help-10

[drifting kernel]

I solved it

Thank you very much once again @spiral knot

.close

[obtuse pebble]

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[spiral knot]

anytime

[obtuse pebble]

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[timid silo]

Hey! I guess I have a reasonably good grasp on the delta-epsilon definition of limits, but when it comes to actually proving limits with $\delta\epsilon$, I get lost. For instance, if I have $f(x)=\frac{1}{x^2}$ and want to prove $\lim_{x\to3}f(x)=\frac{1}{9}$, how would I go about doing that? I know $0<\left|x-3\right|<\delta$ implies $0<\left|\frac{1}{x^2}-\frac{1}{9}\right|<\epsilon$, but how do I establish a relation in between them?

[warm shale]

3317

[cobalt shuttle]

You're missing a part of the definition!

You want to show that given an e > 0, you can produce a delta that satisfies this implication

So usually you give me an expression for delta (usually) in terms of e

[timid silo]

Ooooh.

So something like:
Given $\varepsilon>0$, choose $\delta>0$ such that ...

[warm shale]

3317

[timid silo]

But still, how would I define delta in terms of e?

[cobalt shuttle]

That's the hard part!

[timid silo]

Oof.

[cobalt shuttle]

It's completely dependent on each function so that's what the definition of continuity comes down to

and why we like to refer to rules (sum and product of contiuous functions for eg) instead of actually checking continuity using the e/d definiton

[timid silo]

Ooh, that's cool.

So it's a more case analysis type of thing, amazing.

What about limits at infinity?

I can only imagine it'd be a different process.

[cobalt shuttle]

Yup completely different! There may be a couple of different ways but the way is not delta epsilon (for reasons you can imagine) but rather

the limit of f(x) as x goes to infty is L if given an e, there exists an X so that for all x ≥ X, we have |f(x)-L| < e

so you're saying you can always find an interval (X, infity) where you're within the specified range

whereas usually you're looking for an internal (x-a, x+a) where you're within the specified range

[timid silo]

Oooh, amazing.

Thanks a lot.

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[iron citrus]

how do you formally show that if n variables are independent then any two of of them are independent? so basically if you know P(X1 and X2 and … Xn)=P(X1)…P(Xn). how do you show P(X1 and X2) = P(X1)P(X2)?

[iron citrus]

i’m working with probability from foundations so the only things that can be used for this proof is the three probability axioms, P(A^c) = 1-P(A), and the expression for P(A or B)

set theory of course

i tried doing some basic set manipulations but it all went to nowhere so i have no idea what to do here

<@&286206848099549185>

[obtuse pebble]

@iron citrus Has your question been resolved?

[obtuse pebble]

@iron citrus Has your question been resolved?

[obtuse pebble]

@iron citrus Has your question been resolved?

[trail musk]

Maybe just show it recursively, given that P(X1 AND X2) = P(X1) • P(X2)

Like for instance

P(X1 AND X2 AND X3) =
P((X1 AND X2) AND X3) =
P(X1 AND X2) • P(X3) =
P(X1) • P(X2) • P(X3)

@iron citrus does that work

For any N, you can partition the set into {1,N-1} U {N}, then partition {1,N-1} into {1,N-2} U {N-1}, so on and so forth until each partition has one element

[obtuse pebble]

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[quasi juniper]

can someone explain what i did wrong?

[trail musk]

You only took the derivative once?

Lol

Lmao

[quasi juniper]

did i have to take the derivative twice? i thought dh/dt was the first derivative lol

[trail musk]

Lets be clear

[civic zealot]

h is a function of t, when you took the derivative of h you needed to apply implicit differentiation and included a dh/dt

[trail musk]

Nvm i misread

Ignore me

[quasi juniper]

how do i include dh/dt if h is the only variable? what do you mean, h is a function of t?

[civic zealot]

Since h is a function of t, when you derive h^(1/2) you get (1/2) * h^(-1/2) * dh/dt by chain rule or implicit differentiation (whichever way you think about it)

[quasi juniper]

does that mean i have to put in -sqrt(5h) for dh/dt in that, and plug in h=16?

[digital moat]

yes

[quasi juniper]

thank you!

i got the right answer, thank you wideputin and Zybikron :)

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[digital moat]

i just said yes lmao

[quasi juniper]

lol

[obtuse pebble]

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[glass sentinel]

can someone help me match and explain

.close

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[distant schooner]

State whether there is one, none or infinitely many solutions

[distant schooner]

3x+y=6
6x+2y=7

im not sure how to do this

i know how to substitute and do elimination methods

[zenith raft]

write 3x+y=6 as 6x+2y=12 🙂

[distant schooner]

wait nvm

i got it lmao

lemme just show u what i did

so i made both of them into the standard equations of a linear equation

so

equation 1 is y=-3x+6

and 2nd is y=-3x+7/2 simplified

so since the gradient is the same

but

y values are different

they are separate

but

parallel

so they have no interceptions?

[zenith raft]

good enough

[distant schooner]

alr

ty tho

[zenith raft]

haha np

[distant schooner]

wait can u teach me this method

[zenith raft]

there are no x and y that make 6x+2y=7 and 6x+2y=12 true at the same time

if there were, 12 would equal 7

and that's all

[distant schooner]

ah i see

[obtuse pebble]

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[marsh rivet]

How do i solve for t?

[royal basin]

,rccw

[timid silo]

Log

With change of base.

0.966 you have to change your base from base 10 to base that.

then take the log of both sides

[marsh rivet]

Like that?

[marsh rivet]

Or does it have to be like that? I dont get it with the base 10

[timid silo]

Your calculator will only give you base 10

or base e

To convert you have to convert the answer to base whatever it is.

[marsh rivet]

Its base 0,966 isnt it?

[timid silo]

0.996 is the base yes.

[marsh rivet]

So its correct, right?

The solution

[timid silo]

Don't know is it?

[marsh rivet]

86,6 must be t

[timid silo]

Make sure you check your reasoning

[marsh rivet]

Hmm

My teacher is bad, he didnt explain how log really works, he just said that u need to log in order to get the exponent t

[timid silo]

Log is simply asking what number do I have to raise another number to get the exponent.

[marsh rivet]

Ahh ok

[timid silo]

$\log_b{(x)=n}$

[marsh rivet]

So the calculator tries out?

[warm shale]

[Master Chief [117]]

[timid silo]

b is the base

x is the argument or the number you are trying to find the exponent of

and n is that exponent that raised x to to get that number in x

Simple example.

[marsh rivet]

Ah okay

[timid silo]

$\log_{10}{100\ =2}$

[warm shale]

[Master Chief [117]]

[marsh rivet]

So log isnt some kind of formula or number like pi

[timid silo]

No it's the inverse of exponentiation

it's the reason that log(a) + log(b) = log(ab)

and log(a) - log(b) = log(a/b)

because when you add two exponents together

x^2 * x^2 = x^4 or x^(2+2)

[marsh rivet]

They are additive

Or smth

[timid silo]

When you perform the exponent of a number when they are multiplied together you add the exponents

so if the n value in log which is the exponent raise to something

a^2 * b^2 = log(ab) = log(a) + log(b)

[marsh rivet]

We never had just log(a) we always had it like log b (a) and b is the base and a is the y amount

[timid silo]

no base label

means base 10

[marsh rivet]

Ahh now i get it

[timid silo]

log() = log-base10()

ln() = log-base-e

e = 2.718

@marsh rivet Bare in mind I'm self taught.

[marsh rivet]

No yeah u helped me with that

Thank you

This makes more sense now

[obtuse pebble]

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[cursive citrus]

Does anyone know a proof for the following lemma? I can't seem to find any proof.

[obtuse pebble]

@cursive citrus Has your question been resolved?

[cursive citrus]

<@&286206848099549185>

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@cursive citrus Has your question been resolved?

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[fervent locust]

I hava a 6x6 box. How many different times can i fit a 2x2 box in this 6x6 box. What is the formula? To clarify. It is not 9 becasue the box can cover the cordinates 1,1 2,1 1,2 2,2 and 2,2 3,2 2,3 3,3 and its a different box

[kind hawk]

check in how many spots you can put the upper left corner of the 2x2 box

[fervent locust]

That whould up to 36 and that whould not wotk then becasue when the x cordinate is 6 the 2x2 box will go outside the 6x6 box. or did i missunderstand your answer

The correct answer should be 25 so 5^2 or 6-1 then squre but that whould not work if it was a 2x3 block

Then the answer should be 20

[kind hawk]

well you cant put the upper left corner of the 2x2 box at position 6,6

but you can put it at position 5,5 for example

[fervent locust]

yes but what chould a formula for that be

[whole shale]

If you want the answer in a formula manner then
No.of different ways to fit a "r x s" block in "m x n" box is (m-r+1)*(n-s+1)

[fervent locust]

That was exatcly what i was after, Thank you

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[solemn crater]

Can someone help me understand how this cancellation reveals a hole at x = -3?

[storm heart]

u cant divide by 0

-3+3 = 0

0*3 = 0

[dark mango]

put x=-3 into first equation

you get 0/0

Theres a hole at -3 because the numerator and denominator are both 0 at x=-3

[solemn crater]

How does the cancellation play into that though? like after the cancellation, that no longer works anyway

Or is that just poor wording on the Prof's part?

[dark mango]

it doesnt but after the cancellation if you plug in x=-3 you wont get 0/0

so you have to specify there is a hole there by saying $x \neq -3$

[warm shale]

cantprogram

[dark mango]

otherwise there is a domain error

[solemn crater]

Okay, I think that makes sense. Thank you @dark mango and @storm heart. I appreciate your help

[dark mango]

you can .close

[solemn crater]

.close

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[dreamy copper]

2 questions:

• Ex: does (1/3)² become (- 1/3)² since the power is even?

• In [(1/3)³ × (- 1/3)⁵ × (- 1/3)²] can I do this:

{(1/3)³ × [-(1/3)⁵] × (1/3)²}?

[cedar lichen]

No reason why not

[dreamy copper]

To both questions?

[cedar lichen]

I wouldn't say (1/3)² becomes (-1/3)², they're just equal

[dreamy copper]

Ok so that rule is only if the number is negative?

E.g. (- 1/3)² would become positive?

And also in the 2nd question would it be (- 1/3)¹⁰?

[cedar lichen]

Again, I wouldn't say it becomes positive, it's just equal to the expression with a positive

[dreamy copper]

Sorry I don't get it

Because my teacher taught us that we could do that

[cedar lichen]

(1/3)² = 1/9, (-1/3)² = 1/9

Because they're equal, you can swap them out

[dreamy copper]

Oh wait it's because - × - equals +?

So -² = +?

Typo

[cedar lichen]

Yes

[dreamy copper]

Thanks what about this?

[cedar lichen]

No

The negative is outside the parenthesis

-(1/3)¹⁰

[dreamy copper]

Hmm

Ah thanks so much I get it

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[burnt quarry]

which variables are quantitative and which are quantitative?

[burnt quarry]

<@&286206848099549185>

[cloud berry]

its 3 mins only

no ping

[burnt quarry]

My bad

[cloud berry]

umm.. i can't help sorry

[burnt quarry]

Ok np

<@&286206848099549185> is there someone that can help me and knows how to work with vustat.eu ?

[earnest elk]

just look up the def

of both

that should clear things up

[obtuse pebble]

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[unkempt lotus]

what's a trick to find the lowest common denominator?

[drifting wraith]

the lowest common multiple is a multiple of the largest number, you can look at successive multiples of that number until you find one that divides by the rest of them

it's not going to reliably help, but if that doesn't count there's no trick at all

[kind hawk]

well you could calculate the gcd by the euclidean algorithm and then use gcd*lcm = a*b

whether that's better than just trial and error in most cases you'll encounter? unlikely

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Please don't occupy multiple help channels.

[cold thistle]

Please only open one channel at a time

[tepid urchin]

you need to find two numbers that add to 17x and multiply to 72x^2

what are the factors of 72

both need to have x in them

as x+17 is just x+17

9x and 8x

np

please close both of your chanles

[obtuse pebble]

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[keen pagoda]

can anyone help me confirm the if the boolean is right for this problem?

this is my working

[timid silo]

$F+B\cdot E+D\cdot K+D\cdot\left(PB\vee BPA\vee A\right)+DV+D\cdot S$

Is that it?

[warm shale]

3317

[timid silo]

Just transcribing.

[keen pagoda]

yea that what ive put for it

is that right?

[obtuse pebble]

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[tacit briar]

by finding ways to permute the letters in a word, we are using the permutation formula right?

[tacit briar]

n would be the total letters, and r would be any letters that are repeated in the word

[tardy epoch]

do you have an actual problem.

[tacit briar]

How many ways are there to permute the letters in the word MISSISSIPPI?

dont tell me how to solve it

answer my questions above first

@tardy epoch

[tardy epoch]

there's more than 1 letter that's repeated

[tacit briar]

yes i know

that would be showed by having it in the denominator right?

[tardy epoch]

what's "it"

[tacit briar]

the letters that are repeated

in this case it's I, S, and P

<@&286206848099549185>

[tardy epoch]

the letters are in the denominator?

[tacit briar]

yeah

would that be how we permute letters in a word?

[tardy epoch]

i don't understand what you mean to put letters in the denominator

can you do a simpler example with ABBCCC

[tacit briar]

6!/2!3!

since b and c are repeated theyre going to be r which is under the denominator for a permutation formula

[obtuse pebble]

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[turbid kraken]

Hello I am having trouble understanding the following question:

[turbid kraken]

Do I have to calculate the order of all orders within this multiplication table and say what orders g can be?

[kind hawk]

do you know lagranges theorem?

or eulers theorem?

[turbid kraken]

Reading through Lagranges for lessons now

and I got the following question

and I could not really understand the idea behind it yet

[warm canopy]

The order of an element, is also the order of the subgroup is generates, this should make it more clear how to use lagrange

[turbid kraken]

so after writing the multiplication table

would the order be the range of the set

in this case 1282?

like the length*

[warm canopy]

Youre looking for all possible values orders of elements can take

For instance obviously the order of 1 is one

[kind hawk]

lets start with the definition

[turbid kraken]

exactly

[kind hawk]

what is the order of an element

[turbid kraken]

The smallest positive power of the element

[kind hawk]

no

[turbid kraken]

So if we have a Group A with an identity e

the order of x E A would be the smallest positive integer n such that x^n = e

[kind hawk]

ok

what is the subgroup generated by an element x in A

[turbid kraken]

its the smalles subgroup that contains A

[kind hawk]

no

the smallest subgroup of A that contains A is A itself

[tacit briar]

@tardy epoch you never respnded...

[turbid kraken]

like when A = {1,2,3} the smallest subgroup of A would be {1} right?

or 2 or 3

[tardy epoch]

open a new channel to not bother burd

[turbid kraken]

At least that would by my assumption.

This is my understanding

[kind hawk]

{1} is the smallest subgroup of any group, yes

what does this have to do with the subgroup generated by x tho

[turbid kraken]

ehmmm I am trying to think

My argument makes no sense there whatsoever

You have an x in A and that generates a Subgroup

and in my instance that would be

[turbid kraken]

I am sorry if im not making sense, trying to think hard so that you know what goes through my mind.

If G is a group, and x is an element of G. The set of <a> would be a subgroup of G.

So if a^m, a^n is an element of <a> then a^na^m = a^n+m is a subgroup of <a>

[kind hawk]

a^(n+m) is an element of <a>. Not a subgroup

[turbid kraken]

Ah wait

Thing is, I read through Lagranges theorem for a bit again.

and if we have a group G with 1283 elements. The only possible divisors of 1283 would be 1 and 1283

So the only possible subgroup orders would be 1, 1283

[kind hawk]

Is 1283 prime?

[turbid kraken]

yes

[kind hawk]

But yes that is indeed true

[kind hawk]

But our group does not have 1283 elements

[turbid kraken]

it has even more than that

since its a multiplication table right?

it goes from 0 to 1282

wouldnt the order be 1283?

[kind hawk]

Not sure what exactly you mean with multiplication table

[turbid kraken]

ahhh

something like this

[kind hawk]

Sure you could write down a table with all products. But why

[turbid kraken]

we did it for practice

[kind hawk]

Well any group has a multiplication table

That's different from being a multiplication table

[turbid kraken]

ahh

thanks for that clarification

wouldnt the number of elements of 1283 be 1283?

since its 0 to 1282

which would mean the order is 1283?

[kind hawk]

Do you know what this little star notation means?

[turbid kraken]

its

({0,1,2,3,4,.......,1282}, x)

right?

[kind hawk]

No

Without the 0

[turbid kraken]

since 0n = 0?

[kind hawk]

Yes

0 does not have a multiplicative inverse

[turbid kraken]

Like if we have Z/14Z = {1,3,5,9,11,13} the order would be 6 right?

[kind hawk]

Z/14Z has 14 elements

Did you forget the star?

[turbid kraken]

ehmmm, I know for example

if you have (a)*

you can take as many a's

as you want or 0

[kind hawk]

Z/14Z ={0,1,2,...,13} and this is a group under addition

[turbid kraken]

exactly

[kind hawk]

(Z/14Z)^*={1,3,5,9,11,13} is a group under multiplication

Those two are different

Different notation

[turbid kraken]

ahhh

ehmmm, but like taking the * with my given definition

was that right?

taking 0 or any number you wish?

[kind hawk]

I don't know what you meant by that

[turbid kraken]

so

we had formal reasoning where they said

if you take a*

you can take as many a's or 0 a's

[kind hawk]

What

What is a*

[turbid kraken]

I thought * indicated that (Z/1283Z) could be rewritten as ({1,2,3,4,5,....,1283},x)

but its actually

Z/(1283-1)Z

[kind hawk]

No

[kind hawk]

Well ok it's isomorphic to that in this case but that doesn't help

[turbid kraken]

hmmm

what we need to find are the values of the orders of the set that the element g can generate right?

[kind hawk]

Yes

The element of g always generates a subgroup

What does lagrange say about the number of elements in a subgroup

[turbid kraken]

that its always equal or smaller than the Group its a subgroup of?

or wait

[kind hawk]

Well that's trivial. You don't need lagrange for that

[turbid kraken]

that the number of elements of every subgroup of G divides the order of G

[kind hawk]

Yes

[turbid kraken]

|G| = (G:H) * |H|

[kind hawk]

Ok so the possible orders of g are all divisors of 1282

[turbid kraken]

Ahhh

so I have to find the divisors of 1282

[kind hawk]

I doubt you have to for this exercise

[turbid kraken]

which would be 1,2, 641 and 1282

[kind hawk]

Oh that's all of them?

[turbid kraken]

ye

[kind hawk]

Ok didn't expect that

[turbid kraken]

ye 4 would give 320

320.5*

only ones that do not give a decimal are 1, 2, 641 and 1282

so we take the 1283-1 to find the divisors from right?

[kind hawk]

Yes because 1283 is prime

[turbid kraken]

exactly

if it was not wed take 1283?

[kind hawk]

No

[turbid kraken]

still -1?

[kind hawk]

Remember that for 14 we had 6 elements

So for nonprimes it's even less

Do you know the eulers totient function?

[turbid kraken]

No >.<

[kind hawk]

It tells you the number of elements in (Z/nZ)^*

[turbid kraken]

ah

imma handle that

[kind hawk]

Your course will cover it at some point

[turbid kraken]

ye im sure it will, crypto can be hard sometimes 😦

thanks for taking so munch time to help me out ❤️

[kind hawk]

Oh this is just for crypto

Not a general group theory course?

[turbid kraken]

I have seriously 0 math background, learned most of my math in 2-3 months

nope

its for cryptography

[kind hawk]

Ok then good luck

Crypto courses are not always the best

Cause they don't have the time they need for these concepts

[turbid kraken]

we got a super super super smart teacher, hes just bad at explaining 😦

[kind hawk]

Sadly a lot of smart people are

[turbid kraken]

You might even heard of him, his name is Joan Daemen

worked on AES

its pretty cool, but ye

so we have 1282

The divisors would be 1, 2, 641 and 1282

which would mean that |G| = 1282

and {e} = 1

[kind hawk]

Well other way around but yes

[turbid kraken]

o

{e} = 1282?

[kind hawk]

First this

[kind hawk]

Then this

[turbid kraken]

Ah!

yes

so the trivial group {e} = 1

or the order of |{e}| = 1

with the trivial group, do you just take the smallest divisor in G?

wouold that mean that the g were looking for has either 2 or 641?

[kind hawk]

The trivial group is always {e} with 1 element

Nothing in this says that g cannot be e

g can have 1, 2, 641 or 1282 as order

That's it

[turbid kraken]

ye, would that mean that the order of {e} is always 1?

ah yes

[kind hawk]

That's the solution

[turbid kraken]

sorry my bad, it does mean that

Pff Dena

Thank you so munch for helping me out ❤️

sometimes that click must happen

[kind hawk]

You're welcome

[turbid kraken]

and its difficult 😦

[kind hawk]

Definitely

[turbid kraken]

I spend like 40 hours a week on calculus

and now crypto is breaking my knees

the boys in this channel have helped me out a lot

ill be sure to pass on the good will!

[turbid kraken]

Which you an amazing evening ❤️

.close

[obtuse pebble]

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[turbid kraken]

p.s. thanks for the patience

[obtuse pebble]

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[merry stratus]

I'm stuck proving this

[tardy epoch]

,rotate

[tardy epoch]

can u translate

[merry stratus]

The text?

[merry stratus]

For z^n, we have z^n=a^n...

[obtuse pebble]

@merry stratus Has your question been resolved?

[obtuse pebble]

@merry stratus Has your question been resolved?

[obtuse pebble]

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[opaque galleon]

May I ask for help on what to do next? We were only given these trig integrals and I don't know what to do next 😭

[tardy epoch]

,w integral sec(x) dx

[warm shale]

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[tardy epoch]

oof

[violet sentinel]

gross

[tardy epoch]

https://www.youtube.com/watch?v=JqLLL3CV910

[opaque galleon]

why do we multiply by secx + tanx

nvm ill just follow it

,w integral of sech^2(x)dx

[warm shale]

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[opaque galleon]

why

[obtuse pebble]

@opaque galleon Has your question been resolved?

[tardy epoch]

Differentiate tanh(x)

Probably same as this
https://youtu.be/4Iu9v2f9HrA

[obtuse pebble]

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[fluid bone]

how do i finish the task?

[twin sapphire]

put both n inside the sqrt

and simpliffy the sub fractions

[fluid bone]

whats sqrt?

nad how exactly do i simplify them

[fluid bone]

ah root i see

i have the soltuion but idk whats the process behind simplyfying it

[twin sapphire]

transform the n into $\sqrt{n^2}$

[warm shale]

Benjamin

[twin sapphire]

like this

and then separate each fraction

into n²/n² (+-) 5n/n²

[fluid bone]

thats not how it was solved in my class

hold on

professor skipped like 3 steps so im completly lost

[twin sapphire]

they exactly did what i'm doing now but skiupped one step

[twin sapphire]

exactly this step to be precise

[fluid bone]

so i write this next?

[twin sapphire]

yeah

only the bottom part

[fluid bone]

oks

[twin sapphire]

and then you simplify the smaller fractions

[twin sapphire]

this way

[fluid bone]

like this?

[twin sapphire]

yep but dont forget the 10/(....)

and now you can do the limit easy peasy by pluging in

[fluid bone]

what abt the 3rd part ?

how did that get there

[twin sapphire]

it shouldnt

maybe you wrote it wrong

because look at your last thing

there are only 2 square roots

[twin sapphire]

not 3

[fluid bone]

i think its correct now

[twin sapphire]

yeah right

[fluid bone]

alright thx man

.close

[obtuse pebble]

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[gaunt vigil]

is there a way to mathematically solve without testing one by one the question what is the largest product you can make with whole numbers that sum to 10?

[gaunt vigil]

I know that the answer is 3, 3, 2, 2

and it's somehow related to e

<@&286206848099549185>

[astral oyster]

using calc optimization?

primary - x+ y = 10

Secondary - xy = P

Solve for x or y

plug in primary

take derivative

check with second derivative

plug back in orginal

thats you answers

[gaunt vigil]

what is calc optimization?

[astral oyster]

what math are you in rn?

[wild swallow]

am-gm tells you using n numbers the product is bounded by (10/n)^n

[gaunt vigil]

grade 9 but I started learning a bit of derivatives

[wild swallow]

check that this is maximised between 3 and 4 so that n should be 3 or 4

am-gm then tells you the product is maximised when the numbers are equal

[astral oyster]

yeah idk maybe series?

[gaunt vigil]

I did read about that

can you link me to more about this property

[wild swallow]

just google the am-gm inequality

[gaunt vigil]

yeah I did do that

but I didn't get the part about (10/n)^n

[wild swallow]

write out the am-gm inequality on n numbers

solve for the bound on the product

(product)^(1/n) <= sum/n

[gaunt vigil]

ok thanks

that clears it up

[astral oyster]

.close

[obtuse pebble]

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[bleak dune]

I'm solving the system and I just wanna make sure I don't goof up on the first step, I have
x^2+y^2=4x
x=y^2
step one would be to multiply x=y^2 by (-1) to eliminate the y, and then replace that new equation with which of the two before adding them??

[bleak dune]

I think I might be overcomplicating this

okay yeah I definitely second guessed myself over something simple nvm lol

.close

[obtuse pebble]

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[bleak dune]

.reopen

[obtuse pebble]

✅

[bleak dune]

hold up I just realized something lol

so this is the graph and im solving the system to find all of the intersections

but I'm only finding 2 not 3

.... I am so sorry I figured it out again nvm

.close

[obtuse pebble]

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[gaunt vigil]

sorry I'm an idiot

I still don't get this

[gaunt vigil]

how do I solve for this

[obtuse pebble]

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[ruby skiff]

yo how would it be pie/4

[timid silo]

A until E is 2pi

A until C is pi

[ruby skiff]

wait where did u get 2pie?

[ruby skiff]

?

[timid silo]

it's a periodicity

but if you see accurate we have sin2x so should halve the frequency because it's for sinx

understand?

[nocturne minnow]

But it's not? The period is pi so from A to E, it's pi

[timid silo]

.

[timid silo]

read it

[nocturne minnow]

Are you saying the period for sin x is 2pi? Or the period for sin(2x)?

[timid silo]

im say for sin x ==== 2pi and for sin 2x = ===pi and for sin 4x === pi/2

understand?

[nocturne minnow]

Well you never clearly stated that

You said from A to E is 2pi and for that graph, it's false

[timid silo]

see it if sin x/2 ==== 4 pi

[nocturne minnow]

What I'm saying is, you stated these two lines without specifically stating that it was for the function sin x

One would have assumed it was for the graph in the given problem

[timid silo]

it's true for sin x and cos x remember it

[nocturne minnow]

But you never said that initially

[timid silo]

what your mean?

[nocturne minnow]

.

[ruby skiff]

wait so we take the original value of x for sinx

then we use the b of the new one to manipulate it into the one we have now?

[timid silo]

in first i don't read question exactly

[nocturne minnow]

Given that the period is pi, period is from A to E. Point C is in the middle so that point is half the period

[timid silo]

true

[nocturne minnow]

Then between A and C is point B, and that's halfway point between A and C so you half that value to get the x coordinate at point B

[timid silo]

yes

[nocturne minnow]

More specifically half the value of point C

[timid silo]

surly you learn that well

[ruby skiff]

wait so we just multiply the og value of the sinx to turn it into 3sin 2x?

[nocturne minnow]

You don't necessarily need sin x

You're already given the function

[timid silo]

ok but 3 it's not Influence on x domain but influence in y domine

3 in out of sin so not influence in period

[nocturne minnow]

Stop confusing the kid, the original question was how it's pi/4. I explained how above

[nocturne minnow]

From here

[timid silo]

yes i think you understand it

[nocturne minnow]

I hope you realize I'm not the OP

[nocturne minnow]

@ruby skiff This statement

[nocturne minnow]

And this

Helps you understand why it's pi/4

[timid silo]

AE is a period

understand it

?

[ruby skiff]

yea kind of

[nocturne minnow]

What part are you having trouble understanding?

[timid silo]

x domine dependent on factor x in sinx so if sin x change to sin 2x the domine is halfe then A E is not 2pi is pi

[nocturne minnow]

Seriously stop confusing the kid by involving sin x

[timid silo]

AC = CE , AB = BC

[nocturne minnow]

You're over explaining it when you state that

[ruby skiff]

wait how do we know wut point a is?

wait u said it was 2pi

is it bc of the formula 2pi/b?

[nocturne minnow]

That's the period for sin x

[nocturne minnow]

Use this to find the period for your function

[ruby skiff]

oh k

alr thx guys

[obtuse pebble]

@ruby skiff Has your question been resolved?

[obtuse pebble]

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Channel closed

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[hot hazel]

.close

[obtuse pebble]

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[timid silo]

Question 10 for me

[timid silo]

I’m confused because I’m supposed to find all zeros of the polynomial

(I hust assume this means solve it)

but with synthetic division I plug it in and it doesn’t factor

7x-15 for example the last part

[solar crystal]

try continuing the synthetic division

[timid silo]

how so? i thought i would have to end when i reach 0

[solar crystal]

sometimes the polynomial will end up unfactorable yes

but you can continue the synthetic division to find more than 1 root

if i remember correctly just continue from the bottom line u have 1 7 7 -15

use the same p/q roots and keep going until u get a quadratic

[timid silo]

okay let me try to continue it

its been a while since weve did that

[solar crystal]

its been a while since ive done that too lol

[timid silo]

It seems that worked

Although we didn’t do it in class so I have no clue if it’s technically correct but it looks quite rigjt to me

[solar crystal]

looks good to me lol

you can do synthetic division as many times as you want as long as theres still possible factors to test

[timid silo]

I’ll probably talk to my teacher about if I can use that in tests

Thanks for the help

.close

[obtuse pebble]

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[timid silo]

hi

[cloud berry]

hi

any questions to ask

.close

[obtuse pebble]

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[obtuse pebble]

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[worn yacht]

Hello, Please help, I wrote everything in the image.

[raven spire]

calm down (@_@;) where's the question?

[worn yacht]

calm down?

lol what did I do?

[raven spire]

you didn't send the question and right away bombarded us with an explanation.. I didn't know what to do (@ _ @;)

[worn yacht]

lol

oh oops I didnt even say what I was asking about trigonometric substtution

and I don't know what to do after the last step I showed

$\int \frac{\sqrt{x^2-9}}{x^3}$

[warm shale]

kangaroo rat

[raven spire]

ah

it was that?

[worn yacht]

yes

so what do I do next?

@raven spire

[raven spire]

errr, I'm trying to think about how to proceed from what you did. I'm sure my sensei taught me something relevant but I never paid attention so...

meanwhile, you might want to substitute x = 3sec θ

[dark stirrup]

Are you trying to solve an integral?

[worn yacht]

your Japanese?

[worn yacht]

yes

[worn yacht]

this onw

[worn yacht]

here is my working

[dark stirrup]

what integral are you trying to solve? Sorry but not seeing the original question

[worn yacht]

this one

@dark stirrup

[raven spire]

$\int \frac{\sqrt{x^2-9}}{x^3} , \dd x$

[warm shale]

Arya

[worn yacht]

I think I gtg now but if you could still answer my question that would be great!

Can you keep answering while im gone?

Anyway, thanks

[raven spire]

ah I was ignored

[dark stirrup]

Oh I see it.

Sorry I'm just skimming the channels

[raven spire]

nah I gave the OP their solution but they ignored me so ^^"

[dark stirrup]

I think I ignored you too cuz I don't see what you gave them the solution

the x=3sec thing?

I wouldn't call that "giving". But step in the right direction?

[raven spire]

oh x = 3 cosec θ works better

but do you remember how to solve integral using imaginary numbers :| was wondering if it's possible to take the (cos x) out of square root leaving inside the root(-1) in OP's solution... what do you say @tardy epoch ?

[obtuse pebble]

@worn yacht Has your question been resolved?

[tardy epoch]

Might as well use residue theorem at that point

[scenic sundial]

residue is so powerful.

[obtuse pebble]

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[mortal sun]

So for the lower bound, I am keep getting (2/3)*pi but the answer on the textbook says it is (1/6)*pi

[mortal sun]

let me take a picture of my solution

did I do something wrong in my solution? or is it a typo in the textbook?

[obtuse pebble]

@mortal sun Has your question been resolved?

[mortal sun]

<@&286206848099549185>

[civic zealot]

are you using the lower bound or the left bound?

[mortal sun]

lower sum

so uh

the left bound?

if its like
| | | |
0 1/6pi 1/2pi pi

then I would take 0, 1/6pi, and 1/2 pi right

maybe this is where my error is

Since for sin functions pi = 0 and pi/2 is 1

[civic zealot]

that's why I'm asking, you said lower bound, but then used all the left points on the interval, even though those aren't the lowest values of sin(x)

[mortal sun]

so if i were to calculate the width

would it be
delta x_1 = 1/6pi - 0 = 1/6pi
delta x_2 = 1/2pi - 1/6pi = 1/3pi
delta x_3 = 1/2pi - pi = -1/2pi?

so the first 2 are fine but the last one should be switched to get -1/2pi instead of 1/2pi

?

oh and for the height of the lower bound, I need to use pi instead of pi/2

ok nvm that gets me the right answer

but quick question

[mortal sun]

was this correction done right?

it didnt matter for this specific question since sin(pi) = 0 so it didnt matter what the value of delta x_3 was

but for future questions

[civic zealot]

the width of the last one is still 1/2pi

the width of the interval doesn't change.
the height of the rectangle changes

because if you want a lower bound, you should take the height that corresponds to the lowest point on the function in that interval

[mortal sun]

right

right why did i just say width negative lol

thanks for the help

.close

[obtuse pebble]

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[obtuse pebble]

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[ancient prairie]

How to do functions of zeros?

[urban granite]

do you mean a function where f(x) = 0 for all x ?

[ancient prairie]

yes

f(x)=x2-5x+6

[urban granite]

oh u want an equation

so

you know b²-4ac ?

[ancient prairie]

no

[urban granite]

okok so

f(x) is polynomial form

(sorry for bad english)

[ancient prairie]

is fine

[urban granite]

it's written like : ax²+bx+c

[urban granite]

here we have a=1 b = -5 and c = 6

with this you reach the number alpha

if alpha = 0 there is one root

if alpha > 0 2 roots

if alpha < 0 0 root

fine ?

[grizzled shore]

f(x) is a quadratic

[ancient prairie]

uhhhh I think it's like too hard of it since I am only in alergba 1 but they says is alergba 2

[grizzled shore]

Did you just start quadratics? (Or parabolas)

[ancient prairie]

just functions

[grizzled shore]

What kind of functions

[urban granite]

oh yeah sry, in french we name this polynomial

[grizzled shore]

Give me some examples

[loud tangle]

what exactly do you mean by function of 0

[ancient prairie]

zeros of functions

[loud tangle]

it is a 2nd degree polynomial

[grizzled shore]

It is a polynomial, this one is just a special kind of polynomial

[loud tangle]

so that is correct

[loud tangle]

could you give an example?

[urban granite]

oh great thanks

[ancient prairie]

number 34

[loud tangle]

by 0s i assume the points at which it is 0

so the roots

[grizzled shore]

Have you not learned about quadratics (parabolas, same thing different name)

[ancient prairie]

no

[grizzled shore]

It is a whole topic in and of itself

[loud tangle]

thats odd

here we learn quadratics before functions

weird education system

anyways its kinda complicated

[ancient prairie]

true

[grizzled shore]

You shouldn’t be able to solve quadratics before learning about them

[loud tangle]

i guess there would be a more primitive way to solve it

you could add 10 to the lhs and factor x out of the 2 terms

then case work

thats the only way id solve it without delta

wait no i got a better idea

try to factor

can you really

[urban granite]

could be possible if sqrt(7) was a natural

[grizzled shore]

You can’t solve quadratics without using methods for solving quadratics

[ancient prairie]

i only know about that way

[loud tangle]

so do that

[grizzled shore]

Factorisation is a quadratic solving method

[ancient prairie]

but like sometime the questions says (x-1)

[loud tangle]

i guess they didnt learn delta

[ancient prairie]

like in a step

[grizzled shore]

I think you should ignore it and just ask your teacher

Where do you study? What country

[ancient prairie]

thailand but i am not thai

[grizzled shore]

What grade

[ancient prairie]

8th

[ancient prairie]

is like a private school

[urban granite]

english school ?

[grizzled shore]

do you know the curriculum name?

[ancient prairie]

yes

alergraba 1

[grizzled shore]

ok do you know "Factorization by Middle Term Splitting"

[ancient prairie]

i don't think so

this is all i learnt

[grizzled shore]

what's on page 21

[ancient prairie]

evaluating function

[grizzled shore]

yeah what's on it

[ancient prairie]

function nonation

[grizzled shore]

what the heck this makes no sense

do you know how to turn
$\ x^2+5x+6\ $
into
$\ x^2 + 2x + 3x + 6$

[loud tangle]

no dashes

or not ok

[warm shale]

Frosst

[loud tangle]

goofy ahh latex

anyways

[grizzled shore]

and do you know why you would want to do this

[ancient prairie]

no?

[grizzled shore]

i think you should skip the question and ask your teacher

[loud tangle]

me too

[ancient prairie]

ok thanks I will go ask my teacher right now since I needs to go

thanks for the support

[grizzled shore]

yeah sorry it's a full on big topic you gotta learn

it's not something i can teach you in like 20 minutes

[ancient prairie]

is fine ok

[obtuse pebble]

@ancient prairie Has your question been resolved?

[obtuse pebble]

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[flint ivy]

im trying to find the implied domain

[cloud berry]

of which

[flint ivy]

question i

idk how the working out works

[cloud berry]

x-3x^2 >= 0

[flint ivy]

i know i got it right

yes

[cloud berry]

so what do you want to know

[flint ivy]

why do you take teh sqrt out

and make it larger or equal to 0

[cloud berry]

you can't divide 0 by x in step2

coz sign of x is not known

[flint ivy]

so what do you do instead?

also why

[cloud berry]

solve the inequality by wavy curve method

[cloud berry]

sign of inequality changes if x is negative

and sign of x is not give in question

[flint ivy]

ah ok

whats the wavy curve method?

[cloud berry]

(x)(1-3x)>=0

[flint ivy]

why's it called that

[cloud berry]

put x and 1-3x = 0

and find values of x for both

[flint ivy]

ohh yeah i get it

but why do you change it to (x)(1-3x)

kinda confused

[cloud berry]

we need factors of equation to solve

[cloud berry]

we will get x=0 and 1/3

[flint ivy]

ahh

can i ask why the graph stops at those points

[cloud berry]

now on number line plot 0 and 1/3

[flint ivy]

cus isnt a square root graph supposed to be continuous

[cloud berry]

these are roots of that equation at 0

[flint ivy]

uhh

can you explain in caveman terms

[cloud berry]

?

[flint ivy]

ok

so

why is it 0?

[cloud berry]

who

equation or root

[flint ivy]

oh wait

i got it

equation

[patent jetty]

https://youtu.be/PW5kYqYZQ0w

[patent jetty]

Wavy curve @1:27;45

[flint ivy]

ty ty

i got it now

.close

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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[abstract crow]

H e l p

[cloud berry]

*helps

[small thicket]

*dies in pain

[abstract crow]

hahahaha

[cloud berry]

*trying to close channel

[abstract crow]

one sec

[sage geode]

Post the question

[abstract crow]

iam forming my qesution

[small thicket]

*makes a coffee while waiting

[cloud berry]

*spills coffee on laptop

[abstract crow]

here why did we out n=k twice ?

i understand the series starts from 1 till K

[narrow vault]

it didn't? it's n=k-1 and n=k

remember that the term you're summing is ln(k**+1**)-ln(k)

so for n=k-1 you get ln(k) in front and for n=k you have ln(k+1) in front

the notation is breaking my brain

[abstract crow]

i see i see but in general how do i know which of the following will remain ln(k+1) - ln(k) for example

may you give an example ?

[narrow vault]

you do that by checking the first few values and see that everything in the middle cancels

whether mentally if you have the mental capacity or on paper if you don't

but that's how you observe patterns that you can abuse and simplify

[abstract crow]

the brain is not functioning wait one sec

[narrow vault]

in this case you can also split the sum into two

the you get

$\sum_{x=2}^{k+1} \ln(x) - \sum_{x=1}^{k} \ln(x) = \ln(k+1)$

[warm shale]

IV

[abstract crow]

I see I see

Understood sir

Thank you so much !

hope you have a good day

.close

[obtuse pebble]

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[oak lintel]

does anyone know how to do this pleasee