help-33

[ivory turtle]

It's a stupid question imo

[still temple]

but it isnt an isoceles triangle

[ivory turtle]

I would just answer it cannot be determined

[still temple]

so that wouldnt work

yeah

there is no way there r similar

[solid dock]

Who made this? They fucked up the wordng

Its supposed to be not congruent

[still temple]

is it somehow similar

[solid dock]

Yeah its similar i would say but I sold going through geometry

Nevermind

You're correct

Not similar

[ivory turtle]

How is it not similar?

[still temple]

idk bc if u were to have segments

TS/DF

[solid dock]

I thought it was a dilatation but one side is a little too big

[still temple]

AND SU/FE

or wtv

it wouldn't be the same

making them non congruent

[ivory turtle]

22/33 is not the same as 22/33?

It's asking for similar, not congruent

[still temple]

also 23 does not equal 22 and22

[still temple]

i meant

[ivory turtle]

Ah wait

[still temple]

22/33 23/33 r not the same

[ivory turtle]

I see it

That one side

Is 23

[still temple]

yeee

[ivory turtle]

Mbmb

[still temple]

dw dw

js making sure

[ivory turtle]

I'm on phone so it's small 😭

[still temple]

LOL

thats my guess ngl

the triangles say 62=24 so no

[solid dock]

Not similar correct

[ivory turtle]

But what if it's the other angle?

[solid dock]

Triangle ABC doesn't have an angle 24

Only 98, 62,20

So

[still temple]

i mean

according to AA

[ivory turtle]

Yes I know, but you can't just conclude that 62 is not 24 so not similar

You've gotta make that extra step

[solid dock]

Ah mb

[still temple]

it would seem like the missing angle is different

98+62=160

so x+160=180

but for the other one 24+98=122

so x+122=180

i don't think both would be the sane

.close

[marsh citrus]

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[unkempt herald]

help

R is circumradius

i figured that angle AOB s 90

but idk what to do with it

,cloe

.close

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[scenic quartz]

can yall explain sss sas asa aas and hl to me in drawings or something

[scenic quartz]

cuz i lwk be forgetting them everyday

<@&286206848099549185>

[idle ridge]

The S stands for side and the A stands for angle

[scenic quartz]

yea ik that

[idle ridge]

When you're using the SSS rule, that means you have two triangles where the side lengths of the one match the other

And if so, you can conclude they're congruent

[scenic quartz]

yeah

the o thers got me confused

sss the easiest

ig

[idle ridge]

alright

for reference, here's a pic of sss

now with sas, we have two sides and an angle between them

that would be like if we knew the two side lengths before, and also that these two red angles are equal

if that's the case, then we can conclude by the SAS rule that these two triangles are congruent

make sense so far? @scenic quartz

[scenic quartz]

yeah

[idle ridge]

Alright ASA is basically the opposite, you have two angles and one side between them

[scenic quartz]

ok

[idle ridge]

so like this

you got the blue angles matching, the red angles matching, and the side in between them matching

so you can use the ASA rule to say that these two triangles are congruent

[scenic quartz]

yeha

[idle ridge]

alright, do you feel like you get how AAS works too?

[scenic quartz]

i think

so

[idle ridge]

alright

and then HL is the only one that's not As and Ss

Because it only works for right triangles

But basically if you know two triangles are both right triangles

And they have a matching hypotenuse and leg

Then they're congruent

[scenic quartz]

how would i know which one when im proving

like for example

this

i just found it on the web

[idle ridge]

so this is HL

[idle ridge]

It depends on what info you have available to you

Like for example, in this one, you know RS and QU are the same length

so that's good

you also know TR and TQ are the same length

bc QRT is equilateral

and ST and UT are the same length bc T is the midpoint of SU

so given all that information, which rule do you think it is?

[scenic quartz]

sss?

[idle ridge]

yup!

[scenic quartz]

i dont see an angle lol

[idle ridge]

yeah exactly, we got three sides

that match

so it's SSS

it's all about just figuring out what info you know, and then from that, you can tell what rule to apply

[scenic quartz]

but like sometimes the answer is sas or asa but i dont even see an angle 😭

[idle ridge]

can you give an example

[scenic quartz]

yeah lemme findo ne

find one

this except the angle congrunecy wasnt there

and the line congruency wasnt there iether

[idle ridge]

There's gotta be some pair of matching angles in order to use SAS or AAS or ASA

You mighta just missed it

[scenic quartz]

oh

[idle ridge]

in this one tho, it's SAS

[scenic quartz]

i think BM and MC were congruent then

and AM AND MD were congruent

[idle ridge]

yup

and then

you know that angle AMB is the same as angle CMD

[scenic quartz]

but we didnt know AB and CD was parallel

[idle ridge]

yeah that's what you're trying to prove here

[idle ridge]

but you know this because they're vertical angles

do you know about vertical angles?

[scenic quartz]

yeah

[idle ridge]

okay yea

[exotic osprey]

oop too late nvm

[idle ridge]

Exactly ^

[scenic quartz]

how would i do that question for a two column proof then

cuz we gotta do everything as a two column proof

[idle ridge]

Alright so

[scenic quartz]

so like i would say segment BM and line MC

are congrunet

and line AM and MD are congruent

[idle ridge]

Yea, segment BM is congruent to segment MC because M is the midpoint of BC

Yup exactly

segment AM is congruent to segment MD because M is the midpoint of AD

[scenic quartz]

and then i would say ABM and CDM are vertical angles?

[idle ridge]

yup

except you named them wrong

it's AMB and DMC

those two are vertical angles

[scenic quartz]

i didnt know it mattered 😭

[idle ridge]

okay well

the one that matters the most is the letter in the middle

that's the letter where the angle is located

[scenic quartz]

oh

ight ight

[idle ridge]

here, the angles are located at M

but we can't just say angle M

because there's multiple angles that are located at M

so we gotta be a bit more specific

and say angle AMB and angle DMC

you could also say like angle BMA and angle CMD

[scenic quartz]

oh so this one is SAS? cuz segment AM and then angle M and then segment BM?

[idle ridge]

that would be the same thing

[idle ridge]

yessss

[scenic quartz]

ooh

ight

lemme find another one lol

could u work me through these 2

they the hardest i could find lol

so for the first one we would say segment UW and UY are congruent becuase its given

and then WZ is congruent to YV?

idk why tho

@idle ridge

[idle ridge]

sure lemme see

[idle ridge]

why do you know that?

also, it seems like you're given that angle W is congruent to angle Y, right? or at least that's what the diagram looks like

[scenic quartz]

yeah

[scenic quartz]

idk im guessing lol

[idle ridge]

Lol

so we got one angle and one side

we need one more thing

but luckily both of these triangles share angle U

and angle U is congruent to itself, right?

[scenic quartz]

oh so reflexive property right

or osmething like that

[idle ridge]

yup!

so then what rule do we use

[scenic quartz]

so asa?

[idle ridge]

yup

and that finishes off the proof

[scenic quartz]

ok ok

the second question looks kinda tough

[idle ridge]

yeah it does

let's take a look

are you sure this is a question about congruent triangles lol

[exotic osprey]

looks like angle chasing

[scenic quartz]

idk lol

[exotic osprey]

im tryna do it and its a pain

[scenic quartz]

i serached up congruent triangles proof questions

[idle ridge]

xD

[scenic quartz]

lemme find another then

[idle ridge]

yeah I'm not sure this one is about congruent triangles

[scenic quartz]

so ac congruent to bc

cd is congruent to cd cuz its bisector

ad is congruent to bd

sss ig

cuz there are no angles

[idle ridge]

yup, sss

[exotic osprey]

oh i found a proof for ur second problem but yea its a lot of just angle chasing

[idle ridge]

because reflexive property, not because it's the bisector

[idle ridge]

and this one is bc D is the midpoint of AB

[scenic quartz]

oh

[scenic quartz]

what is angle chasing lmao

[exotic osprey]

you're trying to prove that R=T so the play is just to find as many other angles as possible using properties like how triangles add to 180

[scenic quartz]

do u got alot of time rn @idle ridge or @exotic osprey

cuz i kinda wanna reviwe like 6 questions

or 9

if yall got time

if yall dont its fine

[idle ridge]

I prob gotta go, sorry

[scenic quartz]

yeah its fine

@exotic osprey can u

or na

[exotic osprey]

maybe a couple problems

[scenic quartz]

ok ok

ty

[exotic osprey]

i hate two column proofs tho so i might not know the names of identities lol

[scenic quartz]

same

so this one

ab is parallel to cd

ab is congruent to cd

cb congruent to cb

sss ig

no angles?

[exotic osprey]

SAS

[scenic quartz]

whatt\

[exotic osprey]

because they're parallel, ABC=DCB

[scenic quartz]

wheres the angle 😭

[exotic osprey]

angle ABC

and angle DCB

[scenic quartz]

its not shown tho

how can we say its an angle?

oh

wait

im dumb

nvm

[exotic osprey]

just because they didn't give angles doesn't mean there aren't equal angles (also it's not SSS because you dont know that AC=BC)

[scenic quartz]

sorry

yeah

[exotic osprey]

np

[scenic quartz]

so sas

[exotic osprey]

yea

[scenic quartz]

so j and m are congruent

jk and km are congruent

their vertical angles i think

so

[exotic osprey]

small thing you don't call angles congruent

[scenic quartz]

oh

[exotic osprey]

but yea

[scenic quartz]

do i just say equal

[exotic osprey]

wait nvm

[scenic quartz]

what

i call them congruent or na

[exotic osprey]

you can

[scenic quartz]

ok

[exotic osprey]

ive just never heard it being called that often but you can

[scenic quartz]

lol ok

can we asumme k is the midpoint of nl or no

[exotic osprey]

nop

[scenic quartz]

dang

that woulda been easy

[exotic osprey]

but you have enough here

H=M, vertical angles for K, and the midpoint

[scenic quartz]

asa

[exotic osprey]

yea

[scenic quartz]

cuz k is also an angle on both sides right

or something like that

[exotic osprey]

lowkey you can also just say they both equal 180-J-K

u dont even need congruent triangles

[exotic osprey]

but yes

[scenic quartz]

what

[exotic osprey]

ASA

[scenic quartz]

wdym

[exotic osprey]

because vertical angles

wait wait

one sec sorry

[scenic quartz]

its fine

[exotic osprey]

yes

ur right sorry

[scenic quartz]

ok ok

[exotic osprey]

i keep misunderstanding the problem lmao

[scenic quartz]

lol

[exotic osprey]

but ASA

[scenic quartz]

so x is congruent to w

xt is congruent to tw

xz is congruent to wz

so sas

[exotic osprey]

yea

there are a couple ways to do this

that's one of them

[scenic quartz]

ok

[exotic osprey]

you can also see that ZT is shared, T=90 on both sides, and X=W so AAS

[scenic quartz]

oh 😮

but i would get it correct if i said sas

right

so bc congruent to dc

ac congruent to ac

[exotic osprey]

ya

i think

[scenic quartz]

i think this is

[exotic osprey]

idk if you'd be asked to prove XT=TW but you shouldnt be

[scenic quartz]

sas?

ok

[exotic osprey]

acutally you might

[scenic quartz]

wait why

[exotic osprey]

the problem might be asking you to solve it without knowing that XT=TW for isoceles triangles

[scenic quartz]

i think since its midpoint

or does it not sya midpoint

[exotic osprey]

it doesn't specify the midpoint

[scenic quartz]

oh

:/

[exotic osprey]

and the proof for proving XT=TW uses congruent triangles kinda lol so it's circular

[scenic quartz]

lol

[exotic osprey]

but ur mind is in the right place

[scenic quartz]

ight ight

[scenic quartz]

this is sas right

or am i tripping

[exotic osprey]

yea

because of the angle bisector specifically

[scenic quartz]

yea

since it makes angle?

at the top

at like

[exotic osprey]

C

[scenic quartz]

c

yeah

[exotic osprey]

yea it makes two identical angles

[scenic quartz]

would this be hl theorem

or no

since it doesnt say its a 90 degree angle

[exotic osprey]

nah you cant

because the same conditions are true for parallelograms

[scenic quartz]

so i would say

ad is congruent to bc

and then ab is congruent to dc

db is congruent to db

so its aas?

[exotic osprey]

where does it say it's parallel

[scenic quartz]

i mean

i kidna just assumed lol

[exotic osprey]

🤔

[scenic quartz]

forget i said that

[exotic osprey]

i mean you have three sides that are congruent

[scenic quartz]

its aas tho right

[exotic osprey]

no

[scenic quartz]

😭

[exotic osprey]

you have 3 congruent sides

sooo

[scenic quartz]

what

[exotic osprey]

SSS

[scenic quartz]

ohhh

cuz. the hypotenuse thing

is also a side

thats equal

right

[exotic osprey]

^

[scenic quartz]

yeah

[exotic osprey]

yuh

[scenic quartz]

can we do 3 more

or 2

[exotic osprey]

yea

[scenic quartz]

ok ty

these 3

last 3

ok so for the first one

bc congruent to dc

ac congruent to bc??

wtf

ok

so

then

[exotic osprey]

E

EC

[scenic quartz]

it says bc 😭

whatt

[exotic osprey]

no

E

[scenic quartz]

oh wait

im blind

sory sory

[exotic osprey]

np

[scenic quartz]

ok so

ac is congruent to ec

bc is congruent to dc

its vertical angles

so c ameks an angle

so sas

[exotic osprey]

mhm

[scenic quartz]

ok

next

jk congreunt to lk

jm congruent to lm

km congruent to km

what

its like

sss

i think

cuz there arent angles i can find

[exotic osprey]

i mean

u have three sides

and they're equal

what else are you looking for?

[scenic quartz]

so sss?

yeah idk

[scenic quartz]

idk

[exotic osprey]

i mean yea

SSS

[scenic quartz]

ok

last one

[exotic osprey]

whenever you have three sides u dont need anything else lmao

[scenic quartz]

lol alr

g and j are congruent

fh bsiects gfi

asa

ig

[exotic osprey]

that's an I

[scenic quartz]

since the bisector makes angles

[exotic osprey]

no

[scenic quartz]

what

???

[exotic osprey]

how is that ASA

[scenic quartz]

wait l

lemme rethink

aas?

idk tbh

this one kinda confusing

[exotic osprey]

ur here right

wait the pic didnt send

[scenic quartz]

aas?

[exotic osprey]

mhm

[scenic quartz]

yea

ok

i was thinkg asa

cuz i assumed gh is congurent to ih

but alr

ty for helping me

[exotic osprey]

yea np

[scenic quartz]

imma close it now

[exotic osprey]

sounds good

nice work

[scenic quartz]

thanks

.close

[marsh citrus]

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[marsh citrus]

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[graceful rover]

Hey I got this matrix and i have to calculate the characteristic polynomial, -lambda^3 + 6lambda^2 - 12lambda + 8, ngl i dont remember ever solving polynomials of the 3rd degree or above by hand, so i just did it by guessing one solution and doing polynomial division, is there a cleaner/better way to solve them? Because I got a remainder (which means there is no solution other than 2). So I just want to know if there is a more elegant solution than guessing and doing the division

[marsh citrus]

@graceful rover Has your question been resolved?

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[long temple]

Hello

[long temple]

Anyone there to help

With trigonometry

???

Ok so

[runic temple]

QPS is a right angle

[long temple]

Yes

But for the length of QS what do I do

[runic temple]

use a different angle

[long temple]

?

[runic temple]

the point of trig is to look at a non-right angle of a right triangle

[long temple]

Yea

So can you explain what law to use

And how to get the length using that law

Basically an explanation

?

@runic temple

<@&286206848099549185> I would really appreciate if anyone would come help

[dire wagon]

I believe you use the law of cosine

[long temple]

Can you explain how to get the length of segment qs

In the first question

[dire wagon]

However if you notice one of the angles is 60

So the other side should be 60

So the top one should also be 60

That means its a equilatral triangle and all the sides of the triangle have 10

[long temple]

It’s not equilateral though

[dire wagon]

And since qs is just 2 of those sides its just 10+10

Angle of P and Angle of S are the same

And since all angles of a triangle add up to 60 the last angle on top must also be 60

Same angles on triangle = equalitral triangle

[long temple]

No but

[dire wagon]

You believe angles P and S arent the same?

Well if you insist, you can go the longer route and use law of cosine

[long temple]

Ok

They aren’t the same

Angle t is less than 60 degrees

[dire wagon]

Though u cant use law of cosines cus theres only 2 given variables

Meaning noticing angles P and S are indeed the same angle and finding the triangle is equalatril is the intended route

[dire wagon]

One of the first things teachers tell you is the diagrams arent to scale

Or it will you know... be too obvious

Defeats the purpose ya know

[long temple]

Ya

[dire wagon]

But if you feel relunctend to believe me you can ask for another helper, though i doubt theyll say anything different haha

[long temple]

So what do I do?

No it’s nothing like that

It’s just angle t looks visibly different

Even when they aren’t to scale

So yes

[dire wagon]

Angles p and s are the same angle 60, the top angle then should be 60 becauss it has to add up to 180. 2 steps done so far.
Then just find out both sides for qs are 10 and add up to 10+10

[long temple]

Helpers

<@&286206848099549185> I would really appreciate if anyone came to help

Anyone?

[dire wagon]

Its pretty late here in est, some might be sleep at this time

[long temple]

Yea I’m in wst

So yea

[lone hare]

where are you stuck on

[dire wagon]

@long temple

[lone hare]

ST is 10 yes?

so triangle PTS is isosceles and so angle PST is 60°

[long temple]

Yea

Well I don’t know yet what st is

All I know is the length of rt

And pt

[lone hare]

do you agree that diagonals bisect each other

[long temple]

Yes

[lone hare]

and that the diagonals have the same length

[long temple]

Yea

[lone hare]

so half of a diagonal is 10

?

[long temple]

So you’re saying st is 10

?

[lone hare]

ye

[long temple]

Ok for the first question

So now

For the second

For finding area of pqr

[lone hare]

.

[lone hare]

.

[lone hare]

.

[marsh citrus]

@long temple Has your question been resolved?

[marsh citrus]

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[fossil coral]

How do I find the constant term in the expansion of (2x-(1/x^3))^4

[gentle sentinel]

We can express binomial expansion as

Sigma(n choose k × first term ^ k × second term ^ n-k)

We know the constant term won't have any x

So it must be when the first term is ^ 3 and second term ^ 1

So k is 3

And our constant term is 4c3 × 2^3 × -1

So -32?

I think

[upbeat sable]

Yeah, but giving answers directly is not encouraged here

[fossil coral]

Right, so there would be two answers depending on which term you choose to be the first? (y+x)^n = (x+y)^n ?

[upbeat sable]

No. Both the expansions will be the same

[fossil coral]

I see, can you tell me what I did wrong here then?

[upbeat sable]

Nothing, r=1 is correct

Now plug in r=1 and find the constant term

[elfin berry]

quickdoom

[upbeat sable]

Which is also the answer given by ronush

[fossil coral]

Right, but with different r

Why was his r 3 and mine 1? How we ordered the terms?

[upbeat sable]

Are you aware that $^{n}C_{n-k}=^{n}C_{k}$?

[elfin berry]

quickdoom

[fossil coral]

Right… symmetry in pascals triangle

[upbeat sable]

Yeah, thats why he got 3

[fossil coral]

I get it now I think, thanks

[upbeat sable]

But your answers were both the same

(-32)

You dont get two different answers here

[fossil coral]

Great, I see

Thanks

.close

[marsh citrus]

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[gentle sentinel]

Sorry, mb

[marsh citrus]

@gentle sentinel Has your question been resolved?

[marsh citrus]

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[sand sparrow]

Function y=f(x) is an even function with the given period 6, if f(96)=2
Find
f(-96)+f(-90)+…+f(-6)+f(0)=?

[vernal forge]

hint 1: ||f is even, so f(-96) = f(96)||

[sand sparrow]

im a bit confused about the concept of period

Does it mean f(-90) is also 2 ?

So, to know how many times 2 shows up from -96 to 0, is it logical to divide 96 by the period 6?

ah so f(0) is also 2

so does that mean i just have to not forget f(0) is being left out when dividing 96 by 6?

[mild perch]

I don't see how the function being even matters

Seems like extra info

Since -96=96=0 (mod 6)

[mild perch]

A function f has period 6 if f(x)=f(x+6) within it's domain

In another words x=y (mod 6) implies f(x)=f(y)

[marsh citrus]

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[marsh citrus]

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[placid heath]

i need help

[placid heath]

im trying to do this for revision but i dont understand

[ivory turtle]

which one?

[placid heath]

all

[open kayak]

Focus on one of them first.

E.g. 5)

Do you know what acute means?

[placid heath]

Yes

[open kayak]

Now just try to express what it says using alpha and beta

[placid heath]

okay

and then?

[open kayak]

Well you will be able to solve for alpha and beta

Well, atleast you can think of one more equation that always holds in a triangle that lets you solve for them

[lucid turret]

which one are you doing ?

[open kayak]

She's doing 5)

[lucid turret]

Okay

[placid heath]

Ty

[marsh citrus]

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[unkempt herald]

help

S^(2n+1)=(xn^(2n+1))+(xn-1^(2n+1))+............(x1^(2n+1))

[fathom ridge]

can you use these: () {} []

[unkempt herald]

kk

[fathom ridge]

also whats sigma

wait this still doesn't make sense

[unkempt herald]

so consider a polnomial

[fathom ridge]

^ is exponent

[unkempt herald]

yeh

[fathom ridge]

_ is subscript

[unkempt herald]

there is no sub script

sigma1 is like the sum of roots

[fathom ridge]

[ S^{2n + 1} = xn^{2n + 1} + x(n - 1)^{2n + 1} + x(n - 2)^{2n + 1} \cdots x(1)^{2n + 1} ]

[elfin berry]

neon

[unkempt herald]

sigma 2 is sum of mul of 2 roots

[fathom ridge]

Uh

[unkempt herald]

and so on

itrs like vietas formula

should i explain more?

[fathom ridge]

I'll just wait for someone else to help you

Because nothing is making sense to me

😭

[unkempt herald]

😭

can anyone help?

[unkempt herald]

.

.close

[marsh citrus]

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[unkempt herald]

.reopen

[marsh citrus]

✅

[unkempt herald]

this needs more brain

anyone have more than me

that could help my puny brain solve this

[finite glacier]

this makes S_n seem like a linear function

where does sigma 3 come from

isnt there only 1 root, x=0

[unkempt herald]

wait i made erroe

add another x0 to the thing

[ S^{2n + 1} = xn^{2n + 1} + x(n - 1)^{2n + 1} + x(n - 2)^{2n + 1} \cdots x(1)^{2n + 1} +x(0)]

why aint it doing the thing

[finite glacier]

is the first term x * (n)^(2n+1) or (x * n)^(2n+1)

[finite glacier]

you need $$

$1$

[elfin berry]

KINGRel

[unkempt herald]

the nth term is xn

as in subscript n

[finite glacier]

oh

[unkempt herald]

oh my gof

god

[finite glacier]

ok

i see

[unkempt herald]

i messed up explaining the q

sorry neon

i didnt mean to

sooo...

ummm...

my bad

🫥

ill start fresh later

.close

[marsh citrus]

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[unkempt herald]

srry again

[marsh citrus]

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[unkempt herald]

5. Find the sum of series
   5+3^x+6x^2+8x^3+11x^4+13x^5+16x^6+18x^7+21x^8..... to infinite
   terms where |x|< 0.

[unkempt herald]

help

[lucid turret]

innite?

[unkempt herald]

sorry

[lucid turret]

okay np

[unkempt herald]

the thing became weird

[devout mauve]

|x| < 0 makes no sense

split it up into a few different series

[unkempt herald]

how?

[south smelt]

< 0 means it have to be negative, but you‘re taking the absolute value, so it can‘t. Essentially you can‘t plug a single x that makes |x|<0 true

[unkempt herald]

thats what im not getting

[novel juniper]

|x| is always greater than or equal to zero

The problem is wrong

[unkempt herald]

yeah

[runic temple]

also what the heck is the pattern of coefficients

[unkempt herald]

is it an error

if u take 3x+8x^3 and so on

u get pattern

[runic temple]

oh right

[unkempt herald]

and 6x^2+11x^4 so on

maybe they meant |x|>0

[runic temple]

then thats just all real numbers

[south smelt]

And the thing doesn‘t converge anymore

[runic temple]

if this is a silly troll problem where they meant |x| <= 0, the answers 5

[unkempt herald]

can it be solved after

yeah thatd be nice

but im pretty sure its not

[crude burrow]

Maybe they meant |x|<1

[unkempt herald]

hmm

[crude burrow]

Because if |x|≥1 the series diverges

[unkempt herald]

yeah

but wth |x|>0

we could use arithemetico gerometric formulae

[crude burrow]

But the coefficients are weird to work with lol

[unkempt herald]

no if we take alternate ones they are in AP

like3,8,13 and so on

and 6,11,16 and so on

[lucid zenith]

Yeah that’s the idea

[unkempt herald]

5 is just the odd one out

[lucid zenith]

It’s supposed to be |x|<1

[unkempt herald]

which can be added later

[lucid zenith]

It’s just a sum of two arithmetico geometric series

[unkempt herald]

why <1

[lucid zenith]

Because for |x|>=1 the series diverges

[unkempt herald]

wdym

what does it diverges mean?

[lucid zenith]

A series diverge if either the sum goes to infinity or doesn’t converge to any value

[unkempt herald]

ohh

[lucid zenith]

here it’s the first case, for |x|>=1 the series will tend off to +- infinity

[unkempt herald]

right

[unkempt herald]

ahh...

makes sense

so how does the soln end

i use that super wierd formula

and then calc?

thx

got the answer

well didnt calc but on final step

thx

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[ancient elm]

.close

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[forest scarab]

How to get the 2nd eq from the 1st?

[fickle compass]

ur just basically equating the denominators here

like multiplying and dividing the a/something term by (b-c) and also by (-1)

[marsh citrus]

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[forest scarab]

Could you please elaborate? I don’t seem to understand how to do it.

[forest dune]

the common denominator is (a-b)(b-c)(c-a)
aleast 2 of them are in every denominator
so you gotta multiply the numerator with the 1 denominator that is not there outta the 3, with the respective minus signs

[marsh citrus]

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[inland prawn]

so by quotient rule

there is a problem in simplifying the expresion

[young cairn]

write the top as sinx-(x+1)(sinx)-(x+1)(cosx)

group the sinx together

[inland prawn]

give me asec

[young cairn]

sinx(1-x-1)-(x+1)(cosx)

and then you see

[inland prawn]

thanks

.close

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[south goblet]

hey does anyoone know why this hold, it's not the geometric series right?

[brave marsh]

It's a finite geometric sum.

[devout mauve]

ignore the 1+ at the start

instead of the 3 write some variable like x

write out the sum

then multiply both sides by x-1

[south goblet]

ooh is this a taylor series?

[devout mauve]

well the geometric series is the taylor series of a function. but that perspective doesnt help here

[south goblet]

but I sitll don''t understand

how did he get it

[devout mauve]

have you done all the steps I wrote

[south goblet]

I am doing it now

[south goblet]

wait I wanna know hwo to get it if u on;y know the left side

like the right side is unknown yet

u still here?

[devout mauve]

call the sum S

then given that each term in the sum is the previous one multiplied by x, you might be motivated to multiply S by x

[south goblet]

oh I think I remembered this and then u have S_n-1 or smth

[devout mauve]

then you get nearly the same thing as S back

[south goblet]

but I remember it vaguely

[devout mauve]

subtract S from xS

simplify

[south goblet]

I get x^n - 1

I see it

u divide by x-1 too get S back

[south goblet]

thanks

[devout mauve]

yw

[south goblet]

do u also know aboout recurrence relation?

[marsh citrus]

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[torpid marlin]

sorry the work is all in black

I am looking for someone to check this

cause idk

I always doubt my answers lmao

[ivory turtle]

,w tan^-1(18/15)

[elfin berry]

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[ivory turtle]

,w tan^-1(18/15) in degrees

[elfin berry]

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[ivory turtle]

yeah its right

[torpid marlin]

thank

woops

[ivory turtle]

xd

[torpid marlin]

that is a different problem I'm doing rn

it automatically copy and pastes my snips so I sometimes randomly paste them

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[harsh pumice]

So for this one I think its three but im not too sure. I started by locating the points I got (-5, -4.) and (-3, 4.)

[harsh pumice]

With these points I determined the y interceptr

wrote the equation

y = 1/2x+2

i eventually got y = 7/2x - 17/2

can someone please help with this i feel like im doing something wrong

[vast sandal]

so you have 3 options basically right? We can rule out 2/7 x

we can see that the y has a root < 0

is it possible for all three, that if y = 0 then x < 0?

[harsh pumice]

no

[vast sandal]

in which case is it possible?

i just noticed it's much easier to look at the y-intercept

the y-intercept is clearly positive

so you have only one option

[harsh pumice]

So I'm right

its 7 = 7/2 x * 17/2

[vast sandal]

i don't think so

also isn't that a minus?

[harsh pumice]

OH

I wrote it down wrong on my paper 😭

idk what im doing ok

let me retry

[vast sandal]

lol

[harsh pumice]

it is y = 7/2 x + 29/2

[vast sandal]

yes

[harsh pumice]

ah yers

that makes a lot more snse lol

[vast sandal]

again if you look at the y-intercept it has to be that one

[harsh pumice]

Got u

@vast sandal Would u also agree with this

im pretty sure its right cause i looked at all the points but just want double check

[midnight folio]

Just run it in desmos

[vast sandal]

why not the last one?

[harsh pumice]

ohhh

the last one does work

Thank you!

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[harsh pumice]

I'm not really sure what I'm doing wrong here, can someone help me?

[twilit sable]

Ur meant to draw the graph of those 2 eqs

Like draw y=-8/5x -4

And y=1/5 x +5

And see where they intersect

[harsh pumice]

oh okay

ugh

im still doing something wrong i hate graphs

[twilit sable]

Wait lemme check ur work

[harsh pumice]

That's what I get in demsos

[twilit sable]

For the line y=-8/5 x -4 the x intersect is meant to be -2.5

[harsh pumice]

i cant make it -2.5 on the graph i have

[twilit sable]

Umm well can you make the y instersect = -4?

[harsh pumice]

on desmos

not on my other graph

[harsh pumice]

oh

ok

got it thx

[twilit sable]

Like put the red dot there?

And at (-5, 4)

[harsh pumice]

Got u

[twilit sable]

Aighttt

[harsh pumice]

I think that worked

thanks

.cloose

[twilit sable]

Great

[marsh citrus]

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[marsh citrus]

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[austere wave]

how exactly would you do part B?

[hazy lion]

what have you tried

[austere wave]

nothing

im just stuck 😭

i know it's graph transformations but im confused

[hazy lion]

do you know what a stationary point is

[austere wave]

not really

[hazy lion]

do you have a book

[austere wave]

notebook or?

[hazy lion]

do you have access to google

[austere wave]

yes

[hazy lion]

you should look up a stationary point

because i dont trust the bot

lets see

,w stationary point of a function

CLOSE

not really

B for effort

[austere wave]

when f'(x) = 0

right

[hazy lion]

yea

lets go high-level

what kind of function is f'(x)?

can you describe it in a general sense

what does it look like

[austere wave]

wdym

[hazy lion]

well you have f(x) there

so we take a derivative of it

what does the derivative look like

f(x) looks like a polynomial

you know how to take derivatives?

[austere wave]

ye

3x^2 - 4x - 20

[hazy lion]

sure

so its a quadratic

[austere wave]

ye

[hazy lion]

and ... its concave up

not that it matters

but it has a bottom

somewhere

[austere wave]

right

[hazy lion]

okay

lets say the bottom is at ... x=a

[austere wave]

ye

[hazy lion]

so, f'(a) = 0

[austere wave]

ye

[hazy lion]

now

if i look at the graph of f'(x-a)

[hazy lion]

sorry this is innacurate

and not what i meant to say

i mean to say: f'(x) has a bottom at x=a

a minimum

[austere wave]

alright

[hazy lion]

so now imagine we plot f'(x-a)

wheres the bottom now

[austere wave]

is it just x - a

[hazy lion]

sorry, im being dumb again

https://www.desmos.com/calculator/4y807mhz80

heres what you should be picturing

so, f' has a bottom at x=2/3

then f'(x+2/3) has a bottom at x=0

it shifted it to the left by 2/3

[austere wave]

YE

caps

[hazy lion]

the exact number isnt important

what haapens with f'(x+k)

well its shifted k units left from x=2/3

mb u see where it goes

[austere wave]

ye

so when it's f(x - k) it just moves to the right k times

right?