help-10

[lunar rover]

I have a question that asks to find linear combination for w=-4,2 with u=3,6 and v=3,-1

$$\begin{cases}
& 3\lambda_{1}+3\lambda_{2}=-4 \
& 6\lambda_{1}-\lambda_{2}=2
\end{cases}$$

[warm shale]

Totalani

[lunar rover]

When I solve this im not getting the correct answer and im not sure what im doing wrong

yea

[polar fossil]

show work

[lunar rover]

sure sec

well what I did was I multiplied first one with 2

and subtracted the one below

so I got $7\lambda_{2}=-10$

[warm shale]

Totalani

[lunar rover]

wait

that is correct

what am I doing

[polar fossil]

yeah

[lunar rover]

hold on a gosh darn minute

aight we good

thanks a lot ❤️

I was being too fast I guess

.close

[obtuse pebble]

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[strange summit]

What is $\frac{dy'}{dy}$ and $\frac{\partial y'}{\partial y}$? I am doing ODE right now and I amconfused about uniqueness and existance theorem

[warm shale]

Kintiru

[obtuse pebble]

@strange summit Has your question been resolved?

[strange summit]

<@&286206848099549185>

I am doing second order ode

would this not apply to second order ode?

[obtuse pebble]

@strange summit Has your question been resolved?

[obtuse pebble]

@strange summit Has your question been resolved?

[wary bobcat]

first off, $\partial$ and $\mathrm{d}$ are just different notation for the same thing

[warm shale]

bruhh

[wary bobcat]

$\partial$ usually indicates that the function being differentiated has multiple parameters

[warm shale]

bruhh

[obtuse pebble]

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[edgy needle]

excuse me

[edgy needle]

how would i do this

[coral nexus]

well you know that AB is OB-OA

and u know that CD is OD-OC

[edgy needle]

oh

oh

[coral nexus]

then you can transpose after plugging numberes

[edgy needle]

excuse me

why is it C + B - A?

i dont understand

[coral nexus]

OB-OA=OD-OC

add OC

[edgy needle]

wait

so this is my thinking

I got -5i + 3j for vector AB

and then i have vector OC which is -1i + 0j

now im thinking

vector AB must be equal to vector CD

so i have to find what to add to -1i + 0j to get -5i + 3j

so i get

-4i + 3j

for vector OD

???

[coral nexus]

yuh that should be right

[edgy needle]

oh

did i just do my math wrong then

rip

[coral nexus]

think of it like solving for x

[edgy needle]

ok let me try again

[coral nexus]

its pretty much this but vectors

[edgy needle]

why isnt it this then

the answer is -6,3

when im getting -4,3

[coral nexus]

oh cause u didnt distribute the - to the OC

[edgy needle]

oh

[coral nexus]

it would be 1j not -1j

[edgy needle]

cuz

OD - OC?

[coral nexus]

ye

[edgy needle]

ok thnx

.close

[obtuse pebble]

Channel closed

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[edgy needle]

.reopen

[obtuse pebble]

✅

[edgy needle]

wait

so like this

question B btw

[coral nexus]

yuh

when the coords have zero in them its easier to just not include them in vector format imo

it just leaves u with the ones that u need

[edgy needle]

i like to do them just to be careful

cuz some questions are like this

[coral nexus]

also dont forget the tilde under i,j,k

[coral nexus]

fair

[edgy needle]

tilde

whats a tilde

[coral nexus]

squiggly line

[edgy needle]

whatt

why i need dat

[coral nexus]

these are 2 completely different things

[edgy needle]

do u know what to do if theres a 2 in front of it?

for part C

[coral nexus]

one is in the complex plane the other is in vector plane

[edgy needle]

ohh yes

oh ive heard about that

i cant WAIT TO LEARN THAT... 😭 fake numbers

are u serious

[coral nexus]

its really easy

[edgy needle]

oh

ok good

is it just

[coral nexus]

im assuming that ur at a little bit lower then me considering i just did that

[edgy needle]

2(OC) - 2(OG)

[coral nexus]

and complex is really easy

[edgy needle]

ohh what grade u in?

[coral nexus]

12

[edgy needle]

oh yeh im 11

haha

[rich tapir]

first time i see such thing

[rich tapir]

L

[coral nexus]

really??

[edgy needle]

is this right

[edgy needle]

shut UPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

i hate u.

[rich tapir]

i have done nothing

[edgy needle]

2 am math sessions

[coral nexus]

ye

[edgy needle]

ok thanks

[coral nexus]

but u should keep the 2 outside

[edgy needle]

what u mean outside

[coral nexus]

like 2(x+y)

[edgy needle]

oh

so

2 ( OC- OG)

[coral nexus]

ye

[edgy needle]

ok thanks

[coral nexus]

keeps it clean

[edgy needle]

how was

grade 11 for u

[coral nexus]

im not the right person to ask

[edgy needle]

wow.

are u saying

[coral nexus]

i slept in every class pretty much

[edgy needle]

ur some sort of genius

oh

[coral nexus]

is this speshialist maths or called something diff for u

[edgy needle]

oh

yes

U AUS?

[coral nexus]

perhaps

[edgy needle]

why u up so late man

[coral nexus]

holidays

[edgy needle]

same

but like

[coral nexus]

plus kdrama

[edgy needle]

its 2:31 am

[coral nexus]

oh WA things

5:31 am

[edgy needle]

u vic?

[coral nexus]

mayhaps

[edgy needle]

im moving there

to Kew

[coral nexus]

bruh

[edgy needle]

what

[coral nexus]

kew is horrendous

[edgy needle]

bruh

are u serious

[coral nexus]

nothing there

[edgy needle]

im moving there casue all my family live there

[coral nexus]

thats like a c tier suburb

[edgy needle]

bruhhhhhhhhhhhhhhhhhhhhhhhhhhh

but i like quiet

thats why i like perth

[coral nexus]

vic is the opposite

[edgy needle]

pace of life is really slow in perth

[coral nexus]

ive lived in both

very true

[edgy needle]

theres never traffic unless there was a car accident

BRO

ATAR IS SM HARDER IN VIC

[coral nexus]

its super competitive over here

and the population is like 10 times wa

[edgy needle]

yeh only 30% of students go through the atar pathway

in WA

• english is not counted if its not in ur top 4

and im bad at english

[coral nexus]

bruh

english counts for ours

[edgy needle]

even if theyre not ur top 4

[coral nexus]

i think ur just not getting the right idea about atar

[edgy needle]

^ onto ur aggregate

[edgy needle]

how so

[coral nexus]

top 4 are obvi ur main ones

and 10% of the outer subjects are taken as extra

but all subjects are still scaled

[edgy needle]

oh its not like dat in WA

[coral nexus]

oh

[edgy needle]

they ignore them

[coral nexus]

nvm then

[edgy needle]

what career path u thinking of?

[coral nexus]

uhhh

some engineering

[edgy needle]

do u think toorak or kew is better

[coral nexus]

neither💀

[edgy needle]

bruh

[edgy needle]

damn

• the atar cut offs for uni are higher in vic

im gonna die

[coral nexus]

if u dont get the req atar u can always get in through other means

[edgy needle]

true that

but i dont wanna waste 2 years of my life suffering

just to do more work to get into the course

[coral nexus]

get the atar then🤷‍♂️

[edgy needle]

true

ok thanks for the help

BTW WHAT WAS THE HARDEST TOPIC IN YEAR 11 SPEC?

last question

[coral nexus]

proofs💀

[edgy needle]

what like proving congruency and similarity

[coral nexus]

no

ill show

[edgy needle]

ight

[coral nexus]

simpler version of this

[edgy needle]

uh.................................

is that even math

[coral nexus]

its only hard cause its a newly learned topic

[edgy needle]

what is that upside down U

[coral nexus]

it just means the product of a series

liek the sum symbol

[edgy needle]

oh i see

is it similar to proving congruency and similarity

in triangles

[coral nexus]

thats not in the study design

but its good to know

cause there have been a few questions in the year 12 book that req u to know that for some reason

bruh

can laways drop in year 12 to further

[edgy needle]

but all the kids in my cohort weere choosing it

i got inspired

[coral nexus]

so ur a sheep?

[edgy needle]

wow.

ok

[edgy needle]

WHY BRUH

?

im learning ahead and vectors isnt too bad

[coral nexus]

learning ahead is cool for the right course

what course u going for btw?

[edgy needle]

for uni?

[coral nexus]

yuh

[edgy needle]

uhh

corporate law or electrical engineering or software engineering

[coral nexus]

spesh is like very useless for those engineerings

[edgy needle]

but its a prereq

at my uni

[coral nexus]

??????????????????

[edgy needle]

ou the WA one

[coral nexus]

if ur moving to vic then no

u dont need

[coral nexus]

oh its not req its either or

[edgy needle]

no they make u do a course

[coral nexus]

but ur doing all of them

[edgy needle]

in 6 months

if u dont do it

[coral nexus]

oh thats dumb

[edgy needle]

ikr

so why do that

[coral nexus]

u perma moving to vic?

[edgy needle]

when i can just do over 2 years

yeah unless my dad gets another job change

they wanted us to move to paris

oui oui

[coral nexus]

alright then youll have a bit more space to breathe

[edgy needle]

do u know st catherines school

[coral nexus]

u can add me if u want so we dont keep taking up a channel

[edgy needle]

yeah

[coral nexus]

ye

[edgy needle]

ok thanks anyways

ima do more work

[edgy needle]

is it godo

good

im going st catherines brothers going st kevins

bc hes already going to an edmund rice school in perth

[coral nexus]

its okay from what ive heard

[edgy needle]

ok thanks👍👍👍

.close

[obtuse pebble]

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[mystic finch]

just checking if there is a better explanation

[mystic finch]

<@&286206848099549185>

[fickle turret]

A better explanation than what?

[mystic finch]

what i alr have

as an explanation

[fickle turret]

And what do you already have?

[mystic finch]

i said according to the sum to infinity formula, for increasing values of n, r^n will converge to 0 making the formula a/1-r in which this will only occur when |r| < 1

[mystic finch]

.

tryna see if theres a better explanation for it

bruddah this is taken up

[dull nova]

Oh sorry I’m new

[mystic finch]

np

[dark stirrup]

!15m

[obtuse pebble]

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

[rich tapir]

did you use ratio test?

[fickle turret]

So you are looking at the formula for the partial sums to n and arguing that they don't converge

That's a fine explanation

[mystic finch]

ye basically that r^n for increasing values of n will converge to 0 when |r| < 1

taking place only when |r| < 1

alr thanks

[fickle turret]

Yes

[mystic finch]

appreciate it

[fickle turret]

That's already pretty good. Faster would be to notice that the sequence itself cannot converge to 0

[mystic finch]

could you explain what you mean by that. thanks

[fickle turret]

The infinite sum can only converge if we have a null sequence

Which we don't have here

[mystic finch]

when |r| < 1 ?

[fickle turret]

Yes

[mystic finch]

srry again but what exactly is a null sequence

[fickle turret]

A sequence converging to 0

[mystic finch]

right

makes sense

thanks

[rich tapir]

you can also find the radius of convergence

[fickle turret]

You're welcome. If you don't need this channel anymore you can close it

[mystic finch]

alr sure

.close

[obtuse pebble]

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[rich tapir]

[obtuse pebble]

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[lucid pendant]

hello

[lucid pendant]

i need help for this equation

[leaden ginkgo]

what is the integer on the RHS?

[lucid pendant]

i didnt learn integer

[lament quiver]

is the last number on the right a 9?

[lucid pendant]

its 2.9

[lament quiver]

gotcha so youre trying to find x such that it equals 2.9 right?

[lucid pendant]

yeah

[lament quiver]

in your opinion where do you think we should start?

[lucid pendant]

remove the sqrt(5^x) of the denominator ?

[lament quiver]

how would you like to do that

negative exponents or multiplication or another way?

[lament quiver]

perf

[lucid pendant]

what can i do with this

[lament quiver]

lemme double check smthg before we move on

[obtuse pebble]

@lucid pendant Has your question been resolved?

[lament quiver]

@lucid pendant has your teacher taught any substitution?

sry for how long that took

[lucid pendant]

wdym by substitution ?

[lament quiver]

the only way i found to do it was by u substitution

[lucid pendant]

i substitue what ?

[lament quiver]

u=5^x

[lucid pendant]

i cant solve it with log or idk

[lament quiver]

youll use log in the second half

but theres apparently no way to bruteforce log for the whole thing

not that i found

@lucid pendant

[obtuse pebble]

@lucid pendant Has your question been resolved?

[obtuse pebble]

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[timid silo]

help on the underlined parts

[timid silo]

not rly sure how to explain it

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[timid silo]

hi, can someone recommend me one single resource for studying precalc and calc. level being maybe AP level or a little above

[timid silo]

multiple resources to study the same topics end up overwhelming me when i'm new to a topic

[obtuse pebble]

@timid silo Has your question been resolved?

[tranquil depot]

Khan academy I suppose

Very straightforward learning process

[obtuse pebble]

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[fallen scroll]

P(x) is a polynomial with real coefficients. P(x+a) divided by P(x-b) has a remainder of x+a
P(x-b) divided by P(x+a) has a remainder of bx+a+2
Find a+b

[fallen scroll]

<@&286206848099549185>

[unique bear]

ok so

have you considered what the quotient would be?

like turn P(x-b) into P(x+a)Q(x) + bx+a+2

and same for P(x+a)

and try to figure out what Q(x) should be

[fallen scroll]

I did try that

Also did that for the other

[unique bear]

so what did you get as the quotient?

[fallen scroll]

For one p(x+a)=p(x-b)R(x) + x+a and the other was p(x-b)=p(x+a)Q(x) +bx+a+2

[unique bear]

what do you think R(x) and Q(x) should be?

[fallen scroll]

I have this gut feeling where p is a first degree polynomial

[unique bear]

||the degree of P(x+a)= degree of P(x-b)||

[fallen scroll]

Since the inside (x+a) is the remainder

[unique bear]

if it was a first degree polynomial, P(x+a) = P(x-b)(nx+m) + ..., but then the degree of P(x+a) would be higher than P(x-b), which doesnt make sense

[fallen scroll]

Indeed

[unique bear]

so the remainder for both of them should be constant

and theres a very specific constant

[fallen scroll]

Indeed tried using quotient theorem

There is some value K where p(k)=0

But there wasn't any thing to eliminate k

[unique bear]

(we actually dont need that here, and i'll explain how to get Q(x) and R(x), and we'll see why we dont need it)

[fallen scroll]

Okay

[unique bear]

so P(x) would be in the form of jx^n+kx^(n-1)+... right

[fallen scroll]

Yes

[unique bear]

so how would P(x+a) or P(x-b) look like

||they'd still begin with jx^n||

[fallen scroll]

Same degree but different coefficient

[unique bear]

the leading coefficient doesnt actually change

[fallen scroll]

I know that

[unique bear]

nice

[fallen scroll]

So the qx will have a 1

[unique bear]

yeah

exactly

so Q(x)=R(x)=1

[fallen scroll]

Yes

[unique bear]

So now, we have these equations:

$P(x+a)=P(x-b)+x+a$

[warm shale]

znsn

[unique bear]

$P(x-b)=P(x+a)+bx+a+2$

[warm shale]

znsn

[unique bear]

now it would be really useful to get rid of those P(x+a) and P(x-b)

how would we do that?

[fallen scroll]

I already got that bx+a+2 =-x-a

[unique bear]

oh 💀

alright

ok put everything on one side

and you get bx+x+2a+2=0

now since we want a+b, theres a value we want to plug in for x

[fallen scroll]

2

[unique bear]

exactly

[fallen scroll]

Which gives -2

But asking chat gpt

It replied with 0

[unique bear]

💀

dont rely on chatgpt

[fallen scroll]

And I experienced a stroke

[unique bear]

it's actually so bad at math it's amazing

[fallen scroll]

Quite

Terrible

[unique bear]

i asked it to give me a combination of even numbers that add up to 20

once

it gave me 5+5+5+5

so 💀

[fallen scroll]

Yea

Kinda L

[unique bear]

fr

[fallen scroll]

See i had found it

But gpt threw me

[short ore]

why u checking using gpt lmao

[unique bear]

if ur uncertain just try to just look through your processes and check if you messed anything up

[short ore]

gpt is ass

[fallen scroll]

Felt reliable for a moment

Found like three lapace integrals correct

[unique bear]

it can do higher level math using info online and all but it doesnt have a "foundation" of understanding math

[fallen scroll]

Ah i see

[short ore]

it could solve the riemann conjecture and still fail at adding 1 and 1

[fallen scroll]

So it would be bad to ask him for my bio hw right?

[short ore]

idk how reliable gpt is in other subjects but it isnt in maths

[fallen scroll]

I mean i just downloaded it so i wouldn't know

[unique bear]

💀

[short ore]

ahh yes 3 + 3 = 5

[fallen scroll]

Very well

I guess it would be nice to ask you a very interesting question then

[unique bear]

what is it

[fallen scroll]

P(x) is a 4th degree polynomial with real coefficient where
P(x)>=x
P(1)=1
P(2)=4
P(3)=3
P(4)=?

It was 2002 olympiad round 2 I think

Such a lovely question

[unique bear]

interesting

[short ore]

idk if this is optimal but i would try solving the series of equations

[fallen scroll]

I graphed the thing

[short ore]

a + b + c + d + e = 1
16a + 8b + 4c + 2d + e = 4
81a + 27b + 9c + 3d + e = 3
256a + 64b + 16c + 4d + e = ?

that would be way too hard lmao

[fallen scroll]

The coefficient method will take so long, also youll need to know cramers rule

[unique bear]

cramers rule 😭

[short ore]

whats that?

[unique bear]

using determinant of matrices to find solutions

[fallen scroll]

Long way to solve systems of equations

Good old reliable

[unique bear]

finding the determinants also seem long though

[fallen scroll]

I used like one substitution and a graph, solved it in 5 minutes

[unique bear]

how did u use the information that P(x)>=x

[fallen scroll]

P(x)-x>=0

Q(x)=P(x)-x

Q(x)>=0

[unique bear]

yeah that makes sense

[fallen scroll]

Id plug the points to find qx now

[short ore]

15a + 7b + 3c + d = 3
80a + 26b + 8c + 2d = 2
255a + 63b + 15c + 3d = ? - 1
i dont think you can solve it this way lol

[fallen scroll]

Go on use it

[unique bear]

if we could use that we couldve just taken the difference multiple times

but we dont have enough points for that

[fallen scroll]

Try graphing qx

Youll find something interesting

[unique bear]

there are no more roots

[short ore]

how

[fallen scroll]

For x=1 and 3 qx=0

[unique bear]

and those are double roots

[fallen scroll]

Delighted to hear

Using x=2 youll find coefficients

[unique bear]

k(x-1)^2(x-3)^2

[fallen scroll]

Since qx is never negative it must have double roots

[unique bear]

and plugging in the only nonzero value we know

k=2

[fallen scroll]

Yea

Then undo the substitution

[unique bear]

so P(x) = 2(x-1)^2(x-3)^2+x

[fallen scroll]

Indeed

[unique bear]

and P(4)=22

[fallen scroll]

Congrats

[unique bear]

nice problem

[fallen scroll]

I used to do these like butter

[unique bear]

ngl i fell off 💀

[fallen scroll]

I was smart idk what happened

I suddenly am learning thermodynamics and losing wits

[unique bear]

majoring physics?

wait

im being dumb

[fallen scroll]

Yeah

[unique bear]

oh you are majoring phys?

interesting

[fallen scroll]

Bad mistake

Never do that

[unique bear]

dw i wont 💀

[fallen scroll]

I wanted astrophysics

But no money

[unique bear]

rip

did u do comp math when you were in hs

[fallen scroll]

It was easy ngl

[unique bear]

i keep sillying 💀

somehow my algebra and geo skills fell off from last year

[short ore]

sorry im in hs rn and have never heard of double roots. what do they do for an equation? how can you use that to get k(x-1)^2(x-3)^2

[fallen scroll]

Oh dear

So double roots, they make the x axis work like a mirror

[unique bear]

if it touches and goes up like this, it's a double root

[short ore]

why is it called a double root?

[unique bear]

but be careful of things like this cuz it might look like a double root but it's a quadruple root

[unique bear]

the graph i sent was (x-1)^2

[short ore]

oh wait so its 2 roots

like how the quadratic x^2 + 2x + 1 has 2 roots of 1

[unique bear]

yeah

[fallen scroll]

Yes

[unique bear]

but

[short ore]

oh i just never heard it called a double root before

[unique bear]

it's root of -1

but wtv

[short ore]

-1

i was just thinking x+1 so root is 1 but yeah its when x+1 = 0 lol

[unique bear]

it's pok

ok

common hs mistake (im also in hs 💀)

[fallen scroll]

(Im not)💀

Imma drop out

[unique bear]

💀 become windows ceo

[fallen scroll]

Exactly

I lost half of my hair in first semester of thermodynamics

[unique bear]

😭

i do not like phys ngl

[fallen scroll]

Bro no shit even teachers don't know what they are saying

[unique bear]

idk why i decided to take ap phys c

[fallen scroll]

Ap is simple

[unique bear]

yeah but my teacher 💀

[fallen scroll]

Go electric or sum

[short ore]

im learning ahead of my year on yt and stuff so the order in which im learning stuff is messed up lol. ik how to do synthetic division but never heard of double roots before lmao

[unique bear]

that

that's alright ngl

[fallen scroll]

I do that too

[unique bear]

i havent heard of synthetic division in such a long time 😭

i havent done it in such a long time either

i actually forgot so much of what i learned last year

[fallen scroll]

No such thing as division in physics🔥

Wait till they teach you cal 1-3 in 3 months

[unique bear]

me when $\frac {q_{enc}} {\epsilon_0} $

oops

wrong direction

i dont remember if calc 3 includes mv

multivar

[fallen scroll]

I think it does

I def remember partial derivatives

[unique bear]

i only partially know partial derivatives 😭

we were too focused on suprema and infima

[fallen scroll]

I cease to know those stuff lol

[unique bear]

sup is lowest upper bound of a set and inf is highest lower bound of a set

we had to use it in order to define integrals

[fallen scroll]

I know those

[unique bear]

spivak moment

[fallen scroll]

But all i ever use integrals is dynamic and heat transfer

[unique bear]

do you only do physics in college(or uni)?

[fallen scroll]

(Which i wolframalpha)

[unique bear]

💀

[fallen scroll]

Both i think

You learn all in college

And study one in uni

[unique bear]

interesting

[fallen scroll]

At least Its like this here💀

We needa know biology too💀

[unique bear]

bio 😭

[fallen scroll]

Its so bad bro

[unique bear]

how long are your classes lol

[fallen scroll]

How you mean

[unique bear]

like how long are the lectures you need to attend to

the time it takes

[fallen scroll]

1.30 hour

[unique bear]

how many do you take in a day

[fallen scroll]

4 or 5 I believe

Depends really, sometimes i only have one

[unique bear]

interesting

ngl i gtg now 💀

cya

[fallen scroll]

Sure me too

.close

[obtuse pebble]

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[brittle tundra]

this is just a super tedious question and its getting annoying so i wanna make sure that i didnt make a mistake

[tranquil depot]

Ok

[brittle tundra]

i divided the 6a^3-a^2-12a-5 by x+1 and just factored it, factored everything and i have

i really dont wanna expand this

<@&286206848099549185> is there a way to do tghis without expanding

[obtuse pebble]

@brittle tundra Has your question been resolved?

[brittle tundra]

um

i think i still need help D:

[short ore]

a^2 - a -2 isnt (a-2)(a-3)

[obtuse pebble]

@brittle tundra Has your question been resolved?

[brittle tundra]

oh so what happened was I multiplied a^2-a-2*3a^2-5a, factored it which became a(3a-5)(a-2)(a+1)/2a(a+1)(2a-1)(3a-5) from factoring the 6a^3 stuff

[short ore]

why did you do that?

[brittle tundra]

uhhh to simplify

[short ore]

first thing is cancelling

[brittle tundra]

but i did make an error with factoring

no then i cancelled out

[short ore]

well try again

cancellign and factoring before naything else

[eager niche]

I’d say find the restrictions first

[brittle tundra]

wouldn't i have to factor in the first place in order to find restrictions

This is what I got

[short ore]

correct now you can just cancel a lot on the left

[eager niche]

Now restrictions then cancel

[short ore]

oh yeah you cant cancel 0's lol

[brittle tundra]

for restrictions would i have to make same gcf for the subtraction part

[eager niche]

Or they probably want one fraction

So yeah common denominator

[brittle tundra]

do i have to expand here

[obtuse pebble]

Channel closed

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[brittle tundra]

.reopen

:3

[obtuse pebble]

✅

[hollow solstice]

In denominator 2a+1 **

[hollow solstice]

Why aren't you cancelling 3a-5 too?

[brittle tundra]

what happens to the 2a-1

[brittle tundra]

ones minus ones plus

[hollow solstice]

There is no 2a-1

it is 2a+1 * 3a-5

Nope

Check again

[brittle tundra]

isnt it 6a^2+7a-5

[brittle tundra]

which is (2a-1)(3a+5)

right if multiplied its 10a-3a

which is +7a

oh shit

i messed up the dividion

[hollow solstice]

Yeah

I dont know how you got 6a2+7a tho

[brittle tundra]

i divided it by x+1

like the 6a^3

[hollow solstice]

Den?

Oh

[brittle tundra]

ok i think i got it now

thanks so much

man i didnt see that dumb mistake

[hollow solstice]

Sure

[brittle tundra]

.close

[obtuse pebble]

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[timid vapor]

A quadratic function, leading coefficient is positive. x=2, y=11

[timid vapor]

x=5, y= 12

x=11, y=30

what’s f(8)

possible answers are 18,20,21,24

<@&286206848099549185>

[fallow glacier]

Hello I am here to do what I can to help you out, what's the question is it the one above?

[timid vapor]

yeah

[fallow glacier]

Well there is no way for me to tell you what f(8) is when you only provided two data points, x=11 y=30 and x=5 and y=12. The options for how many functions could pass through those are infinite, are you sure there isn't more information that you are missing.

[timid vapor]

the problem number i mean

[fallow glacier]

Yeah I guess it makes sense since the rest is scratched all out.

[timid vapor]

how are the others scratched out

wdym

[fallow glacier]

????/ The big red marker scratching the next problem in the picture

[timid vapor]

wait so how would i solve number 11

[fallow glacier]

You know I thougth I knew this but this looks hella confusing, algebra is not my strongest point, but just to assure, I would call for help to reassure yourself.

[timid vapor]

this is precal

can you get someone else to help me pretty please

what i notice is that from 2-5 y=1/3x 5-11 y=3x

<@&286206848099549185>

[hollow solstice]

If you're willing to do hard work

assume quadratic y=ax^2 + bx + c = f(x)

put 3 points

play with them

get a b c

and put in the equation and put x=8

Or rearrange them to result in 64a+8b+c = f(8)

[timid vapor]

wait wait wait

how does the rearranging work

[hollow solstice]

Like for example

You were solving those 3 equations

and got 64a + 8b + c itself while solving it

rather finding a , b , c and then putting it in 64 a + 8 b + c

It doesn't work in all questions but just if your luck subsides

[timid vapor]

so is there any way I can do this without guesstimating

[hollow solstice]

.

3 equation 3 variables

[obtuse pebble]

@timid vapor Has your question been resolved?

[timid vapor]

explain

[hollow solstice]

assume quadratic y=ax^2 + bx + c = f(x)
input (5,12)(11,30)(2,11)

Do you see 3 eq 3 var?

[timid vapor]

yeah no no i get what you are saying

Thats very smart thank you sir

may i ask what level of math you are on?

.close

[obtuse pebble]

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[hollow solstice]

High school?

[obtuse pebble]

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[hollow solstice]

Wdym lvl of math

[hollow solstice]

uh

.close

[obtuse pebble]

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[timid vapor]

precal?

calc

alg 2

[hollow solstice]

Well I just know Ive studied calculus

[timid vapor]

Alright

thank you

.reopen

I'm still confused

I have 121a + 11b + c = 30, 25a + 5b + c= 12, so 4a + 2b+ c =6, 64a +8b +c=?

so where do i go from here

[obtuse pebble]

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[rotund raptor]

Hello, I have my geometry midterm tomorrow and I need help on a couple questions.

[rotund raptor]

What equation do I use for these questions?

[timid vapor]

rate of change

[rotund raptor]

For this one I use Pythagorean theorem right

The other paper has the line on it

[timid vapor]

Wait 23 doesnt show any line st

[rotund raptor]

Ik there

[timid vapor]

oooh okay

yeah

[rotund raptor]

Which one is that?

[timid vapor]

change in y/ change in x

[timid silo]

Rise over run gradient equation

[rotund raptor]

Is it y2-y1/x2-x1

[timid vapor]

Precisely

[rotund raptor]

ok cool

So I would do that, get the answer and turn it into slope intercept form?

[timid vapor]

to show the equation for the line

but if it just asks for the rate of change you just show the rate of change nothing more

[rotund raptor]

Ok they have the equation on the practice problems

[timid vapor]

oh okay so yeah you would give it on there!

[rotund raptor]

Any tips for turning it into slope intercept?

[timid vapor]

You just take the slope (4)

times it by the x either first or second it doesnt matter

so (4)(3) + c = 4

12+c=4

4-12

c=-8

[rotund raptor]

Alright cool, thank you.

[rotund raptor]

Could I have help on this one? This one is bugging me a lot.

[timid vapor]

just make sure to use the corresponding y to each x

[timid vapor]

whats your problem with it

[rotund raptor]

I don’t understand the square rooting, and how to setup the equation.

[timid vapor]

okay so the elementary pythag theorm is just a^2+b^2=c^2

[rotund raptor]

Yeah I understand that part

[timid vapor]

Are you trying to understand why the equation is the way it is?

[rotund raptor]

Yeah, so I put the length/ width squared + l/w squared = d

And then I add them, square root and find the multiples?

Here’s the full equation

[timid vapor]

what do you mean leangth/width squared + l/w squared

its just length^2 + Width^2 = hyptoneuse^2

[rotund raptor]

Like in the place for a^2 + b^2

[rotund raptor]

Ok

I understand now

[timid vapor]

yes

[dense imp]

https://www.youtube.com/watch?v=yfGtbNgcrQ8&ab_channel=MathematicalVisualProofs
watch this 1 minute video btw @rotund raptor

[timid vapor]

but it can be used to find both the length and width too!

but you have to be careful as to not break the rules of order of operations

[rotund raptor]

Thank you.

[timid vapor]

so if you are ever concerned that you may have done something wrong just put your answers back into the equation and see if it gives you the same thing

[rotund raptor]

Okay, i understand all that now, why do we square root?

That gives us the answer?

[timid vapor]

yes it gives us the length of the hypotenuse

[rotund raptor]

I understand now.

One second I have one more question

[timid vapor]

the square of the length and the width is just to account for the height gained and distance traveled by a diagonal line

[timid vapor]

Go ahead! 🙂

[rotund raptor]

Thank you

Do you have any tips for proofs?

[timid vapor]

Just know your lingo, and pay attention to detail like the 90 degree angles and such

[rotund raptor]

👍

[timid vapor]

you can also back track like if you dont know where to start

so like well if I knew blank was congruent to blank then that would make this and that equal

[rotund raptor]

Okay thank you very much, I have one last question.

For these, what do I look at to identify the AAS, SSS etc

The curved lines indicate the angles and the straight lines indicate the sides?

We have done it in class and I’ve found sometimes it’s not the case

[timid vapor]

Im sorry for the wait a horrid song came on

[rotund raptor]

Don’t worry about it, take your time.

Sorry, I am terrible at math, probably super easy for you guys lmao.

[timid vapor]

no actually believe it or not geometry was the hardest math for me

[rotund raptor]

Yeah, just trying to get through it, I’ve always struggled with math.

[timid vapor]

besides my burning hatred for such simple 2d figures that make me extrememly frustrated on competition math tests that i always seem to get wrong

[timid vapor]

we arent a judgemental space, the fact that you are reaching out and seeking help shows us all we need to know and what we care to know, I can assure you everyone in here is glad that you are seeking help in areas you dont neccesairly need but are unsure in

but anyways back to the matter at hand

[rotund raptor]

Thank you, and thank you for all of the help also.

[timid vapor]

so this is aas because there are two congruent angles and one side. How I see it if I were to flip the triangle upside down itd be exactly the same as the other

[rotund raptor]

Ah, so it’s like that because of the congruent angles?

[timid vapor]

And the side dont forget!!

[rotund raptor]

Okay so how would I look at it if it was HL

what would one of those look like?

[timid vapor]

What do you mean HL

[rotund raptor]

One of them is hypotenuse leg

[timid vapor]

Oh like the example on the right

[rotund raptor]

Nah, that one is side side side.

I don’t know what an hypotenuse leg one would look like.

[timid vapor]

Ohhhhh

like this

https://www.bing.com/images/search?view=detailV2&ccid=%2FVbibDOH&id=BCA83E7FBE3989A04AA488E777C8F941030EAA07&thid=OIP._VbibDOH8tg0fh1wtlrJWwHaCv&mediaurl=https%3A%2F%2Fdr282zn36sxxg.cloudfront.net%2Fdatastreams%2Ff-d%3Aaeef6d8c5071c39ac97b29401306e2c35316cc3f87c63ae5041cece1%252BIMAGE%252BIMAGE.1&cdnurl=https%3A%2F%2Fth.bing.com%2Fth%2Fid%2FR.fd56e26c3387f2d8347e1d70b65ac95b%3Frik%3DB6oOA0H5yHfniA%26pid%3DImgRaw%26r%3D0&exph=296&expw=800&q=hl+geometry&simid=608016027986363018&FORM=IRPRST&ck=BAB5ED83A60A86B79A86C6D56BD1A57B&selectedIndex=2&itb=0&ajaxhist=0&ajaxserp=0

[rotund raptor]

That should be it, what do i look for in those?

The one side?

[timid vapor]

well if you are looking for if the triangles line up with their right angles and congruent sides

if it shows the hypotenuse for both triangles are congruent and some other side than its most definitely true

or if both sides are congruent than the triangles are most def congruent in that case aswell

[rotund raptor]

Okay, thank you so much.

[timid vapor]

is that all you need?

[rotund raptor]

yep

[timid vapor]

.close

[last pilot]

@timid vapor only the OP can close it

@rotund raptor if you're done, do .close

[rotund raptor]

.CLOSE

[obtuse pebble]

@rotund raptor Has your question been resolved?

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[severe basin]

For what values of n is n!+24 a perfect square?

[obtuse pebble]

@severe basin Has your question been resolved?

[ashen dove]

Use mod 7

[obtuse pebble]

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[fathom flicker]

If we know that dim(U1+U2)=dim(U1)+dim(U2)-dim(U1 intersect U2)

then isn't this statement equivalent to

prove U1 + U2 is a direct sum if and only if, dim (U1 intersect U2)=0

Which it immediately follows that the intersection is empty

?

[obtuse pebble]

@fathom flicker Has your question been resolved?

[fathom flicker]

.close

[obtuse pebble]

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[haughty talon]

What do I have to do?

[haughty talon]

Some surd stuff

[robust sleet]

Multiply both num and denominator by denominator

[haughty talon]

So 5sqrt(5)/5

[robust sleet]

U can simplyify it further

[haughty talon]

Sqrt(5)?

[robust sleet]

Yes

[haughty talon]

So for the rest I just multiply num and denominator by denominator and simplify?

.close

[obtuse pebble]

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[hollow crag]

Hey, I have a question: What exactly is the dot product in vector geometry? (Also known as the scalar product? And for what does one need it?)

[alpine raven]

needed for projection

[hollow crag]

Could you allaborate?

[alpine raven]

I need to draw a picture but man i have nothing to write with right now

[tame python]

itd be nice if you could project that image of yours onto the screen

[hollow crag]

Mine?

[tame python]

no thats a joke for what herels said

[hollow crag]

this is just one of our scripts

[tame python]

youre at 1.6.2 you ought to wait until you actually start using it extensively to then ask questions like this

thats like learning multiplication for the first time then asking "how is it useful"

[hollow crag]

but i don't really understand the definition..

[tame python]

wait

wdym script

[alpine raven]

the length in red should be the dot product of a and b

[tame python]

(this is only true in certain cases)

but thats one of the uses of the dot product

[alpine raven]

only if its an orthogonal projection tho

[tame python]

if its orthogonal the dot product is 0 isnt it

[alpine raven]

nah you dont understand

[hollow crag]

?

[alpine raven]

I mean if we do an orthogonal projection, we get the dot product

[hollow crag]

ah i understood it

[alpine raven]

but if the two vectors are orthogonals, we definitely cant do a projection

[hollow crag]

.close

[obtuse pebble]

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[warm tide]

How would i do #5

Using part 2

Of the fundamental theorem of calculus

[obtuse pebble]

@warm tide Has your question been resolved?

[obtuse pebble]

@warm tide Has your question been resolved?

[obtuse pebble]

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[random olive]

The vectors e1 and e2 form a base in the plane. Two other vectors f1 and f2 are chosen as a new basis. F1 = 7e1 + 8e2. F2 = e1 + e2. Express the vectors e1 and e2 as linear combination of the new basis vectors.

[random olive]

How do I solve this question?

Do I start by switching out e1 and e2 to x and y?

[golden ember]

e1 = xF1 + yF2
e2 = vF1 + wF2
so
1 = 7x +1y
0 = 8x + 1y

0 = 7v + 8w
1 = 8v + 1w

You have to solve for x,y, v,w

[unreal musk]

Alternatively, you could either "solve" those equations for e1 and e2 (similar to a pair of linear simultaneous equations), or equivlaently convert that statement into one about matrices

[random olive]

Oh okay so x = -1 and y = 8?

[dense imp]

you could also just think of the change in coordinate matrix from the first base to the 2nd (it would be the matrix with columns (7, 8) and (1, 1) and i guess going backwards from 2nd basis to 1st would be the inverse of that first matrix

[random olive]

I think that is too advanced for me but what do I do with x and y now?

[dense imp]

if you saw a system like
3x + 4y = 2
4x +3y = 1
you would know how to solve it right?

and get x = ..., y = ... ?

@random olive ?

[random olive]

I think so

[dense imp]

e1 = xF1 + yF2
e2 = vF1 + wF2
ok so this is exactly the same thing, you would be solving for F1 and F2 (analagous to x and y) but you don't have given numbers on the other side, you just leave the solution in terms of e1 and e2

and youll have some coefficients times the e1 e2 vectors which will just be the linear combination the problem is asking for

[unreal musk]

[other way round no: solving f1 = 7e1 + 8e2 and f2 = e1 + e2 for e1 and e2?]

[dense imp]

hm?

[unreal musk]

Question is to express e1 and e2 in terms of f1 and f2

[dense imp]

erm yeah i was just copy and pasting this message, guess it needs correcting

[random olive]

If I solve out e1 and e2 I get e1= (f1-8e2)/7 and e2= f2-e1?

[dense imp]

so you have
F1 = 7e1 + 8e2
F2 = e1 + e2
now solve for e1 / e2 just like you would the simple example with x y, and leave F1 and F2 as unknowns, e1 e2 will just be expressed in terms of them

[dense imp]

https://www.youtube.com/watch?v=oKqtgz2eo-Y&ab_channel=TheOrganicChemistryTutor

[dense imp]

you need e1 and e2 only in terms of f1 and f2, not in terms of each other also

refresh yourself on how to solve systems ^

[random olive]

8e1 and 9e2?

[dense imp]

if you are doing a linear algebra class you better be clear on how to solve systems of linear equations 😄 go watch the video

i'm sure youve done it before and itll come back quickly if you watch it

[unreal musk]

[like here ]

@sage dagger

[random olive]

I understand the video but I don’t know how to solve it when we have f1 and f2 unknown as well

Well when I solve for e1 I get f12 = -e1

[unreal musk]

It's similar to when there are numbers, but you leave them as they are, if that makes sense?

[random olive]

Okay but e1 = -1 then?

[unreal musk]

Say I give you a set of linear equations, $7x + 8y = 4$ and $x + y = 5$, you'd be able to solve that, right? (you don't have to actually solve it for me)

[warm shale]

@unreal musk

[random olive]

Yes!

[unreal musk]

And the steps may be say either multiplying the second one by, say, 7 and subtracting that from the first one, or rearranging one of those equations for a variable and substituting that back in, right?

[random olive]

Yes right!

[unreal musk]

Cool, now, if I now change the question a tiny bit: solving
[
7x + 8y = u \text{ and } x + y = v
]
where $u$ and $v$ can be any numbers of my choosing, and I tell you to solve that for $x$ and $y$ (with those being in terms of $u$ and $v$), would you know how to do that?

[warm shale]

@unreal musk

[random olive]

I don’t know, if I multiply the second equation with -7 do I multiply v with it as well?

[unreal musk]

Yep, you'd need to multiply v by -7 too, but that's the idea!

[random olive]

Oh okay!

So if I for example multiply my second equation with -8 to get rid of e2

I multiply f2 with it as well?

[unreal musk]

Yep, that's it pretty much like that!

[random olive]

So I have this?

And I can cancel out 8e2 and -8e2

And then I combine them

Then I get this

[unreal musk]

Be very careful: f1 and f2 are distinct objects, so you can't combine them like that

[random olive]

Oh okay

[unreal musk]

You should get f1 - 8f2 though

[random olive]

Okay so I have f1 - 8f2 = -1e1

[unreal musk]

Then one small thing to get e1 by itself

[random olive]

Moving over -1?

[unreal musk]

how do you mean "moving over"?

[random olive]

So I get -f1 + 8f2 =e1

Dividing?

Okay!

[unreal musk]

That's it, perfect

[random olive]

So can I use this now and put it in the original equation?

[unreal musk]

Careful, there wasn't a negative so that -56f2 should be +56f2, but otherwise you get the idea

[random olive]

Oh sorry you’re right