What is even: Definition and 664 Discussions

The break-even point (BEP) in economics, business—and specifically cost accounting—is the point at which total cost and total revenue are equal, i.e. "even". There is no net loss or gain, and one has "broken even", though opportunity costs have been paid and capital has received the risk-adjusted, expected return. In short, all costs that must be paid are paid, and there is neither profit nor loss. The break-even analysis was developed by Karl Bücher and Johann Friedrich Schär.

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  1. STEMucator

    If a is even, prove a^(-1) is even

    Homework Statement If a is even, prove a-1 is even. Homework Equations We know that every permutation in S_n, n>1 can be written as a product of 2-cycles. Also note that the identity can be expressed as (12)(12) for this to be possible. The Attempt at a Solution Suppose a is a permutation...
  2. Y

    MHB Odd/Even Functions: Check Symmetry over Y Axis First

    Hello I have a theoretical question. When I check if a function is odd or even, I usually check: f(x)=f(-x) or f(-x)=-f(x) someone told me today that before checking it, I first need to check the symmetry over the Y axis, and if the function is not symmetric over Y, there is no point of...
  3. D

    Prove that the square of any integer, when divided by 3. only by odd and even.

    Homework Statement I know you could prove this by stating every integer is either 3m, 3m+1 or 3m+2. However I am trying to prove this just using either even numbers or odd numbers. so for example, when I try: (2x+1)^2 = 4x^2 + 4x + 1 - expand = 3x^2 + x^2 + 3x + x + 1 - group like...
  4. V

    Hardly even understand problem statement.

    Homework Statement Let f: R → P(R) given by: f(x) = {y ∈ R; sin y < x}. If A is such that f(x) = R for every x ∈ A, then: (i) A = [-1, 1]; (ii) A = (-∞, a] for every a < -1; (iii) A = [a, ∞) for every a > 1; (iv) A = (-∞, a] for every a ≤ -1; (v) A = [a, ∞) for every a ≥ 1...
  5. Government$

    Determine if Even or Odd: (x^2|x-1|)/(SQRT(x-1)^2)

    Homework Statement Show that function is even or odd: (x^2|x-1|)/(SQRT(x-1)^2) Homework Equations The Attempt at a Solution (-x^2|-x-1|)/(SQRT(-x-1)^2) After this i don't know how to procede.
  6. R

    Is the particle still moving at point C?

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  7. marcus

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  8. F

    Why is it not possible for the columns of a matrix to span R^2 even if

    Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?
  9. T

    Can someone please integrate this (hard) (not sure if even possible)

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  10. D

    How Did Einstein Manage To Even Come Up With The Theory Of Special Relativity?

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  11. D

    MHB Prove Evenness of Poisson Kernel for Fixed $r$

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  12. K

    News Extradition of Abu Hamza - is it even a news story in the USA

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  13. I

    Can an even number of Fermions be a Bosonic system?

    Hi everyone, I've just done a problem where we are dealing with two protons with the same spin directions and the system is treated as a fermionic system. I always had the notion that two (or an even number of) fermions, for opposite spin perhaps, act as bosons. Is this true? If so, when...
  14. M

    Prove: Rational Number Squared Has Prime Factors w/ Even Exponent

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  15. R

    Decompose Even & Odd parts of a function?

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  16. R

    Proof that ratio of the products of odd and even numbers converges

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  17. M

    Proving the Energy of Even and Odd Signals

    Hi everyone, In my signals assignment, I'm asked to show that, for a continuous time, real-valued signal x(t): Ex_even = Ex_odd = 0.5 * Ex So here's what I've done: Ex_even = ∫|(x(t) + x(-t))/2|²dt Ex_even = 0.5 * ∫|(x(t)² + 2x(t)x(-t) + x(-t)²)/2|dt Ex_even = 0.5 * [ 0.5 *...
  18. L

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  19. L

    Continuous time signals - Causal signal given even part

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  20. M

    Proof that if 32 -|- ((a^2+3)(a^2+7)) if a is even

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  21. D

    MHB Solving Even Function Integrals: $a_0$ & $a_n$

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  22. J

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  23. C

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  24. D

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  25. L

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  26. N

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  27. M

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  28. S

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  29. R

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  30. L

    MHB Can Division Even Be Allowed In Math If It's Flawed?

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  31. B

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  32. H

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  33. G

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  34. R

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  35. P

    OK to transfer in the middle of undergrad, even if it takes an extra year?

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  36. T

    Even and Odd Eigenfunctions in Sturm-Liouville Problems

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  37. C

    Even though we have enough calorie for day, why are we still hungry?

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  38. M

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    So Euler derived the analytic expression for the even integers of the Riemann Zeta Function. I was wondering if there is a link to his derivation somewhere? Also, is there anyone else who used a different method to get the same answer as Euler? Thank you
  39. N

    Finite difference method for even potential in QM

    Hello to everyone, while solving homework course Nanotechnology and Nanocomponents, I have encountered a problem in FD method that is applied in even potential. In my homework assignment it is explicitly said that it must be done only in x>0 part of the domain, where my problem starts with...
  40. aleemudasir

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  41. P

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  42. N

    Even Differentiable Functions and Linearization

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  43. R

    Prove that every natural number is either even or odd.

    Hello, I'm re-studying calculus using Spivak's Calculus 4ed and I'm stuck in one of the problems. Any help is appreciated. Homework Statement The theorem to prove is "every natural number is either even or odd". The definition of even given by Spivak is the following: A natural number n is...
  44. C

    Evaluating Double Integrals of Odd and Even Functions on a Disk

    Homework Statement Suppose f : ℝ→ℝ and g : ℝ →ℝ are continuous. Suppose that f is odd and g is even. Define h(x,y) : f(x)*g(y). Let D be a disk centered at the origin in the plane. What is ∫∫h(x,y)dA? D The Attempt at a Solution I know there's probably a trick to it. Is it 0...
  45. R

    Discrete Fourier Transform of Even Function

    I'm confused about the DFT of the data, fn = cos(3\pin/N) for n=0,1,...,N. It is definitely an even function, and I read that the Fourier coefficients of an even function is real. But when I take the FFT of this in Matlab I get complex numbers, not real numbers. What am I missing? Thanks ...
  46. H

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  47. T

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  48. D

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  49. C

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  50. Femme_physics

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