help-26

[thorny spire]

it could still be <=

[odd pagoda]

presumably they mean the subset of V, not a subset

[thorny spire]

No

Because when they use this lemma

They don’t make it the subset

It’s supposed to be a

Because they make S_t the empty

set

Which implies that l_t(i) must be greater than 1/n for all i

Which is not necessarily true

stfu monkey

[odd pagoda]

hmm then they might have fucked up. but its hard to judge this without any context in a random discord channel. do you have a prof you can ask?

[thorny spire]

My brother 💀

And the guy who wrote this paper is known

But this kinda destroys the main claim of the paper

[odd pagoda]

known people also make mistakes. is it on arxiv or published?

[thorny spire]

arxiv

I don’t know if it’s published

[odd pagoda]

could check on scholar?

but well, better to talk to someone who knows this stuff

[topaz sinew]

@thorny spire Has your question been resolved?

[thorny spire]

Idk

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[neon iron]

!status

[topaz sinew]

What step are you on?
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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[neon iron]

1

so I was given this worksheet

and we haven't been taught about coefficient of correlation

and I did search my book for problems like these

but they all had data where x had unique values

However, it seems like this one has repetitive values for x

which simply confuses me

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[neon iron]

uh yeah

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[tardy cave]

could someone please explain the 4th step of the solution?

[tardy cave]

it kinda reminds me of

but the rule talks about the ends of the graph

[drifting swift]

is it this step that you want explained?

[tardy cave]

yes!

[drifting swift]

yeah thats different from end behavior

it's behavior near x-intercepts

if the graph crosses the x-axis vaguely like a straight line, the exponent on the corresponding factor is 1 (as in the case for (x-5) )

if it touches the x-axis but doesn't cross it, the exponent is even (as is the case for (x+1) )

if it crosses the x-axis but bends in a manner reminiscent of y=x^3 at the origin, then the exponent is odd and greater than 1

[tardy cave]

where did those rules came from?

I wanna understand the proof, so that i could better remember it 🙂

[tardy cave]

espessialy this one

[drifting swift]

a formal proof would require equally formal definitions for each of these behaviors, which would be hard to write down and equally hard to apply to a graph

but basically look at the graphs of y = x, y = x^2, y = x^3, y = x^4, etc. near the origin

any polynomial, when looked at near one of its roots, will look vaguely like one of these -- up to scaling and perhaps flipping

[tardy cave]

that's intresting

[tardy cave]

just tested, thats correct!

thanks!

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[neon iron]

\textbf{Question:} Prove that $3^n < n!$ if $n$ is any integer greater than 6

\vs{3 mm}
Let's take $\map P n$ to be the statement $3^n < n!$. We can use induction on $n$

\vs{3 mm}
\textbf{Basis step:} For $n=7$, [
3^7 < 7! \implies 2187 < 5040 ]
\textbf{inductive step:} Suppose $\map P k$ is true for $k \ge 6$:[
\map P k: 3^k <k! ]
We want to prove that $\map P{k} \implies \map P{k+1}$:
[
3^{k+1} < 3\cdot k! < (k+1) \cdot k! = (k+1)!
]

[neon iron]

Okay i believe the solution is correct, but i have a question regarding the application of induction itself using the above as an example

[eternal wing]

ye looks right

latex is so good..

[neon iron]

you have to use the fact that $P(k) \implies P(k+1)$ for it to be considered induction, right?

\vs{3 mm}
If we had started off with [
3^{k+1} < (k+1)!
]
instead of [
3^{k+1} <3 \cdot k!
]
Then our application of induction is faulty as we are not using the induction hypothesis, right?

[eternal wing]

i mean

[eternal wing]

your assumption is that 3^k < k!

[pseudo jetty]

what

[eternal wing]

you can't just straight up say 3^(k+1) < (k+1)!

you haven't proved it lol

or ig u can

and then prove for k+2

[pseudo jetty]

[eternal wing]

and change ur base case accordingly

[pseudo jetty]

thats P(k+1) => P(k+2)

[neon iron]

oh i guess thats it yeah

[deep ferry]

why don't just know that 3^6<6! And then say that 3^7 < 7! as the LHS was multiplied by 3 while RHS was multiplied by 7
(Ik it isn't related to the original ques so excuse me)

[pseudo jetty]

[neon iron]

oh yeah thats definitely where i have been messing up okay

i have been kind of subbing in k+1 and working from there, but thats dumb

i see why now

[pseudo jetty]

thats the statement you need to prove

[eternal wing]

snow stop

[pseudo jetty]

but it is not a statement you yet know to be true

[eternal wing]

not everyone is as smart as u

[pseudo jetty]

what

[eternal wing]

Now

[odd pagoda]

3^6=729 and 6!=720 btw

[neon iron]

so basically, use induction hypothesis to transform P(k) to P(k+1)

[deep ferry]

oh, so just start from 3^7 😅

[neon iron]

basically, right?

[pseudo jetty]

ye

[neon iron]

okay

[acoustic tangle]

Yes

[neon iron]

sick

.close

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[pseudo jetty]

induction hypothesis is "P(k) is true"

[acoustic tangle]

"Assume P(k), ... Well if it's true for k then it must be true for k+1 amirite"

[pseudo jetty]

sotru

[eternal wing]

@neon iron btw lex

why r u doing so many topics

at the same time

like once its set theory, then combinatorics, then induction, then...

r u speeding math or something

speedrunning

[neon iron]

yeah thats just how i do stuff dw about it LOL

[eternal wing]

damn

is it set seed

lol

[neon iron]

[eternal wing]

ok next time when u have questions about measure theory make sure to ping snow

[neon iron]

which one

[eternal wing]

the latex god

[neon iron]

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[neon iron]

Quick question, what is so 'dimensionless' about 'dimensionless variables'

[ionic oar]

They don't have physical dimensions

Unitless basically

[neon iron]

oh okay oaky fair enough

ty

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[ionic oar]

both x and L have dimensions $[M^0L^1 T^0]$

[thorny flame]

neonperseus

[ionic oar]

you're welcome lix

[neon iron]

sorry 😭

[ionic oar]

s'all good

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[random charm]

hey guys i am so lost for this question

[random charm]

i dont see how i can use the hint they have given

[flat kindle]

try multiplying r and t

[topaz sinew]

@random charm Has your question been resolved?

[random charm]

okay

wait how do i multiply them if the thing under the root is different for both

ok nvm i can lemme do it

oh

we get 1 by multiplying r and t

@flat kindle what do we do after that?

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@random charm Has your question been resolved?

[flat kindle]

let r and t be the roots of the quadratic equation

then use Vieta's formulas to calculate a and b

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[random charm]

.reopen

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✅

[random charm]

hey, why do they have to be the roots of the equation?

[flat kindle]

we choose t to be the root

it doesn't have to be

but r*t =1 and it makes calculation easy

[random charm]

ahhh

thanks

hey

how do we get r + t? @flat kindle

for the a term

[flat kindle]

I also get stuck here 😦

[random charm]

oh ok

do u have any idea

[flat kindle]

not really

[random charm]

its ok. if you think of a solution do msg. thanks man

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[quartz wyvern]

Can someone help me with anyone of these?

[quartz wyvern]

I'm a bit confused on epsilon delta arguments

[flat kindle]

what are you confused about?

[quartz wyvern]

I've done the first 2, just stuck on C

Idk how to find the limit

I think polar coordinates but idk how

[flat kindle]

try substituting u = x+4y+2z

[quartz wyvern]

oh

of course

thank you!

idk how I didn't think of that

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[potent blade]

Q1a

[keen raptor]

Let's see if we can get a grasp on how to express the amount of food

how many "units" of food left might we say there are

say one unit of food is enough to feed one sheep for one day

[potent blade]

Ok

72*6?

why do we need to know that though?

[keen raptor]

So that's 432

432 "sheep-days" of food, as you call units that are like other units multiplied together

So

How many remaining sheep are there

[potent blade]

oh wait.

how does 72*6= total amount of food?

[keen raptor]

if we have 1 food, we can feed 1 sheep for 1 day

If we have 72 food, we can feed 72 sheep for 1 day

if we have 72*6 food, we can feed 72 sheep for 6 days

[potent blade]

oh..

[keen raptor]

Kind of the nature of multiplication

They'll eat 72 food on the first day, 72 food on the second, 72 food on the third, etc

so 72+72+72+72+72+72

[potent blade]

Oh I see.

but we don't know 72 is 72 food.

[keen raptor]

We're sort of defining a unit of food that way

[potent blade]

Oh

so we assume, one food is for one sheep?

72 sheep= 72 food

[keen raptor]

For 1 day as well

That's why the unit is called sheep-day

[potent blade]

72*6.=432. Total amount of food that sheep eat in 6 days?

[keen raptor]

it feeds one sheep for one day

yeah

it's just a nicer way of expressing the amount of sheep feeding power we have

we already know we can feed 72 sheep for 6 days

this tells us we could also feed 432 sheep for 1 day

or 1 sheep for 432 days

or 72 sheep for 6 days

[potent blade]

oh

so I sheep takes to finish 72 food in 432 days?

1*

[keen raptor]

nah it would finish 432 food in 432 days

food consumed = (number of sheep) × (number of days)

[potent blade]

oh.

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[potent blade]

.close

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[snow spindle]

I find this one a bit difficult so I would like to get a help

[rigid apex]

!status

[topaz sinew]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[snow spindle]

1

[rigid apex]

let's start with a

[rigid apex]

you know what the shape of a tennis ball is right?

[snow spindle]

yes, a sphere

[rigid apex]

so we need to find the volume of a sphere

you know the formula right?

[snow spindle]

\ 4/3πr^3 //

[rigid apex]

yes

[snow spindle]

(sorry for taking long)

[rigid apex]

it's ok

i have all day and nightù

[neon iron]

[rigid apex]

what is r?

[snow spindle]

radius

[rigid apex]

what is the radius of the tennis ball?

[snow spindle]

3

[rigid apex]

3 what?

[snow spindle]

3cm

[rigid apex]

yes

so now it's just calculating the volume :p

[snow spindle]

o

113.10cm^3 (2 d.p.)

[rigid apex]

aren't those 3?

[snow spindle]

for problem b is just times the volume of multiply the volume of the tennis ball by 50?

[rigid apex]

yes

[snow spindle]

what do you mean by 3?

[rigid apex]

nvm i read it wrong

[snow spindle]

all good

[rigid apex]

shouldn't the 10 to be rased to the power of 3?

[snow spindle]

cm^3 means centimeter cubed

[rigid apex]

i'm not talking about cm³ i'm talking about how 10 needs to be rased to the power of 3

[snow spindle]

huh?

[rigid apex]

if you typed the answer with every number you should get 113097.3355 cm³

or simplified 113*10³ cm³

bro nvm

forget what i said

i made a big oopsie

[snow spindle]

it's fine

[rigid apex]

i have put 30 instead of 3 hahah

anyways back to b

you are correct

you gotta multiply answer a by 50

now c

[snow spindle]

apparently the answer is 268.08 m^3 somehow

[rigid apex]

you know what c says right?

'the volume of the box not taken up by the tennis balls'

[snow spindle]

ye

[rigid apex]

we know what the volume of the 50 tennis balls is

[snow spindle]

5655cm^3???

[rigid apex]

5655 nvm you were right

now we only have to find the volume of the box itself

you know the formula for the volume of a cube?

[snow spindle]

height x width x length

[rigid apex]

yes as you see in the question all of them are?

[snow spindle]

well

height x width x length

they gave us height, width, length

which is

30

[rigid apex]

30 what?

[snow spindle]

30cm

[rigid apex]

don't forget it : )

so now we gotta calculate the volume of the box

[snow spindle]

which is 30 x 30 x 30 right?

[rigid apex]

yes

[snow spindle]

27000

[rigid apex]

cm³

[snow spindle]

is that it?

because

I have a feeling that there's something more than that

[rigid apex]

i also have the feeling something ain't right

the answer to c was 260 m³?

[snow spindle]

nope

apparently it's 688.13 m^2, 1697.40 m^3

[rigid apex]

m² why are we working with areas?

[snow spindle]

I'm not sure

the answer page has that on it

[rigid apex]

could you recheck it

maybe you have the wrong answers

[snow spindle]

wait wait

OH

crap

[rigid apex]

you did?

[snow spindle]

It was on the other question

[rigid apex]

i knew it

[snow spindle]

my bad

[rigid apex]

anyways let's go back to the question

c: so we know the V cube and V 50 tennis balls

now we need to find the volume in the box NOT taken up by the tennis balls

[snow spindle]

so just minus 2700 by the volume of the 50 tennis balls?

[rigid apex]

exactly

[rigid apex]

you got the answer?

[snow spindle]

I did

but

it's wrong

[rigid apex]

is it correct?

[snow spindle]

(this time it is actually wrong)

[rigid apex]

did you 27000-565?

yeah it should be 27000-5655...

that's a mistake on my own part

[snow spindle]

there's a decimal

to the answer

21345.1 (rounded up by 1 decimal point)

[rigid apex]

yes you know the volume of the 50 tennis balls?

[snow spindle]

5655

[rigid apex]

with the extra decimals?

[snow spindle]

5654.9

[rigid apex]

so if you calculate it now...

[snow spindle]

21345.1

[rigid apex]

would you look at that

[snow spindle]

oh wait

it saids

[rigid apex]

that's the answer

[snow spindle]

correct to 1 decimal place

not round it up

I'm soo stupid

[rigid apex]

it still corrects to 21345.1

[snow spindle]

yeah

[rigid apex]

sorry for being rusty

sleep is an important thing

[snow spindle]

I also don't sleep well too

I'm doing my hw at night

sooo

I'm trying to get it at least 50% done

[rigid apex]

50 questions?

or 50 percent?

omg i'm actually blind

[snow spindle]

no it's my typo

Sorry for making you confused

[rigid apex]

anyways

you got anymore questions?

[snow spindle]

nope

I believe that's it

actually

can we work on next problem or should I close this channel and get new one?

[rigid apex]

eh we can work on the next problem

[snow spindle]

alright, so I got this one

is 800cm^3 is the capacity of the spherical storage?

[rigid apex]

yea

[snow spindle]

okay

[rigid apex]

so it should be really easy to solve this

[snow spindle]

so just

basically

[rigid apex]

you know what the diamater is?

[snow spindle]

convert capacity into volume

and then find the diameter from the volume

[snow spindle]

yes

[rigid apex]

the double of the radius

[rigid apex]

yes

so we're gonna do a little bit of algebra

so you know the formula of a volume V=(4/3).pi.r³

[snow spindle]

yes

[rigid apex]

we know V but we have to find r

we can already replace V with a number

that being?

[snow spindle]

800

[rigid apex]

just for clarification, have you ever done 'solve x' problems?

[snow spindle]

yeah

[rigid apex]

yeah it's basically that but just with 'solve for r'

[snow spindle]

so basically

it'll be

800/(4/3)π

[rigid apex]

=r³

[snow spindle]

and then we root square right?

[rigid apex]

root cube*

[snow spindle]

oh wait right...

my bad

11.5cm

(corrected to 1 decimal place)

[rigid apex]

correct

[snow spindle]

alright cool

I have no furthur questions

thank you for the help!

[rigid apex]

np

[snow spindle]

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[snow spindle]

wish you luck on helping others :)

[rigid apex]

ty

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[rigid apex]

if you wanna solve the answer make a table where the rows are the possible outcomes of dice 1 (1,2,3,4,5,6) and columns are the possible outcomes of dice 2 (1,2,3,4,5,6)

where the table itself is the sum of the 2 possible outcomes of the 2 dices

[autumn light]

yeah i was gonna give you the answer with a more mathematical approach but that's the best method you should use for similar quesztions in future

[rigid apex]

how do you do it a more mathematically ?

[autumn light]

i don't know if this is correct, but

you have a 5/6 chance of getting a number with a chance of making a sum of 6 (we do not count 6 since adding anything to 6 will not yield 6)

then, the chance of getting the number you need to make the sum equal 6 is 1/6

so 5/36

i might be wrong tho

[rigid apex]

it's right

[prisma mesa]

no, it's fine

[rigid apex]

@neon iron so do you understand what is being said here or do you just want the answer?

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[rigid apex]

eyyy NP

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[torpid dock]

Stuck in proof of chernoffs bound for a poisson distribution. Im having trouble understanding why we arrive at a strict "<" inequality when applying markovs, since markovs inequality states
$$Pr[X\geq t] \le \frac{E[X]}{t}$$. (i.e. the less than or equals, not strictly less than)
Im confused to why we can apply markovs inequality in this case. help would be appreciated ^^
below is part of the lecture slide im having trouble with:

[topaz sinew]

@torpid dock Has your question been resolved?

[torpid dock]

<@&286206848099549185>

I've tried to look at the proof of markov which ive written as the following:

And modified it to use x>t instead of x >= t, but i have a feeling i made a mistake. (im unsure about step 3 below)
i did this to make markovs inequality usable in the chernoffs proof, but i have no idea if this is correct lol

[torpid dock]

<@&286206848099549185>

.close

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[neon iron]

hello

[neon iron]

f'(1) * -3 + f'(ln(e)) * (2/e) + f'(sqrt(5-4)) * (4/(2*sqrt(1))) , I want to isolate f prime

the answer is fprime 1 = e/(e+2)

but how

[craggy haven]

what's ln(e)?

[fallow heart]

What is sqrt(5 - 4) ? And ln(e) ?

[neon iron]

ln(e) is 1

5-4 = 1

wait wtf

now I got more confused

which f prime do I pick

[fallow heart]

They are all f'(1), hence all of them are equal 😅

[neon iron]

but the final answer is e/e+2

[fallow heart]

Try to substitute A = f'(1), then solve for A

[fallow heart]

And so??

I think you're forgetting some basic algebra

[neon iron]

I'm the stupidiest man in the universe

is there an award for that

I found -3 + 2/e + 2 @fallow heart

[fallow heart]

Is there an = 0 somewhere?

[neon iron]

no

[fallow heart]

Mmh very strange, since you can't get x out of that of you don't have = sthg

[neon iron]

I will give you the original before I derivated hold up

x = f(2-xˆ3)+f(ln(-2+e+2x))+f(sqrt(5-4/x))+f(f(1))

derivated everything

since x is 1

i replaced x in the rest of the equation

[fallow heart]

So in the left hand side there is a "1 = "

[neon iron]

yes

but we are looking for fprime 1

[fallow heart]

Yes, but you need the whole equation otherwise you can't solve

[neon iron]

alright

[fallow heart]

The word solve implies there's an = or <>≥≤ symbol

[neon iron]

capiche

can you guide me please?

its already solved I assume

1= 1

ah no there a +

1 = -3*f'(1) + (2/e)f'(1) + 2f'(1)

1 = (-3 + 2/e + 2)*f'(1)

[simple drift]

okay.

[neon iron]

f'(1) = 1 / (-3 + 2/e + 2)

omg

[simple drift]

uhuh?

[neon iron]

e / (e*(-3+2)+2*e)

bruh im so close to the answer

e/e+2

[fallow heart]

You have 1 = f'(1) * (-3) + f'(ln(e)) * (2/e) + f'(sqrt(5-4)) * (4/(2*sqrt(1))). Hence, you get 1 = -3A + (2/e)•A + 2A.

(I put A = f'(1) just for clarity).

From this, you arrive at:
1 = (-3 + 2/e + 2)A, therefore:
1 = (2/e - 1)A, which can be rearranged into:
1 = (2 - e)/e • A, giving us A = 1/[ (2 - e)/e ] , or simply A = e/(2 - e)

[neon iron]

2+e not 2-e

[fallow heart]

Maybe there's a wrong sign, let me check

But those are the steps anyway

[neon iron]

still gives me e/2-e

[fallow heart]

I checked twice but the signs (both mine and yours) are correct

Are you sure you wrote the exercises correctly?

[neon iron]

these are exercises from school

you think they made an error?

[fallow heart]

They could have, because for the function you posted the signs are all ok

But the importante thing is you understand how to do this kind of exercises, the numbers are the last thing to think about

[neon iron]

okeyyy

thank you my friend

for helping me

appreciate it

[fallow heart]

You're welcome 🤗

[neon iron]

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[neon iron]

.helpedme

darn

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[light heath]

Can l get some help

[soft rune]

What's up

What is the question here?

[topaz sinew]

@light heath Has your question been resolved?

[light heath]

Yo

Yeaa so this is mechanics and we are to calculate forces for ox and oy

Of which l didn't really understand

But l do know we are to use the formula of sine and cosine

@soft rune you there?

[soft rune]

Yes

I see two vectors, two forces

Are you supposed to calculate the net force (The sum)?

[light heath]

That's the question

[soft rune]

Or to find the x-component and the y-component of each force separately

[soft rune]

mmmm, so they want the x-component and the y-component of each force separately

[light heath]

Yes

[soft rune]

Let's start with the 8N 60° force vector

[light heath]

Ok

[soft rune]

You can consider that vector as the hypotenuse of a right triangle

[light heath]

The tension force right?

[soft rune]

The other two sides are the x-component and the y-component of the force

[light heath]

Right

So in this case l would be finding the adjacent

Sooo 8cos60?

I was told to be careful when calculating... Considering the angle

[soft rune]

Sorry for the delay, I was drawing this

[soft rune]

Yesss

Fx = 8 . cos(60°)

What about Fy?

[light heath]

I was confused about the angle since it's a different triangle

[soft rune]

How

it's the same

you can use 60° as well

for Fy

[light heath]

In that case it would be 8cos60

[soft rune]

Fy= 8 . cos(60°) ?

[light heath]

Yea that's my confusion

[light heath]

Or do l find the opposite to angle 60 and use the Pythagoras

Oh never mind😅

[soft rune]

:P

when you do cos(60°)

it is the adjacent of 60° / hypotenuse

What is the adjacent leg of 60° ?

[light heath]

It would fx no?

[soft rune]

Yes, right!

$$cos(60°) = \frac{F_x}{F}$$

[thorny flame]

luna7427

[soft rune]

So

$$F_x=F \cdot cos(60°) = 8 \cdot cos(60°)$$

[light heath]

Ok

[thorny flame]

luna7427

[soft rune]

Like you found earlier

Same thing for Fy, how did you confuse!

Apply sine this time, and you get it the same way

[light heath]

8Sine60

[soft rune]

Exactly, because the opposite of 60° is Fy

$$sin(60°) = \frac{F_y}{F}$$

[thorny flame]

luna7427

[soft rune]

$$F_y=F \cdot sin(60°) = 8 \cdot sin(60°)$$

[thorny flame]

luna7427

[light heath]

Ohhhhhh ok am so dumb😂😂

[soft rune]

No, you are not 😝

Just apply the laws carefully!

[light heath]

Alright

[soft rune]

Now do the second force

And show me

[light heath]

Ok

[soft rune]

Yes, correct

But notice one thing

Fx is pointing to the left, not to the right

Fx must be negative, right?

[light heath]

Yeaa

[soft rune]

Fy is pointing down, not up, so Fy must also be negative

[light heath]

Ohh so they are both negative

[soft rune]

Yes, you just append a minus sign to both

[light heath]

As the final answer

Yea l was trying number 9 and l didn't know how to start

@soft rune

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[sterile walrus]

yo

[sterile walrus]

if i have sin(x) = n/m

is x = sin^-1(n/m)

?

im trying to do the inverse but im not 100% sure that thats how the property works

[worthy storm]

it depends on what quadrant the angle is in

[sterile walrus]

its just thetha

but idk how to type that

[worthy storm]

right, but n/m is the same as (-n)/(-m)

[sterile walrus]

it's a physics summer packet

[worthy storm]

so there are two angles with that sine, in general

[sterile walrus]

i dont really think they expect me to know that

it's just variable solving

[worthy storm]

ok

if you're just working with positive m and n, then what you said is true

[sterile walrus]

plus it doesnnt mention quadrants

[worthy storm]

that's how sin^-1 works

[sterile walrus]

mk

thanks

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[lavish sage]

can somoene just give me the answer to this

[worthy storm]

this question makes no sense, none of those are simplifications of the given expression

[lavish sage]

so its impossible?

[worthy storm]

i mean if you just want the roots then the given form allows you to do it easily, solve 2x-1 = 0 and x-4=0

[lavish sage]

ok ty

[worthy storm]

if you really want to use one of these crazy expressions, then multiply out the original formula to get one in the form ax^2 + bx + c

then apply the quadratic formula to that

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[chrome nymph]

P=4s

[chrome nymph]

How do I solve equations with multiple variables

I’m suppose to solve for s

[broken tusk]

Do you have an example?

That's a very broad question

[restive inlet]

pretty much the same rules apply

approach it in the same way you would if you only had one variable

e.g. how would you solve
$$137 = 4s$$

[thorny flame]

ℝamonov

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@chrome nymph Has your question been resolved?

[chrome nymph]

Sorry I meant for solving equations with multiple variables

[restive inlet]

so refer to exactly what i said

make the appropriate reaction if you don't want the channel to abruptly close on you

@chrome nymph

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[undone flicker]

So here i guess x =0 continuity doesn't exist because of h sign

[drifting swift]

h sign?

[undone flicker]

I tried this f(-h) = h/(3h^2+5h) = 1/(3h+5) =0.2

F(h) = h/(3h^2-5h) = 1/(3h-5) = -0.2

So here both values are different so the limit doesn't exist at x=0

[flat kindle]

yes

[undone flicker]

@drifting swift is this correct?
Sorry for ping 🙏

[drifting swift]

correct idea, somewhat bad presentation.

[flat kindle]

true

[undone flicker]

Yes. I didn't write limit and many notation like h tends to 0

[craggy haven]

that's pretty important!

[undone flicker]

Yes true

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[neon iron]

The volume of the shape that is created by this triangle rotating around the y axis is

$$ \frac{1}{2}r^2 2 \pi$$ right?

[thorny flame]

brandon_hu

[neon iron]

$$ \pi r^2$$

[thorny flame]

brandon_hu

[neon iron]

$$ V = \pi \int_0^r (r-y)^2dy$$

[flat kindle]

there's a formula that I forgot

but you can just google it

[thorny flame]

brandon_hu

[neon iron]

$$V = \pi \int_0^r (r^2-2ry +y^2)dy$$

[thorny flame]

brandon_hu

[frail dove]

I got $\frac{\pi}{3}r^3$

[thorny flame]

math_is_fun

[frail dove]

The formula is correct

[neon iron]

yeah

Thank you for help 😭

Still don't have the intuition but i'll figure it out later

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[solemn jay]

Does this infinite series converge or diverge?
3 + 2.1 + 1.47 + 1.029+ ...

[solemn jay]

I think this diveres?

[drifting swift]

... what is meant to be the rule for this tho

until you specify the series as a whole and not just its first four terms there is literally no telling how it behaves

[flat kindle]

oh nvm

so the nth term is $3\times(\frac{7}{10})^{n-1}$

[thorny flame]

_wherewolf_

[flat kindle]

you just need to find $\lim_{n\to\infty}3\times(\frac{7}{10})^{n-1}$

[thorny flame]

_wherewolf_

[solemn jay]

ty

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[hollow oracle]

Does “uniformly” here mean that every egg has the same chance of being picked?

[hollow oracle]

And this is different than the concept of a uniform sample space, where every sample point has equal probability correct?

[woeful drift]

yeah each of the 60 eggs has an equal chance of being selected

and it's slightly different since each individual egg has the same chance, but you don't have the same chance of picking a chocolate vs. plastic egg each time

[hollow oracle]

Alright

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[dapper sparrow]

Hi, I keep getting this one double integral wrong and have no idea where im messing up. I have redone it 3 times and was wondering if anyone can let me know what I am doing incorrectly? Thank you so much:

[junior dock]

Hi i think that in the 7th line instead of +1/4x^4 I should be negative (-1/4x^4) as in the previous step it is subtracted!

[dapper sparrow]

ahh

nice catch

wow yeah i see that

thank you so much

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[junior dock]

No problem!

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[neon iron]

help karlo

I tried applying lagrange's bound

I found m to be ln(1.4)

so at the end I got

$(ln1.4)\frac{\cdot(0.4)^{n+1}}{(n+1)!}$

[thorny flame]

Mushaar

[neon iron]

but this is wrong

[flat kindle]

why are you using lagrange theorem?

[neon iron]

Is there any particular reason why I can't use it?

[flat kindle]

it's not called lagrange theorem I don't think but ok

[neon iron]

ah my bad

I meant lagrange's bound

[flat kindle]

how is your answer wrong though

[neon iron]

If I plug in say even n = 4, I get something < 0.001, but the answer is 5

[flat kindle]

M is the maximal value of f^(n+1)(z) not f(z)

[neon iron]

ah i see

that makes sense

so it's $(-1)^n \cdot n!$

[flat kindle]

1/x is a decreasing function

so it x=1?

[neon iron]

oh right that's what I meant

[thorny flame]

Mushaar

[neon iron]

what do I do from here to find m

[flat kindle]

just plug in M= (-1)^n*n! in to the equation?

what's wrong

[neon iron]

ok yeah I get final answer

thank you

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[ripe pecan]

how do i solve for r

[unborn kiln]

Lol you mentioned you got
8000 = 17000(1-r)^5

You can divide both sides by 17,000 first

[ripe pecan]

yeah but like how do i solve that

ok i did that

[unborn kiln]

Then take the 5th root of both sides

then you can easily solve for r

[ripe pecan]

ok

i got

-0.1399

i hate working with decimals

[unborn kiln]

you should be getting a positive

[ripe pecan]

yeah

i divided 8000 by 17000 and got 0.47058823529

and then i foundthefifth root of that

0.86005893718

and then i did -1

[unborn kiln]

Ok so 0.86 = 1 - r

[ripe pecan]

mhm

[unborn kiln]

How would you get positive r

[ripe pecan]

ohhh

ok

so

it would be -0.13994106281=-r

so i times both sides by -1

and get

0.1399

[unborn kiln]

Or you could switch the position of r and 0.86

r=1-0.86

[ripe pecan]

that answer isnt an option

oh wait

rounded

ok

[unborn kiln]

Yes

[ripe pecan]

i have a few more questions

lemme try to figure out on my own first

[unborn kiln]

sure

[ripe pecan]

so i have

A=5000(1+0.042/4)^16

[unborn kiln]

Didn't this question come up already

[ripe pecan]

yeah

i went to eat

and like forgot about it

[unborn kiln]

😂

The formula looks correct

[ripe pecan]

ok

but like

how do solve

[unborn kiln]

you

plug in to a calculator

[ripe pecan]

i did

into symbolab

and got a bunch of roots

[unborn kiln]

??

[ripe pecan]

imma try desmos

[unborn kiln]

You did something wrong

[ripe pecan]

oh

bruh

i got

5909

what do they mean by

"exclude the comma, round to the nearest penny"

[unborn kiln]

Exclude comma

So

Instead of $1,000

You'd have 1000

[ripe pecan]

oh ok

[unborn kiln]

And the nearest penny is, rounding to the nearest penny

[ripe pecan]

ok

so that would be like

1000.45?

[unborn kiln]

Yes

[ripe pecan]

ok

[unborn kiln]

So if you get 1000.456 or something

You would round to 1000.46

Basically, round to the 2nd decimal point

Because we're dealing with money

[ripe pecan]

ok

@unborn kiln would i include pennies for this?

[unborn kiln]

Well do you get decimal value for your calculation?

[ripe pecan]

umm yeah

[unborn kiln]

Does the question say anything about it

[ripe pecan]

u mean i sent u it

[unborn kiln]

I'd round to pennies then yeah

[ripe pecan]

ok

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[lethal geode]

so

i knwo how to do the question

but i dont understand it

cause

does putting sand 0.7 feet into the box mean that it is

filling 70% of the box

or 30%

OH WAIT

IM DUMB

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[empty sail]

Neither, that's the depth

[lethal geode]

yea

wait so is it

[lethal geode]

is this right

[empty sail]

Yeah

[lethal geode]

yay

thx

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[pulsar sun]

so I seem to have gotten the correct answer, almost (optionA is the correct answer)

[pulsar sun]

I did casework, is that wrong?

also can someone evaluate option A for me?

my answer is ${\frac{10!}{5!}} \cdot {\frac{10!}{5!}} \cdot {\frac{10!}{5!}}$

[thorny flame]

itzkraken.

[frosty cape]

,w sum from 0 to 5 of [5!/(k!(5-k)!]^3

[thorny flame]

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[pulsar sun]

thats wrong (the expression)

[frosty cape]

Ye

,w sum from 0 to 5 of 5!^3/((k!(5-k)!)^3

[thorny flame]

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[pulsar sun]

[pulsar sun]

this comes nowhere near

here's what i did

actually nvm i gtg

thx

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[analog linden]

It’s wrong idk why

[gusty bane]

idk what’s happening

can you explain what you’re doing

[novel echo]

looks like multiplication

[topaz sinew]

@analog linden Has your question been resolved?

[analog linden]

Yea multiplying with decimals

And exponent

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[topaz sinew]

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[bright dagger]

quick question if I have a complex number like so: 4+4i can be further simplified?

[hollow shard]

no

[bright dagger]

so if I say 1+1i is completely wrong?

[sweet shard]

1+1i and 4+4i are two different numbers

[bright dagger]

ok tyvm

.close

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[lunar merlin]

helloo how do i sketch this parabola

[vivid flame]

Look for points of relevance such as the vertex, zeros, and y-intercept.

[lunar merlin]

yeah i’m just having problems finding the x ints

i know i have to factorise it somehow

not sure how tho

complete the square?

[vivid flame]

Factoring would be the way to go, but you can use quadratic formula or completeing the square if u want

[lunar merlin]

how could I factorise?

[vivid flame]

Well the factored form will look like (ax+b)(cx+d).

We also know ac must multiply to -1

And dB would multiply to 9

[lunar merlin]

hmmm ok

[vivid flame]

So list the factors of 9 for ne rq

[lunar merlin]

1 3 3 9

[vivid flame]

Yep

[lunar merlin]

ah

i see

i’ve got it

[vivid flame]

What did you get?

[lunar merlin]

how to factorise it

[vivid flame]

No like as the answer

[lunar merlin]

i’m almost done i’ll be like 20 seconds

(x - 1)(x + 9

[vivid flame]

Not quite

[lunar merlin]

?

[vivid flame]

Here actually, I know what will make this easier on both of our parts

[lunar merlin]

when I check the answer it says postive 1 and -9

hmmm

i mean -1

sorry

and positive 9

[vivid flame]

Well you wanna find out how to get to the answer no?

[lunar merlin]

yup

[vivid flame]

Ok, then Factor out a -1 from -x^2+8x+9 as to get rid of the leading coefficient.

[lunar merlin]

yep

[vivid flame]

What did you get?

[lunar merlin]

-(x^2 - 8x -9)

[vivid flame]

Great now let's factor the inside of the parenthesis only

[lunar merlin]

ahh it’s flipped

(x + 1)(x - 9)

[vivid flame]

Great, now set each of the factors equal to 0 and solve

[lunar merlin]

x = -1,9

[vivid flame]

Great job

[lunar merlin]

middle of those is 4

[vivid flame]

Plot those points now

[lunar merlin]

so x tp is 4

okkk i get the rest now

thank you 🙏

[vivid flame]

Ok, good luck 👍

[vivid flame]

Np

[lunar merlin]

thank you bye!!

.close

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[hybrid raptor]

how can i get the image and the preimage of f(x)=2x²+1?

[fading sparrow]

Preimage what do you think x can be
Image what do you think f(x) can be

[hybrid raptor]

what does that mean

Let me ask you this, so there's a question in my work that says smth like this "the image of 2 is 9"

How can I solve that? @fading sparrow

[fading sparrow]

It means that when x is 2, it is mapped to 9 (f(x) =9)

[hybrid raptor]

so when 2(2)²+1 that's 9?

Oh yeah

Hol on

There's another that says "the preimage of -3 is 19"

is that correct and how can i solve it?

[hybrid raptor]

it's like a true or false type of question

[fading sparrow]

Yea

[fading sparrow]

Then that’s the other way round

If f(x) is -3

What’s x? Isit 19

[hybrid raptor]

huh?

[fading sparrow]

That’s what the qn is asking you

Isit true that when f(x) is -3, is x = 19?

[hybrid raptor]

No?

It isn't 19, right?

[hybrid raptor]

So f(x) is like the whole thing right? Last time f(x) was 2x²+1, and now is just -3

So there's no way it can be 19 i guess

[fading sparrow]

I mean can just sub x as 19
It’s not -3 so false

[hybrid raptor]

I don't understand that, there's no x right?

[fading sparrow]

What do u mean there’s no x?

They gave the preimage

[hybrid raptor]

f(x)= -3, there's no x

[fading sparrow]

What’s the equation of f(x)

[hybrid raptor]

oh

[hybrid raptor]

2x²+1

So x is -3 or 19?

@fading sparrow ?