help-0

[frail rivet]

ive been on this problem for more than 6 hours i think

only for you to tell me that the question text is wrong or what xD

[lime bobcat]

Hahaha

Yes, the continuously differentiable part is clearly wrong and I think the interval too

I'm thinking on what happens with C^1(-1,1)...

[frail rivet]

you can check my conversation with scapeprof in help-1 maybe that will help you?

[lime bobcat]

I read it, it doesn't say anything new

[frail rivet]

can i maybe

I think C^1 includes continuous doesnt it?

[lime bobcat]

Yes

continously differentiable implies differentiable implies continuous

[frail rivet]

Ok then that problem is solved

[lime bobcat]

C1(-1,1) is not even a normed space with the norm of the supremum

One can define functions which are not bounded so the norm would be infinite

So C¹(-1,1) with the sup norm simply does not makes sense so that's definitely a second mistake of the question text

[frail rivet]

wait but ||.|| is a norm on C^1

[lime bobcat]

only when the set is compact

[frail rivet]

thats what i needed to prove for the first one

that ||.|| is a norm on C1( (-1,1) )

[lime bobcat]

Can norms be infinte?

[frail rivet]

umm

[lime bobcat]

(no)

[frail rivet]

xD

i dont know what u meant by that question

[lime bobcat]

Take a normed vector space and v in it

Could be |v|∞

[frail rivet]

honestly ive never thought about it

oh because of the triangle inequality?

[lime bobcat]

No, norms are by detiniton nonnegative real-valued functions

[frail rivet]

nvm

[lime bobcat]

So the sup norm is not a norm for C¹(-1,1)

Consider a C¹(0,1) for simplicity and f(x)=1/x in (0,1)

$\not\exists\sup_{x\in (0,1)} f(x)$

[ocean seal]

jnkena

[lime bobcat]

(or it is infinite)

$f$ is unbounded because $\lim_{x\rightarrow 0^+} \frac{1}{x}=+\infty$

[ocean seal]

jnkena

[lime bobcat]

There does not exist norm for the function f...

So it is not a normed space...

C¹(-1,1) is NOT a normed space
C¹[-1,1] is a non-complete normed space

[frail rivet]

ok

so my proof for C¹(-1,1) is also wrong

although when proving the 3 properties everything seemed correct

[lime bobcat]

You didn't prove that it is $||\cdot ||: C^1(-1,1)\longrightarrow\mathbb{R}$

[ocean seal]

jnkena

[frail rivet]

that was the first question, the one with the banach space is the second

[lime bobcat]

A norm is a map like that which satisfies three properties. (But being a map like that is crucial).

What I trying to say is that you didn't take care that the final set of the norm must be R.

And proving that is crucial for being a norm is the "fourth property" one must prove

1. All objects have norm and the norm is a real number
2. norm is positive defined
3. norm is homogeneus
4. triangular inequality

[frail rivet]

ok i see now

because thats something thats usually true

so we dont prove it?

[lime bobcat]

Yes, but with an open interval (-1,1) continues functions are free to be unbounded (not with compact intervals) and that makes supremum infinite (or doesn't exist)

[lime bobcat]

Yes, I know. But it kinda matters a lot as you see

[frail rivet]

ok...

im so done

[lime bobcat]

:(

You seem to understand everything

Don't lose hope

[frail rivet]

no xD i wasted 7 hours on this

[lime bobcat]

Did you learn?

[frail rivet]

NO

[lime bobcat]

No?mm

Why?

[frail rivet]

ok a little bit

[lime bobcat]

You solved all your doubts, didn't you?

[frail rivet]

hmm

so tomorrow I'll tell my prof that this question is wrong

[lime bobcat]

Yes

And you tell me

[frail rivet]

ok but i need a good reasoning

[lime bobcat]

I gave you...

already...

[frail rivet]

I know

because the interval is open instead of closed

[lime bobcat]

Yes, and one can easily give counterexamples consisting on unbounded continuously differentiable functions for which there is not norm

[frail rivet]

because the supremum of open intervals is infinity

no thats wrong

[lime bobcat]

No, we're not calcuating supremum of intervals

We calculate supremum of functions defined on intervals

[frail rivet]

oh yes with the 1/x example

ok thank u i will ask him tomorrow (5 hours lol)

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[little dagger]

$1 + 1 = 2$

[ocean seal]

megacobblepot83

$1 + 1 = 2$

[remote heron]

#latex-testing

[little dagger]

By proving C^1(5.6,2)
Consider that [(C^1)-1] for 2 = 5
and simplify the current functionated inequality:

$\not\exists\sto_{d/dx\in (1.5,\mathbb{Z})} * f(x)^2$

But what if $\frac{d}{dx}$ was an inequality for $f(x)^2$ ?

[ocean seal]

megacobblepot83

megacobblepot83
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[little dagger]

Or an equality for $(1.5,\mathbb{Z})$ ?

[ocean seal]

megacobblepot83

[little dagger]

So if d/dx was an equality for (1.5,Z), then

$\not\exists\frac{d}{dx} = (1.5*f(x))^\mathbb{Z}$

[ocean seal]

megacobblepot83

[little dagger]

.close

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[maiden compass]

I haven't really tried anything, I just don't understand the question that good

[median dirge]

Hi!

[raven rover]

Throughout the journey, try to describe how far away the boy is from point A as a function of time

[terse thunder]

i suggest making a diagram

[median dirge]

You can make a little graphical representation

[median dirge]

Exactly.

[maiden compass]

ok

[maiden compass]

why did you times 4.5 by 60 tho

is that the distance

oh yea it is

so it would be option E

the boy runs at the same speed backwards

so you minus 270 from 4.5t

t is the seconds

alr bye

.close

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[drifting swallow]

how do I do this?

[drifting swallow]

was thinking that I could use special triangles rules but the answer says that it won't work

that is the answer btw

[terse thunder]

what have you tried so far?

[drifting swallow]

So I thought I could have side lengths of 23, 23, and 23 sqrt 2

and then I also tried 23 sqrt 2 +3

20 sqrt 2 + 3 but that's about

[terse thunder]

try drawing a diagram

[drifting swallow]

ok

[drifting swallow]

here's what I'm at now

23 radius

[terse thunder]

are you sure thats 225 degrees counter clockwise?

remember you start at the bottom

[drifting swallow]

ohhh

wait mb

[drifting swallow]

so here's where I'm at now

[terse thunder]

alright

[drifting swallow]

Not sure what to do next though

[terse thunder]

well we can find the height of the triangle

[drifting swallow]

the neight of the triangle is 23

[terse thunder]

the hypotenuse is 23

but we have to use special triangles to find its height

[drifting swallow]

so should I do 23 = a^2 + b^2 ?

[terse thunder]

its a 45 45 90 triangle

so the hypotenuse is always sqrt2 * leg

basically 23^2 = 2a^2
23=sqrt(2) * a

[drifting swallow]

so the leg is 23

the height is also 23

[terse thunder]

its not the same

https://cdn.discordapp.com/attachments/868674292446027808/981380924627361822/IMG_4178.png

[drifting swallow]

ohh I was thinking of it wrong

so it's 16.26

[terse thunder]

yes

now just add the height of everything below it

[drifting swallow]

ok ty

[terse thunder]

np

[drifting swallow]

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[little dagger]

$x$

[ocean seal]

megacobblepot83

[little dagger]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[little dagger]

$y$

[ocean seal]

megacobblepot83

[little dagger]

I just CAN'T make it.

.close

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[proud crystal]

Maria bought 5 yards of 36-inch wide materail for $7.80 a yard and 2.5 a yard. How much did she play altogether for the material ?

[proud crystal]

How can I figure this out?

What steps can I take to solve it?

[lone heart]

@proud crystal Has your question been resolved?

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@proud crystal Has your question been resolved?

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[ebon fog]

When using the Algebraic method Is there a general rule for what order to use the laws/rules when simplifying.
like a Checklist?

[wary stream]

Not really, you just know what identity to use

[ebon fog]

So you look at the expression that matches with a specific rule.

[wary stream]

Yeah, and with practice. Like the first step, you can easily see that it's distributive law

[ebon fog]

cheers - Just more practise, thanks for the tips .

[wary stream]

.close
If you are done with the channel

[ebon fog]

.close

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[supple crater]

Can anyone help me with this, step by step? How do I solve it? It’s so confusing.

[median oar]

k(x-2)+m - (k(x+1) + m) = -12
k(x-2-x-1) = -12
-3k = -12
k = 4

f(m) = 4(m) + m = 35
5m = 35
m = 7

f(x) = 4x+7

f(x-2) = 4(x-2) + 7
f(x+1) = 4(x+1) + 7
f(x-2) - f(x+1) = 4(x-2) + 7 - 4(x+1) - 7
= -8 - 4 = -12
f(7) = 4(7) + 7 = 35

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[weak fossil]

how would i describe this transformation

[lone heart]

@weak fossil Has your question been resolved?

[weak fossil]

<@&286206848099549185>

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@weak fossil Has your question been resolved?

[fluid eagle]

uwurotate

[weak fossil]

its the last thing i need to be done with this then i can go to sleep 😭

[fluid eagle]

hint: clear the 2x+4 to a constant so you can apply your known transformations

[stone glen]

@weak fossil

@median oar should i close this?

[median oar]

i tink only the person who asked can close it?

[stone glen]

It's been an hour since he last typed

[median oar]

it'll auto close soon then

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@weak fossil Has your question been resolved?

[lone heart]

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[edgy cape]

for question c, using the S= x_0 + vt equation. Why is t=3 used?

[vale wigeon]

how much time passes between 12:00 and 15:00?

[undone spire]

3

[edgy cape]

o i thought it was 1200 hours

[vale wigeon]

question was addressed to OP, not to you.

[vale wigeon]

in the military you do say ONE TWO HUNDRED HOURS

and 15:00 is ONE FIFE HUNDRED HOURS

[edgy cape]

alright, makes sense

[vale wigeon]

but anyway yeah three hours pass from 12:00 to 15:00

[edgy cape]

i'm just supposed to assume that when the velcoity is in km/h the time will be in 24 hours format?

[vale wigeon]

i don't think those two things are related

they could've just as easily said "12 pm" and "3 pm"

in fairness the would have done better to put colons, so 12:00 not 1200 and 15:00 not 1500

[edgy cape]

alrightey, thanks for your help

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[steel hare]

can someone help me with this

[steel hare]

rip no latex

0.5987 is my answer for 3(a)

[lone heart]

@steel hare Has your question been resolved?

[noble sinew]

where does probability 0.5987 come from?

you want P(X<=0), where X ~ N(-0.02, 0.08)

[steel hare]

standard table

[noble sinew]

its wrong

[steel hare]

hmm

[noble sinew]

so read correctly on your table (or use any software, its 2022 not 1970)

[steel hare]

@noble sinew is 0.25 is correct?

[noble sinew]

if you mean converting to z-score, no

recheck formula

[steel hare]

@noble sinew can specify a little details which part where I do wrong

my mean and variance is correct right?

[noble sinew]

You aren’t dividing by variance

When computing z-score

Which you would see if you checked formula

[steel hare]

ohh I need to do a square root right

does the sample size is 10?

wait nvm

@noble sinew is this correct?

@noble sinew my final answer is 0.4721

[primal lintel]

the help of ai, could be wrong but maybe it helps

[steel hare]

oh my

[primal lintel]

The probability that the mean peg fit into the mean hole is P(mean peg fit) = (1.1 cm) / (10 pegs) = 0.8

The probability that the holes into which they are fit have diameters which are normally distributed with mean of 1.12 cm and variance 0.05cm is P(holes) = (1.12 cm) / (10 pegs) = 0.5

[steel hare]

the question are from google?

[primal lintel]

no, artificial intelligence figures it out

[steel hare]

damn

[noble sinew]

Why are you subtracting it from 1?

And have you used what it said? It says mean peg fits into mean hole

So you need distribution of mean peg and distribution of mean hole

[lone heart]

@steel hare Has your question been resolved?

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[dense scaffold]

When do we use mod inside log?

Why is x in mod and not v square + 1

[median dirge]

Hi.

Logarithmic functions dont take negative values

So

log x is defined only if x is positive

In the place of log v^2 + 1

The square on v already turns the number positive

[dense scaffold]

Oh ok

Makes sense thank you

.close

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[chrome shore]

what do i do here?,

[chrome shore]

Do i separate tan x first,

And then substitute sec3 x

[stone glen]

@chrome shore ur in the wrong path , it's simpler than u think

Look at it carefully for 3 more minutes and u might get it

Ping me if need halp

[chrome shore]

Nvm I got it

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[prime ice]

Could someone pls explain to me the process of using the points to determine the equation

[median oar]

ok so you know the roots

so the equation is in some form easily written at y = a(x-b)(x-c)

now you know that -2 and 3 are roots so (x+2) and (x-3)

when x = 0, y = -12 (given) so -12 = a((0)+2)((0)-3)

-12 = -6a, a = 2

then expand and complete the square

[prime ice]

I’m abit confused

[median oar]

this is the most straight forward way, but if u are smarter u can look at the completing the square form to get it easier-ly

[median oar]

which line

[prime ice]

Like how do I substitute it in

So I have 2 x coordinates

And the turning point

[median oar]

you dont have just any 2 x coordinates

you have the roots

[prime ice]

What can I do with the roots?

[median oar]

you can write the equation in the form y = a(x-b)(x-c)

the smart way of doing this requires knowing what the completed square form means

[prime ice]

So after I determine a

Then do I put it back into my equation?

The -12=a(0+2)(0-3)

[median oar]

so u find what a is

[prime ice]

Yeah I got a

[median oar]

ok now write the full thing in this form y = a(x-b)(x-c) without a b and c

[prime ice]

I’m confused again

[median oar]

do you recognise that y = a(x-b)(x-c) is a quadratic

[prime ice]

Yes

[median oar]

do you know what a b c are

[prime ice]

Nope

[median oar]

are you sure?

[prime ice]

Not really

[median oar]

the line i just replied to

you have b and c solved there

what about a

[median oar]

you said you found a here

[prime ice]

B is 2 and c is -3 ?

[median oar]

yes

[prime ice]

Ok yeah I got that

And then a is 2

[median oar]

and what is a

right

ok now write the full thing in this form y = a(x-b)(x-c) without a b and c

[prime ice]

What do I do from here?

[median oar]

a, b and c are the keys to what your quadratic equation is gonna be

[prime ice]

I have a question

[median oar]

so it should be y = 2(x+2)(x-3)

[prime ice]

Yeah I have that

No do I just solve?

[median oar]

why are you solving

[prime ice]

Wait is this the equation?

[median oar]

your objective (what the question is asking) is to find an equation

you are not trying to solve anything

[prime ice]

Ah I see

[median oar]

and there's your equation

[prime ice]

And then if I write it in the other form

Can I give it a try ?

[median oar]

of course yes

after that i can teach you a cool trick to jump straight to part 2 from part a

(if u want)

[stone glen]

@median oar bruh i have just spent hours solving numerous doubts of people idk what I'm doing w

[prime ice]

Is it like that or am I missing something

[median oar]

i dont know let me solve it

[prime ice]

Actually no

I made a mistake I’m

Redoing it

I keep making mistakes 😞

Atleast I’m noticing them

[median oar]

oh i just realised the cool way relies on something you probably havent learned yet so it doesn't matter just ignore that

[prime ice]

I pray this is right

This final answer

[median oar]

yep

[prime ice]

Thanksssss

Helped soo much

I got a couple of other questions

They not functions related though

[median oar]

i should be able to help still

[prime ice]

They ask for which values of x for which f(x) is defined

[median oar]

ok

what rules do you know about dividing

[prime ice]

Dividing?

[median oar]

yeah

[prime ice]

Not sure what that means

[median oar]

there's like 1 rule to dividing

you can't divide by 0

[prime ice]

Yeah I know that

[median oar]

so you see your f(x)

there's a divide

[prime ice]

Yeah I see

[median oar]

so that function is gonna run into problems if u try to divide by 0

aka if the bottom is 0, it wont work

[prime ice]

Yeah I understand that

[median oar]

so you solve for when the bottom is 0

solve for x^2+10x+25 = 0

and say those x values are no good

because the makes the bottom 0

therefore the function doesn't work at those x values

[prime ice]

Ah I see

[median oar]

now SOMETIMES if u factor the top and bottom they can cancel out

you can do that

so say i have (x-3)/[(x-3)(x-4)]

that is the same as saying 1/(x-4)

so you dont have to worry about x=3 here

[prime ice]

Yeah cause x-3 cancel I get that

[median oar]

but you do have to worry that x=4 causes problem

and the problem is that the bottom = 0

[prime ice]

Ok

[median oar]

(x+5)^2 is what the bottom factors into

by inspection XD

[prime ice]

Isn’t it

X-5)^2

[median oar]

it's x^2 + 10x + 25

not -

[prime ice]

Ah I see

[median oar]

if u had (x-5)^2 it'd factor out to -10x

[prime ice]

My calculator idk what it’s doing

[median oar]

you dont need a calculator here

you look at 25, what's the first 2 numbers that come to mind that multiply to 25

[prime ice]

Yeah I know

I just make sure 😂

Not confident in myself at all

[median oar]

gotta drill these basic arithmetic so you can do these fast

and you dont waste time in exams

doubting yourself

[prime ice]

Yeah true

So if I factor it

[median oar]

do u need to graph this?

[prime ice]

What I do after

No

[median oar]

now that you've factored it to (x+5)^2

[prime ice]

They just ask for what values of x for which f(x) defined

[median oar]

you know the bottom can't be 0 cos u cant divide by 0

right?

[prime ice]

Yes it will give a maths error

U defined

Un *

[median oar]

so that means (x+5)^2 cant be 0

there's some x that makes it 0

and that x cant be used

so you solve (x+5)^2 = 0

and whatever u get for x you throw it out

[prime ice]

X=-5

[median oar]

right

so when x = -5, the function breaks

so x can be everything except for -5

[prime ice]

Soo anything that above 5

How would I write all this down

Xer x never equals five?

-5

[median oar]

{x ∈ ℝ : x ≠ -5}

[prime ice]

Ah I see

Do I have to show any calculation?

Like

[median oar]

depends on how many points the question is

[prime ice]

Wait let me write stuff down

Idk they never indicate

[median oar]

they should on the exam

[prime ice]

Yeah

[median oar]

tell you how many points this question is worth

by that you will know how much to show

[prime ice]

In the exams they do these activities they don’t

I think maybe 3 or 4

[median oar]

if it's 1 point then by inspection is good enough

if it's 2 points or above i'd show saying that the denominator cant equal 0

then factorise the denominator and solve it equalling 0

then say x cant equal this, so therefore the domain is ...

[prime ice]

Like this?

It’s not sending

Oh there we go

[median oar]

i would show (x+5)^2 = 0

then x = -5

[prime ice]

Oh ok I’ll rmeber that thanks

[median oar]

also the real number set has a double line on the R

[prime ice]

Oh

[median oar]

ℝ

[prime ice]

Yeah I don’t wanna lose marks for silly stuff like that

[median oar]

you could write "reals"

[prime ice]

Yeah I think ima familiarises myself with that

Mind if I bother u alittle more?

A couple of concepts I’m not too sure of

[median oar]

i dont mind if i dont answer someone else will anyway

just ask away

[prime ice]

Thankssss

[prime ice]

What is the last one?

[median oar]

all complex numbers

[prime ice]

Ah thanks

[prime ice]

So they give this

[median oar]

have u learned calculus yet

[prime ice]

No

[median oar]

would've been super fast to do that with calculus

but that's okay, there's ways without using calculus too

do you know how to do 1.3.1?

[prime ice]

No

I’m confused I’m not familiar with what they trying to represent

First thing that came to mind is the lxw for area

[median oar]

perimeter = 4x+2y = 280
area = 2x * y

that's the information they've given you right?

[prime ice]

Yeah

[median oar]

now you want to show area = 280x - 4x^2

[prime ice]

All the sides add to 280

[median oar]

so first get rid of the y

from 4x + 2y = 280 u can write y in terms of x

so 2y = 280 - 4x
then y = 140 - 2x

[prime ice]

Yeah I see that

[median oar]

now substitute this into the other equation to show the question

area = 2x * y

where y = 140 - 2x

so area = 2x * (140 - 2x)
so area = 280x - 4x^2

[prime ice]

I’m lost

[median oar]

which line

[prime ice]

After the y=140 -2x

[median oar]

ok if the length is 2x and width is y

the area of the rectangle is 2x * y

[prime ice]

Yeah

[median oar]

from the perimeter we found y in terms of x

[prime ice]

Yeah

[median oar]

which is y = 140 - 2x

[prime ice]

Yeah

[median oar]

so with area = 2x * y

we sub in y = 140 - 2x

[prime ice]

Oh I see

[median oar]

now it's area = 2x * (140 - 2x)

[median oar]

and thus u show area = 280x - 4x^2

that's 1.3.1

[prime ice]

I see itttt

Thanks soo much

For 1.3.2

[median oar]

do you know how to graph parabolas?

[prime ice]

Yes

[median oar]

can u graph 280x - 4x^2 = y

i just want to know if u know what the general shape of it will look like

[prime ice]

That would be

Like a

Up side down

[median oar]

what can u tell me about this curve without calculating any numbers

[prime ice]

Smile face

That’s what my teacher would say I think

Like it looks like an up side down smiley face

[median oar]

so it's upside down and has a root at 0, 0

that's what i can tell

[prime ice]

I don’t get the root stuff

[median oar]

well, it's 280x - 4x^2

u can factor x out

so if x = 0, then y = 0

[prime ice]

Is that cause there’s no constant?

[median oar]

yep

[prime ice]

Ok I understand

[median oar]

anyway that's not important for now all im saying is that that's what i see

upside down, root at 0, 0

[prime ice]

Ah I see

[median oar]

so we know that right side up parabolas have a minimum

[prime ice]

So that’s the turning point?

[median oar]

and upside down parabolas have a maximum

[prime ice]

Yeah

[median oar]

no, roots are where it crosses the x axis

[prime ice]

Ah i see

We don’t call it roots here

[median oar]

that's why y=0 is important

[prime ice]

Call them intercepts

[median oar]

you will call them roots later

[prime ice]

Never had them referred to as roots before

[median oar]

for all intents and purposes they are roots of the polynomial

[prime ice]

I see

[median oar]

so since it's upside down

it has a maximum

we need to find where this point is

[prime ice]

Do we make y=0?

[median oar]

we need to find the point (x, y) of this "turning point"

because y is our area

and we will find the maximum area this way

[prime ice]

So

-b/2a?

[median oar]

could be im not sure

are u sure it's minus

[prime ice]

Yeah

[median oar]

ok

[prime ice]

I’m not sure

What I’m doing

But

[median oar]

clearly it cant be -b/2a

[prime ice]

I’m soo confused

[median oar]

can x be negative

[prime ice]

No

[median oar]

so your formula was wrong

it's not -b/2a, it's b/2a

well maybe it's not wrong

actually i think u messed up

[median oar]

why is the top - (-280)

shouldn't it just be -b which is -280

[prime ice]

Ah I see idk why I put -

[median oar]

ok so it is -b/2a you were right

[prime ice]

Yeah x=35

[median oar]

so when x = 35

what is y

y is the area

[prime ice]

Can we do that?

[median oar]

that is exactly what you should do

[prime ice]

So will final answer be 4900m^2

[median oar]

yep

[prime ice]

U should be my teacher

…..

[median oar]

i dont think im good enough to be a tutor lol

i've considered it before but i dont htink my grades were good enough to get students

[prime ice]

Oh

Well your helping me a lot

I have one final question

Or maybe 2 but I think the last one I can figure out

[median oar]

this is pretty simple

[prime ice]

Not sure what they want me to do here

[median oar]

√(a*b) = √a * √b

you know this right?

[prime ice]

No

[median oar]

wait what

[prime ice]

Those are surf laws right?

My bad 😞 I have

[median oar]

(ab)^n = a^n * b^n

n = -1 in this case

[prime ice]

Surd*

[median oar]

ok

now start breaking up 108 and 18

108 is 2 * 54

which is 2 * 2 * 27

[prime ice]

Wait

I’m lost

Completely

[prime ice]

Form here

[median oar]

ok

i mean n = 1/2

[prime ice]

How do we know this?

[median oar]

know what

[median oar]

this?

[prime ice]

Yeah

How do we know n=1/2

[median oar]

well a^(1/2) is the same as √a

that's what √ means

[prime ice]

Oh

Yeah my bad

Forgot about that

[median oar]

all good

so √108 is just 108^(1/2)

[prime ice]

And 18^1/2

[median oar]

yes

108^(1/2) is just (2*54)^(1/2)

[prime ice]

Yeah I see that

[median oar]

which is just (2 * 2 * 27)^(1/2)

which is just (2 * 2 * 3 * 9)^(1/2)

which is just (2 * 2 * 3 * 3 * 3)^(1/2)

which is just 2^(1/2) * 2^(1/2) * 3^(1/2) * 3^(1/2) * 3^(1/2)

and we know a = 2^(1/2)

[prime ice]

Yeah

[median oar]

and b = 3^(1/2)

so 108^(1/2) is just a * a * b * b * b

which is a^2 * b^3

now do that for √18

[prime ice]

Did I write it properly?

[median oar]

uh

dont skip steps

start from the 2nd last line

[prime ice]

Meaning?

[median oar]

from (2 * 3 * 3)^(1/2)

what did i do next

[median oar]

this is where u are up to

[median oar]

you're still skipping steps

[median oar]

this line

where did it go

[prime ice]

Oh

So it’s

a x b x b

[median oar]

which is...?

[prime ice]

a^1 and b^2

Not 3

[median oar]

that's right

[prime ice]

Can I redo 108

Just for practice

[median oar]

of course

[median oar]

yep

[prime ice]

Yay

Thanks I understand it now

[median oar]

hopefully you can see in your head

108 -> a becomes 54

1 more a becomes 27

so a^2

then 27 is 3^3 so b^3

then u get a^2 * b^3 without writing it all down

[prime ice]

Yeah

Can you help with a number patterns question?

[median oar]

sure

[prime ice]

Can I try and do the table

And then work from there

I tried earlier but ended up mixing up myself again

[median oar]

is that all there is to the question

are there no other parts?

[prime ice]

Ok yeah that makes sense

[median oar]

lmao

ok that is a lot easier

haha

[prime ice]

💀 I feel soo dumb rn 😂

I was tryna do it without that

😆

[median oar]

i mean i can kinda tell

from 4 blank 36 blank 144

that's 2^2, blank, 6^2, blank, 12^2

so it's some sort of growing pattern by 4

1 9 49 is also 1^2, 3^2, 7^2

but the figure makes it a lot easier, maybe you can figure it out

[prime ice]

Yeah I’m out i#

Made it that far

[median oar]

did you fill in the thing

[prime ice]

What thing?

[median oar]

the table

[prime ice]

Yeah the I couldn’t finish it though

[median oar]

ok 1 2 3 4 do you see a pattern

[prime ice]

Yeah

[median oar]

the sequence is 1 2 3 4

what is the next number

[prime ice]

5?

[median oar]

uh huh

[prime ice]

But then it’s 11

[median oar]

it's skipping

to 11

[prime ice]

Yeah

[median oar]

becuase you cant draw 11

and u cant count it

they want you to find the equation

so that u know what 11's numbers look like

ie how many shaded, how many white tiles, and how many total tiles when n = 11

[prime ice]

I’m not sure

[median oar]

yes that's what the pattern recognition is about

dont worry about 11 for now

so it's 1 2 3 4 then 5

now 4 16 36 64 144 what's special about these numbers

[prime ice]

They square numbers

Oh cube

[median oar]

who's square numbers

write them out

what squared are they

[prime ice]

4

I see it

[median oar]

what do you see

[prime ice]

Nvm I’m confused again

I though 4^figure number

[median oar]

what is 4

[prime ice]

But that didn’t work

[prime ice]

2^2

[median oar]

what is 16

[prime ice]

4^2

[median oar]

what is 36

[prime ice]

Not sure

…

[median oar]

is it a square number?

[prime ice]

Yeah it is

[median oar]

what squared is 36?

[prime ice]

6

[median oar]

what is 64

[prime ice]

8

8^2

[median oar]

ok do you see a pattern yet

[prime ice]

Yeah

[median oar]

what is the pattern

[prime ice]

Plus 2

Actually

Idek 😭

I know 12^2 will give 144

[median oar]

be confident, what do you think it is

what is the rule

it's fine if you're wrong you can find out why it is wrong

[prime ice]

I honestly have no idea

[median oar]

ok what is the first main thing u recognise from 4 16 36 64 144

[prime ice]

They all square numbers

[median oar]

how do you represent that in math

[prime ice]

X^2

I think

[median oar]

ok

now is there anything special about the x

[prime ice]

+2

Each time

Ah I see

[median oar]

ok what does that mean

in math

what does +2 mean in math

[prime ice]

(X+2)^2

[prime ice]

Increasing

[median oar]

if i have a sequence

0, 3, 6, 9, 12, 15, ...

[prime ice]

+3

[median oar]

how would you express that in math

[prime ice]

3n-3

[median oar]

ok

now what about the numbers 4 16 36 64

you first realise they are something squared

so it's 2^2, 4^2, 6^2, 8^2

[prime ice]

Yeah

[median oar]

so how do you express that sequence in math

rather than just saying +2

[prime ice]

Not sure

[median oar]

remember how you got here

[prime ice]

n+2

[median oar]

so when n = 0, n+2 = 2

n = 1, n+2 = 3

n = 2, n+2=4

that's not 2, 4, 6, 8

we are trying to get 2^2, 4^2, 6^2, 8^2 into a sequence

we know that the ^2 part doesn't change

the part the changes is the base, 2, 4, 6, 8

what's the pattern here

[median oar]

similar to this one

[prime ice]

+2

2n

[median oar]

right 2n

[prime ice]

2n)^2

[median oar]

right

ok so if (2n)^2 = 144

what is n

[prime ice]

6

Yayyy

[median oar]

so is it 1 2 3 4 5

or 1 2 3 4 6

[prime ice]

12346

[median oar]

ok so we had our original assumption that it's 1 2 3 4 5

but it doesn't fit the next row, so now we update the rule and it's now a 6 instead

[prime ice]

Yeah

I can work out the second line for 11 now too

[median oar]

ok so the next row is 1 9 25 49

you need to work it out for 6 as well

[prime ice]

Yeah

So wait

For 11

2(11)^2

And that’s 242

[median oar]

is it (2n)^2 or 2n^2

[prime ice]

2n)

So 484

[median oar]

uh huh

[prime ice]

Wait

I’m not sure now

[median oar]

which part

[prime ice]

2n^2

[median oar]

2n^2 or (2n)^2

[prime ice]

The second one

[median oar]

what are you unsure about

[prime ice]

It is the second one right?

[median oar]

is it? you tell me

[prime ice]

Yeah it is

So 484

[median oar]

uh huh

so row 2 is done

what about row 3

1 9 25 49

what's special about them

[prime ice]

Cube

[median oar]

what cubed?

[prime ice]

No I mean squared

And they the numbers we didn’t use

[median oar]

so what squared

[prime ice]

Previously

1 squared

3 squared

5 squared

[median oar]

ok so what's special about that

[prime ice]

+2

[median oar]

how do you express that in math

[prime ice]

2n

[median oar]

2n is what u had before

2 4 6 8 is 2n

[median oar]

think back to this

0 3 6 9 12 15 -> 3n - 3
1 3 5 7 -> ?

[prime ice]

2n -1

2n-1)^2

[median oar]

okay

so if n = 6, what should be on the 3rd row?

[prime ice]

121

[median oar]

how did you get 121

[prime ice]

(2x6-1)^2

[median oar]

right, that's good

now what about n = 11

[prime ice]

441

[median oar]

and what about the last row

[prime ice]

Add them for now and then determine an equation next question

[median oar]

ok so add them together

[prime ice]

Is that fine?

[median oar]

looks good

so what should the equation look like

for the addition bit

[prime ice]

Is this fine?

[median oar]

what

what's the rule for row 2

[prime ice]

2n^2

Would the total numbers just be

2n^2 +(2n-1)^2

Yeah I think it works

[lone heart]

@prime ice Has your question been resolved?

[median oar]

yeah that's right sorry i had something to do

[prime ice]

Thanks bro

I think ima call it a night

Thanks soo much for ur time

Honestly means soo much

.close

[lone heart]

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[shy breach]

Hi guys, can someone help me to solve?it's about curve length. Thank you <@&286206848099549185>

[lone heart]

Please don't occupy multiple help channels.

[alpine sable]

are you familiar with how curve lengths are calculated?

[lone heart]

@shy breach Has your question been resolved?

[shy breach]

No, I'm not

[alpine sable]

you use integrals to calculate them right?

To calculate the length of a parametric curve you use this formula

you have x and y, so just calculate their derivates, plug them into the formula and solve the integral

[lone heart]

@shy breach Has your question been resolved?

[shy breach]

yes, u're right

[lone heart]

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[north scaffold]

please check my expansion in terms of sintheta

[north scaffold]

expansion of sin6theta in terms of sin^n

Open original + zoom for better vision

[lone heart]

@north scaffold Has your question been resolved?

[lone heart]

@north scaffold Has your question been resolved?

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[woven oak]

X-Y-Z is random coords,
Trying to figure out mathmatically what's the best way to predict X-Y-Z
Currently have, (0, math.sqrt((from.x - to.x) ^ 2 + (from.z - to.z) ^ 2) - 10)

[tacit arch]

What do you mean "predict"

And what do you mean X-Y-Z? that's a minus symbol

[woven oak]

X y z are random coords depending on 2 factors impossible to calculate right now

XYZ are coordinates of a monitor

math.sqrt = square root of (x)
(x) = ((from.x - to.x) ^ 2 + (from.z - to.z) ^ 2) - 10

Is there any other way to mathmatically calculate on a more accurate scale?

[weary wyvern]

do X, Y, Z have some kind of probability distribution?

[tacit arch]

Are they 2 dimensional each?

like X = (1,2), Y = (3,4), Z = (5,6)

[tacit arch]

Also what does from.x, to.x mean?

you said you don't have the coordinates

[woven oak]

Picture there is a random hole in your computer monitor that can randomly appear, A black one and a red one, So unknown X Y Z right now untill it is visable to your eyes,

From.x (red hole)
To.x (black hole)

Mathmatically it is random, This calculation has about a 80% success rate on being correct, I want 99%

[tacit arch]

Are X,Y,Z each numbers or a pair of coordinates like i said above?

[woven oak]

A pair

[tacit arch]

Again, what does from.x measure

[woven oak]

The first from X is me, The to x is to you
We're on random places on the map

From me (black dot) to.x (red dot) you

[tacit arch]

So you know the coordinates of two people

and you know their distances to X

[woven oak]

Pretty much yes,

I know theres and mine, But not currently if that makes sense?

[tacit arch]

no it doesn't make sense

Call A = Person 1 coordinates

B = Person 2 coordinates

[woven oak]

The computer code above, Grabs the positons and the calculation must predict a movement scale on it's movement

[tacit arch]

and A = (a1, a2) and B = (b1, b2)

Is this for a game developer?

[woven oak]

Okay, Ill go in detail
From.x is my person
To.x is your person
^ is times itself

So my cords, To your cords times itself

[tacit arch]

What values can From.x be?

[woven oak]

anything a monitor can be

[tacit arch]

Like a pair of coordinates (1, 2) ?

Just call it A and B

The notation you're picking conflicts with X, Y, and Z

[woven oak]

It does, BUT there are lines of that that seperate them below
to single x > x y > y z > z

[tacit arch]

what does

to single x > x y > y z > z

even mean

[woven oak]

It's so far in depth,
Basically x > x is one calculation
but it's written a different way

Due to fuctions

I'd have to show you in a screenshare or something and explain lmfao

Or i need someone who has experience with lua

[lone heart]

@woven oak Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[alpine sable]

hey i have a question

[alpine sable]

hi

what's your question?

usually you just ask the question right away btw