help-38

[limpid dawn]

,,\lim_{n\to \infty} a_n = \lim_{n\to \infty} \frac{1}{\sqrt{2n+1}}

[solid kiln]

now what (𝔸dωn𝓲²s)

[left oriole]

you had a_n correctly, what happened

[limpid dawn]

what happens as n grows pretty big?

[urban copper]

,, \quad 0 < \frac{1}{\sqrt{2n + 3}} < \frac{1}{\sqrt{2n+1}}

[left oriole]

you want to do that without hte (-1)^n

[urban copper]

0

[left oriole]

a_n is the part without the (-1)^n

[limpid dawn]

i need more hints

[left oriole]

^ correct, so a_n is decreasing

[solid kiln]

calc_and_real_anal

[left oriole]

now show that it decreases to limit zero

[urban copper]

how

[left oriole]

what happens to the denominator as n->inf?

[urban copper]

infty

[left oriole]

right

so what happens to the overall fraction as n->inf

[urban copper]

approaches 0

[left oriole]

right

so the alt test applies

[urban copper]

wdym

[limpid dawn]

if you prove this algebraically yet, then yea

[left oriole]

the two conditions 1 and 2 hold

[urban copper]

but how

[left oriole]

that's what i mean by "applies"

[urban copper]

1 is not proven yet

[limpid dawn]

prove it

[urban copper]

how

[left oriole]

didn't you show that above

[left oriole]

^ here

[limpid dawn]

that's not so obv

[urban copper]

is this enough justification?

[left oriole]

denominator gets bigger --> fraction gets smaller

well it really depends on the context

whether it's enough justification

i would err on being explicit if you're being graded on this

[limpid dawn]

usually you you would wanna work with this until you get a true statement out like n > 1 or something

at least that was the case for me

[left oriole]

you could start with the obvious
2n+1 < 2n+3

then use monotonicity of sqrt

[urban copper]

how to do that

[limpid dawn]

also this comes from squaring both sides and multiply by -1

[left oriole]

and the fact that 1/x is decreasing

[urban copper]

okay a moment

,, 0 < \frac{1}{\sqrt{2n + 3}} < \frac{1}{\sqrt{2n+1}} \ 0 < \frac{1}{2n + 3} < \frac{1}{2n+1}

[solid kiln]

calc_and_real_anal

[urban copper]

how do I flip the fractions

[left oriole]

multiply both sides by (2n+3)(2n+1), which is positive so the < doesn't flip

[limpid dawn]

positive because n >= 1

[urban copper]

,, 0 < \frac{1}{2n + 3}\cdot \frac{(2n + 3)(2n+1)}{(2n + 3)(2n+1)} < \frac{1}{2n+1} \cdot \frac{(2n + 3)(2n+1)}{(2n + 3)(2n+1)}

,, 0 < \frac{1}{2n+1} < \frac{2n+3}{(2n+1)^2}

[solid kiln]

calc_and_real_anal

[left oriole]

wha

[limpid dawn]

you can also apply ()^-1 on both sides

and flip the sign

[left oriole]

^ (2n+3)(2n+1) (the product of the two), not (2n+3) / (2n+1)

[limpid dawn]

,, 0 < \frac{1}{2n + 3} < \frac{1}{2n+1} \quad \big | \cdot (2n+3)(2n+1)

[solid kiln]

now what (𝔸dωn𝓲²s)

calc_and_real_anal

[urban copper]

this?

[limpid dawn]

noo

[urban copper]

no wayyy

[limpid dawn]

this

that's what Bungo means

[urban copper]

what is that big |

[limpid dawn]

commando line

what next operation we are going to do

| ... means we are going to do ... in the equation/inequality

just a notation

[urban copper]

how can we just multiply like that (2n+3)(2n+1) wtf

now that I see this maybe ()^-1 is easier

[limpid dawn]

haha noo

[limpid dawn]

this the common factor

[urban copper]

,, 0 < \frac{1}{2n + 3} < \frac{1}{2n+1} \ 0 < \frac{(2n+3)(2n+1)}{2n+3} < \frac{(2n+3)(2n+1)}{2n+1} \ 0 < (2n+1) < (2n+3)

[limpid dawn]

yea

see how some factors cancel

[solid kiln]

calc_and_real_anal

[limpid dawn]

If you have $$\frac{1}{a} \leq \frac{1}{b}$$ then multiply by the common factor $ab$ on both sides and assume $ab > 0$ yields to $$\frac{1}{a} \cdot ab \leq \frac{1}{b} \cdot ab \implies b \leq a$$

[solid kiln]

now what (𝔸dωn𝓲²s)

[urban copper]

how do you guys know that n > 0

btw

[limpid dawn]

because the series

starts with n = 1

[urban copper]

true dat

[limpid dawn]

and counts up integerwise

[urban copper]

okay thanks

[limpid dawn]

now what

[limpid dawn]

how can we continue

[urban copper]

I mean

,, 0 < \frac{1}{2n + 3} < \frac{1}{2n+1} \ 0 < \frac{(2n+3)(2n+1)}{2n+3} < \frac{(2n+3)(2n+1)}{2n+1} \ -2n < 1 < 3

[limpid dawn]

how about su subtract just 2n on bth sides?

[urban copper]

yes

[limpid dawn]

you then get

but ok

continue

[solid kiln]

calc_and_real_anal

[limpid dawn]

now I would

divide by -2

[urban copper]

that would flip the < though

okay

[limpid dawn]

yes

[urban copper]

,, n > \frac{-1}{2} > \frac{-3}{2}

[solid kiln]

calc_and_real_anal

[limpid dawn]

so for the inequality to hold truth

[limpid dawn]

this has to be

which is the case

our n is at least 1

and that's far greater than -1/2 and even -3/2

and n just gets bigger so you proved

[urban copper]

okay thanks

.close

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[limpid dawn]

only chartbit can use this

[grim sparrow]

why

I've been using it for like 2 weeks now

[limpid dawn]

oh i just associate chartbit with these always haha

[grim sparrow]

fair enough lmao

[trim jolt]

✅

[urban copper]

find $f$ with continuous derivative in $\mathbb{R}$ such that $\\ \begin{cases}f(0) &= 1 \f^{8}(x)f'(x) &= 8x^3 e^{2x^2} \quad , \forall x \in \mathbb{R} \end{cases}$

[solid kiln]

calc_and_real_anal

[final coyote]

chain rule on the left side, as in a similiar example some days ago.

[whole coral]

No no, that's the you're thinking of

[urban copper]

chain rule?

[final coyote]

#help-48 message

[urban copper]

derivative of f^3(x) = 3f^2(x)f'(x)

derivative of f^8(x) = 8f^7(x)f'(x)

[final coyote]

its the same way to solve, the numbers differ.

[urban copper]

how do I figure out the derivative of f^8(x)?

ohh a moment

let h(x) = x^8

h(f(x)) = f^8(x)

its function composition

[final coyote]

take h(x) = x^9.

[urban copper]

but its f^8 tho

wdym x^9

,, \frac{d}{dx} h(f(x)) = h'(f(x))f'(x)

[final coyote]

yes of course, the left side (f^8 times f') is the derivative. as in the last example (we needed f^3)

[solid kiln]

calc_and_real_anal

[urban copper]

no but f^8 means f . f . f . f . f . f . f . f btw

its not referringg to the 8th derivative btw

I forgot to mention mb

[final coyote]

i know. the derivative of x^9 is 9 times x^8. but anyway. take my hint or let it be. good luck.

[urban copper]

,, \frac{1}{9} \cdot \frac{d}{dx} {x^9} = x^8

[solid kiln]

calc_and_real_anal

[urban copper]

h(f(x)) = f^8(x)

[limpid dawn]

i am thinking of all cat appearances lol

[primal steppe]

$\int f^8f' dx = \frac{f^9}{9}+C$

[solid kiln]

Boi

[limpid dawn]

what

[urban copper]

is that due to integration by parts?

how?

[primal steppe]

due to u-substitution

let f(x) = u; then we have f'(x)dx = du

[urban copper]

true

[primal steppe]

oh nvm thats function composition not exponent

is f^8(x) here f(x) * f(x) * f(x) ... or f(f(f( ... ?

[limpid dawn]

ah I see

[urban copper]

f . f . f .f .f . f . f .f

the former

[primal steppe]

oh okay then it still stands what i said

let f(x) = u; then f'(x)dx = du, so that f^8(x) f'(x) dx = u^8 du

$\int f^8(x)f'(x)dx = \int u^8 du = \frac{u^9}{9}+C = \frac{f^9(x)}{9} + C$

[solid kiln]

Boi

[urban copper]

,, \frac{f^9(x)}{9} + C = \int 8x^3 e^{2x^2} dx

[solid kiln]

calc_and_real_anal

[primal steppe]

you need to simplify the integral on the right side using u-sub as well

[urban copper]

u = 2x^2

[primal steppe]

nope

try again

[urban copper]

du = 4x dx

[primal steppe]

yep

[urban copper]

,, \frac{f^9(x)}{9} + C = \int ue^{u} du

[primal steppe]

thats right

[solid kiln]

calc_and_real_anal

[primal steppe]

now the integral easily solves to (u-1)e^u + C'

(integration by parts)

[urban copper]

,, \int f \cdot g' dx = f \cdot g - \int f' \cdot g dx

[solid kiln]

calc_and_real_anal

[urban copper]

f(x) = x

g'(x) = e^{x}

f'(x) = 1

g(x) = e^{x}

,, xe^{x} - e^{x}

[solid kiln]

calc_and_real_anal

[urban copper]

,, e^{x}(x - 1)

[solid kiln]

calc_and_real_anal

[urban copper]

,, \frac{f^9(x)}{9} = e^{2x^2}(2x^2-1) + C

[primal steppe]

now you let x = 0 and find C

since f(0) = 1 is given, it shouldn't be too difficult

[urban copper]

,, \frac{1}{9} = C

[primal steppe]

oh wait nope you made a mistake

the right side here should be e^u(u-1), not e^x(x-1)

since u = 2x^2 is your substitution you must remember to resubstitute

[urban copper]

u = 2x^2

[solid kiln]

calc_and_real_anal

[urban copper]

,, \frac{1}{9} = C

[solid kiln]

calc_and_real_anal

[urban copper]

,, \frac{f^9(x)}{9} = e^{2x^2}(2x^2-1) + \frac{1}{9}

[solid kiln]

calc_and_real_anal

[urban copper]

,, f(x) = \sqrt[9]{9e^{2x^2}(2x^2-1) + 1}

[solid kiln]

calc_and_real_anal

[urban copper]

,w Solve[D[(9E^(2x^2)(2x^2-1)+1)^(1/9), x] == 8x^3E^(2x^2)/((9E^(2x^2)(2*x^2-1)+1)^(8/9)), x]

[solid kiln]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[urban copper]

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✅

[urban copper]

using the identity$\sum_{n = 0}^{\infty} x^n = \frac{1}{1-x} \quad , |x| < 1$ deduce the formula $\ 1 + 2x + 4x^2 + . . . + 2^n \cdot x^n + . . . = \frac{1}{1-2x} \quad , |x| < \frac{1}{2}$

[solid kiln]

calc_and_real_anal

[left oriole]

just replace x with 2x?

[limpid dawn]

more hints

[urban copper]

.close

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[barren ocean]

Any hints for this?: If $G \neq {e}$ acts properly discontinuously on $\mathbb{R}$, show that $G \approx \mathbb{Z}$

[solid kiln]

CoffeeMan

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[mild kernel]

Can someone tell me what I did wrong??

/how to fix it

omg

Omg ur right 😭😭 I thouight i was multiplying for some reason

Tyyyy

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[native radish]

Cos(cosx) min and max value

[native radish]

Pls help

[frail heron]

Do you know the maximum and the minimum value of $cos \theta$

[solid kiln]

Sufferrrrring rn D:

[native radish]

1 and -1 i think

[frail heron]

Alr

Do you know where cosine1 and cosine-1 at?

at which dimension

[native radish]

I have forgotten

Sorry

[frail heron]

No, you don’t need to memorize it

[native radish]

1 at 0 degrees

[frail heron]

It’s not degree, it’s cosine1

[native radish]

Oh sorry

I don't know then

[frail heron]

What’s the approximate value of pi/2?

[native radish]

90 degree i think

[frail heron]

no, I mean value

Like pi is approximate 3.14

[native radish]

I don't know teacher hadn't teach me that

I am little weak in maths so I granted help

[frail heron]

Alr

pi is approximately 3.14, do you agree?

[native radish]

Although my dad is a maths teacher

[native radish]

Yes

[frail heron]

3.14/2 is 1.5~, do you agree?

[native radish]

Yeah approximately

[frail heron]

yeah, that’s all we need

It’s not that hard

[native radish]

Sorry i did not get the answer

[frail heron]

No, it’s not the answer lol

We just started lol

[native radish]

Cospi/2 is 0 and cos(-pi/2) is also zero

[native radish]

Then explain and give the answer

P

Ls

Pls

I request

I need the explanation and answer

[frail heron]

It is

[frail heron]

Is this a test?

[native radish]

No i was solving a problem set and this problem appeared

[frail heron]

I see

How about I just give you how to approach it

And you’ll figure it out yourself

[native radish]

Ok

[frail heron]

Alr

[native radish]

[frail heron]

You shouldn’t find the minimum and the maximum with the concept "with what I plug in, I’ll get the maximum and the minimum"

Instead, see the cosine on the inside as K

-1<K<1

No, I’m not joking lol

[native radish]

Give some more hints

[frail heron]

There you’ll find cosineK -1<K<1

[frail heron]

That’s all you need to know for approaching this question

[native radish]

What does it mean cos function inside a cos function i mean cos(cosx)

[frail heron]

wdym

I did mention it

See cosx as K

[native radish]

Oh

[frail heron]

Since you know the interval of cosx

You know the interval of K

[native radish]

-1 to 1 ?

[frail heron]

yeah

And pi/2 is approximate 1.5

[frail heron]

That’s how you get this graph

[native radish]

I am thinking something

Cosx max value is 1

Then cosk max value at 90 is 1
And minimum is cos1
Pls don't angry i am weak inteligent

[native radish]

If this answer gets wrong

I just think about it and understand this

[frail heron]

No, why would I be angry lol

[native radish]

Is my answer also?

[native radish]

Correct

[frail heron]

I wouldn’t even be here if I would get irritated by helpee’s question

[native radish]

I understand

My answer?

[frail heron]

CosK has the maximum value when K=0

Because cos0=1

[native radish]

That is 1

[frail heron]

Your minimum is correct

[native radish]

And minimum cos1 at k = 90

[frail heron]

The minimum is cos1, but at that moment, k≠90

[native radish]

Yeah you are right

[native radish]

I got the answer

@frail heron thanks for giving me hints

[frail heron]

Alr, congrats

That’s a quick guidance

Hope you enjoyed, have a good one

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[native radish]

It take a little long time as I am fool but ok bye sir you also have a nice one

[frail heron]

.close

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[dark lotus]

I learning desomos and don't understand what the meaning of the f(x) someone can teach what f mean?

[hasty sail]

The f(x) is pretty much just a way to name the function, and for most intents and purposes, is the exact same thing as y

and with that, f(x) and g(x) are two perfectly valid ways to name a function

what's inside the f(x) is what you're trying to solve for

take the function f(x)=2x+6,

say you want to solve for when the x-axis equals 10

To do this, you would use f(10)=2x+6

with Desmos, as far as I'm aware, I don't think you'll be using it too much in that way, but it'd still be useful to know for later when you start getting to use function more often

[dark lotus]

thank you

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[hybrid quiver]

just want to check my answers and i have some additional questions on this

[hybrid quiver]

\documentclass{article}\usepackage{amsmath}\begin{document}The equations of motion for the two-degree-of-freedom system are given by:For the sprung mass ( m_S ):\begin{equation}m_S \ddot{x}S = -k{\text{eq}} (x_S - x_U) - b_{\text{eq}} (\dot{x}S - \dot{x}U) + f{b{\text{eq}}}\end{equation}And for the unsprung mass ( m_U ):\begin{equation}m_U \ddot{x}U = k{\text{eq}} (x_S - x_U) + b_{\text{eq}} (\dot{x}_S - \dot{x}_U) - k_T (x_U - x_R) + f_T\end{equation}\end{document}

[solid kiln]

luke1
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hybrid quiver]

do these equations seem correct

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[marsh forum]

ID?

Oh, linearly indepdent

[rapid horizon]

Yes linear independent

We need scaler so that i can represet one vector in terms of another

[marsh forum]

no idea , sorry

[left oriole]

for the first part, you want to find a scalar c such that $\alpha = \beta c$

[solid kiln]

Bungo

[left oriole]

looking at just the first component you see that you need $c = 1+i$

[solid kiln]

Bungo

[left oriole]

so now just check that $2i = c(1+i)$

[solid kiln]

Bungo

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[mossy cove]

Could someone help me with this question

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[mighty canyon]

ok... consider k = 0, do you agree that it is true?

what makes that true?

what about -100?

what makes that false?

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[mossy cove]

Ill come back to the question later. Im gonna sleep now

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[night estuary]

Any good books for university level calculus and statistics ?
I hope this is the correct channel if not please redirect me to the channel where I can ask this. Ping or reply with ping on so I get notified.
Thanking You in advance.

[stoic iron]

#book-recommendations

@night estuary

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[night estuary]

okie

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[graceful zenith]

My b ii) is wrong can any1 explain why

[graceful zenith]

It’s actually 66

[wraith hinge]

,rotate

[wraith hinge]

think about what can yield a term of order x^3

you can get 2 * term in x^3 - 5x * term in x^2 + x^2 * term in x

I'll do the first term for you. So $2 \cdot \binom{11}{3} \left(x\right)^3 \left(1\right)^8$

[solid kiln]

45

[wraith hinge]

@graceful zenith

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[cyan nebula]

Yo

Need help?

[wraith hinge]

Yes please

[cyan nebula]

Familiar with any formulas u learnt?

Coordinate geometry formulas

[wraith hinge]

No

I don’t know anything

[cyan nebula]

ok one sec

[wraith hinge]

Okayyy

[cyan nebula]

In this vase

You need the disyance

Midpoint and slope

[wraith hinge]

What is that

[cyan nebula]

Which

Slope?

[wraith hinge]

All of that

[cyan nebula]

Ok

So distance between two plints

U get that right

[wraith hinge]

No

What u mean?

[cyan nebula]

Uhh

[wraith hinge]

What is gradient

[cyan nebula]

Wait wair

You don’t get what distance means?

[wraith hinge]

Like

The distance between the point?#

?

I think

[cyan nebula]

Yes

Gradient is the steepness of a line

Get what I mean?

[wraith hinge]

What?

Like how much it goes down?

[cyan nebula]

Ok so

—

What do u think is the gradient of this line

[rugged latch]

He means slope

He’s probably British

[wraith hinge]

What

[wraith hinge]

0

[wraith hinge]

Huh?

[rough frost]

Gradient and slope is the same thing

[cyan nebula]

Yea

[rough frost]

In ur question its gradient

[cyan nebula]

Mb if I got u confused

[wraith hinge]

Huh?

Okay okay

So how do I do that

[cyan nebula]

Ok so u want me to use the term gradient or slope

In this case I’ll use gradient since the question ask

[wraith hinge]

Okay okay

[cyan nebula]

So

Usual formula everyone remembers by

Its rise/run

[wraith hinge]

Oh okay okay

[wraith hinge]

What is that

[rough frost]

Wait Sandra do yk how to read coordinates of ur points

[strange fog]

why is it a png

one second

[wraith hinge]

What is rise over run

[wraith hinge]

No?

What is that

[rough frost]

Bro

[cyan nebula]

oh

[wraith hinge]

Wait yes

Like the y axis and x thingy?

Right

[rough frost]

U understand?

[cyan nebula]

Yea sure

U get that?

[wraith hinge]

Why is it so blurry

[strange fog]

you count the squares

here

[wraith hinge]

Yes yes

[wraith hinge]

I know that

[strange fog]

you count the squares of rise and run

theres

simplifed

[wraith hinge]

Huh

[rough frost]

Girl u rise upwards

[wraith hinge]

What does rise and run mean?

[strange fog]

then you put the value of rise over run

[rough frost]

So u count upwards

[wraith hinge]

Bro what

[strange fog]

do you see how he got 3 and 8?

[wraith hinge]

What is rise and run

[cyan nebula]

How much it rises

And how much it runs horizontally

[strange fog]

yeah

[wraith hinge]

What the flippers

Floppers

[cyan nebula]

AHH

[strange fog]

you can count the squares on the grid

[wraith hinge]

Can u re word that

[cyan nebula]

ok shre

So

[wraith hinge]

Guys ur rise and run makin no sense

ISK what that is

[cyan nebula]

We have a graph yes

[rough frost]

IS IT 7

[cyan nebula]

It’s 6

[wraith hinge]

Huh

[rough frost]

WHOOPS

[wraith hinge]

How did u get that

[cyan nebula]

BRORHER

PH MY

[rough frost]

it’s 6 I counted wrong

[wraith hinge]

What is the 7 for?

[cyan nebula]

😂

[wraith hinge]

Is that rise?

[cyan nebula]

Ur making her so confused

[rough frost]

I MEANT 6

[cyan nebula]

ok here

[cyan nebula]

Ya

Solve that

[strange fog]

so on a grid sandra

[wraith hinge]

So what does that do

[strange fog]

you know how thers squares on the grid

[cyan nebula]

Just fill in the values

[wraith hinge]

No I don’!!

[strange fog]

what the hell

[wraith hinge]

Don’t

[rough frost]

Ofc u don’t

[wraith hinge]

Flipping yes I do

[strange fog]

ok

[wraith hinge]

Where

[strange fog]

now you count how high the triangle goes

[wraith hinge]

What do I solve

[strange fog]

by counting the squares

[wraith hinge]

Okay okay

Is that rise

[cyan nebula]

Doesn’t matter

Just count

Then tell

Ur gonna get urself confused

[wraith hinge]

Okay one sec guys

[cyan nebula]

U got this

🙏

[wraith hinge]

Is it that?

[cyan nebula]

YOO be nice 💀

It’s 6

And 2

Yes

[wraith hinge]

Oh okay okay

[cyan nebula]

You count until the dot

Good

Now

[wraith hinge]

So do I count that small thing?

[cyan nebula]

What small thing

[wraith hinge]

The little thing o the side

[cyan nebula]

???

[wraith hinge]

Yk how for one of the squares

[rough frost]

Yes

[wraith hinge]

There’s only a little bit

Oh okay okay

[cyan nebula]

NO

WHAT R U SAYINF

[wraith hinge]

HUH?

[cyan nebula]

WHAT GRADE R U

[wraith hinge]

BRO

[rough frost]

STOP

[cyan nebula]

BROTHER

[strange fog]

count the squares on the sides

on the grid

[wraith hinge]

8

No

4

[strange fog]

thats run good job

thats rise

good job

now put them in th eformula

[wraith hinge]

Thank you thank you

Which

Huh

[strange fog]

so you foun dout

[wraith hinge]

What formula

[strange fog]

that rise = 8 and run = 4

[rough frost]

Rise/run

[wraith hinge]

Oh okay

[strange fog]

now put it in the formula Rise
Run

[wraith hinge]

Wait so 8/4?

[strange fog]

GOOD JOB

[rough frost]

Yes

[wraith hinge]

2?

[strange fog]

other way around

4/8

[wraith hinge]

Oh

[strange fog]

i think rise is on top

right

persues

@cyan nebula

[cyan nebula]

Brother

[strange fog]

does the order matter

its rise over run

[cyan nebula]

Yes it does

[strange fog]

right

[rough frost]

NO

[wraith hinge]

Oh

[cyan nebula]

Yall need to stop

[rough frost]

RISE IS ON TOO

[wraith hinge]

What?

[cyan nebula]

Everyone stop

[strange fog]

ok

[rough frost]

CAUSE U RISE ON TOO

[cyan nebula]

And just stop msging

[strange fog]

soryr

[wraith hinge]

Y’all are confusing me

[strange fog]

STOP

[cyan nebula]

Yall r confusing

Him

[strange fog]

STOP

[rough frost]

U RISE TO THE TOO

TOP

[strange fog]

STOP

[cyan nebula]

Or hee

[wraith hinge]

HIM?

[cyan nebula]

Stop

[wraith hinge]

HIM?

[cyan nebula]

Her

Mb

Brother

[strange fog]

sandra if you get pressed im gonna lose my shits

[cyan nebula]

I’ll make a video

And watch it

[wraith hinge]

Bro

[cyan nebula]

And learn

And the others need to shut up

[wraith hinge]

What u mean

[strange fog]

ok ok

ill shut up

[rough frost]

Yes

[cyan nebula]

Cause yall also don’t understand

[wraith hinge]

No no the others need to talk

Please

[strange fog]

WHAT

[wraith hinge]

They making me not wanna end it all

[rough frost]

OH MY GYAT

[wraith hinge]

Or I will get super super sad 😞

[cyan nebula]

How old r u guys

[strange fog]

im 14

[wraith hinge]

19

[cyan nebula]

Young af aren’t u

God damn

[wraith hinge]

Nuh uh

[strange fog]

yep

[wraith hinge]

Why u so young

[rough frost]

mummy told me not to tell people on internet my age

[cyan nebula]

19? Dang u learning this late 💀

[wraith hinge]

Yeah…

[cyan nebula]

Ok

[strange fog]

shes a bit behind

just a tiny bit

[wraith hinge]

Your 14

[cyan nebula]

no

[rough frost]

Got pulled back

[cyan nebula]

Ok

Here

[wraith hinge]

Bro

[rough frost]

I don’t know u gf

[strange fog]

shes in grade 9

[rough frost]

Tf

[wraith hinge]

The Evan kid is my brother and the shrunk my sister

[strange fog]

yall shut up

you tryna confuse this guy now

[rough frost]

Me and Evan r twins

[wraith hinge]

We one big happy family

[strange fog]

just fucking do your maths

[wraith hinge]

Yeah

[rough frost]

That why we both 14

[wraith hinge]

Yeahhh

[strange fog]

now hes gone

[wraith hinge]

I’m the oldest

[strange fog]

hes done

good job

[wraith hinge]

Is he actually

[strange fog]

yes

good job

[rough frost]

HE MAKING VIDEO

TRUST

[wraith hinge]

STOP ACTUALLY?

[strange fog]

stfu and he might come back

[wraith hinge]

Please don’t leave

[strange fog]

prolly not anymore

[wraith hinge]

I really need help

[rough frost]

He is trust

[wraith hinge]

Bro are u happy now

[wraith hinge]

I’m gonna fail

[rough frost]

I love u perseus ❤️

[wraith hinge]

YAY

[rough frost]

SEE

[strange fog]

HES BACK

[cyan nebula]

Brothers

Sisters

Whatever

Watch the vid

[rough frost]

1 brother 2 sisters

Why doesn’t a small part of the square count

[wraith hinge]

Wait how did u get the 1/2?

[rough frost]

How do u know when to stop counting the small part

[strange fog]

persues put it on a grid

and show her

how to fucking count the grid

the triangles drawn on

[cyan nebula]

Rise over run

What the fuck

[wraith hinge]

Bro you don’t have to be so moody

[strange fog]

cuz the school dont give you the value of rise or run they put it on a grid

[rough frost]

Because that’s what 2/4 is.

[strange fog]

and you have to find it

[rough frost]

It’s 1/2 or also known as 0.5

[strange fog]

and they teach you to count the grid squares

[wraith hinge]

Wait so how do I find the rise

And run

[rough frost]

TELL ME PERSEUS

[cyan nebula]

No it doesn’t

[wraith hinge]

How did u get that

[cyan nebula]

The dot is on the line

Count the like

[wraith hinge]

Did u divide the 2 and 4?

[cyan nebula]

Line

[cyan nebula]

Divide the 2 by 4

[wraith hinge]

Huh

So that would be 2?

[cyan nebula]

ya I give up

[wraith hinge]

NO PLEASE

[rough frost]

I’m literally telling dad to get u a tutor

[wraith hinge]

Don’t

[cyan nebula]

Where u guys from

[rough frost]

No actuals Perseus can u explain why certain small parts of the small don’t count

[cyan nebula]

This ain’t make no sense that u don’t get this 💀

[rough frost]

Like how do u know when to stop counting it

[wraith hinge]

Amirca

[strange fog]

YOUR IN GRADE 10

ARE YOU SPECIAL

[rough frost]

STOP

I GENIUNELY DONT KNOW WHEN TO STOP COUNTING IT

[wraith hinge]

SAME

[cyan nebula]

Jesus

[wraith hinge]

WHEN DO U STOP COUNTING ?

[rough frost]

why is that square too small

[strange fog]

2/7

what square

the triangle is two units in height

[wraith hinge]

Do I bring a calculator to my test?

[strange fog]

and in length its 7 units

YES

[wraith hinge]

I don’t think I have one

[strange fog]

s

good job

[cyan nebula]

American education is mad

[strange fog]

ask the teacher for one

[wraith hinge]

What am I ment to do

[strange fog]

its australian

[cyan nebula]

Brother I was learning this at 7

[wraith hinge]

The teacher don’t have

[strange fog]

lmao

[wraith hinge]

No way

[strange fog]

its not that hard sandra

[cyan nebula]

How many yrs did u stay back

[rough frost]

WHY DOESNT THIS SQAURE COUNT

[cyan nebula]

What

[wraith hinge]

Then u explain it

[cyan nebula]

Oh my god

[strange fog]

TH EUCK

[strange fog]

I DID

[wraith hinge]

No u didnt

[strange fog]

ok so

[strange fog]

here

[wraith hinge]

Does that small thing count??

[strange fog]

wait

[cyan nebula]

Good luck

[strange fog]

ill explain one sec

[rough frost]

I THINK IT COUNTS

[strange fog]

watch this persues

watch me

[rough frost]

NO STOP

LERSEUS

EXPLAIN

[wraith hinge]

Evan not gonna know

[rough frost]

WHY FOESNT A SMALL BIT OF SWAURE DONT COUNT

[wraith hinge]

BRO DID HE LEAVE?

OH MY GYATT

[cyan nebula]

Ya good luck

[rough frost]

It was 6

Nvm guys I counted it wrong

[wraith hinge]

Are u leaving 😞

[rough frost]

2/6

[wraith hinge]

AHAHAHAHAH

[rough frost]

2/6 is 1/3

[cyan nebula]

Dude

All of u need help

[wraith hinge]

Wait

[rough frost]

Which is 0.3 recurring

That’s ur gradient

[wraith hinge]

How did u get that?

HOW DID U GET THE 1/3?

[rough frost]

U Simplifi the fraction

[strange fog]

surley not me :(

[rough frost]

Both numbers go into 2

[wraith hinge]

WHAT DO I DO TO GET 1/3

[cyan nebula]

All

Of

[rough frost]

So 2/2 is 1

[cyan nebula]

You

[rough frost]

6/2 is 3

[strange fog]

HOW ME

😭

[rough frost]

So 1/3

[wraith hinge]

HAHAHAHHAHAHHA

AHAHHAHAHAHAHAHAH

[rough frost]

Bro just put in ur calculator 2/6

[wraith hinge]

ITS NOT 7

ITS 6

AHAHAHHAHA

EVAN THOUGHT HE WAS SO GOOD

[rough frost]

That’s 6 squares

[strange fog]

why did you write 7 under neath it

i read of the nits

[rough frost]

GUYS I THINK I BECAME STUPID LIKE SANDRA TALKING TO HER

[strange fog]

units

who put the units there

[rough frost]

I COUNTED IT WRONG

[wraith hinge]

AHAHAHHAHA

YALL R SO RUDE

[strange fog]

oh all g

[wraith hinge]

AHAHAHA

[cyan nebula]

This is crazy

[strange fog]

what?

[wraith hinge]

EVAN REALLY THOUGHT

[rough frost]

Okay gradient is 1/3

OKAY SANDRA

[strange fog]

im sorry

on behalf

of al of us

[rough frost]

bro I can hear Evan in his room crying cause he got it wrong

[wraith hinge]

How do I get the fucking 1/3

[rough frost]

Shush twin bro

[wraith hinge]

Same

[rough frost]

BRO

[wraith hinge]

What the flip

[strange fog]

your mistake

[rough frost]

JUSY PUT IT IN UR CALCULTOR

[strange fog]

but sure

[rough frost]

2/6

BRO

USE UR CALCUKATOR

[wraith hinge]

Eva can u like lower ur house

Noie

U so loud

[strange fog]

?

[wraith hinge]

I can hear it from my room

Stop crying

[rough frost]

Okay gradient is 0.3

NOW MIDPOINT

[wraith hinge]

I don’t have a calculator

[cyan nebula]

Crazy crazy crazy

[rough frost]

midpoint is u add all the x axis number

Divide by 2

[wraith hinge]

No persuesu u gotta help

[rough frost]

What r the two x axis bunbers

[wraith hinge]

Trust ill learn

[rough frost]

SANDRA

[cyan nebula]

Ok

[wraith hinge]

WHAT?

[rough frost]

WHAT R THE 2 X AXIS NUMBERS

[wraith hinge]

What?

[wraith hinge]

What

8 and 1

No

[cyan nebula]

Yo

[wraith hinge]

8 and 2

[rough frost]

it’s 2 and 8

GOOD

[cyan nebula]

If I’m teaching

Then fucking listen

[rough frost]

So u do 2+8

Which is 10

[wraith hinge]

Okay I’m sorry

[strange fog]

this guys finished helping other people with harder shit

[rough frost]

And then u divide by 2

[strange fog]

before you understand rise over run

[rough frost]

10/2

Is 5

[wraith hinge]

What the flip

Bro wait

[rough frost]

So the first part of midpoint is 5

[strange fog]

jeneeta shut the fuck up

[rough frost]

Now u gotta find second part

[wraith hinge]

No ur going too fast

[strange fog]

let the other guy do it

[wraith hinge]

Don’t Go so fast

[rough frost]

OH MY GYAT

[strange fog]

she came to this server to get help from another person

[rough frost]

OKAY THEN

[strange fog]

alright

deal

dms

[cyan nebula]

ya gl

[wraith hinge]

Persuadus can u try

[strange fog]

your helping her

its your burden now

im leaving

[wraith hinge]

Filp u guys

[strange fog]

bye ybe

[cyan nebula]

Then shut up

[wraith hinge]

Okay okay

[cyan nebula]

All of u need help

Ok

[wraith hinge]

Okay okay

[cyan nebula]

So

Do you understand a graph

[wraith hinge]

What?

What one

[cyan nebula]

This is a graph

[wraith hinge]

Yes yes

Ik how to look at it

I think

[cyan nebula]

Ok

So

Graph has coordinates

[wraith hinge]

Okay okay

[cyan nebula]

We communicate coordinates by using (x, y)

Ok?

[wraith hinge]

Yes yes

I think

[cyan nebula]

Ok

So do you understand

What I mean by

(6,8)

[wraith hinge]

Yeah I think

X=6?

Y=8?

[cyan nebula]

Yes

[wraith hinge]

Yayyy

[cyan nebula]

Put on X

On (6,8)

And send it

[wraith hinge]

Okay

[wraith hinge]

There

[cyan nebula]

I’m done

[rough frost]

HELO ME

[strange fog]

💀

[wraith hinge]

WHAT?

WHAT DO U MEAN

[strange fog]

thats 5

[rough frost]

hall someone else joined

[strange fog]

on the x axis

[cyan nebula]

@harsh surge 🙏🙏🙏🙏🙏

[strange fog]

please

[wraith hinge]

OH

[strange fog]

faiy

[wraith hinge]

OOPS

SORRYGUYS

ILL RE DO IT

[rough frost]

okayyy

[strange fog]

oh

ri

p

[cyan nebula]

ya good luck

Ok

[strange fog]

you got both x and y right

[wraith hinge]

There

[strange fog]

good joooob

[wraith hinge]

Th Ak you

[cyan nebula]

Ok

[wraith hinge]

Guys I swear that’s just cause I read it wrong

Mb

[rough frost]

OKAY EVACHI SHUSH NOW

[strange fog]

was until you talked

[wraith hinge]

YALL I almost got it

[cyan nebula]

Ok

So

[wraith hinge]

Yes yes

[cyan nebula]

You have to understand how to get a point

Now that u understand how to get a point

[wraith hinge]

What?

[cyan nebula]

When I connect to plints

[wraith hinge]

I’m tweaking

[cyan nebula]

On a graph

What do I get