Form Definition and 1000 Threads

Homework Statement I had to calculate an orbital speed for an arbitrary density ρ(r) I got: V = r*sqrt(G*ρ(r)*4π/3) Homework Equations I am supposed to leave this in integral form, which I don't know how to do as I do not understand calculus. ρ(r) is density of r, hence the...

So how do I convert r=4+4cos(theta) into rectangular form? I know that r^2 = x^2+y^2 and that rcos(theta) = x. Would the start of the solution be: sqrt(x^2 + y^2) = 4+4x If yes, I don't know where to go from there.

Using second mean value theorem in Bonnet's form show that there exists a p in [a,b] such that \int_a^b e^{-x}cos x dx =sin ~p I know the theorem but how to show this using that theorem .

In this note (http://sgovindarajan.wdfiles.com/local--files/serc2009/greenfunction.pdf) the Klein-Gordon retarded green function is derived on the form $$G_{ret}(x − x′) = \theta(t − t') \int \frac{d^3 \vec k}{(2\pi)^3 \omega_k} \sin \omega_k (t − t′) e^{i \vec{k}\cdot (\vec x - \vec x')}$$...

the actual problem is to show that the given matrix is similar to companion matrix here is the companion matrix Companion matrix - Wikipedia, the free encyclopedia ---------------- i know that if same frobenius canonical form then similar but i don't even know how to find the frobenius...

[solved] show all invariant subspaces are of the form i don't even know how to begin (Angry) C_x is a subspace spanned by x that belongs to V C_x = {x, L(x), L^2(x),...} edit: SOLVED

Homework Statement Let G:R2\rightarrowR be a C2 function such that G(tx,ty)=t2G(x, y). Show that: 2G(x,y)=(x,y).HG(0,0).(x,y)t The Attempt at a Solution G is C2, so its Taylor expansion is: G(x,y) = G(0,0) + \nablaG(0,0).(x,y) + \frac{1}{2}(x,y).HG(c).(x,y)t, where c lies on...

Homework Statement Hey guys, Here's the question. For a distinguishable set of particles, given that the single particle partition function is Z_{1}=f(T) and the N-particle partition function is related to the single particle partition function by Z_{N}=(Z_{1})^{N} find the following...

For a system I am studying the following sequence (which I would assume is quite common) came up: n1=1, n2=2, n3=4, n4=7, n5=11, n6=16, n7=22 ... i.e. the difference betweens two successive numbers grows with 1 as we move from (n_N-1, n_N) to (n_N,n_N+1). Is there a closed form expression f(k)...

Homework Statement In each part, the reduced echelon form of the augmented matrix of a system of linear equations is given. Find all solutions to the original system. a.  [1 0] [2] [0 1] [5]  b.  [1 0] [2] [0 0] [1]  c.  [1 0] [2] [0 0] [0]  d. ...

Hi, here is something I can't understand: When you fill a 100% tube with Mercury, close it in one end (the top) and stick it into a bowl of mercury, vacuum forms in the top of the tube. Where does the vacuum come from if it was not there to begin with? The tube was full of mercury to begin...

I have the ODE x''(t)+\frac{k}{m}x(t)=0. Given that the solution is of the form sin(ωt+ø), I plug this form into the original ODE and obtain ω=+\sqrt\frac{k}{m},-\sqrt\frac{k}{m}. And hence, I obtain two solutions of the ODE as follows: x_{1}(t)=Asin(\sqrt\frac{k}{m}t+ø)...

I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

Hi; I've been trying to solve the problem myself but i really don't what could be wrong; The problem says : Make the change of variables x=ucos−vsin y=usin+vcos where the angle 0<(phi)<2 is chosen in order to eliminate the cross product term in x^2+xy+y^2=6 Then find the standard form of...

Homework Statement A system obeys the equations: P=-(NU)/(NV-2AVU) and T=2CU1/2V1/2eAU/N/(N-2AU) Find the fundamental equation Hint: to integrate let s=Dunvme-Au Where D, n, m are constants to be determined. Homework Equations Aside from the given ones, V=Nv U=Nu...

Hello! :) The interpolating polynomial that interpolates at the following data: $f(5)=?,f(8)=14,f(12)=214$ is $4,125x^{2}-32,5x+10$. The corresponding interpolating polynomial in the Newton form is $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$.Which is the value of $a_{2}$? Is it 4,125 because...

I'm doing my homework but I'm lost on one thing. Let's say that we have a systems of equations like so: 2x1+3x2=y1 4x1+2x2=y2 Instead of setting it to a constant our teacher sets it to a variable, he says that to be able to compute this, the augmented matrix should look like: 2 3|1 0 4 1|0 1...

If dr = (dx, dy, dz) so, which is the correct form for d²r? Is (d²x, d²y, d²z) or (dy^dz, dz^dx, dx^dy) ?

Hi, I hope this question is appropriate for this forum - if not can anyone suggest a place to ask it? There is a lot of carbon based matter around, on an in the earth. But,as I understand it, other than gaseous forms all the other liquid and solid forms have been generated/created by living...

Find the slope of the tangent line to the curve f(x)=x-x^3 at the point (1,0) So, I went through and plugged (a+h) in everywhere I saw "x" (a+h)-(a+h)^3 Factoring: (a+h-a^3-3a^2h-3ah^2-h^3) I'm really stuck on what to do next...I don't see anything you can cancel/pull out? I know...

Homework Statement I need to obtain the minimum second order circuit of the function: Homework Equations The Attempt at a Solution I know that in order to get the minimum second order circuit, I need to use K-Map using both miniterms and maxiterm and compare them. My problem is to put the...

According to general relativity, if a remote observer monitors an object falling onto a black hole, (s)he will never see the moment when the object crosses the event horizon. Due to the time distortion, the falling object will hover over the event horizon forever. With that in mind, how...

So this is what I have tried so far playing around with exponent and radical properties to try and solve this textbook problem

Heeeeeeellllllllllllllooooooooooooo, I have a question about HTML and PHP: Firstly, I am using Apache2 and PHP5 (I think) and running it as a localhost. I created a simple HTML form that sends the variables via post to a PHP file; there are two variables with the names "nickname" and...

Hi everyone, :) Here's a question I encountered recently and did partway. I need your advice on how to proceed. Question: What can be said about the Jordan normal form of a linear transformation \(f:V\rightarrow V\) where \(V\) is a vector space over \(\mathbb{C}\), if we know that...

Hello, I'm here for another related intercept form problem of the formula: \displaystyle \frac{x}{a} + \frac{y}{b} \:=\:1 a) Find the equation of the line passing through (-5,-7) AND with y-intercept 3. b) Find the equation of the line passing with x-intercept 1/3 and y-intercept 2/5. I'm not...

Greetings everyone, I need a help since the lecture of intercept form formula is X/A + Y/B = 1 are provied as limited examples and couldn't find exact information regarding for that. 6) Reduce the equation 2x+3y = -1 to intercept form. 7) find the equation of the line whose slope is 3x the...

Homework Statement r = 3sin\theta since x= rcos\theta x = 3sin\thetacos\theta and since: y = rsin\theta y = 3sin^2\theta Then I'm sort of stuck..

I managed to stumble upon a differential equation such as the one above while doing some torque calculations and am wondering if and how to find the solution to it. I'm not that well versed in differential equations, so any help would be appreciated. Edit: A method to graph an integral line for...

A recent post of chisigma rings me the bell of an old problem I thought of posting in a forum (either here or MMF). Is there any particular approach to computing a closed form for derivatives of certain smooth and continuous functions of $\mathbb{R}$? For example, it is easy to find the $n$-th...

Hi, All: Let X be a Reeb vector field, and let ω be a 1-form dual to X. Is ω necessarily a contact form? I know if we have a contact 1-form θ , and Zθ is the Reeb field associated with θ , then from the definition of Reeb field, we have θ (Zθ)=1, which mostly means that θ is...

Ok, so I have been searching around the internet for an answer to this and have not found anything besides the fact that electrons move in a quantum way, that is jumping from one place to another without passing through the space between those two places, which I am aware of. So the two main...

Hey! :o I am asked to convert the following grammar into Chomsky Form $$\Sigma=\{a,b,c,+\}, \Sigma_Q=\{S,V\},I=S$$ $$S -> S+S|V$$ $$V -> a|b|c$$ My idea is the following: $$S_0 \rightarrow S$$ $$S \rightarrow ST|V$$ $$T \rightarrow +S$$ $$V \rightarrow A|B|C$$ $$A \rightarrow a$$ $$B...

In the big crunch scenario, matter would clump together faster and faster, could a blob of this matter form a black hole, even if it had the necessary energy to maintain fusion or if it had no energy to burn up the matter? If the big crunch were to happen, and a single blob of mass existed at...

Hi, (not homework/academic) Is a closed form of the following expression possible? Either way, some pointers in the right direction would be really helpful. H(s)=\sum_{n=-\infty}^\infty \frac{k^n}{k^n+a/s} Thanks, D

I am trying to calculate the dual form of an SVM optimisation problem: Dual Form Optimsation Problem In my algorithm, I have a vector of alphas, vector of target outputs, and a Kernel matrix computing upfront. However, I am stuck as to what indices alpha and j should be taking here...

Hi I'm taking abstract linear algebra course and having trouble visualising bilinear form and inner products. I can visualise vector spaces, span, dimensions etc but haven't managed to figure out how to visualise this yet. Could someone please explain it to me in a visual way? I can't understand...

Homework Statement Complete the square using the symmetric matrix that defines the given quadratic form: ##x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2## and write this quadratic as the sum and difference of squares after completing the square using the matrix. The Attempt at...

Closed form for "geometricish" series (index squared in the exponent)? Hi all, Is there a nice closed form for the following series? \sum_{k=0}^n x^{k^2} Even a decently tight upper bound and lower bound would be nice (obviously it is bounded by the corresponding geometric series \sum...

If I am given an E field E = uniti Asin[w(t-z/c)+pi/4]. Is the phasor form = unit i Aexp(j pi/4) or unit i Aexp(-j(wz/c - pi/4) ?

Homework Statement I need to find i1+i2 Homework Equations for i1=0.092<-98.86 i2=-4i1-j10/25=-4i1-0.4 i1=0.092<-98.86 x=rcosθ=0.092cos(-98.86)=-0.0142 y=rsinθ=0.092sin(-98.86)=-0.0909 i1=-0.0142-j0.0909 Therefor...

I know y is a function of x [i.e. y=f\left(x\right)] with two known boundary conditions, that is f\left(x=A\right)=C and f\left(x=B\right)=D where C and D are known constants (please see figure). I do not know the form of this function and therefore I am trying to find the form of y as a...

Hi everyone, :) Recently I encountered the following problem. Hope you can confirm whether my method is correct. My answer seems so trivial and I have doubts whether it is correct. Problem: Find the Jordan normal form of a unitary linear transformation. My Solution: Now if we take the...

Homework Statement Find all functions for which any tangent in first quadrant "forms" a triangle with constant surface P. (You can assume that y'<0) Homework Equations The Attempt at a Solution Now, I know I should somehow get to differential equation and then solve it but, I...

If $p$ is an odd prime expressible as $$p=x^2+5y^2$$ where $x,y$ are integers, then prove that $p \equiv 1 \text{ or }9\text{ (mod 20)}$.

if the greater of two numbers is one more than twice the smaller and the smaller is x, what is the bigger? if the bigger is x, what is the smaller number? my answer to the first part is 2x+1. but i don't know how to represent the second condition in a mathematical form. and can you also give...

Homework Statement Curious about this ...I have to find the sum. Homework Equations The Attempt at a Solution Ʃ (1/4)(-1/3)^n from 1 to infinity I want to know the proper form and why. Is it (1/4) Ʃ (-1/3)(1/3)^n-1 or (1/4) Ʃ (1/3)(-1/3)^(n-1) You get different answers

Homework Statement Hello, I am trying to put the following equations into matrix form in order to solve the system. If anyone could please explain to me how to do it or show me an example it would be awesome. All material given in question: For the system of inhomogeneous differential...

Hi, quite new in chemistry.. I would like to know the beginning of the atoms in the universe. Therefore I must understand the process from Hydrogen to Helium. But to create Helium you need the isotope(#2) "Deuterium" from Hydrogen. But how did the Deuterium form? From two Protons...

Homework Statement {U_0 = 9, U_1 = -3} U_(n+2) = -(5/4) U_(n+1) + (3/8) U_(n) Homework Equations The Attempt at a Solution First step was to attempt to find the common difference by trying to find the 3rd term: U_(2) = -(5/4) u_(1) + 3/8 U_(0) = -(57/8) This does not...