help-39

[split berry]

it has numerical response as well

but its mainly multiple choice

I no longer have online assessments

[vocal lark]

Are we assuming this triangle, or all triangles in this assignment, are right triangles?

[split berry]

i was told to assume the opposite

unless otherwise stated

[vocal lark]

ok, let's draw another picture. Arbitrary triangle.

label opposite sides/angles with the same letter. Angles uppercase, sides lowercase.

[split berry]

would i use

sine law in this case

[vocal lark]

probably

[split berry]

ok

give me a sec

[vocal lark]

ok

good instinct. Put it together

[split berry]

wdym by put it together

[vocal lark]

use LoS

[split berry]

whats LoS

[vocal lark]

Law of Sines

uh, you can use a calculator, right?

scientific?

[split berry]

ye i have a calcualter

calculator

[vocal lark]

ok

so for LoS to work, one of the ratios needs to be provided

[split berry]

it can do sine law for me?

[vocal lark]

that is, you need a side and its opposite angle provided

[vocal lark]

no, you can do that

[split berry]

ok

[vocal lark]

the scientific has the trig functions

[split berry]

let 30 degrees be angle a

and 12.0 be side a

then

oh

a / sin a would =

c / sine c

wouldn't it

[vocal lark]

it does but you don't have angle C yet

that's easy to fix though

I solved for b since we have angle B

using law of sines

let's do your way though

find angle C first

so you can solve for c

[split berry]

how would we go about that

[vocal lark]

triangle sum law

A+B+C = 180

[split berry]

oh

angle c is 70

[vocal lark]

use uppercase for angles

[split berry]

im having trouble connecting things ive noticed

ok

Angle C = 70

[vocal lark]

$\frac{a}{\sin{A}} = \frac{c}{\sin{C}}$

[jolly parrot]

Disorganized

[split berry]

ok

so

sorry im just copying some sutff into my notebook

[vocal lark]

np

[split berry]

so

12/sin(30)

gives 24

would i just go ahead and do

c/sin(70) = 24

and jsut solve

for c

[vocal lark]

yes

[split berry]

and get 22.5

which is a solution

NICE

[vocal lark]

👍

[split berry]

ok

thank you for all the help

[vocal lark]

np

[split berry]

i really appreciate it

[vocal lark]

you're welcome

[split berry]

have an amazing day or night im gunna continue this assignment

[vocal lark]

sounds good, have fun with it

[split berry]

thank you

math is fun when u understand it

[vocal lark]

Trig is one of the more interesting subjects

[vocal lark]

hell ya

[split berry]

i wish i could agree

but

atleast in the math units ive done so far

quadratics has been the most fun

(since it was my highest mark)

[vocal lark]

what class are you taking

[split berry]

and reciprocal functions

Math 20-1

[vocal lark]

college algebra?

[split berry]

is this college math?

[vocal lark]

is this community college?

or high school

[split berry]

this is grade 11 math

atleast where i am

[vocal lark]

when I was in school (not too long ago) trig didn't show up in hs math until precalculus

[split berry]

Im not sure but i think this is pre calc

my textbook says Pre Calculus 11

so

[vocal lark]

but I could see it popping up in common core II or common core III, or maybe Intermediate Algebra

[split berry]

the course is called Math 20-1 though

[vocal lark]

what's the name given to Math 20

-1 is the cohort

[split berry]

its just called math 20

[vocal lark]

it's not, I promise

[split berry]

i swear its just math 20

[vocal lark]

what school

they have their curriculum posted

https://school.cbe.ab.ca/school/ernestmanning/teaching-learning/classes-departments/math/pages/math-20.aspx

[split berry]

the only thing that has a name to my knowledge

is math 31

which is calculus

[vocal lark]

oh shit you're in Canada

[split berry]

I am

Are you in the us?

[vocal lark]

yes

I was thinking of Integrated Track

when I saw this

anyway

[split berry]

whats a integrated track

[vocal lark]

it's part of the Common Core curriculum

it was designed to teach math subjects in a more sensible and useful order

I mean I guess

[split berry]

I see

my provinces curriculum is significantly harder than others in Canada but that means Canadian universities will bump my average up by 5-6% if i apply outside my province its quite useful icl

[vocal lark]

that's cool

high school math gives you tools to prepare for either (or it was this way in early 2000's) Calculus or Statistics

Statistics is understood to be very important in the US but still doesn't get taught enough in hs

but very few students will learn either

[split berry]

Hm

I think your right

[vocal lark]

they just won't take the classes or won't have the opportunity in high school and never try it

[split berry]

my school board added Math 31 as an option class and it counts as university credit so maybe your right about highschool no longer giving you the tools

to be prepared for uni

since they only added it recently

2013 or 14 i think

i do not think i have ever been taught statistics

[vocal lark]

you will learn about statistical measures, at least

mean, median, mode, quartiles, etc.

probably something about misleading graphs

and bad samples

[split berry]

oh

[vocal lark]

but barely anything else about it

[split berry]

median mode and that stuff

yeah i did learn this

[vocal lark]

I didn't see stats again until undergrad

[split berry]

but we haven't done anything with it even since year 9

[vocal lark]

Yeah, you might not

what kind of job do you want

career

[split berry]

im going into computer science

[vocal lark]

ok good

for programming, networking, or what

[split berry]

I have no idea

[vocal lark]

ok

[split berry]

all i know is that i enjoy coding and that theres a lot of money in it

lol

and it will be much easier to accomplish now with chat gtp and shit

[vocal lark]

you should take a statistics class in college, and it should be an advanced class

or at least better than an intro stats class

[split berry]

I think i will

[vocal lark]

also

you need to take Linear Algebra, preferably with a programming component, but you will probably not have this opportunity right away

that context isn't usually (ever?) the way people are introduced to linear algebra

[split berry]

oh yeah im definetly taking it

its called math 243

I have to take it

[vocal lark]

ok cool

[split berry]

you've already gone through uni right?

[vocal lark]

I have

and it's very, very important

[split berry]

what did you go for?

[vocal lark]

that the program you take

teaches you how to use popular APIs in your programming language

don't go to a college that won't teach you how to do anything useful

I have a BA in Math and an AS in Computer Programming

[split berry]

whats a AS?

[vocal lark]

Associate of Science

[split berry]

and ba is bachelor of arts rrigh

[vocal lark]

yes

[split berry]

ok

ive never really understood the difference between

a BA in comp sci or a BS in comp sci

[vocal lark]

me neither

but Science > Arts

on a resume

bias maybe

[split berry]

it seems like it

comp sci in bs is usually requires a higher gpa

[vocal lark]

what, to graduate?

or to get in?

[split berry]

to get in

[vocal lark]

I never once thought about GPA

I never tried to get into an Ivy League school

didn't even think about it

[split berry]

im not try to go to an i vy league

waste of money

i wanna stay in my home city

bujr

[vocal lark]

huge scam

[split berry]

but

the requirements r pretty high atm

[vocal lark]

how high

[split berry]

the school i wanna attend is UofC

they only offer BsC

in comp sci

[vocal lark]

90 what?

90% of all applications are approved?

[split berry]

no no no

[vocal lark]

sounds like good news

[split berry]

90% competitive admission average

[vocal lark]

idunno what that means

hang on

[split berry]

so the cumulative average of all my classes

must be

90%

to be competitive

so i'd need a 90 in every one of my classes

to be competitive

from an academic stand point

[vocal lark]

https://www.ucalgary.ca/future-students/undergraduate/requirements

fill that out rq

[split berry]

yeah

thats the same site

[vocal lark]

you in Calgary or Alberta or what

[split berry]

alberta is the province

calgary is my city

[vocal lark]

huh

I don't see GPA requirements

[split berry]

yeah

it doesn't use gpa

it uses your cumulative average

the average of all your averages

[vocal lark]

of the cohort of incoming applications?

[split berry]

say u applied with 5 classes

1 80%
1 90%
1 95%
1 60
1 79

it would be the average of those numbers

in this case

your competitive average would be

81%

(80.8)

[vocal lark]

when you say "applied with 5 classes" wdym

[split berry]

you pick 5 classes to apply with

[vocal lark]

like those are your grades from hs?

in 5 courses?

[split berry]

yup

they r not my grades

[vocal lark]

only senior courses?

[split berry]

those r just imaginary

could be 12th or 11th grade

if your doing early admission u can use 11th grade marks

but if ur in 12th you use senior classes

[vocal lark]

can you use any five classes?

[split berry]

if they fit the criteria

yup

ELA 30 is required

math 30 is required

[vocal lark]

ok I see now

[split berry]

yeah

so if i wanted i could get 100% in phys ed

and use it to inflate my average

because it is an approved course

[vocal lark]

cool

[split berry]

but yeah

a 90% competitive average is gunna be hard for me to get

[vocal lark]

you just need 5 A-'s

[split berry]

not use what an A- is equal to

[vocal lark]

low 90%

[split berry]

oh

I highly doubt it will be able to achieve that

but ima try

[vocal lark]

I was a B student and even I coulda self-selected into "low 90%"

[split berry]

if not i can just apply for a different course in the same school and just switch my major the next year

[vocal lark]

...probably

[split berry]

yeah

if i maintain a 3.0> gpa

in uni

[vocal lark]

well here's the other thing

3.0 is B-

[split berry]

ye

[vocal lark]

my GPA, last I checked, was 3.6

[split berry]

thats like a B+?

[vocal lark]

just try to stay motivated in the key courses

that's the most important ingredient for success

[split berry]

yeah

motivation is key

[vocal lark]

ok, I'll let you get to the rest of your hw

I have things to do to

[split berry]

of course

[vocal lark]

you're going to do well

[split berry]

thanks again for your help

[split berry]

thank you

[vocal lark]

no problem

[split berry]

have a good night

[vocal lark]

gn

[split berry]

.close

[pearl pond]

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[pearl pond]

@vast dune Has your question been resolved?

[west sapphire]

can you clarify your question? why not just evaluate (f(x+h) - f(x))/h and plug in x=2?

[pearl pond]

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[coarse sage]

How do I do this?

[midnight haven]

a_n = 2/{n(n+1)}

= 2(n+1-n)/{n(n+1)}

[coarse sage]

This is understood.

How do I find Sum up to 2021 terms

[midnight haven]

using this

[coarse sage]

How did you get that?

[midnight haven]

nothing different about it

1 = n+1 - n

[coarse sage]

Ok

What is S_n?

[midnight haven]

did you get how that a_n is the same as in first step

[coarse sage]

You just said that.

"1 = n+1 - n"

[midnight haven]

YES

so does that make sense or not

[coarse sage]

What is the purpose of doing that?

Explain.

[midnight haven]

= 2/n - 2/(n+1)

a1 = 2 - 2/2

a2 = 2/2 -2/3

[coarse sage]

Ok

Hold up

[midnight haven]

a3 = 2/3 -2/4

[coarse sage]

@midnight haven

Is that right?

[midnight haven]

bruv what

it's not an ap

[coarse sage]

My bad

User defined series smh

[midnight haven]

so do you get it or should I explain

[coarse sage]

I get it, How do I find S_n?

,,S_n= \sum_{n=1}^{2021} \frac{2}{n}-\frac{2}{n+1}

[jolly parrot]

hazysleet

[midnight haven]

all the terms will cancel

[coarse sage]

Wait, I see that

Not all tho.

[midnight haven]

don't interrupt this time, I'm writing it out

a1 = 2/1 -2/2

a2 = 2/2 -2/3

a3 = 2/3 -2/4

a4 = 2/4 - 2/5

....

a2020 = 2/2020 - 2/2021

a2021 = 2/2021 - 2/2022

do you see what terms will get cancelled and which won't

[coarse sage]

Yeah

[midnight haven]

S_n = 2(1-1/(n+1))

[coarse sage]

I get it

Thanks.

.close

[pearl pond]

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[coarse sage]

Hello again, akise

[midnight haven]

4C0 + 4C1 + (4C2)/2

hello

[coarse sage]

How did you get that?

[midnight haven]

so a and b must not have any similar primes

[coarse sage]

Can I not do it without using combinations?

[midnight haven]

because then their g.c.d would be the prime

[midnight haven]

you can, just write the combinations, that's what combinatorics does for you

[coarse sage]

I still don't get how this comes ^

[midnight haven]

do you get this ?

[coarse sage]

Yes

[midnight haven]

and this

[coarse sage]

That's the insight to take from gcd(a,b)=1

[midnight haven]

so now your problem is just arranging four number 2,3,5,7 in 2 boxes a and b

bro wait 1<a<b my answer is wrong then ignore it

but I can tell the method

[coarse sage]

💡

Wait

[midnight haven]

if 2 was separate and 3,5,7 together or 3 was isolated or 5 was we would know they would be smaller

[opal moss]

you're starting to overthink

[midnight haven]

wait no i'm dumb

it doesn't matter'

it will either be in a or b anyway

@coarse sage 1st case is all of them are together

2nd case one of the primes is separated

[coarse sage]

I see 6 combinations possible

[midnight haven]

ok which

[coarse sage]

#Case 1 : Each of one number to the number power the same number as a and rest as b. That adds up to 4.
#Case 2 : Taking two numbers as a and rest as b. There are 2 cases like that.

[midnight haven]

what are you writing

[coarse sage]

Nvm, I get it

.close

[pearl pond]

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[midnight haven]

how to solve this question?

what is the probability that a number will appear on a single dice

and the probability that the same number will appear on a 2nd dice

[hard crystal]

@midnight haven or you can do like n(E)/n(S)
where n(E) is no. Of fav. Outcomes and n(S) is no. Of total outcomes (Sample space)

[midnight haven]

1/6?

the answer is not 1/36

[serene night]

A die has six sides right?

So it has 1/6 chance to get whatever the number is

Like 2

So it asks for two more dices to get the exact same number

[hard crystal]

@midnight haven Have you learned multiplication rule of probability?

[midnight haven]

yo

[midnight haven]

what should be the answer according to you?

[hard crystal]

1/36

[midnight haven]

yes, that is wrong

[hard crystal]

Answer is wrong then

You can search on google

I think that 1/36 is right answer

[midnight haven]

wrong answer on google

the answer should either be 3/28 or 1/36

different answers in different sites

[serene night]

Read the question carefully

The second sentence

It says

Each

Not the total

So the answer is 1/6

Chance for each die

[midnight haven]

read the first statement carefully, it says identical

1/6?

[serene night]

Ye

Because if 1/36 would be the right answer then it would’ve asked the total of the three dices

[midnight haven]

each means all the three dice

🤦‍♀️

[serene night]

Then what was the right answer even

[trim willow]

What is prob all dices are 1? What is prob all dices are 2? … What is prob all dices are 6?

[midnight haven]

it should be

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[pearl pond]

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[stuck arch]

what is C? what does that bracket mean, c is never mention before f is a function

[tropic saddle]

usually C(something, something) means the vector space of all continous functions from the first set to the second

here they specify with respect to what norm they want continuity (although that doesn't matter cause all norms on R^d are equivalent anyway)

[stuck arch]

ah okay thanks

I knew C^1 and C^2 but C was not familiar with and even with the ones I knew I never had brackets following

.close

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[pearl pond]

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[unreal barn]

How do i write this as a FORMAL NEGATION? Discrete Math
"There exists a class that all teenagers hate."

[unreal barn]

this is what i have but I dont think i can write my own variables like this

@vast sluice

[pulsar lark]

What have your tried?

[unreal barn]

I haven't tried anything yet, I spent 15 minutes and couldnt think of or find anything so I moved on... I emailed my professor and he said that we can't write our own variables and sent me an example:

this is a previous test question that was correct

that didnt help me that much though because the question on the practice exam (my orginial question) is asking for formal negation while this example shows something different

so basically i ended up back where i started at rewrite this as a formal negation:
"There exists a class that all teenagers hate."

[pearl pond]

@unreal barn Has your question been resolved?

[unreal barn]

@vast sluice

To anyone who can help: please @ me so I get the notification and respond faster

[pearl pond]

@unreal barn Has your question been resolved?

[unreal barn]

.close

[pearl pond]

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[pearl pond]

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[trail pasture]

,rotate

[jolly parrot]

Results provided by WolframAlpha

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

Requested by عبد الرحمن#9349

[wraith anvil]

Easy you have to change signs to get 116

[pearl pond]

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[midnight haven]

difference means the bigger factor - smaller factor = 13

[keen cradle]

|a-b|

and ab = 48

[midnight haven]

but also, not what you asked for but I'd look again at question 13

what is 10.2 rounded to the nearest whole number?

[midnight haven]

not necessarily

[keen cradle]

hm?

[midnight haven]

a and b are factors of 48, doesn't mean that they multiply to 48

for example if 2 and 3 are factors of 60, doesn't mean 2x3= 60

[keen cradle]

oh yea I see

sorry

[iron basin]

list out all factors

of 48

try that

first

[keen cradle]

look for pairs that differ by 13

[iron basin]

and list them out

youll get sth like 1, 2, 3, 4, 6, ... , 48

[midnight haven]

find one pair that differ by 13

[iron basin]

they are in the form n and n+13, where n is a natural numer

just check with every number

1 is a factor; 1 + 13 = 14 isnt a factor
2 is a factor; 2 + 13 = 15 isnt a factor

yes

n and a number which is 13 more than n

so that their difference is 13

thats whats given here

[pearl pond]

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[midnight haven]

can anyone help me with this please

[buoyant ridge]

,rccw

[midnight haven]

pi is pi radian here

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

<@&286206848099549185>

[buoyant ridge]

what have you tried?

[midnight haven]

i have like no idea how to do this

i did all other questions

but idk how to do this

all ive done is changed cot into cos sin

[rustic apex]

A = pi - (B+C) so use identities to find cos(A) then expand and simplify

[midnight haven]

hmm?

[rustic apex]

cos A = cos (pi - (B+C))

do u know cos (pi - x) identity?

[midnight haven]

no

i mean

[rustic apex]

do u know sum and difference identitiy

[midnight haven]

180-theta?

[rustic apex]

yeah it’s same thing basically

[midnight haven]

yea

but

its 180/4

so wait

nvm

sorry

[rustic apex]

ok

do u still need help with the problem

[midnight haven]

yea

i forgot the question lol

[rustic apex]

ok

[midnight haven]

please continue

[rustic apex]

https://cdn.discordapp.com/attachments/908078029778083872/1061664518222131240/176048095543558147.png

s we know A = pi - (B+C)

so this gives us cos(pi-(B+C)) = cosB cosC

what coes cos(pi-(B+C)) equal?

think of B+C as one quantity, say x

so this is same as cos(pi-x)

[midnight haven]

-cosx?

[rustic apex]

yup

now sub back in x=B+C

[midnight haven]

yee

[rustic apex]

then do u know sum and difference identities

[midnight haven]

so -(cosb* cosc-sinb * sinc)?

[midnight haven]

i think so

[rustic apex]

yep

then distribute the negative

[midnight haven]

wha

cosa+cosbcosc=sinbsinc?

[rustic apex]

no in -(cosBcosC - sinBsinC)

[midnight haven]

ohh

yea i did that

[rustic apex]

okay so it is sinBsinC-cosBcosC

so that is what cosA equal

[midnight haven]

yes

[rustic apex]

so plug it back into the original

[midnight haven]

original?

[rustic apex]

cosA = cosBcosC

[midnight haven]

what i got is cosa=sinbsinc/2

[rustic apex]

plug in sinBsinC-cosBcosC into cosA

[midnight haven]

ohh

but i have to prove cotbcotc=1/2 right?

[rustic apex]

yes

so we have sinBsinC-cosBcosC = cosBcosC

we can simplify this and move everything to one side

[midnight haven]

wdym

[rustic apex]

so there are two cosBcosC terms right

so what happens when you add cosBcosC to both sides

[midnight haven]

cosa+cosbcosc=sinb-sinc?

[rustic apex]

not quite

basically let’s say sinBsinC = a and cosBcosC = b

we are left with a-b=b

[midnight haven]

yea

[rustic apex]

so then we can simplify like a normal equation

add b to both sides

[midnight haven]

yep

[rustic apex]

yeah so then it’s a=2b then we can divide both sides by a

after this what happens when we substitute sinBsinC = a and cosBcosC = b back into the equation?

[midnight haven]

sinbsinc/2=cosbcosc?

[rustic apex]

yup

so divide both sides by sinBsinC

[midnight haven]

1/2=cosbcosc/sinbsinc

ohh

[rustic apex]

yup!

[midnight haven]

thank you very much

[rustic apex]

no problem!

is this a problem from school? seems more difficult than anything i’ve ever been given for class

[midnight haven]

i was trying to solve this since yesterday lol

[midnight haven]

yea

[rustic apex]

oh wow

where are you from if i may ask?

[midnight haven]

asia

[rustic apex]

oh okay yeah im from the US

[midnight haven]

nepal to be more specific but its not a big name

you're really smart

[rustic apex]

ah cool

thank you

[midnight haven]

if you dont mind me asking what grade are you in

[rustic apex]

sophomore

[midnight haven]

damn

same as me

[rustic apex]

cool! ur class seems pretty difficult. most people at my school would also struggle with such a problem

[midnight haven]

yea its like different from the us here

[rustic apex]

yeah the us doesn’t have the greatest math classes lol

[midnight haven]

lol

wait

sophmore is like grade 10 for me here

[rustic apex]

same

[midnight haven]

so 1 year gap from me

but yea this question had me goin for a while thanks for helping

[rustic apex]

no problem!

yeah basically for problems like this you want to try to get rid of A

since it’s not in the final statement

then see what you can do with different identities

[midnight haven]

yea i tried to do that but i did B+C=180-A

[rustic apex]

i see

usually it is best to isolate the quantity you don’t wnat

but that makes sense because 180-A looks nicer, but 180-(B+C) is very similar

i have to study for midterms now but good luck with you math studies!

[midnight haven]

thank you

and good luck with your midterms!

[rustic apex]

thank you!

[midnight haven]

.close

[pearl pond]

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[midnight haven]

I'm a bit confused. Why is 3 subtracted from both sides? Why can't -8x be added to both sides

[hollow cobalt]

So that +3 cancels out

[tough token]

you can do that too

[midnight haven]

adding -8x would make it -16x

[tough token]

or, well not -8x added

[midnight haven]

but i get the idea

[tough token]

but 8x added

[midnight haven]

you can add 8x to both sides

it would still work

.close

[pearl pond]

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[pearl pond]

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[merry stirrup]

Does wave particle displaces?

[merry stirrup]

Need help with this concept?

[foggy mason]

bro is doing quantum mechanics

#old-network

[merry stirrup]

I know but I didn't get any answers from the Physics server

[foggy mason]

and wdym by displaces ?

[mild olive]

Average 14 year old

[merry stirrup]

Displacement

[mild olive]

at 14 I was failing at roller skating, this ones doing quantum mechanics 💀

[honest bough]

What about displacement, and what does it have to do with wave particle duality

[merry stirrup]

Bro I was not doing quantum mechanics it was written in my notebook that particle of medium don't move but then I got the definition of amplitude

[plush bramble]

Show the page you're asking about

[merry stirrup]

I was just talking about sound wave

[merry stirrup]

,ti

[jolly parrot]

The current time for 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛 is 05:18 AM (IST) on Mon, 09/01/2023.

[merry stirrup]

🥲

I haven't sleep

[foggy mason]

?

[merry stirrup]

Can you just correct this concept

If anything is wrong

[foggy mason]

i mean, we have zero context

[plush bramble]

I don't know what your time zone has to do with my question

[honest bough]

The particles in a sound wave don't move, no. They just jiggle around

I mean, they move. They're jiggling

[mild olive]

wait how does it

,ti

[jolly parrot]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[merry stirrup]

Means the net Displacement of a medium particle is 0?

[plush bramble]

Oof

[foggy mason]

Man

[plush bramble]

You're asking in the wrong place

You should know better @merry stirrup

[plush bramble]

.

[honest bough]

There might be a small displacement

But in general the particles will stay in the same general location

[merry stirrup]

Okk I already asked there but I didn't get any responses that's why I asked here 🥲

But still thanks

.close

[pearl pond]

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[abstract junco]

I keep getting 24sqrt(2) but it says it's incorrect

[pearl pond]

@abstract junco Has your question been resolved?

[pearl pond]

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[reef tapir]

I cannot figure out for the life of me how to attempt this

I know im going to need parallel axis theorem

[glacial sequoia]

You should just try conserving mechanical energy between the mean and extreme positions and balancing the forces when it's at the equilibrium position

Oh wait I think I misread the question

It's the larger disc that's rotating?

[reef tapir]

uh

yeah i think both are moving

im not completly sure

but i read do torque

and parallel axis theorem

[glacial sequoia]

Yeah if it's the larger disc that is rotating you need to balance torque

Parallel axis theorem because the moment of inertia of the smaller disc needs to be considered as well

[reef tapir]

net torque is mgsin(theta)?

for total moment of intertial i got $I = \frac{1}{2} M R^{2} + mR^{2}+ \frac{1}{2}mr^{2}$

[jolly parrot]

allarkvarkk

[glacial sequoia]

That's dimensionally incorrect

[glacial sequoia]

Yup

[reef tapir]

:(

isnt there only one force?

gravity?

and torque is r crossed with F which can be rFsin(theta)?

[glacial sequoia]

Yeah you didn't multiply distance

[reef tapir]

oh wups

oh and it'd be negative right? Because of the gang signs?

[glacial sequoia]

Are you familiar with the energy derivative method btw

[reef tapir]

um let me search it up i might be

[glacial sequoia]

Well the torque will keep changing anyways so doesn't matter

[reef tapir]

no i havent seen the energy derivative method

im at this point

[glacial sequoia]

Alright

Just do $\tau = I\alpha$

[jolly parrot]

NEONPerseus

[reef tapir]

$\Sigma \tau : -mgR \sin(\theta) = ( \frac{1}{2} M R^{2} + mR^{2}+ \frac{1}{2}mr^{2}) \alpha$

[jolly parrot]

allarkvarkk

[glacial sequoia]

Yup looks good

[reef tapir]

so im going to hhave to integrate this after chaning alpha to a/r ?

[glacial sequoia]

Yeah

[reef tapir]

lemme try that real quick

[glacial sequoia]

Also sin theta can be approxinated to theta

Since it's small

[reef tapir]

ahh okay ty

let me try that

[glacial sequoia]

@reef tapir

[reef tapir]

yeah?

[glacial sequoia]

Don't write alpha as a/r mb

Write it as the second derivative of theta

[reef tapir]

wait why?

isnt this linear velocity?

also how does the cos(theta) just pop out?

[glacial sequoia]

Because then it can be integrated with theta

[reef tapir]

ohh

[glacial sequoia]

And later on you can write it as v/r

[reef tapir]

wait but there is no way i can get the cosine

[glacial sequoia]

Hmm

Then keep sin theta as is

[reef tapir]

okay ill try that

wait if i leave as angular then acceleration if $\frac{d^{2} \theta}{dt}$

[jolly parrot]

allarkvarkk

[reef tapir]

I dont have a single t in here

[glacial sequoia]

Well you'll perform a substitution

You can write it as $\omega\frac{d\omega}{d\theta}$

[jolly parrot]

NEONPerseus

[glacial sequoia]

Where Omega is angular velocity

[reef tapir]

oh

[glacial sequoia]

I hope you got why I wrote that btw

$\frac{d^2 \theta}{dt^2} = \frac{d\omega}{dt} = \frac{d\theta}{dt} \times \frac{d\omega}{d\theta}$

[jolly parrot]

NEONPerseus

[reef tapir]

wait one sec

For this is the height 1-cos(theta)?

i think i can use energy

[glacial sequoia]

R(1 - cos theta)

[reef tapir]

wait let me try one thing

[glacial sequoia]

Yup you can try conserving the mechanical energy of the smaller disc

[reef tapir]

this is painful to simplify

[glacial sequoia]

Lmao keep th moment of inertia as I

$\int_0^{\omega} \omega d\omega = \int_0^{\theta} -\frac{mgR}{I}\sin \theta d\theta$

[jolly parrot]

NEONPerseus

[glacial sequoia]

@reef tapir this should be it actually

After you integrate this write omega as v/r

[reef tapir]

oh let me see

i dont think so

i couldnt be able to get the 1-cos

[glacial sequoia]

You'll get that when you integrate sin I think

And when you put in 0 cos 0 becomes 1

[reef tapir]

omg im a genius

let me write this out

ty for the help

gn

.close

[pearl pond]

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[latent mortar]

Hello I am looking for help in finding a way to find the volume of a wine bottle (solid of revolution)
I found functions that fits the curve of each of the parts of a wine bottle I used desmos to automatically find the curve and found the equations for it. After that I made them into piecewise functions and put them each into the Disc integration formula (wolfram alpha for calculating). The volume I got after using the disc integration formula was too big. Does anyone know why this is the case? Is there any other way to find the solid of revolution of this wine bottle? I am doing this for my math exploration project.

[pearl pond]

@latent mortar Has your question been resolved?

[reef tapir]

wdym too big? like compared to a real bottle?

[plush bramble]

how do you know it's "too big" ?

[latent mortar]

yes

[latent mortar]

soeme of it is multiplied by 10^8

[reef tapir]

whats the scale?

[latent mortar]

1072.23 + (4.22402 * 10^8) + 54.5657 + (8.56419 * 10^8) = 1,278,822,126.7957

[latent mortar]

I aligned the wine bottle image (in the x-axis) to around 29cm

Do you guys know why it is very big

I am sort of confused

[pearl pond]

@latent mortar Has your question been resolved?

[plush bramble]

Probably your unit conversion

How many cm^3 in a liter

[pearl pond]

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[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
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[bitter night]

Question about tangents and Pythagorean theorem:

[bitter night]

Basically this is not that hard question, but when I use tan(15) = a/b I get the value of tan, then multiply by "b" and get the "a" value. But when I try the same with pythagoream theorem I get totally different answer? I'm doing this from 3 hours already so my brain is like melted.

[inland cove]

What r the values

[keen cradle]

could be a rounding error? also show your results by far

[errant fable]

maybe this isn't a 90° triangle?

considered that?

[inland cove]

It is

The way it looks

[keen cradle]

that's not conclusive

[errant fable]

then just a²+b²=c²

[inland cove]

Yea but this dude says he's getting a different result

[errant fable]

use the cos law for calculating a

[inland cove]

While using trig

[errant fable]

thats why i said "maybe" not 90°

[inland cove]

Omg masters here

Sir oogway

[bitter night]

It is

[ebon skiff]

Yes

[bitter night]

It's 90°

[inland cove]

Bless me mr ooogwayy

[ebon skiff]

Bless you

[inland cove]

My exxams approach

[inland cove]

Tysm

[ebon skiff]

Can you show your work?

So we can see if you made an error

[bitter night]

tan(15) = 0.267949192
tan(15)*2.54 (that is b) = 0,68590948

[bitter night]

also im using c² - b² = a²

[keen cradle]

and what does the pythagorean theorem tell you

[bitter night]

Ok

[keen cradle]

,w tan(15 degrees)*2.54

[jolly parrot]

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[keen cradle]

,w tan(15 degrees)

[ebon skiff]

Yeah thats the answer

[jolly parrot]

Results provided by WolframAlpha

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[bitter night]

−3.7316

[keen cradle]

got the value of tan(15°) right but a little bit off when you multiplyed that by b

[ebon skiff]

,w 2,54^2+a^2=2,72^2

[jolly parrot]

Results provided by WolframAlpha

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Requested by Master Oogway#0599

[ebon skiff]

Wtf

[keen cradle]

what

,w a² + b² = c², b = 2.54, c = 2.72

[jolly parrot]

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[keen cradle]

,w 3sqrt(263)/50

[jolly parrot]

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Upgrade to WolframAlpha Pro!

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[keen cradle]

hmm

[bitter night]

Thats what im getting too, on Microsoft Math calculator

[keen cradle]

yea I don't think the angle is 15 degrees

to check just use cos(15 degrees)

[bitter night]

The angle is straight defined its 90 degrees

[keen cradle]

not that it's not a right angle

the given angle and the given sides contradict

,w cos(15 degrees)

[jolly parrot]

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[bitter night]

Lets just replace some values

[keen cradle]

,w 2.54/2.72

[jolly parrot]

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[keen cradle]

see

[bitter night]

lets accept "b" and "c" are multiplied by 1 Million

[keen cradle]

most likely a rounding error or whatever

[bitter night]

Then "b" is 2540000 and "c" is 2720000

[keen cradle]

uh alright

[ebon skiff]

Why 1 mil and not 100

[bitter night]

I get the answer 973036,.......

When I try with sin, I get 703987.802678856 which is like not even close

[keen cradle]

yeah

[bitter night]

cos's formula doesnt tells me how to find "a" so no need to try it

but the angles are 15 degrees and 90 degrees

[keen cradle]

that doesn't mean the mathematics of geometry and trigonometry contradicts

that rather means the given values are false and doesn't construct the said triangle

the question is set up wrong

[bitter night]

So if we say that its not straight 90 degrees triangle? How do we find "a"

[keen cradle]

cos tells you the adjacent/hypothenuse

which we know the values of

[bitter night]

cos and tan give me different values too

I mean sin

not cos

Tan gives me: 680590.948775051658

Sin gives me 703987.802678856

either im dumb, either something here is wrong

[keen cradle]

law of sines I think

[ebon skiff]

Something is wrong

[keen cradle]

what do you use sin for

[bitter night]

sin = a/c, so if i find sin(15) and multiply it by "c" which is 2720000 then I get "a"

[keen cradle]

rather 10^6 a but yes

[bitter night]

Yes, juts I cant write this, i dont have this symbol on keyboard

Okay lets start again

[keen cradle]

it's shift + 3

[bitter night]

I get #

[keen cradle]

altgr + 3?

anyway

[bitter night]

nothing

wait

its ^ shitf+6

anyways

Thats what we know for now

sin, tan and Pythagorean theorem gives me different results when we accept its 90 degrees

im just dumb or?

[ebon skiff]

So it's not 90

Problem solved

[keen cradle]

yea

[bitter night]

So conclusion: im just idiot

[ebon skiff]

No

[keen cradle]

mayhaps

[ebon skiff]

Your smart

Cuz you figured it out

I wouldnt have tried 2 methods

You did

[bitter night]

xD

the bot deletes my message

where i say my I Q is negative

anyways

.close

[pearl pond]

Channel closed

Closed by @bitter night

Use .reopen if this was a mistake.

[bitter night]

.reopen

Wait

[pearl pond]

✅

[bitter night]

Wait

I still can't figure out "a" value

[ebon skiff]

Lmao

[keen cradle]

you can't

[ebon skiff]

Delete the *10^6

[bitter night]

I must

This is the task

[keen cradle]

oh wait

you can

[bitter night]

Im not 100% sure that the triangle is not 90 degrees... just I proved that im not smart

[keen cradle]

by the cosine law

[ebon skiff]

Bro you just proved that you're smart

[keen cradle]

the triangle does not need to be a right triangle

[ebon skiff]

You cant use cos law

Ww dont know the angle between a and b

[keen cradle]

don't need that

[ebon skiff]

?

[bitter night]

We dont.

[ebon skiff]

Ok...

[bitter night]

We only know "a" and "b"

[keen cradle]

to find the opposite side to the angle we jus need to know the angle and the two lines that construct it, don't we?

[bitter night]

The triangle MAY be 90 degrees, just I'm not sure

[brave mason]

cosine rule thingo

[ebon skiff]

Its not 90

[bitter night]

He said we cant use it

[ebon skiff]

You just proved it

[brave mason]

but he's wrong

So

[bitter night]

Im always wrong .-.

[errant fable]

$a²=b²+c²-2bc\cdot\cos(x)$

[ebon skiff]

Yeah apparently im wrong

So dont listen to me

[errant fable]

just use this

[keen cradle]

nope

you subtract the cos term

[brave mason]

fr

[errant fable]

this works for any triangle in any situation with no hesitation

[ebon skiff]

Yeah you subtract

[bitter night]

a^2+b^2–2abcosC

[brave mason]

We know the angle between b and c so we can make a relationship between all three sides with only one unknown

[keen cradle]

almost

[errant fable]

yeah we subtract sorry

[ebon skiff]

Yeah i understand now

[jolly parrot]

haygiya

[bitter night]

So I just use cosine rule

[ebon skiff]

Yes

[bitter night]

and im done

[keen cradle]

true!

[errant fable]

yup

[bitter night]

Finally 🥹

[ebon skiff]

Green diamond?

[pearl pond]

@bitter night Has your question been resolved?

[bitter night]

I need help lol

So I just need to write answer

tan(15)*b ≈ 680590,948
law of cosine gives me ≈ 709382,338
Pythagores theorem gives me ≈973036.484

@golden bolt

oh sorry

my wrong for pinging you

<@&286206848099549185>

Explain me where im wrong, why im wrong and everything

Im not sure that this is right-angled triangle.

[light jolt]

? is not 90 so you should not use pythagoras

law of cosine gives everything I think

[bitter night]

So law of cosine is right method

[light jolt]

yes the figure may mislead you think that ? looks like 90,

[bitter night]

I know

it looks like 90 degrees

[light jolt]

e.g. $a^2 = b^2 + c^2 - 2bc*cos75$ so you get a, and use it again to get ?

[jolly parrot]

请务必再休息一天

[bitter night]

cos (15 should be I think)

[bitter night]

also

I just need to get "a"

[light jolt]

Oh sorry, yes

[bitter night]

I need to get "a" length

thtas everything