help-39

[autumn fossil]

they are just an extension of reals

[plucky seal]

anything larger and more encompassing than complex?

[vapid cave]

technically you have things like quarternions/octonions/sedenions

the rest of the cayley-dickson algebras

then things like split-complex/split-quaternions/etc

things after quaternions and split-complex are rarely used

[pearl pond]

@plucky seal Has your question been resolved?

[pearl pond]

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
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[midnight haven]

I need to know how can I show if a sequence is convergent or not I n-langugage , using induction , ratio test , or an+1-an test , I need to show that in a strict form

[midnight haven]

I have been stuck on these for the past day lol

i just need help with one or 2 diffferent problems , just to understand this process step by step

[woven matrix]

you have to spam this https://en.wikipedia.org/wiki/Monotone_convergence_theorem

so that your problem often becomes bounding then studying the variations

for example for j, you should prove that 2 <= an <= 2.5, then show that an+1 >= an

so it converges

[midnight haven]

lol , yeah , but with the sqrts for example its kinda confusing , ex , its easy for a_n =1/n that it gets smaller but with ex , a_n= sqrt(2_an-1) it aint that easy (for me )hehe

[woven matrix]

for a) same idea, the first ones are easier than the last
an+1 = sqrt(3an)
if 1 <= an <= an+1 <= 3
1 <= sqrt(3) <= sqrt(3an) = an+1 <= sqrt(3an+1) = an+2 <= sqrt(3²) = 3
by induction, an is bounded and non decreasing

so it converges

[midnight haven]

cool

thank y

.close

[pearl pond]

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[hot mist]

I have a crazy question with a lot of urgency. So basically I’ve been studying super hard for an entrance exam that you have to do in IB Sweden. It’s tomorrow so I’ve been grinding out mock entrance exams but this one doesn’t have an answer key. I was trying to get ChatGPT to make an answer key but it was dumber than me I’m basically asking if anyone smart could complete this mock test so I compare see what I got wrong and what the actual right answer is. Thank you so much.

[hot mist]

@plush bramble does this work?

[toxic lichen]

we don't do your problem(s) for you sorry

[hot mist]

No no no read the message I sent

It’s nothing like that

[toxic lichen]

you should post your answers

it's server policy

[jovial kiln]

i doubt anyone will help will an entire paper. do u not have a markscheme?

[hot mist]

Nah they gave a marksheme for the English not math

[hot mist]

This is like an example test for what may be on the finale that decides if I get into gymnasium, skola

[autumn fossil]

I will, im slightly bored

[hot mist]

THANK YOU SO MUCH MAN 🙏🙏 somehow even I got all of those even though I’m not the best at math to be honest 😂

[hot mist]

Don’t take this the wrong way but I am very happy you are bored 😂🙌

[hot mist]

Ahhh I had I feeling I got the semi circle wrong but if you don’t mind me asking how it 9 5/8 I asked a few other people also and they agreed with 9/16 as well as ChatGPT but one other person also said 5/8

[vapid cave]

you can imagine cutting and pasting the shaded triangles

the blue line denotes the boundary of the shaded part

[autumn fossil]

yep

[hot mist]

OHHH THAT MAKES SO MUCH SENSE NOW THANK YOU

[autumn fossil]

what was your answer to the semi-circle one?

did you count the bottom line too?

[hot mist]

It was 12 cm tbh I don’t know how I got that

[autumn fossil]

it should be pi/2 * 8 + 8 = 3/2 * 8 + 8 = 12 + 8 = 20

[autumn fossil]

Yeah, 12 is just the curved part

you didnt count the bottom diameter

[hot mist]

Ohhhh that would make sense thank you I was sure something looked off but I could figure out what

[autumn fossil]

this one is sus though, x + y should be extremely close to 1

x and y seem to be the same distance from 0.5

meaning their average would be exactly 0.5

and their sum would then be exactly 1

[hot mist]

Yeah this one made zero sense to me even in the slightest I was not taught it at all

[autumn fossil]

the way I would approach is is just observing that x is slightly below 0.5 and y is slightly above 0.5

[hot mist]

I thought it was d send it is like 0.5 of the line if that makes sense

[autumn fossil]

meaning that their total should be around 0.5 + 0.5

[autumn fossil]

yeah, that

wait

D?

[hot mist]

Yeah

[autumn fossil]

I'd say the question is wrong

[hot mist]

I thought sense it was half of the line it’s self it could represent d

[autumn fossil]

it could be either C or D

im 99% sure that if we actually measured it, the sum would be extremely close to 1

[hot mist]

Not possible sense it’s the official 2017 exam of a major IB entrance test

[autumn fossil]

like extremely close, 1mm close

[hot mist]

Ahhh okayyy

[autumn fossil]

I'd probably guess C though

because it's a bit closer to 1 than D

[hot mist]

Yeah but I was thinking sense if you look the line keeps going after to and I can see that D is perfectly centered to the line if you forget about 0 and 2

So I think logically it would make more sense but I may be wrong

[autumn fossil]

red is the x

blue is y

[autumn fossil]

x + y is red + blue (drawn as red + light blue)

[hot mist]

Does this help at all

[autumn fossil]

you probably dont need a ruler

eyes should be enough

[hot mist]

Yeah that’s true, I just asked ChatGPT for a second opinion and it said D so idk

It may be wrong tho

[autumn fossil]

chatgpt is often wrong, yeah

[autumn fossil]

this mark here is exactly 0.5

assuming x and y are the same distance from it, then x + y would be exactly 1

[hot mist]

Yeah it’s weird that they would have a question that is so up for interpretation on a exam like this ngl

[autumn fossil]

it's not up to interpretation, it would be a good question if only one of the letters was exactly at 1

[hot mist]

Yeah that’s what I meant sorry

[autumn fossil]

because x + y is almost exactly 1

[hot mist]

I see it now you’re right

C is 100% closer

[hot mist]

Do you mind me asking how you did b because for the life of me I can’t get it

[autumn fossil]

the best way is probably just guessing what x and y are approximately

x seems to be around 0.4

y seems to be around 0.6

y/x would then be 1.5

[autumn fossil]

hmm its probably more like 0.55

,calc 0.55/0.45

[jolly parrot]

Result:

1.2222222222222

[autumn fossil]

yeah, definitely closer

[hot mist]

Wait that’s the part I don’t get I feel very stupid for not getting it but how does it become 1.5

[autumn fossil]

let's do different estimate

my first estimate was too bad

y = 0.55

x = 0.45

now y / x = 0.55 / 0.45

= 55 / 45

which is slightly larger than 1

[hot mist]

Ohhh I get it now i seeee

[autumn fossil]

or using this, you can ask yourself, how many times is y (the blue one) longer than x (red one)

and you can see that the ratio is definitely above one, since blue is larger

[hot mist]

I see the other way seems easier tho ngl

[rare burrow]

jesus this is such a dumb question

[autumn fossil]

and it's also only slightly larger than 1

[autumn fossil]

the only dumb part about it is part a tbh

otherwise its quite a good question to check your understanding of the number line representation

[hot mist]

Man I’m sorry math is not at all my strong suit I struggle a lot with and moving constantly has not allowed me to really study it well so I lack in math skills

[autumn fossil]

do your answers for the exercise 11 match btw?

[rare burrow]

that's exactly what I was calling dumb

[autumn fossil]

Ye, we can agree on that

[rare burrow]

I'm criticizing the question, not you

you're good

[hot mist]

All except b and d

[rare burrow]

I think the question is just a very silly and poor question to ask

[hot mist]

Ohhhh sorry my bad

[rare burrow]

no no it's alright lol

[hot mist]

I definitely agree with you but ay that’s International baccalaureate for ya

[rare burrow]

wow, and I thought AP was a bad system

[hot mist]

Yeah man tell me about it IB is the worst

And the weird thing is the English part of the test is super easy

[rare burrow]

I wouldn't classify this question as either "hard" or "easy"; just "stupid"

[autumn fossil]

alright, lets check that

[hot mist]

Fair enough but for me all math questions are hard 😂😂

[autumn fossil]

sqrt(bc) - a = sqrt(3*12) - 6 = sqrt(36) - 6 = 6 - 6 = 0

e^2 - b^2 = (-4)^2 - 3^2 = (-4)*(-4) - 9 = 16 - 9 = 7

do you understand where you made the mistake or is sth unclear?

[hot mist]

Tbh still unclear im confused how the answer is zero

[autumn fossil]

Can you show how did you calculate it?

[hot mist]

I got 36 for it but I have no idea where I calculated it my desk is a mess I’ve been doing math for 10 hours straight 😭

[autumn fossil]

36 is just 3 * 12

thats the bc part

then you need to take the square root of that

since there is $\sqrt{bc}$ in the question

[jolly parrot]

MathIsAlwaysRight

[autumn fossil]

and square root of 36 is 6

and lastly, you need to subtract a

and a is 6

and 6 - 6 is 0

[hot mist]

I’m about to ask probably the dumbest question ever

I’ve been doing advanced math for so long I forgot so many basics how do you find square root again? 😭

[autumn fossil]

it's best to remember the square numbers

and if you are lost, you can just guess something

you could start by guessing e.g. 3

3^2 is then 9

too low, guess higher

so maybe try 7

7^2 is 49

too high, guess lower

maybe 5

5^2 is 25

guess higher

6^2 is 36, done

square root of 36 is 6

[hot mist]

Wait but why are you multiplying _ by 2?

[autumn fossil]

$\text{x^2 means} x^2$

[hot mist]

Ohhhh I get it now this makes sense idk how I forgot that

[jolly parrot]

MathIsAlwaysRight
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[autumn fossil]

What the fuck latex

[rare burrow]

lmaooo

[hot mist]

So the square root is just a number that is squared

[autumn fossil]

yeah, square root is the opposite of squaring

if 5 squared is 25, then square root of 25 is 5

[hot mist]

Okay now I get it thank you is there any way you could give me a similar question so I could see if I actually get it or I just think I get it

[autumn fossil]

a = 16
b = 4
c = 14
find sqrt(ab) - c

[hot mist]

Thank you so much ima try it rn

This may be absolutely wrong but is it 30?

[rare burrow]

mildly interesting property of square roots: since $x^{n+m}=x^nx^m$ and you can represent square roots like so: $\sqrt{a}=a^{\frac12}$, a natural consequence is that $\sqrt{ab}=\sqrt a \sqrt b$

[jolly parrot]

00100000

[rare burrow]

it makes the problem marginally easier

[rare burrow]

I believe you've made a mistake in your calculations

[hot mist]

I believe so 😂

[rare burrow]

just check them over carefully again

👍

[hot mist]

Idk where I went wrong but I think it’s at the end maybe

[autumn fossil]

c was 14

so it's sqrt(64) - 14

and you need to respect the order of operations

square root and squaring comes right after parenthesis

[hot mist]

Oh you are completely right

[autumn fossil]

so you should start by calculating sqrt(64) and only after that subtract 4

[rare burrow]

it's better style to use = between lines here

because those 3 dots often are used to mean "therefore"

[hot mist]

Ohhh okayyy I think i get it now should I try the same question again or

[rare burrow]

and you're not really making any implications here, so

it looks better to go
$$2+2$$
$$=4$$

[hot mist]

Oh okay will do

[autumn fossil]

Yeah, i think you should try calculating sqrt(64)

[jolly parrot]

00100000

[autumn fossil]

because the way you did sqrt(60) is incorrect

[rare burrow]

with your style, it looks like "2+2, therefore 4"

which doesn't make sense since neither 2+2 nor 4 are "truth" statements (i.e. true or false)

[jolly parrot]

MathIsAlwaysRight

[rare burrow]

a natural way to use the three dots is anywhere you need a therefore. for instance: a>0 and b>0, therefore a+b>0

(where I take a>0 and b>0 to be assumptions)

ok honestly what am i even waffling about

[hot mist]

I feel like I mess it up again

[hot mist]

I appreciate it though I can’t lie

[rare burrow]

that answer is correct

however, the notation is... odd

[hot mist]

What do you mean by notation 😂😭

[rare burrow]

from line 3 to 4, you wrote
$$=8^2-14$$
$$=-6$$

which is

not true

[hot mist]

Oh wait what was I supposed to do?

[rare burrow]

and then it looks like you added a $^2$ to line 2 as well

[jolly parrot]

00100000

00100000

[rare burrow]

$$=8-14$$
$$=-6$$

[jolly parrot]

00100000

[hot mist]

Oh so I basically put a square on a bunch of stuff that ain’t need it

[rare burrow]

because when you write $$8^2-14$$, it means $$8\cdot8-14$$

[jolly parrot]

00100000

[hot mist]

Is this good now

[rare burrow]

not quite; it turned it into an incorrect expression

which is worse

[rare burrow]

yes

I think i see what you were trying to do

[hot mist]

Ignore my horrendous handwriting btw

[rare burrow]

you were trying to say $$\sqrt{64}-14$$ $$=\sqrt{8^2}-14$$ I think

[jolly parrot]

00100000

[rare burrow]

however, it came out as... something different

[hot mist]

Yeah exactly 😂

[autumn fossil]

but yep, its correct

[hot mist]

Do you think you could give me another one to make sure this was not a fluke cuz I feel like I just got lucky or something idk

[rare burrow]

please note that while $\sqrt{a}^2=\sqrt{a^2}$ for non-negative $a$, you were trying to so $(\sqrt{a})^2=a^2$, which is definitely not generally true

[jolly parrot]

00100000

[hot mist]

Ahh so I got 16 correct and 17 but and 18 a and b but not c also I do not remember at all how I got 17 😭

[autumn fossil]

$\frac{\sqrt{13+12}\cdot\left(2+\frac{6\sqrt{4}}{4}\right)}{5}$

[jolly parrot]

MathIsAlwaysRight

[rare burrow]

oh gosh i committed the terrible latex sin of writing \sqrt{x}^2. i fixed it quickly, but forgive me latex gods

[hot mist]

Huh that looks way more difficult for some reason oh god

Ima try it

But don’t have high hopes

[autumn fossil]

lol

[rare burrow]

ok i need to go study for my own exam tomorrow. for your checking reference, the answer is ||5||

you better not have auto spoilers on

[hot mist]

Ummm

Oops

[rare burrow]

💀

[hot mist]

😂😭

Sorry

[autumn fossil]

doesnt matter lol, see if you get the same answer

[rare burrow]

^

[hot mist]

But thanks so much for helping me good luck on you’re exam

[hot mist]

True I’m going to try rn

[rare burrow]

sorry for spoiling lol, but in my humble defense, spoilers exist for a reason!!

[hot mist]

😂😂you’re good dw

[rare burrow]

thank you! good luck to you as well

[hot mist]

Appreciate it 🙌

[autumn fossil]

here is the last oen

[rare burrow]

wait bro u r straight up giving him all the answers

isn't this like uhhh, not the spirit of the server

[hot mist]

I already did everything and this is a mock test

[autumn fossil]

he already solved those Qs

[hot mist]

Btw i got 82.5 💀💀 something def went wrong

[rare burrow]

oh I see

[autumn fossil]

you missed a dot here

its not 62

its 6*2

[hot mist]

Six times two?

[autumn fossil]

Yeah

[hot mist]

Oops that would make more sense lemme adjust to that

[autumn fossil]

$6\sqrt{4}=6\cdot\sqrt{4}=6\cdot2$

[jolly parrot]

MathIsAlwaysRight

[hot mist]

Wait now I’m getting twenty 😭

Oh wait nvm

[autumn fossil]

you forgot to divide by 4 i think

[hot mist]

I’m actually getting 25 now somehow 😭

OHHH WAIT I GOT IT

WAITT

[autumn fossil]

its almost correct

except you only did the top part

which indeed is 25

25 / 5 then simplifies to 5

[hot mist]

Ignore my terrible hand writing sorry about that 😂

[hot mist]

I’m not gonna lie I completely got this wrong

[autumn fossil]

Lets return back to this one, i think we havent checked it yet

[hot mist]

Ohhh yeah you’re right

I got 840 kr somehow which is super embarrassing cuz that looks like the most simple question ever

[autumn fossil]

for 12?

[hot mist]

Yeah sorry kr means SEK

[autumn fossil]

how did you do it?

[hot mist]

I can send a picture one sec

Sorry it sent upside down

[autumn fossil]

we have tools for that

[hot mist]

Oh damn that’s impressive

[hot mist]

I see 😂

[autumn fossil]

oh so you did 900/15

that's not correct unfortunately

[hot mist]

Yeah I don’t say how tho

I think I know

[autumn fossil]

would you be able to calculate 15% of 900?

[hot mist]

Is it 0.15 x 900?

[autumn fossil]

yep, precisely

[hot mist]

Sorry I think my brains fried so I just got that one wrong

[autumn fossil]

btw one advice regarding the double-checking thing, I suppose that the exam has a time limit, so it might not always be worth it to waste your time double checking, maybe instead just put up marks on the calculations you performed and in case you'll have enough time, you can return to it and verify the calculations

[hot mist]

Yeah I timed my self when doing it and finish with the alarm ringing 😭

[autumn fossil]

Yeah, thats normal, we all get things wrong sometimes

[hot mist]

It’s 90 mins no calculator

[autumn fossil]

,calc 900 * 0.15

[jolly parrot]

Result:

135

[autumn fossil]

and then you'd subtract it

[hot mist]

Yup thanks for pointing that out

Btw to multiple that I just do 900 x 15 and move over the decimal point right

[autumn fossil]

yep

[autumn fossil]

13 is correct, pretty impressive actually, I'd guess that most students would mess that one up

14 should then be 25 and 20

[hot mist]

Yeah I’m not gonna lie I have to admit I waisted a good 10 mins of my time doing that 😭

[hot mist]

Shit I got 20 and 20

I thought it was a trick question and both were 20

[autumn fossil]

when we go to 4 blocks to 5 blocks, we are adding 1 block

and 1 block is 25% of 4 blocks

so we are adding 25% to the 4 blocks

[hot mist]

I see that makes sense

And other way around for b

[autumn fossil]

yep

15 is 4, 11, 1/2, 8

[hot mist]

Yuppp

[autumn fossil]

alright, nice

16 then

that one was a bit more complicated

[hot mist]

I just came to a horrid conclusion I got all of 15 wrong wtf I am so done for

How did I do that

Those are so simple to

I have somehow forgotten the most basic solve for x

[autumn fossil]

It's probably just silly mistakes

[hot mist]

Maybe but idk

Can you tell me how to solve for x somehow someway I got them wrong

[autumn fossil]

17 - 3x = 5

add 3x to both sides

17 = 5 + 3x

subtract 5

12 = 3x

divide by 3

4 = x

(2x-1) / 3 = 7

multiply by 3

2x-1 = 21

add 1

2x = 22

divide by 2

x = 11

3 - 2x = 1 + 2x

try this one

[hot mist]

Wait is there anyway to make that bot write it out it’s so confusing looking at the discord text sorry 😭

[autumn fossil]

$$\begin{align}
17 - 3x &= 5 \
17 &= 5 + 3x \
12 &= 3x \
4 &= x
\end{align}$$

[jolly parrot]

MathIsAlwaysRight
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[hot mist]

Ohhhh I see it now

Thank you for doing the bot thing I really appreciate it

[hot mist]

Okay I’ll try rn

[autumn fossil]

$$\begin{align}
\frac{2x-1}{3} &= 7 \
2x-1 &= 21 \
2x &= 22 \
x &= 11
\end{align}$$

[jolly parrot]

MathIsAlwaysRight
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[autumn fossil]

the general strategy for simple equations is

1. get rid of fractions (by multiplying everything by the denominator(s))
2. move everything with x to one side and everything without x to the other side (by adding / subtracting the terms)
3. at this point you should have sth like 3x = 6, so you just divide by whatever is in front of x

[autumn fossil]

Yep, thats it

[hot mist]

Ahhh i see

[autumn fossil]

now the last step is dividing by 4

[hot mist]

Wait should I divide both by 2?

[autumn fossil]

you could

you would get 1 = 2x

but you need x

not 2x

so you need to divide by 2 again

if you just straight up divide by whatever is in front of x, you will get there in one step

[hot mist]

Wait is the answer a decimal?

[autumn fossil]

in this case, it's 4

[autumn fossil]

yep

or a fraction

1/2 or 0.5

[autumn fossil]

yep

[calm wing]

are you trying to get into MYP 5?

just curious

[hot mist]

Pre DP

[calm wing]

yea same thing

[hot mist]

Yea

[calm wing]

i did IB in sweden lol

[hot mist]

Oh fr

[calm wing]

yea

[hot mist]

That’s cool 😂 what school?

[calm wing]

in Helsingborg

probably doxxing myself rn but oh well

[calm wing]

AYYYYY

[hot mist]

Sorry for the finger not tryna dox

[calm wing]

ISH 💪💪💪

[hot mist]

That’s my third option though can’t lie

[calm wing]

understandable lol

it's not that good

still home

[hot mist]

Yeah not cause it’s not good but because it’s hours away

I just put it down cuz why not

Anyway

[calm wing]

oh wow

[hot mist]

I’m getting a bit distracted

[calm wing]

woops

[hot mist]

The entrance exam is tmr

😭

[calm wing]

this looks good

[autumn fossil]

oh wait

[hot mist]

Any tips

[autumn fossil]

rest

[calm wing]

yeah fr

it's almost 22 here

[calm wing]

(says me who also has an exam tomorrow)

[autumn fossil]

you should def get at least 8 hours of sleep

ideally around 9

[hot mist]

You’re probably right test is tmr at 12:45 I can study in the morning

art do you go any recommendations on what I could study tmr morning from you’re experience

[calm wing]

my exam looked VERY different so i don't think i can help you much (i think it's because i didn't do IB before whatsoever)

but my advice is that you don't have to ace everything

[hot mist]

Ahhh okay makes send do you know at all if bearings would be on it that’s just the one thing I’ve been wondering

You probably don’t know but yea 😭

[calm wing]

i did math aahl and i still don't know how bearings work

so don't worry

[autumn fossil]

It's important to know what you're good at tho, then you can efficiently manage your time during the exam

[hot mist]

Okay well you guys are definitely right I should go to sleep

[calm wing]

absolutely

[hot mist]

Yeah the no calculator is gonna be a pain for tedious stuff only having 90mins

Well wish me luck for tmr ima study in the morning and hope for the best because this makes or breaks my future

[autumn fossil]

Good night and good luck tomorrow!

[calm wing]

hope it goes well! good luck!

[hot mist]

Ohh btw I skipped 2 levels of myp so if I seem a bit dumb it’s cuz I got put hella up

Anyways

Good night yall

Thank you so much for the help

You don’t understand how much you saved me

👍👍

[autumn fossil]

Np, good night :)

(you can close this with .close btw)

otherwise the bot would wake you up with ping

ill just close this, feel free to reopen it if needed

.close

[pearl pond]

Channel closed

Closed by @autumn fossil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[glass schooner]

idk

[orchid heath]

Try to draw it

[glass schooner]

ok

wait

just one more

[orchid heath]

What is slope?

[glass schooner]

idk mAB =?

[orchid heath]

Look at AB and CD

What do u see?

Look at BC and DA

What do u see?

[glass schooner]

AB CD is negative five

BC and DA is negative 1 over 7

[orchid heath]

U need to draw that quadrilateral

[glass schooner]

i dunno how to draw a 1/7 to life in a quadrilateral form in a paper

[orchid heath]

No

I mean, just draw a quadrilateral ABCD

[glass schooner]

ok

this?

[orchid heath]

Slope of AB = slope of CD

What does that mean?

[orchid heath]

PQ = QR = RS = SP, right?

[glass schooner]

ye

[orchid heath]

Isnt is a square?

[glass schooner]

ye

[orchid heath]

Maybe u need parallelism

But i doubt that

Maybe one 90° angle

[pearl pond]

@glass schooner Has your question been resolved?

[pearl pond]

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[thick raven]

I don't know, where did you go wrong?

It looks right to me

You just haven't finished

[orchid heath]

I can barely see something

A B C are equation's notations or variables?

[thick raven]

Did you definitely copy down the equatinos correctly then?

No you didn't, you put a minus sign before the c in line 2

Hahaha

[orchid heath]

It happens sometimes

[thick raven]

Happens to everyone dw

[livid shadow]

yeah just needa be careful

[orchid heath]

At least u used ur brain for a while

[pearl pond]

@livid shadow Has your question been resolved?

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[manic cape]

I need help with these questions

idk how to solve them

[plush bramble]

,rotate

[pearl pond]

@manic cape Has your question been resolved?

[thorny agate]

try rephrasing the questions into equations

[thorny agate]

like for this one, try to make a "can of paint" into a variable like X

,rotate

[thorny agate]

there we go

[pearl pond]

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[thorny agate]

oop

[pearl pond]

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[manic cape]

what

[manic cape]

@thorny agate

[thorny agate]

hel!
o!

hello!

okay so

which one would you like to start with

[manic cape]

first

[thorny agate]

motorcycle?

[manic cape]

,

[thorny agate]

got it

with these sorts of story problems it's best to start by establishing your variables, the things you don't know the exact value for

[manic cape]

Let x be the number of girls in the school

[thorny agate]

and let y be the number of boys

as we don't know how many of those are there either

[manic cape]

the teacher never said y

[thorny agate]

hm

[manic cape]

the question is only asking for girl tho

[limpid lily]

No, with ratios, you can only multiply the sides by the same number.

[orchid heath]

Owh

[thorny agate]

yes, but only using girls, theres no way to find the number

[manic cape]

idk

[orchid heath]

Use boys, but not as variables

[thorny agate]

so lets start with x=number of girls and y=number of boys

[manic cape]

there is a total number of 3460

I thought i could use that

im dumb

[thorny agate]

yes, you will use that

[manic cape]

ok

[thorny agate]

you know that boys+girls=3460

[manic cape]

yes

[orchid heath]

Maybe I'm a middle school student too, explain that to me too

[thorny agate]

is there any other information that can be used to form an equation

[manic cape]

Im a highschool student

[orchid heath]

R u sure?

[thorny agate]

its gonna turn out to be a system of equations, you can't just shove all of the info into one equation

[manic cape]

my teacher used fraction idk and i think he devided

[manic cape]

yeh

[orchid heath]

We can calculate % and use it

[thorny agate]

hm i think he did it in a different way than i'm thinking of doing it

but theyre both valid ways

[manic cape]

I'm afraid of doing your and he gives me 0

this guy is a hard marker

[orchid heath]

Middle School method

[thorny agate]

girl is it possible for you to help people with math without insulting them

[limpid lily]

You've used the sentence "A school has 3460 students." to get x + y = 3460. What other information do they give?

[thorny agate]

are you asking me or the person who needs help? /gen

[manic cape]

shes a girl

[limpid lily]

Oh, sorry.

[manic cape]

k

he gave me the answer its 600 but he told me to solve it and idk how

[limpid lily]

Merai, you've used the sentence "A school has 3460 students." to get x + y = 3460. What other information do they give?

[orchid heath]

Dude, dont invert my purpose, im not insulting

Because you're going to do it differently than I learned in middle school.

[manic cape]

@limpid lily

[limpid lily]

Yes, that information.

[manic cape]

only that

nothing more

ratio

31 and 44

[limpid lily]

OK, 31 what to 44 what?

[manic cape]

31 are the boys and 44 are thi girls

[limpid lily]

OK, so you can write y : x = 31 : 44.

The ratio of boys to girls is 31 to 44.

[manic cape]

yes

[limpid lily]

Does that make sense?

[manic cape]

yes but how did he get 600

[limpid lily]

OK, now you can turn the ratios into normal fractions.

y/x = 31/44.

Then you can solve for either y or x.

What do you get for either one of them?

[manic cape]

no only for girls

[limpid lily]

OK, then solve for x.

[orchid heath]

$\frac{x}{y} = \frac{44}{31}$

[thorny agate]

have patience, this person knows what theyre doing and you need to use boys to find girls, which is why its in the problem

[jolly parrot]

SELVATOR

[manic cape]

do i devide the 3460 with 44

[limpid lily]

It's y/x.

[manic cape]

ok

so what now

do i add 31 + 44

[limpid lily]

Oh, I see.

[manic cape]

it gave me 75

[limpid lily]

What did you get for x?

[manic cape]

i just added them

[limpid lily]

Can you show your work?

[manic cape]

ok

wait

i got 75 as the denominator

but his answer was 600

I still don't know how he got it

[orchid heath]

Girls are 600?

In 3460 students school?

[orchid heath]

The percentage of girls is higher than that of boys

[manic cape]

yeah idk lol

he said its 600

[orchid heath]

It couldn't

[manic cape]

idk im confused

[orchid heath]

3460 ÷ 2 = 1730

[limpid lily]

You have x/y = 31/44.

Multiply both sides by y.

What do you get?

[manic cape]

idk

[orchid heath]

44 + 31 = 75 (total)
3460 ÷ 75 = 46.13

Now multiply 44 × 46.13

[manic cape]

2029.72

[orchid heath]

Let's say 2030

Girls = 2030
Boys = 3460 - 2030 = 1430

Owh

Recheck the question

Asking about the difference between boys and girls

It is: girls - boys = 2030 - 1430 = 600

[manic cape]

ohh

how did you get 600

[orchid heath]

He asks you about the number of girls more than boys.

[manic cape]

oh

wait

so first you multiplied then

minus

@orchid heath

[orchid heath]

I added girls + boys = 44 + 31 = 75

[manic cape]

how did you get 100

[orchid heath]

Lets use orher method

We devided 3460 ÷ 75

$\frac{3460}{75} = 46.13$

[jolly parrot]

SELVATOR

[orchid heath]

That means, we have 46.13 group of 75

[manic cape]

oh

what do we do with the 46.13

[orchid heath]

We multiply it by 44 (girls ratio)

[manic cape]

2029.72

but we round it to 2030 right?

[orchid heath]

It is 43.13333...

So we could say 2030

[manic cape]

ye

so the formula is multplication and subtraction

?

[orchid heath]

We add a + b = T

And we dived Total ÷ T

And multiplying by a or b (depends on what u need)

[manic cape]

so for the veronica question is it the same formula ?

or it depend on the question

[orchid heath]

No, we will use percentage%

[manic cape]

how

[orchid heath]

$5 \to 10$

[jolly parrot]

SELVATOR

[orchid heath]

$? \to 24$

[jolly parrot]

SELVATOR

[manic cape]

4x6

[orchid heath]

5L : 10km
??L : 24km

Do u know square rule?

$\frac{24 \times 5}{10} = ??L$

[jolly parrot]

SELVATOR

[manic cape]

square rule

ohh wait

let me try

[orchid heath]

Fast way to calculate it

[manic cape]

1.2 over 100

[orchid heath]

$24 \times \frac{5}{10} = 24 \times \frac12 = \frac{24}{2} = 12L$

[jolly parrot]

SELVATOR

[manic cape]

wait you got 12

?

[orchid heath]

That's math

Simple way to calcul it

[manic cape]

you got 12 or 1.2

[orchid heath]

Calcul it again, and use () in ur phone calculator

[manic cape]

oh

yes

ur right

hmm arl thx yall

[orchid heath]

U need to understand the idea

So u can use it by urself

If u have 5 : 10
Add 5 to 10
And devide (total × 5) ÷ (10+5)

[manic cape]

so I just gather all the numbers up and multiply to square root

[orchid heath]

Or (total × 10) ÷(10+5)

[manic cape]

why 10 and 5

[orchid heath]

Example

Bc u dont understand y

[manic cape]

oh nvm ur talking about the question

veronica

[orchid heath]

Nope

[manic cape]

lets say ur talking about it won't you use the same formula ?

[orchid heath]

Depends on the situation

Do u know how to calculate %?

[manic cape]

square root

the number with 100

right

[orchid heath]

Let say we have 70 chairs
And we need 30% of them

How to calcul it?

[manic cape]

70 devide by 30

[orchid heath]

I remember solving these problems in primary school.

[manic cape]

23

[orchid heath]

But I forgot about it after I grew up

[manic cape]

Im gr 10

[orchid heath]

Use square rule

$70 \to 100$ %

[jolly parrot]

SELVATOR

[orchid heath]

$?? \to 30$

[jolly parrot]

SELVATOR

[manic cape]

23

[orchid heath]

We multiply 30 by 70, and devide rhe result by 100

[manic cape]

multiply

?

[orchid heath]

$\frac{30 \times 70}{100}$

[jolly parrot]

SELVATOR

[manic cape]

I divided 70 with 30 and then I got 2.3 and then 2.3 squared 100 it gave me 23

ur answer is 21 ?

[orchid heath]

Squared 100?

What is that

Lemme draw square rule for u, i used to use it before

[manic cape]

yeh t

this one

@orchid heath

[orchid heath]

No

We put amount in left

And percentage in right

To find ??

We multiply sideways, and devide them by the opposite sideway of ??

So we get ??

@manic cape

Try it

$\frac{36 \times 100}{50} = ??$

[jolly parrot]

SELVATOR

[pearl pond]

@manic cape Has your question been resolved?

[manic cape]

72

[orchid heath]

72%

Yes

This box ||square|| is useful

[manic cape]

what is square

I have a question

[orchid heath]

This

[manic cape]

the + sign is it x

?

[orchid heath]

It is multiplication

[manic cape]

ok

[orchid heath]

I used same thing with vironica problem

5L | 10km
??L | 24km

[manic cape]

wait i have a question

its a small one

do you mind helping me

?

[orchid heath]

What's ur question

[manic cape]

Ok it says Jill is selling cookie dough. Three tubs cost 22.50. How much will 8 tubs cost ?

does ur formula work for this ?

[pearl pond]

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[manic cape]

.reopen

[pearl pond]

✅

[manic cape]

@orchid heath

[orchid heath]

Yes

3 | 22.5
8 | ??

[manic cape]

4x4

[orchid heath]

?

8 × 22.5

We step sideway

[manic cape]

ohh lol

I thought ur asking the typ of question that ask what two number multpyied by each other makes 8

?? this stand for x

right ?

x=unknown

[orchid heath]

Look here, multiply then divide

This box is about processes that have a connection

[manic cape]

wait devide by what

[orchid heath]

By the rest number

[manic cape]

divide

wait

[orchid heath]

We alr used 8 and 22.5
What is the rest number?

[manic cape]

180

wait

1.8

where did you go

by the rest number do you mean 3

[orchid heath]

Look at here

Yes

[manic cape]

oh

so do i divide with 100

pls quick

[orchid heath]

[manic cape]

..

its confusing

[orchid heath]

That's an example

@manic cape

[manic cape]

ok

let me try

22.50 x 8 = 180

180 divided by 100 = 1.8

@orchid heath

[orchid heath]

We dont have percentage equation here

We only have price and pieces

[orchid heath]

Put price in left boxs

And amount of pieces in right boxs

Just use informations from ur question

[orchid heath]

.

[manic cape]

yeh but idk ur formula doesn't wokr

work

on this question

[orchid heath]

(8 × 22.5) ÷ 3

How much?

[manic cape]

60

[orchid heath]

That's it

[orchid heath]

Did u see what had i done?

[manic cape]

thats the answer ?

[manic cape]

yes last time ur were putting 100 so thats what got me confused

[orchid heath]

100 is percentage

100%

This is for percentage-based operations.

[manic cape]

oh

[orchid heath]

If we got goods and prices
We do this
8 cakes | 20$
3 cakes | x$

We multiply known corners, ( 3 × 20)
And divid them by last corner (8)

As like this:

$\frac{3 \times 20}{8} = x$

Try to see the similarities between them.

And u will understand

[jolly parrot]

SELVATOR

[orchid heath]

I got a good way to do it

3 × 20 = 8 × x

x = (3×20)/8

[manic cape]

ok thx

[pearl pond]

@manic cape Has your question been resolved?

[pearl pond]

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[slow nebula]

How would i. make a formal proof for this? ik its convergent because for large n, an^2 < an. And since an is convergent, an^2 must also be convergent

[versed mica]

part d?

[slow nebula]

am i able to use this if the limit would be infinity

yeah

[vapid cave]

can’t you do term-by-term comparison?

[versed mica]

so a_n convergent implies a_n < 1 for sufficiently large n

see where you can go from there

recall that this holds since a_n convergent implies lim a_n = 0

@slow nebula do you understand what i mean

[versed mica]

well if you did a_n^2/a_n youd get 0 and if you did the other way youd get infinity so no

[versed mica]

this is the idea

then use comparison

[slow nebula]

i think i understand

i have a_n^2 < a_n

[versed mica]

what’s the next step after a_n < 1

mhm

[slow nebula]

then i can use the comparison test?

[versed mica]

yep

[slow nebula]

is there like a formal def for it

[versed mica]

formal definition for what

direct comparison?

[slow nebula]

like intuitively i understand

yeah

like in a proof can i just say its convergent bc of the inequality?

[versed mica]

well you need to be precise

the formal statement is something like

[versed mica]

suppose a_n >= 0. then if |b_n| <= a_n for large n and a_n converges then b_n converges

yea same thing

[slow nebula]

okok thanks

[versed mica]

so

$\sum_{n = N+1}^{\infty} a_n^2 \leq \sum_{n = N + 1}^{\infty} a_n$

[jolly parrot]

knief

[slow nebula]

o i see

N is a lagre number right

[versed mica]

just state that since lim a_n = 0, there exists N such that a_n < 1 for all n > N

[versed mica]

then this result follows immediately

[slow nebula]

ok that makes sense

[versed mica]

and we only care about the tail

the sum up to N is finite

so doesn’t matter

[slow nebula]

okay thanks a lot

[versed mica]

you’re welcome sir

[slow nebula]

.close

[pearl pond]

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[warm elbow]

Is using the MVT the right idea?

[warm elbow]

I'm not sure if i actually proved anything though

but my idea was that x_0 is arbitrary

because a, b are arbitrary

but i feel like im jumping at a conclusion and theres some step im skipping

[tardy reef]

I dont think this is sufficient

Your question asks if you can prove this for all x_0 in R

so, if I provide you with a number x_0, can you come up with the pair (a,b) that satisfy this?

Oh scratch that, on second thought you can infact assume a random a less than x_0 and find a b that satisfies this condition

[rustic gate]

that's still not good

MVT doesn't tell you where the point lies

[tardy reef]

Yea, but for a given random x_0, you can still show that it works out

[brittle tinsel]

MVT generates an x0 given a and b, not vice versa

[rustic gate]

finding a and b such that the MVT value is x_0 is more than just MVT

it takes nontrivial amount of work to show its existence

if it even exists at all

[tardy reef]

We already know that such an x_0 exists

[rustic gate]

you're not asking about the existence of x_0, it is given

[warm elbow]

hmm

[rustic gate]

the question is the existence of a and b

[warm elbow]

my idea was like

given any a, b you will find some x_0

now the question becomes can u find every x_0

[rustic gate]

but you are not given a and b

you are given x_0

[warm elbow]

ah

[rustic gate]

MVT makes no statement about what x_0 is

[warm elbow]

my idea was that wouldn't matter becaue eventually every (a, b) pair would eventualyl. generate every x_0

[brittle tinsel]

iirc the proof involves just using the definition of the derivative at x = x0

[warm elbow]

hm maybe i should just do that then

[rustic gate]

how do you know that? while i don't deny this is true, the MVT doesn't say this

[warm elbow]

yeah it doesnt

[rustic gate]

if it is true at all, it takes non trivial amount of work to prove it

[warm elbow]

so i did jump at a conclusion

it sounds true though i wonder if its possible to prove it

[brittle tinsel]

I think it is true that you can generate a and b for which that is true (from an x0) if f is monotonically increasing

but you'd have to prove that

and that's icky

[warm elbow]

yeah

[warm elbow]

hmm

i might do that problem for fun later on then

[brittle tinsel]

I think contradiction would be your best bet there

[warm elbow]

your reccomendation is just use definition of the derivative for this problem specifically right

[brittle tinsel]

yeah

[rustic gate]

why do you need contradiction

its quite literally a direct proof

[brittle tinsel]

we're discussing a different problem, not this one

[warm elbow]

this

yeah

[rustic gate]

right that one

[warm elbow]

oh

[rustic gate]

i think arctan(x) is a counterexample at 0

[brittle tinsel]

ah that's true. it's probably possible to prove if f is also concave up for all R, that's what I was imagining when i thought it was true lol

or at least has a second derivative that never changes sign 🤔

[warm elbow]

oh thank you!

[pearl pond]

@warm elbow Has your question been resolved?

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[pearl pond]

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

Im not really sure how to figure out b and c,, i received help from my teacher on a and help from a classmate about b (0.00495) but I dont really understand how you appoach the question

[toxic lichen]

have you done part a already?

[elder narwhal]

mhm! its k(52) k(51) k(50) k(49) in that order

[toxic lichen]

52k, 51k, 50k, 49k
are the probabilities in the table

now

what do you know about probability distribution tables?

something that is always true of the probabilities in a correctly formed distribution table?

[elder narwhal]

that adding everything together should always equal 1!!

[toxic lichen]

yes indeed

that's how you find k

from exactly this condition that you just stated

[elder narwhal]

so like k = 1/202?

okayy i think i understand b now and hoq they got that answer!!

[toxic lichen]

yes

[elder narwhal]

do you know how to find out c? :?

i had an idea but i talked to another classmate and im not really sure whats the correct way

i tried 0.00495(100-97) = 0.01485, and 0.00495(100-49) = 0.2525 and then added to get 0.2673

but they only did 0.00495(100-48) = 0.2574, and 0.00495(100-49) = 0.2525 and got 0.5098-0.5099

well that way would make sense because theres already a chance for the probability to be 49 twice

but im not sure if that means i should square 49 or instead use them to divide

because my other idea

was to go like 49/202 -> 0.2426*0.00495 = 0.0012

but that feels like too low of a probability to me

and also when i tried to do 1/49 i got like it to like the power of negative four so i dont think thats super accurate either lol

okay wait i think i understand it now

because of the 1/202 i think maybe it would make more sense to add 48/202 and 49/202 together to make 103/202

because thats just like ummm i forgot what it was called but we learned this im pretty sure

okay so 103/202 would be .5099 whichh would be just a simplified way of getting the same rounded result