help-4

[barren imp]

i⁷⁶= 1?

Am I doing this correctly?

[marble arch]

Yes, you're correct

Both of them are

Also 1/i you can multiply i on both sides

[barren imp]

And i^(-22) is... -1?

[marble arch]

$\frac{1}{i}$ = $\frac{1 . i}{i . i}$ = $\frac{i}{i^2}$ = $-1$

[barren imp]

How so

[honest stone]

oops

[barren imp]

?

[marble arch]

Bloody hell, okay decimal means into

[honest stone]

$\frac{1}{i}$ = $\frac{1 \times i}{i \times i}$ = $\frac{i}{i^2}$ = $-1$

[barren imp]

?

[rocky lotus]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

doctorstrangejr

[marble arch]

omg thanks man, they gotta do something about this astrick stuff

[barren imp]

Where did the other i's come from?

[marble arch]

So this is also correct, 1/-1 = -1

[barren imp]

Ok so what about...m

[marble arch]

Well, we multiplied them on both sides to rationalise the denominator

[barren imp]

$\frac{1}{i^(-11)}$

...

Not what I meant

[rocky lotus]

RainbowOcean

[barren imp]

...

Ok

[marble arch]

Wait I get it

1/1^(-11) yeah?

[barren imp]

Ohhh the denominator cant be i

[barren imp]

Yes

[marble arch]

Yup

Well just make it i^11

[barren imp]

So...

Uh

×1?...

[marble arch]

Just keep the power positive, look for the multiple of 4 JUST before it, and count

so it's i^8*i^3

or 1*i^3

or just i^3

[barren imp]

Does the 1/a and - cancle eachother out?

[marble arch]

Sorry I didn't get that

[barren imp]

Ohhh

So you have to... (whats the term Im looking for...)

[barren imp]

If a`¹² = 1/a¹²

And you have a fraction withing a fraction do they cancle eachother out?

[marble arch]

Yes

Fraction within a fraction?

[barren imp]

Yes

[marble arch]

Can you give me an example of what you're trying to say?

[barren imp]

So the 1/a`² is essentually 1/(1/a²)

Would they cancel eachother out leaving you with a²?

[marble arch]

No no, how did the two come out of the power

[barren imp]

Oh

[marble arch]

did you mean $\frac{1}{a^{-2}}$ = $\frac{1}{1/a^2}$

[barren imp]

Yes

[marble arch]

Okay yes

it just becomes a^2

[honest stone]

Use curly brackets to put the entire thing in the superscript

[marble arch]

Thanks man, let me try

[honest stone]

did you mean $\frac{1}{a^{-2}}$ = $\frac{1}{1/a^2}$

[rocky lotus]

𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³

[barren imp]

Yes!

[rocky lotus]

doctorstrangejr

[marble arch]

Peak stuff

[barren imp]

You guys are pretty good with the commands

[marble arch]

Infinium is definitely better, I started using them rather recently

[barren imp]

I can barely do basic server commands still💀

[marble arch]

You'll soon learn too

[barren imp]

Thank you

I have a feeling (unlike most my servers) I will be using this one very often especially when I jump back in Chemistry and physics

So back to the fraction within a fraction

[marble arch]

Well we'll be here to help you! (BTW you could also ask Physics questions here, some people do)

[barren imp]

Thank you

[marble arch]

Alright

[barren imp]

So... why are we doing it by sum

[marble arch]

Sum, where?

[barren imp]

The exponents.

Off topic

But where did I go wrong?

[marble arch]

Where were you wrong again?

[barren imp]

Here

[marble arch]

Ahhhhhh

Well it'd be -(16 + 1)

[barren imp]

Yeah...

[marble arch]

$(a+b)(a - b) = a^2 - b^2$

[rocky lotus]

doctorstrangejr

[marble arch]

and $-i^2$ = $-(-1)$

[rocky lotus]

doctorstrangejr

[marble arch]

which is +1

[barren imp]

Yeah I got that

Originally I put 17

But then forgot the 16 is negative

[marble arch]

Ahhhh that's fine man, we all make mistakes

Let me show I would do it

oh wait

It's $(4 + i)(-4-i)$

[rocky lotus]

doctorstrangejr

[marble arch]

That's $-16 - 4i - 4i - i^2$

[rocky lotus]

doctorstrangejr

[marble arch]

or $-15 - 8i$

[rocky lotus]

doctorstrangejr

[barren imp]

Ohhhhhh

[marble arch]

me and you both completely missed it!

[barren imp]

We did

Ok check me if Im wrong here- for a different one

[marble arch]

Alright sure

[barren imp]

(8+9i)(8-9i)

I got =145

[marble arch]

It's correct!

[barren imp]

Wait really?

[marble arch]

Yup

[barren imp]

That was fast

[marble arch]

Yup, 64 + 81

[barren imp]

Did you do it mentally?

[marble arch]

Yup, I'm kinda decent at mental calculations

[barren imp]

I used to but when you dont do math for a while you struggle with something basic like 6+8 or 9×7

Im getting a bit better at it again

[marble arch]

That's fine man, it'll come back to you

[barren imp]

But its taking some time

[marble arch]

Well eventually

[barren imp]

Considering I have just started again last month Im having a bit more confidence

But back to 1/i^(-11)

[marble arch]

Alright then

So send it up!

[barren imp]

I

[marble arch]

Well, get the power positive

[barren imp]

So you cant flip it to i¹¹ because of the fractions

[marble arch]

Yup, but you can do so by sending it up

[barren imp]

Eh...make it i⁸ +i³?

[marble arch]

No wait see

[barren imp]

Oh!

Oh.

[tawny moon]

,tex exp rules

nvr mind i thought that was a guild preamble

[barren imp]

[tawny moon]

but do you know what you can do whenever you see a negative exponent?

[barren imp]

But its already a fraction

[tawny moon]

aha. the rule works both ways

[barren imp]

Its a fraction in a fraction

[tawny moon]

ok how about this

do you have a calculator?

[barren imp]

I thought if I cross the numerators cancled out it would leave us with i¹¹

But apparently thats not it

[marble arch]

Well $a^2$ = $\frac{1}{a^{-2}}$ right?

[tawny moon]

this is step 1

you are not done yet

[tawny moon]

whoa what

[barren imp]

I do but itz not adapt for complex numbers

[rocky lotus]

doctorstrangejr

[marble arch]

Whoops!

[barren imp]

???

[marble arch]

So it basically works the other way too

[tawny moon]

anyway you got to the point of i^11

now, I'm going to quote something a helper said to another helpee some time ago, if I may

[marble arch]

Yeah sure!

[barren imp]

So a'²= 1/a²
And
1/a` ²= a² ?

[marble arch]

Oh god no I confused them, when you reciprocate fractions, the signs of the power change

[barren imp]

I loath fractions

[tawny moon]

as long as you remember one simple rule - that flipping a fraction flips the signs of all exponents in the numerator and denominator - you're good to go

there's a reason why the button to flip a fraction on a calculator is x^-1

[marble arch]

like $i^{11}$ = $\frac{1}{i^{-11}} $ and vice versa

[rocky lotus]

doctorstrangejr

[tawny moon]

either way, when you're done pondering on that, this is your next step

[barren imp]

Huh...

[tawny moon]

if you don't believe us

take your calculator right now

[barren imp]

No no I believe you

[tawny moon]

type this in.
1/(3^-1)

[marble arch]

No like if you still have doubts

[barren imp]

Im just trying to figure out HOW its done if you dont get cancle out the fractions

[marble arch]

then do what she's saying, just do it even if it's clear, would help it settle in

Okay so you agree that $\frac{1}{i^{-11}}$ = $\frac{1}{1/i^{11}}$ right?

[rocky lotus]

doctorstrangejr

[barren imp]

I got an error. My calculator is a basic scientific one

[tawny moon]

can you show what you typed?

[barren imp]

Yes

Oh

Theres no /

[marble arch]

Okay, now can't we make $\frac{1}{1/i^{11}}$ as $i^{11}}$ by sending the $i^{11}$ up

[tawny moon]

don't actually type 3^-1 raw in calculators like these

[barren imp]

💀👌

[tawny moon]

either type 3^(-1), or type 3, followed by the x^-1 button

[barren imp]

Ohhh so it flips essentially

[tawny moon]

also, it's supposed to be 1**/**(3^(-1))

[rocky lotus]

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

[hazy pivot]

Use \/

Instead of /

[barren imp]

If it was just i¹¹ it would stay the denominator:O

[tawny moon]

yes, it would (or you can bring it up as a negative exponent too, depending on what you want to do with it)

[marble arch]

Yup, basically we want a positive power, and we do that by switching sides

[barren imp]

Oh ok I got just 3

[tawny moon]

but here, we want the exponent to be positive, so as doctorstrange mentioned, we flip the fraction (formally called taking the reciprocal of the fraction)

[tawny moon]

and 3 = 3^1, and you see that the exponent has changed signs

that's key

[barren imp]

But the negative exponent FORCES it to flip sides

Either way

[tawny moon]

not necessarily

[barren imp]

Now I under- oh

[tawny moon]

you can leave it as a negative exponent if you want to, depending on what you want to do with it

but here we want the exponent to be positive

so flip it is

[marble arch]

But here, for simplicity, we make it positive

[tawny moon]

now that our whole rodeo of burger fraction flipping is over

[barren imp]

XD

[tawny moon]

it's time to get started on this

[barren imp]

Ok

So -1² I thought its just 1?

[marble arch]

Yes

[tawny moon]

but now notice this.

-1 is i^2, and (-1)^2 is 1.

do you see where I'm going with this?

[barren imp]

Yes

[tawny moon]

so, what can we conclude?

[barren imp]

i³=1

[tawny moon]

is that a 3?

[barren imp]

Wait-

[tawny moon]

sure about that?

[barren imp]

Ha... ok no I thought I saw where the direction was going

I was wrong

[marble arch]

Okay, well what would i^3 be (hint - i*i^2)

[tawny moon]

if I write it like this

i^2 = -1
(-1)^2 = 1
can you now draw the correct conclusion?

(hint: make one substitution. your final conclusion should not have a -1 in it)

[barren imp]

Oh- i² (-1) and i² (-1)
(-1) • (-1)=1
i² • i² = i⁴ =1

[marble arch]

Nice!

Okay, so tell me i, i^2, i^3 and i^4 now

(well, you can exclude i xD)

[barren imp]

Ok i² = (-1)
And i³= -i
And i⁴= 1

[marble arch]

Bravo!

[barren imp]

Oh

[tawny moon]

I'm giving you the second part in advance because you more or less found it out

[tawny moon]

this is the key part you were missing in your initial answer of i^11

[marble arch]

Yup, check the multiple of 4 just before it

basically values of i in powers repeat after every 4th power

[barren imp]

Wait if i² is -1
Why is i > (-1)?

Oh wait

[tawny moon]

that is not an inequality chain

that is a pattern marker

don't even think of complex inequalities

[barren imp]

Im overthinking again

[marble arch]

like i -> -1 -> -i -> 1

[tawny moon]

we don't have (at least not at this stage) well-defined orderings for the complex field

so don't try to compare two complex numbers

[barren imp]

i is +
i² ends negative

[barren imp]

Oh

[marble arch]

And this repeats for every 4th multiple of power

[barren imp]

Ok but i¹¹= -i?

[marble arch]

if I ask you i^5, i^6, i^7 and i^8, you'll have the same answer in this very order

[marble arch]

Yup!

[barren imp]

Yayyyy

[marble arch]

Just use the multiple of 4 analogy, and remember that values of i repeat

[barren imp]

Is it 3-8i?

Or wait-

[marble arch]

so $i^{4n}$ = 1, $i^{4n + 1}$ = i, $i^{4n + 2}$ = -1, $i^{4n + 3}$ = -1, if we write it more formally, (where n is a whole number)

[barren imp]

I see

[rocky lotus]

doctorstrangejr

[marble arch]

No it's fine, you're correct

[barren imp]

So in that case its its something like i^((4)(12) +3)= -i

[barren imp]

Why does flipping the sign. Make it a com conjugate ?

[marble arch]

Exactly, so $i^{(4*12)+3}$ = $i^{51}$ = $-i$

[rocky lotus]

doctorstrangejr

[tawny moon]

by definition

[marble arch]

Basically if you multiply a complex number by its conjugate, the imaginary terms cancel out and you're left with only a real number

[barren imp]

Can you show an example?

[marble arch]

Okay

[barren imp]

For instance how does 3+8i ->3-8i

[marble arch]

$(3 + 8i)(3 - 8i)$ = $(3^2 - (8i)^2)$

[rocky lotus]

doctorstrangejr

[marble arch]

You get how right, the identity?

[barren imp]

Yes

[marble arch]

Okay

[barren imp]

What happens to the ²s

[marble arch]

Now i just gets squared, and the imaginary term is removed

$(3^2 - (8i)^2)$ = $(9 - (-64))$ = $73$

[rocky lotus]

doctorstrangejr

[marble arch]

Notice how it gives only a real number (73) and no imaginary term

[barren imp]

Uhhhh

Yes

[marble arch]

That's what a conjugate does basically, and we need the (a + b)(a - b) identity for that

[barren imp]

How does that get it to 3-8i?

Or is the complex congugate just a step

[marble arch]

It is just a step

You could say that

like see

$(3 + 8i)$ does the work of $(a + b)$

[rocky lotus]

doctorstrangejr

[marble arch]

now we need an (a - b) to get only a real number, and that term we call its conjugate

[barren imp]

What about $\frac{10}{-i}$

[rocky lotus]

RainbowOcean

[marble arch]

You got the previous one right?

[barren imp]

Ah...

I see so

This is just a beginner step for later problems

[marble arch]

Alright

[marble arch]

Here you multiply both sides by +i, you get 10i

[barren imp]

So

[marble arch]

no no both sides, both the numerator and denominator

[barren imp]

What would tjat look like

[marble arch]

$\frac{10.i}{-i.i}$ where . is *

[rocky lotus]

doctorstrangejr

[tawny moon]

(brackets are a thing kek)

[marble arch]

Yeah I've tried but it doesn't help

[barren imp]

So why wouldn't i cancle out the one above

[marble arch]

Because we need it for simplification!

[barren imp]

Ah ...

So -i (i) = i²=-1?

[marble arch]

-i^2 isn't it?

[barren imp]

Oh!

Your right

THEN it turns to 1

[marble arch]

Yup!

[barren imp]

Which leaves 10i

[marble arch]

Exactly

[barren imp]

Ok ok now I get that one more

So then... 1 + 7i/1 + i...

[marble arch]

Okay

[barren imp]

$\fract{1 + 7i}{1 + i}$

[rocky lotus]

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

[barren imp]

...

You get what I mean...

[marble arch]

Allow me

$\frac{1 + 7i}{1 + i}$

[rocky lotus]

doctorstrangejr

[barren imp]

Yeah

[marble arch]

Okay, so what do we multiply both sides with (Hint : we want a real number in the denominator)

[barren imp]

1?

Or 7

Or i again?

[marble arch]

Well, what do you multiply a complex number with so that it only leaves a real number?

what's the term?

[barren imp]

Its self?

[marble arch]

well, its conjugate

[barren imp]

i

[marble arch]

with (a - bi) for the (a + bi) we have

[barren imp]

Oh

1 - i

[marble arch]

Yes

Now multiply both sides with (1 - i)

$\frac{(1 + 7i)(1 - i)}{(1 + i)(1 - i)}$

[rocky lotus]

doctorstrangejr

[barren imp]

So then 1 + 7i²

And 1 - i²

[marble arch]

oh god

[barren imp]

Wait

[marble arch]

my fault

Just open the brackets and evaluate it

[barren imp]

Ok

[marble arch]

god I shouldn't have explained with the squaring

[barren imp]

So then

2+6i

[marble arch]

maybe 8 + 6i?

[barren imp]

And 2

Oh. 8?

Where is the 8 from

[marble arch]

well -i*7i gives 7

and there's already a +1

[barren imp]

Ohhh

So we still foil

Oh ok so then its 1-i+7i-7i²

[marble arch]

Sorry but I should sleep now, really sorry if I've confused you, there are people better than me here

[barren imp]

Its ok

Thank you for helping

[marble arch]

Anytime man, and sorry again

@tawny moon can you take over?

[tawny moon]

ah shucks, I just entered a channel

ok, I'll try but Idk where you guys are at atm

[barren imp]

No worries dude

[barren imp]

We are foiling this... thing

[barren imp]

I got this for the top

[tawny moon]

were you distributing this?

[barren imp]

Yes

[tawny moon]

what is the objective here?

[barren imp]

This

[tawny moon]

ah ok

[visual remnant]

Come on

This mad easy

[barren imp]

💀

[tawny moon]

not helping, and #discussion if you're not helping

[visual remnant]

Ok sorry

[tawny moon]

anyway

[tawny moon]

simplify this first.

[barren imp]

I just got back in to math after a WHILE I only have a few weeks under my belt give ke a break

[tawny moon]

let him be, and let's continue

[barren imp]

Ok well...1-6i -7i²

And then below is

[tawny moon]

-6i?

also, do something about that i^2

[barren imp]

Oh-

1 + 6i -7 (-1)

Which makes 1 + 6i +7
8 + 6i

[tawny moon]

now do the denom

[barren imp]

Then the bottom 1-i²

Or

1-(-1) = 2

8+6i/2

[tawny moon]

now divide the numerator by the denom

[barren imp]

Ok

That makes 4 + 3i

[tawny moon]

careful about bracketing: (8+6i)/2 is preferred

and that's the final answer

[barren imp]

Oh

Yayyy

And then the conjugate for -14i is
14i ?

[barren imp]

Thank you

[tawny moon]

nps

[barren imp]

Ok then 11/-i

Eh... 11i?

[tawny moon]

first, state the objective

[barren imp]

I need to put it in standard form

[tawny moon]

a + bi?

[barren imp]

Yes

[tawny moon]

well it's gonna be just bi here only since we don't have an a

[barren imp]

A is 0

So its just 11i?

[tawny moon]

working?

or reasoning?

arguably more important than the answer itself that you know why it is correct

[barren imp]

Ok well if its 11/-i multiply both by i

Leaving 11i

A+ bi form is = 0 + 11i

Technically

[tawny moon]

I was expecting a more thorough explanation of what happens in the denom, but I suppose this works

[barren imp]

Oh! Right the -i (i) = -i²

Which makes -(-1) = 1

[tawny moon]

excellent.

[barren imp]

So its not important

I mean it is

[tawny moon]

can't say it's "not important", we just got lucky it simplified this way

[barren imp]

But it turns it to a whole number

[tawny moon]

specficially, it turns into 1, so we don't have to deal with it

[tawny moon]

but yes, this is right

[barren imp]

True

Hmmm

[tawny moon]

anything else?

[barren imp]

Still working on the top

Ok so far I have 64+32i+32i+16i²

Over 64+32i-32i-16i²

[tawny moon]

if this is the denom, it's wrong

[barren imp]

Wai-

[tawny moon]

remember, we choose to mult by the conjugate of the denom precisely to create a diff of two squares situation

[barren imp]

I thought

I thought I need to foil

The denominator is (8-4i)(8+4i)

[tawny moon]

you do. but you have not simplified the denom

and here's a bit of a pro tip for you

since you know that you're creating a diff of two squares in the denom, you can directly write the denom as a diff of two squares

[tawny moon]

also, correction: it's not wrong, just not complete

my bad

the extra i terms confused me - I was not expecting to see any i remaining

[barren imp]

Do the +4i/-4i cancel eachother out?

[tawny moon]

no

wait what do you mean +4i/-4i

[barren imp]

Well 8/8 is 1?

Oh- the negative

[tawny moon]

ok let's take this again

[tawny moon]

this is correct

[tawny moon]

simplify this and it will also be correct

[barren imp]

Ohhhh

I was just showing you as I was still in the process of working it out in case I made a mistake you saw me me

[tawny moon]

fair enough

appreciate the hard work

[barren imp]

Thank you:) So then so far. 64 + 64i +16(-1)
Over
64-16(-1)

[tawny moon]

continue

[barren imp]

Which then simplies further to 48 + 64i
Over
80

Ugh...

That doesnt... seem right

[tawny moon]

fractions it is

it just so happens that 48, 64 and 80 share a very convenient common factor

[barren imp]

Ok so then... 8-

No

16

[tawny moon]

you will have a and b as fractions

[barren imp]

So then 3+4i/5

[tawny moon]

no, don't combine them

(at least I don't think your site wants it that way)

[barren imp]

It says to divide

[narrow arrow]

just make denominator not be complex by multiplying by (8+4i)/(8+4i)

i mean imaginary part 0*

[barren imp]

Wait...

The example is showing something different

But I dont understand why we are reducing this one

[narrow arrow]

you gotta make the denominator a real number to divide

[narrow arrow]

well

[barren imp]

This wasn't in my notes...

[narrow arrow]

you cant tell me you didnt see 5 as a common factor

brotherr 🙏

well you dont even really gotta factor out the five in the first step if you are okay with more calculation

[tawny moon]

hang on

where are we now

[tawny moon]

if from here, you already divided!

I just said that you should not leave your answer as $\frac{3 + 4i}{5}$

[rocky lotus]

fox(x, y); ∂(fox)/∂x (Flower)

[tawny moon]

we were past this alrd

[barren imp]

Ok so then

[tawny moon]

split the two terms into their own fractions

[barren imp]

Do we make it 3/5 and 4i/5

[tawny moon]

I prefer $\frac{3}{5} + \frac{4}{5}i$

[rocky lotus]

fox(x, y); ∂(fox)/∂x (Flower)

[tawny moon]

because then it's a direct comparison with a + bi

[barren imp]

Oooohh

I guess you can reduce it or jump to complex conjugates

Lets see

[tawny moon]

it's just rewriting the thing so that $\color{yellow}{\frac{3}{5}} + \color{red}{\frac{4}{5}}i$ can be compared with $\color{yellow}{a} + \color{red}{b}i$

[barren imp]

I see

[rocky lotus]

fox(x, y); ∂(fox)/∂x (Flower)

[tawny moon]

so that no one can contest and say that "oh but you didn't write it in the correct form!!!"

[barren imp]

Thats so helpful!

[tawny moon]

yeah, this is a common trick some examiners love to use unfortunately

so I tend to give them what they want to the T

[barren imp]

I see

[tawny moon]

anything else?

[barren imp]

Ok yes

(-7+ 7i)(9 + i)

For the answer I got
56+ 56i

[tawny moon]

let's see

that 56 is defo wrong

the 56i is correct

[barren imp]

Oh-

[tawny moon]

-7 times 9 is so negative that no i^2 can save it

[barren imp]

Its... -70

So -70 + 56i

Uh.. ok this one Im a little unsure of

(-4+6i)²

It just says multipy

I think we still foil but Im a bit unsure

[tawny moon]

yes, foil as usual

[barren imp]

I got... -10?

Wait-

-20

[tawny moon]

what about the imaginary part? can't leave that hanging

[barren imp]

The imaginary- oh...

I see it is -48i

Thats where I went wrong

So its -20 -48i

[tawny moon]

good. anything else?

[barren imp]

There are things but I think its best to call it a night thanks for helping me again getting sleep last night helped alot

I will probably pick up and review before I retake something tomorrow

[tawny moon]

wise choice

oh wait it was you whom I told to sleep last night too

ok lol

[barren imp]

Yep

I was very out of it yesterday

But while it was a bit rocky today I think I am doing pretty decent

Anyway hope you have a good night:)

[tawny moon]

well it's afternoon for me

but yes, have a good rest

[barren imp]

Oh-

Right timezones

Anyway have a good day:) bye

[tawny moon]

aight

[barren imp]

.close

[vale dock]

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[primal matrix]

Hi, I'm starting with derivations, is this correct?

[frozen ledge]

you forgot the +

at the end for 3(-1)x^{-2}

[primal matrix]

Yess, ty

[safe fulcrum]

oh yeah, you're missing a chain rule for $\frac{d}{dx} \sqrt{2x}$

[rocky lotus]

south

[frozen ledge]

that too

[safe fulcrum]

it's better to write it as $\sqrt{2} \sqrt{x}$, so its derivative will be $\sqrt{2} \frac{1}{2 \sqrt x}$

[rocky lotus]

south

[safe fulcrum]

if you apply the power rule you do get 1/(2 sqrt(x))

[primal matrix]

Ok ty, is there any rule to derivate the sqrt?

[safe fulcrum]

that's what I just said

[lucid nimbus]

I think it's easier the second way he wrote it

[primal matrix]

The rule is invert the sqrt + multiply it by 2?

[safe fulcrum]

yes, $\frac{d}{dx} \sqrt{x} = \frac{1}{2 \sqrt{x}}$

[rocky lotus]

south

[safe fulcrum]

cause what does $\frac{1}{2} x^{-\frac{1}{2}}$ simplify to?

[rocky lotus]

south

[primal matrix]

It's complex yes

Ok ty, i close the doubt

.close

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[primal matrix]

.reopen

[vale dock]

✅ Original question: #help-4 message

[primal matrix]

Hi again, why the sqrt of 2 doesn't derivates?

[stark wedge]

what

[stone verge]

the sqrt of two is the coefficient of sqrt(x)

[primal matrix]

Why it's not like this

[primal matrix]

Ahh

Ok

[safe fulcrum]

you're forgetting the constant multiple rule

yeah, $\frac{d}{dx} (kf(x)) = k \frac{d}{dx} (f(x))$

[rocky lotus]

south

[safe fulcrum]

then k = sqrt2

[primal matrix]

I have not studied d/dx yet

I will continue studying, ty everyione!

.close

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[chrome pond]

how do you get the mark circled

[woeful trench]

If the examiner sees that you have a sum of the forms that you've circled, you would get that mark (so either exactly the LHS, or something "similar")

They'll also accept if you forget they mention there's no replacement (hence the "condone...")

Please don't advertise your server in here, and certainly not in the help channels

[chrome spruce]

Sorry

[chrome pond]

ah okay

thanks

.close

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[stone depot]

One message removed from a suspended account.

[stone depot]

One message removed from a suspended account.

[fierce vector]

draw an fbd?

[stone depot]

One message removed from a suspended account.

[fierce vector]

free body diagram

[stone depot]

One message removed from a suspended account.

[vale dock]

@stone depot Has your question been resolved?

[vale dock]

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[jolly sorrel]

I'm not sure if this is correct

Because when I plotted the functions and tbe tangent line it went through y1 at a point

But at (-1,2) they had a shared tangent line

I'm pretty sure my handwriting is readable

[untold oxide]

Hi, form what I see, you've done well. You should write what you've done in addition to the calculation itself.

[jolly sorrel]

Write what I did?

I dont follow

[untold oxide]

that is, first you've made sure both functions pass through the point (-1,2)

[jolly sorrel]

They do!

[untold oxide]

that's the top part of the page

I know they do, they do bc you've made sure of that, butyou need also to wrote it down, that's part of the answer

[jolly sorrel]

?!

I have to write even that

I forget😀

[untold oxide]

So, add it. It will make your text more readable.

[jolly sorrel]

Okay

Thanks

.close

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[leaden portal]

03 - (ITA SP/2007)
Determine the quantities of 3-digit numbers that can be formed with the digits 1, 2, 3, 4, 5, 6, and 7, satisfying the following conditions: repeated digits are allowed, except when the number starts with 0; and no digit can appear more than once (even if it is the first digit). Assign the result obtained.
a) 204
b) 206
c) 208
d) 210
e) 212

[leaden portal]

hey guys! i've solved this exercise in a way i can't understand the logic behind it

[ebon glade]

repeated digits are allowed
no digit can appear more than once

[dreamy scroll]

ye lol

I was thinking the same

[leaden portal]

the answer is correct

i just don't understand how

i missed something

its not subtraction under is multipication

2!.4!

[signal void]

hi @leaden portal i think this figure is not

it's not

okay

okay

[tawny moon]

so what exactly is your question?

[signal void]

i see

[leaden portal]

how is this working

[tawny moon]

first, you might want to address this

[leaden portal]

the transation is poor too, let me re write the question

it can repeat but only whit 7

[signal void]

in here, can rerwithe into 7!/(2! * 4!)*2+2

[leaden portal]

and only when the first digit is 1 or 2

[signal void]

r u ok?

[tawny moon]

at this point

!original please

[vale dock]

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.

[tawny moon]

it's ok even if it's not English

[leaden portal]

1 second

[signal void]

can u leave the this channel?

very busy

[dreamy scroll]

aggressive

[leaden portal]

no worries, hahah

gpt is having a hard time translating it

1 second

[tawny moon]

the original image will do.

[leaden portal]

03 - (ITA SP/2007)
Determine how many 3-digit numbers can be formed using 1, 2, 3, 4, 5, 6, and 7 that satisfy the following rule: The number cannot have repeated digits, except when it starts with 1 or 2, in which case 7 (and only 7) may appear more than once.
Mark the obtained result.

a) 204
b) 206
c) 208
d) 210
e) 212

[signal void]

we can rewrite into 7!/(2! * 4!)2+2
and then calculate the this:
7!/4! +2=7 * 65+2=210+2=212
r u ok? @leaden portal

[leaden portal]

i understand we can rewrite

but what is the logic behind it

why is this working

[signal void]

please "Add friend"
I can explain more detail

[leaden portal]

👀

[tawny moon]

oh nice, evader

[leaden portal]

it gets to the simpler equation later

i get this

[signal void]

evader? @tawny moon
u r evader

[leaden portal]

its like saying it gets to the answer

[signal void]

yeah

[leaden portal]

but how?

[turbid valve]

If you can explain it in a DM, you can explain it here.

[signal void]

okay @turbid valve

[leaden portal]

i used a repetition formula to solve an exercise that can't

[signal void]

what do u not understand?

[dreamy scroll]

jealousy ??

[signal void]

hoho

haha

hi @tawny moon
u r from japan? im japan

[leaden portal]

[!(N+(R-1))/N!.(R-N)!] . 2 + 2

[woeful trench]

You aren't slick, evading your timeout

[leaden portal]

hey guys, i really need help understanding this

[turbid valve]

There's possible mod evasion, i.e. there's precedent

[leaden portal]

😢

[turbid valve]

I've gotta go to work rl quick but very quickly: split it up into cases

One case where the number begins with 1

One where it begins 2

And one where it begins with any other number

[leaden portal]

177 and 277

this would lead to 7!/4! + 2

i get this

but why using a repetition formula on 2 brackets . 2 works?

[dreamy scroll]

[leaden portal]

i'm learnig this topic and it would help me understand

i've solved this one using a method i have not understand why is working

its not good

[hardy coral]

Is this an accurate translation?

[leaden portal]

yes

🙂

[hardy coral]

Ok, here's how I would do it

[leaden portal]

.

[hardy coral]

There is no digit 0, so no problem with the number starting with 0 and not actually being 3 digits

The "except" part only adds two cases: 177 and 277

[leaden portal]

yes! it would lead to 7!/4!

[hardy coral]

The rest is just: 7 choices for the first digit, 6 for the second, 5 for the third

So yes, 7!/4!

To that you can just add 2 for the special cases

[leaden portal]

but i did not solve this way

[hardy coral]

What did you use then

[leaden portal]

i get it that it is the easy way

[hardy coral]

You are missing a parenthesis but alright, this is the same as 7!/4! + 2

I don't quite know how you came up with it though

[leaden portal]

repetition formula on 2 spaces

[!(N+(R-1))/N!.(R-N)!]

how this formula found the answer is hounting me 🤣

[hardy coral]

That formula is incorrect, otherwise you wouldn't have a *2 at the end

[leaden portal]

2 is for the 2 lines

in the exam made sense

pure luck then

[hardy coral]

What 2 lines

[leaden portal]

to be fair i looked at the answers and saw that it was close to 200 something

and i multipyed by 2 to get closer thinking a got something wrong in the way

then added 2 of 277 and 177

at the alternatives

[hardy coral]

Without repetition: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ - with repetition: $\left(\binom{n}{k}\right) = \binom{n+k-1}{k} = \frac{(n+k-1)!}{k!(n-1)!}$

[rocky lotus]

Nel

[leaden portal]

i looked at the alternatives no]t answer

let me get this formula

its not these 2

nevermind

it was

well, i won't wast more of your time

thanks a lot

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[atomic mauve]

[atomic mauve]

[dreamy scroll]

uh huh

what now

[atomic mauve]

[midnight fractal]

@atomic mauve !help

[honest stone]

You opened a help channel.

Do you have a question?

[midnight fractal]

.help

[vale dock]

Commands:

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Type .help <command name> for more info on a command.

[midnight fractal]

.close

[wraith heart]

.close

[vale dock]

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[dreamy scroll]

oh you're a mod riemann

[honest stone]

no he has helpful perms

which means you can pin and use .close

[dreamy scroll]

how do i obtain these powers

https://tenor.com/view/i-need-it-spongebob-spongebob-squarepants-gif-4883506

[honest stone]

Being helpful.

also, why do you need it?

[dreamy scroll]

nothing particular

[honest stone]

yeah probably not.

[dreamy scroll]

aww come on

[honest stone]

[vale dock]

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[proper timber]

@everyone

[proper timber]

I need help

@everyone @everyone @everyone @everyone @everyone @everyone

@everyone

v

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone @everyone @everyone @everyone

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone

@everyone

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@everyone

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@everyone

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@everyone @everyone @everyone @everyone
@everyone

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@everyone @everyone

@everyone

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@everyone @everyone @everyone
@everyone

[sharp whale]

<@&268886789983436800> @proper timber

[glass kelp]

Can u not

[zealous pendant]

Who are they even pinging lol

[woeful trench]

Seems like they're gone

.close

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[glass kelp]

Deleted

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[noble raft]

Need help

[noble raft]

Here’s my failed attempt

<@&286206848099549185>

[zealous pendant]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[zealous pendant]

Oh nvm

Sorry I thought you’d just posted it

[noble raft]

it was 14mins cmon dawg

Failed attempt 2

At my wits end here

[ivory valley]

I think you can use anticommutative property and induce a minus, then it should cancel out, i think

[noble raft]

anticommutative property of cross product?

[ivory valley]

a x b = -(b x a)

[noble raft]

in which failed attempt should I do this

1 or 2

[ivory valley]

the one with the jeans

[noble raft]

okay I'll give that a go

dont disappear on me

then BAC-CAB again?

okay I tried that and wounded up with same answer

@ivory valley

[ivory valley]

yeah i realized

[noble raft]

Am I just cooked

[ivory valley]

let's not give up

[noble raft]

does the unit vector e_r have a derivative and I just have been doing it wrong

[ivory valley]

surely there is something small we overlooked

[noble raft]

idk I'm feeling like I coulda overlooked a lot of things, this is entirely new to me

[ivory valley]

yes

I think differentiating the relation $\bm{r} = r\hat{\bm{e}}_r$ and substituting the derivatives of $r$ might help

[noble raft]

So e_r as r(vector)/r

?

[ivory valley]

yea

[noble raft]

Wait I’m lost

What is the derivative of e_r wrt t

[ivory valley]

well, $\hat{\bm{e}}_r(t) \coloneqq \f{\bm{r}(t)}{r(t)}$

[noble raft]

Oh does quotient rule apply

[ivory valley]

ye

[noble raft]

Okay I’ll try this and get back

Nope still lost I fear

Having spent hours on this I’m giving up for today

If anyone has a solution I’d appreciate it smmm

Anyways thanks for the help

[ivory valley]

what did you get as derivatives

[noble raft]

I do not see this shit simplifying

There’s no m or k

In the derivative of e_r

[ivory valley]

it should be r dot dot x L

i misread

[noble raft]

Wait where

[ivory valley]

So we have $\dot{\bm{e}} = \f{1}{k}(\ddot{\bm{r}} \cross \bm{L}) - \dot{\hat{\bm{e}}}_r$

[ivory valley]

Now we would need Newton's law here

$m\ddot{\bm{r}} = \bm{F}$ and $\bm{F}(\bm{r}) = -\f{k}{r^2}\hat{\bm{e}}_r$ imply $\ddot{\bm{r}} = -\f{k}{m} \cdot \f{\hat{\bm{e}}_r}{r^2}$ \
and $\bm{L} \coloneqq m(\bm{r} \cross \dot{\bm{r}})$ from the textbook.

[ivory valley]

@noble raft

[ivory valley]

this should then work out

[vale dock]

@noble raft Has your question been resolved?

[ivory valley]

Look who disappeared now

[vale dock]

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[thick solar]

help

I dont quite understand

[cobalt crow]

interior angles of a triangle need to sum to wat

[thick solar]

can I just get the answer

[dusky bison]

!noans

[vale dock]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

@thick solar Has your question been resolved?

[vale dock]

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[orchid thistle]

what is simplest form of log5+logx-log4+logy

[orchid thistle]

I got log(5xy/4)

but got marked as wrong and saw that the answer was log(5x/4y)

[honest stone]

bingo.

[honest stone]

oh.

[proud kestrel]

is there parenthesis around the -

[honest stone]

that’s why parens are necessary.

[orchid thistle]

no

[honest stone]

maybe they changed it?

[orchid thistle]

no parenthesis

[eternal osprey]

The software is buggy. Ask your teacher

[proud kestrel]

then ur answer is right lol

[honest stone]

that’s their fault tbh. But we’re just gonna have to go with it.

[orchid thistle]

kk tyall i was doubting myself

ill ask again

[honest stone]

no problemo

[orchid thistle]

.close

[vale dock]

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[brazen cargo]

yo

[honest stone]

hi

[vale dock]

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[wild token]

Im struggling with 3a- we did an example but i didnt really understand it. Can someone walk me thru it

[eternal osprey]

I think you're supposed to do dimensional analysis here

[wild token]

Heres the thing

I learnt two ways of doing it

one in my physics module and then one in my mathematical modelling module( thats where the q is from)

the mathematical modelling module uses a technique im not comfortable w thats why i wanted osmoene to maybe explain to me

i can send an example q if thats helpful

from the lecture notes

[eternal osprey]

Should be the same, right? It boils down to solving linear system.

[wild token]

This is the method used in my physics module-then id find alpha beta and gamma then yeah

this isthe method used in my mathematical modelling module

[eternal osprey]

I think much of the complexity of the mathematical modelling module is that we don't assume ũ to be linear.

[wild token]

I see

I get confused by the division part

It’s just idk

He didn’t really explain it properly

Like here

[eternal osprey]

You mean the $A = [p_0]$ part, or $\tilde{p}=\frac{p}{p_0}$ part?

[rocky lotus]

Xwtek

[wild token]

Yeah

Idk why they done it

And it actually means

And why they r dividing p by p0

Idk😭 man

[eternal osprey]

I think that so they have a dimensionless variable $\tilde{p}$?

[rocky lotus]

Xwtek

[wild token]

Hmm

[wild token]

Hmm so for this would I define some variable H^ and say it’s like H/L?

[eternal osprey]

$\frac{h}{h_0}$ by convention.

[rocky lotus]

Xwtek

[wild token]

So what happens to the dimension L or do we let L=h0

[vale dock]

@wild token Has your question been resolved?

[eternal osprey]

Well, you can look at the dimension of $\sigma$, $\rho$ and $g$

[rocky lotus]

Xwtek

[vale dock]

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