I'm trying to solve a problem my class was given for homework - wherein we have to find the volume of fluid occupying a horizontal cylindrical tank at 100%, 90% and 80% capacity.

Since the hemispherical end caps of the tank are segments of a sphere, I reasoned that I'd have to try and build an expression to integrate with respect to the height of the tank.

The issue is, it's been a while since I've learned integrals, especially problems where I have to triple integrate and take weird boundaries.

I've also been given limited information, as I only have the

• straight length (6000mm)
• length running down the segment radius of the tank (2100mm)
• depth of the segment (x = 145mm)

My attempts so far:

Attempt #1: Try and 'brute force' it - by ignoring the end caps initially, finding the volume of the central cylinder at 100% full. Based on the height of the fluid, I tried working with the ratio of full/empty space in the tank and attempted to use simple arithmetic to work out the remaining volume within the tank occupied by fluid. This effort failed.

Attempt #2: I tried triple integrating with respect to cylindrical coordinates (x,y,z) but got very confused as to how to find the radius of the sphere the segment is a part of.

Attempt #3: Followed some YouTube videos and tried to integrate with spherical coordinates (rho,theta,psi) but got confused again - as I was unsure of how to take my boundaries, since I'm unsure as to if I'm supposed to take my reference point as the centre of the sphere or shift it downward. And after that point I'm just not sure how to proceed.

Any help or advice would be really appreciated.

Thanks in advanced!! :)

idk if this is the right place; this is more general math class advice rather than a specific problem.

I need to get through pre-calc, calc 1, and calc 2 for my degree. The problem is I im in pre-calc/trig, and I feel like I'm just stuck. My big issue is formulas. I could stare at the trig unit circle for a year straight and barely remember when I look away. Thankfully, I found the finger trick for that one, but I still feel stuck on how I'm supposed to get through Calc 1 and 2 when im barely floating in trig/precalc. Does anyone have advice for not being able to memorize formulas, or just advice in general? I feel like I'm up against a brick wall.

I don't really know how to show proof of my prior attempts for rule 2.

I've tried brute force memorization, and it never works. I find that if I am about to have an anxiety attack about learning, I learn the stuff better, but I would rather avoid that., some times tricks work, but only if paired with already being stressed abt it

So I’m writing this math paper for school. I solved it graphically but I really wanted to do it by hand so that the work could be shown, cuz it’s like extra swag yk? Anyways, I reached out to a teacher about it and she was like “I don’t think it’s possible to solve it algebraically” and I was like “I don’t think that’s possible” anyways it goes like this 145.04714x(0.991479)^(x-1)>-1 
Then solving it for x.
If anyone wants to read the paper and give feedback that would be very helpful. (Please if you are like transphobic or something, please just look at the math, this girl in my class is transphobic and it was kinda just a waste of time because her feedback was so obviously biased)
I already know that I don’t have the axis labeled btw.

Title: I study really hard for math tests, understand the material, and feel confident afterward, but still end up getting low marks. What am I doing wrong?

I've been having this problem for a while now, especially in math, and I'm honestly struggling to figure out what's going wrong.

Whenever I have an upcoming math test, I spend a lot of time studying. I go through the homework questions, practice different problems, and make sure I understand the concepts. I also use ChatGPT to help explain things, but instead of just asking for answers, I have it explain the logic behind the math, why certain methods work, and how to approach questions step by step.

The thing is, I genuinely feel like I understand what I'm learning.

For example, I recently studied a lot for a math cumulative exam. I went through the material, practiced the questions, and made sure I understood what I was doing. When I actually wrote the exam, I felt pretty confident. The questions didn't seem particularly difficult, and I even had time to go back and check my answers.

I walked out thinking I had done pretty well.

Then I got my mark back, and it was 55%.

I was genuinely shocked. I wasn't expecting a perfect score, but I definitely wasn't expecting something that low. I was so confident in how I p

As a STEM student, I do a lot of fast handwritten math, and conveniently expressing multiplication has always been frustrating. I also skim over my work and notes a lot, so I do not like notations that are "context-dependent" — I feel like every type of mathematical object should have its own notation. But I swear, there isn't a single multiplication symbol, just for multiplying scalars together, that isn't overloaded.

• Putting them together (e.g. $$xyz$$) works fine for variables, but not for numbers
• Parentheses are annoying to me — I shouldn't have to write 4 strokes like ()() just to multiply two things. Also, parentheses are the same syntax for functions like $$f(x)$$
• × (cross product) looks like x, and it also implies to me that I'm working with vectors
• • (dot product) also implies vectors, and takes a while to fill in
• * (asterisk) is what I use currently, but it's the same symbol for convolution and I've had to abandon it at times

Does anyone have advice?

Hey im starting my undergrad next year and I was wondering to go ahead my syllabus what kind of math do they teach u in your first year fundamental engineering degree and any reccs on how to get ahead

P.S I do mechatronics and robotics

How do I learn math from the beginning? please give me a book that will helps me

Well I'm a nursing student and after 10th grade I chose pcb but now that I'm in nursing and most of the subjects are just learning but not solving. I kinda miss maths. So wanted to start again. Where do I start from to atleast reach 12th level maths as well as maths that'll benifit me in everyday life.

How do I prepare to an Olympiad from a high school math level?

Hi! I'm currently in fifth grade of high school (I'm Mexican, as far as I know is like 11th grade in the US) and want to start keeping in math. I always liked it and in the last year I started learning a bit more, specially on proves, understanding why instead of just copying the teachers formulas.

This year I want to try the olimpiad, my school (the UNAM) makes a yearly math olimpiad and I want to participate in it. It's not top level including deep props, real Analysis, complex analysis, calculus, etc. It is more basic but still impossible for most regular students. I try to solve some problems and solve half of one exam, I really love this kind of problems.

I really want to win an keep learning, not only for the contest, but for my future. I want to study math, so I want to prepare from know into pure math.

What is the path to go from mechanic thinking into abstract logic? I love this kind of thinking but I'm kinda stuck into how to improve my knowledge.

Creo que esta es la mejor forma de aprender Matemática Básica desde cero para Ingeniería Informática. ¿Qué estoy haciendo mal?

Mi teoría es que, para aprender Matemática Básica, no necesito memorizar cientos de fórmulas, sino entender los conceptos desde la base, practicar ejercicios de dificultad progresiva y aprender a reconocer qué método usar en cada problema.

Los temas que necesito dominar son:

- Inecuaciones e intervalos.

- Valor absoluto.

- Funciones, dominio, composición e inversa.

- Matrices, determinantes y sistemas de ecuaciones.

- Otros temas fundamentales de álgebra.

Mi idea es estudiar cada tema en este orden:

1. Entender qué es y para qué sirve.

2. Aprender las fórmulas y reglas esenciales.

3. Ver ejemplos resueltos paso a paso.

4. Practicar ejercicios fáciles, luego intermedios y finalmente ejercicios de examen.

5. Analizar mis errores para no volver a cometerlos.

Pero no sé si este método es realmente el más eficiente.

Si tuvieran que aprender Matemática Básica prácticamente desde cero, con poco tiempo y preparándose para los exámenes de Ingeniería Informática, ¿qué cambiarían de este plan?

¿Qué errores suelen cometer los principiantes? ¿Qué temas debería dominar antes de pasar a los siguientes? ¿Qué recursos, canales de YouTube o métodos de estudio recomendarían?

Me interesa especialmente conocer consejos de personas que hayan tenido dificultades con las matemáticas y hayan conseguido mejorar de verdad.

Pueden corregirme, contradecirme o decirme qué estoy entendiendo mal. Quiero aprender de sus experiencias y encontrar una forma de estudiar que realmente funcione.

I can add/subtract 3 digits in mental math but i cant do any any multiplication/division past 2 digits idk why it seems I forget or something, i wasnt the best at math but i want to atleast be good when I pass, I am 17 in 11th grade I can do long form of multiplication/division addition and subtraction in paper effortlessly but why can't I do the same for mental math? I want to be good at mental math just like how I can do in regular paper

Hey guys, so about 2-3 months ago I decided that I will try to master calculus 1 while self studying and having never taken calculus in high school. I’m still attending highschool tho. Since then I’ve made massive progress I would say. I’m currently reviewing everything I’ve learned in calculus 1 and polishing every skill. Looking back I think this is the best decision I’ve made in a couple of years, honestly. I have also decided that after I master calc 1, I will continue on to calc 2 and 3. And after that I’ll just keep learning math until I complete a full mathematics course that a math minor/major would. I have no idea how long this is going to take me but I’m sure I’ll love every second of it. I was wondering, is it as easy to find free lectures online for further maths such as real analysis as it for calc 1-3? I would greatly appreciate if you guys were able to drop a few link might help my endeavors. 👋

Hello, reaching out to say I’ve been struggling with calc 1 I got a 21/50 on my first exam and I got above the mean with a 27/50 on my second exam, I am currently at a 65% and need a 70% to transfer out of my CC, does anyone have some recommendations on studying and actually understanding the material, I feel defeated right now even though I did better and I’m just stressing out even though there’s about 2 months left I just really need some insight on how to get thru this class and pass. I go to the tutoring the offer and do all the homework and quizzes but when I get to the exam I do good on some and some I feel like I’ve never seen or I forget to study that one part.

I haven't been able to understand math my entire school time ( scored 27 in boards 10th ) . But now i have to understand it.

The problem is i don't know where to begin specifically.

YouTube has too many teachers but no single playlist for a student like me.( Suggest if there's any ?

I want to improve my maths for RRB NTPC and only 70 days i have . I don't know the basic level of mathematics like fast subtraction , multiplication etc . I can't even do a simple

divide.

I hope somebody who's been at my level could understand and guide through this. ,

THANK YOU.

Salut tout le monde !

Je suis en Terminale C au Cameroun, l’équivalent de la Terminale avec spécialité maths. J’aime beaucoup les mathématiques, mais j’ai du mal à être régulier dans ma pratique. Je peux obtenir 15/20 , parfois 17-18/20 à un devoir, puis voir mes résultats baisser par la suite.

J’aimerais apprendre à travailler plus efficacement, à savoir quels exercices pratiquer, comment réviser et comment devenir plus constant en maths, mais aussi en physique-chimie.

Quelles méthodes d’apprentissage et habitudes vous ont réellement aidés à progresser et à obtenir de bons résultats sur le long terme ?

Merci d’avance pour vos conseils !

I havent been in school in over a decade so the finer points of my math is rusty.

Im essentially attempting to graph an additive binary sequence. Numbers for my game lol. Pardon the way I write this, I dont know advanced formatting.

So, the player goes inactive, they lose 2^x tiles each day. 1, then 2, then 4, then 8, 16, etc. I need this graphed, as there's quadrillions of tiles in my game lol

Its not just F(n) = 2^x, right? Surely not...

Thanks in advance for yalls help

Hello my friend needs calculus 2 guidance.
He had homework that is also supposed to be a practice exam prep and it's not looking great. The prof gave hints/answers but he doesn't understand how she got to that point/how to proceed-I cannot help. Guidance on these 8 problem would be great

https://imgur.com/a/Ac4MWUP

Hi,

I did a question in my textbook regarding the cross product of two non-parallel and non-zero vectors a and b.

It asks me to simplify the cross product of (a+b) X (a-b).

I get -2(aXb) but my tutor and the textbook get 0.

My tutor is saying I don't understand cross products but I feel that I do. I'm fairly certain that 0 is incorrect.

Please can someone check my answer and advise what to do because my tutor is totally ignoring me.

I wasn’t able to take my first calc 1 midterm due to a really bad illness and because of that have fallen behind a lot of lectures and haven’t been able to bring myself out of that hole. I feel like I need to go back to the beginning and relearn the first topics from my midterm 1 but i’m not sure if it’s smart to do that and then teach myself the newer topics or if I should be doing both at the same time as the second midterm isn’t cumulative. My first midterm included the topics functions and graphs, polynomials, exponentials and logs, half life, log and linear axes, transformations and compositions and continuity and limits. The next midterms topics include divergent limits and limits at infinity, intro to derivatives, plotting derivatives, the power rule, the product and quotient rules, the chain rule, and the second derivatives. Please give me any advice at all on how you’d approach this and what to do, my prof doesn’t record past lectures and he goes really fast so i’d have to relearn the older lectures alone but any advice is appreciated! Also any success stories would really help me out right now if anyones had any luck in a similar circumstance the exam is worth 20% and I have one other midterm worth 20% as well, the final is worth 35%

I have a math midterm covering the topics(transformations, radical functions, polynomials functions, rational functions and function operations) my average is in the 50s i study for every test like I will do textbook and workbook qs and additional reviews my teacher provides aswell as pratice questions from the SNAP book. Idk what to do, i dont want to repeat math and I dont know what I stuggle with because I will walk into the test confident, anyone have tips on doing well

I wanna ingrain knowing square roots at least 1-50.

First of all, sorry for the poorly worded title. Not sure how to make the question shorter for the title.

Background: am a layman who used to learn and live math in hight school up to early calculus (normal high school syllabus in my homeland). That was about 20 years ago, more I work in a different beach of science which doesn't deal with math being single calculations. I still remember the principles of some things (like basic algebra and geometry, polynomial, very simple differentiation and integral, simple trigonometry), but forgot otherwise most.

So I was trying out a mobile game, which goal is to locate the exact position of n number of cats in a n² grid where each cat must be in their own column and row AND also not adjacent to each other (neither horizontally, vertically, nor diagonally).

Which got me thinking: what is the exact number of all possible solutions for this problem for any given n?

The more I think about it the most apparent it is that this is actually a complicated problem. It's not even a 'simple' (apostrophe because it's not that simple to begin with) probability, or in that sense permutation or combination problem anymore - or at least what I think.

I hope this doesn't break any rule or such. Thanks in advance.

here is the problem: https://imgur.com/a/tmQLdFz

A bit of background: instead of going to high school, I did a vocational training programme. I took maths-based classes, but they were entirely focused on electrical engineering topics (Maxwell’s equations, Ohm’s law, alternating current, direct current, low voltage, high voltage, and related topics). However, we never covered the usual high school curriculum

when it comes to Calculus I, though, I struggle to understand why and how we solve the exercises, as well as how to visualise the graphs, which makes everything extremely abstract and difficult for me to grasp

instead of just the answer or the problem or the mechanicals steps i would love to be able to understand the logic behind it, why x numers of steps were choose to fix this problem, or how can i decide wich "tools" to use to solve it

ill try to put here my understanding( or lack of) the exercise 2 for example

I’m having a hard time figuring out how to get started. In many exercises involving (f(x)), we have conditions like (x>0) or (x<0), which are easier to understand. Those conditions tell you which side to approach from, so you have to calculate the limit from the left or the right depending on the condition.

However, in this case, we have (x=0) and (x=/=0). How am I supposed to determine which side to approach from based on these conditions?

I know that, mechanically, the first step would be to check for continuity, but I’m lost when it comes to actually doing it. You’re supposed to check both sides of the given (x)-value and see whether they approach the same real number. If they do, the function is continuous there, and you can then check differentiability.

However, I’m struggling to understand even the most basic steps involved in solving this exercise.

In part a), you have to determine the value of (a) for which the function is continuous everywhere on (-1,1), but I’m not sure I understand what the question actually means.

I assumed they want me to isolate (a) in the equation that applies when (x=/=0), but how am I supposed to do that when I can’t simply substitute a numerical value for (x)?

i tried calculating the left-hand limit by substituting (x=-1) and the right-hand limit by substituting (x=1), then try to find the value of (a) for each limit, on the left i end up hitting a wall mid way due to having ln(0) and in the right i do end up being able to take out a but even then don’t see how I would be able to solve part (b.1), so I’m guessing that would be the wrong approach to part (a).

And that’s where I’m currently stuck.

Any kind of help would be extremely apreciated!!

I want to rank several countries' characteristics (like economic power, military power, population...etc) in a logarithmic scale.

However, there are some countries that do not have any army (like Andorra) and in that category (and related ones) they have a value of 0. However the log(0) does not exist. So, how could I convert the values into something that could be used to make the logarithmic scale?

I have thought about two methods:

A) To every value in each category, I added the values of the "smallest" or "weakest" country (that does not have a 0 in any category, so that all categories have a non-zero number). In this case, I added the values from Seychelles to all countries.

B) To every value in each category, I added "1", so that in every category that the countries without armies have a "0", the minimal number is "1" instead.

I feel that the first method has the advantage of adding a proportionate quantity in each category, since you will see that for some categories all values are small (like 1,07; 2,08; 3,1...) and in other categories the numbers are much bigger (5, 20, 49, 80...). So in method A the added numbers are proportional to the values of each category

However, it feels arbitrary to add different numbers for each category instead of adding the same for all of them (i.e. 1). However, in this case, adding 1 to the small-values-categories seems to significantly modify these values, while in the case of categories with bigger numbers, the resulting number is almost the same as the original one (like, adding 1 to "1,1 "would increase it by almost the double: "2,1"... however for other categories with a number like "50", after adding the "baseline value", the difference is negligible: "51").

So which method do you think is more accurate?

These are the values: https://docs.google.com/spreadsheets/d/19zjwdoLum0yhIQ2v3m19kz5_IplwSJYZX6e0wMqMHoQ/edit?usp=sharing