You travel at a speed of about 81 kilometers per hour for about 2.0 hours. Stated with the appropriate precision, you have driven _____ kilometers.
the correct answer is 160 but why? why is it not 162???
basically, i’m making an svg, and i now need to find some coordinates for things rotated 45 degress, so i instantly tought that that point is sitting in the midway point on a circle of the 2 equivalents from other polygons, so basically i need the formula for getting the x,y coordinates on a plane of a point midway between 2 other x,y coordinates on a circle in order to finish my svg
edit: to clarify, i need to find the midway point on a circle centered on 32,32 on a 64x64 plane that has 0,0 in the top-left corner between 2 points that lie on that circle while only knowing the x,y coordinates of the points that lie on the circle and not the midway point between then on said circle with the midway point being the one on the shortest path between the 2 points
Seems I can't post any pictures/screenshots here. I want to graph: y=5000(1+0.043)^x
So, a basic compound interest calculation. I put that into the " f: " field of geogebra and I'm not getting anything that makes sense. If I put it into google, the AI puts out the correct graph. Anyone know what I'm doing wrong?
Edit: I put screenshots in the comments.
I understand the logic of reciprocals of whole numbers and vice versa and the logic behind negative powers
As well as that factors are a ratio without without a certain quantity but I don't get the logic or the steps to the flip could anyone help?
Thank you to everyone for the encouragement. I've taken some of your advice and am planning to do some serious Calculus problem-set work in the 2 weeks leading up to the Spring semester. I can fit that in with my current pace without an issue.
A few of you have encouraged me to slow down, not just because math is challenging (and they're non-believers who doubt I can do it (I'll show you)), but because they think I should slow down and enjoy the journey instead of rushing for the destination. I'm sorry to say that mindset just doesn't fit into my reality. I am working to obtain my Associate's and Bachelor's degrees ASAP to support my family.
Now for the actual update! I'm ahead of schedule! I just finished my Algebra 1 review, and I'm moving on to Geometry. I got ahead of schedule due to unexpected downtime at work. I do worry about burnout. I can sense it already trying to get a hold of me. So I'll keep plugging away for now, but I might adjust some of my scheduled review time to give myself a break if burnout starts setting in.
| Course | Progress |
|---|---|
| DONE!!! | |
| Geometry | 1% |
| Algebra 2 | 14% |
| College Algebra | 38% |
| Trigonometry | - |
| Pre-Calculus | 4% |
| Calculus AB | - |
| Calculus BC | - |
| Physics 1 | - |
Taking notes by hand is completely unfeasible for me for personal reasons. I'm soon going to be taking a Linear Algebra and the equivalent of a calc 1 course. I need to be able to take notes live during class, and up until now I've been using Google Docs' built-in equation editor. I've realized that this will no longer be sufficient for my note-taking needs, what are the best alternatives for easy and quick notetaking on a laptop (latex is too much for me to learn imo, but if there's a simplified/similar thing that is as quick that'd be great)? Thanks.
Q= show that if (a,b)=5, then infinite a and b exists for which a+b=100
My answer= via bezout identity
a(x)+b(y)=5
Then as x,y belong to S(non empty set of real numbers)
a(20.x) +b(20.y)= 100
20.x= u
20.y=v
a(u)+b(v)=100
Hence proved.
Ik the method of taking a=100k-5, but I wanted to see how far I've come and measure my progress because I devised the solution on my own.
If I threw a dart at the real number line along the interval between 0 and 1,
P(dart ≠ 0.5) = 1
However, it *could* be 1/2. A probability of 1 doesn't necessarily mean it's impossible for the situation not to occur. That being said, is there a standard way to denote a probability of 1 means it *has* to happen? For example,
P(dart ≠ 2) = 1
This time, it's actually impossible, yet the notation is identical.
I really want to try to study alone and get better by myself. Right now I'm at an average 12th grade level although I notice myself forgetting fundamentals when solving even these simple equations. Does anyone have like a study plan to improve my understanding of basic math? Sorry I'm advance. I know this is an insanely broad question.
Hello, I’m beginning my degree in chemical engineering in the fall, and have spent the summer attempting to solidify my mathematical foundation. For context, my high school offered algebra 1, 2, geometry, precalculus and calculus, all of which I passed, albeit barely. With that said, I have a rough understanding of most high school level mathematics. Moving on, I’ve been utilizing Dolciani’s textbooks to refresh and strengthen the basics(Beginning with the algebra 1 book, and planning to end with modern introductory analysis), but wanted to ask if there exist textbooks more suited to my field. Might be a silly question because at the end of the day, math is math, but any insight would be helpful.
I wanna get back into self studying math but when I pick up where I left off, I am stuck on this problem and end up just staring at the page alot of the time. The textbook specifically says the problem is very difficult but I cant help but get discouraged when I find that its taking a long time. Makes me feel like this problem is impossible to solve or that I will never be able to do it. This makes me very upset because I love math and I want to do it but it feels unaccessible to me which is frustrating.
What do you do when that happens to you?
Finding square root of a number that I don't know was a pain for me.
Using that long division method 😭.
Like 841 it's the square root of 29, I didn't know that I tried many ways to over come but in the end I just used the calculator.
I was furious and curious can I find the square value of any number using (a+b)² expression then maybe I can also find the square root of perfect square numbers using it?
I came up with (10a+b)²= S [I know it's looks similar to that expression and actually it is I'm not claiming I found something new I just got rid of my problem]
100a²+20ab+b² = S (s is the targeted square value of which square root we are looking for.)
Now conditions; a= or < S, b can be only a single digit from 0 to 9.
Example: S=144.
100a²+20ab+b² =144
Then a=1 => 100+20b+b²=144
20b+b²=44
(For selecting b we can guess the number or just divide remaining number by 20a [a=1 in this case].)
44/20 ≈2
Now substituting as a test-
20(2)+(2)² =44
LHS = RHS then
a=1, b=2
(10×1+2)² =12².
I will do further case study related to this stuff.
From what i understood it is jusf math from high school for the entrance exam. I have not touched high school in a few years, so how do i go back to study it?
im at a writers block. im stuck in the prose and i think trying to explain it a second party might help. the paper is about a three-dimensional complex number system. thats my hook and all im going to say here about it, dm me if you want to know more.
I’m taking an undergraduate Ring Theory course and we’re currently using Gallian's Contemporary Abstract Algebra. I really like Gallian, but I’d like to supplement it with another book that has more detailed proofs, worked-out examples, and explanations of how to approach problems.
Our syllabus is roughly:
Unit I – Rings and Ideals
Definition and examples of rings
Properties of rings and subrings
Integral domains and fields
Characteristic of a ring
Ideals and operations on ideals
Ideals generated by a set
Factor rings
Prime and maximal ideals
Principal ideal domains
Unit II – Ring Homomorphisms and Polynomial Rings
Ring homomorphisms
First, second and third isomorphism theorems
Field of quotients
Polynomial rings over commutative rings
Division algorithm and its consequences
Unit III – UFDs and Divisibility in Integral Domains
Factorization of polynomials
Reducibility tests
Mod p irreducibility test
Eisenstein's criterion
Unique factorization in ℤ[x]
Divisibility in integral domains
Irreducibles and primes
Unique factorization domains
Euclidean domains
I’m particularly looking for a book that doesn’t skip too many steps in proofs and has plenty of worked examples before giving exercises.
For someone at the undergraduate level, which would you recommend as the best supplement to Gallian?
Thanks!
I'm relearning math to prep for an engineering degree (comp or cs or environmental) and I wonder when do I add logic and proof to my learning? Sometimes before algebra one?
To begin with, I apologize if this sounds stupid. I already feel like an idiot writing this.
I'm studying at a university in Germany, bachelors, and I used to think I disliked mathematics. But I've realized that I actually enjoy it once I sit down and start trying to solve problems.
My main problem is that after a few months, I tend to forget what I've learned. I know repetition is important, but I feel like the bigger issue is that I often learn how to use an equation without really understanding what's behind it. That is the problem.
I come from Central Asia, where I feel like I've always been surrounded by people who are extremely good at mathematics. Because of that, I've often felt like I'm simply not naturally good at it.
Recently, though, I've realized that I actually enjoy the process of solving mathematical problems and puzzles. I want to develop that way of thinking rather than just memorize formulas and procedures.
I've found these books:
Would these be a good approach for someone in my situation? Are there other books or resources you'd recommend for developing mathematical intuition, reasoning, and problem-solving ability?
Can i pursue mathematics and statistics as my undergraduate course when i am just so so at math.
I am going to uni next year and i am afraid i cant carry it.
Good day everyone, just for context I’m in my senior grade of high school and am taking basic calculus. Simply put, since I was younger I’ve been struggling with visual based math problems, mainly in subjects such as trigenometry, geometry and other mathematical topics that involve visual data. I tend to excel in more number-based topics such as algebra and statistics. Recently, I’ve been struggling in exams as I struggle to understand the graphs and the logic behind functions. I want to overcome this issue as I intend on taking a math-based degree in college and want to be able to have a clear understanding of this so I won’t struggle as much by then. If anyone can help me figure out how to overcome this mental block or frame it in a way that would be easier to understand, it’d be greatly appreciated. Thanks in advance!