help-42

[ancient thistle]

that was not the point

[hybrid drift]

read the other things right after

[keen flower]

[hybrid drift]

i don’t care lol

[ancient thistle]

don't ignore what i said and then reply to me, even if you don't ping

[hybrid drift]

i didn’t mean to

but i did

happy?

[ancient thistle]

[keen flower]

i think coriolanus meant that f being continuous is sufficient but not necessary

[ancient thistle]

"some heavy handed conditions ... but there are weaker assumptions under which the result still holds"

that is exactly what i meant if somebody here took the time to read

[keen flower]

ye

[ancient thistle]

a dumb counterexample is f(x) = 1_{0}(x) and g(x) = 0

lim f at 0 is 0, but f(g(x)) is always 1

[keen flower]

what is 1_{0}?

[ancient thistle]

indicator function of {0}

[keen flower]

oh

interesting

[hybrid drift]

i mean the weaker assumption you stated is not valid either but

it’s a start

[keen flower]

oh brother

[ancient thistle]

bro just can't stop being wrong

https://proofwiki.org/wiki/Limit_of_Composite_Function

i listed hypotheses 1 and 2

proof is provided

[leaden thunder]

Stop. He's already dead

[hybrid drift]

that’s one way to prove it

but not the only way

i will be happy to latex a proof showing you that this can be done without that assumption in some time

[leaden thunder]

Like this was a kill shot already

[ancient thistle]

i literally provided a counterexample to the statement when g fails hypothesis 2 like ???

can you stop trolling in the help channels already

[hybrid drift]

lmao i’m not trolling

i replied to your post

you got pressed

for no reason

[leaden thunder]

Don't attribute to trolling which can be explained with ignorance

[hybrid drift]

y’all really think i would enjoy “trolling” over math i haven’t done since i was 15 😂🤣

[plain bone]

(you'd be surprised how much free time some people have)

[keen flower]

do we use limit of composite functions here at 7:20?
https://www.youtube.com/watch?v=wSMFj0vYul8

[ancient thistle]

looks like it

[keen flower]

thanks

.solved

[calm coral]

Channel closed

Closed by @keen flower

Use .reopen if this was a mistake.

[calm coral]

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.

[patent drift]

For cotg(x)=-4 can I do it as x=alpha+k*pi ?

[calm coral]

@patent drift Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[remote mural]

How do i draw the boundary line for 2x+5y<10

[marble pendant]

first draw 2x+5y=10

then check does (0, 0) satisfy your original eqn which is 2x + 5y < 10

if it does then the side which has (0, 0) is your ans
else the part without (0, 0) is the ans

you can use any point but (0, 0) is the easiest to check for

[remote mural]

Yea how do i draw the 2x+5y=10

Like how to get the point to draw the line so i can shade the region

[marble pendant]

my fav method is to first take x=0 and get corresponding y val
then y=0 and then x val

then draw the line

2 points are enough to get a unique line

[remote mural]

So substitute x=0 to 2x+5y=10

I did that

But then the other point how do i get ?

[desert star]

The last line, @remote mural the next step is to put y=0 to get another point

[remote mural]

Ohh

Ok thank u .

[desert star]

You would have two points, connect them to make a line

https://cdn.discordapp.com/emojis/1335340422142103623.png?v=1

[remote mural]

Ok i got it

Thank u both of u

[marble pendant]

did bro just copy paste an emoji?

[desert star]

Yes sir 😭

[marble pendant]

!done

[calm coral]

If you are done with this channel, please mark your problem as solved by typing .close

[remote mural]

Have a nice dayy

.close

[calm coral]

Channel closed

Closed by @opal rivet

Use .reopen if this was a mistake.

[calm coral]

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.

[opaque rune]

Leg leg congruence theorem.

[opaque rune]

Supposedly my friends told me that the x has to be same value even if you solve it from the two values

x = 2y-4
and
x = 3y+10

And i’m quite confused on how i should be able to get the value of X

or is it my whole solution that’s the problem?

[marble pendant]

um what?

[opaque rune]

It’s The right triangle congruence

[marble pendant]

RHS?

[opaque rune]

uh quite so

[marble pendant]

is it given that the 2 triangles are congruent?

oh wait nvm

[marble pendant]

you need help solving this right?

[opaque rune]

I have to solve the x and y by using the ll theorem

[opaque rune]

yeah

and how i’ll be able to get the value of x

[marble pendant]

this is an LE2V linear eqn in 2 variables

have you been taught how to solve these?

[opaque rune]

yes

the given picture?

or the one you just stated

[marble pendant]

this pair of eqns

[opaque rune]

don’t think so

ive been told to do the elimination method

[marble pendant]

yes good

in this case we can simply equate both the eqns

like we have x = 2y - 4 and x = 3y + 10

as you stated the x has the same value in both

so 2y - 4 = 3y + 10

now solve for y then put the y value in any of the 2 eqns to get x

we call this substitution method as we "substituted the value of x"

[opaque rune]

ohhh

weve been taught to do only the elimination method so that’s probably why

[marble pendant]

we can do this using the elimination method too

we will need to rearrange the eqns first

x = 2y - 4 => x - 2y + 4 = 0

and same for the other

[opaque rune]

so x - 3y - 10?

[marble pendant]

yup

now we need to elimnate x

how can we do that?

[opaque rune]

by eliminating the x from the both

thatd be 0

[marble pendant]

?

[opaque rune]

not it?

thats how we were taught to elimante x

what i did was

3y+2y = 5y

-4+10 = 14

divide

and ill get 14/5

[marble pendant]

yes that is correct

[marble pendant]

you should say coeff of x is 0

[opaque rune]

ah

[opaque rune]

My problem is that,

if i solve for the value of x using the value of y

its not the same answer that i’m supposed to be getting

if i do that

like

3(14/5) + 10
42/5 +10
The value of x would be
92/5

though if i do the other eq

2(14/5) -4
That would be
28/5 -4

24/5

why(

?

[marble pendant]

mb

it should be -14

not +14

[opaque rune]

and i’m supposed to get the same value of x even if i do the two eqs

[marble pendant]

..

i highly recommend doing such problems on paper

[opaque rune]

apologies are you perhaps confused? 😭

[marble pendant]

no but i think we made a mistake here

and it will be hard to point out

so i suggest you do it again

[opaque rune]

is my value of y also incorrect?

[marble pendant]

yup

[opaque rune]

😔

[marble pendant]

any progress?

[opaque rune]

Nope.

I ended up getting 6 as my y

[marble pendant]

ooh

ill show the calculation then gimme a min

$x - 2y + 4 = 0$ and $x - 3y - 10 = 0 \$
Subtractiong the eqns
$\ (x - 2y + 4) - (x - 3y - 10) = 0
\ => y + 14 = 0$
therfore $y = -14$

[opaque rune]

Oh so no fraction?

[marble pendant]

yup

[potent lotus]

Wumpus Man

[opaque rune]

Okay so

What i got for my x is either

-52 and -32

[marble pendant]

were you able to spot your error?

[opaque rune]

yes

seems like i added the 3 and 3

2*

[marble pendant]

oh

[marble pendant]

idts

im gettng only 1 value for x

[opaque rune]

Really?

Is it the same?

[marble pendant]

yup

check once

[opaque rune]

hm

what im doing is multiplying

also triangle method

3(-14)+10

[marble pendant]

sorry had to go

im getting -32 from both the eqns

[opaque rune]

-32?

so 3(-14)-10?

Ah

-42 and with minus positive 10?

[marble pendant]

yup

[opaque rune]

AH

I GOT IT

-28-4

Thats -32

[marble pendant]

LESGO

[opaque rune]

THANK YOUUUU

no fraction right?

[marble pendant]

no fraction

sound:0:4

[opaque rune]

Thank u so much ive been having a breakdown over this lawl

.close

[calm coral]

Channel closed

Closed by @opaque rune

Use .reopen if this was a mistake.

[marble pendant]

ohh

nicee

[calm coral]

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.

[misty nymph]

I’m trying to solve 13

I think I have found the U(n) being U(n)= 28/(1-a) • (1-a)^n-1

[marble pendant]

how will this eat me?

[unkempt drift]

that is correct, but it isn't relevant to the question

[marble pendant]

the thing on paper is correct

[unkempt drift]

yeah try working on "sum of the first three terms is 147", as you did

[marble pendant]

also 147 and 28 have some common factors

[unkempt drift]

ah you should do 147 - 28 - 28 first on the right hand side to make your life easier, before you do the above steps

and then yeah you can further simplify by dividing both equations by a common factor

and only then multiply by (1 - a) on both sides

then expand everything; you get a quadratic eventually

[calm coral]

@misty nymph Has your question been resolved?

[misty nymph]

Sorry I disappeared I had a thing to attend too

I tried multiple methods of doing that

But it didn’t work out

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[misty nymph]

.reopen

[calm coral]

✅

[misty nymph]

I think I got it

[calm coral]

@misty nymph Has your question been resolved?

[unkempt drift]

,w 28/(1-d) + 28 + 28(1 - d) = 147

[potent lotus]

Results provided by WolframAlpha

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

Requested by sooouth.

[unkempt drift]

yeah I was going to say a bit more once you got the two solutions

you need |r| < 1 for a geometric series to converge, for the terms to keep getting smaller and smaller

e.g 1 + 2 + 4 + 8 + .... with common ratio = 2 does not converge, cause it goes to infinity
1 - 2 + 4 - 8 with common ratio = -2 is even worse, cause now it oscillates between -infinity and infinity,

so the answer is r = 3/4 only

[calm coral]

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.

[timid blade]

let $f:\mathbb{R} \to \mathbb{R}$ be a continuous bounded function and $$g(x) = \int_{-\infty}^{\infty} \frac{f(x,t)}{1+t^2} dt$$ comment on continuity and differentiability of g(x)

[potent lotus]

xd_senBugha

[timid blade]

this might be a dumb question but i have no clue how to proceed

[velvet osprey]

did you mean f: R^2 -> R

[timid blade]

This is the original

[velvet osprey]

well then what does f(x,t) mean lmao

they say f takes one real number as input but then shove 2 numbers in

[visual nimbus]

maybe a parameter

still sus tho

[velvet osprey]

mega sus

anyway idk how to prove anything here and bismillah i shall not reveal the answer

[timid blade]

a proof isnt required but an explanation to how you got your answer would be nice

[visual nimbus]

if f is like that :
f : R² --> R
then you need to prove that h : x |--> f(x,t)/(1+t²) is countinuous on R
h : t |---> f(x,t)/(1+t²) is piecewise countinuous on R
and that there exists a piecewise countinous function k such that : |f(x,t)/(1+t²)| < k(t)

thats the proof for continuity

[timid blade]

i dont get it

[calm coral]

@timid blade Has your question been resolved?

[calm coral]

@timid blade Has your question been resolved?

[calm coral]

@timid blade Has your question been resolved?

[calm coral]

@timid blade Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[remote mural]

how to get the quotient

[remote mural]

<@&286206848099549185>

[sweet stag]

cant read shit there @remote mural

[remote mural]

well

[swift dragon]

!15m

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[sweet stag]

use latex

[remote mural]

im so stupid to use it atm

find the quotient for the division of p(x)=(x-3)**2n + (x-2)**n -1 by (x-2)(x-3)

[sweet stag]

ok

[swift dragon]

$P(x)=(x-3)^{2n}-(x-2)^n-1$ What is the quotient of divising $P(x)$ by $(x-3)(x-2)$

[potent lotus]

Bonk

[sweet stag]

i see better now

[remote mural]

thanks

[sweet stag]

what did u try?

[remote mural]

binomial formula

[sweet stag]

show

@remote mural

[remote mural]

wait

[gentle stream]

before you try to do any more painful expanding

[gentle stream]

wait quotient?

[sweet stag]

yes

thats tricky, because, its n-dependent tbh, tryin to find a recurrence relation from that

[gentle stream]

are you sure you mean quotient and not remainder?

[calm coral]

@remote mural Has your question been resolved?

[sweet stag]

good luck solving this recurrence

[calm coral]

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.

[primal sleet]

I have to calculate how far I can send the signal in the fibre optics cable. The reason I have 0,10(x - 1) is because it will be one less splice before reaching the contact.
Have I done the math correctly?

My friend said it should be 66,4 km and he got help with chatGPT and some other ai.

[magic tulip]

!noai

!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).

[primal sleet]

Yea I am thinking it could be some error in the ai. But have I done it correctly?

[calm coral]

@primal sleet Has your question been resolved?

Channel closed

Closed by @primal sleet

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.

[craggy wren]

When writing a proof, is starting with the "given" and ending with the "prove", or starting with the "prove" and ending with the "given" preferred?
As a simple example:

Given: a > b
Prove: a + 1 > b + 1

Option 1:
a > b Add 1 to both sides
a + 1 > b + 1

Option 2:
a + 1 > b + 1 Subtract 1 from both sides
a > b

[velvet osprey]

1 only

[magic tulip]

only option 1

[velvet osprey]

starting with your goal is treacherous and can very very easily lead you to writing complete bs without even knowing it

[craggy wren]

got it, thanks 👍

.close

[calm coral]

Channel closed

Closed by @craggy wren

Use .reopen if this was a mistake.

[calm coral]

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.

[grave isle]

How would I prove the congruence of AB and AC in order?

[magic tulip]

ABE is similar to ACD might be a starting point?

[grave isle]

yes but im not sure on how to get a side from one of those traingles to use for a theorem

okay wait angle A is congruent to angle A because of reflexive property but how to prove angle B is congruent to angle C?

<@&286206848099549185>

[slim knoll]

Ok, let’s start by addressing prerequisite knowledge:

Do you know the sum of all angles of a 3-sided shape? What about the angles of a 4-sides shape

[grave isle]

all angles of a 3-sided shape add to 180?

[slim knoll]

Good! What about 4-sided shapes?

[grave isle]

and 4-sided 360?

[slim knoll]

Correct

What have you observed and inferred so far?

[grave isle]

two traingles are inside of eachother forming two other small ones

and those have vertical angles

also the two big trangles share angle A

[slim knoll]

Here’s something that might help:
Angle A is a right angle, meaning it is 90 degrees

[grave isle]

but thats not given?

im only given BF is congruent to CF and angle ADF is congruent to AEF

[slim knoll]

Fair enough

[slim knoll]

Moving back to this statement, if Triangle ABC exists, then <A + <B + <C = 180

[grave isle]

I think i get it now a little bit

[slim knoll]

I would say there are multiple ways to prove this

[grave isle]

angle A + angle ADC + angle C equal 180 and so same with the other triangle ABE which means angle B and C are congruent because Two angles of both triangles are already equal so the last one must also be congruent

[grave isle]

yeah our math teacher makes us solve it in a wierd order and different theorems can be used for the same shape 😅

[slim knoll]

How does your teacher usually go about solving it

[grave isle]

he usually starts with the given angles and sides and then works with those to use a theorem and then CPCTC

But im pretty sure i figured it out

[slim knoll]

Ok, how did you prove the problem?

[grave isle]

After angle B is congruent to angle C, I also found angle DFB is congruent to EFC (verticle angles) and then triangle BDF is congruent to CEF because of the angle-side-angle thereom

[slim knoll]

Wait

Crap…

I misread the problem

[grave isle]

oh lmao its okay

[slim knoll]

Prove that Line AB = AC

[grave isle]

yeah

[slim knoll]

Well, we can prove that <ABE = <ACD

That does help us

[grave isle]

yeah but i already wrote that

angle A + angle ADC + angle C equal 180 and so same with the other triangle ABE which means angle B and C are congruent because Two angles of both triangles are already equal so the last one must also be congruent

[slim knoll]

I can also explain why <BFD = <CFE

[grave isle]

bc of vertical angloes

[slim knoll]

Yes

Since we proved that two of the 3 angles of each triangle are equal to each other, that means the 3rd angle is also equal

[grave isle]

mhm

[slim knoll]

And since BF = CF, that means all sides are equal, too

So DF = EF

[grave isle]

how does Bf=CF prove that all sides are equal?

[slim knoll]

Have you learned about Sine and Cosine yet?

[grave isle]

yes but my math teacher hasnt used it in this unit yet

[slim knoll]

Ok

[grave isle]

I think i have it figured out thank you for the help

[slim knoll]

You’re welcome

Are you able to figure it out from here?

[grave isle]

yes thanks

.close

[calm coral]

Channel closed

Closed by @grave isle

Use .reopen if this was a mistake.

[calm coral]

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.

[floral turtle]

Are my answers right?

[floral turtle]

If not how do I do it the correct way

[latent steeple]

Why the 1 in c and d though?

[floral turtle]

Because of the 10

10 and 1 is the same colour

10 is blue and 1 is blue

But they can't be next to each other

So I put them opposite to each other yk

And then I'm left with 9,8,7,6 etc

[latent steeple]

Where does it say they must be the same?

[scenic helm]

it doesn't verbatim it says "The only restriction imposed is that no two adjacent regions can have the same color"

[floral turtle]

no where but it can be random doesn't matter

I'm just asking if my answer looks fine

[scenic helm]

Your answer is not correct

[scenic helm]

take a look at b

for example

[floral turtle]

Yea

What about it

[scenic helm]

its wrong

[floral turtle]

There all different colors

[scenic helm]

no

because the rules are very clear

adjacent

the solution is 10, 9, 9, 9

think about it

[floral turtle]

Huh

[scenic helm]

first stripe

[floral turtle]

How

[scenic helm]

you have every color at your disposal

so lets just say you chose blue

right

next stripe

you can no longer choose blue

but you have 9 other colors

lets say you choose red

so now your flag is B, R, -, -

So then next stripe

[scenic helm]

you cant choose red

[floral turtle]

That's my teachers answer

Yea 10 can be blue

9 can be red

The 8 can be green

I don't understand

[scenic helm]

nope

it can go B, R, B, R

thats a valid flag combo

[floral turtle]

But it's not

[scenic helm]

read the rules of the question

[floral turtle]

It's different numbers

[scenic helm]

they dicatate very specific scenarios

B, R and adjacent

[floral turtle]

Different colors

So ur saying my teacher is wrong? 💀

[scenic helm]

they do not share a color

let me reread the rules

I could be psycho analysing it

but

[floral turtle]

Yea ur confusing me

Each number is a different colour

10=blue

9=red

8=green

7=yellow

Or whatever

[scenic helm]

oh what??

[floral turtle]

10 and 1 is blue

9 and 1 is red

Yk

[scenic helm]

is there a pool of ten possible colors to choose from?

[floral turtle]

no but he told us while he was explaing this today

[scenic helm]

its asking for unique

I didnt read that word

[floral turtle]

😭

[scenic helm]

you can have B, R, B, R because it gets repeted more than onc

e

my bad

[floral turtle]

Nah ur good

[scenic helm]

yea then youre correct

essentially

[floral turtle]

Alr lmao

[scenic helm]

each one of those problems is that you have two cases

all unique

or the "repeated" ones

[floral turtle]

yea

Well anyways ty

And cya

.close

[calm coral]

Channel closed

Closed by @floral turtle

Use .reopen if this was a mistake.

[calm coral]

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.

[dusky verge]

Okay i know that this is an extremely silly question is this correct? i dont know where the 5 is coming from... is it log 10 or is it ln..

[upper sparrow]

Multiply and divide that 0.03333 by 10^5

Then log rules

[dusky verge]

could you show me an example pelease

please

i got this -- i found it on google when searching it up. i just want to make sure this is the accurate value.

[upper sparrow]

You are aware of the log property that log(ab) is log(a) + log(b) (whatever log base you’re dealing with) right?

And also that

,calc 0.03333 * 10^5

[potent lotus]

Result:

3333

[dusky verge]

and then i do -log(3333)

??

wait im pretty sure google will give me the accurate value, no?

like am i wrong lol

[upper sparrow]

I mean a calculator would get you the value straight away sure

[upper sparrow]

Tbh not entirely sure why they have it in their form here, but it isn’t wrong

They just did that 0.03333 is 3333 / 10^5 [= 3333 * 10^{-5} ] and the corresponding log rules

[dusky verge]

oh i see! thank you!

[calm coral]

@dusky verge Has your question been resolved?

[calm coral]

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.

[lyric holly]

|300x| = 22

is this correct?

[lyric holly]

or would it be something like 278 ≤ x ≤ 322

[edgy leaf]

what does the question require?

[lyric holly]

x in the range 278 and 322

because x varies

meaning it can be any through that range

[fierce gate]

what is the question

[lyric holly]

Part a is done

[lyric holly]

asks for an absolute value equation soo

idk what im supposed tod o

[edgy leaf]

this is a correct assessment

in equation form, it would be:
|x-300| ≤ 22

your edge cases are the answer to part C

[lyric holly]

why is it <= and not =

[edgy leaf]

it can vary at most by 22 dollars

thats how i interpreted it

[lyric holly]

ohh

[lyric holly]

why is it x-300 and not x300?

[edgy leaf]

an artist can make 300 dollars +- 22 dollars
so lets say the artist makes x dollars
the difference between x and 300 dollars is at most 22 dollars
hence we have
|x-300| ≤ 22

[lyric holly]

OHH

your good at explaining

[calm coral]

@lyric holly Has your question been resolved?

[calm coral]

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.

[marble isle]

Hello

[marble isle]

I have a basic algebra text tomorrow but I am not very prepared at all haha. I can only do the first page. When it starts getting to fractions I get confused.

[tame crag]

What’s your question?

[tame crag]

Algebra is confusing

[plain bone]

can you show some practice problems

[marble isle]

Ya here’s the review. I already answered some stuff but I took these pics before.

Starting from 12 is where I get issues

[plain bone]

Try splitting 9b = 8b + 1b (or 9b = 8b + b)

[marble isle]

What about the 0.5? I don’t see a 1.

[plain bone]

Ignore the 0.5 for now

Actually this isnt a good way

@marble isle pick a side to isolate b

(it can be either, theres no correct answer, but there is a better answer)

[marble isle]

What do you mean by pick a side and isolate exactly?

[plain bone]

I'll show you- first pick a side

(left/right)

[tame crag]

@marble isle do you know how to simplify equations?

[plain bone]

<@&268886789983436800>

[marble isle]

Not really.

For context: I have a pretty bad learning disability and I’ve been trying to get on my colleges assistance program but they haven’t gotten back to me yet.

[marble isle]

Right

[plain bone]

@tame crag you wanna do this or should i

[marble isle]

I’d rather try to do it on my own with assistance the same way I’ll be working with the math resource center on campus tomorrow before the test

[tame crag]

Whatever you want mate,

Sorry if I’m interrupting

[marble isle]

Oh sorry I thought that was @ing me haha

[plain bone]

Ok, so we want to move all the b terms to the right side

And we also have to remove them from the left side

Do you agree with this?

[marble isle]

No I’m getting confused

[plain bone]

Ok which part are you confused with

[marble isle]

I mean by b terms do you mean 8b and put it next to 9b?

[plain bone]

You cant just move terms like that

8b - 0.5 = 9b

[marble isle]

That’s why I’m confused I don’t know what you’re saying

[plain bone]

#help-42 message
we want to remove the 8b from the left side. do you understand this?

[marble isle]

Yes

[plain bone]

Ok, im going to sligthly rewrite the expression

+ 8b - 0.5 = + 9b

Do you understand this?

[marble isle]

Yes

Well actually no I’m getting a little mixed up again lol

The +’s

[plain bone]

Its just adding 0.8b

I'm specifying that the 8b is positive (rather than -8b)

It will help you understand the next step

[marble isle]

Alright

[plain bone]

So, how do we cancel the addition of 8b

[marble isle]

We subtract it

[plain bone]

So, we're going to subtract 8b from BOTH SIDES. we must do the same thing to both sides of the equation to keep it correct

8b - 8b - 0.5 = 9b - 8b

@marble isle can you simplify this? it requires the same skills as the top half of this page

[marble isle]

Which problem specifically?

This is what I did

[plain bone]

Simplifying 8b - 8b - 0.5 = 9b - 8b requires the same skills as problems 1 - 3

[marble isle]

8-8-0.5 gives me -1/2 and I don’t know if that’s right

When I do the S-D button on my calculator it gives me -0.5

[plain bone]

Although it should have been 8b - 8b - 0.5 = -1/2

[marble isle]

I can’t enter the b’s on my calculator

[plain bone]

Then you should know for yourself that 8b - 8b = 0

Because if you right 8 - 8 - 0.5, you will get docked points

[marble isle]

I see

And 9b-8b is 1

[plain bone]

❌ this is why you shouldnt just do 9 - 8

You still need to include the b

[marble isle]

Isn’t the b empty as of now?

[plain bone]

No, b has a value. you just dont know the value yet

[marble isle]

Then I’m just confused here

I don’t know what you’re asking me to do

[plain bone]

Think of it as 9b - 8b = (9 - 8)b = 1b = b

Or rather:
you have 9 apples
you give away 8 apples
you have 1 apple remaining. It doesnt make sense to say "you have 1 remaining"
thus, 9b - 8b = 1b

[marble isle]

Alright

[plain bone]

Sry i forgot about this

So you have:
-1/2 = 1b

Can you solve for b?

[marble isle]

I don’t think this is working out. Thank you for trying to help but I’m going to attempt seeing help from some other people in my life. Have a nice night.

[calm coral]

@marble isle Has your question been resolved?

[calm coral]

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.

[honest geode]

How would you reflect the function y=x^3 across the line y=x? I tried graphing it on Desmos assuming that it would become y=-((-x)^3) but it seemed as though there was an error.

[eternal shard]

that's basically finding the inverse

[brazen elbow]

reflecting across y = x is equivalent to finding the inverse of y = x^3

[honest geode]

so it would become x = y^3?

[brazen elbow]

yes

[honest geode]

thank you

.close

[calm coral]

Channel closed

Closed by @honest geode

Use .reopen if this was a mistake.

[calm coral]

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.

[tame crag]

There's a method I'm using to find the distance between a point (x0,y0,z0) and r(T) = <x1,y1,z1>+<a,b,c>T

[tame crag]

essentially I use a b c to define a plane perpendicular to the line

being ax+by+cz = a(x0)+b(y0)+c(z0)

this is a plane perpendicular to the line containing the point I want

then I find the intersection between r(t) and this plane

and find the distance between two points

[tame crag]

This is a method I kinda just came up with on the spot, so I'm not sure if this works

brother, get your own help channel

👺

[calm coral]

@tame crag Has your question been resolved?

[tame crag]

<@&286206848099549185>

[wary sequoia]

Vector projection or cross product would be more efficient

The method itself seems fine though

[tame crag]

I find it hard to understand these graphacally

is there any source that does a good explanation?

[wary sequoia]

Yes 2blue1brown has excellent material on vector projection look at his linear algebra series.

Another great one is Dr Trefor Bazzet (spelling likely incorrect) but his series on linalg will make this feel more intuitive.

But you can think of a cross product is a direction that is perpendicular to both inputs

The magnitude of a cross product gives the area spanned by the parallelogram of the two vectors

Using this over the magnitude of the direction vector will give the distance between the two planes

[tame crag]

Oh wait, I see it now

we find some point on the line

find a vector from that point to the point we're aftr

since the projection of that onto a vector on the line is the mag of both vectors and cos(angle between them)

we divided by the mag of that other vector on the line and we find the a vector from the point on the line we decided on using this

then we get our og vector minus this new vector to find the shortest vector from the line to the point

and we find mag of that

thanks

https://tenor.com/view/funny-animals-say-cheese-smile-creepy-excited-gif-6564757416229948468

.close

[calm coral]

Channel closed

Closed by @tame crag

Use .reopen if this was a mistake.

[calm coral]

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.

[paper ferry]

can someone tell me why the answer to this

[paper ferry]

is 2pi + 15

[velvet osprey]

did you get something else as your answer?

[paper ferry]

well i wasnt there for my class

so i didnt fully go over the content

my friend sent me the answer, but never gave an explanation

[velvet osprey]

you at least understand that we want to find the area under this graph, yes?

[paper ferry]

yea, of course

[velvet osprey]

yeah so that's made of a semicircle, rectangle and triangle

[paper ferry]

oh wait

i understand it lmfaoo

2*6 = 12, + 2(3)/2 = 3

12 + 3 = 15

and then

[velvet osprey]

and then the semicircle

[paper ferry]

yeah

its 180 so

pi

so why would it be 2pi?

[velvet osprey]

you are confusing yourself...

[paper ferry]

hm

[velvet osprey]

do you know how to find the area of a circle?

[paper ferry]

oh wait

yeah oops

my bad its near 1 am

😭

[velvet osprey]

why are you doing math near 1 in the morning

[paper ferry]

just reviewing

pi(2)^2

so 4 pi

but because its a semi circle

/2

so 2pi

[calm coral]

@paper ferry Has your question been resolved?

[calm coral]

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.

[white tide]

$$

\textbf{(b)} If ( 0 \leq a_n \leq b_n ) for all ( n \geq 10 ), then the radius of convergence of
[
\sum_{n=0}^{\infty} a_n x^n
]
is contained in the radius of convergence of
[
\sum_{n=0}^{\infty} b_n x^n.
]$$

[potent lotus]

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

[white tide]

why is this not true

[velvet osprey]

what if a_n just happened to be 0 for, say, n >= 50

then the RoC of the first series is just infinite

also if you are talking about containment you might wanna speak about intervals not radii of convergence.

[white tide]

oh youre right

about the second statement

not sure i understood

what do you mean

[velvet osprey]

radius of convergence is a number

numbers are not contained in each other, it makes no sense to speak that way

[white tide]

oop youre right

yeah i didnt translate it correctly in the original one it said interval

thanks !

[calm coral]

@white tide Has your question been resolved?

Channel closed

Closed by @white tide

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.

[covert orchid]

What is the difference between a function that is differentiable n times on a point and
A function that is differentiable n times on a neighborhood of the point

[velvet osprey]

single point vs neighborhood...?

like

the former requires only $f^{(k)}(x_0)$ to exist while the latter requires $f^{(k)}(x)$ to exist for all $x \in (x_0 - \ep, x_0 + \ep)$.

[potent lotus]

ann.in.a.teacup

[velvet osprey]

(with k ranging from 1 to n)

[covert orchid]

Yes

[velvet osprey]

not sure how else the difference can be formulated really

!xy

[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.

[covert orchid]

There's no problem I'm trying to understand material

Let's say if I'm given a function that is differentiable on a neighborhood of a and I'm.given that f'(a)>0 could I say that there exists a negihborhood such that f(x)-f(a)/x-a>0 but I can't conclude that if it wasn't differentiable on a neighborhood but on the single point ?

Let's say it's differnetiable on a and I'm given f'(a)>0, could I say the same thing ?

I know if it's differentiable twice on point a, automatically I conclude that it's differntiable once on a neighbirhood of a correct ?

[calm coral]

@covert orchid Has your question been resolved?

[glass heart]

if you take f(x)=1 if x in Q, 0 otherwise

and then take x^n f(x)

that should be n-1 times differentiable at 0 and nowhere else

modulo details

wait no that makes no sense

but works for n=2

but for higher it clearly cant work, if you want to compute the nth derivative you need the n-1th derivative in a neighborhood

[covert orchid]

Does that mean this is right ?

[glass heart]

by definition for something to be differentiable twice, you need to be able to compute the difference quotient of the first derivative in the first place, so it needs to exist in a neighbourhood

[covert orchid]

.close

[calm coral]

Channel closed

Closed by @covert orchid

Use .reopen if this was a mistake.

[calm coral]

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.

[crystal breach]

how would i do this

[calm coral]

@crystal breach Has your question been resolved?

[calm coral]

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.

[remote mural]

why does this equation form a circle

[velvet osprey]

write z=x+iy, square both sides, expand, crunch the numbers until you get down to a quadratic in x and y in standard form

there is not much to say about the geometry of the thing unfortunately

[remote mural]

ohh yess i understand that but im not sure if im looking too deep into it but im trying to understand the geometry part of it

[remote mural]

ohh lol 😭

unfortunate then

because i was thinking if |z-a|=|z-b| i know thats saying a complex number at a distance from z=a complex number distance from b and i understand hwy that forms a perpendicular lines

but then i couldnt understand what the 2 had to do with this on ein this case

but i suppose if it cant be said much about the geometry thats unfortunate then 😅

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

@remote mural Has your question been resolved?

Channel closed

Closed by @vestal sphinx

Use .reopen if this was a mistake.

[calm coral]

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.

[tacit plover]

Can anyone explain why the answer is D to this question? I didn’t learn how to multiply radicals with different numbers but I have a quiz on it today

[edgy leaf]

√a√b = √(ab)

[tacit plover]

Could u also explain why the x is the coefficient?

😢

[edgy leaf]

√(3x)√(2x) = √(3x*2x)

[tacit plover]

Omg wait sorry I think I’m stupid

Tysm!!

So it would be root 6x^2 and then the x goes out because it’s a perfect square right

[edgy leaf]

indeed

[tacit plover]

Tyyy

.close

[edgy leaf]

it doesnt have to be a perfect square

[calm coral]

Channel closed

Closed by @tacit plover

Use .reopen if this was a mistake.

[tidal matrix]

i think the answer is |x|sqrt(6) though

but yeah if x >= 0 then xsqrt(6)

[edgy leaf]

no x is positive from the initial statement

[tidal matrix]

ah

then its fine

[edgy leaf]

√nx for positive n implies x≥0 for x in R

[tidal matrix]

yesyes

[calm coral]

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.

[warm pewter]

Is this right?

[eternal shard]

up until the last line it looks good

[warm pewter]

Which is the last line ur talking abttttt

The 1/4 or the 17…

Oh

Sorry

Misunderstood

[eternal shard]

i am trying to understand the very last line

[warm pewter]

I think

[eternal shard]

1/4 * k^2 (k+1)^2+(k+1)^3

[warm pewter]

AHHHH

[eternal shard]

it at least misses a factor 17

[warm pewter]

It’s for a different question my bad

😅😅😅

[eternal shard]

u silly

well then everything else looks fine

[warm pewter]

Do I replace w the summation formula now

[eternal shard]

w?

[warm pewter]

Ok wait let me send question

[eternal shard]

you can use sum of squares if you want the closed form

[warm pewter]

C)

[warm pewter]

Wat

[warm pewter]

Oh I will need to sub like n=2n and n=n-1 separately right

In that thing

[eternal shard]

yes

then you get rid of the sum symbol

[warm pewter]

Oh

[eternal shard]

and what you have left is a closed form

with that you can work easier

[warm pewter]

Oh it’s called a closed form

[eternal shard]

yes

[warm pewter]

But it’s gonna be long which is normal right 🥲

[eternal shard]

the left sum would have an r^3 term as well, and there also exists a formula for a sum of cubics

[eternal shard]

yea

[eternal shard]

if you need it

[warm pewter]

Ohhhhhgg

Omg thanks

I will try now

[warm pewter]

Will I have to expand everything out

It’s so long oh my god

[eternal shard]

could be

you probably did b)

what you got for b)

yea kinda awful ngl

if you are lucky you end up with some quadratic

although if it's a cubic you can derive the quadratic cause you know

n = 0

so just divide by n

@warm pewter

n = 0 is an obvious solution

oh i forgot a term

[warm pewter]

I’m getting ^4 oh my god

Okay let me try this

[eternal shard]

not really if you divided by n

[eternal shard]

you can try to see if there is another integer solution, like what happens if you plug in n = 1 or n = -1 or n = -2

because then you can get rid of a factor again

optionally you can do a long division with the 2nd integer root and with the cubic polynomial 😄

and then you get a final quadratic

[calm coral]

@warm pewter Has your question been resolved?

[warm pewter]

Wait I actually could get rid of one

[warm pewter]

I got a quadratic luckilyyyyy

Also for this one do I need to prove for n=1,2

it’s hard to see got no space

[eternal shard]

is this a new task

it seems you need prove it for all n silly

not just n=1 and n=2

n=1 could be your base case in your induction proof

[warm pewter]

Yeah

Ohhhhhhhh

LMAOAOAOAOAAOAOAOA

How do I know how many values of n I need for my base case

[eternal shard]

just 1

usually it's the smallest value

so n=1

[warm pewter]

Okay

For every single case

[eternal shard]

wdym

you wann check for each natural number if it's true??

that would take longer than you'd ever live

[warm pewter]

Noooo cos like my teacher told me to do n=1,2,3 for this question but idk why

I mean for another question

[eternal shard]

ok

well it was probably so you see that it works

seemingly

just need to prove it now

[warm pewter]

Ohhh I see

But it’s just unnecessary

[eternal shard]

is it

[warm pewter]

Right

Ugh I don’t have the question w me I can’t show it

[eternal shard]

mathmaticians dont play the game of uncertainty

[warm pewter]

😅

[eternal shard]

if you make a claim, well you prove

it

[warm pewter]

Yes

[eternal shard]

[warm pewter]

But if this given formula is for Un+2

[eternal shard]

we can do i) together

[warm pewter]

Actually this one is not confusing now but I have another question that I need ur help w

[eternal shard]

okk

[warm pewter]

4,5,6,7 any of them

Bc they r different

From what I’ve been doing

[eternal shard]

oh lord

ok let's pick 4

[warm pewter]

Yes

Okayyyy

[eternal shard]

So we are given a recursive formula so we will prob need it in the induction step

[warm pewter]

Yessssss

[eternal shard]

any ideas?

[warm pewter]

Do n = positive number

But idk do 1

I guess

[eternal shard]

yea we can check if it holds for n = 1

and also for n = 2

[warm pewter]

Why n = 2

Like why do I need to do two values

[eternal shard]

because we are given u_2

[warm pewter]

Ohhh

[eternal shard]

yea you have two start values

it's like a double induction

[warm pewter]

So if I do two starting values

I mean if I get two starting values

I need to use two values of n starting from 1

[eternal shard]

yea basically

[warm pewter]

Bruh what

Okkk

[eternal shard]

ya idk how to call it haha

[warm pewter]

It’s ok HAHAHAAHA I have no idea what it means

[eternal shard]

it's like this okay

[warm pewter]

Okkkk

[eternal shard]

you are given a recursive formula that works for sure

[warm pewter]

Yeahhhhh

[eternal shard]

now you wanna prove with induction that the explicit works too

given the two values now you test it

[warm pewter]

Explicit is the other formula right

[eternal shard]

yes

[warm pewter]

Ok

[eternal shard]

so does it work for n = 1 and n = 2

[warm pewter]

Yes

[eternal shard]

can u write it down

[warm pewter]

Write what

[eternal shard]

the base case

[warm pewter]

Ok give me a moment

[eternal shard]

it's enougn if you do it herebtw

[warm pewter]

do I just type here for the explicit one

[eternal shard]

ya+

[warm pewter]

U1 = 1, U1 = 3-2 =1
U2 = 5, U2 = 9-4 =5

True for n=1,2

[eternal shard]

wow well done

[warm pewter]

LMAO

[eternal shard]

no

[warm pewter]

😀

[eternal shard]

many ppl already fail at that step

so

[warm pewter]

What r u sure

[eternal shard]

ye

[warm pewter]

Ok yay I guess

[eternal shard]

now you know for some number n in N that u_n = 3^n-2^n and (because of the second case) that also u_(n+1) = 3^(n+1)-2^(n+1) works

[warm pewter]

Yesssssssssssssssss

[eternal shard]

we will need that now

to prove it for u_(n+2) (which depends on u_(n+1) and u_n)

[warm pewter]

Ohhhhh

[eternal shard]

the induction step is now

to show

u_(n+2) = 3^(n+2) - 2^(n+2)

so far so good?

[warm pewter]

Yes

[eternal shard]

ok any ideas on this

can we somehow rewrite u_(n+2)

[warm pewter]

Wait how I know I use given formula or explicit thingie

[eternal shard]

well that's teh question

in induction we need to use our assumptions

that means

we need to use the fact that
u_n = 3^n-2^n and u_(n+1) = 3^(n+1)-2^(n+1) works

[warm pewter]

Yeppppooo

[eternal shard]

proving u_(n+2) = 3^(n+2) - 2^(n+2)

so i am asking

is there another for we can rewrite u_(n+2) as

[warm pewter]

Yes

[eternal shard]

can u write it down

[warm pewter]

Uk+2 = 5Uk+1-6Uk

[eternal shard]

yes

exactly thats what we need

[warm pewter]

OHHHHHHHHHHHHHHHH

[eternal shard]

Your teacher is so nice

gave you a gift

told you here

use this

[warm pewter]

Yes u

[warm pewter]

Omg yes

[eternal shard]

Now can we rewrite u_n+1 and u_n

[warm pewter]

Yes like I think u can substitute from earlier that we assumed

[eternal shard]

yes!

and you would now try to derive what you wanted to prove

[eternal shard]

using algebra basically

this is also the crucial step

[warm pewter]

Ummmm

[eternal shard]

where we apply our induction hypothesis

[warm pewter]

Whaaaaaaaa

[eternal shard]

our assumptions

like we just used the fact u_(n+1) = 3^(n+1)-2^(n+1) and u_n = 3^n-2^n for some n

[warm pewter]

Ah yep

[eternal shard]

now it's up to us to simplify it

to what we want

[warm pewter]

Yes to get this

[eternal shard]

yesss

try it on paper

and then u are done

[warm pewter]

Okay let me try

[eternal shard]

i mean yea

you are a pro

well done

<@&268886789983436800>

[warm pewter]

How to conclude it?

No u pro

[eternal shard]

conclude what

you mean how to end the proof?

🥹 u there?

[warm pewter]

Yeppp

Sorry

I’m hereeeeee

[eternal shard]

well basically if you write it down nicely what we did then there is your induction proof

base case
hypothesis
induction step along with the algebra

from that follows by induction that the statement is true

[warm pewter]

Hmmmm

Ok so if statement is true for n=k, k+1 then it is shown true for n = k+2. Statement shown is true for n=1,2 so it is true for all positive integers by mathematical induction

[eternal shard]

uhm

you showed that its true for some numbers and based on that you proved it for every successor as well

that results into proving it for all n by the so called domino effect

[warm pewter]

Yes

[eternal shard]

https://tenor.com/view/playing-the-pet-collective-domino-cat-gif-18353123

basically like that

[warm pewter]

Ohhhhhhhhh

Ok I get it a bit

[eternal shard]

a bit🥺

[warm pewter]

What is every successor

[eternal shard]

o

[eternal shard]

like every domino has a succesor in front of that hits it

like 1st domino's succesor is the 2nd domino