help-0

[manic quail]

Ahh, okay. Then just add them and don't multiply by x.

[obtuse charm]

So

May you explain it to me please? What does it mean by give him 2 equations to solve it

[manic quail]

@obtuse charm I am not sure about that, but you could do: $\tan{42}=\frac{x}{23}$ or $cotan{42}=\frac{23}{x}$ xD

[ocean seal]

veryhappyperson

[obtuse charm]

Thanks im guess I’ll try it out

[elder viper]

How many functions f : [12] -> [4] that are increasing?

[manic quail]

f (circle) g means f(g(x))

[alpine sable]

I need help with problem 1 got it? I need the answers and work.

[manic quail]

-3(x²+5)-1

=-3x²-16

But the question asks for the value of the function at 0

so you get -16

It is the same process.

[alpine sable]

I need the answer and work for practice problem 5.

[manic quail]

If you calculate your function correctly, you put 1 into it.

-1+4

-1+4=3

But I don't know if you calculated your function correctly though.

[alpine sable]

can anyone tell what decimal of a unit the top part is PS. Imagine the top part is reaches the full rop of the square

[night jay]

hey i posted my problem here 2 hours ago so uhh what do i do

[glass lichen]

repost it if you havent figured it out

still abiding the rules though

[night jay]

im not sure what its asking for

im using this channel right now...

[alpine sable]

Don't multipost @potent dust

or well at least delete this one

cause you've posted in #help-1

[green marsh]

r we done here

[alpine sable]

no becuase no one answered him

and i dont know the answer

[green marsh]

ok well i have a question in #help-6

[night jay]

<@&286206848099549185> (reposting question cuz its all the way up there)

not sure what its asking for

we can just do 1 question cuz then itll basically tell me what to do for the other ones

[thorn kindle]

give the interval of p values over which the statement is true

in Z and R

[night jay]

wait so its which integers would work

and for R its which real numbers would work

and then just graphing which ones would work

[thorn kindle]

yep

[night jay]

thanks

[alpine sable]

hii, I have a question. How to prove that:

if A, B are sets such as they aren't empty and A-B = ∅, then A ⊂ B

[oak chasm]

@alpine sable Use the definition of set difference and subset.

[tight locust]

∅ ?

[oak chasm]

@tight locust Null (empty) set.

[alpine sable]

I tried by contradiction:

Suppose: A isn't in B and A-B = ∅

for any a in A, a isn't in B
it means that a is in A-B and A-B is ∅

a is ∅, but a can't be null, because ∅ is in B, so A must be in B

but I'm not sure if it has been well done

[oak chasm]

@trail pier Try a dead channel. This one is in use.

[ocean seal]

Chai T. Rex

[oak chasm]

Sorry, the first part is wrong.

[ocean seal]

Chai T. Rex

[oak chasm]

That means there are no elements in A that aren't in B.

[ocean seal]

Chai T. Rex

[oak chasm]

@alpine sable Does that make sense?

Sort of a direct proof rather than a proof by contradiction.

[alpine sable]

It does, but I have even thought about that, but I was trying to show directly that at end it shows a is in B somehow 🤔

thanks though :D

[oak chasm]

No problem.

[alpine sable]

@oak chasm what do you think of it?

[oak chasm]

You can't prove that for any a in A, a can't be in B.

[alpine sable]

wait

[oak chasm]

Or isn't.

[alpine sable]

I corrected again xD

I mean I'm supposing firstly that A isn't in B and A-B = ∅

[oak chasm]

A is a set, do you mean a?

Or do you mean subset rather than not in?

"A isn't in B" means that A isn't an element of B.

[alpine sable]

oh

isn't a subset I mean

[oak chasm]

OK, let's see.

[alpine sable]

and I imagine that every a in A isn't in B (since they don't share any number in common by A isn't a subset of B)

and then I claim:

a is in A and a isn't in B

that leads that a is in A-B

[oak chasm]

Why do you claim that every a in A isn't in B?

[alpine sable]

because I'm trying to prove by contradiction

[oak chasm]

A not being a subset means that one or more elements of A is not in B, not that all elements of A aren't in B.

[alpine sable]

and the contradiction lies on there

[oak chasm]

What are you contradicting?

You already have the contradictory assumption on the first line.

It's that A isn't a subset of B.

But your second line doesn't follow from that.

A isn't a subset of B doesn't mean that for any a in A, a isn't in B.

It means that there's at least one element of A that isn't in B.

At least one isn't the same as all.

[alpine sable]

hmmm

Can I send a pic?

[oak chasm]

Sure.

[alpine sable]

ok wait

ooh forget it

I got it now

[fleet steeple]

For this problem for T2 and T3 how do they know the amount of combinations for their sequences

also why is it 8*4 combinations and not 8 times 4 factorial for the first combination

[oak chasm]

@fleet steeple Try a dead channel like #help-8, please. This one I think is in use.

[fleet steeple]

O I thought you guys were finished

[oak chasm]

I'm not sure exactly 🙂

@alpine sable Did you finish the proof or do you want to continue?

[alpine sable]

I finished it

[oak chasm]

Oh, OK 🙂

[alpine sable]

I'll just write it down and then send here to confirm

[oak chasm]

@fleet steeple There are four possible positions for the square and four possible starting points in each square, and two possible directions (clockwise, CCW).

@alpine sable OK.

[fleet steeple]

ohhhhhhh

so for a square

the number of solutions will always be clockwise and counterclockwise if the requirement is that it has to be adjacnet

[oak chasm]

Yes, that's right. Apparently, diagonally adjacent doesn't count.

Has to be left, right, up, or down.

[fleet steeple]

What about for T2

is there a way to find the number of combinations quickly

without counting

[alpine sable]

hmm

It is wrong 😅

[ocean seal]

Chai T. Rex

[oak chasm]

You should just skip the step with that in it.

Otherwise b can be the empty set.

[ocean seal]

Chai T. Rex

[tight locust]

were you not explicitly given that A,B are not empty

[oak chasm]

Which is a good outcome for when b is assumed to exist.

[alpine sable]

the assumption itself is wrong, cause if we choose:

A = {1, 2} and B = {3, 4}, we have A-B = ∅ and A still isn't subset of B

[oak chasm]

@alpine sable No, what's A - B in that case?

[alpine sable]

this

[oak chasm]

Remember, this isn't intersection.

No, with A = {1, 2} and B = {3, 4}, A - B = {1, 2} - {3, 4}, which is what?

[alpine sable]

oooh true

[oak chasm]

Your proof is almost good.

It's getting there.

[alpine sable]

{1, 2}

[oak chasm]

Yes, that's right.

[alpine sable]

good, good

[tight locust]

-2, -2

[oak chasm]

No, it's not a vector.

[alpine sable]

the only case which it works I can think of is that A = B and then A is surely contained in B

[tight locust]

what's the real difference between a set and a vector? they're both lists of numbers

[alpine sable]

the operation is quite different

and they use sort pairs

(as far as I remember if that is the right name xD)

this

[oak chasm]

@alpine sable Unless you mean $\subsetneq$ by $\subset$, $\subset$ allows for the two sets to be equal.

[ocean seal]

Chai T. Rex

[alpine sable]

I mean the last one

[oak chasm]

@honest echo This channel is taken, try #help-1.

[honest echo]

oh wait i misread that as PM not AM

my bad¨

[alpine sable]

I've taken it from this book:

Given A, B subsets of E, prove that A is subset of B if, and only if, A intersection of Cb = null

and:

[oak chasm]

Does that mean the complement of B?

[alpine sable]

exactly

oh wait

no

hmm

in relation to E and B

[oak chasm]

So, this seems to be the same problem as before.

[rich ether]

can someone help me on setting up a problem,
There is a dome that is placed on top of a building with a height of 50 feet.
The dome has a circumference of 1 - a x^2 - a y^2
a = ?
What is the surface area of the dome?

[alpine sable]

Yeah, but I solved just one side:

x is in A ∩ Cb
x is in A and x is in Cb

x is in A and (x is in A and x isn't in B)

since A is subset of B, then:

x is in A and (x is in B and x isn't in B)

x is in A and x is in ∅

x is in ∅, then A ∩ Cb is subset of ∅

since every set has ∅ in itself, ∅ is subset of A ∩ Cb

A ∩ Cb = ∅

[oak chasm]

No, A is in B means the set A is an element of B, which you probably don't mean.

"x is in B and x isn't in B" reduces to "false", not "x is in empty set".

[alpine sable]

@oak chasm Whatever it is x, x isn't null

For example, we have ... and also ...?

x =/= x 🤔

[oak chasm]

Yeah, all the xs where x doesn't equal itself.

[alpine sable]

it is false tho

[oak chasm]

So, no xs, so empty set.

Right, for nothing is it true.

So there are no elements where it's true, so empty set.

[alpine sable]

as well as {x | x in A and x not in A}, or?

[oak chasm]

Yes, those are a negation of each other.

You have P and not P, which is false.

[alpine sable]

:D

[oak chasm]

"P and not P" is false for all P.

[paper minnow]

Hi, some quick latex help, does anyone know how to put two sets of error bars on scatter plots with pgfplots? So vertical and horizontal error bars (I'm writing up a lab report so I need to put in error bars for all of my measurements).

[alpine sable]

im bad at telling if a triangle is scaled if it dosent have any numbers on it can someone please help?

[magic patio]

if it doesn't say its scaled, then assume its not to scale

[gaunt magnet]

https://tenor.com/view/cat-leaving-leave-oops-bye-gif-17519616

[alpine sable]

its asking me is it scaled or not

pls someone help me

its so late

if my teacher sees how late i sent it its unlikley shell even bother grading it

pleaaaaaaaaase

[paper minnow]

is this about similar triangles?

[paper minnow]

Yep, so this is about similarity

[opal wing]

So imagine it rotated in the position of one of the triangles

[alpine sable]

ok

[opal wing]

If it looks like the other triangle and you have no numbers, then it is probably scaled

Since you are needing to explain, I would redraw the smaller one and make the argument

I can tell you from imaging it rotated in my head to the correct orientation that it is scaled

[paper minnow]

basically if you can rotate it, flip it, and scale it so they look the same, then they are scaled versions of each other

[opal wing]

L->K is the same with P->O

L->M is same as N->O

[alpine sable]

yep its scaled

[paper minnow]

Bingo, you got it

[alpine sable]

thanks

now im confident i wont fail math

hopefully

[alpine sable]

Answer for number 7?

[thorn kindle]

Idk

You try DRAWING IT?

Crazy idea ik

[remote shard]

so for c

the answer is this

i was wondering what the rule was called

when you do dy/dt to dy/d0 * d0/dt

[alpine sable]

Thanks.

[upper ember]

its the chain rule

[rustic tapir]

from here how would you find the exact circular function value?

[alpine sable]

i dont understand this

[thorn kindle]

1 million total coffees with a base value of 1.5

50k of which have a free coffee offer (+1.5)

2 of which have a new TV (+1200)

1 snowmobile (+15k)

1 car (+35k)

find the total value (multiply the price of each item by how many there are)

then divide by 1 million

1mil*1.5 + 50k*1.5 + 2*1200 + 1*15k + 1*35k

divide that by 1 million

[zenith oyster]

I had a question. "If f and g are increasing on the interval I, then fg is not necessarily increasing on I". Is there an example of 2 functions increasing but their products not increasing cause I don't understand

[spare fern]

f(x)=-e^(-x)
And g(x)=-e^(-x)

Or f(x)=x-2
g(x)=x+2

[zenith oyster]

oh okay thanks

[grand portal]

So I have 8 weekly Interest Rates of 0%,-12.50%,-.35%,4.6%,-6.24%, -8.40%, 8.9%, +7.4%, How would I turn these into an effective annual interest rate? Would I average them out and have N=52? or is there a better way

[warped prism]

whats the context

not sure how you are going from 8 weekly rates to annual

[rotund talon]

What would this be in matrix form?

how would I put it in matrix for would be a better question I guess

[acoustic shadow]

Take the help of augmented matrix to solve such questions faster

You can generate 4 cases of D=0, D1=0,D2=0,D3=0

[jagged imp]

Augmented matrix or matrix equation?

[rotund talon]

which ever that means

[jagged imp]

Matrix equation it is

A is a coefficient matrix, it contains the coefficients of x terms in the first column, y in the second column and z in the third. X is the solution vector/matrix [x,y,z] and B is [21,5,-1]

[rotund talon]

Its really that simple. . . .

:')

[jagged imp]

So im too lazy to fill in A but it looks something like this

If you dont know what goes in the coefficient matrix or dont know where something came from just say

[rotund talon]

I think I got it

thanks

[timber geyser]

can someone help with this please

im a little confused about the process

[oak chasm]

@timber geyser They meet if the x and y values can be the same.

The y values being the same is handled by setting y = y and substituting one of them on the left and one on the right.

[ocean seal]

Chai T. Rex

[oak chasm]

Then you can find the xs for which the ys are the same by solving for x.

[timber geyser]

but wudnt that giv the coordinates for the points where they meet?

[desert burrow]

Anyone know calc, areas between curves

[timber geyser]

@desert burrow can u plz get a free channel im using this one

[desert burrow]

oh idk how this server works

[timber geyser]

thats fine, you just have to find a free channel to ask a question

[ocean seal]

Chai T. Rex

Chai T. Rex

[timber geyser]

i cant find x bcs i still dont have the value for m

so its not a complete quadratic

[oak chasm]

m is just a number. Use the quadratic formula or another method to solve for x. The solution will have m in it.

It's OK to have a solution with m in it.

[timber geyser]

ehhh, im not sure how to do that. on the mark scheme they use the discriminant

is there a way using that?

[oak chasm]

Sure. First, get the quadratic equal to zero.

[timber geyser]

done

[oak chasm]

OK, what do you have?

[timber geyser]

2x^2-mx+8 = 0

[oak chasm]

Almost.

[timber geyser]

the discriminant is m^2-64

[oak chasm]

Small error.

[timber geyser]

-mx**

[oak chasm]

Right, your correction is good.

[green marsh]

hi

oh srry

[oak chasm]

Have you seen the quadratic formula?

[timber geyser]

yes

[oak chasm]

OK, use it to find x.

a = 2, b = -m, c = 8.

[timber geyser]

(m +/- sqrt (m^2-64)) / 4

[oak chasm]

Almost.

Remember the part before the plus/minus is -b.

[timber geyser]

yep sorry

[oak chasm]

Good.

Now, how can we ruin this?

Can we make it divide by zero somehow?

[timber geyser]

u cud ruin it by making sqrt(0) ?

make m = 8 ?

[oak chasm]

Well, what's sqrt(0)?

[timber geyser]

m^2-64 where m = 8

[oak chasm]

Sure, but what number is sqrt(0) simplified?

[timber geyser]

0

[oak chasm]

Right, so that doesn't ruin it.

We still have a real number result.

[ocean seal]

Chai T. Rex

[oak chasm]

How can we make the square root fail?

[timber geyser]

ohh, negative number

[oak chasm]

Right!

What values of m give a negative value in the square root?

[timber geyser]

so any number bigger than 8

[oak chasm]

Well, let's try 9.

[ocean seal]

Chai T. Rex

[oak chasm]

10, rather.

[timber geyser]

hm, that doesnt ruin it

[oak chasm]

Nope.

[timber geyser]

ah wait, sorry, yes any number smaller than 8

sorry, im very tired atm

[oak chasm]

It's no problem.

[timber geyser]

so any number smaller than 8

[ocean seal]

Chai T. Rex

[oak chasm]

We're getting there.

[timber geyser]

or bigger than -8?

[oak chasm]

Well, change that or to an and.

[timber geyser]

yup so -8<m<8

[oak chasm]

Yes, that's right.

That ruins it, so there are no solutions for those ms.

[timber geyser]

THANKYOU!!!

[oak chasm]

You're welcome.

[cinder sundial]

Anyone knows what’s the “method” called

[languid verge]

I noticed a symmetry in statistics, and I wanted to make sure it's generically correct

$$ \CDF_X(t) = 1-\CDF_Y(n-1) $$
Where $X$ is distributed according to the sum of $n$ IID inter-arrival time distributions, and $Y$ is a counting distribution over the interval $[0,t]$

[ocean seal]

derp_commander

[languid verge]

So in this particular case, $$ Y \sim \operatorname{Poisson}(\lambda t) $$ and therefore $$ X \sim \operatorname{Erlang}(n,\lambda) $$

[ocean seal]

derp_commander

[languid verge]

Is this true of all renewal processes?

[shell widget]

@languid verge I think you should try the stats discord or #probability-statistics

[languid verge]

It is a question though...

[shell widget]

no just saying

maybe someone will respond to you there more quick

[languid verge]

If it's not addressed by morning then perhaps I will.

[shell widget]

ok

[languid verge]

But do you at least get what I'm asking?

[shell widget]

no 😛 not an expert on stats

[cinder sundial]

Anyone knows what’s the “method” called

<@&286206848099549185>

[alpine sable]

R u American ?

[surreal meteor]

Where do I go from here?

I know it's supposted to be cos(x)

But I don't see what I do from here

[brazen shuttle]

hi

can we for this switch the places of members

is

[surreal meteor]

What you doin @brazen shuttle

Channel occupied 😂

get yo own room 😂

[jagged imp]

Compound angle formula to expand sin(x_0+h)

And youll need to use lim as x approaches 0 of sinx/x=1 at some point

[surreal meteor]

You're going to have to explain what that means 😮

Oh like this?

[jagged imp]

This look familiar?

And sorry for the wait

Combined with $\lim_{x\to 0} \frac{\sin(x)}{x}=1$ that should be enough to do it

a

[ocean seal]

111211211111221312211

[jagged imp]

If you didnt know either of those beforehand thats kinda weird from your teacher

[surreal meteor]

Oh!

Yep!

I got it

[jagged imp]

Awesome

[surreal meteor]

Thanks! 😄

[cinder sundial]

ayyyyyyyyyyy

it said 2x:3y:4z=1:2:3

then x:y:z=?

first question is, i already wrote the answer down below

cuz if 2 3 4 those three numbers all "retreat"(i cant find an better word) one step

it will be come 1:2:3

or in another theory(?) 2 * 1 = 2/ 3 * 2 * 6/ 4 * 3 = 12

its clearly to see that i have no idea how to find the x:y:z

[alpine sable]

I think it's $1/2:2/3:3/4$

[ocean seal]

txkyo

[cinder sundial]

emm

how you find out the answer

the process, and the way you reachin that answer

[alpine sable]

If 2x is 1 then X is 1/2

[cinder sundial]

wait

wait

[alpine sable]

And same for y and z

[cinder sundial]

2x is 1

[alpine sable]

But not sure if that's right

[cinder sundial]

wdym

oh

yes

sorry im trippin

2x is 1

its acceptable, its makes sense

[alpine sable]

Ye I think that's how u do it

[cinder sundial]

yes, and now i cant remember

u know what, i will left it what it is

lets focus on the next

[alpine sable]

Can't remember what

[cinder sundial]

what i did to reached that answer

nevermind, that question is already solved in IMO

lets focus on the next one

i wonder

first i know its exponent

but, its the exponent for 3x or x

[alpine sable]

For x

[cinder sundial]

so its still 3

3x ^2 is 3

cuz x=1

[alpine sable]

U need question 1 for question 2

[cinder sundial]

yes

[alpine sable]

It's not 1:2:3

[cinder sundial]

what

wut

damnnnnnnnnnnn

[alpine sable]

What u wrote in bottom left corner is wrong

[cinder sundial]

no way

[alpine sable]

Ye lol

Look

$2x:3y:4z = 1:2:3$ right?

[ocean seal]

txkyo

[cinder sundial]

yes

thats what it said

[alpine sable]

So that means $2x=1$ right?

[ocean seal]

txkyo

[cinder sundial]

yes

wait

wdym

2x=1 is impossible

like 2=1

or u means the way those numbers arranged

[alpine sable]

x represents an unknown

[cinder sundial]

2 3 4 is 1 2 3

[alpine sable]

Ye the way it's arranged tells us that's $2x=1 , 3y=2 ,4z=3$

[cinder sundial]

no way

[alpine sable]

Wait

It wrote weong

Wait

[ocean seal]

txkyo

[cinder sundial]

i cant take those numbers seriously, when it looks like 2x=3y or sth

[alpine sable]

There look

[cinder sundial]

so its

1:2:3

the answer

1:2:3

i have another idea

lets take a look

[alpine sable]

No

[cinder sundial]

wdym

lets take a look on the idea

[alpine sable]

$2x:3y:4z = 1:2:3$ right?

[ocean seal]

txkyo

[alpine sable]

So that means 2x = 1

Meaning X =1/2

It also means 3y = 2 meaning y=2/3

[cinder sundial]

no way

[alpine sable]

And that 4z=3 meaning z=3/4

[cinder sundial]

i cant

cant understand

lets take a look on my idea

i did noticed

the question did looks similar to this one

[alpine sable]

Ye it is

[cinder sundial]

like 2a:4b:3c=4:12:15

then 2 * 2:4* 3

its eazy right

can we do the same thing to that one which are currently confusin me

it said 2x:3y:4z=1:2:3

then x:y:z=?

like we apply the method to this one

[alpine sable]

Ok so let's do the same

[cinder sundial]

lets gooooooooooooo

[alpine sable]

2 * ? = 1

What's ?

[cinder sundial]

its impossible

[alpine sable]

It's possible

[cinder sundial]

for me

emmm

like how 2 can ever became 1

oh

half of 2 is 1

so its 1/2 in fraction

[alpine sable]

can i ask something please?

[cinder sundial]

@alpine sable can 3 became 2

i cant figure it out, without calculator

in math old im super young

[noble sinew]

3*x=2 then isolate x

[cinder sundial]

i did understand what he said

x=-1

am i right

[noble sinew]

its multiplied by 3

so do opposite of multiply

[cinder sundial]

that one i cannot understand. opposite of multiply

what it means

divide

[noble sinew]

yes

so divide both sides

[cinder sundial]

2/3

[noble sinew]

yep

[cinder sundial]

im too smart for this

how u know it should be divide

what i do is subtract both side by 3

[noble sinew]

you can't subtract that

[cinder sundial]

thats why i got -1 as my answer earlier

[noble sinew]

imagine if x=2 then we had 3*2

you cant subtract 3 on both sides then

if you did you would be saying 6-3=2

(because 3*2=6)

[cinder sundial]

4z is 3/4 right

[noble sinew]

if you have something multiplied by x and you want to isolate x

you always divide

[cinder sundial]

yes, i get what you said now

@noble sinew youre lifesaver

before i do sth advance, i need someone to check the answer for me

[vale wigeon]

(1/2):(2/3):(3/4) is the correct ratio but i think they want you to rewrite it so that the numbers in the ratio are integers

[rigid kettle]

Help

[cinder sundial]

rewrite?

wdym

[rigid kettle]

Is this server got age limit?

Bcoz i got kicked from the other server

[vale wigeon]

no, this server has no age limit, but if you're under 13 you're too young to be on discord in the first place

[rigid kettle]

Oh

Ok

[cinder sundial]

how i write (1/2):(2/3):(3/4) to integers

[vale wigeon]

multiply all by 12

6:8:9

( 12 = LCM(2,3,4) )

[cinder sundial]

yes

why are you so smart

so everytime if i got sth in fraction like 1/2, and i wanna make it to integer

i just get the lcm and multiply em then jot the answer down

no

i live in taiwan

i dont have to use vpn to get access

i think that sentence was wrong "i dont have to use vpn to get access"

grammarly

[alpine sable]

Yes u missed a apostrophe

But it's okay we're here to help

Correct Ur grammar

[cinder sundial]

its diffrent from what i means

[alpine sable]

I think this mine sentence was grammatically wrong too

I'm from korea

North 😡

[cinder sundial]

ohhh

[alpine sable]

Samesies

How did u escape

Yes he is

I love him too

I don't like the south

I like his eyes

[green marsh]

i need help

[cinder sundial]

post it

[green marsh]

in #help-4

ive been asking for hours

no one came :c

[alpine sable]

I know secrets about north korea government but can't tell u

[green marsh]

oki

[alpine sable]

Because u work for them

[green marsh]

how did this person get there

im stuck on that part

the highlighted

yes sir

[alpine sable]

What is it binomial expansion

[green marsh]

its an example problem

[oak chasm]

@green marsh Factoring.

[green marsh]

i can show you the one im doing but

how did he factor

[gray isle]

identify common factor in your terms

[ocean seal]

Chai T. Rex

[wicked ember]

factorisation s

factor out (x+9)^10

[gray isle]

the same way you factorise
ab + ac to a(b+c)

[wicked ember]

yep

[oak chasm]

@green marsh See how they're out on the left now and the rest is inside the parentheses on the right?

[wicked ember]

actualyl

[green marsh]

This is my work

[wicked ember]

factor (x+9)^10(x+4)^3

[green marsh]

this is my problem so far

im up to tht point but

the highlighted

but idk how to factor it

[gray isle]

you're doing calculus

[green marsh]

or simplify

yes

[gray isle]

you should know how to factor by this stage

[green marsh]

c: hi rami

[wicked ember]

you need to solve for that = 0

[green marsh]

i do

i done it before

[wicked ember]

bring the 4(x+8)⁵ to the other side

5(x+4)⁴ = -4(x+8)⁵

[green marsh]

oh

[gray isle]

step 1 when factorisation: determine if all your terms have a common factor.
if so, factor that out

[wicked ember]

wait

idk

[green marsh]

i think spoon is wrong

bc i have to get it = to 0

[gray isle]

also the work on that page is a complete mess

i have nfi what's going on there

[green marsh]

mess as in wrong?

oh

i did the derivative

of the original problem

[noble sinew]

if you don't wanna factor you can also do u=(x+8)^5 and v=(x+4)^4 then use product rule

[green marsh]

but thts how i got the highlighted part

[gray isle]

factorisation comes after differentiating

the stuff on that page is complete trash

[wicked ember]

sorry I’m confused from the working

[gray isle]

do it again, clearly stating what rules you're applying

[wicked ember]

idk what’s happening with the working

idk if that’s the right answer in fact

[green marsh]

idk whts going on

[wicked ember]

idk

[green marsh]

i need help with the highlighted part

im a visual learner

[gray isle]

the stuff on the page is complete trash

i don't even know how you're getting the highlighted part

and is definitely wrong if that's supposed to be the derivative of (x+8)^5(x+4)^4

[green marsh]

it was supposed to be that

[gray isle]

seeing as you started with a degree 9 polynomial
and you highlighted a polynomial with a degree of 5

[green marsh]

wht do i do

i thought my first step

is to find the derivative

of the problem first

[gray isle]

yes. that is indeed the first step

[green marsh]

is that right

yes

you said its wrong..

[gray isle]

yes. i mean what i said

[green marsh]

ill redo it

and show you my work

[gray isle]

finding the derivative is the correct approach
but that's meaningless if you don't do it properly

do it again, clearly stating what rules you're applying
this should include stuff like the product rule, power rule, (and chain rule)

[green marsh]

Here is wht I did

<@&286206848099549185>

[gray isle]

that's still trash

[green marsh]

Why

Where did I go wrong

[gray isle]

you're not applying product rule properly

[surreal idol]

couldn't you just apply product rule in combination with chain rule?

[green marsh]

Oh .. am I doing the power rule or something how am I not

[gray isle]

nor is it clear how
5u^4(1) turned into 5(1)^4

[green marsh]

😦 I wrote it word for word wht I’m doing

I did the derivative of the first part times the seconds part

Then I did the same thing for the second part

And added those two answers together

[gray isle]

nor is it clear how
4u^3(1) turned into 4(1)^3

[green marsh]

Can you show me

Not in words

[surreal idol]

i don't think that's how product rule works

[green marsh]

Wht you are talking about

I’ve been doing that for so many problems prior

And it was fine :/

[coral pagoda]

Yea, there is currently a misunderstanding of the product rule

[gray isle]

what's happening there

[green marsh]

Ok so

[surreal idol]

have you only used it for degree 1?

as in no exponent

[green marsh]

You have to do the derivative of x+8

And I got 1

You times that by the derivative of u^5

And plug 1 into u

[gray isle]

why are you plugigng 1 into u?

[surreal idol]

yeah that only works for degree 1

[green marsh]

I don’t understand

[coral pagoda]

That's not what's going on here huile. We should let them finish

[green marsh]

Can someone write down wht it’s supposed to look like

I don’t understand how I’m wrong

[surreal idol]

right mb

[coral pagoda]

Okay, for $f(x)=(x+8)^5$ and $g(x)=(x+4)^4$, you have successfully found $f'(x)$ and $g'(x)$

[ocean seal]

dackid

[coral pagoda]

However, the product rule is not $(f(x)g(x))'=f'(x)+g'(x)$

[ocean seal]

dackid

[coral pagoda]

The plugging 1 thing was wrong, but you do have the right derivative. So that is good

[green marsh]

$5\left(x+8\right)^4\left(x+4\right)^4+4\left(x+4\right)^3\left(x+8\right)^5$

[ocean seal]

lard

[green marsh]

this is the proper answer

[coral pagoda]

That looks better

[gray isle]

the chain rule here is somewhat simple (du/dx = 1, dv/dx = 1) so i'm gonna skip writing those parts
differentiating the u^5 gets you 5u^4
that part is ok
the issue is you set u (which is supposed to be x+8) to 1 for some strange reason
you even mentioned that you should multiply the derivative of (x+8)^5 = u^5 by (x+4)^4 which would've been fine

[coral pagoda]

I'm not even sure what the 1 thing was because they just replaced it with x+5 and x+4 at the end anyways 🤷

[green marsh]

how do i factor this tho

[gray isle]

and for that part would be
5u^4(x+4)^4 or 5(x+8)^4(x+4)^4
similar idea for the other part

[cursive thicket]

Find the value of x,if Sin[Sin^1(x/5)+Cos^(3/5)]=1

[gray isle]

identify common factors

[cursive thicket]

Anyone know how to solve this

[green marsh]

there are none

im here wielder

[gray isle]

the same way you factorise
ab + ac to a(b+c)

are you implying these terms don't have any common factors?
a^2 + a^3

[green marsh]

yes

oh

no

a^2

[gray isle]

ok

now what about if i added some more stuff like

$a^2b^5 + a^3b^4$

[ocean seal]

ℝamonov

[green marsh]

a^2 and b^4

idk how this relates to my problem

[gray isle]

and would you be able to factor a^2b^4 out from these terms here?

[green marsh]

yes

but how do i factor my problem

[gray isle]

now what if i added even more stuff like
$$a^2b^5cdef + a^3b^4ghij$$

[ocean seal]

ℝamonov

[gray isle]

would you still be able to identify the common factor and factor that out

[green marsh]

This is not related to my blem

my problem doesnt look like that at all

[gray isle]

yes, it is directly related

[green marsh]

i dont see the correlation

[gray isle]

when factorising

the first thing to look for

is

are there any common factors between all your terms

if yes, factor that out

[green marsh]

$\left(x+8\right)^4\left(x+4\right)^3\left(9x+52\right)$

[ocean seal]

lard

[gray isle]

now that wasn't so hard was it

[green marsh]

Well its duckduckgo

[gray isle]

and also related

[green marsh]

but i dont understand it

[gray isle]

which part?

[green marsh]

everything

where we left off

[gray isle]

be more specific

[green marsh]

where we left off ...

the factoring

i got the answer off duck duck go, i didnt solve the factored answer

[gray isle]

now what if i added even more stuff like
$$a^2b^5cdef + a^3b^4ghij$$
would you still be able to identify the common factor and factor that out

[ocean seal]

ℝamonov

[green marsh]

but iyes

yes

[gray isle]

and that's pretty much exactly what you have atm

if you insist, you could consider
a = x+4
b = x+8

$5\red{(x+8)}^4\blue{(x+4)}^4+4\red{(x+8)}^5\blue{(x+4)}^3$

[ocean seal]

ℝamonov

[green marsh]

o

im on a new problem now

[turbid harbor]

this question is driving me up the wall, how is the substitution even helpful?? I would have done t=1+tant so i could easily integrate 1/t... big wat, any geniuses here wanna unravel it for my cute smooth brain

skips with tears in my eyes

[wicked ember]

i am not sure, however i think that this is for the purpose of "reversing" the integral

if you look closely the bounds are 0 to pi/4

so this is sort of integrating backwards

maybe add both versions? im not sure

[turbid harbor]

smooth brain intensifies

[wicked ember]

no dont add them im stupid

[turbid harbor]

i think i might see it, possibly trigonometric identity in the 1+tant

[wicked ember]

yeah probably

i guess tan(pi/4 - u) = cot(pi/4 + u)

but im not sure how that is useful

[turbid harbor]

wolfram is like no heck U hahaha

[sand jetty]

Aw

[gray isle]

looks like you can apply the compound angle identity here

[wicked ember]

oh my god

so we get

[turbid harbor]

tan(A+B)=TanA+TanB/1-tanAtanB?

[gray isle]

and due to how definite integrals work, you can change your dummy variable back to t
after doing the recommended sub

[wicked ember]

(sqrt(2)/2+tanu)/(1+sqrt(2)/2*tanu)

or something

[turbid harbor]

ill give it a spin thank Ram!

and spoon ;3

[wicked ember]

np

[alpine sable]

hi does anyone know how to solve this?

[alpine sable]

My friend told my answer was wrong whats wrong here tho? dont mind the shitty handwriting cuz when i write fast i write dogshit when i take my time i write sorta good

[shell widget]

, rotate

[shell widget]

@alpine sable try writing it in matrix form? apply row operations?

@alpine sable is it $(\sqrt{2x} + c)^2$ or $(\sqrt{2}x + c)^2$

[ocean seal]

Sup?

[alpine sable]

It is that

both the options are same :/

[shell widget]

uh no

look carefully

second is x * sqrt(2)

not sqrt( 2 * x)

[alpine sable]

Second oneee

Idk

Thats the question

[shell widget]

okay

$(\sqrt{2} x + c)^{2} = (\sqrt{2} x)^2 + 2 \sqrt{2} xc + c^2 = 2x^2 + 2 \sqrt{2} xc + c^2$

[ocean seal]

Sup?

[shell widget]

now do it

[alpine sable]

OHHH TYYY yeahhh i forgottt that x gets an square too along the number along side it tyy broo

[dim vine]

What is this even asking

[gray isle]

the constant term here would be the term that doesn't have x in it

[dim vine]

Oh ok

cool ty

[paper temple]

,rotate

[paper temple]

Kinda stumped with this one

[uncut ore]

Can anybody tell me how the limit approaches the specifics?

I'm new... so sorry if I broke some rules

[ripe ginkgo]

been 20 minutes since he had an answer, so

https://en.wikipedia.org/wiki/Successive_over-relaxation

Trying to solve a linear system, but I have elements on the diagonal that aren't non-zero

this is a numerical example of one of the systems

looking at the equation for successive over-relaxation, it includes a w/a_ii term

so if I have any term on my diagonal be a zero, then it'll blow up

what can I do about this?

is there a better way to solve systems like this?

here it is in scientific notation, to show the smaller numbers

the matrix has a pretty awful condition number (5634843.398006929)

seems like Jacobi iteration also includes a 1/a_ii term, which means I can't use that either

[nova anvil]

one way i think u could potnetially try seeing the matrix u got

[ripe ginkgo]

actually, it seems like the determinant is super tiny too, i'm not sure how fsolve is successfully using this as a jacobian

[nova anvil]

is using givens rotation or something

since ur matrix is sparse

or other sparse system solvers but idk much about how to do others

and yea SOR has no guarantee for non SDD matrices that are not positive definite

[ripe ginkgo]

I am very confused

the Jacobian (this matrix I showed) has a super tiny determinant and a huge condition number

but somehow scipy.root() and scipy.fsolve() are both managing to use it to solve the problem correctly

[nova anvil]

sorry i dont use python, is there a fixed method scipy.fsolve uses to solve linear systems? and are you solving a linear system with this matrix or doing something else?

[ripe ginkgo]

this is the jacobian for a nonlinear system of equations

i'm trying to use it to apply newton's method

despite having a terrible condition number and det=0, numpy.solve() can somehow solve the linear system

[hoary anchor]

I have a question can someone help?

I want to find the change in y at a fixed x (x=-d-r) as a function of theta

It is a rotational problem, d is very large

I tried to make an equation of the line as a function of theta

But it did not give me the right answer, maybe what I am doing is wrong, or even the formulation of the problem is wrong in a way

Basically: what I want to find is, how the eye rotation translates the view of an image so far way

[wicked ember]

OH MY GOD IS THIS LENSES

oh my god lenses

[hoary anchor]

There is an error, the correction is: as theta goes from 30 to 90, y goes from h/2 to -h/2

<@&286206848099549185>

[robust flame]

Can someone help me with this

[hoary anchor]

First: Dude, I just asked my question

[hoary anchor]

Second: short tower is (31.7/tan(21.8)), long tower is (short tower + 31.7*(tan(27.5)))

[warm halo]

This is a really interesting problem
(Sorry, I don't know how to solve it, but I hope someone is able to help you with it)

[pale sable]

my dudes I have 2 questions:

how do you study math when you don't know what to google? (I forgot what the operations are called, haven't studied in 6 years)

how do you solve this? n^2 - 2n - 24 = 0

I know it's basic high school stuff but I forgot everything

[jade birch]

Does the term quadratic equation ring a bell?

[pale sable]

yes! I love keywords for me to google

[hoary anchor]

(n - 6)(n + 4)

Please, I posted my question first

Why people keep asking questions after mine, please read rules

[pale sable]

Answer this man's question!

ty

[winged flower]

frank is riding his bike he will ride a total of 20 miles he rode at the speed of 15 miles per hour for the first 0.75 hour, how many more miles does frank have left to complete his ride

so 11.25?

i’m never confident with my answers

[hoary anchor]

No it is 8.75 and READ RULES

[winged flower]

sorry i don’t understand

am i doing something wrong

[ionic jewel]

you solved for how many miles he has gone, not how many he has left

[winged flower]

so 8.75

[ionic jewel]

yes

[winged flower]

am i doing something wro my

wrong

people are telling me to read rules

i have

?

[ionic jewel]

dark is angry his question keeps getting covered

which is fair but idk what he expected posting a hard question in #help-0

[hoary anchor]

where to post it then?

[ionic jewel]

i dont ask questions here but i think higher numbers get less traffic so its more likely someone smart can answer it

[gritty aspen]

the vector plane eq: r . n = 0

does that only represent specific planes?

like

the X-Y plane

or the Y-Z plane

and the X-Z plane?

only these three?

or

any others?

im trying to answer this

[hoary anchor]

Ok guys thanks I found the answer <@&286206848099549185>

[jade birch]

I'm loving the passive-aggressiveness @hoary anchor

[coarse quail]

Can <@&286206848099549185> find mistakes or error in this solution please

and this as well

[alpine sable]

what

A mistake in a solution?

This your working?

from a question

[half panther]

Can someone make me understand the 6th number

[livid adder]

6th number as in 6a?

[half panther]

The 6th question

[sinful spear]

Is m || (parallel) n? Explain your reasoning using slopes.

<@&286206848099549185>

[faint root]

how do I find out a circle's radius and value?

[livid adder]

The radius of a circle is half its diameter

[faint root]

how do I find out the diameter?

[livid adder]

What information were you given about the circle?

[faint root]

I have to make the circle

[livid adder]

I'd assume that the radius and value can be whatever you wish in that case

[faint root]

is the radius the half of the circle?

the length?

[livid adder]

Yes

[faint root]

what is circumference?

[livid adder]

The diameter is the length of the line shown in the image

The circumference means the perimeter of the circle, or the distance around it

[faint root]

does the diameter have to be horizontal or side ways?

[livid adder]

Nope

[faint root]

so it doesnt matter?

[livid adder]

Doesn't matter

[faint root]

what does this mean?

[lusty steeple]

Pie

[faint root]

oh

[livid adder]

It represents a number

[frigid latch]

pie = 3.141xxxx

simplified to be 22/7

or 3.142

[faint root]

for this would r be 4?

[lusty steeple]

How did you get 4

[livid adder]

C means the circumference

[faint root]

would this be 2?

[livid adder]

Yes

[frigid latch]

circumference = 2 pie r

[livid adder]

Both 2 and 3

[lusty steeple]

Ok so 8 is equal to 2 pi r

[frigid latch]

area = pie r^2

[lusty steeple]

It is asking for circumference

[livid adder]

Since d=2r, pi d is the same as 2 pi r

[faint root]

so the 2nd one?

[lusty steeple]

2pir

Pi is 3.14

[faint root]

is this right?

[polar sundial]

Can someone help?

[lusty steeple]

@faint root 108.07

[faint root]

how?

[shell widget]

@polar sundial Multiply/divide the second term by (2 - 3sqrt(x))

and the third term by (2 + 3sqrt(x))

[lusty steeple]

3.14 times 17.2 times 2

[shell widget]

and after that, you'll see that all 3 terms have the same denominator

[faint root]

how come you multipy 3.14?

[polar sundial]

ok, thanks @shell widget

[lusty steeple]

@faint root what is the formula for the circumference of a circle

[faint root]

C=2πr

[lusty steeple]

Yes and pi is not just a symbol it has a value which is 3.14159

[faint root]

k

17.2x3.14x2?

[lusty steeple]

If you have a calculator press the pi button and it will have the number

[faint root]

(3.14x17.2)x2?

[lusty steeple]

Yes because the equation for the circumference of a circle is 2pi r

[faint root]

do I half the number to find out the diameter?

[lusty steeple]

Yes

The diameter is the radius times 2

Are you ready to do this

It isn’t that hard just pay attention

Ok

[faint root]

the diameter is 160.5

radius is 80.25?

[lusty steeple]

No

So you know how to find the circumference so now you have to do it backwards to find the radius

[faint root]

yea

[lusty steeple]

So 321 divided by 2 time pi

So do 2 times pi

6.28

[faint root]

so 160.5x3.14?

[lusty steeple]

Were are you getting 160.5

[faint root]

321 divided by 2

[lusty steeple]

No

[faint root]

yes

[lusty steeple]

That is how you find the radius of you have the diameter

[faint root]

so how do I find the diameter?

[lusty steeple]

You have to get the radius from the circumference

Remember that your c is equal to 2 times pi times r

So if you are trying to find the radius then you have to do your circumference divided by 2 times pi

[faint root]

I still don't get it

how do I get my diameter? what do I do?

[lusty steeple]

And so 3.14 times 2 is 6.28

I will try to show you on paper

[faint root]

yeah I know that

do I mutiply 6.28 by the diameter?

[lusty steeple]



Tell me if you get this

[faint root]

is the diameter 12.54?

[lusty steeple]

No

[faint root]

is the radius 6.28?

?

[lusty steeple]

No

[faint root]

then how do I get radius or diameter?

[lusty steeple]

Your equation for finding r is c divided by 2 times pi

Shown above

Once you do that d your diameter is 2 times r

[faint root]

so 321 divded by 2= 160.5x3.14

[lusty steeple]

2 times pi

Let’s walk through just the math and no explanations

[faint root]

ok

[lusty steeple]

321 divided by 2 times pi

2 times pi is 6.28

Keeping up

Yes no

[faint root]

no

[lusty steeple]

The first thing you asked was what was pi

The symbol

Pi equals 3.14

Right

[faint root]

right