help-27

[pseudo basin]

you seem to be mixing these together

[silver folio]

Nvm I rewrite

,rccw

[pseudo basin]

so you got that R is 10 ohms?

[silver folio]

Ya

[pseudo basin]

ok, so then how did you find the current thru this resistor?

[silver folio]

The last step

(10/10+4)*4.2

If pass thru 4 then (4/10+4)*4

[pseudo basin]

incorrect bracket placement and also incorrect calculation actually

the currents are INVERSELY proportional to the resistances in a parallel connection; you calculated as if the proportion is direct.

but also you can just use V = IR again bc the voltage is the same 12V

[silver folio]

Alright I get this

But how could I show the calculations?

Oh I get it already thx

.close

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[paper radish]

i thought when you solve the derivative, you first have to differentiate f(x) rather than immediately plugging in the value (ln x)

[solar goblet]

that's one way to solve it yeah, by using chain rule

the way they did it is imo bad, they basically are differentiating f(ln x) as a sum

[lavish nimbus]

Notice that $$(x^2)’=2x \cdot (x)’=2x$$ so by first substituting, it’ll avoid missing the $(x)’$.

[woven radish]

Good

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[dull heron]

Hi, I got -6 and was stuck as I didn't see it as an answer choice. I understand the question is vague on purpose probably to make it harder. But am I wrong in thinking the wording should have been "if -2 is one of the solutions to the equation..."(?)

[wraith horizon]

reading

"if -2 is one of the solutions to the equation..."
this is identical to "if -2 is a solution"?

[devout snow]

@dull heron Has your question been resolved?

[dull heron]

ah yes, I guess they're akin to each other... a solution can imply one type of solution that exists for that question.. Thank you

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[pliant hamlet]

guys i am little confused

[final osprey]

write 21 as 22-1 and 12 as 11+1

[pliant hamlet]

yes that will solve it too but

[final osprey]

oh modulo

[pliant hamlet]

according to this if we proove that 21^100 and 12^100 are congurent then then there difference must be multiple of 11

but we very clearly see that they are incongruent so there difference should not be multiple of 11

can someone clearn this for me

in answer key it is stated that the answer is yes

[hollow ice]

try and factorize it first

||difference of squares||

[pliant hamlet]

i know how to solve it without modular arithmetic , my confusion is specifically wrt modular arithmetic

[hollow ice]

once yoyu factorize, applying modular arithmetic gets easier

[pliant hamlet]

bro read what my confusion is exactly above

[hollow ice]

Yea, I read that

[pliant hamlet]

doesn't this produce a contradiction ?

that should not be

[hollow ice]

I'm saying (-1)^2 and 1^2 are equivalent even if they are not congruent

21 is (-1) mod 11, and 12 is 1 mod 11. If you square them individually, they become congruent

[pliant hamlet]

so if the powers were odd , this wont hold anymore ? right

[hollow ice]

for this specific case, yea you are right

[stone stump]

brackets please

[hollow ice]

lol yea

[pliant hamlet]

but if we only consider positive remainders then ? or do we have freedom in modular arithmetic to work with any according to our choice ?

[hollow ice]

You can choose any convenient remainder. They are all equivalent classes

[pliant hamlet]

hmm ok

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[heavy terrace]

quick q, can this be considered a discontinued function?

[heavy terrace]

where it goes down forever, it becomes parallel to the ordinate axis

[wind mason]

Hmm

Well, it seems to be the end of the domain, so I would say no.

[heavy terrace]

right

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[restive river]

heelp

[restive river]

a way to make this easier

[simple seal]

there is a nice factorization but it is quite hard to find cos of the number of factors the coefficients have

its $(2x-9)(3x+10)$ if im not wrong

[woven radish]

ashy!

[restive river]

dude

thanks but I asked how to make my process easier

not asking for the direct factors

[simple seal]

process for what exactly

[winter patrol]

the values you're looking for will be opposite in sign
and based on the sum of -7,
you could focus on factor pairs closer together

or in this case, knowing that 540 = 2 * 270
you should be able to see that = 20 * 27

and technically you should be using ac = 6 * **-**90 = -540

[devout snow]

@restive river Has your question been resolved?

[restive river]

ik thasat

im confused on the x - y = -7/ +

what is that x and y

and how can I use a quadratic formula to find x and y

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[low canopy]

Find the equation

[low canopy]

I've tried formulas in mnd

But my gut tells me im wrong

the main one is if i already know the slope

Which is

$y-y1=m(x-x1)$

[woven radish]

Reuba

[low canopy]

but theres 2 which means (x1,y1) and (x2,y2)

I've tried finding the slope first

But my gut still tells me im wrong

Pls help

[devout snow]

@low canopy Has your question been resolved?

[low canopy]

Yes

/close

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[umbral torrent]

So I must show that v is an eigenvector

Am I tripping or is it not?

Av= [0 0 0] ?

Av= 0v but lapda may not be 0 or am I tripping?

Aaah so v cant be 0?

wait imma look up the theorem

Bonk how are you

STOPPP

hahaha

aaah v cant be 0

but lapda can be alright

alright thank you :)

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[umbral torrent]

So the algebraic and gemoetric multiplicity of each eigen value

I got 3 lambda: 1, -2, 3

[frozen aurora]

off topic but what book/resource is this?

[umbral torrent]

Uhm Lineair_Algebra_Modern_Introduction_4th_edition

u want the author as well?

[frozen aurora]

nah i found it

[umbral torrent]

damn

fast

[frozen aurora]

okay and on which part are you stuck?

[umbral torrent]

So i got my 3 eigenvalues

then I created my 3 matrices?

I dont really understand what those are tho

wait ill show my work

[frozen aurora]

for diagonalisation? or what

[frozen aurora]

no answers, please

[umbral torrent]

that is me ;-;

[frozen aurora]

oh

[umbral torrent]

no worries u are not the first

[frozen aurora]

lmao

[umbral torrent]

so uhm

The E1 and E-2 and E3

What do those tell me exactly

[devout snow]

@umbral torrent Has your question been resolved?

[umbral torrent]

<@&286206848099549185>

[devout snow]

@umbral torrent Has your question been resolved?

[umbral torrent]

.close

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[faint gorge]

bro

[umbral torrent]

?

[faint gorge]

i was just looking at that

[umbral torrent]

Noooooo

.reopen

how did I know ;-;

[devout snow]

✅

[faint gorge]

You were asking what the E matrices represent

[umbral torrent]

I know but no one was responding

so I just gave up and moved to my next question ;-;

[faint gorge]

well when you plug in your eigen values into the matrix then you solve the system and get the eigen vector

[umbral torrent]

eigen values are the lambdas right?

[faint gorge]

yes

[umbral torrent]

but then I get my eigen value matrix but what does that give for info?

Like what is it useful for?

[faint gorge]

it's just the eigen space and by solving the system you are essentially deriving a basis of that eigen space

[umbral torrent]

Aha alright

Thank you :)

Could you maybe help with something else too?

[faint gorge]

i see

[umbral torrent]

Ax=λ1v1? or like what can I do with those eigen vectors?

Hmmm that would not work actually :/

[faint gorge]

ok so you are given the eigen vector and eigen values of some matrix A, now iirc you could diagonalize A under some conditions and thus compute a power of A with ease

[umbral torrent]

diagonalize A?

[faint gorge]

yes

[umbral torrent]

Hmmm never seen that before

[faint gorge]

S contained the eigen vectors, where D contained the eigen values on its diagonals

[umbral torrent]

We use this?

[faint gorge]

i think it was A is diagonalizable if the geometric multiplicity was equal to the algebraic multiplicity

[umbral torrent]

Why did our professor not explain this to us ;-;

Is diagonalizing the only way?

apperently he is going to explain that to us next week ;-;

[faint gorge]

What is Theorem 4.18

also have not seen that before, I believe

[umbral torrent]

Imma check

[faint gorge]

Bonk sucks

[umbral torrent]

nah ur not dw

[umbral torrent]

But for this question I must diagonalize A is there no other way?

Cuz our prof will learn that to us next week so I suppose there must be another way?

[faint gorge]

you can use that method as well, mine might be a bit complicated

Basically you need to see if your eigen vectors span R^3 if i understood correctly

because then you can express x as a linear combination of the eigen vectors and apply the given theorem

[umbral torrent]

Alright imma try that!

[faint gorge]

but like at first glance they are

[umbral torrent]

ye true

so uhm x= c1v1+c2v2+c3v3?

[faint gorge]

yea you basically want to expess x as a linear combination of the vectors v

[umbral torrent]

aaah so now i can do this:

wait is my c1 and c2 and c3 1?

omg

i am dumb

[faint gorge]

i gtg for now

[umbral torrent]

no worries

I think I figured it out

thanks :)

[umbral torrent]

I think this should be it?

[umbral torrent]

what did I do wrong ;-;

Mbbbb

I see

alright thank you

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[undone cloud]

have i done this correct?..

[hollow pulsar]

u can check urself by subbing ur answer in the original equation

[ocean gale]

Don’t forget to divide the negative sign

[hollow pulsar]

youll find it wrong cause on the second line, u removed the negative sign that was originally for x/5

[zenith star]

Intuition says the answer should be negative.

[wind mason]

Negative go r/wooosh

[undone cloud]

Oh, im pretty good at english, so no worry :)

yeah, id realised that after looking at another question :) i just forgot the - in most of them. still, thanks for the confirmation!! :D

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[dense jay]

.close

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[bleak imp]

Hello you great math fellows, got a question regarding algebra.
So let say we have two binary operators ♠, and ♣ over the nonempty set S. I need to prove or disprove if the following equality holds for a,b, and c from S:
a♣(b♠c) = (a♣b) ♠ (a♣c)
So my answer is "It Depends!"
The equality holds iff operator ♣ is distributable in respect to the operator ♠, so just like multiplication, and addition over R.
So I'm asking if it's related to the priority of the operators? or we just need to if two given operator are distributive in respect to each other? I mean is there any subject in algebra that is related to this?

Thank you very much for your time and consideration.

[lusty sapphire]

The parentheses remove ambiguity of priority

Distributive property shows up in Fields, which is an extension of an Abelian Group

[stone stump]

(it already shows up in rings)

[lusty sapphire]

oh oops. I always forget rings

[faint gorge]

who proposes without a ring

[lusty sapphire]

I know a group of people

[stone stump]

but of course you need to know what a♤b♧c is supposed to mean if you want to deal with those operations

[bleak imp]

Awesome, so the definition of the operator matters, and I need to study regarding fields and rings to provide a rigid answer?

[stone stump]

well rings and fields are the most natural objects you encounter which have two operations like that

but from the start in both you assume that one operation has the higher priority and then from there you don't think about it further

[bleak imp]

So priorities are identified just by nature of two operators, no any other way. I mean we need to know what those operator are doing first. (sorry for bad questions)

[stone stump]

yes

or well, also no

you could also just doing "normal arithmetic" but with the priorities flipped

it would just be cursed and lots of properties wouldnt hold anymore

there isnt anything specific that would necessarily prevent you from doing it

its just generally much more natural in most cases do to a particular order

but into the definition of rings and fields the order of the operations is built-in

frankly your question is hard to answer

[bleak imp]

Maybe I asked a stupid question. sorry, I ask many questions. Am not proud of many of them.

[bleak imp]

This is very interesting, and I've not started rings and fields yet, so maybe I'm still early(probably yes).

Awesome. I really really really appreciate your time and consideration. I have a clear path to study regarding this now. Thank you @stone stump , @lusty sapphire, and @faint gorge .
Math bless us all 🍻

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[worldly coral]

Hard Game Theory Question:

You are forced to play a game with 44 other players. Each of you are presented with 5 boxes - each labelled 1 through 5. You must place the value on the box inside one of the boxes (eg. you may choose to put 1$ into box 1, or 2$ into box 2).

After everyone places their money in a box (without knowing what anyone else has placed their money into), the game master comes in, and takes the box with the most money in it, selecting uniformly at random in the case of ties.

Everyone who's money was not in that box gets their money back. Assuming all players are rational, what is the optimal strategy for this game, and what is your EV?

Is this even solvable w/o numeric methods? I tried using monte carlo as well as multinomial to define a loss function and got ~0.54 as EV, not sure if my loss function is right though.

[devout snow]

@worldly coral Has your question been resolved?

[autumn fjord]

I like this question, where did it come from?

my first thought (which might be wrong) is to pick a number between 1 and 15, if i get a 1-5 I'll put it in $1, 6-9 I'll put it in $2, 10-12 I'll put it in $3, 13-14 i'll put it in $4, and on 15 I'd put it in $5.

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[tribal knot]

This is how I solved my firstone

now im stuck on 2

I need help Identifying them Im not sure what all the names are

Aswell as how do I tell if its supplementary or Congruent?

[devout snow]

@tribal knot Has your question been resolved?

[tribal knot]

<@&286206848099549185>

[tame palm]

In 2), those are corresponding angles.

[tribal knot]

Thank you 🙏

Do you happen to know how to solve?

[tame palm]

Corresponding angles are equal to each other.

[tribal knot]

still gotta solve for X

[tame palm]

Yes, so set the two angles equal to each other.

[tribal knot]

okay so 60x=59x+2?

[tame palm]

Yes.

[tribal knot]

W coach whats the next step

Divide?

nvm

cant

60 n 59

[tame palm]

?

[tribal knot]

waitt

59-60x

right?

i mean60-59x

so x=2?

[tame palm]

Yes.

[tribal knot]

so theyre congruent?

[tame palm]

They better be. They're corresponding angles.

[tribal knot]

W Kookie in the chat

lwk dude

[tame palm]

That's a property of a transversal line across parallel lines.

[tribal knot]

love u for explaining it to me in a way that I can actually understand

not sure how to do this

if yk pls explain

[tame palm]

Which one?

[tribal knot]

the F(x)

[tame palm]

Wihch problem?

[tribal knot]

if u can just explain one of each section

if you have time ofc

[rain token]

a

[tribal knot]

I missed a bunch of school and my teacher is making me learn it all by myself

like

for a medical

reason

I was out

and shes just dropping it on me to figure out

[rain token]

Im not good at math but I think you find the points where they both intersect and you plug that in for x and y

[tribal knot]

(-4,-3)

(2,0)?

[rain token]

I think

[tribal knot]

hmm

[rain token]

Shucks they dont make sense when you plug them in

You're just trying to find which values work for x and y right?

[tribal knot]

I think so

[rain token]

I dont know if you've done this before

but if x^2-24 and x-12 both equal y

You can set x^2-24=x-12

[tribal knot]

then u can solve for x?

[rain token]

Yeah

[tribal knot]

+24 on both sides

[rain token]

If you've learned quadratics I think you can do that

[tribal knot]

or no

I mean

square root of x

then gotta do that on the other no?

[rain token]

Do you know how to solve quadratic equations

[tribal knot]

I feel like ive done it

[rain token]

ax^2+bx+c sound familiar

Or the quadratic formula

If you subtract x and add 12 to both sides

[tribal knot]

yes

[summer summit]

for 9 and 10, if you have y = ___ for two equations in the same question, that means that they are equal.

[rain token]

You'd get x^2-x-12=0

[tribal knot]

so the x's on 9 are equal

same as the x's on 10

[rain token]

Factoring you'd get (x-4)(x+3)

I gtg but try that out

[summer summit]

yes

[tribal knot]

thanks dude

ill try that in a bit

[summer summit]

for number 11, if you are given a graph and asked to find the solution, the solutions will be all points where the two intersect

if the two lines are parallel, that means there is no solution.

if the two lines are the exact same and "overlap" each other, then there are infinite solutions.

[tribal knot]

o

Krish'

U sound smart

how do I do these?

[summer summit]

haha thanks im currently trying to get my math degree lmao

[tribal knot]

LMAO DAMN

[summer summit]

this for 9 and 10 btw if that helps explain what i was saying earlier

[tribal knot]

math is very hard for me

[summer summit]

for #7-9, when you find the inverse of a function you switch the x and then solve for y. ill write out an example for you and send that in a sec

also, f(x) and y are interchangeable/mean the same thing if you weren't sure about that previously

[tribal knot]

so F(x) is the same as a variable?

[summer summit]

not necessarily, its more so called a function.

its used more when you are asked to find the value at a specific point

[tribal knot]

ohhhhh

[summer summit]

for example if i had y = 2x and i asked to find the value at x = 4, you would give me the answer of 8, or y = 8.

[tribal knot]

y cordinate

on a plane

[summer summit]

but if i had f(x) = 2x, the question would just say find f(4), and you would say f(4) = 8

here's the inverse example

and when you write the answer, you would put f^-1(x) instead of y

ill try to do it in LaTeX, haven't used it before but ill see if it works

[tribal knot]

why the -1

[summer summit]

its just how inverses are written

[tribal knot]

o?

[summer summit]

if you have f to the power -1 of x, that means its the inverse

[tribal knot]

Do u know how to solve supplementary angles?

[summer summit]

im not the best in geometry, but i can try

[summer summit]

oh yeah

[tribal knot]

I dont think Ill ever fully understand geometry

[summer summit]

so theres like a rule where if angles are like that then they are equal to each other if they are parallel and bisected by a line

let me try to draw it out

[tribal knot]

is it this?

[valid vector]

Yes

[tribal knot]

odds equal

[summer summit]

that doesnt really explain the rule but yes

[tribal knot]

to odds

[summer summit]

oh yeah

yes

so what you have is 6 = 4

so you would set those equal to each other and then solve for x

[tribal knot]

so

do I subtract 83

since it would be 83+x=74

[summer summit]

yes

[tribal knot]

x=11?

[summer summit]

try again, remember youre doing 74-83

[tribal knot]

-11?

[summer summit]

not quite

but close

[tribal knot]

-9

lol

[summer summit]

there you go

[tribal knot]

oops

krish

are u trying to become a teacher?

[summer summit]

i currently teach math as a part time job, and i think ill keep doing that on the side but thats not my main career

i want to be a software developer, programming stuff

because im majoring in both mathematics and computer science

[tribal knot]

ohhh

Teachers don't get paid well

but youre pretty good at explaining

[summer summit]

yeah

thanks lol

i dont teach at like a school but i teach/tutor at like an after school tutor place

[tribal knot]

aye same thing but with tutoring you get less creative freedom

[summer summit]

thats true but also less students at a time

only huge downside for me is i suck at writing upside down

because the paper is facing the student and im on the other side of the desk so to explain so they can read it the instructors have to write upside down

[tribal knot]

I almost didn't understand

lOL

[summer summit]

lmao yeah i assumed it was weirdly worded

i kinda said it like i was on my head, feet up in the air writing upside down

[tribal knot]

LOL

how do I do 5?

since its supplementary

[valid vector]

Adjacent angle add to 180

[summer summit]

Remember, when you have a straight line, the angles add up to 180

[tribal knot]

so 100+89?

[summer summit]

X + 89 + 100 should total 180

[tribal knot]

x = -9?

[summer summit]

There you go

Do you better understand how angles work now

[tribal knot]

Yea

[summer summit]

That’s goos

Good

[tribal knot]

Give me a sec Im going to do 6

then ill see how 7 works

[summer summit]

Alright go for it

[tribal knot]

got it

6 is x=9

y= 1/5x+1

[summer summit]

i'll check it in just a sec to make sure

[valid vector]

What are you meant to do?

[tribal knot]

Undo to find Inverse of the function

[valid vector]

Did you set f(x)=x and x=y?

[tribal knot]

Nope I only did step one

which was y=1/5x+1

[summer summit]

That’s the right first step

[tribal knot]

not sure where to go from there

[summer summit]

Well, switch the x and y

Because remember, when you are finding inverses you switch x and y and then solve for y

[tribal knot]

so x=1/5y+1

[summer summit]

Yes

And now solve for y

[tribal knot]

How do I take away the 1/5?

but first

I need to subtract 1

right?

[summer summit]

What’s the opposite of dividing by 5?

Yes subtract first

[tribal knot]

Multiplying

1/5 times 5?

[summer summit]

1/5 times 5 is 1, because thats like saying 5/5

1/5 y is the same as saying y/5

[tribal knot]

so times 5 on each?

[summer summit]

Yes

[tribal knot]

-5x=y?

1 isnt needed

[summer summit]

Hmm not quite. Can you go through your steps again?

[tribal knot]

Want me to send a picture?

[summer summit]

Sure

[tribal knot]

the top is just swiching it from F(x) to y

[summer summit]

You subtracted 1 on the right side, but multiplied by -1 on the left side

You have to subtract on both sides to keep it equal

[tribal knot]

so -1+x?

[summer summit]

Yes, but its more commonly written with the variable first, like x - 1

[tribal knot]

ohh

[summer summit]

But its the same thing, will give you the same answer

[tribal knot]

so x-5=y?

[summer summit]

When you multiply by 5, you have to multiply EVERYTHING in the equation by 5

[tribal knot]

so x too?

[summer summit]

What is 5 * (x-1)?

[tribal knot]

5x-5

[summer summit]

Yes

[tribal knot]

so 5x-5=y?

[summer summit]

Yes

And remember to notate that with f^-1(x)

[tribal knot]

so 5x-5= f-1 (cant find that thing) (x)

[summer summit]

Yeah

Remember f to the power of -1

[summer summit]

This

[tribal knot]

written as such?

[summer summit]

Yeah

[tribal knot]

should add more spacing fs tho

[summer summit]

Usually written with the f(x) part first, but also doesn’t really matter unless your teacher is strict about that

[tribal knot]

?

OHHH

I see

[summer summit]

Like usually you’ll see f(x) = 2x instead of 2x = f(x)

[tribal knot]

I see

What about when its all on the bottom

like yk

its all divided

by 2

[summer summit]

Same thing, whats the opposite of dividing by 2

[tribal knot]

multiplying

so

y times 2

2y = 14x-18

[summer summit]

Wouldn’t be y, because you switched x and y

[tribal knot]

oh

X

oops

[summer summit]

No

You dont multiply the top by 2 again

[tribal knot]

OHH

[summer summit]

You multiplied by 4 rather than 2

[tribal knot]

because the division

and multiplying

cancels?

[summer summit]

Yeah

You multiplied by 2 twice

[tribal knot]

I see

[summer summit]

So the 2’s cancel

And then you multiplied by 2 on the other side to get 2x

[tribal knot]

so 2x=7y-9

[summer summit]

Yeah

And now solve for y and let me know what you get

[tribal knot]

2x+9/7 =y?

[summer summit]

Yes

What is divided by 7? Is it 9 or 2x+9?

[tribal knot]

both

all of it

no?

[summer summit]

Good there you go

Just making sure

[tribal knot]

W teach

going to try

this

bymyself

[summer summit]

Go for it

[tribal knot]

f to the power of -1(x)=x-10/2

or y=x-10/2

[summer summit]

Can you show me your steps

[tribal knot]

Yes

[valid vector]

Firstly, you expanded wrong. Secondly, do you know the inverse to a squared expression?

[summer summit]

Few things wrong with that. First of all, don’t get rid of the exponent by squaring whats inside. Step 1 would be adding 6 to both side

[tribal knot]

Yea Im cooked

LOL

[valid vector]

^

[summer summit]

What’s the opposite of exponents?

[tribal knot]

Square root?

[summer summit]

Correct

[valid vector]

Yes.

[summer summit]

So you would add 6 to both sides

And then proceed to take the square root of what you have there.

[tribal knot]

wait what

Let me send what I have

done

[summer summit]

Sure

[tribal knot]

like the step

not sure if im following

[summer summit]

That’s right

Now you have one last step

[tribal knot]

Okay

Im ready

what do I do?

add 4

?

[summer summit]

You tell me what you think is the next step

And be confident in it

[tribal knot]

add 4 to both sides

since I need to

get the y by itself

[summer summit]

Yes

So what would be your final answer

[tribal knot]

4 square root x+6 = y

which

is

[summer summit]

4 times that?

[tribal knot]

huh

I put the four on the outside

[summer summit]

You said 4 square root x+6

[tribal knot]

of the squareroot

oh oops

[summer summit]

Would it be multiplied to the square root?

[tribal knot]

I dont think so

Ill send a picture

of what I meant

https://media.discordapp.net/attachments/1320614142935306332/1346980262957027370/IMG_3151.jpg?ex=67ca28a0&is=67c8d720&hm=ed3d0cdaaf1ba9ed93469d0ee3f83360d035c8f1efff9637460d01ca5792a575&=&format=webp&width=503&height=671

[summer summit]

What’s the opposite of subtracting 4?

[tribal knot]

adding 4

[summer summit]

So you would add it, not multiply it

[tribal knot]

wait so where do I put it

like how do I write it

[summer summit]

On either side of the square root

4+ or +4

You could write it like this$f^{-1}(x)=4+\sqrt{x+6}$

[woven radish]

Krish

[tribal knot]

ohhhhhh

I see

I just wrote it wrong

[summer summit]

Yess i finally got the text to work right lmao

[tribal knot]

lmao

the other times were like slightly wrong

[summer summit]

Yeah this is my first time using it so im still learning lmao

[tribal knot]

for 10

its the last one

but its completly different

[summer summit]

So the way you find x intercepts is you set the equation equal to 0

So when you have factors, you would set each factor equal to 0

[woven radish]

Krish

[tribal knot]

alright

sec I need to find paper

[summer summit]

And for two of the options there is a negative in front of the factors, and for two of them there isn’t one. the way you figure out if it should be negative or not is by looking at the graph.

[tribal knot]

got some

[summer summit]

If the graph opens downwards (meaning that the vertex is on top) then it should be a negative. If it opens up, meaning that the vertex is on bottom, then it should not be negative

Try this one with the information I gave you and let me know what answer you get

[tribal knot]

so if it opens up = positive

if opens down = negative?

[summer summit]

Yes

[tribal knot]

10 opens down

so now i needa check which other opens down

f(x)=y

so y=-(x-1)(x+3)

[summer summit]

Yeah, you dont need to change it to y in this case though

[summer summit]

^

[woven radish]

Krish

[tribal knot]

I think

I remember a

way to solve

x=-1

x=3

both should land on it

and it does

first try

[summer summit]

Yeah

[tribal knot]

Its A)

Ill send i

the

way I did it

since its really simple

[summer summit]

^ A is not the answer

[tribal knot]

o?

huh

[summer summit]

Read that explanation

[tribal knot]

It lands on (3,0)

and (-1,0)

no>

?

[summer summit]

What’s the answer for x+3=0??

[tribal knot]

?????

on one

Its f(x)=-(x-1)(x+3)

no?

[summer summit]

Yes. You make it equal to 0

[tribal knot]

so i distribute the x

yes

[summer summit]

Don’t distribute

[tribal knot]

look

[summer summit]

No need to distribute anything here

[tribal knot]

I distribute the - no?

[summer summit]

No you just set the factors = 0

[tribal knot]

why?

C would be the same if A

if we dont distribute

no?

[summer summit]

That’s how you find the solution to an equation if you have factors

No

C opens up because there is no negative

A opens down because there is a negative

[tribal knot]

wait wait

listen to yourself

if were neglecting the -

and only using it

to see if it opens up or down'

then why is it in the equation

whats becoming'

negative

how would something be flipped if the numbers dont become negative?

[summer summit]

Try graphing it and you’ll see that you won’t get the same graph

[tribal knot]

with desmos

[summer summit]

The negative only flips it upside down, doesnt change the zeroes

If you do x+3=0, you get x = -3 which isn’t a zero

[tribal knot]

youre right

[summer summit]

And if you do x-1=0 you get x=1, which is also not a zero on the graph

[tribal knot]

nvm

its like slightly off

to the left

[summer summit]

Not off, but switched around.

[tribal knot]

ITS FLIPPED OHHH

I see

[summer summit]

Instead of having -1 its -3, and instead of 3 its 1

[tribal knot]

like if I flipped a pancake?

[summer summit]

Yeah

[tribal knot]

wait can u show me how to solve

like

using D

as an example

since its for sure not D

D) f (x) = (x + 1)(x − 3)

[summer summit]

X+1 = 0, so x = -1

X-3 = 0, so x = 3

[tribal knot]

Yes I see

[summer summit]

Those are the right zeroes on the graph, however there is no negative so it would open upwards

[tribal knot]

I did the same thing

[summer summit]

So you need those factors but with a negative in the front, which B has

[tribal knot]

just distrubuted

its foresure B

[summer summit]

You can distribute, but its so much longer and takes more steps for no reason

If its already factored, dont distribute

[tribal knot]

thats what I got

[summer summit]

Yeah

[tribal knot]

Thanks dude

[summer summit]

Yeah np

[tribal knot]

Thats all I needed

how do I close

again?

[summer summit]

Just type .close

[tribal knot]

.close

[devout snow]

Channel closed

Closed by @tribal knot

Use .reopen if this was a mistake.

[summer summit]

Have a good one

[tribal knot]

You too

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

Can anyone check if what I did is correct? Mainly F

[dense jay]

pretty much fine, only complaint is the last sentence

it being defined at pi isnt enough, its that its defined and that f(pi)=lim to pi of f(x)

just me being a pedant

[hasty wave]

Ohhh okay ty, I just added that the function and the limit both equal 0 which makes the function continuous

Can u help me with something else ? 😇

[dense jay]

sure whats up

[hasty wave]

The directions states to use direc subsitiom to obtain an undefined expression .
the limit is approaching -2 from the left side. Would I have to plug a number smaller than -2 into the function?

[dense jay]

you would indeed, assuming i interpreted correctly
you should notice it increasing in magnitude quite drastically the closer you get

[hasty wave]

I think I’m not doing it right lol

Wait ignore the bottom

[dense jay]

the stuff youre writing doesnt equal the limit, youre just looking near -2
you can just whack it in a calculator

f(-2.1), f(-2.01), f(-2.001), f(-2.0001) etc

factoring was a nice idea though, should often check if anything will cancel in a limit

wait

sorry im being silly

your first line was actually enough

plug in -2 you get nonzero/0, which is all it needs

[hasty wave]

Wait what

I don’t need to find numbers coming from the left of -2 ?

[dense jay]

the numerator is (x+4)(2x-1), which is 2(-5)=-10 at -2
your denominator is 0
so -10/0, which is undefined (as nothing cancels)

[dense jay]

i just misunderstood im afraid, sorry about that

[hasty wave]

Yeah I noticed that too but what exactly does the question want ?

That I’m not sure of

Like just putting down that’s it undefined is all I need?

[dense jay]

they just want a showing that your limit is undefined

in this case we have a nonzero number being divided by 0, which isnt an indeterminate form so its just undefined

[hasty wave]

In the next question it’s the same question but it’s the 2 approach from the right

I’m confused on why they’re doing that

[dense jay]

ah, so they want specifics

you also need to see what the sign of it will be then

ie +infinity or -infinity

you can do that by checking what sign the factors will have when youre above or below -2

eg for 2^-

(x+4) positive, (2x-1), negative
(x+2), negative, (x-1), negative

so overall negative

must be tending to -infinity from the left side

[hasty wave]

Did I do this right

[dense jay]

looks good

a bit risque with the REDACTED though

well that was odd

the ='s

[valid vector]

Please remove the photos....they gave jumpscare to poor little me....

[hasty wave]

okkkki

[dense jay]

i genuinely had not noticed until you mentioned

[hasty wave]

LMAOO

[hasty wave]

How I feel about math!

[valid vector]

Continue continue

Sorry for interrupt

[hasty wave]

Could u just check one more thing?

Act 2 more things

[dense jay]

sure

[hasty wave]

For D, how do I determine what number to input into the function to find k

[dense jay]

wheres the jump

[hasty wave]

At 1?

Idk.. how do I find the jump LOL

[dense jay]

if there was going to be a discontinuity

where would it be

[hasty wave]

0

[dense jay]

0 doesnt count, its an endpoint, same with 10

why exactly did you set sqrt(kx)=x+1

[hasty wave]

To find k

[hasty wave]

3?

[dense jay]

but why

[dense jay]

yes

thats the jump, and where a discontinuity could be

because you change expression

[hasty wave]

To find where the graph is continuous at K

[dense jay]

what was the question for b?

d looks good though

[hasty wave]

B also asks for the value of K as well

[dense jay]

im afraid you did it wrong

remember, factoring

its the limit of f to the point, not f at the point, rather lim(to a) of f(x)=f(a) is what youre checking

[hasty wave]

Ohhh right

[dense jay]

looks better

[hasty wave]

Wait but there’s no need to add the limit symbols besides that right

[dense jay]

if you wanted to write it out properly it would go like:
$$\lim_{x\to-2}\frac{(x+1)(x+2)}{x+2}=\lim_{x\to-2}(x+1)=-2+1=-1$$
$$f(-2)=K$$
$$\lim_{x\to-2}f(x)=-1=K=f(-2)$$

something like that

[woven radish]

AℤØ

[dense jay]

K=-1, for continuity at x=-2

[hasty wave]

Ohhh okay thank you

.close

[devout snow]

Channel closed

Closed by @hasty wave

Use .reopen if this was a mistake.

[devout snow]

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.

[rustic jetty]

Evaluate $\frac{\sum_{i=1}^{2022} i(2023-i)}{\sum_{i=1}^{2022} (2024-i)(2023-i)}$

[woven radish]

Dork9399

[rustic jetty]

<@&286206848099549185>

[devout snow]

@rustic jetty Has your question been resolved?

[rustic jetty]

<@&286206848099549185>

[tribal knot]

yo....

I cant help bro what is yo teach giving u

🙏

[rustic jetty]

bro please

[tribal knot]

idek where to start dude

[devout snow]

@rustic jetty Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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• 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.

[wind root]

Hi! I just need to know if my answers from 1-20 is correct. This is just statistics and probability. (The bold letters are my answers)

1. Which of the following refers to a normal distribution with mean μ= 0 and σ=1?
   A. Probability mass function
   C. Discrete Distribution
   B. Normal Probability Distribution
   D. Standard Normal Distribution

2. Which of the following is considered to be the basis of statistical inference that represents the distribution of possible estimates of a population parameter?
   A. Statistics
   C. Probability
   B. Normal Variable
   D. Normal Distribution

3. Which of the following refers to a real-valued function defined over a sample space?
   A. Random Sampling
   C. Sample mean
   B. Random Variable
   D. Sample size

4. Which of the following sampling methods groups the population into relatively homogenous subgroups before doing the sampling?
   A. Sample
   C. Stratified
   B. Systematic
   D. Cluster

5. Which of the following refers to the positive square root of variance and is used to measure the spread of distribution?
   A. Standard deviation
   C. Variance
   B. Variation
   D. Mean

6. Which of the following sampling methods involves the selection of elements ordered sampling frame? from an
   A. Sample
   C. Stratified
   B. Systematic
   D. Cluster

7. Which of the following refers to the formula that gives the probability function?
   A. Probability mass function
   C. Discrete Distribution
   B. Probability Histogram
   D. Normal Distribution

8. Which of the following gives the number of standard deviations between a measures x and the mean μ of the x distribution?
   A. Z score
   C. σ value
   B. P value
   D. μ value

9. Which of the following refers to countable numbers such as integers or whole numbers?
   A. Discrete
   C. Poisson
   B. Normal
   D. Binomial

10. Which of the following refers to the specific information collected by the researcher?
    A. Retrospective Data
    C. Primary Data
    B. Observational Data
    D. Prospective Data

11. Which of the following refers to the distribution of a given statistics based on a random sample size n?
    A. Sampling
    C. Sample size
    B. Sampling Distribution
    D. Sample mean

12. Which of the following refers to the science of collection, organization, and interpretation of data?
    A. Data Science
    C. Census
    B. Statistics
    D. Population

13. Which of the following indicates the number of successes that occurs during a given time interval or in a specified region in a Poisson experiment?
    A. Discrete random Variable
    B. Continuous random Variable
    C. Binomial random Variable
    D. Poisson random Variable

14. Which of the following refers to a random variable whose range of possible values is a finite or infinite collection with as many elements as there are integers?
    A. Discrete random Variable
    C. Binomial random Variable
    B. Continuous random Variable
    D. Poisson random Variable

15. Which of the following refers to the graphical way of expressing the probability distribution?
    A. Probability mass function
    C. Discrete Distribution
    B. Probability Histogram
    D. Normal Distribution

16. Which of the following is NOT a main component of Central Limit Theorem?
    A. Successive sampling
    C. Increasing sample size
    B. Increasing sample mean
    D. Distribution of a population

17. Which of the following is NOT an example of a continuous variable?
    A. Amount of rain
    C. Weight of truck
    B. Number of non-productive hours
    D. Number of students

18. Which of the following variables is quantitative?
    A. Time spent of students in an internet cafe
    B. Number of veterans soldier
    C. Number of storms from 2020-2025
    D. All of the above

19. Which of the following refers to the positive square of standard deviation?
    A. Standard deviation
    C. Variance
    B. Variation
    D. Mean

20. Which of the following sampling methods usually based on geographical areas or other natural groupings?
    A. Sample
    C. Stratified
    B. Systematic
    D. Cluster

[pure kelp]

ts a whole ass question paper 😭

[wind root]

It's aquestion in my math book

well not math book but a ppt kind of book

I just need someone to tell me if they're right or if there's something wrong/incorrect

<@&286206848099549185> help 😔

[restive river]

.rjust gpt it

[faint zinc]

!nogpt

[devout snow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[wind root]

oj

then forget it, can anyone just help me in solving? I was absent during binomial and poisson distribution

[faint zinc]

Some of these questions are worded strangely, and I do not know to what they are referring.

[wind root]

and idk what the formula for getting x (probably rawscore) is

[wind root]

it's alright imma just gamble

[faint zinc]

For instance, question 3 "Which of the following refers to a real-valued function defined over a sample space?" is an extremely broad category of functions, and seemingly not actually any of the answers.

[wind root]

oh,..

maybe chatgpt made the questions lol

[wind root]

do u know the formula in getting x in 27?

like this is the formula for z-score

[faint zinc]

No clue. I'm terribly sorry. It is likely that your professor's particular textbook has a slightly idiosyncratic way of simplifying these concepts, which has a side effect of making them technically wrong, but I don't know enough about the book to guess the framing

[wind root]

Oh it's fine!

[faint zinc]

It is probably referring to this formula

But the wording for question 27 is again slightly off

[wind root]

I checked on google and the formula for getting rawscore is mean + z(standard deviation)

[faint zinc]

You just solve for x

[wind root]

but if I solve it the answer is not in any of the choices

like the answer is 52.5

[faint zinc]

45 + 7.5 = 52.5 yeah

[wind root]

but the choices 😭😭

[faint zinc]

I think perhaps 57.5 is the intended wrong answer.

Make a note of it and gripe to your prof.

[wind root]

Alright

[wind root]

but I don't get how the - here became positive when solving for x

[faint zinc]

Z = (x-μ)/σ
σZ = x-μ
σZ + μ = x

[wind root]

OHHHH

I was like dividing them both side by -mean

[wind root]

btw do u know when we divide both sides by the same number?

[faint zinc]

You can divide both sides by the same (non-zero) number any time you wish

(but if you have an inequality, rather than an equality, and the number is negative, you must remember to swap the direction)

[wind root]

ohhh

alright thank you!

now I still have two more things I need help with like this:

[wind root]

this is hurting my head...and I was absent during this topic

like the formula is nCx (p^x) (1-p)^n-x

x as the number of success
p as the probability of each success
n as number of trials

so p = 0.5, n=12 but idk how to solve that

Please help 😭 I rlly Don know it <@&286206848099549185>

[formal delta]

Yo

[wind root]

Hallo how do this binomial distribution thingy

Idk how to get the x

[formal delta]

It’s a good question

[wind root]

I don't think so

[formal delta]

You don’t?

[wind root]

It hurt my head 😡

[formal delta]

E[x]

E[x]=np

[wind root]

That's poisson tho

[wind root]

That's poisson distribution

[formal delta]

So?

[wind root]

This is binomial distribution tho

[formal delta]

E[x]=np=12*1/2=6

So it’s a mean of 6

[wind root]

Oh

Wtf

WHY THAT THOUGH

💀

Thanks

[formal delta]

It’s still a binomial distribution

[wind root]

Oh....

[formal delta]

I gave u the equation bruh

[wind root]

My bad g I was absent that time and my brain aint clockin

[formal delta]

It’s fine…

I forgive you

[wind root]

My head hurts from this country's heat index

[formal delta]

Poisson doesn’t tho

[wind root]

Weally? 🥺

[formal delta]

Literally

[wind root]

It does

Now help me with this!

[formal delta]

K

??

[wind root]

Wait whered it go

[formal delta]

$$idk$$

[woven radish]

Benjamin

[wind root]

Here

[formal delta]

$$did it run away$$

[woven radish]

Benjamin

[wind root]

Nah it disappeared like my dad

[formal delta]

$$ok$$

[woven radish]

Benjamin

[formal delta]

Oof

[wind root]

This the e[x]=np

Right?

So mean is 3

[formal delta]

42.3%

That’s the answer

[wind root]

HOW

HOW 💀😭 HOW R U THAT FAST

[formal delta]

I am sure

Im fast

[wind root]

Please huzz tell me fr 🙏

[formal delta]

Do you want to know the ways?

[wind root]

Yes sir

[formal delta]

But are you sure

[wind root]

Yes

[formal delta]

Once you know, you can never go back

[wind root]

Yes

[formal delta]

🫡

[wind root]

🫡🫡🫡🫡

[formal delta]

First u need to find the probability that there at MOST TWO arrivals

Hence

$$P(X \leq 2)$$

[woven radish]

Benjamin

[formal delta]

K? Buddy?

[wind root]

oh

No I dont understand how u got it

[formal delta]

No I made a statement cuh

[wind root]

Oh my bad g

Ok continue

[formal delta]

u need to find the probability that there at MOST TWO arrivals

Use the poisson probability mass function

[wind root]

Ummmm idk the formula for that 💀🫡😝🥹

[formal delta]

No wonder you got it wrong…

Jkjk

[wind root]

):

[formal delta]

$$P(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}$$

[woven radish]

Benjamin

[wind root]

WHAT IS THAT

WHAT

[formal delta]

The equation buddy

[wind root]

No like yhe upsidedown y

[formal delta]

Lambda

It’s a Greek letter

😭