ma?
>>8048718
what are you talking about?
In an ideal situation where the objects are infinitely rigid, the change of velocity is instantaneous and the acceleration is a dirac, as well as the force.
In a real situation, the objects are not infinitely rigid. Which means there is an interval of time when the two objects are in contact, deforming a bit and then bounce of each other. The speed of each object decreases gradually as the objects deform, and it starts increasing again as the objects take their initial form back. In this case, the acceleration can be very high but not infinite, as well as the force from one object to the other.
If you have trouble seeing this, imagine pressing on a spring or on a very stiff ball put on the ground. If you release it, it might go up if you compressed it enough.
Please help me, /sci/.
So embarrased for asking this.
Why the spark in Layden's bottle?
hey sci. Calculus volume question.
Find the volume of the solid formed by revolving the region bounded by the graphs of the equations about the x-axis.
y=(16-x^2), -4≤x≤4
>>8048760
Wow, so there is acceleration involved in every collision in space rather than just an instantaneous change in velocity since no body can be infinitely rigid?
Which natural numbers have an odd number
of distinct divisors? I said 15; 1,3,5,15?
Second question, find solutions x, y in Z to the given equation, or if doesn't have any...
(a) 91x + 195y = 25.
This is how I've done it...
195 = 2 x 91 + 13
91 = 7 x 13 + 0
Hence, gcd(195,91)=14, the last non-zero remainder, and then by back substitution.
13=195-91(2)
13=195+91(-2)
And then i got stuck here :/...
>>8048923
Btw the second questions uses euclidean algorithm. Forgot to mention, sorry guys.
What structural properties of a protein are you supposed to look at to decide how sensitive or not it will be to heat?
Got to write a report on this shit and I ctrl+f'd all my lecture slides and tutorial sheets and found nothing talking about heat. Google is not giving me anything either. Even ctrl+f'd a pdf of my textbook.
what is the difference between these two notations: [math] \lim_{x \rightarrow \infty} f(x) = L [/math] and [math] \lim\limits_{x \rightarrow \infty} f(x) = L [/math]
ive seen both in my real analysis book, but cant find the distinction between the two
>>8049032
in the first one the x->inf is to the right of lim
in the second one it's below lim
no need to thank me anon, good luck
>>8049034
my bad man. i meant is there a difference in the meaning of the notations. should have been more precise
>>8049032
>>8049032
They're the same, butttttt...don't use \limits for limits in LaTeX
Your first example is for inline equations and the second for equations on their own line (displaystyle). LaTeX will correct this for you if you use it right. (There's other examples of LaTeX code you can force into one style or the other, \frac is the auto for \tfrac and \dfrac, you can also screw with \limits on \sum, \dots is auto for \cdots and...\ldots?)
[eqn]\lim_{x\to c} f(x) = l [/eqn]
PS use \to instead of \rightarrow
>>8049054
i tried using just \lim_ instead of \lim\limits_, but it wouldn't always put it underneath the lim.
>>8049080
In LaTeX or jsmath (4chan)?
For LaTeX:
If you are in the array or equation environment, it will output them under the lim
If you are in the inline environment ($like this$), it will output them to the side.
This is functioning properly. Its a style choice, but one I agree with.
Putting the limit to the side keeps the text visible without screwing up line spacing (which is what LaTeX is programmed to avoid).
In jsmath:
Its probably because you only use math tags. Try [eqn ] [/eqn]
>>8040874
You're missing the z expectation, so missing one third of the expectation.
No one has explained this physically yet? This whole thread dedicated to this shit? Good lord this board...
how do you derive an equation for expected number of collisions using a random distribution?
i think i got most of it after a certain step, but i don't know where the probability [math]\frac{m-1}{m}^{n}[/math] comes from. I'm sure it's something basic but i just can't figure it out.
How do I make animation on flash???
>>8049157
collisions of what?
anal beads?
>>8049293
collisions of whatever is being distributed randomly. i.e. there's 20 people in a room and two share the same birthday, so there was one collision.
anyone feels like people are quick to say they understand something even if they actually dont.
>>8049802
It's called mount stupid
>>8049802
yes, usually when your explanation annoys them.
So I'm revising for my stats exam, and I'm faced with this question:
A paint type has a mean drying time of 95 seconds. After a chemical is added, 16 samples are tested, and results show a 90 second mean with a standard deviation of 4.1
The question is, do these data provide strong enough evidence that the new chemical reduces the drying time?
I figured the answer would be yes, because even one standard deviation away from the new mean is still less than the original mean, but is that the case or the correct way to approach this?
>>8049841
or your questions
second row, the denominator -- why is it not [math]\sigma^2[/math]?
>>8049928
>is that the case or the correct way to approach this?
I don't think so. Looks like you should do a 2 samples t-test and report the p-value
>>8049965
Multiply both sides with sigma, and the other side is still 0.
Not sure why they keep it at all, as the final answer does not contain sigma, either. It doesn't seem like they cancelled it with something in the numerator.
Calculus newfag here. I've been trying to get the derivative of 1 / 3x^2, and I keep getting -1 / 9x^4. But that doesn't seem to match the tangent line.
Is this right? What am I doing wrong?
>>8050004
Just rewrite it as 1/3 * x^(-2) and apply the rule for exponents, x^n.
You only lower the exponent by 1, so if you go from 1/x^2 to something like 1/x^4 you can see you did something wrong.
In simple terms, what information is contained in the Fourier transform of an image?
>>8040874
Is Khan Academy a good chemistry resource?
(basic level, out of high school chemistry)
how long is 10 minutes in dog years
Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression.
The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below:
Boom: Profit = $400,000 with probability = .40
Moderate Growth = $300,000 with probability = .30
Recession = $100,000 with probability = .20
Depression = -$500,000 with probability = .10
(1) The standard deviation of the jewelry store's profits next year (rounded to the nearest dollar) is
A $102,442
B $125,483
C $149,873
D $125,264
E $263,818
(2) The expected profit of the jewelry store during the next year is
A $250,000
B $220,000
C $190,000
D $170,000
E None of the above
