help-27

[wise scarab]

oh they also do it with characteristic functions

[trim shoal]

Well, I'm still in 9th grade 😅 so I'm unable to understand the rigourous proof, could you explain it in simple terms, or would the essense of the proof be lost?

[glossy dew]

basically

for a set of observations

we take the mean

and try bounding it

[trim shoal]

I still have a vauge understanding, I will take some time to further research and understand the proof.

Thanks for taking the time anyways!

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[wise scarab]

no

[wise scarab]

no

ok i didnt mean to open this so uh

.close

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[tropic tinsel]

why is x 3 and not 8

[tall knoll]

It should be 8

[tropic tinsel]

so its an issue with the book?

[tall knoll]

I guess

[tropic tinsel]

alr then ty

[devout snow]

@tropic tinsel Has your question been resolved?

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[summer summit]

because that statement is not true

[misty crest]

this is not how logs work

[summer summit]

log(ab) = log(a) + log(b)

[misty crest]

log of a product is the sum of the logarithms

[summer summit]

no

[summer summit]

^ @restive river

ofc

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[lime plaza]

Did you forget an x? +8x?

So first divide

so guess a number

take like 1, -1 ,2 ,-2

Just put x= that number and see if it comes out to be 0

I don't see any

I normally solve by getting a factor

Like if we get 0 by putting x=1 then we can tell (x-1) is a factor of that polynomial

So we divide that by x-1 but here it is not happening

[winter torrent]

ugh

did you forget an = sign somewhere

[lime plaza]

I think yeah

They are missing a -ve sign

Hey what brings a mod here? hayley?

hmm

wait what

what is the question

find value of x??

....

[urban harbor]

!original

[pseudo basin]

btw @modern pulsar step 0 is to not DM individual helpers asking for help.

[devout snow]

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.

[lime plaza]

did he dm

[pseudo basin]

he tried to DM me yes

[lime plaza]

Don't dm random ppl

And change your name

[pseudo basin]

you can and should post pictures

instead of this bad copypaste that triples all math notation for no reason

[lime plaza]

What is this

[pseudo basin]

If the original problem is not in English, then post it anyway!

[lime plaza]

Why is it triple

Isn't this

This is simple

[urban harbor]

this is just plugging in x = -2 then do arithmetic

[lime plaza]

Just substitute

Exactly

YES

ok close this then

[devout snow]

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[lime plaza]

@modern pulsar if you delete I am not gonna help you again

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[tiny nova]

Hello, I'd like to know if my factorization is correct. I need to create a sign table afterward. If the factorization is correct, should I then isolate the two x values to construct my sign table?

[torn vessel]

the answer is correct, but you left out a + in the middle step.

[tiny nova]

Between (2x + 1) and (3x - 4) ?

[pseudo basin]

yes

you made it look like they were multiplied, but you don't want that

aside from this typo your work is correct so far

[tiny nova]

Okay thank you for the response !!

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[fierce rune]

i have this exercise and made output plots of e_n, but beyond that im not sure how else to talk about it. could anyone help me understand what that function does?

[devout snow]

@fierce rune Has your question been resolved?

[tawny pewter]

maybe compute some x_n n from 1 to say 6-7. Do you recognize a well know sequence F_n? Also it might be useful I think to explicitely compute alpha

[fierce rune]

yeah its the fibonacci sequence, its largest eigenvalue is the golden ratio. i'm just not sure what e_n could represent.

i can see that the numerator is 0 for any eigenvector x_n, but im not sure what else there is beyond that

<@&286206848099549185>

[tawny pewter]

one interpretation I can see for e_n is that it is the multiplicative factor by which the linear map (A - alpha I) stretch the iterates x_n

could you send the plot of the iterates?

[fierce rune]

yea sure

[tawny pewter]

hum for n greater than 90 it does nonsense

[fierce rune]

computation error?

ic

[tawny pewter]

I feel like this is numerical rounding error too

so tentatively the stretching factor of the iterates by the map A -alpha I tends towards 0

[fierce rune]

so up to 90 that's what youd expect?

[tawny pewter]

but I feel there is a better interpretation and this is a linear algebra and numerical analysis skill issue on my part

[fierce rune]

its a computing class so theres no study of linear algebra beyond like what eigenvectors are

i dont think theyd expect any pure analysis

[tawny pewter]

oh I got something

[fierce rune]

ohh so its a way of approximating fibonacci numbers? because then $A^N x_n \approx \alpha^N x_n$

just not true

im lost

[tawny pewter]

x_n seems to converge to the eigenvector associated wit alpha

[fierce rune]

ahhh

[tawny pewter]

and yeah I guess this kinda implies when n is big you can approximate x_n+m by alpha^(n+m) x_n

so you can kinda deduce the asymtotic growth of x_n

it's a bit handwavey

[fierce rune]

wait but x_n =[F_n-1, F_n] which grows

how do you mean it converges?

or just converges to be an eigenvector

ic

okay i can totally squeeze 300 words out of this

thanks so much!

.close

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[sterile ivy]

So, I proved (see attachments):
P1. P(B | A ) > P(B | ¬A )
P2. P(C | B ) > P(C | ¬B )
P3. P(C | AB) = P(C | B) & P(C | A¬B) = P(C | ¬B)
C. P(C | A) > P(C | ¬A)

However, now I want to prove the following and am having a much harder time with it. Anyone any ideas?
P1. P(B | A ) > P(B | ¬A )
P2. P(C | B ) > P(C | ¬B )
P3.* P(C | AB) > P(C | B) & P(C | A¬B) = P(C | ¬B)
C. P(C | A) > P(C | ¬A)

[devout snow]

@sterile ivy Has your question been resolved?

[sterile ivy]

<@&268886789983436800> (I experience this question as inappropriate)
<@&286206848099549185> anyone familiar enough with logic and probability theory to be able to help me?

[misty granite]

How is this inappropriate exactly

I don’t think this constitutes a mod ping, it’s just asking you

[silk falcon]

funny there is no defination of inappropriate

[modest dagger]

With so little context it's not obvious if they meant anything bad by it.

[misty granite]

Unless there are dms but

[modest dagger]

That would count as extra context

[silk falcon]

also
dp literally means display picture, meant to display

[misty granite]

Mhm, door

[modest dagger]

If there is more relevant context definitely share it of course

Fair enough probably just a miscommunication

We should probably let them focus the channel on their question.

It would be good to try and resolve issues between each other before pinging mods though for what it is worth.

[devout snow]

@sterile ivy Has your question been resolved?

[sterile ivy]

<@&286206848099549185> anyone here with knowledge of probability theory/logic? Curious to hear your thoughts!!

[valid silo]

This same should work out

just make sure you put a less then sign here

[devout snow]

@sterile ivy Has your question been resolved?

[devout snow]

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[thin wren]

Linear Algebra problem here, I googled the det(A) and it was -72. What is wrong with how I solved it and how does on get -72?

[sand dove]

wrong line you're expanding on

you want to expand on the "0 4 0" row don't you?

[vital sedge]

the last matrix should be 5,8
3,6

[sand dove]

it's not the row you highlighted

[thin wren]

omg thank you

.stop

.ealve

.leave

leave

how the hell do i get out

[sand dove]

it's .close

.close

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[worthy loom]

I’m not sure how to do this

[potent tusk]

hint connect A and D

[worthy loom]

It has the radius

So it’s an isosceles triangle?

[potent tusk]

yup

[worthy loom]

That’s I all get

[potent tusk]

do you remember the properties of cyclic quadrilaterals?

[worthy loom]

Opposite angles are supplementary

😮

So oad is 38

And so is oda

[potent tusk]

yup

[worthy loom]

Ohhgg

Then I add up 38 and 42= 80

Then 180-80

[worthy loom]

😄😄omg ty sm

[potent tusk]

yw

[worthy loom]

.close

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[nocturne turtle]

In a linear expression, is it possible to cancel out more than one time on the same numerator, example below

[spare crypt]

no you have to take away equal amounts from top and bottom

[nocturne turtle]

Why?

And also what do you mean by take out equal amounts?

[spare crypt]

you crossed off two 2m-n's from the top and one from below, which is wrong

I'm saying you can only cross off one from the top, and the reason this stuff works is (2m-n)/(2m-n)=1 so you can hide them from the fraction

[nocturne turtle]

Phhh ok

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[nova forge]

I am trying to graph this butterfly shape thing around the outer ring of this. how should I make a graph of that? I've been messing with desmos a bit and (cos(t),sin(2t)) was the closest I could get to the shape I wanted

[nova forge]

would I be better off piecing together a bunch of functions until I get the shape I want?

I should just use AI for stupid questions like this

I got my function

.close

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[peak jungle]

select odd functions help

[restive river]

Ye

Reflect over y axis

[thorn perch]

no

[restive river]

Which one looks like same thing but flipped over x axis

[thorn perch]

odd functions are symmetric across the origin

f(-x) = -f(x)

[restive river]

Same thing

[thorn perch]

no

[restive river]

As what i said ye

[crisp tapir]

Wtf

[autumn fjord]

are you sure?

[restive river]

Ye

Flip y

[thorn perch]

no

[restive river]

Then flip x

[peak jungle]

so like

[restive river]

Is same?

[peak jungle]

which one

idk man

its due soon

[crisp tapir]

if you don’t know what it is please don’t confuse the person who has asked the question

[restive river]

😤

[thorn perch]

odd functions are symmetric across the origin, or more strictly f(-x) = -f(x)

i'm pretty sure this is correct

[restive river]

Ye

Both are

[crisp tapir]

Yes

[restive river]

But dont try it yourself

[peak jungle]

which one

idk how to tell

like

ik flipped

acros the orgion

but when i do tht

[restive river]

Draw line y=x

[peak jungle]

it says its wrong

[restive river]

Turn head

[peak jungle]

??????????????

wtf

[restive river]

Does it look like mirror image

[restive river]

Its two steps

What part confusing

[peak jungle]

they all looked mirrored

[restive river]

Yeah but about y=x

Axis of symmetry

[peak jungle]

idk wym

[restive river]

You know how even functions are symmetric about y axis?

[peak jungle]

no

[thorn perch]

no, odd functions have rotational symmetry about the origin

[restive river]

???

[peak jungle]

can someone just give me the answer plz i cant let my grade drop 😭

[crisp tapir]

just take some ‘x’ and note the value if it’s the - of the value at f(-x) it’s odd

[restive river]

Lol y=-x^3 and top right

U dont want to read

Those are the answers

[crisp tapir]

The function won’t be odd due to just one value but you can check

[restive river]

And sin x

So its those 3

[restive river]

They arent reading anything

[thorn perch]

essentially if you rotate the graph 180 degrees around the origin, it should be the same

[restive river]

[peak jungle]

and thats how u tell

if its even

or

odd

?

[restive river]

odd

[peak jungle]

ok ima try ina minute

[restive river]

Just turn ur head

You dont need to try anything

[peak jungle]

im turning my head

and i dont notice anything

am i stupid

[restive river]

If you are on phone

Rotate phone 180 degrees

Does graph look the same

[peak jungle]

yes

@restive river ok i did it and they all look the smae

[restive river]

Easier trick

Reflect over y axis

Does it look same but negative

[peak jungle]

can i do it in vc and u show me what im suppoed to lookk for

[restive river]

No

You can do it in vc

Not with me tho

Ping one of the haters above

[peak jungle]

i wont talk

ok wait look

black is the reflection

what do i do now

they all map onto eachother but the parabola @restive river

[restive river]

Nah they dint

Top right a trick

For both images

[devout snow]

@peak jungle Has your question been resolved?

[devout snow]

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[orchid wasp]

shouldnt it be undefined cus it has ln0

[pastel pasture]

what's the original question?

[vocal tartan]

It's an improper integral, meaning you need to calculate $\lim_{a \to 0} \int_a^1 f(x) dx$.

[woven radish]

Morrow

[vocal tartan]

(Presumably)

[orchid wasp]

But isn’t it still ln0

[orchid wasp]

Lnx/sqrtx

[pastel pasture]

converges alright

[pastel pasture]

if you look at the overall form it's infinity*0 which is indeterminate

so you need to take the limit

[orchid wasp]

What I don’t understand

Where infinity times 0

[vocal tartan]

it's sqrt(x) * ln x with some other stuff mixed in

see if sqrt(x) * ln(x) has a limit as x->0

[pastel pasture]

0*(ln(0) - 2) = 0*(-infinity - 2) = 0*infinity

[orchid wasp]

How’s ln0 equal -inf

[orchid wasp]

Yeah so I plug in x as 0?

[vocal tartan]

no, then you get 0 * (-inf) like neon is saying

[pastel pasture]

,w ln(0)

[woven radish]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by neonperseus

[supple trench]

"ln" is a function whose domain is (0, ∞), so "ln 0" is undefined

[pastel pasture]

to get e to be 0 you raise it to -infinity

[pastel pasture]

yeah like that

the graph goes to -infinity

[vocal tartan]

You're multiplying something really close to zero by something really negative, so it's unclear what you're going to get until you sit down and calculate the limit.

[orchid wasp]

Bruh what I thought this was undefined

[vocal tartan]

The value of the function is undefined

the limit is -inf

[pastel pasture]

if someone ever says a function "equals" -infinity or infinity then they're talking about the limit in general

[orchid wasp]

So this is graph of ln0

[vocal tartan]

wolframalpha is a scheme by big engineering to sell more notational shortcuts

[vocal tartan]

It's the graph of ln x

You can see what happens if x is a really small positive number

ln x becomes a really negative number

,w ln(0.000000001)

[woven radish]

Results provided by WolframAlpha

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Requested by morrowm

[vocal tartan]

So the limit of ln(x) as x->0 is -inf.

ln(0) isn't really a thing, but if you say ln(0) people will assume you're referring to that limit

[orchid wasp]

So how’s it equal -4 when it’s a number - inf

[vocal tartan]

I can plug in an even smaller number if you want to see how it goes to -inf

,w ln(10^(-100000))

[woven radish]

Results provided by WolframAlpha

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Requested by morrowm

[vocal tartan]

Actually does calc work here

[woven radish]

Result:

-Infinity

[vocal tartan]

bah

don't listen to that, it's a precision error

[vocal tartan]

Anyways here you can see that we got -230000 or so
If you try to plug in smaller and smaller numbers you'll get closer and closer to -inf

[orchid wasp]

Ok so how it’s not divergent

[vocal tartan]

It is, but that's plain old ln(x)

[orchid wasp]

If ur minusing infinite

[vocal tartan]

You have a sqrt(x) multiplying it

If you multiply a really negative number by a number close to zero it's unclear what you get as a result

like, 10^(-10000) * -20 is a really small number, for example.
on the other hand 0.01 * -20000000000 is a really negative number

[orchid wasp]

Bruh what am I suppose to do then

[vocal tartan]

What tools do you have for calculating limits

[orchid wasp]

Idk l hopital cus inf times 0?

[vocal tartan]

Yeah lhopital is a good idea

[supple trench]

without l'Hôpital is even better

[orchid wasp]

What

[vocal tartan]

lhopital works, let's go with it

for lhopital you need to get it into the form "0/0" or "inf/inf", can you see how to massage sqrt(x) ln(x) into one of those forms?

[supple trench]

just use a simple substitution like u = ln x, then x = exp(u)

exponential times polynomial power function, so the limit should be easy

[orchid wasp]

Move the 2sqrtx to become 2x^-(1/2)?

[orchid wasp]

But it’s already integrated

[vocal tartan]

Yeah

[supple trench]

so? you're computing the limit

[vocal tartan]

Well, 2ln(x)/x^(-1/2)

[supple trench]

to use l'Hôpital, you need to get the derivatives correct
it's less error-prone to do simple substitutions, and have the basic fact in mind that exponential grows much quicker than power function/polynomials
https://math.stackexchange.com/a/2526702/290189

[devout snow]

@orchid wasp Has your question been resolved?

[devout snow]

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[hot ferry]

bare with me, i am just learning limits now and the lecturer has really bad notes

[hot ferry]

,tex $\lim\limits_{x \rightarrow 3^+} \sqrt{9 -x^2}$

[woven radish]

suds

[hot ferry]

so i had no idea what to do

google said substitute it for x

[pseudo basin]

are you looking for a proof or only for computation?

[hot ferry]

but the teacher said it does not exist since x -> 3+ => x > 3

[pseudo basin]

actually, hold on.

[hot ferry]

my question is why does the limit being x-> 3+ mean that x > 3

prompt is "Evaluate the following limits"

[pseudo basin]

$x \to 3^+$ means $x$ approaches 3 \textbf{from the right}.

[woven radish]

Ann

[pseudo basin]

it's the notation for one-sided limits.

^+ means from the right and ^- means from the left

[hot ferry]

so this was the image of notes that explained it

• more but

the image suggests that the function can be before or after c

so limits actually is its only on this side?

like limit is the asymptote?

[pseudo basin]

i think "limit is the asymptote" is really overthinking it

right so heres the thing

[hot ferry]

i mean if it makes sense 🤷

[pseudo basin]

whether you can talk about $\lim_{x \to c^+} f(x)$ and/or $\lim_{x \to c^-} f(x)$ depends entirely on the domain of $f$

[woven radish]

Ann

[wicked rover]

not all limits involve asymptotes...

[hot ferry]

what i mean by that is the limit is something that the function cannot pass

[pseudo basin]

mmm

no

[wicked rover]

thats a misconception

[hot ferry]

like x -> 3+ means that it goes towards 3 from the positive side, but it cannot reach it

like when u limit x-> 0 in derivatives

[pseudo basin]

i think you're maybe confusing "the limit" with "the value that x goes to"

[hot ferry]

i am

because i dont know the difference lmao

[pseudo basin]

where x goes vs. where f(x) goes

[hot ferry]

these notes are really confusing, even with concepts i already know, they say it in weird ways

[pseudo basin]

when calculating a limit, the former is given while the latter is what needs to be computed

[hot ferry]

oh so the difference is that the limit is the f(x) value given the x -> 3

which u compute with the following expression

[wicked rover]

there are two -> happening

https://i.gyazo.com/3768ac92aebfff95a0f6f33e13b10f62.png

[hot ferry]

ah

ok now i jsut need to write this in a way that makes sense for my notes lmao

but for this question in particular, the limit does not exist because there is no function value fro the function at x = 3

?

[pseudo basin]

more like the domain doesn't extend to the right of x=3.

[wicked rover]

the limit doesnt even make sense to talk about

[pseudo basin]

^

[wicked rover]

you cant even say DNE

[pseudo basin]

there's nowhere for x to even be to approach 3 from the right

[hot ferry]

yea domain

oh true because if x > 3 then its a negatvue root

.close

[devout snow]

Channel closed

Closed by @hot ferry

Use .reopen if this was a mistake.

[hot ferry]

another question

.reopen

[devout snow]

✅

[hot ferry]

I am very confused on limits to infinity

i am trying to say what i think this is trying to say but i dont even know

so a rational function is one in which P(x) / Q(x) = f(x) where P(x) and Q(x) are polynomials

"dividing through by the highest power of x"

what do they mean by that? like if the polynomial is x^5, they use 5? or they divide by x^5

[acoustic leaf]

they mean divide both numerator and denominator by x^5

e.g. [ \frac{3x^3 + 4x^2}{6x^5 - 2x} \cdot \frac{1/x^5}{1/x^5} ]

[woven radish]

cloud

[hot ferry]

so the highest power in either P(x) or Q(x)?

[acoustic leaf]

yes

[hot ferry]

ok

and then I don't know what it means "using the simple results that for any value of p > 0" and the limit notation

[acoustic leaf]

e.g. [ \lim_{x\to \infty}\frac{3x^3 + 4x^2}{6x^5 - 2x} \cdot \frac{1/x^5}{1/x^5} = \lim_{x\to\infty} \frac{3/x^2 + 4/x^3}{6-2/x^4} = \frac{3(0) + 4(0)}{6-2(0)}]
because
[ \lim_{x\to\infty} \frac 1{x^2} = 0 ] and similarly for all other powers

[woven radish]

cloud

[hot ferry]

where did the 0's come from?

[acoustic leaf]

this is because [ \lim_{x\to\infty} \frac 1{x^p} = 0 \qq{and} \lim_{x\to-\infty} \frac{1}{x^p} = 0 ]

[hot ferry]

so p = 2

[woven radish]

cloud

[acoustic leaf]

the result holds for any positive number p, so we apply it for p = 2, p = 3, and p = 4 here

[hot ferry]

i think i see it

so its a way of evalutating the limit?

[acoustic leaf]

yes, it allows us to evaluate the limit of the rational function

[hot ferry]

ok i see

now i just need to think of a way to write that lol

one more thing sorry

as i was checking over my notes for rational functioms

i mostly understand this but theres some weird wording

"which will "cancel out" the problematic indeterminate form"

does it mean it cancels out 0/0 or the expression cancels out?

[wicked rover]

u cancel x-a

[acoustic leaf]

when you evaluate that limit it will be in the form 0/0. but factoring out (x-a) will cancel it out, leaving you with something which is not 0/0

[hot ferry]

ok yeah

[acoustic leaf]

e.g. [ \lim_{x \to 3} \frac{x^2 - x - 6}{x^2 + x -12} ``='' {0}{0} ] but we evaluate it as [ \lim_{x \to 3} \frac{x^2 - x - 6}{x^2 + x -12} = \lim_{x \to 3} \frac{\cancel{(x-3)}(x+2)}{\cancel{(x-3)}(x+4)} = \frac{5}{8} ]

[woven radish]

cloud

[hot ferry]

that was just really bad wording i feel

okay i got it thank you :D

how do you come up with examples on the fly like that

[acoustic leaf]

for this one i came up with the factored forms first and then multiplied them out

[hot ferry]

nice okay

[devout snow]

@hot ferry Has your question been resolved?

[hot ferry]

.close

[devout snow]

Channel closed

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[gritty sandal]

hey can somebody help me solve this linear system of ODE

[gritty sandal]

So far I have managed to identify the repeated eigenvector [-1 2] with eigenvalue 5

so I calculate the generalized eigenvector and i get

[-1 0] + t[-1 2]

yet for some reason this is wrong

[wicked rover]

,w eigenvector [[7,1],[-4,3]]

[woven radish]

Results provided by WolframAlpha

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

Requested by rokettojanpu

[wicked rover]

,w rref[[2,1,-1],[-4,-2,2]]

[woven radish]

Results provided by WolframAlpha

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

Requested by rokettojanpu

[wheat pawn]

!show

[devout snow]

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

[wicked rover]

ur generalized evec looks wrong

[gritty sandal]

hmm ok

uhhh

[wicked rover]

https://cdn.discordapp.com/attachments/903486480075354182/1351460978734268506/wolf.png?ex=67da759e&is=67d9241e&hm=b8c80eb8455f05eda0736b6247c2c295a7b5c2c92496f440fb25f7e78b293ad6&

thats what u solve for gen evec

[wheat pawn]

,rotate

[gritty sandal]

this me solving the

$$(A - 5I)w = v$$

[woven radish]

skm

[gritty sandal]

from the top eq

and then

[wicked rover]

this looks ok

[wicked rover]

just dont forget e^5t in the solution

[gritty sandal]

ye

for now im just solving for the vector

[gritty sandal]

does this vector look ok?

[wicked rover]

yes

[gritty sandal]

ok gimme a sec latex takes a minute

solution wil be

[wicked rover]

e^{5t}(w+tv)

[gritty sandal]

uhh yeah

[wicked rover]

its ok no need to show me if u understand

[gritty sandal]

plus e^{5t}(v)

[wicked rover]

yes

[gritty sandal]

and for some reason I think its wrong

[wicked rover]

well u need c1 and c2 too

[gritty sandal]

yeah

hmm maybe i solved for those wrong

[wicked rover]

i checked v already

https://cdn.discordapp.com/attachments/903486480075354182/1351460838795382835/wolf.png?ex=67da757c&is=67d923fc&hm=eb8e2ba634c8e5c334bb4df326d84621b200c84ec05220f459435a243f475917&

this is how i get w

https://cdn.discordapp.com/attachments/903486480075354182/1351460978734268506/wolf.png?ex=67da759e&is=67d9241e&hm=b8c80eb8455f05eda0736b6247c2c295a7b5c2c92496f440fb25f7e78b293ad6&

if u got these then its right

[gritty sandal]

$$ \begin{bmatrix}
-1 & -1 \
2 & 0
\end{bmatrix}
\begin{bmatrix}
c_1 \
c_2
\end{bmatrix}

\begin{bmatrix}
2 \
-5
\end{bmatrix}

[woven radish]

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

[sterile ivy]

Would you be willing to do it with me? I can’t quite figure it out

[devout snow]

@gritty sandal Has your question been resolved?

[gritty sandal]

¯_(ツ)_/¯

[devout snow]

Channel closed

Closed by @gritty sandal

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[twin frost]

Im so lost

😞

[shell plover]

Hii

[twin frost]

hi

[shell plover]

So did u find that the angle DFC is 90-x

Oops

FDC*

[twin frost]

Yeah

[shell plover]

Good

[twin frost]

Im a little confused on the next steps

[shell plover]

Consider the triangle FDC

It is isosceles

[twin frost]

Ok

[shell plover]

Angle fdc is equal to dfc

Rightt?

[twin frost]

Yep

So c is 180 - all that

[shell plover]

Yaaa

Correct

So u can calculate angle DCB too

Right?

[twin frost]

Erm

Im not to sure

[shell plover]

Why not?

FCB is a straight line

[twin frost]

I got dcf to be -2x

[shell plover]

Yes that's right

[twin frost]

So bcf is 180 + 2x

Oh okk

[shell plover]

What is the sum of the angles DcF aand DCB?

[twin frost]

180-2x

[shell plover]

No

[shell plover]

No

[twin frost]

Oh mb dcb

One sec

[shell plover]

Sure

[twin frost]

90-x

[shell plover]

DCF+DCB= 90-x?

[twin frost]

180

[shell plover]

Yesssss

[twin frost]

Mb mb

[shell plover]

DCF + DCB = 180

And we have already calculated dcf

So we can Calculate Dcb too, right?

[twin frost]

-2x

[shell plover]

Yup

So dcb is what?

[twin frost]

Yh its gonna be

Erm

[shell plover]

Use this

[twin frost]

180+2x

[shell plover]

Umh

Wait

[shell plover]

Angle dcf is negative 2x?

[twin frost]

yeah?

[shell plover]

Why is that negative?

[twin frost]

180 - 2(90-x)

[shell plover]

yes

I becomes positive

When u open the bracket

[twin frost]

So its just x

Kk

[shell plover]

2x*

Ya

[twin frost]

Mb

Ok

[shell plover]

So dcf is 2x

And dcf + dcb is 180

So dcb is?

[twin frost]

180-2x

[shell plover]

Yupp

Now, do you know the special property of cyclic quadrilaterals?

[twin frost]

Opposite add to 180

[shell plover]

yaa

Now try using that

[twin frost]

So 2x + 180-2x = 180

But then the x cancel out and its just 180 = 180

[shell plover]

You have to prove that DAB is 2x right?

[twin frost]

Yh

[shell plover]

why did u already put it 2x

[shell plover]

Here

[twin frost]

Ohhhh ok ok

Thanks

[shell plover]

Ya

:D

[twin frost]

Do u have time for another ?

I have my gcse in 3 months gotta lock in 😅

[shell plover]

Im not that good at geometry

u can give it

[twin frost]

Its part b

[shell plover]

I will try but im not suree if i would be able o do it

ok

[shell plover]

Lemme see

Do u have the answer?

Is it 30 degrees?

[twin frost]

Can u show me how to prove it ?

[twin frost]

No sry

[shell plover]

okk

First of all we need to calculate angle ADC

What do u think, how ccan we calculate it

[twin frost]

Adc is 180 - y

[shell plover]

What is y

[twin frost]

Erm

90-x

As we worked out before

[shell plover]

Yess

Yup

So adc is?

[twin frost]

One sec

90-x

[shell plover]

recheck

[twin frost]

180-90-x

[shell plover]

nope

[twin frost]

90-x ?

Erm

[shell plover]

180-(90-x)

[twin frost]

Adc = 180 - y

Mmm ok

[shell plover]

U forgot the bracketsss

[twin frost]

Oh alr

[shell plover]

It becomes 90+x

Yea

[twin frost]

Kk

[shell plover]

Do u know the sum of angles BAD and ADC?

[twin frost]

180

[shell plover]

Yess

Use this fact

[twin frost]

Kk

[shell plover]

And you'll the answer

[twin frost]

Tysm

[shell plover]

:D welccome daddy dumpling

[twin frost]

Thank you sheesh

[shell plover]

loll byeee

[twin frost]

Do u have time for more if u dint mind

Bye 👋

[shell plover]

Umh

Ok

[twin frost]

Kk

[shell plover]

Just one

[shell plover]

Hmm

[twin frost]

I assume that fkj is also 2x

[shell plover]

Okkk

[shell plover]

Okk

[twin frost]

Jfg is 180-(3y+98)

[shell plover]

i have a simpler solution

But u can give urs a shot

[twin frost]

The triangle

I just red the question

[shell plover]

oh

[twin frost]

Both are radi so its a isosplies

Isoslies triangle

Nvm thats weong

Wrong*

whats ur solution

[shell plover]

U should try first

Do u hv any approach?

[twin frost]

Hkk is 180-( 2x + 7y)

Hjk*

erm

Im lost

Sry

[shell plover]

lemme give u a hint

Do yk that property that states that

[twin frost]

Alternate segmant therom c

?

[shell plover]

The angles formed by a chord on the same arc of a circle are equal

[shell plover]

Lemme google it what's that, idk the names of theorems srry

[twin frost]

Angoes of the same segment throm

?

[shell plover]

yea ig

[twin frost]

I used that to get fkj

[shell plover]

Good

[twin frost]

But hjk

Im confused

[shell plover]

lemme see

Give me a min

[twin frost]

Oki

[shell plover]

Read the question

Again

There's an important information

[twin frost]

Their parallel ?

[shell plover]

Yupp

use that

[twin frost]

Hint ?

All i can think of is alternate segmant therom

[shell plover]

i don't know the name of that property but i can try to tell u

[shell plover]

Noo

Lemmme send u a picc of that property

[twin frost]

Cuz its a Z shape

[shell plover]

Ya that Z shape property

😭 i need to learn there names

[twin frost]

This one ?

[shell plover]

Yes yesss

[sand olive]

Internal alternate angles

[twin frost]

Alternate angle therom

[shell plover]

Ooh smart guyyy

[sand olive]

Lol I just used google translate but thanks

[shell plover]

:)

[twin frost]

So its also equal

[shell plover]

Yess

[twin frost]

Ok thank you very much sheesh

Have a good day

😄

[shell plover]

Night*

[twin frost]

Thanks for your time

have a good night

[shell plover]

:)

[twin frost]

🙂

[shell plover]

Haha byeeeee best of luck

[twin frost]

See ya around

Thanks you too

[shell plover]

Btw what is gse?

[twin frost]

Its the Uk test for people ages 16-17

Its what you need to get into sixform

[shell plover]

oH

[twin frost]

And then sixform to get into uni

[shell plover]

that's cool

[twin frost]

But im taking it early cuz my skl is stupid

[shell plover]

Would u mind telling me ur age?

[twin frost]

14

You ?

[shell plover]

Im 16

[twin frost]

I bet u would get a 9 in gcse

Ur in the year above me

[shell plover]

Hahah thnks :)

Best of luck

[twin frost]

You too have a good night

[sand olive]

加油朋友！

[twin frost]

🙂

[twin frost]

谢谢

[twin frost]

Tryna tutor me in mandarin

要帮我补习吗）

？

我老是不好:(

[sand olive]

我的中文水平不太适合

[twin frost]

我的不好

[sand olive]

我看见了你写的诗，很厉害啊

[twin frost]

太多东西不会认

完蛋了

😭

[sand olive]

没有嘛，你讲的没有那么糟糕啊

也就是慢慢学的过程

[twin frost]

我读你的字也不太懂

我不厉害

但是还知道吧

会听和说不会写合度

[sand olive]

那也算是正常吧

我猜你是英国移民？

[twin frost]

对

[sand olive]

嗯，我是加拿大移民

[twin frost]

但是我是在这出生的

[twin frost]

这么样？

好不好？

加拿大这么样、

？

我没去过

[sand olive]

加拿大还挺好，不过我住在个小城市里

没有几个中国人

[twin frost]

Thanks mate

[sand olive]

当然没有中国卷

[sand olive]

呵呵呵

那你们在英国怎么样？

[twin frost]

对

[twin frost]

蛮好的

持刀犯罪太多

几周前我们学校发生了一起刺伤事件

我没有说谎

😭

[sand olive]

是吗？

英国现在的确比较乱

[twin frost]

对啊

真的

没点都有电话打抢

好我要去睡了

晚安

[sand olive]

哦对，有时差

[twin frost]

谢谢你

[sand olive]

晚安，认识你很高兴！

[twin frost]

希望再见

b ye

[sand olive]

嗯嗯

Bye!

[devout snow]

@twin frost Has your question been resolved?

Channel closed

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[devout snow]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[hallow brook]

how do i copy a photo

[faint zinc]

Try writing it out as a jpg

heic is not a format that is well handled by discord

[supple knot]

https://support.discord.com/hc/en-us/articles/211866427-How-do-I-upload-images-and-GIFs

[devout snow]

@hallow brook Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[full ferry]

I wanna ask if x approach - infinity

Does mean x=0?

Plz help

[astral lodge]

,rccw

[astral lodge]

💀

no

[full ferry]

Oh

lol

[astral lodge]

just means the end behavior as x-> -infinity

so like what is the HA of this graph

[full ferry]

Wait is d

Right

Because it toward negative infinity

[astral lodge]

Yeeep

[full ferry]

Tyty

[astral lodge]

what in the notation abuse

💀

1.5^-

💀

[full ferry]

lol

[astral lodge]

not normal notation

but ok....

[full ferry]

What

That’s funny

.close

[devout snow]

Channel closed

Closed by @full ferry

Use .reopen if this was a mistake.

[astral lodge]

💀

💀

💀

[devout snow]

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[ionic swift]

How can this bound be argued ?

[stone stump]

via induction you could prove a closed form for the sum

or by seeing it as the derivative of the geometric sum

or by some combinatorial argument

(namely the sum is equal to ||k 2^k - 2^k+1||)

[ionic swift]

Yes. Thank you. I was thinking about finding a combinatorial argument but couldnt find it

[ionic swift]

Tried that as well but was unable to conclude something useful

Ok thanks a lot I will try it again

.close

[devout snow]

Channel closed

Closed by @ionic swift

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obsidian plank]

3log3(8) the first 3 is confusing can someone please explain it ?

[obsidian plank]

the instructions are to solve it

[faint zinc]

3 times log base 3 of 8

[obsidian plank]

mhmm

[faint zinc]

What is confusing about this?

[obsidian plank]

nothing

[faint zinc]

It seems to be in its most simplified form

[obsidian plank]

I just didn't know what the 3 was suppose to mean

[faint zinc]

But if you can use a calculator

[frigid jetty]

3 constant

[faint zinc]

Problem solved then?

[obsidian plank]

yeah

thanks

.close

[devout snow]

Channel closed

Closed by @obsidian plank

Use .reopen if this was a mistake.

[obsidian plank]

actually one more question would this apply only to the base or the 8 too ?

.reopen

[devout snow]

✅

[faint zinc]

$a \log_b(c)$ is $a$ times log base $b$ of $c$.

[woven radish]

OmnipotentEntity

[faint zinc]

Doesn't matter what you put into a, b, c so long as they are legal values.

[obsidian plank]

thanks

.close

[devout snow]

Channel closed

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[devout snow]

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[calm fern]

im trying to revise

[calm fern]

and the page im using

doesnt come with answers

could anyone tell me if i got it right please

750.8

to 3 significant figures

surface area btw

cut it out sorry

but yeah you have to find the total surface area of that shape

[weak cove]

,w 6100+2pi38

[woven radish]

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Requested by austinu

[weak cove]

looks good

[calm fern]

thanks so much :)

[devout snow]

@calm fern Has your question been resolved?

[devout snow]

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[devout snow]

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[deep gale]

A rectangular field of given area is to be fenced off along the bank of a river. If no fence is needed along the river, what is the shape of the rectangle requiring the least amount of fencing?

[undone chasm]

we have 2x+y=a

the a doesn’t matter bc we’re just finding the ratios

maximize xy with constraint 2x+y=a

[deep gale]

these were the equations i got

A = xy ; x = A/y
P = x+2y

x is the length and y is the width

[undone chasm]

yes

can you express A with only x’s

[deep gale]

A = xP-x^2 / 2

[undone chasm]

what’s your expression for y?

[deep gale]

y = A/x

[undone chasm]

but we’re gonna use the expression for y in A so it can’t rely on A

[deep gale]

oh is it P = x+2A/x

[undone chasm]

umm

that’s true but we need A in terms of x lol

[deep gale]

how?

[undone chasm]

well P=x+2y so y=(P-x)/2

so we need to maximize A = x(P-x)/2

[deep gale]

idk if my solving if correct but i got
A = 2x+P/2

[devout snow]

@deep gale Has your question been resolved?

[devout snow]

@deep gale Has your question been resolved?

[devout snow]

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[iron holly]

Hello, I’m currently in calculus but have a question about some circle theorem/euclidean geometry problem. I’ve tried asking for help from the most up to date AI models, and even reverse searched this image to no true avail. If know your stuff on this matter I implore you for your assistance.

[iron holly]

I know that angle AOB is 2x due to the isosceles nature of triangle AOB. I know that in triangle AOC, angle OAC and OCA are equal. I need some help and finishing this analysis though.

[gray axle]

Do they mean this shape specifically or any triangle?

[iron holly]

?

Proving that angle w is equal to angle x + 90 is the task.

<@&286206848099549185> (it’s been ten minutes, and if I remember correctly you’re allowed to @ helpers at this time)

[undone chasm]

(15)

[iron holly]

?

[undone chasm]

so we notice AO=BO

bc theyre both radii

[iron holly]

Yes

That is true

[undone chasm]

so CAB=ABC

[iron holly]

How can you deduct that?

[undone chasm]

bc its isoceles

[iron holly]

triangle ABC?

[undone chasm]

ABO

you can also split it into two right triangles and see that theyre congruent

[mortal bloom]

anyone able to help with this😭, me and my friend get different answers

[undone chasm]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[iron holly]

How do you extend triangles ABOs isosceles nature to facts about triangle ABC?

[iron holly]

Inside triangle ABO?

[undone chasm]

yes

[iron holly]

I know ABO is isosceles, and angle AOB would be 180 - 2x, right?

I’m just uncertain on how to get from there to classifying facts about triangle ABC

[undone chasm]

AOB subtends AB

so ACB is half AOB

ACB=90-x

ACD is a straight line so 90-x+w=180

90+w=180+x

w=x+90

[iron holly]

I know that ACB is half of AOB, but how do you then get ACB = 90 - x?

[undone chasm]

bc (180-2x)/2

[iron holly]

180-2x is derived from AOB, right?

[undone chasm]

triangle AOB is isoceles

so with angle x AOB is 180-2x

[iron holly]

Yes

So if you look at angle x

There exist space between line ACD and angle x

[undone chasm]

ya AC

[iron holly]

This here

You’re finding this via angle AOB divided by 2