help-0

[bleak geyser]

Can u give a hint

[wanton umbra]

still factor it and look at the signs

of y at different x

[bleak geyser]

$\frac{x(x+2) + 4(x+2)}{x-2} <= 0$

[ocean seal]

ahaan

[bleak geyser]

It is not the same

[wanton umbra]

it is

[bleak geyser]

How

It denominator is x-2

Numerator is x+2

[wanton umbra]

use distributive

[vale wigeon]

nobody said things would cancel out

also \leq for ≤

[bleak geyser]

Aight

[bleak geyser]

,rotate

[bleak geyser]

,rotate

[bleak geyser]

,rotate

[bleak geyser]

I’m stuck here

[vale wigeon]

,rcw and ,rccw exist

ok, so

[bleak geyser]

I’m not familiar with them

[vale wigeon]

rotate clockwise and rotate counterclockwise resp.

both by 90 degrees

anyway:

answer me this, either YES or NO:

have you solved rational inequalities before?

[bleak geyser]

Yes

[vale wigeon]

ok

have you solved them by way of sign tables and/or wavy curve method?

[bleak geyser]

No?

[vale wigeon]

ok then how did you solve them

[bleak geyser]

I just found x by moving it alone

They were easy before

[vale wigeon]

i said rational inequalities

you didn't think to ask what that meant?

[bleak geyser]

Oh like this one

[vale wigeon]

,rccw

[vale wigeon]

ok so then i see you made a number line

and on it you marked the points where each factor (here x-3 and x+2) changes sign

yes?

[bleak geyser]

Yes

[vale wigeon]

ok then do the same for your current problem.

you'll have more points.

[bleak geyser]

Oh that’s it?

[vale wigeon]

but the principle is the same still.

[bleak geyser]

So the points are

2 and 4

-2 and -4

?

[bleak geyser]

?

[vale wigeon]

no, the list of points {-4, -2, 2, 4} is wrong

your inequality is $\frac{(x+2)(x+4)}{x-2} \leq 0$

[ocean seal]

Ann

[bleak geyser]

Yeah

So it’s 4 2 -2 and -4

[vale wigeon]

are you 100% sure about all four of these points?

"yes i am 100% sure" / "no let me think again" / "fuck you i won't answer"

[bleak geyser]

Oh

I see

ISNT IT THIS

[vale wigeon]

i see you've chosen the "fuck you i won't answer" option.

[bleak geyser]

I picking yea I’m sure

🫠

[vale wigeon]

ok, so then... tell me which factor gives us the point 4, please.

[bleak geyser]

I didn’t mean it that way

[vale wigeon]

BRUH WTF

[bleak geyser]

NO LISTEN

IDK HOW TO MAKE THE SIGN GO UP

[vale wigeon]

YOU ALSO DK HOW TO ANSWER QUESTIONS CLEARLY

[bleak geyser]

I MEANT APPROXH TO -2 and -4 FROM LEFT AND RIGHT

[vale wigeon]

WHEN PRESENTED WITH 3 OPTIONS YOU MANAGE TO PICK THE WRONG FUCKING ONE

"are you 100% sure about these"

simple question

if you arent say you arent

[bleak geyser]

ok in my defense

[vale wigeon]

otherwise its just impossible to communicate

YOU DONT HAVE A DEFENSE

[bleak geyser]

I got scared of u

[vale wigeon]

what were you afraid i'd do?

[bleak geyser]

And when we don’t know what to say

We say Si

[bleak geyser]

Idk

Anyways

[vale wigeon]

so you were scared of me for no reason i see.

of course.

i have a feeling that i might know exactly why you were scared of me.

[bleak geyser]

Why?

[vale wigeon]

cause im a trans woman who was something other than 100% gentle and nice towards you.

subconscious crap.

[bleak geyser]

I didn’t even know u were trans

[wanton umbra]

not like this...

[bleak geyser]

💀💀💀

[vale wigeon]

ok so then if it's not Scary Tr*nny then what was scary about me exactly

like jeez

if you keep getting scared every time ppl help you how tf do you expect to get any help

[bleak geyser]

u saying the fuck again and again made it look like h were mad

At me

For not understanding

[vale wigeon]

not understanding is not something i get mad at

[bleak geyser]

Oh ok

[vale wigeon]

what i do get mad at is muddled communication.

[bleak geyser]

Sorry

[vale wigeon]

when you say one thing and then less than a minute later say the complete opposite.

as if your words have no value.

[bleak geyser]

I got the answer btw 🫠

[vale wigeon]

or you force me to decide for myself which of the things you say i can trust, and which i can't

and it is not just me for sure

[bleak geyser]

Mb

Mb

Is this correct

[wanton umbra]

,rccw

[bleak geyser]

This is the new question

I got

[wanton umbra]

wrong

[bleak geyser]

,tex $-1 \geq 0$

[wanton umbra]

,rccw

[ocean seal]

Something went wrong!

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ahaan

[bleak geyser]

Seriously?

,calc (-5+2)(-5+4)/(-5-2)

[ocean seal]

Result:

-0.42857142857143

[wanton umbra]

,calc (-3+2)(-3+4)/(-3-2)

[ocean seal]

Result:

0.2

[bleak geyser]

Oop I got it

,calc (-1+2)(-1+4)/(-1-2)

[ocean seal]

Result:

-1

[keen plinth]

@valid mortar

[undone jay]

hey I have a question. is cos^2(2x) equal to (cos^2 (x) - sin^2(x)) ^2?

[wanton umbra]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[valid mortar]

Wow that's horrendous

Thanks

I'll give the bots a quick restart

[keen plinth]

[wanton umbra]

oh no, I broke smth

[valid mortar]

No no, that's Discord breaking lol

[wanton umbra]

so what is it?

and why was it wrong

[bleak geyser]

.close

[lone heart]

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[sly yarrow]

is this a function

[sly yarrow]

<@&286206848099549185>

[alpine sable]

no

[devout crest]

I wouldn't consider to be one

[chilly idol]

Nope it fails the vertical line test

[unkempt robin]

Do any parallel lines to the y -axis intersect the graph twice (or more)?

[opal jolt]

what is your definition of function

[mellow grail]

Looks like a horizontal parabola so seems like a polynomial function to me

[lone heart]

@sly yarrow Has your question been resolved?

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[vague gazelle]

!help

[vague gazelle]

uh so

tell me if this is right

nvm idk

pls help

1. -3s² + 9s

[chilly idol]

We need to take out the common terms here, a variable and a coefficent

[vague gazelle]

s?

and 3

[chilly idol]

Yes s and...

good

But I would prefer to take out -3

[vague gazelle]

oh

[chilly idol]

So that we would not need to deal with a negative in front of the s variable

[vague gazelle]

sooo -3s (s + 3)??

or no

or is it negative

[chilly idol]

Well your partially correct it should be (s-3)

[vague gazelle]

ohhhh

alrr

what about in no. 2

common term is 5?

and t?

[chilly idol]

Same thing, take out a coefficent and a variable

[chilly idol]

Well we should take out a -5

[vague gazelle]

why

[chilly idol]

Its -10t^2 +5t

To keep the 10^t2 positive

lets say we did take out 5t instead of -5t

hypothetical scenario here

If we took it out we get 5t(-2t +1)

We have a negative in front of 2t

[vague gazelle]

sooo, -5t (-1 + 2t)

?

[chilly idol]

Yes

[vague gazelle]

ooohh

what about in no 3

[chilly idol]

You could reorder (-1+2t) but its your choice and preference

Anyways 3.

We have x^2 -10x+21

[vague gazelle]

yes

[chilly idol]

The best way to do this is to do the grouping method

[vague gazelle]

oo

[chilly idol]

In the group method you take 21 and find its multiples
1, 21
3, 7

[vague gazelle]

that will sum up 10?

[chilly idol]

Yes but we need a -10

[vague gazelle]

ok so how

+7 -3?

[chilly idol]

We put a negative sign in front of 3 and 7, gets us -3 and -7

[vague gazelle]

oh

[chilly idol]

-3 + (-7) = -10

[vague gazelle]

ohhhhhh

ok ok

how should i write it

[chilly idol]

So now we take -3 and -7 and split the -10 into that

[vague gazelle]

ok ok

[chilly idol]

So we split -10x into -3x and -7x

We get x^2 -7x -3x+21

You could switch the -7x and -3x to make it easier but i beleive you will get same answer

[vague gazelle]

ok so u gonna factor it?

[chilly idol]

But for simplicity's sake I will take x^2 -3x -7x+21

yup

We use the previous skill we learned and factored it

[vague gazelle]

(x² - 3x) (-7x + 21)

hm

sooo

u gonna take out x? on the first parenthesis

[chilly idol]

Yes now time to factor

yup

[vague gazelle]

alr hold on

soo in the second

-7?

[chilly idol]

yup

[vague gazelle]

ok

x (x - 3) -7 (x - 3)

[chilly idol]

We bring it all together and we have x(x-3) -7(x-3)

good

[vague gazelle]

niceee

whats next

[chilly idol]

Since we have (x-3) two times we can take only one of them and combine the x and -7
It would be (x-7) (x-3)

I'll reword this better

[vague gazelle]

ohhh

[vague gazelle]

is it possible that you get 1 term two times

all the time

[chilly idol]

Like (x-5) (x-5) ?

[vague gazelle]

yup

[chilly idol]

well yeah it is possible

[vague gazelle]

but what are u gonna do if u didnt

[chilly idol]

This would be the difference of squares

[vague gazelle]

oh

like (x-5)²?

[summer lance]

Can someone help

[chilly idol]

yes

[chilly idol]

Open your own help channel #❓how-to-get-help

[vague gazelle]

or (x² - 5²)

[chilly idol]

Yeah you could also write it that way

[vague gazelle]

alr

moving on

[chilly idol]

4. 4r^2 +20r+25

Same process as before except we multiply 4 by 25

The coefficent of the first variable and the last constant

4 times 25 should get us...

[vague gazelle]

100?

[chilly idol]

yup

what are the multiples of 100? (numbers that multiply to 100)

[vague gazelle]

1/100
2/50
4/25
5/20

[chilly idol]

yes good

Hold on

[vague gazelle]

ok

would be the factors are 5 and 20

[chilly idol]

Actaully I found out a better way and easier way

[vague gazelle]

ok

what is it

[chilly idol]

Just split the 20r into numbers that can be factored

[vague gazelle]

4/5

2/10

[chilly idol]

Preferrably it would be...

Wait im doing this wrong

[vague gazelle]

oh lol

okay

[chilly idol]

Give me a minute

[pseudo schooner]

ummm sorry to interrupt I just need to go back in this convo
btw why and how did u cancel the cm^3 in the final answer?

[chilly idol]

I get it

I understand why its been a little weird

[chilly idol]

Lets go back to this

We forgot one pair of multiples of 100

Which is 10,10

@vague gazelle You there?

[vague gazelle]

yup

[vague gazelle]

oh alr

10+10 = 20

[chilly idol]

Yup

Same processs as last time

Split the 20 and factor it out

[vague gazelle]

+10 +10

[chilly idol]

remember the x

+10x +10x

[vague gazelle]

4r² + 10r 10r + 25

oh

[chilly idol]

The x is apart of 20x

[vague gazelle]

no x

[chilly idol]

Yes x

[vague gazelle]

uh ok

[chilly idol]

We need the x with the 10

[vague gazelle]

why?

the variable is r tho

[chilly idol]

10 + 10 = 20x

oh

[vague gazelle]

XD

[chilly idol]

I refer to x as the r variable

:/

[vague gazelle]

ok soo

[vague gazelle]

factor time

[chilly idol]

yup

[vague gazelle]

2r (2r + 5) 5 ( 2r + 5)

thereee

[chilly idol]

good

[vague gazelle]

finallyyy

ok 5th

[chilly idol]

well wait

you forgot one step

[chilly idol]

Remember this?

[vague gazelle]

yup

ihh

alr

(2r + 2r) (2r + 5)

[chilly idol]

We will have (2r+5) (2r+5) which equates to (2r+5)^2

[chilly idol]

How did you get (2r + 2r) ?

[vague gazelle]

do u need to write (2r + 5)²

[chilly idol]

yeah fully factorized form

[vague gazelle]

uhh cuz, same terms

hd on

nvm

lol

[chilly idol]

ok

[vague gazelle]

xD

[chilly idol]

So thats gonna be your answer

[vague gazelle]

okkkkk

tyyyyy

tysm

really helps

[chilly idol]

5. 2x^2+3x-14

[vague gazelle]

ok

2x -14

[chilly idol]

🙂 im glad it help

[chilly idol]

Yes

[vague gazelle]

-28

[chilly idol]

ignore the negative

we only want the multiples

[vague gazelle]

ok

[chilly idol]

So what would our multiples be?

[vague gazelle]

-7 +4

?

[chilly idol]

Yup

[vague gazelle]

or +4 -7

nvm

-4 +7

this

[chilly idol]

We want a +3x

[chilly idol]

So it would be this one

[vague gazelle]

ok

(2x² - 4x) (7x -14)

[chilly idol]

Remember the x

[vague gazelle]

oof

yeah

mb

[chilly idol]

Its ok

[vague gazelle]

2x(x - 2) 7(x - 2)

[chilly idol]

good

[vague gazelle]

(2x + 7) (x - 2)

hmm?

[chilly idol]

Yay you did it

[vague gazelle]

YAYYYYY

[chilly idol]

Thats the farthest we can go

[vague gazelle]

niceee tytytyyyyy

[chilly idol]

Your welcome Have a great day

The command for closing channel is .close btw

[vague gazelle]

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[umbral portal]

To start off I first wrote them with the same base

Such as: 3⁷*(3²)^x= 48 × (3²)^y

So 3^7+2x=48×3^2y

however this is where im stuck

[minor needle]

3^2 isn't 6

[umbral portal]

that is true

[minor needle]

so how did you rewrite left side as 3⁷*(3²)^x

[umbral portal]

thats a mistake on my part

So 3⁷×(3*2)^x ?

[minor needle]

yes

that might be

[umbral portal]

(3^7+x)*2^x

(3^7+x)*2^x =48×3^2y

thats where im stuck

[thick lynx]

How did you go from 3^7 * (3*2)^x to that?

[umbral portal]

laws of indices: (3*2)^x=3^x * 2^y

same base: 3^x*3⁷

= 3^7+x

[thick lynx]

Ah, you mean 3^(7 + x)

[umbral portal]

ye

difficult writing on mobile

[thick lynx]

We have that [3^{7 + x} \cdot 2^x = 48 \cdot 3^{2y},] so [3^{7 + x} \cdot 2^x = 2^4 \cdot 3 \cdot 3^{2y},] so [3^{7 + x} \cdot 2^x = 2^4 \cdot 3^{2y + 1}]

[umbral portal]

yes

[thick lynx]

Thus, I'd say we need 7 + x = 2y + 1 and x = 4

[umbral portal]

whys that

why does 3^(7+x)=3^(2y+1)

[hard island]

Are you familiar with prime factorizations?

[umbral portal]

I might be

unsure tbh

[hard island]

It's where we write a number, say, 28, as a product of only primes (7 * 2 * 2)

[umbral portal]

yes I am

I actually use it a lot

[hard island]

Ah, that's good

Since 2 and 3 are both primes, we could consider each side to be prime factorizations:

The number on the left needs to have

• 7+x number of 3's
• x number of 2's

and the number on the right needs to have:

• 4 twos
• 2y+1 number of threes

[thick lynx]

I assume x, y need to be integers

There are infinitely many real solutions

[hard island]

Yeah, this method assumes integers

[umbral portal]

so you assume 3^(7+x)=3^(2y+1)

[hard island]

Yep

[umbral portal]

ah ok ok

[thick lynx]

After assuming that x, y need to be integers, it follows that 3^(7 + x) = 3^(2y + 1)

(Because of what Kiako said)

[umbral portal]

yeah but why doesnt 2 have a role in this

[thick lynx]

It does

2^x = 2^4

[umbral portal]

why isnt that included in the 3^(7+x)=3^(2y+1)

[thick lynx]

That gives you two equations with two unknowns

So you can solve for them

[umbral portal]

and y=5?

alr thanks for the help guys

[thick lynx]

Though did it really ask only for integer solutions?

[thick lynx]

it's probably clear from the context of your course (what you did earlier/...)

[umbral portal]

yeah I can see some correlations

but this is the first instance where I have automatically assumed two equations

anyways thanks for the help

.close

[lone heart]

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[vague fox]

help me

[vague fox]

solution like this

[digital basalt]

X+X

[vague fox]

can you make a solution in more detail

pls

[vague fox]

👉 👈

[lone heart]

@vague fox Has your question been resolved?

[vague fox]

.close

[lone heart]

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[vague fox]

.close

[lone heart]

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[alpine sable]

I’m kinda confused about this whole thing

[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

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[tribal monolith]

where, a(t) is the acceleration vector, κ is the curvature, and N(t) is the unit normal vector.

[tribal monolith]

how could i show this i'm not sure where to start

i tried starting by swapping T(t), N(t) and k[v(t)]^2 in terms of r' and v' and stuff but i get stuck

[tacit arch]

https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/2%3A_Vector-Valued_Functions_and_Motion_in_Space/2.6%3A_Tangential_and_Normal_Components_of_Acceleration

[tribal monolith]

sick

.close

[lone heart]

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[low nymph]

I’m trying to solve the problem: Find all polynomials p(x) such that p(x^n) p(x)^n for all natural n

[low nymph]

here is my solution

is this correct? it would be helpful if someone can verify this for me or find a counter example

[lone heart]

@low nymph Has your question been resolved?

[lone heart]

@low nymph Has your question been resolved?

[lone heart]

@low nymph Has your question been resolved?

[lone heart]

@low nymph Has your question been resolved?

[lone heart]

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[full nimbus]

How me do this?

[median oar]

Draw a diagram

[full nimbus]

I don't really know how

I just need to understand how I get to answer

[median oar]

To get to answer you need to draw a diagram

[full nimbus]

yeah so how do I do that?

[fair goblet]

hyp isn't needed

you know one leg is 5

[median oar]

So first you draw 2 dots

That’s tony and jay

Then you draw a line connecting the 2 dots

Label it with 5 for 5 miles

Because the question tells you tony and jay are 5 miles apart

[full nimbus]

Here

I solved for one side with law of sine, I'm not sure why I did that tho

cus I don't know how to get the altitude part

[median oar]

Well think about this

Consider the left triangle

If we drew a vertical height line, it’s perpendicular to the base

So it makes a 90 deg angle

[full nimbus]

inverse sine times the side

[median oar]

We also know the left angle is 57

[median oar]

Yep

[full nimbus]

did you get 2.53 if you round?

hello?

[lone heart]

@full nimbus Has your question been resolved?

[lone heart]

@full nimbus Has your question been resolved?

[sacred vine]

How do I know which to subtract by without the graph

[full nimbus]

why are you here?

.close

[lone heart]

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[full nimbus]

Is this diagram right?

[jagged cobalt]

not quite

[full nimbus]

cus I don't really understand what south 76 east means

[jagged cobalt]

you have that one right

its the other one

[jagged cobalt]

it means you start south, then rotate 76 degrees towards east

[full nimbus]

what does 26 miles due east mean?

[jagged cobalt]

26 miles away in the eastern direction

[full nimbus]

so its the other way

[jagged cobalt]

no its fine

its more about where you marked the angle 35

[full nimbus]

where would it be then?

[jagged cobalt]

if you do a dashed line directly south from z, then its the angle between that dashed line and your solid one

so on the opposite side of the line to where it is now

youve drawn west 35 south rather than south 35 west

[full nimbus]

what?

so its on the outside of the triangle?

[jagged cobalt]

yes

[full nimbus]

ohhhhhhhhhhhh

so then I need to do 180 - 35 to get the inside angle right?

[jagged cobalt]

90-35

[full nimbus]

thats what I ment

woops

I do that right?

law of sin

oh wait

[jagged cobalt]

where does the angle 26 and side length 111 come from

[full nimbus]

I'm dumb

I just saw that

its the other way around

sin of 111 over 26

[jagged cobalt]

that works

[full nimbus]

did you get 16.76?

if you round

[jagged cobalt]

26/sin(111)=x/sin(55) x=26sin(55)/sin(111)

i dont believe so

[full nimbus]

I put in a wrong number

I got 22.81?

[jagged cobalt]

seems valid

[full nimbus]

ty 😁

.close

[lone heart]

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[crisp hill]

how does this work

[crisp hill]

oh

i c

.close

[lone heart]

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[full nimbus]

how do I?

[tacit arch]

Draw a picture

[full nimbus]

I did, its really bad

[tacit arch]

There's a theorem about lengths of diagonals in parallelograms

Did you learn any in class

[full nimbus]

I don't know that one

this question is about law of sin or law of cos

[tacit arch]

https://youtu.be/At8nkZ37Q3E?si=8TCJJN5UqLBzsSbs

Oh

[full nimbus]

yeah, I don't know

[tacit arch]

https://youtu.be/6qJRnZY5Ee0?si=AwHlKASD_aQ5y_7o

[full nimbus]

I don't have the angle tho

and I need to find the diagonal

wait

yeah I don't have an angle

[tacit arch]

You have three sides of a triangle you can find the angle

[tacit arch]

Show the picture

[full nimbus]

I have no angles

hello?

<@&286206848099549185>

[alpine sable]

You can move the 7 over to the other side since it's a parallelogram

Then yeah you have all 3 sides

[full nimbus]

ok

then what?

<@&286206848099549185>

[tacit arch]

Use law of cosines

[full nimbus]

ohhhhhhhhhhhhh

let me do it rw

rq

I got 94.096 for the angle

wait

I got 18.8391 for the

this angle

then I got 6.375 for half of the diagonal

so the diagonal is 12.75

is that right?

[full nimbus]

hellooooooooo

<@&286206848099549185>

[tacit arch]

Show your work

[full nimbus]

I'm just asking if I'm right

I got one side as 5.5 because 11/2 is 5.5

then one side is 7

then the angle between them is 18.8391

then you us law of cos

then you get 6.375

and then you need to multiply by 2 cus its only half of the diagonal

so you get 12.75

don't leave for another 30 mins, please

he left didn't he

[tacit arch]

I can't follow random numbers without calculations

[tacit arch]

Where does this number come from

[full nimbus]

can you not just solve it yourself?

😭

[tacit arch]

It's your problem not mine

[full nimbus]

thats fair but ur here to help me

so you want me to show all my work?

[tacit arch]

[full nimbus]

inverse cos(((8^2 - 11^2 - 7^2) / 11) / 7)

is where I got 18.8391

just tell me if I'm right

I have waited for like 20 mins

.close

[lone heart]

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[alpine sable]

<@&286206848099549185>

[solemn juniper]

!15m

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[alpine sable]

for why

[alpine sable]

ive never even used that ping before

[solemn juniper]

You just did

[alpine sable]

in the help form i never pinged anyone

its a different question

ur delusional

[fallen verge]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[alpine sable]

exactly an hour ago

wait i never said that like actually

stop meat riding me pls

[alpine sable]

idk how to solve A/B

[fallen verge]

So... status 1?

[alpine sable]

oh my bad

yes 1.

[fallen verge]

When you have A \ B you take out any elements in A that are also in B

Any elements in B that are not in A can be ignored

[alpine sable]

so 5?

[fallen verge]

What is 5?

[alpine sable]

the cardinality of A\B

bc 2 and 7 are cancelled

1 3 4 5 6

[fallen verge]

Yes

[alpine sable]

dope

okay wait

missed class this day utterly no clue whats happening

[fallen verge]

Ngl i havent taken what looks like discrete math so i cant help with this one sorry

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

1

\

[void niche]

Okay first of all, you're a criminal for stealing my username

Now that that's out of the way, what is the current question

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

ive been soup since i opened the account

okay so the directions are under the question

but it doesnt make snese

[void niche]

Which question

You've posted like 4

[alpine sable]

this is the one im currently on

[alpine sable]

this one no one knows how to do and im also stuck on

[void niche]

Okay let's do this one then since I'm not in your class.

What are the three properties you need for a relation to be an equivalence relation?

[alpine sable]

reflexive ,symmetry, trans...

[void niche]

Good. Let's do (a)

Is it reflexive?

That is x~x?

[alpine sable]

i dont understand how that concept relates to birthdays

[void niche]

x~y if x and y share a birthday

This is how they defined the relation

So x~x would suggest that x and x share a birthday. Is this always true?

[alpine sable]

i guess so

x is always x

[void niche]

Yeah, you share a birthday with yourself.

So how about symmetry

That is does x~y imply y~x?

[alpine sable]

yeah it doesnt matter what order the birthdays are in

[void niche]

(Ping me with all responses please, this channel is hiding from me)

Great, now the last one, transitivity

Does x~y and y~z imply x~z?

[alpine sable]

what is z

z doesnt exist

[alpine sable]

z doesnt exist

[void niche]

Sure it does

Watch this

Let z exist

[void niche]

Now answer this

(The actual letters don't matter, just the relation. I could say Bob ~ Calassandra and that would be perfectly valid)

[alpine sable]

if y~z then x~z

so yes?

@void niche

[void niche]

Yes, that is correct, but why?

[alpine sable]

bc if x and y have the same birthday and y and z have the same birthday then x and z have the same birthday

@void niche

its weird pinging myself

[void niche]

Yep, that's it!

So you have established that (a) is an equivalence relation

Why don't you try (b)

[alpine sable]

okay uhh

x cant be older than x

@void niche

[void niche]

Great, that one was easy

So not an equivalence relation

(It also fails symmetry, but passes transitivity)

How about (c)

[alpine sable]

how do i know how many letters are in each word

@void niche

x~x

x does not ~ y

[void niche]

Don't fix specific words, just think of it from an abstract pov

[void niche]

It can. For instance, let x = "soup" and y = "bowl"

Then x ~ y

[alpine sable]

yeah but only in that scenario

[void niche]

That's fine

An equivalence relation does not impose that very many things have to be related

[alpine sable]

so then transitivity is true as well

soup bowl cows

[void niche]

Yep

How about symmetry

[alpine sable]

well yeah u proved it

[void niche]

I didn't

I just showed that there exist some x and y such that x ~ y

[alpine sable]

soup = bowl. bowl= soup

sym is true

[void niche]

Yeah that's the idea

You can't really do it for specific examples like that, you need a more general argument

But that's the point

[alpine sable]

i have a test tmr but i get a note card anything you think i should write

also can u do one more problem section

[void niche]

Problem section? You mean one more problem?

[void niche]

Idk your courses content so there's no way for me to know

[alpine sable]

fair enough

this one is ez i just dont know what set builder notation means

N is natural numbers

im looking at B rn

idk how to convert them

@void niche

[void niche]

Set builder notation is the kind with the colon inside

[alpine sable]

o

[void niche]

So {type of element : conditions element must satisfy}

[alpine sable]

n is within Natural numbers

{1,3,5,7,9...}

[alpine sable]

is that right

[void niche]

Yeah thats the answer to part b

[alpine sable]

how do i do the reverse

[void niche]

For example for (a)

Well, try it. I'll help you correct what you mess up, should that happen

[alpine sable]

{x E R : multiple of 3}

R is real numbers

[void niche]

Yep!

That's it.

[alpine sable]

so there isnt a format it just has to make sense

[alpine sable]

what about the letter one idek where to start

[void niche]

Well there is a format, you did it

[alpine sable]

i appreciate ur help no one else would sit here and help

[void niche]

Just list all the things in the set

No problem, soups gotta stick together

[alpine sable]

frfr

what is the cursive L

{a,e,i,o,u, sometimes y}

@void niche

[void niche]

Ha! Yeah, thats it.

The symbol they use doesn't matter

They could have said {letters in the English alphabet : is a vowel} and it would have been the same set

[alpine sable]

last one on the study guide i swear

idk what this mean

[void niche]

But the symbol is \ell in latex

[alpine sable]

latex??

[void niche]

How people type math usually

[alpine sable]

oh weird

[void niche]

I'm not sure. Probably means equivalent as sets

[alpine sable]

oh the equals sign means its a bijection

[void niche]

Okay

Since both sets are finite, there existing a bijection is equivalent to them having the same cardinality

So what is the cardinality of each side

[alpine sable]

well they cant be the same bc b adds to the cardinality

[void niche]

I feel like you have a typo in there

[alpine sable]

cant

my bad

[void niche]

Are you sure?

Write down A × B as a set

In uhh

[alpine sable]

order pairs

[void niche]

"Roster" notation as your class calls it

Yeah but like

Literallt write it down

Like rn in this chat

[alpine sable]

(a, e) (b,e) (c,e) (d,e)

thats dumb

[void niche]

Good, what's the cardinality

[alpine sable]

they are the same

4

[void niche]

Yep

So there does exist a bijection

[alpine sable]

math is bad

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[wild falcon]

need help

[wild falcon]

increasing -1?

dec 0?

x=2?

h'(x)=0?

[lone heart]

@wild falcon Has your question been resolved?

[wild falcon]

<@&286206848099549185>

[desert compass]

F’(x) = 0 at x= 0 and 2

Decreasing at (0,2)

Increasing for x>2 and x < 0

[wild falcon]

is the bottom 2 correct?

[desert compass]

Ya you have a vertical tangent at x = 2.. but not x=-1

[wild falcon]

it says horizontal

.close

[lone heart]

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[vapid shuttle]

I'm pretty stuck on how to go about this one

likely it has to do with the MVT

I assume

but I tried applying that in a few different ways and couldn't really get a track going where I saw something

so any pointers would be greatly appreciated

[cinder sundial]

what is f:(a,b), is it a function

[vapid shuttle]

yes it is a function from the open interval (a,b) to R

[desert compass]

Idk if im correct.. but f’x is 0 for all values of c.. and so is f’’.. hence the graph should have no local maxima or minima..

[vapid shuttle]

not for all values of c

just for one value of c inside the interval (a,b)

[desert compass]

Oh

[vapid shuttle]

<@&286206848099549185>

[mellow grail]

Can't you just say it doesn't work with second order derivative test

Like it fails the test

[vapid shuttle]

no access to any derivative tests

[mellow grail]

😭

[vapid shuttle]

that'd take all the fun out of it

[mellow grail]

So at c...the derivative and the second derivative touch the x axis right?

But the third derivative doesn't right?

[vapid shuttle]

yes

something like

y=x^3 y'=3x^2 y''=6x y'''=0

at x=0

there is some kind of horizontal slide going on of course

[mellow grail]

But you would have to assume f(x) is a polynomial

[vapid shuttle]

right, I'm not saying that is the only case

just an example

to get a feel for it

[mellow grail]

Well you would have to prove some relation between a local minimum and the derivative to solve this, that is the only thing that pops inside my head

[vapid shuttle]

well the relation is that if f has a local min/max at c and f diff at c then f'(c)=0

but f does not have a local min max at c

so this is useless

[mellow grail]

No I meant a relation with the 3rd and 2nd derivative

Wait what if you let g(x) = f''(x)

[mellow grail]

Then use this

[vapid shuttle]

it doesn't help

it is not an if and only if statement

the reverse implicattion clearly is not true

[near apex]

What if you show that sign of f'(x) is same in neighbourhood of c? Does that work as a proof?
It geometrically clearly makes sense to me but i calculus proofs are often some epsilon delta stuff.

I mean... i can write that formally using limits still but i dunno if it still fits your expectations.

[vapid shuttle]

What do you mean by the sign of f'(x) is same in neighbourhood of c?

[near apex]

That is for x < c, if f'(x) is positive, then for x>c also f'(x) is positive.

Similarly for negative.

Of course, those x's are only in a very small neighbourhood of c.

[vapid shuttle]

and that would help why?

[near apex]

Because sign of derivative changes at maxima and minima.

It goes from positive to negative for maxima, and negative to positive for minima.

[vapid shuttle]

I haven't proven that

[worn fox]

Skill issue

[vapid shuttle]

my knight in shining armour has arrived

[worn fox]

Oh I have no clue

[vapid shuttle]

skill issue

[worn fox]

You've pretty rapidly surpassed the level of analysis I can just recite

I hate analysis

[vapid shuttle]

really

that is good to hear

not the latter but the former

[worn fox]

Yeah I did this shit like 4 years ago now

[near apex]

Just out of curiosity, how does one formally prove that a point c is maxima or minima in calculus then?
Showing that f(c) < f(x)(greater for maxima) for all x in neighbourhood. Like that?

[vapid shuttle]

yes

if there exists a delta>0 s.t for all x |x-c|<delta implies that f(x)<=f(c)

then there is a local max

opposite for min

[near apex]

Ah. Okay.

[lone heart]

@vapid shuttle Has your question been resolved?

[pallid scarab]

name l = f'''(c). Since f''' is continuous, you can find a neighborhood of c where f'''(x) > l/2. then integrating 3 times from c to x...

(distinguish the case where x<c and x > c)

[lone heart]

@vapid shuttle Has your question been resolved?

[lone heart]

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[lone heart]

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[alpine sable]

I have trouble understanding how -cot became tan

[royal meadow]

wtf is that solution

oh wait

ok i see

[near apex]

$\tan{\left(\frac \pi 2 + \theta\right)} = -\cot{(\theta)}$

[ocean seal]

Enemagneto

[royal meadow]

cot(x) = cos(x)/sin(x) = sin(x + pi/2)/-cos(x+pi/2) = -tan(x + pi/2)

oh i'm slow

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Oh I see thank you so much

[lone heart]

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[desert compass]

tan(90 + x ) = -cot(x)

[lone heart]

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[stuck brook]

Can someone help me to create a script for my reporting.. about finding the focus and latus rectum in parabola?🥲

[lone heart]

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[alpine sable]

Can some help me with send

Second*

The only thing I know is that sin60 = sqrt(3)/2

And we have to relate the rest to it

[coral flower]

use those product and sum rules

https://cdn.discordapp.com/attachments/326138757474680852/1071303308175745084/150414892225134592.png

the ones in the end

[lone heart]

@alpine sable Has your question been resolved?

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[paper condor]

Can someone help me with this one?

[lone heart]

@paper condor Has your question been resolved?

[lone heart]

@paper condor Has your question been resolved?

[lone heart]

@paper condor Has your question been resolved?

[lone heart]

@paper condor Has your question been resolved?

[lone heart]

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[knotty oriole]

is "squaring a vector" a well defined operation?

[ocean seal]

madlor

madlor

[mortal trellis]

in an abuse of notation you sometimes write vector^2 for vector dot vector

but that sucks and shouldn't be done

in another abuse of notation it could also mean elementwise squared

[knotty oriole]

ok i see

[mortal trellis]

either way, not nice. don't do it

[knotty oriole]

hmm

this kind of matrix algebra stuff gets me very stressed ngl

are expected values for matrices and vectors well defined?

[mortal trellis]

they are usually elementwise iirc

[knotty oriole]

i believe so too

chatgpt is giving me some nonesense answers here i think, suggesting that the expected value for a vector is a dot product of some probability vector and the vector

[mortal trellis]

dont use chatgpt for math

[knotty oriole]

fair

i would like to use this channel for a question that is technically not the same as the first one i asked

honestly i feel so confused that i dont even know what question to ask to help me lol

i've concluded that it surely means y dot y

.close

[lone heart]

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[alpine sable]

Can anyone give some example clarify 6 f)? It should be true right? (Sorry it's set theory... not much to solve)

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185> ?

XD thats funny because im learning the same thing as you

[forest cobalt]

still need help here?

[alpine sable]

yes pls

[forest cobalt]

consider a set where b = c

and b and c are subset of a

choose the simplest one you can think of so it's easy to visualize

like you said, there's nothing to solve here, so i can't really give you the example without answering the problem

[alpine sable]

i think I get it... its can't be true its false

[forest cobalt]

the key to the argument i'm making is the b=c part

that makes a big difference

[alpine sable]

yea using this I was able to make my argument... its 100% false my hypothesis was wrong

thnx

.close

[lone heart]

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• 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.

[alpine sable]

Hey,
E = {2;{4;5};4}
Why {5} is not included in E

[solemn juniper]

Because it's not one of its elements

Is E coming from somewhere else or is that just how it's defined?

[alpine sable]

Just defined like that

and is {4;5} included in E?

[solemn juniper]

E has 3 elements; two numbers and a set

It is, yes

[alpine sable]

Okay thx for help :p