math-help

[cyan night]

they arent?

[left knoll]

h should come first then g

no?

[cyan night]

no

h is intersection between ac and mn

guys

is anyone there

indian grinder how should i use ∠AHM = ∠BGN

[left knoll]

mahn is this hard or only i am finding it hard?

[cyan night]

its grade 8

[left knoll]

lolllllll

[cyan night]

uh

whats ur approach

[median turtle]

Its not

I just entered the server and saw this problem floating here

@cyan night Have you learnt euclidean geometry?

Its needed for this problem

[left knoll]

Apparently i haven't

[cyan night]

what is that

[median turtle]

Oh

wait

[cyan night]

i dont think so and it doesnt need it

[median turtle]

It does

[cyan night]

my teacher made it possible for grade 8 knowledge

[left knoll]

@median turtle hey is the figure correct?

[median turtle]

that's only under the assumption that he's saying the truth

[cyan night]

he is

🤔

[median turtle]

Nope

[cyan night]

what

it is possible

[median turtle]

Ok let me explain

[cyan night]

😦

[median turtle]

It may take some time, but it should be the solution

[cyan night]

okay

[median turtle]

what is your figure?

reply to the message where you sent it

[cyan night]

this

i added point P

[median turtle]

basically

what you gonna do is

make a random quadrilateral

let me fix one up quick

[cyan night]

ok

[median turtle]

Yes

the E is point N

because ∠AHM = ∠BGN

we can say that

[cyan night]

what are those labels lol

[median turtle]

Yeah I drew it on a screen

like on a webpage

[cyan night]

ok

[median turtle]

so its kinda bad

[cyan night]

ok

[median turtle]

If you see the drawing closely

You realize that by dividing the quadrilateral by AC

You get 2 triangles

so if you can prove that those are congruent

you can say that AC = BD

[cyan night]

yeah

[median turtle]

since ∠AHM = ∠BGN is given

[cyan night]

so

[median turtle]

try it yourself first, proving the congruency of ABC and ADC

[cyan night]

uhh

im having a different approach

[median turtle]

actually no, its ACB and BDC

[median turtle]

what does this say?

like explain

[cyan night]

here is my shape

mn is parallel to dp

[median turtle]

ah ok

I realize

[cyan night]

wait so doesnt that mean g is the midpoint of bd?

oh nvm i thought g,h,n are alligned

[cyan night]

these have nothing but dc common

[median turtle]

Huh.

Your teacher made it pretty easy

Consider the quadrilateral a square

[cyan night]

what

[median turtle]

now draw it and prove its congruency using SSS rule

[cyan night]

no i am figuring out in a different direction

[median turtle]

Ok then, you're on your own

I helped you with my way

[cyan night]

ok

[ember kernel]

I'm at work. Rely on others for now ^^

[cyan night]

ok

im self relying

wait @median turtle are we considering that ac = bd or ahm = bgn

[median turtle]

both are given

use both of them

[cyan night]

what

it said that prove ac = bd if and only if ahm = bgn

[left knoll]

I forgot 😭

[twilit crane]

Hey

@cyan night

I got it

[cyan night]

me too

its actually easy lol

[twilit crane]

It's thales

[cyan night]

yeah

[twilit crane]

Yes too easy

[cyan night]

also known as midline of a trapezium

do u know midline of trapezium?

[twilit crane]

Yes

[cyan night]

yeah so basically what i did was i drew the midline of trapezium abcd

the midline connects the midpoints of ac and bd so its also the intersection of the diagonals of the two parallelograms

[twilit crane]

Medline of triangle

[cyan night]

what

oh

in this problem i used both

[twilit crane]

Qf right

[cyan night]

yeah if thats how u named the midline of trapeziu

qf = 3+5)/2 = 4

qf is also the midline of triangle mnk

qf = 1/2NK => NK = 8

[twilit crane]

Yes

[median turtle]

log

remember?

find all possible cases of x y and z such that

[median turtle]

@cyan night

help

Find all possible cases of x y and z such that the equation

[cyan night]

algebra

[median turtle]

Yes help

[cyan night]

i remember already doing it

[median turtle]

yea so help me?

please?

[cyan night]

but i dont remember how i did it

[median turtle]

bruh

[cyan night]

because i never concentrated in my algebra class

[median turtle]

@left knoll

[median turtle]

any idea?

The question is: find all cases of x y and z such that the equation

nevermind

[cyan night]

u stillneed help?

[left knoll]

yes?

[cyan night]

just algebaically simplify

[ivory pumice]

Hmm

Did you solve it? Or still need help?

[cyan night]

i solved it

[ivory pumice]

Ok

[cyan night]

i neatly solved it

[ivory pumice]

Ok

[cyan night]

do u want to know the solution or do u know how to do it

[ivory pumice]

Nah I did it

[cyan night]

👍

[ivory pumice]

(x²+y²+z²)²= x⁴+y⁴+z⁴+2(x²y²+y²z²+x²z²)

[median turtle]

Yea I figured it out thanks tho

[swift ridge]

Hello

I need help

[median turtle]

hi

send the question here

[median turtle]

can you please translate this?

[swift ridge]

I need to sole this

[median turtle]

this is a test?

read #rules

[swift ridge]

Solve the following initial value problems

Old exam

You know or not

[short rover]

hey someone break mid term in 3x^2 - 4√3x + 4

[ivory pumice]

It is a perfect square@short rover

(√3x -2 )²

3x²-2√3x -2√3x+4

√3x(√3x-2)- 2(√3x-2)

(√3x-2)²

[stray musk]

I have been stuck on this for a fat while

[ivory pumice]

Still need help? If yes then I will do it after 1hr

[swift ridge]

Yes ok no problem I what to see the right answer

[ember kernel]

(a) you can't conclude anything about sum(a_n) because, as a_n > b_n for all n, all you know is that sum(a_n) > sum(b_n) for all n, which tells you little about whether sum(a_n) goes to infinity or not when n is very big. Therefore, there is no way to know if sum(a_n) ever converges or not, it all depends on the expression for a_n

(b) You know that 0 < a_n < b_n for all n. Therefore, 0 < sum(a_n) < sum(b_n). As sum(b_n) converges to a real number, that means the value sum(a_n) is contained between two real numbers, and thus cannot go to infinity (diverge) when n grows infinitely large

That's called the comparison theorem

[ember kernel]

Your second-to-last line is wrong, it should be :
= (2x - 3) * (x + 3)

That's because, from the previous line, you factor out (x + 3)

@left knoll

The last line is just the final, factorized expression for f(x), with all the factors you found : (x-2), (2x-3) and (x+3)

[left knoll]

Ah ty so much bruhh

[ivory pumice]

am getting x+c = (3x+2y)/5 +4/25ln (5(3x+2y)+6)

and put y(-1)= 1

[ivory pumice]

How did I do it :- assumed t = 3x+2y , 3+y' = t` , y' = t/t+2 , and then solved it

[ivory pumice]

5x⁶/y⁴= -9x⁵+89

How did I do it , assume t= 1/y³, divided the whole equation by y⁴ , t= 1/y³, dt/dx = -3/y⁴ dy/dx , substituted this and then used leibneiz form method

[tawny ingot]

Hello Im currently in middle school and would like to learn algebra 1, 2 and 3 online.
Does anyone here knows any good sites?

[hearty tapir]

The links in #useful-links might (and i think they WILL) help you.Take a look.

There are amazing websites that are suitable for learning math, physics etc. like KhanAcademy and Openstax.I recommend them @tawny ingot

[stray musk]

Does anyone know how to do this?

[formal heart]

Can someone help me with this? Its Simplifying Complex Fractions

This is what I have so far not sure if its correct though

[cyan night]

you are correct!

for these problems, just simplify them into a common denominator in both fractions and u can solve it

[formal heart]

Thank you!

[tawny ingot]

Thank you so much

[hearty tapir]

You're welcome 👍

[cyan night]

Given right triangle ABC (AB<AC). On the collinear ray with ray AB, take point D such that BD = AC. On the collinear ray with ray CA, take E such that CE = AD. DC intersects BE at F. Prove that ∠CFB = 45◦

[steel plover]

can someone help me out with a?

[timber scarab]

B part

[swift ridge]

Guys I need someone who knows (matlab)

I need to ask about something

[zenith quarry]

Y u took the exponential function ????? Means in second step

[zenith quarry]

We can also use u / v formula Sloving sinhx and cos hx

[timber scarab]

Yes we can..but I have solved many questions by taking exponential functions so that's why

[zenith quarry]

Can u explain because , I didn't understood !
I have just started doing derivatives .

[steel plover]

thanks!

[mossy fjord]

Glad to help !

[slow cipher]

anyone knows how to solve this?

[timber scarab]

hyperbolicfunctions.pdf
@zenith quarry
This might help u ,if u r learning derivatives

[next viper]

ayo

in exam rn

idk how to do thht

help

[left knoll]

just a sec

[left knoll]

there is an identity a^3 - b^3

use that and also use (a-b)^2

[next viper]

-;

dint understand

my exam

[left knoll]

oh this is an exam

[next viper]

question

stuck LOL

bruh

iam dead

bruh

[left knoll]

i cant help you with an answer

[next viper]

;

[left knoll]

use the identity

[left knoll]

i think a - is like the elements in the universal set which are not in a but im not sure

[next viper]

ayo

If y-1/y =9 find the value of y3-1/y3​

[peak gale]

multiply by y , find the roots of the polynomial then inject in the relationship : y^3-y^(-3)=...

[cyan night]

hes in an exam, its against the rules

[steel plover]

can someone help me out with this problem?

[floral marlin]

hello, i have a problem. I need to calculate the area of a triangle, but I only have this available: a=12cm,α=35 and β=75. I get 113.943 cm^2 but the answers say it's 135.1, can anyone help? bcs idk if the answer in the book is mistaken or if my answer is not correct. Thank you!

[left knoll]

If possible can you send pic of the diagram

Try calculating value of sides using angles and then use Herons formula

[floral marlin]

i did right that and also tried with the height

[twilit crane]

Bro I think the angles ąlpha and Beta are the ones on each end of the line a

[left knoll]

BC= 12cos (beta) and AC= 12 cos(beta) cos (alpha) but those values turn out to be so small that triangles property is violated

So, i guess we need to find suitable triangle and then calculate area

[floral marlin]

ohh i see it now, I actually also turned around the angles

[left knoll]

lol

[floral marlin]

I'll try again lol Thank you!

[left knoll]

Guys can someone from India who studies engineering or medicine please dm me

[alpine escarp]

can someone help me guess what this function is

the value on the y axis that's blurred out is 3

[ember kernel]

y = -1,5x +3, thank me later

Nah seriously, that graph looks strange to me. Maybe we could start by make a list of the info we have :

• tends to 0 when x tends to inf
• global min and max
• f'(2) = -2 (because tangeant to y = -1,5x+3 at x = 2)
• positive with 0 < x < 2
• negative with 2 < x
• roots at x = 0 and 2

Additional (not rigourous) info :

• global min seems to be at x = pi
• only accepts x >= 0, it might indicates a sqrt or log

[hushed talon]

Does anyone know how can I turn this

into this?

Im stuck :c

I need the process

[hushed talon]

nevermind I found the solution :D

[ember kernel]

Treat eaxh term as an independent function. Like this :
f(x) = x³
g(x) = 3x²
h(x) = -9x
i(x) = -7

Therefore, y = f + g + h + i
(I removed the (x) because it's too repetitive

[slate pawn]

hi! can someone help me with this problem?

h(x)=|15-9x|
If h(x)=48, find x.

[ember kernel]

Since (a + b)' = a' + b'

Using the power rule and differentiation of a constant, you can calculate y'= (f+g+h+i)' = f'+ g' + h' + i'

[hardy hare]

help lol

[ivory pumice]

D<0

[hardy hare]

hm?

[ivory pumice]

non negative hmm means it can be 0 too, it should be D<=0

D= 144-4×(-5+2a)×4

[hardy hare]

where did this come from 😭

[ivory pumice]

think it like this, if it had 2 distinct roots the the function had to cross x axis and become negative for values between them

Now to become non negative , it either touches the x axis or does not touch at all, means it can have equal roots or no roots at all

[hardy hare]

ahhhh okok i get this

[hearty tapir]

|15-9x| = 48 ----> 15-9x = 48 , 9x-15 = 48

#1 15-9x = 48 -> 9x = -33 -> 3x = -11 --> x = -11/3
#2 9x-15 = 48 -> 9x = 63 --> x = 7

[ivory pumice]

Oops I took 45 instead of 48

[hearty tapir]

I guess you did a liiiiitle mistake there, sir :))

[ivory pumice]

Yeah

[hardy hare]

it can have equal roots or no roots at all
is this based on the equations discriminant? im lost sorry

[ivory pumice]

Yeah

when it has equal roots then it minimum value will be 0

Which is non negative

For example y=x²

for this discriminant should be 0

[hardy hare]

OHH is this the discriminant LOL

[ivory pumice]

there can be another case when the function does not touch the x axis at all, it means it does not have real roots , for this D<0

[hardy hare]

yeah yeah

[ivory pumice]

Yes

[hardy hare]

can i dm you LOL 😭

[ivory pumice]

Yeah sure , am free for 15 mins

[slate pawn]

thank you!

[hearty tapir]

I'm glad to be helpful!

[hardy hare]

i hate combinatorics help

[ivory pumice]

4!×5c3 , -P-N -C - E -, A's can be filled in any three of the empty boxes , so 5c3, PNCE can be arranged in 4! , So 4!×5c3 @hardy hare

[hardy hare]

so 40 is the answer?

[ivory pumice]

10×24

4! = 4×3×2×1

[hardy hare]

oh

[ivory pumice]

@hardy hare what is the answer?

[hardy hare]

is it 240 😭 bro idk

[ivory pumice]

Oh , I asked to confirm it , yeah I think it should be 240

[hardy hare]

oh okay thank you lol

[left knoll]

Does this also consider the cases of something like AAPANCE

[proven orchid]

help required

[proven orchid]

alpha was found as 60 degrees

is that correct?

[ivory pumice]

I read the question again it says not all hmm , I did it such that every A is apart , well now I have do another case

[left knoll]

Yeaa

[proven orchid]

I didn't do it yet

[ivory pumice]

7!/3!- 5!

[waxen storm]

dude go away

[proven orchid]

can you do it then?

[ivory pumice]

Well uh I made a mistake , lemme do it once again , total number of permutations will be 7!/3! , Which will include everycase, so to get the desired cases , we meed to substract the cases where all three A's are together , which would be 5!

[left knoll]

dw i opened a ticket

[ivory pumice]

@left knoll check this , and lemme know if it's correct

Kindergarten

[hardy hare]

ohhhh

[ivory pumice]

Sadly am not Einstein ;-;

[left knoll]

tbh i dont really know permutation combination and whatever it is 😅 i was just curious because i saw the possibility of 2 of the A's being together

[ivory pumice]

Oh , ty for letting me know

[hardy hare]

duh why would i ask if i did

[hardy hare]

same and i hate it

[ivory pumice]

part a ) divide and multiply by 2 , you would get 2 cos (60°+alpha)
From part a we can see that maximum value will be 2 &minimum -2
2(cos(60°+alpha)) =1
cos (60°+alpha) = 1/2
Now 60°+alpha = 60° or 300
So alpha = 0 & 240°

As I said am not Einstein , I have only 1 brain cell , but you look like a genius so maybe you can?

Then maybe you are blind

[boreal torrent]

Can you help me with this

[ivory pumice]

Cos A -cos A +cos A -cos A = 0

[fringe heart]

Indian

[ivory pumice]

Lemme try this , jee advanced question I guess

Nah , how can I google integration questions lmao

Nope

Ik

No

[left knoll]

Just ignore this guy please, they just want to pick a fight. We're all here to study

[boreal torrent]

Yes it is.

[ivory pumice]

Well tbh idc , what do you think, and try hard you cant even offend anyone , everyone is cringing hard rn at your texts

[ivory pumice]

I will try it , if I will get the answer then will dm you , I have to revise integration first

Nah

Ok

[waxen storm]

ye i got it thx

[ivory pumice]

Well what I did was I took (1-x)²& expanded it into (1+x²-2x)

And then I split this term

I think you can proceed like that

Well lemme try if it actually works or not

Nah i will try it later , it's better to do after revising the topic

[frail geode]

@boreal torrent what grade are you in? When you are in college it is pretty easy

Hope this helps you @boreal torrent

and then, when you use normal integration, then it should me 22/7 - pi

[storm horizon]

help me please

[left knoll]

A path 5m wide runs along inside a rectangular field. The length of the rectangular field is 3 times the breadth of the field. If the area of the path is 500 square metres, then find the length and breadth of the field.
PLEASE HELP ME anyone!!

[ivory schooner]

I got length=100

so for breadth just divide that by 3

take it with a grain of salt tho im not sure

[sonic breach]

^

[sharp ferry]

what specifically do you need to know in this

first part just plot the points second part take 2 points on the graph and find the slope by using y2-y1/x2-x1

[waxen storm]

how did this happen>

?

[sharp ferry]

3rd part H=(V^2)t/R

[sharp ferry]

sin2x=2sinxcosx formula

[waxen storm]

yeah ik but i'm not able to see how they applied that on the rhs

[sharp ferry]

see its
4*(sin2x) (cos2x)(cos4x)
which is 2* 2 *(sin2x) (cos2x)

did you get it now?

[waxen storm]

dude

are u

einstein

thank you so much

[sharp ferry]

now that term in the [ ] becomes sin4x

[sharp ferry]

bruh

[waxen storm]

yah got it

[sharp ferry]

no problem 😊

[waxen storm]

man i sure am grateful

[hollow mauve]

A Lil help with 4(i) pls?

[ivory pumice]

@hollow mauve conver cosx = sin (π/2-x)

sin^-1 (sin (π/2-x))= π/2 -x

Assume tan(z) = X

it would become , z .(π/2-tan(z))sec²(z) dz

[hollow mauve]

Yeah I tried that but got stuck in simplification

😂

[ivory pumice]

Oh

[hollow mauve]

Maybe trigo formula was not clear

Will try again

Thanks

[ivory pumice]

Lemme actually try then

[hollow mauve]

It will be a lot easier if you just open 1-x^4 as a2-b2

[ivory pumice]

I just thought of it like this , and it was working fine

[hollow mauve]

It would cut with the denominator

[hollow mauve]

Yeah, will try again! Appreciate it :)

[frail geode]

@hollow mauve i dont know what level of math he has, so i tried the brute force one

[hollow mauve]

Hahah okay!

[frail geode]

besides its not 1-x^4 but (1-x)^4

[hollow mauve]

Oh

Shit

Sorry

🤦🏻

Hey but I dont understand the first step of your integration

[frail geode]

thats why i used polynomial division in order to break that integral up

[hollow mauve]

My mind tends to simplify things a lot 😂

[frail geode]

simply use binomial fomula und then transform

[hollow mauve]

Oh

Never thought of this way

[frail geode]

then you can cut out everthing that has the form 1+x^2

[hollow mauve]

Yes yes

[hollow mauve]

Alright thanks!

[frail geode]

and after that, you have nice tan^-1(x) which has connections to pi

i hope he understands, what i tried to do xD

[hollow mauve]

Well

I understood

He will too

[frail geode]

he didnt respond so ill wait

[hollow mauve]

Same I am a jee aspirant as well

[frail geode]

whats that?

Never heard that term before

[hollow mauve]

Its and entrance for engineering

In india

[frail geode]

ah nice

[hollow mauve]

Hyped up exam for science students

Very famous for being tough in foreign countries as well

[frail geode]

i wish you luck then 😄

Do you have like old entrance exams?

So you can practice @hollow mauve ?

Because often, you simply take a closer look at these and then you basically know, what they are trying to aim for

[ivory pumice]

Yeah I tried it , it is becoming extremely lengthy , so I just left it

I will dm you if I will solve in much more simpler way

[frail geode]

@hollow mauve could you try send it again but this time rotated?

I can try and solve the integral

Are you allowed to use complex numbers for sin and cos?

[ivory pumice]

Well you will still get the answer , I tried again , it is not too lengthy

[frail geode]

@ivory pumice could you send the trick?

cuz i dont see it

[ivory pumice]

.

[frail geode]

oh bruh

Is someone here good at statistics?

[mellow bramble]

someone speak spanish¿

[steel plover]

need some help with this problem please

seems like asinh(a) would be the answer but I'm not quite sure

[waxen storm]

in trigonometric equations i am not able to understand where u take the x = 2n pie +- a and when to take it as (2n+1)pie/2

can someone explain it to me how it works?

[ember kernel]

I deleted my whole answer because I'm dumb and thought I was wrong.
I got the equation a sinh(a) = cosh(a)

How I got it :

• calculate tangeant fonction f(x) = mx + p knowing that it goes through (a, cosh(a)) and (0,0)
• You get f(x) = (cosh(a)/a)*x
• cosh(x) and f(x) are tangeant, and therefore have equal derivatives at x = a
• Knowing that (cosh(x))' = sinh(x), you get sinh(x) = cosh(a)/a at x = a
• Finally, you get sinh(a) = cosh(a)/a, which is equivalent to : a sinh(a) = cosh(a)

[mossy fjord]

Quentin! (눈_눈;) you are not dumb. You are like the smartest person ever.🙌🏻

[formal patrol]

Can anyone help me with this? Should I convert this to classes?

[ember kernel]

Let's be real, I'm not lol

[covert anchor]

how would i do this

i tried so many times

spent 1 hour on this thing

[ember kernel]

I'll try it in 2h (if I don't forget to do it so don't rely to much on me :P)

But I can already tell you that the diagonals are perpendical (due to the symmetries in the triangles in the kite)

And that Q = (2m, 2n) where (m,n) are the coordinates of the intersection of the diagonals

Maybe a solution would be to get 2 equations you need to solve for x and y :
RQ= PQ
OQ = PR

(notation : OQ represents the linear function that goes through O and Q)

[mossy fjord]

(҂⌣̀_⌣́)in my eyes you are!

[ivory pumice]

slope of line oq =-1/slope of PR

=1/2

Equation of OQ = y=x/2

distance from 4,0= 4(isoceles triangle)

And Q lies on y=x/2

Solve to get positive values of x&y

[rustic sapphire]

hey does anyone have hyperbola notes for jee?

[void badge]

If it helps

[tardy crown]

Hi somebody can help me with this?

Sorry for the spanish hehe

I don't know how solve the second question

If You know a vídeo, please share

[steel plover]

thanks for the help Quentin!

[steel plover]

one question tho, how did you find f(x) (the second step)

[dark sorrel]

To find f(x) you have to find m and p. You are given that the function passes through (a, cosh(a)) and (0,0). The parameter m specifies how much f(x) changes for a change in x. So you can find m by dividing the change in y by the change in x for both coordinates. So m = (cosh(a) - 0) / (a - 0) = cosh(a)/a. Finally you can find p by filling in one coordinate in f(x), for example (0,0). We know that f(0) = 0 must be true, so f(0) = (cosh(a)/a) * 0 + p = 0. That means p = 0.

[steel plover]

ahh I got it. thank you!!

[cyan night]

bezout theorem

[modest compass]

Anybody know what i could do here?

[pearl tusk]

is the three lines = ? cause if yes then i can try solving it @modest compass

[modest compass]

Yeah i think so

[pearl tusk]

okay i'll send it in sometime

[cyan night]

its not equal

[pearl tusk]

then what is it

[modest compass]

Wait it isn't? I've always treated it like it was oops

[pearl tusk]

?

[cyan night]

@modest compass 1+cos^4x-sin^4 x and 2cos^2x are congruent

[modest compass]

What does congruent mean?

[cyan night]

the remainder congruent thing

[pearl tusk]

so they are triangles

[cyan night]

no..

congruence doesnt always refer to triangles

search up modulo congruence

if u think they are equal all the time then uh

[pearl tusk]

dude you are literally in middle school

your role says that

[cyan night]

i learnt it already

so u think im wrong?

[pearl tusk]

which country are in from

[cyan night]

search up modulo congruence and u will see the same sign

[pearl tusk]

idk all im saying is that i learnt something like this in school and its different from what you are saying

[cyan night]

just search it up

[pearl tusk]

yea i looked it up

you're right

[cyan night]

for your information, equal is =

ya they are different

[pearl tusk]

dude you need to leanr what is being taught

[pearl tusk]

yea

ik i thought it was an error

sorry

[cyan night]

no problem

its a little more advanced

[pearl tusk]

i see i don't know about that

[sharp grove]

does anyone know how to complete the square fo 2x^2+5x-8=0

[cyan night]

factorise

[cyan night]

u still need help?

ok so im assuming u dont

[rustic sapphire]

thankyou

[sharp grove]

hii i dont need help anymore, just ealized i didnt need to do it

thank you for checking back!

[cyan night]

sorry for the ping but if ur wondering how to do it, u should try making it factorizable. which in this case, i multiplied the whole equation by 2 (and 0x2 = 0) so that 4x^2 is factorizable (4x^2 = (2x)^2). so i have the equation 4x^2 + 10x - 16 = 0. in these equations where u have to complete the squares, u usually have to make it under the form of (a+b)^2 or (a-b)^2 or anything with a power of 2. here i see that I already have 4x^2 = (2x)^2 and I want to factorize 10x. as known, (a+b)^2 = a^2+2ab +b^2, where a in this case is 2x. so 2*(2x) * b = 10x. => 4 * x * b = 10x -> b = 10/4 = 5/2. and then we want (5/2)^2 = 25/4, but we currently have 16. so the equation turns into 4x^2 + 10x + 25/4 - 89/4 = 0. => using a^2+2ab+b^2 = (a+b)^2, 4x^2 +10x + 25/4 = (2x+5/2)^2 => (2x+5/2)^2 - 89/4 = 0 => (2x+5/2) ^2 = 89/4 => (2x+5/2) = either sqrt (89/4) or - sqrt (89/4), which are (sqrt 89)/2 or - (sqrt 89)/2. thus, x = either ((sqrt 89) - 5)/4 or - ((sqrt 89) - 5)/4

sorry if my explanation is still obscure lol

[ruby tinsel]

Can someone please help me with this question?

[ember kernel]

a + b + c = 23
a + b = c + 3 <=> a + b - c = 3
0.5a + 0.2b + 0.1c = 5.10

These are the three equations you need to solve to get a, b and c

Thus, if you represent the system with matrix, you get Ax = b where :

     1   1   1

A = 1 1 -1 (coefficients of unknowns)
.5 .2 .1

x = [a, b, c] (the vector of unknowns)

b = [23, 3, 5.10] (independant terms)

@ruby tinsel From there, you can apply the Gaussian elimination you've learnt

(Hint : your answer should have c = 10, you can easily verify that using the first two equations)

[ruby tinsel]

Ohhhh I understand it now!! Thank you so much!!

[tardy maple]

how to do these type of questions

i cant wrap my head around it

[cyan night]

where do u need help?

if you need help dealing with fractions, then multiply so u have common denominator

[glacial robin]

probably something like this

[cyan night]

yeah multiply to have common denominator

i can solve with inequalities but whenever you switch sides a negative nmber then u switch the inequality sign

[tardy maple]

i dont understand still

[lofty arch]

You just treat the inequality as an equal sign, unless you multiply or divide by any negative number, then you flip the inequality around

[tardy maple]

ah

so its like solve for x but more fancy

[lofty arch]

yep!

[tardy maple]

how do you know when to flip the sign

nvm

i got it

thanks

[lofty arch]

yeah for this one you don't have to

As long as you keep the rule in your mind for a while it'll become natural

[glossy falcon]

Hi guys I just discovered am stupid I can't solve (5) for some reason

[cyan night]

do u know the formula a^2-b^2 = (a-b)*(a+b)

you multiply so u have common denominator

the answer is 2b/a^2-b^2

[glossy falcon]

i keep getting 2ab and not b

[chilly light]

I am having some derivation/deduction issues with a thermodynamics problem. I want to solve for V2 but cant get it to match with the factsheet. If anyone has the time to explain it to me that`d be appriciated:)

[fierce oasis]

guys, i need help. i got an exam tomorrow and i don't know how to solve this question. it's starting to chip away at my mind slowly the more and more i try with my friend over discord. help us out mate, im sure youse are smarter than the two of us combinedddddd.

[ember kernel]

Send me a dm for the ping, I'll try to do it when I'm done working

[fierce oasis]

aw cheers mate, just in case if anyone else is down to hop in a call with me and help me figure this shit out i'd greatly appreciate it.

[flint crest]

May someone help me?

The question ask to simplify

[wild rover]

https://www.chegg.com/homework-help/questions-and-answers/common-cryptography-work-large-numbers-expressions-simplify-large-numbers-however-computat-q83096228

[mossy fjord]

Radioactive decays are first order reaction
And half life of 1st orser reaction is 0.693/k
Find k then substitute in t=2.303/k log(10/10% 10g)

[mossy fjord]

Is the time 79758 years

[ember kernel]

Let m0 be the initial mass of plutonium-239 (in g), t1 its half-life (in years) and t the time (years)

Let M(t) be the remaining mass of plutonium-239 at time t (in grams)

Using the function of exponential decay, you get :

[ember kernel]

(there's a mistake, I wrote M(x) instead of M(t))

The question gives you m0 = 10, M(t) = 1 (=10% of m0) and t1 = 24000

This gives you the following equation, that you need to solve for t :

[ember kernel]

My answer is different from @mossy fjord's, so one of us (or both) must have made a mistake

@fierce oasis

[mossy fjord]

I might have made some mistake in taking the logarithm value.
But the formulas of chemical kinetics should apply on this question
But it was cool! Different approaches to the same question

[weary granite]

@formal iris help me

[sharp ferry]

can someone help me with this

[coral sierra]

Bit of a late response, but what you want start with is finding the minimum value and maximum value that y could take

[gleaming ridge]

i know this is irrelevant but I love your handwriting

[rustic sapphire]

hey is anyone good with hyperbola, please dm me

[floral marlin]

hello, can anyone help me with this: the sides of parallelogram are a=23cm and b=11cm, the lengths of the diagonals are in ratio 2:3, I need to calculate the diagonals. Pls help

[pearl tusk]

Here dude

@floral marlin

[floral marlin]

Thank you so so much!!

[pearl tusk]

no problem @floral marlin if you find any question difficult then just google it you'll get similar question then you can apply the formula and do it

[floral marlin]

Smart thinking haha thank you, I was stuck on this question for a long time haha

[timid delta]

Oh naiss

[turbid stump]

Hey I'm taking the August sat does anyone have any tips

[gritty agate]

Hello! is there anyone who knows how to write in Latex?

[hardy elk]

Can anyone help solve this Differential Equations question?

[minor rapids]

IM STUDYING FOR SAT

AND FORGOT HOW TO DO THIS BASIC ALG 2 PROBLEM

PLS HELP

the answer is 4x-3 but idk how

[lofty arch]

f(x) = 3-2x

for f(f(x)) you replace the x in the f(x) with another f(x)

so 3 - 2x becomes 3 - 2f(x)

[ember kernel]

Yup, what's your question ?

[dense wadi]

@minor rapids

[weak silo]

TRANSLATION: Find an equation of the spherical surface whose center is contained in the line r: and goes through the points A and B

[weak silo]

nevermind, already did it lmao

[sage cobalt]

I need help

[ember kernel]

What's the meaning of j ?

[sage cobalt]

its just i

[ember kernel]

Oh okay

For the equality to hold, both real and imaginary parts must be equal

That gives you two equations :
32-8a = 0 (real parts)
0 = 7-a-b (imaginary parts)

From the 1st equation, you get that a = 4, and when you substitute that into the 2nd equation, you get b = 7 - a = 7-4 = 3

Therefore, a=4 and b=3

@sage cobalt

[left knoll]

i need help

it's pretty hard

[left knoll]

help

[left knoll]

=infinite ?

[lofty arch]

for large x, you can disregard the +5 and just write it as 5*(4/3)^x, which as x approaches infinity also approaches infinity

[left knoll]

yea is like 5*(4/3)^inf+5/(3^x)=inf+0=inf

tyyyyy <333

[ember kernel]

I'm struggling to find the meaning of "is inverse" in your question

And there may be a typo, since it's odd to separate -3mx² and -9mx² instead of keeping it -12mx²

[left knoll]

6 and 7

I hate word problems with my whole heart

I think my phone is glitching

Lol

Oh ma gawd I feel so dumb rn

Thank u smmmmmm

Your handwriting is beautiful idiot!

It's still beautiful

[brave vapor]

Find the distance from point Q = (10,2) to the
line L: 2x + y - 7 = 0

can someone help me with that problem?

[ember kernel]

1. Find the function f(x) = mx + p, the graph of which is perpendicular to L and goes through Q
2. Find the intersection between L and the graph of f(x) at point P (a,b)
3. Use the distance formula : dist(Q,P) = sqrt[ (10-a)² + (2-b)² ]

Hint for 1 (if you struggle too much) : ||imagine that the slope (derivative) of L is equal to k. For f(x) to be perpendicular to L, you need to use m = -1/k ||

@brave vapor

[brave vapor]

thank you so much

[urban idol]

Hi, I was wondering if someone could help me with this, I don't know how to do it, is function of function or co-function

this is the only example I have to do it but I don't understand:(

[steel phoenix]

you solved it correctly though, what's wrong?

oh that's an example for you to understand. for f(Q(x)), imagine 3x+2, but instead of x, put whatever Q(x) is. so it'll become 3(4x^2-5x) + 2

from there, simplify it

[carmine viper]

If you dont understand dm me

[zenith quarry]

Answer with explaination please

I don't know what to do in next step , is this correct ??

[ember kernel]

Trigonometric functions aren't related only to right triangles ; they're primarily linked to angles

Therefore, you need to find the value of angle BAC to be able to find sin(BAC), cos(BAC) and tan(BAC)

To find BAC, you might want to use the sine or cosine rules in arbitrary triangles (here : https://revisionmaths.com/gcse-maths-revision/trigonometry/sine-and-cosine-rule), since you already have the measures for all the sides and you know that two angles have the same value (isosceles triangle)

⬆️ I'll be honest with you, I won't go through the whole solution, because I'm not that fond of geometry, but here are the main steps to solve the problem

[vapid osprey]

ty friend, i will try to solve now

[limpid lantern]

it seems ok to me

[vapid osprey]

ty bro

[median sapphire]

its of trignometric equations

[fast schooner]

can someone explain how to solve this

[cyan night]

do u know how to convert radians to degrees?

id prefer to solve it in degrees for simplicity but anything works

then u identify the special triangle

if u learnt ratios in 45-45-90 triangles then u can hence find the trig ratios of it

and the coordinates x,y of point A are respective to the cosine and sine of the angle pi/4

[fast schooner]

yes

[cyan night]

u read yet?

[fast schooner]

yes

so if i do cosine that’s is adjacent hypotenuse right

but how do i know what the side lengths are

[cyan night]

its the ratio

u dont need the side lengths because u should be able to recognize the special triangles

have u learnt ratios in special triangles yet

[fast schooner]

ohh i see

i will have to review that then

thank u

[cyan night]

np

[median sapphire]

@cyan night

[cyan night]

no

refuse

[median sapphire]

means

[cyan night]

wdym

i refuse to do that

[median sapphire]

ohk

[harsh schooner]

I am supposed to factorise this using the remainder theorem. Any idea where the value of x=2 came from?

[tidal galleon]

it comes from the Gauss's theorem. It says that for any polynomial with coefficients in Z (integers) if it has any root in Q (rational root) it must be of the form p/q where p is a divisor for the independent term and q a positive divisor from the principal coefficient.
In this case p could be +-1,+-2,+-3,+-6 and q 1 or 3, so trying the differents combinations you arrive to 2, spoiler: ||also you arrive to -3 and 1/3||

[faint citrus]

Pythagorean theorem

@knotty totem

[left knoll]

why would this be 25x24? i don’t get it

[cyan night]

for the first card marie can give 25

one of the 25

and after she gave it

she got 24 left

so she have 24 more choices

<=> 24x25

[left knoll]

okay, thanks

[cyan night]

np

any questions ask clueberry faygo

[charred charm]

https://cdn.discordapp.com/attachments/729656575844810864/878698906739941386/unknown.png

can you help me with part c pls
part a 14.7m
part b 4.1m
i just dont get part c

[left knoll]

Hi everyone, I am looking for a colleague we can support each other, if anyone thinks, please write, thank you

[arctic crater]

Hello everybody. I am currently looking into the statsmodels library, namely statsmodels.formula.api.ols. I read the documentation, it seems everything is clear, but at the same time, no. (i'm a little dumb person lol)
In short, I will be glad if someone can help with understanding the R-style formula, or send a link to useful posts. Have a nice day everyone. thanks
#python

[sharp ferry]

since tan(pi/4)=1

The two sides are equal and the hypotenuse is 1 so
1=x^2 +x^2 (assuming the side length to be x)
2x^2=1
x=1/sqrt(2) [ we dont take the negative value since its the first quadrant]

[fast schooner]

phhh ok thanks

[cyan night]

i already helped him tho

[rustic sapphire]

help!!!!!!!!!!!

[snow eagle]

can some help 2(2x-7)+2(4x+3)=112

how get x?

[silk charm]

I gotchu

[rustic sapphire]

seriously dude just expand and solve:
4x-14+8x+6=112
12x-8=112
12x=120
x=120/12
x=10

[snow eagle]

thanks

also howyou find area

ik b x h but i still confused

[rustic sapphire]

33x

sub the value of x in this

[cyan night]

Is this guy like elementary school

[rustic sapphire]

yeah maybe

[obsidian sage]

1st one B 2nd one D

[rustic sapphire]

thankyou so much btw are you good in organic chemistry?

[obsidian sage]

i dont take chem anm

so no

[rustic sapphire]

k

[left knoll]

Can anyone help me number 21?

[crisp topaz]

anyone pls help me with this! really appreciate it!

[inland sigil]

The answer should be 'x³'

On the left hand side, you take a summation of (1³ +2³+ ....+n³) under the common denominator n⁴

Which gives you (n.(n+1)/2)² on the numerator and n⁴ on the denominator

Solving for the limit for n -> inf

You get 1/4 on the LHS

Integration of x³ on the given parameters gives 1/4

[charred hedge]

Can somebody help me?

[crisp topaz]

thank you so much for answering! but how to get (n.(n+1)/2)²?

[inland sigil]

That's a general formula for summation of first n natural numbers

It's general enough that it can be used without stating its proof

But I'd you're curious about the proof, you can look it up

[crisp topaz]

alright! thanks a lot!

[crisp topaz]

does anyone know how to get this ans? kindly explain it~thanks!

[obsidian sage]

sorry if it looks confusing

the expression is the summation of n rectangles under the e^x curve

so as n approaches infinity the total area of all the rectangle is exactly the area under the graph from 0 to 1

oh oops didnt realize its just a geometric progression with common ratio e^(1/n)

[crisp topaz]

the ans should be the last one, am I right?

[obsidian sage]

the last one here ?

[crisp topaz]

yea

[obsidian sage]

the rectangles have length of base = 1/n and height = e^(k/n)

there are n of them

[crisp topaz]

I see

oops ok..misunderstood

Thanks ya!

[obsidian sage]

np :p

[azure lion]

anyone willing to allow me to send them questions or theory i'm struggling to grasp/understand? <<a level math>> external candidate so no teacher help. pm if u can

[slate pawn]

hi! can someone help me with this problem? “ write a linear equation in slope-intercept form with the given information. slope=4/3; passes through (-5,-6). thonk uu : )

[cyan night]

i can help

[slate pawn]

thank you!

[cyan night]

you can just select that point that the equation passes through which is -5,-6

do u know rise over run?

slope = rise/run

noemi

so u basically rise/run until u get the y intercept

hence u have y = 4/3x+y-intercept

the y intercept here is 2

[slate pawn]

ooh okay i understand now. thank you

[cyan night]

npnpnpnpnp

[indigo field]

Hi can someone help me with this question, I don't understand why dt/dx is less than or equal to 0?

Need help with part f, thanks

Additional info that may help^

[pulsar turret]

-1 does not satisfy the equation so how come (D) is the answer?

If anyone can help, please.

(A) is actually the correct answer but when I looked up, they say solve it to give (D)

[indigo field]

Hey @pulsar turret

I think you might have written the quadratic equation wrong when solving for x

[hollow mauve]

Check with putting the options in the question directly, 200iq 📈😂

[left knoll]

hey...i haven't studied math for 2 years but i have it in my course now (basically stuff like linear equations) so if anyone can clear up my doubts that'll be great . Thanks

[left knoll]

Great idea if options are available

[ember kernel]

Hi ! Whether your questions are about general concepts or precise exercises, you can share them in this channel, and people will explain them to you. (If the answers to your questions happen to be long, you might expect to receive them in your dm's, to prevent flooding this channel 😄)

[left knoll]

cool thx

[hollow mauve]

Yeah..

[ember kernel]

So, what're your questions?

[left knoll]

nothing atm but im sure ill have a lot of doubts as my classes go by, So i just wanted to know if ill be able to get help here. Thx

[cyan night]

ask me

[tiny trout]

Anyone knows how to find xj and fj ?

[ember kernel]

1. Some words on the left and right of the screen are cut out. We don't have access to the whole question.

2. When asking for help, please translate the question for non-French speakers.

3. Considering the time of the year and that you're on a UCL-related website, you're most likely currently taking an online exam. If so, you may have skipped reading rule 5 of #welcome

[tiny trout]

Okay my bad

[ember kernel]

Good luck anyway

[tiny trout]

Thanks but it was to help a friend

[ember kernel]

As the example shows, the geometric mean of 2 numbers (there's a slight difference when dealing with 3 or more numbers) is just the square root of the product of these numbers

[cyan night]

is there any way to solve this algebraically?

quentin what do u think

therer are 9 variables smh

is trying out the only method

this problem is sus

[ember kernel]

There is indeed an algebrical way to solve this

Give me some time to write it on paper

[cyan night]

aight

i am giving a and i the maximum values which are 8 and 9 right

[cyan night]

u there quentin

[mossy fjord]

I m scratching my head over this Q :p

[cyan night]

i am not sure if it could be solved algebraically

its a question from nrich maths

the solution they provided were just students tryin all sorts of combinations

[mossy fjord]

It definitely can be solved algebraically
like it feels like a,b,c... will get cancelled out somehow

[cyan night]

yeah

u tried it out yet

[mossy fjord]

Srry i couldn't do it.

[cyan night]

ok no problem thanks for trying it out

[drowsy fog]

Sorry its a bit blurry, but does anyone know how to solve 1(b)

[thorny flicker]

can help with this

[cyan night]

is that a test

[drowsy fog]

Nope, just an exercise

Although my test coming up tomorrow TwT

[cyan night]

@ember kernel wwhats up?

got it yet?

dang

[ember kernel]

I'll be honest with you, this question just reminded me of how bad I am at discrete math problems

[cyan night]

is it just trial and error?

this is bs

i think trial and error is the only method

Suppose b+d+f+h is divisible by 5.
Min (b+d+f+h) ⇔ 1+2+3+4 = 10
Max (b+d+f+h) ⇔ 6+7+8+9 = 40
B+d+f+h is counted twice => totals of circles are Min or Max when b+d+f+h is Min or Max.
=> Min (all circles) = 1+2+3+4+5+6+7+8+9+Min (b+d+f+h since it’s counted twice) = 55
Max (all circles) = 1+2+3+4+5+6+7+8+9+Max (b+d+f+h) = 85
Case 1: We take min (b+d+f+h) ⇔ b or d or f or h = 1 or 2 or 3 or 4
=> a or c or e or g or i = 5 or 6 or 7 or 8 or 9
From the problem we could identify that a+b = b+c+d = d+e+f = f+g+h = h+i
=> a=c+d
b+c=e+f
d+e=g+h
i=f+g

here is my process so far

[ember kernel]

But I quickly wrote a very unoptimised program to get all possible solutions, so that you maybe could find some pattern in these

Here they are :

4 9 1 3 8 2 5 6 7
5 9 2 3 4 7 1 6 8
7 6 5 2 3 8 1 4 9
7 6 5 2 8 3 1 9 4
8 3 7 1 6 4 5 2 9
8 6 1 7 4 3 2 9 5
9 2 5 4 6 1 7 3 8
9 4 1 8 3 2 5 6 7

[cyan night]

ah

yes the solutions

so

ill just say

i did

"trial and error"

and i got that

PRO
BIG BRAIN MY CLUEBERRY FAYGO

[ember kernel]

You don't need to lie for that

[cyan night]

my friends they just copid the solution from the internet

but i have explanation

[cyan night]

does this sound good?

[ember kernel]

Just be honest, write that you couldn't find a proper pattern and that trial and error didn't give you any satisfactory solution

[cyan night]

there really was no proper pattern

aight

thanks quentin

[ember kernel]

No problemo

[cyan night]

@ember kernel wait are those all of the solutions

[cyan night]

this is bs problem imagine if my teacher doesnt grade this i force her to grade

[ember kernel]

Nah, for such a problem, that thoroughly relies on trial and error, it would be more than unfair to grade

I got them using a Python program I wrote, not by hand

[cyan night]

Ah ok

[cyan night]

that is the property of absolute value?

[vapid osprey]

I'm out of ideas on how to start

[cyan night]

do u know what is absolute value

[twin sluice]

is anyone here good in mathematical logic?

[calm trail]

Do I multiply only pairs of numbers when trying to get a number before the root?

So if there wasn't that one 3, I would only do 22 and its root is 2 so I would write 2√35*7?

I mean 2 * 2 but discord messed up

[lofty arch]

we write it out like that because we can take advantage of sqrt(a*b) = sqrt(a)*sqrt(b)

and we use the pairs of numbers because sqrt(a*a) = sqrt(a^2) = a

[left knoll]

Can someone explain to me why k< -8 as we just brought -8 to the other side, we didn't multiply or divide by a negative number, so the sign would remain the same but they have reversed the sign

[fringe stratus]

Anyone knows why the sum of the nth line of this triangle of consecutive odd numbers is simply n^3 ?
Like, for the 3rd line it'd be 7+9+11 which is 27 which is 3^3

[polar heron]

for product of two integers to be positive, either both of them have to be positive or both of them have to be negative.
k(k+8) > 0 for k>0, also
k(k+8) >0 for k<-8.

[ember kernel]

If you look closely, you'll see that the algebrical mean of each line n is n^2. Then, to get the total sum of the n items (odd numbers) the line, you multiply the mean by the number of items. Thus, you get that the total sum is n*n^2 = n^3

[fringe stratus]

Wow good freaking catch, thanks ! Simple curiosity, how'd you arrive to that conclusion, did you simply observe the triangle and it popped in your mind or ?

[north geyser]

The answer is -2 but I'm not sure if I did the process correctly?

since wouldnt it be (-4)(0+2) which equals 0; therefore, the answer would be wrong?

[fringe stratus]

hmmm I'm a little rusty in maths but I don't think you can remove the h at the line before the last one. Plus you don't really need to, you're calculating the limit when h tends toward 0, -2h + h^2 -8 then tends toward -8, and -8 divided by h then tends toward -∞

[north geyser]

yeah, I figured out my mistake

at the second line,

rather than [9-12-1]-[-4] which equals 0

ive been doing it without that brackets, thinking it was 8

[fringe stratus]

oh yeah then you were right about the -2 limit 🙂

[left knoll]

Anyone?

[polar heron]

f(0)= c = f(-3+3)= 10, then
f(1)= a+b+c= f(-2+3)=2,
f(-1)= a-b+c= f(-4+3)= 24,
solving for a and b gives, a= 3, b=-11, so
4a-2b+c= 44.

[tawny stratus]

Any help pls?

[cyan night]

use pascal triangle to expand (a+b)^n

i think

thats my approach its definitely one of the worst

[fleet agate]

guys do u have a basic math book

for the begginers

[ember kernel]

Convert into spherical coordinates

From there, to get z^10, put mod(z) (the norm) to the power of ten, and multiply arg(z) (the angle) by 10

But are you sure that i is part of the square root ? Because, if so, you must first convert the complex into the format a + bi

(But given the difficulty and nature of the question, I doubt this is the case)

[left knoll]

Thank you

[ivory pumice]

Nais

[craggy plume]

Can someone explain where does the square root of the first x+4 goes?

[polar heron]

the second term has extra square root of (x+4) in the denominator, so you multiply the numerator of the first term with square root of (x+4).

[craggy plume]

But didn't the denominator cancel out the the square root using the square and moves the power(-1/2) x+4 in the numerator down to the denominator to have another square root?

[polar heron]

Yes, but (x+4)^(-1/2) is only in the second term, so to move it down to the common denominator, you have to multiply numerator of the first term by (x+4)^(1/2).

[meager girder]

i have my maths exam on oct 29th /2nd nov it's Pure maths 3 and mechanics 1 (A2) like highschool level maths . so i am looking for advice on how i need to study to get a good grade considering i failed my last exams on this subject . So please i'm really stressing out on how to go about this . i could use all the advice i could get

[ember kernel]

General tips :

• You've still got 2 months to study and get ready. Don't panic, that'd be enough time to study the course twice if needed
• There's no shame in asking questions, and there's no such thing as dumb questions. If you don't feel confident to do so in front of others (although some of them would most likely actually like to get the answers to your questions too), ask them at the end of the class if you have time.
• Making a summary is very helpful and serves as a big role in the learning process. You can even ask you teacher to review it. If you're too shy, you can also ask a friend to do that latter part for you. Teachers' role is to help students after all.
• Practice. A lot. Because there's no better way to remember a formula and how to use it than actually getting familiar with it through many different exercises. Try to adapt the difficulty as well as you get better

Finally :

• Don't get stuck for hours on a problem if you can't concentrate. Take a break, go outside, read the theory again or ask this channel for guidances on how to solve it. But do not just stare at it endlessly

Unfortunately, I don't know what's studied in that "Pure maths 3" course, so I can't give you any precise tip regarding the matter itself

I don't know how to conclude, so I'll just add : never give up !

[cyan night]

ye and ask me for help

[ember kernel]

Ask anyone* for help ^^

[cyan night]

ye

quentin have u ever gone to amcs yet

why take so long

🤔

[ember kernel]

Sorry for the late reply.

It just occured to me that each line had """symmetrical items""".
Take line 3 for example, while searching for patterns in the triangle that could explain the n^3 thing, I didn't look at its items as 7, 9 and 11, but as 9-2, 9 and 9+2 instead, which gave the obvious mean = 9 = 3^2. From there, I quickly checked the result with lines 2 and 4 and got my conclusion from there

[cyan night]

isnt that peroperty of pascal

[ember kernel]

Tbh I can't remember what this property is precisely

[ember kernel]

Idk what that is

[ember kernel]

Was answering someone else's message

[cyan night]

american mathematics competition

like the amc8 amc10 amc12

[ember kernel]

As my role says, I'm European, but I did take part in regional competitions

[cyan night]

hmm oke but the competition is worldwide we also do it in asia

[ember kernel]

Oh I had never heard about it.
But tbh, I think it's kinda off topic in this channel

[cyan night]

ok

[meager girder]

the topics in Pure Mathematics 3 Paper are;
3.1 Algebra
3.2 Logarithmic and exponential functions
3.3 Trigonometry
3.4 Differentiation
3.5 Integration
3.6 Numerical solution of equations
3.7 Vectors
3.8 Differential equations
3.9 Complex numbers

[harsh dragon]

differential equations 😳

i am taking differential equations right now

[meager girder]

also thank you for the tips !! i liked to add

[meager girder]

bro i'm so lost tho

[harsh dragon]

me too

i gotta review my integrals and derivatives again

its been two years since i done that stuff

[meager girder]

4.1 Forces and equilibrium
4.2 Kinematics of motion in a straight line
4.3 Momentum
4.4 Newton’s laws of motion
4.5 Energy, work and power
^ for mechanics my other paper

[harsh dragon]

does paper mean "syllabus"

[meager girder]

well yes the topics for the specific exam

in maths i have 2 sub exams , one is pure math also known as calculus and the other exam is Mechanics

honestly man i'm also lost because i have to self study the syllabus . i don't have school

anyway thank you alot for the tips, i needed at least some guidance to get my mind straight

[harsh dragon]

the topics in your syllabus

are you learning all of the topics in you syllabus for the first time

or are some review

cuz if u already did pre-calc, then it seems like a pretty standard clauclus course

[meager girder]

yes ive done them before but it was months ago so now they're really vague to me

here's the syllabus if you guys wanna check it out

https://www.cambridgeinternational.org/Images/415060-2020-2022-syllabus.pdf

[proven orchid]

any help here would be appreciated

[fringe timber]

Is this right and if so why do i extend the 4 with times 2 instead of + 2?

[winged coyote]

yea u right, +2 would not have gave u the same base of two that you need to solve

[fringe timber]

But why is that? i dont understand it

@winged coyote "+2 would not have gave u the same base of two that you need to solve" why?

cus normaly 2^2 is 4

why is it 2^X x 2 instead of 2^X + 2 when the rule says This "a^2 times a^2 is a^2+2" anyone feel free to help me understand 😄

[cyan night]

ok

[solid anvil]

square has all sides equal

[covert briar]

yes

[solid anvil]

do corresponding wise

ab=ac

[covert briar]

mhm

[solid anvil]

cant we do my way as square has all sides equal?

[covert briar]

u need to find coordinates of a b c d not lenghts of the sides'

[solid anvil]

ahh ohh i need to read question nicely smh

[covert briar]

wait so can u show the process
like what do u find first '
what do u find next and so on

[cyan night]

im confused

im very confused.

[solid anvil]

guitars question?

[covert briar]

uve still got time bud ul learn
i just learned this last week

[cyan night]

equation of ac is 2x+y-5 = 0 <=> y = 2x-5 => slope of y = 2? meanwhile ac's slope is ad/ac = 1??

i am confused

i mean

-1

ad/ac = -1

rise over run not the fraction

uhh

anyone

[covert briar]

wait ha

still tryna figure this out

also it will be y = 2x+5 not -5

[solid anvil]

can we not corelate?

[cyan night]

guys

[covert briar]

pardon?

[cyan night]

teh distance from midpoint ac to a,b,c,d is sqrt 20

[solid anvil]

whom ?

[cyan night]

slope is sqrt 20

or 2 sqrt 5

from midpoint ac to b

i think i got answer

a is (2(3+sqrt.10/2,)-1-2(sqrt.10/2))

b is

(3+sqrt.10/2,-1+2(sqrt.10/2))

im just messing around guys

!!! amogus