help-27

[latent mulch]

Ok

So it's like this

Imma draw it

Wait

This guy

[late kernel]

@latent mulch ah that's simple trigonometry kiddo!

[latent mulch]

And you didn't even help

Though I asked you to help

[late kernel]

i told u "that theta"

[latent mulch]

Yes

That's how I got my doubt cleared

All praise be to praiseworthy

[late kernel]

i'm string theorist, i'm just kidding @latent mulch @boreal helm ?

[latent mulch]

Bruh you nust annoying

What grade you in

11th 12th?

Just get lost for a while

[late kernel]

😂😂🤣🤣🤣🤣

[latent mulch]

I'm just about to get my doubt cleared

And @boreal helm 's just disappeared

You broke my flow

Get lost

@boreal helm You there?

May we continue?

Imma pick on you for a while till he comes

[latent mulch]

You act like you just hit puberty despite being 17

[boreal helm]

Okok

[latent mulch]

Ok hes come

[boreal helm]

Came

Okok

Yes tell

[latent mulch]

So

Where were you?

Why do you disappear?

@boreal helm ?

[boreal helm]

I am waiting

For u

To ask

[latent mulch]

Oh

[boreal helm]

I am here

[latent mulch]

I literally for what I was asking

Ifk

Idk

Wait

Lets see

So

120 is just 30

[boreal helm]

Okok

[latent mulch]

So I find 30

[boreal helm]

Yes 30

Wait imma show

[latent mulch]

In the 1st quadrant

[latent mulch]

Wait

Lemme figure it out

Myself

[boreal helm]

Okok

[latent mulch]

So I find 30

In the first quadrant

And the compare the coordinates

And the only difference there would be is of the signs right?

[boreal helm]

What

[latent mulch]

Since it's th3 same thing positioned in different quadrants

[boreal helm]

Did not understand

[latent mulch]

Wait

[boreal helm]

See it's correct

We add a reference

[latent mulch]

Origin?

[boreal helm]

Like 120 is

90+30

150 is

90+60

[latent mulch]

Yeah

[boreal helm]

We add reference

150 is

180-30

120 is 180-60

Like this

[latent mulch]

Basically what we say in it's just x degrees rtated 90 degrees or whatever

So lemme draw

[boreal helm]

Okok

Draw imma see

[latent mulch]

Is it right?

@boreal helm

@boreal helm

@boreal helm

@boreal helm

@boreal helm

[boreal helm]

Absolutely my guy

[latent mulch]

Now

[boreal helm]

[latent mulch]

I've got a different question apart from my main question

So how we apply the concept of complementary angles to this relation is just derived

[boreal helm]

Okok

[latent mulch]

So -sin(90+30) = cos30 but shouldn't (90-30) be cos30 and not (90+30)

[boreal helm]

See

U had cos(30)

In first quad

[latent mulch]

Yeah

Yeah

[boreal helm]

u added 90 to it

[latent mulch]

Ok

[boreal helm]

Cos is -ve in 2nd

So cos(90+30) becomes -sin30

[latent mulch]

What? You just 17

[latent mulch]

Don't tell me you're a faakin quantum physicist

[boreal helm]

Lol

[latent mulch]

I'm also 17 ok

I'm in 11th grade

[latent mulch]

Ik that

What are you?

A boy who just recently hit puberty?

[latent mulch]

No shouldn't cos( 90-a) give you sina and not cos(90+a)

Good for you

[boreal helm]

Being into something does not guarantee u will excel into it 🗿

[latent mulch]

Lemme study now

You don't even know the conditions ive been through

I just started studying this year

So lemme clear my doubts

[boreal helm]

Oof

U guys

Fight so much chill

[latent mulch]

How do you apply physics to be smarter in social conditions?

[boreal helm]

What if he is saying something

We focus on our work

[latent mulch]

So do that

And stop acting like a child

Conserve energy

Go to sleep chhild

[boreal helm]

Lol

[latent mulch]

So where were we?

[latent mulch]

Here

[boreal helm]

yes

You are correct

Indeed

[latent mulch]

Lol

Ok

[boreal helm]

Yes

cos(90-a) is sina

And cos(90+a) is -sina

[latent mulch]

Wow

[boreal helm]

U can look it in two ways

[latent mulch]

So derive that algebraically

[boreal helm]

As 90+a is

In 2nd quad

And in that cos is -ve

Or u can do this

Cos(90+a)

cos(90-(-a))

sin(-a)

-sina

[latent mulch]

Ooh

I get it now

OK

So onto my main question

Now that I've derived that relationship

How do I extend it to 180-a

[boreal helm]

First mark where will 180-a will be

U will understand

[latent mulch]

Ok

Wait

Do I have to do it on my ownM

Or are you doing it?

@boreal helm

[boreal helm]

Ues

Yes

Do it on your own

Try

Think

[latent mulch]

Ok

So lemme see

This is it

So

What do I know

I wanna write it in terms of theta

What are the coordinates of theta?

The same 180-A

Wait

(Sin180-a, cos180-a) are the coordinates

Now I wanna find in terms of theta

[boreal helm]

U are correct but see theta will be from +ve x axis

[latent mulch]

Theta lies in the first quadrant

[boreal helm]

And 180-a too from the +ve x axis

Yes

[latent mulch]

Here it's just the signs of theta are flipped

Since it's in a different quadrant

[boreal helm]

No

See

See in 2nd quad

The whole x axis

[latent mulch]

Is -ve

[boreal helm]

What

Yes

[latent mulch]

So the trig functions for x axis would be native only

[boreal helm]

See in 2nd quad we have angle from 90 to 180

[latent mulch]

Not for y axis

[boreal helm]

So see

[latent mulch]

Ok

[boreal helm]

If theta like 30 lies in first quad

And we want to write 150

We can write 180-30

We do this

Did u understand

@latent mulch

[latent mulch]

Yeah

[boreal helm]

See if it makes 30 in first quad

And we want to extend it to 2nd quad

We just sub it from 180

And angle comes in 2nd quad

[latent mulch]

Ok

Lets try

150 is also 90 + 60 so i can write it in terms of 60

Just with different signs

[boreal helm]

Bro

[latent mulch]

Is tjisnit?

[boreal helm]

Yes

U can refer it as both

180-30

Or 90+60

Both are valid

[boreal helm]

And both give Same result

It's wrong

[latent mulch]

Where did I go wrong?

[boreal helm]

U have done the opposite

See it's cost and sin t in first quad

So in second it become

cos(180-t),sin(180-t)

[latent mulch]

-cost and sint

Could you draw it yourself

[boreal helm]

Okok

[latent mulch]

And explain each step

[boreal helm]

This

[latent mulch]

Draw a bugger one bruh

[boreal helm]

Ook

[latent mulch]

Stop trynna save pages

[boreal helm]

Lol

[latent mulch]

Don't draw it all at once

Draw and explain each step

And also your line of thinking

[boreal helm]

Ok imma draw each step

[latent mulch]

And also explain what you're thinking to solve it

[boreal helm]

U understand this?

[latent mulch]

Having a cute pfp doesn't imply it's a girl behind the acc. Hes male

[latent mulch]

Yes

Haha diapered

[boreal helm]

1 way to approach it

[latent mulch]

Bruh

[boreal helm]

Other way is

[latent mulch]

What's this

[latent mulch]

Bruh

Your handwritings so nice

Ok

I get it

Yes

[boreal helm]

Yes

[latent mulch]

90+A

[boreal helm]

Yes

Like in 120

90+30

A is

[latent mulch]

Yes

[boreal helm]

30*

[latent mulch]

Oh yes

Ok

[boreal helm]

Okok

Any more doubt

[latent mulch]

Ok

Go

Like 180-A?

How we apply it to 180-A

@boreal helm

[boreal helm]

180 - A is

See do u know the straight has an angle of 180 degree

[latent mulch]

Yes

[latent mulch]

Wtf is this bro

Cant you write any better

[boreal helm]

Okok

[latent mulch]

Draw big

Use pencil

Draw neat

Pls

[latent mulch]

Yes that's better

So what are you tryna say here

[boreal helm]

Counter clockwise theta is +ve

[latent mulch]

Clockwise is

Hahah

[boreal helm]

Lol

See here we took theta with respect to -x

So angle also -ve

[latent mulch]

Yes

Ok

[boreal helm]

U can see angle b/w +ve x and -ve x is 180

So if it makes theta with -ve

[latent mulch]

Yes

[boreal helm]

It should make 180-theta with the +ve x

[latent mulch]

Ok

[boreal helm]

<@&268886789983436800>

[latent mulch]

What happened

[boreal helm]

Wait

[latent mulch]

Ik starting to get a headache

Lol

[boreal helm]

Let someone come imma explain

[latent mulch]

How does it feel to spend 2.5 hours trynna explain something?

[boreal helm]

Good

Lol

[latent mulch]

No

[boreal helm]

Wait

Wait

[latent mulch]

Lol

Ni

[boreal helm]

Wait

[latent mulch]

I dont

I'm tired

[boreal helm]

Wait bro

I m not gonna talk

We need to report this to a mod

[latent mulch]

I'm having a headache

[boreal helm]

Wait

[latent mulch]

What do we need to report?

What happened?

@boreal helm ?

Huh?

[boreal helm]

Wait

[latent mulch]

Man I'm really tired

I swear

And my mother is also asking for the phone

[boreal helm]

Pls wait

[latent mulch]

What is it

[boreal helm]

We need to report toxic behaviour

[latent mulch]

I wanna get in the sun

[boreal helm]

Wait

[latent mulch]

Oh

Who you gon report?

Am I being reported?

[boreal helm]

No

Don't close

[latent mulch]

Ok

So i won't close

[boreal helm]

Wait let a mod come

[latent mulch]

And but I can't stay here e ither

I want to get in the sun

[winter torrent]

[latent mulch]

Keep it open

Oh finally

[boreal helm]

Thanks for coming mam

[latent mulch]

Pass judgment

[boreal helm]

U can see above MEDHAT has been talking trash and showing off toxic behaviour

Anonymous is witness

[latent mulch]

Haha

I'm witnesss

[boreal helm]

Tell anonymous what things did he say

[latent mulch]

Lol

He was talking about solving some equations

Like something like yhat

[boreal helm]

Proof

He has been interfering in this help channel too

[winter torrent]

my judgment is that this channel is a mile long full of both of you speaking past each other, without ever understanding. I'll check the logs and look through the channel some more. @boreal helm it feels like you're holding this person hostage, @latent mulch feel free to go whenever

[latent mulch]

Pass judgment

[boreal helm]

And did not listen when I told him to make another channel and did !occupied

Mam I have given the proof

Pls see it

[latent mulch]

Thanks

[tender cobalt]

entirely relatable if I was 3 years younger

[latent mulch]

It seems so court like

[boreal helm]

I was being professional

[tender cobalt]

the reference triangle you draw for 180 - theta is incorrect

[boreal helm]

Oof

[latent mulch]

Wait

[tender cobalt]

thats pretty much the reason why it doesnt work

[latent mulch]

What?

[boreal helm]

No one saw bout medhat

Why

[latent mulch]

Could ya explain?

But I have to leave

[tender cobalt]

I cant explain if youre not here

[latent mulch]

Could ya explain in dms

[tender cobalt]

oh sure

[latent mulch]

I'll check em later

Can you?

[tender cobalt]

not really

you havent really said how you drew that triangle or why you think its correct

[latent mulch]

Can I tag you later?

[tender cobalt]

yep

[latent mulch]

Ok

[tender cobalt]

you need to "present your evidence to the stand" before I can pass that judgement of what went wrong

[latent mulch]

@tender cobalt

[tender cobalt]

yea thats my tag

[winter torrent]

dead

[boreal helm]

i presented the proof

The ss

[latent mulch]

My lord

[boreal helm]

My lord

[latent mulch]

Forgive that child's child like behavior

[boreal helm]

Did the correct decision i feel

[latent mulch]

Hes a little too ahead of himself

[boreal helm]

No

No he's not

His intention was to make fun and show off his knowledge

He was toxic

[latent mulch]

He thinks he's on top of the world because he's studying some advanced stuff

[boreal helm]

Always be professional

[latent mulch]

It happens my lord

[latent mulch]

Yes

[boreal helm]

And I being a deemed lawyer

[tender cobalt]

of the view posts I saw it didnt seem outwardly toxic, but it does seem customary for anyone who uses discord for too long

[latent mulch]

Hahahah

[boreal helm]

Proved that he was guilty

[tender cobalt]

truly cornered him at the stand

[boreal helm]

Bro he was laughing at a high schooler

[tender cobalt]

justice has served once again

[boreal helm]

He was calling me and him daft

[latent mulch]

Lol

I don't see it

[boreal helm]

A diapered kid and what not

[latent mulch]

What's the judgment

Oh herald of justice

[boreal helm]

He got banned my friend

[latent mulch]

Whaa

[tender cobalt]

and his posts got deleted from here at least

damnatio memoriae

[latent mulch]

Can I tag you later about my question?

[tender cobalt]

yea sure

[latent mulch]

Like what's the time there?

[boreal helm]

Lord Hayley did the judgement

[latent mulch]

Idk I might be online in lime 6-8 hrs

[tender cobalt]

11:15PM PST, what about you

[latent mulch]

Wpuld you be there?

11:46 ist

[tender cobalt]

as suspected

[latent mulch]

Am

So when can I tag you?

[tender cobalt]

just go tag me in DMs

[latent mulch]

Maybe doing you would be better

[tender cobalt]

when I respond, thats when Im ready

[boreal helm]

Okok

[latent mulch]

Ok

[boreal helm]

You add him

So u can get your doubt cleared

Add me too

And then we close this

It's been 2 hours

[tender cobalt]

Ive had longer

[latent mulch]

Almost 3 hrs

[boreal helm]

Lol

Fast

[latent mulch]

Where?

[boreal helm]

Add me friend

So u can dm me

[latent mulch]

Ohk

[boreal helm]

Ohk

Add mtt too

[latent mulch]

Thanks for banging your head on a wall for 3 hrs for me

[boreal helm]

And bye and don't forget

To close

[latent mulch]

.close

[boreal helm]

No prob

[devout snow]

Channel closed

Closed by @latent mulch

Use .reopen if this was a mistake.

[boreal helm]

We always here to help

❤️ yes

[latent mulch]

Yeah thanks

[devout snow]

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.

[willow moat]

Hello if anyone is available I'd like to ask if this is correct. I'm not sure if I did it right. Thank you.

[polar chasm]

Correct

If you mean 33)

[willow moat]

Thank you. Also I need help on this other problem, idk how to do it

No 32

[polar chasm]

I can't see 32)

[willow moat]

Number 13

[willow moat]

Sorry 33

[polar chasm]

Firstly, it's 3*3*3*7

so your a will be 3^3, and your b should be just 7, and not 21.

talking about this

[willow moat]

So it'll just be 3x3x7?

[polar chasm]

not quite, let's do it from scratch then

$-7\sqrt[3]{-189}$

[woven radish]

MæthIsAlwaysRight

[polar chasm]

So we need to simplify this expression here

Firstly, note that there is a minus sign inside the cube root. What can you do to get rid of it?

[willow moat]

I can use imaginary i?

A friend told me the negatives cancel each other, idk if it's true or not

[polar chasm]

That would be if it was a square root. But it's a cube root

first hint

[woven radish]

MæthIsAlwaysRight

[polar chasm]

(they actually will cancel, but I don't think it's obvious enough. Especially because it doesn't happen e.g. in square roots. So it's better to work through it)

[woven radish]

MæthIsAlwaysRight

[willow moat]

Sorry I dont know how to do that method. I was never taught by my teacher

They taught me something like this:

[polar chasm]

You don't know this rule?

[willow moat]

Yes sorry

She said that if I had 4 of the same number then I can take it out since the number to the root sign is 4

[polar chasm]

Right. It actually relies on this rule. $\sqrt[4]{3^{4}\cdot6}=\sqrt[4]{3^{4}}\cdot\sqrt[4]{6}=3\cdot\sqrt[4]{6}$

[woven radish]

MæthIsAlwaysRight

[polar chasm]

root of a product is product of roots

root(ab) = root(a) * root(b)

But you can actually cheat it up a bit, and realize that -189 is same as -1 * -1 * -1 * 189. Now you have -1 there 3 times, so according to the method your teacher taught you, you can take it out

[willow moat]

So then it would be like this?

I took the -1 out so it should multiply to -7 and then I just simplify 189?

[polar chasm]

Yep

So it would be $7\sqrt[3]{189}$

[woven radish]

MæthIsAlwaysRight

[polar chasm]

now can you factorize 189?

[willow moat]

Let me see

Yes

3 and 63 square root

Then I factorize 63

[polar chasm]

right

so what is 63 when factorized?

[willow moat]

3 square root 7

[polar chasm]

3^2 * 7?

[willow moat]

3 (square root 7)

Like the root sign

Or cube root

[polar chasm]

cube root would be better

[polar chasm]

And this is supposed to be what?

$\sqrt[3]{189}$?

[woven radish]

MæthIsAlwaysRight

[willow moat]

3 cube root 21

[polar chasm]

I quite don't see what you are thinking of

but 3 cube root 21 shouldn't arise anywhere during the process

[willow moat]

I got square root 9 times square root 7 times square root 3 for square root 189

Square root 9 is 3 and square root 7 times square root 3 is square root 21

[polar chasm]

*cube root

you need to compute the cube root

not square root

[willow moat]

Sorry I keep forgetting

[polar chasm]

so cube root 9 is not 3

and that one step fails

$\sqrt[3]{189}=\sqrt[3]{3\cdot3\cdot3\cdot7}$

[woven radish]

MæthIsAlwaysRight

[polar chasm]

this is the factorization of 189, you already had this at some point, right?

[willow moat]

Yes

[polar chasm]

how many 3's are there?

inside the cube root

[willow moat]

3

So I take it out to multiply to the 7 outside?

[polar chasm]

right

$7\sqrt[3]{189}=7\sqrt[3]{3\cdot3\cdot3\cdot7}=7\cdot3\sqrt[3]{7}$

[woven radish]

MæthIsAlwaysRight

[polar chasm]

it should look like this

for now

[willow moat]

Yes

[polar chasm]

and 7*3 is 21

so $21\sqrt[3]{7}$

[woven radish]

MæthIsAlwaysRight

[willow moat]

Yes I got the same answer

I will try to do another problem like this but instead of 3 its 7

Thank you for help

[polar chasm]

np

[willow moat]

I got this for 15

I used the same method you used

Number 17

[devout snow]

@willow moat Has your question been resolved?

Channel closed

Closed by @willow moat

Use .reopen if this was a mistake.

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Remember:
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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!

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

[queen pike]

How do i find the latus rectum solely from the curve equation?

[queen pike]

I completely forgot

I know how to get the area, im just having trouble on how to get the latus rectum

[devout snow]

@queen pike Has your question been resolved?

[winter torrent]

put it in the form $x - h = a(y-k)^2$ and your vertex will be at $(h, k)$ with the centerline being the horizontal line going through that so $y = k$

[woven radish]

hayley 🥥 🌴

[devout snow]

@queen pike Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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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.

[vital night]

Hello, I would like an explanation as to why these two linear combinations share the same plane in xyz space?

[devout snow]

@vital night Has your question been resolved?

[magic thicket]

show one plane contains the spanning set of the other

[vital night]

sorry what

I'm taking an introductory course to linear algebra

[magic thicket]

you've never heard the terminology of spanning set?

[vital night]

i have

do I need to see that they have the same spanning set in xyz space?

[magic thicket]

that's one way to prove it yes

[vital night]

alright thank you!

[magic thicket]

(btw, it is not unique, so "the" is inappropriate)

[devout snow]

Channel closed

Closed by @vital night

Use .reopen if this was a mistake.

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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.

[patent abyss]

find the value of √x +1/√x if the value of x = 9+4√5

[dapper fable]

what are you stuck on?

[glossy basalt]

!status

[devout snow]

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

[patent abyss]

the answer is coming in whole value but not mine

[dapper fable]

(i would reccommend turning 9 + 4√5 into a perfect square)

[patent abyss]

its coming sqrt(9+4√5) + sqrt(9-4√5)

is there any property like (a+b) + (a-b)

[dapper fable]

?

[patent abyss]

got it

[dapper fable]

no

[dapper fable]

id reccommend setting this to x, then find x^2

to simplify and sqrt it

[patent abyss]

my answer is coming √18

which is not whole value

[dapper fable]

incorrect

[patent abyss]

i know

[dapper fable]

you missed the 2ab in (a + b)^2 = a^2 +2ab + b^2

[patent abyss]

u r right

36?

[dapper fable]

2sqrt(5)

[patent abyss]

can you wait for 5 min i am gonna create my sol in image

[dapper fable]

alr

[patent abyss]

got it

.close

[devout snow]

Channel closed

Closed by @patent abyss

Use .reopen if this was a mistake.

[patent abyss]

bye

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
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[eternal adder]

tips for finding OD?

[devout snow]

@eternal adder Has your question been resolved?

[eternal adder]

<@&286206848099549185>

[drifting sierra]

There's a solution that uses simple geometry and another that uses a system of equation with vectors

[eternal adder]

tried many ways, seem so close but cant get it

[eternal adder]

can explain both methdosd

prob something with E being the midpoint of AC, it probably gives it some unique properties?

[drifting sierra]

ABC is a triangle. AD is a median, M is the midpoint of AD. BM intersects AC in F.
H is the fourth vertex of the parallelogram ADCH (so AH parallel to CD, and CH parallel to DA).

H is on BM because M is the midpoint of BH by construction

E is the intersection of CH and BA. Triangles AHE and ABD are congruent. That means AE = AB so CA is a median of BCE, and HE = HC = AD, so BH is also a median of BCE

[eternal adder]

what does AD as a median mean

[drifting sierra]

It just means D is the midpoint of BC

[eternal adder]

but its not

it seems like the diagram u made is off

D shouldnt be connected to A in your diagram

assuming E is the O

[drifting sierra]

This diagram is not related to yours

[eternal adder]

o ok

[drifting sierra]

It's a proof that CF = 2AF

You can then use that in your problem, with the appropriate letters

Since you didn't know what a median is, I assume you also didn't know that the medians of a triangle intersect at a point called the centroid, and that this centroid trisects the three medians

[eternal adder]

oh wow

[drifting sierra]

The other solution uses a system of equations: D is on both CB and OE, so, as vectors, CD = pCB and OD = qOE. You can add that OC = 2a+b, and you get the system { OD = q(3/2 a + b), OD = 2a + b + p*b }

It's not really a system, just OD written two different ways

But from that you can find q and p

[eternal adder]

but how does it prove CF = 2AF

algebrically

how does the diagram prove CF = 2AF algebrically

[eternal adder]

seems lik u havent explained completely?

[drifting sierra]

That's a known property of medians

the medians of a triangle intersect at a point called the centroid, and that this centroid trisects the three medians

https://jwilson.coe.uga.edu/EMAT6680Fa2013/Thurston/Write-Ups/Write-up 4/Centroid.html

[drifting sierra]

Anyway you probably want to use this instead, it seems you're not comfortable enough with geometry

[eternal adder]

ok

[drifting sierra]

I'm off, good luck

[eternal adder]

ty

.close

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[eternal adder]

.reopen

[devout snow]

✅

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[devout snow]

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[viral lynx]

I think I know vaguely what im supposed to do but I dont know specifics

Like I thinl I need to ignore either x(t) and y(t) (I cant remember which one) and then take the second derivative of the other one

And set it equal to 0

But yeah not sure

[restive river]

loosely speaking tangent line is vertical if |dy/dx| = infinity. So this happens when dy/dt is finite and dx/dt is zero.

[viral lynx]

loosely speaking tangent line is vertical if |dy/dx| = infinity
Why sry?

[faint gorge]

vertical x'(t) = 0 and y'(t) != 0

[restive river]

I guess if you want a proof, you have to ask what vertical means

but I think that is not the point of this question

[viral lynx]

Yeah im just trying to understand sry

So I can work it out myself next time

[faint gorge]

You can rotate the coordinate system and notice that you would then maximize/minimize now for x

[viral lynx]

like I can remember this but its easier to remember if I understand

[viral lynx]

If x is vertical does that mean x is a max or a min

[faint gorge]

usually you would do y' = 0 for horizontal tangent

now if you flip the coordinate system and flip variables

you would do now x' = 0

if that makes sense

[viral lynx]

Ok I see

[viral lynx]

yeye it does

[viral lynx]

But am I correct that I need the second derivative?

Cause its the max / min of the tangent

[faint gorge]

you can

I mean it's a circle

so you would expect two solutions one with max x and one with min x

graphically speaking

[viral lynx]

Is there a better way?

[faint gorge]

I would ignore the 2nd derivative

I know graphically I can expect two get two solutions because there are two vertical lines

[viral lynx]

Ok I got the answers

(2, 1) and (-2, 1)

Which looks correct

[faint gorge]

yea it is

[viral lynx]

But I am still a bit stuck on this method sry

[viral lynx]

Why not the second derivative? Its the tangent (which we get by taking the derivative) and we want the min / max of the tangent (which we get by taking the derivative again)

Sry I know you already explain it but im still a bit stuck

[faint gorge]

You can calculate the 2nd derivative to really assure that it's a max or min

I just skipped it

[viral lynx]

But then we just have the tangent? Which could be anywhere on the circle right?

[faint gorge]

because looking at the first derivative -4t² + 4 = 0 would get me two solutions

so I could assumme these are the solutions for my vertical lines

[faint gorge]

no

these are vertical tangents

[viral lynx]

Ok.. so derivative of x(t) gives vertical tangents and derivative of y(t) gives horizontal tangents?

[faint gorge]

only if x'(t) = 0

[viral lynx]

Only if we set it equal to zero? or only if t = 0?

[faint gorge]

set it to 0

Let me show you

[woven radish]

𝔸dωn𝓲²s

[faint gorge]

That's your curve right

If we differentiate it wrt time we get the tangent vector

[woven radish]

𝔸dωn𝓲²s

[viral lynx]

Yes the velocity

[faint gorge]

If x' = 0

and y' != 0

in which direction does (0, any number) show

[viral lynx]

Ummmm

[faint gorge]

think about it

(0,1) (0,-2) etc.

[viral lynx]

I mean I'm guessing the answer is 1?

[faint gorge]

???

[viral lynx]

Oh

[faint gorge]

in which direction

[viral lynx]

Ahhh

[faint gorge]

up, left right, horizontal, vertical?

if you draw that vector into the coordinate system

it always shows vertically

[viral lynx]

How come sry

[faint gorge]

draw it

[viral lynx]

OK 1 moment

[faint gorge]

(0,1) means for example 0 steps on the x axis

1 step on the y axis

so we go only up

which is vertical

[viral lynx]

Okkkkkkkk

I get it now

[viral lynx]

But this is true then right?

[faint gorge]

it's vague

Let $t_0$ be a solution so that $$x'(t_0) = 0 \textbf{ and } y'(t_0) \neq 0$$

[woven radish]

𝔸dωn𝓲²s

[viral lynx]

Yepyep I get it

[faint gorge]

Then the tangent vector shows either up or down

on that point

[viral lynx]

Ok I understand now

Haha sry that took a while

Thank you!

❤️

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[humble glacier]

For what value of a, the lines 2x+3y=1, x+y=3, and ax-4y=6 are concurrent?

[restive river]

Well the approach is to find the intersection of the lines 2x+3y=1 and x+y=3, then find the value of a such that the line ax-4y=6 also goes through that intersection point

[humble glacier]

by using matrix

[restive river]

By solving the linear system (substitution, matrix etc.)
Then substitute x and y into ax-4y=6 and solve for a

When solving the linear system use whichever method you want to use or are supposed to use

[humble glacier]

is this correct?

[restive river]

Yes your approach there is correct

[humble glacier]

what do i do from the last step?

[restive river]

You already have ±(58-8a)=0 right

if I read correctly

[humble glacier]

yes

[restive river]

±(58-8a)=0 is equivalent to 58-8a=0 so a = 58/8

[humble glacier]

by doing this way i got -7/4

[restive river]

both approaches should yield the same result unless you made an algebraic mistake somewhere

I'll check the first approach again though

[humble glacier]

thanks

[restive river]

Seems like you made an algebraic mistake in your first image

I still got 7/4 using the first approach disregard

[humble glacier]

i found my mistake

i did mistake in finding the determinant of 3x3 matrix.

[restive river]

I only knew that the matrix approach had a mistake since the second approach seems safer to me and I can easier guarantee that the second result is correct
I can't really check the first one closely because I'm in kind of a rush and the det formula is more complicated

Both approaches should yield the same result if everything is right

[humble glacier]

thanks. the answer is actually -7/4

.close.

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[upbeat isle]

can someone please help me with D (d.1, d.2 and d.3) of this question

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@upbeat isle Has your question been resolved?

[upbeat isle]

<@&286206848099549185>

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[ancient sluice]

Hello i need help solving a biquadratic using Ferraris method

[ancient sluice]

x⁴-8x³-12x²+60x+63 = 0

I have done some work but I think I messed up somewhere coz I'm facing weird values

[dense lynx]

are you required to use ferrari method?

[ancient sluice]

Yeah bro

Else I have a root , -1

By trial method

Can reduce it to cubic and apply cardanos , or straight use Descartes

I am facing really weird values while solving using Ferraris

[dense lynx]

unfortunate but ok fair enough

are u able to post work?

[ancient sluice]

Yeah one moment

Lower part number 4

I also have that lambda is between (-8,-7)

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@ancient sluice Has your question been resolved?

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[restive river]

Problem 8

[solid osprey]

does a,b,c have to be diffrent?

like whats stopping us for a=1 b=0 c=0

[restive river]

🗿

Algebra

[solid osprey]

am i wrong :3

[solid osprey]

wym

[torn bane]

kind of abusing how the question is phrased

[restive river]

Idk how to do it

[solid osprey]

i meannn :shrug:

[solid osprey]

do you know anything related to the question?

[stable cloak]

This should be the answer probably

[restive river]

What if there’s others that give a different final solution

[solid osprey]

then there are multiple answers

[torn bane]

the way it is phrased implies that it's the same

[eager nova]

There are no other solutions

The exercise is correctly written

It says real a, b, c

[restive river]

So for something like this I do that?

No algebra?

[solid osprey]

err

[eager nova]

You have to prove the are no other real solutions than {1, 0, 0}, {0, 1, 0} and {0, 0, 1}

[restive river]

How

[solid osprey]

$a,b,c\leq1$

[woven radish]

Skill_Issue

[eager nova]

Well that is the exercise

[solid osprey]

we can easily get that

[polar chasm]

(Or assume that there is a unique answer)

[restive river]

Yes

[eager nova]

Hint: You have odd number of numbers

[restive river]

I understand not

[eager nova]

What happens when you square or cube a number < 1?

[restive river]

It gets smaller

[eager nova]

So you can know that

a^2 is different from a^3 right?

It is greater

[restive river]

Yea

[eager nova]

a^2 > a^3

b^2 > b^3

c^2 > c^3

[solid osprey]

err wouldnt it be >=

[restive river]

Oh

[eager nova]

So we proved that a^2+b^2+c^2=a^3+b^3+c^3 is false when they are less than 1

[eager nova]

If they are <1

[solid osprey]

0

[eager nova]

Now you prove for >1

[eager nova]

What do you mean

If they are 0 they cant be equal to 1

[solid osprey]

:p ok

[restive river]

That’s just the second degree is larger than the third right

No

My bad

[eager nova]

The opposite

[restive river]

Other way

Yes

[eager nova]

Same reasoning

[eager nova]

And you get the set of answers

[restive river]

Ohh

Okay

I understand

Ty

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[peak imp]

how would I calculate average velocity with the given information?

[peak imp]

I'm covering a section regarding instantaneous rate of change and was cruising along but then I got a curveball asking for average velocity

I calculated the instantaneous rate of change, but from the lecture I'm watching, I'm not sure how I use that info to find the average velocity

the book gives this definition:

so in this question, the time interval "a" would be 0.1 0.01 and 0.001?

and t would be 2.1 2.01 2.001?

[eternal dove]

Ok, to find the AVG velocity. First, tell me what is the initial velocity?

[peak imp]

95 ft/s

[eternal dove]

Good now. Using the equation in the question. What is the value of y when it's t = 2?

[peak imp]

126ft

[eternal dove]

👍🏼. That value will be used as the final velocity.

[peak imp]

thats not a velocity though, thats just a measure of disposition

nevermind i figured it out using the book

(128.94-126) / 2.1-2 = 29.4

position of ball at 2.1 seconds minus position at 2 seconds, divided by the incremental time difference

thanks

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[plucky kernel]

<@&286206848099549185>

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[agile garnet]

i is incenter

g is centriod

r1 is exradius of incenter opposite to A

[grizzled yew]

follows from IG||BC iff AB+AC=2BC

i forgot how to prove it, but idt think theres a super clean way. barybash or lengthbash should work

[devout snow]

@agile garnet Has your question been resolved?

[agile garnet]

thx

[devout snow]

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[solid osprey]

how can i derivate $\frac{x}{x+\frac{1}{x}}$

[woven radish]

Skill_Issue

[solid osprey]

i can see its $x(x+x^{-1})^{-1}$

[woven radish]

Skill_Issue

[solid osprey]

for the outer one, do i do the chain rule first or product rule?

[cold bone]

it's better to use $\frac{x^{2}}{x+1}$

[woven radish]

77²

[cold bone]

it will be kinda messy will it

[solid osprey]

huh how can you get this?

[cold bone]

multiplying x with both numerator and denominator

[solid osprey]

but wont that give $\frac{x^2}{x^2+1}$

[woven radish]

Skill_Issue

[cold bone]

x^2 imean

[cold bone]

yeah mb

[solid osprey]

oh

can i make it $1-\frac{1}{x^2+1}$ to make it even simpler?

[woven radish]

Skill_Issue

[cold bone]

definitely

as you wish

[solid osprey]

ok

[cold bone]

for this you gotta use product rule first

[solid osprey]

for like this

[solid osprey]

or for like this?

[cold bone]

no

[cold bone]

yeah this one

[solid osprey]

oh

[solid osprey]

uh so
$$1-(x^2+1)^{-1}$$
the derivative would be
$$-(x^2+1)^{-2}(2x)$$

[woven radish]

Skill_Issue

[solid osprey]

this?

[cold bone]

almost

it will be positive

[solid osprey]

huh

why

ohh sorry

[cold bone]

-1 times -1

[solid osprey]

$(x^2+1)^{-2}(2x)$

[woven radish]

Skill_Issue

[solid osprey]

so this?

[cold bone]

yeah

[solid osprey]

alr, ty

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[outer talon]

Can anyone help with the first step on part (ii)

I get they use the hint, We know dAt = Wt dt

but not sure how they make Wt dt = d(tWt) - td(Wt)

[hollow ice]

product rule on d tWt

just basic calc

d tWt = t dWt + Wt dt

and rearrange

[outer talon]

ahhh of course

thanks

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[ember patrol]

Does it make sense to say $\abs{f(x)}\rvert_{-\infty}^{\infty}= \sum_ {-\infty}^{\infty} \abs{f(x)}$?

[woven radish]

KySquared

[sand dove]

wut

[ember patrol]

(Also how would I be able to make the “evaluated at” bar larger?)

[sand dove]

the RHS definitely makes no sense

and LHS isn't defined to me either

[ember patrol]

The LHS is just the derivative of the absolute integrability test

$\int_{-\infty}^{\infty} \abs{f(x)} dx < \infty$

[winter patrol]

try \eval_{a}^{b}

[woven radish]

KySquared

[ember patrol]

I took the derivative of this and got to the LHS here

Then I tried to check if f converged absolutely which is how I got to the RHS

[sand dove]

so the LHS stands for $\lim_{x\to \infty}|f(x)|-\lim_{x\to -\infty}|f(x)|$

[woven radish]

rafilou2003

[ember patrol]

Right

I figured since infinity exceeds all possible numbers perhaps I could cheat and write it as a summation

[sand dove]

definitely not

and even so your summation would be over what?