help-0

[placid zinc]

We've got a system of equations, with two unknowns: T and C.

[wheat condor]

than k u

i apprecait eit @placid zinc

[placid zinc]

All good? You can finish from there?

[compact orchid]

I put DNE thinking -7+7=0 so it doesn’t work. But the answer was wrong. I assume it’s to do with the direction but I don’t know where to start if anyone can help. Thank you <@&286206848099549185>

[torpid scaffold]

ay can i ask for help

i dont understand what it means bu dimension of maximum area

[placid zinc]

@compact orchid
Note the limit is from the left

So you can assign infinity or negative infinity to it

[wheat condor]

is the answer D1=D/3

@placid zinc waht did uget

[compact orchid]

@placid zinc If I’m able to treat it as negative infinity and -7. I assume the value must be inf.

However, I’m still unsure how we don’t have to put -7 as the value. I do understand how -inf is apart of the numbers though.if you are able to help.
Thank you for leading me to the answer either way!

[placid zinc]

Yes

[placid zinc]

Consider plugging a number "slightly less than -7" in. Then you get:
-4/(something slightly negative)
= a very large positive number

[proven flare]

Is this channel free?

[compact orchid]

@placid zinc Thank you so much, I think it just hit me. The bottom acts as an asymptote in that regard, and that’s why it’s -inf. So it would be -4/-inf=-inf

[serene jacinth]

how on earth is that the same ?

could someone help me out pls ?

[tacit breach]

caue they both equal 0

[serene jacinth]

how is the first equation transormed in to the second i cant see that

[karmic yarrow]

$$\lambda^2 -1 = (\lambda+1)(\lambda-1)$$

[ocean seal]

Tylertronica

[placid zinc]

@compact orchid
-4/-inf = -inf
Is like, the most sus thing I've seen written today

[serene jacinth]

i see thank you very much sir

@karmic yarrow

[thorn ibex]

So i was doing a review and I wanted to know why my teacher wanted me to multiply by 15 on both sides instead of 5, was this a mistake

[placid zinc]

I'm guiding you towards
-4/-0.000001 = +inf

[tacit breach]

because of common denominators maybe

[thorn ibex]

can you explain a bit more

[tacit breach]

i mean itll cancel them both out leaving you with that 5x-75=3x

[compact orchid]

@placid zinc Sorry I meant +inf. how come we dont like using -inf as a value?

[tacit breach]

then subtract 3x

5x-75-3x=0

=0 cause quadratics

2x-75=0... add 75... divide then x =75/2

[dense trail]

what quadratics

[tacit breach]

idk lol

was just saying stuff

[dense trail]

feel like equating to 0 is unnecessary in this case

[tacit breach]

you didnt have to, could of subtracted 5x

like the teacher did

but most teachers say "you cant have 0"

[dense trail]

lol true

[tacit breach]

like, its not the end of da equation or anything

[dense trail]

i guess practicing equating to 0 here helps learning quadractics in the future maybe idk

[tacit breach]

i said quadratics cause thats what you do right, equal it to 0

@thorn ibex does this help

it turns into 3x becaue you cancel out the 5

[alpine sable]

Just solve it normally @thorn ibex

By taking LCM and then cross multiplying

[tacit breach]

ong bro

[alpine sable]

how does f(x) = 2*x^2 + 2*x + 8 become f ´ (0) = 4*0+2 = 2 ?

[dense trail]

whats the derivative of f(x)

[alpine sable]

can someone please explain how Diana occupies only two positions, when you can have the permutations ANCD, DCNA, CDAN... There are so many more permutations, I thought it would be that Charles and Diana both have 6 permutations. (D-diana, C-charles, A-Albert, N- unnamed people)

[prime fjord]

Because if we have the queue with 4 people (say left side), then it will be Albert and Charles already occupying 2 spots in a line of 4.

Only 2 spots left

@alpine sable

[alpine sable]

so you dont actually count the permutations like ANCD or DCNA

or think about

[prime fjord]

Those permutations have already been accounted for

Because when u put the 4 x 6 x 2 ... It means you are accounting for the 4 possible slots to insert the person into

[alpine sable]

that makes sense thx

[prime fjord]

Nw

[warm patio]

A bundle of P20 bills with serial numbers from TG339659 to TG339728 gives a specific total amount.

Help pls

[tacit breach]

bruh what lol

[pearl galleon]

Hi, im new to letters in math and a video i watched said they hold a value of a number or extra digits, can someone confirm this, and if so what is the default number

[dense trail]

yeah they are called variables

the most common being "x"

[tacit breach]

Yes variables are place holders

unknown numbers, or an expression

[warm patio]

Can some one answer my question :)

A bundle of $20 bills with serial numbers from TG339659 to TG339728 gives a specific total amount.

[tacit breach]

a = 2

a + 3 = 5
or
a = sqrt(4)+6
a + 10 = 18

simply just hidden values until you solve

[burnt wharf]

Can anyone plz solve a maths question of mine

[pearl galleon]

if its simple i can

[tacit breach]

literally everyone lol

[sick torrent]

How do you do questions like this?

[pearl galleon]

you open a caculator

[sick torrent]

I-

But how do you put it in your calculator?

[pearl galleon]

the top part is 10

[dense trail]

just sub x for 3

[sick torrent]

How do u know?

[tacit breach]

he dont know what he talking about

[sick torrent]

Oh

[pearl galleon]

f(x) + g(x) = 10

[tacit breach]

no it doesnt bruh

[pearl galleon]

thats as far as your getting with me

[tacit breach]

thats like saying a + b = 5 when i dont know either number

a could be 3 or 2

[dense trail]

wait but

[pearl galleon]

it says on the top f(x) = 4 and g(x) = 6

[vale wigeon]

lim[x->3] f(x)+g(x) is 10, yes.

[dense trail]

it dfined the function as

yeah

[vale wigeon]

you should not omit the limit notation.

[tacit breach]

oh lmfao

my bad

[dense trail]

although in this case

[sick torrent]

Then what’s the bottom? 6(6)?

[dense trail]

changing "x" doesn't affect anything

[tacit breach]

5/9f

[dense trail]

well its just 6*6

[pearl galleon]

6 multiplied by 6 i assume

[sick torrent]

Oh

[dense trail]

idk its a weird question

in this case having lim and not having it doesn't make much of a difference

[pearl galleon]

your files are open btw

[sick torrent]

So then it simplified would be lim5/18 ?

[dense trail]

yeah ig

[sick torrent]

Files?

[pearl galleon]

files tab

[sick torrent]

What is that

[pearl galleon]

nvm

[tacit breach]

yeah it 5/18

[dense trail]

which would be just 5/18
cuz regardless of what value x is it doesnt affect this function

[sick torrent]

So then how do u find lim5/18

[dense trail]

you dont in this case

[tacit breach]

10/36 = 5/18

[pearl galleon]

i only understood the first part of this math

[dense trail]

dw you will get there

[small trellis]

You're just substituting variables in and the function notation goes away when that's done

[sick torrent]

Wow

Thank you guys

But then

[pearl galleon]

wait, i just noticed it says x = 3

[dense trail]

naw dont worry about it

its limits

[sick torrent]

What does x—> 3 mean?

[dense trail]

it means x approaching 3

[tacit breach]

how you taking that class and not know that

[sick torrent]

What do u do with that information?

[small trellis]

Actually you might have to put a 3 in there somewhere

[pearl galleon]

just multiply by 3 when it has (x)?

[small trellis]

I'm not sure

[tacit breach]

very susballs

[sick torrent]

My bad

[dense trail]

in short, yes, but also not quite

[sick torrent]

Wdym?

[pearl galleon]

i failed but at what cost

[small trellis]

If the lim approaches h, I know you do f(x + h) - f(X)

[dense trail]

because you can do things like lim x -> 0 1/x

[alpine sable]

how do i give another name for a plane??

[dense trail]

remember to divide by h

[small trellis]

And also divide by h

[dense trail]

lol

[small trellis]

Yeah

[sick torrent]

I’m so confused

[pearl galleon]

when something is in brackts youact like its a time table

[dense trail]

watch a video on derivatives I guess

[small trellis]

So surely that would apply for the 3

[dense trail]

or just watch a video on limits

[small trellis]

@sick torrent watch a vid or something on "differentiation by first principles"

[sick torrent]

I did. Multiple videos. But I’m still very confused

[dense trail]

bruh

ok

x -> 3 is just like saying using values closer and closer to 3

lets say

we have f(x) = 3x

[sick torrent]

Uh huh

[dense trail]

what happens when x gets closer and closer to 3?

then f(x) will get closer and closer to 9

[sick torrent]

Oh

[dense trail]

so therefore

[sick torrent]

Where’d the 9 come from

[dense trail]

lim x -> 3 3x=9

[dense trail]

well try and sub in values

try numbers really close to 3

[pearl galleon]

wouldnt it be 6*3 since f = 6 and (x) = 3 so f(x) (f**x)

[sick torrent]

For x?

[dense trail]

because x -> 3 just means having x getting closer to 3

yeah for x

[dense trail]

naw man, f(x) is function notation lol

f is not a variable in this case

[sick torrent]

I get that but what do u do with that information for a question like this?

[alpine sable]

apparently, 2.999... which is probably 3 and 2.999... at the same time

[dense trail]

well

give me a question

[sick torrent]

U put that as x?

[tacit breach]

applied maths bra

[alpine sable]

see limit is not the value of the function at x

it is the value of function as x approaches that value, and approaches as in a infinitely small neighborhood

[pearl galleon]

math is one of those things you like if you understand

[alpine sable]

not like if the limit as x approaches 3, so you take the value at x = 2.5, no the neighborhood is infinitely small

[sick torrent]

What is infinity small neighborhood

[alpine sable]

for example

lets say the real numbers around 3

[sick torrent]

Uh huh

[alpine sable]

for example, 4 or 2 or 2.5 for that matter

okay?

[sick torrent]

Ok…

[alpine sable]

now, since we are considering the real values, the values around 3 whose decimals go on infinitely also come in the category!

[tacit breach]

https://www.quora.com/What-are-real-life-applications-of-limits-in-calculus

[alpine sable]

They are at some point in the infinitely many places the point can be

say, 2.98093460980948309879340

[sick torrent]

Ohh

[tacit breach]

Measuring is exactly how limits work

We measure all the time

[alpine sable]

even though it is ridiculous to even want that value, it still exists at some point of the function

[pearl galleon]

mostly 5 inches when im alone

[alpine sable]

now, things get a bit weird when there isnt a limit

[tacit breach]

We measure outside, wood, in the bathroom,

[dense trail]

you could also have 3.000000000000000123

[tacit breach]

you will always get an aprox but never exact measure

Because nothings exact

[alpine sable]

also, there is a simple proof for the fact that
2.999... = 3

[tacit breach]

theres a proof that 0=1

[alpine sable]

wha

t

[sick torrent]

😃

[tacit breach]

trust me

[pearl galleon]

so i can constanly give you 1 doller

[alpine sable]

ok

[tacit breach]

ye

[sick torrent]

I get that but

[alpine sable]

I hope you understand the concept of a limit @sick torrent

[tacit breach]

https://www.youtube.com/watch?v=P4GgBr-INMk

[sick torrent]

Nvm I give up

[alpine sable]

and he says

that this is a mistake you should avoid

towards the end

[dense trail]

bruh now is not the time for conspiracies

[alpine sable]

😉

[tacit breach]

yes ofc

because its not exactly true

it just works

[alpine sable]

it is not true lol

[tacit breach]

but it is

[alpine sable]

alright

[tacit breach]

https://www.youtube.com/watch?v=hI9CaQD7P6I

[alpine sable]

there might as well be a proof that 420 = 69

[tacit breach]

there probably is

[pearl galleon]

pretty similer irl

[tacit breach]

he boutta prove you can divide by 0

[sick torrent]

Hold up

So if they don’t tell u what f(x) or g(x) equals u sub in x with the x—>number ?

[woven echo]

i mean in that video he does divide by 0 that's why it breaks

[sick torrent]

How do you do a question like this?

[tacit breach]

"Your bill is $400....'
no its 1$ let me prove it

you have chrome bro use it

[sick torrent]

Huh?

What’s wrong with Microsoft edge ?

[tacit breach]

because its microsoft edge

[sick torrent]

My bad

[tacit breach]

people only use edge to install chrome then uninstall edge after

[woven echo]

ah edge is based on chromium anyway

its fine

[sick torrent]

My school used Microsoft apps so it makes everything easy

[sick torrent]

Can anyone help me?

[woven echo]

just plug those values in to the difference quotient

[sick torrent]

It’s so complicated I don’t understand

Where do i put x^2-9x ?

[woven echo]

you use the a and the different h's to plug into that function

(a+h)^2 -9(a+h) is your f(a+h)

use the values for a and h ofc

[sick torrent]

How would the first question look like?

[woven echo]

well like it mentions simplifying first without plugging in a value for h is probably easier so you don't gotta simplify 4 times

so if you plug -5 in for a

(-5 + h)^2 -9(-5) goes where f(a+h) is

[sick torrent]

Ohhhhh so f(a+h) is f(x) ?

[woven echo]

its your f(x) but you are plugging (a+h) in for x

[sick torrent]

Ohhhhh

[woven echo]

you can do it with just the letters, or you could put the numbers in

you'll have some big long thing if you leave the variables

in the future that's actually what you do to solve a difference quotient you just plug (x+h) in

and then - f(x) so it's just the function as is

[sick torrent]

Is this how it would look like?

[woven echo]

well you need to plug it into the actual function

like x^2 becomes

(-5 + 0.1)^2

or (a + h)^2

the -9x becomes -9(-5 + 0.1) or -9(a + h)

[small trellis]

Your h seems to have disappeared for the last part

[sick torrent]

Ohh

[woven echo]

oh shit my bad ur right

i realized that just a minute ago too lol

i was trying to sneakily fix it with that 2nd one and hope no one noticed

[sick torrent]

Like this?

[woven echo]

for the first part yes but the -f(a) needs to subtract the entire function with that -5 or a plugged in

make sure you subtract the ENTIRE function though, you probably want to put parenthesis around it

[small trellis]

you kinda just have to learn that this is how it works

whatever is next to the X as defined as f(x) will then affect everything that is within the function

such as f(x+h)

[sick torrent]

Now I’m confused

[small trellis]

I'm just showing you an example of how it works

[sick torrent]

Like this?

[woven echo]

the - (-5) is not right

[small trellis]

why does the question have f(a)

when there's only a = -5

[sick torrent]

Oh

So what is it supposed to be?

[woven echo]

similarly to how you plugged (-5 + 0.1) into the function for f(a + h)

what do u think u'd do for f(a)

[sick torrent]

I have no clue

[small trellis]

I find this stupid how it's a and not x

but i guess it wouldn't work how it's intended if it were x

[rose fulcrum]

This gives the derivative at x = a

[woven echo]

u gotta work with what they give u

[sick torrent]

Huh?

[small trellis]

I guess I just never really encountered this myself

but I get it

they're combining the function part with a

[sick torrent]

What is f(a) ?

[harsh swallow]

the point is when it says f(a + h) you fill in x = a + h

and when f(a) you fill in x = a

[small trellis]

yeah

you have to use the f(x) equation

[rose fulcrum]

If you have an 'x' instead of 'a', you get the derivative function for all 'x'
If you have an 'a' you get the derivative function for all x = a, same thing?

[sick torrent]

For a?

[small trellis]

yeah

[harsh swallow]

the first one is h = 0.1

[woven echo]

you are plugging "a" into f(x)

similarly as if you were told x = 2

and you put 2 in for every x

[harsh swallow]

(f(a+h)-f(a))/h

[woven echo]

you are inserting the value of a instead

[harsh swallow]

filling it in would be

[small trellis]

The "f( )" part immediately tells you what it's referring to

there's only one function there

[sick torrent]

Like this?

[small trellis]

the part inside the brackets tells you what you need to substitute it for

[woven echo]

there u go

[harsh swallow]

$\frac{(a+h)^2 - 9(a+h) - a^2 + 9a}{h}$

[ocean seal]

Katharine

[harsh swallow]

exactly like that

perfect

[woven echo]

fwiw to make your life easier here you might want to just copy that before you solve it

so you can quickly change that + 0.1

for the others

[sick torrent]

Omg thank you all so much

[sick torrent]

Thx for the tip

[tawdry trench]

Guys

Anyone good in game theory?

[sick torrent]

On my calculator the answer is error. Isn’t x 28?

[acoustic plover]

If it's problem 6
Then ask in #help-6

[sick torrent]

Oh my bad

[echo lodge]

I don't know that XD cool

[split oriole]

Take out x common from deno.

[echo lodge]

yep and ans is 1/28

[sick torrent]

Isn’t the denominator 0?

[split oriole]

First cancle out the terms

Then put the limit

[sick torrent]

How do u put the limit?

[split oriole]

See (x-28)/x(x-28)

Cancle out (x-28) you will get

1/x now put the limit

[sick torrent]

Ohhhhhh

Thank u

[woven echo]

yea if its 0/0 its "indeterminate" and usually you can factor something out to solve it

if its some number over 0 though then it doesn't exist

[sick torrent]

Hold on but

[sick torrent]

How does this = 1/28

I’m still getting an error

[woven echo]

when you cancel the (x-28) you are left with 1/x

if you plug that 28 back in for the x then

you get 1/28

[sick torrent]

Oh gosh I understand

[woven echo]

if you actually graphed this you'd find there is a hole there btw

its not "actually" defined at that point

but 1/28 is what it approaches

[sick torrent]

The numerator is 1 even tho it doesn’t show?

[empty sparrow]

the matrix of the composition in R^2, where it first gets mirrored at the indentity (y = x ) and then mirrored on the y axis looks like what? Can somebody help me

[woven echo]

yeah when you cancel out something you are essentially making a fancy 1/1

so if you cancel everything on the top there is still a 1 there

[sick torrent]

Ohhhhhh

Thank you so much

[woven echo]

np np

[carmine lion]

https://cdn.discordapp.com/attachments/818739351399825459/889774124212297748/image0.jpg

https://cdn.discordapp.com/attachments/818739351399825459/889791706998931476/unknown.png

im asking for part b

[placid zinc]

Combine CC into a new letter like X

How many ways can you arrange FIBONAXI?

@carmine lion

[carmine lion]

8P3/2!

@placid zinc

[placid zinc]

Oh wait, mb

You're turning this into 4 letter codes

[carmine lion]

yes

i thought that was what u meant to ask

so

[carmine lion]

but if this is the qustion u meant to ask, then its 8!/2!

[placid zinc]

Well, I'd go with some hard casework.

• How many ways with no C or I?
• How many ways with no C and 1 I?
• How many ways with no C and 2 I?
• How many ways with both C and no I?
• How many ways with both C and 1 I?
• How many ways with both C and 2 I?

[carmine lion]

wait why

[placid zinc]

Should have some of that already from part A

[carmine lion]

do i have to do all these

[placid zinc]

I admit there's probably a better way. Let me search

[carmine lion]

also

i have a question about the question

can i interpret it such that 2C's will always be chosen

[placid zinc]

Yes I think so

[carmine lion]

https://cdn.discordapp.com/attachments/818739351399825459/889791706998931476/unknown.png

so can i do it like this

[placid zinc]

So then you don't need the first three cases I laid out kek

[carmine lion]

where 2 letters are chosen

and then in the 3 gaps

i can have the 2C's

(one of the gaps)

[placid zinc]

Oh yeah, clever

[carmine lion]

so im just wondering if my calculation for that is right

[placid zinc]

But doing the I's is still weird

[carmine lion]

like accounting for extra I's?

[placid zinc]

Yeye.

[carmine lion]

so 7P2?

[placid zinc]

What is 7P2?

[carmine lion]

how many ways can you arrange 2 objects from 7

given that each object is distinct

[jaunty shard]

hello

[placid zinc]

I mean what are you counting with 7P2 kek

[carmine lion]

this channel is occupied

the 2 places

[tawdry trench]

Guys any help for game theory and linear programming?

[placid zinc]

I think you're counting all possible 4 letter codes with CC with 7P2

[carmine lion]

take away the CC's from the list of letters

so then u have 2 i's and the remaining unique letters

which is a total of 7

[placid zinc]

The problem is that you're not considering FCCB and FBCC as different this way

Only one count for both

[carmine lion]

ah so my method won't work

?

[placid zinc]

You're close, realize that for every count you've made, there's 3 different counts you could have actually made:
CCFB, FCCB, FBCC

[carmine lion]

so i have to multiply by 3

[placid zinc]

So you're up to 3(7P2)

[carmine lion]

yes

[placid zinc]

But there's still a problem, and it is with the I. There's 3 words that include both:
CCII, ICCI, IICC

You're double counting each word as you're considering the two I to be seperate

That's an easy fix, just subtract 3.

You're down to 3(7P2) - 3

[carmine lion]

wait, why are we double counting for the 2nd one

ICCI

[placid zinc]

Because ICCI and ICCI are the same word, despite me swapping the two I

[carmine lion]

ah nvm

lol ok

so now we're down to 3(7P2) - 3

[placid zinc]

Double counting is really hard to explain kekw

I think that's everything

Let me hit it with a method I'm more comfortable with and see if I can confirm

[carmine lion]

okay!

[alpine sable]

Hii can anyone help me with my math practices? It’s pre algebra

[karmic dawn]

any idea what the answer is? I have tried (-infty,infty) not rlly sure where to go from there

[carmine lion]

what is the source of this question

[karmic dawn]

its an assignment/homework

[carmine lion]

assignment?

[karmic dawn]

yea a homework

its not worth anything if thats what your wondering

[placid zinc]

I just realized a problem. Choosing the first I for a word is different than choosing the second I for a word

I think this is overcounting by 30 because of this

[carmine lion]

😱

what. the. heck.

[carmine lion]

why

[placid zinc]

So our counting method is this:

• Take the word FIBONAI
• Choose any two letters, put then in an order (7P2)
• Choose a place for CC in that order (3)

Nowhere in that do we make a rule for the two I being the same

[carmine lion]

so maybe

• Take the word FBONAX
• Choose any two letters, put then in an order
• Choose a place for CC in that order

and then divide by 2!

for the x part

[placid zinc]

Problem is, you're not double counting the words that don't contain any I

Go figure, there's exactly 60 such words

I resuggest my safer method:

• How many ways with both C and no I?
• How many ways with both C and 1 I?
• How many ways with both C and 2 I?

As you can be sure you're not double counting anything here

[wispy olive]

Yo.

[carmine lion]

this is occupied

[carmine lion]

ah so you add each case?

[placid zinc]

Yeye

[carmine lion]

but surely there is an easier way of doing this

especially if the word gets

bigger

like INSTANTANEOUSLY

[placid zinc]

The cases are pretty easy

But I hear you

Maybe there is. I wanna search again

[empty sparrow]

how to i get the normal vector of the plain, which contains a straight line j(x) = (n n n ) + lambda(n n n) that also lays vertical on the plain (n n n)*(m m m), how do u calculate it or do u need exact vectors or numbers?

[carmine lion]

please ask in another channel

thanks!

[placid zinc]

Actually, I did think of an easier way. Use the word FIBONA instead, which gets all words with 0 I or 1 I

Then add the extra case with 2 I

Still not an instant equation. But it gets the correct answer in only two cases and they're both very easy

[carmine lion]

hmm ok

[alpine sable]

halo

i have question

How to describe blue chart with single formula in excel any idea? I have data tables.

is my answer for a and b correct?

<@&286206848099549185>

ping me if yk

[warped jay]

x^(2)+4x=45 help me

[dense trail]

move all terms to one side

letting the other side be 0

[warped jay]

solve by completing the square method

[dense trail]

ok

[warped jay]

what is the standard form of that?

[dense trail]

x^2+4x-45=0

[dense trail]

wdym?

[dense trail]

standard form = ax^2+bx+c

[warped jay]

yeah

so whats the answer?

[dense trail]

oh you guys do it like this

i do it having all terms on one side

you just need the answre?

[warped jay]

yes because i want to correct my self

[dense trail]

then you got it correct

[warped jay]

i have a answer but im still confuse

[dense trail]

1 and -13

what are you confused about

[warped jay]

wait a minute

my answer is x=5, x=-9

bruhh

[dense trail]

can i see working out?

[warped jay]

i use mathway hshshs

Im confuse

[dense trail]

bruh

so which question were you talking about

[warped jay]

that given is standard form right?

[dense trail]

x^2+4x-45=0 this one?

[warped jay]

yeah

[twilit venture]

Hello anyone there to help I am of 9th class

[dense trail]

ohhhh

[warped jay]

same 🙂

[dense trail]

i was solving for the one you sent a picture of lol

[warped jay]

lmao

[dense trail]

then yeah

i got your answer

-9 and 5

[twilit venture]

Pls I want help say yes or nohttps://cdn.discordapp.com/emojis/820714264650055732.png?v=1&size=40

[warped jay]

for how?

can u send your solution

[dense trail]

ok

[twilit venture]

Evr

Do u wanna help me?

[dense trail]

although usually do it slightly differently

[warped jay]

Im confuse with my teacher solution

[dense trail]

on what

[twilit venture]

@dense trail pls

Wait shall I send u question in which I have doubt

[dense trail]

lemme finish helping cosmo first

[oak chasm]

@twilit venture Please read the rules and tips for getting help in #❓how-to-get-help.

[twilit venture]

What's ur doubt Cosmo??

[twilit venture]

This is easy question tbh

[dense trail]

so first you find the perfect square that begins with x^2+4x

in this case it would be x^2+4x+4

but to keep the equation the same, we need to subtract the 4 again

[warped jay]

ok

[dense trail]

so its would become x^2+4x+4-4

now with the 45 itd be

x^2+4x+4-4+45

but now you can simplify the first 3 terms

[twilit venture]

Hello cosmo Multiply the constant with square factories and then common done

That's it

[dense trail]

it becomes (x+2)^2-4+45

[twilit venture]

Can I send my doubt??

[warped jay]

ok noted ty

❤️

[dense trail]

np

go ash

[twilit venture]

These 2 questions

[thin kayak]

I see you bro 👀

[dense trail]

ayo

[twilit venture]

Wait pls he is helping me

[dense trail]

AZ my bro

[thin kayak]

yeah yeah np

[twilit venture]

@dense trail did u get it??

[dense trail]

multiple of 2009

so it can't be smaller than 2009 right

[twilit venture]

What are u talking?it's obv what u r saying bro

[dense trail]

2009*c, for c = all positive integers

[twilit venture]

Ya obv

Any idea how to approach

?

[warped jay]

x^(2)+6x=16 what is standard form of this?

[oak chasm]

@warped jay Sorry, this channel is busy.

[twilit venture]

Substitute everything to the left side

Take 16 to the left

[dense trail]

not substitute

[warped jay]

so this x^(2)+6x-16=0?

[dense trail]

yes

[warped jay]

ok ty again

[twilit venture]

Ya so substitute only right?

[warped jay]

❤️

[twilit venture]

Np

[dense trail]

wait for Q1

couldn't you just set up an equation

[twilit venture]

@dense trail did u get that

Ans

[dense trail]

cuz 2009 is a multiple of 2009 technically

oh but its a natural number

[twilit venture]

Bro politely speaking don't give observations pls tell how to approach what observations u r giving those r obvious

Which class in r u?? @dense trail

[dense trail]

you might not want my help then

i never learnt number theoty

[twilit venture]

https://cdn.discordapp.com/emojis/771287728305471528.gif?v=1&size=40

Ok leave

Thank u for trying

[dense trail]

you were the one demanding my help

[warped jay]

Im still confuse

[warped jay]

why =0

[warped jay]

but this one 0 has a value

@dense trail

[dense trail]

wdym

[warped jay]

this one

[dense trail]

having a 0 there is for null factor law

[warped jay]

why 0 is gone

[dense trail]

??

where

[oak chasm]

@lean night Sorry, this channel is busy.

[lean night]

oh sorry

[warped jay]

x^(2)+5x+6=0

that is a given

[dense trail]

ye?

oh are you following the board

idk why they do it that way

[warped jay]

and the standard form is x^(2)+5x=-6

[dense trail]

no

standard form is x^2+5x+6

[warped jay]

so how x^(2)+5x=-6 is answer?

[dense trail]

wtf

huh

it shouldn't

[warped jay]

Im confuse 🙂

[short peak]

can ratios have a decimal ?

[dense trail]

you were asked to solve using completing the square right?

[warped jay]

My mind is now blowing

[warped jay]

yeah

x^(2)+5x=-6 what form is this?

[twilit venture]

Se bro cosmo shall I explain clearly

[warped jay]

Btw, I'm from Philippines 🙂

[twilit venture]

See the standard form of any quadratic equation that is where the degree is 2 is ax^2 + bx + c = 0

[warped jay]

yeah

so she use another form

[twilit venture]

Ur question was x square plus 5x plus equals to minus 6

Right

So a is 1 bis 5 and c is 6 which is on another side

[warped jay]

ax^(2)+bx=c she use this form

[twilit venture]

Do u want another method

To solve these sums??

[warped jay]

Yeah

[twilit venture]

BTW I am from India 🇮🇳 u??

[warped jay]

My mind is now blowing

[warped jay]

Philippines

[twilit venture]

https://youtu.be/7vjC96TKPXE

@cosmo see this

[warped jay]

ok I will watch

[twilit venture]

Hello u there??

[warped jay]

but I need is Solve by Completing the Square

is that same with that>

*?

[twilit venture]

Ok u need the problem solution by square method??

[warped jay]

Yeah

[twilit venture]

Can u tell the problem once again

[warped jay]

wait

x^(2)+6x=16

so that's correct

Ok got it

[twilit venture]

I have factorization method to solve it because square method works only sometimes

Shall I share that method

?

[alpine sable]

how to do this?

[twilit venture]

@alpine sable just a min

[alpine sable]

okay okay

[twilit venture]

@alpine sable u there??

[alpine sable]

yeppp

[twilit venture]

Draw graph and solve

[oak chasm]

@twilit venture Sorry, this channel is busy.

[twilit venture]

Do u want a video a video

[alpine sable]

yes

can u send it in dms

so i can learn how to do it

[oak chasm]

@twilit venture @alpine sable Please read the rules in #❓how-to-get-help.

[twilit venture]

https://youtu.be/Df-rF_H6ezI

[oak chasm]

Only one question at a time, please.

[alpine sable]

okay thanks

[twilit venture]

Np

[oak chasm]

@warped jay Here's how to do completing the square.

You have x² + 6x = 16.

The x² coefficient is 1, so you don't need to factor that out.

You divide the x coefficient by 2 and write it like this: (x + 6/2)²

Then you find the constant term of that when it's expanded, which is (6/2)².

Then you add that to the other side.

(x + 6/2)² = 16 + (6/2)²

Then you simplify the numbers.

Does that make sense?

[strong karma]

Can i ask a small doubt ?

what is n here

[rigid smelt]

that is hardly readable....

[alpine sable]

can someone help me with this?

[rigid smelt]

channel might be occupied, you should move

[strong karma]

sir wrote sin(0+ 290) . sin (15. 20/2)

then sin (first + last/2)

and common diff n

so whats n ?

[rigid smelt]

is there more context to it?

it looks like they used prod to sum kind of formula

ehh maybe not prod to sum

oh uhh theta is probably the difference of a series? The impression im getting from that terrible handwriting is that sin((first+last)/2).... is a general formula and the first line is the result

[alpine sable]

can anyone help me in this?

[twilit venture]

@oak chasm This server is busy, Pls don't type

[half skiff]

THAT'S EASY

b

[alpine sable]

which is?

[twilit venture]

https://cdn.discordapp.com/emojis/812120204909346876.gif?v=1&size=40

[alpine sable]

how?

[twilit venture]

That's like my boy

[alpine sable]

lol

[half skiff]

shhhsh

[twilit venture]

@oak chasm this server is busy pls don't type

[alpine sable]

how?

[oak chasm]

<@&268886789983436800>

· Refered them to the rules initially here: <#help-0 message>
· They are condescending to helpers here: <#help-1 message>
· Tell them that the channel is busy and referred them again to the rules here: <#help-0 message>
· They mock my asking them to follow the rules twice here: <#help-1 message>

And here they are complaining that I'm typing.

[alpine sable]

lol

[half skiff]

@alpine sable it's actually a cuz it's closest to the orgin(0,0)

[tame falcon]

[strong karma]

hmm ohk

[alpine sable]

B right?

[half skiff]

no A

because it's closet to the orin which is the point (0,0) where nothing exist

so the answer is A

@alpine sable

[alpine sable]

answer is D

my teacher just told

and explained

[half skiff]

tell your teacher he is dumb

[alpine sable]

everyone was saying A

sir explained man

[half skiff]

none is not a point

[small bear]

How does which of the point is smallest make any sense?

smallest compared to what?

[alpine sable]

we can't compare

my sir is saying

so none of these

[small bear]

Exactly

[half skiff]

none of these nuts ; )

i think i understand it now

your teacher is funny

[alpine sable]

how? lol

my sir is giving next question

let's see you can answer

correct

[valid pier]

Pls help

[half skiff]

look

it;s a right angle triganle

just do it

[alpine sable]

what do you all think?

[valid pier]

how

[dense trail]

what are the 2 blacks lines representing

[alpine sable]

fast

[half skiff]

3

[small bear]

Channel is occupied, move to another

[valid pier]

Measure of the whole line

[dense trail]

i think its 1st quadrant

[half skiff]

no it's the 3rd

just look at the boundries

m is negative and so is n

[dense trail]

it cant be third m^2 >0

[half skiff]

doesn't matter

[alpine sable]

hmm

yup

[dense trail]

ok then sub some values in and let me see

[alpine sable]

1 st one is correct

[valid pier]

..

[dense trail]

ok mikey

lemme se

[valid pier]

ok

[dense trail]

ok could you try and find angle BAC

[half skiff]

@gilded oxide ad to ed are right angle to each other so you can find ea then ba-ea = EB

[valid pier]

how Should I find ae

[half skiff]

right angle

[dense trail]

wait is BECD a kite??

[half skiff]

ae^2 = ad^2 + ed^2

@dense trail it doesn't matter

[valid pier]

Do USE PYTHAGORAS THEOREM I NEED AT LEAST MEASURE OF TWO

sorry for caps

[half skiff]

yes you do

right angle = pythagoras

always

[valid pier]

ok got it

[dense trail]

but....if it is a kite, then the question is wrong

modulus

IxI

[half skiff]

just square everything

[dense trail]

modulus is just sqrtx^2 so

[half skiff]

wat is your questin?

[dense trail]

sqrt (x^2)

no it doesnt

[half skiff]

of couse they do

[dense trail]

bro i said sqrt

lol

[half skiff]

?

[dense trail]

no worries

[half skiff]

@alpine sable what you mean

the values do change

so if you squre i you get -1

sqrt i = -1

[dense trail]

bruh why you on imaginery

[oak chasm]

@half skiff With complex numbers, you have x + yi (x and y real numbers) and the modulus is sqrt(x² + y²).

[alpine sable]

What are imaginary numbers?

[oak chasm]

With real numbers, y is zero, so you have sqrt(x² + 0²) = sqrt(x²).

[half skiff]

i don't get what eben is meaning

[dense trail]

number that becomes -1 when you square them @alpine sable

[half skiff]

you siad the vlaue need to change

[oak chasm]

@alpine sable Use the piecewise definition.

[half skiff]

...

[dense trail]

can't you just use a if statment @alpine sable

oh ok

[ocean seal]

Chai T. Rex

[half skiff]

i don't know

i think im dumb tbh

i love induction tho

[oak chasm]

@alpine sable OK, what have you been taught?

[half skiff]

what's computer science?

[oak chasm]

I mean what are you allowed to use.

[half skiff]

wat do you learn?

@alpine sable im still in high school

this is my last yeasr

[oak chasm]

Then you don't need absolute value since they don't ask for distance or absolute difference.

[half skiff]

intergrate it

[oak chasm]

Right, and you should give a negative answer then.

[half skiff]

time cannot be negative

[oak chasm]

Well, you can't get an absolute value if you can't use ifs, sqrts, abs function, etc.

That's what I mean by can't: not allowed.

E-mail your professor. If they say you can, use it. If not, give a negative answer where it fits.

[half skiff]

i learn some calculus

pussy

[dense trail]

Cursed

How eben you just create all the different versions, ones with and without the things you are allowed to use

[alpine sable]

Does anyone know how to go about showing this

[oak chasm]

What is S?

Hmm, I guess it doesn't matter.

@alpine sable Take all the (x, Tom) elements in S.

If x ∈ B, then x ∈ A because B ⊆ A.

So, if the (x, Tom) element has x ∈ B, then the (x, Tom) element has x ∈ A.

So, the (x, Tom) elements where x ∈ B are a subset of the (x, Tom) elements where x ∈ A.

[alpine sable]

Thanks, that makes sense

lads what is this (im studying overseas and i cant speak the local language), i want to know what is the name of this problem and how to solve it if possible please.

[dense trail]

They don't appear to be problems though

They are just examples

For indices laws

[glass lichen]

exponent laws

[cunning sierra]

I came up with my own question,

Particle 1 orbits around a fixed point with a radius of r and with an angular velocity of x.

Particle 2 travels from that fixed point to the orbital radius of particle 1 in a straight line with a velocity of y.

Derive a trigonometric function that expresses the distance between both particles at any given time, t, for 0 < t < y/r.

[sudden garden]

is unionset is same as the universal set(i mean the wya we represent them)

[glass lichen]

no, unions of set need not be U

[sudden garden]

ok,thank you!

[glass lichen]

U={1,2,3}
{1}U{2} != U

[hard walrus]

Can anybody help mw with this math problem?

How many extremum does it have????

[small bear]

If you are looking for local extrema, they are points that are larger (or smaller) in value then the small interval around them, or perhaps visually it is better to understand them as a bump in the graph, or where the function changes from increasing to decreasing or vice versa

[hard walrus]

So can u help me with the math problem?

[small bear]

Sure, look at the table where y is, how many points do you see that change the direction of the graph

[hard walrus]

Hmmmm, thats the graph of f(x)

The question ask fir extremun of f(|x|f(|x|)

[small bear]

Oh sorry, I thought you were asking for f(x)

[hard walrus]

Np? Do u know anyone is an expert of this math type?

[small bear]

Just wait for a bit, if your question isn't answered in 10-15 minutes, you can ping helpers

[hard walrus]

Oh, so how can i ping helpers?

[small bear]

#❓how-to-get-help rule 4

[tardy robin]

It has 2 extremums

Unless you count infinities as extremums

[small bear]

Yes, that is for f(x), the question requires I guess graphing knowledge because it requires the number of extrema for
f(|x| f(|x|))

[hard walrus]

Yes, thank you peaceGiant

[hard walrus]

<@&286206848099549185>

[alpine sable]

how does this make sense wtf

11 : 0,5 is equal to 11 * 2 xD

[obsidian crane]

11 ÷ 1/2

11 x 2

[prisma zealot]

this is the first question I have been able to do since I joined the server

[alpine sable]

I'm not very good at math :(

[obsidian crane]

Let's just say

You multiply 2 both in the numerator and the denominator

[alpine sable]

i got it

[obsidian crane]

The 1/2 cancels in the denominator. There are multiple ways of explaining / understanding it.

[fair karma]

hii

can someone help me

[onyx chasm]

Most ppl would try to help, yes

[fair karma]

if sinα is 5/13 and cosα is 0,28

assign other trigonometric values

[lilac dragon]

quick question. does composition distribute over multiplication?

in particular, if v is L1, w is bounded, f is integrable, is it true that
(vw)°f = v°f w°f

[raw violet]

Can someone explain how is 1 degree equal to 60 minute

[fair karma]

A degree is divided into 60 minutes of arc, while a minute is divided into 60 seconds of arc. DMS notation refers to the use of degrees-minutes-seconds. To complete a full 24 hour cycle, the clock must complete a full 360 rotation twice.

[lilac dragon]

I think if sin(a) = 5/13 then cos(a) = 12/13 and tan(a) = 5/12

[zenith bone]

Am i blind? Are answer 1 and 4 the same?

[raw violet]

Okay ... Thanks

[oak chasm]

Yes, they're the same. Either the site has a mistake or Google transcribed the problem on the site incorrectly.

[zenith bone]

yea i thought so lol i was so confused for a second

[alpine sable]

Channel seems open, can I ask a question?

Why is y(0)=1+c and why is c=1

This is step one of a particular solution for a differential equation

I assume they integrated both sides but I’m not sure where the 1 comes from or why C equals 1.

C is a constant so why wouldn’t it be y(0)=C?

[crisp grove]

y(0) = C+1

but you are already given a value of y(0)

$y(0) = 2$

[ocean seal]

Ryuzaki

[alpine sable]

Right so when integrating both sides is the answer not y=C?

[crisp grove]

you are not integrating y(0)=C. you are just given a specific value of y at a specific point

ex suppose f(x) = x^2 then f(1) = 1. ie for x=1, we have f(1) = 1

doesnot mean f(x) = 1

it's only one point

[alpine sable]

Okay makes sense

[crisp grove]

similarly, y(0) = 2 does not mean y is constant, it's just the value of y at a specific point

[alpine sable]

So how do they find a Y value and where does 1+C come from

[crisp grove]

after solving the ode you put x=0

and y = y(0) = 2(in this case)

that's where you get the value of C

[alpine sable]

Let me try this

The solution to the integration is

I was able to solve this piece correctly. I plugged in x=0 and y=2 and got c=2 not c=1?

[crisp grove]

how are you getting c=2?

$e^0=1 \neq 0$ btw

[ocean seal]

Ryuzaki

[alpine sable]

That is how

Lol

It is always little things like this that get me, my fundamentals are good. I just can’t remember the small details like e^0=1

[graceful lance]

Q 8

I do it by distance formula or mid point ?

[fair karma]

thank u

[alpine sable]

distance formula, mid point formula only works for co-linear points

[graceful lance]

Ohh

What should I do then ?

@alpine sable

[alpine sable]

use distance formula
$$\sqrt{(x-2)^2 + (y-5)^2}=\sqrt{(x+3)^2+(y-7)^2}$$

[ocean seal]

Spica

[graceful lance]

Ohh

Thanks

[jovial edge]

Hello

[jovial edge]

Have you learnt trignometry?

[sour umbra]

no thats why im asking

[jovial edge]

You can use sin to solve it

sin theta = opposite side / hypotenuse side

This is the triangle for your question

Since one of the sides is = 90°, it is a right-angled triangle

which means you can use $sin14=\frac{1.5}{a}$ to solve it

[ocean seal]

DG

[steel hinge]

I'm sorry if this question might sound dumb, but

Is it possible to get a dot product out of matrices and numbers

[alpine sable]

Help

Anyone

The first q

<@&286206848099549185> sorry for the ping

[fresh hatch]

Can someone tell me why definite and indefinite integral both called integral? I mean they do absolutely different things. One is just a antiderivative to a function and other are infinite sum of infinite small chunks of function from one point to another. I cannot see any relation between these two.

[stark trail]

I got 2 different answers for this integration

Am I correct?

[alpine sable]

@fresh hatch go watch 3 brown 1 blue on YouTube for derivatives. Find the video where he discusses finding the formula for volume

It is adding infinitely small strips of pi and the visual shows you why

[fresh hatch]

I understood how it works when you try to find indefinite integral by newton-leibniz formula, but it's more like I cannot find origin to any relation to antiderivative at all.

I always used it but never understood

how can I replace infinite sum of infinite small chunks with subtraction of antiderivaties

[dire whale]

the point is when you add up little bits of functions you get exactly the antiderivative. At a infinitesimal level, the opposite of taking the difference between two "neighbouring" points is to add to the first point the gap between the two points

[coral frigate]

this channel free?

[dire whale]

yeah go ahead

[coral frigate]

can someone please solve this from 0 to 180

[fresh hatch]

yeah, I will process his(her) sentence for a while..

[coral frigate]

I did it in a test and all of my friends got different answers

[dire whale]

$\sqrt{3}=tan(3x+45)$\
$60=3x+45$\
$x=5$

[ocean seal]

Pepa

[astral dagger]

• kpi

[fresh hatch]

the point is when you add up little bits of functions you get exactly the antiderivative
Now I struggle to understand this one. This feels right but I don't know why.

[dire whale]

because taking the derivative was "finding the gaps between neighbouring points", so the opposite is to "add up the gaps between neighbouring points"

[coral frigate]

it said there were multiple solutions

its an angle

and in degrees

x is theta

[fresh hatch]

Here you go
https://www.wolframalpha.com/input/?i=2sin(3x%2Bpi%2F4)%3D2*sqrt(3)*cos(3x%2Bpi%2F4)

[coral frigate]

that doesnt show me the multiple solutions from 0 to 180

(sorry for being an ass this has just been bothering me all day)

[dire whale]

yeah x is 5 degrees. if you shift everything by 360 you get back the same thing, so x can be 5 or 125

[coral frigate]

are those the only 2 solutions?

[dire whale]

between 0 and 180, yes

[coral frigate]

fuck I got 3

[dire whale]

adding 120 gives you more solutions

because 3 times of that would be 360

[coral frigate]

thanks ♥

[dire whale]

oh wait

sorry

adding 60 is fine too i think

so 65 works

[fresh hatch]

why just don't use wolfram alpha?

[gritty tulip]

Can someone help@me super quick

[leaden sundial]

Miss girl i think it is f

[coral frigate]

so there are 3 solutions?

5, 65, 125?

[dire whale]

yep i think so

[coral frigate]

omg I was the only one right LETS GOOOOO