help-28

[unreal wren]

For broken string, what is the row total?

[hard wasp]

100

68.70 of the total guitars had broken string

@unreal wren am i wrong?

[hard wasp]

hey? can you help please?

[unreal wren]

Sorry, I was busy

[hard wasp]

oh its okay

help me when youre free please

[unreal wren]

Yes I'm reading this again rn

[hard wasp]

okay

[unreal wren]

Suppose that acoustic broken strings = Z

We want to find Z

[hard wasp]

okay

[unreal wren]

Z is 61.11% of row total

[hard wasp]

61.11%

yeah

[unreal wren]

And we can figure out row total based on Z

What is the row total in terms of z?

[hard wasp]

idk

i dont understand

[unreal wren]

Hold up

Row total in terms of Z =??

[hard wasp]

z+70?

[unreal wren]

Yeah

And z is 61.11% of the row total

You can use algebra to find Z and the row total for broken string

[hard wasp]

what is row total though? 100 or 68.70?

[unreal wren]

It's z+70

[hard wasp]

wait

how do we calculate z?

[unreal wren]

Algebra

[hard wasp]

please guide me step by step its very confusing for me idk why, i am not stupid but still its confusing for me

[unreal wren]

61.11% of (Z + 70) = Z

[hard wasp]

okay hear me first

61.11% of the guitars that had broken string were acoustic, right?

then

[unreal wren]

Mhmm

[hard wasp]

suppose guitars that were acoustic and had broken string is Z

then Z+70 guitars had broken strings?

[unreal wren]

Yeah 😭

Its basically common sense (not to be insultful)

[hard wasp]

oh okay i get it

[hard wasp]

yeah i am sorry, i am just tired

[unreal wren]

It's alright, happens to me too

Just use some basic alg to solve for z

Once you know z, you can also figure out the column total and total easily

[hard wasp]

z=110?

[unreal wren]

Lemme check

Yess

Then, you should be able to figure out the column total too

It's basic addition

[hard wasp]

131 yeah

[unreal wren]

Then figuring out the total of every thing is easy too

[hard wasp]

yeah filled the table

[unreal wren]

Can you solve for x now?

[hard wasp]

is it

x% of 131 = 82?

[unreal wren]

What

To get things straight, x is the acoustic neck repair column percent

X = $\frac{acoustic neck repair}{column total}$

[glossy valve]

Matcha

[unreal wren]

But in percent

I keep on seeing you type but you haven't sent anything

[hard wasp]

i am confused

you wait

listen me

x% of the guitars that are acoustic had neck repair

and the number of acoustic guitars are 131

[unreal wren]

Yes

Yes

[hard wasp]

so x% of 131 = 21?

[unreal wren]

Yes

Or, x = 21/131

[unreal wren]

Which is the same as what I wrote here

[hard wasp]

yayyy thank you so much

[unreal wren]

Your welcome

Khan Academy I c

[hard wasp]

how?

[unreal wren]

Wdym?

[hard wasp]

where did you see

[unreal wren]

I'm just really familiar with Khan Academy

[hard wasp]

ohh

okay but they dont ask the question related to what they teach

[unreal wren]

What did they teach

[hard wasp]

easy questions they discuss

and ask difficult questions

[unreal wren]

Lol that's normal in Kahn academy atp

I also suffered that when I used it to study

It's also a matter of things looking easier when you are presented the solution than when you are asked to find the solution, i.e. it's psychological related too

[hard wasp]

yeah, thats very bad 😭

[hard wasp]

but no, not in this case

[unreal wren]

Youll get used to it

[unreal wren]

?

[hard wasp]

the questions that are presented is actually easy in khan academy but the question they give us to solvee is difficult

i also dont like statistics and all

[unreal wren]

Why not 😭

[hard wasp]

i am learning it for data science

[unreal wren]

This is still the easy bit of statistics tbh

[hard wasp]

yeah, thats unit 1

[unreal wren]

Ik

The other units are more complicated but less confusing tho

I also found this topic, row and column percent, quite confusing

It was harder than the more advanced topics 💀

[hard wasp]

i like statistics but i dont like whatever this is, i have studied statistics before

[unreal wren]

Ooh

I seee

[hard wasp]

in my university

and also my friend who is studying actuarial science said me to leave this topic 😭

[unreal wren]

Well, if you don't have any more questions you should type ".close"

It was fun helping you out

[hard wasp]

yeah it was fun taking help from you

next time i will tag you

hehe

.close

[full forum]

Channel closed

Closed by @hard wasp

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

yoo

[torn jolt]

@slate glacier

lets start

[slate glacier]

Alright

[torn jolt]

its abt enlargement

dyk it?

i want help with multiple questions of it

[supple bloom]

just send the question

[slate glacier]

I'm not sure, can you send the question

[torn jolt]

this one doctor

[slate glacier]

There's a mod here you idiot

[supple bloom]

people can gauge if they can help you after you send the question

[supple bloom]

its a bot

[torn jolt]

yeah ofc u are here pal

[supple bloom]

I just wanted to check you'd found your way to a new channel okay, but alright

[torn jolt]

https://tenor.com/view/melon-dog-melon-gif-2891417537844027027

[torn jolt]

@slate glacier yk?

[slate glacier]

Not sure, I can do it but not in the traditional way, I'm not familiar with it

You can wait for another helper, not something I'm familiar with unfortunately

[torn jolt]

ok

its alr

[brave ruin]

Polygon with 5 sides is called pentagon, 6 sides - hexagon, 7 sides - heptagon, 8 sides - octagon, 9 sides - nonagon, 10 sides - decagon

Can you now do i?

The shape is a polygon of some number of sides, count the sides and name it.

[slate glacier]

I feel like he needs help with the second part

[brave ruin]

To enlarge it by factor of 2 means to make another similar shape on the grid whose each side's length is 2 times larger than the original shape's corresponding side's length.

So like find length of each side, and multiply the side length by 2 so that now you have measure of each side of the new shape that you need to draw. Just draw it accordingly on the grid with the new measurements.

[full forum]

@torn jolt Has your question been resolved?

[white cave]

Hello Everyone

star is pentagone?

[full forum]

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.

[full forum]

Please don't occupy multiple help channels.

[swift canyon]

<@&268886789983436800>

[full forum]

Channel closed

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

[full forum]

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.

[full forum]

Please don't occupy multiple help channels.

Channel closed

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

[full forum]

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.

[proven lynx]

"Now calculate the probability that the random values lie within one standard deviation of the expected value

[proven lynx]

so i dont understand the P( < x < ) part

what

[whole dagger]

umh

i'm trying to

i can't explain this

[proven lynx]

oh

<@&286206848099549185>

[full forum]

@proven lynx Has your question been resolved?

[languid junco]

which part specifically

[proven lynx]

why did he do the expected value - deviation

this

[languid junco]

"within one standard deviation of the expected value" means that |X - mean| < standard deviation

if you remove the absolute values and solve for X, you get that inequality

mean - SD < X < mean + SD

[proven lynx]

wdym X- mean

oh

u mean the expected value

[proven lynx]

i dont think i quite understand what standard deviation is

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[meager spire]

A farmer encloses a rectangular field by fences into eight smaller identical rectangles in an arrangement of two rectangles by four rectangles. He has 600 feet of fencing to build the enclosure and divisions. What is the maximum area of the field? What are the dimensions
of the field with maximum area?

[plush egret]

What have you tried so far?

[meager spire]

Nothing, I understand I have to use length and width to make an equation but I'm stilll confused as to how

[main vault]

call the length of one enclosure x and the width y

[sonic stratus]

Quick question, do the division share sides or there is a gap between each one?

[meager spire]

they share sides

[uneven birch]

Try drawing it, labelling sides and seeing if you can count the feet of fence he needs

[sonic stratus]

so, you basically have this figure

[meager spire]

yes

[sonic stratus]

Could you identify useful measures for this figure?

as to make an equation based on them

[meager spire]

length and width

[sonic stratus]

Theres multiple options for length or width, you could measure the total length and width of all pens together, or the individual sides

try to be a lil bit more specific

[plush egret]

Do you see how the whole shape is made up of little 'sticks'?

like, we have short sticks, and long sticks

[sonic stratus]

Want me to diagram that?

[meager spire]

Yes, would I just be looking for the length and width of one rectangle to get the area

[plush egret]

oh, idk, im needlessly jumping back in aha

[plush egret]

I'm just trying to give a hint, of how it might be useful to talk about the quantities you said

you said length, and width

[meager spire]

no yeah

okay

[plush egret]

maybe we can talk about length and width, in terms of long or short sides

hope that is helpful you'll have to say if I confused it more

[meager spire]

no, it makes sense,, but how would I use the given information like the 600ft of fencing

[plush egret]

so all of the short and long sides

they're made up of fence

[sonic stratus]

the 600ft of fencing is all the fence you got

IF you use less youre clearly losing area

and you cant use more

[plush egret]

so if we take all of the short sides, and all the long sides, and put them together, we should get 600 ft

That's one equation you can start with

[plush egret]

try to count how many long and short sides you have here

we can draw it more uneven if it helps to count

[meager spire]

would it be 5w * 4l = 600ft ?

actually no

10w * 8l = 600ft because I only counted half of the full thing

[sonic stratus]

Consider that here we are working with lengths

A length * a length = area

Which isnt what we are looking for just now

[plush egret]

here I marked out 4 short

[sonic stratus]

tbh this method is harder

[plush egret]

I think you're right there are 10 short sides in the shape

I guess you end up with bigger coefficients

[plush egret]

but its fine

sure

5 short

3 long

[plush egret]

@meager spire does this make more sense

[sonic stratus]

and just in case

[plush egret]

really you'll get the same answer either way, all thats important is we have a way to count all of the length

[sonic stratus]

yeah

its just that the full w and l make it easier to calculate the area.

[sonic stratus]

Based on this, can you think on how the equation for the whole length of fencing will turn out?

[meager spire]

Im confused lol, so am I getting 3w x 5l = 600ft?

[sonic stratus]

so close

again, the width and length are also measured in ft

but the result is not square feet.

If i tell you one of these lines has a length of 20

What will be the total length of the three together?

[meager spire]

60

[sonic stratus]

How you came to that conclussion?

[meager spire]

I multiplied it by 3 ...

[sonic stratus]

and what about these 5?, suppose they measure 10

[meager spire]

LOL im so sorry, I actually have to go now I have a lecture is in 15 min

its 50 tho right?

[sonic stratus]

yes

So, what will be the combined of these two by themselves?

Again, you just stated the left part adds to 60, and the right part to 50.

[meager spire]

110

[sonic stratus]

I hope you can see whats wrong in here now.

[meager spire]

Yeah, I'm starting to get it

[sonic stratus]

lengths are additive

So you instead get 3w + 5l = 600

[meager spire]

right, okay

.close

[full forum]

Channel closed

Closed by @meager spire

Use .reopen if this was a mistake.

[full forum]

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.

[fallen ivy]

In this week we'll be learning about parabolas, are they difficult? can anyone give me an example of a question?

[unreal wren]

Maybe looking at your textbook will be a better way to find the answer to this

Not everyone in the world goes through the same curriculum

[full forum]

@fallen ivy Has your question been resolved?

[wide sundial]

Find the unique parabola going through (0, 1), (1, 1), (2, 0.5)

There are a lot of interesting stuff about parabolas there’s a lot of theory

They are all relatively simple to understand on their own but there’s much to cover

[fallen ivy]

example?

[little steppe]

this is actually a decent use of chatgpt, a "generate example problems"

don't actually use it to solve problems but it's decently good at generating them

[bright bronze]

until you solve or try to solve it and notice it fucked up somewhere

[little steppe]

right don't use it to solve problems

but it could give you ideas of what kinds you might encounetr

[bright bronze]

considering how op would do anything but open their textbooks, seems like good idea

[full forum]

@fallen ivy Has your question been resolved?

[full forum]

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.

[deep ledge]

.close

[deep ledge]

i need help

.close

[full forum]

Channel closed

Closed by @deep ledge

Use .reopen if this was a mistake.

[deep ledge]

need help with this

it to hard

[vestal kindle]

😭😭

[deep ledge]

what

<@&286206848099549185>

[chrome canyon]

what divided by 5 gives 10 @deep ledge

[deep ledge]

uhm

[chrome canyon]

also use the data given in the qn

[deep ledge]

can i use my calculator

[chrome canyon]

its not a unsolvable qn

[deep ledge]

oh

[chrome canyon]

tell man if i multiply 5 and 10 i get 50?

[deep ledge]

okay

[chrome canyon]

now if i divide 50 by 5 what do i get?

[deep ledge]

10

do i put 50 in the answer box

[chrome canyon]

absolutely

why such confusion in the first place tbh

[deep ledge]

idk but im 15 so my mom yells at me everytime i get an answer worng

so i get kinda scared

[chrome canyon]

MY LORD

[deep ledge]

what

[chrome canyon]

U R 15???

[deep ledge]

yeah

so

[azure onyx]

hang on, I think the channel is closed.

reopen the channel if you want to continue, OP.

[brittle sun]

.reopen

[full forum]

✅ Original question: #help-28 message

[chrome canyon]

man these calculations are expected to b handled from a 6-7 yr old

[deep ledge]

bro

[azure onyx]

so does OP have any other question?

[brittle sun]

Here's some advice: if you don't have anything nice to say, just don't say anything

[deep ledge]

bruh im leaving

.close

[full forum]

Channel closed

Closed by @deep ledge

Use .reopen if this was a mistake.

[deep ledge]

.close

[brittle sun]

It's closed dw

[azure onyx]

you already closed it.

[brittle sun]

If you have another question, feel free to reopen

[deep ledge]

well im sorry imma ask my friend to help me then

[brittle sun]

And it's okay to be behind, we all do things at our own pace.

[brittle sun]

We are happy to help you too

[deep ledge]

arl

[brittle sun]

On behalf of that other user, I apologise

[deep ledge]

okay

[brittle sun]

Feel free to reopen and post another question if you have one

Also hullo Hyacine, sorry for jumping in out of nowhere

[deep ledge]

i only have 12 questions left

[azure onyx]

regardless, if you have a legit question, you deserve to be heard.

[deep ledge]

ok

[brittle sun]

Reopen then?

[deep ledge]

arl .open

[brittle sun]

.reopen

[deep ledge]

.reopen

[full forum]

✅ Original question: #help-28 message

[brittle sun]

I'm gonna go swimming, so all yours @azure onyx

Feel free to tag me to pin stuff though

[deep ledge]

ok

[azure onyx]

I'll be watching, but in case you do have a new question, you can slap it here first, and I'll reply ASAP.

[deep ledge]

arl

[deep ledge]

is it 10

[azure onyx]

yes!

[azure onyx]

okay, this requires knowing how to round numbers.

[deep ledge]

ok

[azure onyx]

have you heard of statements like, "this thing costs $9.50, might as well cost $10"?

oops, ignore that bot.

[deep ledge]

ok

[azure onyx]

this is an example of rounding in action. we round to make calculations simpler to handle.

so here, you are told to round to the nearest ten. do you know what that means?

[deep ledge]

no

wait i think i know it

[azure onyx]

oh? let's hear it. can you round, say, 37 to the nearest ten?

[deep ledge]

2905

[azure onyx]

hm? is this the answer to the problem?

[deep ledge]

yeah this one

[azure onyx]

unfortunately, your answer is too correct for the question.

[deep ledge]

i got it

[azure onyx]

while 35 * 83 is indeed 2905, they want you to round the two numbers first, then multiply them.

[deep ledge]

yay

[azure onyx]

which is to say, your answer is incorrect, btw.

[deep ledge]

ok

brb gotta use the bathroom

[azure onyx]

so first, we have to round 35 and 83 to the nearest ten. this means that you will end up with two numbers ending in 0. round 35 first; what do you get?

[deep ledge]

i got 2905

heres my next question

[azure onyx]

that's... still not the answer to the question, but sure.

[azure onyx]

aha. this question forces you to round.

[deep ledge]

ok

can i use my calculator

[azure onyx]

that defeats the purpose of learning how to round, doesn't it? I know you did it for the last question, but if you use it for questions like these before learning the concepts, you're not learning what's happening.

the idea is that we want to first know why one answer gives a better estimate than the other.

[deep ledge]

idk i just want to go to college...

[azure onyx]

not to belittle or anything, but that's exactly why you should get the basics down.

[deep ledge]

ok

[azure onyx]

sure, you can blaze through these questions with a calculator no problem. but are you learning the concepts behind them?

[deep ledge]

wdym

[azure onyx]

for instance, the previous question. do you know why 2905 is not the right answer?

[deep ledge]

why

[azure onyx]

you are told to round the two numbers to the nearest ten before multiplying. so your answer should end in two zeroes, definitely not a 5. the problem is that you ignored the instructions telling you to round the numbers and calculated them directly.

[deep ledge]

oh

[azure onyx]

that's why I said your answer was too correct.

[deep ledge]

oh

[azure onyx]

they want you to estimate the answer by rounding, not to use a calculator. if you have a calculator, you don't need to round!

[deep ledge]

oh okay

im dumb

[azure onyx]

(of course, if the numbers are still hard after rounding, that's fair game. but round first!)

so do you want to go back to the previous question, or stick on with this one anyway?

[deep ledge]

go back the previous question

[azure onyx]

alright, let's do it properly this time.

[deep ledge]

ok

i feel like im putting preasure on me

[azure onyx]

first, a quick idea on what rounding is. rounding is the process of approximating a number (or in simple speak, the process of turning a number into something that is "close enough").

for example, suppose a product is 37 bucks. if you're asked to find the total value of, say, 50 of them, this is ugly math.

[deep ledge]

ok

[azure onyx]

but instead, you can estimate the number by rounding the price of the product to, say, 40 bucks. now that's a nicer number we can deal with.

[deep ledge]

ok

[azure onyx]

this is called rounding, and this specifically is rounding to the nearest ten (because after the rounding, notice that the last digit is 0).

[deep ledge]

ok

[azure onyx]

so going back to the prev. question. one of the two numbers is 83. what would you round it to?

[deep ledge]

okay

[azure onyx]

(remember: nearest ten, so the number should end in a 0.)

[deep ledge]

okay so

2900

[azure onyx]

no, don't round the final answer. round the numbers individually first!

[deep ledge]

ok

[azure onyx]

note that I asked to round 83.

[deep ledge]

round it to 35?

[azure onyx]

that's too far a round, plus it doesn't end in 0.

[deep ledge]

ok

[azure onyx]

I'll give you two choices: 80 or 90. which would it be?

[deep ledge]

90

[azure onyx]

is 83 closer to 90 than 80?

[deep ledge]

wait no it 80

[azure onyx]

good!

now, round 35 in the same fashion.

[azure onyx]

which is closer: 30 or 40?

[deep ledge]

40

[azure onyx]

excellent.

so now, 35 becomes 40 and 83 becomes 80.

[deep ledge]

ok

[azure onyx]

your multiplication thus becomes 40 * 80. what is the answer to this? you'll find that it is very different from the 2900 you've been insisting on.

[deep ledge]

wdym insisting

[azure onyx]

you kept telling me and showing me 2900. the final answer isn't 2900 for reasons you'll see when you answer the last question I posed.

[deep ledge]

ok

why are my photos i sent pinned

[azure onyx]

because they relate to your question and helps helpers find your original question faster.

[deep ledge]

ok

[azure onyx]

also, don't forget the question here.

[deep ledge]

so multiply 40 and 80

[azure onyx]

yes.

[deep ledge]

well they have 0 so im guessing it 0

[azure onyx]

sure? you can check with your calculator for this one, because it sure isn't 0 (neither 40 or 80 is 0, so).

[deep ledge]

oh it not

[azure onyx]

a product is only 0 if either number is exactly 0.

[deep ledge]

ok

[azure onyx]

so your answer is...?

[deep ledge]

3200

[azure onyx]

and that is the correct answer for that question.

[deep ledge]

10 more questions to go

[azure onyx]

sure. which one next? the one you sent earlier with the division question?

[deep ledge]

it different

[azure onyx]

sure. send it.

[deep ledge]

wait no it is

[azure onyx]

you sent it already, which was why I asked if it was this one.

but either way, let's work on it.

[deep ledge]

oh okay

[azure onyx]

so, the question is just a long way of asking you which expression is wrongly rounded.

[deep ledge]

ok

[azure onyx]

that is, which expression has numbers rounded too far?

[deep ledge]

the second one

[azure onyx]

correct. so the one with the better estimate is the other one.

because rounding too far makes your estimate nonsense.

[deep ledge]

okay so estimate 800 and 40

[azure onyx]

now, you may use your calculator to divide the first expression.

[deep ledge]

gtg

.close

[full forum]

Channel closed

Closed by @deep ledge

Use .reopen if this was a mistake.

[full forum]

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.

[upper silo]

how do you draw in th 3rd bound?

[upper silo]

sorry its a little hard for me to see

[full forum]

@upper silo Has your question been resolved?

[fair oracle]

@upper silo

Can you draw |x + y| = 1, and |x + y| = 2 seperately?

[upper silo]

not sure if its right\

[full forum]

@upper silo Has your question been resolved?

[full forum]

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.

[onyx glen]

didn't you come here with this exact problem some time ago

[thick hedge]

something similar I think

I have a quiz tomorrow, so just reivsing kind of problems I stuggled with earlier

[onyx glen]

no, this exact one

[thick hedge]

oh, okay

[onyx glen]

i distinctly remember it

[thick hedge]

so here all I need is the mariginal of Y, right

[onyx glen]

there are 2 routes:

1. recognize X and Y are independent and just calculate P(X<=1/2)
2. if you don't trust yourself with that, go by the definition the "honest way": P(X<=1/2 & Y>=3/4) / P(Y>=3/4), calculating each one with an integral

[thick hedge]

I'll do the 2nd

or wiat

*wait

yea, the mariganls are 2x, 2y

so just $\int_{0}^{1/2} 2xdx$

[glossy valve]

wai

[thick hedge]

so 1/4

[full forum]

@thick hedge Has your question been resolved?

Channel closed

Closed by @thick hedge

Use .reopen if this was a mistake.

[full forum]

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.

[atomic hare]

<@&268886789983436800> clean up thank you

[full forum]

Channel closed

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

[full forum]

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.

[river goblet]

can anyone show me how to do questions like these?

[low sail]

Do you know how to solve differential equations @river goblet

[river goblet]

roughly but im not very good at them

[low sail]

$$\frac{dy}{dx} - y = 1$$

[glossy valve]

Adarsh

[low sail]

Does this help you? or give you any idea

[river goblet]

would it then just go to dy-y=1dx

[low sail]

$$dy - ydx = 1dx$$

[river goblet]

oh yeah

[glossy valve]

Adarsh

[low sail]

If you do that it would be

Now you can take dx common on the RHS

[river goblet]

so is this the same as the left side in the question?

[low sail]

What do you mean?

$$dy = dx(1+y)$$

[glossy valve]

Adarsh

[low sail]

This is what I meant

[river goblet]

so is this just a rearangement of the question?

[low sail]

Yes

Now you can divide both sides by 1+y then integrate both sides

[river goblet]

sorry im confused with how that rearangement works

[low sail]

From which part are you confused

[river goblet]

just in how it goes from this

[river goblet]

to this

[low sail]

Do you agree that

[low sail]

This is equal to

$$\frac{dy}{dx} - y = 1$$

[glossy valve]

Adarsh

[river goblet]

im not sure sorry

[low sail]

$$\frac{d(y(x))}{dx} - y(x) = 1$$

[glossy valve]

Adarsh

[low sail]

Is this fine?

[river goblet]

so d/dx y(x) is equal to d(y(x))/dx?

theyre essentially the same thing?

[low sail]

In differential equations, yes

[river goblet]

okay i understand

[river goblet]

and then you add the y then times the dx to get there

so then where, do you need the ys on one side and xs on the other?

[low sail]

Yea you want to seperate the vairables

You want dy with the ys and the dx with the x

[river goblet]

so gos to dy/(1+y)=dx?

[low sail]

Yes

[river goblet]

but does integratin not just then give y=x

[full forum]

@river goblet Has your question been resolved?

[river goblet]

.close

[full forum]

Channel closed

Closed by @river goblet

Use .reopen if this was a mistake.

[full forum]

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.

[thick hedge]

This is what I have so far:

$X^2≥Y; X \sim UNIF[-1,1]; Y\sim UNIF[0,1]$\
So $X=1/2;Y=1$

[wide sundial]

\sim

[glossy valve]

wai

[fast peak]

X=1/2 ??

[wide sundial]

where did u get X^2 >= Y

[restive geyser]

I'd first try to find what values X, Y result in the quadratic having real roots in the first place?

[thick hedge]

real solns

[fast peak]

well he did. he just skipped the step

cause...

who knows

[restive geyser]

ah he did yh

Okay, now this amounts to drawing the region of the rectangle [-1, 1] x [0,1] where that inequality holds

Then calculating what proportion of the rectangle that region is

[thick hedge]

The question I had is what's the joint PDF I'm integrating over here

[fast peak]

everything is uniform

[restive geyser]

You don't need a PDF here tho?

[fast peak]

the pdf is just 1/total area

[thick hedge]

is it 2/3

[restive geyser]

Independence allows us to do the joint thing in the first place; UNIF allows us to not worry about weighting

[thick hedge]

$\int_{-1}^{1} x^2dx$

[glossy valve]

wai

[restive geyser]

I feel it is, yeah

[thick hedge]

tq

[restive geyser]

And it's because of there being no weighting that we don't need roads PDFs

[fast peak]

of course we still need weighting

that integral has area 2/3, sure

but the total area is 2

[restive geyser]

(if you really wanted tho, iirc the PDF of a UNIF[a, b] is something like 1/(b-a)?)

[thick hedge]

that's what i used to get X and Y

[thick hedge]

so I divide by 2

got it

tq

So $Y$'s PDF is $1$; $X's$ PDF given Y=y is $1/√y$

[glossy valve]

wai

[thick hedge]

is it just √y

[full forum]

@thick hedge Has your question been resolved?

[full forum]

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.

[charred birch]

is this vector field consercative

[full forum]

@charred birch Has your question been resolved?

[full forum]

@charred birch Has your question been resolved?

[nova briar]

Not if your contour is translated along the x axis
On the given contour, it looks like it though

[full forum]

@charred birch Has your question been resolved?

[full forum]

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.

[forest owl]

Hey, I'm a bit lost on how/why they graphed f0(x) like this. Could someone explain how they did this?

[olive olive]

what must an odd function satisfy

[forest owl]

Oh right, f(-x)

Okay I see now lol

.close

[full forum]

Channel closed

Closed by @forest owl

Use .reopen if this was a mistake.

[full forum]

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.

[languid junco]

I would need to see the work, but i can already tell there's probably an issue since you should have an n in your sines and cosines somewhere 🤔

also what did you mean "pi/2 between pi/2 <t < pi"

[forest raptor]

Ill send my solution

i have a feeling i messed up rlly badly

[languid junco]

okay well your indefinite integral for bn was fine but you didn't evaluate the integral on your bounds

which explains why you have a t in your coefficients

you also forgot to include the second integral (the one from pi/2 to pi) in your final coefficient

[forest raptor]

Omg okay ill redo

[languid junco]

and thank you for having neat handwriting lol

[forest raptor]

is this right now?

i probably messed up again somewhere 😭 so sorry

[languid junco]

all good, that's what we're here for

you forgot to put a t next to the cos(2nt) after integrating by parts (you put the t the first time but forgot this time)

I think you also plugged in 2/pi instead of pi/2 for both 🤔

[forest raptor]

End me

Tysm

[forest raptor]

it cancelled out, hopefully its right now

wait no

i made maths up

they cannt cancel

this does tho, if im not wrong

[full forum]

@forest raptor Has your question been resolved?

Channel closed

Closed by @forest raptor

Use .reopen if this was a mistake.

[forest raptor]

ty for your help

[full forum]

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.

[radiant rampart]

can anyone help me with this?

<@&286206848099549185>

[full forum]

@radiant rampart Has your question been resolved?

[radiant rampart]

ai helped me cuz yall be sleeping or sum 😢

[gritty rose]

!done

[full forum]

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

@radiant rampart Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[fierce roost]

hii im so confused why is this wrong?

[fierce roost]

the derivitive of the equation is -2t-5, right?

[ebon fulcrum]

Yes

[fierce roost]

and then plugging in 4 you get -13

and since its negative it's moving to the left

ok so then what am i doing wrong?

[gritty rose]

you put v(4) = 13

[ebon fulcrum]

You put 13

[fierce roost]

yes but it has the less than 0 after, right?

its 13 less than 0

[gritty rose]

wut

[fierce roost]

wait no you guys are right.

my logic is weird i fear

erm thank you guys have a wonderful night!

.close

[full forum]

Channel closed

Closed by @fierce roost

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.

[thick hedge]

Find the covariance of this dist

[
\begin{array}{c|ccc|c}
& X=1 & X=2 & X=3 & P(Y=y) \ \hline
Y=1 & \tfrac{1}{6} & 0 & 0 & \tfrac{1}{6} \[4pt]
Y=2 & 0 & \tfrac{1}{4} & \tfrac{1}{12} & \tfrac{1}{3} \[4pt]
Y=3 & \tfrac{1}{12} & \tfrac{1}{12} & \tfrac{1}{4} & \tfrac{5}{12} \ \hline
P(X=x) & \tfrac{1}{3} & \tfrac{1}{3} & \tfrac{1}{3} & 1
\end{array}
]

[thick hedge]

oops

this is a mess

.close

[full forum]

Channel closed

Closed by @thick hedge

Use .reopen if this was a mistake.

[glossy valve]

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

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

[full forum]

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.

[jade owl]

when graphing polar equations what would be like a "life hack" that would be really helpfull

[craggy tapir]

graphing polar equations is really no different from graphing cartesian equations, you memorize how common graphs look (circle, cardioids, lemniscate, etc.) and their respective equations, tweak the equation you need to graph into a combination of familiar graphs you can plot, and draw them

[jade owl]

ig without memorization theres no easy way

thanks tho

.close

[full forum]

Channel closed

Closed by @jade owl

Use .reopen if this was a mistake.

[craggy tapir]

i mean, what easy way are you expecting? just like how you would shit your pants graphing (sin(x))^tan(y) = cos^2x, it's manual work if you can't break the equation down into smaller ones

[umbral dome]

if you can graph r vs theta on cartesian axes, you can generally figure out what the corresponding polar plot should look like from there

[full forum]

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.

[tiny anvil]

I don't get it

F(x) belongs to all real other than 1 right?

[fathom saddle]

That's the domain. x is in R - {1}

[tiny anvil]

I mean I understand the note point why it can't be 2 , but then how will I objectively find the sol^n without any help , I mean what kind of exception is this

[onyx glen]

you confuse x with f(x)

also don't auto capitalize

[fathom saddle]

The range can't include 2. f(x) is in R - {2}

[tiny anvil]

Ehhh so this concept involves domains and ranges ?

God......

[buoyant wadi]

R - {1} is all possible inputs to f(x), R - {2} is all possible outputs of f(x)

[onyx glen]

put f(x)=y and do magic to solve for x in terms of y

and explicitly note when you have to divide by zero

[tiny anvil]

Ya when X=1

[onyx glen]

no not like that

[tiny anvil]

bruh

[onyx glen]

when you solve for x in terms of y

[tiny anvil]

X in terms of Y

got it

[onyx glen]

lowercase

[tiny anvil]

X/(x-1)=Y/2

Yea I am lost

[onyx glen]

LOWERCASE

[tiny anvil]

Omg

Sure

[onyx glen]

how would you solve x/(x-1)=69

[tiny anvil]

Pls demonstrate btw

X=69X-69

[onyx glen]

LOWERCASE

[tiny anvil]

68X=69

I am sorry T_T

x=69/68

Habit

[onyx glen]

now do same magic with x/(x-1)=y/2

[tiny anvil]

ohhhh

I get it

x=2/(y-2)

so Y can't be 2

Now pls explain the general approach

I don't get it

[buoyant wadi]

You've essentially done the general approach

2x/(x-1) = y is "y in terms of x"

x = 2/(y-2) is "x in terms of y"

2x/(x-1) says x can't be 1, 2/(y-2) says y can't be 2

[tiny anvil]

Ehhh

so acc to question

what to find

ehhh

Like domain or range

[onyx glen]

. .....

[tiny anvil]

Oh I just got it

ty ya al

[covert heath]

...

[tiny anvil]

for being so nice ;)

.close

[full forum]

Channel closed

Closed by @tiny anvil

Use .reopen if this was a mistake.

[full forum]

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.

[solid ruin]

Given matrices A and B with LU decomposition $A=L_A U , B=L_BU$ prove/disprove that the row space of A is equal to the row space of B

[glossy valve]

prograce

[solid ruin]

How do I start

I think its true

[full forum]

@solid ruin Has your question been resolved?

[fast peak]

when you do gaussian elimination on A, what does that tell you about the row space

[full forum]

@solid ruin Has your question been resolved?

Channel closed

Closed by @solid ruin

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.

[indigo tartan]

The outline of an object can be approximated by a half ellipse with a semimajor axis of 200px and a semiminor axis of 312px

[indigo tartan]

When thwhen the curve is revolved about the xa xis find the resulting surface area

[full whale]

holy shit, you're still at it
you have mentioned enough terms to make me convinced that you know you need integration. have you... tried that?

[indigo tartan]

i know im just stuck

there was a command like

!status

[full forum]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[indigo tartan]

i don't know where to begin to be honest

[full forum]

@indigo tartan Has your question been resolved?

[full forum]

@indigo tartan Has your question been resolved?

[lavish junco]

ok, do you remeber the general equation for an ellipse?

[full forum]

@indigo tartan Has your question been resolved?

[full forum]

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.

[flint moon]

i have been looking at this for like 15 mins and can't think of a relation which fits

[full forum]

@flint moon Has your question been resolved?

[robust slate]

Note that an integer $n$ belongs to the $k$th set iff $T_{k-1}<n \leq T_k$, where $T_k$ is the $k$th triangular number. From here, consider doing some floor/ceiling bounding stuff.

[glossy valve]

Civil Service Pigeon

[sonic stratus]

For some work of mine, i personally did something relatively similar.

The line of thought of it is a bit abstract, but, its analog to the following problem.

Suppose you have n dots you wanna fit in the following structure:
What will be the lowest k st. the n dots will fit without leaving an empty column.

the sequence here is of the form: 2^k

So, you can solve as follows:

Now, in your sequence, the sequence k must look something like this:

From here the notion should be pretty easy, hope that somewhat helps.

[sonic stratus]

Also, as reference, you can use the floor ( log_2 n ) function as your relation

all n st. the result is = k_i are part of the same subset.

[full forum]

@flint moon Has your question been resolved?

[full forum]

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.

[torn jolt]

yo

[torn jolt]

for part e im not sure on how to solve for the solution vector in Ax=0

[glacial pasture]

x=z-5t
-2y+5z-6t=0, y=5/2 z - 3t
z,t free variables [from Bx=0]

from there you should be able to construct your generic null vector - and from that you can make your basis vectors

[torn jolt]

dude I have 0 idea what you just said

[torn jolt]

yeah but

are we not solving for each unknown?

[glacial pasture]

we're finding a general null vector, so having unknowns is fine as we're looking at it in the form of a linear combination of the basis vectors
if we know the vectors have the form
[z-5t , 5/2 z-3t, z , t]
then thats the same as

z[1 , 5/2 , 1 , 0]+t[-5 , -3 , 0 , 1]
in which case what is our basis?

[torn jolt]

i know but do we need to plug back in [x1,x2,x3,x4]^T or ?

[glacial pasture]

z and t are x_3 and x_4

the only thing left to do from where I left it is to write the basis

[torn jolt]

howcome we dont solve for them by subbing

[glacial pasture]

but you can plug it in to check

[glacial pasture]

what do you mean?

[torn jolt]

know how if we have exactly 1 solution we always plug in and solve for each variable seperately

why dont we do that when we have a plane or line as a solution

[glacial pasture]

thats essentially what I did, it just so happens that we have 2 free variables which is why we have a space

I set the vector to be [x,y,z,t]^T, multiplied it by B, and then solved for the variables

[glacial pasture]

theres no way to solve it further than I had here, at most I could change which variables are the free ones

[torn jolt]

wait so whats the point of resubbing anyway? Im trying to understand this so i can see why this worked out

like geometrically whats the point

say you have 1 exact solution

from 3 planes

@glacial pasture did you change your mind?

maybe not

[glacial pasture]

its not that, Im just not great at explaining things in geometric terms

for a single solution of three planes, it would be the planes all intersecting in at one point, in which case we have a definite (x,y,z), no free variables

If we have one free variable, then we have a line - then our planes all intersect along a line e.g [t,2,t+3] is the line [0,2,3]+t[1,0,1]
if i found x=t, y=2, z=t+3

If we have two free variables then our solutions form a plane, so all our planes overlap

if we have 3 free variables then thats just all of R3

[full forum]

@torn jolt Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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 nebula]

Can someone explain the answer

[craggy tapir]

i don't see the answer

[patent nebula]

So basically i checked for the extraneous solution and it should
Root(49) =-7

It saids no real solution is it because
7= -7

Or what

[craggy tapir]

i'm not sure i follow

where is the answer specifically?

[craggy tapir]

!nosols

[full forum]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[patent nebula]

So no real solution?

[zenith hinge]

yes

no real sols

[patent nebula]

Alright

Thx

[unique perch]

you don't need all of this

notice 10-13r >= 0

so r <= 10/13

but r>=4 at the same time so no real solutions

[patent nebula]

Oh thanks for that tip

[unique perch]

does the problem require you to find complex roots?

[patent nebula]

Said to like find the value of n and check for extraneous solutions

[unique perch]

huh

that's weird as hell

[unique perch]

Seems like the problem wants you to square both sides, find the roots then plug them back into the original equation to check

that's horribly inefficient

[patent nebula]

Wdym

[unique perch]

that's a lot more work than just observe r >= 4 and r <= 10/13

[patent nebula]

Alright

.close

[full forum]

Channel closed

Closed by @patent nebula

Use .reopen if this was a mistake.

[full forum]

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.

[stiff pier]

<@&268886789983436800> not sure what this is but it seems fishy.

[twilit leaf]

probably cheating

yeah test proctors usually get the tests a day or two early and amc b is on the 13th

[full forum]

Channel closed

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

[twilit leaf]

thank you lance lance, of lancesquaredland

[full forum]

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.

[charred cedar]

I'm not sure how to approach and solve this problem

[nimble crane]

drawing a few pictures might help

[sonic stratus]

Given that you are working with a very limited amount of elements, you can prove most of these answers "brute-forcing" your way through

As long as you have some knowledge about functions

[charred cedar]

can you guide me?

[sonic stratus]

Well, lets start with r as a function P -> P

Do you understand what its essentially doing?

Beyond the description the problem gives

[charred cedar]

it’s just a function r to P P is a subset of itself?

[sonic stratus]

From the fundamentals,
do you understand why functions are a special type of "relation"?
And what is a bijective function?

[charred cedar]

relations are just functions basically but with multiple input output can be repeated then bijective functions are those that are injective and subjective one to one and on to

[sinful wind]

hi?

[sonic stratus]

!occupied

[full forum]

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

[sinful wind]

PT-BR people?

[sonic stratus]

Tbh you are defining relations as a form of function
While,

1. Its kinda the other way around
2. Still doesnt convey what functions and relations for that are.

Just to give a sense, a Relation (which can be between two sets), is basically a pairing between elements of the two.

[charred cedar]

sorry this was taught way back and I don’t have my notebook on me to properly define, I kind of just do the equations

[sonic stratus]

As a dumb example, lets say we do a relation between the set "fruits" and "colours"

We can say that "Apple" might be paired, to both Red And Green

Well, a function is basically a Relation , but an element from the origin set can only have one pairing from the other set..

[ember slate]

what class is this?

[charred cedar]

ohh I see

[charred cedar]

mathematic logic and reasoning

[sonic stratus]

This section is telling you, element by element

whats the origin, and whats the pairing.

[charred cedar]

yes

[sonic stratus]

So, for a function r(n)
a becomes b
b becomes c, etc...

[charred cedar]

yeah makes sense

[sonic stratus]

Doing some notation abuse, if you applied r to a whole set of elements a to e
{a,b,c,d,e}
it would become: {b,c,d,e,a}
again and its:{c,d,e,a,b}

So its basically cycling through the elements of the set.

We consider that idea a rotation, since, when applied multiple times, youll eventually get back to the original state.

[charred cedar]

ohh

[charred cedar]

tbh we didn’t learn this part

confused me a lot but that’s you this makes sense

[sonic stratus]

Visually it looks like this

[charred cedar]

r(P) means rotation on set P?

[sonic stratus]

again, a bit of notation abuse

Just take it as applying r to all elements

[charred cedar]

okayy

[sonic stratus]

Arguably, from a theorical standpoint, these are arrays in reality

so order matters for our purposes

now, we define another function f_a P -> P

Which is essentially a reflection instead of a rotation

Its described as using a line from a to the perpendicular in cd

[charred cedar]

ohh

can I know how it’s written the reflection?

so I know how to identify

[charred cedar]

like this is on text but haven’t seen how it’s written

[sonic stratus]

You get this

from the set meaning

You have to consider that rotations can alter the absolute order of the array

Meaning: b will always succed to the right a, c will always succed b, etc...

Well, reflection can change that order.

If we start from the rotation
$r: {(a,b),(b,c),(c,d),(d,e),(e,a)}$

[glossy valve]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[sonic stratus]

You get that, as we described, the array $\ {a,b,c,d,e}$ becomes
$\ {b,c,d,e,a}$

[charred cedar]

that’s the origin right?

[glossy valve]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[sonic stratus]

r Is function, functions can be described as a set of "pairs" from the origin to the pairing.

[charred cedar]

is this the rotation f_a

[charred cedar]

yes sorry at first before edited it showed the first set

[sonic stratus]

f_a is a reflection, right now im trying to note down how f_a doesnt work like r

[charred cedar]

oh so is this r(P)

ah gotcha

[sonic stratus]

$f_a$ instead has: ${(a,a),(b,e),(c,d),(d,c),(e,b)}$

[glossy valve]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[charred cedar]

yes I recall now sorry

[sonic stratus]

Which, just in case: doesnt change based on rotation

Since it always uses a as a reference

[charred cedar]

is the reference just another word for starting point?

[sonic stratus]

im mixing a bit general language and actual math words, for reference i mean that f_a is described as being analog to a reflection with a line from a to the perp. in cd

So its uses a and cd as its "frame", which, as we stated previously, the order cannot be changed by rotations

you can probably see that this arrangement is equal to applying r twice.

But the reflection f_a still retains its property of being a line from a to the perp. in cd

With "starting point" i meant the original arrangement from a to e.

Either from geometric reasoning, or set theoretic rational, you should be able to solve for the problem

[charred cedar]

ah got it

thank you for the visuals as well, helps a lot

[charred cedar]

I guess for these type its a good idea to draw then solve for the abcd

[sonic stratus]

if its helps you, both ways are valid

1 its pretty easy to show from a set theoretic standpoint given some of the things i just said

[charred cedar]

yeah for sure

@sonic stratus you're good with your wording I can probably figure it out but what is a) asking for?

[sonic stratus]

Is asking you to check and prove if the composition of r and f_a is equal to the one of f_a and r

in human terms:

If you rotate and reflect, will you get the same as reflect and rotate

[charred cedar]

I believe no?

[sonic stratus]

go check on the diagram, draw in your own

[full forum]

@charred cedar Has your question been resolved?

[full forum]

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.

[crystal tree]

Idk how to do this I fell asleep in class

[onyx glen]

step 0, or in fact -1, would be to uncrop this so that we can actually see the question in full

cause rn im gonna presume that you grabbed sth off Google image search just to troll about "posting a hard question in help channels"

[full forum]

@crystal tree Has your question been resolved?

[torn jolt]

Whats the name of the class

[full forum]

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.

[tidal storm]

Very unsure as of what to do

[tidal storm]

Obviously the quadratic residues mod 5 are 0, 1 & 4, but I’m unsure as of what to do next

I tried splitting up cases of the possible combinations which would create a Q which is divisible by 5 but there are too many cases

[rapid rain]

Really? Have you tried enumerating all cases at least?

Since we're considering sets btw, order in which the numbers appear doesn't matter

So 1112 and 1121 would count as the same instance

[tidal storm]

Oh wow already a mistake

[tidal storm]

I considered these as separate instances

[tidal storm]

Admittedly I gave up half way

Alright I’ll get back to you

If I counted correctly there should be 14 cases

I’m guessing from here we find the total number of possible cases

I’m inclined to say 5^4 but I think that would include permutations of the same set

[full forum]

@tidal storm Has your question been resolved?

[frigid carbon]

0 ain't in the set

[tidal storm]

I wrote 0 as in congruent to 0

Same for all the other numbers

Think I found a bit of a route for myself

There are only 3 possibilities of a Q which is divisible by 5

It depends on the congruency of the individual squares, so there are 3 cases:
#1: 0-0-0-0
#2: 1-4-1-4
#3: 0-0-1-4

I think that if I’m able to calculate the total number of ways that each of these cases occur, then add them together, then finally divide them by the total number of possible choices of 4 numbers from N, I should get the result

Evidently the number of possible choices of 4 numbers from N is N choose 4.

Then based on N I can find how many numbers there are from 1 to N that have squares that are divisible by 5.

And also how many are congruent to 1 & 4 mod 5.