Simplifying Definition and 487 Threads

Hey guys! So I'm self studying Daniel Schroeder's Intro to Thermal Physics and we're to use Stirlings Approximation to simplify the following (assume that BOTH q and N are large, but we don't have a relationship between q and N): \Omega \left( N,q\right) \approx \dfrac {\left( \dfrac {q+N}...

Hello all, I'm trying to answer a question about a meson and a proton interacting to form a neutron and an unknown meson- to be determined. The equation is : (Anti up and strange) + (uud) --> udd + (xy) I arrived at strange and anti down OR anti strange and down. Are both possibilities...

Homework Statement I am trying to understand the simplification between these two block diagrams Homework EquationsThe Attempt at a Solution I understand the 2s+1/s has been moved past the summing junction, resulting in the 2s. But I don't understand where the s/2s+1 block comes from

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] (A+B)&(C+D) + (A+B)&(C+D)' + C (A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans (A+B)&[(C+D)+(C'&D')] + C by Distributive I'm just wondering if I did anything wrong in this simplification or...

Hi all, I'm having a problem simplifying this: [1/(1+x+h) - 1/(1+x)] / h How do you get the common denominators for the top 2 fractions? Thanks

I have been studying the Pythagorean theorem and Fermat’s Last theorem for fun and to brush up on my algebra. I think I’ve come up with an equation for redefining An in terms of B and C. But my math is too rusty to verify if its correct. I hope you look at it and see if there is a mistake...

(tg 570* sin 1469) / (ctg 495 * cos 781) = Its in degrees

I have a question regarding the legality and generality of the following method for simplifying a vector expression. The specific expression that arose my question is ##\left[\left(\vec{P}\cdot\hat{r}\right)\left(\hat{r}\times\vec{M}\right) +...

I simplified a trig equation to \theta=\Big\{sin^{-1}(\frac{1}{2})+2\pi k\Big\}\; and \; \Big\{\pi-sin^{-1}(\frac{1}{2})+2\pi k\Big\} Whereas the book simplified it to \theta=\pm\frac{\pi}{6}+\pi k Obviously these answers encompass the same set of values, with the book's answer being much...

Homework Statement Please find question attached. The context is a lecture course on seismic theory for exploration geophysics. Homework Equations The substitution for the elasticity tensor made in my solution is given in the lecture notes. Please find my attempt at the solution attached...

Homework Statement Hi guys, I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help? I have included a screen shot. Homework EquationsThe Attempt at a Solution Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in...

I need to find the local extrema of \pi r^2(\frac{16}{(r+.5)^2}-1) which I derived and simplified to \frac{16 \pi r}{(r+.5)^3}=2 \pi r which simplifies to \frac {16 \pi r}{2 \pi r}=(r+.5)^3 The radius cannot be zero, so I simplified 8=(r+.5)^3 I used the binomial theorem and more algebra...

Homework Statement [/B] I don't know how to simplify this circuit. Homework Equations [/B] V=IRThe Attempt at a Solution [/B] I thought of this, but I don't know if it's correct, could you help me please?

Homework Statement The linear prediction of one random variable based on the outcome of another becomes more difficult if noise is present. We model noise as the addition of an uncorrelated random variable. Specifically, assume that we wish to predict ##X## based on observing ##X + N##, where...

1) $( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=$?

$$(\sqrt{{\log_{n}\left({p}\right)} +\log_{p}\left({n}\right) +2} *(\log_{n}\left({p}\right)-\log_{np}\left({p}\right)) \sqrt{\log_{n}\left({p}\right)}$$

$$\log_{2}\left({24}\right) / \log_{96}\left({2}\right) - \log_{2}\left({192}\right) /\log_{12}\left({2}\right)$$

$$4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}}$$ I don't even know where to start, I know the teacher said to distribute but distibute what?

Help to obtain a simple form of the following expression: $$\frac{\sqrt[3]{a^2} -\sqrt[3]{ab}+\sqrt[3]{b}}{a+b}$$

I have: sq rt 2 +sq rt 2 over 2 , sq rt 5 + sq rt 5 over 2 I got (sq rt 4 over 2, and 0) = 1, 0 but the answer is actually (sq rt 2, 0) so is my answer still wrong?

Just joined this website for math help like right now :) Background info: I was sick for 2 years before going to university so my level in math is horrible; though I will try my best in all questions which I would ask.1. Simplify 2x^-3 + 9x^-7 Here's what I did 2/x^3 + 9/x^7 find common...

Ok.. What about this one? $$\frac{1}{y+1}+\frac{2}{x+2}+\frac{\frac{x+2}{y+1}-2}{x+2}$$ this is where I am at: \left(\frac{x+2}{y+1}-2\right)

Hello, I am having difficulty solving my math problems. Simplify the expression: (12+r-r^2)/(r^3 +3r^2) The answer is (4-r)/r^2 I know that i can expand 12+r-r^2 as (-r+4)(r+3) But i cannot figure out the rest. Please help me. Thanks

If its not problem for you to check these last two. I got no more of these. If you have some kind a book with tasks like this on internet I would love to print it out so I can have some fun. 1ST answer 20/3 2ND answer -20/3

Homework Statement I want to see if I'm reducing the following circuit correctly. Homework Equations The Attempt at a Solution The two outer resistors are in series: ##R_{56} = R_5 + R_6## Now the outer resistors would be directly wired on each end after simplifying...

In my studies of methods to simplify the Einstein field equations, I first decided to go about expanding the Ricci tensor in terms of the metric tensor. I have been mostly successful in doing this, but there are a couple of complications that I would like your opinions on. At the bottom of...

Hello, Wondering how to simplify this fraction... 3/90 * (36x+54)

I am trying to simplify the expression \not p \gamma^\mu \not p. I believe the answer should be - \frac{1}{2} \gamma^\mu p^2, but I am not sure. Tom

Hey guys, I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For the first one, I evaluated by replacing x for 2+h for f(x). Then I substituted into the givern expression and simplified to get...

Hi everyone. I'm back and happy to be back. I missed math. Anyways, I am taking a college Algebra class as it has been a while, and I definitely want to make sure I have a good foundation for higher maths. But, I have a conundrum. The teacher today gave this example that I thought I had solved...

The problem: (See attachment) I rationalize the numerator and then simplify to get: lim (3(1+sqrtx) - 2(1+cubert(x)))/(1-x) x->1 However, I do not know what to do after this point. If someone could please help me out, that would be great! Thank you! P.S: Look carefully at the...

Homework Statement The length of the curve r(t) = cos^3(t)j+sin^3(t)k, 0 =< t <= pi/2 is Homework Equations AL in polar = ∫sqrt(r^2 + [dr/dθ]^2) The Attempt at a Solution I am having trouble simplifying the terms within the square root. What method should I use to deal with...

Homework Statement Find the arclength of the parametrized path x(t) = (t^2)/2 , y(t) = (t^3)/3 for 1<t<3. Homework Equations Arc Length Formula The Attempt at a Solution x'=t and y'=t^2. Putting them into the arc length formula, I get sqrt(t^2 + t^4) inside. I'm confused...

Hey there! I am getting two completely different equations when I try to simplify one. What am I doing wrong? 1. y=ln(2x) \ \Leftrightarrow \ y=ln(2) + ln(x) \ \Leftrightarrow \ e^y=e^{ln(2)}+e^{ln(x)} \ \Leftrightarrow \ e^y=2+x 2. y=ln(2x) \ \Leftrightarrow \ e^y=e^{ln(2x)} \...

When I multiply out the first line I end up with an extra (dA/dx)*(dσ/dx). Can someone please show me how i get from the first line to the second. Thanks

So, this is probably really simple...but I keep getting the wrong answer when trying to simplify this: $$3\sqrt{\frac{(10x^3)^2}{(10x^6)^{-1}}}$$Could someone show the steps to simplifying it? Thanks so much. (:

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Determine if the following series is divergent or convergent: ## ∑_1^∞ \frac {(2)(4)(6)...(2n)}{n!} ## 2. The attempt at a solution I understand this can be simplified to: ## ∑_1^∞ \frac {(2^n)(n!)}{n!} ## This can easily be seen to be divergent. But when I...

Homework Statement Hey guys, So I have this equation for the entropy of a classical harmonic oscillator: \frac{S}{k}=N[\frac{Tf'(T)}{f(T)}-\log z]-\log (1-zf(T)) where z=e^{\frac{\mu}{kT}} is the fugacity, and f(T)=\frac{kT}{\hbar \omega}. I have to show that, "in the limit of...

Homework Statement $$ \frac{(2n-1)!}{(2n+1)!} $$ How do you simplify this factorial?

Hi, I've attached a screenshot in which a solution simplifies an expression given x>>a. I have been trying to simplify and express the equation as shown, but keep failing to recognize how they reached their solution. If anyone could provide a step-by-step breakdown that would be greatly...

:mad: I really hate these problems. (2+√7)/(3-√-11). What the heck? I start out by multiplying both sides with the conjugate again. This is where I am stuck lol. Can someone tell me what I am doing wrong while multiplying the conjugate? (3 - √-11) is the same as 3 - √11i correct? So I...

Hello, I'm working with a system of equations that has an infinite recursion function, and am wondering if its possible to simplify or remove the recursion in terms of the other functions in the system. Any insight into the framework or family of this system is appreciated. Given two...

[b]1. Homework Statement [/ Simplify: log base 2 x^2*y^3 Homework Equations I know that log base 2 x^2 * y^3 is log base 2 x^2 + log base 2 y^3 The Attempt at a Solution Here is what I thought: 2 log base 2 x + 3 log base 2 y But that does not seem to be simplified, it...

Hi, I have given a complex feedback system in z domain like: Y = 2*W2 + E W2 = z^-1/(1-z^-1) * (W1 + (1-z^-1)*W2 - 1/2*(1-z^-1)*Y) W1 = V - Y + z^-1/(1-z^-1) * 1/2 * (V - Y) where Y is the system output, V is the system input, W1 and W2 are intermediate nodes and E is an error input...

Homework Statement I'm specifically having trouble with taking the Fourier transform of f(t) in order to sketch F(w) and also to move on with the rest of the problem. Homework Equations f(t) = (5+rect(t/4))cos(60pi*t) mixed_signal = cos(60pi*t) The Attempt at a Solution I attempted to...

Homework Statement Hello, I have an answer to my question but I'm not sure if I've simplified it correctly or if it can boil down further. differentiate; y = \frac{z^{3}-z}{\sqrt{z}} Homework Equations Quotient rule The Attempt at a Solution let u = z3 - z let v = z1/2...

Given the following expression \[ \mathcal{P}_{n}(0) = \left.\frac{1}{2^{n}n!}\frac{d^{n}}{dx^{n}} \sum_{k = 0}^{n}\binom{n}{k}(x^2)^k(-1)^{n - k}\right|_{x = 0}, \qquad (*)...

Simplify $$\frac{\Large 1+\frac{1}{2^a}+\frac{1}{3^a}+\frac{1}{4^a}+\cdots}{\Large1-\frac{1}{2^a}+\frac{1}{3^a}-\frac{1}{4^a}+\cdots}$$ where $a>1$ is a real number.

Find the simplified equation (SOP FORM) corresponding to the following circuit (i.e. apply Demorgan's theorem to bring the negations inside the parenthesis). So is it saying W NAND X which means (w!x!) + YNORZ so (w!x!) + (y!z!) = wxyz?