help-19

[weary creek]

Ooh maybe I could use the rate of water

Hang on...

[uneven sable]

A hint is that the ratio of height of water and maximum radius of the water cone is constant

[weary creek]

:OOO alr

😭😭 man can't figure anything out

[weary creek]

How?

We don't know the radius of the height h

[uneven sable]

okay so do you know trigonometry?

[weary creek]

Yes

Oohhh

It makes sense

It's a triangle

Tyyy ima try to find the angle ...

[uneven sable]

no problem

[weary creek]

Yep it worked 💝💝 tyyssmm

Turns out that r = 1/4h from making up a triangle with adjacent h and radius r

I would've never thought about it lol tyyy

.close

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[cobalt reef]

How do I Graph s(t), v(t) and a(t) on the same grid

[lavish jackal]

can you show the actual question

[remote vine]

yeah 😭

[cobalt reef]

its 6 homework questions and the instructions are in the post hold

[remote vine]

Is s(t) relating to displacement, v(t) velocity and a(t) acceleration?

[cobalt reef]

yes

[remote vine]

My initial thoughts would be have an x axis of time, and a y axis not of distance or speed or whatever - but just of numbers, so you can use the same axis, and therefore the same grid for the 3 graphs

Are you alright finding the velocity and the acceleration functions?

[cobalt reef]

i know that you gotta the derivative so the first derivative is velocity

and the 2ncd one is acceleration

[remote vine]

Yup

[cobalt reef]

i got v(t) = 4(t^2-4)

a(t) = 12t^2-16

and i got it graphed on desmos

Now whats MTO and MAFO intervals

[remote vine]

I think that the derivitive comes to 4t*(t^2 - 4)

[cobalt reef]

ye 4t

mb i forgot to type the t

[remote vine]

I'm sorry - I'm not too sure

although im sure someone else will be able to help u :)

[cobalt reef]

okay

[odd edge]

@cobalt reef Has your question been resolved?

[uneven sable]

whats the question?

Oh right

@cobalt reef you still need help or?

[cobalt reef]

Ye what MTO and MAFO intervals

With the

I'm eating rn so mb If I reply late

[uneven sable]

moving towards origin and moving away from the origin\

ping me nextime

[odd edge]

@cobalt reef Has your question been resolved?

[cobalt reef]

The particle is moving away from the origin ( MAFO) in the intervals (-infinity, -2) and (0,2)
And it's moving toward the origin (MTO) in the interval (-2,0).

this is what i got

@uneven sable

[odd edge]

@cobalt reef Has your question been resolved?

[odd edge]

@cobalt reef Has your question been resolved?

[odd edge]

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[desert tree]

!status

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[desert tree]

Where are you

[odd edge]

@echo parrot Has your question been resolved?

[mystic saffron]

She opened two channels and closed rhe second channel

[odd edge]

@echo parrot Has your question been resolved?

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[odd edge]

Please don't occupy multiple help channels.

[fast ivy]

.close

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[ember shell]

The hint said to make it a difference of squares thingy

[summer river]

OMG

[ember shell]

Ah what did I do

11.2.6 btw

Sorry lol

[summer river]

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

[ember shell]

Uhm...

My brain isn't functioning right now

[summer river]

I'll start you off

[ember shell]

U learned it differently

[summer river]

t^2 - 49

that's similar to x^2 - a^2

x = t

a = 7

then subbing stuff in

you get (t-7)(t+7)

[ember shell]

Yes I know how to factor lol

Uhm

Like

Can u read the question I'm bad at explaining

painnn

[summer river]

ac

[ember shell]

Yes indeed

What is up

[summer river]

is this the question @ember shell ?

[ember shell]

yessireeee

[summer river]

it's a p hard challening question that's from the harvard mit math competition

[ember shell]

oh

skully

wellll

its in the aops book

so ig im using it now

haha

[dawn scarab]

@summer river do you want to help or do you want me to?

[ember shell]

i dont know if they are alive rn..

the hint is that you need to find a way to make it a difference of squares

[summer river]

I can help in 15 minutes, but if you can help right now that is perfect

[ember shell]

i flipped to that page

alrighty

[dawn scarab]

Guess I can step in then. So, as your hint said, making stuff into difference of squares is the play here. And I'll give you one more, I started with the x^4 one

[ember shell]

wdym by that

oh the like

x four equals y 4 thingy

[dawn scarab]

The first equation I started working on is the one with x^4 in it

Do you see a way to turn this into a difference of squares?

[ember shell]

Kinda

[ember shell]

Like uj

dont mind the work on top

just look at the spaced out one

starting from x^4 ig

[dawn scarab]

yeah that is the way I went too

[ember shell]

ic

[dawn scarab]

Do you have any idea of how to proceed further?

[ember shell]

doing a system?

how do you do a system of 2 variabels with 3 equations tho

[dawn scarab]

for this one you don't actually have to. I was talking about working with $\ x^4 - y^4 = 18\sqrt{3}\$further

[clever fjord]

Σ balls

[odd edge]

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[ember shell]

oh ok

[ember shell]

thats awkward

[dawn scarab]

eh? Bot's tweaking

[ember shell]

yeah

so you're trying to find x-y

so you just simplify the 18 thingy

[dawn scarab]

oh I see, you posted your question right after the previous question closed, but before the bot could re-mark the channel as free

[ember shell]

the 18√3

and then uhm you do the thingy

[ember shell]

oops

[dawn scarab]

happens ¯_(ツ)_/¯

You don't actually have to touch that for now, you can factor x^4 - y^4 more

[ember shell]

ok

would that be

(x^2+y^2) (x^2-y^2)

[dawn scarab]

yup!

[ember shell]

and then the uh

u can simplify

the second

so thats

(x+y)(x-y)

[dawn scarab]

exactly

Now you just have to look back at the question and you'll notice some things :)

[ember shell]

ohhh

and then they give u like the other htingies

[dawn scarab]

yeah! So you can just plug in and solve

[ember shell]

oh wait

ok so is it like

or am i like tweaking rn

[dawn scarab]

I don't know why a square root appeared on x-y but yeah you're getting there!

[ember shell]

oh wait parenthesis

i went ahead of myself

[ember shell]

I think I got jt

You gotta click the full image tho

[dawn scarab]

That's also the answer I got, congrats :)

[ember shell]

yay ur a life saver bro

😭

[dawn scarab]

Any time :D

[ember shell]

:d

:D

.close

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[mystic saffron]

@olive needle Sorry there's one more thing I'm stuck on

[mystic saffron]

I know the area of a square is s^2

And the derivative is 2s plug in 10 then the ans is 20

But the ans says 5/8 and I have no idea how they got that

+-5/8

[olive needle]

Can you show your work?

[mystic saffron]

That is my work

[mystic saffron]

This and the sentence below

That's all I did

I am lost

[olive needle]

What is f(a)?

[mystic saffron]

10?

I think

[olive needle]

What is the approximation a?

[mystic saffron]

1/32

[olive needle]

No, that is the error in the measurement which you will use later.

[mystic saffron]

So it was 10

?

[olive needle]

Correct.

So what would the linear approximation look like using that information?

[mystic saffron]

Just to make sure

Is the original function s^2

[olive needle]

Yes.

A(s) = s^2

[mystic saffron]

100+20(x-10)

100+20x-200

20x-100

[olive needle]

Ok, now use the error in measurement to calculate what x to use.

You are using 10 inches plus/minus 1/32 of an inch.

[mystic saffron]

,calc 10-1/32

[clever fjord]

Result:

9.96875

[mystic saffron]

,calc 10+1/32

[clever fjord]

Result:

10.03125

[olive needle]

Either should give a satisfactory result.

[mystic saffron]

20(9.96875)-100

,calc 20(9.96875)-100

[clever fjord]

Result:

99.375

[mystic saffron]

Solid.

[radiant gulch]

What 2+2👁️👄👁️

[mystic saffron]

,calc 20(10.03125)-100

[clever fjord]

Result:

100.625

[olive needle]

And you know the area of the square for 10 inches.

[mystic saffron]

How did it get 5/8

[mystic saffron]

Ya

[olive needle]

So the error would be?

[mystic saffron]

100.625-100

0.625

[olive needle]

👍

[mystic saffron]

Oh is that the same

,calc 5/8

[clever fjord]

Result:

0.625

[mystic saffron]

Ah

[olive needle]

The tricky part is understanding what information the question is giving you.

[mystic saffron]

Do u mind if I do 26 real quick

[olive needle]

Go for it.

[mystic saffron]

Alr so area of a circle pi r^2

Derivative becomes 2pi r

,calc 16^2

[clever fjord]

Result:

256

[mystic saffron]

256pi+32pi(x-16)

,calc 32 * 16

[clever fjord]

Result:

512

[mystic saffron]

256pi+32pi x - 512pi

32 pi x - 256pi

,calc 16+1/4

[clever fjord]

Result:

16.25

[mystic saffron]

,calc 16-1/4

[clever fjord]

Result:

15.75

[mystic saffron]

,calc 32(3.14)(15.75)-256(3.14)

[clever fjord]

Result:

778.72

[small ore]

Hi

[mystic saffron]

,calc 32(3.14)(16.25)-256(3.14)

[clever fjord]

Result:

828.96

[mystic saffron]

Hmm

3.14 x 16^2

,calc 3.14 x 16^2

[clever fjord]

The following error occured while calculating:
Error: Undefined symbol x

[mystic saffron]

,calc 3.14 * 16^2

[clever fjord]

Result:

803.84

[mystic saffron]

I mean I guess they're close enough

What do u think

[olive needle]

One moment, let me verify.

You can just type pi when using ,calc.

,calc 32pi16.25 - 256*pi

[clever fjord]

Result:

829.38046054771

[olive needle]

But if you evaluate it by hand, you will find a much easier answer, 264pi.

,calc 264pi

[clever fjord]

Result:

829.38046054771

[mystic saffron]

Oh wow

Wait

It looks exactly the same

Is there no difference?

[olive needle]

From the error to the actual value?

[mystic saffron]

,calc 32pi15.75 - 256*pi

[clever fjord]

The following error occured while calculating:
Error: Undefined symbol pi15

[mystic saffron]

Yeah

[olive needle]

There is an error.

[mystic saffron]

,calc 32pi15.75 - 256*pi

[clever fjord]

Result:

779.11497809027

[mystic saffron]

Oh there is

,calc 32pi16.25 - 256*pi

[clever fjord]

Result:

829.38046054771

[mystic saffron]

16.25 seems fine

But the other one is off

[olive needle]

,calc (16)^2 *pi

[clever fjord]

Result:

804.24771931899

[olive needle]

What is the error?

[mystic saffron]

How'd you get a diff answer here

,calc 16^2

[clever fjord]

Result:

256

[olive needle]

The radius of a circle of 16 inches.

[mystic saffron]

Am I tripping

You did the same thing and got a different answer

,calc 256 * pi

[clever fjord]

Result:

804.24771931899

[mystic saffron]

,calc 256pi

[clever fjord]

Result:

804.24771931899

[mystic saffron]

Holy I'm an idiot

That's a whole different number

Oh my god

Thank you so much @olive needle you are truly a lifesaver

[olive needle]

np

[mystic saffron]

.close

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[gusty sonnet]

Is limit at x = 2 and at x = 5 defined here?

We say that limit is defined if left and right limits are equal

If we take a look at 2-, it seems it's going to negative infinity
If we take a look at 2+, it seems it's going to negative infinity

So does it exist or not?

Yeah

Because they are the same

It should be

Am I misunderstanding something?

Yeah, it exists, but it's not the same you say?

[clever fjord]

woods

[gusty sonnet]

Yes

I thought that's the same thing?

Makes sense

Understood

Thank you very much!

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@gusty sonnet Has your question been resolved?

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[hushed island]

this looks like a change base problem?

[cinder sierra]

can someone confirm if simplifying this gets me 531441n^4 or 1594323n^4

[hushed island]

what...

$9^4^(log_9(27n))$

[haughty fulcrum]

,calc 27^4

[clever fjord]

Result:

5.31441e+5

[haughty fulcrum]

approved 😎 👍

[hushed island]

(9^4)^2/3 + log_9(n)

a

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@cinder sierra Has your question been resolved?

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[crisp flume]

F_A and F_B are linear mappings

[crisp flume]

how can ii show that their composition is also linear?

i can not plug rv+sw so i dont know how to show that

[low locust]

why can you not plug that in

[crisp flume]

better said i dont know where should i plug it in

[low locust]

well into the function

[crisp flume]

what function?

[low locust]

the one you are supposed to show is linear?

[wanton niche]

"map" is another word for function

[crisp flume]

yes i know this but since i dont have any notation for this function i dont know where should i put it

could you please show me

[low locust]

F_B circ F_A is the function

[crisp flume]

yes and should i do something like this? (F_B circ F_A)(rv+sw)=(F_B circ F_A)(rv)+(F_B circ F_A)(sw)=r(F_B circ F_A)(v)+s(F_B circ F_A)(w)

[low locust]

well thats what you are supposed to show, yes

but why do these equalities hold

[crisp flume]

well i dont have a clue

i just did it xd

[low locust]

how does function composition work

[crisp flume]

e is wector with 1 at i position and zero everywhere esle

[low locust]

I mean in general

what does $(f\circ g)(x)$ mean

[clever fjord]

Denascite

[crisp flume]

that you first run that x through function g and then this result you run through f

[low locust]

ok

in symbols?

[uneven sable]

f(g(x))

[crisp flume]

yes

soo then f(g(rv+sw))=f(rg(v)+sg(w))=f(rg(v))+f(sg(w))=rf(g(v))+sf(g(w))

[low locust]

ok, so if we plug our thing into the function we then get $F_B\circ F_A(rv+sw) = F_B(F_A(rv+sw))$

[clever fjord]

Denascite

[low locust]

why do those equalities you wrote hold

[crisp flume]

because we know that g is linear so first step holds and then f is also linear and thats why the second and trird one hold

[low locust]

yes

and thats it

[crisp flume]

alright finally xd

thx for help

.close

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[hollow ibex]

If a/b = c/d, then show that sqrt(a²+c²)/sqrt(b²+d²) = (pa+qc)/(pb+qd)

The third one

[clever fjord]

gwwy

say $\frac{a}{b} = k = \frac{c}{d}$
So a=kb and c=kd
LHS is $\frac{\sqrt{k^2(b^2 + d^2)}}{\sqrt{b^2 + d^2}}$ 
RHS is $\frac{k(pb+qd)}{pb+qd}$

[hollow ibex]

Thank u dudeee

I got it

thanks @uneven sable

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[crisp flume]

what numbers are in this set ${z \in \mathbb{C} \vert |z|=1}$?

[clever fjord]

Slowaq

[desert marlin]

z=1

z=-1

[crisp flume]

numbers like i or 1?

[desert marlin]

numbers of the form a+bi

such that |a+bi|=1

[crisp flume]

yes and can it be just i?

[desert marlin]

what is |i|

[crisp flume]

sqrt(1^2)?

[desert marlin]

why

[crisp flume]

well a+bi so 0+1i thus |i|=1?

[desert marlin]

No

[crisp flume]

😦

[desert marlin]

What is |a+bi|

in general

[crisp flume]

sqrt(a^2+b^2)?

[desert marlin]

Okay

so then |i| being |0+1i|

is?

[crisp flume]

sqrt(0^2+1^2)?

[desert marlin]

=1

yes

it has been 1 this whole time I just wasn't satisfied with your explanation

[crisp flume]

xd alright thx for help

.close

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[crisp flume]

.reopen

[odd edge]

✅

[crisp flume]

wait @desert marlin what can be neutral elemnt in this set

and also inverse

inverse is -z

for z?

[desert marlin]

What do you mean by neutral element

or the inverse

[low locust]

group theory

[crisp flume]

yes

[desert marlin]

Want to take over then

[low locust]

well for starters what is your operation

[crisp flume]

ah yes sorry i forgot to mention it

its multiplication

[crisp flume]

so this is bs

so neutral will be 1

[low locust]

yes

[crisp flume]

and inverse will be 1/z?

[low locust]

yes

why is that again in the set?

[crisp flume]

what do you mean?

[desert marlin]

I got this one

Why is 1/z in that set described above

[low locust]

the inverse needs to again be in the set

[desert marlin]

given that z is

[crisp flume]

ah yes since |z|=1 thus 1/1 is 1 and 1 is in set

[desert marlin]

|1/z|=|1|/|z|=1/1=1

yes

[crisp flume]

yes alright that should be all thx

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[night rapids]

0

[night rapids]

how do i write up the solution set for this marix

[sonic nova]

Go to either 1st or 2nd row and write out the equation it's describing

I'll abitrarily pick the 2nd row

Do you call the variables x, y, z or x1, x2, x3?

[night rapids]

lets just say x1=1

[sonic nova]

Well we cant pick a value for them

[night rapids]

oh

ok

[sonic nova]

Maybe they can take on any value

Maybe theres only 1 specific value

Maybe no values work

Those are the 3 possibilities

[night rapids]

mhh ok

[sonic nova]

So I'll call the variables x1, x2, x3

[night rapids]

sure

[sonic nova]

If you read the 2nd row's underlying equation

It states

x2 + (1/3)x3 = -1/3

[night rapids]

yeah

[sonic nova]

You need to solve for either x2 or x3

In terms of the other

[night rapids]

x2 = x3/3 - 1/3

[sonic nova]

Oh wait ncm

Nvm****

Ignore that

[night rapids]

ok

[sonic nova]

Ok good so far

Now go to the first row

Solve for x1 in terms of x3 as well

[night rapids]

x1 = 4x3/3 - 5/3

[sonic nova]

Ok now you know x1, x2, and x3 in terms of x3

You can write a vector that describes the answers in terms of x3

[ 4x3/3 -5/3, x3/3 -1/3, x3]

Separate that into the sum of two vectors

One that contains all the x3 terms and one that contains the non variable parts

[night rapids]

like so

and now ill seperate them

[sonic nova]

Yea

Perfect so far

Oh wait

No nvm it's good

[night rapids]

we isolated x3 wrong the first time

of wrong +/- in front

[sonic nova]

Correct lol

[night rapids]

but i think i fixed it

[sonic nova]

Should both be negative my bad

x2= -x3/3 - 1/3

[night rapids]

i just didnt write it in my matrix

but only in my calculations lol

[sonic nova]

Ok cool

[night rapids]

mb

[sonic nova]

No my fault too its ok

[night rapids]

right or

[sonic nova]

Not the bottom entry

Does x3 + 1 = x3?

[night rapids]

so 0

instead

[sonic nova]

Yea

Good

[night rapids]

the solution sheet writes it up slighty differnt

[sonic nova]

Well factor out the x3

And then rename it s

And you get the same thing

[night rapids]

yeah, ok, i thought so

[sonic nova]

x3 is a free variable

It can vary across all real numbers

[night rapids]

x3 is the free varialbe because the third row has all 0's?

[sonic nova]

Whenever you have under defined systems, you will.get infinite solutions with free variables

[sonic nova]

There is a free variable because you have 3 variables and 2 equations

[night rapids]

yeah, but it could also just be x1

[sonic nova]

The 0 0 0 row is a useless equation without information

[night rapids]

it is just notation

[sonic nova]

Correct

You would get a slightly different end result

But you can solve with either x1, x2, or x3 free

All answers would give you the same solution set but as the sum of slightly differing vectors

The easiest and shortest way was to choose x3

Since you could directly solve for x1 and x2 in terms of x3 in their respective equations

[night rapids]

alright

many thanks

[sonic nova]

Yw good.luck with your class work

[night rapids]

))

[sonic nova]

A handy rule of thumb, the number of free variables will equal the number of zero rows in your echelon form

[odd edge]

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[gleaming hedge]

Need help understanding this in the ring Z_n of division with equal remainders

[gleaming hedge]

if a1 is in a dash

how did we get to a(dash)=a1(dash)

a1∈a <=> a1=a+ns1 <=> a(dash)=a1(dash)

is confusing me

[sharp oak]

a(dash) is the set of all numbers, where the remainder is the same as a.

a1 being in a(dash) means a1's remainder is the same as a's.

a1(dash) and a(dash) end up being equal sets too.

[gleaming hedge]

could you elaborate on this?

[sharp oak]

I don't think they rigorously show that they're the same set, here. But they are

Every number has a remainder (after division by n)

[gleaming hedge]

right

[sharp oak]

10 is the same as 1, when we are in (mod 3) arithmetic

10 is an element of 1(dash)

10(dash) and 1(dash) are the same set. For example, they both include 13.

[gleaming hedge]

1=0*3+1```

same remainder?

ohh

10=3x3+1

so both 1 and 10 are in 3(dash)

[tall veldt]

(Also lacertae ik you've studied relations in general, this is showing a fact that you already know, if two things are related by an equivalence relation then their equivalence classes are the same)

[gleaming hedge]

yeah

.

[sharp oak]

Note that 1 and 3 do not have the same remainder after division by 3, so 1 is not in 3(dash).

If you're comfortable with relations, then yeah these are just equivalence classes!

[gleaming hedge]

alright I'll try to think this through

it's a little confusing I think it's because of the abstract aspect

ty guys though

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[lethal tulip]

I’m trying to solve this proof via induction and without using the binomial thereom but I have no clue where to start

<@&286206848099549185>

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@lethal tulip Has your question been resolved?

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@lethal tulip Has your question been resolved?

[lavish knot]

it might be beneficial to prove $n! \leq \left(\frac{n+1}{2}\right)^n$ instead.

[clever fjord]

emphatic_wax

[lavish knot]

or $n! \cdot 2^n \leq \left(n+1)\right)^n$

[clever fjord]

emphatic_wax

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[viral frost]

You need to find y'?

[dire garden]

yep

[viral frost]

Do you know what's $\dv{\sin^{-1}(x)}{x}$ in general?

[clever fjord]

! What the hell am I doing here?

[dire garden]

no

1/square root of 1-x2

[viral frost]

yeah

[dire garden]

the formula i think

[viral frost]

What's that no for?

[dire garden]

the picture you sent

im not familliar

is it same to my formula?

[viral frost]

The derivative of arcsin(x) is

[viral frost]

This

(Which is also what I asked)

[dire garden]

yep

[viral frost]

So what's bothering you?

[dire garden]

i mean this if i know this formula

i said no only

[viral frost]

Um, what?

[dire garden]

i mean i dont know that formula

[viral frost]

But you do ...

[dire garden]

noo

[viral frost]

You can derive it if you'd like.

[dire garden]

then how

[viral frost]

By using the definition of differentiation.

Using limits.

[dire garden]

can we use this formula

teach me how to do this

[viral frost]

You can.

Let's start over, what's the issue again?

[dire garden]

in my solution the left side is 3/2 1/√1-(x-1)^2 * 1

how to do the right side

[viscid flint]

do you know what differentiation is in general?

[dire garden]

nope

i mean yess

i forgot how to do it again

.close

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[mystic saffron]

How do I find the derivative of 1/2bh

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[mystic saffron]

In this proof,$ L_1(\mathbb{R})$ refers to f being inside the family of $L_1$ norms, right?

[clever fjord]

radar ashe

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[gleaming hedge]

In Horner's scheme, what does this scheme tell us?

[gleaming hedge]

where a_0-a_n is coefficients

this was the polynomial

divided by x-α where a is a root

we got this

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[gleaming hedge]

<@&286206848099549185>

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[woeful rivet]

hello

[woeful rivet]

is this right?

question C

[pearl snow]

should be

[woeful rivet]

i thought u couldnt divide vectors

[pearl snow]

u can

[woeful rivet]

oh

ok

thx

u just cant divide vectors by vectors?

[pearl snow]

no

what ur looking at is a scalar multple

so it can be divided

[woeful rivet]

i drew this

and it doesnt look like a parallelogram

[pearl snow]

u just havent drawn D yet

[woeful rivet]

.close

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[echo vapor]

How do I compute this? I'm guessing this is the solution but I am not really sure

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[wooden hazel]

Hey everyone,

I'm working on a quizzing application and I'm in need of some statistics guidance. Not sure what terminology to google for, so pointers in the right direction are much appreciated.

I have a record of:

• multiple choice questions
• the answers a user gave
• when the user gave the answer
• whether they were correct

Now, I want to estimate the chance that someone answers correct if they are quizzed X again.

Initially I tried estimating based on the percentage of corrects someone has given for X. All correct? Good chance it'll be correct again, and vice versa. But this has drawbacks:

• Small sample sizes can make the estimate seem confident, when it isn't
• If you've been answering a lot of incorrects for a long while, but have been answering correct in the more recent past, those incorrects still outweigh your recent string of corrects. So somehow I'd like to take confidence or reliability into account based on time.

What branch of statistics should I look into here? How do I incorporate confidence of the samples and sample size into this model?

[sleek moth]

how about this?
https://en.wikipedia.org/wiki/Rule_of_succession

[wooden hazel]

intense reading happening here 😎

(Wait, this is by Laplace Transform's Laplace? nice)

[hardy panther]

The difficulty you have is that you need A LOT of data to make good predictions for this and you are only assuming one variable (scores on the last test) as a predictor for the score on the next test. There are other confounding variables that can affect scores on future tests which you may not have data to track, including study time, homework completion rates, illnesses, etc.

Fun fact: Aeries gradebooks DO predict student performance with a graph and trajectory, but they are able to keep track of all assignments, assessments, tardiness, absences, and illnesses, and have an extraordinary amount of data to tune those predictions to

[wooden hazel]

That's certainly true, though the app isn't testing for anything that will result in certification or anything, it's more for fun

Think more in terms of spaced repetition systems like Anki (if you've heard of that), where the probability of getting asked X again is based on how well you've done in the past

@sleek moth yeah that's certainly in the right direction! Never heard about this, but the paragraph about there being two pseudocounts is super helpful

[odd edge]

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[wooden hazel]

Yeah, I've got enough reading material to continue. Thanks for your help, Stipendi 🙂

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[topaz solar]

Does someone know how to get from that horrible system of equations to these solutions

it was a problem with lagrange multipliers and i have a system of 5 equations but i dont know the method to solve it

<@&286206848099549185>

[quartz walrus]

I wonder if multiplying the first three equations, each by $x$, $y$, and $z$ respectively would help bring the first three equations to fewer variables by elimination. That might be a start.

[clever fjord]

eToThe2iPi

[quartz walrus]

@topaz solar

[topaz solar]

i tried something like that but idk i kinda gave up somewhere, maybe i did something wrong

[odd edge]

@topaz solar Has your question been resolved?

[quartz walrus]

@topaz solar I'm not sure I follow the last half.

Specifically the $y = \frac{-2z+6x}{3}$, etc.

[clever fjord]

eToThe2iPi

[topaz solar]

thats - before the 6x

i expressed y from the first constraint

and plugged it in

which didnt help at all

[stark socket]

What a terrible system of equations

[topaz solar]

my professor is from hell

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[lone heart]

can someone help me with this?
so far ive only simplified the [1+1/2sin(2A)], which is (1+sinxcosx)

[lone heart]

i tried foiling aswell but it didnt take me anywehre

[noble palm]

ok

uh

can you represent 1 in terms of cosine and sine?

[lone heart]

yes

[noble palm]

how would you do that

[lone heart]

sin^2x+cos^2x

[noble palm]

yup

so now we have (sin A - cos A) (sin^2 A + sinA cosA + cos^2 A)

try multiplying this out

[lone heart]

(sin^3 A + sin^2AcosA + sin Acos^2 A -cos A sin^2 A - sinA cos^2 A -cos^3 A)

let me

further

simplfy

[noble palm]

sure

there are terms that cancel

[lone heart]

(sin^3 A -cos^3 A )

[noble palm]

👍

[lone heart]

lmao

ty

[noble palm]

this works because

(x^3-y^3) = (x-y)(x^2+xy+y^2)

np

[lone heart]

yah

[noble palm]

if your question has been solved, do .close

[lone heart]

.close

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[lavish escarp]

help me

[lavish escarp]

e

[tender lagoon]

[lavish escarp]

ok so

we are doing pre algebra in math, and im confused

idk what im confused abt js im confused

[tender lagoon]

Are u trolling mate

:/

[lavish escarp]

no im srs

[copper quarry]

how can we help you if you don’t even know what you’re confused about

[tender lagoon]

Show the question

[lavish escarp]

hold up let me grab my notes

[tender lagoon]

Kul

[lavish escarp]

ok so, i cant send a pic but ill type it here

its like 9 to the power of 6 (9^6) and its like "evaluate and show this in expanded form"

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[lavish escarp]

.close

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[serene urchin]

Part c

What line to draw?

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[mystic saffron]

An airplane flies 110 kilometers from an airport in a direction of 200◦. How far west (the
adjacent side of a reference angle to the direction the plane is traveling) of the airport
is the airplane then? How far south? In navigation, directions are given in degrees
measured clockwise from north.

I have no clue how I can go about this...I been sick ever since school started so have no clue what has transpired over the past 2 weeks. I have a few problems I need help with. If I can learn to solve them, I'm sure I'll be able to solve the rest

[long basin]

I would start with trying to draw this out, helps visuilizing it

[mystic saffron]

alright

[mystic saffron]

ok I got a pen and paper to draw but have no clue what to draw

110 kms from 200 angle?

ok so I unleashed 100% of my brain power and arrived at
37.6km west
103.4 km south

would that be correct?

When Brett and Will ride the carousel, Brett always selects a horse on the outside row,
whereas Will prefers the row closest to the center. These rows are 20 ft 8 in. and 13 ft 1
in. from the center, respectively. The angular speed of the carousel is 2.9 revolutions per
minute. What is the difference, in miles per hour, in the linear speeds of Brett and Will?

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[gleaming coral]

how can i integrate this, is the cos my start?

[fluid tundra]

you want u-substitution

try see if you can simplify this integral a bit by choosing u

[gleaming coral]

we have not learned u substitution offically yet, but i have backgroud with it soooo. Its same properties i assume?

i got stuck again

got to

Sin U + c

now idk

[meager juniper]

Substitute back. However, you missed a step in the u substitution.

You have to replace the inside of your function with u, and then change the dx to an expression involving only u and du

(and constants and such)

So if you have u = 3-5x, then du = -5 dx, so dx = -1/5 du

So you need to integrate -1/5 cos(u) du

@gleaming coral ^

[leaden widget]

and after you're done integrating, you'll have an expression in terms of u, then do a backwards sub to get an expression in terms of x again

[gleaming coral]

how did we come to the conclusion that du = -5?

or dx = -1/5

[leaden widget]

differentiate u = 3-5x in respect to x

du/dx = -5, now separate the differentials (hopefully youre comfortable with that): du = -5dx

[gleaming coral]

we can differntiate du?

[leaden widget]

u?

well u is a variable defined as a function of x, so yes why not be able to differentiate it?

if i gave you more familiar names, y = 3-5x, then you would know how to do dy/dx = -5 right?

it's the same thing but another name, and name isn't important

@gleaming coral i sense you might be a bit confused, anything that needs clarification?

[gleaming coral]

well this is our first day on indefinate intergrals so i would assume i just have to expierence it more

thank you

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[small ore]

What would I do for this problem?

[small ore]

<@&286206848099549185>

Yo can anyone help me

[cursive field]

okay

so you need to figure out the surface area for the shape

dyk how to figure out a cylinder's surface area?

[odd edge]

@small ore Has your question been resolved?

[cursive field]

...

[small ore]

Not really

Sorry

[cursive field]

lol

still playing fn?

;-;

[small ore]

It’s connected to my account and my cousin is playing

[cursive field]

eh idm

[small ore]

I was getting help from someone else but I got confused so I’m going back to here

[cursive field]

anyway do you know how to find the surface area of a cylinder??

[cursive field]

np

[small ore]

Formula?

[cursive field]

well, yes, but also why it works in the first place

[small ore]

2pir^2h

[warm quartz]

they appear to be asking abt the shape’s volume

[cursive field]

yes

[small ore]

We are looking for volume

[warm quartz]

closest to the volume of the 3d shape below

[cursive field]

i am such a bad helper aren't i lmao

okay nvm

[small ore]

The Total surface area is just the other questions

[cursive field]

im dumb ok gimme a break

[small ore]

Its asking which choice is closest to the volume

Idk

[cursive field]

kk

[small ore]

You are not

[cursive field]

eh is fine just woke up

alright anyway you know how to figure the volume out right

[small ore]

Not really

[warm quartz]

so you would just find the volume of cylinder + volume of hemisphere

[cursive field]

okay

[warm quartz]

i think

[cursive field]

yes

let me explain it to yo

*you

[small ore]

Ok

[cursive field]

a shape's volume is (usually) the base's area times the height

[small ore]

Ok

[cursive field]

what's the cylinder's area?

[small ore]

Um

[cursive field]

figure it out using the radius

[small ore]

Ok

Wait

471.24

If I’m correct

[cursive field]

i'm sorry?

[small ore]

Oops

[cursive field]

i meant the base, mb

okay let's go slowly

what's the area of the base of the cylinder

[small ore]

78.54

I think

[cursive field]

just express it in terms of pi

[small ore]

Wait

What is the formula for the area of the base of the cylinder again?

I’m going to try something

[cursive field]

pi x r^2

take ur time

[small ore]

Yeah

78.53

Idk how those are different

But I got that

[cursive field]

in terms of pi?

is fine, dw

[small ore]

I typed pi5^2

[cursive field]

probably floor vs round off

[cursive field]

dw

so 25pi right

[small ore]

Huh

[cursive field]

now what's the height

[small ore]

10

[cursive field]

okay

[small ore]

Do you need a photo

[cursive field]

so what's the volume of the cylinder

[small ore]

Of the question

[cursive field]

no no

[small ore]

Ok

[cursive field]

nah i got it

[small ore]

Wait what

I got

[cursive field]

??

[small ore]

785.4

[cursive field]

yes

[small ore]

Oh ok

[cursive field]

that's perfectly corrcet

*correct

[small ore]

Let’s goo

[cursive field]

don't call me sir lol

im probably younger than u

[small ore]

I’m not

It’s a phrase

[cursive field]

i get it lol

but idk it makes me feel weird sorry

[small ore]

Oh mb

[cursive field]

np

anyway in my suggestion express this as 250pi

for now

[small ore]

Alright

[cursive field]

so dyk the volume of a sphere?

[small ore]

No

Wait

[cursive field]

okay

i'll wait, n

np

[small ore]

Tell me the formula rq

[cursive field]

4/3 times pi times r^3

for a full sphere

keep in mind that this is a HALF sphere

[small ore]

523.6

Divided by 2?

[warm quartz]

i wonder where the equation for volume of sphere comes from actually

[small ore]

261.8

[cursive field]

i can show you a derivation

[warm quartz]

i know its possible to find it w a triple integral

[cursive field]

i made one myeslf

[cursive field]

don't need one, just summation and limits

[small ore]

@cursive field is it 261.8

[warm quartz]

but i was wondering if there was one that didnt require calc

[cursive field]

@small ore don't mind us just nerding out

[cursive field]

one second

[small ore]

Ok

Mb

[cursive field]

DM me @warm quartz

not here

[warm quartz]

because you could technically just integrate 1 in spherical coordinates i think

ok

[cursive field]

@small ore correct!

:D

[small ore]

Let’s go

So do I add them

261.8 + 785.4

[cursive field]

no

[small ore]

Oh.

[cursive field]

remember, 785.4 is 250pi

[cursive field]

nah nah we're just simplifying

actually for this question u can add them

go ahead

[small ore]

1047.20

[cursive field]

it doesn't matter

yes

[small ore]

Which is Answer Choice C

Let’s go

@cursive field thank you for the help

[cursive field]

nice!

np

do .close if ur done

[small ore]

What

[cursive field]

do .close if ur qusetion has been solved

it closes the channel

[small ore]

Oh ok

.close

[cursive field]

so someone else can ask a question here

[odd edge]

Channel closed

Closed by @small ore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

How am I supposed to calcualte?

with the Pytahgoean theorm to check??

Would the numbers be in order of a,b,c?

I got it

[chilly lily]

the 2 smaller numbers should be squared and added to equal the squared number of the bigger one

[lapis nacelle]

The answer is JUST b

thanks

.close

[odd edge]

Channel closed

Closed by @lapis nacelle

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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