help-27

[low holly]

if that makes sense

|x| = 0 and |y| = 0 is one equivalence class

likewise |x| = 0 and |y| = 1

|x| = 1 and |y| = 0

|x| = 1 and |y| = 1

etc.

[restive river]

ohhhhhhhh ok that makes sense

thank you

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[chrome furnace]

Can someone explain why the right hand side is wrong

[lunar harbor]

Prolly cause you should've said something along the lines of 'let f(y)=x'

[chrome furnace]

Yeah but lets say i did that, what would change

Why is the order in which I rearranged wrong

[chrome furnace]

!!!

[lunar harbor]

maybe you were supposed to take the negative case cuz of the domain?

idk I didn't check that deeply

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[restive river]

Does anyone know why for h(x) it isn’t the same answer as g(x)

[midnight dirge]

well

x^2 is always >=0 in R

n for sqrt to b defined in R we need the expression inside to be >=0

so its bit diff

ones -x^2 the other has x^2

[restive river]

wait what i dont understand sorry

[midnight dirge]

kinda like

whats the domain of

sqrt(x^2)

and sqrt(-x^2)

[winter patrol]

you made an error here

[restive river]

anything greater than or equal to 0?

[midnight dirge]

ye

[winter patrol]

no

[restive river]

how then?

[winter patrol]

domain oi sqrt(x^2) would be the set of all real numbers

[restive river]

oh yea

ur right

so all real numbers

[winter patrol]

your end result of [-4,4] was correct for the domain of g(x)
probably due to some pre-knowledge
but you made mistakes in what i screenshotted above

[restive river]

would it be x^2 ≤ 16

[winter patrol]

yes

[restive river]

but then how would i solve for h(x)

i know it would be -4 and 4 when solving for x

[winter patrol]

consider the rough graph of x^2 - 16

you should be able to clearly see where the curve is positive and where its negative

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[forest wind]

Would anyone be able to help me on question 16 a) and b) please

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[devout snow]

@covert pecan Has your question been resolved?

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[green inlet]

I have no idea where to start

is this like a deraitive problem?

[grim agate]

might help if u write the hyperbolics in exponential form

[green inlet]

for sinh(3x) would be it e^3x-3^-3x)/2?

[grim agate]

no, (e^(3x)- e^(-3x))/2

[green inlet]

so it would be (e^kx +e^-kx)/2 / e^3x-e^3x)/2?

[grim agate]

yes

[green inlet]

which would just be (e^kx+e^-kx)/(e^3x-e^3x)?

[grim agate]

yes

[green inlet]

so is it asking which k(x) converges to zero and not infnity?

[grim agate]

no,it need not be zero for it to be finite

[green inlet]

how do you determine the range for finite vs infnite?

[grim agate]

if |numerator| is <= |denominator| then it will converge

[green inlet]

so when it converges if is finite right?

[grim agate]

yes

[green inlet]

and when it divergies it is infite right?

[grim agate]

yes

[green inlet]

ok im not sure if that has been gone in class yet.....

but I know it will likely be covered soon

do I just try and set the numerator equal to the demoantor and solve?

oh, I think I solved it?? I got [-3,3]

[grim agate]

yes looks good to me

[green inlet]

can you go through a quick process just to ensure that I remember the process

[grim agate]

hmm sure

what we did was first written it in exponential form

then for the limit to converge

we need to have

|numerator|<|denominator|

in limiting case

and then u solve it

[green inlet]

|e^(kx)-e^(kx)|<|e^(3x)-e^(3x)|

then you take the natrual log of both sides

to get kx-kx=3x-3x?

is that right?

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[white topaz]

How do I find the mean age of a group?

I am doing a fake ‘research experiment’ and I need to find the mean age of a group. I have ‘300 participants’ who range in ages from 18-25

[zenith jacinth]

by adding their ages and divide by the number of participants

[remote meteor]

literally

[lone ravine]

If it's a fake research experiement you can just invent a number. Instead do as Herels has proposed

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[signal reef]

why is it when dealing with the horizontal stretch/compression we multiply the x cords by the reciprocal (1/k )

like if we have 3 as our k value we divide the x coordinates by 3

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[zealous spruce]

I've written this in every trigonometric form possible

Can't resolve it

[patent marsh]

what's another way to re-write cos(2x)?

[zealous spruce]

So

Multiple ways

wait let me find a photo online

[patent marsh]

bingo

[zealous spruce]

which one

[patent marsh]

now I see there's 1 in there that looks like a good candidate

[zealous spruce]

tan?

[patent marsh]

I would recommend playing around with these

[zealous spruce]

I did

[patent marsh]

but 2cos^2(x) - 1 looks good

[zealous spruce]

Ended up nowhere

[patent marsh]

because we can try that with u-sub

let u = 2cos^2(x) -1, then du = -4sin(x) dx

[zealous spruce]

Where would I go with that

[patent marsh]

not sure if htat would work but just an idea

[zealous spruce]

Oh substitution

[patent marsh]

yep! 🙂

[zealous spruce]

Alright I'll try that

[patent marsh]

sounds good. I gotta head to class so I wont be able to help after but that's the direction I would try first

I think a u-sub is the answer here so play around with that

[zealous spruce]

won't du be 4 cosx sinx

[patent marsh]

whoops yeah you're right

except it'd be -4cos(x)sin(x)

[zealous spruce]

yep

can't go there either

[patent marsh]

oh yeah you're right

yeah u-sub woudlnt' work there

[zealous spruce]

yep

[patent marsh]

well I know that u-sub will work here, it's just finding what would work

maybe play around with tan(x)

[zealous spruce]

k wait

[patent marsh]

I gotta head out, but good luck!

[zealous spruce]

k

Nothing works lol

Ok lemme try splitting it

[bright burrow]

I thought about taking the sinx inside the sq root and doing something with it, what methods have u tried till now💀

[zealous spruce]

every single trigonomentric one

they don't work

But I think I may be onto something

<@&286206848099549185>

anyone? TwT

<@&286206848099549185>

[bright burrow]

Maybe try t=tan(x/2) substitution

[zealous spruce]

it's not that basic

[bright burrow]

The answer i got in maple, seemed pretty long and it had arctans

[zealous spruce]

i got it

[bright burrow]

Howd u do it

[zealous spruce]

Wait I'll take a photo

It was pretty long

@bright burrow

I split the terms in 2 and integrated individually

[bright burrow]

Good work

The main trick was the first step imo

[zealous spruce]

Yeah man

Took me an hour for this question

.close

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[left robin]

like this? $\ \frac{2\cdot \sqrt{x}}{\sqrt{x}}$

[woven radish]

~Martin

[turbid sphinx]

would it just be x=0?

[left robin]

im just trying to understand your equation

$\cos{x}+2\cdot \frac{\sqrt{x}}{\sqrt{x}}$

[woven radish]

~Martin

[left robin]

is that what you mean?

[turbid sphinx]

no

[left robin]

$\cos{(x+2\cdot \frac{\sqrt{x}}{\sqrt{x}})}$

[woven radish]

~Martin

[left robin]

ah ok

when is this undefined?

sqrt(x)=0

therefore when x=0

[turbid sphinx]

Do I just plug in 0 directly?

[turbid sphinx]

Would I have to use the squeeze theorem or anything?

[left robin]

im not familiar with asymptotes and these theorems sorry

thats just what i see here used most commonly

looking when denominator=0

haven't had analysis/calculus yet

but looking at the graph, x=0 looks right

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[tacit cape]

!help

[tacit cape]

i dont get what i did wrong here

so the sum is 1/4x (the 4 isnt x the whole fraction is) +8/5=1/2

so this is how i did it

1/4x times 4/1 + 8/5=1/2 times 4/1

[gleaming socket]

Why did you times only 1/4x but not 8/5 in the left hand side?

[tacit cape]

oh wait

oh yeah

ok hang on ill try that

nope that didnt work either

i got 64/5

but the algebra calculator says -22/5

[gleaming socket]

Show your work

[tacit cape]

WAIT ITS 40

NVM hold on

im a widdle silly boy 🥺

[obsidian elbow]

Check the last second step

It would be (-32+10)/5=-22/5

[gleaming socket]

Yeah you multiplied 32/5 with 2 instead of adding

[tacit cape]

nvm its not

[gleaming socket]

Becareful with the signs

[obsidian elbow]

Dont leave out the signs it hurts the calculation

[tacit cape]

wait 32/5 times 2 is 64/5 right

[obsidian elbow]

No it is not multiplication it is subtraction there

It is -32/5 +2

Not -32/5 × 2

[tacit cape]

oh yeah

[obsidian elbow]

Now try again

By taking lcd and subtracting

[tacit cape]

so its -42/5

[obsidian elbow]

Nope

[tacit cape]

oh wait yeah

because one is positive and ones negative

hang on

so -22/5

[obsidian elbow]

It would be -32/5 +2/1× 5/5

[obsidian elbow]

Yup now its correct

[tacit cape]

alright

thank you

.close

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[obsidian elbow]

Npnp

[devout snow]

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[peak egret]

I’ll translate my problem since its in french

quadratic modeling

A building’s base perimeter is 300m and the area is 4400m2. What are the dimensions of the base?

[peak egret]

i dont know how to find it because usually we focus on one or the other, like y is the area, x is one dimension and a is the other but since its area and perimeter combined im confused

[vivid cliff]

aye aye

hm

[zenith jacinth]

tu viens de donner le périmètre et l'aire de la base là ?

[vivid cliff]

oh nice

[peak egret]

je peux envoyer la question une seconde

numéro 15

[zenith jacinth]

Ok, quand on te demande les dimensions de la base, tu sais de quel dimension on parle ?

[peak egret]

oui, largeur et longueur

genre 2L + 2l = 300

[zenith jacinth]

Nice, tu as l'aire A d'un rectangle qui est :
A = L x l
On sait aussi que le périmètre P est :
P = 2L + 2l

On a là un petit système d'équations

[peak egret]

ouais il faut le modéliser mais je suis tout mélangé

[zenith jacinth]

$\begin{cases} L + \ell = 150 \ L \times \ell = 4400 \end{cases}$

[woven radish]

Ｈｅｒｅｌｓ

[zenith jacinth]

modéliser quoi ?

[peak egret]

complétion du carré pour trouver la valeur de x?

[zenith jacinth]

quel x

tu as vu x où ?

[peak egret]

largeur ou longueur

pardon je l’avais mal expliqué, y est l’aire, x est la longeur et a est la largeur, donc avec ca on peut les transformer en L et l mais en fin de compte je dois les rammener à x

[zenith jacinth]

????????

Tu as juste à trouver L et l

pourquoi tu utilises d'autres variables

[peak egret]

comment je fais ça? est-ce que c’est en isolant une des lettres?

[zenith jacinth]

Bah non, j'y viens justement

[peak egret]

ok

je suis tellement mélangé je m’excuse

[zenith jacinth]

Le mieux serait de déterminer une équation du type :
L+l = s
L*l = p

avec L et l les solutions de l'équation du sécond degré :
X^2 - sX + p = 0

Bon on l'a notre système, donc on l'associe à une equation du second degré :
$X^2 -150X + 4400 = 0$

[woven radish]

Ｈｅｒｅｌｓ

[peak egret]

ohhhhh merci!!

tellement 🫂

[zenith jacinth]

de rien

Si l'equation du second degré n'a pas 2 solutions, il doit avoir un problème

,w x^2 -150x +4400

[woven radish]

Results provided by WolframAlpha

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

Requested by Ｈｅｒｅｌｓ#1420

[zenith jacinth]

Ok bah, ta longueur et ta largeur sont là

[peak egret]

comment es-tu passé de ca à la fonction deuxième degré?

[zenith jacinth]

La magie

Plus sérieusement, j'ai oublié la démonstration, c'est une technique qu'on voit en Première je crois, ça date

Je peux la démontrer vite fait a l'impro

[peak egret]

C’est bon, merci beaucoup pour ton aide, c’est super apprécié!!

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[restive river]

hello, can someone help with this? I've been learning about it but this problem is kinda different from the other ones I have completed and I'm a little confused on how to start it

[devout snow]

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[restive river]

.close

close

.close

[quaint citrus]

alrdy closed

[restive river]

oh

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[tropic rock]

please help

[outer garnet]

Okay

[tropic rock]

i got 7/6 but it was wrong

[outer garnet]

What is 0.6 as a fraction?

[tropic rock]

6/10

[outer garnet]

Yes what is 6/10 + 4/15?

[tropic rock]

10/25

[outer garnet]

There's the problem

You can't just add 6 + 4 and 10 + 15

[tropic rock]

ah ok

[outer garnet]

They need to have the same denominator.

[tropic rock]

30?

[outer garnet]

Yes

[tropic rock]

would the answer be 4/6

[outer garnet]

No

6/10 = 18/30

You multiplied numerator and denominator both by 3

[tropic rock]

alr

[outer garnet]

Now do the same for 4/15

[tropic rock]

8/30

[outer garnet]

Yes

[tropic rock]

26/30

[outer garnet]

Yes

[tropic rock]

then we gotta simpafly

[outer garnet]

Yes

[tropic rock]

by 2

[outer garnet]

Yes

[tropic rock]

13/15

[outer garnet]

Yes

Just saw that you wrote private.

[tropic rock]

😂

all gd

tty

[outer garnet]

np

[tropic rock]

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[civic escarp]

how do i find the probability distribution for (i)

[devout snow]

@civic escarp Has your question been resolved?

[civic escarp]

<@&286206848099549185>

[elfin hill]

Use the property that if you sum all of the probabilities you will get 1

[civic escarp]

i tried looking at the answers and i got this but im not sure how

like why when x=3 is p(x=x) 1/4a

[elfin hill]

You can compute $P(X=n)$ for $2 \leq n\leq 5$ as a function of $a$

[woven radish]

black_couscous

[elfin hill]

Yes

Factorize by $a$ and you have your result

[woven radish]

black_couscous

[civic escarp]

wait but how do u get from 1/2 P(x=2) to be 1/4a

[elfin hill]

It's not

Oh

It is

[civic escarp]

how do you work out the value of it then

[elfin hill]

Because $P(X=2)=\frac{1}{2}P(X=1) = \frac{1}{2}a$

[woven radish]

black_couscous

[civic escarp]

so u multiply the 1/2 by 1?

to get 1/2 a

[elfin hill]

Yes

[civic escarp]

but if u follow that doesnt it mean that when x=3 , you multiply 1/2 by 2

[elfin hill]

No

[elfin hill]

You multiply by the probability that X equals 1

[elfin hill]

Same here with the probability X equals 2

[civic escarp]

OHH

okay

i get it now

thanks!

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[lament raven]

I don't get what angle it wants by counterclockwise of east

[devout snow]

@lament raven Has your question been resolved?

[lament raven]

<@&286206848099549185>

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[analog trellis]

hi, I'm rusty on linear algebra so this might be a dumb q, but I'm stuck on some computations...I tried to use the given eigenvalue to reconstruct the matrix but has been not fruitful.

[analog trellis]

I know that the other eigenvalue is the conjugate

any hints?

what

[rare mantle]

<@&268886789983436800>

[empty tide]

😐

<@&268886789983436800>

[vivid cliff]

aye aye

that’s not cool

hm

[devout snow]

@analog trellis Has your question been resolved?

[hybrid snow]

Ayo what happened

[rare mantle]

some dude said some things

[hybrid snow]

Ah

[devout snow]

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[dull perch]

Is the order correct?

[empty tide]

looks good to me

oh wait

[young fossil]

nope

first line

[empty tide]

watch out for your negatives

[young fossil]

minus minus

[dull perch]

Hmm

[young fossil]

what happens when you take away a negative number?

[dull perch]

You add

[young fossil]

yep :v

[dull perch]

Oh

Thx

[young fossil]

the order is fine gl

[dull perch]

Oh so just the calculation?

[honest meadow]

order of operations is good, just remember negatives

[dull perch]

Ok

Thx

[honest meadow]

so like think of it as -15(4-8m)

instead of 15(4-8m)

[dull perch]

Oh

[honest meadow]

or u can do 15(4-8m) but then after wards multiply everything by -1

[dull perch]

Ok

[honest meadow]

-1(15(4-8m))

[dull perch]

Ok

Thx

You solved my problem thank you

.close

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[devout snow]

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[dry rover]

Hello, can someone help me please, If I know n >= 1 and x >= -1, can someone tell me when (1 + x)^n >= 1 + nx ?? thanks

[dry rover]

no i mean (1 + x)^n = 1 + nx, sorry

[young fossil]

$n \ge 1$
$x \le -1$
$(1+x)^n = 1$

oof my latex sucks

[storm gyro]

This is called bernoulli's inequality, and you need to not let x=-1, i.e. you should have x>-1 as your condition, but if you have that and n>=1 it holds

[storm gyro]

wrap in double dollar signs instead

[young fossil]

ahhh ty

[storm gyro]

or use \\ for new lines

[young fossil]

$$n \ge 1$$
$$x \le -1$$
$$(1+x)^n = 1$$

[woven radish]

Wraith

[dry rover]

wait i dont get it, i let x=-1 and then how do i resolve the equation eqain?

[dry rover]

is this the answer?

so (1 + x)^n sould be equal to 1 ?

[young fossil]

no, this is me writing out the formulas for you

wait

I wrote it wrong, my apologies

$$n \ge 1$$
$$x \le -1$$
$$(1+x)^n = 1+nx$$

[woven radish]

Wraith

[dry rover]

it's okay, so i just take any n and x i want as long as n>= 1 and x <= -1, that's it?

how did you find that please

[young fossil]

this isnt the answer^^^, this is me writing out so its easier to see it written down,
I thought I had it worked out before but I didnt see the "+nx" part.
I probably would have gone about this problem choosing different values for n and seeing where that took me. I'm not entirely sure how to go about it now though. Sneaky said its the bernoulli inequality and says that x>-1 should be your condition. I think he knows a lot about this than me, sorry I can't be more help :I

[dry rover]

ah ok thanks i thought it was the answer, thank you for writing it more clearly 🙂

@storm gyro how do i solve this?

pls

[storm gyro]

I'm sorry what exactly are you trying to solve? are you trying to prove the inequality?

[analog trellis]

it is the Bernoulli's inequality, and don't mean to offend but since now you know the reference, you could easily find a proof online 🙂

if your n is a natural number, you could prove by induction

[dry rover]

i want to solve the equation written by wraith

[dry rover]

yeah true but I just checked and did not really found what i wanted so...

@storm gyro it's the equality i want to solve, not the inequality since it can be proven by induction as amelia said but i wan to know which "x" and "n" lead to (1 + x)^n = 1 + nx

[dry rover]

so basically it's just this equation with the two conditions above

<@&286206848099549185>

@analog trellis any tips? I can't find the answer 😦

[analog trellis]

from wikipedia

[dry rover]

but that's the proof of the inequality, i asked for the solutions of the equation 😦

for example if i take n = 1 and x = 0, I have (1 + 0)^1 = 1 + 1*0 so the equality is correct but now i need to find all the n and x that work

[devout snow]

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[dry rover]

@dry robin

[devout snow]

@dry rover Has your question been resolved?

[dry rover]

@dry robin

@storm gyro

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[marble socket]

hi

[marble socket]

im tryna figure out how to answer this q

A clairvoyant claims that he can tell the suit of any card drawn randomly from a standard pack of
52 cards, without of course seeing it face up.
In a test, he succeeds with 4 out of 6 cards. Carry out a test at the 2.5% significance level, to see
whether his claim is realistic.

how would i even draw the bell graph

nah even thats a wrong starting point

i gotta define if this is 1 or 2 tailed

h0: 1/4 chance every time

i dont know h1 tho

[devout snow]

@marble socket Has your question been resolved?

[marble socket]

<@&286206848099549185>

@violet wind wha would be the alternative?

[marble socket]

i established my h1

p=/=1.4

however whats the sample size?

1?

[devout snow]

@marble socket Has your question been resolved?

[devout snow]

@marble socket Has your question been resolved?

[violet wind]

Alternative is the clairvoyant has >25% probability of guessing the cards

[restive river]

But why not also <25%? He could give intentionally the wrong color to hide the fact that he is a clairvoyant.

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[devout snow]

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[gusty whale]

hi how can i rationalize that

[gusty whale]

?????

[cosmic trail]

conjugate

(a +b)(a -b ) = a^2 - b^2

let a = root 3 and b = 1+root 2

oh wait that doesn't rationalize

well you'll be left with one surd

and then you can rationalize from there, it would be simple

[gusty whale]

okay thanks

[gusty whale]

do i have to write (root 3 + (1 + root2))?

[cosmic trail]

no since addition is commutative

[gusty whale]

ah right

thank you

[cosmic trail]

np

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[old snow]

Hello is my answer for fyx correct

One of my peers said she got fyx=0

i want to know who’s correct

thank you

[loud root]

Yours is correct, it's 36x²y

[old snow]

Okay thank you

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[woven radish]

Results provided by WolframAlpha

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

Requested by e.#6242

[outer garnet]

?

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by e.#6242

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[tame cedar]

.close

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[bitter bison]

i need help on number 10, i can get to 4x/32x^3/2 but iget lost from there

[bitter bison]

ik to move the 32x^3/2 up it has to turn to negatie

so than its (4x)(32x)^-3/2 i believe

but from there i get lost

unless im also wrong on that

[devout snow]

@bitter bison Has your question been resolved?

[bitter bison]

<@&286206848099549185>

[devout snow]

@bitter bison Has your question been resolved?

[devout snow]

@bitter bison Has your question been resolved?

[naive summit]

Remember that the square root affects both terms of the product 32x³

√(32x³) ≠ 32x^(3/2)

[bitter bison]

oh so it would be (4x)(32x^3)^-1/2

?

[naive summit]

yup that's ok

[bitter bison]

than how do i continue from there?

i look at the answer sheet and it says the final answer is (2x)^-1/2

not sure how they get that

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[karmic vigil]

Hello Hi! I have a math question.

So, I'm trying to calculate in-game currency conversion to an 'item' in game.

1000 "Endo" is worth 50$ in game currency.

I'd like to figure out how much is 1575 Endo worth in game.

[karmic vigil]

What formula am I supposed to be using here?

[midnight dirge]

oh yes gamez

i think its multiplication

or ratios?

[karmic vigil]

gamez indeed

[midnight dirge]

like uve to multiply 1000 by

1.575

to get 1575

[karmic vigil]

Yeah, I don't really know. and trying to figure it out online wasn't helping.

[midnight dirge]

similarly multiply the money by that amount

so thats

,calc 50*1.575

[woven radish]

Result:

78.75

[karmic vigil]

why do we want to get 1575 from the 1000 times x?

[midnight dirge]

um

ratio

[karmic vigil]

why'd you multiply :0

[midnight dirge]

like

each endo cost some amt

[karmic vigil]

Also, this is the answer?

[midnight dirge]

in this case each endo costs

[midnight dirge]

ye

[midnight dirge]

,calc 50/1000

[woven radish]

Result:

0.05

[midnight dirge]

but the price is constant

so we can just not calc the ratio

i mean the price

n use the fact that their ratios r preserved

the ratio between cost of endo n cost

[karmic vigil]

I do not understand :^ )

[bitter bison]

alr

ill try to make it a bit easier

so

we need to find the cost of 1 endo

in order to do that

we take the 50$

and divide it by 1000 endo because thats what we are given

so

50/1000

which equals .05

we can make sure of that by doing .05 x 1000=50

once we have figured out that .05cents= 1endo

we can than simply multiply .05x1575

that make it easier or nah, i can try to make it a bit more simple

,calc .05x1575

[woven radish]

The following error occured while calculating:
Error: Undefined symbol x1575

[bitter bison]

opps

its 78.75 anyways

[karmic vigil]

,calc .05 x 1575

[woven radish]

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

[bitter bison]

he did it correct just a bit harder way of understanding

u understand now or want me to try and go in more depth

[karmic vigil]

I see that now

Yeah could we? I'd aprreciate that

[bitter bison]

ok

so we have 50$=1000endo

we need to find how much 1 endo costs correct?

just say like yes to each thing so i can make sure you follow until we find the part you dont understand ✅

[karmic vigil]

Ya that'd be the next step-- I don't know why exactly, but knowing what one cost allows us to multiply by our endo...giving us the amount of money it takes to buy 1575 endo...

[bitter bison]

yes!

[karmic vigil]

I think I get it-- I just need time to let it sink in

[bitter bison]

so in order to figure out how much 1 endo costs

ok!

i can finish if u want or not

up to you

[karmic vigil]

ya pls

[bitter bison]

so

we take the 50$

and are 1000endo

we divide the 50$/1000endo

this will give us how much each endo costs

so its .05cents per endo

after that just simply multiple the .05 x 1575 which will give you 78.75$

understand all that? i cant go into much more detail other then why we first divide the 50/1000

[karmic vigil]

Yeah i got it lol

[bitter bison]

alr cool

[karmic vigil]

Thank you @bitter bison @midnight dirge I know I am not the easiest :^ ) ❤️

[bitter bison]

allg, im not very good at math either

strugglin in hon precalc currently 😆

[midnight dirge]

yayy

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[dry glacier]

Would someone be able to explain what to do with 6ae^a using the quotient rule (differentiation)? I don't understand how to transform this function and the textbook doesn't have examples with this format.

[dry glacier]

Does it just stay in that form as the derivative since e^a would remain e^a?

[proud perch]

Use the linearity of differentiation

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[shadow quest]

with what could i compare it to ?

[spark sleet]

What about (5+2n)/n^4?

[shadow quest]

then ?

[spark sleet]

Then you can distribute 1/n^4

And you get sums that you know their convergence

series in the form 1/n^p , p>1

[shadow quest]

what ?

oh

nvm

i get it

so smart

[spark sleet]

Well, your first reflex should be almost always to compare with power series

When you use the comparison criteria

[shadow quest]

alright ill keep in mind

thank you so much

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[restive river]

$\sqrt{(18)(8)}$

[woven radish]

The guy who asked

[restive river]

Is the correct answer 12?

[midnight dirge]

eh

,calc sqrt(18*8)

[woven radish]

Result:

12

[midnight dirge]

ig

[restive river]

Oh

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[solemn ferry]

guys i have a confusion on cayley hamilton theorem where trying to see what it means but the videos on yt seem very similar to finding eigen vectors and eigen values [the solution process i mean] is it because they use cayley hamilton theory to derive it or is there something else going on?

[solemn ferry]

my first time learning this

[devout snow]

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@solemn ferry Has your question been resolved?

[solemn ferry]

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[midnight dirge]

@arctic field

is this right

[arctic field]

bruh

i thought you were done

[midnight dirge]

the "correct answer"

just wanna

nono

[arctic field]

yes

it is

[midnight dirge]

thrs many Qs

ok

[arctic field]

the correct answer is the correct answer

[midnight dirge]

cuz i dont wanna

look at it understand it

n realise its wrong

as it sometimes is

ok thats all

[arctic field]

lmfao

[midnight dirge]

ill try understnad

bye

.close

[devout snow]

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[midnight dirge]

ye hahhaa

💕

[arctic field]

[midnight dirge]

.reopen

ok yea

[devout snow]

✅

[midnight dirge]

i cant understnad it

@arctic field

whats this mean

the integrand

like say z0=1+i

what would it even mean

[arctic field]

its just constant right

like

[midnight dirge]

OH wait also the prev one, translation invariance

the real part doesnt matter?

[arctic field]

that other one you had integral along the entire real axis

[midnight dirge]

like wed get some parallelogram contour

so its slanted

[arctic field]

so no matter how you translated it left and right it just like doesnt matter

no like

[midnight dirge]

that doesnt rly matter?

[arctic field]

you dont care about the left/right shift

because it covers the entire horizontal line anyway

[midnight dirge]

as long as R is big enough n the contour will just eval into the sum of residues

ye?

[arctic field]

no like

you just

dont care

you just start in the centre

because you're gonna cover from -inf to inf anyway

[midnight dirge]

ok but

[arctic field]

it doesnt matter which finite value you start at

just do substitution to get rid of the constant

doesnt matter

like

[midnight dirge]

so

generally the cond is the blue bit in the top is =0

how do we k the blue bits in the btm=0

given the blue bits in the top=0

[arctic field]

you literally dont care about the translation

[midnight dirge]

thats a nice number

[arctic field]

because it covers from -inf to inf anyway

[midnight dirge]

yea but in this case isnt it just on the real line

[arctic field]

it doesnt matter

it just doesnt matter

[midnight dirge]

dont we hv to do some work

[arctic field]

you dont have to start your integral where your offset is

like

no

[midnight dirge]

to show that the contour of the 2 bits =0

when we slant em

[arctic field]

you dont have to slant them

bruh

[midnight dirge]

btm 2

[arctic field]

the translation doesnt matter

[arctic field]

look

you can just start wherever the hell you want

it literally

doesnt matter

[midnight dirge]

OH WATI

i just realised

ok wait then

so it applies for

[midnight dirge]

if both sides had

x repalced with x+i right

[arctic field]

sure

[midnight dirge]

or just some

x+iy for any real y

[arctic field]

its along the same horizontal line

[midnight dirge]

ok cool

[arctic field]

in the complex plane

you cover the whole thing anyway

[midnight dirge]

i think

im

[arctic field]

doesnt matter where you start

[midnight dirge]

Level 2 translation invariance

WOW

amazing

[arctic field]

gonna just

knock you back down to level -infinity

[midnight dirge]

ok here

what were u sayin

[midnight dirge]

no

[arctic field]

i mean thats what the z0 is supposed to be

[midnight dirge]

at 9 it resets to 0

[arctic field]

do a substitution or something

https://tenor.com/bpZ4K.gif

[midnight dirge]

i dont quite get it

so what r we subbin with

[midnight dirge]

hm

[arctic field]

kinda abuse of notation but whatever

[midnight dirge]

OH WAIT

I JUST REALISED

OK

wow

Level 1 Substituition Jutsu

thanks

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[midnight dirge]

are these 3 not the same? cant we just pick some eps=min(eps1,eps2)

alternatively with R, some great enough R such that 1/R<eps

[devout snow]

@midnight dirge Has your question been resolved?

[arctic field]

@midnight dirge

[midnight dirge]

hi love

[arctic field]

if the definition is given like

the 3 different limits

then yeah you cant really take them together in general

[midnight dirge]

but cant we just pick some sufficiently large one

or small

[arctic field]

no like

you cant take limits together in general

that doesnt work

[midnight dirge]

oh so

this is actually like 3 diff limits

like

lim lim lim

where order doesnt matter

ok wait

what

what does the first mean then

[arctic field]

the first one is a limit in R^2

under the topology of R^2

[midnight dirge]

can u explain it with normal terms

[arctic field]

like if you have

[midnight dirge]

actually

can u give an eg where they differ

[arctic field]

this is an example

[midnight dirge]

o

[arctic field]

if you take like

[midnight dirge]

if we take either x or y first we get 0

?

[arctic field]

yeah

but the limit doesnt exist

because if you set x = y

you get

[midnight dirge]

wdym

u mean for

[midnight dirge]

this?

[midnight dirge]

oh this is x,y approaches 0,0 from any direction rght

[arctic field]

no its

from all directions

more specifically

[midnight dirge]

ye any n all is the same

[arctic field]

in every epsilon-ball of the origin

[midnight dirge]

ok

well

imma go

slp again

bye

thanks

.close

[devout snow]

Channel closed

Closed by @midnight dirge

Use .reopen if this was a mistake.

[arctic field]

👋

[devout snow]

Available help channel!

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[pseudo basin]

@azure elm we don't give answers here.

[devout snow]

Channel closed

Closed due to the original message being deleted

[devout snow]

Available help channel!

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Remember:
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[molten dirge]

15 radical 96 divided by 3 radical 3

[molten dirge]

If that makes sense

Need help with simplifying the answer

[vivid cliff]

aye aye

wassup

eh

er

hm

do u men’s

do u mean*

$\frac{15\sqrt{96}}{3\sqrt3}$

[woven radish]

Springsskateboard

[molten dirge]

Yep

[vivid cliff]

alr so

firstly

do u see

anything

cancelling

[molten dirge]

Not really

[vivid cliff]

alr so

see the

15

in the numerator

and the 3

[molten dirge]

Yea

[vivid cliff]

in the denominator

what is

15/3

[molten dirge]

Isn't it just 5

[vivid cliff]

exactly

so in the numerator

3 is gone

and the 15

becomes 5

[molten dirge]

Ok

Isnt the other answer 32

[vivid cliff]

$\frac{5\sqrt{96}}{\sqrt3}$

[woven radish]

Springsskateboard

[vivid cliff]

wdym other answer

[molten dirge]

For 96 and 3

[vivid cliff]

after this you can simplify

the 96

by thinking

whether it’s

divisible by

a square number

[stuck field]

It's not the other answer but 96/3 is indeed 32. However that's all in the sqrt.

[molten dirge]

Yea. So would the end of the division be pretty much 5 radical 32

[vivid cliff]

eh what

[molten dirge]

Then you simplify

[vivid cliff]

where did

the numerator go

[molten dirge]

I dont know im new to this stuff

[vivid cliff]

denominator*

also

[stuck field]

What do you mean where did it go? The denominator is now 1

[vivid cliff]

??

there’s a sqrt 3

[stuck field]

and there's a sqrt 96 duh

[vivid cliff]

ah I see

what he did

[molten dirge]

Yea

[vivid cliff]

I was slowly gonna

tell him to rationalise

[molten dirge]

I just need to find the simplified answer

[stuck field]

$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$

[woven radish]

What the hell am I doing here?

[vivid cliff]

yeye

I was like

why did he suddenly

skip to that

but ye

[molten dirge]

Because that's where I already am

[vivid cliff]

3sqrt32

[molten dirge]

Ya

[vivid cliff]

bruhh

have a pic of ur work

[molten dirge]

Ok

[vivid cliff]

or is that where

u stopped

[molten dirge]

Thsts where I stopped

[vivid cliff]

alr alr

so

[molten dirge]

I dont know how to simplify it

[vivid cliff]

inside the radical

32