help-0

[jade token]

Another channel, this one is occupied

[alpine sable]

oh

my bad

ill delte

[ocean seal]

şaka şaka

[manic loom]

@alpine sable The internal angles of a Triangle always add up to 180°.

[alpine sable]

what we have done so far is simplified $9$ copies of 6 + 5 copies of 6

[ocean seal]

şaka şaka

[alpine sable]

down to $14$ copies of 6, which we can write as $6^{14}$

[ocean seal]

şaka şaka

[alpine sable]

so the question wants to know how many copies of 36 is equal to 14 copies of 6

Guys i have to find the m here

to the 9 2m

i dont even understand this please help me

[buoyant kayak]

start by getting everything in base 3

[alpine sable]

i dont know whats base this is for the smart peple in class but im not so pls help me i want a good grade for the first time in math

[buoyant kayak]

you have an exponential

which has a base

9 and 27 are your bases

get that in terms of 3^x

[alpine sable]

i dont know much english

how do i turn them into 3

ouuu

like 801

3 and 9 is 801

i dont know

can u just tell me the answer pls

i wanne get a good grade

ok how do i do it

i know this

3?

nonon

ok

https://cdn.discordapp.com/attachments/490557019623915520/899703420531929088/20211018_185951.jpg

i dont know much english and its kinda hard

so its 6

what do you mean by the power it is of 3

.

. i dont understand this

jes

like 3 and 3 its 9

and 3 and 9 its 27

to get all of them in one answer

whats separate

ok

3 3 3 its 9

3 and exponent 2 its 9

like this

or no

3 and exponent is 3

ok

@burnt trench Nice PFP.

pls snipe

x = -4

<@&286206848099549185> ^

the answer is 2x² *

[fringe shoal]

I'm actually at a loss on this one, any help is appreciated I have no idea where to start

[alpine sable]

I got the answer but idk how to type it on Discord lol

You need to determine the derivative

[fringe shoal]

Where do I go from there?

I know the derivative property but how will you compute the FT

[wispy olive]

Channel busy?

Can someone explain the derivation of the formula of Arithmetic Series? Like I understand that Sum of an arithmetic series = Number of Terms * (Average of first and last terms).

But how do you get the Arithmetic Series formula from like just that?

[wispy olive]

<@&286206848099549185> .

[jade token]

Here, I'll explain it

[wispy olive]

Cool less gooo.

[jade token]

so essentially, the folktale is that Carl Gauss was told to add all the numbers from 1-100

*integers

[wispy olive]

Yeah I know that.

[jade token]

so what he did was basically add the first number to the last number

[wispy olive]

His teacher - hard work - he smart - he cool.

Yeah 50 * 101.

[jade token]

and multiply it by the number of numbers and divide it by 2

yeah basically

[short night]

what about my question?

[jade token]

so let's say that we have n elements in an arithmetic series with first element a1 and common difference d

[wispy olive]

Okay yes.

Interesting less gooo.

[jade token]

so the last element would be a1+(n-1)d right?

[wispy olive]

Firstly how do we get last term = (n-1)?

[wispy olive]

Uh what how?

[jade token]

ok

so what's the second term?

[wispy olive]

a-sub-(2).

[jade token]

like

[wispy olive]

a2.

[jade token]

the second term of the arithmetic series

yeah

but like in terms of a1 and d

[wispy olive]

Hmmm.

a1 + d.

[jade token]

exactly!

and 3rd term?

[wispy olive]

a1 + 2d.

[jade token]

yes, so what's the nth or last term?

[wispy olive]

Let me see.

[jade token]

remember that 2 = 3-1

and 1 = 2 - 1

[wispy olive]

Tell me what is it.

Or wait.

Let me try.

[jade token]

||a1+(n-1)d ||

[wispy olive]

a + (n-1)d is formula for Arithmetic Sequences.

[wispy olive]

Ah yessssss.

[jade token]

yes! exactly

[wispy olive]

Now what do we do?!

[jade token]

so when we add the last term and the first term what do we get?

[wispy olive]

Mhm.

Assuming there is a last term.

[jade token]

2a+(n-1)d right? and there are also n elements, so use what Gauss had

[wispy olive]

2a? How?

[jade token]

because the first term is a?

I've got to go, but basically just plug in what Gauss used for 1+...+100

[wispy olive]

Let us see what Gauss did.

1 + 100 = 101.
2 + 99 = 101.
....
....
= 101 * 50.

101 is sum of first and last term.

50 is number of terms.

[jade token]

or you could also write it as 101x100/2

[wispy olive]

Hmmm yeah.

[jade token]

so there are n terms, and the sum of first and last are 2a+(n-1)d

[wispy olive]

Still where did 2a come from?

[jade token]

a+a+(n-1)d

a is the first term

[wispy olive]

Yeah.

[jade token]

a+(n-1)d is the last term

[wispy olive]

So why double it?

[jade token]

so when you add a+a

you get 2a

[wispy olive]

OHHHHH!!!!

[jade token]

I've got to go for now

[wispy olive]

OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[jade token]

I hope that's far enough to get you to understand enough to solve it yourself

[wispy olive]

Damnnnnnnnnnnnnnnnnn!!!!!!!!!!!!!!!!!!

[jade token]

👍

[wispy olive]

Thanks!!!!

[hard garden]

In arithmetic progression this is true: а2=(a1+a3)/2
In geometric progression a2=?

[jade token]

a2=sqrt(a1*a3)

[hard garden]

Thanks

[alpine sable]

How can I find an equilibrium of this network?

c(.) denotes the cost

and x,y,z are fractional such that x+y+z = 10

[wispy olive]

@jade token look what I found -
https://www.chilimath.com/lessons/advanced-algebra/derivation-of-the-arithmetic-series-formula/.

[robust flax]

any advice

for the first one im thinking for the sum to be 0 x has to be 0

[hoary quiver]

Someone expain what to do lmk if u need a better picture

[wispy olive]

See.

Do you need to make the graph?

[fresh parcel]

first sketch y=4/3 x + 4

[hoary quiver]

Ok

[fresh parcel]

then shade all the area above it

[wispy olive]

Then just draw the line replacing the inequality with an equality.

[hoary quiver]

Now how do I do that

Do I have to answer that

[wispy olive]

And then for the inequality, see the x's and and y's and how they work together and act accordingly.

[fresh parcel]

set x to 0 and solve for y

then set y to 0 and solve for x

those are your x and y intercepts

[wispy olive]

||Did you just cheat up in Math when school was online and now you are struggling?||

[fresh parcel]

lmao

[hoary quiver]

Maybe

[fresh parcel]

then just draw a line between them

[wispy olive]

Then.

[hoary quiver]

But not all the time

Cause I was in advanced in 7th

[wispy olive]

Use mathisfun.com to understand.

[hoary quiver]

Now I’m in 9th

[wispy olive]

Or KhanAcademy.

[hoary quiver]

Ok

[wispy olive]

And Desmos to graph.

[fresh parcel]

i commit war crimes but not all the time

im joking

[wispy olive]

[fresh parcel]

yeah so basically thats what you do

lol

[wispy olive]

I should be studying sequences and series But fuck I am here.

[fresh parcel]

lol

[wispy olive]

I want to sleep but not sleep at the same time.

[fresh parcel]

this solution was sponsored by raid shadow legends

[wispy olive]

Path towards Schrodingeratarin.

[fresh parcel]

lmao

[hoary quiver]

What did u mean by sketch

[wispy olive]

[fresh parcel]

draw

it

[wispy olive]

Draw the line and mark/highlight the desired answers.

[fresh parcel]

draw a line

[hoary quiver]

But the answers already have it drawn

[wispy olive]

Wow.

[fresh parcel]

yeah so you look at which one has the right graph

simple

[hoary quiver]

I understand now

[fresh parcel]

good job

[hoary quiver]

I’m so dumb ts is easy 😂

[wispy olive]

👍

[wispy olive]

No, yes.

[floral meadow]

how can you tell that this set of vectors are linearly dependent

is it cause that theres more columns than there are rows, and there needs to be a pivot in each column if it were to be linearly independent?

[vague pecan]

i believe if one or more of the vectors are colinear the set is linearly dependent

[jade token]

Basically if you're able to reduce it to row echelon form, then it's independent

[floral meadow]

is that true for all occasions?

[fluid nest]

hi everyone

[floral meadow]

is this linearly independent?

[fluid nest]

i need help on solving this equation

[alpine sable]

Hey, can anyone tell how to graph y = log (x) to the base a; such that 0<a<1?...need it urgently

[jade token]

Yes

[fluid nest]

Pls

[alpine sable]

differentiate
equate slope = -2
find y coordinate

[fluid nest]

[alpine sable]

when did this cat became happy

[wispy olive]

[alpine sable]

u wrote u hate ICSE the most but I think it's way better than CBSE...altho CBSE gives an edge to entrance prep

[fluid nest]

how do i equate slope

[fresh parcel]

set f'(x) = -2

then solve for x

[fluid nest]

👍

[fresh parcel]

f'(x) means the differentiated version

[fluid nest]

x = -8

so i got my x

now what

[alpine sable]

read the question
Again

[fluid nest]

okay thanks

[alpine sable]

this is wrong

[wispy olive]

Let us talk about it tomorrow in DMs or #discussion .

[fluid nest]

i substitute x with -2

[alpine sable]

bruh

[fluid nest]

im sorry

wha-

[onyx flower]

hmm

someone explain this

[buoyant kayak]

chain rule and product rule

[alpine sable]

should be -2/3

[onyx flower]

you rite

haha

we do a little subtraction mistakes

[alpine sable]

ok non-singular person

[onyx flower]

thsi doesnt make sense to me why is this wrong

how does this simplification even work

[fluid nest]

lmao

i give up with maths

ill sleep

[alpine sable]

chain rule
diff. Of f(g(x)) = f'(g(x).g'(x)

[jade token]

this is because a^2-b^2 = (a-b)(a+b)

where a is sin^2(theta)

and b is cos^2(theta)

[buoyant kayak]

$\sin^4(\theta)=(\sin(\theta))^4$

[ocean seal]

a disappointing son

[jade token]

this is equal to (sin^2(theta)+cos^2(theta))(sin^2(theta)-cos^2(theta))

with the first term equal to 1

🙂

[steep lion]

How do I show that f is differentiable in 0? And how do I go about finding f'(0)? I had no trouble finding a = -1/2, but I had troubles going onwards from that.

[alpine sable]

by showing that LHD and RHD exist at x=0

[fluid nest]

is this problem a related rates?

[steep lion]

no, just a standard continuity problem

[steep lion]

How would I formulate ln(cos x)/x^2 in the lhd/rhd formula? I've never done this before

[alpine sable]

the first principle method

[olive sentinel]

Okay, this is not a hard mathematics question, it is my younger sister's homework. But there is a bit of english to it that I do not understand.

"Every row and every column add up to the same total." I don't grab. I am sorry. Partly ashamed. Help!!!!!!!!!

[glass lichen]

Make a magic square

[olive sentinel]

Much clearer

[olive sentinel]

????????

[wary stream]

Do you know what a magic square is?

[olive sentinel]

Never heard of it

[wary stream]

Look it up

That's the concept you're using

[olive sentinel]

BRB

@glass lichen , @wary stream
Thanks for the reference.
Glad I asked.

[alpine sable]

Hello

I was hoping someone could help explain what's going on to get from left to right?

[glass lichen]

Row reducing

[alpine sable]

r.r. is row reduction I believe, but I've looked it up and I'm not really sure where to go

Row reducing turns a matrix into row-echelon form?

[pallid trout]

Row reduction is using another row to add or substract to another row

It's generally used to try to isolate parameters in an augmented matrix situation, especially when it is used as an equation solver

[pine igloo]

would anyone be able to help with depth first search question?

[alpine sable]

I'm not really sure what is done to get from point a to point b here

[pallid trout]

In general you can swap around rows and add and substract one from another, that's how they did it

I'd start by swapping R1 and R3 since the third column is already isolated

[wary stream]

https://www.youtube.com/watch?v=L0CmbneYETs&ab_channel=KhanAcademy

[alpine sable]

I've watched the video, I'm just confused on how it's done

It feels like he's just guessing which rows to alter

He's not, but I can't see a pattern

[wary stream]

It's just manipulating one of the rows to cancel out a certain term in a different row

Do you know how to get into a upper triangular matrix?

[alpine sable]

Never heard of it before

all 0s

in a triangle on the bottom left?

[wary stream]

Gaussian elimination?

[wary stream]

Yes, this

[alpine sable]

I've done that

[wary stream]

Gaussian elimination to get a triangle of 0s in the bottom left?

[alpine sable]

How do I know when it's not possible

[wary stream]

It's normally always possible to reduce

[alpine sable]

It doesn't seem to have been here?

[wary stream]

It's because the c2 terms cancel out

By observation

[alpine sable]

So, if a triangle is possible it's linearly independent right?

otherwise dependent

[wary stream]

That didn't get it into RREF fully because of the fact that one step before being in full RREF the coefficients of c2 are positive and negative, canceling c2 in the first equation

[wary stream]

RREF will help determine if it is linearly independent or dependent

[alpine sable]

But how

I get that you need to turn it into row echelon form
Not being possible = linearly dependent
possible = ?

[wary stream]

It is possible, as I stated that example in the video did not fully reduce it

In the picture you posted

[wary stream]

https://textbooks.math.gatech.edu/ila/row-reduction.html
If you can view this, read this page that a college created

[white blaze]

a matrix is always 2d right?

like n rows by n columns

[wary stream]

Not exactly, you can have a 3D matrix

[white blaze]

that would become x, y, and z dimensions?

[wary stream]

Yes

[white blaze]

ah ok thank you :)

[rain pagoda]

Hey, im not the smartest guy, im only in grade 10 but i need help

[jade token]

3d matrices would be tensors

[white blaze]

oh interesting

[white blaze]

ok thats what i was thinking

[jade token]

Oh are you talking about matrices with 3 dimensions or matrices containing 3d vectors

[still marlin]

why is there no x intercpet in a slope intercept equation

or why is ti meanignless to talk about the x intercept

[white blaze]

i think dldh was talking 3 dimensions

in my original i didnt specify though

[wary stream]

Think about it like volume, 3D would be length, width, and height

[white blaze]

ahhh that makes sense

thanks so much

[wary stream]

So matrix is row, col, then a height dimension

[white blaze]

ah ok!

at what point would it become a tensor then?

[fluid nest]

guys how do i find the slope of y = 8 / x + 1?

[white blaze]

y = mx + b

look near x

[wary stream]

y = mx + b where m is slope

[jade token]

Yah, but what I was saying is array is 1d, matrix 2d, tensor 3d

[fluid nest]

1?

[white blaze]

ah yes ok thats what i think

thank you!

[jade token]

Np

[wary stream]

No

[wary stream]

y = mx + b where m is slope

[white blaze]

y = mx + b

where does the 1 fit in ? seems to be b to me

m is your slope

[wary stream]

I didn't know the formal term

[jade token]

Also I feel like diffeq is quite late

[white blaze]

yea i think tensor is when u have matrices with a matrix within

[jade token]

Not early uni

Well maybe that's supposed to mean like undergrad

Or elementary

Certainly there's a difference between elementary and advanced mathematics

[still marlin]

im having trouble with this question
"why would it be meaningless to discuss the x-intercept?"

in a y=mx+b equation problem

[jade token]

Uhh

Context?

Oh

[still marlin]

like for example

the qwuestion is

long island city, ny had 2 inches of snow on the ground before a snowsotmr

[fluid nest]

8 then?

[still marlin]

during the storm, snow felt at an average rate of 5/8in an hour

[jade token]

Snowsotmr

[still marlin]

in this problem why would it be meaningless to discuss the x intercept

[jade token]

Ah

[fluid nest]

lol

[jade token]

Because the x intercept would be negative, and the function is only defined for positive numbers, so even though this equation states, there is not like 0 cm of snow around 3 hours prior and negative snow before that

So in this context the domain is non negative numbers

[still marlin]

oh ok

i understand

but what should i like write

for the problem

cuz im only in 8g so ion wanna write some complicated shit

[jade token]

Hmm, just write that it doesn't make sense that around 3 hours prior there's no snow, or that before that time there was negative snow

[rapid grove]

Is this cannel free

?

[jade token]

Or say that the equation is not defined for negative numbers

I guess so

[fluid nest]

why cant i find the slope tho?

[still marlin]

ur writing it wrong

y=mx+b

[sour swan]

theres no slope in that

[still marlin]

u only substitute m and b

[sour swan]

well

you can

[still marlin]

m is ur slope and b is y intercept

[sour swan]

get the instanteanoue slope

[fluid nest]

okay

[sour swan]

d( 8/(x+1))
/
dx

is

[white blaze]

i dont think theyre up to that

[sour swan]

o

[white blaze]

unless they are

but it seems like they wrote it wrong

[sour swan]

-8/(x+1)^2

[white blaze]

are you looking for the avg rate of change @fluid nest ?

of tangential?

[fluid nest]

let me just post the whole question

[sour swan]

yea

they are instantenanosu

sloping

oh wait nvm

waitit you are

lmfao

ok so take the derivative

[white blaze]

oh yea sorry forehead

[sour swan]

which is -8 / (x+1)^2

[fluid nest]

mhmm okay

[sour swan]

and when the derivative is -2

that means the slope at that point

is -2

so -8 / (x+1)^2 = -2

4 = (x+1)^2

x+1 = +2 or -2

so x is either 1, or -3

but the problem limits x from 0 to 6

so it has to be 1

so when x is 1, the slope at that point is -2

[fluid nest]

wow that helped a ton

thanks

[sour swan]

do you know how to get derivatives

[fluid nest]

yes

[sour swan]

kk

[winter pike]

can someone help me with that?

[maiden wren]

how do i graph Quadratic Functions

[alpine sable]

wait there are still questions being asked

[maiden wren]

oh am I in wrong chat?

[alpine sable]

1 question at a time

otherwise everyone spams questions and none get answered

[maiden wren]

ahhh ight mb

[alpine sable]

np

[runic pulsar]

halp

[alpine sable]

Raj takes a test with 20 questions. He gets 5 marks for a correct answer. He loses 2 marks for an incorrect answer. He answers all the questions and gets 51. How many did he get right? Can anyone help me out here?

5x + 2y = 51 where x is the number of correct answers and y is the number of incorrect answers

x + y = 20, where the number of correct answers and number of incorrect answers is the total numbers of answers, which is 20

we want to find how many he got right, so we want to find x

how do I find x from that?

we have two equations. since we only want x, we want to substitute y with something so that we only have x's in an equation

we know that x + y = 20. if we subtract x on both sides, we get y = 20 - x

how would we use the equations y = 20 - x and 5x + 2y = 51 to find an equation with only x's in it?

yes 👍

i know this is simultaneous equations god i forgot

no worries! happens all the time

ill google it then get back to you

i remember do you add the equations when the signs are different?

oh nvm you substitute y into x

[gray isle]

elimination and substitution are methods for solving simultaneous equations

[gritty cave]

how do i figure this out

[gray isle]

depending on what you have, one may be more convenient than the other

[gritty cave]

oh sorry i thought the previous question was answered

[gray isle]

consider the range of the sine function

[alpine sable]

ok thank you

[gritty cave]

3?

[gray isle]

what's 3 supposed to be?

[gritty cave]

amplitude

oh wait nvm

2+3

5?

[gray isle]

yes

[quartz osprey]

i cant fucking udnersatnd usub

wtached like 4 videos and still dont get it

only thing i know is how to find a u and take derivitve of it

then after that im lost

[native knot]

how do I show a epsilion delta function of continuity for 2 functions when they arent defined

Prove, using the 𝜖−𝛿 definition of continuity that if both f(x) and g(x) are continuous at x = 6 then 2f(x)+ 5g(x) is continuous at 𝑥= 6

<@&286206848099549185>

[pliant beacon]

help please

[alpine sable]

the y-intercept is (0, -1). set all of the x's to zero and see which f(x) becomes -1

[steady fox]

yo anyone here familiar with econ

is is the area below the supply curve up to the equilibrium amount the total cost or the total variable cost again?

[native knot]

@alpine sablecould you help with my question?

[alpine sable]

just trying to refresh my knowledge of real analysis real quick

[pliant beacon]

how can i find the equation ?

[native knot]

lol okay

[alpine sable]

for each equation, set x equal to zero. whichever f(x) becomes -1 is the equation

[pliant beacon]

ohh ok

ill try that

[pliant beacon]

thanks for the help

[alpine sable]

this is my proof

oh i should've included that adding functions doesn't affect continuity because if there are no discontinuities in f(x) or g(x), then for h(x) = f(x) + g(x) will also yield no discontinuities

[regal fable]

3 1/2 ?
—- = ——
6 1/4 9
Any help answering this sorry im kinda dumb

[alpine sable]

say our ? is x. this means
$\frac{3 \frac{1}{2}}{6 \frac{1}{4}} = \frac{x}{9}$

[ocean seal]

bertaunth

[alpine sable]

convert $3\frac{1}{2}$ and $6\frac{1}{4}$ to regular fractions

[ocean seal]

bertaunth

[alpine sable]

for 3 1/2, you do (2*3)+1 for the numerator, and for 6 1/4, you do (4*6) + 1 for the numerator

[regal fable]

Ty

[lucid wadi]

Hi

,rotate

[lucid wadi]

So for this, the teacher used ln instead of log on the right side

Ignore the left side

I used log though and got the same answer

Can I just keep using log?

[alpine sable]

no because log and natural log are different kinds of logarithms

[lucid wadi]

Oh

So when do I use ln

And when do I use log

Do I use ln only when we have e

[alpine sable]

you use ln when we're dealing with e

yeah

[lucid wadi]

And then log

For all the numbers?

[alpine sable]

any other time

yeah

[lucid wadi]

Exponential stuff

Ok thanks

[alpine sable]

ln is almost exclusive to problems with e

[lucid wadi]

Like you mean

Only used when e is present

?

[alpine sable]

yeah

[lucid wadi]

Ok thanks

Have a good day

/night

[alpine sable]

thx u too

[worthy adder]

can some hlep me in question 9

[broken ermine]

does anyone know how to get python to return multiple solutions to an equation?

[quartz osprey]

no lcue

but does anyone know how to usub and can walk me through it

ive watched liek 4 videos and none of them make snese to me

[alpine sable]

depends on the equation but I would use recursion or iterative loops to see if multiple numbers are the solution

[broken ermine]

apparently there's a package called sympy that works

[modern dagger]

Is this channel free?

[alpine sable]

oh yeah sympy also works

[quartz osprey]

i need help

super confused on how to u sub

so i have

u=x^9-2

du 9x^8

i mean ig i can do du/9=x^8

if i substitute stuff in sill be intergral of du/9(u)dx

which is 1/9(x^9-2)

right?

[versed dirge]

du/dx = 9x^8

(1/9)(du/dx)=x^8

If u sub that in u get integral of (1/9u) du

[quartz osprey]

so 1/9 lnu

[versed dirge]

Yup

[quartz osprey]

wait whats deritivei of 1/x intergral 1/x is ln right

intergral of ln is 1/x or is it derivitive of ln is `1/x

[odd obsidian]

derivative of ln(x) is 1/x

so integral of 1/x is ln(x)

[quartz osprey]

ah i see

[alpine sable]

can someone help me pls with (2y³) (2y³)⁴

I dont understand exponents that much

[quartz osprey]

exponet rules

idk either lol

[alpine sable]

in the answer key it says that 2⁷ y¹⁵

dk how it got that

[odd obsidian]

should be

$2^{5}y^{15}$

[ocean seal]

QLightningWolf44

[odd obsidian]

I think your answer key for that is incorrect

[alpine sable]

wait how did u get that

[odd obsidian]

so

we have

[fluid moth]

hi

[alpine sable]

oh its a bot

[odd obsidian]

$(2^{1}y^{3})(2^{1(4)}y^{(3)(4)})$

[ocean seal]

QLightningWolf44

[odd obsidian]

by exponent laws

agreed?

[alpine sable]

ohhh

the numbers multiply

like 2, 2 and 4?

[glass lichen]

Not enough info

What field are you working over?

Then can't help you

Then why did you ask?

It's 1

2+2=1 in Z_3

[raw shard]

2/2 = 1

[glass lichen]

2+2=1

Simple as that

[raw shard]

2+1 = 3, 3+1 = 1

[glass lichen]

Wdym

F_n grows to infinity

Shut it

[fluid moth]

hello

[glass lichen]

Oh that

Probably, since explicit formula exists

Just use the explicit formula

There's an explicit formula for the fibonnaci numbers

Yes

So you can probably solve the inequality for n then floor it

No

[warped ember]

Lol.

[glass lichen]

I don't waste my time with pathetic trolls who waste their time

Hard to look when you're blocked

[versed dirge]

Wait does that give the exact answer @glass lichen ?

That's so useful

[raw shard]

some formulas are just really interesting and crazy

[odd obsidian]

and, if you notice, this sequence uses the golden ratio in the terms, just showing how closely they are related

it's really quite something

Yep

(white background)

but essentially, this ratio is found quite extensively in nature

and, it is "the most irrational number"

https://www.youtube.com/watch?v=sj8Sg8qnjOg

here's a really interesting video about it

and it gives an example with flowers and just one example of how this ratio is found in nature

ah didn't read this

nice!

but yeah, it's really quite interconnected when you notice it's part of the sequence to find Fn

<@&268886789983436800>

[sly mantle]

b&

[odd obsidian]

thank you

[formal grove]

can anyone help me puit

<@&286206848099549185>

[versed dirge]

Rate of change is the slope

And that's dollars per minute

[formal grove]

top is dollors per min and bottom is dollars

?

[versed dirge]

Yes

[formal grove]

how i find the values for both

isd top .03

bottom 17

[versed dirge]

Yes lol

U should think of initial value as when n=0

[formal grove]

i am dumb at math i am sorry lmao

[raw shard]

it takes practice to get good

so you probably just haven’t done this tons

[formal grove]

nope

last one

[alpine sable]

If f(0) = 4 and f'(0) = -2, find g'(4). F and G are inverse functions

How do I do this?

[raw shard]

@alpine sable if f and g are inverse functions, and if f(0) = 4, what does that say about g(4)?

do you know what it would equal?

[alpine sable]

0, yea?

[raw shard]

yeah i gotta think about this stuff for a second

[alpine sable]

no worries

[glass lichen]

Yep

[alpine sable]

Can someone explain to me this?

[glass lichen]

do you know volume and SA of a cube..?

[alpine sable]

Nope

[glass lichen]

then google or check your notes

[uncut frost]

I’m factoring polynomials with synthetic division. I did this last year but forgot — how do you find the number on the left side? I have it as a question mark in the pic below

[glass lichen]

it's the root of the linear divisor

[uncut frost]

i feel like u had to find the factors of the first coefficient and the last one but idk

[uncut frost]

sorry, can u explain?

i mena what is a linear divisor

Like x+1=0?

[glass lichen]

the divisor, which is a linear polynomial

x+1 would be the linear divisior, the root of which is -1

[uncut frost]

ok

but how do u find out the root, bc you can’t test every Val

ik that the two fundamental roots are +-1

but what else?

[glass lichen]

...

you dont know how to find the solution of x+1=0?

[uncut frost]

it’s x=-1 lmfao

[glass lichen]

yeah

[uncut frost]

how do you know what values to test?

[glass lichen]

Oh, now you're talking about rational root theorem...

[fickle latch]

The fundamental theorem of algebra???

[uncut frost]

ahhh thats the name

thank you so much

i mean that

[glass lichen]

+- ratio of factors of constant term/leading coefficient

[glass lichen]

no

[uncut frost]

so here would it be +-1/2?

as the root value

or (x-1/2) and (x+1/2)

[fickle latch]

Jkjk

[glass lichen]

you'd test $\pm 1, \pm\frac{1}{2}$

[ocean seal]

Mosh

[uncut frost]

why are you testing +-1?

[glass lichen]

cause 1/1 is valid from RRT

same with -1/1

2 has factors 1 and 2

1 has factors 1

[uncut frost]

ok so thats just something we test all the time right?

+-1?

is something we test every time^

[glass lichen]

I mean yeah...

since 1 divides everything and is thus a factor of all a in Z

[uncut frost]

alr

if the polynomial was 5x^3 +2x^2 +3x +1, would the testing vals be +-1 and +-1/5?

right?

damn ok

[dry echo]

I have a very simple question

[uncut frost]

use another channel pls

@ me when u do

[dry echo]

ok

[uncut frost]

so i can c ur question

[glass lichen]

yes.

[uncut frost]

ok thanks mosh

have a great day

[raw shard]

@alpine sable you’re probably offline now but i might have an answer

[uncut frost]

or whatever it is where u live

[alpine sable]

Sup

[raw shard]

pretty sure i already knew this but i found out that if f and g are inverse functions of each other, then g’(f(x)) = 1/f’(x) @alpine sable

so in this case, g’(f(0)) = g’(4) = 1/f’(0) = 1/-2

could have just looked this up

idk why i tried doing this for 20 minutes

[alpine sable]

Yes its -1/2

[raw shard]

well at least my brain is big apparently

[alpine sable]

Thanks

Lmao

[raw shard]

no problem

[iron forge]

why can't I take ln inside the bracket?

ln(e^3+1)

and get 3+0 ?

[raw shard]

huh?

i think there was more to your question than that

wait no

[iron forge]

i was just wondering

[raw shard]

you can’t do that

[iron forge]

yea I was wondering why you cant

[raw shard]

there’s no rule for addition inside logarithms

[iron forge]

great, gotcha ty!

[raw shard]

just like there’s no rule for adding exponents

well, there is, but not like that

lol

[iron forge]

lmao

yea I just wanted to make sure, thanks!

[raw shard]

no problem

[uncut frost]

yo yo yo @glass lichen how would u do x^3 -5x^2 +23x -51 with rrt?

[robust nymph]

Is this correct or just bad?
i^m = a/100?

[uncut frost]

whats a

*what is a representing

[robust nymph]

So this means r = i^m ?

@uncut frost Forget about that

I asked the wrong quest

[robust nymph]

$$F = P(1 + \frac{i^m}{m})^{mt}$$
vs
$$J = \frac{i^m}{m}$$
$$F = P(1 + J)^t$$

Is this different?

[ocean seal]

BrainDead

[robust nymph]

mt at the end

[odd obsidian]

it's the same except, as you said, there should be an m in the exponent

[lyric terrace]

Can someone help with this?

<@&286206848099549185>

[covert plume]

hello, i neeed help on this, thx

[opaque totem]

5

because sqrt9+16 is sqrt25, hence the answer is 5

[opaque totem]

sorry bro idk

[lyric terrace]

Damn

[covert plume]

wait but its 3^3

[opaque totem]

OHH lol

ups

[meager crest]

yo

[covert plume]

its 43 sqrt right

[opaque totem]

yepp

and tthats the final

[meager crest]

bro

what is a1 in this sequence

is it -6 or -30 or something else

help me

[opaque totem]

-30 right

-6 is a4

[glass lichen]

a1 is the 1st term

so -30, since -6 isn't 1st

[lyric terrace]

I also still need help with this

[brave dagger]

only one big question remains: why life? why not nothing?

[opaque totem]

ahahahaha, ask god

[brave dagger]

ur right XD

[misty sphinx]

for this question i’m confused on how to set up the equation

[brave dagger]

42 is the answer to everything

[misty sphinx]

?

[compact meadow]

Who well versed in US History

[buoyant kayak]

this is a math server

[compact meadow]

nah I'm asking cuz there was a dude who was good at chemistry as well

And this a math server

[buoyant kayak]

math and chem go hand in hand

[compact meadow]

Ah shit you right

[gray isle]

consider properties of an isosceles triangle

[manic sapphire]

Can I get help with this question please

[uncut hull]

hey could anyone here help me with a few linear algebra problems? (vectors)

[opaque totem]

is that khanacademy

[manic sapphire]

Yes 💀

[alpine sable]

he in 3rd grade

[manic sapphire]

Bruh chill

I just want help bruh

[versed dirge]

U could find the length of PW and the length of PZ

If PZ is bigger than PW then you know Z is outside the circle

[summer lintel]

Hello, could someone explain how to solve this? I've been trying to for about 35 minutes and cannot find the correct method of solving it.

It should be pretty simple, but I do not understand how to properly find the domain range or intercepts

[buoyant kayak]

what does the domain represent?

[alpine sable]

All possible x values

[summer lintel]

possible values of x

range is possible values of y

[buoyant kayak]

so, what values of x can we plug into these equations?

[alpine sable]

Are you asking for the answer to homework problem

[buoyant kayak]

huh?

[summer lintel]

any? since x can be lower than 0 and larger or equal to 0

[buoyant kayak]

yes, any

channel occupied

[buoyant kayak]

so your domain is all real numbers

[raw shard]

bruh

[buoyant kayak]

occupied

[buoyant kayak]

now your range is all possible y values... what values does 1-x cover?

actually, that question may be easier once we find the intercepts. do you know how to find x and y intercepts?

[summer lintel]

yeah the locations where the functions intercept the y,x axis or touch it

[buoyant kayak]

do you know how to find them though?

[summer lintel]

not exactly

[buoyant kayak]

well, what's true about the y value when you're on the x axis?

[summer lintel]

uhh

hmm

[buoyant kayak]

what is the y value of the red line?

[summer lintel]

0

[buoyant kayak]

exactly

so when the graph intersects the x axis, y is 0

vice versa with y intercepts... when the graph intersects the y axis, x is zero

[summer lintel]

sorry, english isnt my first language so im having a hard time with math in english

[buoyant kayak]

all good

so, knowing that, can you find the y intercept of 1+x?

x intercept as well

[summer lintel]

give me a minute

so y intercept would be 0,1

and x -1,0

[buoyant kayak]

right, so you found your intercepts for one of the functions

can you do the same for the other?

this one is a bit easier lol

[summer lintel]

im actually dumb

sorry for taking so long lol

[buoyant kayak]

it's all good

[summer lintel]

both intercept (0,0)?

or does origin not count as intercept

[buoyant kayak]

that is correct, origin does count as an intercept

so now you just need the range, correct?

[summer lintel]

so the only intercepts here are (0,1) and (-1,0)

[buoyant kayak]

the origin is an intercept as well

(0,0)

[summer lintel]

oh yeah right

[buoyant kayak]

so for the graph y=1+x, what y values does that cover for all x less than 0?

[summer lintel]

(0, to -infinity)

wait no

any

[buoyant kayak]

not any

remember you told me the y intercept was (0,1)?

[summer lintel]

ohh

yeah

[buoyant kayak]

so you were close with your first answer

[summer lintel]

so [1,-infnitity)

[buoyant kayak]

doesn't include 1 though, since it's strictly x less than zero

not less than or equal to

[summer lintel]

oh

ok

[buoyant kayak]

so now the range for the other function

x^2 with x greater than or equal to 0

what does that cover?

[summer lintel]

[0,infinity)

[buoyant kayak]

right

and those are your answers :)

[summer lintel]

thank you

could I also ask what isolated values of the range means?

[buoyant kayak]

i'm not 100% sure on that to be honest..

[summer lintel]

1 second

I dont understand what exactly they want me to "describe" it as

[civic jungle]

An isolated value is probably an element of the range for which there are no nearby elements that are also in the range

[summer lintel]

Its just that I dont understand what exactly they want me to write

[fresh parcel]

write the range of possible outputs?

maybe write the range of the function

[fast oak]

hello

free?

[summer lintel]

[1,-infnitity)U[0,infinity) then?

[alpine sable]

no it would be (-infinity, 0] U [1, infinity)

[summer lintel]

right. Thank you

[alpine sable]

no problem im just a lurker here lmao

[fresh parcel]

lol

[thick aurora]

how tf is the answer 1

im so confused

someone please help 🙏

save me

[radiant barn]

Which binomial is a factor of f(x) = x^3 – 6x^2 + 3x + 10?
x + 2
x + 3
x - 5
x + 10

[warped phoenix]

i dont get it

what does it mean by "the function is increasing to the left of x = 2 and decreasing to the right of x = 2"?

to the left of x = 2, x becomes more negative and y becomes more negative as it continues

nothing is increasing

[tame stirrup]

@warped phoenix this means that derivative of function is negative in left of 2 so function increases but in the right derivative of function is positive hence function decreases...
X=2 is a critical point

[devout summit]

I think you said the opposite. Derivative is >0 for x<2 and <0 for x>2

[fluid nest]

help

[thick aurora]

<@&286206848099549185> please answer this question 🙏

[raw shard]

@fluid nest what do you need help with

like what exactly confuses you

[fluid nest]

i dont know where to start with this equation

do i derive first?

[raw shard]

implicit differentiation

yes

[fluid nest]

then after that?

[raw shard]

yeah

after that plug in the points

[fluid nest]

4 is x right

[fast oak]

help plz

[alpine sable]

how would i invert an equation like, a mod b=c, a is given c is given i gotta find all possible b

[warped phoenix]

channel in use

[alpine sable]

oh ok mb

[warped phoenix]

what's a derivative?

i dont think thats what we're supposed to use

cuz our teacher didnt say anything ab derivatives

[coral pagoda]

For any two real numbers, x,y that are less than 2, the function is increasing means that f(x)<=f(y) exactly when x<=y.
Now, let's look at the right side, where the function is decreasing. For any 2 real numbers, x,y that are greater than 2 have the property that f(x)>=f(y) exactly when x<=y

Hope this helps

If this is confusing, try to represent my words with a picture.

[unique sand]

can someone help me find the answer to this I think its B but I think I am wrong

[coral pagoda]

We can make some nice deductions. Really, the points that we have to go off of are (-4,-2) and (3,1)

For everything else, the best we can do is estimate. But this is all we need.

[near falcon]

how do I find the area of the sector?

[coral pagoda]

Ah yes, Questions 0. It's about to get crowded

[unique sand]

would that be C

[coral pagoda]

First thing is first. Do we agree that g(-4)=-4 and g(2)=2?

[unique sand]

yes?

[coral pagoda]

Why the question mark?

What y value does the red line hit at x=-4? Same question for x=2

[unique sand]

I am not completely sure

[near falcon]

erm, how do i find the area of the sector?

[coral pagoda]

Please ask in a different channel

[coral pagoda]

Do you know what ordered pairs are?

You there?

Welp, they bailed.

[near falcon]

ok

[coral pagoda]

What class is this for Spooky?

[near falcon]

what

[coral pagoda]

Your question.

[sick scaffold]

these are both the same equation right?

[near falcon]

math

[coral pagoda]

math is a very very broad term

Is it geometry, algebra, calculus...?

[near falcon]

not sure

[coral pagoda]

Okay, so not calculus. Do you know what radians are?

[near falcon]

radius?

[coral pagoda]

Actually, it's still fine. We can do this.

[near falcon]

ok

Im new to pi

[coral pagoda]

Do we agree that the area of the circle is pi*r^2, where r is the radius?

[near falcon]

erm, what

[coral pagoda]

What is the area of the circle with radius r?

[near falcon]

still dont understand..

[coral pagoda]

What is the formula for the area of a circle?

[near falcon]

pi r2

[coral pagoda]

Okay. That is what I said earlier

[near falcon]

ok

[coral pagoda]

• was just multiplication and ^ denotes an exponent

r^2 means r squared

[near falcon]

ohh ok

[nocturne radish]

Write it as pi r²

[raw shard]

that’s basically a special character

[nocturne radish]

Might remove confusion for some

[coral pagoda]

So let's use this circle here

[near falcon]

ok

[coral pagoda]

The circle with a slash is called theta. It is just the angle of our sector

[paper bloom]

ok

[near falcon]

ok

[coral pagoda]

Well, here's the thing. The area of a sector is just a fraction of the area of the circle

Right? It's just a slice of the area we have.

[near falcon]

ok

[coral pagoda]

Does this all make sense to you right now spooky? Ok does not tell me much

[near falcon]

It makes sense

[paper bloom]

thank you this is all i need

i was coming here to ask the same question

[coral pagoda]

Okay cool. Alright, we are in business.

Now the question is, how many of these sectors do we need to fill up the circle

[near falcon]

uhh

[paper bloom]

what is the radius

agian

[nocturne radish]

What exactly is the question?

[coral pagoda]

For these two circles, it takes 2 half slices to fill up the circle, and 4 quarter slices to fill up the circle

[nocturne radish]

Radius is a line drawn from the center of the circle to the edge of it

[near falcon]

ok

[paper bloom]

the value of the radius

[coral pagoda]

So....how many slices with sectors of angle theta do we need?

[nocturne radish]

Radius is a variable here

[paper bloom]

ohh

[coral pagoda]

It is just a variable. The value is irrelevant until the finish line.

[near falcon]

Im confused now

[nocturne radish]

Shall I try to explain?

[paper bloom]

yea

[coral pagoda]

Well, let me continue first.

[nocturne radish]

If you could ask the problem

Yea yea

[paper bloom]

jump into mathmatics

[coral pagoda]

Let's take a look at the simple examples.

[paper bloom]

voice chat pls

[near falcon]

ok

All I want to know is how to find the area of the sector

[coral pagoda]

We are gonna get there

[near falcon]

ok

[coral pagoda]

We are deriving the formula

[near falcon]

ok

[nocturne radish]

I can send a pic

I have already written it

[nocturne radish]

To help dackid