help-17

[manic copper]

Hi, I’m working on an optimization problem

It’s the first time I’ve done one of these with… absolutely no numbers involved

And I’m wondering how I’d even take the derivative of this

Since R and V1 and V2 can all be a multitude of things

[lucid bane]

you should be dividing by velocity instead of multiplying, no?

v=d/t => t=d/v

[manic copper]

...ah

setting that aside -

how do i take the derivative of this

[lucid bane]

well there is only one variable this depends on

think about this more as what you can vary in this problem, what this is a function of

[manic copper]

i had thought it'd be dependent on R

[lucid bane]

what is the one thing you vary in this problem?

[lucid bane]

what is R

[manic copper]

radius

[lucid bane]

do you see what's wrong with that?

[manic copper]

uh... let me think

oh, theta is independent from r

[lucid bane]

r is the radius of the circle

its going to be constant

[manic copper]

ahh...

so theta is the only thing that actually changes

[lucid bane]

indeed!

[manic copper]

okie doke - one further question

if it was just theta and numbers, i could take the derivative

but what's tripping me up is the other variables

how do i account for those when i take the derivative of theta

do i also apply the derivative rules for variables

[lucid bane]

well you seemed to have a good approach in the problem (aside from the not dividing error)

[manic copper]

my question is more just procedure at this point 😅

[lucid bane]

wydm

[manic copper]

i genuinely don't know how to derive when there's two variables in one equation

like if it's x^2+y^2=100, i dont know how to take the derivative of this

[lucid bane]

implicit differentation

treat y as a function of x

[manic copper]

ah...

[lucid bane]

so it would be 2x+2yy'=0

(chain rule)

[manic copper]

why does the chain rule apply here?

[lucid bane]

y(x)

[manic copper]

o

[lucid bane]

d/dx (y(x)^2)=2(y(x))y'(x)

or in shorthand 2yy'

[manic copper]

ohh

that makes sense

so in terms of my equation i'd have to take...

wait, but if R and theta and V dont depend on one another, how can i implicitly differentiate them?

[lucid bane]

say you know dx/dt dy/dt then x^2+y^2=100 becomes 2yy'+2xx'=0

[lucid bane]

R is the radius of the circle

does R change?

[manic copper]

it wont, no

since. it can be for any R

[lucid bane]

so its a constant, so it doesn't matter

[manic copper]

do i treat it like a constant when i differentiate it?

[lucid bane]

yes.

[manic copper]

oh, neat

[lucid bane]

T will be a function of purely theta

[manic copper]

so the 2r^2 part just becomes 0?

[lucid bane]

yes, but remember that your set up was wrong from the beginning

t=d/v

[manic copper]

yeye - so sorry for getting that mixed up

[lucid bane]

or in your case t=d1/v1+d2/v2

[manic copper]

i'll correct it when i go on my second pass through

as for v1 and v2

those can also be anything, and dont depend on theta

so do i treat those as constants as well

[lucid bane]

yea

[manic copper]

wow, everything sure turns into constants real quick

okay, let me try differentiating it and reporting back

[manic copper]

okay, derivative complete!

i think

[lucid bane]

you're supposed to be taking derivative with respect to theta rather than time

[manic copper]

...drat

oohkay give me another uh

five - fifteen minutes

i thought i did, though

unless i

woefully misunderstood how implicit differentiation worked

wait i

genuinely dont understand

what "with respect to theta" means in this case

[lucid bane]

d/dx(x^2+y^2), (d/dx) is read as derivative of with respect to x, in this case it would be 2x+2yy'

say x and y are both functions of t, x(t), y(t), then if we have d/dt(x^2+y^2) (the derivative with respect to t)

[manic copper]

in this case - since all the variables except for time are independent of theta...

oh, i see

so the time part on the left side of the equal sign

[lucid bane]

then this would be 2xx'+2yy' where x'=dx/dt and y'=dy/dt

you wrote d/dt, you're not taking derivatives with respect to time here, you're not supposed to

[manic copper]

i think that's just me... not knowing how to write the thing for derivatives

but i did take the derivatives in respect to theta

i think i just wrote the symbol wrong

[lucid bane]

oh also, why is there pir^2 in n

i just realized

n is a distance around the circumference

[manic copper]

... oops

that one is completely my fault

i'm doing this at 5:30am with very little sleep

[lucid bane]

also you should probably put it in terms of radians

rather than degrees

no neeed to divide by 360 or subtract 180 that way

[manic copper]

all very true

just to confirm something -

after i've rewritten it all

this gives me a formula i can try to find a 0 for, which will be the most optimal point for the boat to dock

well i guess it'll uh

give me a series of most optimal points since it's a sin function

[lucid bane]

theta will be within a given range that makes sense

do you see what range it'll be in

(in radians)

[manic copper]

0-pi, i think?

0 to 180 degrees, so 0-pi

[lucid bane]

yes

so this will narrow your options

[manic copper]

and i'll be able to pick the 0 that falls within that range as my answer

that makes sense! thanks so much for your help

[vocal sleet]

@manic copper Has your question been resolved?

Channel closed

Closed by @manic copper

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>.
• 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.

[jagged rock]

this might be a stupid question but does

[jagged rock]

,,\int_{a}^{b}f^{-1}(x)dy = \int_{a}^{b}f(x)dx

[twin meteor]

daniel naniel

[vocal sleet]

@jagged rock Has your question been resolved?

[vocal sleet]

@jagged rock Has your question been resolved?

[leaden ingot]

It's not always true

But this one is true, though (only if f(x) is strictly monotone)

let c = f(a) and d = f(b), then:

[twin meteor]

TargetVN

[leaden ingot]

You can prove simply by visualization

[vocal sleet]

@jagged rock Has your question been resolved?

Channel closed

Closed by @jagged rock

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>.
• 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.

[near vigil]

when proving a function doesn't have an inverse, it is sufficient if i could show the function is either not injective or not surjective. Or do i have to show it is neither injective nor surjective?

[mental egret]

It's fine to show even one cause both are necessary for it to bijective, thus, have an inverse

[near vigil]

.close

[vocal sleet]

Channel closed

Closed by @near vigil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[twilit sand]

S*S1=T^2 is valid for general conics also to find pair of tangents from a point??
if yes the please open this file the result i am getting is not even straight line
https://www.desmos.com/calculator/xuns99yiap

[vocal sleet]

@twilit sand Has your question been resolved?

[vocal sleet]

@twilit sand Has your question been resolved?

[vocal sleet]

@twilit sand Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sleek flame]

I dont understand how c1-k1m1-k2 would be congruent to 0

do you think of it like basic algebra

if you bring all the terms to the left side, then its 0 on the right side?

ahh ok i see

perfect ok

then how do you deduce that the determinant of the 3by3 matrix would be congruent to 0?

I guess cause its a multiple?

also @dull bear ! hii

long time lol

[dull bear]

Hiii it has been

[dull bear]

And e.g. you have a non zero element in the kernel of said matrix (i.e. something that isn’t zero gets sent to zero when you multiply by the matrix)

[sleek flame]

so any non zero element will do?

so if you have a 3 by 3 matrix and 8/9 are 0s but 1 of them is a num, then you can deduce determinant would be congruent to 0?

@dull bear

[vocal sleet]

@sleek flame Has your question been resolved?

[vocal sleet]

@sleek flame Has your question been resolved?

[dull bear]

Sorry was out and about

[sleek flame]

lol dont worrryyy

[dull bear]

The non zero element thing I was referring to is this, basically:

[dull bear]

(Urgh my internet was acting up )

[sleek flame]

ohh yes

kernel

haha lol

ok

my lin alg skills are bit rusty

😅

[dull bear]

Awwwww it do get that way sometimes

[sleek flame]

gonna stay here again

[sleek flame]

im confused

but wouldnt getting 1000 today be better? cause you get 1000 net

but if you borrow 1000 at 6 percent, you only have net 40, because 1100-1060=40

idk this might be a stupid question

oh is it asking would you rather get 1000 today or 1100 in a yr, but in both cases you borrow 1000 at 6perc, so it would result in 60 loss for 1st case, and 40 gain in 2nd?

[sleek flame]

yes its asking that

[vocal sleet]

@sleek flame Has your question been resolved?

[sleek flame]

here for 30more min

[vocal sleet]

@sleek flame Has your question been resolved?

[vocal sleet]

Channel closed

Closed by @sleek flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[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>.
• 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.

[pulsar star]

how to solve this question

the closes i got to the original graph function was y = 1/2(y-2)^2 - 2 = x

[pulsar star]

i got it wrong

i just noticed that

[ruby slate]

there's a formula for the vertex

[pulsar star]

this question

I need help with this im a bit lost

i thought completing the square and getting the x values

but i dont know if thats right

[ruby slate]

to make it more economic you should find the maximum

since you want the biggest amount of miles per gallon

[pulsar star]

i see

[ruby slate]

have you done derivatives?

[pulsar star]

i dont think so

[ruby slate]

so just use the vertex formua

formula

pay attention and check if the vertex is between 0 and 70

to better understand this you could draw the graph

[vocal sleet]

@pulsar star Has your question been resolved?

[pulsar star]

i dont know if i did the vertex form right

but -1/30(v + 7.5)^2 + 1.875

and i calculated that maximum is 1.875

and smallest is -198.33 which shouldn't be the answer

[vocal sleet]

@pulsar star Has your question been resolved?

Channel closed

Closed by @pulsar star

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[broken orchid]

hi, i'm unsure about what the alpha and beta means in the beta distribution

[flat whale]

They're just parameters of the distribution

https://en.m.wikipedia.org/wiki/Beta_distribution

They're called shape parameters

plot the density for different values to see their effect

[vocal sleet]

@broken orchid Has your question been resolved?

Channel closed

Closed by @broken 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>.
• 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.

[mystic jungle]

what did my teacher do where my pencil is pointing to get the (3x+1) from the equation above

[flat whale]

Factored

[mystic jungle]

thanks

.close

[vocal sleet]

Channel closed

Closed by @mystic jungle

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>.
• 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.

[sullen lintel]

think about it logically, what is 8+8+8?

[vocal sleet]

@autumn oak Has your question been resolved?

[sullen lintel]

@autumn oak do you know how to add?

ok what is 8+8?

great

so what you did is 8x2

[drifting jackal]

Are you trolling?

[sullen lintel]

now we add 8+8+8

what is that?

yes good job

you have solved it

that is 3x8

that is how you can simplify your question into

[vocal sleet]

@autumn oak Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

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>.
• 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.

[fast perch]

Each of the 5 vertices of a pentagon in your notebook is connected to the other 4 points with colored pencils. You get to choose between a blue pencil and a green pencil for each connection. Can you choose a coloring such that no blue triangle nor green triangle is formed?Can it be solved with Ramsey theory?

[vocal sleet]

@fast perch Has your question been resolved?

[fast perch]

<@&286206848099549185>

[vocal sleet]

@fast perch Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[main cosmos]

Find maximum of

[main cosmos]

1-sqrt(x^2+y^2)

123

So the problem i have occured is that that the point where second derivative is 0 is also the point the derivative should not exist

Isn't it?

Also the next derivative does not have any value in thst point

[tidal dock]

you don't need derivatives for this

sqrt(...) >= 0 always

so the biggest 1-sqrt(x^2 + y^2) can be is when sqrt(x^2 + y^2) is smallest

[main cosmos]

Okey but lets assume

I do neet to use

The derivative technique

Is the trick about

Doing it?

[tidal dock]

,rccw

[tidal dock]

i don't understand your question

what is the smallest sqrt(x^2 + y^2) can be?

[main cosmos]

I understand your solution

But

I am not sure if I can do it that way

Its for uni

[tidal dock]

i get it

a maximum of a function can occur where the derivative is undefined as well

[main cosmos]

Okey do this one can't be done using derivatives?

Or will my trick work

?

[tidal dock]

i don't understand you trick, sorry, but it definitely can't be done with derivatives

[main cosmos]

Okey thank you

[vocal sleet]

@main cosmos Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[manic karma]

0=0
20-20=25-25
(4×5)-(4×5)=(5×5)-(5×5)
4(5-5)=5(5-5)
(5-5) cancelled by itself
Hence 4=5
How?????🤥

[lucid bane]

dividing by 0

[manic karma]

So what

It is possible

If we divide zero toffees in zero children everyone will get zero toffees

You must think logically

[hoary umbra]

you can shorten this proof by saying $1=0$ -> $0 * 1 = 0 * 0$ -> $0=0$ so it's true

[twin meteor]

Horsi135

[manic karma]

Aaanyen Baingan

[manic karma]

What's this

I am in 8th standard

[bronze osprey]

everyone implies there even are people in the first place

[manic karma]

Pls speak a bit simple English

[bronze osprey]

more like your English isn't good enough bhai

[manic karma]

Indian?

[bronze osprey]

the reason why 0/0 is undefined is

imagine we make 0/0 = x

then multiplying both sides by 0, we get 0 = x * 0

so like x can be anything, and so there's no single answer to what is x

[manic karma]

I am the question to every answer in the world

But I can't question this answer anymore

😂

[mental egret]

A troll's entered the server. Guess who.

[manic karma]

Who?

[manic karma]

Who is that troll

@Helper I am hosting a helper to owner to tournament, I will type a random question and the helper who answers first wins

[bronze osprey]

your teacher should do this to students in your class

[manic karma]

What is cube of square of cube of square of 66666 - third multiple of 3 * 8382882882288

[mental egret]

457676198201768032629382852705687443566909608973383796930425595934135060199099001682380774093229824241048541823124781754146332224533244756019823362651727816647998719136974224

.close

[vocal sleet]

Channel closed

Closed by @mental egret

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[random knoll]

i am not to sure how to go about this question

[vocal sleet]

@random knoll Has your question been resolved?

[random knoll]

<@&286206848099549185>

[molten imp]

Well I am not totally sure but you could get the moment at C and B and since it is not moving so the force upwards equals the force downwards

Then maybe you cloud resolve the force with the angle to get the tension

[random knoll]

would angle A be 110 ?

[molten imp]

Wouldn’t it be 79

[random knoll]

How ?

[molten imp]

No sorry

It’s 110

It’s a corresponding angle

[random knoll]

yeah i thought so

but i got it now anyways

.close

[vocal sleet]

Channel closed

Closed by @random knoll

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>.
• 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.

[frozen bone]

hi

[reef agate]

Do you have a question

[frozen bone]

i need help

explaining

i cant quite understand

how to solve

uhm it's about trigonometric functions of any angle

[candid magnet]

[reef agate]

!original

[vocal sleet]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[hushed pewter]

@frozen bone you need to share the question for us to help you

[frozen bone]

what I meant is i need tutoring/tips on how to solve

[hushed pewter]

We're not really a tutoring server. We just help you with specific questions

[atomic jasper]

just send the question and we can help you with it

[hushed pewter]

Your best way to utilize this server is to find specific problems you are struggling with, and then we can help you learn from that

[hushed pewter]

But we don't really start teaching anyone from nothing. You have to drive your own learning by coming to us with a specific problem

[hushed pewter]

Perfect

[hushed pewter]

For 1, this looks like an application of knowing your unit circle, and perhaps knowing your half angle formula

[frozen bone]

okay

how about number 2?

[hushed pewter]

That looks like you need to know your sohcahtoa and circle quadrants

[vocal sleet]

@frozen bone Has your question been resolved?

Channel closed

Closed by @frozen bone

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[sudden mango]

i am having trouble with part 9 (iv), i got 3 different answers with 3 different methods, but im not sure exactly how to do the method especially considering that this isnt uniform acceleration

[sudden mango]

this is the closest i could get (the answer is 15.12 m/s)

here is the full speed-time graph

[frozen bobcat]

average of a continuous function is the integral divided by the length of the interval

so you should find the area under the curve and divide by the length of the interval

[finite mist]

Bro this is a simple physic

He probably doesnt know integral yet

[frozen bobcat]

So, use the shapes given by the function to find the area of each region, that's the area under the curve. Then divide by the length of the interval.

[finite mist]

@sudden mango

Well

My writing is very messy

And I didnt use the standard form

But u get the idea

[vocal sleet]

@sudden mango Has your question been resolved?

Channel closed

Closed by @sudden mango

Use .reopen if this was a mistake.

[sudden mango]

thank you 🙏

[finite mist]

lol

[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>.
• 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.

[heady quest]

Yo how did they get cos9x + cosx here

[flat whale]

do you know $\frac{a}{b/c} = \frac{ac}{b}$

[twin meteor]

riemann

[flat whale]

when you divide by fractions, you multiply by the reciprocal

[heady quest]

I dont know abt this

[flat whale]

https://www.youtube.com/watch?v=RAKwouL-lTc

[heady quest]

Do i just watch this?

[flat whale]

it's just basically this with actual numbers

[heady quest]

Bruh i know about this ☠️

Im in college not kindergarten

[flat whale]

so what are you confused about here?

[heady quest]

Yes i meant how did we get cos9x and cosx

From cos5xcos4x

[flat whale]

did you understand the right side

[heady quest]

I understand the rules but i dont know why he added and subtracted the angles

Its multiplied

But we'd just get 2cos5xcos4x in the end

[flat whale]

yes

this

equals 2 times

this

so they divided by 2 to solve for cos(5x) cos(4x)

[heady quest]

How does it equal two times that

sry if i sound stupid but highschool just made me cram

[flat whale]

did you understand this?

[heady quest]

Uh not really... It was multiplied how did they add the two angles

[flat whale]

,tex .sum diff trig/cos

[twin meteor]

riemann

[heady quest]

yeah i know about the law.. im just saying to use it isnt it supposed to be cos(a+b) so we add them?

Theres multiplication between the two cosines

[flat whale]

what is "them"

[heady quest]

Cos5xCos4x

[flat whale]

can you leave? thanks

[heady quest]

no wait if hes explaining it that'd be much better than answering

[flat whale]

also don't ping me for no reason

[spiral mortar]

yeah but he doesnt need to be all "Them" "Define mathematics 🤓 "

[flat whale]

the right side has this term yes

[heady quest]

dont involve urself

[flat whale]

#help-17 message

[spiral mortar]

i can be here if i want i wanna learn too

[heady quest]

How did there become a left and a right side?

[flat whale]

then 🤫

[heady quest]

all they did was add cos(a+b) and cos(a-b) even though the two cosines are multiplied not added

[flat whale]

they're using two equations here to solve for cos(5x)cos(4x)

[flat whale]

use this with theta = 5x and phi = 4x

[heady quest]

Okay but why

I just wanna know why he did this first

[flat whale]

to solve for this

[heady quest]

Yes but it isnt like cos(5x+4x)

It is multiplied

Like cos5x * cos4x

[flat whale]

the right is

[heady quest]

Can u rewrite it on a piece of paper or like on paint

So i can get a better picture of whats going on

[flat whale]

i would just write this

you're solving for cos(4x)cos(5x)

so add the two equations

[heady quest]

Yes... But whyyyyy

[spiral mortar]

Do you know product to sum formula?

[heady quest]

I dont know?

can u show me

[flat whale]

to find the limit

oh i see

[heady quest]

Bro i know i just want to know why they added cos(a+b) and cos(a-b) to eachother even though they are multiplied cos5x cos4x

[flat whale]

you can just plug in 0 here to get 0

[spiral mortar]

cos(A)cos(B)=
1/2 [cos(A+B)+cos(A−B)].

[heady quest]

Thatd be infinity

not what i want

[flat whale]

no

[flat whale]

cos(0) = ?

[spiral mortar]

@heady quest

[heady quest]

Oh

finally a law

[spiral mortar]

yeah

use it

[heady quest]

thank u so much

[spiral mortar]

np

[heady quest]

♥️♥️♥️

.close

[vocal sleet]

Channel closed

Closed by @heady quest

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>.
• 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.

[empty tiger]

So when I solve it I get 1/2 when I put it into a calculator I get 1/2 but the back of the book says the answer is -4 any idea what's going on?

[bitter pilot]

can you describe how you solved it or typed into calculator?

[sly sierra]

you used 5 - - 3^2

instead of 5 - (-3)^2

[empty tiger]

oh yep your right

thanks lol

.close

[vocal sleet]

Channel closed

Closed by @empty tiger

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>.
• 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.

[balmy plaza]

-3 to 3 is the standard deviation?

[atomic jasper]

1 is the standard deviation

[balmy plaza]

how do you know that from there?

[balmy plaza]

so the middle line indicated standard deviation?

[balmy plaza]

in this, it's 1?

[atomic jasper]

the x-axis is in terms of standard deviation

the 1 means one standard deviation

[balmy plaza]

x is vertical or horizontal

[atomic jasper]

2 means 2 standard deviations

[atomic jasper]

horizontal...

[balmy plaza]

horizontal is this

?

[atomic jasper]

yes

| vertical is this

[halcyon imp]

Think about the horizon if that helps

[balmy plaza]

so one SD, two SD is the measurement of how far a something is from the "mean"?

[atomic jasper]

https://en.wikipedia.org/wiki/68–95–99.7_rule

[halcyon imp]

That's what you usually use it for yes, but the SD itself is just a number which depends on your distribution

[balmy plaza]

and 2.1% is SD?

[atomic jasper]

no

standard deviation is just a number

and is calculated as:

[balmy plaza]

you said that the SD is 1

because it's one between each number

[atomic jasper]

$\sigma=\sqrt{\frac{\sum (x_i-\mu)^2}{N}}$

[twin meteor]

Bonk

[atomic jasper]

thats because in that graph its scaled that way

[balmy plaza]

what is the SD?

around 22,5?

[atomic jasper]

its roughly 3

[balmy plaza]

why?

its nearly in the middle of 20 and 25

[atomic jasper]

that distance

is the SD

[balmy plaza]

and there's always 3 SDs?

i think i udnerstand now

[atomic jasper]

wdym?

standard deviation just means how spread out your data is

[balmy plaza]

you said 66 99.7 rule

[atomic jasper]

consider this:
1,3,5
2,3,4

[halcyon imp]

No, there's only one per distribution

[atomic jasper]

what is the standard deviation of the first and second set?

(they both have the same mean)

[atomic jasper]

68% of all the points fall in the range of mu-sigma<x<mu+sigma
99.7% of all the points fall in the range of mu-3 * sigma<x<mu+3 * sigma

thats what that rule means

[balmy plaza]

1.63

0.82

why?

[atomic jasper]

wdym why?

[balmy plaza]

can u show me this on something like this?

[atomic jasper]

do you notice that the SD for the first set is higher than the second set?

[balmy plaza]

or this

[atomic jasper]

that works better with a lot of points

[balmy plaza]

1,63 plus 1,63 is not 3

[atomic jasper]

why would that be the case?

[balmy plaza]

se... those need to be equal

[atomic jasper]

what?

consider this data

the line is the gaussian fit

the peak is at the mean

and how wide it is depends on the SD

you can imagine that if there were more points beyond 6 and 14 that the black line would be further stretched out

[balmy plaza]

ok...

[balmy plaza]

wheres the sd?

[atomic jasper]

you calculate that from the data

its very roughly this

so like 1.2?

very roughly

[balmy plaza]

and people inside this box, qualify in the "standard deviation?

[hybrid cradle]

Sorry guys, can you help me?
Can you do the study of this function "f(x)= 2ln(x) - ln^2 (x)"

[atomic jasper]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[atomic jasper]

idk what you mean by that

what do you know about statistics

[balmy plaza]

so for SD, there isn't "he's below or above SD" like with average,

he's below the average height so he's not attractive

for example

[atomic jasper]

i still dont know what you mean

but you kinda use the sd to compare how far off the average you are

if you have smth like, the average is 24 and your score is 26

doesnt tell you much

but then if you know the standard deviation is 1, then a score of 26 is quite high

[balmy plaza]

how u know that

[atomic jasper]

thats what the standard deviation means

its the spread of the data

high sd = high spread

low sd= low spread

the left has higher SD than the one on the right

[balmy plaza]

here.... are the grades, and the SD is 1,99

what does it mean?

[atomic jasper]

beacuse on the left its more spread out

[balmy plaza]

and how is that getting 1,99?

show me the 1,99

@atomic jasper

<@&286206848099549185>

[atomic jasper]

!noping

[vocal sleet]

Please do not ping individual helpers unprompted.

[atomic jasper]

You can calculate the sd

[atomic jasper]

Right here

[balmy plaza]

and mark sd here

?????

[vocal sleet]

@balmy plaza Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[median knoll]

Need help

[median knoll]

Hello

<@&286206848099549185>

I don’t need help help I just have a question for my work

[sly sierra]

just ask the question

[flat whale]

!15m

[vocal sleet]

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.

[median knoll]

#advanced-lounge

[flat whale]

read and follow this

this is the right place to ask. what you haven't done is ask a question

[median knoll]

Would A and D equal each other or would it be A+D=180

[flat whale]

,rotate

[flat whale]

angle A and angle D certainly don't look like they're equal

[median knoll]

for any problem that I have like this one where A is on the left and D is on the right or it says any letter then it will always be =180

right

and if A was in C’s place instead of being on the bottom left it would still be A+D=180

[flat whale]

yea angle A+ angle D = 180degrees in a parallelogram. they're called supplementary angles
https://www.cuemath.com/geometry/properties-of-parallelograms/

[median knoll]

Alr ty

bye bye

[vocal sleet]

@median knoll Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

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>.
• 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.

[remote hinge]

yo dude whats up....

[reef agate]

Do you have a question?

[remote hinge]

yo dudeee

thoughts dude

does E sound right

@reef agate

[reef agate]

❌

[remote hinge]

do you know the right answer

[reef agate]

Yes, but you need to figure it out

If you dont know how, you can tell me and ill help

[remote hinge]

can you help me figure it out

i dont know how

can you help

[reef agate]

So for each interval:

$\dv{y}{x} > 0$ if $f(b) > f(a)$

[twin meteor]

King Leo

[reef agate]

$\dv{^2y}{x^2} < 0$ if $f'(b) < f'(a)$

[twin meteor]

King Leo

[reef agate]

You might need to change a and b, but make sure b > a

[remote hinge]

c>b

on graph

[reef agate]

Are you saying this is the answer?

[remote hinge]

what

is it B

[remote hinge]

.

[reef agate]

✅

[remote hinge]

Help sir

[reef agate]

Lets look at A first

[remote hinge]

im looking

[reef agate]

On $x \in (0, 2)$, $f''(x)$ changes from $f''(0) = 1$ to $f''(2) = -7$.

[twin meteor]

King Leo

[reef agate]

If $f$ is decreasing on $x \in (0, 2)$, then $f'(x) < 2$.

[twin meteor]

King Leo

[reef agate]

Is this guaranteed to be true?

[remote hinge]

no

[remote hinge]

Is it E

[reef agate]

No

To change concavity, f'' must change signs

But by simply touching 0, you dont know if it has actually crossed into the positive side

[remote hinge]

hmmm

[remote hinge]

D

im FOR THE D

IS IT D @reef agate

[reef agate]

✅

[remote hinge]

yessss

[remote hinge]

IS IT A @reef agate

[reef agate]

,w d^2y/dx^2, y = xxx - 6xx

[twin meteor]

Results provided by WolframAlpha

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

Requested by .king.leo.

[reef agate]

✅

[remote hinge]

C?

[reef agate]

f' is not negative in C.

[remote hinge]

I CAPPED ITS A

YES?

OR IS IT B

ITS ONE OF THOSE 2

@reef agate IS IT A

[reef agate]

f' is positive for half of A

[remote hinge]

so its b

how is it b

can u tell me so i know for the future

[reef agate]

Entire curve is below the x-axis, so f is negative
entire curve is decreasing/going down, so f' is negative
entire curve's slope is decreasing, so f'' is negative

[remote hinge]

i seeeee

Is this A @reef agate

[reef agate]

✅

[remote hinge]

B? @reef agate

[reef agate]

❌

[remote hinge]

can u explain how it isnt b

[reef agate]

What must happen regarding f' for f to have a relative maximum

[remote hinge]

= 0

[reef agate]

Not just that

f' must change from positive to negative for f to have a relative maximum

[remote hinge]

so its not I

@reef agate so c?

@reef agate ^

[reef agate]

✅

[remote hinge]

DUDE LAST ONE LASTO NE

is it d

@reef agate ^

[reef agate]

✅

[vocal sleet]

@remote hinge Has your question been resolved?

Channel closed

Closed by @remote hinge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tropic brook]

Can someone please help me with number 9

im not sure how to start it since the antilog cant be negative

[mental egret]

$a^{\log_a b} = b$

[mental egret]

All you gotta do is solve, then verify value of m

[tropic brook]

bruh im stupid i forgot you could do that

thanks a ton

.close

[vocal sleet]

Channel closed

Closed by @tropic brook

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>.
• 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.

[serene cave]

quick question

[tropic brook]

oops

[serene cave]

all good

.close

[vocal sleet]

Channel closed

Closed by @serene cave

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>.
• 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.

[vast shale]

I was testing for if irrational + irrational is going to be rational or irrational

I came to conclusion it will be irrational but that is not always the case

But where did I do wrong

Oh ohhhh

r + t can be zero

That’s the rational case

And all others are irrational

[hexed needle]

not necessarily

take 2 + sqrt(2) and sqrt(2) for example

but you are right that the sum of irrationals can be rational

[vast shale]

,w 2 + sqrt(2)

[twin meteor]

Results provided by WolframAlpha

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

Requested by gary_29579

[vast shale]

Wait I didn’t get that u added rational with irrational

[hexed needle]

2 + sqrt(2) is irrational

[vast shale]

Yh

[hexed needle]

so is sqrt(2)

[vast shale]

Right

[hexed needle]

2 + sqrt(2) + ( - sqrt(2) ) = 2, which is rational

I was just saying 0 isn't the only time it works

[vast shale]

Ohh now I see

Is there no way to do it using symbols for general

[hexed needle]

Well what is the original problem?

[vast shale]

Is the sum of two irrationals necessarily

Irrational

Always

[hexed needle]

well if you can construct a case where the sum of two irrational is rational, you know the answer

[vast shale]

Right I was about to say may be

I need to do it

By cases

Because solution can be two different things I assume

I just can’t

Prove it

Using logic

[hexed needle]

it's really easy to over complicate things when you're learning proofs and stuff, so lemme give a solid example:

If I said "Prove that you were at the supermarket on Monday", you could easily disprove that by giving evidence that you weren't there on that day, correct?

In the same way, if you are told to prove that the sum of two irrational numbers is always irrational, all you have to do is either prove it OR give evidence that it's false

In this case, you can give evidence that it's false. You just did with the 0 thing you were talking about

Not sure if that helps

[mental egret]

Like doaby said, to prove a statement, you might need to dissect it and justify its truthfulness under given conditions.
However, to disprove, you only need to give one counterexample.

[vast shale]

Well I get ur idea guys but the desperation for proving it so bad. Well I think that’s why the question was in discuss question rather than prove

Cuz it’s just about giving counter

Example

[hexed needle]

Well you can't prove it because it's a false statement. Are you trying to find out exactly when the statement is true just for the sake of it?

[vast shale]

Yeah

[hexed needle]

ohhhh

[vast shale]

Is it possible

[hexed needle]

to find out exactly when the sum of two irrationals is rational? that's probably harder than you think... we can come up with some cases like with the sqrt(2) stuff and the 0 thing you talked about, but finding ALL possible solutions is generally a very hard task

[vast shale]

Looks like a real analysis problem

[hexed needle]

I'd say so too lol

[vast shale]

oh well oh well I was not asked for so I think I would rather prove the addition of rational and irrationals and likewise

💀 ☠️

Oh also same goes for product of irrationals right cuz one can be inverse of other

To give out rational

And that would it

[tender solar]

youre trying to find when sum of two irrationals is rational?

[vast shale]

Yeah

[tender solar]

probably an infinite number of cases

[vast shale]

Or when it’s irrational

[mental egret]

Well, you can certainly try to "prove". But look at this:

=> (p + r) + (a√q + b√s) is always irrational.
Now, as p + r is always rational, this implies a√q + b√s is irrational for all a, b, in R, q, s in R \ {perfect squares}
=> we can pick two a, b, p, q in R s.t. a = -b = v, s = q
=> (v√q - v√q) is irrational, a contradiction```

But this is just redundant

[tender solar]

an immediate thought is that 0.102948589377.... goes on forever added to 0.897051410622..... gives a rational

[mental egret]

You're basically doing a proof where at the end you show contradiction using a counter example

[tender solar]

given any irrational you can probably just construct another irrational number so that when added its rational

[mental egret]

so why not give counterexample before hand and be done w it

[tender solar]

i dont think theres a set pattern to prove

[mental egret]

, the construction is simple. Suppose p is irrational and you want to construct a q such that p + q = r is rational.
Simply, q = r - p passes the bar

[tender solar]

they can certainly either be rational or irrational

[vast shale]

Interesting that’s just like going with counter example first place

[vast shale]

Ah

What’s a set pattern

[tender solar]

theres no pattern, or rule, which you can observe here

irrational + irrational you cant judge beforehand if it will be rational or not

you need to know the two numbers to figure it out

[vast shale]

Oh rightttttt exactly now I get it

It really depends

[tender solar]

yeah

[vast shale]

For the rationals we can judge

Because fractions

Added

Give fraction

Every case

Ohh interesting so there can be problems where output depends on input and they are

Supposed to be

[tender solar]

yeah

[vast shale]

Done with countrr examples

Just give one to say that it can be

Other

Or vice versa

Or can be more if it’s not restricted to real numbers

Oh also it’s the case that additions of irrationals leads to two different results so we can’t disprove it or prove

By contradiction

Because that would mean it is not true for this but for other

But other can say it’s not the case for me

But previous

It’s going back and forth

I was looking for explicit answer to the addition but that’s just not possible

Now I realized

Alright guys I get it now have a good one

Thank you

.close

[vocal sleet]

Channel closed

Closed by @rugged heron

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>.
• 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.

[pliant rose]

help

[vocal sleet]

@pliant rose Has your question been resolved?

[vocal sleet]

@pliant rose Has your question been resolved?

[vocal sleet]

@pliant rose Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vocal sleet]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[vast shale]

AB is 2 cm
CB is 1 cm
It is flipped in half and A becomes A' which is in middle of CB

[vast shale]

Please i need help fast

I need area of A'D'EF

[vocal sleet]

@vast shale Has your question been resolved?

[lost lake]

AE=A’E
AE+EB = 2 therefore A’E + EB=2
If EB is x A’E is 2-x
A’B is 1/2 because mid point
x,1/2 and 2-x make right triangle at A’EN
x^2+1/4 = x^2-4x+4
4x= 15/4
x=15/16 (such an ugly number I might’ve made a miscalculation but these are the first steps)

We have found the lengths of AE (therefore A’E) and EB but we haven’t found DF (therefore D’F) and FC yet

Notice AF = A’F
So AF^2 is A’F^2
So DF^2+AD^2 = A’C^2+CF^2
If we call DF y then FC = 2-y
y^2+1=1/4+(2-y)^2
y^2+1= y^2-4y+17/4
4y= 13/4
y=13/16 (such an ugly number once more, again I might’ve made a mistake in calculation but these should be the steps)

After that area becomes easy

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

Maybe but i dont understand it

[vocal sleet]

Channel closed

Closed by @proven sentinel

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>.
• 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.

[ebon geyser]

"Izza writes a positive integer. The number leaves a remainder of 181 when divided by 2024. Determine the remainder of this number when divided by 88."

whats a remainder and how to do this

[atomic jasper]

the remainder is whats leftover when dividing

for example, 9 divided by 4 is 2 remainder 1

[ebon geyser]

oh so like
= 9 : 4 = 4 x 2 = 8 and then we subtract 9 with 8?

[atomic jasper]

9x4?

[ebon geyser]

o wait

ok there

[carmine token]

bonk can u help me pls

[atomic jasper]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[atomic jasper]

9/4=(8+1)/4=8/4+1/4=2 remainder 1

[ebon geyser]

ahhh okay

but im still confused on the equation

what r we supposed to do

[atomic jasper]

okay, lets call the number that gets divided k

k/2024 leaves a remainder of 181

which means k is of the form k=2024*n+181

now divide k by 88 and look for the remainder

[fluid tide]

show that lnx <e^{x}+x

can you help me

[atomic jasper]

!occupied

[vocal sleet]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[fluid tide]

ok sorry

[ebon geyser]

k = 2024n + 181?

howd u divide it by 88

[atomic jasper]

look what happens when you divide this by 2024

[ebon geyser]

k = n + 181/2024?

[atomic jasper]

yup

so what is its remainder?

divide k by 88, and what do yo uget?

[ebon geyser]

k/88 = n + 181/2024

[atomic jasper]

2024?

\begin{align*}k&=2024n+181\\frac{k}{88}&=\frac{2024n+181}{88}=?\end{align*}

[twin meteor]

Bonk

[ebon geyser]

2024n/88 = 23n
181/88 = 2 remainder of 5??

what you do next

[atomic jasper]

yup

so whats the remainder you have?

[ebon geyser]

2 remainder 5?

[atomic jasper]

whats the remainder

[ebon geyser]

5

?

[atomic jasper]

yup

[ebon geyser]

is that the answer

[atomic jasper]

yes

[ebon geyser]

OHHHHHHHH

ok i thought this had something to do with integrals

thanks for the help

[atomic jasper]

noooo

[vocal sleet]

@ebon geyser Has your question been resolved?

Channel closed

Closed by @ebon geyser

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[north shadow]

i have a math problem which states "how many ways can 5 men and 4 women be arranged alternately in a row where woman comes first". i have come up with 2 answers to this problem, using the formula P = A! * B! you get 2880, however using boxes to represent the amount of men and women i came to the conclusion that there is not enough women to meet the requirements of the permutation, at the 9th square there is 0 women and multiplying them all together = 0, taking out the square would result in 2 men being next to eachother violating the rule they have to alternate. i need a second opinion from someone to verify which answer is correct

[vocal sleet]

@north shadow Has your question been resolved?

[lost lake]

Oh sorry you said alternating

You are right about it being impossible btw

In order for you to alternate you need to start and end with the group of people that have 1 more member

If they had even amount of people you could alternate by starting with a woman and ending with a man

[north shadow]

ah thanks for the response

[lost lake]

You’re welcome

[north shadow]

is there any reason why the formula gives 2880 instead of 0?

[lost lake]

Formula assumes that there are a people where they need to be permutated between themselves and b people where they need to permutate between themselves. It says a! ways to do first and b! ways to do second so multiply. If there were 5 women and 4 men, we’d know it was WMWMWMWMW and you’d only need to permutate genders within themselves, you wouldn’t need to permutate them with each other, so you’d do 5!.4! to see how it is possible. Formula would work
But here no matter how you permutate the women within themselves and the men within themselves, task will remain impossible. You’ll run out of women when you need to put one so you won’t be able to put the last men without breaking alternating

[north shadow]

so if i understood correctly, the formula only works when both groups are equal or when there is 1 more object of the starting group A than group B?

and it doesnt work in this problem because it assumes that there are 5 women and 4 men because of the interchangeability of multiplication?

[lost lake]

The formula works where you have some group A and some group B, you know where A members will be and where B members will be, but not how members of one group will permutate within themselves. A has a members so they can permutate a! ways, B can b! ways so a!b!
If I had some unique math books and some unique history books and I knew I was about to put them in MHHHMMH order, but I didn’t know how books of same class will place within themselves, then I’d do 3!4! bc 3 math and 4 history
If I had 5 women and 4 men alternating with a woman first, that would tell me that I need to do WMWMWMW and id just do the 5!4!, but if it said that we have 4 women and 5 men, id point out that the task is impossible before even I get to use such formula

[lost lake]

In the math and history example formula doesn’t require such thing, you can do 5 and 7, but with people alternating you realize there are restrictions on how bigger one group can be from other and who will start, it is not something algebraic really

[north shadow]

ah well thank you for the help

.close

[vocal sleet]

Channel closed

Closed by @north shadow

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>.
• 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.

[west coral]

someone pls explain ?

i’m so tired my brain can’t think of this stuff nw

[hexed needle]

do you know what even/odd functions are?

[hybrid flicker]

if you know what even/odd means

take an odd function f

an arbitrary point a

and prove f'(-a) = f'(a) by limit definition

[west coral]

even reflected around y axis , odd reflected around origin

[west coral]

but how does drawing graphs explain that

[crude crane]

helo

[hexed needle]

okay cool. take an example, f(x) = x^2

what do you notice about the slope of the tangent line (derivative) at the points x = 1 and x = -1?

[west coral]

it’s reflected too?

or idk it crosses the origin ?

[hexed needle]

what happens when you do the actual calculation

what is the slope at those two points?

[west coral]

y = -2 , y = 2

dy/dx= 2x

idk bro

slope is negative then positive idk bro 🤣

[hexed needle]

yes, that's exactly the point. odd functions are characterized by

f(-x) = -f(x)

meaning when you plug in -1, you get the negative of when you plug in positive 1

[west coral]

yea but the question says show it by drawing a graph

i get the defintion of odd and even

[hexed needle]

just draw a graph and draw the tangent lines, that pretty much explains it

[west coral]

ok

and for c)

not sure what they are asking

[vocal sleet]

@west coral Has your question been resolved?

[hexed needle]

they're just asking why (a) works when you take derivatives of stuff like x^6 or x^3

[west coral]

ight

[vocal sleet]

Channel closed

Closed by @west coral

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>.
• 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.

[leaden ingot]

Suggested by @flat whale , using geometric series
original problem: #help-39 message

[leaden ingot]

can someone check if it's correct

[flat whale]

please don't ping me

[leaden ingot]

sorry

i still gotta give credit tho, i dont wanna be disrespectful

also while you guys check the 1st problem, can someone give a hint for 2nd one

[desert hornet]

aren't these in Valean's book

[scenic ravine]

Here I think king's rule just might work

[leaden ingot]

idk about that tbh

[desert hornet]

I didn't check the specific sums and everything but the method looks right

pretty interesting, this was not the way I did it at all

[leaden ingot]

this one?

[desert hornet]

you do get a lot of terms here which cancel out

[desert hornet]

yea

yes they are question 1.7 from this book

[leaden ingot]

didnt expect the solution to be that short
kinda reminds me of that one cleo's problem on math stackexchange lul

[desert hornet]

lol yeah

another technique for this is to let A=log(1+x) and B=log(1-x) and then write A^2 in terms of (A+B)^2, (A-B)^2 and B^2

log(1-x) is a bit nicer to work with when you're integrating between 0 and 1, because you can do king's rule stuff

and stuff with (1+x)/(1-x) works out nicely many times because you can just substitute that whole term

[desert hornet]

pretty sure this was used in the solution in the book for both of these

[desert hornet]

you probably won't be able to use a similar method as the one you you used for the previous one for this one

[mental egret]

Did you try $2t = \cos^{-1} x$

[mental egret]

Wait

[mental egret]

Didn't you do this already.

$4\ln (1 - x) \ln (1 + x) \ = [\ln (1 + x) + \ln(1 - x)]^2 - [\ln (1 + x) - \ln (1 - x)]^2$

[mental egret]

$4I = \int_0^1 \frac{[\ln(1 - x^2)]^2}{x^2} \dd x^2 - \int_0^1 \frac{\left[\ln \left(\frac{1+x}{1-x}\right)\right]^2}{x} \dd x$

[mental egret]

first looks promising, not sure about second tho

Alr, something clicked

$4I = \int_0^1 \frac{\ln^2 (1 - t)}{2t} \dd t - \int_0^1 \frac{2\ln^2 t}{1-t^2} \dd t$

[mental egret]

Is this workable @leaden ingot ?

You can convert both using expansion for 1/(1-t)

[vocal sleet]

@leaden ingot Has your question been resolved?

[leaden ingot]

yep that's decent enough

.close

[vocal sleet]

Channel closed

Closed by @leaden ingot

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>.
• 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.