help-23

[lean otter]

yup, it's not an inderminate value anymore, you can substitute x=pi/2

[prisma acorn]

doesn't it only work for

0/0

and

inf/inf?

[lean otter]

yes

it's 0/0 here

[prisma acorn]

right

okay thank you so much

.close

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[fleet wadi]

hi, why is this wrong? the answer should be ln(4)

[mortal arrow]

Uhhh

Mistake between step 2 and 3

[sacred wagon]

ln(e^2x-e^x) ≠ ln(e^2x)-ln(e^x)

hint is rewrite e^2x in a different form

[mortal arrow]

Instead use substitution to solve this equation

[sacred wagon]

and substitute

[mortal arrow]

Oops

[fleet wadi]

oh I had done it with substitution and got 4, I was just confused as to why the other method didnt work

[fleet wadi]

this is true ! I got confused

[sacred wagon]

oh ln(e^2x - e^x) ≠ ln(e^2x)-ln(e^x)

you can't split it up

[fleet wadi]

thank you:)

[sacred wagon]

yeeeeeeee

np

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[mint prism]

would it be fair to assume that the particle reaches max height at 3.5 seconds?

[mint prism]

.close

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[desert pasture]

If $x= \alpha$ intersects $xy^2=(x+y)^2$ orthogonally, find $\alpha$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

So I started by raising both sides to the power half, to obtain

$\sqrt{x}=\frac{x}{y}+1$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

On differentiating both sides

$\frac{1}{2\sqrt{x}}=\frac{\left(y-\frac{xdyx}{dx}\right)}{y^2}$

or

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

$\frac{dy}{dx}=\frac{y}{x}-\frac{y^2}{x^{\frac{3}{2}}}$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

I also found $y$ when $x= \alpha$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

which is

[summer wigeon]

you dont even need implicit differentiation here

xy^2=x^2+2xy+y^2

[desert pasture]

$y=\frac{\alpha}{\sqrt{\alpha}-1}$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[summer wigeon]

find where derivative is 0

[desert pasture]

that would still require implict differentiation, no?

[desert pasture]

why 0?

I have to find the point at which $x= \alpha$ is orthogonal

[flat frigate]

ƒ(Why am. I here)=I don't Know

[summer wigeon]

if you bring y^2 to the other side then you can facotr it out

then you can devide by x-1

then square root both sides

eh but then there is a square root so to be safe maybe we should stick with implicit differenciation

[vapid pebble]

You still have a y left over

You will still need implicut

[summer wigeon]

oh yeah lol

didn't even notice

[desert pasture]

just that this feels a bit too long

The steps after this are a mess IMO

[vapid pebble]

Stuff I did 4 years ago

Rip

[summer wigeon]

dydx needs to be 0

[desert pasture]

why though

That would mean it's an inflection point

oo

got it

yeah, makes sense

so 2x=y , when dy/dx=0

[summer wigeon]

you'll have some system of equations i think

so look at all x,y that works for 2x+2y-y^2=0 and the original equation

xy^2=(x+y)^2

expand right

x2+2xy+y^2

wait ill do it out seperatley and show you steps

[desert pasture]

hmm

now I got $2x=y$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

so $2\alpha= \frac{\alpha}{\sqrt{\alpha}-1}$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

oh

so $\alpha=4$

right

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

that checks out

thanks a lot!

[summer wigeon]

yeah

[summer wigeon]

yes**

[desert pasture]

thanks a lot!

.close

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[loud osprey]

How do i do this

[safe radish]

@loud osprey Has your question been resolved?

[thick turret]

Express as summation

let me figure out this syntax stuff

$\sum{i=1}{5}$

thats wrong

hmm

[loud osprey]

as a summation i got

[loud osprey]

1/5 sum (k = 1) -> 5 (ln(2 + k/5))

[thick turret]

yea yea

[loud osprey]

what should i do next

[thick turret]

okay Its starting to come back to me

this is the approximation

and we basically have n right now being 5

[loud osprey]

so b = 5 ?

[thick turret]

thats what I'm not sure about

(b-a)/n should be delta x

[loud osprey]

theres no b-a/m tho

[thick turret]

this should be all the information needed to solve this but im rusty

I don't know how to get the bounds of integration

x_(n+1) = b might help

Maybe 1/5 is our delta x

sum (k = 1) -> 5 { (ln(2 + k/5)) * 1/5 }

[loud osprey]

1/5 is the width?

yeah

[thick turret]

do you agree x_1 = ln(2+1/5)

[loud osprey]

what does x_1 mean?

[thick turret]

the function with k = 1

[loud osprey]

oh yes

[thick turret]

i think we might be able to connect there

becuase x_i = a + (i-1)deltaX

x_1 = a + (1-1)deltaX

ln (2+1/5) = a

but that doesnt work

damn

would it be wrong to use the answer choices and see if they can be expressed as the sum? or do you think thats the wrong order of thinking?

[loud osprey]

i mean

that kinda defeats the purpose

cause im practicing this for the ap exam

so i wanna like learn to do it

yfm

[thick turret]

i see

oooooooh

i think i get it

I think a is 2

[loud osprey]

how

can u explain it pls

oh is it cause a = 2 and ln( 2 + k/n)

waht would i upper bound be tho

[thick turret]

i think we use deltaX = b-a/n to find

bc we know deltaX, b, and n

[loud osprey]

But how would that work

n = 1/5 ?

so b - 2/1/5 ?

[thick turret]

im getting b as 6 so im still doing something wrong as well

oh i made a type

i got b as 3

[loud osprey]

how?

[loud osprey]

wait whys it 1/5 = b-2/5

[loud osprey]

oh

[thick turret]

deltaX is 1/5

i think

I could literally be wrong on all of this 🤣

[loud osprey]

no thats right

i checked the answer bounds are 3 and 2

[thick turret]

so the function should just be lnx

[loud osprey]

ye

[thick turret]

Okay I get it now, lets do another

😄

do u have another 1

[loud osprey]

lemme find one

Wanna try this

[loud osprey]

btw whered u get this reference

[thick turret]

okay whats dx

https://ur.khanacademy.org/math/calculus-2/cs2-integrals-review/cs2-defining-integrals-with-riemann-sums/a/definite-integral-as-the-limit-of-a-riemann-sum

[loud osprey]

2/9

[thick turret]

now we need to think of the summation happening

[loud osprey]

would it be smt along these lines

[thick turret]

yea but I would think of the 2/9 inside the summation just bc it helps see the riemann summ defintion a bit better, but yea thats what i did

[loud osprey]

ok so change in x is 2/9

and a = 4

and the function is 1/x

wait how do i find the function?

[thick turret]

if a = 4 b would be 6 and thats not an option

[loud osprey]

Would i add the 3 + 1 ?

or would a just be 3?

[thick turret]

i would want to add the 1 and 3

[loud osprey]

but then wouldnt that make a = 4?

if we do add the

[thick turret]

the problem is that a cannot be 4 because that isnt a choice

like

this is what I got

[loud osprey]

oh so is the + 1 part just part of the normal function

[thick turret]

i assumed that

[loud osprey]

Wait actually how do i get 9 on top for this summation

i just assumed it was 9 cause 2/9

[thick turret]

I see two ways of looking at it

the first is thinking of the summantion, 2, 4, 6, ... 18. is 2n, 9 times.

[loud osprey]

yeah

[thick turret]

I don't know if you can always assume that the denominator of deltaX is always going to be n.

But for every sitution we have seen so far its been yes.

can you find an example where that isnt the case? maybe look for a problem with an ambigous delta X

[loud osprey]

This one is kinda ambigous

[thick turret]

for delta X?

[loud osprey]

Kinda

[thick turret]

my immediate thought is deltaX is 1/100 and n is 100

[loud osprey]

but its still 1 -> 100

yeah

i think it might be denominator based

cause maybe that represents how many blocks u rectagnesl use?

[thick turret]

well the whole reason for using deltaX = (b-a)/n is to get uniform widths

bc its literally the distance divided by the amount of blocks

so yea

what did you get for this one

[loud osprey]

Gimme a sec

[thick turret]

im pretty confident on my answer

[loud osprey]

i got this

[thick turret]

same

[loud osprey]

alr

i think im getting the hang of this

thanks

[safe radish]

@loud osprey Has your question been resolved?

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[pine owl]

Hello! Pls help me how to prove this statement: From the outlying pentagon, an inner one is reduced by ϕ^2, and finally the inmost pentagon is reduced by ϕ^4 as compared to the outer one.

[pine owl]

Also, if possible, can u please provide another method to verify your answers/explanation? thank you !

I absolutely have no idea abt this but if side lengths are needed, let's assume that the side lengths are 1 (outer pentagon)

[hazy elbow]

find this angle

[pine owl]

that angle is 36 degrees

[hazy elbow]

yes

[spice wing]

Yeah easy one

[hazy elbow]

now what about the angles adjacent to uit

[spice wing]

Bro pentagon

you see symetry

[pine owl]

72

[spice wing]

Each pentagon angle is 144

[hazy elbow]

no

[spice wing]

?

Oh sry

[pine owl]

wont that be 108?

[spice wing]

5*180-360

/5

[hazy elbow]

well each angle of a regular pentagon is equal to 108 degrees

[spice wing]

Yeah 108

[hazy elbow]

this angle?

[spice wing]

Whats the problem then ?

[pine owl]

still 36 i think

[spice wing]

108 - 36 /2

[hazy elbow]

36 is correct

you said 72 earlier

[pine owl]

oh mb

[hazy elbow]

now are you aware of the sine rule?

[pine owl]

yupp

but kinda forgot it

[hazy elbow]

wait, the question talks about area or the sides?

[pine owl]

honestly, I'm not sure what it's talking about either. But here's the source of where I got it: http://www.hypermaths.org/cropcircles/chapter5/

[hazy elbow]

I can't make much of it eithwe

probably it asks to prove that side of inner pentagon/ side of outer pentagon is phi^2

anyways, let's solve for the side

[pine owl]

alralrr

[hazy elbow]

using sine rule

assuming BC to be 'x'

can you calculate the length AB using this

[safe radish]

@pine owl Has your question been resolved?

[pine owl]

oh wait mb im solving it

wait I have a question

oh ok nvm actually mb

[pine owl]

am I on the right track? sorry if I was late, my network delayed for a short while

[pine owl]

im honestly not sure if im doing anything right

<@&286206848099549185>

[safe radish]

@pine owl Has your question been resolved?

[safe radish]

@pine owl Has your question been resolved?

[safe radish]

@pine owl Has your question been resolved?

[pine owl]

y'all 😭

[winter whale]

I feel for you

[safe radish]

@pine owl Has your question been resolved?

[pine owl]

https://tenor.com/view/staring-robert-e-fuller-intense-stare-look-into-your-eyes-look-into-your-soul-gif-23838470

[safe radish]

@pine owl Has your question been resolved?

[safe radish]

@pine owl Has your question been resolved?

[fresh rapids]

What is Sih?

And in case you are referring to Sin, I think you are wrong.

[pine owl]

I may have figured out what it's talking about. It might be referring to the diagonals of the pentagon (which is the pentagram) since we can find the golden ratio there. See that long red line in the first figure? Dividing that line to any of the equal sides of the pentagon will result to the golden ratio (1.618...)

Now what I'm trying to figure out is what will be its value now as the iteration of pentagons continues, considering that the outermost pentagon contains a proportion of 1.618. But let's try figuring out the first inner pentagon tho. I do have some conjectures in mind, can anyone help me try to verify/confirm them? I'm not really sure how to. I have lotta doubts abt my answers lol so please 🥺 🫶

2.618 is 1.618 squared

[pine owl]

here're the figs

[pine owl]

https://www.youtube.com/watch?v=Em90GYNCsK8&t=1s

[pine owl]

I have also discovered suspiciously interesting shi on my own that might have sum connection to this

[pine owl]

there's a counterexample for this though. The result will be different if the side lengths are not an integer

plz help this pitiful lil math idiot here 🥺🥺💟💗

[left gyro]

yes this is correct

[left gyro]

this doesnt make any sense

,align\frac1{\sin108}&=\frac{AB}{\sin36}
\\frac1{\sin108}\cdot\sin36&=\frac{AB}{\sin36}\cdot\sin36
\\frac{\sin36}{\sin108}&=AB

[flat frigate]

mtt

[left gyro]

this is what it looks like to correctly multiply and simplify fractions

compare that to what youre doing and figure out what you did wrong

[left gyro]

"from the outlying pentagon, an inner one is reduced by ϕ²" means "the middle pentagon's sides are ϕ² times smaller than the outermost pentagon"

usually when people talk about resizing or reducing, they are talking about "similar shapes"
if you dont know that "similar" has a specific math-related meaning you should google "similar triangles" and learn what they are
when working with similar shapes, "reduced by #" means "the sides are # times smaller" and also means "the sides are 1/# times the original"

so "from the outlying pentagon, an inner one is reduced by ϕ²" means "the middle pentagon's sides are ϕ² times smaller than the outermost pentagon"
in other words, "if the outermost pentagon has sides 1, then the middle pentagon has sides 1/ϕ²"
in other words, "if the outermost pentagon has sides ϕ², then the middle pentagon has sides 1"

similarly "the innermost pentagon is reduced by ϕ⁴ as compared to the outer one" means "the innermost pentagon's sides are ϕ⁴ times smaller than the outermost pentagon"

[left gyro]

by leaving similar shapes are, whatever youre saying here to "figure out what its talking about" is off track, do not be distracted by other features of the pentagon when reading the english

[left gyro]

same with this

[left gyro]

and this

[left gyro]

with the english out of the way, you shouldnt be attempting to brainstorm further methods or ideas if you dont know how to prove the easier, original statement of figuring out that the middle pentagon has sides 1/ϕ² given the outer pentagon has sides 1
leave that for next time, not this time

[left gyro]

this doesnt help at all
proportions and "this side is X times smaller than this other side" only consider how relatively larger/smaller the sides are, not how big the sides currently are
what youre seeing right now is "ϕ/ϕ² = 1/ϕ = ϕ - 1" and has nothing to do with the problem

[left gyro]

ruler-and-compass constructions will not help you here
this video is walking you through how to draw a pentagon given that you can only draw circles and straight lines
youre not doing that, youre figuring out the side of the middle pentagon given the side of the outer pentagon
ruler-and-compass constructions are notoriously difficult to convert into side lengths and angles

[left gyro]

again youre venturing into unfamiliar territory here
again this is pretty interesting but the way youre describing it is dead wrong

[left gyro]

now with all of those distractions out of the way, we can focus on actually solving the problem
youve figured out so far that AB = sin(36°) / sin(108°)
now since sin(108°) = sin(72°), that means AB = sin(36°) / sin(72°)

theres an argument to make that uses the figures, similar triangles, and the unit circle to figure out that AB = φ⁻¹
its a bit involved, so for now youll have to take it as a given

you can then use sine rule on this triangle to figure out the side of the middle pentagon

you know both long sides are φ⁻¹
use this to figure out a way to calculate the middle side of the pentagon
you should get a number that matches up with φ⁻²

with that down, youll prove how an iteration (going from outermost to middle) shrinks the pentagon down to φ⁻² size,
outermost to innermost = outermost to middle to innermost = two iterations = shrinking twice = φ⁻² * φ⁻² = φ⁻⁴ size
so going from outermost to innermost is φ⁻⁴ just from doing two iterations of shrinking by φ⁻²

[left gyro]

right now this is what youre focusing on
once you figure out this step, the problem is finished - then I show how to do your figure way properly

[pine owl]

Zamn I…

Thanks for making everything clear to me 😭🙏

[pine owl]

Mbmb. Honestly, I wasn’t in the best state of mind when I tried to solve the trigo problem. During that day, we were preparing for a presentation tmr, which has smth to do w/this. And yeah it was rlly stressful for me that it felt like my frontal lobe had a power outage. Given that there would also be a panel of judges and the fact that cooperation was the main area where my group fell short, it added more insult to the injury. Wish I could remove their names from the project 👊

yeahh anyway

[pine owl]

ohhh so the x is out??

alrr that would be 0.61803398….

[pine owl]

thank u mannn I owe u sm 🙏😭😭 I'll give u a shoutout in our study's appendices LOLLLL

[vagrant glen]

.close

[pine owl]

??? Need anything ?

[karmic hedge]

you can find the green pentagon's sidelength over the big pentagon's side length
use ptolemys and similar triangles

[karmic hedge]

ghost ping?

[eternal carbon]

ping of the ghost variety!

[pine owl]

Heyyy soo I've got all the dots connected alr loll and our study's alr completed, thank you for everyone who helped!!

.close

[safe radish]

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[raven heart]

one day this channel will actually close

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[trail otter]

what is derivative of f(x,y)=(x^5+y^5)^1/5 in the (x,y)=(0,0)?

[safe radish]

@trail otter Has your question been resolved?

[foggy acorn]

do you know how to take the partial derivatives

and does it want the gradient

or magnitude

[trail otter]

well first i derive it with respect to x?

that is x^4/(x^5+y^5)^4/5

and now i plug in (0,y)? @foggy acorn

[foggy acorn]

you think like y is constant and then do it respect to x

lemme check it.

[trail otter]

yes i did it like this

[foggy acorn]

it should be correct im still checking it tho

im so lazy

seems correct

[trail otter]

yes

[foggy acorn]

but ^-4/5

bot ^4/5

[trail otter]

and now?

[foggy acorn]

than do it for y aswell

there is your partial derivatives

[trail otter]

yes itl be the same with y in numerator

[foggy acorn]

yep

[trail otter]

but i need to do it in point (0,0)

[foggy acorn]

what does it originally asks for

[foggy acorn]

plug 0

but 0/0?

ooh

[trail otter]

find partial derivatives at the origin for f(x,y)=(x^5+y^5)^1/5

[foggy acorn]

im so confused why it is 0/0

[trail otter]

.close

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[elfin ocean]

can somebody explain to me why the ratio of s to a is equal to the ratio of x to h here? I know it says because they are “similar triangles,” but I don’t see how that applies to this example?

[copper kernel]

Do you see how the triangle with base s and height x is similar to the triangle with base a and height h?

[bleak delta]

descend a line perpendicularly from the top of the prism to its base

Because it's in the middle, will divide into two equal parts

if one side of the square is s

will divide into s/2 and s/2

what you draw from the top of the prism to its base is the height

which is x

and if you pay attention here, a right triangle was formed with lengths s/2, x, and √(x²+s²/4)

If we make a tangent ratio

(s/2)/x is the tangent of that angle

When you draw another prism whose vertex starts from the same place

so like in the figure

[bleak delta]

.

The height you draw towards the base of the larger prism and the height you draw towards the base of the smaller prism overlap each other

so the angle whose tangent we take does not actually change

if we say "a" angle to it, it is still "a" angle because nothing changed in angular

[elfin ocean]

so if i do the tangent ratio for the larger triangle it would be the same?

[bleak delta]

Therefore this ratio is, half of one side of the newly formed square/new height

which is (a/2)/h

so we showed that (s/2)/x = (a/2)/h

sorry

i fixed it

[elfin ocean]

ok because the angles stay the same we are just scaling it kinda

[bleak delta]

yes

exactly

[bleak delta]

and then s/x = a/h

and then s/a = x/h

[elfin ocean]

well what is the side length for one of the cross sections is 2 and the side length of the base was 4

then how would those ratios be the same?

oh wait this is just talking about for the triangle

not the cross sections

[bleak delta]

yes

[elfin ocean]

got it, I understand now

thanks a lot for your help

[bleak delta]

you are welcome

[elfin ocean]

.close

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[cobalt tapir]

when i put vt in quadratic form i get the wrong answer

[cobalt tapir]

can i put vt in quadratic form?

and compute discriminant

[obtuse plover]

for that first equation?

yea why not?

might get a bit messy though

[safe radish]

@cobalt tapir Has your question been resolved?

[cobalt tapir]

i did it but i get a complex answer

[obtuse plover]

show me

thats what i was referring to by "a bit messy" lol

[cobalt tapir]

XI = 50 btw

2XI = 100

[obtuse plover]

$v_t ^2 -2 v_t (50) \cos{\psi} - v_s ^2 + (50)^2 = 0$

this is the equation right

[cobalt tapir]

yup

but i replaced sin with cosine

[obtuse plover]

why?

[obtuse plover]

ok so which one do u wanna use

urs or mine

[cobalt tapir]

Mine

[obtuse plover]

so just this?

[cobalt tapir]

Yeah

[obtuse plover]

ok lets see

so we'd get

$\frac {100 \cos {\psi} \pm \sqrt {10000\cos^2 {\psi} - 4(- v_s ^ 2 + 2500)}}{2}$

bruh ok hold on

[cobalt tapir]

This, no?

,rotate

[obtuse plover]

yea i put that into quadratic formula form

[cobalt tapir]

when i did that i got complex solutions

but the solution is 237...

234,73*

[obtuse plover]

$50 \cos {\psi} \pm 10\sqrt {25\cos^2 {\psi} + 551}$

is there any way to simplify after this @cobalt tapir

like are u given any other values

[cobalt tapir]

vs is 240

[obtuse plover]

oh ok

,calc 240^2

[flat frigate]

Result:

57600

[obtuse plover]

,calc 576-25

[flat frigate]

Result:

551

[safe radish]

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[obtuse plover]

.reopen

[cobalt tapir]

.reopen

[safe radish]

✅

✅

[obtuse plover]

do u know anything else?

[cobalt tapir]

no

thats it

[obtuse plover]

so how did u get a complex solution from here

its not possible

[cobalt tapir]

idk but the answer is still wrong

[obtuse plover]

i have a feeling im missing a lot of context here

[obtuse plover]

why are there two values of cos(psi)

and sin (psi)

and psi Lol

[cobalt tapir]

but we are doing i now

[obtuse plover]

ive never done this sort of stuff with circuits and stuff, but assuming our initial equation was correct, this is the correct simplification.

[cobalt tapir]

cos(x) = sin(x+pi/2) no?

.close

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[neon salmon]

There are two concentric spheres, the inner sphere has radius r = 10 cm and a charge on its
surface of −1 µC, and the outer sphere has a radius of 20 cm and a charge on its surface of +2
µC.
(a) What is the potential at r = 0 cm?

[neon salmon]

would the potential at 0cm be 0 because the electric field would be 0?

[median vigil]

electric field being 0 means the potential is constant, not necessarily that it's 0

[neon salmon]

oh ok

could i just use V = kQ/r then?

[median vigil]

that is the potential caused by the electric field of a sphere, outside that sphere

[neon salmon]

hm

how could i find the voltage then?

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@neon salmon Has your question been resolved?

[neon salmon]

<@&286206848099549185>

[dry pier]

what

[neon salmon]

what

[safe radish]

@neon salmon Has your question been resolved?

[neon salmon]

<@&286206848099549185> pretty please

[neon salmon]

<@&286206848099549185>

@median vigil could you pls help T_T

[median vigil]

if you know that the potential just outside a spherical shell is given by kQ/r, and that the potential is constant inside the shell, then the potential inside the shell must be equal to the potential at the surface

you can also use the superposition principle: the potential at some point is the sum of the potentials due to each object on its own

[neon salmon]

ohh okay

that makes sense tysm

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[gray flame]

Could somone walk me through this

[sharp tiger]

Show your work

Did you draw that triangle

[gray flame]

yes

[thin bridge]

did you do anything else?

[gray flame]

no

im guessing i need sine rule

not rly sure how to go abt it

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[balmy sky]

How do I do this?

[flint pike]

for some integer x, abs(-x)=x and abs(x) = x

all of the options are positive, there are also no options that will give a negative x value

[hollow crest]

The best way is to find the function for each interval

For X>3 every modulus will just vanish

[balmy sky]

that would be too long

[hollow crest]

Actually no

It'll take a few mins at most

[manic dock]

Are you allowed to simply do some brute force method of doing x = 1, x = 2, x = 3, and so forth to see which x gives you the smallest value?

[balmy sky]

nopee

[balmy sky]

thats the point

can't lose time

😅

i found a solution

but can't seem to understand it

[manic dock]

@balmy sky Okay, are you taking calculus?

[balmy sky]

yes

[hollow crest]

Still has to define the function

[manic dock]

So what's the derivative |x| assuming x is positive?

[hollow crest]

1

[balmy sky]

1 or -1

not defined at 0

[manic dock]

(sorry i asked the wrong question... i was thinking of derivatives for some reason)

[hollow crest]

See, for X>3 it'll be 4x

3>X>0 it'll be 2x+6

-1>X>0 is 6

And do like this

[balmy sky]

i know that

[hollow crest]

There is no other way as far as ik

[balmy sky]

but that would take time

there is another way

if you guys could explain it

it would be helpful

[hollow crest]

Hmm

<@&286206848099549185>

[balmy sky]

https://www.youtube.com/watch?v=REL40WGfsZU&list=PLoetsRqdeRZnAjm76z0aZt9XXBCUptjVo&index=3

can you watch the video from

20:29

just 1 minute of it

[hollow crest]

I saw

But I'm not familiar with what he did

[hollow crest]

.

[balmy sky]

i know this method

[balmy sky]

.

i wanna know what he did

[hollow crest]

So what didn't u understand in his method

He's telling mean deviation is minimum abt median

And he found median

But idk how mean deviation will give minimum value

[balmy sky]

yea exactly

[hollow crest]

Hmm try asking your teacher

[balmy sky]

don't have any teacher

😅

i have my entrance exam tomorrow

so i was just doing some past year questions

[granite idol]

https://math.stackexchange.com/q/113270/993372

some complicated explanations

[balmy sky]

ill check

thank you so much

!

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[fleet wadi]

I tried solving this by first separating log(81)

then applied properties and had 6log(2)/6log(16)

change of base, then 6 log16(2) equals to 1/4

multiplied by 6, 6/4, 3/2

3/2 x 4 log(3), and then 6 log(3)

I dont know where is my mistake

[steel marten]

I think it is log(3)?

[fleet wadi]

why is that?

[oak tangle]

there's an extra 6 here

[fleet wadi]

ahh thats true

I was focused on properly changing the base and forgot to divide

is it log(3) then?

[oak tangle]

yes

[fleet wadi]

thanks to the both of you

!solved

[steel marten]

It’s !close

[fleet wadi]

!close

[steel marten]

Wait is it .close

Try this

[fleet wadi]

.close

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[devout shale]

I know the conjugacy classes are the orbits of the conjugation action

so I tried computing those, working on (a) first

but it just seems like way too many cases, so I assume there must be some trick

So I'm not sure how to do this

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[proud plover]

Quick question. Would it be enuf to say that |f(n+1)-f(n)|<=(1/2^n)*|f(1)-1| is cauchy without further statement?

[proud plover]

Oh and of course f(1) is defined and finite

And f is a differentiable function on R to R. The sequence is a(n)=f(a(n-1))

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[sturdy acorn]

How is this function odd pleaseses

[light stone]

what makes a function odd?

[sturdy acorn]

ohh yes f(-x) = -f(x)

here 1-cosx/-x != cosx+1/-x yes?

**cosx-1

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@sturdy acorn Has your question been resolved?

[zinc crown]

Hmm you seem to have applied the function wrong

Notice that

$f(-x) = \frac{1-\cos(-x)}{-x}$

[flat frigate]

Ultimate Chad

[zinc crown]

And because $\cos(-x) = \cos(x)$, do you see how that function becomes odd?

[flat frigate]

Ultimate Chad

[sturdy acorn]

well f(-x) = 1+cos(x)/-x , and -f(x) = cos(x)+1/-x are they same?

**-f(x) = cosx-1/-x ?

[foggy acorn]

you can think of it like cos(x) / x

which is even / odd

= odd

or just plug in -x

[safe radish]

@sturdy acorn Has your question been resolved?

[sturdy acorn]

i was going by definition which says f(-x) = -f(x)

but -f(x) != f(-x) ?

[foggy acorn]

thats the formal sol

[sturdy acorn]

so wouldnit it be neither odd nor even

[foggy acorn]

how tho

it is

f(x) = -f(-x)

sorry for my bad writing.

left is f(x)

right is f(-x)

[sturdy acorn]

then -f(x) is?

hol up its not -f(-x) is it?

[foggy acorn]

its jut f(-x) (right one)

[sturdy acorn]

is -f(x) not = - (1-cosx/x) = -1+cosx/-x

[foggy acorn]

no.

thats for sine

[sturdy acorn]

how?

[sturdy acorn]

so -1-cosx/-x

thats not same still

like we distribute negative right

f(x) = 2x

f(-x) = 2(-x) = -2x

-f(x) = -(2x) = -2x

now thats odd i get it

[foggy acorn]

this is where you make the mistake

[sturdy acorn]

do we not do that?

why

[sturdy acorn]

yes i get that

but what about-f(x)

[foggy acorn]

jsut multiply the denominator

[sturdy acorn]

so f(-x) = -f(x) will not work here?

why -f(-x)

[foggy acorn]

it does work tho

[sturdy acorn]

i just dont understant why we dont distribute the negative over the function

is numerator as a whole a trig function

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[zinc grove]

are they correct?

[hollow crest]

I think first one should be opposite

[zinc grove]

the second one is incorrect idk about the first one

[split ether]

1. The inverse of fog should be g^{-1}of^{-1} ("should" as in "if exists, is")
2. The second equality is true if and only if the domain and codomain of f are the same

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[tribal coral]

how

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[gleaming field]

.open

.close

Dude

[gleaming field]

Im in 12th grade, out of 350 students i placed 5th in my year what is the probability of me getting a grade that offers all colleges if the yearly average of said grade is achieved by top 7% of students?

[foggy acorn]

so

you are in the 1.42th percentile

[gleaming field]

Yeah

I need to corelate it with 7%

I think (1/1.42)7

[hard crest]

you're well within the top 7% of students

at least out of your school

[plucky python]

you're in good shape bro

[gleaming field]

I think its a dud bc individual schools can only predetermine how good you do in fractions of the curriculum

[plucky python]

as long as your year is not terribly worse than previous students at your school, you should be good

[dry pier]

who called helpers?

[gleaming field]

Not here

[dry pier]

k

[gleaming field]

This is actually a textbook question xd

[dry pier]

so what can i help with?

[gleaming field]

Okay so. This message right here

[dry pier]

k alr

[gleaming field]

Im in 1.42 percentile but how to corelate with 7%

[dry pier]

so you are in the top 1.42 percentile

[gleaming field]

Theres a B section of this question but idek what it wants tbh

[dry pier]

what is the yearly average?

[gleaming field]

Uhhh like 70

[dry pier]

k

[gleaming field]

All your "real" grades are determined by endyear entrance exams

Theyre out of 100

Max is 100

[dry pier]

k

so doesn't that just mean you need a 70 or higher?

or is it not that simple

[gleaming field]

Its not a curve to pass

Its a curve with college acceptance rate

[dry pier]

oh

sry i don't understand this stuff im only 13

[gleaming field]

If average was 70 last year and 97.6 went to the best college, it will differ when the average becomes 80 this year

[hard crest]

fyi the helpers ping gets called about 80 times a day

[gleaming field]

Bruh

[dry pier]

it will be smth like 98-99 ish right?

[dry pier]

k

[gleaming field]

Yeah spot on

Maybe i should evaluate average yearly acceptance grades instead of my school grade

[dry pier]

id say about 2-3.5% without knowing the yearly average

[dry pier]

k

[gleaming field]

Thanks for the help this question isnt included for the tests i just wanted to know where im at compared to other students

.close

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[dry pier]

yw

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[idle current]

about this problem

[idle current]

do I use this formula?

[hard crest]

it's way simpler

it's just counting

[idle current]

but am I right sir?

[hard crest]

that formula looks like it's got something to do with standard deviation

which isn't really relevant here

[idle current]

or this dormula

[hard crest]

i'm not actually sure what alpha is for here

you have all of the scores

you can easily check whether 10% of them scored below 20

[obtuse plover]

Ur supposed to do a hypothesis test xd

Alpha is ur significance level

[hard crest]

(as a side note, visually it looks incredibly obvious that way more than 10% of students scored below 20 lol)

[idle current]

this is similar to this problem right?

[obtuse plover]

Wdym

[idle current]

rhis

[idle current]

which of this 2 formulas do I apply on the problem

stats sucks

;((

[obtuse plover]

Probably the first one

Cuz the teacher is saying at most 10%

So it’s proportions

[idle current]

how do I get the value of p hat

[obtuse plover]

Find the sample proportion of students that scored under 20

U have the sample dataset

[idle current]

so I dind the mean?

rawdatascores/37?

[obtuse plover]

That’s not what I said lol

[obtuse plover]

Read this

Find the percentage of ppl that scored under 20

[idle current]

I counted 29 students who scored less thn 20

[idle current]

So 29 is the value of p hat?

[obtuse plover]

Is that the percentage of people that scored under 20?

[idle current]

h

78 percent?

[obtuse plover]

,calc 29/37

[flat frigate]

Result:

0.78378378378378

[obtuse plover]

yea there u go

783/999

[idle current]

so thats the value of the phat?

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[lean otter]

any ideas ?

[desert pasture]

consider the right hand limit and left hand limit

[lean otter]

both sides are same

[desert pasture]

no

[lean otter]

how to factor
|x| from x^3 - |x| ?

[desert pasture]

the RHL of the numerator

for x~0, |x^3-x|= x-x^3

[lean otter]

|x^3 -x | = |x| (|x^2 -1 |) |x| gonna cancelout and |x^2-1| as x--> 0 is x^2-1

[desert pasture]

yes

[lean otter]

thats means it's two sides ?

or what

[desert pasture]

yes

[desert pasture]

I think that's right

[lean otter]

but why wolfram alpha says -1

[desert pasture]

let me work it out myself

I think wolfram is wrong

ask helpers to confirm

[lean otter]

<@&286206848099549185>

[noble ember]

what

[noble ember]

.

lim x → 0 0

[lean otter]

0 ?

[noble ember]

idk

I'm from Peru and they didn't teach me that, I did it by watching YouTube videos

i only know sumatory and integrals

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[carmine granite]

Can somebody help me

[lean otter]

ye

[light gull]

Depends

[carmine granite]

so i have minecraft project where we dig highways. rn we have highway system that is 50k to each minecraft direction and every new road is 5k apart. how long will the highway be if we did it but in 125k? so every road is apart 5k still.
here is map https://highways2b2t.net/map.html where u can see coordinates of them and photo of the highway system we have

weird question xd but idk how to calculate

[carmine granite]

ignore the diagonal roads etc

<@&286206848099549185>

[safe radish]

@carmine granite Has your question been resolved?

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[strong canopy]

hi, I need help with this question
"Factorise the equasion 8ax²-6axy-5ay²"
I know to take the a out to make it
"a(8x²-6xy-5y²)"
but I don't know how to put it into two brackets with this setup
the markscheme says that this is the answer, but I don't know how to get to it (past paper)

[strong canopy]

I thought you could only do that with a squred number then x then a normal number

in that format

I figured it out

I just took the y out

and added it at the end

.close

[safe radish]

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[safe radish]

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• Show your work, and if possible, explain where you are stuck.
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[frail dome]

@light crypt

[frail dome]

I'm so sorry

but remember q42?

this one

[lean otter]

can you post q42

[frail dome]

here

[frail dome]

Ofc!

here ^

[lean otter]

what about it

[frail dome]

let me bring the question

[lean otter]

what do you have to do here

[frail dome]

yea just a sec

[lean otter]

take your time

[frail dome]

It's asking about the arrangement

[lean otter]

i would say a is f(x) b is f'(x) and c is f''(x)

[frail dome]

how did u know

[lean otter]

but i am not sure

[frail dome]

can u pls explain to me

[frail dome]

okay

[lean otter]

i dont know if its correct

[frail dome]

it's okay

[honest perch]

derivative is the slope of tangent

[frail dome]

yep

[honest perch]

find out which function is the derivative of the other

[frail dome]

can u explain how to solve q42

[frail dome]

but it's hard

[honest perch]

look at tangents at each point

[frail dome]

okay

idk how do u decide who is f(2)

not f(2) sorry

i mean second derivative

and first derivative

[honest perch]

in the first graph what's the slope of the tangent at (0,0)?

[frail dome]

it's undefined

oh wait

idk

💀

it's slope is zero

[flint pike]

For the picture we can immediately say that b is right after c, since we have a slope of 0 on c, which means the derivative graph needs to touch the x axis at that same point

[frail dome]

so

[honest perch]

it's tilting downwards a bit

[frail dome]

what's the arrangement

[frail dome]

i don't exactly get what's you're trying to say about b and c

[frail dome]

yes

[flint pike]

Looks like it goes a -> c -> b

[frail dome]

it's tilting both up and down

[frail dome]

how did u know that

can u pls explain it?

[honest perch]

yeah so what would the be slope

roughly

it's not zero

[flint pike]

Look at the slopes at each point on the graph, if one point has a extremely high or low slope, or the slope is zero, you can correlate that to the points position on the next graph

[frail dome]

is it because the slope is not secant?

i think i get it

[frail dome]

what would it be?

[frail dome]

so

[honest perch]

it's tilting downards so negative

[frail dome]

how can we correlate that to the points on the next graphs

[frail dome]

but it's also going upwards

when limit is at x negative = 0

[honest perch]

look at it left to right

[frail dome]

not -x

[frail dome]

okay

[honest perch]

the tangent line is like y = -x

so if suppose the first one was f then f'(0) < 0

or it could be f' then f''(0) < 0

[frail dome]

OH

yesss

OH YES

okay

so what's next

[honest perch]

the only graph such that g(0) < 0 is the last one

so we can guess the last one is the derivative of the first one

[frail dome]

so the last one is the original function ?

[honest perch]

no it's a derivative

so f' or f''

still need to check

let's say it's f'

then first is f, last is f' so middle is f''

can the middle be the derivative of the last?

yeah i think u just need to practice thinking about the slope of tangent

maybe drawing it

that's all the derivative is

[frail dome]

I don't exactly get how is the derivative of f at x = 0 is 0

[honest perch]

it's not 💀

[frail dome]

Oh

lmao

So B is the first derivative then?

is a or c the orgininal function?

[honest perch]

when u say f

what graph u thinking

[frail dome]

A

[frail dome]

cs u were speaking of A here

[honest perch]

why do u think it's 0

[honest perch]

let's call these a(x), b(x), c(x)

@frail dome

[frail dome]

I think it's below zero when the limit is on the right side

[honest perch]

limit on the right = limit on the left

[frail dome]

okay

[honest perch]

the functions are differentialb'e

aafa

sdf

[frail dome]

aafa?

[honest perch]

got a problem

[frail dome]

np

[honest perch]

ok

we continue

[frail dome]

yea they are

so i dont get which one is the original function

[honest perch]

i think

someone said the answer

[frail dome]

okay.

[honest perch]

well i'll leave u to it

ping me if u have a question

[frail dome]

Okay, ty!

[frail dome]

Hi, Cyphercrit, can you please expand on this?

Does it follow that the derivative of graph a is 0 since we're focusing on the tangent line of each graph?

Is that what you are trying to say?

[safe radish]

@frail dome Has your question been resolved?

[flint pike]

Let’s focus on only one point. at x = 0 on graph a, we have a slope that is decreasing, decreases a little less for a little bit, and then decreases fast again. At x=0 on graph c, we have a negative value, a slightly less negative value, and then a more negative value again

Does that make sense?

That is how slope and values are related with derivatives

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[random rivet]

i dont get 10 a

[safe radish]

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

[random rivet]

1

[tardy mango]

• Collinear: the vectors are scalar multiples of each other
• Perpendicular: the dot product is zero

[random rivet]

yea i het that