help-13

[azure swift]

so we want to find (x,y) such that these eqauations hold at the same time

okay

[autumn tusk]

but what would that mean graphically? i would just eval the function at a point. mmm ok the same point where the other eq is true.

[azure swift]

Lets call them (1) and (2)

[autumn tusk]

im following ye

[azure swift]

I can come back to this

Wait uh not these equations

these, when you let them equal 0

so let me just put them here

\begin{align}
x^2=x\sqrt{27-x^2-y^2}\quad\tag{1}\
y^2=y\sqrt{27-x^2-y^2}\quad\tag{2}
\end{align}

[wraith dagger]

Aslan

[azure swift]

Are these correct?

Uh yeah okay they right

so let me start over

[azure swift]

So you have these two equations

we want to find (x,y) such that they hold both (at the same time)

[autumn tusk]

mmm yea but i don't get what those are

[azure swift]

Wait what?

[autumn tusk]

not x^2

just x

yea these

[azure swift]

These?

[autumn tusk]

what are you looking for ? XD

[azure swift]

Lmao what did you mean by this then?

[autumn tusk]

here you wrote x^2 = ..

it's x =

[azure swift]

Yeah!

Well no, who said that?

[autumn tusk]

i dont know where are you getting those from

[azure swift]

Did you try and even solve these?

when they the LHS is zero

Or is this maybe something i missed

[azure swift]

Yes im trying to explain why we end up with these

[autumn tusk]

but i know how to get there

[azure swift]

It seems that was your question from the very start no?

Oh, how?

[autumn tusk]

from the partials

[azure swift]

Right, so whats the problem then?

Im trying to explain how to get to the solution you were looking for

[autumn tusk]

you've helped a lot so far. I was trying to see if i understoo correctly the reasoning

[azure swift]

Just putting it in a (hopefully) slightly different perspective is what im trying to do!

[autumn tusk]

yes

so my doubt was

[autumn tusk]

i have all those separate solutions, (or) and i need to find all combinations where they are all true (and)

right?

that's why i plug

[azure swift]

Think of it like this,

[azure swift]

Yes, so think of it like this. For the fist row. You have two options

Say we picked x = 0

[autumn tusk]

and

[azure swift]

then we're left with the system x=0 and

y=0 or y=sqrt...

we then have a choice for the second row too

say we picked y = 0

then we have the system

[autumn tusk]

yep

[azure swift]

x = 0 and y=0

Cool! thats one solution

[autumn tusk]

i think i understand. it's what i've tried to draw there

so in this case we have 6 systems right?

but x=0 and y=0 ... nothing to do

[azure swift]

I see, i hope my prhasing of it helps. Think of it like a game. The or is a choice while the and is a demand

Yes!

Now we see that one solution must be (x,y)=(0,0)

[autumn tusk]

i meant 4 systems

[azure swift]

Well not really, we have one system

[autumn tusk]

oh hh

[azure swift]

but different paths

[autumn tusk]

yeah tell me more about this, it's the first time i see this

[azure swift]

The part about the system or the game we played above?

[autumn tusk]

system

what is the system here? how would you write it?

[azure swift]

Well by that i just meant its just one system, of equations

[azure swift]

Its this

Maybe you meant something else by system

[autumn tusk]

i think so yes

i mean the classic system of equations 2 variables...

[azure swift]

Yeah me too

Thats what we're dealing with here

it just happens to be the case that we have multiple solutions too

[autumn tusk]

ye but where do you get that written like that from those 4 solutions?

[azure swift]

thats why we end up with or statements

[autumn tusk]

why you get x^2 there?

[azure swift]

Thats the thing, i started from the partials, those 4 solutions is the results from my system

Go back to the partials

let them be equal to 0

[autumn tusk]

ahhh ok i see now lol

i've simplified and ditnt expanded the x^2 ok alright

[azure swift]

So how did we get x=0 and etc?

Well the trouble is when we divide or simplify the equations

we miss a solution

namley when x=0 and y=0

[autumn tusk]

mmok

but i found that in my case

[azure swift]

How did you find it?

[autumn tusk]

cause the partial is
3/2 sqrt(27-x^2-y^2)(-2y) +3y^2 = 0

[azure swift]

Well yes thats equivalent to equation (2)

[autumn tusk]

if factored
y( 3/2 sqrt(27-x^2-y^2+ 3y ) = 0

so y=0

[azure swift]

yes, thats the same reasoning you would do for my equations

nothing is different

[autumn tusk]

and the parenthesys is = 0

[azure swift]

So when you conclude that

its like when you find one of the roots in a quadritc equations

its an or statment because its yet another solution

[autumn tusk]

ok ok

but when i am at that point, goin from or to "and"

it's another system ?

[azure swift]

well think of of this way, in this image

the first row

has the same solutions as our eqaution (1)

and the same goes for the second row with equation (2)

so its really just still a system of 2 eqautions

[autumn tusk]

but i have 2 solutions for each eq here

how do i put this into 1 system only?

i think i need to understand how you see it

[azure swift]

Yes, its just an different but equivalent way of stating the solutions

[autumn tusk]

when you say system i think that is something i need to solve for

so i do all the combinations basically in this case

and i have many ... systems

but i think you see it in another way

[azure swift]

The system has some (or more) solutions. Okay what we do when we solve this system is rewriting this system in equivalent forms to at last see some concrete numbers, we've never changed the solutions but in some sense recovered them

[azure swift]

So the step from this

[azure swift]

to this

is that proccess

of trying to make sense of the solution, this way we can more concretly find them

oh how neat! now we've reduced it to certain cases

etc

As in, we can say pick x=0 from the first row or the other and then do the same for the second row

then we'll recover the solutions

and this process may continue alot further for a much more complex system of equations

[autumn tusk]

but you would do this in with many systems right?

i mean putting those cases into systems

x=0
y=sqrt...

this is one system

x=sqrt
y=sqrt
this is another

[azure swift]

Sure you think of it like that

[autumn tusk]

or how? that's what i dont get

how else

[azure swift]

But its not the same system anymore

its a subset

[autumn tusk]

mmm ok

[azure swift]

these are the subsets youll have to solve, and together they make out the first system we started with

[autumn tusk]

ok so i HAVE to to it this way

i have to solve the subset separately

or are you suggesting there is a way to solve them all together?

[azure swift]

In some cases there are neat elegant ways of avoiding it

[autumn tusk]

in 1 big system?

[azure swift]

Say the equation (x,y) = (1,1)

its just one equation

but can be viewed as the system

x=1 and y=1

maybe not the best example

All of this might become alot clearer once you have say a discrete maths class

or something like set theory and logic

It's all just logic and sets

[autumn tusk]

ok

that's great, thanks a lot for your patience and time

[azure swift]

no worries! I hope i helped you

[autumn tusk]

definetly

[azure swift]

:)

[autumn tusk]

bed time now, see you and thanks again!

[azure swift]

Good night!

[autumn tusk]

.close

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[onyx osprey]

I can tell this is a Game distribution with the given MGF

X ~ Gamma (-10, 1/2)?

I am just confused on how using the general form with lamda and r plugged in get to that MGF provided.

For (b),

σ = E(X) = r/λ

[drifting marlin]

X ~ Gamma (-10, 1/2)?
both parameters have to be positive so double check this part

[onyx osprey]

Well, when I plug in 1/2 to the general form,

I end up getting 1/(1-2t)

[drifting marlin]

i take no issue with the 1/2 parameter

[onyx osprey]

Yea, I see what you mean its Gamma (10, 1/2)

[drifting marlin]

what's your working definition of the gamma distribution (or whatever properties you know about it)

that's better

[onyx osprey]

Mx(t) = (λ/λ−t)^r , t < λ

[drifting marlin]

sure

ok so now that you have the distribution, what's the issue?

[onyx osprey]

I was just trying to prove that its true.

To understand the form instead of just assuming.

So, 1/(1-2t) = (1 - 2t)?

[drifting marlin]

,w 1/(1-2x) = (1-2x)

[wraith dagger]

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Requested by steakanator

[drifting marlin]

alas, no

however, the issue is resolved when you notice the sign of the exponent

[onyx osprey]

Oh, yes so
(1/1-2t)^-10 = (1 - 2t)^-10?

[drifting marlin]

missing a ^10 on the left but that's a basic exponent rule

[onyx osprey]

I guess I just won't bother going into detail about this then.

Thank you.

[drifting marlin]

[onyx osprey]

.close

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[edgy vine]

anyone

[edgy vine]

Which linear graph represents a proportional relationship?

[void sand]

what do you think?

[edgy vine]

BRO IDK

[void sand]

let's start with definitions then

what does "proportional relationship" mean?

[edgy vine]

EXPLAIN WHAT IT IS IM SO CONFUSED LIKE THEY JS THROW THIS PROBLEM AT ME AND DIDNT EVEN TEACH ME WHAT TO DO

[edgy vine]

uhhh

idk.

[void sand]

if y is proportional to x, then what is true about the graph of y?

[edgy vine]

idk

[void sand]

I'll give a hint in the form of a partial definition

[edgy vine]

https://tenor.com/view/im-a-failure-seamus-slasher-i-failed-im-a-disappointment-gif-25655227

[void sand]

a proportional relationship between two variables means that as one variable __, the other __

what goes in the blanks?

here's a word bank for the first blank:

increases
decreases
does not change

here's the word bank for the second blank:

increases
decreases
does not change

try to fill in the blanks

[edgy vine]

errrmmm

a proportional relationship between two variables means that as one variable increases

[void sand]

the other does what, then?

[edgy vine]

back mb

the other does not change?

[void sand]

mhm, not quite.

try again

[edgy vine]

so it decreases

[void sand]

that would be an inversely proportional relationship

[edgy vine]

😭 idk what that is

im just now learning this

[void sand]

it's exactly what you said

x goes up, y goes down!

[edgy vine]

oh

okay

[void sand]

if x goes up, and y also goes up, we say that y is proportional to x

[edgy vine]

OHH

[void sand]

that's the definition of a proportional relationship

so with that in mind, which graph is correct?

[edgy vine]

no negitive ?

[void sand]

wdym?

[edgy vine]

when you said " if x goes up, and y also goes up" does that mean its always gonna be positive

[void sand]

no.

if x goes from -5 to -4, and y goes from -10 to -8, that still means that y is proportional to x

[edgy vine]

ohhh

[edgy vine]

is it this one

[void sand]

you tell me

as x increases (goes to the right), does y increase (goes up)?

[edgy vine]

UH

y always increases?

[void sand]

I don't understand

[edgy vine]

nvm

I dont know

[void sand]

use this.

as x increases, y should too

that's what you're looking for

in other words, as we move from left to right, the height should get higher!

[edgy vine]

this?

[void sand]

ding ding ding!

a winner is you!

[edgy vine]

WWW

THANKS BRO

[void sand]

if you're done here, make sure to close the channel

[edgy vine]

yuh cya

wait is it /close ot

or*

[void sand]

it's .close or .solved

either works

[edgy vine]

alr

.close

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[cedar kiln]

@high harbor Has your question been resolved?

[lavish bobcat]

yes bcs you missed a condition

when 3x-6 < 0 and x + 2 >= 0

you get an interval of [-4/5, 2]

well idk how u did this

little table thing

but you should just do 3x-6 < 0 and x + 2 >= 0

check where that is

and then solve - 3x + 6 -x - 2 <= x + 8

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[spice rose]

Hello

[spice rose]

I am looking for E

6 point m.a.

i get you gotta work back, but how do I do that to find E

[dusky peak]

What does that column stand for?

[mortal hemlock]

that makes it much clearer

you get the 6 pt ma for 2014

you know the average

and you know 5 out of the 6 points of that average

so how would you calculate that last point

[spice rose]

idk

thats what im asking

[dusky peak]

Average = sum of data / number of data points

[mortal hemlock]

if i have points H,I,J,K,L,M, then how would i calculate the average?

[spice rose]

x then divide by amount

Im looking for E

[mortal hemlock]

write it out

write out the sum

and the average

[spice rose]

idk what to do tbh

[mortal hemlock]

sum of A,B,C,D,E,F is (A+B+C+D+E+F)/6 right?

you know a,b,c,d,e and you know the average

so just fill it in and do some algebraic manipulation

[spice rose]

I dont know e though

[mortal hemlock]

these are dummy variables

not the same as the one you have in your example

[spice rose]

oh

[mortal hemlock]

if i have the points 4, 7, 2

then what is the average?

[spice rose]

6.5

[mental trail]

that's not how average works, you divided by 2

but by what are we supposed to divide if there are 3 points in total

[mortal hemlock]

you have 3 points so /3

so, now lets go the opposite way, if we have the average = 8, and the points 2,5,10,5,A

what is A?

$\text{average} = \frac{\text{sum of points}}{\text{number of points}}$

[wraith dagger]

Flappie

[spice rose]

2+5 +10 +5 +A /5= 8

[mortal hemlock]

dont forget the brackets

[mortal hemlock]

and then how do you find A here?

[spice rose]

this is my confused point

[mortal hemlock]

$\frac{2+5+10+5+A}{5}=8\\2+5+10+5+A=40$

[wraith dagger]

Flappie

[mortal hemlock]

if you cant do this, then you need to revise your basic algebra

[spice rose]

oh yeah true

.close

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[mortal hemlock]

(x-3)(x-1)<=-x

mb

should be fixed now

but we've already got rid of the logarithm

we already got the condition that x^2-4x+3>0 from the logarithm

and now we have a second condition that x^2-4x+3<=-x

x^2-3x+3<=0 is one condition, and x^2-4x+3>0 is the other condition

so now we have to find all the x that satisfy both condiitons

[cedar kiln]

@high harbor Has your question been resolved?

[cedar kiln]

@high harbor Has your question been resolved?

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[tardy spade]

If the graph of y = | x-a | + b| x-2 | passes through the points (0.3) and (1,2), find a,b

[mighty shuttle]

!status

[cedar kiln]

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

[tardy spade]

2

I've gotten two equations from substituting the points given

1. | -a | +2b = 3
2. | 1-a | +b = 2

I know i have to examine values of a because of its absolute value, but im kinda stuck on how to do it

[mighty shuttle]

solve both cases

*all cases

[tardy spade]

what cases?

[mighty shuttle]

case 1:- $a \in ( - \infty , 1]$

[wraith dagger]

ƒ(Why am. I here)=I don't Know

[mighty shuttle]

case 2:- $a \in (1, \infty)$

[wraith dagger]

ƒ(Why am. I here)=I don't Know

[mighty shuttle]

I think

[tardy spade]

how do i evaluate

[mighty shuttle]

what is |-a| whena<0

[tardy spade]

a?

[mighty shuttle]

yes

and when a>0?

[tardy spade]

a

[cedar kiln]

@tardy spade Has your question been resolved?

[cedar kiln]

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[slate garden]

i dunno how to do this

[atomic tendon]

Off the top my head

Write tan as sin/cos

Move 1/x to the other

Huh

Nvm dont tvg

[tardy spade]

think about when does tan x doesn't have a solution

and also rewrite as $ tanx =\frac {x + 1} {x} $

[slate garden]

It dosent have a solution

at x = 90 degrees

and that asymptope repaets every 180 degrees

idk how that helps tho

[tardy spade]

do you know what 90 degrees is in radians?

[slate garden]

yeah

pi over 2

wait

yh i think thats right

[tardy spade]

also you have that $tanx=\frac{x+1}{x}$

[wraith dagger]

roi

[tardy spade]

so $x/=0$ right

[wraith dagger]

roi

[tardy spade]

idk how to put the crossed = lmao

[slate garden]

yh i get u lol

i still dunno how the asymptope at pi over 2 helps tho

[tardy spade]

also note that $tanx=\frac{sinx}{cosx}\implies \frac{x+1}{x}=\frac{sinx}{cosx}\implies sinx=x+1,cosx=x$

[wraith dagger]

roi

[tardy spade]

there we go

[slate garden]

sry i have even less clue how that trig identitiy helps

[tardy spade]

dont worry im getting there

[tardy spade]

with this, and the thing i said before, you can find when $cosx \neq 0$ and that is the number of solutions you can have, plus the solutions of $sin(x) = x+1$

[wraith dagger]

roi

[slate garden]

idek how many solutions cos and sin have here

i feel like this is a bit much for a one mark question haha

wait i think i got it now

tan repeats itself every pi degrees

[tardy spade]

yes

[slate garden]

it says anwer is 40 so reciprocal graph must intersect it once every time

but then

how can bii be equal to 5

and not 4

thats what im rly confused about

oh wait

is it cause a bit of it gets cut out

when its only positive

so it loses a solution

it starts from origin when its positive

i think thats it

thx

.close

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[feral crescent]

Im bad at compound interest and need help wuth this question

[cedar kiln]

@feral crescent Has your question been resolved?

[cedar kiln]

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

[feral crescent]

1

<@&286206848099549185>

[cerulean hazel]

@feral crescent you need to use the formula for compound interest

[cedar kiln]

@feral crescent Has your question been resolved?

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[compact epoch]

can we go through this?

[compact epoch]

step by step to understand it better and learn?

basically have to calculate the volume between the 2 functions

on this integration area

[cedar kiln]

@compact epoch Has your question been resolved?

[compact epoch]

i just checked with sympy as well

[cedar kiln]

@compact epoch Has your question been resolved?

[compact epoch]

.close

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[desert bane]

how is this the answer

[desert bane]

i know its not two, didnt know what to do

[odd verge]

How did you get two

What were your procedures

🙂

[desert bane]

i didnt

i just put a random number in

didnt know how to do it

how did they get -0.1 and 0.02

and this

dont know how to dothis

[cedar kiln]

@desert bane Has your question been resolved?

[desert bane]

No

[cedar kiln]

@desert bane Has your question been resolved?

[desert bane]

no

it hasnt

[somber lantern]

Have you looked up the definition of z-score?

[desert bane]

yeah

do you know what stat crunch is

[desert bane]

<@&286206848099549185>

[desert bane]

this is sad

[grim viper]

if it helps morale at all, i'm doing a bunch of research right now on it
(starting with no knowledge on the topic but hey i think i'm getting somewhere)

[ancient lodge]

don't you just use the z score formula

[desert bane]

wtf is x

[ancient lodge]

ex. for part a, $z=\frac{71.5-72.5}{10.5} \approx -0.1$

[wraith dagger]

Civil Service Pigeon

[ancient lodge]

x is the observed value

So for Christina, her test score (or observed value) would be 71.5

[desert bane]

ah..

i see

how do i do it in statcrunch

do you use statcrunch

[desert bane]

what owuld it be for the other

look like

[ancient lodge]

idk you'd have to look it up

but given that doing the arithmetic is one line

just do it

[ancient lodge]

same thing, just copy the different numbers from the question

[desert bane]

what would i replace

[grim viper]

mean = 63.9
alexandria (x) = 64.1
standard deviation = 8.4

refer to this

[desert bane]

the man is diffrent though and so is the standard devation

mean

[grim viper]

oh yeah

just plug those other values in then

[desert bane]

ah i get it

what about the second problem

with percentiles

[ancient lodge]

Find the z-score such that $P(z \leq Z)=0.53$

[wraith dagger]

Civil Service Pigeon

[ancient lodge]

where Z denotes the z-score that makes that work

once you have the z-score, finding the temperature that gives is straightforward

just use this again

[desert bane]

can you do it for a example

[ancient lodge]

well what's the z-score for this

you can prob use statcrunch to find it

[desert bane]

this one

[ancient lodge]

I know what you're talking about

I'm asking you what the z-score for this is

where Z denotes the z-score that makes that work

both b/c it's part of solving it and b/c I don't rlly have a z-score table or a stat calculator on me

[desert bane]

i dont know what a zscore is

what do i put in

[ancient lodge]

a z-score is just the number of standard deviations a given observation is from the mean

ex. a z score of 0.1 would mean that the observed value is 0.1 standard deviations above the mean

[ancient lodge]

https://www.albany.edu/~msz03/sta552/notes/statcrunch_normal.pdf

google is your friend

[cedar kiln]

@desert bane Has your question been resolved?

Channel closed

Closed by @desert bane

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>.
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• 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.

[worn talon]

Why isnt there a minus

isnt f(x)= cosx = -sinx?

[scenic stirrup]

integral of cosine is sine

[worn talon]

yeah but what about the minus

[scenic stirrup]

there is no minus

the derivative of cosine is -sine

i think you got it mixed up

[worn talon]

what if we integrate sinx do we add a minus?

[austere ember]

yes

[worn talon]

Outside the integrals

[worn talon]

Ok so i flip it?

[scenic stirrup]

idk what you mean but the integral of sine is -cosine

[austere ember]

integrals are the opposite of derivatives. d/dx (sinx) = cosx, so integral of cosx = sinx

[worn talon]

So in derviation the minus is cosx = -sinx but in integration sinx = -cosx?

[worn talon]

Got it

thanks

.close

[cedar kiln]

Channel closed

Closed by @worn talon

Use .reopen if this was a mistake.

[cedar kiln]

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.

[frozen hornet]

fuck

just fuck

[flint plinth]

fuck

but why?

[frozen hornet]

i just feel like i wanna die

instead of do this

but here we go

[wintry flame]

Two negatives make a positive

So in reality this expression is

$3/5+1/2$

[flint plinth]

and 1/2 is also known as 2.5/5

[wraith dagger]

MoonCaller27

[frozen hornet]

okay

so we fuck the negatives

got it

[wintry flame]

Simplifying results in 1.1, or 11/10

[flint plinth]

be sure to write that in your solution

[wintry flame]

real

[frozen hornet]

awesome that was the correct answer

i'm not even going to ask how u got it

because who cares

[flint plinth]

not me

[austere ember]

no ask

[frozen hornet]

i won't understand anyway

this one is the current one

two negatives = adding but the answer isn't 18 somehow

[austere ember]

so you have -2 - (-16), and yeah the two negatives mean add

so that becomes -2 + 18

[frozen hornet]

oh

20

[austere ember]

how is that 18?

no

2 + 18 is 20

-2 + 18 is not 20

[frozen hornet]

14

[austere ember]

are you just guessing?

:(

[frozen hornet]

no i already got the answer :c

bc i failed the question

[austere ember]

oh i had made a typo anyway

[frozen hornet]

but let's work the next one together and u can teach me

it's not that i don't want to learn i just get fucking angry/sad

[austere ember]

the best way to think about this is always just moving to the left or right on a number line

[frozen hornet]

so -5 + (-16)

right?

[austere ember]

it's the difference

not the sum

difference means minus, so -5 - (-16)?

[frozen hornet]

oh right

[austere ember]

what do the two negatives become?

[frozen hornet]

positive

[austere ember]

so -5 + 16

two ways to think about this

either rearrange that

-5 + 16 is the same as + 16 - 5

and you can do 16 - 5

or

imagine a number line

-5 is 5 places to the left of 0

adding 16 means moving 16 places to the right

5 of those 16 jumps to the right get consumed to bring your -5 back to 0

the remaining 11 jumps place you at +11

[frozen hornet]

okay that makes sense

so 11

[austere ember]

yes

[frozen hornet]

yay that was right

[austere ember]

[frozen hornet]

so 1200 - 550 + 900

[austere ember]

yes

[frozen hornet]

it probably wants like ...... () or something in the expression huh

maybe around the

900 part

[austere ember]

i don't see why 1200 - 550 + 900 isn't the correct expression

parentheses probably not necessary

[frozen hornet]

lets try it

wow yes finally the common sense wins

it was correct

now 1500 should be the answer

[austere ember]

double check that subtraction

[frozen hornet]

1550 whoops

[austere ember]

right

[frozen hornet]

okay 15

there can't be anything else

well

ofc the -

okayyyyyyyyyy so

[austere ember]

what do you know about the sign of the product of two negatives?

[frozen hornet]

i mean two negatives = positive

that's pretty much all i know

[austere ember]

yes

so mutliplying two negative numbers gives a positive number

then you just multiply the two fractions normally

[frozen hornet]

how do u normally multiply fractions

[austere ember]

multiply the numerators

multiply the denominators

[frozen hornet]

30/70

[austere ember]

yes

maybe your online platform accepts that answer, maybe it wants you to simplify it

[frozen hornet]

the explanation gives a different problem but

this is what it says

i feel like 30/70 is indeed too big

oh

it wasn't

okay

sweet

[austere ember]

you can do that simplification of fractions at the beginning or the end

like you got 30/70 just by multiplying

and you could've looked at it, and divided both the top and bottom by 10 to simplify the fraction to 3/7

or

you could've cancelled out factors when multiplying 5/2 and 6/35 like they do in the explanation

the 6/2 becomes a 3

the 5/35 becomes 1/7

so you get 3/7 that way

[frozen hornet]

multiplying straight across was ez, i don't want to think about the other stuff rn

it's going to get much fucking harder

so i know that power isn't 6 x 2 but 6 x 6 right

because it's 6 two times

but not in the way u would think bc math

[austere ember]

that exponent of 2 means multiplying it by itself 2 times

so (-6) * (-6)

[frozen hornet]

36

[austere ember]

yes

some people make the mistake of saying that (-6)^2 is the same as -6^2

[frozen hornet]

yes

it was tricky for me when he explained it in class

[austere ember]

you understand the difference?

[frozen hornet]

i was like 'dude youre making me wanna fight'

now i understand

can we just make it 9/6

probably not huh

[austere ember]

so the power of 3 means you multiply it by itself three times

first

handle the negative sign

negative times a negative times a negative is what

positive or negative?

[frozen hornet]

positive baby

[austere ember]

negative times a negative is positive

negative times a negative times a negative is therefore positive times a negative

which is negative

[frozen hornet]

okay then fuck

negative

i didn't see the third negative in your question

so 3 x 3 x 3 = 9 but -9

[austere ember]

no

3x3 is 9

3x3x3 is 9x3

[frozen hornet]

ahhhhhhhhhhhhhhh

[austere ember]

so the numerator is 27

[frozen hornet]

-27

yes

[austere ember]

yes

the denominaotr?

[frozen hornet]

2 x 2 = 4 x 2 = -8

[austere ember]

you already accounted for the negative once

so you know that it's 27/8

with either a positive or a negative

[frozen hornet]

okay

[austere ember]

it's easier to just do the numbers first and worry about the sign at the end

[frozen hornet]

that makes sense

okay that was right

hold on i have to get out of my jeans

[austere ember]

dms?

kidding

KIDDING

[frozen hornet]

lmaoooOOOOOOOOOOOOOOOOOOOOOOO

[austere ember]

unless i was fr

[frozen hornet]

i wouldnt blame u

is it really just 40 / 5

[austere ember]

yes

and then just worry about the negative at the end

[frozen hornet]

okay i'm back

had to do ✨self care✨

[austere ember]

um

is that innuendo

[frozen hornet]

LOL no i actually had to wash my face and brush my teeth

silly goose

-8

was correct

[austere ember]

can’t really simplify the fraction

two negatives though

[frozen hornet]

you can't divide 23 by 16

[austere ember]

is that a question

[frozen hornet]

statement

[austere ember]

technically “can’t divide” isn’t true

you can absolutely divide 23 by 16, it’s some decimal that’s a bit under 1.5

[vast vigil]

Yes

[austere ember]

you can’t simplify the fraction 23/16

[vast vigil]

I believe so too

But it can become a decimal

[frozen hornet]

yes but idk what to do w/ decimal

[austere ember]

it looks like they want your answers as fractions

you can’t simplify the fraction 23/16

[vast vigil]

Yea so put

I think

[austere ember]

most simplification you can do here is just cancel the negatives

[vast vigil]

Jus cancel negatuves

Yes

Because negative and negative become a positive

In this case

[frozen hornet]

ah

okay

that was correct

[vast vigil]

Yea

[austere ember]

if a/b = c, that is equivalent to a = bc

if you multiply both sides of the equation by b

right?

if i tell you that 12/3 = 4, that is the same thing as me saying that 12 = 3 * 4

[frozen hornet]

oh

i seee

2 x 3 = 6

[austere ember]

just include your negatives

-2 * 3 = -6

[frozen hornet]

yes

obvi anything divided by 0 is 0 but

in this case -2?

[austere ember]

are you asking what goes in the blank?

they're saying to call it x

[frozen hornet]

yes

oh

[austere ember]

also, when you say a divided by b

the a is the top of the fraction and the b is the bottom

you cannot divide by 0

there are some things that are absolutely illegal in math and dividing by 0 is one of them

having a 0 on the top of the fraction is fine

that's what's happening here

but you said anything "divided by 0" and people generally use that to mean the 0 is at the bottom of the fraction

and dividing by 0 is undefined

[frozen hornet]

in this case it was 0

i tried undef at the end

[austere ember]

let me clarify

0/-2 is 0

dividing 0 by something nonzero is allowed

the answer is always 0

-2 / 0 is undefined

dividing something by 0 is never allowed

in your problem here, they have 0/-2

i'm just saying if it was the other way around it would be undefined

[frozen hornet]

that makes sense

can u explain real numbers and not real numbers

[austere ember]

uh

so complex numbers seem a bit above the level of whatever class this is

if they're still having you add and subtract and stuff, you'll only work with real numbers for a while

did you mean for me to explain something other than real vs not real numbers?

and you're just calling it something different?

[frozen hornet]

no i wanted real vs not real but we don't have to
this is module 1 of the class, i'm redoing it for a makeup exam
idk which module not real numbers is in4

[austere ember]

oh okay if they eventually come up i can quickly explain

you have to understand the hierarchy of the number systems first

you start with the counting numbers

0, 1, 2, ...

when you let these become negative as well, like ..., -2, -1, 0, 1, 2, ..., this forms the integers

the rational numbers are all possible numbers that can be represented as fractions

ratios of two integers

so -1/4, 2/7, etc

there are some other numbers that can't be represented as ratios of integers

like pi, sqrt(2), etc

these are called irrational numbers

if you consider all rational numbers, and combine these with all irrational numbers, together those form the real numbers

any number anywhere on this number line

doesn't have to be on the tick marks, just anywhere on the line

[frozen hornet]

wtf kind of math do u do

[austere ember]

i mean i'm a math major lol

probably more overkill math than most people need to do

now the reason there are some numbers that aren't real (we call these imaginary numbers) is because of this

[snow galleon]

what level of math is this just as a question

[austere ember]

the stuff i'm explaining rn?

[snow galleon]

yeah

[austere ember]

probably algebra/precalculus

[snow galleon]

oh aight

im on trig rn

[frozen hornet]

fucking gross

[snow galleon]

ill do my best to help

[austere ember]

@frozen hornet imagine squaring some number, that number is either positive or negative

when you multiply two positives together, you get a positive. when you multiply two negatives, you get a positive

is it possible to multiply a number by itself and get a negative?

[frozen hornet]

uhhhhhhhhhhhhhhhhh

no?

[austere ember]

not in the real numbers

there is no "normal" number, rational or irrational, that satisfies x^2 = -1

where x is that number

[austere ember]

because of this explanation here

what mathematicians did is defined an imaginary number, called i, defined to satisfy i^2 = -1

it's an imaginary number that gives a negative when being squared

that's where we distinguish between real vs complex numbers

a complex number is of the form a + bi where a and b are real numbers, and i is the imaginary unit

just like the counting numbers are a subset of the integers, and the integers are a subset of the rationals, and the rationals are a subset of the reals, the reals are a subset of the complex numbers

[austere ember]

just the case when b = 0

so there's no imaginary part

[frozen hornet]

oh

i'm sorry i asked

[austere ember]

💀

so if you wanted to solve (_)^2 = -4

you wouldn't be able to fill in the blank with a real number

but if you put 2i in the blank

[frozen hornet]

i'm so convinced that the ppl who created math were on some kind of hallucinogen

[austere ember]

then (2i)^2 = 2^2 * i^2 = 4 * -1 = -4

[austere ember]

some people get super philosophical and say that math wasn't created

just observed, or already existing in the universe

is this math rizz?

[frozen hornet]

this counts as math rizz yes

i am so rizzed rn

coming out of my clothes

[austere ember]

permission to enter dms?

[frozen hornet]

help me w/ this first

[austere ember]

so from left to right

what’s 8/(-4)

remember, just the numbers first, then the signs

[frozen hornet]

2

[austere ember]

then the signs?

positive divided by negative

[frozen hornet]

28

?

[austere ember]

is it positive or negative?

28 is the right numerical part

but the sign

wait

also

i'm slow

it's not 28

8/(-4) = ?

is it +2 or -2

[frozen hornet]

8 / 4 = -2

[austere ember]

great

then (-2) * 7?

[frozen hornet]

-14

[austere ember]

good

[frozen hornet]

soooooooooooooooo

[austere ember]

soooo

[frozen hornet]

so now we divide the 28 by the 14?

[austere ember]

no no

-14 is your answer

your problem is asking what 8 / (-4) * 7 is

that's the same as (8 / (-4)) * 7

which is the same as (-2) * 7

which is the same as -14

[frozen hornet]

ahhhhhhhhhhhh

ugh

@austere ember where am i supposed to start

[austere ember]

division is the same as multiplying by the reciprocal

as in, dividing a fraction by 7 is the same as multiplying that fraction by 1/7

firstly, there's three negatives here

is your answer positive or negative?

[frozen hornet]

negative

[austere ember]

good

now just handle the numbers

dividing by 7 is the same as multiplying by 1/7

so you just need to do 14/3 * 1/7 * 1/6

and then add the negative sign to your answer

[frozen hornet]

so youre saying that 1/7 is 7

[austere ember]

i'm saying that dividing by 7 is the same as multiplying by 1/7

for example, you know that 14/7 = 2

but let's say you didn't know that

14 divided by 7 is the same as 14 times 1/7

which is 14/7

which you could then simplify

i'm saying they're equivalent

likewise, let's say i wanted to know 2 divided by 1/2

how many times can 1/2 go into 2? 4 times

but instead of dividing by 1/2, you can multiply by the reciprocal

flip the fraction

so 2 divided by 1/2 is the same as 2 * 2/1

which is 4

[frozen hornet]

ahhhhhhhhh so you're just saying to make the -7 into a fraction

[austere ember]

yes

and change the division to multiplication

by flipping the fraction

[frozen hornet]

okay so -14/3 x 1/7 x 1/6

and we just multiply straight across?

[austere ember]

yes

[frozen hornet]

so -14/126

[austere ember]

yes

[frozen hornet]

if it was a simp it would be -7/63?

[austere ember]

can you simplify that even more?

[austere ember]

i can be a simp

[frozen hornet]

knew that was coming

i mean maybe idfk

[austere ember]

7 and 63 can be further simplified

63 = 7 * 9

[frozen hornet]

ahhhhhhhhhhhhhhhhhhh

i always just want to simp w/ 2 but it takes long

they didnt ask for simp tho so

okay they do want it

so

2/7?

[austere ember]

where'd that come from?

you got -14/126

you turned that into -7/63

keep simplifying

[frozen hornet]

7/7 = 1, 63/7 = 7

so 1/7?

[austere ember]

63 / 7 = 9

since 63 = 9 * 7

[frozen hornet]

so youre saying the answer is -63/7

[austere ember]

no

i'm saying that 63 = 7 * 9

so -7 / 63 is the same as

-7 / (7 * 9)

and you can divide the 7s

[frozen hornet]

7/9?

or

[austere ember]

try again :(

$\frac{-7}{7 \cdot 9}$

[wraith dagger]

neil

[frozen hornet]

so 7/7

[austere ember]

no

divide both the top and bottom by 7

[frozen hornet]

1/9?

[austere ember]

-1/9

yes

good

[austere ember]

my god

there's more

[frozen hornet]

last one

lmfao

you're doing so good

there's no fractions so fucking yay

so we work from left to right right

[austere ember]

yes

parentheses can't really be simplified here

so you move on to exponents

you have (-6) / (-2) - 5 * 7 + 4^3

what's 4^3

[frozen hornet]

4 x 4 x 16 x 4 = 64 x 4 = 256

?

oo thats only 3 huh

[austere ember]

that's 4^4

yeah you went one multiplication too far

[frozen hornet]

oh lmao so 64

[austere ember]

yes

so (-6) / (-2) - 5 * 7 + 64

now from left to right, division or multiplication

(-6) / (-2) ?

[frozen hornet]

multiplication so 12

wait

ur dividing

bc left to right

[austere ember]

okay i noticed a lot of students make this mistake, where they see the M come before the D in pemdas and assume multiplication has to come first

it's either multiplication or division, whichever comes first, left to right

so in this case moving left to right, the first thing you run into is division

so (-6) / (-2) is?

[frozen hornet]

ahhhhhhhhhhhhhhhh

3

[austere ember]

good