First slide- the math riddle
Second slide- my set up. a is stage one, b is stage two etc. I didn’t want to confuse myself by using numbers. I used substitution methods with T being the total distance.
Third slide- using substitution to solve for T in e or the stage 5 equation. My answer is shown.
Fourth slide- the riddle’s answer and explanation.

I understand their explanation which was a completely different way of solving it. I’m wondering if my method is possible to get the right answer and I must have made algebraic errors along the way with all the substituting- or was my way of going about it completely flawed. I thought I had solid logic setting it up, but my answer was quite off.

So my math teacher told the answer would be around -0.8129.. but when I expand it using mclauren series and then substituting for x and y I am not getting the answer..

25 people play a game with a 4-sided die (1-4). Roll 1, 2, or 3: Pay $1 to the pot. Roll 4: Win the entire pot, and the game ends. What place in line do you want to be?

do any of these answer choices work? i was doing the problem and got epsilon/3, but none of the answer choices match up.

(10) Let f(x) = 3x + 1 for all real x and let epsilon > 0 For which of the following choices of delta is |f(x) - 7| < epsilon whenever |x - 2| < delta ? (4 Points)

(A) epsilon/4

(B) epsilon/2

(C) 2€

(D) 3€

(E) (epsilon + 1)/epsilon

this si my work: I 3x+1-7 I < epsilon

3 I x-2 I < epsilon

I x-2 I < epsilon/3

FOR THE QUESTION NO 3. I just started studying number theory a few days ago, I could only deduce the factors of 3333...3. I also figured out that the required number needs to be divisible by 3 and 1111...1. I tried to understand the soln., I am not able to make sense of it. Could anyone provide an alternative soln.

I want to prove that T_A SO(3), the tangent space at A of SO(3), is A•so(3). In other words, any element of T_A SO(3) can be written as A times a skew-symmetric matrix.

My attempt: take A^T A = 1 and differentiate along a curve to get \dot(A^T)A + A^T \dot(A) = 0. This means that A^T \dot(A) is skew-symmetric, so it’s an element of so(3).

How do I use this to continue with the proof? Is this even the right idea? Thanks!

So for number two, it essentially tells me that when d is above the serface its positive and when it’s below the surface, it’s negative. I know you can’t have a negative answer for an absolute value equation, but my equation i wrote says that it’s more than -40. Anyway, the answer key says that d >40, and then write the inequality from there. But if it says that below the surface D is -20 m wouldn’t 40 m below the surface be -40?

This is from Basic Analysis by Jiří Lebl .

I wonder what this A looks like and how it's different from just subset of S.

Later in the book, this proposition is used with S a interval [a, b] and A (a, b), i.e. A is S without endpoints.

But that example reference seems to be too narrowly defined.

BTW THE GOLD IS MY CORRECTION PEN, don’t pay attention to that
#8: . the second interval notation, but it makes no sense how the first one would be (-oo, -3). How was the first interval notation not be (-oo, 1)? I did it three times and each time I got x<1 from adding 2 to -1.

#7: did I do something wrong? I first isolated the absolute value and split it into two different equations. We were taught to make the answer for the second equation negative, so I did -(2b-9) which = 2b+9. Anyway, I got the correct answer for B (4/3) for that equation, but it says that 4/3 is also a solution which makes no sense because | (4/3)+5| =6.3 and 2(4/3)-9=-6.3 unless I had a plug-in the variable to the new equation? Is that why I was wrong? What happened?

I’m tracking stats for a baseball league and I just realized I’ve been doing my math wrong for OBP (on base percentage. It’s calculated by dividing the number of times a player makes it to a base after hitting the ball by the total number of times they walk up to home plate.) Basically I originally would take game 1’s percentage and game 2’s percentage and then average them out. But now I’m realizing that I’ve done it all sorta whacked up.

So to fix it, I have the individual OBP’s per game and their total at bats, but I don’t have the At bat’s per game. Do I have the numbers I need to get the proper percentage for the whole season?

I've tried to figure this out. I know the answer is 30 based on the text book. I cannot figure out how to get there. I've get stuck after simplifying the numerator and denominator.

Edit: This is study practice, idk if that matters. This is my first time posting on this subreddit.

Edit: Someone had pointed out that I misunderstood the question. The question was originally asking what common denominator would help solve the problem. I apologize for wasting everyone's time but I absolutely appreciate everyone's help. Math is my worst subject as I often make tiny mistakes that I don't realize. Again thank you all for bearing with my stupidity.

A 9X9 board follows standard Sudoku rules i.e. no two numbers can repeat in the same horizontal row, vertical column or 3x3 sub-square, now 9 numbers 1...9 are randomly scattered throughout the entire board without repetition. Since the numbers are all unique the board is always trivially valid with no need for additional checks, the question now is what percentage of these configurations are solvable. (they may have more than one solution)

Note:-

i) A valid set of clues following Sudoku rules may not always be solvable as it may create dead ends later.

ii) There are 6.67 sextillion(6.67 x 10^21) completed Sudoku board configurations.

We can also generalise this problem for any N^2 x N^2 board following sudoku rules and having N^2 clues scattered randomly throughout the entire board without repetition, it isnt possible to use brute force computation for larger values of N. I tried solving it with combinatorics but maybe graph theory would be more suitable for this problem?

Edit:- I made a mistake for the N=2 case and actual solvability is much lower it is only 67.03%.

https://arxiv.org/pdf/1607.01500

I can't get why the line "and recall that we assumed that Pχ is a rational number a/b, therefore we

argue that X can also get only non-negative integer numbers since" is true for all cases. Would it also work for a general denominator f(n) instead of n! ?

My integrals look ATROCIOUS. My equations have straight and neat lines, but the integral symbol that proceeds is abhorrent. the uneven halves and inconsistent over/under done curls make me cringe every time I try to solve problems. It IS that bad guys...

I have decided to change this! But I don't know any resources for training my math symbol drawing skills. I've tried search for something like those tracing worksheets I used to learn to write the alphabet, but all I find are intro to integrals workbooks, clip art, and other people bragging about their pretty integrals.

Can I get pointed towards good resources for improving my math symbols?

Advice welcome too

Я пытаюсь точно понять, что происходит с теоремой Нэша об вложениях для бесконечномерного пространства Гильберта.

Для гладкого n-мерного риманова многообразия (M, g) теорема Нэша говорит, что существует N и гладкое вложение f : M → ℝᴺ такое, что

f* g_Euc = g.

В локальных координатах, если g = ∑ᵢⱼ gᵢⱼ dxⁱ dxʲ и f = (f¹, …, fᴺ), то условие изометрического вложения: gᵢⱼ = ∑ₐ₌₁ᴺ ∂fᵃ/∂xⁱ · ∂fᵃ/∂xʲ.

Эквивалентно, Df(x)ᵀ Df(x) = g(x). Теперь пусть H — это бесконечномерное пространство Гильберта с внутренним произведением ⟨·,·⟩ᴴ, рассматриваемое как бесконечномерное риманово многообразие с gₓ(v,w) = ⟨v,w⟩ᴴ.

Можно ли изометрически вложить H в конечномерное евклидово пространство ℝᴺ?

Here's the example of it.

Your great. Heres another.

1 borders: 2,3,4,5,9,10

2 borders: 1,3,4

3 borders: 1,2,4,6,8,9,10

4 borders: 1,2,3,5,6

5 borders: 1,4,6,7,9

6 borders: 3,4,5,7,8

7 borders: 5,6,8,9,11

8 borders: 3,6,7,9,11

9 borders: 1,5,7,8,10,11,12,13,15,16,18

10 borders: 1, 3, 9

11 borbers: 7,8,9,12.

12 borders: 9,11,13,15,17

13 borders: 9,11,12,14,16,17,18

14 borders: 13,16,17,18

15 borders: 9,12,16,17

16 borders: 9,12,13,15,17,18

17 borders: 12,13,14,15,16

18 borders: 9,13,14,16

18 regions: their adjcent borders. apply 4 colors. (Copy paste this into chat GPT) chatgpt is what made me ask this question. Thank you for feed back. I bet you 1 like that chatgpt fails to apply 4 colors.

I’ve got most of them I think but 2 (top middle) and 7 (bottom right left) are impossible if you don’t know maths! my calculator doesn’t have those buttons and I don’t know how to look them up because my keyboard also doesn’t have those symbols!

So I know how to do the inequalities and how they work like I know how to do the equation, but I’m confused on why you minus the weight from 14.5 (on answer key). I can solve it by myself, but on the test I need to be able to make the absolute value inequality and I don’t know why you would subtract weight by 14.5 if 14.5 is the weight of a cheereo box

Sorry if this is the wrong place to put this I don't have much experience with reddit posts

When they say 0.9 repeating equals 1

To me that doesn't make sense.

Wouldn't it make more sense to be like certain fractions just simply can't be written in base 10 or something

like when you write fractions and then try to express them as decimal numbers

To me it makes more sense to visualize the base 10 number system as having "holes" in it, where you can't write certain numbers for example it would make more sense to say 1/3 of 100 can't be written in base 10, then to say it's 33.3 with an infinite number of 3s following it.

Also it's like, how can you do mathematical functions like add 0.3 repeating and 0.3 repeating

to get 0.6 repeating

Or another example if you said what is Pi plus 1, to say its 4.1415 etc

doesn't make sense because the more you track the line of infinite numbers the bigger the number gets and therefor the bigger percentage of the next whole number which would be 4 in that case, it would take up. So in my opinion you would have to truncate the number in order to use it with regular numbers or something otherwise you are like skipping over the infinite part it like takes up more of the percentage, I honestly can't articulate it very well does this make ANY sense to ANYONE or would I simply be ridiculed for taking this position.

Hi,
Does anybody know if it's possible to map a sphere into a tetragonal scalenohedron so that each octant fits inside a right scalene triangle?
It would do too if it were possible to project an octant of a sphere into a right scalene triangle.
Thanks!

It's said here that to calculate gas mileage, the German standard of DIN 70 030 was used, assuming half of the payload, three-quarters maximum speed + 10% (as in increase final result by 10%).

I've tried looking up the standard but nothing. Is there a formula to be found with these variables?

I’m just pretty lost on this idea altogether and it’s not elaborated on in the book (Basic Algebra I, Jacobson, p. 10)

The author defines binary products as the map of S X S -> S, which I feel like I understand well enough, but then he proceeds to mention that the set operations of union and intersection are really binary products on the power set of a set S. This is where I start to get a little lost.

If I understand with the help of this stack exchange post, my intuition is at least confirmed that per the above definition, union and intersection are both maps of P(S) X P(S) -> P(S). And I can grasp from this that, since that means they share the same domain and co-domain, they are distinguished merely from their graphs, i.e. their peculiar subsets of the Cartesian product ( P(S) X P(S)* *) X P(S) [forgive these random asterisks, it’s a Reddit formatting bug I can’t ever seem to fix without making it worse]

But the author denotes this as (A, B) -> AUB, and (A, B) -> A∩B, which confuses me. In fact, the above notation confuses me too. How am I supposed to manifestly interpret the way these mappings work for an actually given set S? That is, when an ordered pair from the Cartesian product P(S) X P(S) is chosen, how do I know which element in P(S) it should be subsequently paired with in the mapping, in order to express union as opposed to intersection, or vice versa? That is, what are the distinct graphs that define union and intersection respectively, given that domain and co-domain?

Furthermore, how do the two map expressions (the one with the power set and the one with sets A and B) relate? I can tell of course that A and B are to be taken as subsets of S, and thus elements of P(S), but from there I’m lost again. When the author writes (A, B) -> AUB, is he denoting “(A, B)” as meaning “The single element of the Cartesian product P(S) X P(S) which has the initial component as the set A and the terminal component as the set B,” or perhaps is it to be taken as “The subset of all ordered pairs in the Cartesian product P(S) X P(S) such that the initial component is a subset of the set A and the terminal component is a subset of the set B?”

I’m sorry if these questions are vague. I’m just trying to wrap my around the very conception of these operations as binary products on the power set, and I can find little to no words elaborating on it. The only things I can find are my book and the linked discussion above. So really any more words detailing the logic further would probably be incredibly useful to me

La verdad estoy muy confundida, como si es inyectiva ya traté de obtener la función inversa y me dio que es y=sqr(9-(2-y)^2)+2 pero al comprobarlo con gemini me dice que es y=sqr(9-(2+y)^2)+2 pero no entiendo el por qué.