r/mathshelp

I designed this as an original problem combining tangent geometry, calculus, trigonometry, and an unusual auxiliary representation of lines.

The complete problem is in the image. I'd be interested in seeing independent solutions and approaches.

Original problem by Samarth.

https://preview.redd.it/hujik0xy03kh1.png?width=1489&format=png&auto=webp&s=e84076231d01682f594b36b965ee04254004fe4e

Hey,

I'm from Germany and my final exams are getting closer. I have Math and Physics as my advanced courses, so I'll be using my calculator a lot in both.

We use the TI-Nspire CAS at school. I feel okay with the actual math, but I've noticed that knowing the content and actually being quick and confident with the calculator are two different things. So I'd like to change that while I still have time.

I'd be interested to hear how others got to that point. If you've been using the Nspire for a while, what helped you actually get good with it? Anything you figured out late that you wish you'd known from the start?

Any thoughts appreciated.

This has been written for the 'math savvy' audience. It has not been written well enough to present to typical Algebra 2 or PreCalculus students. But, when developed further, what concerns would there be in introducing this idea of parameters to Algebra 2/PreCalculus students?

I do want to start having AP Calculus BC and AP Physics C students consider this, so any feedback, about either the idea or the description, would be appreciated.

Thank you.

https://preview.redd.it/2t023tnio3kh1.png?width=2050&format=png&auto=webp&s=dd5da9e503e7a05934b8d950f79587c413eb6fa7

https://preview.redd.it/o3fqhtnio3kh1.png?width=2050&format=png&auto=webp&s=88ba24268104f34e99395fb023a457943adbc12d

Came up with this today while having a bath, I just changed numbers so its easier. Enjoy!

John filled up a bucket with volume 10,000 cm^3 with water to have a bath. However, by accident, he fills it up with water at 60 degrees Celsius, far too warm. Instead, he wants the water to be 30 degrees.

So, he uses a cup with volume 400 cm^4 to scoop out water and simultaneously fills the bucket conyinuously with water using a tap which has a flow rate of 100 cm^3 per second and the water from tap is 10 degrees Celsius

Assuming that the water from the tap immediately mixes completely with the water in the bucket such that the water immediately becomes a uniform temperature, how many times should John scoop out water using the cup and with what frequency for the fastest time for the water in bucket to reach 30 degrees.

If possible could you also explain a bit on how you solved it? I'm a high schooler, just did basic differentiation and I suspect this involves either integration or differential equations or both.

Thanks!!

I hope this is an appropriate sub to ask this question. I haven't taken a math course in over 5 years so I'm very lost.

I'm writing a sci-fi story where there are two different dimensions. Time moves differently in each and I want to try and figure out how to calculate it.

Problem: Main character lives in Dimension A. They travel to Dimension B and stay there for 6 months (180 days). They go back to Dimension A to visit and find out they've been gone 9 years (3,285 days). If they visit Dimension A for 3 days, how much time would have passed in Dimension B before they go back?

I divided 3,285 by 180 and got 18.25. I then multiplied by 3 (for the days they were gone) and got (~55) 54.75 days. Is that correct or am I stupid?

EDIT: I know my username sounds like something a bot would make but I made this account like 2 years ago to lurk and never expected to post anything. I'm a human probably

I want to qualify for AIME and ideally USAJMO, but I don't know where to start.
For context, I'm a high school freshman currently taking geometry honors, and I'll be taking algebra two honors next semester. I really want to do the AMC 10 and qualify for AIME, and hopefully even the higher levels.
I'm dealing with carpal tunnel right now, so studying is a bit of a challenge, but I'm trying to figure out the most practical way to prep. I know a lot of competition math, like number theory and combinatorics, isn't usually taught in school.
Should I take an AoPS class? Join my school's mathletes team? I already have the AoPS Introduction to Algebra book, which covers some algebra two topics I haven't learned yet, so maybe I should start there. Or should I just grind Alcumus?
I'm feeling pretty confused about the best path forward. If anyone has experience with these competitions, I’d really appreciate your advice!