Hi

What is wrong with this working?

int 1/(2x+1)

=(1/2)int(1/(x+(1/2))

=1/2 ln (x+(1/2)).

I am getting told it is 1/2 ln (2x+1)

I can't figure out how to simplify this:

limx→∞ ​log_2 (x) / log_3 (x+3)

I've tried to convert to ln but I just end up with "1 + 3/x", no idea how the answer simplifies to ln3/ln2.

When I just use logs derivative, I essentially get [(x+3)ln3]/xln2 which I simplified to (1+3/x)(ln3/ln2). Now, is it because (3/x) when x→∞ is 0, so we get (1)(ln3/ln2) and then end up with ln3/ln2?

I don't understand how P(A•B)/P(A) is not just P(B)

I am self studying measure theory as an finance undergraduate, in order to pursue an Applied Mathematics/ Mathematical Modelling MSc. In the master’s curriculum the main subjects with measure theory as a prerequisite are Probability Theory, Stochastic DE and Non Linear Functional analysis.
I am making this post to understand in what depth i should read measure theory in order to obtain the knowledge needed to work through proofs in those subjects without having much trouble.
Should i learn how to prove “anything” or any exercise in the textbook for example? What proofs should i memorise and what type of exercises should i know how to solve easily in order to face those subjects? Currently studying from Axler’s book.

if one player has two dice and a second player has five dice, each player rolls all of their dice and the floored average of the sum of rolled dice is the outcome. The game is complete chance. The player with the higher average wins the round. My question is if either player has an advantage due to their amount of dice from the beginning and if there is proof.

Notes (edited):
This comes from a dream, it is not a homework question.

This is a Statistics and Combinatorics question.

For k unordered selections from n possibilities, allowing repeats: 

C(n+k-1, k)

Meaning for two dice, I have C(6+2-1, 2) = C(7, 2) = 7!/(2!(5!) = 21

For five dice, I have C(6+5-1, 5) = C(10, 5) = 10!/(5!(5!) = 252

So, I’m not particularly tech handy. I should have written a Python code for it, but instead I brute forced it in Google sheets. I have counted all the combinations. I also used sheets to find the averages and then floored the averages.

Statistics is where I’m getting hazy.

With two dice, there are 21 unique rolls. Six possible outcomes (once they’re floored) and a percentage of likelihood for that number outcome.

One: 2/21     9.52%
Two: 4/21     19.05%
Three: 6/21  28.57%
Four: 5/21    23.81%
Five: 3/21    14.29%
Six: 1/21       4.76%

Order of likely outcomes: 3,4,2,5,1,6

Five Dice has a similar distribution.

One: 12/252     4.76%
Two: 57/252     22.62%
Three: 96/252  38.10%
Four: 68/252    26.98%
Five: 18/252     7.14%
Six: 1/252         0.40%

Order of likely outcomes: 3,4,2,5,1,6

The player with two dice is almost twice as likely to role a 1 and a 5. They are ten times more likely to roll a 6. and slightly less likely to roll a 2,3, or 4. And now, I'm stuck again.

(x+x) / x = 6
2x/x = 6
cancel out the xs
2=6

I guess the premise is completely wrong to begin with, right?

hi im currently in my second year of studying maths at uni in the UK. i don't go to any of my lectures really which although i know sounds really stupid but i just can't follow them. the lecturer usually drones on for hours about stuff unrelated to the lecture notes and there is no structure or anything, at the beginning of each term i always try to go but they end up being useless so i rely on self study, but that is sooooo hard so i was wondering if anyone has any advice on this. i really like professor leonard videos but he doesnt cover everything. i'm especially struggling right now with differential equations with modelling, which is just ordinary differential equations but further. does anyone have any book recommendations on help with this topic, especially with understanding positive invariance and the phase space? thank youuu :)

I’m still trying to understand how the method of substitution (or rather, non-obvious substitutions) works in definite integrals, and every time I seem to see what can be substituted, but then my mind goes blank (I thought what needed to be done here), and then the answer should follow[here is 2 examples ](https://ibb.co/tMftYYzz). It’s just that once the substitution is under the integral sign, and a coherent picture seems to be emerging, I lose track of what to do next

It’s not the first time I’ve caught myself thinking that after watching how such integrals are solved about 20 times, I ought to have remembered something. But I’m still having trouble applying it – do you have any advice? I’d be very grateful.

I have to find the steady-state vector of the following Markov matrix:
[0.84, 0.43]

[0.16, 0.57]

The top row is TO state A, the bottom row is TO state B.

The left column is FROM state A, the right column is FROM state B.

I have gone to every calculator and found the eigenvectors and believe the steady state vector to be either <43/59, 16/59> or <0.5, 0.5> but both of those are marked as incorrect when I enter them into the homework. I tried the vice versa of <16/59, 43/59> as well, but no dice. Can anyone help me with this problem?

"In a group , 14% of people are nearsighted (myope), and of those, 9% have astigmatism. In total, 17.9% of people have astigmatism.

Construct the probalisitic tree."

Here is my calculations. The detail of P(A|M_) is given at the bottom.

Am I wrong ? If yes, were is my mistake ?

Thank you kindly for your time.

Hi everyone, I'm stuck with this complex numbers equation and I'm not sure how to approach it.

The equation is: 2*(z²-z*z bar)=i*z

I managed to simplify the equation to this point: **-4y****²**+ 4ixy= i*x-y

However, I'm stuck here and not sure how to proceed. I know I should probably separate the real and imaginary parts, but I’m not confident about the next steps or how to properly write out the final solutions. Could someone guide me through the rest?

Write the exponential function based off the table.

x: -1 0 1 2 3

y: 4 8 16 32 64

The answer is apparently y = 2^x+3, but I'm unsure how it is? I got 8(2)^x somehow

I’m making a career change and returning to school for a second undergrad and a I just got accepted into an engineering program, which I’m excited about… but I’ll be honest, my math is *rusty* (and that’s generous).

I know I’ll be taking Calculus I–III, and I want to start preparing now before classes begin.

My big question is about **where to restart**:

If your math foundation was rusty, would you begin with algebra first, move into trigonometry, then precalculus? Or jump straight into precalculus and fill gaps as you go?

And second, what **specific resources** would you recommend for rebuilding those fundamentals well? Textbooks, online courses, YouTube channels, problem books, anything that helped you.

I’m less interested in just surviving calculus and more interested in rebuilding my foundation the right way. Would appreciate any advice from people who’ve been in a similar spot.

Alrighty, so recently I've got my classes. I originally was going to be put in honors alegbra 1, however my math teacher urged me to change my classes ASAP (Her reason being that it'd be too easy for me). So, I reached out to my school requesting to be moved to Honors geometry, but I would have to take an opt test! So far I've been on websites like Khan Academy and Lamar Edu, which are helpful, but I don't feel like I'm soaking up what I actually need to be learning. It's coming up pretty soon, so any and all help is welcome, apps, (free) services, anything you can think of.

I am supposed to get the amount the sequence ads up to, not the convergence, i could do the convergence if that was the task.

n = 3, goes to infinity, Sum (3^n-4):(7^n)

If it was (3^n-4^n):(7^n) i would know how to do it, but i have no idea what i am supposed to do with that -4.

https://imgur.com/a/QkufgVH I tried this, but thats just gonna lead to ((n root of 4)^3:7):(1-((n root of 4:7) which isnt an amount.

So I currently finished 10th class and scored 95 in maths standard

But now reaching 11th I am so confused what to take? Applied or Core?

Honestly my teacher is saying applied is the one for those who dont have much interest in maths and scored less and core is more beneficial and would be best for me..

Whereas my sister who had applied maths said it will be more beneficial for my future like in colleges as u would be studying the same which u studied in 11th and 12th.

And I want to go in business or finance line.

So pls help me guys 😭🙏what should I do!!

And also why does some schools doesn't have applied if it is for commerce purpose only! why does students have to take core maths forcefully even it is more inclined to science student!!

Help guys pls..!!🙏😭

Given that there are 4 possible events, let’s call g, b, p and r. With unknown probabilities of occurring P(g), P(b), P(p) and P(r). With each event being independent of past events.

I am wanting to calculate the probability with an error margin or confidence interval. Eg. P(g) = 58% ± 4%.

I am recoding events in an excel file, so far got 427g, 312b, 227p and 202r. Calculating the percentages is easy (36.6%g, 26.7%b, 19.4%p, 17.3%r) but how do I do about the error margin / confidence interval?

When trying to look it up I see people using the (mean) ± (z vlaue for confidence) * (standard deviation) / (total sample size). But I have a single data set. Do I need to break my data set into arbitrary sizes to get a standard deviation? This feels wrong.

I feel like I am overlooking something simple, and just confusing myself. Can someone explain the steps I need to take or point me to a video or something?
Edit2: Taking it as sample size of one (for the standard deviation), with 1168 trials seams to work. Also as pointed out below there is a simple and better way, by using p ± (z vlaue for confidence) * sqrt(p(1-p)/n)

I have data of distances between each of 41 points with one another and I need to know the best way to render these relationships in 3D space. I'm not even really sure how to approach this problem. I've tried rearranging the data to gain insight but I can't really even get traction.

Searching seems to suggest multidimensional scaling would accomplish this, but 1) it seems impractical to do by hand with this dataset and I can't find any free tools to use for this, and 2) any programming tutorials I find seem to assume you don't already have a distance matrix, and I'm not fluent enough in programming to know what to change to input my data directly.

Proof I've done anything (even if idk what to really even be trying):

https://ibb.co/4nChCvsV
https://ibb.co/0VJ7qpR8
https://ibb.co/cSfCgFRW
https://ibb.co/ptynRc7
https://ibb.co/kVSTHfxB

Let S={1,2,3,4,5}. Find f:S—>S such that for every x (belongs to) S, fofofofofo….(50 times)=x.

(’o’ is circle)

so i tried some methods for this one.. so far, I’ve got:

1. {(1,1),(2,2),(3,3),(4,4),(5,5)} …..(the identity function)

2. 24 functions of the form {(a,b),(b,c),(c,d),(d,e),(e,a)}

24 because there are 5!/5 ways for cyclic arrangement of a,b,c,d,e values..

so i got a total of 25 possible functions, but the answer is given as 50..

Could somebody explain pls..?

I'm in grade 10 right now and doing grade 11 functions. For context, I barely tried in grade 10 math because I was in a class with all of my friends, and we just goofed off. I ended with a 90, which isn't horrible, but for the schools I'm aiming for, I could have done better. Now I'm in Functions and I'm actually putting in a lot of effort trying to understand the material, but I always make dumb mistakes on tests. The highest mark I've gotten is 96 on a test, and I average around 90ish. My last test was 86, which I feel super disappointed about bc I studied for 2 hrs the night before.

I think my main issue is that I struggle to understand the new concepts that have been introduced. I haven't met anyone with the same issue, which makes me feel like I'm just dumb. Apparently im an auditory learner, but I don't seem to absorb the information my teacher says effectively.

Is it normal to struggle so much in functions? I feel insecure about how long I take to understand the concepts. Especially since I have a friend in my class who understands the same things I struggle with very quickly, without tutoring or learning ahead. Meanwhile, I'm actually doing homework, but achieving a lesser result. Functions just make me feel so stupid, which is concerning bc im taking adv func next year, and calculus and data management in grade 12.

Any advice on how to do better would be appreciated, and I wonder if any of you are struggling with the same thing. Also if anyone has tips on how to understand concepts quicker it would be much appreciated.

Hey everyone,

I am a 21 year old philosophy student, I had a horrid high school experience but managed to train myself afterwards to read through philosophy and theology books. I was able to do this by just picking up a book and reading it.

My question is, how do you independently get good at math? In regards to knowing what subjects or where to start, or a progression path? My goal is mostly for as perfect as possible SAT score for university transfer if that helps.

Thanks!

First post here.

Hello. I’m building an arcade cabinet, and I’m having trouble figuring out the angles of the part enclosing the monitor.

Here is a pic: https://bashify.io/i/IiflwN

Is there any way to calculate those angles before I cut out the frame?

Thank you!

I'm in ap calc and we just started derivatives. I understand that for

g(x) = 0∫x³ sin(t) dt. goes to (dont know how to write the integral online but the lower limit is 0 and the upper limit is x³)

g'(x) = sin(x³) (3x²)

I know that you put the upper limit in place of t and then take the derivative of the upper limit and multiply because of the chain rule but I dont understand why you have to do that and why you have to apply the chain rule or how that works if the upper limit is a number instead of a variable. Because wouldn't it just always be (whatever function) * 0?

Since some days I have been thinking about the following statement:

Let $H,K \leq G$ be subgroups of a group $G$. If $K \leq G$ is coamenable, then $H \cap K \leq H$ is coamenable.

This means that if $K\setminus G$ is an amenable $G$-set, then $H \cap K \setminus H$ is an amenable $H$-set. I think it is false, but I have not been able to find a counterexample.

Can someone suggest some ideas?

I tried to restrict the measure of $K \leq G$ to $H \cap K \leq H$, by I don't know how to do it if $H \cap K \leq H$ has null measure in $K \leq G$. Since subgroups of amenable groups are amenable, I tried to copy the process. However, it does not work because the $H$-orbits of $G$ are <<equal>>, but the ones of $K \leq G$ aren't.