This may sound a bit stupid, but what is the exact definition of a trapezoid? Is it a quadrilateral with EXACTLY one pair of parallel sides or aquadrilateral with AT LEAST one pair of parallel sides? My teacher says it's the first one, but my own textbook (Art of Problem Solving: Geometry) says it's the latter.
I recently attended my college lecture and I was literally told to memorize the algorithm which I couldnt. It would be nice if someone could explain me the algorithm as in from a fundamental apporach
This example is from “A First Course in Probability 6E” by Sheldon Ross:
A class in probability theory consists of 6 men and 4 women. An examination is given, and the students are ranked according to their performance. Assume that no two students obtain the same score.
If the men are ranked just among themselves and the women just among themselves, how many different rankings are possible?
Solution:
(b) Since there are 6! possible rankings of the men among themselves and 4! possible rankings of the women among themselves, it follows from the basic principle that there are (6!)(4!) = (720)(24) = 17,280 possible rankings in this case.
I am having a hard time visualising this example. If it had a factor of 2 multiplied in the solution, I can understand that the rankings would mean [Men rankings][Women rankings] or [Women rankings][Men ranking]. But that’s not the case here.
How would a ranking look like in this example?
let a, b, c, d be integers such that ad-bc=1. prove that the fraction (a^2+b^2)/ac+bd is irreducible
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hi my name is Abdallah and i want to learn mathematics i love space and i think if i learned math well i can understand some theories and formulas of Einstein and Maxwell
So I know that cosecant is 1/sine, secant is 1/cosine, and cotangent is 1/tangent. This is all seems extremely redundant to me and next to useless. I am aware of the geometric reasoning of cosecant and secant. But even that, I don't feel like justifies the need to create 3 new functions for use. So, is there a good reason?
Hi, I am a degree math student and I am struggling with passing my exams.
It's not that I don't study, or anything like that (I study a ton and learn the material perfectly), but when the exam comes around, my abilities suddenly plummet.
To give an example, yesterday I took a theoretical-practical analysis exam and I messed up very stupidly in each of the parts.
In the theoretical part I was doing the proof they asked me for and at one point you took two points x, y from a closed interval and you had to use the fact that their difference was zero, which you could do simply by saying that x = y.
Well, for some reason, my brain couldn't grasp that it could be like that at the time, and I went in a completely different direction, which wasn't right. Anyway, I messed up stupidly, and after the exam, I remembered what I should have written.
And then, in the practical part, I had to calculate the sum of a telescopic series, very difficult, to be honest, but I know how to calculate telescopic series, but at that moment even the initial step (decomposing into simple fractions) didn't cross my mind and then, after the examen, I was like "No way, I knew how to do this"
I've had ADHD diagnosed since I was 7, so that might have something to do with it, but I've never had big problems with it before, academically speaking, so maybe it's related with math?
What may be happening to me. Help.
Hello everyone, I just finished high school and am going to pursue a double degree in mathematics and computer science. There is a 2-ish month gap till I start university. Are there any books that will help me bridge the gap between high school and university mathematics? My high school math course lacked quite a bit of linear algebra such as matrices, etc. If so, how would you recommend to read and practice problems. Any help would be greatly appreciated, thanks! My high school math course lacked quite a bit of linear algebra such as matrices, etc, so suggestions for linear algebra books would also be helpful!
Something interesting I’ve noticed is that many students become comfortable with multiplication after enough practice, but division often still feels confusing even when they know the steps.
With multiplication, learners usually see patterns fairly quickly. Division, on the other hand, seems to create more hesitation — especially when remainders or larger numbers appear.
Sometimes it feels like students memorize the process without fully understanding what division is actually representing.
I’m curious whether others think division is conceptually harder than multiplication, or if it’s mainly the way it’s introduced early on.
dominant right brainer here, creative, etc, had trouble with math since HS i just never got it,
in HS i took it twice, as well as the state exam, barely passed the second time, had a tutor
coming across this same math in college, i failed my math class with D last semester, unacceptable for my career,
i'm awesome in biology in chem which is crazy right? also psych all As so what's up with math?
not to blame the educator but all my math teachers have been wackos i learned more from intelligent students around me, not sure why
i had a lot of hours tutoring in Hs in college i dont use tutors because they all teach different so i stick to my professor , my current professor has a 2 stars on rate my professor lol ,
i have my final tm, didnt do so bad, but i need a 85 to pass, im being stuck on some problems and im just curious
is math really just practice?
is there an easy way to learn math,
since math is universal what country do you think teaches math the easiest?
any tips to grasp numbers
thanks
Lets say i have the equation:
y=5x^2+10x+3
I want to calculate slope at a specific point, im wondering why method 1 is invalid.
Method 1: put it into y=mx+b form
y = (5x+10)x+3
now m=5x+10: it is a variable slope based on x location as expected, but the coefficient is wrong
Method 2: derivative
y'=10x+10
now m=10x+10: this is the correct answer I believe
Any help for me to understand this fundamentally woukd be much appreciated!
I have Provincial Achievement Tests coming up, and I have to do a math test without calculators. Unfortunately I suck at multiplying (mainly because I'm autistic and have a harder time with stuff like that) and we have a maximum time limit of 30 mins to complete 20 questions. I struggle with multiplying a lot even tho I'm 15 and have not said anything about it until now because I'm scared I'll be made fun of for my lack of knowledge. Any tips?
note: I can do my 1-3,5,10-11 times tables if that helps
Soo I'm in grade 10 academic math. My math grade on my midterm report card was a 40% and i got a 41% on my midterm exam. School ends in a month, finals are yet to come, I'm terrified. I got a 30 something percent on my last test. My final is worth 30% of my grade I think but I'm nervous because I haven't been doing great all semester. Is it possible for me to still pass? My attendance is honestly really bad, I'm trying my best to improve it-- it's not that i'm necessarily bad with numeracy but I haven't been there to properly learn everything. We still have another 2 whole units. I'm soo scared for my final exam. I really want to pass. The class I'm taking right now is a pre-req, I'm worried I may have to give that up. Can I still pass or am I for sure gonna fail?
I just passed Calc 2 with an A! Taking linear algebra this summer semester. Any tips or online notes I can take a look at? I have 4 weeks till my summer semester starts so trying to get ahead. Thank you in advance
From what I understand, pemdas is not a rule of math, we use it for uncomplexity between people, then how do we know that the answer to 2×8+4 is 20? Like it's just order made by us, it's like I invented a rule of math that everyone would use, add 1 to everything. The equations would not be right, but that's the rules no? I dont get ittttt
When looking for the GCD of a, b - how do we know we're not just looking for some common divisor?
i straight up hate internet videos and can't watch them but so much of "online how to" is a video now. i'll take books/pdfs too if they're free/inexpensive and reasonably easy to follow in self-learning
i haven't done real math since like 2011 and i'm trying to go back to school for engineering so i wanna make sure i remember it. i got through trigonometry/pre calc in high school just fine i just wanna practice a bit again so i dont go to a calculus class like "lol whats a fraction"
Something I’ve noticed is that many students seem comfortable using the formulas for perimeter and area during practice, but still mix them up surprisingly often in actual questions.
What’s interesting is that even after understanding the definitions, some learners still treat both ideas almost interchangeably unless the question is very direct.
I’ve always wondered whether this confusion happens because the formulas are introduced too early, or because students don’t spend enough time visualizing what perimeter and area actually represent geometrically.
Does anyone else think these two concepts are harder to separate intuitively than they first appear?