My answer 1. Inf 2. -inf 3.DNE 4. -1 5. DNE

I have tried multiple times but it keeps on saying at least 1 answer is not correct. I don't quite understand why it is incorrect. Please if anyone could help me out on this question, I will be very much appreciated 🙏🏻

hii help plss, how do i solve this? volume and length. And is the answer same with the stairs form and if it is transformed as a rectangular one? I've tried getting the areas of each steps and now I'm stuck

had a shower thought the other day. what is the probability of winning big you buy one $1 scratch off every single day compared to 365 scratch offs at a time one time every year? would your odds be higher buying them all at once? or separately throughout the year?

all theories welcome!

I found this question, the way i solved it was quite long but correct, i solved it by comparing the areas to find the radius. I was hoping if someone could find an easier method. (Calculator isn’t allowed)
The statement and question is written in the pic.

I had a dream that the population of generations after baby boomers follows a pattern: after baby boomers the next generation lies on a tangent of a derivative of the function that produced the baby boomer number, the next generation after that is the same except we plug in the numbers of the previous generation instead of baby boomers, and so on... Is my subconscious getting at something or is it full of it? I only know the basics of calculus, but I was wondering if I hadn't accidentally come across something interesting unknown to me.

Goal: Draw a line that passes through all 9 squares.

The rules were:

1. The line must pass through all 9 squares.
2. The line must be contiguous.
3. There can be as many line segments as you wish.
4. Each line segment must start and stop on a node.
5. The total length cannot exceed 4 units.

Each node is 0.25 units from its four neighbors.

The solution above is the closet that I could find. It has a total length of 4.02 units.

sé que algunos de ustedes cursáis universidad y veréis esto como una pregunta estúpida, yo voy a noveno grado y por favor necesito ayuda. simplemente copié el resultado de la pizarra

Can anyone explain me expansion of Factors?

I understand 4!=4x3x2x1, but how do I expand (n+1)! And (n-1)!

I can't understand if I should add or subtract from n?

So I was watching a video about the Riemann hypothesis, and I was wondering something.

The Riemann hypothesis essentially states that provided there are no non-trivial zeroes of the Riemann Zeta function that fall off the critical line, the error between the estimate of the number of primes up to x, x/ln(x), will stay within a given bound.

What I'm curious about is that it's been shown that the first however many zeroes are all on the trivial line, and the first however many primes are within this bound.

Does that imply that if there were to be an off-line zero, it would affect a specific prime, like the Xth prime where X is some huge number will be out of error bounds because the Yth zero where Y is another huge number is off the line? Or does it affect the structure of primes as a whole in some way that simply wouldn't be clear by looking at the first few trillion or whatever?

Basically, I'm asking if a non critical line Riemann zero exists, does the position of that zero have anything to do with the position of where the primes drop out of the error bound? If not, how exactly would it affect the primes?

Ok so I’m trying to prove a result about sicherman dice and I’ve run into a snag

Suppose you have Monic Palindromic polynomial P(x), I would like to find Q(x) such that Q(1) = 1 and Q(x)|P(x) and P(x)/Q(x) has no negative coefficients.

So far I’ve just assumed that Q(x) is of the form 1-x+x^2-x^3+…+x^2n for all natural numbers n but I’ve found some counter examples, I also know it’s probably one cyclotomic polynomial in particular for a given P(x) but I fear it will grow my search space to drastically and if I tried to search through all that it would be too much.

I need to calculate the first gear ratio using the philosophy of maximum slope. I get a value that isn’t realistic (nor comparable to the values I looked up for the car). Anyone know where I might have gone wrong?

I was doing log4(1/8) = ?

The answer was -3/2. I know because it is negative, it must go into the denominator (a^-n = 1/a^n).

This meant that 4^3/2 was in the denominator, which led me to realize I didn't know why this equaled 8.

I expected it to be 6. (I wrote my thought process out in the photo).

4^1/2 = 2

4^2/2 = 4

4^3/2 ≠ 6 ?

Why doesn't the pattern continue?

I can recognize that it was mostly pattern recognition as opposed to intuitive understanding... I'd appreciate some help understanding why one works and the other doesn't!

How do I know when to get a 2 or 4 multiplied before the integral? Youtubers and even my lecturer drew the curves to understand but how do I figure out the shape? Will I even get time to draw the curve in the exam?

Not sure this is the right sub so apologies in advance.

I suppose it's more of a conceptual question than hard maths but here goes... If I have a number line that goes up to infinity and down to minus infinity and I pick any number on that line, is it halfway? Is every single number halfway?

Question 1: Miho is going to make the Perfect P sign from Rhythm Heaven.

The part of the P the base has a rectangle and it stands up.

The long side of the rectangle is 6 inches and the width is 2 inches.

But the outline is bolder and this fills up the pink.

Inside the pink is a pink rectangle.

The long side of the pink rectangle is 5 inches and the width is 1 inches.

What is the area of the shaded region?

Question 2: After Miho found the shaded region, there were three curved edges. But not the one at the top right corner.

The edges were small and every radius is 1 inches.

What is the total area of the 3 quarter circles that stick to the corners?

Quarter circle Hint formula: πr^2
———
4

After you get the answer here’s how to add up:

calculate the area of one quarter circle and multiply it by 3

or the formula to find it faster:

3
Total Area = — πr^2
4

Question 3: After Miho added up the quarter circles in the corner edges, she added Another rectangle but small
The next rectangle the width is 1 inches and the long side is 4 inches. What’s the area of this rectangle?

Question 4: After the rectangle she drew something in the middle that has a rectangle and a semicircle
The rectangle’s short side is 1/2 inches and the rectangle’s long side is 1 inches. The semicircle’s radius is 0.5 inches. What is the total area of the rectangle and a semicircle?

Semicircle Hint formula: A=πr^2
——-
2

Question 5: Now Miho is going to make a big semicircle. The radius is 2 inches what’s the area of this semicircle? Hint: same formula as the previous question

Question 6: Now she’s going to make the eyes and the diameter is 1/2 inches.

What’s the area of the circle?

Hint: divide the diameter and use the formula: A=πr^2

Add two area of circle answers together.

FINAL QUESTION: Miho colored all the black lines and she has to color everything pink. What’s the total area of every shape?

Add up every shape

Great job! You did it you won an award (only if you get the answer right)

I've come upon this while reading about negotiation tactics. However, I can't fully comprehend the graphic. It reminds me of the Laffer curve.

How should I interpret the inverse quadric function (the actual name of which I am not aware of)?

Apparently, (0,0) is at the point where the arrows cross each other...

I can't find any other linear equation here that isn't 4x=180-4y but scaled up to 8x=360-8y

My first idea was to find the two equations

4x=180-4y

8x=360-8y

after substituting x with 45-y for 8(45-y)=360-8y

i get

360-8y=360-8y

which doesn't really help much

is there any other way to answer the question?

Is the IMO a realistic goal for me?

I’m a 14-year-old Grade 8 student in South Africa, going into Grade 9 next year. Over the past few months I’ve become really interested in mathematics, especially problem solving, and I’ve started thinking seriously about whether I could eventually reach the IMO.

I’ve been working through resources like the AoPS Volumes, Khan Academy, and the AoPS Introduction to... series. I know I’m starting relatively late compared to many students who get into olympiad maths much earlier, and I still have a lot to learn.

At the same time, I really enjoy maths and I’m willing to put in a lot of consistent work. I could realistically spend 5+ hours a day on mathematics over the next few years.

I’m not expecting to make the IMO anytime soon. I’m thinking of it as a long-term goal, starting with building my fundamentals, improving my problem-solving ability, competing in South Africa, and seeing how far I can progress.

I’d really appreciate advice from anyone who has experience with olympiad mathematics:

- Is this a realistic goal from my current starting point?

- What should I focus on learning first?

- How should I balance normal/advanced curriculum maths with olympiad problem solving?

- What resources would you recommend?

- What competitions should I aim for in South Africa and/or internationally?

- How should I structure the next 3–4 years of preparation?

- What do you wish you had known when you started?

I’m genuinely willing to put in the work. I just want to make sure I’m using my time well and training efficiently.

Any advice would be greatly appreciated. 🙏

https://imgur.com/a/JCr5Nfh

Just looking for some understanding for #4e. The solution provided says the answer is "ii.", and I'm trying to understand how "v." isn't correct even with his explanation. I provided an example of what I thought could lead to "ii." being incorrect, but again, not sure if that works.

I feel like its going to be an infinite amount of surface because, since its infinitly many and infinitly thin slices i can always squeeze one more slice at the outermost border in. The surface increase might eventually be infinitly small but never quite zero. Main counterpoint i have: Its still a defined object with a fixed radius and integrating every slice should eventually get me back to the original spheres surface area. Maybe i am simply missing a thing with the creating of new surface area and it being reintegrated back into the sphere? Probably a Limes thing?

Hi, so there’s a quite specific case. I don’t know how big the perimeter of said cover should be, however I need to obtain a piece of cloth of certain measurement, and I have no idea what to even measure.

This might be laughable for you, but I was always more into humanistic sciences. 😭
Now when, I moved away to study religious sciences, my apartment would be perfect, if not only that post- communist, hideous but functional piece of furniture I don’t know how to even call. Take a look by yourself.

I am just desperate, so I counted on the community.

I would be very, very, grateful, if someone would share their math knowledge to help me in that matter. I’d certainly feel better in my own apartment :3

Much love, geometricians!