help-26

[vernal vale]

we got p and q and a

[steady vale]

the equation w all these plugged in would be like $-18=-6(-3+6)(-3+4)$ then that into -18=-6(3)

idk what else

[thorny flame]

ariki

[steady vale]

what i js do 😭

[vernal vale]

go way way back to where we started

here

.

y=a(x-p)(x-q)

but we found p and q and a, yea?

[steady vale]

yea

[vernal vale]

so we should be able to plug them back into this

[steady vale]

y= -6(x+6)(x+4)

or sum

[vernal vale]

hmm okay

are we in standard form

[steady vale]

nope

[vernal vale]

what can we do

[steady vale]

we alr have our a value so -6x^2 + bx + c

so

we multiply the binomials

so

give me a sec

[vernal vale]

i think is gonna get you mixed up since its either incorrect or im not sure if youre in the middle of a step or something

[vernal vale]

you have it here

you just need to FOIL

[steady vale]

i am

[vernal vale]

ah, cool

dont let me slow you down

[steady vale]

$-6(x^2+10x+24)$

[thorny flame]

ariki

[steady vale]

now i gotta distribute

right

[vernal vale]

yea

[steady vale]

$-6x^2 - 60x - 144$

oh nah what i do wrong

[vernal vale]

https://www.desmos.com/calculator/wvclpx9btj

plot and check

[thorny flame]

ariki

[vernal vale]

are the points you wanted on the parabola?

[steady vale]

yes

so it's correct ???

[vernal vale]

[steady vale]

i'm albert einstein Fr

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[tacit eagle]

<@&286206848099549185>

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[shut spear]

how would you make an equation for converting the amount of cream to butter churned

[neon iron]

^ @tacit eagle

[tacit eagle]

i dont know

i am confused

[wheat grove]

what are you confused about?

@tacit eagle

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[pine zinc]

hello

[pine zinc]

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[timid forge]

How do you use i in calculus

[empty sail]

Like the imaginary number?

[timid forge]

Yeah

[empty sail]

You can use something like $e^{i \pi} = \cos \pi + i \sin \pi$

[thorny flame]

dldh06

[timid forge]

ok thank you

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[gleaming raft]

I need help with the equation of a straight line:

ax + by + c = 0

What is a, b and c?

[tall wolf]

just values

they alter how the line will look

c is the constant value

b is the linear value

wait wdym equation of a straight line

[signal bough]

that's the standard form for linear equations

[tall wolf]

oh

Right

Yeah just values

[gleaming raft]

What would be a constant and linear values?

[tall wolf]

don't mind that

that's for a parabola

[gleaming raft]

Oh

[tall wolf]

these are just values

Can be turned into y=mx+b form

there's certain rules too for this equation too

[gleaming raft]

Can I use the reduced form on the same cases as I would use the standard one?

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[stuck saddle]

its pretty straight forward but i completely forgot its "solve the following equation for a (the missing side of a right angle)
sin(53)=a over 15

[empty sail]

Do you know how to solve something like 45 = x/65?

[stuck saddle]

i got it nvm

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[topaz lynx]

i asked this question yesterday but still a little confused

so modulus of 2 should be 2

and the argument of w imo should be

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[frosty solstice]

How do I start this problem? I know the volume part

But accounting for the spaces between balls

Idk

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[alpine sapphire]

The radiuses fp the circles are 3 and 10 what is AB?

[alpine sapphire]

<@&286206848099549185>

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[neon iron]

les goooo!

[neon iron]

so um hi :D i am tenshi, ill start of with a introduction, im tenshi, i was kinda busy saving the world from alien life forms during sets topic so idk anything on an atomic level abt it, so someone pls teach me from stratch

[digital river]

Can I assume you know what the symbols mean?

Or should I start there

[neon iron]

so

i know the u means union it think? and n means intersect

[digital river]

Correct.

[neon iron]

and union means everything, intersect means common things

thats all i know :D

[digital river]

Union is "or", intersect is "and", if that makes sense

[neon iron]

i have a question! does universal set mean, all the numbers included in the question

[void yew]

https://kolls.net/venn/

Try using this to visualize the images

[digital river]

The universe is just "everything that can be included in a set". For many questions, the universe will be the integers or the real numbers.

[void yew]

universal*

[neon iron]

(o.o;) okay!

[digital river]

Do you want a book recommendation that will cover all of this?

[neon iron]

one does it mean when it says there B square c?

[digital river]

That superscript c is the conjugate.

$B^c$ is the conjugate of B

[thorny flame]

nHail

[digital river]

It is short for $U - B$, where $U$ is the universal set

[thorny flame]

nHail

[digital river]

So essentially the conjugate of a set is all elements that are not in the set

[neon iron]

hmm, im confused

can u like give a simple example?

[digital river]

Go read the book "How to Prove It", I can't cover a whole introductory course in a help channel.

[digital river]

Sure

Let the universal set be the integers.

Let A be the set {0, 1, 3, 5}

[neon iron]

okay

[knotty ledge]

it is more commonly called the complement

[digital river]

Then the complement (or conjugate) of A is {... -5, -4, -3, -2, -1, 2, 4, 6, 7, 8, 9, 10...}

[digital river]

You're right, thanks

[neon iron]

wait so um, it is bassically, everything excluding the things in A?

[digital river]

Yes

[neon iron]

so the conjugate of B is, everything in the universal set, except for the numbers included in B

[digital river]

Note that $A \cup A^c = U$

[thorny flame]

nHail

[digital river]

Yes

[neon iron]

what does "-" means in sets

minus?

[digital river]

$A - B$ means everything in A which is not in B

[thorny flame]

nHail

[neon iron]

everything in A which is not in B

so if we write it on the other side

it means

B-A, everything in B which is not in A

[digital river]

Yes

[neon iron]

what does ' mean in sets

[digital river]

Also, $A-B$ is often written $A \setminus B$, so just be aware of that notation

[thorny flame]

nHail

[neon iron]

alright!

[digital river]

Honestly, not sure on that one. I would have assumed it was the compliment, but the writer already used c for that

[neon iron]

ohh alright

ahhh

i think it also means complement

its a trick one XD

[digital river]

It might

Again, I recommend you check out the book "How to Prove It", it's where I learned all of this. Some of the later chapters are irrelevant, but the part on sets is a very good introduction

[neon iron]

how long does it take for a channel to close?

[digital river]

15 minutes of inactivity, or you can manually close it

[neon iron]

ohh

i need to go for a bit, ill be back later, also for the book, ill see if i can find it online meanwhile

[digital river]

Alright. Feel free to DM me if you need any help with this

[neon iron]

alright, thanksss

[digital river]

I also know where you can find the book, but I won't link it here

[neon iron]

dm

ohhh

i forgot to ask what the power set of something means

[digital river]

The power set of A is the set of all subsets of A

[neon iron]

so its all the numbers included in A?

[digital river]

So if $A={1, 2, 3}$, $$\wp(A) = { \O, {1}, {2}, {3}, {1,2}, {2, 3}, {3, 1}, {1, 2, 3}}$$

[thorny flame]

nHail

[digital river]

No, it is a set of sets

And the O with a line through it is the empty set.

[neon iron]

woah, thats really confusing,

[digital river]

Power sets are large, yes

[neon iron]

{O, {10},{8},{21},{10,8},{8,21},{21,10},{10,8,21}}

so the powerset of c

[digital river]

Yes

[neon iron]

did i do it correctly?

[digital river]

That is correct

[neon iron]

alrightttt, thankyou

ill dm u later :D

thanks alot

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[neon iron]

Does anyone know which logarithmic laws I would need to use to solve these? Thanks

[neon iron]

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[lunar girder]

I missed class when this was taught and i dont understand how it was done.

[lunar girder]

and dont understand how to start it ?

this is writing one trig in the terms of another

[sweet shard]

what even is the question here

[lunar girder]

to write sin in terms of cos

but i solved it

[sweet shard]

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[tawdry chasm]

Anyone able to proof read this?

I got the correct results with an example before swapping the numbers

Egg on my face, something went wrong somewhere, corrected it, and now it's magically correct

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[neon iron]

where does the circumference value come from?

Is this an optimisation question?

no

its just shell method

in calculus 1

[knotty ledge]

What's troubling you with that solution?

[worthy crater]

do you want a derivation for the circumference or what do u excatly seartch for?

[neon iron]

so I dont know how to get that circumference value?

i know its integral 2pi times the R value and height value

how do u get R? I assume its x in this situation

and h is obviously the sqrt value

[knotty ledge]

Look at the picture, x is the radius, so circumference is 2π*radius which is 2πx

[neon iron]

well thats the answer sheet

but like how do i get the x as the radius

only by looking at the problem

[worthy crater]

you assume it as r-r`

and just call it x

[knotty ledge]

Whenever you have a function of the form y = f(x), x will always be the radius

[neon iron]

oh.. i see

okay thank you for that

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[clear cloak]

i know p series converge for p>1 but im not sure how to proceed with this problem

[cloud jetty]

Ratio test!

then test endpoints, afaik

[clear cloak]

oh

[cloud jetty]

I don’t think this converges for any p though, don’t quote me on that

[wide berry]

Try integral test. For the integral, let u = ln n

[cloud jetty]

^ that’s a smarter idea

[clear cloak]

oh right if i take u = ln n then i see the derivative of it in the problem

[hollow obsidian]

using Cauchy's condensation test is even faster

[clear cloak]

: o

[hollow obsidian]

you don't even needa think about how to do integration

[clear cloak]

i didnt learn cauchy :/

[hollow obsidian]

it's suitable for problems involving log

[clear cloak]

am i doing it right @wide berry

[hollow obsidian]

,ask cauchy condensation test

[thorny flame]

Results provided by WolframAlpha

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

Requested by vin100#3191

[hollow obsidian]

just ,ask and search, and you'd get the answer at undergrad lvl

[clear cloak]

i see

[hollow obsidian]

computing $2^n a_{2^n}$ is simpler than $\int_0^\infty a(x) \dd{x}$.

[thorny flame]

vin100

[clear cloak]

interesting

[hollow obsidian]

$a_2<0$ since $\ln(2) <0$ but that doesn't matter since the rest is positive.

[thorny flame]

vin100

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[rose patrol]

The coordinates of the point C are C(5, 5) , and the coordinates of its image resulting from a rotation of 100° degrees around a certain point are C'(-5, 7.5) , find the coordinates of the center of rotation.

[vale jacinth]

$\begin{pmatrix}cos(t)&-sin(t)\sin(t)&cos(t)\end{pmatrix} \begin{pmatrix}5-a\5-b\end{pmatrix}=\begin{pmatrix}-5-a\7.5-b\end{pmatrix}$

[thorny flame]

Cogwheels of the mind

[vale jacinth]

Where t=5π/9

You can solve a, b now

[rose patrol]

What is that?

I totally don't have any idea what is that

[vale jacinth]

$\begin{pmatrix}cos(t)-1&-sin(t)\sin(t)&cos(t)-1\end{pmatrix} \begin{pmatrix}a\b\end{pmatrix}=\begin{pmatrix}5cos(t)-5sin(t)+5\5cos(t)+5sin(t)-7.5\end{pmatrix}$

[thorny flame]

Cogwheels of the mind

[vale jacinth]

Okay I change my expression

You have
cos(t)(5-a)-sin(t)(5-b)=-5-a
sin(t)(5-a)+cos(t)(5-b)=7.5-b
Solve a and b

The condition gives you
[cos(t)-1]a-sin(t)b=5cos(t)-5sin(t)+5
sin(t)a+[cos(t)-1]b=5cos(t)+5sin(t)-7.5

This is a system of two linear equations of a and b

Where t=5π/9

[rose patrol]

From where we got t value?

[vale jacinth]

100 degree is 5π/9

180 degree is π

[rose patrol]

It is the first time I heard this

I am in the first year in high school, we didn't stduy this

[vale jacinth]

Anyway, you learned trig? $a=\frac{(cos(t)-1)(5cos(t)-5sin(t)+5)+sin(t)(5cos(t)+5sin(t)-7.5)}{2-2cos(t)}$ , $b=\frac{-sin(t)(5cos(t)-5sin(t)+5)+(cos(t)-1)(5cos(t)+5sin(t)-7.5)}{2-2cos(t)}$

[thorny flame]

Cogwheels of the mind

[vale jacinth]

If you didn’t learn trig it’s impossible to obtain the answer

[rose patrol]

Yes, I know trig

[vale jacinth]

Then it’s solved

Just cos(t) is cos(100 degrees) and sin(t)=sin(100 degrees)

[rose patrol]

But how you got this equation

[vale jacinth]

Because (x,y) rotated by angle t around the origin is (cos(t)x-sin(t)y,sin(t)x+cos(t)y)

[vale jacinth]

That’s why I obtained this

[vale jacinth]

Sorry I mean this

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[rose patrol]

.reopen

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✅

[rose patrol]

Thank you @vale jacinth

.close

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[near mist]

can someone help me with this question pls?

[leaden tusk]

what have you tried

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@near mist Has your question been resolved?

[leaden tusk]

i ask again

what have you tried

[near mist]

I think a is equal to 2

@leaden tusk

[leaden tusk]

how'd you determine a=2

[near mist]

x^2 -x =2

i'm not sure

[leaden tusk]

solve this

[near mist]

x = 2, x = -1

[leaden tusk]

wait

your question says x+14 not x+4

[near mist]

oops

[leaden tusk]

looks good

[near mist]

thank you

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[frosty cape]

Hi

[frosty cape]

Is this correct

Oh crap

.close

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

I'm very stuck on this but have absolutely no clue what's going on.

[knotty ledge]

@eternal spoke dont hijack an occupied help channel

[eternal spoke]

icard

didnt we talk yesterday?

[knotty ledge]

maybe

[undone fog]

why is it always me 😭

[eternal spoke]

sry bean

im leaving

[undone fog]

its okay

[knotty ledge]

bean i think you need to enter a number rather than that big expression

so actually work out what number that thing is

[undone fog]

i dont think its correct

[knotty ledge]

you have the same P(x)

uh, not sure why they are calculating the value of $e^\frac{9}{2}$ when the question asks for $e^\frac{1}{2}$?

[thorny flame]

iCaird

[undone fog]

entering the exact answer $\frac{6131}{128}$ is still incorrect

[thorny flame]

beanbeanjuice

[knotty ledge]

,w e^(9/2)

[thorny flame]

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Requested by iCaird#6258

[knotty ledge]

,w 6131/128

[thorny flame]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by iCaird#6258

[knotty ledge]

do you see my confusion

[undone fog]

yes

[knotty ledge]

the question asks for e^1/2, they calculate e^9/2

[undone fog]

,w e^(1/2)

[thorny flame]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by beanbeanjuice#4595

[knotty ledge]

try plugging in x=1/18

[undone fog]

,w 211/128

[thorny flame]

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Upgrade to WolframAlpha Pro!

Requested by beanbeanjuice#4595

[knotty ledge]

does it accept 211/128?

[undone fog]

im scared to enter it because i have 2 attempts left 😭 but it seems like its closer to e^1/2

[knotty ledge]

its very close to e^1/2

[undone fog]

why is it 1/18 rather than 1/2?

[knotty ledge]

because we have the series for e^9x

so to get e^1/2 we need to plug in x=1/18

[undone fog]

9x = 1/2

and solve for x?

[knotty ledge]

yes

[undone fog]

ah

okay so the second part is incorrect

i know you follow the formula

[eternal spoke]

lmao

[undone fog]

$R_{n}(x) = \frac{f^{n+1}(z)(x-c)^{n+1}}{(n+1)!}$

[thorny flame]

beanbeanjuice

[undone fog]

where c = 0, x = 1/18, and z is between c and x

[eternal spoke]

yeah

[undone fog]

yes

$R_{5}(x) = \frac{f^{5}(z)(\frac{1}{18})^{5}}{5!}$

[eternal spoke]

ok and what was that question if you re 12 th

lol

[thorny flame]

beanbeanjuice

[undone fog]

why is everyone always in my channel 😭 this happened yesterday too

[eternal spoke]

cuz

you have anime pfp

it makes you weak

i have rocks

it makes me strong

🤣

yeah bad joke

sry

[undone fog]

<@&268886789983436800>

[eternal spoke]

oh oh

sry mods i wont interrupt again

[vapid lichen]

@eternal spoke @neon iron if ur not here to help then pls leave

also we can see deleted msgs

[neon iron]

ok sorry

[undone fog]

Thank you moderator 😭

[eternal spoke]

ok sorry again

[undone fog]

i was clipping them deleting messages to send here but you can see that

[neon iron]

will not happen again

[neon iron]

they got logs

[topaz sinew]

@undone fog Has your question been resolved?

[topaz sinew]

@undone fog Has your question been resolved?

[undone fog]

actually i figured it out

[undone fog]

z = 1/18

.close

[topaz sinew]

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[drifting needle]

Those d(x) have to be the same

But they arent

Thats them next to each other

[blazing lichen]

it's because the graphs are not perfectly aligned

the red graph is shifted on the x axis

[drifting needle]

Yeah i got that

[blazing lichen]

ok

[drifting needle]

But i want to know where exactly that shift is coming from

Hence that is the problem

This is the task but in german

Its b

[blazing lichen]

oh german

I actually have to start studying German

[drifting needle]

You have the local point of (mentionend in pic) and you have to look for the closest point on the function with the (0|0) coordinate

[drifting needle]

Nice you know something in german?

[blazing lichen]

Ich

ein

[drifting needle]

https://tenor.com/view/mind-blow-galaxy-explode-boom-fireworks-gif-5139389

[blazing lichen]

bein

something like taht

haha

[drifting needle]

XD

[blazing lichen]

OK wait so

what exactly is the q in English?

[drifting needle]

.

The point is at task b

[blazing lichen]

the closest point on the function with the 0,0 coordinate?

[drifting needle]

Yes

[drifting needle]

The down d(x) is the correct one, mine the above

I somewhere made a small mistake and it shifts

[blazing lichen]

can't you just input point H into the eqn to get the formula?

[drifting needle]

With eqn you mean the a²+b²=c²?

[blazing lichen]

so it shifts basically because the correct answer has x-1

and you only have x

[blazing lichen]

how did you get your answer?

what is the original equation?

[drifting needle]

Which i used aswell as the correct answer but i somewhere made a mistake when creating the locus curve

You only have the point H and (0|0)

You are lookin for the closest route

The point H is mentiond in the screenshot

[blazing lichen]

OK no sorry I can't help

[drifting needle]

You use a²+b²=c² for the closest route

[blazing lichen]

what grade is this?

or how old are you

[drifting needle]

19

[blazing lichen]

I'm sorry

good luck!

[drifting needle]

Thanks

Tho

<@&286206848099549185>

[topaz sinew]

@drifting needle Has your question been resolved?

[topaz sinew]

@drifting needle Has your question been resolved?

[topaz sinew]

@drifting needle Has your question been resolved?

[drifting needle]

<@&286206848099549185>

[keen venture]

If you take the first equation and replace every x with an x-1, you get the second equation

That causes a shift to the right by 1 unit.

@drifting needle

[drifting needle]

I could replace it but there would be no conclusion to do so

If you hadn't the answer

So where in my equation did i do something wrong that this shift happen

Not happen dont know which equation is the correct one (graphicaly speaking)

[keen venture]

"correct one"?

[drifting needle]

Yes "correct one"

The one that is true

[drifting needle]

.close

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[jaunty shard]

Let X ∼ Exponential(1). (a) Write the formula of the PDF of X and use integrals in
order to compute E(X). (b) Use the LOTUS Theorem and integrals in order to compute
E(X2
). Use your answer in order to evaluate the Var (X).

[topaz sinew]

Please don't occupy multiple help channels.

[jaunty shard]

<@&286206848099549185>

[keen venture]

Avoid the helper ping before 15 mins

So X has an expressible distribution, what is it?

[jaunty shard]

e^x?

[keen venture]

Close! Check your book or Google if you don't know.

[jaunty shard]

Im really stuck here

[sweet shard]

Do the suggestion

[jaunty shard]

p( X = x)?

or x^e

[topaz sinew]

@jaunty shard Has your question been resolved?

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[vivid adder]

how do i graph y=-1/3x^2+2x-4

[vivid adder]

i cant factor this

so i really have no clue x

xd

wait can i use completing the square method

[leaden tusk]

you can also just plug in points

[vivid adder]

yeah but

like

i need 3 points

the x intercepts and the y intercept

so i can get the vertex

[vivid adder]

that would take way to long dont you think

so

[leaden tusk]

not really

but whatever floats your boat

[topaz sinew]

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@vivid adder Has your question been resolved?

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[frail gyro]

Im not sure if im understanding these

[frail gyro]

For the first one philip wants to have 1 pencil each. So we need to find how many packages we need of each until they hit the common multiple. Which i got 6 pencil packs and 5 erasers. But im not sure how to show my work.

<@&286206848099549185>

can anyone please help

<@&286206848099549185>

<@&286206848099549185>

[split plinth]

First ping helpers after 15 min

And also once

[topaz sinew]

@frail gyro Has your question been resolved?

[frail gyro]

<@&286206848099549185>

Can somon please help

this server litterly sucks

this happens everytime

[gleaming pasture]

which question

[frail gyro]

all

the first one i dont know how to do

but i got 6 packs and 5 packs

the second i got 6

and 3rd i got 36in

[gleaming pasture]

Well, lets start with the first

Pencils come in packages of 10 and erasers come in packages of 12. If you want to have 1 eraser per pencil, what does that mean?

[sweet shard]

Hire a tutor if you don't like waiting for volunteers

[frail gyro]

You need to find when they both come across the same amount of packages

so in other words the lcm

which is 60

[loud dawn]

Yep

So you want to show your work right

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@frail gyro Has your question been resolved?

[topaz sinew]

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[topaz sinew]

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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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[atomic stratus]

how many words i can make with these letters BIBLIOTECARIO if two " i " have to be adjacent

[topaz sinew]

@atomic stratus Has your question been resolved?

[atomic stratus]

<@&286206848099549185>

[topaz sinew]

@atomic stratus Has your question been resolved?

[atomic stratus]

<@&286206848099549185> sorry for pinging again

[tardy jay]

Set X=ii, then you need to count number of words you can create from {B, B, L, O, T, E, C, A, R, I, O, X}, can you continue from here? @atomic stratus

remember to divide by repeated letters as well

[atomic stratus]

but i think I cant have i i i

[atomic stratus]

that would be like 12!/2!2!

[tardy jay]

Okay now subtract the total from the number of words where XI and IX are adjacent

that you have number of words where XI and IX are not adjacent

Set Y=IX and do like similar step

but from the question, it doesn't explicitly mention that 3 i's cannot be adjacent so im unsure if you need to do this or not

[tardy jay]

and yeah i think thats correct unless i missed something

[atomic stratus]

a friend sent me this

[tardy jay]

ah they put another 2! because IX and XI is the same yeah my mistake

your friend is correct if you know for sure the question tells you that III is not possible. But if III is possible you won't be subtracting

[atomic stratus]

i don't understand why the - 11!/2!2!

[tardy jay]

set Y=IX

now you have set {B, B, L, O, T, E, C, A, R, O, Y}

which has 11 letters with B and O repeating twice

now this will give you total words where 3 I's are together

subtracting that from previous will give you total words where 2 I's are together but 3 I's are not together

[atomic stratus]

ooohhh now i got it, thanks you so much!

[tardy jay]

np but make sure to confirm if question is asking you that 3 i's are not together

because from that sentence it may or may not be true

maybe its cuz my english is bad lmao

[atomic stratus]

I'll write both cases just in case!

thx

.close

[tardy jay]

np

[topaz sinew]

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[vapid shoal]

how does this work?

[sweet shard]

you're gonna have to explain what this means

[ruby lintel]

Do you know how these groups work?

[sweet shard]

guessing permutations

[vapid shoal]

this is permutations

this is the answers

[sweet shard]

do you just not get the notation?

[vapid shoal]

i dont get the first line to second

i get the second to last

from what i thought, it was 5 -> 8 -> 5

[sweet shard]

calculate the new permutation of the product of the three terms

[vapid shoal]

so a group is (58)

but in the answers they give 5 is on its own

[ruby lintel]

It goes right to left, usually

So 8 -> 7 -> 6

[vapid shoal]

there are weird differences

but where i am learning permutations we do it from left to right

so its not a universal rule here i dont think

[ruby lintel]

hm

[knotty ledge]

yeah yours are going left to right

[ruby lintel]

but this one works fine if read from right to left

[knotty ledge]

the working out doesnt follow if you do it right to left

[vapid shoal]

do i not get 5 - 8 -5 here?

[knotty ledge]

you do

so that gives you the (5)

[vapid shoal]

oh , i thought that gives you 5 8

[ruby lintel]

wait i am dumb

you're correct

[knotty ledge]

it gives you (5) because 5 ends up back to 5

5 - 8 - 5

[vapid shoal]

okay then for the 6, do i not get 6 -> 7 -> 8 -> 5?

[knotty ledge]

just 6 - 7 - 8

you only go one step in each ()

because you're doing each one after the other

[vapid shoal]

so 6 to 7, then 7 to 8, so we get (68...) and for the new number it gets 8 to 5 then 5 to 6?

so i would get 685?

or do i not count the 5 because its already been taken

[knotty ledge]

you now need to work out where 8 goes

8 -> 5 -> 6

[vapid shoal]

oh shit

[knotty ledge]

so we get (68) yeah?

[vapid shoal]

yeah im dumb, forgot about the 5 going to 6 in the last bracket

yes that makes sense

[knotty ledge]

and then 7?

[vapid shoal]

7 to 6, then 6 to 7

so only 7

[knotty ledge]

yep!

so thats where our (7) comes from

[vapid shoal]

okay thanks

sorry i got one more example i dont get

!closed

nvm i just realised my mistake

[sweet shard]

.close is the close command

[vapid shoal]

i just kept on thinking that if the cycle goes back itself, i write it as two

.close

[topaz sinew]

Channel closed

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[vapid shoal]

thx for the help guys !

[topaz sinew]

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[tidal parcel]

I need to help trying to find the perimeter and area of a circle with diameter 15.6 meters.

[worn inlet]

do you know the formula?

[tidal parcel]

not really learned this stuff today

[worn inlet]

well did you take down some notes?

[tidal parcel]

It would be the area of a circle right

[worn inlet]

huh?

[tidal parcel]

Idk

[worn inlet]

the question is asking for the perimeter and area of a circle

if you didn't jot done the formula try google it to see if they make sense

[empty sail]

What formulas did you write down in your notes?

[worn inlet]

or watch some video cuz it might be helpful visualizing it

[tidal parcel]

Okay

can I like do the problem first and maybe ping you to check my work?

[worn inlet]

yeah sure

[tidal parcel]

Ok thanks

[worn inlet]

no worries~

[tidal parcel]

@worn inlet

how does this look

[worn inlet]

is that a 49 on the third line left

[tidal parcel]

yes

[worn inlet]

how did 2*7.8 give you 49?

[tidal parcel]

Oh wait

I wasn’t supposed to put pi in since 7.8 was supposed to replace that right

[worn inlet]

no

7.8 is r

it's radius

pi is the ratio between radius and circumfrence

[tidal parcel]

I put 2pi7.8 and got 49.0088454

[worn inlet]

yep that's the circumfrence

circumference

[tidal parcel]

then for the area

does the 600 cm look correct

[worn inlet]

no

[tidal parcel]

hm

[worn inlet]

the second last line is the approx answer

you multiplied it by pi twice

[tidal parcel]

yeah for both I did that

just followed the video

might be different though

[worn inlet]

do you mind show me the video you watched?

[tidal parcel]

Sure, I’ll send a dm?

or can I post links here

[worn inlet]

yeah sure either way is fine with me

ok

I took a quick glance

they did it right

I guess

the main problem with your step

is that you multiplied everything including pi at the second last step

[tidal parcel]

so circumference would just be 49

and area would just be 191.1

[worn inlet]

yes

there is two way to avoid the same problem

at least I can think of rn

one way is to come up with the equation and put everything into a calculator

that way you just jot down the answer the next step

but if your school doesn't allow calc skipping step in test

[tidal parcel]

They’ll probably allow them

[worn inlet]

then I would suggest to leave the pi till the end, do everything with the number that you can see (meaning they look like numbers, not symbols lol) , and then multiply it by pi at the very end

which is what they did in the video

[tidal parcel]

alright

I appreciate your help

thank you

[worn inlet]

alrighty

ur very welcome

[tidal parcel]

.close

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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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• Be polite and have a nice day!

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[worn horizon]

hey! i think this is a pretty simple question, but idk how to answer it, please excluse my english, im not too familiar with math terms

[worn horizon]

given the bundle [-5, 5], what are the real numbers?

i know what natural and whole numbers are, just not the real ones

[leaden tusk]

any number on a number line

[worn horizon]

would the answer be 11 then? (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)

or am i missing something

[leaden tusk]

those are whole numbers

any number on a number line is a real number

[worn horizon]

well idk then, if decimals are in, isnt the answer just infinity

[leaden tusk]

there are infinitely many, yes

[worn horizon]

whats the answer then, im just more confused now .-.

[leaden tusk]

you just said the answer

[worn horizon]

O

thanks lol

i was stuck on this

so i just looked for "math" in the discord server searcher

ty

:)

.close

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[unborn kernel]

Hello

[unborn kernel]

may you help me complete this assignment

<@&286206848099549185>

.close

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[mint anvil]

Need help with question 10. Don’t need to show work i just need to know the answer. Also could use help with 11 if possible. Just need the answer

[grim jacinth]

Take a better picture, please

[mint anvil]

Is that not clear enough? I can read it completely

[grim jacinth]

I don't feel like zooming in

Maybe crop it or take a bigger picture

[mint anvil]

Ok

Need help with question 10. Don’t need to show work i just need to know the answer. Also could use help with 11 if possible. Just need the answer

[vernal vale]

if you just want the answer use matlab or something?

seems so silly to wait around for someone to solve it

symbolab and wa do these

[mint anvil]

I have no idea how to use to bot to solve it

[vernal vale]

too

,w y'=5y^2

[thorny flame]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[mint anvil]

and what about 10

?

Thank you so much, im sorry haha

[vernal vale]

id use a bot

i mean no, id probably integrate

well, theres not really any need to i guess

howd you get 0?

[mint anvil]

I have no idea i was very stumped i put 0 bc of the integral being -1 and -1 but they are solving for the derivative so ik that’s wrong

[vernal vale]

so $y(x) = 3 - \int _{-1} ^x e^{-t^3} \dd t$

and youre saying y(-1) = what?

[thorny flame]

jan Niku (@pomodoro role)

[mint anvil]

it’s asking for the line tangent at x=-1

[vernal vale]

okay

whats your internal procedure for finding tangent lines?

[mint anvil]

Find derivative to get slope

[vernal vale]

idk i guess i can spoil and say

you got the right answer

im just trying to explain why its right

[mint anvil]

Ah, so i guessed and got it right?

[vernal vale]

no need to drag it out if you dont care tho

yea but

it should hopefully seem obvious

i mean you saw the integral is 0

so this is the easiest differential equation youll ever have to solve

[mint anvil]

Yes haha, so it’s just a bunch of shit there to trick me up

[vernal vale]

its y'=0

with initial condition y(-1)=3

yup

[mint anvil]

Thank you! This is the last thing i’m learning this year and i’m a senior so that’s why. idont care much to learn

thanks again.

[vernal vale]

np

[mint anvil]

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[radiant ruin]

Hi I was wondering if someone could check if I have the right answer

<@&286206848099549185>

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[thorny flame]

Solceous

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[brittle wharf]

Hi. I'm working on a question about arg and things like that. When I was trying to solve a question, I stumbled across a mistake in my calculation, according to the answer sheet, the right answer is pi/4, yet I don't get that on my calculator.

[brittle wharf]

how do they get pi/4 as the angle?

I understand every step before that, except that final addition part.

On my calculator, 8pi+9pi/4 is not pi/4

i get something like 41pi/4

[wide berry]

When you go around 2pi, you get back to the same point

[brittle wharf]

oh i just realized

yeah

im dumb

oh my god

8pi becomes 0

because you just return to the og spot

and 9pi/4

thats 2.25pi

which is 0.25pi

one fourth of 180

and that is, pi/4

thats quite big brain @wide berry

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[empty sail]

Show work

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[winged rapids]

Welp i dont understand the marked equation.
First of all what do the "||" lines mean?
I also dont understand what is meant by Y0, Y1. (Is it supposed to mean y.x and y.y?)
And there is also atan2. Why is that equation correct? I thought atan2 takes 2 numbers and not 2D vectors.

[winged rapids]

<@&286206848099549185>

[keen venture]

|| might mean magnitude here. That is,
|Y| = √[(Y0)² + (Y1)²]

Or whatever the components of Y are

[winged rapids]

Well thats smth. It would make sense

Didn't know that "||"

Though I know about magnitude of vectors because of programming

Thx @keen venture. That also solves my doubts about atan2. If "||" means magnitude it totally makes sense.

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[vivid rain]

Wut

[vivid rain]

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[mellow venture]

$\int_{0}^{\frac{a}{\sqrt{2}}}dy \int_{y}^{\sqrt{a²-y²}} \sqrt{x²+y²}dx \int_{0}^{\frac{x²-y²}{a}}dz$

[mellow venture]

mannnnnnnn

[thorny flame]

Hyperborean "Fractalogist" Tbh

[mellow venture]

YES

https://tenor.com/view/shrek-fortnite-victory-royale-dance-dancing-gif-17881375

okay so i have to solve this integral by converting it into cylinder coordinates

first time doing it so

at first we have

$$0<=y<=\frac{a}{\sqrt{2}}$$
$$y<=x<=\sqrt{a²-y²}$$
$$0<=z<=\frac{x²-y²}{a}$$

[thorny flame]

Hyperborean "Fractalogist" Tbh

[mellow venture]

Since we are integrating z first, we get
$$0<=z<=\frac{r²cos(2\theta)}{a}$$
hopefully this is correct
how do i find r and theta boundaries now

[thorny flame]

Hyperborean "Fractalogist" Tbh

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@mellow venture Has your question been resolved?

[mellow venture]

<@&286206848099549185>

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@mellow venture Has your question been resolved?

[mellow venture]

nein

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@mellow venture Has your question been resolved?

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@mellow venture Has your question been resolved?

[vale jacinth]

What is the original question? What integral did you originally need to calculate?

[hoary timber]

Well what are the boundaries for x

[mellow venture]

this

how u find x boundaries

[mellow venture]

do u just plug in the cylindrical coordinates like I did with z, or u have to do something different

[hoary timber]

yes just put in the upper and lower bounds for x

and then you can determine what shape it is and therefore how to convert it to cylindrical coords

[mellow venture]

0<=y<=a/sqrt(2)
rsin(theta) <=x<=sqrt(a^2-r^2sin^2(y))

?

[mellow venture]

lol

rcos(theta)=rsin(theta) => r=0
rcos(theta)=sqrt(a-(r²sin²(theta)) =>r²cos²(theta)=a-(r²sin²(theta)) => r²(cos²+sin²)=a => r= sqrt(a)

0<=r<=sqrt(a)

0<=theta<=2pi

lets see

mhhhh

i become (pi*sqrt(a))/10

OMG

i think r boundary is wrong

what should lower limit be for r boundary

[mellow venture]

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[neon iron]

I'm stuck with simplfying this algebraic fraction, I got to step 2 on the right but I'm lost on where to go next

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[neon iron]

@gusty quiverhelp!

[gusty quiver]

why'd you pick me

[neon iron]

ANIME PFP UNITE

PLease

[gusty quiver]

double check if you factorised the numerator correctly in your step 2

[neon iron]

the bottom part of step 2?

Because I wasn't sure how to factorise it

[gusty quiver]

the top part

[neon iron]

its a difference of squares though right

OH

2P RIGHT

[gusty quiver]

so correct that first, then take a look at the denominator (bottom part)

[neon iron]

(2p+3) (2p-3)

[gusty quiver]

what can you factor out of the bottom?

[neon iron]

they both divide by two

[gusty quiver]

that's right

[neon iron]

Leaving me with 2p+3

But the answer says 2p+3/2

Where that final 2 coming from

[gusty quiver]

$\frac{(2p+3)\cancel{(2p-3)}}{2\cancel{(2p-3)}}$

[thorny flame]

dino

[neon iron]

POGGERS

[gusty quiver]

can you manage the rest?

[neon iron]

My hero!

2p+3/2 is the answer

and I understand how to get there now

[gusty quiver]

ah right, no need for the line equation

[neon iron]

I will now always ask you for help

[gusty quiver]

uh- I can't guarantee to always be available

[neon iron]

thas a joke

but I will ask you

ty!

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[neon iron]

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[worldly musk]

I need help finding A and B so that (4,2) is an extreme point for f(x,y)=a/3*x^3-8x*y+b/3*y^3

[worldly musk]

how do i find the gradient to start with, combining the partial derivatives

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[winter lichen]

Hey, how do I solve this system of sigma notations?

[winter lichen]

I need to be getting this answer

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[neon iron]

I know I made a mistake somewhere and I'm unsure of how to factorise this to get the final answer of n/3(n+2)

[neon iron]

what is $n(n-2)$ equal to when expanded ?

[thorny flame]

AimaneSN

[neon iron]

n^2 - 2n?

[neon iron]

Yep! correct

but here you should factorise something in the denominator (what is it?) to get the result you're looking for

3(n-4)^2 ?

[neon iron]

? How did you get this !

write all the steps you followed