help-0

[lunar lintel]

for t

this question t = 1/2 for x

t = 1 for y

oh wiat no i used the dervative

lmao

[faint estuary]

Yeah, so on that one, x=0 has two values of t.

[lunar lintel]

for x

i get

[faint estuary]

But only one of those t's gives 3 when substituted into y.

[lunar lintel]

t = sqrt(t)

[faint estuary]

Yes. That equation has two solutions.

An easier way to see the solutions is to factorise on one side

( t - 1 ) * t = 0

[lunar lintel]

for y

i get

(t-1)(t+2)

so im guessing its 1

since both equations have (t-1)

@faint estuary

[faint estuary]

Yep, correct.

You look for where they each have the same t.

And t=1 is correct, there.

So get dy/dx, and do as you did before.

[lone heart]

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[full briar]

Can someone help me with 89 please?

[echo socket]

Notice that integral from 2 to 4 is the same as integral from 0 to 4 - integral from 0 to 2

[edgy crow]

so first u split the integral into 2 to get the integral going from 2 to 4 of f(x) + the integral going from 2 to 4 of g(x) then the integral going from 2 to 4 f(x) is the same as the integral going from 0 to 4 of f(x) minus the integral going from 0 to 2 of f(x) then U can substitute and evaluate from there the same thing goes for the integral of g(x)

[lone heart]

@full briar Has your question been resolved?

[full briar]

Thanks!

[full briar]

Thank you !

[lone heart]

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[tulip summit]

What would my next step be?

[untold wharf]

I think you can just plug in x=0 at this point.

[tulip summit]

Ik the answer is 4/5 but how would i get there

Because wouldn't 4 be multiplied by zero

?

[untold wharf]

Yea. So maybe theres an error before that?

From the last part I thought the answer was lim = 0

[tulip summit]

Do yk what the error was?

Because yeah on the answer key its 4/5

Or wait could i do (x/sinx)(4/5)

[untold wharf]

How did you get sin4x/4x=1?

[tulip summit]

Sinx/x =1

Would i have to replace it with t?

I wasn't sure because the limit is already to zero

[untold wharf]

Gotchya,

Oh so you would have to multiply by 5x/5x

[tulip summit]

Ooooh

[untold wharf]

Then you can simplify 5x/sin5x as 1

[tulip summit]

Ah ok ok

Thank you that works

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[rustic lily]

Why can’t I multiply 24 by 3 to the power of x?

[rustic lily]

I need a mathematical good reason please

[lament glen]

huh

oh I assume you mean like

[mortal trellis]

what do you mean with "can't multiply"

[lament glen]

24 = 2^3 * 3, so 2^3 * 3 * 3^n = 2^3 * 3^{n + 1} = 8 * 3^{n + 1}

so it can't all be written as an integer power of 3

and I just realised without latex this looks so hard to read

[rustic lily]

So the powers have to be the same

[rustic lily]

To multiply

If there is a variable

[rustic lily]

I mean do the bases have to be the same

[lament glen]

ok so assuming you're working with integer exponents yeah you can't write 24 * 3^x as 3^something unless you have the same exponent

[rustic lily]

So why does 24 x Y work?

[lament glen]

because you can multiply any two real numbers

it's just that you can't write 24 * 3^x as an integer power of 3

[rustic lily]

Wdym

[lament glen]

so e.g. 24 * 3^2 is about 3^4.8927

[rustic lily]

… answer this in simple terms pls

I have gaps in basic knowledge

[lament glen]

you can multiply any two numbers

[rustic lily]

How u know 3^x not finna be real

[lament glen]

3^x is gonna be real

as long as x is real

[rustic lily]

So why can’t I times it by 24

[lament glen]

you can

[rustic lily]

But I can’t

It’s “illegal”

[lament glen]

I multiplied it here

also just think like this

why shouldn't you be able to multiply 24 and 3

24 is 24, 3 is 3 to the first power

[rustic lily]

I can

[lament glen]

exactly

it's not illegal

[rustic lily]

U ain’t answering my question

My teacher told me that I’m not able to multiply 24 by 3^x

U saying I can

?

[lament glen]

your teacher likely means this

[rustic lily]

Yes

[lament glen]

you can't combine this 8 here

you need some other things you likely haven't learned

teachers call what you haven't learned yet "illegal" because it quite literally is illegal for you currently

[rustic lily]

Bro just give me a reason as to why I can’t do 24 x 3^x

Yes

Currently

Give a reason

[lament glen]

this is why

the 8 cannot be written as a power of 3

[rustic lily]

So everything has to have the same “base to multiply”

Is that what u saying

[lament glen]

or the same exponent

since $a^n \dot b^n = (ab)^n$

damn the bot ain't working gimme a sec

[rustic lily]

Ok

[lone heart]

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[lucid nova]

why is it wrong to plug in the value of infinity in x

[lucid nova]

if i do that it will become (1-0)^∞=1

[keen pasture]

You can't calculate with infinity like with a real number

[keen pasture]

Lim x goes to infinity (1+1/x)^x converges to e. So (1 + "0")^infinity is oversimplified

[lucid nova]

ok ty

[keen pasture]

Can you try to write it as e^[something]?

[lucid nova]

yes e^(xln((1-1/x)))

[keen pasture]

Yes 🙂

Now how would you proceed further?

[lucid nova]

then apply l'hopitals rule

[keen pasture]

You move the limit to the exponent first (obviously you already did it), but yes

[lucid nova]

yes ok i understand

[keen pasture]

What do you get with L'hôspital?

[lone heart]

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[buoyant radish]

Can I divide both sides by log_8 leaving it =8? or do I have to divide both sides by log_8(8) have the quadratic divided by 8?

[royal plank]

it wouldn't be division. but if the left log includes the entire left term then you can remove it

[buoyant radish]

so they just cancel? leaving the quadratic = 8?

[royal plank]

yes they cancel

oh sorry

since latex bot dont work I have to draw it, wait a sec

i hope that suffices

[buoyant radish]

yes that makes sense, okay cool

thanks

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[errant stone]

we would only use combination and permutation when we're dealing with any thing collection related right?

[errant stone]

if we're trying to find the combination of something we would use that to know how many ways of picking something

[full sable]

what is the difference between a mathematical model and a physical model

[royal plank]

in a sense, but mind you that they are also needed for any combined calculations

aka pick sets of multiple elements with some rule

[errant stone]

???

[royal plank]

they are lost, dont mind

[full sable]

?

[errant stone]

delete that please

this is my channel

[royal plank]

no need

[errant stone]

post your question somewhere else

[royal plank]

just ignore, they are lost

[errant stone]

kk

[errant stone]

wdym

[royal plank]

let there be numbers from 1 to 10 (10 elements) and you have find all posibilities of picking sets of 2 of those

[errant stone]

a bin. Four balls are drawn one at a time and their numbers are recorded. The winnlng combination
consists of the four selected numbers in the order they are selected. How many winning combinations
are there, if: 
(a) each ball is discarded after it is removed? 

[royal plank]

you also need permutation there, despite it not being the primary rule

[errant stone]

for part a cant we use permutation to solve this

[errant stone]

like pairs right?

[royal plank]

yes

[errant stone]

so we assume order matters for your question?

[royal plank]

it could or could not

[royal plank]

so this is your actual question?
how far did you get?

[errant stone]

i solved it

but im trying to think of another way to solve it

[errant stone]

why do we need permutation there then?

if we arent assuming order matters when selecting sets of 2

[royal plank]

if order matters of course

[royal plank]

elaborate, what did you do and why don't you want to do it that way?

[errant stone]

so why did you say it could or could not when stating that example

[royal plank]

it was an erro

r

[errant stone]

the only way we're using permutation to find when we select sets of 2, is if order doesnt matter

yeah

[errant stone]

so i orginally did 25C4

which is wrong

the answer is actually 25 * 24 * 23 * 22

[royal plank]

yes, beause in a) each 'ball' gets discarded, not laid back

so n changes

[errant stone]

so since n changes because we arent replacing the balls back we can assume order matters right?

[royal plank]

yes, it says the order matters

[errant stone]

where?

[royal plank]

consists of the four selected numbers in the order they are selected.

so what you select first is actually the first element

[errant stone]

oh

so another way to solve part a is to use to permutation

[royal plank]

partly?

did you already learn about binomal distribution?

[errant stone]

since the 4 selected balls matters the way their order is selected

[errant stone]

yeah its a type of pdf

[royal plank]

well, the you can solve it fast (with a calculator)

[errant stone]

why did you mention it?

[royal plank]

i think its just faster to type

26!/22! than 26*25*24*23

[errant stone]

how does that have to do with the binomial distribution?

youre just using permutation and simple counting methods

[royal plank]

wait, why ping

where are you stuck on

[errant stone]

im confused on why you mentioned binomial distribution

what application does it have here?

[royal plank]

because thats when you usually learn the factorial rules

n!/(n-a)! etc

if your question is solved just close

[errant stone]

yeah but it has nothing to do with the question at hand

[royal plank]

you wanted to know another way to solve the question

[errant stone]

if order never mattered when selected the four balls my initial answer using combinations would be right

[royal plank]

the shortest way simply is to 26!/22! and multiply etc

[errant stone]

but i didnt read the question well

[royal plank]

since 26 gets reduced by one every time

[errant stone]

you mean 25?

[royal plank]

sure

[errant stone]

yeah using permutation

[royal plank]

so do you have the right answer now?

[errant stone]

yes

just wanna understand

[royal plank]

understand?

[errant stone]

yeah i understamd

a row of 7 chairs, such that at least 2 boys are next to each other?```

for this question

the answer is 7! - (4!*3!)

does that mean the ordering is SSSSDDD?

[rose mica]

ordering should be BGBGBGB

[errant stone]

how?

we want at least 2 boys next to each other

[rose mica]

And in this ordering we have 4! ways to order the boys and 3! for the girls, so 4!*3!

[errant stone]

that wouldnt give us that

[rose mica]

Yes but we’re subtracting what we don’t want

From the set of all possibilities

[errant stone]

ohhhhhhhh

to get what we do want

[rose mica]

yep

[errant stone]

bro wtf

how did i not know that

is there another way to do this?

[rose mica]

you could count all the cases but that’s more work

AOPS has a good section on this in the intro book

[errant stone]

yeah i got it from that

its chapter 1

you think the wall street book is outdated?

@rose mica

[rose mica]

Never read it idk

[errant stone]

u wanna ask in the server for me?

[rose mica]

Sure, which book in specific?

Or is that what it’s called

[errant stone]

heard on the street

[errant stone]

this would be 4! * 3! since there is a total of 4 boys, 3 girls in that combination right?

[rose mica]

Ok I’ll ask and lyk what they say

Yes

[lone heart]

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[coarse frost]

I'm having trouble understanding how to go about this problem

[coarse frost]

Design a Turing machine with input alphabet {!, ?} that accepts a string if and only if the string has the property described.

a. The input string has exactly twice as many !'s as ?'s.

how exactly do I detect how many ? and !s there are

I'm meant to draw a table for this but i feel like maybe itd be better to draw. graph and translate that into a table

[lone heart]

@coarse frost Has your question been resolved?

[lone heart]

@coarse frost Has your question been resolved?

[coarse frost]

<@&286206848099549185> please help I'm very stuck

[coarse frost]

Can you please mention me when you check this channel

So i know when to look back here

[lone heart]

@coarse frost Has your question been resolved?

[coarse frost]

.close

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[calm relic]

how is this wrong?

[lone heart]

@calm relic Has your question been resolved?

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@calm relic Has your question been resolved?

[alpine sable]

for indians and viets it is

[radiant jacinth]

just join lol

[lone heart]

@calm relic Has your question been resolved?

[errant stone]

I can’t I got banned

Tell him to unban me

[rose mica]

It’s not

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[wheat crystal]

probability

uh

so

13 choose 1 for the rank of the card

then multiplied by 4 choose 3 because 3 of a kind

what after

[rose sigil]

count the possibilities for the last 2 cards?

but i'm wondering if 4 of a kind hands should count here or not

[wheat crystal]

?

[rose sigil]

like you have a card type, and 3 of them

need 2 more cards to make a 5 card hand

i'm just going to assume 4 of a kind hands don't count for now as 3 of a kind hands

it will be a little trickier if they do

[wheat crystal]

i think they specifically need

3 of it

and 2 of any others

[rose sigil]

ok sounds good 🙂

[wheat crystal]

So

[wheat crystal]

Uh

Im not sure how to do this

[rose sigil]

sooo there will be 48 cards that aren't of the rank you're looking at

[wheat crystal]

yes

[rose sigil]

so what do ya think? haha

[wheat crystal]

uhh

13 choose 1

• 4 choose 3

dont u just keep going

like * 12 choose next combo

then stop when it gets to 10

because that would be 5 cards

or is it 11

or wait maybe its 12

[rose sigil]

why that?

[wheat crystal]

because we can only use 5cards

[rose sigil]

where's the 12 from?

[wheat crystal]

the ranks

We start with 13

then use 1 rank

so then its 12

[rose sigil]

i would just think of it as 48 other cards to choose from

[wheat crystal]

oh okay

so

13 choose 1

• 4 choose 3

• 48?

Im not sure

[rose sigil]

almost!

[wheat crystal]

times 4 choose 3

[rose sigil]

nooo 😭

[wheat crystal]

Lol

[rose sigil]

think more about the 48

[wheat crystal]

im not sure 😭

there are 48 cards now

and we have already used 3 cards lol

i mean wait

Have we accounted for 1 card of the hands?

or 5

[rose sigil]

(13 choose 1) * (4 choose 3) accounts for all the ways to make three of a kind (out of just 3 cards)

[wheat crystal]

Wait but i thought we have 5

😭

[rose sigil]

ya haha we're not done yet

[wheat crystal]

13 choose 1 means we chose a rank

and then 4 choose 3

means we chose 3 cards from that rank

Honestly im just confused about the problem now

What it says

What does it want?

how many combinations of 5 cards can have 3 of the same rank in it

[rose sigil]

yea

[wheat crystal]

okay so how does the 13 choose 1 * 4 choose 3

what does that even mean

It means we have a rank and got 3 cards from it? but isnt that just 1 of the possible rank hands

and isnt there 12 others

[rose sigil]

there are 13 ranks (that's the 13 choose 1)

and for each of those we could choose 3 of the 4 cards in the rank

to make 3 of a kind

[wheat crystal]

mhm

so we go through all 13 ranks right?

[rose sigil]

not sure wym but maybe

[wheat crystal]

like

We only accounted for 1 of the ranks

with 13 choose 1

[rose sigil]

we accounted for all of them haha

what if we write 13 instead of 13 choose 1?

13 * (4 choose 3)

[wheat crystal]

13 ranks * 4 choose 3

[rose sigil]

yep

[wheat crystal]

Okay so

[wheat crystal]

sorry so far what does this expression mean?

[rose sigil]

the number of ways to make 3 of a kind (with just 3 cards)

[wheat crystal]

so should we have done 4 choose 5? lol

[rose sigil]

why?

[wheat crystal]

oh wait nvm

But we have 5 cards in our hand

[rose sigil]

ya

so now how many ways to fill in the last 2 cards?

if we fix a three of a kind

[wheat crystal]

lol cant it be anything

oh wait

im not sure

[rose sigil]

48 options for the last 2

[wheat crystal]

oh

because

each combination

would have 3 of a kind from 1 of the ranks

so any other 48 cards can be the last 2

what the 4 cards it cant be depends on which combination we're on which we dont know

okay

so what do we do

after 13 choose 1 * 4 choose 3 * 48

[rose sigil]

almosttttt

there are 48 things to pick from for the last 2 cards

[wheat crystal]

2 choose 48?

i mean 48 choose 2

wait

no

idk

[rose sigil]

haha you were right

[wheat crystal]

oh

so 13 choose 1

times 4 choose 3

• 1128

since 48 choose 2 = 1128

so 13 x 4 x 1128

[rose sigil]

yep 🙂

[wheat crystal]

Oh okayy tysm

Do you have any tips for probability problems?

Because I am always so stumped by them and theres so many 😔

i like dont even know how to start lol

[rose sigil]

oh idk they're hard T_T

[wheat crystal]

ah

[rose sigil]

just a lot of practice helps, idk about any specific tips

[wheat crystal]

ohh okay

ty

.close

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[rose sigil]

np ^-^

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[olive cosmos]

Is this typo or what

[lone heart]

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[barren portal]

.close

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[vivid tiger]

if $f$ is a strictly increasing function on $A\subseteq \bR$, how do you show that $f$ is continuous if $f(A)$ is open or closed?

[ocean seal]

CoolShot

[vague coral]

there is a theorem that says that if f is a monotonic function on A, then it's continuous if and only if f(A) is an interval

[lone heart]

@vivid tiger Has your question been resolved?

[rose sigil]

idt that "theorem" is right

[noble sinew]

Thats only if A is an interval

[rose sigil]

constant functions are still counterexamples?

[noble sinew]

A single point is an interval?

[rose sigil]

eh ok lol

[pseudo ice]

Apparently

[noble sinew]

Yes I know?

[vague coral]

yea true

[lone heart]

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[tardy mango]

What method can you use for this integral? I tried substituting u = ln(x), but it doesn’t really work out

[alpine sable]

take lnx common

then you'll get integral f(x)f'(x)dx

[tardy mango]

With f(x) = ln (x)…?

I feel like i’m missing something obvious

[nimble basin]

You can expand the initial formula to be

$$\int [ln^2(x) + ln(x)] • \frac{1}{x^2}$$

[ocean seal]

hahahxrvy

[nimble basin]

And rather than just substituting u as just ln(x)

you could try substituting

$$u = ln^2(x) + ln(x)$$

[ocean seal]

hahahxrvy

[nimble basin]

@tardy mango

[tardy mango]

Ohh okay thanks, I’ll give it a try

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[cosmic roost]

hi

[cosmic roost]

i need help solving a problem

$sin(theta)=2*cos (theta/2)*sin (theta/2)$

[rose sigil]

you might wanna put that in plain text and/or add some parentheses haha

[cosmic roost]

oops

am sorry

[ocean seal]

M.WALI

[cosmic roost]

idk if this is better

[rose sigil]

yep that's better 🙂

[tight forum]

anyone can help me ?

[wanton tusk]

$\sinθ=(\frac{2cos\frac{θ}{2}}{2sin\frac{θ}{2}})$

[ocean seal]

swaggofishballs

[wanton tusk]

idk why I added parentheses pls ignore hehe

but is that it?

[rose sigil]

idt the 2 in the denominator should be there (actually idt there should be a denominator at all lol)

[cosmic roost]

no..

[wanton tusk]

yeah seemed weird

[cosmic roost]

i will send a picture

[wanton tusk]

okie

[cosmic roost]

am not sure how i was supposed to write that

but anyways

am completely lost in this

[wanton tusk]

oh okie

so basically

you can start from LHS

[fresh crane]

.close

[wanton tusk]

do you know addition formula?

[fresh crane]

what is COS and SIN

[cosmic roost]

yes

[wanton tusk]

so you can express the left side with $sin(\frac{x}{2} + \frac{x}{2})$

[ocean seal]

swaggofishballs

[wanton tusk]

and use addition formula

[cosmic roost]

oh

I didnt think about that

[wanton tusk]

it comes w practice :)

[cosmic roost]

but is it okay to use it in this question?

[wanton tusk]

yes

[cosmic roost]

$sin(\frac{x}{2})*cos(\frac{x}{2})+cos(\frac{x}{2})*sin(\frac{x}{2})$

[ocean seal]

M.WALI

[cosmic roost]

oh wait

yep

its all coming together

is it the same with the b part of the question?

[wanton tusk]

nope

for the part b

it’s a hence question

so you need to somehow use your answer in part a eventually

you in part a we found out that $sinθ= 2sin(\frac{θ}{2})cos(\frac{θ}{2})$

[ocean seal]

swaggofishballs

[wanton tusk]

and in part b we can see that we have 4cos(θ/2)cos(θ/4)sin(θ/4)

we can simplify 4cos(θ/4)sin(θ/4) to 2sin(θ/2)

then use part a to show that it’s = sinθ :)

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[dusty robin]

How do I find roughly the MH's per a GFLOP using this graph or an array I also have.

[limpid turret]

you trying to find MH per GFLOP or GFLOP per MH?

[dusty robin]

GFLOP per MH will work too

both would be good?

[limpid turret]

Using the graph, I would just kinda inspect the tips of the line and measure the slope.

Lines looks pretty tight so should be reliable.

[dusty robin]

I created the graph so I have the array too

first section is MH and second is GFLOP

[limpid turret]

If you have an array of the data, minimizing squares is your most reliable way to get best fit line

https://www.numpyninja.com/post/finding-line-of-best-fit-using-least-squares-method#:~:text=E %3D Y – Y`&text=This method%2C the method of,the best fitting line's equation.

[dusty robin]

do I do this to every data value?

E = Y – Y

[limpid turret]

It's a little more complicated than that.

It's usually a process you automate

Looks like you're using excel

[dusty robin]

can I automate this?

I am using Excel

or google sheets

I'm using Google Sheets

[limpid turret]

Excel can give you a best fit line of data points

The slope will give gflop/mh

[dusty robin]

let me try that

[limpid turret]

worst case, google is your friend

[dusty robin]

I'm not very good with Excel

[limpid turret]

same

I only know it can be done :p

[dusty robin]

Is this equation here relevant?

[limpid turret]

Neither seem to be relevant

But I have to go to bed, so best of luck

[dusty robin]

ok thanks

Anyone know how?

Trying to find GFLOP per MH

hey I think I found the answer

I just summed up both columns and divided them and got 127.451434323 MH per GFLOP

1 GFLOP = 127MH

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[feral valve]

can someone please help me with this optimization question. I literally do not understand where to start this problem

[feral valve]

its oke if you cant solve it all, I just want to know where to start ;-;

[lone heart]

@feral valve Has your question been resolved?

[feral valve]

Lol, guess no one could figure it out. Nw, I got it now lol

[alpine sable]

hi

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[alpine sable]

is this the correct way of completing the square method

[alpine sable]

the answer was right in this case

[alpine sable]

yeah

[proven rune]

yee

[alpine sable]

how do we actually get (x - 3)^2

it came out from x ^ 2 - 6 x

[alpine sable]

(a-b)^2 is a^2 - 2ab + b^2

we have a^2 and -2ab, so we get b^2, so we add and subtract that

oh that’s being used here

completing the square method

alright, thank you.

.close the channel

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[sturdy harness]

How should i solve the tangent of y=sqrt(x+1) at x=3

[sturdy harness]

I have tried to solve through the definition of derviation and i got 1/4

which is the k value in the y=kx+m equation

[vale wigeon]

indeed

[sturdy harness]

then i put the x value in the curve eqution sqrt(x+1) so it became sqrt(3+1) which would be become 2

so the curve would solve to: 2=1/4*x + m

m = 2-x/4

[vale wigeon]

no

plug in both coordinates of your point, not just the y-coordinate as you did

2 = 1/4 * 3 + m

[torpid hare]

Hi excuse me can anyone help me ?

[sturdy harness]

put your question in the avaiable channels

[sturdy harness]

Oh sorry, i actually did that in my soution, i rememberd wrongly

[vale wigeon]

@torpid hare read #❓how-to-get-help for instructions on how to open your own channel

[torpid hare]

Thank you

[sturdy harness]

turns out wrong

idk where i did wrong

[gray isle]

whos saying its wrong

[sturdy harness]

x - 4y = -5
The solution manual says

rewritten maybe?

[gray isle]

did the question ask for the equation in a certain form?

[sturdy harness]

Nope

[gray isle]

the equations are equivalent

[sturdy harness]

Oh, thank you

i have other question that i got wrong, can i ask them here in the same channel?

[gray isle]

sure

[sturdy harness]

y=x^2 at x0

down there i wrote what the manual solution says

[gray isle]

it looks like you messed up substituting your point again

$\underbrace{y}{x_0^2} = \underbrace{k}{2x_0}\underbrace{\red{x}}_{\red{x_0}} + m$

[ocean seal]

ℝamonov

[sturdy harness]

solved correctly now, thank you

[sturdy harness]

.close

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[frail merlin]

I have a project that's due to tomorrow about real life applications of limits, our teacher doesn't want it to be a long professional project, she just wants a simple cool real life application of limits, any ideas?

[wind cloak]

This is kind of cheating but you can use the first principles of a derivative to calculate the rate of expansion of a gas cloud in space 🧠

[lone heart]

@frail merlin Has your question been resolved?

[frail merlin]

why is this cheating?

I'm trying to find "cool" real life applications of limits, is this not allowed for some reason?

i don't know why i can't even find normal real life applications of limits

[steel olive]

calculation profit and loss margins of a company?

or magnetic field

of a magnet

[frail merlin]

yeah but how can i expand on such an application tho

[frail merlin]

that's cool lemme try and do some research

[wind cloak]

Because technically you're using a derivative for that but using the limit definition of the derivative

[frail merlin]

the problem is for some reason i'm not able to find any satisfactory applications online

I think i'm gonna give up

thanks for the help guys

.close

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[south wasp]

Can someone tell me how to check if 2 planes in the xyz *
axis are perpendicular

[south wasp]

?

[royal plank]

how are the planes given?
if they are in some form of $v1+s\times v2+t\times v3$ with v being vectors you can get the cross product of v2 and v3 and compare those

[ocean seal]

Jigglyproff

[south wasp]

They are not with vectors

[royal plank]

so... how are they?>

[south wasp]

5

Like this

[royal plank]

not sure if there is a faster way, but re-writing that function as vectors and then doing the above will work

[south wasp]

Dont mind the language

I have no idea how to right this in vector coordinates

[royal plank]

taking a closer look, with those numbers you could do it imagining how the planes actually look

[south wasp]

I can’t imagine 2 planes

For real

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@sage apex Has your question been resolved?

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[lone heart]

@dusky shuttle Has your question been resolved?

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@dusky shuttle Has your question been resolved?

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[calm belfry]

Doing a review for a test tomorrow but don’t know how to use characteristic equation

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[dim acorn]

help

i have figured out half of it

i just want to know the lenght of straight line

[echo socket]

Aren't these 12 figures all equal?

[dim acorn]

yes

[echo socket]

Oh the perimeter, nvm

[dim acorn]

exactly

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[empty plover]

simplify cos(2arccosx), sin(2arcosx), tan(2arcsinx)

[alpine sable]

Double angle formulas I believe

[empty plover]

Ah

i think youre right

thanks

.close

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✅

[empty plover]

i mean this question

solve for t

[alpine sable]

Oh uh

[empty plover]

t=tanu right?

for some u

in ]-pi/2,pi/2[

[alpine sable]

The insides of the arcsin reminds me of something, I don't remember, let me search

[empty plover]

1+t^2 becomes 1/cosu^2

[alpine sable]

I am not sure how u can particularly solve for x here..

Well t, whatever

Oh wait dude @empty plover

[empty plover]

yeah

[alpine sable]

Dude u transform that arctan(t) to that?

[empty plover]

i think i solved it

i just replace t with tan u

because t is in R

so i can do that

and find the condition on u

i am stuck on this now

f continuous from [0,1] to R and ive got to show its equal to 0 in at least n points

[tribal oxide]

Whar did u get?

I also got a solution, i want to check

[empty plover]

i did not get :/ i didnt fully solve it

[tribal oxide]

Bruh

[empty plover]

ill do it hold on

ive been on my bed for 3 hours and you just managedd to get me up

[tribal oxide]

Okay desmos confirms my answer😈

[empty plover]

its for all t right ? i hope so ;/

[tribal oxide]

Yea i dont think theres any domain restrictions on t

[empty plover]

.

Yeeey

[tribal oxide]

Yea this is what i did essentially, if you do this, you should get it

[empty plover]

yeah i end upp with u=u

[empty plover]

i mean this

[tribal oxide]

u=u wdym?

[empty plover]

if i replace t with tan u

in the equations

[tribal oxide]

Oh there was a t there, i thought it was 1 lol

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[tawny patio]

Hi, I'm studying number theory and I'm a little confused with a specific portion of a proof, if anyone can help me. The initial question is Prove that if 5|n then 5|Fn, Fn is the nth fibonacci num. In the given proof, some algebra is done to get Fn = 5F(n-4)+3F(n-5), which they use to say Fn ≡ F(n-4)(mod 5). This throws me off a little, I'm not sure what steps they took to get the congruency relation out of that equation. I am also confused about one other congruency relation, if it's ok to ask two questions in one go. I see a sequence that goes a≡1 mod 7, b≡1 mod 7, therefore 6ab ≡ 6 ≡ -1 mod 7, a!=b.. Can someone explain the last portion of that to me?

[mortal trellis]

5 = 0 mod 5

so 5*anything = 0 mod 5

uhh wait what

I thought it said something else

[tawny patio]

is there any more information I can post that would help

<@&286206848099549185>

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[final orchid]

need help w the sequence

[lone heart]

@tawny patio Has your question been resolved?

[hard patio]

#❓how-to-get-help

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@tawny patio Has your question been resolved?

[lone heart]

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[alpine sable]

ok so

[alpine sable]

if I have the position vectors:
A = (-2, 4, 7), B = (-1, 3, 8), C = (1, 1, 4), D = (-1, 3, 2)

I want to calculate the area of the parallelogram ABCD using the dot product

[ocean seal]

ZED_118

ZED_118

[alpine sable]

this isn't working...

the method is correct, right?

<@&286206848099549185>

could someone try the question out?

i keep getting 6 * sqrt(2)

the answer is 9 * sqrt(2)

AHHHHHHHHHHHHHHHHHHHHHH

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@alpine sable Has your question been resolved?

[grave carbon]

I see, I think you want to form 4 triangles. Do you have to use the dot product? I could see a cross product being helpful here.

[alpine sable]

4?

[alpine sable]

I'm just finding the area of one triangle here using the (1/2)absinx formula

Then multiplying by 2

[alpine sable]

Also I'm supposed to use dot product here

[grave carbon]

OK, you will need to set up a system of equations here. One property of the dot product is it is 0 when the vectors are orthogonal.

You want to find the vector orthogonal to CA that passes through B. That will be the height of the triangle.

[alpine sable]

Yeah that's a valid method too ig but why does mine not work...?

[grave carbon]

You are assuming that AB and CD are parallel with that method I think

Sorry it is given that it is a parallelogram in the problem.

One sec let me try it myself.

[alpine sable]

👍

[grave carbon]

Also, if this is a parallelogram you can do base times height and get the area.

This isn't really a parallelogram it's more of a quadrilateral with 2 parallel sides.

[alpine sable]

The question says it's a parallelogram

[alpine sable]

Yeah I know but I'm just annoyed by how I can't get my method to work when it should

Anyway I'm going to bed now ill have a look at this again tomorrow

If you want to try it out you can and I'll see tomorrow

[grave carbon]

This site is pretty nice for plotting in 3D, but as you can see AD and CB aren't parallel.

Ok, no problem.

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[granite mortar]

need help with this, all the previous questions had one side with one variable but now both have two variables and now i'm stumped

[gray isle]

set up a system of equations

and solve that system using elimination/substitution

[granite mortar]

i'm trying to do it the blunt way by filling in random numbers and working my way up until i eventually get a whole number, which might be a while.

[frozen tree]

no dont do that

since we know that these two triangles are the same

we can set z+y+22 = 20y-10z

[granite mortar]

yes, but where do I go from there? I might be able to crack it if I'm pushed in the right direction.

[wary stream]

and solve that system using elimination/substitution

[granite mortar]

Solved, thanks guys!

.close

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[mental swift]

Watching this video on finding tangent horizontal and vertical lines for r=e^theta, uhh and I don't understand why when writing the coordinates the input becomes positive when raised by e, could anyone explain?

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[alpine sable]

.open

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[small dome]

Any help is appreciated.

[lone heart]

@small dome Has your question been resolved?

[small dome]

No worries if it’s not resolved tonight though I’m in no rush so help others who need it more.

[lone heart]

@small dome Has your question been resolved?

[last ether]

What's the significance of:

• the first derivative?
• the second derivative?

[small dome]

To get you the critical point and concavity point I believe?

[lone heart]

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[prime pendant]

Hi, I'm doing system of equations

[prime pendant]

I'm confused about this one because not only there's one less term on top, but the y^2 don't line up if I want to cancel

[tall topaz]

You can do first equation - second

And wdym by don’t line up

[merry depot]

move all the constants to the right of the =
just rearrange the terms so hey line up

[prime pendant]

umm could you give a visual

like this?

[merry depot]

y^2 + 4x^2 is the same as 4x^2 + y^2

if x^2 + y^2 - 5 = 0, then x^2+ y^2 = 5

[prime pendant]

wat

could you give steps

[merry depot]

add 5 to both sides

[merry depot]

there are no steps. addition is commutative, 3 + 2 = 2 + 3
you can just rearrange the terms

[prime pendant]

rearrange the bottom equation by adding 5

like this?

[merry depot]

yes

[prime pendant]

what's next

the y still doesn't line up to cancel

<@&286206848099549185>

very helpful

.close

[lone heart]

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[dim trout]

How do we find this W?

With absolute value and all

[lone heart]

@dim trout Has your question been resolved?

[dim trout]

Anyone knows?

[tacit arch]

Do you know the definition of absolute value?

[dim trout]

Ya i think

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[prime pendant]

Hello would like to know the steps for this

[vale wigeon]

write 81 as a power of three

[prime pendant]

the radical is new to me

[vale wigeon]

do you mean "i've never seen radicals before in my life" or "i don't know how to handle the radical in this specific context"

[prime pendant]

in log equations

I'm new to log

just know the basic converting

like this?

[alpine sable]

Either you erased the Root's degree or you erased the 3's exponent

[prime pendant]

I keep that 4?

oh wait

[alpine sable]

Either way, write 4 for the exponent of 3 and rewrite the root of that in exponent form

[prime pendant]

fixed

I think

[obsidian turret]

ya

[prime pendant]

hmm there's no equals sign so I'm guessing it's = X ?

[alpine sable]

$log_3 3^4 \sqrt[4]{3} \to 3^4 \sqrt[4]{3} = 3^x$

[ocean seal]

♡LexQa♡

[prime pendant]

where did that 3 on the right came from?

3^x?

[vale wigeon]

the definition of log_a(b) is "a raised to what power gives b?"

[prime pendant]

some rule because of 3 to the power of 3

lol it's almost 4am, my brain is fried

Here's the problem but done on the board, not sure what's going on though

[elfin tendon]

4 + 1/4 = 9/4?

[prime pendant]

a tutor wrote that and didn't explain anything lol

I found this on my professor notes

doesn't really explain the small steps

.close

[lone heart]

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[dim trout]

How did we get this "note that..." part

[soft quarry]

Mclaurin series of sinx - x

[dim trout]

Why do we need that

[naive valley]

this argument seems dubious

take x = y in $$\frac{|x|^3|y|^{2/3}}{x^4 + y^2}$$

[ocean seal]

Bungo

[naive valley]

you get $$\frac{|x|^{11/3}}{x^4 + x^2}$$

[ocean seal]

Bungo

[naive valley]

which blows up to infinity as $x \to 0$

[ocean seal]

Bungo

[dim trout]

But the answer is 0?

[naive valley]

oh wait scratch that

it doesn't blow up to infinity, the x^2 dominates for small x

carry on 😁

[dim trout]

Also what happened to ln

And to sin lol

[naive valley]

they used the inequality 0 < ln(1+x) <= x, for positive x

[soft quarry]

sinx = x - (x^3)/6 + (x^5)/120 - …

So sinx - x = -(x^3)/6 + (x^5)/120 - …

So sinx - x >= -(x^3)/6

[lone heart]

@dim trout Has your question been resolved?

[dim trout]

Isnt there an easier way i can solve this?

What about here, can i do x=y?

And get lim y->0 (y) which is 0?

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[empty plover]

show that C is connected

[lone heart]

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@empty plover Has your question been resolved?

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[ornate heath]

**Good Morning ... Evening ... or whenever you are ❤️ **

Today in class i just saw this

[ornate heath]

I didn't really understand what it refers to

But it's related with : Polynomes - roots - ...

saw this too

[worn fox]

It's a complex number, that equals 1 when you raise it to the power of n

[ornate heath]

can u give a yt vid link that explains that more

[worn fox]

https://youtu.be/-F-FHNTz4qk

[ornate heath]

Alright

that's a great favor ❤️

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[burnt cargo]

I need help

[lone heart]

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[ornate heath]

Hi there ..
i closed the channel by wrong after they answer my question ... so they are not going to see it

[ornate heath]

1- f(x) + g(x) = 2x^2 + 3x + 1

2- f(x) + g(x) = 2x^2 - 3x - 1

3- 4x ^ 4

4 and 5 the use* previous results ...

[vale wigeon]

@ornate heath do not give out answers

[green folio]

Fr bro gave out straight answers

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[shell urchin]

For 32 do I say that as X increases, y decreases?

[gilded vessel]

show us the graph

[shell urchin]

I don’t have it, the graph is what they are wanting me to plot. My question is more do I just describe what the graph looks like for 32 after I plot the points?

[gilded vessel]

not exactly but its easier to see the relationship between the two with a graph

[shell urchin]

Okay, so instead of describing what it looks like I would describe the relationship I see after graphing it?

[gilded vessel]

yeah

[shell urchin]

Okay, Ty

[gilded vessel]

because you can describe the relationship more precisely depending on the shape of the graph

[shell urchin]

Ah okay, tyvm

.close

[lone heart]

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[steady basin]

for part c, would u need to use a substitution?

[vale wigeon]

define "need"

[alpine sable]

require (something) because it is essential or very important rather than just desirable.

[lone heart]

@steady basin Has your question been resolved?

[steady basin]

so im assuming theres another way