help-27

[jaunty mantle]

when is this true?

well this quadratic clearly is concave up

so it'll be negative between the roots

[broken horizon]

yes

[jaunty mantle]

saying X^2 - X < z is the same as saying X is between the roots of this quadratic

[broken horizon]

do i look at the edge cases so at 0 and at 1 to see if our conditions are met?

[jaunty mantle]

nah ignore the edge cases for now

if you're happy up to here

we essentially have P(a < X < b)

[broken horizon]

where a would be 0 and b would be 1 ?

[jaunty mantle]

if we simplify with z = 0 we get P(0 < X < 1)

but that's the entire support of X so the probability is 1

now if you think about it, this seems weird but it makes sense

every number between 0 and 1 is bigger than its square

[broken horizon]

hmm ok
makes sense

[jaunty mantle]

i wanted to show you this construction because it applies to any change of variables

[broken horizon]

thank you very much

[jaunty mantle]

also we can easily compute for different values of z as well now

like if we wanted the probability that X > X^2 by 0.1, we can just set X^2 - X + 0.1 < 0 which is z = 0.1

[broken horizon]

yes nice

thank you once again

.close

[devout snow]

Channel closed

Closed by @broken horizon

Use .reopen if this was a mistake.

[jaunty mantle]

so for part b

[broken horizon]

ah my bad

[jaunty mantle]

you just break it into cases where X < Y and X > Y

X = Y happens with probability 0 so you dont have to worry about it

[broken horizon]

so it happens at 0

but they meet at 1 tho?

[jaunty mantle]

have you actually studied probability?

[broken horizon]

thats what i am doing atm
we just started

[jaunty mantle]

so you want to know P(X^2 < X, X^2 < Y, Y^2 < Y, Y^2 < X) right

but the X^2 < X and Y^2 < Y both happen always

so it's really just the other 2

you can then condition it on X < Y and Y < X

so P(X^2 < Y, Y^2 < X| X < Y) + P(X^2 < Y, Y^2 < X| Y < X)

[broken horizon]

| is or right?

[jaunty mantle]

no it's conditioning

[broken horizon]

ahh ok

[jaunty mantle]

so given that X < Y, clearly X^2 < Y is always true

because we know X^2 < X and X < Y so X^2 < Y is always true

[broken horizon]

yes

[jaunty mantle]

so it's just P(Y^2 < X | X < Y)

i believe you can just do $\int_{0}^1P(Y^2<X|Y > x),dx$

[woven radish]

frosst

[jaunty mantle]

so for each x, we need Y^2 - x < 0 so we need to solve the quadratic

i think you need to multiply this by the pdf of X as well but the pdf is 1 on this interval

[broken horizon]

Alright 👍

[jaunty mantle]

$\int_{0}^1P(Y^2<X|Y > x)f_X(x),dx$

[woven radish]

frosst

[broken horizon]

So 1/3 then as final product ?

[jaunty mantle]

idk what the final answer is

[broken horizon]

Ok

Thank you 🙏

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fossil raven]

Can someone PLEASE! help

[faint gorge]

Sure, send your actual question in

[fossil raven]

Okay, so, in Theorem 54, if AD = 3, DC = 2 1/2, BE = 4, EC = 3 1/3, is DE || AB?

I'm struggling with Theorems PLEASE 😭

[lunar harbor]

What is Theorem 54? Diagram? What have you tried? Etc.

[last parrot]

bro just screenshot the book or something

no context here

[fossil raven]

alright, I'll try, man. I'm on the computer

gimmie a sec. I'm stressing

[grand siren]

so what's theorem 54?

[fossil raven]

Theorem 54: If a line divides two sides of a triangle proportionally, then it is parallel to the third side

I'm so confused

[last parrot]

sounds like midsegment line of triangle

[grand siren]

i suspect there's more than that

like, what are A, B, C, D and E?

[last parrot]

=Suppose triangle ABC where D lies on AC, E lies on BC

then we need to prove DE//AB i suggest

[fossil raven]

Something like this

[last parrot]

hm ok

what is F for here

[fossil raven]

I think this triangle is an example for a different problem

[last parrot]

Just use Thales theorem

[fossil raven]

What's that?

And I'm so sorry for asking

Wait no, nvm, I'll look it up

[last parrot]

let me find

it is common in vietnam

[fossil raven]

Oh, alright. Ty

[last parrot]

https://www.youtube.com/watch?v=NhSetCrK_5k

[fossil raven]

Ohhh, okay

I should've looked for a video before asking

Tysm 👍

[last parrot]

So, the consequences of this would be if ratio CD/DA = CE/EB, then DE//AB

thales consequence

[fossil raven]

That's the right answer, right?

[last parrot]

CD/DA = CE/EB show these ratios, and already given

[last parrot]

correct

[fossil raven]

Ohhh, alright. BUT, one more question. Is there a formula for this?

[last parrot]

in the video

[fossil raven]

Ok, thank you a lot

[last parrot]

https://loigiaihay.com/ly-thuyet-dinh-li-dao-va-he-qua-cua-dinh-li-talet-c43a5248.html this is vietnamese website, really concise and clarified

but use google translate to translate all site

like this

idk if western countries delve into thales theorem a lot, but viete and thales are fairly importnt

[fossil raven]

Yeah, they haven't said much about it. This site should explain the other equations as well?

[last parrot]

it does

but translate the whole web since its all in viet lmao

[fossil raven]

Okay, thanks again. That's all I needed

[last parrot]

no worries

type .close if you are done

[devout snow]

@fossil raven Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[loud sorrel]

You get to design your own custom pair of 6-sided dice, where on each side you can put an
integer between 1-N, but you cannot have repeating numbers even across dice. If the sum of their rolls of the two dice is is a multiple of 13, you win. What numbers should be put on each dice and what are your chance of winning?
(a) You can choose numbers from 1 to N=12 for your custom dice
(b) You can choose numbers from 1 to N=20 for your custom dice

I am stuck on 1b. For 1a I wrote out all the pairs that add up to 13 because you are limited at 12+11 which cannot reach 26 the next biggest multiple of 13. I got that you should put 1,2,3,4,5,6 on one dice and 7,8,9,10,11,12 on the other in order to seperate the winning pairs. The probability of wining would be 6/36 or 1/6.

Now for part b I understand that now you can have three winning scenarios the dice summing up to 13, 26, and 39. I have written out all the pairs and see that some numbers can be repeated ie. 20+19 = 39 win and 20+6 =26 win. However, I am stuck on how to optimize it so you have the highest chance of winning. I do not know how to conceptually get the best pair of dice without simply brute forcing it. Also I'm unsure about how to optimize which numbers go on which side of the dice because for example if you put the 20 and 6 on the same dice you cannot role a 26 using those two pairs of numbers. Can someone help explain how to approach this problem and explain their thinking.

[devout snow]

@loud sorrel Has your question been resolved?

[loud sorrel]

<@&286206848099549185>

[last parrot]

I think some of the numbers from 1 to 20 all need a number to be the multiple of 13

[loud sorrel]

im sorry i dont understand could you please rephrase?

[last parrot]

For example, 1 and 14 both need 12 to be multiple of 13

Anyways, you need three "double" pairs for Die A and their three corresponding targets for Die B to win

get most win

[candid maple]

that being said, you can ignore 13 itself to shrink your sample space just a little bit.

[last parrot]

And both dices must have elements values less than 20

[loud sorrel]

ok so i've identified the double paris of
(12, 14 or 1) (11, 15 or 2) (10, 3 or 16)... etc.

And for my dice I placed alternated placing on each dice to get
Dice A: 12, 15, 2, 3, 16, 9
Dice B: 1, 14, 11, 10, 17, 4

Is this logic correct?

wait i found a better solution as the previous one only gives 8/36. Because 6 and 7 can combined with each other and 19 and 20 you can have 9/36
Dice A: 6, 19, 8, 17, 4, 1
Dice B: 20, 7, 18, 5, 9, 12

Is this correct and if so how would I verify that this is the best combination

nevermind i think my logic is flawed because I double counted 7 and 6 so this 2nd combination only gives me 8

Is there a better combination than this?

it should be a single arrow between 6 and 7

[topaz axle]

6, 19, 9, 15, 2, 10
20, 7, 17, 4, 11, 3

that's the same 9 arrows

[loud sorrel]

.close

[devout snow]

Channel closed

Closed by @loud sorrel

Use .reopen if this was a mistake.

[woven girder]

What is your question

Nvm

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[chilly owl]

someone help please

i hate algebra 1

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[chilly owl]

1

[supple knot]

Move all the terms with b to one side and then all the terms without b on the other

So subtract 1 to both sides

And then subtract 4b to both sides

[chilly owl]

im kinda still confused

[supple knot]

Then ask

[chilly owl]

im not even sure what to ask😭

[supple knot]

Do this first and show what you get

[chilly owl]

oh wait so why do we subtract 1 from each side?

[supple knot]

See the 1 on the right?

[chilly owl]

yes

[supple knot]

What's 1 take away 1

[chilly owl]

0

[supple knot]

Good

What's remaining on the right side

[chilly owl]

4?

[supple knot]

What makes you say 4

[chilly owl]

i dont even know exactly what your asking twin

[supple knot]

Better to ask than to guess some nonsense

[supple knot]

Right side is
1 + 5b

What's left after you subtract 1?

[chilly owl]

4b

[supple knot]

No

1 - 1 + 5b = 0 + 5b

5b represents 5 times b

[chilly owl]

but we do 1 - both sides right?

sorry if im seeming dumb it might be cause im dumb

[supple knot]

What do you mean 1 - both sides

[chilly owl]

wait

nvm

[supple knot]

Write out the math equation you mean

[chilly owl]

why do we subtract one by itself

[supple knot]

Do you know how to simplify the right side

[supple knot]

Because

[supple knot]

And answer this

[chilly owl]

no

cause im confused why we subtract one by iteself

[supple knot]

0 + anything = anything

[chilly owl]

yeah

thats not the part im confused on tho

[supple knot]

Like I said you need to simplify to understand why

[supple knot]

I'm doing this in smaller steps

[supple knot]

To solve for b

[supple knot]

So after you get 5b on the right, you need to subtract 1 from the left side

[chilly owl]

one minute

wait so the 4b - 5b is b and then 5 - 1 is 4 so 4 = b

i looked this up and this is what i came up with

[delicate jetty]

The eqn is 4b+5=1+5b,so first take 4b to the other side and it will become 5=1+5b-4b now take 1 to the other side which makes the eqn into 5-1=5b-4b then simplify it, it will become 4=1b that is b=4

[supple knot]

4b - 5b does not equal b

5-4 does equal 1 though

[delicate jetty]

Do the steps i said

[supple knot]

!nosols

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[delicate jetty]

Oh we should not give out the ans?

I don't know that bruh

I am new to this

[supple knot]

Yes it's the reason this exists in the first place

[candid maple]

please refer to #❓how-to-get-help; there are some guidelines for how to seek and give help in the channel.

[supple knot]

Also it's in the guidelines

[delicate jetty]

I joined here yesterday only

[supple knot]

It's fine

Happens to a lot of newcomers.

[delicate jetty]

Hmm

[restive river]

@chilly owl do u still need help

[chilly owl]

yes

[restive river]

okay

lets start from the beginning

ill take it super slow

bc i know how hard this shit is

[chilly owl]

very hard

[restive river]

OK SO

i promise you, you are not dumb. and i promise the question i ask is not trying to make you feel dumb. i want to build up to what we're doing in the problem

understood?

[chilly owl]

gang i skipped 8th grade and only did half of 7th i AM dumb

understood

[restive river]

good

1+1= what?

[chilly owl]

2

[restive river]

epic

ok now

do you know what a variable is

[chilly owl]

yup

[restive river]

ok great

explain it

[chilly owl]

its a placeholder for a number right

[restive river]

pretty much

ok so

if i say

x=1

x+x=?

[chilly owl]

2

[restive river]

why?

[chilly owl]

uh

cause you said x = 1

[restive river]

so then how did u get x+x=2?

[chilly owl]

because 1 plus 1

or is it just x because its the same variable

[restive river]

oh i see, so you're filling in x with 1

[chilly owl]

yes

[restive river]

bc x represents 1

as you said earlier

x is a placeholder for 1

[chilly owl]

yes

[restive river]

thanks for your help

OK NOW

Let's say x=1

x+5=?

[chilly owl]

6

[restive river]

why?

[chilly owl]

because 1 + 5

[restive river]

great work

x is a placeholder for 1

as you explained to me earlier

OK NOW

[chilly owl]

yes

[restive river]

let's say we don't know what the variable represents

so x=?

[chilly owl]

1

[restive river]

No

wait

[chilly owl]

1x

[restive river]

No done

not done

I will let you know when Im finished

mb

[chilly owl]

k

your good twin

[restive river]

x=?, we don't know what x represents

But we want to find out

In this instance we don't know, but as an EXAMPLE, let's say:
5+5=x. Here, we are asked to find x by adding 5 and 5 together.

So tell me, what is x?

[chilly owl]

10

[restive river]

why?

[chilly owl]

because 5 plus 5 =x

that means x is 10

[restive river]

so ur saying 5+5=10?

[chilly owl]

yes

[restive river]

so ur saying 10=10?

[chilly owl]

10 is 10

yeah

[restive river]

Thank you.

OK

Now we're gonna step it up

[chilly owl]

your very slow with this your a very good teacher twin

[restive river]

Are you ready?

[chilly owl]

yes twin

[restive river]

it's because i am a very slow learner and i tell mfs to slow the fuck down

OK

[chilly owl]

me too

[restive river]

period

[chilly owl]

continue

[restive river]

anyway

Let's say x=1

NOW...

Tell me

Is this true or false?

x=x+1

[chilly owl]

false

[restive river]

why?

[chilly owl]

wait

true

[restive river]

why?

[chilly owl]

wait

[restive river]

it's okay if ur not understanding yet, i just wanna know ur thought process

be not afraid

[chilly owl]

its false BECAUSE x plus 1 is 2 BECAUSE x equals 1

[restive river]

so ur saying

1=1+1 is false?

[chilly owl]

correct

[restive river]

Thank you.

You're right

Good work

NOW...

[chilly owl]

YAY

[restive river]

Let's say x=2...

[chilly owl]

YES

[restive river]

Are you comfortable with multiplication?

[chilly owl]

its scary sometimes but yes (only with negative numbers)

[restive river]

OK I'll start out with one that hopefully isn't too crazy or scary

You let me know if it is

[chilly owl]

okay

[restive river]

Alright

x=2

Now tell me

Is this true or false?

x+2=2*x

This one is hard

[chilly owl]

it is true

[restive river]

Why?

[chilly owl]

because 2 plus 2 is 4 and 2 times 2 is 4

[restive river]

Ok I want you to show your work by substituting 2 for x

[restive river]

This one

[chilly owl]

same thing

same answer

[restive river]

Yes, but show your work

[restive river]

Like this

[chilly owl]

oh okay so x plus x is 4 and x times x is 4 because x is 2

[restive river]

Sorry, I mean with the symbols

But clearly you're understanding it

[chilly owl]

x+x=x*x

[restive river]

Now fill them in

[chilly owl]

2+2=2*2

[restive river]

And the answers to both sides?

[chilly owl]

4

[restive river]

Lightwork

You got this

OKAY NEXT

[chilly owl]

yes

can you be my full time teacher

[restive river]

Back to basics

No I'm too busy

[chilly owl]

damnit

part time?

[restive river]

For money yeah

And with your parents' permission ofc

I'm a grown man

[chilly owl]

damn twin im broke asl

nvm then

[restive river]

OK NEXT

1+1=?

[chilly owl]

2

[restive river]

OK so

knowing this...

x+x=?

[chilly owl]

2x

[restive river]

NICE

EASY

why?

[chilly owl]

BECAUSE

i think by default if x is undefined then x equals 1x but we just say x so 1x plus 1x is 2x

[last parrot]

you can switch sides

holy long chat

[chilly owl]

wsp minhhh

[restive river]

we going slow

[restive river]

1 variable plus 1 variable is 2 variables

[chilly owl]

yes

[restive river]

sick

thats what u said

[chilly owl]

yes

[restive river]

thank you

ok next

x+1=1. What is the value of x? How do we find it?

[last parrot]

wspp

[chilly owl]

hmm in this case the value of x would be 0 so 0 plus 1 equals 1 so the value of x is 0

[restive river]

True, but how can we show that mathematically?

Show your work

[chilly owl]

can you be my part time teacher on occasion twin

[chilly owl]

hmm

[last parrot]

ok

i think approaching in easy examples would be nice

[chilly owl]

idrk fr

[last parrot]

imagine x +1 = 1. imagine you have a bag contain unknown number of apples, you put 1 apple in. you open the bag and find out there is only 1 apple, then what is the original number of apple?

[chilly owl]

0

[last parrot]

correct, but how do you know its 0?

[chilly owl]

because we put 1 apple in

[last parrot]

you gotta undo by take that 1 apple out right?

if you take that 1 apple out of the bag again, its 0 now right?

[chilly owl]

yes

[last parrot]

so back to x+1=1

what do you do?

if x+1 is the bag with 1 apple added, and since you want to remove one apple?

it would be x+1-1 right?

[chilly owl]

yes

oh shit

i love you dude

[last parrot]

but, we know that operations need to be equal both side, such that x+1-1=1-1, right?

else 0=1, which is wrong

if we subtract 1 on LHS, we also subtract 1 on RHS

[chilly owl]

what

[last parrot]

where LHS is left hand side and rhs is right hand side fyi

[chilly owl]

whats lhs and rhs

[last parrot]

LHS is left hand side and rhs is right hand side fyi

[chilly owl]

k

[last parrot]

for example, you have 2 rooms next to each other, each room have 5 people

so you see the people are equal right?

[chilly owl]

ye

[last parrot]

then, if its 2 room, 4 people each, it still equal, correct?

[chilly owl]

ye

[last parrot]

but you see 5-1=4

[chilly owl]

ya

[last parrot]

then, to achieve equality, we do same operation on both side of equation

in this case, each room have 1 person leave

do you find it logic?

[chilly owl]

yes

[last parrot]

so now, back to x+1=1, to remove 1, then you gotta minus 1 on both side of this equation, true?

[chilly owl]

yes

[last parrot]

so, x+1-1 = 1-1, right?

but 1-1 = 0, so x = 0

[chilly owl]

yes

[last parrot]

so back to the original question

[restive river]

everything you've done up until now has prepared you for this

[last parrot]

if you have an unknown value, you would want to keep them all on one side

[chilly owl]

its different tho

so

[restive river]

i believe in you

[last parrot]

for the equation to be solved, it is best to keep the unknown value on one side of the equation only, like x=1-1

do you agree?

[chilly owl]

wait im confused because the LHS and the RHS both have variables unlike x+1-1 = 1-1

[last parrot]

so now we will cancel them out

firstly, do you notice 1 and 5 are not in terms of b?

[chilly owl]

yes

[last parrot]

but you want to put all of the values not in term of b in one side

so, how do you eliminate 1?

if you have +1, how do you make it become 0? (This is what eliminate means)

[chilly owl]

1-1

i got that from someone else but i dont understand why we do that

[last parrot]

but you learned that just then, if you do an operation on one side, you must also apply it on other side, right?

[chilly owl]

yes

so 1 - 5 is 4

[last parrot]

then, left hand side is 4b+5-1, right?

[chilly owl]

yes

[last parrot]

so it would be 4b+4=5b, correct?

[chilly owl]

yes

[last parrot]

now, you see the values in term of b still on both side

we wants b values to be on one side only, so we need to eliminate again

[chilly owl]

okay so i understand how we do the same thing to both sides

but why do we subtract 1

out of all numbers

[last parrot]

to remove number 1 on the right hand side

you can choose to remove 5, but negative numbers is harder to work with

[chilly owl]

why do we need to remove the one

[last parrot]

you can do 4b +5 - 5 = 1 - 5 + 5b, like this, but it will have 4b = -4 +5b

which is harder to calculate with

[last parrot]

because our mission is to make b values one side (right hand for example), then 1 should not stay there

[chilly owl]

oh my god algebra is so much different

[restive river]

are ya winning son

[chilly owl]

i really need to go to bed i have lwk been trying this for 2 and a half hours can you add me and we finish this tmwr? sorry

[last parrot]

no worries

rest well buddy

[chilly owl]

goodnight twin

please help me tmwr

i NEED to understand this

[last parrot]

okay just ping me

if you are finish, type .close

thanks

[chilly owl]

.close

[devout snow]

Channel closed

Closed by @chilly owl

Use .reopen if this was a mistake.

[chilly owl]

.reopen

[devout snow]

✅ Original question: #help-27 message

[chilly owl]

nvm i can stay up for longer

you still here twin

[last parrot]

yes sir

[chilly owl]

yess

[last parrot]

you understand why we remove 1?

[chilly owl]

wait one second i might have figured everything out!

[last parrot]

what is b then

[chilly owl]

nevermind

[last parrot]

lol

so you still stuck or no

[chilly owl]

yes

[last parrot]

so do you understand why we eliminate 1

[devout snow]

@chilly owl Has your question been resolved?

[chilly owl]

.close

[devout snow]

Channel closed

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[chilly owl]

for now

ill get back to it tmwr

[last parrot]

ok i gotchu

[devout snow]

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[devout snow]

@vital hornet Has your question been resolved?

[vital hornet]

<@&286206848099549185>

Help me🙏😭

Can someone at least add me and I can share my work

[kindred cosmos]

i think it's a reiman sum

you'll turn it to an integral prob

[vital hornet]

Can u add me 🙏

Then I can show you my work

[kindred cosmos]

nah

you can show it here

[vital hornet]

Ok

Lmk if you spot any mistake

[sacred rain]

L=0 is correct

the only 'issue" is that the integral is an asymptotic replacement

[vital hornet]

Is there a fix

[sacred rain]

riemann sum written more properly

nothing structural changes

you just replace the "=" with a limit / o(1) term

[sacred rain]

more prop written $$\frac1\mu\sum_{k=1}^{\mu}\ln!\left(\frac{k}{\mu}\right)=\int_0^1\ln x,dx$$
$$\frac{\ln(\mu!)}{\mu}=\ln\mu+\frac1\mu\sum_{k=1}^{\mu}\ln!\left(\frac{k}{\mu}\right)=\ln\mu-1+o(1)$$
$$\sum_{\mu=2}^{n}\frac{\ln(\mu!)}{\mu}=\sum_{\mu=2}^{n}(\ln\mu-1)+o(n)=\ln(n!)-(n-1)+o(n)$$

[woven radish]

fixer aah

[vital hornet]

🙏

.close

[devout snow]

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[devout snow]

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[velvet swift]

I have a problem with algebra because I missed 2-3 years of important learning because of personal reasons, so now I am left with basically no knowledge and a really important exam in a month or so.

I have tried my best to learn as much as possible these last couple months and my teacher acknowledges my growth but I am stuck with the basic methods. The only method I can without thought is problems with this structure: 4x(2x + 5y) = 8x² + 20xy.

That is it and i wanted to see if anyone got some recommendations on strategies?

[last parrot]

what problem is this?

[rain summit]

wdym by this structure?

like what are you trying to achieve here

[velvet swift]

Structure of the equation

Within algebra there are diffrent type of methods for problems and I only know some of the basics.

[last parrot]

there are many structure

i am not sure, this is vague

[velvet swift]

Gimme a sec I will try to clarify.

[rain summit]

you got any example problems of this?

try giving us one of the problems you have of this structure

[velvet swift]

missed 2–3 years of math due to personal reasons and basically have no algebra knowledge left. I have one important exam in about a month.

Over the last couple of months I've been working hard and my teacher has noticed real improvement, but I'm still stuck at a very basic level. The only thing I can do comfortably and without thinking is the distributive property, like:
4x(2x + 5y) = 8x² + 20xy

That's pretty much it.

I'm looking for practical strategies and a realistic plan to catch up fast. Specifically:
What are the most important algebra topics I should prioritize in the next 30 days?

Best free resources (videos, websites, worksheets) for someone restarting from basics?

Daily study routine that actually works when time is short?

Any tips for quickly moving beyond just distributing to solving equations, simplifying, word problems, etc.?

Any advice from people who have caught up in a short time would be really helpful. Thanks!

(Copied from ai)

[rain summit]

rahhhhhhhhhhhhh

[last parrot]

chat copied from AI

[rain summit]

ahhhhhhhhhhhhhhhhhhhh

[last parrot]

i suggest you read all maths books again

[rain summit]

tính chất phân phối

distributive property

[last parrot]

distributive

[rain summit]

icic

[last parrot]

i think you are lacking a huge bit if knowledge OP

[velvet swift]

Yeah, that is basically the only i know. But only in simple forms.

[velvet swift]

You are correct. I am missing a lot and I made up for it within philosophy but now mathematics is a concern I must engage with so I came here for any tips

[last parrot]

first look up at all multiplicative and additive identity

what are functions, calculations of them

and looks up knowledge depending on which level of education are you taking

[velvet swift]

Do you have any video representing this concept that you would recommend?

[devout snow]

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[twilit comet]

need help with the following question. i need to prove that

[twilit comet]

and so far i have

1. are my steps heading in the right direction?
2. no idea where to go from here

[twilit comet]

thanks in advance, ping when responding, please

[faint gorge]

whats mu and lambda

[twilit comet]

moebius and von mangoldt functions respectively

[woven radish]

ren

[twilit comet]

also

<@&286206848099549185>

does literally nobody have any thoughts on this

[sacred rain]

direction is right

[twilit comet]

and what now

[sacred rain]

wait pls

[twilit comet]

alr

also wait

don't spit out

the whole solution

i mean. just in case. you were going to

i wanna know how to do this kinda stuff in the future

so yeah

thank you for your help though

[sacred rain]

use the identity $$\log(n/d) = \sum_{e \mid (n/d)} \Lambda(e)$$ so the last sum becomes

$$-\sum_{d \mid n} \mu(d)\log^m(d) \sum_{e \mid (n/d)} \Lambda(e) = -\sum_{q \mid n} \Lambda(q) \sum_{d \mid (n/q)} \mu(d)\log^m(d)$$

[woven radish]

fixer aah

[twilit comet]

fucking hell i'm stupid

[sacred rain]

never say that fam

[twilit comet]

i AM

jesus christ how did i miss that

hang on lemme just analyze this rq

[sacred rain]

yh if u need anything js tag me

[twilit comet]

aight

outer sum is 0 if q isn't a prime power
if q IS a prime power then that's log q. if n has m + 1 prime factors -> n/q has m + 1 or m, so that sum reduces to 0.
if q is a prime power, nad n doesn't have m + 1 prime factors then it's not necessarily 0, got it

@sacred rain this work?

[sacred rain]

yup

[twilit comet]

alr

[twilit comet]

thank you!

[sacred rain]

np

[twilit comet]

i'll close this in a bit

.close

[devout snow]

Channel closed

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[devout snow]

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[fast flame]

This is not necessarily a math problem question, but rather on learning a mathematical concept. Coming to the point, what is the best way to understand derivatives and limitations (which I think is Pre-Calc lvl), considering I'm a freshman in Geometry? How to do so if I can? And if not, why not and what are my pre-reqs before learning them? DM or mention me here

[robust bobcat]

What are limitations? Limits?

[fast flame]

i think so

[fast flame]

idk why i phrased it like that, it limits

my fault

[robust bobcat]

I don't think there is a best way just choose some sort of source to learn it from like YouTube or a textbook

[fast flame]

Sure. I'll try it out.

Thx!

[arctic field]

#math-discussion and #study-discussion are also places you can ask for advice

[fast flame]

Alright! Thanks!

[last parrot]

No problems

[devout snow]

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[exotic flicker]

what do I do here bruh

[exotic flicker]

this is the most barebones question I've ever seen

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[exotic flicker]

1

and I don't remember how I got the first option

I tried differentiating both sides, but it doesn't say much, and for all we know, g(x) could be x|x|

[sacred rain]

you ve done a, and b right?

[exotic flicker]

those are the correct options

I'm trying to figure out how to get them from this little info

[sacred rain]

so you set h(x)=g(x)/f(x) on any interval between two roots of f with f(x)!=0 so h is defined

u differentiate h'(x)=(g' (x)f(x) -g(x)f'(x))/f(x)^2. given relation f'(x)g(x)-g(x)f(x) = x^4+2x^2+10

[exotic flicker]

I was going for f(x)/g(x) but that works too

except there's way too little to do anything

[sacred rain]

hence h'(x)= -(x^4+2x^2 +10)/f(x)^2 <0

bc numerator is always pos and f(x)^2>0

[exotic flicker]

yeah I get that

but we don't know any values for f(x) and g(x)

how would showing h(x) is decreasing help?

[valid silo]

Use the sign of g at the roots of f

[sacred rain]

the point of showing h(x)=g(x)/f(x) is decreasing is that it controls how many times it crosses 0

[exotic flicker]

OH

THAT'S BRILLIANT

[sacred rain]

so h(x) = 0 <--> g(x) asl f(x)!=0

[exotic flicker]

f(x) is decreasing at one root and increasing at the other

which means g(x) attains 0 at at least 1 point!

but how do we show there's no other points like that?

huh

I could use a graphical method for this

[sacred rain]

sign argument at the endpoints of the interval; at least one root of g, h decreasing at most one root of g

therefore there is exactly one root of g between two consecutive roots of f

[devout snow]

@exotic flicker Has your question been resolved?

[devout snow]

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[devout snow]

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[chilly owl]

.reopen

@last parrot

[chilly owl]

holy shit

i did it

4b - 5b = b 1 - 1 is - 1 - 5 is 4 so 4b right

oh wait

since we brought it to the other side its 5b - 4b so that would be just b

im confused on the next part tho

with the 5 and 1

uhm

1 - 1

someone else told me that but i dont really get that

can you explain that part please

oh wait

OH YEAH

SO 1 - 1 IS - AND 1 - 5 IS 4 AND 4 PLUS B 4B RIGHT

THATS HOW WE GET 4B

b=4

yes

its not 4 plus b its just 4 = b

[raw cedar]

You always need to have the x in one side and the coefficients in the other side.

[chilly owl]

im starting to kinda get it

[raw cedar]

Do you want another exercise to practice?

[chilly owl]

yes

lemme go to the next problem

ill just do that

[raw cedar]

Ok, try to do that remember t in one side, coefficients in the other side.

[chilly owl]

do we bring the 2t to the other side?

[raw cedar]

Chose one side for t, if you want the right side for t's yes.

[chilly owl]

so we then do 4t - 2t right?

[raw cedar]

No, because when we change a value for one side we need to change his sign.

In this case - to +.

[chilly owl]

is it plus because the + is behind 4t

[raw cedar]

What do you want to do? Move the 4t?

[chilly owl]

no

nvm

[raw cedar]

The -2t?

[chilly owl]

i thought we werent bringing the - part

so when we bring a number over with a sign we change the sign

?

[raw cedar]

Yeah.

[chilly owl]

oh okay

[raw cedar]

Now try to solve. 🙂

[raw cedar]

Were you able to?

[chilly owl]

one minute

[raw cedar]

Take your time if you have questions ask here.

[chilly owl]

i got 7 = 7t but im not sure what to do now

[raw cedar]

Ok, good, you are doing it. Think about the 7 what are they doing, adding, divide?

If they are multipling they pass to the other side dividing.

[chilly owl]

so t=1

[raw cedar]

Right.

Do you have more questions?

[chilly owl]

ngl i got help from chatgpt but im getting it you do 4t plus 2t then add the t so 7t then bring the 9 to the other side and subtract and that would be 7 and then divide it

its starting to make a lot of sense

[raw cedar]

Good.

You're getting this.

[chilly owl]

maybe i will later

.close

[devout snow]

Channel closed

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[raw cedar]

🦁

[devout snow]

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[rich aspen]

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! here is the task. 😢 Below you can see a figure with some vectors and some points. Your task is now to find out as much as you can about the vectors, points, and the figure.

Examples of things you can investigate:
• The coordinates of points
• Vectors between points
• Side lengths
• Dot product (scalar product)
• Length of vectors
• Angle between vectors
• Area of a triangle
• Area of a parallelogram
• Distance from a point to a line
• Parallel vectors
• Orthogonal (perpendicular) vectors
• Cross product (vector product)
• Midpoints

i have found the vectors between the points. and some lenghts. but i dont know what do to now. is it psosible to find the area of the thing?? what do you even do now????????

[chilly owl]

the answer is 66

i think

[rich aspen]

no joke ths is very serious for me

[chilly owl]

oh mb

[rich aspen]

do you know what do to

[chilly owl]

no sorry

[rich aspen]

how do i get someone here

[chilly owl]

@last parrot

help this person!

[rich aspen]

thanks

[chilly owl]

you gotta wait

@final onyx HELP THIS PERSON

[rich aspen]

ok

[raw cedar]

Ok, you have 5 points and you already have the coordinates. Then you need to follow the guide. Vectors between points you already do. You need to see what you have to do and look in tool bar and experimantate and if you don't know how to do something ask here.

[woven vale]

!noping

[devout snow]

Please do not ping individual helpers unprompted.

[chilly owl]

they said i could ping them sorry

[rich aspen]

ooooooooooooooooooooooooo

wait what guide

[raw cedar]

The example that they gave you.

[rich aspen]

i know the vectors between the points

[raw cedar]

Then you can continue investigating the next thing.

[rich aspen]

ok hwo do i know what the next thing is???

[raw cedar]

You can follow the examples.

[rich aspen]

i dont have examples

[rich aspen]

ohhh thx. is side lenght and lenght of vector the same??

would you find area of triangle or pararellogram

[raw cedar]

No, it refers to a figure length.

[raw cedar]

You can do with the program, see in the tools bar.

[rich aspen]

i cant its a screenshot its not mine gabriel

do you knwo hwo to find the
ángulo s

[raw cedar]

In the same tools bar.

In measure part.

[rich aspen]

is the cosinus = 13?

i dont have tools bar i have to use the math in my brain but its not enough

[raw cedar]

But the task is to experiment with GeoGebra, right?

You need to use the app and investigate things with then.

[devout snow]

@rich aspen Has your question been resolved?

[rich aspen]

yes but without geogebra

[last parrot]

Sorry i was sleeping😭

[chilly owl]

I FIGURED IT OUTTTTTTT

I DID IT

[devout snow]

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[devout snow]

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[round tide]

why does the indefinite integral stay

[placid rover]

what is the context

stay?

[last parrot]

i mean he says "Says"

[last parrot]

thats an integral sign

[round tide]

why does it stay

[last parrot]

oh you mean why does it stay

[round tide]

yeah

[chilly owl]

oh hey minhhh whats up

[last parrot]

why not? it can either be e^x or keep at integral e^x

[onyx torrent]

Looks like a typo

[last parrot]

wsp broski

dont think it is

[onyx torrent]

Well either they forgot a dx or kept an extra integral sign it's a typo either way

[chilly owl]

is the first sign different then the circled one?

they look different

[last parrot]

then typo then

[last parrot]

they are the same

[chilly owl]

weird

[placid rover]

if that integral sign on the rhs werent there, it would make a lot more sense

[round tide]

yeah that's what confused me

This will always happen when we integrate functions of a linear function of x.
e.g. \int e^x dx = \int e^x + C

[lament kraken]

i think the \int on the right shouldnt be there

[round tide]

alr

[lament kraken]

so yea might be a typo

[last parrot]

if yes, they must put a dx

anyways

[round tide]

we done here thx for the feedback

.close

[devout snow]

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[devout snow]

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[stone stump]

<@&268886789983436800>

[devout snow]

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[patent wasp]

i need help w/ profit and loss problems

[glossy dew]

such as?

[patent wasp]

i'll send one

a moment

"Jack bought 400 eggs at $8.40 a dozen. At what price per hundred must he sell them in order to make a profit of 15%?"

[glossy dew]

well if a dozen (12) is $8.40 then how much would 400 eggs be

[patent wasp]

ok,by unitary methood, 8.40 divided by 12 is 0.7 per egg, 400 would be 0.7*400= 280

right?

[glossy dew]

yes

for 15% profit, net sales amount would be 115% of the cost of 400 eggs

[patent wasp]

so thats uhh 115/100 full*400

115*4 (00 on denominators cancel)

430?

[glossy dew]

the cost of 400 eggs is $280

115% of that

[patent wasp]

oh uh sorry

322

right?

[glossy dew]

yeah

[patent wasp]

so thats the final answer

right?

[glossy dew]

thats for 400 eggs

[patent wasp]

ok so for per hundred, we need to divide by four

322/4

[glossy dew]

yeah

[patent wasp]

80.5

[glossy dew]

✅

[patent wasp]

finally

can i uh post another one

[ocean haven]

you can

[patent wasp]

ok a sec

a florist buys a 100 dozen roses for $2 a dozen. when the flowers are delivered, 20 dozen are mutilated, and are thrown away. at what price should the florist sell the remaining roses at if he wants to make a 20% profit

[raw cedar]

What did you try?

[patent wasp]

so first the total cp is 200$ (100 doxen*2 per dozen)

and products worth 40$ are thrown away

[raw cedar]

Yeah.

We need recollect 240, but how many flower we have to sell.

[patent wasp]

we can sell 80 dozen

[raw cedar]

Ok, then we need to do a division.

Right?

[glossy dew]

which means you have 160$ worth of items

and you need a 20% profit on the original 200$ you had

[patent wasp]

yep

[patent wasp]

rright

so uhh we need to sell 80 dozens at 20% profit for $2 a dozen as cp

[raw cedar]

How will the division to know the price?

[raw cedar]

No, because if we sell 2$dozen we are losing money.

[patent wasp]

the 2 a dozens is the cp...right...?

[raw cedar]

I recommend you use that formula:

$$\text{Price per dozen} = \frac{\text{Total to collect}}{\text{Dozens available}}$$

[woven radish]

Ga³¹Br³⁵I⁵³9000✞

[raw cedar]

Because you think we want to get 240 dollars selling 80 products. How many dollars will each product have to have to obtain 240.

[patent wasp]

30

[raw cedar]

30*80=2400?

You are near.

[patent wasp]

3

3

[raw cedar]

Right.

[patent wasp]

im sorry

[raw cedar]

Np, do you understand now?

[patent wasp]

yep

[raw cedar]

Do you have more questions?

[patent wasp]

yes... (i apologise in advance)

[raw cedar]

Np, ask here.

[patent wasp]

if the cp of 15 pens is equal to the sp of 20 pens, what is the loss percent?

[ocean haven]

these are for questions no need to apologize

[raw cedar]

Think about, how much you are winning?

[patent wasp]

winning... what exactly?
its a loss..?

[raw cedar]

Yes, because you are losing products right? Because you are not wining money.

Do you understand?

[patent wasp]

yes

[raw cedar]

Good!

[glossy dew]

you can assume cp of a pen to be c if youre comfortable with algebra

[patent wasp]

okey, but we'll need to take sp as a differente variable
so 15c = 20s

s is sp

[glossy dew]

yes

find s in terms of c from here

s = ?c

[patent wasp]

and loss percent is loss/cp *100

[glossy dew]

yes

[raw cedar]

Right.

[patent wasp]

so then we get
c-s/c *100

ill come to that later

[glossy dew]

uhhuh

[patent wasp]

from 15c = 20s we get:
c=20/15 s
c= 4/3 s

and s = 3/4 s

if we substitute s for 3/4 c

we get 15c= 20*3/4 c

and ive obviously sone something very wrong

os so then c-s/c *100 becomes
(c-3/4c) *100

[glossy dew]

why?

[patent wasp]

l% = 1/4c *100

[raw cedar]

Yeah.

[patent wasp]

l% = 20c

which also looks wrong!!

wait a sec ill do this on paper

[raw cedar]

Yes, do in a paper and see.

You are doing it great.

[glossy dew]

$\frac{c-s}{c} \times 100% = \frac{c-\frac{3}{4}c}{c} \times 100%$

/c vanished

[patent wasp]

my bad is l% 25c now

which still... looks wong

[raw cedar]

Use that and do it slowly.

[patent wasp]

oh right

my ba

d

so we now have 25c/c

which is 25

l% is now 25%

[patent wasp]

right

?

[glossy dew]

✅

[patent wasp]

finally

after all this time

[raw cedar]

Correct!

[patent wasp]

so... another question...

if lacie buys lemons for 6 per $1, and sells them at 4 per

$1, what is her profit %

[glossy dew]

find the cost price and selling price first

for one lemon

[patent wasp]

the cp of 1 lemon is $1/6

the sp is $1/4

so clearly we have to convert to like fractions

lcm is 12

so cp is $2/12, while sp is $3/12

the profit is $1/12 for 1 lemon

the p% is p/cp*100

so its {(1/12)/(2/12)}100

[raw cedar]

Right!

[raw cedar]

✅

[glossy dew]

simplify..

[patent wasp]

so how do we simplify when there's a fraction at both the numerator and denominator?

[raw cedar]

Using the sandwich rule.

[glossy dew]

$\frac{a}{b} \div \frac{c}{d}$ = $\frac{a}{b} \times \frac{d}{c}$

[raw cedar]

Sandwich rule.

[glossy dew]

$\frac{1}{12} \div \frac{2}{12}$ = $\frac{1}{12} \times \frac{12}{2}$

[patent wasp]

how do i forget ts

so we got 2*100 now.

[raw cedar]

Don't worry.

[glossy dew]

oh sorry i messed the original order up

[patent wasp]

1/2 by 200 then

[glossy dew]

here

[patent wasp]

50%?

[raw cedar]

Yeah!

[patent wasp]

yay!

[raw cedar]

Do you have more questions?

[patent wasp]

ok ig thats it

no

[raw cedar]

Have a nice day!

If you solve it type .close.

🙂

[patent wasp]

thanks for all your help

.close

[devout snow]

Channel closed

Closed by @patent wasp

Use .reopen if this was a mistake.

[devout snow]

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[gloomy aurora]

the proof is correct, if that's what you're asking.

[indigo anchor]

how do we conclude b^2 - ac = 0 by the fact that p^(1/3) is irrational in equation (3)

[gloomy aurora]

the rationale for (3) is that observe that if it were true.

then the difference between a rational and an irrational would be zero

so a rational number, would be equal to an irrational

which cannot be true.

the only way out is to set $b^2-ac = ab-c^2p = 0$

[indigo anchor]

i dont understand

[woven radish]

Annie Maqionde

[gloomy aurora]

k so let's denote the irrational(the first term ) by $p$ and the $q = ab-c^2p$.

[woven radish]

Annie Maqionde

[gloomy aurora]

Then (3) asserts $p-q=0$

[woven radish]

Annie Maqionde

[gloomy aurora]

$\implies $p=q$

[woven radish]

Annie Maqionde
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[last parrot]

Triple $

[gloomy aurora]

so an irrational p = a rational q

[indigo anchor]

what what what what what

[gloomy aurora]

can that be true?

[indigo anchor]

cant be

but how did we get there

[indigo anchor]

how did we get here

[last parrot]

If p= q then p-q=0

[indigo anchor]

i mean how did we get to p - q = 0 and what is q

[last parrot]

Q is a rational, annie already told you

[indigo anchor]

that was too fast i could not follow

[last parrot]

Read carefully what she said

[indigo anchor]

ok

[last parrot]

Annie go slow a bit so he understand

[gloomy aurora]

$p=(b^2-ac)p^{1/3}, q = ab-c^2p$

[woven radish]

Annie Maqionde

[gloomy aurora]

so then $p-q=0\implies p =q$

[woven radish]

Annie Maqionde

[gloomy aurora]

now $p$ is irrational, $q$ is rational. But $p=q$.

[woven radish]

Annie Maqionde

[gloomy aurora]

that ofc cannot be true.

[last parrot]

He maybe confused how can p-q =0 here

[indigo anchor]

how did p = (b^2-ac)p^(1/3)??

[last parrot]

Read the 2nd statement