help-39

[fathom valley]

is that correct?

[toxic lichen]

how did you get this?

it's wrong, but i want you to explain your process so i can tell you precisely where your mistake is.

[fathom valley]

well

I used this

[toxic lichen]

ok right

[fathom valley]

oh i know

[toxic lichen]

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

[fathom valley]

yeah just realized that

[toxic lichen]

your b is itself 2, but that means the middle term is -2 * 2 * x = -4x

[toxic lichen]

anyway good job remembering these

[fathom valley]

the first time i did it with what i remembered, the second time i used that but forgot the 2

[toxic lichen]

now to apply it back to our whole equation:

from 4(x-2)^2 - x(4x-13) = -5
you get
4(x^2 - 4x + 4) - 4x^2 + 13x = -5

[fathom valley]

yeah

[toxic lichen]

(you handled the other bits correctly so i am just copying those from your work)

ok, do you see how to continue now?

[fathom valley]

im gonna write it out

and then answer

i can do 4(x^2 - 4x + 4) next

and then i can gather them

is that the correct term?

doesnet matter

[toxic lichen]

you can collect like terms as we say in english

[fathom valley]

4x^2-16x+16-4x^2 + 13x = -5

and then

-3x=-21

divide with -3

x=7

done

thanks

.close

[pearl pond]

Channel closed

Closed by @fathom valley

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[bitter pelican]

for the zeroes

why is it only 3pi/2

and not 3pi/2,-pi/2

since sin (pi-theta)=theta

pi-3pi/2=-pi/2

[toxic lichen]

3pi/2 and -pi/2 differ by a full turn

[bitter pelican]

wdym

a full turn is 2pi

oh

if the second value is negative

does that mean you dont use it

[toxic lichen]

... no not really

it's more that sin(theta)=-1 has only one solution on a period

[pearl pond]

@bitter pelican Has your question been resolved?

Channel closed

Closed by @bitter pelican

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tired osprey]

Is $$\frac{d}{dx}f(1) the same as f'(1)$$ ?

[jolly parrot]

Ytterbium

[flat cedar]

f(1) would be a constant value, so no

[indigo pewter]

Is $\frac{d}{dx}f(1)$ the same as $f'(1)$ ?

[tired osprey]

Yea that's what I thought

[jolly parrot]

Dork9399

[tired osprey]

Thank u dork

So is it the same

I had this in my exam yesterday

[indigo pewter]

no its not

[tired osprey]

I didn't write 0

[indigo pewter]

look at this

[flat cedar]

No, it would be zero

[tired osprey]

I put the derivative

[indigo pewter]

this

[tired osprey]

What about partial derivatives

In my exam it was partial derivative

I mean There's no f'(x) notation for partial derivatives

[plush bramble]

Yes there is

[toxic lichen]

$\dv{x} f(1)$ is kinda bad notation

[jolly parrot]

Ann

[toxic lichen]

where did you see that

[plush bramble]

https://tutorial.math.lamar.edu/Classes/CalcIII/PartialDerivatives.aspx

[pearl pond]

@tired osprey Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[lunar bone]

hi, need some help with theese

[hazy pilot]

do you know the derivative and integral of the natural log?

[lunar bone]

nope

i just need the basic formula

[hazy pilot]

ah okay

Are you not interested in why this is true?

[lunar bone]

im in 12th greade so i dont think i need to...

[lunar bone]

is the base of the log 10?

[hazy pilot]

no it's base of log a

[lunar bone]

isnt it ln?

[hazy pilot]

the thing in the bottom is log e

yea ln

ln(a) is in the bottom

[lunar bone]

👍

.close

[pearl pond]

Channel closed

Closed by @lunar bone

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[grizzled pine]

Hi

[grizzled pine]

This the question and I need help to solve it

Rn I’m stuck at 1c😭

<@&286206848099549185>

[toxic lichen]

you need to work out what g(1/x) is

and what g(1-x) is

simplify them both carefully

and show that they're equal

[grizzled pine]

I did the 1/x one

But it’s not ending up as equal😭😭😭

[toxic lichen]

are you trying to compare it against g(x)?

[sudden smelt]

calculate g(1/x) and g(1-x)

to see if they are equal

[grizzled pine]

Is it correct😭????

[toxic lichen]

so you are seeing that it's not equal to g(x) and that's what you're confused by, yes?

[grizzled pine]

I’m supposed to show that g(1/x) is equal to g(1-x)

[toxic lichen]

yes

but where is g(1-x)?

you have not worked that one out yet.

do it.

... i also would have appreciated it if you answered my question of

so you are seeing that it's not equal to g(x) and that's what you're confused by, yes?
directly with a "yes thats whats confusing" or "no its something else"

[grizzled pine]

That’s where I’m stuck

I’m stuck at that part😭

Wait why can’t I message

WHY CANT I MESSAGE

SHSHSJBSBS

Why can’t I message

[grizzled pine]

Im so sorry I didn’t mean to be rude

[toxic lichen]

well you plugged 1/x into g(x) just fine, yeah?

why not plug in (1-x) now instead?

there's no new concepts here just some more algebraic work

[grizzled pine]

It looks confusing😭

[toxic lichen]

$g(x) = \frac{x^3 - 3x^2 + 1}{x(1-x)}$

[jolly parrot]

Ann

[toxic lichen]

$g(1-x) = \frac{(1-x)^3 - 3(1-x)^2 + 1}{(1-x)(1-(1-x))}$

[jolly parrot]

Ann

[toxic lichen]

1-(1-x) on the bottom becomes just x

[grizzled pine]

OHHHHHH

[toxic lichen]

on the top you just have to expand carefully

[grizzled pine]

wait let me solve it further now

I’m stuck again😭

@toxic lichen

<@&286206848099549185>

[toxic lichen]

$(1-x)^3 \neq 1^3 - x^3$

[jolly parrot]

Ann

[toxic lichen]

and $-3(1-x)^2$ is even more not-equal to $-3-x^2$

[jolly parrot]

Ann

[toxic lichen]

but let's take these one at a time

do you know how to expand $(a \pm b)^3$?

[jolly parrot]

Ann

[grizzled pine]

No….

[toxic lichen]

what about $(a \pm b)^2$?

[jolly parrot]

Ann

[grizzled pine]

a^2+2ab+b^2?

[toxic lichen]

the middle term is +2ab or -2ab depending on if the original bracket has a plus or minus

but yes

$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \ (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$

[jolly parrot]

Ann

[toxic lichen]

have you seen either of these?

[grizzled pine]

Yes I’ve

WAIT WAIT ITS EQUAL NOW

THANK YOU VERY MUCH

[toxic lichen]

oh nice that worked then :P

if you want help on other questions from your worksheet it'll be better to close this channel and open a new one for your next question btw

[grizzled pine]

Got it

[pearl pond]

@grizzled pine Has your question been resolved?

[grizzled pine]

Yes✨✨✨✨

[pastel umbra]

If so,

!close

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[hexed ocean]

Help

[hexed ocean]

What does |x| mean

Like

If
|2x+2| = 4

What does it mean

[flint zenith]

that means that 2x+2 is equal to 4 or -4

absolute value

[hexed ocean]

So not -2x -2 = 4

[flint zenith]

that's one of them

thats the same thing as 2x+2 = -4

[hexed ocean]

2x+2 = ±4?

[flint zenith]

yea

[zinc ferry]

Yes

[flint zenith]

and you solve both equations for x

[hexed ocean]

Ok so

Wait

[hazy pilot]

|x| equals x if x is positive and -x if x is negative

[hexed ocean]

That's why the shoelace forumla has an absolute value

To have it positive

[hazy pilot]

y = x

[hexed ocean]

lxl = ℤ+

[hexed ocean]

MY FUCKINF EYES

OMH

ITS NIGHT

[hazy pilot]

y = |x|

[hexed ocean]

FULL BRIGHTMESA

[hazy pilot]

sorry vro 🥀

[hexed ocean]

Why isn't it the -ve

[hexed ocean]

Ts pmo

Icl wanna know a story

[hazy pilot]

always

[hexed ocean]

So like

[zinc ferry]

y=|x| is basically positive part of y=x and mirror image of y=-x mirrored with respect to the x axis.

[hexed ocean]

One time I was trying to scare my old3r cousin

Right

[hazy pilot]

right

[hexed ocean]

I slowly walked to his room

He was home alone

Opened the door to the see him

😔

[hazy pilot]

lmaooooo

[zinc ferry]

Bruh

[hexed ocean]

And the thing is

[hazy pilot]

🥀

[hexed ocean]

It happened twice

[hazy pilot]

💔

[hexed ocean]

💔💔

Like TWICE BY ME not his PARENTS but ME

Yes

😔

[hazy pilot]

🔥

[hexed ocean]

FUCK GEOMETRY COORDINATE

💔💔💔

https://tenor.com/view/car-garn47-garn-47-car-garn47-car-garn-47-gif-13936239128611030573

Ok bye gang

.close

[hazy pilot]

gng

[pearl pond]

Channel closed

Closed by @hexed ocean

Use .reopen if this was a mistake.

[broken fossil]

<@&268886789983436800>

[hexed ocean]

WHAT DID I DO

[hexed ocean]

???

My dearest apologise

I didnt know

[spiral pivot]

Nothing sexual please

[hexed ocean]

Okay

Sorry

[zinc ferry]

Damn a nice mod before gta 6 is crazy

Keep up the good work

[hexed ocean]

Isnt gta 6 out?

[zinc ferry]

Nah it’s delayed

26

[hexed ocean]

...

[zinc ferry]

It’ll come in 2026

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[chrome vale]

number of cyclists that traveled over 50km divided by the total number of cyclists maybe?

[muted sierra]

yeah

[broken fossil]

no??

[muted sierra]

What, wasn't he asking for the method to go for to calc P(E) ?

[broken fossil]

https://tenor.com/view/mac-miller-knock-knock-let-em-in-let-them-in-crazy-kids-gif-18240764032821905828

[muted sierra]

Alr, go on..

[broken fossil]

trust the maths bro

[serene sorrel]

Ahh ok
33/60

[serene sorrel]

tysm L!

.close

[pearl pond]

Channel closed

Closed by @serene sorrel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dense iris]

5a

Confused how to do it

[pearl pond]

@dense iris Has your question been resolved?

[dense iris]

.close

[pearl pond]

Channel closed

Closed by @dense iris

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[neon jolt]

hello

[neon jolt]

This is not a math related but I am having a project in java

and I am having a problem where I really stuck on it for days..

[fringe robin]

probably not the right server if it has nothing to do with maths

[neon jolt]

If anyone can help me I'll really appreciate it

[fringe robin]

!dontasktoask

[neon jolt]

I know sorry in asking here I dont know any other servers

[fringe robin]

#old-network

!da2a

[pearl pond]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[neon jolt]

I am having a 2d maze grid with players where there must be rotating corrdiors (row) for each round. The roation logic does not work

if anyone can help out pls dm me

[pearl pond]

@neon jolt Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[junior vapor]

Hi i dont really understand part i. Answer: 10

[pearl pond]

@junior vapor Has your question been resolved?

[junior vapor]

<@&286206848099549185>

[warm copper]

Well all you really need to do is find the vertical distance covered by the rocket (assuming no acc of gravity) and take away the distance lost from gravity

[junior vapor]

Wouldn't that just be 15? (these questions should all be assuming no air resistance)

[warm copper]

can you show how you obtained 15

[junior vapor]

oh wait distance

[junior vapor]

wait distance is what i tried to do in here

[warm copper]

eh?

I'm ngl I have no clue what you wrote...

First off -10t integrates to -5t²+C

the -10t is the SPEED. Not the acceleration. d²y/dt²=-10, dy/dt=-10t, y=-5t²

The +C is zero since the speed starts at 0, and so does the distance.

You just gotta find the vertical distance upwards by the rocket take away the vertical distance downwards by the gravitational force

[junior vapor]

oh crap yeah ur right idk what i was writing

[junior vapor]

wait how do u find the downwards one

[warm copper]

Well that's the y component

Acceleration=10, speed=10t, distance=5t²

Remember, integrating acc gets speed, and integrating speed gets distance

[pearl pond]

@junior vapor Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[dense iris]

Can I have help doing part B

I have no idea how to start

[pearl pond]

@dense iris Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[buoyant pasture]

8th and 9th question

Will the answer is all of these

[pearl pond]

@buoyant pasture Has your question been resolved?

Channel closed

Closed by @buoyant pasture

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wispy fable]

Im not sure about my answer, I found the gradient as (a, 1)

[wispy fable]

but it needs to be with |delta f| right so the answer is none of the others?

( a/sqrt(a^2+1), 1/sprt/(a^2+1)

[spark parcel]

answer is indeed none of the others

[spark parcel]

as for ur question yes

u need the option for which delta f(-1,0) gives you (-1,1)

i assume u already figured out how to get -1,1

[wispy fable]

yus i just wasnt sure

now im stuck on the continuation of the question tho..

[spark parcel]

I just know the beginning of it

Well what are u stuck on lol

[wispy fable]

i dont know where to start so the beginning is good enough lol

[spark parcel]

whats the formula for the directional derivative

[wispy fable]

u . delta f

[spark parcel]

can you find delta f first

[wispy fable]

okk right i had already found that

it becomes u . (a, 1)

[spark parcel]

find the unit vector

wait

hmm

[wispy fable]

yeahh

[spark parcel]

assume vector u to be u1 and u2 for this

[wispy fable]

u1a + u2 = -sqrt10

now im proper stuck lol

[spark parcel]

remember how the min value of a directional derivative is the neg magnitude of gradient

[wispy fable]

mhm

[spark parcel]

i know something abt that should apply here

hmm

WAIT

[spark parcel]

isolate u2

and we also know that u 1 squared + u 2 squaredshould be 1

my brain is NOT functionign

[wispy fable]

lol its alr

[spark parcel]

that should end up giving you a neat little quadractic

just like a little kitten

hewhehsheshesaea

[wispy fable]

my brain is not functioning x5 im so lost

[spark parcel]

okay

u2 = -sqrt10-u1a

[wispy fable]

yus

[spark parcel]

subbing that in the equation where (u1)^2 + (u2)^2 = 1

[wispy fable]

ohhhhhh

[spark parcel]

yup yup

[wispy fable]

damn

[spark parcel]

🫃

heres an emoji of a pregnant man to make ur day better

[wispy fable]

made my day until, im lost AGAIN

i see the quadractic its here

[spark parcel]

noioce

now

[wispy fable]

its gonna be 1 1

[spark parcel]

what condition does the quadractic have to satisfy such that ur terms are real

solutions

wtv

[wispy fable]

they both need to be 1

or -1

[spark parcel]

bro

think about it again

[wispy fable]

am i dumb

[spark parcel]

what does a quadractic need such that its solutions are real

no ur prolly experiencing brain fog

hint: smth to do with discriminant

[wispy fable]

discriminant needs to be > 0

[spark parcel]

uhuh

UHUH

more than or equal to

actually

equal to

[wispy fable]

i mixed up what quadractic meant my bad 😭

[spark parcel]

😭

[wispy fable]

okkay we just >= the discrimante to 0, its asking a's boundries anyway

[spark parcel]

yes

[wispy fable]

alright thanks a lot 😭

.close

[pearl pond]

Channel closed

Closed by @wispy fable

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[wispy fable]

I keep finding 2x+2z=0

[wispy fable]

dont u just follow the formula, i checked twice for calculation mistakes but didnt see any

[plush bramble]

Gotta show your work like it says here

[wispy fable]

lemme send a photo

found fx, fy, fz

put x, y, z values

[plush bramble]

Show the formula you're using

[hazy pilot]

how is 3 (1)^2 + 1/1 = 2?

[wispy fable]

okay yep

sorry thanks

.close

[pearl pond]

Channel closed

Closed by @wispy fable

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tulip cradle]

,rotate

[tulip cradle]

Trying to differentiate this wrt C1

Do I need to expand

Cause it just seems to get messy

Also they’ve got Y in the final answer but I thought Y gets eliminated when u differentiate

[tulip cradle]

And then equate to zero and solve for C1

For more context I’m trying to get this

[junior loom]

log(ab) = log a + log b

[tulip cradle]

Yeah I just tried that and it didn’t work I just ended up with Y=0

[junior loom]

? you can't solve for Y, this isnt an equality

[tulip cradle]

Optimal solution implies FOC=0 right

[junior loom]

FOC?

[tulip cradle]

First order condition

[junior loom]

Ah, yes, under some reasonable assumptions

let's take this in steps. first find the derivative, and only after that look for roots of the derivative

what does log(ab)=log a + log b look like for this expression

[tulip cradle]

God I finally got it

finals stress has gotten to me😭

Thanks

[junior loom]

🥳

[pearl pond]

@tulip cradle Has your question been resolved?

Channel closed

Closed by @tulip cradle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[stiff forge]

im struggling dude.

[stiff forge]

final unit of stats and im just stuck

[broken fossil]

seems right i cant verify the pcc but i have no clue whats wrong with the rest of it

[stiff forge]

idk where i went wrong bro

lmao

this class dead the end of me

[broken fossil]

sue the teacher

[stiff forge]

Idk bro I need to get this right though ill check back maybe i made a rounding error

.close

[pearl pond]

Channel closed

Closed by @stiff forge

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[ivory basin]

How do we know that (1-sqrt(2))^3000 is smaller than 10^-100?

[sharp vigil]

well that would be about (-0.4)^(3000) compared to (0.1)^(100). since they are both similar size numbers the one with the much larger exponent would be much smaller (since they are less than 1)

[pearl pond]

@ivory basin Has your question been resolved?

[ivory basin]

ohhhhh that makes so much sense thank you!

[pearl pond]

Channel closed

Closed by @ivory basin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[bold mango]

how do I determine the angle between AF and FC

to find the dot product

I cant visualize it

Since they're not on the same plane im not sure how

[dusky glen]

It might help to look at the triangle AFC

[sharp vigil]

you could also do it by components

[bold mango]

im not given the components

im only told each side lenght of the cube is x

[sharp vigil]

well you can make up a coordinate system aligned with the cube

[bold mango]

let me try

A(0,x,0)

F(x,0,0)

C(0,0,x)

?

it works

their dot product would be -x^2

[sharp vigil]

sure?

[bold mango]

Is there a way to do it without components

[sharp vigil]

to do it purely geometrically i would consider buzzing hornet's suggesion

[covert wolf]

Purely geometrical is basicallt deriving the dot product

U would use cosine rule

[bold mango]

Coordinate system:
A(0,x,0)
F(x,0,0)
c(x,x,x)

AF = (x, -x, 0)
FC = (0, x, x)

AF dot FC (by components) = -x^2

AF dot FC = |AF||FC|costheta
-x^2 = (xsqrt2)(xsqrt2)costheta
-x^2 = 2x^2 costheta
costheta = -1/2
theta = 120

For the dot product would 0<=theta<=180 be the restriction for theta

[dusky glen]

You might want to rethink the costheta=-1/sqrt2 step

[bold mango]

oh

bruh

IM STUPID

LMAO

1/2

oops

[bold mango]

typo

[covert wolf]

Yes

[sharp vigil]

generally the angle between vectors will be between 0 and 180, yes

[bold mango]

ty

[covert wolf]

Its because that's the principle angle

[dusky glen]

Right, and so theta will be?

[bold mango]

120 deg

ty guys

.close

[pearl pond]

Channel closed

Closed by @bold mango

Use .reopen if this was a mistake.

[dusky glen]

Wait, how did you get this?

[bold mango]

by components

oh wait i forgot to mention

im given the side lengths of the cube

which is x

so asume E is the origin

I put.A F C into coordinates

[dusky glen]

Ok I will point out as a sanity check that AFC is an equilateral triangle

[bold mango]

oh

💀

that would be the easier way

[sharp vigil]

just as a side note we should note that there is a distinction between the angle between AF and FC as vectors vs the angle between them as line segments

[covert wolf]

Its not

Its isoscoles

[bold mango]

How would it be as line segments

[dusky glen]

...I'm pretty sure it is? All of its sides have length xsqrt2?

[covert wolf]

No the AC =2x

[bold mango]

its isoscoles

[sharp vigil]

well as line segments you can get two different angles which will be supplementary to each other, and one of those will be the angle between them as vectors

[dusky glen]

Am I going completely insane here? Is this not obviously false?

[bold mango]

120 deg and 240 deg?

[dusky glen]

It's the diagonal of a square of side length x isn't it?

[sharp vigil]

i was thinking more 60 and 120

[sharp vigil]

this is correct for the record

[bold mango]

no you're right

[covert wolf]

Nah when thinking about the angle

[bold mango]

yeah

[covert wolf]

Wouldn't u flatten the shape

[bold mango]

wait if i identify the equilateral triangle can i also find the angle that way

[covert wolf]

Like think about it as planes

Flattened

[sharp vigil]

you would think about the shape existing in the diagonal plane

[dusky glen]

Well, what is every angle in an equilateral triangle equal to?

[bold mango]

60

erm

[dusky glen]

Right.

[bold mango]

💀

but how would i identify the angle between the vectors

[covert wolf]

Dot product works

I don't see a problem with that?

[bold mango]

60 or 120

[covert wolf]

Oh its obviously 60

U filter

It

Using logic

U want the Accute angle

That's tje only way to go about it

[bold mango]

the angle between AF and FC is 120

in the equilateral its 60

[covert wolf]

Yh they're all 60

[covert wolf]

Also depends on the segment you chose btw

[bold mango]

yk when you have a question but you dont know what to ask

[covert wolf]

If you want that specific angle u want u do FC. FA

[sharp vigil]

the yellow vector is a copy of AF that i placed starting at F

[bold mango]

this answered the question i didnt know what to ask

[bold mango]

ya

thats sick

can I do the same with AF and BG

thats acc so sick

i just unlocked a new point of view

.close

.close

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[modern marlin]

A rectangle with one side on the x-axis has its upper vertices on
the graph y = cos (x) as shown in the figure to the right. What is
the minimum area of the shaded region?

A. 0.799
B. 0.878
C. 1.140
D. 1.439
E. 2.00

anyone know how to do this optimization?

[gray lantern]

do you have a picture of the figure by any chance

just for clarification

[modern marlin]

Yes

Been stuck on this for hours

[gray lantern]

oh alright

well first you can start with modeling rectangle width and height with expressions based on x

what would rectangle width be here

in terms of x

[modern marlin]

thats all the info i was given

the one i sent above

[gray lantern]

you can just call x the end position of the rectangle

on the x axis

in that case what would the width expression be

[modern marlin]

2cos(a)?

[gray lantern]

nope

remember the distance from the origin to one end of the rectangle is just x

there are ends on both sides of the origin

so the width would be?

[modern marlin]

x

[gray lantern]

almost

[modern marlin]

2x?

[gray lantern]

remember there are two sides

yes

now what would the height be modeled as

[modern marlin]

so then how do i minimize that

[gray lantern]

in terms of x

[modern marlin]

2x

[gray lantern]

no

[gray lantern]

remember the height is just y here

[modern marlin]

2y

[gray lantern]

no

[modern marlin]

y

[gray lantern]

yep

because it only intersects y

not 2y

[modern marlin]

ahhhh

[gray lantern]

but y is just equal to?

[modern marlin]

cosx

[gray lantern]

yep

width = 2x
height = cos(x)
area = ?

[modern marlin]

2x cosx

[gray lantern]

good

[modern marlin]

(2x)(cosx)

[gray lantern]

now you can optimize it

[modern marlin]

thats the thing

i dont know how

where do i go from the area

[gray lantern]

what's the derivative of the area

[modern marlin]

-2xsinx

[gray lantern]

product rule applies here

[modern marlin]

-2sinx + 2cosx

[gray lantern]

close

[modern marlin]

-2xsinx + cosx

2cosx*

[gray lantern]

2cosx - 2xsinx is what i got

yes

[modern marlin]

yep u just put cos first

so whats the minimization

[gray lantern]

2cosx - 2xsinx = 0

[modern marlin]

let me pout in calc rq

0.860

is what i got

[gray lantern]

sadly have to go now

[modern marlin]

nooo

i need u

[gray lantern]

im sure someone else will be able to help

sorry

[modern marlin]

.close

[pearl pond]

Channel closed

Closed by @modern marlin

Use .reopen if this was a mistake.

[modern marlin]

.reopen

[pearl pond]

✅

[modern marlin]

A rectangle with one side on the x-axis has its upper vertices on
the graph y = cos (x) as shown in the figure to the right. What is
the minimum area of the shaded region?

A. 0.799
B. 0.878
C. 1.140
D. 1.439
E. 2.00

anyone know how to do this optimization?

Anyone know how to do this

please builder left me to rot

🙏

[radiant terrace]

Did they see those things you posted/deleted?

[modern marlin]

No i made an executive decision to delete before he saw them!

🫡

[radiant terrace]

Okay yeah def don't do that kind of stuff. Thank you for deleting it.

[modern marlin]

yes sir!

can u help

uwu

[radiant terrace]

For your problem, do you know how to integrate?

[modern marlin]

yes

i just dont know how to minimie

to get the value

minimize

because from the area equation

2cosx - 2xsinx = 0

where do i go from here

[radiant terrace]

You see how you can integrate to get area under curve then subtract out the box area right?

Then you have some goofy function you want to minimize?

[modern marlin]

do u thunk u could get that asnwer for me, i keepo doj git wrong

[radiant terrace]

I'm not gonna do that.

[modern marlin]

keep doing it wrong

[radiant terrace]

After you do what I mentioned you would just minimize in the same way you'd do when you learned derivatives. So you want to solve f'(x)=0 where f is whstever goofy area function you had, to find local maxs/mins on your given interval.

The general strategy is that. The actual calculation might just be ass. But you can also use wolfram alpha for a lot of this stuff if you keep messing it up.

[modern marlin]

all the ais give different answers

thats why i needed help

cuz i know how to get to the area equation

the actual calculation is dif on everyhting

[radiant terrace]

Wolfram alpha isn't a literal ai afaik

I wouldn't recommend using ai tools to begin with compared to a real cas or something.

[radiant terrace]

Where it says "Interpreting as", you see how it isn't interpreting what you put correctly?

Mmm

Is the lhs of this equation your area function?

[modern marlin]

yes

we took the derivate of the originakl equation alr

thats the derivivative

[radiant terrace]

Oh okay

,w solve 2cosx - 2xsinx = 0

[jolly parrot]

Results provided by WolframAlpha

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

Requested by dootdooter

[radiant terrace]

Not sure if this is right

[modern marlin]

A. 0.799
B. 0.878
C. 1.140
D. 1.439
E. 2.00

these r the MCQ answers

its so weird

[radiant terrace]

Yeah also the - is nonsense

[modern marlin]

yea

[radiant terrace]

Possibly your area formula is wonky

[modern marlin]

thats why i am so confused

every AI has the same area formula

im pretty positive its correct

builder dolphin also got same formula

[radiant terrace]

The fact that some AI gave it to you doesn't inspire confidence in me

[modern marlin]

i would usually agrre, but when 10 dif do, and the helper in this discord as well, and my friends

i feel like it has to be

the only thing is, we all got different values for the minimize

and thats where the MCQ doesnt make sense

its either between A, B, or C we think

[radiant terrace]

Was your original area formula something like 2-2xcosx?

,w 2xsinx-2cosx = 0

[jolly parrot]

Results provided by WolframAlpha

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

Requested by dootdooter

[radiant terrace]

Oops

,w solve 2xsinx - 2cosx = 0

[jolly parrot]

Results provided by WolframAlpha

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

Requested by dootdooter

[modern marlin]

ye

it was a product rule or smth

[radiant terrace]

See the graph here?

The red dots minimize your function. The bottom numerical solutions in the screenshot are the x coord approximations for those red dots

Check those in your area function

[radiant terrace]

Idk wtf this x value was lmao

Worth pointing out

Not all of the x values make sense to try in the screenshot

The box only uses values lying somewhere between -pi/2 to pi/2 in your figure (which is approx 1.57) so anything outside that range doesn't need to be checked.

[pearl pond]

@modern marlin Has your question been resolved?

[modern marlin]

okay

i tjink its C i

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[ripe pagoda]

If A works 3 times faster than B and C takes half of the time which A take. How much work they will do in one day?

theres no answer given so im confused
my and my friends are getting different answers

[pure rapids]

wdym work

There's no quantifiable unit in the question

[ripe pagoda]

yeah thats the point, i need to assume ig

[signal atlas]

What did you get and how

[wise flicker]

Is it related to some aptitude kinda stuff?

[dusty flame]

ahh

we use ${A, B, C}$ to represent the rate of each person, respectively

[jolly parrot]

k

[dusty flame]

therefore, ${B = \frac{1}{3}A}$ and ${C = 2A}$

[jolly parrot]

k

[dusty flame]

therefore, the total rate when they all work together is

$\frac{10}{3}A$, and the total work is ${\frac{10}{3}A}$ where ${A}$ is the amount of work ${A}$ can do in a day

[jolly parrot]

k

[dusty flame]

unless specified what "work" is, we cant really say

[ripe pagoda]

i was considering that B does the work in 12 days

A will do it in 4

and C in 2

then 1/12 + 1/4 + 1/2

[dusty flame]

yes

so

,w 1/12 + 1/4 + 1/2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

[dusty flame]

the total rate is 1/(6/5)

[ripe pagoda]

i just need to find how much work they do in a day

so its just 5/6 right

[ripe pagoda]

ohh right same thing

my bad

so 5/6?

[dusty flame]

ye

[ripe pagoda]

cool cool

thank you so much

also i had a doubt, my friend was considering that B does the work in 1 day and following the same procedure
he got 10 as an answer

hows that so

@dusty flame

[dusty flame]

we cant really answer

unless we know how much one person is actually doing in terms of work

[ripe pagoda]

oh

right

that makes sense

cool cool thank you

.close

[pearl pond]

Channel closed

Closed by @ripe pagoda

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[nocturne night]

Part B, how did they get the ø bounds?

Or more generally, how it it possible for it be be ABOVE the ø = π/3 cone?

[sharp vigil]

if it's above the φ = π/3 cone that would imply 0 ≤ φ ≤ π/3

[pearl pond]

@nocturne night Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[plucky zenith]

guys is this contradicting,both serve approximate to 3 decimal place but one said rn<0.001 another rn<0.0005 (barron ap book)

[pearl pond]

@plucky zenith Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[gentle lichen]

I have a question regarding this proof of the taylor series

$Let f(x) = a_0 + a_1 x + a_2 x^2 + ... \newline
=> a_0 * 0! = f(0) \newline
a_1 * 1! = f'(0) \newline
a_2 * 2! = f''(0) \newline
... and so on$

Didn't we assume that f(x) can be represented as a polynomial at the start and we never actually proved that this was true?

[gentle lichen]

Bruh

How do I

Latex

[broken fossil]

[oak ivy]

Don't leave space

[gentle lichen]

Wait

Let me fix the formatting

[rough stream]

So maybe your class didn't prove this to be true, but proofs of this fact do exist

[jolly parrot]

Dhruv

[rough stream]

I wouldn't use the word "polynomial" though, since polynomials are finite.

[gentle lichen]

Alright

Thank you

[rough stream]

Oh wait I see, this is supposed to be a proof

You'd need to get into Taylor's theorem. That is, the error gets smaller as n gets larger

[gentle lichen]

👍

.close

[pearl pond]

Channel closed

Closed by @gentle lichen

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[fickle blade]

how do i write this in spherical coordinate?

[fickle blade]

i did it in cylendrical coord and got pi

[fickle blade]

when i tried in spherical i got undefined??????

I tried it another way and still getting the same thing

[fickle blade]

im pretty sure p2 is incorrect, is there even a p2??? do i even have to split this?

and my phi value are also wrong but i have no clue on how to get them

<@&286206848099549185>

Calc 3 in spherical triple integral

[fickle blade]

I feel like this should = pi

like the phi going from the paraboloid(2cos/sin^2) to the red cylinder(2/sin)

and the region being from pi/4 to pi/2

[pearl pond]

@fickle blade Has your question been resolved?

[fickle blade]

you know what

proof that pi = 2.8739

.close

[pearl pond]

Channel closed

Closed by @fickle blade

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[buoyant pasture]

What is isolated essential singularity

[broken fossil]

does bro know picards theorem

[pearl pond]

@buoyant pasture Has your question been resolved?

[buoyant pasture]

Not yet

But would love to know?

[buoyant pasture]

.close

[pearl pond]

Channel closed

Closed by @buoyant pasture

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[indigo agate]

Is this right?

[west sapphire]

can you put a screenshot

not gonna open some random file

[minor meteor]

Yes

[indigo agate]

ok

[west sapphire]

tx

i get what you're doing but be careful how you write it, these are not actually equalities:

like 32^2 does not equal 2^5, but 32 does

but your answer is correct

[indigo agate]

its (2^5)^2

[west sapphire]

right, but you didn't write that here

[indigo agate]

in the next one it is

[west sapphire]

the left and right sides of the two equality chains are equal but some of the stuff in the middle is not

[indigo agate]

so i have to put it directly?

[west sapphire]

yea the end result is fine and i get what you're doing, i'm just pointing out that you have some false equalities in the middle and you could restate it a bit to clean it up, like:

$$32^2 = (2^5)^2 = 2^{10}$$

[jolly parrot]

Bungo

[indigo agate]

ohh ok

thanks for the help

[west sapphire]

yw

[indigo agate]

im preparing for the exam

[west sapphire]

cool, gl

[indigo agate]

thanks

.close

[pearl pond]

Channel closed

Closed by @indigo agate

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[green perch]

goodness me

[dusty flame]

Definition of e (so maybe take ln)

And Riemann sum definition

[royal pier]

thanks for replying. Yes i did that and then proceeded with Reimann sum definition as well, but getting stuck somewhere in the manipulation or something

[dusty flame]

May I see?

[nimble socket]

!show

[pearl pond]

Show your work, and if possible, explain where you are stuck.

[nimble socket]

this is definetely just an ln case lol

$\ln\qty(\prod_{k=1}^na_k)=\sum_{k=1}^n\ln(a_k)$

[jolly parrot]

ooaa

[royal pier]

Stuck at the thing in the end box

[nimble socket]

oh heck no

i aint dealin with no analysis bs

[royal pier]

hahahaha, no worries

[quasi bramble]

what grade are you in?

i wanna learn all this

[royal pier]

this is undergraduate mathematics

[quasi bramble]

ohh

ill be passing highschool next year like my finals will be there in feb

so soon

[royal pier]

all the best buddy

[quasi bramble]

yessir thank you!

[pearl pond]

@royal pier Has your question been resolved?

[pearl pond]

@royal pier Has your question been resolved?

[pearl pond]

@royal pier Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[short path]

for the ODE y'' + 3y' + 2y = 2e^(-2t) + 2e^(-3t) I get the particular solution as -2te^(-2t) + e^(-3t) but chat gpt insists the particular solution is 2te^(-2t) + e^(-3t). Can someone verify which one is right?

[spare lark]

You can check by plug in back the equation

[short path]

what do i plug in and where

[spare lark]

Your answer in the equation

[short path]

just the particular solution?

[spare lark]

Yeah

[short path]

into the original?

[spare lark]

Y

[junior loom]

make sure youre using the wolfram alpha gpt, not the regular one

it outsources the math to wolfram alpha

[spare lark]

There is a wolfram in the server, you can do :

,w y'' + 3y' + 2y = 2e^(-2t) + 2e^(-3t)

[jolly parrot]

Results provided by WolframAlpha

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

Requested by yakubros

[short path]

ohhh ok thank you

[junior loom]

yeah but it's nice to be able to upload pdfs or images to chatgpt, or to explain what you want to do in plain english

[spare lark]

Just make sure to do it in the #bots channel if you just want to check by your own

[short path]

oh ok i see thanks

do i just type w, and then the equation?

[spare lark]

Yeah its ,w

[short path]

oh ok thank you

is there a way to check with initial conditions?

[spare lark]

Yep

Just add , (initial condition) it will understand

[short path]

ok thank you guys for your help

.close

[pearl pond]

Channel closed

Closed by @short path

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[ivory glen]

hey

[ivory glen]

Assume that $a$ is a fixed integer, and let $a=1$. Then we ought to show the property $$\sum\limits_{i=1}^{n}(2i-1)=n^{2}$$
holds in this case. $$\sum\limits_{i=1}^{1}(2i-1)=1^{2}$$
$$2(1)-1=1$$
$$1=1$$
We know $1=1$, so the property holds in this case.

Now, lets hypothesize for some $k \geq a$, the property $$\sum\limits_{i=1}^{k}(2i-1)=k^{2}$$
is true. Then if the property holds in the general case, we ought to prove that $$\sum\limits_{i=1}^{k+1}(2i-1)=(k+1)^{2}$$
By expansion, $$[2(k+1)-1]+\sum\limits_{i=1}^{k}(2i-1)=(k+1)^{2}$$
By substitution and algebra:
$$[2k+1]+k^{2}=(k+1)^{2}$$
$$k^{2}+2k+1=(k+1)^{2}$$
$$(k+1)(k+1)=(k+1)^{2}$$
$$(k+1)^{2}=(k+1)^{2}$$
So we have proved the inductive step holds, and therefore that the property $\sum\limits_{i=1}^{n}(2i-1)=n^{2}$ holds in the general case.

[jolly parrot]

pyrate

[ivory glen]

any criticisms on this proof that 1+3+5 + ... (2n-1) =n^2

i was thinking about explicitly labeling each part

im doing mathematical induction so the basis case, inductive hyp, inductive step

i think my conclusion could also be more clear

[fossil jewel]

what is a

you have all the right steps you just write like 5 lines that are unnecessary

[ivory glen]

a is the value for the basis case, im pretty sure its important to specify that it does not change

i guess you can just shove an immediate value

[junior loom]

but you never use the symbol until the IH

[ivory glen]

oh dang

i skipped showing that its supposed to be in the basis

but yeah i see how its redundant either way and a bit useless

thanks guys

.close

[pearl pond]

Channel closed

Closed by @ivory glen

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[pearl pond]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[earnest finch]

,w solve for a, (-1)^(n - 1) * 3^(2n + 1) / (10^(n - 1)) = a^n

[jolly parrot]

Results provided by WolframAlpha

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

Requested by en.ratham

[earnest finch]

,w true or false? -30 * (-9/10)^n = (-1)^(n - 1) * 3^(2n + 1) / (10^(n - 1))

[jolly parrot]

Results provided by WolframAlpha

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

Requested by en.ratham

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[short path]

When solving second order non homogeneous linear ODEs and you're trying to find the particular solution, will there ever be a situation where one of the constants you're trying to find cancels out and only gives you the solution to one of the constants?

[hazy crypt]

probs depends how ur solving it

[pearl pond]

@short path Has your question been resolved?

[junior loom]

by cancela out, do you mean equal 0?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[short path]

sorry i can't explain it well, but for example if you had constants A and B that you're trying to find, and all the B terms added together were 0 so the equation is just the A terms = to the forcing function

.reopen

[pearl pond]

✅

[junior loom]

maybe giving an example would help me understand your question

[short path]

What i'm trying to say doesn't happen here, but let's say in the equation 2A + 3At + 3B = 3t that the A's cancelled out and just left the B

so you would find the value of B but can't for A

i'm not sure if this can even happen but i wanted to check just in case it can

[junior loom]

,rotate ccw

[junior loom]

so youre asking if sometimes you'll not be able to find unique answers for A, B, etc , some might stay undetermined?

[short path]

Yes

[junior loom]

yeah, thats possible if youre not given enough initial conditions but you have partial initial conditions

[short path]

what does partial initial conditions mean?

[junior loom]

let you have y''-3y'-2y=0 , y(0)=2

and thats it

[forest sigil]

Help

[junior loom]

normally youd need y(0)=2, y'(0)=3

2 initial conditions

[short path]

wait that's not what i meant

i mean for a non homogeneous equation

[junior loom]

same thing

let you have y''-3y'-2y=cos t , y(0)=2

[short path]

i think i may have said the wrong term for something

for the part of the solution that's based on the cos(t)

the initial conditions don't matter for that part right?

[junior loom]

i think they still matter, sure.

,w solve y''+y=cos t, y(0)=1

[jolly parrot]

Results provided by WolframAlpha

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

Requested by gfauxpas

[junior loom]

see

,w solve y''+y=cos t, y(0)=1, y'(0)=-1

[jolly parrot]

Results provided by WolframAlpha

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

Requested by gfauxpas

[junior loom]

see

[short path]

the way i was taught was that Y= Y of the homogenous equavalent + Y of the particular solution

[junior loom]

yes

[short path]

and for the Y of the particular solution for the cos(t) you send Yp= Acos(t) + Bsin(t)

then you find the first and second derivative

does that sound right so far?

[junior loom]

yes and im.saying

if you dont have enough initial conditions ,you may end up with some coefficients not uniquely determined

simple example:

y''=x

has solutions of what form

[short path]

1/6(x^3) + C1x + C2

[junior loom]

great

now i suppose i tell you y(1)=-3 and thats all i tell you

[short path]

i'm talking about different unknown constants for just Yp

[junior loom]

yes