help-4

[stark wedge]

do you think Zoe is right or do you think she's wrong

[verbal sentinel]

i dont know what the statment is even saying

where did shoe size come from

im confused

[stark wedge]

you're given extra info in part b: among your 25 women, 3 of them have shoe size 7.

Zoe says,

"The probability that a randomly selected woman from our group has shoe size 7 or dress size 14 is 3/25+6/25=9/25."

[verbal sentinel]

there is no dress size 7 tho

[stark wedge]

who said anything about dress size 7?

are you getting your wires crossed?

[verbal sentinel]

ok i read that wrong

yh

then she is not wrong

bc from the the table is 6/25+3/25 as she stated

which is 9/25

[stark wedge]

ok that's gonna be a nope

[final adder]

but what about the women who have both shoe size 7 and dress size 14?

they would be counted twice, no?

[verbal sentinel]

yh

[verbal sentinel]

but then you multiply bc is and

[final adder]

why would you multiply?

[stark wedge]

tfw memorized "and means multiply"...

[verbal sentinel]

why are we adding the fractions when it says or

[final adder]

this is a set theory "or"

aka a union of sets

[verbal sentinel]

but zoe says or so 1 of then condition need to be met

we are saying what about the people that have shoe size 7 and dress 14 zoe didnt say and

[safe fulcrum]

so here for example

there's 5 + 6 = 11 people who play hockey

[verbal sentinel]

yes

[safe fulcrum]

and 6 + 3 = 9 people who do gymnastics

[verbal sentinel]

yes

[safe fulcrum]

so if the left circle = shoe size of 7 and right circle = dress size of 14

you can't just add both circles and call it a day

[verbal sentinel]

no

[safe fulcrum]

you'd be double counting

you'd have something like (5 + 6) + (6 + 3)

[safe fulcrum]

so what do you have to do to make sure the middle is only counted once?

[verbal sentinel]

u dont add

[final adder]

but lets just say you were given that 11 people play hockey, and 9 people do gymnastics, but 6 people do both

[safe fulcrum]

there's one easy step you can do after you add though

[safe fulcrum]

you want to have 5 + 6 + 3 here right?

then that would be all good

[verbal sentinel]

yh

bc 6 come together

both

[safe fulcrum]

yep so after you add (5 + 6) + (6 + 3)

you just need to subtract 6

[verbal sentinel]

yes

[safe fulcrum]

you just need to subtract the middle (the intersection of both)

[verbal sentinel]

ye

so how about zoe

[safe fulcrum]

you tell me then

based on what we discussed

[verbal sentinel]

😭

[safe fulcrum]

the point is we don't know how many people have both that dress size and shoe size

[verbal sentinel]

we dont know the shoe size people

but we know dress

[safe fulcrum]

exactly

[verbal sentinel]

is 6

[safe fulcrum]

if the intersection has 0 people, then we can have 3/25 + 6/25 - 0/25 = 9/25, sure

but what happens if the intersection has 1 person?

2 people?

5 people?

[verbal sentinel]

yess

[safe fulcrum]

all 25 people??

[verbal sentinel]

we substract

[safe fulcrum]

yeah

[verbal sentinel]

them

[safe fulcrum]

so then it wouldn't be 9/25 right?

[verbal sentinel]

yh

[safe fulcrum]

it'd be something less than that, more specifically

[verbal sentinel]

but there might be people in the middle

[safe fulcrum]

that's my point

[verbal sentinel]

we dont know

[safe fulcrum]

so then Zoe's just wrong

[verbal sentinel]

how do i word this then

[verbal sentinel]

yh i get it now

[safe fulcrum]

"Zoe is incorrect; she didn't subtract the intersection"

[verbal sentinel]

both the people can have shoe size 7 and dress size 14

smth like tht

?

[safe fulcrum]

yeah

[verbal sentinel]

ok

thats fine

[safe fulcrum]

there may be people with shoe size 7 and dress size 14

that would also work

[verbal sentinel]

yes thank you for your time

[safe fulcrum]

no worries!!

[verbal sentinel]

.close

[vale dock]

Channel closed

Closed by @verbal sentinel

Use .reopen if this was a mistake.

[vale dock]

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.

[signal chasm]

help

[signal chasm]

im really

slow on this

[stark wedge]

which step do you think is invalid, if any?

[modest kettle]

theres a property

[signal chasm]

i didnt really think

none of them were invalid

[modest kettle]

for inequalities

[signal chasm]

but turns out

[stark wedge]

don't call me "bro".

[signal chasm]

the first ones wrong

[stark wedge]

ah fuck

[modest kettle]

i didnt call you bro..

[stark wedge]

wrong reply

[modest kettle]

💔

anyways

[stark wedge]

yeah sorry i misclicked

don't call me "bro"

[modest kettle]

logarithms are monotonic

meaning always increasing or decreasing

perfect for inequality abuse

[stark wedge]

logarithmic functions with base between 0 and 1 are decreasing

to be more specific

so you would need to reverse the sign

@signal chasm still here?

[signal chasm]

ok so?

idrk where we going with this

[stark wedge]

can you delete or edit this msg

also reread what i wrote earlier

[signal chasm]

but

it doesnt matter right

cos

well

the left side

gna equal to 2 or greater

[stark wedge]

.....

[signal chasm]

and the right

will be less than that

so is that

the wrong step?

[stark wedge]

yes it does, the sign was supposed to be flipped but it wasn't, that was the mistake

[signal chasm]

how

[stark wedge]

how what.

[modest kettle]

if a > b\
then $log_{n} a > log_{n} b$, IF the base n is greater than 1

[signal chasm]

wait.

[modest kettle]

this is because in that range the logarithm is an increasing function

[signal chasm]

wait

do all log graohs

[modest kettle]

on the contrary if n is between 0 and 1

[signal chasm]

cross x axis

at same point

[modest kettle]

yes

[signal chasm]

which is

[modest kettle]

why ask that

[signal chasm]

well

wait it crosses at what

how do u work that out

[signal chasm]

cos then

u can see

so

well

[signal chasm]

yk the right hand side is gna be 6

[modest kettle]

at (1, 0)

[signal chasm]

and if its n=1 by any chance

that means x=2

so

both of these coordinates

are to the right

of 1,0

meaning a negative y

so that means

the sign should flip

when using the logs

is that logic correct?

[modest kettle]

um do you mean the n in the question?

[signal chasm]

oh yh im slow for that

[signal chasm]

yes

cos n has to be a positive integer

so the left hand side smallest value possible can be 2

both points must be on the right side of x intercept

meaning y value is negative

so the overall log value

is negative

so sign should switch right?

idk

if that makes sense

or not

[modest kettle]

can you say which log values youre stating negative here

[signal chasm]

ok

so

log 1/2 to the 1/4

=2 right

wait

im an idiot

i think

i confused myself

[modest kettle]

so that step is actually correct

the tomfoolery happens when you bring a logarithm on both sides

you know 1/4 < 1/2

but is $log_{1/2} 1/4 < log_{1/2} 1/2$?

[signal chasm]

erm

no

bro

i dont get this

[modest kettle]

what about this

[vale dock]

@signal chasm Has your question been resolved?

[vale dock]

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.

[worldly stirrup]

why are these the values for x

[worldly stirrup]

the fractional part of x when k=2,4,6,8

why is it 1/2,1/4,2/4,3/4,....

[rough talon]

whats the original question?

[distant steppe]

gm

[craggy girder]

@worldly stirrup pls send a ss of the whole thing

this doesnt give enough context

[vale dock]

@worldly stirrup Has your question been resolved?

[vale dock]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vale dock]

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.

[midnight pier]

0≤{x}≤1, so other values that don't fit in the domain don't enter in the sequence

[tawny moon]

you've opened this channel btw

remember to close it when you're done, unless you have a question

[midnight pier]

Sorry :p

[midnight pier]

How to close?

[tawny moon]

!done

[vale dock]

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

[midnight pier]

.close

[vale dock]

Channel closed

Closed by @narrow jolt

Use .reopen if this was a mistake.

[vale dock]

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.

[gilded timber]

hi, need help finishing this need to make a drawing using various things on desmos trying to make a bear please help me finish it!!

[oak crane]

thats so cute

[gilded timber]

this assignemnt is actaully pissing me off likec razy

[oak crane]

u are asked to make this on desmos?

[fickle rose]

(btw you can add images in desmos for easier reference)

[gilded timber]

yes

ik

[opal pendant]

Ngl just use chatgpt

[gilded timber]

bro i alr tried LOL

he gets hella confused and the equations never work

[opal pendant]

"He" is crazy 💀

[opal pendant]

Ohh

[gilded timber]

mb

they them

[oak crane]

average gpt

its really bad advice

[gilded timber]

okay so i have my three circles right

and im missing everything else?

[oak crane]

I personally use equations like $p_{0}=\left(p_{01},p_{02}\right)$

[rocky lotus]

アキラ (>⩊<)

[oak crane]

and i can move the points closer to the image

[gilded timber]

r u joing im cnfused

when i copy and paste that it doesnt work

[opal pendant]

Alr alr

[oak crane]

u need to make it up

let me share my sample

[gilded timber]

okay let me elaborate i have 0 knowledge of what i am doing!

[oak crane]

i draw things like this https://www.desmos.com/calculator/ec00589750

just a sample 🙂

once u do that u can hide the points when u make ur equation

[gilded timber]

okay but i have 0 idea on how to do that

theres not like an equation i can just copy and paste?

[oak crane]

first try writing up 3 points

[gilded timber]

[oak crane]

like this

[gilded timber]

wth is a point

like a coord?

[oak crane]

ya

[gilded timber]

uh theres a yellow triangle

[turbid valve]

why is there an anime villain in my maths
-# and why is he looking at me like that

[oak crane]

for triangles i think u need to make coordinates like $A = (x_1, y_1), \quad B = (x_2, y_2), \quad C = (x_3, y_3)$?

I forgor

[rocky lotus]

アキラ (>⩊<)

[oak crane]

its a fanart 🙂

[turbid valve]

he's a fan of me!? /s

idk whether to be grateful or fearful

[oak crane]

idk about that

[gilded timber]

so how do i put that into desmois

also how di i make it so this parabola ends at a certain point?

[oak crane]

something like this $y = x^2 {0 \leq x \leq 3}$ for example

[rocky lotus]

アキラ (>⩊<)

[gilded timber]

i was trying something like this but it wouldnt worjk

[oak crane]

u need to add {}

[gilded timber]

ohh

wheres the other side LOL

like i literally have no idea how these numbers work

if i dont do this today i get kicked out of college so im like tweaking out rn'

[oak crane]

ah shit

let me do something rq

[timid wagon]

nosebleed

[oak crane]

https://www.desmos.com/calculator/yhcx8jisi2

[gilded timber]

okay how do i get it lower LOL

[oak crane]

are u familiar with parabolas?

u could do this $y=x^{2}\left{-1<\ x\le1\ \right}-5$

[rocky lotus]

アキラ (>⩊<)

[gilded timber]

no! i am not

[oak crane]

https://tenor.com/view/huh-cat-cat-huh-small-cat-huh-what-gif-2593177363967991691

[gilded timber]

ok how do i get that into my freaking desmos

my keyboard doesnt work that way

[oak crane]

freaking desmos?

wdym

dont tell me ur just copying things

[gilded timber]

u said to try that no?

[oak crane]

i never said copy it tho

sometimes it doesn't work

u have to type it

[gilded timber]

okay did it

bro looks so happy

[oak crane]

ya u can play around with desmos until u get it 🙂

[river shale]

[gilded timber]

ok am playing with some of the numbers how can i close that gap

can i get some like lines

[oak crane]

just bring the numbers closer like change that -3 and -2.7 to something tighter like -3 and -2.9 and maybe let the x-values chill together more see if that works

also do u mind giving me ur thing i wanna test the triangles

here's how u could start with triangles

[gilded timber]

https://www.desmos.com/calculator/l4luc9zixs

[fickle rose]

that looks like a quadratic bezier curve

[oak crane]

i gotta go something come up

u can continue lama

[gilded timber]

a curve is a curve right

i just need a c

[fickle rose]

a c where?

[gilded timber]

on the grade

lol

\

[fickle rose]

oh I thought you meant an actual c on the graph 😭

alr well then let's shoot for an A

[gilded timber]

at this rate

im not sure

[fickle rose]

nah you got this, lock in

so what company logo are you drawing?

[midnight pier]

parabolas ftw

[gilded timber]

bruh

i just realized it needs to be a logo and not any drawing

omg im gonna cry

what logos have a bear 🙁

[midnight pier]

make mcdonalds logo

[gilded timber]

wont fit the requirements

[midnight pier]

what r they

[fickle rose]

no cricles

[midnight pier]

damn

I'd go insane if i had to do this

[gilded timber]

dude i am

like actaully having a breakdown

[midnight pier]

I'd be dead by now

[gilded timber]

and get this!!!

if i dont do this plus 150 other questions of hw plus 5 more assignments with the same type of vibe i cant go to college !!

all due tonight btw.

[midnight pier]

honestly?

You are cooked.

[gilded timber]

bro

[vale dock]

@gilded timber Has your question been resolved?

[gilded timber]

.close

[vale dock]

Channel closed

Closed by @gilded timber

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.

[brave urchin]

heya. if i have this equation: x^3-x^2-3^(x-1)+4^(x-1)=0 , can I do anything with those simmilar powers?

[brave urchin]

i know common bases disappear when the exponents are the same when equating two terms, but i'm not sure if theres any of that magic i can pull here

it also looks to be a polynomial with a 3rd degree as the highest, and we've not done too many of those

[vast dove]

It is NOT a polynomial

[brave urchin]

i need to find its roots by the way

hmm

[vast dove]

This seems quite difficult on first inspection

[brave urchin]

okay i might have gone about it wrong

let me restart with the problem

i have to prove the continuity of a function on the R interval. the function takes two forms: x^2+3^(x-1) and x^3 + 4^(x-1). to prove that it's continuuous, i have to prove those two are equal

[ebon glade]

well there is an obvious solution

which turns out to be the only one

but thats not obvious

you definitely fucked up the question

cause that makes no sense

[brave urchin]

i have to prove those two are equal... when x goes towards 1

[ebon glade]

ok so a completely different question

[brave urchin]

it's the continuity question

[ebon glade]

well the limit x->1 for both functions is easy to calculate

[brave urchin]

yeah... i got the answer 2=2 which proves it's continuous

but i need to find all the x's in which it is

eyeballing it gives me one and zero i believe

[ebon glade]

can you post the original statement please

[brave urchin]

okay

Determine the interval of points where the following function is continuous: f:R->R, f(x)={x^2 + 3^(x-1) x is < than 1
{x^3 + 4^(x-1) , x is > or = to 1

[ebon glade]

its continuous for all x!=1 by just general knowledge of continuous functions

so you only need to care about x=1

[brave urchin]

i see

i think the interval thing threw me off

thanks

.close

[vale dock]

Channel closed

Closed by @brave urchin

Use .reopen if this was a mistake.

[vale dock]

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.

[quaint gull]

im drawing a blank and i dont want to looking it up because i want to know how to solve it

[civic sedge]

What can you do to isolate theta here

well first of all, what have you tried

[quaint gull]

dude idek ive stared at this and i genuinely cant think of anything

[civic sedge]

Well, I feel it would help if we could get the theta term on one side, so what can we do about that square root?

[late cypress]

cot(x) = 1/tan(x) so you should use that and you would get (tan(x)) = 1/sqrt(3)

then u gotta lowk remember the unit circle thing

[civic sedge]

Don't give them the solution

[quaint gull]

i was gonna try to square -3 for -1.73 and move it to the other side

[civic sedge]

it'd do you better to just move the root 3 by itself

[late cypress]

mb

[quaint gull]

so cot0 = - sqrt3

[civic sedge]

yes, good

now there's two ways you can get rid of the cot

well technically one

because the other is just a longer way of doing the first

[quaint gull]

with unit circle its like 30 degrees i thought

or whats what i got

idk if i did it wrong

[civic sedge]

You are close

you have that (\cot \theta = \sqrt{3})

now

[rocky lotus]

Ryan + James (TCC)

[civic sedge]

let's take the arccot of both sides to get rid of the cot

(\arccot \cot \theta = \arccot \sqrt{3})

[rocky lotus]

Ryan + James (TCC)

[civic sedge]

(\theta = \arccot \sqrt{3})

[rocky lotus]

Ryan + James (TCC)

[quaint gull]

following

[civic sedge]

now the arccot here is asking you "what value's cotangent is \sqrt 3"

now the definition of the cotangent is (\cot = \frac{1}{\tan} = \frac{\cos}{\sin}) right?

[rocky lotus]

Ryan + James (TCC)

[quaint gull]

yeah

tan0 = sqrt 3/3?

idk how to make theta sign

0 is supposed to be theta

[civic sedge]

$\theta$

[rocky lotus]

Ryan + James (TCC)

[civic sedge]

correct

[quaint gull]

okay

[civic sedge]

so what angle gives you a tan theta of sqrt(3)/3?

[quaint gull]

30?

[civic sedge]

yes

[quaint gull]

or pie/6

if i recall

[civic sedge]

You got it right earlier, I just wanted to see your thought process

yes

(\frac{\pi}{6})

[rocky lotus]

Ryan + James (TCC)

[quaint gull]

okay

[civic sedge]

do you understand how to approach this sort of problem now?

[quaint gull]

yeah thank you

youre amazing lmao

[civic sedge]

Meh, I had to go look up a unit circle table myself, it's been a while since I've had to actively think about this stuff

(last I did was multivariable calculus over a year ago) -Ryan

[quaint gull]

well u def helped

ty again

[civic sedge]

it's no problem

if you need anything further, feel free to open a new help channel

[quaint gull]

.close

[vale dock]

Channel closed

Closed by @quaint gull

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.

[brittle epoch]

how do i solve $\log_x{3} + \log_3{x} = \ln{x}$

[rocky lotus]

General_Jacob

[shadow moss]

use change of base to make everything natural logs

[charred fulcrum]

or log base 3, it doesn't matter, as long as all the x's are in the same log base

[brittle epoch]

okay thanks

.close

[vale dock]

Channel closed

Closed by @brittle epoch

Use .reopen if this was a mistake.

[vale dock]

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.

[thorn kernel]

wait

[thorn kernel]

for this

if z = 0 we get -1 = y^2

so how do we know what y is like?

[chrome beacon]

for that k there is no z = 0

as you can see

but for a different k (-1 i think) there will be

[thorn kernel]

what

if i set z = 0

-y^2 for 2 cases k = -1 and k=0

for k = 0 its just -y^2 = 1

for k= 1 its just -y^2 = 0

k=1 makes sense its just 0 at the origin

[thorn kernel]

but k = 0 doesnt make sense

[chrome beacon]

the graph that looks like ) ( which is labeled k = 0

[thorn kernel]

yea

[chrome beacon]

is different from the graph that looks like X which is labeled k = 1

[thorn kernel]

yeah i get that

k = 1 is the X

k = 0 is the )(

but how do we draw the )( from

[chrome beacon]

and is also different from the graph that looks like ⩆ which is unlabeled but should probably be like k = -1 or something

[thorn kernel]

u said to set z = 0 and y = 0

what im asking is how to draw )( where do they get this from

for the )( in z axis we get that of k = 0 and set y = 0 right we get z = +-1/3

but how do we do that for y

[chrome beacon]

did they mislabel that

weird, if x = 0 and y = 0 then z does have real solutions, so the ≍ graph should be the x = 0 graph

[thorn kernel]

wot

[chrome beacon]

if x = 0, then your equation is 9z^2 - y^2 = 1, which is a hyperbola that goes through the points (y = 0, z = 1/3) and (y = 0, z = -1/3)

right?

[thorn kernel]

yea

[chrome beacon]

so that describes the ≍ graph

[thorn kernel]

its these ones right here

yep

[chrome beacon]

yea

that should be labeled k = 0

[thorn kernel]

now how do we get )(?

[chrome beacon]

try k = 2

see what that gives you

[thorn kernel]

why would k = 2

its 1-k^2

[chrome beacon]

wdym why would k = 2

yes....

[thorn kernel]

k is betwee -1<k<1

[chrome beacon]

is it?

does it say that somewhere

[thorn kernel]

1-k^2, how can u have negative hyerbola

[chrome beacon]

try it.....

does the x axis not go beyond 1?

i'm fairly sure the x axis goes beyond 1

[thorn kernel]

hm ok

ig that rule only applies for spheres and circles

[chrome beacon]

https://www.desmos.com/3d/rjzop2zg3c

[chrome beacon]

yes bc they eventually become purely imaginary

whereas a hyperbola always has at least some real solutions

[vale dock]

@thorn kernel Has your question been resolved?

[vale dock]

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.

[muted bridge]

Hi

the transformation would be 3 units to the left

and 1 unit down

idk i just guessed D is the correct graph because

it looked the most like what it should be

but im so confused

[frozen ledge]

?

[muted bridge]

oh shit

[frozen ledge]

and it’s 3 units left for what function?

[muted bridge]

log

[frozen ledge]

not log_4(x)

no

[muted bridge]

no?

[frozen ledge]

nope

2(x + 3/2)

(x, y) —> (x, y + 1) —> (x + 3/2, y + 1) —> (2x + 3, y + 1)

[vale dock]

@muted bridge Has your question been resolved?

[vale dock]

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.

[agile island]

hi im back, could i get some help with this problem?

7. A piece of work can be completed in 30 days by 10 men. If the work is to be completed 5 days earlier, how many more men are needed? (Assume that the men work at the same rate.)

[agile island]

so far i have '1 man = 30 x 10'

but im not sure where to put 25 (5 days earlier)

since they have to work at the same rate i cant make it '1 man = 25 x 10'

[sharp whale]

it should be 1 work = 30 days x 10 men instead

now we have 1 work = 30 days x 10 men = 25 days x ? men

[agile island]

ohhh ya

[sharp whale]

presumably for less days we need more manpower, so you have to figure that out with algebra

since we know 30 days x 10 men = 25 days x ? men,

that means 30 x 10 = 25 x ?, right

[agile island]

ya

[sharp whale]

now can you find out what ? is

[agile island]

300 = 25x?

[sharp whale]

sure, then?

[agile island]

x = 12

[sharp whale]

yep

[agile island]

wait im not sure if im allowed to use algebra tho

[sharp whale]

30 days x 10 men = 25 days x 12 men

[agile island]

or like variables

[sharp whale]

then you can think about it this way

you can think of 25/30 as a factor for how smaller the time we have is

25/30 = 5/6

so we only have 5/6ths of the time given, right

[agile island]

ya

[sharp whale]

30 days x 10 men

= 30 days x 5/6 x 6/5 x 10 men

since 5/6 x 6/5 = 1, right

[agile island]

ahhh

i see

[sharp whale]

this is a bit of a strange trick

but the more common way to think about it is

5/6x the time, so we need 6/5x the manpower

[agile island]

so reciprocal?

[sharp whale]

like with "double the manpower in half the time"

[sharp whale]

sure

[agile island]

ok i think i got it

tysm for the help!

[sharp whale]

np

[agile island]

.close

[vale dock]

Channel closed

Closed by @agile island

Use .reopen if this was a mistake.

[vale dock]

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.

[silk jacinth]

Help

[tawny moon]

do you have a question? if so, do post it

[stoic adder]

What is your question?

[vale dock]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[silk jacinth]

I'm in need of help with fictional currency translation.

How much would Vash's double dollar bounty be worth translated to Woolong?

In the series "Trigun", the main character, "Vash", has a bounty of $$66,000,000,000. ($132,000,000,000 translated to USD)

According to the internet, one double dollar in Trigun is worth around $2 USD.

However, in the series "Cowboy Bebop", due to hyperinflation, 1 Woolong is worth $0.000031 USD.

So, if I'm correct, $$1 = $0.000062 correct?

according to someone on Reddit, I got this conversion backwards, though I didn't understand their explaination.

[vale dock]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tawny moon]

i think we know where OP's at rn

[silk jacinth]

2 and 3?

[stoic adder]

hmm

[tawny moon]

what are you trying to find?

the conversion rate between what and what? i see three currencies here and some contradictions

[copper stump]

You already know $$1 = $2, so where did $$1 = $0.000062 come from

[silk jacinth]

I'm trying to convert one fictional currency to another.

Double Dollars (from Trigun), wherein $$1 = $2 USD.

to Woolong's (from Cowboy Bebop), wherein W1 = $0.000031 USD

so according to my math, $$1 (double dollar from Trigun) should be worth 0.000062 Woolong.

According to Reddit, that conversion is backwards, and I don't know where I'm going wrong.

To put simply, I'm trying to translate Vash's $$66,000,000,000 double dollar bounty to Woolong. And since $$1 = $2, his bounty in USD should be $132,000,000,000 in the real world.

So, I'm trying to figure it out for Cowboy Bebop

[copper stump]

So you have, 1W = $0.000031. That would mean for $1 you need approx 32258W (if reddit is correct)

and so, for $2, you need 64516W

and $2 = $$1

[silk jacinth]

Correct

[copper stump]

well?

do you see how yours is the other way round?

64516W = $$1

[silk jacinth]

Oh

Yea, I see

The calculation I got was that Vash's bounty would only be W4,092,000, and I knew that had to be incorrect.

Though I'm still struggling to figure out what it'd actually be.

[tawny moon]

you have the bounty in USD

just go from there

[copper stump]

,calc 132000000000 / 0.000031

[rocky lotus]

Result:

4.258064516129e+15

[copper stump]

this much

[silk jacinth]

4,258,064,516,129 Woolong?

Someone on Reddit managed to get 4,258,064,516,129,032 Woolong

(unless that additional 032, was supposed to be 32 cents

[copper stump]

4,258,064,516,129,000 Woolong

[silk jacinth]

Oh

[copper stump]

yea, the calculator is not very precise

that may be 032

in the end

[silk jacinth]

I see, so my answer is over 4 quadrillion

[copper stump]

yep

[silk jacinth]

Thank you, that answers my question.

How do I close this out?

[tawny moon]

.close

[silk jacinth]

.close

[vale dock]

Channel closed

Closed by @silk jacinth

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.

[raven token]

i know my answer is wrong but i dont get why

what i did was

i know the volume is area of triangle times height

so i know the height of the triangle is 6 and height of prism is 15

so if i assume b is the base of the equilateral triangle

isnt the volume (6b/2)*15

which is 45b

and if i swap the heights

i also get 45b

so i got the answer as 1

but i def did smth wrong

[copper stump]

sure, but b is gonna be different when you swap the H and h

[raven token]

wait why didnt he use the right number for the base either way even if he swapped the H and h

[copper stump]

the height of an equilateral triangle is related to its base

[copper stump]

swapping H and h would lead to different values of b as well

[raven token]

i dont get it wouldnt he already know b?

[copper stump]

you need to calculate it from the correct height

*base

you only know h and H

you dont know b

[raven token]

ohh

so i cant assume that he knows b

[autumn whale]

write out the equation to calculate b and I think that'll help you understand

[raven token]

how would i do that

[copper stump]

Why are you talking in 3rd person, aret you the david in the problem

[raven token]

lolll i js realized

[autumn whale]

well you know it's an equilateral triangle and you're given h

[raven token]

ohh so i split it into like

two triangles

and then like

[autumn whale]

yea

they are 30 60 90 triangles

so that makes the calculation part easier

[raven token]

so( b/2)/6=tan30

[autumn whale]

or you can just use the 30 60 90 triangle rule

[raven token]

which would make the equation b/2sqrt3=tan 30

wait im lost

[autumn whale]

dont mind my bad drawing skills

[raven token]

so if h is 6

[autumn whale]

the sides in a 30 60 90 triangle are x, 2x, and x root 3

[raven token]

yeah i get that so far

[autumn whale]

so if $h = x\sqrt{3}$

[rocky lotus]

satvik

[raven token]

ohh then sub in either 6 or 15 first for h

[autumn whale]

$x = \frac{h}{\sqrt{3}}$

[rocky lotus]

satvik

[autumn whale]

you should be able to do the rest

[raven token]

so if i say 6 then x= 6/root 3

[autumn whale]

yea

[raven token]

and the base is 2x

oh i see yeah i could do the rest

thank you

[autumn whale]

indeed

[raven token]

.close

[vale dock]

Channel closed

Closed by @raven token

Use .reopen if this was a mistake.

[vale dock]

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.

[hardy temple]

been doing this for a long time

[magic lynx]

uhh

is the problem to calculate it exactly

[hardy temple]

i rewrote it the fraction as
$\frac{(-1)^n x^{2n}}{(2n+1)}$
to solve the sum at x=sqrt1/3

[magic lynx]

or prove convergence

[hardy temple]

calculate it exactly

[hardy temple]

nah

[rocky lotus]

haveaniceday12

[hardy temple]

so it looks a lot like the taylor series for ln(1+x) and ln(1-x)

[magic lynx]

uh is this taylor series

[hardy temple]

not exactly but with i believe we're supposed to turn it into one through some integration and or differentiation

it's just the odd terms of the taylor series for ln(1+x) with alternating signs

i think i got it one escond

[low frigate]

sure is

[magic lynx]

wait you can get all of the even terms in the taylor series by like using ln(1-x^2) right or something like that

[low frigate]

this is a direct sub into one of the common taylor series formulas

does the ln series have a 2n+1 on the bottom?

[hardy temple]

unfortunately no

[magic lynx]

wait so we have all terms even and odd from ln(1-x)

[hardy temple]

it's all of the odd terms from ln(1+x) with alternating signs

or ln(1-x) technically

[magic lynx]

wait just use ln(1-x)

ok now we need to get rid of the even terms

[hardy temple]

indeed

[low frigate]

I think you’re getting distracted chasing a shiny object

this is not the way

[hardy temple]

yup

that's what i thought with that too i tried it and i couldn't get anywhere with it

[magic lynx]

the taylor expansion of ln(1-x^2) will be the same thing for ln(1-x) except each exponent will be doubled

[low frigate]

all of the even terms have the same sign, how are you going to cancel those out with the alternating series for ln?

[magic lynx]

subtract ln(1-x^2)/2

[low frigate]

that doesn’t work

the (-1)^n term is independent of the x term

[magic lynx]

oh i see

yes you are right

[hardy temple]

the answer to it is $\frac{\pi}{2\sqrt{3}}$

[rocky lotus]

haveaniceday12

[hardy temple]

acccording to wolframalpha

[magic lynx]

oh wait what is the expansion for ln(1+x^2)

[low frigate]

you were blazing hot right here you’re one step away from the key to the solution

[hardy temple]

hm

because then i made it
$\displaystyle \frac{1}{x} \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)}$

[rocky lotus]

haveaniceday12

[low frigate]

what’s the taylor series expansion for $\frac{1}{1+x^2}$? what happens when you integrate it?

[rocky lotus]

cytos

[hardy temple]

arctan

[low frigate]

yes

[hardy temple]

it's the same as 1/1-x where x is -x^2

wow i think i see it now

thank you so much

.close

[vale dock]

Channel closed

Closed by @hardy temple

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.

[gray patrol]

is this role can be used into this question ?

[gray patrol]

or should i use this one ?

[jovial edge]

it's the same

[stiff lily]

pretty much the same thing

[tacit ore]

i think you can intergrate separetly

[gray patrol]

but i wanted to use this because it is easy to save in my mind

thx alot

.close

[vale dock]

Channel closed

Closed by @gray patrol

Use .reopen if this was a mistake.

[vale dock]

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.

[fair wing]

R(x)=x²-2x+2 and Q(x)= 2x²-4x+3, how do i use completing the square here

[oak crane]

,tex .cts

[rocky lotus]

アキラ (>⩊<)

[tawny moon]

why not simplify the 2/2

[stiff lily]

why are you adding/subtracting the x term

[sharp whale]

@fair wing you here?

[blissful sinew]

Always add and subtract a constant term

Not a variable term

[vale dock]

@fair wing Has your question been resolved?

Channel closed

Closed by @fair wing

Use .reopen if this was a mistake.

[fair wing]

.reopen

.reopen

[sharp whale]

.reopen

.close

[vale dock]

Channel closed

Closed by @sharp whale

Use .reopen if this was a mistake.

[sharp whale]

.reopen

[vale dock]

✅

[sharp whale]

@fair wing looks like thats fixed

[fair wing]

ok so

i am doing x2-2(1) (x) +2-2+2

x²-2(2x/2) + (2x/2)² - (2x/2)² + 2

This is correct ig ^

[glass kelp]

wait

whatare we doing here

completing the square for ${R(x)}$ and ${Q(x)}$ indpendently, right?

[rocky lotus]

k

[glass kelp]

@fair wing

[fair wing]

Yes @glass kelp

Both are different

[glass kelp]

alrighty

so

[fair wing]

this is very basic thing but i am stuck here

[glass kelp]

ok

what do u notice abt the term containing x^2 and x

can u think of a perfect square containing x^2 + 2x?

[fair wing]

x-2) ²

(

[glass kelp]

nope

(x-2)^2 = x^2 - 4x + 4

[fair wing]

it should be +

[glass kelp]

still

the middle is 4x not 2x

[fair wing]

x+1) ²

[glass kelp]

yup

so

${(x+1)^2 = x^2 + 2x + 1}$, right?

[rocky lotus]

k

[fair wing]

Yes ofc

[glass kelp]

subtracting 1 on both sides

${(x+1)^2 - 1 = x^2 + 2x}$.

[rocky lotus]

k

[fair wing]

Yes

[glass kelp]

We can substitute this back into our original thing

${x^2 + 2x + 2 = (x^2 + 2) + 2 = (x+1)^2 - 1 + 2}$

[rocky lotus]

k

[fair wing]

Yeah

[glass kelp]

combine the last two terms

all should be done

now

could u do a similar thing for Q(x)?

[fair wing]

Yes

[glass kelp]

cool

after u're finished, could u send me ur working so i can check

[fair wing]

Yes

4x/2 -2) ²

Nah

It's not

[stiff lily]

first factor out 2 from the first two terms

[vale dock]

@fair wing Has your question been resolved?

[vale dock]

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.

[brazen zephyr]

why is the decreasing interval (-infinity, -1]u(0, 2) and not (-infinity, -1)u(0, 2) ?

[brazen zephyr]

i dont understand why -1 is included in the decreasing interval, but not included in the increasing one (-1, 0)u(2, infinity)

[sharp whale]

theres no real reason for this, presumably they want -1 to either be in the increasing interval or in the decreasing one, so they just chose one of them

[jovial edge]

I have taught to not include -1 or 2 here

[chrome beacon]

shouldn't really be included in either

[sharp whale]

the correct way is to stick to "dont include them at all"

or to stick to "always include them (in specific contexts)"

instead of halfway inbetween like here

[brazen zephyr]

so the second answer i mentioned technically wouldnt have been wrong?

[sharp whale]

yea, thats what Id expected to see

decreasing would also be (-inf, -1) U (0, 2)

[brazen zephyr]

oh okay thanks 😄 i was overthinking that one bracket

.close

[vale dock]

Channel closed

Closed by @brazen zephyr

Use .reopen if this was a mistake.

[vale dock]

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.

[lusty crystal]

I wanna learn how to do algebraic division T -T

[lusty crystal]

like I'm shit at ut

*it

Ping me anytime

[stiff lily]

wdym by algebraic division?
do you have a specific math problem you're stuck on

[warped shale]

You mean polynomial division.......?

[frank spindle]

@lusty crystal could you elaborate on your problem

[lusty crystal]

Like

Wait

Lemme copy the sums

[stark wedge]

you can (and should) send a picture

[lusty crystal]

Like these

Idk how it works

[stark wedge]

do you know how long division for regular numbers works?

[lusty crystal]

Like, normal long division method is easy but idk how to do this

[lusty crystal]

Yes sir

[stark wedge]

please don't call me "sir".

[lusty crystal]

I did this but idk what I did

[lusty crystal]

I forgot to check the pronouns 😭

Sorry

[lusty crystal]

I copied it from my friend's notebook

[stark wedge]

ok right so

maybe we should revisit long division for regular numbers to think about what you're really doing

[lusty crystal]

I'm good with regular division

[stark wedge]

wow wtf is that \

uhhh ok so

[lusty crystal]

2/131

Try it someday

[stark wedge]

can i have you work out 5238 / 7 and stop when you hit the remainder

[lusty crystal]

Sure

[stark wedge]

just for demonstration purposes, this should be large enough to work while not being absurdly large

[lusty crystal]

I'mma do it real quick

[stark wedge]

to clarify i dont want any decimals

when you hit a remainder just stop

[lusty crystal]

Alright

[stark wedge]

i'll be right back

[lusty crystal]

I would've gone to the depths of hell for the answer with decimals

@stark wedge 748

[stark wedge]

i want to see your process and work lol

i was gonna comment on it and show you how it relates to polynomial division

[lusty crystal]

I think

I might've understood how an algebraic long division method workss

The only difference is that, it goes + - +-

That's it

[stark wedge]

mmmmm

[lusty crystal]

Can you give me an algebraic long division question

[stark wedge]

sure.

divide x^5 + 8x^4 - 3x^3 + 9x^2 - 10x + 25 by x - 2. show all work.

[lusty crystal]

you should've gone a little easier 😭

Either ways i'mma do it

[stark wedge]

it isn't that hard tbh, just takes some careful work

[lusty crystal]

I can't do it anymore 😭

My head is like a maze rn

@stark wedge

First divide x by x⁵ then I get x⁴, then I multiply x-2 by x⁴ and write x⁴ at the top

Then I repeat it

[stark wedge]

ok lemme check your arithmetic

[stark wedge]

you mean divide x^5 by x though

[modest kettle]

you copied it as +9x^3..

[stark wedge]

also yeah you miscopied the dividend

[lusty crystal]

Wha

[stark wedge]

also if we ignore that, 94x+25 requires one more step

[lusty crystal]

Like like terms?

[stark wedge]

you miswrote the x^2 term as if it were x^3

[lusty crystal]

3x³

Oh

damn

I just added the like terms (Cuz I wrote them wrong, so they became like terms Cuz x³

so yea)

But did I do it right tho?

[stark wedge]

you had one step to go

94x+25 requires one more step

subtract 94x - 188

[lusty crystal]

I know it takes one more step, but my brain isn't braining enough to add 188 with 25

yk what, i'mma add it

213

[stark wedge]

do you know column addition

[stark wedge]

honestly there is no reason to despair

if i saw anything wrong with your arithmetic i would have said it

"stopped one step short" is one of the easiest things to correct

[lusty crystal]

What's that

[lusty crystal]

Lmfao

So basically, I just need a bit (alot...) of practice

[stark wedge]

 188
+ 25
----

like this

[lusty crystal]

Yea

I know

[stark wedge]

yeah that

[lusty crystal]

But writing it like that vs doin it in brain is uh

I choose the latter

[stark wedge]

don't do things in brain except if you are 120% certain you could do them at gunpoint flawlessly

after being woken up at 3 in the morning

[vale dock]

@lusty crystal Has your question been resolved?

Channel closed

Closed by @lusty crystal

Use .reopen if this was a mistake.

[lusty crystal]

I can

[lusty crystal]

I. Can.

Hesitation kills the bird

[vale dock]

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.

[lime bone]

I bet there are some unconventional way to identify independent two events

[lime bone]

Let’s say I roll a fair dice, and A is the event where I get 1,3,or 4as the result. B is where I get even numbers

Are A and B independent

[turbid valve]

A and B are independent events if P (A and B) = P(A) x P(B)

That's sorta the definition of independence

[lime bone]

What is the intuition? Can I tell if they are independent by reasoning

[jovial edge]

Yeah, rolled 1,3,4 didn't affect the out come of when you roll even

If the one event affect the outcome of other event then they're not independent event

[turbid valve]

it sorta does though

oh come on it's a PNG

The probability that A, given B, will happen is definitionally the probability of both happening over the probability of B happening

But if they're independent, then P(A|B) = P(A)

Rearrange

[lime bone]

Yes, I know that. But I wonder if I can solve their relationship by reasoning

Like whether I take a poop now is doesn’t affect whether you eat a sandwich

These two events are independent

Can I do it the same way? Can I tell if A and B are independent by reasoning

Or there another way that do not rely on this formula?

[tawny moon]

i believe we have to be careful about the difference between independent events and mutually exclusive events

[pine prairie]

P(A) = 1/2, P(B) = 1/2, P(A ∩ B) = 1/6

[spice bluff]

Hi

[lime bone]

What if you are deprived of the ability to do math

[pine prairie]

Uhh what do you mean

[lime bone]

Like any mathematical definition is took away from you

[pine prairie]

So let me clarify what you want

You want a solid unambiguous definition of a mathematical concept without using the technical terminology constructed for the sole purpose of precise mathematical arguments

[lime bone]

Yes

[pine prairie]

Okay build a rocket with nothing but pebbles

Do you see the absurdity of your request

[drifting hornet]

well, in this specific case B is obviously less likely to happen if we know that A happened. If A happened, then there is only a 1/3 chance of landing at even number

[vale dock]

@lime bone Has your question been resolved?

Channel closed

Closed by @lime bone

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.

[stark wedge]

how did 3x grow a ^2

[deft condor]

ik i could just put y value in second buh

[stark wedge]

also i think you kinda made your own life difficult

would you like an easier thing to do or do you want to continue with this specific method

[deft condor]

yea

[stark wedge]

... so which one is it

@deft condor

[deft condor]

what did i do wronh

[stark wedge]

how did 3x grow a ^2