help-36

[final saddle]

@leaden crypt Has your question been resolved?

[lean thicket]

The laws I found relevant for this kind of problem were

1. Distributive laws (sounds like you know these already)

2. De Morgan’s laws:
   In words, the negation of a logical expression negates every statement and flips the operators. For example,
   “not (A and B)” is equivalent to “(not A) or (not B)”.

3. Insertion (my term, not a standard term):
   You can insert a false statement into an “or”/disjunctive expression without changing its validity. For example, “A or B or FALSE” is equivalent to “A or B”. Similarly, you can insert a true statement into an “and”/conjunctive expression, that is, “A and B and TRUE” is equivalent to “A and B”.
   The use for these problems is that “A and (not A)” is always false, while “B or (not B)” is always true. Inserting these allows you to construct minterms and maxterms from terms that don’t contain every statement.

For example, for question 1:

[final saddle]

@leaden crypt Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[zealous oar]

Guys can anyone help with this

[supple mantle]

Hi could you please translate?

[zealous oar]

So it says x and y are two real numbers ≠ 0, proov:

[supple mantle]

So we should prove $2x+4y=1 \implies \frac{1}{x^2 + y^2} \le 20$?

[soft zealot]

VulcanOne

[zealous oar]

Yeaah

[supple mantle]

Alright

Did you try your hand at it?

[zealous oar]

Replacing x with $(1-4y)/2$

[soft zealot]

AymanRhz

[zealous oar]

Then tried the same with replacing y

But I just couldn't go anywhere

[supple mantle]

Hmm

Hmm

Try doing AM >= GM

[zealous oar]

Aand what's that

[supple mantle]

$\frac{x_1 + x_2}{2} \ge \sqrt{x_1 \times x_2}$

[soft zealot]

VulcanOne

[supple mantle]

You're given 2x+4y = 1

This is the condition you need to use and manipulate to prove the inequality you need to prove

[opal plinth]

Seems unnecessarily complicated

[supple mantle]

Yeah now that I think about it, I think it won't work properly

[zealous oar]

And we didn't study it yet so I dont think it's the way I should go with

[supple mantle]

But an inequality is needed using the equation given

[opal plinth]

If $x \ne 0$ and $y \ne 0$, what can you say about $x^2 + y^2$?

[soft zealot]

Nel

[supple mantle]

Yeah don't worry about it now

[zealous oar]

X² + Y² >0

[opal plinth]

Exactly, so $\frac{1}{x^2 + y^2} \le 20 \iff 1 \le 20(x^2 + y^2)$, right?

[soft zealot]

Nel

[zealous oar]

Yeah?

[opal plinth]

Replace x by something with y (or y by something with x), and you get a quadratic

[zealous oar]

Okk I'll do it now

But I need the first one implies The second one

So can I use the contrapositive?

[opal plinth]

I guess but why would you

[zealous oar]

The equivalent is gonna break at one point

[opal plinth]

No

[zealous oar]

It wouldn't do a problem if I replaced x?

[opal plinth]

2x + 4y = 1 is your premise, you can assume it's true while proving the inequality

[zealous oar]

Ohhh

Okkk

[opal plinth]

Show me the inequality you get once you've done the substitution and simplified

[zealous oar]

,rotate

[opal plinth]

Not sure how you got 380y^2 here

[zealous oar]

Ohh it's 320

I wrote it incorrectly

[opal plinth]

And simplify the fraction at the end

[zealous oar]

It would be 400y² total then

[opal plinth]

It's all divisible by 4

[zealous oar]

It's
100y² - 40y +5

[opal plinth]

Right, now you should make one side 0

[zealous oar]

0 =< 100y² - 40y +4

[opal plinth]

Great

Can you find a way to factorize that quadratic?

[zealous oar]

I can re dévide by 4

[opal plinth]

Either that or we can discuss the discriminant

Yes, you can

[zealous oar]

Can we do both?

[opal plinth]

Sure

So we have 25y^2 - 10y + 1, right?

[opal plinth]

Ok right, the discriminant equals 0

What does that mean for the quadratic?

[zealous oar]

25(y-(1/5))²

?

[opal plinth]

Yeah, that's correct too

[zealous oar]

It's a(x-x0)²

So I dévide by 25?

[opal plinth]

No need, all you want to know is whether it's positive (or zero)

Can a square be negative?

[zealous oar]

Oh no

So

[opal plinth]

Yes, and so you're done

[zealous oar]

Yeaah because it's always true

Thank you so much 🙏🏻🙏🏻

[opal plinth]

Without factoring, you can also argue that because the discriminant is zero, the quadratic is either always negative or always positive (and zero at exactly one point)

Just try one value to figure out which one it is

So like if y = 1 then 25y^2 - 10y + 1 = 25-10+1 = 16, which is positive, so the quadratic is always positive (or zero)

[zealous oar]

Ohhh

Thank you so much

[zealous oar]

That's my first time noticing that

[opal plinth]

But tbh the discriminant being zero basically gives you a factorization, so it's just as easy

[zealous oar]

Thanks, it helped so much 🙏🏻

[opal plinth]

You're welcome

[zealous oar]

.close

[final saddle]

Channel closed

Closed by @zealous oar

Use .reopen if this was a mistake.

[final saddle]

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.

[quartz flame]

i got it wrong and idk what to do

i thought it was a hyperboloid of 2 sheets

hang on

i thought in lecture my prof did completing the square for each variable but i dont see how i'd do that

i know it's one sheet

[crude island]

divide by four

[quartz flame]

i did that

[crude island]

one minus sign

so hyperboloid of one sheet

[quartz flame]

well ik that part

[crude island]

two sheets would have two minus signs

well what else do u need?

[quartz flame]

it said it was wrong when i did the eqn

[crude island]

-(1/4)x^2+8y^2+...

= 1

[quartz flame]

yeah

thats what i did

[crude island]

u sure?

I'm not sure what else would constitute as a standard form then

make sure u include = 1

[quartz flame]

well evidently i had an error somewhere, i retried it and it was correct

thanks

.close

[final saddle]

Channel closed

Closed by @quartz flame

Use .reopen if this was a mistake.

[quartz flame]

.reopen

[final saddle]

✅

[quartz flame]

?? why is this wrong

i also left it as x^2+3y^2=6z^2

and that was wrong

<@&286206848099549185>

[crude island]

um

[exotic shale]

try with z^2 in the left side

[crude island]

is this not already in standard form?

[quartz flame]

oh

okay

[exotic shale]

yea

ah idk

[crude island]

yeah sure

try that

but I've seen it presented that way with = 0

as the "standard form"

[exotic shale]

isnt this the general format

[quartz flame]

well it's accepting others not like that

like this for an ellipsoid

[exotic shale]

oh

standard form for the specific equation

[quartz flame]

i am confused why these answers arent working for the cone

[exotic shale]

try

root 6 squared

[crude island]

Don't worry too much i'm not sure why they are emphasizing this standard form so much

[exotic shale]

like this

[quartz flame]

i did that

[crude island]

if you can identify the shape and know how to rearrange it you should be fine

[quartz flame]

here

[crude island]

I honestly don't know what they are looking for because it seems that it is already in standard form to me

[quartz flame]

yeah idk either

[exotic shale]

they mean like for a specific equation

not for quadric surfaces in general

[exotic shale]

for example this is for cone

[quartz flame]

yeah i did it for a cone

[crude island]

so not this?

[crude island]

oh okay

[quartz flame]

this is in cone format

imma try this one

damn looks like that's what it wanted

idk why it couldnt accept for first 5 attempts since they're all equivalent

[exotic shale]

thats for all general one

[exotic shale]

didnt you already use it

bro

[crude island]

lol

[exotic shale]

isnt that what it already has

[quartz flame]

yeah idk

[crude island]

a = 1, b = 1/sqrt(3), c = 1/3

[quartz flame]

it really wanted it =0

[exotic shale]

you just had on other side

[final saddle]

@quartz flame Has your question been resolved?

[quartz flame]

.close

[final saddle]

Channel closed

Closed by @quartz flame

Use .reopen if this was a mistake.

[final saddle]

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.

[lofty mist]

Can someone please explain factoring to me, ik it’s so basic but I literally don’t know how to do it all and this is my last resort 😭

[lofty mist]

This is my best attempt

[tiny gorge]

the numerator is right

[lofty mist]

Thank god I’ve been trying for like 30 minutes 😭

[tiny gorge]

you can always multiply it out to confirm

[lofty mist]

I don’t know what to do with the bottom part though

Please help 😭🙏🏼

[tiny gorge]

well first a general observation

you know it will be of the form (x + a)(x + b) where a and be are numbers (positive or negative, we don't know yet)

you have +3 constant term so you know ab = 3

so a and b have the same sign

(otherwise their product would be negative)

you also have -4x

so a and b can't be positive

so they're both negative

[crude island]

when a =1, find two numbers that multiply to the constant term and that sum to the coefficient of x

[tiny gorge]

hopefully that reduces the effort a bit

[crude island]

always try integers first

[tiny gorge]

yea and if you know the rational root theorem, that can help narrow it down to just a few possible numbers

here it should be pretty obvious since you want two integers whose product is 3

there aren't many choices that work

[lofty mist]

Thank you guys, I’m still very lost but it was worth a shot😭

[bleak granite]

if anything I would like to give my 2 cents: -4 can be broken up into 4 ways:
-2*2
2*-2
-1*4
1*-4

take each of these pairs, add them up, if one of them is positive three then you have identified your factors

[lofty mist]

So it’s the 3rd one?

Are most problems like that when factoring 😭

Or does that just depend on the front number

[bleak granite]

wait I did a stupid 3 can be broken up these 2 ways:
3*1
-3*-1

take ach of those pairs, and add them to get -4, that's your factors

[final saddle]

@lofty mist Has your question been resolved?

[lofty mist]

I’m still lost but thank you guys for trying it really means a lottt

[final saddle]

Channel closed

Closed by @lofty mist

Use .reopen if this was a mistake.

[final saddle]

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.

[hexed smelt]

pls help me guys. so far i understand that the inverse function would have the reciprocal derivative.

so -6x^2-3 is the derivative of f(x)
inverse: 1/-6x^2-3

what I then did was plug in 1 since thats where they ask for the point but then i got it wrong

[formal trail]

,, (f\inv)'(x) = \frac{1}{f'(f\inv(x))}

[soft zealot]

κλαουντ ☁ (cloud)

[formal trail]

in other words you need to plug in the value of y such that f(x) = y to your inverse derivative

[hexed smelt]

can you show me plz with the question?

[formal trail]

if you know $(a,b)$ such that $f(a) = b$ i.e. $f\inv(b) = a$, then [ (f\inv)'(b) = \frac{1}{f'(f\inv(b))} = \frac{1}{f'(a)} ]

[soft zealot]

κλαουντ ☁ (cloud)

[hexed smelt]

wait okay

i thought the derivative of the inverse is just the reciprocal?

[formal trail]

it sort of is, but it's the reciprocal evaluated at a different value

[hexed smelt]

Oh

Yikes

Sorry can u just explain to me really quick why thats the case

is it like chain rule??

[formal trail]

yes, the proof is due to the chain rule

[hexed smelt]

so the deriviative of the inverse function

is 1/the deriviative of f at the point of the inverse

[formal trail]

yes

[hexed smelt]

ok

thank you

i think i got it

do i do the close thing

.close

[final saddle]

Channel closed

Closed by @hexed smelt

Use .reopen if this was a mistake.

[final saddle]

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.

[sand patrol]

for this question,

[sand patrol]

I did half it of it, is it right so far

I want to make sure this is right before I show containment on the other direction lol

[plush quiver]

Looks good to me 👍

[sand patrol]

tyyyyyy

.close

[final saddle]

Channel closed

Closed by @sand patrol

Use .reopen if this was a mistake.

[sand patrol]

.reopen

[final saddle]

✅

[sand patrol]

uh i think something is going wrong with the other direction

I’m not sure where is wrong but it’s not making sense

I changed the wording a bit

Uhm….

for the second part, im getting a intersection instead of a union...

wait

no i still dont get it what went wrong

okay im not understanding my instructor's proof now (nvm i get it again)

[plucky rover]

Wait no

Lemme go over it once again

[sand patrol]

i changed it to for every i in I, x is a member of A\Bi

im still thinkingif thats right lol

[plucky rover]

Yes that is correct

So for every i, x is a member of A and NOT a member of B_i

[sand patrol]

yurrrrr and im thinkig wut to write next

well i wrote

im thinking this line lol

[plucky rover]

x is not in the union either

Cuz the intersection is contained in the union

[sand patrol]

how did you change from a intersection to a union

uhmmm since x is not a member for all Bi when i in I... we have uhmm

[plucky rover]

x is not in the intersection yes

But it's also not in the union

Because the intersection is a subset of the union

[sand patrol]

how?

wai

[plucky rover]

Do you understand now

[sand patrol]

ohhhhh

is it because

x is not in any of Bi's

[plucky rover]

Yes

[sand patrol]

so its not in union either

cause there's not a single one in there

[plucky rover]

Yes

[sand patrol]

omg thank you so much

[plucky rover]

That works better than what I was doing lol

Nah this was mostly you

Give yourself the credit

[sand patrol]

i was stuck trying to think through this thank youuuu

.close

[final saddle]

Channel closed

Closed by @sand patrol

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frank folio]

Im a little confused by this explanation, elements in $F^S$ are not lists while elements in $F^n$ are?

[soft zealot]

BOSS

[frank folio]

or sorry, functions that go to lists

[formal trail]

there is a natural correspondence between a list in F^n and a function {1,...,n} -> F

[frank folio]

hmm

wait so for any set S, does the function need to take all elements to some element in R (in F^S)

like would it be something like

{1,2,3} -> {20,5,3}

[frank folio]

im trying to understand this more fully

Like i understand that if we had some $x = (x_1,x_2, ... ,x_n) \in F^n$ this can be thought of as a function $x$ where $x(i)=x_i$

[formal trail]

let's take F = R for concreteness. then we can identify the list (1, 1.4, pi) with the function f: {1,2,3} -> R with f(1) = 1, f(2) = 1.4, f(3) = pi

[frank folio]

ok yeah sure

but thats the thing, functions in R^S would go to R right, like a single element in R

not multiple elements like a list

[soft zealot]

BOSS

[frank folio]

idk if my question makes sense

[formal trail]

functions in R^S are simply functions with domain S and codomain R

there's no obligation for them to have the same output for every input

[frank folio]

I just dont see how the function x is the same as the element x in f^n if the element x in F^n has multiple values and the function x in F^S has 1

oh hmm

nvm i think it makes more sense

the function technically does return 4 elements

so some x+y = (x_1,x_2, ... ,x_n) + (y_1,y_2, ... ,y_n) can be tought of as adding the functions (x+y)(t) for some t in S

Meaning, $(5,3,8)$ is just a function taking 1 -> 5, 2->3, 3->8

[soft zealot]

BOSS

[formal trail]

yes

[frank folio]

and they both just have inputs from {1,...,n} and outputs in R

[formal trail]

yes

[frank folio]

ok bet yeah just needed to talk it out

tyty

@formal trail

[final saddle]

@frank folio Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

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.

[slender jackal]

help

🙏

can you tell me the order from 1-9

[craggy plank]

Is this some sort of meme? I’ve been finding this question in this server a lot lately XD

[slender jackal]

its neal.fun game

its like captcha game

[craggy plank]

I see

[slender jackal]

and i suck at maths

[craggy plank]

I’m too old for this, anyways which box do you need help with?

[slender jackal]

so er

[jagged flare]

theres this website called desmos, you can just plug all of these in and it will give you the value

[slender jackal]

it needs to be ordered

from lowest to highest

[slender jackal]

which type of calculator

do i click

[jagged flare]

i use 2d graph

[slender jackal]

@jagged flare

how do i make the 6 go above 3

[jagged flare]

first

[jagged flare]

6 go above 3? which one

[slender jackal]

i accidently changed it

waaaa

😭

[jagged flare]

could you ss your screen

[formal trail]

find the integral sign in the functions menu (above the text entry)

[slender jackal]

screenshare?

[jagged flare]

the integral, you can also write "int" and it will make it

[formal trail]

in the pc version you will want to pull up the on screen keyboard (bottom left)

and then press the functions button on the top right of the keyboard

[slender jackal]

ok

how do i get this sign

@formal trail

[jagged flare]

the same method you get the integral

it should be right next to the integral sign

[formal trail]

all of the symbols you need are in the functions menu or main keyboard

[slender jackal]

ok

ok i have put all the things in

now what

yay i got it

.close

[final saddle]

Channel closed

Closed by @slender jackal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tribal robin]

I need help with this problem

[tribal robin]

Also idk why the image looks so cinematic 😭

Anyway

I think I know where to start

I know that the cube root of x needs the $(a - b) (a^2 - 2ab + b^2)$

[soft zealot]

Adrift

[tribal robin]

But idk where to go from thete

There*

[dire solar]

Haha it does

Think about rationalizing denominator

[tired walrus]

substitute t := x^(1/6)

[tribal robin]

?

its not an infinite limit

Why would I need to substitute?

[tribal robin]

So multiply by the conjugate?

[dire solar]

Its a very fast way to get the answer

[dire solar]

Yes

Mine is slower

[tribal robin]

I got

$x^1/3 - 1 (sqaure root of x + 1) / x - 1$

[soft zealot]

Adrift

[dire solar]

$\sqrt{x}$

[soft zealot]

Cindered

[tribal robin]

oops

[ornate tree]

$\frac{x}{3} - \frac{\sqrt{x + 1} }{x-1}$

[soft zealot]

This is sad 😢

[ornate tree]

is this what you're looking for?

[dire solar]

Do you mean $\frac{(x^{1/3}-1)\cdot (\sqrt{x} -1)}{x-1}$

[soft zealot]

Cindered

[tribal robin]

yes

[dire solar]

ok nice

[tribal robin]

how did u do that?

[tribal robin]

Ok let me stick with your thing

[ornate tree]

back slash frac{numerator}{denominator}

[dire solar]

Great

[ornate tree]

back slash sqrt{} >> square root

[dire solar]

Now, rationalize the numerator thing as well

Do you remember a^3 - b^3 identity?

You need to use that

[tribal robin]

Ye but I forgot how to use it

thats the question I have

[dire solar]

You will put a=x^1/3, b=1 there

[tribal robin]

where do I start?

ye I get that

[dire solar]

welp its a formula so you will have to memorize it most probably

[tribal robin]

but then what is a^2 - 2ab + b^2?

[dire solar]

its not -2ab its +ab

[tribal robin]

why plus?

the identiy is a^3 - b^3

[dire solar]

Thats the formula a-b times a2 + ab + b2

Yeah the formula you told me is wrong

[dire solar]

yep exactly

Its +ab as you see

Multiply numerator and denominator by the second term

[dire solar]

And use these substitutions

[tribal robin]

Bro then what was the formula with 2ab

is that (a+b)(a+b) /

?

[dire solar]

Yes

(a-b)^2

You probably got confused

[tribal robin]

Okok got it

Ye

so its

never I'm still confused

what do I plug in?

[dire solar]

x^1/3 - 1 is the a - b term here, you want to make it into x-1

So multiply numerator and denominator by x^2/3 + x^1/3 + 1

[tribal robin]

what

im so lost 😭

what $x^2/3$

[soft zealot]

Adrift

[tribal robin]

why?

[dire solar]

$x^{2/3}$

[soft zealot]

Cindered

[dire solar]

Sorry i am phone and its painful to type any sort of math so i am handwaving stuff

[tribal robin]

O see

I see*

but why that?

what makes it x^2/3 ?

[dire solar]

Please use this

[tribal robin]

Ok

I understand that

but where did u get x^2/3 ?

[dire solar]

Its the a^2 term

[tribal robin]

Right ok

Ok let me see what I can do

I got $(x^1/3 - ) (x^2/3 - x^1/3 + 1) ( \sqrt{x} + 1)$

[soft zealot]

Adrift

[tribal robin]

all divided by x-1

[tribal robin]

first term supposed to be $(x^1/3 - 1)$

[soft zealot]

Adrift

[final saddle]

@tribal robin Has your question been resolved?

Channel closed

Closed by @tribal robin

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tranquil pine]

Can someone help me with question 2 and 3

[umbral steppe]

may I know what you've tried?

[tranquil pine]

<@&286206848099549185>

[umbral steppe]

!15m, please.

[final saddle]

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.

[tranquil pine]

Alrighti

[tranquil pine]

Cozs^-1 (0.2)=78.46

I have no idea wha t to do from there

[umbral steppe]

you have one of the two answers.

now, consider in which other quadrant is cosine positive.

[tranquil pine]

Uhh 281.5?

[stoic temple]

,w cos 281.5

[umbral steppe]

,calc 281.5 + 78.46

[soft zealot]

Result:

359.96

[umbral steppe]

hm...

,w cos(281.5 degrees)

[soft zealot]

Results provided by WolframAlpha

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

Requested by shiningsage

[umbral steppe]

you're a tiny bit off.

[stoic temple]

But it works though

[umbral steppe]

not sure if this is within rounding acceptability or not though.

[tranquil pine]

Ohhhb

[tranquil pine]

Lemem check the answer

[umbral steppe]

if you're allowed to round to 4sd, yeah, this works.

[tranquil pine]

Ahhh i see thanks

[umbral steppe]

,w cos(281.54 degrees)

[soft zealot]

Results provided by WolframAlpha

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

Requested by shiningsage

[umbral steppe]

technically this would be a more precise answer.

by the way, OP, are you still around?

[tranquil pine]

Ahhh i see

Btw how about the third question

Is it the same?

[umbral steppe]

reading it now.

q3 requires you to sketch the function's graph. part c) is the same as what you've been doing in q2, but the graph will make your checking easier.

[tranquil pine]

Ahhh i see thanks

[umbral steppe]

my pleasure. anything else?

[tranquil pine]

Nope thank you

[umbral steppe]

alright. please remember to close the channel when you're done, and see you around.

[final saddle]

@tranquil pine Has your question been resolved?

[craggy plank]

.solved

[final saddle]

Channel closed

Closed by @craggy plank

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[onyx smelt]

what this mean ?

[worldly mesa]

What is your question

[onyx smelt]

i dont understand this

(1) is for all x p(x)

we use p(c) for some c

but (3) is there exists some x for p(x)

we still use p(c) for some element c?

how ?

@worldly mesa

whats it tryna say

[worldly mesa]

1 is wrong

It means P(c) for arbitrary c

[onyx smelt]

for all c is same as arbitrary c ?

[worldly mesa]

Yes

The difference is \forallx.P(x) is a statement and has no meaning by itself.

When you add semantics to it gets a meaning.

[onyx smelt]

okok

thanks bro

.close

[final saddle]

Channel closed

Closed by @onyx smelt

Use .reopen if this was a mistake.

[final saddle]

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.

[harsh hawk]

I have this figure, if i want to make a parameter equation for the plane, can i just use points H=( 5,93, 14,27, 0), G=(7,62, 9,79, 0), E=(10,9, 14,27, 0).

[final saddle]

@harsh hawk Has your question been resolved?

[thin cloud]

I'm not sure why you want to make an equation but yeah

That works

[final saddle]

Channel closed

Closed by @harsh hawk

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[radiant carbon]

not sure how to do this

[barren hound]

i'd start by figuring out how many tandems were built

since that column goes 1 1 1 2

[radiant carbon]

but why does it have to be tandems

[barren hound]

well like

[radiant carbon]

couldn't it be other combinations of products

[barren hound]

look at saddles vs total number of cycles

[radiant carbon]

hmm

ur right

[barren hound]

then i'd probably figure out how many unicycles, using the handlebar number

just kinda logicking it out yfm

[final saddle]

@radiant carbon Has your question been resolved?

[verbal viper]

u can use the matric method for solving these 4 equations

idk whts it called

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[nocturne torrent]

i’ve answered this last time, but i didn’t quite get it since i think like a monkey. so i’m going back to it to practice

[umbral steppe]

you have the right idea, but you were a little excessive with it.

the two marked factors are unnecessary.

[nocturne torrent]

soooooo

it should be multiplied by (x+2) only

and the other one

(x-2) only?

[umbral steppe]

each fraction should be multiplied by what's missing from its denominator to form the common denominator.

for the left fraction, it already has an (x-2) factor. it only needs the (x+2) factor to reach the common denominator.

likewise for the right, it already has a denominator of (x+2) - it only needs the (x-2) factor to reach the common denominator.

[nocturne torrent]

ooooh

omg

this is the first time

i get something

[umbral steppe]

well done.

[nocturne torrent]

soooo

wait

YES YES YES?

[umbral steppe]

correct, but you should bracket your x+3 as well.

[nocturne torrent]

ah yes

[umbral steppe]

otherwise, super pedantic people would misread it as x+[3(x+2)] and that'd be the end of your marks.

[nocturne torrent]

is thisss

complete

i can move on to step 2 by getting

the critical point

s

or not yet

cuz last time i tried to solve this

someone said i can factorise it(?)

[umbral steppe]

you can.

[nocturne torrent]

do i have to

[umbral steppe]

wait let me actually check.

never mind, you can't factor the numerator.

[nocturne torrent]

so this is it?

um how do i get the critical points

with this

[umbral steppe]

good question. look at the poly in your numerator.

[nocturne torrent]

yes

quadratic

[umbral steppe]

then tell me what you think its roots are.

[nocturne torrent]

1

4

8

wait am i right

what are roots again

[umbral steppe]

no.

values of x for which the poly = 0.

[nocturne torrent]

how do

i get the roots

AAAGSGHWHSHSHSWP

oh man i hated quadratic equations back in grade 9

now i’m back

[umbral steppe]

well, the most direct method is the quadratic formula, but before we even do that, it might be a good time to check the discriminant of the numerator.

[nocturne torrent]

which is -16

[umbral steppe]

what does this tell you?

[nocturne torrent]

um

it’s less than 0

[umbral steppe]

sure... but what else does it tell you?

[nocturne torrent]

no idea, ma’am..

it doesn’t cross 0?

or never crosses 0

[umbral steppe]

correct. that's the answer I'm looking for - more properly stated as no real roots.

so if the poly doesn't have a real root, do you agree with me that it is either always positive or always negative?

[nocturne torrent]

um

maybe

no

yes

no

[umbral steppe]

settle on one answer and tell me why.

[nocturne torrent]

i

don’t know, ma’am

pls explain

[umbral steppe]

polynomials with positive exponents are generally continuous functions. at your level, it suffices to know that these functions can be completely graphed without lifting your pencil.

(or pen, if you roll that way.)

[nocturne torrent]

AH

so

the parabola

never crosses the x-axis

or wtv

[umbral steppe]

yes.

[umbral steppe]

then, do you see why now?

[nocturne torrent]

no

why

uum

why is it alwyas positive or negative

if it can’t be graphed properly or something like that

[umbral steppe]

now, in order to change sign from positive to negative or vice versa, you have to cross the x-axis. the other way of changing signs is to lift your pencil-
oh, we can't do that, because polynomials are continuous.

so if a polynomial never even touches the x-axis, let alone cross it, there's not a chance that the polynomial can change signs.

[nocturne torrent]

what does it mean if polynomials are continous

[umbral steppe]

^

[nocturne torrent]

continuous

[umbral steppe]

the precise definition of continuity requires knowledge of calculus and thus will not be discussed here.

[nocturne torrent]

oh

[umbral steppe]

but suffice to say that at your level, you can think of continuity as that last part of what I said there.

[nocturne torrent]

alright alright

sooo

since it’s not a real root

we can’t change signs

i suppose?

[umbral steppe]

reconsider this.

do you now agree or disagree with me?

[nocturne torrent]

disagree

[umbral steppe]

why?

[nocturne torrent]

becuz -16 doesn’t cross 0 or if you tried to graph it, it wouldn’t cross the x axis. and if it doesn’t cross the x axis, the sign can’t be changed..?

[umbral steppe]

what do you think the phrase "either always positive or always negative" means?

[nocturne torrent]

uhm

[umbral steppe]

also, wrong reasoning there, but I'll save correcting it for later.

[nocturne torrent]

it can be positive or negative..?

i don’t get the always

part

[nocturne torrent]

obviously

[umbral steppe]

always positive means that no matter what x I use, the result is positive.

same goes for always negative.

[proper dagger]

hint for xuo: you're actually agreeing with Lute.

[nocturne torrent]

I AM?

[proper dagger]

if a graph is positive, will it be above or below the x-axis?

likewise, what about a negative graph?

[nocturne torrent]

above

and a negative

below

[proper dagger]

so a positive graph is above the x-axis, and vice versa for negative graphs.

[nocturne torrent]

i’m losing my brain

just when i started to understand rational inequality

[proper dagger]

you then agree that the poly will not cross the x-axis because of its discriminant

so that means the entire graph must either be above or below the x-axis!

which is exactly what always positive or negative means!

[nocturne torrent]

OOOOH

but

isn’t the discriminant negative

therefore

it’s below?

[umbral steppe]

no.

the discriminant will not tell you where the graph is located.

[nocturne torrent]

oh

right..

[umbral steppe]

the discriminant's job is only to tell you the nature of the roots.

but it's alright. we have another way to find out where it is.

[nocturne torrent]

i got it now, thanks

[umbral steppe]

consider a general quadratic $ax^2 + bx + c$.
do you recall how to determine which way the parabola opens?
(hint: it's related to a.)

[soft zealot]

Lute

[nocturne torrent]

by the sign of the

uuuh what its called

the x^2

coefficient of the x^2

which is positive

meaning it’s upwards

[umbral steppe]

exactly. also known as a.

so it opens upwards.

[nocturne torrent]

yes

[umbral steppe]

can you then tell whether this graph will be always positive or always negative?

[nocturne torrent]

do

i have to give a reasoning again

if i say yes

[umbral steppe]

if you say yes, tell me whether this poly is always positive or negative.

[nocturne torrent]

both

[umbral steppe]

I hope you're joking.

[nocturne torrent]

i’m just stupid beyond comprehension

[umbral steppe]

a poly cannot be always negative and positive at the same time. this isn't Schrodinger's polynomial or something.

[nocturne torrent]

it’s

always positive

[umbral steppe]

there we go.

[nocturne torrent]

since it’s upwards

[umbral steppe]

so now, the numerator polynomial is always positive.

this will limit the values the denominator can take.

[nocturne torrent]

uhuuhh

[umbral steppe]

specifically, what kind of numbers is the denominator forced to have if the whole fraction is to be less than 0?
(positive/negative)

(hint: less than 0 = negative.)

[nocturne torrent]

forced to have

wait

am i supposed to give u numbers

or am i supposed to answer with

[umbral steppe]

no, I gave you two answer choices.

[nocturne torrent]

positive or negative

positive

[umbral steppe]

well, bad news for you then.

a positive number divided by a positive number is itself positive.

[nocturne torrent]

so

it’s negative?

[umbral steppe]

correct. that's the only way to get a negative quotient (and thus satisfy the inequality).

now, put the numerator aside and focus on the denominator.

we have (x-2)(x+2), meaning our roots are x = +/-2.

[nocturne torrent]

yes

[umbral steppe]

so we need to do some interval checking here to see where this poly is negative.

[nocturne torrent]

how do we interval check

[umbral steppe]

there are three intervals to check here: x < -2, -2 < x < 2, and x > 2.

[nocturne torrent]

wh

[umbral steppe]

pick some random number in the interval, put it into (x-2)(x+2), and calculate the answer.

[nocturne torrent]

aren’t they the same thing

x < -2, x > 2 to -2 < x < 2

[umbral steppe]

no.

in words, the intervals are: x is less than -2, x is between -2 and 2, and x is greater than 2.

[nocturne torrent]

oh

so basically like this……..

wait

[umbral steppe]

to check each interval, pick a random number that fits the description of each interval, then see the sign of the number you get.

note that here, we are not interested in the actual answer, but only the sign (positive/negative).

I'll do one for you as an example.

in the interval x > 2, let's pick x = 3.
then, (3-2)(3+2) = 1(5) = 5
this is positive, so it's not the interval we want.

do the same for the other two intervals.

[nocturne torrent]

all negatives

[umbral steppe]

the interval that gives you a negative sign is the one you want.

[nocturne torrent]

wait what

u got a positive

[umbral steppe]

indeed I did.

[nocturne torrent]

WHAT

aait

isnt it

so 3+2

positive yeah

3-2

positive

OH

[umbral steppe]

and positive times positive is?

[nocturne torrent]

YEAH

OMG IM GOING CRAZY

anyway

[umbral steppe]

continue.

[nocturne torrent]

SO

its

positive negative positive

[umbral steppe]

correct.

so which interval gives you the negatives?

[nocturne torrent]

the middle

which is

[umbral steppe]

state it again.

[nocturne torrent]

-2<0<2

[umbral steppe]

that's not a 0 in the middle.

[nocturne torrent]

wha

OH

x

mb

[umbral steppe]

correct.

and that is the answer interval to the inequality.

[nocturne torrent]

so

what about the numerator

wait

so there’s no critical points

WAIT

[umbral steppe]

there are none. this fraction will never hit 0 at any point.

[nocturne torrent]

so we just disregard numerator

because…?

[umbral steppe]

regardless, it still has an answer interval. that's all that matters.

we did not disregard the numerator.

[nocturne torrent]

i mean

like

focus on denominator

[umbral steppe]

we noted that the numerator is always positive.

[nocturne torrent]

AH

RIGHT

[umbral steppe]

and used it to find out the sign we want out of the denominator.

[nocturne torrent]

because we’re finding negative

below negative

i mean

below 0

so the numerator cant be used

since it always positive

AAAAAH

[umbral steppe]

the numerator is used.

[nocturne torrent]

I MEAN

[umbral steppe]

just not to find the critical points.

[nocturne torrent]

YEAH

[umbral steppe]

it is still used to determine the sign of the denominator given the inequality we have.

[nocturne torrent]

oh man i need to fix my choice of words

before i text

[umbral steppe]

completely unused is definitely wrong.

if we did not know the numerator is always positive, we'd have to do a lot of sign work.

[nocturne torrent]

i’m so

happy

omg

i finally understood

okay wait

let me do it all over again

let me reflect on this

can i ping u when i’m back if ever the channel closes

[umbral steppe]

try not to.

[nocturne torrent]

i got it..

[nocturne torrent]

sooo

the answer has no -infinity or infinity

just

-2<x<2

[umbral steppe]

yes.

[nocturne torrent]

how do i

determine

wait

so this one has an arrow going to the left

and one to the right, right

how about for the problem we solved

this one

[umbral steppe]

two open circles with a line segment connecting them.

[nocturne torrent]

where do i put the open circles

[umbral steppe]

where do you think?

[nocturne torrent]

um

on the -2 and 2?

[umbral steppe]

there we go.

[nocturne torrent]

going towards…?

the middle

or the same

[nocturne torrent]

as the one i showed here

[umbral steppe]

what do you think?

[nocturne torrent]

OH

CONNECTING THEM

so like this

[umbral steppe]

it's rather hard to see, but yes.

[nocturne torrent]

i hope fortune brings upon you, kind ma’am

[umbral steppe]

likewise. is that it?

if there's nothing else, remember to close the channel when you're done.

[nocturne torrent]

well

i have one final problem, but

i can answer it

[umbral steppe]

if there's something else, I'll pass to the next helper along.

[nocturne torrent]

on my own, probably

but

oh.

[nocturne torrent]

alright, thank you, lute

i suppose i can search how to make a sign chart online

.close

[final saddle]

Channel closed

Closed by @nocturne torrent

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brazen stump]

hello is this right?

[worldly mesa]

f(1) is not 10

you did 3 * (1)^2 + 1 = 3^2 + 1 which is not true

[brazen stump]

how should it be

[worldly mesa]

1^2 = 1

3 * (1)^2 + 1 = 3 * 1 + 1 = 4

[brazen stump]

i see

so is 4/16?

[worldly mesa]

yes

[brazen stump]

ty

.close

[final saddle]

Channel closed

Closed by @brazen stump

Use .reopen if this was a mistake.

[final saddle]

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.

[dull laurel]

I don't exactly understand how this is done?? Like how do I get started??

[fallen vigil]

what is 1 OR 0

u work it out from the left to the right. then repeat for the next rows values of A, B, C, D

[plush mulch]

oh these are logic gates, like used in computers

is the "OR" box, that is a "OR" gate

[dull laurel]

gate

[plush mulch]

A and B to the "OR" gates are the inputs

[dull laurel]

1 stands for true 0 stands for untrue

[plush mulch]

they are either True or False (have voltage or have 0 voltage in electronic)

[plush mulch]

So to process the first gate (the OR gate), we would check to see if A OR B is true. If either of them is true, the output of that gate (the "wire" on the right hand side) would be true....

[dull laurel]

ohhh

[plush mulch]

Yh

[plush mulch]

or if we are doing electronics, there is a set of transistors you can wire together that will do the same thing with voltage instead of true and false, this is how computers do math.... True or False, 1 or 0, voltage or no voltage... logically the are the same thing
Or if

[dull laurel]

[plush mulch]

so you would wire up an "OR" gate with a few transistors and other basic electornic components (or just buy a chip with them all built in already)

[dull laurel]

I see

[plush mulch]

Yeah
For the AND gate, we check the inputs (B and C in this case) to see if both B AND C are true (or are 1, or have voltage), if so, the output is also true, for all other possible inputs, the output is false.

[sage meteor]

look up their boolean expressions, it makes more sense with that

is there anything i left out to say? Just look up the boolean expressions, it makes the problem easier to solve

[plush mulch]

the other gates are similiar but each has a different "truth table" (rules for what the output is, based on the input)and some of them don't translate well to english/human speech lol

[dull laurel]

ohhh

yeah I think I get it now

thank youuu

[plush mulch]

Welcome ✋

And for clarification XOR and OR are similar. I only know English so I don't know if happens in other languages but sometimes someone will tell you: "you can have apples or oranges for lunch". And it isn't 100% clear if you can have both or not?

If you can have both, that is logical OR
If you can only have one, but not both, that is logical XOR
So I hope this would help 🙏

in English or can mean either, which sucks 🤷 hahahaha

[dull laurel]

oh yeah my teacher also said something like that

thx

[plush mulch]

You can close the channel

[plush mulch]

another one in English you might hear:
"pick a number between 1 and 6"
assuming they mean integers, does that mean I'm allowed to pick 6? Or is 5 the largest possible choice? In English it isn't always clear (although I'd argue between means you 1 and 6 aren't allowed).

in math:
If 1 and 6 are acceptable choices, its written [1,6]
if 1 and 6 are not acceptable choices, it is written (1,6) ---meaning everything inbetween 1 and 6, but not 1 and 6 themselves. sometimes you'll see really weird ones like:

[1,6) ---meaning 1 is acceptable, but 6 is not!

the most subtle (and hardest) is the difference between IF and IF AND ONLY IF (abbreviated as IFF. I'm not going to touch that one as it tends to confuse the f out of people.

[plush mulch]

I'll just say that in English, if is used for both, as ususal lol

[final saddle]

@dull laurel Has your question been resolved?

Channel closed

Closed by @dull laurel

Use .reopen if this was a mistake.

[final saddle]

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.

[golden cave]

idk how to od

do

it might be 792

[wind orbit]

how many ways are there to top one slice

[golden cave]

um

[golden cave]

4

no

16

[wind orbit]

ya

mb i gotta go for a sec'

[golden cave]

ok

[wind orbit]

k do how many ways are there across four slices

including rotations

[golden cave]

256?

[wind orbit]

no

[golden cave]

oh u multiply by 4

[wind orbit]

what

[golden cave]

or 6

[wind orbit]

no you mutiply it by itself four times

[golden cave]

ok

[wind orbit]

do you get why?

[golden cave]

yea

[sturdy cypress]

it should be 4^5

[golden cave]

what abt 1/2 pizza

[sturdy cypress]

5^4

[wind orbit]

youre not supposed to just give answers

and i think thats wrong

explain

[sturdy cypress]

I can think of 2 types of symmetry, AAAA and ABAB
so like an ABCD would appear 4 times among 625

but AAAA would appear once

and ABAB twice

[wind orbit]

its aaking for rotational

thats just 4

[sturdy cypress]

i don;t know if that's enough

[wind orbit]

abcd dabc cdab bcda