help-0

[jagged raptor]

for a circle you can use that the tangent line at a point is perpendicular to the radial line through that point

and that can be proved without calc

[chrome plank]

There's a formula to find the tangent of an ellipse, but you still need to know that the point is on the ellipse

$\frac {x \cdot x_p} {a^2} + \frac {y \cdot y_p} {b^2} = 1$

[ocean seal]

Nonna

[chrome plank]

This is what it looks like, xp and yp are the coords of the point

[alpine sable]

oh thats kind of based

[chrome plank]

I have no clue where that formula comes from, it's just so nice to remember haha

[alpine sable]

lol yea

[chrome plank]

Works with hyperbolas too!

[alpine sable]

ok well im not sure if i will never use, but at least ik it now

[chrome plank]

and circles

[alpine sable]

ooh nice

[chrome plank]

But for circles it's overkill

[alpine sable]

lol yes

[chrome plank]

Also there's a way to make it work with parabolas, but that's too much

[chrome plank]

(of course, just switch the + with a - and it will work)

One downside is that the line is in a terrible form and usually some calculations are required to bring it to y = mx + c

[alpine sable]

yes

.close

[lone heart]

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[void trout]

Help plz

Can you send pic if working out I think answers wrong

[fathom kite]

hi

[void trout]

Yo

[fathom kite]

what i would do is split the triangle into two right angle triangles

right in the middle

from A to D

basically to find the angle ABC

[void trout]

Can you send me workingoyt plz

[fathom kite]

ok

you understand?

[void trout]

Ye how bout b

[fathom kite]

i would calculate the area of the whole triangle ABC

and then calculate the area of the non shaded part, and then subtract the non shaded part from the area of the triangle

[void trout]

Sorry bro can you plz send a pic

I am better visual

[fathom kite]

yes but i hope u are not just using the answer lool...

[void trout]

I’m not bro my exams in 4 weeks not now

[wary stream]

Don't do the work for people, like this, even if they ask for it. You should ask them what they did first and you can check to see if it's done correctly

[fathom kite]

ok @void trout you have to find the full area of the triangle

and then find the area of the non shaded part

[void trout]

What form

Do you use

[fathom kite]

whats a form

[void trout]

Formula you use

[fathom kite]

oh

[wary stream]

What's the area of a triangle formula?

What's the area of a sector?

[fathom kite]

yeah

[wary stream]

It's just those two formulas you need

If you don't know them, I suggest Googling it instead of getting spoonfeed

[void trout]

Ok but what radius

For both

Cause they are diffeent

[last ether]

Well you should know that the altitude of an isosceles triangle is also the median of the triangle. This means that you'll have a right triangle with sides 2sqrt(3), the altitude, and 6

The radius is 6 if you look at the diagram

[void trout]

For both trajnhjes

[last ether]

Well here, what I would do is find the area of the entire triangle and then subtract the area of the sector

Do you have the area of the isosceles triangle?

[void trout]

No

Not sure how

To find area of big

[last ether]

You can use Heron's formula or find the height

Which one you wanna do?

[void trout]

Haven’t learnt that

I think height

What wjuks you do

[last ether]

This

Reverse Pythagorean

[void trout]

Haven’t learnt that

[last ether]

It's literally just Pythagorean theorem

What's your hypotenuse of one of your right triangles

[void trout]

6

[last ether]

What's the length of the leg of the right triangle

[void trout]

6 root 3

[last ether]

No

That's the whole base

[void trout]

What wield it be

[last ether]

Well you should know that the altitude of an isosceles triangle is also the median of the triangle.

The median bisects the base

So what would the leg length be

[void trout]

6 root 3 minus 6

[last ether]

Buddy I just said it bisects

It cuts the base in two

[void trout]

Not sure

[last ether]

What is $6\sqrt{3}$ divided by 2?

[ocean seal]

Umbraleviathan

[void trout]

3 root 3

[last ether]

Yeah, so that's your leg length

You know Pythagorean theorem right

I'm gonna let $b$ be the height/altitude of the isosceles triangle:

$$(3\sqrt{3})^2 + b^2 = 6^2$$

Find $b$.

[ocean seal]

Umbraleviathan

[void trout]

Ye it’s 3

Then after what do you do

[last ether]

Well you know your formula for the area of a triangle?

[void trout]

Ye can you send me what you minus

[last ether]

You don't subtract anything yet

We're just finding the area of the isosceles triangle for now

So what's the area of the isosceles triangle

[void trout]

Not sure what do I sub in

[last ether]

You know your formula for the area of a triangle?

$A = \frac{1}{2}bh$

I'm an idiot

[ocean seal]

Umbraleviathan

[last ether]

No

What's your base

Of the isosceles

[void trout]

3 root 3

[last ether]

Of your isoceles

[void trout]

3

[last ether]

Look at your diagram

[void trout]

6 root 3

[last ether]

Yes

What's your height

[void trout]

3

[last ether]

Plug it in

[void trout]

9 root 3

[last ether]

Yup!

Good, save that somewhere

[void trout]

Ok

[last ether]

So now we need to find the area of the sector

[void trout]

Ye

[last ether]

What's the radius of your sector

[void trout]

6

[last ether]

Yup

What's the measure of angle ABC, in degrees?

[void trout]

Pie over 6

[last ether]

That's in radians

Are you gonna use radians or degrees?

[void trout]

Any

[last ether]

Alright well if you're gonna use radians, then yes, it's π/6 rad

[void trout]

Yep

[last ether]

You know your (radian) formula for sector area?

[wary stream]

I'm assuming radians since part A asked for radians

[last ether]

$A_{\text{sector}} = \frac{1}{2}r^2\theta$

[ocean seal]

Umbraleviathan

[last ether]

Ah

[last ether]

So just plug it in

You have your radius and your angle (in radians)

@void trout

[lone heart]

@void trout Has your question been resolved?

[last ether]

Whelp they dead

At least they got the area of the triangle lol

@wary stream don't you love it when this happens

I was this close to finishing it

[wary stream]

When they die? Yes

[last ether]

Well no not literally die

[jagged raptor]

how do u know

[last ether]

Well I mean that is a possibility but a very small one

[lone heart]

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[main zephyr]

Given 3 points A(a, a+1), B(-6, -3) and C(5, -1). Find the possible value(s) of a if the length of AB is twice that of AC.

answer: 2 or 16 over 3

below is my working, i have no idea how to get 16 over 3

[main zephyr]

!close

.close

[lone heart]

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[karmic spoke]

how do i derive (x-5)/x

[karmic spoke]

answer is 5/x^2

[fallen verge]

Its differentiate

But anyway

You can do two things

The first one being quotient rule if you know that already

[karmic spoke]

i wsnt taught the quotient rule

[fallen verge]

Or you can split the fraction based on the numerator

[karmic spoke]

and i tried the nx^n-1 rule

[karmic spoke]

so like

OH

I GOT IT

like this? @fallen verge ?

[fallen verge]

👍

[karmic spoke]

okay thanks

!close

[fallen verge]

No prob

[karmic spoke]

.close

[lone heart]

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[alpine sable]

this doesn't need quiotent rule

[fallen verge]

...

[alpine sable]

$\frac{x-5}{x}=1-\frac{5}{x}$

[ocean seal]

Normal Zeta

[fallen verge]

......

Did you see the work

Also its closed already

[alpine sable]

oh wait mb didn't see

I was on the top messages

didn't notice

[fallen verge]

Ok

[lone heart]

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[tranquil brook]

Hello,
So I have trouble with my linear inequalities homework and I need help with part h till p
I still don't quite get fractions of linear inequalities so it would be nice if someone helped me

[native cloud]

What help do you exactly need?

[tranquil brook]

With my homework and I still don't grasp the concept of linear inequalities

My teacher explains really fast and I'm kind of a slow learner so😫

[native cloud]

What's x = 4x + 8?

[gray isle]

are you comfortable with linear equations?

[tranquil brook]

Linear equations yes

[gray isle]

linear inequalities aren't that much different

[tranquil brook]

I thought you meant simultaneous

I only learnt simultaneous equations
Haven't gotto that chapter

[gray isle]

how...

simultaneous equations HAS to come after linear equations

[tranquil brook]

I learned simultaneous equations first

My first chapter was linear graphs and simultaneous equations

[gray isle]

linear equations is pretty much a prerequisite for doing simulatenous equations

[tranquil brook]

or is the chapter during the 7th grade?

[gray isle]

these don't even have two variables, only one

[tranquil brook]

Cause I doze of during 7th grade

[tranquil brook]

Ohhh

[gray isle]

by linear equations i'm referring to stuff like solving

x = 4x + 8

[tranquil brook]

Oh yea I already did

[gray isle]

which i am 100% sure that you've done before

[tranquil brook]

Yea sorry

[gray isle]

manipulating inequalities using basic algebraic operations is very similar to manipulating equations
except that you reverse the direction of the inequality when multiplying/dividing both sides by a negative amount

[tranquil brook]

ohhh

Thanks

How do we know how to reverse the signs?

@gray isle

[gray isle]

wdym

[native cloud]

If there's a minus

[lone heart]

@tranquil brook Has your question been resolved?

[tranquil brook]

Like if it's > how did it suddenly turn to <
I still don't understand that
Is it because of multiplying by a negative number or?

[gray isle]

except that you reverse the direction of the inequality when multiplying/dividing both sides by a negative amount

[lone heart]

@tranquil brook Has your question been resolved?

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[lone heart]

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[sharp nebula]

Can anyone help me with this problem?

[marsh rapids]

This isn't a strong condition, a lot of numbers verify that. It's pretty easy to start at 1000 and find the smallest one

[sharp nebula]

Can you write the answer down for me?

I can’t seem to find a way to solve it

I was going to use Chinese Remainder Theorem but the gcd isn’t 1 so i’m unable to solve it

[marsh rapids]

Noticing it's periodic modulo 18 can help

Then you find the set of solutions quite easily

[sharp nebula]

Can you at least write it down i don’t quite understand what you’re saying

[marsh rapids]

1000 doesn't work. 1001 is solution. Therefore 1001 is the smallest 4-digit number that works

That ought to be the shortest solution to this problem, though quite a disappointing one

[marsh rapids]

This idea is that if k is solution, so are 18+k and 18-k. Therefore you can just find the solutions in [0, 17] and transfer them to [990, 1007]. Since 10 isn't a solution, 1000 isn't, but since 11 is solution, 1001 is

[sharp nebula]

So the problem isn’t this?

1001 doesn’t satisfy this system

[prime badge]

no it's any combination of 1,2,5

not specifically 1,2 and 5

[lone heart]

@sharp nebula Has your question been resolved?

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[gritty verge]

Is something wrong with my working

[deft python]

How does this work?

[gritty verge]

Wait oop its not liddat

OOh isssit 1/4 then becomes -4 ??

[lost coral]

,flip

.flip

[deft python]

im confued?

[alpine sable]

,rotate

[gritty verge]

Oh boy sorrry for that bad photo

May it which line is wrong?

Ik*

[lost coral]

hmm can u take another photo?

[gritty verge]

Sure

[lost coral]

ok nice

[gritty verge]

Is this bttr?

Okie

[lost coral]

u finding derivative of xy-sqrt(1+y^2)?

[gritty verge]

Yup

Implicit differentiation

I’m tryna find dy/dx to be exact

[lost coral]

i think the 3rd line is wrong

[gritty verge]

Oh which tho I cant tell what’s wrong oof :,>

[gritty verge]

Mhm

I was tryna use product rule did i use it wrongly?

[lost coral]

hmm u only use product rule for xy

product rule is used when theres multiplication

[gritty verge]

Hmm i see

I thought (xy) was gettingmultiplied to the thing after it

[lost coral]

it is?

it seems like xy - sqrt(1+y^2)

[gritty verge]

Oml nope

My bad writing

It’s getting multiplies hehe

[lost coral]

oh its right

[gritty verge]

I cant draw square root for dear life

Haha so is my end solution correct too??

[lost coral]

hmm

[gritty verge]

Bcos the answer sheets answer is diff

Idk cus ifi did wrong or some simplification has to be done

[lost coral]

what did u do in the 4th line?

multiply y on both sides?

[gritty verge]

I kinda expanded o.0

[lost coral]

o

[gritty verge]

Oh line 5

Missing a minus

1 mistake I fount lol

Found

[lost coral]

oo

[gritty verge]

But stilll doesn’t help to Make a difference

Mhm

[lost coral]

theres no problem in line 4

[gritty verge]

Oh then maybe my ans is right but it looks wrong oml

[lost coral]

but theres a problem in line 5

[gritty verge]

Mhm which part

[lost coral]

this extra open parentheses

no wait

wait what

[gritty verge]

AHHA dis is what I’ve been thinking too

Wait unless u wanna try ur way then see if my ans is wrong I Guess?

[lost coral]

the open parentheses is fine

[gritty verge]

Yep

I just forgot to close it

[lost coral]

u did

[gritty verge]

Mhm

Lol math is diff

And my working

[lost coral]

hmm ill try to find dy/dx in my way and see if theres any difference

[gritty verge]

Okey sure

[tribal oxide]

Whats happening in the 7th line?

[gritty verge]

I cancelled common terms

Is that wrong

[tribal oxide]

Which ones? Maybe i just cant see it in my head

[lost coral]

ok

heres my calculations

[gritty verge]

The square root 1 plus y square

[lost coral]

ye its diff from yours

[gritty verge]

Oop

Can dy dx be simplified more?

[lost coral]

hmm i did a mistake

🤦‍♂️

[gritty verge]

Oop

Differentiation is scary

[lost coral]

i think i see your problem

[tribal oxide]

I cannot see how u can write this

[gritty verge]

Ooh oops careless mistake

[lost coral]

theres another mistake

u didnt add the parentheses i think

[tribal oxide]

Theres a minus mistake before

[gritty verge]

Yep i got that one

[tribal oxide]

How does that matter?

For this as well, how does it matter

[lost coral]

wait it doesnt matter

[gritty verge]

So like dis?

[tribal oxide]

5th step the sign is still wrong

Oh wait

[gritty verge]

O.0 I changed it i think?

[tribal oxide]

Bruh its in multiplication i see

Why do u write it like that☠️

[gritty verge]

Eh yo which part o.0

[tribal oxide]

3rd to 4th step the -✓something times y, why do u write it like y-√, very confusing, id definitely use -y√

[gritty verge]

Wait there’s no minus

I write the bracket that way

I don’t even know how i got that habit

[tribal oxide]

....

[lost coral]

btw try not to use power of fractions but write it in radicals instead

[gritty verge]

Also I realised the one at the end shld be x

Oh okay

[lost coral]

hmm

[lone heart]

@gritty verge Has your question been resolved?

[lost coral]

@gritty verge u cant just move it up like this

e.g

[gritty verge]

I cancelled it

Ty btw

[lost coral]

np

can u send all the answer options on the answer key?

[lost coral]

try this

[gritty verge]

Sure

Part c

[lone heart]

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[lost coral]

missed one close parentheses at the 2nd last line

type .reopen?

[lone heart]

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[tidal zealot]

guys

v

why is it plus/minus

i thouhgt its only plus minus when u root both sides

am i dumb

[vale wigeon]

sqrt(cos^2(x)) is not always equal to cos(x)

this is your graph

[alpine sable]

as an aside, wouldnt -sign(cos(x)) be better notation lol

[lone heart]

@tidal zealot Has your question been resolved?

[lone heart]

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[honest kindle]

hello, i am doing Try Hack Me and i am on the Crypto 101, i struggle to understand the concept of cryptographic hash function
to be more specific the question is

If you have an 8 bit hash output, how many possible hashes are there?

i got the answer from the internet but i didn't understand why it is 2 power 8

i tried to read that Article but i don't understand really
https://nakamoto.com/hash-functions/

my math is bad so sorry in advance lol

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@honest kindle Has your question been resolved?

[lone heart]

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[slow wasp]

help in ii) one
confused kind of

[slow wasp]

,rotate

[hard thorn]

now those x1 and x2 means the value of cos(x) now solve for x

[hard thorn]

for the second one it's -1/3 not 1/3

[lone heart]

@slow wasp Has your question been resolved?

[slow wasp]

wait how?

ah yes

sorry MB

[hard thorn]

so

[slow wasp]

okay thanks

[hard thorn]

cos(x)=1/2

[slow wasp]

i will convert them into Cos

[hard thorn]

huh?

[slow wasp]

I get it now

[hard thorn]

x must pi/3

[slow wasp]

I get it now

[hard thorn]

nice

[slow wasp]

.close

[lone heart]

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[lone heart]

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[bitter crater]

You have decided to borrow the remaining money from Commonwealth Bank which is $1,170,000. The rate is 4 % p.a over 20 years using simple interest. Assume you decide to pay monthly repayments. Calculate the monthly repayments you will make for the next 20 years?

[bitter crater]

<@&286206848099549185>

<@&286206848099549185>

[lone heart]

@bitter crater Has your question been resolved?

[gray isle]

what have you tried?

[bitter crater]

what do you mean?

Like ways to solve it

[gray isle]

supposedly you would have made some sort of attempt before coming here

what did you try doing and where did you get stuck

[bitter crater]

I don't even know where to start the formula i have tried things that I even know are wrong

[gray isle]

regardless show me what you've done

[bitter crater]

When i put it all in a calculator

Well first I divided

the

Rates by 12

4% ÷ 12

then I did

1,170,000(1+4%/12x20)

[gray isle]

why divide the rate by 12

[bitter crater]

12 is the months

I googled it

I know i did something wrong

alot of things wrong

[gray isle]

you unnecessarily divided by 12

that's what you did wrong

[bitter crater]

How do i find monthly rate then

[gray isle]

you don't?

or at least you don't need to

[bitter crater]

It says calculate the monthly repayments

[gray isle]

yeh

[bitter crater]

I really dont understnad this qestion

[gray isle]

and to do that you can consider the total amount you would need to repay

and divide that by the number of months

[bitter crater]

so 1,170,000 ÷ 12?

[gray isle]

well you ignored the interest there

do you have access to the simple interest formula?

[bitter crater]

pxrxn

[gray isle]

no

[bitter crater]

PxRxN

wait

no

no

P(1+rn)?

[gray isle]

final amount = P(1+rn)
yes

[bitter crater]

ye sorry bout that'

um

[gray isle]

#❓how-to-get-help this channel is occupied

[rain trench]

@gray isle I’m new sorry

It’s says all are occupied

[rain trench]

Nvm

[bitter crater]

So where were we @gray isle

[gray isle]

final amount = P(1+rn)

[bitter crater]

so 1,170,000(1+4%x20)

?

[gray isle]

you are given P, r, n
which allows you to determine the final/total amount you would need to repay

yes

[bitter crater]

2106000

Is what i got

what do i do next

[gray isle]

and divide that by the number of months

[bitter crater]

175500

[gray isle]

total number of months

not just the amount of months in one year

[bitter crater]

In 20 years?

[gray isle]

remember you're paying this back over 20 years

[bitter crater]

887.5

[gray isle]

not quite, how are you getting

887.5

[bitter crater]

12x20

is 240

so

2106000÷240

877.5

i mean

[gray isle]

is not 877.5 either

[bitter crater]

what did u u get and how did u get it?

[gray isle]

not 877.5

what exactly are you putting in and reading on your calculator

that number is too small

[bitter crater]

8775

sorry

i

[gray isle]

yes, that's better

[bitter crater]

its dark in here

Okay so how do i present my answer

[gray isle]

that's the answer

monthly repayment: $8775

[bitter crater]

Ok really thank you so much

how do i close this channeel again

[gray isle]

.close

[bitter crater]

Ok thankyou

.close

[lone heart]

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[lyric gust]

hello, world

[lyric gust]

So, i have some data. It looks like this
{54: {240: 80, 24: 1}, 126: {91: 79}, 151: {183: 43}...
Where as,
50 is mistaken as 240 80 times, and 24 1 time
126 is mistaken as 91 79 times, 151 is...

I need a graph to show the correlation between these numbers as the numbers they're mistaken as

but im not quite sure which one fits most

i cant quite do a range because, only specific values are correlated

[alpine sable]

Bar chart?

[lyric gust]

what

how would that be a useful way to represent data

i was thinking about this

[alpine sable]

That’s a bar chart

[steady bough]

yeah thats a bar chart

[lyric gust]

but it wouldn't be good at represented overlaps

[steady bough]

a "stacked bar chart"

[lyric gust]

thats great, beautiful, I love it, i appreciate the name

but uh

no

[alpine sable]

?

[lyric gust]

its not good at representing potential overlaps with numbers

[alpine sable]

How would someone mistake 50 as 240 anyway

[lyric gust]

what are you... talking about

[alpine sable]

You can use stacked bar chart without overlaps

[lyric gust]

indeed

i can

yes

what is your point

why are you here

[alpine sable]

I don’t see a problem with using the bar chart

Could you clarify the problem you see there

[lyric gust]

.close

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[wide loom]

Isn't the answer C?

[marsh rapids]

It's not C

It is B

[wide loom]

how I found C everytime

[marsh rapids]

Use the Pythagorean theorem better

[wide loom]

probably I miss something

[marsh rapids]

5^2 = 25 makes it way too big

[wide loom]

yeah guess what did I miss

I understand it which one is longest

I have to read it more carefully thanks for answering

just skipt the question part

.close

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[remote heron]

wait are you talking abt matrix powers or each element

oh, this may be above me sorry

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[serene flame]

what did i get wrong

i' tryna get 2πr

i'm doing path integral and converting it from a dx dy integral to a dφ one

yes i suck at terminology i'm sorry

but what is it that's wrong here

the reasons i think it's wrong are:

[alpine sable]

is $y=isin(\theta)$

[ocean seal]

Normal Zeta

[alpine sable]

I don't think this goes by the name path integral

[serene flame]

1. i can't solve this
2. pluggin π/2 in sqrt(cos(2phi)) gives sqrt(-1)
3. even using modulus i don't get the right result

[serene flame]

no it's r sin phi

[alpine sable]

oh

[serene flame]

ye i just can't remember words

[alpine sable]

well then how are u getting -sin^2(psi)

I think it will be +sin^2(psi)

[serene flame]

d/dφ of cos gives -sin

[alpine sable]

don't u have the r as well?

[serene flame]

squared, it's -sin2

[serene flame]

i factored it out

[alpine sable]

$(-sin(x))^2=sin^2(x)$

[ocean seal]

Normal Zeta

[serene flame]

oh

bruh

[alpine sable]

coz (-1)^2=1

[alpine sable]

oh

[serene flame]

i'm stupid, yea thank

[alpine sable]

np

[serene flame]

.close

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[cyan mountain]

What would the variable be

[sly vessel]

Can i ask some basics why do we multiply with the conjugate, and in what situations... Example of where this is coming from was rationalizing expression, then I saw in calculus we multiplied..

With the conjugate

[abstract fractal]

#❓how-to-get-help

[sly vessel]

👍

[cyan mountain]

<@&286206848099549185>

.close

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[leaden hound]

Hi I don't get the third step, where |e^(jkwt)|^2 becomes 1

[mortal trellis]

I assume j is the imaginary unit and k, omega, t are all real?

then e^(j k omega t) is on the unit circle and has norm 1

[leaden hound]

correct

[leaden hound]

ok, how does that lead to 1? I might be missing something here

[mortal trellis]

every point on the unit circle has absolute value 1

that's the definition of the unit circle

[leaden hound]

yes I get that, so basically |e^(jkwt) |^2 has ben rewritten as the module of this complex numer?

being the module 1, the square root is one

at that point though, I would expect that the evaluation of the integral of 1 from 0 to T, which I don't see anywhere there

[mortal trellis]

well first you are forgetting about the gamma_k

second, the integral of a constant is equal to the length of the interval times the constant

here the constant is |gamma_k|^2 and the length of the interval is T, so the value of the integral is T|gamma_k|^2

but you can do it the usual way with integrating to |gamma_k|^2 t and then evaluating that at the boundaries 0 and T

[leaden hound]

very interesting I didn't know this

[leaden hound]

I am going through this because is the usual procedure I would follow

[mortal trellis]

it just saves like 1 step in which you could make a mistake with signs etc. not a huge deal etc but still a nice trick

[leaden hound]

It is, in fact with the lengthier procedure I get: - T |gamma_k|^2

[mortal trellis]

yup classic sign mistake

[leaden hound]

can you explain please?

[mortal trellis]

well you got an extra minus

maybe evaluated the bounds in the wrong order or something, dunno

[leaden hound]

the evaluation would be |gamma_k|^2 * 0 - |gamma_k|^2 * T

[mortal trellis]

nope. other way around

upper bound minus lower bound

[leaden hound]

whoops stupid mistake

thanks a lot, you've been very helpful

.close

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[sacred flax]

in dont understnad

please help

[lone heart]

@sacred flax Has your question been resolved?

[gray isle]

is that stuff above your work?

[sacred flax]

yes

wait nvm

.close

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[junior talon]

This makes absolutely no sense to me guys

[junior talon]

Is it a typo?

should it be n <= N？

[copper stone]

no there's no typo

[junior talon]

Really? I mean I tried big N = 13 and I wrote em all:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. and calculated the square root of 13 and it's around 3.60555

if I'm to stop at n<= sqrt(13) I can't even cross out 4

alright welp, I realized how big dum dum I am, I should cross out all numbers that are multiple

until reaching n<= sqrt(13)

logic works

[copper stone]

no i don't think that's what they meant

[copper stone]

yeah that's it

[junior talon]

Alright this is the next thing, but my book didn't even address this at all for colouring in discrete math, would this case be false if the graph wasn't a cycle one? would vertice colouring be independant from edge colouring if the graph wasn't a cycle?

This is the correct answer btw ^

[lone heart]

@junior talon Has your question been resolved?

[junior talon]

Eh I guess I'll have to uuuh wing it?

.close

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[floral zephyr]

How can i prove this function is bounded

[copper stone]

what is the domain ?

[floral zephyr]

R2-{(0,0)}

[naive valley]

maybe rewrite the numerator as x^2 + y^2 - 3y^2 and then manipulate accordingly

or just write it as the sum of two fractions and show that each one is bounded

[floral zephyr]

O sure thanks

And what about the limit (x,y)---->(0,0)

[naive valley]

do you have any thoughts about the limit?

have you tried approaching (0,0) from different directions?

[floral zephyr]

My intention was to use bounded*0

[naive valley]

check the value on the x axis and on the y axis (except the origin of course)

[floral zephyr]

1 and -2

?

[lone heart]

@floral zephyr Has your question been resolved?

[naive valley]

yes

therefore?

[lone heart]

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[agile condor]

What is the value of Min(k) such that $$ (2ab+bc+ca) (2bc+ca+ab) (2ca+ab+bc) \leqslant k (a+b+c) ^6$$ for positive reels a;b;c?

[ocean seal]

عزالدين لقام

[agile condor]

@oak perch

[lone heart]

@agile condor Has your question been resolved?

[agile condor]

<@&286206848099549185>

[agile condor]

any help plz

[lone heart]

@agile condor Has your question been resolved?

[lone heart]

@agile condor Has your question been resolved?

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[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[urban pine]

this a cool question, but not sure how i would start...
do you have any potentially relevant theorems lying around?

[alpine sable]

Nop

[urban pine]

just realized a min ago they make some parallelograms too which makes things nicer

the sections

gonna play with it 😄

[urban pine]

nothing proven yet, but something i noticed:

we have

\begin{align*}
\sqrt{T} &= \left( \sqrt{T_1} + \sqrt{T_2} + \sqrt{T_3} \right)^2 \\
T &= T_1 + T_2 + T_3 + 2 \sqrt{T_1 T_2} + 2 \sqrt{T_1 T_3} + 2 \sqrt{T_2 T_3}
\end{align*}

and if you call the three trapezoids formed t_k then you also have

$ T = T_1 + T_2 + T_3 + t_1 + t_2 + t_3 $

maybe worth expressing the trapezoid areas in terms of the triangles

[ocean seal]

citrusmunch

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[true skiff]

.reopen

[lavish pier]

Could someone latex wrap these for me separately

[worn fox]

@alpine sable

[urban pine]

you want to learn latex?

[alpine sable]

,tex {\textbf{\color{pink}Rules for Powers/Exponents}}\[3pt]
%v1_050822_764959481070616617
\colorbox{gray}{\begin{tabular}{l|l}
\hline
\[-10pt]Product Rule&$a^xa^y=a^{x+y}$\[5pt]\hline
\[-10pt]Negative Exponent&$a^{-x}=\frac{1}{a^x}$\[10pt]\hline
\[-10pt]Quotient Rule&$\frac{a^x}{a^y}=a^{x-y}$\[8pt]\hline
\[-10pt]Power of Power&$\left(a^x\right)^y=a^{xy}$\[5pt]\hline
\[-10pt]Distributivity&$(ab)^x=a^xb^x$\[5pt]\hline
\[-10pt]Zero Exponent&$a^0=1$\[5pt]\hline
\[-10pt]Fractional Exponent&$a^{\frac{x}{y}}=\sqrt[y]{a^x}$\[5pt]\hline
\end{tabular}}

[ocean seal]

Toby

[alpine sable]

hi lol

[worn fox]

This is literally your calling lol

[alpine sable]

yeah :D

[lavish pier]

Thanks Toby

[alpine sable]

yw :)

[lavish pier]

Toby

You missed the last one can you do that

@alpine sable

[lavish pier]

The last one

<@&286206848099549185>

[alpine sable]

I didnt type it from scratch, it was an old paste i had

(also it follows from distributivity)

[lavish pier]

Yeah but I have draconic teachers

[alpine sable]

anyways: $\left(\frac xy\right)^m=\frac{x^m}{y^m}$

[ocean seal]

Toby

[lavish pier]

Thank

[tacit arch]

damn dude did you really tex all that

https://www.cuemath.com/algebra/exponent-rules/

[alpine sable]

I was procrastinating last week

[urban pine]

is there a discord macro thing, or do you just copy+paste from a file?

[worn fox]

He just writes it rly fast

[alpine sable]

i have my own macros

[tacit arch]

no sadly. i just make my own discord and store there

[ocean seal]

Toby

$1i\rotatebox[origin=c]{180}{w}_{o\leftarrow f}x(\text{f})=\rotatebox[origin=c]{180}{7}$ $\Leftarrow\hspace{-15pt}\raisebox{1pt}{$\implies$}$ \rotatebox[origin=c]{180}{A}$\in\gneq O$, {\Huge\rotatebox[origin=c]{180}{$\in$}}6$\not\leq$O, such\\tHat f\,\rotatebox[origin=c]{-90}{$w$}\,\rlap{b}\rotatebox[origin=c]{-180}{$d$}$\phantom{.}_\delta$($\emptyset$) $\rlap{=}>$ $|\mid \times(f)-\rotatebox[origin=c]{180}{7}||<\epsilon$

[tacit arch]

what da eff

[worn fox]

Yeah I want to die?

[tacit arch]

might be the worst notation i've ever read in my life

[worn fox]

The iff is a nice touch

[lavish pier]

.close

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[tacit arch]

but there is more opportunity. could be better "such that" instead of letters

[worn fox]

It's time for "who will accidentally open this help channel" roulette

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[bleak island]

Hi, can someone tell me why this + turns into -?

[alpine sable]

because of this minus, you distribute it to the entire equation because it is in parentheses

[little nimbus]

what pesadao said ^

you notice how -7x -> + 7x right? yeah it's distributing the negative sign to every term

[bleak island]

Ohhh aight now I get it, didn't think about that

Thanks a lot

.close

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[bleak island]

.reopen

[lone heart]

✅

[bleak island]

hold up

[little nimbus]

?

[bleak island]

Does it only apply to the parenthesis after the -

[little nimbus]

yes, the distributing of the negative sign only applies to the terms that were in the parenthesis

[bleak island]

so everything before the - stays the same? like this

[placid zinc]

• sticks to whatever is to the right, correct.

Everything to the left of - does not care about the -

[bleak island]

ok cool

[little nimbus]

oh yeah, because they're not being distributed into it

[bleak island]

Thanks again

[little nimbus]

I believe it's called the "distributive property" ? might want to check that to fully understand it

[bleak island]

Yea im watching some videos to understand, ty all

.close

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[frosty bone]

Hello, I know how to find the conditonal distribution but Im not sure about the segmented bar graph part or more of what that is

[lone heart]

@frosty bone Has your question been resolved?

[tacit arch]

Of the 85 men, how many fly?

[alpine sable]

thanks

[frosty bone]

18

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@frosty bone Has your question been resolved?

[lone heart]

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[lost coral]

idk what i can do here

[lost coral]

i know that tan(x)=sin(x)/cos(x) tho

but idk what to do with sin(2x)

[placid zinc]

Right, you can't use that tan identity

There's a good identity for sin(2x) though

[lost coral]

hmm

i dont know any identities that involves with the angle

can u send some good identities that i should remember?

[gray isle]

pinned in #geometry-and-trigonometry

[lost coral]

ok thanks

.close

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[oak perch]

Hi, jus woke up. So it’s the same as solving maximal value for left hand side divided by $(a+b+c)^{6}$ . Now we can assume that $c=1$ since both above and below have degree 6, next let $r=a+b,t=ab$, that thing becomes $\frac{2t^{3}+2r^{3}+7r^{2}t+7rt^{2}+2t^{2}+rt}{(r+1)^{6}}$ now notice that when r is fixed, t has maximal value $\frac{r^{2}}{4}$ so let $t=\frac{r^{2}}{4}$ , this becomes a rational function of r. Finally the derivative of this is negative something multiplied by $r^{3}+25r^{2}-60r-27$ and it has only one positive real root, so this function goes up and down, maximal is when you let r be the only real root of $r^{3}+25r^{2}-60r-27$, for this we can use formula. So it’s done

[oak perch]

.close

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[ocean seal]

Cogwheels of the mind

[oak perch]

Sin(π/2)=1 dude

So 2

?

I don’t like repeating, so last time: sin(π/2)=1

.close

I am done

Really annoying

Yeah that’s why I said really annoying

If it was your channel I would just leave

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[mild saffron]

Hello, I have to integrate the function g(r)

Do y'all have any idea of integrating it

I tried the u-substitution method but... not sure if that would work

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@mild saffron Has your question been resolved?

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[woven spade]

so the answer is d

though my calculations say it's c

i tried dv/dt=(h)(dl/dt)(dw/dt)

but apparently that's incorrect

apparently the correct equation is this (with h=10):

why is this?

help appreciated

nvm it's just the product rule

?close

!close

.close

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[little nimbus]

When having absolute values
$|\pi - 6| \rightarrow 6 - \pi$
Is this valid?

[ocean seal]

OceanBro

[fervent timber]

no (edit: only if pi - 6 < 0)

[urban pine]

yes?

i would use equals instead of arrow though

you're just evaluating

since the inside of the abs value is negative, you negate

[little nimbus]

hm does this apply to everything?

If there's only 2 values in the absolute value, we change their signs?

[urban pine]

as long as you follow the definition of absolute value, you can compute with it i guess

no

for instance

$|6 - \pi| = 6 - \pi$

[ocean seal]

citrusmunch

[little nimbus]

it's going to give the same ans as $|\pi - 6|$ tho

so does it actually matter

[urban pine]

your first question was more like |-3| = 3 and my example was like |3| = 3

[ocean seal]

OceanBro

[little nimbus]

oh, so they're the same

[urban pine]

they reduce to the same value yes

[little nimbus]

alright then, I guess it doesn't matter. Thanks

.close

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[urban pine]

please no one attack me for saying π = 3 😨

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[alpine sable]

I just did this, the problem is and the answer is actually -13.721 can anyone tell me how to solve this when the answer is a negative?

[elfin snow]

[urban pine]

should get -13.719
but for these if you subtract a bigger number from a smaller number then you get a negative number

[alpine sable]

How I do it by hand

[tacit arch]

How old are you

[alpine sable]

25

[tacit arch]

https://youtu.be/MdthGCQfC0o

[alpine sable]

I just watched that video and he doesn’t say how. Can you try and do the problem by hand because that way doesn’t work

[sinful wolf]

@thorn plaza

do the calucator ma boy

[fervent timber]

video seems pretty clear to me

[sinful wolf]

use a clactor

pre algebra 0

[alpine sable]

It’s not it doesn’t say what to do when your answer is a negative

[sinful wolf]

do u not have acaluctor

[alpine sable]

What do I when I get kid napped and I can’t use a calculator

[tacit arch]

Kidnapped? You mean adult napped because you're 25

[alpine sable]

No one can answer it

[tacit arch]

https://youtu.be/g1xCB7B1jtI

[tacit arch]

Read server rules

[sinful wolf]

That is so mean

[tacit arch]

No one is giving you the answer because it's against the rules

[alpine sable]

@thorn plaza do you have a job ?

[sinful wolf]

Yea

we cant give u the answer

Only motivation

[tacit arch]

Not because people here don't have the skills

[alpine sable]

What job you doing?

[sinful wolf]

she working at dairy queen

so died

answer ma boy

ma boy u know?

[alpine sable]

Thanks @tacit arch

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@alpine sable Has your question been resolved?

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[mossy tusk]

what are the steps to get to the answer?

I have to find the total surface area

[urban pine]

you'll need the radius/diameter eventually

we can assume this is a right cylinder so that's a right triangle hiding in there

and the missing side is the diameter to that circle 🙂

[mossy tusk]

yes your right

thanks citrusmunch

.close

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[surreal hull]

A circle with a radius of 4 has points at 20, 49, and 180 degrees. What is the area of the triangle composed of lines connecting each point

[gray isle]

what have you tried

[surreal hull]

something like this i thought

[gray isle]

that diagram isn't clear enough

the diagram is open to interpretation and i am unsure if you fully understand the setup

[surreal hull]

gimme me a moment to write my thought process

[gray isle]

ideally you should have something to clearly mark the centre and make those angle labels less ambiguous

[surreal hull]

alright but can i just have it solved and you tell me your thought process and how you would do it

its a math question my friend asked me and we cant figure it out

[gray isle]

make another attempt at drawing a proper diagram

[surreal hull]

alr one sec

that diagram is what my friend had in his mind and roughly sketched it,i want you to focus on the written part of the question and tell me your answer

[gray isle]

and i'm saying the before you start any calculations at all

you should have a clear diagram

[surreal hull]

alr will do in the future but can i just get the answer now

[gray isle]

make another attempt at drawing a proper diagram

don't beg for answers, it doesn't help

a clear diagram makes it much easier to understand what's going on

[surreal hull]

alr the lowermost point is 180 degrees right

so there is that

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@surreal hull Has your question been resolved?

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[worthy verge]

Question 14.
Answer for A and B is both 1/3

This is what i have tried

[marsh rapids]

f(xi) = (i/n)^2 not (1/(n+i))^2

Then you can use the summation formula that was provided

[worthy verge]

i did

summation of y * change = 1/n edited

but im missing smth

[half epoch]

Change?

[worthy verge]

0 to 1 split into n strips

so 1/n

[half epoch]

And why do you have an extra 1/n there?

Each of the strips have area y * 1/n

[worthy verge]

where

[half epoch]

Here

[worthy verge]

this is summation of y * change x is it not

[worthy verge]

i meant change = 1/n mb

[marsh rapids]

If you actually start from the Riemann sum formula, you'll notice it's over n^3.
Then you can have 2n^3 ( + lower terms) / 6n^3 -> 1/3

[worthy verge]

how do u get n^3 at the denominator

[half epoch]

$\lim_{n \to \infty} \sum_{i = 1}^n f(i) \Delta x$ is what we want

[ocean seal]

Learath2

[half epoch]

You correctly figured $\Delta x = \frac{1}{n}$

[ocean seal]

Learath2

[worthy verge]

and they gave me the summation of y

[half epoch]

Now notice 1/n is constant w.r.t the summation index

So it can leave the sum sign

So we have $\lim_{n \to \infty} \Delta x \sum_{i=1}^n f(i)$

[ocean seal]

Learath2

[half epoch]

Notice that sum is nothing but the sum you’ve been given to use

[worthy verge]

ok

[half epoch]

Plug in the given sum, plug in the deltax, take the limit, let me know if stuck

[worthy verge]

yea

thats whaat i did

[half epoch]

Oh, I misread there, it’s not f(i) it’s f(i/n)

Which is nothing but (i^2)/(n^2). You get another 1/(n^2) out of the sum

[worthy verge]

i cant get it lol