help-17

[elfin moon]

This line

[proven garden]

I changed it

[elfin moon]

3^1/10 =3
3^2/10 =9
3^3/10=7
3^4/10=1

[proven garden]

and |<a>| divides |G|

thus |G| must not divide 2

try to find n such that |U(n)| doesn't divide 2

[elfin moon]

Why

2

[proven garden]

x^2=1

so 2

[elfin moon]

Mind blank

🙄

[proven garden]

hmm

learn some group theory

[elfin moon]

The thing is that you can see in my work

The work we did for n=10

What is wrong there?

Order is 4

So we should not take it?

Because 4 is divisible by 2?

[proven garden]

so we have 2 elements such that x^2=1

if |U(n)| is not divisible by 2

then only 1^2=1

all other elements would not square to 1

[elfin moon]

Divided by?

What is n?

N=1?

[proven garden]

no

|U(n)| is the order of U(n)

i.e how many elements are in U(n)

[elfin moon]

For n=10 we got 4 elements

[proven garden]

so if U(n) have 3/5/7/9...elements only 1 would square to itself

[elfin moon]

Yes it will

What about mod 10?

[proven garden]

what mod 10?

[elfin moon]

X^2=1 mod 10? Is this what we are doing?

[proven garden]

yes

[elfin moon]

I guess i am confusing. Myself

[proven garden]

generally we are doing x^2=1 mod n

[elfin moon]

x^2-1 / n
1^2-1/n =0

Only 1 will give the remainder 0 so this is the only solution

[proven garden]

when |U(n)| is not divisible by 2 ye

s

for other case like n=10 we might have more solutions

[elfin moon]

You mean when we don't see co prime?

[proven garden]

??

[hard atlas]

kinda useless condition. you might aswell say n!=2

[proven garden]

what

[elfin moon]

n!2

What is that factorial?

[proven garden]

!= means not equal to

[elfin moon]

Okie

[proven garden]

you know this if you code

[elfin moon]

I don't

[proven garden]

how though

[elfin moon]

What will we do if n!2

[hard atlas]

|U(n)| is always divisible by 2 except for n=2.

[proven garden]

how??

[elfin moon]

I guess no

[hard atlas]

phi(n) is always even

[elfin moon]

Co prime and phi(n) aren't same?

[hard atlas]

since when

[proven garden]

ohh

[hard atlas]

if k is coprime, then n-k is also coprime

so they come in pairs (k,n-k)

[elfin moon]

I'm lost somewhere

I need to learn many things

I'm very new in group theory

So i see things with examples

[proven garden]

so |U(n)| is always divisible by 2 for n>2

therefore at least 2 elements satisfy x^2=1 mod n

[hard atlas]

(we can explicitly say them anyway, 1 and -1)

(or 1 and n-1 if you prefer)

[vocal sleet]

@elfin moon Has your question been resolved?

[untold surge]

You remember I told you to read that section 4.11

This used it too

n=(2^e)m, m odd having k many prime factors. Then U(Z/nZ) is product of k cyclic groups (all having even order), if e=0,1, k+1 cyclic groups if e=2. k+2 cyclic groups if e>=3

To achieve the minimal, k=0, e=1, U(Z/2Z). 1

Sorry didn’t see condition n>2

k, e smaller the better, so k=1, e=0, or e=2, k=0 (meaning m=1), both cases give you two solutions

?

So answer is 2

You want me to give you the cases when it’s two or what?

[hard atlas]

yes lets overkill this

[untold surge]

n=an odd prime number or n=4

It’s just that he asked a different question, also involving structure of U(Z/nZ) weeks or months ago, I don’t remember. I asked him to read about it, and I said basic algebra I by Jacobson , section 4.11 has it. It seems like he still hasn’t started

Giving him a reminder

[elfin moon]

I guess the book is written too much above my level of understanding

[untold surge]

… then this kind of questions is bit advanced for you

[hard atlas]

it really isnt

[untold surge]

This case isn’t last time he asked

number of solutions of x^2=1 mod n when n=(2^e)m, m odd having k many prime factors , e>=3. I explained why it’s 2^(k+2).

It’s just that I saw he asking a question also involving U(Z/nZ). If he is going to ask more questions about it, also to solve the last question , he will have to read about it

[hard atlas]

for this particular question he has to know precisely nothing about what you said. it's doable much more elementary. I don't know the other questions he asked

[untold surge]

Yeah. I am just giving him a reminder

[elfin moon]

I'll get back to these type questions after some days

Once i grab the idea of it

[untold surge]

Okay. And again, 4.11 is independent with other stuffs in chapter 4

[elfin moon]

I am just a chinese remzider thorem level

[untold surge]

It’s exactly what 4.11 requires

Only cyclic group and CRT

nothing else

[elfin moon]

I tried right now but failure

[untold surge]

Don’t worry, try again in the future

If it really involves things you don’t know I would have mentioned earlier

[untold surge]

No

Section 4.11

Not theorem 4.11

Section

The 11th section in chapter 4

[elfin moon]

Here we go

[untold surge]

Yes this section

You don’t need the beginning

Jump right to theorem 4.19

By CRT U(Z/nZ) is product of U(Z/p^rZ), you can ignore everything before theorem 4.19, starting from theorem 4.19 this section proves U(Z/p^rZ) is cyclic when p>2 or p=2, r=1 or 2. Is product of a cyclic group and Z/2Z when p=2, r>=3

You need to read those to solve your last question about it. But Denascite is right, you don’t have to use those for this question you asked today

[elfin moon]

Can we not solve today's question with any numbers?

U(10) ={1,3,7,9}

Nevermind. I need to work on it more then retry thanks again

.close

[vocal sleet]

Channel closed

Closed by @elfin moon

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.

[proven garden]

!show

[vocal sleet]

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

[elfin moon]

I am confused with the currency

I can help you if they convert into indian currency

[vocal sleet]

@timid leaf Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[viral galleon]

I need some help understanding this

i dont understand

[exotic linden]

hey guys

[karmic imp]

What part?

[exotic linden]

i need help to understand something

[vocal sleet]

Please read #❓how-to-get-help

[viral galleon]

where -2(800)(600)cos(60) comes from

[karmic imp]

Law of cosines

[viral galleon]

ok but what about r squared

how does r squared turn into this

[karmic imp]

Do you know the formula for law of cosines?

[exotic linden]

can anyone tell me When do we add and when do we subtract of linear simultaneous equations

[vocal sleet]

Please read #❓how-to-get-help

[viral galleon]

you need to open another channel

read the how to get help

[viral galleon]

well

i ggoogled it

so now i do

i took a year break in between physics classes so i forgot it

[exotic linden]

oh my bad

[karmic imp]

Does it make sense now?

[viral galleon]

hm

maybe

ok so for the image right

its divided into two triangles

the 30 degrees turns into 60 degrees for obv reasons

its very hard to explain my question

let me think

ok so this is the image im looking at when i looked up law of cosines

but if you look at the image

its a parallelogram

in the problem

[karmic imp]

Yes, that just uses that general triangle, and forms 3 similar equations based on what side you are looking for

[karmic imp]

Yes

[viral galleon]

ok so for this problem how do i know that i need to use 60 instead of 30

why not 120

which is the whole angle

[karmic imp]

The parallelogram rule, you can parallel shift the lines, ie shift F2 so the tail is where the head of F1

[viral galleon]

ok

so if i do that then it looks like a mirror z yes?

[viral galleon]

I guess my question is how do i know what to plug in because the example here was a triangle

[karmic imp]

You're looking for R, the dotted red line, I shifted F1 and F2 but it does not matter which you do, but if you notice in law of cosine, you are using the angle across the unknown side. So in the image there, F2 is the orange, F1 is the purple. If you were finding R using the red F2, purple F1, then you use the angle in between, the pink one. Same logic with the other way, if you have the red F1 and orange F2, then the angle used to find R is the green one. Both the green and the pink angles have the same measure

[viral galleon]

oh

so you dont treat this like a parallelogram necessarily

you can use the properties of a parallelogram to make a triangle like this

ok i think i understand now

well ok i have one more question

would alpha angle not just be 60 as well?

[karmic imp]

No because it's not an equilateral triangle

[viral galleon]

then how do we know what the pink angle is

or the green one

[karmic imp]

The line where the 30 degrees is, draw it down until it reaches that purple line, that angle is a right angle

The sum of interior angles in a triangle equals 180

[viral galleon]

wow ok now i feel stupid

i didnt see the right triangle

[karmic imp]

You have 30, 90, and the pink angle

[viral galleon]

yes

so 60

i understand now thank you

[karmic imp]

Don't forget to .close if you are done with the channel

[viral galleon]

.close

[vocal sleet]

Channel closed

Closed by @viral galleon

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.

[viral galleon]

For this i know i need to use -600cos(some angle) to find the x component of f2

However I am struggling to figure out which angle to use

There is a 60 degree angle, 90 and 30 on this right triangle

[proven garden]

use the angle that is formed by F_2x and F2

[viral galleon]

so 60 degrees?

[pallid forge]

yes

[vocal sleet]

@viral galleon Has your question been resolved?

[viral galleon]

can someone help me understand this

so i was told to use the angle formed by the vector and the component

so for example

f2y and f2 forms an angle of 30

so you would do -600sin(30)

however the answer for this problem does 30 degrees for cosine as well

if we look the triangle is a right triangle

the angle formed by f2 and f2x would be 60 degrees

[viral galleon]

<@&286206848099549185>

[proven garden]

this is if you use cosine

if you use sine it's different

[viral galleon]

ok

so what do i do for sine

[proven garden]

also sin(30)=cos(60)

[viral galleon]

ir ealize that

which is why im confused

[proven garden]

learn trigonometry

[viral galleon]

is that not what im trying to do?

[harsh wolf]

It sounds like you're dealing with a physics problem involving vectors and trigonometry. Let me break down what's happening to help you understand it better.

[viral galleon]

really the only problem i am having is with using what angle for cosine and sine

everything else i can do on my own

[proven garden]

you are learning forces using trigonometry as a tool

but you don't know how to use the tool

[viral galleon]

dude what is the point of this server then if i am supposed to know how to use the tool

if ur not going to help dont respond

[harsh wolf]

Okay, lemme help you with that as well

[viral galleon]

ok thank you

[proven garden]

I want you to focus on trigonometry itself

[harsh wolf]

Given angle between F2 and F2y: 30 degrees
F2y component: -600
You need to find F2x, the horizontal component of F2.

Vertical Component F2y:
You're correct in using sine for the angle of 30 degrees:
F2y = F2 * sin(30°) = -600

[viral galleon]

ok makes sense

what about cosine

[harsh wolf]

Horizontal Component F2x:
The angle between F2 and F2x should be the complementary angle to 30 degrees, which is 60 degrees. This is because F2 and F2x are orthogonal (perpendicular), and in a right triangle, the angles must add up to 90 degrees.
Now you can use cosine for the 60-degree angle:
F2x = F2 * cos(60°)

[viral galleon]

yes but the problem is that -600cos(60) is same as -600sin(30)

and according the answer posted on the slides

he used cos(30)

[harsh wolf]

In a right triangle, the angles are complementary, meaning the sum of the angles is 90 degrees. If the angle between F2 and F2y is 30 degrees, then the angle between F2 and F2x should indeed be 60 degrees. This is because 30 degrees + 60 degrees = 90 degrees.

Given that the angle between F2 and F2y is 30 degrees, you should use sine to calculate F2y, and for the angle between F2 and F2x (which is 60 degrees), you should use cosine to calculate F2x.

However, in this specific case, since the triangle is a right triangle, it turns out that the sine of 30 degrees is equal to the cosine of 60 degrees: sin(30°) = cos(60°)

This is why you're observing that -600sin(30) is the same as -600cos(60).

[viral galleon]

No I understand the logic and I am in agreement with you. I am just confused because the answers my professor posted for the problem did not follow this logic

professor used 30 degrees for both cosine and sine

[viral galleon]

this is the answer he posted

u see he used 30 degrees for both

[harsh wolf]

Okay, if your professor used 30 degrees for both cosine and sine in the solution, it suggests that there might be a misunderstanding or error in the provided solution. Based on the information you've provided and the principles of trigonometry, using the same angle (30 degrees) for both cosine and sine does not align with the correct approach for calculating the components of the vector.

To ensure accuracy, it's generally necessary to use the correct angles for the corresponding trigonometric functions. In a right triangle scenario with complementary angles, using the sine of one angle and the cosine of the other angle is the appropriate approach.

[viral galleon]

Yeah that is what I thought too. I might ask him next time. This could just be a mistake

I know for sure the answer is 721 N though because I did the same problem with another method using parallelogram law

in which i got same answer he did

[harsh wolf]

Yeah, you should clarify with him.

[proven garden]

Ray you sound like chatgtp to me lol

also I don't see how is using sin30 and cos30 incorrect

[harsh wolf]

Remember i have an Masters in maths lol

[viral galleon]

That goes against what you said earlier. Earlier you said for cosine you used the angle formed by the x-component and vector. That would mean then the angle would be 60 degrees because that is literally the angle formed by the two. Now you are saying you dont see how cos(30) is incorrect

[proven garden]

cos30 is used for F2y

and the 30 degree is formed by F2y and F2

[viral galleon]

ok because

when i look at my notes from earlier classes

they use cosine for x component

and sine for y component

[proven garden]

in that case the angle should be formed by F and Fx

[viral galleon]

the angle formed by f and fx is 60 degrees

there is a 90 degree angle because it is a right triangle

i am just so confused because i had a quiz on this which i got a 100% on where there was a problem like this

and i used cosine for x component

and sine for y component

i know everything about this problem but the angle is tripping me up

it confuses me even more when this guy with masters in math agrees with me

but the thing is I know for a fact

the answer is 721

because again I did this same problem using law of sines

i will show u

[harsh wolf]

It is possible there could be a discrepancy in the specific problem you're facing, based on what you provided, your original understanding seems accurate.

[viral galleon]

yeah but

its frustrating

[harsh wolf]

Sorry, for that

[viral galleon]

do you think

it is maybe related to it being in the 3 quadrant

i am jus throwing out random ideas I have no idea to be honest with you

it is past 5pm so my professor wont respond to my question for a while

and to be honest with you i literally am skipping the gym to figure out this problem because I am so frustrated by it😂

[vocal sleet]

@viral galleon Has your question been resolved?

[vocal sleet]

@viral galleon Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[light hare]

I don’t understand what the units are supposed to be in part A and I’m confused on part B.

[paper depot]

well

you're dividing a distance in feet by a time in seconds

what units is that supposed to be?

[light hare]

Velocity?

[paper depot]

"velocity" is not a unit.

what units do you measure velocity or speed in, generally?

if you think you don't know, just say "I don't know" and i will try to jog your memory a bit further. @light hare

[light hare]

Yea, I’m raking my brain but I just don’t remember

[paper depot]

well ok

have you ever been in a car, whether as a driver or as a passenger?

[light hare]

Yes

[paper depot]

right

so you've seen a car speedometer, yes?

[light hare]

Yes

[paper depot]

ok now are you from america or from not-america

[light hare]

America

[paper depot]

ok

so you have seen the abbreviation "mph" at some point in your life, yes?

[light hare]

Sure have

[paper depot]

do you know what that stands for?

[light hare]

Miles per hour

[paper depot]

yes

that's a unit of speed

and generally ALL units of speed are "<length unit> per <time unit>"

m/s, km/h, mi/h, etc.

here you will want ft/s naturally.

[light hare]

So here it would be feet per second?

[paper depot]

that's what i just said.

[light hare]

Ah, sorry

It’s just that I remember trying to type that and it didn’t work

Gimme one sec

Is there another way to write ft/s? I’m trying to type it and it doesn’t let me

Wait, I got it

But how would one estimate the velocity at t=0.2?

[flat whale]

Use average rate of change formula from your previous problem

[light hare]

Thank you

If you don’t mind, would it be alright if you checked my answer for another problem and tell me if it’s right or not?

For question 5 I put figure 7 as my answer. Was that correct?

Actually I’ll just open up a different channel since the original question was solved.

.close

[vocal sleet]

Channel closed

Closed by @light hare

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.

[remote sorrel]

Why is the ans 70, im getting 35 ... ?

[flat whale]

Show your work

[remote sorrel]

<@&286206848099549185>

[loud pier]

what kind of mall has a parking capacity of 11

[remote sorrel]

idk lol

[loud pier]

goofy aaa

[remote sorrel]

btw what am i doing whong here why is the ans 70 ?

[loud pier]

tbh i dont get 70 or 35, i get 1, which is: they left

[remote sorrel]

bruh why r u here then

[loud pier]

i can identify whats wrong

just not whats right

[outer warren]

10 + 1 = 11 total cars

[remote sorrel]

yes 11 slots in total

[outer warren]

11 cars in total at the start as well

[remote sorrel]

no 10 only

[loud pier]

for once i can identify whats right

[outer warren]

don't think the 10 there includes his own

[remote sorrel]

yes it does

[loud pier]

i guess it doesnt specify

duck

[remote sorrel]

it says he parked it amongst the 10 parked

[loud pier]

https://tenor.com/view/good-luck-good-luck-gif-20034388

i gtg

bye

[remote sorrel]

finally thx

[outer warren]

there are 10 parked already there

if he parks there as well, it'd be 11

[remote sorrel]

nah after john parked itll be 10

[remote sorrel]

read it again carefully (the eng)

[remote sorrel]

cause the probability that im getting is right

[outer warren]

probability of what

[pure bone]

idk

[remote sorrel]

the next part of the ques was find probality that on his return he finds 5 cars parked such that 2 of the neighbors are empty

btw i got it

Irrespective of where John parks, his car occupies 3 parking spots, effectively, cuz "neighbouring parking spots are empty". That leaves 11-3=8 spots for others.

Total cars = 5
Other cars = 5-1 = 4
Available spots = 8
Therefore number of ways that there are 5 cars in the parking lot = 8C4

.close

[vocal sleet]

Channel closed

Closed by @remote sorrel

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vast shale]

laws of motion problem

[vast shale]

,rotate

[vast shale]

finally

im having trouble in the second one

i know block B will be moving down and block A will be sliding leftwards so block C goes up but i cant proceed from there

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

<@&286206848099549185>

[gray yarrow]

im eating right now, i have an idea i can show you after

sry for the wait

[vast shale]

aight

[quiet hatch]

Patrick Bateman asking for help.THATS AMAZING.

[gray yarrow]

ok im back

i would start by ignoring block A completely

we have a pulley system

here:
F_Z=1/n F_L
where F_Z is the pull force and F_L is the Force of the Mass (here C)
so we get F_B=1/2 F_C
notice though that we have ignored the gravitational force on B
so actually we would get F_B=F_C/2 + 2mg (2m because that is the mass of B)

and F_C is just m*a_C

then we can use

$\tan\theta=\frac{F_A}{F_B}$

[twin meteor]

Martin

[gray yarrow]

but i dont know if that is going to help us

ok i dont know how to continue
what i did pretty much:
look at B and C and get the force that acts on B (depending on the acceleration of C)
then look at A and C
that way we can get the force acting upon A, but that will depend on the acceleration of C as well

[vast shale]

is f_z the tension in the string

and f_l the normal force

i dont know what you mean by force of the mass

[gray yarrow]

i got the variables from another website
f_z was the force with which we pull on B and f_l is the force that pushes C downwards, so f_l should be the gravitational force of C

pulleys are confusing

[vast shale]

no C isnt going down

actually idk if its going down or up

[gray yarrow]

ah i did it wrong

im gonna try it again

[vast shale]

but i'd think it was going up because if it was going down then block C would be completely useless

im assuming C is pulled up by the string, and B is being pulled down by gravity, such that A is being moved leftwards

if i assume block C is going down, block A becomes irrelevant, and i get acceleration of C as g/3 ms^2 downwards

and that can't possible be the answer because this question has a single digit answer from 0-9

[gray yarrow]

ok this is what i got thus far

this is what i used

here we have F_Z=F_L/n
so in our case F_Z=F_L/2

but somehow i think i did it wrong again

but even if i find my mistake, i still think i cant solve for a_C like this...

yes in fact, i am pretty sure i did it wrong

im gonna try it the other way round next

ok sry, i have no idea how to proceed

[vast shale]

🥲 me neither

[gray yarrow]

maybe this discord can help better: https://discord.gg/physics

[vast shale]

banned

[gray yarrow]

haha, how is that possible

[vast shale]

i dont want to say it

[gray yarrow]

damn

[vast shale]

this question has been fucking me up for days

and its not even that hard

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

no it has not been resolved <@&286206848099549185>

[stoic drift]

I mean. The solution is online.

[vast shale]

nevermind i solved it

this is such a convoluted one

.close

[vocal sleet]

Channel closed

Closed by @still phoenix

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[delicate totem]

all trigometric identites

[hard rose]

What about them

[delicate totem]

give me

[vast shale]

google

[hard rose]

Ss fron google a bit unnecessary

[delicate totem]

its blur

[vast shale]

its not

[delicate totem]

ok'

1+1=3?

welp

[obtuse sierra]

head to #geometry-and-trigonometry and see pins

[vast shale]

??

[vocal sleet]

@delicate totem Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[brittle peak]

help!

[dull maple]

How did you get 0?

Didn't you just calculate the limit expression to be (8+h)?

[vocal sleet]

@brittle peak Has your question been resolved?

[brittle peak]

I just guessed ngl assuming h = 0

do i replace h with (8+h)

[dull maple]

You have (8+h), and your h is approaching zero, so you are supposed to replace h with 0.

[brittle peak]

ooohhhhh

you're right

[dull maple]

That's how you are supposed to do it.

Make sure that you understand.

Once you find the expression for limit by solving $\frac{f(c+h) - f(c)}{h}$, you put 0 at the place of h. Then, limit will either exist or not.

[twin meteor]

Enemagneto

[vocal sleet]

@brittle peak Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[frail hornet]

I dont understand this ive looked at my notes but i cant seem to figure it out

[paper depot]

@frail hornet are you familiar with basic algebra?

like solving equations of the simplest kinds

[frail hornet]

uhh not really

i was never really good at math

[vocal sleet]

@frail hornet Has your question been resolved?

Channel closed

Closed by @frail hornet

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[frail hornet]

again :)

[wraith venture]

Only 27 numbers to check

[frail plinth]

is this where i go for help

someone plz

[wraith venture]

No. Use an available channel
#❓how-to-get-help

[frail hornet]

im sorry?

[empty frigate]

check if 1 is perfect, then check if 2 is perfect, then check if 3 is perfect, and so on

since we're checking them in order, whichever perfect number we find first is the smallest one

[frail hornet]

and how would we find the perfect number

[empty frigate]

...that's literally what i just explained how to do? or am i not understanding what you mean

you check if 1 is perfect, then you check if 2 is perfect, then you check if 3 is perfect, etc.

[frail hornet]

ohh okay

[untold surge]

You wrote n=Π(p^r) , then the sum of its divisors other than itself is (Π(1+p+p^2+…+p^r))-n

Might help examining whether n is “perfect”

[wraith venture]

Look at her previous question just above
You're definitely overshooting with that explanation. Both for the helpee and for the problem

[vocal sleet]

@frail hornet Has your question been resolved?

Channel closed

Closed by @frail hornet

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.

[restive hawk]

Hi,
would someone be so kind and help me with this problem.
Which of the following formulas correspond to the statement about the natural number n, n>1 : "n is a prime number."?

1. (∀k∈N)(∀l∈N)((n=k⋅l)⇒(k=n∨k=1))
2. (∀k∈N)(∀l∈N)((n=k⋅l)∧(k=1∨l=1))
3. (∀k∈N)(∃l∈N)((n=k⋅l)⇒(k=1))
4. (∀k∈N)(∀l∈N)((n=k⋅l)⇒(k=1∨l=1))

I am trying to understand why for example in the first option n couldnt be something like 12
if I get it right: k can be either n or 1 if n = k * l following this logic I dont really see the reason why k cant be 6

[untold surge]

Which one do you think is correct

Sorry
Which among them do you think are correct?

[dull maple]

Hey, i have a question.||In those (k=1 v l=1), does it not mean that they both can be 1 at the same time? That would create problem.||
I'm not well versed with logic so excuse me if it's trivial. Lol

[untold surge]

||I think he wrote slightly not rigorous , he should have written them as ()()(()) -> () not ()()(()->()). And you are right, that’s why logically all of them can deduce the statement n is prime because 2,3 are actually false. False statements can deduce any statement. But since he used the word “corresponding” I am okay that they are actually looking for 1,4||

[dull maple]

I think i get it. ||All it means that when truth value of n=kl is true, then truth value of (k=1 v l=1) should be true as well, and that it is.|| Right?

[untold surge]

Yeah

[dull maple]

One more question, please. ||What about the second one? I don't know the proper terminology, but it seems like they made no statement there. Just stated the premise. Like - for all natural k and l such that kl =n, and either k is 1 or n is 1, then <missing part>. I am just wondering if there should be a claim afterwards. Or, does it tacitly go that the claim is - then n is a prime?||

[vocal sleet]

@restive hawk Has your question been resolved?

[untold surge]

||all of them are statements, if he asked which statements satisfying the statement-> r is correct where r:”n is prime” then the other three are like (p->q)->r, second is like (p Λ q)->r, all of them -> r are actually correct because 2,3 are false statements but yeah since he used the word “correspond”, 3 doesn’t correspond and 2 is more like a condition yeah, so directly crossed off||

[dull maple]

Okay. Thank you.

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[untold surge]

||on second thought I think 3 isn’t false, it’s just saying a completely irrelevant thing I think. 3:p->q, p is false, so what 3 actually is simply “k=1”, so 3->r isn’t true but it doesn’t “correspond” r anyway||

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[knotty kettle]

is there something im missing

this looked pretty straighforward

.close

[vocal sleet]

Channel closed

Closed by @knotty kettle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[echo patrol]

I have a question and two invariants I feel satisfy the question but I am not sure if there is a possible counter example to it

Question
To make learning more interactive and fun for students, a math teacher decides to teach a concept to students by using Lego blocks. There are 2 rows of legos, rowA (of length n) and rowB (of length m).
Both rows hold legos with positive integer values printed on them. However, some values (possibly, none) are missing. The missing values are denoted by 0. Students need to incorporate the missing values. The task is to replace each O with a positive integer such that the sums of both arrays are equal.
Return the minimum sum possible. If it is not possible to make the sums equal, return -1
e,g a = [1,0,2] b = [1,3,0,0] -> 6
a = [1,1] b = [0,0,0] -> -1

Answer
Invariants

1. if either of the rows does not have a 0 then it becomes impossible iff the non-zero rows sum is less than the sum of the other row + its count of zeros e,g a= [1,1,1] b = [2,2,2,0] aSum = 3 and bSum + 0s = 9 so impossible
2. other than that we simply get the maximum of the sum of each row + its count of zeros a=[1,2,0] b=[3,1,0] aSum + 0s = 4 bSum + 0s = 5 therefore min possible is 5

[vocal sleet]

@echo patrol Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[kind shuttle]

Given x=cos(theta) and y=2sin(theta) with -pi/2<=theta<=pi, eliminate the parameter. I got y=2sin(cos^-1(x/5)) and it said it was wrong

[kind shuttle]

Can someone help me figure out where i went wrong

If it helps, the website for this assignment is strict in formatting of the answer input. So if I do have the right answer, does anyone have an idea as to how I can format it better?

[echo patrol]

.reopen

[kind shuttle]

please

<@&286206848099549185>

[vocal sleet]

@kind shuttle Has your question been resolved?

[kind shuttle]

.close

[vocal sleet]

Channel closed

Closed by @kind shuttle

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.

[hoary kestrel]

2B i dont get how to integrate it

[hoary kestrel]

I’m stuck here

[loud heath]

No need to square both sides

Do separation of variables

[hoary kestrel]

Like this?

@loud heath

[loud heath]

Yes

[hoary kestrel]

Thx

.close

[vocal sleet]

Channel closed

Closed by @hoary kestrel

Use .reopen if this was a mistake.

[loud heath]

Wl

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[rugged vortex]

Determine the quadrant that θ terminates in first

[velvet cove]

isnt it 3

[rugged vortex]

Yup

[rugged vortex]

So is sine positive or negative in quadrant 3

[velvet cove]

its negative i think

can i just change tan to sin/cos

and say sin(theta)=4 and cos(theta)=3

[rugged vortex]

No

how can sine and cosine be greater than 1

Draw a triangle in Q3 that has the property such that tan(θ) is 4/3

Determine the hypotenuse

[velvet cove]

is it sqrt(3^2+4^2)

oh wait thats 5

[rugged vortex]

Find sine

[velvet cove]

k ty

.close

[vocal sleet]

Channel closed

Closed by @velvet cove

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[cunning shuttle]

A company, which is making 200 mobiles phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N.
(a) Find the value N.
(b) The company then plans to continue to make 600 mobile phones each week.
Find the total number of mobile phones that will be made in the first 52 weeks starting from and including week 1.

[cunning shuttle]

Is this correct?

[paper depot]

,rccw

[gritty zenith]

First one looks good

[paper depot]

sees ok to me assuming no arithmetic bs

[stray dawn]

the second one is wrong
the formula for sum of terms in an ap is
n/2[2a + (n-1)d]
the given n is 21 so with the values put in the formula would look something like
21/2[2(200)+(20)(20)]

[vocal sleet]

@cunning shuttle Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[digital veldt]

Hi so in this question I've proven -b/a = -c/b = h but the last photo is as far as I've gotten for d/c. How do I get d/c to be in terms of the (a,b) and hence equal h. Is it just simple algebra I'm not seeing? Lol

[vocal sleet]

Please don't occupy multiple help channels.

@digital veldt Has your question been resolved?

Channel closed

Closed by @digital veldt

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.

[tame mason]

Might anyone be able to explain how to do this? I understand how to find the unit vector, I just don’t know what it means by smaller and larger i component

[vocal sleet]

@tame mason Has your question been resolved?

[vocal sleet]

@tame mason Has your question been resolved?

[somber portal]

You've said you have found "the" unit vector.
There are two.
Assuming you have found "one" unit vector, i'm gonna call it u, it can be decomposed as u=ai+bj, with "a" and "b" being reals, i and j the unit vectors aligned with x and y axis.
Since you got two vectors, each of them is gonna have a different "a" value.
It asks for those two, different, "a" values.

[tame mason]

But it asks for 2 i components

It doesn’t mention any sort of j

[somber portal]

read the answer again, carefully. I've slightly edited it to be clearer

[tame mason]

I assume you mean the increasing and decreasing one?

[somber portal]

no. I'm gonna put an example with two (wrong) vectors.
Let's say that the vectors parallel to the line are u=(1, 2) and v=(-1, -2)
You could write u=1*i+2*j
The "smaller" i-component would be the one from v, -1;
The "larger" i-component would be the one from u, 1

[tame mason]

Yeah that’s what I meant, the one increasing and the one decreasing

[somber portal]

i would not call it "increasing" and "decreasing" since they are constant, but it might be a language difference

[tame mason]

I submitted 1/7 for a similar one and got it wrong, this one specifically. (Also tried without the i)

Tried the negative version too

[somber portal]

gimme one sec

maybe it needs both to be correct to evaluate as right? i'd submit -1/7 and 1/7

[tame mason]

I just tried on the first problem and got it wrong too

Oh wait I put it in wrong

One sec lemme retry

[somber portal]

sqrt(145) is not a possible value.
You're told to find unit vectors. The components of unit vectors need to be within the [-1, 1] range

[tame mason]

Yeah I put it in wrong

I tried again and same thing

[somber portal]

If it's not accepting the answer i'd go to the teacher with it fully solved by hand, say "these are the unit vectors" and ask what the field actually wants inputted

[tame mason]

Ah ok, will do

[somber portal]

you can solve the math problem, it's not your job to fix the input field :)

[vocal sleet]

@tame mason Has your question been resolved?

Channel closed

Closed by @tame mason

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.

[zealous remnant]

What is wrong with my calc

[outer warren]

seems to be in radians mode

based on the angle values, seems you want degrees mode

[vocal sleet]

@zealous remnant Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vocal sleet]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

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

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

[simple urchin]

what.?

[simple urchin]

it is not a function when the vertical line intercepts 2 points

what the hell does the 4th and last option have to do with any of that..

[dense stump]

exactly

try looking at the other options

[simple urchin]

uhh

so

[dense stump]

oh wait it says 2

[simple urchin]

hold on give me a minute please so i can sketch it out

yeha...

one moment

[dense stump]

okay I’ll have to think abt this

[simple urchin]

i have other questions

this is just one

i have 1 more

but this is like

hold on

this is the correct answers

but

[dull maple]

Well, for the last one, it fails the vertical line test.

[simple urchin]

i get the 2nd one

but the 3rd one

i dont get it

[simple urchin]

how did you solve the last one?

[heady ibex]

,w plot |y| = x

[twin meteor]

Results provided by WolframAlpha

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

Requested by kathlijn

[dull maple]

Well, it's by simple analysis.
You have $|y| = u(x)$, so if for some x = a, let's say u(a) = b.
Then, $|y| = b$.
Don't you think that you are getting more than one values for y here?

[twin meteor]

Enemagneto

[simple urchin]

oh

wait

let me see

okay but

what about this

if i put for example 1 as the square root

the domain and y would both be 1

no?

[heady ibex]

remember what a function is

one to one

[simple urchin]

oh

[heady ibex]

one input means one output

[simple urchin]

so the other example you gave me

its y = x

that means if x was 1

y would be 1, correct?

[heady ibex]

the graph i showed

if i input x = 1

then y = 1 or -1

[simple urchin]

dont get it 😭

here

theres another uh

activity of the same concept

the first 2 i understand

the 3rd one

i still dont get the | y | = x thing

[dull maple]

Just so you are not confused, this is a function.

[simple urchin]

why?

😭 😭

[dull maple]

Why do you think it's not?

[simple urchin]

i mean

how would it be graphed

i dont think its not

i just dont know how this would be graphed

because i have no numbers

[dull maple]

Do you know any two positive numbers whose squares are same?

[simple urchin]

Nope

[dull maple]

Good

So, there is no such x for which we'll get two different square roots.

[simple urchin]

corrct

correct

but

[dull maple]

That means that for each one x, there'll be one unique y.

[simple urchin]

i get that now

yeah because

like

if the domain was 16

[dull maple]

So, it doesn't violate any properties of function.

[simple urchin]

y would be 4

right?

[dull maple]

Yes

[simple urchin]

okay now

about the other example

[dull maple]

Important thing to notice is that y won't be -4.

[simple urchin]

well yeah obviously

wait

what if there was

a +- before the square root

that would be different

that wouldnt be a function, right?

[dull maple]

Yes

[simple urchin]

okay cool

[dull maple]

That would make it not a function.

[simple urchin]

as there are... 2 different ys for 1 x?

okay.

[simple urchin]

so THIS

why is that not a function

[dull maple]

Try to think about this.

[simple urchin]

okay

[dull maple]

Are you familiar with absolute value functions?

[simple urchin]

so theyre saying that y = x and x can be any number greater than 1

what is that?

[simple urchin]

like

if i pick 2 domains

say 3 and 5 for example

[dull maple]

You see these || around y?

[simple urchin]

3, 3
and 5, 5

no, what is that?

[dull maple]

That's the absolute value function.

[simple urchin]

what about it

[dull maple]

You should know it in order to be able to do the question.

Just in case, do you know the modulus function?

[simple urchin]

Nope

maybe

what is it

like

going back to the question

as i said if i picked

2 domains

3 and 5

3 = y

there is only one

uh

one y

for 3

which is 3

3, 3

no?

[dull maple]

It says that regardless of whatever value you put inside me, i'll give you the positive value with same magnitude.

So, |5| = 5

and |-5| = 5

as well

[simple urchin]

oh wait..

OH WAIT..

YEAH

THAT'S TRUE-

I'M SO STUPID

oh

so now i should be able to

solve the whole second question

lets go 1 by 1

f = 1, 0 and 1, 1

that's not a function so yeah

2nd one is a function

NWO the 3rd one

its what we just studied

its not a function because the domain can have 2 y's

[dull maple]

So, you got the third one?

[simple urchin]

yup

[dull maple]

Cool

[simple urchin]

now

the 4th si a function

now 5TH one

its a function because

if the domain was 16, the "y" would be 4 and 4 only correct?

okay good

the last one is interesting

[dull maple]

We already did that too.

[simple urchin]

is it wrong because there is a + and - before the square root

which would giv

2 y's

for one domain

[dull maple]

Yes

[simple urchin]

okay

oh SWEET

you're an amazing person!

okay uhh

[dull maple]

Lol. Happy to be of help.

[simple urchin]

❤️

let me check if thre are

other questions

that ih ave

oh yeah

theyre asking

which of the following functions has a domain equal to the set of real numbers

wait

the ones that restrict or say > or < than 0 are all wrong

is it because they want all real numbers

[dull maple]

Yes

[vocal sleet]

@simple urchin Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[wary mantle]

Solve the inequality $\sqrt{1 - x} \geq - \frac 1 2 - x$ for $x \in \mathbb R$. \
We can break this up into two cases: \ $(1)$, $- \frac 1 2 \geq x$ and $(2)$, $- \frac 1 2 < x$. \
In the first case, we could square both sides and so on, but in the second case, how would we proceed? We wouldn't be allowed to square, since the RHS would be negative.

[paper depot]

i mean in the second case it's auto satisfied

because you have sqrt(1-x) ≥ 0 > -1/2 - x

[hard atlas]

well if the RHS is negative then the inequality is always true

[paper depot]

btw is there a reason you wrote the case conditions backward?

[hard atlas]

if anything you should be worried about taking sqrt of something negative

[wary mantle]

Oh, right. Thanks!

[wary mantle]

Kinda, I wanted to make the first case the one where we can square and the latter the one I'm asking about

.close

[vocal sleet]

Channel closed

Closed by @wary mantle

Use .reopen if this was a mistake.

[wary mantle]

.reopen

[vocal sleet]

✅

[wary mantle]

Wait, in the second case, the RHS is not necesarily negative

[worthy citrus]

He means the RHS of the original inequality, which your second case is precisely the one that says its negative

[wary mantle]

Oh, yep, thanks

.close

[vocal sleet]

Channel closed

Closed by @wary mantle

Use .reopen if this was a mistake.

[worthy citrus]

Provided you're not square rooting a negative

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[wheat sinew]

How do i prove gcd(a,b) = gcd(b,a-b)?

[brittle robin]

this is good

try to do the opposite way

now

[brittle minnow]

you have proved that d divides b, a-b ie d is a divisor

all that remains to show is that it's the greatest divisor

[brittle robin]

hint :- if x divides y and y divides x then x = y..try to think and apply this

[wheat sinew]

both d and d' divide a, b , a-b

[brittle minnow]

this just proves that the gcd's are a divisor

you still need to show that they are the greatest

divisors

[wheat sinew]

how would i do that

[brittle minnow]

take a common divisor (say c) of b, a-b then show that c divides d

[vocal sleet]

@wheat sinew Has your question been resolved?

[wheat sinew]

im sorry im dumb

[hard atlas]

in any of your previous stuff, have you actually used that d is the greatest common divisor?

if you can show that the sets of the common divisors are the same, then also the greatest elements in those sets have to be the same

[wheat sinew]

sorry im a beginner

could you explain step by step how i could do this?

[brittle robin]

let's get down to the basic
tell me about this
assume 3 integer x, y and z

now x divides y and x divides z..can we say x = gcd(y,z)??

[wheat sinew]

no

[brittle robin]

good

[wheat sinew]

it has to be a multiple of x though

[brittle robin]

why not? if not gcd then what can we comment about x then?

[wheat sinew]

it is a factor of the gcd

[brittle robin]

hmm..true..well done!

now let's assume gcd(y,z) = p..then can we say x divides p?

[wheat sinew]

yes

[brittle robin]

okk

now can we say that x divides (y + z)??

[wheat sinew]

yes as y = ax and z = bx, y + z is ax + bx = x(a+b) so yes x divides y and z

[brittle robin]

okay cool

can we say the same about (y-z)?

[wheat sinew]

yes

[brittle robin]

great!!

now we have the base level understanding

now to solve your original problem

assume d = gcd(a,b) and g = gcd(b,a-b)

[wheat sinew]

okay

[brittle robin]

now start from d divides a and d divides b..and find way to relate d and g ... like whether using can we say d divides g or the opposite way around

try to apply what I have explained just now..that will be enough

[wheat sinew]

either d is a multiple of g or g is a multiple of d

[brittle robin]

how? explain me that?

[wheat sinew]

so d divides a,b,a-b, g divides a,b,a-b also, and so earlier we said d must be a multiple of g, or g must a multiple of d

[brittle robin]

you are merging everything together..

see d divides b and a - b and we know that gcd(b, a-b) = g..now what can we say about d and g?

[wheat sinew]

but d and g dont have to be equal

do they?

g = kd

OH WAIT

i think i got it

if g = kd

d must equal kg

g = kkg

divide by g to get k = 1 because g cannot be 0

g = d

[brittle robin]

yea true

that's way to solve this problem..

[wheat sinew]

is it the way you had in mind?

[brittle robin]

but you could have used this too

anyways since you are a beginner it's good

[wheat sinew]

explain

d divides g

[brittle robin]

using this? you tell me..I can explain but you have to learn right? think and tell

[wheat sinew]

i think i got it

so d divides g as said before, and since g divides a and b, and gcd(a,b) is d, g divides d

and d divides g and g divides d

g = d

[brittle robin]

great! excellent work!

you are free to close this now

[wheat sinew]

thank you so much!

i appreciate it, im only 15 and i want to become better at olympiad maths so thank you so much!

.close

[vocal sleet]

Channel closed

Closed by @wheat sinew

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[vocal sleet]

Please don't occupy multiple help channels.

[chilly pawn]

.close

[vocal sleet]

Channel closed

Closed by @chilly pawn

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[twin meteor]

General_Jacob

[jagged gorge]

what

[mild flower]

x can be almost anything

[jagged gorge]

that’s an expression not an equation

[twin meteor]

General_Jacob

[vocal sleet]

Channel closed

Closed by @orchid beacon

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.

[soft walrus]

How can I show:
$\lim_{p\to\infty}\frac{(p+1)\text{round}\left(\frac{p!}{\ln^{p+1}2}\right)}{\text{round}\left(\frac{(p+1)!}{\ln^{p+2}2}\right)}=\ln2$?

[soft walrus]

I don't even know where to begin :(

[twin meteor]

MrFancy

[soft walrus]

these round functions are giving me a headache 🥴

[hidden kelp]

you have a knack for finding weird ahh limits and sums

[soft walrus]

$\frac{\lim_{p\to\infty}(p+1)\text{round}\left(\frac{p!}{\ln^{p+1}2}\right)}{\lim_{p\to\infty}\text{round}\left(\frac{(p+1)!}{\ln^{p+2}2}\right)}$?

[twin meteor]

MrFancy

[soft walrus]

tis my specialty! 🙃

[flat whale]

Uhhh do you know Stirling's formula

[soft walrus]

stirling's approximation, yea

[flat whale]

Use that

[soft walrus]

on the factorials? ok

[mild flower]

oh like (ln 2) ^ p

not ln repeated p times

that makes more sense now i think

[soft walrus]

$\frac{\lim_{p\to\infty}(p+1)\text{round}\left(\frac{\sqrt{2\pi{p}}\left(\frac{p}{e}\right)^{p}}{\ln^{p+1}2}\right)}{\lim_{p\to\infty}\text{round}\left(\frac{\sqrt{2\pi{(p+1)}}\left(\frac{p+1}{e}\right)^{p+1}}{\ln^{p+2}2}\right)}$

ok converted

waiittt

can I move the limits inside the round() function?

[soft walrus]

ln(2) times itself p+2 times :)

[twin meteor]

MrFancy

[flat whale]

Is the round a floor function or a ceiling

Not 100% sure if it makes a difference

[soft walrus]

rounds to the closest integer

round(0.3)=0

round(0.9)=1

[flat whale]

Man

[soft walrus]

I assume you know that lol

[flat whale]

I guess you can do upper and lower bounding using floor and ceiling

[soft walrus]

all this just to show log(2)

[flat whale]

Or just solve it by pretending the round isn't there at all

[soft walrus]

omg holy shit i have spent 2 hours and did not even consider that

the factorial and logs cancel

and you end up with ln2

@flat whale ty so fucking much

now I feel like an idiot smh

.close

[vocal sleet]

Channel closed

Closed by @soft walrus

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.

[gritty mountain]

Do I have to solve the equation

Or can I just say it's undefined

and no solution

because it becomes 1/0 when you input the initial condition

which is undefined

[oblique leaf]

whether a solution exists or not, you would have to justify it properly, which you do by solving the eqution either way

but im not quite sure where you got 1/0 from

[gritty mountain]

I just plugged in 1 for x

[oblique leaf]

oh i see, but the gradient at the point doesnt rly matter;
suppose the solution to a differential equation is y= tanx
surely y' approaches infty as you approach pi/2 from the left right
but that doesnt mean that a solution doesnt exist

gradient/slope whatever idk where youre from

[gritty mountain]

I'm suppose to use Picard's theorem

And I think that since it's undefined and not continous at the initial condition, then it doesn't have a solution.

I think

.close

[vocal sleet]

Channel closed

Closed by @gritty mountain

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.

[unique jolt]

need help with precacl!