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[alpine sable]

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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[safe vine]

ok

lets take an algebraic approach to this

since we know they have the same number of books in the beginning

we can set the number of books each to x

so raj has x books and samuel has x books

so if raj gives samuel 29 books

...

what grade are you

ok

so for the first one

in order for samuel to get 29 more books

raj has to lose 29 books

ok so what do you think the answer is?

no

since samuel gets 29 more

and raj loses 29 books

key word loses

try again

[stuck geode]

maybe put it in a algebraic format

but i think it might help you understand

are you fr?

uh

well

so samuel and raj are both x

they have the same number of books

[safe vine]

check dms

[stuck geode]

no

its just

it doesent even need math its just logic

yes

exactly

he just has a bit more books

29 more books

wait sorry

no lmao

im stupid

58

because samuel gave him 28 of his books

[safe vine]

29*

ok

lets say i have 29 books

and you have 29 books

i give you 29 of mine

how many books do you have

and how many do i have

yes

but liek

number

you have 29

i give you 29

how much do you have

yep

58

so how many do i have

i just gave away 29

29-29 = 0

so i have 0 books

[stuck geode]

i think its a troll

[safe vine]

i originally has 29

so how much more do you have than me?

you have 58 books

i have 0

yes

58

[elfin tapir]

.close

D:

[stuck geode]

no problem i barely helped

[elfin tapir]

!close

[safe vine]

its .close

[elfin tapir]

[lone heart]

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[lone heart]

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[wet vector]

need help finding an anti derivative for this function

i wanna use integration by parts but that z^2 is making it tricky

[alpine sable]

try integration byparts

oh

[alpine sable]

take the other way

[wet vector]

ohh

ok

[alpine sable]

z on diff and sinh(z) on integration

[wet vector]

ok

[wet vector]

nah

so when i use the integ by parts formula

i now get

intgeral of z^3 cosh(z^2)

[alpine sable]

:/

show me your working

[wet vector]

ok

[alpine sable]

bruh

nvm

i didn't see the z^2 in sinh

there is no need to byparts

try solving it by substitution

[wet vector]

u = z^2?

[alpine sable]

u =z^2

aye

[wet vector]

ok

then do parts?

[alpine sable]

there is no need to byparts

[wet vector]

i get sqrt (u) x sinh(u)

oh wait

[alpine sable]

what did you get after substituting u =z^2

[wet vector]

one sec

[alpine sable]

you forgot to change dx into du

[wet vector]

ye

[wet vector]

got it

thanks a lot

.close

[lone heart]

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[crisp sun]

!help

[lone heart]

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

[broken charm]

yeah whats the question

[broken charm]

alr

lets say a is the first term

[crisp sun]

i know the formula

[broken charm]

alr what is it

[crisp sun]

a is your first term

r is the common ratio

n is the power to

first 6 terms is equivalent to to the power of 6

but when i plug it into the formula i know ym aswer is not right

why??

[broken charm]

r=5

[crisp sun]

yes

[broken charm]

5^6 is 15625

[crisp sun]

61027344

[broken charm]

so 1-5^6=15624 which cancels out with the sum

[crisp sun]

u get this number

but thats wrong

[broken charm]

whats this

[crisp sun]

the number

[broken charm]

a?

[crisp sun]

when u put the formula into the calculator

61027344 this is the number when u plug and chug all the numbers into the formula

and put it into the calculator

but thats obviously wrong

so what i do

[broken charm]

well dont use the formula calculator

we have r=5 and n=6

[crisp sun]

yes

[broken charm]

5^6 is (use a normal calculator) 15625

so 1-5^6 is -15624

[crisp sun]

ok

[broken charm]

so -15624a/(1-5)=15624

so a =4

[crisp sun]

ohhh

i see what i did wrong

i put it into the formula wrong

u see this is how ur suppose to doit

because a is the first term

[broken charm]

yes.

[crisp sun]

and they never gave us the first term so we solve for the unknown a

but instead i put 15624 as my a

so i got that big number

[broken charm]

oh lol

[crisp sun]

ok thx

[broken charm]

np

[crisp sun]

but

the formula calculator does wrong

its just human error

actually

i feel likei m cheating

using the calculator :/

[broken charm]

lol but the formula calcultor is both a normal calculator and a ready result

so its more cheating

[lone heart]

@crisp sun Has your question been resolved?

[lone heart]

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@wicked sedge Has your question been resolved?

[acoustic solar]

You need to differentiate w?

[lone heart]

@wicked sedge Has your question been resolved?

[alpine sable]

chain rule

used repeatedly

for w

[lone heart]

@wicked sedge Has your question been resolved?

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[flint mist]

$\log_{2}{\frac{x+1}{x}} = 3x-2$

[ocean seal]

Ctrl

[flint mist]

find X

[hard aspen]

try writing 3x and 2 as a logarithm with base two

[flint mist]

tried

[hard aspen]

show your work

[median pelican]

you can split x+1/1 into two products

[alpine sable]

would end up with 2^3x anyhow

[median pelican]

then use the principle log(xy)= log x + log y

[flint mist]

the left hand side is already modified

it originally was written as log2(x+1) - log2(x)

[median pelican]

dang then tbh i cant see any answers

if you raise both sides by 2, it'll go in a loop

[flint mist]

yep i tried that

i was going in circles

<@&286206848099549185>

[alpine sable]

wait 15 mins atleast

before the ping

[flint mist]

sorry

[runic glacier]

[ \log_a\left(\frac bc\right) = \log_a(b) - \log_a(c) ]

[ocean seal]

shsgd

[flint mist]

and how to use it there?

[runic glacier]

Use on LHS

[flint mist]

i did and it didnt help

[runic glacier]

Where did you get up to

[flint mist]

1s

[livid forge]

This is what we got, sorry for the horrible writing

[flint mist]

this is the furthest we got

so far

[median pelican]

u actually can't do anything to it without doing log base 2 on RHS without dot x

[alpine sable]

expand it by logxy= log x + logy
2 would get cancelled out

[median pelican]

what do you mean?

[alpine sable]

then need to do smth bot 3x on RHS

[livid forge]

Sorry, this

[median pelican]

one way to do this is by doing newton raphson method to approximate x

assuming you know that

[alpine sable]

oh wait nvm bruhhh

[alpine sable]

this two right here is base right ??

[livid forge]

yeah

[median pelican]

all in all if your prof haven't taught u that method then there has to be a mistake

[livid forge]

Probably

[alpine sable]

then this is complicated

[median pelican]

there's no rational answer to this i guess

[storm ridge]

I just plotted it on desmos,
||(1,1)|| is a solution

[alpine sable]

bruuuuuuuuh

[median pelican]

can you shows us

[flint mist]

1, 1 is solution, now prove it

[storm ridge]

Just saying

[median pelican]

prove it

[livid forge]

Yeah, we know that the solution is 1

[flint mist]

can we ping helpers now?

[storm ridge]

"we"?

[storm ridge]

Idts

[median pelican]

nvm

[flint mist]

certain group of people

[alpine sable]

it is :/

[median pelican]

jk it's not valid

1-1/1 is 2?

oh its a postive

[alpine sable]

wtf 1 is the solution dude

[median pelican]

nvm

[flint mist]

ok im pinging helpers thats it

<@&286206848099549185>

[median pelican]

if you try to prove it

hold on

this is a fucking transcendental

well u need to actually use graphs and analyze the answer

[livid forge]

This is from an exam, which I took today

[flint mist]

does any1 have wolframalpha premium whatever account? https://www.wolframalpha.com/input?i=log2(x%2B1)+-+log2(x)+%3D+3x-2

[alpine sable]

tbh we cant really solve it by doing anyything
its just analytical problem

[median pelican]

indeed

a transcendental equation cannot be solved through "normal" means

[alpine sable]

we cant solve exponential with linear that easily if nothing gets simplified

transcendental equation yup

[flint mist]

its from an exam from a school, 11th grade.

it has a solution

[median pelican]

yeah

[flint mist]

or either exam had a mistake

[median pelican]

u need to use graphs bud

make the equation equals 0

[alpine sable]

can you ask your teacher for its solution ?

[median pelican]

then find the what x makes the RHS equals 0

[livid forge]

I will

[livid forge]

.

[median pelican]

so u have x • 2^2x-3=x-1, then x•2^2x-3-x+1=0

now

u need to find what value of x makes it 0

or find the roots of that equation

you'll find out it's 1

i guess that's one logical solution

@livid forge

do you understood that?

i can explain further

[livid forge]

1Yeah, I got it

[lone heart]

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[alpine sable]

virus ?

[rain finch]

sorry it was uploaded from my phone

the paper says it all, i need to use formulas to make a clock. my teacher is terrible and never taught us this well.

im familiar-ish with Special right triangles, Right traingle trig, trig identities, but i dont know what "Measurement" and parallel line cut by a transversal are

please help me solve this project or understand how to do it

[sleek girder]

you are very much compelled to ask the assignor

[rain finch]

ask my teacher? hell no

he doesnt help

[sleek girder]

complain about the point value, for example: 7 times 12 ain't 80

this needs clarification, or it won't be neat at all

[rain finch]

wdym point value, pls explain

[sleek girder]

the grading part
you get 7 points per formula, and you have to fill in 12
however, you'll only get 80 points maximum, while you should have got 84

[rain finch]

wait i didnt even notice that

your right, that doesnt make any sense

i was less concerned about the grading than the actual problem solving though

[sleek girder]

then you can complain about unclear questions

[rain finch]

? i came on here to get help with my math, because no one else (including my teacher) would help. I dont care about how the grading system is bad, i just want to know how to make special right triangle, measurement, right triangle trig, trig identities, and parallel lines problems and equations to solve for a certain number

[lone heart]

@rain finch Has your question been resolved?

[real gazelle]

I think the assignment is pretty vague, so it gives you a lot of room to do whatever you want

This is what parallel lines cut by a transversal look like

You could maybe do something involving corresponding angles

No idea what your teacher means by "Measurement", you should probably just ask them

[rain finch]

thank you, you explained that better

[lone heart]

@rain finch Has your question been resolved?

[lone heart]

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

f(x) = 2x - 1

f(1-9/16)

[slate vortex]

Find what is 1-9/16

then plug it into f

[zealous tree]

I'm sorry but I don't understand

can you please explain it a bit more

[slate vortex]

Like if I wanted to find $f(1)$, it'd be $f(1)=2(1)-1$.

[ocean seal]

Ari

[hard aspen]

whereever you see a x, replace it with the given x value (1-9/16)

[zealous tree]

i know that part

idk how to finish it

like finish whole problem

[slate vortex]

just compute it?

[ocean hawk]

then you simplify/compute

[zealous tree]

wait I'll try to do it then send it here

and yall can tell me if I did it right ok?

I'd appreciate it

[ocean hawk]

ok

[zealous tree]

is it done right?

[ocean hawk]

7/8 - 1 = ?

[zealous tree]

mb

it's supposed to be negative right

[ocean hawk]

the answer is negative, yeah

[zealous tree]

it's right tho?

did i do it right?

[ocean hawk]

yeah until the end

the second to last line should be 7/8 - 1

[zealous tree]

i don't understand why

oh sorry I actually do

can't believe I made that dumb mistake

[ocean hawk]

no worries

[zealous tree]

I have one more problem if someone could help me too

I'll send

is this correct?

[ocean hawk]

you can't solve it like that

[zealous tree]

how should I solve it?

I'm not really good at maths

[ocean hawk]

there's nothing to solve. you did the first few steps right. the final answer would be f(x - 1) = 2x - 3

[zealous tree]

last time my teacher didn't accept it lile tjat

and I got F

[ocean hawk]

what was the question

[zealous tree]

actually not that one but similar one

I'll have to find it first

I'll be here in five mins when I find it

it's D)

that I did like that and teacher didn't accept

[zealous tree]

@ocean hawk

[ocean hawk]

is that a colon next to 16/3?

[zealous tree]

uhh sorry english is not my first language I don't understand what sre you trying to ask

[ocean hawk]

is that a : next to 16/3, on the second (and later) lines?

[zealous tree]

it's deviding

this

is what : means

[ocean hawk]

hmm, so (16/3) divided by (8 + 1/3)?

[zealous tree]

yeah

photomath said I did that correct but teacher said no

[ocean hawk]

yeah your work looks correct

[zealous tree]

What's wrong with my teacher then

idk what to do

[ocean hawk]

you should ask your teacher why it was marked wrong

[zealous tree]

i did she yelled at me

she's known for that typa stuff

usually over half of class fails that she teaches

[ocean hawk]

sorry, I don't know. it looks right

did she provide a mark scheme?

[zealous tree]

no she just put big X over it

[ocean hawk]

or you could ask someone who got it marked correct?

[zealous tree]

so it means it's incorrect

[zealous tree]

everyone else did that exam like 6 moths ago

I got F so I had to fix it now

if I don't want to fail

[ocean hawk]

well you should have gotten that one right

[zealous tree]

I mean I can go and learn some other math problem so I still get positive grade

but It'll take way too much time

and test is tomorrow

can someone please explain how to do this

[alpine sable]

AUB contains elements of both Set A and Set B

[zealous tree]

thanks

what do other ones do tho

[alpine sable]

The second one is read A intersection B, contains elements that are common to A and B

The third is all the elements of A that do not belong to B

[junior vigil]

so for example ${1,2} \cap {2,3} = {2}$

[ocean seal]

🫎 Chmoosey 🫎

[alpine sable]

The fourth is all the elements of B that are not in A

[zealous tree]

thank yall soo much

I got another question tho if one of you have time

it's same type of question

[alpine sable]

Sure, go ahead

@zealous tree make it quick

[zealous tree]

here it is, had to write it on paper as my book is in different language

[alpine sable]

Cartesian product

A X B is the set that contains the tuples (x, y) where x belongs to A and y belongs to B

A X B = { (1, a), (1, b) , (2,a) , (2,b), (3,a), (3,b)}

So you understand?

[zealous tree]

I'm sorry but not really

[alpine sable]

Each element of A must be paired with each element of B

[zealous tree]

ohh I get it

what about BXA

it should be same right?

[alpine sable]

The reverse

Order matters

[alpine sable]

Look here, 1, 2, 3 come first in each bracket, they belong to A

Because in A X B , A is in the beginning

[zealous tree]

so on B X A it would be { (a, 1), (a, 2)...

right?

[alpine sable]

Yesss!

You got it!

[zealous tree]

thanks I get it now

[alpine sable]

A ^2 would be A X A

Like { (1,1), (1,2), (1,3)....(3,3)}

Got it?

[zealous tree]

oh yes

[alpine sable]

Okay

[zealous tree]

thank you

[alpine sable]

Yeah no worries

[lone heart]

@zealous tree Has your question been resolved?

[zealous tree]

can anyone help me with these two

that are inside line I drawn

<@&286206848099549185>

[lone heart]

@zealous tree Has your question been resolved?

[round stratus]

what is your confusion

[ocean hawk]

you just have to compute them

[lone heart]

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[lusty nimbus]

Hey

[lusty nimbus]

I need help with this question 👇

[forest marsh]

what question ?

[lusty nimbus]

Let's say I choose a Ferris wheel for example

I'm not sure how to set up the question

Let's say it takes 15 minutes to make a full circle

It's like 10 meters high

@forest marsh

[forest marsh]

okay so it's a period of 15min

[forest marsh]

okay but let's say it start from 2meters from the ground

[lusty nimbus]

Ok

Then it's 12 meters in total from the ground to the top

[forest marsh]

ok np

so the middle is 6 meters above the ground do you agree ?

[raw swallow]

You need to make a sin wave with a period of 15 minuted and an amplitude of 10 right?

[lusty nimbus]

alr

Yes I think

[lusty nimbus]

Yes

Why did u put the pi icon?

[forest marsh]

okay so it would looks like this

[lusty nimbus]

Beside the 2?

Alr

[forest marsh]

when you have a periode of 15, for example, you put 2pi / your period to get your expression

in the cos

[lusty nimbus]

Oh ok

[forest marsh]

-4 is the 'a' which represent the distance of the boxes(idk how to say it) from the center of your wheel

[lusty nimbus]

Yeah alr

How would I word that?

Now what about the sin?

I really appreciate u

This is due tomorrow so ty

Also may u label the graph?

Like the t in minutes

And the x axis or whatever

[forest marsh]

yes imma answer question by question to be as clear as possible, So :
The 'boxes' of the Ferris wheel are 4 meters far from the center of the wheel, the distance from the point where you hop in and the ground is 2meters, then the wheel do a full turn in 15min, the distance from the hop in and the go out is represented by a sinusoidal function.

[forest marsh]

x is horizontal and y vertical

[lusty nimbus]

Alr

So that's for cosine?

[forest marsh]

yes and i'm writing for sin now

[lusty nimbus]

Alr ty

@forest marsh u got it?

[forest marsh]

some trouble for the sin

[lusty nimbus]

Oh

U think u can do it tho?

If not I can try asking someone else

[forest marsh]

go for it but i'm sure about the cos one

[lusty nimbus]

Alr

Ty tho

Wait @forest marsh

What's the a,k c and d?

[lusty nimbus]

U got it figured out? @raw swallow

[forest marsh]

it's more written like y = a sin (ωt + ϕ) or asin(b(x−h))+k

[lusty nimbus]

I'm confused

[lusty nimbus]

Sin?

What about the cos?

[forest marsh]

acos(b(x−h))+k

[lusty nimbus]

The given function is
𝑦

−
4
cos
⁡
(
2
𝜋
15
𝑥
)
+
6
y=−4cos(
15
2π
​
x)+6. This function is a cosine function of the form
𝑦

𝑎
cos
⁡
(
𝑘
𝑥
−
𝜙
)
+
𝑑
y=acos(kx−ϕ)+d. Let's identify the parameters
𝑎
a,
𝑘
k,
𝑐
c, and
𝑑
d:

Amplitude (a): The amplitude is the coefficient in front of the cosine function.

𝑎

−
4
a=−4
Frequency (k): The frequency is the coefficient of
𝑥
x inside the cosine function.

𝑘

2
𝜋
15
k=
15
2π
​

Phase Shift (c): The phase shift is given by
𝜙
/
𝑘
ϕ/k. In this function, there is no horizontal shift term (
𝜙
ϕ), so:

𝑐

0
c=0
Vertical Shift (d): The vertical shift is the constant term added to the cosine function.

𝑑

6
d=6
Therefore, for the function
𝑦

−
4
cos
⁡
(
2
𝜋
15
𝑥
)
+
6
y=−4cos(
15
2π
​
x)+6:

𝑎

−
4
a=−4
𝑘

2
𝜋
15
k=
15
2π
​

𝑐

0
c=0
𝑑

6
d=6

Got it

Ai

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[austere charm]

is that what i was suppost to do in that box?

.close

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[marsh bane]

How to do this?

[limpid turret]

Do you know to find $3^{2x}$?

[ocean seal]

SWR

[marsh bane]

no

[limpid turret]

Then it sounds like you need a review on general exponent rules.

Are you familiar with exponent rules?

Like, say, $a^{b+c}=a^b a^c$?

[ocean seal]

SWR

[marsh bane]

oh i see so it will be (3^2x)/3^5

[marsh bane]

nvm $3^{2x} = 4$

[ocean seal]

haridev

[marsh bane]

thanks i got the answer

.closer

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[golden elk]

finding the discontinuities here is trivial--its not continuous where x^2 = 1 + y^2 and when xy <= 0, but theyre in terms of both variables. how do i convert that to intervals

[round stratus]

maybe I'm misremembering, but don't you need an initial value to determine the interval of validity

[golden elk]

i think she wants a list of all the intervals?

[pseudo ice]

(wait, why xy being strictly less than zero?)

[golden elk]

bc ln isnt valid for negatives or 0

right?

[pseudo ice]

There's an absolute value there though, no?

[round stratus]

it doesn't matter, we're taking the log of |xy|

[golden elk]

oh so true

so just xy=0 then

[round stratus]

intervals of validity can depend on starting conditions tho

[golden elk]

true

okay so ill just list the discontinuities and thatll have to be good

thanks

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[elfin iron]

Hello I am back with a few more questions regarding my assignment they are the final ones, can you grade them if they are right or not again rq please and ty.

[lone heart]

Please don't occupy multiple help channels.

[elfin iron]

helloo.

[small lance]

sup

[elfin iron]

could you grade a few more questions again for me

[small lance]

Just post them

[elfin iron]

d

c

c

a

b

d

c

thats it

[round stratus]

only checked up to here, but they're all correct thus far

all of these look correct

[elfin iron]

ty

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[median mulch]

Hey i need help with a matrix problem (im new here)

[alpine sable]

question

what level are matrix problems

[limpid turret]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[median mulch]

classic ig

i dont get how my teacher put -(1-m)^2

[median mulch]

ty!

cuz that wouldnt make sens with the (m-1) and (1-m) ?

[hushed locust]

the -1 came from a row swap and they factored out (1 - m) from two rows

[median mulch]

yes but how did it factored by (1-m)^2 with the (m-1) and the (1-m) ? Did he used the - to only swap one of them ?

[hushed locust]

well he used the fact that m - 1 = -(1 - m)

[median mulch]

indeed that why we dont use the -, but with the - in the (1-m)^2 become a + after ?

[keen plinth]

i hope you realise it says 1 - m^2 not (1 - m)^2

[median mulch]

wit

indeed

why the ()

i didnt saw

just admit it

lmao

sry about that

but that still doesnt explain the sign change?

[median mulch]

so if we have 1 - m^2 how do we end up with (1 - m)^2 ?

[keen plinth]

there are two factors of (1 - m) being taken out

[median mulch]

oh yeah i always forget about that thx !

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[smoky meteor]

Can someone tell me if this is right

[lone heart]

Please don't occupy multiple help channels.

[runic glacier]

No need for step 3, but looks good

[smoky meteor]

can someone guide me through solving this question?

[runic glacier]

Can you send the original question

[smoky meteor]

that is the original question

[runic glacier]

Is the graph supposed to be f(g(x))?

[smoky meteor]

yes

[lone heart]

@smoky meteor Has your question been resolved?

[runic glacier]

The vertex (a,b) of a parabola is given by
(x-a)^2 + b
In this case, that would be:
(x-(-3))^2 + 4 = (x+3)^2 + 4
But notice the parabola is negative, so we multiply the term with the x^2 in it by -1. So we have:
f(g(x)) = -(x+3)^2 + 4

We are told that f(x) = 4 - 2x^2
So we have that
f(g(x)) = 4 - 2(g(x))^2 = -(x+3)^2 +4
Now just solve for g(x)

4 - 2g(x)^2 = -(x+3)^2 +4
Take 4 from both sides
-2g(x)^2 = -(x+3)^2
Divide by -2
g(x)^2 = 1/2 (x+3)^2
Square root both sides
g(x) = sqrt( 1/2 (x+3)^2 )

@smoky meteor Now plug g(x) into f(x) to check it yields -(x+3)^2 +4

[smoky meteor]

thank you!

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[opaque pulsar]

need help specifically with c

in my answer i got a ring in the first bit in the third quadrant but the second bit is an empty set

so it cancels out

[icy sphinx]

Are you getting something like this

[opaque pulsar]

third quadrant so bottom left

but Re(z)>0 isnt that only in the right side half

so it cancels out to become an empty set

[icy sphinx]

For re(z) >0 I guess we should go for the common region

Are we getting a common region?

[opaque pulsar]

i dont think so because isnt Re(z)>0 positive in the x axis or am i wrong

so maybe the ring placement is wrong

[icy sphinx]

Whats your principal argument

[opaque pulsar]

w?

[icy sphinx]

Arg(w)

[opaque pulsar]

-2pi/3

might be wrong but i found w = 8e^-2pi/3i

and w = -4-4sqrt(3)i

the two forms

[icy sphinx]

So it's in the 4th quad and lies bw - pi and pi so ig it's correct

[opaque pulsar]

il definitely double check it but answer this does Re(z)>0 mean in the right half?

not including 0

[icy sphinx]

Nope it just means this part

now just tell me if the arg is - 2pi/3

[opaque pulsar]

how does that drawing represent re(z)>0

[sour verge]

If the original statement is as is, then yes, the intersection is empty. The annulus in the third quadrant doesn't have any point with positive real part.

[icy sphinx]

I still doubt abt the argument

[opaque pulsar]

w definitely is equal to -4-4sqrt(3)i

[icy sphinx]

Otherwise the intersection is null

[opaque pulsar]

yeah i put it into a complex number calculator and my w in both forms is right

so what does that mean for the question tho?

for the ring i let z = a+bi

then the ring is the function of |z-w|

right?

[icy sphinx]

Yes

[opaque pulsar]

when plotting the x axis is a and imaginary axis is b right>

?

[icy sphinx]

Yep

[opaque pulsar]

and the ring centre should be -4,-4sqrt(3)

as that is the w function and the ring is translated there

by those amount

[icy sphinx]

Yes

[opaque pulsar]

and as |z-w| is between 1 and 2 the sketch is circle radius 2 minus circle radius 1

[icy sphinx]

Shift this in 4th quad

[icy sphinx]

Yes

[opaque pulsar]

well it sounds like the ring bit is right but it just seems unlikely that the answer is an empty set

idk

[icy sphinx]

Two are on the opposite side ig we can't get the intersection

[opaque pulsar]

damn

[icy sphinx]

yes

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[restive oriole]

what graph is this and what is the equation of the graph???

[normal bone]

looks like a cubic

probably x^3+2x^2-3x

[restive oriole]

thanks man

someone told me it was a squiggly graph and i was about to smash my computer

[normal bone]

nice

well it is a squiggly graph

[restive oriole]

your not wrong

[hot hatch]

Since the roots are 0,1,-3

x(x-1)(x+3)

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[safe jay]

how do i get started with this question?

how can i get a vector and a f(x,y) from this information

[median oar]

well thing about what that's telling you

the plane they've given you is the tangent plane at the point (1, 5)

so let's pretend we're standing on the function f, at point (1, 5), and we face the origin and ask what's the gradient in this direction?

but actually that's the same as asking for the gradient when you stand on the plane

so you have a plane, at (1, 5), a unit vector in the direction of the origin, how much do you "go up" or "go down" when traversing the plane?

[safe jay]

so my function would be f(x,y)=3y-2x+17

and the vector would be [-1,-5]?

[median oar]

i think when they say direction they mean a unit vector

[safe jay]

well yeah sorry the unitvector for that vector

[median oar]

so you'd need to normalise the vector [-1, -5]

[safe jay]

okay i will work this out

[median oar]

it's good to have a geometric intuition where you can, here it's a surface over the x-y plane which is very visualisable

[safe jay]

yeah I got the answer

i also didnt read correctly seeing the "towards the origin"

but your explanation does help with the conceptualising of this stuff

thanks

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[steep sentinel]

Hi! I have a problem understanding indicator functions in statistics.
Here is an indicator function
1_[0,\theta](x) is equal to 1 if x in [0,\theta] and to 0 if x not in [0,\theta]
How do I transform this function such that it is a function of \theta? Basically I need to put theta as an argument of the function and the x must go into the interval.

[peak bough]

What is the purpose. This seems like a question that can have many different answers depending on it

[steep sentinel]

So this often appears in statistics where I have a distribution that looks like :
f(x) = 1/ theta * 1_0,theta
The goal is to estimate the value theta with a MLE

to me it seems obvious that max(X_1, ..., X_n ) should be a decent estimator of theta , but I am confused, I don't know how to prove it

basically the distribution is a Uniform([0,\theta])

[peak bough]

You could just define the likelihood-function to be\

$f_{x}(\theta) = \mathbb{1}_{[0, \theta]}(x)$

[ocean seal]

Mikkel Angelo

[peak bough]

There isn't a need to transform anything

[lone heart]

@steep sentinel Has your question been resolved?

[steep sentinel]

Sometimes I do need to transform it , for example if I need to check if the statistical model satisfies regularity conditions with respect to theta

let me give you an example.

there is a question where they ask to find the MLE

and you see in the last image the indicator function is with respect to theta

in my course they use it all the time

[peak bough]

That is not a transformation of $\mathbb{1}_{[0, \theta]}$. That is just using the identity\

$\prod_{i = 1}^{n} \mathbb{1}{[0, \theta]}(X{i}) = \mathbb{1}{[X{(n)}, \infty)}(\theta)$

[ocean seal]

Mikkel Angelo

[peak bough]

Or said in words: all X_i being in [0, θ] is the same as θ being bigger than or equal to the maximum of the X_i

[steep sentinel]

I am struggling to understand that, is there a way to prove it by hand?
to me it is still a change of perspective - before we looked at the indicator function as a function of X and now as a function of theta. I understand that this is the same thing, but I am not able to do this switch myself

sorry if the question is dumb

[peak bough]

$\prod_{i = 1}^{n} \mathbb{1}{[0, \theta]}(X{i})$ is 1 if and only if all the indicator functions $\mathbb{1}{[0, \theta]}(X{1}), \hdots, \mathbb{1}{[0, \theta]}(X{n})$ of the product are 1.\

All of them being 1 is true if and only if $0 \leq X_{i} \leq \theta$ for all $X_{i}$. Specially, the maximum $X_{(n)}$ is less than or equal to $\theta$.\

The function that is 1 if and only if $X_{(n)}$ is less than or equal to $\theta$ is the indicator function $\mathbb{1}{[X{(n)}, \infty)}$.

[ocean seal]

Mikkel Angelo

[steep sentinel]

thanks!

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[opaque dock]

how many numbers are there from 51 to 100

[cinder tundra]

Depends, you will have to specify more

[gray jewel]

Do you know the term count formula?

[opaque dock]

no i dont

i know the answer is 50

[jagged cobalt]

what kind of numbers

[opaque dock]

but it confuses me cuz 51 to 100 its like my intuition is telling me 49

[jagged cobalt]

integers?

[opaque dock]

yea

[storm ridge]

They mean whole numbers ig

[opaque dock]

like 1 to 50

theres 50 numbers

but 51 to 100

[jagged cobalt]

its inclusive of 51, i presume

[cinder tundra]

?

[storm ridge]

If you do 100-51, you're actually counting from 52, till 100
That's why you get 49

[cinder tundra]

You will have to give original question

[opaque dock]

i know but it just feels weird

[cinder tundra]

With all the context

[gray jewel]

Maybe the easiest way to think is realise that numbers between [a, b] are same as [a + c, b + c]

So 51,100 is same as 1,50

Subtracting 50 from both bounds*

[opaque dock]

i see this makes sense

[gray jewel]

Which is quite obviously 50

[opaque dock]

but its just something weird like intuition makes me feel like 100-51

[gray jewel]

Yeah same even though it isn't

[opaque dock]

but if u count 51 to 100 u get 50

[cinder tundra]

If the context doesn’t say, the question is ambiguous but

If you want to imagine theyvare included u can think this way

Choose a number between 1 and 2

How many numbers u have to choose? If I dont give all context?

2? Or 2-1?

[gray jewel]

I think Samuel is talking to you

[gray jewel]

If you like memorizing formulas it is: (Last - First) / Increment + 1

And the +1 is explained by Samuel

[lone heart]

@opaque dock Has your question been resolved?

[opaque dock]

this math is like counter math

i just wanna see like 51 to 100 is 50 numbers

its not common in the sense that if u ask non math ppl how many numbers are there from 51 to 100 (inclusive)

there is a chance the majority is gonna answer 49

[cinder tundra]

Irrelevant

If those people answer 49 that means they don’t know what inclusive word means

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[long panther]

How would I know to use radians or degrees in this question

[runic glacier]

It doesn’t matter which one you use unless they specify

[livid sage]

almost always radians

so yes it matters

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[leaden tusk]

I have exactly 30 minutes of time, so id like to practice and learn how exactly to do Linear equations just to be safe

[leaden tusk]

Could someone maybe give me some tasks for practice?

Something along the lines of part 1. Task A), B), C)

[wheat isle]

do u have a better screenshot

[leaden tusk]

Maybe but my gallery is messy rn

[leaden tusk]

Tasks in part 1. A to C. Can someone just ask me questions like those?

And if i get something wrong maybe lil guidance?

Ive asked alot of help before. But i wanna try doing it by myself

?

Im running out of time so ima just ask at the evening after school.

.close

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[raw jetty]

status 1

[lethal belfry]

you can find the minimum value of the denom using AM-GM

[alpine sable]

Use am gm and find the range of product abcdef and then using am gm again on the equuation below find the min value

[raw jetty]

how

[alpine sable]

Do u need solution??

[raw jetty]

kinda

[alpine sable]

It's not alloweded here

I can explain

[raw jetty]

how did you get a+b+c+d+e+f/6>=(abcdef)^1/6

oh

.close thanks

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[autumn mist]

why do we say that a vector that is tangent to the curve of intersection of two 3d surfaces has to be tangent to both surfaces? trying to visualize this but can't come up with a solid explanation

[gray jewel]

Because it's on the surfaces of both shapes?

Maybe think about two spheres intersecting

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[unreal mango]

Hello guys, I have to find a function that looks similar to this. I tried picking 3 points and finding an exponential function but it didn't work.

[modest gyro]

doesn't it look linear?

[unreal mango]

Thought about that one but wouldn't it be too inaccurate?

[modest gyro]

line of best fit?

i think there should be room for error?

wait do you have a desmos

[unreal mango]

I am using GeoGebra.

[pliant estuary]

you can either approximate it as linear or try to do some curve fitting

[unreal mango]

How would curve fitting work?

[modest gyro]

could you send link?

[pliant estuary]

you give fitting function your data and it spits out the best approximation of which method you use

maybe like lest squares wold work nicely, but some others may give better answers

[unreal mango]

https://www.geogebra.org/calculator/j2qdegnj

[lone heart]

@unreal mango Has your question been resolved?

[unreal mango]

That worked well, thank you very much. 🙂

[lone heart]

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[echo socket]

!status

[lone heart]

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

[frozen sentinel]

i got

but idk what to do after that

[sudden burrow]

Take the derivative and set it to zero.

[echo socket]

To get rid of square roots, we could minimize the square of the distance rather than the distance

I.e., minimize x^2 + (x^2 - 1)^2

[frozen sentinel]

hmm

so you don't need the square root?

[echo socket]

Do you know how to find the minimum/maximum value of a quadratic function?

[echo socket]

Not necessarily, no

[frozen sentinel]

yes

but isn't it a quartic function?

@echo socket

[echo socket]

It is not quadratic in x, but it is quadratic in x^2

[frozen sentinel]

so i got x^4 - x^2 + 1

[frozen sentinel]

can you help me on that?

[echo socket]

If you find it difficult, you can denote x^2 with a new variable and find the value of that variable for which x^4 - x^2 + 1 is minimal

[frozen sentinel]

so A=x^2, then A^2 - A + 1 right?

[echo socket]

Yes

Minimize A^2 - A + 1 with A >= 0

[frozen sentinel]

theres no solution?

[echo socket]

There is

[frozen sentinel]

for a^2-a+1=0?

[echo socket]

For a^2 - a + 1 = 0 there is no real solution, but why would you be looking at that equation in the first place?

[frozen sentinel]

so the minimum is (0.5,0.75) ?

[echo socket]

Yes, but we aren't interested in the minimum value, only in the value of A for which that minimum is obtained

Anyway, you have A = 0.5

What does that make x equal to?

[frozen sentinel]

sqrt(1/2)?

[echo socket]

Yeah

There is another value of x though

[frozen sentinel]

wait what

[lone heart]

@frozen sentinel Has your question been resolved?

[echo socket]

There are two values of x satisfying x^2 = 1/2

[lone heart]

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[shy dove]

What contour and complex function should I use for $\int_{0}^{\infty}\frac{\ln^2(x)}{1+x^2}\dd x$? I tried having f(z) the same as f(x), and a quarter donut looking contour but I couldn‘t get it to work nicely

[ocean seal]

ℑμΤ𝛄𝛗θ

[cinder compass]

mabe x = tan(theta)

[shy dove]

I want to solve it using contour integration (:

[lone heart]

@shy dove Has your question been resolved?

[shy dove]

<@&286206848099549185>

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@shy dove Has your question been resolved?

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[lean portal]

hello

[lone heart]

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[lean portal]

I have a question on recurrence relations. Am i in the right place?

[modern sedge]

Yes ig

[lean portal]

So im asked for the best asymptotic time bound. I've tried generalising this after subbing the formula into itself a few times, and found that

T(n) = T(1/(2^(2^k))+k

Now, i tried doing:

let n^(1/(2k)) = 1

But I'm struggling to rearrange for k

Even after attempting that, I was told that this step doesn't work

So tbh i'm a bit lost and not sure how to continie

[modern sedge]

hmm maybe let n = 2^2^k

[polar prism]

u mean 2^(2^k )?

right?

[modern sedge]

yeah, i think that's the standard grouping

[polar prism]

same ye

good idea

[modern sedge]

then T(2^2^k) = T(2^2^(k-1)) + 1 if im not mistaken

[polar prism]

ye

[modern sedge]

uh

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[atomic sky]

Ye three's still work to be done

Don't believe that's solving it for him

[modern sedge]

what's strange is the assumption T(1) = 1

[atomic sky]

I mean in algorithms that's what we often use, make it 0 if you will

[modern sedge]

From mathematical perspective, it looks weird because T(1) = T(1) + 1 by the condition, but idk the context behind all that

[atomic sky]

Seems like am algorithm question, you need an initial value

Usually the formula is for n>= initial 0 or 1 with T(initial)=1

Doesn't change it much either

[lean portal]

Whoops

It wouldve helped if i shared the start of the thingy too

one moment please

[lean portal]

Sorry my friend

I will reattempt the question

[atomic sky]

Doesn't change what I did much dw

[lean portal]

So the answer they were looking for was O(log log n)

[lean portal]

Right

[atomic sky]

Yep

[lean portal]

Let me share this:

I will try to "get" what they did, through the working out like you did

There's like ten of these questions, so this should be fun

[atomic sky]

You should see a master theorem coming after what I did

[lean portal]

Should i attempt this question using that?

*reattempt

[atomic sky]

Yes, and what I just gave you

The idea is to get a form with T on one side and then using the theorem

[lean portal]

Ok I'll try both ways

Direct (substitution) method and Master Theorem

Hmm

I will there was a VC here

wish*

so much typing rn ------

so basically

note: _2 means base 2

i got to:

log_2 (logn / log2) = k

So you know how we have some log(n) divided by some constant

can we just discard that [because the log of some n divided by some constant will still be log of some n] and say, okay,

Its O(log log(n))

Could i ask another question

Or is it limited to 1

[lone heart]

@lean portal Has your question been resolved?

[lone heart]

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[old yew]

how do I show this is not prime without having to chuck in numbers

i actually find it really interesting that this generates primes for so many numbers though

[empty moth]

what

(n+1)^2 -n^2 = 2n+1

[old yew]

like what i did was uh 3b^2 + 3b + 1

[empty moth]

ohw ait

it's ^3

[old yew]

ye

[empty moth]

(n+1)^3 - n^3

[old yew]

yes

but i cant relaly break that up

(doesnt have any real roots)

[empty moth]

lmao

it's a polynomial

there is a trivial way to find prime outputs

[old yew]

hmm

[empty moth]

3n^2 + 3n + 1

[old yew]

do you just plug in numbers for n till you find a composite number?

[empty moth]

let me walk you through it @old yew

[old yew]

kk

[empty moth]

find f(n) for some arbitary n

f(n) = 3n^2 + 3n + 1

[old yew]

ye

[empty moth]

let's say f(1)

compute f(1)

don't be lazy here

[old yew]

7

[empty moth]

now compute f(f(1) + 1)