# 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. ### NPN transistor overheating even when used with appropriate parameters

I have been trying to build a simple Current control circuit using a NPN TIP35C transistor but have run into the problem of it constantly over heating and being destroyed. The transistor is the only component that heats up whilst it is on. The supply voltage is 10V, well below the Max and at the...
2. ### A Is MOND Inadequate for Explaining Vertical Oscillations in Galaxy Motions?

Stacy McGaugh's blog post of 7-Apr-2023: A Few Words About the Milky Way left me gobsmacked. A "few" words? Ha! Here follows my "short" version... Stars in a galaxy don't have just a flat orbit around the galaxy centre. During their orbit they also do small oscillatory motions up and down in...
3. ### I Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction

There is a proof that shows by induction (and by contradiction) that the identity permutation decomposes into an even number of transpositions. The proof is presented in the first comment here...
4. ### The linear spring having even forcing pull/push

How do we have linear spring direction (mostly a spherical spring) to have pull/push force evenly across some points within a range? Or is it possible to create spring material with anomaly property capable of performing so?
5. ### Express a function as a sum of even and odd functions

I am refreshing on this; of course i may need your insight where necessary...I intend to attempt the highlighted...this is a relatively new area to me... For part (a), We shall let ##f(x)=\dfrac{1}{x(2-x)}##, let ##g(x)## be the even function and ##h(x)## be the odd function. It follows...
6. ### Set properties of even (##E##) and odd (##I##) integers

Problem Statement : I copy and paste the problem as it appears in the text (Lang, Basic Mathematics, 1971). Attempt : There are several questions in both a) and b) above. I type out the question and my answer each time. a) (i) Show that addition for ##E## and ##I## is associative and...
7. ### How do you even cheat in chess?

https://www.cnn.com/2022/09/28/sport/chess-how-to-cheating-explainer-spt-intl/index.html
8. ### Problem set with 5 proofs involving odd, even, parity, etc.

help me in my problem set qs
9. ### Show that ## 11\mid R_{n} ## if and only if ## n ## is even

Proof: Suppose ## 11\mid R_{n} ##, given a repunit ## R_{n} ##. Let ## R_{n}=1\cdot 10^{m}+\dotsb +1\cdot 10+1 ## and ## T=(a_{0}-a_{1})+(a_{2}-a_{3})+\dotsb +(-1)^{m}a_{m} ##. Then ## T=(1-1)+(1-1)+\dotsb +(-1)^{m}a_{m}=0 ##. This means ## 11\mid R_{n}\implies T=0 ##. Thus, ## n ## is even...
10. ### B Does a body behave as a point mass even at rest?

Hi, A body with center of mass behaves as a point mass when a force is applied. So when ##F_{ext}=0## then does it also behave as a point mass with ##a_{com}=0##, at rest. If yes, How can we prove this? (And can somebody please answer my other question I posted a week ago...
11. ### But in the end, it doesn't even matter

in the grand scheme of things, our life is an imperceptible blip on the universe's timeline. we are insignificant, and we don't really matter. no matter how successful we are in life, or how our lives end, all our accomplishments will be erased during the heat death of the universe, along with...
12. ### Prove that the Goldbach conjecture that every even integer....

Proof: Let ## n ## be an integer. Then ## 2n=p_{1}+p_{2} ## for ## n\geq 2 ## where ## p_{1} ## and ## p_{2} ## are primes. Suppose ## n=k-1 ## for ## k\geq 3 ##. Then ## 2(k-1)=p_{1}+p_{2} ## ## 2k-2=p_{1}+p_{2} ## ## 2k=p_{1}+p_{2}+2 ##. Thus ## 2k+1=p_{1}+p_{2}+3 ##...
13. M

### Prim's algorithm: pick-up and drop-off locations for packages

This question statement is below, but I can't find out what it's even asking. Any help? [chegg link redacted by the Mentors after the content was posted below. Please avoid posting low-quality chegg links]
14. ### MHB Parity: Show that the sum contains at least one even number.

Hello, guys! I have a question that need help! A number with 17 digits is chosen and the order of its digits is inverted, forming a new number, These two numbers are then added up. Show that the sum contains at least one even number.

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16. ### The given function is an even or an odd function?

I think the answer is an even function as the function ##x^2## is an even function and thus, is symmetrical w.r.t. Y axis. The question I have is how to do this problem algebraically. I tried to graph some functions on GeoGebra to verify my answer. a) ##y = ln(x^2)## b) ##y = sin(x^2)##...
17. ### I When does an even potential give both even and odd solutions to Schrodinger's Eqn?

I don't understand this statement about potential energy V(x) from Griffiths Intro to Quantum Mechanics, 3rd Ed. Problem 2.1c: If V(x) is an even function (that is V(-x)=V(x)) then psi(x) can always be taken to be either even or odd. psi(x) refers to a solution of the Time Independent...
18. ### I Is the odd root of an even number always an irrational number?

Is the odd root of an even number always an irrational number? For example the 7th root or the 11th root, etc. of an even number.
19. ### How can I scan this kind thing, I can't even look up online?

I am not good with smart phone, I know people scan this kind of thing. How can I do it. I did point the phone on it and it did nothing. I must have to load some sort of app. to do that. Can anyone kindly give me some guidance? I don't even know what this call to look online! Thanks
20. ### Can I power things even after Zener breakdown?

I understand that Zener Breakdown occurs when the reverse current starts flowing in the junction because of which depletion region entirely vanishes. Can I power things using this reverse current ? Or will it damage the appliance?
21. ### B Will entropy eventually destroy even an open and efficient system?

I'm no expert but, as I understand it, in an open system, one that can take in energy and matter from outside of itself, the overall entropy level can be prevented from increasing (and can actually decrease) under the right conditions. I have three questions: 1. Can the kinds of quantum...
22. ### Determine whether the given function is odd or even

##f(x)=x^3+3x−1##
23. ### MHB This isn't even funny how hard it is

https://assets.learnosity.com/organisations/154/a4840bb5-1a32-4997-8d1f-28992a862a2b.PNG
24. ### When something is scratched, even slightly

When something is scratched, even slightly, from what I understand by common sense, they would lose its atoms from the surface even if it's trace amount and not possible to measure, is that right? In that case, where do they end up? Are they lost to the air, carried by wind and then combined...
25. ### MHB Finding Even Natural Numbers w/ No Repetition: 0-5 & 6

The number of even natural numbers less than 100000 that can be formed from the digits of the set (0,1,2,3,4,5,6) so that the digits in the number are not repeated is? Here I understand that the even number in the last place is an even number, that is, it has 4 possibilities, but won't the...
26. ### Identity permutation as product of even number of 2-cycles

The book I'm following (Gallian) basically says: r can't be 1 since then it won't map all elements to themselves. If r=2, then it's already even, nothing else to do. If r>2, Then consider the last two factors: ##\beta_{r-1} \beta_r##. Let the last one be (ab). Since the order of elements...
27. ### If the lightest metal around were iron, would aerospace even be possible?

I was reading about an old project I was involved in (X-33), and it got me thinking. It seems that without aluminum (or something as strong per unit mass), modern aerospace vehicles would not be possible. As everyone here knows, the most important design criteria is weight, and iron is much...
28. ### Odd and even extension of sine function

Hi everyone, We've been looking at Fourier series and related topics in online class, touching upon odd and even periodic extensions. However, we haven't looked at what this translates to for sine and cosine functions - only sawtooth and line examples. So, I'm trying to do my own investigation...
29. ### MHB Gre.al.13 sum of even and odd numbers

$\tiny{gre.al.13}$ For which of the following conditions will the sum of integers m and n always be an odd integer.? a. m is an odd integer b. n is an odd integer c. m and n both are odd integers d. m and n both are even integers e. m is an odd integer and n is an even integerI chose e just...
30. ### Is an interpreter without an intermediate representation even possible?

I was reading the page about interpreters on wikipedia and one particular section caught my eye: "An interpreter generally uses one of the following strategies for program execution: Parse the source code and perform its behavior directly; Translate source code into some efficient...
31. ### Powers with fractional exponents that have an even denominator

(If I should have posted this in the Math thread instead of the Homework thread, please let me know.) I have three questions which I will ask in sequence. They all relate to each other. I've typed my questions and solutions attempts below. I've also attached a hand-written version of this...
32. ### Prove that if a is even & b is any positive integer, then ab is even

Proof: Let a be a even positive integer of the form a=2m & b of the form b=2n (This is where b is a even positive integer) ab = 2m*2n = 2(mn) = Let k = mn = 2k Therefore, ab is even. Let a be a even positive integer a=2m & b be a odd positive integer b = 2n+1 ab = (2m)*(2n+1)...
33. ### Prove that if a & b are odd then a+b is even

Summary:: Prove that if a is an odd integer and b is an odd integer then a+b is even. Theorem: If a is odd and b is odd then a+b is even. Proof: Let a and b be positive odd integers of the form a = 2n+1 & b = 2m+1 a+b = 2n+1+2m+1 = 2n+2m+1+1 = 2n+2m+2 = 2(n+m)+2...
34. ### Why does a symmetric wavefunction imply the angular momentum is even?

I looked in the instructor solutions, which are given by: But I don't quite understand the solution, so I hope you can help me understand it. First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...
35. ### B Can You Fall Into a Black Hole? Exploring Time & Decay

It takes infinite amount of time to cross the event horizon from an outsider's perspective. But black holes eventually decay from Hawking radiation. So if you wait long enough a black hole won't exist anymore, as it would have decayed into nothing. The in-falling observer witnesses infinite...
36. ### MHB Why I Can't Stand SAS (and even R)

I found learning SAS to be one of the most infuriating learning experiences of my life. Here's the contrast: I learned basic Python from this webpage in one week. At that point, I was good enough to be productive, and I had learned enough to do the code for TestScript, a LabVIEW/Python...
37. ### MHB Largest Even Integer: Impossible Sum of Two Odd Composites

Find the largest even integer which cannot be written as the sum of two odd composite numbers.
38. ### Other How to get research experience even though I’m in a unique situation?

I received a bachelors degree in physics in 2018 . Due to circumstances out of my control , I did not learn as much physics and math as I should have. My grades were very mediocre , but I realized later that I was being pushed through the system because I was a first generation minority student...
39. E

### Why do we even need the term 'conventional current'?

If we take electric current to be the rate of flow of (signed) charge past a certain point in a given reference direction, this unambiguously tells us all the information that we need to know. If we label a current arrow with ##-6A##, then in ##1## second we either think of a charge of ##-6C##...
40. ### Prove that the set of all even integers is denumerable

Now, set of even integers is ## A = \{ \cdots, -4, -2, 0, 2, 4, \cdots \} ##. We need to prove that ## \mathbb{Z}^+ \thicksim A##. Which means that, we need to come up with a bijection from ##\mathbb{Z}^+## to ##A##. We know that ##\mathbb{Z}^+ = \{1,2,3,\cdots \} ##. I define the function ##f ...

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42. ### B Odd or Even? -1/x: Origin Symmetric?

Is the function -1/x an odd or even function? Is it origin symmetric? For a function to be origin symmetric, must it lie in the 1st and 3rd quadrant or can it lie in the 2nd and 4th quadrant? I suspect it is odd and origin symmetric, but I don't know if I am missing some fine math...

50. ### B Understanding the Odd and Even Nature of sin(x^3)

Hello, would you please explain how to determine if sin ##x^3## is odd or even? Is there anyway to understand it without drawing the graph? Thank you.