Formula Definition and 1000 Threads

$$b_{k} = b_{k - 1}/2 +b_{k-1} $$ $$b_{0} = 1 $$ What would be the sequence for this expression, I calculated it to be 1, 2/3, 2/5, 2/7 ... Is it right? My explicit formula is $$b_{n} = 2/n+2 $$ What would be the explicit formula in your view and how can that formula be proved by...

Algebra in this answer does not seem to flow right. Firstly, the 16, secondly the n term. Can someone explain or show me the right answer?

Could someone please write out or post a link to the Riemann Tensor written out solely in terms of the metric and its first and second derivatives--i.e. with the Christoffel symbol gammas and their first derivatives not explicitly appearing in the formula. Thanks.

https://www.asi.edu.au/wp-content/uploads/2015/03/PhysicsASOE2013soln.pdf Q12 e) Working backwards, P = Ae^kt form, i.e. EAts = Emin e^(ln2/τ x t). Not sure how they get this formula in the first place with these values.

Dear Everyone, I am wondering how to use the integral formula for a holomorphic function at all points except a point that does not exist in function's analyticity. For instance, Let f be defined as $$f(z)=\frac{z}{e^z-i}$$. F is holomorphic everywhere except for $$z_n=i\pi/2+2ni\pi$$ for all...

Dear Everyone, I am wondering how to use the integral formula for a holomorphic function at all points except a point that does not exist in function's analyticity. For instance, Let $f$ be defined as $$f(z)=\frac{z}{e^z-i}$$. $f$ is holomorphic everywhere except for $z_n=i\pi/2+2ni\pi$ for...

To estimate the cost of an item of equipment or plant from another of a known cost and size or capacity , we use a well known formula Cost B = Cost A * ( CapacityB/Capacity A)^n, where n is a factor usually around 0.5-0.8 depending on the plant or equipment involved. These exponents are...

I am looking for a formula that will them me how many possible connections between 2 sets of objects. Ex: 12 on left and 4 on right, how many possible states can it be in? state one: top on left connected to top on right state two: top on left connected to 2 on right state three: top on left...

I derived (trivially) an expression for the variance of a random variable (which I had never noticed before). Let ##X## be a random variable with cdf ##F(x)## then (assuming finite second moment). ##Var(X)=\frac{1}{2}\int\int (x-y)^2dF(x)dF(y)##. Is this expression of any use?

This is the question. The following is the solutions I found: I understand that the first line was derived by setting one vertex on origin and taking the transpose of the matrix. However, I cannot understand where the extra row and column came from in the second line. Can anyone explain how...

Reference frame is an accelerated frame in SR (uniformly accelerated with "g" in flat spacetime). An object is falling with relativitic velocity of up to 0.8 c in the pseudo-gravitational field in this frame. From Newton's theory, I know the formula for potential energy in such a scenario: ##W...

Hello. I am working this formula. I= 1/L∫Vdt . The following website have the best explanation of it. http://www.learningaboutelectronics.com/Articles/Inductor-current-calculator.php I am confused with a few things about it. One is that this website says If the current is Ac then the value...

I'm pretty lost on this one. I think he needs to drive the second mile at 75 miles per hour to average 50 miles per hour. So he needs to drive the second mile at a rate of 1.5 minutes which would = 75/1.5 = 50 So my answer for 1. 1.5 minutes, and my answer for 2. is Yes, at 75 miles per hour...

Admittedly Euler was a genius and I am a noob, but I sometimes feel that there must have been a method or process that he followed to go about such problems and came up with these elegant solutions. It couldn't have been just a sudden flash of genius. For example, I wonder how he could have come...

Hey everyone, I have generated a nice little velocity vs time graph that I would love if somebody could help me put to use. I have marked data points on the x-axis for the Y-value for every second on the function. Just to be clear: X-axis = time in seconds & Y-axis = velocity in meters/second...

number of moles of CO2 =0.089moles (using 2/22.4) number of moles of water = 0.067 (using 1.205/18) I know that all the carbon from the hydrocarbon is in the CO2 and all the hydrogen from the hydrocarbon is in the water and water creates x2 hydrogens so number of moles of C : H = 0.089 ...

How can I' be the formula above? Is there any formula to get this same

Hello, i am testing batteries for a project of mine. I first measure the voltage on the battery (OCV, Open Circuit Voltage), and then i place a load resistor over the battery. This results in a voltage drop with a exponential decrease in voltage like in the image. But i am working with a...

In a paper published in the JOURNAL OF MATHEMATICAL PSYCHOLOGY 39, 265-274 (1995), formulas are provided on page 272 for the expectation E(Tn) of a random variable T as dependent on n (formulas 28 and 29). Now I would like to know what these formulas look like for the variance i.e. Var(Tn).

Hey! Let $\mathbb{K}$ be a field and let $1\leq n\in \mathbb{N}$. Let $a_0, \ldots , a_{n-1}\in \mathbb{K}$ and let $m_n\in M_n(\mathbb{K})$ be given by \begin{equation*}m_n:=\begin{pmatrix}0 & 0 & \ldots & 0 & -a_0 \\ 1 & \ddots & \ddots & \vdots & \vdots \\ 0 & \ddots & \ddots & 0 & \vdots...

Below are equations/formulas/text from https://en.wikipedia.org/wiki/Schwarzschild_geodesics https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html I apologize for not remembering the source for the "v=" equation, or for my inability to find it again. For a circular orbit, the distance r and...

The following is the questions given. I solved the first one, which steps are shown below. But I am not sure if this is how the question wants me to solve the problem. Would you tell me if the way I solved the problem is the proper way of simplifying the expression using euler's formula...

Hello! (Wave) Suppose that we have the recurrence relation $a_k=3^k-a_{k-1}, a_0=1$. By replacing the terms of the sequence we get that it is equal to $a_k=3^k-3^{k+1}+3^{k+2}-a_{k-3}$. How do we get that it is equal to $a_k=3^{k}-3^{k-1}+3^{k-2}- \dots+ (-1)^k$ ? :unsure: Also, why is the...

I was studying how to derive the cross-section formula in the CoM frame from Mandl & Shaw QFT's book, and they state the following formula for the relative velocity (I'm going to use Vanhees71's notation though) $$\omega_1 \omega_2 v_{rel} = [(p_1 p_2)^2 - m_1^2 m_2^2]^{1/2} \ \ \ \ (2)$$ Then...

We work in natural units. Let's assume in this post that the differential cross-section of two particles that, after collision, yield ##N## particles is given by the following formula: $$d \sigma = (2\pi)^4 \delta^{(4)} (\sum p'_f - \sum p_i) \frac{1}{4 E_1 E_2 v_{rel}} \Pi_l (2m_l) \Pi_f...

Please let me make questions after showing what I am studying. We first consider two particles (they may be either leptons or photons) with initial (i.e. before collision) four momentum ##p_i = (E_i, \mathbf p_i)##, ##i=1,2##. These two collide and produce ##N## final particles with momentum...

Dear Everyone, I am having trouble with finding a formula of the multiplication 3 formula power series. \[ \left(\sum_{n=0}^{\infty} a_nx^n \right)\left(\sum_{k=0}^{\infty} b_kx^k \right)\left(\sum_{m=0}^{\infty} c_mx^m \right) \] Work: For the constant term: $a_0b_0c_0$ For The linear...

Hi, Can someone please help me in understanding few parameters of cubic equation formula for solving polynomial of degree three. I attached the formula in the screenshot. My questions are: (1) what is ". " dot in the end of the formula and what does it mean? (2) I want to use it only for real...

Tong proposes the following exercise in this lecture (around 25:30, section b)): Exercise statement: Prove that the stress-energy tensor is given by the functional derivative of the action with respect to ##\delta g^{\mu \nu}## $$T_{\mu \nu} = \frac{-2}{\sqrt{-g}} \frac{\delta S}{\delta...

Hi, I have this formula, What I want is to find the value of "x" (without trying all possibilities) so that the result of the formula will be the lowest possible value under the constraint when x !=0, and x<n. Here, values of A,B,C, Q, R,n are already known and fixed...

Centripetal force is defined as the force causing the body to follow a curved path, acting towards the center and always orthogonal to the direction of motion. For uniform circular motion the formula for centripetal acceleration is $$a_c = \frac{v^2}{r}$$. But my understanding of centripetal...

how can i write a function that calculate math formula using void function-recursion in C?

Prove that the stress-energy tensor is given by the functional derivative of the action with respect to ##\delta g^{\mu \nu}## $$T_{\mu \nu} = \frac{-2}{\sqrt{-g}} \frac{\delta S}{\delta g^{\mu \nu}}$$ Tong suggests (around 25:30) we could get the desired tensor by performing a...

Hello! Can someone point me towards some papers/readings providing formulas (derived theoretically or based on experimental data) for the nuclear charge radius? Almost all the papers where I found a formula for that are of the form ##aA^b+c##, where a, b and c are constants and A is the mass...

i want to ask about my homework im not understand what to do with this formula :

Let´s suppose we are observing the sun and measuring some spectral lines. Does the velocity correction´s formula for the Earth include the rotational velocity components of the Sun as well? or rather are we basically measuring both velocity contributes of Earth and of Sun together (receeding...

Hello all I was hoping someone can help with the following problem. I am trying to create a parabolic formula to give me target weight. For example:- Day 1 = Target Weight 100kg Day 112 = Target Weight 67kg Each day is consecutive - can anyone help me to create a parabolic formula that goes...

Here is a diagram of experiment: Here is the results: Average distance between nodes (cm) Frequency (hz) Line 1 Line 2 Line 3 500 253 176 105 1000 333 438 None My analysis: ƛ/2=D ∴ƛ=2D where ƛ=wavelength (cm) D=distance between nodes/antinodes (the average,cm) 500hz: Line 1...

So, two wave fronts leave adjacent "slits" in a grating and head for a screem When they get to a point of local maximum, they will have interfered constructively, and so they must be in phase. Therefore the path different will be a whole multiple of the wavelenth. People routinely draw a right...

The values calculated was nowhere near the theoretical values, though I guessed they won't be as the results recorded was incredibly inaccurate. My teacher acknowledged the fact the final values won't be close to the theoretical ones but also said that my formula was wrong, that it works to find...

Hello, everyone. I am trying to find an aberration of light formula in Einstein's writings that is given in terms of tangents. I did a fairly thorough internet search and all I could find was the formula he wrote in terms of cosines. Yet I have a vague memory that somewhere he did give the...

the equation is not equal not to anything (example: 3x = 6) and i don't know how to resolve [e ^ - (b / 2m) t].

Hi everyone, please could someone assist in the formula for the above A, B, C, D, E and F in order for me to try and resolve the maths questions, I'm just a little stuck on the formula, Thanks in advance all :-)

Wikipedia gives, "The relative velocity ##{\displaystyle {\vec {v}}_{B\mid A}}## is the velocity of an object or observer B in the rest frame of another object or observer A." Suppose the coordinate system being used in the rest frame of ##A## is has its origin slightly displaced from ##A##...

Summary:: Is there a formula to determine when watch hands overlap? The other day, I was sitting on the can and, as I am won't to do, pondering matters of import to the known and unknown universe at large. During the event in question, I happened to notice my watch - and I am having the most...

Moved from technical math section, so missing the homework template Summary:: Find a general formula for the nth derivative Hi everyone! How would I approach and answer a Q such as this I began by rewriting the expression in a different form, then used chain rule to each given term I...

Recently I created a spreadsheet that generates Phythagorean triples. Curious, instead of using only positive integers for the values of m and n, I found that as long as m>n, the sides 2mn, msq + nsq, msq - nsq, still form the sides of a right triangle even though m and n are non-whole...

I have the STRESS , YOUNG S MODULUS ,and the LENGTH . How can you discover the CHANGE IN LENGTH when you don t have the FORCE and AREA unit ?

Hello, In high school, I had been taught about finding substitution resistance from Wheatstone bridge. The formula: a. If the cross product of ##R1## and ##R3## is same as ##R2## and ##R4##, the galvanometer in the middle (##R_5##) can be omitted and use series-parallel principle to solve for...