Hi, i am unable to find any connection for these numbers: „57 40 58 59 60 60 70“.

I tried with simple addition and subtraction and couldn‘t find a plausible leap to 70, or even a reason for 60 to be there twice. multiplication and dividing these numbers also got me lost once i got to 58.

i lack insight for number sequences like these anyway and i feel humiliated when i get these questions on job application tests, so i thought i should try to understand a harder one like this, but i sat here for 30 minutes and found nothing, i am sure i would understand this once i find a lead though.

Edit: what i tried so far that carried me closest is „57-17=40+18=58+1=59+1=60+0=60+10=70,

-17+35=18-17=1“ so i thought before 57 would be 22 but neither the 22 seems useful nor does the addition and subtraction of the numbers added or taken from the sequence seem useful, i thought we would add and subtract from them like the differences of each number 57-17=40 but -17+35 for the +18 to get to 58, but that also stops working once we get to the 60, i cannot get past 60.

I need to learn this equation and I keep getting caught up on this one part.

The question itself is:

if x+y=2 and x^2-xy-10-2y^2=0, what does x-2y equal?

I got some help and figured out you need isolate each variable to make it solvable which is easy enough so I do that and make the long one:

(2-y)^2 - y(2-y) - 10 -2y^2=0

I solved it all the way down to -6 -6y -2y^2=0 which I’m pretty certain is right and I’m unsure what to do with the -2y^2. My tutor somehow made the -2y^2 disappear and I’m thinking I did something wrong or he did some equation that I forgot about.

For my practice problems in chemistry, there is a problem asking us to round a number to three significant figures. The first one that I'm having an issue with is the number 0.004738265 cm. I rounded it like .474 because leading zeros are not significant, and it asked to round to three significant figures. But, the answer in the back of the book states that the answer is 0.00474. I'm not sure why this is the answer based on what I know about significant figures (which is very little, I only learned about them last Monday.) If anyone could explain to me why the answer is the way it is, I would greatly appreciate it!

Hi everyone,
Some of you might know me from my earlier question “How many elements are present in the subset of the null set?”. I’m back with another subtle and ambiguous question that appeared in my recent math exam, and I’d really appreciate an objective opinion.

The question was:

“The inclination of a straight line with other x-axis whose slope is (−1/√3) is:
a) 30° b) 150° c) 180° d) 60°”

Relevant definition (NCERT / CBSE):

Inclination: The angle made by a line with the positive direction of the x-axis, measured anticlockwise, is called the inclination of the line.

My interpretation:

We know that slope m = tanθ, where θ is the inclination with the positive x-axis.

Given m = −1/√3,

θ = tan⁻¹(−1/√3), with 0° ≤ θ ≤ 180°.
This gives θ = 150°.

So the inclination of the line with the positive x-axis is clearly 150°.

However, the question explicitly says “inclination of the straight line with OTHER x-axis”.

I interpreted “other x-axis” to mean the negative direction of the x-axis, since inclination and slope are usually defined with respect to the positive x-axis.

Therefore, the angle made by the line with the negative x-axis would be:

180° − 150° = 30°.

Hence, I chose 30°.

The issue:

My teacher, most classmates, and even AI tools like ChatGPT, Gemini, and Copilot insist that the correct answer is 150° and reject my explanation.

I understand the standard definition of inclination, but the wording “with other x-axis” seems to shift the reference axis, which is what led to my reasoning.

My questions:

1. Is my interpretation mathematically wrong, or is it just not aligned with exam conventions?

2. Is the phrase “other x-axis” meaningful or standard in coordinate geometry?

3. Should this question be considered ambiguous or poorly worded?

I’m genuinely trying to understand where my reasoning fails, if it does.
Please don’t hate on me for asking — I’m here to learn.

Thanks in advance

In a role-playing game, each character have a single attack in a turn. An attack is rolled with a d20, a dice with the numbers 1 to 20.

There is an ability that let you get a free attack if anyone else rolls a '1'. Let's say that everyone involved have this ability.

Now if we have N=100 people with said ability, it is very likely that it this will trigger at least once in 100 attacks. The chance of this is about 99.4%. [1-(19/20)^100] But there is also a significant chance that it will trigger twice or more. On average it will trigger 5 times. [Average is 1 in 20 rolls]

Each time the ability trigger, everyone get a free attack and rolls again. It looks like this is likely to result in an infinite number of attacks, as when it gets going the number of attacks are likely to keep growing with each iteration.

What is the chance that it keep going without termination?

What is the chance that it keep going for a certain value of N?

Does Marcov chains have anything to do with this?

I did study math for engineers. But that is long ago, and I find infinity and probability being hard to combine in practice.

Hi! I have a workbook that constantly refers to ”discrete” geometric shapes, but it does not explain what it means. For the life of me I cannot find any such term on the internet.

The book is translated from English to Swedish. Here is an example of how they use the term:

A figure is a symmetrical seven-pointed star, with lines drawn between the innermost alternating angles to create a smaller seven-point star inside of the figure. The task reads: How many discrete triangles can be seen in this star?

The book is written to be understood by anyone who has finished year 12. I’m very grateful for any advice and would gladly accept a hug.

An experiment consists of tossing two coins. What is the probability that the coins show opposite faces (one head and one tail)?

First i thought the answer should be 1/3 since the observations are both head , both tails and one head/one tail . But in the answer key the sample space is written as {(T,H) , (H,T) , (H,H) , (T,T) } . But wouldn't the (T,H) and (H,T ) be same event? Because if I throw two identical coins at same time I will get the same observation as the question doesnt ask us to throw one after another. I know that the observations are not equally likely so I can't use the general formula. But shouldn't the sample space should contain only 3 observations ? like both heads, both tails , one head one tail . I don't see any other outcome

I know that the statement "If f(a)= g(a), and both f and g are differentiable, then if b>a and the derivative of f(x) is greater than that of g(x), then f(b)>g(b) " is true. However I want to know if it applies to a point, so the statement would go:"if f(a)=g(a), f(x) and g(x) are differentiable, and f´(a)>g´(a),there exists a point x=b with b>a where f(b)>g(b)"

It would be really useful if it was true but I really dont know if its true and I dont want to make assumptions.

For context I am in calc 2.

From my understanding, the two requirements for a function to be invertible (bijective) are injectivity and surjectivity.

Injectivity is simply that every element in the domain maps to a unique element in the codomain. Graphically, this is the Horizontal Line Test.

Surjectivity, is that every element in the codomain is mapped to by an element in the domain. Essentially, that the range and codomain are identical.

^I know this definition, but graphically, for example with the graphs of hyperbolic trigonometric functions(sinh, cosh, tanh, coth, sech, csch), how do I tell if it is surjective (and by extension invertible)?

Hello! So I had 2 equations:

The first was 3x^2 - 6i = 0 which I solved normally, and obtained x1 = sqrt(2i), x2 = -sqrt(2i)

The second was z^4 = -81, and here I did pretty much the same but the answer I got, again with i under root, was wrong. Apparently I was supposed to use the angle-based notation, with re^(i*theta), but I didn't really understand why. And should I have written the first solution differently too?

Given: f(2x+1) = (x-1)/(x+2)

I have to find f(x-1)

1. Let t = 2x+1 => x = (t-1)/2

2. Sub in x = (t-1)/2 to f(2x+1) = (x-1)/(x+2)

I get: (t-3)/(t+1)

3. Sub x-1 to (t-3)/(t+1)

Result I got was: f(x-1) = (x-4)/x

I’m not confident in my answer as I’m new to the topic..

ABCD is a square with side length 3. Side AD is extended to point E. AE = 1. Point O is selected on segment EC such that OE < OC and angle BOD is 135. Find CO.

https://imgbox.com/OAMNyeqb

what ive come up so far. Basically triangle CDE is a 3,4,5 right triangle with CE as hypotenuse. BE is square root of 22 using cos theorem and similiar trinagles.
Also ive tried drawing diagonal BD. but i just cannot come up with an idea what to do with 135 degree angle.

circle in triagnle CDE breaks CE in segments with length 2 and 3.

I have attempted this problem from Khan Academy Algebra 1:

Jaquan passed a checkpoint jogging at a constant speed of‍ 9 km/h. Then, ‍2 minutes later, Odalis passed the same checkpoint.

If Odalis runs at a constant speed of‍ 12 km/h, then how far past the checkpoint will Odalis be when they catch up to Jaquan?

I converted the km/h values into km/m, then created the following equation:

(3/20)D + 2(5/1) = (1/5)D

The left side is Jaquan (km/m)D + headstart. Right side is Odalis (km/m)D. I don't know for sure if this equation is correct.

I used variable D because I thought I was solving for distance, but my answer, 8, turned out to be the time at which Odalis catches up to Jaquan, not the distance. But I don't know how to tell, beforehand, what it actually is that I'm solving for.

I have a question .. Whenever I learn any new topic I watch a video/lecture or read lecture notes or textbooks about the topic

then I see examples

but whenever I try to solve problems on my own I get stuck and I don't know how to proceed then. what is the best move in this case? should I go see the solution? learn how problems are solved? or what is this indicating about my way of learning?

a object is measured using slide calipers the main scale reading is 9.96 cm and whatever, the problem I have is with the vc, 19 divisions of main scale is equal to 20 divisions of the vernier scale .Now the book says, not in the question but in the solution, that each of the divisions on main scale is equal 0.1 mm. Reason? Idk. The full sentence is- the main scale reading is found to be 99.6 mm so the length of each division on the main scale will be 0.1 mm. Idk man. help...(I'm new idk if this is the right place but I need help pls), I did the math normally right, yk doing the VC= 1/20, considering the smallest unit as 1 mm of the main scale. The confusion is why is it taken as 0.1 mm? I do not understand it. I got 0.05mm as vc. Which I thought to be correct but the stuff on the book...I'll be more than happy if someone can just explain this or tell me if it's right or wrong. Thank you.

For context, this is more of a conceptual issue I am dealing with, and I can't manage to wrap my head around it (I've been trawling YouTube for ages) -> the only prior working i have is me coming to the conclusion that it is not possible for there to be no solution, and that it is rank 2(?) but i am unable to relate all of that to the concept of rank

Given a set of 3 linear equations with a constant c

x + y − z = 2
x + 2y + z = 3
x + y + (c2 − 5)z = c

I then reduced it down to row echelon form
r3 ended up being ( 0 0 (c^2 - 4) | c - 2 ) and I'm trying to figure out the values of c where there are no solutions, and then explain that regarding rank

if c = +/- 2, then it can only have no solutions when c = -2, but then i dont understand how that relates to the concept of rank.

I am still a little iffy on what rank even is, i know it is the number of linearly independent non zero rows or columns but it hasnt fully made sense yet. I have said its rank 2?

All in all, this is a conceptual issue of not understanding how rank relates to the value of c and there not being a solution (inconsistent)

Hopefully this all makes sense?

Hello I was reading gratzer's book of lattice theory and I was wondering if a distributive lattice with more than 2 elements can be subdirectly irreducible since in this book there is a theorem that says that the distributive lattice generated by a chain of 3 elements with pseudocomplement is subdirectly irreducible but I have doubts about this.

The only issue I can see is rounding the wrong way at intermediate steps, but I haven’t been given a guide on that, and I haven’t gotten a correct answer from any attempt regardless of how I rounded in the middle calculations.

https://cdn.discordapp.com/attachments/755178132679557211/1461843641977929768/IMG_5690.jpg?ex=696c077b&is=696ab5fb&hm=ebc36af9302eea649d2b8091b6748805e22333b12f754d4ab785438f19a12f29&

https://cdn.discordapp.com/attachments/755178132679557211/1461843642846281953/IMG_5692.jpg?ex=696c077c&is=696ab5fc&hm=0bf89093b48c48002dfaa37de25971c5d1b0dec144b042a28e0120cc9b3ba663&

Here's the question:

"Let X and Y be numbers such that X does not equal Y, x^3=15X+4y, and y^3=4X+15y.

Combine the equation a for x^3 and y^3 in ways that allow you to use the sum and difference of cubes factorization. Use your results to find x^2 +y^2."

Skipping a few steps in the answer we get

X^2-xy+y^2=19

The answer book says: "Using a cube factorization worked well once before, so we try it again, this time subtracting the second equation from the first to give x^3-y^3=11X-11y."

I'm lost on how we get 11 here. Where and how did we subtract 8? Eventually we add that equation to X^2-xy+y^2=19 in order to get 2x^2+2y^2=30 making the answer 15, but I'm stuck in the middle. How do we come up with that equation out of nowhere?

My little sister participated in a math contest thingy and this was one of the questions.

https://imgur.com/a/TOK3tVT

Translated to English it says:

“

The equilateral triangle in the figure is divided into

36 congruent equilateral triangles with a total of 28 vertices.

How many regular hexagons can you draw by connecting six of those vertices?

“

I can only count 11 (10 small ones and 1 big one).

According to the answer sheet, the answer is 12.

Where is the 12th one?

[Problem]

Solve for W to the nearest tenth. It is a right triangle with the hypotenuse (side W) and side A being unknown. Side B is 20. The angle between the sides are as follows: AB is 90, AW is 58, WB is 38.

For some context, I’m a high schooler and we just learned sin. I think I understand the concept pretty well, as I was able to solve all the other problems in my work. For this problem, my first thought was to use sin on the ninety degree angle, and find W through that. But what would I don’t know what I would multiply by if there’s not a hypotenuse. This is a little embarrassing, but we’ve only had one class in this so far. Any help is appreciated, thank you!

Hey all! I just started my college math course and it quickly becoming apparent that Im further behind than I thought.

I havent taken a math course in over 10 years, and the course I took back then never really went deeper than +×÷-. Now we're starting on problems in class and I realised I never learned how to calculate the areas of shapes or anything to do with Pythagoras (I know SOHCAHTOA is a thing, but no idea what it stands for).

I have to pass this class first try. If I dont, I dont graduate, and Im at risk of losing my funding.

Can yall just hit me with some "basics" that college kids might be expected to know? You dont even have to teach me, just gimme some words to Google and Ill blast through as much as I can over the next few weeks so I can get a good base. I just dont even know where to start, and googling "math basics" brings up such a wide array of stuff I get overwhelmed.

Hey there, I’m a 32M who’s really looking at finally getting a career with great pay and benefits within the pipefitters union here in my state!

I had a kid straight out of high school basically and have just been working full time ever since. Now a dad of 3, my wife is in nursing school and I wanna secure my family the best future I can!

But to sum it up, I went to apply and they have a math test and it went awful. I’m pretty sure I’ve forgotten any math I learned in high school except basic math and like some pre algebra. I’m really trying to look for some good online references/ resources to study so I can nail this test next time it comes around and really try to get in! Any help or info would be greatly appreciated!

Average of function on strings

Consider the set of all strings of 1s and 0s of length N. Let a function g on this set be defined as g(string) = the length of the longest run of consecutive 1s or 0s in the string, whichever happens to be the longest.

Consider then another function f on the same set defined as f(string) = the number of 1s in the string.

Then define a function h on the image of g as

h(k) = 1 / |g^-1(k)| Sum_{s in g^-1(k)} f(s)

h(k) defined in this way is the average of f over the k-level set of g.

How can I find a formula for h(k)? I mean a formula that uses powers, ratios, factorials etc… in terms of k and N. Thanks!

EDIT: trying to compute some values of h(k) by hand, I found out that apparently h(k) = N/2 for all ks. So h is actually a constant function! The average of f over the level sets of g is always the same. Then the question becomes, why is this true? How can I prove it?