help-23

[clever pawn]

x/srt(1+x^2) becomes srt(1+x^2)

[odd arch]

Let $u=1+x^2 \implies $du=2x dx$
$\implies x , dx = \dfrac{du}{2}$

[flat frigate]

jesko
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[clever pawn]

ok thanks

and the last thing

[odd arch]

Yes

[odd arch]

Every row is an integral

Integral of -1 is -x

[clever pawn]

where is the 1 from?

[lean otter]

Nice

[safe radish]

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[lean otter]

My answer doesn't match the answerkey. I am getting 2903040 but the correct answer is 2902080. Can anybody pls solve so I can see what I am missing out

[plain sky]

rack 1: 9 possible gadgets
rack 2: 8 remaining possible gadgets
rack 3: 7 remaining possible gadgets
rack 4: 6 remaining possible gadgets
rack 5: 5 remaining possible gadgets
rack 6: 4 remaining possible gadgets
rack 7: 3 remaining possible gadgets
rack 8: 2 remaining possible gadgets

for the final remaining gadget, you can place it in any one of the 8 racks, making it 8 possible placements

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 8

[lean otter]

So your answer is also 9!*8=2903040

[plain sky]

whoops, i read your question wrong, i mixed up the ans key and your answer, my bad :')

[lean otter]

But the correct answer is 2902080

It's okay! If you get it right, pls share the solution

[safe radish]

@lean otter Has your question been resolved?

[vagrant ice]

,w (9 choose 2) * 2 * 8 * 7!

[flat frigate]

Results provided by WolframAlpha

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

Requested by sooouth.

[lean otter]

The answer is supposed to be 2902080

[vagrant ice]

I know

weird, maybe the answer has a typo?

,calc 3040 - 2080

[flat frigate]

Result:

960

[vagrant ice]

I'm not sure

[vagrant ice]

this seems like it is doublecounting somehow though

[lean otter]

I also thought that earlier but it was again asked in test and again our answer 2903040 was marked wrong so i think the correct ans is indeed 2902080

[vagrant ice]

definitely seems like a typo

[lean otter]

I think so too

[lean otter]

let's see I will confirm then

[safe radish]

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[lean otter]

Thankyou guys for your efforts! I will recheck with the anskey

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[cold forge]

slight issue

[pseudo scroll]

Do you know determinant properties

[flat frigate]

neon

[median vigil]

this is from a roblox quiz so i'm not sure he will

[pseudo scroll]

third time i've helped someone with roblox math

[fading solar]

Roblox has math now?!

Damn times are changing

[pseudo scroll]

I considered making a game myself but cba to learn Lua and their editor

[bronze gust]

As someone who has done just that it's like alright

[pseudo scroll]

maybe one day when I have a freee afternoon

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[fathom plume]

lf for an explanation of what a matrix is, like ik how they add multiply and doing determinents etc and using them for ijk vectors, but rn i completely cant make sense of the steps im doing and why im doing them

[fathom plume]

i been told they are juts a store of numbers sometimes

sometimes they say they represent vectors

[desert pasture]

You can view them as linear transformations

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[deft vigil]

Hi, I have an issue understanding this image?
Why does it look like the function is defined for a set of which not a whole domain is used? and why would "Afbeelding" aka Image be an apart term? I though the idea of an image came hand in hand with the defintion of a function

[plucky elk]

Can you translate

[deft vigil]

Relation, Function, Image, split up with Surjection and Injection and finally Bijection

I thought Image refered to the set onto which a function gets mapped to

Could it be that this diagram we got in class is just wrong?

I mean it's either wrong or I just don't get it

A function is defined as f: A -> B where every element of A gets mapped to a single element in B

which the image doesn't show considering A has an element that isn't mapped

and the third diagram translates to "image"

which should be the subset of all elements in B in f:A->B for which an element in A gets mapped to, so it's not even a relation type

[fallen heart]

The function in that diagram appears to be a partial function--a function which is not defined by all elements of A but only by a select amount (its natural domain).

[deft vigil]

Ah okay, so if it were to be more accurate it should be ssomething like
Reltion, Partial Function, Function, ...

thanks!

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[coral shoal]

hi sooo i did -4r1 + r2 = r2new

but i get {0 7 -2}

how did he get 15 here

how is this reduction working in here.. i dont get it

[oak tangle]

16-1=15?

how did you get 7

[coral shoal]

oh fuck

im stupid

thx

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[bleak cradle]

Looking to practice trigonometric identities
Does anybody know of something?
I need to remember all of them and really well
Things like converting x/2 and 4x within sin(2x)
is something that's also very important

[icy lance]

are you referring to the double/half angle formulae?

[patent flame]

Especially if you have to memorise (if you don’t get a formula sheet, etc), look to memorise just a couple of basic identities, and then you can relatively easily derive the rest

But yes obv prioritise intuitive understanding as opposed to rote learning

[safe radish]

@bleak cradle Has your question been resolved?

[bleak cradle]

Yes, these are also very important

I need to memorise all sorts of trigonometric identities, including half angle and not only:
like converting half angle (when they are displayed like 4a 2/3a etc)
where can I practice it?

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[remote harness]

What is the geometric place that makes this equation?
I found only 2 solutions but I can't find the other 2.

[vagrant ice]

you're forgetting that if $a^4 = b^4$, then $a = b$ or $a = -b$

[flat frigate]

south

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[ancient steeple]

Is what I wrote in this image true?

[ancient steeple]

like i think i have a misunderstanding of inverses

[icy lance]

are you saying arcsin(y) would be arsinh(x)?

if so no

[ancient steeple]

is this also true?

[ancient steeple]

is arcsinh(x) the same thing as (sinh(x))^-1 ? 😭

[icy lance]

the inverse of sinh is arsinh
so you would be free to say arsinh(y)=x

[ancient steeple]

this is what my professor wrote

which I'm trying to figure out right now

and i already have an issue at the start

arcsin(y) = (sinh(x))^-1

[ancient steeple]

yeah exactly

so why did my professor write that

or i'm reading wrong

or it has to do with the inverse function derivative formula

[icy lance]

i must admit im confused also, its not very clear to me

[ancient steeple]

well most likely case is he wrote wrong

the way the formula was written kinda had me confused as well but

figured out what it means from chemistry tutor thumbnail

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[somber kite]

i dont know how to solve this question first though was to solve simultaneosly by making k or a subject but didnt work

[somber kite]

plz i need help my brain isnt braining

[icy lance]

12/5=2sin(a)+k
-3/5=2sin(-a)+k=-2sin(a)+k

if i add the two i get 12/5-3/5=2k

or you could make 2sin(a) the subject:
2sin(a)=12/5-k
2sin(a)=3/5+k 12/5-k=3/5+k 12/5-3/5=2k

making k the subject would only help to eliminate k, but we want to find it

actually nvm you could

k=12/5-2sin(a)
k=-3/5+2sin(a)

add them, 2k=12/5-3/5 +2sin(a)-2sin(a)

[somber kite]

This is what i did is it correct?

[icy lance]

your = scare me greatly

[somber kite]

sorry my handrwiting isnt that good

[icy lance]

what did you do on the third line?

your result of k=9/10 is right, im just struggling to follow your process

it looks like you found sin(a)?

[somber kite]

i eqauted the two equations

yeah i did

[icy lance]

in that case its alright

[somber kite]

since k =12/5 -2sina and k = -3/5 +2sina

[icy lance]

your = does look like an s though and some other symbols, id be careful with that

[somber kite]

damn thx for the roast

thx for the hel[ though

[somber kite]

i got used to it

[icy lance]

no worries

its more for other people to understand better

[somber kite]

especially since i started studying mechanics too

ahh ok

[icy lance]

thought it might be a < at first

[somber kite]

sorry if i troubled you

[icy lance]

and in the third line its hard to see, thats why i was confused

tis no problemo

just a note heh

[somber kite]

thx alot

btw how do i close a help channel

[icy lance]

'.close'

[somber kite]

'.close'

.close

[icy lance]

without the '

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[somber kite]

lmao

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[hardy silo]

I need help

[haughty sphinx]

Is that a incenter and centroid?

[somber kite]

dafuqq

[haughty sphinx]

The dot in the center

[tardy mango]

Direct question: https://en.m.wikipedia.org/wiki/Menelaus's_theorem

[hardy silo]

Ab=ac

Answers

What happened?

Couldn't you find it?

[tardy mango]

Did you read the theorem that I sent? It’s a direct application of that.

[safe radish]

@hardy silo Has your question been resolved?

[hardy silo]

Is it 1/6?

So

[hardy silo]

I read

But answer is 2/7

Ad/db=ad/dc=ag/ge

[charred saffron]

and why is that?

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[rain dagger]

how is this conclusion statisfactory?

[rain dagger]

whole thing

[mint citrus]

sorry, what's the question?

or is it just how to get from the epsilon chase to the inequalities?

[rain dagger]

why l-epsilon <= L implying l<=L

for every epsilon > 0

[mint citrus]

ahh, okay

assume otherwise, that l-ε <= L but l > L for all ε > 0

[rain dagger]

but does it not just imply EQUALITY?

rather than the weaker inequality <=

[mint citrus]

let l be 0 and L be 1

it's still true

[rain dagger]

but ive proved l-eps<=L

[mint citrus]

yeah, and 0 - ε <= 1 for all ε > 0

[rain dagger]

i can just do l-L<=eps

[peak estuary]

but not |l-L|<eps

you might be confusing it with that

[rain dagger]

i am

why do we need < and not <=

it should be the same for every eps>0

[mint citrus]

we don't

it's the absolute value we need

[peak estuary]

I just wrote < because I was lazy

[rain dagger]

then my point still stands?

[mint citrus]

we've shown that l is less than or equal to L

[peak estuary]

l-L can easily be negative

[mint citrus]

and equivalently that l - L <= ε

[peak estuary]

so then l-L<0<eps for example

[rain dagger]

so we get l-L<=|l-L|<=eps for every eps

[mint citrus]

but not that |l - L| <= ε

[rain dagger]

so l=L

[mint citrus]

we can't justify the second inequality here

[peak estuary]

write down the inequalities you are claiming for this example

[rain dagger]

i see

[mint citrus]

0 - ε <= 1 for all ε > 0

but clearly 0 \neq 1

[rain dagger]

btw, do i need to prove that? i am going to try now, but none of the other solutions did

which is weird cause it feels neccsary

[mint citrus]

I don't think you can prove it in general

not that I have a counterexample

it just feels like one should exist

[peak estuary]

if l>L then there exists an eps with l-eps>L

for example eps=(l-L)/2

[mint citrus]

sorry, I was meaning a sequence such that lim inf x_(n+1)/x_n is strictly less than lim inf \sqrtn

[rain dagger]

1. so this statement works for every l,L that are reals right?
2. how did u know to choose this l?

[peak estuary]

you mean this eps?

l-L is the distance from l to L

so if I just travel half the distance then I am still bigger than L

[rain dagger]

yes

[rain dagger]

r u assuming l,L>=0?

since it's not the distance if not

[peak estuary]

well |l-L| in general but here l>L so its fine without the absolute value

whether l and L are positive doesnt matter

[rain dagger]

alright, ty mate

[rain dagger]

ty too

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[lean otter]

Am I dumb or is this question worded poorly?

[solid shell]

It's certainly worded in a slightly odd manner

[lean otter]

Don’t mind the 2.25 I guessed

[solid shell]

What was your thought process?

[rustic goblet]

it seems worded decently, minus some grammar issues

the intent of the problem seems clear

[icy lance]

is it implying you walk from one side to the other? Or that you walked to the center and back, since its all the way around (start=end)

the result is the same i guess

but odd

[solid shell]

I think it's meant to convey the blue line here

[lean otter]

I couldn’t figure out what “walked through meant. Like he walked around a crop field in the shape of a circle which makes the circumference 5.5. “He walked directly through it” makes me think the answer is the diameter.

But now that I wrote this out I get it

[solid shell]

Starting at one end and going to the other by means of passing the center, i.e. a diameter

[icy lance]

if its this i would consider it half circumference.
comparative to diameter rather than full

[lean otter]

The question is just essentially saying “the walk of the diameter is how much shorter than the circumference walk” but I was tripping myself up assuming he wanted to get back to where he started

[solid shell]

I believe that to be the correct interpretation

[lean otter]

I just try to read into things too much

[solid shell]

It's really just asking how long the diameter of a circle with circumference 5.5 is

Sometimes reading into it is a good thing because some math problems are based on very specific intended interpretations

Especially in probability

[lean otter]

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[lean otter]

Hi. Is it possible to prove the red entailment without using RAA?

[lean otter]

I googled what are the negations of the quantifiers in intuitionistic logic but I didn't found any results

Nvm i just found it can't be done

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[lean otter]

I can’t figure out the y^5 part

shouldn’t the negative sign distribute it and make it negative or is that incorrect?

[heavy frost]

looks like you distributed the negative correctly, just combine like terms

[lime dust]

No he did not

[heavy frost]

oh yeah i missed that

[lime dust]

He added some extra - for some reason

[heavy frost]

keep the - off the y it is the same term

[lean otter]

At the end?

[lime dust]

Read what I said

[lean otter]

You’re saying it shouldn’t be 3x^3-y^5

[lime dust]

That is what i am saying, and also for the other one

[lean otter]

Why wouldn’t that be negative?

[lime dust]

-(4x^5y^3) is -4x^5y^3 and not -4x^5-y^3

Idk why u separate that

Is like you say -(8 * 3) is not -24 but -8 -3

Doesnt make sense

You have to apply distributive over a sum or a substraction, not over a product

[lean otter]

So 3x^3y^5 is 1?

And not

3x^3 y^5

[sly finch]

can someone help me?

[lime dust]

3x^3y^5 is a single thing

[lime dust]

#❓how-to-get-help

[lean otter]

Okay I see now. If it doesn’t have an operation in between then it is 1

[lime dust]

So when you multiply with -1 you just change the sign

-1 * (x^3y^5) = -x^3y^5

[lean otter]

I see the answer I think as D. But why is it not 2y^5?

I see actually, never mind

[lean otter]

I got it now. Thanks

[lime dust]

Perfect

[lean otter]

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[covert yoke]

@rich dawn are you aware of the geometric interpretation of the dot product?

[rich dawn]

is this right?

[rich dawn]

I hope so

[covert yoke]

Cool. That is how I would approach it, and how you did approach it

I don't see an error

[rich dawn]

so the method is right okay Thank you a lot

[covert yoke]

,w arccos(sqrt(5/14)) in degrees

[flat frigate]

Results provided by WolframAlpha

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Requested by omnipotententity

[covert yoke]

Lgtm

[rich dawn]

whats meant by minimal in part (b) that it can't be further simplified?

[covert yoke]

Minimal means that you can't remove an equation from the system of equations and still get the same answer.

[rich dawn]

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[halcyon panther]

claim

[icy lance]

claimed✅

[halcyon panther]

there are so many theories and unsolved problems stating that "every" number under x set is of x properties

e.g. the goldbach conjecture

these will never be solved

because there are an infinite number of x sets of x properties,

numbers can always get bigger, which means that these theorems will NEVER be solved unless some ultimate upper bound number is found

which i doubt there will be

[halcyon panther]

or if you can somehow manage to find a resolute factor of infinity

but by mathematical instance, every number is a factor of infinity?

[flat frigate]

Death on Two Legs

Death on Two Legs

[halcyon panther]

or if you can manage to create a series that extends to the reals to define everything within the set, but even then, there are strict limitations on infinite series

[rustic goblet]

why does this mean they can never be resolved?

[halcyon panther]

like how the series of 1-1+1-1+1...±1 is technically 1/2

[halcyon panther]

there are exceptions, but the reason they can't be completely solved is because there is an infinite number of solutions

[halcyon panther]

i.e. you're trying to count to infinity

[rustic goblet]

the Polya conjecture stated that at least 50% of odd numbers less than a given number contained an odd number of prime factors, and it was resolved with a counterexample on the order of 10^361

[halcyon panther]

"less than a given number"

[rustic goblet]

and that given number goes to infinity

[halcyon panther]

the conjecture itself gives you a bound that does not include infinity

[rustic goblet]

no

the conjecture was for all natural numbers n

[halcyon panther]

if a bound is given, then it makes sense on why it can be solved

[rustic goblet]

it was not a bound

[halcyon panther]

oh

[halcyon panther]

what was the resolution btw

[rustic goblet]

read the end of the message

there was a counterexample

[halcyon panther]

oh

[rustic goblet]

I'm honestly unsure as to what the question is too

there is no reason why Goldbach will never be resolved

it is not impossible to prove statements for all natural numbers

[halcyon panther]

if there is an infinite number of numbers in sets, then how are conjectures without bounds able to be solved?

[rustic goblet]

conjecture: 2^n < 3^n for all natural numbers n

this is easily verified by induction

despite there being infinite numbers to check

[halcyon panther]

well that's just basic algebra

[rustic goblet]

to prove it, one uses induction

induction is a proof technique that lets you start at a base case, and subsequently prove a statement for all natural numbers greater than the base case

[halcyon panther]

so you just lim(n>inf) 2^n and lim(n>inf) 3^n

[rustic goblet]

Goldbach cannot be verified with induction, but that's besides the point

[gusty trench]

we can also sometimes reduce the space we look at to a finite set of numbers if possible

i was once solving a fairly difficult problem that asked for which natural numbers a statement was true, and there was this neat trick involving the prime number theorem that let me show that the statement would guaranteed fail for any n > 18

i went from having to check a space of infinite numbers to 18 cases

[rustic goblet]

there are a lot of powerful techniques to help us prove things for infinitely many elements of a set

[halcyon panther]

but why were you able to

[gusty trench]

why were you able to what?

reduce the space i was looking at?

[halcyon panther]

set yourself a bound

yes

[gusty trench]

well that's problem dependent lol there's no guarantee that you can find a bound

a lot of number theoretic questions might have asymptotic upper bounds

this particular problem required placing the numbers from 1 to n^2 in an nxn grid, and i found a particular observation that any primes would be forced to be placed on the main diagonal

in other words, if you could show that there were more than n primes between 1 and n^2, it would be impossible to arrange the numbers in a way that works

and we have asymptotic lower bounds for the prime counting function, which i was able to use

[rustic goblet]

being able to prove universally quantified statements is really important in math

maybe another number theoretic example would be

show that if 2^n - 1 is prime, then n is prime

once again, n ranges from 0 to infinity (there are infinitely many n to check)

but this statement is provable

[gusty trench]

that's a different problem from the example he wanted to make

[rustic goblet]

oh, typo wtf

[gusty trench]

oh nvm 💀 i thought you were talking about it being true vacuously

[rustic goblet]

how

oh nvm

[safe radish]

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[fervent hatch]

No clue how to start 45

[abstract ore]

Okay wait I maybe got this

Choose a parameter

[fervent hatch]

Uh

Theta

[abstract ore]

x = AQ = 2 cos 0 (horizontal distance of A fromO) Y=2-ABsin0, where AB can be determined using the relationship AB times OA =(AQ)^2

Find OA, AB, and substitute into the equations to express x and y expliciylu in terms of 0

Sooooo the parametric equations in terms of 0 are: X =2cos(0)

and

y = 2 - 2sin(0)cos^2(0)

That describes the curve traced by the point P and 0 with a line through it varies

@fervent hatch

[fervent hatch]

Hmmm

[abstract ore]

Does that seem right

[fervent hatch]

Uhm kind of

[abstract ore]

What seems off

[fervent hatch]

Nothing I’m just still following it

[abstract ore]

Oh, you got this champ

I usually watch youtube videos to explain somthing for me when I dont understand

[fervent hatch]

How did you determine the 2 in $$2cos(\theta)$$

[flat frigate]

Nathan

[fervent hatch]

@abstract ore

[safe radish]

@fervent hatch Has your question been resolved?

[safe radish]

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[abstract quail]

I have a question for part d

I know in 2nd quadrant is where sin is positive and cosec is positive
so in the 2nd quadrant cos is negative
tan is negative
cot is negative

so $cosec \theta = \frac{|k|}{\sqrt{k^{2}-1}}$
as |k| >= 1 or -1 =< k =< 1 and since theta is obtuse as obtuse lies 90 =< theta =< 180 in the 2nd quadrant then $cosec \theta = \frac{k}{\sqrt{k^{2}-1}}$
why is the answer the negative?
$cosec \theta = - \frac{k}{\sqrt{k^{2}-1}}$

[flat frigate]

CodingDude

[safe radish]

@abstract quail Has your question been resolved?

[abstract quail]

<@&286206848099549185> can anyone please help me?

[sand willow]

If k>0 and subbing into $\csc\theta =1/(\sqrt{k^2 -1)$ produces a
negative result for $\csc \theta$.
This negative value does not match the second quadrant, where $\csc \theta > 0. $ Therefore, the correct expression becomes:
$\csc \theta = -\frac{k}{\sqrt{k^2 - 1}}.$

This correction make sure that the value of $\csc \theta$ reflects the positive nature of the second quadrant.

So basically, the negative sign is introduced to correct for the sign of k , ensuring that $\csc \theta > 0$ in the second quadrant. If $k$ is inherently negative, the negative sign in the final formula compensates for it.

[sand willow]

Does that help

[flat frigate]

Benjamin
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[abstract quail]

thanks

[abstract quail]

thanks it does

.close

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[noble kiln]

Hello

Alright lets see

So we can group the books according to size

@carmine seal

[sleek wolf]

the correct answer is already circled tho

was that your answer?

[compact rampart]

u can use the gap and block method

make a block of all the different sizes

and find number of ways to arrange that

[sleek wolf]

@carmine seal has not indicated the progress

[noble kiln]

Yea

[safe radish]

@carmine seal Has your question been resolved?

[compact rampart]

@carmine seal

[void path]

@carmine seal make a help thread if you don't want it to be closed automatically fast

[carmine seal]

no sorry im in class so i couldnt answer im really sorry

[safe radish]

Channel closed

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[carmine seal]

no its not its the correct answer though

[noble kiln]

Hello

Do reopen if need

[safe radish]

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[carmine seal]

okay

[carmine seal]

yeah but shouldnt it be 3!×5!x4! i just dnt understand where that last 3! came from

[noble kiln]

3 small books combinations you understand?

Last 3! is how to permute the different groups of book sizes

[solid shell]

All the books of the same size are grouped together, so the three categories of groups can be ordered in 3! ways on top of the number of ways to order individual books

[carmine seal]

oh okay i get it now

[noble kiln]

[carmine seal]

thank you sm 🙏 @noble kiln @solid shell @compact rampart

[noble kiln]

np

[carmine seal]

okay so here the first digit could be 1,2 or 3 right so 5C3 then the second digit could be any of those numbers so 5C5 then the same with the last two digits 5C5 but i get 10 and the answer is 375

[noble kiln]

Why 5C3 in first step

[sleek wolf]

should have reopened and reclosed
if I were being jokey, the first digits could have been 0
I have a serious question, however: can digits be duplicated?

this question does not make it clear 🤔

[noble kiln]

Why 5C3 you only have 3 choices

[carmine seal]

because it should be greater than or equal to 1000 and less than 5000 so we cant choose 4 as the first digit or 0

[noble kiln]

Blud you have 3 choices

1, 2, 3

[carmine seal]

ik 😭

yeah yeah i get what you mean idk why i did that

[noble kiln]

Ok

[sleek wolf]

so it's not 5C3
it's just 3

we have space for 3 digits remaining out of 4/5 :3

[carmine seal]

yeah

[noble kiln]

Yup

So qn remains: can we repeat

If no: ans is 3 x 5 x 5 x 5

[sleek wolf]

yeh

[noble kiln]

Wait thats the answer

[carmine seal]

yeah

[sleek wolf]

375

[carmine seal]

so we cant repeat

[noble kiln]

Oh i guess we can repeat ig

[noble kiln]

Can

[carmine seal]

wait

cant

[sleek wolf]

so we can repeat

[carmine seal]

oh

[sleek wolf]

it doesn't say that the digits have to be unique

if they had to, the answer would have been 3 × 4 × 3 × 2 = 72

[noble kiln]

Ya

@carmine seal you understand?

[carmine seal]

no not really 😭

[noble kiln]

Oh

Which part

[carmine seal]

why is the first one just three

oh wait

[noble kiln]

We have 3 choice

This question dosent use C

Its just multiplication

[carmine seal]

yeah yeah i understand now im sorry

[noble kiln]

No is ok

Sorry if i rude

[sleek wolf]

I was joking about adding 0s infinitely before the number

so yeah, you must pick 1/2/3 for your thousands' place

[carmine seal]

no no you werent not at all

[carmine seal]

yeah

[sleek wolf]

then the remaining three places, you pick anything out of the 5

so 3 × 5³

:)

[carmine seal]

yep thanks guys 🙏

[noble kiln]

Np

[sleek wolf]

any other questions?

[carmine seal]

nope

[sleek wolf]

!done

[safe radish]

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

[carmine seal]

.close

[safe radish]

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[carmine seal]

.reopen

[safe radish]

✅

[carmine seal]

the answer is 111

[vagrant ice]

you need to split into cases

case 1 is when the first digit is 3 or 5

case 2 is when the first digit is 4

[carmine seal]

okay imma try that

the first case is 48

[vagrant ice]

ah interesting so you can stop anytime

so yeah there are numbers with 3 digits, 4 digits, and 5 digits

[carmine seal]

yeah so if its 5 digits there will be 48 ways

[vagrant ice]

4()2 has 3 ways
4()()2 has 3 * 2 = 6 ways
4()()()2 has 3 * 2 * 1 = 6 ways

so 15 ways for that case 2

48 + 48 + 15 happens to be 111, interesting

[carmine seal]

Yeah I understand now thank you

[vagrant ice]

np!

[carmine seal]

.Close

Uh

.close

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[safe radish]

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[pale bane]

hello, i'm stuck in this question :,)

[vagrant ice]

okay, what have you tried

[pale bane]

this is what I did so far

[vagrant ice]

wait

no that's correct sorry

[vagrant ice]

great, so 45/360 = 1/8

[lean otter]

try finding the area of oab then divide by two

[vagrant ice]

cancel out the pis on both sides and then multiply both sides by 8

you get a quadratic after expanding and moving everything to the same side

[lean otter]

oh and radius is positive so use the value which gives r-2 as a positive answer

after solving the quadratic

[pale bane]

would " r^2 + 112r +392 = 16r^2 -16r +64 " be correct?

after cancellings the πs and multiplying by 8

[lean otter]

yes bring it all to one side now

[pale bane]

so 15r^2+96r-328 = 0

[lean otter]

-96*

[lean otter]

r^2 + 14r + 49 = 16r^2 - 64r + 64

[pale bane]

so is the answer 8.9?

[lean otter]

15r^2 +15 - 78 so 5r^2 + 5 - 26

um one sec

r should be 5

[pale bane]

wait so how did I get my quadratic equation wrong?

[lean otter]

on the left side you didnt cancel out the 1/8 mutiplied by 8

it was 1/8 ( r^2 ....) = 2( r^2 ...)

multiplying 8 both sides on the left sides 1/8 * 8 is 1

[pale bane]

oh I also messed up on the multiplication on the right side

[lean otter]

yes

[pale bane]

oh now I got 5

ty

.close

[safe radish]

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[rotund dew]

I got 0 clue for part b

well okay that is a lie

What i tried is this

i inducted on n
and then realized that I want to show that 2m+1 choose k is odd using m choose k is odd for k=0, 1, ..., m
I tried reducing them to odd * odd using factorial definition but that seemed like a dead end

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[lean otter]

In the plot of y=x^2

[lean otter]

all values for y will be positive

similarly when we put the value of x, say (-1)

it'll get squared....

so all values of x will be positive as well

[queen ingot]

x is -1

[solid shell]

x is the input so in that case it's -1

[queen ingot]

when it gets squared, it's y

[solid shell]

That's why the graph can stretch into the second quadrant

[lean otter]

hmm

[lean otter]

okay got it 👍

.close

[safe radish]

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[leaden tundra]

what formula should i use ? help please

[severe pond]

$V = \pi \int_c^d [R(y)]^2 dy$

[flat frigate]

knief

[lime dust]

Pi?

[severe pond]

yep

[leaden tundra]

thank you

[lime dust]

I was thinking 2pi

[severe pond]

nope

[lime dust]

Bad memory then

[leaden tundra]

sorry, for what should i replace R ?

[severe pond]

i don’t speak spanish but i assumed they wanted you to revolve around the x axis right?

or did they want you to revolve around the y axis

[leaden tundra]

around the y axis

[severe pond]

ahh ok then you’d integrate dy instead

so R is just the radius to whichever axis you’re revolving around

$V = \pi \int_c^d [R(y)]^2 dy$

[flat frigate]

knief

[leaden tundra]

r(y) being clearing x from the original function?

[severe pond]

it’s the radius to the y axis in terms of y so essentially you’re just solving for x or finding the inverse of the function they gave

because the distance to the y axis is just x

so solve for x in terms of y

[leaden tundra]

and then just replace and integrate ?

[severe pond]

put it in here

and integrate with the formula

[leaden tundra]

how do i get c and d ?

[severe pond]

they are the limits of integration and since we are integrating dy they will be the lower and upper bounds of y values for the region we are revolving (just find the lowest and highest values of y for the region)

[leaden tundra]

in geogebra shows 0 and 0.57 aproximately

its there any other way to get it exactly?

[severe pond]

yea so the lower bound is 0 since they give y = 0 and then set x = 1 to find the other, you’ll get 1/sqrt(3)

,calc 1/sqrt(3)

[flat frigate]

Result:

0.57735026918963

[leaden tundra]

wow thank you bro

really aprecciate that

[severe pond]

you’re welcome

[safe radish]

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[last crater]

Hello

[last crater]

Where is the mistake in here? Help

[plucky elk]

You used x twice?

[last crater]

Its not the same x sorry

Its just to say a² = that

I should have put something else

[lean otter]

Whys ab =3

Or is that a given

[last crater]

Its a problem from the internet and I was just curious to solve it

[plucky elk]

They're asking what is the problem

[plucky elk]

We can't tell from your work

[last crater]

I Saw in Youtube another answer

[lean otter]

Where does the question end

[last crater]

In every video basically

So I did not know if there was a mistake

[plucky elk]

You're still not answering this

[lean otter]

I'm asking what's the question exactly.. I can't tell the question and your answer apart

[pseudo scroll]

,w xy = 3, x^2 - y^2 = 9

[flat frigate]

Results provided by WolframAlpha

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

Requested by neonperseus

[last crater]

https://youtu.be/CzkrdUoZIMg?si=dea2108hFYaPRi-l

[pseudo scroll]

hm

[lean otter]

Thanks

[last crater]

I mean I Saw the problem here and I wanted to solve it

[pseudo scroll]

that is NOT an olympiad problem

[lean otter]

Fr 😭

[last crater]

Sure but I was curious lol

Because the videos said another answer

And I was like 1 hour checking

So I came here

[quick crater]

could be if lower level

[last crater]

Umm

Do i close this?

[solid shell]

You type .close whenever you're ready

[last crater]

Well ill see another day

.close

[safe radish]

Channel closed

Closed by @last crater

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[lean otter]

@last crater

Nvm he closed the ticket

[last crater]

What

[lean otter]

Was gonna explain to you how it's solved

[last crater]

.reopen

[safe radish]

✅

[last crater]

I would like to know thanks

[lean otter]

Alr 1 second

Do you understand this?

[last crater]

Yes

[lean otter]

Understand this?

[last crater]

Yes I do

[lean otter]

@last crater do you want an exact value?

[last crater]

Oh

The value of a+b

My request was because my solution was not matching the Youtube solution

So I thinked I had a mistake

[lean otter]

Idk what you did but what I'm doing gets you the answer

You just get the value of b by square rooting the value of b^2 then a=3/b then just add those

You get two solutions incase you didn't realise

[last crater]

My logic was that if ab=3 then 3/a is b, and if what i want is a+b then is also a + 3/a which is (a²+3)/a

[quick crater]

heres another idea:
a^2-b^2=(a+b)(a-b)=(a+b)(sqrt((a-b)^2))=(a+b)(sqrt((a+b)^2-4ab))=(a+b)(sqrt((a+b)^2-12))=x(sqrt(x^2-12))

[lean otter]

In your solution you did (a+3)/a

Not a + 3/a

At least that's what I understood from a quick look

[last crater]

Wasn't It (a²+3)/a

Because the problem said a+b

[lean otter]

Ph I missed the square at a

Lemme recheck

Your answer isn't wrong?

Just not simplified

[last crater]

I checked in websites to simplify it

But It says longer things

[lean otter]

No need just evaluate it with a calculator

It's the same answer

[last crater]

Dmmit

Youre right

Well dude Im going to sleep

Here is 2am

Thanks you

.close

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[lean otter]

Np

[safe radish]

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[little mountain]

((x+3)(x+1)) / (x+1) = (x+3)
What kind of equality is broken here? Since the left side is undefined at x = -1

[tardy mango]

dividing by (x+1) makes the assumption that (x+1) is not equal to 0

[little mountain]

What inequality sign would I put to convey that? Is there a special symbol for it

[tardy mango]

$$\text{your equality}, x \neq -1$$ is what I would do

[flat frigate]

Civil Service Pigeon

[tardy mango]

this specifies that it's true for all x except -1

[safe radish]

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[lean otter]

simplified answer (not mine):
\sqrt{-i \sin(x) + \cos^2(x) + 1} - \log\left(1.0 \cdot \sqrt{\cos^2(x) + 1} \cdot e^{ix} + 0.5 e^{2ix} + 0.5\right) - \pi \cdot \tanh\left(\frac{\cos(

[lean otter]

pic is sending

there

im trying to see if the answer is wrong

[plucky elk]

Answer to what question

[lean otter]

i feel like it is tho since the logarithmic and hyperbolic tangent terms are incomplete

[lean otter]

simplified

some dude was trying to simplify it

[lean otter]

here it is

is it wrong tho?

[plucky elk]

Plot both and see

https://www.desmos.com/calculator

[lean otter]

like the logarithms and dilogarithms are not fully simplified

[lean otter]

ive used desmos like once and that was in 5th grade

i dont think it works

desmos doesn't have imaginary numbers

[plucky elk]

Nope. See
https://help.desmos.com/hc/en-us/articles/31103542590733-Complex-Numbers

[lean otter]

mb

[acoustic mulch]

what do you use for plotting functions?

[lean otter]

i don't

maybe mathway

[acoustic mulch]

oh!

[lean otter]

thanks guys

.close

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[lean otter]

.close

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[terse light]

help me solve this pls, it just easy with you guys

[desert pasture]

You have to solve for $x$?

[flat frigate]

ƒ( wai ina teacup)= I don't know

[terse light]

yes solve for x

its Vietnamese, pp say let it at original language or it will dif to understand

[bronze gust]

For a.) and b.) consider squaring both sides

[desert pasture]

for (c) consider factoring the right hand side

what do you think the best way to do d is

[terse light]

idk??

square both sides

i think?

[desert pasture]

yup!

[terse light]

okay tyman, if i can solve all the x imma close server:)

[desert pasture]

close the server ?

[terse light]

breh

how about b/?

[desert pasture]

square both sides

[terse light]

so: x2 -2x +4=2-x
<=> x2 - x + 2
Then what?

all i wrong-_-

maybe-_-

[desert pasture]

quadratic formula

[terse light]

The curriculum here doesn't allow you to use it, just solve it by hand

[desert pasture]

uh

try $x=1,2 $ etc

[terse light]

nope cant

breh maybe knowledge only goes there

[desert pasture]

what do you mean

you just sub x=1, x=2

to try to see if any of them are roots

[terse light]

not equal

i mean iam not gud at eng tho

[desert pasture]

,w solve $x^2-x+2=0$

[flat frigate]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by physicsrocks

[desert pasture]

,w x^2-x+2=0

[flat frigate]

Results provided by WolframAlpha

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

Requested by physicsrocks

[desert pasture]

okay, so no real solutions

[terse light]

nvm ty so much bro

hav a gud day tysm

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[slow lily]

is this a good proof

and how the hell am i gonna prove this

o wait i have an idea

nvm

i was gonna say smth about triangles but

how am i to prove DB perpendicular AC 😭

<@&286206848099549185>

they just are 💀

[topaz tree]

Just prove <AED = <DEC

since they're on a line

<AED + <DEC =180, or <AED = <DEC = 90deg

[neat tendon]

Prove the congruency in DAB and DCB (SSS test)
From there you'll get that angle ADB is equal to angle CDB ..now shift the focus to triangle ADE and CDE and prove the congruency by SAS

We get angle AED =CED=90

[slow lily]

is this good 😭

[charred saffron]

if you have two points where each one is equally distant from the extremities of a segment, the two points form the segment's perpendicular bisector

[charred saffron]

for this one

[slow lily]

what are extremities again

[charred saffron]

yk how a segment has a beginning and an ending

[slow lily]

yes

points right

[charred saffron]

the beginning point and the ending point

are the extermities

yes

[slow lily]

oh ok

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[halcyon light]

why is the 2a being multiplied by n

[topaz tree]

what do you get when you add [1] and [2]

[halcyon light]

i thought the 2a is just by itself

[topaz tree]

a+ a(n-1)d + a+d + a + (n-2)d +........ = 2a + (n-1)d + 2a + (n-1)d +..... n times

[halcyon light]

oh shoot

thanks

.close

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[green fjord]

My doubt is regarding the interval of the range in the following question

[lean otter]

You get all the real numbers from 0 to 1 in option d

Which aren't included in option b

[green fjord]

Wait so in option d
Which has (0,infinity)

It means ill get 0.0000001......

Am i right?

But u wont get that in [1,infinity)

[lean otter]

Sorry I mean (0,inf) means every real number from 0 to 1 included

Which isn't included in the other option

[green fjord]

Ahhh i see

I now relaize

[lean otter]

Which is [1, inf)

[green fjord]

Okay that cleared up my doubt

Ty

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[brazen parrot]

how am i supposed to know to do this

can someone walk me through their thought process when they see this q

i left it blank in a test 😭

[lucid stream]

they're just substituting the solution in for z

[vagrant ice]

since the coefficients of the quadratic are all real, you can just use sum and product of roots actually

(p - 2i) + (p + 2i) = 2p = -(-q)/2 = q/2
so yes 4p = q

and (p - 2i)(p + 2i) = 40/2

basically like the working above assumes you do not know sum and product of roots

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[spare sand]

ok

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[warm sentinel]

Hi, I am not sure how I should transform the ↔ part.

[potent roost]

i maybe wrong but I don't think that changes

[warm sentinel]

Do you think my last line is right and it is the solution?

[potent roost]

i mean your second line is correct aswell, i don't think you have to simplify the expr

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[warm sentinel]

Thank you!

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[queen mango]

How both angles $\alpha$ are qual

[flat frigate]

<rajel />

[queen mango]

We are given the one In the bottom

<@&286206848099549185>

Sorry to bother found why

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[topaz tree]

AHH

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[queen mango]

Even better thx

[queen mango]

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[split fulcrum]

If theta can reach negative values since -pi/2<theta<pi/2 then why is sec(theta) assumed to be > 0

[rich elm]

omg bro is diligently studying post hsc

🫡

[split fulcrum]

noo wayy

dootud

whatchu doing upp

[rich elm]

am travelling rn but im doing tutoring stuff and studying at night

[split fulcrum]

i gott my uni offer brooo hbu

[rich elm]

nice thats good ot hear

and also i got mine as well

[split fulcrum]

wow studying post-hsc 🫡

[split fulcrum]

awesome

what course

[rich elm]

math + compsci (hon math) as first offer

also got acturarial studies + math

[split fulcrum]

holy

math demon

[rich elm]

nah nah

anyhow

[split fulcrum]

bro honor math and actuarial is crazy

are u gonna be a math professor

respect

[rich elm]

not that good at maths but anyways bac kto the q

[rich elm]

whats sec theta also equal to

[split fulcrum]

1/cos

[rich elm]

ok ok good

so if are angle is bounded on -pi/2 to pi/2

which quadrants are those?

and what do we know about vlaues of cos for those quadrants

[rigid hazel]

first and fourth

cos is positive for those

oh ur not the guy asking for help nvm

[split fulcrum]

well 0 to pi/2 is first and -pi/2 to 0 is the fourth or something i havent done quadrant stuff in awhile

my trigonometry is clapped asf

[split fulcrum]

well since cos is an even function even if the angle is negative youll always get a positive output

oh so thats why sec > 0

[rich elm]

ok u are half correct here, only if its negative in the correct range of values

like cos(-pi) is sitll negative output

[split fulcrum]

ohh yeah

true

[rich elm]

but if u are discussing betwene -pi/2 to pi/2 u are correct

also are u doing a bridging course atm?

or just self studying maths for ur own leasure

*leisure

[split fulcrum]

nah im not im self studying for leasure lmao

i want to finish calculus 2 before the first semester of uni starts

so ill have all of calc covered

[rich elm]

what course are u doing (if u dont mind me asking)

also isn't it 2am in australia T=T

[split fulcrum]

BsC and major in physics minor in math

they also offer an astrophysics program which ill enroll in

[split fulcrum]

ya

are u not australian 🤣

[rich elm]

ok ok damn

[rich elm]

im overseas atm so i keep forgetting timezone

[split fulcrum]

Ohhhhhhh true

[split fulcrum]

ya im excited

im like half way through the book

a little over halfway

[split fulcrum]

im assuming the math demon that u are youve already done calc 2

[rich elm]

again, not rly a math demon and idk what calc 2 is

i feel like calc 1 2 3 is like an american thing

so i have no idea what it equates to

[rigid hazel]

in us calc ab includes limits discontinuity derivatives integrals

bc also includes series, taylor series, tests for convergence and divergence of series

[split fulcrum]

ya but i think its mostly universal what it includes

but yeah calc 2 is what the person said

taylor series stuff like that

[rigid hazel]

https://apstudents.collegeboard.org/courses/ap-calculus-bc here is a list of topics of calc 2

(bc)

it's done in a more superficial way though and the principal behind why it works isnt really explained

[winged flare]

calc 2 the electric boogaloo

[rigid hazel]

but i recommend taking bc if you want to take calc, its not much harder and it makes you look better

[rich elm]

i was gonna just recommend studying off an ex2 textbook but then i realised ex2 doesnt cover infinite series

[rich elm]

well i would recommend not speeding through calc too fast

try to get a deep understanding of whats happening