Formula Definition and 1000 Threads

I would like to understand how the Euler constant elevated to fractional exponent gave this result? 958mV someone please!?

Homework Statement begin with ##H = U+PV##. Manipulate it into the form: ##(\frac{∂H}{∂U})_P## hint: you might find the resulting expression from part a useful) the resulting expression that I found was ##(\frac{∂U}{∂V})_P = \frac{C_V}{V*a} + π_T##Homework Equations ##π_T## =...

Apologies if this is in the wrong section. Wasn't sure where to put it. While this is technically homework, I don't think it fits in the homework section In a paper I'm writing, I need to estimate the cost to society of future pollution. Reading relevant academic articles, it seems pretty clear...

Hi,thanks in advance for your help Ive been given the task to transpose To make x the subject from y=7-2x Which in my mind x= 7+y / 2 But my book is saying X=7-y / 2 Is the book correct if so where / why am I going wrong ?

Homework Statement i know that the formula of head loss is (V^2) / 2g , where v =velocity , but , why did the author want to change it to k[(Q)^1/n ] ? Homework EquationsThe Attempt at a Solution

Homework Statement is the equation in the 3rd photo wrong ? since there are 2 exits , why shouldn't the eqaution become (P1 / y) + z + (8.33^2) / (2x9.81) = 0 + z +[ 2 (12^2) / (2x9.81) ] ? Homework EquationsThe Attempt at a Solution

We have tried to convert a petrol engine into a compressed air engine back in our graduation project. At that time we only measured the RPM of engine using tachometer and pressure of compressed air using pressure gauge. Now, we need to know the power of wngine at those readings. As the setup is...

http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ] a(t) : the angle in instant t . t : time g : gravity . Pi = 3.14 k = Fixed (Friction ) l : longer of pendulum...

can you please explain me why don't we use arc length formula to calculate wavelength? seems a bit confusing...

[FONT=PT Sans]how to get the formula of shear stress (tau) ? i got (-dp/ds -ydz/ds )(r/2) instead of -d(p+yz)/ ds (r/2) as in the book , if it's d(p+yz)/ ds (r/2) m , i would get (-dp/ds -ydz/ds-z(dy/ds) )(r/2) ,, right ? The Attempt at a Solution P/s : I'm concerned about the derivation part ...

My book says this: I don't understand how this works. I learned that the usual sunisoidal function looks like sin(wt+phi), where w is frequency, t is time, and phi is some offset. EQ 17.1 doesn't match the bolded formula above. How does this work?

Hello! I took a quality certification test yesterday and there was a question on there about torque wrench formulas. I didn't have anything about that in my notes, so I took some time this morning to create a cheat sheet based on what I could find on the web. 1) In some of the forums, they...

Homework Statement is I/ V ( in the second picture)submerged is a valid formula of metacentric height ? i have never seen this in my textbook . This is just another notes given by my senior. Homework EquationsThe Attempt at a Solution

Is it true that we can't use the formula ##f##= ##\frac{-dU}{dx}## when external source of energy or some external force is present? I think it should rather be "we can't use ##f##= ##\frac{-dU}{dx}## when non conservative force is present" because potential energy is defined only for...

Homework Statement what is the 2.1 and 0.35 refers to in the equation of (9810)(2.1)(4.2)- 9810(0.35)(0.7) -Fx = 1000(5.88)(8.4-1.401) ?? is it the width ? but , the width is not given ? Homework EquationsThe Attempt at a Solution

Homework Statement This formula we've been using recently, I don't understand where it comes from. Homework Equations T = 2pi * sqrt(m/k) The Attempt at a Solution Hooke's law: F = -kx E(total) = .5mv^2 + .5kx^2 Circumference of a Circle: C = 2 * pi * r I figure these piece together, but I...

Homework Statement why the y ſ P dA will equal to P yc A ? why not P (yc^2) A ? since yc = ſ y dA / A Homework EquationsThe Attempt at a Solution

Hello! (Wave) A force $6N$ forms an angle $\frac{\pi}{4}$ with the y-axis, showing to the right. The force is opposed by the movement of an object along the line that connects $(1,2)$ with $(5,4)$. I want to find a formula for the vector-force $F$. The line that connects $(1,2)$ with $(5,4)$...

I want to convert a recursive real formula to rational number representation, but I get the wrong response. For the real formula: k = 1.9903694533443939 u1 = -12.485780609032208 u2 = -6.273096981091879 u3 = k * u2 -u1 /// 1st iteration u3 = -1.7763568394002505E-15 // approx. zero /// 2nd...

Homework Statement why the alternative formula of viscosity not = (mass x length ) / ( time x area) ? for force x time , we would get (mass x length ) / time ... Homework EquationsThe Attempt at a Solution

Homework Statement A bullet with a mass of m=15.5 g is shot out of a rifle that has a length of L=1.02 m. The bullet spends t=0.16 s in the barrel. Write an expression, in terms of given quantities, for the magnitude of the bullet's acceleration, a, as it travels through the rifle's barrel...

I'm talking about equation 22, Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it. L would be the length, F would be force, and μ would be mass per unit length. f is the frequency Thanks

1. Homework Statement how to get R=Vi 2 sin2θ/g y=x*tanθ-[x2*g]/[2(Vi*cosθ)2] Homework Equations Vy=Vi*sinθ-gt y=Vi*sinθ*t-1/2gt^2 Vx=Vi*cosθ x=Vi*cosθ*t The Attempt at a Solution I use this formula to find the expression for t Vy=Vi*sinθ-gt gt=Vi*sinθ t=Vi*sinθ/g I substitute it into...

Hello! (Wave) Given two vectors $a$ and $b$ why does it hold that the vector projection of $a$ on $ b$ is $$\frac{\vec{a} \cdot \vec{b}}{||\vec{b}||^2} \cdot \vec{b}$$ ? Could you explain to me why the formula holds?

Good day to you all, I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...

Homework Statement Verify that a) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}\bar z}{1-\bar z e^{it}}dt = 0##, if ##f(w)## is analytic for ##|w|<1+\epsilon##, and that b) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}}{e^{it}-z}dt = f(z).## for ##z = re^{i\theta}## with ##r <...

Homework Statement The formula being derived is N=No*e^k*t, from the equation Nn=No/2^n where No is the initial number of particles and the lowercase n in the second equation is the number of half lives. The n in Nn just indicates the number of particles after so many half lives. You might also...

Homework Statement 2. Homework Equations [/B] De Moivres Theorem/ Eulers formula The Attempt at a Solution Honestly don't know where to go with this now. I already applied De Moivres theorem at the very end. It feels like I have to do something more with either De Moivres theorem or...

Homework Statement Derive the Breit-Rabi equation in the case that the quantum number j is equal to 1/2, specifically the 1S_1/2 state of Hydrogen. This is the equation describing hyper-fine and Zeeman splitting of the energy levels in an applied magnetic field. Homework Equations We are given...

what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure

can someone explain how you go from (4.25) to (4.26) using Euler's formulas in the attachment?

Not saying this is fake, but it seems pretty incredible to me. Can anyone shine some light on this?

Homework Statement what does the gamma in the formula mean ? since the other terms in the formula are the same , i can just cancel it, leaving μ / γ = v /g . So , γ has unit of kg(m^-2)(s^-2) ? Homework EquationsThe Attempt at a Solution

What does this formula measure? c= \sqrt{2EY/\pi} This topic is from fracture mechanics. Does this formula tell you how much stress is required to cause the crack to increase?

Find $ \oint\frac{e^{iz}}{z^3}dz $ where contour is a square, center 0, sides > 1 There is an interior pole of order 3 at z=0 CIF: $ \oint\frac{f(z)}{(z-z_0)^{n+1}}dz = \frac{2\pi i}{n!} f^{(n)}(z_0) = \frac{2 \pi i}{2}f''(z_0) = -\pi i $

Homework Statement The picture attached appeared in my powerpoint for my class. It's been a long time since I took calculus 1, but if I remember correctly this formula is wrong correct? I mean thinking about it limit k-> inf ( cos(theta)^k ) = 0 if theta is not a multiple of pi OR +/- 1 if...

Please go to this Wikipedia article on Lift Coefficients, and behold the first formula. The last part of the equation has a "S" which is supposed to stand for "relevant plan area". Now, there was no explanation of what this "relevant plan area" is or means. I was guessing that it means the...

Edited by moderator In the attached file it says that the formula for when n=2 implies the next one but I don't understand why it suddenly became (s-t0)^2 inside the integral instead of (s-t0) in the next one and keeps this pattern, it doesn't seem to be implied anywhere for me.

Homework Statement I'm reading the book Relativity, Gravitation, Cosmology by Ta-Pei Cheng. I'm in the part where he derived the gravitational time dilation formula for static gravitational field, τ1=[1+(Φ1-Φ2)/c2]τ2. This implies that clocks at a higher gravitational potential will run...

Homework Statement Why the weight of water at water surface is given by formula 2(pi)Rσ(cos angle) ? Homework EquationsThe Attempt at a Solution

So, unless you've been living under a rock, you should know the jackpot for the powerball is at 1.5 billion dollars. I was looking up the distribution of annuity payments and the website said that the payments are not equally distributed. They are incremented by 5% each year. Like the nerd I...

Homework Statement How many moles is 0.01 gram formula weight of NaCN?Homework EquationsThe Attempt at a Solution I thought it meant 0.01/49 moles of NaCN. The solution simply says 0.01 moles. Why?

Problem A now solved! Problem B: I am working with two equations: The first gives me the coefficients for the Laurent Series expansion of a complex function, which is: f(z) = \sum_{n=-\infty}^\infty a_n(z-z_0)^n This first equation for the coefficients is: a_n = \frac{1}{2πi} \oint...

How does (6.79) satisfy (6.70)? After substitution, I get $$(1-w^2)\frac{d^{l+2}}{dw^{l+2}}(w^2-1)^l-2w\frac{d^{l+1}}{dw^{l+1}}(w^2-1)^l+l(l+1)\frac{d^{l}}{dw^{l}}(w^2-1)^l$$ Using product rule in reverse on the first two terms...

I'm doing my HSC physics course and I was playing around with the algebra in space unit and came upon something that confused me (note this isn't required to know by the syllabus except knowing that escape velocity is the velocity to escape from a planet's gravitational field) Ok, so from the...

Homework Statement The motion of an electron is given by x(t)=pt^3 +qt^2 +r, with p = -1.9 m/s^3 , q = +1.3 m/s^2 , and r = +9.0 m. What is the velocity at: a) t=0s b) t=1s c) t=2s d t=3s Homework Equations v=x/t The Attempt at a Solution I have tried plugging in the time to equal to t, in...

Quick question: is the following a correct integral formula? $$\int \! \frac{1}{(-x + a)^2} dx = -\left(\frac{1}{-x + a}\right)$$ I couldn't find it on the integral tables, so I just extrapolated from a similar integral formula I've found there. That formula being: $$\int \! \frac{1}{(x + a)^2}...

I am trying to understand N-spherical cap area formula (surface area of blue part), but it seems to give wrong answers. for 1 dimensional cap obviously ## \frac{l_{cap}}{l_{sphere}}=\frac{l_{arc}}{l_{circle}}=\frac{r*θ}{r*2π}=\frac{θ}{2π} ## But according to wikipedia formula...

Homework Statement In a certain carnival ride, visitors enter a circular room with radius r=9.1m. The room then begins spinning around its center, reaching an angular speed of 1.7rad/s. What centripetal acceleration do the riders experience? Homework Equations ac= v^2/r The Attempt at a...