help-33

[hazy lion]

yea but your problem is +k

oh, wait, no its not

yea you got it

[austere wave]

so do i just use the value x = -2?

from the quadratic of course

alr i got it

thanks for the help

.solved

[marsh citrus]

Channel closed

Closed by @austere wave

Use .reopen if this was a mistake.

[marsh citrus]

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.

[marsh citrus]

@stone summit Has your question been resolved?

[twilit geyser]

what have you tried

[twilit geyser]

where did you get these questions from in the first place

[marsh citrus]

@stone summit Has your question been resolved?

[marsh citrus]

@stone summit Has your question been resolved?

[marsh citrus]

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.

[willow vault]

Hi can someone help with a combination question

[ivory turtle]

!da2a

[marsh citrus]

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

[willow vault]

So I want to find the number of combinations to reach a sum of 10 with integers 1-9

I get 2^9-1

Minus 1 because I want to sum at least 2 numbers

[ivory turtle]

you will always need two numbers to sum with integers 1-9

*at least

[willow vault]

Yes I know that

Say I want the number of combinations for the above with a new condition

Where I cannot repeat the numbers summed

[unborn condor]

how did you get this

[crystal lintel]

the problem is unclear to me

[slender bobcat]

so
1+2+3+4 is allowed
but
1+1+1+1+1+5 is not allowed

[willow vault]

Yes

[ivory turtle]

why is 1+1+1+1+1+5 not allowed?

[slender bobcat]

.

[ivory turtle]

oh right

mb

[willow vault]

Okay so I got 2^9

[ivory turtle]

2^9 seems way too high

[willow vault]

Cuz at most it’s 9 plus signs between 10 numbers

Like visually

[unborn condor]

again, how did you get that

[slender bobcat]

2^9 is 512 which seems like a lot

[willow vault]

ok let ‘o’ be like representing 1

ooooo+ooooo is like 5+5

[ivory turtle]

is the answer not just 9?

[crystal lintel]

,w expand \prod_{i=1}^9 (1+x^i)

[elfin berry]

Results provided by WolframAlpha

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

Requested by slayyla

[willow vault]

I can insert a plus sign between every o

That’s two options I pick 1

[unborn condor]

ummm... wtf?

[ivory turtle]

but then you use multiple numbers, no?

[high edge]

are permutations allowed or not?

[willow vault]

Combinations

[ivory turtle]

is this a sudoku question?

[willow vault]

Uh no it’s me trying to figure out an Olympiad question

[ivory turtle]

!original

[marsh citrus]

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.

[willow vault]

{1,2,3…2000} find the total amount of subsets whose sum is divisible by 5

But like I don’t just want someone to tell me the answer yk

So I’m guessing ish through my way

[celest girder]

I would just do cases 💀
Case 1: Two Integers
9 + 1 = 10
8 + 2 = 10 ....

Case 2: Three Integers
7 + 2 + 1 = 10
...

[ivory turtle]

thats a wildly different question

[willow vault]

I understand but the number can go up to 2000

In the original question I want to solve

[crystal lintel]

you should reduce the numbers in {1,2,3…2000} mod 5

and see how many of each residue there are

[celest girder]

3Blue1Brown covered this in a video :D

[willow vault]

Yes I just don’t wanna look 😅

[willow vault]

Hm

[ivory turtle]

this is why i was asking if this a sudoku question, in killer sudoku you need to use unique numbers that sum to a certain value

[willow vault]

Any thoughts I’ll listen just please don’t leak the answer aha

[crystal lintel]

like throwing 1 into a subset and throwing 6 into a subset does ”the same thing” for the value of the sum of the set mod 5

so you only need to care about the values of the elements in the set mod 5

[willow vault]

I’ll look into that thank you

[crystal lintel]

https://projecteuler.net/problem=250 see also 🙃

[willow vault]

My temptation to just type up a program to do it haha >::C

[celest girder]

hmmmmm
I think this can get pretty messy and hard to deal with

bc you'll get sets of numbers of different resides
like
{7, 3 1}, { 8, 4, 2} but then also
{1, 2, 3, 4, 7, 8}

[crystal lintel]

what?

[celest girder]

I'm just saying idk how reducing by mod 5 will help? 😭

[crystal lintel]

:hmmge:

well my idea was to do it with dynamic programming but that’s probably not acceptable

the reducing mod 5 thing makes bookkeeping easier

[celest girder]

!!

ahhh, in that case, that would probably be my first choice too!

[crystal lintel]

it would be like… keep track of how many subsets for each residue mod 5 there are, starting with just 1 element available to use, and make one more element available in each dp step

[crystal lintel]

on second thought this may not make bookkeeping any easier

[celest girder]

Step 1:

2000/ 5 = 400
so 4000 numbers in [0], [1], [2], [3], [4].

Step 2:

subsets of size 1:
400 choices -- all elements of [0]

subset of size 2:

• 400 C 2
• [1] + [4] = [0], thus 400*400
• [2] + [3] = [0], thus 400*400
• (I think that's it)?

subset of size 3:

• 400 choose 3
• uhhhhhhhh

[crystal lintel]

not what i had in mind

[marsh citrus]

@willow vault Has your question been resolved?

Channel closed

Closed by @willow vault

Use .reopen if this was a mistake.

[crystal lintel]

start with
S = {1}
dp = [1,1,0,0,0]
where dp[i] represents the number of subsets of S with sum i mod 5

now imagine we wanted dp for S = {1,2}. we just keep the old subsets and also get new ones by adding in the element 2 to them

and we only need to keep track of the sums of the subsets mod 5, not the actual subsets

and we can repeat this adding 3, 4, etc to S

[marsh citrus]

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.

[novel juniper]

if gcd(a,b)=1; c|a+b then prove gcd(a,c)=gcd(b,c)=1

[novel juniper]

so to start $a+b=ck$

[elfin berry]

ƒ(Why am. I here)=I don't Know

[still temple]

looks like you'll need ||Bezout's lemma||

[slate yarrow]

Didn't we do this earlier

[novel juniper]

i haven't marked it as done in my book, so idts

[still temple]

or a proof by contradiction?

[novel juniper]

I'm more comfortable with the lemma

so xa+yb=1

[slate yarrow]

Hmm want to do it again?

[novel juniper]

yeah, sure

[slate yarrow]

(a,b)=(a+b,b)=(c,b)=1

[novel juniper]

right

[lucid zenith]

why is (a+b,b)=(c,b)?

I think you mean to say (c,b) | (a+b, b)

[slate yarrow]

c|a+b

[slate yarrow]

I mean that also works

[lucid zenith]

it doesn't just work, that's the only thing you can conclude directly

[slate yarrow]

Sure you are right

[lucid zenith]

you can't say (c,b)=(a+b, b) just because c|a+b

[slate yarrow]

Hmm ok

Imma stop it

[novel juniper]

so how would I use bézout's lemma here?

[slate yarrow]

Wai I'll help you with NT when I gitgud

[novel juniper]

👍

$so ax+by=1$

[lucid zenith]

let $ax+by=1$

[elfin berry]

ƒ(Why am. I here)=I don't Know

kheerii

[lucid zenith]

lmfao nice timing

and let $a+b=ck$

[elfin berry]

kheerii

[novel juniper]

yup

[lucid zenith]

then, a=ck-b

so, $x(ck-b)+by=1$

[elfin berry]

kheerii

[novel juniper]

mhm

[lucid zenith]

$b(y-x)+c(kx)=1$

[elfin berry]

kheerii

[lucid zenith]

let $y-x=k_1, kx=k_2$ where $k_1, k_2\in\mathbb{Z}$

[elfin berry]

kheerii

[novel juniper]

doesn't this imply ck-b and b are coprime ?

[lucid zenith]

oh yeah also state that $x,y,c\in\mathbb{Z}$ somewhere here

[elfin berry]

kheerii

[lucid zenith]

does it?

okay yeah you're right

but

that's not what you're after

[novel juniper]

hmm

one minute

[lucid zenith]

ck-b is just a, so you just restated your original thing

[novel juniper]

ah right

[lucid zenith]

so this gives you $k_1b+k_2c=1$

[elfin berry]

kheerii

[novel juniper]

oo

so b and c are co prime

[lucid zenith]

yes

[novel juniper]

got it

thanks!

[lucid zenith]

a symmetric proof works for (a, c)=1

[novel juniper]

yeah, makes sense

[lucid zenith]

you can remember that $(a,b)=\text{min}{ax+by: x,y\in\mathbb{Z}, ax+by>0}$

[elfin berry]

kheerii

[novel juniper]

👍

thanks

.close

[marsh citrus]

Channel closed

Closed by @novel juniper

Use .reopen if this was a mistake.

[lucid zenith]

[marsh citrus]

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 steppe]

how do i graph something if theres no x-intercepts but i know the max/min points?

im confused

[vagrant gull]

did you find the vertex

you could still graph it by just knowing the vertex and y-int

[rocky steppe]

in the previous problem

thats like the same as this one, just differnt numbers

they only asked me to find x intercepts

and the max/min

and i was able to graph it

but this problem it doesnt ask me to find vertex

so im not sure, do i need to do extra work outside the problem?

usually the problem has all the steps to graph

[vagrant gull]

does it say you have to graph it?

[rocky steppe]

yes

did u see the pic above?

[vagrant gull]

you could do this in your head

you don't need to show it

[rocky steppe]

isnt the 4 the vertex?

thats the max/min value

[vagrant gull]

vertex is (h,k)

you found k, which is 4

try doing this problem in vertex form

[rocky steppe]

whats the vertex form?

[vagrant gull]

y=a( x − h ) 2 + k

[rocky steppe]

erm im not sure how

i just did it the way my teacher taught

[vagrant gull]

do you know completing the square?

[rocky steppe]

yes

[vagrant gull]

did you teacher not taught you how to convert a standard form to vertex form

you should do this to get this

[rocky steppe]

ok

i got it

im doing antoher problem rn but ill comer back to it

thank you for th ehelp

[vagrant gull]

no problem

[rocky steppe]

.close

[marsh citrus]

Channel closed

Closed by @rocky steppe

Use .reopen if this was a mistake.

[marsh citrus]

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.

[dull sable]

How do I find the sum of this series

[lyric bay]

Convergence test?

[dull sable]

No like find the value it’s supposed to be pi^3/32

Is there a way this can be connected to a special function like the digamma function or gamma function

[limber hearth]

Fourier ?

[dull sable]

I don’t mind a Fourier series but I don’t know much about it other than you have to find the right function on some interval

[marsh citrus]

@dull sable Has your question been resolved?

[naive fox]

I think this paper might related to what you are doing https://www.ams.org/journals/qam/2018-76-03/S0033-569X-2018-01499-3/S0033-569X-2018-01499-3.pdf

and there is a nice discussion here https://math.stackexchange.com/questions/359667/sum-sum-n-0-infty-frac-1n2n13

[marsh citrus]

@dull sable Has your question been resolved?

[dull sable]

I guess for now I’ll have to remember that sum as pi^3/32 , I did see in that link you can use residues but I only know residues theorem for integrals not how it applies to an infinite series

[naive fox]

yeah... it is quite a common one, actually. There is no quick way to derive that

[marsh citrus]

@dull sable Has your question been resolved?

Channel closed

Closed by @dull sable

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 oyster]

can you check my work and answers please

[raw hawk]

||Chain rule||

For the first part

[marsh citrus]

@misty oyster Has your question been resolved?

[misty oyster]

that's the same answer i got, but with the parts in parentheses in a different order

are you saying i need to show more steps?

[raw hawk]

Why is x² multiplying everything

[raw hawk]

Is it required?

[misty oyster]

for which question? 1,2, or 3?

[misty oyster]

nope, it doesn't earn any extra points

[raw hawk]

Derivative of 2√x -1 is 1/√x

Not x^(3/2)

[misty oyster]

so that's what f'(x) is for question 3?

going by the formula

[raw hawk]

Sorry I have to gts

😴

make g(x) a function of i(x)

h(x)=f(x)xg(i(x))

[marsh citrus]

@misty oyster Has your question been resolved?

[warm abyss]

yo which question

3?

@misty oyster

[marsh citrus]

@misty oyster Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[mortal lintel]

I am in calculus 1 and trying to learn how to create a graph of a function but I feel like I don't have enough information so I can't make sense of it. How can f(3) = 5 but the limit as x ->3 of f(x) != 5 at the same time and how would I graph that?

[fervent rampart]

you can make a function defined piecewise, for example: [ f(x) = \begin{cases} \frac 2x & x \ne 3 \ 5 & x = 3 \end{cases} ]

[elfin berry]

cloud

[fervent rampart]

then you would make a hollow circle at the place the function "should be" (the limit) and make a solid circle at the value of the function

[mortal lintel]

for full context these are the conditions:
lim x-> 0- f(x) and lim x-> 0+ f(x) are infinite
f(3) = 5, but ;im x -> 3 f(x) !=5
lim x -> -3- f(x) != lim x-> -3+ f(x)

wouldnt the circle be in the same location though? How do I make a hollow and a solid circle both at (3,5)

[fervent rampart]

the limit should be somewhere other than y = 5

something like this

[mortal lintel]

I don't understand how I am supposed ot know that. I feel like I dont have enough information

do I just put it literally anywhere else?

[fervent rampart]

you're free to make the limit anything as long as it isn't 5

[mortal lintel]

So the only thing I know for sure is there is a vertical asymptote at x=0
the second rule tells me there is a solid point disconnected from the function where f(3) = 5 and then I can make a hollow point at basically any value other than 5 for the limit of f(x)

so so far I am looking at something like this

[fervent rampart]

yes, then the hollow point is the one that the graph should pass through

[mortal lintel]

oh oops right I mixed it up

so then for the last part lim x -> -3- f(x) != lim x-> -3+ f(x)
do I just pick any 2 values that are different at x=-3?

like would this work?

[marsh citrus]

@mortal lintel Has your question been resolved?

Channel closed

Closed by @mortal lintel

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.

[lucid zenith]

I'm trying to prove the fundamental theorem of Algebra (for fun). Specifically what I'm trying to prove is that the polynomial $$P(z)=a_nz^n+a_{n-1}z^{n-1}+...+a_0$$ with $a_i\in\mathbb{C}, a_n\ne 0$ can be factorised as $$P(z)=a_n(z-z_1)(z-z_2)...(z-z_n)$$ with $z_i\in\mathbb{C}$

[elfin berry]

kheerii

[lucid zenith]

I realised that I only need to prove that P(z) has at least one root, after which I can prove that that factorisation must exist using the factor theorem and strong induction

[stark trail]

assuume P(z) != 0 for all z in C

then what can you say about |P(z)|?

[lucid zenith]

|p(Z)|>0

[stark trail]

yes

denote g(z)=|P(z)|

it will have some minimum value right?

[lucid zenith]

yeah

non-zero

[stark trail]

actually, before I continue

do you want me to just give you the method

or are you trying some things

[lucid zenith]

no, maybe some sort of hint

[lucid zenith]

we need to prove that g(z) has a root

[stark trail]

its fairly unintuitive imo

heres the first 2 steps without any work as a hint

there are certainly other better methods to prving this btw, this is just what I know using CA

[static quarry]

there is actually a book with nothing but proofs of the FTA

[lucid zenith]

hmm

[stark trail]

I think even if I give you all the steps, its still some working out to do

incase i go away

open this if u want later

[lucid zenith]

can we write $p(z)=c+a_r(z-z_0)^r+a_{r+1}(z-z_0)^{r+1}+...+a_n(z-z_0)^n$

[elfin berry]

kheerii

[lucid zenith]

wow

.close

[marsh citrus]

Channel closed

Closed by @lucid zenith

Use .reopen if this was a mistake.

[still temple]

[marsh citrus]

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.

[valid hinge]

69

a=a/2+a/2
b=b/3+b/3+b/3
C=c/4+c/4+c/4+c/4

a+b+c/9 >= (a^2b^3c^4/(4^5×3^3)

2^9 4^5 3^3>=(a^2b^3c^4)

[stoic slate]

First, let’s clarify a,b,c > 0

[valid hinge]

Yes

[stoic slate]

When the factors are equal u will get your max

So

a/2 = b/? = c/??

[marsh citrus]

@valid hinge Has your question been resolved?

[valid hinge]

Why?

[stoic slate]

No problem, we can do your way too. Give me a moment

[valid hinge]

Yes sir

[stoic slate]

So you have this (a/2+a/2+b/3…+c/4)/9 >= ((a^2b^3c^4)/(2^2 + * 3^3 * 4^4))^(1/9)

Numerator is 18

18/9 = 2

2 >= right side

Can u continue from here?

[valid hinge]

Yes sir

@stoic slate

[stoic slate]

Ok so

[valid hinge]

...

[stoic slate]

We have 2^9 = 2^4 * 2^3 * 2^2

Right?

Now lets take 2^3 and 3^3

[valid hinge]

Yes right

[stoic slate]

What do u get

[valid hinge]

6^3

[stoic slate]

2^4 is 4^2

And 4^5 * 2^2 how much is it?

Start by making 4^5 in base 2

Then multiply and then let raised another base to 4

[valid hinge]

I got it now

B

[stoic slate]

U mean (2)?

[valid hinge]

Yes

[stoic slate]

Yes thats correct 4^5 is 2^10 and 2^10 * 2*2 is 2^12, which is (2^3)^4 = 8^4

[valid hinge]

.close

[marsh citrus]

Channel closed

Closed by @valid hinge

Use .reopen if this was a mistake.

[valid hinge]

.reopen

[marsh citrus]

✅

[valid hinge]

@stoic slate

I would like to know your method too

[ivory sundial]

They have utilized a manipulation of the AM-GM inequality

[valid hinge]

Like how?

[ivory sundial]

Look up the AM-GM inequality

[valid hinge]

I have solved the whole question with am gm

[valid hinge]

I am looking for another method which they intrduced

@ivory sundial

[ivory sundial]

The AM-GM inequality has equality when all terms are equal, hence its minimized when they are equal

[valid hinge]

I see

[ivory sundial]

You should always look for using these inequalities instead of calculus in questions like this

[valid hinge]

a+b+c=18

[ivory sundial]

I'm sure you could use vector calculus here but it would be so lengthy

[valid hinge]

Vector calculus 🥺

I thought derivative

a/2=b/3=c/4=k

a=2k
b=3k
c=4k

[shadow warren]

lagrange multipliers moment

[valid hinge]

Yes

But i will not do that because it is competitive exam

What should I next?

Help

.close

[marsh citrus]

Channel closed

Closed by @valid hinge

Use .reopen if this was a mistake.

[marsh citrus]

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.

[sweet pawn]

why

[golden pecan]

11c^5

Sorry

[sweet pawn]

why

[golden pecan]

4c^3 + 7c^5 is 11c^8 sorry

[stoic slate]

?

[golden pecan]

Is the ans 11c^8 d^5

[stoic slate]

The answer to what, i don’tsee any question

[proud basin]

no

[golden pecan]

.

[stoic slate]

That is not a question

That is a picture of a product and you should say what you want to do with that

[golden pecan]

What would it be

[stoic slate]

For example expand

[golden pecan]

Simplify

Sorry

[stoic slate]

What do you do when you have a product?

[proud basin]

$4\cdot7\cdotc^3c^5d^5$

[elfin berry]

Skill_Issue
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[stoic slate]

Of 2 bases with different exponents

[golden pecan]

Add

[stoic slate]

So make the product here

And let me see your working

[golden pecan]

Is it 4x7 because of the ()()

[stoic slate]

What is 4 * 7?

You can take them out cause product is commutative

[golden pecan]

C^8 d^5

[golden pecan]

Ty

[stoic slate]

What happens with 7 * 4?

[golden pecan]

Why is it multiplication instead of addition

[stoic slate]

What does 2b means?

It means 2 * b, right?

[golden pecan]

What

[stoic slate]

When u have a number close to a variable you multiply them

[golden pecan]

Oh

[stoic slate]

For example 4c^3 means 4 * c^3

This * means multiply

So (4c^3d^5)(7c^5) means 4 * c^3 * d^5 * 7 * c^5

And here you use commutative property to multiply

[golden pecan]

Okay

Tysm

,close

[stoic slate]

4 * 7 = 28

[golden pecan]

.close

[marsh citrus]

Channel closed

Closed by @golden pecan

Use .reopen if this was a mistake.

[marsh citrus]

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.

[novel juniper]

using euclid's algorithm obtain integers (x,y) satisfying the following

[novel juniper]

gcd(56,72)=56x+72y

now using EDA I got the gcd=8

[versed storm]

Right

[novel juniper]

so 8=56x+72y

or 1=7x+9y

[versed storm]

You will gave to use the process of algo

[novel juniper]

hmm

ok

thanks

[versed storm]

Did you got it

[proper zodiac]

You "work backwards" through euclid substituting jnto the equation above

[novel juniper]

let me try

[glacial hedge]

or say the numbers are small and notice they're easily found by hand (||91-90||)

[novel juniper]

could you elaborate ?

the steps are

[versed storm]

Write your process of euclid

[novel juniper]

72=56+16

56=48+8

48=6*8

[versed storm]

Yea

[proper zodiac]

Youre better off watching a vid of.someone doing it

[versed storm]

Now sub a and b at the place of 72 and 56

[novel juniper]

ok

instead of telling me the steps, could you give me a hint, like what'

what's the idea here

[glacial hedge]

You gotta see it once

16 = 72-56
8 = 56-3*16

So 8 = 56 - 3*(72-56)
= 4*56 - 3*72

and you keep subsituting

making bigger numbers and distributing at each step

reading the gcd computation backwards

[novel juniper]

hmm

ok

thanks

[glacial hedge]

it's much easier to see than to convey

if you think you understood, just try with other numbers, there's infinitely many practice examples for this

[novel juniper]

Yeah, will do have 4 more problems like this in my book

thanks

.close

[marsh citrus]

Channel closed

Closed by @novel juniper

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.

[plush blaze]

,, \frac{1}{x} + \frac{1}{p} + \frac{1}{q} = \frac{1}{x+p+q} solve for x

[elfin berry]

CrazyGamer547

[plush blaze]

my textbook answer says x = -p or x = -q

but i hv no idea how it got there

[spark lagoon]

you can move everything to the left

then find lcd

then multiply everything with it

then set the numerator equal to 0

factor and then you will have a quadratic equation

and by using the quadratic formula you can find the solutions

[plush blaze]

what does lcd mean?

lowest common denominator?

or wat

[spark lagoon]

yeah

your textbook answers are correct btw

its just a very long and tedious process to do

[plush blaze]

if i move everything to the left, the lcd will be (x)(p)(q)(x+p+q) ???

[plush blaze]

oh

[spark lagoon]

its because the lcd will be (pqx)(x+p+q) and then for the quadratic equation a= q+p , b- 2qp+q^2+p^2 and c=qp^2+pq^2

the methodology is quite simple but the process of doing everything correct is the hard part

[plush blaze]

onesec

lemme try

,, pq(x+p+q) + xq(x+p+q) + xp(x+p+q) - xpq = 0

[elfin berry]

CrazyGamer547

[plush blaze]

is this correct?

after i multiply by lcd

so like i just simplify it now?

[spark lagoon]

yeah pretty sure its correct

[plush blaze]

so now just simplify?

[spark lagoon]

remove the parentheses

[plush blaze]

ok

onesec

[spark lagoon]

and then remove the opposites and collect like terms

and then factor everything and then identify the coefficients of the quadratic equation

[plush blaze]

kk

,, x^2(p+q) + x(p+q)^2 + pq(p+q) = 0

[elfin berry]

CrazyGamer547

[plush blaze]

now i just treat it like a normal quadratic equation?

and use quadratic formula?

[spark lagoon]

yeah

[plush blaze]

will i be able to factorize it tho?

like is it compulsarily needed to use formula

[spark lagoon]

yeah since the answers are -q and -p you can factorize it

the discriminant will factorize to $(p^2-q^2)^2$

[elfin berry]

Miliski

[plush blaze]

oh

[spark lagoon]

it will be way easier with the quadratic formula in my opinion

[plush blaze]

ohk

btw i can remove (p+q) right

cuz all 3 terms hv it

divide the whole thing

so

[spark lagoon]

you dont know if p+q is zero or not

[plush blaze]

oh

right

so i cant factor it

[spark lagoon]

just do the last parentheses here

[plush blaze]

so i expand $(p+q)^2$ and then use quadratic formula?

[elfin berry]

CrazyGamer547

[spark lagoon]

you need to distribute pq through the parethenses

you can also expand $(p+q)^2$

[elfin berry]

Miliski

[plush blaze]

oh

[spark lagoon]

and then identify the coefficients of the quadratic equation

[plush blaze]

ok

a = p+q

b = p^2 + q^2 + 2pq

c = p^2 q + pq^2

???

[spark lagoon]

yeah that is right

then use the quadratic formula

[plush blaze]

ok

onesec

,, discriminant is (p^2 + q^2 + 2pq)^2 - 4(p+q)(p^2q+pq^2)

[elfin berry]

CrazyGamer547

[plush blaze]

,, = (p^2 + q^2 + 2pq)^2 - 4(p^3q + pq^3 + 2p^2q^2)

[elfin berry]

CrazyGamer547

[plush blaze]

how do i take the root of this?

[spark lagoon]

you need to expand everything and then do the operations that are possible and then you will be able to factor it

[plush blaze]

oh

ok

[spark lagoon]

it should factor to $(q^2-p^2)^2$

[elfin berry]

Miliski

[plush blaze]

lemme see

[spark lagoon]

so then you can simplify the root with the exponent

[plush blaze]

what joy does school get with giving these kind of problems to 10th graders 😭

,, ok yeah it simplified to (p^2 - q^2)^2

[elfin berry]

CrazyGamer547

[spark lagoon]

you can now simplify the root and then just seperate the solutions and find them

[plush blaze]

ohkk

thxxx

got it

x = -p or -q

tysm

[spark lagoon]

np

[plush blaze]

that was the lengthiest sum i hv ever solved till date

.close

[marsh citrus]

Channel closed

Closed by @plush blaze

Use .reopen if this was a mistake.

[marsh citrus]

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.

[pure compass]

AD = AE = BF
Prove that G = 90 degrees

[pure compass]

And I figured out that ADE is congruent BCF

But what now

And i know that E = F

But i don't know how much is e or f

something like that

<@&286206848099549185>

[vital forge]

Is AD = AE = BF all that was given? I don't see how you arrived at the fact that ADE congruent to BCF.

[pure compass]

yeah

me too

oh

ohh i forgot to tell its a parallelogram

[vital forge]

Did you assume/is it given that ABCD is a paralelogram?

Ah okay

Well, you have that the opposite angles are congruent in ABCD

[pure compass]

oh really

[vital forge]

And you have a bunch of angles that are equal to each other bc of isosceles triangles and angles opposite to each other like AED and GEF.

[pure compass]

mhm

[vital forge]

Perhaps start by calling at these angles x, and if you have an angle that you dont have info on, you can call it y, z, ...

[pure compass]

alright

[vital forge]

Yeah. Do you know Thales Theorem?

[pure compass]

no

[vital forge]

Ok, nw.

[pure compass]

wait so how should the angels should be

instead of ADE is congruent BCF

[vital forge]

As long as angle A matches angle B is shouldnt matter the other, as they are isosceles triangles.

So like, ADE congruent BFC or ADE congruent BCF

[pure compass]

so i got it right?

[vital forge]

Yeah, this is right.

[pure compass]

oh good

mhm so what should we do now

I don't see what we can do

[vital forge]

Well, say that angle ADE and DEA are x, given that the triangle is isosceles.

[pure compass]

alright

[vital forge]

If angle A is y, it follows that y + 2x = 180

[pure compass]

right

yeah

mhm wait why D = y

Isn't it just 2x?

oh right

yeah

so you called b as y

alright

[vital forge]

Give me a moment, go back to this.

[pure compass]

alright

mhm i think i solved it @vital forge

C = 2x

A = 2x

2x + x + x = 180

x = 45

[vital forge]

Thats the asumption I made, but I made a mistake in the process.

[pure compass]

if E = 45 AND F = 45

oh

mhm

[vital forge]

ADE is not congruent to BCF.

[pure compass]

oh

mhm

[vital forge]

I thought the congruent theorem was SS for some reason.

Anyway.

Lets go one-by-one.

[pure compass]

alright

[vital forge]

We know that ADE is isosceles, so the equal angles we denote them as x and angle A as y such that y + 2x = 180

[pure compass]

alright

[vital forge]

Similarly, is BCF, we end up with angles a and b such that 2a + b = 180.

[pure compass]

yeah

[vital forge]

Now, the little trick here is to notice that triangle GEF is congruent to triangle GDC.

Can you see why?

[pure compass]

oh

i think i see it

[vital forge]

Why is that correct?

[pure compass]

wait but i see only two angels

c1 = f1

and d1 = e1

[vital forge]

Well, the third angle is G itself.

[pure compass]

oh

why?

[vital forge]

Angle G is in both the triangle GEF and triangle GDC.

And I believe we can agree that angle G = angle G.

[pure compass]

oh right

yeah

[vital forge]

Angle GDC equals angle GEF because AB is parallel to CD>

[pure compass]

yeah

[vital forge]

These are called corresponding angles.

As per US books, had to google it.

[pure compass]

lol

[vital forge]

Well, because these two are congruent, and angle GEF = x, then it follows that GDC is also x.

Now you can see the euqations that I put in the bottom of the paper.

[pure compass]

b = 2x?

oh 2x + 2a = 180

[vital forge]

But basically, y + 2x = 180 and b + 2a = 180 bc of angles of a triangle. b = 2x because of opposite angles of a parallelogram.

Substituting back yields 2x + 2a = 180 => x + a = 90.

Now we look at triangle GDC.

In that triangle, we have the relationship G + a + x = 180. Given that a + x = 90, it follows that G is 90 degrees.

[pure compass]

wait why a + x = 90

[vital forge]

2x + 2a = 180, right?

[pure compass]

yeah

[vital forge]

If we divide both sides of the euqaiton by 2, it yields x + a = 90

[pure compass]

oh right

oh i see now

alright

thanks man @vital forge

[vital forge]

No worries.

Have a good one.

[pure compass]

i appreciate it a lot

same to you

.close

[marsh citrus]

Channel closed

Closed by @pure compass

Use .reopen if this was a mistake.

[marsh citrus]

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.

[terse dove]

pls help me with this integral

[terse dove]

its 4x cube plus 5x squared

[quaint elm]

factor the bottom then use partial fractions

[terse dove]

ok got it

thnks

.close

[marsh citrus]

Channel closed

Closed by @terse dove

Use .reopen if this was a mistake.

[marsh citrus]

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 lion]

,rotate 3

[cinder lion]

Is this a good way to approach this question?

I might have drawn something on wrong

Or this may be completely wrong do I make an equation for the car and the trailer and solve simultaneously

Because I need a, but I have an r in the way

<@&286206848099549185>

[marsh citrus]

@cinder lion Has your question been resolved?

[next crystal]

the net force on car is Fe - T -2r = ma

and on trailer is T-r=Ma

Your diagram is corect but your equation arent

[cinder lion]

What does Fe mean sorry?

[next crystal]

Force by engine

[cinder lion]

So at this point I should exclude the trailer?

And write an equation for the car only

[next crystal]

yes for writing equation on car you only see force acting on the car

[cinder lion]

So it would be like this?

My problem is I don’t have a value for the tension on the trailer

[next crystal]

yes

in second equation T will be same 2400 as the rope is light

[cinder lion]

Ohh so when it’s light, the tension is the same

[next crystal]

yes for a string having mass the force changes

[cinder lion]

That’s my answer

Looks right to me

[next crystal]

ya mee too

[cinder lion]

Do you think I could ask you another quick question?

[next crystal]

ya sure

[cinder lion]

I believe I did the first part right

But I’m honestly not sure where to start on part b

And is the displacement allowed to be negative or would I change it to a positive?

[next crystal]

as you have taken the upward side possitive the displacement should be possitive

but in the question the total time of particle till it hits the ground is 10sec

thus the time at which the particle reaches the top will be half of that

[cinder lion]

So it goes up, then down past 0 and then hits the ground

Wait, so I’ve done something wrong there?

[next crystal]

no it hits the O at t=10sec

[next crystal]

yes

you have taken total time = time of ascent which is wrong

time of ascent = (total time)/2

[cinder lion]

It says it hits the ground when t=10

[next crystal]

wait I read the question wrong my bad

ya 1st part is correct

[cinder lion]

Alright

I’m fairly sure I’d need to use two equations but I’m just not sure how

Not my strong point

[next crystal]

for 2nd part 1st find when the velocity is equal to 24.5

[cinder lion]

Alright so I’d just say u=24.5

[next crystal]

v=24.5 u=39.2

[cinder lion]

Oh right yea

I’m eating now, I’ll do that right after, what would the next step be?

[next crystal]

you will get two times when v=24.5

lets say it to be t1 and t2

now as the particle moves between t1 and t2 you will its speed will always be less than 24.5

as gravitational accelration will pull it down

[cinder lion]

Oh right yea

[next crystal]

then just find the time for which its greater by subtracting

[cinder lion]

Gotcha

Thanks so much!

[next crystal]

No prob

[cinder lion]

.close

[marsh citrus]

Channel closed

Closed by @cinder lion

Use .reopen if this was a mistake.

[marsh citrus]

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.

[wary bluff]

I dont rlly understand how they got "n"

How exactly did they get log_10 a + log_10 b for this

[narrow epoch]

how many repeetitions does the program make?

with a given b = n input

repetitions/calculations

[marsh citrus]

@wary bluff Has your question been resolved?

[wary bluff]

are you talking about the while loop here?

like how many iterations

[whole sleet]

I think they're defining n, not getting n

n is the number of digits of both numbers.

[outer lodge]

Bits not digits

[wary bluff]

shoudnt it be log_2(a) + log_2(b)

[whole sleet]

Oh, I see the comment defines it as bits

In that case, yes it should be log2, not log10

Not that it makes a difference to the final statement

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[winter osprey]

Is this correct?

[vagrant gull]

yes

[scarlet steeple]

Yes

But square root of 2 can be 1.4

[winter osprey]

If I drew a graph, would there be a line curing right of the Y axis top right ?

[vagrant gull]

you could leave it as exact number too

[vagrant gull]

ye

[winter osprey]

Is this correct ?

[vagrant gull]

,w 5=\sqrt{4x-3}

[elfin berry]

Results provided by WolframAlpha

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

Requested by kensukeken

[vagrant gull]

it is

[winter osprey]

Is this good

[vagrant gull]

,w (6-5i)/(1-6i)

[elfin berry]

Results provided by WolframAlpha

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

Requested by kensukeken

[vagrant gull]

it looks good

[vagrant gull]

are you doing a test or smth?

[winter osprey]

It’s a review

[vagrant gull]

I see

just use wolfram to check your answers correctly

[winter osprey]

Do I need the pro to do it. Or just regular

[vagrant gull]

just regular

since you're checking last answer

[marsh citrus]

@winter osprey Has your question been resolved?

Channel closed

Closed by @winter osprey

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.

[calm vessel]

I kept getting different answers for 6 and 7, is someone able to look over my work? Thank you

[kind solar]

How did you get d=48^2 ?

[calm vessel]

Wait that doesn’t make sense, I re did it and now I’m getting d= 144 feet

[stoic slate]

The problem in 6 is that u replaced wrong number

[calm vessel]

I think I did it completely wrong. I’m getting 144 feet which makes more sense

[marsh citrus]

@calm vessel Has your question been resolved?

[calm vessel]

<@&286206848099549185>

[inland prawn]

in problem 6, you missed the square root in the 16

remember that the square root is for the whole fraction

[calm vessel]

I thought I did that whole question wrong

.close

[marsh citrus]

Channel closed

Closed by @calm vessel

Use .reopen if this was a mistake.

[marsh citrus]

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.

[bitter terrace]

hi im having trouble figuring how to do this concisely

[leaden monolith]

What have you tried

[wind token]

...

Ok

So there are 6^3 possibilites

216 possibilites

with the highest being 216

How many perfect squares are in 216?

[wind token]

?

[sleek lake]

i don't think you can

[wind token]

I'd say that's consice

[sleek lake]

because you gestured at the solution

the solution would be three times as long

wait what are you suggesting

there's 14 sqaures or something

that doesn't help

[wind token]

So its 14/total

[wind token]

isn't it?

or am i getting the wrong interpretation?

[empty saffron]

$P(PS) = #PS / \omega$

[elfin berry]

Max-Cat

$P(PS) = #PS / \omega$
```Compilation error:```! You can't use `macro parameter character #' in math mode.
l.49 $P(PS) = #
               PS / \omega$
Sorry, but I'm not programmed to handle this case;
I'll just pretend that you didn't ask for it.
If you're in the wrong mode, you might be able to
return to the right one by typing `I}' or `I$' or `I\par'.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l
ocal/texlive/2023/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/local/texli```

[empty saffron]

you have omega (6^3), now you just need the perfect squares

not, here, ask in a free channel

as, I was saying,

if you had 2 dice you could do a double entrance table, but with three it gets exponentialy more difficult

[wind token]

I dont get it

isn't it just 14/216?

[empty saffron]

the Probability of getting a perfect square is the number of possible perfect squares over all the possible outcomes

how did you get 14?

[sleek lake]

product means multiplication

[wind token]

yeah

and there are 1-6 in a die

oooh

right

mb

oh

so i have to factor each

[empty saffron]

ok, how many ways can we multiply numbers to get a PS?

[wind token]

and consicely

[sleek lake]

like, 121 is a square

[wind token]

i get it

[sleek lake]

how do you multiply 3 numbers to get 121

[wind token]

i have to factor those

[empty saffron]

you can't, sqrt121 is 11, which is a prime number

[sleek lake]

i think you count 4 x x and 1 x x and an extra special case

it's concise but also totally guessing

[bitter terrace]

thing is im not even sure if it goes to 216, like the highest square probs isnt 216

ah

i have no idea how to do this

find all of the combs that are sqrts and just over the whole prob

but the sqrts

do i need to just list the combs out

or is there a way or formula that shows it more concisely

[wind token]

it is

6x6x6

[bitter terrace]

thats a cube tho

[sleek lake]

i suggested a way, there's 18 − 2 combinations that look like 1 x x

[bitter terrace]

i thought the higest would be 4x4x4

[sleek lake]

6×3 − two repeats of 1 1 1

there 16 more that looks like 4 x x, and there's 3! that look like 2 3 6

[bitter terrace]

is the 6x3 6 x 3!/2?

[sleek lake]

the problem is it relies on luck, maybe it's missing a combination

yeah

[bitter terrace]

yea thats the problem

idk if theres a surefire way to get all the combs instead of like this

yea i think this is the most concise its going to get

thanks

.close

[marsh citrus]

Channel closed

Closed by @bitter terrace

Use .reopen if this was a mistake.

[marsh citrus]

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 gust]

how do i negate this with the negation symbol and without it?

[marsh citrus]

@rugged gust Has your question been resolved?

[simple plover]

@rugged gust Hey. What are we doing here?

[rugged gust]

trying to negate this

[simple plover]

Got it. My tip is to try to negate it step by step, starting from the very left.

[rugged gust]

ive never seen it where the for every x in the set of real numbers is in the middle of problem though

normally i substitute everything to f(x) and work from there but here im confused

[simple plover]

Ah, I see what you normally do. I wouldn't remember "formulas" for negations. Always treat it by parts, it'll be easier.

[rugged gust]

so is it ¬∃ M > 0 --> f(x)

[elfin berry]

BH

BH

[rugged gust]

oh okay

[simple plover]

👍

[rugged gust]

what about that implies at the end there

[simple plover]

Yes, for that you treat it as an implication. P implies Q.

And negate it as a whole.

[rugged gust]

not left and not right

[simple plover]

Not quite.

[rugged gust]

left and not right

[simple plover]

Perfect.

[rugged gust]

so does that turn into left implies f(x) less than or equal to M?

[simple plover]

Yes, that's exactly the negation for that implication.

[rugged gust]

thank you so much

[simple plover]

Not a problem.

[rugged gust]

.close

[marsh citrus]

Channel closed

Closed by @rugged gust

Use .reopen if this was a mistake.

[marsh citrus]

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 monolith]

What have you tried

[spice widget]

i tried to expand the r^2(r-1), which ended up as r^3-r^2, then i split the summations as the sum of r^3 - the sum of r^2

[leaden monolith]

And then?

[spice widget]

then, i expressed the sum of r^3 as 1/6(n^2(n+1)^2) and the sum of r^2 as 1/4(n(n+1)(2n+1))

then i subtracted them and tried to factorise but failed

[stray fern]

you put the 1/6 and 1/4 in the wrong expressions

[spice widget]

ah

[spice widget]

so would you end up with this

[leaden monolith]

Perhaps we could factorise that

[spice widget]

should i take out n from the polynomial

and then factorise the cubix

[leaden monolith]

Look at this

And think to yourself

There’s an n outside in the answer

Yes, I should factorise an n out

[spice widget]

i did factor the n out, but idk if i can factorise it further

i checked on mathway and apparently the expression isn't factorisable with rational numbers

[leaden monolith]

Well

The it looks like the m is gonna come in handy

[spice widget]

so what should i do with it then?

[leaden monolith]

Try solve for it

Make the 2 things equal and figure out what m must be

[spice widget]

do you mean i have to set the equation equal to m?

[leaden monolith]

No set it equal to the right hand side here

[spice widget]

i'm still stuck

[marsh citrus]

@spice widget Has your question been resolved?

[marsh citrus]

@spice widget Has your question been resolved?

[marsh citrus]

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.

[azure peak]

i was actually trying to diffrenciate data type values between integer and float, i.e. 5 and 5.0, and gpt helped this with using epsilon value , so for variable b = 5.0, b - int of b (type casted) is less than a epsilon value than its integer else float. so my question is that 5.0 is bigger than 5 if epsilon take in account to compare?

[devout mauve]

you are taking the absolute value of the difference

so it doesnt matter whether b or (int)b is bigger

[vernal forge]

moreover, 5.0 happens to be exactly 5.0 when represented as a float!

https://www.h-schmidt.net/FloatConverter/IEEE754.html this is a handy tool

[sleek lake]

i don't understand what you're asking

[glacial hedge]

yeah this is a bad way of testing this

why would you even do this?

[sleek lake]

it's the only way what do you mean

[devout mauve]

well there could be lots of situations where you might want to check whether a number is an integer

[azure peak]

curiosity

[glacial hedge]

just type things properly

[devout mauve]

what

[static quarry]

this isn't gonna work well if b is something like 4.9999999

[devout mauve]

you might have intermediate results for which you need to use floats

[static quarry]

const double tol = 1e-6;
const double remainder = fmod(some_num, 1.0);
if (remainder > 1.0 - tol || remainder < tol) {
    // close enough
}

[glacial hedge]

I'm struggling to come up with a convincing example where this can't just be attributed to bad programming

[azure peak]

so the absolute diff i.e. 0.0 is less than epsilon value

[proven geyser]

Yeah, so 5.0 is an integer

Kind of makes sense 😂

Because computer use binary systems so it can't represent some numbers exactly. That is why b - int(b) doesn't always equal 0 so we need to compare it to a small number epsilon

[azure peak]

i see

[proven geyser]

The common case is 0.1 + 0.2 = 0.3000000000004 😂

[azure peak]

ye i remember that xD

the concept is straight forward but still put me in confusion

[azure peak]

thats actually helpful thnx

[idle ridge]

Do you still have any questions or nah

[azure peak]

im done , thnx for the help :>

[idle ridge]

kk

.close

[marsh citrus]

Channel closed

Closed by @idle ridge

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.

[open kayak]

Is there a mistake in this?

Didn't this person mean AA' not unit matrix?

Wikipedia gives me

[idle ridge]

Probably yes

Actually I'm confused, what does ' mean?

Does it mean transpose or conjugate transpose?

[open kayak]

It should just mean transpose, the person wrote $\overline A'$ for the hermitian condition, so that should mean conjugate transpose

[elfin berry]

Kepe

[open kayak]

Ok so you also agree with the German Wikipedia article and not what the person wrote

Thanks

.close

[marsh citrus]

Channel closed

Closed by @open kayak

Use .reopen if this was a mistake.

[idle ridge]

it doesn't make sense then, AA' = I for an orthogonal matrix, not unitary

[open kayak]

.reopen

[marsh citrus]

✅

[open kayak]

That was never claimed..?

Everything is correct just not the second line I think, no?

It should say "AA' \neq E so not unitary"

First and last line seem fine?

[idle ridge]

It should be a conjugate transpose.

[open kayak]

Oh

True

Thanks

.close

[marsh citrus]

Channel closed

Closed by @open kayak

Use .reopen if this was a mistake.

[marsh citrus]

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.

[bold creek]

I have a question. how would you solve this question. A man walked 440 m [50.0° N of E] and then 580 m [5.0° S of W]. The entire trip took 150.0 min. whats his displacment.