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field produced by a straight curre. 8 Magnetic Vector Potential 163. Computation of magnetic field intensity. In all other cases the law is incorrect unless Maxwell's correction is included (see below). Alternatively: this observations shows that during charging/ discharging, the circuit is (momentarily) complete and t... | {
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# If both integers $x$ and $y$ can be represented as $a^2 + b^2 + 4ab$, prove that $xy$ can also be represented like this …
There is a set $Q$ which contains all integral values that can be represented by $$a^2 + b^2 + 4ab$$, where $a$ and $b$ are also integers. If some integers $x$ and $y$ exist in this set, prove th... | {
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# how many ways of arranging given 7 two digit positive integers so that the sum of every four consecutive integer is divisible by 3?
in how many ways can I arrange the numbers: 21,31,41,51,61,71,81 such that the sum of every four consecutive numbers is divisible by three?
Though I am not an expert on modulo math, I ... | {
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All of these work. Once you've chosen one of these sequences you can fill it in by replacing the $0$s with $21,51,81$ in some order, the $1$s with $31,61$ in some order, and the $2$s with $41,71$ in some order. There are therefore $6\times6\times2\times2=144$ ways to do this in total.
• why is it 6x6x2x2? I understand... | {
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# Discrete Math: Set Theory
Can anyone help me check if my solution is correct?
Link here, sorry it kinda look too messy when i tried to paste
d) A class has 175 students. The following table shows the number of students studying one or more of the following subjects.
Subject ... | {
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Thanks to brian for pointing the arithmetic error :)
-
I think you needed to provide more context and actually wrote out where you are having issues. Some people find "check my homework" to be rude behavior and items are better posted as questions asking for guidance and help. Regards – Amzoti Mar 9 '13 at 17:39
@Nat... | {
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# perpendicular distance from $ax-by = 1$ to origin
I have a problem from a basic number theory book that asks for the perpendicular distance from the line $ax - by = 1$ to the origin.
My approach was to find the area of the triangle formed by the line and the axes, find the base of the triangle situated at the diago... | {
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Thus, the minimum of $\left|\,(x,y)\,\right|$ is $\frac1{\sqrt{a^2+b^2}}$.
Perpendicular Distance
If $ax_1-by_1=1$ and $ax_2-by_2=1$, then $$(a,-b)\cdot(x_1-x_2,y_1-y_2)=1-1=0$$ Thus, $(a,-b)$ is perpendicular to the line containing $(x_1,y_1)$ and $(x_2,y_2)$; i.e. the line $ax-by=1$.
This means the vector from the... | {
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# How to find the total number of pages which a book has when the clues given indicate a range?
This problem doesn't seem very complicated but I got stuck at trying to understand what is the meaning of the last clue involving an integer and a range. Can somebody help me?
The problem is as follows:
Marina is reading ... | {
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Therefore:
$$53x<4200$$
$$x<\frac{4200}{53}$$
However this fraction is not an integer.
There is also another piece of information which mentioned that she always read no less than $$14$$ pages.
If during the first day she read a third of the novel then this would be:
$$\frac{1}{3}x>14$$
So $$x>42$$
But, on the ... | {
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• I would really like to understand what you meant. But the thing is you ommited some steps and I don't get very clearly where do those fractions come?. I don't get the idea in the second step for day 2. I understand the part of $\frac{1}{4}\times\frac{2}{3}$ but why should I multiply $\frac{2}{3} \times \frac{3}{4}$? ... | {
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• Thanks for the confidence boost. I really needed it. I think the source of my confusion was that I did not consider the passage mentions each day individually and not the number of pages that had been read until that day. Hence for each day I need to account what it was read on the prior day. Because of this for the ... | {
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• Thanks for that but I have a question. Does it mean that given the conditions at itself it cannot be found the number of pages without checking the alternatives given?. – Chris Steinbeck Bell Mar 5 at 22:29 | {
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# How can I answer this Putnam question more rigorously?
Given real numbers $a_0, a_1, ..., a_n$ such that $\dfrac {a_0}{1} + \dfrac {a_1}{2} + \cdots + \dfrac {a_n}{n+1}=0,$ prove that $a_0 + a_1 x + a_2 x^2 + \cdots + a_n x^n=0$ has at least one real solution.
My solution:
Let $$f(x) = a_0 + a_1 x + a_2 x^2 + \cdo... | {
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• There's a standard lemma that if $f$ is a strictly positive (negative) function, then $\int f$ is strictly positive (negative). I suppose you could prove this easily with Riemann sums. Then apply the contrapositive to conclude that $f$ changes sign (or is identically zero), and invoke continuity.
– user296602
Jul 28,... | {
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Why not write it the other way round?
The polynomial function $$F(x)=\sum_{k=0}^n\frac{a_k}{k+1}x^{k+1}$$ is a differentiable function $\Bbb R\to\Bbb R$ with derivative $$F'(x)=\sum_{k=0}^na_kx^k.$$ We are given that $F(1)=0$, and clearly $F(0)=0$. Hence by Rolle's theorem, there exists $x\in(0,1)$ such that $F'(x)=0$... | {
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# Concerning the solution to the non-homgeneous second order ODE
Does any second order linear differential equation have two linearly independent solution ?
What about the non-homogeneous DE of the form $$y''+ay'+by=f(x)$$ I know that it has as solution $$y=c_1y_1+c_2y_2+y_p$$ where $$c_1y_1+c_2y_2$$ is the solution ... | {
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In fact, it's not really great to talk about the space of solutions of a non-homogeneous ODE as being "linearly independent", since this implicitly invokes the idea that they are vectors that we can add together. For a homogeneous linear ODE, this is valid, since the linear combination of any two solutions is also a so... | {
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Note that $y_p$ is certainly linearly independent of $y_1$ and $y_2$, otherwise the ODE would be homogeneous.
• So the rule that says "the general solution of the second order ODE contains 2 independent solutions " is not correct unless we are talking about an homogeneous ODE. Right ? – MCS Oct 24 '17 at 20:50
• @Sous... | {
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y(x) = yh(x) + yp(x)
The relation between the solutions are as follows: 1. The sum of a solution of y" + p(x)y' + r(x)y = r(x) and a solution of y" + p(x)y' + r(x)y = 0 [yh(x) + yp(x)] is a solution of y" + p(x)y' + q(x)y = r(x) 2. If there are two solutions of y" + p(x)y' + r(x)y = r(x), the difference is a solution ... | {
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# If $f,g$ are quadratic forms over $\mathbb{R}$ and $f$ is positive definite, can you reduce the both simultaneously to sum of squares?
If $f,g$ are quadratic forms over $\mathbb{R}$ and $f$ is positive definite, can you reduce the both simultaneously to sum of squares?
This question appeared from a friend of mine a... | {
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Because $f$ is positive definite, $\lambda_i > 0$ and you could modify the basis so that $\lambda_i = 1$. But of course, there is no way to change the signs of the $\mu_i$. Alternatively, you could change the basis so that $\mu_i \in \{-1,0,1\}$, but you have to make a choice: you cannot have a simple form for both the... | {
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# Sets and Venn diagrams
#### bergausstein
##### Active member
the associative axioms for the real numbers correspond to the following statements about sets: for any sets A, B, and C, we have $(A\cup B)\cup C=A\cup (B\cup C)$ and $(A\cap B)\cap C=A\cap (B\cap C)$. Illustrate each of these statements using Venn diagra... | {
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View attachment 1151
Good job!
- - - Updated - - -
here's my try.
View attachment 1154
is this correct?
To me this is okay. But as Evgeny.Makarov pointed out this might not be okay to someone else. Cuz he might say that 'no this does not illustrate the identity correctly' and no one can do anything about it. Don't ... | {
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# How can I plot histogram with the same number of values in every bin?
For example I have 100 values sample. I'd like to build histogram in which every bin contains, for example, 10 values. How can i do that? Thanks.
You can use the values of the quantiles of your sample as bin delimiters for your histogram. You can... | {
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• Wow, thanks for help. One more question: how to change y-axis value from 'number of values in each bin' to 'probability density function value for each bin'? – instajke May 16 '15 at 18:02
• Histogram can do that for you: just add "PDF" as the bin height specification, as the following: Histogram[ sample, Table[Quant... | {
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Row[Histogram[datab, bF[10][First@Union@datab], #,
PlotLabel -> Style[#, 16, "Panel"],
ChartElementFunction -> "GlassRectangle", ImageSize -> 400,
ChartStyle -> {Red, Blue},
ChartLegends -> Placed[{"data1", "data2"}, Bottom]] & /@
{"PDF", "Count"}]
• That's absolutely amazing. Thank You a lot. – instajke May 16 '15 a... | {
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# How many possible numbers do I have?
Stupid question from stupid non-math-orientated person here.
I have a list of four-digit sequences. These sequences consist of and iterate through a letter of the alphabet followed by a range of numbers from 100-999. So the list starts at A100, followed by A101, A102... A999, B1... | {
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• Your answer is incorrect, there are not 899 numbers but 900. – RGS Jan 10 '17 at 23:45
• @RSerrao fixed. I read the question, and still did it wrong myself. – Travis Jan 10 '17 at 23:46
• Haha, I'm glad to hear it wasn't just me. Thanks for the extra info about the range vs total. I also didn't know that about the la... | {
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# Expressing $12\sin( \omega t - 10)$ in cosine form
$$12\sin( \omega t - 10)$$
I understand how it's solved when using the graphical method, however I'm having trouble understanding something about the trigonometric identities method.
The solution in the text book goes like this (It wants positive amplitudes) : (Al... | {
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The identities you can use are: \begin{align} \sin x&=\cos(90°-x)\\ \cos x&=\cos(-x) \end{align} Therefore $$\sin(\omega t-10°)=\cos(90°-(\omega t-10°))= \cos(100°-\omega t)=\cos(\omega t-100°).$$ Of course, you could also directly use $$\sin x=\cos(90°-x)=\cos(x-90°).$$
• What about $-10\cos(\omega t+50)$ to sine? $-1... | {
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# Proving a recurrence in Mathematica
I have
$$j_n=\int_0^1 x^{2n} \sin(\pi x)dx.$$
How do I show that $$j_{n+1}= \frac{1}{\pi^2}(\pi- (2n+1)(2n+2)j_n)\, ?$$
I keep getting a recurring integration by parts and I can't simplify it. Please tell me where I'm going wrong.
-
Welcome to Mathematica.SE! I suggest the fol... | {
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The first two terms are exactly what we would be integrating when evaluating $(2n+1)(2n+2)j_{n} - \pi^2 j_{n+1}$ in order to check the equality we're trying to prove. The last term is a problem: how to make it go away? Well, still motivated by integrations by parts, we ought to examine a similar derivative,
D[x^(2 n +... | {
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Let us define
J[n_] := Integrate[ x^(2 n) Sin[Pi x], {x, 0, 1}]
(* (Pi*HypergeometricPFQ[{1 + n}, {3/2, 2 + n}, -Pi^2/4])/(2 + 2*n) *)
and
Clear[JJ];
JJ[n_] := JJ[n]=1/Pi^2 (Pi - (2 n ) (2 n -1) JJ[n - 1]) // Simplify
JJ[0] = J[0];
We have
Table[J[n] - JJ[n], {n, 0, 6}] // Simplify
(* {0,0,0,0,0,0,0} *)
w... | {
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Finally put everything together :
en = FullSimplify[int[n] /. recursion, Assumptions -> {n \[Element] Integers, n > 0}] ;
enp1 = FullSimplify[int[n + 1] /. recursion /. recursion /. recursion,
Assumptions -> {n \[Element] Integers, n > 0}];
FullSimplify[enp1 - 1/Pi^2 (Pi - (2 n + 1) (2 n + 2) en),
Assumptions -> {n ... | {
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# What is the difference between kernel and null space?
What is the difference, if any, between kernel and null space?
I previously understood the kernel to be of a linear map and the null space to be of a matrix: i.e., for any linear map $f : V \to W$,
$$\ker(f) \cong \operatorname{null}(A),$$
where
• $\cong$ rep... | {
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The context should make things clear and every claim about, say, dimensions of kernels/nullspaces should still hold despite the ambiguity.
As manos said, "kernel" is used more generally whereas "nullspace" is used essentially only in Linear Algebra.
- | {
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# Rigid body equilibrium word problem
In my 100-level university physics course, we are just starting to touch on rigid bodies and tension. While I am fairly certain that I approached this the right way, I would appreciate if someone could look at my work and confirm that this is a valid solution to the following prob... | {
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I suppose what has me second-guessing myself is that the magnitude and direction of the force exerted by the bolt are the same as the tension, just flipped about the y-axis. Assuming this is correct, is this because the sign is in static equilibrium and the net forces must be zero, so the only way for that to be possib... | {
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I hope that this also shows that this sort of problem can be solved in a few lines using the sine rule.
$\dfrac{16\;g}{\sin 40}= \dfrac{\text{tension}}{\sin 70}= \dfrac{\text{bolt force }}{\sin 70}$.
• Yay for using diagrams. Funny thing is, I had a different picture in mind (where the sign was between two walls). Yo... | {
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# 2.8.2 Stephen Abbott : Absolute convergence for double series
So here is the problem. Given absolute convergence for a double series (infinite sum over $|a_{ij}|$) , show the double series $(a_{ij})$ converges . The proof strategy is: 1) keep one index fixed - so given i is fixed we know the series over j converges ... | {
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The comparison test can only be used if the terms of the series are nonnegative.
Suppose the series $\sum_{i,j}|a_{ij}|$ converges. Let $b_{ij} = \max(a_{ij},0$) and $c_{ij} = \max(-a_{ij},0)$.
Since $0 \leqslant b_{ij} \leqslant |a_{ij}|$ and $0 \leqslant c_{ij} \leqslant |a_{ij}|$ we can now apply the comparison te... | {
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Find all Pythagorean triples $x^2+y^2=z^2$ where $x=21$
Consider the following theorem:
If $$(x,y,z)$$ are the lengths of a Primitive Pythagorean triangle, then $$x = r^2-s^2$$ $$y = 2rs$$ $$z = r^2+z^2$$ where $$\gcd(r,s) = 1$$ and $$r,s$$ are of opposite parity.
According to the previous theorem,My try is the foll... | {
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What we need to solve is
$$21^2=441=3^2\cdot 7^2=(z+y)(z-y)$$
that is we need to try with
• $$z-y=1 \quad z+y=441\implies (x,y,z)=(21,200,221)$$
• $$z-y=3 \quad z+y=147\implies (x,y,z)=(21,72,75)$$
• $$z-y=7 \quad z+y=63\implies (x,y,z)=(21,28,35)$$
• $$z-y=9 \quad z+y=49\implies (x,y,z)=(21,20,29)$$
• My method wor... | {
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# Find $k^{th}$ power of a square matrix
I am trying to find the $$A^{k}$$, for all $$k \geq 2$$ of a matrix, $$\begin{pmatrix} a & b \\ 0 & 1 \end{pmatrix}$$
My approach:
$$A^{2}=\begin{pmatrix} a^2 & ab+b \\ 0 & 1 \end{pmatrix}$$
$$A^{3}=\begin{pmatrix} a^3 & a^{2}b+ab+b \\ 0 & 1 \end{pmatrix}$$
$$A^{4}=\begin{p... | {
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Not the best way, but you could also try diagonalisation. The caveat with diagonalisation is that for certain values of $$a$$ and $$b$$ (in particular, if $$a = 1$$ and $$b \neq 0$$), the matrix won't be diagonalisable. However, if we make the assumption that $$a \neq 1$$, then we should end the process with a perfectl... | {
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Hint: Use Cayley–Hamilton: $$A^2-(a+1)A+aI=0$$.
• I got the same results using Caley-Hamilton. Then what will be next step? Sep 6, 2019 at 0:18
• I guess, this method is not a good one for finding large powers of A. Sep 6, 2019 at 0:19
• @Barsal, it is. Just reduce $A^2$ every time. Try the first few powers and you'll... | {
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# Integrations by parts
Calculate $\int \cos (x) (1− \sin x)^2 dx$ .
Can you integrate the different products separately?
Does it have something to do with integration by parts?
I have tried letting $u=(1− \sin x)^2$ but I don't think I'm heading in the right direction! Can anyone help?
Thanks
• You have asked se... | {
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# Two circles with the centre on each others circumference
• Sep 1st 2006, 12:58 AM
a4swe
Two circles with the centre on each others circumference
Problem: Two circles, both with the radius of R (and in the same plane) intersect so that the centre of one circle lies on the circumference of the other circle. Calculate ... | {
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Quote:
Two circles, both with the radius of R (and in the same plane) intersect
so that the centre of one circle lies on the circumference of the other circle.
Calculate the area inside both of the circles.
The intersection is a lens-shaped region.
Code:
* * /:::* * /::::::* /:::::... | {
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Originally Posted by malaygoel
Hello to all of you!
I have a question relating to circles. It is like this:
There is a grass field in the circular shape, with the fence along the boundary. A goat is tied to the fence(at a stationary point) with a rope such that she can graze half of the area of the field. The problem i... | {
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# Convergence of Ratio Test implies Convergence of the Root Test
In Elias Stein and Rami Shakarchi's Complex Analysis textbook, we have the following exercise:
Show that if $\{a_n\}_{n=0}^\infty$ is a sequence of complex numbers such that $$\lim_{n\to\infty}\frac{|a_{n+1}|}{|a_n|}=L,$$ then $$\lim_{n\to\infty}|a_n|^{... | {
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By definition of limit, for all $\varepsilon>0$ there exists $N$ s.t. $$n>N \implies \left| \left| \frac{a_{n+1}}{a_n} \right|-L \right|<\varepsilon.$$ So $$|a_n|=\frac{|a_n|}{|a_{n-1}|}\cdots \frac{|a_{N+1}|}{|a_N|} |a_N|<(L+\varepsilon) ^{n-N} |a_N|$$ Take the $n$th root of both sides of an inequality, we get $$\sqrt... | {
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# Solving for probability of dependent events
I was reading A First Course in Probability by Sheldon Ross. I read one of the problems and then tried building logic for it. Then read books solution which was completely different. So was guessing if my logic is wrong.
Problem: An ordinary deck of 52 playing cards is ra... | {
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My logic was below and I feel it more intuitive and natural
1. First pile will contain 13 cards out of 52. Thus sample space will be $^{52}C_{13}$. The first pile is to contain 1 of 4 aces and rest 12 cards can be any of remaining 48. Thus the event space will be $^4C_1^{48}C_{12}$ Thus the probability that first pile... | {
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4. Is the book's approach more sort of defining the events recursively? If yes, does this means that problem involving any sequence of dependent event can be solved in the way given in the book thus effectively defining the desired probability recursively and solving to the probability of base condition (in this partic... | {
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## 1
But I feel this is what we need to find. So the desired probability is $\mathsf P(E_4)$. But book says its $\mathsf P(E_1E_2E_3E_4)$. Is it like the probability $\mathsf P(E_4)$ cannot be standalone? and we cannot specify/calculate $\mathsf P(E_4)$ independently. Or $\mathsf P(E_4)=\mathsf P(E_1E_2E_3E_4)$
The e... | {
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# In how many ways can $20$ distinct students be placed in four distinct dorms if each dorm needs to have at least one student?
Question: $$20$$ distinct students are to be placed into four distinct dorms named: A, B, C, D. In how many ways can they be assigned to the four dorms, with the restriction that each dorm ne... | {
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I appreciate it very much if anyone could help me out on this problem. Thank you.
• Just to be clear. The rooms are distinguishable, and the students are distinguishable. Is that correct? Label the students 1,...,20. If students 1 and 2, swap dorms that changes the arrangement? And if all the students in dorm A move t... | {
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but your method would give us $$3\times 2\times 2^1=12$$
The usual way to do is via Inclusion Exclusion. There would be $$4^{20}$$ ways if we allowed empty dorms. We first correct this by subtracting off the cases in which one specified dorm is empty, to get a correction of $$-\binom 41\times (4-1)^{20}$$ and then we ... | {
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# Fourier Series Of Piecewise Function | {
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In fact, for periodic with period , any interval can be used, with the choice being one of convenience or personal preference (Arfken 1985, p. the Gibbs phenomenon, the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity. 32) x t e dt T x t e dt T a T jk T t T jk ... | {
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at the early graduate level or, in some cases, at an upper undergraduate level. Produces the result Note that function must be in the integrable functions space or L 1 on selected Interval as we shown at theory sections. In particular, if L > 0then the functions cos nˇ L t and sin nˇ L t, n =1, 2, 3, are periodic with ... | {
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following advice can save you time when computing. Fourier Sine and. libasan4 (7. They introduced so called “concentration factors” in order to improve the convergence rate. To start with, Amazon chose the wrong flag: the. Sine series. If I compute the antiderivative of the piecewise version of the abs function. Electr... | {
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the. In this instance, the Fourier coefficients can be computed in closed form, segment by segment. Theorem Let f be a piecewise smooth function on the interval [0, L]. Find the Fourier series of the following functions. Fourier Series Calculator is a Fourier Series on line utility, simply enter your function if piecew... | {
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transform algorithm. 10 DEFINITION (Fourier series). Since the function F (x) is continuous, we have for any because of the main convergence Theorem relative to Fourier series. Relation Between Trigonometric and Exponential Fourier Series. Find the Fourier series of the following piecewise defined function, on the inte... | {
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sinc (infinity) 1 & Max value of sinc(x) 1/x Note: First zero occurs at Sinc (+/-pi) Use the Fourier Series Table (Table 4. Fourier series summation and symbolic representation for algebraic functions. For convenience we use both common definitions of the fourier transform using the standard for this website variable f... | {
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of f. Fourier Series Expansions of Functions. a) True b) False View Answer. Again, using MathView to handle the detailed manipulation allows Let's have a look at a simple notebook example where the Fourier series approximates a unit step function at x=0 and calculate the coefficients. Then the function. determines a we... | {
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discontinuities in any interval, and f(c+) and f(c−) exist for all c in the domain of f. Functions - What Does the Pharynx Do. The discrete-time Fourier transform is an example of Fourier series. Decompose the following function in terms of its Fourier series. It is noted that, like and , the weighted average is discon... | {
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additional conditions (such as piecewise differentiability), this Fourier series of an arbitrary function by the orthogonal system with Fourier coefficients converges to on an interval at the points of continuity of , and to at the points of discontinuity of , where ). The piecewise linear function based on the floor f... | {
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Convergence of Fourier series. Learn about our use of cookies, and collaboration with select social media and trusted analytics partners hereLearn more about cookies, Opens in new tab. In mathematics and statistics, a piecewise linear, PL or segmented function is a real-valued function of a real variable, whose graph i... | {
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command floor(y). The Crown series four: Princess Diana pleads 'to be loved' by the Royal Family as Gillian Anderson recreates Margaret Thatcher's brittle tone in new trailer. For any a > 0the functions cosat and sinat are periodic with period 2ˇ/a. If you are a student in one of the mathematical, physical, or engineer... | {
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is therefore eliminated, this program will run much more quickly than the general form for Fourier series expansions. introduce one of the many ways that Fourier series are used in applications. A function is called C 1 -piecewise on some interval I= [a;b] if there exists a partition. Find the Fourier series of the fol... | {
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equal the function. Given an integer n ≥ 0, the n -th cosine coefficient of the Fourier series of f is defined by an = 1 L∫L − Lf(x)cos(nπx L)dx, where L is the half-period of f. IEEE Trans. For now we are just saying that associated with any piecewise continuous function on [ ˇ;ˇ] is a certain series called a Fourier ... | {
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function is discontinuous, its Fourier series doesn't necessarily equal the function. Fourier series summation and symbolic representation for algebraic functions. Symbolic computation of Fourier series. Even and odd functions. This apps allows the user to define a piecewise function, calculate the coefficients for the... | {
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that ""any reasonable [piecewise continuous] function of period 2pi has exactly one expression as a Fourier series"" is analysed. We consider Fourier series of and in the form of where and are Fourier coefficients defined as Then we propose a weighted average of and as follows: for. Theorem: L2 convergence. Solution: S... | {
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convergence. Then its Fourier series converges everywhere (pointwise) to f. In other words, if is a continuous function, then. If we are given a function f (x) on an interval [0, L] and we want to represent f by a Fourier Series we have two. the n the approximated function shows amounts of. The following advice can sav... | {
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independent variable. Ø Complex Exponential Fourier Series. Conversely, the Fourier sine series of a function f : [0,L] → R is the Fourier series of its odd extension. The following theorem, which we state without proof, says that this is typical of the Fourier series of piecewise continuous functions. 2) The entries a... | {
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f(x) has only a finite number of discontinuities and only a finite number of extreme values (maximum and minimum). When a function is discontinuous, its Fourier series doesn't necessarily equal the function. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms. Can ... | {
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of the given interval. UNIT IV: Fourier Series Periodic functions; Fourier series of Periodic functions; Euler‟s formulae; Functions having arbitrary period; Change of intervals; Even and Odd functions; Half range sine and cosine series. Fourier Cosine Series of a piecewise function - Duration: 26:46. Introduction to F... | {
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doubt for West Indies series after injuring right thumb. A number of things that follow on one after the other or are connected one after the other. Time limit: 0. (Received Pronunciation) IPA(key): /ˈsɪə. function f (x) =π, π∈[]−π, π, , extended periodically on the real line; this function is discontinuous at x =(2k +... | {
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Fourier series 165 8A Real Fourier series on [−π,π] 165 8B Computing real Fourier coefficients 167 8B(i) Polynomials 167 8B(ii) Step functions 168 8B(iii) Piecewise linear functions 170 8B(iv) Differentiating real Fourier series 172 8C Relation between (co)sine series and real series 172 8D Complex Fourier. clearly sugg... | {
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+ P ∞ k=1ak cos(kx) + P k=1bk sin(kx) We take it for granted that the series converges and that the identity holds at all points x where f is continuous. Daileda Fourier Series Introduction Periodic functions Piecewise smooth functions Inner products Definition 1: We say that f(x) is piecewisecontinuousif f has only fini... | {
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Value Problems, 6th ed. It’s easier to say what the Fourier series does exactly at a discontinuity. larity as the sum of a piecewise polynomial function and a function which is continuously differentiable up to the specified order. f(x)={1 0) is an example of _____ operator. If f(x) is an odd function with period , the... | {
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2. Fourier Series Of Piecewise Function 1 Orthogonal Functions 12. is continuous and is -periodic if and only if ,i. Both of those shifts will affect the fourier series in a predictable way, so that if you can find the fourier series for the shifted function, you can easily convert to the fourier series of the original... | {
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(CNAM, Paris A Ranking-based, Balanced Loss Function for Both Classification and Localisation in Object Detection A random matrix analysis of random Fourier features: beyond the Gaussian kernel, a. With simpy like : p = Piecewise((sin(t), 0 < t),(sin(t), t < pi), (0 , pi < t), (0, t < 2*pi)) fs = fourier_series(p, (t, ... | {
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associated with the function. Appendix 0). Relation Between Trigonometric and Exponential Fourier Series. Get the free "Fourier Series of Piecewise Functions" widget for your website, blog, Wordpress, Blogger, or iGoogle. I'm trying to do problem 3, section 24. As an odd function, this has a Fourier sine series f(x) ˘.... | {
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de-scribed in this document all of which are based on series of independent Bernoulli trials. If you are a student in one of the mathematical, physical, or engineering sciences, you will almost certainly find it necessary to learn. Problem1 Find the fundamental period and deduce and plot the magnitude and the phase of ... | {
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equations. m that is similar to coef_legen and has signature function [z,s,c]=coef_fourier(func,n) % [z,s,c]=coef_fourier(func,n) % more comments % your name and the date to compute the first coefficients of the Fourier series using Equation. The Fourier series of a piecewise continuous function with 8 segments and no ... | {
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but the ones we want to focus on are. November 2019; Issues properties of discrete and continuous finite Fourier series. Piecewise Constant Function. Travel and explore the world of cinema. Derivative numerical and analytical calculator. Free piecewise functions calculator - explore piecewise function domain, range, in... | {
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L-functions and higher-order generalized Bernoulli numbers in near future. 3 Fourier Cosine and Sine Series 12. Let f(x) be a piecewise C1 function in Per L(R). Aug 30, 2020 an introduction to laplace transforms and fourier series springer undergraduate mathematics series Posted By Ry?tar? ShibaPublic Library TEXT ID 2... | {
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- Duration: 17:54. Mathematica for Fourier Series and Transforms Fourier Series Periodic odd step function Use built-in function "UnitStep" to define. Do exponential fourier series also have fourier coefficients to be evaluated. For a distribution in a continuous variable x the Fourier transform of the probability dens... | {
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or the average of f on [ L;L]. The Fourier series for a number of piecewise smooth functions are listed in Table l of §21, and Theorem 2. Proposition (i) The Fourier series of an odd function f : [−L,L] → R coincides with its Fourier sine series on [0,L]. Signal Processing : Fourier transform is the process of breaking... | {
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multiples of the base frequency. An improvement of the Beurling-Helson theorem. We shall shortly state three Fourier series expansions. By using this information and choosing suitable values of θ (usually 0, or s), derive the following formulas for the sums of numerical series. Compute Fourier Series Representation of ... | {
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# [SOLVED]3.3.003 Find the equation of the curve that passes through the point (1,2)
#### karush
##### Well-known member
Find the equation of the curve that passes through the point $(1,2)$ and has a slope of $(3+\dfrac{1}{x})y$ at any point $(x,y)$ on the curve.
ok this is weird I woild assume the curve would be an ... | {
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And the ODE becomes:
$$\displaystyle \frac{e^{-3x}}{x}\d{y}{x}-\frac{e^{-3x}}{x}\left(3+\frac{1}{x}\right)y=0$$
$$\displaystyle \frac{d}{dx}\left(\frac{e^{-3x}}{x}y\right)=0$$
$$\displaystyle \frac{e^{-3x}}{x}y=c_1$$
$$\displaystyle y(x)=c_1xe^{3x}$$
$$\displaystyle y(1)=c_1e^3=2\implies c_1=2e^{-3}$$
Hence:
$$\... | {
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# Thread: Calculate Tangent Line to 2 Circles
1. ## Calculate Tangent Line to 2 Circles
I am trying to calculate the equation of line tangent to 2 circles. I have attached a picture to give a better idea.
Circle 1 has a center at (3,4) and radius of 5
Circle 2 has a center at (9,19) and radius of 11,
So far I have ... | {
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--Kevin C.
3. Originally Posted by CaliMan982
I am trying to calculate the equation of line tangent to 2 circles. I have attached a picture to give a better idea.
Circle 1 has a center at (3,4) and radius of 5
Circle 2 has a center at (9,19) and radius of 11,
So far I have wrote the equation = of the 2 circles, and ... | {
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7. Originally Posted by CaliMan982
How would I calculate a point on the cirlce the tangent line touches, i just calculated the slope.
Have a look here: http://www.mathhelpforum.com/math-he...348-post1.html
8. ## Complete solution to the four tangent lines of two circles
Tangents to Two Circles gives complete expressi... | {
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# Solve $\sin x + \cos x = \sin x \cos x.$
I have to solve the equation:
$$\sin x + \cos x = \sin x \cos x$$
This is what I tried:
$$\hspace{1cm} \sin x + \cos x = \sin x \cos x \hspace{1cm} ()^2$$
$$\sin^2 x + 2\sin x \cos x + \cos^2 x = \sin^2 x \cos^2x$$
$$1 + \sin(2x) = \dfrac{4 \sin^2 x \cos^2x}{4}$$
$$1 + ... | {
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"openwebmath_score": 0.8731548190116882,
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