even Definition and 650 Threads

Homework Statement Let a\inZ. Prove that 3a+1 is even if and only if (a+1)/2 \inZHomework Equations We know that C is an odd number if there exists: C=2k+1 Even: C=2kThe Attempt at a Solution I think I figured it out, but I'm terrible at Discrete Math, so I was hoping for some input. We...

Homework Statement a 100kg bicycle and rider initially move at 16 m/s up a 15 degree hill. The rider slams on the brakes and skids to rest. The coefficient of friction is (0.8, 0.7) Homework Equations I have a few but nothing to do with a coefficient of friction. The last ones given to...

Homework Statement Show that the only function which is both even and odd is f(x)=0 2. The attempt at a solution Since f(x)=0 is f(x)=0x it is not hard to show that it is odd and even. In order to complete the proof I need to show that this is the only funcion. I know intuitively that if in...

http://www.reuters.com/article/2011/11/11/us-science-meat-f-idUSTRE7AA30020111111 It is only a matter of time until this starts popping up in our food supply. My opinion: Absolutely in no way what so ever would I ever eat this or want the government to allow it in our food even...

Homework Statement For a given periodic function F(x), the coefficients An of its Fourier expansion can be found using the formulas (Form1) and (Form2). Consider a periodic square pulse and verify that the Fourier coefficients are as claimed: An =(\frac{2}{πn})sin(\frac{πan}{λ}) for n≥1 and...

Cheers everybody, the Hamiltonian of an even anharmonic oscillator is defined as H_N(g) = - \frac{1}{2} ∂_q^2 + \frac{1}{2} q^2 + g q^N (N even). In a paper (PRl 102, 011601) I found that to determine the eigenenergies of this system the Euclidean path integral formalism is used. They...

to get a Complex Conjugate of a #, is it ok to just replace i by -i even in denominator or inside argument?

Is there anything in the physical world that is actually random even after we were given every single bit of information needed to calculate an outcome? Rolling a die or flipping a coin doesn't count, because if we did all the calculations, we would be able to calculate what the outcome would...

Can someone please help me with a Fourier series equation for a even square wave shown below: F(t) = 0 when -2ms <t < -1ms k when -1ms <t < 1ms 0 when 1ms <t < 2ms T=4 Im after finding the first 10 harmonic components. To be honest struggling with...

I like to know in one dimensional symmetric potentials, can we have any even wave functions which be zero in the origin?

In the symmetrical potentials the Eigenstates are either even or odd. why the even states have less energy than odd states?

What I mean is are there things traveling so fast in outer space that we don't exist in their FoR? Or we haven't even been born yet in their FoR?

Homework Statement A function f is an even function is f(-x)=f(x) for all x and is an odd function is f(-x)=-f(x) for all x. Prove that the derivative of an odd function is even and the derivative of an even function is off. I get what even and odd functions are but I'm not sure how to...

Here's my situation. In the math program now. Finding it's ok.. Not the best. Just ok.. I'm wondering if i should just join the army instead. Alot of my time, i think about getting laid or how to get into a girl's pants. I'd rather be doing jiu jitsu, mma and salsa than math sometimes. If i...

Am I correct in thinking exp(−x^2 ) is an even function? Thanks

I watch a lot of cooking shows and the misuse of the term au jus drves me crazy. In the last 30 minutes 8 people have misused the term 20 times. Au jus means "with juice", you can serve something "au jus" but you cannot serve something "with au jus", you cannot make an "au jus", AAARRRGHH...

A function f is an even function is f(-x)=f(x) for all x and is an odd function is f(-x)=-f(x) for all x. Prove that the derivative of an odd function is even and the derivative of an even function is off. I get what even and odd functions are but I'm not sure how to rigorously prove this. Thanks.

I got confused.. XD "Under Einstein's theory of relativity, an object accelerated close to the speed of light gains a tremendous amount of mass.That is why no amount of energy can suffice to accelerate any object, even an elementary particle, to the speed of light - it becomes infinitely...

This really surprised me. >> format rat >> 1/3-1/2+1/6 ans = -1/36028797018963968 Even school student knows that the answer is 0. Even format short does not give a correct answer. >> format short >> 1/3-1/2+1/6 ans = -2.7756e-017

I have been given a problem to make a problem for x!. The only restriction is, "But omit odd numbers given x is even" Another is for x! is, "Omit even numbers, x is divisible by 3". Is it even possible? I've thought of several manners, but I don't think I'm correct. Thanks in advance...

If I was in a bio class, I wouldn't even complain. But physics? My teacher does not teach why things work, just throw random formulae and show how to 'plug-in' values. I know one must learn a skill to deal with this type of teacher but I have never had this kind before. How did you cope with...

Hi, I'm not sure this should go in homework of here as this was a test question, but the question itself isn't a test question. I got this question marked wrong, for the record. Question For each statement below, determine if the statement is true or false. If true, provide a proof...

I've got a shaft that rotates at about 1 rpm and handles a radial load of approximately 25 lbs, a thrust load of 17 lbs, and a bending moment of about 150 lb-in. The shaft and joint will be submerged in lakewater. A shaft diameter of 1.5 in would be nice, but in general a larger shaft would be...

Homework Statement For every non-negative integer z, z2 - 3z is an even integer. Prove this statement. So far, I have learned about direct proofs and indirect proofs such as contraposition and contradiction. Homework Equations An integer z is odd when there is an integer a so that z = 2a+1...

Homework Statement For a,b, \in Z, prove that if ab is odd, then a^2 + b^2 is even question 1 ab = 2k + 1 for some k is integer (1) It doesn't seem logical to rearrange some a and b on (1) So I need the following product of two odd numbers is always odd,product of two...

Homework Statement Two skaters, one mass 65kg and one mass 40kg, stand on an ice rink holding a pole of length 10m and negligible mass. Starting from ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 40kg skater move? Homework Equations...

Hi guys, I am noobie in number theory so if something exists better than this equation I did please don't bash me this is my first equation. Today I was thinking of a way to count all even from 1 to n,so this way I thought about is like this. Let me first write the equation,then I will...

So high school was easy. I didn't go to an elite high school like many people at my university, but senior year I took 8 ap credits and got by with minimal work. BC calc was easy. I thought it was interesting though...and I thought I was good at math. but I'm not. I found that out quickly in...

Homework Statement Show for any metric space (S,d) and  e> 0 that N(e, S) <=  D(e, S) <= N(e/2, S) Homework Equations none The Attempt at a Solution Can somebody please tell me what does N(e,S) or D(e,S) even mean so I can at least know what I am asked to prove? I dig...

1. Homework Statement : A function f : R → R is called “even across x∗ ” if f (x∗ − x) = f (x∗ + x) for every x and is called “odd across x∗ ” if f (x∗ − x) = −f (x∗ + x) for every x. Define f (x) for 0 ≤ x ≤ ℓ by setting f (x) = (x^2) . Extend f to all of R (i.e., define f (x) for all real x)...

show that the square of any odd integer is odd, use this fact to justify the statement "if p2 is even , then p is also even

Complex analysis gives us theories about functions that u can't get without the complex algebra, could there be an extension to complex numbers that might solve important problems in mathematics.. Thanks to all..

Homework Statement [PLAIN]http://img703.imageshack.us/img703/8599/physicsks.png Homework Equations I'm considering cross product and dot product rules, yet I don't know where to begin with this one. The Attempt at a Solution I have two pages of scratch paper that is littered with...

1)-why is x(t)+x(-t) always even??..no matter if x(t) even or odd? 2)-when we talk about unit step function...u(t)..and we add..u(t)+u(-t)..the value of both is 1 at t=0..so does'n't that gets added twice??..and it becomes 2 at t=0... 3)when we have x(-t) and we time shift it say x(-t-3)...

1)-why is x(t)+x(-t) always even??..no matter if x(t) even or odd? 2)-when we talk about unit step function...u(t)..and we add..u(t)+u(-t)..the value of both is 1 at t=0..so does'n't that gets added twice??..and it becomes 2 at t=0... 3)when we have x(-t) and we time shift it say x(-t-3)...

some times I am kept awake till like 1am, oops sry spelling error.

Do you dream constantly? Does "dreamless sleep" even exist? We know that... We can dream in all 5 stages of sleep (not just REM) We move around very often throughout the night (all in nREM since you're paralyzed in REM) Memories are sorted out constantly in all stages of sleep. And if you...

Given that \zeta (2n)=\frac{{\pi}^{2n}}{m} Then how do you find m with respect to n where n is a natural number. For n=1, m=6 n=2, m=90 n=3, m=945 n=4, m=9450 n=5, m=93555 n=6, m=\frac{638512875}{691} n=7, m=\frac{18243225}{2} n=8, m=\frac{325641566250}{3617} n=9...

The media is always seeming to portray it like http://tvtropes.org/pmwiki/pmwiki.php/Main/NuclearPhysicsGoof" waiting to go off. Now I've done a fair amount of research into nuclear power and it's readily apparent to me that this is not the case. I was wondering what, if any circumstances...

I can't tell whether this guy is serious... https://www.youtube.com/watch?v=AYEzhRbVDC0 or... https://www.youtube.com/watch?v=794i35FBPog

Hi, New member, first post. Is a Grand Unifying Theory even possible? If there is evolution on our planet, why would there not be an evolution of the laws of the universe? What we theorize, test and measure may be true of our universe at this time point, but could it not be that at...

I can't even find words on how to ask this question. My father brought it up to me and I don't know how to answer it... I am at a fixed location you take off at near light speed away from me, 5 years later I look up in the sky and you would almost be 5 light year away from me. Now because...

Odd number of terms so there is a middle term. It is equal to 0. Since C(n,k)=C(n,n-k), abs(k/n - 1/2)=abs([n-k]/n - 1/2), and what's in the abs() increases and is positive k goes from 0 to n/2 -1, the sum is twice the sum of the first n/2 - 1 terms, 2*(1/2 - k/n)*C(n,k). Added C(n,k) from 0...

Hi! I have calculated various eigenstate wavefunctions for a one-dimensional system of a particle in a potential. The potential is an even function. All the wavefunctions have become either even or odd functions which I understand why. The ground-state wavefunction has always been even, is...

Homework Statement Prove: If a and b are prime numbers larger than 2, then a + b is even. The Attempt at a Solution Can i just say that prime numbers larger than 2 are odd and then prove that the sum of 2 odd numbers is even. And can i say that prime numbers larger than 2 are odd because...

I am illustrating this via both questions and an experiment both of which are conceptually are dealing with the same idea. http://en.wikipedia.org/wiki/Coincidence_counting_(physics ) Question: 1 a) if there were zero noise, and only single photon was sent, do we need a co-incidence...

This is in my book: exp[2\pi i(hx+ky+lz)][1+exp(\pi i(h+k+l))]=2exp[2\pi i(hx+ky+lz)]\cos^2[\frac{\pi}{2}(h+k+l)] And in order for the cosine not to be zero, h+k+l must be even when we want to see the reflection. But I think that the result should be exp[2\pi...

take a cunductive wire. coil it (for conventional space) then run electrons through it with 8.98755179 × 10^16 J (the same number for the speed of light squared) of energy. ( i realize that doing that is nearly or completely impossible). using the equation m=e/c^2 e and c^2 are the same...

Homework Statement Prove by direct proof that 5x-3, where x is an integer, is odd for all even x. Homework Equations N/A The Attempt at a Solution Let x=2a, where a is an integer. It follows that 5x-3=10a-2-1=2(5a-1)-1. Although it is obvious, I don't know how to logically prove...

Hello all, I am about to go into my 2nd year at my university and all I can say is that my first year was incredibly stressfully and filled with depressing downturns. Here it goes: 1.) I did not pass any placement exams for the maths (was not paying attention in High School) and was unable to...