help-0

[small bear]

which means when you divide, and then put the x inside the square root, you must keep a negative sign in front

makes sense?

[alpine sable]

hm

i didnt know that

thank you

[small bear]

so what would the limit be when x-> -inf?

[alpine sable]

i suppose

-1/2

[small bear]

exactly

[alpine sable]

ty so much ur a life saver

[small bear]

No worries, anytime

[alpine sable]

wait but also, a follow up question

um

wouldn't the denominator be negative as well?

if its x approaches -infinity

[small bear]

x already is negative, the sign is inside x as well

in a sec, this channel is occupied

[small bear]

so in the denominator, when you divide by x, you are dividing with a negative number and the sign of x is there

x could be -4, -100, it doesn't matter, we still write +x

the problem was the square root function

we can't put negative values in it, since the square root of a negative number is ill-defined

so instead, we opt out to represent x as -|x|, which as an example would be x=-5, x=-|x| means -5 = -|-5| = -|5|

[alpine sable]

i understand the part in the numerator

from my understanding this is how the function would play out

so wouldnt the negatives cancel out

[small bear]

-x is positive when x-> -infinity

take x=-100, -x = -(-100) = 100

[alpine sable]

oh i kinda get it

[small bear]

I think you should play around with numbers and see what happens, maybe that would help

[alpine sable]

so when im appraoching any limit problem where x is approaching negative infinity

should i treat the x as a negative number?

or

i know im missing something here

[small bear]

Yes, however -x doesn't mean the value -x is negative

[small bear]

because x could be negative itself, as i mentioned here ^^^

so positive numbers are |x| and negative are -|x|

that is the best you could do

[alpine sable]

hm ok

i think im getting it

[small bear]

great, if you have further question just ping me

[alpine sable]

for sure

[small bear]

yeah, channel is now free

[ocean seal]

marc

[golden nymph]

Check whether the channel is occupied or not before posting 🙂

[gilded python]

my bad.

[small bear]

Number theory is my greatest weakness, though I can do some googling and maybe see if that is true

in order to not spoil the solution that is

[small bear]

This should be correct, the gap between primes can be shown to be arbitrarily large

consecutive primes*

do you want a hint?

You need to consider a sequence of integers (or rather find a construction) so that the number between the primes are composite (hint: use the factorial)

yeah, perhaps another way to do it, consider finding N consecutive numbers that are composite

yeah, since from that sequence you are guaranteed to have a smaller number that is going to be a prime, as well as a larger one making the gap larger than N

yeah, how would consecutive numbers with the factorial look?

[jagged ginkgo]

im having problems with this

[small bear]

can you algebraically write a few out?

[small bear]

Occupied, please find a different channel

if I tell you it's a major spoiler

maybe work with those hints for a little bit, if you get stuck for like 10-15 minutes you can ask me again

since it is a wonderful problem

so 1) use the factorial function to 2) construct a sequence of N composite numbers

I should be online

you can also DM me in order to not keep this channel occupied

yw

[empty sparrow]

Hey guys can someone help me, I just cant get to the matrix from the answer

I just dont get it, why the second row from the matrix T_B is influenced by T_A and not both

[glass lichen]

Cause one of the columns in T_A is 1 0

So when you do the multiplication, it'll just keep that column from B the same

[empty sparrow]

How does the composition work? If i remember correctly, u have to use T_A first and then use the outcome in T_B?

[glass lichen]

Yeah you do, but the composition of transformations is the multiplication of their matrices

[empty sparrow]

do we know the size of T_A ? e.g R^3x3 ?

[glass lichen]

Yes, A is an operator on R^2, so it's 2x2

[empty sparrow]

as u mentioned before that one column is 1 0 , then the second column should be 0 1 right, since they are both standard vectors for 2x2?

[glass lichen]

No, A is not identity

The 1st column is where (1,0) maps, which is itself

[empty sparrow]

okay

[glass lichen]

2nd is where (0,1) maps

[empty sparrow]

could be give me a simple example i cant follow after "2nd is where.."

or could u recommend me a good video about that topic

[glass lichen]

(0,1) clearly maps to (0,-3) under A

[empty sparrow]

yes

[glass lichen]

So the 2nd column is (0,-3)

[empty sparrow]

thats it?

[glass lichen]

Yes.

[empty sparrow]

lol i knew that but i thought u meant something more complicated

im sorry for being dumb

[glass lichen]

Nope

[empty sparrow]

thank you very much, i think i got it

[torpid delta]

Does there exist $n \in \bN s.t. (d\cdot n + c)|(a\cdot n + b) ; \forall a,b,c,d \in \bN$

[glass lichen]

Yes...

[torpid delta]

wait, not this exact form

also no

[ocean seal]

TC159

[glass lichen]

Yeah you have an expression not an equation

So yes, N exists

[torpid delta]

?

No

[glass lichen]

Your question makes no sense

[torpid delta]

d > a and c > b

[glass lichen]

Still doesn't make sense

[torpid delta]

Duh doy smart guy I said It wasn't in that exact form

give me a sec

$\exists m \in \bN ; s.t. ;(m \cdot (2k-1) - (k-1)) | (m \cdot n + k-1) \forall n,k \in \bN$

[ocean seal]

TC159

[torpid delta]

n such that n geq 2k - 1

[glass lichen]

Ok...

Still, what's the requirement on the expression

[tiny minnow]

Help me 1+1x0=?
I say 1 but my teacher say 0

[fair vine]

@tiny minnow "operator precedence" is they keyword, multplication before addition, so 1+(bllah*0) = 1+(0) = 1

[empty sparrow]

are u for real?

[tiny minnow]

yeah that why

[golden nymph]

Did you forget including parantheses somewhere?

[empty sparrow]

no way ur teacher said its 0

[golden nymph]

Coz (1+1)x0 is sth different

And old calculator which do one operation at a time (like the one in google for example) do not respect pemdas

[tiny minnow]

LOL i trick my teacher:/

[golden nymph]

?

[unique ingot]

Can someone explain how step 2 got to step 3 thanks

[golden nymph]

I say magic

There is sth wrong

Probably just a typo

[tiny minnow]

Hes typo

[unique ingot]

So many typos in this textbook ;-;

[golden nymph]

It meant (a-4)(a+2)

[tiny minnow]

a^a-2a-8 = (a-4)(a+2)

[unique ingot]

Okay thanks

[golden nymph]

[empty sparrow]

If I have three Points A = (4 4) , B= (2 4) and M= (3 -10), how can i calculate the distance between M and the straight line that goes through A and B ?

[tiny minnow]

[golden nymph]

Good question

Classic

You can do a simple sketch to help you

Take notice that there isn’t such a thing as the distance between a point and a straight line

A straight line is a set of points

So you can draw a line joining the point with any other point in the line to find its distance

But the thing is

We are said to find the “shortest” distance between a point and a line

[empty sparrow]

the distance will change depending in the point i choose right

[golden nymph]

That’s probably what your question asks

[golden nymph]

I just wanted to give you a heads up to this point

[empty sparrow]

thats the thing it just says , the distance nothing more or less

[golden nymph]

Yeah so it actually means the shortest distance

[tiny minnow]

Am I youngest here?

[golden nymph]

The teacher omitted it because it is “obvious”

[tiny minnow]

I am 11

[golden nymph]

Yes

[golden nymph]

You have to be 13+ to use discord delete

[empty sparrow]

alright, i will see, thanks mate

[tiny minnow]

jk lol

[golden nymph]

Thanks what?

I didn’t help you yet?

You know how to find this shortest distance?

[tiny minnow]

no 11 can algebra:/

[empty sparrow]

between any point and shortest distance is already a help

[tiny minnow]

execpt math guy

[golden nymph]

Wait wait

I think a misunderstanding happened?

[empty sparrow]

what happended?

[golden nymph]

I mean that what you have to find is the shortest distance from the point to the straight line

That’s what your question actually wants

[empty sparrow]

yes thought the same

[golden nymph]

But you can’t choose any point on the straight line

Not all will give you the shortesy distance

There is a certain point

So the thing is

[empty sparrow]

alright im listening now it gets interesting

[golden nymph]

What you use is that the shortest distance is the perpendicular distance

You can draw a sketch to make sense of this

[golden nymph]

You see that?

[empty sparrow]

just looking it up

[golden nymph]

You mean googling? Don’t do that just draw a sketch

[empty sparrow]

alright did

[golden nymph]

So what you have to do is

Find the equation of this line

This line has a gradient perpendicular to the line AB and passes through point M

Using those information you can construct the equation

After that make the red line intersect with AB and find the point of intersection

Now the shortest distance is the distance from your M to the point of intersection

[empty sparrow]

hold on give my brain a minute to follow up

[golden nymph]

Using distance formula

[golden nymph]

Ok

[empty sparrow]

can i use this formula?

[golden nymph]

You can point out to your teacher that they didn’t include the “shortest” in the question 😉 if they are easy and won’t get mad at doing so

[golden nymph]

Where did you find this?

[empty sparrow]

internet

[golden nymph]

Internet is bad

[empty sparrow]

thats true

[golden nymph]

We can’t just use formulas from the internet

[empty sparrow]

sometime u find sth good though

[tiny minnow]

@empty sparrow not Recommend

[golden nymph]

This formula is true but you can’t just “use” it

It’s not inside your tool box

Your teacher wants you to work through all the steps to reach your required

[tiny minnow]

Its to hard for simple question

[empty sparrow]

i mean its an online task, so they just want the answer

[tiny minnow]

if u relly-relly maxed make 1;1 scale

[empty sparrow]

i dont think that he wants to see the actual way

[golden nymph]

That would be considered cheating in some sense

[empty sparrow]

🙃

[golden nymph]

Like entering a paintball fight with a tank

You won’t learn if you use ready formulas

[tiny minnow]

Yeah

[golden nymph]

You as a person doing math is the one supposed to come up with the formulas

So you should do it in steps and reach the answer using your math skills

[empty sparrow]

alright ZossDude, i will try it out without using given formulas from the internet , if i dont succeed will message u again 🤝

[golden nymph]

Sir?

Don’t call me that please I am not even an adult yet

[tiny minnow]

if u want use formula u must know where its from

[empty sparrow]

now better?

[golden nymph]

ZossDude 🤣 yes that’s good

[empty sparrow]

🤝

[golden nymph]

Okay good luck!

[empty sparrow]

Thanks!

[golden nymph]

That’s not my point. I’m saying you can’t use sth your teacher didn’t “allow” you to use

[tiny minnow]

yes

[golden nymph]

Wlc

[tiny minnow]

Zozz how old are u

[golden nymph]

Young

[lethal pike]

Is there a faster way to calculate this besides using partial fraction decomposition ?

[rigid wind]

what's x+1 - (x-1)

[lethal pike]

well it'll be (x^2-1)^4 but I quess it won't reduce to a mucc more simpler form

[tiny minnow]

its (x-1)^2(x+1)^2 ?

I Think There is ffaster

but its hard

what grade are u

[lethal pike]

12 th grade

[tiny minnow]

I Cant

[lethal pike]

Why ?

[tiny minnow]

Its to OP

But there is exepction

i scare u will use on wrong number

[lethal pike]

Well then I'm up for it

[oak hound]

come on vc

[alpine sable]

What exactly does the classical adjoint of a matrix mean?

In a geometrical sense.

[alpine sable]

I understand how linear transformations and the determinant works but idk for the adjugate.

[tiny minnow]

@alpine sableThe determinant of a square matrix is a single number that, among other things, can be related to the area or volume of a region. In particular, the determinant of a matrix reflects how the linear transformation associated with the matrix can scale or reflect objects.

That i can help

[alpine sable]

Anybody know ?

[tiny minnow]

Can take better pic?

[alpine sable]

yeah

@tiny minnow

[tiny minnow]

4,5

[alpine sable]

what do i do here

[tiny minnow]

@alpine sable 4,5

just do 3/2 log_y^x

[alpine sable]

you know how to say the calculations i need too

?

@tiny minnow

[tiny minnow]

x = 3
y = 2

[alpine sable]

oh thx

[tiny minnow]

and change to 3/2

[alpine sable]

i must

help to solve questions

but they are way too hard

because im only at grade 8..

[alpine sable]

logʸ x = 3 logʸ² x³ @tiny minnow

[tiny minnow]

for future

[alpine sable]

okay

simplify or solve-

[tiny minnow]

solve

[alpine sable]

well

the calculation in the photo and this

Is it really 4.5?

[tiny minnow]

Not 100%

[alpine sable]

ah

so

9x - 7i > 9x - 21u

from this we know that 7i < 21u

very thanks @tiny minnow

[tiny minnow]

@alpine sable nope

[alpine sable]

i think

i cant go any further

i only know that

7i < 21u

[tiny minnow]

divided by 7

[alpine sable]

oh-

forgot abt that

so

i < 3u

[tiny minnow]

LOL

[alpine sable]

whats so funny

wait-

is that a

trap?

i < 3u roughly equals to i < u

[alpine sable]

i < u means i luv u tho

so...

frick.

[alpine sable]

The answer is right but my teacher asked for the calculations.

😦

[oak hound]

bruh im stuck....if u have 5/6 : (-25/18) what do u do?

can someone help me?

[alpine sable]

but

[oak hound]

u multiply 5/6 x (-18/25)?

[alpine sable]

how does 5/6 relate to -25/18

[oak hound]

and then simplify

[alpine sable]

@tiny minnow

[oak hound]

oohh ok thx

[alpine sable]

what?

[oak hound]

divide*

[alpine sable]

oh

why dont you put a slash instead;

[tiny minnow]

5/6 x 18/-25 = 90/-150 = 3/-5

[alpine sable]

'-'

oh wow

well

[tiny minnow]

wait dif question

its -3/5 instide of 3/-5

[wary stream]

Btw $$\frac{1}{2}$$
\frac{}{}

[alpine sable]

no

thats only test

dont be awkward

[wary stream]

Also, test it in #latex-testing

[alpine sable]

ok

[scenic dew]

WHO PINGED?

Absolutely UNACCEPTABLE! I cannot begin to comprehend why you just pinged me on the Discord app. It seems the divide between you and I (on intellectual levels) is greater than I could have ever imagined. While I was busy creating the next big thing, you and your underdeveloped brain decided to humor me with “comedy gold,” as others have said recently. Well, you certainly have failed to humor me — in fact, you have actually made me quite upset. It is for that I applaud you, I truly do. You may have just been the first of the cesspool of commoners to finally pique my attention, the first whose utter retardation has finally caught the interest of a higher being. Well, I’m listening. What is it today, “Funnyman?” Is it another mediocre meme? Another “le epic copypasta?” This is the first and last time I acknowledge a Funnyman. In fact, this is the last time any Funnyman will be acknowledged. Image permissions will be removed starting immediately, and a one minute slow mode is being enacted in that very moment. You’ve done God’s work, Funnyman. You finally broke the last straw and ruined it for everyone else. I grow gleeful at just the thought of you writhing in pain the next time you go to shitpost, realizing quickly that this liberty is no more; know it is not a liberty, it is an act of insubordination, treason, terrorism.

[alpine sable]

I RIGHT THE QUESTION YOU SAID
@tiny minnow

very thanks

[alpine sable]

actually

can you chill a bit

ping isnt that bad

and it is allowed

[wary stream]

I feel like you typed this in the wrong server because I don't think anyone pinged you, except for these recent replies

[simple gazelle]

This is the question, I have no way to prove that the exam is over. Maybe answer tomorrow

[oak hound]

(1/10 - 3/2) ^2

[alpine sable]

3/2 = 3/2 * 5/5

15/10

(1/10 - 15/10)^2

(-14/10)^2

[oak hound]

7/5

[alpine sable]

(-7/5)^2

[oak hound]

49/25

• X - = +

[alpine sable]

(-7/5)^2 = (-7/5)*(-7/5)

(-1)(7/5)(-1)(7/5)

(-1)^2 (7/5)^2

(7/5)^2

[simple gazelle]

Can yall just help me with that? I swear the exam is over

Its nagging me constantly

[alpine sable]

just find 3^(100) mod 11 and you should be done

[unreal kettle]

how do i approach 2iv? am i correct to just take all the points in S2 to form a homogeneous linear system and subsequently solve for p,q,r,s?

I got p = 0, q = -s, s= s, r= s. how should i proceed?

[alpine sable]

I'm not even mad, this is just funny.

[fresh relic]

Anyone know how to solve this? I keep getting 80 but it’s wrong

[spark zinc]

should be 2*4 + 5 = 13

[fresh relic]

oh I was doing 4^2

also you know how to do this one?

[warm patio]

Need help

:)

[spark zinc]

x^3 increases faster than x^2 so it should converge to zero

[kindred hull]

Which part

[warm patio]

Whole part

[fresh relic]

That very weird because I put 0 and it says it was wrong

[warm patio]

I forgot this whole part

[tropic sail]

didn mean to interupt sorry

[warm patio]

Its quadratic equation

[kindred hull]

So what did u put for part 1

[warm patio]

I didn't put any

I forgot all

[spark zinc]

weird, maybe i am missing something but this looks quite simple actually. dont really now what else it would be

[warm patio]

The question is on the right side

[kindred hull]

If the width is x and the length is 3 longer than the width, then the length is 3 longer than x. So how would u express the length

[warm patio]

Multiplying?

[kindred hull]

No

Brb imma get on my pc

[warm patio]

Ahh 3m:)

[kindred hull]

close

its 3m and the width together

[zenith bone]

Practicing for my ged and i’m trying to figure out what type of math is this?

[kindred hull]

so what would that be

[warm patio]

7m

Ahh

[kindred hull]

how 7

[warm patio]

Nvm that

So L=W+3 am i right or wrong

[kindred hull]

ur right

but u would replace w with x

since the width is x

[warm patio]

Hmm okay

No. 2?

[kindred hull]

just replace the letters with the info u know

so u know the length and width

[oak hound]

someone wanna go on vc?

just chillin

[gentle prism]

If two lines are perpendicular to the same plane, they are
(1) Congruent
(2) Perpendicular
(3) Coplanar
(4)Skew

Someone help

[kindred hull]

area = length x width. IN this case the length is x+3 and the width is 3

so what would are be equal to

[warm patio]

28m²=x(x+3)

Is it right?

[kindred hull]

ye

[warm patio]

And then?

[kindred hull]

now u can rearrange it into standard quadratic equation

[warm patio]

x²+3x -28=0 ?

[kindred hull]

right

now factorise and find x

[warm patio]

Ahh

Thats my question

How to factor quadratic equation?

I don't know how

[alpine sable]

Do you know the discriminant formula?

[kindred hull]

u dont need to use that here

u wanna get into into the form (x+y)(x+z)

[alpine sable]

you never need it, but it's an easy what out of any quadratic equation

[warm patio]

Ahh okay and then?

[kindred hull]

(x+y)(x+z)=x^2+(y+z)x+yz

x^2+(y+z)x+yz ur expression is in this form

[alpine sable]

when you got something like x² - ax + b, the 2 solutions (if they exists) have their sum making a and their product making b

[kindred hull]

where y+z=3 and yz=-28

so u need to find values that satisfy that

[warm patio]

(x+7)(x-4)=0 like this?

[kindred hull]

ye thats right

so now we can use the fact that for two factors product to be 0, one of the factors must be 0

so eitehr x+7 or x-4 can be 0

for the equation to be satisfied

so now just find the two values of x

[warm patio]

So the answer is width is 4 then the length is 7

Right?

[kindred hull]

no

[warm patio]

Ohh

[kindred hull]

x+7=0 x-4=0

what two values of x does this give

[warm patio]

x²+4x+7x-28=0

x²+3x-28

[kindred hull]

no ur going backwards

(x+7)(x-4)=0

for this equation to be true either x+7 or x-4 has to be 0

[warm patio]

I don't get it

[wary stream]

Aka zero product property

[kindred hull]

if two factors products is equal to 0 then at least one of the products must be 0

shit i

i mean on of the factors must be 0

think about it like x*y=0

if x is 0 the equation is true

and if y is 0 its also true

[warm patio]

So x+7 must be zero

[wary stream]

Or?

[kindred hull]

thats one solution

[warm patio]

x-4

[kindred hull]

ye

so what values of x give that result

[warm patio]

Ahh i get it

[warm patio]

Then question 3

[kindred hull]

what values of x did u get

[warm patio]

3

[kindred hull]

how 3?

ur two solutions are

x+7=0
and
x-4=0

so just rearrange them to make x the subject

and thats ur two solutions

aka find x

[warm patio]

x=7 and x=4?

[kindred hull]

close

4 is right

but not 7

7+7 isnt 0

[warm patio]

Wait

Ahhhh

-7

[kindred hull]

ye

so ur solutions are x=-7 and x=4

[warm patio]

So thats the answer of number 3

[kindred hull]

almost

remember its lengths

so x=-7m or x=4m

in the context of length

-7m doesnt make sense

so we can disregard that solution

so that just leaves us with x=4

[warm patio]

Oh

Thats done?

[kindred hull]

not quite that gives the width only

the width is x and the length is x+3m

so u can sub x in

[warm patio]

width

[wary stream]

Also known as extraneous solution, I believe. Correct me if I’m wrong

[kindred hull]

im not really familiar with fancy terms xd sorry

[wary stream]

Didn’t mean to ping you, message was too far back so had to ping reply for the context

[kindred hull]

its ok

its ok

[kindred hull]

ye this is right also i googled it

[wary stream]

No, not free

[kindred hull]

so have u got ur length and width?

[warm patio]

No

How?

[kindred hull]

u know the width is x cos it tells u

and the length is x+3

but now we know the value of x

so we can replace it with a number

[warm patio]

What number

[kindred hull]

remember the solutions we found the the quadratic

?

[warm patio]

Ahh

[kindred hull]

its the same variable

[warm patio]

W

L

[kindred hull]

so whats the width if its just x

and we know x is 4m

[warm patio]

x=-7

[kindred hull]

remember we disregarded that solution

i feel like ur overthinking it

its right infront of u

[warm patio]

Ahh tell me the answer already so that i can understand how answer is made

[kindred hull]

if width=x
and x=4m

then width=4m

i mean width

not length

[warm patio]

So x=4,x=4?

[kindred hull]

were trying to find the dimensions of the pool

the dimensions would be like
width=
length=

thats the dimensions of a rectangle

width=x
length=x+3m

x=4m, all u need to do is sub this value in

@warm patio

[warm patio]

Wait

Im overthinking

[kindred hull]

ik u are lmao

[warm patio]

So thats the answer?

[kindred hull]

sub x in

width=4m
length=4m+3m

so length=7m

so u understand

[warm patio]

Ohh ty

[kindred hull]

so for u answer u would just write width=4m length=7m

[warm patio]

This is right

Im just taking a shortcut

[kindred hull]

thats not right tho

x isnt 7

omag

[warm patio]

Why?

[kindred hull]

cos it just isnt 7

thats not a solution to ur quadratic

[warm patio]

Ahh ok

[kindred hull]

are u trying to represent the width and length by x and x

cos u cant do that

if u wrote w=4 and l=7 that would be right

[frigid coyote]

can i ask?

[lapis valley]

anyone knows logistic regression

[final ferry]

can someone help me factorise this 😀

[alpine sable]

you've not got any common factors to take out

[scarlet leaf]

I would appreciate some help solving this: 2-(2-(2-(2-(2-(2-(2-2))))))

[final ferry]

the answer is this, but i just dont get how to get to this answer

[scarlet leaf]

It says that the answer is 0 in the exercise but I get lost when trying to prove it.

Great

[hushed pasture]

THIS IS NOT MULTIPLICATION, THEY ARE ALL SUBTRACTION

[scarlet leaf]

Yeah I realize that the last 2-2 inside the paranthesis will be 0. But where does the multiplication come in?

[hushed pasture]

WRONG

$2+(4-3)$

[ocean seal]

Salah

[hushed pasture]

is this multiplication?

[final ferry]

3

[scarlet leaf]

Damn, this one is giving me such a headache lol

Channel is busy @alpine sable @sour umbra

Pls

[undone dock]

Wrong angle, theta is on the top

[alpine sable]

oh shit yeah I read it wrong way around

[scarlet leaf]

I guess ill just repost

[alpine sable]

16/13 then

[scarlet leaf]

I would appreciate some help solving this: 2-(2-(2-(2-(2-(2-(2-2))))))

Yeah but i get lost in the brackets lol

The last 2-(2-2) = 2

[kindred hull]

no

[scarlet leaf]

Hmm

I’ll dream of brackets tonight lol

[empty sparrow]

#help-4 message

can someone look over and help me?

[alpine sable]

a(x) = 450 + 17 x
how do i do it so that 20 times as much until i get 2000

[empty sparrow]

u want 450 + 17 x = 2000 ?

[alpine sable]

yeah

[empty sparrow]

and u want to know for which x?

[ocean seal]

WhipStreak23

[alpine sable]

I think i got it, is it 91.18?

[empty sparrow]

yeah should be

[peak cloud]

Can anyone tell me what is done here?

I know it's the divide multiply thing(idk what it's called) but why can't I just divide it simply?

[empty sparrow]

is it $\sqrt{\frac{1}{1,732}}$ ?

[ocean seal]

SSJ_Sammy

[peak cloud]

Yeah

[empty sparrow]

why did u include the Square Root again if u already did it once

from sqrt(1/3) to sqrt(1/1,732) it should be just 1/1,732

[torpid flax]

Hey could i get some help with

[alpine sable]

How do?

[solemn juniper]

Compute the limit at x=0

[alpine sable]

Good book about combinatorics?

#book-recommendations

#books-old

@alpine sable

[alpine sable]

still need help?

[torpid flax]

Very much

[alpine sable]

\everymath{\displaystyle}

Apply the fractional rule $\frac{a}{\frac bc}=\frac{ac}b$

[alpine sable]

i think you're supposed to take the limit of sin2x/2x as x approaches 0

[alpine sable]

@torpid flax do you get that ^?

[torpid flax]

Not exactly

Wait a min

[alpine sable]

soo do you get it now?

[torpid flax]

Ima try something, 1 min

[alpine sable]

alr

If you wanna know more just search up complex fractions

or nested fractions

[torpid flax]

Alright, thanks for the help

[alpine sable]

nah but do you get it tho?

[alpine sable]

i can continue on

[severe pond]

Thought you were done

[alpine sable]

¯_(ツ)_/¯

up to him

[torpid flax]

I can show you what i got

[alpine sable]

alr

[torpid flax]

Just give me 2 min

I can read this entirely fine, until (24x+60)/6

[severe pond]

It factors out a 12

So 12•2=24 and 5•12=60

[torpid flax]

5•12=5?

[severe pond]

My bad

Then 12/6=2

So when you factor out the 12 you can divide it by 6 to get 2(2x+5)

[torpid flax]

ahh is see, (5x/6)12=60/6

[alpine sable]

i'd just apply that rule, factor x, cancel x

,w simplify \frac{\frac{x^2}{3}+\frac{5x}{6}}{\frac{x}{12}}

[ocean seal]

Results provided by WolframAlpha

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

Requested by Tasmav#3708

[alpine sable]

yeah so you're good

I just left it 1 step before here

or well a few steps actually

anyways they're both the same except the top the 2 is factored out

second they distributed 2

[torpid flax]

Makes way more sense now

[severe pond]

So you’re good?

[torpid flax]

Yeah im good, thanks a lot

[severe pond]

Np

Can someone help with this

[torpid flax]

@alpine sable @severe pond Life savers

[severe pond]

Q30

[severe pond]

I got you

[severe pond]

I know the answer but I don’t understand how to show the answer

[alpine sable]

i dont want to raid yall biut

would anyone mind

[severe pond]

I already asked my question wait your turn

[alpine sable]

bet sorry

[hoary shell]

Can you factor the polynomial in the denominator and then plug in 1?

[severe pond]

Yah I didn’t think about that

[hoary shell]

Or I think u can just plug in Q

1***

[severe pond]

You can’t because it gives a negative under the root. And factoring doesn’t do anything

This channel busy

[hoary shell]

Wouldn’t the number under the root be 10?

I don’t see a negative?

[severe pond]

Nvm plugging in 1 gives you 1/0

[hoary shell]

Oh I see there is a negative higher up lower down you wrote a plus sign XD

[severe pond]

Yah my writing is shit

It’s -5x

[alpine sable]

How can i make this a proper function

450 + 17 * 2000 wouldn't work obv

[severe pond]

This channel is busy

[alpine sable]

I'm not talking to you.

This is a follow up to my older question

[empty sparrow]

450 +17x = 2000 , then minus 450 => 17x = 1550 , then divide with 17

x = bla bla...

[alpine sable]

yeah thx

[ocean seal]

∫(Daman)dx
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[severe pond]

?

[alpine sable]

#help-1 I am getting help already

[severe pond]

Does no one know limits

I can’t solve this limit

I know it’s infinity but I don’t know how to evaluate it

No we haven’t learned that yet so I assumed the teacher didn’t want that method

How does that help

[alpine sable]

It's a one handed limit so you can use graphical or numerical methods. To use algebraic methods I think you'd need to prove that the left-hand limit is equal to the right-hand limit, correct me if i'm wrong

[acoustic plover]

Can anyone quick tell me what's 2+2

[alpine sable]

funny

Does anyone know how to model quadratics

[stray estuary]

might be 1

no calculus

got it

yeah it looks like it

its not even an infinity lol

you cant approach 0 from the right for that function anyways

I know it’s infinity but I don’t know how to evaluate it

it legit doesnt exist because we cant approach that function from the right

of 1 at least

also btw that problem that we were solving yesterday had the stupidest solution

legit did reverse product rule

yeah

IT WAS SO DUMB

like

you could rewrite it as the derivative of two functions

"its supposed to be easier than ibp" shut up ur making me feel bad for not seeing something obvious

nah i ended up turning it in with that rewritten solution

thank god

now i wait for the other questions to get graded

yeah

cuz remember we were getting sin u/u+ln u cos u

you can rewrite that as (sin u ln u)'

so lame

i just did u =sqrtx

hold on

i can send my work

found my work for that pepepega

also note that the formula for the circle is $$(x-h)^2+(y-k)^2=r^2$$ where $(h,k)$ is the center and $r$=radius

[ocean seal]

blanket

[stray estuary]

you can easily find the radius by finding the distance between the point given and the center of the circle

since the radius is just the length from the center of the circle to a point on the circle

[ocean seal]

∫(Daman)dx

[empty sparrow]

what did i wrong here?

[stray estuary]

cough

[alpine sable]

is this still busy

[gilded aurora]

im not good at math 😦 (a computer nerd), can anyone give me an explanation regrading the 2nd question, like step by step pls 🥺

[rigid wind]

a sphere center at (x0, y0, z0), radius r is given by (x-x0)^2 + (y-y0)^2 + (z-z0)^2 = r^2

[alpine sable]

well how can i do this the fastest way

i did it

[stray estuary]

just realized this was posted

[alpine sable]

and it worked but it took like 30 seconds

[stray estuary]

i dont think you did anything wrong there

[alpine sable]

i need something faster

[stray estuary]

dont think there is anything faster other than flipping them all over and just adding regularly

[empty sparrow]

but why is my solution so different than the actual solution

[stray estuary]

what matrix are you acting on with those transformations?

[empty sparrow]

only got the information until "What i Did"

[alpine sable]

well i did

1*5/2*5+1*2/5*2+1/10=0.8 

there must be something faster

[stray estuary]

other than knowing the fact that 2^-1 is 0.5, 5^-1 is 0.2, and 10^-1 is 0.1 then adding them together, there really isnt much to do

you could factor out a 1/10

and realize that you get 1/10(5+2+1) which is 8/10 which is 0.8

[alpine sable]

wait

explain more

that's an intresting way

[stray estuary]

if you factor out a 1/10

so

$$\frac{1}{10}\left(\frac{10}{1}\cdot\frac12+\frac{10}{1}\cdot\frac15+\frac{10}{1}\cdot\frac{1}{10}\right)$$

[ocean seal]

blanket

[stray estuary]

you see how the inside of the parenthesis will be 5+2+1?

[alpine sable]

AWWW

You're clever

[exotic wigeon]

if you look at it, 2 and 5 are factors of 10. SO you should be able to instantly work out that its 5/10 + 2/10 + 1/10 which equals to 8/10 or 0.8

[alpine sable]

yeah @stray estuary mentioned it

and it's a lovely way

[stray estuary]

👍

[exotic wigeon]

mhm

anyways gl

[scarlet leaf]

I’ve been trying to simplify this for ages but I cant get it to work. Would really appreciate if someone could help me out and walk me through it..

[stray estuary]

yeah im looking at it and i dont see anything wrong with your work

[alpine sable]

GREAT WAY

[stray estuary]

what can you write (a^2+2ab+b^2) as?

[stray estuary]

and what can you rewrite a^2-b^2 as on the bottom?

[alpine sable]

I solved the followup question in like 10 seconds

[scarlet leaf]

(a+b)^2?

[stray estuary]

yep

try rewriting it like that and you should see something cancel

you can also keep things factored and get common denominators but

¯_(ツ)_/¯

[scarlet leaf]

and (a-b)(a+b)

[small trellis]

Difference of two squares

😉

[stray estuary]

there you go!

[scarlet leaf]

yeah idk what's the better method, my head is absolute shambles rn lol

[stray estuary]

either one would work to be honest

[scarlet leaf]

been sitting way to much w/o any breaks but I just wanna finish this problem

[empty sparrow]

just got notified that the task has a mistake

thanks fam

[stray estuary]

what was the mistake?

was transformation a wrong?

thats what i had a problem with

even if you multiply those two transformations together you wouldnt get a 2x2 matrix

awkward

[empty sparrow]

the solutions was wrong thats what i got told

[scarlet leaf]

what do you mean by that?

[empty sparrow]

just discussing it with my friend

[stray estuary]

ah i see

[stray estuary]

he meant you could multiply everything out

[exotic wigeon]

Process

[gilded aurora]

question

is this correct ?

😦

[exotic wigeon]

just remember that (a+b)^2 can be broken into (a+b)(a+b), and that (a+b)(a-b) can turn into (a^2-b^2), and vice versa

[alpine sable]

make easier?

[gilded aurora]

well, did my best 😦

[stray estuary]

@scarlet leaf

[alpine sable]

@scarlet leaf swedish?

how

?

[gilded aurora]

yeah

[stray estuary]

btw you could factor the difference of squares on the left term

[gilded aurora]

oh

i have got something like this 😦

ohh, reallyy, all i just need to do is plug the r^2? the radius ?

oke, brother :>

[rustic rock]

._.

hmmm

[gilded aurora]

@alpine sable Thank you 🙂

[frigid coyote]

Free?

[crude musk]

how do you find the equation of a line that is equidistant from 3 points in the xyz plane

[rustic rock]

(x,y,z)

[crude musk]

what?

[rustic rock]

like that cords ?

like function or something ?

[empty quarry]

can someone get me a ticket to Australia?

[misty jasper]

anyone have a good tutorial video for solving x on a right triangle

[vocal kindle]

help :P?

[rain path]

Let me ask a stupid question,

Isnt a recurring number infinity?

[sleek elbow]

no, the definition of infinity is "a number greater than any assignable quantity or countable number". A recurring number like 0.333...... is not larger than all other numbers and therefore not infinity

[small trellis]

A recurring number has an infinite number of the same number/s

but it's not infinity

[rain path]

Well ok what if you times it by 2

[small trellis]

if you times what by 2?

[rain path]

A reoccurring number

[small trellis]

then it gets twice as big

[sleek elbow]

0.333...... * 2 = 0.666......

[rain path]

With a whole number

[small trellis]

Same thing

gets twice as big

Multiply it the same way as you would with any other decimal

[severe pond]

No it’s not DNE it’s infinite

[rocky lantern]

Someone help

[severe pond]

Look up on wolfram alpha

The right side is negative infinite left side is positive infinite

Double side limit DNE

[rocky lantern]

@alpine sable

Can u help me

[terse coral]

I feel like I did this wrong

Im supposed to find length of vector |v| and the vector is (1,1)

can someone confirm that I did this right?

[sinful relic]

looks fine

[terse coral]

ty!

[sinful relic]

length of a vector is $\sqrt{a_{1}^2 + a_{2}^2}$

[ocean seal]

Lil Sachi

[autumn plank]

is x ln(x) - x the same as ln(x)^2

[alpine sable]

no its same as ln((ex)^x)

[autumn plank]

but when intigrating ln(x)

Sometimes I have to use x ln(x) - x and sometimes ln(x)^2

[west wave]

Someone who can help me with this: Calculate the volume of a cylinder of revolution circumscribed to a cube of volume 8m ^ 3.

[alpine sable]

its xln(x) - x where you got ln(x)^2 ?

[autumn plank]

No

I have to integrate ln(x) + 2 / x

[alpine sable]

then its xln(x) -x + 2ln(x) = xln(x) -x + ln(x^2)

[autumn plank]

Nvm i figured i think

its 2 ln(x) + ln(x)^2

cause u have to integrate 2/x and ln(x)/x

here’s the question I just dont grt it

[red ledge]

Guys

Can someone explain this

9Pn-4 = 9!
Find n

How to find n?

[alpine sable]

substitute 2 + ln(x) as u

[red ledge]

Can u help me?

[alpine sable]

Basically I'm proving that for this specific problem that Z is unbounded. I was just wondering if it's the case that Z is always going to be un-bounded when Non-basic Variables > Basic variables in terms of the amount of them is always true.... Because it essentially leaves no possible leaving basic var? Or is there a case where NBV > BV but it can be bounded still?

[red ledge]

Um guys can somebody solve my question?

9Pn-4 = 9!
Find n

[alpine sable]

You just rub the magic conche and it'll tell you

[red ledge]

Rubbing the magic conche

Now pls tell me

[alpine sable]

lmfao

[red ledge]

and why, I need an explaination for the problem

[alpine sable]

So you want us to do your hw

lol

[red ledge]

No man I just need an explaination

Why everybody says that

I just simply don't understand the concept so I'm trying to get someone to explain it to me

Why do you have to always attach it to homework

Fuck's sake

[alpine sable]

I don't think there's an answer since (9-n)! will give a fraction and factorial can't be fraction

[red ledge]

This world will never help u

[red ledge]

No U are wrong

There's an actual answer

[alpine sable]

and what's that?

[red ledge]

Wait man

[alpine sable]

lol this kid

[red ledge]

What are u talking about

There's no 9-n in the question

Bro read the question again

The question says

[alpine sable]

9Pn is same as 9!/(9-n)!

[red ledge]

9Pn-4 = 9!

[alpine sable]

lmfao

[red ledge]

Yeah u are right

[alpine sable]

He doesn't know how to substitute a formula

[red ledge]

Please stop I'm serious

Stop being rude

I'm trying to learn

[alpine sable]

What are you in discrete mathematics rn, doing combatorial math

[red ledge]

Please stop

[alpine sable]

Thats.... a question

Literally asking what class this is for

[red ledge]

Yes bro u are right so what?

[alpine sable]

You didn't even state what area of math this is. Or ask how to start solving the problem. He just wants the answer and explanation so he doesn't have to do ti

it

[alpine sable]

so 9Pn never equals 9! + 4

[red ledge]

Bro it's 9 P n-4

[red ledge]

n-4

[alpine sable]

bruh

[red ledge]

Not just n

What?

[red ledge]

What am I missing?

[alpine sable]

How do I calculate average velocity

[alpine sable]

nothing I considered it as 9Pn -4 instead of 9p(n-4)
so
just remember if nPr = n!
then r = n-1

[red ledge]

So...?

[terse coral]

can someone help me solve that?

Im confused

for (z1,z2) I got (3,2)

[alpine sable]

so as given 9!P n-4 = 9!
that means n-4 = 9-1

[scarlet torrent]

guys i need help i dont understand how to do (10^-3)^4
if some one can explain to me and help me

[red ledge]

So n equals what?

[alpine sable]

can't you solve n-4 = 8?

[red ledge]

12?

Okay bro but how did u know this rule

[alpine sable]

yes

[red ledge]

"just remember if nPr = n!
then r = n-1"

Where did u get this from?

Take ur time

[alpine sable]

$$^nP_r = n!$$
$$\frac{n!}{(n-r)!} = n!$$
$$(n-r)! = 1$$
$$n-r = 1 ~or ~0$$

[ocean seal]

Spica

[red ledge]

Wow that's awesome

[alpine sable]

so answer can be 12 or 13

[red ledge]

Yes exactly

How did u know all of that man?

[alpine sable]

was mentioned in my textbook

[red ledge]

Like is is there a book that explains this rule specifically or a Youtube channel?

[red ledge]

Please tell me what's ur textbook

[alpine sable]

idk about yt channel but

[alpine sable]

my boards book XD

[red ledge]

What? Wdym?

Please I wanna buy that book

Are u in high school?

[alpine sable]

It was my boards book so that's not available worldwide

[red ledge]

Like ur teacher's book or something?

[alpine sable]

yes for your info its mentioned in almost any algebra book conatining p and C

[red ledge]

Wow

[alpine sable]

yeah kinda

[red ledge]

Okay are u in High school?

[alpine sable]

yes

[red ledge]

Senior?

[alpine sable]

yes

[red ledge]

Okay there's another one do u want it?

[alpine sable]

ok

[red ledge]

it says

[alpine sable]

btw you can refer hall and knight but that'll be too high for your lvl

[red ledge]

$$\frac{n+2!}{(n)!}+3n = 74$$

[ocean seal]

Abstract

[red ledge]

Oh I forgot to put like brackets

[tawny lion]

parentheses

[red ledge]

Yeah parentheses

My keyboard is broken

[oak hound]

can someone look at #help-1 ? pls

[alpine sable]

$\frac{(n+2)!}{(n)!}+3n = \frac{(n+2)(n+1)(n)!}{(n)!}+3n= (n+2)(n+1)+3n$

[ocean seal]

Spica

[alpine sable]

now its quadratic in terms of n just solve it

[red ledge]

Bro I was stuck at this point

I didn't know I have to like do the quadratic

Because our teacher always taught us that we like factor the 74

To axbxc

For example 120= 5 x 4 x 3 x 2

What do u mean?

I dunno man.. Yeah it helps in other problems

But u can't factor the 74 here

Then u equal n+1 = 5

Then it's an equation or something

[alpine sable]

there's 2 in lhs so it'll become 72 then factor it in 12*6 cause there will be a 6n term in lhs

[red ledge]

Do it on calculator

[red ledge]

What is "Ihs"?

[alpine sable]

left hand side

[glass lichen]

Obviously

[red ledge]

Yes u can do fractions on calculator.

[ocean seal]

WhipStreak23

WhipStreak23

[red ledge]

Then what do I do?

Wait why don't u equate it to zero

[glass lichen]

You need 1 side 0, yes

[red ledge]

like put = 0

Yeaaah I'm right

[alpine sable]

yes

[red ledge]

But why tho?

Umm

[glass lichen]

To apply zero product property in the general sense

[red ledge]

Hmmm

[ornate lintel]

hi guys new here