Natural Definition and 1000 Threads

Hello everybody I have a mass production project for a new product . The thing is to be made in foam , sheets...it is some material involved . To visualize the idea think about the Yoga mat sort of material but much thick.. Natural or Synthetic ?..provided there is to be found a natural...

Homework Statement Given M \in N, show that there exists an X \in N such that for all n \geq X , n^2+n+1 \succ M Homework Equations The Attempt at a Solution Since both M and X are natural numbers and I am just trying to prove the existence of a certain natural number X, I...

It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?

Homework Statement I am trying to calculate the natural frequency of a steel beam. Homework Equations I=1/12*W*T^3 Volume= T*W*L M0=V*ρ K=(3EI/L^3) Meff=(33/140)*M0+Mend ωn=√(k/Meff) The Attempt at a Solution This should be a simple plug and chug problem but I can't see what...

Homework Statement Solve for x xln(x)-24+6ln(x)-4x=0 My attempt at the solution I first moved "-24" and "-4x" to the right side of the equation yielding xln(x)+6ln(x)=24+4x I then converted the natural logarithms to exponent form and product form yielding ln(x)^x+ln(x)^6...

Homework Statement N refers to the set of all natural numbers. Part 2: From the previous problem, we have σn : N → N for all n ε N. Show that for any n ε N, σ(n+1)(N) is a subset of σn(N), where we have used n + 1 for σ(n) as we defined in class. 2. The attempt at a solution For Part 2, I...

Any information on the following formula for natural logarithm (I looked in wikipedia and Mathworld but didn't see it). It came from another equation I was working on a bit ago, and I was curious about it as I didn't recall seeing it before (which doesn't mean I haven't), although it reminded...

Homework Statement I wish to find the following integral over the rectangle [-a,a] in u and [-b,b] in v using Mathematica. The constants a and b are positive (and non-zero). The variables x and y are in Reals. A(x,y)=\int_{-a}^a{\int_{-b}^b{\log{\left[(u-x)^2+(v-y)^2\right]}{\rm d}v}{\rm...

I have a spring-mass system with 200 masses and 199 springs. All masses are 100 tonnes and stiffness 20 MN. The boundary conditions are fixed-free. I have constructed a lumped mass matrix and stiffness matrix and calculated the lowest natural frequency. Including the boundary conditions I...

Is the following relationship true?: \frac{\partial (ln(k))}{\partial P}=\frac{1}{k}\frac{\partial k}{\partial P} I am getting both of these terms from a paper on mineral physics and they seem to use both terms interchangeably. If so, how are these related?

Hi I am using Ansys to find the natural frequency of a structure but this has meant that my understanding of vibrations has become unstuck. When I last studied natural frequencies, it was under free vibration. I formed the impression that one structure can have only one natural frequency...

Homework Statement Show that \frac{1}{x} \ln \frac{x+1}{x-1} = \sum_0^\infty \frac{2x^{2n}}{2n+1}. 2. The attempt at a solution I tried to use the relation \frac{1}{1+x} = \frac{d}{dx}\ln (1+x) and expand as a geometric series, but this did not lead anywhere since I then ended...

What is the meaning of a frame of reference where $c=1$ ? Are these the so called natural units?? And which is the purpose of this??

Hi I want to rewrite the following equation in terms of t: X=\exp(-At)-\exp(-Bt) Where X,A and B are positive numbers. The problem is, I have a -exp() term... so I can't take the natural log of this... ie. as far as I am aware the following is not allowed: \ln(-\exp(-Bt)) So...

1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test. 1...

Homework Statement Prove that the product of any three consecutive natural numbers is divisible by 6. Homework Equations The Attempt at a Solution wat

Homework Statement Calculate the following: \int^{-4}_{-6} (x^-1+5x)dx Homework Equations The Attempt at a Solution I've worked this down to ln(-4) + 5(-4) - ln(-6) - 5(-6) =ln(-4)-ln(-6)+10 The answer to the left half (the ln parts) of the equation is undefined, and the...

Homework Statement State and prove a natural generalization of "prove that for any three positive real numbers x1, x2, x3, x1/x2 + x2/x3 + x3/x1 \geq 3. Homework Equations AG Inequality is used in subproof (x1/x2 + x2/x3 + x3/x1 \geq 3) The Attempt at a Solution I don't know what...

Homework Statement Find the integral to the following expression \int\frac{1}{x-1}dx Homework Equations \int udv = uv - \int vdu \int\frac{1}{x}dx = ln(x) The Attempt at a Solution Given the information above, would a correct answer to this problem be ln(x-1) ? If not...

Homework Statement Differentiate, f(x)=71+x/1-x Homework Equations The Attempt at a Solution Working this out, hoping it's right as I was going along, my final answer is 71+x/1-x * (2ln7)/1-x

when we talk about the phenomenon of resonance, we use the term 'natural frequency'. What actually is natural frequency of an object?...what is meant by matching of natural and applied frequency and why does it produce vibration with maximum amplitude?

natural log helpp! Homework Statement ln(x+10)+ln(x+4)=2 2. The attempt at a solution okay so i took it down to (-14+-(14^2 - 4(e^2 - 40))^1/2) / 2 which i broke down to 356 - 4e^2 inside the sqrt. am i on the right track and if so Whats the next step?

Black holes are believed to be scattered throughout the universe. These ultra-dense bodies have a gravity field so dense that nothing, not even light can escape. If these bodies are able to consume everything that enters its event horizon than over the billions of years that the universe has...

so I've got this equation down to x*ln(2/x) = 5 Can someone show/point me to a page where I can see how to solve this. I am under the impression it requires some type of ratio computation. thanks!

A mass m is confined to move in a channel in the x-direction and is connected to four identical springs with spring constant k, which are oriented at angles \phi = 45° as shown, if the system is in static equilibrium. a) Ignoring friction, determine the natural frequency of vibration of the...

A fundamnetal question here; IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?

How do we formalize the following: For all natural Nos : n^2 is even\Rightarrow n is even

I believe that Fibonacci primes are infinite. Currently there is no proof that there is an infinite number of Fibonacci primes. I was wondering why we couldn't compare the set of Fibonacci primes to the set of Natural Numbers and demonstrate that both have cardinality aleph null? Indeed, why...

Color Rendering Index is said to measure the extend to which lights behave as natural light .It is said that Incandescent have CRI of 100 and Florescent have around 60-70. However, I find the lights from Incandescent yellow-reddish and I find that objects are rendered yellowish on its light. I...

Hello everyone. I am the author of "Wormwood Forest: A Natural History of Chernobyl" and stumbled upon your very interesting forum when googling Genn Saji, a Japanese nuclear scientist who has been sending out daily email updates about Fukushima. I am fortunate enough to be on his list and...

How is the net driving pressure difference within a PWR a function of T and H delta P = delta T(Core) * g * partial Rho(T, P(RCS))/partial T * delta H I get how this correlates to the pressure differential and is found with bernoulli's equation but how does the temperature dependence get...

Homework Statement Prove by natural deduction ((X \Rightarrow ¬Y)\vee(¬X\RightarrowY))\Rightarrow(¬(X\wedgeY)\wedge¬(¬X\wedge¬Y)) Homework Equations The Attempt at a Solution i understand basic natural deduction and how to prove via it but this one has me stumped as there is no...

Homework Statement Prove by both natural deduction and by resolution ((X \Rightarrow ¬Y)\vee(¬X\RightarrowY))\Rightarrow(¬(X\wedgeY)\wedge¬(¬X\wedge¬Y))Homework Equations The Attempt at a Solution as far as natural deduction on this goes i have no idea since there is no ' I- ' looking symbol so...

Find the largest natural number m such that n^3 -n is divisible by m for n element N. Prove your assertion. How exactly do you begin this im thinking the largest m could possible be is n^3 -n, but I am not sure. To be divisible we know that mk=n^3-n for some k

Hi, I was reading Lemon's Perfect Form and it talked about "natural boundary conditions". But I don't understand exactly how one determines them. It seems to me that one imposes some random condition then deduce stuff from it...?! Advanced thanks for any enlightenment!

Homework Statement Describe Lack's experiments with Swiss starlings, and state what these experiments tell us about the effect of natural selection Homework Equations Lack's studies / experiment was that he marked the nestlings of the starlings and then he recaptured them months later...

Most public intellectuals who are critics of society and speak out about their knowledge often come from the social science realm. Why aren't there any from the hard sciences?

i have a basic question about the natural frequency of a system. for a mass (M), spring (k constant) undamped system the natural frequerncy is: w_n=sqrt(k/M) the units of w_n according to a lot of resources i found on the internet & textbooks are [rad/sec], my question is why? if i use...

Hey, I was having this very silly problem in heat transfer. Please could you see what's going wrong ! I am working on defrost water tray modelling. In that, the water collected during defrost is heated by the compressor o/p coil so as to aid evaporation. I was trying to find out the heat...

I found two different versions of equations to find natural frequency of a cantilever beam. I am not sure which one is right. I would appreciate if someone could make things a bit clear here F1= k^2*sqrt(E*I/(mpl*L^4))/(2*pi) where k=1.875 for first natural freq and I= b*d^3/12; OR is...

Homework Statement Let log z be the principal branch of the logarithm function defined −pi < arg z < pi the domain to define f(z)=loglog z?? Homework Equations The Attempt at a Solution I already know how to represent the arg z by arctanb/a+2pi*k how can I get arctan [Re (log...

A natural draught cooling tower is designed to have a 3% loss of the mass of the water entering the tower by evaporation into the atmosphere. Atmospheric air enters the tower at a volume flow rate of 4 m^3/s a temp of 10C and a relative humidity of 50%. Air leaves the tower in a saturated...

Hi all ! i want to know some of the devices that measure natural frequency of solids/vessels, etc ! with regards! take care !

Homework Statement [PLAIN]http://img840.imageshack.us/img840/553/unled0016.jpg Homework Equations The Attempt at a Solution can you sujjest me some articals to read (what knowladge do i need) before attemptiong this question?

Homework Statement For every epsilon > 0, there exists an N\in N such that, for every j >= N, |f(i,n) - g(n)|<epsilon for every n\in N. In addition, for every fixed j\in N, (f(i,n)) converges. Prove that (g(n)) converges. Homework Equations f: N x N --> R, g: N --> R The Attempt at...

natural isomorphism from V to V** It is known that there is a natural isomorphism \epsilon \rightleftharpoons \omega^\epsilon from V to V**, where \omega: V \times V* \rightarrow R is a bilinear mapping. So given a certain \epsilon \in V, its image under the isomorphism is actually a set of...

I downloaded the Crysis natural mod, installed it, and not only does the game look mind-blowingly spectacular, But I think the framerates increased very slightly. Beforehand, playing Crysis on very high spec/1920x1080 gave me 25-45 fps. Now it's at 35-60+ fps with the natural mod installed. Did...

SORRY FOR THE LACK OF FORMATTING, I SPENT 30 MINUTES TRYING TO FORMAT AND IT KEPT GETTING MESSED UP. Homework Statement Evaluate by substitution. Integral of dx/xln(x^2) Homework Equations integral of 1/u du = ln(u) + C The Attempt at a Solution u = ln(x^2) du = 2/x...

Homework Statement Evaluate the derivative of the following function: p(x) = (5x)-ln(5x) Homework Equations \frac{d}{dx}lnx = \frac{1}{x} Not sure what else... The Attempt at a Solution I know that I will have to use the chain rule in this problem, but actually...

Hi everyone, Say, I was wondering if you could explain something to me. I have two examples to share: 1) I drive by several enclosed bus stops on my way to work. The enclosure consists of a solid roof, but the sides are a metal mesh screen with circular holes less than the diameter of my...