help-0

[glass lichen]

which is clearly a composition of functions

This is also why just doing chain rule on sin(x+y) is more efficient, as opposed to compound angle then differentiate

[alpine sable]

wtf is a composition of functions

[glass lichen]

1st graders dont do calculus so... no

$f(g(x))$ is f composed with g...

[ocean seal]

Mosh

[alpine sable]

i said explain like I’m a first grader

[glass lichen]

use chain rule when function inside function.

[alpine sable]

where am I supposed to use chain rule in my equation

[glass lichen]

answered that already.

[alpine sable]

Ykw

I’m skipping this question

[glass lichen]

Ok

[alpine sable]

bye

[cunning obsidian]

Idk how to explain with a simple manner xd

Uhm so you see that’s cos y right

[glass lichen]

Eh leave it

[alpine sable]

shut up mosh

ur a horrible tutor

[cunning obsidian]

[alpine sable]

pls dont ban me i need more help

sorry

[wary stream]

Do you know know chain rule?

[cunning obsidian]

Maybe be a little more polite

[alpine sable]

yes

[devout totem]

You should be more involved in your learning. You just threw a question out and clearly aren’t trying to learn how to do it and just want an answer. You should also be more polite to people who are able and willing to help you…

[alpine sable]

"you should be more involved in your learning" i sent an ss where im clearly needing help with the SECOND LAST question

[wary stream]

You sent a screenshot with no context

[alpine sable]

yea and when yall were being annoying about it i sent the whole screenshot

[shut socket]

ikr

[alpine sable]

i thought it would be obvious since u guys are "smart"

[cunning obsidian]

= =

Let’s get back to the q first = =:;

So do u understand this >_>

[glass lichen]

smart and telepathic are different things btw

[wary stream]

If someone just sent you an equation with no context, would you know what to do?

[alpine sable]

why do you keep talking about it when i clearly sent it after u asked r u stupid

[glass lichen]

Do you want help or no?

[alpine sable]

no

[glass lichen]

Ok

[wary stream]

Then good bye

[glass lichen]

remember to .close the channel then

[alpine sable]

🍆

[wary stream]

.close if you're done with the channel

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @plain plaza

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[slate kayak]

Why is it at 90 degrees: pi/2 ?

The circumference of the circle is 2pi right

[wary stream]

Yes

[slate kayak]

I dont get where the 2 comes in to place then when dividing pi by 2 for 90 degrees

[glass lichen]

so 2pi radians=360 degrees

[wary stream]

90 degrees is 1/4th of the circle

[slate kayak]

Oh

So 1/4 times 2pi

[wary stream]

So 2pi/ 4

[slate kayak]

Isd what they did

[glass lichen]

yep

[slate kayak]

Okay i get it thnxc

.close

[lone heart]

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[alpine sable]

im stuck on ii)

[alpine sable]

ik that when the denominator = 0, then thats the vertical asymptote

but im not sure what to do with trig functions

[upbeat gorge]

if that’s the case, then you need to find the values of x between 0 and 2pi inclusive for which cos x is 0

[alpine sable]

ive drawn the graph

but havnt found the intersections

[upbeat gorge]

What function did you graph?

[alpine sable]

y=cos x

[upbeat gorge]

ok

[upbeat gorge]

Have you discussed trig functions before?

[alpine sable]

yea

[upbeat gorge]

And have you encountered the unit circle?

[alpine sable]

but long time ago

[alpine sable]

yes

wait would 45 degrees be zero

[upbeat gorge]

no

Remember that cos corresponds to the x-coordinate

[alpine sable]

$\frac{\pi}{4}$

[upbeat gorge]

backslash frac

[ocean seal]

Bread

[alpine sable]

lol

new to latex

[ocean seal]

CST

[alpine sable]

$\frac{\pi}{2} , \text{and} , \frac{3\pi}{2}$

[upbeat gorge]

[ocean seal]

Bread

[upbeat gorge]

You are correct

[alpine sable]

ah ok

is it ok if i leave this channel open

if i get stuck again

[wary stream]

In my opinion, if you're not stuck with anything for more than 15 minutes, then you should just close the channel, and when you are stuck with something just open up a new one

[alpine sable]

👍🏻

i need help with iv)

[alpine sable]

^

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[sand pawn]

You here?

[alpine sable]

ye

[sand pawn]

in which part you need solution?

[alpine sable]

iv)

[sand pawn]

At x=0, secx=1

cosx= 1/secx

Using this, you can prove from the previous information to the question to the question

[alpine sable]

isnt it asking for sec x =1

oh i see

ty

[sand pawn]

Np

[lone heart]

Channel closed

Closed by @shadow elbow

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[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

for v)

do i just say negative parabola

at $\frac{\pi}{2} < x < \frac{3\pi}{2}$

[sand pawn]

You can take help from desmos. Here, see an example

[alpine sable]

the other way around

[sand pawn]

Your question is not making sense. Are you sure it is complete?

[alpine sable]

yea

its asking for vertical asymptotes

[sand pawn]

Just reading the question, I think the range is 0<=x<=2*pi

[ocean seal]

Bread

[alpine sable]

yea within there is 2 asymptotes

u can see it in the desmos

[sand pawn]

Yep, there is

[alpine sable]

alr ty for ur help

[bleak ridge]

Bread

[alpine sable]

yes?

[bleak ridge]

We are both bread

[alpine sable]

ofc

im ur son

[bleak ridge]

True

[sand pawn]

How you got that Active role?

[bleak ridge]

Uhh

Idk I just talked

The channel says its automatically given by a bot

[alpine sable]

alr u guys can talk somewhere else

ama close

.close

[lone heart]

Channel closed

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[lucid wadi]

hi

[lucid wadi]

how would I find -146 degrees

it doesn't land on one of the things in the unit circle

[wary stream]

Do you know what coterminal means?

[lucid wadi]

it lands on 214 degrees in the clockwise direction

not 100% sure but

I think it means the angle that is the same thing as

I forgot how to explain it but I kinda get what it means

it's the angle that helps you locate

[sand pawn]

nope

[wary stream]

Yes, so given -146 degrees, how would you get that into a range of 0 and 360?

[lucid wadi]

things that are not on the unit circle

so I know that you go -146 degrees in the clockwise direction

which would put you at 214 degrees

which is in between210 and 225 degrees

but how would I know the exact value of the radian if it's not on the unit circle

[sand pawn]

BTW, the answer will also be in radian

[lucid wadi]

like -360 and 360 are coterminal angles

yea

but im not sure how to get the exact radian

it's between 7pi/6 and 5pi/4

[sand pawn]

A circle is equal to 2pi radians

[lucid wadi]

yea

[wary stream]

It doesn't want a radian answer for 214

It just asks for a coterminal angle of -146

[sand pawn]

Now subtract that and get the answer for b

[wary stream]

Nothing with that question has anything to do with the unit circle

[lucid wadi]

360-146?

that's the same thing

214

[wary stream]

Yes, or -146 + 360

Yes

214

[lucid wadi]

WAIT

I CAN CONVERT TO RADIANS

by pi/180

multiply by that

right

[wary stream]

Dude, it has nothing to do with radians

Those are two separate questions

[lucid wadi]

oh

im so stupid

I just saw it

it wants degrees

[wary stream]

It just wants a coterminal angle for -146

[lucid wadi]

214

[wary stream]

Yes

[lucid wadi]

I got it sorry I thought they wanted radians

thanks a lot

[sand pawn]

BTW, he is asking for help for the 2nd question probably

[wary stream]

Nah

They got the second question

[lucid wadi]

no I think I got the second one but actually

[wary stream]

Notice how it's filled in?

[lucid wadi]

is there any easier way to do the second one without looking at the unit circle?

[wary stream]

Yes

[lucid wadi]

cause I had to look for that one

[wary stream]

Subtract multiples of 2pi

Until you get between 0 and 2pi

[sand pawn]

What filled in?

[wary stream]

3pi/4

[lucid wadi]

oh so basically you want to get a radian measure between 0 and 2pi

[wary stream]

Yes

[lucid wadi]

cause we don't care about how many rotations there were

[wary stream]

Same thing with degrees

[lucid wadi]

what if u do

[wary stream]

If given an angle 720. the coterminal is 360

[lucid wadi]

7pi/4

[sand pawn]

19/4pi = four rotations - pi/4. That's basically 270 degrees

[wary stream]

You just subtract multiples of 360 to get the angle between 0 and 360 degrees

[lucid wadi]

so 19pi/4 -7pi/4 -7pi/4

that's 5pi/4

which is 225

degrees

right?

[wary stream]

No

Where is 7pi/4 coming from?

You subtract multiples of 2pi

[lucid wadi]

u said 3pi/4

how is that a multiple of 2pi?

[wary stream]

I was saying you put in an answer of 3pi/4

[lucid wadi]

oh mb

ok so u subtract by multiples of 2pi

[wary stream]

Yes

[lucid wadi]

but what r the multiples of 2pi

are they the 4 quadrants?

[wary stream]

2pi, 4,pi, 6pi, ... 2pi * n

[lucid wadi]

oh

so in this case we have 19pi/4

which one should I subtract it by?

[wary stream]

Just keep subtracting multiples of 2pi

[sand pawn]

That's 4 rotations + pi/2

[wary stream]

That's just memorizing

You can just do 19pi/4 - 2pi - 2pi... so on

[lucid wadi]

ok so 19pi/4 -2pi

[wary stream]

Until you get a number between 0 and 2pi

[lucid wadi]

that's 19pi/4 -8pi/4

which is 11pi/4

then

[sand pawn]

Just put it in the calculator. works fine either 🤷‍♂️

[lucid wadi]

11pi/4 - 8pi/4

that's 3pi/4

that's between 0 and 2pi

which is at 135

[wary stream]

The concept is coterminal, not using a calculator

[lucid wadi]

right?

[wary stream]

Where you have to add/subtract multiples of 2pi to get an angle between 0 and 2pi

[wary stream]

Yes

[lucid wadi]

thanks so much

I get it now

have a good day/night

[wary stream]

Same thing for degrees, it's multiples of 360

[lucid wadi]

ok

so keep subtracting

till u get between 0 and 360

[wary stream]

So 360, 2 * 360, 3 * 3600, etc

[sand pawn]

Ikr, the calculator helped me anyway

[lucid wadi]

alright thanks

https://tenor.com/view/thumbs-up-double-thumbs-up-like-agreed-yup-gif-11663223

[wary stream]

So what? Some teachers don't allow calculators and want you to do it by hand

[lucid wadi]

should I close this

yea my teacher doesnt allow a calculatpr

calculator

[wary stream]

Hence adding/subtracting multiples of 2pi or 360

[sand pawn]

where you live in?

[lucid wadi]

richmond, VA

[wary stream]

Irrelevant

Some teachers design a test that it can be done with no calculator

[lucid wadi]

Khan sorry but I think most students nowadays have to learn it without a calculator

[wary stream]

But if you are done, you can close it

.close

[lucid wadi]

ok thanks

.close

[lone heart]

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[fresh parcel]

Guys i have a question

[fresh parcel]

oops

Bob and Alice both have identical decks, 3 red 3 blue 3 green and 3 yellow. They take turns removing cards from their deck, Alice going first. What is the chance that Alice removes all three red cards before Bob removes any?

[empty ridge]

What have you tried so far?

[fresh parcel]

i dont really know how to approach the problem

for previous problems ive done casework

because it was easier

but in this question theres too many cases

[empty ridge]

Ok, do you see any way you could simplify this problem?

[fresh parcel]

well all the non red cards could be grouped together

so its 3 red and 9 non red

for each

[empty ridge]

Good. What are the cases you figured out so far?

[fresh parcel]

alice can draw a red card first or she draws a non red card

yeah but then there are too many cases to keep track of

[empty ridge]

I agree. Can Alice win with just 3 cards?

[fresh parcel]

yes

if she draws all red cards

[empty ridge]

The probability of that is...

[fresh parcel]

1/12 x 1/11 x 1/10?

oh wait

no

[empty ridge]

Wait! Good!

[fresh parcel]

3/12 x 2/11 x 1/10

[empty ridge]

But this is just alice right... what would happen to bob?

[fresh parcel]

uh

bob would draw 2 cards

[empty ridge]

You are now thinking about two things happening right.. not just alice drawing reds, but bob drawing non reds

[fresh parcel]

hm

im still confused

how does that help?

[empty ridge]

Ok, have you learned about independence and joint probabilities? P(A and B) = P(a) * P(b)?

[fresh parcel]

ye

[empty ridge]

Since Alice's deck and Bob's deck are independent (Alice can't change the probabilities that Bob would be facing when drawing cards, right?)

[fresh parcel]

yes

[devout summit]

But if Alice picks a red, chances of Bob picking red decreases too

[fresh parcel]

nono they have seperate decks

[empty ridge]

They have separate decks

Yeps

[devout summit]

Oh yes read just now

[fresh parcel]

oh wait so its just the probability of alice drawing 3 reds multiplied by the probability of bob drawing none?

[empty ridge]

Yes, but Alice may not be that lucky right?

[devout summit]

I didn't know they had separate decks

[fresh parcel]

hm

[empty ridge]

Initially I understood the same as you, but this less messier...]

[empty ridge]

What else could happen?

[fresh parcel]

alice doesnt draw 3 red cards on her first go?

[empty ridge]

Or, maybe she needs 4 cards to win... what would be the probability of that?

[devout summit]

You could try a tree diagram of the possibilities

[fresh parcel]

4 cards would mean 3 are red and 1 is not red

[empty ridge]

Think about what @devout summit is suggesting as you are building your intuition about the problem

[fresh parcel]

hm okay

[empty ridge]

Right, what would be the probabilty of the 4 cards case?

[fresh parcel]

uh

[empty ridge]

At least for bob, nothing changes right? But what would be different for Alice?

[fresh parcel]

can i calculate it using combination?

is it possible to do that

[empty ridge]

But do you understand why?

[fresh parcel]

im sorry i dont understand what you mean

bob's card draws are independent

[empty ridge]

The combination idea is correct. It is needed because there are more than one way to get 3 reds and 1 non red.

I was just checking if we were on the same page

[fresh parcel]

so should it be 8/(11x5x9)?

because there are 8 ways to get 3 reds and 1 non red from 12 cards

[empty ridge]

I mean ~~RRRN ~~RRNR RNRR NRRR right

[fresh parcel]

oh

yeah

[empty ridge]

ops, the first doesn't count (she would have won...)

[fresh parcel]

oh yeah true

so there are 3 ways she can draw 3 reds and 1 non red

[empty ridge]

Good! And each has a probability equal to what?

[fresh parcel]

so RRNR has a probability of 3/12 x 2/11 x 9/11 x 1/9

oh wait they all have the same probability

[empty ridge]

Great! Yes. So what is the probability of Alice wining with 4 cards?

[fresh parcel]

2/11 x 9/11 x 1/9

because the 4 and the 3 cancel out the 12 on the denominator right?

so do i have to do the same thing all the way up to 12?

[empty ridge]

No, this is just alice side of the thing right. Don't forget about Bob...

[fresh parcel]

thats quite tedious

oh yeah bob

he needs to get 9/12 x 8/11 x 7/10 x 6/9 right?

[empty ridge]

That's right (again P(A and B) = P(A) * P(B)

[devout summit]

<@&268886789983436800>

[empty ridge]

Dude, can you imagine the type of people that is spending their night on a saturday solvind math problems?

[sly mantle]

b&

[fresh parcel]

so its (2x8x7x6)/(12x11x10)?

wait a second

ima redo my math

oh wait

nvm

[empty ridge]

That is a good idea, Check alice's numbers.

I don't think i follow the 2/11 x 9/11 x 1/9

[fresh parcel]

okay

[fresh parcel]

wait but is this correct?

[empty ridge]

I think this is the situation right? 3 * (9/12 * 3/11 * 2/10 * 1/9)

[fresh parcel]

oh yeah its 10

my bad

[devout summit]

But Bob also has to consistently not pick a red right?

For three turns

[empty ridge]

Yes, this is just alice's side of the thing...

[fresh parcel]

yeah

i think i calculated that already

[empty ridge]

Just steping back to summarize the thing:
Alice can win with 3 cars with the probability of:
P(A winning 3 cards)*P(B not gettin red)

Alice can win with 4 cards with probability:
P(A winning with 4 cards)*P(B not getting red)

[fresh parcel]

3 * (9/12 * 3/11 * 2/10 * 1/9) * 9/12 x 8/11 x 7/10 probability correct?

oh crap just realized

bob only draws 3 times

okay so the edited message should be the probability

[empty ridge]

Yep, now I want you to think when our logic will break. I mean, we can repeat this same logic for Alice winning with 5 cards, then 6 ... But this logic has a limit, do you see why?

[fresh parcel]

after 9

because then bob cannot draw more than 9 cards with all of them being non red

[empty ridge]

Great, you solved it!

[fresh parcel]

wat

[empty ridge]

You just have to compute the probabilities and you are done.

[fresh parcel]

oh yeah

alright then

thanks for your help!

[empty ridge]

It may be tedious, but at least it makes sense right?

[fresh parcel]

im going to close the channel now since its solved

yeah

alr thanks!

.close

[lone heart]

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[serene osprey]

how do you do this question

[serene osprey]

i tried expanding out the cos with compound angle formula

but couldn't get anymore

[thorn kindle]

Might be worth a shot to use complex exp

[serene osprey]

huh?

what?

i don't think i have learnt that

[placid zinc]

You'll want to get both with θ/2, or with θ

I don't remember the double angle formulas off hand oof. Maybe worth a look up

[serene osprey]

i wanted to try double angle

but you need the term to be squared

i think

[placid zinc]

One thing at a time haha

[serene osprey]

oh

right

sorry thats half angle

hahaha

[placid zinc]

The angles definitely have to match, so double angle/half angle happens somewhere

[rigid smelt]

double angle for cos(2x) is cos(2x)=1-2sin^2(x)

[devout summit]

Yeah and,\\$\cos(\theta)=\cos\left(2\cdot\frac{\theta}{2}\right)$

[ocean seal]

Euclid31415

[lone heart]

@serene osprey Has your question been resolved?

[serene osprey]

no i did this expansion

but then how do you equate this?

[devout summit]

You get a quadratic in terms of sin(theta/2)

$1-2\sin^2\left(\frac{\theta}{2}\right)+3\sin\left(\frac{\theta}{2}\right)-2=0$

[ocean seal]

Euclid31415

[devout summit]

Then you can factorise and solve for sin(theta/2) and hence, theta

[lone heart]

@serene osprey Has your question been resolved?

[lone heart]

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[lone heart]

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[wispy olive]

Should not pi be a rational number?

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

p = 22, q = 7.

[wispy olive]

.close

[lone heart]

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[alpine sable]

.close

[lone heart]

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[lethal ore]

Share your question once again. I wanna copy it

[lone heart]

@lethal ore Has your question been resolved?

[lone heart]

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[wild snow]

Just need help with part B. I haven't done anything like this before so I'm not sure how to start it. All I know is it has to do with 5! and 4! but I dont know how to set up the equation.

[alpine sable]

help pls

use an empty channel

empathy i'll try to help later if i can, i'm helping some other people
sorry about that

[wild snow]

All good, no rush ^^

[fiery bronze]

Do you know about counting principles?

[wild snow]

That terminology doesn't sound familiar but I may know about it

[fiery bronze]

Did you already do question A?

[wild snow]

Yes

[fiery bronze]

Did you use combination or permutation?

[wild snow]

Permutation

1 x 1 x 1 x 6!

[fiery bronze]

So the word eloquence is a 9 letters word right?

[wild snow]

Yes

4 consonants and 5 vowels

[fiery bronze]

having 5 vowels right?

exactly

So, there is no repetition of letters - neither vowels nor consonants.

[wild snow]

Isnt E a repetition

[fiery bronze]

Therefore, the arrangement pattern of letters shall be:

vowel-consonant-vowel-consonant-vowel-consonant-vowel-consonant-vowel.

I'm not sure tho

do you have the answer with u?

[wild snow]

Yea I have the answer

It says it should be 480

[fiery bronze]

i think ur right. E is a repetition.

i would wait for somebody

what grade are you?

[wild snow]

Year 11 maths methods

[fiery bronze]

I'm in year 11 as well mate

doing the same thing as u

we are on the same boat my brother

[grizzled path]

since there are 3 E's there are 3! ways to rearrange them so that the word stays the same

which means that the 2880 overcounts each word 3! = 6 times

so 2880/6 = 480 distinct words

[fiery bronze]

@grizzled path is right

[wild snow]

Oh

Thank you @grizzled path

[fiery bronze]

thank you @grizzled path

[grizzled path]

your welcome

[wild snow]

.close

[lone heart]

Channel closed

Closed by @wild snow

Use .reopen if this was a mistake.

[wild snow]

oops

.reopen

[lone heart]

✅

[wild snow]

how do i make this channel available

[fiery bronze]

@grizzled path what grade are you in?

[wild snow]

.close

[lone heart]

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[weary hazel]

Is the answer 17/7 hrs?

[fiery bronze]

let me help you with this question

he spent 3/7 of his time grocery shopping and the remaining 2 hours buying furtniture right?

remaining 2 hours must therefore equale to 4/7 as both added together should equal 7/7

[grizzled path]

in the polish system it's grade 2 of middle-high school so like 10th in normal units

[weary hazel]

Is the answer 3.5 hrs ?

[quaint trout]

@weary hazel yes, please stick to one channel next time and use .close to close this channel if your question is resolved.

[fiery bronze]

Yes sorry my wifi went off. So if we divide 2/4 we get the value of 1/7 which is 0.5

to then find 3/7 we multiply 0.5 by 3

which is 1.5

we then add 4/7 (2) and 3/7 (1.5) which is as you said 3.5hrs

[lone heart]

@weary hazel Has your question been resolved?

[lone heart]

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[harsh belfry]

I was wondering how I could approach this problem
https://media.discordapp.net/attachments/486841106298961930/904325971765788704/unknown.png?width=1247&height=526

[harsh belfry]

I am searching for the rate at which the light on the car travels along the wall.

I believe that would result in me having 2Πr as my x and 70ft as my y with 30 degrees as my theta

https://media.discordapp.net/attachments/486841106298961930/904328420727619615/unknown.png

This should be my equation if I'm not mistaken to find z

[harsh belfry]

But would I differentiate this statement to find the rate at which it travels?

Calc 1 Related Rate problem

Would appreciate any help

[celest solstice]

what exam board r u doing

[lone heart]

@harsh belfry Has your question been resolved?

[harsh belfry]

<@&286206848099549185> Would really appreciate any help on this related rates problem. Need some guidance.

[woeful pulsar]

Firstly you'll need to come up with an equation that relates the angle and position, then differentiate both sides with respect to time.

@harsh belfry

[harsh belfry]

Any chance you could help me out in setting that up?

[harsh belfry]

I'm not used to doing that part I guess.

[woeful pulsar]

Start by setting up the equation relating angle and position

you sort of have it, just need to not put in the specific angle

[austere gale]

guys anybody help

[harsh belfry]

Hey, this is an occupied channel. Currently solving a problem

[austere gale]

ok sry

[harsh belfry]

This should work right? @woeful pulsar

[woeful pulsar]

there's no dt on the left hand side

you have to differentiate both sides with respect to time

[harsh belfry]

ah would I perhaps end up with dtheta/dt

[woeful pulsar]

what would the expression be? remember to use chain rule

[harsh belfry]

I was originally thinking this

but perhaps I need to re-do it

[lethal tapir]

An 8 × 12 board is divided into colorless unit squares. Determine the minimum number of squares that need to be painted black such that each 3× 3square contains at least two red squares?

what is the ans

[harsh belfry]

Hey man, this is an occupied channel.

#help-11 is available

[lethal tapir]

ok

[harsh belfry]

@woeful pulsar This should be it

[woeful pulsar]

yeah looks like it

[harsh belfry]

Now I would plug in my theta?

[woeful pulsar]

now what information do you have to plug in?

yeah theta

and?

[harsh belfry]

I would guess theta/dt

but not sure what that is

hmm

[woeful pulsar]

read the question, is the information there for d theta/dt?

[harsh belfry]

dtheta is the revolving rate of the light right?

2pir's derivative?

[harsh belfry]

No its not right?

[woeful pulsar]

there is information about d theta/dt

[harsh belfry]

Thats what we're solving for.

[woeful pulsar]

what we are looking for is dx/dt

[harsh belfry]

2pi38

is the only thing I can think of

[harsh belfry]

I must be missing something major

[woeful pulsar]

yeah 76pi radians per minute

( and yeah, we do things with radians)

now can you solve for dx/dt?

[harsh belfry]

I believe I can

give me a moment

[woeful pulsar]

be careful about your units

[harsh belfry]

or 22284.3639

Which is the rate at which the light travels along the wall in ft/sec

That should be correct @woeful pulsar

[woeful pulsar]

for which angle?

[harsh belfry]

angle of 30 degrees

ah I see

will try punching in the answer to see if I'm right

[woeful pulsar]

incorrect, be careful about your units

[harsh belfry]

😅

OH

this is in revolutions per minute

its asking for seconds

[woeful pulsar]

yeah that looks reasonable

[harsh belfry]

very good this should be my answe

Thanks a bunch @woeful pulsar really!

[woeful pulsar]

I guess you can .close now lol

[harsh belfry]

.close

[lone heart]

Channel closed

Closed by @harsh belfry

Use .reopen if this was a mistake.

[night geyser]

Just an FYI: honorables have access to .close!

(so do helpers and trusted)

So you don't need to own the channel to close it

[lone heart]

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[alpine sable]

Need help with confirming if I got this matrices equation correct

[alpine sable]

<@&286206848099549185>

Just need confirmation

[lone heart]

@alpine sable Has your question been resolved?

[empty ridge]

I suggest you to organize this solution better and do the math with no rush (slow is smooth and smooth is fast...)

[alpine sable]

What you mean by that

Actually when you said

Nvm now Ik what u mean

[empty ridge]

I don't know what you are trying to solve there... (I had to struggle just to understand that there is system of equations somewhere there, some determinants everywhere and some cryptic variables D, Dx,Dy,Dz ... to help you and the person that will have to read this, I suggest you write some small notes on the solution... Things like: I have to find the solution to ... write the system of equations.
Then, to solve this I will apply this method that uses some determinants ... Write D, then Dx, then Dy, then Dz
Finally, using the determinants, x is ... , y is ... and z is ...

What I mean by slow is smooth and smooth is fast is that It seems that you know what you are doing, but there are some determinants that are not computed correctly. For instance, det((-4,-1),(6,5)) isn't -26

[alpine sable]

Yeah Ik

I got -14

Nvm

[empty ridge]

My bad, check D

[alpine sable]

Now Ik what I did wrong

Yeah what I did was unorganized

But Ik what I did wrong now

[empty ridge]

The value of D is not -480... where are you calculating D? I can't find it on the solution.

[alpine sable]

Yeah the first part I didn’t calculate it correctly

I did 20+-6

It was supposed to be 3(-20- -6)

Which would be 3 (-14) is -42

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[fiery bronze]

I'm doing the IB

[wary stream]

Just fyi, you opened this help channel with that response

If you didn't mean to, just close this

[fiery bronze]

.close

[lone heart]

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[alpine sable]

IB gang

[fiery bronze]

😂 😂 😂 you taking it as well mate?

[alpine sable]

mhm

year 2 for me

[fiery bronze]

i can imagine all the pain mate lol

subjects taken?

[alpine sable]

Maths AA HL
Economics HL
Business HL
Chemistry SL
English SL
French SL

you?

[lone heart]

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[alpine sable]

Hi, I have been reading a book about algorithms and realized I also need an understanding of maths to be able to solve that algorithms, can you recommend me a book that emphasizes the math needed for solving programming algorithms?

[fiery bronze]

Maths AA HL, Biology HL, Chemistry HL, Italian HL, Economics SL, English SL

[wary stream]

Ask in #book-recommendations

[lone heart]

@alpine sable Has your question been resolved?

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[icy dagger]

super quick question

[icy dagger]

if a number is not prime does that mean its composite?

it does right?

[plain nexus]

yes

[icy dagger]

thanks i appreciate it

.close

[lone heart]

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[glass lichen]

if the number isn't 1, then yes

[lone heart]

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[alpine sable]

Shouldn't be the answer 8 ?

[charred flint]

no I see the answer there, what values do you get for each part?

[alpine sable]

√3, 2 and 1/√3

3+4+1

[charred flint]

correct with the first line

but cosec isn't squared :v

[alpine sable]

Oh ryt

[charred flint]

np

[alpine sable]

Silly mistake 😅

Tnq

.close

[lone heart]

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[dense tangle]

studying for trig test, could someone walk me though how to solve this?

[dense tangle]

Yes I do

SOH CAH TOA

And the reciprocals

Like y/r x/r and y/x

[placid zinc]

Consider putting this line on the unit circle. Can you point out what the sides need to be?

[dense tangle]

Well would it be on the y axis since it’s y = 3x?

[placid zinc]

"it"?

[dense tangle]

Wait I’m sorry

Ok my bad so if I put 3x on the line what would I do from there?

[placid zinc]

"Put 3x on the line" is a very weird way to say it, haha.
So you want to graph y = 3x.

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Kaynex#7520

[dense tangle]

I know I’m sorry

[placid zinc]

That should be no problem. If you are having trouble with graphing lines, check up a YouTube

[dense tangle]

Ok so once you plot that what do you do from there?

Do you just find where it is on the unit circle?

So as long as it’s more than 0?

Ah gotcha

[placid zinc]

That's a better picture. You want to find the coordinates of that intersection

[dense tangle]

Oh ok

So then the coordinate would be(1, 3) and you would be able find the trig functions cuz your given x and y?

[placid zinc]

The point is not (1,3) haha

However, you have noticed that the y-value will be 3 times larger than the x-value

Actually, fair. You're right you can construct any triangle

So yeah a triangle with base 1, and height 3 works

[dense tangle]

Alright gotcha

So just plot that and then find a point that’s more or equal to 0

Just making sure so I know how to do it by myself haha

[alpine sable]

How do you differentiate 12 / (x - 3)

?

Hm, we didn't get that yet

wait

[dense tangle]

Ok well thank you for the help

.close

[lone heart]

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[novel sinew]

can i have help please?

yeah, im not really a pro at math

[lone heart]

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[rustic delta]

i need help

[wary stream]

Do you have a book? Because using that will help

[rustic delta]

no

[wary stream]

You can Google the definitions

Do you know what domain means?

Or rate of change?

[rustic delta]

The domain of a function is the set of all possible inputs for the function

its not asking for the definitions

hello?

[lone heart]

@rustic delta Has your question been resolved?

[lone heart]

@rustic delta Has your question been resolved?

[alpine sable]

How do you differentiate ((x-3)(x-1)) / x-1

?

[wary stream]

Don't ask in an occupied channel

[alpine sable]

Oh, I didn't think it was occupied

[wary stream]

#❓how-to-get-help

[cinder sorrel]

But it's not a right triangle?

[lone heart]

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[alpine sable]

what is this?

[next chasm]

smh

sqrt(40)+sqrt(90)

2sqrt(10)+3sqrt(10)

5sqrt(10)

5 is your answer

[alpine sable]

these questions blow my mind lol

[next chasm]

bruh

what grade you in

just google square roots

[alpine sable]

i think in america its 12

[next chasm]

see what you can find

and study

[alpine sable]

i have and i dont fuckin get it

[cobalt palm]

Mind if I chip in? You're just multiplying it out

[next chasm]

like imagine 4

it is 2 times 2 right

[alpine sable]

yes

[next chasm]

so imagine a number x

the square root of it

is a positive number

(sometimes negative works, but positive is the correct way)

that if you multiply it

by the same number

you get x

so

some examsples

sqrt(1)=1

since 1*1 is 1

sqrt(4) is 2

since 2*2 is 4

sqrt(9) is 3

[alpine sable]

yes

[next chasm]

since 3*3 is 9

and so on

sqrt(100) is 10 since 10* 10 is 100

but some numbers

[alpine sable]

yes

[next chasm]

have irrational square roots

for example

square root of 2

or square root of 10

theres no specific number to find their square root

so basically square root of prime numbers are irrational, and some other numbers square roots are irational as well

so here

you have square root of 5 times (square root of 8 + square root of 18)

since its in () try opening it u

p

we get square root of 5 times square root of 8 + square root of 5 times square root of 18

and when we have

square root of a times square root of b, we can multiply to get square root of ab

so her

e

we are going to use that

square root of 40 + square root of 90

so now we can write 40 as in 4* 10

so square root of (410) + square root of (910)

sorry i meant to put * 2 times

discord messes it up

basically

square root of 4 is 2

9 is 3

so we can write 2 sqrt(10) + 3sqrt(10)

add it up

5 sqrt(10)

[alpine sable]

i hate to be that guy

but im confused

[next chasm]

hm ok

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/understanding-square-roots

[cobalt palm]

mind if I have a go?

[next chasm]

fosho

[alpine sable]

i know the square roots part

[cobalt palm]

@alpine sable ok so to start off simple

do you know how to expand out

like, multiply a(b + c)

[next chasm]

mans 12 grade

[cobalt palm]

i'm just verifying foundation before i continue

[next chasm]

lmao

[alpine sable]

you lost me from here

[cobalt palm]

and idk what 12 grade means lol

[next chasm]

wym

[cobalt palm]

ok so cigar

[next chasm]

anyways

[alpine sable]

alright no need to take the piss because i dont understand something

[cobalt palm]

let's say you have 5(4 + 1)

how would you do this

[alpine sable]

20+5

[cobalt palm]

right cool

which is 25

[next chasm]

im not saying nun, im saying you would know expanding

[cobalt palm]

okay so with square roots, it's exactly the same

[alpine sable]

i do

[cobalt palm]

multiply it out before anything

[next chasm]

yes

[alpine sable]

not with square roots

[cobalt palm]

root 5 x root 8 = root 40

[next chasm]

anyways

listen to dyre

[cobalt palm]

root 5 x root 18 = root 90

you now have root 40 + root 90

[next chasm]

maybe try opening 18 as 2*9 then write 3 root 2 then multiply

so its easier

[alpine sable]

ok

[cobalt palm]

well, either way round works

i'm just trying to explain it level by level

[alpine sable]

yeah, thank you

[cobalt palm]

so root 40 is the same as root 20 x root 2

equally it is the same as root 10 x root 4

equally it is the same as root 8 x root 5

which would be written as root and then 8 x 5 inside of it

[next chasm]

root 80 x root 1/2 works too

basically anything

[cobalt palm]

yeah

[next chasm]

that multypling gives 40

[cobalt palm]

now, of all of those roots i have shown, which do you think simplify into a rational number

[next chasm]

rational

like 1 2 3 4

[cobalt palm]

root 10, 4, 20, 2, 8 or 5

[alpine sable]

4

[next chasm]

correct

[cobalt palm]

cool because that makes two

[next chasm]

right

[alpine sable]

yes

[cobalt palm]

so now you know it's root 10 x root 4

this can now be turned into 2 root 10

because instead of it being root 4 x root 10, it's 2 x root 10

now to add them, you need 90 to also have a root of 10

[next chasm]

and what about 90 45 30 15 9 6 3 2

[cobalt palm]

so you turn 90 into root 9 and root 10

conveniently, root 9 also simplifies down into 3

[alpine sable]

9

[cobalt palm]

as such, you have 3 root 10 + 2 root 10

do we agree

[next chasm]

correct

i agree

[alpine sable]

ok

yes

[cobalt palm]

now do you know what you can do with that

[next chasm]

so add up

[alpine sable]

make it 5 root 1

10

[next chasm]

since it wants some form of

[cobalt palm]

aye, because both numbers inside the root are the same you can add

nope,

[next chasm]

a root 10

[cobalt palm]

sorry i meant yes

i'm tired

[next chasm]

lmao

[cobalt palm]

anything there you don't understand @alpine sable

[alpine sable]

no

you explained it well

im gonna be honest

[next chasm]

so whats root 25

[alpine sable]

im here because i couldnt find a way to put this in a calculator

tbh

but thanks alot

[next chasm]

whats root 25

[alpine sable]

5

[cobalt palm]

absolutely no worries mate

oh also just for reference

[alpine sable]

i have never revised maths, neither anything else

[cobalt palm]

these are called surds so you can cross reference

surds = roots which don't become rational

[alpine sable]

the irrational square roots are yes

[cobalt palm]

yea

[alpine sable]

been learning it for a while

[cobalt palm]

alright yeah

[alpine sable]

in the beginning i understood

but now i dont

so i just put shit in the calculator

and write down what my teacher writes

[cobalt palm]

lol

i know the feeling mate, but yeah, if you have the time always look for help

anyway, was great meeting you man

have a good one

[alpine sable]

thanks

[cobalt palm]

👍

[next chasm]

🍪

heres a cookie

for your efforts

[alpine sable]

thanks

this is the next hurdle

[next chasm]

now

you know this formula

(a+b)^2

=

a^2+2ab+b^2

if not i can explain

so imagine you are multyplying some number by itself

and lets say a+b=n right

for the moment

so (a+b)^2= (a+b) * (a+b)

which equals

(a+b) * n

so when we expand

we get an+bn

[cinder sorrel]

Tell it to Me pls

[next chasm]

but we said that n is equal to a+b

so an+bn is equal to

a(a+b) + b(a+b)

so when we expand

we get the following

a^2 + ab + ab +b^2

which becomes a^2+2ab + b^2

so now we have a =1

b= root 3

so their (a+b)^2 = 1 + 3 + 2 root 3

which equals to 4 + 2 root 3

so a

is equal to 4

b is 2

since we have 4+ 2root3= a + b root 3

[raw shard]

remember that (a+b)^2 = a^2+2ab+b^2 @alpine sable

[next chasm]

yeah

[rancid blade]

you need not remember this

[raw shard]

a = 1 and b = sqrt3

[next chasm]

imma write some formulas to remember

[rancid blade]

you don't need to memorize

[raw shard]

yes you do

[next chasm]

1. (a+b)^2= a^2+2ab+b^2
2. (a-b)^2= a^2-2ab+b^2
3. (a+b)^3= a^3+3a^2b+3ab^2+b^3
4. (a-b)^3= a^3-3a^2b+3ab^2-b^3
5. a^3+b^3=(a+b)(a^2-ab+b^2)
6. a^3-b^3=(a-b)(a^2+ab+b^2)
7. a^2-b^2=(a+b)(a-b)

[rancid blade]

just apply the definition of the square

[alpine sable]

that shit alone confuses me

[rancid blade]

ignore it

you don't need it here

[raw shard]

unless you wanna derive literally everything that would have just been easier to remember

yes you do

[ocean seal]

grist bundle

[rancid blade]

then FOIL multiply as usual

[raw shard]

which gives what i already said

[rancid blade]

yes

no need to memorize now though

especially if the problem is conceptually difficult to begin with

it's better to work through it using the tools we already have, if possible

tricks can come after

[next chasm]

here remember these

[rancid blade]

don't

just remember binomial theorem when you get to that point

[raw shard]

yeah don’t remember all those

[alpine sable]

i have no fuckin idea what any of that means tbh

[rancid blade]

it subsumes all of the ones davo mentioned

ignore it

it's not of use to you now

do you know how to carry out the multiplication here?

[next chasm]

yeah not now

just like over time

[ocean seal]

grist bundle

[next chasm]

its useful to know

[alpine sable]

i dont know anything

to me its just a bunch of letters

[rancid blade]

ok what's 2+7

[alpine sable]

9