help-42

[eternal shard]

2nd domino's successor is the 3rd domino

like a chain

and like

you had n = k and n = k+1 now you flip the succesor n = k+2

[warm pewter]

Ohhhhhhhhhhhh

Very good explanation

Ok understood

Can u help me w one more

By the way thanks a lot I actually get it

[eternal shard]

okk

[warm pewter]

This one is divisibility

ii) I am stuck

[eternal shard]

yes

what are your thoughts on approaching this

[warm pewter]

We just do the same thing which is a base case

N=1

And then we assume for n=k that like it is divisible by 16

[eternal shard]

yeeeeeeeeeeeeeeedsssss

can you tell what happens for n = 1

[warm pewter]

Yes the result gives 112 and we can factorise the 16 out to show that it is true

So 16(7)

[eternal shard]

yesss

well done

now we know for some n f(n) is divisible by 16

[warm pewter]

Yessssssss

[eternal shard]

now we need to show for f(n+1)

using the fact that f(n) is divisible by 16

[warm pewter]

Yes

[eternal shard]

,, f(n+1) = 5^{(n+1)+2}-4(n+1)+9 = 5^{n+3}-4n+5

[eternal shard]

this is what we wanna show now

[warm pewter]

Yes

But aren’t they the same thing

[eternal shard]

no

so we basically want to show this

using the assumption that f(n) is divisible

[warm pewter]

Is it f(n+1) - f(n) bc if both r divisible by 16 then subtracted would be divisible too

[eternal shard]

well yes

but we want to prove f(n+1) is divisible by 16

[warm pewter]

Try to factorise 16 out

[warm pewter]

Why can’t I prove it this way

[eternal shard]

uhm

i dont know how you would go about it that way

[warm pewter]

Bc we found f(k)

Idk too

[eternal shard]

My try would be to use the assumption instantly like we know that f(n) is divisble by 16 which means f(n) is some multiple of 16

like

f(n) = 16m for some m

[warm pewter]

Yes

Ok I under

Stand what u mean

[eternal shard]

then i would try to algebraically derive f(n+1)

and see what happens

[eternal shard]

ok we need a 5^n+3 and instead of 9 we need a 5

we could multiply by 5

[warm pewter]

Yepppo

[eternal shard]

now we need a -4n and a 9

so we can write -20n as a difference that has -4n

same with 45

we can write 45 as a sum of two numbers where one is 9

can u do that

[warm pewter]

-4n-16n + 9 + 36

[eternal shard]

ooooooooooooooooooooooooooooooooooooooooooooooooooooooo

[warm pewter]

Omg

[eternal shard]

now let's bring 36 and 16n to the other side

[eternal shard]

winnie what can you conclude

[warm pewter]

Idk bc -36 cannot be factorised

[eternal shard]

we now have f(n+1) on the left

and on the right

some terms with 16

[warm pewter]

😅

[eternal shard]

remember

you are almos at the finishing line

it's almost wonnie

o shoo

[warm pewter]

5x16m + 16(n+1)-48

[eternal shard]

😭

[warm pewter]

Wait

HAHAHAHAHAA

[eternal shard]

i thought 36 was divisible by 16 i am so dumb

[warm pewter]

HHAAHAHAHAAHAHAHHAAHAHAHAHAJAA

NOOOO

Ur so smart

[eternal shard]

hmm

we did a mistake

we dont need a 9

we need a 5

[warm pewter]

Ohhhhhh

Ok so

[eternal shard]

but uhm

[warm pewter]

5+40

[eternal shard]

yea 40 is also not good

[warm pewter]

Hmmmm

Omg wait

Omggggg

I think ik what we did

Wrong

It’s not 5 it’s -13

[eternal shard]

😭

i wrote it down wrong

[eternal shard]

+9 not -9

[warm pewter]

I didn’t even see that

[eternal shard]

i did

ok let's restart ok 😄

[warm pewter]

Ok!!!

[warm pewter]

Is it n+3

[eternal shard]

we make it multiplying by 5

[warm pewter]

Ohhhhhh

Ok got it

[eternal shard]

Keep in mind

[eternal shard]

THATS whaat u said with 13

todays is the 13th too

[warm pewter]

Omg yes

[eternal shard]

so we need 45 asa difference with 13

can u do that pro

[warm pewter]

Omgggggg

32

Omggggfddssss

[eternal shard]

YA

yea you are done basically

q.e.d

can u finish it

[eternal shard]

yea i believe u

u had it right

[warm pewter]

5^n+3-20n-45 = 5x16m
How do you type so fast?

[eternal shard]

discord likes me?

i guess

[warm pewter]

Is this the same for all divisibikity rule questions

[eternal shard]

yesss

[warm pewter]

I’m on phone it’s so hard

Ok I will just do this

[eternal shard]

if something is divisible by some number

then you can write it as a multiple of that number

[warm pewter]

Ahhhhhh

This makes sm sense

[eternal shard]

f(n) divisible by x means f(n) = xm where m is an integer

[warm pewter]

Ohhhhhhhhhhhh

Omg yes

I will try this for other questions tomorrow

By the way thanks sm u spent so much brainpower and time

[eternal shard]

you deserve it!

you are a very good student

[warm pewter]

If I have questions can I dm u 🥲 but not frequent or else I’m gonna disturb too much

[warm pewter]

Yes I know

😂

[eternal shard]

it's easier to help u with the texit bot here, so i would prefer to help you on the server instead

[calm coral]

@warm pewter Has your question been resolved?

[calm coral]

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[calm coral]

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[junior zodiac]

i have a question

[junior zodiac]

19c

k = 2 btw

i get all these seperate cases

case 1, the cdf is always 0

case 2 we can integrate with the given bounds

but i dont really understand case 3 (and case 4, but they look pretty symmetrical)

why do we fill in F(x,y) with y = 1 is my question

[glass heart]

F(x,y) is the probability P(X<x,Y<y). but thats the same as P(X<x,Y<1) cause Y>1 has prob 0

[calm coral]

@junior zodiac Has your question been resolved?

[junior zodiac]

oh right thank you

[calm coral]

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[manic timber]

what do they mean actual value?

[manic timber]

do we just make another estimate with more subdivisions and call that the actual value?

[leaden thunder]

just pick an arbitrary increasing function that goes through the same points

[manic timber]

how

should i just use a power regression on desmos?

[leaden thunder]

just draw it on paper

the picture will give away the estimates being under or over

[manic timber]

ohh

thanks

.close

[calm coral]

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[calm coral]

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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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• Be polite and have a nice day!

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[cloud gyro]

hello

[cloud gyro]

im trying to change the bounds of integration

this is what i have so far

[cloud gyro]

but its the wrong answer

[wary tundra]

bro is just googling lmao

lemme check

[calm coral]

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.

[verbal pumice]

we are the same person

[cloud gyro]

sorry that is just my ipad discord

[wary tundra]

thats cool... an alt account... you are banned

jk

[cloud gyro]

oh naur

it says in the solutions

that the leftmost x value should be 0

but i dont know how to get that

help

[wary tundra]

lemme think

[cloud gyro]

i think i remember my professor saying that i cant have a function as bounds for my outer integral

[wary tundra]

wait a sec

[cloud gyro]

should i ask chatgpt he frustrates me when i ask him math questions

sorry yes

[wary tundra]

hows this?

[cloud gyro]

oh woah i think youre right

wait why sinx on the bottom

[wary tundra]

The given bound x=arcsin(y) can be written as y=sin x

since

x ranges from

arcsin(0) = 0 to pi/2

[verbal pumice]

but in the original equation it’s the area under arcsin

oh wait is it not?

i might have misinterpreted

[wary tundra]

who are you know?

[verbal pumice]

i am hi sorry

[wary tundra]

aah same guy , my bad

[verbal pumice]

it’s okay lol!

[verbal pumice]

wait i’m pretty sure it’s the bound underneath the curve because in the original equation it says the arcsin graph is the leftmost bound

[kind axle]

what book are you using for multivar calc

[verbal pumice]

oh these were just problems my professor wrote down for us to solve

i don’t think she’s got them from the book but i use multivariable calc 8th ed

mc

[wary tundra]

Since x= arcsin(y) was the lower bound in the original integral, this means that y starts at sin(x) where we can wite in term of x

[kind axle]

Stewart?

[verbal pumice]

mcgraw*

[kind axle]

Hm never heard of that one

But alright

[verbal pumice]

sorry mccallum huges hallet

i got the names mixed up from a different textbook

[wary tundra]

originally, x starts at arcsin(y) meaning for a fixed y, we must solve for the corresponding lower x value

bruh.... are you good at Binomial?

[verbal pumice]

not good

[wary tundra]

i'm cooked

[verbal pumice]

your question looks too big brain form me

for*

[wary tundra]

ig its not

lmoa

what you doin rn?

[verbal pumice]

i’m trying to ponder at this

[cloud gyro]

this is the answer im sorry i should have posted this earlier

but it looks like she forgot to switch the dx dy

[wary tundra]

soo... my answer isn't correct?

[verbal pumice]

ah man

you had the x bound right

better than me

[wary tundra]

nah, sin x whould be in lower limit

your sir is wrong here

[verbal pumice]

i shall ask chatgpt

wait

how did you get the 0 to pi/2

you could be right, there were a lot of errors in the solutions manual

[wary tundra]

bruh, you also did the same thing.. don'tchu know that?

[verbal pumice]

no i got this answer 😭

[wary tundra]

ig you should get some rest for now

[verbal pumice]

what do you mean my friend 😭

i’m still confused

[wary tundra]

get some sleep

[verbal pumice]

wouldn’t the x left most x bound depend on the function?

it’s only 7pm for me, but i will let you go

what is your chess elo

[wary tundra]

2308

[verbal pumice]

WOAH

chess.com? fide?

[wary tundra]

chess.com... fide 2249

[verbal pumice]

NUH UH

wow that’s impressive

[wary tundra]

UH HUH

[verbal pumice]

good for you man

alright thanks for the help

[wary tundra]

whats yours?

[kind axle]

@tame quail wants to play

[tame quail]

damn

[verbal pumice]

i’d rather not disclose 😔

[tame quail]

that's high

[verbal pumice]

that’s IM level. you’re crazy good

[wary tundra]

ohk.... but i'm not currently loggin in this device... soo if you got some opensource chess website... i'm in send me link

[tame quail]

I can't play rn

about to work

sorry

[kind axle]

aw i was hoping you could do a quick game

[tame quail]

you would probably crush me though

[wary tundra]

lemme make some arrangements

[wary tundra]

how about, i play without my queen?

[tame quail]

well I would win then

I'm like 1500 USCF

[wary tundra]

let see.... time will tell

[tame quail]

depends on the time control

in blitz maybe

[wary tundra]

choose one.... bad opening or without queen?

[tame quail]

anyway I can't play right now unfortunately

depends on how bad the opening is

in some openings you lose your queen

so

[kind axle]

Halloween Gambit

[verbal pumice]

do any of you big brain chess players know why the left bound doesn’t depend on the function

[tame quail]

that's not as bad as being down a queen

[tame quail]

because that's the upper bound

[verbal pumice]

the upper bound is pi/2

oh you mean for y

oh i get it

[tame quail]

yeah

[wary tundra]

a4 Ra3 capure my rook with your bishop.... i'll take that ith knoght then... same goes for h1 side

[verbal pumice]

oh that really just cleared all my questions

[tame quail]

that's not even that bad lol

[wary tundra]

damn

[tame quail]

you get more development and arguably the bishop pair is better in the opening/middle game

[wary tundra]

exachange rooks with bishop... that aint bad?

[tame quail]

no

being down a piece is significantly worse than down an exchange

[verbal pumice]

that’s what the 11 year old kid i’d babysit used to play

[wary tundra]

soo... tell me what should i play

[tame quail]

not to mention down a queen

[tame quail]

I would just take the queen honestly lol

[wary tundra]

ohk... i'll give you my queen in few moves...

[tame quail]

but maybe like

the fried liver?

let me be the attacker and allow it

[verbal pumice]

cow opening 😏

[wary tundra]

wanna play as white.... I LITERALLY GAVE YOU MY QUEEN

[tame quail]

under what conditions?

[wary tundra]

i'll play as white...

[tame quail]

ok sure

I can't now though

[wary tundra]

https://buddyboardgames.com/chess?room=MDA3

[verbal pumice]

when will this tournament take place

[wary tundra]

fuck

[tame quail]

dude I can't play now 😭

just started working

[wary tundra]

you in for chess?

[verbal pumice]

DOWN

i’m 1700 chess.com!

[wary tundra]

ohk... same goes for you... take my queen

[verbal pumice]

so uh maybe a worse opponent for you

[wary tundra]

thats actully good

[verbal pumice]

…bullet

i just spam play bullet and hope the time runs out

that’s my strategy

[wary tundra]

i'm dead for real then... 5min blitz

[verbal pumice]

i’m ashamed to say

ok i’m down for that

[wary tundra]

ohk ohk

[verbal pumice]

where do you want to play

[wary tundra]

https://chess.org/play/5dc20fc5-0726-4c88-9335-7c2cbf979a70

[verbal pumice]

let’s go!

wait i’m getting nervous knowing you’re 2300

I MESSED UP

IM OUT FOR YOUR CLOCK BUDDY

that was a good game

i liked your strategy not letting me take any pieces

being down a whole queen is just too unfair i think

oh did you want white?

[wary tundra]

i should have grinded more

[verbal pumice]

do you want white

i’ll resign

[wary tundra]

nah

i'm fine with black

just don't take my pawn

[verbal pumice]

okay

[wary tundra]

only the queen at first

[verbal pumice]

are you sure?

[wary tundra]

then you can take as much as pawns you want

[kind axle]

close this channel move to #chess-go-shogi

[wary tundra]

after you get the queen

[verbal pumice]

i could trade the queen for 2 bishops

[wary tundra]

nah... no trading... full sacrifice... lmao

[verbal pumice]

LOL

your wish

[wary tundra]

get back to game

[verbal pumice]

i can’t move for some reason

ok

scholars mate attempt

oh shake my head 😦

[calm coral]

@cloud gyro Has your question been resolved?

[wary tundra]

lets do one proper

[verbal pumice]

oh man

okay

can you send another challenge i think i lost the page

[wary tundra]

https://chess.org/play/1c405b05-e491-4294-b775-831f3fb93837

[verbal pumice]

uh i think it’s lost 😞

good game

you destroyed me

it’s back to studying for me.

[wary tundra]

i think so

[verbal pumice]

yes lol

thanks for the games

[wary tundra]

hats the time there?

[verbal pumice]

and the help with my math

[wary tundra]

whats*

[verbal pumice]

it’s 7:30pm

[wary tundra]

nice.. ^AM here

6

AM

i should sleep no

now*

[verbal pumice]

NOW?

yes you should

[wary tundra]

yes?

should i?

[verbal pumice]

YES

have a good night

or morning..?

[wary tundra]

good morning

[verbal pumice]

good morning

thanks for the help!

.close

[wary tundra]

i'm not sleeepy

[verbal pumice]

GO TO BED

😭

6am 😭

[wary tundra]

plz... let me stay

[verbal pumice]

.close

.close

WHY WONT THIS THING CLOSE

[wary tundra]

hehe

[verbal pumice]

YOU NEED TO SLEEP

[wary tundra]

i'm find dude... i woke up at 4

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[verbal pumice]

goodbye friend!

[wary tundra]

whats your age?

[cloud gyro]

im 19

[wary tundra]

damn... same

[cloud gyro]

AND YOURE 2300??

ive failed as a person

man

[calm coral]

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• Show your work, and if possible, explain where you are stuck.
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[hardy sail]

hi guys

I've been looking for an hour to figure out how to solve this operation without giving me a coherent result.

(It's not for me, it's for my sister who is in third grade and goes to high school)

[manic hawk]

What do the symbols mean?

!original

[calm coral]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[icy parrot]

Help

[hardy sail]

!occupied

[calm coral]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hardy sail]

pls help

<@&286206848099549185>

[calm coral]

@hardy sail Has your question been resolved?

[calm coral]

@hardy sail Has your question been resolved?

[calm coral]

@hardy sail Has your question been resolved?

[keen flare]

are you trying to solve for x or just rearrange?

since this is just an expression

doesn't seem to equal anything

[calm coral]

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[stable hollow]

Okay so for c

Ik how to find reflections and stretches

How do I find the verticle and horizontal translations?

Like how many units it moved up/down and left/right

Do I need to draw out the stretch first?

Or how tf

<@&286206848099549185>

[calm coral]

@stable hollow Has your question been resolved?

[calm coral]

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[stable hollow]

So how do I do 15

First find the inverse?

So

(X+2) over 4 = f^-1 (x)

[wanton wave]

yeah

[velvet osprey]

use a slash for fractions. (x+2)/4

also lowercase x not uppercase X, careful w/ that

otherwise yes f^-1(x) = (x+2)/4

[stable hollow]

Then what

[velvet osprey]

well you have yourself a formula for the inverse now

all that's left to do is to find its values at the points they want

[stable hollow]

(X+2)/4 = 4

So solve for x?

Is this written correctly?

[velvet osprey]

no you are overthinking it.

do you know how to evaluate a function at a point?

[stable hollow]

Idk

Can someone just tell me

I should've been sleeping 5 hours ago 😭

(4+2)/4 = 4

This?

[buoyant ridge]

when you say f(3), what is 3? what does it represent

[velvet osprey]

(4+2)/4 isn't equal to 4

[stable hollow]

Nvm

Bro

Just what do I put where

[velvet osprey]

f^-1(4) = (4+2)/4 = what you want

[velvet osprey]

please do not call me bro.

[stable hollow]

Mb

Can someone just

Idk

[velvet osprey]

f^-1(4) = (4+2)/4 = what you want

for letter a

[stable hollow]

??

I don't see a

[velvet osprey]

letter a) like in the question

it has four subproblems

[hasty mulch]

Question 15a).

[stable hollow]

You want the inverse when x is 4

Idk

[velvet osprey]

you asked to show what needs to be done, i showed you what needs to be done

if you are deliberately depriving yourself of sleep this is only your problem but not ours

[hasty mulch]

What is $\frac{4+2}{4}$.

[potent lotus]

Omega

[stable hollow]

I think I understand

3/2

[stable hollow]

I wasn't planning on needing to do a bunch of stuff and not being able to sifsy

Study

[hasty mulch]

$f^{-1}(x) = \frac{x+2}{4}$.

[velvet osprey]

f^{-1}

[potent lotus]

Omega

[stable hollow]

(x+2)/4

So for this example

You plug in whatever you want to find

Into x

And whatever it = is the answer

[hasty mulch]

No, they give you x. Just calculate the value.

[stable hollow]

Exactly

So let's do 9c

15c*

(8+2)/4

10/4

5/2

?

[hasty mulch]

Exactly.

[stable hollow]

Ok thank you so much 🙏🏻

I need to sleep now

[hasty mulch]

You're welcome, and be sure to get enough sleep.

[stable hollow]

Yeah

Well

I'm waking up in Leeds than 6 hours

Normaly I get 6.5-7 before tests and do fine

This might be bad though

[velvet osprey]

definitely very bad

[stable hollow]

Anyways cya

Sleeping rn

[hasty mulch]

Alright, bye!

[stable hollow]

I function very well on 6.5

So idk

[hasty mulch]

.close

Wait, can someone close the channel-

[velvet osprey]

only OP or a green name can close

i'll just do it myself

.close

[calm coral]

Channel closed

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[hasty mulch]

Oh, I see.

[calm coral]

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[south obsidian]

Someone can help me in this please

[hasty mulch]

Is the question asking to simplify?

[desert star]

@south obsidian

[south obsidian]

Yes

[hasty mulch]

Wait a minute. If the question is asking to simplify, there wouldn't be two sides to the equation.

Oh, it's asking to solve for x.

[south obsidian]

Yes

My bad

[hasty mulch]

OK, question 2b, right?

[south obsidian]

Yesyes

[hasty mulch]

First, simplify the left-hand-side.

Do you know how?

[south obsidian]

I did the whole exercise but my teacher got a different result from mine and I asked chat got but now I'm confused so I just need you to tell me if I did it right

[hasty mulch]

!nogpt

[calm coral]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[hasty mulch]

How did you do it?

[south obsidian]

Wait

Im transcripting my letter is trash

[hasty mulch]

Take your time, no worries.

[south obsidian]

Here is

[hasty mulch]

And what was the result your teacher got?

[south obsidian]

-1/3

[hasty mulch]

Let's see if we can recreate your teacher's result.

$$\frac{1}{2}(\frac{10}{3}x-\frac{2}{9})-\frac{1}{3}=\frac{7}{3}x$$
$$\frac{10}{6}x-\frac{2}{18}-\frac{1}{3}=\frac{7}{3}x$$

[potent lotus]

Omega

[hasty mulch]

...

I gotta go, sorry...

[south obsidian]

Ouuuh

Ok 😔

Goodbye

.close

[calm coral]

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[hasty mulch]

Try redoing the question until you get it. Sorry I can't help you...

[south obsidian]

.reopen

[calm coral]

✅

[south obsidian]

Its okay

.close

[calm coral]

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[calm coral]

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[zenith summit]

#help-48 message

how do I show A is orthogonal and that A can be chosen s.t. det(A) = 1

i can only show that det(A) = ±1

[quick talon]

Hey

I gave you an answer yesterday and you said A is supposed to be a matrix

Well the answer I gave you IS a matrix

Just try the product will you ?

[zenith summit]

w and v are column vectors so w^T v will give me a scalar

@quick talon

[quick talon]

This is w v^T

[zenith summit]

oh ok

yeah fine that makes sense

[zenith summit]

is there a way to continue from here though

[quick talon]

How do you show a matrix is orthogonal

[zenith summit]

A^T A = I

is one way

or the columns of A form an orthonormal basis of R^n

[quick talon]

Try this

[zenith summit]

yeah but i can't figure out how to do the multiplication

[quick talon]

Just write it and I’ll tell you

[quick talon]

That’s not how you write it

Lose the basis B, it’s just adding complexity

[zenith summit]

what do you mean?

[zenith summit]

ok sure

[v]_B is a column vector on its own (coordinates of v in the standard basis)

[zenith summit]

no that's not what i was talking about

[zenith summit]

this is a different matrix i came up with

it does but i had already worked out this much so it would be nice if there's a way to continue on from there

[calm coral]

@zenith summit Has your question been resolved?

[calm coral]

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[summer mica]

im confused on how ther side splitter works

[calm coral]

Show your work, and if possible, explain where you are stuck.

[summer mica]

so ive got that 25/x+9=10/x

I believe thats right

[rustic osprey]

Put parentheses around your first denominator, but yes

[summer mica]

and then you cross multiply i believe

[rustic osprey]

Yeah you can do that

[summer mica]

But im confused on whats next

[rustic osprey]

$25x=10(x+9)$

[potent lotus]

Civil Service Pigeon

[rustic osprey]

I would use the distributive property on the right hand side

[summer mica]

so 25x=10x+90

so 15x=90

so x= 6

using that info i can tell y is the mid segment

so y=20

and then would z be 25/10=z/20

so z/20 comes from y and then 25/10 comes from the sides

[rustic osprey]

What

Those sides don’t correspond with the similar triangles

25 and 10 are sides of the larger triangle, y is a side of the smaller triangle, and z is a side of the larger triangle

[summer mica]

thats how my math teacher explained the last one

[rustic osprey]

Uh

[rustic osprey]

20 and 25 correspond

y and z correspond

So 20/25 = y/z

Done

[summer mica]

she explained it like this

on a previous question

[rustic osprey]

That’s what I did just now

😕

[summer mica]

16/12 is from the sides?

[rustic osprey]

Yeah

[rustic osprey]

16

[rustic osprey]

12

[summer mica]

So why can’t I use 25/10

5)-(/ from the sides

I meant that’s from the sides

[rustic osprey]

.

You need to set the ratio of the corresponding side lengths equal

As I said earlier, those side lengths don’t correspond.

[summer mica]

Wdym they don’t correspond

[rustic osprey]

They don’t “match up”

[summer mica]

I’m confused

[rustic osprey]

Here, AB and DE match up, as do AC and DF

And BC and EF

So we can set each of those ratios equal to each other

What we can’t say is something like AB/DE=AC/EF

Because while AB and DE correspond, AC and EF don’t

[summer mica]

Oh ok that makes more sense

How can I tell if they’re corresponding

[rustic osprey]

Look at the figure

They’re opposite the congruent angles

[summer mica]

Wouldn’t angle c angle b and angle a be confruent same for e f g

[rustic osprey]

??

We’re using the convention that same number of arcs -> congruent

Ex. Angles C and F are both marked with three arcs, hence they’re indicated to be congruent

[summer mica]

Like this

[rustic osprey]

Uh

[summer mica]

I can’t draw my hands are cold

[rustic osprey]

It looks like you drew a river pattern 💀

Just refer to the angles with the vertex names (ex. Angle ABF)

[summer mica]

This might be better

Those angles are congruent is what I’m saying

And the top one is a similar angle for all the triangles

[rustic osprey]

All I’m seeing is a creative interpretation of an ear 😭

[rustic osprey]

.

Also you got like 5 minutes before I gotta dip

So you’ve been warned

[summer mica]

So cbf is congruent to dce and bag

Same goes for other side

They all share the common angle of m<d

And y is parallel to bf and ag

[rustic osprey]

(and z, which is what I was implicitly using earlier)

[summer mica]

Z is bf

[rustic osprey]

Oh is it

Maybe I should stop using the marked up figure lol

[summer mica]

Oh I am to 😭

Oh I get it now on the first one the lengths are pairs but on the second one they’re not

So 25/20=z/ what would go on the denominator of z

Or 20/25 mb

[rustic osprey]

.

(Since 20 and y are part of the same triangle, DCE)

(And 25 and z are part of the same triangle, DBF)

[summer mica]

So z/25

So 20/25=z/25

[rustic osprey]

???

Where is z/25 coming from

[summer mica]

You said z and 25 are same triangle

[rustic osprey]

Ok let me rephrase

You can’t mix and match

20/25 is taking the ratio of a side of DCE to the corresponding side of DBF

So you need to do the same for your second proportion

[summer mica]

So z/10?

[rustic osprey]

Do z and 10 correspond?

Also they’re both part of BDF

So that has the same issue as I just said (namely that if one proportion is taking the ratio of the sides between the two triangles, so must the second)

[summer mica]

What would z denominator be then

[rustic osprey]

Since you put the side for DBF in the denominator for the first proportion, z should be in the denominator, not the numerator.

But work with what I’ve been saying

[summer mica]

Oh ok

[rustic osprey]

Your numerator in the first proportion was the side corresponding to BD in triangle DCE

The same exact logic applies.

[summer mica]

Oh so would it be 5?

[rustic osprey]

??

[summer mica]

Or no

[rustic osprey]

Remember what I said earlier about corresponding sides and angles

What angle is side z opposite to (in triangle DBF)

[summer mica]

It would be 20?

Z is in the middle

[rustic osprey]

That’s not an angle.

[summer mica]

Ik

I’m asking if the numerator would be 20

[rustic osprey]

No

[summer mica]

Oh

Side z’d angle would be opposite to angle d right?

[rustic osprey]

Yes

So what angle must the corresponding side in triangle DCE be opposite to

[summer mica]

Dec?

[rustic osprey]

.

[summer mica]

There’s no other angler

Angles

In triangle dce

[rustic osprey]

My point earlier (and now) is that the corresponding sides are opposite the same angle.

So since z is opposite angle D, the corresponding side in triangle DCE is also opposite angle D.

[summer mica]

Than I don’t get what’s opposite of dce

Angle

[rustic osprey]

Mate.

[rustic osprey]

(That’s an arrow btw - ik the pointing part looks kinda flat)

[summer mica]

Yea d is opposite of angle 180

[rustic osprey]

So hence y is your corresponding side

[summer mica]

Yea

[rustic osprey]

That’s all I was asking for this whole time

[rustic osprey]

And as a result, you get this ^

[summer mica]

I’ve got to go temporarily

[calm coral]

@summer mica Has your question been resolved?

[calm coral]

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[calm coral]

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[spare kettle]

What's the difference between all of these distributions?

[calm coral]

Please don't occupy multiple help channels.

[bleak peak]

you see the normal distribution has a 'bell shape'

For the uniform one, in terminology, the standard derivation would be very small

The mean of the skewed left one is very close to the maximum value of x and vice versa for the skewed right

[calm coral]

@spare kettle Has your question been resolved?

[calm coral]

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[calm coral]

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[remote mural]

Im just asking for g(x) how am i supposed to factorise it

i tried x(2x^2 - x) but then i dont know how to factorise whats inside the brackets

i mean i can do x(2x-1) but what do i do with the second x

[eternal shard]

why not x^2

[remote mural]

then i just get x^2 = 0

[eternal shard]

2x³-x² = 2x(x²)-1(x²)

[eternal shard]

what is that supposed to argue

you want to factorize

you look for the gcd in each term

[remote mural]

sorry let me try to explain why im confused i input the equation into desmos and i get 3 points

[eternal shard]

you mean 3 roots?

[remote mural]

Yeah

no not 3 roots

3 points

[eternal shard]

the in between is not a root

yes

[remote mural]

why would they show me it

[eternal shard]

x²(2x-1) = 0

[remote mural]

okay thank you

[eternal shard]

and y = x²(2x-1)

y = x²(2x-1) shows you all points that satisfy this equation

which resembles that curve

x²(2x-1) = 0 this gives you the solutions of x-intercepts which are two roots (one double)

[remote mural]

ohhh thats why

okay thanks

.close

[calm coral]

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[calm coral]

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[frank jungle]

I've taken trivial examples in my head so I think it's true

But Im not sure how to prove it

[old falcon]

i think you need more here

right

[frank jungle]

Wdym?

[old falcon]

like if W1 = W2

[frank jungle]

It kind of makes intuitive sense right

[old falcon]

but B1 != B2

[frank jungle]

Hmm

Counter example?

😂

[old falcon]

i mean can you think of one

[frank jungle]

I mean that's literally it right

[old falcon]

try to think of a subspace with 2 possible bases

not super hard

[frank jungle]

Let W_1 = W_2 = R

[old falcon]

simpler lol

[frank jungle]

and B_1 = {1} and B_2 = {2}

[old falcon]

but sure yea

thats what i was thinking

so youd need some kind of qualification i think on the basis

[frank jungle]

I'll clarify it with my teacher

[old falcon]

in order to make this true

but clearly as written not true

[frank jungle]

Thank you for your help!

.close

[calm coral]

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[calm coral]

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[lost elm]

In how many ways can you arrange the word "HONULULU" (the spelling is intentionally made incorrect such that it has 3U's) so that no 2 Ls and no 2Us are together

[bronze adder]

[lost elm]

I dont think there are 2760 cases(above 50%)in which the condition might be true, and i do not understand where i have went wrong

[bronze adder]

generating function?

[lost elm]

what

[bronze adder]

nvm

you're manually counting the cases up?

[next mesa]

hey

what kind of this question

[lost elm]

no

atleast I wouldve

but idk how to reliably count that much with less innaccuracy'

[lost elm]

permutaions and combinations

also is there a reliable computer program to list and eliminate all cases for a given word so that you can check urself if what the anser u got is correct

[calm coral]

@lost elm Has your question been resolved?

[magic tulip]

that is to say, LL and UU are forbidden

but LU is not?

[lost elm]

yes LU is permitted

[magic tulip]

,w \frac{8!}{3!2!} - \frac{3 \cdot 7!}{2!} - \frac{7!}{3!} + 3 \cdot 6!

[potent lotus]

Results provided by WolframAlpha

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

Requested by radmeerkat62445

[calm coral]

@lost elm Has your question been resolved?

[calm coral]

@lost elm Has your question been resolved?

[calm coral]

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[wheat wyvern]

I first made the triangle

Then did trig sub

.close

[calm coral]

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[potent igloo]

Your sin/cos^2 integral is wrong

[calm coral]

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[next fossil]

Hi

[next fossil]

Have not learned trig inverses properly, can someone help me

[eternal shard]

,rcw

[remote mural]

What are you trying to do with this equation? Send the full problem?

[next fossil]

Derivative

I further simplified to 8x/ (8x^2)(root8x^2 -1)

Ye

How

Conjugate it?

Or do you multiple the denominators

The 2 should just be for the radical inside

Ik I wrote it wrong but I did it right

The arrow is pointing at what I’m on

So left with 1/xroot8x^2 -1

Ah I see

Got one more

Do I have to do both derivatives separately

[dull wagon]

wdym by separately

[next fossil]

So then idk how to take the inverse of 2x

I know trig inverses derivatives

I haven’t learned actual inverse derivatives

[dull wagon]

the idea is that you don't need to explicitly find the inverse function

[dull wagon]

apply the formula given to you, (its a good exercise to derive or look up where it comes from)
plug x=1 into that

[next fossil]

2 - sin(x)

2 - sin(1)

[dull wagon]

not what i asked you to do

[next fossil]

What am I supposed to do

[dull wagon]

apply the formula given to you, (its a good exercise to derive or look up where it comes from)
plug x=1 into that

you're given a formula for derivative of an inverse function
(f^-1)'(x) = ...

start by plugging x=1 into that

[next fossil]

Idk how to do that

[dull wagon]

literally replace all x in that with 1

[next fossil]

From what I can’t even take the derivative of the inverse tho

[dull wagon]

you're literally given the formula for it

[next fossil]

I literally have not learned how to do it

[dull wagon]

don't overthink this first step

$(f^{-1})'(\red{x}) = \frac{1}{f'(f^{-1}(\red{x}))} \ \
(f^{-1})'(\red{1}) = \ ?$

[potent lotus]

ℝαμOmeganato5

[next fossil]

What id do is like take y = 2x flip it so it’s x= 2y and have y = 1/2x and take the derivative of that

[dull wagon]

no

you can't ignore the cos(x)

and as i've said before, do not make any attempt to find f^-1(x) itself

its not needed and quite complex

[next fossil]

So what would my first step be

[dull wagon]

please read what i've said above

[next fossil]

I have been but it doesn’t make sense

I need to see it happening I can’t understand just from words

Just a first step

[dull wagon]

if you were given
g(x) = x + 7
how would you find
g(8)

[next fossil]

Plug 8 as x

[dull wagon]

yes

same idea here

[next fossil]

So do I just do 2(1) + cos(1)

??

[dull wagon]

you are given the formula for
(f^-1)'(x)
and you want to know
(f^-1)'(1)

no

forget about the rest of the question and focus on only that

[next fossil]

Yes

[wheat wyvern]

thank you!!

[dull wagon]

same idea as

if you were given
g(x) = x + 7
how would you find
g(8)

[wheat wyvern]

🏃 sorry to interrupt carry on

[next fossil]

But I haven’t learned any of the steps of how to take undersea derivatives

[dull wagon]

undersea?

[next fossil]

Plug 8 in and get g(8) = 15

[dull wagon]

exact same idea here

[next fossil]

So what do I plug 1 into

[dull wagon]

you're given the formula for
(f^{-1})'(x) right?

[next fossil]

IDK HOW TO USE THE FORMULA atleast tell him how to apply the equation into the formula

[dull wagon]

use it the same way you used

if you were given
g(x) = x + 7
how would you find
g(8)

you wanted to know
g(some specific value)
replace all x in your given equation with that value

[next fossil]

Bro please is there any other way you can explain this

I’m not understand this way

Like show me what the first step is instead it’ll make more sense to me that way

The theory I’ll understand from the application and the steps

[dull wagon]

this is simply evaluting functions at a value in general

[next fossil]

Rather than learning the theory first

[dull wagon]

please don't overthink this

do the same thing you did

Plug 8 in and get g(8) = 15

exact same idea applies

[next fossil]

Are you saying make 2x + cosx = 1

[dull wagon]

no

forget about f(x)

Plug 8 in and get g(8) = 15
you replaced all x in the equation with 8 to achieve that

the same applies here, replace all $x$ in the equation with 1
$$(f^{-1})'(\red{x}) = \frac{1}{f'(f^{-1}(\red{x}))}$$
$$(f^{-1})'(\red{1}) = \ ?$$

[potent lotus]

ℝαμOmeganato5

[dull wagon]

don't worry about anything else at this stage

more steps will come after

[next fossil]

1/f prime (f inverse at 1)

[dull wagon]

yes

good

[next fossil]

Okay

[dull wagon]

$$(f^{-1})'(1) = \frac{1}{f'(\blue{f^{-1}(1)})}$$

[potent lotus]

ℝαμOmeganato5