help-19

[tropic shadow]

how

[south plume]

but r is correct

because first term is n=1 according to the sum

[tropic shadow]

i see that

[south plume]

substitute n=1 to 1/3*(5/6)^n

[tropic shadow]

5/18'

[south plume]

yes

that's your a

[tropic shadow]

so to find any a in any geometric series substitute the index in

then the r is whatever is to the power of n

[south plume]

yes

[tropic shadow]

what makes these geometric?

[south plume]

because it's a constant to the power of variable

and the ratio of 2 consequent terms is the same

[tropic shadow]

but E is a constant to the power of a variable

and also F is alternating so how can it be geometric

[south plume]

huh

um

ah

E is a sum

not a sequence

it's already a sum of a sequence

[south plume]

$(-1)^n \left(\frac{2}{5}\right)^n = \left(-\frac{2}{5}\right)^n$

[clever fjord]

artemetra

[tropic shadow]

oh

A is not geometric cause the numbers dont increase by the same multiple, B is geometric with the common ratio 1/3, C is not geometric because 1/n is not constant D is geometric because it simplfies to (9/5)^n E is not geometric sequence because its a geometric sum, F is geometric because the (-1)^n combines for a common ratio of (-2/5)

@south plume

[south plume]

yes

[tropic shadow]

how do i evaluate that limit

@south plume

it alternates between - and positive inf because 3n > 2n+1

[south plume]

yes

use a convergence test

[tropic shadow]

so the limit != 0 so it diverges

how did t hey make this conclusion

@south plume

[south plume]

1. why are you tagging me

[tropic shadow]

do yo want me to not?

[south plume]

2. idk how you learn it at your level but i personally just know that n! grows faster than 3^n

so idk how to show this

[tropic shadow]

oh its a sequence not a series

[south plume]

no need to tag specifically me

[tropic shadow]

i like u though

[south plume]

thank you

[light burrow]

2n!=3.4....n
3^n/n!=2.3^n/(3.4....n)<=2(3/n)

[tropic shadow]

yeah i didnt realize it was a sequence

i thought it was a series

lim r -> 2- ln|r-2|

2- gets closer and closer to 2

1.99999

1.99999-2 = -0.000001

abs avlue

0.000001

ln(0.000001) = -inf

not positive infinity

[odd edge]

@tropic shadow Has your question been resolved?

[odd edge]

@tropic shadow Has your question been resolved?

[quasi sparrow]

yes -inf is correct

[tropic shadow]

Answer says inf

[quasi sparrow]

i can see that

[odd edge]

@tropic shadow Has your question been resolved?

Channel closed

Closed by @tropic shadow

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.

[odd edge]

@silent isle Has your question been resolved?

[odd edge]

@silent isle Has your question been resolved?

[odd edge]

@silent isle Has your question been resolved?

[odd edge]

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.

[echo ginkgo]

thoughts ?

@spark cargo

[spark cargo]

A closure = A U L

[echo ginkgo]

closure is the set with its limit points yeah that's true

[spark cargo]

I think its true

[echo ginkgo]

you're already thinking of stuff a bit sophisticated

think ultra simple

[spark cargo]

[2,3] is closed

[echo ginkgo]

the closure of a set is always closed right

[spark cargo]

yes

the complement

of a closed

set is open

[echo ginkgo]

yeah

[spark cargo]

thank you

.close

[odd edge]

Channel closed

Closed by @spark cargo

Use .reopen if this was a mistake.

[odd edge]

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.

[wraith nexus]

How to graph K in a inversely proportional equation

[odd edge]

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.

[wraith nexus]

It’s not a spicfic question, I just want to know how you would Graph K on a chart

With any inversely proportional question

Okay if you need a question

"Suppose you are driving a car at a constant speed. The time it takes to travel a certain distance is inversely proportional to your speed. If it takes you 4 hours to travel 240 miles, how long would it take to travel the same distance at a speed of 60 miles per hour?"

I need help graphing that and identifying where K is on the graph

[odd edge]

@wraith nexus Has your question been resolved?

[wraith nexus]

<@&286206848099549185>

I need help still

[odd edge]

@wraith nexus Has your question been resolved?

[odd edge]

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.

[rugged hamlet]

What should I do next?

Or am I on wrong path?

[odd edge]

@rugged hamlet Has your question been resolved?

[odd edge]

@rugged hamlet Has your question been resolved?

[odd edge]

@rugged hamlet Has your question been resolved?

[odd edge]

@rugged hamlet Has your question been resolved?

[rugged hamlet]

.close

[odd edge]

Channel closed

Closed by @rugged hamlet

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.

[rancid basin]

got no idea where to start

[lament walrus]

just draw the circle:
|z-2i| >= 1

sub z = x + iy

so:
|x + iy - 2i| >= 1

[rancid basin]

its a circle radius 1 from centre 2i right

but what do you do from there

[lament walrus]

find the line:
argz = pi/3

[rancid basin]

thats just the ray at angle π/3 from origin right

what do i do w the info tho

is it √3 cis π/3

√3 isnt the length tho

not sure mate

<@&286206848099549185>

[manic horizon]

There is an equilateral triangle, how to find the length of the segment from the corner to a random point on the other side?

[odd edge]

@rancid basin Has your question been resolved?

[rancid basin]

ik that π/3 are the interior angles of an eq. triangle

but how does that help with the length

[odd edge]

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.

[mystic saffron]

how do we get from the top to the very bottom?

I understand that we derive it

but then? How do we go from that long line to the short line

[tardy lagoon]

are you differentiating?

why do you ignore the step though

[mystic saffron]

wdym ignore

I derive the top one

then get the whole 4(x-2)...

then I don't know how to get from the second to the third line

[tardy lagoon]

from second line to thrid you factor (x-2)

[mystic saffron]

I thought about that but I didn't know how I'd do it

for me I didn't do the same as the top line

I had (x-2)^2 * (4x-2)

[tardy lagoon]

show your work

[mystic saffron]

so I got 2(X-2) * (4x-2) + 4(x-2)^2

[mystic saffron]

sure, one sec

[tardy lagoon]

it's correct

[mystic saffron]

hm

[tardy lagoon]

just factor (x-2)

[mystic saffron]

I had difficulty with that

one second

[mystic saffron]

I don't get the same as the solution sheet

if I factor out (x-2) then I get 2*(x-1) + 4(x-2)

because the (x-2) is squared

[tardy lagoon]

2*(x-1)?

[mystic saffron]

yea

[tardy lagoon]

how

[mystic saffron]

it was (4x-2)

so it'll become (2x-1)

no wait

Idk man

[tardy lagoon]

2(x-2)(4x-2)

after factoring it should become 2(4x-2)

[mystic saffron]

(x-2)^2 no?

[tardy lagoon]

you had 2(x-2)(4x-2)+4(x-2)^2

??

[mystic saffron]

correct

[tardy lagoon]

2(x-2)(4x-2) becomes 2(4x-2)

4(x-2)^2 becomes 4(x-2)

[mystic saffron]

but when I factor with something don't I have to include that something somewhere?

like if I factor with (X-2) shouldn't there be an (x-2) somewhere

ab + ac = a * (b+c)

so the a is still there for example

[tardy lagoon]

yes

so we have (x-2)(2(4x-2)+4(x-2))

[mystic saffron]

wait

how do we factor x-2 out of 4x-2

is it just 4 then

[mystic saffron]

wait so 2(x-2)(4x-2) turns into (x-2) (2*4)?

@tardy lagoon I get (x-2) * 8 + 4 (x-2)

[tardy lagoon]

???

[mystic saffron]

what

[tardy lagoon]

this

[tardy lagoon]

how'd it become this

[mystic saffron]

but this isn't what the book got either

[tardy lagoon]

it's the same after simplifying

[mystic saffron]

because of the (x-2)

there's 2(x-2)*(4x-2)

so if I take out the (x-2) it becomes (x-2) * 2 * 4

no?

[tardy lagoon]

??????

how

2(x-2)(4x-2)

take out (x-2)

2(4x-2)

???????

[mystic saffron]

but that's not factoring anymore

how do I just "take it out"

idk if there's some language barrier here or something but that's not what I imagine under factoring

[tardy lagoon]

when factoring you have ab+ac=a(b+c)

I'm saying 2(x-2)(4x-2) is ab here

factor out (x-2) being a

we're left with 2(4x-2) which is b

[mystic saffron]

Ohhhhhhhhhhh

so 2(4x-2)+4(x-2)?

[tardy lagoon]

yes that's (b+c)

[mystic saffron]

hm

so:

@tardy lagoon what's the mistake here?

[tardy lagoon]

no mistake here

simplify more

[mystic saffron]

(x-2)(12x-12)

[tardy lagoon]

last step factor out 12

[mystic saffron]

(x-2)12(x-1)

[tardy lagoon]

bruh no one write like that

do you write x2y

[mystic saffron]

12(x-2)(x-1)

[mystic saffron]

sometimes when I'm lazy

[tardy lagoon]

so cursed

[mystic saffron]

I know

I used to also do xa^2 instead of a^2x

it happens

[tardy lagoon]

that's acceptable

[mystic saffron]

my teacher didn't like it very much

[tardy lagoon]

when you have a varaible

[mystic saffron]

alphabetically or whatever

my issue is honestly just with the small stuff

like I get the whole derivation thing

then I get stuck on the factoring

do you have any tips on how to fix that

[tardy lagoon]

when you can do calculus but not basic algebra

[mystic saffron]

I still have today, tomorrow, saturday and sunday

[mystic saffron]

suffering from success

[mystic saffron]

exam's on monday so there is still hope

I just need to know what to practice

[tardy lagoon]

practice factoring polynomial

[mystic saffron]

noted

wait let

let's try getting the third derivation

it's also necessary

12(x-2)(x-1)

I'd personally unfactor here

wait small question

if I wanted to do 12 * (x-2)

would I write 12x-24 in parenthesis or without

[tardy lagoon]

with

[mystic saffron]

What's the rule behind that

when do I put parenthesis and when do I not

[tardy lagoon]

associativity

[mystic saffron]

which means?

[tardy lagoon]

when multiplying a,b and c we write abc

but technically it's kinda abusing notation

rigorously we either have (ab)c or a(bc)

but since (ab)c=a(bc) we just write abc instea

d

associativity basically means the order of multiplying doesn't matter

[mystic saffron]

ah

so technically there are always parenthesis

[tardy lagoon]

yes

[mystic saffron]

thank you

when doing the third derivative I get (12x-24)(12x-12)

which is 12((x-2)+(x-1)) right

[tardy lagoon]

NO

[mystic saffron]

one sec one sec

12(x-2)+12(x-1)

[tardy lagoon]

noooo

[mystic saffron]

wait what

no?

(12x-24) turns into 12(x-2) tho

[tardy lagoon]

what

[mystic saffron]

and (12x-12) into 12(x-1)

[tardy lagoon]

^

[mystic saffron]

great

[mystic saffron]

idk

I tried summing it all up under one

ig not

why does that not work though

would it not just turn into 12(x-2)+12(x-1)?

[tardy lagoon]

idk why you think 12(x-2)(x-1)=12((x-2)+(x-1))

[mystic saffron]

if I put 12((x-2)+(x-1))

[mystic saffron]

no with another parenthesis

[tardy lagoon]

oh wait

you're talking about after taking derivaitve

[mystic saffron]

yeah

[tardy lagoon]

mb

[mystic saffron]

all good

what's the difference though

with before or after taking a derivative

[tardy lagoon]

I just misunderstood

[mystic saffron]

ah

all good

[tardy lagoon]

hmm

[mystic saffron]

I'm going to now take a shower then redo the whole thing from the beginning and I am hoping that it'll be right from the first try

[mystic saffron]

what's up?

[tardy lagoon]

you're still wrong though

[mystic saffron]

wait how

[tardy lagoon]

this is correct

[tardy lagoon]

not this

[mystic saffron]

but I got that from this

[tardy lagoon]

wut

[mystic saffron]

(12x-24)(12x-12) turns into 12((x-2)+(x-1)) when I factor 12 out

or just 12(x-2)+12(x-1)

same thing

[tardy lagoon]

how'd you get the correct result while being completely wrong

[mystic saffron]

I'm not wrong tho

the book has the same thing I think

what was the second derivative again

[tardy lagoon]

(12x-24)(12x-12)=12(x-2)(12x-12)=144(x-2)(x-1)

[mystic saffron]

wtf

12(x-2)(12x-12)'

now say I want the derivative of this

waht I did was "unfactor"

to (12x-24)(12x-12)

because I wanted to just use one product rule

and not a chain rule

if I'd kept 12(x-2) I'd need to do u(x)=12x and v(x)=x-2

[tardy lagoon]

ahh

[mystic saffron]

and I didn't wanna do that

then the whole u'(v(x)) * v'(x) thing

just too much unnecessary work

so then I got (12x-24)(12x-12)

and did the whole u'(x)*v(x) + u(x)v'(x)

(12x-24) (12) + (12x-12) (12)

wait one sec no I didn't do that

let me look back at my notes

[tardy lagoon]

but the second derivative is 12(x-2)(x-1)

[mystic saffron]

was it?

I forgot to highlight it on my tablet

so now it's stuck in a mess of god knows what

then I did (12x-24)(x-1)

yeah that makes more sense

(12x-24)*1 + 12 (x-1)

yeahhh

see

that's how I got there

so then I got to (12x-24) + (12x-12)

and from there I went on to do 12((x-2)+(x-1)) aka 12(x-2)+12(x-1)

any problem with any of that?

[tardy lagoon]

ok now this is correct

[mystic saffron]

yea I had the wrong derivative lol

but this is what I did

and the 12((x-2)+(x-1)) = 12(x-2)+12(x-1) thing is correct right

[tardy lagoon]

yes

[mystic saffron]

great

now I can actually do the goddamn exercise

of finding turning points and local maximum/minimums

[mystic saffron]

thank you by the way

this was a very daunting exercise

[tardy lagoon]

no problem

[mystic saffron]

.close

[odd edge]

Channel closed

Closed by @torn swan

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.

[rocky juniper]

Hello, sorry but I'm really lost with proving this exercise. Can't I just say that as the semi-infinite binarysequence are uncountable, it implicates that this set is uncountable as well?

[odd edge]

@rocky juniper Has your question been resolved?

[rocky juniper]

Or can you just help me with how the functions look like? Are there only two functions because of {0,1}?

[odd edge]

@rocky juniper Has your question been resolved?

[weary pelican]

it would work saying that ${0,1}^\infty$ is uncountable, as then the amount of possibilities $f(0)$ can be is already uncountable

[clever fjord]

rafilou2003

[odd edge]

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.

[karmic girder]

Just learned the concept of "at least one" probability. And was told the formula is P(at least one)=1-P(none)

Can i interpret "none" as complement of A ?
P( at least 1 A)=1-P(all possible A' )

[tardy lagoon]

what's A?

complement of "none" would be "at least one"

[odd edge]

@karmic girder Has your question been resolved?

[karmic girder]

event A

[karmic girder]

ah ok, ty!

[tardy lagoon]

it's more natural to think that P(A)=1-P(complement of A)

[karmic girder]

yeah i know this, but when an "at least" probability problems come up, i got kinda confused

[karmic girder]

thats why i asked if i can think of it this way to help me remember it more intuitively, instead of just using the formula

[late dust]

The complement of "at least n" would be "strictly fewer than n"

[tardy lagoon]

I see

[late dust]

In the case of n=1, that's just "none"

[karmic girder]

like 0 n?

[tardy lagoon]

yeah it's better to learn taking complement

[leaden raft]

It can be half

[late dust]

No n is a number not an event

[karmic girder]

oh

[tardy lagoon]

instead of at least one A, think of it as A happened at least once

[odd edge]

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.

[proper quail]

Hi what would be the best way to solve system of equations with 3 unknowns?

[manic sleet]

Elimination

[proper quail]

Can anyone provide any good tutorial?

[manic sleet]

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/09%3A_Systems_of_Equations_and_Inequalities/9.02%3A_Systems_of_Linear_Equations_-_Three_Variables#:~:text=A system of three equations in three variables can be,one equation to another equation.

[proper quail]

So elimination method is the easiest?

[manic sleet]

For systems of 3, the method which is most elementary and efficient, elimination is your best bet, yes

[proper quail]

ok so do I have to learn how to solve with 2 unknowns first?

if yes, what would be the best way to do it?

[odd edge]

@proper quail Has your question been resolved?

Channel closed

Closed by @proper quail

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.

[weak portal]

idk what i screwed up, can someone solve this and explain

I just mutliplied (1+root3+root5) to the LHS

<@&286206848099549185>

[slow light]

This has infinite solutions

The kernel is dim 3

One equation of 4 variables is not enough for a specific solution

[spiral basalt]

he's got the pre-uni role

[slow light]

Shoot

[spiral basalt]

don't you talk about linear forms like he'll understand

[slow light]

idk how to find the right answer w/o row reduction

[spiral basalt]

his method looked sound

[spiral basalt]

oh it's a she

[slow light]

… ah it’s a gimmick problem then? ie the method only works on this specific one?

[spiral basalt]

idk
It could have been they're looking for integer solutions but the answers don't match that

,w expand (1+sqrt(3)+sqrt(5))(P+sqrt(3)Q+sqrt(5)R+sqrt(15)S)

[clever fjord]

Results provided by WolframAlpha

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

Requested by mateo713

[spiral basalt]

we want that to equal 1

[slow light]

… I truly see no way other than linalg

[spiral basalt]

it's (P+3Q+5R) + (P+Q+5S)sqrt(3) + (P+R+3S)sqrt(5) + (Q+R+S)sqrt(15) = 1

then just linalg this

[slow light]

That’s the same equation as you started with silly

[spiral basalt]

except I can turn this into a simple equation

[slow light]

Oh?

[spiral basalt]

By saying I hope for a solution of the form 1 + 0 + 0 + 0

,w solve ((1, 3, 5, 0), (1, 1, 0, 5), (1, 0, 1, 3), (0, 1, 1, 1))(a, b, c, d) = (1, 0, 0, 0)

[clever fjord]

Results provided by WolframAlpha

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

Requested by mateo713

[spiral basalt]

rip

[snow marten]

cant you just rationalize the fraction

[slow light]

yes

you are right lol

that’s exactly how you get the solution 😭

[spiral basalt]

You take the conjugate in Z[sqrt15] ?

[slow light]

Because answers are rational I assume

[spiral basalt]

time to use Galois theory to figure out how to rationalize fractions

[spiral basalt]

is that just 1 - sqrt(3) - sqrt(5) ?

or do you have to multiply by all 3 conjugates then ?

[slow light]

All three

[spiral basalt]

dammit

[slow light]

afaik?

[spiral basalt]

me too

but I don't want to

[snow marten]

(1+sqrt(3)+sqrt(5)(1-sqrt3-sqrt5) = 1-(sqrt3+sqrt5)²

[slow light]

@weak portal you can use this

Just set coefficients equal to each other

[spiral basalt]

isn't that literally the original problem ?

[snow marten]

what

[spiral basalt]

to do this

[snow marten]

but you have pqrs now

[spiral basalt]

well yeah just skydrop the solution

but that's not interesting

[spiral basalt]

but neither is algebra in Z(sqrt(3), sqrt(5))

= Q[sqrt(3), sqrt(5)] ? When is a field extension a field ?

[slow light]

,rotate

[spiral basalt]

I hate your sqrt notation but thank you

[slow light]

No @spiral basalt bc we assume rational coeffs so we just take 3/11 as sqrt3’s coeff = Qfor instance

Then sum all

[spiral basalt]

so we don't have equality ?

[odd edge]

@weak portal Has your question been resolved?

[odd edge]

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.

[slender solstice]

Is there a trigometric identity 1- cosx or 1 + cosx?

[mystic saffron]

Hi!

[cold sage]

you could apply the half angle identity

let 2theta =x

[mystic saffron]

By formula ,

Cos(A) - cos(B) =2{sin(A+B)/2}.{sin (B-A)/2}
1-cos(x) = 2{sin(0+x)/2}.{sin(x-0)/2}
1- cos(x) = 2sin(x/2).Sin(x/2)
1-cos(x) = 2sin^2(x/2)
= 2sin^2(x/2)

Do the same thing for 1 + cosx

[odd edge]

@slender solstice Has your question been resolved?

[odd edge]

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.

[mystic saffron]

Hello?

[mystic saffron]

I'm in the middle of reconstructing a rational function and I'm unsure about the significance of a constant in the numberator

[zenith tartan]

yea so? its a constant whats wrong?

[mystic saffron]

It's because I have to reconstruct the constant in order to graph the funtcion

[tight crescent]

Well it is most definitely important since you are asking about its significance

[mystic saffron]

Yeah

This was apart of the problem I'm trying to solve

[tight crescent]

Well you simplified incorrectly.

You get (x+3) * (x-2) in the denominator

and (x+3) cancel out, not (x-3)

[mystic saffron]

So the new numerator is -3(x-3)?

[tight crescent]

Yes

[mystic saffron]

Ok

And then when I divide the numerator do I redistribute the -3?

Or does it become a parameter?

[tight crescent]

What

We've got $f(x) = \frac{-3 \cdot (x-3)}{(x-2)}$

[clever fjord]

USS-Enterprise

[mystic saffron]

Yeah

And then I have to rewrite it in this format

By using long division

Because I still need to find vertical and horizontal asymptotes

.stop

.closd

.close

[odd edge]

Channel closed

Closed by @slow crypt

Use .reopen if this was a mistake.

[odd edge]

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.

[weak portal]

basically a follow up question

I didnt understand what happened before

[weak portal]

from here i guess

[noble forge]

do you know how to rationalise the denominator?

[weak portal]

ye

i did thatt

[weak portal]

I mean, I don't get exactly what I've to rationalise, the original RHS of the question?

[noble forge]

yes. denominator of the RHS

[weak portal]

Alright, what's the next step?

[slow light]

what did you get for it? (the rationalised RHS)

[noble forge]

well, show your work

[weak portal]

Ok, one min

[weak portal]

How do I type it out here

[slow light]

you can use latex

in this case

[noble forge]

well, just write out what you get as values of P,Q,R,S

[weak portal]

1-root3-root5/-7+2rooot15

[slow light]

$\frac{NUMERATOR}{DENOMINATOR}$

[weak portal]

^

[slow light]

or that works too lol

shhh bot

[slow light]

ok now rationalise it completely

[weak portal]

k

[slow light]

the root15 is still in the denominator

[weak portal]

one min

[noble forge]

Okay, seems like I'm too used to LaTeX

[weak portal]

k got rid of it

got 11 in the denominator

i think i can simplify the numerrator

I will do that

[slow light]

good good

[weak portal]

ok so idk how to use latex yet

[slow light]

no worries

[weak portal]

ill type it out normally

[slow light]

https://media.discordapp.net/attachments/903463355619110912/1169658864048808087/444537905919164428.png?ex=655634b4&is=6543bfb4&hm=8f9ad15d9465a862817df73bcb011261a090c39a52286224e560843c9ac823e3&=&width=1442&height=1082

did you get this?

[weak portal]

yep

[slow light]

hooray

ok so we can rewrite that...

we have

[1P + \sqrt{3}Q + \sqrt{5}R+\sqrt{15}S=\frac{7+3\sqrt{3}-\sqrt{5}+2\sqrt{15}}{11}]

[clever fjord]

Astral

[slow light]

do you have any idea how to solve for rational PQRS from here? (I say rational bc otherwise we're back where we started, with infinite solutions)

[weak portal]

simplify till we get P+Q+R+S = something?

ok no im confused let me figure this out

[slow light]

hint: ||compare coefficients||

[weak portal]

yeah we can take the coefficients common

multiply 11 first to both sides?

[slow light]

no

this is ostensibly our last step before getting the values

let's put it this way

what rational values of P will let it be $k\sqrt{3}$ for rational k

[clever fjord]

Astral

[slow light]

(rational is just a fraction)

so sqrt(3) is irrational, but 12312/238479812 is rational, as is 1/2 or 2/1 or 3

P cannot "contribute" to the square root terms

because it cannot be irrational, and its coefficient is 1

[weak portal]

so we just need a rational solution

p is rational

[slow light]

so now matter what P is, it will never help sqrt(3)Q becomes 3sqrt(3)/11

[weak portal]

but we need the other 3 to be rational

[slow light]

[1P + \sqrt{3}Q + \sqrt{5}R+\sqrt{15}S=1\frac{7}{11}+\sqrt{3}\frac{3}{11}+\sqrt{5}\frac{-1}{11}+\sqrt{15}\frac{2}{11}]

lemme write it this way

[clever fjord]

Astral

[weak portal]

oh so Q is 3/11

[slow light]

all I did was separate the numerator into different fractions

[weak portal]

R is -1/11

And S 2/11

[slow light]

ok, so you see the patterns yes?

[weak portal]

and I just add them up

[slow light]

but do you know why it's the solution?

[weak portal]

It's rational?

[slow light]

I mean yes

but like,

do you know why P can only contribute to the "1" term, and not the sqrt(3) or sqrt(5) or sqrt(15) terms?

why Q cannot contribute to the "1" sqrt(5) or sqrt(15) terms?

[weak portal]

cuz if u multiply a constant by root 3 ull get smth irrational?

product of a rational number and irrational number?

only if u multiply with that exact root will u get a value corresponding?

the value of P cannot be irrational, similarly value of Q can't be a something of a prooduct of root5 or root15

[slow light]

yes! you can multiply 1 by an irrational number like root 3 to make 1(k) irrational! But in this case, 1P can never be irrational because P is rational

if P was irrational, again, infinite solutions, it's out of scope for your level of the problem

[slow light]

yes exactly

you seem to understand

[weak portal]

:D thank you so much for the help

[slow light]

you'll see more of this concept in partial fraction decomposition

which solution did you pick? (ABCD?)

[weak portal]

I didn't understand what you mean?

[slow light]

in your original question

[weak portal]

d

it was a practice paper

[slow light]

ah ok

[weak portal]

I spent about an hour on it

[slow light]

it happens

[weak portal]

But I could not understand how to solve it

[slow light]

.... though looking back when I sum PQRS I get 1....? 11/11

idk lol

the process was correct

unless there are infinite solutions 😭

[weak portal]

I will add it up and check, its quite likely the question is wrong, Ill just ask my teacher to show me the correct answer and how they got it

[weak portal]

The answer 1 should be correct right?

[slow light]

I'll be honest the sum should be 11/11=1, which doesn't correspond to any of the provided answers 😭

why would it be likely the question is wrong?

[weak portal]

I found 2 more errors on the same paper (was a science +math paper)

[slow light]

ahhh ok

that's reassuring

[weak portal]

I will resolve it, perhaps the rationalisation may have been wrong

[slow light]

I don't think so, we got the same answer independently

[weak portal]

But if it's the same, it's prolly the question

[weak portal]

alr thanks a lot for the help, really appreciate it

[slow light]

no problem!

distracted me from my lectures which is good

never calculate the jacobian of a spherical function in cartesian coords plz

it's not worth it

[weak portal]

lmao ill understand that in a few years or months I hope

,close

.closse

.close

[odd edge]

Channel closed

Closed by @weak portal

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.

[plain pendant]

Using the arc length formula and integral

Algebra and integrating

Now what do i do

What does the question mean by find all of f(x)?

[quasi sparrow]

you missed a constant of integration here

once you include that, that'll be "all f(x)"

[odd edge]

@plain pendant Has your question been resolved?

[plain pendant]

ah good point

[plain pendant]

can you explain to me how this works?

is this right/.

[quasi sparrow]

no

$\int du = u + C$

[clever fjord]

riemann

[plain pendant]

(\int dx = x + c) also right

[clever fjord]

hamr

[quasi sparrow]

correct

[plain pendant]

so what is the full equation? can you explain how the equation could be used to find all f(x) that satisfy the requirements?

[quasi sparrow]

use this before you sub back in for y

instead of " =u" should be "= u + C"

[plain pendant]

( = u + c = arcosh(y) + c)

[clever fjord]

hamr

[plain pendant]

im confused?

[quasi sparrow]

why

[plain pendant]

How does this euqation define all f(x) that satisfy the constraints?

what even is the full equation

[quasi sparrow]

the + C makes it "all of them"

what constraints are you talking about

[quasi sparrow]

i don't see the word constraint there

[plain pendant]

properties

the properties are the constraints i mean

f(x) has a property that area under curve is euqal to length of curve

and there are infinite f(x) that have this property

the goal is to find an equation that helps us find these f(x)?

[quasi sparrow]

yes this +C makes there infinitely many

yes i thought you did that with your integral

isn't this your work

[plain pendant]

yes

one second

[odd edge]

@plain pendant Has your question been resolved?

[tight crescent]

It's, in fact, been 2040 seconds

[odd edge]

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.

[clear tree]

Hello how can I evaluate the following it's either telescoping or geometric

[wooden python]

it is neither

instead it is a sum of two different geometric series

[clear tree]

Can you elaborate

I split

to two series?

[odd edge]

@clear tree Has your question been resolved?

[ripe imp]

For compact two-dimensional surfaces without boundaries, if each loop can be continuously compressed to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré Conjecture, proven by Grigori Perelmán, states that the same is true for three-dimensional spaces.

Someone to solve it

[clear tree]

@wooden python

[wooden python]

$\sum_{n=1}^{\infty} \frac{3^{2n-1}}{4^{2n+2}} - \sum_{n=1}^{\infty} \frac{2^{3n}}{4^{2n+2}}$

[clear tree]

Or ratio test?

[clever fjord]

Ann

[wooden python]

ratio test only tests convergence, it tells you nothing of the value

you can take my word that both these series converge, or apply the ratio test yourself to establish the same -- but applying ratio test to a geometric series is a bit silly.

[clear tree]

But the thing is I don't know how to solve this geometric serie

[clear tree]

.

[wooden python]

what is $\sum_{n=0}^{\infty} ar^n$?

[clever fjord]

Ann

[clear tree]

a geometric serie

[wooden python]

no, what is its value

[clear tree]

but the one you sent is quite different

a/1-r

[wooden python]

missing parentheses

a/(1-r)

[clear tree]

Yes

[wooden python]

both my series can be rewritten into the same firm

form*

think about how

i know you are able to do it

[clear tree]

2^3n can be rewritten as (2^3)^n

[wooden python]

keep thinking in that direction.

i don't rly want to hold your hand all throughout here.

[clear tree]

4^2n+2 can be rewritten as (4^2)^n+1 which is (16)^n . 16

my answer is 1/16

[odd edge]

@clear tree Has your question been resolved?

Channel closed

Closed by @clear tree

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.

[gleaming wharf]

Is this correct mathematical notation?

[low locust]

yes

[gleaming wharf]

Alright

because normally you cant use = when doing row operations

[low locust]

well you arent doing row operations here

[odd edge]

@gleaming wharf Has your question been resolved?

Channel closed

Closed by @gleaming wharf

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.

[vague shard]

he wrote 12cosx = 5sinx but when he get to the dividing he wrote the opposite

why?

also, how he decided to put 5-12-13 at which part of triangle?

[cold sage]

what do you mean?
if 12cos=5sin
12=5sin/cos
12/5=sin/cos

[cold sage]

sin/cos = tan
if tan=12/5 then 12 is the opposite and 5 is the adjacent

the 13 as the hypotenuse can then just be found by pythagoras

[vague shard]

he wrote sin=12 and cos=5

but at the start he wrote sin=5 and cos=12

[cold sage]

show me, because sin=12 and cos=5 is impossible

sin and cos are bounded by -1 and 1

so you must be misunderstanding something

[cold sage]

thats a fraction

sin/cos=12/5 does not mean sin=12 and cos=5

[vague shard]

yes im talking about that

[cold sage]

it means the ratio of them is 12/5

thats like saying 5/6=30/36 means 5=30 and 6=36

doesnt work that way

[vague shard]

so, he can also write like sin/cos=5/12 right?

[cold sage]

yes thats the same equation as i showed here

[vague shard]

okay thanks

.close

[odd edge]

Channel closed

Closed by @vague shard

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.

[tepid spear]

Hey, I don't understand the exercise 3, how can I calculate the distance from a point to a function

[odd edge]

@tepid spear Has your question been resolved?

[tepid spear]

Better question, how can I calculate the minimum distance of a point to a function?

<@&286206848099549185> maybe

[odd edge]

@tepid spear Has your question been resolved?

[mystic saffron]

does the task require to find minimum distance from point P to the point on 2(1-x)(x+2)?

[odd edge]

@tepid spear Has your question been resolved?

[sullen ferry]

think about the distance formula between two points, and how a point on a function can be described

[odd edge]

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.

[stiff pewter]

This is just very confusing to me. Geometry is not my strong point at all

[odd edge]

@stiff pewter Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

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.

[sand zephyr]

My math question is simple: I want to know if a table of values is correct or not. A teacher presented me with a table of (x,y) values that looks like this: (0,1) (1,4) (2,10)(3,20)(4,35). This to me appears immediately to be a tetrahedral function/sum of triangular numbers. y=1/6x(x+1)(x+2). Simple. However, of course, a true tetrahedral would have a slightly transposed table of values: (0,0)(1,1)(2,4)(3,10)(5,20)(6,35) etc. So what's up? Did the teacher just mistype the list of values or do I need to figure out a different function? This is just precalc, nothing fancy.

[odd edge]

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.

[sand zephyr]

Wait, I'm confused. Why did I get put in this channel with a new question if someone is here qith a question already?

[cold sage]

?

[sand zephyr]

Oh, hello! Can you help me?

I don't mean to bother anyone. I'm just a little baffled by this discord.

[spring relic]

Oh oops sorry lol I didn’t notice the channel name lol

[sand zephyr]

Oh

well, can anyone help me with my question: I want to know if a table of values is correct or not. A teacher presented me with a table of (x,y) values that looks like this: (0,1) (1,4) (2,10)(3,20)(4,35). This to me appears immediately to be a tetrahedral function/sum of triangular numbers. y=1/6x(x+1)(x+2). Simple. However, of course, a true tetrahedral would have a slightly transposed table of values: (0,0)(1,1)(2,4)(3,10)(5,20)(6,35) etc. So what's up? Did the teacher just mistype the list of values or do I need to figure out a different function? This is just precalc, nothing fancy.

[spring relic]

This one is confusing lol this is a guess but could it be shifted or stretched. I’m not sure to be exact lol

[sand zephyr]

it can't be shifted or stretched, because the output for x=0 would still be y=0 given any difference in coefficient. And if a constant were added it would alter the whole function.

I think the teacher made a mistake!

THANK YOU for your help 🙂

[spring relic]

Yeah true lol

[sand zephyr]

ok I guess the teacher made a mistake so !close

!close

.... lol I give up

[odd edge]

@sand zephyr Has your question been resolved?

[slender rain]

.close*

.close

can I do it?

nope

@sand zephyr do .close

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

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 pollen]

A 240 pF planar capacitor with distance of 0.2mm, find the area.

I keep getting the answer of 5.42 but the answer is 54.21

[tawdry cave]

!show

[odd edge]

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

[vast pollen]

I have C and d over E but when i calculate it, it gives me like 5.4 and when i convert to cm, it doesnt not give me 54, and the answer is supposed to be 54 in cm

[tawdry cave]

You forgot to change the unit of distance to SI unit.

It's in mm. You are supposed to put in metre.

[vast pollen]

so 0.0002?

[tawdry cave]

Yes

[vast pollen]

it gave me 0.00542

[tawdry cave]

,w 240 * 10^(-12) * 0.2 * 10^(-3) /(8.85 * 10^(-12))

[clever fjord]

Results provided by WolframAlpha

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

Requested by .enemagneto

[tawdry cave]

That seems correct.

[vast pollen]

yes but the answer is supposed to be 54.2 cm

im not sure what i am doing wrong

[tawdry cave]

It can't be cm.

It is area. It would be cm^2.

[vast pollen]

yes that is what i meant sorry

54.2 cm^2

[tawdry cave]

Also, what you have gotten is in m^2. Convert to cm^2. It's same.

[vast pollen]

ohh i see

thank you

i was converting m to cm and not m^2 to cm^2

thank you so much, have a nice rest of your day

.close

[odd edge]

Channel closed

Closed by @vast pollen

Use .reopen if this was a mistake.

[odd edge]

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.

[gaunt stratus]

why is it n^3?

[south plume]

what's T(n)?

[gaunt stratus]

T(n) = T(n-2) +n^2

[south plume]

oh

[echo ginkgo]

what part are you confused abt ?

[gaunt stratus]

how the summations are \theta(n^3)

[echo ginkgo]

the first summation gives $\frac{n^3}{2}$, so obviously it's $\Theta(n^3)$

for the second, you have $4n \sum_{i=0}^{n/2}i = 4n\frac{(\frac{n}{2})(\frac{n}{2}+1)}{2}$, so that's also $\Theta(n^3)$

for the third, use the formula for the sum of squares $4\sum_{i=0}^{n/2}i^2 = \frac{(\frac{n}{2})(\frac{n}{2}+1)(n+1)}{6}$

[void yew]

oh ye

[echo ginkgo]

@gaunt stratus

[gaunt stratus]

oh

[clever fjord]

aPlatypus

[gaunt stratus]

why is it theta and not big o?

[echo ginkgo]

they all have a non-zero n^3 coefficient here

so they're all bounded below by a constant multiple of n^3

[gaunt stratus]

oh because it grows faster than n^3?

big o would be n^4?

nvm

thanks for the answer how do i end this?

[echo ginkgo]

no big theta means you have roughly the same order of growth as n^3

being bounded above and below by constant multiples of n^3

that's what being theta(n^3) means

[gaunt stratus]

yea

ok so O(n^3) would also be correcT?

[echo ginkgo]

yes

and big omega n^3

[gaunt stratus]

because that is the best case right?

[echo ginkgo]

wdym?

[gaunt stratus]

big omega is the lower bound so the best case

[echo ginkgo]

ah yeah

yes

[gaunt stratus]

ok thanks makes sense now 🙂

[echo ginkgo]

but you could also say n^3 is big omega n^2 if you want

the bound doesn't have to be tight

[gaunt stratus]

uh

[echo ginkgo]

time to revise your big O etc... notations then

[gaunt stratus]

oh because big omega is just at least as fast right?

[echo ginkgo]

yes

[gaunt stratus]

cool

thanks for the help 🙂

.close

[odd edge]

Channel closed

Closed by @gaunt stratus

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.

[leaden light]

Can someone explain how to solve this problem

[leaden light]

Consider the figure below. Find an expression for the maximum value of teta such that the person does not slip.
so that the person does not slip.

Here is the translation

[pallid tinsel]

is the coefficient of friction given?

[leaden light]

Nope

I suppose that we should find all the forces that are applied to the body and then equal it to zero

Ff + Fn + Fp = 0

And then make protections to ox and oy

Ffx+ Fnx = 0 and Ffy - Fpy - Fny = 0

But I don’t know what I should do next

[odd edge]

@leaden light Has your question been resolved?

[odd edge]

@leaden light Has your question been resolved?

[odd edge]

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.

[dreamy escarp]

How would you prove n−(m+k)=(n−m)−k.

Like, I know It is true and I can substitute these with numbers and solve it and it will be equal. But, how do I actually go about proving it.

ps, very noob here, be gentle.

[smoky dove]

hello

can someone explain what's the difference between relation and mapping

[odd edge]

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).

[echo ginkgo]

what are n, m, k here ?

[dreamy escarp]

They are arbitrary, could be any number.

[echo ginkgo]

yeah but what type of number

[dreamy escarp]

natural numbers

[echo ginkgo]

natural, integer, ...

well you'd need some kind of definition of natural numbers

otherwise you can't really prove stuff

you can look into the peano axioms for example

[dreamy escarp]

I am following a specific youtube playlist and it is building numbers from string of ones to roman then into hindu.

At this stage, Natural numbers are a string of I's. I, II, III, IIII, IIIII etc. S(n) = N + I ==> S(I) = I + I = II, or S(II) = II + I = III

[echo ginkgo]

and if you want something more guided, the first few chapters of Tao's Analysis 1 go through the construction of natural numbers, integers, rationals, real numbers, ...

[dreamy escarp]

I am not that good with Math to learn analysis. Does what I told above helps? I don't think this question is supposed to be something advanced. I somehow need to prove using what I have been taught in previous lectures. In lectures, author has developed, natural numbers, addition, multiplications and their laws.

But, I am unable to prove this using the things I have learned up until now.

I guess I will re-watch the videos where author proved laws of addition and multiplication. Maybe, that will give me a hint.

[echo ginkgo]

what I'm saying is the first few chapters of Tao aren't analysis in a strict sense

it's just constructing numbers

[dreamy escarp]

Alright, I will take a look.

<@&286206848099549185> please look at pinned message.

[odd edge]

@dreamy escarp Has your question been resolved?

[odd edge]

@dreamy escarp Has your question been resolved?

[odd edge]

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.

[humble meadow]

Hello, I'm having a hard time with this question. I understand formula for Variance and that our expectations in this case just our mean but how do go about finding E(X).

[quasi sparrow]

use z score

$Z = \frac{X - \mu}{\sigma}$ will be $\sim N(0, 1)$

[clever fjord]

riemann

[humble meadow]

How am I supposed to find the Z-score when I don't have X?

[quasi sparrow]

you know the form of X

"normal rv with mean 5, ..."

[humble meadow]

I don't know how I'm supposed to get X just from that information.

[quasi sparrow]

you don't need to get X

you just need var(X)

[humble meadow]

Var(X) = E(X^2)-u^2 right?

[quasi sparrow]

yes but that's not useful here

[quasi sparrow]

you keep sigma as a variable after this step

[humble meadow]

That's the only formula for Variance I know

[quasi sparrow]

then use your P(X < 9) = 0.2 formula

that'll give you sigma

$\sigma^2 = Var(X)$

[clever fjord]

riemann

[humble meadow]

Var(x) = omega^2 is this the one I'm supposed to use?

[quasi sparrow]

the variable name is sigma, not omega

[humble meadow]

Sorry I meant sigma.

Okay but if Z= (X-u)/sigma

I still have X as an unknown.

I'm sorry if being dumb but I don't get how I can do this without X

[humble meadow]

If I keep sigma as a variable, the most I get is -0.84= X-5/sigma.

[quasi sparrow]

this is incorrect

X isn't a single value, it's a r.v.

your first step should be P(X-mu > 9 - mu) = 0.2

[humble meadow]

I don't get it.

I don't have the random variables. I just know that P(X>9)=0.2

And the mean is 5

I don't know how to use that in the formula for the Z-score

[quasi sparrow]

yes from here

[quasi sparrow]

you can subtract something from both sides of the inequality to get this

[quasi sparrow]

You don't work with X directly like this, you need to work with probabilities of X

[odd edge]

@humble meadow Has your question been resolved?

Channel closed

Closed by @humble meadow

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.

[molten bough]

Hello! How would I go about solving this problem? I don't know what the professor is asking for here, as the plot of a real function in the complex plane.. would just be dots on the horizontal(Real) line, right?

[odd edge]

@molten bough Has your question been resolved?

[odd edge]

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.

[proper quail]

what is difference between matrix and determinant

[proper quail]

I have to calculate inverse matrix 3x3

how I can do that and why is it different than calculating determinant

they look almost the same

[lament walrus]

when u calc det u get a number

not matrix

a single number

[weary pelican]

a matrix is a collection of elements (here numbers) arranged in rows and/or columns, the rows all have the same length.
The determinant is a function that inputs a SQUARE matrix and outputs a single number

[proper quail]

Ok so when I calculate determinant i get single number

but how I can calculate matrix 3x3?

I can't find a good tutorial on that

[weary pelican]

You have 2 ways that I know are easy

[lament walrus]

A = | a b c |
| d e f |
| g h i |

u can find the inverse of A like this:

A⁻¹ = (1/det(A)) * adj(A)

[proper quail]

wait wait

so to calculate inverse matrix

i have to calculate determinant first right?

[weary pelican]

yes

[lament walrus]

not always

there is another way

[weary pelican]

well...

[lament walrus]

idk its hard to explain here

im giving up good luck

[proper quail]

Ok because we did that in class

A⁻¹ = (1/det(A)) * adj(A)

i don't understand this

what is adj?

[lament walrus]

adjoint

or we say aswell adjugate

[weary pelican]

Adjugate matrix which is done finding the determinants of the minor matrices

But

Let's not do that

Here's an easier way

so your matrix is
a b c
d e f
g h i

[lament walrus]

u know the "de morgan's rules" ?

[weary pelican]

We'll write a second matrix on the right, which is Identity

[lament walrus]

exactly ..

[weary pelican]

a b c | 1 0 0
d e f | 0 1 0
g h i | 0 0 1

Now, your job is to row reduce echelon the matrix on the left

[subtle fern]

What is the second derivative for x^2+y^2=2xy

[weary pelican]

!occupied

[odd edge]

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).

[proper quail]

wait

so

1 0 0
0 1 0
0 0 1

[lament walrus]

open ur channel..
and its depends on which u need y or x

[proper quail]

is some standard i will always use?