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@trim tendon Has your question been resolved?

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[acoustic wave]

When multiplying series, do the two series indicies have to start at the same point?

[acoustic wave]

<@&286206848099549185>

[plucky sluice]

Example?

[acoustic wave]

I am wanting to multiply these series together

Should I pull out the first term in the second series first?

[plucky sluice]

I think that will make it simpler, yes

[acoustic wave]

Okay sweet, I will definitely take simpler 😭

This whole problem is very arduous

.close

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[slate vortex]

I don't really get how to explain these types of problems. Could someone help?

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[empty pelican]

Hello!

I am trying to prove that for a binomial raised to a prime power, the binomial expansion of that binomial will only have coefficients that divide that prime power.

I started working on it, by trying to prove it directly but....given the equation for the coefficient, wouldn't it just be true more generally for any binomial raised to a power, not just a prime power?

[empty pelican]

Sorry, I meant for any coefficient between 1 (incusive) and p-1 (inclusive)

Oh, nevermind lol!

[tardy stag]

,w expand (x+1)^4

[ocean seal]

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Requested by kitten.in.a.teacup

[lone heart]

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[tribal valve]

okay so its improper

so just limit t approaches infinity and the staff is t and 1

and then just use usub, u = lnx to get $\frac{1}{2}(lnx)^2$ from t and 1

[ocean seal]

dabbingpotato

[tribal valve]

now just sub in 1 and you get 0

if you sub in t you get ln infinity

is that possible

or is this divergent

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[celest stump]

does no acceleration mean no one speeds up/slows down the entire time?

without much understanding, i think the answer would be D by counter example, if there is no acceleration then Charlie could of just sat still at the start of the race

making the race 18 meters long

isnt it all dependent on how far charlie went?

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[raven shale]

I just wanted to know if this is correct?

[placid zinc]

Try subbing it into the original DE to check

There is a sign error

[raven shale]

How do I deal with the sign?

[raven shale]

How do I sub it?

[placid zinc]

Using your solution, what's dV/dP?

[raven shale]

Its -C

[placid zinc]

And then, what's -V/P?

[raven shale]

Its dV/dP ?

I don't get it

[placid zinc]

V = -CP
So
-V/P
= -(-CP)/P
= C

But dV/dP should be the same as -V/P, as per the question. So, the solution doesn't work

The problem is when you take the exponent of both sides. The negative is out of place

[lone heart]

@raven shale Has your question been resolved?

[raven shale]

Hmm

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@raven shale Has your question been resolved?

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[vale wigeon]

you know you can select a thing in paint, and ctrl+c ctrl+v it directly into discord right

[icy herald]

Ok didint know ty

[vale wigeon]

also are these meant to be two different problems?

[icy herald]

I have to brb

[icy herald]

Ya

[vale wigeon]

for which you've done the working out and want it checked?

[icy herald]

Ye

[vale wigeon]

well im gonna tell you that the top problem is wrong all around

[icy herald]

I have to go for 5 min

Brb

[vale wigeon]

also for the second problem, 1/3 is not equal to 0.3330

also x^(-4)/x^(-2) ≠ x^(-4/-2)

[lone heart]

@icy herald Has your question been resolved?

[icy herald]

i will look at chat soon

back

[icy herald]

why not

[icy herald]

then its x^-6?

[vale wigeon]

expressing 1/3 as a decimal would require the threes to go on forever

[icy herald]

ya

so cant solve it then?

[vale wigeon]

"solve" is a strong word

there is absolutely no reason here to convert 1/3 into a decimal

[icy herald]

just let it be as 3^-1 or 1/3

ok

(2xA^6)/(X^6 x 3^-1)?

[icy herald]

i have so simplify btw

@vale wigeon

[vale wigeon]

there are many things wrong with how you are writing this

1. don't mix UPPERCASE and lowercase
2. don't use the letter x as a multiplication symbol

[lone heart]

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Channel closed

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[covert kiln]

Function 4x^2+8x-9

[lone heart]

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[hollow niche]

yo

[hollow niche]

nvm!!

.close

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[amber frigate]

hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no counterexample

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[halcyon mirage]

no idea what the question means

[halcyon mirage]

but i still need a starting push to start

[vague coral]

show that a_{2022} <= 1

[halcyon mirage]

ye but

fk

[vague coral]

?

[halcyon mirage]

ill figure it out

.close

[lone heart]

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[icy herald]

@languid gust

[icy herald]

Yo i forgot one thing

can you help me?

[frozen blaze]

Hey

[languid gust]

wassup

[icy herald]

40 billion monkeys per milliliter

how many monkeys volume = 1.5 dl

[frozen blaze]

40money/ml

[icy herald]

40x10^9?

[languid gust]

ok how many mililitres in a litre

[icy herald]

1500

i think

[languid gust]

theres 1000ml in a L

how many L in a dL

[icy herald]

then 40x10^9 x 150

[languid gust]

stop stop no jumping ahead slow down

[icy herald]

10 dl in a L

[frozen blaze]

Unitary method

[icy herald]

monkey*

[languid gust]

there are 40x10^9 monkeys per mL

thats 40 billion

now

you are trying to find how many in a decilitre

[icy herald]

how many monkeys in 1.5 dl

40 billion x 150ml

[languid gust]

no

we need to convert mL to dL

because they are not the same measurement

[icy herald]

40 billion monkeys is per mL

[languid gust]

now, there are 1000ml in a litre

and 10 litres in a dl

[icy herald]

ya

[languid gust]

so therefore there is 10,000 ml in a decilitre

[icy herald]

no

[languid gust]

because 10 x 1000

[icy herald]

ye

10 ml?

10 dl is 1l

[languid gust]

other way around

its implied in the word decilitre

10 litres

[icy herald]

decimal

deci?

[icy herald]

10 DL is 1 Liter

[languid gust]

its not though

[icy herald]

how ?

[languid gust]

HOLD ON HOLD ON

[icy herald]

lol

[languid gust]

some random source telling me wrong

1dl is 0.1L so 1.5dl is 0.15L which would be 150 mL you are correct my friend

my mistake

[frozen blaze]

How's 40 billion monkey in litre ?

sorry i mean in ml

It must be volume

[languid gust]

mL is volume

[icy herald]

yep

so

[frozen blaze]

Yes

[languid gust]

monkeys aren't 2 dimensional

[frozen blaze]

Sorry i mean

[icy herald]

40 billion monkeys in 150 ml

[frozen blaze]

Is money a liquid to put in tank

Anyway

[icy herald]

they are not asking for monkeys i just said it because its easier to explain

[languid gust]

because 40 billion in 1 ml

you need to times 40 billion by 150

[frozen blaze]

Bruh

[icy herald]

ye and the answer i need to write in weird way

[languid gust]

probably scientific notation

[icy herald]

i get 6x10^13

but book says

6x10^12

wtf?

[frozen blaze]

40×10^12 money per 1 d

L

Wait

[languid gust]

whats 40 x 150

[icy herald]

420

150 x 10 = 1500

1500 x 10

=

15000

[frozen blaze]

4×10^10 moneky per 1dl

[icy herald]

15000 x 10 = 150000

150000 x 10 = 1500000

[icy herald]

1500000

fact or cap?

[icy herald]

you cant split it up?

[languid gust]

very cap

[icy herald]

and multiple by 10

just 4 times?

[languid gust]

definitely not

[icy herald]

it made sense tbh

[languid gust]

just out of curiosity what grade are you in

[icy herald]

12

[languid gust]

so you're trolling

[icy herald]

no

[frozen blaze]

Wtf

[icy herald]

I am not

I study math 18 hours a week now

self study

[languid gust]

you have a calculator right...

use it

[icy herald]

ye

[frozen blaze]

Good then

[icy herald]

so

[languid gust]

gives you the asnwer

[icy herald]

why type 40 x 150

its 40 billion x 150

[languid gust]

we're forgetting the billion for now

6000 x 10^9

6000 is like 6x10^3

[languid gust]

6x10^3x10^9 is 6x10^12

[frozen blaze]

How you get 6

[icy herald]

because

it get lower value you do ^+

[frozen blaze]

4 trillion monkey per 1dl

ain't it

[icy herald]

??????????

[languid gust]

6 trillion

[frozen blaze]

Ohh

[icy herald]

3+9 = 12

6^12

[frozen blaze]

4 trillion in 1 dl
And
6 trillion in 1.5dl

Thats why

[icy herald]

@languid gust how did you make it into 6 again?

because 40 x 10^9?

[frozen blaze]

1.5 dl

[icy herald]

x 150

[frozen blaze]

Thats why

[icy herald]

= 600000000000000000

then 6 x 10^9

[languid gust]

yup

[icy herald]

ok make sense

but then

[icy herald]

how do i make it into 6 x 10 ^12

wait dont answer

i will check something

[frozen blaze]

Sorry 1.5 dp

[icy herald]

its not the problemm lol

,rotate

[icy herald]

my calculator dont let me see what 40 x 10^9 is in numbers

[frozen blaze]

I solve same problem using unitey method

[languid gust]

ok im gonna write this out for you, and then i have to go because i have other things to do

[icy herald]

ok t

y

[icy herald]

idk what that is

but thanks i can look back at chat

[frozen blaze]

Do u know about cramer's rule

[icy herald]

no

[frozen blaze]

6Trillion

[icy herald]

ty bro

[icy herald]

ty

[frozen blaze]

?

[icy herald]

for help too

[frozen blaze]

I didn't help actually

I just came because i was suprised from question

40 billion monkey in 1 ml ?

[icy herald]

ye original question didint say that

i just changed from bacteria to monkeys

[lone heart]

@icy herald Has your question been resolved?

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[shadow igloo]

Analytic geometry, I'm suck at understanding the question

[halcyon mirage]

hey

[shadow igloo]

Can anyone change the wording of the question? I don't know how?

[halcyon mirage]

ah

let me see

give me 1 mimnute please

[shadow igloo]

Sureee no need to rushh

[halcyon mirage]

oh ok i see how this wors

so you have point P correct?

you want the distances $PR=PQ$

[ocean seal]

i like cheese

[shadow igloo]

Yes, but what should be my point P?

[halcyon mirage]

there is a line, whch for all points fits the equation

you need to find that line

if you dont know how to solve it algebraically, i would recommend finding 2 poitns which are along the line, then figure out the equation.

does that help?

or do you want me to clarify furhter

[shadow igloo]

But on the graph it looks like PR is not equal to PQ, soo I need to find a point that would give me two equal distance?

[halcyon mirage]

yes

note, dont trust graphs

they arent always drawn to scale

sometimes they are

well

usually

but

if it doesnt feel correct

dont trsut it

[shadow igloo]

Oohhh okaayy Okayyy

[halcyon mirage]

so

let me get on desmos rq

[shadow igloo]

Aightt I'll tryy noww if it would work soo two distance formula equal to each other?

[halcyon mirage]

just find the nromal

then make it pass through the middle of QR

thatll be my idea

yk what the normal is correct?

[alpine sable]

Excuse me, is 9x+y = 7 the answer?

@shadow igloo

[halcyon mirage]

no, i dont think so

[shadow igloo]

I still don't know the answer xD

[halcyon mirage]

\

i think

[shadow igloo]

It would look like this but not twice of the distance??

[halcyon mirage]

the constant is wrong

the gradient of the equation is -9/5 btw

[shadow igloo]

OOHHHH THAT LINE in the middle

[halcyon mirage]

yes

[alpine sable]

Thanks

[shadow igloo]

Yeahh it would give both equal distancee

Alright, I think I can do it noww, Thanks guyss

[halcyon mirage]

here we go @shadow igloo

u should be able to figure out the working

[snow sail]

oh dang.....

[halcyon mirage]

[snow sail]

[shadow igloo]

XD, I'm a suckass at graphingg @halcyon mirage

[snow sail]

damn im suck at math

[halcyon mirage]

nup

ur good

layla its ok

haha

@shadow igloo do u know how to

uh

calculate the gradient

of P

[shadow igloo]

Nooo but I think I can get the equation I think, anyways what is gradient? :0

[snow sail]

IM FEELING nervous today cuz of this test math

[shadow igloo]

First time hearing thaat @halcyon mirage

[shadow igloo]

It's okay to be feeling nervous thoughh soo no worries

[halcyon mirage]

gradient is

uh

the gradient

;-;

ok so

go to desmos

now type in equation y = mx

m would be the gradient

now add a slider of m

and see what the gradient does

ooh i have an explanation

the gradient is practically the angle of th eline

[shadow igloo]

Ohh like slopee or no?

[halcyon mirage]

mhm

[snow sail]

uck myself

[halcyon mirage]

ur good

[snow sail]

WHATTTT

WHAT should i do if i cheat on test

[halcyon mirage]

haha dont

if u need help just ask

👍

[shadow igloo]

Yeaahh don't xD

[halcyon mirage]

aries did u figure it out?

[shadow igloo]

It's better if you know how

Yeahh the equation and distance, I'm kinda working on it

[halcyon mirage]

aight

tell me if u ned further help

[shadow igloo]

Yepp, thanks a bunch to youu

[halcyon mirage]

no probs!

dont close it yet haha, in case u mess up somehow :)

[alpine sable]

Just wanted to ask if we can do it this way (Sorry for disturbing)

[halcyon mirage]

hmm

[snow sail]

my brain didnt make it

[halcyon mirage]

aditya let me have a look

how do you classify the direction of a point?

how do you get a

uh

the equation

of the point

cuz i dont think that works

@shadow igloo anything else you need help with?

[alpine sable]

uhh, I don't know much about this, I just used distance formula in coordinate geometry. I equated the distance between P point to r and q point as it is given in the question

[snow sail]

i already cheat on test i calculator it

[halcyon mirage]

skull

@alpine sable that is a good idea, and it along the way

basically here are the steps

1. find the gradient of QR

[alpine sable]

From this I got a equation in which when we put the x and y coordinate of the point it gets solved.

[halcyon mirage]

2. get the normal of QR

3. find the midpoint of QR

get the equation of P using the normal as the gradient

[shadow igloo]

Nopee I'm good for noww xD, but maybe moree laterr

[alpine sable]

I haven't learned it till now but I will try learning it

[halcyon mirage]

aight

.close @shadow igloo

[snow sail]

i just download the math to cheat and learn

[shadow igloo]

Aightt

Thanks a bunch again guyss

[halcyon mirage]

gl with whatever u need to do

i need to sleep now

lmao

gn

[shadow igloo]

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[snow sail]

good night have a good sleep

and sleep well

[lone heart]

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[marsh echo]

,rotate

[marsh echo]

questikon b

[snow sail]

damn....

[marsh echo]

?

[snow sail]

nothing.....

[zealous lichen]

what is J+

[marsh echo]

a positive integer

[zealous lichen]

just show that $\frac{1}{1+t^n}\leq \frac{1}{1+t^{n+1}}$ for $0\leq t\leq 1$

[ocean seal]

WhereWolf(ping if needed)

[marsh echo]

do i work each individualy/

?

[zealous lichen]

wdym

[marsh echo]

im also confused about the equal to part

also where do i start

[zealous lichen]

you can start from $t^n\geq t^{n+1}$

[ocean seal]

WhereWolf(ping if needed)

[marsh echo]

oh i see

wait

but the inequality is flipped right

cause hes my concern

if f(x) > g(x) for the domain

[frozen blaze]

We can use any opreation on both side right

[marsh echo]

then in the area under f(x) > area under g(x)

right?

so i just need to prove that f(x) > g(x) for 0 < x <1

for for the function

how are the areas equal to each other

only as n approached infinity

do the integral of them equal each other

[frozen blaze]

How ?

[frozen blaze]

Yes

If ranges of f(x) is greater then g(x)

while we input same domain

[marsh echo]

how do i prove $\frac{1]{1+t^{n+1}} \geq \frac{1}{1+t^n}$

[lone heart]

@marsh echo Has your question been resolved?

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[paper sage]

Why I’m getting two different answers since it same equation

[pale kestrel]

Why are you sure they're different.

[paper sage]

Hmmm they seem different

[paper sage]

Is there any way to verify that

[coral flower]

both answers are same

from left side they just factored out e^(2x-2) from numerator and denominator and canceled them

[lone heart]

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[cyan mountain]

hello kind souls, can anyone help walk me thru this problem?

[tardy stag]

evaluate from the inside out

first find f(4)

[cyan mountain]

that is 5

f(4)=5

[tardy stag]

great, so now go the other way, look for x such that f(x) = 5 [this is how you calculate f^-1(5)]

[cyan mountain]

such x that f(x) =5

x=4

?

[tardy stag]

yeah lol

[cyan mountain]

so the inverse

is 4

[tardy stag]

yep

[cyan mountain]

HAHAH

[tardy stag]

since it's a one-to-one function, $f\inv(f(x)) = x$

[cyan mountain]

like

[ocean seal]

jan Hayley

[cyan mountain]

yes

i knew

but i thought

maybe it would be

more complex

thank you so much

LOL

[tardy stag]

nah but it's good to do it by hand to check

[cyan mountain]

i really appreciate it 🙂

ty

.close

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[raven shale]

Is this right

[wind cloak]

yes

[raven shale]

Thanksss

How about this?

@wind cloak

[wind cloak]

looks good

[raven shale]

I don't know if that's the right thing
To multiply both sides to 6

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[frosty swift]

Is the answer zero (question is to evaluate this limit).

[coral flower]

yeah pretty sure

lne = 1
ln 1 = 0

[frosty swift]

Ok.

Thanks.

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[alpine edge]

How to calculate the grey area

What I did is set the dotted lines to 2 making the grey area 8cm^2

but I did that from observation

[manic flame]

you can start by calculating the area of the entire square

and you can see the 2 smaller triangles are 2 x 2

[alpine edge]

that would be 36cm^2

[alpine edge]

how do I know that the dotted line is actually 2 cm

[manic flame]

You know the triangle is right angle (90) and the sides are equally long. (8) This means the small triangles are 45c

[alpine edge]

I see, since the top angle of the small traingle is also 45° then the sides must be equal

[manic flame]

yea, and you will see if you remove the 2 smaller triangl they still maintain their 90 angle

[alpine edge]

Gotcha, cheers!

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[magic cipher]

Can some

[magic cipher]

Can someone help me with this please?

[lone heart]

@magic cipher Has your question been resolved?

[manic flame]

you know how to get the y=kx+m from those 2 points?

[magic cipher]

for the line?

Yes

Y=2.0625x-3.3

[manic flame]

ok

and you know the circle equation?

[magic cipher]

X^2 +y^2 = r^2

[manic flame]

ok

so you have the equation if its in origo

and it gives you the radius

[magic cipher]

So i plug in the line equation?

[manic flame]

yea once you have both equations

you replace the y in the circular equation with the line y

[magic cipher]

I can solve for x and then plug in the x points into the line to find y values?

[manic flame]

yea

since it a line, you can get 1 or 2 x

depending if it tangens or goes through it

[magic cipher]

Oh ok

Ty ima give it a shot

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[rugged sail]

.open

[fallen shuttle]

Are these the same?

[wind cloak]

what

Left is a real number right is an expression

Is it meant to be an equation?

[fallen shuttle]

I am working with taylor series

so I want to create a taylor series for the one on the left, I want to know if I use the one on the right would it be the same for the series

[vale wigeon]

this does nothing, you're supposed to post your own question right away no commands
but now you need to do it in your own channel

[vale wigeon]

the left thing is literally just a number

[fallen shuttle]

I am sorry, I am lost with that

[wind cloak]

Well

What does a definite integral give you?

[fallen shuttle]

This is what I am working on

[last ether]

Do you know the Taylor series for cos(x)

[fallen shuttle]

yes

[last ether]

Yeah so just replace every x with πx^2 and that'll be your polynomial

[fallen shuttle]

I was thinking that, but the stuff on the left had me confused

[tardy stag]

the idea here is that you replace the $\cos(\pi x^2)$ with the series

[ocean seal]

jan Hayley

[fallen shuttle]

Ok I will give that a try

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[half flicker]

Any idea how to solve this eq?

[half flicker]

Its w

i have found solution

i had to take the power -1 and then substitue

.closed

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[mellow mica]

I am supposed to change the equation r^2 -z^2=0 into spherical coordinates and then simplify

[mellow mica]

I changed it into P^2sin^2p - P^2cos^2p = 0

Then, I grouped into P^2(sin^2p - cos^2p) =0

I then went P^2(1/2 - 1/2 cos 2p - 1/2 - 1/2 cos 2p) =0

I am currently at P^2(-cos2p) = 0.

I am told it can be simplified further, but I do not see how

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[paper sage]

I found the stationary points which is (2,1) I don’t know what to do else

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[fringe mist]

Every how many zeros is next number?

Like 1.000.000 this is one million, you’ll need one thousand millions to be a billion?

[umbral cosmos]

1.000.000 million
1.000.000.000 billion

[fringe mist]

So like 10 millions

And then 1000 millions would be billion?

[wind cloak]

yes

[green knoll]

1 one
1000 one thousand
1000000 one miion
1000000000 one billion

if thats what youre asking evrry 3 zeros you go to the next “number”

[ionic jewel]

This is true in English but not true in all languages

in chinese for example, it's every 10000 gives you a new "word"

[fringe mist]

What’s after billion?

[ionic jewel]

trillion is a thousand billions

(in English)

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[toxic mulch]

I am unsure what this question is asking I understand that a) is asking df/dL but I am unsure how to utilize implicit differentiation to specifically get the answer as for b) it would be df/dT. I guess I am just not sure how these would differ.

[alpine sable]

please open another channel first. This channel is closing because you deleted Ur original message

[toxic mulch]

Alright thank you! Sorry just joined the server

[alpine sable]

no worries it happens

[toxic mulch]

Thank you!

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[lilac jolt]

Scientific Notation: is it possible to have a negative coefficient

[lilac jolt]

I mean, does that violate the rules of sn

[gray isle]

something like
$$-5.7 \times 10^3$$
is valid in scientific notation

[ocean seal]

ℝam()n()v

[lilac jolt]

what's not valid then

[plucky sluice]

Do you mean negative power? If so, yes. If you mean can scientific notation represent negative numbers, also yes

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[dawn quail]

I don't understand this last step

x^5

isn't it supposed to be ln(x)^5?

[gray isle]

bad/wrong notation

[dawn quail]

not ln(x^5)

[dawn quail]

where?

[gray isle]

first step

[gray isle]

eeep. Leonard done fked up

[dawn quail]

where exactly?

i see that he wrote lnx

which I don't like

I prefer ln(x)

this is suuuper confusing.... is it ln(x)^5 or ln(x^5)??

[gray isle]

power should be in the argument
especially for the second and third term

ln(x^5)
ln((x^2+1)^(1/2))
ln((x-2)^4)

[dawn quail]

damn, i misread this

I thought power 5 is for log, not the argument

wow, brackets are super needed here

dunno why he's teaching without them

[gray isle]

yes

[dawn quail]

we are talking about arguments

brackets = requirement, not optional

alright ty

I will try this again

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[sinful fossil]

Had this question in geometry/chem. "You are hired to count the number of ducks in three northern lakes during the summer. Describe the procedure you would use to go about this task. Then, suppose your answer is around one million ducks. What would you do if, you are driving away from the lakes and see 15 more ducks fly in from the south and land on the last lake. Do you change the number of ducks that you report? Justify your answer."

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[naive valley]

what's the context? this doesn't seem like a math question

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[visual nest]

$1.4.6 Convert is a function to change equations into their variable form, For example
ℂ(x) = 45x → y = ℂx
Shows that the normal equation was converted (ℂ) to it’s variable form. ℂ replaces the number 45 and the ℂ(x) was replaced by y, the common variable change.$

[ocean seal]

Umbe

[visual nest]

actuall

nvm

.close

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[radiant silo]

I thought I proved x_(n+1)-x_n tends to zero implies it’s convergent as it’s Cauchy but this ain’t true can someone tell me why my proof is flawed

[radiant silo]

I have a counterexample I just dk why my proof is wrong

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[radiant silo]

<@&286206848099549185> elp

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[lone heart]

@alpine sable Has your question been resolved?

[icy crane]

yeah kaz

what you posted already seems simple enough

maybe you can divide everything by -3 to make it even simpler

woahh dude

not cool

i didn't say divide by 0 😄

I said divide by -3

zero divided by anything (except zero) will remain 0 indeed

but coming back to the equation you posted, it depends on what you want to do

solve for x? solve for y?

ah

yes. not -3

that would be if you wanted to solve for x

what does it look like now?

heh you mean divide everything else by the coefficient 😄

and yes, that sounds good

I mean

you haven't solved for y yet

that's just a step

yep. ok so you know how to cancel terms and move them from one side to another

cool

what else?

don't you mean the "height" of the equation when x = 0?

like, the slope is something that's always the same in linear equations

it's that "m" in your example

you mean depend on x? not in linear equations

how about you also show exactly what the exercise is asking

so we're clear on that

I think you want to find the value of y when x = 0

ok

so two different things

first: find the slope

well, solve for y and you'll see the slope appear

it will not have a specific value

right

yep

its value depends on x

yes

yes but don't do that part yet

just get y alone and tell me what the equation looks like

ok and divide by the coefficient like you said before

so you have y = .....

all of it

divide every term by -5

yea, except you keep jumblin numerator and denominator

it should be y = (-2)/(-5)x - 4 instead

haha make sure to be careful with that stuff in the future

alright so now you can see the slope

what is it?

no!

check again

ok the y stuff is correct

you put in x = 0, then y = -4

yes

you're welcome but you still gotta do the slope

yes, so what is M equal to

M is the slope

nope 😄

actually

yes it is

you are correct

this time I mixed numerator and denominator

you can also simplify it by cancelling the two -

-2 / -5 = 2/5

glad to help

[lone heart]

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[alpine sable]

Do I just ignore the square root for this?

[stark crater]

What do u think it is

even if you cant show algebraically

[alpine sable]

Lemme solve rq then

Even I think

[stark crater]

Yeah

Do you know the formal definition of even

[alpine sable]

But only looked at the exponent so lucky guess lol

[stark crater]

Oh lol

[alpine sable]

If you put f(-x)

It should come out the same

I think that’s what it was

[stark crater]

Yeah

[chrome silo]

ya it is even

[stark crater]

So check if sqrt(x^2-4) = sqrt((-x)^2-4)

[alpine sable]

So could I do the -x thing without looking at the square root and just solve like that every time?

[chrome silo]

ya it

[stark crater]

No

[alpine sable]

Fuck Alr

[stark crater]

Informally, a function is even if when you flip it across the y axis it overlaps

Formally it is f(x)=f(-x)

[alpine sable]

Yeah and other one if you flip it 180

Should be the same

[chrome silo]

and 0 is the only function that is both even and odd

[alpine sable]

Just the algebraically that’s a pain

[alpine sable]

Huh?

[stark crater]

Once you understand it is probably simple. You just literally plug in -x to the function

for x

[stark crater]

thats how I got this

[chrome silo]

f(x)=0 is both odd as well as even function and it is the only one of its kind

[alpine sable]

Yeah I get that but what would there need to be for the square root to fuck things up?

Just plug it into the calc and check?

[stark crater]

The square root is irrelevant

[alpine sable]

Ok so I can just ignore it then

That’s what I was wondering

[stark crater]

You are just confirming if this is true

[chrome silo]

because of the square root the value of x can't be less than modulus 2

[stark crater]

(-x)^2=x^2 agree?

[alpine sable]

Yuh

[chrome silo]

yup

[stark crater]

so then sqrt(x^2-4) = sqrt((-x)^2-4) implies sqrt(x^2-4) = sqrt(x^2-4) which is obviously true since theyre the same thing

so you have algebraically shown the function is even

[chrome silo]

true

[alpine sable]

Alr thanks g

[stark crater]

if you were trying to show it was odd you would do -f(x)=f(-x) which in this example would be confirming -sqrt(x^2-4)=sqrt((-x)^2-4) but this is false

so it is not odd

[chrome silo]

ya and also one function can't be both

[stark crater]

Ye

[chrome silo]

r u guys in school

[alpine sable]

What if it was a fraction

F(x) = 1/x

How would I do that

[chrome silo]

odd

[stark crater]

Im not IN school rn but I take school

[alpine sable]

Ik it’s odd

[stark crater]

first determine if u think it is odd or even or neither

[alpine sable]

Cuz it’s from my notes

[stark crater]

then check if -F(x)=F(-x)

[alpine sable]

But like idk how I’d solve it lol

[stark crater]

You know what F(x) is

[chrome silo]

i know

[stark crater]

and F(-x) is just F(x) evaluated at -x

F(x)=1/x evaluated at -x is 1/(-x)

[chrome silo]

r u both in high school

[stark crater]

im in college

[alpine sable]

I just started college

This math is bs

[chrome silo]

ohhh

i am also in college

[stark crater]

college gang

[chrome silo]

didn't you guys had maths inhigh school

[stark crater]

yeah

[alpine sable]

Yuh id hope so

[chrome silo]

all of us are same

i also didn't had maths in my 12th grade

but i am now learning calculus

[alpine sable]

I’m in pre calc

Idk why I’d need this for my degree

But wtvr

As long as I don’t gotta take more math after pre calc

We chillin

[chrome silo]

r u in business degree

it is really necessary bro

math is fun

[alpine sable]

Don’t rlly know what ima major in but got told I had to do this no matter what so

[chrome silo]

in which uni do u study

[alpine sable]

In a community college rn cuz got scholarship for it

[chrome silo]

great

if you have any questions you guys can ask

[stark crater]

rip I didnt know what to major in either but I like math so I did that (do not like the risk of not getting a job)

[chrome silo]

r u guys teen

[alpine sable]

I could see math being fun if you already know it 😂

[chrome silo]

indeed

[alpine sable]

I can’t for the life of me keep up with this math man

Like every class so much shit and I’m supposed to just know it by the next day like bruh

Out here studying like 6 hrs a day and still not keeping up

Yet alone my other classes smh

[chrome silo]

whats your name bro

[alpine sable]

Ion rlly give my name out sorry

Never know these days

[chrome silo]

true

i can be a murderer

[alpine sable]

Fr

[chrome silo]

who knows

atleast tell me whether you r a girl or boy

[alpine sable]

Boy lmao

Anyways I gotta get back to my math but thanks for the help both you guys

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[lone heart]

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[mystic nebula]

i got h = 16 +/- sqrt144/-32

so far

is that right

[placid zinc]

I don't think it's quite right. Note you don't need the quadratic equation here

[mystic nebula]

well im supposed to use the quadratic equation here

cause thats the way they're doing it

[placid zinc]

I think you set b = -16. The correct solution would set b = 0, and a = -16

[mystic nebula]

OH

[mystic nebula]

so is it +/- sqrt 768/-32?

[placid zinc]

Yes that's it

[mystic nebula]

so what next

16sqrt3/-32?

i get -0.87 and +0.87

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[waxen turtle]

Idk where to start

[winged lava]

i assume the “weight” M is actually the mass. mass is proportional to volume, the constant of proportionality being density.
M = kV where k = vol
losing 200 ml meant losing ( 590-400) = 190 g of oil
therefore:
190 = 200k
k = 19/20
therefore:
M = (19/20)V

does this make sense,

?

[waxen turtle]

Umm it says that's wrong

[sour dove]

Oh!

yeah it's just a linear equation

[proven leaf]

hey Mellow!

[sour dove]

hey Pajama! ❤️

[waxen turtle]

Mellow from death note

https://tenor.com/view/mello-near-hate-deathnote-anime-gif-19141762

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[mystic nebula]

how do i factor 2x^2 - 92x - 3360

[lone heart]

@mystic nebula Has your question been resolved?

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[waxen turtle]

@cunning frost

I have no clue

[cunning frost]

well, how many heartbeats occurred in the graph

and how many seconds passed in the graph

[waxen turtle]

Umm including the one going into the 2nd quarter thingy

I forgor

Quadrant

[cunning frost]

maybe a better way to do it is

can you tell how often the graph repeats horizontally

[waxen turtle]

Idk like every 7/10 seconds

@cunning frost

[cunning frost]

nahh this one is pretty easy to see

look at where it aligns with the grid

[waxen turtle]

WDYM

Uhh

8/10

A second

[cunning frost]

ok so

how far apart are the peaks

if you had to guess

pick two adjacent ones and look at the horizontal distance

[waxen turtle]

3/5

[cunning frost]

that’s a good guess

one way to check if 3/5 is exactly right is to count the number of pulses in 5 seconds

because 3/5 means 3 pulses every 5 seconds

wait

sorry that’s wrong lol

[waxen turtle]

Does the one on 0 count as a beat

And before it

[cunning frost]

actually this explanation doesn’t work as well as i thought

but yeah count the one on 0

it would be 3/5 means 5 pulses every 3 seconds

[waxen turtle]

So like

100 beats a minute fr

Wait

12 beats

Fr

A minute

[cunning frost]

well if it were actually 3/5

but the gap is actually 2/3

[waxen turtle]

Oh

So

40/3

[cunning frost]

notice how between x = 0 and x = 2 there are three pulses (non-inclusive of the end)

[waxen turtle]

Per minute