help-27

[restive river]

in the example u can find them ?

[plush grail]

well no

i mean x power n

that's about it

or the first iteration of the series there will be an x

wait

[restive river]

im firstly making a simple example that will lead to the problem, im trying to find where you stuck

[plush grail]

should i get the first iteration of the series and then equal it to one

?

damn

oh

[restive river]

missclick

[plush grail]

no worries

that would be a seperate equation though i wont be playing around with the one i wrote earlier

like the picture i sent

[restive river]

the one equation that you sent gives several other equations

[plush grail]

yeah

i have 3

now

[restive river]

lemme see

i mean send a pic

[restive river]

,rotate

[plush grail]

last one is after i got the first iteration of series

making n=1

[restive river]

yes good

[plush grail]

that's it >

mind if i add you ?

might need you

[restive river]

yes ok

[plush grail]

thanks i appreciate it

[devout snow]

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[cerulean scarab]

why can we just do E=E_n ?

why can we just ignore the possible dependance of x on the first n coin tosses

nvm first sentence in the proof

still doesnt seem intuitive to me

ah wait

so this says that if $g$ is defined as above, then $E_n(yapyapyap)(\omega_1\dots\omega_n)=g(0.5yapyapyap)(\omega_1\dots\omega_n)$???

[woven radish]

>_<

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[faint gorge]

@arctic pendant
yours was correct

[arctic pendant]

Really? I was having self doubt though 😭😭😭😭😭😭

[faint gorge]

You can see here why I chose these bounds specifically

[arctic pendant]

This integral has been so tricky I don’t know the area of unshaded part omit whenever it’s not half

[faint gorge]

the only tricky part is to figure out the correct bounds

The problem is I couldn't find bounds where you capture exactly one whole petal because of the way the curve is moving

This is why I suggested it with a half petal and multiply by 12

[arctic pendant]

I was actually thinking a more elegant solution to bound it with a circle of radius of 1 and one with the radius of sqrt2/2 then add them together and divide it by 2

Tbh it’s a tricky integral I encountered for a while

[faint gorge]

I don't get that,

are you trying to resemble the "petal" curve by a circle

[arctic pendant]

Yes I will get the shaded area and then use the full circle to subtract it and the circle of radius sqrt2/2 to subtract it again

Either way the unshaded part preserved

[faint gorge]

,w 12 * Integrate[r, {theta, pi/3, pi/2}, {r, 0, cos(3/2 * theta)}]

[woven radish]

Results provided by WolframAlpha

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

Requested by adoniszgks

[faint gorge]

checks out

[faint gorge]

Getting the shaded part is also tricky

[arctic pendant]

Yes true

But the integral I am confusing what’s the area being integrated at this point?

[faint gorge]

https://www.desmos.com/calculator/8b72ul4ugq
try to see how the curve is moving or being drawn with the slider

[arctic pendant]

If I do it from 0 over 4 pi

[faint gorge]

The blue lines represent the angle with r

This is how it's being integrated

now you can imagine if you go from 0 to 4pi you would integrate regions twice

[arctic pendant]

So I should integrate it over 2 pi will I get all the shaded area?

[faint gorge]

You could do it that way

From 0 to pi/3 for one half shaded piece, and then you subtract a whole petal

and that times 12

[arctic pendant]

Then this will be the same as looking for unshaded petals 😭😭

[faint gorge]

I am just trying to go the safe route

[arctic pendant]

I must have been a genius to really figure the method, ChatGPT can’t even provide a hint on this one😭😭

[faint gorge]

Yeah you are a genius for taking the hint from me 😛

[arctic pendant]

Is there like more elegant way to integrate this in one go like stunningly?

[arctic pendant]

You’re right!!!

[faint gorge]

I don't know right now, you could try to figure it and compare

[arctic pendant]

Must revenge on teachers remember

[faint gorge]

It just have to make sense what you integrate and what's being integrated

[alpine python]

you're trying to find the area of the flower?

[faint gorge]

no

[alpine python]

oh

[arctic pendant]

This integral is very tricky

[faint gorge]

lmao

my solution is so perfect

[arctic pendant]

I am thinking if there’s a way I can get somehow the whole region of the curve, then I can use circle to restrict it

[arctic pendant]

Good latex skill though even take proper care of the font of boundary

Usually guys won’t do that

[faint gorge]

that's why you deserve the best help

[arctic pendant]

🥰🥰🥰 seriously I must let the teacher pay by making a super tricky solution

Like we all do Econ I wonder how my classmates do this 😂😂😂😂

Without ChatGPT they can barely work 😩😩😩

[faint gorge]

They pay mathematicians on fiverr

[arctic pendant]

Mathematician???? Aren’t they some creeps inside the ivory tower I mean some

My thought on the integral was fairly easy though, the big angle big loop, the interval for which the curve travels at 0 isn’t even

I found the small interval

In which it gives me the correct region… 🥰🥰🥰

[faint gorge]

When you get rich give me a cut

[arctic pendant]

Have to say these days people from ai gets rich easier 😭😭😭😭🤯🤯🤯

Though I am gold digging otherwise who would I ever take so many math classes 😭😭😭

[faint gorge]

anyway I just wanted to let you know your first solution is correct imo

gtg take care

[arctic pendant]

?

[faint gorge]

.solved

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[jagged orbit]

I keep getting this problem wrong. The answer should be 9π/8 - 9/4, but I keep missing the 9/4. Would anyone mind taking a look?

[tame palm]

One moment ...

[nova glen]

Shouldn't the final area be 2* A?

Since even 5pi/4 is to be considered?

[jagged orbit]

I'm not sure. Should I have taken the integral from π/4 to 5π/4?

[nova glen]

Nah nah, you can take advantage of the symmetry in the first and third quadrant

[jagged orbit]

Ok i'll try using symmetry and multiplying by 2, but I think the non-π fraction would still cancel out the way i'm doing it, and it shouldn't

i'll try again

[charred zodiac]

Hello. Two times the first integral you got results in the correct answer

The limits in the second integral are incorrect

[timber ore]

It will almost certainly help to draw the functions out first, especially because they're quite simple in this case (they're going to be two overlapping circles, one pointing upwards, one pointing to the right)

[charred zodiac]

I agree, in this case finding the "intersections" is not enough

[jagged orbit]

Ok thanks. I'll try again. Still unsure at times exactly what i'm doing when say, setting both r = to one another

[timber ore]

From the graph, the region you're interested in actually is not really "between" the two functions in the normal sense, i.e. it's not the case that the radial segments of the area of interest are from r1(theta) to r2(theta)

Your first integral got you this region (which is why it's half the answer):

[jagged orbit]

So to get the second half, would I take the second integral from π/4 to 5π/4?

[tame palm]

It would be easier to use r=3cos(theta) from theta=pi/4 to theta=pi/2 to find half of the intersected region.

[timber ore]

From pi/4 to pi/2, but by symmetry it'll give you the exact same answer (which you could motivate algebraically by just shifting theta in your first integral)

[jagged orbit]

Ok great. thanks a lot for all the help everyone

.close

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[lilac dawn]

Hi, can someone help me with this? I have no idea where to start

[devout snow]

@lilac dawn Has your question been resolved?

[restive river]

@lilac dawn

[lilac dawn]

?

I cannot see how this has anything to do with my problem

[restive river]

OH FUCK

WRONG THING

HOLDON

[lilac dawn]

😭

[restive river]

here u go lol

[lilac dawn]

lmao

[supple knot]

!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).

[lilac dawn]

Yeah I know, I am not following that solution, because it is AI

which is why I haven't closed this help yet

[restive river]

mbb i didint know

[devout snow]

@lilac dawn Has your question been resolved?

[crude wasp]

ig compute the probability that X <= x, Uf(X) <= y and show that it's given by the integral you expect

and then it'll follow by the uniqueness of finite measures

[lilac dawn]

Thanks!

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[idle coral]

Hello, does anyone know how to solve this type of problem?

[rocky carbon]

bro

what

just do (a + b+ c)^7/7 which is 0 ^7 / 7

0 / 7

for the other side they just factorized it its the same thing

or no wait

nvm forget what i said

[idle coral]

🤔

[devout snow]

@idle coral Has your question been resolved?

[devout snow]

@idle coral Has your question been resolved?

[idle coral]

<@&286206848099549185>

[subtle isle]

is it a^5+b^5+c^5 multiplied by a^2+b^2+c^2 ?

and a,b,c are real numbers?

[idle coral]

yes

[idle coral]

I think so, the problem does not specify it

[devout snow]

@idle coral Has your question been resolved?

[raw knoll]

i think you can try to sub in

c=-a-b

then from there i believe you are able to derive the other eqn from the first

$\frac{a^7+b^7-a^7-7a^6b-21a^5b^2-35a^4b^3-35a^3b^4-21a^2b^5-7ab^6-b^7}{7}$

[woven radish]

Kai The Cat

[raw knoll]

$-a^6b-3a^5b^2-5a^4b^3-5a^3b^4-3a^2b^5-ab^6$

[woven radish]

Kai The Cat

[raw knoll]

consider that $c^5=-a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$

[woven radish]

Kai The Cat

[raw knoll]

therefore

you get

$(-a^4b-2a^3b^2-2a^2b^3-ab^4)(ab)$

[woven radish]

Kai The Cat

[raw knoll]

then u can see they are equal

since

$-a^6b-3a^5b^2-5a^4b^3-5a^3b^4-3a^2b^5-ab^6=(-a^4b-2a^3b^2-2a^2b^3-ab^4)(ab)$

[woven radish]

Kai The Cat

[raw knoll]

$=\frac{a^5+b^5+c^5}{5}\frac{a^2+b^2+c^2}{2}$

[woven radish]

Kai The Cat

[raw knoll]

@idle coral

you can also notice that a+b+c=0 and the divisions result in the removal of the sole a or sole b terms, and rebases everything to kab^n-1 where k is 1

[hollow zealot]

how do i graph this i need to know the equations asap Pls help

[devout snow]

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[limber forum]

I need help with a question in probability that has been destroying my friend group.

If we assume the rules of mine sweeper were that the numbers only give information about cardinal directions (not diagonals) then what is the probablilty of a bomb being in the given spot

[limber forum]

The discussion is split between 1/5, 2/5, 2/6, and 1/2.

1/5 because there are 5 possible board states and only one has a bomb in that spot

2/5 or 2/6 is because the given information has two reasons to think there would be a bomb in the given spot.

1/2 is cause one of my friends is silly

.

When we ran a simulation there was a 1/5 chance that the board ended up with a bomb in the given spot. However I am unsure the simulation was ran accurately

[wise storm]

1/5 is the only case that makes sense to me

[limber forum]

But how is that calculated? How do you get there?

[wise storm]

same way as you it sounds, there are only 5 possible board states

as far as I know, they're all equally likely to occur

[limber forum]

So then the safest option is to choose that spot right?

[solid osprey]

i mean there are 5 cases

[solid osprey]

i belive so

[limber forum]

Thats fair ig

It just seems so counter intuitive

[wise storm]

way I counted was 2 ways to do bottom left, and 2 ways to do top right independently so that's 2*2 then +1 for that shared spot, so 5 possibilities

[limber forum]

Yeah it checks out

I really didn't want it to be correct but I guess it is

We needed to know for rewards in our game

Thank you

[wise storm]

I guess a similar experiment you can do with similar intuition is flipping two coins, since they're independent events

if that helps convince them

write out all 4 possibilities HH, HT, TH, TT and then start flipping coins

maybe try to hedge it in such a way that makes it seem unlikely or unknown coming into it, idk if that helps at all lol

[limber forum]

Nah we just need optimal understanding for rewards

[wise storm]

but seeing "a heads and tails" represented by HT and TH as two possibilities instead of one is the kind of key idea

[limber forum]

This helped alot

[wise storm]

for conveying the probabilities

cool

[limber forum]

Thank you

[wise storm]

you're welcome

[limber forum]

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[idle coral]

.reopen

a

[idle coral]

.close

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[craggy sequoia]

I don’t know if I’m over thinking this piece wise function but would the answer be 0?

[misty crest]

yep

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[floral badger]

i need help making a TM for L2 = {1^a 01^a 0^a 10^a | a ≥ 0} where a is an integer and Σ = {0, 1}

[devout snow]

@floral badger Has your question been resolved?

[floral badger]

<@&286206848099549185>

[devout snow]

@floral badger Has your question been resolved?

[faint zinc]

@floral badger use two extra symbols: 1* and 0* to walk forward through the string one quadruplet of 1, 1, 0, 0, at a time, marking them with the asterisked versions as you go, until you reach an inconsistent state or you have exhausted the string. You can assume that the string is bordered by x symbols or something to make the edges easier to detect.

[devout snow]

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[limpid shale]

i’m supposed to find the derivative of the top y= function

where did I go wrong?

[misty crest]

(3x^2+3)^2 ≠ 3(x^2+1)^2

[modest geyser]

yeah when you factor out the three.

it was inside a square, so should be factoring out a 9

[limpid shale]

ohhh, got it, thank ygs so much!! :))

.close

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[solid osprey]

find all positive integer $n$ such that $2^n+12^n+2011^n$ is a perfect square

[woven radish]

Skissue ping4response

[solid osprey]

taking mod 4 for n>1 it would be $3^n\equiv -1^n \mod 4$

[woven radish]

Skissue ping4response

[solid osprey]

so n is even (or 1)

n=1 works btw

$-1^n+1 \mod 3$ implies n has to be odd

[woven radish]

Skissue ping4response

[solid osprey]

wait whar contradiction???

.close bruh

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[weak cove]

.close

bruh

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[trim kiln]

Hi guys! Can someone help me answer these? I’m having a hard time right now, I’m doing my all my backlogs in all subjects. I’m an extracurricular student so I was not present in class when they discussed this huhu I only have 3 hours left to finish all my works 😓🙏

[simple seal]

there are many questions in there, have you tried any of them?

[trim kiln]

No, not yet.. I’m also doing stuck on my other subjects 😓

[simple seal]

try it first

we arent here to give answers

[trim kiln]

Well, ik. I just wanted someone to like answer one because I don’t know what to do 😓

But it’s fine

I’ll js try to do it once i’m done with earth science

Thanks

.close

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[astral pagoda]

how are these two equal
ive tried to think out the first equation but i just end up with x(x-4)/x^2+8x-16 which isnt equal to the 2nd one
i feel like im missing something super obvious

[acoustic helm]

• 4x - 4x

[fair juniper]

what are your steps for multiplying the factors in the denominator?

[fair juniper]

check your second red line

[astral pagoda]

oh my god i am actually so dumb

sorry guys

thank you

😭

[fair juniper]

negative signs are easy to miss

[astral pagoda]

yeah

thank you so much

.close

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[solid osprey]

find all primes $a,b,c$ and positive integer $n$ such that $a^2+b^2+16c^2=9n^2+1$

[woven radish]

Skissue ping4response

[solid osprey]

ok for this one i genuenly have 0 clue

my only slight idea is mod 3 so $a^2+b^2+c^2\equiv 1 \mod 3$

[woven radish]

Skissue ping4response

[solid osprey]

so two of them must be 1 mod 3, and one of them must be 2 mod 3

thats it im out of ideas 😭

[final drift]

um lets see

wait this implies that 2 of the primes are 3

no squares can be 2 modulo 3

[solid osprey]

wait...

huh is that really it?

wait thats not it yet

[final drift]

yeah although there is still a bit of work to do

[solid osprey]

so 2 of them are 3

[final drift]

either $16c^2+17=9n^2$ or $a^2+152=9n^2$

[woven radish]

Arnavutköy

[final drift]

or $b^2+152=9n^2$

[woven radish]

Arnavutköy

[solid osprey]

so it can be $18+16c^2=9n^2+1$ or $a^2+153=9n^2+1$

[woven radish]

Skissue ping4response

[solid osprey]

a and b are interchangable

[final drift]

yeah

if $9n^2-a^2=152$, then $(3n-a)(3n+a)=152$

[woven radish]

Arnavutköy

[final drift]

152=2^3*19

which implies that $a=37$, and $n=13$

[woven radish]

Arnavutköy

[final drift]

or if $(3n-4c)(3n+4c)=17$, then

[woven radish]

Arnavutköy

[final drift]

$n=3$, and $c=2$

[woven radish]

Arnavutköy

[final drift]

Thus, the answers are $(3,3,2,3)$, $(37,3,3,13)$, and $(3,37,3,13)$

[woven radish]

Arnavutköy

[solid osprey]

makes sense

[solid osprey]

why only this?

this only is for (2,76)

what about (4,38)

(3×7-17)(3×7+17) right?

okay thanks

.close

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[vestal bay]

How do I find B?

[alpine python]

there's a geometric series

[vestal bay]

Oh okay

[limpid basin]

yeah and use the formula

[vestal bay]

Yep alright thanks guys

.close

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[polar chasm]

A more interesting approach would be realizing that the product is a factorization of 2021^10 - 1

Wait nvm its not

But it almost is

It could be converted to it easily tho

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[untold pivot]

Let $C$ be the collection of basic open sets with the desired property. A basic open set $B \in C$ of $2^X$ is some finite intersection of the subbasic elements, and we can show inductively that only for finitely many elements $x_1,x_2, \cdots x_n, y_1,y_2,\cdots, y_m \in X$, $f\in B$ if and only if $f(x_i)=1$ and $f(y_j)=0$.

[woven radish]

somethingwrong

[untold pivot]

Could anyone give me some hints on how to continue this

or if the line of reasoning wont going anywhere

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[candid timber]

I was trying to solve this question for my exams and I got stuck

[faint hearth]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[candid timber]

1.I don't know where to begin

[leaden mantle]

can you prove 1 => 2?

[faint hearth]

Just work by definitions

[candid timber]

I'm not that smart

[leaden mantle]

then 2 => 3, 3=>4 4=>1

[faint hearth]

How about trying first

[leaden mantle]

so all of them are equivalent

[candid timber]

Let me try and I'll come back

[faint hearth]

Clearly write what you want to prove and what is given to you as true

[orchid axle]

95% patience 5% knowledge 0% smartness

is required

to do maths

mostly

[candid timber]

I'll try

[devout snow]

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[raw sandal]

i need help w these 10 questinos

[raw sandal]

<@&286206848099549185>

idk how i got this wrong but im a bit confused

[royal radish]

ur not suppose to ping helpers

for 15min

and send ur work

[raw sandal]

mb

ion got it

[royal radish]

well you said you dont know how you got it wrong

so you have to have had some thought process

about the correct answer

[raw sandal]

ima be honest

ian locked in at all this semester

im so behind so idek these

[raw sandal]

so what im thinking is

125/ac is the same as 10/20

so it would probably be double it?

250

bc theyre similar triangles

but i reset this test and last time i got it wrong and i cant get it wrong again

its been 15 minutes can anyone help me w this one?

<@&286206848099549185>

i assume its #3 bc its the only one that has the correspoding sides? im confused

[devout snow]

@raw sandal Has your question been resolved?

[supple knot]

did you try drawing a picture

[devout snow]

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[quick cloak]

The last exercise, how can I solve it based on the question that directly precedes it?

"I apologize for the language in which the exercise was presented; I couldn't translate it."

[restive river]

what is T ?

[devout snow]

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[quick cloak]

No

[dense jay]

[quick cloak]

https://youtu.be/f_Q0qlwlclQ?si=nnWV1BoH4pveEKQi

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[robust hemlock]

I was wondering how to graph this equation onto the graph?

[opal spear]

Find any points this function gets through(the most convenient ones are x and y intercepts) and draw line that connects them

also extend that line

[robust hemlock]

Thank you

[devout snow]

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[devout snow]

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[sonic igloo]

i need help

[sonic igloo]

... im cooked. man

[verbal vector]

yikes man

[sonic igloo]

i need help badly

[verbal vector]

topic?

[sonic igloo]

its 4 classes 7th grade stuff

i need to get atleast b's to pass

i got till thursaday

but i keep getting distracted

[devout snow]

@sonic igloo Has your question been resolved?

[violet wind]

You don't even have a question

Idk what u want

[devout snow]

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[devout snow]

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[tawdry meteor]

How do I do this? I missed this lesson in class and I have zero clue

[torn violet]

You know this?

[tawdry meteor]

I think so

[torn violet]

Then u can apply it

[tawdry meteor]

But idk what d is…

[torn violet]

Ur goal is finding d

U have an, n, a1

n=5 an=389 a1=-11

[tawdry meteor]

Ok-

So how do I find d?

[tawdry meteor]

Thank you

@torn violet could you help with geometric?

[devout snow]

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

[torn violet]

Alr

What u need ?

[tawdry meteor]

Idk the sequence

[torn violet]

The formula?

[tawdry meteor]

Yeah

[torn violet]

U could search those on internet

https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/09%3A_Sequences_Series_and_the_Binomial_Theorem/9.03%3A_Geometric_Sequences_and_Series

Try that

[devout snow]

@tawdry meteor Has your question been resolved?

[tawdry meteor]

I tried with the formula and I can’t figure it out

[torn violet]

Show me ur problem

[tawdry meteor]

5

[torn violet]

U need to use this

U have a1 is 4

an is 1024

[torn violet]

Keep going

Now u need solve for r

[tawdry meteor]

Ok but what’s the first step in doing that-

[tawdry meteor]

Oh

Duh

[torn violet]

U know what to do next right ?

[tawdry meteor]

Divide by 4-?

[torn violet]

Ye

[tawdry meteor]

256 = r^4

Is that the answer or do I need to 4th root it

[torn violet]

Or u take logarith

[tawdry meteor]

I have a calc (short for calculator)

[torn violet]

Oh alr lol

[tawdry meteor]

Thank you

[torn violet]

Np

[tawdry meteor]

Ok I also have this?

Arithmetic and geometric

If you can

[tawdry meteor]

<@&286206848099549185>

[devout snow]

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[crystal sierra]

Can anyone please explain to me how to solve this?

[empty moth]

what do u initally get when u plug in the values

[lost laurel]

pretty sure the limit is ||doesn't exist||

so are you sure it;s right

[lost laurel]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[crystal sierra]

how did you get that

[lost laurel]

Well, what did you try first

[crystal sierra]

muiltiply x on both bottom and top

[lost laurel]

nice

and what does that give you

[crystal sierra]

and cancel sinx square

but it became 1 over x

so i was like

errrrr

[lost laurel]

Yup, doesn't exist

You were righ!

[crystal sierra]

i thought i just didn't think of another solution

thx for the help

how to close it

[lost laurel]

.close

[crystal sierra]

.close

[devout snow]

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[crystal sierra]

Can anyone explain how to do this question please?

[clear kindle]

hiii

are u familiar with the graph of cot(x)

or the behavior of cot(x) in general?

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[devout snow]

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[ivory torrent]

plz hrlp me with this

[final drift]

ok um

can you use polynomial division first to try and find $ax^5+bx^2+c/(x^2+px+1)$ in terms of quotient and remainder

[woven radish]

Arnavutköy

[devout snow]

@ivory torrent Has your question been resolved?

[ivory torrent]

how can this be proven?

[final drift]

.

[ivory torrent]

Is there any other method

[devout snow]

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[devout snow]

Please don't occupy multiple help channels.

[warm breach]

!show

[devout snow]

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

[fiery zenith]

I dont know where to start

i found deriative

which is

x/2 +1 +8sin2x

[warm breach]

correct

equal it to 0 to find critical points, and which will include maxima too

so your ans is B

[fiery zenith]

answer is B?

answer key says the answer is D

[warm breach]

uhm

wait a sec

[fiery zenith]

how would u know randomly the ans is B

[fiery zenith]

np

[warm breach]

^

[warm breach]

^

[fiery zenith]

o ok

lol sry

it says its D idk

[warm breach]

i think ans in B

maybe ans. key is wrong

lemme try simplify opt d

[fiery zenith]

Na its from college board its legit

it couldne be wrong

[warm breach]

recheck i think

[fiery zenith]

wait D is the second deriative of the function

but how does that make sense for the question 🤔

[warm breach]

2nd derivative is generally used to check the nature of critical points

,w x/2 +1 +8sin2x=0

[woven radish]

Results provided by WolframAlpha

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

Requested by cool_vansh

[warm breach]

,w 1/2 + 16 cos (2(-14.59))

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by cool_vansh

[fiery zenith]

@warm breach I think i get it

its asking for the maximum slope

[warm breach]

yeah it's in -ve, but how the hell will you check in examination

that it's -ve

[fiery zenith]

the first deriative only represents slope of f(x). The slope of f(x) is maximized or minimized when f ′ (x) itself has critical points.

[warm breach]

but since it has asked maximum

we cannot be sure

[fiery zenith]

it said possible maximum

act idk what im saying

[warm breach]

• in D they made it equal to 0, so still it would be indecisive

[fiery zenith]

right

[warm breach]

for local maxima it must be -ve

[fiery zenith]

what is ve

[warm breach]

-ve = negative

+ve = positive

[fiery zenith]

o

ok

[warm breach]

it could be both B & D
but more appropriate answer is B

[fiery zenith]

bro what

[warm breach]

what

well where are you stuck at?

[devout snow]

@fiery zenith Has your question been resolved?

[devout snow]

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[devout snow]

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[reef solstice]

every time i use different approach i am get diff ans how

[sand dove]

what have you tried so far?

[devout snow]

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[silver hollow]

is this good enough proof?

[devout snow]

@silver hollow Has your question been resolved?

[silver hollow]

<@&286206848099549185>

[devout snow]

@silver hollow Has your question been resolved?

[devout snow]

@silver hollow Has your question been resolved?

[restive river]

Hello, how can I help you?

[silver hollow]

yesss

can you check if my proof is correct?

and maybe also this one?

[devout snow]

@silver hollow Has your question been resolved?

[devout snow]

@silver hollow Has your question been resolved?

[gloomy latch]

yes! the proof is correct

[gloomy latch]

this proof is also correct, but I would be more careful with notation after your second "if and only if": the T (for transpose) symbol on A seems like it's applied to the whole parenthesis

[devout snow]

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[summer knoll]

I always forget how to do this does anyone know the steps?

[misty crest]

first find the point at which the left side equals the right side

[summer knoll]

Do you mean set equal together

[misty crest]

yes

then from there you could do a few things

but find the points that satisfy left = right

[misty crest]

mhm

and now you should set the right side to be zero

by adding 3

then solve the quadratic

you can just factor it

[summer knoll]

Like factor

Bet

Thanks bro imma do that

Okay so I got -1, and 5

But how do we know where the arrows goes

And if we gotta shade or nah

[misty crest]

ok great now let’s look back at our original inequality

$x^2-4x-8 < -3 \iff (x-5)(x+1) < 0$

we determined that it equals zero at 5 and -1

so those i guess you could say are "critical points"

[summer knoll]

Wait the thing is pointing this way tho <

[misty crest]

or just points where we need to analyze how the sign of the product of those two terms changes before and after

[summer knoll]

Like the inequality sign

[misty crest]

oh right my fault

[summer knoll]

All good bruh I make the same mistake err day

[woven radish]

knief

[misty crest]

ok so we want the product of two numbers to be less than zero which is the same thing as being negative

if i multiply two numbers together and get a negative number, what must be true of those numbers

as in

are they both positive? both negative? one positive one negative?

[summer knoll]

One positive one negative

[misty crest]

mhm so what we can do is first determine for what x values each individual factor is positive/negative then use that to determine when the product of the two is negative

so we want intervals where the factors have opposite signs

now

can you tell me the intervals for the first factor, x-5

where is that negative and where is it positive

if it helps

[summer knoll]

My bad when say interval what do you mean

[misty crest]

x-5 being negative means x - 5 < 0

[summer knoll]

Like is it closed or open?

Ohh

[misty crest]

x-5 being positive means x - 5 > 0

solve those two inequalities

[summer knoll]

like set equal?

[misty crest]

well i’ll do the first one

x - 5 < 0 means x < 5

just add 5 to both sides

can you do the other one

[misty crest]

^

[summer knoll]

Okay so then x < 1

No?

[misty crest]

where did you get that from

[misty crest]

^

[summer knoll]

Wait

Wait is it x<-1

[misty crest]

you’re doing the other factor for some reason

[summer knoll]

Oh I thought you wanted me to do that one cause u did x=5

[misty crest]

i asked you to determine when each factor was positive/negative

well i only showed where x-5 < 0

i asked you to determine where x-5 > 0

[summer knoll]

Oh like show it on the number line

[misty crest]

no like write it like this

[summer knoll]

oh so

wait I’m Cooked if x-5 <0 means x<5 why doesn’t x-1<1

[misty crest]

what

[summer knoll]

Im so cooked 😭

[misty crest]

x-1 < 0 does mean x < 1

[summer knoll]

wait so what r we looking for I thought that’s what u wanted

[misty crest]

but that’s not relevant, x-1 isn’t even a factor

[misty crest]

we want to find the intervals where one factor is positive and the other is negative, to do that we need to first determine where each factor is positive/negative individually

remember that the intervals where one is positive and the other is negative means their product will be negative which is what we want from the inequality

[summer knoll]

ohh so waot

U wanted me to look at both of them and see which is positive and negative

okay so 5 is positive and 1 is negative

[misty crest]

first find where x-5 is positive then where it’s negative and do the same for x + 1 then our solution to the inequality is the region where one is positive and the other is negative

[misty crest]

no

the factors are x-5 and x+1

i’ve told you already that x-5 < 0 when x < 5

i just added 5 to both sides

similarly x-5 > 0 when x > 5

now do the same for x + 1

[summer knoll]

so copy this

but for x+1

[misty crest]

yes

[summer knoll]

So x+1<0 when x<1

Is this what u want

An interval is (x-1) right

[misty crest]

again, the factor is x+1 not x-1

[summer knoll]

ohhhhhh

sorry

On my paper I had it x+1=0 my bad

[summer knoll]

Is this correct?

[misty crest]

no

subtract one from both sides

[summer knoll]

so x=-1

[misty crest]

we already had that but we want intervals where that factor is positive/negative

[summer knoll]

can you explain what a interval is i feel like that’s what is stumping me

Like this is getting embarrassing ngl

or when u say “where that factor is positive/negative what do you mean”

x-1 < 0 I did the less than sign cause it’s negative

I had to reread

[misty crest]

when i say interval i mean a particular set of values

you can think of it as a region on the number line

[misty crest]

i mean the set of values that satisfy the inequalities (factor) > 0 for positive and (factor) < 0 for negative

[summer knoll]

okay so u just wanted me to look at the equation

and choose the right sign

[misty crest]

not an equation

an inequality

[summer knoll]

or inequality sorry

but that’s what u wanted me to do no?

[misty crest]

yes

as i was doing above

[summer knoll]

I’m sorry bro

I sold you

[misty crest]

lol

tbh i have to go

i don’t have much time for this

but i’ve done the first bit for you

[summer knoll]

Cant blame you it’s all good

[misty crest]

now it’s time for you think for yourself or have someone else help you

[summer knoll]

Imma think myself ngl and just reopen if I need help

Thanks bro

[devout snow]

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[alpine python]

break it into two integrals

you want the min to be x^2+y^2 on one integral and sqrt(3/4-x^2-y^2) for the other

[void knot]

Ye but I'm confused bc i think that sqrt3/4 -x- y this one is always the min

Isn't it?

[alpine python]

no

did you forget the squares?

you wrote -x-y

[void knot]

Just for convenient

[void knot]

Look at that graph

[alpine python]

okay i see two circles

[void knot]

Doesn't this graph represent these two separately?

[alpine python]

yeah

the inner circle is the domain on which x^2+y^2 is the min

the outer circle is the domain on which sqrt is the min

i'm not sure what you mean

[void knot]

How can I split it into two intergal? I can't find the split point

[alpine python]

at the radius of the inner circle

[void knot]

Sqrt3/2?

[alpine python]

try solving an inequality with x^2+y^2 and sqrt(3/4-x^2-y^2)

[alpine python]

not quite

[void knot]

What inequality?

[alpine python]

x^2+y^2 > sqrt(3/4-x^2-y^2)

but use r

r^2 > sqrt(3/4-r^2)

[void knot]

r^4>3/4-r^2

[alpine python]

r^4

👍

we are only concerned with r in (0,3/4) so we can assume r is positive while manipulating this inequality

[void knot]

r^4+r^2-3/4>0
1/2

[alpine python]

not quite 1/2

[void knot]

1/sqrt2

[alpine python]

yeah

greater or less than?

[void knot]

If x^2+y^2 is the min, then it's greater

[alpine python]

if x^2+y^2 is the min, r<1/sqrt(2)

[void knot]

Damn why am I so dumb

[alpine python]

[void knot]

Ok i seem to get it

[alpine python]

the upper bound on the last integral seems wrong

[void knot]

Why?

[alpine python]

it's just 3/4

wait

oh you're right

[void knot]

Tysm

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[radiant cosmos]

So I'm looking for a formula that basically defines X and Y based off a table where:
10 = 10; basically X = Y
20 = 110; basically if X plus 10, then Y plus 100
30 = 1110; if X plus an additional 10, then Y plus 1000
I'd like to be able to graph this on like, desmo or similar so I could see what X would be if Y was 82, for example

[lusty sapphire]

Looks like exponential growth

[radiant cosmos]

i realize there's a difficulty because the rate of change doesn't start immediately but after X = 10

[lusty sapphire]

So, (40,11110) would be next?

[radiant cosmos]

yes

[lusty sapphire]

gave away the ending

[radiant cosmos]

yeah this looks like what I'm looking for

[lusty sapphire]

,w plot y=(10^(1+x/10)-1)/9-1

[woven radish]

Results provided by WolframAlpha

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

Requested by spelwerdzrite

[lusty sapphire]

thanks wolfram...

[radiant cosmos]

and related to the question, what would I do to change the formula so Y starts at 32 years

[lusty sapphire]

[radiant cosmos]

so thiss same line but it starts y = 32, x = 0

[lusty sapphire]

add 32

[radiant cosmos]

soo +31? since it says -1?

thanks a bunch

.close

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[vivid wing]

Hi

[vivid wing]

I had a quick probaility question

so the question is you hae to create a security password

8 characters. You must have two special symbols [#, $, !] in any position and they cannot repeat but the rest can be any lower case letter or digit and can repeat

I had 2 different solutiosn for thsi one but don't know which one is right and why

1. 3 choose 2 * 8 choose 2 * 2! * 36^6

2. (3x8) * (2x7) * (36)^6

I don't undersatnd why my second answer is wrong

[restive river]

So if there are 23 people then what amount of people in an relationship that will maximize amount relationships?

[vivid wing]

2?

[fair juniper]

youre double counting in the second case

if you choose # first and $ second, and place them like #$______, it will also be counted when you pick $ first and # second

[vivid wing]

OH

I see

thanks so much

[fair juniper]

youre welcome

[vivid wing]

.close

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[restive river]

If the partial derivatives of a scalar field $f: \mathcal{D} \subseteq \mathbb{R}^n \to \mathbb{R}$ exist in one coordinate system, are they guaranteed to exist in every coordinate system? For example, if the partial derivatives $\frac{\partial f}{\partial x^1}(\mathbf{a}), \dotsc, \frac{\partial f}{\partial x^n}(\mathbf{a})$ with respect to Cartesian coordinates exist at some $\mathbf{a}$, then is it true that $\frac{\partial f}{\partial \phi^1}(\mathbf{a}), \dotsc, \frac{\partial f}{\partial \phi^n}(\mathbf{a})$ exist for every other coordinate system $\phi$? If not, then does the term "partially differentiable" at $\mathbf{a}$ mean that all of $f$'s partial derivatives in all coordinate systems exist at $\mathbf{a}$ or that $f$'s partial derivatives with respect to Cartesian coordinates exist at $\mathbf{a}$?

[woven radish]

mkovachev

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[balmy dragon]

when i’m solving trig identies what should i always look for

[balmy dragon]

ik to swap tan out with sine and cosine but what are some other things to look out for

[minor perch]

remember three identites like
sin^2 + cos^2 = 1

1 + tan^2 = sec^2

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[full ferry]

Can some one tell me how to do

[full ferry]

What’s the x function and y function

<@&286206848099549185>

How do I start

[full ferry]

🙏🙏🙏plz help

<@&286206848099549185>

[polar chasm]

can you also use graphing calculators?

Or just paper

[full ferry]

I can

Is a assignment

[full ferry]

But i dont know how to calculate the y function and x function

[polar chasm]

https://www.desmos.com/calculator/4hffyxijyk

maybe try to play around with it

and plot some functions

this one is pretty bad at modelling the bottom part

[full ferry]

Can I just do linear

Even though there’s like a mis number

[polar chasm]

you could, but the bell doesnt look like a curve

I'd at least try to compose it of polynomials

that's decent enough

[full ferry]

Hmmm

[wheat pawn]

how close does your bell need to match? pieces of polys of degree 2 or 3 seem close enough for most parts

[full ferry]

10%

Prior

Error

[polar chasm]

thats pretty interesting

i have a really stupid solution in mind

[full ferry]

I think the easiest way are like plug in triangle

[full ferry]

What

[full ferry]

Oh

[polar chasm]

lines will be better though

and they should be more than enough to keep the error < 10%

[wheat pawn]

i mean... if he's expected to use integration, i doubt stepwise is gonna be accepted

[full ferry]

That will be a lot of work

[cinder bobcat]

the problem says it wants you to write out all of the integrals for calculating the volume, so that might not be ideal lol

[wheat pawn]

because otherwise is just "count squares"

[polar chasm]

indeed

[full ferry]

Yeah we need to use integral

[polar chasm]

it could be written as an integral, but its stupid as I said

lines are better

[full ferry]

That what I do

[polar chasm]

looks good

[wheat pawn]

i mean, that should be under 10% error

[full ferry]

How to plug in to integral ?

I forgot

😁

[wheat pawn]

you need the equations of each of those lines

[full ferry]

Yeah

☹️

[wheat pawn]

you would consider the "top" line of each step as f, the "bottom" as g, and then integrate (f-g)

each of your intervals would be when either the top or bottom line changes

for example: from 0 to 1, you'd integrate a-b

from 1 to 8, you'd integrate c-b

from 5 to 8, you'd also integrate d-0

and so on

[full ferry]

That’s what I thinking but just too much work

😭😭😭

[wheat pawn]

well, it's a complex shape

[full ferry]

Alr thx

Ill try

[wheat pawn]

and if they complain about the error, you can simply turn your lines into higher degrees of polys

[full ferry]

Ok ok

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[twin swan]

Please solve this , and tell me how you did it

[royal radish]

erm

i dont think thats how this works

u should prob say where ur confused

or what ur confused about

and someone will probably clarify

[twin swan]

I don't know any of it about circuits

[royal radish]

well if thats the case this server is to help you with specific problems not teach new material

someone might wanna teach u

but i wouldnt count on it

[twin swan]

Well can they solve this one then

Just this one

[royal radish]

possibly if they want to

[heavy current]

@twin swan heads up, this channel is going to close soon

you've deleted your original message

in case that happens, open a new one

anyways, a circuit is a path in a graph that starts and ends on the same vertex

so if you want to find circuits of length 2 starting at, say X, then you need to look for paths of the form XYX

where Y is some other vertex connected to X

@twin swan does that help?

for example, BDB is a circuit of length 2 since it starts at B, ends at B, and D is connected to B

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[modest tapir]

Why x^2 - x isn’t x?

[eager nova]

Because $x^2= x * x$

[woven radish]

Samuel

[eager nova]

Being * the product

@modest tapir

[tame palm]

For the same reason the 3^2 - 3 ≠ 3.

[modest tapir]

But like

x^2 - x

[static raft]

The other way would be true but not like this, because 2^2-2=2

[modest tapir]

You’re left with ^2