help-33

[queen sun]

If you wrote it back to equations you’ll see how it works

[fervent rampart]

gauss-jordan requires about 50% more operations for large matrices

and is also numerically unstable

[queen sun]

What does that mean? Edit: I can search things up

[fervent rampart]

so it's good for hand calculations (which use small matrices and precise fractions) but not suitable for computer algorithms

[queen sun]

Floats be like: $0.1+0.2\ne0.3$

[elfin berry]

BBMaths

[queen sun]

Start from the bottom row and work backwards (it’s in the name “back substitution”)

Like z=-1 then put that in the next row up and get y

[elfin badger]

z doesnt equal that

[fervent rampart]

the equation at the bottom is just z = -1

so how could z not equal -1

[elfin badger]

i was looking at the one above it

the green one

[fervent rampart]

you do the back substitution process on the yellow one (since it's in REF)

[elfin badger]

.

[queen sun]

-32z=32

[fervent rampart]

you could do it on the second to last one as well but then you get -32z = 32 which can still be solved for z

[queen sun]

So z=-1

[elfin badger]

oh

so for y=

[fervent rampart]

to find y, you go to the next equation above, which is y + 3z = -1, and plug in the value of z you got previously

[queen sun]

The green one is 2y+6z=-2 which will give the same answer it doesn’t matter which you choose, you could even switch back and forth between the different matrices here!

[elfin badger]

oh ok

[queen sun]

Only because they relate by row operations

Since row operations are about keeping the same x, y and z solutions but changing the system of linear equations

[elfin badger]

.close

[marsh citrus]

Channel closed

Closed by @elfin badger

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[devout charm]

Hi guys does this look correct? This is for conic sections and I use the matrice function on my calculator for it

[queen isle]

Did you already verify by hand? As in plug your x and y values in and find that the equation holds?

[devout charm]

let’s just say…. No

[queen isle]

Do that. It's the best way to do so because you can do this without using some fancy technique. Just put it in your calc and see.

[devout charm]

Hmm much more simple thank u

It was wrong btw gulp

Thanks so much!!

[queen isle]

yes it was

[devout charm]

Do u have any idea how I might’ve done the matrices wrong?

[queen isle]

If I'm not mistaken the first column is the given x, the second column is the given y, and what is the third column for?

[devout charm]

I’m not all too sure, when my teacher taught it she Included the column but it always was the same number in the examples

[queen isle]

That's a problem if this test question is calc required.

[devout charm]

Gulp

[queen isle]

Alson in your written solution A and C seems to have disappeared.

81-36

How did you get the fourth column?

[devout charm]

It’s a^2 + b^2

[queen isle]

Beyond the verifying by hand I am of no help here since I never used a calculator for this purpose. Sorry. You should call for other helpers.

[devout charm]

Ah, I understand. Thank you for the help regardless

[queen isle]

Btw it's not 81-36

(-6)^2 =36

[devout charm]

Oh my god 😭

[queen isle]

same for the 81-16

Your mistake is likely that

[devout charm]

Should’ve learned my algebra rules probably

Went straight to calculus instead

AH THAT WAS UT

THANK YOU WAHAHAHAHA

[queen isle]

Make sure though.

[devout charm]

Yes! Will verify

.close

[marsh citrus]

Channel closed

Closed by @devout charm

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[quaint arrow]

i need help on b. i used a hessian calcualtor online and i can easily see that not all of the entires of the hessian will be positive

[marsh citrus]

@quaint arrow Has your question been resolved?

[quaint arrow]

<@&286206848099549185>

[marsh citrus]

@quaint arrow Has your question been resolved?

[quaint arrow]

<@&286206848099549185>

thank you for the response. this makes sense to me, but the directions say to use the second-order definition of convexity

thank you so much for the response. I understand most of it. But i think i am slightly confused on differentiating matrices. Specifically, how did you go from 2·a(s)·w -> 2·a(s)·I + 4·a'(s)·w wᵀ?

im sorry, i'm having a bit of trouble doing product rule. did i set u v improperly?

[quaint arrow]

@chilly valley thank you so much for your help

you really helped! Have a good day mate

.close

[marsh citrus]

Channel closed

Closed by @quaint arrow

Use .reopen if this was a mistake.

[past thicket]

dear god I really hope chatgpt was correct.

@quaint arrow this guy was caught using an LLM on nearly all the questions he answered. I hope you’re able to able to double check every thing you got from him…

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hard laurel]

If a sequence is bounded and it is converges to A then every subsequence of this sequence will Converse to A

[hard laurel]

I guess it is true

[stoic saddle]

where is question

[wary kite]

i mean why do we need it being bounded

[hard laurel]

Actually i am reading some notes

So doubt arises in mind🙈

We need to be bound otherwise we can't say anything

[wary kite]

no?

[hard laurel]

(-1)^n

[wary kite]

that doesn’t converge

it’s just redundant

[hard laurel]

ohh wrong example

Hmm

[wary kite]

no need to mention it

[stoic saddle]

you are reading notes and you are only certain enough to say "i guess it is true" about something that you yourself wrote in your own notes written by your own hand?

[hard laurel]

n^2

[wary kite]

that’s not bounded and diverges

if it converges then it’s bounded

[hard laurel]

I didn't write these notes. I am reading coaching notes

[wary kite]

no need to mention it being bounded

[hard laurel]

Let me show you hang on

7 point

[wary kite]

this is not what you said before

[hard laurel]

They also mentioned bounded?

[wary kite]

saying "and it converges"

is not the same here

[hard laurel]

Ohh my bad sorry

Iff?

[wary kite]

saying it’s a bounded sequence is a preliminary assumption

also what is cps

are you trying to prove 7 btw?

[hard laurel]

Yeah

[hard laurel]

I am asking about it only

[wary kite]

have you tried either direction?

one direction is very trivial

[hard laurel]

Wdym?

[wary kite]

proving either direction

[hard laurel]

I don't need to prove just need to understand

[wary kite]

same thing

perhaps you don’t understand subsequences?

[hard laurel]

subsequences is part of sequence

so sequence is converges to L then all points are travelling to that limit slowly

[wary kite]

why slowly?

[hard laurel]

Subsequences will also travel in that direction

[wary kite]

what do you mean by slowly

[hard laurel]

nothing specific

Slowly fast

[wary kite]

🤔

[hard laurel]

I mean points which is very close to that limit can be Faster

[wary kite]

closer = faster?

i’m not sure i follow sir

[hard laurel]

Nevermind my words

[wary kite]

think back to the definition of convergence. it requires that regardless of the distance from the limiting value, beyond a certain point eventually all of the sequence members will be within that distance from the limiting value. now since any subsequence you choose "extends" into this tail part of the sequence where all of the sequence members are hanging around the limiting value, we can just as easily say this subsequence also converges to the limiting value because it’s also in those neighborhoods

does this make sense?

[hard laurel]

yeah makes sense but please write more in simple English

[wary kite]

i didn’t use big words

[hard laurel]

If I have a bounded sequence

I can't say it is convergent

(-1)^n

we have two limit points

[wary kite]

ok sure what’s your point?

notice that we can find two subsequences that don’t converge to the same value

[hard laurel]

So for convergent we need unique limit?

[wary kite]

take one subsequence to consist of the even terms and one to be of the odd terms

[hard laurel]

If the sequence is convergent then what can we say about convergence of subsequences

This is my doubt

I mean each and every subsequence is converging so they will Converse to the same limit am I right

[wary kite]

they don’t lie in the same neighborhoods but together they form the entire sequence and since they don’t hang out in the same neighborhoods the entire sequence certainly doesn’t converge because it needs all of its homies in one place

[wary kite]

they all converge to the same value that the entire sequence converges to

[hard laurel]

I am asking in rerverse

My doubt is about subsequences

1/n...it converse to 0

if I take finite subsequnces

1,1/2,1/3

is this converging to 0?

I'm sorry my doubt is messy and not clear

Maybe i am mixing lots of unfruitful things

[wary kite]

subsequences are not finite lists

[hard laurel]

I see. They need to be infinite?

[wary kite]

they are sequences within the sequence

[hard laurel]

Great!!

[wary kite]

yes. it doesn’t make any sense to talk about convergence for finite lists of numbers

[hard laurel]

Hmm

Thanks

I got it

.close

[marsh citrus]

Channel closed

Closed by @hard laurel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hearty dust]

is the ans to both just that f(x) and g(x) that they are continuous for which those statements hold

that seems too short of an ans

[marsh citrus]

@hearty dust Has your question been resolved?

[cunning fiber]

Yeah

[hearty dust]

am i missing smth to my ans?

[cunning fiber]

Nothing I can think of

That’s the main thing

[hearty dust]

great tysm

.close

[marsh citrus]

Channel closed

Closed by @hearty dust

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[near elbow]

guys, i dont understand f and h

[near elbow]

for f, isnt Central Limit Theorem only applied when n is large and when distribution is unknown?

and for h, why is it false?

[marsh citrus]

@near elbow Has your question been resolved?

[hearty dust]

i dont think f and h are even related to central limit theorem

those equations are related to the distribution of a sample population

another helper can mistake me if im wrong

[near elbow]

oooo

alrightt thankyouuu

[hearty dust]

ye no worries

[marsh citrus]

@near elbow Has your question been resolved?

[hearty dust]

bro wut 😭

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[still temple]

Find domain

Shud i convert x to given, or given to x?

[proud basin]

what?

[patent sandal]

whats the domain of cos-1 y

[still temple]

[-1 ,1]

[patent sandal]

so then what is the interval in which |x-1| lies

[still temple]

Uhh

How do i do

[patent sandal]

think about it

[still temple]

2 less than or equal to x and x less than or equal to 0?

[patent sandal]

yeah pretty much

[still temple]

Shud i switch signs if i apply mod?

[still temple]

But its the opposite

[patent sandal]

yep

[still temple]

Ans is given opposite to what i got

How?

[patent sandal]

whats the answer

[still temple]

[0,2]

[patent sandal]

its just what you said

i mean thats just the proper way of writing it

cus if you say 2<=x<=0 that means 2<=0

which isnt true

so you write 0<=x<=2

[still temple]

Oh

2cos inverse of 2x + sin inverse of x

How to find for this?

[patent sandal]

try it for yourself once

[still temple]

Btw

Will 2 in front of cos inverse of 2x affect domain?

[patent sandal]

yes

[still temple]

Oh

Ok ill try

[patent sandal]

oh sorry

if you meant the 2 in 2x

then it will affect the domain

the 2 of 2cos-1 2x doesnt

[still temple]

So coeff has no effect?

Ok

[-1/2,1/2]

[patent sandal]

correct

[still temple]

,rccw

[still temple]

In this

I get [-1,0]

But ans is [-1,1]

How so

[patent sandal]

because its x^2

if x is negative then (-x)^2 = x^2

so its symmetric

(-1)^2 = (1)^2 = 1

(-1/2)^2 = (1/2)^2 = 0.25

[still temple]

No

But here it is given as

-x², not (-x)² right?

[patent sandal]

alright

even so

-x^2 = - (-x)^2

so - (1/2)^2 = - (-1/2)^2 = -0.25

-(1)^2 = - (-1)^2 = -1

basically we have that -1 < -x^2 < 1

[still temple]

Wait wait

[still temple]

I dont understand this

[patent sandal]

oh the minus sign became a bullet

[still temple]

Oh

[still temple]

Ye

[patent sandal]

so -1 < -x^2 < -1 then -1 < x^2 < 1 then -1 < x < 1

i skipped a step, should i elaborate that?

[still temple]

But for +x², doesnt -1 become 0 since x² always greater than or equal to 0

[patent sandal]

yeah so we have 0<x^2<1 we dont even need to care about the -1 part

since 0<x^2<1

x must be between -1 and 1

[still temple]

Oh

If the question is given as x²

Is it [0,1]¿

The hell is this?

.close

[marsh citrus]

Channel closed

Closed by @sudden musk

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[near elbow]

guys i dont get the question of 1b

[near elbow]

this is 1a

[spark otter]

what's the probability that the confidence interval doesn't contain the actual population mean, and in fact the population mean is bigger?

so P(mean > 13.0)

[marsh citrus]

@near elbow Has your question been resolved?

[near elbow]

ohhhh

thats 0.005

i was thinking of 0.01 but since it should be bigger than 13.0 then it is 1/2 of 0.01

[near elbow]

but how do you know that the population is bigger?

[marsh citrus]

@near elbow Has your question been resolved?

[tough sapphire]

"...confidence interval will be below the population mean."

[near elbow]

ohhh

okkk i get it

[near elbow]

thankuu sm

[near elbow]

thankyouuu sm

.close

[marsh citrus]

Channel closed

Closed by @near elbow

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[compact crescent]

.close

[marsh citrus]

Channel closed

Closed by @compact crescent

Use .reopen if this was a mistake.

[stoic saddle]

step 0 is to take off that literal fucking HITLER PFP. <@&268886789983436800>

[weak surge]

my man what is that pfp 💀

[oak oxide]

ig he just got rejected from art school

[ruby mulch]

But why the question is also closed?

[stoic saddle]

op closed it irrespective of the hitler-wannabe that showed up.

[ruby mulch]

Hell, even a blank pfp is better than that pfp

[calm harbor]

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[rich isle]

if i(n,a) =(1-2x)^(a-1)(x-x^2)^(n+1)/(n+1)+2(a-1)i(n+1,a-2)/(n+1) where i(n,a)=\int (x-x²)^n (1-2x)^a dx find i(14,28)

[rich isle]

i used various sources and got it as-

$\frac{(28!)^{2}}{57!}$

[elfin berry]

.

[stoic saddle]

can you send a picture or write what this i(n,a) thing is in proper LaTeX please

[rich isle]

if $$I(n,a) =\frac{(1-2x)^{a-1} (x-x^{2})^{n+1}}{n+1}+\frac{2(a-1) I(n+1,a-2)}{n+1}$$ where $$I(n,a) = \int_{0}^{1} (x-x^{2})^{n} (1-2x)^{a} dx$$ find $I(14,28)$

[elfin berry]

.

[rich isle]

HERE

[stoic saddle]

aight wait

you give two different defns for I(n,a)

one of which is a function of x and another which isnt

inconsistent much?

[rich isle]

the second one was given

i derived the 1st one

easy

???

[stoic saddle]

show your derivation

[rich isle]

i first did it for my actual expression, for 1-2x whole to the power 28, hence got 54 in that 2nd term involving i(n)

[rich isle]

but otherwise, generally, the 1st expression is the recurrence relation needed here

[marsh citrus]

@rich isle Has your question been resolved?

[marsh citrus]

@rich isle Has your question been resolved?

[marsh citrus]

@rich isle Has your question been resolved?

[rich isle]

<@&286206848099549185>

@stoic saddle

[earnest canopy]

Can you send the question again?

[rich isle]

.

[past thicket]

check pinned meessages

[twin pike]

have you tried substitution

like

taking x-x^2 as some variable z

the expression becomes [(z)(1-4z)]^14

smthing like that mybe

[rich isle]

no

[rich isle]

<@&286206848099549185>

[rich isle]

ask sm1 to pin the LaTeX one

the present one is messy

[brave knoll]

Notice that d(x-x²) = (1-2x)dx and that here 2n = a

[rich isle]

<@&286206848099549185>

[brave knoll]

You may find errors but it really is the idea

[rich isle]

illse sire

well i am a pre-uni fella so maybe i cant understand all of it but still

[brave knoll]

there is a small sign error in the IBP but the computation remains coherent

[rich isle]

[rich isle]

<@&286206848099549185>

[hollow urchin]

I would write $(x-x^{2})^{n}$ as $x^{n}(1-x)^{n}$ and then do ibp

[elfin berry]

డ్ర్యాగ్లొక్స్

[solar elbow]

can anyone solve these

[cunning fiber]

!occupied

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[brave knoll]

A way to solve I(14,28) is to expand the terms raised to the power 14 / 28
It demands a lot of computation (using Newton Binomial formula) but it gives the solution

[stone shale]

help please

[worldly crag]

maybe draw it out on a paper so u can visualise better

and id say also write out the formulas for area and pythagorean theorem on an equation

[heady forge]

<@&268886789983436800>

[stone shale]

PELASE HELP!!EEEE

[simple crane]

its there?

the question stated what to do.

[marsh citrus]

@rich isle Has your question been resolved?

[cunning fiber]

!occupied

[marsh citrus]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[true notch]

i give up on this can someone pls explain the entire thing like how did your brain work through finding patterns to figure this out

[true notch]

like i was thinking after the 3rd term, we can see that it becomes 2^1, then 2^2, then 2^3

and we also notice that the difference between the terms after the 2nd and 3rd also go up by 2^1, 2^2

for example, 5-3=2, 9-5=4, 17-9=8 and so on

so what i came down to was (2^(n-4)) / (2^(n-2)) but obviously this doesnt work for the 2nd term

then i looked at them seperately and still couldnt figure it out

so i give up and require help

https://tenor.com/view/british-cop-screaming-screaming-sad-gif-1879411192175791821

[iron marlin]

Yeah you already guessed a formula right, try getting it right for everything from the 2nd term onwards

[fringe nacelle]

just use OEIS

on the numerators and denominators

<@&268886789983436800>

[true notch]

what is OEIS?

[iron marlin]

Though you could argue the formula is
n=1...6: these 6 terms
n=7...: always 19

[fringe nacelle]

https://oeis.org/

the answer is not unique, so, any answer will do

this isnt a math problem

[true notch]

im ngl to you idk what this means 😭

[fringe nacelle]

it means the following is a valid answer:

[iron marlin]

It's just saying the first 6 terms are as given and any further terms are 19

[fringe nacelle]

1/4, 1/3, 2/5, 4/9, 8/17, 16/33, 19, 19, 19, 19, 19, 19, 19, ..., 19, ...

[slim shard]

one pattern i noticed for every term other than the first and second:
the sum of the denominator of the previous term and the numerator of the current term is the denominator of the current term

[true notch]

ohhh

[iron marlin]

which is a valid continuation of a sequence, just probably not what the person who set the question had in mind

unless that person is me

[iron marlin]

But try this, carefully

the first term might be a bit problematic for now

[iron marlin]

like these differences - can you modify the numerator and denominator of your fraction to match the sequence, from the second term onwards?

[true notch]

idk

i mean i couldnt figure out a way to modify it so that it would fit

the entire series

it always breaks on the second term

[iron marlin]

Fit second term onwards first

Ignore the first term for a bit

[true notch]

ok

let me try with that in mind

[wary kite]

consider multiplying each of the fractions for n >= 2 by 2/2

pattern should be clear

$\frac{1}{4}, \frac{2}{6}, \frac{4}{10}, \frac{8}{18}, \frac{16}{34}, \frac{32}{66}, \dots$

[elfin berry]

knief

[haughty zephyr]

1/4, 2/6, 4/10, 8/18, 16/34, 32/66, ...
Numerator: 2^(n-1)
Denominator:
6 - 4 = 2 = 2¹
10 - 6 = 4 = 2²
18 - 10 = 8 = 2³
34 - 18 = 16 = 2⁴
66 - 34 = 32 = 2⁵
...
T(n) = 4 + (2¹ + 2² + ... + 2^(n-1))
T(n) = 4 + 2(2^(n-1) - 1)/(2 - 1)
T(n) = 4 + 2^n - 2
T(n) = 2^n + 2

Thus f(n) = 2^(n-1) / (2^n + 2)

[true notch]

ty

so it just comes down to figuring out if its possible to unsimplify the numbers

then going for patterns from there?

[true notch]

ima try this tw

ty*

[wary kite]

yea the idea was that we have a nice sequence of powers of 2 from the second term onwards but the first term breaks that so we multiply by 2 to all of the fractions from the second term onwards

[haughty zephyr]

np

[true notch]

.close

[marsh citrus]

Channel closed

Closed by @true notch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[opaque sleet]

im so stuck after this part

[wary kite]

what about it?

split the fraction

do you know how to integrate 1/2 and 1/2 cos(2x)?

[opaque sleet]

so

its

1/2 times 1/2 and then + 1/2 times cos2(theta)

[winged delta]

yes

[wary kite]

no

[opaque sleet]

what

i got the 1/2 from the 1+ cos2theta / 2

[winged delta]

$\int (f + g) = \int f + \int g$

[elfin berry]

Médicis

[wary kite]

yea but you have an additional 1/2 on the 1/2 which presumably comes from the factor outside the integral

if you want to distribute it inside the integral then it also needs to be multiplied by the 1/2 cos(2x)

[opaque sleet]

lets do it step by step my brain is not getting it

[wary kite]

$\frac{1}{2} \int \frac{1}{2} + \frac{1}{2} \cos 2\theta \dd{\theta} = \int \frac{1}{4} + \frac{1}{4} \cos 2\theta \dd{\theta}$

[elfin berry]

knief

[wary kite]

what is written here is wrong

[opaque sleet]

so u got that first 1/2 because it was already from 1/2 cos^2 theta d theta

then after the integral

the 1/2 is the 1+ cos2theta / 2

[wary kite]

what is unclear?

[opaque sleet]

\

the 1/2s

[wary kite]

what about them

[opaque sleet]

i understand the 1/2 before the integral

[wary kite]

that comes from splitting the fraction

$\frac{1 + \cos 2\theta}{2} = \frac{1}{2} + \frac{\cos 2\theta}{2}$

[elfin berry]

knief

[opaque sleet]

okay i understand

the splitting fraction part

now we integrate

[wary kite]

yes

[opaque sleet]

so i want the first 1/2 to go out

making the 1/2 outside 1/4

[wary kite]

sure

[opaque sleet]

but theres an extra theta idk where that came from

[wary kite]

$\frac{1}{4} \int 1 + \cos 2\theta \dd{\theta}$

[elfin berry]

knief

[opaque sleet]

wait whered u get the 1

[wary kite]

🤔

didn't you just say you wanted to pull the 1/2 out

as a factor

[opaque sleet]

well yeah

wouldnt it be

1/ 2 times 1/2

[wary kite]

$\frac{1}{2} \int \frac{1}{2} + \frac{1}{2} \cos 2 \theta \dd{\theta} = \frac{1}{2} \int \frac{1}{2}(1 + \cos 2\theta}) \dd{\theta}$

[elfin berry]

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

[wary kite]

its 1/2 times everything inside the integrand

[opaque sleet]

is this right so far

[wary kite]

i mean yea

[opaque sleet]

okay i see now u bascially factored out the 1/2?

so now

u kick out that 1/2

and then whats left inside is the

1 + cos2theta

now we integrate

step by step

1 is just theta

and multiply by 1/4 so thats how u got 1/4 theta

so now we have cos2theta

which is sin^2 / 2 times 1/4

[wary kite]

what

[opaque sleet]

wops

i forgot what the integral cos^2 theta is

[wary kite]

its not cos^2

its cos(2theta)

[opaque sleet]

oh crap right

so i kick out the 2 there from cos2theta

that makes my 1/4 into a 1/8

i have it written down as

1/4 times cos2theta

i get it wrong sometimes and do 2/8 instead of 1/8

how do i avoid that

[wary kite]

take the factor of 1/4 then divide by 2 for reverse chain rule on cos(2theta)

cos turns into sin

because sin differentiates to cos

[opaque sleet]

oh timeout

this part

didnt we kick out 2 on the sin

to make our 1/4 to 1/8

[wary kite]

by kick out do you mean divide by 2 because of the 2theta

[opaque sleet]

would this be written as

1/ 4 times sin 2theta / 2 + c

[wary kite]

what

why not make it 1/8

[opaque sleet]

yeah but before it becomes a 1/8

i mean

[opaque sleet]

im just going stepbystep to make sure im doing it right

[wary kite]

i mean if it helps you then sure

[opaque sleet]

so

this part here

[wary kite]

what about it

[opaque sleet]

i mean this whole part here

we got the one on the left side fine

[wary kite]

sin(2x) = 2sinxcosx

[opaque sleet]

whats this called again

[wary kite]

double angle identity

[opaque sleet]

ok great

this part is the part where u go back to x is what i understand

i think i got it from here

thank you

.close

[marsh citrus]

Channel closed

Closed by @opaque sleet

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[umbral moon]

help?

[umbral moon]

its not 92.9697

or 93.0093

[fervent rampart]

caan you show how you got your answer?

[umbral moon]

i didn't

[nimble prairie]

what have u tried?

or, what do u need help with?

[wary kite]

was it gpt?

[nimble prairie]

Notice that u have a geometric series

[umbral moon]

https://tenor.com/view/shh-cats-gif-14317670277085954258

[umbral moon]

yes

[nimble prairie]

Do u know how to compute a convergent geometric series?

[umbral moon]

i don't have my notes with me i forgot at friends house so it's hard to do the hw rn, like for me to do, ykwim

[wary kite]

search up sum of infinite geometric series

you'll find some videos

[umbral moon]

!close

.close

[marsh citrus]

Channel closed

Closed by @umbral moon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lusty island]

i did some rough work

just to visualize

the question a little bit

but dont know how to even begin proving here

[ruby mulch]

Tips: there should be a neat bijection by marking "1" as the "start of the number"

[marsh citrus]

@lusty island Has your question been resolved?

[lusty island]

hm

is this for if the compisition starts with 1 or 2?

[ruby mulch]

You first prepend the composition with "1"

[lusty island]

ok...

[ruby mulch]

Note that:

1 = 1
3 = 1 + 2
5 = 1 + 2 + 2
7 = 1 + 2 + 2 + 2
...

[lusty island]

right

[lusty island]

i think i need a little more elaboration

[ruby mulch]

For example, for n = 5, the possible compositions are:
5, 3 + 1 + 1, 1 + 3 + 1, 1 + 1 + 3, 1 + 1 + 1 + 1 + 1 = 5
Rewrite it in the above rule results in:
1 + 2 + 2, 1 + 2 + 1 + 1, 1 + 1 + 2 + 1, 1 + 1 + 1 + 2, 1 + 1 + 1 + 1 + 1 = 5
Now, if you drop the leading one, you get:
2 + 2, 2 + 1 + 1, 1 + 2 + 1, 1 + 1 + 2, 1 + 1 + 1 + 1 = 4

Sounds familiar?

[lusty island]

oh if you drop the leading one it gives you the composition for the previous one?

[ruby mulch]

Yes

[lusty island]

i think i get it

let me write some stuff and send a solution

[lusty island]

@ruby mulch

ignore the visuals

thats for me

to understand lol

thanks for the help

i dont know how you guys come up with proofs so well

.close

[marsh citrus]

Channel closed

Closed by @lusty island

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[clear crane]

i ran through this problem and dont know what to do

[clear crane]

Find the absolute extrema of the function on the closed interval.

[agile karma]

What have you tried?

[clear crane]

i tried solve for the derivate of that problem

set it = to 0

and put x = -3 , x = 6 for the derivate

[agile karma]

Did u try using the x value from when u set the derivative to 0?

[clear crane]

yea

this is my work

[gusty flame]

It's x=0 and x=1

[clear crane]

oh i forgot x= 1

yea my bad

js saw that too

[agile karma]

your maximum looks right

[gusty flame]

Happens

[agile karma]

well- the x value is right

make sure u remember to plug your x value into the original function, not the derivative

[clear crane]

oh

[agile karma]

Do u know why?

and your minimum x value is wrong

[clear crane]

nope...

i try to put it to canvas

idk what graph to look for

[agile karma]

Okay

Do u know what the derivative means in context of the original function?

[clear crane]

hmm just one degree less?

[agile karma]

Not quite

[clear crane]

i actually dont know what is the derivate, i just apply the formula lol

[agile karma]

Okay

[clear crane]

or sometime they ask to find a slope

[agile karma]

You're getting warmer

[clear crane]

i do the derivate, put given x into the derivate to find slope

and do y-y1 = m(x-x1)

[agile karma]

Okay

so, if, for example

i have a function f

and i evaluate the derivative of that function at, say, x=3

i get..?

[clear crane]

f'(3)

you get slope??

[agile karma]

exactly

you get the slope of the curve at that point

give me one second...

[clear crane]

okk....

[agile karma]

say the blue graph is my function

and the red line is a tangent to the function at x=3

then the derivative of f at 3, f'(3), will give me the gradient of that tangent

So what do you think happens when I take the derivative of a function, and set it equal to 0?

[clear crane]

you will get the minimum

or it will give you a x value

[agile karma]

It will give me an x value, yes

but what does that tell me about the original function at those points?

[clear crane]

oh ...... a tangent line pass through the point

[agile karma]

Not quite

The derivative always tells me the gradient of the tangent for a graph

so if my derivative is 0, then the gradient of my tangent is..?

[clear crane]

would probably to 0 as well

or would it be constant

[agile karma]

it would be 0, yes

which would mean it's a straight line

so if we look at this function, the derivative should be equal to 0 where?

try imagine the tangent at different points

[clear crane]

i think that is where slope = 0

[agile karma]

exactly

[clear crane]

its a constant line

[agile karma]

exactly

so, for any function f, setting the derivative to 0 and solving for x will give me the x-values for..?

[clear crane]

oh

minimum and maximum

[agile karma]

yes, (and stationary points of inflection, but we dont need to worry about that here)

So if we go back to your original function

[clear crane]

wait....

is this correct

[agile karma]

$f(x) = x^3 - \frac{3}{2} x^2$

[elfin berry]

Hyper

[agile karma]

absolute minimum and relative minimum are correct

are you sure that's the absolute maximum though?

[clear crane]

yea i would say unsure as well

because the graph goes infinity

i think that is relatve max

[agile karma]

yes

[clear crane]

i was gonna ask you about that question but idk how to say

[agile karma]

let's pretend that's the whole graph

[clear crane]

so abs max = DNE

[agile karma]

if the graph was defined for all x, yes

so if we go back to your original function- how would you approach finding the absolute minimum and maximum?

(remember the closed interval)

[clear crane]

i just plugged in x to the original function

because that is where the line touch the lowest close interval

and would do the same thing to find max

hmm for this problem is it true that i wasted time doing the derivate, i just plugged in x = - 3, x=6 i have my min and max already

[agile karma]

For this specific one- yes

But that might not hold true for every function

[clear crane]

yea

usually odd function right

[agile karma]

it's useful to know how to find minimums and maximums with the derivative

[clear crane]

ok i have a similar problem

let me try to do it

[agile karma]

Go for it

[clear crane]

the problem with this is that , i got the minimum wrong

i try to set the problem = 0

hmm i think i forgot the set the orinigal equation x = 0

[agile karma]

Nah, you wouldnt set the original equation to 0

There's an error in your working when u set the derivative to 0

2/(3sqrt(x)) cubed isn't x/8 * 8/x

instead of cubing, try squaring

[clear crane]

like ()^2 ?

[agile karma]

yes

[clear crane]

....

ok here

oh oh then i just multiple both side with denominator

i found x =0

now plug it in to find the minimum value

[agile karma]

waitt my bad i misread your original working

Nevermind- u were right the first time

that's my mistake

The derivative is 0 when x=1, yes

[clear crane]

oh ok

[agile karma]

But it's not quite the minimum still

[clear crane]

but that isnt the answer for the minimum

[agile karma]

yes, it's not

there's one more point u might want to check

u were close

[clear crane]

is it factor??

[agile karma]

nah not quite

think about it graphically

what does the graph of $3x^{2/3} -2x$ look like

doesnt need to be technical, just a rough drawing is fine

[elfin berry]

Hyper

[clear crane]

hmm

no idea

but i can use desmo

i mean

using desmo

it gave the sauce already

my bad on this one i do not what the graph looks like without desmo

it would take me years

[agile karma]

lol

[clear crane]

actually not years, i just plug in x = 0,1,2,3

[agile karma]

if u ever want to graph it without desmos

think of the graph as two different functions

3x^(2/3)

and -2x

and you're just adding them together

you can graph both of those by themselves, then draw your function

[clear crane]

yea

[agile karma]

So what have you got for your minimum?

[clear crane]

i put 0 in for x

lowkey it tells me that 3(0)^2/3 - 2 ( 0 ) would just be 0

anything time 0 = 0

i got (0,0) for minimum

[agile karma]

That sounds right

[clear crane]

yea thanks to desmo for that

but it lowkey works for me

thanks for the help !! really appriciate it

[agile karma]

no worries

good luck

[clear crane]

https://tenor.com/view/plato-kramnik-chess-philosopher-philosophy-gif-17492842099697542220

.close

[marsh citrus]

Channel closed

Closed by @clear crane

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hexed sigil]

in linear algebra, if i know the standard matrix representation of two linear transformations $K, S$, is the standard matrix representation of $K + S = [K] + [S]$?

[elfin berry]

dis_da_mør

[crisp lagoon]

I ended up getting the correct answer but I am not convinced with the method I used to solve I am sure there are plenty of mistakes
Someone pls tell me how can I better approach questions like these

[hexed sigil]

sorry this channel is occupied

[crisp lagoon]

Ohh my bad

Are there any free ones?

[hexed sigil]

yep check the above category, like #help-45

[crisp lagoon]

Thanks

[hexed sigil]

re-sending the original question:

in linear algebra, if i know the standard matrix representation of two linear transformations $K, S$, is the standard matrix representation of $K + S = [K] + [S]$?

[elfin berry]

dis_da_mør

[hexed sigil]

from what i can see if both transformations have the same origin and destination vector spaces (so their matrices are the same size) then yes

.close

[marsh citrus]

Channel closed

Closed by @hexed sigil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[halcyon elk]

"the ratio between the reading of the ameter before and after closing K"

[halcyon elk]

how is it any of these options...?

before closing k, the whole current would go thru the ameter

so it would be I""

after closing K, the current is gonna be split in half

so... 1/2 I

I / (1/2 I) is 2

which is not in the options

[fervent rampart]

but the current is also higher after closing the switch because the whole circuit has less resistance

[halcyon elk]

oh... 2/3

1 / (2/3)...?

I calculated the overall R, did Vb/R, split that into two

I : 2/3 I

yeah its right

ty cloud

.close

[marsh citrus]

Channel closed

Closed by @halcyon elk

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[clear arrow]

Hello! I am working on a proof of this exercise from Herstein's "Topics in Algebra":

[clear arrow]

Sketch of my proof goes as follows. The first sentence in the problem is basically a fancy way of saying that left coset equals right coset for all elements of G, i.e. Ha = aH.

And if so, we can easily prove that gHg^{-1} = H for all g from G. (because gH = Hg means that for every h from H, there is a h' from H such that gh = h'g, then we can multiply by g^{-1} on the right and get ghg^{-1} = h' which would eventually establish that gHg^{-1} = H for all g. So as a side effect we will establish what is asked in the exercise (i.e. that gHg^{-1} is a subset of H).

[elfin cairn]

Yes

[clear arrow]

my question is: why does Herstein ask for something milder?

i.e. why doesn't he ask to prove a stronger result (equality of sets rather than just A is subset of B)?

am I missing something in the statement?

[elfin cairn]

First, these are equivalent

This inclusion implies equality

[clear arrow]

because there is a bijection between the two?

so they have equal number of elements, hence there can't be anything missing on the left?

[elfin cairn]

In the finite case that will work

[clear arrow]

well, in the finite case, yes

[elfin cairn]

But generally the double cosets form a partition of your group

And so if any two (double) cosets have a non-empty intersection then they are equal

[clear arrow]

I haven't got to double cosets yet 🙂

is that like aHa{-1} ?

[elfin cairn]

Really it just aHb instead of aH or Ha

[clear arrow]

ok

OK, I see, so basically we are saying that H is a double coset (with a=e, b=e) and gHg^{-1} is a double coset (with a=g, b=g^{-1}), and they have non-empty intersection (because one is included in the other and is not empty), and since they form a partition (just like normal cosets) - they are equal

[elfin cairn]

Yes

[clear arrow]

OK, so the summary is that Herstein is asking us to prove something equivalent (that looked weaker to me, because I didn't know that it was equivalent -- or at least I have to prove that). I suspect though that he may have had some other proof in mind, that would more naturally lead to that subset formulation...

but there is no way to tell because there are no official solutions from Herstein himself 🙂

[elfin cairn]

Maybe yeah

Ptobably something like, take x=ghg^-1

And take a look at the coset Hx

Showing it must be equal to H somehow

[clear arrow]

but then elements of that coset would be hghg^-1?

i.e. with two "h"s

I found this exercise quite confusing overall, especially before I reformulated the first assumption to simple aH=Ha. Actually I came to this from the end, i.e. I've just seen this property of cosets (that aHa^-1 = H if aH=Ha) in another book and then I realised that I just need to show that aH=Ha and then I am done. And then I realised that the assumption of the problem is just equivalent to that -- it took some time to persuade myself 🙂

[elfin cairn]

Maybe its a good idea to gather your reasoning on why is this statement is equivalent

[clear arrow]

on equivalence of "aH=Ha" and "whenever Ha != Hb then aH != bH"?

[elfin cairn]

Yes

[marsh citrus]

@clear arrow Has your question been resolved?

[clear arrow]

my reasoning went like this. Let's reverse Herstein's statement (i.e. make a contrapositive statement). Then it becomes "if aH=bH then Ha=Hb" (for all a,b from G). In words, alternatively, "if two elements are in the same left coset, then they are in the same right coset". We know (from previous exercises or the book) that left cosets (and right cosets too) form a partition of G. A partition of a set is fully defined by specifying for each pair of elements whether they are in the same part or not (because this relation "a and b are in the same part" is basically the same relation for corresponding equivalence relation). And our statement said that "if two elements are in the same left part, then they are in the same right part", so this relation is defined identically on one partition and and on another, leading to the same parititions for all a and hence aH=Ha in general. But this one is somewhat messy (and also it looks like our statement about pairs goes only in one direction A -> B, not necessarily A=B, so I need to do some workaround for that too)

there is probably a simpler way of demonstrating this...

[elfin cairn]

Using this observation and using a two sided inclusion to prove aH=Ha can work

If you want to go through the details

if x in aH then xH=aH and and so Ha=Hx, and so x = e * a in Ha

The one sidedness of the given statement is not a problem as if aH=bH then
Ha^-1=Hb^-1 by taking the inverse

[clear arrow]

yeah, makes sense

[elfin cairn]

Oh I see you are a factorio gamer xD

Love this game

[clear arrow]

haha, yes, it's good, but I only played a little, should come back to it at some point, it was fun

[elfin cairn]

I have 1300h on it 😵‍💫

And I am always just messing around

Late game of the new dlc is tough

[clear arrow]

wow 🙂 that's definitely not "a little"! 🙂

for me it was like this: I liked the game and started to "sell" it to my friend, who got hooked, and then somehow I myself almost stopped playing it 😅

[elfin cairn]

The ability so sit down an truly enjoy gaming has been going up and and down in phases

Right now I found two new games to add to my top 10 ever.

[clear arrow]

what are they?

[elfin cairn]

Finished one already, and having fun with the other

[elfin cairn]

Clair obscur: expedition 33 and blue prince

[clear arrow]

ah yes, got those two on Game Pass, but haven't played yet, only watched some let's plays on YouTube 🙂

I recently played Baldur's Gate 3 and Kenshi 🙂

[elfin cairn]

Barely know anything about these tbh

When the time comes I might play one of them

I have enough things related and not related to gaming to do

[clear arrow]

yeah, so many games to play!

so many areas of math to study 😄

[elfin cairn]

Yeahh and group theory is just the begginning of abstract algebra

you have rings, fields and then dozens of ways to continue

I am currently battling Algebraic Geometry

[clear arrow]

I also wanted to discuss my study plan, but that's probably something that's better to do in the relevant channel for abstract algebra

[elfin cairn]

#groups-rings-fields

[clear arrow]

and another time, because I need to get back to work 🙂

[elfin cairn]

Cya

[clear arrow]

thanks for your help, see you!

.close

[marsh citrus]

Channel closed

Closed by @clear arrow

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[stone hound]

lim f(phi) = f( lim phi )

[indigo nest]

!original please

[marsh citrus]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[stone hound]

Help me with the last property

[indigo nest]

Ah limits commute with continuous functions

[stone hound]

Wait

Can you elaborate?

Please look at this

I somehow did it

.

[marsh citrus]

@stone hound Has your question been resolved?

[stone hound]

<@&286206848099549185>

[marsh citrus]

@stone hound Has your question been resolved?

[stone hound]

.close

[marsh citrus]

Channel closed

Closed by @stone hound

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[leaden peak]

Official explanation

my answer: 16 sqrt 2

my reasoning: side is 32, center of the circle would be center of the square, so find half diagonal length

$\frac{\sqrt{32^2 + 32^2}}{2}=16\sqrt{2}$

[elfin berry]

UCYT5040

[stoic saddle]

that is the distance from A to the center

and not to the circle itself

[leaden peak]

so it means like, to the nearest point on the circle?

[ionic ferry]

Ahhh yeah, they're not asking to centre of circle, only the circle

[leaden peak]

oh so then since the radius is 16

just subtract that from half diag

[ionic ferry]

Yup

[leaden peak]

ok that makes sense

just kinda confusing cause i always saw circle notation as like O(x, y)

but i guess it makes sense its not talking about the center, thats just a way to identify the circle

[ionic ferry]

That's fine dude even I was confused there for some time

[leaden peak]

ok thank you so much, guess this problem wasnt that hard lol

.close

[marsh citrus]

Channel closed

Closed by @leaden peak

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[fervent burrow]

hi, can anyone help me understand this concept? its factoring quadratics, ive tried different explanations but none of them really make sense to me.

[fervent burrow]

i promise im in college 😓 i just have difficulty understanding formulas

[past thicket]

,rccw

[brave knoll]

for this particular case I would just have computed the roots

otherwise it's about guessing and training

[slim shard]

lol with such an unclear explanantion i dont blame you for not understanding

[fervent burrow]

yes exactly lol

im mostly confused on how to get the last two terms on the last step

i dont really understand where the 2 and -8 came from other than the -16, and if thats the case whats the point in multiplying the first and third number 😓

[obtuse umbra]

do you know about the complete the square method?

i think this one is easier for you to follow

[fervent burrow]

would that work if its not an equation?

[obtuse umbra]

it works for most of the quadratics

so take the quadratic $9y^2 - 18y - 16$ as what it said

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

do you notice that $(3y)^2 = 9y^2$?

[elfin berry]

1 divided by 0 equals Infinity

[fervent burrow]

writing down rn

yes

[obtuse umbra]

the purpose of this method, is to make a square

and what is $(a + b)^2$ and $(a - b)^2$?

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

if you can't remember the formula, then just distribute it all out

[fervent burrow]

wdym?

[obtuse umbra]

what i mean is that

[obtuse umbra]

this method's purpose is to make a square, which is in form of $(a + b)^2 \pm c$ or $(a - b)^2 \pm c$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

and $(a - b)^2 = a^2 - 2ab + b^2$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

so the $3y$ here can act as $a$

[elfin berry]

1 divided by 0 equals Infinity

[fervent burrow]

?

[obtuse umbra]

wait

3y acts as a

and we want 18y to act as 2ab

notice that 18y = 2 . 3y . 3

so b can act as 3

since we only need b^2 left, we can seperate -16 into 9 - 25

so it should be something like

$(3y)^2 - 2 \cdot 3y \cdot 3 + 9 - 25$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

turns into $(3y - 3)^2 - 25$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

do you get what i mean now?

[fervent burrow]

not really

its not the correct answer and im guessing thats why i have to use that formula

[obtuse umbra]

wait

that's not the answer yet

now do you know the difference of squares?

[fervent burrow]

im just more confused now

idk

[obtuse umbra]

if you are confused about the formulas

try to discover why they are true

for example: $(a + b)^2 = a^2 + 2ab + b^2$, why?
because $(a + b)^2 = (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

the same reason applies for $(a - b)^2 = a^2 - 2ab + b^2$

[elfin berry]

1 divided by 0 equals Infinity

[obtuse umbra]

that is one way to remove your confusion of the formulas

they exist because they have proven it

[marsh citrus]

@fervent burrow Has your question been resolved?

Channel closed

Closed by @fervent burrow

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[past thicket]

Huh?

<@&268886789983436800>

[ionic ferry]

ummmm

[quiet anvil]

no

[past thicket]

Also using an llm to scam is pathetic lmfao

[marsh citrus]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[oak oxide]

huh

[main idol]

💥

[past thicket]

Bars

[oak oxide]

What's Q4

Ehhh I can't understand

[past thicket]

Also asking the same question

[quiet anvil]

quarter 4

it's financial bullshit

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vital yew]

Find the number of ways in which two small squares can be selected on the normal chessboard if they are not in same row or same column.

[vital yew]

My answer is 64*49 , but idk the answer is given 32X49

[vagrant raft]

You overcounted each position twice

[vital yew]

Yes , that's written int he solution......

But why

I mean normall

y

when I use principle of counting I don't think of overlapping

Why for this specific case I have to

[vagrant raft]

Think about how you picked your squares

[vital yew]

Yes....... i had 64 choices for the 1st square and for each correspond square I had 49 choices