help-42

[sage cosmos]

Then T=0

And block is at rest at g=0

[pliant scarab]

oh yeah it makes sense

see

geff at eqm is 0

so T = infinity

yes

[sage cosmos]

Yeah

But actual me toh g = infinity nhi hota

Analogy tha sir ka dekha jaye toh

[pliant scarab]

ohhh accha

[sage cosmos]

Lekin sir ye bhi bole ki T=0 means infinite frequency that is infinite oscillatios in 1 second

For a object at rest, oscillation never ends so that analogy should also be true and both gives T=0 and T= infinity

Lekin sir T= infinity bol diye toh wo me convention le lunga lekin pure clarity nhi mili sigh

[pliant scarab]

same lol

i am also confused

but good thing is

it is never used

so i dont care

[sage cosmos]

I can give you the video

[pliant scarab]

kk

[sage cosmos]

Do you have telegram

[pliant scarab]

no

issok leave it

[sage cosmos]

I watched video on telegram

[pliant scarab]

ohh

[sage cosmos]

Okay

.close

[calm coral]

Channel closed

Closed by @sage cosmos

Use .reopen if this was a mistake.

[calm coral]

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.

[strong dew]

Suppose a population of wolves grows according to the logistic differential equation dP/dt=3P - 0.01P², where P is the number of wolves at time t, in years.

Find the number of wolves in the population when the population is growing the fastest.

[strong dew]

I know when the population is growing the fastest, but do i just take the integral of dp/dt from 0 to 150 or something?

that kinda feels wrong

[stray tundra]

When is it growing the fastest? how did you obtain it?

[strong dew]

L/2 right?

i factored out 0.01P and got 300 for L

so it’s growing the fastest when t=150?

[stray tundra]

what is L?

[strong dew]

the kP(L-P)

thats the formula i remember for differential logistical growth

its the carrying limit right

also pls hurry, i only have like 4 mins left

[stray tundra]

is this homework to deliver?

[strong dew]

quiz in 2 mins

or less i forgot

@stray tundra could you just quickly explain what i do

is it an integral?

wait can i use the L/1+Ce^-Lkt thing

actually idk what C is

yea no idk what to do

time to fail the quiz

[calm coral]

@strong dew Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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 mural]

do you have a specific problem

[calm coral]

@remote mural Has your question been resolved?

[steep pebble]

Say you have some infinite sequence of numbers $(a_n){n=0}^{\infty}$ indexed by the natural numbers (you can start at 1 if you want).
The sums $S_n \coloneqq \sum{k=0}^n a_k$ are called \emph{partial sums} for the series $S \coloneqq \sum_{k=0}^{\infty} a_k$, and if they converge to a number, we define $S$ to be this number.

[potent lotus]

LemonGeneSorcerer

[steep pebble]

Specifically, in the question, the sum is the \emph{geometric sum}, for which there is a specific formula (that you can find e.g. on Wikipedia)
There's also a formula for the partial sums

Ahm.

Did you learn about limits anywhere?

My answer would depend on whether or not you did.

[calm coral]

Channel closed

Closed by @steady ridge

Use .reopen if this was a mistake.

[calm coral]

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.

[red spear]

I have to approximate the value of arctg0,2 using Taylor series with Lagrange reminder

[red spear]

how to evaluate the last inequality?

what value of c should I consider

<@&286206848099549185>

should i pick a value of c, looking at the range of c (0;0,2) for which the inequality is correct?

like that I mean

What am i doing wrong

<@&286206848099549185>

[next thistle]

Hello there

[red spear]

hello!

[next thistle]

Hmm

Interesting

[half jolt]

What error do you need?

[red spear]

0,01

[half jolt]

And you took p(x) = f(0) + f'(0)x?

That should be enough for this case

[red spear]

well i took n=1

should still be good, no?

[half jolt]

That's n = 1 isnt it

[half jolt]

this

Why did you plug in c = 0.2 though, that doesn't give you an upper bound

[red spear]

but I have to calculate n+1 expressions

what you wrote would be for n=0, no?

[half jolt]

For n = 1, p(x) = f(0) + f'(0)x, r(x) = f''(c)/2 * x^2

[red spear]

ah i see what you mean, then yes

[half jolt]

$\abs{R_2(0.2)} = \abs{\frac{\frac{-2c}{(1+c^2)^2}}{2!} 0.2^2} = \abs{\frac{c}{(1+c^2)^2} \cdot 0.04} = \frac{c}{(1+c^2)^2} \cdot 0.04$

[potent lotus]

RedstonePlayz09

RedstonePlayz09

[half jolt]

And you are done

To get the upper bound, I replace the c in the numerator with 0.02

[red spear]

where did you get 0^2 in the denominator?

[half jolt]

And the c in the denominator with 0

Because 0 < c < 0.02

Making the denominator smaller would increase the fraction

[red spear]

oh i see

[half jolt]

Honestly you should start taking n = 2 and above more often

[red spear]

when picking the c should i always pick at the edges of range of c?

either 0 or 0,2 in this case

[half jolt]

The whole idea is to find an approximation using simple methods

Using the bounds on c is very easy

Sometimes it might not be enough, and that's why I always recommend taking at least n = 2

[red spear]

I see

[half jolt]

In this case, 0 is very close to 0.02 so you only needed up to the first derivative

[red spear]

my biggest problem is knowing what value to replace c with

[half jolt]

Just use the bounds on it..

[red spear]

so in this case 0 or 0,02?

[half jolt]

Which side depends on the expression

I chose to replace the c in the numerator by 0.02 because that gives me an upper bound

And the denominator with 0, because it again gives me an upper bound

Replacing the c in the denominator by 0.02 would only give you something smaller, meaning your inequality will be >=

Instead of <= which is what you want

[red spear]

I see

but the values themselves, that you replace c with

are on the edges of the range of c

[half jolt]

Yes

[red spear]

I understand now

thank you

[half jolt]

np

[red spear]

Now, that I have n, is the expression itself wrong?

[half jolt]

Idk what you wrote here

[red spear]

here

[half jolt]

Now that you know |R_1(0.2)| < 0.01

Meaning the error of the expansion for n = 1 is less than 0.01

You can approximate arctan(0.2) using it

arctan(0.2) is about f(0) + f'(0)x = 0 +1 * 0.2 = 0.2

so arctan(0.2) is about 0.2 lol

[red spear]

ah I see

because arctan(0.2) is 0,197 and when I approximate it to the second decimal place

it's just 0,2

[half jolt]

Yeah I guess

[red spear]

Got it

thank you!

.close

[calm coral]

Channel closed

Closed by @red spear

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 mural]

he

[calm coral]

Please don't occupy multiple help channels.

[remote mural]

lp

[calm coral]

Please don't occupy multiple help channels.

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

GET UR CAMERA BITCHH

[leaden thunder]

?????

[remote mural]

?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[heavy cairn]

Why is the graph falling from the point -pi/6 i tought it would rise because A is positive.

[leaden thunder]

There's a negative number multiplying theta

[heavy cairn]

Okey Thank you

.close

[calm coral]

Channel closed

Closed by @heavy cairn

Use .reopen if this was a mistake.

[calm coral]

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.

[rose fox]

I have to do 4-27a

[rose fox]

Well I need help writing an equation for the graph

I got a(x+3)(x+1)(x-2)^2 but i’m not sure what a is

[kindred estuary]

It's y = a(x + 3)(x + 1)(x - 2)^2, use a point from that plot, plug it in, and solve for a

A point that isn't a root to the function

[rose fox]

What do you mean by root to the function?

Can I use (2,0)

[kindred estuary]

No, because that's a root

If you plugged in that, the right side results in 0, making it not useful to finding the value of a

[rose fox]

Okay, I found my answer

Thx

.close

[calm coral]

Channel closed

Closed by @rose fox

Use .reopen if this was a mistake.

[calm coral]

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.

[blazing coyote]

TP and TQ are tangents to $y^2=4ax$ at Pand Q. If the chord passes via(-a,b), then find the locus of T

[potent lotus]

Why am. I here

[blazing coyote]

I would like a hint

I mean I could startby finding general tangent equations, the points wt which the tangents intersect the parabola and so on

but is there any other better way

[quaint sphinx]

what is b

[blazing coyote]

a fixed point

-a,b is a fixed point

[quaint sphinx]

is the a in (-a, b) the same a that is used to define the parabola

[blazing coyote]

yeah

nvm, I've got to go

thanks though

.close

[calm coral]

Channel closed

Closed by @blazing coyote

Use .reopen if this was a mistake.

[calm coral]

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.

[old falcon]

Okay, I'm stuck on a simpler problem, maybe this will be a good chace to figure out how this epsilon business works

bonk

bot?

[old falcon]

Assume $|E|_e < \infty$. Then $E$ is measurable iff $|E|_i = |E|_e$.

[potent lotus]

jan Niku

[old falcon]

I'm working on the forward direction now

[potent lotus]

jan Niku

[whole hinge]

PIN

What's PPT?

PowerPoint?

[old falcon]

previously proven theorems

is that not standard

[whole hinge]

Ah

I have never heard this

[old falcon]

[whole hinge]

But which previously proven theorems do you have

Lol

[old falcon]

idk its too many to list

[whole hinge]

This was more or less the definition of measurable that I had while reading Folland

[old falcon]

we have nothing about the inner measure

this problem is actually the first time ive seen it

[whole hinge]

Can you write down the definition of measurable again then

[whole hinge]

Okay

[old falcon]

we have some equivalent theorem

[whole hinge]

Makes sense

[old falcon]

thats probably a better form

basically identically as above, up to Closed F subset E such that |E-F|_e < eps

[whole hinge]

So you're assuming E is measurable and trying to prove that the inner and outer measure are the same

[old falcon]

right

so clearly theyll just be the measure

[whole hinge]

Use both of these theorems

The closed one relates to the inner measure, the open one relates to the outer measure

[old falcon]

that the outer measure is the measure for sets of finite measure is PPT

[old falcon]

but it doesnt, it relates outer

theyre both defined using outer

[whole hinge]

I'm not sure that that matters

The definition of inner measure is based on closed subsets

[old falcon]

i guess im asking

i had no idea what the other person was talking about with the epsilons

[whole hinge]

Let's see

So I mean the intuitive idea here is

"You can get closed subsets as close as you want to the set E. You can also get open supersets as close as you want to the set E. Therefore, you can get the inner measure and outer measure as close as you want, i.e. they're equal."

Obviously you have to formalize this but

That's the gist of the argument

[old falcon]

supersets?

[whole hinge]

Yeah, you take open supersets when you define the outer measure right?

Like open G such that E is a subset of G

[old falcon]

ive never seen that word before

[old falcon]

i dont think so

[whole hinge]

we're both learning

[old falcon]

we use volumes

[whole hinge]

But the volumes are of open sets, no?

[old falcon]

no

[whole hinge]

Or, sums of open intervals

[old falcon]

no

[whole hinge]

What

[old falcon]

theyre volumes of closed intervals

[whole hinge]

That's weird, but that should be basically the same idea

[old falcon]

'intervals' are hard-defined as being closed at least in my notes

[whole hinge]

Do you have a theorem relating open supersets to the outer measure

[old falcon]

im not sure what supersets are, so i dont have anything like that

[whole hinge]

superset is just the opposite of subset

[old falcon]

we have that defn of measurable that has the word open in it

and the paired one for closed

this one i posted a moment ago

[whole hinge]

Okay

[old falcon]

but both use the outer measure

so im not sure its applicable

[whole hinge]

Hmmmm

[old falcon]

can we do like

okay so clearly F and E are mble

then |E-F|_e < eps

i think i can say that E-F is measurable?

so |E-F| < eps

then |E| - |F| < eps

[whole hinge]

That seems like it should work yeah

[old falcon]

but idk where youd go from here

[whole hinge]

Well then you know that |E| - eps < |F|

but you also know that |F| ≤ |E|

[old falcon]

[whole hinge]

and then make eps arbitrarily small, and you're good

[old falcon]

idk i can actually assert all this

[whole hinge]

Which part are you shaky on

[old falcon]

|E-F|_e = |E-F|

[whole hinge]

So, the difference between two measurable sets is measurable, right? Have you proven that previously

[old falcon]

because |E-F|_e < eps doesnt mean E-F is measurable

oh wait but were assuming E is measurable

[whole hinge]

Yeah

[old falcon]

but we dont know F is measurable

[whole hinge]

F is closed

So we do

[old falcon]

ah

[whole hinge]

BTW have you proven the Lebesgue measure is additive

so |A disjoint union B| = |A| + |B|

[old falcon]

no, its an assignment on this pset

[whole hinge]

Can you use it for this problem

[old falcon]

and we arent allowed to use stuff on the current pset

[whole hinge]

Oh

I'm not sure how you assert that |E| - |F| < eps then

maybe subadditivity suffices?

[old falcon]

well first i need to show that difference thing

[whole hinge]

Oh you haven't shown that the difference of measurable sets is measurable yet either

[old falcon]

ah we have

[whole hinge]

Okay wait

[old falcon]

i have it checked off as ok i did it myself

okay so then

|E-F| is measurable apropos basically the entirety of this problem

[whole hinge]

I don't think you even need to switch to Lebesgue measure here as long as you know about subadditivity of the outer measure
|E|e ≤ |E-F|e + |F|e < |F|e + eps
so you can pick F so |F|e gets arbitrarily close to |E|e

I think we're overcomplicating this

[old falcon]

if E1 E2 are measurable, E2 subset E1, |E2|<inf, then |E1-E2| = |E1| - |E2| is good too

[whole hinge]

I just didn't know which facts you've already proven

[old falcon]

im not sure i track all this

[whole hinge]

Are you okay with the first inequality? (Subadditivity)

[old falcon]

it doesnt look like subadditivity to me

you have a difference

[whole hinge]

Hint: write E as a union of two sets

[old falcon]

right you could write it as union E and F

[whole hinge]

Close, not E and F

[old falcon]

[whole hinge]

I wanna introduce the set difference in there somehow right

So what should I write E as a union of

[old falcon]

sorry im not really sure

we ultimately want to write it as a union of sets that have a positive distance

but im not seeing how to do that

[whole hinge]

Please stop spamming, this is a help channel

[whole hinge]

Here, fill in the blank: E = (E-F) U ?

[old falcon]

right, i know this

but they dont have positive distance

so it breaks the chain of equalities

E = E-F U F

[whole hinge]

You still have subadditivity, no?

[old falcon]

but d(E-F, F) = 0

it doesnt matter

[whole hinge]

Why do you need a positive distance

[old falcon]

dont we need that | E-F U F |_e = |E-F|_e + |F|_e ?

[whole hinge]

No, we only need subadditivity (as far as I know)

≤

I mean unless something about this argument is broken, but I don't see it

[whole hinge]

^

[old falcon]

well we can get to |E|_e <= |E|

im not sure what you mean with the chain you have written

[whole hinge]

Our end goal is to show that |F|e can get arbitrarily close to |E|e, i.e. for each eps, there exists F such that |F|e > |E|e - eps, right?

That would prove the inner and outer measures of E are equal

[old falcon]

? no we wanted to show that the inner and outer measure are equal

oh

I'm not sure how that would show what we are trying to show

[whole hinge]

The outer measure is just |E|e

[old falcon]

how did you construct it

right

[whole hinge]

The inner measure is ≥ |F|e

If the two get arbitrarily close together, then |E|i = |E|e

Also out of curiosity, is this a first course in analysis? Or a second course

Measure theory seems like a pretty advanced topic lol

[old falcon]

I had real analysis back in 2020

[whole hinge]

Ah okay

A while ago

[old falcon]

there is literally no reason for ppl with my major to take this class

it makes 0 sense that its included as part of the degree

my last proofs-based course was that real analysis class

although ive done proofs here and there

[old falcon]

I'm sorry im dumb and stupid, i still dont see

|E|e is the outer measure

[whole hinge]

You're not dumb

Do you agree that |E|i ≥ |F|e for every closed subset F of E?

[old falcon]

I guess I havent shown that

[whole hinge]

It's the definition of |E|i, right?

[old falcon]

it is?

[whole hinge]

It's the supremum of all such |F| s

[old falcon]

one second

its defined using the lebesgue measure

the sup doesnt stop us from using outer measure does it

because F is otherwise measurable

[whole hinge]

Yeah, F is measurable so |F|e is the same as |F|

[whole hinge]

So we get this right

[old falcon]

sure

[whole hinge]

Okay

So we have a chain |F|e ≤ |E|i ≤ |E|e for every single closed subset F of E?

Does that make sense

[old falcon]

how do you get the second?

im sorry this is probably like pulling teeth

[whole hinge]

I think it was a previous part?

[old falcon]

oh

[whole hinge]

Like the last question you asked

[old falcon]

wait we arent allowed to use stuff on the pset though

[whole hinge]

You're all good

Wait isn't this the same question

[old falcon]

but its the second part of the problem

[whole hinge]

Yeah

You should be able to use it, I'd expect

[old falcon]

maybe that means youre actually supposed to

okay sure

so chain chain chain

|F|e <= |E|i <= |E|e <= |F|e + eps

does this actually show equality

is this a standard way to do it

can you just say this shows equality or is there something else to do

i think ill stop here

i appreciate it eric

.close

.close

[calm coral]

Channel closed

Closed by @old falcon

Use .reopen if this was a mistake.

[whole hinge]

no problem!

[whole hinge]

yes

make eps as small as you want

[calm coral]

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.

[vapid aspen]

can someone help me determine the chromatic number for this graph?

Since it has an odd cycle, I know we will need at least 3 colors. I seem to require 4, but I am not sure if that is the real chromatic number, if it can be done with 3, or how to tell

[calm coral]

@vapid aspen Has your question been resolved?

[vapid aspen]

<@&286206848099549185> anyone up for helping with some graph theory?

[calm coral]

@vapid aspen Has your question been resolved?

[vapid aspen]

.close

[calm coral]

Channel closed

Closed by @vapid aspen

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.

[chilly oak]

how do i solve this integral?

[sinful pasture]

factorize the 4

where's the integral?

[chilly oak]

it got cut off

[calm coral]

@chilly oak Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

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

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

[odd knot]

Is it correct to say that all 3 cases could be binomial distribution?
like, in question (a) the number of days in april is constant (30) so n=30 and p=1/2 (either it rains or it doesn't.)

for question (b), there are 12 months in a year, and this holds true every year, so n=12, and p=1/2.

for question (c), here I am a little unsure, but IF we set n=number of years, and p=1/2 it's still OK for a binomial distribution since both n and p are fixed values. BUT, since the Easter sunday may vary between mars and april for different years, I assumed there were some trickery by my teacher and so maybe it's not optimal for a binomial distribution?

[left bay]

Yeah, good observations - but have a look at your argument that p = 1/2, because either it rains or it doesn't.

You can say the same thing about playing the lottery. The chance that I win is 50 %, because either I win or I don't.

[odd knot]

ahh ofcourse... How do I think of p in the correct way then?

[left bay]

For a given day, there is some probability p that it rains that day. It might be p = 0.05, if you're in Qatar, or p = 0.7, if you're in London (I'm making these up).

The probability of rain will vary depending on where you are and the season.

So for the first one (the one with April), I would say that it is reasonable enough to assume that the probability of rain is the same every day in April.

(as long as you always measure at the same location :))

For the binomial distribution, you also need independence between different measurements. I'm no meteorologist, but I would assume there is some correlation between it raining on consecutive days.

So that's another assumptions you have to make - besides the probability p of rain being the same for all days in April - there is independence between whether it rains or not on any given days.

[calm coral]

@odd knot Has your question been resolved?

[calm coral]

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.

[hexed ginkgo]

I did not understand this whole topic in my lecture

[hexed ginkgo]

Please start from explaining this condition for the uniqueness of solution
I have 0 idea where in the world this came from and what does this even imply

[calm coral]

@hexed ginkgo Has your question been resolved?

[calm coral]

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.

[calm coral]

Please don't occupy multiple help channels.

[digital swallow]

I don't understand how to find these points

<@&286206848099549185>

[half jolt]

Either AM-GM inequality or derivatives

[digital swallow]

What

is that

[half jolt]

Are you learning derivatives right now?

[digital swallow]

no

I have bo clue what that is

[half jolt]

So what are you learning?

[digital swallow]

functions

graphs of rational functions

[half jolt]

Well be more specific

[digital swallow]

what's that

I'm learning every single function

[half jolt]

But what tools have you learned for analyzing these functions?

[digital swallow]

tools?

[half jolt]

What have you learned that lets you know stuff about these functions

[digital swallow]

uhhh

asymtote

x and y ints

the type of line

[half jolt]

Okay, anything else?

[digital swallow]

we didn't learn the tp of the lines

[half jolt]

How do you usually find min/max points

[digital swallow]

I've never learnt thay

the teacher only teaches easy stuff

and expects us to learn the hard ones

[half jolt]

Learn how

Huh

[digital swallow]

can u send me a videos on it

I've been searching youtube

and I can't find one for this type of graph

all of them are for normal graphs

[half jolt]

I find it hard to believe you're expected to learn that yourself

[digital swallow]

me too

I find it hard to believe as well she is such a bitch

[half jolt]

AM-GM inequality is the easiest way to solve this one, but it might not work for other examples

[digital swallow]

she only teaches this class because she is the coordinator

[digital swallow]

for Rectangular hyperbolas I always use AM-GM?

can u send a link to a yt video I dunno how to learn that

also I have another question

[half jolt]

Google AM-GM inequality

[digital swallow]

okok

also I have to ask

why is there no x ints

y≠0 is just what I copied but I don't understand it

[half jolt]

x intercepts is when y = 0

[digital swallow]

yeah but apprently there's no x int of this

[half jolt]

But the fraction is never 0 because the numerator is never 0

[digital swallow]

so whenever there is no other numbers

and only a fraction

there will never be a x int?

[half jolt]

What

No

The numerator is just 1

The fraction can't be 0

[digital swallow]

ohh

so if any fraction has a numerator

of 1

it can never be 0

[half jolt]

I guess

Just try to understand why

Not memorize patterns

[digital swallow]

how does am-gm

help me find the tp

[half jolt]

y = x + 4/x >= 2sqrt(x * 4/x) = 2sqrt(4) = 4

So y >= 4

(When x > 0)

And AM-GM also tells you that when x = 4/x, there is equality.

Meaning x = 2 is when y = 4, and for all other x values, y > 4

So (2, 4) is a minimum point

[digital swallow]

I don't undersatnd

I just watched a yt video

I have no idea how u applied it

😭😭😭

[half jolt]

You understand this?

[digital swallow]

not really

I feel like they don't have a coknection

I don't understand the connection between am-gm and this graoh

[half jolt]

y is equal to x + 4/x

For every point on the graph

But x + 4x is greater than 4 according to AM-GM

(when x is positive)

So y >= 4 for every point on the graph

[digital swallow]

why is y eql to x+4/x

[half jolt]

That's the function..

You sent it

[digital swallow]

isn't the function

[spark stratus]

y-coordinate = x-coordinate + 4 / x-coordinate

also y = f(x)

so theres no difference between y = and f(x) = for your problem

[digital swallow]

x+2+(4/x-1)

[half jolt]

That's what you sent

It says y = x + 4/x there

Unless you have a different problem

[spark stratus]

and its x + 4/x thats ≥ 4 (if x > 0)

[half jolt]

alr @spark stratus u can take over

[spark stratus]

whatd I do wrong

[half jolt]

nothing, but it seems you want to help him

[spark stratus]

on second thought Im gonna send an image and go

[digital swallow]

ok

[spark stratus]

,,\text{AM-GM: }{\color{yellow}a}+{\color{cyan}b}\ge 2\sqrt{{\color{yellow}a}\cdot{\color{cyan}b}}\
{\color{yellow}x}+{\color{cyan}\frac4x}\ge 2\sqrt{{\color{yellow}x}\cdot{\color{cyan}\frac4x}}=2\sqrt{4}=4\
x+\frac4x\ge4

[potent lotus]

mtt07734

[half jolt]

Nice latex

[spark stratus]

thanks

[digital swallow]

how does this help me find the max min

I'll look tmr

I'm so sleepy

[spark stratus]

alr

[digital swallow]

it's so hard

idk why my teacher didn't teach this

[spark stratus]

thats because youre asking a question youre not supposed to be able to answer

most likely they marked the point with the coordinates on there so you know that its there

you dont need to know how to get one

from what it sounds like, this is something you can get to later on when youre more familiar with algebra

and with what a min or max is

[calm coral]

@digital swallow Has your question been resolved?

[calm coral]

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.

[blazing coyote]

Why exactly is this the same as the thumbtack definition of an ellipse?

[blazing coyote]

https://youtu.be/pQa_tWZmlGs?si=piZgHfqas1pk7Tlf

[blazing coyote]

I'm not sure I understand grants explanation

More specifically the this is vaguely remeniscent of the thumbtack definition

6:48 is the timestamp

[thorny stump]

The thumbtack thing is when you fix the ends of a string onto two thumbtacks and then pull on the string with a pen, and draw a figure that way

It draws an ellipse because the sum of distances to the foci remains the same

[blazing coyote]

Why does it in this case

[thorny stump]

In which case? Thumbtack or cone slice?

[blazing coyote]

Thanks

Conic slice

[thorny stump]

Well that's kind of what this whole video is about

Once you slice the cone with a plane, you can add the two spheres such that they are tangent to both the cone and the plane

Call each of the points where the spheres touch the plane "focus"

[blazing coyote]

Hmm, ok just re-watched that section, I think I got it

Hmm, ok,

[thorny stump]

Cool, need me to continue?

[blazing coyote]

No need, thanks!

[thorny stump]

[blazing coyote]

I'll close this now ?

. close

.close

[calm coral]

Channel closed

Closed by @blazing coyote

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.

[grave condor]

yeah

[flat pumice]

Yeah

[calm coral]

@flat pumice Has your question been resolved?

Channel closed

Closed by @flat pumice

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[proper berry]

assistance please

[round helm]

follow normal algebraic logic while substituting x into the expression

keeping in mind that i^2 = -1

[proper berry]

i did that and got -32+18i

but that was wrong

[round helm]

show your work

[proper berry]

i did it for a different equation

but one sec

[round helm]

that isn't the given question i suppose

it seems like you worked out the solution for a different question

[proper berry]

no i get to retry questions if i am wrong

i think the correct answer was -32-6i but I am not positive

[round helm]

for which question?

[proper berry]

the one i tried to solve first

[crude pecan]

[proper berry]

its a different equation

the other one x =-2+6i

[round helm]

share the work for the question you're trying to solve along with the correct question

[proper berry]

ok i gotta do it so one sec

[round helm]

you haven't opened the brackets properly in the x^2 term

$(-a-b)^2 \neq a^2 + b^2$

[potent lotus]

Talent Unlimited

[proper berry]

is it minus?

[round helm]

$= a^2 + b^2 + 2ab$

[potent lotus]

Talent Unlimited

[proper berry]

ok but why

[potent lotus]

Talent Unlimited

[proper berry]

ohhh

[round helm]

now try to simplify it again

[proper berry]

-16+12i?

[round helm]

yes, good!

[proper berry]

thank you

.close

[calm coral]

Channel closed

Closed by @proper berry

Use .reopen if this was a mistake.

[calm coral]

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.

[torn gorge]

maybe it could be useful to try integration by parts, by integrating 1/x+1=ln |x +1|+c

that is equal to ln2 when it is been intgrating fro 0 to 1

[leaden thunder]

Show what you tried

This is only half the formula

Write out the entire formula for geometric series for 1/(1-q)

[calm coral]

@remote mural Has your question been resolved?

[leaden thunder]

It does if you choose q correctly

This is just a finite sum. Series means infinite sum which is what you have.

[leaden thunder]

Well then do this instead

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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.

[finite quest]

why the answer for b 2?

[potent igloo]

It's not 2

[finite quest]

-2

sorry

why is it -2?

[fathom shuttle]

approch f(-1) from the positive side

h(-1) whoops

[finite quest]

hmmm

i dont get it

[potent igloo]

Look at what h(x) gets close to as x gets close to -1, considering only values to the right of -1.

[finite quest]

OHHH

ok

so for a its 1 cause thats whats it getting close to from the left

and for b its -2 cause thats what its getting close to from the right

?

[median oyster]

yes

[potent igloo]

Precisely

[median oyster]

importantly, what the function actually does at the point doesn't matter

[finite quest]

ohhhh

okk

thank u

.close

[calm coral]

Channel closed

Closed by @finite quest

Use .reopen if this was a mistake.

[calm coral]

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.

[magic olive]

How many different equivalences on a 7-element set with three equivalence classes of sizes 4, 2, and 1 exist?

[magic olive]

How to calculate it

I know definitions of equivalance on a set and equivalance class, but this is some combonatorics so i need help

[glass heart]

well first you need to choose 4 elements to be in the big class, then 2 elements to be in the middle class and then the last one is left over

[magic olive]

So its 7 choose 4 . 3 choose 2?

Since 1 choose 1 is left

[median oyster]

yes

another way to think about it is, for every permutation of 7, identify any permutation of the first 4 and any permutation of the next pair, so it's 7!/4!2!

these both give the same total, just different ways of counting it

[magic olive]

Alright

Thanks

.close

[calm coral]

Channel closed

Closed by @magic olive

Use .reopen if this was a mistake.

[calm coral]

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 cobalt]

Let $a \in (0, 1)$. Find all solutions $x: \mathbb{R} \rightarrow \mathbb{R}$ to the IVP $\dot{x} = sgn(x) |x|^a, x(0) = 0$ and justify that these are all the solutions.

[digital cobalt]

For this question, my thought process was to break it up into 3 cases: $x = 0, x > 0, x < 0$. Clearly, $x(t) = 0$ for all time is a solution to this IVP. When $x > 0$, $\dot{x} = x^a$; this is separable, so we can do some algebra/calculus to eventually get $x(t) = (1 - a)t^{\frac{1}{1 - a}}$. I'm struggling to work with the $x < 0$ case, when $\dot{x} = -|x|^a$. Is breaking the problem up into three cases likes this the right approach?

[potent lotus]

murkii

murkii

[calm coral]

@digital cobalt Has your question been resolved?

[digital cobalt]

<@&286206848099549185> any help is greatly appreciated! 🙏

[median oyster]

splitting into cases seems sensible

if you have x<0, you should be able to remove the modulus in that case, like how you did with the x>0 case though

i.e., x' = -(-x)^a

[calm coral]

@digital cobalt Has your question been resolved?

[digital cobalt]

oh i see; ok that was simple lol

as for justification, do you think it'd be enough to say that these are three distinct cases that cover all possible choices for x?

i think one of my confusions also makes me question this casework; can't a solution x fluctuate between being positive, negative, or zero depending on time?

hm idk

[calm coral]

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.

[pallid halo]

!status

[calm coral]

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

[eternal bluff]

1

yeah no

[pallid halo]

try expanding (x+y)^2

[eternal bluff]

yeah so

x^2+2xy+y^2

right

[pallid halo]

yea

now is that >= 4xy?

try subtracting 4xy from it and find out

i'm assuming OP doesn't have amgm available

and needs an elementary proof

[eternal bluff]

yeah so u get x^2-2xy+y^2

yeah i do

[pallid halo]

and can you write that another way

[eternal bluff]

idk do you factor it?

(x-y)^2 >= 0 ?

okay

so how tf do i do the next part

<@&286206848099549185>

<@&286206848099549185>

.close

[calm coral]

Channel closed

Closed by @eternal bluff

Use .reopen if this was a mistake.

[calm coral]

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.

[turbid canyon]

<@&286206848099549185>

[turbid canyon]

<@&286206848099549185>

my bad

[grim latch]

Man waits for 15 minutes then pings.

💀

[turbid canyon]

me?

ok so who's helping me?

no

wha are u saying

oh shi

i sent the wrong problem

thats the one

they make triangles?

@remote mural

ok

ngl

i have work thats hard but simpler than this, this one is the hardest of them all

thats why im asking u it first

tell me numbers bro

this why i be confused

im literally confused

i would undersand this one @remote mural

[calm coral]

@turbid canyon Has your question been resolved?

[turbid canyon]

it was 9

u were supposed to round it ig

[calm coral]

@turbid canyon Has your question been resolved?

[calm coral]

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.

[fierce cradle]

Could someone help me with this?

[leaden thunder]

Use the definition of fixed point

[fierce cradle]

I got this...do you agree?

Anyone?

<@&286206848099549185>

[calm coral]

@fierce cradle Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[flat pumice]

It should be divergent no?

[swift laurel]

what kind of convergence test could you use for this?

[calm coral]

@flat pumice Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[flat pumice]

.reipen

.reopen

[calm coral]

✅

[calm coral]

@flat pumice Has your question been resolved?

Channel closed

Closed by @flat pumice

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[odd egret]

can anyone help me derive a, c and d in terms of b. the equations are : a+b = d , 2ab= cd, c/b = (a+b)/a , b+c = a

[odd egret]

<@&286206848099549185>

[modern peak]

!15m

[calm coral]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[remote mural]

can you show your work

[odd egret]

it is a mess

[remote mural]

its okay

[odd egret]

ill send

[calm coral]

@odd egret Has your question been resolved?

[calm coral]

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.

[remote mural]

,rccw

[calm coral]

Please don't occupy multiple help channels.

@remote mural Has your question been resolved?

Channel closed

Closed by @small musk

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.

[eternal bluff]

help

[eternal bluff]

x^3-13x+12 =< 0

im not sure what again to do with the x^3

[empty tartan]

Have u tried subbing in numbers

[eternal bluff]

wdym

[celest stream]

try to guess a root so u can factorize it

[empty tartan]

For example 1 is clearly a solution to the cubic

[eternal bluff]

12 and -1

sorry

--12 -1

for a+b axb

[calm coral]

@eternal bluff Has your question been resolved?

Channel closed

Closed by @eternal bluff

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.

[amber wedge]

When finding local/global maxima/ minima of a function

[amber wedge]

Does the derivative at those points have to be 0?

What about when finding extreme points

[median cloak]

I think so

[amber wedge]

Or is it simply the point where the function has the highest value?

[calm coral]

@amber wedge Has your question been resolved?

[calm coral]

@amber wedge Has your question been resolved?

Channel closed

Closed by @amber wedge

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.

[mild saddle]

man where'd 1 and 2 come from in (x-1)^2 and (y+2)^2

[brazen elbow]

is this chatgpt

[mild saddle]

ye,,,, lmao

[pure kayak]

[brazen elbow]

you never ever use chatgpt for math

it is a language model, it sounds smart but it contains innumerable fallacies

[mild saddle]

my bad g

ima ask sm1 else then

.close

[calm coral]

Channel closed

Closed by @mild saddle

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.

[wanton dove]

is anyone able to make sense of the solution

[wanton dove]

I mean i guess its the Maximal value of our sample but how is that using the Maximum Likelihood Estimate lol

.close

[calm coral]

Channel closed

Closed by @wanton dove

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.

[unborn stone]

Is 1 correct??

[unborn stone]

And how to do 2

[remote mural]

Let's set the width as "x", and length as "3x"

That's going to make it a lot easier

[unborn stone]

Ok

So 2x

Is answer?

[remote mural]

No

[unborn stone]

Also is 1 right

X=3x idk what to do after

[remote mural]

Length = 3x
Width = x

The perimeter of a rectangle is length + length + width + width right?

Since we have the perimeter, how can you try and solve this

[unborn stone]

6x+2x

8x

[remote mural]

1 should be correct, but I would suggest assigning 2 or 3 more values for x and y, 2 is not a lot

[unborn stone]

I think it’s enough

[remote mural]

Yes! 3x + 3x + x + x = 2600

Solve it from here

[unborn stone]

What I thought it was 1200

[remote mural]

Why?

[unborn stone]

The total

It says 1200 ft of material

[remote mural]

Oh sorry

I read that as 2600

My bad

[unborn stone]

Ok so it’s 8x=1200

[remote mural]

3x + 3x + x + x = 1200

[remote mural]

Yup, solve from here

What you'll get is the width, and the length is 3x. Plug in x to find the length

[unborn stone]

Ok I got 150

So that’s length?

[remote mural]

Yes that's the width, now find the length

[remote mural]

Width is x
Length is 3x

You have found x now

What do you do to find length?

[unborn stone]

It says length three times the width tho

[remote mural]

Yes, you already have the width, 150

3 times the width

What do you get

[unborn stone]

450

[remote mural]

Yup, good job!

Those are your dimensions

150 and 450

[unborn stone]

I still don’t get this tho I thought width is 3x length

Wait so is L=3W wrong then?

[remote mural]

Length is equal to 3 times the length. We set x as the width above

[remote mural]

It's correct

Width is 150

Length is 150 × 3

[unborn stone]

So is my drawn rectangle wrong

Cus I have length on all 4 sides basically?

[remote mural]

Yes

Instead of 3w, write w

Or just replace L with 3W

[unborn stone]

👍

[calm coral]

@unborn stone Has your question been resolved?

[calm coral]

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.

[torpid dune]

Let n be a positive integer. Prove that n * sqrt(19) * {n * sqrt(19)} > 1, where {x} is the fractional part of the number

[torpid dune]

,rotate

[torpid dune]

this solution is wrong but it's just there to "inspire" some ideas

[calm coral]

@torpid dune Has your question been resolved?

[lime harbor]

what exactly has to be done here

[surreal wave]

show the question

[lime harbor]

.

@surreal wave

[surreal wave]

mb

[lime harbor]

pretty straightforward answer ig

[modern peak]

hang on, n*sqrt 19?

you mean the nth root of 19?

[torpid dune]

no

n times sqrt(19)

[modern peak]

so (n sqrt 19)^2 > 1 for any int n?

for pos integers

that's just 19n^2

[torpid dune]

thats not the full qn

[modern peak]

?

[torpid dune]

thiis is the full quetsion

it looks confusing cuz its typed out

[modern peak]

where is "x"

[torpid dune]

wdym

[modern peak]

you never mentioned "x"

[torpid dune]

its just explaining what {} does

{4.2} = 2

{x} = fractional part of x

[modern peak]

so... {x} = x - floor x?

[torpid dune]

yes

[modern peak]

okay

so how is that needed

it's obvious

(n sqrt 19)(n sqrt 19) = 19n^2

since n > 1, n^2 > 1

so 19n^2 > 1, and actually 19

[torpid dune]

do u need me to screenshot the actual question?

,rotate

[torpid dune]

if the fractional part is really really tiny, then it's not > 1

@modern peak

if any of you have an answer, dm me, im going to bed

[calm coral]

@torpid dune Has your question been resolved?

[calm coral]

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.

[spare ore]

.help

[calm coral]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[median crypt]

is there a quick way without calculator to check which is bigger

[sacred valley]

yes

you know that $\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}$

[potent lotus]

DerTheo

[sacred valley]

so you can say that $3\sqrt{6}=\sqrt{9\times 6}$

[potent lotus]

DerTheo

[sacred valley]

and $6\sqrt{3}=\sqrt{36\times 3}$

[potent lotus]

DerTheo

[sacred valley]

and now you can compare it

[median crypt]

wheres 36 and 9 coming from

[sacred valley]

because of this rule

you can add an additional step $3\sqrt{6}=\sqrt{3^2\times 6}=\sqrt{9\times 6}$

[potent lotus]

DerTheo

[median crypt]

could you show how it would be with 4 diffrent variables

like a * b^0.5 vs c * d^0.5

[sacred valley]

$a\sqrt{b}$ vs $c\sqrt{d}$

?

[potent lotus]

DerTheo

[median crypt]

yeah

formal for which wpould be bigger

[sacred valley]

assuming that a, b, c, d >0

you can say that $a\sqrt{b}=\sqrt{a^2}\sqrt{b}=\sqrt{a^2\times b}$

[potent lotus]

DerTheo

[median crypt]

and the same for cd i gues

[sacred valley]

and you can say that $c\sqrt{d}=\sqrt{c^2}\sqrt{d}=\sqrt{c^2\times d}$

[potent lotus]

DerTheo

[sacred valley]

now you just have to compare the two

[median crypt]

thx

[sacred valley]

youre welcome

you can use .close now

[median crypt]

.close

[calm coral]

Channel closed

Closed by @median crypt

Use .reopen if this was a mistake.

[calm coral]

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.