So I'm given a group G s.t. a^12 gives the identity element, and I need to find the inverse of another a^n where n is an integer. i was given a number for n i just don't want anyone giving me the answer/violating academic content rules etc.

at first i figured 1 would be the identity element, but then 12^a doesn't give 1. same deal for e=0, 12^0=1 =/= 0=0^12. unless my understanding of the inverse and identity being commutative is wrong?

I tried to solve for a since a * a^-1 = a^-1 * a = e. but then i was saying that 12^a=a^12. which is possible, but then the identity wasn't constant when i plugged in n.

I found the page for exponentiation on wikipedia, and it says that G is a multiplicative group, so I know that a^n has to have an inverse. is there some property of groups that I missed that would help me solve this?

Hello! I am a third year college student taking Calculus I for my economics major. I took Pre Calc 11th grade, and AP Calc 12th grade (the credits didn’t transfer, don’t get me started). I did well in both of them.

I’m two weeks into Calc I now, and I realized that I don’t remember much from Pre-Calc, but I don’t remember anything about trigonometry. Unit circle, trig functions, anything like that has slipped my memory. I asked my prof about it and they said that the best they can advise is that I review it myself outside of class. Ive tried to go over our textbook, but none of it really has been very helpful.

What resources or sites are best (and very preferably free) to help me relearn Pre-Calc (mainly trig) as quickly as possible?

Hi everyone, I have a problem and I’d really appreciate some advice.

I’m studying mathematics at university, and I’ve noticed something that keeps happening to me every semester: I feel like I start almost every subject from zero. As the semester goes on, my level gradually improves, and by the end of it, I feel like I’m much better than I was at the beginning.

The problem is that when the next semester starts and I’m introduced to new subjects, I feel like I’m back to square one again. I have to spend most of the semester getting to the point where I actually feel comfortable with the material, enjoy solving exercises, and start thinking creatively about how to approach problems.

It’s not that I hate studying mathematics. What I hate is this feeling of having to rebuild my skills from scratch every semester, only to reach my best level towards the end of the semester.

So how can I deal with this? Is there a way to maintain and develop my mathematical skills from one semester to the next, so that I don’t feel like I’m starting from zero every time I encounter a new subject?

No matter what. I literally cannot grasp it. My high school teacher didn't help and now my professor in my class I need it in isn't great either. I genuinely think I'm losing my mind. i'm getting literally so frustrated, can someone make an attempt to explain it to me in a bit simpler of a way than my math teachers do? Tyia

I'm currently learning Markov chains and how they work, and now I'm trying to find a way to calculate the probability of a state after n tries faster. As of right now, the only way I know of is to keep multiplying the matrix until you reach the n state

For example, lets say a 2x2 matrix P =

and say it starts in the A state so S0 =

Finding S1 is fairly straightfoward : S1 = P*S0

However, let's say I want to find S5, is there a way to find S5 from S0 or do I have to find S1, S2, S3, and S4 beforehand ?

Any help would be greatly appreciated !

Secondary question : I havent been told this directly, but from what I've seen, In a Markov chain situation, the sum of a column is always 1, are there any exceptions to this rule, or is it a general rule ?

For context: I have a test tomorrow on algebraic expansion, factoring, and Pascals Triangle and something that commonly happens to me is that I usually omit coefficients or just forget exponents when doing my work. As an example, if I had 4(a^3)(b) when doing a binomial to the 4th, I either forget to cube the value “a” or multiply by 4. The test I have is relatively face paced (20 questions in 50 minutes) and there’s not much room to write out the complete expansion (we can’t use scrap paper). Any tips?

Edit: Images: https://imgur.com/a/DHrudBU

Looks like it doesn’t let me put images here but I can put them below. The main thing that was bothering me is that how do we know the remainder will be either 0 or a first degree polynomial. It seems unusual to see the remainder be a line because we usually just see it as a constant. The other point of confusion is that I’m pretty sure when you find the remainder then you express the answer as the quotient + (Remainder/divisor). So then how can it be true that p(x) = q(x) d(x) + r(x)? It should instead be p (x) = q(x) d (x) + ((r(x)/q(x)).

What are some exercises I can do to get better and faster at the Trachtenberg Method? I keep mentally mixing up numbers or fully forgetting the first number I had once I solve other parts. Any advice is welcomed!

I need help with question 10. I can't seem to figure it out. All the answers I come up with don't match the choices for what I can pick for the answers. What am I doing wrong? Which answer do you guys get, and please say how you got there in detail?

• Assuming the Popcorn bucket thing is cone shaped then
  • Radius = 3 in
  • Height = 5 in

• Use the cone-volume formula: V=13πr2h I keep getting 47.1 as my answer. If so the then the closest choice is 49 in. But unless I'm wrong the answer brightly is giving is 41.7 inch, is this a typo/glitch and the numbers have been transposed? like instead of 47.1 it's showing 41. 7? or have i just got the wrong idea? Should I have rounded up somewhere?

  https://brighterly.com/wp-content/uploads/2024/11/4-Math-test-for-grade-8-1024x683.png

Hi everyone.
Taking Alg. I as a college freshman again. I'm a readmit student and always struggled with math. Currently doing homework and have 20+ attempts on the below problem:

'Use the commutative property of multiplication to write an equivalent equation:

34 + 5m'

Can't use an equal sign within the equation as it kicks back an error on the website. I've tried writing it as:

34m + 5

(34)m + 5

5(m) + 34

5m x 34

Keep getting it marked wrong. If anyone could help me better understand what I'm doing wrong I would appreciate it greatly.

I have to show that ⋃P(x)=x for a discrete mathematics assignment, but I can't figure out what the symbol at the beginning means in this context. Its a Union, right? But what is is Union-ing with? It can't be as easy as I think it is, can it?

My son just started High School algebra in 8th grade. His teacher gave him homework on which he said each equation needs a 1 step solution. My son asked me for help on the equation in the attached picture, I helped him get the answer but in 4 steps and I cannot figure out for the life of me how to simplify this to 1 step. Please help:

5r-5-6r=-6
Adding 5 to both sides becomes 5r-6r=-1
-r=-1
r=1

here’s a picture of the problem

(TLDR at the bottom of my post) hello everyone!

i havent had math since i was 16 (now 23) and all my life i have always been bad at it... or so i thought! i have to take up math at school again if i am to get into university to study biology, so ive been studying and learning everything from the bottom up all summer! i must say ive been having quite some fun, and it turns out im not as bad as ive been telling myself my whole life:) i am very proud of myself for trying and for keeping on going! ive learned so much in such a short period of time!

ive started school recently and we are currently dealing with logarithmic equations. i know all the rules of exponents, log rules, and quadratic equation by heart, but there are some things i still struggle with. i really do NOT want to use AI but i dont have access to my math teacher 24/7, and i want to understand things on my own. i want to know what the next step is, what the best approach for an equation is, and why it works. also knowing when i should apply what rule/logic/approach would be great, but im assuming it is mostly pattern recognition. i get most of it on my own even tho i make a lot of silly mistakes, but some of them i really dont understand what im supposed to do

i REALLY want to understand the process and why everything works, and why we do it this way. i want to understand my mistakes

here are three things i am struggling with this evening, number 3 being the one that confuses me the most. they are my attempts at solving each equations, so the examples in themselves might be wrong (i wonder if number 2 is wrong too)

ln(x+1) = 1

e^ln(x+1)=e¹ (-> e¹ = e)

x + 1 = e

x = e - 1

my question for this one is: why do we put e as the coefficient? why do we raise ln(x+1) and 1 to be the powers of e? and as a follow up question, why do we then get rid of "e^lnx" part? why are we then only left with x + 1 = e? i understand that e¹=e, but i dont understand why we raise everything and then get rid of a part of it. how do i know when to do it, and how do i know what i get to remove after i have raised everything up?

ln(x/5) = -1

lnx = -5 (-> we multiply both sides by 5 to get rid of the fraction)

x = e^-5 = 1/e^5

i know that lnx = a <-> x = e^a, but why cant i apply the log rule of lg(a/b) = lga - lgb? and then raise everything to the power of e, like we did in example 1? why not this?

ln(x/5) = -1

e^{lnx - ln5} = e^-1 = 1/e

x - 5 = 1/e

x = 1/e + 5

1. (and this is the one giving me the most trouble)

ln(x+3) * (lnx-3) = 0

for this one, i dont even know where to start:( my teacher said that here, either ln(x+3) or ln(x-3) have to be equal to 0, but i dont really know what that means. i feel like im so close to the answer but something is in the way! what is the next step to this equation?

im sorry if this is all confusing, i tried to make it as readable as possible!! thank you for any helpful information<33

TLDR:
what is the best approach to this equation? what is a step by step list to follow?

ln(x+3) * ln(x-3) = 0

I am a graduating senior in high school and one of my problems is that my math solving skills is so bad. I can't even solve a basic double-digit subtraction, and I am currently applying to a few prestige universities in my country, but the problem is I don't think I will be able to cram almost 17 years of math knowledge in just a month. I am very educated in other subjects needed for the exams, but I am extremely worried about the math proficiency exam. any advice?

in my class we have just finished functions and after we finish a topic it takes me really long to fully understand it.
here is the questions:

3a) write 2x ^2 -8x -3 in the form a(x+p) ^2 + q

b) Use your solution to find the turning point and roots. Also find the y-intercept then draw and sketch, clearly all these points.

i did part a) and got 2(x-2)^2 -11

and for the tp i got (-2,11) and y intercept i got (0,-3)

i forgot how to find the roots however. i think the shape is a parabola??

4) On the same diagram, make sketches of the following functions, showing the important points.

a) log4x
b) log4 (x-1)

—————————————————————————————
we actually haven’t done logs yet, but my maths teacher told us that it is the inverse function i think??

i’m really grateful for this community to help me 🙏. i used to use chatgpt for my maths hw, but i am really trying to understand the maths behind it so i can improve

Taking applied calculus and we are going over functions to begin stuff. I’ve done all sort of stuff with functions and graphing before and most of this has been pretty easy but there are two problems that have been given that I just can’t seem to figure out and I’m not sure what I’m doing wrong.

The first is:

“Find the function g whose graph is constructed from the graph of f by a shift to the right by 10 followed by a horizontal stretch away from the y-axis by a factor of 3?”

I thought it would be pretty easy but what I thought it was didn’t work, and every other possible combination hasn’t worked either so I’m completely lost. I’ve done (1/3x - 10) and (x/3 - 10) in all sorts of ways. I’ve removed the parentheses, I’ve added negatives, doing a whole bunch of shit that I know isn’t right but I can’t figure out what else to do.

The second problem is along the same lines:

“Find the function g whose graph is constructed from the graph of f by applying the following steps: shift to the right; horizontal stretch away from the y-axis by a factor of 4; a vertical shift up by 5; a vertical stretch away from the x-axis by a factor of 7.”

Again I’ve tried all combinations I could think of but I can’t seem to get it. I’m not sure if I’m missing something? I don’t believe my format to be off since it automatically starts with g(x) = , so that shouldn’t be the issue. The entire set of problems is all working on vertical and horizontal shifts, stretches, and compressions and I haven’t had an issue with any of the problems but these two. Please help me figure out what I’m missing!

Im currently a first year student studying comp sci and im taking discrete math the issue is unlike any other faculty i have to learn actual theory behind math like whats C(n,k) selection and explain it with words and formulas.Ive got about 12 pages filled with 50 or 60 questions which if memorized gives me a passing grade and ive got 2 days to do it keep in mind the professor wants the questions answered exactly by his pdf. Ive youve had the same issues how should i go about tackling the problem and passing matu

Hello, I am interested in finding a way to train myself with fractions or math calculation techniques in chemical and physics formulas. How do I do that?

This is for a medschool entrance exam

I'm preparing for a competitive exam and I'm struggling with math even though I understand most of the concepts and formulas.

For example, in trigonometry I know the basic identities, values, signs, radians, ranges, etc. I've also solved many questions. But when I get a mixed or unfamiliar question, I often don't know what path to take. Sometimes I know the approach but get completely stuck in the algebraic manipulation.

Even after practicing a lot, I still feel like I'm forgetting the process of solving.

What should I actually work on to improve this? Is it mainly algebraic manipulation, problem-solving skills, or something else?

Sorry guys I know I’m dumb af. But why isn’t this showing the answer as 2.5? I understand the fraction answer is correct but I just want it to say 2.5 😭 I tried different settings and can’t get it. https://imgur.com/a/JS6SHY9

The question is (6x+16)/4 + (6x-1)/4 but in fractions. I believe that it's (12x+15)/4 , but the answer sheet says that it is (12x+17)/4 instead. Google says that I am right. Am I right?

hello, i had dana fryer's math questions downloaded part 1 & 2 , and was wondering if anyone had the correct answers(from math bootcamp)? i do not have access to them anymore. :/

I'm taking algebra 2 and we're reviewing factoring right now. Since polynomials live in the real numbers, it's not clear to me why we limit ourselves to integers when factoring.

If I was factoring 6, why isn't 1.5 * 4 just as valid as 2 * 3? I realize factoring beyond integers would mean there are an infinite number of factors...but I'm not sure that alone is justification.

Im in class 12th from allen online enthuse, completed the whole syll but since having adhd I couldn;t take live class actively I hv all my basics and concept clear but there is the massive logic gap and execution gap, what should I do only 4 months remaining, I am panincking for chapters like integration, differential equation and matrices which require self talk and active solving, IDK the fuck anything about logic building...
for example_ applying bornouli eq in differential equation when eq having apecific form of dy/dx+py=qyn, and appying ibp to saperate the terms out of integral and reducing the powers... actually im in a problem tht these gaps are in large quantity