help-0

[thin stag]

i was able to show this result with the hint (for small positive epsilon) but i dont know how i can combine the two integrals from here

[lone heart]

@thin stag Has your question been resolved?

[lone heart]

@thin stag Has your question been resolved?

[placid zinc]

So we gotta assume the integrals are convergent, and so the ε isn't necessary

I think you'll see a negative on the right side as well, since the bounds were swapped

My apologies, you don't see that negative

Yeah, the next steps are to add the integrals. You know that:
2I = ∫ ln(sin(x) + ln(cos(x)) dx

[thin stag]

why do we assume the integrals converge first before working on it? is the mindset like 'If this integral converges, then...'

i omitted it but the question was phrased like "evaluate if it exists"

okay, assuming that the integral $I$ exists i get $I = -\frac{\pi}{2}\ln(2)$, using the double angle formula which i missed when working independently. but this strikes me as odd because the original integral looks very divergent.

[ocean seal]

Dominic

[lone heart]

@thin stag Has your question been resolved?

[thin stag]

ill look at this again later

.close

[lone heart]

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[violet iron]

Hello?

[violet iron]

Can anyone help me please?

I need help with letter C

And in the second picture is the data. I’m just not sure how to do the “figure out the increments” part

<@&286206848099549185>

🥺

Help please I’m stressed 😦

[tacit arch]

Read this

[violet iron]

I did

[tacit arch]

Then don't ping until after 15 minutes

[violet iron]

I did it a bit too early sorry

<@&286206848099549185> nowww my 15 minutes are over, once again I apologize

[buoyant kayak]

well don't ping helpers again

you already did

[violet iron]

But no one is helping me 😂 but okay

[nimble fiber]

@violet iron do you know what the increment of the graph means

[violet iron]

Not really

How the waste of money increased maybe?

[nimble fiber]

well it basically means, in the x and y axises, how far apart the numbers are

for ex.

you can notice that the time goes by 2s, 0, 2, 4, 6, etc

[violet iron]

Right

[nimble fiber]

"will we have to go to the penny or the nearest dollar"

which do you think is more reasonable

[violet iron]

Hmm I think I’m understanding just a little bit

Penny?

[nimble fiber]

why do you think so?

[violet iron]

Because it’s money and every cent matters

😅😓

I’m not sure though

[nimble fiber]

i would say that you can just round to the nearest dollar, because the numbers are large enough that they a couple of cents doesn't really matter

[violet iron]

Ohh okay

So first do I have to order them from least to greatest?

[nimble fiber]

i'm not sure

[violet iron]

Like, to plug them in the graph

I just ignore the decimals right? I just round to the nearest whole number?

[nimble fiber]

yeah

[violet iron]

This is what I’m doing

I’m putting the amount spent in order from least to greatest

Wait, how do you find the increment? 😨

In the case of my problem

[nimble fiber]

i would go by 5s or 10s

up to you

[violet iron]

What do you mean

[nimble fiber]

also your graph is wrong

[violet iron]

Do I not have to plug in all the money spent on the right side?

Oh why?

[nimble fiber]

it's not to scale

[violet iron]

Oh yes this is only the rough graph it says there

[nimble fiber]

ok then if you don't care about scale then yeah that's good ig

[violet iron]

I’ll use this for the original one

[nimble fiber]

but make sure to fix it for the final one

[violet iron]

Yeah I will

So what is the first step?

[nimble fiber]

so the vertical axis represents how much money you have, and the horizontal axis represents time

[violet iron]

Whattt

What is the time in my problem?

[nimble fiber]

each bank statement

is one time unit

[violet iron]

And the amount of money I have is 600

[nimble fiber]

mhm

[violet iron]

Ohhh so they areee let me see…

12 time units

[nimble fiber]

yeah however many bank statements there are

[violet iron]

Okay

Can you show me how it would be?

Or help me to know

[nimble fiber]

so you start with 600, so a point would be (1,600)

[violet iron]

Where do I write the 600

[nimble fiber]

then you withdraw 15 dollars, meaning you subtract 15, so the second point would be (2, 585)

[violet iron]

Ohhhh

[nimble fiber]

you graph points

[violet iron]

I kind of get it

[nimble fiber]

so x axis is time, y axis is how much mone you have

[violet iron]

Is there a way to send voice messages

I can’t explain myself very well texting

[nimble fiber]

you can try using voice input? but that's not very accurate

[violet iron]

I’ll try

Wait nah

So comparing it to the example you gave me

The 0 in the vertical axis would be 600 right?

[nimble fiber]

yeah

[violet iron]

And then the 0 in the horizontal axis would be 0 too, the 2 in the horizontal axis would be 15

[nimble fiber]

no

the 2 in the horizontal axis should be 600 - 15 = 585

[violet iron]

So I subtract 15 from 600 and then the 92 would be 585?

Ohhh

[nimble fiber]

yeah

[violet iron]

Crap I’m confused

[nimble fiber]

also, if you are going to call the starting 600 0, then the 15 dollar withdraw would be x = 1

[nimble fiber]

it's really up to you (or your teacher) on whether you start the 600 as x=0 or x=1

[violet iron]

How is the graph gonna look like that if the only number or unit I have in the vertical axis is 600?

[nimble fiber]

anyway

[violet iron]

😭

I’m so confused

[nimble fiber]

what does your graph look like right now?

you need to finish all the rest of the bank statements

and then you'll have a lot of points, which youll be able to connect just like that

[violet iron]

How many other points do I put under the 600

I have to subtract the bank statements first right?

[nimble fiber]

yeah

[violet iron]

OHHHHHHH

hold on

And then, when I plug all the numbers in, the money is gonna go down right?

[nimble fiber]

yeah!

[violet iron]

Like that?

But it’s gonna go straight down 😂😂

[nimble fiber]

mhm the dude in this example is not good at managing money lol

[violet iron]

And then, instead of 167.72 should I just put 168?

Yeah he’s gonna go homeless

[nimble fiber]

mostly good, except you dont write 15 in the bank statements

you can just label 1 2 3 4 5 etc

[nimble fiber]

yes

[violet iron]

Ohh okay okay

Alright

Oh my god thank you so much, and I’m sorry for the pinging again 😓

[nimble fiber]

no problem :)

[violet iron]

Have a nice day man or woman 😎

[nimble fiber]

u2

[violet iron]

Or however you identify as 😨

.close

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[minor bloom]

how do i draw the graph of the first derivative when you are given the graph of the second derivative? this is for polynomail functions

[lone heart]

@minor bloom Has your question been resolved?

[covert agate]

@minor bloom

one question at a time.

[open folio]

Omg!?!?! It's?!?!@?! Chromium!?!?!??#?!?@!

[covert agate]

please either close this channel or help-20

[minor bloom]

o sory

[covert agate]

@minor bloom

[minor bloom]

i choose 20

[covert agate]

.close this one

[minor bloom]

.close

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[twilit rivet]

Hi how can i do this qs ?

[twilit rivet]

how to find the value of a ?

[lone heart]

@twilit rivet Has your question been resolved?

[zenith compass]

Can you input two numbers

In the answer

[twilit rivet]

I got it tks

the ans is 8

i did not read the qs clearly

[zenith compass]

Ok good

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Channel closed

Closed due to the original message being deleted

[zenith compass]

What

The channel is closed

I am not sure

But i suggest u to open a new channel

Otherwise the channel will close suddenly

The channel is already closed

Yes

Just use a new room

[lone heart]

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[glass lichen]

No clue how to do this, and my textbook doesn't give examples for how to do a continuity proof.

[glass lichen]

.close

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[next cliff]

Hey There!

[next cliff]

Can anyone explain what "the average of every outcome" is supposed to mean?

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@next cliff Has your question been resolved?

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@next cliff Has your question been resolved?

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[alpine sable]

How to move forward

[serene junco]

Your sin(y) changed to a sin(x) in the second line. Which is it supposed to be?

[alpine sable]

Sin(x) mybad

[serene junco]

Just checking lol

You want to solve this for y, right?

[alpine sable]

Mhm

[serene junco]

So all that's left to do is take the arctan on both sides

[alpine sable]

mhmm

how would I do that to cot

[serene junco]

You wouldn't do it to cot alone, you'd just have to wrap the whole RHS in arctan

I don't know of any clean ways to simplify that

[alpine sable]

Should I apply that to a calc or is it a rule I hav e to know

Ah ok

ty!

[serene junco]

No problem

[alpine sable]

.close

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[vagrant fractal]

Need help determining the possible outcomes and their values here

took a break before answering this assignment again and everything just fell out of my mind

[lone heart]

@vagrant fractal Has your question been resolved?

[tacit arch]

What have you tried

[lone heart]

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[vagrant fractal]

i kinda don't get the "cards are drawn, without replacement, until a card is drawn that matches the color of the first card" part so i don't know tbh

[lone heart]

@vagrant fractal Has your question been resolved?

[remote heron]

try to think like

how many different possible outcomes can you have?

we have ten cards, and we draw one

its either red or black

there are now 4 "matching cards" left, and 5 "nonmatched" cards

say without loss of generality the first card is red

whats the worst case scenario for cards we have to draw to get another red?

whats the best case scenario?

@vagrant fractal

[vagrant fractal]

OHHHHH

shit im dumb

thanks a lot

😄

[remote heron]

u got it?

[vagrant fractal]

kinda my teacher told us he would have a rediscussion of the lesson next week cus a lot of ppl in my class got almost everything wrong

but yeah i think i got the gist of it

[remote heron]

nice

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[tight locust]

What are the constraints on the ratio of side lengths in a pythagorean triple

[tight locust]

Basically look at this

$(ak)^2 + (bk)^2 = c^2$

[ocean seal]

EndTimes

[little drum]

the pythagorean triplets

[tight locust]

And tell me what the restrictions must be on the ratio a/b

[little drum]

are always of the form

[woven whale]

the m,n form

[little drum]

$${(r^2 - s^2), 2rs, (r^2 + s^2)}$$

[little drum]

the primitive triplets at least

[tight locust]

Actually the factor k doesn't matter haha

We just need to find the ratio of a/b in a^2 + b^2 = c^2

Maybe a bit of context might help

[little drum]

yes

[tight locust]

Can an HDTV with aspect ratio 16 by 9 ever have integer side lengths and diagonal?

[little drum]

what's the equation

what's the condition you're looking for

[tight locust]

Yeah so that means for some k there must be

(16k)^2 + (9k)^2 = c^2

Which i don't think is possible?

[little drum]

._.

[tight locust]

k can be real

[little drum]

$$256k^2 + 81k^2 = c^2$$

[little drum]

$$337k^2 = c^2$$

[little drum]

$$c = \sqrt{337} k$$

[little drum]

[tight locust]

Right exactly

So we're letting k be any positive real quantity

So its possible

so k = n/sqrt(a^2+b^2) where n is any integer

.close

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[alpine sable]

Hi

[lone heart]

Please don't occupy multiple help channels.

[alpine sable]

can someone helpy with python

[alpine sable]

Python is a programming language

And this is for maths

Ig

wait only maths i thought ive

seen people ask about progrmming

in the sevrer

my bad \

[alpine sable]

You should #❓how-to-get-help

It's for math only

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[sturdy dust]

What would I need to know to find the area of the shape in red? The size of every side and the angle of the roof? And then what would the formula be to work it out?

[alpine sable]

um

you have to use the pytagtherom

[buoyant kayak]

well that's 3d

do you mean surface area or volume

[sturdy dust]

surface area and volume i guess

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[grim vessel]

values of a and b so that function of f(x) is continuous for all real values of x

[gray isle]

what have you tried?

[grim vessel]

um i dont know where to start

I don't understand the question

this was on my limits unit test for pre calculus

[gray isle]

start with the (limit) definition of continuity

[grim vessel]

oh so for x^2 i would write limit as x approach -2 form the negative side ?

[gray isle]

yes, that will be part of your work for investigating continuity around x=-2

[grim vessel]

what numbers do i plug in for a and b. I got the limit of x^2 and 2^2+2

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@grim vessel Has your question been resolved?

[gray isle]

you don't plug in any numbers for a and b

you'd also want to consider the limit as x→-2 from the right
and the limit as x→2 from the left

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[alpine sable]

If I prove that, forall x, y in N, (y != 0 -> exists ! z, x = y * z), how do I define division as the right-inverse of multiplication? I'm confused because of the "y != 0" condition.

Is it just, forall x,y,z, z = y:x iff y = x*z?

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@alpine sable Has your question been resolved?

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[wet spindle]

this method works every time right? Watched a math video that says you should isolate the expression inside the abs first then solve for it, but here I didn't and got the right answers as well

[alpine sable]

It's correct

What you did was a piecewise function

[untold crescent]

You're using the definition of absolute value here, it's 👌

[lone heart]

@wet spindle Has your question been resolved?

[little drum]

no it does not work all the time

At times you'd have to note the interval in which you're working

so that extraneous solutions can be defenestrated

[wet spindle]

@little drum ah I didn't give you the full picture

,rotate

[little drum]

hmmm

so the idea is

to check your final solutions after solving each cases, with the interval of interest

if they agree with the solution or not

if they do, you're fine like in this case

it only takes an extra 10 seconds of caution to be honest

And saves your day (ヘ･_･)ヘ┳━┳

[wet spindle]

here's how he did it in the video, which one is better?

[wet spindle]

@little drum here, is the only way to check for extraneous solutions is to plug it back into the equation?

[little drum]

nope

it's to check if the initial interval(w.r.t. which you split cases) agrees with the solutions

for example

here, you split into cases x - 1 > 0, x - 1 < 0

and since 4 and -2 fall in those intervals respectively

those solutions are correct

[wet spindle]

isn't it ≥ 0?

[little drum]

yha, pardon me I don't have the geq symbol in my phone keyboard

anyways, so

[wet spindle]

try holding it

[little drum]

say if you somehow solved and the equation got you the solution 0.5 when solving in the interval x - 1 > 0

then, you can reject it

because it doesn't agree with the interval

[wet spindle]

so it's the same as this @little drum

upper right part

[little drum]

yep

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[lone heart]

@flint sphinx Has your question been resolved?

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[flint sphinx]

;-;

Am I doing this right? I feel its kinda wrong but idk in what way.. Please help

Sorry for the double

<@&286206848099549185>

[placid zinc]

Check the rules on helper pings. I'm not certain if you claimed the channel correctly, it may be closing

[flint sphinx]

Oh

Maybe I should close it and open another one..

Mhmm

.close

;-;

Did i broke the command..

[glass lichen]

when you deleted the original message, it closed already.

[flint sphinx]

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[twilit dune]

how to prove in any field for arbitrary element $a$, $a+a=0 \implies a=0$

[ocean seal]

alshfik

[vale wigeon]

you can't because that isn't true

for example, in the field with two elements, 1 + 1 = 0

@twilit dune a+a=0 => a=0 is equivalent to char(K) ≠ 2

[twilit dune]

oh right

.close

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[alpine sable]

How do I get the eigenvector from this???

[alpine sable]

I'm always confused with the free variable way of expressing a vector

This is why I'm confused hehe

[raw latch]

i cant read what you have written there, but if you're asking why the answer isnt [3/7 , 1]. That is just a choice they are both linear dependent vectors

[alpine sable]

Yeah well i don't understand that

I'm sorry

Are they the same?

[raw latch]

yes

look at the last equation it gives you the value of x1 if you know x2

so whatever x2 is, you immediately know how to choose x1

you made the choice of x2=1 and they made x2=7

[alpine sable]

Ah shit

They choose 7 as the free var

[raw latch]

yes

so that both are integers

it just looks nicer

no other reason

[alpine sable]

Makes sense

Easier to work with

[raw latch]

yes exactly

[alpine sable]

Thank you bro

. close

[raw latch]

no problem

[alpine sable]

.close

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[lucid olive]

In a meeting, the ratio of the no. Of boys to that of girls is 37:72. When 98 more boys joined the meeting, the ratio of the no. Of males to that of girls will be 80:63. Now how many more girls should attend the meeting such that the no. Of boys and girls are equal?

[lucid olive]

What will be the answer?

[sudden hinge]

How about you let X be the numbers of boys and Y be the number of girls. Then construct some equations? @lucid olive

[lucid olive]

I tried that answer is coming in decimal

[sudden hinge]

Show what you did

[lucid olive]

Wait

These are the solution I got, not very clear but b and g values are highlighted

Answer is 68

Clueless

[sudden hinge]

I see, you indeed get decimals

Hmm maybe they just want us to round?

[lucid olive]

Question might be wrong or something maybe?

[sudden hinge]

Yeah feels weird to get decimals here

[lucid olive]

Even if we round its far from 68

[sudden hinge]

if we round the no. of males will be X = 66.62 and females Y = 129.64 (approximately) before anyone joined

[lucid olive]

Hmm weirdge question

[gray isle]

did you copy down the values of the question correctly?

[lucid olive]

Yes i copied it correctly

Not sure if its visible?

[sudden hinge]

bold is the correct answer?

[lucid olive]

Yes

¯_(ツ)_/¯

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[dapper patio]

not sure how to do this question

[gray isle]

consider the factorisation of z^3 - 1

[dapper patio]

mhm....

z would be 1 right?

but i'm still so lost 0-0

[gray isle]

z = 1 is the real solution to
z^3 - 1 = 0

[dapper patio]

apologies, I understood that part, but I am unsure what to do with that next?

[gray isle]

what's the factorisation for z^3 - 1

[dapper patio]

(z-1)(z^2+z+1)?

[gray isle]

yes

(z-1)(z^2+z+1) = 0
now considering the zero product property and that
w is a non real solution to this equation, what does that tell you?

[dapper patio]

w cannot be 1??

or w can be 1...

[gray isle]

why do you think w can be 1?

[dapper patio]

oh wait

z can be 1

which is a real solution

and w is a non real solution

meaning that w can not be 1

[gray isle]

and then...

[dapper patio]

doesn't that just mean the value of 1+w+w^2 is w =/ 1

[gray isle]

no

that doesn't make any sense

[dapper patio]

ok im sorry im completely lost, so we determined that w can not be 1

[gray isle]

supposing that =/ is an attempt to represent the not equal to symbol

[dapper patio]

yeah

[sudden hinge]

if (z-1) = 0, that implies z = 1 which is a real solution. you have to consider the second factor

[gray isle]

saying that the value of an expression is an statement is nonsense

ok, lets take a step back

what does it mean for w to be a solution to

(z-1)(z^2+z+1) = 0

[dapper patio]

im not sure i understand that question...

[gray isle]

what part of that don't you understand

[dapper patio]

just the question

what do you mean "for w to be a solution"

[gray isle]

if w is a solution to

(z-1)(z^2+z+1) = 0
what information does that give you?

[dapper patio]

that there are other roots?

[gray isle]

not what i want from you

how do you know/determine if something is a solution to an equation?

[dapper patio]

by solving the equation

oh wait

[dapper patio]

so that means solving this equation (z-1)(z^2+z+1) = 0 will get us w right?

or am i misunderstanding this completely

[gray isle]

not what i want from you

don't overthink this

[dapper patio]

(z-1)(z^2+z+1) = w ?

[gray isle]

no

if you couldn't immediately tell whether 5 was a solution to

(z-1)(z^2+z+1) = 0

what simple approach would you use to determine if it is

[dapper patio]

substitute 5 into z

[gray isle]

yes

[dapper patio]

oh so

[dapper patio]

this tells me that if i substitute w into z i should get 0?

[gray isle]

yes

and since you are told that w is non-real,
that's the conclusion you can reach from that?

[dapper patio]

that substituting w into z should give me an answer that is <0?

[gray isle]

no

that completely contradicts what you just said

perhaps we should go back a step

this tells me that if i substitute w into z i should get 0?
yes

[dapper patio]

that w is an imaginary number?

[gray isle]

what happens when you do that

[dapper patio]

then (z-1)(z^2+z+1) = 0 becomes (w-1)(w^2+w+1) = 0

[gray isle]

yes

and what would be the first step you'd take to solve:

(w-1)(w^2+w+1) = 0

(or any other factored polynomial equation)

[dapper patio]

i mean i know (w-1)=0 so I guess factor (w^2+w+1)=0?

[gray isle]

that's not quite what i asked for

all i wanted was for you to apply the zero product property to get
w - 1 = 0 OR w^2+w+1=0 and nothing else

[dapper patio]

oh

sorry

[gray isle]

now what would solving that first equation give you?

[dapper patio]

w=1

[gray isle]

and you were told that w is non-real

so in fact w cannot equal 1

and then putting that all together

you have
w^2+w+1=0

which gives you exactly what the question is asking for

[dapper patio]

OHHHH

so the final value is just 0 then

[gray isle]

yes

[dapper patio]

understood understood, thank you so so much, sorry for the time it took

but then for part 2 of the question, is the final value still 0?

it asks me to use the conjugate but...

there is no imaginary part theres only the real part which is 1

so i assume the answer would still be 0?

[gray isle]

it will still be 0 by complex conjugate root theorem

[dapper patio]

okiii, tysm again

.close

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[alpine sable]

Anybody can help me understand why this works ?

[alpine sable]

Does this not assume that there always exist a solution ?

So for every input it's possible to get the exact output value

I am not seeing how that is the same as this:

I dont understand how that matrix operation creates values for W that minimize the difference between (w * x - y)^2

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

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[lone heart]

@alpine sable Has your question been resolved?

[wide raven]

what's the problem ? Where are you stuck?

[lone heart]

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[grizzled tusk]

Can I get help on figuring the formula

[tacit arch]

What help do you need

[grizzled tusk]

I need to find the formula

.close

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[spare ibex]

AD=?

[limpid spade]

what did u try

[spare ibex]

everything

[limpid spade]

show work

[spare ibex]

i threw it away

but i tryed making a line from A parralel to DB

nothing

i trying to play with angles

nothing

Everytime i don't use that DOA=90

[limpid spade]

you can find the angles of CBE

with the intrtesevtion being E

[spare ibex]

ok let me try

i just dont know how sin and cos work

but ill try to get it

[limpid spade]

after that u can find the size of CE and BE

[spare ibex]

so

CBD=42.709 :/

CDB=47.291

is it right?

[limpid spade]

is that the angle of D

[spare ibex]

i think so

tan(CBD)=12/13

yes?

[limpid spade]

yes

[spare ibex]

and how to get this?

[limpid spade]

x=arctan(12/13)

find the and of b with tangent

tanx=13/12

then u can find angle of C in CEB

then u can find the sizes

[spare ibex]

aaaaa

i dont understannd

how??

im liek

at 8th grade

i have no idea about trigonometry and how it works

yes

a^2+b^2=c^2

DCB and DBA?

ok

and how we could get something from it

yep

bruh

from where did you get that ABCD is parallelogram

its a trapezoid

[lone heart]

@spare ibex Has your question been resolved?

[crimson carbon]

are you given any other information?

Not that we might need them

Okay so I just want to state that this an orthodiagonal quadrilateral (the face diagonals are perpendicular, non adjacent vertices) and we could apply the formula a^2+c^2=b^2+d^2, but we do have two missing lengths (if we had one we could apply this formula then solve for the remaining)

• the sum of the squares of two opposite sides equals that of the other two opposite sides

Well you should pretty much notice that every triangle aside from ABD is an orthogonal triangle

So you could apply theorems

Such as the pythagorean theorems and your trigonometric ratios

@spare ibex what have you been taught in order to do this?

Does it say line segment CA is a bisector of angle CDB

[spare ibex]

What?

im actually los

lost

[spare ibex]

nope

like BC || DA but its kinda obv

[crimson carbon]

How do we know it's parallel?

Assuming it isn't, I've happened to do it another way

But I did assume that line CA is a bisector of angle CDB

and then things got a little outta hand

anyhow you could probably apply your properties of angles in parralell lines

Recall them

your face diagonals are your transversals

Okay let's find the obvious angles and lenghts

Given that BCD is an orthogonal triangle we can apply the pythagorean theorem to find the face diagonal BD

Wait is @ocean seal even working

,tex test

damn

anyways BD=sqrt(13^2+12^2)

which is sqrt(313)

We can find our angles of triangle BCD using our trigonometric ratios

So recall them again

m<CDB (< denotes angle here, but unfortunately @ocean seal stopped working it's a little less convenient for me) = arctan(13/12), and m<CBD=arctan(12/13)

we could use any trig ratio as we have every side length

So using the alternate interior angle property m<CBD=m<BDA

I think most of the inscribed angles share the AAA similarity

[lone heart]

@spare ibex Has your question been resolved?

[lone heart]

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[craggy shoal]

Help

[craggy shoal]

My teacher for extra credit gave us abunch of weird questions, it doesn’t have anything to do with what we are learning but I really need the extra credit

<@&286206848099549185>

<@&286206848099549185>

[tacit arch]

CHILL

[craggy shoal]

AH SORRY

I’m new to this Channel

And I’m freaking out

[tacit arch]

read the rules

[craggy shoal]

OH

ok! Sorry :))

This is what I think it is

But I need help bc The #s are throwing me off

[twin vale]

Can Some One Help Me

[craggy shoal]

This is my server

You gotta get your own

[twin vale]

ok

[craggy shoal]

Go to the open servers

[twin vale]

can u pin one please

[craggy shoal]

Dude idk I’m still waiting to get help

<@&286206848099549185>

<@&286206848099549185>

It’s been 20 minutes

[abstract fractal]

Your answer seems fine. There's a clear pattern that you followed. I can't imagine there's only one answer

[craggy shoal]

That’s what I’m hoping, I wanted to make sure tho

Thankyou!

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[wise basin]

Just need help with the first one I’m very lost

[knotty spire]

Well, what have you tried/thought of so far?

[wise basin]

I tried googling how to do it my teacher doesn’t have any examples or even a start of how to do them

[knotty spire]

well how do you understand transformations

[placid zinc]

If you have seen literally nothing on the subject, start here:
https://www.mathsisfun.com/sets/function-transformations.html

[wise basin]

Thanks

[twin vale]

i neek help

need

[limpid spade]

is it hard for u to read #❓how-to-get-help

go claim a help channel in MATH HELP (AVAILABLE)

[lone heart]

@wise basin Has your question been resolved?

[wise basin]

.close

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[frosty tendon]

Where do I even start

[pine kettle]

just the sum of all those circles, no?

you don't even need to use an integral

you have the radius of each semicircle ;)

[lone heart]

@frosty tendon Has your question been resolved?

[bright hedge]

complete the square to find the radius

noting that

The area of a semicircle with radius $r$ and center $(h, k)$ is
$$y - k = \sqrt{r^2 - (x-h)^2}$$

[ocean seal]

Shuri 4 honorable (Yottachad)

[bright hedge]

(you can get this just by rearranging the normal equation)

[frosty tendon]

.close

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[tacit arch]

read this and give it a try!
https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html

right

just attempt all of them

write down your answer to all the questions and stop pinging me 4 times a minute

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[lone heart]

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[runic lava]

Determine the next term of the sequence 12, 17, 15, 21, 18, 25, 21,

[runic lava]

how is this?

[gray isle]

consider every second term

[runic lava]

21+8 = 29!

thanks!

.close

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[burnt flume]

Hi! The question is state all angle coterminal with 497. I have 370n degrees-497

[burnt flume]

I’m not sure if that’s right?

[gray isle]

is wrong

where's 370n coming from and why are you subtracting 497

[knotty spire]

hopefully a mistype

(regarding the 370)

[burnt flume]

Ohh

Sorry 360

Also, plus 497

Sorry I’m so bad at typing on a small screen

Is it 360n+497 then? Or is there also another option with an equal reference angle?

[gray isle]

360n+497
would be acceptable

[burnt flume]

Okay thank you!

[gray isle]

and there are infinitely many ways to express an equivalent answer

[burnt flume]

Okay thank you again!:)

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[violet surge]

can someone help me solve this

i tried using variables for unknown angles and stuff but this trig problem is too hard for me

<@&286206848099549185>

hello????

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@violet surge Has your question been resolved?

[violet surge]

<@&286206848099549185>

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@violet surge Has your question been resolved?

[lone heart]

@violet surge Has your question been resolved?

[lone heart]

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[grizzled hawk]

How can I solve x^2 = lnx, wolframalpha says, but how do I get to this solution
I know what the lambert function for background

[tight locust]

If y = xexp(x) then W(y) = x

[grizzled hawk]

Yes I know that, but how do I get to what wolframalpha says

[tight locust]

Its usually pretty difficult to get it into that form though

Lets see

[grizzled hawk]

Yea I have tried a lot of things, square root both sides, take e to both sides.

divide by x on both sides.

It doesn't have any real solutions btw

I don't know if thinking it as a quadratic would work some how. x^2 - lnx = 0. I'm not sure.

[tight locust]

Let's work backwards

ln(x) = -W(-2)/2

-2ln(x) = W(-2)

[grizzled hawk]

Yep.

[tight locust]

Then

[grizzled hawk]

inverse of W.

[tight locust]

-2lnx * exp(-2lnx) = -2

lnx * 1/x^2 = 1

lnx = x^2

Lol

[grizzled hawk]

so it works?

[tacit arch]

Accidentally did the whole thing

[grizzled hawk]

let me try get my head around it

[tight locust]

?

[grizzled hawk]

Ok. I kinda go close to it.

[tight locust]

Ok

You good?

[grizzled hawk]

so I've go x^-2 * lnx =1

[tight locust]

Υερ

[grizzled hawk]

e^ln(x^-2) is the same as x^-2

[tight locust]

Yes

[grizzled hawk]

bring the -2 outside.

times both sides by -2 so then its.

-2lnx * e^-2lnx = 1

[tight locust]

= -2

[grizzled hawk]

ohh yea my bad

W both sides now.

-2lnx = W(-2)

divide by -2?

and raise both to the e

and i get

x = e^(W(-2)/-2)

my bad forgot you can move the negative out front

well thats really nice solution.

Thankyou very much EndTimes

.close

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[weary mango]

Hi, can anyone help me with this?
Find the minimum value of the expression (x ≠ 0)

[full vine]

Where did you get stuck?

[weary mango]

nvm i solved it

.close

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[fathom cypress]

How is this question solved?

Ive been stumped on it for the past 30 minutes

[fathom cypress]

Thanks also

<@&286206848099549185>

uhm

am i doing something wrong?

[pale kestrel]

Not so much math as a guessing game

guess the pattern

[fathom cypress]

oh

i wAs trying to solve it with math

[pale kestrel]

Well yes, there probably is some math to the pattern

not my kind of problem though

[fathom cypress]

yeah thats where im stuck

[pale kestrel]

Guess the pattern? Technically any answer fits if you justify it
#chill message

[fathom cypress]

its usually (A+B)^2= the center number

so im stumped

[fathom cypress]

thanks though!

idk how to guess im stuck on 100-126

[fathom cypress]

whats the embed link?

[full vine]

It’s the difference between the external numbers, times 2, squared

Just guessing really

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[fathom cypress]

i solved it

your guess was right i presume

thanks!!!'

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[rose gate]

So I've been working through the integration chapter for my further maths a level course, and we just started integration by parts

[rose gate]

and in the textbook it says to just accept that the integral of tanx is ln|secx| + c

but i wanted to derive it

https://cdn.discordapp.com/attachments/395232269805289493/946874656114217010/unknown.png

[vale wigeon]

have you covered substitution?

[rose gate]

so i thought i should do it by integration by parts

which i realised later is wrong

you're meant to do it by substitution

[vale wigeon]

ibp probably won't work here

[rose gate]

but why does doing it by parts end up with seemingly 0 = -1?

[vale wigeon]

it doesn't

[bright hedge]

integral has + C

[vale wigeon]

^

[bright hedge]

got something right for once

[rose gate]

I understand that, but how does that relate to this result?

[alpine sable]

i can help if I understand your writing

[rose gate]

is the +c = to 1 in this case?

[rose gate]

yeah sorry, what part don't you understand?

[bright hedge]

different C's on both sides

[rose gate]

handwriting's always been a bit scruffed

[alpine sable]

Ye

[bright hedge]

pretty much you get

the antiderivative of tan(x) + C - (antiderivative of tan(x) + K) = -1

so C - K = -1

this works normally because C - K is just another constant so we ignore it

[rose gate]

that makes sense yeah

[bright hedge]

C + K**** sorry

[rose gate]

so if i added a + c, and then a different constant of integration after i integrate the second nested tanx it would make sense?

but it wouldn't lead to the final answer of ln|secx| + c bc i used the wrong method

is that the tldr here?

[bright hedge]

yes

and you should see how it would be ln|sec(x)|... dont try to make it super complicated just write tan(x) using its sin and cos

[rose gate]

i mean yeah i did that here and messed it up

bc i used the wrong method

but i know how to get there from integration by substitution now

[bright hedge]

okay

[rose gate]

.close

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[regal ridge]

I need some help with this problem :

by increasing the length of the side of a square by 6 cm, we obtain a new square whose area is 84 cm² more than the first square, what's the length of the side of the first square?

I have problem finding the equation ( it should be a first degree equation )

[vale sapphire]

Well, let's give a name to the side length of the first square

To be unoriginal, let's pick x

[vale sapphire]

So then,

1. what is the area of the second square using its side length?
2. what is the area of the first square?
3. how are these two related according to the statement of the problem?

[regal ridge]

1. i think its x²+12x+36-x²

1. 12x+36
2. x²
3. second square area is 84 + x²

@vale sapphire

[vale sapphire]

Uhh, 1) is wrong

If you know the side length is x+6, the area is (x+6)², right?

(if you see an area that's a multiple of x and not x², that should raise some red flags)

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[reef iris]

halp

[oak perch]

Is solving by drawing diagram allowed?

[reef iris]

weird thing is, the previous question is literally definite integral of x

So you'd think the answer should be simple 🤔

[oak perch]

Oh so you can’t use that cycle thing…

Oh got it you let

t=x-2

Sqrt(4-t^2) dt

[reef iris]

I looked it up online, and I have to do trigonometric substitution?

[oak perch]

Then do it again,t=2sin(s)

Oh yes same as I thought

[reef iris]

this progression curve is friggin weird

[oak perch]

? It’s half of a cycle

[reef iris]

Alrighty, I'll go along with that then, mostly wanted to be sure if there was an easier answer

[oak perch]

Easier answer is drawing diagram then area of half a cycle

[reef iris]

Oh that sounds interesting 🤔

how would one go proving that?

[oak perch]

y=sqrt (4x-x^2) , so y^2=4x-x^2, therefore (x-2)^2+y^2=4

That’s easier to get the answer but if steps are required then

[oak perch]

Better this way I guess

[reef iris]

Lemme graph it then

it's literally a half a circle

Well

I feel I could be smarter now lol

[oak perch]

Yes it is, half a cycle

[reef iris]

thanks again Coggy!

[oak perch]

Np

[reef iris]

.close

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[hybrid pulsar]

Yo I need help with fhis question

I-

[wet spindle]

@random rain #❓how-to-get-help

[hasty elk]

to get help, you need to read #❓how-to-get-help

[hybrid pulsar]

Oh-

I didnt see mb

[lone heart]

@hybrid pulsar Has your question been resolved?

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@hybrid pulsar Has your question been resolved?

[pale kestrel]

We gathered, but not possible it you don't say what the problem is

[hybrid pulsar]

Oh, I dont know how to express it, everytime I try to I just end up with 10 percent

0.9x assuming x is fhe original price, is the discounted price

I dont know what to do after that

[pale kestrel]

Right try some real examples

Just make up an actual example with real numbers in it

ideally nice, of course

and try to work through it

[hybrid pulsar]

Oh okay

[pale kestrel]

There's also something else to consider.

If the bills are 50% off, do you think that means they can eat 50% more?

[hybrid pulsar]

No

I know that, but I dont know how to find how much more they can actually get

[pale kestrel]

ok, then work through an example made with real numbers

Post here.

[hybrid pulsar]

Okay

X is original price, P is perfrntage off and Q Amount extra that can be added into the discounted one

But original price is like 100

100p +q = 100

[pale kestrel]

huh?

real example, not algebra

[hybrid pulsar]

Oh-

So like

100 dollars

10 percent off it would be

90 dollars

Uh

[pale kestrel]

yes

[hybrid pulsar]

10 dollars extra to spend

Uh 10 dollars is 1/9 of 90 dollars

Wait

Yeah I think thats it

[pale kestrel]

well yes.........

How about this

a meal costs $10

Your wallet has $90

This is what I wanted you to come up with

[hybrid pulsar]

Ohh

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[karmic dawn]

Is this countable or uncountable? ⋃n∈ℕ ℚ^n

[pale kestrel]

what do u think

[karmic dawn]

So from my understand its basically saying Q U QxQ U QxQxQ U....

[pale kestrel]

ok

[karmic dawn]

But im not sure where to go after that

Like how to decypher if its countable or uncountable

[pale kestrel]

any intuition for the answer?

what you think