help-27

[robust ermine]

so is it all - (less than 7k + even - less than 7k and even)

all is 5P4

less than 7k+even is 4*4P3

less than 7k AND even is 3*4P2

5P4-(4*4P3-3*4P2)

its 60

i was missing a bracket

WHT AM I DOING WRONG

[uncut crow]

the digits are 2,3,7,8,9.
the 4 digits numbers less than 7000 and even look like 2xx8 or 3xx2 or 3xx8

do you see an issue in your expression?

[robust ermine]

oh crap

i was

i was ooking at a different question when i did the last part

[uncut crow]

we have 3 left to choose 2 from and permute, not 4

[robust ermine]

i read 6 digits

42

ITS CORRECT

LETS GOOOOOOOOOOOOOOOOOOOOOOO

FINALLY

bless ur soul fam

ur patient as hell

LOL

tysm

.solved

[devout snow]

Channel closed

Closed by @robust ermine

Use .reopen if this was a mistake.

[robust ermine]

never again

complementary counting

to hell with with it

[uncut crow]

lol no sometimes it is the simplest way

just not here

[solid perch]

if complementary counting leads to some weird inclusion-exclusion bs, then might wanna consider direct counting.

[robust ermine]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaai will

thank u peepole

[uncut crow]

[devout snow]

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[tender kite]

.close

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[devout snow]

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[latent hedge]

IM SORRY MY PHONE CAMERA IS BROKEN I CANT TAKE A PHOTO OF THE QUESTION BUT ILL TRY EXPLAIN IT AS WELL AS POSSIBLE

"in the coordinate system the parabola y= x² + k and the line y= -6x - k is shown below. If the parabola is tangent to the line at point (m,n), what is the sum of m+n+k?"

[latent hedge]

i got 27 as an answer and its none of the choices...

[solid perch]

can you please show your work? (typing it out is fine if you cannot take a picture of your written work.)

[tepid kestrel]

is it 15?

[latent hedge]

x²+k = -6x -k
x² + 6x + 2k =0
its tangent therefore ∆=0
6²-4(1×2k) =0
k= 4.5
y= -6x -k
y= -6(4.5) - 4.5
y= -31.5
4.5 + (-31.5) = -27... 😭😭

[latent hedge]

YEAH

PLEASE SHARE THY KNOWLEDGE

[solid perch]

y= -6x -k
y= -6(4.5) - 4.5

where did you get x = 4.5 from?

[latent hedge]

isnt b²-4ac supposed to equal 0 if its tangent

[solid perch]

that's k.

using the discrim should only give you the value of k.

[latent hedge]

oh woops

[solid perch]

you still need to find the point of intersection.

[latent hedge]

😭

[solid perch]

try doing that.

[tepid kestrel]

do you know basic diffrentiation?

[latent hedge]

holy crap im stupid

[tepid kestrel]

wait nvm ill let chiakiwxplain it

[latent hedge]

no i havent learnt calc yet 💔

[solid perch]

calculus is not necessary for this problem, don't worry.

[tepid kestrel]

Its not just makes it easier

[solid perch]

anyway, substitute k back into x² + 6x + 2k = 0, and then proceed.

[hollow ice]

||or just use -b/2a as the x||

[latent hedge]

so x would be -3?

[solid perch]

there's also that, yeah.

[solid perch]

correct.

[latent hedge]

what 💔

[solid perch]

now you can find your y.

[latent hedge]

y= 13.5

[solid perch]

if a parabola is tangent to a straight line, its vertex must be on that straight line.

so...

[hollow ice]

recall your quadratic formula and put discriminant as 0 there

[latent hedge]

ohhh

[solid perch]

looks right. now sum x, y, and k.

[latent hedge]

dude im gonna fail math atp

[latent hedge]

FIFTEEENN

[solid perch]

and there you have it!

[latent hedge]

YAAAAAAY

[sand quarry]

Merhaba hemşehrim

[latent hedge]

😮

paşam

yarına mat projesi var onu yetistiricm

ANYWAY THANK YOU CHIAKI

❤️❤️❤️😭😭😭

[solid perch]

glad to have helped!

[sand quarry]

iyi sanslar

[latent hedge]

.close

[devout snow]

Channel closed

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[devout snow]

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[maiden cloud]

@polar chasm Are you there?

[gloomy aurora]

um so firstly please post your question.

and secondly even though MathIsAlwaysRight may appreciate it, as a general rule,

!noping

[devout snow]

Please do not ping individual helpers unprompted.

[maiden cloud]

It’s a continuation bro

[gloomy aurora]

It doesn't matter

||and do not call me bro||

[maiden cloud]

why

[gloomy aurora]

I'd prefer not to disclose.

Please post your question.

[devout snow]

@maiden cloud Has your question been resolved?

[devout snow]

Channel closed

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[jaunty moat]

Can anyone help on how to do part c or like those questions in general

[jaunty moat]

answer for part a is x < 4

part b = 3 < x and x < -1/2

[neon folio]

well you probably just intersect the answers from a) and b)

right

[jaunty moat]

Idk I have no idea how to do these types of questions

[neon folio]

draw a number line

[neon folio]

and colour these intervals

[neon folio]

and this

for a) colour it blue

and for b) colour it red

and see in which intervals you have both colours

thats the answer

[jaunty moat]

Is there a faster way?

Cause like spening 5 mins on a num line for 1 mark is not worth in my opinion

[neon folio]

the faster way you learn by yourself after mastering this method

[jaunty moat]

Alr

[neon folio]

and doing it in your head

[jaunty moat]

Thanks

.close

[devout snow]

Channel closed

Closed by @jaunty moat

Use .reopen if this was a mistake.

[jovial fox]

i have a test tomorrow

[jaunty moat]

Good luck

[jovial fox]

thanks

can you give me some tips about probability?

like those tree diagrams and stuff

[neon folio]

if you have a specific question we can help you

!help

[devout snow]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[jaunty moat]

What grade or what lvl

[jovial fox]

i don't have questions

me grade 7

[jaunty moat]

For tree diagrams watch 1stclassmaths, he has a 20 min video on tree diagrams and other probablity stuff. You'll basiclly be set for the entire topic if you watch that

[jovial fox]

Thank you so much

I will ace that test for ya

😄

[jaunty moat]

Yesssir

[reef copper]

@jaunty moat you got your answer???

[jaunty moat]

gl

Yep

[jovial fox]

thanks bye

[jaunty moat]

bye

[reef copper]

@jaunty moat

[jaunty moat]

Yes

I already closed it

[reef copper]

Ok

.close

[jaunty moat]

.

.close

Yeah it wouldn't work

[devout snow]

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[modern thistle]

could I get help with this?

[modern thistle]

I know that prism vol = area of base x height

and area = l x w

but im not sure how to do this with it slanted?

[coarse flume]

You can think of the trapezoid (the face with sides 2.5, 4 and 25) as the area and 12 as the height

[modern thistle]

I'm sorry I don't understand

are you saying it would be 1/2 x (2.5+4)x12 =39? is that right?

[vestal surge]

1/2 x (2.5+4)x25

not 12

thats the area of the trapezoid in the q

[vestal surge]

after that you can use 12m to find the volume and convert it into gallons and well you can find the cost then

[modern thistle]

ah so vol = 81.25 x 12

[vestal surge]

yeah

[modern thistle]

okay thank you

.close

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[devout snow]

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[buoyant verge]

hi

[buoyant verge]

Is this proof valid?

Is for a topological space (X,T) where A,B are a subset of X

[uncut thicket]

isnt that statement itself wrong??

[buoyant verge]

it shouldn't

[uncut thicket]

it is

[coarse flume]

Definitely is

[buoyant verge]

have in mind that $\overline{A}$ is the Adherence of A

In a topological space

[woven radish]

S0S4 - Feel free to ping

[uncut thicket]

is this complement of set??

[buoyant verge]

nope

[coarse flume]

Ok that makes more sense mb

[heavy current]

closure of a set

[buoyant verge]

Adherence of A in a topology (X,T)

[uncut thicket]

ok sorry this is not what i meant ok nevermind

[buoyant verge]

where A,B are subsets of X

[buoyant verge]

Don't worry, is my bad for not specifying it

I have rewrited it

[heavy current]

why is that last set the same as cl(A) U cl(B)?

[heavy current]

you’ve just asserted it without explaining why

[heavy current]

hm, that still doesn’t explain why

[buoyant verge]

I know that is from that there

that you can distribute it

[heavy current]

mhm!

that’s the key step you should show explicitly

in fact, I’d recommend changing the style of the proof to double inclusion

instead of working with the entire set

[buoyant verge]

Should I say like: Distributing G intersection (A U B) gives you...

[heavy current]

ideally yes

[buoyant verge]

I have never done a double inclusion proof

[heavy current]

but it would be super clunky to write that with the entire set

[heavy current]

it’s the standard way to to show that two sets A and B are equal

show that A is a subset of B and B is a subset of A

[buoyant verge]

I'll try my best

would you help me through it?

[heavy current]

you can do it c:

sure!

do you know how to show one set is a subset of another?

[buoyant verge]

Thanks, give me a bit of time and I'll try to came back with something decent

[buoyant verge]

nope

[heavy current]

right, you need to fix an arbitrary element of the first set and show that it lies in the second set

[brittle inlet]

Long time no see

Dropping a little hint here: fairly sure the definition of closure I gave you last time should work out here as well

[heavy current]

and then conclude that because the element you chose was arbitrary, the entire first set lies within the second set

[buoyant verge]

I have noted it and I have studied it xD

[brittle inlet]

Which should also allow you to train yourself a little with intersections

[buoyant verge]

Let me try it and come back with something consistent 🙂

[devout snow]

@buoyant verge Has your question been resolved?

[buoyant verge]

Would this be valid?

I'm sorry Prim for not using your definition😔

@heavy current

[heavy current]

in the => paragraph, you need to be careful when you say that "this is the definition of cl(A) U cl(B)", because that isn't the defn

in fact, you need another sentence

since $(G \cap A) \cup (G \cap B) \neq \emptyset$, either $G \cap A$ or $G \cap B$ is nonempty, hence $x$ is either in $\operatorname{cl}(A)$ or $\operatorname{cl}(B)$ by definition

and hence x is in cl(A) U cl(B)

[buoyant verge]

wow

well

[woven radish]

higher!

[buoyant verge]

I'm happy I did like 90% of the proof

and how do you know when you have to explain more?

it is until you get to the basic definitions?

[heavy current]

as for the second paragraph, you've written two equalities and taken the union of them, which isn't good notation

your idea is right, and I can tell what you're trying to do, but the notation is kinda made up

you can't take the union of equations

[buoyant verge]

[heavy current]

you want to say that $G \cap A \neq \emptyset$ and $G \cap B \neq \emptyset$, hence $(G \cap A) \cup (G \cap B) \neq \emptyset$

[woven radish]

higher!

[heavy current]

and then you can more or less continue as you already did from there

[heavy current]

well, in this case, you had to explain more because the conclusion hadn't been reached yet, because what you claimed was the definition wasn't

[buoyant verge]

It now we be valid?

[heavy current]

yeah, this looks great to me c:

...with one exception you should replace "which is the definition of cl(A U B)" with "which means x is contained in cl(A U B)" :p

[buoyant verge]

thank you very much 🙂

I'll close the channel, you probably see me again in like an hour because I got a hell of large topology exercise sheet xD

thanks also to prim

.close

[devout snow]

Channel closed

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[primal ferry]

i have this exact miku sticker irl! this was so cute to see

[devout snow]

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[wet berry]

(im doing the college panda sat math textbook and) i have no idea how they simplified x^3 inside the parenthesis

how did we get (x+1)((x^3 )+1)?

[supple knot]

factor out (x+3) from the previous line

[heavy current]

if you treat x + 3 as an variable itself, say y, then your express is x^3y + y = 0

then it becomes more clear to factor y out

[wet berry]

im sorry im still trying to understand how we removed x^3 and the y and got x^3+1😭

[heavy current]

the x^3 wasn't removed at all, wdym?

[wet berry]

it went inside the parenthesis right

[heavy current]

it didn't really move anywhere, I guess it's more that x + 3 moved out :p

if you relabel $x + 3$ as $y$, then $x^3(x + 3) + (x + 3)$ can be written as $x^3y + y$, agreed?

[woven radish]

higher!

[wet berry]

yes

[heavy current]

then now we can factor y out!

$x^3y + y = y(x^3 + 1)$

[woven radish]

higher!

[wet berry]

OH

😭😭

[heavy current]

convert back by using y = x + 3, and we get the result

[wet berry]

thank you so much

[heavy current]

no problem

good luck with the SAT c:

[wet berry]

thank you im taking it in like 3 days😭😭

[heavy current]

I hope it goes well

[wet berry]

.close

[devout snow]

Channel closed

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[devout snow]

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[glossy dew]

hmm

[glossy dew]

wait a moment

these are the cases i got

[devout snow]

@glossy dew Has your question been resolved?

[devout snow]

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[errant hatch]

aaaaand we're back

[errant hatch]

div both sides by 10 and we now have 25^(t-3) = 625

[misty crest]

write 625 as a power of 25

[smoky rapids]

25^t/25^3=625=25^2
25^t=25²*25^3=25^5
t=5

[errant hatch]

25^(t-3) = 25^2

oh

uhm

[misty crest]

or just t - 3 = 2

[smoky rapids]

yeah

[misty crest]

never do this

[errant hatch]

wait u lost me at the 2nd line

[misty crest]

don't bother

[misty crest]

you have this

bases are equal so exponents must also be equal

[misty crest]

^

[smoky rapids]

https://tenor.com/view/chill-guy-chill-guy-just-a-chill-guy-relax-gif-1579445140409713118

Yeah actually just listen to knief

You have same bases

[misty crest]

,av carlos19zy

[woven radish]

carlos19zy's Avatar

Click here to view the image.

[smoky rapids]

[errant hatch]

uhmmm

oh

OH

same base

so the exponents

[errant hatch]

have to be the same

ok

wow

brain openeing

[misty crest]

guh suck out yuh madda chessmaster57906. wid a straw!

[errant hatch]

oh

@misty crest

ariseee

[misty crest]

hello

[errant hatch]

greetings

[errant hatch]

im at

log y = x/3

[misty crest]

good start

now use the definition of log y

do you have a definition from your notes?

[chrome sky]

The answer is C

[errant hatch]

whats a note?

[chrome sky]

Just a simple application

[errant hatch]

clown~1

[errant hatch]

which idk how to do

[errant hatch]

wdym?

log b10 y?

[misty crest]

$\log_b x = y \iff b^y = x$

[woven radish]

knief

[errant hatch]

hmmm

[misty crest]

have you ever seen something like this

[errant hatch]

maybe

yeah

[summer summit]

!nosols

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[misty crest]

so here the base is 10

if they don't write it then you can assume it's 10 i guess

at least for this class

[chrome sky]

3Log y=x
Log y^3=x
The base of the log is not specified so we assume it is base 10 generally
Solving it will be y^3=10^x
Y=10^x/3

[misty crest]

🍪

🏅

[errant hatch]

how did we get y^3?

[chrome sky]

Hmm this is an advance way of writing on discord but have to explain able

[misty crest]

he applied a log property for no reason

what you did is perfectly reasonable

[chrome sky]

That is a rule In logarithms

[misty crest]

bro what

[chrome sky]

Log a^x=xLog a

[misty crest]

just leave dawg

you're not being helpful

no one cares that you know how to do it

[summer summit]

this is a formatting language called LaTeX. it's actually a lot easier than typing it out on a discord chat.

[chrome sky]

Okay brr just trying to explain

[chrome sky]

Yeah

[errant hatch]

still mentally at log y = x/3

[misty crest]

refer to what i wrote earlier

[misty crest]

here

[chrome sky]

For which one

[chrome sky]

Okay I understand

[summer summit]

refer to the top two here, these are general log rules

[errant hatch]

log y = log b10 y = x which is = to 10^x = y?

[misty crest]

nono

not sure what you're saying actually

[chrome sky]

No 10^x=y

[summer summit]

yes

[chrome sky]

It is 10 raised to the power of x

[errant hatch]

yeah mb

forgot the ^

[chrome sky]

Okay Scholar

[summer summit]

?

[errant hatch]

so 10^x = y...

wait what abt thr x/3

[misty crest]

it isn't 10^x = y

[summer summit]

replace x with x/3

[misty crest]

you have $\log y = \frac{x}{3}$

[woven radish]

knief

[errant hatch]

maybe i should write it down

[summer summit]

you will have a fraction as your exponent which may seem/look weird at first but is correct.

[chrome sky]

It going to be 10^x/3

[summer summit]

this is not helping. nobody learns if they are given solutions to every problem

[errant hatch]

ok

about this

im just gonna call x y and y x to make it less confusing for me

[misty crest]

mhm

[errant hatch]

if log y = x what happens to the other x

from the x/3

[misty crest]

other x?

x is just a placeholder

log y = anything implies that 10^anything = y

[errant hatch]

for what? whatevers on the pther side?

[misty crest]

yes

logs are inverses of exponentials. given some base, they take as input some number and output what exponent you need to raise the base to to get that input

[errant hatch]

am i raising x to the power of x/3?

[misty crest]

read this a few times if you have to

[misty crest]

and compare what i said to this

i can give examples if you'd like

log 100 = 2 because i need to raise 10 (which is the base of the log here) to the power of 2 to get 100

[misty crest]

nice

[errant hatch]

ok so what now?

[misty crest]

nothing

circle the answer

they asked you to find y

you did that

[errant hatch]

OH

hey chat

actually wait

.close

[devout snow]

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[devout snow]

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[red hornet]

hello

[red hornet]

Moey needs help

got a test tomorow

on Polynomials

and quadratics

[south oxide]

hi

[red hornet]

hi

[hollow vine]

pls ask the exact question straight away

[red hornet]

the question that makes me question everything is( part b)

m teacher used diistance formula idk why

[summer summit]

.pin

[red hornet]

omg why does this always happen

[summer summit]

<@&268886789983436800>

[red hornet]

people spam random stuff and never help

please @ me

[hollow vine]

do u have to use it? it'll help with explaining

[red hornet]

yes

[summer summit]

well first of all, maximal vertical separation means both points will have the same x value

[red hornet]

ok

[summer summit]

you can set point $A = (x, x^2-3x)$ and $B = (x, 2x - \frac{x^2}{2})$

[woven radish]

Krish

[summer summit]

so use distance formula on that first

and let me know what you get (yes it will be an expression involving x)

[red hornet]

but why do i use x,x^2-3x instead of x^2-3x

[summer summit]

what do you mean?

its a point, not an expression

some coordinate value on the graph (x, y) where we set y equal to each of the equations you have

[red hornet]

so x is x1 and x^2-3x is x 2?

[summer summit]

no.

they correspond to the x values of each

distance formula is $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

[woven radish]

Krish

[red hornet]

ok

[devout snow]

@red hornet Has your question been resolved?

[red hornet]

i still need the rest of th explanitation

<@&286206848099549185>

[heady vapor]

what do you need ?

[hard shoal]

What even is the question

[red hornet]

check the pinned bar

[red hornet]

.

i need an explanation for part b using distance formula

[summer summit]

did you do what i mentioned?

[red hornet]

i already have the answer i just wanna get the explanation

[summer summit]

explanation for which part?

[red hornet]

i used f(x)-g(x) but my teacher wants me to use the distance formula

[summer summit]

yes that's what i told you to do... did you plug in point A and B into the distance formula?

[summer summit]

that shows exactly what i said. can you elaborate what part are you confused on?

[hard shoal]

I see it but whats it asking for all i see is graph and some algebra

[summer summit]

this is the "(y2 - y1)^2" in the distance formula

[summer summit]

it's stated in the picture.

[hard shoal]

i was talm bout the previous one butyes i see the solution now

[red hornet]

and why do we use (x-x)^2 instead of just plotting x in

if that makes sense

[summer summit]

i know, its stated in the original picture

[summer summit]

because we don't know x yet.

[hard shoal]

ohh at the bottom i overlooked that i just saw grid

[red hornet]

after using distance formula why do we use axis of symmetry formula?

[summer summit]

your professor has incorrectly done a step.

when they do -b/2a, it should evaluate to 5/3, not 5/2.

[red hornet]

hmm

[summer summit]

-b/2a is the formula to find the vertex

[red hornet]

ok

[summer summit]

so your professor's final answer is slightly off from what it should be from what i can see

[red hornet]

but why we using axis of symmetry formula

[summer summit]

read this.

the vertex of a quadratic is defined as $(\frac{-b}{2a}, f(\frac{-b}{2a}))$

[woven radish]

Krish

[summer summit]

@red hornet do you understand this?

[red hornet]

so a vertex is 2 axis of symmetry?

[summer summit]

no... a vertex is the minimum or maximum of a parabola

[red hornet]

ok makes sense

[summer summit]

the axis of symmetry is a vertical line that passes through the parabola

the axis of symmetry is the equation for a line, whereas the vertex is a singular point on the graph/plane (x, y)

[red hornet]

yes

[summer summit]

yes. so you understand the question then?

[fresh imp]

hi moey how u doing

[red hornet]

good

how about you dash

[fresh imp]

i have been good

[red hornet]

now this?

[red hornet]

rn are u good?

[fresh imp]

yeah

[fresh imp]

have a nice day i gtg busy day

[red hornet]

ok cya

[red hornet]

@summer summit

[summer summit]

literally just plugging in x

except x should be 5/3

[red hornet]

ik but i want the reason

to why we use distance formula twice

im a very logical person

@summer summit

[summer summit]

there shouldnt need to be distance formula twice

you can just straight up plug it into d = 3x^2 / 2 - 5x

[red hornet]

$3x^2/2-5x$

[woven radish]

Moey

[red hornet]

?

[summer summit]

yes, that is what i said.

[red hornet]

$1.5x^2-3/5x$

[woven radish]

Moey

[summer summit]

?

where did you get this from

[red hornet]

thats the answer to 3x^2/2-5x

[summer summit]

huh?

[red hornet]

wait no nvm

i thought u can divide 3x^2 with 2

im dumb

[summer summit]

this is literally all you need to do to get your answer

[red hornet]

it doesnt do that here

[summer summit]

that is literally what your professor did.

[red hornet]

i dont see any division

[summer summit]

what do you mean

fractions are division

although it is wrong, your professor is plugging in 5/2 into d

@red hornet is there anything else you don't understand?

[red hornet]

thats it

[summer summit]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[red hornet]

thank you

.close

[devout snow]

Channel closed

Closed by @red hornet

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[brazen scarab]

Could someone teach me how to do number 5 I am lost

[brazen scarab]

x^2+xy+x-y+2=0

ok

I did that

I got y= ((-x-2)(x-1))/x-1 -((4)/x-1)

here I am thinking that x=1 is a removable discontinuity

but AI told me no

and idk why

but basically I got y= -x-2 -((4)/x-1)

y=-x-2 is my horizontal asymptote and x=1 is my vertical asymptote

[winter patrol]

missing some () in your plain text representation
you should have () around the whole denominators when typing in text
anyway

$$y = \frac{(-x-2)(x-1)}{x-1} - \frac{4}{x-1}$$

[woven radish]

ραμOmeganato5

[winter patrol]

y= -x-2
would be an asymptote, however that is a slanted line
would be referred to as an oblique asymtptote, not horizontal

[brazen scarab]

so would the horizontal asymptote be converted to an oblique?

when we get a slanted line?

[winter patrol]

wdym converted

[brazen scarab]

like I feel like a horizontal asymptote existed in the equation before

[winter patrol]

it exists or it doesn't
here you don't have a horizontal one

[brazen scarab]

but because of the xy component the asymptote that once was a straightline became slanted

[brazen scarab]

oh

ok

[winter patrol]

there isn't a removeable discontinuity at x=1
because that isn't a restriction in the original equation

in the process of manipulating the equation to a form with easier to identify key features,
that was self created

actually 1 sec

[brazen scarab]

I did long division

and ended with a remainder

[winter patrol]

due to the /(x-1)
in the second term

[brazen scarab]

original was this

[winter patrol]

you'd actually have a vertical asymptote tehre

[brazen scarab]

yes

same thing

I just prefer the x-1

[winter patrol]

there was real issue with the work

[brazen scarab]

I don't like dealing with 1-x

I am asking why is x=1 not a removable discontinuity .

[winter patrol]

$$y =-x-2 - \frac{4}{x-1}$$

[woven radish]

ραμOmeganato5

[winter patrol]

the equation would simplify down to that

no issue cancelling out those (x-1)/(x-1) since that same restriction is still present in the 4/(x-1) term

[brazen scarab]

wdym

like because the x-1 is still present in the remainder

(4)/x-1

[winter patrol]

x-1 is still present in a denominator

[brazen scarab]

therefore we do not have a discontinuity?

[winter patrol]

indicating a restriction that x can't be 1

and (x-1)/(x-1) = 1 when x isn't 1

[brazen scarab]

oh so basically the asymptote already included the discontinuity?

or we shouldn't phrase it like that

[winter patrol]

you have a vertical asymptote there, which would make the curve discontinuous there

[brazen scarab]

ok

I get it

so what is the next step to graphing the equation?

should I create an interval?

[winter patrol]

wdym by interval method

[brazen scarab]

my teacher taught us this

[winter patrol]

,rotate

[winter patrol]

2nd image yes
first is for something different

[brazen scarab]

its the same concept

my teacher taught us to create graphs using it

[winter patrol]

i suppose,
essentially plug in values of x to identify which section your graph is in

[brazen scarab]

yea

but Im really confused

[winter patrol]

and also identify other key parts like intercepts if they exist

[brazen scarab]

yeah thats the scary part, IDK what to do if I don't have a factorable equation and I can't find intercepts cus of skill issue

or sometimes intercepts don't exist

and idk what to do

cus I don't have another method

[winter patrol]

for the y-int simplify plug in x=0

[brazen scarab]

right..

[winter patrol]

for x-intercepts plug in y=0
and if you can't find a way to factorise or can't be bothered
you can use the quadratic formula

[brazen scarab]

mmmm you right

[winter patrol]

here there won't be any x-intercepts

[brazen scarab]

oh yeah I can set things to y if I get the quadratic formula

[winter patrol]

you can check yourself

and then you can also just plug in other x values to get a few other points of the curve

to identify which section they lie in

[brazen scarab]

uhhh so I plugged in y= 0 so in my original equation I got x^2+x+2=0

[brazen scarab]

you mean like plugging in x=1,2,3... and x=-1,-2,-3....

and see if values exist?

[winter patrol]

the values will exist (except at x=1 where your asymptote is)

[brazen scarab]

right

[winter patrol]

plug it into that equation

[brazen scarab]

why not the original?

[winter patrol]

you want the y-coordinate to get your points

more efficient

rather than having to rearrange for y every time

[brazen scarab]

wait if I am determining my x/y intercept should I always use it from my modified equation?

[winter patrol]

doesn't really matter

[brazen scarab]

does it ever matter?

[winter patrol]

but if you're goal is to get the y-coord where x= something
and you already have an equation of the form
y = ...
then its more efficient to use that

[brazen scarab]

ok I'll just try to determine which is more efficient to use

my algebra might be wrong

but I got x-intercepts to be (-3,0) and (2,0)

[winter patrol]

algebra is wrong

[brazen scarab]

when I plugged into y=-x-2-((4)/x-1)

uhh y= 0

I get x+2=(-4)/x-1

multiply both sides by x-1

I get x^2+x-2

add 4 over

oh

nvm

yeah its not factorable

[winter patrol]

should view that as adding 4 to both sides

"move" is quite vague and not recommended

[brazen scarab]

mb bad habit

[winter patrol]

are you expected to graph other key details like turning points?

[brazen scarab]

no but I should know what I am doing

like I probably need to know symmetry, domain, asymptotes, intercepts to graph

I don't need to provide it

[winter patrol]

mmk.
any other issues?

[brazen scarab]

yeah Idk how to graph it

[winter patrol]

did you plug in some values of x into your manipulated equation?

x=-3, y = ?
x=-2, y = ?
x=-1, y = ?
x= 0, y = ?
x= 2, y = ?
x= 3, y = ?

[brazen scarab]

so I shouldn't use interval method?

oh I remember what I was confused about

so I was unsure whether or not -x-2 belonged in the interval

[winter patrol]

interval method you showed is for identifying signs

the principle is more or less the same
but you aren't really interested in just the signs

but rather which section of the point you obtained and graph will be in

[brazen scarab]

well -x-2 is part of the manipulated equation

[winter patrol]

after you've identified your asymptotes, you should start drawing that on your graph

then you'd want to test a few values before/after 1 to identify which section your graph will be in

[brazen scarab]

it used to look like this, but we removed x-1 and could 4 , x-1, exist in the interval

[winter patrol]

wdym

used to look like this

[brazen scarab]

cus we could get x-1, -x-2, x-1, x-1

[winter patrol]

over complicating

did you plug in some values of x into your manipulated equation?
x=-3, y = ?
x=-2, y = ?
x=-1, y = ?
x= 0, y = ?
x= 2, y = ?
x= 3, y = ?

[brazen scarab]

perhaps it is for the best

maybe I'll just stick to interval when we have bounces in our curve

I don't think conics have bounces

[winter patrol]

technically for what they're asking,
one point on each side of x=1 is sufficient
they more you use more accurate your graph will be / the better it will look

[winter patrol]

depends on the conic

[brazen scarab]

WhAT are you serious... conics can have bounces in the curve?

Im actually cooked for my test

I didn't learn conics well

[winter patrol]

so as mentioned, just plug in some x values and tell me what you get

[brazen scarab]

(-1,1), (-2,1.33), (-3, 2), (0,2), (2,-8), (3,-7)

[winter patrol]

plot those points on your graph

[brazen scarab]

btw I just need a rough shape

[winter patrol]

and even just one on each side would indicate that your curve will be in the top left and bottom right

[brazen scarab]

oh

is that how you can always determine which quadrants the graph will exist in?

[winter patrol]

yes

[brazen scarab]

fire

[winter patrol]

and if they don't care about find the exact turning point
you can just draw something where the ends tend towards those asymptotes

[brazen scarab]

ok

[winter patrol]

and also note that since you determined that there are no x-ints
that part in the top left shouldn't cross the x-axis

[brazen scarab]

yes

ok thank you it makes more sense now

yippie

.close

[devout snow]

Channel closed

Closed by @brazen scarab

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[devout snow]

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[lament wigeon]

i get the numbers but what symbol would the answer have

[lunar harbor]

... does this question even make sense

Take $x=-2$ and $y=-0.99$. Then $xy=1.98$, so A, D are out. C literally says $-1>1$, which is obviously bullshit, so that's out. And taking $x=-2$, $y=4$ yields $xy=-8$, so B is also wrong.

[solid perch]

one way to find out is to draw the two inequalities on a number line, I suppose, for the 'proper' way to do it.
wait, I did not see the nature of the answers. ignore this.

[woven radish]

Civil Service Pigeon

[lunar harbor]

Hello?

[lament wigeon]

this is what the explanation shows but i dont understand it

[lunar harbor]

Read what I said above. The answers are all bullshit, so any explanation justifying one of them is inherently wrong.

[lament wigeon]

alright then ill skip it

[solid perch]

ah okay, I see what they're doing.

[solid perch]

they're doing this mistaken idea.

basically they want to find out the compound inequality without noticing that the notation that they used means the product of x and y.

[valid silo]

Ok, this question is technically not bullshit

{xy : -1 < xy <= 1} is just the set of values xy can take give -1 < xy <= 1, the set {a : a = 2} is just the set {2}

They are just giving you two sets, and asking for intersection.

[devout snow]

@lament wigeon Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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[devout snow]

Available help channel!

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[icy wagon]

I did this sin and cos like wave test HOWEVER how do I know when it goes up or it goes down

[icy wagon]

I’ll do a small sketch hold on

Really horrible drawing Ik but the 1st one goes up and the 2nd goes down

[solid perch]

what do you mean, wave test?

[summer summit]

sin starts "halfway up the wave" at (0,0) and cos starts "at the top of the wave" at (0, 1)

[icy wagon]

Idk the name tbh

It was just some like waves that’s what it looks like fr

[sturdy palm]

The period you mean

[summer summit]

the red wave is sin, the blue is cos

[solid perch]

then I'll let Krish handle this.

[icy wagon]

Well yes but like drawing one cuz they made us draw one how do I know to like draw it up or draw it going down the midline

[summer summit]

im not sure im understanding your question.

[icy wagon]

I think I’m confusing myself too

ILL TRY TO FIND A BETTER WAY TO SAY IT AND THEN MAKE THID AGAIN BUT THANKS A LOT FRIEND

How do I close this

-close

!close

Uh

[sturdy palm]

,close

[summer summit]

its .close

[icy wagon]

,close

[sturdy palm]

Oh hahaha

[icy wagon]

.close

[devout snow]

Channel closed

Closed by @icy wagon

Use .reopen if this was a mistake.

[sturdy palm]

Blind leading the blind

[dim perch]

eventually

[summer summit]

72 special characters later

[last parrot]

You knew it would be .close

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[bronze void]

how do I go about this? I've gotten an answer although im pretty sure my process is quite wrong

[solid perch]

there is an alternate interpretation for c).

might want to check that.

in fact there might be many interpretations for c).

[bronze void]

yea

its a bit ambiguous

[sand quarry]

i think you are misinterpreting what 'unique' means here

[bronze void]

decode the string of numbers into letters, which ever is unique lettering is the answer no?

[sand quarry]

No

that's not what the question means by unique

[solid perch]

but see, you have alternate interpretations for at least one of them. what does that tell you?

[bronze void]

the one with many interpretations cannot be the answer ?

[solid perch]

oh okay, I kind of misunderstood what OP misunderstood about uniqueness.

[bronze void]

what a sentence

[solid perch]

well yes. after all, if a string of digits arose from multiple sets of letters...

[bronze void]

so like how 12 can be A B or L

but wouldn't that apply to like all 3 cases we have?

[solid perch]

can you find an alternative interpretation for a)?

remember, 0s cannot stand alone and cannot be the leading digit of a two-digit sequence as stated in the instructions.

[bronze void]

ah no, since none of the strings are 26 or higher

there is only 1 interpretation for a.

[solid perch]

mhm.

[bronze void]

a. 4, 5, 10, 6, 2, 7, 1

b. 2, 8, 3, 10, 40, 1

huh

[solid perch]

b. 2, 8, 3, 10, 40, 1

[solid perch]

what happened to the initial 4? I could have sworn I saw it before you edited it.

[bronze void]

i missed it i think

yea i missed it when typing over

b doesnt work bc 40 is only possible number and there isnt 40 letters in alphabet

c. 10, 9, 2, 3, 1, 14

all of these are unique

[white elk]

c isn't unique

[bronze void]

how...?

[white elk]

there's a few different groupings

[bronze void]

OH bc u can group it as 10, 9, 2, 3, 1, 1, 4

[white elk]

the first digit would havae to be either a 1 or 2

yeah that also works

I was thinking 23 personally

[bronze void]

how did u get 23??

[solid perch]

^^^

[white elk]

2, 3

[bronze void]

oh grouping it like that

ic

[solid perch]

between the (2, 3) pair and the (1, 4) pair I can see at least four interpretations of c).

in fact there might be more, because the (1, 4) pair is preceded by another 1.

[white elk]

there's also 11

ye

so 6?

[tall linden]

Ah, yes. <ab> and <l> is definitely the same letter sequence.

[sand quarry]

there are six combinations

[white elk]

actually I don't think it matters though

[sand quarry]

but anyway this is besides the point i guess

[white elk]

since it just asks for unique

[solid perch]

mhm. sorry for the wild goose chase.

[sand quarry]

did you catch the goose

[white elk]

lol it's a fun goose chase though

[bronze void]

it is a "group" challenge paper lol

[white elk]

sorry I don't get it

[bronze void]

oh the questions im doing

are from a competition

and this part is the group based task

and im using it as study material for the actual thing

[white elk]

oh I'm sorry I thought you were making a joke for some reason lol

[bronze void]

part joke part serious

[white elk]

well I guess I mean wordplay somehow

anyways

I am very distracted rn

[solid perch]

I guess you have enough helpers now so I think my job here is done. all the best!

[bronze void]

tysm for the help!

[white elk]

did you need anything else?

[bronze void]

ill probably be back later

tbh

[white elk]

okie doke

[bronze void]

these are some hard problems (for me at least)

[sand quarry]

hey you did all the work we (I) did nothing lol

[solid perch]

I did nothing as well. all nanojumper here.

[white elk]

you did a bunch before I got here

[bronze void]

you all helped out a bunch

[white elk]

don't fret it

yeah

[bronze void]

i should be fine with this one but ill check in later

[white elk]

ah yeah these are called gnomons btw

I'm not sure why but it's a fun name lol

[bronze void]

?

gnomons

[white elk]

like the outside part of a shape

yeah

[bronze void]

uh

intersting...

[wooden roost]

its c

[bronze void]

?! its a

[wooden roost]

oh

[white elk]

yeah, I'm fairly confident it's a

[wooden roost]

wait im geeking

[white elk]

lol

[bronze void]

allg

[wooden roost]

yeah its a

i see it

[solid perch]

but just as an aside, you might not want to jump directly to solutions next time.

!nosols is a thing in this server.

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[bronze void]

oh so for the inital "skin" for this problem

1*\1*1 just makes 1 cube right

then 2*2*2 makes 4, 1 cubes

[solid perch]

I think your escapes are not working the way you think it would.

also what's 4, 1 cube?

[white elk]

yeah you got it now

[bronze void]

like 4, 1*1*1 cubes

[white elk]

as in the skin of the cube is made up of 4 1*1*1 cubes

[solid perch]

are you sure?

[violet wind]

Here take this ×

[white elk]

maybe x for * is less cumbersome

[solid perch]

or am I misinterpreting?

[white elk]

oh wait no I am being dumb

yeah it is not 4

recount the number of cubes in a 2x2x2

[solid perch]

also sorry to jumper, that was not directed at you and I realize it might sound a little too pointed.

[bronze void]

something like this

[white elk]

no worries

[solid perch]

but yeah OP, reconsider the 2x2x2 case.

better, if you have such cubes on hand, count the number of cubies present.

[bronze void]

the skin would just be the uhh amount of visable cubes

[white elk]

mhm

so how many could you see in a 2x2x2?

[bronze void]

4 per side, and 6 sides so 4*6 = 24

[white elk]

I believe it asks for the number of cubes you can see

not the square faces

[bronze void]

The skin of ‘Cubik’s cube’ consists of those building blocks which lie in at
least one face of the constructed cube

so just one face then

[white elk]

hmmmm

well okay how about this

how many of the 2x2x2 cubes can you not see

[bronze void]

none

[white elk]

exactly

so that means all of them are visible

which is how many?

[bronze void]

4*6 = 24

[white elk]

well how many cubes are there in the figure?

[slim rose]

Why you trol

[bronze void]

??

4 cubes per face, and 6 faces

[solid perch]

so you're saying each corner of the 2x2x2 is a different cubie?

[bronze void]

yes

[white elk]

so think about labeling each of those cubes with a number

[solid perch]

very sure?

[white elk]

if you were to count them

[slim rose]

There is form

[white elk]

you have to make sure that you aren't counting the same one twice

[bronze void]

Oh

right

they can share

[white elk]

ngl should've thought to get a picture by now

[solid perch]

my bad, sorry.

[white elk]

so how many cubes are there?

[solid perch]

also I'm sorry for stepping back in and interrupting, will step back for now.

[white elk]

all good

[bronze void]

so if they share the corners then we get.... (lemme think rq)

[white elk]

not a problem at all

[bronze void]

just 8 no?

[slim rose]

So firist 2 number goes x2 and 3 th goes / 2

[white elk]

yes!

[slim rose]

And number this is / is number of figure

[white elk]

none of them are invisible which means there's 8 total cubes

[white elk]

now what about cubik's rubik's cube

[bronze void]

well we have 1 unique per face

so we have at least 6 to start with

[slim rose]

So g=1xn2x4/n

[bronze void]

we have 1 in the centre that isnt visable

[white elk]

so do you remember how it was a little annoying to think about it like this because we overcounted

[bronze void]

and we have 8 remaining cubies, so 2(8) + 6

22?

[white elk]

yes, this is the right approach

not exactly

[white elk]

thinking about the faces gets quite complicated

[slim rose]

What is problem

[white elk]

there's actually a little simpler way

[white elk]

you can but there's a much easier method I'm hinting at

[slim rose]

Why don't we just use formule

[solid perch]

I think it's best we let nanojumper help without interruptions unless to add something.

[solid perch]

formulas without understanding is not very helpful imo.

[white elk]

when we count things it can be easier to count the opposite of what the problem asks and then leveraging some extra information to find what we're actually looking for

[bronze void]

kudos for finding a formula tho

[solid perch]

if I may jump back in to offer a general piece of advice though.

[white elk]

so instead of how many cubes we do see, let's look at a simpler question for how many you don't see

[white elk]

yeah go ahead

[bronze void]

just the 1 in the centre

[white elk]

mhm

now we know the opposite problem

[bronze void]

3^3 - 1

so 26?

[slim rose]

From where comme this one in centar?

[white elk]

yes!

[solid perch]

well that, and after discounting invisible cubies, consider fixing a face and counting from there, then counting surrounding faces, remembering which cubies have already been counted from previous faces.

[white elk]

and now it generalizes

[solid perch]

then you can rediscover whatever formula you can use for this.

because there is a sort of pattern to this that you can glimpse from counting it that way I feel.

[bronze void]

oh so for 4*4*4 we get 4^4 - 2^2

[solid perch]

as long as you remember you're not done, yes.

alright, said my piece. I'll back off for now.

[white elk]

not squared

[white elk]

it's slightly different

[bronze void]

there isnt 4 cubies in the centre we cant see?

[white elk]

I'm not sure I understand exactly?

[bronze void]

or is it bc theres now stuff in the centre of each face

[solid perch]

that was directed at OP.

[white elk]

well okay what are the dimensions of the inner cubies?

[white elk]

oh mb

[solid perch]

I'm just using your message to say that OP should first discount the invisible cubies, then start counting outer faces.

[slim rose]

They all are same

[solid perch]

mb.

[white elk]

I guess I should say: what shape is the invisible part

[slim rose]

So i think inner one most be 2x2x2

[white elk]

sorry but can you not answer questions without spoilers

[fluid stag]

that question is for OP. please do not answer questions not meant for you

[white elk]

this is kinda their problem and we're tryna guide them to the solution

[fluid stag]

and if possible, just let nanojumper help for now

[slim rose]

I don't even understand questions

[fluid stag]

then please let nanojumper and KB discuss this

[bronze void]

oh yea it is 2*\2*2 bc its 3d not 2d