help-19

[tacit elm]

Let’s move on to the next example

[dusk moon]

I'm just copying it again

well n by n zero matrix all columns and rows are lines of zeroes

well wouldn't Ox =0 if you did the multiplication

you'll get the zero vector as output

[tacit elm]

Let’s take the definition

If Ox = 0 for all x

[dusk moon]

well I would get N(O) = {x: Ox=0, x in R^n}

[tacit elm]

What does that mean ?

[dusk moon]

Null space of zero matrix N(O)

I know it's a weird notation but that's how book uses it capital N for null space

[tacit elm]

What is the null space then ?

[dusk moon]

well Ox=0 works for any vector x in R^n so maybe it's R^n?

[tacit elm]

Yes !!

What is the range now

[dusk moon]

would it be zero

since Ox=y=0

[tacit elm]

Yes !!!

The only possible output is 0

I need to go to bed but you’re starting to get it

[dusk moon]

No worries, thanks for the help

[odd edge]

@dusk moon Has your question been resolved?

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[robust olive]

Regarding the solution to this question, we got possible limits of 1/3 and 2/3. Why are we choosing that the sequence is bounded below by 2/3? Wouldn't it make more sense to pick 1/3 because if the sequence is bounded below by 1/3 then it can also be bounded by 2/3 ?

[forest sky]

that would give us a usable lower bound, but would be unlikely to give us a limit since these sequences don't tend to "cross" potential limit points

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[unique arrow]

geometry proofs just confused of the last step is right

[odd edge]

@unique arrow Has your question been resolved?

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[tranquil elk]

does anybody know what error i made here?

[tranquil elk]

im confused about b and c

[small dune]

u have to use divide rule of differentiation

[short terrace]

Well for the first one you entered the answer wrong

[small dune]

division rule*

[tranquil elk]

i did do that though

you mean the quotient rule right?

[small dune]

yeah quotient

[hearty fossil]

it may help

[tranquil elk]

the one thats (f*g'-g*f')/g^2

[small dune]

ur quotient rule is wrong

the one in numerator is differentiated first

u did the opposite

[tranquil elk]

what do you mean?

[small dune]

d(u/v)/dx = (vu' - uv')/v^2

the one in numerator is to be differentiated first for the first term in numerator

'u' is in numerator of the function so 'u' will be diff first

[tranquil elk]

oh

[small dune]

yeah

[tranquil elk]

wait, but how does that change my answer

[small dune]

the value inputs would be different then

[tranquil elk]

wdym?

[small dune]

try putting -31/49 for B and 31 for C

lets see if its correct

[tranquil elk]

alright

[tranquil elk]

oh you were right

tysm

[small dune]

nice

did u understand the mistake though?

[tranquil elk]

no

[small dune]

ok lemme try to explain

in part B

the function was f/g

so u wrote the differentiation which was f(5)g'(5)-g(5)f'(5) for numerator

what u should actually have done was g(5)f'(5) - f(5)g'(5) for numerator

ur denominator is correct but ur numerator was wrong

[tranquil elk]

ohh i think i get it

[small dune]

in the first term u have to write the differential of numerator function i.e f

[small dune]

yeahh

numerator comes first and then denominator

[tranquil elk]

i didn't know that was a thing lol

[small dune]

its ok now u know right?

[tranquil elk]

thanks so much bro

[small dune]

thats what matters

[small dune]

no problem

[tranquil elk]

yeah

tysm <3

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[tulip fiber]

might be pretty messy but the original inequality is number 3.

UUGGFSSGAHAH i might just rewrite this

so it’s more understandable

[brazen hare]

,rotate

[tulip fiber]

i wanted to ask if what i did here is right

for the interval on the most left part

it’s undefined

so it got no sign

[orchid torrent]

$\frac{2x-x^2}{x^2-2x-15}$ is undefined at $x=-3$, but that's irrelevant to determining the sign on the interval $(-\infty, -3)$ since $-3$ isn't in that interval. You should substitute something, like say, $x=-4$.

[clever fjord]

Civil Service Pigeon

[orchid torrent]

,w \frac{2x-x^2}{x^2-2x-15}, x=4

[clever fjord]

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[orchid torrent]

gonna dip soon but hope this helps

[tulip fiber]

oh, yeah. i actually substituted -3 by accident

so it's positive, positive, positive, positive, and negative

and since i'm trying to find greater or less than 0

the answer is

(-8,-3) (-3,0) (0,2) (2,5)?

[orchid torrent]

no

,w \frac{2x-x^2}{x^2-2x-15}, x=1

[clever fjord]

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[tulip fiber]

oops, or equal*

[tulip fiber]

oh

positive, positive, negative, positive, negative?

or did i calculate something wrong again..

[orchid torrent]

good 'ol typo

[tulip fiber]

isn't it

snd then

[orchid torrent]

,rotate

[tulip fiber]

divide 2 negatives

[orchid torrent]

,rotate 180

[tulip fiber]

divide 2 negatives = positive

[orchid torrent]

the numerator isn't negative

[tulip fiber]

ah wait

-(1) is -1

-1(-1)

is positive

mb..

[tulip fiber]

did i get anything else wrong

so it's (-infinity, -3), (-3,0), and (0,2)

[tulip fiber]

yeah

it's still a positive either way

right....

[orchid torrent]

,rotate

[orchid torrent]

,rotate 180

[tulip fiber]

wait no

its positive 9

[orchid torrent]

mhm

[tulip fiber]

AAAAGHHHHH

so it's negative

wjwhebwkwd

SO

-,+,-,+,-

[orchid torrent]

,w graph (2x-x^2)(x^2-2x-15)

[tulip fiber]

and the answer is (-3,0) and (0,2)

[clever fjord]

Results provided by WolframAlpha

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[orchid torrent]

yes

[orchid torrent]

it says $\geq 0$, not $>0$

[clever fjord]

Civil Service Pigeon

[tulip fiber]

oh right

[orchid torrent]

also your second interval is completely off

[tulip fiber]

w

[orchid torrent]

you probably copied the wrong one

[tulip fiber]

my second interval

which one is that

(-3,0)..?

[orchid torrent]

I meant the second interval in your answer

(0,2)

[tulip fiber]

oh

i meant to say (2,5) oops

[tulip fiber]

wait

so what

how do i

AAAGGGH

i just know that (-3,0) and (2,5) is one of the answer

but since it's or equal to 0

how do i find the other answers

[orchid torrent]

you found where the left hand side is > 0

so now include where it's = 0

[tulip fiber]

can

u give me an example

on how to do it

[orchid torrent]

mate

when is $\frac{2x-x^2}{x^2-2x-15}=0$

[clever fjord]

Civil Service Pigeon

[tulip fiber]

i got it now

thanks, kind sir

.close

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[timber river]

how is this not E

3:2 so last year, the basic cost would be 198 and taxes 132. 198 * 1.2 = 237.6. 132 * 1.1 = 145.2
237.6 + 145.2 + 25 = $407.80

[wooden python]

last yr total of 330 includes the booking fee

so it's 280 you should be splitting 3:2, and not 330

you really should be reading these questions carefully

@timber river

[timber river]

ah

[timber river]

yeah i feel like this is my biggest problem

im scared of running out of time on the real exam

[wooden python]

do they give you negative marks for wrong answers

[timber river]

nope

[wooden python]

ok then you should take the time to read through the qs carefully

and if it happens that you are truly completely out of time for any that remain, then guess randomly

[timber river]

yeah

thanks

.close

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[onyx gate]

Ok so I need to factor this and the GCF is x+8

[onyx gate]

I’m pretty sure I’m doing this wrong but I’m unsure what to do with the extra x+8 and the - sign between the two

[onyx gate]

OH OK

how about the rest of it

[devout hedge]

where did this come from too?

[onyx gate]

Since I started with the (X+8)^2 and only factored out X+8 don’t I put the other there

I was unsure with that

[devout hedge]

the (x+8) in front of the (3x+2) is exactly where you're meant to put it.

[onyx gate]

But what about the other X+8

It’s still there right

X+8 is just the GCF

[onyx gate]

But I can’t just forget that originally it was (x+8)^2

[devout hedge]

one copy of (x+8) was used to cancel against the denominator. you're left with one only.

[onyx gate]

Is that complete then?

[devout hedge]

to answer that, we'll need to see your original question.

[devout hedge]

and the instructions? include them too.

[onyx gate]

Original question which I had written down too

[onyx gate]

Factor completely

I can’t factor further right

I’m pretty sure

[devout hedge]

wait, if you were asked to factor completely, your notation here is wrong in the first place. you need one more (x+8), and this whole expression inside is going to be in a big pair of brackets.

[devout hedge]

also, I would try expanding the (x+8)(3x+2), then subtract the (5x - 2) from it, and try to factor that quadratic. if that cannot be cleanly factored, I suppose you can just leave it as is, after recalling what I mentioned here.

[onyx gate]

Like this?

[devout hedge]

the big pair of brackets must include the -(5x-2), because you factored an (x+8) from that too.

[onyx gate]

Alright

[onyx gate]

I fixed that could I do anything else?

[unkempt lichen]

.

[onyx gate]

I can’t factor here

[unkempt lichen]

nvm, this is not a nice factorization

technically can but it's ugly as fuck

[onyx gate]

Yeah

[unkempt lichen]

so return to your second line

[onyx gate]

Got it so that’s the answer?

[unkempt lichen]

that shld be your answer

[onyx gate]

👍

So I’m looking at this
Can I factor this anymore?

[odd edge]

@onyx gate Has your question been resolved?

[atomic hornet]

No, you're done

That's all you need

Anymore question you want to ask after this one?

lmk if there's any

[wicked olive]

@onyx gate close the channel if you’re satisfied with the answer

[onyx gate]

i will

[atomic hornet]

Alright

[onyx gate]

ty

[atomic hornet]

Have a good one

[onyx gate]

i will finish this assignment and see if i come across any problems

[atomic hornet]

bet :))

[onyx gate]

How does this look

[atomic hornet]

Looks good

yeah, I don't see any problem

[onyx gate]

Thank you

Looking at number 7

I need to factor this but should I distribute first

[atomic hornet]

not really

You can manipulate the exponent like how you did in the previous question

try to make this guy 1/3

[onyx gate]

Like that

?

Is that alright?

[onyx gate]

@atomic hornet

[devout hedge]

is this still ongoing?

[onyx gate]

Yeah just wondering if I factored correctly

[devout hedge]

I don't think you did. for starters, the fraction in the exponent should not be flipped.

[onyx gate]

Oh 😭

I’m noticing but I suppose I can continue to distribute the final answer I had

[devout hedge]

I did it another way, but my answer matches yours, minus that mistake.

[onyx gate]

👍

I’m lost for number 10

[devout hedge]

can you show the original question please?

[onyx gate]

It’s there

Factor completely

[devout hedge]

it's a little hard to see, but alright.

[onyx gate]

Sorry 😭

[onyx gate]

Better image

[devout hedge]

no, it's fine, I just have poor eyesight. sorry.

anyway, what do you think you will factor out here?

(hint: use the denominator as a guide.)

[mystic saffron]

highly recommend drawing a bracket here

[onyx gate]

It’s ok I’m blind too

[mystic saffron]

since theres a subtraction in between

[devout hedge]

so have you gotten your common factor?

in particular, one common factor kills this problem straight away.

[onyx gate]

(2x+1)^-2/3

?

[devout hedge]

correct.

now factor that from the numerator. what do you get?

(ignore the denominator first.)

[mystic saffron]

i have an easier method

ngl

[mystic saffron]

why not solve this here

[devout hedge]

in that case, you can take over from me.

[onyx gate]

Thx for your help still :)

[mystic saffron]

(2x+1)^2/3 will be gone

[devout hedge]

I apologize for not knowing the method you mean.

[mystic saffron]

i mean i just gave an advice....

[frosty quiver]

can someone help me im french

[onyx gate]

Wdym

[devout hedge]

!occupied, sorry. please take another channel like #help-46.

[odd edge]

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).

[mystic saffron]

so till what point am i supposed to show btw

[mystic saffron]

solve the bracket

[onyx gate]

Just normally?

[frosty quiver]

ok

[onyx gate]

Aren’t I factoring

[mystic saffron]

is your final answer in a quadratic form?

like is it supposed to be in a quadratic form

[onyx gate]

It can be - it just needs to completely factored

[mystic saffron]

hmm

works

[onyx gate]

Should I just continue with what u said

[mystic saffron]

yep

[onyx gate]

So deal with the exponent first, then distribute the 9, and then expand the 2

[mystic saffron]

write that term with -ve exponent as a fraction

and solve the subtraction

[onyx gate]

-ve?

[mystic saffron]

negative

till u do this ill try another method

[onyx gate]

Yeah I’m 101% I messed up
I’m really confused now

Ignore the 9. Part
Bottom left is where I wrote

[mystic saffron]

what no no no

i think you went wrong

1s

[onyx gate]

O wait I shouldn’t have just ignored those

[mystic saffron]

yk what

do this

take out (2x+1)^-2/3 common out of the numerator

and remove it from the denominator

instant answer

[mystic saffron]

@onyx gate ^

[onyx gate]

I moved this above
I shouldn’t have done that?

To become this

[mystic saffron]

no need of that

start from the beginning

and take out (2x+1)^-2/3 out of the numerator

show me once you take it common

btw

[onyx gate]

Ok

[mystic saffron]

denominator isnt needed

[mystic saffron]

it wont be 1

because its an exponent right? so it wouldnt be 1 unless the terms were equal

[onyx gate]

So what would it be then

[mystic saffron]

try again using laws of exponents

then ill tell

[onyx gate]

So what did I do wrong?

[onyx gate]

Just this?

[mystic saffron]

rest seems pretty good, only that term is wrong

[onyx gate]

How did I do the rest of it fine and just get that wrong

[mystic saffron]

because when you took that out common, you didnt use this identity correctly, and got that term wrong

understood the mistake?

[onyx gate]

So it’s (2x+1)^4/3-6/3

Instead of (1)^6/3

[mystic saffron]

????

4/3 - 6/3?

[onyx gate]

😭

[mystic saffron]

no

[onyx gate]

I’m sorry sleep deprivation

[mystic saffron]

no its alr dw

if you have the fraction a^2/a^3 then it can be written as a^-1, which is a^(2-3)

somewhat like this

so use this in that q

got it now?

[onyx gate]

^4/3 - -2/3

Then

?

[mystic saffron]

yessir

now solve

[onyx gate]

So the 1 is 2x+1

Right

[mystic saffron]

yep

[onyx gate]

Huh 😭

[mystic saffron]

yeah thats correct!

now simplify it

further

[mystic saffron]

also as i advised, draw a bracket because the two terms i marked with different colours are different terms

[mystic saffron]

yeah cancel the common term

[mystic saffron]

no 😭

these 2 terms are the same right?

[onyx gate]

[onyx gate]

Yes

[mystic saffron]

cut em off

its division so it'll be 1

also why not write this 6/3 as 2

[mystic saffron]

yep correct

[onyx gate]

Should I square into a quadratic and see if I can factor that?

[mystic saffron]

yea you can

but you can also use a^2 - b^2 identity

[devout hedge]

you won't be able to factor the result.
ignore this message.

[mystic saffron]

the quadratic in the end is solvable

but identity easier imo

[devout hedge]

my apologies, I was thinking of full expansion. sorry for intruding again.

[onyx gate]

Yeah you right I think

[mystic saffron]

no bro its solvable 😭

[devout hedge]

ignore that message. I'm just being stupid.

[mystic saffron]

you expanded it incorrectly

[onyx gate]

Ofc I did

Wait how

[mystic saffron]

what about the 1

[onyx gate]

O so it’s -8

[mystic saffron]

yep

[onyx gate]

Right

[mystic saffron]

yeah yk how to solve a quadratic right?

[mystic saffron]

yeah

now solve the quadratic

make it simpler by taking 4 out as a common factor

im assuming yk how to solve a quadratic, if not tell me

[onyx gate]

We good

[mystic saffron]

yessir!

thats the final answer

[onyx gate]

Thank you
U amazing

[mystic saffron]

you cant simplify it further

[mystic saffron]

np alg 👍

though i felt this was easier

but yea anything works

[onyx gate]

Is this correct btw?

[mystic saffron]

yo

sorry i didnt see your msg

lemme check

[mystic saffron]

in the 1st q

you made a blunder

they both are negative signs

so why is this negative too?

@onyx gate 2nd line is not the answer

its a clean factorization

it should be -5x + 2

because of two negative terms

[onyx gate]

The circled answer is the factored answer

Not the last 2

[mystic saffron]

its not

[onyx gate]

Ignore those

[onyx gate]

Oh

[mystic saffron]

homie

you did it wrong

thats not the answer

[onyx gate]

Oh😭

What did I do wrong

[mystic saffron]

^

now thats a clean quadratic which is solvable

[onyx gate]

Got it
(ATP the questions I did on my own I don’t even have faith I did right

I was so confident with this one 😭

[mystic saffron]

its a minor sign mistake dw

[unkempt lichen]

shit, my apologies for missing this earlier

[onyx gate]

NWS

[mystic saffron]

just keep in mind multiplication of 2 negative terms is positive

otherwise the steps followed in this answer were correct

[onyx gate]

Better?

[mystic saffron]

um

[onyx gate]

How did I mess up that bad

What

[elfin meteor]

Why is it the 28th

How are u in the future

[onyx gate]

Oh yeah I am

Sleep deprived behavior

[mystic saffron]

ok 1st mistake i saw, you took 8 common which should be 18

[onyx gate]

I’m blind

[mystic saffron]

yea rest seems well

only that

[onyx gate]

I’m looking at 2 and it looks wrong

But I don’t see how

[mystic saffron]

you are supposed to add them

[mystic saffron]

no that 3x+4 is correct but hes supposed to add the other 2

because he took that out as common factor

[devout hedge]

oh okay he's doing that dividing to take it out as common factor, my apologies once again.

[devout hedge]

I probably will not intrude any more after this. sorry to both of you.

[mystic saffron]

yea you can take 3 out

[mystic saffron]

i dont mind...

[onyx gate]

Don’t worry about it I always appreciate you trying to help

[devout hedge]

I do mind, the last three times I stepped in I made a mistake. I'll just react if I see something wrong. sorry once again.

[onyx gate]

Don’t pressure yourself like that
It’s completely fine and everyone can help each other

How is that?

[mystic saffron]

yeah

write it as one term

3(3x+4)^2

[onyx gate]

👍

[mystic saffron]

dw my maths also sucks

[onyx gate]

@mystic saffron I’m just gonna bother u about this one - I’m having u check my entire math hw at this point

[mystic saffron]

can u send the original q

[onyx gate]

Number 3

[mystic saffron]

yeah thats correct

[onyx gate]

Amazing I will try my best to deal with the rest of the proof reading myself- I appreciate your help

[mystic saffron]

aight np

[mystic saffron]

which grade are you in if you dont mind me asking

[onyx gate]

Wait one more thing I’m sorry can you look over number 8 😭

[onyx gate]

I’m taking algebra 2/trig h I’m in 10th grade

[mystic saffron]

looks correct to me

[mystic saffron]

i see

[onyx gate]

Why lol

[mystic saffron]

curious

lol

[onyx gate]

Wait number 8 is correct?

Ok thank you

U can close this I am so done with math

[mystic saffron]

yeah

[onyx gate]

Actually I need to oops

Till next time cya 👋

.close

[odd edge]

Channel closed

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Use .reopen if this was a mistake.

[mystic saffron]

cya

[odd edge]

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[swift heron]

we havent learned determinants yet, how would you approach this?

[swift heron]

would you have to check each case of elementary matrix

[merry finch]

i mean what is an elementary matrix and what is a row swapping elementary matrix

[swift heron]

from my understanding an elemenatary matrix is just an invertible matrix

in the form of row swapping, row scaling, row addition (to antoher row)

[unkempt lichen]

i did a quick check

an elementary matrix seems to be any matrix formed from one (and only one) elementary row operation applied to the identity

[swift heron]

hmm

in that case

[swift heron]

Because EE is row swapping, then

EE * EE = I

Then

E^-1 = E^3

If E is an elemenatary matrix, then so is E^-1. But E^-1 = E^3 which is multiple operations applied to the identity? idek if that makes sense

[unkempt lichen]

think you might need to do some casework here mate

[odd edge]

@swift heron Has your question been resolved?

[swift heron]

so it is casework

💀

.close

[odd edge]

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[odd edge]

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[jagged maple]

Hello, I'd like to check if my proof is correct. The problem was as followed:

[jagged maple]

Somebody actually managed to prove that there existed some $f$ such that $v_n / u_n \to c\in \mathbb{R}$ :

https://math.stackexchange.com/questions/5091558/nature-of-prod-n-fau-n-over-fu-n

[clever fjord]

Médicis

[jagged maple]

However I somehow proved the countrary, which is that $\forall f, f(\infty) = \infty, v_n / u_n \to \infty$, so who is right?

[clever fjord]

Médicis

[jagged maple]

my proof was as followed: for any real number $u_0 > 0$, by the growth of $f$ you get $u_1 > u_0$, hence you can take any real number $v_0$ such that $v_0 \in (u_0, u_1)$. Since you get $v_1 > w_1$ as well, you can take another real number $w_0$ such that $w_0 \in (u_1, v_1)$

[clever fjord]

Médicis

[jagged maple]

As such :

$\forall f, \exists (u_0, v_0, w_0), v_1 > w_0 > u_1 > v_0 > u_0 >0$

[clever fjord]

Médicis

[jagged maple]

you also can prove that $forall f, \forall (a_0, b_0), b_0 > a_1 > a_0 > 0, b_n / a_n \to \infty$ :

[clever fjord]

Médicis

[clever fjord]

Médicis

[jagged maple]

now, assume that there exists $f$ such that

$\forall a_0, \exists b_0 > a_0, b_n / a_n \to c \in \mathbb{R}$

since you can take any $v_0$ such that $v_0 > u_0$, and any $w_0$ such that $w_0 > v_0$, let's say that:

$v_n / u_n \to l_1 \in \mathbb{R} \ w_n / v_n \to l_2 \in \mathbb{R}$

[clever fjord]

Médicis

[jagged maple]

However, since $w_0 > u_1$, you get:

$w_n / u_n \to \infty$

Which implies: $\underbrace{w_n / u_n}{\to\infty} = \underbrace{{w_n\over v_n} {v_n\over u_n}}{\to l_1 l_2}$

[clever fjord]

Médicis

[jagged maple]

Which contradicts #help-19 message

hence $\forall f, \forall (u_0,v_0), v_0 > u_0 > 0 \Longrightarrow v_n / u_n \to \infty$

[clever fjord]

Médicis

[jagged maple]

are we done?

[woeful briar]

hmm your proof somehow only relies on v0,w0,v1,u0,u1 etc

i.e the first few terms of the sequences

this doesn't describe at all the behaviour as n approches infinity

[jagged maple]

It describes it well for v_1 > u_0, which is sufficient to prove that v_n/u_n goes to infinity, which was all that was necessary to guess the behavior of u_n, v_n and w_n, at least from what I think

[woeful briar]

the main thing that I think is the problem is the deduction that $w_0 > v_1 \implies \frac{w_n}{v_n} \to \infty$

[clever fjord]

ExpertEsquieESQUIE

[woeful briar]

which is simply not enough

[jagged maple]

how is this proof wrong / not enough?

[woeful briar]

You probably meant to take $v_n = u_{n+1}$

[clever fjord]

ExpertEsquieESQUIE

[woeful briar]

and the problem with this is that this is a specific case which may not happen

[woeful briar]

to prove this you have to show this for every u0, v0 and f

[jagged maple]

assume $v_0 = u_1$, therefore $v_n / u_n \to \infty$

Now take $w_0 \geq u_1$: this implies that $w_n \geq v_n$, therefore ${w_n \over u_n} \geq {v_n \over u_n} \to \infty$

Which isn't that specific since we used it to prove that there existed some contradiction #help-19 message

[clever fjord]

Médicis

[jagged maple]

since you can take v_0 as close as possible to u_0, and w_0 as close as possible to v_0, it means in my eyes that the divergence of the ratio holds true for any u_0 and v_0

[woeful briar]

this works to show for v0 >= u1

but the problem is what happens when v0 < u1?

[jagged maple]

I agree, but if you assume that there exists f such that there existed v0 < u1 such that vn/un converges, you get a contradiction #help-19 message

[odd edge]

@jagged maple Has your question been resolved?

[woeful briar]

ok

but this still leaves v0 < u0

[jagged maple]

we assumed at first that v0 > u0

[woeful briar]

true

[odd edge]

@jagged maple Has your question been resolved?

[odd edge]

@jagged maple Has your question been resolved?

[summer wave]

Are we sure that un diverges?

[jagged maple]

yes : $u_{n} \geq u_0 (1+f(u_0))^n \to \infty$

[clever fjord]

Médicis

[jagged maple]

actually I think I’ve just found a much simpler proof

$u_{n+1} \sim u_n$

Thus ${v_n\over u_n} \sim {v_n \over u_n} {1+f(v_n)\over 1+f(u_n)$

[clever fjord]

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

[jagged maple]

granted that $v_n / u_n \to c \in \mathbb{R}^*$, it means that ${f(v_n)\over f(u_n)} \sim {1+ f(v_n) \over 1+ f(u_n)} \sim 1$

[clever fjord]

Médicis

[jagged maple]

however $v_n / u_n$ is strictly growing, so is $f(v_n) / f(u_n)$, however $f(v_0) > f(u_0)$. Therefore there is a contradiction

[clever fjord]

Médicis

[jagged maple]

So $\forall f, \forall (u_0, v_0), v_0 > u_0 > 0 \Longrightarrow v_n / u_n \to \infty$

[clever fjord]

Médicis

[summer wave]

How is un ~ un+1

[jagged maple]

isn’t that true for all sequences?

[summer wave]

No

Especially when un goes to infinity

[jagged maple]

oh yeah x^n

my bad

Well the second proof is wrong then

[summer wave]

Can we be sure that wn/vn doesn't go to infinity ?

*doesn't go

[jagged maple]

It’s an assumption

if it can’t happen then you got your proof by contradiction

[summer wave]

I thought the assumption was that vn/un converged

[jagged maple]

vn/un and wn/vn converged

[summer wave]

What if only one of them converges

Another thing, why must w0 be > u1?

[jagged maple]

we took some w0 such that w0>u1

[summer wave]

But then how did you make sure that wn/vn converges

To me it feels like you're enforcing both w0>u1 and wn/vn converges, at the same time

[jagged maple]

yes

[jagged maple]

is this a problem?

[summer wave]

I think you just showed that such wn doesn't exist

[jagged maple]

how is this incorrect then #help-19 message

[summer wave]

From what I get what you did was

1. Let u_n be a sequence
2. Suppose v_n is a sequence such that vn/un tends to l1
3. Pick wn such that w0>u1 and wn/vn tends to l2
4. Then l1* l2= infinity

But you can't do step 3 because wn doesn't exist

The conditions are mutually exclusive

You can always pick w0>u1 but then you need to show that "wn/vn goes to l2" is a reasonable assumption

[jagged maple]

I see

[odd edge]

@jagged maple Has your question been resolved?

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[near swan]

how do we prove this?

[woeful briar]

this is the prime number theorem

pretty difficult proof

usually takes half a course to develop

using elementary methods, you can prove a slightly weaker result

that $\pi(n) = \Theta \left (\frac{n}{\ln(n)} \right )$

[clever fjord]

ExpertEsquieESQUIE

[near swan]

i do not see how they're related

ah wait

got it

okay, how do we prove that, then?

okay

[clever fjord]

ExpertEsquieESQUIE

[near swan]

why did we do this?

also i am sorry; my wi-fi is acting up so my replies will be a little slow

[woeful briar]

we choose an optimal t to make the RHS in the row above as small as possible

we have freedom over t after all

[near swan]

well, fair enough

[clever fjord]

ExpertEsquieESQUIE

[woeful briar]

https://metaphor.ethz.ch/x/2021/hs/401-3110-71L/ex/eighth.pdf this is a free resource that takes a slightly difference approach

but same ideas

pages 4-6 here

[near swan]

i see

well, i did not follow that completely but i think i got the idea

thank you!

.close

[odd edge]

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[karmic arrow]

!status

[odd edge]

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

@weary nebula Has your question been resolved?

[short terrace]

Since it's an MCQ my first instinct would be to plug in some values and see

[karmic arrow]

The only issue is nCr isn't really easy to compute, especially like that many. Ofc you can use the Pascal triangle but for a good sample size, that would still not be enough

[odd edge]

Channel closed

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[granite bramble]

Can someone help me with my maths

[granite bramble]

🥺

[vernal yacht]

Yes post

[fluid bluff]

send your question first so that the bot pins it

[granite bramble]

For my homework

Idk how to do it

[golden sonnet]

section formulae

[granite bramble]

What

What

What does this mean

I can't comprehend this

😭😭

[fluid bluff]

figure out C

[golden sonnet]

well wait

oh shit

[fluid bluff]

then from that figure out D

[granite bramble]

How do you figure out c

💀

[fluid bluff]

because C is midpoint of AB then C = (A+B)/2

[golden sonnet]

yes using section formulae

[fluid bluff]

dont overcomplicate

[granite bramble]

Wtf is this 😭😭

[brazen hare]

do you recall how to calculate the midpoint?

[granite bramble]

Smt plus smt divided by 2

[golden sonnet]

well watch a 5-min video on it

wait

[fluid bluff]

it can be solved by just ratios

[granite bramble]

Whatt

Guys I promise I'm trying my best

I'm grade 10

[golden sonnet]

coordinates are here too

[granite bramble]

You have to go easy on me

[fluid bluff]

yea

[golden sonnet]

it is indeed grade 10

never panic

[fluid bluff]

it is not

[golden sonnet]

https://www.youtube.com/watch?v=VvINYLS4Gys maybe watch this

[brazen hare]

$$M_{AB} = \left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right)$$
where $M_{AB}$ is the midpoint of A and B

[golden sonnet]

grade 5?

[granite bramble]

No that's wrong

[fluid bluff]

for me yes

[golden sonnet]

brilliant

[fluid bluff]

for normal ppl, grade 9 maybe

def not grade 10

[golden sonnet]

our edu system is a joke

[fluid bluff]

why

[brazen hare]

tf you mean that's wrong 😭

[granite bramble]

This is basic maths

Grade 1 at best

And I'm being generous

[fluid bluff]

yea basic maths

hear me out

[granite bramble]

I could solve in 0 seconds

[fluid bluff]

bruh

[brazen hare]

so i assume you have point C then?

[granite bramble]

😔

I'm watching the video

[fluid bluff]

ok then figure out D

[golden sonnet]

yes see it

[fluid bluff]

why in china thats max grade 7

[golden sonnet]

without it doing it will be lenthy and maybe too much effort taking

[golden sonnet]

idk man our country is a piece of dust against yours

we cant compare

[brazen hare]

you from china?

[fluid bluff]

yea

[brazen hare]

oh cool

[granite bramble]

Guys

I feel like

Ur over complicating things

This is basic maths

I still don't get it

Not even with the video

I'm trying my best j swear 😭😭

[brazen hare]

okay

[brazen hare]

so this formula right

you take the x-coordinate of point A as $x_A$, x-coordinate of B as $x_B$ and so on

[granite bramble]

Ik how to find c

[granite bramble]

I found c

But how do I find d

And

[brazen hare]

use this formula

[granite bramble]

Is c 12,11

[granite bramble]

Can you help me use the formula 😔

Bro tf is mx²

[brazen hare]

m and n are the ratios of the two line segments that divide CE

DE*

[granite bramble]

Ahh

🤔

So what would the equation look like

Cuz I am beyond lost

[brazen hare]

so you want to find the x- and y- coordinates of D

[granite bramble]

Yes

[brazen hare]

choose two variable names for them

[granite bramble]

Uhh

Who's them

💀

You have to be specific with me 😭😭

[brazen hare]

for the x and y coordinates of D

[granite bramble]

I don't get anything 😭

[brazen hare]

choose one variable name for the x-coordinate of D

[granite bramble]

I just call the x and y

[brazen hare]

choose one variable name for the y-coordinate of D

[brazen hare]

okay that works ig

[granite bramble]

Them*

[brazen hare]

just make sure you didn't use x and y earlier in your working for point C

[granite bramble]

What

Okay I wanna change my answer then

[brazen hare]

go ahead

[granite bramble]

X can be called jasmin

[brazen hare]

no.

[granite bramble]

And y can be called feet

[granite bramble]

Hu

Huh

Why!?

[brazen hare]

Let's just go with a and b

[granite bramble]

Okay 😔

[brazen hare]

Let D be the point (a, b)

[brazen hare]

now substitute into the formula given here

[granite bramble]

🤔

Uhh

Ohhh

[granite bramble]

What's x¹ and y¹

And x² and y²

Am I a lost cause

[brazen hare]

no

[brazen hare]

first of all

those are supposed to be written below the line

the 1s and 2s

[granite bramble]

Oh

[brazen hare]

since youre typing them out

you can settle for x_1 or x1

but write it as $x_1$

[brazen hare]

x_1 and y_1 are the coordinates of the first point

[granite bramble]

That makes it so confusing

[brazen hare]

what grade are you btw?

[granite bramble]

10

U?

[brazen hare]

higher

[granite bramble]

Likee

[brazen hare]

anyways do you get this?

[granite bramble]

Ye

[brazen hare]

and x_2 and y_2 are the coordinates of the second point

[granite bramble]

And the point B us x_2 y_2

Okay

[brazen hare]

we're considering the line segment DE

and the division of the line segment into DC and CE

[granite bramble]

Yes 🤔

[granite bramble]

🤔

Yes

[brazen hare]

right

so can you name the coordinates of D, C, and E?

[granite bramble]

No🥺

I need to look at it again

Ik c and e

[brazen hare]

yep

and you let D be something earlier

[granite bramble]

We're finding d

[granite bramble]

No I didn't

🤔

E is 29,5

And c is 12,11

And

Do we do

[brazen hare]

^

[granite bramble]

What's a b

a,b

[brazen hare]

they are just variables

that represent the x-coordinate and y-coordinate of D respectively

!occupied

[odd edge]

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).

[brazen hare]

thanks

[granite bramble]

Ohhh

I get it now

Alr

[brazen hare]

so

[granite bramble]

D is (x, y)

Uhhh

[brazen hare]

?

[granite bramble]

What do I do now

[brazen hare]

anyways the section formula that the other guy posted will give you the coordinates of the point along the line segment

i.e., C

[granite bramble]

Is the point along the line segment, D

[brazen hare]

wait

[granite bramble]

Tf is the first image bruh

[brazen hare]

compare these two images to see what i mean

[granite bramble]

What is m+n

[brazen hare]

m and n are the ratios of one length to the other

so here m = 2 and n = 3

[granite bramble]

Oh

That's so smart

[exotic notch]

Am I scary?

[granite bramble]

🙁

I don't get it anymore

[exotic notch]

Oh nice I use that for my homework too

[granite bramble]

U actually understand this 😔?

[low inlet]

this gcse?

[brazen hare]

then can you help this guy out

[brazen hare]

ya like sec 1 work i think

[granite bramble]

Ye

[exotic notch]

Absolutely not

[granite bramble]

That is not 1 second work

[brazen hare]

secondary 1

i meant

[low inlet]

im intrested in this question

[granite bramble]

😭

[low inlet]

ill try myself

[exotic notch]

I hate maths

Am I getting banned now?

[granite bramble]

👆 🤔

[granite bramble]

Occupied

[exotic notch]

Nah

I don't feel like it

[granite bramble]

So is the equation

[exotic notch]

You have given me great insight

729+12x(9x32)1=67

[granite bramble]

No

[exotic notch]

Am I right or right?

[granite bramble]

6 7!!

You said 6 7!

[exotic notch]

Ikr I'm so smart

[granite bramble]

The equation is too hard to type

So I'll pic

The bottom one

With the D =

Also rate my handwriting

😎

[exotic notch]

-1/999

[granite bramble]

I bet yours isn't any better

[brazen hare]

Nope

[granite bramble]

😨

[brazen hare]

C is the point that is given by the formula

[granite bramble]

Hu

[brazen hare]

The point in between the two input points

[granite bramble]

Ik what c is

12,11

[brazen hare]

yes

[granite bramble]

I used the formula for d

[brazen hare]

you know C

so you can use the formula to 'reverse-engineer' D

[granite bramble]

They didn't teach us that yet

[brazen hare]

form the equation that relates D and E to C using the formula

[granite bramble]

😔

Idk how

[fluid bluff]

still not finished?

lol

i have to go bye

[granite bramble]

😔

[exotic notch]

I rate it like 6-7/10 honestly
Pretty decent handwriting
I said -1 for the funniz

[granite bramble]

6 7!!

You said 6 7!!

[exotic notch]

Depending on what I'm feeling like my handwriting can be ass or amazing

[brazen hare]

...

[granite bramble]

Do u need a ping

[granite bramble]

Imma be deadass with you rn

[exotic notch]

I recognise the joke but I actually think it's between 6 and 7

[granite bramble]

I didn't understand anything

[brazen hare]

are you very sure your school hasnt taught you the section formula yet

[granite bramble]

I'm so sure

I just started grade 10

And I'm in top set

[brazen hare]

you dont recognise anything similar to it?

[granite bramble]

And they didn't teach us 😔

[brazen hare]

okay since it's your first problem with it, i'll give you the equation.

[granite bramble]

No

I'm absolutely clueless

[warped urchin]

maybe take the distance between C and E divide by 3 then times by 2 then create a circle at C with that radius and solve for the leftmost intersection between the circle and the pink line

[granite bramble]

What

There's no circle

But ik the dividing by 3 and multiplying by 2

[warped urchin]

im just saying you can construct one to solve the problem

[brazen hare]

this is way too complicated than it needs to be

[granite bramble]

I'm a noob

🥺

I'm gonna shower rq

[warped urchin]

unfortunately im a circle glazer

[odd edge]

@granite bramble Has your question been resolved?

[granite bramble]

@brazen hare I'm done showering

Give me the equation mush 💔

Nvm I figured it out

You can close this btw

@brazen hare

[ember oak]

.close

[odd edge]

Channel closed

Closed by @ember oak

Use .reopen if this was a mistake.

[odd edge]

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.

[onyx jay]

could i get help with this problem? i know that i have to make a diagram of some sort to solve it but im not sure where to start

2. John was travelling to B city via A town. At 10:30, he noted from a road sign that A town was 105 km away and B city was 155km away. At 12:30, he stopped for lunch at a place midway between A town and B city. At what average speed did John travel before he stopped?

[bronze canyon]

do you know how distance time and speed relate to each other?

also, we dont have to make a diagram to solve this, but if you do, im assuming you want the plot of distance and time

[odd edge]

@onyx jay Has your question been resolved?

[onyx jay]

hmm ok

so he uh

so he sees the sign at 10:30

then 2 hours pass and he stops in the middle of the two places

[bronze canyon]

wait

[bronze canyon]

first we should write out all the formulas we need

just so we know what were looking for

[onyx jay]

we need to find avg speed i think