help-0

[chrome plank]

What's the formula to find the distance between two points

[foggy shale]

Uh idk

Sorry 😅

[chrome plank]

The distance between a point A and B is
$\\sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}$

[ocean seal]

Nonna

[chrome plank]

^ You should probably learn this

[foggy shale]

Ohh

Whats x b then

Only one point tho

[chrome plank]

I write the general formula

You use that when you know the coords of two points, A and B

As you said, we only have one point

That's (5, 0)

Here's where something nice happens

The point we are given has y = 0 (so it's on the x axis)

You can divide the circle in two parts (one with y positive and the other one with y negative), and if you pick the same x value, the two points of the circle will have the same distance

Here's what I mean

Do you understand?

[lone heart]

@foggy shale Has your question been resolved?

[lone heart]

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[shrewd marsh]

Anyone knows what this inverted A means?

[clear stump]

for all

[shrewd marsh]

c inv(a) c means c such that all values of c?

or what

[clear stump]

idk I just googled that shit

lemme see some more

[gray isle]

for all c in what I'm assuming is supposed to be the set of reals

[shrewd marsh]

Also there is one another symbol that looks like laterally-inverted 'E' in maths

which means "atleast one"

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[edgy flare]

Also means “there exists”

[gray isle]

$\exists$

[ocean seal]

ℝamonov

[lone heart]

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[alpine sable]

i needed help on this

[lone heart]

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[alpine sable]

.reopeb

.reopen

this is the question

[raven rover]

Try drawing a picture

[alpine sable]

on a aplne?

plane

[clear stump]

Ok I have no idea how you supposed to do them but I see a pattern

[alpine sable]

what is rti

it

[clear stump]

Look at the changes in A and A' and so forth

[alpine sable]

should i calculate the scale factor?

[clear stump]

idk

[alpine sable]

nvm then

[lone heart]

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[zinc dove]

so im doing algrbra 1 to skip it and im stuck on factorzing. I dont know how to do 2 methods, the completeing the sqaure and the sqaure root one. can anyone help me fast pls

[clear stump]

No

I just guess till it works

[wary stream]

Why fast?

[zinc dove]

its coming soon

ive been stuck on it for a long time, fast help would be helpful

[wary stream]

What does that mean, it's coming soon?

[zinc dove]

the tes is

test

[wary stream]

Watch videos

Plenty of videos

[zinc dove]

i did and it didnt help me, i just dont understand

[wary stream]

https://www.youtube.com/watch?v=yk-3ZRG0YAU&ab_channel=TheOrganicChemistryTutor
Did you try that one?

[zinc dove]

probbaly not

ill watch it

were do i find practive problems for this

i think i get it

but i need to see if i can solve

[wary stream]

Look them up on the internet

Khan academy might have some

[zinc dove]

.close

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[inland yacht]

I'm self-studying basic proof writing with the 3rd edition of How To Prove It. I'm stuck on question 13a of chapter 5.4, which is the chapter that introduces closures. Suppose F is the set of all functions on the set A. The task is to prove that, for any subset B of A, B has a closure C under F, or in other words C is closed under every function in F. I'm struggling to figure out how to find and represent the closure. From the examples given in the previous problem, it seems clear to me that the union of the closures of B under each function of F may end up being the closure of B under F, but it's not guaranteed. I'm thinking that maybe a proof by condradiction would be a good approach here, but I can't figure out how to actually find the contradiction.

[lone heart]

@inland yacht Has your question been resolved?

[inland yacht]

Here's the actual question from the book:
If F is a set of functions from A to A and C ⊆ A, then we will say that C is closed under F if ∀f ∈ F∀x ∈ C(f(x) ∈ C). In other words, C is closed under F iff for all f ∈ F, C is closed under f. If B ⊆ A, then the closure of B under F is the smallest set C ⊆ A such that B ⊆ C and C is closed under F. Suppose F is a set of functions from A to A and B ⊆ A. Prove that B has a closure under F.

[lone heart]

@inland yacht Has your question been resolved?

[inland yacht]

<@&286206848099549185>

[lone heart]

@inland yacht Has your question been resolved?

[novel night]

There's a common technique for this kind of argument (showing there is a minimal set with some property, and containing a given set). In this case, try to (1) show there exists some closed set containing B... it doesn't have to be minimal (so it might not be THE closure). Then, (2) show that intersections of (arbitrarily many) closed sets are still closed. From those two ingredients, you can show the closure exists.

@inland yacht Ping me if you need a hint on the last part, or clarification on the bit above.

[inland yacht]

@novel night Thanks for the response. For the first part, A should satisfy the requirement since the fact that it contains B is one of the assumptions and since ∀f ∈ F (f: A → A), it's closed under F. When considering just a single function f to be closed under, I know that the intersection of all sets that both contain B and are closed under f is the closure of B. But I can't make that leap to closing under a set of functions. Is it a natural extension of the intersection strategy and I'm just overthinking it?

[novel night]

Correct on part a. I guess a bit of both on part b? :) It helps to set things up right. So imagine you have a bunch of sets C_a, each closed under F, and each containing B. You want to show the intersection of all of the C_a's is closed under F.

(and I guess you shouldn't forget to check: the intersection of the C_a's still contains B... but that one is easy)

And: to show a set (like the intersection of the C_a's) is closed under F, according to the definition, you have to show this:

For any element c in the intersection and any f in F, f(c) is also in the intersection. You can use the fact that each C_a is closed under F.

[inland yacht]

That makes it a lot clearer and not feel like I need to reinvent the wheel. Thanks for your help.

[novel night]

👍

[inland yacht]

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[lone heart]

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[wind bloom]

how do i find x

[clear stump]

meth

theres probably some kind of theorem you use

[wind bloom]

pythagorean theorem lmao

[clear stump]

sure lol

[wind bloom]

uhh

so

how do i do this bc i did 14.1^2+x^2=15^2 and got it weong

[clear stump]

does that line cut the other line in half?

[wind bloom]

idk

but i assumed

it did

[clear stump]

idk either

I havemt slept

[inland yacht]

14.1^2+x^2=15^2 solves for the line segment above x, but not x itself.

[wind bloom]

oh

then how do i find x

[inland yacht]

Let's call that line segment y. y and x equal the radius of the circle. You should be able to find x from there.

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@wind bloom Has your question been resolved?

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[oblique pier]

,rotate

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[alpine sable]

Oops

It was closed by mistake

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[little berry]

How can you factor these?

[little berry]

like that? then factor the perfect square binomial?

[vale wigeon]

this is not equal to either of the expressions in the first screenshot

are you doing #93 right now?

[little berry]

ye

[vale wigeon]

the best you can do is to factor $x^{1/2}$ out to get $x^{\color{red}1/2} (x-1)$

[ocean seal]

Ann

[vale wigeon]

not x(x-1) as you just wrote

[little berry]

oh

okay thanks

.close

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[normal hazel]

How do i solve a system of polynomial equations on a calculator?

[normal hazel]

3x^2+5y=17
5y^2+3x=13

[fossil gate]

depends what calculator you are using

[normal hazel]

For isntance

I have a TI-84 Plus

I have seen so many videos but they never bring that topic up

[alpine sable]

Usually you input the coefficients of x and y and the constant, in standard form

You do it for both equations

[fossil gate]

Go to menu and 'equations', you should be able to find simultaneous

[alpine sable]

That’s what I’ve seen on most calculators

[fossil gate]

And polynomials

[normal hazel]

okay 1 sec

oh yaeh

poly

root finder?

[fossil gate]

should be it

[normal hazel]

i see one with simult eqn solver although

[fossil gate]

Or you can literally go to graphing and graph both equations, then click 'intercepts'

[normal hazel]

yeah i'll try that

ty

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[alpine sable]

How should I approach this?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[novel night]

As a dumb example, 1/6 + 1/6 + 1/6 + 1/2 is a solution. I believe you're supposed to consider 1/2 + 1/6 + 1/6 + 1/6 as a different solution... if so, think about ways to permute solutions, and pay attention to the possibility some numbers in a solution may repeat (like 6 did above) and how that affects the number of permutations for that solution.

[oak perch]

I guess: solutions are divided into two cases: a=b or not, if a doesn’t equal b, then (a,b,c,d) is a solution implies (b,a,c,d) is a solution, they appear in pairs, so even number many, we consider the case where a=b, then two cases again similarly, c=d or not, we count how many solutions there are such that a=b, and c=d, 2/a+2/c=1, (a-2)(c-2)=4, 3 solutions, (6,6,3,3),(3,3,6,6),(4,4,4,4) so odd many in total

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

ahhh I see, so I could divide the problem into different cases? and determine if they are pairs or not, if one of them is odd, the entire thing will be odd?

[alpine sable]

I think thats it, thanks!

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[vale wigeon]

you know $|P(A)| = 2^{|A|}$, yes?

[ocean seal]

Ann

[kindred anchor]

yes

number of subsets

[vale wigeon]

then what's the issue? this problem is pretty clearly $2^{2^{2^{2^0}}}$

[ocean seal]

Ann

[kindred anchor]

Answer is 16.

Ok

Im too dumb.

Overthinking in every kind of simple questions

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[viral cedar]

mathematically, what is the term of this cell ?

[tender dew]

supremum and infimium?

local maxima/minima

[viral cedar]

Im really have no idea about what you said, but according to google, I did research with your terms

somehow its make sense

[viral cedar]

this one

appreciate your time, have a good one

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[twilit cypress]

Can someone help me understand how this is turning into....

[twilit cypress]

this

[clear stump]

Math

[twilit cypress]

I don't understand where that 4xh is coming from

[twilit cypress]

lol the magic of math?

[clear stump]

I do

whats (x+h)²=?

[twilit cypress]

the same as x^2 + h^2?

[clear stump]

Hell no

[twilit cypress]

(x+h)(x+h)?

[clear stump]

yeah

[twilit cypress]

so FOIL that bitch out?

[clear stump]

now you expand that shit

Yeah

[twilit cypress]

aight, one second

but then I still end up with x^2 + 2hx + h^2

wait, nvm

I'm an idiot

I forgot to multiply it by the 2 after

[clear stump]

I see

Lol

[twilit cypress]

That makes more sense. Thank you @clear stump I appreciate it!

It's too early for me to be doing math

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[warm berry]

how do you make different bases the same to solve for the exponent?

[warm berry]

the question is 9^x = (square root 3) ^ x +2

[vale wigeon]

do you mean $9^x = (\sqrt{3})^x + 2$ or $9^x = (\sqrt{3})^{x+2}$?

[ocean seal]

Ann

[warm berry]

the second one

[vale wigeon]

right

as it happens

9 = 3^2

and sqrt(3) = 3^(1/2)

[warm berry]

yes

[vale wigeon]

so use that to express both sides as 3^something

[warm berry]

so i put it as

3^2x?

[vale wigeon]

9^x = 3^(2x) yes

[warm berry]

why is sqrt3 ^ x+2 turn into 3 ^2x

or is that in reference to 9^x

if so then why is the other side 9^x also

[elfin snow]

it doesn't

[elfin snow]

yes, read ann's last message

what fo you think (√3)^(x+2) will turn into

[warm berry]

i think i need to make both sides bases √3

since 3 is also √3 x √3

.close

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[elfin snow]

what no

@warm berry

reopen it

because √3=3^(1/2)

you can use that

[warm berry]

.reopen

[lone heart]

✅

[elfin snow]

so what would (√3)^(x+2) turn into based on what I just said?

[warm berry]

3^x?

[vale wigeon]

do you know your exponent laws

[elfin snow]

let me write it with latex

[warm berry]

these are it but im not sure how they apply in this scenario

[elfin snow]

$\sqrt3=3^{\frac12}$

[ocean seal]

gmod

[warm berry]

negative exponent rule?

[elfin snow]

so what does $\left(\sqrt3\right)^{x+2}$ become?

[ocean seal]

gmod

[elfin snow]

just make this substitution first

[warm berry]

kk

[elfin snow]

so what do u get

[warm berry]

im going to be honest i am completely lost

[warm berry]

i understand this

but im not sure what sqrt 3 ^ x becomes

[ocean seal]

What the hell am I doing here?

[warm berry]

multiplying the 2 exponents

oh

[vale wigeon]

$(\sqrt{3})^{x+2} = (3^{\frac{1}{2}})^{x+2}$

[ocean seal]

Ann

[elfin snow]

yeah, does that help?

[warm berry]

yes a lot thank you

[elfin snow]

so now you can distribute the 1/2 into x+2

[warm berry]

so x/2 + 1

[elfin snow]

and then ur able to proceed

yep

so now we have $3^{2x}=3^{\frac x2+1}$

[ocean seal]

gmod

[elfin snow]

so now are u able to solve?

[warm berry]

since its the same base you just do 2x = x/2 + 1

yes thank you

[elfin snow]

yep

[warm berry]

im so sorry for being such a dumbass 😭

[elfin snow]

awesome

[warm berry]

thank you for helping me

[elfin snow]

nono

ur good

ofc

[warm berry]

have a good night or day

.close

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[thorn stone]

Friend got 10 i was wondering what the answer is

[slender gull]

What do you get?

[thorn stone]

I didnt do it yet

Solving rn

[slender gull]

Then do it smh.

[thorn stone]

15

If soemone could check that would be great

[languid bolt]

can you show your work?

[thorn stone]

Since 23 are left i subtracted 23 by 8

[languid bolt]

ok so

[thorn stone]

Yes?

[languid bolt]

hmm

i got 18

[thorn stone]

Oh

Can you please explain

[languid bolt]

ok so

13 student didnt take recess

[thorn stone]

Yup

[languid bolt]

so just 40 - 13 it first

27

[thorn stone]

Yup

[languid bolt]

9 people took recess and go to canteen

27 - 9

18?

[thorn stone]

Oh ok

Ty

[last ether]

Holy shit Marvel's a cube now

Oh hell naw

[thorn stone]

Lol

[languid bolt]

i feel offended

i identify as a rectangular prism

[last ether]

Shut up bitchh

[languid bolt]

ok 😢

[fresh parcel]

plot twist: marvel is hexagon

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[azure trout]

What did I do wrong here?

[fresh parcel]

what formula r u using

cosine law?

[last ether]

Cosine bingus

[fresh parcel]

haha what

[azure trout]

yes cosine lol

[fresh parcel]

okay so that should be c^2 = a^2 + b^2 - 2ab cos(C

so where r u getting confused?

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[terse oak]

(pi/a)rect(2at)

[terse oak]

how to plot this

rect is the rectangular function

[true pulsar]

Like a unit pulse rectangular function?

[karmic rapids]

,w plot pi/a rect(2at)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by illuminator3#0001

[terse oak]

.close

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[rose blade]

i alr found the equation for the parabola in vertex form

I just dont know what to do next

[karmic rapids]

is your course sponsored by mcdonalds

[tacit arch]

i prefer my courses sponsored by In N Out

[lone heart]

@rose blade Has your question been resolved?

[waxen flame]

Find the position of the top-corner of the truck and see if it is under the parabola.

[lone heart]

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[tawdry saffron]

can someone give me a hint for this

[abstract fractal]

u sub, maybe

[weary wyvern]

u = ||the denominator||

I would ||multiply the num and denominator by e^(2x)|| but that's probably not necessary

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@tawdry saffron Has your question been resolved?

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[tawdry saffron]

.reopoen

.reopen

[lone heart]

✅

[tawdry saffron]

I thought I had it but the outcome should be this

between the parentheses it says (substitution+partial fraction decomposition)

[weary wyvern]

Did u try this sub

[tawdry saffron]

in the $$1+e^{-x} = u$$ sub I got the integral $$-\int \frac{u-1}{u}du$$

[ocean seal]

Ruffy🎄

[weary wyvern]

Ok

Can you integrate that

[tawdry saffron]

yea

-u + ln(u)

is what I got

[weary wyvern]

Yes

Now what would you do?

The answer should be in terms of x

[tawdry saffron]

well plug it back to 1+e^-x

but how did they get 1+e^x in the ln

[weary wyvern]

If you do this then your answer should be the same as the one given but they might differ by a constant

Because remember in an indefinite integral you have a plus c

You can try to get your answer in the form given plus some constant

Technically there should be a plus c in the answer btw

[weary wyvern]

Hint: || add and subtract x from your answer ||

[tawdry saffron]

ohh

ty

.close

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[abstract swallow]

im trying to do this and am realising i have no clue how negative exponents work

[raven rover]

Here's a long list of identities you can use

The one at the bottom is likely most useful for you

[abstract swallow]

so would the answer to my question be 1.33?

[raven rover]

Show steps

[abstract swallow]

my though with that is 4^ 1/3 is 1.33

[raven rover]

I don't think that's the right application

a^(-b) isn't equal to a^(1/b)

[abstract swallow]

ohhh i see

lemme re do

[abstract swallow]

so to start i make it 1/4^-3?

or do i now take the negative sign away?

[raven rover]

Well, what is the thing you are trying to calculate? the number you are trying to find?

Show each step - from where you start and each step you take to get to the end

[abstract swallow]

so. would it be. 1/4^3. wich 4^3is 64 so 1/64?

[raven rover]

You can plug it into a calculator to check 🙂

[raven rover]

But yes

[abstract swallow]

okaey thanks. o think i got it now

.close

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[woven ginkgo]

how to 232

[raven rover]

What?

[alpine sable]

Idk how to 232

Jk

@woven ginkgo ???

What is your question

[clear stump]

the question is how to 232

[raven rover]

Don't try to help him if he's not even going to share his question

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@woven ginkgo Has your question been resolved?

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[lone heart]

@candid lichen Has your question been resolved?

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[heady pollen]

which outcomes follow the statement?

if you know all these outcomes

then you calculate the probabilities of these outcomes

and add them up

[summer bluff]

Is it C,C C,M M,C

@heady pollen

Or no

[heady pollen]

correct

[summer bluff]

Alr

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@summer bluff Has your question been resolved?

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[modern maple]

Why is this equal to

[modern maple]

x^12 y^4

[clear stump]

do the division

[modern maple]

I did

[clear stump]

cool what you get

[modern maple]

I got x^4 y^5

[clear stump]

Theb you fucked up

do it again

[modern maple]

I already know I messed up

I’m trying to figure out where

I got the same thing again

Help@me

[clear stump]

$\frac{x^m}{x^n}=x^{m-n}$

[ocean seal]

dotcom

[clear stump]

so lets say you do the x first

show me the steps

[modern maple]

This is what I did:

I timesd the x^4 to x^8
And@the x^-2 to x^-4 and then minused the x^-4 by the x^8 and got 4

[clear stump]

so you just did 8-4?

but m=8 and n=-4

[modern maple]

Yeah

8 -4 is 4

[clear stump]

yeah but you did things wrong

$x^{m-n}$ m=8 and n=-4 so $x^{8-(-4)}$

[ocean seal]

dotcom

[modern maple]

Yeah eight minus negative four is four isn’t it

[clear stump]

whats -2*(-3)

@modern maple

[modern maple]

-8

[clear stump]

What?

How

[last ether]

The fuck

[modern maple]

I’m just doing what my teacher taught me in grade 7

[last ether]

Lmao how did you get -8 from -2 • -3

[modern maple]

8 not 7

[modern maple]

Well 2 times 3 is six

[last ether]

Yeah

[modern maple]

So -2 times negative 3 is -6

I made a typo

[last ether]

Then what is negative 2 times negative 3

[tacit arch]

,calc 8 - (-4)

[ocean seal]

Result:

12

[tacit arch]

,calc 8 - 4

[ocean seal]

Result:

4

[last ether]

Buddy this is like

Sign multiplication

-2 • -3 = 6

[modern maple]

This is how I was taught it in grade 8

Was I taught it wrong

[last ether]

No you weren't

[clear stump]

probably not

[tacit arch]

unlikely. you just remembered wrong

[last ether]

Its just that both signs are negative

[clear stump]

your teacher would be out of a job

[last ether]

That logic can only applies if both factors were different signs

[modern maple]

My teacher has a physic degree

[last ether]

Physics entails calculus

I think your teacher knows what they're doing

-2 • -3 = 6

[modern maple]

Why is that positive tho

[last ether]

Because a negative times a negative equals a positive

[modern maple]

Likely, I once forgot my name

[clear stump]

lmfao

[terse oak]

bruh 💀

[placid zinc]

Physics entails some pretty solid math

[modern maple]

Not joke I really did

[clear stump]

how

[terse oak]

physics is actually just maths in a mask

[placid zinc]

sus

[clear stump]

I was sick once and I thought I had slept for over 24h when I sleot for like 2 hours

[terse oak]

sus

[last ether]

@modern maple

[last ether]

If it helps, split this up

[modern maple]

My brain hurts

[terse oak]

which grade are u?

[modern maple]

I once did sleep for 24 hours

[terse oak]

in

[modern maple]

8

I just finished 8

Canada

[terse oak]

u should know -1*-1 = +1

somethings fishy

[last ether]

People forget stuff

Or they have a hard time applying patterns

[clear stump]

yeah

[modern maple]

It was a hybrid class

[last ether]

It's gotta be really out there to be fishy

[terse oak]

um this is over the top, no?

[modern maple]

Grade six and sevens and eights learning the same things

[last ether]

No

[terse oak]

this is like grade 3 or 4 stuff

[clear stump]

he has just learned it so it really isnt

What

[last ether]

Yeah idk what kind of grade shit you're doing

[modern maple]

Excuse me

When I was in grade 4 I just learnt division

[clear stump]

we went over these like 7-8

[last ether]

Sign multiplication is typically, in the US for normal classes, is 7-8, maybe 9th grade

[terse oak]

oh

[last ether]

Whatever math you're learning, that's some accelerated shit

[terse oak]

yeah ig lol

[modern maple]

I gotta go in five minutes

[clear stump]

My screen be pressing shit and I almost called umber

[last ether]

Split this up

[modern maple]

Wait just explain negative multiplication and addition to me pls

[clear stump]

well

-2*(-3)=6

so -(-4)=4

[last ether]

$\left(\frac{x^4}{x^{-2}}\right)^2\left(\frac{y^{-1}}{y^{-3}}\right)^2$

[modern maple]

So do the 2 negatives like cancel each other out

[clear stump]

cause -1*(-4)=-(-4)

that shits 4

[ocean seal]

Umbraleviathan

[last ether]

What multiplying by a negative does is switch signs

• to -, and - to +

So if you take the negative of a negative you're switching signs from - to +

[modern maple]

So it becomes positive

[last ether]

They don't cancel out

[clear stump]

So if you have an even number of - its positive

uneven is negative

[modern maple]

So like -5 * -5 would be 25…?

[clear stump]

yes

and -5* -5* -5=-125

and so on

[modern maple]

And -5 * -3 * -4 would be -60…?

[clear stump]

yes

[modern maple]

Thanks

What about negative addition

Or subtraction

[clear stump]

wdym

like -(-4)?

[modern maple]

Like the 8 - -4

[last ether]

$$a - (-b) = a+b$$
$$a + (-b) = a-b$$

[clear stump]

well thats just -1*(-4)

[vernal thunder]

Subtracting a negative means you add the number (delete the negative)

[ocean seal]

Umbraleviathan

[modern maple]

Thanks

This has been super helpful

[clear stump]

oh yeah that

[vernal thunder]

@modern maple ^ here’s the universal law

[lone heart]

@modern maple Has your question been resolved?

[lone heart]

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[heady pollen]

f(x)=(450+50x)(11-x)

this is defined from x=0 to x=11

[molten lotus]

Wait thats all?

How do I graphically show it then?

[heady pollen]

you plot that graph

[molten lotus]

Do I draw it on the thing though?

[heady pollen]

the thing?

[molten lotus]

Yeah

Like for the question do I just put (450+50x)(11-x)

[heady pollen]

(450+50x)(11-x)=-50x^2+100x+4950

but yeah i would use the factored form
(450+50x)(11-x)

[molten lotus]

Okay

[heady pollen]

but if you take the form
-50x^2+100x+4950
you can easily take the derivative

to find the maximum value

[molten lotus]

Huh

Im so confused

[heady pollen]

you want the ticket prize (x axis) such that you get the most money (y axis)

the maximum will have a slope of 0

so you take the derivative

and set it to 0

you will find that the maximum is at x=1

note that that is not the price of a ticket

we have
price=11-x

so the most efficient price would be
11-1=10

[molten lotus]

Okay

Is that all?

@heady pollen

[heady pollen]

i would say so

[molten lotus]

Okay

I also need help with this question

@heady pollen

<@&286206848099549185>

.clos

.close

[lone heart]

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[raw sequoia]

I don’t get the question and I don’t know where to start

[lone heart]

@raw sequoia Has your question been resolved?

[real gazelle]

hint: the original equation has y intercept -1 (how would you verify this?)

[raw sequoia]

3x^2+4x-2= -1 ?

[real gazelle]

what does y-intercept mean?

[raw sequoia]

The coordinate of y intersects at the y-axis

[real gazelle]

right and what is x equal to when it intersects the y axis

[raw sequoia]

0

[real gazelle]

yup so you find the y-intercept by plugging in x=0

[raw sequoia]

but the y intercept is -1 ?

[real gazelle]

yes how would you figure that out

[raw sequoia]

Wait by plugging in x=0?

[real gazelle]

yea

[raw sequoia]

I'm kind of getting it but at the same time i'm not

Wait

Hold on

I just have to find the y intercept

that's it

?

I verify by finding the y-intercept

Isolate it then plug in 0

It just clicked

Thank you!

[real gazelle]

yes that's the y-intercept but then what's the "second equation" you should pick

[raw sequoia]

well I isolated, 3x^2/2 +0 - 1?

[real gazelle]

wait I'm confused what did you do

[raw sequoia]

I put 3x^2 and 2 as a fraction from 2y and then minus 4x-2 which leaves 2x-1

[real gazelle]

let me ask you a simpler question

if I have the two equations
2x + y =0
and
2x + y =0
how many solutions does it have

[raw sequoia]

2

[real gazelle]

how did you get 2

[raw sequoia]

Wait graphically ?

Or like

if we're talking abt graphics, there's none

But I got y=-1 though?

3x^2+4x-2 = 2y
I isolate the variable
y= 3x^2+2x-1
And then you told me to find the y intercept plug in x as 0
3x0^2+2x0-1 = -1

Or is that the wrong formula?

[real gazelle]

(0, 0) is one solution, (1, -2) is another, (2, -4) is another

how many solutions does it have?

[raw sequoia]

3

[real gazelle]

can you find any other solutions?

another way to think about this is:
how many times does the line 2x+y=0 intersect with the line 2x+y=0

[raw sequoia]

well it intersects w many lines, it's infinite

it goes down

all the way

[real gazelle]

right it's infinite because they are the same line

[real gazelle]

going back to this original question, can you think of a second equation which intersects the original equation at an infinite number points

[raw sequoia]

Wait so I don't have the calculate that equation they gave???

[real gazelle]

you do in order to check that the y-intercept is -1

but that's all you have to do

once you know that, you can give the second equation easily

[raw sequoia]

Okay, I thought of one hopefully this will work
3x - 2y = -1

[real gazelle]

wait how did you get that

[raw sequoia]

I just randomly made it up

[real gazelle]

you want to find an equation that

1. overlaps with the original equation at an infinite number of points and
2. has y-intercept -1

but that equation doesn't satisfy either of those

[raw sequoia]

3x^2-4x-2

Oh hold on

[real gazelle]

hint: you already know the original equation has y-intercept -1, from what we already talked about

[raw sequoia]

3x^2+4x-2= -1 ?

[real gazelle]

uhh almost

you know that if we have two graphs with the same equation

then they overlap at infinitely many points right?

[raw sequoia]

y= 3x^2+4x-2
y= - 1

[real gazelle]

answer the question though

if we have two graphs with the same equation

then how many points do they overlap at

[raw sequoia]

infinite

from what I graphed, infinite

oh

wait

hold on

[real gazelle]

right, so if we want a second equation which overlaps with the first equation at infinitely many points

what should we pick

[raw sequoia]

an equation that = -1

[real gazelle]

no, that will only overlap with the first equation at x=0 (and possibly a few other points)

we want to overlap at infinitely many points

[raw sequoia]

-1+3x^2+4x-2??

[real gazelle]

if you look at this example again

what do you notice about the two equations

they're the exact same, right?

[raw sequoia]

Yeah

They're both the same

[real gazelle]

yep

so what should we make the second equation in this case

[raw sequoia]

the same

[real gazelle]

yep

so what should it be

[raw sequoia]

3x^2+4x+2?

[real gazelle]

well close that's not the same as the original equation, is it?

what's the original equation

[raw sequoia]

2y=3x^2+4x-2

[real gazelle]

yep

so what should our second equation be

[raw sequoia]

2y= 3x^2+4x+2

[real gazelle]

remember, you want to find an equation that

1. overlaps with the original equation at an infinite number of points and
2. has y-intercept -1

[real gazelle]

why +2?

[raw sequoia]

Oh i just realized the mistake

[raw sequoia]

2y= 3x^2+4x-2

[real gazelle]

yep!

and now we know that this satisfies property 1 that we want, it overlaps with the original equation at an infinite number of points

and we also know from earlier that it has property 2, it has a y-intercept of -1

so this is a good answer

[raw sequoia]

Ohh that makes sense

Thank you so much!

[real gazelle]

no problem!!

[raw sequoia]

.close

[lone heart]

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[frozen dragon]

help pls

[lone heart]

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[candid lichen]

Hi can someone please help me <@&286206848099549185>

[iron mulch]

BRO

!15min

[lone heart]

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

[iron mulch]

READ RULES PLEASE

[candid lichen]

if you don't calm down. i wont figure it out in 15 mins which is why i pinged

[wary stream]

Or you could have read the rules and understand that you post your question, wait 15 minutes, and if no help comes, you get to ping

[candid lichen]

wow u rlly slayed me dldh06

[wheat breach]

what's the time pressure? is this a test?

[candid lichen]

no its cus i had like 2 other tickets w no one talking it in

😭

throughout the day

[wary stream]

So?

[candid lichen]

which is why i pinged quicker

seemed like people responded now 😭

[wary stream]

People responded because you prematurely pinged

[candid lichen]

yha and no one responded when i didnt

so like..

[wary stream]

This wouldn't have happened if you actually waited

[candid lichen]

what would have happened was me not getting an answer naur

[wary stream]

Then you wait

Simple

[candid lichen]

yay thats what i did

and waited hours

[wary stream]

Okay, and?

[candid lichen]

well its a homework id like to,... do it

[lean depot]

I might give answering this a shot 😊

[candid lichen]

ur so real boytjie ❤️

[wheat breach]

unless you deleted messages you haven't asked this question in this server yet

so

[candid lichen]

i defo did

[wary stream]

You're not special, you don't get privileges that allows you to ping early. You wait , like everyone else

[candid lichen]

if u dont calm down

u r a discord mod please 😭

[lean depot]

So, your question has some information about how often something occurs, and it wants you to infer a probability distribution. What are your first thoughts on how to answer this?

I don't think discussing what happened is going to be helpful :)

[wary stream]

Also, this server is all voluntarily, meaning no one is obligated to help you, if they don't want to

[last ether]

This is funny

Entitled people in discord

[wary stream]

Just saying

[last ether]

You know, I never thought I'd see that shit in here

But like

[candid lichen]

im assuming i have to multiply games played w/ frequency

[last ether]

Y'all funny just saying

[lean depot]

Can you explain this a bit more?

[candid lichen]

multiply these values to get a mean

or something like that

im horrible w stats

[lean depot]

I still don't understand what you mean by multiply, so maybe I'll talk about what I think is going on here

The frequency is the number of times that a particular outcome has occured

one interpretation of probability is the following

The probability of an event is the number of times this event has occured, divided by the number of times anything has happened

So let's do a specific one

let's work out P(4)

What do you reckon this will be?

[candid lichen]

4 x 18 ?

[lean depot]

Why's that?

[candid lichen]

because the 4 games have a frequency of 18

[lean depot]

So the probability of 4 games being played in a tournament is 4 x 18 = 72?

There's something awry with this.

Can you see what the issue is?

[candid lichen]

no girl i cant

[lean depot]

Okay, here's a very important rule

[candid lichen]

i have 0 clue what is happening in the equation 😭

[lean depot]

Probabilities are always between 0 and 1

[candid lichen]

ok slay

[lean depot]

And 72... it's a bit far away from that

OK great

So I can see you're confused about the question

[candid lichen]

ik i prob have to divide by something i just have no clue what it is

[lean depot]

Yeah that's cool we'll get there

Like, do you know what the numbers 4,5,6,7 are supposed to mean?

bc it's a bit of a trick: those numbers don't matter

the setup is like this, if you read the question carefully

Every year there is a tournament. Some number of games are played at this tournament.

Every year there are either 4, 5, 6, or 7 games played

You cool with that?

[candid lichen]

yes

[lean depot]

So when I ask, what's P(4), I'm asking... what is the chance that if I chose a random year, that year would have 4 games played

Let's have a look at this table one more time

https://cdn.discordapp.com/attachments/490557019623915520/999139426682806293/unknown.png

So in the column where it says 4 then 18 underneath

That's saying that in 18 different years there were 4 games

[candid lichen]

okay yha

[lean depot]

OK

Just wanna be 100% clear on this bc it's important for the calculation

[candid lichen]

peri

[lean depot]

Now can you calculate for me

How many tournaments have there been in total?

[candid lichen]

so

its 18 x 4

[lean depot]

Really?

[candid lichen]

to find

[lean depot]

Why?

[candid lichen]

how many

omg

im sorry i cant take this just tell me what to do mama 😭

cus what im seeing

is

if there are 18 times 4 games were played

thats 4 x 18

[lean depot]

So the numbers on top (4, 5, 6, 7) is the number of games in a particular tournament

But I asked

how many tournaments were there in total

[candid lichen]

4+5+6+7

[lean depot]

Why is this?

[candid lichen]

IDK

like please just tell me

i just wanna find this mean

[lean depot]

I don't want to just tell you, because if I do, then you won't understand.

But I'll start with this

[candid lichen]

no because i will

#promise

[lean depot]

let me try a different method

Let's forget these numbers 4,5,6,7

So every year there's a tournament, and we'll call it a bad tournament if there are only 4 games in it

So the table says there were 18 bad tournaments

right?

[candid lichen]

SO 18 x4...... to find how many games played

[lean depot]

Not asking that yet! Please just bear with me!

So again

if there were 5 games in the tournament that year, it's just OK

So the table says... how many OK games were there?

Whoops, bad language

I mean

how many OK tournaments were there?

Can you tell me that from the table?

[candid lichen]

like 5

[lean depot]

5?

[candid lichen]

or 12

[lean depot]

No, this is not right.

[candid lichen]

one of the two

[lean depot]

Please tell me which one

[lean depot]

Can you quickly explain to me why

[candid lichen]

im gonna b so real if u just tell me how to find the mean with this chart i will understand

what ur doing is confusing me way more

[lean depot]

I'm sorry, if you don't understand this then I cannot believe that you will understand this from the chart.

[candid lichen]

ok

[lean depot]

But you agree right, there were 18 tournaments with 4 games, and 12 tournaments with 5 games

We're good with that?

[candid lichen]

yes

okay

[lean depot]

So now let me ask, how many tournaments were there in total?

This will be used later

[candid lichen]

this is a 6 part question

I HAVE NO CLJHEU

proaBBLY

ALL OF THEM

[lean depot]

Okay

[candid lichen]

added together

[lean depot]

That's right. Because the table lists all the tournaments, ranked by the number of games in each one, it lists all the tournaments

so can you calculate the total number of tournaments?

This is your cue!

OK, well when you're ready to continue do ping me

[autumn oyster]

@lean depot im back on a different account

im ready to continue

[lean depot]

OK cool!

[autumn oyster]

so the number of tournaments, is it 4?

[lean depot]

Okay, no it isn't.

I need to ask you this, are you guessing? Please don't guess. It's very important that you don't just guess.

What I've figured out is the first confusion you have is how to read the table

So can we go through this quickly? I promise it'll be worth it.

[autumn oyster]

yes

[lean depot]

Ok. So the setup, again, is that we have a tournament every year. Games are played during these tournaments

Every tournament has either 4, 5, 6, or 7 games

This table counts how many tournaments there have been of each type

[autumn oyster]

I thought there are 4 tournaments in this data set

[lean depot]

No, but there are 4 kinds of tournaments

ones with 4 games, ones with 5 games, etc

do you see that?

[autumn oyster]

yes

[lean depot]

OK great!

[autumn oyster]

so is the number of tournaments in each of the frequencies

[lean depot]

That's correct

so the first row, labelled "x (games played)" is just listing the kinds of tournament

[autumn oyster]

That means 74 tournaments

[lean depot]

the second row, Frequency, is counting the number of tournaments of that type

Yes that's right!

OK wonderful

And of course, that's the sum of the frequencies

So OK

Let's move on to probability

The question doesn't say this explicitly, but it wants you to calculate the probability like so

the probability of something happening is the total number of times it's happened divided by the total number of times it could have happened

[autumn oyster]

so it would be each of the frequencies divided by 74

?

[lean depot]

That's exactly right.

Perfect!

[autumn oyster]

yay

so

for the first p(x)

it would be

18/74 = .2432

[lean depot]

Yeah that's right, you could write this as p(4) = .2432

[autumn oyster]

ohhh

okay

I think i have it now

thank you so much

[lean depot]

OK good stuff

Do you want to give the other parts a shot?

[autumn oyster]

I got

.2432
.1622
.2568
.3378

[lean depot]

Looks right to me

[autumn oyster]

perf

[lean depot]

alright nice

I need to get to sleep so I will have to leave you, but good luck with the other parts

[autumn oyster]

Thank u!!!

[lean depot]

hopefully another person will give you a hand

no worries

[autumn oyster]

Have a good night

[lone heart]

@candid lichen Has your question been resolved?

[lone heart]

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[lone heart]

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[severe quartz]

Can someone explain the process of solving this question?

Do I need to use the circumference for this question too

[chrome plank]

When does a tire do a complete rotation?

[severe quartz]

Doesn’t say and it’s not necessary information for this problem

[chrome plank]

Answer this

[severe quartz]

.close

[lone heart]

Channel closed

Closed by @severe quartz

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[chrome plank]

Bruh

[lone heart]

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.

[tropic oasis]

this is a problem i have a question with

the one i know how to do is with the table and we're given the subinterval

and with the table i can find the points x and y

but in this problem with the geometric formula

how would i go about finding my x and y points?

i know my x points are from [0,3]