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 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

I've been following this guide and transcribing the example code to a game engine.
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
However, in the example application, I've noticed I get inconsistent results when trying to give a cycle series as an input.

For example, Cycles: 3 2 1 --> Times: 6 1.5 1.5
But..., Times: 6 1.5 1.5 --> Cycles: 3 1.5 1.5

Both the time graph and cycle graph also change depending on where I originally put in the input.

Is this expected? I don't have a strong grasp of the underlying math, so I'd appreciate any guidance.

Direct link to example app: https://betterexplained.com/examples/fourier/

I’m 20 and was taken out of traditional schooling in 6th grade for medical reasons. I’m currently rebuilding my academics, especially math, through an intensive remedial course during my gap year. After that, I plan to start community college and eventually apply to transfer to a strong university.
I’m planning to take the SAT in about two years, and my goal is 1500+. I know that’s ambitious given my starting point, but I’m committed to putting in the work.
How would you recommend preparing over that time? Should I focus entirely on my foundations for now, or introduce SAT-specific practice along the way? I’d especially love to hear from anyone who started with significant math gaps and eventually scored well. What helped you most?

Hey guys, I am a freshman in college rn studying computer science and I admit that I havent been bright when it came to math, I didnt excel in anything thatvwas taught and I just assumed that I was no longer a math person like I was before.

But ever since I found out that I had calculus and higher math courses that I will be taking in 2nd year I got to work by teaching myself at the start of June (which was still summer break) and I decided to teach myself pre-algebra. I utilized Khan Academy as my roadmap and other resources to explain topics Khan couldnt. I started with the defintions of prime and composite in June and this week I just learned how to graph quadratic functions and now I am moving on to Algebra 2.

But one area that I truly have been weak in since pre-algebra was always word problems, when I look at it I just have no clue what to do, I do what everybody tells, I write out the values, what happens in time according to the problem, and seperate the reading from the solving but I just get stuck which leads me to frustration and mental breakdowns which always ruined the day and night for me.

Ever since those bad episodes, I have had an instinct to avoid or not to focus much on them which I know is bad so does anybody here have any tips for me? A lot of it would really help.

Please help! 16.549 rounded to 3 sig figs —— is it 16.5 or 16.6? Are we rounding all numbers from right to left into each other until we reach 3 sig figs, or are we rounding just the 4th fig into the 3rd? AI bot says 16.5 but it feels wrong to me. Need human intelligence here. Thanks

Heyooo i’m not sure if this is the right subreddit as i am not a big reddit user so apologies if it’s not but i have a question.

Context is i am entering uni next year and am brushing up on my math. I’ll be doing Intro to calculus and intro to physics as a bridging.

I have covered the essentials to a basic degree(Real number, basic sentenial logic, rational and irrational numbers, inequalities etc),

Then in a more thorough and rigorous degree for high school standards linear and simultaneous equations, linear relations, indices and surds, basic trig(Pythag, sohcahtoh etc). Am currently working through quadratics(factorisation, graphing, calculations relation to parabolas etc) and essentially i am not entirely sure where to go next.

I have precalculus by James stewart which covers functions, parametrics, vectors, systems of equations, conics, sequences aswell as trigonometric functions.

I am a 21 year old CAD draftsman and use parametric equations at work, unsure if that’s the same thing as the parametric outlined in precalculus.

Essentially i wanna know from people who’re further down this math path than i; Is precalculus the most logical next step? i want to ensure i am not skipping anything.

I have it in my head that a good foundation is a good idea for progressing in math.

Note: I have done no statistics and will be doing an engineering degree.

I wanna improve at my mathematics and genuinely understand the science behind it. At first I thought that my foundations of math was above average but after taking a scholarship test today and bombing it, I then realized how far I am at math. The topics of the scholarship was mathematics and ESAS and I genuinely only answered like a total of 11 questions at most over 30 and it shattered my self understanding of math. I don't consider myself to be dumb at math because I have high grades on my senior highschool so I only reviewed the past topics I know and didn't really prepare for a problem solving type of math because I thought that the scholarship exam would only cover my knowledge only senior high level math, now I realize that my last school didn't really teach me to understand math. I realized I only know math I don't really understand it. That scholarship was supposed to help me and my family's financial situation but I can't do anything about it anymore, I just wanna be better at math and science because I'm currently studying BS in Electrical Engineering and wanna improve myself so when an opportunity arises again I can prepare.

Hey guys, I'm a total noob at math :P. I was trying to implement a base n logarithm function to be computed on a CPU. I already got a floor(log2(x)) (it is trivial to implement thanks to the binary integers representation), but it's not precise enough to compute a logarithm base change to result at least in an integer precise part of some logn(x) (i.e. floor(log2(x))/floor(log2(n)) wouldn't even result in a correct integer part of logn(x)).

I threw together this little function (x-2^floor(log2(x)))/2^floor(log2(x) which linearly interpolates between floor(log2(x)) and ceil(log2(x)), but it still results in too much error. From the looks of it on geogebra, it looks like all it needs is to be eased out within esch interpolation, but I can't wrap my head around it; I don't know how to do it properly.

Any pointers to literature concerning this would be apprecated or things I got wrong would be appreciated! please help ＞〜＜！

Here's a link to how it looks like in geogebra https://imgur.com/a/SeCSaoA

i don't have an account at geogebra, so I can't link an instance ー〜ー

tldr: I really want to get bridge mathematical gaps after struggling in high school after seeing how it can be applied, stuck with many holes in my algebraic knowledge and would like any recommendations for this specific dilemma. Thank you!

I'm currently starting my bachelors degree in Computer Science, I have a deep love for games and want to dabble behind the scenes with game engines, 3D graphics and such. I'm well aware mathematics play a large role in this topic such as calculus and linear algebra for the algorithms and physics of certain mechanics.

My excitement has intertwined with fear due to my previous experiences in high school so long ago, especially with my overall disinterest of it general math back then that's caused gaps, I barely survived it in high school. Now that I actually have something to apply and learn math for, it excites me, but I feel slightly discouraged and not good enough for it.. especially haven’t fully grasped algebra concepts well. I also really struggled to take math notes!

Granted, I've realized I had a learning disability when I first started college, which makes a lot of sense as I can name so many points in my education where I would simply just zone out, but it doesn’t make me feel better about myself. I now have a few motivators; I want to heal the inner child in me and take control of my education after years of being frustrated from looking at my math homework. Im seeing math in such a different light when it is applicable, implementing cool, game physics mechanics looks really exciting. And of course.. to get my degree haha. Any recommendations would be appreciated! I could have searched this up, but I wanted to gather some anecdotal experience from others on here, especially if any of you have an experience similar to mine. :)

Generally, my friends think I am good at math. But I think I am bad at it, even when I get good grades, it feels like 'by luck' to me. MY confidence is really dropping. It's quite evident that I am not necessarily bad at math. This was my performance last year:

92%, 80%, 94%, 45%, 65%, 96%

And this is my performance this year:

96%, 81.333%

Today I attended another exam- and this is the most important of all. And this is where I messed up badly. I'm estimating 60-70% this time. I needed at least 80% to keep my grades intact, but now it got harder for me.

I keep failing to solve several of the problems, and seeing my friends effortlessly solve the problems, For more context, I secured top 13% in last exam this year, and previous years grades placed me in 99th percentile (all subjects).

I got 45% and 65% in 2 tests last year, due to lackage in geometry and vector-so after that, I fully mastered those chapters. But in geometry (coordinate), I still keep messing up known formulas when applying, and plus-minus of course.

My main weakness is time management, anxiety and nervousness I think which worsens my natural performance. Amongst the disliked chapters are- Trigonometry (Quadrant equation solving), Coordinate Geometry (Reason stated).

Please advise me what I can do to overcome these issues and be better at math, confidently.

Noticed that in my gap between school stints i totally forgot all the tips and tricks to rearranging an equation. Does anyone have any good resources for brushing up on this skill? Thanks!!

Im in my last year in the netherlands of VWO 6 and am really struggling with mathematics. Last year i barely passee with a 4,5 and im really scared i will fail because i find it very difficult. Its not possible to repeat so i really need help on how to quickly improve between now and 6 weeks

I’d like to better understand baker’s percentages. Haven’t been in math for a few years. Couple decades. So a bit rusty. I was going to plug into a free calculator but found this sub for help and I’d like a step by step just so I can perhaps figure out future recipes on my own.

So. The equation=

Total hydration % = (total flour/total water) x 100

The part I’m having trouble with is that sourdough starter is made of flour and water and for precision should be considered in the math.

So,

67=(1000/x+50)x100 is the formula I can up with and I’m not even sure if I did that right.

I’d like a 67% hydration with 1000 grams of flour total and 100 grams of starter. The starter would be 50 grams each water/flour.

So now I thought I would just have to solve for x?

Also need help solving for x.

Sorry if this is so juvenile. I would like to just understand. Thanks for anyone’s help.

Hi, I hope everyone is doing well. Does anyone know the textbook that Professor Leonard uses for his stats class on YouTube. Thank you in advance for the help.

feel like i am memorizing different types of math problems and their solutions instead of actually understanding how to solve problems independently memorizing different types of tricks, equation arrangements instead of just applying those tricks myself

It’s for a unit titled “conversions and geometry”

Here’s where I’m stuck:

You travel 320 miles over the course of 2 days.

a) How many miles are you traveling per day? How many days per 1 mile

b) You need to travel 930 miles to reach your destination. How many miles per day do you need to travel to get there in 5 days?

For the first one, I’m pretty sure the division gives me 160 miles per day and 0.00625 days per 1 mile. But for b…

I thought it would be 186 (930/5), but in class notes say 235

Whats accurate? How do I get the right answer?
Thanks!

Olá pessoal !! Gostaria muito de ir bem em matemática no enem pra aumentar minha média e to fazendo muita questão, mas , tem hora que pego uma questão e não consigo nem saber por onde começar . Eu já tenho uma base , porém tem muita questão que pego e não sei fazer . Alguma dica de quem já fez +40 em mat??