Formula Definition and 1000 Threads

I'm currently writing up a homework assignment on a Hidden Markov Model. This involves long strings of conditional probability formulas and lots of subscripts. Here is an example of one that I think is really hard to read. Any ideas how I can condense the spacing in the subscripts or make it...

Imagine two space ships each with thrusters that can accelerate them .1c or .3c almost instantly. The velocity addition formula indicates that if one spaceship applied the .1c thruster 3 times then if c is estimated to be 300,000,000 m/s the velocity of the ship after the accelerations the ship...

For the formula A=A0(1+r/k)^(kt) does it only work if t is in years and k is how many times per year it is compounded?

Hi, I am trying to derive the Sherman-Morrison formula for the following expression: a*x*(b*AAH+I)-1*y, where a, b are non-negative scalar values. Also, vectors and matrices are represented by lowercase bold typeface and uppercase bold typeface letters, respectively. Also, (.)H and (.)-1 are...

The formula for Helmholtz coil is given by mu*(0.8^1.5)*nI/R, where I is the current, n is te number of coil and R is the radius of the coil. Now assume the bunch of coils have a small 'thickness' w (so it looks like a hollow cylinder with a very small height), and the the two coils are...

I know torque is defined as r x f , but how did we come to define it in this way? Sorry if question seems a bit noobish but i haven't been able to find the answer

I've a small confusion about formula ##\log^3 n = \log \log \log n## or ##\log^3 n = (\log n)^3 ##

Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...

One semester I was asked to find the inverse of $\,f(x) \:=\:\dfrac{3x - 5}{2x+1}$ Later, I had to find the inverse of $\,f(x) \:=\:\dfrac{2x+7}{4x-3}$ It occurred to me that a general formula would a handy tool. Especially since I planned to teach Mathematics and I might be teaching this very...

Homework Statement Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ Homework Equations x = Rcosθ y = Rsinθ The Attempt at a Solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...

I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop. But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that? Thanks

108 pages of physics formula goodness! Print off the pages you need and start studying!

Just a general inquiry, and not for any personal gain and or theory, I would like to know if anyone has developed a formula for measuring the vibrational rate of an atom.

Is the General Formula of benzene and diacetylene the same?:nb):nb):nb)

Okay so I'm using Coloumb's law and the defining equation of electric field strength to find a proof (for my own satisfaction) for the electric potential formula: V_A = \frac{PE_A}{q}= \frac{Q}{4πε_0r} (where A is the position configuration of a point charge q in an electric field) My derivation...

Homework Statement If arg(\frac{z-ω}{z-ω^2}) = 0, \ then\ prove \ that\ Re(z) = -1/2 Homework Equations ω and ω^2 are non-real cube roots of unity. The Attempt at a Solution arg(z-ω) = arg(z-ω^2) So, z-ω = k(z-w^2) Beyond that, I'm not sure how to proceed. Using the rotation formula may also...

How was the formula for kinetic energy found, and who found it? My questions mostly concern the history of physics. Who found the formula for kinetic energy ##E_k =\frac{1}{2}mv^{2}## and how was this formula actually discovered? I've recently watched Leonard Susskind's lecture where he proves...

I was wondering if anyone could like explain these formulas listen in this document. Thanks http://teachers.ausd.net/devor/cprepp/Formulas/P1TestMTp.pdf -Kevin 11 Grade

Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...

Guys, when utilizing the electric field intensity formula ( Fe=qE), do we use the sign of the charge (q)? I think we do, but I remain confused!

Okay, so I've messed about with this for a while now and I've found that the following formula works on how to get the speed. A car has covered 27 miles in 120 minutes. What is the speed it is traveling at? I add three zeros to the 27, making it 27,000. 120/27000 = 225. I then put a decimal...

Find a formula for g(x)= sin(arccos(4x-1)) without using any trigonometric functions. I have the answer key right in front of me, but i still get how to start it off or the steps in solving these kind of questions or how to do it at all :/ Thanks!

This is a classic case of using the wrong formula for the question. My problem is that, using the given information, both formulas could've been used (to the best of my knowledge) 1. Homework Statement A car traveling at 22.4 m/s comes to a stop in 2.55 s. Determine the stopping distance of...

Hello, I have the haversine function within my C++ program to calculate the distance between to points, the two tester points I have chosen are Swansea and Cardiff both located in Wales. Swansea lat = 51.622559, long = -3.934534 Cardiff lat = 51.475661, long = -3.174688 The problem I am having...

hey, can someone suggest where will a get a detailed proof of stirling's formula (related with gamma function). I read it from PRINCIPLES OF MATHEMATICAL ANALYSIS Walter Rudin,but in it many shortcut steps are there, which is either beyond my knowledge, or i m not getting it.

Hello, I am new to electronics and am having trouble understanding this formula for capacitance: Could someone please break this down into layman terms? Interestingly π appears? I'd like to understand why that exists in capacitance. Thank you all in advance!

Is there a simple formula to find the amount of money in an account given a situation like this... You deposit x into the account Each year you get interest Year one the interest is 1% Year two the interest is 2% Year three the interest if 3% and so on Is it possible to get a simple general...

On problem #6, when using the Vrms formula, does the mass have to be in kg because the constant used uses J, which is kg?

Homework Statement This is a real basic question I am sure. Maybe I just missed something. so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared. Homework Equations T = 1/2 m v^2 a^2 + b^2 = c^2 The Attempt...

In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...

Under the standard form of dimensional analysis, I know that we relate a dependent variable to a function of the independent variable(s). However, what if there is some additive variable needed in the equation? How does this method, which expresses all of the independent variables as a product...

Hello, Suppose there is a $\delta > 0$ such that $f(x) = g(x)$ when $0 < |x - a| < \delta$. Prove that $\displaystyle \lim_{x\to a} f(x) = \lim_{x \to a} g(x)$. $|f(x) - L| < \epsilon$ for $|x - a| < \delta_1$ $|g(x) - M| < \epsilon$ for $|x - a| <\delta_2$ Let $\delta' = \min(\delta_1...

Homework Statement Two bars are placed between plates whose temperatures are Thotand Tcold . The thermal conductivity of bar 1 is six times that of bar 2 (k1 = 6k2), but bar 1 has only one-third the cross-sectional area (A1=1/3 A2 ). Ignore any heat loss through the sides of the bars. Which...

Hi, Just curious if anyone knows of a formula that would show how mass changes in a gravitational field? I have seen the formulas for gravitational time dilation and length contraction (which are rather similar) and was wondering is mass changes the same way. Thanks

https://courses.physics.illinois.edu/phys406/Lecture_Notes/P406POM_Lecture_Notes/Derivation_of_the_Sabine_Equation.pdf I can't understand anything from the above link. Is there any alternative way to derive Sabine's formula. I searched in google but coundn't find anything.

Homework Statement If I know the work function of various metals in eV and need to find the largest wavelenghts required to emit photoelectrons from the metals would i just use ɸ=hf0=hc/λ0? Homework Equations ɸ=hf0=hc/λ0 The Attempt at a Solution The formula only gives the threshold...

Homework Statement Given a pendulum with fixed length, at what angle does the pendulum have to be released at in order to not follow the standard formula for frequency? Homework Equations P = 2pi*sqrt(l/g) The Attempt at a Solution I know that this equation holds for "small" angles (theta <...

I am having some issues with the derivation of the Planck Radiation Formula, as for instance given in http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html . My point is that the assumption of cavity modes implies the formation of standing waves inside the cavity walls. In most situations in...

Homework Statement I need to derive this formula, and I'm basing it upon the following method (this has the diagram which I will be talking about below) http://isites.harvard.edu/fs/docs/icb.topic1214926.files/Purcell-appendix-B.pdf The Attempt at a Solution I'm fine with everything apart from...

Homework Statement In classical electromagnetism, an accelerated charge emits electromagnetic radiation. In non-relativistic limit, where the velocity of the electron is smaller than c, the total power radiated is given by the Larmor formula, to wit P=2/3*e2*a2/c3, where a denotes the...

I've always been interested by the pattern within venus' orbit around the sun. I found this image and the formula of its retrograde motion in the upper right hand corner which confused me. What does it mean? can someone break this down in layman's terms...

Hi I was wondering say for example you had this simple current divider circuit. I was wondering if R1 for example had zero resistance it would have all current dropped over it. However pertaining to the current divider formula. ##I_i = Is (R_T / R_i)## Thus if R1 = zero the equation is not...

Homework Statement How much time does the object use to travel 12m down a plane. The object has a constant acceleration of 1m/s2 and the starting velocity is 5m/s. Homework Equations S=V(starting velocity)*t+1/2*a*t2 The Attempt at a Solution Here I struggle with changing the formula. I could...

P(A/B) is defined to be P(A∩B)/P(B) Why is this true? When A and B are dependent events, I can understand why this is correct. It is clear when you see the venn diagram. But for independent events, why is the formula correct? Any intuition or formal proof?

< Moderator Note -- moved from Academic Guidance to Homework Help >[/color] Hey, I'm new here, I decided to register because one of the threads has helped me in the past and I'm hoping for some answers; to get into it, I'm doing research on the physics of being hit by a car/truck, and I've got...

Hi, I am trying to find an equation that would give the mechanical advantage of this system: I am fairly new to this kind of analysis, but my understanding is that to determine the MA I need to consider that: W_{in} = W_{out} F_{in} d_{in} = F_{out} d_{out} F_{out} / F_{in} = d_{in} /...

Homework Statement Problem: A car's rear window defroster uses 15 strips of resistive wire in a parallel arrangement. If the total resistance is 1.4 ohms, what is the resistance of one wire? Solution: rearrange formula to $$ R nR_{T} = (15)(1.4 \Omega) = 21 \Omega $$ Question: What is the...

Homework Statement t=2v/g the AAMC used this formula to solve a problem that was asking what would happen to time if the gravity becomes g/6. the answer is that the time increases by a factor of 6. Homework Equations v=v0 + at The Attempt at a Solution I got the wrong answer by thinking...

Homework Statement When reacted with a small quantity of water, SiCl4 produces an oxychloride X, SixClyOz. The mass spectrum of X shows peaks at mass numbers 133, 149, 247, 263 and 396. You should assume that the species responsible for all these peaks contain the 16O, 35Cl and 28Si isotopes...