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# /sci/ - Science & Math

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 >> Anonymous Tue Nov 7 07:28:22 2017 No.9280930 Starting us off with an easy one.How exactly do I show a sequence is Cauchy? Example: Prove $x_{n} = \frac{1}{n}$ is CauchyWriting the definition: $\forall \hspace{0.2cm}\epsilon > 0 \hspace{0.2cm} \exists \hspace{0.2cm} N \in \mathbb{N} \hspace{0.2cm} \text{such that} \hspace{0.2cm} \forall \hspace{0.2cm} m,n,\geq N, \hspace{0.2cm} |x_{n} - x_{m}| < \epsilon$One can write: $\left| \frac{1}{n} - \frac{1}{m}\right| <\epsilon$ but how do you generally proceed from here?
 >> Anonymous Tue Nov 7 07:34:20 2017 No.9280933 >>9280930Is this correct? Choose epsilon to be $\frac{\epsilon}{2}$ Since $m, n > N$, $\left| \frac{1}{n} - \frac{1}{m} \leq \left| \frac{1}{n} \right| + \left| \frac{1}{m} \right| < \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon$
 >> Anonymous Tue Nov 7 07:35:35 2017 No.9280935 >>9280933$\left| \frac{1}{n} - \frac{1}{m} \right| \leq \left| \frac{1}{n} \right| + \left| \frac{1}{m} \right| < \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon$
 >> Anonymous Tue Nov 7 07:36:00 2017 No.9280936 File: 16 KB, 652x96, reimannhypothesis.jpg [View same] [iqdb] [saucenao] [google] [report] can someone help? I have absolutely no clue how to do it other than by solving the recurrence which I doubt we'd be asked to do for this given the wolfram alpha result.
 >> Anonymous Tue Nov 7 07:38:02 2017 No.9280938 >>9280930 but how do you generally proceed from here?It depends on the situation.On this one for example you can write $| \frac{1}{n} - \frac{1}{m} | < | \frac{1}{n} | + | \frac{1}{m} | = \frac{1}{n} + \frac{1}{m} < \frac{\varepsilon}{2} + \frac{\varepsilon}{2} = \varepsilon$ for some m and n greater than some number. $\frac{1}{n} < ε$ when n is greater than some number follows from the Archimedean property of the real numbers.
 >> Anonymous Tue Nov 7 07:38:51 2017 No.9280940 >>9280936Write out the first few terms of the sequence to get an idea of what's going on. Can you show it's bounded and monotone? Then you will know if it is convergent or not.
 >> Anonymous Tue Nov 7 07:43:45 2017 No.9280945 >>9280927Consider an insulating sphere with +q surface charge. Can a Gaussian surface within the sphere prove the field inside is zero for: (a) a uniform surface charge distribution; (b) a variable surface charge distribution?
 >> Anonymous Tue Nov 7 07:45:01 2017 No.9280946 >>9280933You don't choose epsilon. You choose N as being larger than 2/epsilon.
 >> Anonymous Tue Nov 7 07:47:26 2017 No.9280948 >>9280936$f(x)= \frac{1}{2} x + \frac{1}{x}$The sequence given a $x_0$ is $x_0, f(x_0), f^2(x_0), \ldots$ .Use Banach's fixed point theorem.You can prove Lipschitz continuity using derivatives.
 >> Anonymous Tue Nov 7 07:50:03 2017 No.9280950 >>9280948Oh and the fixed point is the limit.You can find it solving this $x=\frac{1}{2} x + \frac{1}{x}$ .
 >> Anonymous Tue Nov 7 07:52:29 2017 No.9280952 >>9280930Use the equivalence relation that says a sequence in $\mathbb{R}^n$ is convergent iff it is Cauchy. To prove that it is Cauchy it is enough to prove that it converges. In the case of $x_n=\frac{1}{n}$, it's clear that $0n$, meaning it's decreasing (i.e., it is monotone). The monotone sequence theorem tells you, then, that this sequence is convergent, and therefore it is Cauchy.
 >> Anonymous Tue Nov 7 08:02:27 2017 No.9280966 >>9280948those things are new to me and it's supposed to be solveable with what we've already done in class >>9280940seems right but don't I have to solve the recurrence to do that?
 >> Anonymous Tue Nov 7 08:05:36 2017 No.9280969   >>9280948You need a compact set for Banach's fixed point theorem.You can use Banach to prove that it converges if you start inside the set $A_N = [-N,\sqrt{2}] \cup [\sqrt{2},N]$ for $N > 2$.Then use that fact to conclude it converges if you start in the set $A = (-\infty, \sqrt{2}] \cup [\sqrt{2},\infty]$ and only then prove the general case.
 >> Anonymous Tue Nov 7 08:20:29 2017 No.9280981 File: 53 KB, 978x307, Screenshot_20171107-142246.jpg [View same] [iqdb] [saucenao] [google] [report] Reposting. Can anyone show how to get this solution?
 >> Anonymous Tue Nov 7 08:31:55 2017 No.9280990 >>9280966Let's consider an easier example.Only difference here is I have selected an initial condition.Let $x_{1} = 1$ and $x_{n+1} = \sqrt{1+x_{n}}$.First show the sequence is increasing by doing induction. Recall what it means for it to be increasing, $x_{n+1} \geq x_{n}$ for all $n$. These problems are great for induction.Next, the boundedness. It should be obvious that $x_{n} \geq x_{1}$ for all $n$. The upper bound then is the challenge. Claim: $x_{n} \leq 2$ for all $n$. This is another proof by induction.Now you've shown it's monotone and bounded, therefore it converges, and this it's limit exists (and it's value is quite interesting).
 >> Anonymous Tue Nov 7 08:37:04 2017 No.9280994 >>9280936Put x[n+1]=x[n]=x, to getx=x/2+1/x=> x^2=x^2/2+1=> x^2/2-1=0=> x^2=2=> x=+/-sqrt(2)If x[n] is +ve, x[n+1] must be positive. If x[n] is negative, x[n+1] must be negative.Note that the recurrence is a specialisation ofx[n+1] = (x[n]+k/x[n])/2for k=2. The generalised form is known as the "Babylonian method" or "Heron's method" for calculating the square root of k. If x=sqrt(k), then x=k/x=(x+k/x)/2
 >> Anonymous Tue Nov 7 08:41:06 2017 No.9280997 >>9280927If $f : E \rightarrow F$ and $B$ is a subset of $F$, how does one show that $f^{-1}(F$\$B) = E$\$f^{-1}(B)$ ? I guess I have to use double inclusion, but I don't really see where to go from there...
 >> Anonymous Tue Nov 7 08:42:58 2017 No.9280998 >>9280994this works, thanks.
 >> Anonymous Tue Nov 7 08:44:04 2017 No.9281001 >>9280997f^(-1) (F\B) = {x in E | f(x) in F\B}= {x in E | f(x) in F} \ {x in E | f(x) in B}= E \ f^(-1)(B)
 >> Anonymous Tue Nov 7 08:45:20 2017 No.9281003 >>9280969Not really. You have to break it to two cases. Case 1: x0 is in the interval $[ \varepsilon , + \infty )$ . xn converges to $\sqrt{2}$ . Contraction can be proven by the mean value theorem and the fact that the derivative is always less than 1/2.Case 2:x0 is in the interval $(- \infty, - \varepsilon]$ . xn converges to $- \sqrt{2}$ .
 >> Anonymous Tue Nov 7 08:48:52 2017 No.9281007 >>9280998This "works" yeah, but you have to prove that it converges.You really have to use >>9280948 , >>9281003 to actually prove it.
 >> Anonymous Tue Nov 7 08:55:32 2017 No.9281011 File: 25 KB, 780x109, 123.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Tue Nov 7 08:55:50 2017 No.9281013 >>9280981Two forms solutions are $e^{\pm \sqrt(\epsilon)}$ and then using the boundary equations you get the correct constants, so you can write it into the form cosh
 >> Anonymous Tue Nov 7 08:56:32 2017 No.9281016 >>9281003>the derivative is always less than 1/2The derivative at x=0.1 is -99.5 for example.
 >> Anonymous Tue Nov 7 08:56:53 2017 No.9281017 >>9281013I meant 1/squareroot
 >> Anonymous Tue Nov 7 09:03:33 2017 No.9281024   >>9281016Oh fuck it needs to be |x|>1.Well, in [-1,1] |f(x)-f(y)| = 1/2 |x-y| |xy-2|/|xy| bla bla bla ... bound
 >> Anonymous Tue Nov 7 09:35:38 2017 No.9281048 Prove: Suppose $(x_{n})$ is monotone and has a convergent subsequence. Prove that $(x_{n})$ converges.Suppose $x_{n+1}\geq x_{n}$ . We're also given, $\forall \epsilon > 0 \exists N \in \mathbb{N}$ such that $\forall k \geq N , |x_{n_{k}} - L | < \epsilon$$(x_{n})$ converges, so $\forall \epsilon > 0 \exists N \in \mathbb{N}$ such that $\forall n \geq N , |x_{n} - L | < \epsilon$How do I relate these two?
 >> Anonymous Tue Nov 7 09:36:49 2017 No.9281050 >>9281048It's a basic theorem.Fucking google it.
 >> Anonymous Tue Nov 7 09:42:12 2017 No.9281052 >>9281048Proof: ThinkBecause the sequence is monotone you can bound every term in the sequence between two of the terms of the convergent subsequence. And then as n goes to infinity, the distance between the terms of the convergent subsequence go to 0.So you can proceed in either of two ways: Use this to prove the general sequence is Cauchy or even better: conjecture that the limit of the sequence is the limit of convergent subsequence and then do your epsilon magic.
 >> Anonymous Tue Nov 7 09:42:35 2017 No.9281053 >>9281048Bolzano-Weierstrass theorem.By the way, which book are you working out of?
 >> Anonymous Tue Nov 7 09:46:10 2017 No.9281057 >>9281055Proof: Think.If the charge is distributed along the sphere, a Gaussian sphere with the same center but smaller radius will enclose exactly 0 charge. Apply Gauss law and then think.
 >> Anonymous Tue Nov 7 09:47:13 2017 No.9281062 >>9281057*If the charge is distributed along the surface
 >> Anonymous Tue Nov 7 10:07:08 2017 No.9281090 >>9281057Why do they make the distinction of considering a uniform and a non-uniform charge distribution as separate cases then?
 >> Anonymous Tue Nov 7 10:45:20 2017 No.9281131 >>9281090To test if you are stupid
 >> Anonymous Tue Nov 7 10:50:46 2017 No.9281133 File: 16 KB, 653x231, 438b218a1e7cf4745b627d9b0b577aa5.png [View same] [iqdb] [saucenao] [google] [report] >>9280870The answer on my exam key is 2, so that is incorrect. Pic related is the problem. I set my bounds as stated in my stack exchange post here: https://math.stackexchange.com/questions/2506874/triple-integral-bounded-by-a-cylinder-and-a-planeCan anyone tell me why my bounds are wrong?
 >> Anonymous Tue Nov 7 11:23:08 2017 No.9281159 File: 3.39 MB, 5312x2988, 20171107_112106.jpg [View same] [iqdb] [saucenao] [google] [report] The book says the answer to this problem is e^7 - 1I get where the e^7 comes from but not the 1
 >> Anonymous Tue Nov 7 11:31:16 2017 No.9281167 >>9281159It is a telescopic series.Write out a partial sum and you'll see why. Everything except the first term e^7 and the last term -e^(n+1) cancel out.
 >> Anonymous Tue Nov 7 11:32:30 2017 No.9281169 >>9281167>last term -e^(n+1)-e^(7/(n+1))
 >> Anonymous Tue Nov 7 11:54:27 2017 No.9281198   File: 3.48 MB, 5312x2988, 20171107_114918.jpg [View same] [iqdb] [saucenao] [google] [report] Thank you for the explaining the last problem.The book also has a problem similar to this but n =0 making easier to find r if I am correct.To find r you usea_1r=a_2But this series starts at n=1 making it more involved and I want to make sure im not missing something before I continue
 >> Anonymous Tue Nov 7 11:56:51 2017 No.9281201   File: 9 KB, 250x180, 1499464258015.jpg [View same] [iqdb] [saucenao] [google] [report] >tfw you realize .05 seconds after posting
 >> Anonymous Tue Nov 7 12:49:49 2017 No.9281286 File: 64 KB, 539x426, 8493572_orig.png [View same] [iqdb] [saucenao] [google] [report] Someone can explain to my why the phase spectrum of the sinc function is $\pm \pi$ when $\sinc(x) < 0$?Sinc is real so it shouldn't be all 0?
 >> Anonymous Tue Nov 7 13:06:56 2017 No.9281318 Can you expand conditional probability expressions like that ? P(A) = P(c2) + P(c3) - P(c2) x P(c3)P(c2|A) = [P(A|c2) x P(c2)] P(A)Can I then expand - P(A|c2) by replacing where c2 occurs in A with 1? 1+ P(c3) - P(c3)x1 Is there anything wrong with this ?
 >> Anonymous Tue Nov 7 13:31:31 2017 No.9281367 Simple question, why is $\phi_2=180°-\phi_0$ in the second quadrant of a unit circle? I understand if ex. you have 180°, and the first angle fills one portion, while the other fills the rest of the 180°. But doesn't make sense if both have the same starting point.
 >> Anonymous Tue Nov 7 14:30:36 2017 No.9281487 I'm new to general relativity and I am confused by notationwhat's the difference between$\Gamma^a_{\ bc} \quad \quad \Gamma_{ab}^{\ \ \ c}$?
 >> Anonymous Tue Nov 7 14:35:45 2017 No.9281494 File: 1.26 MB, 2576x1932, 20171107_133340.jpg [View same] [iqdb] [saucenao] [google] [report] Am I doing this wrong, feel like I am doing this wrong.
 >> Anonymous Tue Nov 7 14:44:20 2017 No.9281520 >>9281494They want me to show if I know how to get a trig identity. I am trash at them so I came here. The stuff on top is the original identity.
 >> Anonymous Tue Nov 7 15:18:25 2017 No.9281577 How does one derive the recurrence formula $T_{n+1}(x) = 2xT_n(x) - T_{n-1}(x)$ using the generating function $g(x, t) = \frac{1 - tx}{1 - 2tx + t^2} = \sum\limits_{n=0}^\infty T_n(x)t^n$ without using cosines in any way? The basic idea is clear: derivative wrt t and then playing with the coefficients, but I can't do this in practice for some reason, or maybe I'm just too blind to see how to do it.
 >> Anonymous Tue Nov 7 15:27:08 2017 No.9281595 >>9281494It's literally multiplying both sides by the denominator. Then you see they are equal.After that just work backwards: adding the stuff and then dividing it.
 >> Anonymous Tue Nov 7 15:30:26 2017 No.9281606 >>9281494Anyway, you're doing it right.
 >> Anonymous Tue Nov 7 16:18:51 2017 No.9281717 File: 2 KB, 368x38, imabrainlet.png [View same] [iqdb] [saucenao] [google] [report] ?
 >> Anonymous Tue Nov 7 16:24:58 2017 No.9281733 >>9281606Thx
 >> Anonymous Tue Nov 7 16:34:21 2017 No.9281761   File: 49 KB, 1781x277, Screenshot_20171107-163035_01.jpg [View same] [iqdb] [saucenao] [google] [report] By what method can I evaluate this limit?
 >> Anonymous Tue Nov 7 16:36:33 2017 No.9281771 >>9281717Did you try anything?
 >> Anonymous Tue Nov 7 16:37:57 2017 No.9281774   >>92817171/n^(1/3) < 1/n
 >> Anonymous Tue Nov 7 16:38:53 2017 No.9281779 File: 49 KB, 1781x277, limit.jpg [View same] [iqdb] [saucenao] [google] [report] By what method can I evaluate this limit?
 >> Anonymous Tue Nov 7 16:40:06 2017 No.9281780 >>9281779derivative
 >> Anonymous Tue Nov 7 16:41:44 2017 No.9281784 >>9281774there was an attempt
 >> Anonymous Tue Nov 7 16:47:24 2017 No.9281798 1/n^(1/3)<ε <==> 1/n<ε^3 <==> n>1/ε^3 Ν:=Ceiling[1/ε^3]>=1/ε^3n>N ==> n>1/ε^3 ==> 1/n<ε^3 ==> 1/n^(1/3)<ε
 >> Anonymous Tue Nov 7 16:55:22 2017 No.9281815 If two expressions are equal, is it a guarantee you can manipulate either one into the other form algebraically? An example would be (n-1)*(n-3)*(n-5)...*(n-(n-1)) == n! / ((2/n)! * 2^(n/2)).Is there a rigorous definition for equality between algebraic statements? Is the left hand side of that equality I posted even an algebraic statement if I have to include "..." to show what I mean?
 >> Anonymous Tue Nov 7 17:00:34 2017 No.9281830 >>9281815Also: f(n) = (n/n) has a discontinuity at 0 but n/n = 1 and g(n) = 1 does not have a continuity.If 1 = n/n then doesn't f(n) = g(n) but if they're equal why does f(0) not equal g(0)? Or does it?Is this just a case of attributing more to the idea of equality than is there?I would ask one of my profs this but I feel like this is something I should understand from elementary school....
 >> Anonymous Tue Nov 7 17:01:40 2017 No.9281835 >>9281780Using l'hopital's rule?
 >> Anonymous Tue Nov 7 17:03:16 2017 No.9281840 >>9281835nodefinition of derivative, the limit
 >> Anonymous Tue Nov 7 17:03:52 2017 No.9281841 "In the card game of poker, each player is dealt 5 cards. Assume the game is played with all 52cards. In how many ways can a player have a ‘four of a kind’ (that is, 4 of the 5 cards must befrom the same ‘denomination’ (e.g. the four 8s) - the fifth card can be any other card)?"The answer is 624 but I don't know how this was reached.Can someone do like a step-by-step?
 >> Anonymous Tue Nov 7 17:07:45 2017 No.9281849
 >> Anonymous Tue Nov 7 17:09:34 2017 No.9281856 >>9281841There are 13 denominations in a 52 card deck so you can get 13 different sets of 4 cards of a kind.For each of the 13 possibilities, you will have 52 - 4 = 48 cards remaining. So then there are 48 possible 5th cards for each 4 of a kind.If there are 48 "versions" of each and 13 possible 4 of a kind hands, then you have 13 * 48 = 624 possible 5 card hands with 4 of a kind.If you didn't follow that then you need some basic combinatorics knowledge: https://en.wikipedia.org/wiki/Rule_of_product
 >> Anonymous Tue Nov 7 17:09:35 2017 No.9281857 >>9281841Judging by the answer, the order that the cards were dealt doesn't matter.How many tetrads are there? 13Pick one of them. 13 possible ways.You are left with 52-4=48 cards.Pick one of them. 48 ways.13*48=624
 >> Anonymous Tue Nov 7 17:16:59 2017 No.9281878 >>9281487There are two types of Christoffel symbols, one with only lower indexes (first kind) and one with one upper index (second kind). So long as you don't mix them, whichever way you write it is fine. I've seen it written both ways and also with the upper index in the middle.
 >> Anonymous Tue Nov 7 17:52:20 2017 No.9281960 >>9281878so $\Gamma^a_{\ bc} = \Gamma_{bc}^{\ \ \ a}$ then?
 >> Anonymous Tue Nov 7 17:58:21 2017 No.9281967 why is every SQT just a bunch of math proofs questions that can be googled? ask questions here that cant be googled and get ppls opinionsill start: what causes cell apoptosis?
 >> Anonymous Tue Nov 7 18:05:30 2017 No.9281979 >>9281967Sometimes having a dialogue with someone over a topic provides a deeper understanding of the concept, or allows understanding to take place at all. >ill start: what causes cell apoptosis?What do you mean by "causes" it? The mediating mechanism or the initiating one? Maybe neither, since both of these questions can be easily googled or found in the Wikipedia page on apoptosis and you said your question can't be.
 >> Anonymous Tue Nov 7 18:07:27 2017 No.9281981 13 dollar bet you go play again after big win
 >> Anonymous Tue Nov 7 18:08:03 2017 No.9281982 Can someone explain math/formulas? What are we actually doing here? Are we trying to find relations between some elements of a system and connect them through a formula? I wouldn't know how to get a formula on my own, even though it may make sense.
 >> Anonymous Tue Nov 7 18:13:54 2017 No.9281997 >>9281960Yes, but don't quote me on that.
 >> Anonymous Tue Nov 7 18:17:13 2017 No.9282003 >>9281997>>9281960An addendum: just look at the definition of the Christoffel symbol, it really doesn't care where you write the upper index. The only thing it cares about is the order of the lower indexes.
 >> Anonymous Tue Nov 7 18:35:21 2017 No.9282042 >>9281840why not l hopital?
 >> Anonymous Tue Nov 7 18:43:19 2017 No.9282069 >>9281815Equality is essentially defined as a relation where, if two things are equal, then you can substitute them for each other arbitrarily and everywhere: $(x=y)\Longrightarrow \left(P(x)\Leftrightarrow P(y)\right)$, no matter what proposition P represents.In your case however, $f(n) = \frac{n}{n} = 1$ only when $n\not = 0$, and so $f(n)=g(n)$ doesn't hold when n is zero.
 >> Anonymous Tue Nov 7 18:46:05 2017 No.9282076 File: 25 KB, 549x97, problem 3.png [View same] [iqdb] [saucenao] [google] [report] The generating function of a standard tetahedra die is: x^1 +x^2 +x^3 + x^4 and a standard cubic die is x^1 +x^2 +x^3 + x^4 +x^5+x^6.So the sum would be: 2x^1+2x^2+2x^3+2x^4+x^5+x^6How do I come up with the other dice that would generate this?Am I even on the right track?
 >> Anonymous Tue Nov 7 19:23:07 2017 No.9282149 >>9282042It can only be used in 0/0 etc type cases.
 >> Anonymous Tue Nov 7 19:24:41 2017 No.9282158 Should I study ODE with Boyce book or Tenenbaum book?
 >> Anonymous Tue Nov 7 19:25:11 2017 No.9282160 >>9282076>UpdateWell I figured out that the probability distribution of the sum of the two standard dice would be:x^2+2x^3+3x^4+4x^5+4x^6+4x^7+3x^8+2x^9+x^10Is there any way to find possibilities other than guessing and checking. Sorry if I am dumb.
 >> Anonymous Tue Nov 7 19:33:15 2017 No.9282182 >>9282158Simmons if you're not a brainlet.
 >> Anonymous Tue Nov 7 19:44:42 2017 No.9282206 File: 1.04 MB, 3120x3120, IMG_20171107_174422.jpg [View same] [iqdb] [saucenao] [google] [report] >>9281133Your bonds are wrong. It tells you z is bound by the plane z = 0. That means your first set of bonds should be 0, sqrt(4-y^2). That gives you the right answer.
 >> Anonymous Tue Nov 7 19:49:16 2017 No.9282213 >>9281494Write neater. Always. it doesn't matter if this is your rough work. That's illegible.
 >> Anonymous Tue Nov 7 19:49:24 2017 No.9282215 >>9282182but I am a brainlet
 >> Anonymous Tue Nov 7 19:50:56 2017 No.9282219 >>9282149I evaluated it using l'hopital's rule.Given that F(gamma) = F0(cos(gamma*t) - cos(omega*t))and G(gamma) = omega^2 - gamma^2limit as gamma approaches omega for F(gam)/G(gam) evaluates to 0/0.
 >> Anonymous Tue Nov 7 20:05:12 2017 No.9282247 >>9281982Entirely depends on what your talking about. 2+2 = 4 is simply simplifying the equation on the LHS into the RHS. This is often the case for equations including calculus. An integral is solved from its integral form into an equation to make it understandable. When we make a formula given elements of a system we are finding a relation between the elements and then expression that relation as a mathematical formula. If for every 3 apples I have I can trade those apples for 4 pears a formula would be:3a = 4p
 >> Anonymous Tue Nov 7 20:24:56 2017 No.9282300 >>9282160Figured it out. There are four possibilities including the standard dice.
 >> Anonymous Tue Nov 7 21:17:22 2017 No.9282393 >>9282069So then the statement "n/n = 1" is incomplete, or at least the "for n not equal to 0" is implicit. It seems like there is an analogy to the congruence relation in modular arithmetic, like a ≡ b (mod n), b ≡ c (mod n) then a ≡ c (mod n). Similarly f(n) = n/n = 1 = g(n), when we say f(n) = g(n) by the transitive property, we can't do so without maintaining the implicit restriction that they are equal WHEN n != 0, which arose when we set n/n = 1.I've seen congruence modulo written with the modulus over the triple bar, so there is some sense in which the restrictions under which an equality holds are "attached" to the equality?>>9281982I think this question is hard to answer both well and concisely.If you think a bunch about the rules of chess, you can come up with some theorems about how chess works. Maybe you can develop some new rules which follow logically from the "basic" rules which are set out in the definition of the game. Furthermore, maybe you can extend those idea outside of chess to tell you things about systems which are related to chess. Mathematics is about doing that, in general, for all kinds of different sets of rules. You may find this channel interesting? https://www.youtube.com/watch?v=R7p-nPg8t_g
 >> Anonymous Tue Nov 7 22:59:51 2017 No.9282549 File: 14 KB, 554x59, problem 8.png [View same] [iqdb] [saucenao] [google] [report] Any help on this would be appreciated. Obviously a rectangle (2n, 3m) or (3n, 2m) would work. What about other possibilities?
 >> Anonymous Tue Nov 7 23:14:03 2017 No.9282561 >>9282549Both n and m have to be at least 2 and their product must be divisible by 6.
 >> Anonymous Tue Nov 7 23:26:16 2017 No.9282576 >>9282549Key observation: A rectangle can be tiled by $2 \times 3$ if and only if that rectangle can be constructed by stitching together $2\times 3$ tiles. So lets instead investigate all the ways to stich together these tiles.The easiest way would be by putting a $2 \times 3$ tile on the plane and calling that the main corner. And then stitching together some tiles next to it horizontally and some other tiles next to it vertically. You can then proof that the rest of the rectangle can be filled in properly.If we let there be $x$ horizontal rectangles and $y$ vertical rectagles, the rectangle we created will have side lengths $m = 2x, n=3y$ so the set of pairs we are looking for is simply[eqn] \{ (2x,3y), x,y \in \mathbb{Z} \} [/eqn]
 >> Anonymous Tue Nov 7 23:40:15 2017 No.9282598 >>9282576You can very easily tile a $5 \times 6$ rectangle.
 >> Anonymous Tue Nov 7 23:40:52 2017 No.9282599 I found a story here some months ago about a hypothetical Russian rocket that used some insanely dangerous fuel/oxidizer combo because the CIA leaked that the US had found a way to make the combination work with use of a top secret stabilizer.Anyone have a link to the story?
 >> Anonymous Wed Nov 8 01:14:23 2017 No.9282712 The probability density functionfx(x) = 1/((1+x)^2) for x>0, and 0 elsewhere.How do I show that 1/x has the same distribution as x?
 >> Anonymous Wed Nov 8 01:25:47 2017 No.9282725 Brainlet incoming, shit deflectors activated.What do you do when you're on the verge of failing (D or F) towards the end of the semester? I have three classes that are giving me a huge death wish. For one class I may get an instructor withdrawal because of circumstances, the other two have just been really difficult for me to balance with my stupid life and on top of that getting intuition has been difficult to me. If anyone has any good resources that take things a bit slow for an engineering statistics and first course in linear algebra, please send. YouTube can be helpful sometimes, but there seems to be so many different approaches to these courses that not every video is directly relevant. LA has had a really bad exam average, but the hw is super long and I will probably have 2/3 of the total grade for that. Going to office hours for both classes tomorrow to be a little crybaby. Anybody here fail out of uni before? If I actually pull my shit together I could be fine, but long term gf just left me so last week I did almost nothing (made my situation a lot worse).
 >> Anonymous Wed Nov 8 01:32:55 2017 No.9282730 >>9282712[eqn] P(X \leq t) = \int_0^t \frac{1}{(1+x)^2}dx \\= \int_{\frac{1}{t}}^\infty \frac{1}{(1+x)^2}dx \\= P\left( X \geq \frac{1}{t} \right) \\= P\left( \frac{1}{X} \leq t \right) [/eqn]
 >> Anonymous Wed Nov 8 01:46:26 2017 No.9282747 >>9282730I see. Thank you...these are a little confusing for me.How about..If X has distribution R(0,1) and Y has distribution (-1/a)(lnX) with a>0,how can I show that Y has the same distribution as the exponential distribution of a?
 >> Anonymous Wed Nov 8 01:49:36 2017 No.9282751 >>9282747Stop asking other to do your homework.Fucking do it yourself. It's done the same way the other guy showed you.
 >> Anonymous Wed Nov 8 01:55:45 2017 No.9282758 >>9282751I don't know how to.
 >> Anonymous Wed Nov 8 01:59:12 2017 No.9282763 >>9282758You know the definition of a cummulative distribution function is.Compute the cummulative distribution function of Y.P(Y <= y) = ........
 >> Anonymous Wed Nov 8 02:03:18 2017 No.9282770 >>9282763= int from 0 to y of (-1/a)(lnX)dx, no?then what?
 >> Anonymous Wed Nov 8 02:44:03 2017 No.9282799 >>9282770>then what?Then solve the integral. But you can also do thisy ranges from 0 to infinity.P(Y-ay) = P(X>e^(-ay)) = 1-P(X
 >> Anonymous Wed Nov 8 02:55:35 2017 No.9282818 Anyone can recommend me a book on power electronic? About step down/up converter and half/full bridge inverter and fly-back SMPS converter?
 >> Anonymous Wed Nov 8 03:44:14 2017 No.9282853 File: 2 KB, 149x18, MSP14952123e8772545b7b6d00000g52ah46dbba4eh2.gif [View same] [iqdb] [saucenao] [google] [report] There is supposedly a trivial solution to this but I can't see how to do it without simplifying everything to the same base. Plz help
 >> Anonymous Wed Nov 8 03:46:17 2017 No.9282855 >>9282853try $x = 0$
 >> Anonymous Wed Nov 8 03:57:39 2017 No.9282869 File: 109 KB, 1667x348, Capture.png [View same] [iqdb] [saucenao] [google] [report] >>9280927How the heck do they draw that graph or whatever you call it? Half of those numbers seem like they were pulled from magic. Is there anyway to get good at drawing them? I can't find any tutorials for them.
 >> Anonymous Wed Nov 8 04:10:43 2017 No.9282884 >>9282869law of sines
 >> Anonymous Wed Nov 8 04:27:29 2017 No.9282889 >>9282884I get that part though where did they pull the 50 and 30 degrees from?
 >> Anonymous Wed Nov 8 04:37:15 2017 No.9282895 File: 93 KB, 1053x478, Capture.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Nov 8 04:39:37 2017 No.9282901 File: 92 KB, 878x295, Untitled.png [View same] [iqdb] [saucenao] [google] [report] Pretty sure this can't be done as the two events are dependent, and you need them to be independent to do the first part,,,Why am I wrong?
 >> Anonymous Wed Nov 8 04:49:06 2017 No.9282911 P(X=3,Y=2) = P(Y=2|X=3) P(X=3)= 3 (0.6)^2 (0.4) (0.25)
 >> Anonymous Wed Nov 8 04:59:22 2017 No.9282922 >>9282901Calculate binomial distributions where p=.6 and n=0,1,2 and 3. Multiply these by the p m f value for the corresponding X to get joint pm f. Rest is easy then
 >> Anonymous Wed Nov 8 05:08:10 2017 No.9282927 >>9282911correct>>9282901Joint pmf: $P(X=x,Y=y) = P(Y=y | X=x) P(X=x) = \binom{x}{y} {0.6}^y {0.4}^{x-y} p_X(x)$ Marginal of Y:$P(Y=y)= \sum\limits_{x=0}^{3} P(X=x,Y=y) = \sum\limits_{x=0}^{3} \binom{x}{y} {0.6}^y {0.4}^{x-y} p_X(x)$
 >> Anonymous Wed Nov 8 05:10:07 2017 No.9282930 >>9282895Thanks for the help anon. I see the error in my ways now.
 >> Anonymous Wed Nov 8 06:07:10 2017 No.9282967 Can someone explain to me how the raising operator $a^\dagger=\frac{1}{\sqrt{2}}\left(-\frac{d}{dq}+q\right)$ is the adjoint of the lowering operator $a=\frac{1}{\sqrt{2}}\left(\frac{d}{dq}+q\right)$. This suggests that $\frac{d}{dq}$ is a pure imaginary operator, but I don't understand why this is the case.
 >> Anonymous Wed Nov 8 06:10:59 2017 No.9282968 Why is$g^{bc}\nabla_b\nabla_cx^a = g^{bc}\left ( \partial_b \partial_c - \partial_d x^a \Gamma^d_{bc}\right )$Does the metric kill all terms from $\nabla_b\nabla_c x^a$except for$\partial_b \partial_c - \partial_d x^a \Gamma^d_{bc}$?
 >> Anonymous Wed Nov 8 06:22:20 2017 No.9282975 >>9282967You can write d/dq as d/dq = ip where p is the momentum conjugate to q. q is a real observable, thus p is real as well. So d/dq is imaginary as you say.You can also verify from stipulating that [a,a^\dag] = 1 (since you said they are raising operators). Then you can show [d/dq,q]=1 and since you know [x,p]=i, you can work out the rest.
 >> Anonymous Wed Nov 8 06:48:28 2017 No.9282993 >>9282968Doesn't that just follow directly from the definition of the covariant derivative? You can see all the other terms cancel.
 >> Anonymous Wed Nov 8 08:31:23 2017 No.9283085 >>9282855How does that help in any way?
 >> Anonymous Wed Nov 8 08:32:46 2017 No.9283087 Is the probability of getting HHT and HHH the same on a fair coin? That doesn't sound right but if it' fair then they all = 0.5 so wouldn't it just be 0.5^3?
 >> Anonymous Wed Nov 8 08:36:41 2017 No.9283090 >>9283087>Is the probability of getting HHT and HHH the same on a fair coin?Yes.>That doesn't sound rightIt does, you are just confused. {HHT} is not {HHT, HTH, THH}.
 >> Anonymous Wed Nov 8 10:41:56 2017 No.9283230 >>9282993I don't see how everything else cancels, maybe I'm doing something wrong$\nabla_b\nabla_cx^a = \nabla_b(\nabla_cx^a) = \partial_b( \nabla_cx^a)-\Gamma^d_{bc}(\nabla_dx^a)+\Gamma^a_{bc}(\nabla_dx^a)\\=\partial_b(\partial_cx^a+\Gamma^a_{ce}x^e)-\Gamma^d_{bc}(\partial_d(x^a+\Gamma^a_{de}x^e)+\Gamma^a_{bd}(\partial_cx^d+\Gamma^d_{ce}x^e)\\=\partial_b\partial_cx^a+\partial_b\Gamma^a_{ce}x^e+\Gamma^a_{ce}\partial_bx^e-\Gamma^d_{bc}\partial_dx^a-\Gamma^d_{bc}\Gamma^a_{de}x^e+\Gamma^a_{bd}\partial_cx^d+\Gamma^a_{bd}\Gamma^d_{ce}x^e$Is it just some clever way of relabeling indices and most of this vanishes?
 >> Anonymous Wed Nov 8 10:49:33 2017 No.9283238 >>9283230messed up a bit, rightmost term of uppermost equation should be$\Gamma^a_{bd}(\nabla_cx^d)$
 >> Anonymous Wed Nov 8 10:54:31 2017 No.9283245 File: 51 KB, 865x84, untitled0.png [View same] [iqdb] [saucenao] [google] [report] What the hell?Is this as obvious as I think? Can someone help me out?
 >> Anonymous Wed Nov 8 11:00:56 2017 No.9283250 >>9283230What the fuck is this mess?
 >> Anonymous Wed Nov 8 11:02:48 2017 No.9283252 >>9283245Yes, it is obvious. Are you supposed to proved it or what?
 >> Anonymous Wed Nov 8 11:03:39 2017 No.9283253 >>9283252Time for you to go backto reddit
 >> Anonymous Wed Nov 8 11:04:07 2017 No.9283255 >>9283252Yes and I think I did although I can't figure out LaTeX to share. So I come here to see if someone else will verify their proof with me
 >> Anonymous Wed Nov 8 11:06:30 2017 No.9283257 >>9283255$f_{\vec{X},\vec{Y}}(\vec{x},\vec{y})=f_{\vec{X}}(\vec{x})f_{\vec{Y}}(\vec{y})>0$
 >> Anonymous Wed Nov 8 11:12:06 2017 No.9283264 >>9280927Humanities brainlet struggling with optics here.>At what distance from a converging lens with a focal distance of 40cm must an object be situated, in order to get an image 4 times larger than the object?>The focal distance of a camera is f = 5cm. The image of a 6m tall house is 24mm large. From what distance was the house photographed?
 >> Anonymous Wed Nov 8 11:18:41 2017 No.9283279 How is the subgroup $nA$ in $A/nA$ defined exactly? Where $A$ is an abelian group.
 >> Anonymous Wed Nov 8 11:31:37 2017 No.9283297 i have a function from R^2 to R^1, how do i find its equivalent matrix operator?
 >> Anonymous Wed Nov 8 11:38:05 2017 No.9283301 >>9283279nx = x+x+x...+x (n times)
 >> Simon Troy Cosgrove Wed Nov 8 11:39:13 2017 No.9283305 >>9280927I Have Never Deserved My Own Thread.For I Gave You My Position in the Cosmos, for US.I do mean 'all' of US.
 >> Anonymous Wed Nov 8 11:44:37 2017 No.9283311 >>9283230Move to a geodetic coordinate system at x, all the non-differentiated Christoffel coefficients vanish.
 >> Anonymous Wed Nov 8 11:45:50 2017 No.9283314 >>9283279nA is the identity element of A/nA. Therefore {nA} is the trivial subgroup of A/nA.
 >> Anonymous Wed Nov 8 12:04:23 2017 No.9283340 >>9283301Yeah, but how is $nA$ itself defined? $nA := \{ na | a \in A \}$? So all "multiples" of n?>>9283314Sorry if I wasn't clear, I meant something different.
 >> Anonymous Wed Nov 8 12:44:58 2017 No.9283432 >>9283085$8^0 = 0.6*18^0+0.4*3^0$$1 = 0.6*1 + 0.4*1$$1 = 0.6 + 0.4$
 >> Anonymous Wed Nov 8 12:56:00 2017 No.9283450 >>9283340>Sorry if I wasn't clear, I meant something different.Oh I see.Well, if there's no other context, then it kinda Has to mean what you wrote.
 >> Anonymous Wed Nov 8 13:03:59 2017 No.9283466 How high in the atmosphere can a person live and not suffocate?
 >> Anonymous Wed Nov 8 13:17:27 2017 No.9283492 >>9280936Separate the cases x_0 > 0 and x_0 < 0. Then, compute $x_{n+1}-x_n$ and deduce that (x_n) has a limit. Then, see what that limit must be.
 >> Anonymous Wed Nov 8 13:17:32 2017 No.9283493 >>9283466mount everest is almost too high, they need oxygen masks to climb up there
 >> Anonymous Wed Nov 8 13:23:48 2017 No.9283508 >>9283492>Then, compute xn+1−xnxn+1−xn and deduce that (x_n) has a limit.that does not deduce that
 >> Anonymous Wed Nov 8 14:19:51 2017 No.9283626 File: 68 KB, 960x720, serveimage.jpg [View same] [iqdb] [saucenao] [google] [report] for an NMOS, how come the drain current saturates after passing a certain drain voltage?
 >> Anonymous Wed Nov 8 16:55:22 2017 No.9283871 Thoughts on a non thesis M.S.? Will it help getting a reasonably good job? I have no plans to get a phd and i dont really want to stay in school for 2 extra years rather than 1
 >> Anonymous Wed Nov 8 17:07:44 2017 No.9283894 >>9283508yes it does, but it requires a little something
 >> Anonymous Wed Nov 8 17:13:59 2017 No.9283902 >>9283626The channel pinches off.https://en.wikipedia.org/wiki/Channel_length_modulation
 >> Anonymous Wed Nov 8 17:14:51 2017 No.9283905 If I know the mean free path between particle collisions and between particle-photon collisions, in some part of the solar photosphere, and I know the average temperature difference between once such collision and the next, how do I tell if the system is in Local Thermodynamic Equilibrium? The temperature difference between particle-particle interactions is tiny, say 1e-6 K, but the temperature difference between photon-particle interactions is a few thousand K. Is this LTE or not?
 >> Anonymous Wed Nov 8 17:15:25 2017 No.9283907 >>9283466A few miles, about 5 or 6.
 >> Anonymous Wed Nov 8 19:17:32 2017 No.9284105 >Every positive integer greater than one can be written uniquely as a product of primes, where the prime factors are written in nondecreasing order.What’s important about the non decreasing bit. Why not omit it?
 >> Anonymous Wed Nov 8 19:24:37 2017 No.9284124 File: 27 KB, 628x290, d or a.png [View same] [iqdb] [saucenao] [google] [report] >>9280927What are two different methods to distinguish between a dissociative and associative pathway leading to the same product? I don't think that labelling with deuterium would work here.
 >> Anonymous Wed Nov 8 19:50:54 2017 No.9284169 File: 25 KB, 1080x464, HALF-ADDER-FULL-ADDER-FIG-2-compressor[1].jpg [View same] [iqdb] [saucenao] [google] [report] Here's my assignment: Design a combinational circuit that adds two 4 bits binary numbers together.Steps given to design a combinational circuit:1. determine # of inputs and outputs2. derive truth table to get the relationship between input and output3. obtain a simplified boolean function for each output4. draw a logic diagramSo I'm guess there's going to be 9 inputs and 5 outputs. Right now I'm specifically wondering if I have to make a truth table for all the 9 inputs and outputs. And if not, can someone give me some suggestion on what to do? I'm completely lost.
 >> Anonymous Wed Nov 8 19:52:21 2017 No.9284172 Let's say that I have three vectors a,b,c that define the corners of a triangle. Now I want to show that the three medians of the triangle meet at the center of 1/3(a+b+c).How do I show this? I don't know where to start at all.
 >> Anonymous Wed Nov 8 20:01:28 2017 No.9284190 Can I figure out if a linear transformation is orthogonal by running i-hat and j-hat through it and seeing if they retain distance? Or are there cases where this wouldn't work.
 >> Anonymous Wed Nov 8 20:02:45 2017 No.9284192
 >> Anonymous Wed Nov 8 20:04:40 2017 No.9284198 >>9284124One of the methods is to determine rate dependance by with varying reactions. 1st order reaction versus 2nd order.
 >> Anonymous Wed Nov 8 20:05:01 2017 No.9284200 >>9284105>uniquely
 >> Anonymous Wed Nov 8 20:08:39 2017 No.9284205 >>9284198So, for 2nd order reactions, I should ask: "is the rate affected by the depletion of [B]"? And if it is, then it is indeed a 2nd order reaction. THank you anon.
 >> Anonymous Wed Nov 8 20:11:10 2017 No.9284212 >>9284190wouldn't you just take the inner product of your input vector and the vector it maps to?
 >> Anonymous Wed Nov 8 20:13:29 2017 No.9284218 >>9284172the median from a is the line from a to the midpoint of b and cthe midpoint of b and c is b + (c-b)/2 = (b+c)/2the intersection is located on this line a+ ((b+c)/2 - a)*t for some t st 0
 >> Anonymous Wed Nov 8 20:22:42 2017 No.9284236 >>9284212Consider a linear transformation that simply scales i-hat by 5 and j-hat by 5. The inner product for the image and original will be zero, but distance between vectors is not conserved.
 >> Anonymous Wed Nov 8 20:36:12 2017 No.9284276 >>9284218now I see. it actually isn't that hard. thanks.
 >> Anonymous Wed Nov 8 21:17:08 2017 No.9284370 >>9283894>but it requires a little somethingso... it doesn't
 >> Anonymous Wed Nov 8 21:31:22 2017 No.9284396 File: 79 KB, 1004x773, Axler.jpg [View same] [iqdb] [saucenao] [google] [report] >>9284190No, it would not work. A map T is orthogonal iff ||Tv||=||v|| For All v in the vector space; not just the basis vectors.For example consider the map which takes i to i=(1,0) and j to 1/sqrt(2)(1,1). It's obviously not orthogonal.But, if the images of i and j are orthonormal, i.e. have unit length like i and j do AND they are orthogonal, then the map is orthogonal.
 >> Anonymous Wed Nov 8 21:31:34 2017 No.9284397 >>9284169The easiest solution is a ripple-carry adder: 4 full adders where the carry-out from one stage is fed to the carry-in of the next stage. Each full adder has 3 inputs, so that's only 2^3=8 rows in the truth table.The disadvantage of ripple-carry adders is that the propagation delay from the least-significant input bit to the most-significant output bit is proportional to the number of bits.More advanced designs avoid this at the expense of requiring more gates. The extreme is a minterm (disjunctive normal form, sum of products) solution which is only 2 gates deep but requires an exponential number of gates.
 >> Anonymous Wed Nov 8 22:51:19 2017 No.9284548 >>9284396Much appreciated
 >> Anonymous Wed Nov 8 22:54:44 2017 No.9284554 >>9284190Just take the determinant of the transformation.
 >> Anonymous Wed Nov 8 22:57:57 2017 No.9284561 File: 1.00 MB, 2404x751, 1486474084121.png [View same] [iqdb] [saucenao] [google] [report] How do I calculate the arc length of this?I got to a weirdish integral and I do not know if I'm on the right way.
 >> Anonymous Wed Nov 8 22:58:03 2017 No.9284563 File: 35 KB, 652x258, opera_2017-11-08_22-44-50.png [View same] [iqdb] [saucenao] [google] [report] How do I pass my midterm on Friday?
 >> Anonymous Wed Nov 8 22:59:38 2017 No.9284567 >>9284554Can you elaborate?
 >> Anonymous Wed Nov 8 23:03:09 2017 No.9284573 File: 2.00 MB, 3120x4160, 1499987398857.jpg [View same] [iqdb] [saucenao] [google] [report] >>9284561I have to calculate the arc length between x=0 and x=5 btwThis is how far I got manually. The integral is right but not sure if it's the proper way to do it "humanly". Wolframalpha got the same integral when solving it.
 >> Anonymous Wed Nov 8 23:03:29 2017 No.9284576 >>9284561ez, Y=6*cosh(x) just solve it like a regular trig function then. Hyperbolic functions and regular trig functions have similar integrating rules.
 >> Anonymous Wed Nov 8 23:06:11 2017 No.9284583 >>9284576Sorry but I'm the average calc II retard. Could you show me the trig identity you just used?
 >> Anonymous Wed Nov 8 23:08:21 2017 No.9284588 File: 3 KB, 415x170, opera_2017-11-08_23-07-37.png [View same] [iqdb] [saucenao] [google] [report] >>9284583I'm guessing you haven't covered hyperbolic functions yet. I suggest reading this link.http://tutorial.math.lamar.edu/Classes/CalcI/DiffHyperTrigFcns.aspx
 >> Anonymous Wed Nov 8 23:09:51 2017 No.9284590 >>9284588Yeah, we haven't. Hope I can learn it by myself pretty quick so I can get some hours of sleep before class.Thanks for the help, anon.
 >> Anonymous Wed Nov 8 23:10:16 2017 No.9284591 >>9284590No problem
 >> Anonymous Wed Nov 8 23:21:47 2017 No.9284611 >>9284591What would the square root of 1 + 36sinh2(x) be?
 >> Anonymous Wed Nov 8 23:39:42 2017 No.9284631 File: 99 KB, 225x335, 1509527885766.png [View same] [iqdb] [saucenao] [google] [report] Is there a single book that covers all of the following:Banach algebrasAffine Hecke algebraBeurling algebraDuffin–Kemmer–Petiau algebraExterior algebraFiltered algebraGerstenhaber algebraHall algebraKoszul algebraPoisson algebraRota–Baxter algebraWeyl algebra
 >> Anonymous Wed Nov 8 23:53:58 2017 No.9284652 >>9284591Reporting back. I tried as hard as I could and I failed. I got the length as 40.1 or 38.43.Wolfram alpha said it's 439.56 from the start though.
 >> Anonymous Thu Nov 9 00:05:30 2017 No.9284673 >>9284652seems like there is no simple closed form for this according to https://www.wolframalpha.com/input/?i=sqrt(36cosh%5E2(x)-35)so the best you can do is approximate but if you really want the exact answer https://www.wolframalpha.com/input/?i=-i+EllipticE(i+5,+36)but i may be wrong
 >> Anonymous Thu Nov 9 00:10:04 2017 No.9284680 >>9284673I can't believe I just wasted ~5 hours on a teacher's typo.No way this was intended in any way.Can you spoonfeed me the steps up to the "exact answer"? I really don't know how to work my way there. I tried to use what I learned from the link you sent me while following what I learned about calculating curve length.
 >> Anonymous Thu Nov 9 00:31:17 2017 No.9284714 >>9284611you can't simplify that. But it was probably meant to simplify in order to allow you to use 1 + sinh^2(x) = cosh^2(x)
 >> Anonymous Thu Nov 9 01:51:16 2017 No.9284796 >>9284680It's fucked up. Mathematica took like 30 seconds to solve the indefinite integral and after like 2 minutes in, it still hasn't solved the definite one and I aborted it.There's most certainly a typo.
 >> Anonymous Thu Nov 9 04:13:07 2017 No.9284936 File: 382 KB, 640x480, Asuka_smiling.png [View same] [iqdb] [saucenao] [google] [report] What is the exact meaning of quotient spaces? i mean i know the definition, but what is the essence of it? take $\mathbb{R} / \mathbb{Z}$ for example.
 >> Anonymous Thu Nov 9 04:21:57 2017 No.9284943 >>9284936It's just [0,1)
 >> Anonymous Thu Nov 9 04:32:40 2017 No.9284951 >>9284943yeah i get it its homeomorphic to $\mathbb{S}^1$.... but what does it mean? something with translations...
 >> Anonymous Thu Nov 9 04:49:21 2017 No.9284966 >>9284936You consider Z as zero...., -2+c, -1+c , 0+c , 1+c, 2+c, ... are considered as the same thing.
 >> Anonymous Thu Nov 9 04:53:30 2017 No.9284972 >>9284966i see..thats why its the equivalence classes of $x\sim y :\Leftrightarrow x-y\in \mathbb{Z}$
 >> Anonymous Thu Nov 9 04:59:14 2017 No.9284979 >>9284972yep
 >> Anonymous Thu Nov 9 06:15:47 2017 No.9285024 > link jumping on wikipedia> land on cadmium> leading source of cadmium poisoning is tobacco/smoking How the fuck does a toxic metal like cadmium end up in tobacco? I tried to find an answer but most hits seem to be around the percentages in various types of plant/cigarettes, but nothing on where it actually enters the chain? Non-smoker, but just curious.
 >> Anonymous Thu Nov 9 07:30:43 2017 No.9285070 I don't understand how the Cantor set is uncountable. $\mathbb{Q}$ is countable, so if the Cantor set is uncountable that would mean it's not a subset of $\mathbb{Q}$, so my question is why is the Cantor set not a subset of $\mathbb{Q}$
 >> Anonymous Thu Nov 9 07:37:34 2017 No.9285078 File: 358 KB, 552x543, 1510230564682.png [View same] [iqdb] [saucenao] [google] [report] I have a real analysis exam on monday spanning from chapter 3 on baby rudin till chapter 5 and I've barely started studying, will I make it?
 >> Anonymous Thu Nov 9 08:14:11 2017 No.9285122 File: 91 KB, 1420x599, 6543654584.jpg [View same] [iqdb] [saucenao] [google] [report] How do I go about solving this? I thought about breaking up the nonparallel plates into infinitesimal parallel strips, but I got nowhere. Please help.
 >> King Brainlet Thu Nov 9 08:34:21 2017 No.9285146 File: 366 KB, 583x608, 1508341370410.png [View same] [iqdb] [saucenao] [google] [report] Here's a step in the proof of $f(x) = x^{2}$ being continuous at $x=2$:Let $\delta \leq 1$ Then $|x-2|<1 \implies |x-2|\cdot |x+2| < \epsilon$. Note $|x+2| \leq |x-2| + 4 < 5$, so $|x-2|\cdot |x+2| < 5\delta$What's the reasoning behind: $|x-2|\cdot |x+2| < 5\delta$?
 >> Anonymous Thu Nov 9 08:36:20 2017 No.9285148 >>9285146wtf is this nonsense
 >> Anonymous Thu Nov 9 08:42:37 2017 No.9285153 >>9285146If $|x - 2| < 1$ then $|x+2| < 5$. In this case, if $|x - 2| < \delta$ we have that $|x-2| |x + 2| < 5 \delta$. The second sentence is wrong; $|x-2||x+2| < \epsilon$ is something you want to prove, rather than an implication. You can do this by putting delta less than 1 and also less than epsilon / 5.
 >> Anonymous Thu Nov 9 08:45:03 2017 No.9285155 >>9285078Try these problems:https://ocw.mit.edu/courses/mathematics/18-100b-analysis-i-fall-2010/exams/Also try the problems from the UCLA "Basic Qualifying Exam" or "Berkeley Problems in Mathematics" on the relevant topics (the Berkeley Problems in Mathematics book is arranged by topic).
 >> Anonymous Thu Nov 9 08:47:20 2017 No.9285156
 >> Anonymous Thu Nov 9 08:48:30 2017 No.9285157 >>9285156Do you think I don't know how to Google, you dipshit? The problem isn't asking for capacitance, it's asking for potential. Kys.
 >> King Brainlet Thu Nov 9 09:13:23 2017 No.9285174 File: 457 KB, 772x804, 1508341079554.png [View same] [iqdb] [saucenao] [google] [report] >>9285153I see. Thanks.
 >> Anonymous Thu Nov 9 09:16:32 2017 No.9285177 what is>t. me?It looks like a citation or something but I've never heard of it being done that way. Is it a new thing?
 >> Anonymous Thu Nov 9 09:21:22 2017 No.9285181 If the instructor doesn't include a grading scale on the syllabus does that mean that usually mean they curve the entire class's final grades?
 >> Anonymous Thu Nov 9 09:21:45 2017 No.9285182 Given the pipe diameter, the volumetric flow rate of the water and the viscosity of the water, how do I calcualte the reynolds number? Re=(D) (U) / V d=diameter, u = fluid velocity and v=viscosity.I just need to find the value for U but the only information I have is the volumetric flow rate, so I have to convert it to linear fluid velocity. How do i do this? What is 0.2L/min in m/s?
 >> Anonymous Thu Nov 9 09:24:07 2017 No.9285183 Why is it when two elements are placed next to each other with no operator, it is assumed to mean multiply? So 2a is 2*a. What's so special about multiplication?
 >> Anonymous Thu Nov 9 09:35:56 2017 No.9285193 >>9285024Cadmium, and others heavy metals, accumulates in the tobacco plant, but given the shit they put in cigarettes, I wouldn't be surprised if it also comes from other sources. Also, tobacco is pretty good at accumulating heavy metals. https://www.google.it/url?sa=t&source=web&rct=j&url=http://www.globalsciencebooks.info/Online/GSBOnline/images/0712/TAET_1(1%262)/TAET_1(2)46-53o.pdf&ved=0ahUKEwjCrdfR2rHXAhXJmBoKHeFMDGEQFgg8MAU&usg=AOvVaw09uZFhf0nG1KowgNpt62_XApparently plants can be used to clean contaminated soils. (keywords: bioremediation, phytoremediation)
 >> Anonymous Thu Nov 9 09:52:01 2017 No.9285205 >>9285177It's a meme from /int/ that comes from the way Finnish people sign messages such as letters, e-mails, etc.>>9285183It doesn't necessarily mean multiplication. I'd argue that it's more notation for addition as 2a means that you have a quantity of 2 of whatever a is. For example, $4\lambda$ could be interpreted as 4 $\lambda$'s -- i.e., $\lambda+\lambda+\lambda+\lambda$ -- or $\lambda$ 4's -- $\sum_0^{[\lambda]}4+([\lambda]-\lambda)4$ where $[\lambda]$ is the greatest integer in $\lambda$.
 >> Anonymous Thu Nov 9 09:53:59 2017 No.9285207 >>9285205I meant $(\lambda - [\lambda])$ not $([\lambda] - \lambda)$.
 >> Anonymous Thu Nov 9 11:51:30 2017 No.9285321 >>9285183Nothing is special about it. You just do it to write less.
 >> Anonymous Thu Nov 9 12:47:42 2017 No.9285405 How difficult can I expect a course in projective geometry (undergrad) to be? The course description says it will cover: projective space, the principle of duality, mappings in projective space, conics and quadrics. I did okay in linear algebra.
 >> Anonymous Thu Nov 9 13:02:11 2017 No.9285429 >>9282149Not him but it really does look like that limit is creeping up on 0/0. That also looks like trig identities night be helpful.t. Guy who models oscillations
 >> Anonymous Thu Nov 9 13:19:51 2017 No.9285452 www2.lawrence.edu/fast/GREGGJ/Math150/032Work.pdfcan anyone tell me why they don't multiply gravity in finding work here? they eventually get 1.38*10^12 ft-lbs and I understand everything they went through to get it except I thought work would have to be Ms*g*y (where Ms is mass of slice of pyramid) making the integral be ∫(0,h)Ms*g*y (and since Ms=p*x^2dy and x=(b/h)(h-y) the integral is ∫(0,h)p*((b/h)(h-y))^2 *g*y dy = p*g*∫(0,h)((b/h)(h-y))^2 *y dy) but they have the integral as just ∫(0,h)Ms*y (or p∫(0,h)((b/h)(h-y))^2 *y dy), literally the same thing just without being multiplied by g. it took me like 2 hours to go through all this since i suckbut the point is that they have W=1.38*10^12 ft-lbs and I think it should be 32.2(1.38*10^12) ft-lbs. (since 32.2 ft/s^2 = 9.8 m/s^2 probably obviously) W=Fd so what gives? where is the F in what they did?
 >> Anonymous Thu Nov 9 13:23:31 2017 No.9285458 >>9285452learn latex you mong
 >> Anonymous Thu Nov 9 13:28:47 2017 No.9285466 >>9285458sorry But I kind of think all the shit is besides the point Almost, or maybe it isn't idk. But they're just calculating the work done to get a slice of a pyramid up to a point y. And they don't multiply gravity by that y to get W. I don't know why they don't
 >> King Brainlet Thu Nov 9 13:31:40 2017 No.9285471 File: 13 KB, 225x225, 1503247350492.jpg [View same] [iqdb] [saucenao] [google] [report] how do I show $x_{n} = \frac{1}{2^{n}}$ is cauchy using the definition: $\forall \hspace{0.2cm} \epsilon > 0\hspace{0.2cm} \exists\hspace{0.2cm} N \in \mathbb{N}\hspace{0.2cm} \text{such that}\hspace{0.2cm} \forall\hspace{0.2cm} m,n \geq N, |x_{n}-x_{m}| < \epsilon$I get as far as $\big| \frac{1}{2^{n}} - \frac{1}{2^{m}} \big| = \big| \frac{2^{m}+2^{n}}{2^{n+m}} \big|$
 >> King Brainlet Thu Nov 9 13:33:14 2017 No.9285475 >>9285471* $\big| \frac{2^{m}-2^{n}}{2^{n+m}} \big|$
 >> Anonymous Thu Nov 9 14:44:56 2017 No.9285611 File: 160 KB, 629x645, Capture.jpg [View same] [iqdb] [saucenao] [google] [report] any german speaking anons here who can help with anything here, literally any help would do since I'm really lost
 >> Anonymous Thu Nov 9 14:48:00 2017 No.9285620 >>9285611Really would help you but I'm too busy. Just run it throughhttp://imtranslator.net/compare/ and check individual words with https://www.dict.ccall the best
 >> Anonymous Thu Nov 9 14:53:10 2017 No.9285637 >>9285620thanks german speaking anon, but could you help with the examples that are in question, since I'm not only looking for help with the translation but some help with solving these fuckers
 >> Anonymous Thu Nov 9 14:55:01 2017 No.9285643 >>9285637bin ein Hirnlein, also kann ich nur übersetzen
 >> Anonymous Thu Nov 9 14:55:15 2017 No.9285645 >>9285471wlog let n
 >> King Brainlet Thu Nov 9 14:59:55 2017 No.9285655 File: 291 KB, 750x750, 15092396555577.png [View same] [iqdb] [saucenao] [google] [report] >>9285645t-thanks
 >> Anonymous Thu Nov 9 15:02:53 2017 No.9285663 brainlet here, I have trouble multiplying matrices together
 >> Anonymous Thu Nov 9 15:07:39 2017 No.9285672 >>9285663think of it as a dot product of the rows of A with the columns of B
 >> Anonymous Thu Nov 9 15:09:17 2017 No.9285673
 >> Anonymous Thu Nov 9 15:14:08 2017 No.9285683 >>9285672this is a very good advice
 >> Anonymous Thu Nov 9 15:24:01 2017 No.9285707 >>9285663The n-th column of a matrix is where it sends the n-th dimension. A*BTake the columns of B, break them up into the sum of their dimensions, see where A sends each dimension individually, sum them together to find the net effect, and you have the columns of the result AB.
 >> Anonymous Thu Nov 9 16:09:45 2017 No.9285800 >>9285452>>9285466Okay I asked a friend It was an issue of unitsPounds are not mass, but are basically newtons. So that's why they don't need to multiply by g, they already have their dimensions correct
 >> Anonymous Thu Nov 9 16:37:18 2017 No.9285854 aerospace engineering senior brainlet here. How hard is it going to be getting an internship with sub 3.0 GPA?
 >> Anonymous Thu Nov 9 17:09:10 2017 No.9285936 I'm in EE, and I'm thinking of going into grad school to specialize in microprocessor systems, or semiconductor physics. Do either of these require any proficiency in digital systems, or combinatorial circuits?
 >> Anonymous Thu Nov 9 17:18:07 2017 No.9285953 What's a good book on signal processing?
 >> Anonymous Thu Nov 9 17:40:08 2017 No.9286010 >>9285953The Analytical Theory of Heat
 >> Anonymous Thu Nov 9 18:04:11 2017 No.9286073 Is it possible for the joint probability distribution of two purely random variables to have a greater variance or standard deviation than either one of the distributions its composed of?
 >> Anonymous Thu Nov 9 18:06:25 2017 No.9286078 How hard would it be to get a master's in Mech E if I have a bachelors in EE?
 >> Anonymous Thu Nov 9 18:36:49 2017 No.9286132 >>9285936I'm just a second year EE, but shouldn't microprocessor systems? That sounds like it would be a lot of digital/combinational/sequential circuits.
 >> Anonymous Thu Nov 9 18:43:05 2017 No.9286139 >>9285611hey girlI have a phd in spurtopologie
 >> Anonymous Thu Nov 9 18:43:17 2017 No.9286140 >>9286132I'm more interested in the physics of things, but you're probably right.
 >> Anonymous Thu Nov 9 18:50:53 2017 No.9286149 File: 67 KB, 736x736, 1447542508836.jpg [View same] [iqdb] [saucenao] [google] [report] >>9280927One of the exercises in this textbook has the solution listed as (-∞,3) U (3,∞), while my answer was (-∞,3) U [4,∞)Would a professor mark that wrong? I obviously see why the former is the superior choice, but they both describe the same set, right? It's like in programming (int i = 0;i<=10;i++) vs (int i = 0;i<11;i++), right?
 >> Anonymous Thu Nov 9 19:14:35 2017 No.9286174 Was there any follow up to that /sci/ anon who made the hypothesis of some steroid being able to cure cancer?
 >> Anonymous Thu Nov 9 19:19:44 2017 No.9286184 Please help a brainlet. The volume of toothpaste has an average of 3.4 ounces with a standard deviation of 0.1. What is the probability that arandom sample of 9tubes is within 0.05 of the stated average?
 >> Anonymous Thu Nov 9 19:21:20 2017 No.9286186 >>9286139sup my man, then these examples should be no-brainers for you tbqh, help out
 >> Anonymous Thu Nov 9 19:44:07 2017 No.9286220 File: 92 KB, 959x617, math +.png [View same] [iqdb] [saucenao] [google] [report] >>9286149Think about 3.5 and where it is.
 >> Anonymous Thu Nov 9 19:45:27 2017 No.9286223
 >> Anonymous Thu Nov 9 19:47:35 2017 No.9286230 >>9286010>implying anyone will get the start with the Greeks reference
 >> Anonymous Thu Nov 9 19:50:45 2017 No.9286234 >>9286220tfw im a brainlet
 >> Anonymous Thu Nov 9 19:57:22 2017 No.9286251 TeX question:What happened in this post:>>9280933and how did he fix it so quickly:>>9280935?
 >> Anonymous Thu Nov 9 19:57:54 2017 No.9286252 >>9282818Check the sci wiki for books, I think they have a few recommended texts for power electronics
 >> Anonymous Thu Nov 9 20:02:54 2017 No.9286261 Need to pick my specialty for MS in EE soon, torn between photonics and optics or RF/mixed signal. Which might be better for the long term? I plan to get a PhD after my MS if that matters
 >> Anonymous Thu Nov 9 20:03:45 2017 No.9286263 >>9286251\left| \frac{1}{n} - \frac{1}{m} \leq \left| \frac{1}{n} \right| + \left| \frac{1}{m} \right| < \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon\left| \frac{1}{n} - \frac{1}{m} \right| \leq \left| \frac{1}{n} \right| + \left| \frac{1}{m} \right| < \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilonhe forgot "\right|"
 >> Anonymous Thu Nov 9 20:08:56 2017 No.9286272
 >> Anonymous Thu Nov 9 20:22:24 2017 No.9286299 >>9286272It's what started Fourier Analysis (which is used heavily in signal analysis):https://en.wikipedia.org/wiki/Joseph_Fourier#The_Analytic_Theory_of_Heat
 >> Anonymous Thu Nov 9 20:27:02 2017 No.9286307 >>9286299What is "Start with the greeks"?
 >> Anonymous Thu Nov 9 20:45:45 2017 No.9286335 File: 71 KB, 600x493, 1433662924954.jpg [View same] [iqdb] [saucenao] [google] [report] >>9286307The beginning (and end) of Philosophy.
 >> Anonymous Thu Nov 9 20:47:55 2017 No.9286337 >>9286335I dunno, I could make a really good case for Blaise Pascal...
 >> Anonymous Thu Nov 9 21:05:38 2017 No.9286359 File: 66 KB, 662x580, 1509496616332.jpg [View same] [iqdb] [saucenao] [google] [report] Would increasing the oxygen content in our atmosphere by 1% have any noticeable effect?
 >> Anonymous Thu Nov 9 21:15:52 2017 No.9286371 >>9286359That picture is depressing pls delet
 >> Anonymous Thu Nov 9 21:21:02 2017 No.9286376 >>9280927I've been trying to get a grip as to why I shy away from math even though I can understand the big picture type of concepts.I have pinned it down to my mental processing speed in regards to reducing fractions like 135/168 to their lowest whole number form.I know the steps to perform in my head, but I easily get lost.Should I just cave and use a calculator for this, so that I could progress quickly through my math learning? Or should I try to memorize some type of fraction table?
 >> Anonymous Thu Nov 9 22:55:29 2017 No.9286495 What bands does Ammonia (dissolved and nitrated) absorb? Trying to build a coloriometer to monitor aquarium ammonia levels. Maybe there is a better solution? I already have a pH probe.
 >> Anonymous Thu Nov 9 23:15:37 2017 No.9286521 In epsilon delta proofs, why do we always start with the epsilon expression and then go <= ... <= ... until we arrive at the delta expression? Why does that work?
 >> Anonymous Thu Nov 9 23:22:24 2017 No.9286528 >>9286521Because less than is transitive and therefore a partial order
 >> Anonymous Thu Nov 9 23:31:55 2017 No.9286539 >>9286528huh
 >> Anonymous Fri Nov 10 00:15:46 2017 No.9286581 >>9285471>this fucking retard againhere you brainlet, here: >>9280935 >>9280938
 >> Anonymous Fri Nov 10 01:40:23 2017 No.9286667 bro how the FUCK do i get LaTeX to work? and DONT just say read the wiki, i dont get it. there is just a guide on how to type with no links to whatever extension/plugin i need.
 >> Anonymous Fri Nov 10 02:41:42 2017 No.9286713 Can a diverse population of a single organism go for several generations of still having the exact same allele frequencies? If so, how?
 >> Anonymous Fri Nov 10 03:20:02 2017 No.9286752 >>9286667open your .tex document and compile it to a pdf.A VERY basic document looks like this:\documentclass{article}\begin{document}Your text goes here.\end{document}Then use a compiler such as pdflatex to compile it to pdf.If you are on windows you should probably download texworks/texstudio/texmaker. They should allow you to easily install a tex distribution.On linux (or others) you should just run pdflatex mydocument.tex and look at the created pdf, of course you can also use an editor with built in pdf viewer.
 >> Anonymous Fri Nov 10 05:57:09 2017 No.9286916 >>9285663Take the first row of your A matrix and multiply it by the first column of the B matrix, the sum of the products will give you your first entry for AB. Then multiply the first row from A into the second column of B and continue until you've run out of columns. This forms your first row for AB. To get your second row, take the second row from A ..... and I think you get the pattern.
 >> Anonymous Fri Nov 10 06:04:04 2017 No.9286929 >>9285663It's simple as the other guys told you.To understand why it is defined that way see here:https://www.youtube.com/watch?v=XkY2DOUCWMU
 >> Anonymous Fri Nov 10 09:01:10 2017 No.9287163 >>9286376a-anyone?
 >> Anonymous Fri Nov 10 09:23:07 2017 No.9287191 >>9285193Thanks man, will read when I sober up
 >> Anonymous Fri Nov 10 10:50:29 2017 No.9287312 File: 394 KB, 649x524, 5Ha0Ypd.png [View same] [iqdb] [saucenao] [google] [report] i have to prove that this is true for my homework. M and N are sets that contain other sets.$(\cap M) \cup (\cap N) \subseteq \cap(M \cap N)$but to me this makes no sense at all so i've been thinking that my lecturer might have made a mistake when he created the assignment. does anyone else think this isn't true or am i just an idiot?
 >> Anonymous Fri Nov 10 10:54:07 2017 No.9287322 >>9287312Not once in my life have I seen this notation.What does ∩N mean?
 >> Anonymous Fri Nov 10 10:55:07 2017 No.9287323 >>9287312Yeah it is wrong.Consider M={A} and N={B} with A not empty or B not empty.You get non-empty set subset of empty set.
 >> Anonymous Fri Nov 10 10:56:10 2017 No.9287326 >>9287323oh and A cup B = empty
 >> Anonymous Fri Nov 10 10:57:26 2017 No.9287330 >>9287312>sets that contain other setsdo you mean an intersection of an indexed family of sets?
 >> Anonymous Fri Nov 10 10:59:34 2017 No.9287333 >>9287322it is an intersection of every set that is an object of N.For example if N={A,B}, then ∩N is A∩B.
 >> Anonymous Fri Nov 10 11:07:39 2017 No.9287347 >>9287333Thank you. Never saw it before.
 >> Anonymous Fri Nov 10 11:23:51 2017 No.9287384 >came from one of the worst school districts for math in my state >never cared about studying in high school >played video games from 4 pm to 1030 pm every day >never took precalculus in high school >now a junior in college>C in precalculus >C in calc 1>terrified to take calc 2 Have been held back by math my entire life. I fucking suck at algebra mates. That’s all there is too it. In calc 1 I was phenomenal at integrating and deriving equations but I couldn’t get correct answers because I couldn’t simplify complex algebraic expressions. The only test I did well in for precalculus was logarithms. How can I truly fucking finally get good at algebra and beat this monster that has been on my back since 7th grade?
 >> Anonymous Fri Nov 10 11:25:09 2017 No.9287386 >>9287384It's really nothing to learn precalculus.Just take a book and read it for 1-2 weeks and you'll be done with it.
 >> Anonymous Fri Nov 10 11:36:23 2017 No.9287404 >>9287386Any book you recommend?
 >> Anonymous Fri Nov 10 11:44:22 2017 No.9287418 >>9287404Dunno. check math.stackexchange.com
 >> Anonymous Fri Nov 10 11:51:32 2017 No.9287427 File: 206 KB, 1600x1201, joker-prison-close-there-s-a-secret-hidden-behind-heath-ledger-s-joker.jpg [View same] [iqdb] [saucenao] [google] [report] Why do mathematicians assume infinity even exists. Literally nothing we know of is infinite in the real world. Also geometry is bullshit too. Why the hell are we using points and lines to build more complex geometric shapes. Points and lines don't exist in the real world either. Someone please convince me math isn't a bunch of dumb rules some fag from ancient greece made up.
 >> Anonymous Fri Nov 10 12:10:28 2017 No.9287459 I get the idea of prime implicants in boolean algebra, but I don't quite get which terms are the essential prime implicants.
 >> Anonymous Fri Nov 10 13:31:24 2017 No.9287599 >>9287384unironically make an account on khan academy
 >> Anonymous Fri Nov 10 13:35:56 2017 No.9287606 >>9287427maybe the only reason you believe in a real world is that you left out the infinite your real world can't see?
 >> Anonymous Fri Nov 10 14:21:51 2017 No.9287700 >>9287323kinda late but yeah, that's what i've been thinking
 >> Anonymous Fri Nov 10 14:22:42 2017 No.9287703 File: 56 KB, 514x432, 1498992183284.jpg [View same] [iqdb] [saucenao] [google] [report] Which grad school rankings are the best? Looking for top schools in EE, specifically photonics/optics related
 >> Anonymous Fri Nov 10 14:32:50 2017 No.9287725 >>9286713yes, if those allele combinations that aggrandize are regularly thinned out by environmental factors or even by the colony itself
 >> Anonymous Fri Nov 10 14:34:19 2017 No.9287729 >>9286359yes
 >> Anonymous Fri Nov 10 14:38:19 2017 No.9287738 >>9285611If I'm really gonna translate THAT for you, I'm afraid I'm going ask you to pay for that.
 >> Anonymous Fri Nov 10 15:01:09 2017 No.9287789 With the word "Deleted", what is the probability that the two Ds in a permutation of the word will be separate?I got 300/420. Is that right?
 >> Anonymous Fri Nov 10 15:14:41 2017 No.9287824 >>9287789Yes.$1-\frac{6!}{3!1!1!1!}/\frac{7!}{3!2!1!1!} = 5/7$
 >> Anonymous Fri Nov 10 15:20:50 2017 No.9287842 File: 55 KB, 619x247, Untitled.png [View same] [iqdb] [saucenao] [google] [report] Hello I am struggling with this classic mechanics question, The first part I am fine with.ai) a=F/m so a=4/3ms^(-2)ii)W=1/2mv^2 so v=sqrt(2W/m)=sqrt(2*96/18)=4sqrt(2/3)ms^-1b) P_initial=F*v=24*0=0Wp_final=24*4sqrt(2/3)=96sqrt(2/3)WNow for part c I am getting different results of time pulling due to the velocity changing, how do I go about calculating this? or have I completely fucked up as I go along now? Thanks in advance.
 >> Anonymous Fri Nov 10 15:57:36 2017 No.9287895 >>9287842$P = F \cdot \frac{S}{T},\space 96 = 24 \cdot \frac{4}{T}, \space T = 1 \space s$I didn't check your numbers, though. But unless you got a multiplication or a square root wrong, everything seems fine.
 >> Anonymous Fri Nov 10 16:09:01 2017 No.9287912 >>9287895I missed the square root there, it's actually 96 sqrt(2/3). So the answer is 1,225 s.
 >> Anonymous Fri Nov 10 16:37:18 2017 No.9287959 plz, how do you prove that lim cos(n) ( or sin(n) ) when n goes to infinity is 0 ( in the distrubitions sens).
 >> Anonymous Fri Nov 10 16:48:41 2017 No.9287980 File: 23 KB, 600x484, helper.jpg [View same] [iqdb] [saucenao] [google] [report] >>9287959>( in the distrubitions sens)
 >> Anonymous Fri Nov 10 17:04:07 2017 No.9288007 >>9287912But why would the velocity/acceleration time be different? I am getting root 6 for that as a result.
 >> Anonymous Fri Nov 10 17:07:35 2017 No.9288012 File: 45 KB, 821x869, 1510158230500.jpg [View same] [iqdb] [saucenao] [google] [report] >>9287980>distrubitionsno bully plz.
 >> Anonymous Fri Nov 10 18:11:41 2017 No.9288128 File: 2 KB, 134x23, heyho.png [View same] [iqdb] [saucenao] [google] [report] Help this brainlet whos getting into ODEs out. Tried using integrating factors and now stuck at e^(1/2(-x^2))
 >> Anonymous Fri Nov 10 19:07:31 2017 No.9288233 >>9288128looks like you picked one hell of an ugly ode
 >> Anonymous Fri Nov 10 19:09:04 2017 No.9288236 File: 15 KB, 642x194, Unbenannt.png [View same] [iqdb] [saucenao] [google] [report] >>9288233forgot pic
 >> Anonymous Fri Nov 10 19:32:33 2017 No.9288294 >>9288233>>9288236wow had no idea it was going to get this complicated, thanks for the help though
 >> Anonymous Fri Nov 10 20:18:28 2017 No.9288342 File: 95 KB, 564x401, equilibrium.png [View same] [iqdb] [saucenao] [google] [report] What would be the approach to this question? I tried substituting the value of mew given to obtain the respective partial pressures but my Kp value is 6.649 instead of 6.049
 >> Anonymous Fri Nov 10 20:30:10 2017 No.9288364 >>9281815Depends on what you consider an "algebraic manipulation". Consider f(n)=(-1)^n, and g(n)=1 if n is even, and -1 if n is odd. It also depends on what you consider to be an "expression". Consider that x^2-x=0 for all $x\in\mathbb{Z}/2\mathbb{Z}$.
 >> Anonymous Fri Nov 10 21:12:10 2017 No.9288451 What's the proper latex symbol that represents the relationship between $SO(3,1)^+$ and $x^2 + y^2 + z^2 - t^2$
 >> Anonymous Fri Nov 10 21:49:47 2017 No.9288512 I belatedly realized, if one can do such a thing and revert to basic knowledge, that 'range' and 'domain' are essentially synonyms intentionally chosen as specific separate terms
 >> Anonymous Fri Nov 10 21:53:50 2017 No.9288519 How are you supposed to insert latex into a word doc? (i'm using libreoffice btw)
 >> Anonymous Fri Nov 10 22:00:54 2017 No.9288546 What is the "acceleration of acceleration"?If acceleration is the change in velocity over time, then what's the term and the symbol for the change in acceleration over time?
 >> Anonymous Fri Nov 10 22:13:09 2017 No.9288576 >>9288546That's jerk, which is acceleration applied over time. Acceleration is the instantaneous tangent (derivative) of jerk. Yank is jerk times mass.
 >> Anonymous Fri Nov 10 22:16:48 2017 No.9288588 >>9288576These terms sound suspicious.Are you yanking my chain, anon?Please don't jerk me around like this.
 >> Anonymous Fri Nov 10 22:18:34 2017 No.9288592 >>9288576>>9288546>do my due diligence and look them up>yank and jerk are real professional terms even though they sound like a three-year-old coined themThe world gets weirder every day, and I get slightly less stupid. Ever so very slightly.
 >> Anonymous Fri Nov 10 22:19:54 2017 No.9288598 >>9288576>Acceleration is the instantaneous tangent (derivative) of jerkother way around, also a derivative is the slope of the tangent, not the actual tangent itself
 >> Anonymous Fri Nov 10 22:25:13 2017 No.9288607 >>9288592look up snap crackle and pop
 >> Anonymous Fri Nov 10 22:45:19 2017 No.9288655 File: 18 KB, 232x254, i guess.jpg [View same] [iqdb] [saucenao] [google] [report] >>9288607>look it up>still not being fucked withScience has gone too far.
 >> Anonymous Fri Nov 10 23:31:26 2017 No.9288731 If air pressure lowers with wind speed, then how come box lids only fly off if wind gets under them?Surely having stationary air below and moving air above should lift the lids?
 >> Anonymous Fri Nov 10 23:40:07 2017 No.9288741 File: 272 KB, 600x600, __doremy_sweet_and_yakumo_yukari_touhou_drawn_by_kuroba_rapid__d1957fc2c6003338387fb4a418dde6c9.png [View same] [iqdb] [saucenao] [google] [report] >>9284631>single bookNo.>Banach algebrasAny functional analysis.>Affine Hecke algebraAny mathematical text on conformal field theory.>Exterior algebraAny differential topology book.>Koszul algebra Any homological algebra text.>Poisson algebraAny classical mechanics text.>Weyl algebraAny mathematical text on quantum field theory.>>9284936Let $X$ be a $G$-space and denote the action of $G$ on $X$ by $g \mapsto (x \mapsto g(x))$, then the $G$-quotient is the space of orbits $\mathcal{O}_x = \{y \in X\mid y = g(x) \}$.>>9287959Let $f\in\mathcal{S}_c$ be a test function and suppose $\phi$ satisfies the equation $\phi'' + \phi = 0$, then [eqn]\int_K dxf(x)\phi(x) = -\int_K dxf(x)\phi''(x) \rightarrow_{x \rightarrow nx} -\frac{1}{n} \int_K d(nx) f(nx)\phi''(nx) = -\frac{1}{n}\int_K dx f(x)\phi''(x) = -\frac{1}{n}\int_K dx f(x)\phi(x) \rightarrow 0[/eqn]Remember that scalings of compact sets are still compact so $f_n(x)\equiv f(nx) \in \mathcal{S}_c$.
 >> Anonymous Sat Nov 11 00:38:25 2017 No.9288792 >>9288741See global rule 13.
 >> Anonymous Sat Nov 11 02:25:31 2017 No.9288880 >>9287895>>9287912>>9288007Ive gone back through and had a look and I still cant see why the time calculated through power and work is different to my acceleration velocity time? can anyone clarify why this it the case or at least check if I have fucked up in prior calculations?
 >> Simon Troy Cosgrove Sat Nov 11 03:59:54 2017 No.9288946 >>9280930Starting us off with an easy one.How sequence a Cauchy sequence exactly ? Example : Prove $x_n=\frac{1}{n}$ is CauchyDefinitely Write : Writing the definition: $\forall \hspace{0.2cm}\epsilon > 0 \hspace{0.2cm} \exists \hspace{0.2cm} N \in \mathbb{N} \hspace{0.2cm} \text{such that} \hspace{0.2cm} \forall \hspace{0.2cm} m,n,\geq N, \hspace{0.2cm} |x_{n} - x_{m}| < \epsilon$You can write : $\left| \frac{1}{n} - \frac{1}{m}\right| <\epsilon$ ; But how do you generally proceed from there?Sequence Complete.
 >> Anonymous Sat Nov 11 04:07:56 2017 No.9288951 File: 2 KB, 252x55, unknown.png [View same] [iqdb] [saucenao] [google] [report] >>9280927I can't solve this, I think I'm not cut out for math. Help.
 >> Anonymous Sat Nov 11 04:23:38 2017 No.9288962 >>9288951solve what?
 >> Anonymous Sat Nov 11 04:26:22 2017 No.9288967 >>9288962finding the minimum or maximum
 >> Anonymous Sat Nov 11 04:27:33 2017 No.9288971 >>9288967wait the max.
 >> Anonymous Sat Nov 11 04:32:46 2017 No.9288981 >>9288967>>9288971How the fuck can you not find that? The problem is as simple as it gets.Open your textbook and read the relevant chapter.
 >> Anonymous Sat Nov 11 05:13:44 2017 No.9289030 >>9288880Post your calculations. It's hard to guess what you did.
 >> Anonymous Sat Nov 11 07:03:13 2017 No.9289121 Are there legal restrictions to making your own medications (in the US primarily but also generally)? Like, I imagine with an understanding of fundamental chemistry it's easy enough to make something that's already been made, tested, mass produced and sold.There's obviously the risk of getting no-knock raided as a suspected illigal substance lab but people have gotten raided for less.I ask because I take medication daily and it would be comforting to know that, should I run out of refills in a wierd situation (come to think of it, that's exactly what I'm dealing with right now...) or there's a disaster of some sort preventing pharmacy access, that I could just make a batch.I'm not talking about controlled substances like testosterone or opiates, things like antidepressants and dermatoligy meds that require a perscription but aren't "monitored" or restricted.
 >> Anonymous Sat Nov 11 07:56:27 2017 No.9289194 >>9287427>Why do mathematicians assume infinity even existsBecause math has nothing to do with reality.You have to ask the physicists why they use mathematics which relies on infinities to describe the real world.>Why the hell are we using points and lines to build more complex geometric shapes.Physicists use them because they are a good approximation, if you are talking about the distance from NYC to LA and you are not using a point somewhere in the middle, then you had to describe the distance as m +-100km or something, which is absolutely retarded.>Someone please convince me math isn't a bunch of dumb rules some fag from ancient greece made up.That is easy, the "dumb rules" were made up by a German and a German/Isreali jew.
 >> Anonymous Sat Nov 11 10:45:49 2017 No.9289391 >>9289030okayai) $F=m\cdot a[\math] so [math]a=\frac{F}{m}[\math] which ends up giving me an acceleration of [math]\frac{4}{3}ms^{-2}[\math]Then [math]W=F\cdot s[\math] which gives work as 96.0Jii) so assuming that W=E here its going to be [math]v=\sqrt{\frac{2W}{m}}[\math] which gives a speed of [math]4\sqrt{\frac{2}{3}}ms^{-1}[\math]b) the power applied at the start is nothing right due to the initial velocity being 0 seeming it starts from rest so the ending power will be calculated as [math]P=F\cdot v[\math] which I get as [math]96\sqrt{\frac{2}{3}}W[\math]c) This is where things get fucked up and the prior power calculation gives me the same value as you and my acceleration and velocity time gives me root 6, so where am I going wrong. Also sorry if my latex typing is shit, fingers crossed and I typed it correct, if not you will have to puzzle it out.  >> Anonymous Sat Nov 11 10:47:49 2017 No.9289398 >>9289391Cool I did backslashes like a retard, oh well.  >> Anonymous Sat Nov 11 12:21:30 2017 No.9289516 File: 10 KB, 1331x80, Capture.png [View same] [iqdb] [saucenao] [google] [report] I'm getting confused with the algebra of this problem. I am able to break the hypothesis to: (1-(-7)^(k+1)/4) + (2(-7)^(k+1) at that point, I find a gcd with 4 and multiply to get (1-(-7)^(k+1)/4) + (4*2(-7)^(k+1)/4) I don't actually get how I would simplify that to equal (1-(-7)^(k+2)/4)  >> Anonymous Sat Nov 11 12:43:20 2017 No.9289570 Could someone explain to me what a force actually is? Is it just to describe a transfer of energy?  >> Anonymous Sat Nov 11 13:36:45 2017 No.9289707 >>9289516[math]2\sum_{k = 0}^{n+1}(-7)^k =$$2(-7)^{n+1}+2\sum_{k = 0}^{n}(-7)^k =$$2(-7)^{n+1}+\frac{1-(-7)^{n+1}}{4} =$$\frac{8(-7)^{n+1}+1-(-7)^{n+1}}{4} =$$\frac{1+7(-7)^{n+1}}{4} = \frac{1-(-7)(-7)^{n+1}}{4}= \frac{1-(-7)^{n+2}}{4}$
 >> Anonymous Sat Nov 11 13:39:26 2017 No.9289713 >>9289707beautiful. Thanks anon.Thinking from a simplification standpoint and not an induction standpoint, I was unable to see the 8 turning into 1+7.
 >> Anonymous Sat Nov 11 15:59:54 2017 No.9290056 Is it trivial that $[a,b)\cup=[a,b]$?  being the singular point $b$
 >> Anonymous Sat Nov 11 16:03:57 2017 No.9290067 How do you solve1 / (2 + x) = 1/4I get it, it's the most basic algebra.
 >> Anonymous Sat Nov 11 16:15:27 2017 No.9290094 >>9290056pretty much. If you want to do it riugorously you have[math] [a,b) \cup \{ b \} = \{x\in \mathbb{R}~|~a\leq x >9290067multiply by (2+x) and 4 and you get 4 = 2+x, subtract 2 and you get x = 2
 >> Anonymous Sat Nov 11 16:28:22 2017 No.9290122 >>9290056yeah [math][a,b)\cup\{b\}=\{x\in R:a\leq x
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