help-13

[tropic oxide]

of 1080?

[hexed vortex]

yeah I think that should be 1080

[tropic oxide]

,calc 2^3 * 3^3 * 5

[wraith dagger]

Result:

1080

[tropic oxide]

so it is

what about the divisor, 180

... well it's 2^2 * 3^2 * 5

@hexed vortex still here or what

[cedar kiln]

@hexed vortex Has your question been resolved?

[tropic oxide]

rip

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[patent hull]

Hi! I'm wondering how to show that dim(V) even implies ker(F)=im(F) for this question I've done the other direction, but I'm a little stuck here.

[patent hull]

Do image and kernel have to be of equal dimension for even dimensional spaces? And I would have to show that the image and kernel equal and not just their dimensions, so maybe I'm starting from the wrong place. Any advice would be greatly appreciated!

[tropic oxide]

implies that there EXISTS such an F that its ker and im have the same dim

that's important

you need to construct F

[patent hull]

ooohhh ok that makes more sense

thank you!

.close

[cedar kiln]

Channel closed

Closed by @patent hull

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 pumice]

This is a mathematical question, really.

[frozen pumice]

It is a question of the function y(t) being finite or infinite. t is a real number.
I want clarity on option 3.
t is not an explicit factor in the equation.
I made a y vs x graph, and it's like a concave hill with (0,1) as its peak

What do you think?

[tropic oxide]

yeah so in fact you can say 0 < y(t) <= 1

regardless of what x is doing

option c is... confusingly worded even for me

[frozen pumice]

Thank you, Miss Ann. Good day to you.

.close

[cedar kiln]

Channel closed

Closed by @frozen pumice

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[limpid glacier]

if you are given two integers a and b (a <= b)
where:
gcd(x,y) = a
lcm(x,y) = b
the sum x+y is minimum (have the lowest value)

** how do you find the 2 integers x and y? **

Heres what i tried:
define k = b/a , the coprime factors of k are (m,n) where values of m&n is closest to the square root of k

we will have gcd(m,n) = 1

so x = a.m , y = a.n

Example: a = 6 , b = 36

k = 6 , where we will find the pairs (2,3) ; (3,2)
then x = 6.2 = 12 ; y = 6.3 = 18 (or x = 18 and y = 12) and the sum will be 30, which is minimum.

(just asking if there is a better way of solving this problem mathematically)

Theres also special cases where theres no solutions for x and y.

[cedar kiln]

@limpid glacier Has your question been resolved?

[limpid glacier]

<@&286206848099549185>

[gentle echo]

🤔 you could use the fact that lcm * gcd = product

could

[limpid glacier]

how would that go

[gentle echo]

x * y = a * b

you have a * b as constants so uhhh

that's somewhere

then you have a problem of minimising x+y with a constraint of x * y = a * b

the lowest integer solution is your answer

i don't know much number theory a whole lot so this is the best i could help you with 😔

[limpid glacier]

i appreciate the help though

i think im gonna close this soon if it doesnt gain any activity

[gentle echo]

happy to help

[limpid glacier]

well i just retake a look at my notes and thats what i mean by the square root of k part

because of AM-GM we will have (x+y)/2 >= square root of xy

[surreal cave]

I think x=am and y=an with gcd(m,n)=1 is good, then if lcm(x,y)=amn=b then surely mn=b/a=:k (as you said). Then intuition tells me that take the closest two factors of k and that would minimize the sum like when k=6 the two closest factors are (2,3), and x+y=30 but if you chose (6,1) or (1,6) (equivalent) x+y=6.1+6.6=42

but that's just intuition I would not have a good idea of how to prove it rigorously...

but maybe to show that choosing the factor pair (d1,d2) is equivalent to (d2,d1)

so picking d1 closest to sqrt(k) but also smaller than it

and then d2=k/d1

surely d2 integral because d1|k by definition

[limpid glacier]

[surreal cave]

idk that's just spitballing, but could be a direction

[limpid glacier]

a question, (5,1)?

[surreal cave]

oh wait I meant 6

[limpid glacier]

well expanding on a little bit , theres no solutions if k is not an integer

The reason i have posted this problem is that for big numbers this method is not too optimal so yeah

im also not sure about negative numbers but they are not something to be worried about

[cedar kiln]

@limpid glacier Has your question been resolved?

[limpid glacier]

welp

.close

[cedar kiln]

Channel closed

Closed by @limpid glacier

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[vital jolt]

Hello

[vital jolt]

I need help understanding my solution

[cedar kiln]

@vital jolt Has your question been resolved?

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hexed mist]

hey! I was wonder what went wrong? I checked over it and re-did the whole problem and I am still getting the samw answer

[tropic oxide]

uhhh your numerator is not the same as that of the problem mate

question says 3x^2 + 2x - 3 but you went for x^2 - x + 6

so you... kinda went the opposite way lmfao

[hexed mist]

LMAO okay thank you

did not notice that

and this is why I am getting evalutated for dyscalcula

thank you!!

can't even spell

let me solve the correct problem and then I'll come back

okay it should be the correct problem now. Did i mess anything up?

[ancient nova]

Nope

All good

and your handwriting is gorgeous

[hexed mist]

wooo! And thank you!!!

.close

[cedar kiln]

Channel closed

Closed by @hexed mist

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hexed mist]

i'm back 20 mins later

[hexed mist]

I am on another probelm and I'm confused about what my next step is?

[crimson sedge]

i think u expanded it wrong

[sacred anchor]

put brackets around the (Bx + C)

[pastel vault]

yeah clearly should be +Bx(x - 1) + C(x - 1)

[sacred anchor]

also are you sure $1^2 + 9 = 9$? lol

[hexed mist]

where would the x-1 come from?

[crimson sedge]

denominator of A

[hexed mist]

pfft-

ohh

so it would distribute

okay

one sec

[crimson sedge]

yeah just expand it and put in evidence x, x^2 and the constant term

then u can make a system of equations with the 10

[hexed mist]

I see, will try that out ty!

[sacred anchor]

Let x = 0, to find C, and then let x = anything else to find B

[hexed mist]

i need to really work on partial decomposition bc i don't think i did it right?

[cedar kiln]

@hexed mist Has your question been resolved?

[sacred anchor]

just from your working it looks correct

might be some arithmetic error i didnt catch, double check it on your end

[hexed mist]

okayy i'll keep looking over it ty

[sacred anchor]

i think you did something wrong wih solving for C

[hexed mist]

ohh wait i see

it

i didn't put x^2+9 into the equation when solving for C

[hexed mist]

update:

no idea what's wrong bc I even pulled up integral calculator to check my final answer and it has teh same answer

[dire geode]

,w int 10/((x-1)(x^2+9))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by rie.mann

[dire geode]

wrong sign on arctan term

[dire geode]

your C=-9 was correct but somehow it became positive in your answer box

[spark carbon]

hola

[hexed mist]

the program marked that as wrong as well

[dire geode]

oh your |x/3| is wrong in arctan

|stuff| is only for log

,w int 1/(x^2+1)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by rie.mann

[dire geode]

no abs val

[hexed mist]

ah

there we go ! thank you!!

.close

[cedar kiln]

Channel closed

Closed by @hexed mist

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hollow star]

Hey -- I made a program that produces the nth catalan number given n. I got it to work for n=2*10^9, and the hash of the output in sha-256 is as follows:

8CE88BC5287AF643ADAE6988300B7DF8CED71EC3875F34AEC85D55799ECD68CB

I couldn't find any result online about the exact value of the number, so I have no way of knowing if i'm truly correct (AFAIK the code and everything else is all good). could anyone try to reproduce this number and see if they get the same hash?

[twilit escarp]

Catalan(2*10^9) has quite a lot of decimals

[crimson delta]

casually about 10^9 decimals

thats like 500 mb just to store the number

[twilit escarp]

Not sure i can on my side

[crimson delta]

frankly no surprise you couldnt find that anywhere. who would put that anywhere

[hollow star]

its 1.2 gb

for 1.2 billion decimals

[crimson delta]

well its 4*10^9 bits

[hollow star]

to clarify, i put the number in a plain text file, for each digit representing a byte

wouldn't that be 1.2 billion bytes = 1.2 gb

[crimson delta]

ok yeah thats not very efficient

[hollow star]

i know, i just wanted to see the number for the sake of the work i put in to come up with it

it was just 12 minutes for i/o anyway so its wtv

[crimson delta]

well you could just try to compute the last 100 digits or so of the number

and then compare

compute with some CAS I mean

[hollow star]

could you guide me on how to do that? i'm pretty new on using coding for math

[crimson delta]

well its just coding but in a language that has more built in stuff for math

[twilit escarp]

Yeah you can work mod (a storable number)

[hollow star]

which language? i'm kind of hopeless if it's anything outside of python. i'll definitely try learning C because python is not built for math, but i'm looking for an immediate solution

[crimson delta]

sagemath is basically built on python

you can use a sagecell on the internet

maybe

if its fast enough

[twilit escarp]

Well python math library is probably made in C

[crimson delta]

what formula did you even use to compute C_n

recurrence should never finish

[hollow star]

if you use legendre's formula for 2n choose n for each prime and subtract the p-adic valuations from multiplicities of factors of n-1 then you get a prime factorization

then the bottleneck is getting a seperate program to read the output txt file and actually crunch the number

i got it the number in around 9.3 minutes in python, i bet it would be a lot faster using C

[hollow star]

for Cn = 2n choose n times 1/n-1

[twilit escarp]

• no?

[hollow star]

sorry, what are you asking?

[twilit escarp]

1/(n+1)

[hollow star]

times

[twilit escarp]

Yeah but you wrote -

Is it typo

[hollow star]

oh shoot

yeah typo

[floral arrow]

Maybe post your code if it's not too long

[hollow star]

if someone could implement this and then take the prime factors modulo 10^10000 (or even 10^100 is fine as a minimum) and then multiply them all together (you should get the last ten thousand digits that way, correct me if i'm wrong), that would be great

[crimson delta]

frankly if the result is wrong even five digits are probably enough to tell

[red igloo]

Store it in a raw binary format rather than a plain text file

[hollow star]

i'll try to get the code on my github today and i'll share the link

once i do that

[red igloo]

You’re wasting bits the way you’re doing it right now since you only need like 3-4 bits per digit

[hollow star]

i know there are more efficient ways to get the number, i only did it the way i'm doing it right now on a whim since i wanted to see the number for myself

[red igloo]

Also this, I don’t think you should be using an interpreted language, something like C, C++ or C# would be more favourable for this case

You can ask AI to transpile the code if you aren’t familiar with them

[hollow star]

sure

where would i go from there in terms of verifying my result, though

[cedar kiln]

@hollow star Has your question been resolved?

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.

[errant rock]

@austere rune since the lines are parallel, what does that indicate with regards to the slope?

[austere rune]

same slope?

[errant rock]

Yes!

So, how do we find slope using two points?

[austere rune]

using the slope formula y2-y1/x2-x1?

[errant rock]

Yep; so all you have to do is just set the slopes equal to each other. You have two separate sets of two points, so calculate the slopes for the first section of two points and the second section, then set them equal to each other.

[austere rune]

thank you so much!

[errant rock]

No problem! Just remember to type .close to free the channel if you're done.

[austere rune]

.close

[cedar kiln]

Channel closed

Closed by @austere rune

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.

[onyx jolt]

Wh

I'm going to send my question didn't mean to click that sorry-

I'm not sure what I did wrong I thought I've been doing everything right and even followed the example they gave

[ember geode]

,rotate

[onyx jolt]

I think it's S that I'm getting wrong

Well S '

[cedar kiln]

Channel closed

Closed due to the original message being deleted

[onyx jolt]

The original message was a sticker-

[cedar kiln]

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.

[cosmic olive]

Could someone walk me through and explain this? I'm not sure what to do - thanks so much!

[ancient grotto]

show that any arbitrary vector in V can also be represented with C as basis

[cosmic olive]

how can i do that

[ancient grotto]

you already have B as basis so you can take any arbitrary vector and then use the properties of inner product to show a correspondence from B to C (by using the linearity of inner product)

[cosmic olive]

could you help me with that? what arbitrary vector can i use

im lost with this topic

[stuck jolt]

[ancient grotto]

did I do an oof ?

smh the anxiety

[ancient grotto]

you would take a tuple of n-scalars corresponding to n-basis vectors to depict your arbitrary vector with basis being B.

[cedar kiln]

@cosmic olive Has your question been resolved?

Channel closed

Closed by @cosmic olive

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.

[fallen furnace]

Please can someone help me with this?

I have tried to use Kirchoffs first law, second law and ohms law

and got a set of equations

in the end

but after I tried to solve the equations, apparently no solution exists

wait lemme try smtn

wait nbm

nvm*

still not sure

<@&286206848099549185>

[cedar kiln]

@fallen furnace Has your question been resolved?

[fallen furnace]

hm

[cedar kiln]

@fallen furnace Has your question been resolved?

[main needle]

@fallen furnace still there?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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

Closed due to the original message being deleted

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.

[indigo quartz]

Observe

63 - 24 = 39

52 - 48 = 4

39 + 4 = 43

verify this hypothesis for the second square

then find ? yourself

@crimson sedge

[crimson sedge]

okk

[cedar kiln]

@crimson sedge Has your question been resolved?

[tropic oxide]

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

[crimson sedge]

i am stuck with right side rule of dice , there's no written work here

[peak relic]

Think about the first 2 positions only. What do the positions of the 6 and 2 tell you about the relationship between 3 and 4?

[crimson sedge]

4 is opposite to 3?

[peak relic]

Yeah. You can think of taking the first die, picking it up and turning it. The 6 will stay on top, the 2 will move to the left, and the 4 comes into view.

Can you find a similar situation to try and understand what's opposite to 5?

[crimson sedge]

1?

[peak relic]

Well, our 5 is next to 6 and 4, right?

[crimson sedge]

yea

[peak relic]

Do you see another number that is next to 6 and 4?

[crimson sedge]

2

[peak relic]

So now imagine taking that second die, picking it up, and rolling it toward you. The two turns from the front to the bottom, the 6 comes to the front, and the 5 goes from the back up to the top. This brings you to the third picture.

[crimson sedge]

ohhk

[peak relic]

(another way to see this is: from the first 3 pictures, 6 is next to 2, 3, 4, and 5. So it must be opposite to 1).

(that only leaves 2 and 5 left to be a pair, since we knew 3 and 4 were opposite)

[crimson sedge]

Ok thanku

[peak relic]

Sure! Remember to type .close once you're done.

.close

[cedar kiln]

Channel closed

Closed by @peak relic

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.

[hasty lion]

a = 1 + 2 + 3 + 3² + ... + 3¹⁰ + 3¹¹

a) prove that a is even
b) prove that a can be divided by 10

Ok so, would I calculate that whole thing and is there a formula / expression I could use to do so?
I have done an exercise earlier which required me to only focus on the last digits of the numbers and I think this one would require this too.

[cedar kiln]

@hasty lion Has your question been resolved?

[azure horizon]

why is there a 2

[hasty lion]

Well, that's the exercise

[azure horizon]

very strange

but anyway yeah a is even iff the last digit is even

and a can be divided by 10 iff the last digit is 0

so just do the same sort of thing again

[hasty lion]

do I check the last digit for all 3ⁿ

[cedar kiln]

@hasty lion Has your question been resolved?

[tired charm]

a)for all 3^0 * 3 + 3^1 * 3 + ... + 3^10 * 3 is odd

you can say so after calculating the amount of numbers

if the amount of number is odd, then the whole 3 stuff is odd

+1 + 2 => even

[cedar kiln]

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.

[steel shore]

can anyone help?

[frozen valve]

huh

[graceful karma]

[cedar kiln]

@steel shore Has your question been resolved?

Channel closed

Closed by @steel shore

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.

[crimson sedge]

what's the difference between these two?

[crimson sedge]

regular expressions

[graceful karma]

What kinda regular expressions

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

@graceful karma this was the whole question.

I just don't know the difference between c & g

[graceful karma]

I'm not familiar with this kinda math sorry

[crimson sedge]

No prob

[potent gorge]

is this an exam

[crimson sedge]

assignment

[cedar kiln]

@crimson sedge Has your question been resolved?

[stuck jolt]

0* 1* is the concatenation of 0* with 1*

if $L_1$ and $L_2$ are languages, then $L_1L_2$, their concatenation, sometimes denoted $L_1 \circ L_2$, is the set ${uv \mid u \in L_1, v \in L_2}$

[wraith dagger]

mniip

[stuck jolt]

@crimson sedge

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

@stuck joltty

[cedar kiln]

Channel closed

Closed by @fresh olive

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.

[crimson sedge]

wouldn't these two be the same though basically? because both would accept 0000111 for example.

I can see (01)* being a different case as thats 01, 0101, 010101

vs (0 U 1)* which I imagine could be 0101011...etc

[stuck jolt]

no, the second will not accept 0000111

[crimson sedge]

doesn't 0star mean as many 0s then union 1star as many 1s?

[cedar kiln]

@crimson sedge Has your question been resolved?

[stuck jolt]

no?

what do you mean "then"

you take the union of two languages

the word has to belong to either 0* or 1*

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[cedar kiln]

@wicked berry Has your question been resolved?

[cedar kiln]

@wicked berry Has your question been resolved?

[cedar kiln]

@wicked berry Has your question been resolved?

[errant rock]

Please read #❓how-to-get-help

[rustic coyote]

um

[crimson sedge]

[rustic coyote]

please don’t keep occupying the channel if nobody is helping

it is better to try again in an unoccupied channel after opening this back up

.close

[cedar kiln]

Channel closed

Closed by @rustic coyote

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

So, i hmave been able to complete part a up until the quadratic, but im not sure how to factorise it with another factor to = z^3 + Az^2 + 26

[dense wing]

do you know vieta's formulas?

[crimson sedge]

No

i am unfamiliar

[dense wing]

have you heard "sum and product of roots" before?

[crimson sedge]

are they simple? i just need to learn how to finish these questions by monday and my revision is complete

oh yeah

like alpha + beta + gamma = -b/a?

[dense wing]

yes

those are vieta's formulas

[crimson sedge]

hhh okay

well the thing is, i only have roots alpha and beta, i dont have root gamma

nor do i have the value of A

[dense wing]

which one would be easiest to use here for part a? Given you dont know A and B?

roots 1,2 or 3 at a time?

[crimson sedge]

im not too sure, i thought it would be best to factorise and solve for the third root that way

[dense wing]

you cant factorise

you dont know A or B

[crimson sedge]

why not?

for the roots you can

[dense wing]

you do that for part b

you need the 3rd root though

[crimson sedge]

it's just, i saw the worked solution, and he factorised by inspection to find the third root

my working is the same up until by inspection and it really confused me

[dense wing]

I suppose you could do that, however I think vieta's formulas is more straight forward and "obvious"

[crimson sedge]

ah okay

im not familiar with the rest of them, only -b/a

what are the others?

[dense wing]

$\alpha\beta\gamma =\frac{-d}{a}$ is the revelvant one here

[wraith dagger]

Mosh

[dense wing]

you can google the rest

[crimson sedge]

ohh okay

that makes a lot of sense really, makes it quite simple

[dense wing]

and by CCRT, you know 2 of the roots are 1+i and 1-i

so you have (1+i)(1-i)(gamma)=-26

But yeah, Vietas generalizes nicely for any polynomial

[crimson sedge]

so yeah, y = -13

alright, im going to try part b, is it okay if i keep this channel open just incase i have trouble?

@dense wing Okay, i got it

thanks

that clears things up

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @ember 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.

[mystic island]

Ik ik its easy

but how do i do 3

Number 3

<@&286206848099549185> sorry for ping idk if i am allowed

[zinc blaze]

only after 15min bro

[mystic island]

oh sorry

[cedar kiln]

@mystic island Has your question been resolved?

[cedar kiln]

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.

[crimson sedge]

is this the proper way to solve for the error in the adjacent side of the triangle?

[crimson sedge]

using differentials

Here is the original question

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @tame quest

Use .reopen if this was a mistake.

[cedar kiln]

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.

[torpid wren]

So I need to figure out to do substitution, here is one of my problems: -4x+3y=-2

[torpid wren]

and y=x-1

[livid hound]

replace something with something of equivalent value
add stuff like parentheses / multiplication symbols if needed to maintain the order of operations

try "substituting" y = x-1
into the first equation

[torpid wren]

ok

so like this:

-4x+3(x-1)=-2

[livid hound]

yes

[torpid wren]

oh okay

thank you

[cedar kiln]

@torpid wren Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[normal hound]

How do I prove that this returns the optimal solution? I'm assuming by induction by the number of subtrees where the base case is 1 subtree? Any tips to get me started?

[cedar kiln]

@normal hound Has your question been resolved?

[cedar kiln]

@normal hound Has your question been resolved?

[normal hound]

<@&286206848099549185>

[cedar kiln]

@normal hound Has your question been resolved?

[cedar kiln]

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 sage]

i need some help

[eager elk]

SYW

[main sage]

?

oh show your work

[cedar kiln]

@main sage Has your question been resolved?

Channel closed

Closed by @main sage

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

Closed due to the original message being deleted

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.

[crimson sedge]

how do i do this?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[fluid kestrel]

so this is in one of my practice exams for specialist but I have no idea what to do

[quartz leaf]

have you learnt about binomial coefficients?

[fluid kestrel]

no...

[quartz leaf]

the notation refers to combinations

https://mathworld.wolfram.com/BinomialCoefficient.html

[fluid kestrel]

like nCr

[quartz leaf]

yeah

[crimson sedge]

well what's 5C2

and what's 4C2

[fluid kestrel]

5C2 = 5!/2!*3!

= 10

[crimson sedge]

good

[fluid kestrel]

4C2 = 6

ohhhh

[crimson sedge]

now show that they equal

[fluid kestrel]

then 3X10 = 30 and 5X6 = 30

[crimson sedge]

mhm

[fluid kestrel]

Thank you!

[crimson sedge]

you are welcome

[fluid kestrel]

.close

[cedar kiln]

Channel closed

Closed by @fluid kestrel

Use .reopen if this was a mistake.

[cedar kiln]

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.

[violet pebble]

im kind of confused on how to start b

I originally tried replacing x with x=y^3 but I dont think that thats right

[cedar kiln]

@violet pebble Has your question been resolved?

[main needle]

x=y^3 will work, turn everything into an x

[violet pebble]

ohhh i see! that ended up working, thank you!

.close

[cedar kiln]

Channel closed

Closed by @violet pebble

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.

[wheat jewel]

How to find which octant a (x,y,z) coordinate lies in?

[tropic oxide]

are octants not simply defined by the signs of the x, y and z coordinates?

[wheat jewel]

yes but is there a way to figure it out instead of just remembering these signs mean 3rd octant, etc.

like ik there is a table which u can memorisr

memorise*

[tropic oxide]

oh, you mean remembering which octant gets which number?

[wheat jewel]

yes

like ik u can just use this table

but is there a trick or something instead of just memorising a table?

[tropic oxide]

A convention for naming an octant is to give its list of signs, e.g. (+,−,−) or (−,+,−). Octant (+,+,+) is sometimes referred to as the first octant, although similar ordinal name descriptors are not defined for the other seven octants.

this is what wikipedia says

however, your table is based on the following naming scheme:

octants 1-4 are the 'upper' octants (z>0), starting from (+,+,+) counterclockwise

octants 5-8 are the 'lower' octants in the same order

[wheat jewel]

for when z<0?

[tropic oxide]

yes

[wheat jewel]

ok thank you for the help

.close

[cedar kiln]

Channel closed

Closed by @wheat jewel

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.

[smoky stump]

1(a)

what is the general rule in finding the values for k?

because in (d), the solution has 0, +- 1 and 2 as the answer

not -2

i know them being conjugate pairs

and also how would you visualise this sort of thing like k = 0, +- 1, -2 on the argand diagram

[granite ridge]

find k such that the final expression is between -pi and pi

make a bunch of inequalities and solve

[smoky stump]

if so then how would you get the k = 0 +-1 and 2 in this?

[wraith dagger]

A Fellow Human

[granite ridge]

cleaned everything up sry

where did 2 come from?

[smoky stump]

i mean -2

how did you go by finding k equals to ?

[granite ridge]

use the bounds

[wheat jewel]

can i take over? lol

ok firstly, do you know how to convert a complex number to mod-arg form ?

[smoky stump]

yes

[wheat jewel]

so what is the modulus and what is the argument of i?

[smoky stump]

the mod would be 1

and the arg would be 90

pi/2

[wheat jewel]

correct

and to find the roots theres a very simple formula

are u in aus?

[smoky stump]

Yeah how do you know?

[wheat jewel]

4U ?

[smoky stump]

Yeah

[wheat jewel]

the textbook is NSM ?

[smoky stump]

No advanced terry lee

[wheat jewel]

ok im doing my hsc in 2 weeks lol

ok back to the question

theres a really easy basic formula that i highly recommend memorising

[smoky stump]

okay, please tell me

[wheat jewel]

n is the root u r trying to find... so in this case 4

r is the modulus

theta is the argument

and if ur finding 4th root, u sub in k=0, 1, -1, -2

if u were finding 5th root it would be k=0, 1, -1, -2, 2

etc.

[smoky stump]

then the question here is which values of k would you know what to sub in?

[wheat jewel]

u start from 0 and go up

so 0, -1, 1, -2, 2 etc...

in that order

[smoky stump]

If you take a look at (d)

[wheat jewel]

depending on how many roots ur finding

[smoky stump]

the values of k is 2 as well

instead of the -2

[wheat jewel]

u can use 2 if u want but it wont be within the mod-arg limits

u know how the angle in the mod-arg form has to be in between -π and π

[smoky stump]

yeah

[wheat jewel]

if use 2, it wont be within that and u will have to convert it

but if u -2 then it will

so always use the negative number first

[smoky stump]

but then why did (d) use 2?

not negative 2

[wheat jewel]

it didnt

must be a typo since new textbook

because if u check the 4th answer they got.... its -23π/24

[smoky stump]

yeah i see

[wheat jewel]

if they used 2 it would be 25π/24

but as i said, even if use 2, its still the right answer

just not within the limites

limits*

so u'll have to convert it

[smoky stump]

Another question is how does doing this to find the roots this way work in the textbook?

[wheat jewel]

i dont understand

[smoky stump]

What i meant is that through using the way of the textbook, like finding the kth values when multipled by 2pi k such that it will be in the same quadrant no matter what values of k

how does dividing by the nth amount of root suppose to wrk?

If possible, please refer back to some like argument and mod rules

[wheat jewel]

since ur dividing by the nth amount, u wont repeat the values until u have extra solutions (that is, more solutions than 'n')

because if u look at roots of unity etc. graphically

[smoky stump]

yeah, they are evenly spaced

[wheat jewel]

yes exactly and when u finish going around the circle

and get to initial spot again

thats when u repeat the values

[smoky stump]

yeah but when you times them together, how do they form the solution

in this case i?

[wheat jewel]

wait i take it back

have u learnt de'moivres yet?

[smoky stump]

yeah

[wheat jewel]

yeah well if u take any of the solutions u get to the power of 4 then u will get i

[smoky stump]

yeah

[wheat jewel]

idk if im understanding ur question

but they're just 4th roots of i...

[smoky stump]

okay thanks

.close

[cedar kiln]

Channel closed

Closed by @smoky stump

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.

[misty gyro]

hiya, this is a past paper question. I am suppose to find the tangent plane to this parametrised surface, however I am not too sure where I went wrong with my working as the answer for the normal is (2,-2,1) and the equation is 2x -2y + z = 0

[tropic oxide]

you didn't go wrong

your normal is simply -27 times their normal

[misty gyro]

Oh yeah you’re right, thank you very much @tropic oxide

.close

[cedar kiln]

Channel closed

Closed by @misty gyro

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.

[civic coral]

ayy

[civic coral]

i have a question

there are how many parallelograms on this pic?

let me show you my work

i got 288 but the correct answer is 72

i split it into three areas area A, area B, area C

first just look at the A

[civic coral]

PLEASE LOOK AT THE "A" IN THIS PIC AT THE FIRST LINE
how to form a parallelograms in this case? we need 4 sides right?

first we pick 1 from those 4 lines in this case i choose the blue. then there's 3 lines left for you to choose so pick one randomly e.g the yellow. then do the same thing to red and green

I WANNA KNOW WHERE I DID WRONG, I AIN'T WANT THE ANSWER OR "HOW TO DO IT PROPERLY (HOW TO DO IT YOUR WAY)"

its Permutations, everyone have their own way. i need to know where i did wrong so i wont do the same mistake next time

[civic coral]

HERES THE PICTURE aka THE PIC

<@&286206848099549185>

[cedar kiln]

@civic coral Has your question been resolved?

[civic coral]

i need help

SOS

[cedar kiln]

@civic coral Has your question been resolved?

[civic coral]

<@&286206848099549185>

[cedar kiln]

@civic coral Has your question been resolved?

[tropic oxide]

you're making two mistakes here, one major and one minor
the minor mistake is that you're writing C(n,1) where you could just write n, which makes your expressions look obscure and hard to parse both for yourself and others
but the major mistake is that you're picking two sides but you aren't accounting for the fact that order doesn't matter. if you'd picked the green and then the red you would've ended up with the same parallelogram

and the same goes for the other pair of parallel sides, of course, so in total you end up overcounting by a factor of four

[civic coral]

yes ure right, im gonna end up double-count those things

i should take a note on this, i keep fallin on the same mistake

[civic coral]

then the Area A will be 72/2!2!

which gives you 18

[tropic oxide]

yes, exactly.

[civic coral]

and sorry i don't know how to describe the problem i think thats the reason why it took 2 hours till somebody replies to my question

[tropic oxide]

i was busy with other things so that's why i only saw it now

also, grammar thing: "ain't" means "isn't" (except "ain't" can be used with any pronoun, not just 3rd person singular), not "don't"

[civic coral]

thank you i will take it to my note

[tropic oxide]

of course, it must be said that "ain't" is strongly informal in terms of style.

[civic coral]

thank you it helps a lot, now i can continue my course

i think the question is solved

.close

[cedar kiln]

Channel closed

Closed by @civic coral

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.

[crimson sedge]

how do you do this without conjugate root theorem

is it even possible?

because the second part of the question asks for you to deduce that alpha is equal to the conjugate of beta, so i assumed they dont want you to use conjugate root theorem in the first part of the question

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @muted obsidian

Use .reopen if this was a mistake.

[tawdry rivet]

You can use the fact that
sum of roots = -b/a
Product of roots = c/a

[cedar kiln]

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.

[little stag]

how to solve this?

[potent gorge]

what did u try

[flat tapir]

（a+b）（a-b）=a^2-b^2

this may helpful

[cedar kiln]

@little stag Has your question been resolved?

Channel closed

Closed by @little stag

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

.close

[cedar kiln]

Channel closed

Closed by @rough gazelle

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.

[simple cairn]

I got it right but I dont under stand how an 18 sided polygon is equal to 2880

[livid hound]

bad wording

the interior angle sum of an 18-sided polygon is 2880°

consider the formula for the interior angle sum (derived from splitting a polygon into triangles)

[simple cairn]

Ik how to get the answer

But how do I find out the angle is 2880

?

[livid hound]

consider the formula for the interior angle sum (derived from splitting a polygon into triangles)

*interior angle sum

[simple cairn]

I haven't learnt that

[livid hound]

start with a regular polygon

[simple cairn]

So 360

[livid hound]

pick a vertex

[simple cairn]

Vertex?

[livid hound]

corner

[simple cairn]

Ok

[livid hound]

and draw segments from that to every other vertex

note the number of triangles formed this way

[livid hound]

draw lines from that vertex to every other vertex

[simple cairn]

Ok

[livid hound]

you don't really need to bother with the adjacent vertices,
anyway how many triangles are formed this way

[simple cairn]

3

[livid hound]

and what's the interior angle sum of a triangle

[simple cairn]

16

0

[livid hound]

no

the interior angle sum of a triangle is none of 0,16 or 160

[simple cairn]

2880

[livid hound]

the interior angle sum of a triangle is NOT 2880

[simple cairn]

What is it?

180

[livid hound]

yes

[simple cairn]

Triangle

[livid hound]

pls read my questions carefully next time

[simple cairn]

I didn't see that

Ok

[livid hound]

and note that if you add up all the angles in the triangles you'll get the interior angle sum of your polygon

i.e. in the case of a pentagon, you have 3 triangles for a total angle sum of
3 * 180° = 540°

[simple cairn]

Ok

[livid hound]

and in general for an n-sided polygon, you'll have (n-2) triangles

for an angle sum of (n-2)*180°

[simple cairn]

Where did the -2 come from

[livid hound]

n-2 will be the number of triangles formed by connecting one vertex to every other vertex for convex polygons

[simple cairn]

Ok

So for it to be convex it has to be 180?

[livid hound]

wdym by it

[simple cairn]

Polygon

[livid hound]

wdym by polygon has to be 180

[simple cairn]

For it to be convex

[livid hound]

that question doesn't make sense

don't know what you're trying to say

[simple cairn]

Dont mind me

I got it now ty

[cedar kiln]

@simple cairn Has your question been resolved?

[cedar kiln]

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.

[crimson sedge]

simplifying the power

not entirely sure how they got to this answer. if I combined my way I just got t-6

nope the picture is correct

(2t-1)-(t-5) = 2t-1-t+5 = t+4

you probably forgot to change the - to a + when expanding the - into the brackets

i know but i dont understand how they even got a +5

or what they even did

well i just said, since you are subtracting t-5, the -5 will become +5

because two negatives make a positive

[obsidian coral]

-(t -5) = -1 * (t - 5)

Distribute

[crimson sedge]

so the negative in the middle of the problem is -1?

starting to understand i think

[obsidian coral]

That's how you can think of it

$$(2t-1)-(t-5) = (2t-1)-1 \cdot (t-5) = (2t-1)+ -1 \cdot (t-5)$$

[wraith dagger]

dldh06

[crimson sedge]

im just not fully understanding where the -1 comes from or why i have to distribute but i think i just have to stop getting stuck over this one and accept it

[obsidian coral]

Because everything has a constant of 1

Like x = 1x

Or -x = -1 * x

So -(t -5) = -1 * (t - 5)

[crimson sedge]

and i only distribute to that second one because the - is only in front of that one right

[obsidian coral]

Yes

[crimson sedge]

ok thanks for the help really helped me :D

.close

[cedar kiln]

Channel closed

Closed by @twilit rampart

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 fox]

my teacher replied to this question

so does that mean the height of ABC is 2.5 and BC is 1

[crimson sedge]

yes

[sleek fox]

thanks for the confirmation

.close

[cedar kiln]

Channel closed

Closed by @sleek fox

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.

[cinder fox]

So for 3-8 how exactly do I figure this out?

[crimson sedge]

,rotate

[crimson sedge]

re-write each function in terms of powers

[cinder fox]

Right, I just don't even know where to go about it or how to start

[crimson sedge]

oh I see

do you know exponent laws?

[cinder fox]

Not really, teacher is kind of a goofball and didn't explain them

[crimson sedge]

okay, this is them

#7 doesn't look like a power function

[cinder fox]

Hmm so separate the negative from the 3

And yea ik 7 isn't, since it has the exponent has to be x

Yea lol

Hm kk

So for q3, I would separate the x^-3 into x^-1*x^3?

Oh its not a -3

Sorry, the x is neg

Gah this is terribly confusing

I know the answer to the q3, its (-1/6)x^9

But other than multiplying the exponent of x and the exponent outside the parenthesis i have no clue how to figure out the rest

Like, how does the 6 randomly come up to the top and put itself in the parenthesis with the -1? No fuckin clue

I mean sure but that doesn't help me solve the problem

I've figured out 1 part of the problem, what rule is allowing the 6 to swap sides of the fraction and insert itself into the parenthesis

Okay so you multiply 1/6 to the x^9

Gotcha

And I assume the 1/6 becomes negative in my problem since the x is negative in the parenthesis

Gotcha, thanks!

.close

[cedar kiln]

Channel closed

Closed by @cinder fox

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.

[glass chasm]

Taking the derivative and solving for dR

[cedar kiln]

@glass chasm Has your question been resolved?

[main needle]

yeah take the derivative of R = k/r^2

you'll get a relationship between dr and dR you can use

[glass chasm]

k thx

.close

[cedar kiln]

Channel closed

Closed by @glass chasm

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.

[crimson sedge]

1/cot = tan ?

[dense wing]

yes.

[crimson sedge]

And 1/cos = sec ?

[dense wing]

yes.

google reciprocal trig

[crimson sedge]

Ok tysm

[dense wing]

you're asking stuff that is easy to google.

[crimson sedge]

Okkie

[crimson sedge]

I tried

Bu it showed the trig table

[dense wing]

did you google "1/cot=tan"?

[crimson sedge]

Or sin^2 + cos^2 = 1 concept

[crimson sedge]

Yeaahh

It showed ncert sums

[floral thistle]

just look into trig identities

[dense wing]

One of the first results for "1/cot=tan" was mathisfun.com...

[crimson sedge]

Okeii

[crimson sedge]

Oh okk

Tnq its done

.close

[cedar kiln]

Channel closed

Closed by @cinder cedar

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.

[silk sail]

How are these 2 equal?

[mighty oar]

can i have help please?

[pulsar folio]

That sum has a well-known form
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯

[silk sail]

Dude channel occupied just real the rules.

[pulsar folio]

in this case, it's missing the last +n term, so the n(n+1)/2 becomes n(n-1)/2

[silk sail]

Oh let me see.

[silk sail]

Uh what?

Can you please elaborate?

[pulsar folio]

in the equation you posted, it's only 1 + 2 + ... + (n - 1)

the formula is for 1 + 2 + ... + (n-1) + n

the formula on the wikipedia page, specifically

[silk sail]

Yes.

Then?

[stuck jolt]

just apply the formula at k=n-1

[silk sail]

Uh what?

[stuck jolt]

sum from 1 to k is k(k+1)/2

k=n-1

[silk sail]

Yes.

Oh let me see.

Then it is n²-n.

[stuck jolt]

/2

[silk sail]

Oh yes.

That.

[stuck jolt]

are you satisfied

[silk sail]

I will read and comprehend and tell.

I think I will be.

Ohhh thank you very much.

They just did not expand it I see.

.close

[cedar kiln]

Channel closed

Closed by @silk sail

Use .reopen if this was a mistake.

✅

[silk sail]

.close

[cedar kiln]

Channel closed

Closed by @silk sail

Use .reopen if this was a mistake.

[cedar kiln]

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.

[fervent osprey]

Ok just to check im not being stupid and im right

[fervent osprey]

Theres 47 players in 2021

And 82 in 2022

It says find the percentage increase

So i do 82-47

Is 35

35/47*100

74%

And its not on there

What they have is just 82/47 which is where they got 58 from

Am i just an idiot

[frozen valve]

nah you are not wrong

it should be 74%

but maybe there were 82 in 2021 and 47 in 2022

maybe you read it wrong

[cedar kiln]

@fervent osprey Has your question been resolved?

[cedar kiln]

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.

[low rune]

.Ask

.Ask A boat sails d1 = 40.0 km 60.0° North of East and then travels d2 = 70.0 km west.
a)
d1East =
d1North =
d2East =
d2North =

what

[low rune]

A boat sails d1 = 40.0 km 60.0° North of East and then travels d2 = 70.0 km west.
a)
d1East =
d1North =
d2East =
d2North =

For d1East I put 40.0kmCos(30) = 34.6 km

For d1North I put 40.0kmSin(30) = 20 km

Why are they wrong

and for d2East and d2North I need help with

[cedar kiln]

@low rune Has your question been resolved?

[obsidian coral]

Angle is wrong

60 degree north of east

You did 30 degrees of east of north

If you did that way, you have the trig functions wrong

[cedar kiln]

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.

[marble dagger]

I have a list of characters and numbers which when joined together create a string of 6 letters. The final 6 letter string uses 4 elements from the initial list.

Example:

Password: q400dc```

[marble dagger]

I am unable to devise an algorithm to enlist the number of possible 6 digit combinations.

[main needle]

you need to do a bit of casework

sometimes it's a three single characters and a 3 digit number

sometimes it's two single characters and two 2 digit numbers

do you allow repeats? like qqq400?

[cedar kiln]

@marble dagger Has your question been resolved?

[cedar kiln]

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.

[brazen root]

Find all real solutions to the equation x^2+2y^2=xy

[broken swan]

<@&286206848099549185> I need help with this

[obsidian coral]

You have to wait at least 15 minutes before pinging helpers

[brazen root]

give me my channel back pls!

[broken swan]

ok sry.

[obsidian coral]

Also #❓how-to-get-help

This is a new system

[broken swan]

no I used one of the availables, got thrown here

[true glade]

Try dividing the entire equation by y^2 and taking (x/y) as t

[brazen root]

ok

then t is complex

[true glade]

True

Well from the get go you can tell that one real solution is (0,0)

Since all terms contain either x or y or both

[brazen root]

mhm

[true glade]

And since the quadratic you get is complex you can tell that there are no other real roots

[brazen root]

ah okay

[true glade]

So (0,0) should be the only real solution

[brazen root]

oki

thanks!

.close

[cedar kiln]

Channel closed

Closed by @brazen root

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.

[uncut urchin]

Subject: Differential Equations - Hi, I'm having a bit of trouble figuring out finding equations from solutions, specifically this 2x part. I get the other part. I wrote it out in paint to help illustrate better. Thanks

[heady breach]

are you trying to find anti-derivative?

[uncut urchin]

I don't know.

[heady breach]

from the looks of it I feel like you are trying to integrate it... <@&286206848099549185> can anyone spot me on this?

In your case C0 is 7

[uncut urchin]

yea

that's waht I gather

I can provide another example, maybe it will help you guide me

[heady breach]

this is your initial coefficient

that would be nice

[uncut urchin]

ok one sec

[heady breach]

from what I see, I can tell that your c0 value is the coefficient in front of your variable or e. The c1x is simply the coefficient in front of your variable (which in our case is 3 and 0). Our variable is the exponent of e. For the second part (2x), you have no e terms in this. Because of this, your e value will be e^0x. For the first term the e value is e^3x where 3 is the coefficient of x

This is for the first problem^

D is c0

I am not too sure what this is lol. I am in high school and this is like trying to understand quantum mechanics 😅 . I understand where all of the terms are coming from but I am not sure what this is or how to explain the concept of this... sorry :(

I hope you find what you came for though...

<@&286206848099549185>

Best of luck!

[zinc blaze]

as you have two solutions, you may need to find a second order differential equation

knowing it is linear and homogeneous makes it way more easy

just make a_2 y'' + a_1 y' + a_0 y = 0, then using y = 7e^(3x) + 2x, calculate its derivatives and solve for the coefficients

[uncut urchin]

For context, this is part of the method of undetermined coefficients

[zinc blaze]

then it is exactly what you should do

first

what is y'

[uncut urchin]

?

where is y at all

isn't that what we're finding?

I'm just trying to understand where c0 came from in (c0+c1x)e^0x

i understand how to get D-0 from it but don't understand why it would be squared. because there's two solutions so it would need to be order 2? So I suppose my main question is how do you know 2x is correlated from two solutions of the DE?

[zinc blaze]

I think that y is that 7e^(3x) + 2x

it is the solution, right?

[uncut urchin]

When I solve the equation, I do obtain the solutions, but I don't understand how to get from 2x to (c0+c1x) backwards

[cedar kiln]

@uncut urchin Has your question been resolved?