help-0

[glass lichen]

f(5)=2(5)+7=17

so do that for the rest.

[wary stream]

Mosh is saying don't use x as multiplication sign in text because it gets confusing in if it is used as a variable or multiplication. The assumption is normally a variable because x is a commonly used variable in math

[glass lichen]

[wary stream]

What?

[glass lichen]

??

[raw shard]

uh

[wary stream]

Isn't the function f(x) = 2x + 7?

[raw shard]

yeah

wait never mind

[glass lichen]

Given I said f(5)=17 was correct... why the hell are you changing the entire equation

we know how to read

[raw shard]

you said it wrong

[glass lichen]

what you said is wrong

[wary stream]

You're multiplying 2 times x, why would you do 7 times x?

[fresh parcel]

find the critical points

[glass lichen]

They already know how to do it, they just don't know the algebra

[fresh parcel]

find the places where the derivative is 0 to find the max and minimas

[glass lichen]

You don't

you just said 2x+7 is equivalent to 7x-2

it isnt

in case you haven't noticed, 7 and 2 are different numbers

[wary stream]

If the equation is f(x) = 2x + 7, you do not do 7 times x minus 2 because as mosh said, you stated f(x) = 7x - 2

[fresh parcel]

aljebra 100

it isnt equal lol

[glass lichen]

Even if you, for some reason, wanted to find the inverse of f(x)... that still isnt 7x-2

[signal oak]

📝

[wary stream]

And 7x - 2 isn't even the inverse of 2x + 7

[fresh parcel]

dude

when someones trying to help you

LISTEN

you asked the question

[wary stream]

We know math better than you, apparently

[glass lichen]

Just let them get the question wrong if they're just gonna deny their error

[wary stream]

Good luck getting it wrong then, because that ain't correct

Algebra

[fresh parcel]

hey plug in 2

and see if thats correct

[glass lichen]

@fresh parcel no point in trying

[wary stream]

Using algebra concepts

[fresh parcel]

2(2) + 7 isnt equal to 2 + 7(2)

[glass lichen]

You were given the function, if you want people to help you don't be stubborn.

[raw shard]

this went on for so long i forgot the question

[glass lichen]

plug in the values from the domain, and the set of outputs will be the range.

[fresh parcel]

its a linear equation with a positive slope

so you don't even need to find critical points

just plug in the rightmost value

[wary stream]

You plug numbers into equation, then do algebra

[full marsh]

T...t.the range is 17 ?

[wary stream]

And it's the biggest and smallest value

[fresh parcel]

the range should have 2 values

[gray isle]

plug in each possible input to get each possible output

[fresh parcel]

but the domain

bruh

[full marsh]

what even is that domain

points ?

[gray isle]

from my interpretation of what you posted, the domain is a set of 3 values that for some reason weren't ordered

[wary stream]

This makes no sense

[fresh parcel]

set of 3 values?

thats range

[gray isle]

domain of {5,18,-5}

[full marsh]

in that case range will be a set of 3 values at those x values

[wary stream]

I think the goal was determine the range given a certain set of values

How?

[full marsh]

w/e youre trolling peace

[wary stream]

Peace, you mean?

[full marsh]

haha

dont worry youre correct

17 is the answer

😄

[glass lichen]

@heady kindle lose the cockiness if you want help

[full marsh]

indeed

[wary stream]

Yet you are here asking for help. If you were smart, you wouldn't be here

[glass lichen]

You thought 7 and 2 were the same numbers, so shut it and lose the cockiness

[fresh parcel]

that was not required

[glass lichen]

Albert Einstein* and yes, cause everyone asks for help at some point in education

[gray isle]

who the FK is that

[glass lichen]

Yeahh Im chalking you up to a troll at this point

[fresh parcel]

until you solve the collatz conjecture shut up and chill

[wary stream]

You can still Google the name if you don't know how to spell it

[glass lichen]

With the excessive disrespect and cockiness, no one in their right mind would willingly help you. I suggest, if you want help, to simply start showing respect to the people trying to help you

[wary stream]

Or use speech to text

[gray isle]

based on what you posted, I already gave you an idea of what to do

[full marsh]

you've been feeding the troll for how long at this point ? isn't that kinda obv ?

[gray isle]

if you're still interested in solving, sift through the chat logs

[glass lichen]

That's still cocky.

[alpine sable]

help me plz

[fresh parcel]

what grade are oyu

[alpine sable]

help me

plz

help me 🙏

[glass lichen]

what have you tried...?

[alpine sable]

nothing

i have no idea

[glass lichen]

so go attempt it

[alpine sable]

i need help

[glass lichen]

google

read your notes

[alpine sable]

its a submative

[wary stream]

One, stop spamming messages, two actually attempt the problem

[alpine sable]

sorry

ok

I wont

[wary stream]

You didn't have to repost, we still see it

[fresh parcel]

think about it like this: every x it moves right the y moves up 33

[alpine sable]

I dont understand what it means

[alpine sable]

OH THX

[gray isle]

how much coordinate geometry have you learned so far?

[full marsh]

@alpine sable https://en.wikipedia.org/wiki/Function_(mathematics) that should do it

[fresh parcel]

it isnt that difficult

sus

[wary stream]

It says graph the equation, do you know how to graph?

By plugging in numbers

[fresh parcel]

plug in x = 1 and x= 2

[alpine sable]

No I dont

[fresh parcel]

what is y for each of them?

[alpine sable]

I know the slope formula tho its m= y2-y1 and x2-x1

[fresh parcel]

mhm

[alpine sable]

33x

[fresh parcel]

but you wont need that right now

so when x=1 y= 33

[alpine sable]

yes

[fresh parcel]

and when x=2 y=66

correct?

[wary stream]

Then I honestly suggest looking at Khan Academy, and paying attention in class, if you don't know what graphing an equation means

[alpine sable]

yes

[alpine sable]

Yes I would I regret playing in class now

[still sundial]

really simple question, im a newb

[fresh parcel]

now draw a point at both points

[still sundial]

is this a proper way to write this down?

[alpine sable]

its good 👍

[wary stream]

Do you even know what that means?

[still sundial]

im a bit confused about where im supposed to use the ","

between the premisies?

and the conclusion?

[fresh parcel]

yes

[alpine sable]

''Given any real number, there is a number that is greater'' (Author)

[glass lichen]

$\forall r\in\mathbb{R}, \exists s\in\mathbb{R}|s>r$

[ocean seal]

Mosh

[still sundial]

Ohhhh

[fresh parcel]

replace the second comma with s.t.

[subtle palm]

this one got me baffled

[still sundial]

so the conclusion follows the "|" ?

[glass lichen]

the pipe is "such that"

alternatively a semi-colon

[still sundial]

Oh

okay

thanks guys <3

[fresh parcel]

could you also replace that with that backwards E symbol

like the curved one

[glass lichen]

No

[fresh parcel]

doesn't that also mean such that?

[glass lichen]

No

$\exists$ is existential

[ocean seal]

Mosh

[fresh parcel]

i meant this one

[high lintel]

hello could i have some assistance

[fresh parcel]

wheres the graph

[high lintel]

it wasnt given

[still sundial]

💀💀💀

[wary stream]

You're given coordinate points, use that to determine the equation

[alpine sable]

I got it! so heres what I wrote

x = 1 y = 33

[high lintel]

(2,7) and (4,14) right

[fresh parcel]

good job :)

[wary stream]

Where did 7 and 14 come from?

[alpine sable]

thx

[still sundial]

do you guys find math to be fun?

[ocean seal]

pingu

[high lintel]

she is 13 miles away from the campground so it would be 7 miles into hiking
she is 6 miles away from the campground after 4 hours so its 14 miles into hiking

[wary stream]

Yep, sounds good

[surreal meadow]

uncalled for

[still sundial]

i asked do YOU

[glass lichen]

Still uncalled for

[high lintel]

no we use savvas realize for tests AND homework

which i think is cringe

[fresh parcel]

yeah

math.fun = true

[still sundial]

niceq

[surreal meadow]

what you consider a fact is just an opinion

[still sundial]

i feel like i do so too as long as I have a solid foundation, which the school didnt really give me so im starting over

[surreal meadow]

let’s just try to keep it amicable, no need to say stuff like that

[wary stream]

The intersection point

[alpine sable]

hi

[surreal meadow]

don’t give away answers

[wary stream]

Don't give out answers

[surreal meadow]

consider reading the rules @heady kindle

[scenic kestrel]

I think it would be yellow

[fresh parcel]

roblox programmer

imagine

[fierce turtle]

Its in the 3rd quadrant

[wary stream]

What's the coordinates of the intersection of the lines?

[fierce turtle]

Where both x and y are negative

Think abiut taht

[scenic kestrel]

(8.-3)?

-8.-3)

[fresh parcel]

bruh could you just stop

you're violating like 18 rules

[alpine sable]

programming 😩

[fresh parcel]

lol

[alpine sable]

maths 😩

[wary stream]

You're just guessing until someone states the right answer

[fresh parcel]

you

[scenic kestrel]

i mean to put the neagitve

infront

[alpine sable]

POP QUIZ EVERYONE TRUST ME THIS IS NOT A TEST

[scenic kestrel]

of the e

[alpine sable]

its very easy

[scenic kestrel]

8

[fresh parcel]

trolling isnt allowed

if you read the rules

[alpine sable]

y = 80 -10 x = 20$

[fresh parcel]

then dont troll

[wary stream]

The output is 20

[alpine sable]

correct

congrats!

👑

here you go

cya later

wait

no

[fresh parcel]

well you were

[alpine sable]

how many video games i bought

you should probably stop chatting for a bit because it seems people are angry

80-10x=20

[wary stream]

Use basic algebra and the fact that the output is 20

[alpine sable]

🤨

[alpine sable]

no its 2

[wary stream]

No

[alpine sable]

x = 2

wait no

sorry wrong

iits 6

its 6

80-10x = 20
80 = 20 + 10x
60 = 10x
x = 6

i think this is the answer

🤨

[glass lichen]

just ignore them

They dont have anything better to do

[alpine sable]

he doesnt bother me

[wary stream]

Plug 6 back in for x and see if it matches the output

[alpine sable]

im a greater troll than he is

[alpine sable]

it does

6×10+20 = 80

it's the definition

[wary stream]

Then you found the answer

[alpine sable]

this is as much mathematics as i can do

i cant

it's too complicated

it's the symbols

so many symbols

[lapis valley]

Is there a term for two function that create "a chain" for its antiderivatives? Idk how else to say this but what I mean is what do you call an example like this:
$$\int sinh(x) = cosh(x) + C$$ $$\int cosh(x) = sinh(x) + C$$

[ocean seal]

hduxueiwkwnxudi

[placid zinc]

No this isn't named

[lapis valley]

ok

[fading zephyr]

you are temporarily muted for trolling. if you continue to do this, matters will escalate.

[alpine sable]

nice

[fresh parcel]

oofed

[harsh swallow]

who?

[alpine sable]

some guy

[fresh parcel]

bruh that guy literally asked a problem and when we answered he said we were wrong

[alpine sable]

he's also a roblox programmer

so that adds up

[fresh parcel]

lmao

[fading zephyr]

use modmail again if they keep it up. have fun with your studies 🙂

[harsh swallow]

👍

[fresh parcel]

pog

[harsh swallow]

you know what absolute value means for complex numbers right? @snow pawn

[snow pawn]

the length?

[harsh swallow]

yeah the size of the vector

aka length

you can calculate that using a+bi

[snow pawn]

yes thank you. I just cant get my head around how to solve the question

so substitue z with a+bi?

and then just solve it?

[gray isle]

you could also consider the geometric interpretation

[harsh swallow]

ramonov is onto something

i didn't think of that

[alpine sable]

can someone help me out with this

[harsh swallow]

one sec

[alpine sable]

alr

[surreal meadow]

try figuring out a few different values

what is the cost at 0 hours?

[alpine sable]

50?

[harsh swallow]

yes

[alpine sable]

Ok

what now

[harsh swallow]

,rotate

[surreal meadow]

what about 1 hour in?

[alpine sable]

90?

[surreal meadow]

yes

and I’m sure you can guess the value for 2 hours in

so, can you express this as a function?

or an equation

[alpine sable]

uhh

[surreal meadow]

what are you doing to the value “y” every time an hour passes?

[alpine sable]

adding 40?

[surreal meadow]

yes

#book-recommendations

[alpine sable]

y = 50x + 40?

[surreal meadow]

the x is in the wrong spot

we charge 40$ every hour

and x is the number of hours

what you wrote means that we charge 50$ every hour

[alpine sable]

y = 50 + 40x?

[surreal meadow]

yes

[alpine sable]

so thats the equation?

[surreal meadow]

yes

[alpine sable]

and how would i graph that

[surreal meadow]

do you know how to make a graph?

[alpine sable]

theres already one in the paper

[surreal meadow]

yes, but labeling and drawing in the lines

do you know how to do that?

[alpine sable]

oh yh

like x y?

[surreal meadow]

so ok, plug in some of those points we talked about

yeah, x and y

[surreal meadow]

and then join these together with a line

[alpine sable]

alr

[whole path]

Guys, If a person has read 15 questions out of 25
If the exam consists of only 2 questions, what’s the probability that he has read those questions ?

[strange rampart]

the probability that he has read both questions?

[whole path]

yeah

[strange rampart]

15/25 * 14/24

[whole path]

could you elaborate ?

[snow pawn]

so how would I go about doing that?

[strange rampart]

the probability that he has read the first problem is 15/25
for the second problem there are only 24 problems it could be. 14 of which he has read.

[whole path]

wouldnt the probability for the second problem be the same ?

15/25 I mean

[glass lichen]

the exam wouldn't have the same question twice

[strange rampart]

if the same question can be asked twice then yes

[whole path]

Yeah right

I get it now tysm

[strange rampart]

no problem

[fresh parcel]

Im confused about the third step

what does it mean to raise y(i) to a negative power?

and what is it doing

like explain the 3rd step in a simpler way

also this is describing the chinese remainder thereom where n(1) .... n(k) are modulos

<@&286206848099549185>

[hushed pasture]

it's the inverse of $y$, we say that $b$ is the inverse of $a$ if: $a\cdot b \equiv 1 [n]$

[ocean seal]

Salah

[alpine sable]

Inverse means if not p then not q

[fresh parcel]

oh okay

[snow pawn]

im gonna need someone to walk me through a complex numbers equations cause ive literally been at it for 6 hours now and Im not close to anything 😆

[alpine sable]

What is d/dx log(x)

[empty sparrow]

do u mean log_10(x) or ln(x)

[alpine sable]

log_10(x)

[empty sparrow]

should be 1/xlog(10)

if u mean ln(x) then 1/x

[snow pawn]

∣x+iy−i∣=1
⟹x^2+(y−1)^2 =1

i dont get why this is happening

[placid zinc]

That's:
|x + (y - 1)i| = 1

[raw shard]

seems to imply you need to solve for the variables

wait i might misunderstand

[placid zinc]

And, you should know that
|u + vi| = √[u² + v²]

[snow pawn]

THANKS! 😄

[nova otter]

What grade is this

[brisk lantern]

Can someone walk me through this? I’m not sure where to start

[raw shard]

you put the point at -3,1

wait why did you scratch out the original coordinates

@brisk lantern

[snow pawn]

what happens to the i`s? do they become -1?

[raw shard]

it’s just the coefficients

the i isn’t included

[snow pawn]

oh

[placid zinc]

It's weird to say anything "happens" to them

Simply,
|u + vi| = √[u² + v²]

Or that | | takes a complex number and produces a real

[snow pawn]

and I cant for the life of me understand this

[alpine sable]

My apologies it is occupied here

[snow pawn]

What ive done is put z=x+yi into that equation

[placid zinc]

You're better off looking at it geometrically

[snow pawn]

This is what ive heard

and Ive made some points in geogebra and thats about it

what am I looking for?

[placid zinc]

|z - 5|
Is function that takes a complex number z, and returns the distance from the complex number 5

Likewise
|z - (-3 - 4i)|
Takes a complex number z, and returns the distance from -3 - 4i

You're looking for complex numbers z that are equidistant from 5, and from (-3 - 4i)

[snow pawn]

🥰

[placid zinc]

You can probably get these points algebraically too. But, you should be able to see there's a line of solutions

[snow pawn]

so basically a parallell line from these poitns

[earnest cairn]

Is this right? I thought it'd be 14C2

Because

There r 12 balls n two sticks to distribute them so (12+2)!/2!12!= 14C2

Balls n stick model

Can u ask in another channel

Kek

[lost glade]

hey can someone help me for my exercise ?

and if someone speak french it's good

[alpine sable]

Hey i have question. Does anyone know any site that have every( or just basic) math rules? cuz i think i have holes in that

[snow pawn]

Omg m8 is 5 = 5+0i?

[earnest cairn]

😢

[snow pawn]

Is this the reason Ive been struggling all fuckin day lmaoooo

please

[earnest cairn]

Yea all real numbers r complex aswell

[snow pawn]

well shit

[earnest cairn]

If that's wut ur askin

[green wadi]

Q12 please ? Thanks

[earnest cairn]

Ale

Alr

cos-1(-x) = pi-cos-1(x)

Use that

And you get tan(pi/2 + cos-1(2/7))

Which becomes cot -(cos-1(2/7))

Do u know how to do the rest urself?

[green wadi]

This is actually where im stuck

[earnest cairn]

You need to convert cos-1 to cot-1 using right traingles

Imagine a right traingle with a base 2 and hypotenuse 7

[green wadi]

Ok ok yes

Thanks a lot 🙏🏻

[earnest cairn]

The angle between that base n hypotenuse is cos-1(2/7)

[green wadi]

Great help 👍🏻

[earnest cairn]

So u can get cot-1 from taht

No worries

[strange rampart]

Find the value of

lim -2sin3t / (sin3t + 2tcos3t) as t-> 0

[thorn kindle]

Let 3t=u

Then t=u/3

Then it becomes

-2sin(u)/(sin(u)+ 2/3 u cos(u))

[dim oasis]

I never learned u-substitution that’s actually pretty neat

[thorn kindle]

-2u/(u+2/3u) = -6/5

Not exactly the most rigorous way to go about it

But sin(u) ~ u about 0

And cos(u) ~ 1 about 0

In fact you can say that ucos(u) ~ sin(u)

About 0

[wraith trout]

How do you calculate B if B^2 = A ?

[onyx pawn]

is it diagonal?

you can diagonalize and takes sqrts of eigenvalues

if they are non-negative, otherwise ain't no sol

[fresh parcel]

idk

olympiad gr8 maybe

[wraith trout]

i diagonalized it but i dont know how to calculate that B

[onyx pawn]

just square the diagonal part

and remultiply

I mean, take the square root of the diagonal

So like, if you get A=UDU^-1 then B = Usqrt(D)U^-1

but sqrt(D) is just term by term since it's diagonal so it's all good

[thorn kindle]

[onyx pawn]

why u hating on me bruda

[thorn kindle]

No hate

[onyx pawn]

oh ok 🙂

[wraith trout]

Like this?

I mean D is the diagonal i got

[onyx pawn]

sure, but you need your U and U^-1

you need to get those while you are diagonalizing

no, B is not D

B is UDU^-1

fuck I messed up

Well, B is not that

B is that but conjugated

[tender reef]

Any way to link (cosx)^3, (sinx)^3 and cos(2x)?

In some form of identity

[onyx pawn]

you need the eigenspace in essence

is what I'm saying

you need U

[wraith trout]

i have to study way more these things

[onyx pawn]

you just need to diagonalize like a pro

so that you still have the U and U^-1

[wraith trout]

in the first part of this exercise i calculated D=P^-1AP

So i have rn A, P and D

[onyx pawn]

oh cool

U is P

[wraith trout]

oh

[onyx pawn]

ok great

[fresh parcel]

are those vectors

[onyx pawn]

D,P and A are matrices

square

[wraith trout]

so for me to get that B when B^2=A i just have to do this PDP^-1 ?

[onyx pawn]

you have A = PDP^-1 right?

[wraith trout]

yeah!

[onyx pawn]

ok

now look at the matrix Psqrt(D)P^-1

do you know what sqrt(D) is?

it's term by term, it's a diagonal matric

by the way the thing that we are doing is called functional calculus

[wraith trout]

it would be
(1 0 )
(0 sqrt2)

[onyx pawn]

sure

well, the matrix P(sqrt(D))P^{-1} squared gives you A

you can check it

so the matrix that you need is that one

[wraith trout]

thank you so much!!

[onyx pawn]

my pleasure

[alpine sable]

can someone help me in dms

please

i have a test tmr

[strange rampart]

How does this

[strange rampart]

Become this?

[strange rampart]

Because if sin(u) goes to 0 as you mentioned here

Shouldn't the whole equation become 0/0?

-2sin(u) = 0 because sin(u) = 0?

[final ferry]

can someone help me factorise this step by step?

[amber iron]

so i decided to do this w/ implicit differentiation

so basically

[lapis sluice]

for $z \in \bC$, i was wondering then if $z^z \in \bR$

@glass lichen

[glass lichen]

why did you ping me?

[lapis sluice]

idk

misclick

what do you think

^^

[glass lichen]

not helping

[lapis sluice]

ugh

[civic jungle]

$z^z=\bR$?

[ocean seal]

Icy001

[lapis sluice]

yes?

idk, thats what i am asking

[civic jungle]

I think you made an error in your notation there

[lapis sluice]

yeh my notation is fucked up

lemme fix it

levi ffs

in use channel

[ocean seal]

Danajax

[lapis sluice]

happy?

[civic jungle]

Nice, are you in high school or college?

[lapis sluice]

high school, studying complex analysis

and calc

[civic jungle]

Damn that's pretty wild

So you learned like the fact that $i^i=e^{-\pi/2}$ I assume

[ocean seal]

Icy001

[lapis sluice]

yes

which is real

[civic jungle]

Ya

[lapis sluice]

which got me wondering if any complex number to the power of complex number is real

[civic jungle]

Try a complex number that's neither real or purely imaginary

[lapis sluice]

like z = 3+ 4i

sure

[civic jungle]

Yep that works

[lapis sluice]

so it works for any complex number???

[civic jungle]

Nooooo

I don't know if it works

I meant that works to try

[lapis sluice]

ah ok

one sec then

lemme just do it

ahaha okay, I assume it doesn't work RIP

would of been cool though

[civic jungle]

The life cycle of a conjecture

You still did something valuable

[lapis sluice]

yes, perhaps I should of tested it myself before asking

but I was so confident it would be real

[civic jungle]

That'd be a good idea

[lapis sluice]

well I guess I learn't from that then

[civic jungle]

ya 🙃

[lapis sluice]

OOOOO

wait

but it seems that any imaginary number to the power of imaginary number is real though

am i correct?

[civic jungle]

imaginary number being an element of $i\bR$?

[ocean seal]

Icy001

[lapis sluice]

it for sure seems so

[civic jungle]

That sounds plausible

[lapis sluice]

yes

[civic jungle]

Try to prove it!

[raw shard]

just saying, but you know i^i is real right

[lapis sluice]

yes

it for sure works

now "i" am happy

[civic jungle]

Did you prove it or something?

[lapis sluice]

yes

[civic jungle]

I wonder how I got this then

[lapis sluice]

wtf

i see my mistake in my proof

hold on one quick sec

yes, ok

[raw shard]

could you maybe represent it in terms of e^x?

[lapis sluice]

i agree

you for sure could

[raw shard]

i didn’t mean is it possible lol

[lapis sluice]

ik, but idk who you are asking

,ask (e^(i*pi))^2

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Danajax#1235

[lapis sluice]

makes sense

eulers identity i guess

are there any other fun stuff with complex numbers?

,ask (2e^(ipi/2))

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Danajax#1235

[dapper frost]

hello

can someone clear something up for me

basic finding the domain

x^2 right

do i square both sides?

after x^2 != 4

hello?

https://tenor.com/view/stalker-hamster-creepy-gif-10750644

i just need clarification

<@&286206848099549185>

i'm 90% sure you square but was just asking to make sure

i'll just submit (-infinity, -2)U(-2,2)U(2, infinity)

[wheat rock]

Hey is this room available for a question

[rigid kiln]

Real quick, what does it mean for this vector here to be squared? Is it the dot product with itself?

oh, it says it's a scalar quantity, maybe it is

[alpine sable]

when a quesstion asks for the exact value of $tan\frac{7\pi}{6}$ what exactly does it want you to do? am i finding the angle in radians?

[ocean seal]

Bouldering

[glass lichen]

evaluate tan(7pi/6)

[alpine sable]

so just type into my calculator when in radians mode $tan\frac{7\pi}{6}$?

[ocean seal]

Bouldering

[alpine sable]

if i do that i get: a long decimal answer, im not sure if thats what im supposed to get

[cedar bloom]

Brandon bought a jacket on sale for 40% off the original price and an additional 25% off the discounted price. If the jacket originally cost $60, what was the final cost, without tax, that Brandon paid for the jacket?
then what's the answer

[zinc sable]

Excuse me how many way A to z?

[alpine nacelle]

Constraints of not being able to go down or left ?

[zinc sable]

Say just cant use left

[alpine nacelle]

Infinitely many, unless you can't walk several times on the same segment

[zinc sable]

Diameter is allowed
And up and right

[alpine nacelle]

What's diameter in a grid ??

[zinc sable]

Alike ddduuurr
Maybe

[mild plover]

wouldnt it be 13!/7!6!

[zinc sable]

Yes for part1

[mild plover]

ok cool

[zinc sable]

For 2 question i should use diameter

[mild plover]

whats it asking

[zinc sable]

how many way A to z?( Diameter is allowed)

[mild plover]

oh

[zinc sable]

For diameter have formula?

[arctic blade]

What's the best way to say all elements of a vector belong to a set? E.g. a 3d vector where all values are non-negative.

I thought of or $\vb{w} \subset \mathbb{Z}^{n}_{\geq 0}$

[ocean seal]

clr

[arctic blade]

or $w_i \in \mathbb{Z}_{\geq 0}$ for all i

[ocean seal]

clr

[alpine nacelle]

Your vector w belongs to $\mathbb{Z}^{3}_{\geq 0}$

[ocean seal]

Mélo

[arctic blade]

so would the first one be the best?

i thought it may be an abuse of notation, since i used a subset when a vector is not a set

[alpine nacelle]

What is w ? A vector ? If so, the first one doesn't make sense

[arctic blade]

yea it's a vector

[alpine nacelle]

$w \in \mathbb{Z}^{3}_{\geq 0}$

[ocean seal]

Mélo

[arctic blade]

so that's okay?

[alpine nacelle]

Since 3d vector

[arctic blade]

yea i just thought, $\mathbb{Z}^{3}_{\geq 0}$ isn't a set of vectors, but if it's alright i'll use that

[ocean seal]

clr

[nimble frost]

hello, I have a point A (0,2,4) and a line where x=-1+t, y=3t, and z=-2-2t, the line contains point B. im trying to find the projection of AB onto the line L

how would I go about finding point B? just use dot product to find an orthogonal vector?

[median crag]

Four points on a grid are A( 4, 2), B(2, 6), C( 4, 6) and D(5, 6). Does line CD bisect line AB?
Prove algebraically.

[atomic torrent]

Do you know how to get the equation of a line from 2 points?

[nimble frost]

hey my question hasn't been answered yet so this channel isnt open :/

[median crag]

mb

[quartz osprey]

so i know chainrule

f=u^5g=e^-u
f'=5u^4

oh i see my mistake now

oh nope i dont nvm

i need guidence

[nimble frost]

maybe find an open channel

[quartz osprey]

better get used to it homie not everyone has to answer your question along with mine

[sour dove]

remember that the chain rule is f(x) = g(x)h(x) f'(x) = g'(x)h(x) + g(x)h'(x)

so g(x) = u^5 and h(x) = e^-u

[grand garnet]

can you show us your work?

[quartz osprey]

Oh this clears things up for me

i did the derivitve of u^e wrong

or e^u

-u

thanks

[sour dove]

yep no worries!

[nimble frost]

to find a vector with magnitude 6 parallel to -3i + k

would I just divide both components by 6??

theres no exact scalar multiple

[violet jetty]

a/|u| u where a is the desired magnitude

so like 6/(magnitude of u) times vector u

[tawny dawn]

How many pounds of coffee worth $9 a pound should be added to 20 pounds of coffee worth $3 a pound to get a mixture worth $7 a​ pound?

[nimble frost]

thank you

[violet jetty]

(20 • 3+n • 9)/20+n = 7 @tawny dawn

[nimble frost]

im trying to find the intersection of these

and i know i need to set them equal to each other

im stuck on -13+2s=1-4t, it becomes 2s+4t=14

[violet jetty]

What’s the problem?

[nimble frost]

so they intersect at (7/3)?

[violet jetty]

What

[nimble frost]

theyre lines that intersect

im trying to find the point of intersection

[violet jetty]

You do a system of equations

[nimble frost]

so x=7/3 is correct?

because im trying to find one value for both s and t right?

[violet jetty]

Yeah

But you used one equation there, not two

You can’t add up 2s and 4t

so y=y
-t=-6+s

and z=z
2-s=-3

Right off the bat we know s = 5

Plug that it

[nimble frost]

ahhhhhh i see now

[violet jetty]

t=1

[nimble frost]

thank you

[violet jetty]

Check with first eqtn

Np

Meant to be solved through the corollary to Taylor’s Theorem, I got to here but I don’t know how I can use the interval to solve for A

[halcyon wolf]

can someone help me with my test of binominal distribution? :c

[placid zinc]

@violet jetty
You care about the largest value of the 5th derivative on that interval

Largest magnitude, I should say

[alpine sable]

Can you just use division property of congruence when you're given 2 midpoints?

For example:
Y is the midpoint of XYZ and E is the midpoint of AEF

XYZ is congruent to AEF

so can i just use the division property of congruence and say XY is congruent to AE

[violet jetty]

Why the 5th derivative?

[alpine sable]

wdym by similar

XYZ and AEF are segments btw

2 seperate segments

yeah sorry abt that

Oh and i forgot to say they're both congruent

wait no

i already did

[alpine sable]

^

[placid zinc]

@violet jetty
Well, that's just what it is, kek. Should have seen that in your notes?

[alpine sable]

they're just marked as congruent with a dash mark

[placid zinc]

If you're asking "how to derive Taylor error formula", that's on Google

[alpine sable]

alright thank you

@alpine sable do i have to define midpoint first before the division property though?

@alpine sable ??

[placid zinc]

Oh yeah that's it

Sorry I misunderstood kek

Yeah it's the missing term, with a coefficient that is the max of the next derivative

[alpine sable]

alright thank you

[violet jetty]

His notes on this were a bit choppy, it's his first year teaching. So the "A" value I'm trying to find would just be the maximum value of the n+1th derivative in the interval?

Gotcha, thanks a lot!

[placid zinc]

Well, max magnitude

[violet jetty]

yeah, absolute value

[placid zinc]

Whatever y-value is furthest away from 0

[violet jetty]

hold on

you mean derivative when x=1/2

and in the second question, it would just be the derivative when x=3/2?

[placid zinc]

So the 5th der is 24/(x + 1)^5, I think

[violet jetty]

and I plug in the maximum value that |x| takes upon the interval there?

[placid zinc]

Max value of f⁵(x) over the domain

[violet jetty]

so not necessarily the maximum value x takes on, rather the maximum value of the derivative.

[placid zinc]

And when I say "max value" I really mean max magnitude kek

So consider minimums as well

[violet jetty]

magnitude just means absolute value right

yup

[placid zinc]

That's okay! This discord is great for learning

[violet jetty]

Youre talking about the A coefficient, Kaynex is talking about the bound of the remainder i believe, so it means the same thing

[placid zinc]

No, I am specifically talking about the A coefficient

[violet jetty]

other way around

[placid zinc]

Yeye

Okay I see the mistake

Even still, the entire error needs not be the max possible value of the missing term

[violet jetty]

The entire error would be less than Ax^5/5! (a=0) where a would be the maximum value of the 5th derivative

[placid zinc]

Couldn't have said it better myself haha

[violet jetty]

Gotcha, thanks for everything guys, yall are lifesavers

[halcyon wolf]

😦

[hardy geyser]

https://gyazo.com/ffa9bd950e47cf2e56653c47755f3e60

someone help me why is my math flawed what i do

oh is this channel used mb

9^1/2

OH PEMDAS

oops

nvm i see

[ocean seal]

bernoulli

[hardy geyser]

yeah i got it

i forgot to do pemdas

[tawny dawn]

How many pounds of coffee worth $9 a pound should be added to 20 pounds of coffee worth $3 a pound to get a mixture worth $7 a​ pound?

[fast wraith]

I need to find the derivative of f(x) = (x+1)/(x-1) using the definition of the derivative and I know what the definition of the derivative is but not how to substitute f(x) in

[uncut smelt]

have you heard of the quotient rule? you use that to diffrentiate it

[fast wraith]

yeah I know the quotient rule but that's technically in the next unit and I don't think I'm supposed to use it

[uncut smelt]

okk do you know the the product rule

[fast wraith]

yes but that is the same unit as quotient

which is why I'm in a pickle

[uncut smelt]

you can re write it as (x+1)(x-1)^-1

[fast wraith]

cause I'm not sure how to use the definition of the derivative with f(x) in this scenario

[uncut smelt]

derivative of f(x) is f'(x)

[fast wraith]

yes

[uncut smelt]

so i would use the product rule or quotient rule to find the derivative

[fast wraith]

yes I would too

[uncut smelt]

so u would be (x+1) and v would be (x-1)^-1 then you diffrentiate each of them

and use the formula

so u'(x)= 1 and v'(x)= -1(x-1)^-2

[fast wraith]

yes I know the quotient rule

but my problem is I'm at a question where I have to use the quotient rule but can't if that makes sense

[uncut smelt]

product rule?

thats different to the quotient rule?

[fast wraith]

not really

[remote heron]

👀

[fast wraith]

the ^-1 turns the quotient rule to the product rule

[uncut smelt]

yh product is y=uv quotient is y=u/v

[fast wraith]

yes

[uncut smelt]

both diff formulas

[fast wraith]

yes

[uncut smelt]

i dont know any other way you were to do it if you didnt use either one of them tbh

[full frost]

can someone help me with linear algebra problem

[lapis hedge]

Yeah

[full frost]

ok

@lapis hedge

I have to do this w/o a determinant

I have this so far

from my row reduction

not sure what to do after

[charred flint]

if that bottom right corner wasn't zero, you could scale it to 1 and get rid of the entries above it

[full frost]

how do i know if it is zero or not?

[charred flint]

well you have to consider both cases, zero or not

if it's not zero I said how to make it have all 1's on the diagonal, so independent

[full frost]

what do i do for the case where it is zero

its asking for dependent tho

[charred flint]

if it's 0 I don't see any way to do that, so dependent

yeah so the problem just becomes -k^2-k+12=0

to get your answer

[full frost]

whats the reasoning?

because if i get a zero row then i would have a free variable?

[charred flint]

right, that 3rd row would be all zeroes

[full frost]

and a free variable means dependent right?

[charred flint]

right, that's exactly what the definition is

[white crown]

maybe this makes a bit more sense...

[full frost]

yeah i said i had to do it w/o a determinant

[white crown]

oh my bad

[full frost]

also i thought for it to be linearly dependent that the determinant has to equal 0

u have do not equal

[white crown]

cannot equal zero

[tawny dawn]

4?

[blazing rose]

what math is this

[full frost]

If the determinant is not equal to zero, it's linearly independent. Otherwise it's linearly dependent.

[white crown]

nevermind youre right

[full frost]

u lying to me

xD

[full frost]

its linear algebra

[white crown]

lol at least the answers are still right

[full frost]

yea

i got -4 and 3

[white crown]

yeeee

[late ivy]

How would I factor x+y+3x^2-3y^2

[amber depot]

Well

[full frost]

combine the x's and y's

[tired axle]

u can take out an x and a y

yes^

[amber depot]

@late ivy It just asks to factor?

[tired axle]

or u can take out x's and y's

[late ivy]

Yes

[tired axle]

u cant combine thoes btw^ becuase they are x^2 and x

[amber depot]

oh my bad

[late ivy]

I think I have to factor by grouping but with this problem, I’m unsure how to do so

[tired axle]

u can also try factor by gruoping

oof ^

[full frost]

??

[late ivy]

Lol

[full frost]

i meant grouping them

[tired axle]

once you gruop then u can find a gcf in the ( ) and then find ur new # ( ) and # ( )

[late ivy]

The answer is supposedly supposed to be (x+y)(1+3x-3y); assuming the first group to be the sum of greatest common factors

How would I get (x+y)?

By grouping

I am probably overlooking something

Is it possible for you to walk me through the steps?

[tired axle]

ok so

lets bring the x and y's together

so we have x+y+3x^2-3y^2 right?

lets rearrange it to be

x+3x^2 |||| y-3y^2

for the left hand side what can we take out ?

an x right?

so far we have x(1+3x) <-- by taking an x out....

now lets do that for the y (the right hand side)

we can take out a y becuase there is a y in both terms

so rigt hand side would be

y(1-3y)

now we have by gruyoping x(1+3x) + y(1-3y)

[late ivy]

I see

[tired axle]

the x and the y are its own polynoimial

so we get the (x+y)

and then from the ( ) we combine them both

with the like terms....

to get the (1+3x-3y)

is that lear?

clear*

[late ivy]

But wouldn’t we get 2 + 3x - 3y?

[tired axle]

you would think that

BUT

the 1 appear twice

so u ujust use it OCNE

ONCE*

[late ivy]

I see

Interesting

[tired axle]

yeeee

and since the 3x and -3y are unique

u se them both

u use them both*

[late ivy]

Thank you very much, I didn’t realize that when grouping I could just re arrange the terms

[tired axle]

yeee

no worries

[sage cloak]

Hey i got a matrix that represents a graph and show the probability of going from 1 point to another point

And i was wondering how could i get the distribution, if i put X objects at each point and let them walk (same number of object for every point)

Could i find the stationnary distribution and multiply the probability by X objects to find how many objects end up at wich point please?

[mellow canyon]

Can someone help me with this?

[devout summit]

You understand f(g(x))?

[mellow canyon]

Yes

[devout summit]

Ok so what is g(-1)?

[mellow canyon]

the g of x

[devout summit]

Specifically putting x=-1

[mellow canyon]

Yea

[devout summit]

So what g(-1) evaluates to?

[mellow canyon]

x=-1

Ok nvm I don’t know

[devout summit]

g(-1)=5*(-1)-3

[mellow canyon]

Said it evaluates in yea

Yea I was about to say that lmao

So now do just connect them?

[devout summit]

So, f(g(-1))=f(-8)

[mellow canyon]

where does the -8 come from?

[devout summit]

This

[mellow canyon]

ohh

[devout summit]

And now we just put x=-8 in f(x)

[mellow canyon]

so -8=x^2+3x-7?

[devout summit]

No.
f(-8)=(-8)^2+3(-8)-7

[mellow canyon]

Would the answer just be false?

Wouldn’t*

[devout summit]

We can calculate this

What is (-8)^2?

[mellow canyon]

-16

no wait. 64

[devout summit]

Yes

[devout summit]

So yeah we just do 64-24-7 and we get f(-8) which was f(g(-1))

[mellow canyon]

33

[devout summit]

Yep

[mellow canyon]

ok thanks man 💯

[dim oasis]

That's what I got :P

[dawn prairie]

can anyone help model a graph?

[untold kestrel]

@raw shard ?

[raw shard]

<@&268886789983436800>

[glad compass]

Imagine spamming

lol

[raw shard]

wow i was about to ping mods again

lucky timing

thanks

[glad compass]

Can you help me

[raw shard]

yeah

[violet hemlock]

b&

[raw shard]

@untold kestrel um

it’s 26/5

[glad compass]

@raw shard

[shut plover]

hey, im doing this problem and i think the answer is k = 1/9

however, another possibility is 2/3?

Not sure which one is right

[untold kestrel]

@raw shard ya ur right 26/5 corrected

What’s wrong here

[raw shard]

nothing

[alpine sable]

is this channel free?

and if so, could someone please walk me through this question

[alpine sable]

ur handwriting makes me wanna cry

[glass lichen]

what's $AA^{-1}$?

[ocean seal]

Mosh

[alpine sable]

i have no clue

is it [A^2]^-1

[modest wyvern]

hello can someone help me

[glass lichen]

so you dont know what an inverse is..?

[alpine sable]

well the inverse is just

1/det[M]

[glass lichen]

?????

no

not at all

[alpine sable]

what?

if A = abcdf

abcd*

shouldnt the inverse be

[glass lichen]

the inverse is a matrix

not a scalar

[modest wyvern]

.

[alpine sable]

1/det(A) x [d -b -c a]

[glass lichen]

yes, but I wanted the general answer.

the inverse is what you multiply by to get identity.

that is the definition of the inverse of a matrix

[alpine sable]

oh

i see what you are asking now

[glass lichen]

Y is X's inverse iff $XY=YX=I$

[alpine sable]

did you mean A * A^-1?

[ocean seal]

Mosh

[glass lichen]

that's what I wrote...

AA^(-1)

[alpine sable]

well yeah, but it was just poorly notated

confused me

[glass lichen]

it wasnt

it was common notation.

[alpine sable]

r u trying to help me or are u feeding ur ego

im confused

[glass lichen]

Im trying to help you, however I'm telling you that's how multiplication is written for matrices.

[alpine sable]

alright

[glass lichen]

so anyway, what's $AA^{-1}$?

[ocean seal]

Mosh

[alpine sable]

it should be the identity matrix

of A

[glass lichen]

identity matrix of R^(2x2), not of A

yes $AA^{-1}=I$ so that means their dets are equal.