help-27

[lavish sigil]

sqrt(6) - sqrt(2)

[restive river]

okay thanks guys i get it now

.close

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[vivid kite]

Is 5 and 6 asking me to solve the diff eq and sketch on the slope field?

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[vernal grail]

hi

[vernal grail]

Can anyone explain the cauchy sequence to me, pls

[supple knot]

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

[vernal grail]

im not english 😦

[supple knot]

...

[vernal grail]

i need the proof

[upper schooner]

"proof"

[supple knot]

"need"

[vernal grail]

I don't understand the proof

i already have one

[upper schooner]

Proof of? You've just said "Cauchy sequences", and no statement about them

[vernal grail]

to demonstrate that the cauchy sequences are bounded, every convergent sequence is cauchy and that if a sequence is cauchy a_n it is convenient to extract a_n_k convergent towards l, then a_n also converges towards l.

[upper schooner]

If you show the proofs and explain the parts you don't get, we can explain them?

[vernal grail]

ok!

$\textbf{PROPOSITION.}$ Every convergent sequence is Cauchy.

$\textbf{Proof:}$ If $a_n$ converges towards $a$, then for every $\epsilon > 0$, there exists $v$ such that $|a_n - a| < \frac{\epsilon}{2}$. From the triangular inequality, it then follows, for $h,k > v$:
\begin{align*}
|a_k - a_h| &\leq |a_k - a| + |a - a_h| \
&< \frac{\epsilon}{2} + \frac{\epsilon}{2} \
&= \epsilon.
\end{align*}

[woven radish]

alee

[vernal grail]

<@&286206848099549185>

[upper schooner]

Which part is the confusing bit?

[vernal grail]

I don't quite understand why a_n transforms into a_k and a_h

[upper schooner]

Remember the definition of a Cauchy sequence

[vernal grail]

what?

a_k - a_h < epsilon

[near trout]

do you know what a cauchy sequence is

[upper schooner]

Absolute value, and some missing things, but I'll take that

[vernal grail]

I also didn't understand what a_h and a_k are

[vernal grail]

a_k - a_h < epsilon

[near trout]

ok

so you have some sequence a_1, a_2, a_3, ...

then a_k and a_h are just some random terms of the sequence

they're the h'th terms and the k'th terms

so then that sequence is cauchy if

so long as h and k are large enough

|a_k - a_h| < epsilon

for any h, k

h and k are just big numbers

[vernal grail]

ok

im thinking

so the terms a_h and a_k tend to the same limit given that they are part of the same sequence?

[near trout]

not necessarily

[vernal grail]

what

[near trout]

in certain cases there can be cauchy sequences that aren't convergent

[vernal grail]

i blundered 😦

[near trout]

but if a cauchy sequence does converge to a limit

then a_k and a_h clearly go to the same limit

because the whole sequence goes to that limit

if you see what i mean?

[vernal grail]

last 2 questions

but if I took like ε/4, would I still have found with the proof?

[near trout]

?

sure it doesn't really matter

[vernal grail]

ok

[near trout]

you would get e/2 instead

which is still as small as you want

[vernal grail]

Can I move on to part two?

thx !

[upper schooner]

Share the next part if you're happy!

[vernal grail]

I'm just placing the first part in my notebook for a moment

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[vernal grail]

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[devout snow]

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[cinder bobcat]

i forgot the command, but where are you stuck at?

[upper schooner]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[cinder bobcat]

thank you lol

[humble shuttle]

I am on 1

I'm confused on how to use u sub

and u intergration

whatever it is called

[cinder bobcat]

okay, well they tell you the first step luckily

do you know why they want you to use u sub?

[humble shuttle]

No

well yes

it tells you to but idk why

@cinder bobcat

[cinder bobcat]

okay i think all the symbols will just be more confusing

[humble shuttle]

Yea now im rly confused

[cinder bobcat]

you use u substitution when the derivative of u is already inside your integral

here, they say u = 4x^2 - x

what is du/dx?

[humble shuttle]

8x-1?

[cinder bobcat]

yep! and would you look at that, that's inside the integral already

[humble shuttle]

ohhhhhhh

wait then

what do i do with that

[cinder bobcat]

so now you have du/dx = 8x-1

[humble shuttle]

yes

[cinder bobcat]

multiply by dx on both sides

[humble shuttle]

8x-1dx

[cinder bobcat]

so du = (8x-1)dx

[humble shuttle]

+C?

[cinder bobcat]

yep

no, that only happens after you integrate

we haven't integrated yet

[humble shuttle]

ohh okay

[cinder bobcat]

so wherever you see (8x-1)dx in your integral, replace it with du

and anywhere you see 4x^2-x in your integral, replace it with u

since that was your substitution

[humble shuttle]

okay

for the original intergral?

[cinder bobcat]

yep

[humble shuttle]

?

[cinder bobcat]

first of all, the integrand is everything excluding your differentials

differentials are the du and the dx

so get rid of those

second of all, you were supposed to replace (8x-1)dx with du, but you still have a dx there

and third, you were supposed to replace 4x^2-x with u everywhere you see it, remember?

[humble shuttle]

OH

wait

sorry im confused so do I not have any du in it?

(8x-1du) e^u 8x-1du?

[cinder bobcat]

read this again

wherever you see (8x-1)dx in the original integral, replace it with du

[humble shuttle]

just du not the actual numbers

[cinder bobcat]

wdym?

[cinder bobcat]

this

you correctly replaced it before, then you went backwards

[humble shuttle]

so do I keep the 8x-1du or is it just du

oh i got it

its just e^u

[cinder bobcat]

yes there you go

[humble shuttle]

yay

thank you

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[quick lichen]

can someone help with this pls?

[cinder bobcat]

there are a couple of nice ways to do this. you could calculate p1 using your initial condition, then calculate p2, etc, and notice a pattern

that might be the easiest way

just don't multiply anything out while doing this method, or the pattern won't be obvious

[quick lichen]

wdym by p1?

[cinder bobcat]

$p_1$

[woven radish]

doaby

[cinder bobcat]

I'm just lazy lol

[quick lichen]

im completely new to DTDS so im still not sure where to plug in the 3000?

[cinder bobcat]

if you have a recurrence like $p_{t+1} = 2p_t + 5, \ p_0 = 1$, then $p_1 = 2p_0 + 5 = 2(1)+5$

[woven radish]

doaby

[cinder bobcat]

basically replace t with 0 wherever you see it

that gives you $p_1$. then $p_2 = 2p_1 + 5 = 2(2(1)+5)+5$

[woven radish]

doaby

[cinder bobcat]

repeat that pattern and you can get to a formula. OR if you wanna take an easier route, keep calculating your recurrence and see if each of the formulas work

[quick lichen]

so would mine be P3000 = 1900-0.9(3000) = -800?

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@quick lichen Has your question been resolved?

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@quick lichen Has your question been resolved?

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[gray ivy]

hi, im stuck on this problem. the second screenshot shows my work- i am not sure where to go from here. a guide online says to let 2x+1=cosh(x), but i am not sure where that comes from or what to do from here in general lol. thank you!

[devout snow]

@gray ivy Has your question been resolved?

[gray ivy]

<@&286206848099549185>

[devout snow]

@gray ivy Has your question been resolved?

[restive river]

Hi

[gray ivy]

hello :)

[restive river]

have you tried using the exponential representation of hyperbolic functions

[gray ivy]

the e^x form?

[restive river]

ye

[gray ivy]

i have not i will try that right now

[gray ivy]

i just wrote it all out, i dont understand how to isolate the a variable when it's in the exponent of e

[restive river]

https://math.stackexchange.com/questions/205770/hyperbolic-functions-and-the-saint-louis-arch

11 years ago

there seems to be solution

except graphing

[gray ivy]

i was actually looking at that link earlier, but the solution didn't really make sense to me

[restive river]

where is this from?

is this test graded?

have you tried asking your teacher

[gray ivy]

.close

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[raven storm]

suppose f(x) = g(x) + (x-3)

i want to find out number of maxima points and minima points of f(x)

[raven storm]

i already know number of maxima points and minima points of g(x)

so my question is, if i add an increasing/decreasing function to g(x) .in this case (x-3). will my answer change?

or does number of maxima/minima remain same

[lusty sapphire]

You can start to see the answer to your question if you consider how the derivative of f would be different from the derivative of g

[devout snow]

@raven storm Has your question been resolved?

[raven storm]

yea it changes the maxima and minima value itself. but my question is "number of them"

which i believe remains the same

[lusty sapphire]

Hint: let g(x) be a polynomial

[raven storm]

this was the original question

i think the answer is 3 only

cuz g(x) looks like this as it is a cubic equation

and (x-3) wont affect the answer

ahh its fine my brain is too fried forget it. it doesnt affect this one specifically, idk about universal situations.

[lusty sapphire]

Consider g(x)=1/3*x^3-0.5x

[raven storm]

ohhh yea you're right, i see

the maxima minima number changed

ohk good to know.

thanks!

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[quartz lodge]

find the integer x such that C(x,100) = C(2400,100) + C(2400,99)

[quartz lodge]

this is for discrete math

I entered 2400 for my answer to what x was and I got it incorrect

<@&286206848099549185>

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[rugged sparrow]

C represents combination right?

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[calm hamlet]

need some help with a financial math question

<@&286206848099549185>

[solar goblet]

!15min

[devout snow]

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.

[calm hamlet]

<@&286206848099549185>

.close

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[candid lance]

No idea how to do it

[devout snow]

@candid lance Has your question been resolved?

[late rose]

did you find the composite function

try checking if the fuction is increasing or decreasing

then you'll get to know if its one-one or not

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[frank rock]

yr 9 algebra

[frank rock]

if x = 1 wouldn't the area just be the same with/without padding?

wait is this a binomial product?

ohhh

ive been doing it all wrong then

how do I know if it's a binomial prodcut

sorry I'm new to this

of the same?

like terms

ok

yes u correct

okay let me retry

and ill let u know

(x+3)(x+5)

binomial product?

for example

oh ok

[frank rock]

for this it would be (2+1)(3+1)

o

so what would it be

I've been on holidays and just came back to school and she slaps me with this hw

tb?

oh no

I did but it didnt make sense

how 2?? it says x = 1

yes i know

yes i know

but it's area so it doesnt matter it's just length x width

so we only need to use the one on top and one on right

or am I wrong

the length is 3m without the padding

but with the padding it's 3m and 1m

no

3 and 1

OH

I get it

yes

because the 1m is only for half of the padding

bro I just need like 2 weejs to full recalibrate

then ill be fine

ok so (3+2)(2+2)

then

3x2+3x2+2x2+2x2

?

3(2+2)+2(2+2)

[frank rock]

i think tthat the correct method we learnt

ok

so area with the padding is 20

oh

thts my answer

bruv im tryna do my math hw while eating my fish

nawh hold on

I need sum more help

is the missing number 5

only thing is idk where thye got 6 from

how did I miss that

💀

wait so where did they get 5x from

oh yeyeeyey 😭

we learnt tht today

it's so whack

first time hearing abt it

yes

[frank rock]

x*x

thts first

then x*3

is outer

2*x

innter

2*3 outer

last one

this would be 6?

just double checking

[visual hazel]

yes

[late rose]

6

[frank rock]

ok ty

close

?close

.close

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[fervent sapphire]

James Cooke, an undercover agent, has received a tip from an anonymous entity. It’s come in the form of a code, and with enemies around every corner, Agent Cook must decipher the hidden number before it’s too late. Unfortunately, Agent Koek is, uhm… Not the tallest tree in the forest, so he’s going to need your help!

[To: Agent Cake]

{ 3 X 2ABCDE = ABCDE2 }

I can’t even start it please help

[grizzled hazel]

Which letter do u think u could find first?

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[sand junco]

what is 2 and 3 even asking me? im so confused 😭

.close

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[winged coral]

how do i know the quadrant where 2x terminates?

[winged coral]

the question is tan(x)=5/3, sin(x)<0

[candid lance]

U learnt the general form of all four quadrants

ie the signs for x and y coordinates

[winged coral]

what do you mean

[candid lance]

like for example

[winged coral]

yeah i know the signs but what do these have to with that question

[candid lance]

lemme tell u smt

sin theta less than 0

means

its either on 3rd quadrant or 4th quadrant

[winged coral]

and tan is positive so

it’s 3rd quadrant

[candid lance]

either 1st or 3rd quadrant

yeh

[winged coral]

but what i do with that information

[candid lance]

use it

tan is 5/3

[woven radish]

❄ѕησωƒℓαкє❄

[candid lance]

@winged coral

wait

u dont even need that

[winged coral]

um

the question is find the quadrant where 2x terminates but i don’t even know when a 2x terminates

i saw a video explaining and he didn’t say anything about that so i’m confused

but i know the other stuff

if that makes sense

[candid lance]

could u once tell me

what the question exactly wants us to find

[devout snow]

@winged coral Has your question been resolved?

[devout snow]

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[swift sinew]

1. (2 points) On the side AN of triangle AMN, point K is marked such that ∠AKM = β. Find MK, if AN = a, ∠A = α, ∠M = φ

[restive river]

i dont think thats possible

[rugged sparrow]

well you can not find side lengths with only angles

You need at least one side to be able to get an exact value for the side MK

There are infinite such triangles (triangles similar to this one) that can be formed with same angle dimensions

[outer spade]

But AN = a is given

@swift sinew Apply law of sines 2 times

[swift sinew]

can you show examples please

is MK/sina = AN/sin(fi)

i don't think so

they are two different triangles

[outer spade]

Let me type for you

[swift sinew]

would be much appreciated

[outer spade]

$\frac{MK}{\sin\alpha}=\frac{AM}{\sin\beta}$ and $\frac{AN}{\sin\phi}=\frac{AM}{\sin(\alpha+\phi)}$

[woven radish]

kitten

[outer spade]

Now you can exclude AM and find MK

[swift sinew]

aw

i see

thank you very much

yep that's quite easy actually

[outer spade]

[swift sinew]

but how have we found the ∠N?

[outer spade]

It's 180 - \alpha - \phi

[swift sinew]

asjkdanslkdasjda

yes

i see

ok tysm

you are the best

:Fire:

[outer spade]

Happy to help

[swift sinew]

.close

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[proper osprey]

How do we get the $1^k \cdot 1^{n-k}$ part?

[woven radish]

キマイラ

[late rose]

(a+b)^n
general term

they are showing you nCk is (1+1)^n

[proper osprey]

No i mean where does the $1^k \cdot 1^{n-k}$ part come from?

[woven radish]

キマイラ

[late rose]

thats what im saying

they are trying to show you

that nck is nothing but (1+1)^n

[rich summit]

$1^k \cdot 1^{n - k} = 1$, it doesn't add anything, because it's multiplying by 1

[woven radish]

Jelle

[proper osprey]

I'm not sure if i understand it yet, give me a second

[rich summit]

do you understand why the first step is true?

[late rose]

they have the written the same thing

in a different way

[proper osprey]

yes

1^anything is always 1

Is it because of this?

that we can just insert the 1^k * 1^n-k ?

[grim pumice]

its from this formula

[rich summit]

yeah, and x = y = 1

[proper osprey]

oh okay
The thing is, what i posted wasn't supposed to explain

its a problem we were supposed to solve

and i didn't know how to solve it so i looked at the solution

[rich summit]

oh, you want to know how they got to this solution?

[proper osprey]

Yes exactly

it seems unintuitive

[rich summit]

well, if you have a sum of binomial coefficients, it should remind you of this formula

[proper osprey]

okay i'll keep this one in mind

[rich summit]

and once you have this, you need to choose some x and y that make it work

(there is also a combinatorial approach)

It's all the ways you can choose subsets out of a set with n elements

You either pick 0 elements, 1 element, 2 elements, etc..

and then add all those possibilities together

[proper osprey]

okay i understand

but this would be a little harder right

[grim pumice]

the summation is just giving you each term when you expand the (a+b)^n

I think you should look up pascals triangle it links both of this things

[proper osprey]

okay thank you

have a great one

.close

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[merry lily]

you mean what should you label as A, B, C?

go clockwise or anticlockwise, the math will work either way :)

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[graceful lava]

How can we show that G1 x G2 -> G2 x G1 is bijective?

[uneven solar]

You have to show that it is both injective and surjective.

[graceful lava]

ok i think i have an idea

do i do rando elements

like for injective

f(a1,b1)=f(a2,b2)

and we WTS that a1=a2 and b1=b2?

wait or just do we show that (a1,b1)=(a2,b2)

im confused on how directprod works

also if we show one is the other automatically proven? since there are same elements crardinality

[uneven solar]

For injective: f(a) = f (b) implies a=b for all a and b in your domain.

[uneven solar]

yes

[graceful lava]

can u check this
f(a1,b1)=f(a2,b2)

wts a1=a2 and b1=b2

lets make our function

G1 x G2 -> G2 x G1

so f(a1,b1)=(b1,a1)

so then going back

=> (b1,a1)=(b2,a2)

so b1=b2 and a1=a2 proven

since its injective is also surjective since same number of elements

or can also prove by f(a,b) = (b,a)

[uneven solar]

if f(a1,b1)=f(a2,b2), then you want to show that a1xb1=a2xb2

[graceful lava]

or in other words, a1=a2 and b1=b2

[uneven solar]

Yes, if the groups are finite and have the same number of elements it would suffice to show injective

[uneven solar]

I believe so.

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[restive river]

Hey i have a question from physics! what exactly is Q in this case?

[restive river]

electric charge?

[somber panther]

yeah, Q almost always denotes electric charge in this context

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[restive river]

I'm lost on a)

Estimating the values

I know that g(0) = 0

But I am unsure about g(2), g(4), g(6), g(8)

Ping me when respond please

[tame palm]

What are you having difficulty with?

[restive river]

Like I know I have to find the area between 0-2

But how would I do it

It's like this part

[tame palm]

You don't need to be precise, it's just asking for an estimate.

Have you learned about Riemann Sums?

[devout snow]

@restive river Has your question been resolved?

[restive river]

Yes

Please ping me when you respond

[tame palm]

Usea Riemann Sum to calculate the area.

[restive river]

I got 7

Is it correct

[tame palm]

Looks like a good estimate.

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[dry rover]

$D = \left{ \frac{n}{10^k} \mid n \in \mathbb{Z}, k \in \mathbb{N} \right}$. Show that for every ideal $I$ of $D$, there exists $a \in \mathbb{Z}$ such that $I \cap \mathbb{Z} = a\mathbb{Z}$.

[woven radish]

lilisworld.

[magic thicket]

Can't you just say that I n Z is a subgroup of Z ? Since an ideal is a group

[dry rover]

yes actually

i think i can just use that thanks 👍

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[lament schooner]

im a bit confused by the instruction

[dense jay]

-1 isnt in the domain of ln(x)

[crisp niche]

look:

[lament schooner]

so would this me right

[crisp niche]

yes, but , it is ok to write parenthesis in your case, 2 ln ( -x ) + 1

[lament schooner]

if ln of a negative number an error occurs can i still write it with parenthesis

[crisp niche]

i said, you write 2 ln ( -x ) + 1, parenthesies refers to minus x

no need to write absolute value now

[lament schooner]

ohhh okay ty

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[halcyon yew]

Ik this isnt math but can i get help with. Hs chemistry? 🙏🏽

[halcyon yew]

I have a test to

Tom

[restive river]

there is a chemistry server in #old-network i do know some things about chemistry if you need it rlly quick

[halcyon yew]

I just was wondering if u could test my conceptual understanding

About stoichiometry 11

[restive river]

try the chemistry server

[winter torrent]

elements in = elements out

that's it

you put two hydrogen atoms in, you better get two hydrogen atoms out

[halcyon yew]

Idk how to work that server

Can someone quiz me plz

If thas alr

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[proud plover]

i think this is 200 but the answr says 300

[devout snow]

@proud plover Has your question been resolved?

[proud plover]

@tranquil iron

[heady tulip]

hi

show steps

or why you think the answer is 200

[devout snow]

@proud plover Has your question been resolved?

[proud plover]

So if a square ends in 5 or 6 the root must also end in 5 or 6

7 and 8 can't be units digits in squares

So I found out how many numbers ending in 5or6 up to 1000

Since 1000 is sqrt of 1000000

[heady tulip]

so you know there are at max 1000 numbers that are perfect squares

you have to check from 1 to 1000 if it ends in 5,6, 7 or 8

1^2 --> 1

2^2 --> 4

3^2 --> 9

4^2 --> 6

5^2 --> 5

6^2 --> 6

7^2 --> 9

8^2 --> 4

9^2 --> 1

0^2 --> 0

[heady tulip]

if a square ends in 5 or 6 the root must also end in 5 or 6 OR 4

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[heady tulip]

@proud plover

for every 10 numbers there are 3 perfect squares with that property

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[restive river]

guys i need help

[restive river]

this is my work so far

idk how to find x now

[tall stirrup]

Use inverse trig functions

[restive river]

how

[proud plover]

Oh ty

I forgot about 4

[restive river]

bro

dont talk in my channel

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[serene steeple]

(iii)

[serene steeple]

could i please get a hand

[dense jay]

with?

[serene steeple]

(iii)?

[serene steeple]

not sure what to begin

what does it mean by the plane y = xsin(theta)?

[dense jay]

might be sketching the intersection, not too sure to be honest

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[static linden]

ay boys

[static linden]

google is no help so could anyone explain

[weak cove]

What does the sign of the first derivative tell you about a function's increasingness /decreasingness

[static linden]

the slope of the tangent line at that point

i think

[weak cove]

That is what the first derivative evaluated at a point is

but I'm asking you specifically about what the sign tells you

positive first derivative vs. negative first derivative

tells you what about your function

[static linden]

not too sure on that one

[weak cove]

If the first derivative is positive your function is increasing

If it is negative your function is decreasing

heard that before?

[static linden]

well yeah thats intuitive

[weak cove]

Okay then this google search should be just as intuitive

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[sand rivet]

This are the lecture notes about Finite Element Methods to solve PDEs. We have defined several things in general and now want to use them on a specific problem. We are showing, that a boundary problem has a unique weak solution. One step is to show, that a in F(u) = 1/2 a(u,u) - <f, u>_0 is H_0^1-elliptic on page 14. In the proof, there is one step, which is not further explained (the one after using Cauchy-Schwarz). Can you help me understand why we can use this inequality?

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[sand rivet]

<@&286206848099549185> Anyone that can help me with this FEM for PDEs?

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[slim mural]

Ok so, for permutations and combinatorics, are there any fixed formulae for specific conditions?

For example, Consider the word 'domestic'
a) how many arrangements of 4 letters can be made if M is included and the C is not?

[slim mural]

Btw, is anyone open for dms to discuss my permutation question doubts?

I need help with a)

<@&286206848099549185>

[patent thistle]

there are lots of combinatorics formulas

[slim mural]

Which one is relevant here then?

[patent thistle]

well the “C is not” condition basically just says the word is “domesti”

don’t need a formula for that

[slim mural]

So it's just 7C4?

[patent thistle]

no

[slim mural]

Then?

[patent thistle]

“M is included” and there are 3 other letters that go into an arrangement

[slim mural]

____ 4 spots, 7 letters?

[slim mural]

___ 3 spots 6 letters, so 6C3?

[patent thistle]

arrangements sounds like order matters

[slim mural]

6P3?

[woven radish]

Sb

[slim mural]

that's why I am confused

[patent thistle]

there are 6 choose 3 ways to choose the other 3 letters

[slim mural]

WAIT what?

Oh yes that makes sense

[patent thistle]

there are 4! ways to scramble up the m and those 3 letters

[slim mural]

Why can't we do that with Permutations?

If we want to scramble up anyway and have order?

[patent thistle]

you’d just be permuting the 3 not m letters or something

[slim mural]

How would that work?

[patent thistle]

how would what work?

[slim mural]

How would we permutate 3 not m letters and get the same answer as 6C3 * 4!?

,calc 6C3 * 4!

[woven radish]

The following error occured while calculating:
Error: Undefined symbol C3

[patent thistle]

do we though?

6P3 is 120, 4!*(6C3) is 480?

[slim mural]

Idk because I typed a bunch of stuff on calc with Perms and did not get anything close to 480.

Yes so I am wondering if I didn't notice the combs method and wanted to do with perms, how would we do it?

[patent thistle]

going to sleep sorry

[slim mural]

np

<@&286206848099549185>

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[hollow elbow]

Please address this issue in detail 🥲

[odd lantern]

Workings?

[hollow elbow]

yes

[devout snow]

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@hollow elbow Has your question been resolved?

[hollow elbow]

<@&286206848099549185>

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@hollow elbow Has your question been resolved?

[umbral phoenix]

Take x^4 +1 as t^4 and solve

[late rose]

add and subtract 1

in the numerator

and then sperate it accordingly

[late rose]

x still gonna remain

also this is an even function

[umbral phoenix]

no, its not...

wait 2 mins..

[late rose]

x^4+1 = t^4
4x^3 dx = 4t^3dt

then?

numerator there's x^4 not x^3

x still gonna remain in the numerator

[umbral phoenix]

its literally the same... {4x^3 dx = 4t^3dt}
So you can just take, dx=dt

[late rose]

how is that gonna help

you dont even need substitution

[umbral phoenix]

just try it

[late rose]

,rotate

[late rose]

oh

okay okay

[umbral phoenix]

...yeah

[late rose]

alright

my bad

thanks

[umbral phoenix]

dw

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[dense lynx]

oof

it’s possible to solve this integral and to do so without any advanced methods but the process is extremely long and tedious

[devout snow]

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[near trout]

you just do it

it basically gives you 1/(u^2 + 1) and then you know how to do that

are we good or what

[supple knot]

If you don't want people to talk to you, close the channel

Just block them then

[weak cove]

What is wrong with what they said?

x/3 = x *(1/3)

There is no need for quotient rule

[weak cove]

Multiplication?

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[weak cove]

Do you know how to multiply fractions.

x*(1/3)=x/3

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[restive river]

How do I know if a function is one to one just by looking at it?

Like how do I know if f(x) = 2x - 1 is a one to one function (each input only goes to one output)?

[magic thicket]

because you can find an inverse

[restive river]

Uhhh

How do I know that tho

[magic thicket]

in this case because affine functions are very simple

[restive river]

Okay

[patent thistle]

strictly increasing functions are one to one

[lusty sapphire]

Make sure no two points on the graph gave the same y coordinate.

[restive river]

There’s no graph

[restive river]

What do you mean by strictly increasing

[lusty sapphire]

You wanted to know just my looking at it.

You could memorize what the basic one to one functions are.

[restive river]

Okay, what are the basic one to one functions?

[lusty sapphire]

For any two points on the graph, the larger x coordinate will also have a larger y coordinate

[restive river]

Okay

[lusty sapphire]

$y=x^n$ for any odd integer $n$, $y=\sqrt[n]{x}$ for any integer $n$, $y=e^x$ and $y=\ln{x}$. And any of the inverse trigonometric functions

[woven radish]

SWR

[restive river]

Can you teach me how to solve these, idk what to do , where to start. I do know how to solve composite functions, but no idea how to do this inverse stuff

[lusty sapphire]

,rccw

[restive river]

@lusty sapphire

[lusty sapphire]

!noping

[devout snow]

Please do not ping individual helpers unprompted.

[restive river]

Apologies

[lusty sapphire]

Do you know how to do function composition?

[restive river]

Yes

[lusty sapphire]

So what do you get for a)?

[restive river]

That’s for f(g(x))

[lusty sapphire]

Looks good.

[restive river]

What do I do next ?

How do I determine whether the functions are inverses of each other..?

[lusty sapphire]

They're inverses if and only if f(g(x))=g(f(x))=x

[restive river]

Pls explain

I don’t understand

[lusty sapphire]

If f(g(x)) simplifies to just x, and so does g(f(x)), then f and g are inverses of each other

[restive river]

So do I expand these to find out?

[lusty sapphire]

Yes

[restive river]

And if I get an x val as an answr, example: x=2 then they are inverse?

I don’t quite understand this part

[lusty sapphire]

Not "an x value", just x

It just needs to simplify to x and nothing else

[restive river]

Ohh okay I got it

[restive river]

I only need to expand the right side of the equals sign right ?

[lusty sapphire]

Yes exactly

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[sonic crystal]

What is the preferred method.

The method on the left, or the method on the right.

And why?

[near trout]

it's the same thing, use whatever you like

[sonic crystal]

Ok, how would the second method be used on a problem like this?

[restive river]

if i understand it correctly, first you would rearrange the right side to 5/x + 2 and then move the + 2 to the other side as -2

[devout snow]

@sonic crystal Has your question been resolved?

[devout snow]

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[haughty yacht]

Can someone help explain this problem

[inland seal]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[inland seal]

@haughty yacht

[haughty yacht]

Im not sure if Im right. I think the answer if false because you can also have an augmented matrix with no solutions. This is the counterexample i came up with

[inland seal]

Yup

That's right

[haughty yacht]

thank you

For this question idk where to start

[inland seal]

Have you learned about matrix multiplication?

A matrix times a vector

and about transformations?

If not, just start by row reducing the matrix

[haughty yacht]

yeah we have

wait i think ik how to do it give me a sec

[inland seal]

If you have, then ||try representing this as a matrix * a vector, and think of another way to describe w||

||Think of the matrix as a linear transformation||

[devout snow]

@haughty yacht Has your question been resolved?

[haughty yacht]

Im confused on what i should do next

would I think of the augmented part as all individual vectors? and check if its a space space?

[inland seal]

You want it to be consistent

What needs to be satisfied then?

Also remember that w_1, w_2, w_3 are real numbers. They are the components of w

[haughty yacht]

3w1 + w2 + w3 = 0?

[inland seal]

Yes

That's the necessary AND sufficient condition for the system to be consistent

Now you need to check if the subset of all such w, is a subspace

[haughty yacht]

Okay so i think it is a subspace

I get (2, -4, 1)

It has the zero vector, closed under multiplication and addition

How do i find a basis for it

[devout snow]

@haughty yacht Has your question been resolved?

[haughty yacht]

<@&286206848099549185>

[modern gulch]

7-2 = 10/x + 15/x

[haughty yacht]

Not my question 😭

[haughty yacht]

@inland seal

[inland seal]

??

Your answer needs to be yes/no, is it a subspace or not

[inland seal]

And if you want a basis, use this

Write w in its general form, and find the span

[haughty yacht]

wait

im so lost

lemme show u my work

i used to the t values to get a vector

OH

@inland seal would (2, -4, 1) be the basis of the sub space?

[devout snow]

@haughty yacht Has your question been resolved?

[devout snow]

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[prisma elm]

nine units up

why it -9

?

[silent steppe]

im pretty sure the question is incorrect

i plotted it

see it went down

there is a reflection in the x axis and it is moved 2 units to the RIGHT but it is moved 9 units DOWN

[prisma elm]

this is the same

[silent steppe]

i recognize this website

what is the name again?

also i plot this [part 3] still its coming out wrong

Purple is correct

[prisma elm]

ok thanks

.close

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[urban matrix]

Guys how do I write a rule for the sequence 1,6,11,16 first diff is 5

[dense jay]

all diffs are 5

its an arithmetic progression

[urban matrix]

I get that but idk how to make the rule

[dense jay]

have you seen the general form of the terms of an arithmetic sequence before?

[urban matrix]

gimme an example of what ur saying

[dense jay]

An=a1+(n-1)d, where a1 is the first term, and d is the common difference

[urban matrix]

yes

[dense jay]

An is the nth term

[woven socket]

Im not sure how to find my limits

[urban matrix]

I was taught about that 2 days ago lmao

[dense jay]

thats all you need

[urban matrix]

shit I am so dumb, thanks!

.close

[devout snow]

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[urban matrix]

.reopen

[devout snow]

✅

[woven socket]

some of the example solutions just showing the limits, my brain bout to fry

[dense jay]

welcome back

[urban matrix]

wait

lmao

[dense jay]

ashborn go to your own channel

[woven socket]

ohhh mb

[urban matrix]

what is n in the case of An=a1+(n-1)d?

[woven socket]

how can I find my chanel

[urban matrix]

I forgot

[dense jay]

n=1,2,3,...

its the term number

[urban matrix]

?

[dense jay]

1 is term 1 (n=1)
6 is term 2 (n=2)
...

[urban matrix]

you will see it above math help availiable

you can ask ur question there @woven socket

[urban matrix]

oh

so it can be any term for n?

[dense jay]

if you have a1 and d then sure, whatever n you want

[urban matrix]

ex term 1 so the formula in this case would be a_n=1+(1-1)5?

that does not seem right?

[dense jay]

how not?

[urban matrix]

cuz it can be any term

ex a_n=1+(2-1)5

or

[dense jay]

you said term 1

A1=1+(1-1)5=1

A2=1+(2-1)5=6

[urban matrix]

but how do i make a rule

I am so dumb rn sry

[dense jay]

An=1+(n-1)5 is the rule

[urban matrix]

ohhhhhhhhhh

[dense jay]

or equivilently

[urban matrix]

n is aribtary

it could be any term basically

[dense jay]

An=-4+5n ig

[urban matrix]

ye

thanks

[dense jay]

could even say its 5n-4

oh thats what i wrote lmao

nw

[urban matrix]

LOL

.close hopefully

[devout snow]

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[urban matrix]

Thanks @dense jay

[devout snow]

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[smoky gyro]

The rate of change of angle sum S of a polygon with n sides is a constant 180 degrees. If S = 360 degrees when n = 4, find S when n = 7

[smoky gyro]

so I don’t even know what’s going on here to be honest

would like for someone to explain

[distant harbor]

180(n-2)

[smoky gyro]

What

I don’t understand

[glacial valve]

thats the formula for sum of interior angles

when n = 4, 180(4-2) = 180(2) = 360

you can do the rest for when n=7

[smoky gyro]

So S = 180(n-2)?

All I have to do is plug in 7 for n? And get 180(5)?

[smoky gyro]

@glacial valve am I right here?

Well that was easy

.close

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[queen dirge]

Uhh

Tried applying squeeze theorem to both

[wicked turtle]

what happened when you did that?

[queen dirge]

Then since f(x)<=g(x)<=h(x)

I took one of the f(x) and h(x)

And tried finding the equations which satisfy the inequality

I think i might have the right direction but one thing im not sure of is how to get the squeeze theorem of that absolute

Since lim approaches 5, i guess tgat means -[g(x) - 8]

Although im not sure with that

Since i got wrong answers

[queen dirge]

So that i could find g(x)

[queen dirge]

i assumed that if x>8 the equation would be positive, and if x<8, it would be negative

Maybe if i assume g(x) <= 3(x-5)^2 i could find something?

[cinder bobcat]

I think this is simpler than you think.

$|g(x)-8| \leq 3(x-5)^2 \iff -3(x-5)^2 \leq g(x) - 8 \leq 3(x-5)^2$

then immediately apply squeeze Theorem

[woven radish]

doaby

[devout snow]

@queen dirge Has your question been resolved?

[devout snow]

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[plucky kernel]

hi

[fair juniper]

if x-1 is a factor of the polynomial, what is a root of the polynomial?

[queen dirge]

the question was < instead of <= though

how did you come up with <= ?

[cinder bobcat]

Oops, I just misread. shouldn't make a difference tho

[queen dirge]

alright, but why tho

Does it have something to do with R / {5} ?

[cinder bobcat]

they could just as easily include 5 and use <=, so pretty much

all it means is exact equality isn't possible

[queen dirge]

But if you substitute 5, the inequality falls

I think

[cinder bobcat]

we don't even know what g is lol, so we don't know that for certain

[queen dirge]

So basically... In this context, < is the same as <=?

[cinder bobcat]

the only reason they are using < instead of <= is because your domain does not include 5

so you can think of it as the same sure

[queen dirge]

So how does one find g(x) in this

With the squeeze theorem, it's gonna be one of the two bounds right

Or would there be more manipulation

[queen dirge]

Or more possibly i find which one of the two equations satisfy that inequality

[queen dirge]

right?

[cinder bobcat]

as x approaches 5, each side of this inequality goes to 0. what does that tell you about the middle?