help-27

[fossil locust]

your denominator is 4 - 3/2 d + d = 4 - d/2

[deep gale]

ohhhh

[fossil locust]

you want to clear the fraction by multiplying everything by 4 - d/2

[deep gale]

so it should be

64-8d

[fossil locust]

yes

also then (4 - 3/2 d)(4 - d/2)
= 16 - 2d - 6d + 3/4 d^2
= 16 - 8d + 3/4 d^2

that's another mistake

so you should end up with $\left(16 - 8d + \frac{3}{4} d^2 \right) + \left(16 + 4d + \frac{1}{4} d^2 \right) = 64 - 8d$ overall

[woven radish]

higher's secret twin brother

[deep gale]

pls hold

i'm dying as we speak because my head hurts

[fossil locust]

should be $d^2 + 4d - 32 = 0$ actually

but anyways, $(d + 8)(d - 4) = 0$ gives $d = -8, 4$

[woven radish]

higher's secret twin brother

[deep gale]

OH YES MY BAD

[fossil locust]

so the d = -8 solution was the one you didn't want, cause you would get 16, 8, 0 and so the 4th term = 0 as well

and then d = 4, try again and you'll get it

[fossil locust]

ITS OK

[deep gale]

WELL

-2 SORRY

[fossil locust]

it's okay no need to apologise

yeah so -2, 2, 6

then the last term is 18

congrats, the sum of the 1st and 4th is 16
and the sum of the 2nd and 3rd terms is 8

[deep gale]

yehey!!

but then 13. is also hard and i'm stuck with it as well 😭

[fossil locust]

13?

I only see 10, 11, 12

[deep gale]

it's similar to 12 but i solved 12

[fossil locust]

oh that's neat

[deep gale]

the difference is that in 13. it didn't give the common difference

[fossil locust]

I mean if you let the terms be a, a + d, a + 2d, a + 3d as usual

the common ratio condition of the GP gives

$\frac{a + 2d + 5}{a + d + 2} = \frac{a + d + 2}{a + 4}$ and $\frac{a + 3d + 18}{a + 2d + 5} = \frac{a + 2d + 5}{a + d + 2}$

[woven radish]

higher's secret twin brother

[fossil locust]

oh maybe using a - d, a, a + d, a + 2d will make the arithmetic easier

algebra bash

well actually the great mathematicians would gladly toil away on problems and do all the computations in order to arrive at their insights

not saying you need to be exactly like them

but it's in the spirit of maths to keep on trying

(if you take breaks and rest ofc)

[deep gale]

okay, sorry for the late reply! was rewriting my answer for 10

[deep gale]

yupp!! i really like math, algebra specifically but for some reason this is making it hard for me 😭

so i cross multiply?

[fossil locust]

yes

[deep gale]

i got this

@fossil locust

[fossil locust]

yes that's correct

and then you need the other equation too

[deep gale]

ohh that's why you sent this as well

[fossil locust]

yeah you need both equations! otherwise it would be unsolvable

[deep gale]

right, since 2 variables 2 equations

[fossil locust]

hey that's pretty neat

I've noticed you've been collecting the coefficients mentally, so that you don't need to write all 9 terms on the paper

[deep gale]

i can see that i can eliminate the d^2 and d

[fossil locust]

that's a sign you've practiced algebra

[deep gale]

yes because of a previous exam 😭

[fossil locust]

yeah so (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca and so on

[fossil locust]

excellent that skill is really useful

yeah that's correct

[deep gale]

okay that's good to hearr

[deep gale]

do i do this?

[fossil locust]

jesus, so equating both equations we have $5a_1 + 4d + 16 = 10a_1 + 4d + 11$

[woven radish]

higher's secret twin brother

[fossil locust]

yeah

like make the d^2 the subject in both equations

oh brilliant

that's such a relief

[fossil locust]

it seems the question maker has taken pity on you

then you can sub in a and get a quadratic in d

[fossil locust]

yes

[deep gale]

where do i substitute a?

[fossil locust]

in any one of the equations

they should give the same thing

[deep gale]

theree

[fossil locust]

wow congrats

[deep gale]

actually, there's more to this problem set like harmonic and infinite geometric sequence

i know how to do harmonic and i'm assuming it won't be as hard but i don't have a clue on how infinite geometric sequence works

[fossil locust]

ah you know how the sum for a regular geometric series is $\frac{a(1 - r^n)}{(1 - r)}$

and we need $-1 < r < 1$ for convergence as well of course

[woven radish]

higher's secret twin brother

[fossil locust]

if we have say 0.99^10, 0.99^100, 0.99^1000 and so on

we are going to be multiplying by a number (with absolute value) less than 1 every single time

so as $n \to \infty, r^n \to 0$

[woven radish]

higher's secret twin brother

[deep gale]

convergence?

[fossil locust]

this will become $\frac{a (1 - 0)}{1 - r} = \frac{a}{1 - r}$

[woven radish]

higher's secret twin brother

[fossil locust]

for the sum to exist

[deep gale]

hmmm

are you willing to help me out on the questions for infinite geometric sequence?

[fossil locust]

I need a break, but no worries

you can close this channel and open a new one

[deep gale]

oh actually i'll just go and make a new one, maybe other helpers are free

[fossil locust]

so that other people see your question haha

ye

[deep gale]

just wanna say thank you for helping me out! you genuinely helped me out

see you aroundd!!

.close

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[sinful tinsel]

help I'm not getting 20.99 angle

[hollow ice]

that theta is in radians

convert it

what you have is 20.99 degrees

[sinful tinsel]

so 0.366 is the one with π, like π/4

also, how will I know when theta comes in degree or when it comes in radian?

@hollow ice

[hollow ice]

inverse functions give answers in radians

[devout snow]

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[dapper quail]

what would i fill this in with

[dapper quail]

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

[polar chasm]

Yes

and to rationalize it, try multiplying the numerator and denominator by sqrt(x^2 + 7) + 4

[dapper quail]

so multiplying by the conjugate right

i never really understood that concept

like why

[polar chasm]

sqrt(x^2+7)-4 will be 0 when we plug in x = 3

[dapper quail]

like where do they use a difference of squares here?

[polar chasm]

and so we need to get rid of that part

[polar chasm]

(cos(x) - 1)(cos(x) + 1) = cos^2(x) - 1

[dapper quail]

ohh

thats such a weird way to use it in my head

[polar chasm]

and to do that, we multiply it by conjugate. This will get rid of the square root, which might result in some cancelling, although it will add a new square root in the denominator, but the expression with that will probably be non-zero, so we dont mind it as much, as it wont result in 0 / 0 situation

[dapper quail]

ah yeah

[devout snow]

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[surreal stream]

What is the difference between these two formulas?

[faint gorge]

Substitute h=x-a

[surreal stream]

into both?

[faint gorge]

They are both the same

It's just you can make a change of variables

[surreal stream]

so it doesnt matter which one i choose im assuming?

[faint gorge]

yes

[surreal stream]

ok thx

[faint gorge]

they are equivalent

[surreal stream]

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[spark hound]

Straight up, don't gimmie the answer, just answer this:

1. When you read this, how easy is it for you to formulate an equation that can approach this problem?

[supple knot]

draw a picture

translate the information into equations

[spark hound]

Hard asf I like that

Ty

.solved

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[faint gorge]

first one to compliment riemann 💀

[wary slate]

hi

[lone ravine]

I think Layla was first

[faint gorge]

actually I was the first

[devout snow]

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[cursive shuttle]

Hello

[cursive shuttle]

What does this symbol mean?

[fossil locust]

in, so x is in the set of the real numbers

excluding 3

[cursive shuttle]

Ohh

[fossil locust]

that's what the entire statement means

in maths we like to think of things using sets, collections of objects

so instead of 'x is real' which is what we do say, informally

[cursive shuttle]

How would I represent/type it on a regular keyboard tht symbol

Or do I not need to show it?

[fossil locust]

we say that x is in the group that contains all real numbers

[cursive shuttle]

Ooh

[fossil locust]

you should learn LaTeX

so we would type $\in$

[woven radish]

higher's secret twin brother

[fossil locust]

$x \in \mathbb R$

[woven radish]

higher's secret twin brother

[cursive shuttle]

Ohh ok

[agile elbow]

Also read as "belongs"

Means the same

[cursive shuttle]

Does that work on google?

[cursive shuttle]

Kk

[agile elbow]

If you want to use it on Google to ask smth you have to most prob copy it first by searching the term belongs symbol in math or you can just write belongs. It will be the same input

[cursive shuttle]

Ohh ok !

Ty!!

[devout snow]

@cursive shuttle Has your question been resolved?

[devout snow]

@cursive shuttle Has your question been resolved?

[cursive shuttle]

How would I enter that symbol into here?

[devout snow]

@cursive shuttle Has your question been resolved?

[supple knot]

$\cup$ means union

[woven radish]

riemann

[supple knot]

so $(0, 1) \cup (2, 3)$ means all numbers between 0 and 1 or between 2 and 3

[woven radish]

riemann

[cursive shuttle]

Okay

[devout snow]

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[jade girder]

(x-9)(x-4)(x-9)(x-15)(x-20) = 0
Solve for x

[rotund umbra]

!status

[devout snow]

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

[jade girder]

3

[rotund umbra]

what's your answer?

[jade girder]

4 9 15 20

[rotund umbra]

looks correct to me

what did they think the answer is?

[jade girder]

they havent said its meant to give me numbers and then a message

but i got no clue

[rotund umbra]

well, you've got the correct values of x for your polynomial. perhaps it's somewhere else in the question that's wrong?

I presume there was more to the question?

[jade girder]

just that and the key says "A=1 B=2 C=3"

thats it

[rotund umbra]

now I'm confused XD

mind posting the full question?

[jade girder]

they said its 4 9 9 15 20

[jade girder]

Theres nothing more than just:

Solve for x
(x-9)(x-4)(x-9)(x-15)(x-20) = 0

A=1
B=2
C=3

[rotund umbra]

this is a very poorly written question

maybe they wanted you to write 9 twice, because the graph "crosses" at 9 twice (technically only touches at 9, but that counts as crossing twice).

https://www.desmos.com/calculator/qwfwmfogg0

[jade girder]

ive got no clue icl i think the question is just wrong

they saying its right and others got it

i got no clue tho

[rotund umbra]

I've no idea what the A=1 etc thing is about

[jade girder]

only thing i can think is quadratic formula LMAOOOO

but idk how that fits in

i think its just the code

icl i dont think it makes sense

i appreciate your help tho sorry for wasting ur time

[rotund umbra]

quadratic formula doesn't fit here, nor should it be needed even if it was a quadratic.

[rotund umbra]

all good 🙂

I think it's just a badly written question.

[jade girder]

same

but apprecioate the help either way

[devout snow]

@jade girder Has your question been resolved?

[devout snow]

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[soft roost]

can someone help me put this in vertex form

the top is my attempt but i think i got it wrong

oh never mind it was supposed to be 6

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[distant mural]

im a little suck on this:

[distant mural]

this is my working so far

[left relic]

i think it would be easier to combine it into one power

[distant mural]

oh so how do i do that

[distant mural]

would this not work?

[quartz nova]

Dif of squares

[left relic]

Think of it as $\left(\left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)\right)^{40}$

[woven radish]

Luke

[distant mural]

ohhhhhh

[left relic]

and expand the inside

[distant mural]

ohh i see

[distant mural]

is there no way to do it like this tho?

[quartz nova]

U probably could but it’s inefficient

[distant mural]

huh 💀

[idle goblet]

I dont mean to interupt Dr. Pepper, but i just want to say i love your name.

[distant mural]

omg ty!

[idle goblet]

Im actually wearing a Dr. Pepper shirt rn 💀

[lone kiln]

you can do it the way luke is saying which has a fairly straightforward answer

[idle goblet]

anyways, good luck on your maths! :D

[quartz nova]

Btw can I send the answer

[lone kiln]

that is equivalent to your approach

[quartz nova]

@distant mural

Or nah

[distant mural]

sure

[quartz nova]

So r=20 s=20 so it checks out with ur work

But uhh ur way would be bashing for like hours

[distant mural]

wait how did you get this

[quartz nova]

So dif of squares

Then binomial theroum

[distant mural]

ohhh using ur method?

[quartz nova]

Ye

[distant mural]

yep

[quartz nova]

I can’t think of a ez way to do it ur way

Other than guess and check

[distant mural]

well i tried asking ai

and this is what it said

[quartz nova]

Wolfram?

Or chatgpt

[distant mural]

chat

[left relic]

i think you might be able to use this to solve it the other way

but honestly idk

[quartz nova]

Bro chatgpt is so bad for math

[left relic]

nvm they alternate

[quartz nova]

Like I would only rec wolfram

But u gotta pay for sol

[distant mural]

ohh

[quartz nova]

So 😔

[distant mural]

oh dang

[quartz nova]

Ye just use like math stack exchange or smth

Or this server

[distant mural]

do u have any idea why it simplified to (40 20)

[distant mural]

frfr

[quartz nova]

Basically it uses the observation that the 1/x terms & the x terms need to same powers to fully cancel each other out

[lone kiln]

no idea why you're asking gpt

[quartz nova]

So under binomial Theorem u would have to do 40 choose 20

Since u set both powers to 20

[distant mural]

wait could u explain that

[quartz nova]

U can easily see this by combining the two binomials

[distant mural]

oh

[quartz nova]

What abt it?

[distant mural]

like why is it 20

i dont understand

[quartz nova]

^

[distant mural]

so they need the same power

how does making it 20

give the same power

[quartz nova]

If one is 20 then the other has to be 20 bc it needs to add up to 40

[distant mural]

OHHHH

[quartz nova]

20 = 20

[distant mural]

omg

im so sorry

i get it

[quartz nova]

It’s fine

Np

[distant mural]

ohhhh omg that makes so much sense

thank you everyone for helping!!

how do i close this?

[quartz nova]

U like wait or smth

[distant mural]

oh oh

[quartz nova]

And it ping u abt close

The u click the check

[distant mural]

👍

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[viral rapids]

how can you find directional vectors for a plane in ax+by+cz=d form

[glossy basalt]

you mean like normal vector?

normal vector of plane ax+by+cz=d is given by vector (a,b,c)

[devout snow]

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[leaden radish]

I got f(t) but i'm having trouble figuring out how to find C

[lone kiln]

by C you mean the constant term?

you have two conditions which you can plug in to f

[leaden radish]

ye ik but it gives two different C's, what do I do with those two

[winter torrent]

well you ought to have two free variables

[leaden radish]

For f(0) = 6 the C is 4 and for f(pi) = 3 the C is 3-2e^pi?

But then what do I do witht hose two to make the final expression

[winter torrent]

can you show your entire work

[leaden radish]

wait i think ik my mistake, i've been combining C1 and C2

just to make it C

so if it's two integrals we need to have two separate constant terms? we can't combine

[lone kiln]

so say you do one integral, there's one constant

you do another integral on the result, ...

[leaden radish]

oh shit cause C1 becomes C1t since it was a constant in the integral

Clutch

lemme try this jawn again

THank you team

.close

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[viscid marsh]

How to do b(ii) I tried a oot but couldnt

[viscid marsh]

Its a corcle theorem question

[lone kiln]

something something inscribed angle theorem

[devout snow]

@viscid marsh Has your question been resolved?

[viscid marsh]

Alternate angles?

[viscid marsh]

Oh yea the angles ive drawn I did after finding the solution to reverse engineer which theorem was used but didnt get it

<@&286206848099549185>

@lone kiln could u tell me how to do it i have my ig exam in a couple hours and wont be able to use my phone soon

[lone kiln]

the theorem says QOR is double some other angle

[viscid marsh]

OHHHHHH

Thanks so muxh

[devout snow]

@viscid marsh Has your question been resolved?

[devout snow]

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[restive river]

How is my number 3, wrong?

HOW is it not 8x10^9

May anyone explain

<@&286206848099549185>

[celest pasture]

liters to gallons?

[restive river]

Giga Liter

Giga liter

This is what i followed

[radiant anvil]

its u again

with the bad teacher

[restive river]

Exactly

[radiant anvil]

giga should be a capital G

not a small g

[restive river]

i forgot but

it is supposed to be GL

how is my answer wrong anyways

[sage burrow]

1 Gl = 10^9 l

[radiant anvil]

yea

for sanity check u can just convert it to base units

[restive river]

so is my answer right or wrong, not including the unit

[celest pasture]

its to the negative of -9 due to L being smaller than a GL

if it was the opposite conversion than your awnser is right

[restive river]

Ah ok

Sorry

Thats

Thanks

.close

[devout snow]

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[eager magnet]

.open

[devout snow]

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[eager magnet]

so i'm going to ask a question for how to solve a question

[radiant anvil]

just ask the question directly

[eager magnet]

how'd i get this wrong?

[radiant anvil]

it looks fine

[eager magnet]

yea but it says i got it wrong

[fresh elbow]

justify your first answer

Why SAS

[eager magnet]

idkkk. i didn't learn this and it was in a test

[fresh elbow]

What is SAS

[junior chasm]

geometry sucks fr

(im very bad at it)

[eager magnet]

agreed. i just don't like it as well as algebra

[junior chasm]

is it saying that the congruency should be by SSS and not SAS?

[eager magnet]

yep

[junior chasm]

both are right

[eager magnet]

i thought so. i put only one since it one answer only

[junior chasm]

what else is wrong

AC=DB, yeah thats wrong

diagonals of a kite arent same length

[eager magnet]

oh

.close

[devout snow]

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[devout snow]

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[vocal oar]

Any hints？

Im not exactly getting it :')

[uncut crow]

do you see how the hint would help? do you have any ideas on how to prove the part in the hint?

[vocal oar]

thats the problem

i genuinely have never heard of a finite ring

or what it exactly indicates

[uncut crow]

for another hint on the hint, consider the elements x, x+x, x+x+x, ...

if R is finite then...?

[vocal oar]

they sum to a finite number

[uncut crow]

no 😭

[vocal oar]

it stops at nx

eventually

n is some natural number

[uncut crow]

R is a ring, doesn't have to be numbers

what does stops mean?

[vocal oar]

its capped

[uncut crow]

hmm well i would just say x, x+x, x+x+x, ... is an infinitely long list and there are only finitely many elements in R so there must be an element in R that shows up twice in the list

which means there exist distinct integers a and b such ax = bx

[vocal oar]

i iwll be thinking at my desk

thank you for the hint

[uncut crow]

loll ok lmk if you need more help

[devout snow]

@vocal oar Has your question been resolved?

[vocal oar]

i think i got it after looking at finite fields

x+x+... x n times gives some finite number

but say 2x+x...+x m times gives some finite number equal to previous

so i can set that equal

move on both sides and that would be the k in the question

[devout snow]

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[sinful tinsel]

in first picture, tan inverse gave angle in radian because it was less than 0. and second picture, it gave answer in degree because angle is bigger?

[fossil locust]

well you should be using radians for all trig functions actually

tan inverse gives you an angle in radians cause that's what your calculator mode is set to

,w -4000/3600 = tan(2 theta)

[woven radish]

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[fossil locust]

,w -1/2 arctan(10/9)

[woven radish]

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[fossil locust]

,calc 0.41899 * 180/pi

[woven radish]

Result:

24.006358658186

[fossil locust]

yeah so it's just your calculator settings

that answer for the 2nd question is correct in degrees

[sinful tinsel]

and wbu adding 90°

angle was negative so we add 90° to -24, so other angle was 66 and 156

[fossil locust]

cause tan theta has a period of 180 deg

so tan(2 theta) has a period of 90 deg

and for tan, there's one solution per period

[sinful tinsel]

so it'll be that for all sin cos

also

[fossil locust]

no

[sinful tinsel]

I want to know if it comes other than tan

[fossil locust]

sin and cos have two solutions per period

so for sin, you have sin(x) = sin(180 - x)

then you have
.... x - 2pi, x, x + 2pi, x + 4pi ......
.... (180 - x) - 2pi, (180 - x), (180 - x) + 2pi, (180 - x) + 4pi....

and for cos, cos(x) = cos(-x)

so you have
.... x - 2pi, x, x + 2pi, x + 4pi ......
.... (-x) - 2pi, (-x), (-x) + 2pi, (-x) + 4pi....

oh I am mixing degrees and radians my bad

[sinful tinsel]

yes

[fossil locust]

but yeah sin(x) = sin(pi - x) in radians

[sinful tinsel]

what is x-2π, x, x+2π

[fossil locust]

sin and cos have period 2pi

so you can add or subtract 2pi to the solutions as many times as you want

[sinful tinsel]

can you please write in figures instead of variables, I don't understand

angles

[fossil locust]

in figures?

[sinful tinsel]

all I know is sin repeats after π

[fossil locust]

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

watch this video

[fossil locust]

that's wrong

sin and cos repeat after 2pi

[sinful tinsel]

yes

[fossil locust]

tan repeats after pi

[sinful tinsel]

but sin0 = sin180

[fossil locust]

one example doesn't prove anything

any other angle will be a counterexample

for example, sin 30 is not sin 210

sin 30 = -sin 210 actually

[sinful tinsel]

one sin wave is between 0 and 180

[fossil locust]

https://www.desmos.com/calculator/31iekundxp

[sinful tinsel]

or should it be 360

[fossil locust]

it's 360

the graph of sin x doesn't repeat after 180 degrees

[sinful tinsel]

pls I want to know where I'm wrong

wait

I get it

so tan repeats after 90, and sin repeats after 360?

[fossil locust]

no, tan repeats after 180

tan = sin/cos = y/x
so tan theta is the slope of the black line right?

[sinful tinsel]

then wbu this

are we doing this because our scale on graph is of 2theta

[fossil locust]

yes!

cause f(2x) is a compression of f(x) by a factor of 2

so if tan(theta) originally has a period of 180 degrees

tan(2 theta) will have a period of 180/2 degrees

= 90 deg

[sinful tinsel]

so if we had been calculating for tanθ instead of tan2θ our angle would be -24, -24+180

[fossil locust]

yes!

[sinful tinsel]

thank you 😭

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[devout snow]

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[restive river]

hey guys. I need help with the following question. In particular, the B part

the question asks us to find the volume of the region y = f(x), the x-axis, the y-axis and the line x = 2.8

the part about the region being enclosed by the y-axis really confuses me

[restive river]

if I plot the graph of the function that is given hre

,w plot y = x\sqrt{9 - x^2} + 2 \arcsin(x/3)

[woven radish]

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Requested by alison_burg3r5

[restive river]

we can see that the area to be rotated to find volume can either be enclosed by the x-axis or the y-axis

but not both

am I missing something here?

[fossil locust]

I see another AAHL sufferer here lol

[restive river]

:(

I got the answer correctly

so this is the equation I used:

$$V = \pi \int_{0}^{2.8} f(x)^2 dx$$

[woven radish]

Edmund Cloudsley

[restive river]

the answer is right

= 181

[fossil locust]

the y-axis part is to say that they want the region where x >= 0 and y >= 0

or conversely, where x <= 0 and y <= 0

[restive river]

ahhh I see

[fossil locust]

since f(x) is an odd function the two volumes will be the same

[restive river]

that does make sense

cheers mate thanks

[fossil locust]

cheers!

[restive river]

also I'm curious how did you know this was an aahl question?

did you also do the IB or something?

[fossil locust]

1. the style looks very familiar
2. there's a tiny bit of your screenshot where I can read MAA

[restive river]

ahh cool

[fossil locust]

yes I'm an IB graduate

[restive river]

noice

thanks so much

have a good day

.close

[devout snow]

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[devout snow]

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[knotty musk]

HELP

[faint zinc]

What have you tried?

[knotty musk]

Nothing

Ill start now

Share Your ideas ill try that too

[faint zinc]

Ok, so do you see that there are similar triangles here?

[knotty musk]

Yes

But I didnt think of that cuz can similarities help to get angle?

[faint zinc]

They can if you can get the ratios of side lengths

[knotty musk]

But I haven't explored it

[knotty musk]

Mmmmm

I haven't even read the question properly :/

Ac = 2bd

[knotty musk]

Ok

Have you solved it ?

[faint zinc]

I haven't, because I am currently just on my phone without a pen and paper.

[thin basin]

Do you still need help?

@knotty musk ?

[knotty musk]

Yes

I dont see a way 💀

[thin basin]

As the other guy said they are similar

Now write the ratios of all the sides

[knotty musk]

Ywah?

Ok

[thin basin]

Do you know any of these?

[knotty musk]

Any of these?

[thin basin]

Like the ratios

[knotty musk]

Actually i haven't tried the question yet

Im just trying to plan a algorithm rn

But none seems assuring

[thin basin]

Ok so basically you will get the ratio between AD and AM

Then you can use trigonometry

Cause it's a right triangle

[knotty musk]

Ohh

Leeme try

[thin basin]

Kinda unique question

Ping me if you need help

[knotty musk]

May I dm if I get stuck?

[thin basin]

Yeahh

@knotty musk status?

[knotty musk]

Cant find ratio

Is there any way I can get the value of BA in terms of Ac or Bd?

@thin basin

[faint zinc]

@knotty musk Pythagorean theorem.

[knotty musk]

Where

[faint zinc]

Both triangles

Crudely, you have a total of 7 unknowns. These are the length of the 6 sides and the similarity ratio.

You have 6 constraints. These are the similarity ratio equations (3 of them). Pythagorean theorem (only one of which gives new information). And AB = 2AM, AC = 2BD

Between these 6 you can find all of the values of the sides up to a scaling factor. In other words, you can set one of the sides to x, and get the rest in terms of just x.

In order to find angle A you only need to find any two of AD, AB, and BD, or any two of AC, AM, and CM.

[knotty musk]

Okay

WAIT

I GOT CA= BA

Oh Ywah

Sin x = 1/2

X IS

30

Thanks

@faint zinc

@thin basin

[faint zinc]

Hmmm... That doesn't seem reasonable

@knotty musk ^

[knotty musk]

Why?

[thin basin]

I think that x is 15 degree

[knotty musk]

Wait What

@faint zinc whats the answer is per you?

[faint zinc]

Let me put pen to paper

[knotty musk]

We have to solve this without trigonometry, pure geometry

Any ide

Idea?

[faint zinc]

That is a very clever method of finding the angle. Doing this without trig seems to be a tall ask

[knotty musk]

Yeah but its asked so

.close

[devout snow]

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[knotty musk]

Thanks for the help guys

[devout snow]

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[wanton wigeon]

join the event stage

[twilit comet]

what...?

do you have a maths question-

[supple knot]

if you don't have a question close the channel

[twilit comet]

okay he doesn't

.close

[devout snow]

Channel closed

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[twilit comet]

it's some sort of channel apparently

[wanton wigeon]

thats mean

[twilit comet]

AHAHAHAHA

[wanton wigeon]

🔪

[fervent hornet]

if you have no question then dont occupy the help channels

[twilit comet]

@formal latch how many times do we have to tell you to stop advertising

@upper schooner I'M SORRY WHAT IS THAT REACTION

[formal latch]

its urgent

[twilit comet]

that does not justify it.

[upper schooner]

Which one, the cat shoot one?

[twilit comet]

...
i hate you

/j ofc

[fervent hornet]

gello chartbit

[upper schooner]

Gello to you too

[upper schooner]

hehe

[devout snow]

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[tender hound]

help

[tender hound]

beef shawarma or chicken shawarma

[junior chasm]

math

[tender hound]

math shawarma?

[junior chasm]

i meant meth*

[twilit comet]

...?

[tender hound]

ah i see

[small jackal]

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[twilit comet]

do you have a question?

[tender hound]

ill see if thats on the menu

[small jackal]

mathematics help

[twilit comet]

<@&268886789983436800> troll *sighs*

[small jackal]

Bro

[celest dock]

.close

[devout snow]

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[twilit comet]

yeah

just post your question

for a, the extreme point of a parabola is always the vertex

for b you can calculate it using like i said the vertex

for c just input t = 0

[brisk panther]

the vertex of a parabola occurs at t = -b/2a

[twilit comet]

nw

[devout snow]

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[somber citrus]

how do i go from line 1 to line 2?

[acoustic leaf]

get the fractions from line 1 on a common denominator

[somber citrus]

ok

turns out it was an algebra skill issue on my part

thank you!

.close

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[hollow jasper]

What do I do here

It says this but idk how

[agile elbow]

Take (x+1) common in the second denominator

[hollow jasper]

And?

[agile elbow]

You get that (x+1) (x-2a)

Are you having problems in understanding how to get that x(x+1) - 2a(x+1) from the x² + x - 2ax -2a

[hollow jasper]

No I’m having problem with how the first red denominator changes into the 2nd red one

[agile elbow]

If we take (x+1) common from x(x+1) - 2a(x+1) we get (x+1)(x-2a)

[restive river]

it's x(x+1) - 2a(x+1). They both have x+1 in them, so you can take them out. and put the remaining parts together. (x+1)(x-2a). x-2a is what's left

[hollow jasper]

And then why is there still (x+1)

[restive river]

Because it still exists

[hollow jasper]

But didn’t I just cancel it?

[restive river]

no

It will cancel out, but not in the step we just explained

[hollow jasper]

You just said x-2a is left

[restive river]

My mistake. I meant that the remaining parts are the x - 2a

[hollow jasper]

Ok now I just don’t get where does the x+1 appear from

[restive river]

Are you aware of the distribution property?

[hollow jasper]

Yes

[restive river]

Okay, I'm going to give you an example.

Let's say instead of x+1, we have the variable h

if you were to write that out, you'd have h(x-2a)

When you use the distribution property, you multiply the x and the 2a by the h

so it will then become xh-2ah

Does that make sense?

[hollow jasper]

Yes

[restive river]

You're doing the same thing with (x+1)

It's just being done in the opposite order

(x(x+1)-2a(x+1))

[hollow jasper]

Wdym by opposite order

[restive river]

So using the example again

it's like you're starting with x(h)-2a(h)

They've already been distributed to both terms, so now you want to take the h out

[hollow jasper]

So I have x-2a

Or?

[restive river]

You have (x+1)(x-2a)

If you distribute (x+1) into x and 2a, you get x(x+1)-2a(x+1)

Which is what we started with

You're basically just doing reverse distribution property

[devout snow]

@hollow jasper Has your question been resolved?

[devout snow]

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[supple knot]

plug in the numbers to b(x)

[ruby wolf]

i have

i got it wrong three times

im crashing out

[supple knot]

did you plug in -2?

[ruby wolf]

yes

[supple knot]

to b(x)?

to get b(-2)?

[ruby wolf]

yes

i got 17

its wrong

i feel dumb

i want to cry

back

hello

you there

nope alr

[steel flint]

its 19 not 17
18 - 0.5 * -2 -> 18 - -1 -> 18 + 1 -> 19

[ruby wolf]

i am stupid

[steel flint]

did u understand this?

[ruby wolf]

i dubtracted

sub

yes

[steel flint]

okay good

[steel flint]

no, it happens, its okay :)

[ruby wolf]

its so simple oml

.close

[devout snow]

Channel closed

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[ruby wolf]

.reopen

[devout snow]

✅

[ruby wolf]

thx

.close

[devout snow]

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[ruby wolf]

.close

.close

[devout snow]

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[balmy oracle]

If you have the equation y=x+3 and y=x+1 and they are parallel how would you solve the perpendicular intercept

[balmy oracle]

I think I did it but idk

Im stuck

[wooden charm]

If they have same a and different b they are not intercepting

[balmy oracle]

I know

but the problem says I have to make a perpendicular line inbetween them where the largest distance is

if it has a slope of 1x the perpendicular line has a slope of -1

[wooden charm]

Can you show it on desmos bc I hate a math naming in english

[wooden charm]

What do you mean by the largest distance?

[balmy oracle]

my bad wrong wording

[wooden charm]

The equation for making perpendicular lines is -1/a

[balmy oracle]

Like a place of interception that the perpendicular line would run through

i know

let me show you my current work

[wooden charm]

Oke

[balmy oracle]

I used (0,3) for one of the perpendicular intercepts

since we know (0,3) is one of the points the parallel line runs through

and if you do y-y1=m(x-x1) you get y=-x+3

Is that right so far

heres a pic

[wooden charm]

And you need to get this second point of interception?

[balmy oracle]

yeah

I can substitute

[wooden charm]

Ooo

x+1=-x+3

[balmy oracle]

yep

[wooden charm]

2x = 2

[balmy oracle]

and I'm using x+1 because we already used x+3

x=1

[wooden charm]

So that all

(1,2)

[balmy oracle]

(1,2)\

now distance formula

(1,2) and (0,3)

[wooden charm]

Pythagoras

[balmy oracle]

pretty sure its this

[wooden charm]

Yup

So yea thats all I think

[balmy oracle]

like this

[wooden charm]

Bro

1^2 is 1

[balmy oracle]

rly?

1x10 is 1?

oh nvm

its 1x1

[wooden charm]

Yea

[balmy oracle]

its sqrt 2

[wooden charm]

Yup

[balmy oracle]

1.4142135624

Did it in my head

[wooden charm]

👏

[balmy oracle]

I guess I know it all

But

I have a test tomorrow so

Im kinda overdoing it ig

[wooden charm]

The funcs are easy

It should go well on test

[devout snow]

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[long plume]

For the (iii) part will we do 3 cases

1. Albert, No Tracy
2. Tracy no Albert
3. No Albert no Tracy

Or just the first two

[long plume]

Because the mark scheme only did the first two cases and I'm confused..

[warped jay]

ㅂㅅ들

[long plume]

I only speak English 😥

[devout snow]

@long plume Has your question been resolved?

[long plume]

<@&286206848099549185>

[atomic nacelle]

Hello

question iii?

@long plume It says EITHER

So one or the other

so the answer should be 4494

[devout snow]

@long plume Has your question been resolved?

[devout snow]

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[spiral walrus]

Can someone help me finish this problem? I have already found one matrix that satisfies this but I believe there are more. For the 3x3 Matrices I believe that there is no such matrix because the dimension of Col A will never equal the dimension of Nul A

Find all 2 x 2 matrices A such that Col A = Nul A. Could there be a 3 x 3
matrix with this property? Why or why not?

[wicked turtle]

"the dimension of Col A will never equal the dimension of Nul A" - true, but can you explain why?

[spiral walrus]

yeah because dim Col A + dim Nul A = 3 for the 3x3 and also dim Col A = dim Nul A as they are the same

so that never happens unless the dimension is 3/2, which can't happen

[wicked turtle]

yep that's right

[spiral walrus]

okay but what about the other part

"Find all 2 x 2 matrices A such that Col A = Nul A"

[wicked turtle]

you said you found one, right?

what was it?

[spiral walrus]

a -a^2/b
b -a

but that only works if a is not 0 and b is not 0

[wicked turtle]

should be ok if a=0

[spiral walrus]

wouldnt that give the zero matrix_

?

[wicked turtle]

$\begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$

[woven radish]

Bungo

[wicked turtle]

is what you get with a=0 and b=1

and that has the desired property

[spiral walrus]

i tried doing that example in the way I solved for the other one

0 0s
b bs

where s is a scalar. but that only got me to

sb^2=0 so either b=0 or s=0, then i get

0 0
b 0

or

0 0
0 0

and im not sure how to show that those satisfy the conditions (especially the zero matrix)

[wicked turtle]

well the zero matrix definitely doesn't work

its null space is R^2 and its column space is trivial

[spiral walrus]

yeah

[wicked turtle]

i suspect that the answer is $\begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$ and any matrix similar to that matrix, but you should verify that

[woven radish]

Bungo

[spiral walrus]

does it need to be 1 or can it be any number?

bc i have the matrix

0 0
b 0

and im trying to see how to prove that but im struggling

[wicked turtle]

yea similarity will give you any nonzero scalar multiple of that (and many others)

[spiral walrus]

i know that Col A = span ((0,1)) but what is Nul A?

[wicked turtle]

well you can just do the multiplication
$$\begin{pmatrix}0 & 0 \ b & 0\end{pmatrix}\begin{pmatrix}x \ y\end{pmatrix} = \begin{pmatrix}0 \ 0\end{pmatrix}$$

[woven radish]

Bungo

[wicked turtle]

this tells you exactly that bx = 0

[spiral walrus]

yes i did that and I got bx=0

[wicked turtle]

since b is nonzero, this means x=0

[spiral walrus]

so is nul A the y axis or the x axis_

?

the y right?

[wicked turtle]

any vector with x=0, so the y axis

[spiral walrus]

got it got it

and col A is also the y axis bc of 0,b

[wicked turtle]

yep

[spiral walrus]

thats so cool

[wicked turtle]

you can find similar examples for 4x4, 6x6, 8x8 etc

any square matrix with even number of rows/cols

[spiral walrus]

that makes sense

wait so there's only two unique matrices that satisfy Col A = Nul A right? the first one I told you and the one we just did

or are there more?

im going to try

0 c
0 0

someone told me that worked

[wicked turtle]

no it's any matrix similar to $\begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$

[woven radish]

Bungo

[wicked turtle]

that includes $\begin{pmatrix}0 & c \ 0 & 0 \end{pmatrix}$

[woven radish]

Bungo

[spiral walrus]

by traspose?

[wicked turtle]

any matrix of the form $A \begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}A^{-1}$ where $A$ is any invertible 2x2 matrix

[woven radish]

Bungo

[wicked turtle]

i believe that's the complete characterization but again, you should probably check that as i could be wrong

[spiral walrus]

okok how about this one>

a -a^2/b
b -a

thats the one i derived first

[devout snow]

@spiral walrus Has your question been resolved?

[devout snow]

@spiral walrus Has your question been resolved?

[spiral walrus]

<@&286206848099549185>

[spiral walrus]

.close

[devout snow]

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[devout snow]

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[barren ledge]

yes?

[slate ocean]

[winter torrent]

.close

[devout snow]

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[stable nymph]

drowning in this problem because I do not get it

[stable nymph]

I've been trying the product rule

w a double product rule in the mix

and do not know why I'm not getting it right

[misty crest]

alternatively you could turn 5sinxcosx into 5/2 sin(2x)

[stable nymph]

I can but I'm horrible at remembering my trig idens so I doubt I would remeber it in a test

😭

[restive river]

what 50x50

[misty crest]

well then

polo g

[stable nymph]

polo g lowk mid

[misty crest]

https://tenor.com/view/polog-liltjay-genius-popout-live-gif-26128013

2019 was peak

[stable nymph]

noname is fire bro

[atomic dome]

Do you know the product rule for 3 functions?

[stable nymph]

💀

[stable nymph]

is it the chain rule?

or is it the product rule

within a product rule

[atomic dome]

$\frac{d}{dx}(fgz) = f'gz + fg'z +fgz'$

[woven radish]

mari

[atomic dome]

Zed font doing the most

[stable nymph]

zed font?

[misty crest]

brit

[atomic dome]

I am actually American

[misty crest]

"zed"

[stable nymph]

im cooked for tmmr dawg 🙏 :sobb

[misty crest]

tyler the goat fr

[stable nymph]

he needa drop sum

[misty crest]

nah you’re chilling bro

[stable nymph]

trig stuff is acc killin me

too much rules an remembering

[misty crest]

fundamentals kills everyone

[stable nymph]

can you teach me the trig iden method

ts double product rule is confusing me so imma js pray I remember how to do that

[atomic dome]

Just one, triple product rule

[stable nymph]

I aint understanding that way of doing the triple product rule

I learnt it by

p prime x p+ q prime x p

and then if thiers a product rule in between that

just do that for that one

[misty crest]

the only trig identities you really need are double angle, pythagorean, and angle sum/difference

[quaint citrus]

ln f = ln(5x) + ln(sinx) + ln(cosx)
f' = f (1/x)(cosx/sinx)(-sinx/cosx)
f' = -f/x

this is the chad method

[misty crest]

https://tenor.com/view/mujikcboro-seriymujik-gif-24361533

mogged