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[zinc haven]

ignore everything written in blue, thats my writing

[zinc haven]

translation: given a trinominal f(x) as shown in the graph

how many extrema does $y = f(|x+1|-1)$ have

[ocean seal]

FungusDesu

[zinc haven]

my educated guess is A, but im not sure

[lone heart]

@zinc haven Has your question been resolved?

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@zinc haven Has your question been resolved?

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[lone heart]

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[inland ocean]

The goal was to find the last 2 digits of the equation and I got the answer right which is 8 but is there any other faster way to solve this other than getting the last 2 digits of each number then multiplying to get the last total 2 digits?

[exotic canopy]

last 2 digits?

and the correct answer is 8?

what is the other digit?

[lone heart]

@inland ocean Has your question been resolved?

[inland ocean]

08

Thats the last 2 digits

[exotic canopy]

oh

then yeah

[inland ocean]

Theres no other ways to solve? 💀

[exotic canopy]

i mean what you did was essentially a modular arithmetic argument

[inland ocean]

Ahh I see

[lone heart]

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[neat dragon]

Guys im back hehehehehehhe

[neat dragon]

If im being honest I didn't understand the lesson

[grizzled gulch]

Bruh its just polynomials ;-;

[neat dragon]

Sorry but i dont really understand it

[grizzled gulch]

Its fine

Do uk how to factorise?

I mean they need solutions in terms of factprs right?

[neat dragon]

Yea

[grizzled gulch]

Ok..

1 sec ill solve and show

Check if its correct

[neat dragon]

I dont know 😭

Slr im doing other assignments

[grizzled gulch]

I actually gtg somewhere

Is it fine if i finish this sometime later

[neat dragon]

Its okk

[fickle heath]

Not a very helpful factorization if you intend to find roots

[zenith hound]

x^3 - 3x - 2
= x^3 +2x^2 - 2x^2 + x -4x + 1
= x^3 + 2x^2 + x - 2x^2 + 4x + 1
= x(x^2+2x+1) -2(x^2+2x+1)
= x(x+1)^2 -2(x+1)^2
= (x-2)(x+1)^2

[grizzled gulch]

Ojh ok

Thanks for rectifying me!

[zenith hound]

wont claim credit for it

wolfram alpha's work

these are not easy

[neat dragon]

True

Hahahaha

[fickle heath]

You can always try some values

x = 1 is a pretty obvious one

[zenith hound]

adn then polynomal division right

*and

[fickle heath]

If you need to

[zenith hound]

*-1

[fickle heath]

Yeah sorry

[zenith hound]

x^4 -13x^2 + 36
= x^4 -4x^2 -9x^2 + 36
= x^2(x^2-4)-9(x^2-4)
= (x^2-9)(x^2-4)
= (x+3)(x-3)(x+2)(x-2)

easier one

[fickle heath]

You can just use the quadratic formula for that one

[zenith hound]

ye

[fickle heath]

3rd one is pretty bad

[neat dragon]

Cherry Man you can do it hahahahaha

Moral support

Jokeeee

[grizzled gulch]

In 3rd one

Leave 1st term as it is

Factorise the squared term

Amd then factorise the 1st term

Wouldnt that be good?

[grizzled gulch]

Ohh did u mean zero of the polynoimal

If yes then equate the equations to 0 and find all solutions of x

[fickle heath]

Isn't it pretty much the same problem?

[neat dragon]

Omg i dont know anymore

[grizzled gulch]

I thought by root u meant the factors

[alpine sable]

I did like this...

[grizzled gulch]

Thats hit and trial method

[neat dragon]

Thissss is what my teacher did

[grizzled gulch]

Thatll work too

[alpine sable]

Oh...

[fickle heath]

The roots are used to build the factors; or the other way around, you get the roots from the factorization

[grizzled gulch]

Ohh ok then

[alpine sable]

I can explain the method if you want

[neat dragon]

Yes pls

[fickle heath]

That's pretty evil

[alpine sable]

Join the call

[grizzled gulch]

When we get the factors then we can just equate them separately to 0

[grizzled gulch]

Ikrr

[neat dragon]

Waitt

[alpine sable]

Ok

[fickle heath]

Right but finding all the roots is equivalent to finding the full factorization

[grizzled gulch]

But after factorisation ull get ans like (x+1)(x+2)

Etc

So to find x just equate them to 0

Which is same as equation the wjole polynomial to zero

IF ITS GIVEN TO FIND ZEROS OF A POLYNOMIAL THAT IS

[fickle heath]

Sure, that's just the obvious step

[grizzled gulch]

Yepp

So i thought tao asked to find factors

Not the zeros of p(x)

[fickle heath]

What I meant is that those two things are equivalent up to that obvious step

[grizzled gulch]

Sure thats right

[neat dragon]

Guyss i get it nowww 😭

Ill try to answer it

Pls tell me if its wrong

[grizzled gulch]

Sure

[lone heart]

@neat dragon Has your question been resolved?

[neat dragon]

Oh i forgot to add 2 there haha

Got too excited

[neat dragon]

Guys need help can you give me the factor that ill use on num 2

[neat dragon]

Can i mention some of you? Hahahah

Is it -2 or -3?

@grizzled gulch

Hehe

<@&286206848099549185>

Hehehe

What factor will i use on number 2?

[clear stone]

1 and 2?

[neat dragon]

What factor will i use

@grizzled gulch @fickle heath @alpine sable Where you at 😭

Hahahahaha i cant

Im going crazy

[fickle heath]

Just use X = x^2 and solve a quadratic

Then solve x^2 = X for whatever value of X you get

And this is wrong, (x-1) should be (x+1)

[neat dragon]

Ohhhh ok ok

[neat dragon]

How?

[fickle heath]

If you can't solve x^2 - 13x + 36 = 0, I can't help you

[neat dragon]

Wait a sec ill figure it out

You mean by quadratic is -b +/- sqrt 4ac all over 2a?

So 9 and 4?

[fickle heath]

Yes

So x^2 = 9 or x^2 = 4

[neat dragon]

Ohhhh

[fickle heath]

Looks fine

[neat dragon]

Wait the question tho is x⁴-13x²+36...

[neat dragon]

Nice niceee

Only num 2 has no answer 😭

[fickle heath]

?

[fickle heath]

Read again

[neat dragon]

Ohhh so ill use synthetic division

Ok ok

Hahahaha

Oh wait i think i got it

Answer is 13, 4, and 9????

@fickle heath

[fickle heath]

No? Where does that 13 come from

[wind ibex]

Improve ur handwriting 😂

[neat dragon]

4+9?

[neat dragon]

I know????

[fickle heath]

Is that you just making things up?

[neat dragon]

No??

[fickle heath]

Then what's the reasoning behind adding 4 and 9?

[neat dragon]

I dont know anymore???

[wind ibex]

Let x^2 = t
THen the equation will be
t^2-13t+36
Solve for t and after getting the value of t put x^2=t

[fickle heath]

Guess I'll repeat myself

You solved x^2 - 13x + 36 = 0

You found x=4 and x=9

[wind ibex]

Yaa

[fickle heath]

You have x^4 - 13x^2 + 36 = 0

So x^2 = 9 or x^2 = 4

[fickle heath]

.

[wind ibex]

Ya

[neat dragon]

??

[wind ibex]

Opps

U didn't understood

[neat dragon]

Yea

[wind ibex]

Okk

Let x^2 = t

@neat dragon

Then the equation will be
t^2-13t+36

Ok

@neat dragon

?

?

[neat dragon]

Yea?

[wind ibex]

Understood these 2 steps?

@neat dragon

[neat dragon]

Yea

[wind ibex]

Then solve the equation

U will get t=(9, 4)

Then x=t^2

So, x=(81, 16)

Okk

@neat dragon

Solved

[topaz goblet]

lol

[neat dragon]

didnt ask for your opinion on my handwriting...but thank you for "helping"

.close

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[wicked bridge]

So this is a question in my Linear Algebra exercise sheet: Solve the lower triangular system Lc = b, and then Ux=c. What is the role of A in the equation Ax=b? I already solved the first two equations with the given matrices L and U and the given vector c. I don't understand what they mean by "the role of A".

[wind ibex]

Sorry baby

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[wicked bridge]

.close

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[whole flame]

about question 11

[whole flame]

.close

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[silver coral]

Yes

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[vocal tapir]

For P(A∪B)=P(A)∪P(B)
Let x∈P(A∪B), then x⊆(A∪B)
In x can be elements only from A, only from B, but not elements from both.

[vocal tapir]

this is false, but I'm looking for the correct statement

Tried writing down my lecturer's notes, but I got it wrong

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@vocal tapir Has your question been resolved?

[vocal tapir]

<@&286206848099549185>

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@vocal tapir Has your question been resolved?

[vocal tapir]

<@&286206848099549185>

[vocal tapir]

.close

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[vocal tapir]

let f : N → N, f (x) = 2023
I need help finding out if it's injective/surjective function

[vocal tapir]

so by my reasoning, if it's from natural numbers to natural numbers

there has to be 2023 back in the natural numbers

so it should be surjective?

[tall topaz]

Write down the definions of injectivity and surjectivity

see if this function satisfies them

[vocal tapir]

hmm ok

[tall topaz]

im not sure what you mean by this.

[vocal tapir]

nothing

this?

[tall topaz]

mhm thats injectivity

not check with ur f

[vocal tapir]

alright so

if f(x)=2023

for any x it will always be 2023

yeah?

[tall topaz]

yes

[vocal tapir]

so even for a1 and a2, it will equal 2023

which makes it not injective

[tall topaz]

right any elements will give 2023

not injective

now surjectivity

[vocal tapir]

for all b in B, there exists an a in A such so f(a)=b

[tall topaz]

is it true that $\forall b \in N, \exists a \in N, f(a) = b$

[ocean seal]

$Pure$

[vocal tapir]

yeah so

by my reasoning

let me think this through for a moment

we have b already

so there must be an a such so f(a)=b

but any a gives 2023

this means that there's an a that does give 2023

[tall topaz]

all this means is every element in the codomain is hit

but is this true

take 2024 in N then can you find f(x) = 2024?

[vocal tapir]

yes

2024

well

any x is 2024

yeah?

[tall topaz]

what?

[vocal tapir]

idk

[tall topaz]

what do you mean any x is 2024

[vocal tapir]

x1, x2, ..., xn

1,2, ..., n being indexes

so uh

am I right?

[tall topaz]

your function is a constant function

for any input it gives 2023

[tall topaz]

i have no idea what you mean by x1 , ... xn

[vocal tapir]

that makes it surjective, yes?

[tall topaz]

no

do you understand what surjective means

tell me in words

[vocal tapir]

for all b in the range of values, there exists an a such so f(a)=b

so in this case x

x=2023

[tall topaz]

for all b in the codomain

[vocal tapir]

yeah codomain

[tall topaz]

theyere not the same thing

[vocal tapir]

yeah yeah

ik

ik ik

[tall topaz]

well so ?

[vocal tapir]

well f(x)=2023

so x in this sense?

[tall topaz]

?

[vocal tapir]

?

[tall topaz]

what do you mean x in this sense

[vocal tapir]

well it's given that f(x)=2023

so x?

or idk

help

[tall topaz]

what do you mean so x?

[vocal tapir]

well it's already given

no?

f(x)=2023

[tall topaz]

do you acutally understand what this is saying

[exotic canopy]

$\forall x f(x)=2023$

[vocal tapir]

ig idk

[ocean seal]

artemetra

[exotic canopy]

whatever x you pick, it will be 2023

[vocal tapir]

oh yeah

that's true

[exotic canopy]

surjective means that there is a value (or values) of x such that f(x) is any natural number

is this possible?

[vocal tapir]

yes

it is

[exotic canopy]

well find me an x such that f(x) = 2024

[vocal tapir]

x+1?

[tall topaz]

for any input the function gives you 2023

[exotic canopy]

f(x+1) = 2023

[tall topaz]

f(49234192493) = 2023

[exotic canopy]

f(0) = 2023

f(bajillion) = 2023

[vocal tapir]

yeah

[exotic canopy]

no matter what you pick it's 2023

[vocal tapir]

Ik, yeah

[exotic canopy]

???

[vocal tapir]

proved that with injectivity

[exotic canopy]

so can you find a value of x such that f(x) is 2024 if regardless of x the value of f(x) is 2023?

[vocal tapir]

any

[exotic canopy]

any what

[vocal tapir]

?????????

?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????v

any value

as you said

no?

[exotic canopy]

what?

no

[vocal tapir]

dude idk help

[exotic canopy]

by any i mean arbitrary

[vocal tapir]

surjectivity is for when all values of A have a value in B

[tall topaz]

no

[exotic canopy]

no

[vocal tapir]

uhh B in A

[tall topaz]

for all values of B we have some number in a such that f(a) = b

you pick any value in the codomain you can always find at least 1 a in A such that f(a) = b

in your case its a function from N to N

pick any natural number m

can you always find another natural number x such that f(x) = m

[vocal tapir]

yes

[exotic canopy]

here's the graph of the function. can f(x) be anything but 2023? no. so is there anything that could make the value of f(x) anything but 2023?

[vocal tapir]

ohh

I think I get it

[exotic canopy]

like

[vocal tapir]

I mean visually like this I do

but how do I apply it in the definition

there isn't

[exotic canopy]

surjective means that it "covers" the whole of codomain (natural numbers)

but your function, regardless of input, "covers" just one value, 2023

[vocal tapir]

right

[tall topaz]

the negation of surjectivity is $\exists b \in B \forall a \in A, f(a) \neq b$ if this helps

[ocean seal]

$Pure$

[vocal tapir]

yeah it does

[tall topaz]

$\exists m \in N , \forall x \in N, f(x) \neq m$ in your case

[ocean seal]

$Pure$

[vocal tapir]

this makes sense

ty both

.close

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[tall topaz]

[lone heart]

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[unkempt compass]

this question was so confusing. idk if i solved it or got lucky or what. can someone show me the right path to doing this?

[molten pivot]

y = log(x)
x = 10^y

log(10^(-2)) = -2 log(10) = -2 * 1 = -2

[novel sand]

it's actually just the identity , f of f inverse (x) is just x

[unkempt compass]

im just a little confused but dont you have to like take the log of both sides or something? so log(10^(-2) = log(x)

[ionic jewel]

The definition of the inverse of a function is literally $f(f^{-1}(x)) = x$

[ionic jewel]

well surely its the other way actually

[unkempt compass]

are my steps the correct ones in proving the identity?

for this particular problem

[ionic jewel]

your work looks right for this problem

[novel sand]

yea

[unkempt compass]

all i really learned is that you should swap the x and y variables when taking the inverse. my understanding isnt much beyond that i think

is there something else i should know to make things more clear or concrete?

[limpid turret]

Mostly true, but there are also domain considerations that need to be mentioned, depending on the context of discussion.

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[somber spade]

hey i need help with figure numbers

[somber spade]

i am confused on how to find the formula of this, i though it was just to ger the formula for square which is n^2

and add it with 2 of the formulas for triangle

[somber spade]

which gives me n^2 + 2*n(n+1)/2

but im not getting the right answers so what am i doing wrong?

[keen pasture]

The triangle has a smaller base

n-1 is the base not n

[somber spade]

oh because it has nothing on figure 1?

so the formula for triangle in this is (n-1)((n-1)+1)?

[keen pasture]

Yeah, and there is always the square in the middle and the triangle with a base of n-1

[somber spade]

alright so for square the base is n

[keen pasture]

Yes, so you get n^2 + n(n-1)

[somber spade]

wait what

now im confused

[keen pasture]

Your approach was completely correct, but the bases of the triangles didn't fit

[somber spade]

but isnt the whole formula n^2 + 2* (n-1)((n-1)+1)?

/2

[keen pasture]

So instead of n^2+n(n+1) (that is what you got) it is n^2 + (n-1)*n

[keen pasture]

Yeah, you can simplify this

[somber spade]

what do you simplify

[keen pasture]

2/2 = 1

[somber spade]

right yeah

[keen pasture]

And n-1+1 = n

[somber spade]

oh right

makes sense

thanks anyways

have a good one

[keen pasture]

You're welcome. You almost didn't need help 🙂

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[jolly lily]

this is a misprint right?

it says the domain = -pi/2 < y < pi/2

how can the domain be in terms of y

this should be range?

Also shouldnt the domain be all real numbers
-infinity =< x =< +infinity

[rustic coral]

x is a function of y here, not vice versa

[jolly lily]

ok and itt says
-infinity < x < infinity

Shouldnt it be

• infinity =< x =< infinity

[rustic coral]

No, because infinity isn’t finite

So you can never equal it

@jolly lily

[jolly lily]

Ok thank you

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[wind turret]

hi, can someone help me with this please

[fickle heath]

Sign error?

[limpid turret]

plug in x=0

[lone heart]

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

[wind turret]

-2/-2?

[lone heart]

@wind turret Has your question been resolved?

[ocean seal]

chef

[lapis goblet]

@wind turret

[wind turret]

ty i got it

its -2, right ?

[lapis goblet]

Yes

[wind turret]

tysm

[lapis goblet]

np

[wind turret]

.close

[lone heart]

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[alpine sable]

hello

[alpine sable]

ok

I don't understand this problem

[limpid turret]

Looks like you need to express x in terms of the other variables.

proportionality rules seem to be what you want to use.

[alpine sable]

how do I do that, I think it's x the square root of wy

[limpid turret]

Do you know any properties of similar triangles?

[alpine sable]

barley

barely

[limpid turret]

Those are what you want to review then

[alpine sable]

So like for this problem what would be the answer?

The problem I already put in chat

hello?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[alpine sable]

are you joking?

[timid marlin]

You will have to use the Pythagorean theorem and write down a system of equations from it.

I think

[timid marlin]

x is the square root of w^2+y^2 so its an incorrect answer

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[dapper echo]

Am I on the right track to find the area of a rectangle with a semicircle, which had a perimiter of 44?

[tribal haven]

that does not seem like the correct perimeter of a semicircle

[dapper echo]

OOps, should've worded it better. The whole thing's perimiter is 44

[lone heart]

@dapper echo Has your question been resolved?

[tribal haven]

that’s still not the perimeter of a semicircle

[dapper echo]

I know...

The perimiter is given to me

Of the whole thing

I just need to find the area

[tribal haven]

what im saying is
πr^2/2 is not the perimeter of a semicircle

[dapper echo]

ohhh

Is this right

[tribal haven]

why do you keep writing the perimeter and area of a circle as the same expression

they are absolutely not the same

equation at the bottom seems fine

[dapper echo]

Is this better?

[tribal haven]

your optimised equation is still wrong

what are the formula for area and perimeter of a semicircle?

[dapper echo]

pir^2 / 2

[tribal haven]

and what’s the perimeter

[dapper echo]

πr + 2r

[tribal haven]

right, and are you optimizing for area or perimeter

[dapper echo]

for area

[tribal haven]

right, so why is πr + 2r in your optimised equation

[dapper echo]

because I already tried using area...

[tribal haven]

what

you can’t say you’re optimizing for area then randomly throw in a perimeter
then you’re optimizing the wrong quantity

[tribal haven]

and your problem here is that the restricting condition also has the area while it’s supposed to be the perimeter

[dapper echo]

I see

[dapper echo]

I tried tweaking the restricting equation a bit, so that only one y is counted, and the semicircle takes the upper y

Still gives me no answer

.close

[lone heart]

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[shell narwhal]

Can you justify the vector space dimension by the number of pivots in the row echelon form of a matrix? ping me if you reply

[ionic jewel]

number of pivots in rref is the dimension of the column space

[shell narwhal]

what does rref mean

[ionic jewel]

reduced row echelon form

[shell narwhal]

so... yes ?

[median oar]

Your question is nonsensical

[shell narwhal]

why so

[median oar]

The matrix has nothing to do with the dimension of “the” vector space

What vector space are you talking about

[shell narwhal]

changed it

so

now ? ?

yes ?

[median oar]

The “column space” of a matrix is a subspace of the codomain

It still makes no sense

The matrix has nothing inherently to do with vector spaces

[ionic jewel]

isnt column space the span of the columns

[shell narwhal]

Can you justify the vector space dimension by the number of pivots in the row echelon form of a matrix? ping me if you reply

[median oar]

Usually you need to first be like: let T be a linear transformation from V to W (where V and W are vector spaces)

Then let A be the matrix representation of T such that T(v) = Av

[shell narwhal]

wtf

this is supposed to be a yes or no answer

[median oar]

The matrix itself has nothing to do with vector spaces

[shell narwhal]

and to move on

[median oar]

But the matrix represents a linear transformation

From 1 vector space to another

[shell narwhal]

i have no clue wtf ur talking about

im doing basic linear algebra

[median oar]

So your question of “the vector space” doesn’t make sense

[ionic jewel]

Im pretty sure my answer is what they are looking for

[shell narwhal]

look buddy, english isnt my native language

[ionic jewel]

even though it doesnt answer the question as stated

[shell narwhal]

thats my translation of things

[median oar]

What is “the vector space” you’re referring to

Which vector space

[shell narwhal]

vector space

[median oar]

Which one

[shell narwhal]

this one

[median oar]

It is important to ask sensical question in maths using the language and terminology

So you can read things and write things in a logical manner

[shell narwhal]

mhm

[median oar]

The number of pivots in a matrix A in rref is equal to the dimension of the column space of A, which is a subspace of the codomain

[wicked pewter]

The codomain refers to domain after transformation is applied right

[shell narwhal]

k thanks

[median oar]

Let f: A -> B be a function

A is the domain

B is the codomain

[wicked pewter]

So if T(A) is R2-R3 codomain is real space

[median oar]

The range of f is a subset of the codomain

[median oar]

What’s T(A)

[wicked pewter]

Transformation represented by matrix A

I’m in basic linear alg course as well just trying to get my terminology correct

[median oar]

Usually you write [T] for the matrix representation of T

If T: ℝ² -> ℝ³

Then ℝ³ is the codomain

Not ℝ

[wicked pewter]

Right

R^3 is called real space though right

[median oar]

But obviously by linearity the range of T here is at most dimension 2

[median oar]

I don’t think that’s a convention

You could define “real space” to mean ℝ³ sure

[wicked pewter]

I see

[median oar]

But also, ℝ³ itself isn’t a vector space

You need the addition and scalar multiplication shenanigans to make it a vector space

ℝ³ is just an ordered triplet of real numbers

(But you’ll often encounter ℝⁿ with the addition and scalar multiplication in your course)

[wicked pewter]

When would it not have addition and scalar multiplication?

Actually nvm I think I get it

[median oar]

If you don’t say that it does then it doesn’t

[wicked pewter]

Yeah I see

In math you just need to define everything precisely 😭

[median oar]

Well it’s because sometimes we might not need the idea of adding things

[wicked pewter]

Hmm I see

So vectors in R^3 would form a vector space but R^3 in general isn’t

Or R^n

[median oar]

Itd be proper to say the triplet (ℝ³, +, •) forms a vector space

But it’s very troublesome to write

So usually they either just go ℝ³ or let ℝ³ be a vector space

And obviously with linear algebra it’s pretty much implied that we’re working with vector spaces

Otherwise it all makes no sense

[wicked pewter]

I see I see

Thanks

[lone heart]

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[normal holly]

How would i solve b

I tried plugging in 18 as y

Then as the y intercept

I’m a bit lost

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@normal holly Has your question been resolved?

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[torn thorn]

In a dice game, there are 9 piles of money valued from 1 to 9. The game involves rolling two dice multiple times. If the total of the dice is 10, 11, or 12, you re-roll until the total is between 1 and 9. For example, if you roll a 3+4=7, you can either take pile 3 and pile 4, or just pile 7. If two dice have the same result like 3+3=6, you can just take pile 6.If either option is not available, the game ends. The goal is to maximize the amount of money taken.

I think as for the distribution of the outcome of two dice, it has larger probability that the sum lying around 7, so maybe if the sum is near 7 I should take the split piles instead of the sum pile? Still very confused about what's the best strategy.

[lone heart]

@torn thorn Has your question been resolved?

[pure jasper]

Ok ur def right about 7 has teh highest %

2 (1+1)
3 (1+2, 2+1)
4 (1+3, 2+2, 3+1)
5 (1+4, 2+3, 3+2, 4+1)
6 (1+5, 2+4, 3+3, 4+2, 5+1)
7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
8 (2+6, 3+5, 4+4, 5+3, 6+2)
9 (3+6, 4+5, 5+4, 6+3)

The strategy to max $ is preserving the piles that are most likely to be rolled (which are around the center, like 6, 7, and 8) and instead taking the piles that correspond to the individual dice whenever possible.

you want to keep your options open for as long as possible and avoid ending the game prematurely by running out of available piles\

if that makes sense

[torn thorn]

Thx for that. But it's an interview quetion and the interviewer was hoping that I could give an intuitive quick answer of what's my strategy and what's the rough expectation of my strategy. I wasn't able to answer the expectation lol. Could you give me some insight into the expectation?

[pure jasper]

sorry I'm not versed in interviews so maybe someone else can give tips

[torn thorn]

No worries.Thx for your analysis

[ocean seal]

$Pure2$

[tall topaz]

Yeah I interviewed the interviewers once

That’s how you show dominance and confidence innit

[pure jasper]

^

[torn thorn]

So do you know how should I tackle the expectation of the problem during the interview

[tall topaz]

No I only interview the interviewers

[lone heart]

@torn thorn Has your question been resolved?

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[limpid cove]

Why is 9 being multiplied here

[limpid cove]

is 9 the multiplicative inverse?

[lone heart]

@limpid cove Has your question been resolved?

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[limber harbor]

write the equation of a line that is parallel to y=-4x+1 and has the same x intercept as y=-1/2x+7

[limber harbor]

<@&286206848099549185>

$$y=-4x+1$$

[ocean seal]

ynwsk

[limber harbor]

$$y=-1 / 2+7$$

[ocean seal]

ynwsk

[limber harbor]

someone help me man

[marble surge]

☺️ Type

y = \frac{1}{2}x+7

[limber harbor]

$$y = \frac{1}{2}x+7$$

[ocean seal]

ynwsk

[limber harbor]

thanks

does anyone know how to do this

write the equation of a line that is parallel to y=-4x+1 and has the same x intercept as y=-1/2x+7

in slope point form

[old cedar]

so, what's the x intercept - do you know how to calculate that?

[limber harbor]

x intercept is -4

I think

[old cedar]

umm not quite.. x intercept is value when y is 0 so if you put y=0 in y=-1/2x+7 what do you get for x?

[limber harbor]

14

[old cedar]

yep.. and what is the form of lines parallel to y=-4x+1?

they should have same slope

[limber harbor]

i'm not sure

[old cedar]

so when you have y=mx+c, m is the slope, you ok with this?

[limber harbor]

Yes

[old cedar]

so line parallel to y=-4x+1 would be y=-4x+c, this make sense?

same slope (m)

[limber harbor]

Ok yes.

[old cedar]

ok so now when you put y=0 in y=-4x+c you want to get x as 14 (same intercept as the other line)

so you can solve for c?

[limber harbor]

Yes

shit man i give up have a great day sorry for distrubing you

[old cedar]

umm that didn't help? i thought you got it done?!

[lone heart]

@limber harbor Has your question been resolved?

[lone heart]

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[hearty citrus]

Is the spring constant 3 or -3?

[lone heart]

@hearty citrus Has your question been resolved?

[lone heart]

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[frosty gull]

How do I solve these questions?

I am confused which is the base and index?

[fervent timber]

yeah why is the notation so weird

[frosty gull]

Ikr ig there's a typing error

[eternal blaze]

so werid

[frosty gull]

In the first question what if we take base 5 and 20

Like this?

<@&286206848099549185>

This is 2nd question.

[frosty gull]

..

[chrome plank]

I'd use the change of base formula for logs, but you can also use others

[charred plover]

Square both sides by 27

or change of base yeah

Personally i prefer using swuaring and using ln to bring the x down

wait nvm that doesnt work

[lone heart]

@frosty gull Has your question been resolved?

[frosty gull]

?

I am confused

<@&286206848099549185>

[shrewd carbon]

I'm here

What is the question you wanted to solve again

[frosty gull]

Second one

[shrewd carbon]

The second one right?

ok

[frosty gull]

Yeah

Thanks

[shrewd carbon]

Let me type for a sec

$\log_{27}^{x}$is, $\log_{3^3}^{x}$

[ocean seal]

diaas_(yt)

[shrewd carbon]

So now, you can use $\log_{a^b}^x=\frac1b\log_a^x$

[ocean seal]

diaas_(yt)

[shrewd carbon]

So that becomes $\frac13log_3x$

[ocean seal]

diaas_(yt)

[shrewd carbon]

So let's revisit the first equation

$\frac13\log_{3}x+\frac12\log_3x$

[frosty gull]

Is this correct can you check once again?

[shrewd carbon]

Yes it is bro, It's log x to the base 3 on the right

[frosty gull]

Ok

[shrewd carbon]

What seems to be the problem?

[frosty gull]

I thought the question was a but twisted

[shrewd carbon]

Not really

[frosty gull]

Alright

[shrewd carbon]

So you understood how $log_{27}x=\frac13\log_3x$ right?

[ocean seal]

diaas_(yt)

[frosty gull]

Is this?

[frosty gull]

Yes I did

[shrewd carbon]

Ok so let's substitute that in the first equation

[ocean seal]

diaas_(yt)

[shrewd carbon]

This is equal to 5/12

Put $t=\log_3x$

[ocean seal]

diaas_(yt)

[shrewd carbon]

$\frac t3+\frac t2 = 5/12$

[ocean seal]

diaas_(yt)

[shrewd carbon]

Solve this to get the value of t

[frosty gull]

I can do the resr

[shrewd carbon]

Ok

Hope I helped

[frosty gull]

Thanks

[frosty gull]

I was not aware of this formula

Thanks anyways mate.

.close

[lone heart]

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[loud solar]

hi, im not sure how to solve any of these

[loud solar]

that's what i tried, but i have the answers so ik my solution is wrong

[charred plover]

a?

[wanton nova]

chain rule

[charred plover]

yeah

let me try and latex it

$\frac{dy}{dx} = \frac{d \cos^{4} 6x}{dx} = (\frac{d \cos^{4} 6x}{d \cos 6x} ) (\frac{d \cos 6x}{d 6x}) (\frac{d 6x}{dx})$

[ocean seal]

habuki (dms open)

[loud solar]

ye i was trying to do chain rule, i think i did it incorrectly

[charred plover]

(4cos³6x)(sin6x)(6)

= 24sin6xcos³6x

my working should be correct

[loud solar]

yee thats the answer, i def misunderstood chain rule. could you explain it more?

[wanton nova]

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/a/chain-rule-review

[loud solar]

ohh okk, ye i was using a different formula. tyy

.close

[lone heart]

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[noble kayak]

the ratio of the sum of n terms of two Arithmetic Progressions is (7n+1):(4n:27).Find the ratio of their mth terms

[finite flax]

Did you state the problem exactly as it was given to you?

Please restate the problem using the exact wording. You have a typo in your expression as well

[lone heart]

@noble kayak Has your question been resolved?

[noble kayak]

um yes it was given this way

[vapid shuttle]

!original

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[wind ibex]

Wait a min

[finite flax]

Ok so there was indeed a typo

[wind ibex]

(7m-6) : (4m+23)

[noble kayak]

ok

but ho

how

[wind ibex]

Is this correct @noble kayak

Because answer can be in more forms

[noble kayak]

its (14m-6):(8m+23)

so there's a certain step in this problem

[wind ibex]

Yaa

Let me think

[noble kayak]

it tells me to equate n = 2m-1

but there is no relation of m and n in this problem

[finite flax]

I'm sorry, what tells you this?

[noble kayak]

i was able to get till equation 1

but after that

[wind ibex]

Ya it is true

[finite flax]

Why

I see they are assuming n is odd

(by doing this)

I was just gonna write that

But thought it was too many variables

[noble kayak]

so this is the ratio that we have to find right

[wind ibex]

Ya but it will be 2m

Acc

[noble kayak]

so when we divide this first equation by 2 in both the numerator and denominator

[finite flax]

$\frac{\frac{m}{2}(2a_1 + (m-1)d_1)}{\frac{m}{2}(2a_2+ (m-1)d_2)} \
= \frac{2a_1 + (m-1)d_1}{2a_2 + (m-1)d_2} \
= \frac{a_1 + \frac{(m-1)}{2}d_1}{a_2 + \frac{(m-1)}{2}d_2}$

[wind ibex]

Yaa,

[noble kayak]

ok but how do I know if those 2 equations are the same

the n and the m one

like is there any rule

I can see 'a' and 'd' are common in them

[wind ibex]

Nooo

[noble kayak]

uh

[wind ibex]

Same because of ap

[noble kayak]

not this equation

the sn equation

[noble kayak]

yes

so what is the least amount of things I must see common in them to compare them

[wind ibex]

U don't need, because ratio is given and u can use ratio acc to ur ease

[noble kayak]

um can you please elaborate on that

I dont understand

[wind ibex]

😊

[noble kayak]

uh

[ocean seal]

Disorganized

[wind ibex]

Ok

[finite flax]

https://tenor.com/view/hmm-gif-19410752

[noble kayak]

ye so same for the n equation as well

if we replace the dashes with 2

[wind ibex]

See, u know the general form of ap, RHS is in solved form, but in RHS only n is variable, so only n is changed

[noble kayak]

yes

a = (n-1)d

[wind ibex]

What

[noble kayak]

I mean the a dash and d dash

[wind ibex]

Because there are two different ap

[noble kayak]

yes

I understand that

so n remains same

in both aps

[wind ibex]

So the first team and common diff will also be diff

[wind ibex]

Right

[noble kayak]

for m too

thats the case right

m remains same

[wind ibex]

Smart, I was going to say it😅

@noble kayak I have a trick to check your answer for these types of questions

Do u wanna know that?

[noble kayak]

sure

[wind ibex]

See, u can check your answer by putting any value of m and n (as 1)

[noble kayak]

ok

yea thats alr

but

I just have some confusion

in comparing

[wind ibex]

Tell

[noble kayak]

you know its like a quadratic equation

[wind ibex]

Ok

[noble kayak]

where u have to compare with ax^2+bx+c

to know what a, b and c are

[wind ibex]

Ok

[noble kayak]

so here we have

this one

[wind ibex]

This is not a quadratic equation

[noble kayak]

and this one

[wind ibex]

I think I didn't understood what r u trying to say

[noble kayak]

yea I know that

what im trying to say is how to compare two equations

so that

we can tell they'

are equal

[noble kayak]

this is sn/sn'

[wind ibex]

Ok

See, first compare the coefficient of variables(m and n)

And try to make the coefficient same

@noble kayak

[noble kayak]

ok

[finite flax]

how does the reader know that n should be interpreted as 2m-1?

[noble kayak]

yea thats the problem

I couldnt think that way

I thought I was dumb

[wind ibex]

It's not a big problem

[finite flax]

Doesn't seem implied anywhere

[wind ibex]

🥲 nope

[finite flax]

How did you know? What gave that away

[noble kayak]

the solution

otherwise I wouldnt have known

and I still dont understand

[finite flax]

Diwali didn't have the solution

[wind ibex]

😂

[noble kayak]

so they're basically telling us

[wind ibex]

I can solve and send u

[noble kayak]

to compare

the n equation and the m equation

there everything is the same

[finite flax]

Why can't we just stick with n???

[noble kayak]

except

[finite flax]

Isn't the given expression the ratio???

[noble kayak]

n-1/ 2 and m-1

so 2 goes to the other side

n-1 = 2m-2

take one to the other side

n = 2m-1

[wind ibex]

Yaa, I have told u to compare the variables first

[noble kayak]

thats how they arrive at n = 2m-1

[finite flax]

Oh I kind of see where I was going wrong

[noble kayak]

can this method be used everywhere else too

cause this seems new to me

[wind ibex]

Yes

But answer will not be same everywhere 😅

[noble kayak]

ok

I think i have a bit of an idea now

[wind ibex]

@noble kayak if u will face any other problem, then dm me, I will send u detailed solution, because here I can only help u, if I send solution , they will ban me from the server

[noble kayak]

oh

ok

.close

[lone heart]

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[vestal tulip]

what is cos 30

[wanton nova]

1/2

Wait no

Its (sqrt(3)) / 2

[lone heart]

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[vestal tulip]

why do we have to memorise this

[worn fox]

Memorise what

[mortal trellis]

.

well it just comes up from time to time. useful to know it

[prime badge]

it's not like it comes up more often than cos 50

maybe the idea is that you memorize some, so you can derive arbitrary ones

that's why they also give all these identities

[lone heart]

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[vestal tulip]

https://tenor.com/view/thank-you-gif-25358104

[lone heart]

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[trim summit]

im not sure

[grizzled gulch]

Join AD

[trim summit]

and then?

@grizzled gulch

[alpine sable]

bro it's very easy

[trim summit]

not for me

[alpine sable]

after we joined AD we will see that angle ABD and angle ACD are angles subtended by same chord which makes angle ABD = angle AC

[alpine sable]

sorry was typing answer

[rigid sail]

Hmmm, seems like you assumed what was to be shown

[alpine sable]

how?

[rigid sail]

You cannot use Inscribed angle theorem you are supposed to prove it

[alpine sable]

??

sorry could you explain in simple words

[rigid sail]

You just used the inscribed angle theorem to prove the inscribed angle theorem.

[alpine sable]

ohhhhhhhhhh

[rigid sail]

Don't worry, this is not easy and I don't think the diagram is very helpful.

[alpine sable]

hey just asking but can't we join A and D to the centre of circle (suppose O) and let angle AOD be x. So by this angle ABD will be x/2 and angle ACD will also be x/2. So they will be equal.

...

@rigid sail

[rigid sail]

Now you are still using an equally strong theorem

Here is a vauge proof outline:

1. Use the definition of the circle to find one (or more ) isosceles triangles with verteces at the center of the circle.

2. Note that two angles in these triangles are equal.

3. Do some angle chasing using common method like supplementary angles and angle sums.

[rigid sail]

Hope this helps

[trim summit]

alright i will try now then

thank you both

[alpine sable]

welcome and sorry

[lone heart]

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[unkempt sundial]

I'm trying to study this parametric curve, supposed to follow these steps but i hit a wall

[unkempt sundial]

aaa think i got it

what's the Human way of solving this

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[unkempt sundial]

.reopen

oops

[lone heart]

✅

[lone heart]

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[mellow wing]

im stuck on part b of this question.

im not sure how to progress beyond P(-0.732 =< z =< 0.732). am i supposed to plug it into the calculator or is there another way to go about solving the problem?

[lone heart]

@mellow wing Has your question been resolved?

[lone heart]

@mellow wing Has your question been resolved?

[lone heart]

@mellow wing Has your question been resolved?

[mellow wing]

oh my

[lone heart]

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[soft stratus]

How do changes in the proportion of athletes doping affect the probability that an athlete whose medical test shows doping is actually doping?

probabilities:
(a competitor is doping: 0.1) = x
(medical test shows doping|x) = 0.9
(medical test shows clean|x) =0.1

(a competitor is clean : 0.9) = y
(medical test shows doping|y) = 0.2
(medical test shows clean|y) =0.8

i need to change x and y

[lone heart]

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[lone heart]

@soft stratus Has your question been resolved?

[grizzled gulch]

<@&286206848099549185>

[lone heart]

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[fickle tinsel]

What's the proper name for this?
E.g.
$P_0(a,b,c,d)=abcd$
$P_1(\dots)=abc+abd+acd+bcd$
$P_2(\dots)=ab+ac+ad+bc+bd+cd$
$P_3(\dots)=a+b+c+d$

[ocean seal]

7aman

[fickle tinsel]

And by 'this' I mean the function P for any number of parameters