even Definition and 664 Threads

I'm going to fail my first proofs class. How do people even learn this!? A bit of cheese with my whine perhaps but I'm more frustrated because I don't know what to do. I am going to fail this class unless I figure it out before our first exam. I read the chapters, take notes, try to understand...

Homework Statement There is a charged wire aligned/centered along the Y 2L in length. A test charge is placed D distance from the wire on the X axis. The wire has a total charge of Q. calculate the integral to figure out how much force the test charge experiences. a semi decent pic of the...

I've been trying to understand some basic stuff about cosmology for years, and I still can't quite get there. I'm not even sure which part of it I'm misunderstanding, and don't know what questions to ask, so I'll just start blasting out the questions and see if anyone can help me make sense out...

Homework Statement Suppose x = (x1, x2, ..., xn)T ∈ Rn is a random vector drawn from the n-dimensional standard Gaussian distribution N(0, I), where 0 = (0, 0, ..., 0)^T (0 vector transpose) and I is the identity matrix. (a) What distribution does ||x||^2 follow? Justify your answer. (b) On...

I know it's a dumb question but I can't figure out why the totient of n is always even (I've read in a book that it "follows immediately from the definition of the totient function", so it should not require any theorem to prove). It is clear to me that it holds true for n = pk, where p is a...

if god is omnipotent, could even he make a rock so big that he could not move himself?

I was at a new year's party and the people who hosted it own a cat. Apparently, I'd been sitting on its chair and I got mewed off. How rude! Stupid creature. Question to you guys: How do you even like cats? They are such arrogant creatures. The look they give you seems to say "Listen human! I...

\varsigma(s) = \sum^{\infty}_{n=1}n^{-s} If you substitute a trivial zero, let's say -2. Wouldn't it be \varsigma(s) = \sum^{\infty}_{n=1} = 1^2 + 2^2 + 3^2 + 4^2 + . . . How would this series be equals to zero? Thanks

Determine all possible even perfect number(s) C such that each of C-1 and C+1 is a prime number.

Homework Statement Given that n independent tosses having probability of p of coming up heads are made, show that an even number of heads results is 0.5(1+(q-p)^n) where q is 1-p, by proving the identity Sigma from i=0 to n/2 of (n choose 2i) (p^2i)(q^(n-2i))=0.5(((p+q)^n)+(q-p)^n)...

Say I get a Ph.D in Physics and hopefully Mathematics as well later. I want to know whether either of them are necessary for this "ideal" job. 1. Very little (hopefully none) social contact whatsoever. 2. Working with very very little people. So I am not really looking to teach 3. Money...

I've always wondered if it is actually possible for the universe, and all of known reality and space-time to suddenly collapse, or cease to exist. Modern theoretical physics points to multiple universes, other dimensions, etc... Is it actually scientifically possible for all of space-time and...

i can't understand the transistor completely i can understand how it works but this stupid conventional current is confusing me completely please can anyone give a lengthy explanation on working of transistor CE CB CC types. i don't understand all these types of transistor i.e how current...

Homework Statement given the equality a2+b2+c2+d2+e2=f2 prove 2 out of the the 6 variables must be even.Homework Equations can use quadratic residues and primitive roots if it helps but don't think i need them. The Attempt at a Solution assume f is even. then f2 is even. and not all 5 numbers...

Homework Statement Its a problem from a foreign book. It sounded simple to me but I am confused now. If V(x), a potential energy function, is known to be an even function, what can you say about wave function for any stationary state? What shall be the expectation value of x for any...

Homework Statement I am to find the partial derivatives fxx, fxy, and fyy off(x,y)=The integral from y squared to the square root of x of cos(t squared) dt Accidentally posted, was editing to get the TEX to work Homework Equations The Attempt at a Solution All rules of integration I know...

Hi, I need to evaluate \int e\stackrel{-(r/R)}{}sin(qr/h)dr between r=0 and r=\infty but I keep getting stuck. I hae tried integrating by parts but the integral just keeps getting more complicated, and I have tried substituting in sin(x) = (1/2i)(e^ix - e^-ix) but that gave me the result...

Homework Statement Integrate the definite integral \int_{-2}^{2}{\frac{x^2}{4+x^6} dx Homework Equations The Attempt at a Solution (1) The integrand f is an even function, therefore: 2\int_{0}^{2}{\frac{x^2}{4+x^6} dx (2) I re-expressed the denominator as...

Hi, I'm sorry if I post this thread at the wrong section. I have a question regarding sequences. Qn: if there is a sequence x(n) = (0.5)^n u(n), find the energies of the latter sequence of x(2n) and x(0.5n). Also, how the even and odd sequence of x(2n) and x(0.5n) relate to those of x(n)...

Homework Statement a) Let k be any integer. Prove that if k3 is even, then k is even. Homework Equations The Attempt at a Solution Proof by contradiction: If the hypothesis is true, then k3 cannot be even if k is odd. Assume k is odd: k = 2n + 1, such that n is any...

Homework Statement Let f(x) = a_{1}\sinx + a_2\sin(2x) + ... + a_Nsin(Nx) where N\geq1 is an integer and a_1, ... , a_N \in\Re. Prove that for every n = 1, ... , N we have a_n = \frac{1}{\pi}\int{f(x)\sin(nx)dx} with the integral going from -\pi to \pi (sorry I don't know how to write...

Homework Statement Suppose g is a function defined for all x > 0 which satisfies the following properties for all a, b > 0: g(1) = 0 g(a/b) = g(a) - g(b) Determine whether the function f(x) = g(x+ root(x^2+1)) is even, odd or neither, and justify your answer. Homework...

Hey guys. I came upon this problem in the professor's recommended problems, and I have no idea how to solve it. After spending an hour on it, I've got nothing. Any suggestions would be much appreciated! A function f : R -> R is called even just in case f(-r) = f(r) for every real number r. f...

is '0' an odd or even number,i mean in my maths book it was given it is neither odd nor even

what is the location of the higgs boson?

Homework Statement 13. (a) Prove that any function f with domain \mathbb{R} can be written f = O + E where E is even and O is odd. (b) Prove that this way of writing f is unique. Homework Equations N/A The Attempt at a Solution (a) Suppose that f is some function with domain...

1.if f and g are odd and even functions , respectively, such that f(a)= b and g(c) = b, b cannot equal 0, then [f(-a)/g(-c)] + f(-a) - g(-c) = A. -1 B. -1-2b C. -1+2b D. 1-2b E. 1+2b 2.if r= 4 sin(angle) is converted to rectangular coordinates , then A. x^2 + (y-2)^2 = 4 B. (x-2)^2...

Before deciding to pursue physics I was on track to complete an A.A. in business admin. As it stands I have 4 more classes If I still wish to do so. However, being that I'm now completely uninterested in anything even remotely related to this discipline, I don't think I can stomach it. I'm...

Homework Statement Let S be a set of Natural numbers with the property that every even number in S is divisible by 5. Which of the following must be true. a. 2 is not in S b. 5 is not in S c. S contains all multiples of 10 d. Every even number in S is divisible by 10 e. S contains no...

Hi, if let's say that there's an even function f(z) then how do we know if its Laurent decomposition (i.e. f(z) = f0(z) + f1(z) ) will be even functions and have even powers of z? Any help will be greatly appreciated.

Homework Statement Suppose that the function f has domain all real numbers. Show that f can be written as the sum of an even function and an odd function. Homework Equations f(-x) = f(x) is even and f(-x)=-f(x) is odd The Attempt at a Solution If g(x) is an even function it can be...

Can the universe itself develop awareness or even omniscience? How could we know?

Homework Statement Prove that every Natural number is either even or odd. Homework Equations Mathematical Induction Even: n = 2k where k is an integer Odd: n = 2k + 1 where k is an integer The Attempt at a Solution I think I have a relatively complete proof, however, it doesn't...

It might be a silly question but I was just wondering if this was unprovable or false... Thanks guys

Hi, I put my question in the attached file... could you please look at it... it is very simple quiestion... thank you :shy:

Homework Statement Let R be a ring and suppose there exists a positive even integer n such that x^n = x for every x in R. Show that -x = x for every x in R. Homework Equations The Attempt at a Solution I solved the case where n = 2. Let x be in R. (x+x)^2= x+x = 2x...

For example, in the double slit experiment, is momentum transferred to say, the wall in between the slits even when the particle manifests on the wall behind the slits? In other words: Is momentum transferred to places where the particle does not manifest? Thanks! Jake

Show that the Cardinality of a set which doesn't include inverse elements from a group G is always even. So the set with all g in G, which includes no inverse elements from G. (g=!g^-1) I can get this in every example I've done, checking mainly with dihedral groups, it's always been true but I...

Hi, I have no idea on how to start to do this question. If the square of an integer is even,then the integer itself is even I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2). Thanks!

Homework Statement A syringe of volume 20 ml has just been used and now lies empty on the doctor's desk. The pressure in the office is 100,000 Pa. Assume that the air is an ideal gas consisting of nitrogen N2 (80%) and oxygen O2 (20%) molecules. k=1.38×10-23 J/K and the molar mass of oxygen is...

Changed to a different question: Can anyone provide a proof for the order of alternating groups |An| = ½(n!)?

I know that GR says that gravity is caused by a curvature in spacetime, but why would matter have to move into the curve, why not just site there on the curve.

Homework Statement A 500 g model rocket is being accelrated at 24.8 m/s/s. How much force is the engine producing? A go cart is producing a force of 750 N. The friction opposing the cart is 600 N. The go cart is being accelerated at 12.6 m/s/s. 1.) What is teh total force causing the...

Homework Statement 1. (top picture) Mass A is 30 kg, Mass B 15 kg, Mass C 5.0 kg. Mass A is 0.50 m away from pivot and Mass C is 1.5 m away from pivot. seesaw at a 30 degree angle from horizontal. Calculate torques of A and C and where B should be placed for equilibrium 2. (middle picture)...

Homework Statement Prove that for all integers n and m, if n-m is even then n3-m3 is even. Homework Equations Definition of even: n=2k The Attempt at a Solution Proof: Let n, m \in Z such that n-m=2k n-m=2k n=2k+m m=-2k+n...

Is there a general formula for the even partial derivatives of a ratio, where both A and B are functions of f? \frac{\partial ^{(2n)}}{\partial f^{(2n)}} \left( \frac{A}{B} \right) Thanks

Homework Statement Let F be the set of all continuous functions with domain [-1,1] and codomain R. Let A be the algebra of all polynomials that contain only terms of even degree (A is a subset of F). Show that the closure of A in F is the set of even functions in F. The attempt at a...

webassign even my ta's didn't know what to do... ?... and I am in intro to physics Homework Statement A 33 ohm resistor is made from a coil of Cu wire whose total mass is 12g. (a)What is the diameter of the wire and (b) how long is it ? ( give you answer in m) Homework Equations one...

Tension on a rope--no idea how to even start. Homework Statement A rope is used to pull a 10kg block across the floor with an acceleration of 3m/s^2. If the frictional force on the black is 50 N, what is the tension on the rope? M=50kg A= 3m/s^2 Frictional force is 50 N. Homework...

Homework Statement It's a modeling question, the question itself doesn't matter because i know how to do, but stuck on one of the equations Homework Equations Q'(t)=15- 3Q(x)/800, Q(0)=2, The Attempt at a Solution I'm stuck at e^(3t/800) *Q(t) = 9/109 *e^(3t/800) +c but the...