help-33

[fallen iris]

oh sorry i was checking anyway i have doubt in complex no.s question

[lofty gyro]

any examples?

[fallen iris]

wait

[lofty gyro]

nice question

[fallen iris]

and

[tribal tree]

See what happens when u square both sides of the equation you start with

Actually sorry

Wait would that work

[lofty gyro]

and think about conjugate

[tribal tree]

Yeah that

Tho finding the conjugate of the right part seems tough

[fallen iris]

do it for me!

[tribal tree]

Can't sorry

[fallen iris]

🥲

[tribal tree]

Usually if I do someone's labor I get a payment in return

But I'll help you come up with your own answer for free

[fallen iris]

i can give 0.1$

[tribal tree]

Tho in this case I might not know how

Nvm I forgot how OP the conjugate operator is

Try multiplying x-iy by it's conjugate

And then the right side by its resultant conjugate

Note that $\overline{z^n} = \overline{z}^n$

[elfin berry]

hiidostuff

[marsh citrus]

@fallen iris Has your question been resolved?

Channel closed

Closed by @fallen iris

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[misty wing]

hello ,does anyone know hoe to do excel ? i did some in elementary school and i dont remember anything and i need it now if yes please text me ill see it probably after uni !

[marsh citrus]

@misty wing Has your question been resolved?

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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]

I still cannot understand what is so called proof of work through his explanation

Can someone elaborate the term

[devout mauve]

any reason you didnt just link the yt vid itself?

anyway, you should elaborate on what you dont understand

[compact crescent]

https://www.youtube.com/watch?v=bBC-nXj3Ng4&ab_channel=3Blue1Brown

[compact crescent]

what is proof of work exactly

I'm so confused, the explanation is so vague

[devout mauve]

there is a hash function. you can put values into it and get "random" values out

its impossible to "predict" what you get out

so if you want to get some value with a special form, then the only option you have is to try over and over again

this is a lot of work

eventually you succeed with getting a special input so that the relevant output has the form you want

and the fact that you even know this input is "proof" that you went through a lot of values to find it

because its very unlikely that you found it quickly

so the fact alone that you have it says that you did a lot of work

[compact crescent]

I do not have to put a lot work to find the number with 30 0s at its beginning. Maybe, I'm a lucky guy, I just throw a value randomly into it and get what I want

So the term "proof of work" is so vague, for people are not necessarily put a lot effort to find a special number.

[devout mauve]

its very unlikely that you got lucky

yes, its only a "proof", not actually a proper proof

but in practice its very much good enough

[compact crescent]

It is so vague!

[devout mauve]

well its tech, not math

what do you expect

[compact crescent]

Like I said earlier a number with more zeroes doesn’t necessarily mean ppl put more work to find the number!

[devout mauve]

it doesnt have to

but with like 99% probability or something it does

[compact crescent]

Then how do I know which ledger has more computational “work”

TF

[devout mauve]

I dont know the actual numbers but you are legit just very very unlikely to be lucky

and this isnt just once, dont forget that

getting lucky once is easy

[compact crescent]

How do people tell which ledger got more computational “work”

[devout mauve]

getting lucky twice or more often? on average you just will have to do a lot of work

[compact crescent]

Let’s say I have 2 numbers which are 00001 and 10101

Which number has more computational work

That’s BS

[devout mauve]

this isnt about 2 numbers

this isnt about a coinflip

this is about billions of numbers

[compact crescent]

How the computer judge which ledger has more computational work

The video did not explain it well

But vague his way through it

[sleek lake]

@compact crescenteach hash counts as 1 hash

it's only about quantity

there's a target difficulty, but it's either met or not met

[compact crescent]

so more transaction in my ledger, the more proof of work it has.

Am I correct

[sleek lake]

yes

and no

like the target that the hash was going for is part of it

[compact crescent]

hello

what is a target?

is that a special term

related to bitcoin

[sleek lake]

it's what people call "tha amount of zeroes" for some reason

[compact crescent]

ohhh

[sleek lake]

it's actually just compared against a number

target = 5
i make hashes that equal 3,4,5,6,7
3 and 4 get counted

now my ledger has 2×5 work

i guess 2 × (1/5)

[compact crescent]

what do you means you make that hashes equal 3,4,5,6,7. Hash is just some 256 bits of 1s and 0s with random order.

[sleek lake]

yeah they are large numbers

[compact crescent]

how can you make them equal 3,4,5,6,7

[sleek lake]

they are equal something

[compact crescent]

but not 3,4,5,6,7. Hash only contains 1 or 0.

[sleek lake]

i mean i convert the binary number to decimal

[compact crescent]

I see

[compact crescent]

how do you know it is 2*5 of work

how could you tell

[sleek lake]

lets say we have 7 bit numbers 0−127

(so the examples are easy to write)

if the target is 10, then each hash has 10/127 chance to be correct

[compact crescent]

what do you mean 0-127? from 0 to 127?

[sleek lake]

yes

then we count work that goes into each hash as 127/10

[compact crescent]

0 to 127 converted to 7 bit numbers that mere contains 1 and 0

is that what you mean

[sleek lake]

yes

[compact crescent]

would you mind explaning the term "target" like why each hash has 10/127 chance to be correct.

[sleek lake]

if the hashes were 2 bit, there would only be 4 difficulty settings

25%, 50%, 75% or 100% chance to meet the target

so like at maximum difficulty
00 counts
01 doesn't, 10 doesn't, 11 doesn't

which means if i show you 6 hashes it "proves" I actually "made" 24

and in my example my target is 10, so like the smallest 10 hashes count

[compact crescent]

That makes no sense, 6 hashes are 6 hashes.

would you mind explaining why the 6 turn out to be 24

[sleek lake]

if i want to find 6 blocks i would expect to make 24 hashes on average

because the chance is 1/4

the hashes have more bits, so the chance can be granularly adjusted

[compact crescent]

I see

[sleek lake]

difficulty is literally hash per block

(except in bitcoin they use units of 2^32 traditionally)

[compact crescent]

I see.

When we mention target in bitcoin, it would be a string made out of 1s and 0s.

[sleek lake]

yes

but it's just a number that the hash must be less than

and that number divided by 2^128 is exactly the chance to do that

or 256

i don't remember

yeah 256

target = 1/difficulty essentially

[compact crescent]

the more zeroes in the beginning of a string imply a harder target difficulty, am I right?

[sleek lake]

so yeah, you literally prove you made half quadrillion hashes by showing just one

yes more zeroes would imply harder difficulty

it's just that zeroes don't matter

it just sounds less boring i guess

so people don;t bounce off the explanation

[compact crescent]

I see it now

So the proof of work of a hash depends on how many zeroes are in the beginning of string

For example, there are two 4 bit numbers which are 0001 and 0011. The former have more proof of work done to it.

[sleek lake]

no

it matters what the target was

what was the chance that the hash is correct

i can;t tell from the hash how hard it was, it was easy if half the range was accepted when it was found

[compact crescent]

does it mean these two numbers have same amount of proof of work

[sleek lake]

yes

unkown amount

literally depends on the date

[compact crescent]

I see

if the target has more bit, then the target difficulty would get higher. And if the bits of a hash matches the target more then it has more proof of work.

[sleek lake]

nah

[compact crescent]

I'm so sad, I'm an idiot sandwish

Then what is proof of work exactly

[sleek lake]

the bits don't matter, just think of decimal nuimbers

and it's hard to write examples with realistic numbers, so i used 0 to 127

and then you think it's not how it works, like it's only an analogy

you show me a hash that says 7, the target was 10, so you hit the target, the size of the target is 10/127 of the range

[compact crescent]

I show you a hash of 7 while the target was 10 and I hit the target?

that is quite singular

[sleek lake]

why thank you

[compact crescent]

the target was 10, I'm supposed to get a hash that encoded the number 10 so I can hit it.

[sleek lake]

10 or less

[compact crescent]

ohhh

[sleek lake]

otherwise the target size doens;t change, it would only have one difficulty setting

you can imagine a literal target with a certain size

i don't care where you hit it

i care that you did

i can estimate how many arrows you had to shoot

[compact crescent]

I see

[sleek lake]

it's not harder to hit a 7 than a 9

but it's harder to hit a small thing than a large thing

so the amount of work is the sum of difficulties

inuitively it should actually estimate what happened, how much work was done by people

but of course luck is involved

[marsh citrus]

@compact crescent Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[marsh citrus]

@buoyant jetty Has your question been resolved?

[buoyant jetty]

dim(W) < dim(S+T)

dim(S+T)=dim(S)+dim(T)-dim(S n T)

S :

1. 4x1 + x2 - x4 = 0
2. x 1 + x3 = 0

x1 = -x3

x2 = x4-4x1 = x4 -4(-x3) = x4 + 4x3

(x1,x2,x3,x4)=(-x3,x4+4x3,x3,x4)
x3(-1,4,1,0)+x4(0,1,0,1)
S = <(-1,4,1,0),(0,1,0,1)>

[tulip idol]

Which book so you follow for lin alg?

[buoyant jetty]

S n T :

a(-1,1,0,0)+b(4,0,1,1)
(x1,x2,x3,x4)=(-a+4b,a,b,b)

4x1+x2-x4 = 0
4(-a+4b)+a-b=0
-4a+16b+a-b=0
15b-3a=0
15b = 3a
5b = a
x1 + x3 = 0
(-a+4b)+b=0
-a+5b=0
5b=a
(-a+4b,a,b,b)=(-5b+4b,5b,b,b)
(-b,5b,b,b)=b(-1,5,1,1)
S n T = <(-1,5,1,1)>

[buoyant jetty]

the bibliography of the course is based on multiple books

[buoyant jetty]

[buoyant jetty]

dim(S+T)=dim(S)+dim(T)-dim(SnT)
dim(SnT)=1
dim(S)=2
dim(T)=2
dim(S+T)=2+2-1 = 3

dim(W) < dim(S+T)

dim(W) < dim(R^3)
dim(W) < 3

we need dim(W) not equal to 3 because then dim(W)=dim(S+T)

and if dim(S+T)=dim(W)
and W ⊂ S + T
then W = S+T

if W intersects with the orthogonal complement of S
and W is contained in S+T
then the orthogonal complement of S intersects with S+T

if W intersects with the orthogonal complement of T
and W is contained in S + T
then the orthogonal complement of T intersects S + T

[marsh citrus]

@buoyant jetty Has your question been resolved?

[compact moon]

Did I do anything wrong? I think I’m missing a term

I’m supposed to use a Pascal’s triangle to expand

But I’m unsure if I’m doing this right

I used to wrong one

That’s why

This can be closed now

Same issue

Am I doing the wrong row on the triangle?

[marsh citrus]

@buoyant jetty Has your question been resolved?

[digital field]

is this question from like last year still

[buoyant jetty]

wdym

[digital field]

how long has this question been unsolved for

[buoyant jetty]

like a lot of time

[digital field]

I remember this question was active before I deleted discord lol

[buoyant jetty]

I am solving it

[digital field]

did you find the basis of S?

[buoyant jetty]

ye

[digital field]

can I have that for free

[buoyant jetty]

S :

1. 4x1 + x2 - x4 = 0
2. x 1 + x3 = 0

x1 = -x3

[digital field]

basis vectors?

[buoyant jetty]

x2 = x4-4x1 = x4 -4(-x3) = x4 + 4x3

(x1,x2,x3,x4)=(-x3,x4+4x3,x3,x4)
x3(-1,4,1,0)+x4(0,1,0,1)
S = <(-1,4,1,0),(0,1,0,1)>

[digital field]

oh don't worry

oh thanks

I thought you didn't have the basis vectors when you sent that first message

[buoyant jetty]

,w rref {{4,1,0,-1,0},{1,0,1,0,0}}

[elfin berry]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[digital field]

I'm just lazy lol

and I know the basis vectors aren't unique

[buoyant jetty]

x1 + x3 = 0
x2 - 4x3 - x4 = 0

i) x1 = -x3

[digital field]

have you found any W yetm

[buoyant jetty]

ii) x2 = 4x3 + x4

[buoyant jetty]

I found one vector from it

like, W is

dim(W) < dim(S+T)

because it cant be dim(W)=dim(S+T)

because W ⊂ S + T

[buoyant jetty]

dim(S+T)=dim(S)+dim(T)-dim(SnT)

dim(S+T)=2+2-dim(SnT)

S n T :

a(-1,1,0,0)+b(4,0,1,1)
(x1,x2,x3,x4)=(-a+4b,a,b,b)

4x1+x2-x4 = 0
4(-a+4b)+a-b=0
-4a+16b+a-b=0
15b-3a=0
15b = 3a
5b = a
x1 + x3 = 0
(-a+4b)+b=0
-a+5b=0
5b=a
(-a+4b,a,b,b)=(-5b+4b,5b,b,b)
(-b,5b,b,b)=b(-1,5,1,1)
S n T = <(-1,5,1,1)>

dim(S+T)=4-1 = 3

since dim(S+T)=3

and W is not S + T

dim(W) < dim(S+T)

dim(W) < 3

[digital field]

• is the union?

or intersection

[buoyant jetty]

well is a little bit more complicated than that

is the span of the union

[digital field]

yeah that's fine

[buoyant jetty]

you know the span is the set of all possible linear combination of the vectors

[digital field]

ya

[buoyant jetty]

so S + T is the span of all the possible linear combination of the basis of S with the union of T

but strictly speaking union of subspaces does not exist because is not closed under addition

so S+T = span{S ∪ T}

[digital field]

yeah that's fine

[buoyant jetty]

anyways, lets assume W is dim 2

like if its dim(W)=1 then there exists a vector

v that intersects (S+T)∩(orthogonal complement of S) ∩ (orthogonal complement of T)

but thats too complicated

its simpler to find a W that is dim(W)=2 that satisfies this

let W = <w1,w2>

w1 ∈ (S+T)∩(orthogonal complement of S)

w2 ∈ (S+T)∩(orthogonal complement of T)

I can find a basis for S+ T

that is just placing the vectors S and the vectors of T as rows in a matrix and eliminating the redundant vector

[buoyant jetty]

.solved

[marsh citrus]

Channel closed

Closed by @buoyant jetty

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[flat bear]

This question is wrong right? The pdf given doesnt integrate to 1? Also i cant find a cdf that works

[cobalt sentinel]

,w int (x+2)/3 from 1 to 4

[elfin berry]

Results provided by WolframAlpha

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

Requested by northsteve

[cobalt sentinel]

oofington

[flat bear]

i knew it!

bastards

tyvm

.close

[marsh citrus]

Channel closed

Closed by @flat bear

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[muted patio]

question about sobolev spaces:
we know that delta dirac function is not in Lp hence not in Wmp and int he other hand we know form the definition of the sobolev space Wmp functions in Lp that have their derivatives in Lp. but for discontinuous functions that their derivative includes delta dirac function thus it iz not in Lp ? i need help to see how to deal with this

[proud ice]

I would ask in #diff-geo-diff-top

[muted patio]

thank you good sir

[marsh citrus]

@muted patio Has your question been resolved?

Channel closed

Closed by @muted patio

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[split vigil]

how did we come with 2^5

[limber hearth]

Det(2B) = 2^5 * det(B) where 5 is the number of column in B

[limber hearth]

For A in M_n(K)

[marsh citrus]

@split vigil Has your question been resolved?

[split vigil]

Ohhh

Is this for any lambda in R

[limber hearth]

In K

So yeah in R

[split vigil]

What is K

[limber hearth]

A set

It can be R

Also C

Its used in proprety

Writing

[split vigil]

So it depends on the context right

[limber hearth]

Its just to make a generalisation

[split vigil]

And what is n? Amount of columns in matrix

[split vigil]

Got it

[limber hearth]

you matrix is a square so either column or row

As you want

[split vigil]

Is the determinant of a nonsquare always zero

[limber hearth]

None

Non square doesn't have a det

[split vigil]

Ow

Thank you so much for your help

.close

[marsh citrus]

Channel closed

Closed by @split vigil

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[abstract cosmos]

How to change y = -x² + 4x - 3 into a vertex form?

[abstract cosmos]

I know the basic but for this one it seems I can't factorize because -x² confused me

-x² + 4x + 4 -3 - 4 = y

[signal pine]

if it helps you can factor out -1

[clear oak]

you can rewrite it as -(x³-4x+3)

[abstract cosmos]

I see

[ripe badge]

X²-4X-4+3+4= -y maybe

Oh nvm

[abstract cosmos]

-(x² - 4x + 4 - 3 - 4) = y
-([x - 2]² - 7) = y
-(x-2)² + 7 = y

Alright thank you

.close

[marsh citrus]

Channel closed

Closed by @abstract cosmos

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[native seal]

So the rule for inverting a circle is Rz (In this case I’m inverting the admittance, admittance is the inversion of impedance, Y = 1/Z, Z=1/Y)

Rz = (Zmax-Zmin)/2, where Zmax = 1/Ymin and Zmin = 1/Ymax. in this case we just read these values off the already drawn in circle. So let’s say Ymin is 0,11 - 0,26i and Ymax is 0,43 - 0,54i. For the calculation of Zmax and Zmin respectively, do I need the value of the Ymin and Ymin arrows, aka, would the answer to Zmax and Zmin be 1/sqrt(a^2 + b^2)?

Rz is the radius of the inverted locus/circle

[native seal]

Yellow here represents Siemens and blue represents ohm, but for the sole purpose of this being essentially maths, just think of the y axis as the imaginary axis and x axis as the real axis

[marsh citrus]

@native seal Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[spring tree]

is 5 the only positive integer $n$ s.t. there exist positive integers $x>y$ satisfying $n=\frac{4xy}{x-y}$?

[elfin berry]

babario

[amber birch]

clearly not, try $x = 3, y = 2$ for example

[elfin berry]

south

[spring tree]

oh right, so any x=y+1, x=y+2, x=y+4 anymore?

also is there a way to generalize all $n$?

[amber birch]

yes but I have no idea if that's exhaustive

[elfin berry]

babario

[spring tree]

7 cant tho

[tulip idol]

Yes there is, but I won't guarantee there's a closed form

But first

!xy

[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.

[spring tree]

find all positive integers as such

[tulip idol]

Do you have a pic or screenshot perhaps?

[spring tree]

there

[tulip idol]

Hmm, start by cross multiplication and try factorising

[spring tree]

uhh like b(4a+n)=na?

[tulip idol]

4ab - na + nb - n² = -n²

[spring tree]

ohh

nvm i still cant get it

@tulip idol ?

[crude vine]

we can consider a and b as any two consecutive +ve integers right

or also a-b=2p or a-b=4p

and we wud get inf values of n?

[spring tree]

p is?

[crude vine]

any +ve integer

like we take 10-8 = 2
12-8 = 4 = 2(2)
14-8=6=2(3)

[tulip idol]

Suppose a = dm, b = dn with (m,n) = 1, it follows that (mn, m - n) = 1 => N = 4dmn/(m - n) => (m - n) | 4d, or 4d = k(m - n), for some positive integer k

=> a = km(m-n)/4, b = kn(m - n)/4 and thus, N = kmn for positive integers k,m,n

From here, can you introduce a step to make sure a, b are integers indeed? As, for now you can see the 1/4 part sticks around

[spring tree]

So for any +ve k,m,n s.t. m-n=0 mod 4 or k=0 mod 4?

Or like u said no closed form?

[tulip idol]

No, GCD(m,n) = 1, so m - n can't be even

[spring tree]

So 4|k?

[tulip idol]

We must have 4|k or k = 4k'

Replace and we have, n = 4k'mn for any positive integers k',m,n

[tulip idol]

Mb. This can indeed be considered a closed form ig.

[spring tree]

Yep thanks so much

.close

[marsh citrus]

Channel closed

Closed by @spring tree

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[brisk saffron]

How do I deal with question c?

[brisk saffron]

This is the progress I got so far

[marsh citrus]

@brisk saffron Has your question been resolved?

[brisk saffron]

<@&286206848099549185>

[summer grove]

im pretty sure there is a physics and/or electrical engineering discord

probably going to get more responses there

[brisk saffron]

this question was in my differential equations course assignment lol
but fair enough i'll try asking there too
thanks

[marsh citrus]

@brisk saffron Has your question been resolved?

[marsh citrus]

@brisk saffron Has your question been resolved?

[marsh citrus]

@brisk saffron Has your question been resolved?

[marsh citrus]

@brisk saffron Has your question been resolved?

Channel closed

Closed by @brisk saffron

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[long cape]

is it too late at this point to find difference of squares for denominator?

i should have done that first to get (x + 4)(x-4) and cancel the (x-4) factor on the numerator?

so there's no going back at this point?

how do you know what order to do things? i started here with the conjugate but it screwed me

[crude vine]

someone asked the same question a while ago

[long cape]

it was probably me lol

i've been trying to understand this question for days now

[crude vine]

u can put x as 4 wherever it doesnt make a difference

[long cape]

but if I put x as 4 i will get 0 at the numerator

[crude vine]

not there

like replace it in such a place so that it doesnt create any problem

[long cape]

i dont understand

[crude vine]

like in the denominator

[long cape]

you can find the limit of just the denom?

[crude vine]

for the 1st term

[long cape]

i didn't know you could do that

i thought you had to find the limit of everything once you start plugging in the limit value

[crude vine]

not always

it comes with experience

but u can still revert back from ther

[long cape]

wait that doesn't make sense tho, lets say i find limit when things are scaled by 1000, now my answer is 1000 times bigger
i shrink that and find the limit again
wouldn't it mess things up if i am just using limit for one term only?

[crude vine]

u can just use L hospital after cancelling the red ones

[long cape]

oh

so L'hospital can save me

if I forgot to find difference of squares to begin with

[crude vine]

it depends

[long cape]

i prefer plug and chug, i don't wanna be second guessing everything

[wary kite]

bruh

[long cape]

lol, wrong advice?

[crude vine]

bruv

[main idol]

they don't cancel when they're still x

[crude vine]

or just take x-4 out common and cancel

[long cape]

https://tenor.com/view/michael-jackson-comendo-picoca-gif-9669437860846841235

here we goooo, let's get to the bottom of this

[tulip idol]

No you so cannot do that

[long cape]

hahaha

[tulip idol]

That's bs

[crude vine]

same shit bro

[long cape]

lol

[wary kite]

no

[crude vine]

[main idol]

did you try plugging x=4 into this?

[tulip idol]

Cancelling just a part of the expression in denominator by plugging whatever is bs

[wary kite]

also why are you expanding the denominator

[crude vine]

he told he expanded bymistake

[wary kite]

the whole point of doing what you did was to eliminate the factor of x-4

[crude vine]

like he didnt think much abt it

[wary kite]

did you?

[crude vine]

huh

[wary kite]

🥱🥱

[tulip idol]

Yes, $\frac{2\cancel{(x-4)}}{\cancel{(x-4)}(x+4)(\sqrt{2x+1}+3)}$

[elfin berry]

Arya

[wary kite]

whattt

$\cancel{69}$

[tulip idol]

After cancelling you can go on with the plugging

[elfin berry]

knief

[crude vine]

fuck it

[wary kite]

that’s useful

[long cape]

that would be ideal first, before conjugate. but my question is, am i screwed if I do conjugate first?

[wary kite]

you can’t do it before conjugate

[tulip idol]

No, that would not be possible as you do not have a (x-4) factor before rationalising

[long cape]

isn't it already tho? check the original

[tulip idol]

So rationalising, then cancelling is the right call

[long cape]

this is difference of squares for den before conjugate

[wary kite]

the 2x-8 came after you multiplied by the conjugate

[long cape]

ya but difference of squares first is what i mean

[wary kite]

what?

[crude vine]

well where was i wrong 😭

[long cape]

before it becomes this mess

[wary kite]

brother

[tulip idol]

Yeah, you need to do only that, just don't multiply conjugate in denominator also @long cape

[long cape]

this is FOIL before difference of squares

[shrewd dove]

you could multiply by conjugate and then do difference of squared but you don't want to expand the demoninator. no FOIL needed

[wary kite]

$\frac{2}{(x+4)(\sqrt{2x+1}+3)}$

[elfin berry]

knief

[wary kite]

what difference of squares are you talking about

we canceled the x-4

[shrewd dove]

the x^2-16 to the (x-4)(x+4)

[long cape]

this difference of squares

[wary kite]

that was canceled already

again, why are you expanding??!

[shrewd dove]

we're talking about before then

[long cape]

no, just listen for a sec

i used conjugate first

multiplied everything by 1, but it screwed my denominator

made it messy

[wary kite]

no it didn’t

it made it nice

[shrewd dove]

you're not following lmao

[wary kite]

because you are supposed to leave it in factored form

[long cape]

ya, you really need to check original @wary kite

[wary kite]

no dingus, you are not following

what they did was utterly useless

[shrewd dove]

yes, whenever you multiply by the conjugate DO NOT FOIL. leave it in factored form

[crude vine]

[wary kite]

and counterproductive

[shrewd dove]

i agree with that

[long cape]

this is the original question

[shrewd dove]

but they're asking a question and you're not answering it

[wary kite]

yes

[long cape]

just gimme a sec to ask it again knief

one minute i will ask it

ready?

before we jump ahead

[shrewd dove]

so essentially you did the right think by multiplying by the conjugate. your mistake was that you foiled the denominator when you should have left it in factored form

[long cape]

yes exactly

[wary kite]

$\frac{(\sqrt{2x+1}-3)(\sqrt{2x+1}+3)}{(x-4)(x+4)(\sqrt{2x+1}+3)} = \frac{2(x-4)}{(x-4)(x+4)(\sqrt{2x+1}+3)}$

then cancel the x-4

[long cape]

you are not listening knief

this is how to solve it yes

[elfin berry]

knief

[long cape]

but i am asking if i ONLY do the multiplication of conjugate first, leaving the den exactly as it is

[wary kite]

i understand exactly what you did but as we tried explaining, what you did was wrong

[long cape]

you are doing both in that step

[shrewd dove]

it doesn't matter which one comes first 🙂

[long cape]

i am trying to tell you that i did conjugate first, i did foil, and i ended up with a mess. is it too late to salvage it at this point?

[shrewd dove]

yes. foiling it messed it up

[wary kite]

$(x^2-16)(\sqrt{2x+1}+3) = (x-4)(x+4)(\sqrt{2x+1}+3)$

[elfin berry]

knief

[wary kite]

it doesn’t matter if you decide to factor it later

[long cape]

dang, so even L'hospital's rule can't save it after foil?

[wary kite]

why lhopitals rule

😭😭

[long cape]

it was suggested, i dunno

[shrewd dove]

i dont see a way it could

[wary kite]

he didn’t know what he was talking about

[long cape]

read above, someone else said it could be salvaged that way

[wary kite]

the whole point of doing it this way was to not do lhopital

[shrewd dove]

i'd argue that's incorrect

[tulip idol]

Yes, erase the second step, do not foil in den, only num, cancel the common factors, voila bon appetite

[main idol]

don't listen to whoever told you to use l'hopital

[long cape]

alright, so FOIL totally screwed me here

[shrewd dove]

yes

[wary kite]

after doing it with the algebra and canceling the x-4 it is no longer 0/0

[long cape]

OK

[wary kite]

🙈🙈

[tulip idol]

[long cape]

so my question here is: how do you know which to do first? start with conjugate, game over
start with difference of squares, you can solve it

[wary kite]

it doesn’t matter what you do first

[crude vine]

i just realised how wrong my answer was 😭 😭 😭

[shrewd dove]

you're going to have to do both either way. multiply by conjugate and then factor the difference of squares, or factor difference of squares then mutliply by the conjugate

[long cape]

so why does FOIL mess it up?

[main idol]

knief told you like 5 times

[long cape]

that's the added step that is not wanted here

[shrewd dove]

because then you lose the difference of squares and the (x-4) which went on to cancel

[long cape]

but even if we FOIL theres no method to UNFOIL?

say the question comes in that messy form

[shrewd dove]

factoring, which would get you right back to where you started

[long cape]

ah, but it's just not too obvious here. no magic method to do it easily

[shrewd dove]

right. foil just makes things messy

[long cape]

i always like to think of math as having equal forward and backward operations, you can always undo or redo, like a computer
but maybe some math doens't work like that?

[wary kite]

brother the entire point of multiplying by the conjugate was to be able to cancel a factor in the numerator and denominator which was leading to the 0/0

[wary kite]

sure it does but why would you ever distribute it just to go back to factored form?

[long cape]

ya i know, i'm just asking if i mess up and use FOIL by accident

[shrewd dove]

then erase it and go back to the point where you didn't use foil

[long cape]

distributing never helps when we are finding limits?

[wary kite]

almost never for these problems

[shrewd dove]

in the denominator, distributing after rationalizing rarely helps

numerator you're usually good (but not always) to distribute

[tulip idol]

Bruh, we distributed in the numerator

[long cape]

sometimes it does?

[long cape]

any reason for that?

[tulip idol]

Similarly, you might need to distribute to rationalise the denom sometimes instead of the num

[shrewd dove]

i hate to make a general statement that may be not true, so I didn't say never. I have not found a situation in which it is a good idea to distribute

[shrewd dove]

so the denominator is usually the problem. we want to keep the factor that causes issues alone so we can find a way to cancel. often in these problems simplifying the numerator allows us to find a factor that will cancel

[long cape]

but like @tulip idol we did distribute in the numerator already

[wary kite]

i mean it’s entirely possible that we have the reverse scenario though, where the radical expression is in the denominator

[shrewd dove]

yes i was talking about the denominator, my bad

[wary kite]

the whole point of distributing in the numerator was to utilize the difference of two squares to get rid of the sqrt

[shrewd dove]

true, which is why i didn't make a general statement in the first place 😭

[wary kite]

so you can’t generalize it to be exclusively forbidden to do so in the numerator/denominator

[long cape]

so it could be 50/50 chance to distribute or cancel in num/den?

[wary kite]

it depends on the problem

there is no chance here..

you don’t just wing it lol

you use it when appropriate

[shrewd dove]

essentially what I think we're getting at is you have to know what you're after. you find a problematic factor, and then simplify the other part (numerator or denominator) to cancel that factor

[long cape]

https://tenor.com/view/i-have-no-idea-what-im-doing-linus-sebastian-linus-tech-tips-i-dont-know-what-i-am-doing-i-am-not-aware-of-what-im-doing-gif-20668620

[shrewd dove]

multiplying by a conjugate is designed to simplify the place where you have the conjugate, so it makes sense to distribute there

distribuiting in the other place often makes it worse

so as knief said, if you had the rational in the denominator, and you multiplied by the conjugate, you would want to distribute the denominator and i would hold off on foiling the numerator

[wary kite]

consider going for a run

[main idol]

it's not a good use of time to try to generalize a method to all problems. you generalize more the more problems you do

[long cape]

OK, I think I just gotta find patterns maybe

I see something that can be factored (difference of squares) I should do it when finding the limit

[main idol]

and there's almost no way you're going to generalize from one problem alone

[crude vine]

[wary kite]

just use lhopital bro

[main idol]

the x-4 cancelling should be a common pattern as you do more problems. so go do more problems avid

[main idol]

if you don't use /s they might take it seriously

[long cape]

https://tenor.com/view/danny-devito-gif-21664201

[crude vine]

broo 😭 i get, my mistake 😭

[smoky siren]

You should really understand what it means for something to be of the form 0/0. You are just multiplying by the conjugate and doing arbitrary algebraic manipulations without a sense for what the end goal is.

[long cape]

True, I am trying things out to cancel variables wherever I can, but FOIL expansion in denominator just makes a mess of things

[shrewd dove]

Following off what hexicle said, i think it's really important in math to understand why you're doing what you're doing so it doesn't lead to issues like this. before FOILing, ask yourself why you're foiling, and what you're hoping to get out of foiling.

[long cape]

Math is interesting where not every operation is reversible
for example integration and derivative, we lose the exact value of whatever C is

[smoky siren]

You are not trying to cancel whatever you can, there is only one thing that you are trying to cancel.

[long cape]

oh

[long cape]

what is that one thing I am trying to cancel called?

[smoky siren]

If you multiply three numbers together and the result is 0, do you agree that one of them is zero?

(and possibly more than that)

[long cape]

yes

So I will know I am finished whenever the den doesn't = 0

otherwise it's DNE and limit doesnt exist

[smoky siren]

so if you have something of the form 0/0 you agree there is some part on the top that is causing the zero, and some part ont he bottom that is causing the zero?

[long cape]

yeah, the top part is fine afaik, it's just the bottom that is the issue?

or both should not be 0? to find limits

[smoky siren]

You are trying to read ahead, and its not helping, you either agree or not

[long cape]

oh sorry

I thought I was following your logic

what do you need me to say here? agree or disagree?

[long cape]

agree

[smoky siren]

Okay, so if you plug in x = 4 in this case, some piece is causing the top to go to zero

and some piece is causing the bottom to go to zero

So your goal is to write it of the form (x-4) multiplied by some junk in the numerator, and (x-4) multiplied by some junk in the denominator

[long cape]

OH

[smoky siren]

because something that looks like (x-4) is causing the 0/0 and once that is gone, it won't go to zero anymore

[long cape]

to cancel whatever is causing that 0

interesting

[smoky siren]

now the denominator in your example

is (x-4)(x+4)*some_junk

and it doesn't matter what some_junk is

[long cape]

so most likely if the limit is 4 i wanna try to find a factor (x-4) to cancel that becoming 0
or if the limit is -2 i wanna find a factor (x+2) to cancel that becoming 0

[smoky siren]

all that matters is that it doesn't go to zero when you plug in x = 4

because your whole goal was to deal with the 0/0

[long cape]

so what you are saying, it's no coincidence that the factor i cancel for this function is (x-4) to find the limit towards 4

[smoky siren]

yes

[long cape]

interesting

I never thought about it that way but it makes sense

[smoky siren]

and that's why distributing on the denominator is a waste of time

[long cape]

ya

[smoky siren]

you have (x-4) times something times something else

and you don't care what those 2 "somethings" are

as long as they are not 0

[long cape]

so I should be checking for both top and bottom of fraction? does numerator equal 0 at lim, does denominator equal 0 at lim

[smoky siren]

I don't really know what you are trying to say

[long cape]

is it more important i cancel bottom of fraction to not equal 0 at limit?
or is it just as important to have top of fraction not equal 0 at limit?

[smoky siren]

there are some number of terms on the top that are taking it to zero, and the same for the bottom

[long cape]

0/something is 0
but something/0 DNE which is a big problem

[smoky siren]

if there are more on top, like (x-4)^2/ (x-4) then the limit is going to go to 0 because you will have canceled all the terms causing the 0 on the denominator

[long cape]

ya

[smoky siren]

but either way, once you no longer have a 0/0 case after canceling, you now have separate problems that teach you how to deal with 0/nonzero, nonzero/0 etc

[long cape]

OK

I will have to review this for limits:
you now have separate problems that teach you how to deal with 0/nonzero, nonzero/0 etc

.close

[marsh citrus]

Channel closed

Closed by @long cape

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[void heart]

Does anyone know what theorem is this (sorry it in my language)

[ancient copper]

what exactly is it saying?

[hazy lion]

is this the intermediate value theorem

[void heart]

function f is continuous and have derivative between I that have real number m,M and m<= f'(x)<=M and all a,b is in I, a<b
We have a inequality ... (Sorry for the bad translation)

[ancient copper]

yeah, thats what i thought too

[ancient copper]

this is intermediate value theorem (IVT)

or something similar to it

yes, its just the inequality version

$f'(c)=\frac{f(b)-f(a)}{b-a}$ for $c\in[a,b]$ for differentiable $f$ on $[a,b]$

[void heart]

I see

[elfin berry]

;(

[ancient copper]

<@&268886789983436800>

[marsh citrus]

@void heart Has your question been resolved?

Channel closed

Closed by @void heart

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[earnest python]

I need help with homework simply because I don't understand and would prefer is someone could help me step by step

[ancient copper]

post problem pls!!!

[earnest python]

23 chicken wings were bought for 25.30$ what was the cost of each of the wings in dollars per wing ( asking me to write problem on the double number line then telling me to use multiplication and division to find the missing value )

[ancient copper]

use dimensional analysis

[earnest python]

What??

[ancient copper]

we are given dollar and wing and we want dollar/wing

so what do u think we are going to do

[earnest python]

I thought divide the 25.30 by 23

[ancient copper]

yeap

[earnest python]

So 1.1 dollar per wing?

[ancient copper]

yeap

[earnest python]

What about the then use multiplication and division part for finding missing value??

[ancient copper]

thats what it was.

[earnest python]

And how do I write this?? I'll, send picture

Nvm

[marsh citrus]

@earnest python Has your question been resolved?

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[austere scroll]

Does anyone have a explanation/video of why in implicit differentiation you have the dy/dx multiplied by your derivative of the y value?

[proud ice]

wdym

[silk garnet]

how come this does not work?

[proud ice]

!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 peak]

Do you mean why differentiating f(y) with respect to x yields f'(y) dy/dx?

[austere scroll]

I think that’s what it is yea

I just didn’t know how to formulate it lol

[silk garnet]

im new, is it one person needing help per channel or osm

[austere scroll]

Ye

[marsh peak]

Then it's by chain rule

[silk garnet]

alr

[proud ice]

yeah. Check #❓how-to-get-help

And welcome to mathcord

[austere scroll]

Can you elaborate a bit?

[ancient copper]

dy/dx=dy/du*du/dx

[marsh peak]

Can you state what the chain rule says?

[ancient copper]

where u can be a function in y

[ancient copper]

so basically, let’s take y^2

2y*y’

our “outer” function is u^2

“inner” would be y

[austere scroll]

d/dx f(g(x))=f’(g(x))*g’(x)

[marsh peak]

Right, replace g(x) with y

[austere scroll]

I’m not familiar with the u symbol

So for example y^2 it would be 2y*dy/dx

[ancient copper]

it’s just another variable

[austere scroll]

Is this utilizing the chain rule?

[ancient copper]

yes

y doesn’t have an exact derivative w.r.t. x so we just notate it y’

[proud ice]

This is misleading

It does

But it is not expressable in just terms of x

[ancient copper]

???

what i mean is that d/dx y=y’

[proud ice]

yeah but how you said it implies that the derivative of y does not exist

[austere scroll]

Ok ummm……. Why is y^2 a composite function that requires an outside and inner function?

[proud ice]

because y is a function of x, and you compose that y function into a function that squares its input

[ancient copper]

“exact derivative” i didn’t say it doesn’t have one

[proud ice]

I said how you worded it implies that.

[proud ice]

you said "y doesn't have an exact derivative w.r.t x"

you make it sound like dy/dx does not exist

[austere scroll]

Okay I think my roots of calculus aren’t super strong so I dont really comprehend it. But dy/dx means how much y changes at a very small movement in change of x?

Or like the slope of y with respect to x?

[proud ice]

yes

[austere scroll]

Ok for y^2 we are imagining it as f(x) because we are trying to find the derivative of the value with respect to x

[austere scroll]

So how does that plug into the chain rule if we use this

A video I’m watching says that the f(x) becomes the squared value and g(x) is the y

[ancient copper]

yeah

[ancient copper]

reference from here

[austere scroll]

So when you take the derivative of y (the inner function) what do you get?

[ancient copper]

y'

like, you cant explicitly take the derivative of y and get an output in terms of x

[marsh citrus]

@austere scroll Has your question been resolved?

[brave spire]

Do you understand what explicit differentiation is?

[marsh citrus]

@austere scroll Has your question been resolved?

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lavish breach]

anyone please example this

[lavish breach]

i'm so confused by the calculation

how a=02c and how it turn into 004c^2 while substituting

<@&286206848099549185>

[true crescent]

(0.2)^2=0.04

[lavish breach]

can you explain fully i'm still confused
as per your answer 0.04 still have ^2

first of all how does a = 0.2

a/c = 0.2

[true crescent]

There is a mistake there, tan Θ should be equal to a/b not b/a.

[true crescent]

I think that’s a typo.

[lavish breach]

ok but what about the equation under the "by the pythagorean thoerem"

[true crescent]

That one is correct.

[lavish breach]

should i change to other book for learning trigo or contince this one

[lavish breach]

ok

[true crescent]

I would recommend you change.

There are better trigonometry books out there.

[lavish breach]

ok

thanks for help

.close

[marsh citrus]

Channel closed

Closed by @lavish breach

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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]

hi

[still temple]

i have problem on proving traingle as similar

[tulip idol]

!original

[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.

[tulip idol]

!xy

[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.

[summer grove]

!da2a

[marsh citrus]

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

@still temple Has your question been resolved?

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[limpid lagoon]

could someone please help me with this?

[tulip idol]

Mock Exam ?

[limpid lagoon]

yes its so gay

genuinely need help w it

@tulip idol can you help me?

[marsh citrus]

@limpid lagoon Has your question been resolved?

[limpid lagoon]

<@&286206848099549185>

[marsh citrus]

@limpid lagoon Has your question been resolved?

[cloud field]

3 is also a factor of 15 btw

[limpid lagoon]

.close

[marsh citrus]

Channel closed

Closed by @limpid lagoon

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[woven condor]

*In interviews with 200 individuals in these workplaces, it was found that 85 suffered from mental illness, 80 suffered from alcohol addiction, and 60 suffered from both.

a) Fill out the table.
b) Calculate the proportions.*

[woven condor]

Suffer from alcohol - 57,5%
Both - 42,5%

But only from mental illness?

[marsh citrus]

@woven condor Has your question been resolved?

[marsh citrus]

@woven condor Has your question been resolved?

[ancient copper]

P(A and B)=P(A)+P(B)-P(A or B)

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[upbeat hound]

$6x^2 + (m-1)x - m = 0$ find m knowing that x is 1/2

[elfin berry]

Simon James B

[upbeat hound]

okay so we have $6(1/2)^2 + (m-1)(1/2) - m = 0$

[elfin berry]

Simon James B

[upbeat hound]

i am doing something wrong somehwere idk where tho

so then we get $6(1/4) + (m-1)/2 -m = 0$ right?

[elfin berry]

Simon James B

[upbeat hound]

then we get $6/4 + (m-1)/2 -m = 0$

[elfin berry]

Simon James B

[upbeat hound]

okay so now $3/2 + (m-1)/2 - 2m/2 = 0$ ?

[elfin berry]

Simon James B

[upbeat hound]

thanks:) ok now $2 -m /2$?

[elfin berry]

Simon James B

[upbeat hound]

3 -1 would give us the 2 and m-2m would be -m?

[merry hill]

It should be (3+m-1-2m)/2 = 0

[elfin berry]

Arya

[upbeat hound]

yes and 3-1 is 2 and m-2m is -m

oh

yea

so 2m = 0

no

2-m = 0

-m = 2
m=2

[merry hill]

Nice

[upbeat hound]

but there is more to it

[merry hill]

If you want to check, you can substitute the m you get to the original equation and check if its right

[tulip idol]

NOooooo

[upbeat hound]

-2

typo

[tulip idol]

-m ≠ 2, only m = 2

Oh

[upbeat hound]

if you multiply - on both sides don't you get -2

[tulip idol]

2 - m = 0 => 2 = m ✓✓✓✓

[upbeat hound]

2 - m = 0.

divide 2 on both sides

2/2 -m = 0/2
-m = 0

divide by - on both

m = -2

oh i see it

bruh

i am so dumb

how am i getting so stuck on a equation that easy😭

can i please get a explanation why is m 2 and not -2 i do not understand this

nevermind i got it

.close

[marsh citrus]

Channel closed

Closed by @upbeat hound

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[serene cloud]

Hi

[serene cloud]

Does anyone know how to solve through Jordan normal forms?

I need to . Write the Jordan normal form of the matrix A, if
A = [[2, 0, - 2, - 1],
[2, 3, - 4, - 2],
[- 1, 1, 1, 1],
[3, - 2, - 2, - 2]]

[marsh citrus]

@serene cloud Has your question been resolved?

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[lethal bridge]

What is exactly is the purpose of this equation? I sort of get how they are equal since both find the integral from -inf to +inf but if you can break down the integral from -inf to a and a to +inf, what’s the purpose of breaking it down even more with a point b?

[summer grove]

you can break up the interval into finitely many segments, and the integral will still be the same

[lethal bridge]

oh is that what its trying to show

ok thanks

[marsh citrus]

@lethal bridge Has your question been resolved?

Channel closed

Closed by @lethal bridge

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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[minor cipher]

HI

[minor cipher]

HELP

brother go to another free channel

Dis ones mine

[coarse cove]

sorry

[minor cipher]

Its ok tro ❤️

[coarse cove]

do u need any help

[minor cipher]

yes

tan(3x + pi/4) = cot(2x)

Ive been ripping my hair out over this How are you supposed to solve this

tan(3x + pi/4) = 1/tan(2x)
tan(3x + pi/4)tan(2x) = 1 assuming tan(2x) is not 0
and then what.

And then i tried

[ancient copper]

have you converted tan(x+pi/4) into something get

[severe owl]

cot x = tan(pi/2 - x)

[minor cipher]

how does that make any sense

[coarse cove]

u should get pie over 20

[minor cipher]

hold on

[minor cipher]

Oh my god this works because x is negative

[ancient copper]

you can convert the cot into a tangent, then just solve the inside equations

[severe owl]

Now this is a single solution to a transcendental

Eqn

[minor cipher]

This so stupid Omg I hate trig so much

OKay thank you

ik how to do the rest

[coarse cove]

good luck

[minor cipher]

.close

[marsh citrus]

Channel closed

Closed by @minor cipher

Use .reopen if this was a mistake.

[minor cipher]

.reopen

[marsh citrus]

✅

[minor cipher]

Nevermind

UHm

How am i supposed to do this

Im trying to use the general solution but i think i fucked up

i got ( (pi * n) + (pi/4) ) / 6.....

Which does not look right at all

[ancient copper]

i’m assuming you did tan(3x+pi/4)=tan(pi/2-2x) then equated the insides

[minor cipher]

yeah

Was that a mistake

[ancient copper]

3x+pi/4=pi/2-2x+npi

[ancient copper]

not at all

[ancient copper]

now try this

[minor cipher]

Wait how did i get division 6

[ancient copper]

idk lol

[minor cipher]

Holddddddd onnnn

[minor cipher]

3x + 2x = pi/2 - pi/4 + npi
5x = pi/4 + npi
x = pi/20 + pi/5 * n

OHHhhhhhHHh wait i just realized what idid wrong

[ancient copper]

yeap

👍

[minor cipher]

Thank U again

I shall throw my maths homeokr at the wall now

.close

[marsh citrus]

Channel closed

Closed by @minor cipher

Use .reopen if this was a mistake.

[ancient copper]

yw!

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[potent reef]

If a sphere is in equilibrium and is not moving in a liquid of two liquids where a liquid of lower density than the other floats on top of the other one and the sphere's m/n volume is in the upper liquid and 1-m/n part in the lower liquid, how can we find it's density in terms of the m/n and the densities of the liquids?

[potent reef]

I understand that we have to equate the weight of the sphere by the resultant force (which is 0) of the two liquids, but I fail to understand how the upper liquid is exerting any buoyant force on the sphere that is beneath it.

[marsh citrus]

@potent reef Has your question been resolved?

[fervent rampart]

it is exerting a buoyant force downward

the buoyant force described by archimedes' law is the net force from the liquid pushing from all directions

[potent reef]

Is the weight of the liquid exerting the buoyant force?

How can it even exert a buoyant force from above?

.close

[marsh citrus]

Channel closed

Closed by @potent reef

Use .reopen if this was a mistake.

[potent reef]

I will come back later.

Thanks for you words and time.

[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.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• 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.

[hot cloud]

yo so for question 3

[hot cloud]

this was the system i put

and then i graphed it. this is the correct graph right? if so, how would i find the vertices

<@&286206848099549185>

pls ping me when u respond

[summer grove]

!15m

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hot cloud]

can u help tho

[summer grove]

i can barely read the question

[hot cloud]

this is the system i did

[hot cloud]

this is my question

<@&286206848099549185>

pls ping when u respond i don’t have notifs for regular mssgs

<@&286206848099549185>

[summer grove]

!15m

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hot cloud]

bro it’s been 15 mins

can u js help tbh

[summer grove]

ping once, did you even read it?

[hot cloud]

yes it hasn’t been answered for 15 mins

that’s why i pinged

lol

maybe u needa read it

[summer grove]

what does this say?

[hot cloud]

pls stop trying to mini mod

[summer grove]

!volunteers

[marsh citrus]

Helpers are just people volunteering their time to help you. Be polite and patient.

@hot cloud Has your question been resolved?

[hot cloud]

no

[glossy flint]

<@&268886789983436800>

[peak fiber]

people might not be inclined to help if you insult them lol

[normal moss]

The helpers are volunteers

[peak fiber]

I think it's fine in this case

[hot cloud]

im sirry im js mad

[hot cloud]

chill bro

mb i didn’t mean to insult no one

[peak fiber]

okay

[hot cloud]

i would appreciate help

[peak fiber]

to find the vertices you would have to solve for when the lines touch, so e.g. solve
7x+4y=168
14x+2y=210
to get one vertex, then
7x+4y=168
14x+5y=252
for another, and so on until you've done all combinations

[peak fiber]

I think this is fine, at a glance

[hot cloud]

so to get a vertex we find the intersection of 2 lines

[marsh citrus]

@hot cloud Has your question been resolved?

[hot cloud]

<@&286206848099549185>

[hot cloud]

☝️

[hot cloud]

i’m kinda confused can someone walk me through this

<@&286206848099549185>

[hot cloud]

i’m wondering how to find the vertices from a system

[willow owl]

didnt they answer you above ?

[hot cloud]

i’m still kinda confused tho tbh

wait

[willow owl]

do you know how to solve systems of equations ?

[hot cloud]

so we solve

7x+4y<=168
14x+2y<=210

7x+4y<=168
14x+5y<=252

14x+2y<=210
14x+5y<=252

so we should have 3 vertices?

wait so

(12,21) (8,28) (13,14)

are these the vertices?

[hot cloud]

<@&286206848099549185> this is the question and for the vertices i got (13,14) (8,28) and 12,21 is that right

[tight furnace]

How many times are you going to use that ping

[hot cloud]

it’s been 15 mins

[tight furnace]

That's certainly a creative interpretation of the ping rules

[hot cloud]

that’s what it said lol

wait 15 mins before using the ping if no response

[willow owl]

for this question i didnt work it out but given what has been told to you by the others then yes these are the systems that you need

[hot cloud]

so we should have 3 vertices correct?

based on the fact we’re solving 3 system questions

[willow owl]

although you are solving 3 systems of inequalities right ?