help-27

[woven radish]

Dumbest Being

[restive river]

In the other triangle

That $l_1$ is scaled by some value $l_1*s$

[woven radish]

Dumbest Being

[restive river]

Where s is the value by which it got scaled

And infact all the lenghts will get scaled by the same factor

U can see that 3 became 6 after scaling

So the factor which it got scaled is 2 right @rain quiver ?

[rain quiver]

Yes.

[restive river]

So now look at the side length x

After scaling[multipying by 2] it became 18

So $2x=18$

[woven radish]

Dumbest Being

[restive river]

right?

[rain quiver]

yep

so x = 9

[restive river]

Yup

Now what do u think about $y$

[woven radish]

Dumbest Being

[restive river]

Can you figure it out

[rain quiver]

4

[restive river]

Yes

[rain quiver]

Alright. Thanks for the help. Very much appreciated. 🙏

.close

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[devout snow]

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[winter patrol]

post embeded pic instead of heic file extension

[chilly hornet]

try screenshoting it

and sending the screenshot

[spiral mural]

ok downloaded the image for you guys

[chilly hornet]

oh ty

I assume these are all line segments

oh

that's going to be pretty complicated

best way to go would probably be setting f(x)=ax+b|x+3|+c|x-2|+d

and doing a lot of math

[zenith glacier]

a piecewise would have made it so much better

ye

[chilly hornet]

aight this works

just need to use the gradient of the line

when x<-3, the slope is 3 on the graph

on our f(x), the slope is a-b-c

repeating that for -3<x<2 and x>2 gives

solve this, then use any random point to find d

idk why you can't just do piecewise functions

[chilly hornet]

an expression like this should rarely be practical to do anyway

either way

yes that should be correct

now use any point to find d

np

lmao

don't think that's a thing

[devout snow]

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[zenith glacier]

smort

[devout snow]

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[nocturne nimbus]

Need help with these steps

[vagrant mural]

Where's the problem?

[nocturne nimbus]

(3x+2)/x(x^2+1)

bottom of the snippet

[vagrant mural]

i mean where are "you" facing a problem

[nocturne nimbus]

Where to begin. Really not understanding partial fractions

[vagrant mural]

your teacher didn't teach?

[nocturne nimbus]

Not in a way that landed with me. The class is remote and im not hearing back. I believe the formula goes a_0/x + a_2x + a_1/x^2 + 1

@vagrant mural Im not understanding which formulas equate to the numbered instructions

<@&286206848099549185>

[devout snow]

@nocturne nimbus Has your question been resolved?

[nocturne nimbus]

Gotta get to work.

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[onyx merlin]

Guys i have this absolute value equation,
3|x-1|-2=7
does the 3 infront of the absolute value sign means multiplication?

[zenith jacinth]

ab means a times b

basic algebra

[chilly hornet]

also that equation doesn't have a solution

but anyways

[onyx merlin]

did a typo, sorry

so its basically 3x-3 right?

[oak harness]

if x-1 >= 0, sure

[zenith jacinth]

who told you that

[oak harness]

But x-1 could also be less than zero (unless you're given some weird restrictions)

[sonic smelt]

Yeah but there's no need to rewrite 3|x - 1| as |3x - 3|

3|x - 1| = 9
|x - 1| = 3

[onyx merlin]

my teacher told me theres 2 solutions, i did the first way where i get 4, and the other way is to make the 7 negative

im not really sure here

[sonic smelt]

From here
x - 1 = 3 or x - 1 = -3

So x = 4 or x = -2

[oak harness]

If you think about what the absolute value means, it makes more sense

|x - 1| = 3

What number(s) have the absolute value of 3? Well, that'd be 3 and -3.

so x - 1 =3 OR x - 1 = -3

[onyx merlin]

ah, i think im understanding now, ill ask more questions if i run into problems

thanks guys

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[obtuse slate]

My work

I know I messed up on the ordering

It should be 0.5 + other stuff

But I’m confused on the other stuff

<@&286206848099549185>

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[boreal night]

Can anyone help with this

[devout snow]

Please don't occupy multiple help channels.

[distant harbor]

Factors of c that add to equal b

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[covert pendant]

How would i solve this

[placid rover]

substitution

[covert pendant]

Would the whole denominator be u

[placid rover]

if you let it be u, then why not.

I wouldnt recommend it though

Also that integral is written badly

There is a missing dx

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[pliant tiger]

can i use fundamental theorem of calculus to evaluate integrals on the complex plane?

[pliant tiger]

i found this scary integral online

[pliant tiger]

can it be evaluated this way?

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[lone gazelle]

One message removed from a suspended account.

[main gull]

It's n to the n power

What exactly are you questioning?

[lone gazelle]

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[main gull]

Do you have the actual question to post?

[lone gazelle]

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[copper mango]

n^n is... n^n

If that's not what you want to ask, don't ask it

If you have an actual question relating to n^n, you should ask that... other than that you got the answer you asked for, .close

[main gull]

You provided the text format. If you have the actual document on where the question came from, screenshot it and send it

[lone gazelle]

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[copper mango]

Screenshot the entire page

[lone gazelle]

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[main gull]

That gives so much more details now

You're finding the first 5 terms of n^n

Probably starting with n = 1

[lone gazelle]

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[main gull]

Do you know how to do the first one?

[lone gazelle]

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[main gull]

Explain how you would do it

[lone gazelle]

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[main gull]

Because if you can do the first one, it's the same process for n^n

[lone gazelle]

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[main gull]

FYI, when you ask a question, post something like this, with all the details

[main gull]

Because this gives no context

[lone gazelle]

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[devout snow]

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[silent scaffold]

I have a question regarding strong induction if you can help me.

What's wrong with the following proof.
Show that for all n > 0, n2 is even.
Base case: n = 0 --> 02 = 0 = 2p*0
Assume by strong induction the proof is true for all n upto k.
Show that (k+1)**(2) is even.

1. (k+1)**(2) = ((k-1) + 2)**2
2. ((k-1) + 2)**2 = (k-1)*2 + 2(k-1) + 4
3. By inductive hypothesis, (k-1) is even, thus 2*(k-1) + 4 is even.
4. (k+1)**(2) = ((k-1) + 2)**2

[narrow plank]

What is x**2

[silent scaffold]

x squared

[graceful cosmos]

Ah yeah no don't use that, haha

x^2 is safer

[silent scaffold]

I apologize is there latex on this server?

[graceful cosmos]

There is!

$Latex$

[woven radish]

Kaynex

[silent scaffold]

I will be back haha, let me rewrite this

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[restive river]

.

[narrow plank]

Try assigning variables to 1) Areas and 2) cutting rate

Cutting rate can be thought of as some area per second

[restive river]

@narrow plank

alright

A = 2B
A = 3C

[narrow plank]

Is that area or cutting rate?

[restive river]

area

and I assign a new variable for cutting?

shen

[narrow plank]

yup

[restive river]

C(x)=2B(x)

C(x)=3A(x)

@narrow plank

how does this help me?

[narrow plank]

Note:

Area cut = cutting rate • time

[restive river]

hmmm

but I don't get how to use that because I don't have cutting rate or area cut

and like I can't combine like terms since there are 2 variables

[narrow plank]

You can express area cut and cutting rate in terms of scalar multiples of 1 variable

[restive river]

not sure what a scalar multiple it

@narrow plank

can you help me

[restive river]

are we solving for time here?

[narrow plank]

Oh - everything is expressed in terms of 1 variable - different variables are just 2 times (that variable) or 3 times (that variable)

[narrow plank]

Yup

[restive river]

oke

[narrow plank]

We want to see who is the fastest (lowest time)

In comparison to the others

[restive river]

ya

area cut

A = 2B
A = 3C

which one do I use?

@narrow plank

[narrow plank]

area cut / cutting rate = time for each person to cut their lawn

[restive river]

since we have A then I'll use A

2B /(area of Carlos)/3 = time

@narrow plank but this just looks weird and confusing

and idk where to go from there

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[viscid crown]

im learning discrete distributions and im confused about when to use what

[viscid crown]

4 of them are releated to success and failures, (hypergeometric, binomial, negative binomial, geometric), last one (Poisson) is related to interval

Hypergeometric is used when we are given a fixed number of dataset N and we have decided to sample n points from N. And we want to determine how many of them are success and how many are failures.

Binomial is used when we repeat an experiment N times which has probability of success of P and we want to determine how many of them are success

Negative Binomial is just Binomial but we keep experimenting until we reach at least K successes

Geometric is just negative binomial? I dont get it

Finally Poisson is used when we want to determine number of times an events occurs in an interval

im kinda confused of when to use what and if my understanding of those distributions is even correct

[devout snow]

@viscid crown Has your question been resolved?

[supple knot]

if geometric was exactly the same as negative binomial, it wouldn't have a different name

the only way to learn when to use what is to solve problems

[viscid crown]

hm so is my understanding on Hypergeometric and binomial kinda correct?

[supple knot]

you've oversimplified it

just read the first sentence of each wiki

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).

and so on

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[sonic coyote]

On a 100 question true/false test, what is the probability of getting 0 answers right?

O used a Binomial Probability Calculator where n i wrote number of trials 100 probability 0.50 which is 50% of getting a correct answer and successes 0. Am i doing it right? Is answer correct?

[sand thorn]

@sonic coyote can't you think of it like, there's exactly one way to get all the questions wrong, and there are 2^100 ways to answer all the questions, so it's 1/2^100

[sonic coyote]

Oh nice. Thanks

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[gilded radish]

I know how to normalize a vector but I am not sure what is a normalized matrix and how to do it?

[gilded radish]

I cannot find this, all what I find is for vectors

The question is: what is a normalized matrix and how to normalize a matrix? any good reference is appreciated

[supple knot]

you're just looking for a definition?

like you don't have an actual problem to solve?

the answer is there are lots of answers

divide it by determinant for example

https://en.wikipedia.org/wiki/Matrix_norm

[gilded radish]

Does it depend on the problem?

[supple knot]

yes

there is no single definition of "normalized matrix"

[gilded radish]

hmm, for example I had an exam where they asked me to find the normalization of a matrix X whose eateries are generic x_11, x_12 ... x1d etc

It was machine learning exam(so you can think of the matrix as data matrix) and I didn't know what they want me to do

[supple knot]

screenshot the original question

[supple knot]

if it's ML then it's probably none of the ones listed

https://towardsdatascience.com/understand-data-normalization-in-machine-learning-8ff3062101f0

non-math people fuck up math terms all the time

i wouldn't ask math people definitions for words from non-math classes

[pallid peak]

^^^

[gilded radish]

😂

I see thank you for your help!

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[manic gull]

I've tried several times but the result is either contradiction or wrong.
What should be the answer?

[manic gull]

Or should it be insufficient data?

:<

anyone?

plz help

[velvet notch]

U got it

I mean the answer is probably E because there no way to tell who are two truthtellers and two liars.

[manic gull]

ok tq

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[uncut narwhal]

how to solve this?

[sonic smelt]

You mean how to evaluate that?

That's just taylor expansion for e^x

if I'm not mistaken

[uncut narwhal]

ohh

how do we know that it is taylor expansion for e^x?

[sonic smelt]

Generally taylor series for some function f is this

In this case f(x) = e^x

So f^(n)(a) just becomes 1 (a = 0)

And so the series just becomes sum of x^n/n! from n = 0 to infinity

[uncut narwhal]

so can i just write like this?

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[tribal lantern]

I need help

[tribal lantern]

This has something to do with mean value theorm

[placid rover]

Sketch a graph.

Deduce the answer.
Use this to help write the formal argument

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[tame bridge]

I have no idea how did they solve this

maybe i know but cant remember

mmmnnn hello?

any one here

any one reading this, just look at the immage i shared above, im confused

[tribal lantern]

Im confused too

What equation did they plug the value

[tame bridge]

lemme show you

hello?

[lilac heath]

whats wrong

[spiral mural]

They just made an equation given the info

[tame bridge]

please lookat the first image

[spiral mural]

then they just sub'd in the value and solved for the indeterminate

[lilac heath]

ya they just solved for V my homie

[spiral mural]

an explanation is even provided there

[tame bridge]

in the first image: $R=275-v*13$

[woven radish]

mugohan bae

[tame bridge]

how did it become : $13V=65$ in the next step

[woven radish]

mugohan bae

[spiral mural]

You didn't sub in your R value

[tame bridge]

wdym

[spiral mural]

Let's just swap sides so V ends up on the LHS

What they did was subtract 210 by 275

[tame bridge]

65

[spiral mural]

that'll give you -13V=210-275

Whic his -13V=-65

apply 1 more step

V=5

[tame bridge]

ok and them divide by 13?

[spiral mural]

nope

-13

[tame bridge]

ahhh yea i meant that

[spiral mural]

ye that's about it

[tame bridge]

wait so..

[spiral mural]

1. Learn how to make equations given the info
2. Learn how to algebraically manipulate

[tame bridge]

i can do the 2nd

[spiral mural]

ok

If you can why'd you ask?

[tame bridge]

I was confused

sorry

for

bothering

if

i

[spiral mural]

I'm not bothered

[tame bridge]

did

[tame bridge]

cool

alrighty

[spiral mural]

You gotta learn how to do 1.

Cause you'll come across many questions that require you to set up an equation

[tame bridge]

Hmmm yea i have math class today so ill talk to him

by the way?

how long does it take to complete covering a topic like "linear equations" in alg1 for a newbie student

thanks man!

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[restive river]

Hi! I have a problem and in it I did something I'm really not sure of, here's the problem:
y = 5sin³(𝑥)cos²(𝑥) for 0 ≤ 𝑥 ≤ ½π, its maximum point is M.
i) Find the 𝑥-coordinate of M.

[restive river]

I differentiated and got:
dy/dx = 5[sin²(𝑥)cos³(𝑥) - cos(𝑥)sin⁴(𝑥)]
and equated it to zero to get tan²(𝑥) = 1

Is what I did correct?

the dy/dx looks a little too simple

one sec

dy/dx = 5 cos(x) sin^2(x) (3 cos^2(x) - 2 sin^2(x))

we can consider the case where 0<x

as it is obviously not the solution

and x<1/2*pi

now we want to find the critical points, just as you realised we need to do

0= 5 cos(x) sin^2(x) (3 cos^2(x) - 2 sin^2(x))

divide by 5 cos(x) sin^2(x) because it does not equal zero on the domain

0=(3 cos^2(x) - 2 sin^2(x))

3-2*tan^2 (x)=0

tan^2(x)=3/2

Okay I follow everything except how to reach dy/dx

your solution actually seems prettier. I will double check mine

Alright take your time, but when you check it can you send the steps you took?

all you really need to know is
d/dx ( f(g(x)) )= g'(x) * f'(g(x))
d/dx ( f(x)*g(x) ) = f'(x)*g(x)+ f(x)*g'(x)

and the derivatives of trig and power functions

Okay I think I fell short in implementing the first rule of those

because for example in sin³(𝑥)cos²(𝑥) I'm supposed to do 3sin²(𝑥)cos(𝑥)cos²(𝑥) + .... but I forgot the 3 in the beginning

am I getting you right?

tbh I used Wolfram the first time

one sec

5* sin³(𝑥)cos²(𝑥)
5* (sin^3(x))' * cos^2(x) + sin^3(x) * (cos^2(x))'
5* [cos(x) 3* sin^2(x) * cos^2(x) - sin^3(x) * sin(x)* 2*cos(x)]

this is done by hand

Let me try and reach it

you almost got it

but please pay attention that the g(x) inside the f'( ) is not differentiated

Okay

[restive river]

.

[restive river]

5* [3* sin^2(x) * cos^3(x) - 2sin^4(x) * cos(x)]
5sin^2(x) * cos(x) [3 * cos^2(x) - 2 * sin^2(x)]

I finally came back to the result

5* [3* sin^2(x) * cos^3(x) - 2*sin^4(x) * cos(x)]

Ok I reached this

enough thinking for me for now ima go get a glass of water

thank you so much

now factor out everything you can

Alright

yeah factoring is a smart idea usually I just divide and rewrite the equation

this is beautiful lol

yeah factor everything then divide by it

tan(x)=sqrt(3/2) , (because) 0<x<pi/2

why do you say that last part?

because otherwise it can be -sqrt(3/2)?

(thanks dude)
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[unreal obsidian]

May I ask how should i start

do i use mean value theorem

[graceful cosmos]

Yeah

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[mortal gyro]

Hi all, I have this question for the assignment and I am confused about the way of approaching the problem. For J(z) = log(sigma(2y-1)* z) should I apply the chain rule? If I apply the chain rule I get sigma(2y-1)/(z*ln10) . Should I evaluate the behavior based on this result? Thanks!

P.S. I am new to this server, if question is not relevant to this channel, please let me know.

[devout snow]

@mortal gyro Has your question been resolved?

[elfin drift]

you can ping the helpers role

like this @dry robin

<@&286206848099549185>

dont ping or dm people specifically @mortal gyro

[mortal gyro]

<@&286206848099549185>

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[honest rover]

how do i do this?

[polar bolt]

Find the ways to get M=1,2,5

Find the probability of those events

[honest rover]

ye but

idk how

@polar bolt

[polar bolt]

Start with this like I said

[honest rover]

ok

@polar bolt

[polar bolt]

Huh? Start with this like I said - what you wrote doesn’t make much sense

[honest rover]

i dont what u man by that

[polar bolt]

What combination of coins gives median is 1?

[honest rover]

in terms of probability?

[polar bolt]

No just ways rn

[honest rover]

if u add 20% and 30%?

2 and 5?

[polar bolt]

Ways to get it

No probability rn like I have said

[honest rover]

maybe i dont get what the median is

in this case

[polar bolt]

,w what is median math

[woven radish]

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Requested by ScapeProf#9427

[honest rover]

ye lol ik that

[polar bolt]

Then what is the problem?

Give me a combination that gives median 1

[honest rover]

0, 1, 2

[polar bolt]

Is 0 a possible value?

[honest rover]

no

[polar bolt]

So why not give combinations that are actually possible?

[honest rover]

2, 3, 1, 4, 5

[polar bolt]

Is 3 a possible value? Is 4 a possible value? Is median even 1? Are we doing 5 draws?

[honest rover]

2, 1, 5

[polar bolt]

Like what

[honest rover]

this?

[polar bolt]

Is median 1?

[honest rover]

no 3

[polar bolt]

No

[polar bolt]

You clearly don’t even know what median is

[polar bolt]

Read here or check wiki or whatever

[honest rover]

i do know tho, its the ordered list of ascending numbers

and u want the middle value

[polar bolt]

So how did you arrive at median is 3?

Seeing how 3 isn’t even in the list

[honest rover]

nah i was getting confused cos i kept on thinking i was wrong

so i read the q again

and said 3

[polar bolt]

So what is the actual median of this?

[honest rover]

1

[polar bolt]

No

[polar bolt]

.

[honest rover]

is it 2

[polar bolt]

Yes

[honest rover]

u should have just told me

from here

[polar bolt]

Told you what?

[honest rover]

acc nvm

mb

ok so

now what

[polar bolt]

Now do what I said

[honest rover]

is there a specific formula for this?

[polar bolt]

No just write down the ways

Like I have tried to tell you

[honest rover]

for m=1 do i times all of them together

0.2, 0.3, 0.5

[polar bolt]

Sounds like you haven’t done what I have said (at least not correctly)

What ways are there to get median equal to 1?

[honest rover]

2, 1, 5 and 5, 1, 2

[polar bolt]

Didn’t we just agree median of this was 2?

You really don’t know what median is do you?

[honest rover]

if median is 2

how am i meant to make m=1

[polar bolt]

Find ways to get median 1

[honest rover]

0.5^3 + 0.2(0.5)^2 + 0.3(0.5)^2

[polar bolt]

Better but still missing some

1,1,2 - 1,2,1 - 2,1,1 are all ways to get median 1

[honest rover]

oh so my first was wrong

and third

[honest rover]

but that means they were all the same probabilities

[polar bolt]

3 ways to get it, so multiply by 3?

[honest rover]

u mean each one?

[polar bolt]

No only the ones that have 3 ways to get it

Only 1 way to get 1,1,1

[honest rover]

oh ok

true

do i multiply by 3?

[polar bolt]

What?

[honest rover]

nvm lol

this is awns for m=1?

[polar bolt]

No

Isn’t 1,1,1 a way to get median 1?

What about 1,1,5?

Ways to arrange 1,1,5?

[honest rover]

oh

5,1,1 and 1,1,5

[polar bolt]

No

[honest rover]

5,1, 1 and 1,1,5 and 1,5,1

[polar bolt]

Yes

[honest rover]

ok

what now

[polar bolt]

Now you can find probability?

You managed to find all ways to get median equal to 1 which was step 1

Like I said at the beginning

[honest rover]

ye

i got 0.5

for m=1

what do i do for m=2

ok i understand

.close

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[honest rover]

.reopen

[devout snow]

✅

[honest rover]

.close

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[restive river]

Having trouble with the 3 red boxes

[narrow plank]

I think it wants you to distribute and find a common factor of 2 among all terms you can

[devout snow]

@restive river Has your question been resolved?

[restive river]

How do I do that

[narrow plank]

Distribute?

(2k + 1)^2 = ?

[restive river]

I did and got 4k^2+4k+1

What do I do after that

[devout snow]

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[restive river]

Need help with the red box I’ve tried everything pls help

[glad valley]

Im pretty sure you made a typo

a = 2k, for some k

if they want you to plug in for a, you can't forget about the k

[restive river]

Nah that didn’t work either

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[devout snow]

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[amber brook]

is the answer

$y=ln(sqrt(x)+C)$

[woven radish]

qiz69k

[graceful cosmos]

,w solve y' = e^(-y)/(2sqrt(x))

[woven radish]

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[graceful cosmos]

Ye

[amber brook]

sesh thats fancy as

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[graceful cosmos]

Check out WolframAlpha on google

[amber brook]

ok thanks

.close

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[idle ice]

I'm struggling to set this one up, I know you have to make it in the form of a function and then take the derivative of it and find where the derivative = 0 to find a max/min, but i have no idea how to set it up from this information

[idle ice]

I put all the stuff together but to me it feels like everything has different variables

[devout snow]

@idle ice Has your question been resolved?

[devout snow]

@idle ice Has your question been resolved?

[devout snow]

@idle ice Has your question been resolved?

[devout snow]

@idle ice Has your question been resolved?

[proud zenith]

@idle ice

Are you still here?

[proud zenith]

You can try expressing one of the variables in terms of the other

From the linear equation

Considering a side's length of the triangle to be a and b for square

3a + 4b = 6

Now write b in terms of a

And then use the area formula for each and add them to find the total area

Then find the derivative with respect to a and equate it to 0 to find an extremum

(You'll probably have to find the second derivative as well to check whether the extremum is the minimum of the function or not)

[marsh linden]

3a + 4b = 6
3a = 6 - 4b

[marsh linden]

now, put that in the area formula

and differentiate and equate to zero

to get minimum

[devout snow]

@idle ice Has your question been resolved?

[dull egret]

Hi can anyone explain me midpoint theorem?

[marsh linden]

open your own page my friend

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[blissful elk]

Henlo everyone,

Having a bit of trouble here with part (b). I've completed (a) with no issues.

[blissful elk]

Sent that a bit too quickly but oh well.
I'm struggling a lot with group functions or at least...combining them?
I thought I had it in lesson today but I can't seem to make it work properly

I understand that you need to read from right to left rather than the other way around and how to map a number to another but I can't seem to get p such that (sigma)(rho)(tau inverse) becomes (1 2 3 4 5)

[devout snow]

@blissful elk Has your question been resolved?

[blissful elk]

<@&286206848099549185>

Any of you peeps able to assist me with this bit of Group Theory?

[gilded mason]

Do you know what (sigma)^-1 would be?

[blissful elk]

I believe that would be (4 3 2)?

[gilded mason]

Yes, so how could you use that to solve for rho?

[blissful elk]

I ended up applying both tau and sigma to the right hand side. Giving me;

(4 3 2) (1 2 3 4 5) (1 3) (2 4 5)

So we have - (Sigma)^-1 (1 2 3 4 5) (Tau)

Well, sigma-1 to the left side of both sides

And then tau to the right side of both sides

If that makes sense

[gilded mason]

Yes

So what would remain on the LHS of the equation?

[blissful elk]

That would leave just rho and 2 identity elements

[gilded mason]

which would further simplify to

[blissful elk]

Just rho?

[gilded mason]

Yes.

So, without using variables, what do you have on the RHS?

[gilded mason]

nvm you have it here

[blissful elk]

Yeah, 4 disjoint (I hope) cycles

Or at least that's what they look like to me

[gilded mason]

Well, the first three all have 3 in them, so they arent disjoint. Have you learned how to compose permutations?

[blissful elk]

I believe so. I think that's what I had to do in a previous question so I'm gonna go with yes

Read the thing backwards and find say where 1 starts and what it gets composed into

Or...something along those lines

[gilded mason]

Yes, you work from right to left

[blissful elk]

For 1 I get...
1 -> 3, 3 -> 4, 4 -> 3. therefore 1 ->3?

Or after my workings... rho = (3 5 4 1 2)

[gilded mason]

this is correct

[gilded mason]

I got something different

[blissful elk]

Oh no

[gilded mason]

what is the path you take for 5?

[blissful elk]

5 -> 2, 2 -> 3, 3 -> 2?

[gilded mason]

Yes.

[blissful elk]

So 5 -> 2 overall?

[gilded mason]

Yes

[blissful elk]

I got this before and ended with (5 2 3 4 1) after applying it at the start. Trying to figure out where I've gone wrong

[gilded mason]

I think you got your notation a bit off, where should 2 go?

[dull egret]

Means?

[blissful elk]

The route I got for 2 was:
2 -> 4, 4 -> 5 and that was it

[steep brook]

#❓how-to-get-help

[gilded mason]

Yes, but in this, it says that 2 goes to 3

[blissful elk]

That was my final answer after applying rho = ( 3 5 4 1 2) back into the original (sigma)(rho)(tau)^-1

In a previous attempt at doing the question

Let me send what my compositions were

[gilded mason]

do you see how you have one loop that does 5->2->5, and another that does 3->4->1->3? this has the right order, but not the right parentheses

[blissful elk]

1: 1 -> 3, 3 -> 4, 4 -> 3
2: 2 ->4, 4 -> 5
3: 3 -> 1, 1 -> 2, 2 -> 4
4: 4 -> 5, 5 -> 1
5: 5 -> 2, 2 -> 3, 3 ->2

I can see the loops sort of, like for 1: and 5:

[gilded mason]

if you just look at the first and last of each, that is your resulting permutation. Do you know how to write it using disjoint cycles?

[blissful elk]

So you'd actually have
(1 3 4) for 1: and for 5: you'd have (5 2 3)?

[gilded mason]

ignore all the numbers in the middle, you have:
1->3
2->5
3->4
4->1
5->2
How would you write the cycles for this?

[blissful elk]

(1 3 4) (2 5)

I seeeee now

[gilded mason]

Yes.

[blissful elk]

And judging by Tau being a disjoint cycle in the question

Rho must be (1 3 4)(2 5)

[gilded mason]

Well, the reason rho is that, is because you had rho on the LHS, and combined permutations to get (134)(25) on the RHS, so its equal

I dont think it matters whether or not tau is disjoint, as it was cancelled out on the left already

[blissful elk]

True, true. I just missed that there was a cycle and thought that rho would be a group of 5 things rather than splitting it

Now onto Part (c) where I'm thinking of generator stuff yet that was learnt...after this work was set

[steel sage]

(1 2 3 4 5 6 7 8) is odd so can’t be a square

It almost fed you the answer

[blissful elk]

I'm not exactly full of energy and also struggling with GT.
How is it odd? Is it down to expanding it to it's permutations and finding the total to be even or odd?

[steel sage]

It equals (18)(17)…(13)(12)

Odd many transpositions

[blissful elk]

Ooohhhh...I seee

I think that's all I've got to ask today

Thanks to both of you for the help on those questions. Glad to see there are those who can help with Group Theory lel

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[sacred cairn]

i solved using the difference quotient but for some reason the answers still dont match up

i dont kno what i did wrong here

[devout snow]

@sacred cairn Has your question been resolved?

[graceful cosmos]

Indeed, you've made a mistake somewhere

Happen to have your work? Can easily correct it

[sacred cairn]

It’s supposed to match the structure in the question but I can’t tell what I did wrong

My notes are very messy sorry

[graceful cosmos]

Is part of it cut off? Lol

[sacred cairn]

Yea lemme get the full thing rq

I simplified a lot it’s not in here tho

[sacred cairn]

Bro?

[devout snow]

@sacred cairn Has your question been resolved?

[sacred cairn]

@graceful cosmos

[graceful cosmos]

Oh I see

So notice the + 5 in the question. You've factored so that becomes + 1

-35 / (5x + 5h + 5)(5x + 5)
Is the form they want

@sacred cairn

[sacred cairn]

Omg thank u so much

that had me so confused

if u dont mind i have one more question

[devout snow]

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[restive river]

What does this symbol mean

[late island]

Hello
how can I get an equation for a curve with a horizontal asymptote (I have about 50 points for that curve) and it has a decreasing slope

[coral pecan]

symbol ⊆ means is a subset of

[restive river]

Oh

[coral pecan]

Sorry, this is already occupied go grab a new one!

😄

Yes

[restive river]

What does U to the side without the I mean then

[copper mango]

Proper subset

[restive river]

Oh I see

[coral pecan]

[restive river]

Thank you both 👍

[coral pecan]

damn tat is fast 👀

Mosh

Sure, you are welcome!

If you are done then please go ahead and close this

[restive river]

Oh sorry about that

.close

[devout snow]

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[heavy terrace]

help
Translation: "Given: Triangel ABC, AL is bisector
Prove: S(ABC)/S(ACL)=AB/AC=BL/CL"
the topic is congruent triangles
the theorem is any point from a bisector is in equal distance from the arms of the angle which it halves
"S" is for surface
I'm overall confused
Is the problem saying I have to find the ratio
or idek

[devout snow]

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[smoky cloak]

hey I was wondering if I could do this with a factorial.
[ (n+1)*(n!) ]^3 = (n+1)^3 * (n!)^3

[proud notch]

yeah u can

[smoky cloak]

okay thanks!

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[civic oak]

How to go from left to right

What's the steps

[polar bolt]

(Sqrt(x)-1)/sqrt(x)=sqrt(x)/sqrt(x)-1/sqrt(x)

[copper mango]

(a-b)/c=a/c-b/c

[civic oak]

Ty, that actually made sense

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[restive river]

So im suppose to use the x answer from the previous problem in the next problem

I got 5.05 but idk if thats right

i did 46 = 1/2(20x-9)

and got 5.05

but idk how to solve next problem with that 5.05

[wanton star]

uwu rotate

[wanton star]

wow what is this kind of question

[restive river]

i gotta find x

i use the x in the previous question to fill in the box in the next question

[wanton star]

that feels very error-prone

[restive river]

oh ya it is

1 wrong x then entire thing is wrong

[wanton star]

so you're asking about the top right?

[wanton star]

exactly, just make separate problems

[restive river]

so

im asking abut

wether or not the problem where the x+4 is, is 5.05 correct?

and

how do i solve the next problem where i put 5.05 in for the blank

[wanton star]

so the first question is whether x=5.05 is correct assuming 4 is correct?

[restive river]

ya

im like 99% sure 4 is correct

previous proiblems were easy

[wanton star]

hmm i realize i don't know my angle theorems anymore, lemme try harder :P

[devout snow]

@restive river Has your question been resolved?

[wanton star]

@restive river oh yeah this is the idea

5.05 is correct

https://cdn.discordapp.com/emojis/622030615923130408.webp?size=48&quality=lossless

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[thin hull]

The answer should be 4/29 but without the minus I am unable to see where is the mistake

[wanton star]

check this step

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[limpid junco]

Need to solve for x and y

[deft wagon]

for x and y?

[limpid junco]

yes

[cinder marten]

Expand out then equate Re and irrational parts

[limpid junco]

Re?

[cinder marten]

*Real

[limpid junco]

Well once i expaned it out i got 9x +2x(sqrt(8)) = 54 + y(sqrt(2))

But i dont know what to do from there

[cinder marten]

Simplify the LHS further

[limpid junco]

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[agile narwhal]

100 sheep are on the island. The wolf eats at least one sheep per day and eats them all in N days. Determine the smallest value of N for which there is a guarantee that there is a continuous stretch of days on which the wolf eats exactly 20 sheep. (1 day is also a continuous stretch of days)
Any ideas ?

[agile narwhal]

answer is 60

is it possible to apply pigeonhole principle on this ?

[wanton star]

are you sure the answer is 60?

[proud notch]

prbly not 60 since the wolf could eat 2 sheep per day for the first 40 days and then 1 sheep per day for the remaining 20 days?

[wanton star]

then there is a continuous stretch right

day 1 thru day 10

[proud notch]

ohh i see that's the continuous stretch ok

[agile narwhal]

i think its is like 1...1 (19 days), 21, 1 ... 1 (19 days), 21 1...1(20 days)

[wanton star]

wait exactly 20 sheep

rip

[agile narwhal]

not 100%, but probably it is correct

[wanton star]

if it's just a multiple of 20 the answer would've been 20 lmao

anyway

[proud notch]

so what is meant by continuous stretch?

like the wolf eats 20 sheep per day?

[wanton star]

several days that follow consecutively

[agile narwhal]

contiguous period of days

[wanton star]

so days a, a+1, a+2, ..., b-1, b

for a <= b

[proud notch]

and the wolf has to eat 20 sheep on day a, 20 sheep on day a+1, etc?

[wanton star]

no

the sheep eaten on a, a+1, ..., b has to total 20

[proud notch]

okay yep makes sense

[wanton star]

so if the wolf goes like 1, 5, 7, 8, 2 then there is a continuous stretch of days on which the wolf eats 15 sheep

[restive river]

yea

[agile narwhal]

i dont know how

[wanton star]

oh wait

pigeonhole works out nicely

i think?

[restive river]

consider the sequence $S_1,S_2,....S_N$
where $S_n$=number of sheeps eaten till the end of nth day

[woven radish]

Arkos

[restive river]

so $1 \leq S_1,S_2.....,S_N \leq 100$\
now include another set of sequence $(S_n+20)$\
so we have
$1 \leq S_1,S_2....,S_N, S_1+20, S_2+20,... S_N+20 \leq 120$

[woven radish]

Arkos

[restive river]

we have 2N elements in 119 holes

we need 2 elements in a hole
so we get $$S_i=S_j+20$$\
$$S_i-S_j=20$$

so the min value of N has to be 60

[restive river]

@agile narwhal

[agile narwhal]

hmm

im thinking about it

[woven radish]

Arkos

[restive river]

eh why right align

[agile narwhal]

hmm, tbh i don get it

maybe its too abstract for me

[restive river]

yea thats true, but the main idea is that we need to create a scenario where u can have 2 pigeons in 1 hole
and that we want a streak of days where total kill count is 20

[wanton star]

||consider the cumulative number of sheep eaten at each day. two days differing by 20 are banned, since otherwise we can take days totaling S+20 minus the days totaling S to get a stretch of 20 sheep eaten. now put each day in groups 20k+t for a fixed 0 <= t <= 19, so {0, 20, 40, 60, 80, 100}, {1, 21, 41, 61, 81}, ...., {19, 39, 59, 79, 99}. We have 20 of these groups and in total we have N+1 days (including the 0th day). For each set we can have 3 days at most (since otherwise we have two days differing by 20). So we may only have 60 days (including 0) at most, so N <= 59. For N = 59 notice that (19 ones), 21, (19 ones), 22, (19 ones) won't generate any stretch of 20 sheep, concluding the answer||

:D

the construction at the end was wacky

this doesn't invoke the pigeonhole principle explicitly but it does use its ideas

[agile narwhal]

ok thanks guys a loot

i will definitely use your thoughts when I will be writing my solution

[wanton star]

'your' being plural? kekw

arkos' idea is basically the same as mine but written differently

[restive river]

yea unless u've done something similar in class its hard to come up with this

[wanton star]

it was used in a math olympiad once i think

[restive river]

hmm

[wanton star]

i mean the same idea

not the same flavourtext

https://cdn.discordapp.com/emojis/715701345092370544.webp?size=48&quality=lossless

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[jade smelt]

Why doesn't this work?

[wanton star]

the square root of a sum is not always the square root of its terms

For example, \[ 2 = \sqrt{4} = \sqrt{2 + 2} \ne \sqrt{2} + \sqrt{2} = 2\sqrt{2} \approx 2.82843 \]

[woven radish]

Lance

[wooden zodiac]

only two exceptions

[wanton star]

1. where one term is 0

what's the other?

[wooden zodiac]

i

[jade smelt]

ok thanks

[wanton star]

hmmm, sqrt(a+b) = sqrt(a) + sqrt(b) implies a + b = a + b + 2sqrt(ab)

so sqrt(ab) = 0

so either a=0 or b=0

which clearly works

\[ \sqrt{a+b} = \sqrt a + \sqrt b \] if and only if at least one of $a$ and $b$ is $0$.

[woven radish]

Lance

[jade smelt]

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[dusky brook]

i’m super lost with evaluating limits using a graph and algebraically

[dusky brook]

problems i’m referring to

[devout snow]

@dusky brook Has your question been resolved?

[dusky brook]

no

[proud notch]

to evaluate the limit using a graph

first graph the function

then see what y value approach as you get closer to x=2

[dusky brook]

x=-3? that’s the value of the graphing problem. the other one is algebraically

[proud notch]

sry yeah x=-3

[dusky brook]

okay thank you what about algebraically?

that’s the one that i’m suck on bc i know you can’t substitute the x for 2 bc the denominator would be 0

but i’m not sure where to go from there

[proud notch]

good observation

the numerator looks like it can be factored though

[dusky brook]

okay once i factor it’s - (x+1)(x-2)/(x-2)

then the x-2 cancel and i’m left with - x+1

[proud notch]

yup

so you got it?

[dusky brook]

but then what’s the limit

[proud notch]

just plug in x=2

[dusky brook]

so -3

[proud notch]

ya

[dusky brook]

okay thank you

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[ember shard]

I wuickly need help

[ember shard]

This is my last question

My brain hurts

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[gleaming herald]

I have to find the distance between coordinate A(-1, 3) and B(-2, 5)
Above it is there an example written, but I dont understand it

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[amber edge]

,rotate

[amber edge]

what part do you need help with, all of it or one step?

[gleaming herald]

Ohh, I got it now, but actually have a different question

I have to check if the triangle is rectangular

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[ornate tree]

I'm doing logics and algorithms homework and have a question about permutations.
The question is
I have a string with 6 characters, each character can either be a digit or a lowercase letter. The first character must be a letter and at least two characters must be digits. How many possible strings? I'm not sure if I have the correct understanding because of the fact that the first character must be a letter and there must be at least two digits. From what I understand that means we have 26 * 10 * 10 * 36 * 36 * 36 = 121305600

[ornate tree]

I think that is right but I'm not sure because of the wording

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[ornate tree]

<@&286206848099549185>

[devout snow]

@ornate tree Has your question been resolved?

[timber pebble]

the first character must be a letter

this means that out of the gate we know the front multiplier is 26

then we have 5 characters left

at least 2 must be digits

[timber pebble]

so you need choose in there

problem is duplicates

either way

the way you have it undercounts

$\binom 5 2 10^ 2 36^3 26$

this overcounts

[woven radish]

jan Niku (Shuri for Honorable)

[timber pebble]

but is closer

it must just be

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[restive river]

In an examination of maximum marks 250, Arun scored 75. What is the percentage of marks scored by Arun ? If 40% is the passing mark, did Arun pass his exam?

[restive river]

can anyone tell how to solve this??

<@&286206848099549185>

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[restive river]

<@&286206848099549185>

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[restive river]

@restive river what have u done

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