help-49

[boreal geyser]

g(3)=2 and g'3=6

so we can sub those in

F'(3)=f'(2)6

F'(3)=f'(12)

[still nacelle]

f'(2) is a number, you can't just multiply f'(2) x 6 = f'(12). It is given to you in the question what f'(2) is

[boreal geyser]

F'(3)=6(6)

so F

F'3=36

[boreal geyser]

is this sound reasoning?

[still nacelle]

yup!

[boreal geyser]

thanks for the help

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[novel herald]

believe so ye

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[desert wagon]

Im getting no solution 💀💀??

[tacit jackal]

to solve an inequality you first solve $\sqrt{9x - 20} = x$

[grand pond]

joren

[tacit jackal]

first step would be getting rid of the square root, do you know how to do this?

[desert wagon]

Ah well our teacher taught us this method

[tacit jackal]

not sure why he wants to solve it that way if im being honest

anyway, I can help you get the same results in a different way, its quite simple

[tacit jackal]

to get rid of the square root we, square both sides to remove the square root: $9x - 20 = x^2$

[grand pond]

joren

[tacit jackal]

re-order to get them all on the same side: $x^2 - 9x + 20 = 0$

[grand pond]

joren

[tacit jackal]

then unbind the factors to solve the quadratic formula: $(x-4)(x-5) = 0$

[grand pond]

joren

[tacit jackal]

so the solution is x = 4 and x= 5, then you could graph the functions and see where $\sqrt{9x - 20}$ is smaller than $x$

[grand pond]

joren

[tacit jackal]

is both of them graphed, you can see they intersect at 4 and 5, and you can see which one is smaller visually.

[tacit jackal]

@autumn canopy I dont understand why one would take this approach, would you be able to explain why you'd take this approach with root inequalities? Solely because checking the results of intersect result(s) and see if they are valid after squaring can get annoying?

[desert wagon]

Yea got it

[midnight plank]

@desert wagon Has your question been resolved?

[autumn canopy]

Well it's more analytical than "graph the function and see which is smaller"

[tacit jackal]

fair enough

[autumn canopy]

Essentially, it's the same, it's just that I keep it in inequality form and you convert it, then convert back

[autumn canopy]

But yeah, with your way, you should definitely look at the domain too

Don't forget about that

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[tacit jackal]

so ive got the line l and the line m

i need to prove both have the same distance to A(5,0)

so I did this:

oh wait i did it correctly

had a typo

.close

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[lime cairn]

$ If f(x) = ln x, then \lim{x}{3} \frac{f(x)-f(x)}{x-3} = $

[lime cairn]

$ If f(x) = ln x, then \lim{x}{3} \frac{f(x)-f(x)}{x-3} = $

[cedar mason]

If $f(x) = \ln(x)$, then $\lim{x}{3} \frac{f(x)-f(x)}{x-3} =?$
?

[lime cairn]

whats wrong with the bot

[grand pond]

Percy

[lime cairn]

oh

[cedar mason]

x approaches three?

[lime cairn]

Lim as x approaches 3

[queen ermine]

Texit hates you

[tiny drum]

it's asking for f'(3)

[cedar mason]

idr how limits worked

but yeah

[lime cairn]

would that be the same as the deriv of ln x

[cedar mason]

the derivative lmao

yep

[lime cairn]

that would be 1/x * x'

so 0?

[cedar mason]

uh

[tiny drum]

no...

[cedar mason]

why x'

[tiny drum]

what is the derivative of ln(x)

[cedar mason]

what the hell is x'

[lime cairn]

1/x

[cedar mason]

yes so

1/x

[tiny drum]

yes, so just plug in 3

[lime cairn]

so no chain rule in here?

[runic hamlet]

its the spaces before and after the $. the bot doesnt like those

[cedar mason]

no

[lime cairn]

Because normally we do

1/f(x) * f'(x)

[cedar mason]

chain rule is for when you differentiate a function in some variable with another variable

[lime cairn]

ahh

reviewing unit 1 i competely forgot limits lol

makes sense, thank you

[cedar mason]

$\frac{d}{d \theta} \cos(\phi)= sin(\theta) \frac{d \phi}{\theta}$

[grand pond]

Percy

[cedar mason]

And stuff like that.

[lime cairn]

yea so only deriv with respect to another var

[cedar mason]

something you can expect to see in physics

[cedar mason]

yessir

[lime cairn]

also, lim as x approaches infinity of $\frac{ln(e^{3x+x})}{x}$

[cedar mason]

you're bad at latex

dont blame the bot

[grand pond]

lxve

[cedar mason]

$\frac{\ln(e^{3x+x})}{x}$

[lime cairn]

simple mistake

[grand pond]

Percy

[cedar mason]

yeah okay so

[lime cairn]

anyways, this would be infinity right?

[cedar mason]

yeah i guessssssss?

[lime cairn]

because 3x is a higher co-eff than x?

[tiny drum]

no...

[lime cairn]

would ln and e not cancel out, leaving 3x + x / x essentially?

[cedar mason]

wait no

not at all

[cedar mason]

yes

i think so

[lime cairn]

then wouldn't that mean the top is bigger

[tiny drum]

3x + x = 4x. 4x / x = 4

limit is 4

[cedar mason]

3x+x/x is 4 yeah

[lime cairn]

so bigger on top wouldn't apply here?

because 3x + x is bigger than x

[cedar mason]

x cancels out sir

[tiny drum]

they are of the same degree

[lime cairn]

ohh

degree not co efficient

use co efficient for when the degrees are the same

[cedar mason]

in general, try not to generalise math like that

it's better to understand stuff

than memorise it

just like

as something you should aspire to do

it's fine to memorise for now lmao

[lime cairn]

i would try but i have the final and its basically memorize for tmr

[cedar mason]

Mmmm

[lime cairn]

im decent at calc, just unit 1 i forgot a lot

[valid fiber]

Just remember that you have to be able to tell when top and bottom have same degree then use co efficient

If this not the case look for the bigger (top or bottom)

[lime cairn]

i see

also, on my paper i ended up doing it like this

$\frac{x(3+1)}{x} = 4$

[grand pond]

lxve

[lime cairn]

canceled the x

did i do wrong way for right answer?

[valid fiber]

Why would it be wrong way?

[lime cairn]

or should i strictly focus on it being $\frac{4x}{x} = \frac{4}{1}$

[grand pond]

lxve

[valid fiber]

4/1 = 4 there no question here

you’re right then

[lime cairn]

yea, but i canceled it out rather than focused on the degree

just wondering if this method wouldnt work on a different equation

[valid fiber]

When you have something that simple don’t bother searching for other longer method

[lime cairn]

okay, i was just making sure if that simple method was the right way

but i got it now

thank you all

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[near ermine]

Hello! I was just curious if anyone here did accounting math or math regarding finance and stuff like that if they could help me with with it, much appreciated!!

[near ermine]

Ill explain more in detail if I find someone who does that type of math, if not I have some regular math questions as well that can be answered!

Or if anyone does business statistics too that would be great!

[dull yoke]

Just send ur question and someone may help

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[near ermine]

@dull yoke okay thank you!

So in accounting the numbers have to balance out

So I was wondering if accounts receivable is an asset or a liability account and what would miscellaneous expenses be

Like what counts as miscellaneous expenes

*expenses

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@near ermine Has your question been resolved?

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[bleak pier]

Please suggest books for these topics

[midnight plank]

@bleak pier Has your question been resolved?

[last slate]

Books are ass

Look on Khan Academy

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[pearl hull]

!status

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[sullen hollow]

dont know where to begin

[orchid vault]

do you recognise what kind of polygon this is

[pearl hull]

Do you know the sum of angle of a square?

[midnight plank]

@sullen hollow Has your question been resolved?

[sullen hollow]

no

[sullen hollow]

360

<@&286206848099549185>

<@&286206848099549185>

[unborn pecan]

answer is 52 degrees

since it is a quadrilateral,the sum of all of those interior angles is 360,right? so add all those interior angles and subtract it from 360!

360-(230+42+36) = 360-308
=52 degrees!

[sullen hollow]

thanks!

[unborn pecan]

what grade mathematics is this? btw

[lethal path]

middle school, like 6th grade

[unborn pecan]

i guessed it lol
anyway,hope you got the answer~!

[midnight plank]

@sullen hollow Has your question been resolved?

[pearl hull]

My apologies, I wasn’t available

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[limpid ember]

can anyone please teach me how this works

[flat spire]

What you don’t understand

[limpid ember]

i dont understand how it work

like the stuff she did

[flat spire]

The whole thing?

[limpid ember]

after the factoring

yeah

please help :(

pleaes anyone

please someone help me

i need help

please

im begging

[burnt flame]

well you know sin(270 degrees)=-1

hence 2x=270

[limpid ember]

i see

how did they get the rest of it though

[burnt flame]

the period is defined by f(x+T)=f(x) where T is the period

[limpid ember]

i see

thanks

im a bit confused on how they got y=sin2x

[burnt flame]

so they add the period to get another solution. there are technically infinitely many, because you are purely lookin in the interval 0 to 360

because you have simplified the equation to sin(2x)=-1

so 270 is a solution to this

but you can also get another solution by adding the period

i.e. sin(2x)=-1=sin(2x+T)

[limpid ember]

ok i see thank you

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[solar yew]

How would I go about creating my migration matrix?

[midnight plank]

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[jagged hare]

[] brackets are greatest integer function

[jagged hare]

is this true for g.i.f.

can't think of a way to prove/disprove this

[midnight plank]

@jagged hare Has your question been resolved?

[jagged hare]

nope

[novel herald]

consider b = 1, x = .5

LHS is 2 but RHS is 1

[jagged hare]

rhs would be uh infinite right

but yeah thanx for this example

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[novel herald]

greatest integer?

ceil(.5) = 1

[jagged hare]

despite what it sounds like its actually a floor function

not ceil

[novel herald]

i see

well the counterexample still holds i suppose

[jagged hare]

yes

thanx 👍

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[prisma narwhal]

what is the formula for solving this, if there is any

[marsh grove]

you know the surface area formula for a sphere right

$4 \pi {r}^2$

[grand pond]

Potatomonke

[marsh grove]

You are given the diameter and circumference of the objects

So just find the radius by using the given diameter and circumference, plug them into the formula, and find the difference

$\mathrm{Diameter} = 2r$ and $\mathrm{Circumference} = 2 \pi r$ just for reference

[grand pond]

Potatomonke

[prisma narwhal]

.close

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[cursive oyster]

are all rotational matrices orthogonal? 3x3, 2x2?
thanks

[cursive oyster]

proof would be appreciated (link or if you could do it here :D)

[midnight plank]

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[midnight plank]

@cursive oyster Has your question been resolved?

[sage olive]

any linear transformation when composed into its SVD can be thought of as three successive linear transformations: a rotation, a scaling, and another rotation

transposing the SVD gives you the SVD of the transpose, and while transposing a scalar multiplication doesn't do anything, transposing a rotation results in a rotation in the opposite direction

effectively undoing a rotation

in other words, the transpose of a rotation matrix is exactly its inverse

A^T = A^-1 is exactly the condition for a matrix to be orthogonal

[cursive oyster]

SVD?

[sage olive]

singular value decomposition

[cursive oyster]

ok i'll have to look into that

suppose i have a circle with a normal vector n2 and another with normal vector n1

if i rotate n1 about n1xn2, what exactly happens? does c1 get rotated onto the same place as c2?

[sage olive]

here's a slightly more straightforward proof btw, this will get you to the A^T = A^-1 result which directly defines an orthogonal matrix

[cursive oyster]

after i apply the rotation matrix to all the points on the circle ofc

[cursive oyster]

thank you

[cursive oyster]

.close

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[primal heron]

do you guys think u is a typo for w?

[jagged saffron]

Must be

[primal heron]

fair enough

[uncut cloud]

could also be that v means u and w means v

can you ask whoever gave you those questions?

[primal heron]

stop making it complicated

[primal heron]

nope

T-T

[uncut cloud]

well you can't really be blamed for a typo in the question, so pick one and go with it (or do both if you want to play it safe)

[primal heron]

aight

maybe 2u=w

because double u

🇼

win

imma close this

[last slate]

Is that a wronskian lmao

[primal heron]

can i even

nah just standard vector with random input for matlab/octave

dont mind bout it

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[obsidian hedge]

can i get sm hint on proving these

[obsidian hedge]

i think (b) is implied by (a) so with (a) please

[last slate]

hi man

[lilac nebula]

could be an induction thing

[last slate]

or you can just do the algebra

but more nicer way is to think combinatorially

[fierce thunder]

just expand it by binomial theorem dude

nCr

[obsidian hedge]

yeah. also hi

[obtuse basin]

Would be helpful to know which definition of C you are using

[obsidian hedge]

im trying to do it without biomial theoremvsince im not yet supposed to have learned it

[last slate]

alright basically, consider that you have n+1 balls, and you want to pick r+1 balls

[last slate]

now the number of ways to do that, is basically n+1 C r+1 right?

[grand pond]

SirGareth

[obsidian hedge]

yeah

[obtuse basin]

Of course

[last slate]

now, try to count it a different way:

say you have the first ball,

[obtuse basin]

In that case you just prove it by induction and through a lot of algebra

[last slate]

we can say, the number of ways to choose r+1 balls = no. ways to choose r+1 balls not choosing 1 + no. of ways to choose r balls while 1 is chosen right?

[obsidian hedge]

yes

[last slate]

now, you know the lhs is n+1 C r+1

the RHS is: n C r+1 + n C r

[obsidian hedge]

yeah i get it now

ty

combi is

.close

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[last slate]

combi ❤️

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[wraith oriole]

Can someone check my work

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[lapis elm]

The average of two numbers can be found by adding them and then dividing the result by 2.
The average of 7 and p is −3. Find p by writing and solving an equation.

[lapis elm]

I don't understand how to start^-^

[worthy wing]

Do you know what is average of two numbers?

[lapis elm]

yea

u add them than divide them by how many numbers they are!

right?

[worthy wing]

So if I had numbers x and y, what would be the average?

[lapis elm]

um

x+y/2

[worthy wing]

(x+y)/2

Ok so

[lapis elm]

yea

[worthy wing]

What so lets call average A

So (x+y)/2=A

Agree?

[lapis elm]

yea!

[worthy wing]

Now, read your exercise and tell me what information do you have.

[lapis elm]

u need to find out what p is

[worthy wing]

So here what info u got?

Can you replace x, y or A with any info?

[lapis elm]

7 and p

[worthy wing]

What would be 7 and p?

[lapis elm]

7 would be x

and p would be y?

[worthy wing]

Ok so

(7+p)/2=A

Reqd the exercise again, maybe you can find more information

[lapis elm]

u need to find the average of them- so u divided them by 2?

[worthy wing]

Read out loud this. The average of 7 and p is -3

Do you need to find the average or they already told you the average?

[lapis elm]

u have already been told the averge

[worthy wing]

So in our equation

[worthy wing]

Which letter represents the average?

[lapis elm]

A

[worthy wing]

And the average how much is it?

[lapis elm]

2?

oh wait

no

u divid with 2.

umm

[worthy wing]

Read this again.

[lapis elm]

-3

[worthy wing]

Great

So now write the equation

Using that info

[lapis elm]

7+p/2 -> A = -3

?

[worthy wing]

A bit strange way to write

[worthy wing]

Write the final equation like this

But using the info u have about A

If you know A, just replace it

[lapis elm]

but wait

oh

got it

(7+p)/2=-3

[worthy wing]

Perfect

Now this is the equation to find p, the other number

Do you know how to solve this equation?

[lapis elm]

um not quite.srry.

[worthy wing]

Ok so what is bothering you most in the equation?

[lapis elm]

umm just what i should do first ig..., do i bring all the numbers one side? or do i uhh bring divide or add the numbers??

and what about the p?

[worthy wing]

You want to find p right?

So you want your equation to become something like this

[lapis elm]

yep!

[worthy wing]

p=something

But now p is with other stuff near so we need to isolate p

For now, the most problematic this is the fraction

[lapis elm]

yea

[worthy wing]

We are dividing by 2 and that doesnt allow us to work essily

[lapis elm]

which is basically dividing the numbers

[worthy wing]

So we are gonna remove it

[lapis elm]

yea

[lapis elm]

where do we put it than?

[worthy wing]

By doing the same thing in both sodes lf the equation

I will show you the method with an easy example

[lapis elm]

oh ok

[worthy wing]

Imagine D=G

If we multiply D by 2, do you think 2D=G or not?

[lapis elm]

no?

[worthy wing]

No, to make it equal, we should multiply also G by 2, like this. 2D=2G

Right?

[lapis elm]

yep!

[worthy wing]

Ok so we are gonna use this technique in our equation

If you have one side dividing by 2

What operation is the inverse of division,

[lapis elm]

we need to divide the other side by 2!

[worthy wing]

But remember

We want to get rid off the division

Not adding more divisions

[lapis elm]

oh ok

um

do we do the oppisote and times 2?

[worthy wing]

Yes, but remember you have to do in both sides

Like this

2(7+p)/2=2(-3)

Now, do you know how to simplify in the left side of the equation?

[lapis elm]

14 + p = -6

[worthy wing]

$\frac{2(7+p)}{2} = 2(-3)$

[grand pond]

Samuel

[worthy wing]

Look at this

What happens in the left side?

2 is multipliying (7+p) but (7+p) is also being dividing by 2

[lapis elm]

oh

[worthy wing]

Do you see a way to simplify?

[lapis elm]

14 + 2p/2 = -6

[worthy wing]

Do not distribute the parenthesis

Do like this

$\frac{\cancel{2}(7+p)}{\cancel{2}} = 2(-3)$

[grand pond]

Samuel

[worthy wing]

Do you understand this?

I will explain with objects

Everybinside the parenthesis is one thing

Lets call (7+p) = potato

If we have 2 popatoes and divide them between 2 people

How many potatoes get every person?

[lapis elm]

1

[worthy wing]

And 1 potato was equal to (7+p)

So 2(7+p) divided by 2 has to be 7+p

Do you see now?

[lapis elm]

i get it.

i got it with my dad

the answer is p = 13

[worthy wing]

No

The answer cannot be 13

Because 13+7 is 20 divided by 2 is 10

Not -3

[lapis elm]

-13

[worthy wing]

Yeah that is correct

[lapis elm]

.close

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[last slate]

how to do (C)

[dull path]

For both triangles
What is common?

[last slate]

area

idk how find mn distance

[dull path]

That doesn't matter tho

[last slate]

Wot

[dull path]

Because its same for both triangles

Say mn = x

[last slate]

oh so p is 5/2 ?

[dull path]

Now what is the area of the triangle interms of x ?

[last slate]

UHhhh, idk

[dull path]

A = ½ BH

The base we consider X

Or rather then x lets call it z so to not confuse with the coordinates system

[last slate]

Ok

[dull path]

Do you know the hight of one of the triangles ?

[last slate]

it is 5/2 i think

[dull path]

How are you getting 5/2

[last slate]

Wait let me check

midpoint of cn

[dull path]

How does that give you the hight ?

[last slate]

cuz m is x,0

[dull path]

Can you draw the hight on the diagram?

[last slate]

idk how

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[frozen spire]

A regular A nine-sided polygon, if given: the radius of the inscribed circle is 96 cm

[frozen spire]

Calculate scope and area

I cannot figure out the way to get how much one triangle is

Can anyone help?

[midnight plank]

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[frozen spire]

<@&286206848099549185>

[cobalt sigil]

@frozen spire hey

You @frozen spire there

See we have AB

Triangle ABC is right angled triangle

We can draw 16 triangles like ABC

So angle BAC = (180/16)°

Now you can find CA using trig identities

Area (ABC) = 1/2 ×BC ×CA

Total area of nonagon will be , 16×1/2 ×BC ×CA

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[last slate]

How do I turn fractions into decimals that don’t evenly equal 10 or 100? I was doing khan academy and they only did ones that evenly equal 10 or 100

[slender walrus]

do long division

[last slate]

Could you maybe show an example please?

[slender walrus]

there should vids on khan about it

have you done any long division before?

[dreamy lichen]

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-dividing-decimals/v/long-division-with-decimals

here is with decimals

it's better prolly

[last slate]

So basically do this?

[dreamy lichen]

Yeah, and then you'd do the standard division algorithm you were probably taught

[last slate]

Ohhhhh I thought it was way more complicated than it was. Thanks both of you!

[frozen spire]

Yes??

[last slate]

.close

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[frozen spire]

@cobalt sigil

Can you continue?

[frozen spire]

360/9 and then by /2 no?

[frozen spire]

18 triangles no?

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[frozen spire]

hm

[frozen spire]

what

[midnight plank]

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[novel herald]

what

[midnight plank]

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[weary adder]

Mine is this

[weary adder]

Guyz what will be the answer to this question

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[lime silo]

pinaszőr

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[stable halo]

limit as Beta goes to infinity?

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[weary adder]

Guyz what will be the answer to this question

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[spark nebula]

what's the difference between this ^ and dW

[midnight plank]

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[main current]

Context is everything here

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[spark nebula]

.reopen

[midnight plank]

✅

[spark nebula]

actually it's from thermo dynamics

look

ther's alot of that symbol sometimes it's interpreted as a d

but i think it's different from d

[main current]

Yeah I remember thermo being full of cursed notations that don't actually matter to the problems haha

[spark nebula]

i that it does matter 💀 (i have to understand it )

[main current]

dU is definitely referencing a differential form over a manifold, and δw isn't. But for the average problem, they certainly both mean "difference between"

Well, maybe I can dig a bit more into it. Which book are you using?

[spark nebula]

it's not a book i have the lesson pdf

and our university made it

i can send you the pdf

[main current]

Surely your class has a book though?

But yeah I'll take a look at the pdf if that's cool with you

[spark nebula]

i don't know they give us lessons that's all, in papers and as a pdf file

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[iron zephyr]

Hey guys, my teacher used AM-GM inequility to say the following:

[iron zephyr]

I can't really understand what is happening here

he basically did it to find a smaller denominator for the fraction at the top

[tribal temple]

Using $\frac{a + b}2 \geq \sqrt{ab}$ but with $a = 1$ and $b = n^2$, then rearranging?

[grand pond]

@tribal temple

[iron zephyr]

ohhh its the AM-GM inequlity for 1 and n^2

then he multiplied by 2

okay i did not see it at all lol

[tribal temple]

Yep yep

[tiny drum]

that's a plus sign?

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[prisma narwhal]

does anyone know how to do these, even one would help

[slender zenith]

ye u gotta find the apothem

for question 2

[midnight plank]

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[prisma narwhal]

whats the apothem and how do I find it

[prisma narwhal]

<@&286206848099549185>

[ripe nova]

D

[prisma narwhal]

?

<@&286206848099549185>

[midnight plank]

@prisma narwhal Has your question been resolved?

[fickle oriole]

@prisma narwhal

just use the equation

a=.5ap

where a is the apothem

and p is the perimeter of the polygon

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[last slate]

I’m so confused on similar triangles

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[last slate]

.reopen

[midnight plank]

✅

[last slate]

<@&286206848099549185>

[midnight plank]

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[midnight plank]

@last slate Has your question been resolved?

[viral dagger]

@last slate which question?

ima go for the unanswered one then, for d, you can say that $$\frac{x^2+16}{4}=\frac{(4+9)^2}{x^2+16}$$

[grand pond]

Skill_Issue

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[last slate]

58th

[lavish venture]

what have you tried

this should scream mean value theorem to you

[last slate]

yes but i am not getting what to do

[lavish venture]

well what does the MVT say

[last slate]

it just says what it says

[lavish venture]

🤔

[last slate]

finite derivative must exist in (a,b) given that function is continuous and diff

For some c

[lavish venture]

well it says that if a function is differentiable on the open interval (a,b) and continuous in the closed interval [a,b] then there exists some c in the interval such that f’(c)=average rate of change over that interval

so what’s the average rate of change

[last slate]

Or chord joining f(a) and f(b) must have same slope as tangent drawn to curve at c inn (a,b)

[lavish venture]

yes

so

what is that slope

[last slate]

Slope of secant

[lavish venture]

mhm

[last slate]

Derivative

[lavish venture]

which is what mathematically

no

derivative is slope of tangent line

f(b)-…

[last slate]

oh you mean I should write the lmvt expression for f in (a,b) but what do I do about the (a^2 + b^2 + ab) I get their hanging

How do i express it in terms of c

[lavish venture]

well

the average rate of change

is

(f(b)-f(a))/(b-a) yes

[last slate]

Yes

[lavish venture]

so you have f(b) and f(a)

[last slate]

Yeah

How do I open one of these thingys I forget

[lavish venture]

so what would f’(c)=

[lavish venture]

go to the unused help channels

[last slate]

Go to help

thank you

And type something

[last slate]

This would equal that

Which you wrote before

The average rate of change

[lavish venture]

mhm but with numbers

[last slate]

For some c

[lavish venture]

because we know

f(b)

and f(a)

[last slate]

4/b-a

[lavish venture]

so just put that in for f’(c)

[last slate]

yeah

Then

[lavish venture]

you get (b^3-a^3)(4/(b-a))

[last slate]

Right

[lavish venture]

you should notice that difference of two cubes

which can be factored

[last slate]

Yeah

[lavish venture]

do you remember how

[last slate]

I got until here but then went blank

[lavish venture]

(b-a)(b^2+ab+a^2)

[last slate]

yes

[lavish venture]

so the b-a cancels

[last slate]

yes

now ??

[lavish venture]

ok so

we have

4(b^2+ab+a^2)

[last slate]

Right

[lavish venture]

they want it in terms of c?

[last slate]

Yeah look at the options

lol

[lavish venture]

hmm

[keen hill]

use the form (a^2+ab+b^2)/k = c^2 where k is some integer and solve for k

[last slate]

huh

[last slate]

Solve for k how

[keen hill]

all the answers are multiples of c^2

so you can set your original equation

4(b^2+ab+a^2)= kc^2

[last slate]

I think they want us to apply lmvt for some different function which already includes c^2

[keen hill]

where k is some constant

[last slate]

nice

yeah it's good for exams but that's not how those mcqs are designed we must get a cancer even if we didn't use the options

in terms of c

Answer*

Funny autocorrect

@lavish venture hey is this enough math to start integral calculus

Or I should know some more things

[lavish venture]

what else do you know

i’ve never seen this formula before tbh

what book is this?

[last slate]

I did monotonicity minima maxima rolles theorem lmvt cauchys mean value theorem

[last slate]

It's an exam preparation book used in my country not a famous one

[last slate]

Tangent and normals

[lavish venture]

ahh that makes more sense

[last slate]

Curve sketching

[lavish venture]

you did inverse functions?

all the derivatives obviously

[last slate]

Yeah I did inverse periodic and composite functions

[lavish venture]

exponentials logarithms trig functions inverse trig functions etc

all the derivative rules

[last slate]

But I didn't do a chapter called matrices and determinants it's pretty big I started calculus before that

[last slate]

Yeah

And functional equations

[lavish venture]

related rates?

optimization?

[last slate]

Yeah but yet to practice problems on those

Optimization

[lavish venture]

what country are you from if you don’t mind me asking

[last slate]

India

[lavish venture]

ahh so is this like JEE prep

[last slate]

Yes but I still don't wanna miss anything which is not included in jee either because like next year after jee I will directly start learning multivariable calc

So I just wanna make sure I know just enough stuff before that

[lavish venture]

integration shouldn’t be challenging so long as you know your derivatives

[last slate]

Because after jee I would have plenty of time to just devote it to math and not other subjects

[lavish venture]

i enjoyed integration more

more of a puzzle

[lavish venture]

how many other subjects are there

chem

physics

bio?

[last slate]

Chemistry and physics yes but there's alot in it like physical organic and inorganic chemistry

Thickbooks for each

[lavish venture]

organic!!

oof

[last slate]

And physics in itself is huge

[lavish venture]

man to high school students is crazy

[last slate]

No it's an engineering entrance exam so no bio

[lavish venture]

ahh right

india is nuts

[last slate]

Yes but we have pretty experienced chemistry teachers here

[lavish venture]

you should see american standardized tests

lol

[keen hill]

its a joke!

[last slate]

Yes literally nuts

[lavish venture]

if you saw the sat math section

💀

i’ve seen JEE exams

ridiculous

[keen hill]

the standardized tests are formalities if you actually take your education seriously

[last slate]

why

[keen hill]

(in america)

[last slate]

Why is it that easy

[lavish venture]

🤷🏼‍♂️

[last slate]

Do you guys not require extreme problem solving skills in unis

[lavish venture]

americans are stupid

[keen hill]

this is just a guess and check method

oops

[keen hill]

i meant to reply to this

[last slate]

But you guys have best universities and best facilities

India dosent have shit

[keen hill]

there is a large gradient in the population

[last slate]

Literally research is 0 here education is a joke here

[lavish venture]

yea ik it doesn’t make much sense when thinking of it at first

[keen hill]

it isn't the most difficult to get into any university

but for the best of the best

[lavish venture]

american universities have a lot of funding

[lavish venture]

this as well

[keen hill]

it's more difficult

[last slate]

You mean if I were in USA I would easily get into Harvard or mit

[keen hill]

not neccesarily

[lavish venture]

well

there’s a lot more than just testing

[keen hill]

because our admissions don't just care about academics

[lavish venture]

yup

all about extracurriculars

[keen hill]

a really really really big part of it is extracurriculars

[lavish venture]

they do test optional nowadays lol

unreal

[last slate]

Wtf why would they give 2 fucks about art or sport extracurriculars if I wanted to major in theoretical physics

[keen hill]

research experience is good, participation in clubs that are relevant, competition math, volunteer hours

[lavish venture]

they want this

they like leadership

and just getting involved

[last slate]

Wtf

[keen hill]

for theoretical physics they'd want to probably see early participation in higher level physics like college classes

[lavish venture]

they want the next bill gates

[last slate]

Why

[keen hill]

and maybe physics olympiad

[lavish venture]

the next president

[keen hill]

maybe participation in some engineering clubs

or leading your own

[last slate]

Why not next stephen hawking or Oppenheimer

[keen hill]

and research is a massive +

[last slate]

Why bills gates

[lavish venture]

because bill gates is rich and they want notable rich alumni

[keen hill]

MIT and caltech probably want the next hawking or oppenheimer more

oh and notably your grades are a baseline

[last slate]

Lmao but what does education have to do with riches

[keen hill]

you need to have good enough grades

[lavish venture]

funding!!

[keen hill]

but grade inflation is rampant here

thats what we say but

in reality

they want that because they like having well rounded students

[last slate]

Here grades don't decide anything if you get a 75% in your high-school graduate test and you Crack a competitive like jee you're just well off compared to someone who got 90% on graduate test

Because 90% guy won't get any good uni

[keen hill]

students who demonstrate grit and adaptability

[lavish venture]

grades are just the bare minimum

[keen hill]

^

[last slate]

Unis only care for competitive

[lavish venture]

being valedictorian guarantees you nothing

[keen hill]

generally for competitive admissions to test-required schools

you do want to look for an almost perfect score

[last slate]

So should I move to America or Europe after undergrad lol I don't see a point staying here for higher education as it's a joke

[keen hill]

like 1520+/1600

[lavish venture]

yea

[lavish venture]

you should

don’t most indian kids do that

[last slate]

only rich ones

[keen hill]

if you can afford the living costs

yea

[last slate]

And some poor ones who get scholarship

[lavish venture]

a lot come even for undergrad

[last slate]

Nah I can't afford undergrad it's too expensive

Only rich people do undergrad there

[lavish venture]

if you get a scholarship

[last slate]

I have some friends who will move right after jee

[keen hill]

did you apply to any american schools?

[last slate]

no why would i

[lavish venture]

well he didn’t take the JEE yet

[keen hill]

oh thats true

[last slate]

It's unaffordable

[lavish venture]

so i’d assume he’s like 16

[keen hill]

i mean with aid

[last slate]

Turning 17 in 3 days

[keen hill]

that is understandable though

[last slate]

No aid programs for undergrads

[lavish venture]

depends on your family income

[keen hill]

there are plenty

well

not all schools do it

but if you shoot for some of the prestigious ones

there are plenty

for international students

[last slate]

Yeah that's the point it's not less or more

lol

[lavish venture]

you’re right in the middle?

[last slate]

upper middle

[lavish venture]

that’s unfortunate for college costs

[last slate]

yes

[keen hill]

truly

[last slate]

Are you guys math grads

[keen hill]

nope!

[last slate]

then

[lavish venture]

i’m a senior in high school

[keen hill]

im about to graduate from high school, i just like studying math on my own and in college

[last slate]

Only if I had much time as you guys I could do the same

Lol

[keen hill]

indeed!

[lavish venture]

yea the most work i had this year was just aps

i took 6

self studied 2

[keen hill]

i took on a heavier load this year so i was a little swamped

[last slate]

What's aps

[keen hill]

they're our advanced courses

college level

which are not insane honestly

[lavish venture]

advance placement program

you take courses for college credit

while in high school

[last slate]

Nice do you guys have complex numbers

In school

[keen hill]

nope!

[lavish venture]

no

[last slate]

Wtf

[keen hill]

i am taking it next semester though

[lavish venture]

barely

[last slate]

It's my favorite chapter until now

[keen hill]

wait

hold on

ohhh

yes

we do have complex numbers

i thought you were talking about complex analysis

[last slate]

Not like the complex number geometry and root analysis de movire and all those stiff

Stuff

[lavish venture]

no

complex numbers ended with i^4=1

💀

[last slate]

💀

[keen hill]

and complex roots to polynomials

[last slate]

That was first 5 minutes of cn class which lasted for 2 weeks and 6 days

[keen hill]

yup

[last slate]

lol

[lavish venture]

yup

america is quite terrible

especially if you don’t go to a private school

[keen hill]

my teacher did cover de Moivre's but honestly

when we did

I was checked out

2 years ago

or 3

[last slate]

lol

[keen hill]

in precal

i only really got into math a year or so ago

[last slate]

What's precal

Limits?

[lavish venture]

precalculus

[keen hill]

its like

algebra and trig

and brief coverage of limits

[last slate]

How is that calculus

[keen hill]

and matrices

[last slate]

Okay

[keen hill]

pre-calculus

so taught before

its generally just a fundamentals class for calculus

thats where my teacher covered complex numbers too

[keen hill]

this in theory

should have all been covered

[last slate]

This is precal for me in that sense

[keen hill]

in precalculus

though A LOT of cirriculums leave it out now

[last slate]

They leave out alot of beauty

Then

[lavish venture]

yea that looks about right

[keen hill]

yes this is indeed precalculus

though many teachers don't think students are ready for alot of the vocabulary

[last slate]

Hmm they covered it as the first chapter in jee

[keen hill]

so they're really dumbed down in how they're referred too

[last slate]

Do you guys had analytic geometry

[lavish venture]

that’s uni

[last slate]

Indepth analysis of 2D curves

[keen hill]

that's with calculus for me

yes

[last slate]

I had that last year

It was fun aswell

[lavish venture]

what calc class did you take

not AP?

[keen hill]

I took it at a college