help-13

[weary vessel]

Same thing for y and z

[rigid gulch]

Okay

[weary vessel]

Tell me what you find

[rigid gulch]

Y is 0

And 1

[weary vessel]

nnnnope

[rigid gulch]

Yes

It is

[weary vessel]

nooo

[rigid gulch]

Yes it is

[weary vessel]

You want y to be minimum

[rigid gulch]

Yes

[weary vessel]

y=u-v

[rigid gulch]

Okay

It’s still 0

[weary vessel]

0<=u<=2
0<=v<=1

[rigid gulch]

0-0

[weary vessel]

u=0 and v=1

[rigid gulch]

-1

[weary vessel]

gives the true minimum

yess

[rigid gulch]

Is this sort of like Jacobian?

[weary vessel]

No, just finding out ranges :P

now, max of y

[rigid gulch]

So what work do I erase and work do I start writing

[weary vessel]

what do you say!

[rigid gulch]

Max of y is 1

[weary vessel]

Nooo

[rigid gulch]

2?

[weary vessel]

yes, 2

when u=2 and v=0

that's when you get y's max

😃

[rigid gulch]

Z max is

6?

And min is

[weary vessel]

yess

[rigid gulch]

1

[weary vessel]

right right

There you go, you have them all

$$0 \le x \le 3$$
$$-1 \le y \le 2$$
$$1 \le z \le 6$$

[rigid gulch]

why is this significant?

[wraith dagger]

LUNA

[weary vessel]

Because

When you divide the integral into 6 integrals

Each integral will have its own bounds

depending on the face

of the paralellogram

[rigid gulch]

Wdym 6 integrals

3 double integrals?

[weary vessel]

6 double integrals

6 because paralellogram has 6 faces

and double because it is a surface integral

takes forever honestly

that's why the divergence theorem is used

[rigid gulch]

my professor said

idk

for the final

we can use either stokes theorem or divergence theorem for one of the problems

whatever we are more comfortable with

so divergence theorem is prob the more comfortable one

for our final boss problem?

[weary vessel]

That's awesome!

[weary vessel]

Yeah, look

instead of computing 6 double integrals

and involving vector fields and normal vectors

you only do 1 triple integral

involving SCALAR field and no vectors

[rigid gulch]

Actually divergence theorem sounds kind of nice

[weary vessel]

i have a picture of it, wait

[rigid gulch]

Just the name

Sounds like the movie

Divergent

[weary vessel]

Oh you know it!

[rigid gulch]

I haven’t watched that tho

[weary vessel]

Nice

[rigid gulch]

I hate

How

I’m studying over the weekend

And I’m not watching Oppenheimer

[weary vessel]

😛

You can still do it using ordinary method

but 6 double integrals

Wanna do one of them for practice?

[rigid gulch]

Yes

I have like

9 more problems left

For this section

16.7

I still gotta do 16.8 Stokes’ Theorem

[weary vessel]

mhmm

Can you imagine the paralellogram we are dealing with?

imagination is key

[rigid gulch]

I gotta graph it

[weary vessel]

$$0 \le x \le 3$$
$$-1 \le y \le 2$$
$$1 \le z \le 6$$

[wraith dagger]

LUNA

[weary vessel]

just imagine it, don't graph

it's like a box in the middle (origin) of 3D space

length from x=0 to x=3

width from y=-1 to y=2

and height from z=1 to z=6

[rigid gulch]

its just railroad tracks

[weary vessel]

I will try, wait

i can't lol

just imagine a box

around the origin of 3D space

length from x=0 to x=3
width from y=-1 to y=2
and height from z=1 to z=6

[rigid gulch]

let me graph it by hand

[rigid gulch]

I prob butchered it

[weary vessel]

Something like this

it's okay, it's just to observe

what we doing

does not need to be exact

[rigid gulch]

K

[weary vessel]

Let's do these 2 surfaces for example

The surface integral across S1

$$\iint_{S_{1}} \vec{F} \cdot \vec{dS_{1}}$$

[wraith dagger]

LUNA

[weary vessel]

Let's start with F

$$\vec{F}=z , e^{xy} , \hat{i} -3z , e^{xy} , \hat{j} + xy , \hat{k}$$

[wraith dagger]

LUNA

[weary vessel]

Do you think we can simplify F here?

Like do modifications to it

Only valid for the surface S1

[rigid gulch]

Maybe

Let me think

From S1

Y=2

[weary vessel]

All points in S1 have one thing in common, which is consant

[rigid gulch]

Z=1 to 6

[weary vessel]

All points in S1 have one thing in common, which is consant

[rigid gulch]

X=0 to 3

Y

[weary vessel]

x=3

all points in S1 have x=3

can you see it?

imagine it

[rigid gulch]

How

[weary vessel]

⬆️

The S1

[rigid gulch]

Isn’t it Y

[weary vessel]

y is varying, z is varying

[rigid gulch]

That is constant

[weary vessel]

but x is 3

no, look at axes!

i labeled them

[rigid gulch]

Oh yeah

X is 3

I have mine drawn incorrectly

Then

[weary vessel]

it's constant, 3, for all points in S1

[rigid gulch]

So plug in 3 for any thing

I see having x in it?

[weary vessel]

Therefore, only within this integral, you can substitute x=3

instead of leaving it variable x

[rigid gulch]

Okay

Doing that now

[weary vessel]

$$\vec{F_{1}}=z , e^{3y} , \hat{i} -3z , e^{3y} , \hat{j} + 3y , \hat{k}$$

[wraith dagger]

LUNA

[weary vessel]

Notice that I am naming it F1

Because it is valid only for S1

[weary vessel]

,rccw

[weary vessel]

Noice

That's the F1 part

[rigid gulch]

Now take curl?

[weary vessel]

$$\iint_{S_{1}} \vec{F_{1}} \cdot \vec{dS_{1}}$$

[wraith dagger]

LUNA

[weary vessel]

We simplified F, to F1

Now, what is dS1

The differential normal vector to S1

?

[rigid gulch]

Yes

Which I got 3 1 -2

[weary vessel]

it's not the normal vector

it's differential normal

[rigid gulch]

0 0 0?

[rigid gulch]

Then that would be

Idk

How would I go about calculating that

[weary vessel]

you don't calculate it

it's given by

Since the normal vector is in direction of x

you use dSx

$$\vec{dS_{1}}=dy , dz , \hat{i}$$

[wraith dagger]

LUNA

[weary vessel]

Did you digest it?

[rigid gulch]

No

[weary vessel]

I think this is all new to you

[rigid gulch]

I’m not getting it

Yes

[weary vessel]

D:

I suggest you consult your professor then

[rigid gulch]

I mean I don’t think my lecture notes has that

[weary vessel]

This is how you express differential surfaces

we're just evaluating the integral right

We simplified F

[weary vessel]

now, dS

[rigid gulch]

He doesn’t have that anywhere

[weary vessel]

eeeeh, you should do it the way you guys do it then

this one is direct

substitute F, substitute dS

integrate

check with your classmates for example, how they did it

or consult your professor

[rigid gulch]

My class mate has 21 done

I just don’t think his writing is legible

[weary vessel]

mhmm

what can i say, this is the method I know

the direct way

but stick to how you guys did it

you must learn mine though!

even when you use the divergence theorem, you will need to express differential volume

[weary vessel]

stokes' theorem, you express both differential length and differential surface

no way to get around it

😛

[weary vessel]

Why is your teacher making it tedioussss

[rigid gulch]

Lol

Idk

He’s seem like the guy

Who wants us to learn the hard way

[weary vessel]

i seeeeee

Allright, then

Better stick to the notes :3

[rigid gulch]

Well

[weary vessel]

I wish you luck!

[rigid gulch]

Yeah

Idk if you can help me the way we learned

[weary vessel]

I'll help you when it gets a little bit more advanced

I hate the way your teacher is doing it tbh

😆

do i send you some of the laws?

save them for later use

i have them written in latex already

[rigid gulch]

Yes please

Oh wait what

[weary vessel]

Divergence theorem

Divergence computation

Stokes' theorem

Curl computation

How to express dl, dS, and dV

Save them for later use, you will need them

[rigid gulch]

Idk how to email my professor about this

He prob doesn’t want us knowing this

[weary vessel]

Yeah yeah, im just saying, have them, not use them

Someday you will encounter them

You will have the laws ready

[wanton sail]

Are you saying doing surface integrals isn't your passion??

[rigid gulch]

So basically

I’m not in higher level math yet

To even be using those laws?

[weary vessel]

i understand, i understand

someday

[primal pendant]

chris i feel you

[rigid gulch]

Okay

Soo my buddy texted me this

That one is for a later question about a cube (saw it in answer guild while checking my work) but what you do after finding the crossproduct is replace all the x, y and z parts of the intial F forumla with the intial S parenters given (in this case x= u+v y = u-v z=1+2u+v) and then multiply it by the crossproduct you got

[cedar kiln]

@rigid gulch Has your question been resolved?

Channel closed

Closed by @rigid gulch

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.

[ripe wasp]

help

it an eaz question so wont take more than a minute

[zenith sail]

What have you tried so far?

[ripe wasp]

Tried getting value of R in terms of other values and stuff

didnt really work

and the trig to find sides doesnt work either

[zenith sail]

yeah without knowing another angle I don't think trig functions are going to be much help

but what else could we do with a right triangle?

[ripe wasp]

idk pythag?

oh I might have an idea now

[zenith sail]

awesome, go for it

[ripe wasp]

.close

[cedar kiln]

Channel closed

Closed by @ripe wasp

Use .reopen if this was a mistake.

[zenith sail]

I didn't mean you had to close the channel lol

unless you already got it, in which case, nice job 👍

[cedar kiln]

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.

[distant adder]

if anyone is around to help with this again i could use some

[dire geode]

Just repost it here

[distant adder]

I know nobody is going to want to help with this but I was trying to work through some of the details in a paper by Knuth and couldn’t work out the step notated by the blue arrow https://media.discordapp.net/attachments/886483914410049556/1135765501797224671/IMG_2040.png

not really sure where the $\tau_j$ terms pop out from

[wraith dagger]

rubixcyouber

[distant adder]

from $$ \frac{\sqrt{2 \pi}}{e^m} \sum_{1 \le k \le m-1,;; j \ge 0} \frac{\sigma_j}{m^j} \frac{k^{k-1} e^{-k}}{k!} \left( 1 + k/m\right)^{\frac{1}{2} - j} \frac{1}{k+m-1}$$ , we can swap order of summation and sum j first to get something like

$$ \frac{\sqrt{2 \pi}}{e^m} \sum_{j \ge 0} \frac{1}{m^j} \sum_{k=1}^{m-1} \frac{k^{k-1} e^{-k} }{ {k! (k+m-1)}} \sigma_j (1 + k/m)^{1/2-j}$$

kinda looks like the result but not really - thats currently where im at

[wanton sail]

wow knuth really didn't like writing out his steps did he....

[distant adder]

trying to expand it out

[wraith dagger]

rubixcyouber

[distant adder]

Yeah I got no ideas

[wanton sail]

If it makes you feel any better, you're definitely not missing anything obvious....

[distant adder]

I think riemman was onto something earlier but not sure

If anyone has any suggestions I’m all ears

[cedar kiln]

@distant adder Has your question been resolved?

[cedar kiln]

@distant adder Has your question been resolved?

[distant adder]

I don’t think will be answered

[cedar kiln]

@distant adder Has your question been resolved?

[cedar kiln]

@distant adder Has your question been resolved?

[wraith dagger]

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

[brazen grove]

Hi, instead of trying to get the 3rd line from the 2nd you can do a reverse approach and try to get the 2nd one from the 3rd. I'll leave you the steps to follow:

Prove that the 3rd line is equal to
$$
\frac{2 \pi}{e^{m}} \sum_{k=1}^{m-1} \frac{k^{k-1} e^{-k}}{k!} \frac{\sqrt{k+m}}{(k+m-1)} \sum_{j=1}^{\infty} \frac{\tau_{j}}{(k+m)^{j}} (k+m-1)
$$
Just reducing terms and swapping the order of summation

After this check that

\begin{align*}
\sum_{j=1}^{\infty} \frac{\tau_{j}}{(k+m)^{j}} (k+m-1) &= \sum_{j=1}^{\infty} \frac{\tau_{j}}{(k+m)^{j-1}} - \frac{\tau_{j}}{(k+m)^{j}} \ &= \sum_{j=1}^{\infty} \tau_{j} (\frac{1}{(k+m)^{j-1}} - \frac{1}{(k+m)^{j}}) \ &= \tau_{1} - \sum_{j=2}^{\infty} \frac{\tau_{j}-\tau_{j-1}}{(k+m)^{j-1}}
\end{align*}

Finally use the definition of $\tau_{i}$ to obtain the 2nd line.

[wraith dagger]

BillyTheDancingKid

[distant adder]

Bruh

that’s smart

[cedar kiln]

Channel closed

Closed by @distant adder

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.

[keen nova]

why can't we 1) solve a^2 and sqrt(a) separately to begin with and 2) how can we perform the last simplification?

[keen nova]

if we did a^2 and sqrt(a) separately they would be 2a and 1/2sqrt(a) , which gave me a v different answer

and i cannot understand exactly how the last simplification is performed. I know sqrt(a) = a^(1/2) . But I just see the variable removed from its exponent and magically there's a square root

[simple plume]

It's a raise to the power 3/2

3/2 can be written as (1+2)/2

Which will give you

1/2 + 1

Powers of the same base add when they are mutiplied

It's kinda the reverse of the procedure of step 2 and step 3

[keen nova]

the way i see it is we take a^(2/2) away from the right quotient and multiply it to the left, leaving us with a^(1/2)

is that right

[keen nova]

and still can't see why we do the multiplication of powers. I know it's a rule and that we CAN do that, but I don't see why we HAVE to do that instead of solving them by themselves

[simple plume]

Like the 1st one why we add powers during multiplication with same base??

[keen nova]

a^2 * a^(1/2)

i know we CAN do 2+(1/2) giving a^(5/2)

but why do we HAVE to do that instead of solving them by themselves

[simple plume]

So really don't have to add powers you can solve it without that as well

[keen nova]

.

[simple plume]

Just use the multiplication rule of derivatives

[keen nova]

oh

so then they would be separate derivatives?

[simple plume]

Lemme see ans should be same

[simple plume]

Like we treat them as different functions a^2 and a^1/2

But I'll recommend this method only. It's way more simpler and efficient

[keen nova]

so if we don't add powers during multiplication, we have to do derivation for these functions separately, and then it would be the same?

what is the multiplication rule of derivatives btw ? maybe i know but

nvm, found it

[keen nova]

then i get $(a^2 * 1/(2sqrt(a)) + (2a * sqrt(a))$

[wraith dagger]

marty

[simple plume]

Now combine them using LCM

[simple plume]

Either way you'll have to use these rules

For the first term you'll get (a^3/2)/2

[keen nova]

i rearrange and get a^2 (which can be seen as a^4/2) multiplied with sqrt(a) (which can be seen as a^1/2). Thus I get a^(5/2)

and then i multiply a^5/2 with 1/2 and get 1/2a^5/2

thats my left term

what am i doing wrong

ah wait

it should be a^2 * 1/a^1/2

which is equal to 4/2 - 1/2

that gives a^3/2

divided by 2

but for the right term i get 2a^3/2

$(1/2a^(^3^/^2^)) + (2a^(^3^/^2^))$

[wraith dagger]

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

[keen nova]

which i guess would give

$5/2a^(^3^/^2^)$

[wraith dagger]

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

[keen nova]

how can we turn this into

$5/2a * sqrt(a)$

[simple plume]

So now you are on second last step??

[wraith dagger]

marty

[keen nova]

i did the terms through using the derivative mulitplication rule

and now added like terms

[simple plume]

So what you have right now is (5*a^3/2)/2

??

[keen nova]

well yeah if that's the same as 5/2a^3/2

5 halfs a to the power of 3/2

[simple plume]

Nah that's now same

Here

a is in denominator

You can share the pic of ur work

It's kinda confusing

[keen nova]

where the last term in my eyes could also be 1/2 * a^3/2 which would be 1/2a^3/2

is correct?

[simple plume]

Waitttttt

Where have you used the product rule??

Alright got it give me a sec

[simple plume]

Alright

So now

a^3/2

See you can write

3/2

As

(1+2)/2

Right??

[keen nova]

ohhhhhhhhhhhhhhhhh it's reverse power addition rule

[simple plume]

Yeahh

That's what I was saying from start

[keen nova]

a^3/2 = a^2/2 * a^1/2

[simple plume]

Yeahh

[keen nova]

which equals a * sqrt(a)

[simple plume]

Yupp

And I'll still say

[keen nova]

but now i learned how to do it from scratch, used the product rule for the first time lol, and got more experience with powers

yes its faster

[simple plume]

1st method is more convenient

[keen nova]

but now i learned more

[simple plume]

Instead of product rule

[simple plume]

Ohh good for ya!!!

[keen nova]

not saying i disagree but i learned more

thank u a lot

[simple plume]

No issues!!

[keen nova]

wow

[keen nova]

this is so cool lmao

magic

[simple plume]

Btw where are you from?

[simple plume]

Yeahh maths is magic in itself

[keen nova]

i'm from norway but live in netherlands how about u

[simple plume]

India

[keen nova]

nice 🙂

now math break

have a nice day!

[simple plume]

Same to you!!!

[simple plume]

Sure!!

[cedar kiln]

@keen nova Has your question been resolved?

[cedar kiln]

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.

[mystic abyss]

how do i do B?

[cinder shard]

Did you solve a ?

[mystic abyss]

yes

(200, 30)

[cinder shard]

give me a moment

Is B not just the value 200 then

[mystic abyss]

?

[cinder shard]

second

one sec

[mystic abyss]

it's asking for the domain

[cinder shard]

yeah yeah

one sec

i misread

[mystic abyss]

alr

[cinder shard]

okay, consider this thought

here is a suspension bridge diagram

[mystic abyss]

mhm

[cinder shard]

the turning point is in the middle

[mystic abyss]

yeah

[cinder shard]

what is x representing in your question?

[mystic abyss]

the horizontal length

[cinder shard]

well

almost

[mystic abyss]

the horizontal coordinate?

[cinder shard]

yes

logically, what would be the minimum value for x?

[mystic abyss]

0

[cinder shard]

okay

and the turning point is in the centre, no

[mystic abyss]

OH

[cinder shard]

xD

[mystic abyss]

0 ≤ x ≤ 400 right

yeah that's the answer

[cinder shard]

Yeah

[mystic abyss]

ok i get it now ty

.close

[cedar kiln]

Channel closed

Closed by @mystic abyss

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.

[unkempt bison]

How to find the extremum of f(x)=x^2-6x+5

[unkempt bison]

?

[sand meadow]

derive them

[dusk finch]

Do you know differentiation?

[gritty galleon]

*differentiate it

[sand meadow]

yp

[mighty shuttle]

Given that it's a parabola, I suggest you find its vertex instead of using calculus

[unkempt bison]

.close

[cedar kiln]

Channel closed

Closed by @unkempt bison

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.

[nova snow]

whats the tips with these sorts of probability questions

[tropic oxide]

these ones in particular are combinatorics questions in disguise tbh

[nova snow]

really?

[tropic oxide]

yes really

they can all be solved without pain by doing the (favorable outcomes)/(total outcomes) thing

btw i really dont like the wording of question 9

[nova snow]

what part about 9

[tropic oxide]

the use of "female" and "male" as nouns

it's creepy and basically incel-ese

[upper ruin]

Where's the problem?

[gritty galleon]

that too, but that isnt fully combinatrics

[tropic oxide]

should i repeat myself as to the grievance i take with how question 9 is written

[junior dome]

the permutation questions i have in my book have a similar wording

[upper ruin]

I don't understand what is not correct

[tropic oxide]

it's not about correctness, alberto!

it's about creepiness!

[upper ruin]

I still don't understand what's wrong with it 😅

[tropic oxide]

@gritty galleon don't sotrue me when i'm being 100% serious and genuine.

[gritty galleon]

isnt sotrue supposed to mean 'so true'??

or is it sarcasm

[tropic oxide]

it's ironic/sarcasm

genuine agreement is

[nova snow]

so to start simple with q7 what should be my approach

[tropic oxide]

using "female" as a noun when you mean "woman" is creepy

[gritty galleon]

can we please help OP

[gritty galleon]

sorry i didnt know

[nova snow]

[tropic oxide]

find the number of ways to draw 2 balls from the bag -- for these purposes, all 9 balls count as distinct
then find the number of ways to draw 2 balls of the colors specified

[upper ruin]

Well, but females includes girls, women and so on, so I don't see why they should use women instead of females

[tropic oxide]

...

do you think "girl" and "woman" are disjoint categories or what

[gritty galleon]

I am worried about the other genders ...we forgot abt them

[nova snow]

so 3 yellow, 4 pink, 2 black

if 2 balls are randomly chosen find probability of getting a yellow and black ball

a) with replacement.

so 9 balls in total but i think i need a little more help

so do i do 3/9 * 2/9 * 3?

[tropic oxide]

where did the last 3 come from

[nova snow]

from the three different colours

[tropic oxide]

well ok let's forget that you didn't follow my instructions here but like

if you're gonna do 3/9 (for yellow) * 2/9 (for black)

then surely you will want to do that times 2 for the two orders in which you could get them

(BY vs YB)

[nova snow]

is this product rule?

[tropic oxide]

if you wanna call it that

[nova snow]

may i ask why the order matters here

isnt getting a black yellow and yellow black the same thing

[tropic oxide]

drawing a black then a yellow is a different event than drawing a yellow then a black

[nova snow]

are we drawing them at the same time

[tropic oxide]

no

we are drawing with replacement

this means we draw 1, record its color, put it back, and only then draw the second one

[nova snow]

okay

[nova snow]

so how about without replacement

[tropic oxide]

well, if you want to go the non-combinatorial way then you still have to account for the different drawing orders

since you do still conceptualize your drawing as happening one by one, you just don't put the balls back

so P(B, then Y) = 2/9 * 3/8 and P(Y, then B) = 3/9 * 2/8

[nova snow]

do i multiply by those 4?

[tropic oxide]

???

sorry, i do not understand your question.

[nova snow]

2/9 times 3/8 times 3/9 times 2/8

do i do that?

[tropic oxide]

no

you add these two products.

[nova snow]

hm

[nova snow]

i dont understand why we're doing what we are doing

[tropic oxide]

ok let's try this

if $A$ and $B$ are disjoint (mutually exclusive) events, then $$P(A \cup B) = P(A)+P(B).$$ agree or disagree?

[wraith dagger]

Ann

[nova snow]

agree

[tropic oxide]

"we draw a black and a yellow in some order" = "we draw B, then Y" union "we draw Y, then B"
and the union is disjoint

agree or disagree?

[nova snow]

im confused here so P(A) and P(B) can have multiple things happening? not just a single thing

[tropic oxide]

P(A) and P(B) are not events but numbers. do not conflate an event with its probability!

also A and B are events. i am naming the events im talking about by their plain-english (but precise) descriptions.

said descriptions can, and routinely do, involve "multiple things happening".

[nova snow]

okay

[nova snow]

agree

[tropic oxide]

i mean you don't need to agree to the same thing a second time...

[nova snow]

oh

i forgot i said agree

so whats next

[tropic oxide]

wym what's next

i told you how to do problem 7, you said you got confused, now i am uncertain as to whether or not your confusion has been resolved

[nova snow]

ok

i would like to try question 8 now this time with the combinatorics approach

[main hazel]

help

[nova snow]

@tropic oxide how can i do this

[nova snow]

get your own channel in #❓how-to-get-help

[tropic oxide]

a deck of 100 tickets, 2 winners, 98 losers, we draw 4 w/o replacement

there are 100C4 ways to do that

er wait no ok

[nova snow]

what is a c4

[tropic oxide]

it's not 2 indistinguishable winners

it's a gold and silver again

100C4 means 100 choose 4

variously written as ${}_{100}C_4$ or ${}^{100}C_4$ or $\binom{100}{4}$

[wraith dagger]

Ann

[nova snow]

ill just resend it here

with these n choose k stuff i dont how how to really apply it to the questions

can we start with a

[dreamy sleet]

Ok, how would you start for a?

[nova snow]

4/100 * 4/100

.close

[cedar kiln]

Channel closed

Closed by @nova snow

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.

[old basalt]

Can someone please tell me why is this true if the sequence of (An) is increasing

[old basalt]

The union sign with a dot on top means that the events are incompatible

[tropic oxide]

the events are disjoint, you mean..?

[old basalt]

Meaning the intersection of the two sets is the empty set

[tropic oxide]

yes, disjoint

[old basalt]

Yes

[tropic oxide]

ok

[old basalt]

Yes thank you

[tropic oxide]

have you attempted writing out a proof of this equality?

[old basalt]

Yes ,what I don’t understand is how a serie became a limit

[tropic oxide]

there are no series or limits...

there are only indexed unions

$x \in \bigcup_{n \in \bN} A_n$ iff $(\exists n \in \bN)(x \in A_n)$

[wraith dagger]

Ann

[old basalt]

Yes but we can work with sequences,and series of sets the same as with ordinary ones

[tropic oxide]

not really

[old basalt]

Since the relation of intersection and union are relations of order

[old basalt]

Really?

[tropic oxide]

union and intersection are not even relations, they are operations.

the notion of 'limit' is somewhat... involved for sets.

union and intersection are like 100 times more elementary.

[old basalt]

I see

I am sorry for my mistake

So what are the first and second sides of the equality

I mean I can understand the first one as a union of n sets but what about the second one

[tropic oxide]

no, it's not a union of n sets, it's a union of infinitely many sets

as is the right-hand side

[old basalt]

Alright it worked since I can form any An from the union of the other sets

Thanks for your help

.close

[cedar kiln]

Channel closed

Closed by @old basalt

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.

[turbid spoke]

why

[vague rapids]

which step you don't understand?

[turbid spoke]

Why is a2 transformed together with the trigonometric function?

[vague rapids]

Like you mean RHS of steps 2 and 3?

[turbid spoke]

tes

yes

[turbid spoke]

thx

.close

[cedar kiln]

Channel closed

Closed by @turbid spoke

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.

[carmine pilot]

Hi

[carmine pilot]

I wanna ask why can system of linear equation can be represent by matrix

[smoky idol]

https://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html

[carmine pilot]

Got it

Tks

.close

[cedar kiln]

Channel closed

Closed by @carmine pilot

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.

[crude gale]

Kind of confused whats going on here

the 3rd matrix there seems like it would be inconsistent

since i have 4x_2=3 and 6.5x_2=4

oh wait nvm

.close

[cedar kiln]

Channel closed

Closed by @crude gale

Use .reopen if this was a mistake.

[cedar kiln]

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.

[spring owl]

Let the matrix A ∈ R 3×3 have the eigenvalues 0, i and -i. Then the linear system y'(x)= Ay(x) is:

stable and asymptotically stable

stable and not asymptotically stable

unstable and asymptotically stable

unstable and not asymptotically stable

I choose stable and not asymptotically stable because we only have 0 as a real eigenvalue. Am I right?

[cedar kiln]

@spring owl Has your question been resolved?

[spring owl]

<@&286206848099549185>

[cedar kiln]

@spring owl Has your question been resolved?

[spring owl]

No one??? damn

<@&286206848099549185>

[frozen meadow]

gotta wait for the smart people

[spring owl]

lmao

[dire geode]

https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Chemical_Process_Dynamics_and_Controls_(Woolf)/10%3A_Dynamical_Systems_Analysis/10.04%3A_Using_eigenvalues_and_eigenvectors_to_find_stability_and_solve_ODEs

Zero Real Part

[spring owl]

wow this hits the nail on the head, thank you!

.close

[cedar kiln]

Channel closed

Closed by @spring owl

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.

[spring coyote]

guys

does this mean Square of sum?

[austere merlin]

yes

[spring coyote]

🇮🇱 👍

.close

[cedar kiln]

Channel closed

Closed by @spring 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.

[lament kelp]

I’m tryna understand the question of my book. It says determine the period for the following rational number

[lament kelp]

What is the period

[vestal bear]

it would be awesome if you could show us the rational number in question

usually period is a term for trig functions

[lament kelp]

It shows diffrent numbers

Like 2/3

-63/99

16/7

[vestal bear]

send a picture of the question please

[lament kelp]

2

[lament kelp]

Its on swedish

[uneven matrix]

then tl it

or send pictures of the nonswedish parts

[lament kelp]

tl?

[vestal bear]

translate

[lament kelp]

I just translated

[vestal bear]

I looked up period of rational numbers and it said it is the repeating digits of the rational number

of its decimal expansion

[lament kelp]

I dont have a great calculator

[vestal bear]

so 2/3 I assume it's period is something along the lines of 66

[lament kelp]

No on my book it says 6

[vestal bear]

ah

then just the first part that repeats

[lament kelp]

But the weird part is

-63/99

[vestal bear]

,w compute 63/99

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Arctic#1647

[vestal bear]

63

[lament kelp]

Here book Says its 63

[vestal bear]

yeah

[lament kelp]

,w compute 16/7

[wraith dagger]

Results provided by WolframAlpha

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

Requested by sonner.

[lament kelp]

Oh shit

,w compute 2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by sonner.

[lament kelp]

[vestal bear]

2 doesn't repeat

[lament kelp]

Thank you

[lament kelp]

Thank you

[lament kelp]

Yeah its 0

.close

[cedar kiln]

Channel closed

Closed by @lament kelp

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.

[crimson sedge]

Hmmm trying to find the inverse laplace transform of [
\cmap {\mathcal L}{\map f t} = \map \log{\f{s^2+1}{s(s+1)}}
]

[crimson sedge]

It's kind of weird though because I'm unsure on how to deal with that log

[smoky idol]

I'm not sure, but is it like with limits where you can bring it outside since it's continuous or smth?

[royal loom]

log(a/b)=?

[crimson sedge]

Yes loga - logb but you still have to deal with the log

Do you take e^log or something

[royal loom]

so log here is natural log

?

[crimson sedge]

Yes

[royal loom]

do you this identity

$\mathfrak{L}^{-1}(F(s))=\frac{-1}{t}\mathfrak{L}^{-1}(F'(s))$

[wraith dagger]

Austin

[crimson sedge]

Darn I guess not

First time I see it

[royal loom]

try deriving it

so you can use it

[crimson sedge]

Well definition of Laplace here we go

[dire geode]

Is it in a table you have

[crimson sedge]

no

Okay I'm a bit lost with the derivation I won't lie

I'd appreciate a hint

[dire geode]

https://grdp.co/cdn-cgi/image/f=auto/https://gs-post-images.grdp.co/2022/5/laplace-transform-img1652263785631-45.JPG-rs-high-webp.JPG?noResize=1

Do you have something like 17-19

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

No truth be told I am familiar with all of those except 17-19

Any link for me to understand them?

[dire geode]

Just follows from integration by parts
https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/6%3A_The_Laplace_Transform/6.2%3A_Transforms_of_derivatives_and_ODEs

[cedar kiln]

@crimson sedge Has your question been resolved?

[royal loom]

@tough sand

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crude scroll]

Im not sure how to do this?

Do we have to re parameterize t in terms of something else?

[wanton sail]

what is the question?

are there more instructions

[crude scroll]

oh sorry

[wanton sail]

ah

Okay so yeah what does stokes's theorem say?

do you know

[crude scroll]

it says we can turn the line integral into a flux integral

i think

[wanton sail]

yeah, can you write out the equation?

[crude scroll]

was gonna type it out, but here it is.

[wanton sail]

yup, so what's the curl of F?

[crude scroll]

<Ry-Qz, Pz-Rx, Qx-Py>

I could calculate that one

<0,0,2x^2>

[wanton sail]

awesome and then how can we parameterize the disc?

[crude scroll]

that im am not sur

[wanton sail]

okay so we have a parameterization of the circle already

we need to figure out how to turn it to a disc

[crude scroll]

maybe in terms of cylindrical or spherical coordinates?

[wanton sail]

hmmmm well

first let's start with this

what are the parameterizations of the unit circle and unit disc in 2d?

[crude scroll]

$(r\cos\theta, r\sin\theta)$

[wraith dagger]

KN

[wanton sail]

yup

so the circle comes from setting r=1

and the disc comes from letting r range between 0 to 1

right?

[crude scroll]

right

hmm so, like $(r\cos\theta, r\sin\theta, r)$?

[wraith dagger]

KN

[crude scroll]

idt that is correct.

[wanton sail]

almost

so like

in 2D we went from (cos t, sin t) to (r cos t, r sin t)

now we have (cos t, sin t, sin t)

how should we "fill in the circle" to make a disc?

[crude scroll]

Based on how we did that in 2d, it should be (rcos t, rsin t, rsin t)?

[wanton sail]

yes!

[crude scroll]

i see.

that makes senes.

thanks

[wanton sail]

no problem, do you know how to do the surface integral from there?

[crude scroll]

Yep

Thanks.

.close

[cedar kiln]

Channel closed

Closed by @crude scroll

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.

[crude scroll]

actually

[crude scroll]

What would the parameterized bounds be

would 0 <= r <= 1 and 0 <= t <= 2pi?

[wanton sail]

yes!

r=0 corresponds to the center

and r=1 corresponds to the outer ellipse

[crude scroll]

i see

thank you for the help

[wanton sail]

no problem!

[crude scroll]

.close

[cedar kiln]

Channel closed

Closed by @crude scroll

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.

[sharp viper]

can some1 explain to me this answer

like how did that prove they r equal

[dire geode]

Is there more to the answer

[sharp viper]

nope

just that

[dire geode]

Which part exactly is confusing

[dire geode]

What's below the last line

[sharp viper]

nothing

like its another question

[dire geode]

Can you show it anyway

[dire geode]

How annoying

Yea they used demorgans law for intersection of two compliment sets

Did you learn demorgans laws yet

[sharp viper]

yep

so there is more to the answer?

like doesnt wut he just proved just show that x is subset of AUB(complements) so then its also of AnB(complements) since its not in AuB?

[slate lintel]

this is asking you to prove demorgan's law

surely

[wanton sail]

Yeah I think the answer given there is just incomplete

[cedar kiln]

@sharp viper Has your question been resolved?

[cedar kiln]

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.

[lethal bison]

how can they determine this?

[lethal bison]

here's the problem

[violet flume]

this is a known property of normal RVs

https://www.statlect.com/probability-distributions/normal-distribution-linear-combinations

see example one

it also contains a proof

[lethal bison]

oh ok I'll look at that thanks

[violet flume]

ah, yours is slightly different

let me see

[lethal bison]

it's a minus

[buoyant latch]

It’s still a plus

It wouldn’t make sense to have minus

[lethal bison]

yeah Ik

[violet flume]

well generally $var [aX+bY] = a^2 var X + b^2 var Y$

[lethal bison]

I meant in the question

[violet flume]

what

[buoyant latch]

LMAO

HAHA

[wraith dagger]

jan Niku

[violet flume]

forgive the typesetting

notice the squares, and what this means in your case

[lethal bison]

the minus becomes a plus

because when they do this in the proof

[violet flume]

yes, but i think its better you just use the linear combo form i posted

[lethal bison]

alright thank you for the explanation

.close

[cedar kiln]

Channel closed

Closed by @lethal bison

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.

[crimson sedge]

Can someone please explain me the red underlined part?

[violet jay]

I don't have a slick way of seeing it, but one thing to note is that if t > s then t/(1-t) > s/(1-s), so you can check the two cases t > s and t <= s.

[crimson sedge]

I see. That I realised, but I don't understand how they came up with these terms?

[austere merlin]

If t < s, then E(BtBs) = (1-t)(1-s)t/(1-t) = t(1-s) = min(t,s)(1-max(t,s))
If t > s, then E(BtBs) = (1-t)(1-s)s/(1-s) = s(1-t) = min(t,s)(1-max(t,s))

[crimson sedge]

Many Thanks!

.close

[cedar kiln]

Channel closed

Closed by @ocean wolf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[soft wagon]

if my mom say my dad not at home to get milk yesterday, when will he get the milk today? and how many milk he have?

[nimble mulch]

exactly e^(pi*i)

[soft wagon]

not a logical answer tho,

e^(pi*i) is not logical

[nimble mulch]

but it's -1, he stole exactly 1 milk

e^(pi*i) = -1

[soft wagon]

i know it equals -1 but where he stole it from? need the answer for that

[nimble mulch]

from somewhere he wants to keep secret from you ofc

[cedar kiln]

@soft wagon Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

how do i solve this? it's a calculus concept that i haven't really learned much about

[restive shard]

just undo each log

not much calculus

[crimson sedge]

how would i do that?

[restive shard]

well what's the inverse of log base 10?

[crimson sedge]

is it just ten?

sorry im not good at this

[restive shard]

yea it's 10^x

now how about log base 6?

[crimson sedge]

6^x?

[restive shard]

exactly

now look at the problem

imagine that everything inside log base 6 is equal to a variable u

giving you log6(u)=0

try solving for u

[crimson sedge]

okay so u = 1

[restive shard]

alright now substitute u for whatever was in log base 6

[crimson sedge]

okay i think i understand

so i just keep doing that until i get my answer

[restive shard]

yep

[crimson sedge]

alright, ty

[restive shard]

np!

[crimson sedge]

wait also sorry one other thing

for this one, is it the same method or do i start from like the inside?

[restive shard]

you should start from the inside

[crimson sedge]

okay, ty

[crimson sedge]

wait would the one on the inside be equal to x too or a different number?

oh wait would i just set it equal to a different variable

[rich mason]

you can calculate from the inside

log5(25) is 2

log2(2) is 1

[crimson sedge]

well i got to 1=3^x, im not sure how to solve that

[rich mason]

x = 0

anything to the power of 0 is 1

[crimson sedge]

ohh

alright thank you

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @signal hollow

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.

[crimson sedge]

i can use a calculator on this, but im not sure how to interpret the given function because of the subscript 0 and the k next to the t. how should i go about solving this?

[magic solar]

The k is constant subscript is no. Of bacteria at t=0

[crimson sedge]

do i need to know the value of k?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

never mind

[hearty arch]

did you end up figuring it out

[crimson sedge]

not really

no one showed up but i asked this question somewhere else

i have another question though

but its unrelated to this problem

does anyone know what it means when it says to say what values of theta does it intersect the pole? because isn't the pole the center of the polar graph? im not sure how it can have an angle measure

[ember halo]

Math sucks

[hollow trail]

a 0 subscript typically indicates a starting condition. To find the function, start by setting t=0. When t=0 then eᵏᵗ = 1, so n = n₀ (we are given the start amount in the problem).

then solve for k with the value you have for n₀, and with the given information (n = 1200 when t = 1)

[hollow trail]

for certain values of θ the function will return r = 0. remember that multiple different polar coordinates can point to the same spot

[crimson sedge]

oh okay, thank you

also do you know what it means when it says to tell the values of theta that make it so the graph is drawn only once

[hollow trail]

for some of the graphs once you get a high enough value of θ it will go over the exact same points over again (because sin and cos are periodic functions), so you want to find a range for θ where it draws the whole function without going back over itself

[crimson sedge]

do you know how i would figure that out?

[hollow trail]

probably easiest to work it out from the graph

[crimson sedge]

oh okay

so would a circle just have the range of 0 to 2pi

[hollow trail]

yes

[crimson sedge]

okay - and would that be for any circle or just a circle that isn't touching the pole

[hollow trail]

it would be true for the usual form of a circle in polar coordinates, which is a constant radius (e.g. problem 60)

[crimson sedge]

so it wouldn't be true for 61?

[hollow trail]

it wouldn't, no

[crimson sedge]

is there another way to figure it out for that type of problem then? or do i just need to look at what polar coordinate lines the graph touches?

[hollow trail]

it can be difficult to tell purely from where the graph touches since any given angle can put you in one of 2 quadrants. if the graphing software you use supports it, try changing the angles used as inputs until you find the smallest range that still has a complete graph

[crimson sedge]

i can't use any technology on these types of problems though

for this specific assginment

[hollow trail]

in that case i'd start drawing until it seems like it "completes a loop". that may be before or after you reach 2π

[crimson sedge]

i drew out the graph and it's just a circle thats on the right side of the y axis

[hollow trail]

while you're graphing, try to keep track of which angles you're going through. in that case, it started in the first quadrant, then went to 0 at θ=π/2 and completed the circle at θ=π

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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.

[hot python]

is this a good enough tesselation?

[whole bloom]

Yeah

[tropic oxide]

wym by "good enough"?

@hot python what do you want from this tessellation?

[cedar kiln]

@hot python Has your question been resolved?

[cedar kiln]

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.

[quasi plover]

/

[quasi plover]

Idk what to start

[lunar lynx]

#❓how-to-get-help

[quasi plover]

...

Nicr

[hollow trail]

generally in statistics when we look at a sample we're trying to use the data to find a statistic (calculated from the data in the sample) to estimate a parameter (calculated from the population, difficult to measure).

[quasi plover]

Parameter?

Idk, but if i answer. Ill answer B, but the answer A and C i dont understand

[hollow trail]

just because the mean number of dramas was 15 doesn't mean many people watched exactly that number. It may be that none of them watched exactly 15 dramas.

remember we're talking about the mean, or average

[quasi plover]

Ya

But like

It also say like margin of error of 3

Thats the part i felt most uncomfortable with

[hollow trail]

basically we couldn't interview every single student. but we want to have some idea of what the average is for every student anyway.