I feel everyone knows the answer to the riddle, “You walk one mile south, one mile west, and one mile north. You end up exactly where you started. Where are you?” The answer is the poles of the Earth which is an interesting way to get thinking about non-Euclidean geometry.

I was wondering, if you assume that Earth is a perfect sphere, why would this answer not be true at any point on the Earth’s surface and not specifically have to be the poles?

I made this question in school

Question is simple. Just finding the red angle
ABCDE is a right pentagon and EFGD, CIHD are squares.

I am finding a solution without computing and approximation.

I'm holding this for over a month please help me

I've tried using congruence and similarity and none helped

Let's suppose I play a fair game of Russian roulette.

We only play 1 round, if the 6-shot gun doesn't fire for me nor my opponent the game is a tie.

After a coin toss it is decideded I play second. The barrel is rolled, the bullet has an equal probability to be in the first or second slot, both at 1/6.

My opponent plays and lives, it's now my turn.

May I request the barrel to be rolled again or would it make the game unfair ?

I know it's fine, but what bothers me a bit about Faà di Bruno's formula is that its analytical expression is not entirely explicit in a closed way because the summation does not have clear defined limits and makes it somewhat ambiguous and leaves something to mathematical convention and I would like more to know if there is an explicit analytical expression of formula, because it would be useful to me. I don't know if it is possible or if there is some other more explicit version or another type of expression of formula that fixes that, it would be excellent for me

Bonjour. Je suis élève en première qui aime bien faire des exercices hors-programme. Voici mon premier exercice (que j'ai trouvé sur le Web) et ma résolution, où il faut faire une récurrence forte.

Je me demande si j'ai bien redigé? (Il m'a pris environ 35 minutes de réflexion. J'espère m'améliorer.)

J'apprécierais tous vos remarques et conseils.

I just got out of highschool and I am interested in how to formally write a mathematical solution. This is a problem I tried to solve and I want to ask a few questions:

1. Is my solution valid and rigorous? Let me know what my mistakes are

2. Is my way of writing the solution formal enough? What words, phrases, symbols, or anything, can make the tone more formal?

3. What can I do to improve my ability to write solutions/proofs formally?

okay so on the top of the first image is the original problem, where I'm supposed to find the zeros of f composed of g. I've found that f(g(x)) is (x^2-10)^3 + (x^2-10)^2 - 100(x^2 -10) - 10 which after expanding the binomial and trinomial and then simplifying comes out to x^6-29x^4 -180x^2 and I confidently understand how we got there. then in step 7 it tells me to find the zeros by solving for (f(g(x))=0, and we see it sets up x^6-29x^4+180^2=0, then it says to start by factoring out x^2 which makes it x^2(x^4-29x^2+180)=0. I understand the process here like I get how we factored that out I just don't know why we're doing that, like Idk why I couldn't have just left it as is, but anyway I get the process of that step so whatever. Then we move to step 8 where it says to "set each factor equal to zero. solve for x" and I just straight up don't understand the expressions beneath that, like first off why are we setting both x^2 equal to 0 and x also equal to 0? and next to each of them it says "or [expression]" which is where I'm really lost. where did x^4-29^4+180=0 come from?? in the previous step 29x has the exponent 4 BEFORE we factored out x^2, but now with x^2 on the outside of the parenthesis how is the 29x on the inside to the fourth power instead of squared? also both expressions next to "x^2=0" and "x=0" are the exact same. like i followed everything clearly up until step 7 and 8. 8 I'm entirely lost on, I've tried solving it on my own, I've tried googling tutorials, I've asked my friends, i'm still lost.
And yes this is an example problem and yes it does technically give me the correct answer at the end of these steps but I need to understand how we get there so I can do it myself to solve my actual homework problem. I've done composite functions before without trouble, but this is my first time encountering a composite function that's asking me to fine the zeros.
Can anyone break down step 7 and 8 for me step by step to help me understand what the hell is going on here?? any help would be greatly appreciated. Last image is just me showing my work of correctly following everything up to step 7.

A podcast I listen to, "A Problem Squared" (ep. 146), recently answered this question and I'm trying to see if I understand it correctly.

Assumption 1:

0.0499999.... = 0.05.

Assumption 2:

If a number is rounded to the nearest place value, you add 1 to the nth place to be rounded off if the digit to the right is 5 to 9, you truncate if 0-4.

Therefore

0.449999 = 0.45

Rounded to the nearest tenths, it is equal to 0.5.

Is this correct?

Thanks!

And suggest videos/tutorials, please.

I do pop-up books, and I have a tutorial I really want to follow. But the tutorial's shape and my desired is not the same. For one, the tutorial is based on a square; I need a thinner rectangle to fit into a notebook. So my question is, what's it called when you scale something up or down, and what's it called when you change its shape in addition to scaling it up or down? The problem with pop-up books is that you have to keep some of the 'gears' the same while changing the areas for others. While retaining the same functions.

PLEASE suggest tutorials for this type of math

I'm working through the Book of Proof.

Exercise 1.4 asks that we write listed sets by listing their elements between braces.

The set for #11 is { X ∈ P({1,2,3}) : |X| ≤ 1 }

My answer was { ∅, {1}, {2}, {3} }

But the textbook's answer is { ∅, {∅}, {{1}}, {{2}}, {{3}}, {{1,2}}, {{1,3}}, {{2,3}}, {{1,2,3}} }

It seems to me this would be correct for { X ∈ P(P({1,2,3})) : |X| ≤ 1 }, but not { X ∈ P({1,2,3}) : |X| ≤ 1 }

Thoughts?

Long story short, I was in care as a child and now while I'm at university, the social services pay £135 of my £186 p/m rent. This year, because of the government I'm having to pay in monthly installements (as opposed to previous years where you pay a lump sum per term).

The problem is this: I can get the social services to pay their part 3 months in advance (£405). So that should cover 2 months of rent, and then by the 3rd month I'd be outstanding £72. But then I get the social services to do it again. And then when I eventually in the summer next year, I'd have to pay the last three months, right? So the question is, how long can I do this until I'd eventually have to pay?

I've tried to solve this so far by doing (744×2)-(540×3), with 744 being a total month's rent, 540 being how much the social services pay and then the other two numbers are the months. But I'm not really getting a visual sense of how long I can do this for.

Each standard deviation is 15 numbers above the mean if that’s what it’s talking about. For MENSA I would expect this to be more clear.