help-23

[safe radish]

@silent roost Has your question been resolved?

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[cursive pivot]

.close

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[silent roost]

how important is sleep

[silent roost]

so like i dont wanna go crazy researching this myself idk why im asking here lol but y not

how necessary is it really

like how accurate are the guidelines from sleep medicine foundation or whatever and how much sleep do people actually need

its a confusing topic because its very individualized but how does one find

a good amount of sleep

[cosmic grove]

is maths related to sleep ?

[silent roost]

idk

[cosmic grove]

[silent roost]

definitely not ;-;

[cosmic grove]

its a math server tho

[silent roost]

ya

that means everyone is smarter than me

[cosmic grove]

definitely not

[silent roost]

XD

[worthy hemlock]

It means you should ask math related questions

[silent roost]

true 😭😭

but im losing sleep and im already paranoid that i wont remember what ill learn tmmrw if i dont sleep but at the same time i gotta miss sleep ugh

its a mathematical dilemma cuz then thereforee

[worthy hemlock]

https://sph.umich.edu/pursuit/2020posts/why-sleep-is-so-important-to-your-health.html#:~:text=Sleep is essential to every,touches every aspect of health
https://www.sleepfoundation.org/how-sleep-works/why-do-we-need-sleep
https://thesleepdoctor.com/how-sleep-works/
Literally just found 3 articles

[silent roost]

lmfao

[worthy hemlock]

It's not hard to google

[silent roost]

yess but how reliable is it

maybe the better question i should be asking is how to do proper research

[cosmic grove]

you think we are more reliable than articles ?

[silent roost]

its a rabbit hole when i google things

[cosmic grove]

[worthy hemlock]

Sleep deficiency can interfere with work, school, driving, and social functioning. You might have trouble learning, focusing, and reacting. Also, you might find it hard to judge other people's emotions and reactions. Sleep deficiency also can make you feel frustrated, cranky, or worried in social situations.

Sleep deficiency is linked to many chronic health problems, including heart disease, kidney disease, high blood pressure, diabetes, stroke, obesity, and depression.

[silent roost]

yesyes

[thin bridge]

#discussion #chill

[silent roost]

but what are the differences in amount of sleep specifically

[silent roost]

o ya i should do that

[worthy hemlock]

Anyways, ram is right, this isn't a math question

.close

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[supple gale]

Can we write -4cos^3 as -4^1/3cos

[cosmic grove]

[supple gale]

?

[cosmic grove]

your expression lacks

[supple gale]

What is that symbol

[cosmic grove]

parenthesis

[supple gale]

Oh ok

[cosmic grove]

dirty mind

[regal swift]

[supple gale]

Lel

[cosmic grove]

rewrite it, i cant understand it

[supple gale]

(-4)cosQ^3 = (-4^1/3)cosQ

Am i correct

[regal swift]

do you mean something like

$-4\cos^3{Q}=-4^{\frac{1}{3}}\cos Q$

[supple gale]

No

[regal swift]

i cant read ahaha

[supple gale]

No not theta in brackets

Just cos

[regal swift]

[cosmic grove]

$\cos^3 (x) = (\cos(x))^3$

[flat frigate]

Ｈｅｒｅｌｓ

[supple gale]

YES SOMETUING LIKE THIS

[flat frigate]

3_n

[supple gale]

YES THIS ONE

[regal swift]

uwot

[cosmic grove]

which one

[cosmic grove]

cuz this one is wrong af

[regal swift]

yes it is

[supple gale]

How

[cosmic grove]

it doesn't follow the property of cos at all

[supple gale]

a number multiplied by itself 3 times gives 4 is 4^1/3

[cosmic grove]

yes and ?

[supple gale]

Right?

I wanted to convert the cos cube into a normal cos

Lol

[regal swift]

it's more of like RHS^3=LHS

[supple gale]

No i mean

See my question is this

[cosmic grove]

wdym ?

$(-4^{\frac{1}{3}} \cos(Q))^3 = -4\cos^3 (Q)$

[flat frigate]

Ｈｅｒｅｌｓ

[supple gale]

So can write like this

Or no

In the above img

[cosmic grove]

this ?

definitely no

hell no

[supple gale]

No the one

You sent

[regal swift]

pls no

[cosmic grove]

the one I sent is true

[regal swift]

oh it works then

but the cube is still there

[cosmic grove]

I dont see the problem

[regal swift]

that's not a problem ahah

[supple gale]

https://photos.app.goo.gl/xQSM3Yidvt6FpPDn6

PLEASE JUST SOLVE THIS FORGET MY PREVIOUS QUESTION

I i can easily solve this useing pythogaras

But the cube

AAAAAAAAAAAA

[cosmic grove]

why should we solve it 🤔

[supple gale]

CUZ I NEED HELP

PLS I BEG YOU

MY TEWCHER WILL KILL ME

[supple gale]

Ok

[cosmic grove]

you need to do this for today or what

[supple gale]

My school is going to start in 2 hours

My 2nd period is maths

Pls pls pls

[cosmic grove]

you can factor by cosα first

[supple gale]

How

[regal swift]

pyth? hmm you can try constructing a right angled triangle with property sin alpha = 1/2

Since alpha is acute you will end up with something like this

[cosmic grove]

since im tired, ill do it asap

$\cos(\alpha) (1-4\cos^2 (\alpha)) = \sqrt{1-\sin^2 (\alpha)} (1-4+4\sin^2 (\alpha))$

[flat frigate]

Ｈｅｒｅｌｓ

[regal swift]

^ this works too

[cosmic grove]

$(\cos(\alpha) - 4\cos^3 (\alpha)) = (-3+4\sin^2 (\alpha))\sqrt{1-\sin^2 (\alpha)}$

[flat frigate]

Ｈｅｒｅｌｓ

[safe radish]

@supple gale Has your question been resolved?

[supple gale]

Nvm i got it

https://photos.app.goo.gl/ArMhc19vBiyrfDcr6

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[left agate]

Can someone explain me the correct answer thanks!!

[buoyant shadow]

i can't find any correct answers

[left agate]

Ahmm i think the correct answer is the last choice?

[buoyant shadow]

you want ~P ∧ Q which could be ~(P V ~Q)

just don't make sense any of those

[left agate]

Okayy thank u!!

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[light mauve]

how do u find that length ?

[lean otter]

big radius + small radius = 18

big radius - small radius = 6

[light mauve]

simultaneous equations?

[lean otter]

yea

[light mauve]

oh ty

b-s=6

2b=24
b=12

12-s=6
s=6```

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[trim jackal]

Anyone able to help me with question 7?

[safe radish]

@trim jackal Has your question been resolved?

[trim jackal]

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[trail pasture]

Can anyone please show me how to find this

[sage galleon]

Have you learnt/tried L'Hopital rule?

[dense lynx]

Do you know what x/sin(x) at limit close to 0

[trail pasture]

tried l'hopital, doesnt work because I can't get rid of either sin(1/x) or cos(1/x)

do you mean I should try l'hopital on just (x^2)/sin x first?

[sage galleon]

you can try using squeeze theorem,
|sin| <= 1
x^2|sin| <= x^2
then do

[sage galleon]

yes

[trail pasture]

how do I solve 0 * lim{x->0} sin(1/x) ?

ah, nvm, its just 0 * {0 < sin(1/x) < 1} right?

so 0

thank you very much

but can you please show me more of the alternative way with squeeze?

never mind, I got it!

thank you again

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[lean otter]

Can someone please explain the wording of this question to me?

[lean otter]

I have some questions to ask about it.

The first question is what value am suppose to use for solving it. Is it the 1203 alumni or 510 scores?

If your answer is 1203 alumni, please explain why?

Also, if the question were to be altered a little to say exactly 4 people had that grade, how will i go about it?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

I believe it would be 1202 alumni because the person who got 510 would be included in the 1203 meaning you would have to subtract him leaving you with 1202 scoring higher than 510

[lean otter]

subtract 4 from 1203

[lean otter]

no

what did you end up with?

902

explain

are you familiar with quartile.

not really

the median is have of the population

602

oh

wait

I may or may not have misread the problem

the first quartile is median of 601

301

hence above 301 is 1203-301=902

i dont really understand it.

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@glacial badger Has your question been resolved?

[safe radish]

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[rugged hearth]

Hello

[rugged hearth]

One question

When I have a fraction do I use >=0 or =/ if something is under the square root?

Anyone?

[split ether]

What does =/ mean?

"not equal"?

[safe radish]

@rugged hearth Has your question been resolved?

[rugged hearth]

Yep

[split ether]

x^2 >= 0 for all x
Is this what you're asking about?

[rugged hearth]

Nah

Wait pls I will attach pic ture

Picture *

How I do the bottom part?

[split ether]

if a/b = 0, then a = 0

(also you need to make sure that b is nonzero)

So, in this case,

Find values of x for which 4 + 4x - 3x^2 = 0 and sqrt(2x + 4) isn't 0

[rugged hearth]

Do I need to write that 2x+4 is not equal to zero or equal to >=0 and why?

[split ether]

2x + 4 =/= 0

[rugged hearth]

But why tho if I have log why not >=?

[split ether]

You don't want it to be 0

[rugged hearth]

I know it can't be zero but when I look at youtube the guy is doing it with >=0 because of log

[split ether]

Is he doing the same question?

[rugged hearth]

Yeah

[split ether]

Ah

2x + 4 > 0

Yes

But not >=

[rugged hearth]

If u had log from smth would you do it with >= no matter if its the bottom part?

[split ether]

You don't need log though

[rugged hearth]

Just >?

[split ether]

You just need 2x + 4 to be positive so that sqrt(2x + 4) exists

[rugged hearth]

I see

[split ether]

But usually if sqrt(x) exists, then x >= 0

In this case we don't want sqrt(x) to be 0, so x > 0

[rugged hearth]

Oh I understand 🙂

Thanks

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[safe radish]

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[twin solar]

I have do find D(f) of
$$\left(\frac{x}{x+1}\right)^{\tan(x)}$$

[flat frigate]

marejak023

[split ether]

Rewrite it as e^(tan(x)ln(x/(x + 1)))

[twin solar]

done

[split ether]

Now just apply product rule

[twin solar]

whats that?

[split ether]

(ab)' = a'b + ab'

[twin solar]

I dont want to find derivative

[split ether]

Ahh

Domain

[twin solar]

yeea

[split ether]

mb

[twin solar]

nw :)

[split ether]

Well first you'd like tanx to be defined

and x+1 not to be 0

[twin solar]

tan is sin/cos so for tg all R\cos(x)=0

so R{(2n+1)pi/2} is what ive foun

[split ether]

Yes

And exclude -1 as well

[twin solar]

and x\neq0

ah yes sorry

-1+1

so -1

[split ether]

Ah and yeah the expression shouldn't be 0^0

So x =/= 0

[twin solar]

so thats all?

[split ether]

Yeah

[twin solar]

exclude zero and cos?

great, thanks!

[split ether]

and -1

[twin solar]

yes, i messed up again xd

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[manic nexus]

I somewhat figured out the formula to the first part of this question and I understand the thinking behind Simple Induction, but I don't get how a binary string with length zero can exist?

[manic nexus]

If f(0) = 1, that'd imply there's a binary palindrome of length 2*0 no? How does that work?

<@&286206848099549185>

[peak estuary]

the emptry string "" is a palindrome

same thing forwards and backwards

[manic nexus]

Ohh, ah.

Okay, that's interesting, I actually had no idea.

Thank You @peak estuary

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[smoky lava]

do i solve for w?

[upper folio]

what is something that you know is constant throughout?

[smoky lava]

the time?

[upper folio]

A hint would be the fact that he went down the same path

[upper folio]

Not necessarily since he could've been going faster downhill

[smoky lava]

w = (y-z) * x

[smoky lava]

hm

[upper folio]

He took the same path

that means the distance travelled up and down was the same

and you know how fast and how long it took to go up and down

x amount of time at y speed

so xy gives you the distance travelled uphill

what would give you the distance travelled downhill?

[smoky lava]

zw

[upper folio]

not quite because he took a different amount of time to go downhill

oh wait

[upper folio]

yeah it's correct now

[smoky lava]

well the problem with this is that it's not an equation

it doesn't equal anything

[upper folio]

yes but you know that the distance up and down the hill is the same

[smoky lava]

there is no variable for distance

[upper folio]

and xy is the distance uphill and zw the distance downhill

[smoky lava]

yeah

[upper folio]

but since they're the same

you have xy=zw

[smoky lava]

thank you

[upper folio]

no problem

[smoky lava]

t= x*n

do you think this is valid?

[safe radish]

@smoky lava Has your question been resolved?

[smoky lava]

i failed

[safe radish]

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[lean otter]

idk

like what are the p,a, and b

im just confuse

d

[mortal sandal]

p is part of the quadratics

a² and b² are made up

[lean otter]

isnt it q?

in the quadratic

oh

im blind

[mortal sandal]

This is a really dumb question lol

p is an integer

so a=p and b=0 works

probably whoever wrote this just missed that

[lean otter]

does thie answer the question??

wut

[mortal sandal]

yeah

not the solution they had in mind but

ig you could challenge yourself and say non-zero a,b

[lean otter]

u havent determined q in terms of a and b

right?

[mortal sandal]

nah

it's probably not really possible in this case

that part of the problem was designed with the other harder solution in mind

[mortal sandal]

Trying to prove you can't now

OH JUST HAD A RANDOM UNRELATED REVELATION

I am the greatest

not entirely unrelated

[lean otter]

chris approved

help room 38

moni i feel like ur so much beter at advanced math stuff than algebra, thats my take

[mortal sandal]

ok we need to find integer solutions to 2a²=b²+c²=d²+e²

[lean otter]

just do help 38

[mortal sandal]

ok 1 minute

[lean otter]

@idle parrot @feral linden @proper crypt @steep dove

maybe snow too @toxic stratus

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

.close

[safe radish]

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[plucky elk]

read #❓how-to-get-help

[dusk vapor]

u gotta help me with riemann😭

[plucky elk]

don't spam other people's help channels

[dusk vapor]

i crush fairy closed it,

[dusk vapor]

^^

lol why did u delete the guy's question

[safe radish]

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[warped heart]

is it one?

i drew out all the possibilites

for if we started with a red bead and a blue bead

and from both of it, i can only see one

for the third place

the options are also:

[fierce trench]

From what I see it’s one

The center would be red and the rest blue

[warped heart]

yes

[fierce trench]

As the center one connects to every other circle

[warped heart]

did u check it by yourself?

i'm not sure if my possibilities are accurate

[fierce trench]

Yeah that’s just my impression

[warped heart]

okay, thanks

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[tight dove]

i need help

[safe radish]

Please don't occupy multiple help channels.

[tight dove]

why is 2x ≠ 0

@admin

<@&286206848099549185>

[obsidian oracle]

what's f and g ?

[tight dove]

f(x)= 2x

g(x) = -3x + 1

[obsidian oracle]

what's Dg ?

[tight dove]

R

[obsidian oracle]

isn't it R* ?

[tight dove]

no

[obsidian oracle]

then Dgof = R

[tight dove]

thats the problem

the teacher just poped that 2x € R*

[obsidian oracle]

what is Df ?

[tight dove]

(i used € cuz i cant find the symbol)

R

i think she just made a mistake

sorry for wasting your time

[safe radish]

@tight dove Has your question been resolved?

[safe radish]

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[verbal willow]

Consider the following argument:
I will buy a car or take a vacation.
I will buy a car.
Therefore, I will not take a vacation.
(a) Write the argument in symbolic form, (b) State the name of this form of argument, (c) Is the
argument valid or invalid?

[lean thorn]

hi what have you got so far?

[verbal willow]

Nothing yet

havng a hard time understanding

[lean thorn]

okay so have y'all gone over an exclusive or yet?

[verbal willow]

Nope

[lean thorn]

so this is an example of an exclusive or

it basically means "one or the other, but not both"

an inclusive or means "or or the other, both is okay"

[verbal willow]

oH

[lean thorn]

For example:
"At the concert, I will get a coke or a hotdog". In this case, you can get a coke, a hotdog, or even both. This is an inclusive OR.
"Turn right or turn left up the road". You can turn right or turn left, but you can' t do both. This is an exclusive OR

[verbal willow]

i SEE

So in symbolic form

wait

which one do I even write in symbolic form

[lean thorn]

well they're separate statements

[verbal willow]

oh

[lean thorn]

Let $P$ be "I will buy a car" and $Q$ be "I will take a vacation"

[flat frigate]

MellowDramaLlama

[lean thorn]

The symbol for exclusive or is $\oplus$

[flat frigate]

MellowDramaLlama

[lean thorn]

So the symbolic statement would be $P \oplus Q$

[flat frigate]

MellowDramaLlama

[lean thorn]

There are other symbols for exclusive or but this is the one I'm familiar with

[verbal willow]

I see

[lean thorn]

Do you know how to do truth tables?

[verbal willow]

yes

[lean thorn]

okay so this truth table will be this:

-----------------
| P | Q | P ⊕ Q |
|---|---|-------|
| T | T |   F   |
|---|---|-------|
| T | F |   T   |
|---|---|-------|
| F | T |   T   |
|---|---|-------|
| F | F |   F   |
-----------------

sorry that took a second to draw lol

notice that it's the negation of "If and only if" 🙂

?

[verbal willow]

Yes I do

[lean thorn]

so those are inverse of one another

[verbal willow]

so

[lean thorn]

This covers part (a)

[verbal willow]

really

[lean thorn]

This covers part (b)

[verbal willow]

All they wanted was a truth table?

[lean thorn]

no not the truth table

I was just showing the truth table to show you what the rules were

[verbal willow]

so

the symbolic form would be

P↔Q

?

[lean thorn]

no

that's if and only if

it's the circle plus above

[verbal willow]

I dont think we've covedrd that

is that the only symbolic form?

[lean thorn]

for XOR yes

oh

well then I think I made this too complicated. The teacher probably only wants you to play with OR then

it's a weird question though because exclusive or exists

anyways

then I think how to approach this is this

I will buy a car or take a vacation.
I will buy a car.
Therefore, I will not take a vacation.

Let P = "I will buy a car" and Q = "I will take a vacation".
Symbolically this is P V Q

so that's (a) and (b)

then to answer (c), the statement "Therefore, I will not take a vacation." would be invalid because with or you can do both (this is the inclusive part I was talking about)

so ignoring all the above with the exclusive or

and only working with the OR you've probably learned about so far in class, then the statement above is not correct

make sense?

[verbal willow]

Absoulety

do you have time to help me with one more?

or do I have to create a ticket?

[lean thorn]

I have to run soon. so I reccomend closing this out and reopening with your other question 🙂

[verbal willow]

Thank you regardless you explained it perfectly

[lean thorn]

yep no worries!

best of luck

[verbal willow]

how do i close ?

[lean thorn]

.close

[verbal willow]

.close

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[raw bobcat]

how do i open a q?

[lean otter]

its open now haha

[raw bobcat]

I asked someone alrdy and they said something along the lines of a cartesian product

i need to solve for the

system of equations with answer in order pair form

[raw bobcat]

not sure what that is or how to get the answer

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[patent vault]

How many distinct 3-letter words can one make out of the letters in the word PARABOLA? Each letter may be used as many times as it appears in PARABOLA, and any 3-letter combination is a word—for example, AOA is a word.

[patent vault]

is my solution correct?

We can use complementary counting. There are a total of 8^3 distinct words we can make. But this overcounts, because some letters were used more times than they appear in the word PARABOLA. 
        We can do casework for each letter and count how many incorrect words are there for that letter:
            P: P appears once, so when it appears twice there are 3C2 * 7 words, and when it appears three times there is 1 way. Thus a total of 21+1 words.
            A: A appears three times, and we are making three letter words, so there are no incorrect words with too many A’s.
            R: P appears once in PARABOLA, so it also has 22 incorrect words.
            B: B has 22 incorrect words as well.
            O: O has 22 incorrect words as well.
L: Lastly, L has 22 incorrect words.     
    In total we have 22+22+22+22+22=110 three letter words that don’t work. Thus, there are a total of 8^3-110=402 distinct three letter words made out of the letters from PARABOLA. 

anyone?

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@patent vault Has your question been resolved?

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[waxen heart]

cN SOMEONE explain why im getting A wrong??

this is the work i have which consistently gives me 4/3

[hardy lion]

your quotient rule is reversed

low dhigh first

also for this problem it doesnt matter bc theyre the same, but its low^2

you may want to remember it by (low dhigh-high dlow)/low^2 because i think youre just applying a formula where the fraction is flipped

[waxen heart]

what doss low and high meN

[hardy lion]

low is the denominotor and high is the numerator

but it wouldnt be as easy to memorize/right if you had to say that every time

[waxen heart]

low dhigh is first tho

oh it a trick buh

.close

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[solar verge]

How do I find the answer in terms of z?

[solar verge]

I just tried to solve in terms of y is it correct?

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[merry sleet]

which part confuses you?

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[lean otter]

Let p = False and q = False. Then (p <-> q) = True.

[lean otter]

Why is this true?

nvm

i got it

.close

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[foggy salmon]

lol

[lean otter]

circle shut up

[foggy salmon]

false iff false

[lean otter]

im studying for my midterm

rn

its tomorrow

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[hard sandal]

im not too sure where to start with this question

[hard sandal]

plz

what about these?

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

bruh, ive been here for half an hour

<@&286206848099549185>

please I really need help, I have no clue where to start

.close

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[lean otter]

whats one trillion to the tenth power

[lean otter]

bro

can someone help me

what is one trillion to the tenth power

[merry sleet]

one trillion is 10^12

so one trillion to the tenth

is

[lean otter]

.close

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[merry sleet]

[lean otter]

.close

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[boreal ore]

I am trying to find determinant of this matrix only with using determinant properties. I know, that answer is not 0, but when i starting solve that, i get result 0. What i do wrong? My solution: third column i multiplied on second column, and second and third columns now are equals => determinant = 0

[peak estuary]

I assume you mean you multiplied the columns pointwise? you can't do that

you can only multiply a column by a scalar

you could multiply the second column by 1 but that doesn't do anything

[boreal ore]

When i calculate determinant by column,i multiply which column by another column, multiply by a number so that zeros appear in the column, why i cant make it in this case?

[quasi bison]

you don't multiply two columns together...

you multiply a column by a number and add/subtract that to another column

[boreal ore]

I realized my mistake, what should I do with this matrix of variables, how can I get the determinant from it, without direct calculation by row

[quasi bison]

well as a first step you could add -a^2 times col 3 to col 1

that'll leave you with $\vmqty{x^2 & ax & 1 \ y^2 & ay & 1 \ z^2 & az & 1}$

[flat frigate]

Ann

[quasi bison]

then factor a from the second column

and you'll be left with what is almost the vandermonde matrix for x, y and z

[boreal ore]

Thank you

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[mossy sequoia]

Me

[safe radish]

Please don't occupy multiple help channels.

@mossy sequoia Has your question been resolved?

[mossy sequoia]

.close

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[modern lynx]

How do I find f^(-1)'(8) when f=x^3+4x^2+(64/12)x+8

[modern lynx]

I tried derivating first then inverting but that didnt work

I know the answer btw, I just dont know how to get to it

[obsidian oracle]

First you gotta find x such that f(x) = 8, and that x will be f^-1(8)

So you want to find x such that :
x^3 + 4x² + (64/12)x + 8 = 8

You don’t have to look too far for a clear solution...

[modern lynx]

but I'm looking for the derivative of f^-1(8)

[safe radish]

@modern lynx Has your question been resolved?

[modern lynx]

<@&286206848099549185>

[coarse cape]

do you know the inverse function rule $$f^{-1}'(a)=\frac{1}{f'(f^{-1}(a))}$$

[flat frigate]

Enoo58
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[modern lynx]

Yes, but I'm not sure how to use it here

also very nice profile picture btw

[coarse cape]

its not that hard tbh the main thing is what is f^-1(8)

[coarse cape]

thanks lmao

[modern lynx]

yeah thats the part that I'm stuck at

Im only used to solving quadratic expressions not ^3 (dont know the proper english words)

[coarse cape]

yeah thats a nightmare to do for everyone

but look at your function cloesly

[modern lynx]

is the first step to make it into x^3+4(x^2+4x/3+2), then solve the quadratic part? what do I do with the x^3 outside it?

think I messed up some numbers in there but the idea haha

[coarse cape]

plug in some easy values

you make it too hard

think waaay easier

whats the easiest value to plug in for x

[modern lynx]

oh my

0 then it is 8

[coarse cape]

yesss

[modern lynx]

hahahaha holy shit

[coarse cape]

and with that use this rule

that should be it

[modern lynx]

yepp just checked that correct, thank you so much man

[coarse cape]

np glad to help

[modern lynx]

I have another one similar to this, is it okay if I dm you if I cant figure it later?

[coarse cape]

yeah sure

[modern lynx]

thanks man ❤️

.close

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[halcyon carbon]

This is the SMC today?

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[azure basalt]

dont know how to find where it is continous

[azure basalt]

to me it makes sense that it would be cont when y+cos^2(x) is > 0

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[stiff kayak]

Just checking if I got the right answer

[quasi bison]

checks out, assuming the handwritten asterisk stands for multiplication

[stiff kayak]

they do, hanks

the asterisks in 3*6 is struggling rn

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[topaz urchin]

Alex decided to go to Washangton. At 10 o’clock he went ⅕ of the way. Two hours later he went ⅚ of the way. How long did it take for the whole journey to Washington assuming he held the same speed the whole way. Round to the nearest ten minutes.

[idle parrot]

oops @modest cloak looks like u lost to them by couple of seconds, open new channel

[topaz urchin]

Hi, how do i solve this?

<@&286206848099549185>

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@topaz urchin Has your question been resolved?

[topaz urchin]

no

<@&286206848099549185>

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[unkempt pecan]

What's the difference between these?

[unkempt pecan]

for f), is it because it's not {{∅}} ⊂ {∅, {{∅}}} ?

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[oak glen]

U have a deck of cards. U have to pick 6 cards from the deck. In the 6 cards there must be exactly 2 Aces and the number of red cards and black cards must be the same.

[oak glen]

How can I solve this question

[compact ferry]

in how many ways can you pick 6 cards from 52 cards

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[tight dove]

.close

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[dawn elbow]

I need a hint of where to start on how to find the eigenvectors of a householder reflector

[dawn elbow]

Defined as: $F = I - 2uu^*$

[flat frigate]

Maxerature

[peak estuary]

try picking a good orthonormal basis of V

[dawn elbow]

V?

I don't know what you mean by orthonormal basis either (I'm still rusty on some concepts, since it's been a while)

[peak estuary]

I assumed your vector space would be called V

[dawn elbow]

I understand that the eigenvectors need to be orthogonal since householder reflectors are hermitian, but I don't know how to define that (probably in terms of u, I imagine).

I don't know anything about my vector space. I haven't dealt with them in 4 years, since I was a freshman undergrad, so I don't even really remember what they are unfortunately

[peak estuary]

well thats a very weird set of knowledge you have there

knowing the implications of a operator being hermitian but not knowing stuff about vector spaces

do you remember gram schmidt

[safe radish]

@dawn elbow Has your question been resolved?

[dawn elbow]

yes

[dawn elbow]

I'm taking computational linear algebra for my PhD but haven't done any linear alg in 5 years

So I'm a bit lost at points 😅

You mean for QR factorization, right?

[peak estuary]

you can use it for QR factorization

but in general its an algorithm to turn a basis of a space into an orthonormal basis of that space

[dawn elbow]

I only know it in terms of QR factorization

[peak estuary]

if you set $A=(v_1, \ldots, v_k)$ and get a QR factorization $A=QR$, then $Q=(q_1, \ldots, q_k)$ with $\operatorname{span}(v_1, \ldots, v_k) = \operatorname{span}(q_1, \ldots, q_k)$ and $q_i$ are now an orthonormal basis of that space

[flat frigate]

Denascite

[peak estuary]

and q1=v1 which we need here

(up to scaling)

[dawn elbow]

I don't know how you'd do that based on just the vectors u

[peak estuary]

so we have the vector u

[dawn elbow]

I need to base it all on the basis of the householder reflector

[peak estuary]

do you know that you can extend any linearly independent set to a basis of the vector space?

[dawn elbow]

That'll be a no

[peak estuary]

uhm ok

I'm gonna pull a "trust me bro" cause I don't really wanna go through that stuff

[dawn elbow]

I kinda need to actually understand what I'm doing

[peak estuary]

just to give you the outline of what you will do

and then you can read up on the stuff later

cause I wanna go to bed soon

[dawn elbow]

The problem is that I still have my notes from when I took linear alg as an undergrad and that's not in it anywhere

[peak estuary]

I doubt that

[dawn elbow]

Is it more advanced than something an undergrad would learn in a 1000 level course?

[peak estuary]

that's a super basic theorem

that you need for a lot of shit

[dawn elbow]

okay I guess

[peak estuary]

so we can extend ${u}$ which is a linearly independent set to a basis ${u, v_2, \ldots, v_n}$ of our vector space $V$

[flat frigate]

Denascite

[peak estuary]

now we can apply gram schmidt and get an orthonormal basis ${u=q_1, q_2, \ldots, q_n}$ of $V$

[flat frigate]

Denascite

[peak estuary]

and now check what F(q_i) is for each of those

[dawn elbow]

How would I do this for an arbitrary u?

Like I don't have any actual numbers

Just the formula for F

[peak estuary]

have you ever done proofs?

this abstract kind of reasoning without actually doing anything to specific vectors?

when I say "apply gram schmidt", I don't actually mean going through the algorithm by hand and calculating stuff

[dawn elbow]

I'm really bad at proofs but I do them for this course

I can do induction fine, but other kinds make me want to fucking scream

[peak estuary]

I mean in the abstract sense, I would take that set as input and then I would get something out of the algorithm with some properties

[dawn elbow]

Okay I guess, yeah

[peak estuary]

out of interest, what is your phd about. and what was your masters about. if this kind of reasoning is strange to you

(fair ifyou dont wanna say of course)

[dawn elbow]

No masters, I'm starting straight from a computer science bachelors in data science and machine learning. My PhD is in the same field

[peak estuary]

from a bachelors to a phd? that's possible? TIL

[dawn elbow]

Yeah it is at most universities in the US at least

I'm in no way a mathematician. I struggle with trig substitution in integrals and still don't know times tables beyond 12. I suck at proofs in any field because I don't have that kind of mind. I can't visualize anything - aphantasia is a bitch in many ways it seems, and I need to see something done (or do it) to actually understand it, which isn't the case in this kind of course. Occasionally an algorithm will be shown, which I do understand, but I can't do abstract logic well. I always have no idea where to start and then get stuck at steps because I can't see how to get where I want from where I am

If proofs require more than algebraic logic, I get stuck, essentially

[peak estuary]

well you will have a rough time during your phd I think

[dawn elbow]

Yeah probably. This is the only pure theoretical math course I need though. I'm good with everything else like data science, statistics, and applications of the linear algebra used in actual machine learning structures

[peak estuary]

I wish I could offer helpful advice but really not sure what to say. a lot about proofs is about practice

practicing how to think

which math students usually do during their bachelors and masters

you didn't get all that

[dawn elbow]

Yeah it's a pain. Like I can do proofs for set theory-style discrete math, because that's all induction. This is just beyond me

[peak estuary]

oh I wish discrete math was all just induction

[dawn elbow]

It's not all induction, but a large portion of it was

It was also 3 years ago pre/early-covid with an 85 year old professor who died from cardiac arrest during one of our lectures so I don't remember much of it

[peak estuary]

well that is some time to die

well I wish you good luck. Im gonna go to bed

[dawn elbow]

thanks for the help!

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[pliant inlet]

Completed a)

dont understand what the other questions are asking

[foggy salmon]

um

do uk what r linear combinations

[pliant inlet]

kindof?

[foggy salmon]

yea

in this case u can show that

r1 r2 r3 make up r4

or

r4 is a linear combi of r1 r2 r3

[pliant inlet]

is r1 r2 and r3

the col vectors?

[foggy salmon]

oh wait

oops

[pliant inlet]

i.e. ( 1, 0, 1, 1) , ( 1, 1, 0, 1), (0, 1, 1, 1)

?

[foggy salmon]

err

well

i think imma get out

im bad at matrices

[pliant inlet]

lol gotcha

thanks anyways

[foggy salmon]

op Q, b onwards

[pliant inlet]

<@&286206848099549185>

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.

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[dark wolf]

Help

[lean otter]

That’s just
2(6) = 6/6 + 6²-2

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[kindred vault]

you can choose the cubes in 27x26x25 different ways. Now how many of these would give you 4 black faces.

You have to know how many cubes are coloured on 1, 2, 3, or 0 sides

If you have any urge to solve this, let us now, or im off !

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[next shadow]

<@&286206848099549185>

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[keen idol]

Hello could someone please help me simplify this expression which I got from a definite integral?

[keen idol]

I'm not sure how to simplify that further

To get an answer in exact form

<@&286206848099549185>

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<@&286206848099549185>

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[keen idol]

<@&286206848099549185> if you want me to rewrite it clearer or anything please just say

[plucky elk]

,w integral sec^3 x

[flat frigate]

Results provided by WolframAlpha

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

Requested by riemann#2529

[plucky elk]

[keen idol]

@plucky elk nono I've got that

I've subbed in the limits 1 and 0

Which is what the last line is

But I don't know how to simplify that further

Because in the textbook it says that should simplify to 1/2(sqrt(2) + ln(1 + sqrt(2)))

[plucky elk]

,calc log((cos(1/2)+sin(1/2))/(cos(1/2)-sin(1/2)))

[flat frigate]

Result:

1.2261911708835

[plucky elk]

https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Algebra_and_Trigonometry_(OpenStax)/09%3A_Trigonometric_Identities_and_Equations/9.03%3A_Double-Angle_Half-Angle_and_Reduction_Formulas

[keen idol]

.close

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[signal granite]

i have to prove the following $\sum_{j=1}^{n} (2j-1)^{3} =n^2 (2n^2-1)$ for every natural number n \ge 1 by induction. I proved the statement for n = 1 and im trying to prove it for k+1 by splitting the sum: $\sum_{j=1}^{k} (2j-1)^{3} + (2(k+1)^{3}$. the result is $\sum_{j=1}^{k} (2j-1)^{3} +8k^3 - 12k^2 + 6k - 1 but i cant go further from here

[flat frigate]

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

[plucky elk]

[signal granite]

cant do latex yet haha, still learning

[plucky elk]

send your messages and equations separately

$\sum_{j=1}^{n} (2j-1)^{3} =n^2 (2n^2-1)$

[flat frigate]

riemann

[plucky elk]

$\sum_{j=1}^{k} (2j-1)^{3} + 2(k+1)^{3}$

[flat frigate]

riemann

[signal granite]

thanks for the tip! any idea how i can go further with what i have? Or did i go wrong somewhere

Also i think you got the second term wrong, its (2k+1)^3

<@&286206848099549185>

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[lean otter]

How do I prove that on this Delta symbol the Delta is as big as all the other angles combined?

[hardy lion]

What is the sum of the angles in a quadrilateral?

[lean otter]

360 I think.

[hardy lion]

And second hint: what is the sum of angles around a point?

[lean otter]

The same

[hardy lion]

Exactly

Try labeling the angle the shares a point with d and compare two sums

[lean otter]

Excuse me?

I don't think I understand

[hardy lion]

Ok hold on

You can set up an equation using the two sums

The red angle appears in both

[lean otter]

So 360/2?

or 160 times 2?

[hardy lion]

No it has nothing to do with value

Red+delta=red+the three angles in the quadrilateral

We can do this because 360=360

Then we can cancel the red on both sides to prove
delta=the three angles in the quadrilateral

[lean otter]

Why is the red angle even necessary?

Isn't it basically the same with or without?

[hardy lion]

It shows equivalence more clearly

[lean otter]

Sure, but I need to prove why it is equal.

[hardy lion]

I just showed how

[lean otter]

.close

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[hardy lion]

...ok

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[lean otter]

Thanks @hardy lion

[hardy lion]

No problem

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[lean otter]

Wait sorry, does this mean the value of Delta is 180 if Red+delta=red+the three angles

[lean otter]

For that would mean that would mean that both would have the same value so 360/2.

So both are 180.

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[kind dove]

what is asymptotically equal to x^x ?

is there something other than the functions below?

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<@&286206848099549185>

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.close

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[plain hedge]

I am trying to figure out how chain rule works with matrices

or product rule

is it dot product, Hadamard product, or both

[plucky elk]

where's your matrix?

[plain hedge]

I thought for chain rule u use hadamard product

Oh

u want me to right out the actual matrix

[plucky elk]

oh each term is a matrix i missed that

what's y?

is w_0 a matrix too?

[plain hedge]

oh sorry

y is a 1 X 3 matrix

yea w_0 is a 3 X 3 matrix

@plucky elk

[plucky elk]

i think your formula should be somewhere here
https://www.doc.ic.ac.uk/~ahanda/referencepdfs/MatrixCalculus.pdf

Is E a scalar?

$E = \frac{1}{2} (x_3 -y)^T (x_3-y)$ ?

[flat frigate]

riemann

[plain hedge]

kind of lol

this might be more complicated than I thought

let me send u the website I was referencing off of

[plain hedge]

https://sudeepraja.github.io/Neural/

[plucky elk]

yea you left out the || || in the definition of E

[plucky elk]

so that does equal this

[plain hedge]

ok so E is a scalar for total error but the equation I am actually using for backpropagation is

$E = \frac{1}{2} (x_3 -y)^2$

[flat frigate]

jpjthunder

[plucky elk]

how do you square a vector?

you have to define that

[plain hedge]

that is a good question actuallyt

tbh I didnt pay much attension to that part since it was going to become this when derived

$(x_3 -y)$

[flat frigate]

jpjthunder

[plucky elk]

you mean differentiated?

[plain hedge]

yea

[plucky elk]

use this website instead
https://explained.ai/matrix-calculus/

[plain hedge]

@plucky elk I think there are a lot of details that I need to learn to fully understand matrix calculus, but for now I just need to know how chain rule and product rule works

I could be wrong but when u do chain rule u multiply hadamard product and when u do product rule u use dot product

ty for sending me this

[plucky elk]

Derivatives involving scalar expansion
read that section

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[thin briar]

anyone who can help me get rid of 1010
1 0 1 0
1 1 0 0
1 2 4 0
0 2 2 1

[thin briar]

idk what i should do

i just need to get rid of that 1 and im done

[lean otter]

R1+(-1/4)*R2 -> R1

[thin briar]

thanksss

[obsidian oracle]

Actually, C3 -C1 -> C3 is better

But whatever pleases you

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[lean otter]

How would you go about changing the fraction : —(2/x^3) to the form -2x^-3

[nova creek]

What have you tried

[lean otter]

I’ve tried using the index laws

[nova creek]

Such as?

[lean otter]

A^m-n, A^m+n, A^0-1,

[nova creek]

How would you write 1/xⁿ so that the x is not in the denominator?

[lean otter]

Wouldn’t you multiply by x^n?

Or by x rather

[nova creek]

You can't just multiply things

[lean otter]

1/x^n x x^n = 1

[nova creek]

I mean, we can multiply 2 by 2 to get 4, but 2 ≠ 4

So we can't just multiply willy nilly

What does $x^{-n}$ mean?

[flat frigate]

Gamer Dio

[lean otter]

1/x

[nova creek]

Where'd the n go?

[lean otter]

It’s the numerator no?

Nah I’m dumb

1/x^n