help-38

[rapid horizon]

b
a+b+c
It is not a basis

[shrewd vessel]

you can't split a 2x2 matrices into 1x1

[rapid horizon]

Order 1

[shrewd vessel]

?

idk how to give more clue without blantantly giving the answer away

think about the vector
$\begin{bmatrix}
x_1 \
x_2
\end{bmatrix}$

[solid kiln]

lgkoo

[shrewd vessel]

where x_1 and x_2 are real

you can write that vector as a linear combination of basis vectors

i.e. in terms of $\begin{bmatrix}
1 \
0
\end{bmatrix}$
and
$\begin{bmatrix}
0 \
1
\end{bmatrix}$

[solid kiln]

lgkoo

[shrewd vessel]

once you figure out how to do this, then apply similar method to the matrix

[trim jolt]

@rapid horizon Has your question been resolved?

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[rapid horizon]

Do you mean
1 0
0 1
?

[shrewd vessel]

for one of the matrix yes

there's more though

[rapid horizon]

0 1
1 0 ?

@shrewd vessel

[shrewd vessel]

no

you have to split it based off the given matrix

basically try to this split that matrix so that each matrix has only 1 letter

[rapid horizon]

0 1
1 2
?

[shrewd vessel]

no

[shrewd vessel]

how did you get that?

[rapid horizon]

I put a=0
B=1

C=1

[shrewd vessel]

the point is a,b,c are general

and distinct

so you can't just pick a,b,c as you want

I'll demonstrate how to do this with vectors and see if you can work it out for your question

[rapid horizon]

Yes please 🙈

[shrewd vessel]

Given $\begin{bmatrix}
a \
b
\end{bmatrix}$, we can split it as
$\begin{bmatrix}
a \
0
\end{bmatrix} + \begin{bmatrix}
0 \
b
\end{bmatrix}$, or equivalently,
$a\begin{bmatrix}
1 \
0
\end{bmatrix} + b\begin{bmatrix}
0 \
1
\end{bmatrix}$

[solid kiln]

lgkoo

[shrewd vessel]

where $\begin{bmatrix}
1 \
0
\end{bmatrix}$ and $\begin{bmatrix}
0 \
1
\end{bmatrix}$ are the basis vectors that spans a vector subspace of the form $\begin{bmatrix}
a \
b
\end{bmatrix}$

[solid kiln]

lgkoo

[trim jolt]

@rapid horizon Has your question been resolved?

[shrewd vessel]

@rapid horizon if you have more questions you should really just ask mate

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@rapid horizon Has your question been resolved?

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[knotty rain]

hi guys, for question 5c, i dont get it, why do we subsitute 12 into the equation? i remember we solved this question in class like 3 months ago and im revising since math final is tomorrow. but yeah i remember when we solved this we substituted 12 but i dont remember why and i dont write notes in class since math is genuinely really easy to me.

[nimble stone]

,rccw

[nimble stone]

i presume thats just where the vertex of T is

at t=12

so thats the time of the min temp

and you just get the temp by subbing that in

[knotty rain]

wait

oh my gosh

you’re rifht

wtf why didnt i think of tgat

smh nvm

thanks a lot tho

.close

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[solid kiln]

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

[tawny obsidian]

to check that X and Y are independent it's sufficient to check that the value of Y doesn't affect the value of X

if X has n possible outcomes we actually only need to check this for n-1 of those outcomes, the last we get for free

(why)

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[lilac cloud]

Does anyone know where to start in sketching a proof that all non-defective square matrices can be diagonalized?

[grim estuary]

interesting

if a square matrix is non-defective then alg multiplicity = geom multiplicity

hence the eigenvectors of the matrix is linearly independent

then det(P) must exist

hence P is invertible

I'll leave the rest to you

[lilac cloud]

Ah I see

That makes a lot of sense

[wooden plover]

what does defective mean here ?

non-invertible ?

or something else

[grim estuary]

when the algebraic multiplicity is not equal to the geometric multiplicity

that is #eigenvalues > dim

[wooden plover]

ok ok

[marble wharf]

det(P) always exists for square matrices. and it being zero or nonzero doesnt matter at all

[marble wharf]

not quite, but for each eigenvalue you can find alg multiplicity many linearly independent eigenvectors

[trim jolt]

@lilac cloud Has your question been resolved?

[grim estuary]

shi mb what I meant was the solution to Px = 0 exist

I haven't revised in sometime

im kinda rusty

[grim estuary]

yea thats what I meant my bad

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[static beacon]

what does the graph of this function look like?

$E(r)=\frac{4}{3}k\cdot\frac{\pi \rho}{r^2}\cdot (r^3 - r_1^3)$

[solid kiln]

thunder7

[static beacon]

k, pi, rho, r_1 are constants

all != 0

$\E(r)=\frac{1}{r^2}\cdot (r^3 - 1^3)
\E(r)=\frac{r^3}{r^2} - \frac{1}{r^2}
\E(r)=r - \frac{1}{r^2}$

[solid kiln]

thunder7

[static beacon]

should be like this right?

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[static beacon]

.close

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[indigo lintel]

Is there any video resources like 3blue1brown, or text materials, that explains what exactly are we doing with expanding a matrix (specifically a 3x3 one in my example) and why?

[lilac cloud]

Do you mean for finding determinant?

[hallow kite]

yeah what do you mean by expanding?

[lilac cloud]

I’m assuming laplace expansion

[trim jolt]

@indigo lintel Has your question been resolved?

[indigo lintel]

Yeah for finding the determinant

Well it says it's for finding the determinant.

But I don't understand.

Why by doing that complicated procedure can I find the determinant?

Is there any way I csn understand it in an intuitive way?

[hallow kite]

there unfortunately isn't any intuition for it that i can think of or that i've seen, the internet seems to agree with me

the formula is more of a result from the multilinear properties of the determinant, so it's kind of hard to get some geometric intuition for it

https://textbooks.math.gatech.edu/ila/determinants-cofactors.html

there's a brief proof here of how the cofactor expansion recovers the unique defining properties of the determinant

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[wraith hinge]

.close

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[south latch]

this isn't a quiz or a test, is it?

these questions are pretty scattershot

[solemn thorn]

its homework

[south latch]

well kind of. It's all functions I guess

[lusty delta]

if a student gets an assessment that has a "CHECK" button that's just asking to be cheesed

so business as usual here

[south latch]

@mellow robin why don't you try all of these and get back to us when you get stuck?

[solemn thorn]

according to them they have 1 minute left

its been 2 minutes so

[lusty delta]

incredible

[mellow robin]

....

[mellow robin]

nah

it is imagine math

💀

[solemn thorn]

did you try it

[south latch]

use your 🌈IMAGINATION!

[mellow robin]

YEs

my brain is very slow

[south latch]

imagine math sucks

[mellow robin]

yeah....

POV: You got one wrong and if you get this wrong you have to do the whole lesson... AGAIN

(You failed the last time💀 )

[south latch]

it sucks because it doesn't integrate well with grade books

[south latch]

well...maybe you should then

[solemn thorn]

anyways whats your answer here

you said you tried it already

[south latch]

OP, what is "domain"?

what does that name mean?

[mellow robin]

the x value of the function

[solemn thorn]

not quite

[south latch]

close but too specific

it's the set of all possible inputs

[mellow robin]

like the list of x values that will satisfy the function

[south latch]

what is the meaning of "range"?

[mellow robin]

domain for y-values

[south latch]

yeah, alright

it's the set of all possible outputs of the function

what do you think x represents in this context?

[mellow robin]

I only have to worry about the simple domain

x is the number of times the firework splits

[south latch]

yes.

what set of numbers makes sense for the inputs?

they gave you the function, btw

f(x) = 2^x

[mellow robin]

It can't be 1 because 1*2 = 2 and doesn't equal 5

[south latch]

but we need the context to restrict the inputs

[mellow robin]

yeah..

[south latch]

of course it can be 1

it can split once

and if it does, you get 2^1 = 2 new bursts.

[mellow robin]

I am just confused

I thought it had to be equal to the number of firework bursts in total??

[south latch]

we are trying to identify the domain.

[mellow robin]

Yeah I got that

[south latch]

x is "the number of times the fireworks split"

what set of numbers would that be?

what numbers would be included?

[mellow robin]

multiples of 5??

[south latch]

what numbers definitely wouldn't be included?

[south latch]

no dip

[mellow robin]

because each 0

[south latch]

what else

[mellow robin]

-numbers

[south latch]

right

how about decimals?

[mellow robin]

no

[south latch]

how about fractions?

[mellow robin]

nah because you can't have 3/4 of a burst of fireworks

[south latch]

how about roots?

$\sqrt{3}$

[solid kiln]

Melvin Eugene Punymier

[south latch]

?

👋

[mellow robin]

only

if they are perfect squares

[south latch]

which would make them...

(positive) integral.

[mellow robin]

just integers

ye

[south latch]

ok, so list the numbers

that are in the domain

[mellow robin]

(5, 10, 15, 20, 25....)

[solemn thorn]

not quite

[south latch]

why 5's?

no love for 4's?

or 3's?

or 2's?

or 7's?

or 13's?

[solemn thorn]

f(x) = 2^x

[south latch]

why are you so picky

[solemn thorn]

wrong function

ok is correcr now

[south latch]

we are doing the domain

not the range

[mellow robin]

OH MB

\

I understand now

I was looking at the output

[solemn thorn]

btw

[mellow robin]

and thinking it was the input

[solemn thorn]

5x ≠ 5^x

[mellow robin]

not the input as the input

[solemn thorn]

nvm what am i saying

[south latch]

@mellow robin let's get through this

list the numbers

for the inputs (domain)

start with the smallest number that makes sense

[mellow robin]

All integers including 0

[solemn thorn]

all of them?

[south latch]

which is the nonnegative integers

yes.

{0,1,2,...}

[mellow robin]

yeah

[south latch]

by the way, is this set finite or infinite?

[mellow robin]

infinite

???

[south latch]

yes, it is "countably infinite", because we can order these elements

{0,1,2,...}

this is a "discrete" set because there is space between the numbers. That is, we are not including ALL the numbers between 2 and 3, for example.

we just have a bunch of points on the number line. 0, 1, 2, ...

anyway, that's your domain.

[mellow robin]

so it is all positive integers??

[south latch]

yes

most texts say that "positive integers" includes zero. Some say it doesn't though 👀

you know what, I guess it MUST split

so 0 actually isn't in this set anyway

my bad

[mellow robin]

ok.

[south latch]

alright, now list the outputs.

plug your set of inputs, one at a time, into f(x), and write the list of outputs

[mellow robin]

(2, 4,8...)

[south latch]

sounds good

looks like they aren't giving you that option

oh, that's the old question

[mellow robin]

so did I select the right one??

[south latch]

you posted the same question again.

[mellow robin]

ik

I reshowed it

so is that good??

[south latch]

how are you still not sure what we are talking about here

the domain of f(x) is the set of all viable inputs

you already listed them and said which one describes it

[mellow robin]

I understand now I just want confirmation that I chose the right answer

[south latch]

be brave.

[mellow robin]

If I get this wrong...

💀

NOOOOOO

WHYYYY

GOD

WHY

What have I done

to deserve this

[south latch]

nothing.

[solemn thorn]

Back to square one

[south latch]

the question is worded strangely and this was the correct answer regardless

[solemn thorn]

Well at least you have more knowledge so it shouldnt be that hard

[mellow robin]

Yeah

[solemn thorn]

the question says "one type of fireowkr splits 5 times after it is fired into the air"

[south latch]

the function should be written as f(x) = 5^x, but the domain is still the list of positive integers

[solemn thorn]

meaning it can split a maximum of 5 times probably

[south latch]

the question asked about the domain, not the range

[solemn thorn]

yeah the number of splits

it can split a number of 5 times

thats x

the number of splits (x) of the firework is up to 5

[south latch]

...

wouldn't that mean the domain is just {5}?

[solemn thorn]

no

by my understanding it can split up to 5 times

[south latch]

it didn't say "up to" 5 times, it just says it happens 5 times.

[solemn thorn]

yea so 5 times

[south latch]

I hate third party math question writers

[solemn thorn]

split once (1)
split again (2)
split again (3)
split again (4)
split again (5)

[south latch]

that's fine

but that's not how the question is written

[solemn thorn]

I guess

[south latch]

I think that's what they intended

[solemn thorn]

Better luck next time

[south latch]

but it isn't what they wrote for our math student here

(or their math tutor here)

@mellow robin be nice to your teacher about this, it isn't their fault and they would much rather write these themselves or pick them out of a book than a website

@mellow robin it's only 7 questions, let's jump back on and get through the first 6

[trim jolt]

@mellow robin Has your question been resolved?

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[plush ether]

if the population of a bacteria grew double every 15 years how long does it take to triple? assuming exponential growth

[plush ether]

i kinda forgor how to do these rip

[raw magnet]

okay

[plush ether]

helloo

[raw magnet]

so what kinda equation

do you think it would look like

[plush ether]

ummm

its like

the

a=p(1+r)^t

that oen i think?

[raw magnet]

yeah sure we can work with this

[plush ether]

alrighty

[raw magnet]

let's not wory abt the principal

[plush ether]

alrighty

[plush ether]

so im a little bit lost here what should i start with

[raw magnet]

cuz we don't care about the inital population right

[plush ether]

right yeah

we just care about time

:D

[raw magnet]

yeah 😄

[plush ether]

indeed

:D

the issue is that i am a little bit stupid and idrk what im doing :D

[raw magnet]

don't worry okay

[plush ether]

yay

[raw magnet]

hmm I have to settle some stuff for my quant club so give me 5 mins 😭

[plush ether]

lmaoo np

[raw magnet]

I'm not getting into any decent quant 😭

but anyway

mathematics

2^{t/15}

how does this function look

[plush ether]

ripppp

[plush ether]

confusing

very very confusing

[raw magnet]

what's up

llike the /15 is for every fifteen years

2^x is for the doubling

[plush ether]

i mean yeah

i guess

but

r u sure thats just it

[raw magnet]

well we have to solve for when 3 = 2^{x/15}

p sure

@plush ether any ideas

[plush ether]

uhmmmmm you just likeeeeee

go to the power of 15 and then idk

see????

😭

im not too sure

[raw magnet]

okay

let's do it two ways

pull up desmos

see when this happens

[plush ether]

im not allowed to use desmos 😅

[raw magnet]

the other way is not desmos

dw

[plush ether]

okk

[raw magnet]

taking log_2 on both sides we get

log_2(3) = x/15

x = 15 log_2(3)

= 23.774

[plush ether]

AHHHHH

ok

:D

[raw magnet]

😄

[plush ether]

okkk

thank you so much

uhm

[plush ether]

do you know half life btw

[raw magnet]

does it match with ur answer key?

[raw magnet]

yes

[plush ether]

yessss

exactly

[raw magnet]

half life is same thing

but /2

[plush ether]

oh okk

huh

[raw magnet]

like

(1/2)^{t/{amount of time})

[plush ether]

oh oh ohok

uhmmmmmm

freak

😭

[raw magnet]

urmmmm what a sigma ☝️

[plush ether]

im really bad at these problems if you couldnt tell

:D

[raw magnet]

idk ignore that I'm just addicted to saying that

[plush ether]

ermmmm what the sigma

[plush ether]

its ok if you say it in a way where its the greek symbol people will just clal u a nerd

:D

lmao

[plush ether]

oki holdon

so

like

can i send the problem

or

do you want to leave

lmao

[raw magnet]

urmmm

sure

[plush ether]

yey

if a radioactive substance has a halflife of 10 years how long would it take for 2 grams to decay to 0.01 grams assuming an exponential decay

[raw magnet]

0.01 = 2 * (1/2)^{t/10}

solve for t

[plush ether]

HEH

hwod u get that

[raw magnet]

hmm

we decoded the problem

[plush ether]

wait also uhm

[plush ether]

im bad at processing what this looks like

😓

can u write it on wolfram alpha or paper

sorry

ahehahehaehhahahehahehehehaehaehah

[raw magnet]

hehehe

[plush ether]

please halp

😭

[raw magnet]

sorry I'm just coping with my possible unemployment

[plush ether]

ah

arent we all

:D

[plush ether]

hmmmmmmm

[raw magnet]

nah ur def getting employed

[plush ether]

cant even do basic alg

feeling useless asl rn

lmao

[raw magnet]

I mean u got a couple years b4 job

[plush ether]

true haha

[raw magnet]

also these problems more about decoding

[plush ether]

ah ic

oh well

lol

[plush ether]

is this correct btw?

[raw magnet]

yes

[plush ether]

how do i change that into log form 😅

[raw magnet]

leap of faith

[plush ether]

what the fweak

zawg

[raw magnet]

lmao

[plush ether]

please help kind sir

i will be forever indebted to thyselves services

[raw magnet]

0.01/2 = (0.5)^{t/10}

[plush ether]

heh

what

[raw magnet]

I divided by 2

on both sides lmao

[plush ether]

oh

well yeah

but

thats not log is it

[raw magnet]

lol

yeah but now

we do the leap of faith

[plush ether]

oh

[raw magnet]

I'm jst going to do natural log here

[plush ether]

heh ok

[raw magnet]

ln(0.005) = t/10ln(0.5)

[plush ether]

ok ok

[raw magnet]

t = 10 * ln(0.005) /ln(0.5)

[plush ether]

wait idk how to do that

😭

i only know how to do it like

log3^3

for example

like really simple ones

😓

[raw magnet]

oh

[plush ether]

sorryyyy

do. you have any idea how to do those or

[raw magnet]

yes

I do have an idea

lmao fine we can do it

[plush ether]

yey

:D

[raw magnet]

we log1/2

log1/2(0.005) = t/10

t = 10 * log1/2(0.005)

[plush ether]

hmm

okk

so its

5log0.5^0.01=t?

im bad at formatting

😅

[raw magnet]

huh

why 5

[plush ether]

1/2*10?

[raw magnet]

no no

it's log based 1/2

[plush ether]

ok

so its

1/2log0.5^0.01*10=t?

[raw magnet]

no

[plush ether]

ahhahahfoeahdsahefshafhdjkas;fhe[8ayoihefnasofiejnapsi

[raw magnet]

it's okay

[plush ether]

i dont know sorryyy

im so confused

[raw magnet]

it's okay

[plush ether]

ok sooooo

please help

😭

pain

[raw magnet]

pain

I gotchu tho

[plush ether]

i cant english right no more

:D

[raw magnet]

hmm do you have free tutoring services in your university

just in general

I'll help you get through this q

[plush ether]

huhhhhhh

im going to highschool next year

😓

[raw magnet]

oh then ur chilling

[plush ether]

lol

i dont get how

0.01=2(0.5)^t/10

turns into a log

[raw magnet]

oh

divide by 2

what do you get

[plush ether]

huhhhhh

0.01/2

but i cant do it in this format

i dont think

[raw magnet]

you can get a numerical result

please do the math

[plush ether]

ok sure??? so

uhm

0.01/2

[raw magnet]

0.01/2 = 0.005

0.005 = (0.5)^t/10

take log based (0.5) on both sides

[plush ether]

HUH

how did you get 0.005

0.01/2=0.5^t/10 is what i thought

[raw magnet]

yes

but 0.01/2= 0.005

[plush ether]

ohhh

alright i got that

0.005=0.5^t/10

what next :D

[raw magnet]

take log based 0.5

on both sides

[plush ether]

how do i do that

😓

[plush ether]

sorry if this is frustrating haha

uhm

[plush ether]

oki so

uhm

do you have like a visual of that or

.close

[raw magnet]

hmm

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[raw magnet]

https://www.youtube.com/watch?v=oR9RwYvAlbM&list=PL0G-Nd0V5ZMpyjKOkfXDoJPG7bT9rh3Q4

check this out

not exactly relevant but could be helpful

[plush ether]

oh uhm

i had a formatting thing but

it really just didnt work bruh

😓

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[sudden drum]

!help

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[sudden drum]

this doesnt make sense

oh nvm

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@sudden drum Has your question been resolved?

[sudden drum]

!help

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[sudden drum]

i need help

is the answer

HELP

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[formal meteor]

someone explain how he factors studd out

[unique minnow]

They just factored e^x out of the whole numerator : you get e^x(3^x + 2 -3^x*ln(3))

Then they factored the 3^x on the inside to get e^x ( 3^x(1 - ln(3)) + 2)

[formal meteor]

oh

okok

and for this

like idk how to practice stuff like this

i get the dericitive

i don’t know how to simplify it to well

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@formal meteor Has your question been resolved?

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@formal meteor Has your question been resolved?

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[marsh forum]

if G is the centroid of a triangle ABC and O is any point then Vec(OA)+Vec(OB)+Vec(OC) is?

[marsh forum]

options

vec(O)

vec(OG)

3vec(OG)

none of these

Position vector O

[wraith hinge]

!status

[trim jolt]

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

[marsh forum]

1

[wraith hinge]

try taking an equilateral triangle

[tawny obsidian]

What is vec

[wraith hinge]

1,w.w^2

[marsh forum]

I know that works

[wraith hinge]

nope

proof?

[marsh forum]

I want to prove for the general case

[marsh forum]

vector

[tawny obsidian]

Hint: vec(OA) = vec(A) - vec(O)

[marsh forum]

So that would give

Vec(OA)+vec(OB+Vec(OC)=-3vec(O)

[tawny obsidian]

How do you figure that

[marsh forum]

Vec(A)+Vec(B)+Vec(C)=0

[tawny obsidian]

Why is that

[marsh forum]

oh

that's wrong here

right

[tawny obsidian]

What is the centroid in terms of vecA, vecB, and vecC

[marsh forum]

Vec(A),vecB,vec(C)/3

[tawny obsidian]

Cool yes good

[marsh forum]

oh

it's that simple

got it

tq

[tawny obsidian]

👍

[marsh forum]

.close

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[dire crystal]

<@&286206848099549185>, may I know what are the next steps in this question?

[pulsar dust]

! status

[trim jolt]

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

[dire crystal]

I'm in 2.

[pulsar dust]

So what you are supposed to do is to separate 5 cos²x into 4cos²x+cos²x

[woeful siren]

Take 4tan2(x/3) to rhs

And it's done

[dire crystal]

I am supposed to show that 5 + 4 tan(x/3) is 4 sec2(x/3) =1 like I need to use like different identities on whether right side or left side to compare and ye

[dire crystal]

umm if you dont mind can you show me how it is done like the working?

@woeful siren

@pulsar dust

[woeful siren]

Just a sec , I will send

[dire crystal]

oh ok 👍

[dire crystal]

Ohh i see

thank you so much 🙂

.close

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[drowsy kraken]

HI

[drowsy kraken]

NEED HELP QUICK PLEASE

<@&286206848099549185>

[wet dragon]

[drowsy kraken]

question 5

i cant remember how to do this

i need to get 5 7 8 done today

[wet dragon]

y=8/x

x=8/y

try replacing either x or y with 8/y or 8/x respectively

[drowsy kraken]

i have to get x and y values

by forming a quadratic equation

then factorizing into brackets

and using those to get values

[wet dragon]

great

you know what to do

[drowsy kraken]

I KNOW WHAT TO DO BUT I CANT REMEMBER HOW TO

FREAKING RIGHT HAND SIDE TO LEFT HAND SIDE

[wet dragon]

y = x + 2

[neon basin]

7. 9x = x² + 2x + 1
   x² - 7x + 1 = 0
   Solve for x i suppose

[wet dragon]

replace y with 8/x (because y = 8/x)

8/x = x + 2

now solve for x and y

ok?

[drowsy kraken]

No thats the problem

i have to move all of them to one side

im confused with that part

thats it

[wet dragon]

try multiplying both sides by x here

[drowsy kraken]

so its 8 = x^2+2?

[wet dragon]

2?

you mean 2x

yes

[drowsy kraken]

mb yes 2x

[wet dragon]

now solve

[drowsy kraken]

alright js standby for me please

i will get this done rq then i might need help

[wet dragon]

ping me when you return

[drowsy kraken]

sure

@wet dragon

um so now im at

(x-2)(x+4)

x=2 x=-4

how do i get the y vals

[wet dragon]

y = 8/x

or

y = x+2

https://tenor.com/view/think-mark-invincible-omniman-gif-21416554

handshake is fine

or fist bump

[drowsy kraken]

im so cooked rn my brain has had horrible math burnout

https://tenor.com/view/theoffice-michael-scott-jim-halpert-gif-27622036

the office gifs do NOT stop

[wet dragon]

good work

[drowsy kraken]

@wet dragon

so

question 7

[wet dragon]

ye

[drowsy kraken]

the

[wet dragon]

3sqrt(x) = x+ 1

square both sides

[drowsy kraken]

x+1=3sqrtx

square both sides?

[wet dragon]

yes

[drowsy kraken]

so 3 = x^2+1

?

[wet dragon]

no

[drowsy kraken]

9

?

[wet dragon]

no

(ab)^2 = a^2 * b^2

[drowsy kraken]

ab?

[wet dragon]

where a and b are any numbers

so

[drowsy kraken]

so in this equation it would be?

[wet dragon]

( 3 * sqrt (x) )^2 = 3^2 * sqrt(x) ^2

=9x

also

[drowsy kraken]

hUH

[wet dragon]

ill send an image

[drowsy kraken]

too many brackets

brain is abt to explode

[drowsy kraken]

yeah thats better

[wet dragon]

in general

[drowsy kraken]

x+1 = 3sqrt(x)

would come out to

[wet dragon]

squaring both sides gives

[drowsy kraken]

3^2 x sqrt(x)^2 = 9x?

[wet dragon]

ya thats 3sqrt(x)^2

now square x+1

and make them equal each toehr

[drowsy kraken]

okay and then?

can you js run through this question

[wet dragon]

nuh uh

do it urself

[drowsy kraken]

one example would be helpful

😭

PLEASEE

@wet dragon -x^2+9x-1

or

x^2-9x+1

POCKLE

IMA GONNA CRY

@wet dragon

[wet dragon]

are confused as to what (x+1)^2 is

[drowsy kraken]

x^2

+1

[sweet hare]

(x + 1)^2 = (x + 1) * (x + 1)

[drowsy kraken]

which is x^2 +1 isnt it

[sweet hare]

no

you can use FOIL: multiply the First terms together, and the Outer, and the Inner, and the Last terms, then add them all

[drowsy kraken]

@sweet hare

can you help w question 7

please

im lost here

<@&286206848099549185>

[half mural]

lemme look

x+1=3√x?

@drowsy kraken

(x+1)²=(3√x)²

Hint ^

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[twilit hatch]

hey i'm looking through past MAT papers (this is from 2016) and cannot figure out why the length of this side is a/b. nagged me for 2 days

[twilit hatch]

i feel like it's something to do with a similar triangle with sides a, b, and c with scalar multiple 1/b

[verbal stream]

I think you can also use the AM-GM inequality

[twilit hatch]

i'm not familiar with that

[verbal stream]

Basically for positive reals, the arithmetic mean is always greater than or equal to the geometric mean

But the geometric solution also works

[twilit hatch]

i'll check out AM-GM, but i'm lost on how they got a/b

[verbal stream]

The right triangle formed by the origin and x/y intercepts has legs c/b, c/a

So the ratio of leg lengths is a/b

And the similar triangle has one of the legs as the radius of the circle, which is 1

so the other leg is a/b

[twilit hatch]

damn

that's wack

appreciate it :)

.close

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[past comet]

Whats wrong?

And?

no

What?

When does a power series converge?

So write when it converges in terms of |z|?

|z|

Yes didn't you just find it?

And what is definition of radius of convergence?

The question asked for radius of convergence?

If you know definition you did yes

so answer is...

indeed

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[brisk pebble]

Hi

[brisk pebble]

sin a = 1/root 10 and sin b = 1/root 5 find a plus b

So uh I cant use calculators

so I cant just use the sin inverse function

any other leads?

[main sigil]

maybe find sin(a+b)

and then it might look familiar

just guessing, i need to try it btw

[brisk pebble]

no I did sin (a plus b) I got it as root 5/50

then I would have to use sine inverse

[main sigil]

that looks incorrect

[brisk pebble]

Oh I messed up?

[main sigil]

I think so

[brisk pebble]

what are u getting?

[main sigil]

havent tried it yet, im just guessing based on how small root 5 / 50 is

[brisk pebble]

Oh alr let me check again

[main sigil]

what did you get for cos a and cos b?

[brisk pebble]

cos a as 3/root 10

cos b as 2/root 5

[main sigil]

that looks correct

[brisk pebble]

alr hmm then i substituted it in sinacosb plus cosasinb

[main sigil]

Hmm

will a+b even have nice close form

oh ye

it does

[brisk pebble]

what does that mean?

[main sigil]

ignore it, i messed up one line, it has a nice solution

[brisk pebble]

alr

[main sigil]

Wait im idiot

[main sigil]

this is correct

no its not, misread it

im idiot twice in a row

[brisk pebble]

all good man

[main sigil]

alright, so what do you get?

with the formul

sin(a+b)

[brisk pebble]

root 5/50

no sorry

5 / root 50

[main sigil]

thats the one

[brisk pebble]

I am an idiot

[main sigil]

now root 50 can be simplfieid

[brisk pebble]

alr

[main sigil]

note that 50 has a nice square factor

[brisk pebble]

which would be?

[main sigil]

25

:]

so sqrt(50) = sqrt(25 * 2)

[brisk pebble]

Oh I dont know nice square factors

Alr I think I got it now tho

[main sigil]

It's not a mathematical term, I just meant "a factor that's a square"

25 is a factor of 50 and it's a square of 5

it's good to consider the prime decomposition when simplifying roots

[brisk pebble]

oh u mean 5 root 2?

alr then what do we do

[main sigil]

$\frac{5}{5\sqrt{2}}$

[solid kiln]

MethIsAlwaysRight

[main sigil]

this is what you should have now

[brisk pebble]

Correct

OH SO 1 ROOT 2

[main sigil]

yes

[brisk pebble]

OH and sin 45 is 1/root 2

[main sigil]

1 / root 2

yep

[brisk pebble]

Thanks a lot man

[main sigil]

np

[brisk pebble]

really helped me

[brisk pebble]

people told me it wasnt possible without calculators

[main sigil]

sorry for my messy messages at the start lol

[brisk pebble]

no its all good

[brisk pebble]

if I have doubts can I dm them to u?

[main sigil]

If it's related to this problem, then sure

otherwise please avoid it

[brisk pebble]

alr no problem

Thanks again meth

[main sigil]

I am usually helping in this server when im not busy

[main sigil]

np

[brisk pebble]

So uh now that my doubt has been resolved what do I do?

[main sigil]

.close

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Channel closed

Closed by @main sigil

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[brisk pebble]

.close

[main sigil]

already done :]

[brisk pebble]

Ok its closed

[brisk pebble]

alr bye man

[main sigil]

bye, have a nice day

[brisk pebble]

u too

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[stone comet]

Hi.

[stone comet]

$\lim_{x \to 0} |x|^i$

[solid kiln]

Mary

[stone comet]

I need a hint to begin with.

[past river]

Probably write |x| as e^ln|x|

[grim estuary]

for any i?

[stone comet]

i is sqrt(-1)

[grim estuary]

oh shit my bad I thought i is a variable

[grim estuary]

have you tried doing this?

[stone comet]

yes, but doesnt look like i can do too much

maybe i dont see something obvious

[grim estuary]

can you evaluate $\lim_{x \rightarrow 0}\ln|x|$

[solid kiln]

N(μ,σ²)

[stone comet]

shouldnt it be ilnx?

[past river]

If you apply what I said you‘ll get $\lim_{x\to 0}e^{i\ln|x|}$

[solid kiln]

ℑμΤ𝛄𝛗θ

[past river]

And you can evaluate this as x aproaches 0 from both sides to confirm your result

Or rather, no. I‘m mixed here, because I‘m not sure you‘d want to assume i * inf = inf

[grim estuary]

yeah but start from evaluating the limit of that

[stone comet]

that is the main problem i have

[past river]

What happens when you evaluate it from the right? And what about the left?

[stone comet]

-i * inf

i mean e^ that

but it is not a closed form

or 0^i

which is undefined

[past river]

Recall that e^(ix) = cosx + isinx

In your case x = ln|x|

This should help clear out why it‘s undefined

[stone comet]

wait this limit has no solution?

ok i see now

thx

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[copper dagger]

Could anyone help with this?

[exotic jetty]

Plug f(x) into x

Then expand and simplify

[wraith hinge]

f(f(x)) = f(x^2 + 1) = (x^2 + 1)^2 + 1

[copper dagger]

So it would be x^4 + 2x^2 + 2 right?

[exotic jetty]

Yes

[copper dagger]

It was correct thank you, I thought I was doing something wrong but forgot to add one

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[scarlet totem]

How do I solve this

[prisma kayak]

alpha' + delta + gamma = 180
this gives u gamma

epsilon = 180 - alpha : this gives you alpha

see if you can do the rest from there

which is basically only beta

[scarlet totem]

Why minus alpha

[prisma kayak]

its the opposite exterior angle
no wait i might be wrong

you can find out the supplementary angle of delta

which gives you two angles of the small triangle on the left

epsilon, 180-delta, 180-alpha

^ 3 angles

sum them to 180

you get alpha

is this confusing ?

[scarlet totem]

A bit Ill try to process it in my head

[scarlet totem]

Why this step?

[prisma kayak]

this is what i was referring to

now sum these up and you should have 180
solve for alpha

[scarlet totem]

So gamma would be 50

right?