help-49

[midnight plank]

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[dire thorn]

<@&286206848099549185>

<@&286206848099549185>

[lavish venture]

@dire thorn

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@dire thorn Has your question been resolved?

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[limber acorn]

Where did I go wrong in part 3?

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[last slate]

How did they come up with these differential equations?

[last slate]

yes

double differentiation

yeah

what?

no

[last slate]

how did they write the differential equations

OH

xD

.solved

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[last slate]

.reopne

.reopen

[midnight plank]

✅

[last slate]

sigma F = ma

first is T cos(theta) T being the tension in the string

and the other is the restoring force of the spring kx

@dense flax

https://tenor.com/view/mujikcboro-seriymujik-gif-24361533

no

its just tension and wright

well then i will close it

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[last slate]

also restoring force

[midnight plank]

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[last slate]

The 1 is Unit matrix

[last slate]

1 min

[last slate]

The 1 is Unit matrix

[last slate]

How did they come to this conclusion?

the variable matrix is ,this(epsilon) ?

for context

[last slate]

its a typo ?

because in the next line they took the det of the whole thing and not just [M]

[midnight plank]

@last slate Has your question been resolved?

[sharp coral]

it should say $\det([M] - \omega_i^2 I) = 0$

[grand pond]

cloud

[sharp coral]

that would be the correct statement of the characteristic equation

[last slate]

thank you

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[twilit field]

Is this LA

[midnight plank]

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[last slate]

.no physics SHM

[sour cedar]

Teach me how to do this and fast please

[midnight plank]

Please don't occupy multiple help channels.

@sour cedar Has your question been resolved?

[sour cedar]

No bruh

<@&286206848099549185>

[next granite]

@sour cedar what do you need help with?

Reply in 10s or I'm leaving cause I gtg in a bit.

[sour cedar]

Bruh

[midnight plank]

Please stick to your channel.

[sour cedar]

No shut up

No one likes you

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[midnight plank]

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[simple sinew]

hey guys this is a reversible process right?

[tidal badger]

It's reversible, you can refreeze water

[simple sinew]

alright thanks, thts good enough im just making sure

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[buoyant slate]

pretty sure its irreversible

@simple sinew

[simple sinew]

why?

.reopen

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[buoyant slate]

there would be a change of entropy in the system

[simple sinew]

is it because the melting of ice is spontaneous due to heat flowing from the room into the ice?

so theyre not at equilibrium?

[buoyant slate]

yup

[simple sinew]

ohh

alright, thats just it right

thanks

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[simple sinew]

WAIT

.reopen

[midnight plank]

✅

[simple sinew]

@buoyant slate assume that the room is large enough for its temperature to be ignored

so constnt temperature

heat is not constant

wouldnt it make this reversible

[buoyant slate]

the room is in constant temperature yes, but the ice (now water) has had a change in entropy

another reason why its irreversible is that it would take energy to reverse the process, so there is a change of energy in the system

[simple sinew]

ahh

ok i understand it now

thank u v much

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[severe cloud]

You‘d have to distribute the minus sign though. That‘s why the logz is negative

Well, first you have a division in the log, so it becomes log(ax)-log(yz). Then for log(yz), you are right, it‘s multiplication, so we‘d add, but we have to be careful with the negative sign, doing it like so: log(ax)-[logy + logz]

[midnight plank]

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[midnight plank]

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[terse pasture]

I need help in question 3

[buoyant slate]

any way to get a better image? kinda far away cant really read it

[terse pasture]

Sure hold on

Is that better?

[buoyant slate]

what have you done so far?

[terse pasture]

Honestly I have no clue what to do

I tried like 3 different methods but idk if they correct

[buoyant slate]

what methods?

[terse pasture]

Trapezium rule

And the other two are like just some random crap I made up 😭

[buoyant slate]

well you will need to use normal integration here

[terse pasture]

Oh ok

So this?

[buoyant slate]

,rotate

[buoyant slate]

its a good start yes

[terse pasture]

Alright now I'll solve that and get back to you

Ok so I found c

Now lemme input the two values then subtract it

[buoyant slate]

you dont need to find c when computing definete integrals'

[terse pasture]

Oh ok

[buoyant slate]

they cancel out when putting in the limits of integration

[terse pasture]

Cause like they minus each other right

Ye

@buoyant slate

[buoyant slate]

,rotate

[buoyant slate]

where did the ln go?

[terse pasture]

It's there bro

[buoyant slate]

your answer should be in terms of ln

[terse pasture]

Oh ok

Nah bro idk how to do from there

From when we integrated it

[buoyant slate]

well

$3\ln{5}$

[grand pond]

caspar

[terse pasture]

How did you get that bro

[buoyant slate]

what is that representing

ill type it out hold on

[terse pasture]

When X is 1?

[buoyant slate]

$3\ln{(2\cdot6 + 3)} - 3\ln{(2\cdot0 + 3)} = 3(\ln{15}-\ln{3}) = 3\ln{(15/3)} = 3\ln{5}$

[terse pasture]

Oh ok bro

[grand pond]

caspar

[buoyant slate]

the integral represents the area under the curve

[terse pasture]

Ohhh ok

Thanks

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[midnight plank]

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[leaden matrix]

Can someone explain why what I did is wrong

I know in the solution they factored the numerator into an s+3 and that makes sense, but I don’t understand why what I did is wrong and why im not allowed to just split it like I did

[buoyant slate]

well the s in the numerator has to be (s+3) aswell to use the t-shift

or s shift i always mix those up

[midnight plank]

@leaden matrix Has your question been resolved?

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[safe onyx]

,, \int x \sqrt{8-x^2} dx

[grand pond]

smeagol

[safe onyx]

how can I put this into calc?

it kept giving me errors

I want to check my work

[leaden matrix]

So you need the form (s-a) in both the numerator and denominator?

[gaunt otter]

what calc

[buoyant slate]

yup

[leaden matrix]

I see thanks

[buoyant slate]

np

[safe onyx]

,calc \int x \sqrt{8-x^2} dx

[grand pond]

The following error occured while calculating:
Error: Syntax error in part "\int x \sqrt{8-x^2} dx" (char 1)

[safe onyx]

the bot

,w \int x \sqrt{8-x^2} dx

[grand pond]

Results provided by WolframAlpha

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

Requested by iamsmeagol

[gaunt otter]

I think its just ,c

[buoyant slate]

wolfram alpha on top

[safe onyx]

how can I see the steps that it used

[gaunt otter]

upgrade to wolfram alpha pro

[safe onyx]

i don't have a job :/

[gaunt otter]

https://www.integral-calculator.com/

works for most integrals

but for some you need wolfram alpha

[safe onyx]

thank you

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[gaunt otter]

https://mathdf.com/int/ also good

@safe onyx

[leaden matrix]

Wait but when u split it wouldn’t the rhs be 10 over (s-a)? It wont have the form (s-a) in the numerator

[buoyant slate]

im not following, can you show work?

[leaden matrix]

When u factor the numerator you get -3(s-3) + 10 right?

[midnight plank]

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[buoyant slate]

oh yeah

[buoyant slate]

hold on ill try to solve it

[leaden matrix]

And then if you split that into -3(s-3) as one fraction + 10 as another fraction

The one with the 10 doesn’t have the form (s-a) in the numerator

[buoyant slate]

thats not needed

[leaden matrix]

Wdym?

[buoyant slate]

$\mathcal{L}^{-1} \left[\frac{b}{(s-a)^2 + b^2}\right] = e^{at}\sin{bt}$

[grand pond]

caspar

[buoyant slate]

$\mathcal{L}^{-1} \left[\frac{b}{(s-a)^2 + b^2}\right] = e^{at}\sin{bt}$

[grand pond]

caspar

[buoyant slate]

you just use this formula

@leaden matrix

[leaden matrix]

So you take out the s-a from the whole eqn before splitting it?

[midnight plank]

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[verbal kindle]

idk where and how to solve for the energies

i know theres elastic, graviational, kinetic, and frictional energy but i dont know how to apply them

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[verbal kindle]

idk where and how to solve for the energies
i know theres elastic, graviational, kinetic, and frictional energy but i dont know how to apply them

[midnight plank]

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@verbal kindle Has your question been resolved?

[verbal kindle]

<@&286206848099549185>

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[tawny beacon]

Without using calculus and derivatives, I need to find the instantaneous rate of change of the function p(x) -0.05x^2+350x-45000 at x = 1000

In the end I got 0.250 but the answer is 250.

I’m trying to find my mistake. My initial guess was the number I chose that is close to x2 = 1000, x1 = 999.999

[livid python]

Learned derivatives yet ?

[tawny beacon]

naa not yet and I’m dumb again sigh

my steps are right i just put it in the calc wrong

[livid python]

Don’t be harsh on yourself it’s ok

[tawny beacon]

haha

I just tried it again and I got 0.25/0.001 which = 250

which makes sense when I look carefully at my steps

[tawny beacon]

thanks for offering to help tho 🙏🏽

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[umbral sparrow]

am i right with A here

[oak slate]

yep

[umbral sparrow]

it made most sense to me

thank you agai

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[midnight plank]

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[static lion]

how to do this

[oak slate]

do you know the formula for 1 + 2 + ... + n

[static lion]

whaat about it?

its just n

[oak slate]

no

its n(n + 1)/2

[static lion]

oh

i didnt saw that

ok

[oak slate]

sub that in

then you can do partial fraction decomposition

[static lion]

its not U sub?

I mean like

cannot use Integral test?

oh nvm

[oak slate]

are you trying to evaluate the sum or determine if it's convergent/divergent?

[static lion]

just conv or div

i thought it be easier to do ratio test but ok

[surreal moon]

Ratio test would be indeterminate i think

[humble torrent]

consider the limit of the terms

does it approach 0?

nvm thought u had something not approaching 0 lol

[static lion]

yes

I already found it with comparison test

thanks

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[static lion]

how to do this

[fallow scarab]

what is the question

[static lion]

test conv/div no need to get sum

[fallow scarab]

do you know comparison test

[static lion]

yes

but

what if use ratio test?

[fallow scarab]

sure you can try

comparison test makes it easier

[static lion]

i cannot cancel anything after getting an+1/an

yes maybe I use comparison test

what i do with 2^n and the n!?

i cannot do anything with n!

do I just straight up analysis say that n! grows too fast therefore converge to 0?

[fallow scarab]

yea compare your sequence to something simpler and then do ratio test

[static lion]

how I compare if there is n!

[fallow scarab]

use the definition of n! to find what to compare to

[static lion]

what about n! ?

[fallow scarab]

?????

do you know the definition of n!

https://www.mathsisfun.com/numbers/factorial.html

[static lion]

if I use comparison test, so like, DT = 2^n / n! --> r = infinite > 1, converge????

[fallow scarab]

you need to look this up

write out 2^n and n! for a few small natural n

[static lion]

I sub with this one?

[remote glade]

if you are trying to use limit comparison test. then the limit should be one to draw a conclusion. not infinite

[static lion]

no, Im using P test comparison test

[fallow scarab]

that would be wrong

2^n / n! is not a p series

you can use ratio test once you get here

[static lion]

what is the rotated i symbol mean?

[remote glade]

dude thats factorial

never heard of that ?

[fallow scarab]

.

[static lion]

the i that is rotated like 90 degree, the one on the end

[remote glade]

that is factorial sign

[fallow scarab]

You should have said no when I asked this

[static lion]

I know what factorial is bro

but like

[fallow scarab]

????

[static lion]

what is that????

I never see this before

[fallow scarab]

That was from your message

[static lion]

whatttttt

[remote glade]

ah you meant that 😂 😂 😂

the -- was cropped such that second dash is half in the picture

thats why it seems like that

[static lion]

so what i do here is, comparison test, get the DT, from the DT I use ratio test inside the comparison test?

[static lion]

ngl, when u guys said that it was factorial, I contemplated all the things I learned from pre calc bro

[midnight plank]

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[midnight plank]

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[barren onyx]

can someone tell me the difference in these two questions and why is the answer different

[barren onyx]

The word is aaagnpit

[fossil knot]

(c) asks for (X or Y) and (d) asks for (X strictly or Y)

where X is starts with G, and Y is ends with I

[barren onyx]

so x is must in d?

[fossil knot]

No

In (d), you have to exclude any word that starts with G and ends with I

whereas in (c), you merely just have to avoid overcounting

[barren onyx]

why did we subtract twice id d

in*

[fossil knot]

You subtract once to avoid overcounting
and subtract another time to exclude the cases where it starts with G and ends with I

[barren onyx]

how is not accounted when substracting for the first time

i can't solve a basic problem after doing many advanced ones...

[fossil knot]

Basically, what you're doing is

1. Counting how many words start with G
2. Counting how many words end with I

But in both steps 1 and 2, you count words that start with G and end with I.

So you have to subtract it twice, once for each step.

In (c), you only need to subtract from one step, because you want to include words that start with G and end with I, but you don't want to count it twice.

[barren onyx]

ohh

because it counted the words starting with g and i twice

in c

[fossil knot]

right

[barren onyx]

ye i understood ty

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[upbeat plinth]

One message removed from a suspended account.

[upbeat plinth]

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[hushed glen]

its horizontal velocity is going to mimic a sim wave

it'll be moving at its peak velocity at the top and bottom of the circle

and won't be moving at all on the two sides of the circle

horrizontally

[upbeat plinth]

One message removed from a suspended account.

One message removed from a suspended account.

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[hushed glen]

you need to find an equation that relates its horizontal velocity to its vertical velocity

then differentiate it with respect to t

[lavish venture]

what’s the equation for the circle

🙈🙈

in terms of position

[upbeat plinth]

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[grand pond]

Kenzo

[lavish venture]

yea sure but it’s the unit circle

centered at the origin

it isn’t that complicated

[upbeat plinth]

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[lavish venture]

🤔

x^2 + y^2 = 1

[upbeat plinth]

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[lavish venture]

just differentiate dt

[upbeat plinth]

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[lavish venture]

yea but who cares about the h k and r

[upbeat plinth]

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[lavish venture]

yea

[upbeat plinth]

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[lavish venture]

with respect to time

[upbeat plinth]

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[lavish venture]

nope

close

[upbeat plinth]

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[lavish venture]

x and y are both functions of t

[grand pond]

Kenzo

[lavish venture]

yep

[upbeat plinth]

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[lavish venture]

just solve for dy/dt

[upbeat plinth]

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[lavish venture]

dx/dt, x, and y are given

[upbeat plinth]

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[lavish venture]

guess

[upbeat plinth]

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[lavish venture]

yuck

no be fr

[upbeat plinth]

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[lavish venture]

yep

[upbeat plinth]

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[lavish venture]

steak is clearly the best food

no contest

[upbeat plinth]

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[lavish venture]

you’ve clearly never been to a premium steakhouse

🤌🏻🤌🏻🤌🏻

[upbeat plinth]

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[lavish venture]

i eat steak 4-5 times a week usually

[upbeat plinth]

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[lavish venture]

rarely 3 times

[upbeat plinth]

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[lavish venture]

bugging

[lavish venture]

you’re dense

[upbeat plinth]

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[lavish venture]

man really fell for the red meat bad shit

brother

[upbeat plinth]

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[lavish venture]

carbs are not the enemy

[upbeat plinth]

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[lavish venture]

also, steak doesn’t even have carbs

[upbeat plinth]

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[lavish venture]

wtf are you on about

[upbeat plinth]

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[lavish venture]

carbs are your energy source sir

[upbeat plinth]

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[lavish venture]

bro you’re probably like 120 pounds

relax

[upbeat plinth]

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[lavish venture]

no chance

[upbeat plinth]

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[lavish venture]

interesting

[upbeat plinth]

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[lavish venture]

i fluctuate

atm i’m around 175

5’11

[upbeat plinth]

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[lavish venture]

just eat less

it’s so easy

[upbeat plinth]

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[lavish venture]

poor genes

i have a high metabolism tbh

[upbeat plinth]

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[lavish venture]

lemme read

[lavish venture]

yes

[upbeat plinth]

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[lavish venture]

dh/dt = 2

[upbeat plinth]

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[lavish venture]

dV/dt = 0

[upbeat plinth]

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[lavish venture]

$V = \pi r^2 h$

[grand pond]

knief

[lavish venture]

differentiate that bitch

dt

[upbeat plinth]

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[lavish venture]

huh

product rule

[upbeat plinth]

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[lavish venture]

yea

[upbeat plinth]

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[grand pond]

Kenzo

[upbeat plinth]

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[cunning inlet]

It's so boring, no one to chat with

[upbeat plinth]

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[upbeat plinth]

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[cunning inlet]

hello

[upbeat plinth]

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[lavish venture]

you’re flirting

[lavish venture]

rizz bro

🔥🔥

[upbeat plinth]

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[cunning inlet]

Can I be your friend?

[upbeat plinth]

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[lavish venture]

bruh

dr/dt

[lavish venture]

\pi

[upbeat plinth]

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[lavish venture]

also just no

[cunning inlet]

Seems cool

[lavish venture]

wrong

[upbeat plinth]

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[lavish venture]

good

[upbeat plinth]

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[lavish venture]

what is it then

[upbeat plinth]

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[lavish venture]

nah that’s your wife bro

[upbeat plinth]

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[cunning inlet]

What are you talking about?

[lavish venture]

AI generated

[woeful cloak]

Give me a recipe for pancakes

[upbeat plinth]

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[lavish venture]

😟😟😟

[upbeat plinth]

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[lavish venture]

so many things..

[upbeat plinth]

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[lavish venture]

why is there an x, why is it 2r^2

[upbeat plinth]

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[upbeat plinth]

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[grand pond]

Kenzo

[upbeat plinth]

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[lavish venture]

yea and please stop spamming parentheses

[upbeat plinth]

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[lavish venture]

just use h’ and r’

[upbeat plinth]

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[lavish venture]

or don’t use parentheses

[upbeat plinth]

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[lavish venture]

$\pi(r^2\frac{dh}{dt} + 2rh\frac{dr}{dt})$

[grand pond]

knief

[lavish venture]

this is just much cleaner

[upbeat plinth]

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[lavish venture]

like why are there parentheses around (r^2dh/dt)

or around dr/dt

[upbeat plinth]

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[upbeat plinth]

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[lavish venture]

don’t accept it lol

[upbeat plinth]

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[lavish venture]

your teacher is bogus

[lavish venture]

you can..

[upbeat plinth]

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[lavish venture]

readability is important

[lavish venture]

good series

[upbeat plinth]

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[midnight plank]

Channel closed

Closed by @upbeat plinth

Use .reopen if this was a mistake.

[cunning inlet]

You all are awesome.

Is there anyone to chat with?

It's a bit boring now

[midnight plank]

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[young bane]

https://cdn.discordapp.com/attachments/936100524531523594/1309009675332620401/image.png?ex=674005c2&is=673eb442&hm=ca40cca1ee1098af8db27093dc22b0fc91cbfbec0aef35922b5015fd14692813&
https://cdn.discordapp.com/attachments/936100524531523594/1309009675584274452/image.png?ex=674005c2&is=673eb442&hm=ed5ab26999327d464f3cabf748d975197f49a054eae41ca8b2dfc9115725ca64&
https://cdn.discordapp.com/attachments/936100524531523594/1309009675794251826/image.png?ex=674005c2&is=673eb442&hm=b3f2be07083ea85a1535126c621e5811165558a8f2f164f60ccd93f9a4243c11&
Hello,

I am currently working on part E of the above problem. I have the solutions, but I am not quite sure how to obtain them. I have been able to successfully complete parts A-D of this problem. Information about this problem is listed in the images above, along with graphs and the solution from the solutions manual.

[young bane]

<@&286206848099549185>

[last slate]

Bro it's simple asf try doing by urself

[young bane]

okay

[azure sonnet]

just chatgpt it bro

[young bane]

Yeah, but could you explain how you would get these solutions? I just don't know how to get them.

[last slate]

In which grade are you

[young bane]

10th

[last slate]

Ohk

[midnight plank]

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[young bane]

.reopen

[midnight plank]

✅

@young bane Has your question been resolved?

[midnight plank]

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

.close

[midnight plank]

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[opaque igloo]

i dont know where to start

[south stag]

try using special angles

like tan(pi/6)

[fallow scarab]

,tex .half angle

[grand pond]

riemann

[opaque igloo]

oh i realised how to do it

thanks guys

.close

[midnight plank]

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[primal nexus]

can someone tell/teach me about Lines, Line Segments, Angles and its theorems cause tmr am about to do a quiz on it

[grizzled blade]

Google

[peak ridge]

I got u

(Youtube)

[midnight plank]

@primal nexus Has your question been resolved?

[midnight plank]

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[midnight plank]

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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[grand pond]

a5667.
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[midnight plank]

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as this action is irreversible, and this channel may abruptly lock.

[hollow stratus]

$f(x) = \frac{(3x+1)^{2x} \cdot 2^{4x+1}}{\cos ^54x \cdot \sqrt[3]{5x+1}}$

[grand pond]

a5667.

[hollow stratus]

I want to find the derivative of this function. I think it would be a good idea to take the natural log of both sides and simplify it, then use implicit differentiation.
The question I have is: Should I take the absolute value of the denominator when I do it?

Or should I just go ahead and use the quotient rule first?

The quotient rule seems like too much work

[tribal temple]

(open another channel, you may lose this one)

[vale sigil]

I don't know how to help you but ^

Yeah exactly

[hollow stratus]

oops

.reopen

[tribal temple]

You can't reopen it

[hollow stratus]

ok I will go to the channel help-4

[midnight plank]

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[twilit field]

Base case : $24 \mid 5^2-1 $ this is trivially true
\
Inductive hypothesis $24 \mid 5^{2n}-1$
\
We wish to show that $24 \mid 5^{2n+2}-1

[grand pond]

A dense set(Ping when reply)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[twilit field]

We thus know by inductive hypothesis that $(5^2n-1)=24k$
\
We have $5^{2n} =24k+1
\
$5^{2n+2} = 25(24k+1)$

Now what

[grand pond]

A dense set(Ping when reply)
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[carmine void]

Now consider 5^(2n+2)-1

You're almost done

[twilit field]

ah

oh

$5^{2n+2}-1=24(24k)$

[grand pond]

A dense set(Ping when reply)

[twilit field]

Well, that finishes it

thanks

[carmine void]

Isn't it 25•24k + 24

[twilit field]

oops

Well, that still works

yes

[carmine void]

Factor

[twilit field]

$n^3-n=6k$
\
$(n+1)^3-(n+1) = n^3+3n^2+2n$

[grand pond]

A dense set(Ping when reply)

[twilit field]

hmm, now I factor this ye?

[carmine void]

No, I would just factor the original one

Then the task becomes easy

[twilit field]

$6 \mid n(n+1)(n-1)$
\
$6 \mid (n+1) (n+1-1) (n+1+1)$

[grand pond]

A dense set(Ping when reply)

[twilit field]

oh

wait

$n^3-n=6k$
\
We also have $(n+1)^3-(n+1) = n^3+ 3n^2+3n+1-n-1 = n^3-n + 3n^2+3n$
\
$n^3-n + 3(n^2+n)$

[grand pond]

A dense set(Ping when reply)

[twilit field]

Bad idea?

[carmine void]

Not the most efficient way to do this, but it works and is almost a full solution 👍

[twilit field]

Hmm

so I prove n^2+n \mid 6 by induction

[carmine void]

No, you only need to prove it is divisible by 2

[twilit field]

on right

cool

thanks

[carmine void]

You're welcome

Do you want to know how the short solution looks like?

[twilit field]

sure

[carmine void]

So you have already shown that it is the product of 3 consecutive integers. One of them needs to be divisible by 2 and one of them is divisible by 3. Since gcd(2,3)=1 this shows the statement

[twilit field]

ah

awesome

[midnight plank]

@twilit field Has your question been resolved?

[twilit field]

$2^n+1 \leq 3^n$
\
We wish to prove that $2^{n+1}+1 \leq 3^{n+1}$
\
This is equivalent to proving that $1 \leq 3^{n+1} - 2^{n+1}$
\
$3^{n+1}-2^{n+1} = 3\cdot 3^n-3\cdot 2^n+ 2^n$
$3(3^n-2^n)+2^n$
$3^n-2^n>1$ by inductioon hypothesis, we're done

[grand pond]

A dense set(Ping when reply)

[twilit field]

Is thsi fine?

.close

[midnight plank]

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[chilly cobalt]

Triangle ABC has AB = 459, BC = 460, CA = 461, and is inscribed in circle O. Circle P is tangent to O at point A and intersects AB and AC at points M and N respectively. If circle P is tangent to BC, find MN

[chilly cobalt]

ive made some points and named some angles, idrk what next

<@&286206848099549185>

[midnight plank]

@chilly cobalt Has your question been resolved?

[graceful drum]

wait

how did u get anm = acb

cus by exterior angle = sum of opposite interior angles property

we would get

a+c = a+b

=> b=c

@chilly cobalt

[feral sedge]

this is just. not possible lol

for circle P to be tangent to both BC and O it would be true that the centers of O and P are collinear with A, which is obviously false

[graceful drum]

why not

it seems quite possible from the innacurate but close enough diagram

[feral sedge]

tbh maybe i just forget how to do geometry

[graceful drum]

relatable

honestly

the circumcircle of abc looks like it isnt important

doesnt it suffice to say that circle p contains A and is tangent to BC

[feral sedge]

ok no i was correct

[graceful drum]

tell us

[feral sedge]

i already did before

if it is wrong, then ok let me know, but the explanation is there

[graceful drum]

but the last part

where u say that centres of O,P and A are abviously not collinear

doesnt make sense

if u consider the perpendicular to the common tangent of the two circles at A

it contains the radii of both circles

and thus that line contains all three of A,centre of O and centre of P

@feral sedge

[feral sedge]

ah thank you i see my error

[midnight plank]

@chilly cobalt Has your question been resolved?

[midnight plank]

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[alpine gyro]

How to solve $$\int_1^\infty \frac{x+2}{\sqrt{x^3+x^5}}dx$$

[grand pond]

Good

[alpine gyro]

Like, which function should I use for limit-test (if that's the name).

$f(x)=\frac{1}{x^{\frac{3}{2}}}$

[grand pond]

Good

[alpine gyro]

But why choose $\sqrt{x^3}$ from $\sqrt{x^3} \sqrt{1+x^2}$?

[grand pond]

Good

[alpine gyro]

.close

[midnight plank]

Channel closed

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[midnight plank]

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[onyx cedar]

Need help for 16

[onyx cedar]

The answer is 86.81 rad/s

I just have no clue how to get there

[gaunt nimbus]

$v = \omega r$

[grand pond]

k

[gaunt nimbus]

Do u know this

[onyx cedar]

Yeah

[gaunt nimbus]

Use that

Make sure that everything is in meters

[onyx cedar]

Yeah and v = delta s / delta t right

[gaunt nimbus]

Yes

[onyx cedar]

Alr

[onyx cedar]

Just curious why change everything to meters

[gaunt nimbus]

So that unit can cancel out

[onyx cedar]

cm to meter and km to meter then they cancel right

Alr I see now

[gaunt nimbus]

Yes

Then the meter unit on both sides will cancel

This is imporant cuz radian is a dimensionless unit

[onyx cedar]

Alr I understand

,rotate

[onyx cedar]

Just curious how would I express time here

Sry I don’t know much abt this cus I didn’t take physics yet but a question like this came up in my maths class

[gaunt nimbus]

Time in seconds

U should get

This many seconds

[onyx cedar]

Oh I did 23400 instead of 24300 sec

[gaunt nimbus]

Yes

After division u should get 27.78 or smth

[onyx cedar]

Yeah

[gaunt nimbus]

u can use arc length = angle x radius still

[gaunt nimbus]

Divide by r and u’re essentially done

[onyx cedar]

Would the angle of displacement be the distance times circumference

[gaunt nimbus]

And then try to find angle/time

[gaunt nimbus]

?

[onyx cedar]

Wait nvm nvm

[onyx cedar]

I’m confused how would the arc length represent time

[midnight plank]

@onyx cedar Has your question been resolved?

[midnight plank]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obtuse totem]

and the sol

I dont understand why X~ Binominal has these values

or bernoulli even

binomial is supposed to be Binomial(n,p) where n is the sample size and p is the probability of success

[fallow scarab]

P(X=0) = p00 + p01

[obtuse totem]

yup

[fallow scarab]

because P(X=0) = sum_y P(X=0 | Y = y)

[obtuse totem]

but i dont know what X stands for

like how do you know prob of success is p10+p11

[fallow scarab]

X and Y ~ Bernoulli

[obtuse totem]

yes but why p10+p11, not p00+p01?

[fallow scarab]

bernoulli is just Binomial with n=1

This is P(X=1)

X ~ Bernoulli(p) means P(X=1) = p

[fallow scarab]

Because p + (1-p) = 1

[obtuse totem]

oh I see, guess that makes sense because I think bernoulli is a type of binomial right?

so it wouldnt make sence to have a sample size of 0 in the binomial

[fallow scarab]

yea

n=0 in binomial is an edge case you shouldn't need to worry about

[obtuse totem]

thank youuu

[fallow scarab]

but it is defined. just not very intersting.
https://en.wikipedia.org/wiki/Binomial_distribution

[obtuse totem]

also @tribal temple Hiiii👋

another question,

I thought V(Y) is sum of x in D, (x-mean)^2p(x)

so shouldnt it be (p01+p11)(1-p01-p11)^2?

[obtuse totem]

wait no, this is only for discrete rand var, not jointly

wait whattt

no

no this is for E(X), so it is a discrete rand var

I'll send the whole question and solutions

solutions in that order

[obtuse totem]

i get it now, its asking for E(X) and V(X) where X is a binomial distribution

so mean would be np, and variance would be np(1-p)

[midnight plank]

@obtuse totem Has your question been resolved?

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[last slate]

what are the bounds ?

region is easy but boounds are hard

in x-y

[obtuse basin]

Swap to polar

[last slate]

hehe

i got it in polar

is it not possible in x-y ?

[obtuse basin]

It is, but it's gonna be painful

Cut into regions by the line x = 1

[last slate]

it would be sum of 2 or more double integrals right ?

yeah

okay

thanks

.close

[midnight plank]

Channel closed

Closed by @gleaming geode

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[last slate]

.reopen

[midnight plank]

✅

[last slate]

one small thing

we can write dA as either dydx or dxdy right ?

because area of rectangle

[obtuse basin]

Depends on your order of integration

[last slate]

do you mean bounds?

[obtuse basin]

Yeah

dA is either of those sure but when you turn the double integral into an interated integral, the order of dx and dy should correspond to the bounds

[last slate]

like in this case ,
double integral over region R (x+y) dxdy = double integral over region R (x+y) dydx

it is the same

?

[obtuse basin]

That yes

[last slate]

okay thanks!

.close

[midnight plank]

Channel closed

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[midnight plank]

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[dense arch]

a function is homogeneous if f(kx,ky) = k*f(x,y)?

[obtuse basin]

Yes, specifically you would call f homogeneous of degree 1 in that case

[dense arch]

okay

the degree changes depending on the degree that k has

[obtuse basin]

What do you mean by the degree of k?

Ah you mean the power of k?

[dense arch]

yeah

like k^2 would be degree 2

[obtuse basin]

Yes

[dense arch]

okok perfect

thank you

.close

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[lyric scroll]

hi can anyone tell me what i did wrong

[lyric scroll]

please.

[grim vector]

-2- 5/3 ?

[lyric scroll]

?

where

[grim vector]

Last pic

[lyric scroll]

yeah

my bad

[grim vector]

But you can't get that e out

you have e^3x

[lyric scroll]

oh

fuck

yeah i forgot that

but i included it

in the calculator

wait

let me recalculate it

please dont leave.

[grim vector]

Dw

[lyric scroll]

also

i accedently flipped the plus to minus

for some reason

[grim vector]

Why ?

Well nvm

[lyric scroll]

okay

umm

idk if its correct

like idk where to find the answer

to this

[grim vector]

Let e^3 as e^3 don't simply

You should have 2/3*e^3 - 5/3

[lyric scroll]

where?

[grim vector]

,w integral from 0 to 1 of e^{3x}*(3x^2-4x+3)

[grand pond]

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Requested by yakubros

[grim vector]

Instead of writing 13.39

Don't simplify e^3

[lyric scroll]

i dont understand

but

holy shit

im gonna cry

its nearly correct man

i was struggling for hours

[grim vector]

Let e^3

Don't write 13.39

[lyric scroll]

ohhhh

because the thing

the answer

will be wrong

because of rounding

[grim vector]

Exactly

[lyric scroll]

ok you mean

[grim vector]

Thats why never simplify e^

[lyric scroll]

just write e^3times1

[grim vector]

yes so 2/3 here

When you evaluate the brackets

It gives 2/3

So 2/3*e^3

[lyric scroll]

ok yeah

ty

tysm

life saved