help-49

[frosty veldt]

could be what they expect

[clear tusk]

They are saying justify the statememt and solve it

Anyways I will research it furtger everybody thanks for your kind help

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[orchid siren]

can someone help me with this and its entirety i dont understand a thing about it

[steel snow]

can i help you with it in a couple hours

[orchid siren]

Yes please

[steel snow]

okay

[gray bolt]

i can help in like 2 min if you want

[steel snow]

i would do it now but its 3 am

[orchid siren]

can you help me

[gray bolt]

yeah

[orchid siren]

i just wanna understand it

[gray bolt]

okok gimi like 2 min

[orchid siren]

okay thanks

[gray bolt]

ok this is for quadratic stuff right?

[orchid siren]

yes

Quadratic Functions

[gray bolt]

ok so you should start by representing that word problem as a quadratic function

in general rev=(number of things sold)(price)

[orchid siren]

okay

[gray bolt]

so do you know how to set it up

[orchid siren]

r=(50)(7,200)

r=(50-1x)(7,200+200x)

right

[orchid siren]

is this correct or wrong

[gray bolt]

this is correct

so you want to find the maximum revenue

if you draw a parabola when is it at its max

like if you look at it

[orchid siren]

is there an app to draw a parabola

[orchid siren]

how do i put this on desmos

[gray bolt]

wait hold i think somthings wrong with the equation

but just put in desmos y=-x^2

[orchid siren]

okay what to do after

[gray bolt]

ok nvrmind its good

do you see the shape

[orchid siren]

yes

[gray bolt]

of the parabola

[orchid siren]

how do i determine the a, b, and c

[gray bolt]

so it goes up thats the revenue going up then it hits its max then starts going down again

we need to foil this

get it into a form like ax^2+bx+c

do you know how to do that

[orchid siren]

nope sorry

but i do know how to foil

[gray bolt]

its ok you just have to multiply those two terms together

foil stands for first outside inside last

ill write an example one sec

[orchid siren]

okay

[gray bolt]

Like this

multiply the first two

then add that to the product of the things on the outside then add that to the producs of the things on the inside then multiply it by the last things

[orchid siren]

why is it (5+x) and (8+x)

or is that just an example

[gray bolt]

this is just an example

[orchid siren]

okay

[gray bolt]

try it with r=(50-1x)(7,200+200x)

[orchid siren]

its too big but

hold on

ill do it

r = -200x²+2800x+360000

[gray bolt]

yes god job

[orchid siren]

what do we do next

do i put teh a b and c on desmos?

[gray bolt]

we need to find the vertex

do you know how to put it in vertex form

[orchid siren]

x=-b/2a

[gray bolt]

yes

what does that give you

[orchid siren]

the vertex is (7, 351800)

[gray bolt]

yes good job do you know what those numbers represent

[orchid siren]

they're the cords of the vertex

the x, y

[gray bolt]

yes but they mean something for the word problem

[orchid siren]

then nope

what do they represent

[gray bolt]

the 7 is the number of times he increased the price and the y is the money hes getting

[orchid siren]

OHHHH

[gray bolt]

yes and we want the vertex because that is when y is at its higest point

therefor the maximum revenue

[orchid siren]

maximum revenue is 351800

[gray bolt]

yes

[orchid siren]

so to answer it would be

7,200 plus 1400

[gray bolt]

the answer would be 7200+200(7)

because he raised the rent 7 times

[orchid siren]

Ohh okay

to solve it

first we foil

and then we get the vertex?

[gray bolt]

yes set up the word problem as an equation

foil it so its in standard form

convert it to vertex form

[orchid siren]

wait i understand it a little bit

can we answer a different question

[gray bolt]

yeah sure

[orchid siren]

If 600 people will attend a concert when the admission price is P 450, and if the
attendance decreased by 60 for each P150 added to the price, then what price of
admission price of admission will yield the highest gross receipts?

so first we display the word problem as a quadratic function

[gray bolt]

yes

[orchid siren]

rev=(number of things sold)(price)

r= (600)(450)

and then

r= (600-60x)(450-150x)

and then we foil it

[gray bolt]

yes good job

[orchid siren]

9000x² - 117000x + 270000

[gray bolt]

wait

one problem

in r= (600-60x)(450-150x)

[orchid siren]

yes

ios the 600-60x supposed to be positive

[gray bolt]

yes

wait

sorry

no

its 450 dollars

[orchid siren]

oh oaky

[gray bolt]

and every time you add you add 150

[orchid siren]

oh okay

[gray bolt]

so what would r=

[orchid siren]

9000x² + 117000x + 270000

[gray bolt]

r=(600-60x)(450+150x)

it should be this because you add money every time

[orchid siren]

okay

[gray bolt]

foil that

[orchid siren]

this

and then i found the vertex

its (6.5,159750)

[gray bolt]

just make sure its -9000x^2

[orchid siren]

okay

-9000x² + 117000x + 270000

[gray bolt]

yes good job

[orchid siren]

450+150(6.5)

then what price of admission price of admission will yield the highest gross receipts?

the answer is 6.5 right

but how do i say its 6.5

would this be correct 'the admission price that yields the highest gross receipts is 6.50.'

[gray bolt]

ok wait sorry i just double cheaked all the calculations

try to re foil

[orchid siren]

oh wait

its

[gray bolt]

you should get -9000x^2+63000x+270000

[orchid siren]

is it not 9000

[gray bolt]

sorry im tired

it is

[orchid siren]

okay

[gray bolt]

but b should be 63000

[orchid siren]

the vertex is (3.5, 380250)

would this be correct 'the admission price that yields the highest gross receipts is 3.5.

[gray bolt]

almost

the 3.5 is how many times they incresed the price

(450+150(3.5))

[orchid siren]

the admission price that yields the highest gross receipts is (450+150(3.5)

this?

[gray bolt]

yes

450 dollars originally plus 150 3.5 times

[orchid siren]

okay thanks

[gray bolt]

so 975

and then the revenue is 380250

total

one tip is if its asking for maximum a will always be negative and if its asking for minimum a will always be positive

in ax^2+bx+c

[orchid siren]

brb

[gray bolt]

ok i think ima go to sleep now good luck though

[orchid siren]

okay thanks bro

you're a savior

[midnight plank]

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[twilit field]

find the range of $sin^2(x)+cos^4(x)$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

is there any way to do this sans trig

sorry I meant calculus

I know how to maximise and minimise it

but beyond that, not too sure

[shy ice]

u probably could do calculus but i think that would be hard? idk

[twilit field]

Yeah, that's what I thought

how would I do this with trig though

[shy ice]

idk thats why i was guessing

[long sleet]

i think you can use sin²x=(1-cos(2x))/2 and cos²x=(1+cos(2x))/2

[twilit field]

hmm

[feral sedge]

use pythagorean identity

[long sleet]

it should give a quadratic in cos(2x) i think

[twilit field]

ok

thanks

$sin^2(x)+(1-sin^2(x))^2$

[shy ice]

probably

[grand pond]

ƒ(Why am. I here)=I don't know

[long sleet]

oh yeah that looks easier

[twilit field]

let $sin^2(x)=u$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

$u+(1-u)^2$

[grand pond]

ƒ(Why am. I here)=I don't know

[twilit field]

which simplifies to

[last slate]

Then find their maxima or mininma perhaps

[twilit field]

u+(1+u^2-2u)

or 1+u^2-u

which is easy enough

thanks

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[feral sedge]

tbh i'm pretty sure someone posted this exact question some weeks or months ago

i remember helping them using this approach but i can't seem to find it

[twilit field]

#help-6 message

here

[feral sedge]

fun

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[last slate]

Guys, can u share a video about what exactly is dot product?
Because I am aware that it deals with geometry and trigonometry so will be a bit difficult to explain in text
So... Pls

[last slate]

Dot product of vectors btw

[midnight plank]

@last slate Has your question been resolved?

[long sleet]

https://youtu.be/LyGKycYT2v0?si=QMT6jAXLhjpTmBEA

its a bit beyond the standard explanation but i think its still okay

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[willow sundial]

this is linear algebra, im just trying to understand the logic behind how they got those numbers at the right end

the task gives me a vector (-3,2,-1)

and i need to find matric A

that belongs to the mapping of that vector

[lethal path]

Do you know how to do the cross product? If not, search it up

[willow sundial]

like with determinant ? im familiar with that but i dont see it working here

[lethal path]

Yeah so for the i component of A(i), they did i(2 * 0 - (-1) *0) = 0i

[willow sundial]

everywhere where there is a 1 the number is 0 and the other 2 switch places

[lethal path]

And for the j component they have -(-3 * 0 - (-1 * 1)) = -(-1)

[willow sundial]

ah thanks, for saving me from wasting more time on this

[lethal path]

No worries

[willow sundial]

close.

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[last slate]

I didn't understand 1 thing
WHAT will we get after doing a•b•cos theta

Like what?

[long sleet]

its a number

thats basically it

that video already shows a geometric interpretation

[midnight plank]

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[obsidian hedge]

find all x satisfying |sin(2x)|=1/2

[obsidian hedge]

so 2x = $\pm30$

[grand pond]

SirGareth

[obsidian hedge]

or using sinx = -sin(-x)

huh not that

sinx=sin(pi-x)

so we get 150 and 210

as valid values for 2x

[warm pollen]

draw sin(30) on the unit circle

how many angles on the unit circle satisfy the following: $$ sin(2x)=\pm(1/2) $$

[obsidian hedge]

just 4 right?

[grand pond]

dindu

[warm pollen]

yep

[obsidian hedge]

ah thanks

the answer key said there would be 8

prolly the answer key is messed up

thanks once more

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[old shell]

hello im doing review at the moment but there's a question that requires drawing the angle of 4 rads to the nearest tenth, however im unsure of how to get to this

[old shell]

i understand how to find degree and radians, however i do not understand how to find rads

[unique stream]

rads ≠ radians?

[old shell]

sorry for the confusion, i know how to find questions with pi over a set number

[severe cloud]

What‘s an equality that you‘re sure of between degrees and rads?

[old shell]

im sure they both share similar formats

[severe cloud]

No I mean, an equality like x rads = y degrees

I‘m sure you know one

[unique stream]

k if rads = radians then you know
2π = 360° which is the main principle you need for the conversion

[old shell]

yes

[severe cloud]

Dude

[unique stream]

which you can use to derive a formula

[severe cloud]

Let them think of it themselves

[unique stream]

sry :3

[old shell]

i see

[unique stream]

Well what can you come up with?

[old shell]

sorry if you dont mind me asking, is rad the same as radian?

[unique stream]

Usually it's abbreviated that way

I was rather unsure whether you meant it

since you first wrote rads then radians

[old shell]

ah i see

[unique stream]

but if you know
2π = 360°,
how can you find a conversion formula for 1 radian or 1 degree?

[old shell]

oh radian conversion i know

let me remember

radian x 180/pi right?

for radian -> degree

[unique stream]

ys

[old shell]

and then degree x pi/180 for degree -> radian

[unique stream]

ys

[old shell]

by chance whats the difference between the single radian and radian / #?

[unique stream]

notice that if you simply add a factor of 2, it'll make more sense:

x * 180°/π = x * 360°/2π

[old shell]

i know how to do the latter but the single radian confuses me

[old shell]

i see

by chance do you need to convert the radian into degree for this question?

[unique stream]

Well then let's convert:
What's 4 radian in degree?

[unique stream]

Hm it can be helpful ys

[old shell]

is it 229?

[old shell]

i see, is it possible to solve the question with radians alone?

[unique stream]

229.183118...°

[unique stream]

Sure, in the end you only need to "draw" the angle

[old shell]

by chance how would you go about the question with radians if you dont mind me asking?

[unique stream]

which tools are you allowed to use for drawing it?

[old shell]

i have a calculator i think

[unique stream]

but you shall draw it? 🧐

[old shell]

yes

[unique stream]

well if you shall 'draw' it to the nearest tenth then it sounds like you'd have to draw it accurately

if I get the task correctly

[old shell]

im a bit confused im sorry i dont understand

why is calculator bad with drawing?

[unique stream]

"drawing the angle of 4 rads to the nearest tenth" is what you initially stated

[old shell]

yes

[unique stream]

so it's unclear to me whether you mean the precision in drawing

or the precision in calculating the angle in degrees

So 4 = 229.183118° ≈ 229.2° is what they probably want to hear?

and then we can draw that angle

[old shell]

i think so yes

[unique stream]

well we know 180° < 229.2° < 270° so that angle has to be in the lower left quadrant

If you have a triangle ruler then you can just draw it precisely

[old shell]

the answer key said 4+2pi is ~ 10.3 rad & 4-2pi ~ 2.3 rad however im unsure why pi is added

[old shell]

i think i understand! thank you lunatic

[unique stream]

Hm don't see that from the given question either

If something remains unclear just keep it open :]

[old shell]

i tried to work backwards but i dont quite understand the method

thank you once again i appreciate all the help

[unique stream]

Yh it's unclear why they did +2π & -2π from the given task

[midnight plank]

@old shell Has your question been resolved?

[midnight plank]

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[ocean socket]

uh I have a doubt from chemistry

[ocean socket]

Find the Volume of Oxygen gas from 25g sample of CaCO3 at NTP

the answer is 8.4 L but I don't get how

[midnight plank]

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[dry spruce]

Guys

[dry spruce]

How does it become ^3 here

Idont get it

[midnight plank]

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[proper coral]

I was wondering what I got wrong?

[prime hornet]

did you draw pictures for all of these?

[proper coral]

I did now, is it because concavity doesnt matter just about if its increasing or decreasing

[prime hornet]

well, here's 1 and 3 drawn out

left endpoints for concave up and down

the right endpoints are pretty similar

with this, I think you can answer your own question

[proper coral]

ye

ty

[prime hornet]

[proper coral]

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[last slate]

inverses (opposites) always cancel out coz they give the negative number effect?

[last slate]

examples like

[novel herald]

don't know what the negative number effect that you're referring to is, but yes, you can cancel inverses like that

just make sure you're not cancelling a 0 out

[last slate]

like having 1 apple (+1) and someone taking it back (-1)

[prime hornet]

well I wouldn't call that an effect per se

that's just how negative numbers work lol

there's two types of inverses: additive ones and multiplicative ones

[novel herald]

not sure how cancelling inverses leads to a negative number i see what you were trying to say now

[last slate]

??

[last slate]

no

im askim

like

[last slate]

can u give a real life

example

[novel herald]

cancelling -1 and +1 has nothing to do with cancelling 1/2 * 2/1

[last slate]

to those 3 ppints

[prime hornet]

oh

[sinful trout]

higher and chebyshee she's referring to a previous conversation we just had

[prime hornet]

if I have two halves of a pizza, then I have an whole pizza

1/2 * 2 = 1

[novel herald]

if oyu weigh 100 lbs and double your weight, and then halve , how much do you weigh

[last slate]

oooo

[sinful trout]

oops

#help-16 message

there

[last slate]

huh

double my weight?

[latent elk]

I told u to let me cook, u didnt, now she messed up multiplication and addition

[novel herald]

finish the cook

[last slate]

huuh

[latent elk]

Im busy with someone else

[novel herald]

unlucky

[last slate]

what

[last slate]

real life examples to these three pointss

guyss

[latent elk]

Do u want to hear the true?

The harsh truth?

[last slate]

ok tbh

i just want an wxample of

3x1/3

in rl

3 people x 1/3 of those ppl =1̄?

[latent elk]

You lack the understanding of very basic math foundation

[last slate]

no

[last slate]

this rifht?

[last slate]

wait

nvm

[latent elk]

Unless u can accept it, no one can help

[last slate]

ok

i

[last slate]

is dis rifht doe @warm dock

[latent elk]

I will

But she need to know the truth first

@last slate

x + 2 = 5

Whats the value of x

[last slate]

bro

ik this

lol

[latent elk]

Just answer it

[last slate]

i jusr want an example

[latent elk]

Like for real

[last slate]

3

now su

[latent elk]

How?

Where the 3 comes from

[last slate]

coz

it went to the other side

but idk why

to leave x alone but

why did the sifn change

[latent elk]

When the 2 jumps

the sign change

[last slate]

[sinful trout]

i agree... that statement is true, but there was no need to say it or state it as it was irrelevant

[latent elk]

right?

[sinful trout]

my lord

@latent elk

[last slate]

[sinful trout]

this is WHAT I EXPLAINED BEFORE

[last slate]

jump

[sinful trout]

JESUS CHR7ST MAN

[last slate]

[sinful trout]

who me

[latent elk]

Cause thats the rule

[last slate]

3 oranges x 1/3 of those three orangez givd us 1 oeangw

[sinful trout]

@latent elk

"that's the rule" is not helpful

[last slate]

right????

GUYS

RigHT

[sinful trout]

rote memorization isn't learning or teaching

tell her the REASON

[sinful trout]

that spelling tho

💀

[latent elk]

She need to accept it first, then she will realize why its true

[sinful trout]

oh my god

you don't just "realize"

that's your responsibility

[latent elk]

If we want to prove it, right, lets start with set theory

[sinful trout]

to teach her

not necessarily, blues

[last slate]

3 oranges when added 1/3 times, give us 1 orange
but why

[sinful trout]

inverse functions EXIST

[sinful trout]

not added...?

this isn't real analysis

we don't need to explain set theory to her

[last slate]

lemme edit it

[last slate]

wdym
3x1/3

3 got added to itself

1/3 times

uh

yea

@sinful trout

[latent elk]

Look at what u've done @sinful trout

[last slate]

ill turn u pink

[last slate]

where did u go

):

[latent elk]

He gave up

[prime hornet]

hm

what's going on here now?

[last slate]

or he went to the toilet

[prime hornet]

@last slate what do you need help with now

[last slate]

3 oranges when added 1/3 times, give us 1 orange
but why

[prime hornet]

I left for a while

[prime hornet]

think about slicing an orange into three pieces

[last slate]

mhm ❤️

[prime hornet]

if I take a knife and cut up an orange into three pieces, don't I still have an orange when I put the pieces together?

"putting the pieces together" is adding them together

[last slate]

mhm

[prime hornet]

I have three thirds of an orange, and I piece them back together to get...

the same orange

[last slate]

Oh yea ratio

[glossy garnet]

I don't think this was necessary.

[last slate]

its 1/3

[prime hornet]

yeah 1/3 of an orange means "one third of an orange"

[last slate]

1/3+1/3+1/3

[prime hornet]

yeah

[last slate]

yea!

[prime hornet]

I take my three slices and put them together

and I have my 1 orange again

[last slate]

thank youuuuu😊

[sinful trout]

@prime hornet tysm bro

[last slate]

ure mean

[sinful trout]

?

how am i mean

what did i do :(

[last slate]

i feel like i got made fun of

[sinful trout]

how?

[last slate]

by blue

[sinful trout]

no im thanking higher bc he could explain

i couldn't

[sinful trout]

im not blues, yk that right

[last slate]

u supported him

and told me to chill

):

[sinful trout]

that was so long ago

and u called him annoying when he didn't do anything

recently i agree he was definitely being unnecessarily condescending

you hadn't done anything wrong, not knowing maths isn't wrong

[last slate]

he was annoying cause he was getting impatient coz he wasnt trying to understand my problem ):

[sinful trout]

i know

i didn't see that

sorry :(

[last slate]

coz hes ur friend -.-

[sinful trout]

no?

i just met him

don't make assumptions

[last slate]

oh

yea

okay sorry

[prime hornet]

ren is not associated with Blues lmao

[sinful trout]

it's alr

[prime hornet]

anyways... you're done here right? @last slate

[sinful trout]

anyway ru done?

[last slate]

okay

[prime hornet]

you can close the channel

[sinful trout]

timing

[last slate]

ye

[sinful trout]

ahahaha

alr

bai

[last slate]

baiii

[sinful trout]

:)

[last slate]

.close

[midnight plank]

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[midnight plank]

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[last slate]

how do you get this?

this problem driving me nutts

shown is the correct answer.

500/20

[novel herald]

do you know what lhopital rule is

[last slate]

yeah

[novel herald]

do you know how to apply it?

[last slate]

yeah

but how do you apply it to this? its not a fraction

[novel herald]

move (x^3/7) to the denominator by dividing by its reciprocal

so Numerator is just 10/x - sin(10/x)

and denom is 7/x^3

[last slate]

alright

right?

I don't see how this helps

what if i multiply

oh so you mean i can be like

f(x) = the top bit and g(x) = 7/x^2?

sorry for slow reply

[still nacelle]

you meant 7/x^3 not x^2

[last slate]

yes

[still nacelle]

but the point is to get the thing into the form of a fraction

[novel herald]

g = 7/x^3 but yes

[still nacelle]

where the limit of the numerator = denom and specifically 0/0 or inf/inf so that you can apply l'hopital

[last slate]

derivative of sin(10/x) is cos(10/x)

[novel herald]

no

[last slate]

this still has the problem you are dividing by 0

[novel herald]

chain rule

[last slate]

well

yeah true

but part of it is cos(10/x) i mean

and that's not defined

[novel herald]

i know

[still nacelle]

dividing by 0?

[novel herald]

but there will be a nice cancellation

just try/ keep going

[still nacelle]

it's inf that is the limt

so dividing by inf, which is 0 (very informally speaking)

[last slate]

dont see it

looks like more of a mess to me

how do you get rid of the cos(10/x)?

[still nacelle]

you're messing up some of your signs

tip: always write smth/x in terms of x^-1

easier to read and do calc

[last slate]

its not me its the tool im using to draw it

probably should use something else

better i guess

¯_(ツ)_/¯

https://tenor.com/bDLuZ.gif

i think thats good

idk

but anyways, back to the question. how do i cancel cosine?

there is only one cosine in the entire thing

am I just stupid?

[lapis dew]

it looks easier using a sub u=10/x

[last slate]

what do you mean

[last slate]

what's the u?

oh

what

how is this easier?

[lapis dew]

mmmm

[last slate]

so you get the lmit of 10/x on its own?

[lapis dew]

wdym

[last slate]

get limit of 10/x then plug it in?

[lapis dew]

that limit isn't there anymore

[last slate]

what

[lapis dew]

ok do this sub u = 10/x

[last slate]

sorry

[lapis dew]

if x-->inf, u-->?

[last slate]

0

[lapis dew]

ok

so calculate the limit as u-->0 using u instead of lim as x-->inf using x

[last slate]

damnit

that's it

should have thought of that

[lapis dew]

ok you still need to use lhopital for u

but is easier

[last slate]

what do you mean?

[last slate]

oh

x is the reciprocal

x = 10/u, u = 10/x

[lapis dew]

yes

[last slate]

so weird

[lapis dew]

you can do whatever substitution you want

[last slate]

brilliant

[lapis dew]

i mean not any there are some restrictions which i dont know but still

in general yes

just to build intuition here's an example with a simple limit

or just search on youtube something like limit using change of variable

https://www.youtube.com/watch?v=VBHCiTU0HRI

[midnight plank]

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[last slate]

(3^x-2)(3^x-3) = 2*3^x Hidden Quadratic? I've solved this, substituing y=3^x and got a completey different answer from the answer key, x={0, log(subscript 3, base 6). Am I on the right track or it has something to do with exponenets?

[last slate]

For refernece I got x=1,x=6

[dull yoke]

$(3^{x-2})(3^{x-3}) = 2 \cdot 3^x$

[grand pond]

Stephen

[dull yoke]

is this the problem

@last slate

[last slate]

no, it's 3^x, but the -2 is not a power

$(3^x -2)(3^x - 3) = 2\cdot 3^x$

[grand pond]

Slurp

[last slate]

@dull yoke this is right^

[dull yoke]

so (u-2)(u-3) = 2u, thus u^2 - 7u + 6 = 0

then (u-6)(u-1) = 0

u = 1, 6

[last slate]

yeah thats what I got

[dull yoke]

now u have to do the substitution again

[last slate]

but the answer key is diff

[dull yoke]

u = 3^x

[last slate]

Oh

[dull yoke]

3^x = 1, 3^x = 6

solve for x

u should get ur answer

[last slate]

Ahh okay

wow that was obvious

Tysm

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[heady parcel]

The solution given to this was
PSR = 65 °* 2 = 130 °
PRS = 180 °- ( 20 + 130 ) = 30°

How is PSR twice of PQS?

[midnight plank]

@heady parcel Has your question been resolved?

[heady parcel]

<@&286206848099549185>

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@heady parcel Has your question been resolved?

[midnight plank]

@heady parcel Has your question been resolved?

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[last nebula]

what does this question mean

[blissful ether]

do you know what the difference of 2 squares means

[last nebula]

uhh no

I don’t think so

[blissful ether]

ever seen this before

[last nebula]

oh yea ik what that is

[blissful ether]

good

where can we use it

[last nebula]

uh

is that what I’m looking for?

[blissful ether]

yeah

[last nebula]

I think B?

[blissful ether]

yes

[last nebula]

ok yay

[midnight plank]

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[warm hearth]

What formulas/methods can i use to estimate the value an oscillatory graph will converge to? (example below)

[warm hearth]

its not a harmonic oscillation and its discrete, meaning i dont have a formula to evaluate a limit for

I can think of a couple approaches off the top of my head, like curve fitting, or finding which y-value reduces the mean offset by the most

but id like to know of like a 'named' way to do this

cause im writing a paper and it came up

[crude pier]

are the data values given or just the graph?

[warm hearth]

so ideally id be like "hmm yes and we can find the expected value by the sillyman's method"

[warm hearth]

i have the data, this is a graph from matplotlib (a python data visualizer)

[crude pier]

you can try a least squares regression using that data

[warm hearth]

like pearson's and then i cut off data till the slope is zero and use the intercept?

[crude pier]

this sounds like a solid idea

and you can probably try some interpolation method that gives you a point where the slope is closest to zero for a given tolerance of your choice

[warm hearth]

question is how do i know thats the best way to do this for my situation?

its why i'd like to have a named method

something thats been tested by alot of people

and whose strengths and weaknesses i could mention in my write-up

[crude pier]

you can try looking at newton-raphson

which gives you an approximate x-value that you can then use in basic interpolation to find its corresponding y value

[warm hearth]

isnt that for roots of a function?

i might be wrong

i was just reading up on it

[crude pier]

it is, and tbh I'm not sure if it's applicable in this context, but it could

[warm hearth]

i mean there's gotta be a standard mathematical approach for doing specifically this

its not too out there of an ask

no way im even close to being the first person who wants to do this

the closest thing i could find from a search was stuff relating to "damped oscillation"

but most of it is harmonic

like modeling springs over time

[midnight plank]

@warm hearth Has your question been resolved?

[warm hearth]

does anyone know of a mathematical approach to achieve this specifically?

maybe like a moving median? idrk

[prime vector]

Can anyone help ne

[midnight plank]

@warm hearth Has your question been resolved?

[fallen vigil]

whats the data for

[midnight plank]

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[keen seal]

could it be \int _0^1:\left(5+sqrty\right)^2-\left(5+y^2\right)^2

this is the graph

oh nvm

i just forgot to add pi

wtf

i acc got it

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[placid marlin]

V

[placid marlin]

oops

how do i approach this?

[robust sigil]

Could you try your best best to do it? I could show you the mistakes if you do any!

[placid marlin]

ohh i just need to sketch the graph?

ok wait

[robust sigil]

Yup!

[placid marlin]

this?

its such a bad drawing but

am i on the right track

@robust sigil

[robust sigil]

Hey, yes yes i am reading

[placid marlin]

oh my bad haha

[robust sigil]

Its good, but I think its better if you remove the point on x=2

You can not differentiate a point

[placid marlin]

sorry lol it was just for reference

[placid marlin]

also what do you mean by this?

[robust sigil]

Think of it as 0 of y=absolute value of x

You cant differentiate it right?

[placid marlin]

i guess but how does 0 of y=absolute value mean the same thing as what i posted

[robust sigil]

If its too pointy there is no derivative

So try making it more round, if it is for an exercise

[placid marlin]

oh i see, thanks!

[robust sigil]

You welcome!

[placid marlin]

.close

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[placid marlin]

ok so i lied im back

.reopen

[midnight plank]

✅

[placid marlin]

this would be easy if i just had to graph the derivative but how do i graph the original one?

<@&286206848099549185> :)

[winter nimbus]

there is a link between the values of the derivative and the original function

do you know about it ?

[placid marlin]

yeah i mean i know the rule on how to get the derivative

just not vice versa

[winter nimbus]

ok so if the derivative is positive when x < -5 (your first condition), what does that tell us about the original function ?

[placid marlin]

theres an inflection point?

there

idk

its negative when x <-5??

im just guessing at this point im not sure

[midnight plank]

@placid marlin Has your question been resolved?

[winter nimbus]

when the derivative is positive, it means that the original function is "going up"

the informal link between the two is that the derivative tells you how the original function evolves over time

the bigger the number, the faster it increases or decreases

and the sign tells you if it decreases or increases

[midnight plank]

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[sweet sparrow]

What dimensions is this even asking for? Volume or surface area? Also how would I even start?

[runic python]

The volume is fixed at 400 cm³ so you want to minimize the surface area

[zenith stone]

start by constructing 2 systems of equations based on the given data. One for volume and one for surface area. Both beign expressed in terms of 2 variables

[sweet sparrow]

V= pi x r^2 x h and

SA = 2 pi x r^2 + 2pi x r x h

[zenith stone]

okay good

now choose one variable

h or r?

which one do u wanna isolate from the volume equation

[sweet sparrow]

h

[zenith stone]

so what do u get if u make h the subject of the formula for the first equation?

[sweet sparrow]

so h = 400/(pi x r^2)

do i substitute it then?

for the second equation

I think i do actually

let me try that

[zenith stone]

yes

then dS/dr = 0

then boom

[sweet sparrow]

perfect thanks

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[copper yew]

I dont know which next integration rule to use

[slender walrus]

sub again

[copper yew]

Wdym?

[zenith stone]

sub in e^u = m

[copper yew]

I dont understand

Wait i solved it na

Thank you !

!close

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[twilit field]

try rationalising the denominators

[midnight plank]

@olive heron Has your question been resolved?

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[olive zinc]

i tried like 5 times

[olive zinc]

ik the mean

14.084375

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[olive zinc]

14.053 – 14.185

i get this

sample SD: 0.075258059

Sample mean: 14.11928571428

[midnight plank]

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[pure compass]

I try to use 3 parameter which are a7(start point for integral), e7(end point for integral) and A7 (control percentage of area from point a7 to e7) for function y= f(x) in the image
Want to use this for random weight.
when a7=0, e7=0.5 and A7=0.5, the result will be like the first image.
1.I'm not sure, I solves it correctly or not because I don't touch this lv of math more than 10 years now
2.and is it possible to get p7 that have a7 in the equation too?

[pure compass]

when a7=0, e7=0.5 and A7=0.1, the result will be like this image.

here is what I try to solve for p7

3. I think for some value it isn't work like intend. a7=0, e7=0.1, A7=0.78. I don't think area from 0 to 0.1 is 78% from area under the graph

[midnight plank]

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[pure compass]

.close

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[pure compass]

<@&286206848099549185> I think I should ask this on early university but in which channel?

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[real eagle]

Estimating the population mean, stats and prob

[real eagle]

I wanna know how can I caculate the p value

since the way that I've been taught to get the p value requires something more

[sour narwhal]

is this under a normal distribution?

[midnight plank]

@real eagle Has your question been resolved?

[real eagle]

it is, the question said to assume that it is a normal distributed population. So yes

[sour narwhal]

what is alpha in this case

[novel herald]

how have you been taught

[real eagle]

0.10

if your gonna ask more questions regarding the mean, and other stuff, its been laid out in the question description

[sour narwhal]

no i mean what is alpha

like what does it represent

[real eagle]

level of confidence...

[sour narwhal]

ah

[tribal tartan]

you can either use a calculator to get this value or a t distribution table

calculator is more accurate whereas for the t distribution table, we would have to estimate

seems like it wants an actual value so i would recommend using the calculator

[real eagle]

yeah realized it earlier

I have to use the tcdf function

got the answer but its a whole 1

the question demands an answer with decimals

[tribal tartan]

also your t statistic seems wrong

that seems way too big for a sample mean that it quite close to our hypothesized mean

[real eagle]

yeah I think the sample mean/x-bar is wrong when I tried to compute the test statistic

I assumed the 77.6 liters is the x bar

[tribal tartan]

yeah that’s right

and mu would be 87

and the sample size and standard dev is given

[last slate]

Problem 3. Jack tore several successive pages from a book. The number on the first page he tore out was 183 and it is known that the number on the last page was written with the same digits in some order. How many pages did Jack rip out of the book?

Why can he only give 136? I got several responses

[tribal tartan]

so $t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$

[grand pond]

y0shi

[midnight plank]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[real eagle]

yeah I inputed the mew, standard deviation, and the sample correctly

[tribal tartan]

hmm but i got around -1.759 for it

[real eagle]

yeah tried on a desmos caculator

and got that...

[tribal tartan]

alright

[real eagle]

idk why I'm inputing it wrong then on my ti-84...

[tribal tartan]

maybe you forgot a parenthesis or something

anyways your p value should be less than the alpha value

[real eagle]

oh like paranthesis the entire thing?

[tribal tartan]

parenthesis the numerator

[real eagle]

or parathesis the numerator

[tribal tartan]

and the denominator

[real eagle]

yep

oh the denominator

aight lemme try

yeah got it

[last slate]

Problem 3. Jack tore several successive pages from a book. The number on the first page he tore out was 183 and it is known that the number on the last page was written with the same digits in some order. How many pages did Jack rip out of the book?

Why can he only give 136? I got several responses

[real eagle]

@tribal tartan thanks a lot bro

[tribal tartan]

yw!

[real eagle]

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[flat spire]

so i took the conjugate and got

[flat spire]

$\frac{-2+2i}{1+i}=\frac{\left(-2+2i\right)\left(1-i\right)}{1^{2}-i^{2}}$

[grand pond]

water beam

[flat spire]

but what do i do then?

[neon rune]

expand and simplify

[flat spire]

$\frac{\left(-2+2i\right)\left(1-i\right)}{2}$

[grand pond]

water beam

[flat spire]

$\frac{-2+2i}{1+i}=\frac{\left(-2+2i\right)\left(1-i\right)}{1^{2}-i^{2}}=\frac{\left(-2+2i\right)\left(1-i\right)}{2}=\frac{4i}{2}$

[grand pond]

water beam

[flat spire]

is this right?

so its 2i?

[flat spire]

i found it to be 2i but what next?

[neon rune]

well 2i is purely imaginary

and that's the goal of your question

[flat spire]

ohh

right okay

and for this one

how do i approach this?

[neon rune]

can you express z bar (basically conjugate of z) in terms of w and v?

[flat spire]

z bar is a - bi right?

so isnt z = w - iv already in that form?

[tribal temple]

Yes and no not for the given z you have, but if z were a + bi sure

[flat spire]

CHARTTTTT

i missed u

[tribal temple]

Missed you

[flat spire]

im trying to learn something new, complex numbers hahah

[tribal temple]

Awwww

[flat spire]

[twilit field]

are you familiar with (a+b)(a-b)=a^2-b^2

[flat spire]

yeah

[twilit field]

use that here

[flat spire]

im confused is z bar a - bi or is it (a-bi)^2

[twilit field]

z bar is a-ib

sorry

I meant id z=a+ib

then z bar is a-ib

[flat spire]

i dont get it

why we square?

[tribal temple]

Basically the complex conjugate changes the sign of the imaginary part btw

[tribal temple]

So as per before the conjugate of a + bi is a - bi, right now you basically instead have z = w + (-v)i

[tribal temple]

Anyways, if you work out what z * zBar is...

[flat spire]

so z bar is w + iv?

[flat spire]

$z=w+\left(-v\right)i$ then $z_{barrrr}=w-\left(-v\right)i$?

[grand pond]

water beam

[jagged saffron]

$\bar{z}$

[grand pond]

ΣAC

[jagged saffron]

but yes

[flat spire]

ohh

okay

[jagged saffron]

the bar is really just replacing the i with -i, whatever your complex number looks like

[flat spire]

so $\bar{z}$ = $w + vi$?

[grand pond]

water beam

[jagged saffron]

when z = w -vi yes

[flat spire]

so $z\bar{z}$ = $\left(w+vi\right)\left(w-vi\right)$

[grand pond]

water beam