help-10

[slate warren]

i tried doing it log3(y)=x but i dont know if that is how you should do the inverse of 3^x

[sage geode]

Your question is really unclear, can you define what log form of a number is?

[devout sable]

well you could write something like $3^x = 10^{x \log_{10} 3}$

[devout sable]

although yes question is bit unclear

[slate warren]

i mean making an exponential equation become logarithm, like 2^x=4 is the same as log2(4)=x

[sage geode]

Ye but you just gave us 3^x, that's not an equation

[slate warren]

i know, thats why i was confused, because my teacher said we had to make 3^x into log form

so i just assumed you could turn it into an equation with 3^x=y then make it log3(y)=x

[slate warren]

but i think this would work

[devout sable]

[slate warren]

thanks mate

.close

[obtuse pebble]

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[devout sable]

np

[obtuse pebble]

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[timid silo]

I am given a set question that says in a class of 50, there are 23 males. Is it safe to assume that the number of number of females are 27 or can a person be both male and female as in the case of a bisexual? I am confused.

[sage geode]

Most of the textbooks refer to binary genders, so I guess it is safe to assume that

And no you can't be male and female at the same time

[high lily]

bisexual isn't a gender

[timid silo]

thank you.

[devout sable]

Uhhh

Wut

[high lily]

there could be non-conforming

[sage geode]

I guess bisexuality is an attraction and bigender is a gender

[royal basin]

ive seen probability problems explicitly specify "this many boys and this many girls" to avoid ambiguity on this matter

or set theory whatever

[timid silo]

I am preparing for an exams that isnt a textbook question. It is a quantitative reasoning maths question.

[timid silo]

They dont always, especially when things are grouped into more than one categories.

they just give you the total and ask you to solve for the unknown.

[royal basin]

nyeh

i'd assume male and female are supposed to be complementary here

simply bc that's just commonplace

[timid silo]

okay.

[obtuse pebble]

@timid silo Has your question been resolved?

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[obtuse pebble]

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[rich moon]

Whats the right name to use when a function is a variable in an expression?

[rich moon]

i.e the function is unknown

If there is a proper notation for this that would be good to know, but I was thinking of something like $f^X$ where in this case X is the function

[warm shale]

FargothUrIsOnline

[rich moon]

This is a bespoke notation where something like the above would be useful, so it would be good if there was a standard I could use instead of making something up to avoid bespoke notation

[obtuse pebble]

@rich moon Has your question been resolved?

[obtuse pebble]

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[near rock]

A bacterial culture grows exponentially and the number of bacteria triples in one hour. After 4 hours, the culture contains 10 million bacteria.
How many bacteria were there originally?
10,000,000 = b * 3^4
b = 10/81

[near rock]

anyone that can check my answer because i think this is wrong

[daring rock]

Your equation is right

[near rock]

the question should be easy but my teacher didnt rly explain it well

[daring rock]

Your equation is right but 10/81 is not

You lost a factor of a million somewhere

[near rock]

i just used symbolab to calculate that

yh the answer is probably wrong aha let me redo that

[daring rock]

3^4 = 81

so

10,000,000 = b*3^4 becomes

10,000,000 = 81b

[near rock]

10,000,000 = b * 3^4
10,000,000 = b * 81
10,000,000 / 81 = b

[daring rock]

right

[near rock]

that's so easy, i just don't know why the calculator gave me that answer before, but anyways thanks

[daring rock]

no problem

[near rock]

@daring rock can i ask you one more question

which function has the biggest t_2 value

of f_2 and f_3

im pretty sure its f_2

[daring rock]

I'm not sure what you mean by t_2 value

The growth factor?

[near rock]

the doubling constant

[daring rock]

so as in $y=a\cdot b^x$, you're referring to $b$?

[warm shale]

tatpoj

[daring rock]

If so, then yes

[near rock]

no

the doubing constant is like

if you have t_2 = 3, that means if you go 3 out on the x-axis the y value will be the double

but in that picture its different

[daring rock]

Ahh I see, I've never heard that term before

Since f_1 is decaying, its doubling constant would be negative then, right?

[near rock]

yh

[daring rock]

And f_3 is growing more slowly than f_2, so wouldn't you have to go out farther in order for f_3 to double?

[near rock]

thats what i thought

so f_2

[daring rock]

Wouldn't that make it f_3?

You said the doubling constant is how far the x needs to change in order for y to double

in f_3, x needs to change more in order for y to double, because it's growing more slowly

[near rock]

wait, so it's f_3?

im gonna do smth, but ill read it after

it's gonna take 5 min or so

[daring rock]

I've never heard the term doubling constant, but based on your definition, yes, it's f_3

[obtuse pebble]

@near rock Has your question been resolved?

[near rock]

ight i see

[obtuse pebble]

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[glass folio]

Having trouble w this. Probability question. I used formula but unsure where each number goes

[chrome mesa]

show what you've done so far

[obtuse pebble]

@glass folio Has your question been resolved?

[glass folio]

Did this

[obtuse pebble]

@glass folio Has your question been resolved?

[glass folio]

.close

[obtuse pebble]

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[bold grotto]

lol wtf is this
where do i even start?

[tidal hawk]

u can simplify the inside first

[devout sable]

$d^m \cdot d^n = d^{m+n}$

[tidal hawk]

or factor 81 and take it out of the fourth root

[bold grotto]

Do u have to do 81×81?

[tidal hawk]

no

[tidal hawk]

^^

[gusty halo]

yes

you do

its multiplication you cant factor it out

[tidal hawk]

u can if u want but very troublesome

[bold grotto]

Ohh okay

[tidal hawk]

if it’s multiplication u can factor

[devout sable]

and $\sqrt[p]{d^q} = d^{\frac qp}$

uhh

[tidal hawk]

omg @devout sable I want coloured latex

give me

[gusty halo]

ab*ac does not equal a(bc) it equals a^2(bc)

[devout sable]

thats not available publicly

[tidal hawk]

):

[warm canopy]

At no point do you need to calculate 81*81 lol

[devout sable]

81=3^4 btw

[gusty halo]

you dont have to calculate it but you cant just factor out an 81 you need to have 81*81 or 81^2

[bold grotto]

Erm did i do it right? It looks wrong

[tidal hawk]

how did you get d^2 for the second term

to make it easier maybe u can split it up

into 2 fourth roots

[stable rain]

omg u r here

hiii

queen

[tidal hawk]

HI QUEEN

[bold grotto]

Lool

[tidal hawk]

why ur name different

colour

[stable rain]

me?

[tidal hawk]

ya

[stable rain]

ye

i think

they changed helper color

[tidal hawk]

oooo

HAHAHA

[stable rain]

OMG

[tidal hawk]

looks good on u <33

[stable rain]

i got

very active

at last

[tidal hawk]

what’s that

[stable rain]

its

a role

like

how u r active

whats

theQ

[tidal hawk]

oooo

[tidal hawk]

^^

indices

[stable rain]

i can

visually tell the ans

hahaha

[nocturne minnow]

Not helper, but helpful. New role

[stable rain]

oh

[stable rain]

whats rhe diff

[bold grotto]

What about now?

[stable rain]

did they just change name

[tidal hawk]

better

but

[stable rain]

wait isit

[devout sable]

,rotate

[stable rain]

wait no

[tidal hawk]

forgot to subtract the power

[stable rain]

one of the powers is

neg

ye

[tidal hawk]

and also

[nocturne minnow]

Same abilities as helper but without getting pinged

[tidal hawk]

it’s -5/4

[stable rain]

hahhaa

then

[bold grotto]

Why -5??

[stable rain]

who has helper

[tidal hawk]

four question

has -5

[stable rain]

the original Q has ^-5

[tidal hawk]

ur**

[wild swallow]

circle straight up just going off topic

[tidal hawk]

SNOW

the queens are here

too much charm for me to handle

[bold grotto]

Ohhhhhhhhhhhhh

[wild swallow]

no more ping simulator

oh wait

[bold grotto]

That the answer

[wild swallow]

im green D:

[stable rain]

I WOULD NEVER

[tidal hawk]

errr

[stable rain]

oh wait

[bold grotto]

💀is it not?

[stable rain]

then i can finally enable server pings

[tidal hawk]

1-5/4 is

[bold grotto]

Why 1-

Where did 1 come from

[stable rain]

its from the

^4

[stable rain]

then when we took it out of the

4th root

it became ^1

[tidal hawk]

first rule

[bold grotto]

Is the answer 9

1-5/4=-1

-1

3d×3d^-1
=9

[warm canopy]

1-5/4 is not -1 😦

[stable rain]

ok

im bacc

[stable rain]

yea this is

not really right

i think u r thinking of

(1-5)/4

but its

1-(5/4)

u gotta

add dem brackets

normally division comes first without

but can be a bit amibigous

[bold grotto]

Oh okayy

[stable rain]

oo

seems right

yayyyy

[bold grotto]

Is it??
I am still sus

[stable rain]

nono

i think its right

,w (81x^4*81x^-5)^(1/4)

[warm shale]

Results provided by WolframAlpha

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

Requested by Circle#0025

[stable rain]

well

its

hahaha

tbh u cant take it out of the sqrt

but ur Q kinda

forces ubto

[bold grotto]

I texted my friend
This is the answer??

[stable rain]

forces u to

[bold grotto]

Yea exactly

[stable rain]

sry whats that

[bold grotto]

Idk I think he is wrong

[stable rain]

oh

no its like

ye

hes wrong

its like

wait

no

hes right

im wrong

[bold grotto]

Am I wrong?

[stable rain]

HAHAHA

um

errr

slightly

but like

the

way they want u to ans ur Qs

u dont rly hv a choice

u just gotta

use ur ans ig

[bold grotto]

Ohh okayy!!
I will take you word that that's the right answer

[stable rain]

yea

its cuz

its like

sqrt

u cant do

sqrt (neg number)

so thats y sqrts is

bit diff from

[bold grotto]

Ohh

[stable rain]

^(1/2)

but they want indices

so no choice

[bold grotto]

Ohh

Thank you!!!

[stable rain]

npp

[bold grotto]

Thank you everyone!!!!

.close

[obtuse pebble]

Channel closed

Closed by @bold grotto

Use .reopen if this was a mistake.

[stable rain]

❤️

[obtuse pebble]

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[charred latch]

Hi! I don’t really know what I should be doing or what i’m doing wrong (#9) and for (#1) i don’t even know where to start

[wooden cipher]

show your work pls

wait im dumb

nvm

[charred latch]

😭

[wooden cipher]

so for #9, you were basically there,

you just need to simplify the fraction

[charred latch]

i do not understand

[wooden cipher]

since they are parallel, you match slopes whidh you did

the small problem is that you plugged it into the formula not quite correctly

[charred latch]

oh what should i do instead?

[wooden cipher]

the -p-(-p) needs to be changed into p-(-p)

[charred latch]

i had it wrong in the original photo and then i fixed it so this is what it looks like rn

[wooden cipher]

yeah that looks good

so now combine like terms

[charred latch]

does p = 3.5?

[wooden cipher]

yup

[charred latch]

Omg thank you

[wooden cipher]

for #1, this one requires a little more intuition

[charred latch]

i wasn’t sure how to start, one of my friends told me to plug in values but i didn’t know how

[wooden cipher]

we know the y intercept of the second line is 3 right

[charred latch]

why would the y intercept be 3?

[wooden cipher]

you rewrote the equation in the form y=mx+b, the b was 3 (aka the y-int)

[charred latch]

Oh wait sorry i was still looking at the previous question

yes

[obtuse pebble]

@charred latch Has your question been resolved?

[obtuse pebble]

@charred latch Has your question been resolved?

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[devout fern]

Can someone explain this to me?? I just need an explanation to number 1

[cedar lichen]

Is (1, 2) a solution to x + y = 11?

[devout fern]

Idk

How can i know if (1,2) is the solution to x + y = 11

[cedar lichen]

What's x in (1, 2)?

[devout fern]

1?

[cedar lichen]

Yes

What's y?

[devout fern]

2

[cedar lichen]

If x is 1 and y is 2, what's x + y?

[devout fern]

3

Oh

[obtuse pebble]

@devout fern Has your question been resolved?

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[timid silo]

I don’t understand afar im doing wrong

[solemn osprey]

The number that makes the (f+g) undefined isn’t 3

Hint hint

[stable rain]

its when the

bottom is 0

[solemn osprey]

^^

[solemn osprey]

I think they’re afk

[stable rain]

[timid silo]

No Im thinking : , )

[stable rain]

hiii

[solemn osprey]

Oh oh my bad

[stable rain]

welc bac

[solemn osprey]

Hallo

[timid silo]

I still don’t understand 😔

[stable rain]

we want to

exclude the val where

[solemn osprey]

Whatcha thinking about? When is the fraction undefined? When the denominator is zero? When 3x=0? When x=0?

[stable rain]

3x=0

what val is x

when denom

aka 3x

=0

[stable rain]

3x=0

[solemn osprey]

The domain should exclude 0, not 3

[stable rain]

yuppp

:

[timid silo]

Is it 1/3?

[stable rain]

no its

like

3x=0

u divide both sides by 3

so

3x/3 = 0/3

x = 0

[solemn osprey]

Can u walk us through your thinking? How did u get 1/3?

[stable rain]

[solemn osprey]

Dam cute emoji

[timid silo]

Ohh wait I understand I think

Im just making it overly complicated

[wild swallow]

[solemn osprey]

:

[stable rain]

OMG

[solemn osprey]

[stable rain]

ANOTHER ONE TO ADD

[timid silo]

[solemn osprey]

Hehehe

You got it now Cracker Jack?

[timid silo]

Yesh

[stable rain]

yayy

.close

[obtuse pebble]

Channel closed

Closed by @stable rain

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[wise agate]

Need help on factoring

[gusty halo]

do you have a specific problem?

to solve

[timid silo]

do middle term split

[nocturne minnow]

Did you try anything?

[wise agate]

(x+7)(x+8) right

[timid silo]

yup

[wise agate]

how bout this

[timid silo]

what did u try

[wise agate]

(3x )(3x )

[gusty halo]

try factoring out a 3 first and see if that makes it easier

[timid silo]

nah

[idle swallow]

3(x^2-x-2)

[idle swallow]

Agree

[wise agate]

ik its not answer but idk what to put in

[timid silo]

after factoring 3 do middle term split

[wise agate]

hmm

wouldnt I factor 6

[gusty halo]

what do you get when you factor out just a 3 from the whole expression?

[night fox]

Uh have you thought of finding it roots first?

[wise agate]

3(x^2-x-2)??

[gusty halo]

yes

so how can you factor x^2-x-2?

[wise agate]

(x-2)(x+1)?

[gusty halo]

yep

and when you put the three back in?

[wise agate]

3x^2-3x-6 = (x-2)(x+1)

[gusty halo]

not quite

we determined that x^2-x-2 = (x-2)(x+1)

so whats 3(x^2-x-2)?

[wise agate]

hm

3x^2-3x-6

?

[gusty halo]

you have to replace (x^-x-2) with its factorized form

thats just the original problem

[gusty halo]

we first factored the original to be this

[gusty halo]

then we factored x^2-x-2 to be this

so what happens when you put those together?

[wise agate]

It's not asking for that

but can you show me

how

[gusty halo]

3x^-3x-6 = 3(x^2-x-2) = 3((x-2)(x-1))

so its 3(x-2)(x-1)

does that make sense?

[wise agate]

a tiny bit, but can't you just put the 3 infront of (x-2)(x-1) to save time?

[gusty halo]

yes

[wise agate]

ok

lemme try another problem

lemme try this on my own

you try to find answer

[rough knoll]

Is that right?

[gusty halo]

he said he wanted to do it on his own

[wise agate]

its cool

ill do another

[rough knoll]

Oh mb

[gusty halo]

but thats not the final answer only the first step

[gusty halo]

try and explain your thought process as you solve it

that will make it more clear what part you struggle with and what part you understand

[boreal condor]

adding on, if you really want to test your knowledge, try to teach the concept to someone else

if u can teach it, u know it thoroughly

[wise agate]

I got (x^2-x-20)

i just divided it by 3

[gusty halo]

you have to keep the three as a factor in front

you have the right idea though

3(x^2-x-20)

[wise agate]

oh

[gusty halo]

you cant just divide by 3 like that unless its an equation and you divide both sides by 3

[wise agate]

then do we factor

it by 3?

[gusty halo]

yes

[wise agate]

just divide or multiply ?

[gusty halo]

you had the right idea here

how can you factor this expression?

[wise agate]

tbh idk

[gusty halo]

when you factor it, you should get (x+a)(x+b)

and we know that a+b=-1

and a*b=-20

[wise agate]

where did u get a +b

[gusty halo]

(x+a)(x+b) = x^2 + (a+b)x + a*b

if a+b = -1 and a*b = -20 then what are a and b?

[wise agate]

hmm

oh

2 x 10

-4 x 5

20 x 1

[gusty halo]

sorry it should be -20 my bad

but one of those is close

[gusty halo]

almost

[wise agate]

flip it?

[gusty halo]

very very close

remember a+b = -1

[wise agate]

oh

-5 + 4

[gusty halo]

yes

[wise agate]

so 3(x-5)(x+4)?

[gusty halo]

yes

now remember to include the original 3 we had

[wise agate]

ye i got it

alright I now believe I can do it on myself

imma try 1 more

[rough knoll]

Now do another one by yourself

This time we won't give hints.

[wise agate]

here the problem i'm doing

[gusty halo]

this is the exact same process as the last two, only with different numbers

you should be able to do it

[wise agate]

got it

3(x-3)(x+2)

[gusty halo]

that looks right

nice job

[rough knoll]

Nice 👍

[wise agate]

Ok I did 2 others and it says im right

i got it

thanks

👍

[gusty halo]

You're welcome, also remember to do .close so that other people can use this channel for help @wise agate

[wise agate]

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

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Remember:
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[upper sequoia]

Guys I'm stupid pls help

[upper sequoia]

question 6

[stable rain]

which

[upper sequoia]

a and b

[stable rain]

um

6a

it says list

so u have no choice but to

write them down slowly

[upper sequoia]

isit like

257

275

725

752

527

572

[stable rain]

i think

u can repeat?

i feel u would be able to

but then u would have 27 stuff

which is bit long

hahha

generally the Q wld specify

[upper sequoia]

i think thats all for a

[stable rain]

but yea i think we just wrok with this 6

else itll be a bit long

haha

[upper sequoia]

ya hahaha

[stable rain]

ok so

part B

u want 1 group

[upper sequoia]

i dont understand b

[stable rain]

even numbers

and another group

middle digit is a 5

do uk what are even nummbers

[upper sequoia]

yes\

even and odds

even

so it be like

257

only ?

[stable rain]

w8w8

no

257 is odd

even numbers are

those that end with a

0,2,4,6,8

[upper sequoia]

ohh

so

275

?

[stable rain]

no thats

odd as well

[upper sequoia]

or just 2

[stable rain]

END with

[stable rain]

one of these

[upper sequoia]

oh ok

so 752

[stable rain]

yesss

[upper sequoia]

or 572

[stable rain]

yuppp

[upper sequoia]

only these two?

[stable rain]

so those are in group A

yup

then now group

B

those whose middle digit is a 5

can u identify those

[upper sequoia]

i dont understand wdym by middle digit is 5

[stable rain]

so like

123

the middle digit is a 2

or like

749

the middle digit is a 4

like there are 3 digits, the digit in the middle would be the 2nd one

[upper sequoia]

urm

ok

[stable rain]

[upper sequoia]

oh

ok

[stable rain]

got it now?

[upper sequoia]

then i put the others in b?

[stable rain]

yepp

so whats in B?

[upper sequoia]

like

275

257

[stable rain]

nono

the

middle

or 2nd digit

has to be a 5

so like

_5_

[upper sequoia]

oh

so i put

257

[stable rain]

no

[upper sequoia]

752

[stable rain]

yepp

257 yes

correct

so

we have

[upper sequoia]

so i put those two in b?

[stable rain]

A: 572, 752
B: 257, 752

so now we have to put it in the venn diagram

[upper sequoia]

what do we putt

[stable rain]

so first we should start with those that are not in A or B

[stable rain]

so from here

which numbers are not in A or B

[upper sequoia]

ohhh okk

275

[stable rain]

do uk where to draw them?

[upper sequoia]

725

[upper sequoia]

its on the right of the question

[stable rain]

so

those that is not in A or B will be like

the white part here

[upper sequoia]

oh ok

so

the middle i put

275

527

725

[stable rain]

um

the white part

i wouldnt call it middle

but yea those 3

now

back to this

A: 572, 752
B: 257, 752

are there any numbers in both A and B?

[upper sequoia]

yes

[stable rain]

what is it

[upper sequoia]

these

A: 572, 752
B: 257, 752

[stable rain]

nono

i mean

overlap

is there any number in

set A

AND

also in

set B

[upper sequoia]

i dont understand 😭

[stable rain]

so like

if i have

A:1,2

B:2,3

then

the number 2 is in both A AND B

so now we have

[upper sequoia]

oh

[stable rain]

A: 572, 752
B: 257, 752

is there any number in both

A AND B

[upper sequoia]

what i have wrote i put in the middle?

752

[stable rain]

yep

so

in this yellow bit

[upper sequoia]

then i dont put 275 527 725 in the middle?

i just put 752 in the middle

[stable rain]

yes just that 752

[upper sequoia]

ok thats all?

thank you

[stable rain]

nono

lastly

weve the

last 2 numbers

[upper sequoia]

which is?

[stable rain]

so we had

A: 572, 752
B: 257, 752

but now we filled in 752

so we are left with

A: 572
B: 257

so just fill those into the

middle ish bits of both of their sets

[upper sequoia]

ok

is there anything esle?

[stable rain]

um

i think thats it

[upper sequoia]

ok thanks

[stable rain]

npp

❤️

.close

[obtuse pebble]

Channel closed

Closed by @stable rain

Use .reopen if this was a mistake.

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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>.
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• Be polite and have a nice day!

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[rough knoll]

What r u stuck with?

[timid silo]

this question

[night fox]

What have you tried so far?

[rough knoll]

Ok yea but what do u not understand about it?

[devout sable]

adding-5 is same as going left 5 steps

[night fox]

Look for 4, go 5 steps back.

[timid silo]

• moving forward

-moving backward

by defintion

[rough knoll]

4+(-5) is the same as 4-5

[timid silo]

+(-5) is -5 / going back by 5 steps

[devout sable]

yes

[timid silo]

now idk if +*-=- has some proof in ring theory

so dont trust me when I say by defintion

[rough knoll]

There's 4 people here helping you with math. Lmao

[timid silo]

so it’s -1?

[rough knoll]

Yes

Now do it on the number line

[timid silo]

aha thanks

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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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.

[devout sable]

,rotate

[devout sable]

thats 3*a^3b^3 right?

oh i see

yes my b

yes feels alright to me

[obtuse pebble]

Channel closed

Closed by @ember nova

Use .reopen if this was a mistake.

[devout sable]

lowercase c

[obtuse pebble]

✅

[warm shale]

Retrieving the previous image failed.

Sep 24, 2022, 5:29 AM

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[obtuse pebble]

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.

[feral sentinel]

@wild swallow hi mother can u explain this 2 me pls i didnt get the explanation lol

[wild swallow]

oh right

this thingo

[feral sentinel]

HELLO

[wild swallow]

hello

[feral sentinel]

lets do dis

[night fox]

I have done these problems.

[wild swallow]

do you have the other person's explanation

[feral sentinel]

no i lost it

[wild swallow]

i literally

[night fox]

Is this taken from Hall and Knight?

[wild swallow]

sent it to you

how could you lose it LOL

[feral sentinel]

nu

OH RIGHT

[wild swallow]

anyway

[feral sentinel]

findingsouth: but basically, let x = t, y = at, z = bt which represents the parametric form of the intersection curve
findingsouth: this gives 6 + 4a + 3b = 0, 4a + 2ab + pb = 0
findingsouth: now the gradient of 6 + 4a + 3b = 0 is -4/3, and implicitly differentiating, 4 + 2b + 2a (db/da) + p (db/da) = 0
findingsouth: substituting db/da = -4/3 gives the tangent point as (-3, 2)
findingsouth: and so 4(-3) + 2(-3)(2) + p(2) = 0 gives p = 12
findingsouth: now we should confirm that p = 12 gives more than one real solution
findingsouth: and if this has infinitely many solutions as we conjectured, substitute in x = 1 and you will find y = -3, z = 2, which is not the trivial solution (x, y, z) = (0, 0, 0)
findingsouth: (the general solution is (x, y, z) = (3t, -9t, 6t) btw)

ok wait

[wild swallow]

yes that

[feral sentinel]

so i wanna do this

to train my meth problem soling ksills

skills

ok so hmm

[wild swallow]

im not actually sure where the db/da = -4/3 comes from

but it works

[feral sentinel]

wait can u tell me what am i supposed to look at first

[wild swallow]

but i have a different solution

which doesnt use differentiation

[feral sentinel]

lets say im a total retarC

[wild swallow]

C

[feral sentinel]

oh ok lai

[wild swallow]

well

okay so

do you know what happens

[night fox]

welp

[wild swallow]

when you do something like

[feral sentinel]

yes

[wild swallow]

what happens

[feral sentinel]

a^2 + b^2

• 2ab

[wild swallow]

LOL

[night fox]

It's get squared.

[wild swallow]

you had me there

[feral sentinel]

[wild swallow]

and so you see

you get 2ab

[feral sentinel]

dharr mann moment

[wild swallow]

thats

[feral sentinel]

wait how does that help

[wild swallow]

the product of two of the terms right

[feral sentinel]

ye

[wild swallow]

thats the stuff hanging out in the second equation

here

[feral sentinel]

i donut see it

wait

dong tell me

[wild swallow]

dong

[night fox]

got it lol

[feral sentinel]

i seriously dont see it

watafak

[night fox]

a+b+c^2

Lmao

[wild swallow]

the xy

the yz

and the xz

right

[night fox]

Ywh replace them

[wild swallow]

they are products of two terms

[night fox]

Fuking phone user 💀

[devout sable]

[feral sentinel]

wattttt

wait

we are making use of

(a+b)^2 = a^2 + 2ab + b^2 right

[night fox]

No lmaao

[feral sentinel]

heh

[wild swallow]

im just throwing out ideas

[night fox]

We got three terms.

[wild swallow]

so like

the idea is

when we do (a + b)^2

we get a^2 + b^2 + 2ab

[feral sentinel]

ye

[night fox]

it get sqaured.

[wild swallow]

and thats how we can get access to these "cross terms"

which look like ab

thats exactly whats appearing in the second equation

[feral sentinel]

o

[wild swallow]

does that make sense?

[feral sentinel]

i get this

but i dont get how it applies here

lmao

[wild swallow]

currently the two equations dont really like

want to talk to each other

[feral sentinel]

yea

[night fox]

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca).

[wild swallow]

because one of them is just x, y, z by itself

and

one of them has xy, yz, xz terms

[feral sentinel]

wait tbh i dont even get what the question wants

[wild swallow]

so you want to make them "talk to each other"

[feral sentinel]

it wants me to find the value of p

so that theres inifnte solutions

[wild swallow]

okay lets explain the question first then

[night fox]

see the last terms.

[wild swallow]

we have the two equations

[wild swallow]

and we want to find the smallest positive integer p such that there is more than 1 solution

the reason why we want more than 1 solution is because

there is a really easy solution that works for any value of p

can you spot it

[feral sentinel]

0?

[wild swallow]

0 what

theres 3 variables

x y z

[feral sentinel]

wait but i tot were only finding p

[night fox]

Guess

[wild swallow]

when it says solutions to the two equations

it means solutions for x, y, z

[feral sentinel]

ohh

[wild swallow]

p is a parameter that we can tune

but its not something we solve for

[feral sentinel]

everything 0?

[wild swallow]

yes

everything 0

x = y = z = 0

[feral sentinel]

yes

[wild swallow]

so that is the trivial solution if you will

that will always satisfy the equations

[feral sentinel]

yes

but thats only 1 right

[wild swallow]

we want to find the smallest value of p

[feral sentinel]

so now we wanna find

[wild swallow]

such that there is at least 1 more

[feral sentinel]

other slutioss

p

o

hmm

[night fox]

🥴

[wild swallow]

so actually

say for example

when p = 3

there are no other solutions

they just dont exist

and it can be proved

[feral sentinel]

nani

why

[wild swallow]

well thats part of the solution

so i wont explain it just yet

but just know

[feral sentinel]

yessir

[wild swallow]

that for certain values of p

there are actually no other solutions

okay so

how do we even solve equations

we have 2 equations that we're trying to solve simultaneously

so sort of similar to row reduction in linalg

we need to make them talk to each other

[feral sentinel]

OKAY

[wild swallow]

and so as i was explaining earlier

[feral sentinel]

ye

[wild swallow]

the equations sort of dont talk to each other rn

because the first one is has x, y, z terms

but the second has xy, yz, xz terms

[feral sentinel]

why not we multiply both sides of the equation with x

[wild swallow]

because that has awful symmetry

it sort of

[feral sentinel]

wait wut

[wild swallow]

doesnt let you do stuff

[feral sentinel]

o

how do u know tho

how did u eyeball ti

[wild swallow]

algebraic intuition i guess

well

maybe if you multiply by x

you get something

but

then youd need to multiply by y

and then z

and you end up back to squaring

[feral sentinel]

o

okay

so what should be my next intuition

[wild swallow]

well

to get access to the xy yz and xz terms

like with (a + b)^2 = a^2 + b^2 + 2ab

we can do

the first equation squared

[feral sentinel]

but we dunno whats (a+b+c)^2

[wild swallow]

do you not

just

expand it out by hand

its not hard to calculate

[feral sentinel]

is there

a formula for this

[wild swallow]

well there is

but i mean

[feral sentinel]

oh lmao wait

[wild swallow]

you gotta discover it

[feral sentinel]

we can just separate them

lmao

[wild swallow]

at some point in your life

yeah

[feral sentinel]

its so long

[wild swallow]

did you collect

[feral sentinel]

O

[wild swallow]

you should only get 6 terms in the end

[feral sentinel]

A ha

[wild swallow]

are you

missing a term

wait no

you just forgot the ^2

[feral sentinel]

Oop

[wild swallow]

,w simplify (6x + 4y + 3z)^2

[feral sentinel]

Wowowow

Wtf

[warm shale]

Results provided by WolframAlpha

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Requested by 夢雪#2250

[wild swallow]

nice

[feral sentinel]

Ez

[wild swallow]

looks like it matches