help-10

[heavy frost]

yes, that what i told u in other question

😄

[merry cave]

i did 72 x 2 got 144 but halve then get the same 72

[frail junco]

just use the other dude's thing where (8x+12)+72 = 180

it makes sense bc the lines make the full circle

[merry cave]

12?

[frail junco]

angle PXW + angle PVW = 180 ddegrees

so it goes to 8x+12 + 72 = 180

and then you can solve from there

[merry cave]

yes i got 12

[frail junco]

oh i thought you were questioning where i got it from

yeah that should be it

[obtuse pebble]

@merry cave Has your question been resolved?

[obtuse pebble]

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[ancient drift]

is A the correct answer?

[ancient drift]

im confused

[sullen turtle]

Let me check

[ancient drift]

alright

[sullen turtle]

For me it's A

Let me explain

[ancient drift]

please do

[sullen turtle]

You can change the value of x in the expression, and you'll get an y

[ancient drift]

ohhh

i’m dumb for not trying that

[sullen turtle]

In every occasion, the result will never equal to the "expected result"

But it's similar

[ancient drift]

can i ask you

one more thing

[sullen turtle]

For example:
$3.48*(-4)^2+1.22(-4)+3.44 = 54.24$

[warm shale]

186_

[sullen turtle]

Check with the others results

[warm shale]

ilytimm

For example:
$3.48*(1)^2+1.22(1)+3.44 = 54.24$

[ancient drift]

okay thank you

.close

[obtuse pebble]

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[ember swallow]

In the midst of the Cold war, in the 1950s, a sleek aircraft known as the Avro Arrow was built to intercept Soviet bombers that might have entered North American air space over the North Pole. The Arrow was scrapped in 1959 and the planes were ordered to be destroyed. Nine model aircrafts were launched into Lake Ontario and were never recovered.

In the summer of 2017, a mission to recover the nine models of the Avro Arrow was launched. It was a collaborative effort by several private companies in collaboration with the Canadian Coast Guard and the Royal Canadian Military Institute.

A Newfoundland company, Kraken Sonar Systems, was awarded the $500,000 contract which will involve deploying its state-of-the-art ThunderFish underwater vehicle and AquaPix sonar system to capture high-quality images of the lake bed.

**The high probability area that was to be searched included 64 square km.

The Thunderfish and crew can map and analyse 1 square km at a time, doing 5 in a week. Assume each of the 9 model Avro Arrows would occupy it's own square km. Meaning, there cannot be two Arrows in the same square km.

What is the probability that, after the first week, the crew find at least one of the Avro Arrows?**

[ember swallow]

i'm learning about permutations and combinations, but I am confused about how to apply it to this

A lot of this question is just setup, so i bolded the main thing being answered

[obtuse pebble]

@ember swallow Has your question been resolved?

[ember swallow]

<@&286206848099549185>

[hard phoenix]

Imagine the high probability area to be 64 tile square space.

[ember swallow]

alright

[hard phoenix]

What is the probability of finding an avro in a tile

[ember swallow]

9/64?

or would it just be 1/64

[lone dirge]

So let's simplify. 64 squares, there are arvos in 9 random squares, and you are searching in 5 squares?

@ember swallow

[ember swallow]

sorry for the late response, yes

[lone dirge]

So why 9/64?

9/64 would be the probability of finding 1 if you are searching in 1 square

[ember swallow]

so would it be 9/64 x 9/64 x 9/64 x 9/64 x 9/64 for 5 squares?

[lone dirge]

no

Why do you multiply?

[ember swallow]

i was thinking of another example i've done similar to this

1/2 was one coin being flipped, 1/4 was too coins being flipped 1/8 was 3 coin, etc.

i thought it would be similar

[lone dirge]

You are referring to the probability of two events to happen together

such as getting two Heads when two coins are flipped

Then you can multiply the probabilities if the events are independent.

Pr(A and B) = Pr(A) * Pr(B).

But this is not the case here

This is the case with the coins... In your question you don't have 5 events

And even if you do, you are not looking for the probability of all of them to happen together

Say if you define the events A_i = the i-th crew finds an arvo

You are looking for the probability of A_1 or A_2 or A_3 or A_4 or A_5

@ember swallow right?

[ember swallow]

Yeah

[lone dirge]

OK, here's a way to think about this. Let's fix the 5 square the crews are searching in

And now you can imagine that 9 squares are chosen randomly out of the 64

These where the arvos are

So what is the probability that at least one of the 5 squares we are searching in will be chosen

[ember swallow]

1/9

[lone dirge]

How many ways are there to choose 9 squares?

64C9 right?

[ember swallow]

Oh. Yeah

[lone dirge]

Now, it would be easier to calculate the probability of the compliment

That is the probability that we don't choose any of the 5 squares the crews are searching in

Can you find it?

How many ways are there to choose 9 squares out of the squares the crews aren't searching in?

@ember swallow

[ember swallow]

27540584512?

[ember swallow]

like your asking for this right?

[lone dirge]

What is this?

Oh no

64C9 is the number of ways to choose 9 squares out of all the 64 possibilities

[lone dirge]

this is different

[ember swallow]

I actually have to go right now

Sorry

[lone dirge]

Bye

[ember swallow]

I think what you explained makes sense, I’ll try to see what I can do

Thanks

.close

[obtuse pebble]

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[merry cave]

how do i get d?

[urban patrol]

quadliteral's interior angles add up to 360

[obtuse pebble]

@merry cave Has your question been resolved?

[obtuse pebble]

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[remote timber]

can somebody please explain what this means 😓 How do I even graoh it

[remote timber]

or this please help

<@&286206848099549185> how do you even graph this..

[obtuse pebble]

@remote timber Has your question been resolved?

[remote timber]

<@&286206848099549185> ? D:

[fierce lagoon]

Do you know how to do shell or washer/disc method?

[remote timber]

yeah of course, I've been painfully learning about it all day

but like what is the third variable how do I even like graph it

I feel so hopeless hah

I know how to do both though

[fierce lagoon]

"a" is just a constant of some sort

[remote timber]

that's what I thought, but how do you graph that? Or are ya not supposed to?

[fierce lagoon]

If you want, go to desmos and substitute sqrt(a) with some random ass number and see what it'll look like

[remote timber]

but won't the volume change depending on the number

[polar fossil]

yeah

but that's just for intuition

[fierce lagoon]

But I wouldn't even graph it

[remote timber]

hm.. okay, how do you do this without GRAPHING??..

[lost salmon]

Which third variable?

[remote timber]

the a^1/2

@lost salmon

[polar fossil]

all you need to know are the bounds, you have the left bound already

the right bound comes from where it intersects the x axis ie y = 0

[lost salmon]

The third variable it’s there just to say that it’s a constant… when you integrate you treat “a” like a constant

[remote timber]

mannee

so then how do you go about it like

true we do have one pound

bound

lord

[polar fossil]

if you need a sketch, just figure out where it crosses each axis and draw whatever shape you want

[lost salmon]

$\int{a \cdot dx} = a\cdot x + C$

[warm shale]

pcheese2010

[remote timber]

yeah so 0 is one, but how is the SOFTWARE gonna know which number i randomly choose

[polar fossil]

you would presumably type in some expression containing the variable a

[remote timber]

yeah in desmos you can have a slider

where the picture slides

[polar fossil]

... into the software you would type this

like, the answer to this question will not be a number

[remote timber]

so when you revolve it over the x axis for example

you know the first bound is zero,

you get it in terms of x ? so maybe y = sqrt(a) - sqrt(x)

[lost salmon]

You shouldn’t, that’s why you professors actually put that way… Knowing this is probably something that is an exam or test (which shouldn’t be posted here) he put that way to you work out an algebraic expression.

[remote timber]

no it's my homework :( HW 7.3

[polar fossil]

you would solve for y yes

[remote timber]

it's Chapter 7 applications of integration it's killing my brain n makin me sad

[lost salmon]

Look, $a$ could be any number you want

[warm shale]

pcheese2010

[polar fossil]

if you want you can start with a = 4

[remote timber]

yeah but I can't use that in the final software answer, right?

[polar fossil]

correct

you'd essentially have to do it again without putting a number in there to get the expression

[lost salmon]

You’ll substitute 4 by $a$ in the final answer

[warm shale]

pcheese2010

[remote timber]

alright so I have a FUNCTION now

y = a - x

[lost salmon]

Integrate this

What you’ll find?

[polar fossil]

,tex .freshman

[warm shale]

Hayley

[remote timber]

from 0 to ?..........

wait is it a

0 to a maybe

ax - x^2/2 ?

[lost salmon]

Incorrect expression

[lost salmon]

Right logic

[lost salmon]

See this

[remote timber]

oh shit so it is (a-x)^2

but I still don't know the top bound

I guess I'll use disk so just normal pi

[lost salmon]

Nope see what you’ll find

:

[remote timber]

a^2 - 2ax + x^2 ?

[lost salmon]

Correct

Actually

Incorrect

[polar fossil]

show your work in solving for y...

[lost salmon]

$\sqrt{x} + \sqrt{y} =\sqrt{a}$

[polar fossil]

,rccw

[polar fossil]

$2^2 \neq 1^2 + 1^2$

[fierce lagoon]

I KEEP FORGETTING TO DOWNLOAD HIS STUFF

[warm shale]

Hayley

[polar fossil]

even though 2 = 1 + 1

[fierce lagoon]

FUCK IRS BEEN 6 MONTHS LOL

[remote timber]

shoot ur right

so you cant square the entire expression to make the roots go away?

[warm shale]

pcheese2010

[polar fossil]

you can square the entire expression

but the roots won't go away

at least not all of them

[remote timber]

so what's the educated way of doing it? 🧠

🤯

trippy

mane idk why he put this on here this is a calc 2 class

he just wants us to suffer even though he doesn't teach us at all how to do somethin like this

[polar fossil]

squaring both sides of the equation

[remote timber]

but which ones does that get rid of then

[polar fossil]

the one you care about

[remote timber]

ahh makes sense actually, so if I square

okay here

like that

[polar fossil]

what

what did you do to get from the first eqn to the second

[remote timber]

but I thought that's how it worked 😂

squaring the whole equation!!

[polar fossil]

if you squared the whole equation (ie both sides) you would get $(\sqrt x + \sqrt y)^2 = \sqrt a^2$

[warm shale]

Hayley

[remote timber]

I also moved x over with a so we have it in terms of x

[polar fossil]

ah okay so you had $\sqrt y = \sqrt a - \sqrt x$ and you squared both sides?

[warm shale]

Hayley

[remote timber]

yes !

[polar fossil]

,tex .freshman

[warm shale]

Hayley

[remote timber]

shit

so hold up

@polar fossil boom😎

,rccw

[remote timber]

got chu

[polar fossil]

+x

[remote timber]

oops.. yeah

[lost salmon]

Yeap

[remote timber]

OKAY WOW

so THAT'S the integral function

but I STILL don't unerstand HOW there can be a top bound

unless it's like a - x or some random

[polar fossil]

that's the original function you started with

[remote timber]

no ik that's what I put in the integral i guess

[polar fossil]

there's a top bound because the target function crosses the y axis, hangs out in quadrant 1, and then dips below the x axis

[remote timber]

interesting

[remote timber]

so now you put that in an integral and evaluate the antiderivative

WHY does

how do you know it looks like that ?! in desmos it's totally differet

[polar fossil]

i don't have a clue what it looks like (lie)

but it doesn't matter what it looks like

[remote timber]

damnn

okay so how do we KNOW the bounds then ?!?

[polar fossil]

well, where does it cross the x axis?

[remote timber]

y=0

[polar fossil]

yes that is what it means to cross the x axis

[remote timber]

so the bounds are 0 and 0 ?!

[polar fossil]

at what value of x does it cross the x axis

[remote timber]

I wouldn't be surprised at this point

y=0

wait

shit

hold on

[polar fossil]

am i speaking spanish

[remote timber]

so you INPUT 0 for y

IM SORRY NO

😩

SO YOU can input 0 for y and liek pick a random number for a

[polar fossil]

no don't pick a random number for a

just put in 0 for y and solve for x

[remote timber]

but a is also an unknown variable

[polar fossil]

yes

[remote timber]

so how do we solve with two unknown variables?!

I keep forgetting it's a constant

so you could just like get the x and as on seperate sides

[lost salmon]

Actually no it isn’t an unknown variable , as a matter of fact its just an arbitrary number that doesn’t change

[polar fossil]

$\sqrt x + \sqrt y = \sqrt a$ \
let $y = 0$
$\sqrt x + \sqrt 0 = \sqrt a$

[warm shale]

Hayley

[polar fossil]

... can you solve that second eqn for x?

your answer will be an expression involving a

[remote timber]

WAIT

X = A /!

okay so

sqrt(x) = sqrt(a)

THEN you can SQAURE BOTH SIDES

THEN X = A

DAMNN

biggest plottwist

[polar fossil]

ah yes never would have guessed that in an equation involving square roots we might have to square something to solv eit

anyway

so now we know our bounds for the integral

reminder that we're doing a solid of revolution here

[remote timber]

definitely!

0 to x

or 0 to a

I guess they the same thing

,rccw

[remote timber]

WHAT?!? WHAT DOES

THE PI IS THERE

[polar fossil]

yeah, is the area of a circle equal to $\pi r$?

[warm shale]

Hayley

[remote timber]

yes?...

n o

maybe

hold o

[lost salmon]

Maybe?

[remote timber]

its squared

pir^2 ??

oh shit

YOU GOTTA SQUARE IT

OKAY

YEAH I forgot y bad

oh jesus this is gonna make my brain hurt gimme like 1 min

certified algebraic

,rccw

[remote timber]

wait but if x = a can we not just put everything in terms of a or x

is this what multivariable calculus is like

[polar fossil]

a is a constant, x is the variable we're integrating over

why do you think x = a?

[remote timber]

we solved it earlier?!

wait

[polar fossil]

randy

[remote timber]

that's when it's zero

🫠

[polar fossil]

...yes

x = a when y = 0 that was how we found our integral bounds

[remote timber]

hmm okay

so now what?! do we like evaluate it

from a to 0

[polar fossil]

yep! from 0 to a

[remote timber]

jesus

so like how the fuck

do you do that like

does a become ^2

a^2

[polar fossil]

please
randy
a is a constant
it is not the variable we are integrating by

when you see a

replace it with "9" in your head

we are integrating dx (which you should write as well)

[remote timber]

but don't write it down as 9?..

so like

a^2 becomes a^3 / 3 like normal?

[polar fossil]

what i mean is like
treat it like you would the number 9, or 4, or 16, or 25

if you integrate 9^2, does it become 9^3 / 3?

[remote timber]

hm no?

WAIT

[polar fossil]

$\int a\dd{x} = ax$

[warm shale]

Hayley

[polar fossil]

• c

[remote timber]

so we juwt add an x okay

to everything basically

[lost salmon]

What

[remote timber]

so a^2 becomes a^2x >:)

[lost salmon]

What

[polar fossil]

to all the constants, yes... but not to anything involving x

[remote timber]

yeah it'll go up a power

or like

what about 2asqrt(x)sqrt(a) wtf happens there

does the x become like x^(3/20

[polar fossil]

$2a\sqrt a\sqrt x = 2a\sqrt ax^{1/2}$ and just use power rule

[warm shale]

Hayley

[polar fossil]

so, yes

[remote timber]

so the dx INFECTS the xs wah

okay give me a sec

wait shit

what about 2xsqrt(x)sqrt(a)

do BOTH the xs increase?!

or only one

[polar fossil]

,tex .exp rules

[warm shale]

Hayley

[lost salmon]

At this point i dont even think your doubt is at calculus

[remote timber]

wym?!

what's that mean

[polar fossil]

means you need to practice algebraic manipulation

[remote timber]

shit yeah I forgot you can just ad the x's alright omll

[lost salmon]

Means you need to review basic math and pre calculus

[remote timber]

I'm just really tired okay 🥺

[lost salmon]

It’s okay, it’s just an tip

If you don’t understand the basics you can’t do the advanced

And I conclude that probably you’re on an Engineer course or computer science

[remote timber]

,pccw

yes!

[lost salmon]

This will follow you for the rest of the course, so you can’t escape

[remote timber]

I was Algebra 2 and pre-calc during covid

so that's probably why my algebra understandings are mid

[remote timber]

wait wym?

like this weird algebra thing?! no way?

,pccw

WHY ISNT IT DOING THE THING

,rccw

[remote timber]

damn

@polar fossil AM I RIGHT

[lost salmon]

I mean that this will still appear in every other subject apart from calculus

[remote timber]

yeah that's why calc 1 was DIFFICULT cause I didn't know any algebra rules

like I did't know that 1/2 * 1/2 is just 1

[polar fossil]

it... isn't

1/2 * 1/2 is 1/4

[remote timber]

1 / 2

wait no no

NO HOLD

1/2 / 1/2

t h a t thing

yeah >:)

causei t's ACTUALLY 1/2 * 2/1

which was trippy in first semester

[polar fossil]

that's not even algebra that's like fourth grade

[remote timber]

I KNOW

so idk where I got my math skills from but

like ionkno it's a work in progress

so WAIT AM I RIGHT

WHAT NOW??

do I plug this entire fuckin expression into my software

no way it

it's finna take it

[polar fossil]

the antiderivative is correct

now remember how to do a definite integral?

[lost salmon]

Everything it’s wrong Randy

[polar fossil]

,tex .FTC1

[warm shale]

Hayley

[remote timber]

yeah FTC pt 1 ?

wait but the first part

F(a) is just 0

[lost salmon]

Integration correct

[polar fossil]

yep F(a) = 0 [to be clear, what I mean is F(0) = 0... we've got a as our top bound which gets confusing]

[remote timber]

cause there's a x in everything which is 0

so now?.. I plug in A for all the Xs?

[polar fossil]

yes

[remote timber]

YOO

HOLD ON

[polar fossil]

and s i m p l i f y

[remote timber]

I CANDO THIS NOW i've EVOLVED

[timid silo]

Trouvez une solution générale à l'équation de Navier-Stokes en trois dimensions pour le mouvement d'un fluide visqueux incompressible !!!

[polar fossil]

you'll get an answer with just one term

[timid silo]

I need help

[remote timber]

Trouvez une meilleure salope de langue. Votre pays était fortement gonflé en 1790 !

[remote timber]

YES HOLD ON

IM WORKING

this is gonna be CRAZY

[polar fossil]

that's fine! keep going for sure i just wanted to give you something to check against

[timid silo]

Bro

[remote timber]

I didn't mean it :(

[lost salmon]

What is happening here?

[remote timber]

,rccw

BOOM

[remote timber]

OKAY there!

now what do I

don't tell me I gotta balance the fracions ns hsit

[polar fossil]

s i m p l i f y

[remote timber]

SO THAT MEANS BALANCE THEM

[lost salmon]

Why there are French ?

[polar fossil]

it means combine like terms

[remote timber]

wait

wait a^3 / 2 PLUS a^3 / 2 is like

a^3

[polar fossil]

yes

[lost salmon]

Integration is incorrect also

[polar fossil]

you sure? it looked right to me

[lost salmon]

He Integrated x two times for some reason

[polar fossil]

which term?

[remote timber]

Wtff

,rccw

[remote timber]

WHY is it like that

[lost salmon]

It’s so messy I can’t even identify to you

[polar fossil]

hmm well it should be positive

[remote timber]

WELP it's okay I'll just skip the question I still got a 90% on the homework tbh

mane so igot a 3.9 over freshmen year but like

idk if it's finna stay that way this math is really starting to math

welp, I appreciate the help regardless I've learned today!

<3 .close

[lost salmon]

Hey

[remote timber]

. close

huh?!

Hey? 😭

[lost salmon]

It’s not wrong having doubts but staying with them

Like i said

[polar fossil]

here's how i did it

$\int_0^a (\sqrt a - \sqrt x)^4 \dd{x} = \int_0^a a^2 - 4a^{3/2}x^{1/2} + 6ax - 4a^{1/2}x^{3/2} + x^2$

[warm shale]

Hayley

[remote timber]

why tf is it to the fourth power

[lost salmon]

Yeap that’s right

[remote timber]

oh wait

is it because you already squared it from before

[polar fossil]

$= a^2x - \frac83a^{3/2}x^{3/2} + 3ax^2 - \frac83a^{1/2}x^{3/2} + \frac13x^3$

[warm shale]

Hayley

[remote timber]

jesus then waht

then what

it's like a movie

[polar fossil]

then substitute a, so

$= a^3 - \frac83a^3 + 3a^3 - \frac83a^2 + \frac13a^3$

[warm shale]

Hayley

[polar fossil]

but I'm a little confused because I thought it would be one term and this is two

[remote timber]

so it seems I messed up like one term somewhere

h u h

so what happens in the end

[lost salmon]

Why?

[polar fossil]

because I threw it into wolfram and it gave me one term 😄

[lost salmon]

Oh

[lost salmon]

You Integrated $x^{\frac{3}{2}}$ but forgotted to add

[warm shale]

pcheese2010

[polar fossil]

ahhhh ty

[lost salmon]

Yeah that makes sense

[polar fossil]

that explains where the 5 came from...

$= a^2x - \frac83a^{3/2}x^{3/2} + 3ax^2 - \frac85a^{1/2}x^{5/2} + \frac13x^3$

[warm shale]

Hayley

[polar fossil]

anyway literally everything here is a^3

so $1 - \frac83 + 3 - \frac85 + \frac13$

[warm shale]

Hayley

[polar fossil]

all times a^3

[lost salmon]

Let me think for an sec

Ok that’s fair

Yeap

Like i said he Integrated wrong at some point

But i cant even find where

[polar fossil]

he had the 5/2

[lost salmon]

Yeah

But where the mistake starts?

[remote timber]

Wtf

What’s the answer?!

[lost salmon]

You need to organize better your resolution

so $(1 - \frac{8}{3} + 3 - \frac{8}{5} + \frac{1}{3}) \cdot a$

[warm shale]

pcheese2010

[lost salmon]

@polar fossil definitely is an math bachelor because she don’t put {} on latex functions

[polar fossil]

time waste

i've got things to do

i don't have time to type {8}{3}

[polar fossil]

*a^3

[lost salmon]

Yeah your call

[lost salmon]

Thx

[novel onyx]

gotta find angle theta and length of x

[polar fossil]

i think \frac12 looks better than \frac{1}{2}

[lost salmon]

The problem is when you need to put something like an variable…

[polar fossil]

\frac a2

[lost salmon]

$\frac\beta2$

[warm shale]

pcheese2010

[lost salmon]

Fair enough

[polar fossil]

you can even $\frac\beta{\alpha+2}$

[warm shale]

Hayley

[polar fossil]

$\sqrt a^2$

[warm shale]

Hayley

[lost salmon]

Ha!

This one doesn’t work

$\sqrt2^2$ or $\sqrt{2^2}$

[warm shale]

pcheese2010

[lost salmon]

That’s my point

[polar fossil]

oh i know, i used it intentionally earlier though

[lost salmon]

Oh

Fair enough

[polar fossil]

$\sqrt a^2 = a$ for all $a \in \mathbb{R}$

[warm shale]

Hayley

[lost salmon]

$\sqrt a^2 = a$ for all $a \in \mathbb{N}$

[warm shale]

pcheese2010

[lost salmon]

Actually

I can’t remember how to use the command to express exclusion of a set

Moreover now i got to an point that even I can’t figure

[lost salmon]

I Would like to try this but excluding an set

[polar fossil]

#latex-help

[lost salmon]

Right

[obtuse pebble]

@remote timber Has your question been resolved?

[obtuse pebble]

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[noble pollen]

just want to make sure I'm doing this right

[noble pollen]

5x(x^3-x+8)=

5x^4-5x^2+90x

is the first part

[grizzled shore]

Where did you get 90x

[noble pollen]

2nd part 5(x^3-x+8) = 5x^3-5x+90

[grizzled shore]

Where did you get 90 from

[noble pollen]

5x*18

[grizzled shore]

5*18 is 90 yes

[noble pollen]

whoops

I messed up

40 lol

[grizzled shore]

Yep

[grizzled shore]

Same for this

[noble pollen]

okay now I have to collect like terms next?

[grizzled shore]

Yes

Although normally I do these kind of expansions by looking at the powers

[noble pollen]

5x^4-5^2+18 + 5x^3-5x+40

so I rearrange them like this.....

[grizzled shore]

You’re missing an x in the first part

You’re missing 2 x’s actually

5x^4-5x^2+ 18 40x + 5x^3-5x+40

[noble pollen]

5x^4-5x^2+40x for the first part

[grizzled shore]

Yes

[noble pollen]

aaaaah I always make these stupid mistakes lol

[grizzled shore]

Are you writing it out on paper

[noble pollen]

yes I think that I just have bad eye coordination

[grizzled shore]

Try see if different ways of writing your working helps

[ashen totem]

Hii

[grizzled shore]

It’s easy to blame something “out of your control” for your problems, but it’s more useful to try fix them

[noble pollen]

good point

let me try it again for the first part

5x^4-5x^2+40x

2nd part 5x^3-5x+40

5x^4-5x^2+40x+5x^3-5x+40

rearranged is ....

5^4+5x^3-5x^2+40x-5x+40

5x^4+5x^3-5x^2+35x+40

okay I got it right

thank you

.close

[obtuse pebble]

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[worthy cargo]

why is (x-a)^2 = (a-x)^2? I can understand it from a number line point of view where a-x and x-a is the distance between the two points on the number line and then squaring it will yield the same value whether its positive or negative, as well as by expanding it algebraically, but is there a way to manipulate the terms inside the parenthesis only such that it makes sense

[ruby path]

$$(x - a)^2$$ $$(-(a - x))^2$$ $$(-1)^2(a - x)^2$$ $$(a - x)^2$$

[warm shale]

neonperseus

[worthy cargo]

ah okay thats what i was looking for, thanks idk how i didnt see that

.close

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[jagged blaze]

Does anyone know how to use psuedocode? For my RAPTOR program? Idk if this is the right server to ask

[wooden cipher]

Perhaps try computer science in #old-network

[jagged blaze]

alright

[obtuse pebble]

@jagged blaze Has your question been resolved?

[tardy epoch]

.close

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[zenith drift]

A plane is about to land. by the time the wheel touches the ground An airplane has a speed of 180 km/hr, how much deceleration will it take to stop it at a distance of 500 m?

[zenith drift]

It's 2.5

just figured it

.resolved

[obsidian isle]

.close

that's the command

[spark stump]

LMFAO HI GARLIC

[wooden cipher]

Hi

[spark stump]

ITS ME

MIRUKA

[obtuse pebble]

@zenith drift Has your question been resolved?

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[steel parcel]

hi i need help evalutating the intervals

[steel parcel]

i got up to here

do you guys think its possible with the tan(2x) = 2tan(x)/1-tan^2(x) identithy?

[spark stump]

may i out of interest ask what level of education this is @steel parcel

[steel parcel]

year 12 math

[spark stump]

country?

[steel parcel]

aus

[spark stump]

LMAOO

[steel parcel]

specialist math

[spark stump]

ME TOO

LMFAOOO

[steel parcel]

besties

[spark stump]

LMFAO

me rn

XD

NO WAY

[steel parcel]

i remember doing this last year

[spark stump]

4/15

that was last last term which is term one

now im in term 3

and i got unit 1,2 for physics, specs, methods and chem exam

im legit fucked this term

@steel parcel state?

[steel parcel]

oh lol we'll talk in dms because i don't want this ticket to get flooded

[spark stump]

ok

[obtuse pebble]

@steel parcel Has your question been resolved?

[steel parcel]

<@&286206848099549185>

[obtuse pebble]

@steel parcel Has your question been resolved?

[rotund rune]

find the value of sin(pi/12) and cos(pi/12)

[rotund rune]

and also tangent is an odd function so tan(-pi/24) = -tan(pi/24)

you can use the half-angle formula to find tan(pi/24) and then tan(pi/48)

[steel parcel]

hmm

[rotund rune]

or, you can find tan(pi/12) and then set up an quadratic equation to find tan(pi/24) and then tan(pi/48) (but i think that's quite hard with the numbers)

i couldn't think of an easier way...

[steel parcel]

ok i’ll see what i can do

[rotund rune]

if you choose this method and require a hint: ||pi/12 = pi/4 - pi/6||, or you can ||apply the half angle formula to sin(pi/6) and cos(pi/6)||

[obtuse pebble]

@steel parcel Has your question been resolved?

[obtuse pebble]

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[celest zodiac]

does anyone know the reasoning why this equation is modified

[haughty coyote]

That's just the general projection formula

[obtuse pebble]

@celest zodiac Has your question been resolved?

[celest zodiac]

ah okay, thank you!

[obtuse pebble]

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[wise galleon]

anyone help with this

[shy vigil]

what have you tried so far, @wise galleon?

[obtuse pebble]

@wise galleon Has your question been resolved?

[obtuse pebble]

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[visual sluice]

.open

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[visual sluice]

In an ap if I know the first and last term, can I find out the sum of all the terms ???

[rich plume]

no

you need to know number of terms

[visual sluice]

Ok thanks

.close

[obtuse pebble]

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[deft sun]

how am I supposed to solve a Recurrence relation?
for example I have
an = 3an-1 + 10 an-2

[deft sun]

I want to get f(n) = an

[kind hawk]

do you know linear algebra?

[deft sun]

no

like I know something which is related

[kind hawk]

discord seems sucky

doesnt send my messages

lets try anyway

[deft sun]

yee I know

me 2 😦

[kind hawk]

so, we first assume that a_n=r^n is some geometric sequence

[deft sun]

I know Generating function
I am pretty sure its related

oh finally

ye okay I am listening

[kind hawk]

plugging that in, we get that r^2=3r+10

this you can solve for r

[deft sun]

now we use the root thing right?

[kind hawk]

"root thing" ?

quadratic formula

[deft sun]

english is hard 😦

x1= -2
x2 = 5

and know we do
Ax1 + Bx2?

when A,B are natural numbers

[kind hawk]

now we know that a_n = A(-2)^n + B(5)^n for all n, where A and B are determined by the initial conditions

not necessarily natural numbers

[deft sun]

ah right
a0 = 1
a1 = 3

I think we need that 2

[kind hawk]

this fact holds because of linear algebra, I'm not sure how to argue for it otherwise

yes we need 2 initial conditions

[deft sun]

my teacher told me to just take it as a fact until I learn linar algebra

[kind hawk]

ok. so now we know a0 = 1 = A (-2)^0 + B (5)^0 and a1 = 3 = A (-2)^1 + B (5)^1

in other words, A+B=1, -2A+5B=3

which you can solve

[deft sun]

ok thanks a lot 🙂

and what are these A and B values?

what do they mean

[kind hawk]

well they are coefficients that give you what you want

a_n = A(-2)^n + B(5)^n

[deft sun]

so this is the final solution (after pluging A and B)?

[kind hawk]

in terms of linear algebra, they are the coordinates with respect to a certain basis. but that doesnt mean anything to you

yes

[deft sun]

okay thanks again
have a nice day

[kind hawk]

u2

[deft sun]

.close

[obtuse pebble]

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[obtuse pebble]

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[teal python]

i dont understand this at all

[obtuse pebble]

@teal python Has your question been resolved?

[teal python]

<@&286206848099549185>

[timid silo]

ever heard of the sign of the function ?

[tulip prawn]

1. or 2.

what have you tried? what do you understand? what do you not understand?

we're not math solvers, we're math helpers

[wintry swift]

you wont get solutions her.e we help to get the solutions yourself

[teal python]

ok

so I dont get how the intervals make the "breaks"

[timid silo]

It's not the intervals that makes the breaks it's the x's values

[teal python]

then what is it

is that just declared?

[timid silo]

the question stated that the function is a rational one which means it's in the form of a/b

[teal python]

yeah

[timid silo]

yes you find the continuity through the x values

[teal python]

ig theres holes and vertical asymptotes

[timid silo]

exactly

[teal python]

but I cant visualize it

and I dont kknow how to put this in desmos

I know how to find them in a rational function but I dont get how to do it with these table of values

holes and asymptotes I mean

[timid silo]

he already gave you the asymptotes from the x values where the function is discontinous, the fact that the function is rational and the table values

[teal python]

yeah but Im stumped on what kind they are

and how to even find that out

[timid silo]

It's easy to find the vertical asymptotes

[teal python]

is a vertical asymptote a type of discontinuity?

[timid silo]

Take a closer look at the table values and the behavior of the function at each interval

[teal python]

can you like tell me how to graph this

cuz i cant visualize it

is it squiggles

or

[timid silo]

It's where you'll find discontinuity

[timid silo]

If the function is positive it's above the x-axis if not its below

[teal python]

yeah

a rational function is like

this

[timid silo]

Yes exactly

Even 1/x is a rational function

[teal python]

ok so how would I graph it based on the points

like

ohh nvm graphing is easy

but type of asymptotes

[timid silo]

For this question it's a vertical asymptote

[teal python]

an infinite discontinuity for all points?

[timid silo]

How did x+2=y3 turned to the one Below it

[timid silo]

There only one point I'm not sure if it is asymptote or a hole

[timid silo]

You needed to find the inverse function for g(x) so you simple take the inverse of the cube which is the cubic root to get y and y will be the inverse you're looking for

[teal python]

so ive come to the conclusion that -3 and 4 are infinite discontinuities and 2 is removable

[timid silo]

For -3 and 4 you're right but for 2 I'm not sure

[teal python]

for 2 im thinking it could be infinite and removable

does this place have latex?

$\frac{1}{(x+3)(x-2)^2(x-4)}$

[warm shale]

bagel123

[teal python]

and

$\frac{x-2}{(x+3)(x-2)(x-4)}$

[warm shale]

bagel123

[timid silo]

<@&286206848099549185>
Can somebody tell us if 2 is removable or infinite ?

[timid silo]

Your guesses are as good as mine 😅

[woeful sentinel]

Removable it is

[fervent kiln]

Bro it doesn't exist

It's an indeterminate form

[woeful sentinel]

otherwise it will be 0/0 inderminate form .

[timid silo]

I'm not sure if the value 2 is a hole or asymptote both are possible

[teal python]

bro 💀

[fervent kiln]

You can find limiting values

But at 2 it's irremovable

[timid silo]

We don't know the numerator how can we be sure that it is equal to zero

[woeful sentinel]

At 2 it will be 0/0 , so i think x should not be equal to 2 , but we can find approaching value at 2 using L hospital rule .

[teal python]

chill out only algebra allowed

[woeful sentinel]

Ohk then , x= 2 not allowed nah .

[teal python]

soo removable or nonremovable

[woeful sentinel]

not removeable .

[little cedar]

Try the partial fraction method

[woeful sentinel]

at x= 2 function is not defined

[timid silo]

How is that even possible we don't know that the numerator will be zero at x=2

[woeful sentinel]

what are you saying , in numerator it is x-2

so at x=2 numerator will be 0

[teal python]

no I just put that there as an example

[timid silo]

Exactly this is one possibility if 2 had asymptote the other is that 2 is a hole

[teal python]

yeah

[timid silo]

How did you know ?

[timid silo]

im sorry but wut does that mean

[timid silo]

What is the inverse of x^3 ?

[woeful sentinel]

X^1/3

[timid silo]

Let him answer 😅

sorry but im kinda new on the inverse thing

how do u inverse

[timid silo]

It's ok

i got f-1(x)=3 cube root x

[teal python]

.close

[obtuse pebble]

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[small cave]

can someone explain me the last line?

why CD*CB = CB * CB?

[pseudo swift]

well the basic thing to see here is that $\overrightarrow{CD} = \overrightarrow{CB} + \overrightarrow{BD}$

[warm shale]

_aplatypus

[pseudo swift]

CD is the sum of CB and something orthogonal to CB

and the dot product behaves nicely with sums of vectors

$$ \overrightarrow{CD}\cdot \overrightarrow{CB} = (\overrightarrow{CB} + \overrightarrow{BD})\cdot\overrightarrow{CB} =\overrightarrow{CB}\cdot \overrightarrow{CB} + \overrightarrow{BD}\cdot \overrightarrow{CB} $$

what

[warm shale]

_aplatypus

[pseudo swift]

the dot product distributes over sums of vectors

[small cave]

I understand it now with the distribution

thanks

.close

[obtuse pebble]

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[dull matrix]

Suppose that the orders for a certain product produced by a factory in the next four months are shown in the table below. The contract stipulates that the product should be delivered before the end of the month. The Fixed cost of each batch of products is 3000 yuan, and the number of products produced in each batch is unlimited. The variable cost of each product is 1000 yuan, and the maximum production capacity of each batch of products is 5 pieces. The monthly storage cost for each product is 500 yuan. There is one item in stock at the beginning of January, and no products will be left at the end of April. How to organize production to minimize the total cost while meeting the needs. it's a dynamic programming question.

[dull matrix]

Are there any parts of this text that you dont understand? I can explain it to you

[radiant halo]

!status

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[radiant halo]

@dull matrix

Chk the chart.

[dull matrix]

yeah

[radiant halo]

choose numbe

[dull matrix]

how

[radiant halo]

type

do !status and type

[nocturne minnow]

@dull matrix pick what option

Like type it

1, 2, 3, 4, 5, or 6

[dull matrix]

i know it but it's so hard to calculate

[rocky goblet]

it's difficult to calculate whether you know where to begin or not?

[dull matrix]

my teacher told me use programming language to solve it

but i cant write it out

[dull matrix]

it's diffcult to calculate by hand

[nocturne minnow]

We aren't asking you that. You pick what part of the math process you are in

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[nocturne minnow]

Do you see how it's a 6 step process?

Pick what step you are on

[dull matrix]

i want to hear from you. Our methods may be different

[dull matrix]

I have defined five states

[nocturne minnow]

That's not how the server works. We help you where you get stuck. We don't provide our answer to you

If you want help, provide to the people helping, the proper info

Meaning, where are you stuck, did you try anything, and if you did present that work

[dull matrix]

got it.

thank you

.close

[obtuse pebble]

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[karmic hedge]

https://i.imgur.com/LyhOiqj.png

[karmic hedge]

I got the second derivative 12ax^2 +2b and set it equal to 1/4, I dont really know what im supposed to do next or what I can do with the point [-1,-1] though...

[high lily]

you' shouldn't be setting the second derivative itself to be equal 1/4

[karmic hedge]

oh

I thought the inflection points were what you got when you got the second derivative and set it equal to zero

Thats why I thought i should set it equal to 1/4

since its an inflection point

[high lily]

that doesn't mean you set the second derivative itself equal to 1/4

which seemed like what you were seaying

the second derivative is 0 when x=1/4

[karmic hedge]

aaaah

[high lily]

and you get another piece of info from the graph passing through the given point

then solve a system of equations to determine a,b

[karmic hedge]

Wym sry

I dont understand passing through the point given point

[high lily]

typo, typed an extra point

through the point given point

[karmic hedge]

But I still dont understand really what im supposed to do

[karmic hedge]

Does this even help?

[high lily]

consider a simpler example

[karmic hedge]

I mean like does them telling us the x=1/4 even help

[high lily]

y = mx + 3
what is m if (3,6) is a point on that line

[karmic hedge]

1

[high lily]

and how did you reach that conclusion

[karmic hedge]

I subbed in 6 for y and 3 for x

[high lily]

same idea applies here

[karmic hedge]

but we dont have it in that form

[high lily]

doesn't matter

its still a relation between x and y

[karmic hedge]

But we still have 2 unknowns right

[high lily]

yes

you get an equation from each piece of info

you'll end up with a system of equations with two variables

then proceed with stuff like substitution/elimination

[obtuse pebble]

@karmic hedge Has your question been resolved?

[karmic hedge]

I think so im just solving haha

I got it thank you

❤️

.close

[obtuse pebble]

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[radiant frigate]

Explain the difference between stationary and critical points. It is written everywhere that these are the points where the derivative is 0 or does not exist, but then what is the difference between these points, if by definition they are the same?

[timid silo]

Stationary is where the derivative is only equal to zero

Critical point can be zero or DNE

[radiant frigate]

It is also interesting to ask about the extreme points. As I understand it, these are the points of the local minimum and maximum, that is, the points of some "inflection" of the graph of the function, where the local minimum is the transition from a negative derivative to a positive one, and the local maximum is the same, but the opposite. At the same time, the extremum points also have a derivative that is zero or does not exist. Did I understand this correctly?

[radiant frigate]

Thank you!

[obtuse pebble]

@radiant frigate Has your question been resolved?

[obtuse pebble]

@radiant frigate Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[stable apex]

who determines the

+ - +
- + -
+ - +

[dull rune]

For each cofactor you use $(-1)^{i+j}$

[warm shale]

zander_a

[dull rune]

And multiply this by the minor $M_{ij}$

[warm shale]

zander_a

[stable apex]

what is i and j?

[dull rune]

Each entry is a_ij

[nocturne minnow]

The matrix elements

i for row, j for column

Btw it's called Laplace expansion

[stable apex]

row 1 column 1
so
(-1) ^1*1

row 2 column 2
so
(-1)^2*2

[nocturne minnow]

Add

[stable apex]

like this?

[dull rune]

addition

[nocturne minnow]

Not multiply

[stable apex]

ah ok ok

[nocturne minnow]

1 + 1

[stable apex]

so I can just remember the pattern right?

since its same for every 3x3 matrices?

[nocturne minnow]

Yes

[stable apex]

great great

thank you guys @nocturne minnow @dull rune

.close

[obtuse pebble]

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[long hedge]

Im lost

[limber quartz]

What is the definition of tangent

[long hedge]

y/x

nothing on the unit circle makes the point

[limber quartz]

Ok, draw a right triangle where the legs have those lengths

[limber quartz]

Trig ratios reduce to ratios on the unit circle but they can scale up and down

[long hedge]

https://tenor.com/view/jim-halpert-teary-eyed-john-krasinski-the-office-facepalm-gif-15090727

[limber quartz]

Does this mean you know what to do now?

[long hedge]

ok so once i find the hyp of the triangle what do i do

[limber quartz]

Hmm actually I don't have this ratio memorized

[timid silo]

Umm, can’t we just reduce the fraction inside and use the standard trigonometric values?

[limber quartz]

Yeah it's 1/sqrt(3)

[timid silo]

Yeah

[limber quartz]

@long hedge divide every side by sqrt(3)

[long hedge]

ok