SQT

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Did I fucked up? Proof of orthogonality of plane waves

Prove that n^5 - 5n^3 + 4n is divisible by 120.
I tried factoring it and I got n(n+1)(n-1)(n+2)(n-2) but I still have no idea why it's divisible by 120. Any help?

>>8495521
how do i implement a hashtable using only arrays?

>>8495750
Put arrays in your array.

>>8495722
n(n+1)(n-1)(n+2)(n-2)
Put it in order:
(n-2)(n-1)n(n+1)(n+2)
Now, it's supposed to be n> 2 otherwise it is impossible.
See that for 3 we have:
(1)(2)3(4)(5) = 6*20 = 120.
For 4 we have:
(2)(3)4(5)(6) = 6*120 = 720
For 5 we have:
(3)(4)5(6)(7). As you can see by now, you'll always have a multiple of 5, 3 and 8(a multiple of 2 and 4 every time). So it'll always divide by 120.

>>8495757
Why is it impossible for n to be 0, 1 or 2? Isn't 0 divisible by 120?

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>>8495755

>>8495761
> Isn't 0 divisible by 120?
yes it is

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If you increase an objects energy, you increase it's gravitational pull. But kinetic energy is just relative, so how does the universe ensure that me moving towards another galaxy wont collapse it? Or is the increase in kinetic energy(and thus gravity) perfectly cancelled with time dialation?

Apologies if i didn't explain correctly, this isn't my field of expertise.

>>8495792
In general relativity the position of energy is kind of fucked up.The gravity due to the kinetic energy is not directed towards the galaxy like if it was mass, since the momentum causes some dragging effects, this wont cause the galaxy to collapse since the kinetic energy isn't 'in' the galaxy. On the other hand, if some 3rd person saw you and the galaxy moving towards each other and combined you 2 would co;apse due to the kinetic energy, then you 2 will.

>>8495539
Check lines 2 and 3

Is [eqn]\frac{1}{2}||f(x)||^2[/eqn] continuously differentiable? I thought it was not differentiable at 0 but I'm not sure anymore

>>8495946
what conditions do you have on f?

>>8495948
No explicit conditions, but I think it's continuously differentiable

>>8495952
why do you think its not differentiable at 0 if there's no given condition on it at 0?

>>8495989
Cause the absolute function is not differentiable at 0 and I thought there's some relationship

Why is [math]\{0\}[/math] a linearly dependent set?

>In the theory of vector spaces, a set of vectors is said to be linearly dependent if one of the vectors in the set can be defined as a linear combination of the other

There are no other vectors in the set that could define 0

dont use definitions from the start of a wikipedia page

the standard definition is the one here
https://en.wikipedia.org/wiki/Linear_independence#Definition

and you have c*0 = 0 for any scalar c, so the set is linearly dependent

>>8495992
yes but [math]\|x\|^2[/math] is differentiable, because [math]\|x\|^2=x^2[/math]

>>8495750
select a hash function, implement it, and use it to determine the index. youre confined to an array so youll obv need to use some probing technique since you cant just chain in the event of collisions. may as well just use linear probing.

Why do people get sweaty at temperatures at or above 80 F when our core temperatures are 98.7 F?

>>8496042
the body is trying to maintain a temperature of 98.7F. it also naturally produces heat. hence, it needs an ambient temperature below the core temperature to maintain a temp of 98.7F.

>>8496042
The rate of heat transfer due to conduction is proportional to the temperature difference. As the air temperature rises, the temperature difference drops and heat transfer by conduction alone becomes insufficient, so evaporation (i.e. sweating) is used.

What kind of mental deficiency causes people to think that Beatles are a good band?

>>8495722
120=5*3*2^3
From you factorization, it's clear that at least one term is divisible by 5, and one is divisible by 3. One must be divisible by 4 as well, and then a different one by 2. That's all you need.

>>8495946
||f||^2 is a sum of squares. It's at least as smooth as f is.

If I'm travelling at the speed of light in one direction and I fire off some electromagnetic radiation in the opposite direction what is its velocity? How can it travel at the speed of light if its source is on an opposing vector also at the speed of light? it would have to have a subjective velocity double that of light?

>>8496062
You made me do this.

Ahem,
"The fact that so many books still name the Beatles as “the greatest or most significant or most influential” rock band ever only tells you how far rock music still is from becoming a serious art. Jazz critics have long recognized that the greatest jazz musicians of all times are Duke Ellington and John Coltrane, who were not the most famous or richest or best sellers of their times, let alone of all times. Classical critics rank the highly controversial Beethoven over classical musicians who were highly popular in courts around Europe. Rock critics are still blinded by commercial success. The Beatles sold more than anyone else (not true, by the way), therefore they must have been the greatest. Jazz critics grow up listening to a lot of jazz music of the past, classical critics grow up listening to a lot of classical music of the past. Rock critics are often totally ignorant of the rock music of the past, they barely know the best sellers. No wonder they will think that the Beatles did anything worthy of being saved."

When will science artificially create women who are not dumb cunts?

Haha how are imaginary numbers ever real my man just close your eyes nigga haha.

Anyone know what this file is?
http://pastebin.com/bebTpGKN
it appears to be a key or encrypted data on a stack.

>>8496240
Basic statistical analysis on the data (excluding the first and last 16 bytes) indicates that it's quite close to random

Shannon entropy = 0.99016, distribution is quite close to binomial.

So either random, pseudo-random or compressed.

>>8496086


It would be traveling at c with regards to your reference frame.

>>8496354
Also smartalec answer; an object that could 'give off' radiation wouldn't be traveling at c anyways.

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I thought the Borel sigma algebra on R^n was just the intersection of all the sigma algebras on R^n that contained the standard topology.

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How the fuck do I solve this shit?

>>8496527
Draw a line through D, perpendicular to AB. Let P be the point of intersection with AB.

The area of the rectangle PBCD is a^2*sin(30)*cos(30)=a^2*sqrt(3)/4.

The angle ADP is 45, so the area of ADP is (1/2)*a^2*sin(30)^2=a^2/8.

Total area is a^2*(1/8+sqrt(3)/4) = a^2*(1+2*sqrt(3))/8.

>>8495891
I cant see where I fucked up, any more tips?

Prove that all natural numbers with the form of n^3 + 17n are divisible by 6.
I have a tip to express 17n as 18n - n. But how does that help?
Help?

>>8496000
0 is a nontrivial combination of itself, namely [math]0 = 1\cdot 0[/math]

>>8496675
n^3+17n = n^3-n+18n
= n(n^2-1)+18n
= n(n-1)(n+1)+18n
= (n-1)n(n+1)+18n

What follows may seem familiar from the answer to your previous question.

(n-1)n(n+1) is the product of 3 consecutive numbers, n-1, n and n+1.

At least one of those will be a multiple of 2, and exactly one of them will be a multiple of 3. So their product must be a multiple of 6.

And 18n=6*3n, which is clearly a multiple of 6.

>>8496693
Did you never wonder why the binomial coefficient C(n,r)=n!/(r!(n-r)!) (for r<=n) is always an integer?

>>8495521
Does the analytification of the hilbert scheme coincide with the douady space of the analytification?

>>8496693
Thank you, divisibility is hard for me for some reason but I'm almost done with it, just 2 more problems.

>>8496675
(n^3 - n)+ 18n

n^3 - n is divisible by 3 by Fermat's theorem, and also is even, thus is divisible by 6

>>8495521
Is this a valid way to argue pic related, or is a bunch of words a babby-tier way to prove a proposition such as this?
Translation:
"G is a simple undirected graph containing more than two vertices. Show that G contains a vertex v such that (the inequality) holds."

My approach would be the following:
Note that the RHS is equivalent to the mean degree of the vertices in G (seems fairly obvious to me in this setting). The LHS is equivalent to the mean degree of the nodes adjacent to v, as it sums the degrees of the neighbours and divides by the degree of v, the latter of which is simply the number of neighbours.
Thus, if the inequality didn't hold, the mean degree of the neighbours of any v would be strictly less than the mean degree of the graph, a contradiction. Hence, the inequality holds.

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>>8496729
sorry, forgot pic.

Would it be feasible for a layman to understand this?

https://oeis.org/A000262

>integrals of parabaloids in spherical coordinates

wew lad, how the fuck is overcomplicated bullshit like this allowed?

>>8495521
Is Engineering a branch of Science?

>>8496988
No, Science is a branch of Engineering.

True or false: let R be an arbitrary ring, and x [math]\epsilon[/math] R with x [math]\neq[/math] [math]0_R[/math] then x is either a unit or a zero divisor. The answer if false, but I don't know why.

>>8497066
Is it not obvious? Just consider the integers.

Can you propel yourself in space with a lantern

Guys did I fuck up?
>didnt get a good enough rank for top 5 IIT in core branch
>Could've taken mining but its not good
>applied abroad and go into uni of sydney and got in easily
Did I do good considering I want to apply to top american unis for masters?

>>8495521
>>8495521
I have a transformation [math] x_ { \mu } \to \alpha x_ { \mu } [/math] and I need to deduce that it can be generated by [math] D = i x^{ \mu } \partial _{ \mu } [/math] I don't know how to go about doing this, other than I should expand near the identity so [eqn] x_ { \mu } \approx I + i \beta \partial_{ \mu } x_ { \mu } [/eqn] Which has a passing familiarity to what I'm supposed to show.

How would you differentiate a function like [eqn] \frac { \partial } { \partial x^{ \nu } } \frac { 1 } { x^2 } [/eqn] The way I've been going about it is to write [math] x^{-2} [/math] as [math] x^{ -2 } = \left ( x^{ \nu } x_{ \nu } \right )^{ -1 } [/math] where the index was chosen so that it coincided with the index on the derivative. The just apply the chain rule and product rule, giving [eqn] \frac { \partial } { \partial x^ { \nu } } \frac { 1 } { x^2 } = \frac { \partial } { \partial x^ { \nu } } (x^{ \nu } x_{ \nu })^{-1} = - \frac { x_{ \nu } } { (x^{ \nu } x_{ \nu })^2 } [/eqn] Which seems right.

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Can someone help me here?
In 3, how did the 2 went to the denominator of fraction below?
In 4, where he came up with the ax on the denominator of the fraction above and the bx on the denominator of the fraction below?

>>8497940
It's a trig identity [math] 1- \cos (x) = 2 \sin ^2 ( x/2 ) [/math] then it looks like they re-wrote it, since in general [math] 1/a/b = b/a [/math] so you could think of it as [eqn] \frac { 1 } { \frac { x } { 2 } } \sin ^2 \left ( \frac { x } { 2 } \right ) = \frac { 2 \sin ^2 \left ( \frac { x } { 2 } \right ) } {x }[/eqn]

Similar idea with 4), he re-writes so you can use the previous result. Notice that [eqn] \frac { \sin ( \alpha x ) } { \frac { \alpha x } { \frac { \sin ( \beta x } { \beta x } } } = \frac { \sin ( \alpha x ) } { \alpha x } \times \left ( \frac { \sin ( \beta x ) } { \beta x } \right ) ^{-1} = \frac { \sin ( \alpha x ) } { \alpha x } \times \frac { \beta x } { \sin ( \beta x ) } = \frac { \beta \sin ( \alpha x ) } { \alpha \sin ( \beta x ) } [/eqn] So now if you multiply it by [math] \alpha / \beta [/math] then you'll get your original limit.

>inb4 jsmath fail.

>>8497944
Thank you, anon.

>Let X, Y and Z be sets. Draw Venn diagrams to illustrate the sets (X u Y) n Z' and blah blah blah...

I get how to answer the question, but how do I actually draw Venn diagrams on a computer? Every online editor wants data sets, and you can't shade intersections in WordArt. Right now I'm seriously leaning towards just using mspaint, but surely there's gotta be a better option.

>>8497939

why would you choose the index to coincide with the derivative's index, isn't that a divergence? moreover, it isn't clear what the x^2 term is, its ambiguous.

>>8496700
Yes. Quite remarkable from just looking at the formula.

>>8496362
Isn't that what the text is saying?

>>8497969
That's a good point, so suppose that I introduce a new index [eqn] \frac { \partial } { \partial x^ { \nu } } \frac { 1 } { x^2 } = \frac { \partial } { \partial x^ { \nu } } (x^{ \rho } x_{ \rho })^{-1} = - \frac { \eta ^{ \rho } _{\nu} x_{ \rho } } { (x^{ \rho } x_{ \rho })^2 } = - \frac { x_{ \nu } } { (x^{ \rho } x_{ \rho })^2 } [/eqn] Which would explain how I managed to end up with the right answer with the wrong method, thanks. Although I'm annoyed that it didn't occur to me sooner.

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How do I prove that this system is linear and not time-invariant?

y(t)=3tx(t)

Seven digit number 6pqpqpq is divisible by 18.
Five digit number pqpqp is divisible by 6.
What is p?

No matter what I try I can't solve it.

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>>8498022

I dunno, it's late where I am and I've been up all night, so I might be wrong here, but when I did it I got an extra factor of 2.

[eqn]\partial_{\alpha}[(x^{\mu}x_{\mu})^{-1}]=-x^{-2}\partial_{\alpha}[x^{\mu}x_{\mu}]=-x^{-4}(x_{\mu}\partial_{\alpha}x^{\mu}+x^{\mu}\partial_{\alpha}x_{\mu})=x^{-4}(x_{\mu}\partial_{\alpha}x^{\mu}+x^{\mu}\eta_{\mu\sigma}\partial_{\alpha}x^{\sigma})=...=-x^{-4}(2x_{\alpha})[/eqn]

>>8498078

heh, fugg

[math]\partial_{\alpha}[(x^{\mu}x_{\mu})^{-1}]=-x^{-2}\partial_{\alpha}[x^{\mu}x_{\mu}]=-x^{-4}(x_{\mu}\partial_{\alpha}x^{\mu}+x^{\mu}\partial_{\alpha}x_{\mu})=x^{-4}(x_{\mu}\partial_{\alpha}x^{\mu}+x^{\mu}\eta_{\mu\sigma}\partial_{\alpha}x^{\sigma})=...=-x^{-4}(2x_{\alpha})[/math]

>>8498068
0 (mod 3)

>>8498085
Nevermind. I really misunderstood that question.

>>8498079
>>8498078
That's it, I missed the factor of two in the example. Thanks a lot anon, that looks right to me. Also when using tex on 4chan it's best to just throw in whitespace everywhere.

If you do a melting point test in a pan over a candle using an ir thermometer will your results be anywhere near accurate?

I really need to know before I take these drugs

>>8497700
Brehs...

>>8498068
Okay so I looked at the answer because after an hour I still couldn't do it and p = 4. So I think q is 6, since 6464646 (6pqpqpq) is divisible by 18 and 46464 (pqpqp) is divisible by 6. But I still have no idea how to solve it. Help?

>>8498027
x'(t)=k*x(t) => y'(t)=3*t*x'(t) = 3*t*k*x(t) = k*y(t)
x'(t)=xa(t)+xb(t) => y'(t)=3*t*(xa(t)+xa(t))=3*t*xa(t)+3*t*xa(t)=ya(t)+ya(t)

y(t+dt)=3*(t+dt)*x(t+dt)
x'(t)=x(t+dt) => y'(t)=3*t*x(t+dt) =/= y(t+dt)

>>8498184
Dammit it also works if q = 0. Now I'm lost.

>>8498068
> Seven digit number 6pqpqpq is divisible by 18.
6000000 + 101010*p + 10101*q = 0 (mod 18)
> Five digit number pqpqp is divisible by 6.
10101*p + 1010*q = 0 (mod 6)

>>8498260
I tried something like this, but I don't know how to go from there.

is being a geneticists worth it

>>8498260
>>8498266
6000000=6, 101010=12, 10101=3 (mod 18)
10101=3, 1010=2 (mod 6)

6 + 12*p + 3*q = 0 (mod 18)
=> 12*p + 3*q = 12 (mod 18)
=> 4*p + q = 4 (mod 6)

3*p + 2*q = 0 (mod 6)

[4 1][p]=[4]
[3 2][q]=[0]

Note that matrix is its own inverse:
4*4+1*3=19=1 (mod 6)
4*1+1*2=6=0 (mod 6)
3*4+2*3=18=0 (mod 6)
3*1+2*2=7=1 (mod 6)

[p]=[4 1][4]
[q]=[3 2][0]

=> p=4,q=0

>>8498418
Dammit dude, I just solved it haha. But thank you, anyway.

>>8498438
Also, because mod 6, q=6 is also a solution.

Verify that the set of complex numbers of the form [math]x+y sqrt{2}[/math]
where x and y are rational, is a subfield of the field of complex numbers.

Note: I've found that the solutions online haven't been very useful so please give me a new explanation and thorough solution.

Also, Why is this a set of complex numbers? Aren't complex numbers only x+yi?

>>8498720
Correction: [math]x+y \sqrt{2}[/math]

>>8498720
>Aren't complex numbers only x+yi?
yes, every complex number can be written as a+bi for some real numbers a,b.

in this case you have a=(x+ysqrt2) and b=0

to see that its a subfield you just need to check that products (a+bsqrt2)(c+dsqrt2), quotients (a+bsqrt2)/(c+dsqrt2), sums a+bsqrt2 - c+dsqrt2 can be written as e+fsqrt2 for some e,f

>>8498720
> Why is this a set of complex numbers?
It's a set of real numbers, and the real numbers are a subset of the complex numbers.

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What is this 'Co' operator?

>>8498744
>>8498727
Ah yes, like all naturals are also complex numbers. right?

>>8498787
yes but not a subfield or even a subring of course

>>8498768
I think I figured it out as being a convex combination of the set.

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How would I do ii) here? I've done i) easily enough, but not too sure where to go with ii)

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I know the area of a tetrahedron is 3^1/2 a^2.

How do I find the beginning and endpoints ?

>>8498910
I think that the easiest way to do is:
1.Because the Gram matrix is symmetric, it can be diagonalized, and using the properties of the determinants det(AB)=det(A)*det(B) the determinant of the diagonal matrix is the same as the determinant of the original one. Therefore we only have to prove the statement for an (non-normalized) orthogonal basis.
2. And it's easy to prove that the Gram matrix for an orthogonal basis (not necessarily normalized) has det>0, because the norm is positively defined.

>>8497837
No takers?

>>8497837
>>8498995
Let's take a function [math]f(x^\mu)[/math], if we apply that transformation what we have is [math]f(\alpha x^\mu)[/math] but if we expand it near [math]\alpha\approx 1[/math] we get
[math]f(\alpha x^\mu)\approx f( x^\mu)+(\alpha -1) x^\nu \partial_\nu f(x^\mu) [/math]
Therefore the generator of the dilatations is x^\nu \partial_\nu, and we add an extra i because we are physicist and not mathematicians.

>>8499111
Thanks anon.

>>8498910
If V is the matrix you get by putting the vectors into columns of a matrix, then G = V^t V.

If the vectors are linearly dependent, there is a non-zero x such that Vx =0. Then G x = V^t V x =0, so G is singular and so has zero determinant.

If the vectors are linearly independent, then for any non-zero x, V x is not zero, so x G x = || Vx||^2 >0 , so G is positive definite and so has positive determinant.

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How would I go about starting this?

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>>8498727
I found this solution online. Can you explain it? You answer doesn't seem to cover the multiplicative inverse which I need to check.

>>8499381
the solutions makes sure the additive and multiplicative identities are present, and notes closure under + and *

when i wrote
>quotients (a+bsqrt2)/(c+dsqrt2)
if you set a=1 and b=0 you get
1/(c+dsqrt2)
which is the same as checking closure under inverses

>>8499393
thanks man I got it now 100% luv u

>>8499268
the integral grows pretty fast
show it has for some x (maybe x=1) that it has a lower bound greater than two
easy if you split the integral

What is the difference between the Box Topology and Product Topology. They seemed to be defined in exactly the same way. I can't really catch the difference.

>>8499268
Use e^t>=1. When x=0 you get zero. When x=1 you get something larger than e-1. Intermediate value theorem.

>>8499521
>>8499268

>Intermediate value theorem. Your function is continuous since it's the sum of two continuous functions. When x = 0, your function is equal to 0. When x = 1, [math] (-1)^2 + \int_{0}^{x} e^e > 1 [/math] and therefore, there exist an x s.t. your function is equal to one.

How do I get good at thermodyanmics and physics (e&m)

inb4 read the book

i have read the book like several times. the questions at the end of the chapter are not covered in the text.

>>8499536
I'm probably one of the worst people to answer since I can barely into thermodynamics but when I was studying it, I made great strides through the lectures on MIT opencourseware.

How do I go about proving that:
[eqn]\sum_{k=1}^{\infty}\alpha_{mk}^{-2}=\frac{1}{4(m+1)}[/eqn]
where [math]\alpha_{mk}[/math] is the kth zero of the mth bessel function? I've seen this stated in a few papers and applications of Bessel functions but i'm not quite sure where to start.

>>8499536
I'd argue get a better book. For emag Griffiths and Jackson are both great and I know for a fact that the problems in Griffiths are possible to do after reading the chapter. For thermo I'd recommend Concepts in thermal physics by Blundell. The problems in Blundell are pretty dang hard but also doable if you read the chapter and honestly work out each step that is skipped in each derivation and proof.

[eqn]
\Sigma ^{0} \rightarrow p \space + \space \pi ^-
[/eqn]

Is this decay path possible?

is this solvable
[eqn]\int f(x)g(x)dx=\int f(x)dx\int g(x)dx[/eqn]

Can someone give me a good example of using big Oh notation, how it is used to see if an estimate is good when doing Taylor expansions or whatever.

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Does anybody else feel discouraged in their studies because they attend a shitty university and they feel that their courses aren't hardcore enough?

I go to a bumfuck state school for EE and always get bummed out when I see schools with much more rigorous curricula. I can't go at the pace I want because of the shitty ass retarded scheduling and advising system here. And it doesn't help that most of the faculty are shit at research so I have jack shit to do outside classes either, which puts the prospects for me going to a real school for grad straight in the can.

Should I just off myself?

>>8499907
deconvolution

>>8499927
>grad school
>for EE

Use your normie school for practising your network + social skills, and/or getting assistance in applying for certifications/qualifications/accreditations or whatever it is you faggots have.

You may even be able to go the route of industry/applied research, where (unlike theoretical masturbation) you actually get paid well and funding is seldom an issue.

Learn the advanced rigorous shit by reading textbooks (and lurking on websites frequented by faculty and students of the top schools).
If you're serious about doing research the autodidactism should be no problem for you.

how do i solve for the minimum voltage necessary needed in a electrolytic cell where,

Anode: [math] \text{Ni}\textit{(s)} \rightarrow \text{ Ni}^{^{2+}} \textit{(aq)} + 2 \text{e}^{^{-}} [/math]
E[math] _{\text{an}}^{\circ} = -0.28[/math]
Cathode: [math] \text{Cd}^{^{+}} \textit{(aq)} + 2 \text{e}^{^{-}} \rightarrow \text{Cd}\textit{(s)} [/math]
E[math]_{\text{cat}}^{\circ} = -0.40[/math]

Doesn't [math]\text{E}_{\text{cell}}^{\circ} = \text{E}_{\text{cat}}^{\circ} - \text{E}_{\text{an}}^{\circ}[/math] ?

That would mean
[math]\text{E}_{\text{cell}}^{\circ} = -0.40 - (-0.28) = -0.12[/math]
but the back of the book says [math]\text{E}_{\text{cell}}^{\circ} = 0.17[/math]

>>8499981
actually, E[math]_{\text{an}}^{\circ} = -0.23[/math]

still doesn't make sense though, unless i just reverse the signs for some reason...

I have a deck of 32 cards.
How many 5 card hands containing exactly 1 pair can I form?

>>8499987
>reverse signs for some reasons
Maybe Ecell is defined the other way around? Or you just take the positive value because it doesn't matter whether you define it as positive or negative

Can anyone git gud in math or is it the same way some are just naturally better in sports etc etc?

I'm having trouble with math because I can't visualize or put a context on what's going on.

In (R, T) for T the lower limit topology (which means, the topology that includes all subsets of the form [a, b) for a and b real), what are the closures of (0,1], (0, 1) and [0, 1]?

I think these are the answers but I am not sure:

(0, 1] -- (-∞, 0) ∪ (1, ∞) is an element of T so [0, 1] is closed in (R, T). As [0, 1] is the smallest closed set containing (0, 1], the closure of (0, 1] is given by [0, 1].

(0, 1) -- By the same reasoning (-∞, 0) ∪ [1, ∞) is open so the closure of (0, 1) is [0, 1). This is also an open, though. Is this correct?

[0, 1] -- From above, [0, 1] is closed. So [0, 1] is its own closure.

Can someone check these for me?

m years ago Mary was n years old. How old will Mary be after k years?

I think the answer is n + m + k, but the solution says n + m - k.
Is the textbook wrong or am I retarded?

>>8500074
the sets [a,b) are both closed and open
once you have thus result it is easy to prove that all of those sets are themselves closed desu (by arbitrary intersection)

>>8500122
Right now Mary is n+m years old, as she was n years old m years ago. So in k years, she will be m+n+k years old. Your textbook is probably retarded.

>>8500137
Yeah I thought so too. Thanks for confirming.

>>8500130
except probably the first one desu

>>8500142
>>8500130
disregard this I suck cocks

>>8499907
Let the right side be F G and take derivatives of both sides to get F' G' = F' G + F G'. Rearrange to get G'/G = something involving F and F'. Integrate to get log G on the left, exponentiate to get G as a function of F related things. Derive to get g. Plug in any f.

>>8495521
>>>/g/57715029

/g/ didn't want to help me, could you give me a hand, /sci/?

>>8500243
Doesn't look too bad. You have lines row + 2* column = 4* k and a simple formula for above the "diagonal" and another for below.

>>8500243
First, it's only defined if (2*x+y)%4==0.

In which case, it's the maximum of (2*x+y)/4 and y/2.

This assumes that you only need distances for x>=0 and y>=0, i.e. to the right of and below the origin. If you need distances on all sides, then you also need to consider (2*x-y)/4, and the negatives of all 3 (for 6 cases in total; cells of equal distance from the origin form hexagons).

Let [math]X \in \operatorname{Sch} /k[/math].

Show [math]{\operatorname{Def} _X}:\operatorname{Art} \left( {\Lambda ,k} \right) \to \operatorname{Set} [/math] defined by

[math]{\operatorname{Def} _X}\left( A \right) = \left\{ {\begin{array}{*{20}{c}}
X& \to &{{X_A}} \\
\downarrow &{Cartesian}&{\mathop \downarrow \limits_{flat} } \\
{\operatorname{Spec} k}& \to &{\operatorname{Spec} A}
\end{array}} \right\}/ \cong [/math]

is a deformation functor.

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Why don't I get streamlines starting from each of the red stars, why do they only start from some of them?

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Can someone explain what an "Intersection Graph" is?

>OR MORE IMPORTANTLY
How do I go about drawing one from this information?
How does an Intersection Graph relate to a regular Graph and its Adjacency Matrix??

Is accounting a bad major? I tried engineering, but I failed out after the first semester. I was thinking of changing to accounting.

>>8500700
I don't know how to explain it more clearly than how it is written right there...

>>8495750

if u are asking this question you clearly doesnt understanding hashing....

>>8495521
How do i solve:
[eqn] \int_0^1 (\frac{-1}{x})^{\frac{1}{4}} dx [/eqn]

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Stupid Question: How do I foil this equation? That's a question mark after the Equal sign, not a 2 or Z.

(3x+1)^2 +2^2 =9x^2+6 right?

>>8500040
If you mean 52 card deck, its
[math] \frac{ {{13}\choose{1}} \cdot {{4}\choose{2}} \cdot {{12}\choose{3}} \cdot {{4}\choose{1}}^{3} }{ {52}\choose{5} } [/math]

I think...

>>8501028
take the anti derivative.

>>8501028
solve the integral from [math] a\epsilon (0,1] to 1[/math] and then take the limit if it when a tends to 0

>>8501036
no.
square [math] \sqrt{3x+1} [/math]
square [math] +2 [/math]
multiply [math] \sqrt{3x+1} [/math] by [math] +2 [/math] and then multiply again by [math] +2 [/math] since you're adding together two identical terms.
then add all of that shit up and that's your solution

>>8501042
>>8501046
>>8501052
i'm sorry, i should have been more specific.
how do i relate >>8501028 to [math] \Gamma(x) [/math]

>>8501054
>>8501046
>>8501042
>>8501028
also i wrote down the problem wrong:

[eqn] \int_0^1 (\frac{1}{x} -1)^{\frac{1}{4}} dx [/eqn]

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>>8501059
not to be rude, but quick reply window has a LaTeX preview

>>8501036
No, if you put [math] a = \sqrt { 3 x + 1 } [/math] and [math] b = 2 [/math] then [math] (a+b)^2 = (a+b)(a+b)=a^2+2ab+b^2 [/math] Now just substitute the definitions of a and b.

It might be a bit easier for you if you put [math] d=(a+b) [/math] then distribute over [math] (a+b) [/math] giving [math] d(a+b) = da + db = (a+b)a+(a+b)b [/math] and then distribute one last time.

>>8501060
Yeah, but there's still an issue with how 4chan parses the tex commands, so something like [eqn] \int^{\infty}_{-\infty}\nabla\vec{x}dx [/eqn] might not work (although I bet that it's going to now I'm trying to break it) even though it looks fine in the preview window.

This is unless Hiroshima fixed it since it's been implemented.

>>8501060
appreciate it, now excuse me while i cry in a corner

>>8500511
trivial

>>8496116
when the proteome is decoded, and not a day sooner
the cure for dumb will absolutely shake this world

>>8500700
draw a dot for each A_i.
Now draw an edge between A_i and A_j if they have at least one element in common.

>>8501058
set [math] \frac{1}{x} -1 =t^4[/math]
you get a rational function, innit?

>>8501179
that leads me to
[eqn] \int_0^\infty \frac{4t^4}{(1+t^4)^2} dt [/eqn]
which also isn't easy to solve

>>8501232
but you can solve it by the fractions thingamajig
which is a pain in the ass but still

Scientifically speaking, why does carbonating a sweet drink make it taste so good?

>>8501244
No. you can't. [math] \frac{1}{(1+t^4)^2} [/math] does not have a simple anti-derivative. there are factors of [math] \pi [/math] in the solution.

>>8501232
Can you use contour integration for this? You have a good bit of residues but it shouldn't be that awful.

>>8501261
the hint was equate it to the gamma function

>>8501058
do you need a closed form solution?

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>>8501244
>>8501256

>>8501279
final thing simplifies to pi/2sqrt2

>>8495521

Is there a methodical way to do optimizations in calculus?

It seems like you just have to try an approach and work from there. I hate that, it feels like im stabbing in the dark.

t 2nd year chemo student

When speciation occurs, where does the new specie get a mate to mate with.

>>8501281
Setting the derivative to 0?

are there glasses for people with already good vision? I have 20/13 but I want to see what it would be like to have like 20/5 or 20/1.

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>>8501302

Whats a good resource to learn SQL?

>>8501279
thank you, but that didn't help

>>8501460
stackoverflow

hey i dont know whats going on here so this may be a stupid question, but what does "SQT" stand for?

>>8501579
stupid questions thread

>>8495521
I can't seem to figure out this question. Are there any integers x,y,z so that x^3+y^3+z^3=33?

>>8501460
any lecture plan from a decent university should do, but learn database theory first (basically functional dependencies, normalisation and a few of the basic algorithms to reach normal forms, relational algebra and the ACID principle).

You cannot know sql without knowing at least the basics of db theory, even if you already "know" how to program

How do I define a sine wave that climbs up the Y axis (like arcsin but without domain being limited to pie half)?

>>8501620
x=sin y?

>>8501620
y = x + sin x?

>>8501623
Correct!
>>8501625
Also a bretty cool function

But... if a function has many y coords for one x... doesn't that strictly make it a non function? Or is the role reversed for x = sin(y)? Can I have both on my graph without teachers being butthurt?
Also thank you this is the first step towards a completely sinusoidal swastika

>>8501640
So long as every element in the domain of the function has a unique value in the range then its ok. As for your teacher being butthurt, depends on what your assignment is?

>>8501640
in this case, x is a function of y, but y is not a function of x (because, like you said, there are multiple points with the same x value but different y values). i don't know what bizarre rules your teachers have about graphing conventions.

>>8501646
>>8501648
Thanks. I was referring to the ">hurr durr u cant habe 2 y values for a single x on the graph" meme, but now its resolved.

do u guys take notes when you study maths?

>>8501726
Yes. But I almost never look at them, it just helps me pick up little things during class. If I ever need to review something I use the textbook.

What are the chances of actually seeing this tech for civilian use
https://www.youtube.com/watch?v=b6ME88nMnYE

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I applied for a web data analyst job. I said in my application that I have minimal html/css/php experience, but I can code, I am good at statistics, and I'm willing to learn as I go.

Now I have an interview. Should I try and fake my front end skills? Or just be brutally honest?

The job description said "really good front end skills" which I certainly do not have.

>>8501613
It is expected there is a solution, but it has not been found yet.

Can anyone help me out with this partial derivative? How do you do it? :(


[eqn]
\frac{\partial \sum_i a_i(\mathbf{b_i} - \mathbf{x})^T(\mathbf{b_i}-\mathbf{x})}{\partial \mathbf{x}}
[/eqn]

My guess is something like [math]-2\sum_i(\mathbf{b}_i - \mathbf{x}_i)[/math] but desu matrix calculus never really clicked for me

>>8502232
Oh and in my guess there should be an a_i between the bracket and the sum

>>8502232
Your guess is correct (except that the x shouldn't have a subscript).

>>8502254
... and the a_i

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I already made a thread about it but I'll ask here anyway

How am I supposed to do these two radii? A construction line at the top and just two circles with edges at the same spot on the left side?

>>8502270
have you tried putting the centre of the R5 circle at (-0.5; 3.75) taking the centre of coordinates as that rightmost corner? that's what it seem to imply to me desu

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top matrix is multiplied by q1,q2,q3 and is equal to 0

what row operations were done to get to the bottom matrix to solve the system?

>>8502442
nevermind my dipshit teacher copied the problem incorrectly

good shit

I know vectors and magnitude are pretty much bros but why is magnitude ||v||?

What is more 3^500 or 7^300 and why?

>>8502473
>>>/b/

>>8502477
Nevermind, I got it.

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How do I interpret changes in an independent variable if the dependent variable is the weighted distance change from the previous 12 months average when pic related is the formula used? I previously considered it without the logarithm of the distance but it makes more sense in the context of the application when the log is used which on the downside makes the interpretation quite difficult.
Ive no clue so far and would be very grateful for any comment.

>>8502636
absolutely disgusting

>>8501058
[math]\displaystyle \int_0^1 (\frac{1}{t}-1)^{1/4} \mathrm{d}t[/math]
[math]\displaystyle \int_1^\infty \frac{(t-1)^{1/4}}{t^2} \mathrm{d}t[/math]
[math]\displaystyle \int_0^\infty \frac{t^{1/4}}{(t+1)^2} \mathrm{d}t[/math]
[math]\displaystyle \int_0^\infty t^{1/4} \left( \int_0^\infty e^{-s (t+1)} s \, \mathrm{d}s \right) \mathrm{d}t[/math]
[math]\displaystyle \int_0^\infty \left( \int_0^\infty e^{-s \, t} t^{1/4} \, \mathrm{d}t \right) e^{-s} s \, \mathrm{d}s[/math]
[math]\displaystyle \int_0^\infty e^{-t} t^{1/4} \mathrm{d}t \int_0^\infty e^{-s} s^{-1/4} \mathrm{d}s[/math]
[math]\displaystyle (1/4)! (-1/4)![/math]
[math]\displaystyle \frac{\pi}{4} \csc ( \frac{\pi}{4} )[/math]
[math]\displaystyle \frac{\pi}{4} \sqrt 2 [/math]

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How much of a correlation is there between serotonin deficiencies and the mental state?
Does it really lead to depression, or is it just a meme?

i despise physics. how do i get a BS in physics? what are upper div physics courses like?

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Whats ''the'' book to learn Thermodynamics?

I consider it to be a very important subject, although my calculus aint that good, I would like to start learning it.

pls respond

>>8502749
what substitutions did you use?

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This problem is sort of like the counterfeit coin problems, but you can use a geiger to detect if there is a radioactive potato in a pile of potatoes. It is not able to tell you which one in the pile is radioactive or how many of the potatoes are radioactive.

Cool question, but i've been having trouble when the piles aren't uniform.

>>8502749
Wow! How'd you come up with that?

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What's going on here? Surely line 4 and 6 are wrong? It's meant to be a transformation from basis vector e_i to e'_j (Einstein summation convention)

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Could someone help me prove this? I know to find M_{k}, the supremum of f on [x_{k-1}, x_{k}] a subinterval of [a, b] I need to use the fact that there exists a rational r with (1/2)(x_{k} + x_{k-1} < r < x_{k}, but I don't know why this inequality is true, where it comes from or where to go from here.

>>8502869
if your calculus isn't very good you aren't ready for "the" book. You'll be better off with a text suited for chem majors (though these will still require some calculus).

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is this a typo by the book or am I missing something? Where the fuck did this 1 come from?

>>8503102
it should be a plus

>>8503048
>handwriting your homework
for the love of god learn to tex

So I came out of the closet. For a long time I thought myself as an Engineer, but I just couldn't lie to myself anymore. I finally admitted that I am an accountant. What do?

alright lads, I don't know where the fuck else to ask so I guess I'll ask here
I have bunch of stress-strain (Green Strain, 1st and 2nd Piola-Kirchhoff) data that I want to fit to a constitutive model. Something like the SLS model would probably be easier but I want to use a hyperelastic model for better representation. How do I fit resultant data to this model? Do I need to somehow calculate principle components or am I going to be approximating those?

Not a question, I just had a huge breakthrough in my research (molecular dynamics) and made my calculations ~50 times faster. I've been doing this for a year and a half and just realized how to massively improve my script, feeling really good right now.

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It's just stupid questions.
This is true? Can we really blow up the energy of the vacuum?

Destroyed by vacuum energy detonation (It is the number 6)
http://www.livescience.com/17875-destroy-earth-doomsday.html

I found this other paragraph, which was put a few years later to the previous one, which also includes "Methods to destroy the earth" But "Blow up the vacuum energy" is in "Things that will NOT destroy the earth"

https://qntm.org/destroy#sec7

>>8495521
>>>/k/32141147

My sides

>>8501874
just be upfront about it, but make sure to stress your relevant experience and express a willingness to learn on the job. if you try to fake your skills, there's a very good chance you'll be found out.

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shouldn't it be impossible for me to integrate sqrt(cos(2θ))? You use the identity to change cos(2θ) to 2(cosθ)^2 - 1, but you can't square root that cause of the -1
What's wrong here?

>>8501874
Honest, but don't be self-deprecating, you still want to play up your skills.

>>8503500
Hint: you aren't trying to find the indefinite integral

>>8503507
A full loop is 2pi, so half of it is 0 to pi, I already know that much
I figured out that I'm not squaring the r, but then I get 2(cosθ)^2 - 1 in the integral, and solving that gives me sinθcosθ which given the limits just gives me zero

>>8503521
check your integration limits for what value of θ is r equal to 0?
remember that in polar coordinates you have to integrate r^2/2 dθ
so r being a square root, the function you end up integrating is pretty easy desu

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>>8503539
Here's the "work" it's number 3
Not sure why my limits are wrong

>>8503543
your integration limits are wrong. what's the value of r when theta is π/2, for example?
your actual integration limits should be [-π/4, π/4]
also using that trigonometric identity is useless, you can integrate right away

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>>8495521
How do you prove this Mathematically? In other words, how do you prove this without using assumptions in Probability?

>>8503571
but then integrating 0.5cos(2x) from [-π/4, π/4] gives me 0.5 and 0.5a is still wrong

>>8503580
inductively?

>>8503586
a^2/2 is wrong?

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>>8503597
>a^2
That was right, the tiniest god damn things
I fucking hate this class I'm glad it's almost over

>>8503302
anyone?

>>8503580
looks like you take (1+x)^n, take two derivatives and then plug in x=1. standard trick.

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I need a no bullshit app for memorizing and practicing multiplication times tables, roots, and logarithms.

Not sure if this warrants its own thread.

I'm making a simulation of a double pendulum for an undergrad physics class. My system consists of two point masses attached to one another by a massless spring, and the higher mass is attached to a fixed point by another massless spring. The whole thing is in a vacuum.

Simply plowing ahead, I started with an impulse-based simulation for the position and velocity of the two masses. A quick google search turns up a wealth of literature on this topic, deriving the equations of motion for similar systems from the Lagrangian, but this was quick.

Anyway, what was surprising was that when I animated the simulation, the result looked pretty, well, plausible. And when I increased the spring constants to very high values, the animation looked just like the gifs on wikipedia for "Double Pendulum."

Why does the literature emphasize Lagrangian mechanics so much? Does solving the Lagrangian and using Euler's method result in a better approximation than an impulse-based simulation? How much better is it?

>>8503302
Sorry, don't have an answer, but what's your field? I'm stats and this looks interesting

>>8503670
jessicababyfat for anyone else who needs to know who this semen demon is. Jesus fucking christ.

>>8503696
Biomedical engineering. More specifically biomechanics. I need to figure this shit out since its make or break on the grading. All the constitutive modeling is based on tensors and shit but I have no idea how derive the tensors for a cylindrical system with no dimensions given from a dataset.

The models from this page look like they'd work but I have no idea how to fit a model to the data I have.
http://www.umich.edu/~bme332/chap11bloodvessel/bme332bloodves.htm

>>8503699
praise kek, paradise found

>>8503759
Stats guy here. I can't suggest anything that you haven't already tried but don't waste any more time waiting for help from this board. Threads like these are dominated by engineering underclassmen and mathfags, tough luck finding someone who's familiar with this specific problem. Good luck senpai

>>8503795
No worries, I figured I'd throw it out on the off chance some anon here got a meme degree in bioe/mede and could help me with biomechanics. Worst comes to worst I model it with a viscoelastic model and come up with some bullshit justification and lose points. Or stop being an autist and ask the TA/Prof for help.

>>8498303
>geneticist
You're going to have to be more specific, son...

What's the best way to bring milkshakes to school? For context, everyday I blend the following into a milkshake:
>Protein powder
>Oatmeal
>Milk
>Peanut Butter
>Banana

If I blend it all at around 11 AM, will it still be good to drink at around 3 PM? It's just going to be sitting in my backpack. If this isn't safe then I'll invest in a good ice pack to keep it cold.

>>8503833
Why not just drink it at the time of creation? Or before you go to the gym would be better. If you want to keep it cold try putting ice into the shake itself, you can never be too hydrated. This seems like a question better suited for /fit/

>>8498184
p,q are both even
3(p+q)+6=9n (multiple of 9)
3(p+q)=3,12,21,30,39,48,57
or p+q=1,4,7,10,13,16,19 (all greater multiples would not be the sum of 2 single digit numbers)
2(p+q)+p=3n ie 3p+2q=3n
q is a single digit even multiple of 3; ie 6
Since p is even, p+q must be even too therefore, p+q=4,10,16
The only one of these that satisfies q=6 is p=4

>>8503048
[math]M_{k}=2|q_{k}|+1[/math] where [math]q_{k}[/math] is some rational number in [math][x_{k-1},x_{k}][/math] such that [math]f(q_{k})[/math] is the within that panel. Then [math]U(P,f)=\sum_{k=1}^{n} (2|q_{k}|+1)\Delta x_{k} = \sum_{k=1}^{n} 2|q_{k}|\Delta x_{k} + \sum_{k=1}^{n} \Delta x_{k} \geq 5[/math] because the right sum is 5 and the left sum is always positive hence the upper and lower integrals are not equal.

>>8503862
*is the max within that panel

>>8503838
Ahh, I never thought of putting ice into the shake! I'll make the shake then add ice cubes before I leave. I won't blend the cubes because that would yield higher surface area which makes them melt faster.

Why does stress and anxiety fucks us up so much? Even if they know it's all on your head, there are thousands people suffering

Not sure where to post this but basically I have my RN psychometric test coming up and my numeracy and mechanical skills are rusty at best.

Could someone point me towards the right modules i'd need to learn to ace it?

Here's an example of the test. I only need 50% to pass but i'd like to impress by getting full marks if possible
>inb4 wow this is piss easy you must be a retard
n-no bully pls
http://www.royalnavy.mod.uk/Careers/Royal-Marines/~/media/AB74D461DD2741EE9517CFD73E668FA0.ashx

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Diffeq problem here:

How do you know to place these Rs into this problem? Above the black line is the first example problem I did, so I just figured "oh, U must just be the product of X(x) and T(t)," so I tried doing the second problem like that only to see that they took a completely different route. How do I know to do that? I feel like I don't get what U is on a conceptual level.

Assuming you had enough anti-matter, could you throw enough into a black hole to annihilate enough of the mass in the singularity that the gravity wouldn't be enough to cause the singularity anymore and the black hole would dissapear?

Bonus question: Does fusion occur inside the singularity?

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Any ideas for this one? I got that P=210N and that it would be tipping. But that's was after I changed my original answer of 120N so I wasn't sure

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>>8502869
Pic related has a fuck ton of good problems and is very in depth and clear for the most part. Hundreds of great example problems and currently using it right now for my thermo class. Would recommend

>>8498078
>>8498079
Let's see if I got the source of the problem right.
[eqn]\partial_{\alpha}[(x^{\mu}x_{\mu})^{-1}]=-x^{-2} \partial_{\alpha}[x^{\mu}x_{\mu}]=-x^{-4}(x_{\mu} \partial_{\alpha}x^{\mu}+x^{\mu} \partial_{\alpha}x_{\mu})=x^{-4}(x_{\mu} \partial_{\alpha}x^{\mu}+x^{\mu} \eta_{\mu\sigma} \partial_{\alpha}x^{\sigma})=...=-x^{-4}(2x_{\alpha})[/eqn]

Has science ever truly made anyone's life better?

>>8498068
p, q are even
3(p+q) is congruent to 12 mod 18
(p+q) is congruent to 4, 10 or 16 mod 18
p+q = 4 or 10 or 16
2p+2q = 8 or 20 or 32
We know that 3p+2q is divisible by 3. And since p, q are even, 3p+2q is divisible by 6.
Thus:
p = 4, q = 0
p = 4, q = 6
p = 4, q = 12 (impossible)
So we have p = 4 and q = 0 or 6.

>>8501070
Certain symbols need a space between them for /sci/'s LaTeX to work properly. The TeX preview doesn't take this into account.

Examples:
}} to } }
}\ to } \

>>8504457
As I thought.

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

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

What's this principle (perhaps fallacy) called?

Duplicate reply.

>>8504288
>>8504493
Sorry, responded in the other thread. >>8504548
I should have stuck here since I got dubs.

>>8504493
its common sense and nothing else
you could find an example of something not working under improved conditions (for example, a poor student might be better than a rich student becasue his necessity makes him more disciplinated or whatever)

sounds like something greek philosophers would argue about, aka sophism and bullshit.

>>8504461
I wouldn't have a cushy job where I barely get any work done on a given day without science, so yes.

>>8504566
>that's trivial

>>8504493
Well, it's sort of a tautology. In the absence of any other context, you'd assume "bad" conditions to be whatever would impede the working of "it".

For other definitions of "bad", it can be a fallacy. E.g. some electronic circuits may only work because of parasitic properties (the deviation of a component from its theoretical ideal), meaning that replacing components with "better" alternatives causes the circuit to stop working.

>if I can run at least 15 km/h, I can also run more than 10 km/h.
15 km/h is more than 10 km/h, so you can run at a particular speed which is more than 10km/h

>everyone answers this instead of the initial problem

What's a differential equation?

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Not sure if this is the right place to ask, but how do I choose the point for the instantaneous center of zero velocity? In this case it's perpendicular with A and B's velocity, but what about P? I tried to solve it using the "other end" of therectangle triangle between A and P and the results were different.

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>>8504632
>I tried to solve it using the "other end" of therectangle triangle
To make things clearer, this was the point that didn't work.

>>8504607
An equation which includes both variables and their derivatives.

Hi
I have this exercise about polynomials :

Let P and Q be in Z[X], show that there is a polynomial D in Z[X] that divides both P and Q if and only if P and Q have a common root in C.

I showed that if D divides both P and Q then D has a complex root which is common to P and Q.
I don't know how i'm supposed to show the other implication

>>8504632
if the angular velocity is 2 rad/s, then P should be moving with tangential velocity of 1000 mm/s or 1 m/s. Point A would also have this tangential velocity, but it is constrained to move in the x direction. So you need to take the component of the tangent that is moving in the x direction, which is 1*cos(45) m/s or sqrt(2)/2 m/s. A would be moving in the y direction with velocity 1*sin(45) m/s or sqrt(2)/2 m/s, but it is constrained. So instead we have that B is moving downward with velocity sqrt(2)/2, so that A's movement with respect to the system in what it should be. But this movement of B affects the movement of P, adding some downward y velocity. We already have that the downward velocity of y is sqrt(2)/2 m/s, so if we add the additional sqrt(2)/2, we get sqrt(2). The x component is still sqrt(2)/2, so the final speed of P is sqrt(2.5).

>>8504566
>>8504601
Okay. Let's try a different example

If I can get an offer from Oxford University (hard conditions),
I can certainly get an offer from University of West London (easier "improved" conditions,
by the principle of ___________ (if it works in worse conditions it works in better ones or something....)

It makes logical sense but it might be a fallacy as UWL may still reject you if you are overqualified and they anticipate your decision making.

>>8504632
> how do I choose the point for the instantaneous center of zero velocity?
Er, what?
If a is the distance of a to the right of the corner, and b is the distance of b above the corner, then
a=cos(θ)/2
b=sin(θ)/2

θ=pi/4
dθ/dt=-2
da/dt=da/dθ.dθ/dt=-sin(θ)/2*-2=sin(θ)=1/sqrt(2)
db/dt=db/dθ.dθ/dt=cos(θ)/2*-2=-cos(θ)=-1/sqrt(2)

px = -a
py = 2b
dpx/dt=-da/dt=-1/sqrt(2)
dpy/dt=2*db/dt=-2/sqrt(2)
|dp/dt|=sqrt((-1/sqrt(2))^2+(-2/sqrt(2))^2)
=sqrt(1/2+2)=sqrt(5/2)

>>8504697
>>8504702
What you guys did is correct, but what I'm asking is where to put the "c" point while using this method (page 382 of this pdf): https://docs.google.com/file/d/0Bw8MfqmgWLS4V0NFR2dVUWpuYzg/edit?pli=1

Thanks for replying.

>>8504673
If P and Q have a common root C then z-C divides P and Q.

>>8504771
Yeah but if that root is sqrt(2) for instance then D(x)=(x-sqrt(2)) is not in Z[x]

>>8504771
proof of that?

>>8504765
it looks like in the picture in the pdf, the point C will always be on a line perpendicular to the velocity. So looking at pic related, the velocities of A and B are shown in red, and I connect their normals in grey. The tangent velocity of P is in orange, but because B is moving downward the actual velocity is shown in red. It can be seen that this too is normal to the line that connects P to C. Hope this helps.

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>>8504795
Forgot pic

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If (G, +) is an abelian group, how do I use a), b) and d) here to show that c) is true?

>>8504795
>>8504796
Thanks! I think I've finally got it.

There's something that has been bothering me for a while now related to the divergence theorem. Can someone tell me if this holds and why/(not)?
[math]\int_V (\nabla \cdot \vec{F})\ g\ d\tau = \int_A g\ \vec{F} \cdot \vec{dS}[/math]
Where F, g functions of spatial coords.

>>8503862
>>8503864
Most appreciated anon.

>>8504779

Sorry, I'm an idiot. I think you have to take the minimal polynomial of C and show that divides P and Q. You know it's degree is less than the degrees of P and Q. Call the minimal polynomial R, divide P by R. Then there can't be a remainder or the remainder would be of lower degree than R and also have C as a root.

>>8504939
No. Integrate by parts.

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>shower equations

Just for fun:

Given an arbitrary circle of radius R centered at location (X , Y) whose radius is less than the distance from the origin to its center, and an arbitrary ray with initial point at the origin which makes some angle with the x-axis, find a general equation that can be used to determine whether the ray passes through the circle.

In other words: given a circle which does not include the origin, find the bearings of its two tangent lines that pass through the origin. Then if the ray's bearing lies between them, it must intersect the circle.

Solution here: http://i.imgur.com/tcMRt3L.png

>>8503042
g-guys p-please

[math]\sin^3 x = \left(\frac{e^{ix}-e^{-ix}}{2i}\right)^3
= \frac{e^{i3x}-3e^{ix}+3e^{-ix}-e^{-i3x}}{-8i}= \frac{\sin 3x - 3\sin x}{4}[/math]

Help. I trying to understand how from the second to the third step. How is there a two to factor out to get four in from -8i?

>>8505396
the identity used is the one here:
https://en.wikipedia.org/wiki/Euler%27s_formula#Relationship_to_trigonometry

[math]\text{Is there a name for this property? For some matrix A and all vectors x, y}\\ \textbf{A}\textbf{x}\cdot\textbf{A}\textbf{y}=\textbf{x}\cdot\textbf{y} [/math]

>>8505399
Yes, im trying to deduct the identity. What i don't understand is the missing step(s) between two and three, that is how to simplify two in order to factor out two and get to step three

>>8505412
e^{i3x}-3e^{ix}+3e^{-ix}-e^{-i3x}
=e^{i3x}-e^{-i3x}+3e^{-ix}-3e^{ix}
=2i*sin(3x)+3(2i*sin(-x))
=2i*sin(3x)-6i*sin(x)
=2i(sin(3x)-3sin(x))

>>8505409
https://en.wikipedia.org/wiki/Unitary_matrix

>>8505422
Thank you

>>8505396
sorry this should read
[math]\sin^3 x = \left(\frac{e^{ix}-e^{-ix}}{2i}\right)^3 = \frac{e^{3ix}-e^{-3ix}-3(e^{ix}-e^{-ix})}{-8i}= \frac{\sin 3x - 3\sin x}{4}[/math]

>>8505422
see>>8505430

>>8505430
>>8505422
>>8505434
Ugh. Its getting late

[math]\sin^3 x = \left(\frac{e^{ix}-e^{-ix}}{2i}\right)^3 = \frac{e^{3ix}-e^{-3ix}-3(e^{ix}-e^{-ix})}{-8i}= \frac{\ 3sin x - \sin 3x}{4}[/math]

>>8505442
see
>>8505422 (You)

need to the find the equilibrium conentration of Hg+2 in a galvanic cell with:

>Hg electrode immersed in 1.2L of 0.122M Hg+2 solution
>Ag electrode immersed in 1.2L of 1.52M Ag+ solution
>25 degrees temp

what do i do
someone please hold my hand
im literally at electrochemistry

Am I correct in saying that 1+2+3+4... = -1/12 because they are using a formula that works for convergent series on a divergent one just for the lulz

>>8497700
Fuck off we're full

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In all these problems you can use a Geiger counter that can detect if there is a
radioactive potato in a pile of potatoes, but cannot tell how many there are.

>>8505874
Well, I managed to do the counterfeit coin problems, but this is probably beyond me.

In passing, I note that there are (2^m+1)*(2^n+1) = 2^m*2^n+2^m+2^n+1 = 2^(m+n)+2^m+2^n+1 possible combinations, and m+n+1 checks have 2^(m+n+1) = 2^(m+n)+2^(m+n) > 2^(m+n)+2^m+2^n+1 (except for m=n=1) possible outcomes.

Basically, it's a matter of chopping the set of combinations roughly in half with each check.

As m and n get larger, the number of outcomes asymptotically approaches twice the number of combinations, so that provides some amount of slack.

>>8505935
> this is probably beyond me.
Or maybe not.

Consider laying out out all of the possibilities in a (2^m+1)×(2^n+1) grid.

Checking one potato from each pile either
a) removes one row and one column, leaving you to check 2^m×2^n possibilities with m+n checks, or
b) isolates that row and column, leaving you to check 2^m+2^n+1 possibilities with m+n checks.

a) is straightforward. Split one pile (of size 2^k for some k) into two size 2^(k-1) piles. Check one of them. Repeat until you've found the radioactive potato. This takes m steps for the 2^m pile and n steps for the 2^n pile.

For b), check one of the two potatoes from the first check. If it's radioactive, the remainder of the pile it came from is clean. Now you just need to check the other pile (including the potato you removed for the first check, so 2^k+1 potatoes), and you still have m+n-1 checks left. Easy (unless m=n=1, which would mean 3 potatoes with 1 check).

I'm dying here guys. Trying to solve a system of differential equations but I fell pretty far behind in the class and have no idea what I'm doing. The system is
[eqn]x'=x+y^2[/eqn]
[eqn]y'=-y[/eqn]
I know that this means [math]y(t)=y_{0}e^{-t}[/math], but I'm at a dead end trying to solve for [math]x(t)[/math] other than knowing that [math]x'(t)=x(t)+y_{0}^2e^{-2t}[/math]. Help?

>>8506113
>[math]x'(t)=x(t)+y_{0}^2e^{-2t}[/math]
Weird that it worked in the preview but not my post.

>>8506113
>>8506116
Leltex strikes again. Let's see if this works.
[math]x'(t)=x(t)+y_{0}^2 e^{-2t}[/math]

>>8506113
x'=x => x=e^t
So it's going to be a linear combination of e^t and e^-2t.

x(t) = a*e^t + b*e^-2t
=> x'(t) = a*e^t - 2b*e^-2t

x'(t)=x(t)+y(0)^2*e^-2t
=> a*e^t - 2b*e^-2t = a*e^t + b*e^-2t + y(0)^2*e^-2t
=> -2b*e^-2t = b*e^-2t + y(0)^2*e^-2t
=> -3b*e^-2t = y(0)^2*e^-2t
=> -3b = y(0)^2
=> b = -y(0)^2/3

=> x(t) = a*e^t - (y(0)^2/3)*e^-2t
=> x(0) = a - y(0)^2/3
=> a = x(0) + y(0)^2/3

=> x(t) = (x(0) + y(0)^2/3)*e^t - (y(0)^2/3)*e^-2t

are solutions of a differential equation graphed as x on the horizontal axis and dy/dx on the vertical?

>>8506145
Usually t on the horizontal and x(t) on the vertical. Or x and y(x), or whatever; independent variable on the horizontal, dependent on the vertical.

Differential equations are solved for the variable, not its derivative.

>>8506143
Alternatively, using Laplace transform:
x'(t)=x(t)+y(0)^2.e^(-2t)
=> s.X(s)-x(0) = X(s)+y(0)^2/(s+2)
=> (s-1).X(s) = x(0) + y(0)^2/(s+2)
=> X(s) = x(0)/(s-1) + y(0)^2/(s+2)(s-1)
= (x(0)(s+2) + y(0)^2)/(s+2)(s-1)
= (x(0).s + 2.x(0) + y(0)^2)/(s+2)(s-1)

= a/(s-1) + b/(s+2)
= (a(s+2)+b(s-1))/(s-1)(s+2)
= ((a+b)s+(2a-b))/(s-1)(s+2)
=> a+b = x(0), 2a-b = 2.x(0) + y(0)^2
=> 3a = 3.x0+y(0)^2, 3b = y(0)^2
=> a = x0+y(0)^2/3, b = y(0)^2/3

=> X(s) = (y(0)^2/3+x(0))/(s-1) - (y(0)^2/3)/(s+2)

=> x(t) = (y(0)^2/3+x(0)).e^t - (y(0)^2/3).e^-2t

>>8506143
>>8506166
Thanks anon! Following your process was very helpful!

>>8506166
> = (x(0).s + 2.x(0) + y(0)^2)/(s+2)(s-1)
> = a/(s-1) + b/(s+2)
Residue method for partial fractions:

y/(x+p)(x+q)(x+r) = a/(x+p) + b/(x+q) + c/(x+r)
= (a(x+q)(x+r) + b(x+p)(x+r) + c(x+p)(x+q))/(x+p)(x+q)(x+r)
Multiply by (x+p)
= (a(x+q)(x+r) + b(x+p)(x+r) + c(x+p)(x+q))/(x+q)(x+r)
Set x=-p => x+p=0:
= (a(x+q)(x+r) + b(0)(x+r) + c(0)(x+q))/(x+q)(x+r)
= a(x+q)(x+r)/(x+q)(x+r)
= a
Likewise for b, c, ...

So:
(x(0).s + 2.x(0) + y(0)^2)/(s+2)(s-1)
Multiply by s-1:
(x(0).s + 2.x(0) + y(0)^2)/(s+2)
Set s=1:
(x(0) + 2.x(0) + y(0)^2)/(1+2)
= (3.x(0) + y(0)^2)/3 = x(0) + y(0)^2/3

Multiply by s+2:
(x(0).s + 2.x(0) + y(0)^2)/(s-1)
Set s=-2:
(-2.x(0) + 2.x(0) + y(0)^2)/(-2-1)
= y(0)^2/-3
= -y(0)^2/3

i.e.
(x(0) + y(0)^2/3)/(s-1) - (y(0)^2/3)/(s+2)

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Someone help me on this. Since distance to B with rowing is R and running is piR, won't it be fastest to row as near as you can to B and then run? So C will be nearest point to B?

Can anybody recommend any books for learning about the mathematics behind NURBS and B-Splines?

Please help a retard understand how to solve this equation;

5ln(x^2)=4ln(x^3)+6

I know the result but I'm having a hard time figuring out how to get there.

>>8506500
Use the fact that ln(x^n) = nln(x) to get 10ln(x) = 12ln(x) + 6. So, ln(x) = -3 and x = e^-3

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Thoughts on adrafinil?

How do I get the two angles, B?
SinB = (5sin(70))/7

whats more efficient a speaker singing or a human singing

>>8504367

What college are you going?

Does anyone have the chart of /sci/'s version of a better American education system?