help-39

[pearl pond]

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[pearl pond]

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[lucid ibex]

Hey this is more of a syntactical question. What is the correct way of writing that a part of this expression converges to 0(or infinity or whatever)? For example in this example i know that 5/x converges to 0 but how would i write that correctly?

[versed mica]

i usually don’t write it tbh but you can just put 0s in place of them or draw a slash through them with an arrow saying 0

[elfin stirrup]

and the limit of a sum is the sum of the limits, again only if both limits exist

[lucid ibex]

ok i wasnt sure if that was "allowed" ty both

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[young cloak]

How can I evaluate this multiple integral using polar coordinates if x = rcos and y=rsin? I've been trying to figure it out for quite a while and I just keep getting zero as the result when it's 2/3 supposedly

[pearl pond]

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[young cloak]

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[remote tusk]

Hi!
How to simplify this expression:
X = A' ⋅C ⋅ D+B ⋅(C ⋅ D)+ A ⋅ ( C' ⋅ D ) + A ⋅ B ' ⋅ D
I'm stuck at D(A'C + CD + AC' + AB)

[spiral pivot]

Consider the second term in the parentheses

We can rewrite just this term along with the D as DCD = CD, yes? So we can simplify it to just C

Oh wait

[remote tusk]

i see now that i wrote it wrong*
it should be: D(A'C + BC + AC' + AB')

[spiral pivot]

You've made a mistake already yeah

Well, one thing you can do is do a K map

And see if that helps any

I don't see anything obvious from here

[remote tusk]

yeah right

can consensus be used here?
C is used several times

[spiral pivot]

So the form of consensus is xy + x'z + yz = xy + x'z

Our complement pairs are BC and AC' so for consensus we would need AB, but instead we have AB'

We also have BC and AB' so we would need AC but instead we have AC'

[pearl pond]

@remote tusk Has your question been resolved?

[remote tusk]

D( C ( A' + B ) + A ( C' + B' ) )
there's nothing else to do i guess?

[spiral pivot]

I cannot see anything else.

[remote tusk]

ok thank you so much 🙏

[spiral pivot]

However, did you draw out a k map?

Just in case?

https://en.wikipedia.org/wiki/Karnaugh_map

[remote tusk]

i did but might've done it wrong, i'll take a look at your link
thank you again

[pearl pond]

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[alpine haven]

Can anyone help me with 25 and 26 would be nice if you explained too thanks

[tall flint]

,rccw

[edgy wren]

Show circle D with the question

[pearl pond]

@alpine haven Has your question been resolved?

[toxic fractal]

,rotate

[pearl pond]

@alpine haven Has your question been resolved?

[clear moon]

for 25:
we know angle A and C are equal. then you can get angle ADC and then angle BDC.

for 26:
same reasoning, start with angles A and C are equal. and arc BC is across from angle A

[pearl pond]

@alpine haven Has your question been resolved?

[pearl pond]

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[daring bay]

what did i do wrong ( im trying to find out the concavity switch

[daring bay]

(wp is the point)

[versed mica]

,rotate

[versed mica]

are you looking for point of inflection

$f(x) = \frac{7}{2}e^{-2x}(7+x)$

[jolly parrot]

knief

[versed mica]

this yea?

@daring bay

mistake here

should be 7/2

ok i’m going to go eat

[pearl pond]

@daring bay Has your question been resolved?

[daring bay]

bro

omg

im sorry

its 1/4

not 7/4

and why 1/2

x derived is 1

[sterile flame]

from the 1/2 e

in original equation

[daring bay]

i put it outside the brackets?

[pearl pond]

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[sterile flame]

it’s just not how maths works

[sterile flame]

imagine you differentiate 9x^2

you can’t separate 9 and x^2 then differentiate

same here

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[pearl pond]

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[daring bay]

so

i cant put the number outisde

[sterile flame]

you can’t do half of everything you did

[daring bay]

what the hell man

so i write a exam on friday

and integrals all that stuff

and now i get this info bro

i sm cooked bro

[sterile flame]

it’s a harsh world

[pine jay]

sorry what?

you can infact do that

[sterile flame]

not what I meant

[pine jay]

well what did u mean?

[sterile flame]

you have to read the whole context

he is differentiating 9 to nothing

[pine jay]

Oh lol

[daring bay]

what

where?

[pine jay]

.reopen

[pearl pond]

✅

[pine jay]

incase it gets closed

[daring bay]

where did i do thar

[pine jay]

uh idk if im missing anything but you did nothing wrong for f'

[pine jay]

idk what part u were reading, but theyre not doing that

[daring bay]

what did i do wrong for f‘‘

f‘‘

[pine jay]

im just saying you did nothing wrong for atleast f', havent checked the others

[daring bay]

alright sir ty

i think

[pine jay]

but let me check while im at it

[daring bay]

when i was solving the f‘‘

for the zero points

i didnt use the 1/4 before the e

but its 3 am for me

i gotta sleep man

[pine jay]

same

[daring bay]

can i still see this channel

when i wake up

[pine jay]

probably not

[daring bay]

i got school at 8 am bro fuck me

[pine jay]

same

you can just open a new one

its fine

take ur time and sleep now

and youll have a fresh mind to think about this

[daring bay]

i gotta leaen

im writkg. a exam

friday

i still gotta learn integral tomorrow

of e finction

[pine jay]

i mean i gotta learn too, but i procrastinate by helping lmao

but sleeping is like top prio

you wont learn if you dont sleep

[daring bay]

ok ty

im gonna skip physics

fuck physics

[pine jay]

there is nothing really deep going on here, it seems you already got the concepts down but just made a calculation error (atleast for this problem)

[daring bay]

yeah

but sre the derivatives good

i mean

correct

or what did i do wrong

[pine jay]

now checking

it seems like you only made a simplifcation mistake?

for f''

like you computed it correctly

but then the line after seems wrong if im not just too tired

let me double check lmao

[daring bay]

so

[rose robin]

for f' too
these 2 terms disappeared on the next line

[pine jay]

he simplifed

[daring bay]

yeah

the -2 too

[pine jay]

oh wait

yeah

[daring bay]

i simplified

[rose robin]

it should be (-2x-1) not -2

[pine jay]

yeah that too

the simplifications is the mistakes here

[daring bay]

why -1

[pine jay]

factor out e^(-2x)

what do u get?

[daring bay]

-2

[pine jay]

so we have e^(-2x)(-2)(1+x) + e^(-2x) inside the bracket from the 2nd line right?

3am be hitting

[daring bay]

i guess bro

[daring bay]

wait

what was wrong here

[pine jay]

im just reading off ur 2nd line

[pine jay]

ur simplification

[daring bay]

why is it wrong

[pine jay]

because e^(-2x)(-2)(1+x) + e^(-2x) = e^(-2x)(-2x-2 + 1)

you wrote e^(-2x)(-2x -2)

missing the +1

[daring bay]

OHHHH

YES

OMG

I GOT CONFUSED

[pine jay]

and the same misstake again in f''

[daring bay]

BECAUSE its times 1

[pine jay]

🫂

yes

[daring bay]

but

in f‘‘

i did subtract -2

[pine jay]

oh u did

maybe im too tired

[daring bay]

ok beo

go to sleep bro

[pine jay]

u too!

[daring bay]

@rose robin hey bro

i need ur help for 3 minutes bro just really wquick bro

[pine jay]

u got the concepts down, its fine

these are just calculation mistakes

nothing deep

sleep over it!

[daring bay]

alright beo

im stressing

cuz i gotta leanr integrals too tomorrow

[pine jay]

im trying to make u not stress, its better if you actually have sleep to learn

you wont learn anything

if u dont sleep

[daring bay]

yeah

[rose robin]

it's (-2)(-2x -2) is (4x+4) then there's the -2 from the other term
so it should be (4x+2)

[daring bay]

oh

right

so first times -2

then -2

oh ok

[rose robin]

oc that derivative will be wrong bc you simplified f' wrong

[daring bay]

yeah

but ty

alright im glnna sleep now

[rose robin]

yea np

[daring bay]

ty guys

[rose robin]

gn

[pine jay]

i mean whats the point in correcting a mistake in a mistake that cant be corrected (vaguely)

yes sleep!

[rose robin]

I feel like that wouldn't let me sleep if I was him

[pine jay]

lmao

.close

[pearl pond]

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[iron shore]

is this right?

[tall flint]

seems fine

[pearl pond]

@iron shore Has your question been resolved?

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[radiant lake]

I need urgent help on this similarity problem for geometry.

[radiant lake]

<@&286206848099549185> Been 15 Minutes

[woven oak]

just matches letters

like letter 1 * letter 2 must be over letter 1 * letter 2 on other side

[radiant lake]

Ok, Oh so then its first one and last one

[woven oak]

exactly

[radiant lake]

Right?

[woven oak]

yea

[radiant lake]

Ok thanks!

[woven oak]

good job

[woven oak]

np

[radiant lake]

Also what would this be?

Wouldnt HL be “solving for more”

Plus we dont have hypotenuse

Oh its SAS

.close

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[alpine haven]

Do u know how to get the X

[pearl pond]

@alpine haven Has your question been resolved?

[pearl pond]

@alpine haven Has your question been resolved?

[pearl pond]

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[rugged ocean]

This is a dumb one but I’m confused on how a simple formula works. The question is “there are two pizza ovens. Oven 1 burns 3 times as many pizzas as oven 2. If 12 totals pizzas were burnt, how many pizzas did oven 2 burn?”
The formula is easy, it’s 3x+x=12. What I’m confused about is how this formula answers the question, and how I know when to use it or how to change it for different scenarios. I have the answer, it’s 3, but I really don’t get how this formula answers the question

[bitter lynx]

oven 1 burns 3 times as many pizzas as oven 2

so we can say the amount of pizzas burnt by oven 2 is x

do you agree?

[rugged ocean]

Yea

[bitter lynx]

and since oven 1 burns 3 times as many as oven 2, we can say the pizzas burnt by oven 1 is 3x

so we have

3x + x = 12

[rugged ocean]

But then aren’t we sort of solving for either oven? 😭

Like what part of this says “yes this solves for oven 1”

[bitter lynx]

yea, we are

if we know x = 3

then we know oven 2 burnt 3 pizzas

and if oven 1 burnt 3 times as much

then 3*3 = 9

oven 1 burnt 9

9+3 = 12 pizzas burnt total

[rugged ocean]

I’m struggling on how to word what my question is

So this solves for oven 1

but how do we know that outside of just…knowing

[bitter lynx]

we know that because the formula tells us, and we set the variables ourselves to represent the ovens

[midnight haven]

Oven 1 + Oven 2 = 12
If Oven 2= x
And oven 1 burns 3 times as oven 2 then Oven 1 = 3x
Let's substitute in our original formula which is oven 1 + Oven 2 = 12
So it'll be 3x + x = 12
4x=12
Divide both sides by 4 to get x = 3
And oven 2 = x = 3

If we wanted to find for oven 1 we'd substitute in oven 1 formula which is 3x so 3 * 3 =9

So oven 2 burns 3 while oven 1 burns 9

Which is 12 in total

[rugged ocean]

This one makes way more sense to me

[midnight haven]

Glad to hear

[rugged ocean]

Sorry I know it’s a dumb question but like

[bitter lynx]

no dum questions

[rugged ocean]

I need to take this and then apply it to more stuff so it was really confusing me

[bitter lynx]

we here to learn!!

[midnight haven]

No question is a dumb question

[midnight haven]

^^^

[rugged ocean]

Well, I appreciate it

[midnight haven]

If you need help with other questions we'd be glad to help

[rugged ocean]

I’ve been doing circles and velocity and stuff and all that made sense but for some reason THIS messed with me so much

[midnight haven]

Ahaha trust me I can relate it's always the simple stuff that makes your brain go null for some reason

[pearl pond]

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[untold pebble]

can somebody please explain why the -n/k term disappears

[pearl pond]

@untold pebble Has your question been resolved?

[steep saddle]

is this big O time complexity

[untold pebble]

yes

[pearl pond]

@untold pebble Has your question been resolved?

[pearl pond]

@untold pebble Has your question been resolved?

[pearl pond]

@untold pebble Has your question been resolved?

[midnight haven]

Have you tried to expand the series?

[coarse harbor]

Because O(n^2/k - n/k) = O(n^2/k)

[untold pebble]

What do you mean sorry?

[untold pebble]

Why?

[coarse harbor]

$\lim_{n,k\rightarrow\infty}\frac{n^2/k-n/k}{n^2/k} = 1$

[jolly parrot]

EQUENOS

[untold pebble]

From this property

[coarse harbor]

alright

[untold pebble]

If we remove -n/k because max(n^2/k, -n/k) = n^2/k, then shouldnt we remove n too then?

[coarse harbor]

No because k might grow as O(n), for example

And so O(n^2/k) will be the same as O(n) in this case

Or even worse, if k grows as O(n^2), then O(n^2/k) = O(1), while O(n^2/k + n) = O(n)

So indeed O(n^2/k + n) and O(n^2/k) mean different things

[untold pebble]

Okay got it

Thanks very much

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[barren sphinx]

Heya! Does anyone know how to solve this? I really appreciate any help.

[spiral pivot]

Here's a question, is 21! divisible by 21?

what about 22!?

[nova spindle]

$a+ b \mod c = ((a \mod c) + (b \mod c)) \mod c$

[spiral pivot]

Starting from which value is n! divisible by 21?

[nova spindle]

oh wait its a sum not a product

[jolly parrot]

Karma

[barren sphinx]

I mean both are divisible by 21 since it contains 21.

[spiral pivot]

Yes, this is true.

Is 15! divisible by 21?

[nova spindle]

hint: prime factors

[barren sphinx]

yeah

[spiral pivot]

so what's the smallest number n, such that n! is divisible by 21?

[barren sphinx]

7!

[spiral pivot]

exactly, so for all values 7 or larger, the remainder is 0 when divided by 21.

So you only need consider values smaller than this

[barren sphinx]

ohhhh

so n > 6

[nova spindle]

there's actually another hidden factor of 21 in (6! + 5!), not necessary to spot to do the problem ig but maybe makes it easier

[barren sphinx]

okay so since its 1!≡1, 2!≡2, 3!≡6, 4!≡3 and 5!≡15
1+2+3+6+15=27
27/21=1≡6 so last digit is 6 is it correct?

[nova spindle]

no

[nova spindle]

.

rule is "mod early mod often"

[spiral pivot]

sorry what I'm dumb

[nova spindle]

24 lol

[spiral pivot]

4! = 24 = 3 mod 21, yeah

[nova spindle]

1+2+3+4 = 10, 4! = 24

5! is also not 15

[nova spindle]

if you were curious

5! = 5*4*3*2*1 = 20*6
6! = 6*5! = 20*36
20*36 + 20*6 = 20(36+6)
20(42)
20(21 * 2)

[spiral pivot]

5! = 120 which 21 * 5 = 105, so 15 mod 21

but yeah, you can actually make your life a little bit easier.

by just doing 5! = 4! * 5 = 3 * 5 = 15 mod 21

then 6! = 5! * 6 = 15 * 6 = 90. And then 21 * 4 = 84, so 90 is 6 mod 21.

[barren sphinx]

ohh

[spiral pivot]

So you have 1 + 2 + 6 + 3 + 15 + 6 overall

[barren sphinx]

can u explain bit more abt last 6 im kinda confused now

[nova spindle]

n-no

6! is 720

[spiral pivot]

yes

6! is 720

however, we're only caring about mod 21

so because 6! = 5! * 6 and we know that mod 21 5! is equivalent to 15, we can use that instead.

[nova spindle]

oh yh my b. dont be putting equal signs where they dont belong tho

[spiral pivot]

difficult to manage on keyboard. And I didn't feel like latexing stuff.

[barren sphinx]

thanks guys 🙏

.close

[pearl pond]

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[pearl pond]

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[hoary wharf]

how do i find the rule for the sequence 7/8 5/8 13/24 1/2

[hoary wharf]

i know that between a1 and a2 is 6/24 , a2 and a3 is 2/24, and a3 to a4 is 1/24

but idk how to put this into an explicit sequence

[pearl pond]

@hoary wharf Has your question been resolved?

[fallow veldt]

not rlly sure if I understood what u want

could u rephrase it

[pearl pond]

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[pearl pond]

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[daring bay]

hi what happens to the ax in the abx here?

[tender gate]

in which step?

[daring bay]

the one

where i marked ??

like

the ax just disapears

[tender gate]

oh

my bad i didn't see the ??

in II the value for a was found

so it was plugged in

[daring bay]

its solved

but

[tender gate]

and you get 2 + 2*(1/2) *b

[daring bay]

bro

i got a question

[daring bay]

yes

so 1b

right

[tender gate]

yeah

[daring bay]

ok bro

so

listen

i just realized

exponential functions

coming in tomorrows exam

so

[tender gate]

uh oh

[daring bay]

im just gonna sleep

[tender gate]

😂

[daring bay]

i cant study anymore

i swear

so much shit

[tender gate]

nah hol on

[daring bay]

now i gotta learn ln()

and stuff

[tender gate]

just remember these couple things

very important for exponential

ln (e^x) = x

leme write it in latex hol on

[daring bay]

ty

[tender gate]

$ln\left(e^x\right)=x$

[jolly parrot]

eggman

[tender gate]

thats an important rule

[daring bay]

yeah i just had that stuff

eait

wait

let me show u something

[tender gate]

becasue you can use it by multiplying the whole equation with ln and you can drop the x

and everything up there in the e

[daring bay]

tbh bro e functions and exponential functilns kinda the same

[tender gate]

these too

[tender gate]

eeh kinda yeah

[daring bay]

look

e^-3b

then he does ln

what does ln even do bro

[tender gate]

ln is a function ?

leme double check

its like e^()

yeah it is a function

ln(x) = number

ln(e^x) = x

ln(e^xy) = xy

you can also write xy*ln(e^1)

yeah like if on your exam tomorrow you're solving an equation and you get e^(...) = number

you can multiply both sides by ln and you would get ... = ln(number)

and then solve ln(number) your calculator or keep it as it is

aight imma go sleep

good luck on your test tomorrow

[daring bay]

wait

[daring bay]

so ln basically just gets rid of the e?

[tender gate]

Yeah

[pearl pond]

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[pearl pond]

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[raven spade]

What do I do after this?

[prime pier]

L'Hôpital's Rule

[raven spade]

I'm new to the concept

How do I go about using it here

[strange veldt]

does phyisics count as math

[prime pier]

yea but pls open up a new help channel instead of hijacking someone else's

[prime pier]

nvm i didnt read ur question

but now i did

u dont need L'Hôpital's Rule

just apply the limit by subbing in 0 for x

and thats ur answer

[raven spade]

-4/3?

[prime pier]

L'Hôpital's Rule is when subbing in 0 for x results in 0/0 or infinity/infinity
i wrongly assumed ur equation would lead to that since u were stuck

[prime pier]

correct

assuming ur simplification was correct

in the earlier steps

[raven spade]

The 8th question is the og q btw

Forgot to mention this mb

Cus I directly used binomial expansion

For the exponential parts

[unborn abyss]

,rccw

[strange veldt]

rude muc?

[raven spade]

It does convert to 0/0 here

[prime pier]

what

happened to the powers

in ur one

[raven spade]

Used binomial expanion

(1+x)^n = 1 + nx

Is that valid

[prime pier]

no

[raven spade]

Why so

[prime pier]

maybe it is valid, but no, thats not how you should approach the question
instead apply L'Hôpital's Rule
differentiate the numerator
differentiate the denominator
then apply the limit with the derivatives

[raven spade]

Ah okay

[main oxide]

factor the denom as difference of squares

[raven spade]

We don't differentiate the entire fraction as a whole with lhopital yes?

[prime pier]

no let
numerator = f(x)
denomiator = g(x)

then u find f'(x)
and g'(x)

then apply limit with
f'(x)/g'(x)

[raven spade]

Yeah I'm getting -1/6

Tysm

[prime pier]

perfect

nws

[raven spade]

. close

Gottverdammt

.close

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[coral lava]

It’ll be a scalar

You want the dot product of ai+9j and <3,1> to equal 0

[shut shard]

Oh ok thanks

[coral lava]

Np

[pearl pond]

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[midnight haven]

Hi

[midnight haven]

I only need question 15

And I don't even know where to begin

[vocal isle]

well

when you don't know where to start

define variables

so we can call $m\angle A = x$

[jolly parrot]

rain

[midnight haven]

Measure of A = x

[vocal isle]

well ignore that actually

they tell us that A is thirteen less than C

can u make that an equation

[midnight haven]

A=c-13

[vocal isle]

yes

can u make the second statement an equation too

[midnight haven]

B=4c-11

I need to know what angle C is, but I don't know how to with angle A and B

[vocal isle]

you have a third equation

what is a+b+c in a triangle

[midnight haven]

180

But I can't do that equation without angle C

You there?

[vocal isle]

you have three equations

and three variables

its solvable

[midnight haven]

Yeah, and I'm having trouble trying to solve for angle C

Can you help me solve for angle C?

If you're just gonna keep leaving and coming back telling me the equation is possible, I'll just get a different tutor

.close

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[stuck hamlet]

hi

[vocal isle]

hi whats ur question

[stuck hamlet]

Could you explain for part d why there is no acceleration

For fnety = ma

[sick latch]

the object is not floating or falling

so vertically there is no acceleration

as its vertical velocity is at 0

all the time

[stuck hamlet]

but even if it is on the floor isnt there still gravity pushing it down?

[sick latch]

ye

what is vertical acceleration?

[stuck hamlet]

0

[sick latch]

mb

like what is acceleration?

definition

[stuck hamlet]

how much it speeds up over time

[sick latch]

which is basically a change in velocity

so rn the object is resting on the floor meaning its vertical velocity is 0

the object continues to rest

its position doesnt change

[stuck hamlet]

ah

[sick latch]

so we can infer there is no change in velocity

and therefore no acceleration

[stuck hamlet]

but if the object is moving on the floor then there is gravity

[sick latch]

but that gravitational force is countered by the normal force

[stuck hamlet]

ok i get it tysm

'

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[plush moss]

You can express any nth root with an index

Where
$\sqrt[n]{x} =x^{\frac{1}{n}}$

[jolly parrot]

denzio321

[royal gull]

I understand that part but i dont understand if k times x^n is asking for k to be simplified to a single number so in a. 2x^-4/3 is simplified into a whole number

[plush moss]

By k they probably mean a constant

A term without x

[royal gull]

theres no constants tho

[plush moss]

There is you see the 2 and 3 in a.)

[royal gull]

oh

so i jus multiply the 2 and 3 , remove it from the x's and then multiply the 6 with the x's after i simplify it into x^n?

so 6 times x^-1

[pearl pond]

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[lament dagger]

How can I prove that every isometry is a topological embedding?

[lament dagger]

I have proven that isometries are continuous and injective. Do I need to show anything else?

[pearl pond]

@lament dagger Has your question been resolved?

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[hard locust]

Apparently the first one is incorrect but I can't seem to figure out how?

[pearl pond]

@hard locust Has your question been resolved?

[tropic saddle]

I'll ignore the obvious issue with the first equality sign

the terms you need to divide are $\frac{(n+1)x^{n+1}}{2^{n+1}}$ and $\frac{nx^n}{2^n}$

[jolly parrot]

Denascite

[tropic saddle]

you forgot about the n+1 in the first one and when dividing them you forgot about the n in the second one

[pearl pond]

@hard locust Has your question been resolved?

[hard locust]

Oh, thx

.close

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[scarlet glen]

Where did I go wrong

[scarlet glen]

it's derivative only using first principle

it's little off from the answer

<@&286206848099549185>

[autumn trellis]

You forgot the square root

[pearl pond]

@scarlet glen Has your question been resolved?

[pearl pond]

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[scarlet glen]

.reopen

[pearl pond]

✅

[scarlet glen]

can u re-elaborate

where is the square to begin with? or am i missing one?

sorry i was afk

[autumn trellis]

It was there in the line and went away in the next line

[autumn trellis]

Look at the tips of the arrows

[scarlet glen]

u meant square roots?

ah

[autumn trellis]

Yes that is what i said here

[scarlet glen]

sorry

i only read squar

extremely sorry

i will retry

tq alot

it got solved

:)

i am dumb

sorry and thank you

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[pearl pond]

@naive marlin Has your question been resolved?

[ivory swallow]

what do you get when you take the dot products?

yes but you should get an equation

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[rich jolt]

how will u do this without vector inequalities?

[pearl pond]

Please don't occupy multiple help channels.

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[green dew]

n and q are integers

my work is this

the remaining integral after doing IBP, if i keep integrating it by parts, the exponent q of ln(t) will keep going down by 1

while tⁿ stays the same

idk if thats useful info

[pearl pond]

@green dew Has your question been resolved?

[green dew]

<@&286206848099549185>

[pearl pond]

@green dew Has your question been resolved?

[green dew]

<@&286206848099549185>

[pearl pond]

@green dew Has your question been resolved?

[green dew]

<@&286206848099549185>

[vocal isle]

whats ur question

whether ur work is right?

or asking the answer

[green dew]

how to solve it

i showed what i did

thats all

[vocal isle]

that is a hard integral

have to write it out

you can u-sub $t = e^{-u}$ and then the integral becomes the gamma function

[jolly parrot]

rain

[vocal isle]

i think you can also do this by integration by parts

[pearl pond]

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[midnight haven]

if arcsine(y) = theta
Can we say sin(theta) = y?

[timber tartan]

Yeah

But y should be from -1 to 1 only

[vestal tapir]

which it is

[midnight haven]

If sin(theta) = y, then can we say arcsine(y) = theta?

[vestal tapir]

or the first line is not true

no, this one doesn't work

[timber tartan]

No we can't say that

|arcsin(x)| ≤ 0.5π

That statement is only true for |y| ≤ 0.5π

[midnight haven]

y?

lol

[midnight haven]

....

[midnight haven]

....

since theta can exceed the daily limit, but arcsine can't, we get a contradiction, showing that we can't say this is true always

[vestal tapir]

it's literally like the square roots
if sqrt(x) = a then a² = x
but if x² = a, then sqrt(a) may be something else and not x

[midnight haven]

wait

won't x be either -a or a?

[vestal tapir]

yes? idk

[midnight haven]

ok

I get it

Thank you

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[junior vapor]

how do u do part i?

[scenic marsh]

Since the absolute value of anything has no complex part, you know the complex part on the other side of the equals sign must equal 0

[warm current]

!nosols

[pearl pond]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[scenic marsh]

@warm current ? Is this fine now

[junior vapor]

ohhh that makes sense

to find z do i hv to sub in a-12i and then expand everything?

i feel like there's as faster way cus its only 2 marks

oh wait i think ik

thanks you!

[scenic marsh]

Not necessarily

[junior vapor]

do i do like a-12i+8=sqrt(a^2+144)

but since the right hand side is all real

i can disregard the 12i?

[scenic marsh]

Not exactly I think

Wait

Maybe

[junior vapor]

oop

[scenic marsh]

Actually yes I think you’re right

Or on the right track

[junior vapor]

ohh ok thats good

[scenic marsh]

It relies on
|a+bi|=sqrt(a^2+b^2)

[junior vapor]

yep

[scenic marsh]

so if a+bi=z then you can do some work

Perfect

[junior vapor]

yep got it thank you very much

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[static wasp]

Could I get some help on these two questions? They're the last hw questions I've got

[static wasp]

For problem 2, I wasn't sure if we needed to find x= something or just be able to use the bounds. So I used the bound but I believe my answer is very wrong

I'm a little closer on 3, currently doing the determinant for u and v but I got stuck since I need to find them in terms of u and v

[dusk horizon]

problem 2 is just about finding the bounds.

[static wasp]

so like the lines that make the shape?

I saw an example and it looked super complicated so I got very scared

[dusk horizon]

once you know where the bounds are, it's just evaluating 3 separate polynomial integrals.

[static wasp]

Ahhh okok! Let me try to do that then!

I haven't gotten the bounds yet but I think I got the equations, so far I have this:
yz: z=-3/2y + 3
xy: y=-2x+2
xz: z=-3x+3
does that sound right?

Also, I'm trying to get the bounds but, how do we know which one is the bottom bound and which is the top one?

for example, I just solved for x and got 2 equations: -y/2 +1 and -z/3+1

how do we know which is the top bound?

[dusk horizon]

I don't know what you're doing here. What's t?

[static wasp]

oh oops, I meant to put y there, sorry!

[dusk horizon]

having bounds in 2 dimensions isn't really that helpful.

[static wasp]

would these be okay bounds: 0 to -y/2 + 1 for dx, 0 to -2/3z+2 for dy and 0 to 3 for z?

[dusk horizon]

this is a strange question in context because of where the tetrahedron is. The lower bound is always 0 and you know it's the lower bound because the rest of the tetrahedron has positive coordinates only.

[static wasp]

yeah, I realized the better bound would be 0 to something but I'm still a little confused on which one to use

[dusk horizon]

Work from outside in. 0 to 3 is good for z.

[static wasp]

ohhhhh okokok

outside in? how so? sorry I'm confused by that

[dusk horizon]

figure out z first, then y, then x

z is the easiest because it has constant bounds

[scenic marsh]

Your z bounds should be constants
y bounds should be one in terms of z and the other 0 (since a vertical part of it isn’t a function of z, just 0)
x bounds in terms of y and z for one of them, and the other should be 0 for similar reasoning above

[dusk horizon]

0 to -2/3z+2 for dy
This looks good too.

[static wasp]

OHHHH! okay! That makes sense! Thank you!

so I've gotta fix my dx one then since it only hay y

*has

[scenic marsh]

Every bound should only contain variables that are farther inwards on the integral, otherwise they wouldn’t go away when integrating

[static wasp]

ahhh okokok, that makes sense!!

[dusk horizon]

in theory, it's possible to have integrals where the inner bounds don't use the outer variables (like if you're integrating over a rectangular prism), but that's not the case here

[static wasp]

ahhh gotcha gotcha

so to find the upper bound of dx, would we use some type of tetrahedron equation?

[scenic marsh]

My way of thinking about it that is easiest to explain is if x and y are on the outside because then the last direction is z, and you can just think of filling the shape with water. What function tells you the shape of the bottom? Which the top? The same idea applies to other orders or integration but easiest to say vertically

[scenic marsh]

The equation of the plane in terms of y and z

[static wasp]

ohhhhhhh! okay! that makes sense!

[static wasp]

OHHH! but wouldn't we need a vector for the equation of a plane? I'm googling it rn since I don't know it off the top of my head

[scenic marsh]

Yes and honestly I don’t remember how to do that but I have my calc iii final coming up

Something something normal vector I know

[static wasp]

ahh okokok, I'm using geogebra rn trying to find this plane lol

I'm just not sure where the vector would come form since we only have vertices n stuff

[scenic marsh]

It’s perpendicular to the plane

The vector that you need

Idr how

[static wasp]

would the plane x=1 - y/2 - z/3 work?

it has both y and z

[dusk horizon]

I think that's good. You can do some quick checks that it goes through the vertices that you want it to.

[static wasp]

sick! and yeah I checked it and it does go through the vertices

now I've just gotta do the integration

also for problem 3, we need to do a determinant for it right?

[dusk horizon]

why a determinant? Not saying it's wrong, but I don't see it.

[scenic marsh]

I would guess it wants change of variables

So blah blah blah determinant Jacobian whatnot

[static wasp]

yeah, that's what I remember anyway, I don't remember any of the steps to get to the determinant but I remember there being one

[dusk horizon]

wouldn't the change of variable just be a rotation though? So it would have determinant 1. But the actually changing of variables sounds like a nightmare here.

[scenic marsh]

I do think you’re right

[static wasp]

wait, so it could be done with just the equations of the sides?

[scenic marsh]

I don’t think it would be a rotation

I think it’s something like squishing a parallelogram to be a rectangle or something like that

[dusk horizon]

it's already a square

that touches the origin

[scenic marsh]

Gulp what

A rotated one

I guess

[static wasp]

its slightly tiled tho? dunno if that matters tho

[dusk horizon]

you could do it the same way that you just did the other question, though you might have to split it into more than one integral.

[scenic marsh]

It does matter because then to set up your bounds youd have issues

[dusk horizon]

Yes, it's rotated. That's why we might want to rotate it back. 😄

[static wasp]

ah dang 😭 so more than the two it already has? just looking at it is 💀

[static wasp]

ohhhh okok! So would that happen through a change of variables? or something else?

[dusk horizon]

I don't mean like a triple integral. I mean it would be 3 separate double integrals.

[scenic marsh]

As things stand (before change of variables) you would need to set up 3 different integrals because the equations for your bounds are changing

[static wasp]

ooohhhhhhhh! Okay! that makes sense and sounds like a nightmare ngl lmao

[dusk horizon]

the dotted lines here show the regions of those 3 separate integrals

[scenic marsh]

It is a nightmare! Thats why we are lazy and don’t want that

[static wasp]

https://tenor.com/view/skeleton-reaction-information-my-reaction-to-that-information-my-honest-reaction-to-that-information-gif-613275461876515673

frfr

like hell naw, my brain would explode w that

[scenic marsh]

The region sucks but that’s not to mention the integrand pre-change is also… gross

[static wasp]

https://tenor.com/view/david-rose-gif-3214199033367100027

[dusk horizon]

Oh wait, the numerator and denominator both look like they're chosen to make the change of variable nice

[scenic marsh]

Exactly

[static wasp]

actually 😭🙏

[dusk horizon]

the 2, -1 is the same vector as the sides of the square

it's nice to see your options though, even if some are less appealing

makes you appreciate doing rotations

[scenic marsh]

Change of variables problems are some of the most obvious no brainers ever when you see the alternative

[static wasp]

HONESTLY like damn

still, not what I expected linear algebra to end w lmaoo

[scenic marsh]

wtf 😭

[static wasp]

yeah...

[scenic marsh]

Why is that in linear algebra?

[static wasp]

idk man 😭😭😭

the last section thingy is this

like bruh-

I thought I did my time 😭😭😭 shit is coming back for blood frfr

it could be worse tho so it is what it is

also also, this, would you just conceptually do this problem?

[scenic marsh]

That kinda sucks

Uhhh

[static wasp]

Like, you could literally look up area of ellipse and it should be the same I think

[scenic marsh]

Yes for sure but there’s probably a way to show it

[static wasp]

I know 😭😭😭

[scenic marsh]

No the hint is actually helpful I realize

You say like

u=x/a, v=y/b

Then unit circle

[static wasp]

that a problem for later, I'm still doing these intergrals for #2 😂

wait wait wait

[scenic marsh]

Polar

[static wasp]

how'd you get those equations?

[scenic marsh]

It’s just like

x^2/a^2

Idk you just feel it

[static wasp]

ahhhh

well

you did

lmaooo

I felt certain doom and skipped it LMAO

that makes sense tho!

[scenic marsh]

An ellipse is just like a squishing or stretching of the unit circle and when you just have like a constant in your transformations like that it works

I’m working out #2 and 😵

By golly!

[static wasp]

OHHH! Wait that's such a good mental visual!!

[static wasp]

https://tenor.com/view/brain-dog-brian-dog-cooked-wallahi-im-finished-cooked-dog-gif-1849480349705279416

please no 😭😭😭

[scenic marsh]

It’s not awful I guess

But definitely not fun

[static wasp]

bruh

😭😭😭😭

[scenic marsh]

It’s different from we’ve done them in class normally the changes are obvious and the bounds too because they won’t give points but instead they’ll say it’s restricted by like xy=2 and xy=5 and something else like ok obviously one of them is u=xy then

[static wasp]

ohhhhhh

that makes sense

I put it into symbolab and the answer is like... damn okay, all that work 😭👍

[scenic marsh]

It doesn’t feel right but my final answer was -175/18

[static wasp]

👀 gimme a little, I'm almost done lolol

[scenic marsh]

Right or wrong I’m just happy I got an answer on a problem like that past midnight

[static wasp]

lmaooooooo frfr! Like man, your brain working so well rn 😭👍

[scenic marsh]

Idk about that that problem took forever but eh

If you mean explaining things I think it just comes down to how I think about stuff I try to make it simple to explain so that I can explain it to myself

[static wasp]

its a lot better than how I'm doing, I'm at the second integral and trying to multiply everything out and I forgot a +2 somewhere like 😭💀💀💀

[static wasp]

that's big brain frfr! I just do enough problems still my brain gets it (takes hours)

[scenic marsh]

I’m no psychologist but I think a lot of peoples big pitfall is overdoing things

I won’t lie when I think about some of this stuff for too long jt makes less sense

If it works for you it works for you though

[scenic marsh]

I avoid that and ik sleep makes a huge difference for how well I can think overall but especially math stuff

[static wasp]

yeah, indeed it does 💀, I can moderate it but I hibernate so much so 😎😎👌👌

it takes a lot for me to understand something but once it clicks in some random ass problem then its smooth sailing fr

[pearl pond]

@static wasp Has your question been resolved?

[static wasp]

well, I'll keep going at these questions till I get the right answer (in the morning tho!)

Thank yall so much for the help man 😭🙏🙏🙏 I really REALLY appreciate it!!! You guys are amazing!!! THANK YOU AGAIN! 🙏🙏🙏🙏🙏🙏

[static wasp]

.close

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[static wasp]

.reopen

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✅

[static wasp]

.close

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[soft oxide]

hi i need help visualising all dimesions of simplexs using dots
to get what i mean here is a representaion of a 3 simplex (tetrahedron)

[soft oxide]

<@&286206848099549185>

bruh

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[rough forge]

why is this true

[tropic saddle]

its the def for continuity at x=0

or what do you mean

[rough forge]

the blue underline

they are only equal if x is non-negative

[sharp vigil]

that's fine because we are only considering x in the domain of sqrt(x)

[rough forge]

that makes sense thank you

that leads me to another question

according to delta epsilon the limit exists

what if had a piece wise function where I have y = 1 for x < 0 would the limit still be 0

[cunning comet]

no.

in this case the function would not be continous at x = 0.

[rough forge]

uhm i asked if the limit would be still 0

[cunning comet]

as i said: no.

[rough forge]

why

[cunning comet]

you cant do this:

for this function. the limit f(x) for x->0 would not exist and therefore the function is not continous.

[rough forge]

why wouldn't the limit exist

[cunning comet]

take epsilon, for example epsilon = 0.01, can you determine a delta such that for all x in ]-delta,delta[ f(x) is in ]-epsilon, +epsilon[?

[rough forge]

no

[cunning comet]

so the limit does not exist.

[rough forge]

the thing is, when i am looking at this, it always seemed to me that the limit must exist from both sides, so that the limit exists

so then with only sqrt(x) i thought it would only exist from the right, because how else would you construct it

[cunning comet]

in the above sketch it is ok, that the limit must exist from both sides, as the function is defined on both sides.

in the example f(x) = sqrt(x) for x>=0, the function is only defined on x >= 0., so for all x > 0 you would have to check both sides for the limit, but for x = 0 you only need to check approaching from the right side.

if you extend your function f(x) = sqrt(x) to a function g(x) with g(x) = f(x) for x>=0 and g(x) = 1 for x < 0, then you have to check both sides at x = 0 as g(x) is now defined in the negatives.

continous function is defined with respect to the domain of the funtion.

[rough forge]

so in the case of sqrt(x) at x = 0 it wouldn't make sense to say it is right side continuous

but actually continuous

[cunning comet]

it is continous and therefore it is also right continous. but to be honest. i would use the term "right continous" only in cases of functions like g(x). you can say, g(x) is not continous at x = 0, but right continous at x = 0.

[rough forge]

so then this doesn't make sense I should just consider 0 < x < delta instead of 0 < |x| < delta

[cunning comet]

you can use 0 < x < delta to clarify but 0 < |x| < delta is also correct as by the domain of f x cant be negative.

[rough forge]

but wouldn't 0 < |x| < delta imply -delta < x < delta

[cunning comet]

i would use 0 < |x| < delta, as this comes from the epsilon-delta-definition, but in the next step i would omit the | . | and would mention that we can omit it because x has to be nonnegative by the Domain of f. this should avoid any possible misinterpretation.

[rough forge]

ok I think that's it, i just had some conceptual misunderstandings, thanks ThM

and to the others as well

[cunning comet]

youre welcome

[rough forge]

.solved

[pearl pond]

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[rough forge]

.reopen

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✅

[rough forge]

this is also basically what confused me
https://youtu.be/DvM9i1xL_Zw?si=uesuXLoxq2P36mbz&t=314

[tropic saddle]

ja das ist minimal ungenau

achte in der ersten zeile auf das x in D

nur die x in der domain sind relevant

[rough forge]

ja, genau das was du und der andere meinten

danke

kuss geht raus

.solved

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[cobalt plume]

I need help with this two way annova sum, how do they take the coding method value which is used to subtract all the value in the table with, like the second image below:

[cobalt plume]

they took 40 as a coding method value in here but i dont know why and how? so if someone please help me to figure this out I can able to clear my arrear exams atleast this time. Thank you.

• I mean with the knowledge I can clear if that sounds like I am trying to cheat, no.

[compact ridge]

yes this looks like the chi squared test

so to find the mean, they simply found the mean of all the values in the table

,calc (44+38+47+36+46+40+52+43+34+36+44+32+43+38+46+33+38+42+49+39)/20

[jolly parrot]

Result:

41

[compact ridge]

oh that is weird

I think that's a mistake then in your notes

or like the assumption that mean = 40 was stated elsewhere

look elsewhere in the slides

[cobalt plume]

okay, let me try that with other question and let you if that works. thank you!

[pearl pond]

@cobalt plume Has your question been resolved?

[cobalt plume]

if i did summation of column total of A,B,C and D for this I am receiving 0 and also for row total summation too its 0

after subtracting the 41 for all the values in the table

[compact ridge]

yeah so I think it shouldn't be 41 then

I think this process relies on the row and column summations not being 0

[cobalt plume]

yes thats correct

it shouldn't be 0 to continue the other steps

[pearl pond]

@cobalt plume Has your question been resolved?

[pearl pond]

@cobalt plume Has your question been resolved?

[pearl pond]

@cobalt plume Has your question been resolved?

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[sudden zinc]

Having trouble solving this, this is what I wrote:

$\int _0^1\int _0^1\frac{x}{1+xy:}:dxdy$

[jolly parrot]

Chuti | Argentina