help-27

[misty crest]

you’re correct it’s b

or wait

[grim escarp]

ooh okay

?

[misty crest]

no yes that’s right

they’re both decreasing

[grim escarp]

ok so the stuff from sum of functions also applies to differences?

[misty crest]

i thought it said g was positive AROC for a second

[grim escarp]

😅

[misty crest]

yes

difference is a sum

technically

[grim escarp]

yeah

[misty crest]

think of it like this

do you do know about derivatives at all

[grim escarp]

umm i’ve heard of them

oh i think it’s the slope?

that’s what another of my teachers said

[misty crest]

ahh wait no i’m tripping lol if it’s h=g-f and they’re both decreasing then h’=g’-f’ thus g’ if g’ is negative and f’ is negative then you have a negative-(negative) which could be positive

it’s d because positive-(negative) is always positive

i’m on 3 hours of sleep

forgive me

💀

[grim escarp]

[misty crest]

the difference does matter

[grim escarp]

what’s the ‘ ?

[misty crest]

prime is notation used for the derivative function

which models the slope of that function

thus

if g’ is negative it means the slope of g is negative

does that make sense

[grim escarp]

yeah

[misty crest]

a negative slope minus a negative slope can be positive

but

a positive slope minus a negative slope is always positive

because +-(-)=+

[grim escarp]

ohh

[misty crest]

sorry about that

[grim escarp]

so h could be increasing on 0 to 5?

[misty crest]

could be

might not be

you don’t know

since you don’t have values for the slopes

[grim escarp]

so it’s not100% true

yeah

[misty crest]

but it must be increasing on (5,10)

[grim escarp]

so then the increase from 5 to 10 is guaranteed

from the + - -

[misty crest]

yes because in no instance is a positive - negative not positive

[grim escarp]

ohhh okay

thank you!! i get it now

get some sleep

[misty crest]

lol today was my last day of the summer term and i had to cram all of my writing assignments in

i procrastinated finalizing my essays

and had to stay up all night

[grim escarp]

💀 kinda deserved then

[misty crest]

no fun

[misty crest]

yup

[grim escarp]

hahaha

well thanks again!

.close

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[misty crest]

you’re welcome

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[lapis mirage]

4

[formal valve]

did you try graphing it?

[lapis mirage]

Yes

[formal valve]

do you notice anything about how the triangle looks?

[lapis mirage]

Oh it’s an 90 degree angle right

[formal valve]

yes

[lapis mirage]

How do we figure big the sides on since it’s on an graph

[formal valve]

do you remember the distance formula?

[lapis mirage]

No

He dog left me

Done

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@lapis mirage Has your question been resolved?

[lapis mirage]

):

[flint spire]

$A(x_A, y_A) \hspace{1cm} B(x_B, y_B) \ \ AB = \sqrt{(x_B-x_A)^2 + (y_B-y_A)^2}$

[woven radish]

Emily

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[cerulean rover]

hi, I could use some help with this
these are my very messy notes from my last class. I think I was out of it at the time, so I just wrote stuff down without trying to understand it 😅 now I'm not sure if my confusion is because of sloppily written notes, or I'm missing something. why do I have that the top and bottom were both multiplied by 1/x, but then it looks like the top was multiplied by 1/x^2 in the next step? Is that right? If so, why?

[cerulean rover]

sorry if it's hard to read

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[swift knoll]

What does it mean for a point not to be an isolated point of a metric space X? The definition I am working with is that an isolated point is a point in X such that there exists an r>0 for which B(x;r) \cap X={x}. So is the negation that a non-isolated point is possibly not a point of X such that for all r>0 the intersection is not {x}? Seems kind of ambiguous, but maybe I didn't negate correctly

[jaunty mantle]

it sounds like for non-isolated point, every ball around these points include at least some other points

[uncut crow]

that sounds fine to me

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[swift knoll]

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[unborn rune]

how is this solved?

[unborn rune]

this is a practice exam

[dense lynx]

first find the boundary points (i.e. where x^2(x^2 + 4) = 21)

[unborn rune]

how’d i do that. expanding just gets a 4th degree polynomial

[dense lynx]

it's a 4th degree polynomial yes but notice how everything is written in terms of x^2

so instead of solving for x directly, you first solve for x^2 (i.e. use y = x^2)

[unborn rune]

answers are fishy

taking roots i get x = squareroot(3) and x = squareroot(-7)

but answers have -squareroot(7)

[dense lynx]

remember x is a real number

[unborn rune]

.close

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[unborn rune]

logic of sin. makes sense, but tan doesnt

firstly they’re asking for interval of -1 to 1 for tan, but in Solution they’re using -1 to -1

[upper schooner]

.reopen

[devout snow]

✅

[upper schooner]

(If you close channels and type in them afterwards, you run the risk that they may lock on you)

[upper schooner]

And that’s a typo, and they meant to put 1 on the right there

[unborn rune]

-1 to 1 in tan starts from -pi/4 to 0 then 0 to pi/4 no?

[olive snow]

You right but x is in 0 <= x <= pi so you cant use negative values, hopefully its pi periodic so you just add pi to -pi/4, which gives 3pi/4

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[unborn rune]

.open

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✅

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[unborn rune]

sorry to bother, but when u look at the graph

[unborn rune]

graph

u see at 3pi/4, tan is 1, not -1

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[tranquil flower]

can someone explain why its +3 and not +2

[cold bone]

'coz 2(n+1)+1 = 2n+3

[tranquil flower]

isee

and could you explain how theyve simplified the 4

is it because when you cancel the 2n+1 you're left with 2

and 4^2 is 16

@cold bone

[cold bone]

yeah

[cold bone]

kinda yes

[tranquil flower]

ty

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[pliant axle]

if the equation asymptotes of a hyperbola are y=±2x and it passes through (1,2), what is the equation of hyperbola

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[coral tulip]

How to do this qstn

We have to find x

!status

[devout snow]

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

[coral tulip]

3

[dry rune]

The integral in the que has a formula I think

[devout snow]

@coral tulip Has your question been resolved?

[coral tulip]

Yes i know that

But i am geeting x=φ

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@coral tulip Has your question been resolved?

[restive river]

not sure how

the integral comes out as arc sec of t

and with limits applied, arcsec(x)-arcsec(root 2) = pi/2

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[loud pine]

can some1 help

[devout snow]

@loud pine Has your question been resolved?

[devout snow]

@loud pine Has your question been resolved?

[devout snow]

@loud pine Has your question been resolved?

[loud pine]

@jagged harbor

[jagged harbor]

fiiine

explain what you're stuck on

[loud pine]

(T' ∩ P') ∪ (P ∩ A)

can u show me this as a

3 way ven diagram

[jagged harbor]

who are T, P, and A?

[loud pine]

i send photo wait

[jagged harbor]

how come we don't get any leverage over the top of the page

we can barely see

[loud pine]

its 12

[jagged harbor]

that whole paragraph surely doesn't just say "12"

ah

[jagged harbor]

I understand what you're saying lol

[loud pine]

yeah

[jagged harbor]

ok

each of T, P, and A are pictured

fine

who are T' and P'?

[loud pine]

the region

[jagged harbor]

which region?

[loud pine]

is it not (T' ∩ P') ∪ (P ∩ A

like the photo

[jagged harbor]

I'm asking what T' and P' even mean to begin with

[loud pine]

isnt that like we don't shade in

[jagged harbor]

that sounds plausible

but could you be more specific?

target T' first

who is T'?

[loud pine]

set

[jagged harbor]

lots of things are sets

which set is T'?

[loud pine]

idk sorry

[jagged harbor]

what does it mean for an object to be an element of T'?

[loud pine]

Set 𝑇T: This is a specific set containing certain elements.

[jagged harbor]

ok chatgpt

which elements do they contain?

[loud pine]

T

[jagged harbor]

T is probably not an element

it's a set

[loud pine]

OR IT CAN be object

or am i wrong

sorry for caps

[jagged harbor]

I mean yeah the set T could be an object in your universe

but the specification of what is in the universe isn't important here

I have a set X

there is notation that defines another set X'

what is X'?

[loud pine]

can u tell me

[jagged harbor]

I can't because I'm asking you

maybe you've written it down somewhere but I won't accept a regurgitated definition

I need your definition

[loud pine]

for me it's a set but for other it might be different

complement

[jagged harbor]

lots of things are sets

it's a complement? ok

what's a complement of a set?

[loud pine]

The complement of a set refers to all elements in the universal set that are not in

[jagged harbor]

sketch a universe and a set contained in that universe

show me what the complement of that set is

[loud pine]

wait i meant the ven diagram

[loud pine]

the one i circled

i mean ijs need help because i don't get the U

and how t odo 3way ven diagram

[jagged harbor]

there are many parts to the task of shading the requested region in that venn diagram

we are doing the reasonable thing of picking it apart, piece by piece, and determining whether or not we know what it means

[loud pine]

can u show me what it'd look like

[jagged harbor]

otherwise we won't understand the question

you can show yourself what it'd look like

sketch a universe

denote a set inside that universe

and shade its complement

[loud pine]

can u do it for me

[jagged harbor]

no

[loud pine]

r u aus

[jagged harbor]

also no

[loud pine]

time

oh

is it likethis

[jagged harbor]

what have you shaded exactly?

[loud pine]

well

(T' ∩ P') ∪ (P ∩ A)

(T' ∩ P')

means u only shade everything but the circles

only outside

so i did that

then i did p n a

but left the t

[jagged harbor]

how could we possibly know any of this data if we don't know what T' is?

seriously

do what I'm saying

new universe

one set

complement

go

[loud pine]

is it like this

[jagged harbor]

that's not even your handwriting

[loud pine]

i got that online

yeah ik but is it like that?

[jagged harbor]

I mean... you tell me?

is it a new universe?

with one set?

[loud pine]

yes

[jagged harbor]

and its complement denoted?

[loud pine]

yes

[jagged harbor]

where is its complement?

describe it to me

[loud pine]

the circle

[jagged harbor]

your internet privileges have been revoked

paper

pencil

universe

set

[loud pine]

the one outside the circle

[jagged harbor]

complement

do it

outside the circle?

[loud pine]

yrsh

the box

[jagged harbor]

to be clear

which part is the set A

and which part is its complement?

[loud pine]

a circle

A' COMP

[jagged harbor]

so we're saying that A is the circle

[loud pine]

yes

[jagged harbor]

and A', the complement, is everything outside of the circle

[loud pine]

yes

[jagged harbor]

now,

I'm a new person and we've just met

I can't see pictures

what is the complement of a set?

[loud pine]

the complement of a set is is the set outside of the circle

[jagged harbor]

what circle, I don't see a picture

[loud pine]

If 𝑈 is the universal set, then the complement of 𝑋 is given

[jagged harbor]

you copy pasted that

italicized U's don't even look like that

[loud pine]

i can't get te symbol

[jagged harbor]

it's the letter U, it's on your keyboard, so it's unnecessary

[loud pine]

the complement of the set

it's

where one set

is apart from another set

[jagged harbor]

apart from

explain this

[loud pine]

imagine a unverise and a set

the unverise is ooutside the set

[jagged harbor]

that's probably not what you mean

you want the set to live in the universe

and that there's stuff in the universe outside of the set

but go on

[loud pine]

uh

so

the set

lives in the unverise

they're apart

[jagged harbor]

what do you mean by apart?

[loud pine]

they're in each other but they're seperate

[jagged harbor]

in each other?

[loud pine]

wait

5 mins

i not use google trust

[jagged harbor]

trust

[loud pine]

sorry i'm tryna find a pen to write

im back

[jagged harbor]

welcome back

[loud pine]

so

what i mean by theyr'e in each other

is like

think of a unverise

a set lives in there

but

theyre live there

but they are not apart

A N B for example

a lives in b

but they're seperated

[jagged harbor]

you've used 'in each other' to define 'apart', and 'apart' to define 'in each other'

with some 'separated's floating around

it's funny that you've adopted my 'lives in' however lol

anyway, this definition doesn't make sense because of the circular reasoning

I need a careful definition of what you're talking about

[loud pine]

can i use the words circl

[jagged harbor]

you can use the word set

some sets are circles

every circle can be described as a set

so 'set' is stronger

[loud pine]

Okay

So

Set

Sets are in

Unverified

Universe

Like rectangles for eg

But they’re in each other

But they don’t live with each other set

So

A universe n set like circle

They’re together

But they’re different

@jagged harbor

[jagged harbor]

needs a lot of improvement

do you know the word "subset"

[loud pine]

No

[jagged harbor]

have you verified that the word "subset" has not appeared in your course thus far?

[loud pine]

Yes

[jagged harbor]

alright

it's not required at this stage

but whenever we say a set "lives in" another set, we mean that one is a subset of another

every element of one is also an element of another

e.g. every set is a subset of the universe

[jagged harbor]

scratch this. whenever I say "lives in", that's what I mean. it's not universally accepted vocabulary, and it's not technical

hell sometimes I say an object "lives in" a set if the object is an element of that set

[loud pine]

Okay

[jagged harbor]

it's just

context

[loud pine]

So what should I do now

[jagged harbor]

I would never write that in a paper, only say it casually

you still need to give me a consistent definition for the complement of a set

[loud pine]

Well

Let’s say

A rectangle

That’s your complement

There’s gonna be a circle inside

Which is ur set

[jagged harbor]

stop

what you've just said is that the set, a circle, is inside of the rectangle, which you're calling the complement (presumably the complement of the circle)

is this true?

[loud pine]

Yes

[jagged harbor]

this is not true

a set is not contained in, i.e. a subset of, its complement

a set and its complement have no elements in common at all

so try again

[loud pine]

What do you want me to tell you

And I’ll tell you

For the set

Component

Conplement

[jagged harbor]

give me a functioning definition for the complement of a set

[loud pine]

The complement of a set is basically all the elements like you said that are not in the set.It's like the set's "oppoite in a way, containing everything tgat the set does nyt include

[jagged harbor]

that's a functioning definition, I'll fuckin take it

[jagged harbor]

you're allowed to revisit this image

this image kinda sucks because the shading is inverted from what I'd like

the set A is denoted by everything in the universe with an orange shading

[loud pine]

<<

[jagged harbor]

the complement A' is denoted by everything that is left unshaded

i.e.

everything that is not orange

i.e. everything that is not in the set A

[loud pine]

Okay

Or if u can find a better photo

Cuz I don’t got good ones

[jagged harbor]

it was good enough

next question

[jagged harbor]

on the left there is an upside down U

in the expression T' n P'

what does that symbol denote?

[loud pine]

Intersect

[jagged harbor]

we call A n B the intersection of two sets A and B

what elements does it contain?

[loud pine]

All elements that are present

In both set?

[jagged harbor]

that's correct

[loud pine]

A B

[jagged harbor]

last character is the rightside-up U

I'll just write it as u

[loud pine]

That I don’t know

[jagged harbor]

it denotes the union of two sets

A u B is called the union of A and B

[loud pine]

Okay

[jagged harbor]

have you heard of that?

[loud pine]

Not before

[jagged harbor]

ok

the union of the two sets A and B is the set of all elements present in at least one of A or B

[loud pine]

Okay

[jagged harbor]

an object x in the universe is in the set A u B if and only if x is in A or x is in B

[loud pine]

Okay

[jagged harbor]

so that's all of the symbols present in the task of question 12

I ask that you do the left component first because it's easier to troubleshoot

shade the region T' n P'

[loud pine]

Hold on I need to draw it

[jagged harbor]

go ahead

[jagged harbor]

that's not what I asked

left, not the right

[jagged harbor]

this is somehow worse

the left image, in question 12, depicts two sets T and P, drawn as circles

this image contains three circles

two is not equal to three

we should see two circles here

[loud pine]

I chose the 3 circles one

[jagged harbor]

you're not being serious

I requested the first part, with two circles

[loud pine]

Okay

Like this

[jagged harbor]

those are definitely two sets drawn as circles called T and P

and the number of circles is correct this time, so it's a good start

use a different color in your shading

[jagged harbor]

thanks

this is supposed to be T' n P'?

[loud pine]

Left side

I mean

I did the left side but

[jagged harbor]

hmm

[loud pine]

Didn’t fill it in all

[jagged harbor]

there's probably not a fill tool is there?

I can accept that

[loud pine]

There’s no

Ne

[jagged harbor]

then yes, this is correctly shaded

[loud pine]

Okay

What about the right one

[jagged harbor]

$(T'\cap P)\cup(P\cap A)$

[woven radish]

Flip

[jagged harbor]

I need that for reference

[loud pine]

Ok

[jagged harbor]

I disagree with your shading

how did you go about determining what was shaded?

[loud pine]

?

I thought u said u were accept

[jagged harbor]

this is correct

[jagged harbor]

this is not

[loud pine]

I didn’t see the

‘

I mean I thought I saw it

On the P

[jagged harbor]

word

yeah, I thought I saw that typo at some point

[loud pine]

Yeah same

But

Now that’s it’s different

Do I leave

Hold on I’ll show

@jagged harbor

[jagged harbor]

staring again

[jagged harbor]

I still disagree with this

[loud pine]

Why?

[jagged harbor]

not trying to be silly, it's because there's at least one thing wrong; the first thing I'm currently looking for is the shading in the set P

if you explain how you're getting these solutions, I could give you more feedback

[loud pine]

Trying to shade the part part outside a

I mean

P they is outside T

[jagged harbor]

ok that looks like you've shaded everything and that doesn't feel right either

[loud pine]

Can u help me

[jagged harbor]

you haven't explained how you're getting these yet

[jagged harbor]

still disagreed

[loud pine]

Can u show me

I get it because

I thought it’s meant to overlap

The circle of a

Over lap p and a

[jagged harbor]

alright here's some advice

not like life advice or anything just advice for how to do this kind of exercise

you're tasked with shading the union of two sets, T' n P and P n A

in two separate colors, shade each of these sets first

why? because breaking things apart like makes the whole scope of the problem easier

[loud pine]

Okay

[jagged harbor]

this is T' n P?

[jagged harbor]

in response to this

[loud pine]

Yes

Can u do it for me

[jagged harbor]

nope

[loud pine]

Or tell me if one of the circle is correct

[jagged harbor]

this is not T' n P

[jagged harbor]

this is correct

now in a different color, shade P n A

[loud pine]

@jagged harbor

[jagged harbor]

I disagree with the blue shading

[jagged harbor]

now you're just guessing

[loud pine]

P and A

[jagged harbor]

nope

[jagged harbor]

this is quite wrong

at this rate we're going to go through all of the possibilities

that's not what we want

ah, I was right before, all 2^8 possibilities

[jagged harbor]

no

and let's reclarify

the blue region is meant to be P n A, correct?

[loud pine]

Yes

[jagged harbor]

so why in the world are we shading things that aren't in either of them?

[loud pine]

Are you English

[jagged harbor]

yes

[loud pine]

Like uk Timezone?

[jagged harbor]

this is the same as an earlier response, and is wrong

nah I'm in the US

it's 12 pm

[loud pine]

Ignore blue

Do I just leave it

[jagged harbor]

no?

so you've tried everything and now you're trying nothing?

[loud pine]

There’s no ‘

Before I had ‘ I knew what to do

[jagged harbor]

you want to shade the region that denotes the intersection of the sets P and A

[loud pine]

In a diff colour

[jagged harbor]

uh

can you do it in blue again

and shade more of it

it's hard to see

[jagged harbor]

that's not blue

wait... that might be blue hang on

no they're the same color nevermind

it's too messy

do it a bit more carefully

[loud pine]

To messy,

[jagged harbor]

yeah that's still too messy

color inside the lines please

[loud pine]

There’s no fill

[jagged harbor]

I know there isn't a fill, just stay in the dang lines lol. anyway this is correct

now unfortunately I'd just seen that the white region T' n P is slightly incorrect as well, and it should have some overlap with the purple region

I don't care about this however

shade the union of the two shaded regions in a new color

carefully

[loud pine]

Can I show u in 6 hours

I’m gonna sleep

Don’t close the chat

@jagged harbor is that good with you

[jagged harbor]

the chat will automatically close

[loud pine]

@jagged harbor

I can’t get it more perfect they that

Is that good

[jagged harbor]

that wasn't the task, you just made the shading more dense

where is their union?

[loud pine]

U said there was a problem with the lines

[jagged harbor]

that isn't even what I said

it's your shading and staying inside the lines

the lines did nothing wrong

where is the union of the two sets?

[loud pine]

The blue

[jagged harbor]

are you suggesting that the blue region is the entirety of the union of the two regions, T' n P and P n A?

[loud pine]

A

[jagged harbor]

who the hell is yellow

[loud pine]

Union

In different colour

[jagged harbor]

you're telling me that the union of these two regions has parts of it that are in neither of the regions?

[jagged harbor]

good grief

what is happening now

[jagged harbor]

here's what I'm gonna suggest

let's take a long break

does that sound good?

[loud pine]

I js needed it for my cheat sheet that’s all

[jagged harbor]

let's take a break

[loud pine]

Don’t close this chat yeah 👍

[jagged harbor]

it'll close automatically

[loud pine]

Oh shi

Ight

[devout snow]

@loud pine Has your question been resolved?

[devout snow]

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[scenic surge]

I thought I understood this yesterday when I was going over it but I forgot/didnt understand properly

[scenic surge]

How is S_n finite here if n isnt even bounded

the solution sheet simply said S_n is finite

[torn bane]

s_n is finite since each string has fixed length

and the alphabet is, presumably, finite

[scenic surge]

each string has length n here?

[static ember]

each S_n by itself is bounded yes, you can however choose n arbitrarily large, doesn't change that fact though

[scenic surge]

oh alr now I get it

ty

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[scenic surge]

For this couldnt I create a dfa with states q1, q2

self loop on q1 for any alphabet that isnt "a". For "a" it moves to q2 (finish state) and then theres a self loop on q2 for any alphabet

[devout snow]

@scenic surge Has your question been resolved?

[scenic surge]

@autumn fjord 🙏😭

last one fr

exam in 15 mins

[autumn fjord]

lock in

[scenic surge]

tbh I couldnt understand the solution they gave for this

but would mine be good too?

[autumn fjord]

they are using "a" twice here, the "a" in the set builder notation refers to a word in the language A.

so you can't just have a state that says "the letter a moves to q2"

[scenic surge]

ohhhhh

shit

I misunderstood the question

[autumn fjord]

yeah that was just rather poorly worded.

[scenic surge]

mhm how would you do this then

coz I honestly dont rlly get the soln

[autumn fjord]

okay so we just want to make an NFA from some DFA for the language A.

usually proving some "function" of a language is regular will have us pick an arbitrary DFA for A

[scenic surge]

wdym by "some function"

[autumn fjord]

like S(A) is a new language built out of A

S is a function of the language

so you input A and get a new language out.

[scenic surge]

ah

[autumn fjord]

if you want to prove that S(A) is regular, you don't have much to go off of except that there's a DFA for A

(and the fact that there's a DFA for A is usually what you want to use)

now, how do i check that there's a substring x of w such that x is in A

well, i just ignore some amount of the letters in the string

but ignoring a letter is a self loop

[scenic surge]

wait why? shouldnt I ignore the letters that arent in x?

[autumn fjord]

we want to check to see if there is such an x

we don't know anything about the potential substring

we just check to see if, ignoring some of the letters in the input string w, we get a string in A

[scenic surge]

ohh I see

[autumn fjord]

that's what it means to have a noncontiguous substring

[scenic surge]

wait Im kinda lost one sec

so w is the string. We want to check if there exists a substring within w that is in A right

[autumn fjord]

yeah

so like we want to make an NFA that's based on the DFA for A, that takes in w, and outputs whether the thing you said holds

[scenic surge]

right

and then

oh

alr

makes sense

tysmmm

[autumn fjord]

🫡 lmk how it goes #computing-software

[scenic surge]

https://tenor.com/view/black-guy-whtie-and-black-cry-praying-looking-up-gif-553441503240360994

bet

.close

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[devout snow]

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[timber estuary]

i need helpp

[timber estuary]

is the answer 36pie or we have to simplfy pie too?

<@&286206848099549185>

[sick wagon]

lemme search my notes

[acoustic leaf]

it's spelled pi, not pie

[timber estuary]

o

mb

lol

[acoustic leaf]

it says "express your answer in terms of pi", so you should leave pi in

[timber estuary]

so 36pi?

pi=symbol

[acoustic leaf]

yes

[timber estuary]

so this?

[sick wagon]

I can’t find notes

I’m so lost now 😭

[timber estuary]

😭

[drifting hearth]

did this answer work?

or have you not tried it yet?

[timber estuary]

o i have to finish all to submit

[drifting hearth]

that answer looks correct enough to me

[timber estuary]

ty

.close

[devout snow]

Channel closed

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[timber estuary]

guys'

another help

[drifting hearth]

use .reopen

[timber estuary]

.reopen

[devout snow]

✅

[timber estuary]

then proportional is 50 mile per hour

what do i write 😭

[drifting hearth]

do you think it's a proportional relationship?

[timber estuary]

yes

[drifting hearth]

why?

[timber estuary]

because

the line is straight

and it start at (0, 0)

[drifting hearth]

another thing to note is that both axes also increase linearly

instead of exponentially

[timber estuary]

btw

Short-Response: 1 point each. Be sure to write the answer only.
Extended-Response: 2 points each. Be sure to include math vocabulary in your explanation.

directions

[timber estuary]

?

whats that mean

[drifting hearth]

instead of going like 10, 100, 1000, it's going 1, 2, 3, 4, 5

[timber estuary]

yea in time

so what do i write for answer?

[drifting hearth]

the things you mentioned above should be good enough

instead of straight line, maybe constant slope

and crosses through the origin

that should be good enough

[timber estuary]

can u pls write me a good sentane use vocabulary words

pls

pls

pls

[drifting hearth]

that's ur job buddy

[timber estuary]

.

"the graph represents proportional relationship because the starting point is in (0, 0) and it has constant slope. The propotional relationship is 50 miles perm hour"

good enough?

[drifting hearth]

ur proportional relationship is wrong

it's not 50 mph

[timber estuary]

it is 50mph

[timber estuary]

wat is it then?

[drifting hearth]

check ur calculations

we don't hand out freebies here

[timber estuary]

look

the point is on 1 and 50

1 is hour

50 is mile

50mph

i think u made mistake

[drifting hearth]

it is not on 50

wait nvm that is 50

[timber estuary]

then wat?

[drifting hearth]

mb gang

[timber estuary]

.

broski

.close

[devout snow]

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[timber estuary]

guys

[timber estuary]

help

my work

w handwriting

what do i write for the answer

|<@&286206848099549185> |

[trim marsh]

Don't ping

Look at step 2

[timber estuary]

mb

i forgot step 2

but it alr

[trim marsh]

The first part

(3+2)(-20-25) u think that's right?

[timber estuary]

he did wrong not me

step 2 is incorrect

[trim marsh]

Yeah

So what's ur problem now

[timber estuary]

mean all other step in correct

[timber estuary]

idk what to write for answer

[trim marsh]

Only step 2 has a mistake

[rigid gorge]

They only asked for the first one

[trim marsh]

Just simplify the expression how you usually would

[timber estuary]

do i say that his second step was incorrect and i tell them how to solve then expression?

[trim marsh]

Yes

[timber estuary]

bruh

it will take forever to explain 😭

[trim marsh]

You can't simplify ab + cd as (a+c)(b+d)

[trim marsh]

Forever

[timber estuary]

yess

[trim marsh]

I just did

[timber estuary]

can u pls write me a sentace

pls

[trim marsh]

I'm not gonna give you the answer

[timber estuary]

i know the answe thp

[trim marsh]

I explained to you how it works now u write it urself

[timber estuary]

😭

[rigid gorge]

"The mistake in step two is incorrect use of distributivity" maybe

Doesn't read right

[timber estuary]

do i have to give then the real answer?

[rigid gorge]

Yes

[timber estuary]

.

and btw

is my work even corect?

[timber estuary]

.

[rigid gorge]

Seems correct

Can check with a calculator

[timber estuary]

how will i show work on google form-_-

[rigid gorge]

Ig paste the picture you took

[timber estuary]

u cant

[rigid gorge]

Is it a slot to enter an answer?

[timber estuary]

u just type

[rigid gorge]

You could write with equals or steps like they did

2*(-20)+3*(-25)+100+200=-40-75+300=something...

Or just write the answer with no work

Might be acceptable

[timber estuary]

good idea

lol

.close

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[bold kraken]

It's all about Quadratic formula and using extracting square roots

And factoring

[elfin atlas]

yes, the first five are literally basic definitions though. should be able to do them at least

[bold kraken]

I kinda forgot what term is b on the fourth question

[elfin atlas]

I think they call it a middle-number, not so important to know though dw

[elfin atlas]

I hope your bio is a joke man

[bold kraken]

it's a joke dw

On the test 2

[elfin atlas]

fair enough 😭

which one do you not understand in the test 2, you just need to apply the quadratic formula btw

[bold kraken]

The 4-5th question, on the second picture, I kinda forgot how to extract the square roots

[bold kraken]

4-5

[elfin atlas]

oh okay

[woven radish]

penguin

[elfin atlas]

@bold kraken get it now? knowing a^2 - b^2 = (a+b)(a-b) should do it

[bold kraken]

yeah, kinda

[elfin atlas]

nice so d = 10/3 or d = -10/3

[bold kraken]

Hey man, thanks for the help

Unfortunately, I passed my quiz because it has a time limit

And it was unfinished

Although, It's okay

[elfin atlas]

no worries man, good luck for the next quiz 💪

[bold kraken]

alright

.close

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[native basalt]

here again I am to unrust my brain I need help I compleatly forgot how to do this

[winter torrent]

do you have some kind of formula for stdev of Y?

[native basalt]

mhh

well I know that VAR(Y) is E(Y^2)-(E(Y))^2

[winter torrent]

yep, and do you have a formula for E(X) of a continuous rv

?

[native basalt]

is it some long formula or is it something I should know ?

[trim bronze]

You should know its definition

For continuous rv

[native basalt]

well E(X) is like the mean so its all of the numbers added up together divided by the amount of numbers

is that what you mean?

[trim bronze]

No

[winter torrent]

that's (sort of) true for a discrete rv

[native basalt]

yeh I cant find the formula

[trim bronze]

It’s the first one in the question

[native basalt]

oh thats what the mean is?

[winter torrent]

that's the expected value

[native basalt]

so the first one Is E(X) and the second one is E(X^2) So i need to do 1040-16^2 and then root the answer ?

because id get the variance if I didnt root?

[winter torrent]

yep

[devout snow]

@native basalt Has your question been resolved?

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[lost laurel]

So to solve this I first compute the rank. And then compare the rank to the number of variables, right>

[acoustic leaf]

you are trying to solve the equation
[ x_1 \vb a_1 + x_2 \vb a_2 + x_3 \vb a_3 = \vb y ] which can be expressed as a system of linear equations

[woven radish]

cloud

[lost laurel]

yes

So I get a 3 by 5 matrix

Namely

$\begin{bmatrix}
-1&3&1&|1\
2&1&1&|2\
0&2&1&|4\
1&0&1&|0\
\end{bmatrix}$

this would be the coefficent natrix

[woven radish]

f(why am i here )= I don't know

[lost laurel]

would be the augmented matrix

I now convert this to RREF

right?

[misty crest]

well this isn’t a 3x5

[lost laurel]

my bad

[misty crest]

but yes this is how you’d do it

[lost laurel]

Now I solve for each varibale

right?

[misty crest]

putting it in RREF should do that for you

what did you get

[lost laurel]

I'll do that now.

Was wondering if there's a shorter method

tbh, I don't even need a matrix here

I know x=-z

yeah

thanks !

[elfin atlas]

I get that this needs to be solved with a specific method but x = -z makes it so easier

[
\left(\begin{array}{@{}ccc|c@{}}
-1 & 3 & 1 & 1 \
2 & 1 & 1 & 2 \
0 & 2 & 1 & 4 \
1 & 0 & 1 & 0
\end{array}\right)
]

[woven radish]

penguin

[lost laurel]

Yeah

Thanks!

[elfin atlas]

yeah better to write latex code this way for such problems

[lost laurel]

x=-z reduces it to LE2V

[elfin atlas]

but in the exam, you'll need to convert it to RREF completely. no finding ways to avoid them or be ready for someone to deduct points for no reason 🤷

[lost laurel]

I'll ask my prof

Thanks

.close

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[radiant anvil]

hiiiiiiiiiiiiiiiiiiiii

[vivid stream]

Can someone please help me understand how the two highlighted expressions are equivalent?

Hi!! Thank you

[radiant anvil]

r-s is a real number. real numbers squared is non negative

so the abs can be removed

[vivid stream]

I’m a bit confused but not sure if it’s just a notation thing. Like why the change between || and ()

[acoustic leaf]

this is a vector equation

[radiant anvil]

oh true

[acoustic leaf]

for any vector, for example v, we have that |v|^2 = v * v (for the dot product)

[vivid stream]

Thanks you. I’m thinking on this. Don’t fully understand but not sure exactly what I don’t understand 😂

[radiant anvil]

x dot y=|x||y| cos theta

in this case theta=0 and cos 0 = 1. so when when do dot product on the same vector we can ignore the cos

[vivid stream]

Why is this not accurate?

[radiant anvil]

dot product isnt defined on numbers

[misty crest]

dot product is between two vectors

[radiant anvil]

yea

well dot product is kinda defined on numbers trivially as normal multiplication ig

[misty crest]

what you just sent is equivalent to a scalar dot scalar

[vivid stream]

So what’s the equation that gives the relation between magnitude and dot product?

[misty crest]

which is not an operation

[misty crest]

^

[radiant anvil]

wdym?

[vivid stream]

Maybe do y’all have a search recommendation where I could read up on this to understand it? Just confused about that jump between magnitude squared to dot product

[vivid stream]

Wondering if there’s an equation that is used to derive this jump between magnitude and dot product

[radiant anvil]

its how dot product is defined

with theta being 0

so cos theta is 1

[acoustic leaf]

for any two vectors $\vb x$ and $\vb y$ we have [ \vb x \cdot \vb y = \abs {\vb x}\abs{\vb y} \cos \theta ] if we take the dot product with itself, the angle must be 0: [ \vb x \cdot \vb x = \abs{\vb x}\abs{\vb x} \cos 0 = \abs{\vb x}^2 ]

[woven radish]

cloud

[vivid stream]

Thank you!!!!

Thank you all!

.close

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[hollow walrus]

may someone help me with part b

[spiral geyser]

it's possible to find the solution without actually calculating the grid

all you need is the total sum

and each square of the same size contributes the same amount to that sum

[hollow walrus]

how do you find total sum

[hollow walrus]

and this

[radiant anvil]

maybe u can start by writing the value of a generic square in a 10 by 10 grid