help-10

[toxic harbor]

yeh but how do i find it

[gaunt current]

Now That's wrong

[toxic harbor]

well good thing u finally told me

[gaunt current]

$4\sqrt{2}x -10\sqrt{2} = x+3$

[toxic harbor]

let me fix it

[warm shale]

Coder decoder

[gaunt current]

$(4\sqrt{2}-1)x = 3+10\sqrt{2}$

[warm shale]

Coder decoder

[gaunt current]

Now you have to rationalise

I'll leave the rest to you

[gaunt current]

Yes

[toxic harbor]

what does rationalise mean again?

[gaunt current]

Solve for x an you get an answer multiply and divide that answer by the conjugate of the denominator

[toxic harbor]

can u belive idk what does conjuate mean

[gaunt current]

Conjugate of$ a+\sqrt{b} = a-\sqrt{b}$. Its ok

[toxic harbor]

$a+\sqrt{b} \is\ a-\sqrt{b}$

[gilded drift]

when you have something in the form a-b, a+b is the conjugate or if you have something in the form a+b, a-b is the conjugate

a conjugate is something you multiply to something in order to get a^2-b^2

if that makes sense

since (a-b)(a+b)=a^2-b^2

[gaunt current]

Exactly

Correct

[toxic harbor]

so the opposite

[gaunt current]

Yes not exactly but

Opposite is like $a+b
,,-a-b$

[warm shale]

Coder decoder

[toxic harbor]

i mean opposite signs

oppositeof + is -

opposite of / is *

[gaunt current]

a has a + as well it is $+a+b$

[warm shale]

Coder decoder

[toxic harbor]

isnt that just the opposite sign

[gaunt current]

a+b as a whole has a +

[toxic harbor]

-a-b is the opposite

[gaunt current]

Yes and a-b is the conjugate

Or b-a is conjugate

[toxic harbor]

lemme just see if theres a diff word we use here in AUS

opposite of the sign of the middle term

[gaunt current]

Australia? Do you use Americans or British English

[toxic harbor]

upgraded british

[gaunt current]

On then you call it conjugate its a standard mathematical term

Even Americans call it conjugate

[toxic harbor]

one sec lemme show u what i think it means

right?

[gaunt current]

Thats conjugate

[toxic harbor]

yes

!!!

i was low key confused i was like where did conjuction come from??

[gaunt current]

Nowhere it's a typo

[toxic harbor]

lol

[toxic harbor]

lets go back here, how do i solve for x

do i do 2sqrt2 x-x?

[gaunt current]

Divide by $(4\sqrt{2}-1)$

[warm shale]

Coder decoder

[gaunt current]

It'll be useless you are expected to combine the terms

[toxic harbor]

uhhh why?

[gaunt current]

You need to divide both sides by say c and cx= b. Then writing ax+dx= b is not helpful

[toxic harbor]

i am very confused

[gaunt current]

It'll make it worse

Leave it divide by 4√2-1

[toxic harbor]

why do i divide i see no reason to

[gaunt current]

To find x

[toxic harbor]

umean to get rid of x i need to divide?

[gaunt current]

(4√2-1) x = 3+ 10√2

[toxic harbor]

i see no equal sign

do i just spawn one in?

[gaunt current]

The last step you forgot to equate to zero

[toxic harbor]

ohh i think i get it

[gaunt current]

You do what I said at 2nd last

I think I made a typo 4√2-10

[toxic harbor]

uhh i dont think i get it

[gaunt current]

Move 3 to rhs

[toxic harbor]

ok

[gaunt current]

I think an error

[toxic harbor]

i see the error

do we need more helpers

[gaunt current]

Something is wrong

Wait it is (4√2-1/x = 3+10√2

Now divide by 4√2-1

[toxic harbor]

where did -1 come from

[gaunt current]

4√2x -x taking x common

[toxic harbor]

https://giphy.com/gifs/myemotionalsupportanimal-tired-sleepy-sleepingatwork-V7KF1ZHIdjurHIwkkp

[gaunt current]

Try pinging some helpers

[toxic harbor]

this is how im feelin rn

<@&286206848099549185>

[gaunt current]

Sorry

[toxic harbor]

we all make mistakes

[gaunt current]

I tried to help. But I had to teach you concepts from scratch

[toxic harbor]

all good

i do have the solution

wanna see it?

[gaunt current]

Anyway I think that x = (4√2-1)/(10√2+3)

[gaunt current]

Yes

[toxic harbor]

we werent even close

[gaunt current]

I think Mercury made an error

[toxic harbor]

we all do

[gaunt current]

,w (4√2-1)/(3+10√2)

[warm shale]

Results provided by WolframAlpha

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[gaunt current]

,w 8+ (11/2)*√2

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by codingdecoder

[toxic harbor]

why am i so stupid

[gaunt current]

Same for me

Am I stupid

[toxic harbor]

were stupid

[gaunt current]

Which class you're in ? Are you're core concepts clear as rationalisation is taught in 9th I our country

[toxic harbor]

11

lets say i forget alot

[gaunt current]

Ok. Then let's retry. I think you said to me that you don't want to use sin 45 is the problem

It is 1/√2

And sin 30 is 1/2

[toxic harbor]

i can do that with a calc not in my brain

[gaunt current]

They're values that are supposed to be remembered in 10th I presume

I've them affixed in my brain

Just like the formula of water is in my brain

[toxic harbor]

i wasnt in 10 methods, i was in 10 general

rn im in 11 methods

[gaunt current]

Whats that

[toxic harbor]

methods is stage 3
general is stage 2

[gaunt current]

We've mathematics standard and basic here

[toxic harbor]

let me ask a class mate

[gaunt current]

Good idea

Bye

[toxic harbor]

cya

.close

[obtuse pebble]

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[obtuse pebble]

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[edgy needle]

how would i read thsi

[edgy needle]

i have 0.75 and then do i just find when both of them line up?

[olive oxide]

first check vernier scale reading

what is the first vernier scale division coinciding with the main scale?

[edgy needle]

i think like

here

[olive oxide]

hmmm close but i would take the one just 2 to its left

like 2.7

[edgy needle]

hmm oki

wat do we do with this info

[slate island]

I think it's an physics question

[olive oxide]

do u know the least count of the vernier?

[olive oxide]

since it coincided on 2.7 it is the 27th vernier scale coinciding

so

we get Vernier Scale Reading= 27x Least Count of Vernier Scale

[edgy needle]

so just 0.01 x 27?

oh and i add it to the 7.5?

[olive oxide]

yep

[edgy needle]

sry i did 0.75 instead of 7.5

oh ok

thanks so much

[olive oxide]

7.5+ 27x0.01

=7.77

!done

[obtuse pebble]

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

[olive oxide]

no bigie :p

[olive oxide]

!done

[obtuse pebble]

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

[edgy needle]

.close

[obtuse pebble]

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[edgy needle]

.reopen

[obtuse pebble]

✅ Original question: #help-10 message

[edgy needle]

srry i have 1 more q..

is this 1.35

im getting confused because of the 5 on the left

[olive oxide]

yepp its 1.35

that 5 is there for when there is a positive zero error

[edgy needle]

whats the 15 for on the right?

[olive oxide]

<@&268886789983436800>

[olive oxide]

i think its since the cylinder has a smaller circumference they etched 2 rows of readings due to not enough space

[obtuse pebble]

@edgy needle Has your question been resolved?

[obtuse pebble]

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[desert pulsar]

Can someone help me visualise the difference between multiplying something by two and squaring it?

Like is there anyway I can visually see the difference between 2r and r^2? I know they're not the same.

[versed stratus]

,w graph 2x and x^2

[warm shale]

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[desert pulsar]

I don't know why graphing it, didn't come to mind for me lol

thanks

[stoic breach]

Take a line, length 10. If you double it, you make a length 20 line. If you square it. You make a square with length 10 each, with 100 units.

[desert pulsar]

thats another great way to put it

Thanks guys, i think my doubt is pretty much cleared now.

.close

[obtuse pebble]

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[stoic breach]

No problem.

[obtuse pebble]

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[distant dawn]

I am stuck in both

In second one I got a condition

$$1+q=\frac{3p-2}{4p-3}$$

[warm shale]

Double_mytrouble

[distant dawn]

after this I am unable to solve

[obtuse pebble]

@distant dawn Has your question been resolved?

[distant dawn]

<@&286206848099549185>

<@&286206848099549185>

[restive gorge]

Double the ping

[distant dawn]

haha. very funny. Please help

[restive gorge]

I took a look but it's out of my scope

[restive gorge]

How did you get that

[distant dawn]

found x and y in terms of p usind first 2 row

then simplified third row to y(1+q)=1

then replaced y

[restive gorge]

How does that constraint guarantee exactly one solution

I'd row reduce but it seems painful

[distant dawn]

idk where to use that

3p not equal to 2 is enough in itself that there is unique sol

idk why it is mentioned exclusively again

[restive gorge]

,w p^2x^2+4y^2+4pxy=6px+12y-9 and x^2+9y^2+6xy=8x+24y-16 and px^2+3y^2+3xy=3x+1-(q-3)y

[warm shale]

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[restive gorge]

are p and q real numbers or integers

[ prpl begin{cases} p^2x^2+4y^2+4pxy &= 6px+12y-9 \ x^2+9y^2+6xy &= 8x+24y-16 \ px^2+3y^2+3xy &= 3x+1-(q-3)y end{cases} ]

[restive gorge]

seems like you get some perfect squares

(px+2y)² and (x+3y)² at least

[distant dawn]

yeah

first two equation

[restive gorge]

Yeah no clue, where is this problem from?

[distant dawn]

idk. My teacher gave it to us

[obtuse pebble]

@distant dawn Has your question been resolved?

[distant dawn]

<@&286206848099549185>

[regal hazel]

31 or 32

[distant dawn]

32

31 I got it

after a hour

[gilded sail]

[ begin{cases} (px + 2y + 3 )^2 &= 0 \
(x + 3y + 4)^2 &= 0\
px^2+ 3 (y^2+ xy - x) + (q-3) y - 1 &= 0 end{cases} ]
From first and second equations we have
[ (3p - 2) x + 1 = 0 ]

why

[distant dawn]

你好.

[gilded sail]

I'm bad at dc latex

[distant dawn]

Relatable

[gilded sail]

nihao

[distant dawn]

Did I write it correctly 😭

[gilded sail]

yes

[distant dawn]

🙏🙏🙏🙏🙏

[gilded sail]

(px + 2y + 3 )^2 &= 0
(x + 3y + 4)^2 &= 0
px^2+ 3 (y^2+ xy - x) + (q-3) y - 1 &= 0

From first and second equations we have
(3p - 2) x + 1 = 0

[distant dawn]

Just write it in a copy and send bro. It's not worth the hassle

[gilded sail]

lol

or maybe I just leave it like this

[distant dawn]

I am stuck for 2 hours. What's 24 more gonna do...

[gilded sail]

lemme continue

[restive gorge]

You forgot the backslashes, \begin and \end

[gilded sail]

from first and second equation we have px = -2y - 3 and x = -3y - 4
we can sub into third equation
(-3y - 4) (-2y -3) + 3y^2 + 3(-3y-4)y - 3(-3y-4) -1 - (q-3)y = 0
(x,y) has unique solution if 3p \ne 2, means the discriminant is 0

ok I hate calculating it so left it for you

but here you should find what is q , then p is easy

[restive gorge]

It astounds me that we have essentially 4 variables and 3 equations anyway

[restive gorge]

,w simplify (-3y - 4) (-2y -3) + 3y^2 + 3(-3y-4)y - 3(-3y-4) -1 - (q-3)y

[warm shale]

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[restive gorge]

this is linear not quadratic

[gilded sail]

it is of course quadratic, the left hand side is quadratic

having matrix does not means it is linear

I see

[restive gorge]

You also seem to have a sign error when you completted the squares

[gilded sail]

then you need to work together with the two lines above

yeah

,w simplify (-2y+3)(-3y+4)+ 3y^2 + 3y(-3y+4) - 3(-3y+4) + (q-3) y - 1

[warm shale]

Results provided by WolframAlpha

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[gilded sail]

why is it linear anyway

[restive gorge]

What seems to be missing for me (a 4th constraint) would be that p and q are integers, then the story changes

[gilded sail]

hmm

ok it does missing something

[distant dawn]

I am back. Is the question wrong?

[restive gorge]

,w gcd(3p-2,4p-3)

[restive gorge]

Suppose p,q are integers. Then 1+q=(3p-2)/(4p-3) implies that (4p-3) | (3p-2) since 1+q is an integer. Now gcd(3p-2,4p-3)=1 so by Euclid (4p-3) | 1 => 4p-3 in {-1,1} so 4p-3=-1 <=> p=0.5 or 4p-3=1 <=> p=1

That's the only way I see it working out

[obtuse pebble]

@distant dawn Has your question been resolved?

[distant dawn]

I am gonna close it ig. I will just ask sir

Thanks y'all for trying 🙏😄

.close

[obtuse pebble]

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[obtuse pebble]

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[tulip dawn]

Guys

[tulip dawn]

What’s 6 plus 7?

[willow flax]

bud. do you have a real question?

[digital hound]

2.5 next question

[round nova]

-# please dont troll if u have an actualy question ask otherwise you should close this

[tulip dawn]

Aight mb

I was js doing a dare

[willow flax]

are @fiery olive ?

[tulip dawn]

Got 10 bucks

[willow flax]

blud. we saw that

also close this

[round nova]

whenu are done please type .close

[hardy widget]

<@&268886789983436800> troll

[olive yew]

.close

[obtuse pebble]

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[obtuse pebble]

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[white pollen]

Representing functions in power series

In blue was my first attempt, it got me +41
The red was an alternative path, where I differentiated before changed x-1 to 1-x, and in that I got that right answer by getting a -1 out

Did I miss a step in blue or is there a specific order of things I should be following?

[white pollen]

Nvm lol

Differentiating 1-x gives -1

.close

[obtuse pebble]

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[obtuse pebble]

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[fallen stag]

How do you go about isolating y in $\log_y x = x$?

[warm shale]

Quinn

[gilded drift]

change the base to something you'd like

[fallen stag]

Oh wait i figured it out

[solar meadow]

$a^b = c \iff \log_{a}{c} = b$

[warm shale]

Erebus

[fallen stag]

wait what the hell

[gilded drift]

oh yeah forgot this also worked

[fallen stag]

i dont remember learning that right expression

[gilded drift]

I was thinking too weirdly

[fallen stag]

figured it out tho

.close

[obtuse pebble]

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[clever mango]

hi!! im learning about networks right now and im confused about question 3c

[stoic breach]

Which question, OP?

[clever mango]

like what does it mean “a new path of length 20m will be built in between the reptile exhibit and the giraffe exhibit” im so confused on the wording

[clever mango]

3C

[stoic breach]

Would you mind justifying what were the answers you got for 3b, 3a?

Normally they would help to solve 3c.

[clever mango]

3a) entrance - p - s
45m
3b) entrance - l - t - m
110m

Lemme just double check that

[clever mango]

Yeah this is correct

Lowk im js confused on where this reptile exhibit is

[mystic folio]

All you need to care about is that RG has length 20 and Rcafe has length 35

[clever mango]

Thats rlly it???

Do i add the entrance distance to the giraffe exhibit too??

[mystic folio]

Add to what?

[clever mango]

Like to the distance from the entrance to the monkey exhibition

wait im confused are we not starting from the entrance anymore🤨🤨

[mystic folio]

The question is simply asking if you can find a shorter path, aka either give an example of a shorter path or prove it can't exist

[clever mango]

OHH

OH

I got it now lowk

[mystic folio]

Oh also note that R only connects to cafe and G, so for all intents and purposes all we care now is that there's is a new path of length 55 from G to cafe

[clever mango]

Yess okok

So basically this path doesnt reduce the shortest distance its actually longer

OKAYY yess i got it tysm

.close

[obtuse pebble]

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[willow folio]

my value of a+b+c = 3, but teacher's value is coming ±√3

[willow folio]

What have I done wrong?

[hardy widget]

are you sure this bit is correct?

I'm assuming you added the three equations to obtain this

[willow folio]

Yes

[ember spade]

-# genuinely need 2016 ver

hey @willow folio how are you?

[hardy widget]

yeah recheck that then

[willow folio]

Hey, I actually got stuck to that problem when I thought I finally understood 😅

[ember spade]

let me explain

[willow folio]

We take minus common

[ember spade]

do you rember multiplying?

[willow folio]

I am currently on some other part : )

[ember spade]

multiply
a(a-b)=1
b(b-c)=1
c(c-a)=1

by b, c, a

just for fun

[hardy widget]

My point was that you should have $a^2+b^2+c^2$ instead of $a+b+c$.

[warm shale]

Civil Service Pigeon

[hardy widget]

But since the help channel is getting sniped, I'll let y'all have fun

[ember spade]

you get
ab(a-b)=b
bc(b-c)=c
ca(c-a)=a

do you understand?

[willow folio]

Oh my bad

[willow folio]

Yes

[ember spade]

now add them up together

ab(a-b)+bc(b-c)+ca(c-a)=b+c+a

idk why but it may be helpful then

no now i see what to do

sum
a(a-b)=1
b(b-c)=1
c(c-a)=1

do you remember ab+bc+ca=0

now if sum
a(a-b) + b(b-c) + c(c-a) = 1 + 1 + 1

a² - ab + b² - bc + c² - ca = 3

a² + b² + c² -(ab + bc + ca) = 3

since ab+bc+ca=0

a² + b² + c² = 3

do you know formula (a + b)² = a² + 2ab + b²

now let's use it

(a + (b+c))² = a² + 2a(b+c) + (b+c)²

so
(a + b + c)² = a² + 2(ab + ca) + b² + 2bc + c²

_ _
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

again, ab + bc + ca = 0

(a + b + c)² = a² + b² + c²

but we have (a + b + c)² = 3

@willow folio do you understand all that?

[willow folio]

Wait, lemme read

[willow folio]

Okayy

But what do I do with it?

[ember spade]

you have some value squared equal to 3

what do you think?

[willow folio]

How will I get a²+b²+c²

[willow folio]

I

Ahm

a²+b²+c² = 3

Then

[ember spade]

No

[willow folio]

Am I right?

[willow folio]

[ember spade]

This

do you understand how we got this

[willow folio]

Yes

ab + bc + ca = 0

Therefore

[ember spade]

Now this, do you understand this?

and previous messages

[stoic breach]

How did you get this?

[ember spade]

few previous messages

[ember spade]

this

ab + bc + ca = 0 in our case

[stoic breach]

Ah true.

In that case then you are correct.

[obtuse pebble]

@willow folio Has your question been resolved?

[obtuse pebble]

@willow folio Has your question been resolved?

[willow folio]

Thanks @ember spade! Now I am on next problem. I haven't completed this. But I think It's not necessary. I have extracted some thinking, and put my brain a lot already.

[ember spade]

im sorry to hear this

bad part is that you doing this because video

while i do it other way, which is not so helpful

[willow folio]

Please come to next channel

.close

[obtuse pebble]

Channel closed

Closed by @willow folio

Use .reopen if this was a mistake.

[ember spade]

-# so my fault here

[obtuse pebble]

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[forest wind]

HELP HELP HELP

[obtuse pebble]

Please don't occupy multiple help channels.

[mystic folio]

You already had a help channel

[digital path]

you can try induction for 8 - (i)

[tardy epoch]

close one of your duplicate channels

[obtuse pebble]

@forest wind Has your question been resolved?

Channel closed

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[obtuse pebble]

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[abstract sapphire]

The page itself even tries to explain how to get the answered but with its wording I am failing to understand. It says to rewrite each term as it's product of primes (I assumed that meant factorization), so it shows how it can be done but the equation suddenly changes from the one shown to 8k^3+12k^2+20k.

There's more about this I don't understand but I'll start here.

[wild glade]

whats the GCF of the 3 numbers

[surreal plover]

Four

[wild glade]

yes

[abstract sapphire]

Yeah I think that would still be true for the first one but it's weird

[short crescent]

they were trying to ask OP, in order to help them.

[surreal plover]

Mb

[wild glade]

whats weird

[short crescent]

once you find the GCF, just factor it out. in other words, divide every term by that gcf and that'll be what's on the inside.

[abstract sapphire]

I understand the steps but am confused why the 4k and 32k changed to 12k and 20k. I'll take more pictures, hold on

[surreal plover]

Oh that

[wild glade]

ignore that for now
dont think thats right

[short crescent]

? show what you mean

rewriting this as its product of primes should look something like the following

$2^3(k^3) + 2^2(k^2) + 2^5 (32)$

[warm shale]

Krish

[abstract sapphire]

Ok so the primes are still the same just the og is different?

[wild glade]

I think they are using another example

to show how it works

[short crescent]

that looks like a mistake or a different example

it's trying to tell you: here is a similar problem, now apply the same logic to the one you are given.

[abstract sapphire]

Ahhhh! Cool nevermind then lol.

.close

[obtuse pebble]

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Closed by @abstract sapphire

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[obtuse pebble]

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[ebon pecan]

What is the intution behind the Lagrange method for solving a PDE?

[ebon pecan]

.close

[obtuse pebble]

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[obtuse pebble]

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[quasi escarp]

I really need help with sequence and series pleaseee.... I am really bad in it 😭

[surreal plover]

Please state your question

[quasi escarp]

Shall I send the question ?

[stoic breach]

Please do.

[quasi escarp]

Mm lemme send

First can you guys explain me the topic... If you guys are free... Please...

It's called difference method...

[stoic breach]

Well, what have your teacher taught you about it?

[quasi escarp]

Wait lemme send...

[obtuse pebble]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[stoic breach]

What's your thought, idea, or understand of it.

[slender orchid]

Oh yeah ik

[inner sierra]

we're here to help you with specific questions

[quasi escarp]

Please do explain easily 😭 🙏🏻

[inner sierra]

so like if you can give us an example question

we can try to help you

[quasi escarp]

Ik that... But it would really help if someone devotes their time and explain me this plsss

[slender orchid]

Look at the S =

[quasi escarp]

Mm I did

The topic is up and question is down..

[slender orchid]

In the 2nd line they just added a zero

Think of it like that

[quasi escarp]

? Can you come again... Wdym zero ?

[slender orchid]

Wait do you want to know the concept or
You're stuck at a question?

[quasi escarp]

Idk my teacher just yapped something and now I am stuck there in the concept 😭

[quasi escarp]

Yea I don't know the concept...

[slender orchid]

First let's understand the concept

[quasi escarp]

Mm

[slender orchid]

Let's say we have a series of n terms

[quasi escarp]

Mm

[slender orchid]

We called it "S"

[quasi escarp]

Okie

[slender orchid]

So let's say
S = a1 + a2 + a3 (and so on).....+an

[quasi escarp]

Mm I understand

[glossy shard]

wavy curve method denotions are so confusing

[slender orchid]

Now we will right this same series

[quasi escarp]

Next ?

[glossy shard]

how do i denote after ploting

[slender orchid]

But we will add a zero

[slender orchid]

Not here

[glossy shard]

wdym

[slender orchid]

Use other help channels

This one is taken

[quasi escarp]

Ooo so the empty space is 0 ?

[slender orchid]

Yes

[glossy shard]

ok

[slender orchid]

Exactly

[quasi escarp]

Okie go on please

[quasi escarp]

😁

[slender orchid]

So we just added a zero

So the series is still the same

[quasi escarp]

Okie 👌🏻

[quasi escarp]

Yup !

[slender orchid]

Adding zero changes nothing

[quasi escarp]

Yes !

[slender orchid]

So now we will just subtract it

In a different way

[quasi escarp]

Mmm like those algebraic subtraction ?

Like changing signs down ?

[slender orchid]

Wait lemme send u a pic

[quasi escarp]

Mm please that would help

[slender orchid]

We just wrote these two series right?

But in a different way

[quasi escarp]

Mm yess

[slender orchid]

Now we will subtract the 1st one from second

What will be the LHS?

[quasi escarp]

0?

Cuz S-S is 0 ?

Or am I tripping 😭

[slender orchid]

Correct

[quasi escarp]

Oo

[slender orchid]

Now be smart while subtracting the RHS

Subtract like this

[quasi escarp]

Wait 🫷🏻 it is basically like an - an-1 right ?

[slender orchid]

So
0 = (a1-0) + (a2-a1) + ..... And so on

[slender orchid]

Yes!

[quasi escarp]

Yay

[slender orchid]

And the end

[quasi escarp]

Mm

[slender orchid]

Now look carefully at the very last term

[slender orchid]

It's
-an

We just took it to LHS
Which became +an

[quasi escarp]

😮 it makes sense now

Yaya

[slender orchid]

an = (a1-0) + (a2-a1) + (a3-a2)+ ...... (an-an-1)

Yeah that's it

Now you'll probably get something useful while solving actual question from here

[slender orchid]

Now try to solve the question at the bottom with the way we derived

[quasi escarp]

.... So we subtract each term from preceding ?

I am kinda confused...

[slender orchid]

The series is
5+7+13+85....
Right?

[slender orchid]

Let's say that the series is "S"

[quasi escarp]

Mm

[slender orchid]

So
S = 5 + 7 + 13 + 85..... And so on

Now we will write the same series but add a zero in the front

[hardy widget]

.pin

[quasi escarp]

Wait lemme try and send brother...

[slender orchid]

Now just subtract like we did earlier

[slender orchid]

I missed the 31

Shit

There's a 31 after 13

[slender orchid]

5 + 7 + 13 + 31 + 85...

[quasi escarp]

Oh so we get 2,6,18,..?

[slender orchid]

Yes we get
5 + 2 + 6 + 18...

Now remember when I told you you'll get something useful after subtracting

5 + (2+6+18+ ...)

If we ignore 5

The rest of the terms are in GP

[quasi escarp]

Ooo

Common ratio is 3 ?

[slender orchid]

Yes

And don't forget the Tn and the end

[quasi escarp]

Yes sir

[slender orchid]

Yk the formula for the sum of GP right?

[quasi escarp]

I got
5 + 3^n+1 - 1

[quasi escarp]

Yup ik dw

[quasi escarp]

How do we get n ?

[slender orchid]

Check question

[slender orchid]

I think that's the answer...
They wanted it in terms of n

I think it's supposed to be

5 + 3^(n-1) - 1

Not n+1

So 4 + 3^(n-1)

[quasi escarp]

Oh yea srry

I have the option

Thank you so much

You are the god 😇🙏🏻 😭

You really helped me a lot

They should remove my teacher and hire you

Thank you so much from the bottom of my heart rlly 🙏🏻

[slender orchid]

It's not over yet tho
We have to find the sum

[slender orchid]

Yw 😭

[quasi escarp]

Ik that how to do dw

But rlly thanksss

[slender orchid]

Okay

[slender orchid]

Yw 🌚

[slender orchid]

When you're done type ".close"

[quasi escarp]

Okiee thanksss so much < 3

.close

[obtuse pebble]

Channel closed

Closed by @quasi escarp

Use .reopen if this was a mistake.

[slender orchid]

Yw

[obtuse pebble]

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[cyan lodge]

we have a conraption that looks like this

[cyan lodge]

the triangle has equal sides

and it is known that the perimeter of the pentagon in 10

we have to find its maximum area

that's all we know

[woeful pebble]

Do uk if the rectangle in the bottom is square

But either way

U can just use calculus

[cyan lodge]

I don't know that

[woeful pebble]

Let side length of rectangle be y and side length of triangle be x

[cyan lodge]

this is the furthest I got

[woeful pebble]

Yeah it's fine

[woeful pebble]

Yeyeye

Basically

U can write y in terms of x

Then, get an expression for the area

[cyan lodge]

y= (10-3x)/2

[woeful pebble]

And sub the equation for y u got

[high grotto]

Ez af by glance

ques

[woeful pebble]

Bro not everyone is euler

The goal is to learn

[high grotto]

I'm Ramanujan

[cyan lodge]

Idk man, this was the last problem on our test

if it's as easy as you say im gonna ctfo

[woeful pebble]

BRO

ITS FINE

ILL EXPLAIN IT

Did u get an expression

For the area

Of the pentagon

[high grotto]

Of complete pentagon u meant?

[cyan lodge]

is this the equation that calculates the full area?

[cyan lodge]

yes

[woeful pebble]

Yeah

And now that u have this

U have 2 choices which are basically the same

But idk if u guys know calculus

[cyan lodge]

hmmm

tell me the solution, I'll tell you if I'm following

[lime verge]

find equation of area in terms of X(side of equilateral triangle) and then A'(X) = 0 for maxima

[woeful pebble]

The most intuitive way to maximize the expression would be to complete the square and find max value of x

[cyan lodge]

what is A'(x)=0

[lime verge]

with the help of perimeter you can find the side Y in terms of X

[woeful pebble]

But if u use calculus

[woeful pebble]

Yeah u should just complete the square

[lime verge]

derivative of A in terms of X = 0 for the maxima

[high grotto]

Wsp

[lime verge]

hi

[cyan lodge]

wait a second

ohhhhh

I think I get it

so I turn this formula into a graph

[lime verge]

you know how to differentiate or you doing it without it

nvm

[cyan lodge]

y = the equation above

[lime verge]

without it

[woeful pebble]

You can do that

[cyan lodge]

and then find the tup

tip

[woeful pebble]

Yeah

[high grotto]

@cyan lodge bro

I have

The method for uwithout calc

[woeful pebble]

But u can also try completing the square

[high grotto]

See

[high grotto]

Without calc

See

@cyan lodge

Its doable for u

[woeful pebble]

Zawg

[cyan lodge]

why did you write z

[high grotto]

Heron formula

[cyan lodge]

the triangle is equal sided

[high grotto]

Equilateral

[lime verge]

rather than finding the tip via graph, just make it into a quadratic and find its vertex

[cyan lodge]

yes, english is not my first language, sorry

[high grotto]

Bruh

[woeful pebble]

Get yo brahmagupta formula Outta

[high grotto]

I thought Isoceles

[cyan lodge]

is that when two sides are equal?

[high grotto]

Yea

[woeful pebble]

Yeah

[lime verge]

yeah

[cyan lodge]

no

[high grotto]

But it's equilateral nvm

Leme do again

[woeful pebble]

@cyan lodge just complete the square for the expression u have

[lime verge]

you can actually find A(X) and then its vertex will be the final ans

[woeful pebble]

For the area

And get the value of x at which it occurs

[lime verge]

well any method works

ig

[woeful pebble]

He dk calculus

[lime verge]

no like the 2nd approach was

to find vertex

of the quadratic

-b/2a

because A(X) is a quadratic

[high grotto]

@cyan lodge yk Heron's Formula for area?

[lime verge]

no dont use heron's formula

[woeful pebble]

HOW DO U THINK U GET -B/2A

[high grotto]

Vertex

[woeful pebble]

Yeah it's a lot harder to deal with

[woeful pebble]

No like

[cyan lodge]

I think I do

[woeful pebble]

The derivation

Is the same

Ultimately

[lime verge]

thats why i said any method works

🥀💔

[woeful pebble]

IM NOT DISAGREEING WITH U VRO

[lime verge]

(except heron's formula)

[woeful pebble]

💔🥹

[lime verge]

lets not take this into consideration when i meant any

[woeful pebble]

But @cyan lodge did u get it

[cyan lodge]

yes, half perimeter minus each side's length, square root, and so on

[lime verge]

dude heron's formula will make it harder

just follow @woeful pebble

[high grotto]

Wait

Its ezier

Equi ∆ area formula

[lime verge]

yes

thats what im saying

[cyan lodge]

could you guys explain what you meant by "completing the square", I think there might be a language barrier

[lime verge]

@woeful pebble

[woeful pebble]

Like

For any general quadratic ax²+bx+c

[high grotto]

Bro try this every1

[woeful pebble]

U can express it as a(x+h)²+k

[lime verge]

let the op proceed with 1 method pls

[high grotto]

Okay

[lime verge]

hes prob doing it by the chinese dude's way

so let it continue

[high grotto]

Ig so

[woeful pebble]

I mean u seem smart so get the answer by am-gm

[lime verge]

yes

i got by am-gm

[high grotto]

Wth

Idk

Tell me some 1

[woeful pebble]

Its in inmo prep book 💔💔

[high grotto]

Bruh I'm not INMo LVL rn

Ioqm

[lime verge]

ok

find the area

the equation of area

of the entire thing

or actually create another help channel

ill tell you there

this is occupied

mb

[high grotto]

Np it's same problem

[high grotto]

Can I use above equn

[lime verge]

yes but its the op's channel

not ours

[lime verge]

#help-44｜stanley-🌲-v2-dans

@woeful pebble yall can continue

sorry bout the little invasion

[woeful pebble]

Its calm

@cyan lodge u still here?

[cyan lodge]

yes

I'm trying to find it with the -b/2a method

but the answer is a mess

[woeful pebble]

Yeah it's not gonna be pretty with this one

Unless u have an answer already?

[lime verge]

wht u getting

[cyan lodge]

the area formula

and this is the quadratic equation I get

[woeful pebble]

It appears to be correct

Is this not the answer u were expecting?

[cyan lodge]

not really

I expect something without square roots an divisions

usually is the answer in these kinds of problems

[woeful pebble]

Did ur teacher give u ans

[cyan lodge]

no

[woeful pebble]

It doesn't have to be

Sometimes theyre just like this

It's so u can deal with the numbers better

[cyan lodge]

yeah, but in the test, I have to write my own version of the answer on the sheet. If I got this answer during a test I would be hesitant to write it.

there's no a b c or d

[woeful pebble]

Yeah I get that. That's why u should check all your steps to make sure you didn't make any mistakes

[cyan lodge]

ok

[woeful pebble]

Welcome to the club fr

[cyan lodge]

so the answer is whatever the y0 and x0 gives me when I plug it in

[woeful pebble]

Yeah

[cyan lodge]

great

[cyan lodge]

Thanks alot

[woeful pebble]

NP

[cyan lodge]

hope to be able to solve it with calculus in the future

[woeful pebble]

GLAD TO HELP

[woeful pebble]

YOU WILL

[cyan lodge]

see ya

[woeful pebble]

ALR

[cyan lodge]

.close

[obtuse pebble]

Channel closed

Closed by @cyan lodge

Use .reopen if this was a mistake.

[obtuse pebble]

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• Be polite and have a nice day!

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[rocky nymph]

Heyo! I have a question regarding this exercise which i havent finished yet.
In my sketch i point the vector (1 -2 1), the normal of the plane) in the direction of the line l1, im afraid that this assumption is completely arbitrary or if it even is correct in the first place, how can i know? i didnt finish answering cause i dont want to make a mess because of a missing negative sign

[rocky nymph]

if my sketch is correct, then AFa should be the opposite of what i wrote (the same for BFb), if my sketch is incorrect and the normal actually points away from the line then my reasoning should be correct :P

my guess would be that ofcourse it depends on the position of A and B, so would i need to plug in the coordinates of A into the equation of the plane, if its >6 then the angle formed with the normal is positive and thus its above plane, meanwhile if its <6 its beneath the plane? but im not sure if this makes sense or not

anyways, if someone answers please ping me :) thanks!

[obtuse pebble]

@rocky nymph Has your question been resolved?

[pearl spruce]

Actually the orientation of the vector doesn't matter, all that matters is that the normal vector is parallel to the one that defines the plane

[rocky nymph]

<@&268886789983436800>

[pearl spruce]

Strictly speaking the same plane has infinitely many normal vectors, as long as its not a scale factor of zero

[rocky nymph]

for calculating AFa i multiply the distance between A and Fa by the normal vector (not considering the 1/sqrt(6) as it is not normalised) so do i not need to be careful on whether or not i need a negative sign?

[pearl spruce]

To be clear AFa is a distance right?

[rocky nymph]

its a vector

[pearl spruce]

Ah

[rocky nymph]

its the vector that i denote AF_A

[rocky nymph]

in this picture

sry im on mobile so its a bit of a pain to use latex

to reflect l1 across the plane i first reflect two points A and B across the plane and then build l2. The issue is when reflecting a point P across the plane i do it by finding its distance to the plane, create the vector PFp where Fp is the foot of p on the plane, and then find P' (the reflected point) by doing OP' = OP + 2PFp.

The issue is finding the vector PFp knowing only the distance from P to Fp and the afformentioned facts, i do this by multiplying the numerator of the distance (so not including the norm of the normal as it is not necessary normalized) by the normal, the issue i found is that im not sure wether or not to i need to add a negative sign as the normal of the plane is not necessarily in the same direction as PFp

but more then likely im just confusing things and there is probably a better way to finding the vector PFp

ach is alright im just in pre exam craze so im probably not making any sense

thanks anyways :)

.close

[obtuse pebble]

Channel closed

Closed by @rocky nymph

Use .reopen if this was a mistake.

[rocky nymph]

i found a better way to solve the problem anyways

[obtuse pebble]

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• Be polite and have a nice day!

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[obtuse pebble]

Please don't occupy multiple help channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[austere gazelle]

Can someone help me with these 3 questions? I tried them on my own but I don't know where I went wrong

[vestal steppe]

Hi! Actually your answer for Q14 is worked quite well, you just mixed up your functions.

[gilded drift]

-# how did you read that so fast

[vestal steppe]

Like, you are given that f(x) = 1 - 2x - 5x^2, but you instead expanded f(x) = 5x^2 - 2x - 1 for some reason

[vestal steppe]

Wat I swear it wasn't that long 😭

Don't you have to read like paragraphs for comp maths or smth

[austere gazelle]

The answer key says it's 40, even if it's a plus 1 it wouldn't make sense

[vestal steppe]

Let's first look back at your expansion

The function is

f(x) = 1 - 2x - 5x^2
Agreed?

[gilded drift]

-# I'm not smart enough for comp math I'm just a casual person nowadays + my preferred comp math is mental

[austere gazelle]

Agreed

[vestal steppe]

doubt

[vestal steppe]

Nice

[surreal plover]

<@&268886789983436800>

[vestal steppe]

How would you calculate
f(x + 2) based on this?

[austere gazelle]

Well I would turn it into [5(x+2)(x+2)] - 2(x+2) +1

Hindsight idk why I put -1

[vestal steppe]

Very close

Why [5(x + 2)(x + 2)]?

You are actually missing something here :)

[austere gazelle]

Because x squared, so (x+2) times itself

Which is (x+2)(x+2)

[vestal steppe]

Wait wait

The squared part is fine

But look at the function very closely

I'll give you a hint: what is the number in front of x^2?

In f(x) = 1 - 2x - 5x^2?

[austere gazelle]

Oh it's a -5 not 5

[vestal steppe]

There you go :)

So! What should our expression become?

[austere gazelle]

[-5(x+2)(x+2)] -2(x+2) +1

Right?

[vestal steppe]

Perfect

So, what do we get when you expand this?

[austere gazelle]

[-5(x²+4x+4)] -2x -4 +1

[vestal steppe]

Yep, go on...

[austere gazelle]

Then (-5x² -20x +4) -2x -4 +1

Ooops

(-5x²-20x -20)

Mb

[vestal steppe]

You're good

Perfect!

You seem to know what you're doing here, I'll let you finish that off

[vestal steppe]

Once you are ready;
For Q5.
What does 5^-1 mean?

,rotate

[austere gazelle]

Wait for the last question still I got -5x² -22x -19

[vestal steppe]

How'd you get -19?

[austere gazelle]

-20 +1

[vestal steppe]

uhuh

I think you are forgetting something else

[austere gazelle]

What?

Ohhjh

The -4

[vestal steppe]

Indeed

[austere gazelle]

So -23

[vestal steppe]

Perfect

So, what's the answer?

[austere gazelle]

But that is =-50 and not 40

Ts is so confusing

[vestal steppe]

Really?

Show me

[vestal steppe]

a - b - c is -50... reallllly now?

Alright

Prove it to me :)

[austere gazelle]

The question states and if f(x+2) is written in the form ax² +bx +c the value of a-b-c is blank

Oh wait

[vestal steppe]

Yep yep skip to the part where you calculate a - b - c

[austere gazelle]

I did it the wrong way

[vestal steppe]

Ooof

[austere gazelle]

I lowkey read right to left and not left ot right

[vestal steppe]

Rip

[austere gazelle]

So it's basically 45 -5

Which is 40

Okay, onto the next question

[austere gazelle]

^

[vestal steppe]

For this question, you were actually doing fine

You just didn't finish it

[austere gazelle]

Idk how

[vestal steppe]

I.e what's -2/3 + 6

[austere gazelle]

Uhmmmm gimme 1 moment for the multiplication

[vestal steppe]

Take your time 👍

[austere gazelle]

16/3

Which is = to b

I lowkey spld that one

And how do I do the last one now?

Cause like I lowkey barely understood the question

Here's the question again

[vestal steppe]

oof

[vestal steppe]

You had the right idea basically

The thing is,

[austere gazelle]

Yeah I don't deserve my 94

[vestal steppe]

What's 5^-1 equal to?

[austere gazelle]

1/5

[vestal steppe]

Nice

So

How do you calculate 5^-1/(5^-1 + 4)?

[vestal steppe]

You honestly just need a little bit more practice, and also taking your time with each question

You clearly know what you are doing

[slow wolf]

Bro it’s 1/5 divided by (1/5 + 4)

[austere gazelle]

But like since they're both to the power of negative 1 don't they literally just swap?

[slow wolf]

It’s reciprocal

[austere gazelle]

Yeah Ik that

[vestal steppe]

The thing is - there's a + 4

Whenever you have an addition term in a fraction (with no brackets), then you can't "swap" the positions of reciprocals.

[slow wolf]

Wait is it 5 to the power -1+4

[vestal steppe]

It's the same reason what 2/(2 + 3) is not the same as 1/(1 + 3)

[vestal steppe]

Yes on the denominator.

[slow wolf]

Oh then it’s different

[austere gazelle]

?

Huh

[slow wolf]

Then add the outer and inner power

[vestal steppe]

[ \frac{5^{-1}}{5^{-1}+4} ]
The fact that the $+4$ is in the denominator means you \textbf{can't} swap the terms around.

[warm shale]

Average Maths Student

[slow wolf]

The way u wrote it is confusing

[slow wolf]

Ohh it’s this

[vestal steppe]

In general, you cannot move terms between the numerator and denominator unless you are multiplying and dividing.

[austere gazelle]

Cause like 5to the power of negative 1 plus 4 is different to 5 to the power of negative 1?

[vestal steppe]

Yes

To keep things simple, addition or subtraction in the denominator is bad - it messes up a lot of things.

[austere gazelle]

Cause it's like 20/5 which isn't the same as 1/5

Rough estimate btw

I think it's roughly 20/5

[vestal steppe]

roughly 20/5 wait wdym

[austere gazelle]

Well cause like you can't swap them around because it's roughly 1/5 over 20/5 which are not the same numbers

[vestal steppe]

Ngl I'm not sure what you are saying

[austere gazelle]

🙁

[vestal steppe]

I think you might be overcomplicating this a little

[austere gazelle]

I'm trying to say that like you can't swap them cause they're not the same base

[vestal steppe]

You can't swap them because there's an addition sign 😭

[austere gazelle]

?

[vestal steppe]

You can still "swap" numbers if they have different bases

$\frac{5^{-1}}{7^{-1}}=\frac{7}{5}$

[warm shale]

Average Maths Student

[vestal steppe]

The reason we can't swap here is purely because there's an addition sign

Between 1/5 and 4

[austere gazelle]

But when I was doing a different unit we could still do the switch even when there was a +4 though

Like exponent laws unit or smth

[vestal steppe]

yeah, nope.

I mean I can always show you it calculator wise

You can see the answer to both fractions are different, so you can't "swap" them.

The reason that you can't swap them is because the swapping rule only applies when there isn't addition.

You'll see it somewhere on your index laws

[austere gazelle]

No I mean for the 5^-1/5^-1+4

[vestal steppe]

wdym about it

Like

Okay let me just ask straight up