help-17

[sly basin]

(0,0) (5,0) (0,7)

[tired gorge]

So what does y vary from

In terms of z

[sly basin]

(y,z)

so

y2-y1=m(x2-x1)
7-0 = m(0-5)
7=-5m
m=7/-5

y= -7/5x + b

b = 7

s= y=-7/5x + y

so y =-7/5z+7

[tired gorge]

I think we have y/5 + z/7 = 1 right?

So y = 5 - 5/7 z

[sly basin]

uh ye

but where is x?

oh u used equation of plane

[tired gorge]

This also works for lines if you have two variables!

But yes it does look like the equation of a plane

[sly basin]

but thats where u got it

from right?

u just plugged in x=0

[tired gorge]

It's the intercept form for a line

It looks the same as the intercept form for a plane but only has two variables instead of 3

(It does technically define a plane as well but that doesn't matter here I used this equation to get the equation of the line)

[sly basin]

im so confused

sorry

[tired gorge]

It's fine! The important bit is we have the equation for that line

You can use whatever method is comfortable to you to find it

[sly basin]

wait so

if u didnt know the plane

how u getting y equation

[tired gorge]

What do you mean

[sly basin]

like

u used a/x b/y c/z = d formula

other way around

x/a y/b z/c = d

let x = 0

so ur left with y/b + z/c = d

[tired gorge]

I mean that works here because of our circumstance yes

https://byjus.com/maths/intercept-form/

But I used this directly since I knew the y and z intercepts, it works the same way as the plane version

And looks the same since it uses the y and z intercepts

Since we're in the x=0 plane we can find the equation of the line by plugging x=0 into the plane equation, the two methods are exactly equivalent

Sorry if I confused you by that you can use the typical method to find the equation of a line if you'd like

[sly basin]

okay okay

nono that makes sense

so basically u used plane u just set x to zero (cuz we smoosh it)

so left with y/a + z/b = D

[tired gorge]

In this case yes

With more complex shapes it's not that simple but it works here

[sly basin]

is there

like certain formula

i can use to abuse these types of problems

like derivtives

u cant always use 1 formula

there are few but if u know them

u can get derivitive of anything

product, chain, quotient

like that

power

same here, doing these types of rpboelms setting up integration bounds, setting up paramters

are there Formula I can just use?

[tired gorge]

I haven't done enough integrations like this to know of any shortcuts

The most intuitive way I've found is to work it from first principles, I also don't like to memorize arbitrary equations though

Sorry

[sly basin]

okok

so if u didnt use plane equation here

howd u solve it

using y =mx+b

formula

it should give u same answer no?

[tired gorge]

Yes

I think you did something wrong above

When you tried that

Ah you solved for z in terms of y but swapped the variables

[sly basin]

yee

exactly

[tired gorge]

Yes

[sly basin]

okok

OKOK

[tired gorge]

Anyways you should now have your y bounds

[sly basin]

I THINK i have an idea kind of

[tired gorge]

Good!

[sly basin]

so lets say im doing dxdydz

Outter = EZ PZ 0 to 7

it should have no variables

[tired gorge]

Correct

[sly basin]

then (For me) i find middle easier than inner

because MIDDLE can ONLY have z

so very variale should be Z

y=something Z

[tired gorge]

Yes

[sly basin]

since YZ plane has (0,5,0) and (0,0,7)

im gonna see it like (5,0) (0,7) because its not really in 3d when i view it from there

m=y2-y1/x2-x1

so x1=5
x2 = 0
y1= 0
y2 = 7

7/-5
so m = 7/-5

[tired gorge]

You've swapped your variables again

You want y in terms of z, so your slope should be (y2 - y1)/(z2 - z1)

Then y = mz + b

[sly basin]

ye but im seeing it like

y is just x

z is just y

since its 2d

[tired gorge]

No in this case you want y as a function of z so z is like x

You've swapped your vars

z is the independent variable

[sly basin]

its just a place holder

tho

no?

wont matter what i call it

i know whats y and whats z

interms of finite number

[tired gorge]

Try plugging in your values of z for the equation you got

[sly basin]

that was the wrong equation

[tired gorge]

It won't agree with what you should get

[sly basin]

this is the way i see it

Given points :(0,0,0), (4,0,0), (0,5,0) (0,0,7)
Since we squashed the X.
There are no X in a yz plane

Given points :A(0,0,0), B(4,0,0), C(0,5,0) D(0,0,7)

these are points

so POint A and Point B are useless

or they lead is ut samething

both are 0

so its orgin

A and B are both orgin

(5,0) and (0,7) two points we an work with

regardless what we call it xyz

my first focus should be to get y=mx +b formula

(y,z) cuz yz plane

im gonna treat it liek (x,y) so i can solve it without visualizing too much

so given those 2 points I think i can solve for y=mx+b equation

m=y2-y1/x2-x1 = 7-0 / 0-5 = 7/-5 = -7/5
m = -7/5

now to solve for y

y-y1=-7/5(x-x1)
plug in 1 point
y=-7/5(x-5)
y=-7x/5 +7

thats what i got

(x,y) = (y,z)
so z=-7y/5 + 7
7y/5 = 7-z
7y=35-5z
y=5-5z/7

is that the same answer u got?

[tired gorge]

Yep

[sly basin]

super mechanical way of doing it

[tired gorge]

Convoluted a bit maybe but if it makes sense to you that's all that really matters!

[sly basin]

okok

but if im given plane equation

i should abuse it huh

y/5 + z/7 = 1
y/5 = 1-z/7
y=5-5z/7

[tired gorge]

Again if you want to think of it as the plane equation that works here but will not for general shapes

[sly basin]

thats MUCH easie

easier

[tired gorge]

Yeah

If all you're doing is integrating over these particular tetrahedra it works fine but will not for more general shapes

Really the method should be smoosh along the x-axis and find the equations of the boundary lines in whatever way you can

[sly basin]

so

divergence theorem

is always

triple integral

huh

[tired gorge]

Yep

[sly basin]

and we just do the div(f)

thats it

[tired gorge]

Yes

[sly basin]

its pretty easy

then

its just setting up integral thats hard

[tired gorge]

Definitely

[sly basin]

hey u think

u can help me thru more problems?

or u busy

if not its cool

[tired gorge]

It's pretty late here and I've been putting off some of my own work but I could quickly give you a pointer or two if you need it!

[sly basin]

u help with

differnetial equations?

[tired gorge]

Sure

[sly basin]

Ohh quick question

on the last question

for divergence theorem

lets say it was pointing inward

or outward

all it does is flip the final answer

correct?

[tired gorge]

I think so

Yeah

[sly basin]

so after integrating

if i got a negative answer

i would just flip sign?

[tired gorge]

No you don't have to worry about that in this case I don't think your answer should be correct

The divergence theorem assumes outward pointing normals

[sly basin]

i got some problems pointing IN

[tired gorge]

Oh interesting

Then your answer for those problems SHOULD be the negative of what you'd get from what you did before

But the flux integral isn't always positive

[sly basin]

bbso

so if its pointing OUT

= ALWAYS POSITIVE

if i get negative answer = FLIP

if positive = keep same

IF POINTING IN then..
Answer = negative
If i get positive answer = flip to negative?

[tired gorge]

No

Perform the divergence theorem as normal. If the normals are pointing outwards do nothing, but if the normals are pointing inwards flip the sign

[sly basin]

what if its pointing outward

i get negative answer

[tired gorge]

That's fine in some cases

Sometimes the flux integral is supposed to be negative like I said

[sly basin]

okok

[tired gorge]

Like for the field <-x, -y, -z>

If you had a sphere say with outward pointing normals then the flux integral would be negative

[sly basin]

okok

make sense

alright

I APPRECIATE IT!!

[tired gorge]

No problem!

[sly basin]

can i hit u up for questions later

cool if i shoot u a dm

[tired gorge]

Sure but I may not respond all the time!

[sly basin]

if not it cool

its aite

[tired gorge]

It may be more convenient to just open a chat here, I'm not active often lol

[sly basin]

forsure

.close

[vocal sleet]

Channel closed

Closed by @sly basin

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[deep plume]

Guys I have a number series and its first 5 terms, i dont know its logic but i was able to predict its polynomial due to the crazy growth.

[tidal dock]

okay

[deep plume]

For n = 1: 0.0
For n = 2: 6.72
For n = 3: 32.0
For n = 4: 93.06
For n = 5: 210.0

[deep plume]

could u tell me how to solve it?

[tidal dock]

show the full problem, i don't know what you are talking about rn

[deep plume]

thats all I know

i have the first 5 terms of a number series

[astral pilot]

You want to find a polynomial given its values?

[deep plume]

i need to find first 10 terms

all i know is the logic to gain the next term is a polynomial logic

due to the growth of the terms

[twin meteor]

Result:

2.2566086395874

[deep plume]

huh? anyone there?

<@&286206848099549185>

[vocal sleet]

@deep plume Has your question been resolved?

[deep plume]

<@&286206848099549185> Anyone? Help me please

Heello anyone??

help me

[atomic summit]

Can you find any pattern?

If n = 1 is 0

That means you’re dealing with at least a 2 part equation

Or some other way to cancel

Or ln(n)

[deep plume]

thats the thing

i hv only dealt with simple ones before

like (where u make two variables or do multiplication or basic squares)

where its logically easy to tell

[deep plume]

no so all i know is it involves exponenets(duh) and the growth rate decreases

like its first 300%, then 200% and so on

[atomic summit]

Path looks exponential

1 - e^n-1 maybe?

Something along those lines

[deep plume]

i just want idea on how to solve

is it even possible?

[atomic summit]

Find an inductive step proof

Come up with some thesis

[deep plume]

Im in grade 9

idk wtf iit is

[atomic summit]

And see how it performs against the given data

Oh true

[deep plume]

inductive step proof

[atomic summit]

Okay

Induction says that if you can prove it for n = 1 then you can prove it for n+1

[deep plume]

so i make a formula in which if u apply it on 1 u get 0

and then apply the same formula?

[atomic summit]

Yeah essentially

And hope that it holds

[deep plume]

but logicaly it makes no sense? because many logic cn hv same answer

[atomic summit]

That’s true, then you’ll have a formula that fits the sequence, it doesn’t imply that it’s unique

You can have a lot of ways to get to the number 27

Doesn’t mean the paths a wrong

So yes there may be several equations that make that sequence work

I think you just need one

[deep plume]

so since the question never said ifnd the orginal formula, i just need to find the remaining terms

[atomic summit]

I don’t remember year 9

[deep plume]

it could work

is that what u remember?

[deep plume]

oh no

this is not part of my syllabus

iim solving an ARG

[atomic summit]

What’s the question state?

To find the first 10 terms?

[deep plume]

yes

[atomic summit]

So you need answers for n=6 through 10

For that you’ll need to create an equation

That holds for the first five terms

[deep plume]

so ill do it for 1

then test if same formula works for 2

if it doesnt, give up

make another

(thats basically bruteforcing math?)

[deep plume]

?

[atomic summit]

Yeah essentially brute forcing

[deep plume]

so i make an equation so it holds true for one

[atomic summit]

There’s probably a better way

[deep plume]

try same on 1

if it doesnt work

try another equation

and so on

wont that take VERY long?

[atomic summit]

It shouldn’t because it only needs to hold for n-1,n,n+1

If it works for those it will work for all

[deep plume]

isn't that only three terms?

what?

so i assume n as 1 first

test it for -1 and 2

and if it works

it will work for all the terms

since i dont know -1 according to the series

ill take n as 2

[atomic summit]

So n=2

[deep plume]

so i need to test only for 1

and 3

[atomic summit]

Yes

If it holds both ways

[astral pilot]

[ 400.616 683.856 1078.33885714]

[atomic summit]

It should continue to hold

[deep plume]

should 😭

Thanks love ya mate

[atomic summit]

Lol no worries

[deep plume]

il keep this open till i confirm it works ig

[astral pilot]

I wrote a program and got these

[deep plume]

1078.33 IS THE SUm of the 10 terms?

[astral pilot]

no those are values for n=6,7,8

[deep plume]

oh?

i dont think its correct

but i cant confirm

it feels off by a bit

[astral pilot]

OH reallly?

seems good to me

[deep plume]

then could u find the rest of the terms?

ill check

[astral pilot]

for 9 and 10, 1602.72457143 2275.67314286

[atomic summit]

Is it like

[deep plume]

the sum?

is what i need to find

sum of the 10 terms

[astral pilot]

let me double check

[atomic summit]

Ln(n)^10n

That’s very close

Not 10n

Something else

[atomic summit]

But ln(n)^n*coefficient works

Ln(2)^5*2 is close

For n is 2

Ln(3)^10*3

Is close for n is 3

[astral pilot]

,calc 0 + 6.72 + 32 + 93.06 + 210.0

[twin meteor]

Result:

341.78

[atomic summit]

Mmm doesn’t work

[astral pilot]

,calc 341.78+400.616+683.856+1078.338+1602.724+2275.673

[twin meteor]

Result:

6382.987

[astral pilot]

@deep plume Is answer close to like 6300 or 6400

[deep plume]

6400 close to it

wait i mean

6600<x<6700

[astral pilot]

$y=3.11x^{3}-9.68857143x^{2}\ +14.22142857x--7.684$

[twin meteor]

Pro_Hecker

[deep plume]

how are u doing this btw

what method?

[astral pilot]

numpy in python has polyfit function

[deep plume]

idk what polyfit is but alr

[astral pilot]

import numpy as np
n_values = np.array([1, 2, 3, 4, 5])
sequence_values = np.array([0.0, 6.72, 32.0, 93.06, 210.0])
coefficients = np.polyfit(n_values, sequence_values, deg=3)
polynomial = np.poly1d(coefficients)
next_n_values = np.array([6, 7, 8, 9, 10])
predicted_values = polynomial(next_n_values)
print(predicted_values)
print(coefficients)

[atomic summit]

xe^x-e^x

[astral pilot]

$$y=18.30142857x^{2}-59.17457143x+44.564$$ this is the closest quadratic i could find

[twin meteor]

Pro_Hecker

[deep plume]

hecker

could u tell me how do i create a function to do it(mathematically) other than induction

how is the polynomial function created

[astral pilot]

idk I saw it in a data science course for trend fitting

,calc 341.78 + 348.368 + 527.112 + 742.45885714 + 994.40857143 + 1282.96114286

[twin meteor]

Result:

4237.08857143

[astral pilot]

ah shit here we go again

its not a polynomial then

[deep plume]

well ur approxed answer first one was like 250 off

findinig the precise answer is not possible?

[astral pilot]

,calc 341.78 + 405.8 + 706.32+ 1140.3+ 1739.36+ 2538

[twin meteor]

Result:

6871.56

[astral pilot]

😮

[deep plume]

6654.89

is the answer

[astral pilot]

let me do it to a degree 10 polynomial

,calc 341.78 + 404.67538228 + 699.57229369 + 1116.6830279 + 1676.38140774 + 2396.29816742

[twin meteor]

Result:

6635.39027903

[astral pilot]

hey this is dangerously close

,calc 341.78 + 401.32249787 + 677.40432437 + 1031.91781527 + 1431.20132069 + 1801.57905147

[twin meteor]

Result:

5685.20500967

[astral pilot]

closest i can get

a degree 5 polynomial -0.00937181x^5 + 0.26057721x^4+ 0.87339578x^3 -1.63134178x^2 + 1.88212288x - 1.37538228

fits almost perfectly

I am having a seizure by solving this monstrosity by trial and error

[deep plume]

is there any other way tbh

lol

[astral pilot]

I think you can do it manually

say y = ax^4 + bx^3 + cx^2 + dx+ e

and then you can do like put x = 1 and y =0, then you will get a linear equation in 5 variables

since you have 5 values you can get 5 equations and solve them

then you will get the values of a, b, c, d and e

[deep plume]

how did u assume its power is 4 tho?

and not a cubic

or square

also how do u know it follows the general form

what if the equation is random bllshit

[astral pilot]

that can be true

but if we have a degree 4 equation we can guarantee that it passes through those 5 points

just like line a degree 1 can pass through 2 points

parabola a degree 2 can pass through any three points

a degree four can pass through any 5 points

[deep plume]

(no offense but idk wtf u said)

[astral pilot]

if given 2 points can you draw a line(first degree)?

[deep plume]

thru them? ye

[astral pilot]

line is a first degree polynomial

see, given 2 points we can draw a degree one polynomial

similarly given 5 points we can draw a degree four polynomial

[deep plume]

alr

[astral pilot]

and even if it is square then we can the quartic and cubic coeffiecients to be zero

that's the way to do it manually

I'll never do it by hand

[deep plume]

so we assume general form

[astral pilot]

yeah

[deep plume]

like for square

ax^2 + bx + c

then?

[astral pilot]

we put x= 1,2,3,4,5,etc and y=0,6.72, and so on

so for e.g.

a(1)^2 + b(1) +c =y =0
i.e. a +b +c =0

so we got one equation in three variables

[deep plume]

then i assume x as 2

and so on?

[astral pilot]

yeah

[deep plume]

and after hving 3 equations

we do the same with a this time?

then wut bout b and c/

[astral pilot]

no after 3 equations its enough to solve 3 variable equatino

what is your grade?

[deep plume]

9

[astral pilot]

omg, how did they give you this question then??

this seems like a 11th grader question

[deep plume]

(im solving an ARG)

[astral pilot]

Alternative Reality Game?

[deep plume]

yes

[astral pilot]

which one?

[deep plume]

a random one

and i need to solve series for this

[astral pilot]

[deep plume]

bro i get it we make 3 equations, cuz 3 terms in the standard form of a quadratic equation

after we make the 3 wut do we do

[astral pilot]

suppose you get equations like
a+b+c =0
3a+2b+4c -3=0
2a-4b+3c-2=0

then you can solve this and get a,b and c

[deep plume]

so we equate y in the 3 equations into 1 value?

[astral pilot]

yeah

[deep plume]

could u show example using this stupid series itself?

(cuz u alr solved it basically)

[astral pilot]

its soo hard to do by hand man

It'll take hours

[deep plume]

perfect

(im jobless)

[astral pilot]

I'll have 3 seizures before I solve this by hand

[deep plume]

if i get the logic to do it by hand

fully

i can do it using computational power

and hand

[astral pilot]

let's get something easier then

[deep plume]

so i can cook next time

[deep plume]

alr

[astral pilot]

n=1, the value is 0
n=2, the value is 1
n=3, the value is 2

[deep plume]

mhmm

[astral pilot]

now what we'll do is put x=1,2,3 and y = 0,1,2

assuming y = ax^2 + bx +c

0 = a + b + c (by putting x =1 and y=0)

1 = 4a + 2b + c (by x=2 and y =1)

2 = 9a + 3b + c (by x=3 and y=2)

now there are many ways of solving these three eqn^s

we can use substitution for this one

[deep plume]

and solving it gives me the integer or constant

[astral pilot]

from Ist equation c = -a -b

yeah then you'll get the values of a, b and c

then you can the equations

let's solve this now

[deep plume]

after getting the constant

what do i do?

(also i can assume the values as anything right?)

for y and x?

[astral pilot]

y = ax^2 + bx +c

[astral pilot]

you have to assume the values you know of

[deep plume]

alr, so in my case i know y is (The term of series) and x is N?

[astral pilot]

yeah

x=1 and y =0

x=2 and y= 6.72

https://tenor.com/view/me-dead-now-cat-kitty-pretending-to-be-dead-gif-15587136

[deep plume]

so after i get abc?

the constants?

[astral pilot]

yeah

then you can make the equation

[deep plume]

and then again use same values

for the y

i meanx

where x ==n?

[astral pilot]

yeah

[deep plume]

(hey bro no offesne but wtf u mean it will take hrs)

it seems like the typical questions i do in my spare time

[astral pilot]

It will

[deep plume]

how.

[astral pilot]

this was simplified case

[deep plume]

for this case for example

[astral pilot]

It already has took me 3 hours since you began this question

[deep plume]

3: 32

equation will be

32 = a * 3^2 + b * 3 + c

no?

[astral pilot]

yeah

[deep plume]

also how do u graph this?

we only learn

basic co ordinate geometry

[astral pilot]

Basic coordinate geometry? USE A GRAPHING CALCULATOR

[deep plume]

alr ty man

i owe u

ALOT

u wasted 2 hours

helping a rando

on a rando server

YOUR GOATED

[astral pilot]

I learned a lot

[deep plume]

so win win?

(oh funfact: the ARG game was mine i just wanted to solve my own problem without fkin my sanity up)

cuz i didnt know how exactly to solve it efficently

[astral pilot]

you fked my sanity tho

[deep plume]

and chatgpt is dumb

[deep plume]

(bro i was gonna do rando shit)

i was calc percentage of growth

and shit

idk wtf i was doin

was improvising

[astral pilot]

np, It was fun

not worth the wait tho

[deep plume]

Well now time to do 900 series program ewaully autistic manually

[astral pilot]

this was basic data science

[deep plume]

So I ACHIEVE greatness

[deep plume]

u wanna try solving my arg game

🙂

[astral pilot]

yeah

[deep plume]

Thats how it starts

everything is mine btw

nothing ripped off

even the quote

im a poet i know

(i used chatgpt to make it a bit more spicy thats it)

[astral pilot]

This chatgpt?

[deep plume]

nah i gave it a quote made paragraph

and asked it to spice it up

and it spawned dis shit

the orginal quote which i mde was

[astral pilot]

You can make a game, but not program polyfit wtf??

[deep plume]

😦

lol im the dumbest/smartest guy type shi

idk why

[astral pilot]

this game coded by you?

[deep plume]

its not code

its like a mini cicada

[deep plume]

but yeah im a good programmer

i have made rats

rootkits

ransomware

CHAT platform

[astral pilot]

Nice man

[deep plume]

Sick shit i know

[astral pilot]

69 chan 🔛🔝

[deep plume]

my friend did front end

im the backend goat

he slacked off a while ago

he didnt send the front end for chatting pages

[astral pilot]

He did front end? wtf did he do?

[astral pilot]

centre a div?

[deep plume]

no we both 9th graders

[astral pilot]

this kinda good

[deep plume]

@astral pilot hey but u hv a goodstart in the riddle

cuz u solved

one of the hardest parts

(u aproxxed answers but i gave the real one so lol0

u hv less work to do

[astral pilot]

how did you get that answer?

[deep plume]

i know the logic

orginal

[astral pilot]

tell me

[deep plume]

rules.

[astral pilot]

based

[deep plume]

((n^2 + 3)/n) * ((n^3 -n)/(n + 3)^2) * 4n

[astral pilot]

no shit, i didn't consider the possibility of it being a rational function

[deep plume]

( i ddi give a hint tho)

"what if the user just put a random ass equation"

[deep plume]

in this case using standardform will work right

cuz of the angle thru line shit

[astral pilot]

yeah

[deep plume]

ig ill close this now?

.close

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[tribal mulch]

Help

[tribal mulch]

This is not an exam Btw

[fringe smelt]

the top of the page: description of question will help you solve part a)

there is a relationship between size of angle and length of arc

[tribal mulch]

how to know which angle

[fringe smelt]

so clearly the size of angle on a point is 360 degree, then what if i draw some line that intersect on that point, then i divided the angle into several part and they add up to 360 degree

then intuitively, larger the arc, larger the angle

then what can you think of that might be true?

[tribal mulch]

Is it 108

[fringe smelt]

yes

I believe u get it

[tribal mulch]

wut is (b)

[fringe smelt]

do you know what an angle bisector is?

[tribal mulch]

Nope

[fringe smelt]

let say i have angle BAC=100 degree, then the angle bisector divides BAC into two equal part, each 50 degree

let say!

so it bisects the angle

as its literal meaning

[tribal mulch]

Oh ok

what to do next

[fringe smelt]

so it is asking you if straight line BD is angle bisector of angle ABC, which is essentially asking you if straight line BO is angle bisector of angle ABC

to prove this, you need to find angle CBO and ABO respectively and prove that they are equal/not equal

[tribal mulch]

idk what is (b)(i)

[fringe smelt]

honestly idk how to give hint to bi) as i cannot think of a way that skip bii) to do bi)

[tribal mulch]

.close

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[cerulean lichen]

How can I derive the automorphism of annulus with r < |z| < R

[cerulean lichen]

I know the result but I can’t find how

Is there any conformal map that maps annulus to other domain like plane or disk?

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[cerulean lichen]

<@&286206848099549185>

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[nova solstice]

can anyone help with this

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[rare swallow]

can anyone draw me this rectangle and triangle? i don't get how it should looks like

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[crisp zenith]

I’m not confident on my answer, could someone check if it is correct, trying to find a eigen basis with a generalized eigenvector

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[vast shale]

how do you find the remainder in long division for polynomials

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[void vigil]

How to factorize? What steps were done?

[hushed pewter]

RRT would work

[void vigil]

Could you explain how that works simply? I dont quite get it

[hushed pewter]

Don't get what?

[void vigil]

I need to find the eigenvalues for this matrix

I found the determinant, but now im stuck on how to find the eigenvalues using this determinent

[desert hornet]

you just set it equal to 0 and solve for the values of lambda

[void vigil]

Thats the part I dont get, how do I solve for the values of lambda

Ah, I think I got it from chatgpt

ty

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[tidal hazel]

need help with this one

[marsh elk]

this is one ugly limit

[brittle umbra]

that looks goofy bruh

prob taylors expansion or something

[tidal hazel]

i haven't studied that yet

[left lichen]

hey

we can use this property

a^x-1/x where x tends to 0 is lna

now lets convert the numerator to this form

add and subtract 1 in the numerator

youll get ( (a^tanx - 1) - (a^sinx-1) ) / (tanx - sinx)

now

we need a^x-1/x right

so multiply and divide tanx for a^tanx - 1 term

similarily for a^sinx-1

and then youre good to go

[rancid flicker]

can solve this in another way

it's equal to (a^(tanx - sinx) - 1) * a^sinx)/(tanx-sinx)-> lna(x->0)

[left lichen]

oh yeah this better

[rancid flicker]

hi, how are you?

[left lichen]

im fine, you?

[rancid flicker]

fine too

Did you major in math?

[left lichen]

nah

[rancid flicker]

just hobby?

[left lichen]

i learnt this in school

so yeah

[rancid flicker]

ah, ic

[left lichen]

im currently in university 1st year

[rancid flicker]

ic, ic

which university did you enter?

[left lichen]

Ah you wouldnt know

where ya from?

[rancid flicker]

im from China

what about you?

[left lichen]

India

[rancid flicker]

education level in India is very high, I think

[left lichen]

maybe

im cs student btrw

[rancid flicker]

what are you majoring in?

[left lichen]

computer science

[rancid flicker]

sounds good

can we stay in touch further?

[left lichen]

Sure sure

ill add ya

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[bleak prawn]

Im stuck on something

sin^2(x)cos^2(x)

((1-cos(2x))/2)((1+cos(2x))/2)

(1-cos(2x)(1+cos(2x))/4

(1 - 2cos(2x) - cos^2(2x))/4

So now I want to convert 2x into u

But before that can I take the 1/4 out and just integrate that to x/4?

Or does it get integrated to u/4 ?

Or u/8?

[vast shale]

"(1-cos(2x)(1+cos(2x))/4"
"(1 - 2cos(2x) - cos^2(2x))/4"

[bleak prawn]

Theres a mistake?

[vast shale]

Where did -2cos(2x) come from?

[bitter pilot]

You can reduce it down to (sin(x)cos(x))² = sin²(2x)/4 = sin²(u)/4 then use the identity with cosine for sin²(u)

[bleak prawn]

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

[vast shale]

What? No.

[bleak prawn]

Hi adonis ❤️

[vast shale]

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

[bleak prawn]

Oh youre right

[bleak prawn]

Ahhh I see

[bleak prawn]

But ok, lets pretend I did have this

My im still wondering about my original question

What is the next step?

Hi Chartbit ❤️

[bitter pilot]

You could do the same trick, rewrite the cosine square term

[bitter pilot]

this identity

[bleak prawn]

Hi Xbz! ❤️

All my favourite people here today hehe

[bleak prawn]

Okay yeah true...

Im still just wondering tho haha

Like if I WAS to do it the other way

Does it become x/4 or u/4 or u/8?

I guess x/4 and u/8 are the same in this case...

[bitter pilot]

If you do this substitution you get x = u/2 and for dx = du/2

If you also pull the 1/4 factor before the integral you get a total factor of 1/8 before the integral, if that's what you are asking

[bleak prawn]

Wait I dont fully understand sry

Like i still need to integrate the 1/8?

Or before the integral as in to the left of it (as in its already integrated?)

[bitter pilot]

No it'd be a factor

[twin meteor]

𝔸dωn𝓲²s

[bleak prawn]

Okkkkkkkk

I see now

Thank you so much haha

Sorry that took a while for me to get 😅

Thanks again!!

❤️

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[vast shale]

Can anybody help me with 3rd

[bronze osprey]

if you draw out a diagram for q3

using a coordinate system, the parabola passes through (0, 6)

it also passes through (-50, 30) and (50, 30)

[vast shale]

That's where i stuck

[vast shale]

Ah thanks

[bronze osprey]

so naturally vertex form

once you have the equation in vertex form sub in x = 18 and the length of the vertical wire will be the y

or x = -18, it doesn't matter by symmetry

[vast shale]

The answer I solved is 9.11m approx

And It's the right answer I guess

Thanks man for ur help

. close

/close

[bronze osprey]

nicely done I get the same

.close

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[fringe smelt]

I believe MI+factorization might help

[quick vigil]

Why is this even asked as a proof

[undone burrow]

imma be honest

idk what that means 🔥

Im an a level student for context

this showed up in one of the interview prep qs

[fringe smelt]

well, MI=mathematical induction

[undone burrow]

is it doable with the knowledge I would have at an A level/12th grade

[undone burrow]

oh well

nvm that makes sense

Ye ik what induction is

[fringe smelt]

it is fun function btw, riemann zeta function

[undone burrow]

isnt the zeta function to infinity?

[fringe smelt]

yes so it is a partial sum

[undone burrow]

ah

i was thinking i could put bounds on certain intervals

[fringe smelt]

anyways it doesnt matter in this proof lol

[undone burrow]

but it is the harmonic series and diverges

[bronze osprey]

https://math.stackexchange.com/questions/2746/is-there-an-elementary-proof-that-sum-limits-k-1n-frac1k-is-never-an-int

[undone burrow]

so that plan fell apart

[bronze osprey]

proof is not easy

[undone burrow]

ight ill move on then

[bronze osprey]

not easy to come up with this yourself

[undone burrow]

fair

[bronze osprey]

but then you can certainly try understanding the solutions

[undone burrow]

yep ill have a look at this

thanks

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[lilac sluice]

how do i continue 2a

[astral pilot]

use the fact that largest angle is twice the smallest one

what is the largest angle in this case?

[lilac sluice]

so T5 = 2(108 - 2d)

[astral pilot]

yeah

[lilac sluice]

and would u solve for d

by equating the two

[astral pilot]

yes

[lilac sluice]

ok

but then i just get -a = -T5

hello??

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[lilac sluice]

.close

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[lilac sluice]

.reopen

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✅

[elder scaffold]

yo

@lilac sluice still here?

[lilac sluice]

yes

[elder scaffold]

still on 2a?

[lilac sluice]

i still need help yes

[elder scaffold]

how'd u come up with this?

[lilac sluice]

bc largest angle is twice the smallest angle

[elder scaffold]

ah sorry, didnt read what u had on ur paper already

[lilac sluice]

allgs

[elder scaffold]

also use the fact that t5 is a+4d

[lilac sluice]

oh true

[elder scaffold]

is that dr du?

[lilac sluice]

yep

[elder scaffold]

interesting, isnt sequence and series advanced?

[lilac sluice]

it is but they still teach us

idk why

but i’m just following along

[elder scaffold]

fair

[lilac sluice]

i thought summations was an ext 1 topic tho

[elder scaffold]

nah it should be advanced

[lilac sluice]

oh alr

what else do i have to learn

cus this week is the final chapter on sequences and series

[elder scaffold]

uh idk what they do at dr du

[lilac sluice]

btw d = 18 right

[elder scaffold]

yeah thats correct

[lilac sluice]

ok

[lilac sluice]

i just wanna know what else there is to learn

in terms of the syllabus

[elder scaffold]

like for sequence and series?

[lilac sluice]

mhm

[elder scaffold]

have u touched on geometric progressions?

[lilac sluice]

yes

that was first chapter

i’ve gone over GP AP general sequences

so last last week was sequences

last week was series

[elder scaffold]

limiting sums?

[lilac sluice]

uhhh yes

that was last weeks content

[elder scaffold]

hmm, weird order

[lilac sluice]

is it?

[elder scaffold]

yeah idk what much else there is to it, maybe you'll touch on financial mathematics

[lilac sluice]

oh yea true

applications of sequences and series

that’s gonna be annoying

[elder scaffold]

financial definitely has to be the worst topic

[lilac sluice]

would u know how to do the next question

[lilac sluice]

i agree

i’ve solved b i

i got n/2 (99-3n)

but idk how to do ii

[elder scaffold]

set that to <0

then ur going to have to solve for n

[lilac sluice]

so i’ve done this

but i’m lost

is n > 33 in this case?

did i just write the notation wrong

[elder scaffold]

they want the least value of n

n>33 is true

but the lowest value would be 34

[lilac sluice]

so in this case n>33 or n>0

[elder scaffold]

n<0

[lilac sluice]

how so

3n/2

n = 0 here

so n>0

if that makes sense

[elder scaffold]

nah

its a quadratic

with a negative leading coefficient

[lilac sluice]

oh true

[elder scaffold]

i meant positive

but case in point

[lilac sluice]

so 3n/2 (n-33) > 0 still holds?

[elder scaffold]

still holds for what?

[lilac sluice]

like is it true

[elder scaffold]

yes

[lilac sluice]

and n>33 but n<0?

[elder scaffold]

yes

[lilac sluice]

but we can’t have -n terms so only n>33 is true

right

[elder scaffold]

yep

[lilac sluice]

okay

do u mind helping with 2a as well

[elder scaffold]

yeah i can help

[lilac sluice]

ight

[elder scaffold]

so there is a geometric progression

but it doesnt start with 420

[lilac sluice]

oh

oh it’s 430

right

[elder scaffold]

not exactly

[lilac sluice]

oh crap

mm and cm

[elder scaffold]

uuuhh

nah

[lilac sluice]

wait what

420 mm is when it was first observed

[elder scaffold]

its the fact that each successive growth is 70% of the previous week

[lilac sluice]

but grows 10 cm

oh

[elder scaffold]

oh yeah ur right actually, the units are different lol

[lilac sluice]

so it’s 14.2 in the first week

14.2 cm

[elder scaffold]

uhh

52 cm

[lilac sluice]

what the sigma

can u explain

[elder scaffold]

so its originally 42 cm

[lilac sluice]

OH

crap i got the conversion wrong

[elder scaffold]

lol alg

[lilac sluice]

ok so S8 = 163.34….

[elder scaffold]

so what equation do u have at the moment?

[lilac sluice]

which isn’t right

[elder scaffold]

let me do it real quick

[lilac sluice]

ight

[elder scaffold]

yeah so

back to my original point

it shouldnt start with 42 or any other number we discussed

[lilac sluice]

okay

[elder scaffold]

because 42 isnt in geometric progression

[lilac sluice]

so first term is 70% of 42 or 52?

[elder scaffold]

neither

it grows 10 cm

but each week its only 70% of what is was last week

so the 2nd week should grow by 7 cm

[lilac sluice]

ohhhh

so 3rd week would be 49/10

[elder scaffold]

yes

[lilac sluice]

so it’s a decreasing sequence

wait no

oops

[elder scaffold]

the amount is growing by is getting smaller

but the plant is still growing larger

[lilac sluice]

yes that’s what i meant to say

[elder scaffold]

what u have is fine, just split up the 52

it should be 42 + 10(1-...)

[lilac sluice]

wdym split up the 52

oh

[elder scaffold]

so that the 10 is in geometric progression

[lilac sluice]

but the formula only uses T1

ohhhh

true

is it 1-30%?

[elder scaffold]

nah its basically what u have now

but with a 10 instead of 52

then just add the 42 to the end