help-28

[half remnant]

since f-1(b) = a

i mean whoops

the other way around

[onyx glen]

no your correct

[half remnant]

oh right

[onyx glen]

but yeah for the f(x) its the integral from [0, a] with respect to dx

for f^-1(x) its the integral from [0, b] with respect to dx

and those areas end up being the same

[half remnant]

I think theres some logic where if u integrate about the y axis

with the bounds between a and b swapped

its the same as integrating the normal function along the x axis

[onyx glen]

yep

but the tricky thing to understand with this problem was it was still with respect to the x axis

the inverse function kinda tricked me into taking the wrong integral the first time i looked at the problem

but if u can put that into words, i think you will get full credits for a good explanation

[half remnant]

yea

[onyx glen]

or u can prove it how i did it by using linear functions and triangle area

[half remnant]

Ill probably do it with the inverse function integration

thanks a lot for the explanation

helped me understand it better

[onyx glen]

np

[half remnant]

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[granite torrent]

statement appears to be false

[jolly flint]

i thought so

it doesnt simplify

thanks

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[white delta]

Bit stuck of where to start

[white delta]

nvm just saw it

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[undone pendant]

can someone give me some ideas on how I can start this question 3(b)?

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[left hamlet]

I am getting the following solutions:
Quiz 1 - 4 (option b)
Quiz 2 - 144 (not in option)

But the given solutions are option (a) and (c) respectively.

Can anyone help me solve them? Thank you

[serene hazel]

we don't help in quizzes

[left hamlet]

it's a quiz from a book though, not a real quiz

self learning

Full snippet

[hoary ember]

for number 1 if x^2=16, then x=±4, thats a hint

[left hamlet]

Ah got it, thanks @hoary ember
I just took the absolute values at first and didn't check for others.

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[minor crater]

would you mind translating the question?

[barren stirrup]

Well, it is asking what should be in the blank

theres not much to translate

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[minor crater]

open a new channel

this one got closed because you deleted the original message

[barren stirrup]

Oh yes thanks

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[hard gate]

.reopen

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[sacred sparrow]

what's the issue

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[torn jolt]

I’m working on number 5 and basically have idea where to start. My professor thought that giving us a couple of massive assignments over spring break would help us take a break from homework. Its for diff eq

[idle kelp]

Plug in Ayp into the left hand side and use your knowledge of basic algebra, calculus, linear algebra or whatever to show that it is equal to AQ(x).

[torn jolt]

aight

i was trying to work through it audibly and that's the direction it was heading. i'll see what happens and if i solve it i'll close the tab

yea that worked

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[frail elbow]

Hi

[kind jay]

Hello

[frail elbow]

Can u verify if this is correct

@kind jay

[kind jay]

I can't check works right now

[frail elbow]

What do u mean

[kind jay]

First one u can use wolfram and second one desmos

[frail elbow]

Ohh

I don't have them

At This moment

Can u check

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[small barn]

Stop

Are you mad or something

[frail elbow]

Yea

I am getting impatient

[small barn]

So leave the server

[frail elbow]

Cuz every channel I open

I don't get

Any attention

For help

[small barn]

Use latex

[frail elbow]

It's been more than 1 hour

[frail elbow]

What is that

. close

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[brittle parcel]

I need help with this

[brittle parcel]

uhhh about 4 A4 pages of identities

so uhhh yeah

is there like a quick trick to get this to an easier integral?

[nimble ridge]

Integration by parts of the Integral with cos(x)^n * sin(x) leads to another Integral with cos(x)^n * sin(x) , bring both to one side and you get the result for that integral.
Use this to solve your problem with integration by parts ( u = cos(x), v = cos(x)^5 )

[stiff musk]

which identities did you try

[brittle parcel]

I almost had it

but I think I have miscalculations somewhere

can you help me cehck where I was wrong?

[deft tulip]

instead of integrating by parts, you can also use cos^2 identity and you'll get (1+cos 2t)^3 which you can expand, then each of the terms of that is easy to integrate (for the cos^3 one, write it as (1-sin^2)cos, the cos^2 one apply the identity again, other ones are basic integrals of a constant and cos

[brittle parcel]

no thanks

[deft tulip]

i think this is the more common method 🤷‍♂️

[brittle parcel]

alright do it then

see if it doesn't take you an hour or more

[deft tulip]

it really isnt hard lol

[brittle parcel]

I give up on the common methods

[deft tulip]

i think you are just intimidated by expanding the cubic, but for no good reason?

[brittle parcel]

integrating is a godsent mathematical instrument

wow it helped me a lot

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[vapid garnet]

Can anybody review and see if I did this proof correctly?

[nimble ridge]

the brackets in the line 9(9^n - 1) = 8k are wrong. Without brackets, the line wolud be correct.

[tacit siren]

interesting writing format

Ik u didnt ask for style tips but the "OK!" is just kinda out there

Then full sentences r preferable

and idk why u middle-aligned everything

sounds nitpicky now but when u start submitting things it'll matter

[vapid garnet]

Why?

Hold on let me check

I see now, damn me

[north shell]

Just as a side note

You could've done it without recurrence

[vapid garnet]

There's no recurance formula being used, it's an explicit formula?

unless

if you're talking about something else

[north shell]

a^n-1=(a-1)(a^(n-1)+

1s lemme find it in google

Hurts to type it

[vapid garnet]

Uhh... Why are we speaking about recurance?

[vapid garnet]

Oh fuck, I realized. It's not distributive, it's splitting up the exponent.

[nimble ridge]

yes!

[north shell]

I said you could've used it without induction

But I just realised they forced you to do it

Mb

[vapid garnet]

Yeah they did

lmao

i don't know if there are other methods, but to be honest. eerm

yea

[nimble ridge]

But one other point

[north shell]

Yeah there are

Alot

[nimble ridge]

You should write the last part like: 9^(n+1)-1 = 9 * 9^n - 1 = .... = 8 * (9^k + 1) and not start the proof with the result (9^(n+1)-1 = 8k) which you want to show.

[vapid garnet]

this part?

[nimble ridge]

yes, this part.

[vapid garnet]

The reason why I wrote it out is because I wanted to make it abdundantly clear that this is the proposition I'm using.

for myself, mostly

[nimble ridge]

the proposition used is 9^n - 1 = 8k NOT 9^(n+1) - 1 = 8k

[vapid garnet]

yeah this

This is what n = p + 1 is

and, I'm checking if n = p + 1 is true based out of n = p

[nimble ridge]

But you can not assume, that your first line in this proof is actually true.

[north shell]

Yeah use the n=p propriety and prove it for p+1

It's a staircase

Not a magical staircase

[vapid garnet]

Problem is, according to my course litterature: "assume" is literally used. I don't even know if my course litterature is dumb

Like, at this point I don't even know how to use the right language because everything is so damn scuffed and vague

[vapid garnet]

My brain hurts from reading multiple explenations of what this principle means xD

[north shell]

I'll explain it

So there's two main things you have to keep in check in order for the proof to be valid

The property for n = 0

[vapid garnet]

or, any n could work technically

depends what the question is

[north shell]

Yes good

In this case it's 0

[vapid garnet]

Right

0 is divisible by 8

oh wait

[north shell]

Yup

[vapid garnet]

hold on

yeah, that's 0

1-1

[north shell]

Yup

And you assume it's right for a random p and prove that it's right for p+1

[vapid garnet]

But, what did I do wrong here, by assuming n = p?

[north shell]

This works because if you prove it for 0 you can immediately assume it's right for n =1 using p=0

[vapid garnet]

I said I assumed it was equal(n=p), like you did right?

[north shell]

You should assume n=p but you are not allowed to use n=p+1

You have to prove it by using n=p

[vapid garnet]

Well, we have to get to n = p +1 somehow

idk how

[north shell]

The problem is you did a deduction that I don't even understand but for the most part

You used the p+1 equality

Which is in itself incorrect

Because you don't know if the equality is there or not

[vapid garnet]

Well, I said "testing"

after n = p

so like:

Assume ( n = p ) --> Test (n = p + 1)

[north shell]

Testing as in

[vapid garnet]

checking if it's true

[north shell]

Trying to find contradiction?

[vapid garnet]

Trying to see if the statement is true

[north shell]

Yeah but it doesn't work like that

How do u do that

OK tell me how

[vapid garnet]

By using our n = p statement to substitute a part of n = p + 1

and, check for equality

if there is equality:

n = p + 1 is proven, (true)

in an old proof I did, I used this principle

have to define L and R, but I am kinda lazy there xD

[north shell]

You are using équivalences or what ever it's called in English

[vapid garnet]

yes

[north shell]

Personally

I don't advise because

It's not usually gonna have the other sense or

Other way

You might get stuck

Althought it's fast

[vapid garnet]

At this point I don't know what to do

[north shell]

Back to the topic

Look here

[vapid garnet]

yes?

[north shell]

What the hell did u prove

[vapid garnet]

I was so lost

xD

[north shell]

I respect it lmao

OK so

Let me do it for you this time okay?

[vapid garnet]

aight

[north shell]

Using the n=p

We have

9^p-1 =8k

Then 9^(p+1)-9=98k

That's 72k

I just multiplied by 9

Then

[vapid garnet]

...wait

So by adding n, you go up

[north shell]

U think u can continue?

No I multiplied by 9

To go up

[vapid garnet]

Hold on, let me show my teacher's solution

He's doing the same thing I did

its in swedish

He's going straight to say: It's true for n = p

[north shell]

Yeah what he did is correct

Althought it was similar to yours

It makes perfect sense

What he did was

Take the 6^(p+1)-1 and proved it to equal the thing below

That thing below has a side as a factor

Thus divisible by 5

[vapid garnet]

uh

[north shell]

And he used the n=p

[vapid garnet]

I don't know what I did wrong here

[north shell]

Do u understand

[vapid garnet]

I don't think I do at this point, because I don't know what to say

[north shell]

Okay

I think the deduction is a little bit off

[vapid garnet]

like, I could straight out throw an n=p, but that doesn't make sense, (assuming I have my base case)

[north shell]

But I think your idea is correct

See if u removed all the =8k

And say the rhs is divisible by 8

It would've been perfect literallu

[vapid garnet]

I don't even know when to not use the LHS

is this like, a pattern thing? Where, if you see the same question then you do not use 8k

[north shell]

I meant lhf

Lhs

Not rhs

Fuck I can't tell the difference between left and right

[vapid garnet]

Lul

like, when do you not do this?

[north shell]

About everytime

Équivalences are

Very tricky

I really suggest you do as your teacher

Try not to memorize but to appreciate the maths

This is my advice to you

[vapid garnet]

cause, in other induction proofs when it comes to sequences. I always do stuff like this.

[north shell]

Only then you will improve much better

[vapid garnet]

For proofs, I have to memorize how to work with them.

Other then that, I don't have to memorize the literal proofs

[north shell]

This time it worked because you barely used équivalences

[vapid garnet]

I have no idea what équvilences are

[north shell]

U just did it the standard way but in the équivalence shape

Okay I'll explain what they are but

[vapid garnet]

cause, at this point I don't think I understand anything anymore. Probabaly better to memorize how to do proofs for each type of question.

[north shell]

Nvm I'll just explain

So when u have a statement that says

If and only if

You can use équivalence to prove it without going back and forth

[vapid garnet]

I have never seen such statements in my math book

[north shell]

You are using an implicit type of equivalence rather using the right hand side simplifying both sides to get a true statemeent

This true statement directly implies that the first one is correct

Since the mathematical reasoning implies that an implication is correct in three cases

Nvm

I'm yappin

[north shell]

How old are u

[vapid garnet]

I'm 18

[north shell]

That's nice

[vapid garnet]

and here I am, not knowing what I'm doing xD

[north shell]

It's hard to grasp all at once

I suggest taking your time

And Do not be discouraged

If you have more questions I'm free to help

Ask me what you didn't understand from what I said

[vapid garnet]

I'll take a little break

maybe my dumbo teacher can finally nut it into my head, cause explaining stuff online isn't the same as explaining in person (for me)

[north shell]

Ping me when you are ready for round 2

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[fallow sage]

uploading work in a sec i keep trying to find slope and getting 0 probably did usm wrong

[fallow sage]

Hopefully this is understandable

[umbral dome]

is (-1,1) even on the curve?

[fallow sage]

idk i think i did it wrong

how was i supposed to start

[last locust]

first step is the hint

[fallow sage]

oh thats what i tried

and i got 0

[last locust]

take the derrivatice of both sides with repsect to x

[fallow sage]

so i did sum wrong

[last locust]

then you need to solve for y'

you also have a mistake

[umbral dome]

i think there is a mistake in the question, because (-1,1) is not on the curve. they may have meant (1,-1) (which is on the curve), but as it stands the question doesn't have a real answer

[last locust]

the 3x should be just 3

[fallow sage]

apparently this the answer

oops

not the

e)1

[last locust]

but @umbral dome is right. the question is wrong. Plug in x= -1 and y=1 to proove that its wrong

[fallow sage]

just y =-2x-1

damn

maybe ill ask my professor

[last locust]

no mistakes happen in textbooks or problems. dont focus too much on them

just continue

[fallow sage]

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[plain gate]

is this the same as

$y \in \mathbb{R}^+$

[glossy valve]

pixel

[torn jolt]

Ambiguous

that symbol can mean to say "positive real numbers" or "non-negative real numbers"

the latter is kind of dumb in my opinion, but it is used

if you want to remove the ambiguity, you can say $\R_{>0}$

[plain gate]

mm

but is it the same as saying $y \in (0, \infty)$

[glossy valve]

pixel

[torn jolt]

yes

,, y \in (0,\infty) \equiv y\in\R_{>0}

[plain gate]

alr

thank yo

you

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[ashen karma]

Find the number of ways in which 5 teachers (Arnel, Mark, Ralmond, Joy, and Edith) can be seated at a round table, such that Arnel and Ralmond must NOT seat together.

[ashen karma]

formula is P = (n-1) !

question got me confuse

do I count arnel and ralmond as 1 entity?

then n=4

[plain fox]

id first calculate how many ways the 5 ppl can sit and then calculate the number of ways arnel and ralmond are together (considering them 1) and then subtract

[ashen karma]

ah okay

Let me try

that would be zerooo

[plain fox]

0?

[ashen karma]

yeah

[ashen karma]

used n=5 in this formula

[plain fox]

ok

[ashen karma]

then counted arnel and ralmond as together plus the rest = 4! = 24 as well so P = 24 - 24 equals 0

[plain fox]

if arnel and ralmond are together u consider them as single

so n = 4

[ashen karma]

Yeah but must not be together..

[plain fox]

so the total ways they can sit together is (n-1)! = (4-1)! = 3! = 6

[ashen karma]

Or what if the question was just meant to confuse me, and the number of object is 5

[ashen karma]

hmm wait

I'm so confused. whether the answer is 72, 12, or 24 lol

[plain fox]

btw we will have to multiply this by 2

[ashen karma]

yeah

[plain fox]

so total ways they can sit together is 6 * 2

which is 12

total ways all 5 ppl can sit together is 24

so total number of ways they dont sit together is 24-12 which is 12

[ashen karma]

oh so I'm right, thanks

[plain fox]

u said 0 first tho

[ashen karma]

Well I had 3 answers haha

24 which I got by only using 5 as number of objects

[ashen karma]

I'm still overthinking whether this is the answer or the 12.

[plain fox]

thats the total number of ways all 5 teachers can sit together

we need to find total number of ways Arnel and Ralmond dont sit together

[ashen karma]

nevermind 12 is right haha thanks

[plain fox]

ik

[ashen karma]

So smart of you thanks again mister/ma'am

Wait I have another one

[plain fox]

tbh the blue square thing next to my name tells that im a boy

np tho

[ashen karma]

yk how people are on disc

[plain fox]

btw whats ur other question?

is it related to this or is it of another topic?

[ashen karma]

wait

[ashen karma]

related it's repeated permutation

Find the number of permutation in the word SUPERCALIFRAGILISTICEXPIALIDOCIOUS

lol

[plain fox]

is that really a question?

[ashen karma]

yeah

number 8

If you can't answer it that's fine haha, I'll just ask my teacher

[plain fox]

answer or help?

[ashen karma]

Help and answer what's the difference?

Well I meant to say help answer so mb

[plain fox]

help is i try to make u understand how we got the answer

[plain fox]

ok first we count the number of letters in this word

[ashen karma]

That'd be n ice

[ashen karma]

32?

[plain fox]

no

[ashen karma]

how many?

[plain fox]

34 letters

[ashen karma]

thank youu

[plain fox]

that was pretty basic question :/

that isnt the answer

[ashen karma]

Sorry, I ask because I'm dumb that's kind of obv

[plain fox]

im telling u that the word has 34 letters which means there are 34! ways to arrange this word

but there are few letters that repeat

like i

e

a

[ashen karma]

You know for a man you're kind of sassy

Okii

can you help me identify the letters that are repeated? 😊

[plain fox]

i dont think im sassy tho D;

[plain fox]

e o p r u a c l s i

[ashen karma]

You are for me, it's kind of cute lol

[plain fox]

we now need to find how many times each letter is repeated

like e is repeated 2 times same with o p r u

btw check if i make any mistakes tho , im also human

[ashen karma]

Nah you didn't

[plain fox]

a c l and s are repeated 3 times

and i is repeated 7 times

[ashen karma]

thanks, what's next sir?

[plain fox]

find how many ways those letters can be arranged

like i can be arranged 7! times in the word

and then we divide them by 34!

we get something like this
34! / (2! * 2! * 2! * 2! * 2! * 3! * 3! * 3! * 3! * 7!)

btw if u dont get smthing , u can let me know ill explain it

[ashen karma]

Oof...

34! is a lot

[plain fox]

34! is total number of ways u can arrange SUPERCALIFRAGILISTICEXPIALIDOCIOUS

[ashen karma]

34!/209018880

Can you help me solve mister ));

[ashen karma]

Ehh....... should I just put 1.4125 x 10^30

[plain fox]

yeah

[ashen karma]

Last question

[plain fox]

1412469529257855275311104000000
exact if u want

the answer is from wolframalpha

,w 34!/209018880

[glossy valve]

Results provided by WolframAlpha

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

Requested by justtopro

[ashen karma]

too many numbers

[plain fox]

yes

[ashen karma]

it hurts my eyes

[plain fox]

big letts = big numbers

they should have given a small letter like the mississippi state

thats good enough difficulty

[ashen karma]

kind of easy, anyways last question

[plain fox]

how many more btw?

[ashen karma]

last one

What's your instagram 😚

[plain fox]

dont have 1

[ashen karma]

):

[plain fox]

not too much social on anything except discord

[ashen karma]

How old are you even?

mid 20s?

[plain fox]

18

i dont like these apps , not my interest

[ashen karma]

Aw ):

Add me then mister

[plain fox]

nah

[ashen karma]

Please

🥺

[plain fox]

nah

[ashen karma]

🥺🥺🥺

Please ?

Pretty please?

Why not ):

[plain fox]

!done

[full forum]

If you are done with this channel, please mark your problem as solved by typing .close

[ashen karma]

Wha-

[plain fox]

dont want to

[ashen karma]

):

[plain fox]

already have decent amount of ppl in my friend list

dont want it to be too overcrowded

[ashen karma]

That's a lame excuse...

[plain fox]

im a lame person irl

[ashen karma]

I don't care

Add me, please );

[ashen karma]

What will make you add me?

[plain fox]

by u not asking to add me and not giving me a request

[ashen karma]

I think mister likes talking to me though ❤️

[plain fox]

not really

[ashen karma]

If you don't then why are you still here talking to me?

[plain fox]

cuz all the rest of the questions are too advanced for me to help them

the top question is partial derivative , havent started learning them

the 2nd one is about mean which i wont learn for a long time

and 3rd one is already being helped (i think)

same with 4th and so on

[ashen karma]

Oh, so you're all about learning

[plain fox]

i like maths

[ashen karma]

Makes sense why mister does not have other social media

[ashen karma]

I like you sooo 😊😊😊😊

hello?

):

@plain fox I still have one more problem I need help solving mister

🥺 @plain fox

Please help @plain fox 🥺🥺🙏🙏

I was only kidding, I'm a guy frfr

I still need help, I'll be serious this time fr

@plain fox 🥺

<@&286206848099549185> How do I solve for n in this: The permutation of n object taken 6 at a time = 12 multiplied by The permutation of n object taken 4 at a time

[tender shore]

I know I am a helper, but I have no clue...

[ashen karma]

Haha it's fine wait let me send a picture of this

[tender shore]

n!
(n - r)!

Is what I got from that

[ashen karma]

that's circular permutation

[dark bay]

send a photo

[ashen karma]

wait

There

[ashen karma]

this one is actually right

[dark bay]

ok so

[tender shore]

Oh I didnt know I thought I got it wrong.. I usually fail those kinds of tests..

[dark bay]

use the formula to simply this equation

[tender shore]

I love how everyone in this server is math nerds LOL.

[dark bay]

n!/(n-6)! = 12 x n!/(n-4)!

[dark bay]

☠️

[ashen karma]

Okay what now?

[dark bay]

hmm

[tender shore]

Oh I got the first part right!

[ashen karma]

Take your time guys I'm multi tasking 2 subjects

[tender shore]

I'm trying to do something hold on

[ashen karma]

alright take your time

@plain fox ahem ahem

[plain fox]

u could close this channel and post ur question again cuz this one is too below and many wont see it

[ashen karma]

Why not help me instead? 😚

[plain fox]

also
${n}P{6}$ can be written as $\frac{n!}{(n-6)!}$

as the previous guy said

[glossy valve]

JustToPro

[ashen karma]

I know so what now?

[plain fox]

simplify this and sovle for n

[plain fox]

cuz ur annoying

also pls stop pinging me

[ashen karma]

Not unless you accept my friend req

[ashen karma]

I can't simplify that

Since I don't know how mister

I know 12 needs to be left alone but how?

[plain fox]

ok ill help with this but dont ping me or disturb me

[ashen karma]

Yes sir ^^

[plain fox]

$\frac{n!}{(n-6)!} = 12 \frac{n!}{(n-4)!}$

[glossy valve]

JustToPro

[plain fox]

u can divide both sides with n! and cancel those out

let use consider a example a! can be written as a(a-1)!

similarly (n-4)! is equal to (n-4)(n-4-1)(n-4-1-1)! which is (n-4)(n-5)(n-6)!

multiply both sides with (n-6)!

u are left with something like this
$$\frac{1}{1} = 12 \frac{1}{(n-4)(n-5)}$$

solve for n , now this is very simple

[glossy valve]

JustToPro

[ashen karma]

Eh..

That's a little wrong from what I know, now I'm confused

one sec

[plain fox]

i explained it above

[ashen karma]

Just explain this for me

[plain fox]

thats exactly what i explain above

thats exact same thing i wrote above

and explained above that

[ashen karma]

okay but that didn't help in making me understand how the second step happened

[plain fox]

thats cross multiplication

if u understood this

then no need to understand that , both are exact same

[plain fox]

this is basically $(n-4)(n-5) = 12$

[glossy valve]

JustToPro

[ashen karma]

nevermind my writing sucks, wait

Yeah, I got it, thanks.

Thank you mister 🥰🥰

You are so smart

Mind adding me now mister?

[plain fox]

no

[ashen karma]

Why? );

If you give me a valid reason, I'll stop pestering you mister

[ashen karma]

@plain fox 🥺

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[glossy valve]

ren

[rugged void]

just factorize top and bottom and ur good to go

i mean factorize first frac

then cancel

i guess

[rugged void]

mhm

good

so just... divide now

i guess

[blissful vine]

yeah just flip the divisor

and then simplify

[gusty carbon]

@blissful vine

[blissful vine]

so simply put

u have the original

and the divisor u just flip

because then itll be multiplication

and then u can eliminate the (x-2) and (x-3) from both

because they are each on opposite sides

[gusty carbon]

so is it just x+2 divided by x+5?

[blissful vine]

yep

good job

[gusty carbon]

yay

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[sleek quest]

im really confused on how i would solve these

[sleek quest]

we never learned a rule or proceduce for cot and csc

[unique timber]

What's the derivative of cscx ?

[thick hedge]

try a u-sub

also known as integration by substitution

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@sleek quest Has your question been resolved?

[sleek quest]

-cot(x)csc(x)

[sleek quest]

on what?

[thick hedge]

cosec(x)=u

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@sleek quest Has your question been resolved?

[sleek quest]

what about the next one?

would using the same u work

oh wait i just use u=cot(x)

now how would i do it for the last one

i would need to do du^2

or something

if i use u=cot(x)

or wait

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[void jackal]

apologies if this is a stupid question but is the model answer wrong or did I miss something blitheringly obvious?

[glad hound]

Granted, it looks a little further off than most rounding errors, but I believe that's all this is

Replace 0.0468 with x and solve, and you get...

.04674

Somewhere in the model answer, they rounded and got .04675 or something, which rounds up to .0468, and it leads to their answer of 7.45% and your (and my) answer of 7.59%

But remember.. that ".45" and that ".59" are the thousands place and the ten-thousands place, after the decimal

.0045 and .0059

@void jackal

[void jackal]

oh okay, thank you so much 😊

in retrospect, i think they are more "accurate". because they used the raw values of P(X<7.5) and P(X<8) to calculate it, while i used the 3sf rounded values

thanks anyways :)

[glad hound]

Yeah, it happens sometimes

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[dim marlin]

Can someone pls help me with this.im literaly dying trying to figure out

[dim marlin]

I know the equation for sin,cos and tan

How do i put it in tue exercise i dont understand

The 1st question 1st(a) triangle i got correct

2nd (b)triangle i got wrong

[torn jolt]

\e{alignat*}{{2}
\m\sin\theta &= \f{\t{opp.}}{\t{hyp.}} & \q \m\csc\theta &= \f{\t{hyp.}}{\t{opp.}} \\
\m\cos\theta &= \f{\t{adj.}}{\t{hyp.}} & \q \m\sec\theta &= \f{\t{hyp.}}{\t{adj.}} \\
\m\tan\theta &= \f{\t{opp.}}{\t{adj.}} & \q \m\cot\theta &= \f{\t{adj.}}{\t{opp.}} 
}

[torn jolt]

its repetitive application of the above pretty much

so for the second triangle, what kind of sides are you considering. Can you name them?

[dim marlin]

Wdym

[torn jolt]

in the second triangle your sides of interest are b and the side with 16cm. Can you label them under opposite, adjacent, or hypotenuse?

[dim marlin]

Ohhh wait nvm

I got ut

Thx

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[lunar lynx]

For this question, i've found the vector form equation for the first given line, but i dont understand why they have given 2 equations for the second line (which looks like the equation of a plane)

[simple totem]

what shape is the intersection of two planes?

[lunar lynx]

a line?\

[simple totem]

yes

so they gave you two planes, the line is defined by their intersection\

[lunar lynx]

ohh right thank you

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[coral vortex]

How do I do 5a

[torn gust]

here's what it's talking about

once you plug in 1/2 you'll have to use -sin^2 = cos^2-1 later

[coral vortex]

Yeh I got that bit but I don’t know what to do after wards

[buoyant ivy]

Show your workings

[coral vortex]

I didn’t know what to do next

[hot herald]

Pythagorean trig identity

[crisp girder]

Sin^2 seems awfulllly familiar 🙂

[coral vortex]

Is this correct, I swapped out the x in the trig identity for x/2 and then subbed out the sin

[crisp girder]

Why the -1/2

It should just be -(1

[coral vortex]

Oh ok

I thought because it was x/2 you have to divide the 1 by 2 aswell

[crisp girder]

Nah dw

[coral vortex]

Thanks for the help

[crisp girder]

Thank them not me 🙏

But cheers

[coral vortex]

Could I have some help with this question aswell? I understand that at the x intercept y = 0 so do I just set tant = 0 and then sub t into x to get the x coordinate

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@coral vortex Has your question been resolved?

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[celest valve]

HELP NEEDED! what is these || ||_1 || ||_k and || ||_inf I am studying the convergency in metric space and cant make anything out of these symbols.

[brisk obsidian]

L_k norms

https://en.wikipedia.org/wiki/Norm_(mathematics)

[celest valve]

what does it mean to be an infinity norm intuitively?

[brisk obsidian]

The infinite norm implies a limit as n goes to infinity that results in x_i, or the largest value in the set.

[celest valve]

i see that supremum norm is equivalent to the supremum of all the distance between two function say f and g in a given domain

[brisk obsidian]

Yes.

[celest valve]

that arises a question that metric is the idea of different kind of distance while norm is the measured length between two vectors in the given space. How can they become equivalent when n tends to infinity?

[full forum]

@celest valve Has your question been resolved?

[stiff musk]

"how can they become equivalent" - which "they" are you talking about?

the infinity norm is not the same as the euclidean norm

[celest valve]

that is something I dont understand. I am very new to metric space and I cant make much out of the definitions and relate with each other

[stiff musk]

for example, in 2 dimensional euclidean space:
||x-y||_2 is the usual euclidean distance between two points
||x-y||_infinity is either |x_1 - y_1| or |x-2 - y_2|, whichever is greater (where x_1 and x_2 are the components of x and similarly for y)

to take a concrete example:

if x = (3,5) and y = (1,4)
then ||x-y||_2 = sqrt((3-1)^2 + (5-4)^2) = sqrt(4+1) = sqrt(5)
and ||x-y||_infty = max(|3-1|, |5-4|) = max(2, 1) = 2

[celest valve]

the euclidean distance i get

what does the last formula even imply?

[stiff musk]

about what?

[celest valve]

what do we understand by getting ||x-y||_infty = 2

[stiff musk]

is just the greater of the "x coordinate" distance and the "y coordinate" distance

[celest valve]

like by taking euclidean distance we understand the smallest distance between the two points, how does the infinity norm help us?

[stiff musk]

it helps us when that's a suitable measure of distance for our problem
for example maybe i want to fit a curve to some data, and i want the worst-case fit not to exceed some threshold

"worst-case fit" = the infinity norm

[celest valve]

okay i understood that

can you also tell me what does it mean to find the infinity norm between two continuous function?

[stiff musk]

yes

it's just the maximum of their pointwise differences

in other words, compute |f(x) - g(x)| for every x in their domain

and take the maximum of those values

[celest valve]

okay okay okay now i understood. Oof finally the dots connected in my head lol

thank you very much @stiff musk

[stiff musk]

sure, cheers

[celest valve]

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[tired shell]

Hallo

[tired shell]

I need some help trying to find a unit vector of a function

v = L(-cos0, -sin0) where 0 represents theta

Just dont have a greek keyboard :P but if someone could provide insight bc im very stuck

[stiff musk]

what is L?

[tired shell]

I think L is an unknown

This is the entirety of what is given

[stiff musk]

(-cos(theta), -sin(theta)) is already a unit vector

just use cos^2 + sin^2 ...

[tired shell]

So the unit vector in the same direction would just be L?

[stiff musk]

L is not a vector

L is a positive real number

they're asking you to find the value of L that makes v a unit vector

[tired shell]

Im confused now

[stiff musk]

what is your doubt?

[tired shell]

The whole thing 😢

Could someone explain further Ive been stuck for 20 mins :/

[sacred sparrow]

you know that the vector (-cos(theta) -sin(theta)) has length 1 right

[tired shell]

Ye

[sacred sparrow]

which means v has length L * 1

and a unit vector has length 1

so you can just take v / L

which gives you a vector of length L / L = 1

which is a unit vector

and it points in the same direction as v

because we just multiplied v by a factor (1/L)

[tired shell]

So then the unit vector is L , L

Yes?

Sorry if im being dumb its my first time learning vectors

Ohhh okay bc pythagorean identity the hypotenuse is 1 of -cos(theta) -sin(theta)

So then therefore the vectors add to one

so then v = L * 1

So then to find unit vectors isnt it v^ = v/|v|

[sacred sparrow]

nw not an issue

L is a constant

v is a vector

so your new unit vector would be v * 1/L

the vector v times a constant 1/L

which yields another vector

[tired shell]

And to find |v| it is sqrt(-Lcos(theta)^2 + (-Lsin(theta)^2

[tired shell]

What if I do it this way

Is it possible?

[sacred sparrow]

yes that would be the process of normalisation

and you know that |v| = L

as I've mentioned before

which means v^ = v/L

just like above

[tired shell]

How did you come to that conclusion though

[tired shell]

Yes so v = L(1)

[sacred sparrow]

well |v| = L*1 = L

[tired shell]

How does that make |v| = L

[sacred sparrow]

v is not equal to L times 1

[tired shell]

Wait its not?

[sacred sparrow]

L times 1 is a number

v is a vector

if we want to find |v|:

[tired shell]

hmm okay

So then the finalised vector is v^ = v/L

[sacred sparrow]

ys

[tired shell]

So strange man

So difficult for my head to figure out

So this looks correct?

[sacred sparrow]

yep!

definitely experiment with vectors

once you have the graphical intuition

everything becomes simpler

[tired shell]

Phew okay

Thanks very much man

Definitely got more study to do

[sacred sparrow]

don't necessarily get strangled by tasks, try a bit with graphical software or just play with the concepts a bit

anything that keeps you motivated will make you better at it quickly

[sacred sparrow]

the basic concepts of algebra and analysis tend to be not that simple, but once you dig into them you'll feel like a mastermind :)

[tired shell]

Will for sure do

Need to get a very strong grip on them for my degree

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[stiff wagon]

Could someone help me with these 2 problems?

<@&286206848099549185>

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[final relic]

Is the statement for the lemma here correct?

[modern osprey]

Looks like it

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[high scroll]

if anyone can help me out i’d appreciate it :)

[full forum]

@high scroll Has your question been resolved?

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[pliant void]

How would i end up getting something where i can get to 100% this is non calculator

[tawny nest]

brother this is my channel

[pliant void]

Mb bro

Idk how this shit works lmao

[brisk obsidian]

#❓how-to-get-help

[pliant void]

I got it thanks

[tawny nest]

u good

[brisk obsidian]

Can you show your work? I'll try to help you while I can. Gotta step out for about two hours in about 20 minutes.

[tawny nest]

basically i did this but with my own numbers

so integral of 0 to 5

[tawny nest]

?

[brisk obsidian]

It looks like you calculated the volume incorrectly

I gotta step out. Let me post an example of how I solved a similar problem.

[brisk obsidian]

Take a look. Compare notes.

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@tawny nest Has your question been resolved?

[tawny nest]

<@&286206848099549185>

I dont get where Im going wrong

.close

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[carmine mango]

stuck on c d e?

[iron cradle]

u = 1/y, so u(1) = 1/y(1)

[iron cradle]

this helps us get c right, if u = 1/y, then u(1) = 1/y(1), and we know that y(1) =1, so u(1) =1

[carmine mango]

👍

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[lethal mirage]

I dont understand how to solve for f(x)

I did the differentials thing but it's wrong so idk what else to do

[fathom saddle]

You correctly solved for f(x). Notice the question isn't asking you to do this, though

[lethal mirage]

Okay, what is the question asking me to do

Oh

Do i sub (2, 1) into f(x)?

[open zinc]

Plug (2,1) into dy/dx to get the slope of a line going through (2,1) then evaluate that line at y=0

[lethal mirage]

Ok so the slope is 3

So what do i do after that?

Do i take my point slope form line of tangent line approximations and solve for y like that

Essentially that y-1 = 3(x-2)

And then solve for y= 0

Wait was the entire differential equation thing unnecessary for this question?

I didnt have to do separation of variables and solve for y did I

<@&286206848099549185>

[naive drum]

So if you are trying to solve for the x intercept, make y 0

[main trellis]

@lethal mirage wassup

[naive drum]

And vice versa

[lethal mirage]

yeah but the whole solving for y using differentials was not at all needed for this question right

[jovial radish]

It didn't tell you to find f(x) so no

[main trellis]

@sterile oxide jump in

[lethal mirage]

I just needed to solve for dy/dx with (2,1) and make a tagent line approx from it

[jovial radish]

It just told you what that the name of the solution was f(x)

[sterile oxide]

hi

[lethal mirage]

and get the y int?

[jovial radish]

Yes

[jovial radish]

X-int

[lethal mirage]

right bc its the zeros

ok that makes sense

I have a few more questions

[jovial radish]

ok

[lethal mirage]

what would be the correct setup for Q11, radioactive decay question?

would it be y= y_0 e^kt

and k= ln(2)/276 because 276 is the half life

its also asking for the rate of decay so Im assuming that I need to solve for dy/dx, but idk how to

[jovial radish]

Did you remember to add a constant when integrating

That's something that gets people a lot of the time

[lethal mirage]

but for exponential decay, don't I just use the y= y_0 e^kt formula; no integration?

for the first question on the page

[jovial radish]

Gimme a sec

[lethal mirage]

alr

I tried redoing the question and i got -0.002

[jovial radish]

I got A

[lethal mirage]

how?

[jovial radish]

Give me a second to check to see if that's right or not

[lethal mirage]

what do I take the derivative of?

[jovial radish]

Alright I'm pretty sure A is right

Let me send my work

[lethal mirage]

okay

[jovial radish]

Read from top left to the bottom and then go to top right and down

[lethal mirage]

ohhhh ok now I see where I went wrong

I solved for K and assumed that that would be the rate

i had to sub k into dy/dt = ky

that makes soo much more sense thank u so much

sorry one more quick question

I also reworked the 2nd question on the sheet I sent a picture of, and got A; 8

would that be correct?

[jovial radish]

Uh

Pretty sure it's B

Mb wrong images

It's B though

[lethal mirage]

but why

[jovial radish]

Because if it were A that means it would add 16

You have to think about the change being double the integral

[lethal mirage]

bc distance from a-c is 18 and displacement is 10

[jovial radish]

Because one half of the change is cancelling out the negative area and the other half is adding that area but positive

[lethal mirage]

ohhhhh

[jovial radish]

Yeah see

[lethal mirage]

so 2x is the actual area in + units

[jovial radish]

Yeah I guess

[lethal mirage]

that makes sense

thanks!

.close

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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.

[hybrid nexus]

x = 60 is correct

[torn jolt]

do you know how they got that

cause what i got is 40

i did