help-23

[quiet vector]

...way to teach

[summer ice]

Hope this helps!!!

[ruby cloak]

Hello

Is this correct to

It’s called x formula

You are very smart goerg

[quiet vector]

idk that method but you got the right answer so 🤷

seems to work

[safe radish]

@ruby cloak Has your question been resolved?

[safe radish]

@ruby cloak Has your question been resolved?

[safe radish]

Channel closed

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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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[uneven kelp]

hi

[uneven kelp]

can anyone help

[worthy hemlock]

No, no one in a math help server can help you /s

[uneven kelp]

sorry

[lost lodge]

wow, MEAN!

[uneven kelp]

ill post the question

moment

[worthy hemlock]

Hope that's sarcasm, I put /s for a reason, meaning I was being sarcastic

[lean otter]

Lol

@uneven kelp he dldh6 was joking

What’s ur question

[uneven kelp]

sorry for the wait, I need to find a b and c so that
a^b+c is a perfect square and a^b-c is a perfect square

and c is prime

i tried looking at like if it is odd or even or rewriting it but didnt get anything

[uneven kelp]

(a^b)+c

[broken yew]

$$a^b+c = n^2$$
$$a^b-c = m^2$$

[flat frigate]

Shuri2060

[uneven kelp]

yea

[lean otter]

Yes these are ur equations

[broken yew]

Alright

Well I think I gave you a big hint

[uneven kelp]

merge them?

[broken yew]

Because of how I wrote it

yes

what do you get?

[lean otter]

Yes

[uneven kelp]

2a^b = n^2+m^2

maybe the other way around

[broken yew]

👌

what u just wrote doesnt look helpful

[lean otter]

One sec

Do u think c is prime

[uneven kelp]

you would get 2c=n^2-m^2

[broken yew]

you're given that c is a prime

[uneven kelp]

it says in the task that it is

[broken yew]

$$2c = n^2-m^2$$

[flat frigate]

Shuri2060

[broken yew]

Alright, I think we've given enough hints 👀

[lean otter]

Yeh

[uneven kelp]

i only know that (n-m)(n+m) cant be divisible by 4 ( if c is not 2 )

[broken yew]

$$2c = (n-m)(n+m)$$

[flat frigate]

Shuri2060

[broken yew]

I think.

You know a lot more than that.

[uneven kelp]

do i try making primality cases?

[broken yew]

I think you're overthinking

[uneven kelp]

but that would get me to the same thing i just said

[lean otter]

c is prime

[broken yew]

There really is something more you can say than what you just said.

Just give it a few thoughts.

[uneven kelp]

hmm

[lean otter]

Think over this

[broken yew]

@uneven kelp If it helps, let c = 5 (as a random example)

[lean otter]

C is prime and it’s a product of sum and difference of two Integers

And it’s divided by 2

[broken yew]

I think they'll get it 🤐

[lean otter]

@uneven kelp are u there

[uneven kelp]

im thinking

[lean otter]

Ok

[uneven kelp]

it could be that either n-m or n+m is a prime and the other factor is 2

[lean otter]

Yes

[uneven kelp]

so you cancel out 2

[lean otter]

And not just a factor of 2

It is 2 itself

[broken yew]

you've missed out a case.

[uneven kelp]

hm

[broken yew]

Do you realise if I told you $$ab = 21$$

[flat frigate]

Shuri2060

[broken yew]

What a b could be?

[uneven kelp]

yea but a and b are integers

could be -

1, 21, -1 -21, -3,-7, 3, 7

[lean otter]

Disregard the negative numbers for now

It’s number theory here

[broken yew]

that's not many cases

[uneven kelp]

okay so what do i go from now
c = n-m case 1
1 = n+m/2 case 1 still?

and
c = n+m case 2
1 = n-m/2 case 2?

[lean otter]

n+m = 2 means both numbers are 1

n and m

we solving this in natural numbers afaik

[uneven kelp]

but it would be 0 then

n-m

[lean otter]

Yes

Which doesn’t exist in natural numbers

So …. What do u think

[uneven kelp]

but its whole numbers

[lean otter]

Ok fine

My point still stands

0 is not prime

Or composite

Primes and composites are defined in the set of natural numbers afaik

[uneven kelp]

why cant n = -1 and m = +3

[lean otter]

Is there any constraint on a,b,c

Which set they belong to

[uneven kelp]

only that a and b are whole

[lean otter]

So c is prime

[uneven kelp]

yea

[lean otter]

Which means it is whole as well

Or rather natural

[uneven kelp]

well primes cant be negatie

yea

[lean otter]

And since a and b are whole

And c is prime

They cannot get added to a negative number

[lean otter]

Or subtracted which is what u are saying here

[uneven kelp]

a = -3, b = 3

and c = 3

[lean otter]

U just said that a and b are whole

[uneven kelp]

you have (-3)^3 + 3 which is negative

isnt whole like -infinity, 0, + infinity

[lean otter]

No bruh

Whole numbers are 0,1,2…..

[broken yew]

whole numbers generally refer to natural numbers

[lean otter]

With 0 included

[uneven kelp]

ooh then its an integer

[lean otter]

Not an integer

A positive integer

Integers are not whole either

[uneven kelp]

it says in task integers a,b

[lean otter]

U just said a,b are whole

[uneven kelp]

im sorry, language barrier

[lean otter]

Post the original question picture

I’ll translate

[uneven kelp]

well its not in the same language

[lean otter]

Ik

That’s why I’ll translate

[uneven kelp]

and it uses the exact word "whole numbers" but it means idfferent

in my language

i just googled it, its integers

[lean otter]

What language it is

Of yours

[uneven kelp]

it is romanian

[lean otter]

Pls post a picture of the exact question

[uneven kelp]

😦

[lean otter]

Just do it

Hello ?

[uneven kelp]

i dont think it is neccessary but i think i figured it out so will go

[lean otter]

Ok cool

Should I close the channel

[uneven kelp]

yea

[lean otter]

.close

[safe radish]

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[tranquil hollow]

how do I get from the first to the 2nd line ?

[tranquil hollow]

ah just multiply by (1-p) and p

.close

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[vocal prawn]

how would someone approach a problem like this:
$$I = \int{\frac{\int{e^{\int{tan(x)dx} \cdot cos^2(x) \cdot sin(x) - sec(x)}}}{e^{\int{tan(x)dx}}}}$$

[flat frigate]

Khazali

[lean otter]

Ayo wtf

[vocal prawn]

that actually shouldn't look like that, i made a mistake somewhere in the synax

[lean otter]

Ok

[opal knot]

Hahahaha

[vocal prawn]

$$I = \frac{\int{e^{\int{tan(x)dx}} \cdot cos^2(x) \cdot sin(x) - sec(x)}}{e^{\int{tan(x)dx}}}$$

i think that's it

[flat frigate]

Khazali

[vocal prawn]

you can see it comes from a DE

[opal knot]

Ok

[lean otter]

I see

Well e^tanx is a standard integral

[vocal prawn]

yeah that just becomes
$$e^{\int{tan(x)dx}} = e^{ln(sec(x))} = sec(x)$$
i believe

[flat frigate]

Khazali

[lean otter]

Also I forget to add a dx in denominator

Over the entire integral

[vocal prawn]

oh right, always forget it

so it becomes
$$I = \frac{\int{sec(x) \cdot cos^2(x) \cdot sin(x) - sec(x)}}{sec(x)}}$$
hopefully that's right

[flat frigate]

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

[vocal prawn]

oh it's become so much easier, what am i doing

$$I = \int{cos^2(x) \cdot sin(x) - 1}$$
right?

[lean otter]

I don’t think so

[flat frigate]

Khazali

[vocal prawn]

should be cos squared

[lean otter]

Yes

[vocal prawn]

then it's trivial from there

[lean otter]

Yuppp

[vocal prawn]

i just needed to look at it piece by piece

i let its size intimidate me, smh

what a way to use my first question on the help channel

but thank you anyways

.close()

oops, programmer hands

.close

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[median kestrel]

lmao gg

[median kestrel]

.close

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[wary veldt]

I forgot how to solve this type of question, getting back to Mechanics again and doing some exercises:

F1 = 2i + 3j , F2 = i + j | F1 and F2 are measured in Newtons, what is the magnitude of their resultant?

[inland ivy]

You should just be able to add them together and use pythagorean theorem

On the real part of the components

[wary veldt]

So it'd be (3, 4)

Alright, hold on

nevermind i'm a little too stupid for this right now

[inland ivy]

Yeah (3,4) is right

Then you can either use one of the special triangles you prob learned 10 years ago

Or just plug it into pythag

[wary veldt]

my issue is how would i find alpha?

the angle between them?

and what is (3,4) right now

[inland ivy]

Do you mean as part of another question?

[wary veldt]

really sorry for being dumb, i haven't picked up mechanics in ages.
no.

we usually use this rule

https://cdn.upload.systems/uploads/l3708K1u.png

[inland ivy]

Oh

You can just assume they're perpendicular I think

The real axis, i and j are always perpendicular

So 90 degrees

[wary veldt]

ah that makes a lot more sense now

i'm confused why this wasn't mentioned

[inland ivy]

Yeah some nice solid review helps me a lot too

[wary veldt]

alright thank you dude!

.close

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[inland ivy]

Np

[safe radish]

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[shell cobalt]

is this equation impossible?

[shell cobalt]

I applied laws until I end up with (x+3)(x-4) = 0 but both end up with a negative in one of the logs in the base

[broken yew]

Can you show working

[split ether]

Yeah, that equation has no solutions

If you want to write rigorous proof of that, that'd be a proof by contradiction

[broken yew]

you can try wolfram to check

[inland ivy]

50% chance it gives up

[broken yew]

nvm wolfram will probably say those are valid

in complex

Probably desmos I guess 😅

[shell cobalt]

alright

.close

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[noble beacon]

Help

[safe radish]

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[lean otter]

I don’t understand the wording at all

[lean otter]

,rotate

[broken yew]

$$ax^2+bx+c$$

[flat frigate]

Shuri2060

[broken yew]

They want $$a^2+b^2+c^2$$

[flat frigate]

Shuri2060

[broken yew]

you don't have quadratic ofc, but you get it.

[lean otter]

Ah ok

When I simplify it all out I get -7^3+4x^2+13x+1

I put 4 but that is wrong

[broken yew]

how is it 4???

what

heck are you adding

[thin bridge]

wheres -7^3 coming from

[lean otter]

There is only one x^2

How do I solve this the

[broken yew]

what?

$$\sum^n_{k = 0}a_kx^k$$

[flat frigate]

Shuri2060

[broken yew]

If this is your polynomal

$$\sum^n_{k = 0}a_k^2$$

[flat frigate]

Shuri2060

[broken yew]

This is the sum of the squares of the coefficients??

[thin bridge]

write out your expansion properly

and simplify if you haven't already done do

[lean otter]

I did

[quasi bison]

so what do you get after simplifying

[lean otter]

When I simplify it all out I get (-7)^3+4x^2+13x+1

[thin bridge]

wheres (-7)^3 coming from

[quasi bison]

yeah, where are you getting a constant term equal to negative three-something hundred

do you have written work to show? @lean otter

[lean otter]

Aren’t we subtracting

I honestly do t see where you don’t understand where it is coming from

[quasi bison]

do

you

have

[thin bridge]

tell me in as much detail as you can what you're multiplying or whatever to get
(-7)^3

[quasi bison]

written

work

to

show

yes or no

simple question

simple answer

[thin bridge]

no matter how trivial you may deem the description to be

[lean otter]

4x^2-8x+8-7x^3-21x+7

There

[quasi bison]

your work boils down to one (1) line?

(and even so, there is already an error here)

[lean otter]

I’m just doing math

[quasi bison]

why aren't you answering simple yes-no questions directly?

[lean otter]

Yes

[quasi bison]

so your work does contain one line and one line only. got it.

and this one line does not at all answer ramonov's question either

[lean otter]

Why not

[quasi bison]

your work contains no mention of (-7)^3, which both ramonov and i are curious as to how you got.

are you being purposefully antagonistic to the people trying to help you?

[lean otter]

But it does

I can show you

[quasi bison]

the line 4x^2-8x+8-7x^3-21x+7 has no mention of (-7)^3.

[lean otter]

Oh

[quasi bison]

and you confirmed that this line was your entire work.

[lean otter]

I made a typo

[quasi bison]

so maybe you lied somewhere.

[lean otter]

With this

[quasi bison]

okay, so what is your expansion supposed to be after you fix all the typos?

[lean otter]

(-7x)^3+4x^2+13x+1

[quasi bison]

no, this is not correct.

but if we ask you how you got that (-7x)^3 term, doubtless you're going to drag your feet about showing your work...

[lean otter]

Hmmm

[quasi bison]

like

you do understand why people here always ask help-seekers to show their work, right?

[lean otter]

I do

[thin bridge]

^preferably a pic
and if you type it, be 100% sure that it accurately represents what you have written

[quasi bison]

100% is not enough

you need to be 110% sure you've copied your work EXACTLY as it was written, and then you need to double- and triple-check it, lest a typo ruin everything.

[quasi bison]

so then why are you being so stubborn about showing yours?

[lean otter]

-7x^3+4x^2+13x+1

[quasi bison]

what is this?

[lean otter]

I fixed it

[quasi bison]

did you mean "this is what i get after expanding and fixing all of my typos"?

[lean otter]

I’m having some trouble seeing what I did wrong

[quasi bison]

for fucks sake

[lean otter]

😦

[quasi bison]

how much of a lowly scumbag am i in your eyes that you continually refuse to give me the bare minimum of respect by answering yes-no questions with "yes" or "no"

[lean otter]

I do not view you as a lowly scumbag at all!

[quasi bison]

then why do you keep refusing to answer yes-no questions as you're supposed to?!?!!!

[lean otter]

It’s hard to explain

But I apologize

[quasi bison]

what could possibly be hard to explain

and how hard could it possibly be

to type "yes"

or to type "no"

[lean otter]

Ok, I get it

I will answer yes or no

[quasi bison]

so, you say that after fixing all of your typos and all of your mistakes, you end up with $-7x^3+4x^2+13x+1$. do i understand you correctly?

[flat frigate]

Ann

[lean otter]

Yes

[quasi bison]

okay

see, was that so hard?

now i can actually confirm to you that you have indeed done the simplification correctly.

now, the problem asks you to compute the sum of the squares of the coefficients. have you done so?

[lean otter]

No

I honestly don’t really understand what that means

[quasi bison]

do you understand what the words "sum", "square" and "coefficient" mean?

[lean otter]

Yes

But the wording is weird

[broken yew]

sum of the (squares of the (coefficients))

[lean otter]

So that should be 4

[quasi bison]

how are you getting 4?

[thin bridge]

and please show work

[broken yew]

I'm finding it hard to get 4 with those numbers 🤔

[thin bridge]

and not just give seemingly random numbers (that without work would only be interpreted as guessing)

and will yield the response "how did you get that" regardless of whether it's actually correct or not

[lean otter]

16?

[broken yew]

Show working.

[lean otter]

Ok

[quasi bison]

and not just give seemingly random numbers (that without work would only be interpreted as guessing)

[lean otter]

-7+4+13

Do I have to add the one as well?

[quasi bison]

no, crabbo. you should be adding the squares of the coefficients. not the coefficients themselves.

but yes, the 1 is a coefficient and so should be accounted for.

[lean otter]

Ah

[broken yew]

This was very helpful in seeing how you went wrong.

[lean otter]

235 then

Let me show my work

[broken yew]

,w 49+16+169+1

[flat frigate]

Results provided by WolframAlpha

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

Requested by Shuri2060#9525

[broken yew]

You're good

[lean otter]

Yay!

[quasi bison]

communication

there is so much difficulty in communication

[lean otter]

Is this 4?

[broken yew]

I agree.

[lean otter]

So it was meant to trick me

[broken yew]

🤔

[quasi bison]

so what was meant to trick you?

[broken yew]

I really don't think so.

[quasi bison]

what do you think was put there to trick you in either of the two problems at hand?

[lean otter]

With the pi, sqrtw

[lean otter]

Only the second one

[quasi bison]

this is not trickery

this is testing whether you can recognize that 2pi and sqrt(10) are just numbers

[pulsar condor]

Just use the definition of degree of a polynomial 🤨

[lean otter]

Right

[quasi bison]

if you consider this trickery then everything that isn't a rational number must be written off as "things meant to trick you"

[lean otter]

Thanks everyone

.close

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[woeful zinc]

Hello

[woeful zinc]

Can someone help me solving the part 2 using de moivre's theorum?

[broken yew]

Show picture.

[woeful zinc]

I sent above

[broken yew]

No

That's a picture of the question

Where's your picture

[woeful zinc]

Means?

[broken yew]

Also, close the other channel,why double post?

[woeful zinc]

Im new in the server

Im stuck on this question

[broken yew]

Firstly, draw the argand diagram.

Hint: drawing what z^4 is first helps.

[woeful zinc]

Wait

I usually solve it this way

[broken yew]

,rotate

[woeful zinc]

This is different qstn

[broken yew]

Alright, sure.

What's the issue with this question

[broken yew]

I don't see how it's any different

[woeful zinc]

For this qstn i want to substitute it like the answer i showed

Like use - i as cis(-pi/2)

I cud have solved it if its z^4=-i

How to solve it for z^4=1-i

[broken yew]

Ok, then draw z^4 on an argand diagram

figure out what it's argument and modulus is

[woeful zinc]

Im not sure how to do that

Can i convert the 1-i to cis?

[broken yew]

well yes?

What does

argument

and modulus

mean

[woeful zinc]

$z^4 = {r(z)}^4 * {cis(z)}^4 = {r(z)}^4 * {cis(4z)}$

[flat frigate]

ChickenWing

[woeful zinc]

Is this correct?

[broken yew]

well yes, but that's not helpful (yet)

What does 'argument' and 'modulus' mean

[woeful zinc]

Argument is the angle

Modulus is sqrt2

Right?

[broken yew]

no.

oh

well yes

Modulus is the distance to the origin

which is sqrt 2 here

[broken yew]

My point is, if these 2 are the things you want to find

Drawing a diagram... might help?

[woeful zinc]

Argument is - pi/4

[broken yew]

ok.

[woeful zinc]

.close

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[safe radish]

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[sonic galleon]

Hi guys, I wanted to clarify something about degrees of freedom.
If I am doing a t-test on a linear regression with multiple parameters, is my degrees of freedom n-1 or n-k-1?

[velvet nebula]

k is the number of parameters and n is the number of data points?

[sonic galleon]

yes

[velvet nebula]

yeah probably not n-1

[sonic galleon]

so n-k-1?

[velvet nebula]

i guess? not very sure about this

[sonic galleon]

hmm okay

thanks anyway

ill try have a google or wait and see if anyone else is sure

google is giving very confusing answers

[velvet nebula]

maybe because sometimes t-test is also used for determining if population mean is different from some guess m

so there's where you tend to get the n-1 from

[safe radish]

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@sonic galleon Has your question been resolved?

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[wary veldt]

Hi.
Volume of a regular quadrilaterial pyramid is 400 cm^3, and it's height is 12 cm, then the lateral surface area = ?

[ember bough]

the lateral surface area is basically the area of the base

[wary veldt]

I did the following:
Base Area = S . S
100 = S.S
50 = S

Perimeter = 50 x 4 = 200

I'm confused how I can get the lateral side, I tried using Pythagoras's but it didn't work out.

https://cdn.upload.systems/uploads/4IRtiQs8.png

Got the base area from the volume rule

wait a moment

got it! that was a slow brain moment for me, solving maths questions at 3:32 AM is not a good idea

thank you

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[lean otter]

How would I be able to separate the trapezoid into two areas and combine them to result in the formula: Delta d= 1/2 times the (quantity of velocity final minus velocity initial) times Delta t

[lean otter]

That helps a bit but I am still struggling to write it as a formula

“The semi-complicated area can be separated into two easy-to-find areas.” I have to write an expression of that but I am not quite sure how to get the area of a triangle and a rectangle to form the formula I previously mentioned

[ember bough]

well

that's what my intuition says

or just use the formula for the area of a trapezoid

[lean otter]

We have it as a requirement to use both though

But thanks for the help anyways

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[fluid hare]

Just wondering if I’ve done a and b correctly

[humble surge]

yes, you have done those correctly

[fluid hare]

Sickk

Thanks

I’m confused about h though

• shifts right and - shifts left yet positive on this graph is shifting left and - shifting right

[humble surge]

desmos.com

go there^ and enter that equation

play around with the values of p and q

[fluid hare]

Yeah I did that

[worthy hemlock]

If I recall correctly, h is in the parentheses, y = A(x - h)^2 + k

[fluid hare]

Yeah

[worthy hemlock]

Notice the sign of h, it's the opposite

So if h was positive, then it's a shift left

[fluid hare]

Oh

So I’ve written it back words

[worthy hemlock]

No, you have it right

Wait

[fluid hare]

Ok

[humble surge]

you have it right, its just that the sign of h is reversed

[worthy hemlock]

You might have plotted wrong here, that's why it's the opposite

[worthy hemlock]

That's because h is positive

If you were given (x - 5) then you know that h = 5, but if given (x + 5) that's equivalent to (x - -5) making h = -5

Also, I skipped typing the exponent, k, a, etc

[fluid hare]

Yeah

Because the vertex listed is (5, -7)
But h has to be -5 to make it (5,-7) on Desmos

I think I get it

[worthy hemlock]

No, h = 5 on desmos

[fluid hare]

Now I’m lost

The vertex listed in the question is (5, -7)

[worthy hemlock]

Yes

[fluid hare]

But if it is 5 on Desmos then the vertex is -5,-7

[worthy hemlock]

That's if you typed in (x + 5)

But don't forget, the equation is y = A(x - h)^2 + k

[fluid hare]

Yeah

[worthy hemlock]

And because the point is (5, -7), h = 5

[fluid hare]

Yes

[worthy hemlock]

So when you plug that in, it's (x - 5)

[fluid hare]

Ah

Okay

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[cerulean relic]

How do i factor -x²+2x+63

[crisp lodge]

you can use x1,2 formula

and find your roots

[lost lodge]

find the factors of -63 that add up to 2

[cerulean relic]

I have to factor it by grouping

[crisp lodge]

, this is your method

[lost lodge]

yeah, it is

[crisp lodge]

but if you can't manage to find them by looking, then x1,2 will help you figure out the roots

[crisp lodge]

No no no I meant like, as a statement "this is the method that will help @cerulean relic"

[cerulean relic]

-x²-7x+9x-63

[lost lodge]

lol, i was joking, dw. i'll leave you to it

[cerulean relic]

@crisp lodge wdym x1,2 formula?

[crisp lodge]

you know

the root formula

(-b+- sqrt(b^2-4ac))/2x

[cerulean relic]

Oh

Well i have to factor it by grouping and not using the quadratic formula

Nvm ill figure it out on my own lol

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[night sandal]

yo

[night sandal]

i got a question

what does ; mean ?

1 = 5p – 100; –5p = –101; p = 101 ÷ 5 = 20,2.

this is economy math btw eu

but what does the ; mean

<@&286206848099549185>

[worthy hemlock]

You have to wait at least 15 minutes before pinging helpers

[night sandal]

dang

lol

didnt know that

but @worthy hemlock do u know the answer?

[worthy hemlock]

Probably used as separation method

Because between these two 1 = 5p – 100; –5p = –101, it's demonstrating getting terms with p on one side and everything else on the other

[night sandal]

nvm

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[jade pier]

.reopen

.reopen

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[tropic wharf]

can someexplain me

how they used r^2=x^2+y^2

and rsintheta=y

into x^2+y^2 = 2y

?

this part ^^

[winter pivot]

ok. this is a bit involved so pay attention

[tropic wharf]

okkk

[winter pivot]

there are two ways to describe a point in 2D space: by its horizontal and vertical displacement (x,y)
or by its distance from the origin and angle from the positive x axis (r, theta)

[tropic wharf]

okkk

[winter pivot]

so now i want you to derive a formula for r in terms of x and y only

[tropic wharf]

sqrt(x^2+y^2)

?

[winter pivot]

yes

now i want you to derive a formula for y, and another formula for x, in terms of r and theta only

[tropic wharf]

y=r sin theta

x- r cos theta

?

[winter pivot]

yes

now you see. you will do this a lot in your later courses. especially when you get to vectors

[tropic wharf]

mm

ohh i got it i think

r^2 = 2r sin theta

r^2 = 2(y)

X^2+y^2 = 2y

right?

[winter pivot]

yep

[tropic wharf]

oh okkk, thanks

ill be learning vectors next

so 🙂

thanks.

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[radiant junco]

Can anyone help me with Algebra?

Question:

Make v the subject
w = 1⁄2mv²

[winter pivot]

impossible

there is no v

[radiant junco]

sorry i typed it wrong

[winter pivot]

ok now we can solve (up to sign)

we have v^2 on the right being multiplied by some factors

how do we undo multiplication?

[radiant junco]

We divide

[winter pivot]

right. do so.

[radiant junco]

What next?

[winter pivot]

what do you have now?

[radiant junco]

I need to get rid of the exponent

Does that mean I square root?

[winter pivot]

sure try that

[radiant junco]

ok thank you

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[tropic wharf]

can anyone help me with this

the answer is

but i got (x-ax)^2+y^2=(ax)^

so my center would be instead (ax,0)

What did I do wrong?

[winter pivot]

Not quite

What is the standard equation of a circle?

@tropic wharf

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@tropic wharf Has your question been resolved?

[tropic wharf]

Aorry

@winter pivot

Standard equation is x^2+y^2=r^2

I did r^×=2a(rcos theta)

= r^×= 2ax

Right? @winter pivot

[winter pivot]

Not quite

The standard equation is

(x-h)^2 + (y-k)^2 = r^2

[tropic wharf]

Ohh

Mb

[winter pivot]

For a circle centered at (h,k)

[tropic wharf]

Yep

[winter pivot]

Note how each term appears only once

[tropic wharf]

Ues

How do I do it then

Set (x-h)^2 + (y-k)^2 = 2ax

?

[winter pivot]

r = 2acos(θ)
sqrt(x^2+y^2) = 2acos(θ)

rcosθ = x.
cosθ = x/r = x/sqrt(x^2+y^2)

sqrt(x^2+y^2) = 2a x/sqrt(x^2+y^2)
x^2 + y^2 = 2ax
x^2 - 2ax + y^2 = 0

(x-a)^2 = x^2 - 2ax + a^2

(x-a)^2 + - a^2 + y^2 = 0
(x-a)^2 + y^2 = a^2

@tropic wharf

[tropic wharf]

Im looning at it

Mm

Sqrt(x^2+y^2) × (sqrt(x^2+y^2) = 2ax

How did u get this ( x^2+y^2 = 2ax

?

[winter pivot]

That's not what I wrote

[tropic wharf]

Soz I missed the division sign

[winter pivot]

I could tell you that 5 = 10/2. Then does that mean 2*5 = 10?

[tropic wharf]

Yes?

[winter pivot]

Exactly

[tropic wharf]

(sqrt(x^2+y^2) × (sqrt(x^2+y^2) = 2ax?

[winter pivot]

Mhm

[tropic wharf]

This part

I don't understna dhow the top line

Go into the 2nd line

[winter pivot]

Ok. Let me ask you a question.

What is sqrt2 * sqrt2 ?

[tropic wharf]

4

[winter pivot]

No

[tropic wharf]

Wait 2

Mb

Sqrt4 =2

2

Oh

Ohhh

Mmm

Last qristion

No

This part

(A-x)^2 = x^2-2ax + a^2

Where would u get this? If u weren't given

Ohh wait

Nvmmm

[winter pivot]

This is called completing the square

[tropic wharf]

Yes but

U could have completed the square this eqaurion

X^2-2ax+y^2=0

U could have completed the square of this right?

[winter pivot]

Yeah sure

Doesn't really make a difference

I was just showing you the identity

[tropic wharf]

= (x^2 - 2ax + a^2x^×) + y^2 = 2ax

?

Right

If I was to compete the square

So thus ( x-ax)^2 + y^2 = 2ax

[winter pivot]

Wtf u doin haha

[tropic wharf]

Completing the square

?

(-b/2)^2

?

[winter pivot]

What does ^× even mean

[tropic wharf]

Where?

Ohh

I mean = (x^2 - 2ax + a^2x^2) + y^2 = 2ax

Sorry

X^2

[winter pivot]

You've changed the equation now

[tropic wharf]

But this would be valid

[winter pivot]

No.

[tropic wharf]

If the question as (2ax,0)

Wait n

Just (ax,0)

[tropic wharf]

Circle with centre

Right?

[winter pivot]

The center cant vary with x

Then it's not a circle

Recall the standard equation

[tropic wharf]

So how did I change the equation?

I did same as u

[winter pivot]

No you did not

First of all, a circle cannot have center (ax, 0)

That is not a circle

So you have changed a circle into something that is not a circle

[tropic wharf]

Ohh

So I would need to use the identity to do so?

[winter pivot]

Which identity

[winter pivot]

Yeah use that identity

[tropic wharf]

Oh 8kkk

[winter pivot]

Just take half of the coefficient of the linear term

[tropic wharf]

Mm oh okkk

Thanks yoy alotttttttyyyy

[winter pivot]

A circle with center (ax,0) is an ellipse

That is a cool way to interpret ovals. A circle with variable center

[tropic wharf]

Ohh wow

[winter pivot]

Yeah you should read up on conic sections

The fascination of the ancient greeks

[tropic wharf]

Yss

I have

I learnt like the topic on conic sections

But I didn't realise waht u saud

Thanksss

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[lunar roost]

if an apple tree grows 3 apples and there is an 8% chance of an apple to be purple what are the chances of two out of three apples to be purple

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@lunar roost Has your question been resolved?

[marble marlin]

3 * 0.08 * 0.08 * 0.92

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[granite frigate]

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then what is the equation of the parabola?

[granite frigate]

I got the diagram and all but how to find the equation

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[granite frigate]

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[lean otter]

Hello. What is 12x6x3 in lengh?

[candid lodge]

What do you mean?

[lean otter]

Like these are sizes and lenghes, which is lengh, width and height?

[pulsar condor]

doesn't matter

[lean otter]

How? Im literally asking the question here

[worthy hemlock]

If you're responding to mosh, he is saying it doesn't matter how to label length, width, height

[pulsar condor]

the volume is invariant under however you have it oriented

it doesn't matter what side the length is

[lean otter]

The question is, which numbers means height, width and lengh?

[worthy hemlock]

As stated, it doesn't matter

[pulsar condor]

Read what was said

[lean otter]

It does, because this is mentioned for a product i bought

[pulsar condor]

multiplication is commutative

order doesn't matter

you're asking something similar to:

Out of the numbers 1,2 and 3, which is x?

[lean otter]

Pretty sure if this is written on an item, each number is a specfic size code

Specific

[worthy hemlock]

If it's for a product you bought, and you have it, measure it

[pulsar condor]

Yeah, and you're not talking about anything specific

you wrote an arbitrary product of numbers

[lean otter]

Im talking about my product which is written with this sizes

[worthy hemlock]

Like we know what product you have

[pulsar condor]

and again, it doesn't matter what you call the length

hypothetically:
Let's define the height of an object as how tall it is.
If I turn it on it's side, the height changes

[lean otter]

How? Lets say 3 mesns cm, of course that cant be the lengh as the product is much longer than that

[pulsar condor]

so it doesn't end up mattering what side I call the height specifically, as the orientation changes the definition

[pulsar condor]

Ok, so turn the object around

[lean otter]

I get it, i just need to know what is what to know the sizes of the product

[pulsar condor]

Your question is poor at best bluntly

it doesn't matter what you call the length

end of story

[worthy hemlock]

It's based on how you label it yourself

[lean otter]

Why cant you just be a nice person and help with what i need help with, instead of always mocking

[worthy hemlock]

The length could be any of the 3 values

[toxic skiff]

what is the product you bought.

[pulsar condor]

We are helping, you're not listening

[lean otter]

I am listening, u just dont want to listen to me, u want to listen to urself

[worthy hemlock]

You're not listening though

[pulsar condor]

Yeah cause you're still stuck on the fact length is a well defined concept when we're both saying it isnt

the length of a prism is free to be chosen

[worthy hemlock]

If given 12x6x3, the length could be 12 units, or 6 units, or 3 units. It's all based on how you decide to label it

[toxic skiff]

i dont think he is asking this question from a mathematical point

[lean otter]

Look i totally get it, but im pretty sure if a seller has written such sizes, he means in a specific way

[toxic skiff]

what is the object you bought

[worthy hemlock]

It's based on your perspective

[lean otter]

Its a doll for my little sister

[toxic skiff]

a fridge cant be 10 meters wide and 1 meter tall

[worthy hemlock]

Yes it can

If you rotate it

[toxic skiff]

why would you rotate a fridge

for practical use

[lean otter]

True man, but lets say we are giving each site a specific ankle

[worthy hemlock]

To move it

[toxic skiff]

lol okay

[worthy hemlock]

If it's a doll, and you have it standing vertically, the length could be from toe to heel. If it's laying on it's side, the length could be head to toe

Like I said, it's based on perspective

[lean otter]

Its laying on its back

[worthy hemlock]

The length could be 12, but if you have it standing, the length could be 3

Perspective is the key word

[lean otter]

Okay but its laying on its back…

[worthy hemlock]

Doesn't matter, rotations are a thing

[lean otter]

I know man but can we please just look at it as its on its back?

[toxic skiff]

if youre 6' tall standing up youre gonna be 6'ft long laying down

[worthy hemlock]

Yes, your height would be 6' standing, but laying down, your height could be 1' tall but the length is 6'

[toxic skiff]

yes thats what i said

[worthy hemlock]

No, because you're being illogical. Mosh and I told you, it doesn't matter

[lean otter]

I totally get ur mentallity, but lets just look at the object when its on its back.

[worthy hemlock]

What if I wanted to view it vertically?

[lean otter]

Lets say its on its back RIGHT NOW, now what is lengh and so on

[toxic skiff]

grab a measuring tape and act like if you were the doll

[lean otter]

It feels like you just want to fight me lol😂

[worthy hemlock]

It's based on what you want the dimensions to be

[lean otter]

The thing is from the product, i dont know what the seller means is lengh and so on

[toxic skiff]

you said it was laying on its back

[lean otter]

Yes i dont have the product yet

[toxic skiff]

logically, height would be like ceiling to floor and length would be like wall to wall

if its laying on the ground

[worthy hemlock]

The seller could mean whatever they want

As I have been saying, it's based on perspective

The seller could have had it vertically and you decide to have it laying on its back

See, two different lengths

Based on perspective

[lean otter]

Okay then but is 12x6x3 cm big sizes ( already know the answers but ill see if im right)

[worthy hemlock]

There is no right answer, if it's based on perspective

[lean otter]

But lets take it from laying down perspective

[worthy hemlock]

No

I don't want to

I want it standing

Why not from my perspective?

[lean otter]

@toxic skiff are u seeing this?

[lean otter]

Well im the one asking the question and its my product🤔

[toxic skiff]

what

[worthy hemlock]

Then view it from your perspective and determine which is the length yourself

[lean otter]

I can, but i asked here cause i wasnt sure, and idk whats lengh etc

[worthy hemlock]

Do you not understand that it is a perspective thing? So every one will have a different perspective on what length is

So you can use your own perspective and determine that yourself

[lean otter]

Yes i know that. But you can choose which perspective and then work there. Now, IF its laying on its back, what is what then, IF its laying in its back, IF

[worthy hemlock]

Then you determine that yourself

[lean otter]

It dosnt hurt to actually be a nice person, you know? But whats to be expected nowdays

[worthy hemlock]

It doesn't help that you don't understand what it means by perspective

[lean otter]

I do

[worthy hemlock]

If you do then you can determine length yourself

[lean otter]

I will leave this, there might be someone whos actually a nice person and want to help, and not make this into some kinda weird fight

[worthy hemlock]

It's because you don't understand perspective

[lean otter]

I think u rlly need to buy urself a gold metal

[worthy hemlock]

I think you should relearn what perspective means, so you can determine your answer

[lean otter]

Are u done?

<@&268886789983436800>

Can you pls warn him for mocking

[knotty sigil]

Bruh r u serious

[lean otter]

What

[knotty sigil]

To answer ur qn btw , generally from a maths problem view , it is generally lxbxh

So 12 units is ur most probable length

[lean otter]

Thx!!! And can u write it in full words ?

[knotty sigil]

But yeah as dldh said it depends on perspective as well

[knotty sigil]

Wdym full words

[lean otter]

L b and h

[knotty sigil]

If u want
But remember it depends on perspective very much
And what I'm telling is from the math problem general perspective

[lean otter]

Can u write it in full words

[knotty sigil]

Bro IF U WANT U WRITE

Wth

[lean otter]

No i mean so i know what words they are

[knotty sigil]

What are u even saying xD

[crisp lodge]

length breadth height?

[worthy hemlock]

Larry Ben Harry?

[lean otter]

Thank u so much, didnt know what the b was for as i would say width

[knotty sigil]

Oh my u asked that

Yeah write it if u want

[crisp lodge]

Lartin Buther Hing?

[lean otter]

Lol😂

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[cobalt lily]

hello

[cobalt lily]

is letter (c) correct

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[cobalt lily]

<@&286206848099549185>

[modern jolt]

hmmm

How did you arrive at that value?

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@cobalt lily Has your question been resolved?

[cobalt lily]

I got it

I should do 1-1/p

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[tepid hatch]

How do we change the discrete time functions from [n] to continuous (t), and how do we evaluate this? Using point/slope I get (1/3) * -2, which isn’t a possible solution

[tepid hatch]

This is my work so far, the answered make sense besides 12 b

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[arctic thicket]

Hello,I don't understand this question hope somebody helps .

How would you color part of the points in a plane so that any circle of unit radius would pass through exactly 4 color points?

[tepid hatch]

.reopen

[stoic dune]

Color a grid

Horizontal and vertical lines that are 1 unit away from eachother

Ah wait that doesn't even work. A circle can pass through an intersection

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[stoic dune]

Just vertical lines 0.5 units away from eachother

[arctic thicket]

Can you explain it?

<@&286206848099549185>

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[midnight hare]

How do I prove that f(x) = x - cosx has a zero using the Bolzano Cauchy theorem

[crisp lodge]

bolzano cauchy?

is that the intermediate vlaue theorem?

can you define it?

[midnight hare]

yeah

it's the intermediate value theorem

[tall acorn]

Wdym by "has a zero"

[midnight hare]

has a root

[tall acorn]

Well you take two any x's in your interval and multiply them

If it's <0, there's at least 1 root

[broken yew]

thats not the thm.

[midnight hare]

thats a special case of the theorem

[broken yew]

you just solve it like any other ivt problem?

MVT

i think

cant remember

[crisp lodge]

can you define it here?

[midnight hare]

Let f: [a, b] -> R be continuous and f(a)*f(b) < 0. Then there is c e(a, b) such that f(c) = 0

[broken yew]

oh so this is the thm ..

[pulsar condor]

IVT

[broken yew]

🤔 i dont remember it being worded like this

[crisp lodge]

yea that's the one

[tall acorn]

I know Bolzano theorem as this

[lament beacon]

let x = 10000 and x = -10000 and look at the signs of the function values in both those cases

[lament beacon]

responding to this

[crisp lodge]

I think there's a more generalized version claiming that if f(a)<d<f(b) there there exists some value c s.t. f(c)=d

[broken yew]

maybe lets pick pi and -pi