Terms Definition and 1000 Threads

Homework Statement "In a geometric sequence, the sum of t7 and t8 is 5832, the sum of t2 and t3 is 24. Find the common ratio and first term." Homework Equations d = t8/t7 or t3/t2 tn = a * rn-1 The Attempt at a Solution So I thought of developing a system of equations then solving...

Prove that $\tan \left( \dfrac{3 \pi}{11} \right)+ 4\sin \left( \dfrac{2 \pi}{11} \right)=\sqrt{11}$. I know this problem may be stale as it has been posted countless times at other math forums, but I've seen one brilliant method to attack this problem recently, and I'm so eager to share it...

I was trying to design some GUI for a tool I'm making and I noticed there's a hidden math problem somewhere in there. Not being one to let the opportunity slide, I decided it's worth exploring. Basically there's 3 buttons that add to a variable. What are the best values to put on those...

Hellow! I was noting that several definitions are, in actually, expressions of vector calculus, for example: Jacobian: \frac{d\vec{f}}{d\vec{r}}=\begin{bmatrix} \frac{df_1}{dx} & \frac{df_1}{dy} \\ \frac{df_2}{dx} & \frac{df_2}{dy} \\ \end{bmatrix} Hessian: \frac{d^2f}{d\vec{r}^2} =...

There are multipliers that can be used when building infinite series that can create several different orders for the signs of consecutive terms by, for example, (-1)^n to get, - + - + - +... but I have been having difficulty figuring out any beyond the following, + - + - + -... + + -...

Homework Statement Sum the series 1 + 2a + 3a2 + ... to n terms This series consists of an a.p. (with general term n) and gp general term a^(n-1) right? So the series general term is na^(n-1) So is the sum the sum of each progression times each other? i.e (1-a^n)/(1-a) *...

Hi, All: Sorry for the length of the post, but I think it is necessary to set things up so that the post is understandable: I'm going through an argument in which we intend to show that a given vector field [ itex]R_ω [/ itex] (actually a Reeb field associated with a contact form ω) is...

Evaluate the sum $\displaystyle \sum_{i=0}^n \tan^{-1} \dfrac{1}{i^2+i+1}$.

In a previous thread I showed how to express $\zeta'(-1)$ in terms of the Glaisher-Kinkelin constant. http://mathhelpboards.com/challenge-questions-puzzles-28/euler-maclaurin-summation-formula-riemann-zeta-function-7702.html This thread is about expressing $\zeta(3)$ (sometimes referred to as...

Homework Statement . Let ##f:[a,b] \to [\alpha,\beta]## be a bijective function of class ##C^2## with an inverse function also of class ##C^2## ##g:[\alpha,\beta] \to [a,b]##. a)Calculate ##g''(x)## for every ##x \in (\alpha,\beta)## in terms of ##f## and its derivatives. b)If ##f'(x)>0##...

As I understand it, the value of a 4-vector x in another reference frame (x') with the same orientation can be derived using the Lorentz boost matrix \bf{\lambda} by x'=\lambda x. More explicitly, $$\begin{bmatrix} x'_0\\ x'_1\\ x'_2\\ x'_3\\ \end{bmatrix} = \begin{bmatrix}...

Hello (Smirk) Given the x^{2}y''+axy'+by=0,I have to show that with replacing x with e^{z},it becomes a second order differential equation,with constant terms. I tried to do this and I got this: y''+\frac{a}{e^{z}}y'+\frac{b}{e^{2z}}y=0 . But,at this equation the terms aren't constant...

Homework Statement Given the following wave function for hydrogen: psi(r, t=0) = (1/sqrt(10))*(2*psi_100 - psi_210 + sqrt(2)*psi_211 + sqrt(3)*psi_21(-1)) where the subscripts show n, l, m_z, respectively, and the psi_nlm_z are already normalized. - At t=0, we measure and find l = 1...

Hi All, I'm working through the theory of the strong interaction and I roughly follow it. However I have some questions about the meaning of the terms. The book I use gives the gauge transformation as: \psi \rightarrow e^{i \lambda . a(x)} \psi First question ... What are the a(x)...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

Let f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2} first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary u + iv : u(x,y),v(x,y) and then partially differentiating wrt x and y and just show that \frac{\partial...

What is Schwinger terms that related with commutator of currents and what is the origin?Why the infinities appear when we consider the product of operators of fields at the same spacetime point?

How does one calculate the number of terms in the sequence \sum\limits_{a=2}^k \sum\limits_{b=a}^k of 1/(a*b).

Hi guys, i need your help to go about his question, Question: $$\text{Show that the coefficient }C_n \text{in the Laurent expansion of }$$ $$f(z)=(z+\frac{1}{z}) \text{ about z=0 is given by}$$ $$C_n=\frac{1}{2\pi}\int^{2\pi}_0 \cos(2cos(\theta))cos(n\theta)\, d\theta ,n\in\mathbb{z}$$

Homework Statement Find an expression for the moment of inertia (I) of the platform in terms of acceleration of the mass (a), the value of the hanging mass (m), the radius of the spindle (r) and the constant (g). Diagram: http://i.imgur.com/rv3zFYG.jpg Homework Equations F=ma t=Iα...

What Is The Difference Between These "Dielectric" Terms? Can someone please explain to me what the difference between these terms are? 1. Dielectric constant 2. Relative dielectric constant 3. Dielectric loss I came across them on this website: http://www.lsbu.ac.uk/water/microwave.html#pen...

This is a spin off from another thread: First there are a couple of mathpages http://mathpages.com/rr/s8-04/8-04.htm and http://mathpages.com/rr/s8-03/8-03.htm that discuss the refractive index model and highlights the differences. The first obvious objection is that the 'medium' must have...

Hi, I need to let an operator act on a scalar function. The operator is however in a very cryptic form, so I would want to work it out a little bit. I get stuck in the process. The operator is: \vec{u}\cdot\left[\vec{L}\times\left(\vec{u}_r\times\vec{L}\right)\right]f Where \vec{L} is...

If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...

how would i go about properly grouping terms to start my factoring? 1. $12x^2y^3-24y^3z-6x^6+30y^4-15x^4y+4x^2y+12x^4z+10y^2-8yz$ thanks!

I want sthg I can visualize in order to understand , I keep asking and am always told time , so how is time a 4th dimension ? I try my best but my mind is too weak to visualize things more complex than disney (so please , I want sthg in that standard ,consider me a curious 6 year old child)

Hi MHB, This problem vexes me until my mind hurts. Problem: Find the sum of the first 11 terms of the series $$\frac{19}{99}+\frac{199}{999}+\frac{1999}{9999}+ \cdots$$ Attempt: I managed only to find the expression of the nth term of the given series and I got...

Homework Statement If \displaystyle \int_0^1 \dfrac{e^t}{t+1} dt = a then \displaystyle \int_{b-1}^b \dfrac{e^{-t}}{t-b-1} dt is equal to Homework Equations The Attempt at a Solution I used the definite integral property in the second integral \displaystyle \int_{b-1}^b...

1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...

Homework Statement 3x+cos 2x = c c is an unknown constant. how do i solve x in terms of c?

This was something I noticed as I was trying to practice solving PDEs using the method of characteristics. The text has the following example: $$\frac{\partial u}{\partial x} + x \frac{\partial u}{\partial y} = 0$$ This should be easy enough. I let p(x,y) = x and solve for \frac{\partial...

I posted this question over at the QM page, https://www.physicsforums.com/showthread.php?t=714076 but I realized I am really looking for a hard Mathematical proof ... A description of a numerical way of proving this would also be very helpful for me. or a reference covering the...

Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...

Solve for $x$ in terms of $a$ in the equation $x^4-3ax^3+3a^3x+a^4=0$.

Dear all, I am stuck with the problem which is given below; In this problem the equilibrium equations of the given functional must be derived in u, v, and w directions from which the boundary terms must be found. I think that i have derived the equilibrium equations( 5 equations), but i...

Hi All, Thanks again to all the great mentors and contributors to this forum. I wanted to ask a question about the Gauss's law/Ampere's law equations in Maxwell's Equations: \nabla \bullet \textbf{E} = \frac{\rho}{\epsilon_0} \\ \\ \nabla \times \textbf{B} = \mu \left( \textbf{J} + \epsilon...

Problem: Rewrite the indefinite integral ## \iint\limits_R\, (x+y) dx \ dy ## in terms of elliptic coordinates ##(u,v)##, where ## x=acosh(u)cos(v) ## and ## y=asinh(u)sin(v) ##. Attempt at a Solution: So would it be something like, ## \iint\limits_R\, (x+y) dx \ dy =...

Express the vector <1,0,0> in terms of I,J,&k. (a)*I + (b)*J + (c)*K You have to find a,b, and c. I know that I,J,&K are unit vectors and so I thought that a = 1, b = 0, c = 0. But the answer has radicals and fractions in it. I don't understand how to arrive at the solution.

The article is about something spinning at an incredibly high rate, with a blurb from the scientist saying that the spin rate is so high that the angular acceleration is compared to gravity - which makes no sense since gravity is a linear acceleration, and as well, if it were the tangential...

What is the difference between: Atomic mass Relative atomic mass Atomic weight Relative atomic weight People misuse these so many times that I've confused myself. Somebody please confirm their definitions please, thanks.

Hi there, the problem says, an n-gon is circumscribed around a circle so the mid point of each side is tangent to the circle. Prove the triangle consisting of one side of the n-gon and the sides from the end points to the middle of the circle has area tan(pi/n) Cheers!

I'm going to be taking a course in differential equations and I'm nervous. From previous calculus courses I know the derivative is the ratio of how one quantity changes with respect to another the integral is the area under the curve So what's a differential equation? According to here "A...

what if the evolution of the universe over time and the expansion of space a series of binary events such that the same quantity of energy is divided geometrically from one into two, four, eight, sixteen pieces, such that each Planck time is equivalent to one such split and each Planck length is...

I am a bit curious about how pedagogical terminology, say what you found at the glossary of your science (or non-science) textbook gets established. My guess is that you have a pioneer in the field come up with some concepts, write articles etc. on those concepts and gives it a name, and then...

The vectors $\vec{i}$ , $\vec{j}$ are unit vectors along the x-axis and y-axis respectively. The vectors $ \vec{u}= –\vec{i} +2\vec{j}$ and $\vec{v} = 3\vec{i} + 5 \vec{j}$ are given. (a) Find $\vec{u}+ 2\vec{v}$ in terms of $\vec{i}$ and $\vec{j}$ . $–\vec{i} +2\vec{j} +...

Homework Statement A tangent line at point A with coordinate (a,f(a)) of function f(x) intersects f(x) at point B coordinate (b,f(b)) . A vertical line is drawn from point p (a<p<b) and intersects f(x) at C. From C a perpendicular line to the tangent line is drawn which intersect the tangent...

Homework Statement A gun is shoot straight up. Assuming that the air drag on the bullet varies quadratically with speed, and the equation of motion for the bullet is (m/2)(dv^2/dx)= -mg-(cv^2). Find for the downward motion , v^2 in terms of x. Taking that upward direction is positive...

Homework Statement I am trying to understand game of roulette through kinematic equations of circular motion. Roulette is game where a ball spins in circular motion. Initially it is accelerated such that velocity of ball increases with time however after reaching its peak value it starts to...

So i realize that the integral of [f(x)dx] is pretty much the height of the rectangle f(x), multiplied by the width dx. But that is the area of 1 infinitesimally skinny rectangle. How does the integral sign add up an infinite amount of rectangles? I've taken cal 2 so if you could show what the...

I need to find the value of the first term for this geometric series. Sn = 33 tn = 48 r = -2 I know that I have to take the formulas tn = t1 x r^(n-1), and Sn = [t1 x (r^n) - 1] / (r - 1), and isolate t1 for the first formula and then input that into the second, but I don't know the actual...