help-0

[wanton holly]

this problem seems unsolvable to me as its a nonlinear system

[lone heart]

@wanton holly Has your question been resolved?

[marble gazelle]

What are x' and y' with respect to? Are they the total derivatives?

[wanton holly]

yeah total derivatives

nothing else is given in the problem

[wide moat]

hi can u help me

[marble gazelle]

Please see #❓how-to-get-help

[wide moat]

i did

oh oops

nvm

[wanton holly]

open up a channel and ill see but no promises

[wide moat]

mmk

its on the forum

[marble gazelle]

Sorry, I thought I could help but seems like I can't

[wanton holly]

haha its alright

the only thing i could think of is straight up guessing solutions

[marble gazelle]

I'm just confused how x is a function of x

[wanton holly]

x and y are both functions of time

like uhh x(t) and y(t)

but its just written shorthand

[lone heart]

@wanton holly Has your question been resolved?

[finite spindle]

hi

[vagrant lily]

hi jobbers

[lone heart]

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[dusk tinsel]

I wanna x with steps

[tribal field]

Have you considered similar triangles?

Also, you really don't need to post this in two places

[dusk tinsel]

Sorry

[tribal field]

You're good, but once again
Similar triangles?

[dusk tinsel]

Yes

[alpine trench]

split the big triangle down the middle to get to smaller right angled triangles

[dusk tinsel]

Sorry i can't understand

Its already splited

[alpine trench]

k

[tribal field]

There are 3 triangles at are similar, do you know which sides correspond with which

?

[dusk tinsel]

No

Can u answer it in a paper

And show me

[tribal field]

uh, my phone ran out of battery, so I can't take photos

give it like a few min to charge

[lone heart]

@dusk tinsel Has your question been resolved?

[dusk tinsel]

Not yet

[tribal field]

you have to click the red x

it'll automatically close in a bit if you don

@dusk tinsel phone is alive again, lemme draw this out

[winged hinge]

Hello guys, I have a math test on Sunday. I found this document:

https://www.studocu.com/in/document/mahatma-gandhi-university/mathematics-ii/math-quiz-and-answers/29647037

online and it will be very helpful for me. However, the version I found is incomplete and I'm unable to purchase the full version. Does anyone happen to have the full version that they could share with me?

[tribal field]

get your own channel

read #❓how-to-get-help

sorry, @dusk tinsel I'm in like 6 places at once right now

[dusk tinsel]

No worries

[lone heart]

@dusk tinsel Has your question been resolved?

[tribal field]

actually, in hindsight, forget the similar triangles

there's a faster way to do this

The area of the triangle

consider AB as the base, then AC would be the height

actually, you still need the similar triangles

[lone heart]

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[dire terrace]

what did i get wrong in these questions?

[tribal field]

I don't think 4 is wrong

might be a formating issue

maybe the quotation marks are necessary? have you had issues with this before?

[dire terrace]

yes I have

I was just making sure I did it correct before emailing my professor, so all is correct just wrong formatting?

[lone heart]

@dire terrace Has your question been resolved?

[lone heart]

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[lone heart]

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[hot hatch]

What do you mean rationalise?

Is the inside part 5- root 21?

[wintry sluice]

multiply it by conjugate

[hot hatch]

Don't u do that for denominator irrational no.?

[wintry sluice]

oh wait

it isnt 1/

fuck

my bad

sorry

[hot hatch]

It's fine

I was wondering what's wrong with the question too

[tawdry urchin]

is it $\sqrt{5 - \sqrt{3\sqrt{7}}}$ or $\sqrt{5 - \sqrt{3}\sqrt{7}}$

[ocean seal]

Dork9399

[wintry sluice]

the latter i think

[tawdry urchin]

ight so

[hot hatch]

.

[tawdry urchin]

lol

@alpine sable wanna clarify

[tawdry urchin]

.

ty

$\sqrt{5 - \sqrt{21}}$

[hot hatch]

Do u have any idea what to do?

[ocean seal]

Dork9399

[tawdry urchin]

yea yea ik

[hot hatch]

...what can we do

[tawdry urchin]

so we have x = sqrt(5 - sqrt21)

[lone heart]

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.

[hot hatch]

It doesn't from a perfect square too

[tawdry urchin]

x^2 = 5 - sqrt21

[hot hatch]

[tawdry urchin]

bro calm down

[hot hatch]

Let him explain

[tardy tapir]

.

[tawdry urchin]

5 - x^2 = sqrt21

[hot hatch]

Which year and advanced?

[tawdry urchin]

25 - 10x^2 + x^4 = 21

$x^4 - 10x^2 + 4 = 0$

[ocean seal]

Dork9399

[tardy tapir]

bro

!original

[lone heart]

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.

[tardy tapir]

can you?

[wintry sluice]

bruv

send the original question

[hot hatch]

@alpine sable

Send a screenshot of pic

Of question

[tawdry urchin]

ight idt that will give us anything

lets try something else

$a + b\sqrt{21} = \sqrt{5 + \sqrt{21}}$

[ocean seal]

Dork9399

[tawdry urchin]

a^2 + 21b^2 = 5, 2absqrt21 = sqrt21

a^2 + 21b^2 = 5, 2ab = 1

[wintry sluice]

how long is it taking for you to send a pic of the question

[tawdry urchin]

b = 1/(2a)

[wintry sluice]

💀

[hot hatch]

Which year question?

[tawdry urchin]

$a^2 + \frac{21}{4a^2} = 5$

[ocean seal]

Dork9399

[hot hatch]

And is it advanced or mains

[hot hatch]

Is this imaginary root?

Bitc-

[tardy tapir]

i dont see the 'question' anywhere

[tawdry urchin]

I won't bore you with solving the equation but the sols are $\pm \sqrt{\frac{7}{2}} and \pm \sqrt{\frac{3}{2}}$

[ocean seal]

Dork9399

[wintry sluice]

bruv 💀

[hot hatch]

Ask him the answer then...

[tawdry urchin]

does the question really matter

we can get a sol

its fine

[hot hatch]

Yeah

What do u even get here?

It's not even square root of complex number

To simplify

[tawdry urchin]

so taking a = sqrt(3/2)

we get b = sqrt(7/2)

[hot hatch]

I'm pretty sure the question is flawed but you continue

Nvr seen a JEE question like this

[tawdry urchin]

,calc sqrt(7/2) - sqrt(3/2)

,calc sqrt(5- sqrt(21))

they are the same

[hot hatch]

Wasn't the question 5- root 21?

Not 5+

[tardy tapir]

@alpine sable try multiplying and dividing it by sqrt(2)

and show us what you get

[hot hatch]

@alpine sable I checked in google and I don't see a similar JEE question

[ocean seal]

Result:

0.64608382199538

Result:

0.64608382199538

[tawdry urchin]

mb mistyped

so simplified is $\sqrt{\frac{7}{2}} - \sqrt{\frac{3}{2}}$

[ocean seal]

Dork9399

[hot hatch]

See this

[hot hatch]

You got same

[tawdry urchin]

yea

[tardy tapir]

🤷‍♂️

he multiplied and divided by sqrt(2)

not 2

[hot hatch]

2 inside root

So root 2

[lone heart]

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[tawdry urchin]

bro this is some mathemagic right here

[lone heart]

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[alpine sable]

Representacion Verbal :
Todos los números reales
mayores que -3 y menores
o iguales que 5
Representacion Simbolica:
(−3, 5]
−3 < 𝑥 ≤ 5

Representacion Verbal:

Representacion Simbolica:
−4.5 ≤ 𝑥 < 3
__
Representacion Verbal:
Todos los números
menores o iguales que -7
Representacion Simbolica:

__

Representacion Verbal:

Representacion Simbolica:
[3.8, 5.6)

__
Representacion Verbal:

Representacion Simbolica:
(1.9, ∞)

[lone heart]

Please don't occupy multiple help channels.

[alpine sable]

@hardy path

[hardy path]

Fuera de mi nivel de habilidad

[alpine sable]

:c

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[vast tapir]

Square both sides

[alpine sable]

how?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[lone heart]

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[raven field]

im learning about polar coordinates, why is (-3,-7pi/2) placed at the bottom instead of the top?

[tribal field]

With negative radiuses, they'll be on the side opposite of where you'd expect

[raven field]

tysm

.close

[lone heart]

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[lone heart]

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[shell narwhal]

how do i find the normal vector on z=x^2-y^2

[shell narwhal]

or on 3x^2+y^2-8

one of them you can choose

[wanton peak]

Use gradient vector

[shell narwhal]

why ?

[wanton peak]

Normal vector is just gradient vector right?

[shell narwhal]

c

[wanton peak]

💀

[remote heron]

you should be careful with chatgpt and math

[wanton peak]

Its so powerful yet sometime so stupid, when it's first come up, I tested it with a calc 3 problem with mid-level hard; somehow, chatgpt got it correctly

[remote heron]

thats not the problem

[shell narwhal]

.close

[lone heart]

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[hallow dome]

Hey

[lofty heart]

hey akti

[hallow dome]

Let $a_1,...a_n$ all strictly positive and distinct $\$
I wanna prove that it exists $b_1 \le ... \le b_n$ and ${b_1,...,b_n}$={a_1,...a_n}$

[ocean seal]

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

[median oar]

Well, let $b_1 = \min(a_1, …a_n)$

[ocean seal]

Frosst

[hallow dome]

We can use $\sigma$ a permutation of ${1,...n}$ but I'm not familiar with that that's why I ask help

[ocean seal]

Akti

[median oar]

Let $b_2 = \min({a_1, …,a_n} \setminus {b_1})$

[ocean seal]

Frosst

[hallow dome]

$b_k = min({a_1,...a_k} \setminus {b_1,...b_{n-k}$ ?

[median oar]

Something like that yeah

[ocean seal]

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

[hallow dome]

ah ye I didn't think it like that

but yeah it should works

[median oar]

I mean it should be possible right

You just pick the list in increasing order

The a_n’s are in R and R is totally ordered

[hallow dome]

a_n are in N

[median oar]

Those are also totally ordered

[hallow dome]

yep

[median oar]

Same thing

[hallow dome]

For all k in {1,...n} right?

[median oar]

Yeah

[hallow dome]

that's a good idea ty

[median oar]

But you can’t setminus b_0

Be careful of the notation

[hallow dome]

I was lost with permutation

n-k+1 then?

[median oar]

Just define b_0 to be something negative

So when you set minus it doesn’t do anything

[hallow dome]

It still works if we say $A \setminus {\emptyset}$ ?

[median oar]

The empty set is not a number

[ocean seal]

Akti

[median oar]

Eh it should still work

You’ll be doing {a₁, …aₙ} \ {{}}

Which is something the a set doesn’t contain

So it won’t change anything

[hallow dome]

I mean at first we have $b_1 = min({a_1,...,a_n} \setminus {b_1}$ but at this moment $b_1$ doesn't exist

[median oar]

But still

But we don’t

[ocean seal]

Akti

[median oar]

Oh

I misread

Sorry

Nevermind

[hallow dome]

me too

I just realised

a_{n+1-k} is wrong actually

[median oar]

Yeah no you wrote it right the first time

[hallow dome]

this you mean?

if so, it's wrong

for exemple, with n=10 and b=5, we have b_4=min(...) \ {b_1...b_6} and we want b_3 not b_6

So it's k-1

$bk = min({a_1,...a_n} \setminus {b_1,...b_{k-1}})$ ?

[median oar]

Omg

Ok I’m just saying random things without thinking

[ocean seal]

Akti

[hallow dome]

but we needs to say b_1 = min({a1,...a_n})

cuz b_0 doesn't exist you were right

[median oar]

Following this, clearly $b_k = \min({a_1,…a_n} \setminus \bigcup_{i=1}^{k-1}b_i)$

[ocean seal]

Frosst

[median oar]

And it is often useful to define unions from 1 to 0 as the empty set

[hallow dome]

yep

[median oar]

I guess

[hallow dome]

it's a bit weird to use union for one element each time but it works

[median oar]

I just like the bigcup command and reduces the \{\}

[hallow dome]

$b_k = \min(\bigcup_{i=1}^na_i \setminus \bigcup_{i=1}^{k-1}b_i)$

[ocean seal]

Akti

[hallow dome]

we got it

ty

@median oar are u here I have a last question

[median oar]

I’m here yeah

[hallow dome]

can we say ${b_1,\ldots,b_n}={a_1,\ldots,a_n}$ ? $\$
Or should we say $\bigcup_{k=1}^nb_k=\bigcup_{k=1}^na_k$ ?

[ocean seal]

Akti

[hallow dome]

.

[median oar]

They mean the same thing

Sets are not ordered

[hallow dome]

I wasn't sure

[median oar]

The only thing here in the question was to show you could actually pick an order

[hallow dome]

Also how can I prove $\sum_{k=1}^n \dfrac{a_k}{k^2} \ge \sum_{k=1}^n\dfrac{b_k}{k^2}$

[ocean seal]

Akti

[median oar]

Aren’t they the same set

Or is this a different question

[hallow dome]

same a_k and same b_k

but it doesn't mean when we divide by k^2 it's still same

[median oar]

Oh but they aren’t the same

Because b is a reordering of a

Ah that’s why it’s important they were positive and integers

[median oar]

This doesn’t hold otherwise

[hallow dome]

all we can say is $\sum a_k = \sum b_k$

[median oar]

Not =

[ocean seal]

Akti

[median oar]

Well

[hallow dome]

reordonned or not, they have same sum

[median oar]

So I’m thinking

[median oar]

Ok

I got it

So if a_k <= b_k for all k

Then by comparison test, the inequality is held

But since b is the ascending reordering of a_k, you can never have a_k > b_k

Since there are only k-1 numbers before a_k and there are exactly k-1 b’s less than a_k before b_k

Does that make sense?

[hallow dome]

U sure? if a_3 = max(a_k) we don't have b_3 >= a_3

[median oar]

There’s 2 parts to it

[median oar]

Then k = 3

[hallow dome]

I mean

of a_n

[median oar]

Oh

[hallow dome]

We should use rearrangement inequality ig

[median oar]

The inequality is the other way lmao

It’s b_k <= a_k

[median oar]

Why did I write this lmao

[hallow dome]

still not

[median oar]

Why

[hallow dome]

if a_3 = min(a_n) then..

[median oar]

Then b_1 = a_3

[hallow dome]

ah ye

b_3 >= b_1

cuz it's ordonned

[median oar]

Yep

[median oar]

This is wrong

[median oar]

This is right

[median oar]

This is wrong at the end

[median oar]

This is correct

[hallow dome]

can I just say

For all $k \in {1,\ldots,n}, a_k \ge b_k$ since $b_1,\ldots,b_n$ is ascending order $\$
So $\dfrac{a_k}{k^2} \ge \dfrac{b_k}{k^2} \$
So $\sum_{k=1}^n\dfrac{a_k}{k^2} \ge $\sum_{k=1}^n\dfrac{b_k}{k^2}

[ocean seal]

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

[hallow dome]

What do you think @median oar

[median oar]

yes

[lone heart]

@hallow dome Has your question been resolved?

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[stark hawk]

ive solved this question in two ways but i want to know why one way doest work

[stark hawk]

the first way was correct- i used the cosine rule to find the velocity
but with the second way i converted the velocities in i's and j's and worked it out from there

wait ill show a picture

[lone heart]

@stark hawk Has your question been resolved?

[stark hawk]

<@&286206848099549185> vectors help pls I just want to know why one method works and the other doesn’t

[stark hawk]

<@&286206848099549185> 😢

[limpid hazel]

method 2 might not have worked because it might not have correctly accounted for the angle between the two velocities

[lone heart]

@stark hawk Has your question been resolved?

[lone heart]

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[real seal]

Can someone help me with these two questions?

[graceful pawn]

do you wanna solve it in factored form or completed square form

do you know what (h, k) represents

[real seal]

x intercepts

right

[graceful pawn]

thats for the factored form

but in the completed square form, (h, k) represents the turning point

[merry iris]

(vertex)

[real seal]

oo

i see

so I gotta

find the vertex?

[graceful pawn]

yes

[real seal]

ok lemme try something

Ok that did nit work

Im in need of guidance what to do

😭

<@&286206848099549185>

[vast cradle]

For 2a and 2b?

[real seal]

Yea

[vast cradle]

I think for 2a

You can try to use a system

[real seal]

system?

[vast cradle]

like you know the basic form

of a quadratic right

just ax^2 + bx + c

[real seal]

ye

[vast cradle]

and ur given two points

here

the y intercept

and what looks to be (6,10)

[real seal]

i only see one

Oh

Ye

[vast cradle]

then

starting with the yint

(0,10)

i can plug in 0 for x in the quadratic

[vast cradle]

plug x into this

i mean 0 for x

oh shucks

what would that do

yeah it would be better with three points

this lowkey is weird

OH

[real seal]

math is weird like that 🤷‍♂️

[vast cradle]

hmm

[graceful pawn]

im back

[real seal]

😮

[graceful pawn]

you should start with 2b, it's easier to solve

[vast cradle]

it says y = x^2 transformed

[real seal]

What that mean

🤔

[vast cradle]

prob jst saying its a quadratic

ye this is weird lowkey

might as we do 2b as other guy suggested

[real seal]

ight

[vast cradle]

only issue with 2b that i cant think of is the scaling

only issue is that you dont have a third point

[graceful pawn]

?

what scaling

you dont need a third point

[vast cradle]

cuz if u use intercept form

you have two zeroes

[graceful pawn]

use factored form

[vast cradle]

but theres some scalar

[vast cradle]

yeah but theres prob a scalar

[humble tartan]

Slope

[humble tartan]

The facts it’s not on a grid there probably isn’t

[real seal]

So just use factor form to try and figure it out?

[vast cradle]

prob yeah

[humble tartan]

Apply the transformations to the base power function

[graceful pawn]

yes

(h, k) for 2a = (3, 1)
(h, k) for 2b = (2, -8)

now just put that into the equation and find a, where y = a(x-h)^2 + k

@real seal

[real seal]

howd u get 1 in 2a

[graceful pawn]

you can see it by lookinkg at the graph

i can also give u a mathematical proof

[real seal]

do dat

i gotta open my eyes

[graceful pawn]

y = (x - h)^2 + k right, and there are 2 points (0, 10) and (6, 10)

[graceful pawn]

so you get

[real seal]

ye

[graceful pawn]

10 = (0 - h)^2 + k
10 = (6 - h)^2 + k

[real seal]

wait what 0-0

[graceful pawn]

so after simplifying everything, you get 36 - 12h = 0

[real seal]

I thought it would go in h,k

[graceful pawn]

and h = 3

[graceful pawn]

what is 0-0?

[real seal]

oh thats just a

little discord emoji

😮

[graceful pawn]

so you know that h = 3, u substitute into teh equation

[real seal]

like shocked

[graceful pawn]

10 = 3^2 + k

and k = 1

so i just used simultaneous equation, because in every quadratic graph, there are 2 points where y is the same

[real seal]

Lemme write all this down and see if I got any questions

[graceful pawn]

so now you know (h, k) = (3, 1)

[real seal]

How did you solve these

[graceful pawn]

so like

[real seal]

like 6-h

[graceful pawn]

(6-h)^2 = (6-h)(6-h) = 36 - 12h + h^2

[real seal]

OHH

Yo thats something i remember my teacherr sayin

[graceful pawn]

its just a mathematical proof to show that (h, k) = (3, 1), dont overthink it

[real seal]

Yea but i think im gonna need thag

Because my teachers gonna give me half a mark if I say

[graceful pawn]

oh, that's true XD

[real seal]

yea you get it

and im assuming you would do the same thing

for the other equation

and add it

?

[graceful pawn]

wdym add it

[real seal]

like the uh

the “like terms”

[graceful pawn]

so

do you understand how to get (3, 1) now

[real seal]

wait how did u go from

[real seal]

this

to

H=3

Wait is it ebcause like

3 makes the equation

[graceful pawn]

so (0-h)^2 = (6-h)^2

[real seal]

true

[graceful pawn]

so h^2 = 36 - 12h + H^2

[real seal]

Ye

[graceful pawn]

and after you simplify it, 36 - 12h = 0

and h = 3

[real seal]

oh

Wait how are u simplifying it

[real seal]

into this

[graceful pawn]

bruh im overcomplicating this shit

ok ykw

[real seal]

lmaoo im might be cooked

[graceful pawn]

in (0, 10), the x is 0

in (6, 10), the x is 6

the x coordinate of the turning point is (0+6)/2 = 3

wait bad explanation

[real seal]

Nah wait

I actually

Understoood that

cause thats how u find midpoint

[graceful pawn]

yep

but they have to be on the same line

[real seal]

Go on

[graceful pawn]

if you get what im saying

[real seal]

Yea

[graceful pawn]

so y = (x-3)^2 + k

substitute (x, y) = (0, 10) into the eqn

10 = (0-3)^2 + k

and find k

[real seal]

I see

what about a

[graceful pawn]

now you know y = a(x - 3)^2 + 1

[real seal]

Oh

So i just leave a

[graceful pawn]

todays your lucky day a = 1

[real seal]

Ight bet

Lemme try the second one

[graceful pawn]

ok but how do you get a = 1

[real seal]

Oh

[graceful pawn]

y = a(x-3)^2 + 1

you substitute (x, y) = (0, 10) into the eqn

and solve for a

same thing

[real seal]

Ohh so you solve a last

[graceful pawn]

yes

you can choose any point on the graph

and substitute it into the eqn

[real seal]

Man my indian teacher cant explain shit 💀

[graceful pawn]

XD

[real seal]

Alr lemme try 2b

Alr

Tell me if im doing this right

[graceful pawn]

i think im not qualified to be a helper ☠️

[real seal]

still helping me out

thats all that matters

🤷‍♂️

[graceful pawn]

whered you get 1.5

[real seal]

uhhh

3/2

So like

The two “zeroes”

[graceful pawn]

man whattttt

[real seal]

were (-6,0)

(9,0)

OH

[graceful pawn]

its (10, 0)

[real seal]

THATS NOT 9

FUC

Hold up

Gimme a sec

[graceful pawn]

idk how to get k for 2b though ☠️

[real seal]

BOOM

Oh

[graceful pawn]

lemme thinik

are you sure you can't just look at the graph and go

teh turning point is (x, y)

[real seal]

i mean i think i could but like i feel like being able to explain it

would make sure I dont get

half a mark

Wait

What if I just used factor form

them figured the vertex form of it

[graceful pawn]

you can try

[real seal]

Ight

this all i got so far

not sure how i would change this to vertex form though

[graceful pawn]

you probably have to just eyeball it

and howd you get -16 dawg

also i gtg

sorry if i made you more confused XD

[real seal]

it ight

[frozen scarab]

is ur question answered?

[real seal]

not the second one

“2b”

Heres where im at but im not sure if im doin this right

[frozen scarab]

resend the question

[real seal]

Oh the question

[frozen scarab]

in standard, vertex, or x-intercept form?

[real seal]

vertex i think

[frozen scarab]

ok so you did (x+6)(x-10) but it should be a(x+6)(x-10) because the function could be dliated by a factor of a

[graceful pawn]

he pretty much knows how to solve it, he just needs a way to find out the turning point instead of eyeballing it

[real seal]

https://tenor.com/view/que-gif-27530657

[graceful pawn]

the (x+6)(x-10) that he did washim just tryna find y-coordinate of turning point

[frozen scarab]

can you not say (2, -8) is turning point?

or does the question want you to find that mathematically

[real seal]

my TEACHER wants me to find it mathematically

[graceful pawn]

im pretty sure the only way to solve it is eyeball it XD

[real seal]

o wrd

😈

[frozen scarab]

theres no way to find the turning point mathematically you have to eyeball it and say it is (2, -8) then find the standard form of the quadratic

[real seal]

bet

[frozen scarab]

then use completing the square to change it to vertex form as u said vertex is the preferred answer

[real seal]

elaborate rq

[frozen scarab]

alr let me clarify my response better

easiest way is

start with y = a(x - 2)^2 - 8

cus turning point is (2, -8)

then find the dilation factor a by substituting one of the x-intercepts into the equation

[graceful pawn]

everything we did for 2a basically @real seal

[frozen scarab]

this works but it is more complicated than it needs to be lol, dont do this

[real seal]

Oh

Did i do it

[frozen scarab]

yea ur good

[real seal]

https://tenor.com/view/arms-wide-open-parker-mccollum-handle-on-you-song-outstretched-arms-open-arms-gif-4050047577086926131

les go bois i just finished question 2 out of 27 at 12pm (im actually fucked)

alright my questions been answered for today

[lone heart]

@real seal Has your question been resolved?

[lone heart]

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[slim mica]

hi

[slim mica]

i dont understand step 2

of question a at all

like i integrated it myself and i got m = 2.19 which appears to be the correct answer

but idk how to get it into the form of 2m^2 - 24m + 43

like how did their x become x^2

and their 6 become x

did they integrate it or something..!?!?!?!!

[frozen scarab]

this is a probability density function so the area under the curve represents the probability

to find the median value which we let m, we know that the definite integral from 1 to m will equal to 0.5 (probability from 1 to m will be 0.5)

evaluate the definite integral and you find that x becomes (x^2)/2 and 6 becomes 6x

use the formula for definite integrals by substituting m and 1 and evaluate to get your answer

[lone heart]

@slim mica Has your question been resolved?

[slim mica]

i dont get that part

i integrated it but i’ve never encountered a x

x^2

[wispy geyser]

you have always kept this factorized in (6-x)². developing that gives you the x and x²

[frozen scarab]

you integrated incorrectly

[slim mica]

ohh

so i was supposed to expand it

instead of just evaluating them right away
?

[wispy geyser]

you can

[frozen scarab]

no

integral of 6 - x is 6x - (x^2)/2

[slim mica]

but my final answer turned out correct

m = 2.19

[wispy geyser]

but you have it right at the end too if you want

no integration is fine

[frozen scarab]

no its not fine

[wispy geyser]

it's weird but

[frozen scarab]

its incorrect

[wispy geyser]

it's a constant off

[slim mica]

i used the

(ax+b)^n

and fit it into (6-x)

[wispy geyser]

I would integrate like you did Isaiah but his answer is just a constant off

so it's fine

[slim mica]

[(6-x)^2]/(-1 * 2)

was this wrong

[frozen scarab]

yeah

[wispy geyser]

It's not wrong but everybody integrates polynomials by first developing it then itegrating every term

[frozen scarab]

wait no its right

[wispy geyser]

yes

[frozen scarab]

so youve done chain rule in reverse

thats weird

[wispy geyser]

yes very weird x)

[slim mica]

wait

[frozen scarab]

you should just integrate each term individually for 6 - x lol

[wispy geyser]

yes

[slim mica]

so after this i was supposed to expand the numerator?

to get like a x^2 and 6x or something?

[wispy geyser]

no right at the begining

[frozen scarab]

if it was (6 - x)^20 or something i would understand lol but like just 6 - x

[slim mica]

ohh hold on let me try

[wispy geyser]

You've basically used a formula that is right but that nobody uses for this kind of integrals

[lone heart]

@slim mica Has your question been resolved?

[lone heart]

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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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[frank gate]

im stucked at g(2x-3)=4x^2-12x+11

i continued but cant get the answer

anyone?

[gray isle]

consider doing a sub like
u = 2x-3

[frank gate]

wdym by 'u'

[gray isle]

a new variable

[frank gate]

Oh

lemme try

[gray isle]

choose whatever you want, (within reason)
i just prefer u

[frank gate]

is it like let y=2x-3

or f(y)=2x-3

[gray isle]

i'd advise against using y
due to how its linked to function values when graphing

[frank gate]

My teachers suggest us using y

and books used y too

[gray isle]

use whatever then, end result doesn't change

[frank gate]

ok

so is it

let y=2x-3

or f(y)=2x-3

[gray isle]

let
your choice of variable = 2x-3

and then express
g(2x-3)=4x^2-12x+11
in terms of that variable

after this step you shouldn't see any more x in your equation

[frank gate]

then the next step is g(y)=4x^2-12x+11

right?

[gray isle]

no

if you're choosing to use
y = 2x-3
then y=2x-3

[frank gate]

yeah

[gray isle]

oh edited now

[frank gate]

i dont get it

[gray isle]

you'd now also want to express the right side of that equation in terms of y

[frank gate]

ok

[gray isle]

from

y = 2x-3
x = ?
then sub that in

[frank gate]

x=1.5

[gray isle]

no

how are you getting x=1.5

[frank gate]

i solve the

[gray isle]

solve what

[frank gate]

4x^2-12x+11

[gray isle]

show me exactly what you did that lead to getting
x=1.5

[frank gate]

this equation

i used calculator

[gray isle]

how?

[frank gate]

to solve this equation

calculator give me x=1.5

[gray isle]

what exactly did you type into the calculator

[frank gate]

a=4,b=-12,c=11

[gray isle]

you shouldn't be solving 4x^2-12x+11 = 0
nor will that get you x=1.5

[frank gate]

then what should i do

[gray isle]

from
y = 2x-3
x = ?

[frank gate]

oh

y+3/2

[gray isle]

no

[frank gate]

wtf

[gray isle]

if you mean $x = y + \frac32$, that is incorrect

[ocean seal]

ℝαμΩℕωⅤ

[frank gate]

no

i didnt mean this

the divide 2 is for both y and 3

means y/2+3/2

[gray isle]

oh

you should use () then

to indicate that

[frank gate]

oh sorry

[gray isle]

(y+3)/2

[frank gate]

then after this i sub in?

[gray isle]

yes

[frank gate]

i got -4y+17

how do i continue

after this

[gray isle]

that doesn't look right
show exactly how you're getting that

[frank gate]

4<(y+3)/2)>-12<(y+3)/2>+11

2y+6-6y-18+11

-4y+17

[gray isle]

you're missing the ^2 on the first term

[frank gate]

OH

SHIT

i got the answer already

thankyou so muchhhh

.close

[lone heart]

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[lone heart]

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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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[stable lantern]

Two unidentified flying discs are detected by a receiver. The angle of elevation from the receiver to each disc is 39.48°. The discs are hovering at a direct distance of 826 m and 1.296 km from the receiver. Find the difference in height between the two unidentified flying discs, to the nearest metre.

[stable lantern]

i used tan to work out the height of both

disk 1 was 680.41m

and disk 2 was 1067.58m

then i subtracted to get the difference in height

387m

but the answer says its 299m so idk what i did wrong?

plz help

[frozen scarab]

direct distance

so wouldnt that mean the hypotenuses?

[stable lantern]

wait lemme try

if i was to find out the hypotenuse

i would have to use cos right?

[frozen scarab]

for the first disc, sin(39.48) = h/826

where h is its height above the ground

and 826 is the direct distance

[stable lantern]

wait so 826 is the height from the ground

not the recepter?

[frozen scarab]

no

ill draw a diagram for you

[ocean seal]

Couldn't find an attached image in the last 10 messages.

Apr 21, 2024, 7:36 AM

[frozen scarab]

,rotate

[stable lantern]

ohhh ok i got it

[frozen scarab]

so its sine

answer will be 299m

[stable lantern]

yup thx i accidently drew my diagram wrong 😭

.close

[lone heart]

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[lone heart]

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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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• Be polite and have a nice day!

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[loud anvil]

i had nothing better to do so i started doing maths can someone help answer this with working out cuz i can't work it out for some reason and chatgpt is fcked when it comes to decent working out

[viral oracle]

you don't use chatgpt for maths

[vast cradle]

fr

its p much

the area of the bottom + area of side of the cylinder + area of the hemisphere

[viral oracle]

^^^^^^^^^^^

[storm badge]

GPT be like: "Oh sorry, i didnt know 2+2=4, let me correct myself by saying 2+2=6"

[vast cradle]

and they gave u radius as 15 cm and height as 10 cm

surface area of a sphere u gonna have to look that up cuz i got no clue

and its half a sphere

but thats that

[loud anvil]

can some1 write working out on paint or smth?

[loud anvil]

i understand that but my answer is always incorrect i want to know where i was wrong

[vast cradle]

ion know ur answer tho

[loud anvil]

nah alg im stupid i got the answer thx

[vast cradle]

make sure to close the channel

[loud anvil]

.close

[lone heart]

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• 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!

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[atomic steppe]

This is a common diagram used to show where the formula for a determinant comes from.

[atomic steppe]

I have rotated this diagram, and I get a different formula for the area.

= ab + ad + bc + cd - cd - ab
= ad + bc```
However if I use -c instead of c. Then I get the correct answer?
```(a+(-c))(b+d) - (-c)d - ab
= ab + ad - cb - cd + cd - ab
= ad-cb```
Why is this?

Can a, b, c and d not represent negative values anyway?

[echo socket]

You changed the sign of c by the rotation

[atomic steppe]

I don't quite get this. Imagine you've never seen the first diagram and you see the second one now. Could c not represent a negative value? I don't get how it makes a difference

[echo socket]

c can be negative, yes, like in the same diagram

The formulas are different because you are calculating the area, which is not the same as the determinant

Also I think the only difference between the diagrams is that the sign of c changes rather than an actual rotation since [a, b] stays in the same quadrant

[atomic steppe]

I thought the determinant was the area?

[echo socket]

No, the determinant's magnitude is the area and it's sign is dictated by orientation

But with that the formulas would still differ so nvm

[lone heart]

@atomic steppe Has your question been resolved?

[atomic steppe]

.close

[lone heart]

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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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[celest pulsar]

how do you write each set of these measurements in order of size, starting with the smallest

76cm, 745mm, 0,074m

[frozen scarab]

convert all to the same unit then compare

[celest pulsar]

i keep getting confused when converting

[frozen scarab]

i recommend converting all to cm

so 76 cm remains same

10 mm is 1 cm

so 745 mm is 74.5 cm

100 cm is 1 m

so 0.074 m is 7.4 cm

[celest pulsar]

after that do you just order it from smallest to largest according to the numbers

[frozen scarab]

yes so what would u order it

[celest pulsar]

uhm

7.4 cm , 74.5cm and 76 cm

is that right

[frozen scarab]

yes...

[celest pulsar]

i need to get this in my brain could u give me an equation

[frozen scarab]

equation? u mean a question like that one?

[celest pulsar]

Yup

[frozen scarab]

alr uhh

0.045m, 4.8cm, 48.66mm

[celest pulsar]

Okay so since you suggest converting all of them into cm

4,8 stays the same

4.8 cm

0.045 into cm is...

uhm

you multiple it by 100

MULTIPLY

MY BRAIN ISN"T BRAINING OMG

soo

that's 4.5 cm

it turns into*

then 48.66mm into cm is..

how do you do that

divide by 10

[frozen scarab]

10 mm is 1 cm

[celest pulsar]

Oh ok

so then

that's 4.866cm

the answer is

0.045m, 4.5cm and 48.66mm

smallest to largest

uhm

[frozen scarab]

yeah

[celest pulsar]

the answers correct?

[frozen scarab]

well 4.8 cm

but yeah

correct

[celest pulsar]

4.8cm sorry

typo

[frozen scarab]

ur allgg

[celest pulsar]

I need more help

[frozen scarab]

may i ask

what maths is this for?

[celest pulsar]

the same thing but it's now cm squared

[celest pulsar]

I have a test 😭

[frozen scarab]

give me the question

[frozen scarab]

uni ?

[celest pulsar]

No this is easy level math

Middle school

[frozen scarab]

u have a middle school test?

[celest pulsar]

i'm in 8th grade..

HELPP

[frozen scarab]

oh..

then why did u choose undergraduate role

that means ur in uni bruh

[celest pulsar]

what was i suppose to pick

[frozen scarab]

pre-uni

[celest pulsar]

Oh

[frozen scarab]

cus this stuff is way way way too easy for uni

[celest pulsar]

exactly 😭

[frozen scarab]

i was confused lol

anyways give me the question

[celest pulsar]

1km², 1m², 1cm²

smallest to largest

[frozen scarab]

thats the question?

[celest pulsar]

eah

y

[frozen scarab]

thats even easier lol

what do u think

the answer is very obvious

[celest pulsar]

you still convert them into cm?

[frozen scarab]

no...

[celest pulsar]

Math is my weakest subject you're gonna have to bare with me 😭 sry

[frozen scarab]

look at the list

1km², 1m², 1cm²

order it

from smallest to largest

u know how to start? or should i start you off

[celest pulsar]

help me PLS

[frozen scarab]

ok ill start you off

obviously 1 cm squared is the smallest

[celest pulsar]

whys that

[frozen scarab]

do you know what a cm is

[celest pulsar]

centimeter

[frozen scarab]

yes but do you know how big it is

[celest pulsar]

no

[frozen scarab]

centimetre, metre, kilometre

whats the biggest?

[celest pulsar]

kilometre

[frozen scarab]

whats the second biggest

[celest pulsar]

metre

[frozen scarab]

whats the smallest

[tulip bone]

2 cm is average

btw

[celest pulsar]

centimetre

[frozen scarab]

@tulip bone this is the hardest question ever

pls help

[tulip bone]

LMFAOAOA

[tulip bone]

oh

[frozen scarab]

yeah so for 1km², 1m², 1cm²

[tulip bone]

damn

[frozen scarab]

whats the smallest

[tulip bone]

pull up your scale

js pull up yo scale

[celest pulsar]

what scale

[tulip bone]

your

[celest pulsar]

1cm squared, 1m squared and then it's 1km

[tulip bone]

simple scale??

ruler

[frozen scarab]

yeah thats the answer

easy

thats why i said it was obvious

[tulip bone]

not necessarily

in the question its 0.076 m

[celest pulsar]

What's the difference between non squared questions and squared

[frozen scarab]

this is a different question

[tulip bone]

oh

mb

</3

[frozen scarab]

squared dimensions is about area

[celest pulsar]

oh

so you dont have to convert anything ..

[frozen scarab]

for that one yeah

but for this one: 76cm, 745mm, 0,074m
you do have to convert

[celest pulsar]

Oh

I'll get that in my brain

Give me a question now

[tulip bone]

1 m is how many centimeters?

[frozen scarab]

good question

[celest pulsar]

I MEANT A PROBLEM 😭

[tulip bone]

tell me tho

how much is it

[celest pulsar]

100

[tulip bone]

correct

[celest pulsar]

1,000

[frozen scarab]

alr ill give a problem

[tulip bone]

i kilometer is how many meters

1

[celest pulsar]

I don't know 😭

[tulip bone]

boy

cmon

[celest pulsar]

that's the thing i keep forgetting, it's hard for me to get it in my brain 😭

[tulip bone]

alright

theres a very

[celest pulsar]

i have to learn it by heart how do you guys do it

[tulip bone]

VERY CUTE PATTERN

bring your ruler up

[celest pulsar]

I dont have one