help-23

[shadow sparrow]

and its just a quadratic and an absolute with the same y int

so potentially a 3rd right in the middle

not sure if that counts though

[gentle shoal]

ok

[safe radish]

@gentle shoal Has your question been resolved?

[gentle shoal]

<@&286206848099549185>

please

.close

[safe radish]

Channel closed

Closed by @gentle shoal

Use .reopen if this was a mistake.

[gentle shoal]

.reopen

[safe radish]

✅

[shadow sparrow]

smart

[gentle shoal]

please

someone

[shadow sparrow]

that shit was genius yo

[gentle shoal]

ik]

cause

now

[shadow sparrow]

😭

[gentle shoal]

it on top

so ppl see it

<@&286206848099549185>

please

[lean otter]

hello

who needs help

can u send the question again too much scrolling up @gentle shoal

[gentle shoal]

#help-23 message

so im on this

what to do after

the question is
How many times could
f(x)=a(x-h)^2+k
and
g(x)=a|x-h|+k
intersect?

[lean otter]

well u need to find the xs for which

a(x-h)^2+k = a|x-h|+k

u simplify both k's

a(x-h)^2 = a|x-h|

[gentle shoal]

i did

[lean otter]

u can divide all by a

[gentle shoal]

click this link

[lean otter]

(x-h)^2 = |x-h|

[gentle shoal]

to see what i have done so far

[lean otter]

u gotta

its easy

1 sec

so where u struggle

is i guess

on

|x-h|

u gotta make 2 cases

if x<0

if x>0

ur functions depend on x

[gentle shoal]

i did not learn

[lean otter]

so u know h is just a

[gentle shoal]

partial

[lean otter]

constant

[gentle shoal]

factoring

@lean otter

[lean otter]

do u have any information on h

[buoyant epoch]

3, just simplify the expression to
(x-h)^2 = |x-h| and then isolate this into (x-h)^2 = x-h and (x-h)^2 = h - x and then you get h, h -1, h+1

it's petty easy

also stop spamming

[gentle shoal]

where

[buoyant epoch]

you were going into other channels asking for help

just be patient or do it yourself

[gentle shoal]

ONLY ONE

[lean otter]

how do u get (x-h)^2 = x-h, isnt it x^2-2xh+h^2

[buoyant epoch]

you split up the absolute value expression into plus/minus and then it is a simple algebraic expression

[lean otter]

oh

i see what you made

i split it too but differently

[gentle shoal]

how

[buoyant epoch]

expand (x-h)^2, turn it into a quadratic equation, and solve

[gentle shoal]

i got the quadratic equation

now what

x^2-2xh+h^2= |x-h|

@buoyant epoch

[buoyant epoch]

you split the absolute value into two expressions
x^2-2xh+h^2= x-h
x^2-2xh+h^2= -(x-h)

[gentle shoal]

ok

[buoyant epoch]

cause if (x-h) is negative and is made positive by the absolute value, it is the same as doing -(x-h)

[gentle shoal]

ok

next

[buoyant epoch]

? do you no how to solve quadratic equations

[gentle shoal]

find the roots?

ok

but how u get x=h

and

[gentle shoal]

i got x= 1

@buoyant epoch

[buoyant epoch]

x^2 - 2xh - x + h + h^2 = 0
x^2 - 2xh + x - h + h^2 = 0

then factor and then solve for x

so the answer is h, h +/- 1

[safe radish]

@gentle shoal Has your question been resolved?

[celest trellis]

Hi I need some help with something

I understand how to do everything until the last step. I don’t understand how they got the 4.57899231

[safe radish]

Channel closed

Closed by @gentle shoal

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[stray storm]

2. [TMC Regional 2012 Q4] Find the sum of all numbers less than 120 which are the product of exactly three different prime factors.

[stray storm]

I dont understand a method to get to the answer

I have written a chart from 0-120

and i eliminated everything under 30

because the smallest possible combination is 235

2x3x5

which is 30

i also eliminated the primes

as they only have 2 factors

and cannot possibly be divided by another prime

i am currently trying to find the multiples of primes up to 120

thanks

actually common multiples

i was just wondering are there other ways

more thinking:noticed a trend where lots of them are around prime numbers

P+1 or -1

<@&286206848099549185> i believe it is 15 minutes

sorry for the ping

[buoyant charm]

huh

[stray storm]

hi

why the huh

i saw you typing before too

but u dissapeared

[buoyant charm]

Sorry, I can answer now.

[stray storm]

oh alright

thanks

[buoyant charm]

I assume you know all prime numbers and that the lowest are 2, 3 and 5 so you've probably eliminated numbers below 30, and you must have eliminated all primes.

[stray storm]

yes

that was in the typing

hi?

oof

<@&286206848099549185>

:)

[hybrid wedge]

2×3×5 = 30
2×3×7=42

@stray storm

You need to check like this

You need to multiply 3 primes and check if the no. Is <120

[stray storm]

yes

checking

but i want to know are there other methods

[hybrid wedge]

I don't know

[stray storm]

ok

[hybrid wedge]

I think there is 1 way using coding

[stray storm]

uh

ok

<@&286206848099549185>

[young nexus]

you are searching for all numbers < 120 which are the products of 3 primes.

[stray storm]

Ok

[young nexus]

name them a, b anc d and assume they are sorted a < b < c.
case a = 2, b = 3 -> 3 < c < 20.

[stray storm]

What

[young nexus]

case a = 2, b = 5 -> 5 < c < 12

[stray storm]

Sorry i dont get it at all

[young nexus]

name them a, b and c and assume they are sorted a < b < c. is this clear?

[stray storm]

The primes?

[young nexus]

yes

[stray storm]

Alright

[young nexus]

assume a = 2 and b = 3, then ab = 6 and abc < 120, clear?

[stray storm]

Yess

[young nexus]

solve for c.

[stray storm]

I think i need to show you my existing work

[young nexus]

ab = 6, abc < 120 -> 6c < 120 -> c < 20

[stray storm]

Yep

OHHH

I SEEE

SO WE CAN MAKE AB 2*5 OR SOME TING???

[young nexus]

exactly. and this will end very fast, as we assumed a < b < c, so you wouldnt find any (3,7,c)

[stray storm]

THANKS YOU SO MUCH

YOU ARE THE BEST GUY EVER

.close

[safe radish]

Channel closed

Closed by @stray storm

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[stray storm]

uh woops

[stray storm]

@young nexus once that runs out

what happens?

example 2* 7 * 9

is that it

cuz it feels kinda insecure

[young nexus]

let me explain:

[stray storm]

yes

[young nexus]

with 2,3 you will get c = 5, 7, 11, 13, 17, 19

[stray storm]

mhmm

[young nexus]

all primes greater the 3 (as we assumed they are sorted) and we got c < 20.

[stray storm]

yess

[young nexus]

with 2, 5 you will get 7, 11

[stray storm]

mhmm

loHH

cuz 11 cant go any larger?

because 11*11 is 121

so invalid

the next smallest possible one is 2,5,9

so

[young nexus]

2x5 = 10 -> abc < 120 -> 10c < 120 -> c < 12

[stray storm]

what no

nvm

[stray storm]

what

im dumb sorry

[young nexus]

9 isnt a prime

[stray storm]

yeah

i forgot

thats why the nvm

[young nexus]

with 2, 7 you will get nothing, since c > 7, and c < 120/(2x7).

[stray storm]

i see

kind of

[young nexus]

then go on with starting 3 -> 3,5 -> c < 8, so only 3,5,,7

[stray storm]

120/15

=8 i guess?

[young nexus]

yes

[stray storm]

aha

[young nexus]

and now we are finished. no more combinations possible.

[stray storm]

sorry to disturb

[young nexus]

no problem

[stray storm]

ok

how do we know this

very very very very sorry

im dumb

[young nexus]

we assumed a, b, c are sorted. if we do not find a solution for a = 3, b = 7 how should there be a solution for a = 3, b = 11?

[stray storm]

lemme process

ohh

ok

still feel dumbfounded

but thanks

[young nexus]

you are welcome.

[stray storm]

thanks

.close

[safe radish]

Channel closed

Closed by @stray storm

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[brave wolf]

1. is incorrect

[rancid gyro]

If you're reflecting across the y axis, change the sign of the x coordinates

so for the 1st one, the coordinates are (0,-1), (1,-1), (1,-3), (3, -3) right? So change the sign of the x- coordinates

and you get (0, -1), (-1, -1), (-1, -3), (-3, -3)

Lmk if you're confused

[brave wolf]

Or just keep in mind that all the reflected points must have same distance from Y axis, as their original version

As you can see, W and W reflected have distance 1 unit from the axis. (Which is correct) But E has 0 distance, and E reflected has 1 for some reason (Which isn't correct)

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[magic gale]

I need help with 26, 28, and 30

[magic gale]

I will be checking back in 30 min

[stark idol]

isosceles ∆ and pythagoras

[magic gale]

For 26 and 28?

[sleek merlin]

use pythagorean theorem for numbers 28 and 30

[safe radish]

@magic gale Has your question been resolved?

Channel closed

Closed by @magic gale

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[safe radish]

@little aurora Has your question been resolved?

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[minor hatch]

can't differentiate it:

[minor hatch]

that's correct, but then I need to simplify it and I don't manage to do it.

I mean

that's what I get:
f(x) = (x=1) [4x-2(x-1) * 2x^2]

[inner nest]

Considered using quotient rule?

[minor hatch]

I did differentiate it

but the issue is the simplification

can't simplify the damn thign

[inner nest]

tell me how did you differentiate it

then I can understand why it becomes tough to simplify

Did you do quotient rule first then power rule? or power rule first then quotient rule?

[minor hatch]

you mean f' * g - g' * f?

[inner nest]

although answers will be same nevertheless, but one will be pretty neat and efficient than the other

[inner nest]

no

[minor hatch]

so that's what I did

[inner nest]

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

[minor hatch]

yeah

that's what I mean

f' * g - g' * f \ g^2

[inner nest]

You should first do the power rule then the quotient rule therein

[minor hatch]

idk what that means

[safe radish]

@minor hatch Has your question been resolved?

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[upbeat galleon]

Hi

[upbeat galleon]

There are 5 white and 7 black balls in the box. two consecutive balls are drawn from the box (provided they are not returned to the box). Find the probability that the first ball drawn is white and the second ball is black.

Isn't this supposed to be found like this C(5;1)*C(7;1)/C(12;2)

[dull sequoia]

,w (5 choose 1) * (7 choose 1) / (12 choose 2)

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Frosst#1111

[dull sequoia]

,w 5/12 * 7/11

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Frosst#1111

[quasi bison]

no, since for your purposes it matters which ball comes first

[dull sequoia]

surely it's just this

i feel like you're overcomplicating it

[upbeat galleon]

Oh ty but in what condition should I use the C

[dull sequoia]

nCr is for how many ways to choose r items from n items

[upbeat galleon]

Thanks

.close

[safe radish]

Channel closed

Closed by @upbeat galleon

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[deep musk]

i have no idea what this is asking for me to get

[prime nacelle]

"what is the height of the image"

thats ur image

how then what would be the height?

[deep musk]

so just convert 15 in. to ft.?

[prime nacelle]

na

[deep musk]

hmmm..

[deep musk]

idk :/

[prime nacelle]

thats the 15 inc

[deep musk]

ohhh

[prime nacelle]

the height of the image

what would u use to find the height

[deep musk]

idk 😭😭😭

[prime nacelle]

it says

that light entering the opening reflects his image on the wall

right

[deep musk]

ya

[prime nacelle]

it reflects

[deep musk]

oh

[prime nacelle]

so it means

its the same image

just

[deep musk]

the theorem?

[prime nacelle]

sized down

what theorem

[deep musk]

ya

oh i thought u meant the image would be like this..?

[prime nacelle]

does that help u in finding the height?

[deep musk]

no

[prime nacelle]

r u familiar

with similar triangles

[deep musk]

ya

but im trying to figure out this..?

hold on

[prime nacelle]

because the question states this

[deep musk]

this height?

[prime nacelle]

no.

the

[deep musk]

the 4ft 6in?

[prime nacelle]

height of the image

where is the image

[deep musk]

the kid?

[prime nacelle]

here

whats the height

[prime nacelle]

yea the reflected kid

[deep musk]

5ft 5in

but u circled the box and thats 15in

[prime nacelle]

fahjwoiuerfjwaejfoiweajfwa

[deep musk]

[prime nacelle]

love spoon feeding

[deep musk]

i hate proving units 😫

[prime nacelle]

this is

the height

[deep musk]

yes

[prime nacelle]

of the image

do we understand

[deep musk]

yes

iah

ah

[prime nacelle]

i circled this because i hoped u would realise that is where the iamge is

and what the height of the image would mean

so does similiarity seem like somenthing u could apply to this quesetion?

[deep musk]

wait so

[deep musk]

the 15 in is

ohhh

ok i get it

thanks

[safe radish]

@deep musk Has your question been resolved?

Channel closed

Closed by @deep musk

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[neat halo]

Hello I have a question

[neat halo]

It's not about math but it is related to math in someway

[stray socket]

Hmm

Just post it

If it's about some discussion maybe it's better in #discussion or #chill

[neat halo]

Alrightt holdon

oh no its missing

Found itt

How did it become 32-36 ATP

This is cellular respiration by the way

[stray socket]

Oh i don't remember biology all too well

Is there some equation

[neat halo]

Not reallyy

All I know is

2NADH = 5 ATP

So Glycolysis has 7 ATP

Kreb's has 20 ATP

While ETC produces around 28 ATP

But why is the over all total 32-36 if you add all of the ATP it will be 60+ ATP

[stray socket]

It produces ATP right

Is it possible it takes ATP to produce more ATP

[safe radish]

@neat halo Has your question been resolved?

[neat halo]

I don't know as well

Thank you for your help though

[safe radish]

Channel closed

Closed by @neat halo

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lone snow]

im not very sure how to do this question

[lone snow]

these are what i have so far but im sure im wrong

<@&286206848099549185> help please

[safe radish]

@lone snow Has your question been resolved?

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lean otter]

what method do i use to integrate 5 sqrt(3−2𝑥− x^2)

[lean otter]

complete the square

and then do a trig sub

like under the sqrt?

yep

like

spoilers alert

you want to get something that is like sqrt(a^2 - u^2)

u can do that by completing the square

and from there, just do standard trig subbing

this is kinda frusturating

[lean otter]

alright whats wrong

i always do trig sub wrong

yeah no worries just like

share what u have been doing

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[winged pumice]

Hello, I am trying to figure out a solution for how many games I would need to play for 2,000 tokens. So far I've figured out you need two and a half 20 minute losses, or one 34 minute win for 20 tokens. With a win/loss rate of 50% how many games in total would you need for 2,000, and how much time would that be?

[safe radish]

@winged pumice Has your question been resolved?

[brave wolf]

Lemme explain first part, I made an equation that models what you said, then I substituted for tokens, using 50-50 probability I made W=L (Wins and Losses are approx. equal) and solved for Wins

Now in second part, I will solve for L and then model new equation with time

Well I actually already solved for L since L=W

(W=71 I made small mistake while rounding)

[winged pumice]

this is awesome

[brave wolf]

Second part is here

[winged pumice]

ok, so in total you would need 71 wins, and with a 50/50 average that would be 142 games

[brave wolf]

That's approximately this in minutes. This scenario will never happen, but it's average of all possible scenarios

t is in minutes

[winged pumice]

cool, makes sense

thanks a lot man you're awesome

.close

[safe radish]

Channel closed

Closed by @winged pumice

Use .reopen if this was a mistake.

[brave wolf]

Here is day hour minutes seconds format ;)

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hybrid wind]

Hi guys,
How to derivative this x^2/(1+x^2) by using the definition of the derivative

[hybrid wind]

I tried solving it, but don't know if I did right

[safe radish]

@hybrid wind Has your question been resolved?

[safe radish]

@hybrid wind Has your question been resolved?

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[haughty sleet]

Could anyone help me with this i have stuck on this one for 3 hours

[bold ferry]

Send your work

[haughty sleet]

ok give me a second

it should look something like this

[bold ferry]

,calc 1/2 * 4/3 * 11^2

[flat frigate]

Result:

80.666666666667

[bold ferry]

oh that’s cubed

my bad lol

[hybrid wind]

.

[bold ferry]

your channel was auto closed unfortunately, please make a new one

[hybrid wind]

Ok

[bold ferry]

,calc (6437/3) - (887 + 1/3)

[flat frigate]

Result:

1258.3333333333

[bold ferry]

@haughty sleet calculation error here

it isn’t 1850pi

perhaps the mixed number mixed you up, I’d recommend using improper

[haughty sleet]

thank you

wait so 121pih

is equal to 1258(pi)?

@bold ferry

[bold ferry]

yeah

[haughty sleet]

ok

[bold ferry]

well 1258.3333(pi)

or 1258 1/3

[haughty sleet]

easier as 1/3

[bold ferry]

(or make that improper)

yeahh but it can mess you up on a calc

[safe radish]

@haughty sleet Has your question been resolved?

Channel closed

Closed by @haughty sleet

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[wind osprey]

I have a probability question

[wind osprey]

We have 7 players, how many "battles" can we generate if regrouping the players in 2 teams of 3 ?

The answer is 7C3 * 4C3 but we need to /2 because of symmetry

Can someone try and explain this symmetry concept in combinations so that i can notice it next time around ?

Let me give an easier example

4C2 = 6 using the general formula

But the answer is 6/2 because of symmetry

Why does this apply in the previous case ?

[past aurora]

Do you understand why it's (4C2)/2 and not just 4C2 in this case?

[wind osprey]

Yep i do

Logically but nor rigorously

[past aurora]

Can you explain it in your own words, and then we can try to figure out why it also applies in the 7 player case

Or, we can try to make it more rigorous and that may help

[wind osprey]

Ok sounds great !

So when I’m searching for my different possible combinations, when i create one an other is created. But with the general formula i will eventually count the set create "in the background" again

English isn’t my first language so hopefully this makes sense 😂

[past aurora]

I'm a little uncertain but I think I see what you mean by "when I create one another is created"

For the 4-player case let's do it out really explicitly

Let's say the players are W,X,Y, and Z-- then what does 4C2 count?

[wind osprey]

WX, WY, WZ, XY, XZ, YZ

Oh

I think it’s starting to click

Wait no nevermind

But when i pick out WY, ZY are left alone

[past aurora]

OK, so what we're doing with 4C2 is choosing the two players who are on the first team

For example, when we do that first one, WX, the other team is YZ, right?

[wind osprey]

So when i pick out WY, YZ has already been "created"

[past aurora]

Right.

[wind osprey]

So wait i’m confused now haha is the answer 6 or 3 ?

[past aurora]

So using the 4C2 solution, we can make a little table:
WX, other team is YZ
WY, other team is XZ
WZ, other team is...

I think the answer is 3, because "WX vs YZ" is the same battle as "YZ vs WX"

[wind osprey]

Yes absolutely makes sense

[past aurora]

If you go through, you'll see that every battle is shown twice in that table (once in each order)

[wind osprey]

So we’re /2 because of the nature of the question ?

[past aurora]

Hence we need to divide by 2

If they were playing a different game where the two sides are different, like hide-and-go-seek, we wouldn't divide by two

because the first time we'd generate WX(hiders) vs YZ(seekers), and later YZ(hiders) vs WX(seekers)

[wind osprey]

Makes complete sense !

Ok so the question is why we’re /2 that’s already huge thank you bro !

But why does it apply when the number of players is 7 ?

No wait i think i know why

Same thing, it’s just because when we pick out 3 players they need to be versing another 3 players in order for the game to start

I think ?

[past aurora]

Right

If you wanted, you could go through the options with 7C2, although it's a lot

You can try it with 5 instead of 7

But I think you get it

[wind osprey]

I think i do damn thank you so much man

[past aurora]

Happy to help 🙂

[wind osprey]

Take care thx again for the massive help, was bothering me for ages

[past aurora]

np, keep on mathin'

[wind osprey]

❤️❤️

.close

[safe radish]

Channel closed

Closed by @wind osprey

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[umbral solar]

Hi

I hope this is the truth

Does anyone know the truth?

[glass carbon]

why 2sqrt(390) and why in the denom?

[umbral solar]

Its not rule of derivating ?

oh

its constant?

so i treat it as 0?

but not really

because its constant * function?

so i just keep sqrt(390)?

very nice?

[glass carbon]

now it's ok

[umbral solar]

Woah

this is too hard

always some complication

[shut inlet]

[umbral solar]

tomorow test college

this is the hardest part

the actual calculationing

formula is not hard

pls give me pro tip number#1

[shut inlet]

good luck

[safe radish]

@umbral solar Has your question been resolved?

Channel closed

Closed by @umbral solar

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[obtuse parcel]

this is discrete math but im unsure on how to solve these two problems

[zinc token]

either truth table or prove => and <=

[safe radish]

@obtuse parcel Has your question been resolved?

Channel closed

Closed by @obtuse parcel

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lean otter]

How does this equal cosθ + 1

i get sinθ+ 1

[zinc token]

recall what tanx means

[lean otter]

sinx/cosx

[shut inlet]

$\frac{\sin(\theta) + \tan(\theta)}{\tan(\theta)} = \frac{\sin(\theta)}{\tan(x)} + \frac{\tan(\theta)}{\tan(\theta)}$

[flat frigate]

Mehdi_Moulati

$\frac{\sin(\theta) + \tan(\theta)}{\tan(\theta)} = \frac{\sin(\theta)}{\tan(x)} + \frac{\tan(\theta)}{\tan(\theta)}$

[lean otter]

ohhh

makes more sense

[shut inlet]

sin(x)/tan(x)=cos(x)

[lean otter]

i got it

thanks again

.close

[safe radish]

Channel closed

Closed by @onyx hull

Use .reopen if this was a mistake.

[shut inlet]

anytime

[shut inlet]

tnx to him too

[zinc token]

[shut inlet]

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[dense tiger]

Can someone help me out with this statistics problem

[safe radish]

@dense tiger Has your question been resolved?

[safe radish]

@dense tiger Has your question been resolved?

Channel closed

Closed by @dense tiger

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lofty elbow]

Could somebody help me understand what I should be studying other than 'algebra' for me to understand this question better?

[lofty elbow]

Dont really have a clue on how to start

specifically, the 'factor of 9' stuff

[empty gyro]

Exponential functions

[lofty elbow]

hmm thankyou

.close

[safe radish]

Channel closed

Closed by @lofty elbow

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[granite cape]

can anyone help me out with this, here is my working.

the value I get for area is negative for some reason, can anyone check my working?

[dense galleon]

you got the top and bottom functions flipped

[granite cape]

wdym?

[sudden forum]

you're doing bottom-top

[dense galleon]

sqrt(x) is larger than x/3 for the interval (0, 9)

[granite cape]

but how?

oh I see now

my bad

I still get a negative value

@dense galleon

[sudden forum]

send working

[dense galleon]

why is the integral of x^(1/2) negative

[granite cape]

Oh true my bad

So is the final answer for the area

9/2 units squared

[safe radish]

@granite cape Has your question been resolved?

Channel closed

Closed by @granite cape

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[mild lion]

I need help answering question 4M, the topic is functions but I don't understand how to determine the value of p

[coarse birch]

hey

Okay cool

can you talk me through how to do question a)

[mild lion]

This is my working out but it’s wrong

yep ill send a pic of A

[coarse birch]

So you have said f(p) = 33

[tame smelt]

they are asking you about f(p), not f(33)

[coarse birch]

which is correct

but then on line 3, you are doing f(33)

[tame smelt]

33 is supposed to be the output

not the input

[coarse birch]

which is not what you need

the goal of m, is to instead of putting 33 in for x, you find what the p value is to get 33 as your answer

Ill ask you same question with more familiar terminology ebony

If I tell you f(x) = 2x for example AND I tell you f(x) = 4
Could you tell me what x is?

[mild lion]

Uhhh

Not rlly no 😭

[coarse birch]

Or rather, I ask this:
For what value of x is f(x) = 4 if f(x) = 2x

[mild lion]

4 or 2x isn’t it

I’m not too sure still

[coarse birch]

I have a function, f(x) = 2x.

What x value makes it equal to 4?

[mild lion]

2

?

[coarse birch]

ok cool

yes

now, that process is differnt to me asking you for example, what is f(2)

For you to work out f(2), you need to take the 2 and place it in where the x was in the original equation, right?

so f(2) = 2(2) = 4

[mild lion]

Okay

[coarse birch]

Okay, so what m is saying, is the previous question

for a function f(x), what value of x makes the answer equal to a number

its just using math language to communicate it, rather than words

so for my function f(x) = 2x

instead of me asking you, what value of x makes it equal to 6

ill ask you this:

For the function f(x) = 2x,
if f(p) = 6, what is p?

[mild lion]

3

[coarse birch]

Yes

So the process you follow when doing these questions is this

f(x) = 2x

f(p) = 2p = 6

2p = 6

p = 6/2

the second line is the important one

you arent putting the 33 as the p-value, you dont know what p is

You put p in for x, and make it equal to 33

then solve for p

try yours now, if you feel confident?

[mild lion]

okay I’ll try it now

[coarse birch]

https://cdn.discordapp.com/attachments/903481106819612714/1070661401602949200/Screen_Shot_2023-02-02_at_7.03.17_pm.png

Can you remove this message, it isnt appropriate here

[digital ember]

can i do these aswell

[digital ember]

sorry

[mild lion]

Is this correct

[coarse birch]

This isnt a chat channel, its a channel where someone is asking for help. If you want to chat go to a discussion channel please

So ebony, the problem is you are replacing x from the original equation with the number 33

[digital ember]

sorry

[coarse birch]

but x isnt 33.

x = p

so instead of x, you substitute p

[mild lion]

Ahhh ok

[coarse birch]

try writing your f(x) function, with p substituted for x

<@&268886789983436800> can you ban this guy? @digital ember

[digital ember]

why bro

[mild lion]

Do you mean like this? 😭

[coarse birch]

yes!

[digital ember]

im sorry bro

please forgive bro

i am sorry bro

[coarse birch]

now what else is f(p) equal to, aside from 5p-2?

[mild lion]

33

[coarse birch]

cool

so make that into an equation

[coarse birch]

What does that look like as an equation

if f(p) = 5p-2 and f(p) = 33?

[mild lion]

Idk I’m srry 😭😭😭

It’s taking a while to get my head around it

[coarse birch]

Okay

If i tell you x = 2y

and i tell you 2y = 3

can you tell me what x equals?

[mild lion]

Uhhh 3

??

[coarse birch]

yes

so how do you do that?

[coarse birch]

yes!

now, repeat that line, without including the f(p)

[mild lion]

5p-2=33

[coarse birch]

perfect

now solve for p

[mild lion]

5p-2=33
5p=35
p=7

[coarse birch]

yes!!!

thats it

so this is just the "math language" way of asking

[mild lion]

Okay tysm

[coarse birch]

if f(x) = 2x, what is the x value that makes it equal to 4

and you saying 2

instead the math language is
for f(x) = 2x

If f(p) = 4, what is p?

Thats the concept you are learning - communication of what they want you to do in this type of question.

[mild lion]

Do I do f(p)=4=2x
4=2x
x=2

?

[coarse birch]

99% yes

but when you do f(p) it is 2p not 2x

the idea is x becomes p

[mild lion]

okay

f(p)=4=2xp
4=2p
p=2

[coarse birch]

2xp meaning 2 times p, yes

as loong as that x is times, and not the algebra x, that is correct

[mild lion]

yes that’s what I meant

[coarse birch]

perfect

it makes more sense, when you start to think of a function not like a math equation

[mild lion]

is it ok if I do the next question by myself and send it here to check I’ve got it

[coarse birch]

absolutely

[mild lion]

okayyy

[coarse birch]

https://cdn.discordapp.com/attachments/903481106819612714/1070661401602949200/Screen_Shot_2023-02-02_at_7.03.17_pm.png

brb for one second

[mild lion]

Okay

This is 4n btw

[coarse birch]

Perfect!!!

You’ve got it nice work

[mild lion]

Tysm Warmazta

🥳🥳🥳

.close.

Oh

.close

[safe radish]

Channel closed

Closed by @mild lion

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

Channel closed

Closed due to the original message being deleted

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hasty oak]

The probability of winning a game is 2/23 and the probability of losing a game is 7/23. How many games were not played

[hasty oak]

prob of winning is 2/23 prob of losing is 7/23 how many games were not played

.close

[safe radish]

Channel closed

Closed by @hasty oak

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lean otter]

is there any pattern? i see none

[safe radish]

@lean otter Has your question been resolved?

Channel closed

Closed by @dark yew

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[long flame]

A basketball player has a 80% chance of making each free throw. What is the probability that the player makes at least 4 of their next 8 free throws?

[marsh walrus]

what have you tried?

[safe radish]

@long flame Has your question been resolved?

[long flame]

i don’t know where to start

[hollow phoenix]

Remember, the 80% applies to every single one of the 8 free throws

[marsh walrus]

it depends on teh class the exact logic to get there but

usually youd start by classifying the trails or whatever

to see if you can figure out a distribution

so youd want to ask stuff like

is the chance of making a shot independent of previous throws?

does the probability stay the same?

is it a binary success/failure

[safe radish]

@long flame Has your question been resolved?

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[marsh cloud]

hi

[quasi bison]

Sonom and Anu each deposited 1500 currency units in some bank. Sonom received interest [at] a rate of 15% per annum compounded annually, and Anu received interest at a rate of 16% per annum compounded half-yearly. Find the difference in the interest received by Anu and Sonom at the end of the year.

@marsh cloud did i transcribe the problem correctly?
your handwriting (or that of whoever wrote this) leaves much to be desired in terms of legibility...

i can't decipher the currency symbol you used, though it should not really matter

[safe radish]

@marsh cloud Has your question been resolved?

[quasi bison]

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[desert cedar]

Hello so this is the graph

[desert cedar]

After inputting f(x) = 9x

What would be the end behavior

[unborn mist]

What do u want to know?

[desert cedar]

How to determine the end behavior

And what that would be

[unborn mist]

Wdym with "end behavior"?

The lim x-> infinity?

[desert cedar]

What would be the coresponding end behavior that matches it

Yeah essentially

Where the function would approach

[unborn mist]

So, lim of 9x as x approaches +infinity is +infinity indeed

The graph will continue to increase endlessly

[desert cedar]

No like towards these answers

[unborn mist]

5th one seems right

That's what I said

Positive infinity

(negative infinity when x approaches -infinity, of course)

Do u understand why?

[desert cedar]

Kinda but I don’t understand how you got the negative infinity part

[unborn mist]

Imagine, f(x)=9x

And x approaches -infinity, your number is very big, but negative

So if x = -99999999999, f(x) = -9*999999999 so it will be bigger (but negative)

The biggest number u can pick, 9 times it will be a bigger one

That's why the infinity

[desert cedar]

Yeah but why wouldn’t it be positive

Ik about the infinity part but what makes it negative

[unborn mist]

Well

If x<0

9x is >0 or <0?

[desert cedar]

9x<0

Oh

[unborn mist]

Yeah

Did u understand the negative infinity now?

[desert cedar]

Yeah can I solve a question on how you did it to double check real quick

[unborn mist]

Yes sure

Go on

[desert cedar]

So b would be the second one correct?

I meant first one*

[unborn mist]

Approaches 0?

[desert cedar]

Yes

[unborn mist]

Yep, correct

[desert cedar]

And c would be the third?

[unborn mist]

Nope

Hint: if u have same thing multiplying in numerator and denominator, u can "cut" both with some restrictions

Like

(123*456)/456 = 123

So, if you have (999*x)/x, what u get?

[desert cedar]

-9999999999?

[unborn mist]

What

[desert cedar]

Since ur multiply 999 by x?

That’s what I thought it’d be

[unborn mist]

And divide by x after

[desert cedar]

So approaching 999?

[unborn mist]

Yep

Because both x will cut

So (999*x)/x = 999

[desert cedar]

So it basically cancels out since your multiply and dividing after?

[unborn mist]

Yes

For example (2+x)/x you cant cut because x in numerator is add to 2, not multiplying

[desert cedar]

That makes sense

So d would be fourth one then right?

[unborn mist]

Hmmm no

[desert cedar]

No but d would be adding I forgot

[unborn mist]

Yeah

[desert cedar]

So how would you approach d

[unborn mist]

Try separate the fraction

(a+b)/c = a/c + b/c

And then try again

[desert cedar]

So 99/x and x/x

[unborn mist]

Yes

[desert cedar]

Wouldn’t it be just 1 then since x/x

[unborn mist]

True

[desert cedar]

So d would be the second one, e would be the third and f would be the fourth following that same concept of like splitting it up

[unborn mist]

e and f are wrong

[desert cedar]

99x/x and x/x for e

[unborn mist]

What

[desert cedar]

Splitting it up

[unborn mist]

99x/x + 9/x

[desert cedar]

Nvm I’m blind yes that

[unborn mist]

That is d)

[desert cedar]

99x/x + 9/x the x would cancel out 9 to x makes it 1 then 99 times 1 = 99?

[unborn mist]

Yes

[desert cedar]

I tried doing that with f as well but how would that become 9

[unborn mist]

999/x + 9x/x

999/x is 0, right?

At the limit

[desert cedar]

Yeah

[unborn mist]

So 9x/x

[desert cedar]

X would cancel out and just leaves the 9?

[unborn mist]

Yep

x cut

[desert cedar]

So this would essentially be the same concept

[unborn mist]

Yeah there u have to do some stuff

Do u know oblique limits?

I recommend to you watch some videos about it because for what I saw you don't have much knowledge about the basics

[desert cedar]

graph of a function approaches a line that is not veritical or horizontal I’m pretty sure

[desert cedar]

Alright I’ll watch some videos after like 20min I’ll try doing this by myself and are you able to correct it?

[unborn mist]

Ywah, that's not vertical or horizontal

[unborn mist]

https://youtu.be/qGCKjuhA4eQ

I recommend this one

[unborn mist]

Yep

Ping me when u are done

[desert cedar]

Alright thank you

[unborn mist]

Uw

[safe radish]

@desert cedar Has your question been resolved?

[safe radish]

@desert cedar Has your question been resolved?

[desert cedar]

Alright I’m finished but there’s a bit of understanding

Most of the answers he does is just bottom heavy equations

I get the general concept but all the ones above are top heavy

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[wind osprey]

Hello i have a probably question

[wind osprey]

So we have 10 balls, 6 whites and 4 black.
The probably to draw out BNBN when you place back the balls after drawing them is lets say a = 6/10 * 4/10 * 6/10 * 4/10

Now why is the probability of drawing exactly 2 black balls ( lol ) when placing them back each time = a * 4C2 ?

And not = a ?

[quasi bison]

B = blanc, N = noir?

[wind osprey]

Because BBNN = a or NBNB = a etc so a guarantees that i have exactly 2 black balls ?

[wind osprey]

Yes sorry

[quasi bison]

drawing exactly 2 blacks means drawing one of WWBB, WBWB, BWWB, WBBW, BWBW, or BBWW

you need to account for all 4C2 possibilities of their order

[wind osprey]

I get that logic

[wind osprey]

But then this makes sense to me as well

So why is that line of thought wrong ?

[quasi bison]

you are confusing the event "draw 2 blacks" with the more specific event "draw balls in WWBB order"

"a guarantees that i have exactly two blacks" is nonsensical as is

[wind osprey]

But that last event guarantees me 2 black balls ?

[quasi bison]

it is true that {draw BBWW} is a SUBSET of {draw 2 blacks} but that's a strict inclusion

{draw 2 blacks} = {draw BBWW} union {draw BWBW} union ...

[wind osprey]

I see

I think i got it

Thank you @quasi bison love you ❤️

.close

[safe radish]

Channel closed

Closed by @wind osprey

Use .reopen if this was a mistake.

[safe radish]

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[dreamy ferry]

also I have a question, can the regular expression 0* + 10*1* be further minimized?
like we can't take 0* common from it, right?

[brave wolf]

0* what?

[dreamy ferry]

wdym?

[brave wolf]

what does 0* mean?

[past aurora]

Are these regular expression?

[dreamy ferry]

none or more occurrences of 0 in the regex

[brave wolf]

ah it's regex

[dreamy ferry]

so can we minimize it anyhow?

[past aurora]

I don't think you can factor that out, you'd need to write like (1+0)0*...

But then you're stuck

Because what you can do after the 0* depends which branch of the + you took before

And you can't express that in regex

[dreamy ferry]

ok so it stays like that

[past aurora]

I think so yeah

[dreamy ferry]

i have one more question

how is epsilon + RR* = R*

[past aurora]

epsilon is the same as "zero copies of R", so the left hand side says "either 0 copies of R or at least 1 copy of R" and the right hand side says "at least 0 copies of R", and those are the same

Does that help?

[dreamy ferry]

how is RR* = R+ ??

i dont get this part

[past aurora]

Ah I see

Can you say what R+ means in your own words

[dreamy ferry]

closure of R minus epsilon

[past aurora]

Right so like (1 + 00)+ matches

1, 00, 100, 0000100, ...

Right?

[dreamy ferry]

the + in between 1 and 00 is union or like the closure minus epsilon thing

[past aurora]

Union

Yeah I was worried that was going to be confusing, do you use superscript for that?

[dreamy ferry]

yeah

[past aurora]

$(0+11)^+$

[flat frigate]

RSB

[dreamy ferry]

how 🥲

[past aurora]

Well it's the closure except the empty string

[dreamy ferry]

how do u take the closure of a union?

[past aurora]

Like, $(0+11)^*$ matches all those too

[flat frigate]

RSB

[past aurora]

As long as you can divide up the string into a bunch of substrings each of which matches the closured expression, you're good

So (0+11)* matches 01100011 because you can divide it up like this: 0 11 0 0 0 11

[dreamy ferry]

i see

[past aurora]

I think of $R^+$ as meaning "you can divide the string into a bunch of substrings each of which matches R, and there's at least one substring

[flat frigate]

RSB

[past aurora]

Whereas $R^*$ means at least 0 substrings

[flat frigate]

RSB

[dreamy ferry]

(0+11)+ wont match 11

right?

[past aurora]

It will

[dreamy ferry]

there's no substring of 0

[past aurora]

That's okay, you just need to divide up "11" into substrings each of which is matched by (0+11)

[dreamy ferry]

hmm okay

[past aurora]

And in this case there's no dividing up to do, you can use one substring which is the same as the whole thing

Like if I say "Pogram please go to the store and buy at least one fruit. Please make sure each fruit is either a banana or an apple" and you come back with an apple, you've followed the instructions

If you come back with ten bananas you've followed the instructions

But if you come back with no fruit at all you've not

[dreamy ferry]

ok i got it now

so hows rr* = r+

?

[past aurora]

rr* means "something that matches r, followed by at least 0 things that match r"

Actually how about this, let's be more explicit

Expression a is $(0+11)(0+11)^*$, expression b is $(0+11)^+$.

What's a string that's matched by a but not b, or by b but not a?

Oh hang on, I missed that up

[flat frigate]

RSB