help-17

[north totem]

ok

61*60/2

i can say this is

61*30

[upper shell]

yeah

1830

[north totem]

which is pretty easy to do in the head

[upper shell]

then subtract 2

[north totem]

610+610+610

which is 1830

so final ans is 1828

[upper shell]

Correct!!!!

[north totem]

DUDE I WANT TO KILL MYSELF

bro how did i not get it

[upper shell]

bro you got the answer yourself only

its all in the confidence

[north totem]

yeah but not in the test

[upper shell]

any other questions?

[north totem]

there were also a q if there is a 10by 100 chess board in how many way can u out bishops without them atacking eachother

]i think i said 119

bc i thought that was the amount of diagnold there are

[upper shell]

u sure it is 10 x 100?

[north totem]

yeah

[upper shell]

ok youre right here

10x100 chessboard

has 100 diagonals which go top right from the base of the chessboard

• 9 more to the left

there are 109 north east /south west diagonals

but we also gotta consider north west/ south east diagonals

which is also 109

[north totem]

so the ans was 218?

[upper shell]

no no

we gotta consider if there are certain diagonals where u cant place bishops without attacking each others

for example

there are 1x1 diagonals

at the cornals

*corners

lets try to look at a simpler problem

where instead of a 10x100 diagonal

we have a 3x5 diagonal

so we can draw it and see how the bishops interact

[north totem]

i think its 5

[upper shell]

yeah this is wracking my brain

yeah im getting the same

but did u see how its not about the no. of diagonals

[north totem]

yeah its the number of distinct ones

like where there are no cuts from othere ones

ok o no no

its the amount of squares that only one diagonl gets to them

devided by 2

i think

[upper shell]

i dont think so

how about a 4x5 chessboard?

[north totem]

7?

[upper shell]

wait i think i get the trend

in the 10x100 chessboard

[north totem]

4+5-2

so 100+10-2

[upper shell]

if we line the bishops all along the bottom row

nono

wait

[north totem]

yes yes

i swear

[upper shell]

if we line the bishops all along the bottom row

[north totem]

yeah

[upper shell]

then there are just a few squares wehere we can place bishops

and actually there are 0 squares where we can place any more bishops

its just 100

[north totem]

nah i dont think so

ok check a 3x3 and see if its 4

[upper shell]

3x3 is 3

[upper shell]

nvm

[north totem]

its k+n-2

[upper shell]

not true for 3x5

[north totem]

it will be 6

[upper shell]

nah its 5

[upper shell]

here

bbtw i gtg and im 100% sure the answer is 100

[north totem]

ok ty for helping

[vocal sleet]

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[stoic anchor]

subject: epsilon-delta definition of a limit

this is my first time doing proof and latex so I want to make sure that what I'm doing is correct, could someone check if this is right, or provide a way to verify my answers? tyia

[wary mantle]

First one looks good, other than the typo in the first line, it's 5 - 2x. Also, at the end, you forgot a | after 'we have ...'. You don't really need the last part at all, it's enough to show you can pick such a delta for all epsilon. The last part is just checking your answer (much like plugging back a solution into an equation; it's not necessary)

Second one looks good too, you can cancel x + 2 because x is not -2 per epsilon-delta definition of the limit

[stoic anchor]

oh yeah I did forget the |, for the first one, do you mean I should write (5-2x) without parenthesis?

nvm I found it

[wary mantle]

I guess I don't like the 'suppose' in the third one, it sounds as if you are going to do cases. Instead, we can just set delta < 1 (we can always do that), then |x - 2| < 1 follows

[wary mantle]

No, I mean this

It's not 5x - 2x, it's 5 - 2x

[stoic anchor]

gotcha

[wary mantle]

Yeah ok you do that with the min condition, that's fine

[stoic anchor]

um how would you recommend I rewrite it?

[stoic anchor]

or is it fine already?

[wary mantle]

It's fine like this, I didn't read the last part yet when I wrote that

[stoic anchor]

ah alright

[wary mantle]

I meant that I would right away write "Let delta < 1"

Instead of "Suppose |x - 2| < 1"

But then you'd still have to see if epsilon/19 is less than your chosen delta or not, so it would lead to the same thing

So yeah, just keep it like this

Maybe one thing if you want to be very nitpicky: use \ before min in LaTeX

[stoic anchor]

which is the same as | x - 2 | < 1, right(?)

[stoic anchor]

ohh didn't know that was a thing, I'll try it

[wary mantle]

Well, if you say "Suppose |x - 2| < 1" then it sounds like you are going to do cases, and continue your next paragraph with "Now suppose |x - 2| >= 1". If you say "set delta <= 1", you know you only have that one case

But with your min condition, it's really equivalent

[stoic anchor]

I see

[stoic anchor]

thank you for the help, and for being really meticulous!! I still don't fully understand the language used in proofs so I don't rlly understand this but thanks a lot

oh do you have any recommendations for what to learn (basics, particularly the language/words used) when getting into proofs?

[wary mantle]

The proofs are very good, these were just minor things

[wary mantle]

I don't think one should imagine proofs as something mysterious, you're really just arguing that a certain thing is true

You can write it however you want, you just want every step to be justified

[stoic anchor]

interesting, so I suppose it's smthn like a philosophy paper

ig I have to practice reading them to get used to their structure

[wary mantle]

There are different proof techniques like induction, contraposition, contradiction

They can make it easier to argue a certain thing

You are (or should be) made familiar with these techniques when you begin studying mathematics at uni

[stoic anchor]

our math classes just started at uni so I guess we haven't reached the topic yet

[wary mantle]

Are you a math major?

If you're studying something else like physics and only take maths as minor, then proofs are from what I've heard a bit underrepresented

[stoic anchor]

I'm about to be, I'm a freshman taking a different program rn but I plan to shift to a math major after this sem (compsci; they say the program's like a double major prog in our uni lol, computers + math)

[wary mantle]

Yeah, then if you're doing 'real math' (maybe not in Calculus but in Real Analysis and basically everything beyond) everything needs to be proven and books read like Definition - Theorem - Proof

You will quickly get familiar with it

[stoic anchor]

yeah our couse rn is called "elementary analysis"-

I was struggling at first bc we weren't taught 'real math' before in high school but I'm getting used to it

[wary mantle]

That's normal

[stoic anchor]

finding it more fun too

than just memorizing arbitrary rules

[stoic anchor]

loving math actually, which I didn't rlly expect lol

oop I hope chatting beyond the "help" part is allowed here, would you mind if I send a friend request?

[wary mantle]

oop I hope chatting beyond the "help" part is allowed here

It is lol

You can send me a frq sure

[stoic anchor]

thanks !!

I think I should close this now

.close

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[tidal dock]

Suppose that there exist invertible n×n matrices A and B such that AB = −BA.
Show that n is even.

[tidal dock]

no clue where to start really

this is a chapter on determinants

[tidal umbra]

hi

[tidal dock]

hello

[tidal umbra]

take determinants on both sides

[tidal dock]

yes

OH

[tidal umbra]

and use properties

[tidal dock]

i see it

thank you

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[tidal umbra]

welcome

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[atomic jasper]

<@&268886789983436800>

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[steep shard]

I need help solving this I've done abit of it

Ig it needs checking

[vocal sleet]

@steep shard Has your question been resolved?

[prisma prism]

hey @steep shard do u still need help ?

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[steep shard]

.close

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[nocturne shale]

dk how to solve this

[gentle nimbus]

differentiate

then f'(2)=7 so you get the value of a

[nocturne shale]

yo why is the new discord layout so weird

[bitter pilot]

y = f'(2)(x-2)+b

[nocturne shale]

ok so f'(x) = 2ax + 3

[bitter pilot]

set them equal make sure discriminant equals 0

[nocturne shale]

ok thanks

.close

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[honest gale]

I need help with some hw rq

[honest gale]

.close

[paper depot]

wait so do you need help or not

[honest gale]

nvm i got it

srry

[paper depot]

k

[honest gale]

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[timber gyro]

If I know that the square root is always greater than or equal to zero, how can I mathematically prove that the cube root is greater than or equal to zero?

[quick spire]

the cube root has no such restrictions in R

for ur particular question though

try cubing both sides then squaring both sides

then simplifying and solving for roots of the leftover polynomial

[timber gyro]

But thx for the help

.close

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[steep shard]

needs checking for part a

is this the simplest form

[vocal sleet]

@steep shard Has your question been resolved?

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[steep shard]

.reopen

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✅

[steep shard]

<@&286206848099549185>

[twin horizon]

check the final answer

[steep shard]

does it need simplifying?

[twin horizon]

Sin(5t)-0.3≠-0.3sin(5t)

[twin horizon]

look at these parts

[twin horizon]

Yes

[steep shard]

so

[twin horizon]

.

[twin horizon]

Yup

[steep shard]

and so

this is the simplest form?

[twin horizon]

Yes

[steep shard]

alright now

i have to differentitate this to get acceleration

[twin horizon]

,w diff (e^(-0.3x))sin5x

[twin meteor]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[twin horizon]

You can change the +- to -

[steep shard]

hmm

[twin horizon]

Nope just with 5e^{-0.3t} factored out

[steep shard]

shall I differentiate this

[twin horizon]

Yes

[twin horizon]

This is way easier to differentiate

Nah nvm

[steep shard]

ok ill try

[twin horizon]

Either one is okay.

[steep shard]

Ok'

[steep shard]

correct so far?

[twin horizon]

U is correct

[steep shard]

Oh ok

[steep shard]

O

so

use the chain rule?

[twin horizon]

V=cos a - 0.06sina

[steep shard]

oh

[twin horizon]

Yes on both cos and sin

[steep shard]

okay

[twin horizon]

Yup

[steep shard]

Hmm

[steep shard]

I don't understand

H

oh

[twin horizon]

Compare the top and bottom and you will notice...

[steep shard]

I do

[twin horizon]

[steep shard]

is this the simplest form

[twin horizon]

Multiply through by 5

[steep shard]

hmm

but that would be expanding

[twin horizon]

,w diff cos(5x)-0.06sin(5x)

[twin meteor]

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Requested by ishigamisenku_

[steep shard]

oh ok

[twin horizon]

Ok now for the product uv

Use the product rule and you're done

[twin horizon]

Seems correct

,w diff 5e^{-0.3x}[cos(5x)-0.06sin(5x)]

[twin meteor]

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Requested by ishigamisenku_

[twin horizon]

Collect like terms (the sin terms on one side and the cos terms on the other)
Then simplify.

[twin horizon]

Yes

[steep shard]

hmm

wait

[twin horizon]

Sorry gtg

[twin horizon]

Anyways you can check your final answer with this

[steep shard]

Oh

<@&286206848099549185>

[flat whale]

did you do this yet #help-17 message

[steep shard]

my final answer isn't this

[flat whale]

use sin(x)cos(x) = (1/2) sin(2x) to make derivatives easier

[flat whale]

in this step

[steep shard]

what do you mean

[flat whale]

what don't you understand

[steep shard]

how to simplify

[flat whale]

did you see this

[flat whale]

and this trig identity?

[steep shard]

I havnt learnt

wait

[flat whale]

trig identities are a prerequisite for derivatives of trig functions

sometimes called "double angle formula"

[flat whale]

this one that is

[flat whale]

uh huh and

[steep shard]

do I need to simplify

becus the answer will still be the same

[flat whale]

its fine as is

just plug in t=2

you're asked for a number in part b), not a function

[vocal sleet]

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@steep shard Has your question been resolved?

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[nimble spindle]

im not sure what to do

[hollow kite]

PEMDAS

[vocal sleet]

@nimble spindle Has your question been resolved?

[nimble spindle]

Already tried it

None of the answers line up

You try to solve it and tell me what you get. I get 1448 point something

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[nimble spindle]

No <3

[drifting jackal]

I was able to get an answer that is one of those choices. What did you do to get 1448?

[nimble spindle]

i did 8.5 times 13, then that times the number in from of the parenthesis, and then added

from there i dont get what it wants me to do

i followed pemdas

[drifting jackal]

Did you follow sig fig rules as you were doing the calculations?

[nimble spindle]

how am i supposed to?

theyre all numbers i cant really do that with

[drifting jackal]

Do you know the sig fig rules when you add/subtract and multiply/divide?

[nimble spindle]

Is this right?

[drifting jackal]

Yes

So if you follow that for multiplication/division, if you do 8.5 * 13, how many sig figs should the result be?

[nimble spindle]

2

but

then id have to do a bunch of exponents

which
there are none in any of the answer choices

[drifting jackal]

Where are exponents coming from?

[nimble spindle]

the ^-10 or ^10 rule or something like that

[drifting jackal]

No need for that

So if you know that 8.5 * 13, the result is two sig figs, what is the result?

[nimble spindle]

i literally dont know

110.5

thats it

thats the answer

[drifting jackal]

What's 110.5 to two sig figs?

[nimble spindle]

Thats another thing i dont know

i literally dont know what it wants

Id say 11 but thats nowhere near the value its asking for

[drifting jackal]

It's not 11 because trailing zeros are not sigificant unless there is a decimal. So 110.5 to two sig figs is 110

[nimble spindle]

well if id have thought for more than 5 seconds maybe i wouldve figured that out
god im dumb
lol

thank you

so it is 1442?

[drifting jackal]

No

You're not done yet

So you have 110 * 13 now

[nimble spindle]

yes
plus the other thing

[drifting jackal]

How many sig figs shoul 110 * 13 be?

[nimble spindle]

oh god

2

[drifting jackal]

So 110 * 13 is?

[nimble spindle]

1430

[drifting jackal]

And two sig figs would be?

[nimble spindle]

Dont know, and holy shit youre patient

[drifting jackal]

It's the same idea with 110.5

[nimble spindle]

so i just hae to remove numbers

that make it notits value anymore

[drifting jackal]

You use the first two digits and buffer with 0s since trailing 0s aren't significant

[nimble spindle]

this question doesnt make sense and i dont see how itd reflect itsactual value

i mean

it does

but
its stressing me out bc this will never apply to real life

ever

[drifting jackal]

.

[nimble spindle]

1400

which would leae me with 1412

[drifting jackal]

Well the thing is, that website is kinda stupid too because ideally, you're suppose to round at the end but to get an answer that matches, it rounds at every step

[drifting jackal]

Yes

[nimble spindle]

which i hate 😭

bc i have to add extra steps to pemdas

[drifting jackal]

Or it's whatever that last option means

[nimble spindle]

p (oh yeah do the sig fig thing) e (sig fig thing!) m (sig figgggg) d( sig fig!!!)

etc

[nimble spindle]

she didnt delete it

meaning its not supposed to be there

thank you

[drifting jackal]

It did say be careful and do the problem slowly

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

[nimble spindle]

.close

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[sonic glade]

given a 3D vector v, how would I go about rotating it by an angle theta in a uniform random direction?

[sonic glade]

the tips of all vectors theta away from v make a circle, so I suppose I could try to pick a random point along that circle? but how would I find where that circle is exactly

[vocal sleet]

@sonic glade Has your question been resolved?

[deft oar]

Okay I may be wrong

But, if we have a general matrix for rotating a vector an angle about phi and and an angle about theta

I think we can rethink this in the context of your question

To apply the construction that (phi)^2+(theta)^2 = angle you want squared

Thin this case, we’re rotating by the angle you want each time about a circle

This is a pretty unique problem, and I haven’t worked it out much, so I could totally be wrong

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[frozen smelt]

I need help for setting the values for the 2nd pics part

[frozen smelt]

Its a partial fractal decomposition problem

Also don’t mind the doodles

What should I set A+C and the other systems of equations equal too?

🙏

I was wondering if I should set it equal to the x values of the deonomiatora of the respective letter

So for A and c, both of them have been multiplied by x-2^2 and x+2^2

So if I multiple the real zeroes and get -4

Would that be what I set the a+c equal to?

Or do I set it all equal to the amount of times the specific degree shows up

The original problem is the make 5x^2/ (x-2)^2(x+2)^2

A proper fraction

I also wondered if I should set it equal to the coeffs of the distributed version of the denominators factors

I tried reading my textbook but they weren’t clear

[uneven flicker]

,rccw

[twin meteor]

Couldn't find an attached image in the last 10 messages.

Feb 12, 2025, 7:47 AM

[uneven flicker]

💀

[twin meteor]

Couldn't find an attached image in the last 10 messages.

Feb 12, 2025, 7:48 AM

[uneven flicker]

i highly recommend using a pencil for such maths

so you can erase what you did wrong

[errant citrus]

We need to find the values of A, B, C and D , right?

So we can make Partial Fractions

[vocal sleet]

@frozen smelt Has your question been resolved?

[errant citrus]

I think that it had be much easier if you obtain equations in A, B, C and D by putting various values of X.

Put X where other Unknowns like, A, C and B, D becomes 0 together. That would give you an equation and so on.

For this problem, you should check X = 0, 3, 2 and -2.

These 4 equations should be enough to solve for A, B, C and D easily. Tho it is lengthy and calculative still.

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[grim sequoia]

I have no idea how the 9/10 can become 19/10?.

[atomic jasper]

where is 19/10?

[grim sequoia]

this is what the answer should look like

how does he get from 9/10 to 19/10

?

[outer warren]

1 + r = 1 + 9/10

[grim sequoia]

but why is that?

[outer warren]

because you're gaining 9/10 * current value

current value + 9/10 * current value = current value * (1 + 9/10)

[grim sequoia]

ohh

i see

thanks

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[gilded badger]

Can I just square root the whole function then put it into my calc?

From 0 until pi with 30 degree steps?

Would that give me the correct shape?

Cuz I don’t get what the ms means

Wait I get it now mb

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[mystic canyon]

is it possible to get help with physics here as well? or only maths

[mystic canyon]

oh fk i didnt mean to make a thing

[oak magnet]

Depends the physics

[mystic canyon]

its energy/heat

[oak magnet]

If its enough math related then why not

[mystic canyon]

it is mostly

calculations

[oak magnet]

Also i don't know any physic don't count on me kekw

[mystic canyon]

Problem 7:
40.0 g of molten lead at a temperature of 328°C is placed in a container with 1200 cm³ of water, where the initial temperature of the water is 8.2°C. The mass of the glass container is 180 g. Determine the final temperature of the water after the lead has cooled down. The glass jar is considered to be insulated, and heat exchange with the surroundings is negligible.

𝐶 glass=840J/kg

[oak magnet]

But you can show sure

[mystic canyon]

ah okay

i translated the question

from swediosh to enlgidh via gpt

so hopefully itrs accurate enough

If you could use the m1 * c1 * (t1-tf) = m2 * c2 * (tf - t2) with tf being the temperature of the mixture

m = mass and c = heat capacity of the

ssbuject/substance

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[old zinc]

anybody want to help me with kinematics

[reef agate]

!da2a

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[old zinc]

what does this mean

[pallid temple]

It's a bot command..

Don't need to ask whether someone can help

[old zinc]

gotcha

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[small flame]

<@&286206848099549185>

[flat whale]

!15m

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[atomic summit]

!15m

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[iron summit]

hello, this is the integral but im stuck on how to solve this

[iron summit]

i managed to reduce this to a form

root of cos2x/sinx

but unsure as how to proceed

[reef agate]

,w true or false csc^2(x) - 2 = cos^2(x) / sin(x)

[twin meteor]

Results provided by WolframAlpha

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[paper depot]

evidently the reduction was incorrect

but also this is one very ugly integral

[iron summit]

no, its root of cos 2x/sin x

uhh idk how to write in mathematical notation on discord

[reef agate]

Ya but i cancelled out the root from csc^2(x) - 2

[reef agate]

$\sqrt{\csc^2(x) - 2 } = \sqrt \frac{\cos(2x)}{\sin(x)}$?

[twin meteor]

King Leo

[iron summit]

here lemme send

ignore me not writing dx every step lol

[reef agate]

Oh i see

[paper depot]

oh so the sin(x) was not under the root

[reef agate]

,w sqrt(csc^2(x) - 2) = sqrt(cos(2x))/sin(x)

[twin meteor]

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Requested by .king.leo.

[reef agate]

That seems right

[iron summit]

soo

how do i proceed further 😭 been tryna scratch my brain

[reef agate]

Try using double angle identities on cos(2x)

[iron summit]

i did

but the root makes it difficult to use substitution

[reef agate]

Oh wait one sec

[iron summit]

its always the sum or difference of 2 terms, so idk how to remove the root

[reef agate]

Idk this :(

[iron summit]

if i use

double angle identity twice

i can reduce numerator to

root of (-2cos^2 x/2 +1)

but again its a fucking sum of 2 termss

uh

@reef agate do i ping helpers?

[reef agate]

Ya but you need to wait 15mins before

!15min

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[iron summit]

lmao exactly 15 mins have passed

<@&286206848099549185>

[vagrant kraken]

uh i think this integral is impossible

[iron summit]

apparently this is the answer

[iron summit]

💀

must be some way

[vagrant kraken]

thats diabolical

[iron summit]

yea

root tan x is easier than this

and i thought that was tough lol

[vagrant kraken]

lemme cook

nvm

[iron summit]

my

teacher sent me smth

but

im having doubts

altho i cant find the fault

[vagrant kraken]

how did he get from end of first col to second col

or is that dif ways of doing it

[iron summit]

nope

one method

[iron summit]

express cot^2 x as 1/tan^2 x
and 1 as tan sq x/tan sq x

[vagrant kraken]

oh

[iron summit]

one friend is telling me this is apparently

hyperbolic subs

i have 0 clue

[vagrant kraken]

u dont hv to

just do

integration by parts and an inverse sine sub

its hard to see but it should work

[iron summit]

can you send me

how would that look?

yea nvm this, she made a mistake

[vagrant kraken]

o

gg gl

[iron summit]

wdym gg 😭

i thought u got it

[vagrant kraken]

🙏 😭

[iron summit]

damn bro

teacher did it

welp ig doubt is no more lmao

@vagrant kraken @reef agate thought i'd tag you since you both were also trying to solve it.

.close

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[vagrant kraken]

huh

forced substitution... interesting

[iron summit]

what works it works

heh

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[sudden marten]

need help with le evil bonus questiomn

[sudden marten]

where should i start? ibp on the left?

[vast shale]

x = g sub

[errant citrus]

Let A = integration of inverse of f(x) wrt x from f(b) to f(a)

Let inverse of f(x) = t

Then find dx, substitute it, integrate it with the help of by parts.

[sudden marten]

did i mess up this look weird

also got this

[errant citrus]

A little bit, wht I meant was:

Inverse of f(x) = t
x = f(t)
dx = f'(t)dt

Substitute this all in A, A at first is written absolutely fine.

[sudden marten]

uhhh

oh right cuz an inverse is just x and y switch

so if f(x) = t

then x = f(t)

[errant citrus]

Yes

[errant citrus]

It would be nice if you share me the Final A we get before applying by parts

https://cdn.discordapp.com/emojis/1335340422142103623.png?v=1

[sudden marten]

?

i see the ibp now

[errant citrus]

Yes, but the upper and lower limits will change as well because of the substitution we did

[sudden marten]

true

[errant citrus]

f(b) would be changed to b and f(a) would be changed to a

[sudden marten]

aight i see how the left becomes bf(b) - af(a) but how to do tjat last integral

[errant citrus]

The last integral is

@sudden marten

[sudden marten]

yes but how

[errant citrus]

Because we did our substitution like that, f of inverse of f(x) is x

x = f(t)

Inverse of f(x) = t

f(inverse of f(x)) = f(t) = x

[sudden marten]

would u be able to write out the steps to rewrite int(f(t)dt) in that form

in still havin a hard time i apologize

[errant citrus]

Maybe, let me write it

[errant citrus]

It's fine

@sudden marten is it better

[sudden marten]

oh yeah that makes sense :) thank you !

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[errant citrus]

No worries ^^

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[dense fulcrum]

can someone help me with boolean algebra?

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@dense fulcrum Has your question been resolved?

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@dense fulcrum Has your question been resolved?

[hard atlas]

.

you wont get anything unless you ask your question

dont just say no to the bot

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[dense fulcrum]

i asked it yesterday but nobody answer me

[civic otter]

Well, here no question appears

[hard atlas]

and you thought you would have better luck now without even asking the question?

no one is going to search through your post history

[dense fulcrum]

ok i'll ask it

[dense fulcrum]

nono i don't mean that

[atomic jasper]

we cannot read your mind

[dense fulcrum]

hi, I'm stuck in this step of simplifying minterms in boolean algebra (the first photo). In the attachment I leave the 2 possible results obtained from the Karnaugh maps (second and third photos) and the initial function where I obtained the 2 maps (fourth photo)

[dense fulcrum]

yea i know but yesterday i asked the question and no one aswerd me, i was just asking if in this server people also help with boolean algebra

[atomic jasper]

if you have a specific question in a certain area then perhaps its better to ask in the early-university channels

[dense fulcrum]

where can i find it?

ops

[atomic jasper]

its below the help channels, scroll further down

[dense fulcrum]

i just find it

[dense fulcrum]

yep

[atomic jasper]

im not sure in what category this would go though

but you probably know better

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@dense fulcrum Has your question been resolved?

[dense fulcrum]

nope

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@dense fulcrum Has your question been resolved?

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[ember verge]

this is a pretty simple problem but

im confused for c

it says to find when v(t) = 0

i could also do a(t) = 0

[chilly condor]

When the particle is at rest, it’s not moving.

[edgy kayak]

what an insight

[ember verge]

but i chose to do v(t) = 0 but im getting $sin(2{\pi}t) = 1$

[twin meteor]

gamer75431

[chilly condor]

This wouldn’t be right. Throw a ball into the air. At some point it will be at instantaneous rest and then it will come back down but it is always accelerating with -g.

[tidal umbra]

acceleration being 0 doesn't mean something ain't moving

[ember verge]

oh

nvm then only velocity

[edgy kayak]

indeed

[ember verge]

but how can i evaluate this

[chilly condor]

If you find it easier let q = 2pi t, find the values of q then rearrange to get t misread your question I think

[ember verge]

first deriv gets me $2\pi - 2{\pi}sin(2{\pi}t)$

[twin meteor]

gamer75431

[ember verge]

oh i see

[chilly condor]

Wait, what exactly is the thing you are confused about doing?

[edgy kayak]

arcsin(1)/2π = t
that is how you solve it

[ember verge]

so im trying to find for what values of sin(x) = 1

which would be pi/2

and then do i say 2pit = pi/2

cuz x = 2pit

[chilly condor]

That’s how you get one of the solutions. It would be good practice to check there are no more within range to be sure

[ember verge]

yeah i have to check the domain of 0 and 3

[chilly condor]

Yep

[ember verge]

alr

[chilly condor]

But make sure you adjust your range accordingly.

[ember verge]

t = 1/4

[ember verge]

wdym

[chilly condor]

If you have sin(t) = 1 for t in range 0 to 3, that would actually be sin(q) = 1 for q in range 0 to 3/2pi

[edgy kayak]

arcsin(1) has multiple solutions yes

[ember verge]

how did you get this?

[chilly condor]

As I understand it, arcsin(1) has one solution, otherwise the function would not be… a function

[ember verge]

you mean domain when you say range right?

[chilly condor]

Oh sure.

[ember verge]

yeah so how are we manipulating the domain when we assume q = 2pit

[chilly condor]

Oops- I believe I got it wrong. 0 < t < 3, then 0 < 2pit < 6pi. Just multiply by 2pi

[edgy kayak]

ah yes I stand corrected

[ember verge]

oh i see

so we are saying that since the argument is 2pit (instead of t) that the domain is also equivalent to what you've said

[chilly condor]

Yep, you find the solutions for your new variable where that lives and then translate them back to be solutions for your old variable where it lives.

[ember verge]

right ok

so now what bounds do I check still?

do i also have to check when 2pit = 6pi

and when 2pit = 0

i mean check t = 3 and 0 into v(t)

see if they are also 0

[chilly condor]

You find the solutions to v = ds/dt =0. Luckily you already have v(t), so just set v(t) = 0.

[ember verge]

no i have found that t = 1/4 when i set the derivative = 0

[chilly condor]

Sure.

[ember verge]

don't i have to check when t = 3 and t= 0 now?

[chilly condor]

Why?

[ember verge]

like v(3) and v(0)

couldn't they also be at rest there

[chilly condor]

I believe you only have to use the solution(s) to v(t) = 0. There’s no need to check 3 and 0 separately if they aren’t solutions to v(t) = 0 because then of course if you sub them in you won’t get 0

[ember verge]

oh yeah fair enough

thank you

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[ember verge]

.reopen

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✅

[ember verge]

if it asks for max velocity then i'd have to check them right

[chilly condor]

The maximum velocity would at a(t) = 0, then you obtain some time and substitute that into v to see what the velocity is. Alternatively the acceleration might be constant or something in which case it would occur at an endpoint. So yes

[ember verge]

okok thank you

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[bold laurel]

I'm reading bagging predictors paper. And I came across this notation. It almost my first time encounter such notation in set theory like this. How it is different than the usual I studied and where it came from?

[bold laurel]

https://link.springer.com/content/pdf/10.1007/BF00058655.pdf

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@bold laurel Has your question been resolved?

[cyan talon]

How it is different than the usual I studied
hard to say if you don't tell what's your usual

[bold laurel]

{(y_n, x_n) | n ∈ {1, 2, 3, ..., N}}

[cyan talon]

it's literally the same thing really

[bold laurel]

I know, but I'm not sure it got me confused

[cyan talon]

a dataset with N examples, and each example consists of a vector of inputs x, and an output y you wish to predict

[bold laurel]

Okay, do u know why he used this notation?

[cyan talon]

no

it's just a purely stylistic difference, you're paying attention to it too much

[bold laurel]

Oh yeah that's what I want to know

[cyan talon]

like n in {1, ..., N} or n=1,..., N represent the same thing, n ranges from 1 to N

[bold laurel]

Is there any reference or sources could help with that?

Like history of math notations or anything

[cyan talon]

I'm not sure reading a source about history of notation would necessarily help with day-to-day paper reading

unless you're reading centuries-old sources

in this case why not

[bold laurel]

Yes

[cyan talon]

1996 isn't centuries old afaik

[bold laurel]

I'll close this channel. Thank u

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[rugged orchid]

<@&268886789983436800>

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[summer mortar]

Pls help
23x(x²×2×53)[2x+7(2x×4)+21]÷2

[vocal sleet]

Please don't occupy multiple help channels.

[flat whale]

#help-1

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[charred mirage]

So recently I made a question in my maths book and I was off by about 11 degrees. Did I do something wrong in my calculation or is it just wrong from the start?

[charred mirage]

Bgtan is arctan btw

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[paper depot]

well even if your calculation is correct it looks very painful to have trig functions of 90-x in there

so i think the way you did it isn't worth the effort

[charred mirage]

Alright

I can do the way the book did it I just tought it was easier that way but it didn’t work out

[charred mirage]

Quick question , could you explain why it’s painful to have it there

[paper depot]

does not let you simplify much

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[acoustic patio]

How would I find the area?

[acoustic patio]

I had to solve a similar one before, but all I got was 5=5 and things like that

[edgy kayak]

is that all the information you have?

[acoustic patio]

Yes

[edgy kayak]

as far as I know, you cannot solve this with just that much information

[acoustic patio]

I'll try to assume something, thanks

.close

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[shadow orchid]

Hi, could I have help w/ this

[reef agate]

Do you know how to approximate the slope of P(t)

[shadow orchid]

y2-y1/x2-x1?

[reef agate]

Since we care about t = 9 and t = 11

Or rather:

[tepid fern]

..

.reopen

[reef agate]

We care how much P(t) will increase betwen t = 9 and t = 11

[tepid fern]

.close

[shadow orchid]

right

[reef agate]

This is a diff channel now

[shadow orchid]

ya get ur own channel

[tepid fern]

Idk how

[shadow orchid]

the ones that say available

#help-30

[reef agate]

So, ideally, we would have the slope of the line at t = 9 and t = 11, right?

[tepid fern]

Where

[reef agate]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[shadow orchid]

right

[reef agate]

But since we dont have those slopes, we need to estimate the slope. We must use the closest given datapoints to find an estimate

Do you understand this?

[shadow orchid]

mhm

so we would use 3 and 4?

[reef agate]

For purposes of this $P(t)$, I'll modify the change:
$$\frac{P(b) - P(a)}{b - a}$$

[twin meteor]

Unban il798li

[reef agate]

So whats the average slope between t = 3 and t = 4

[shadow orchid]

One sec let me calculate it

0.4

0.4 mil/hour

[reef agate]

So we're going to assume that 0.4 is the slope for all t > 4

Do you understand this?

[shadow orchid]

Yep but i have a question

we know that the slope between 2 and 3 is 0.7 so is it still ok to assume that its 0.4

oh wait

i read that wrong

t greater than 4

my bad

i understand

[reef agate]

So whats the total change in P between t = 9 and t = 11

[shadow orchid]

0.8

Ohhhhh

that makes so much more sense

i thought we had to do like some sort of complex math

thank u so much!!

[reef agate]

Np

[reef agate]

There will be better ways to estimate as you progress further in math

[shadow orchid]

right that makes sense

I guess i should close this now right

[reef agate]

Ya

!done

[vocal sleet]

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

[shadow orchid]

.close

[vocal sleet]

Channel closed

Closed by @shadow orchid

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sudden delta]

where would i start with this

[bitter pilot]

n divisible by 13 means n = 0 mod 13

try to solve for x

||you will need to find the inverse of 10 mod 13||

[sudden delta]

sorry for late response

what does mod 13 mean

[bitter pilot]

mod means modulo

which gives the residue of a number divided by 13

since n is divisible well the residue is 0

but if you are not familiar with modular arithmetic then you'd probably have to consider different means

if n is divisible by 13 then for some integer k you have n = 13k

10x+y = 13k

now my suggestion is try to recreate x+4y on one side and see if the other side factors 13

[vocal sleet]

@sudden delta Has your question been resolved?

Channel closed

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[surreal bear]

help

[flat whale]

!show

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

@surreal bear Has your question been resolved?

[vocal sleet]

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Closed due to timeout

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

[azure fox]

genuinely confused

[tidal salmon]

well lets try writing this out

and slowly simplify

do you know cos and sin law?

or the ratios at least?

[azure fox]

no

im in geometry 😭

we didnt learn any of that yet

[tidal salmon]

ok thats fine still

i just have to think of diff way to explain it

[azure fox]

i know pythagorean

so thats how i got the one

and im assuming its the same for the other one aswell

[tidal salmon]

thats all you need lol

and other things

do you know similar triangles?

[azure fox]

yeah thats what we r working on

[tidal salmon]

ok perfect

there are two triangles here

can u name them?

[azure fox]

uhhh idk

wed have to make a point

at the

middle part

[tidal salmon]

no i mean

if you look at it

theres triangle 1, the big one, with sides cbd

then the small one

with sides

16,12,20

[azure fox]

ohh

[tidal salmon]

now

similar triangles state

when there are two triangles

with the same angles

the sides have the same ratios

[azure fox]

yeah

[tidal salmon]

so why dont you take those two triangles

and draw them side by side

because they both share the same angles

right angle, angle A and then the last one

[azure fox]

the uhh

angle there

[tidal salmon]

doesnt matter lol

think about it

the actual values about the angles dont matter

as long as you know they are the same

[azure fox]

yea

so angle A and C?

[tidal salmon]

not C

just A

[azure fox]

oh

[tidal salmon]

because C gets cut in half, for the smaller one

[azure fox]

ohhh yeah

[tidal salmon]

or not half exactly

[azure fox]

but they share the

[tidal salmon]

Angle A

[azure fox]

yes

[tidal salmon]

so now you have two triangles, with the same angles and the values of all sides for oen triangle

and one side of the big traingle

all you have to do is solve for them

[azure fox]

so uh

16 12 and 20

im so confused

how to find side a

[tidal salmon]

alr do you want me to draw it out for you?

[azure fox]

sure

[tidal salmon]

gimme a sec

here you go

lemme know if anything i wrote doesnt make sense

@azure fox

[azure fox]

sorry

[tidal salmon]

?

sorry for what?

[azure fox]

i was lowk unfocused

[tidal salmon]

nah its all good

[azure fox]

ohhh so

[tidal salmon]

as long as you get the problem and how to do it thats all that matters

[azure fox]

wait so do i find numbers

😭

[tidal salmon]

i thought u learned similar triangles?

its pretty much small/big = small/big

so in this case, 16/20 = 12/d

it also works the other way

like big/small = big/small

[azure fox]

yeahh ik that

i know how to decipher if they are similar triangles

[tidal salmon]

well i showed you how

as long as you know

that they have 2 smae angles

they are similar

then you just put the side by side, with the angles in the same positions

and ur good to go

[azure fox]

ohhh ok

thanks

[tidal salmon]

np

[azure fox]

ohhh i understand it now

d is 15

[tidal salmon]

and c is?

[azure fox]

ohhh i understand

i have to do pythagorean