help-41

[grizzled pagoda]

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[split sail]

,w integrate 1/(x+3) from -2 to 1

[grizzled pagoda]

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[amber wasp]

@split sail Has your question been resolved?

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[keen pawn]

Decide if the following is possible or not by providing an example or explaining why it's not possible : A sequence of nested empty intervals, $J_1 \supset J_2 \dots $ with $\bigcap_{ i \in \N} J_i$ being nonempty but only consisting of a finite number of elements. I feel it is possible, but I'm unable to come up with any example

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[quick spoke]

nested empty intervals
i think you mean non-empty lol

anyway if you're unable to find any counterexamples then maybe the statement isn't true

[keen pawn]

yeah

[quick spoke]

what attempted counterexamples have u made?

[keen pawn]

Then I'll have to think of a reason why it isn't true

[keen pawn]

(0, (n+1)n)

(0, 1/n]

[quick spoke]

what's the problem? what do you always end up with?

[keen pawn]

Either an empty set or an interval

[quick spoke]

wait hang on i should probably check

[quick spoke]

does the question specify the type of interval?

i.e open, closed etc.?

[keen pawn]

non-empty open

my bad

[quick spoke]

yeah ok nw

[quick spoke]

right so maybe we can prove it always has to be an interval

draw a picture and see what happens - can u prove it?

[quick spoke]

(btw there does exist an example if we have a nested sequence of closed intervals - can u think of one?)

[keen pawn]

[n-1]/n, (n+1)/n]

[keen pawn]

This is not possible as the intersection of two open intervals is either empty or an interval

it can never be a point

They just asked for an argument, not a proof

for now

[pseudo crescent]

can the intervals be closed? nvm, i just read your ans above

[quick spoke]

i guess that's fine for now, although this is very much a loose handwavy argument rather than a rigorous proof

if u tried turning that into a proof, u'll have issues cus a finite intersection and an infinite intersection behave very differently

[keen pawn]

yeah, i realise

[unborn plaza]

what is an infinite intersection?

can you not take a sequence (-1/n, 1/n) approaching {0}?

[keen pawn]

I haven't done sequences yet

I have some work to do now

gtg

sorry

.close

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[knotty grotto]

If the bisectors of triangle ABC intersect at point I and we know that the area of ​​triangle BIC is equal to 9 and AB = 7 and BC = 6, then what is the area of ​​triangle AIB?
1)9
2)10
3)19/2
4)21/2

[knotty grotto]

What is the solution to this question?

[tired girder]

Diagram ?

[neat wind]

use fact, area of small triangles is proportional to the sides

[knotty grotto]

This question has no diagram

[knotty grotto]

ok wait a minute

[tired girder]

You need to draw that

[knotty grotto]

S(BIC) = 9 -> this means IH * 6 / 2 = 9 so IH = 3 and i think here IH = IH' = 3 and if we do IH' * AB / 2 it will be 21/2

I don't know this is correct or not

thank you guys that was correct

.close

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[light ridge]

if theta = 130 and x = sin(theta) + cos(theta)
A) x > 0 (+ve)
B) x < 0 (-ve)
C) x = 0

[left spire]

yo

do u have any thoughts?

[light ridge]

yup

Like i know that sin is +ve is 2nd quad and cos is -ve in 2nd quad So

[left spire]

yup

[light ridge]

x < 0

Beta option

[left spire]

and ur reasoning

?

[light ridge]

(+) + (-) = -

As sin is positive and cos is negatice

[left spire]

right but how does that intuitively make the answer negative?

[light ridge]

I think so that way that why I mark the option

[left spire]

right but 3 + (-2) is still positive?

[light ridge]

hmm

then how we know if it is positive or negative

[left spire]

well we have to think about which one has a larger magnitude

[tired girder]

sin 50 , -cos50 crosses 45 so sin > cos

[light ridge]

???

[left spire]

yeah u can pretty much think about a 45 degree angle in the 2nd quadrant, which would be at 135 degrees

[light ridge]

but sin(45) and cos(45) both have value 1/ sqrt(2)

[unborn plaza]

Another method would be to look at the graphs of y=sin x and y= cos x

[light ridge]

they have range for -1 to 1 both function

no offense but they did not allow graph in the exam

[unborn plaza]

Yes but you can see which magnitude is greater

[unborn plaza]

This works too

[light ridge]

How can u explain

[unborn plaza]

Draw a unit circle and a ray at 130 degrees

Wait your doing the other method

[light ridge]

supplementary angle of 130 is 50

no I am going for easy method which I use in exam ( in every question )

[unborn plaza]

Yeah so the vertical leg is taller than the other leg

[light ridge]

sorry?

[unborn plaza]

I'm on my phone and I can't make pictures now

[light ridge]

hmm which one we are doing graph or other

[unborn plaza]

Up to you

[light ridge]

I prefer other bu the way but I love to learn both

[unborn plaza]

Then use the other method

[light ridge]

first we do toher then graph okay

[unborn plaza]

OK

[light ridge]

so ya we got angle = 130 which is in second quad and sine is positive in second quand and cosine is negative in second quad

[unborn plaza]

Yeah and the vertical leg is taller

Because they're equal at 135

[unborn plaza]

Put 135 on the picture too

And the unit circle

[light ridge]

is thsi right

[unborn plaza]

I meant in the same coordinate system

But this might be ok

Anyway you need triangles too

Right triangles

[light ridge]

where right triangle in the diagram

<@&286206848099549185>

if theta = 130 and x = sin(theta) + cos(theta)
A) x > 0 (+ve)
B) x < 0 (-ve)
C) x = 0

<@&286206848099549185>

[amber wasp]

@light ridge Has your question been resolved?

[amber wasp]

@light ridge Has your question been resolved?

[light ridge]

.clsoe

.close

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[sharp dock]

yo

[sharp dock]

So I had to make a graph and graph it on desmos

From the years 2015-2024

And how the prices changed over time

I used a trigonometric function

And got this

y=13793.8241sin(0.585195(x-1.28605))+51317.0035

Now how do I find the price of the car during the year 2030?

[split sail]

bruh is it me

[sharp dock]

<@&286206848099549185>

I see Alberto typing

Maybe he got it

[split sail]

ill leave you alone if you ask you know

._.

i swear its between 45k and 50k

[true jackal]

I thought you just need to substitute x = 2030 but seems you said it's incorrect

[split sail]

i know that was wrong

[sharp dock]

Let him answer

[split sail]

ik

[sharp dock]

Here's what chatgpt said 👇

[grizzled pagoda]

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

[true jackal]

Don't trust this gpt stuff

[sharp dock]

Ok

Yk how to answer it tho?

[true jackal]

It seems that chatGPT thinks your regression equation starts from x = 2015

[true jackal]

Replace x with 2030 and you're done

At least that's what I understood you want to do

[sharp dock]

The x doesn't start at 0

Here's the question the teacher asked me

Part 2: Modelling Depreciation

Next, we will be modelling car prices using Desmos. You will do this part of the assignment on your own. This website shows the history of car prices for different makes and models of a car:

https://www.cargurus.com/research/price-trends

Choose a car make and model that you would like to analyze. Choose a car with the model year 2015.

You can edit the start and end date to see the price of the car over a given period of time.

Enter the price of your chosen car in June of each year. If you can’t find the cost in June of a given year, write down the cost on the day closest to June.

Name of car (make and model): BMW M5

[true jackal]

Still don't understand

Let's see if some other helpers can help you

[sharp dock]

Alr

[true jackal]

<@&286206848099549185>

[sharp dock]

Ik someome else who can help its fine

.close

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[pallid canopy]

Why is xy both a vector and a component in a vector

[past pawn]

Idk anything about matrices

We didn't take them

But the professor gave us that question in a quiz

And idk how to proceed

[pallid canopy]

Uh then you wrote it down wrong

[past pawn]

No

That's a pic

Of what he wrote

And he couldn't have wrote it wrong

Why the fire emoji

[split sail]

Mb sorry

[past pawn]

Lmao

It's alright

So what do I do

[pallid canopy]

Then he should have explained what types of objects the variables were and you need to tell us.

[past pawn]

He has a quite...fiery personality

[vernal surge]

this makes no sense

[quick spoke]

lmao wtf is this

[pallid canopy]

no cents no cap frfr

[past pawn]

The thing is
He's in the top 2% of mathematians and got his doctorate from Stanford so yeah

It has a solution

[dull pike]

[vernal surge]

give us more context

[dull pike]

That has nothing to do

[plush fjord]

that doesnt mean anything

he still could be wrong

[past pawn]

that's what he wrote in the test

[quick spoke]

and i study at cambridge but my professors aren't dicks!

[vernal surge]

what was the test about

[pallid canopy]

Nobody asked about qualifications

[past pawn]

BRO I'M NOT SAYING ANY SHIT
WHAT I'M SAYING IS
I SENT ANOTHER QUESTION THAT HE GAVE US BEFORE AND NO ONE COULD HELP ME HERE AND I FOUND IT'S SOLUTION

[pallid canopy]

Just what the variables mean

If you can't answer then nobody can help

Blud is mad

[dull pike]

You gotta stop the scream now

[past pawn]

No

[quick spoke]

what was the previous q u sent and what was the soln?

[dull pike]

Not asking tbh

[past pawn]

Hold on

This one is alot easier tho

[quick spoke]

nvm it has nothing to do with the current q, but this problem is actually well posed lol

[fluid sentinel]

are those brackets vectors or combinatorix?

[past pawn]

I didn't study matrices so idk what you are taking about
Sorry lmao

[quick spoke]

but uh yet we need to know ^ otherwise we can't really help you

[past pawn]

I'll ask his assistant for the answers
Hopefully he gives us them this time

Thanks for trying

[dull pike]

!done

[amber wasp]

If you are done with this channel, please mark your problem as solved by typing .close

[past pawn]

Blud has been waiting

.close

[amber wasp]

Channel closed

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[past pawn]

Can someone give me a video explaining integration really well

Like what exactly is it

How it gives us the area
How it is the anti derivative

And the Sum of dx

.reopen

[amber wasp]

✅

[proud tusk]

Create new channel at this point

You won’t get answered otherwise

[past pawn]

Oh

Okay thanks

[unborn plaza]

i think the .reopen command worked though...

[past pawn]

Idk

What he meant but I'm new here

[proud tusk]

It’s just a mess on the channel

[past pawn]

So yeah

Now I have two

AHAHHAHA

[unborn plaza]

yeah...

[past pawn]

Just kidding

.close

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Channel closed

Closed by @past pawn

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[amber wasp]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[untold torrent]

Help

[untold torrent]

Do i add 0 to 10?

[sterile nymph]

I am not sure what you are asking here

Can you be a little more explicit with your question?

[untold torrent]

For the cost interval

The data is at the top of the page

[sterile nymph]

Ah

There do not seem to be any products within that interval

[untold torrent]

So i dont need to have 0 to 10 in intervals?

[sterile nymph]

I would consider it unimportant and OK to leave out, like the interval from 50 to 60 which is also empty.

[untold torrent]

Ok

[untold torrent]

Can you help correct my istogram when i finish doing it

[sterile nymph]

Well wait

Your intervals are 40 ≤ x < 50

And you have a product that is exactly 50

So you do actually need the 50 ≤ x < 60 range for that one product

[untold torrent]

Ok

[amber wasp]

@untold torrent Has your question been resolved?

[sterile nymph]

@untold torrent looks good to me, sorry about the delay, I had to go AFK a bit

[untold torrent]

Is the skew positive

[sterile nymph]

Crudely based on the histogram, it is very slightly skewed positive, but I would call this approximately no skew qualitatively. And insist on calculating the skew explicitly if pressed for an answer.

@untold torrent

[untold torrent]

So for d do i say no

[sterile nymph]

The skew is the third moment

[untold torrent]

Skew

[untold torrent]

What does that mean

[sterile nymph]

Oh

[sterile nymph]

"make sure you have at least 5 bins that contain data"

[untold torrent]

What does bin mean

[sterile nymph]

You'll need to make your bins smaller

Those are the intervals

[untold torrent]

What should i do

[sterile nymph]

[10, 20) is a bin

Maybe make your bins size 5?

[untold torrent]

Doi do 10 to 15

Ok

[untold torrent]

Is it good now

[untold torrent]

<@&286206848099549185>

[untold torrent]

.close

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Channel closed

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[amber wasp]

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

Help

[mild zephyr]

On what

[untold torrent]

Is my histogram and frequency tabel correct

[quick ridge]

what’s this for bro

[untold torrent]

Its due in morning its night time for me

[quick ridge]

but what is it

[mild zephyr]

Yeah it looks good

[untold torrent]

My math statistic thing

[quick ridge]

right but like what kind of assignment

[mild zephyr]

Don’t forget to label the x axis tho

[untold torrent]

Is my answers for two last questions correct?

[mild zephyr]

One sec

I’ll check

[untold torrent]

What do i label it?

[quick ridge]

^

[untold torrent]

Its for using statistic k owledg in real world

[mild zephyr]

Cost intervals

[quick ridge]

yes but quiz, test?

[untold torrent]

Kind of a test but we have 3 days

[quick ridge]

<@&268886789983436800>

[unborn plaza]

so a take-home test

[untold torrent]

We choose the city and research stats

[untold torrent]

Yes

[quick ridge]

this dude has been asking for verification of his answers on tests for hours at this point

[mild zephyr]

How did you get part 5

[quick ridge]

stop helping

[mild zephyr]

I don’t see any correlation

[untold torrent]

Theresultiple pages

[mild zephyr]

Why

[quick ridge]

because it’s cheating

[mild zephyr]

How

[quick ridge]

its a test

[mild zephyr]

Oh

Mb

[quick ridge]

brother why did you call this a test

😭

ya know what i don’t even care

[untold torrent]

Its to use stat mnowledge for real world

[quick ridge]

whatever lol

[untold torrent]

Did i say the right thing for d

[mild zephyr]

Yeah it’s positive

This doesn’t look like a test so ima help out

[quick ridge]

yea i have no idea why he called it a test

[untold torrent]

Thanks also im allowed to search how to do the stuff on internet but im bad at that

Its not the test like the one in class that you cant have the books

[quick ridge]

specify that

[untold torrent]

Huh?

[quick ridge]

don’t just say it’s a test or a take home test

elaborate on what the assignment actually is, this doesn’t appear to be a test at all

more like a project

[mild zephyr]

For part 5, it doesn’t look like there asking you to list your data straightforward

[untold torrent]

What it ask for?

[mild zephyr]

They’re asking you to describe how it would feel to live there

[untold torrent]

Can i write its expensive to live there?

[mild zephyr]

For instance, “it would be very cold in Toronto as the avg temp is 4 degrees”

[mild zephyr]

Yes

[untold torrent]

But i can only use data i found

[mild zephyr]

I know

It was an example

[untold torrent]

Oh

[mild zephyr]

Yeah, other than that everything looks good

[untold torrent]

Is 230$ expesnive everyday?

[mild zephyr]

Yes

[untold torrent]

And is 685 mm of rainfall a lot?

[mild zephyr]

Id say yes

[untold torrent]

How do i describe rainfall? Do i say it rains a lot

[mild zephyr]

Say something along the lines of “there would be more rain than the average with an annual average precipitate of 685mm”

If you don’t mind me asking what grade are you in

[untold torrent]

10

Im doing pre ib

[mild zephyr]

I see

Good luck

[untold torrent]

Thanks

[untold torrent]

What is your education?

[mild zephyr]

I’m in college rn

[untold torrent]

What are you stufying

[mild zephyr]

I’m in forensic science right now

[untold torrent]

Whats forensic science

[mild zephyr]

It’s pretty broad, better just to google it

[untold torrent]

What job do you do with it

[mild zephyr]

Forensic scientist

Anyways do you have anything else or are we done?

[untold torrent]

Did i do the box wisker plot right?

[untold torrent]

Was i supposed to make the line more specific with numbers

[amber wasp]

@untold torrent Has your question been resolved?

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[keen pawn]

Find the points of local maxima and local minima

[keen pawn]

$f_x(x,y)+ f_y(x,y) = e^xcos(y) -e^xsin(y)$. We now equate this to $0$ , to obtain $e^x=0$ and $cos(y)=sin(y)$ as points of local extremea

[honest dagger]

points of local maxima extrema

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[mellow hornet]

why are you adding f_x and f_y

[keen pawn]

$e^x=0$ i absurd, so the point of local maxima or minima are those points where $cos(y)=sin(y)$. In other words $y = 2n \pi+ \frac{\pi}{4}$

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[keen pawn]

ah, my bad

[mellow hornet]

Ye you need both to equal 0 to have a critical point

[keen pawn]

so $e^xcos(y)=0$ and $-e^x sin(y)=0$

both can't happen at. the same time

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[honest dagger]

This makes sense, given the e^x growth.

[keen pawn]

yeah

let me graph it to confirm

,w e^x cos(y)= f(x,y)

[grizzled pagoda]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[honest dagger]

[keen pawn]

[honest dagger]

If you want to be certain, consider the magnitude of the gradient

[keen pawn]

🙏

I don't think I've read about the relationship between the gradient and extrema points yet

will probably do that later then

TYSM!

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[viscid cobalt]

I get the first step here

but i cant rearrange it to the right form

I just did 1-x/8 = 1-2y^2/81

move the one to the other side

and divide through by 2/81

and then square root both sides

.close

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[echo mirage]

Since u want the x part to be positive u can proceed by multiplying ( -) to both the side
Then u will get -1+x/8 = -1+2y^2/81

[viscid cobalt]

yeah no i got it thanks

I just had to write it as one fraction

[echo mirage]

Yess

U can use this aswell

[amber wasp]

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[calm pewter]

i need help with this

[restive orchid]

what have you tried

[dull pike]

What is your question

[calm pewter]

i have a question do i just substaute the value of x?

[dull pike]

Not the value

You substitute x

[calm pewter]

oh ok i think i got it thanks

tysm

.close

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[eternal summit]

Past what decimal place is it not important to consider?

[amber wasp]

Please don't occupy multiple help channels.

[primal holly]

you need to elaborate

[restive orchid]

depends on context

[split sail]

depends

[eternal summit]

What decimal place is not important

[primal holly]

look into the concept of significant figures because "decimal place" is very arbitrary

[sinful sapphire]

it's whatever you like

[eternal summit]

After hundreds decimal place?

[restive orchid]

what is "important" is subjective

[eternal summit]

So low that it doesn’t matter?

[restive orchid]

it means there's not one answer to this question

[solar gust]

It will matter anyway

[primal holly]

are you taking a measurement? is this a computer program? what are you doing

[solar gust]

It will matter for someone at some point

[eternal summit]

Just in general

[primal holly]

well it depends from place to place

and more often than not it will be obvious enough and you can decide there

[solar gust]

The real problems with rounding or forgetting about a certain threshold of decimals is that when you do operations on, it became wrong

[frozen glacier]

I'd say it depends on the accuracy you wanna achive, like in normal text book problems one may approximate π to be 3.14 while NASA uses 15 to 16 digits (I don't know the actual figure)

[solar gust]

15

It was also proved that with more decimals it bring nothing useful tho

[eternal summit]

Like 15 decimals is so little…

That it doesn’t matter

[solar gust]

Not that little

[restive orchid]

there are times where using digits make the answer worse

[solar gust]

Its cs

[eternal summit]

No?

[restive orchid]

for instance sin(pi)=0 but sin(3.14) isn't 0 and probably not what you want

,w sin(3.14)

[grizzled pagoda]

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[solar gust]

Js moment

[solar gust]

Do you think that 0.1 + 0.2 = 0.3 ?

[frozen glacier]

,w 0.1+0.2

[grizzled pagoda]

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[eternal summit]

What is sin again?

[solar gust]

Sinus

[frozen glacier]

sin

Bad deeds

[eternal summit]

And what’s that?

Ratio between the a/c?

[solar gust]

Air conditionning ?

[eternal summit]

Omg

$\frac{a}{c}$

[grizzled pagoda]

ariana😍

[solar gust]

Ok but what is a and c

Opposite / hypothenus ?

[eternal summit]

Ye

[frozen glacier]

SohCahToa

[primal holly]

spit on that thang

[eternal summit]

The sin of <A is

[primal holly]

,w sin 49 degrees

[grizzled pagoda]

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[frozen glacier]

I think I would be rather interesting to find a

[eternal summit]

Okay

So

[eternal summit]

The tg of gamma

[frozen glacier]

I don't have the proof but c =√52

[eternal summit]

The ratio of tg

In here

Is

,calc 4/6

[grizzled pagoda]

Result:

0.66666666666667

[eternal summit]

0.6666666

That’s the ratio of tg

@primal holly

[primal holly]

yes

[eternal summit]

Ok

I know this

Bb

.,•+{

.Close

Ret

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[fallen chasm]

Are these accurate?

[signal furnace]

,w differentiate (t+1)(t-3)^3

[grizzled pagoda]

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[signal furnace]

,w increasing 4(t-3)^2 t

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[signal furnace]

yeah they both look good to me

[fallen chasm]

TYSMM

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[split sail]

w, integrate (2x^2-15x+5)/(x-7) from 1 to 5

[split sail]

w, integrate (2x^2-15x+5)/(x-7) from 1 to 5

[brisk leaf]

,w

[split sail]

WHY

ok

,w integrate (2x^2-15x+5)/(x-7) from 1 to 5

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[shadow stump]

if all you need to do is ask wolfram alpha a question i would recommend the website https://www.wolframalpha.com/

[keen pawn]

or #bots

[split sail]

okkk my bad

.closee

.closed

.close

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[keen pawn]

.solved works too btw

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[viscid cobalt]

can somoene explain part b?

i forgot how to do it

dont i set the deravative equal to 0?

[quick ridge]

y decreasing -> dy/dx < 0

[viscid cobalt]

so basically

I got this

so i would make

x less than a half right?

like x = 1/2 or 5/2

[quick ridge]

,w derivative 3x(2x-5)^4

[viscid cobalt]

when dy/dx = 0

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[viscid cobalt]

or like less than 5/2

idk

that doesnt make sense

[quick ridge]

since we have a product we should consider when only one of the factors is < 0 so find where (2x-5)^3 < 0 and (2x-1) > 0 or where (2x-5)^3 > 0 and (2x-1) < 0

[viscid cobalt]

oh that makes a lot of sense

[quick ridge]

for the first one we would have x < 5/2 and x > 1/2 so 1/2 < x < 5/2

now you do the other one

[viscid cobalt]

2x-5 cubed greater than 0

x >5/2

and then the other one is x less than a half

j the other way around innit

?

nice

thanks!

.close

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[viscid cobalt]

.reopen

[amber wasp]

✅

[viscid cobalt]

wait i dont get the less than/ greater than or equal signs

[quick ridge]

they considered endpoints to be decreasing when in fact it would have dy/dx = 0 so i guess they just accepted those

[viscid cobalt]

ohhh right

technically less accurate then

cool

thx

.close

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[viscid cobalt]

.reopen

[amber wasp]

✅

[viscid cobalt]

this is how the mark scheme gets it to cartesian form

i dont understand why they need to use the identity tho

[quick ridge]

is this the toy problem?

[viscid cobalt]

no xd

j parametric integration

like I just tried to plug sint = x/4 into sin2t

to get 3sin1/2 x

idk why they have to use the double angle formula

[quick ridge]

because we want to express y in terms of x and y can be written in terms of sint and hence can be written in terms of x

using double angle

[viscid cobalt]

ah alright

ty

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[solemn escarp]

i need to find the value of tan( 3pi/11) + 4sin(2pi/11)

[solemn escarp]

i dont really know the approach

cause 11 is prime

[keen pawn]

huh

$\tan(3π/11)+ 4 \sin(2π/11)$

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[keen pawn]

this?

[solemn escarp]

yeah

[keen pawn]

interesting

to start, re-write it in terms of sin and cos

I suppose

[solemn escarp]

idk if that gets me anywhere

maybe im just bad at trig

chat what about

11th root of unity stuff

<@&286206848099549185>

[mystic plover]

subsitute pi/11 as some variable and then simplifiy?

[solemn escarp]

huh?

wolfram alpha says its sqrt(11)

[mystic plover]

$\tan(3k)+ 4 \sin(2k)$

[grizzled pagoda]

Waqar

[mystic plover]

like here k=pi/11

[solemn escarp]

yeah?

[mystic plover]

and then suppose that this thing is equal to a number which u said is sqrt(11)

suppose that number is z

[solemn escarp]

okay

[mystic plover]

then z is equal to this

then you expand and do trig identities

[solemn escarp]

i

[amber wasp]

@solemn escarp Has your question been resolved?

[amber wasp]

@solemn escarp Has your question been resolved?

[amber wasp]

@solemn escarp Has your question been resolved?

[mystic plover]

$\tan(3k)+ 4 \sin(2k)$ =t

[grizzled pagoda]

Waqar

[mystic plover]

convert tan3k to sin3k/cos3k then cross multiply and apply identities

[solemn escarp]

yeah i got this

not sure what to do next

[harsh python]

<@&286206848099549185>

did I do the right thing

[mint nacelle]

,rotate

[mint nacelle]

when you add (2/2)^2 you should subtract (2/2)^2 to keep everything the same

[solemn escarp]

find your own help channel bro😭

[mint nacelle]

yes

[solemn escarp]

my channel has been up for 4 hours wth

[mint nacelle]

https://math.stackexchange.com/questions/11246/how-to-prove-that-tan3-pi-11-4-sin2-pi-11-sqrt11

more results online

[solemn escarp]

oh what thanks

tysm

middle school competitions be wilding

.close

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[mint nacelle]

JEE 12th grade....

it said that online

[solemn escarp]

this was in 2016 TUMSO where i found it

its a school's math and science olympiad for middle schoolers

im taking it on jan 10th

[mint nacelle]

good luck

[solemn escarp]

yeah its hard lmao😭

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[rose hearth]

this was taken from Ali's channel since its pretty much dead

my attempt:
replace x = e^t, such that 4y = 4z follows. remains to show z" = x^2 y'' + x y'

[rose hearth]

$z' = \frac{dz}{dt} = \frac{dz}{dx}\frac{dx}{dt} = \frac{dy(e^t)}{d(e^t)}\frac{d(e^t)}{dt} = \frac{dy}{dx}e^t = x\frac{dy}{dx}$

[grizzled pagoda]

violet

[rose hearth]

my argument for the first eq in the solution but I don't feel confident about it

[amber wasp]

@rose hearth Has your question been resolved?

[rose hearth]

.cloee

. close

.close

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[spark iris]

Can someone help prove that d=1/3 of the height? I’m pretty sure it is but I can’t prove it and my working is based of the points being a third of the height

[mild zephyr]

,rotate

[spark iris]

u got any ideas? cuz im kinda stuck

[abstract pine]

It looks like Thales' theorem applied 47 times

[abstract pine]

Well yes, so you can find the areas of BDG, FGC and AEF then simply substract them from ABC

[spark iris]

yeah but how do i prove that d=1/3 height of that f= 1/2 height

srry had to eat breakfast so i wasnt here

@abstract pine

[abstract pine]

Either divide all sides in 6, or extent the thirds beyond the triangle.. if you get what i mean

And maybe useful to use base × height/2 somewhere in there

[spark iris]

wdym by that?

im js trying to prove the height cause i think i got the right answer already

[abstract pine]

Though i don't quite understand what you mean by this

[spark iris]

like

does d line up with 1/3 of the triangles height

like in a straight line

[abstract pine]

Oh if it's saying D is located 1/3 of the height above the base, then you can use similar triangles

[spark iris]

how can we do that?

[abstract pine]

Well say AC is divided in 3: A-I-J-C, then ABC and ADJ are similar, so their heights are also proportional

[spark iris]

and d is 1/3 above the base

?

because sf is 2/3

@abstract pine is that the reasoning cuz im kinda dumb

[abstract pine]

What is s and f lol

But yeah smth like that

[spark iris]

scale factor

[abstract pine]

Yeah makes sense, maybe another more direct way is similar triangles on the right-angled triangles BDX and BAY where X and Y are at the heights at D and A

[spark iris]

oh yeah

makes more sense

tysm for helping

[abstract pine]

Nw!

[spark iris]

.close

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[wispy ingot]

This problem seems like a variant of the 100 green eyes riddle, but I think this version is flawed? Even with only two professors A and B, professor A doesn't know that professor B knows whether professor A's work has a mistake or not, and therefore can't conclude anything by professor B not resigning. And likewise, professor B can't conclude anything by professor A not resigning. In the green eyes riddle with two people, each person know that the other person can see their eye color, which is a fundamentally different situation. Is my analysis correct? (The riddle I'm referring to https://www.youtube.com/watch?v=98TQv5IAtY8).

Also, for question 28, if we apply it to the green eye's riddle, the knowledge gained is that "everyone knows the everyone knows that everyone knows... x100 that at least one person has green eyes," is that correct?

[wispy ingot]

oh I just realized the professor added "which has been discoverd by others in the department." Strictly speaking, doesn't he have to say "discovered by all others"?

otherwise the induction works for n = 2 but not n = 3 I think

[amber wasp]

@wispy ingot Has your question been resolved?

[wispy ingot]

@split kraken You might be interested in this

[split kraken]

is too much words >.<

and I'm not generally into the puzzly kind of path

[wispy ingot]

Oh ok sorry

<@&286206848099549185> i think it breaks down for n = 3 unless professor X says “discovered by all others” yeah?

[lusty saffron]

yeah
it's impossible that anyone will resign on the first iteration, because no matter what information they have, it's consistent that only one mistake exists and it was made by someone else (either a mistake they know about, or a mistake that they don't know about and the third person does)
so when that in fact happens it gives nobody any information, and so the next step (and by induction every step afterwards) plays out identically to the first one

[wispy ingot]

Right, but I think even after 17 weeks they don’t have sufficient information based on what Prof X said

[lusty saffron]

...although a possible interpretation is that they all already have common knowledge that, if there was a mistake, everyone except the person who made the mistake would know, and so prof X didn't have to say that explicitly

[lusty saffron]

well yes, that's my conclusion

after 17 weeks, or n weeks for any n, they have no information, because in each week they gain no information

[wispy ingot]

Ok but if they have that common they already would have resigned I think right? Depending on what precisely you mean by common knowledge

[lusty saffron]

well knowing that that's the hypothetical policy doesn't imply that any mistakes have ever actually happened

[wispy ingot]

Oh I see what you’re saying

Yeah then that should be sufficient

Given what the prof says

But not sufficient without what the prof says

Like given 3 people A, B, C; the knowledge gained would be “Person A knows that person B knows that person C knows that there’s at least one mistake “

That would be the answer to question 28 right?

[lusty saffron]

yep, it's that kind of thing

"everyone knows that P is true" and "everyone knows that everyone knows that everyone knows that everyone knows [...] that P" are in general very very different

[wispy ingot]

right right

ok thanks, I think that answers all my questions!

.close

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[storm portal]

How do I know what the angles a b and c are

[keen pawn]

You can find angle A as a+112=180

[storm portal]

How about c

[vocal isle]

this is easy

[solar gust]

Then find C with that value

Sum is 360

[vocal isle]

b + c = 180

[storm portal]

Okay Okay I got it

Thanks

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[robust willow]

What have you tried?

[empty lintel]

i dont even remember am trying to solve for 1 day

[robust willow]

Best method here is integration by parts if you remember it

[empty lintel]

ye i propably already tried it

if anyone can solve so i can see what i did wrong will be much appreciated

[jaunty eagle]

it's better if you had shown what you tried

[empty lintel]

its like 15 papers than i through to garbage from last night i dont have time to solve it rn my deadline is finishing i must work on others too

[jaunty eagle]

it's your responsibility to time your answers 😭

[empty lintel]

exactly thats why am asking for help

[jaunty eagle]

😅
don't tell me you're here only for the solution

[empty lintel]

no i want to see what is the right way to solve it

after everything i tried

[jaunty eagle]

remember, you told us that you wanted to compare answers to show what you did wrong

you must show your work first

[empty lintel]

ok

[jaunty eagle]

hey, not too bad

how did you get dv tho 🤔

[empty lintel]

i might even mest up the integration

idk

[hidden basalt]

dv is what is in the original integral

[empty lintel]

ye i get it

[amber wasp]

@empty lintel Has your question been resolved?

[modest chasm]

ncice approach

you could do it better tho

[empty lintel]

how can i

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[topaz river]

Can someone explain why the value ln10/ln2 = 2.303/2.303x0.301 instead of 2.303/0.301

[topaz river]

It's been 8 months since I revised logarithm so idk if I'm missing out on something

[vocal isle]

,calc ln(10)

[grizzled pagoda]

The following error occured while calculating:
Error: Undefined function ln

[vocal isle]

,w ln(10)

[grizzled pagoda]

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[vocal isle]

,w ln(2)

[grizzled pagoda]

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[topaz river]

Yo myf

I misunderstood ln2 for log 2😭

ty

[vocal isle]

no prob.

[topaz river]

.close

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[tough mica]

The sum of two positive integers $a$ and $b$ is $1001$. What is the largest possible value of $\gcd(a,b)$?

[grizzled pagoda]

938c2cc0dcc05f2b68c4287040cfcf71

[frank zealot]

first off, do u view 0 as a positive integer?

cause for everyone, this idea differs

[tough mica]

0 is not positive nor negative

[frank zealot]

alright then

u can consider GCD(a,b) = δ

in that case, u can conclude that:

a = a'δ

b = b'δ

a' and b' are coprime

[tough mica]

ok

[frank zealot]

add both equations and try to find possible values for δ

of course u want the biggest one

[tough mica]

how

[frank zealot]

ok so

a + b = δ(a' + b')

yes?

ur given a + b

[tough mica]

ye

[frank zealot]

1001 = δ(a' + b')

[tough mica]

1001

[frank zealot]

now we want to know possible values for both delta and (a'+b')

since they both divide 1001

we decompose 1001 into prime factors

and deduct the possible values for each of them

does that make sense

[tough mica]

why prime factorization helps

[frank zealot]

cause u can know the possible values for each of δ and (a' + b')

[tough mica]

, calc 1001 / 7

[grizzled pagoda]

Result:

143

[tough mica]

1001 = 7 x 143

,calc 143/13

[grizzled pagoda]

Result:

11

[frank zealot]

1001 = 7 × 11 × 13

yes

alright

now

[tough mica]

7 x 11 x 13 = ∂(a'+b')

[frank zealot]

okay

[tough mica]

, rotate

[frank zealot]

delta or a'+b' wpuld be any of these

(sorry if i took a bit too long)

u would want the largest value of delta

so what would the answer be

[tough mica]

1001

[frank zealot]

u mean 11 × 13 × 7

if u choose delta = 11 × 13 × 7

[tough mica]

,calc 11137

[grizzled pagoda]

Result:

1001

[frank zealot]

then a' + b' = 1

which means that one of a' or b' would have to be 0

and thus one of a and b would have to be 0

and thats why i asked you before if u see 0 as a positive integer or not

[tough mica]

11x13

[frank zealot]

no its 11 × 13

oh

yeah gj

thats it

[tough mica]

,calc 11*13

[grizzled pagoda]

Result:

143

[tough mica]

thanks for the help

.solved

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[frank zealot]

npp

[tough mica]

subaru kun

[frank zealot]

thats me

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[stray lodge]

Hi, so for 9c, I've figured out the equation for the circle, but I'm not sure why its domain is restricted to x < 0, can someone shed light on this?

[unborn plaza]

this is like arg(z-i)-arg(z+i) right?

[stray lodge]

This is my working out

[stray lodge]

Yeah

Another way to express it

[unborn plaza]

in the first and fourth quandrant, the order of subtraction switches

[stray lodge]

uh

whaaaat

[unborn plaza]

i mean

it doesn't switch

[stray lodge]

what doesn't

[unborn plaza]

in the step where you got rid of arg() you introduced extraneous solutions

[stray lodge]

so what should I do

<@&286206848099549185>

[unborn plaza]

you also solved for arg = 5pi/4

[stray lodge]

where

[unborn plaza]

when you set (x^2+y^2-1)/(x^2+(y+1)^2) = (-2x)/(x^2+(y+1)^2)

[stray lodge]

so how does that solve for arg = 5pi/4

[unborn plaza]

"for arg to be pi/4, Re(z) and Im(z) must be equal"
this is true, but
if Re(z) and Im(z) are equal, arg is either pi/4 or 5pi/4

[stray lodge]

yeah

so i'm solving for pi/4

[unborn plaza]

so you introduced extraneous solutions

it's like squaring both sides of an equation

[stray lodge]

oh

so how do i NOT do that

[unborn plaza]

the arg is pi/4 when Re(z)=Im(z) AND Re(z)=Im(z) > 0

use Im since it's simpler

[stray lodge]

why do Re and IM have to be above 0 for pi/4

[unborn plaza]

so you write down the condition (-2x)/(x^2+(y+1)^2)>0

because pi/4 is in the first quadrant, where x and y are positive

[stray lodge]

i see

thank you

wait but

if I also do Re(z)

and get

$x^2+y^2>1$

I get a domain and range of

[-1,1]

however

in the answers, it shows the range beyond that

oh wait

[grizzled pagoda]

Ram

[stray lodge]

oh nvm

I think that just means both can't be

plus or minus

1/root2

to 0

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[vagrant acorn]

two questions here, what gives it away that (0,0) is a point of interest and how can i paramatize this below to find the boarder points?

[pallid canopy]

What even is the problem

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.close

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[tough mica]

Three different natural numbers $x$, $y$ and $z$ each have exactly three natural-number factors. How many factors does $x^{2}y^{3}z^{4}$ have?

[grizzled pagoda]

938c2cc0dcc05f2b68c4287040cfcf71

[junior vector]

Doesn’t really make sense

A number has to have an even number of factors right ?

[tough mica]

wdym

[junior vector]

Cus factors come in pairs

[quartz sapphire]

factor 30

into a product of primes @junior vector

[junior vector]

It’s not asking about prime factors

It’s asking about natural number factors

“Have exactly three natural number factors”

[quartz sapphire]

first time i hear of factors coming in pairs

[junior vector]

What

Factors come in pairs

For example factors of 6

(3,2) are a factor pair

(6,1) is another pair

[quartz sapphire]

only true if you divide it by ONE factor

[junior vector]

What

[quartz sapphire]

factors of 30= {1,2,3,5,6,10,15,30}

[junior vector]

Yeah that’s an even number of factors

[quartz sapphire]

(30,1), (15,2), (10,3) etc.. but 10, 15 and 30 can clearly be factorized further

[junior vector]

But the way the question is phrased

“Has exactly 3 natural number factors”

Not sure how that’s possible

[quartz sapphire]

that just means that x can only be written as a product of three natural numbers that are not necessarily different

example: 8 = 2x2x2

wheras any prime number or multiple of a prime number composed with another prime, cannot

21= 7x3, 7 and 3 cannot be decomposed further

well, it depends on if you count 1 in the factorization or not

thats a choice you have to take to solve this

[junior vector]

Idk

[quartz sapphire]

but the question is still vague

the number of factors varies depending on if you consider powers or not

[rose hearth]

perfect squares

e.g. 4 = 2^2 has factors 1, 2, 4

you got the pair (2,2)

if that helps in respect to numbers that have 3 factors

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[vagrant acorn]

how does the -sin(t) - cos(t) = 0, turn into tan(t) = -1?

[vestal hatch]

adding sin(t) to both sides and then dividing by cos(t)

[vagrant acorn]

And the -1?

[bronze locust]

add sin t to both sides -> - cos t = sin t -> divide by cos t -> -1 = sin t / cos t = tan t

[vagrant acorn]

Thanks

.close

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[rocky tendon]

the intersection is D_2

but the problem is

when you fix the x

it's 1 <= x <= 0.5

and the y is

$\sqrt{\frac{1}{4} - x^2 } + \frac{1}{2} \le y \le \sqrt{x - x^2}$

[grizzled pagoda]

RulzerFly

[rocky tendon]

this is what i found but in the solution