help-49

[neat cedar]

u shouldn’t drink and do calculus

it’s bad to drink and derive

[low garden]

oka that was a good one

[dawn dagger]

you got big nostrils

[neat cedar]

☠️

[low garden]

wow im hurt

wait

[neat cedar]

bro is hurt

bro is hurt in 2024

[low garden]

whats r6

[dawn dagger]

6th wait

[neat cedar]

bro feels pain

[low garden]

painful fr

[neat cedar]

I thought maths would’ve numbed it but apparently not

[dawn dagger]

Oh I can't read the table

then use R(2) and R(7)

[low garden]

bacc made a mistake

hheheahahha

[dawn dagger]

wait actually

[neat cedar]

don’t put bacc down like that

[low garden]

wow

[dawn dagger]

how did you get

[low garden]

stop pointing fingers at me

[dawn dagger]

the area in the first place

[low garden]

hm

[neat cedar]

he’s just a human, we all make mistakes

[low garden]

omg

bacc

if i got part a wrong

[neat cedar]

HAHAHAHAHAHAHA

[low garden]

(60⋅2)+(90⋅2)+(110⋅2)+(120⋅2)

[dawn dagger]

ok I see

[low garden]

is it okay

because if its not im throwing hands at someone

[neat cedar]

hey!

violence isn’t the answer!

[low garden]

localbassman can have it

[dawn dagger]

I am kinda confused

[low garden]

WHAT

GANG

[dawn dagger]

how are you supposed to do this using subintervals

[neat cedar]

probably multiply by 2 to get normal intervals

[low garden]

uhh

[dawn dagger]

(R(0)+R(2)+R(5)+R(7)+R(8)) * (8-0)/2

[low garden]

💀

[dawn dagger]

this doesn't make sense

[low garden]

theres no way

[dawn dagger]

but maybe it's

R(2) to R(5) is 3 and R(7) to R(8) is 1

[low garden]

yes

[dawn dagger]

so maybe that's the compensation

[low garden]

so waht my friend did was right?

[neat cedar]

ahh so e^iπ in this sense goes to 0 as the derivative of x^2 is 2x and plug in y

I get it I get it

[dawn dagger]

I need a drawing

[neat cedar]

draw

[low garden]

eh

[dawn dagger]

no

[low garden]

hm

[neat cedar]

maybe ask teacher and or professor

[low garden]

idk for part b he integrated idk what he cooked

let me send

part c

[low garden]

idk what that erf is i dont rlly get how he integrated that

[neat cedar]

that seems right ngl

[dawn dagger]

💀 bro used wolfram

erf(u) lmao

[low garden]

😭

idk wth erf is

[neat cedar]

erf

[low garden]

never seen in my life

[dawn dagger]

errorfunction

[low garden]

WHAT

[neat cedar]

like the planet we live on?

[dawn dagger]

anyway irrelvant

[low garden]

LMAO

[neat cedar]

oh what

[low garden]

so thats wrong

[low garden]

why did u say it seems right

u gave me hope

[neat cedar]

it does

[low garden]

it does until i see erf

[neat cedar]

(Idk what ur doing I’m just being supportive)

[low garden]

(oh)

im dying rn

[dawn dagger]

,calc (0+2+5+7+8)/4

[grand pond]

Result:

5.5

[dawn dagger]

ok I think i know

[neat cedar]

good luck guys !!!!

[low garden]

okay

[neat cedar]

he thinks

therefore he is

[low garden]

so we need to rewind first to a and b...

[dawn dagger]

we wanna have 4 itnervals

[low garden]

mhm

[dawn dagger]

meaning 4 rectangles

[low garden]

yes

[neat cedar]

how many rectangles in a square

[low garden]

4

no

wtf

what are you asking me fr

[dawn dagger]

actually it's simpler than thought

[low garden]

hm

[dawn dagger]

Delta_X = just the difference of x_i and x_j

[low garden]

uh yes

[dawn dagger]

for example

for R(0) you have width 2-0

For

R(2) you have 5-2

[low garden]

r3 7-5

r4 8-7

[low garden]

Yes

[dawn dagger]

So we sum up

[neat cedar]

integration

[dawn dagger]

R(0) x (2-0) + R(2) x (5-2) + R(5) x (7-5) + R(7) x (8-7)

[neat cedar]

never mind then

[low garden]

l*b?

[dawn dagger]

60 x 2 + 90 x 3 + 110 x 2 + 120 x 1

[low garden]

yuh

WHAT

oh

[dawn dagger]

,calc 60 * 2 + 90 * 3 + 110 * 2 + 120 * 1

[grand pond]

Result:

730

[dawn dagger]

730

[low garden]

not 760

[dawn dagger]

yup

[low garden]

grrr

let me update that

[dawn dagger]

Now for D(t) it is still fine the way we did it

it is an estimation after all

[low garden]

yup didnt seem any other way around that

[neat cedar]

did u figure it out guys

[dawn dagger]

,w 100 + Sum[2 * 400e^((-(2k)^2)/4), {k, 0,3}] - 730

[grand pond]

Results provided by WolframAlpha

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

Requested by adoniszgks

[low garden]

uh mayb

[dawn dagger]

For The approximated integral of D(t) we used 4 subintervals but used Delta_t = (8-0)/4 = 2

A consistent Delta_t instead of having a new width everytime

[neat cedar]

real real

[low garden]

okay and the width is 2 is that the change in t

[dawn dagger]

and left point rule, not to forget

[dawn dagger]

what

[low garden]

delta t

[dawn dagger]

oh ye

mb

[low garden]

ok nvm yuh

yuh

yuh yuh go on

[dawn dagger]

Ok I would go with that

[neat cedar]

well done

[dawn dagger]

for the R'(5)

I find it better to use R(2) and R(7)

instead of R(5) and R(7)

[low garden]

okay thats fine

we can use r2 and r7

[neat cedar]

what about r3

[low garden]

no leave r3

[neat cedar]

but r3 is cool beans :((

[dawn dagger]

undefined

[grand pond]

bacc (unhelpful)

[low garden]

yup

[dawn dagger]

ok good

pro

[low garden]

so its just that

[dawn dagger]

if you simplify yea

30/5 = 6 approximated

[neat cedar]

bacc just figured out his own question

chad

[dawn dagger]

it's not deep but i am fried today

[low garden]

am i deadass getting 6 marks for writing tis though

[dawn dagger]

from me yes

[low garden]

why does it have such a high mark allocation

[neat cedar]

big tricky

so

if u solve

big reward

[dawn dagger]

The fact that your friend used erf(u) is so funny

[low garden]

hes such a bozo

[dawn dagger]

like he wants to be special in class

Mr. Teacher, I actually integrated it

[low garden]

that made no sense Lmao

[dawn dagger]

also we got clean numbers

most of the time a good indicator

[neat cedar]

cleanliness is next to godliness

[low garden]

yuh

whats aroc

stand for

[dawn dagger]

average rate of change

didnt mind to write it out

[neat cedar]

derivative

[dawn dagger]

average derivative

[low garden]

oh also

since part a is 730

part b answer is going to change

need to add 30 more

[dawn dagger]

.

yea

[low garden]

oh wow ur already ahead

[dawn dagger]

nah

you just missed it

[low garden]

this discord bot thingy is fast

ok real

[dawn dagger]

every anime girl calls it thingy

love it

[low garden]

🤗

okay tysm bacc person

change unhelpful to helpful

[dawn dagger]

they took my helpful

for unknown reasons

[low garden]

why

they are evil

[dawn dagger]

haha

[neat cedar]

bacc is super helpful

[low garden]

real

[neat cedar]

such liars

[low garden]

localbossman u were her for emotional support

i didnt cry

[neat cedar]

exactly

but now u will

[dawn dagger]

and what about my emotional support

[low garden]

true

[low garden]

u were the brain

[neat cedar]

π = 3 and also e = 3

😄

[dawn dagger]

i was both sides of the brain :D

[low garden]

where was i fr

!!!

[dawn dagger]

the heart

[low garden]

so real

[neat cedar]

such kind words

[dawn dagger]

😂

[dawn dagger]

@shadow scaffold

[low garden]

okay can i bother you again later when i study in an hour or 2

i will take a break now

[sinful trout]

okay bacc

don't just randomly ping modmail

[dawn dagger]

just open a help channel

[sinful trout]

and second you're supposed to message the bot lmfao

[low garden]

okay bet

[sinful trout]

@Moderators instead

and not for smth as trivial as this

[dawn dagger]

bro you are really lost ngl

[neat cedar]

not trivial

fact

🌚

[dawn dagger]

aight enough internet

.solved

[midnight plank]

Channel closed

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[midnight plank]

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[modern frigate]

Anyone know how to calculate newton polynomials?

[midnight plank]

Please don't occupy multiple help channels.

[modern frigate]

Sorry i don;t see my topic

[sinful trout]

close one of your channels

[modern frigate]

when i close one i close two

[sinful trout]

#help-32 is the other one

[modern frigate]

i don't see this channel

[sinful trout]

i literally just sent you a link to that channel

[modern frigate]

Can guys close this channel 32 because i dont see

[sinful trout]

go there and close it lol

sure

i'll do that for you

all done

[modern frigate]

ok thanks

[main current]

Go to "channels and roles" at the top of the channel list, you may be hiding the channels

[modern frigate]

.close

[midnight plank]

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[midnight plank]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[uneven sandal]

hey I'm quite lost here and would appreciate some help

[uneven sandal]

with L being the angular momentum operator, fulfilling $[L_j,L_k] = i \varepsilon_{jkl} L_l$

[grand pond]

tobi

[uneven sandal]

should I look at each matrix entry?, I just dont see how these are equal to one another if i write down the taylor series

already found a way of solving this

.close

[midnight plank]

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[midnight plank]

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[real pivot]

for this example how would you draw the graph?

[real pivot]

Im trying to draw it but there seems to be an additional tri edge {a, s, c} but its not in the set of tri edges

[midnight plank]

@real pivot Has your question been resolved?

[midnight plank]

@real pivot Has your question been resolved?

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[dense bay]

hi i just want to confirm that my approach is correct for this question

[dense bay]

what i have:
$$F_U(u) = P(min(X,Y) \leq u) = 1-P(X>u, Y>u)$$
(taking the complement above)

$$= 1 - \int^{\infty}_u \int^{\infty}_u ye^{-(x+1)y}dxdy$$

[grand pond]

jack

[dense bay]

and then solve by fubini? hpoefully this looks fine

[merry pewter]

Yeah seems good to me

[dense bay]

thanks

[dawn dagger]

looks good

[midnight plank]

@dense bay Has your question been resolved?

[midnight plank]

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[twilit field]

Let $a>b$, then by the mean value theorm there exists $c \in (a,b)$ such that $f'(c) =\frac{sin(a)-sin(b)}{a-b}$
\
$cos(c) = \frac{sin(a)-sin(b)}{a-b}$
\
but $-1 \leq cos(c) \leq 1$
\
so
\
$-1 \leq \frac{sin(a)-sin(b)}{a-b} \leq 1$.
\
we now multiply across by $(a-b)$
\
We thus get
\
$-(a-b) \leq sin(a)-sin(b) \leq a-b$
\
$sin(a)-sin(b) \leq |a-b|$

[grand pond]

A dense set

[twilit field]

This is what I've done so far

[dawn dagger]

Can you simply multiply by (a-b) without affecting the inequalities tho

[twilit field]

$a-b$ is positive

[grand pond]

A dense set

[dawn dagger]

it says for all a and b?

[twilit field]

Oh

right

then I split it into cases

[dawn dagger]

Actually I cannot read, you assumed a > b mb

[twilit field]

I mean by the acrhemedain property, for every a there is a greater b, that enables me to cover all a,b

Got it

thanks

.close

[midnight plank]

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[midnight plank]

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[viral dagger]

$f(f(x))=\frac{x^5+5x^4+10x^3+10x^2+5x+1}{x^3+3x^2+3x+1}$
if $f(1)=3$ then find $f(25)$

[grand pond]

Skill_Issue

[viral dagger]

i noticed that the fraction can be simplified to $x^2+2x+1$ but im not sure what next

[grand pond]

Skill_Issue

[viral dagger]

what

[tawdry laurel]

i think we can do some substitutions

f(f(1)) = 4

f(3)=4

[viral dagger]

f(3)=4
f(4)=16

[tawdry laurel]

think so

[viral dagger]

not 25 tho

[tawdry laurel]

yea

f(f(25)) = 576

[viral dagger]

[tawdry laurel]

fr idk how to continue

[eager geyser]

envien ph

[midnight plank]

@viral dagger Has your question been resolved?

[merry pewter]

Wait f(f(4))=25, so f(f(f(4)))=f(25)

And you can find f(f(f(4)))

It’s (f(4)+1)^2

So it’s 17^2

@viral dagger

[fleet axle]

,c 17^2

,w 17^2

[grand pond]

Results provided by WolframAlpha

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

Requested by ginger4557

[viral dagger]

how did you get this

[merry pewter]

f(f(x))=(x+1)^2

[viral dagger]

oh

[fleet axle]

isn't another way to say

you know f(4) = 16

so f(f(f(4))) = f(f(16))

then you can plug into the equation for f(f(x)) givne

idk

[fleet axle]

oh

this is the same thing

[viral dagger]

ty guys

.close

[merry pewter]

Yeah

[midnight plank]

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[merry pewter]

https://tenor.com/view/krill-issue-skill-issue-krill-issue-gif-25572478

[midnight plank]

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[twilit field]

Is this proof too terse

[twilit field]

We wish to proceed via induction
\
Base case : $\sum_{k=1}^{1} \binom{k}{r} = 1$
\
Inductive hypothesis $\sum_{k=1}^{n} \binom{k}{r} = \binom{n+1}{r+1}$
\
we wish to prove that this implies that $\sum_{k=0}^{n+1} \binom{k}{r} = \binom{n+2}{r+1}$
\
\
$\sum_{k=0}^{n} \binom{k}{r}+ \binom{n+1}{r} = \binom{n+1}{r+1}+ \binom{ n+1}{r}= \binom{n+2}{r+1}$
\
This concludes our proof

[hollow oyster]

yes this works

[twilit field]

isn't it too terse?

thanks convergence !

[hollow oyster]

have you seen rudins books?

[twilit field]

[hollow oyster]

also why did your question have k=0

ik that you corrected it but yeah...

[twilit field]

wait

oops

[grand pond]

A dense set

[twilit field]

That's the book

c(0,n)=0

[hollow oyster]

so thats how its defined

[twilit field]

yeah

makes life easier

[hollow oyster]

oh wait that's the same as not choosing anything why did i not think of that...

[lunar ocean]

your base case here doesn't make any sense

or wait maybe it does

ok nevermind it works assuming the restriction in the question that isn't actually necessary for this result to be true

[solid iris]

@twilit field k=1 in base case

[lunar ocean]

with r=0 both sides evaluate to n+1, with r > n both sides evaluate to 0

so there's no actual reason for the condition that 1 <= r <= n

[twilit field]

We wish to proceed via induction
\
Base case : $\sum_{k=1}^{1} \binom{k}{r} = 1$
\
Inductive hypothesis $\sum_{k=0}^{n} \binom{k}{r} = \binom{n+1}{r+1}$
\
we wish to prove that this implies that $\sum_{k=0}^{n+1} \binom{k}{r} = \binom{n+2}{r+1}$
\
\
$\sum_{k=0}^{n} \binom{k}{r}+ \binom{n+1}{r} = \binom{n+1}{r+1}+ \binom{ n+1}{r}= \binom{n+2}{r+1}$
\
This concludes our proof

[grand pond]

A dense set

[twilit field]

Thanks everyone!

.close

[midnight plank]

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[midnight plank]

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[drifting root]

q is to evaluate this integral

[drifting root]

this is what i did

$2\ln \left| \sec{\frac{x}{2}} \right| + C$

[grand pond]

Sho

[drifting root]

am i just bad or are ans wrong

[hollow oyster]

lol this is correct

-ln|x|=ln|1/x| you forgot about the - sign in your answer it is supposed to be -2ln|cosx/2|+c @drifting root

[drifting root]

AHHH

Thank you, i was so confused cause i copied it down as cos in class as well

.close

[midnight plank]

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[drifting root]

Will fix

[midnight plank]

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[verbal kindle]

im. not too sure how to begin

[stiff shard]

Wait a Min

[lethal path]

those are some big numbers

let's work with a simpler problem first:
if A takes 2 hours to fill a bathtub, and B takes 3 hours to fill a bathtub, how many hours does it take when A and B both fill the bathtub?

[lethal path]

hint: think of how many bathtubs A and B fill in 6 hours

[uneven crystal]

chatgpt

[lethal path]

!nosols

[midnight plank]

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.

[stiff shard]

yea yea

[lethal path]

yeah

[stiff shard]

Okay then.

it's not chatgpt btw

[fleet axle]

there is a trick you can do

there is a normal way and a trick way

[stiff shard]

do the normal way

[fleet axle]

the trick way is so coool though but

[stiff shard]

he/she may get confused

[fleet axle]

yeah if you only know one way, do the normal way

[lethal path]

yeah I can get to the trick way from this

[fleet axle]

normal way has more use

[lethal path]

it generalises really nicely if you cancel out the 6 in the numerator and denominator
denominator is ||6/2 + 6/3||

[fleet axle]

yeah

[fleet axle]

i think this is a good way to start, either way, too :p

[uneven crystal]

is the answer 6/5 hours? i've completely forgotten about inverse proportions

[lethal path]

yep!

[uneven crystal]

alr thnx!

[verbal kindle]

does it take

work = rate x time right

[lethal path]

yeah

[verbal kindle]

so 1 bathtub = 2hr/bathtub x 2hrs

the other one would be

1 bathtub = 3hr/bathtub x 3hrs?

[fleet axle]

$\frac{2 hr}{bathtub} \times 2 hr$?

[grand pond]

Ginger

[fleet axle]

is the left fraction the right direction?

[verbal kindle]

idk

wai

wait

0.5 bathrubs/hr

there

[lethal path]

yeah, now that's correct

[fleet axle]

yess

bathtubs/hour

[verbal kindle]

other is 0.33 barbrubs /)4£;!:

0.33 bathrub per hour

god

i cant yype

[fleet axle]

1/3 barbeques per hour yes

[verbal kindle]

so i can multiply thenm

1 bathrub takes

[lethal path]

yeah so 1 hour = 1/2 bathtubs and 1 hour = 1/3 bathtubs

[verbal kindle]

yes

now what

im sorry im slow i have such a bad headache rn

[fleet axle]

you're not doing bad

[lunar ocean]

wait no

[verbal kindle]

k so their rate together is

[lunar ocean]

"1 bathtub is 1/2 hours" would correspond to 2 bathtubs every hour, not 1 bathtub every 2 hours

[lethal path]

yeah I confused myself

[verbal kindle]

5/6 bath rubs na hour

[fleet axle]

you can add rates to get the rates when they both act together @verbal kindle

yes

[lethal path]

hold on let's get the correct equation from what you did

[obsidian bay]

simultanous in CAS

[fleet axle]

5/6 baby back ribs per hour

[verbal kindle]

H bz z .!? hrrngh

[lethal path]

so now 1 hour = 1/2 + 1/3 bathtubs

okay so now what is 1 bathtub

[verbal kindle]

1 bathru = 5/6 bath/hr x T

6 abth = 5bath/hr x T

what the gell am i doing

takes 6/5 hrs

?

[obsidian bay]

what are you guys talking about with bathtubs

[lethal path]

breaking down this rate problem

[fleet axle]

we're talking about barbeques

[verbal kindle]

is it 6/5 hours

[lethal path]

once you can do it for 2 bathtubs, it generalises really nicely

[lethal path]

yep

so it is actually 1/(1/2 + 1/3) and you can simplify that to 6/5

[karmic sundial]

Hey Im new to this server

[verbal kindle]

can i resent the og provlem here

[lethal path]

try convincing yourself that if A takes 2 hours, B takes 3 hours, and C takes 6 hours

then it's 1/(1/2 + 1/3 + 1/6)

[verbal kindle]

i get it

because we are adding their rates

and we take reciprocal because

[lethal path]

cause 1 hour = 1/2 + 1/3 + 1/6 bathtubs

and now divide by the same thing on both sides to find ? hours = 1 bathtub

[fleet axle]

welcome

[verbal kindle]

in the end we want time for 1 abthrjudb not their rate

right

[lethal path]

yep!

[fleet axle]

yes

[verbal kindle]

Ok

so for thsi

[lethal path]

so nearly there, if you add all the people up in the original question, you get 2 * (M + A + T + H)

[fleet axle]

abthrjudb

[verbal kindle]

wait wait wait

[fleet axle]

this was kinda the "trick" method to me (x but yes it's nice

[verbal kindle]

ok then

wgat

[lethal path]

so if you want to find the time taken for just (M + A + T + H)

what must happen to the time?

there is twice less manpower but the same work to do

[verbal kindle]

divide 2

[lethal path]

no, the time wouldn't be quicker

[verbal kindle]

time s2

[lethal path]

yes, times 2

ok now you have all the info you need to solve the original question

[fleet axle]

wait really their names spell math

this keeps getting deeper

[lethal path]

yeah lmao they do

someone posted GPT output and I realised

[fleet axle]

that is amazing lol

[verbal kindle]

takes

uhhhhhhhhh

6004

so

[lethal path]

remember this?

[verbal kindle]

12008 rate

[lethal path]

do the exact same thing for these 4 people

[fleet axle]

(4 pairs of people)

[verbal kindle]

i cant fkign do thsi shfit

M and A takes 1188

so M and A rate is 1/1188

[lethal path]

like you can treat M + A as one person
and A + T as another person

[fleet axle]

ok idk if this helps like
Mathis and Anders

• Andres and Tellis
• Tellis and Hal
• Hal and Mathias
  all working on it at the same time. so yes they ahve twins

[verbal kindle]

A T takes 1/1540 TH TAKES 1890 and hM takes 1/1386

so the time it takes

for all of then togthehrr is

god do i need to multiply them

[fleet axle]

no it's the bathtub thing

[verbal kindle]

i know but

[fleet axle]

1/2, and 1/3

[verbal kindle]

i need a common denominator

im gonna divide by 5

[fleet axle]

wait what are you calculating tho

[verbal kindle]

1/1188 + 1/1540

etc

[fleet axle]

ok yes

good

[verbal kindle]

Fuck

how to add thsy

[fleet axle]

is a calculator not allowed

[verbal kindle]

no

[fleet axle]

the answers are in decimals

[verbal kindle]

no calculote

[fleet axle]

😠

[verbal kindle]

https://tenor.com/view/rage-gif-24341837

HOW DO I DO THUS

[fleet axle]

with a calculator

imo

[verbal kindle]

I CANT USE

[fleet axle]

or with not a headache

[verbal kindle]

HOW DIO

HOW DO

[fleet axle]

bc it's just you know adding fractions

you know how to add fractions

[lethal path]

just find the expression, don't worry about the no calculator bit

[fleet axle]

but it just

those are huge fractions

[verbal kindle]

ok irs just

1/2(1/1188 + 1/1540 + …)

[lethal path]

actually the super trick method is that you know you need to multiply by 2

so it has to be D, cause 364.7 * 2 = 729.5 nearly

only A and D are separated by a factor of 2

[verbal kindle]

How

[fleet axle]

🪦

[lethal path]

2 * 1/(1/1188 + 1/1540 + 1/1890 + 1/1386) to be exact

[fleet axle]

bc he knows the test creators will try to trick you

by creating one option that is if you forgot to multiply by 2

[verbal kindle]

Shit SHIT

[lethal path]

but then that's not teaching you about maths

that's just teaching you how to get good at MCQs

if it's short-answer where you need to show work you'd be screwed

[verbal kindle]

Ok so

so

theres these people

that take some time to fill Peach or some shit

[fleet axle]

so this is the problem done

pretty much

[verbal kindle]

but these peoole are actually 2 people

duplicates

[fleet axle]

yess

[verbal kindle]

but we dont care about duplicates

because we only want

[lethal path]

yes

[verbal kindle]

each 4 individually

so the rate of the 4 dupes are

just 1/however long takes them to fuck

but that means its 2 times the speed of the actual 4 people

so if we want how fast to do 1 peach but with half the manpower

u need to fond 1/shit and muiplty the time it takes by 2 since half less people

[fleet axle]

this is the first time i'm realizing the original problem is about peaches

[verbal kindle]

yr allowed to times half less people becaus it loses each dupe but IF IT LOSES not a dupe it fucks the proboke up

right

[fleet axle]

what the ||fuck|| is gaffney peach

[verbal kindle]

I dont fakign know

[verbal kindle]

is this right

[fleet axle]

yeah that sounds right

[verbal kindle]

Ok

[fleet axle]

it's the same as dividing by the rate by 2

before you do the 1/everything

anyway yes

sounds good

[verbal kindle]

can u hekp me witj 1 more problm

oe are u busy

[fleet axle]

i can try

[verbal kindle]

ylets goo

for this

doesnt it keep going

i tried case work

but is dumb

[fleet axle]

interestingg

i'm not a mathematician

i might be too dumb for this one

without hints

[verbal kindle]

Fuck

[fleet axle]

but now i'm probably going to keep thinking about it

[verbal kindle]

But u solved the other one

easily

[fleet axle]

the other one seems easier to me

[verbal kindle]

Shit

[fleet axle]

i'm thinking about the wording actually

let me check something

,w 1 - .4 - .6 * .4

,w 18/25

ok so

they. jus tmean

what is the probability that alejandro won?

ok i can do this one

but idk if i can do it in a simple way

[verbal kindle]

I seep

I tried case work

like if we wins first

wins second time

etc

[fleet axle]

yeah

that sounds similart to what i was thinking

there are two "groups" of cases

well you can think about it however lol

[verbal kindle]

there must be a faster way tho no?

[fleet axle]

but either he can win first, or she can win first

after that, they must alternate

[verbal kindle]

cuz they expect this solved in 2 mins

[fleet axle]

until the double win

[verbal kindle]

eactly

[fleet axle]

hmmm

this way maybe could be done quickly?

[verbal kindle]

idk sounds like a lot to me

[fleet axle]

group 1 is like: start with .6^2, then multiply by .6*.4

[verbal kindle]

unless u can simply some cases

[fleet axle]

group 2 is .4 multiplied by group 1

[lethal path]

wait where are these questions from btw

[fleet axle]

group 1 = .6^2 * 1 / (1 - .6*.4)

[verbal kindle]

wait its a geometric sequence no?

[verbal kindle]

my teacher

[fleet axle]

just wrote the formula for that. exactly

[lethal path]

yeah these look a lot like contest maths

[verbal kindle]

wait wai

can you ru. me thorugh the logic again

i gtg

@fleet axle

so we have 2 groups one is if he jusy wins in the 2 rounds

and other is alternating and then he wins

[fleet axle]

it always alternates so

you have 2 geometric series

one is if he wins first

other is she wins ifrst

but then it always laternates

[verbal kindle]

if he wins first its

[fleet axle]

and ends with him winning

[verbal kindle]

0.6 x 0.6

[fleet axle]

so, the series where she wins first, the whole thing, is just 0.4 X the series where he wins first

[fleet axle]

yes

exactlu

[verbal kindle]

so we have

0.6 x 0.6 +

basically

[fleet axle]

but there's a whole series, so, 0.6^2, or 0.6 * 0.4 * 0.6^2, etc

[verbal kindle]

0.4 x 0.6 x 0.6

[fleet axle]

0.6 * 0.4 is always the multiplier in the series

perfect

[fleet axle]

one more 0.6 here

[verbal kindle]

or 0.4 x 0.4 x 0.6 x 0.6

…..

[fleet axle]

0.6 * 0.4 * 0.6^2

[verbal kindle]

ok

yeah so

[fleet axle]

(he win)(she win)(he win)^2

etc

[verbal kindle]

the common ratio is

[fleet axle]

(he win)(she win) = 0.6 * 0.4

is the common ratio

[verbal kindle]

i see

[fleet axle]

right cause

Group 1: (he win)^2, or (he win)(she win)(he win)^2, orrrr (he win)(she win)(he win)(she win)(he win)^2

Group 2: Same, but add an extra (she win) in front of everything

[verbal kindle]

i see

[fleet axle]

e

,w (1 + 0.4) 0.6^2 / (1 - 0.6*0.4) fraction

[grand pond]

Results provided by WolframAlpha

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

Requested by ginger4557

[verbal kindle]

ok so

win is always 0.6 squared

but they alternate

every 0.6 and 0.4

which makes that the common ratio

[fleet axle]

rightt

[verbal kindle]

and theres 2 ways

one is first he win the other is

lina go first

soi just add the two cases

ok i grg cya

tysm

.close

[fleet axle]

yes [erfect

[midnight plank]

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[fleet axle]

lina win first

glgl

lina barbeque first*

[midnight plank]

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[twilit field]

cna I have a hint for (b)

[twilit field]

I've tried playing around with some inequalities

but that doesn't help much

like $e^x \geq -(1+x+x^2/2)$

[grand pond]

A dense set

[twilit field]

e^x>1+x-x^2

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

<@&286206848099549185>

Ohh

Let $x=ln(y)$

[grand pond]

A dense set

[runic hamlet]

what tools do you have available?

[twilit field]

MVT, rolle's theorm and the first and second derivatve tests

and differential calculus

[runic hamlet]

compare the derivatives

[twilit field]

$e^x \geq 1+2x$

[grand pond]

A dense set

[twilit field]

isn't always true

[runic hamlet]

check again

[twilit field]

let x=1, $e \ngeq 3$

[grand pond]

A dense set

[twilit field]

oops

ojay

okay

[runic hamlet]

check your derivative again

[twilit field]

1+x is the derivative

e^x is always more than 1+x

oh right

okay

thanks

I suppose i can use the same for the last problem

Thanks!

.close

[midnight plank]

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[idle phoenix]

help

[stiff shard]

This is physics and not math

[idle phoenix]

yeah

but

physics is basically math

right?

nvm

.close

[midnight plank]

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[twilit field]

Trying to prove this

[twilit field]

The lower bound I have is $2\sqrt{2}$

[grand pond]

A dense set

[twilit field]

as per my calculations

[carmine void]

How did you get to it?

[twilit field]

using this property

[carmine void]

Ah, that looks to weak

[twilit field]

Hmm

could probably comare it with another integral

[slow thorn]

Hint: $x^2$ is always lesser than $\sqrt{x^4+1}$

[twilit field]

yeah, that's probably it

[slow thorn]

you can just remove the one inside and figure it out too

[twilit field]

just 4 months ago, I would have figured this out in a snap 😭

[slow thorn]

i got lucky guessing the function though 😂

[twilit field]

,w \int_1^3 x^2

[grand pond]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[twilit field]

yup

[slow thorn]

i saw 26/3 = 27/3 - 1/3 and thought it was x^3/3

[twilit field]

that's it

lol

that's not luck

that's smarts

[slow thorn]

works only sometimes though

[twilit field]

I'll compare this with $\int_0^{\pi/2} x$

[grand pond]

A dense set

[slow thorn]

makes sense

inequality holds exactly until pi/2

[twilit field]

.close

[midnight plank]

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[twilit field]

thanks

[midnight plank]

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[oak granite]

is (-1)^(1/3) = -1 or 1/2 + i√3/2 ?

[worthy wing]

Depend on the context

[oak granite]

wdym?

by context

[worthy wing]

Context is whats around the question.

[oak granite]

The principle root?

[oak slate]

the principal root is the root with the biggest real part

bprp has a video on it

[oak granite]

what about the imaginary part?

[sinful trout]

doesn't really matter

[oak granite]

because there is also 1/2 - i√3/2

[oak granite]

link pls

[sinful trout]

principal root is essentially the root of unity with lowest arg

[oak granite]

so it is 1/2 + i√3/2 ?

[wild lark]

for instance n_/x means the nth principal root of x in most contexts.

[oak slate]

https://youtu.be/44kBz2-rfhM?si=sKjs6I3OW0OuYkXF

its presh actually, not bprp

[oak granite]

so (-1)^(1/3) is not -1

[worthy wing]

🙏

[oak granite]

?

my objectif is to know the domain of x^x
what I want to know is for exemple (-1/3)^(-1/3) is real or not

[midnight plank]

@oak granite Has your question been resolved?

[midnight plank]

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[grim ridge]

AE =2, AC=4 , AB=3 , AD= ?

I've solved it myself

But my answers wrong

[dreamy lichen]

How did you solve itt?

[grim ridge]

What how

[worthy knoll]

ohh nvm

[grim ridge]

A lot of doing stuff lol

Let me explain

[worthy knoll]

but, is 6 correct tho?

[grim ridge]

Nuh

[worthy knoll]

hmm wrong theorem then

[grim ridge]

I solved it by using similar triangles

So BD = EC

[dreamy lichen]

How do you know that?

[grim ridge]

ED=EC=CB

[grim ridge]

Angles

Angels

[nova pike]

?

ED = EC ?

[grim ridge]

Sorry

Dc

[dreamy lichen]

okay so ED = DC = CB

[grim ridge]

Yep

AD cuts the EB line in a place, name it G
Same for AC , name it F

[midnight plank]

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[gaunt nimbus]

** High School Math Question **
Define ${f: \mathbb{N} \rightarrow \mathbb{N}}$ such that ${f(x) = x^3 + 2}$ and for any positive integer ${n}$, define:
\begin{enumerate}
\item $f_1 = f$
\item $f_{n+1} = f \circ f_n$
\end{enumerate}
Find the number of integers ${x}$ over the closed interval ${[2023, 2566]}$ such that $(f(x))^{f(x)} - f_{f(x)}(x)$

[grand pond]

k

[gaunt nimbus]

Answer key: 271

i have the full solution but i dont understand it

and it's in my native language

[last slate]

What language?

[gaunt nimbus]

thai

[last slate]

bruh

I recommend you look for a way to translate it

[gaunt nimbus]

let me pull up latex

gimme around 10 minutes

[tawny hedge]

send pic

im not fluent in thai but i can read it well enough

[gaunt nimbus]

my attempt at translation

i dont even understand

this notation tbh

<@&286206848099549185>

[midnight plank]

@gaunt nimbus Has your question been resolved?

[midnight plank]

@gaunt nimbus Has your question been resolved?

[midnight plank]

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[night gyro]

why is this wrong

[hearty rune]

'perimeter'

[modern shard]

which would be pi(r) in this case

[night gyro]

wht m i meant to do

[hearty rune]

you found the area

you merely need to sum the lengths of the sides

[night gyro]

do i find the sector?

[hearty rune]

do you mean arc length?

[night gyro]

yh

[hearty rune]

sure

[night gyro]

wht do devide 360 by

[hearty rune]

since its half a circle we can just do this

half the circumference of a whole circle

[night gyro]

so pi/2?

[hearty rune]

no

if we're using l=r theta, theta would be pi

[night gyro]

idk

whts l

[hearty rune]

arc length

[night gyro]

x/360 * 2pi*r

[hearty rune]

im not a fan of that formula

but x would be 180

[modern shard]

yeah can be used

[night gyro]

arc lentgh/theta = r

[night gyro]

ok

wht do we do

[midnight plank]

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[night gyro]

.close

[midnight plank]

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[safe onyx]

Optimization -- minimum distance between two points
Find the point on y^2 = 2x that is closest to (1,4)

d = sqrt (x-1)^2 + (y - 4)^2
x = 0.5 y^2
d = sqrt (0.5y^2-1)^2 + (y - 4)^2

then instead of minimizing d, the textbook says to minimize it's square so
d^2 = f(y) = (0.5y^2-1)^2 + (y - 4)^2

why do you square everything?

[safe onyx]

I get that squaring d removes the sqrt . But why do we change to d^2

[sudden yacht]

Because working without roots is (usually) easier. And in this case minimizing d or d² is the same, because you're finding the point that minimises d, and not the minimum of d

And note that his works because d is non negative, as d² is

[safe onyx]

And in this case minimizing d or d² is the same
how can I know this, I don't want to always assume

my textbook says "you should convince yourself that the minimum of d occurs at the same point as the minimum of d^2, but d^2 is easier to work with"

[sudden yacht]

Exactly, indeed

[safe onyx]

since the variable is always positive, it's minimum is the same?

in this case, 0,0

[sudden yacht]

Well, if d is the minimum it means that d < D for whatever other distance D you consider
If you square this you get d² < D²
So d² is the smallest among all other distances square

Note that I'm not saying that the the minimum d has the same value of the minimum d²

[safe onyx]

so if I find the minimum of d^2 it is the minimum of d?

[sudden yacht]

In other words d can be different from d². What matters is that d and d² are the minimum at the same point (x, y)

[sudden yacht]

Yeah, if you find for instance that d² has minimum value of 3, it means that the minimum value of d is √3

The key concept here is that minimum ≠ point of minimum

[safe onyx]

i'm trying to sketch it out, sorry I don't fully get it

we want to find the (x,y) (blue) where distance (d orange) is the smallest

[sudden yacht]

You can't actually visualise d²

Or better said, it doesn't have a geometrical meaning in this case

[safe onyx]

so what other way can I represent it

is it like going from 2d to 3d kinda thing

[sudden yacht]

The fact is that you can do that because d ≥ 0 and on d ≥ 0 the function d² is monotonically increasing

[sudden yacht]

You simply don't

[sudden yacht]

No no

It's something quite trivial, I don't actually know how to explain it

[safe onyx]

I think I'll close this for now, if you know of any resources or have an idea for an explanation would you mind pinging me or dming me?

Thank you so much

[sudden yacht]

I think you can wait for other helpers, before you close the chat

Probably some helpers turn up, they might be going around here

[safe onyx]

Sounds good I can wait

I am currently trying to understand

• How d^2 can be understood in the pinned equation
• Why does minimizing d and d^2 occur at the same point

[sudden yacht]

I'll tag helpers, so that they know they can directly read the questions here

[sudden yacht]

<@&286206848099549185>

[safe onyx]

thank you :)

[safe onyx]

https://youtu.be/lx8RcYcYVuU?t=2670
I followed along to this and noticed that he did not ignore the square root. I tried seeing what happened when I did and there was no change in where D = 0 since the deriving the square root divided everything in the numerator by 2 and since the numerator determines where D' = 0 that seems to make some sense. (this doesn't fully resolve the questions, but I think is helpful)

I personally just set
D^2' = 2(7-x)(-1) + 2(2+x)
= 4x - 10
x = 10 / 4 --> 5/2 (when set to 0)

he has the same ratio except divided by 2, which I guess is negligible in finding the critical point

and the denominator can never be 0 since you are adding two squared numbers, so d^2 is defined in all real numbers

[flint rock]

im confused too now

[sudden yacht]

Yeah exactly, here when you solve derivative = 0 you can eliminate the denominator, which actually is the derivative of the inside of the square root, due to chain rule. But what is inside the square root? If you think about it for a while, it's exactly d^2

[sudden yacht]

You spotted on! We're not interested in the value of d (or d^2) but rather in the value of x that makes d have the minimum value (whatever that value is)

I think you're getting it now 👍

[safe onyx]

sorry I basically noticed that d^2 is the same as the numerator of the derivative

[flint rock]

ok

i think its just that the minimum value's position doesnt change

x-axis wise

[safe onyx]

though technically it's 2* greater, you can factor it out and it's ignored in critical points

thank you both, I'm still a little scared for the test but it's decreased today XD

.close

[midnight plank]

Channel closed

Closed by @safe onyx

Use .reopen if this was a mistake.

[midnight plank]

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[untold oyster]

Is it right?

[sleek cloud]

Find (f(x) = (-2)?

Did you mean f(x) = -2?

Then it's wrong

I see so it's probably F(x) = -2, where F(x) is the derivative of f(x). So it's still wrong.

[untold oyster]

Yes

[sleek cloud]

Send the original question

[untold oyster]

F(-2)

[sleek cloud]

F(-2) and F(x) = -2 mean two different things

[sleek cloud]

,rotate

[sleek cloud]

So it's not derivative

[untold oyster]

Its function

[sleek cloud]

So your answer right

[untold oyster]

Ty

How about the 2nd one?

How can i simply it?

[sleek cloud]

Wait the first one isn't correct calculation

The result is correct but a step wrong

Should be -4 not +4

[sleek cloud]

Try factoring more