help-13

[upper laurel]

u u^T is another way of writing u * u

but either can be used

whats more important is

this formula is easier to use and is usually what you learn

[chilly bolt]

but in matrix multiplication u cant just multiply two 2x3 matrices right, they need to be 2x3 and 3x2

[upper laurel]

yes

the * is dot product

the * does not mean matrix-multiply

matrix-multiply does not have a symbol

[chilly bolt]

ive only done dot product when its like (1,2) dot (2,3)

does this extend to larger matrices as well

[upper laurel]

(1, 2) and (2, 3) are vectors

[chilly bolt]

yeah

[upper laurel]

dot product is for vectors only

u is also a vector

[chilly bolt]

oh

[upper laurel]

u * u is between two vectors

nothing new is happening

oh wait

@chilly bolt I made a big mistake

u^T u is u * u

u u^T is something else entirely

[chilly bolt]

what

explain

[upper laurel]

lets say $u=\begin{bmatrix}1\2\3\end{bmatrix}$

[wraith dagger]

mtt

[upper laurel]

so $u^T=\begin{bmatrix}1&2&3\end{bmatrix}$

[wraith dagger]

mtt

[upper laurel]

now $u^Tu=\begin{bmatrix}1&2&3\end{bmatrix}\begin{bmatrix}1\2\3\end{bmatrix}=\begin{bmatrix}1\cdot1+2\cdot2+3\cdot3\end{bmatrix}$

[wraith dagger]

mtt

[upper laurel]

when you matrix multiply u^T and u together, you get what is essentially a single number

that single number is the same thing as dot product: u * u

[chilly bolt]

oh yeah they will be diff cause matrix multiplication isnt commutative

[upper laurel]

yea

,,\begin{bmatrix}1\2\3\end{bmatrix}\cdot\begin{bmatrix}1\2\3\end{bmatrix}=1\cdot1+2\cdot2+3\cdot3

[wraith dagger]

mtt

[upper laurel]

so u^T u is u * u

compare this to doing u u^T instead

,,u;u^T=\begin{bmatrix}1\2\3\end{bmatrix}\begin{bmatrix}1&2&3\end{bmatrix}=\begin{bmatrix}1\cdot1&1\cdot2&1\cdot3\2\cdot1&2\cdot2&2\cdot3\3\cdot1&3\cdot2&3\cdot3\end{bmatrix}

[wraith dagger]

mtt

[upper laurel]

you get a 3x3 matrix out of u u^T

for reasons you can ask me later, uu^T v = (u * v) u

uu^T is matrix multiplication
u^T v is also matrix multiplication

u * v is dot product, which gets you a number
(u * v) u is multiplying u by a scalar, which gets you a scaled version of u

[chilly bolt]

ok

[upper laurel]

oh wait

Ive got a good way

we say earlier u^T u = u * u right

[chilly bolt]

yeah

[upper laurel]

u^T v = u * v

there was no need to have the second vector also be u

[upper laurel]

so this is true in general

right

[chilly bolt]

yeah

[upper laurel]

now I u on the left on both sides

u u^T v = u (u * v)

since theyre both equal, attempting to multiply them by u should also remain equal

on the left, u^T v is technically a 1x1 matrix, so multiplying by u gets you a 3x1 matrix

on the right, u * v is a number, so multiplying by u gets you a scaled version of u, also a 3x1 matrix

so u u^T v = u (u * v) in general

do you believe that

[chilly bolt]

oh ok

[upper laurel]

yea

then u (u * v) = (u * v) u

(u * v) is a number so this is valid

u u^T v = (u u^T) v, so you can do the u u^T first

you get a matrix out of that

[chilly bolt]

is this to do with assoicative property

[upper laurel]

yep

[chilly bolt]

ok that makes sense

[upper laurel]

now what this all ends up meaning is

we have two different formulas that do the same calculation

weve shown that they are the same

however this is a number

and this is a matrix

[chilly bolt]

ok

[upper laurel]

so the bottom one is a matrix way of doing proj_u(v)

uu^T / ||u||^2 is the matrix you multiply v by

[chilly bolt]

is this projection of u onto v

[upper laurel]

proj_u(v) is

this is a projection of v onto u

[chilly bolt]

or the other way around

ok

[upper laurel]

you can think of it as u being what you base things off of

and v being some vector that could partly face parallel or perpendicular to u

proj_u(v) lets you see how "u-wise" v is

[chilly bolt]

yeah

alright

[upper laurel]

anything else?

[chilly bolt]

nah all good

[upper laurel]

nice

.close

[cedar kiln]

Channel closed

Closed by @upper laurel

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.

[fervent jackal]

I understand how it works for a single variable (one dimensional x and y) but I dont seem to understand how it translates to multiple dimensions, can someone explain the proof to me? and why the equality holds?

[fervent jackal]

I especially dont understand this part

I get that probability density functions must be positive so we take the absolute value, but why do we take the determinant?

[cedar kiln]

@fervent jackal Has your question been resolved?

[autumn fox]

Notice first that\

$F_{\mathbf{Y}}(\mathbf{y}) = P(Y_{1} \leq y_{1}, \hdots, Y_{n} \leq y_{n}) = P(g(X_{1}) \leq y_{1}, \hdots, g(X_{n}) \leq y_{n}) = P(X_{1} \leq g^{-1}(y_{1}), \hdots, X_{n} \leq g^{-1}(y_{n})) = F_{\mathbf{X}}(g^{-1}(\mathbf{y}))$\

Then you can use that\

$F_{\mathbf{Y}}(\mathbf{y}) = \int_{-\infty}^{\mathbf{y}} F_{\mathbf{Y}}(\mathbf{s}) ; \dd \mathbf{s}$\

To deduct the rest

[wraith dagger]

Mikkel Angelo

[autumn fox]

With $\int_{-\infty}^{\mathbf{y}} F_{\mathbf{Y}}(\mathbf{s}) ; \dd \mathbf{s} = \int_{-\infty}^{y_{1}} \hdots \int_{-\infty}^{y_{n}} F_{\mathbf{Y}}(\mathbf{s}) ; \dd s_{1} \hdots \dd s_{n}$ that is

[wraith dagger]

Mikkel Angelo

[fervent jackal]

Ah so thats where you get the jacobian matrix when you differentiate afterwards

but where did the determinant come from

[cedar kiln]

@fervent jackal Has your question been resolved?

[cedar kiln]

@fervent jackal Has your question been resolved?

[cedar kiln]

@fervent jackal Has your question been resolved?

[crimson sedge]

Where did the determinant come from? 🗣️🗣️

[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.

[river latch]

this is false right?

[worldly chasm]

@river latch well, with true false questions you have a 50/50 shot of guessing correctly. Why do you think it is false?

[stoic crystal]

Btw

[worldly chasm]

!nosols

[cedar kiln]

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

[worldly chasm]

Oh lol

[worldly chasm]

Yes, it's obviously false because the proposed tangent line is not a line 🙂

[river latch]

thank you

.close

[cedar kiln]

Channel closed

Closed by @river latch

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.

[wicked stag]

@sturdy island hi

It would be helpful if you divide it in cases

1 WC 3 B
1WC 4B
2WC 3B
2WC 4B

[wicked stag]

For all cases you can calculate ways and add them

[cedar kiln]

@sturdy island 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.

[still moss]

how to start this guys

[cedar kiln]

@still moss Has your question been resolved?

[still moss]

.close

[cedar kiln]

Channel closed

Closed by @still moss

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.

[rare magnet]

How did we end up with a single R variable here? I cannot figure out what they did inbetween these steps

[ancient lodge]

$$\frac{1}{\sqrt 2} (R+h)=R$$ $$\frac{1}{\sqrt 2} R+\frac{1}{\sqrt 2}h=R$$ $$\frac{1}{\sqrt 2} h=R-\frac{1}{\sqrt 2} R$$ $$h=\sqrt 2 \left(R-\frac{1}{\sqrt 2} R \right)$$

[wraith dagger]

Civil Service Pigeon

[rare magnet]

distribute the squareroot 2 and then factor out the R, yes I see it now

thank you

.close

[cedar kiln]

Channel closed

Closed by @rare magnet

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.

[river ivy]

is solving for theta possible

[river ivy]

cant tell if there is insufficient information or i am insufficient

[elder wyvern]

You've just described exactly how I feel right now. I can not help, but I wanted you to know that you are not alone.

[river ivy]

thanks for the support

how should i approach this

considering i feel like there is either insuffiecient information, or it is 4:50 am

Help

[mint thistle]

sunrise duration = 11:55 am - 06:58 am

that's 4 hours and 57 minutes

[river ivy]

correct

[mint thistle]

now estimate the time frame that the whole ferris wheel will be in sunlight sicne the ferris wheel is likely to be in sunlight for a portion of the day so we can assume that it will be in sunliught for approximately haft of the duration of the sunrise

[river ivy]

because the entire question is that there is a ferris wheel and tower kind of blocking it

but thanks for explaining

[cedar kiln]

@river ivy 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.

[gritty oxide]

I got this question in my online pre-calc course and I don't know how to combine the 4x with the rest of the expression when finding the equivalent expression:

"Which of the following is equivalent to 4x+5lnx-ln2xy?

A: ln(8x^7y)
B: ln(4x^6-2xy)
C: (5ln4x)/(ln2y)
D: ln((2x^5)/y)"

I know that I can turn the term 5lnx into lnx^5, and that you can turn the logarithms being subtracted into a division, so my guess is that it would be D, but I can't figure out what happened to the 4x.

Any help would be greatly appreciated.

[restive shard]

4x can be written as ln(e^4x)

[gritty oxide]

ok, so then I can turn everything into ln(((e^4x)*x^4)/2y), but what can I do after that?

[restive shard]

you could take out the exponent of 4 on the numerator but i don’t know what you’d do with the denominator

like 4ln(xe^x) - ln(2y)

[gritty oxide]

so the program is saying that $ln({2x^5\over y})$ is correct, and it is the one that made the most sense, but I don't understand why it works and the graph doesn't look the same to me.

[wraith dagger]

adjxst

[floral salmon]

if you mean $4x+5ln(x)-ln(2xy)$ and:\
A: $ln(8yx^7)$\
B: $ln(4x^6-2xy)$\
C: $\frac{5ln(4x)}{ln(2y)}$\
D: $ln(\frac{2x^5}{y})$\
Then there is no correct answer, as a counterexample consider $x=e$,$y=1$\
$4x+5ln(x)-ln(2xy) = 4e+6+ln(2)$\
A: $ln(8e^7) = 7+ln(8)$\
B: $ln(4x^6-2xy) = 1+ln(2)+ln(2e^5-1)$\
C: $\frac{5ln(4x)}{ln(2y)} = \frac{20}{ln(2)}$\
D: $ln(\frac{2x^5}{y}) = 5+ln(2)$\
As you can see none of A,B,C,D matches $4x+5ln(x)-ln(2xy)$, for $(x,y)=(e,1)$, so there can no be any equivalent expressions among the alternatives.

[wraith dagger]

Crystopher

[gritty oxide]

ok, I guess the program just decided to be strange. Thank you for the help.

.close

[cedar kiln]

Channel closed

Closed by @gritty oxide

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.

[sturdy island]

!status

[cedar kiln]

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

[sturdy island]

2

[odd verge]

Are you to calculate the number of possible cricket teams

[sturdy island]

yup

Doy you know how to do this

I try to do this with ombination

combination but not working

[cedar kiln]

@sturdy island Has your question been resolved?

[odd verge]

Notice a certain amount of players must be included

[sturdy island]

ya

Here keyword is Al least with bowler

[odd verge]

1 wicket keeper right and at least 3 bowlers

[sturdy island]

ya

[odd verge]

Lemme solve it

[sturdy island]

2(4C3 * 2C1 * 9C7) + 2( 4C4 * 2C1* 8C6) = 688

I try to do this

[odd verge]

Isn't it meant to be 7c5

[sturdy island]

????

there are total 13 players so i subtract 4

and from 11 i subtract 4 also

?

did i do that wrong?

[odd verge]

And 2

[sturdy island]

there are 2 wicket-keepers so if we are selectinG 1 then WE do not know which one we are selecting like K1 or K2

btw 22 is right answer

<@&286206848099549185>

[sturdy island]

<@&286206848099549185>

@everyone

Anyone of you help me

[cedar kiln]

@sturdy island Has your question been resolved?

[odd verge]

So sorry man

I was doing something

[sturdy island]

do not worry

it ok

What you are doing

Like which level you are in

Graduate

Are you Graduate?

[odd verge]

I am like in 11th but I am taking undergrad engineering math physics and chemistry

[sturdy island]

Are you Indian

[odd verge]

I was rushing I Couldn't find neater paper or ise better handwriting 😞

[odd verge]

No

[sturdy island]

Pakistani

Or Bangale

[odd verge]

, rotate

[odd verge]

Neither

[sturdy island]

then which country

You are Asian i think that much

[odd verge]

Nigeria

[sturdy island]

great

btw i am in 12th class

[odd verge]

Cool

[odd verge]

This is solution

My 1 is actually 7

[sturdy island]

Why 7C7 or 7C6

[odd verge]

Select the required remainder of people from the unselected people

[odd verge]

Lol

[sturdy island]

Wait i have a question

In Case : 1

We select 3 bowler and 1 keeper

ya right?

[odd verge]

Yes

[sturdy island]

So there are 13 players in total

right?

[odd verge]

Yes from the available people

[sturdy island]

We already select 4 player in which 3 are bowler and 1 is keeper

so 13-4 = 9

wdym Available one

?

Aall 13 player are available

[odd verge]

No we use the available combination required

[sturdy island]

hmmm

not getting your point

[odd verge]

Which is why i split it into total players or available and required players

[sturdy island]

i know you are saying that there are 4 bolwer in total and 2 keeper in total so when we subtract 13 -4-2 it is 7

[odd verge]

Yes

[sturdy island]

but why are we taking them all toghter and make 7 pepole out 13

[odd verge]

Lemme re dolve with details

Ok?

[sturdy island]

ok

[odd verge]

I am slow at writing

Almost done

[sturdy island]

noo

not worry

[odd verge]

Part a

[sturdy island]

but why are we taking the remaining player 7

Like if we add 3 bowler and 1 keeper in team

[odd verge]

We have to find no of ways for selecting each group of players from the available

[sturdy island]

Bro wait

let me explain to you what i understand

then correct me

ok?

[odd verge]

Ok

[sturdy island]

Listen

We have total 13 players

out of which we have to find 11

[odd verge]

@ ..... Please do contribute if there are mistakes

[sturdy island]

No your answer is correct

[odd verge]

Yessir 😊

[sturdy island]

now

we are given 4 bowler and 2 keeper

We have constraint that we must have to add 3 bowler in team

and 1 keeper

If we add 3 bowler and keeper in team

[odd verge]

We must consider 3 or more bowlers because it says at least 3

[sturdy island]

ya i am taking about case 1

if we take 3 bowlers and 1 keeper then 7 places left for other players

right

[odd verge]

Yes

[sturdy island]

so to find these 7 players we subtract selected players

right or worng

wrong

So if we select B1 ,B2 ,B3 and K1

[odd verge]

11-3-1=7slots remaining

[sturdy island]

then

ya

[sturdy island]

ya

but what about 13 - 4 = 9?

[odd verge]

13-4-2=7 residual players in the original team

[odd verge]

No 😔 its 13-4-2

[sturdy island]

but why

we select only 4 players

not 6

[odd verge]

We selected these four from a total of 6 players

[sturdy island]

We select B1 ,B2 ,B3 out of B1,B2,B3,B4

[odd verge]

6=no of wickets + no of bowlers

[sturdy island]

what??????????

[odd verge]

Unassigned

[sturdy island]

not worry

[odd verge]

Look at the solution you'll see I separated the team into required and total

[sturdy island]

ya

Thanks for you help

[odd verge]

The thing is we have assigned 4 and 2 to be selected to fill other spaces

So the remaining 7 is unassigned

[sturdy island]

i am so confuse

Thanks btw

i will try to understand it later

[odd verge]

You can check 3B1B and organic chem tutor for combination and permutations

[sturdy island]

ok

which one is great

cuz i sometime watch Organic Tutor

what is 3B1B???

.close

[cedar kiln]

Channel closed

Closed by @sturdy island

Use .reopen if this was a mistake.

[restive shard]

bro is about to be mind blown from 3b1b

[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.

[dense tide]

What does the following article mean by the highlighted statement?

[cedar kiln]

@dense tide Has your question been resolved?

[worldly chasm]

@dense tide it means if you have a polynomial given by $\sum_{i=0}^n a_i x^i$ you can write it as $a_n \prod_{i=1}^n (x - r_i)$ for some sequence of coefficients ${a_i \in \mathbb{C} }$ and roots ${r_i \in \mathbb{C}}$.

[wraith dagger]

OmnipotentEntity

[dense tide]

thank you

[worldly chasm]

No worries. Is it clear? Or too convoluted?

[dense tide]

well, could you elaborate please?

[worldly chasm]

Sure thing

Essentially, if you have a polynomial with real coefficients, in order to solve all of them, such as x^2 + 1 = 0, we need to use complex numbers.

But if we have polynomials with complex coefficients, we can solve them still with only complex numbers.

If we limited ourselves to real numbers only, there would sometimes be quadratic factors that cannot be split further.

But for complex numbers we can always get down to linear factors.

To be more explicit.

If you have ax^3 + bx^2 + cx + d with a-d complex numbers then there exists r1-r3 such that ax^3 + bx^2 + cx + d = a(x-r1)(x-r2)(x-r3)

Where r1-r3 are also complex

This is true for any degree polynomial.

The idea is with real numbers there was "something else" we needed to solve polynomials, and the something else is complex numbers.

So it's not closed.

But with complex numbers we can't make something else using polynomials. We can only make other complex numbers. And because we can only make other complex numbers, and not other things, it is closed.

I hope that's clear?

[dense tide]

yes that's clear. Thank you

and a linear factor is essentially just a polynomial of first degree?

[worldly chasm]

Yes, it's the (x-rn) that I've been writing everywhere

[dense tide]

right..

thank you

.close

[cedar kiln]

Channel closed

Closed by @dense tide

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.

[abstract thicket]

in part a, I got 1/2 but it is incorrect for some reason

there are 18 even numbers out of 36

18/36

=1/2

<@&286206848099549185>

[wanton harness]

0 is even

[alpine knot]

It's 19/37 I'm pretty sure

[dull oxide]

!15m

[cedar kiln]

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

[abstract thicket]

ye

[alpine knot]

The way I like to approach this kind of problem is to do it for 0 to 2, then 0 to 4, etc

See if you can spot (and of course verify) a pattern

That way you can be more confident

[abstract thicket]

I can see the patern

0 to 6, 0 to 8

etc

yes, I dentify the pattern

what's next?

there are 18

[wanton harness]

I didn't use the ping also I am not helper

[abstract thicket]

oh ok

Im still confused

[dull oxide]

Sorry I fat fingered

[abstract thicket]

there are total of 37 possible outcomes because the 0 doesnt count

[wanton harness]

It's ok

[abstract thicket]

nvm I got it

0 is an even number

so it's 19

this case is dismissed

.close

[cedar kiln]

Channel closed

Closed by @abstract thicket

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.

[vernal kite]

how do we do b ii

[cedar kiln]

@vernal kite Has your question been resolved?

[cedar kiln]

@vernal kite Has your question been resolved?

[crimson sedge]

.close

[vernal kite]

<@&286206848099549185>

l.close

.close

[cedar kiln]

Channel closed

Closed by @vernal kite

Use .reopen if this was a mistake.

[vernal kite]

.reopen

[cedar kiln]

✅

[nimble axle]

Ok, got it

[vernal kite]

soooo?

[nimble axle]

this one you don't suppose to find what R and r is, but write it so that the form change into something usuable

first we know the formula of the annulus as this

if you look closely, you can factor it

[nimble axle]

can you try factor it?

[crimson sedge]

use pythagorean theorem on the triangle

[nimble axle]

yeah that will come in the later part, when we're dealing with diagram

[vernal kite]

but how??

[crimson sedge]

I mean it's already drawn our right there

[vernal kite]

so then what's R and r?

[crimson sedge]

R and r

[vernal kite]

pi (R^2 - r^2)

[nimble axle]

correct

[vernal kite]

and how does that help us

[crimson sedge]

Use pythagorean theorem on the R, r and 7 triangle

See what comes up and how it can help

[nimble axle]

look at this diagram and tell me 1 Pythagorean theorem equation

[crimson sedge]

I would literally be telling you the answer

Just apply it

[delicate umbra]

thx

[crimson sedge]

Are you folding kidding me?

[nimble axle]

yo chill

he's trying, geometry is hard when you don't see the connection yourself

[vernal kite]

i see R^2 = r^2 + 7^2

[crimson sedge]

Correct

R^2-r^2 is 49

[vernal kite]

yes

[nimble axle]

now back to this area formula

[crimson sedge]

Put 49 into the this

[vernal kite]

ohhh

thanks guys

[nimble axle]

np

[crimson sedge]

Oh shi

I thought Tara was asking the question

God damn it

[nimble axle]

sorry if I come off as aggrsive

yeah I was the one helping

[crimson sedge]

no no i thought I was telling you to apply the equation and you kept sending me closer pics 😭😭

i was getting annoyed at you for now reason lmao

Sorry

[nimble axle]

This is funny as hell 💀

np, it's all fun and game, and our friend got the answer now so all good 😂

[crimson sedge]

@vernal kite sorry😭😭

[vernal kite]

na na itt's chill

thx for helping

[nimble axle]

I'll be going then, don't forget to close channel

[vernal kite]

yep

.close

[cedar kiln]

Channel closed

Closed by @vernal kite

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.

[teal geyser]

Is there a name for this? https://cdn.discordapp.com/attachments/844681108473118750/1257381169901731993/896758879176785930.png?ex=668432f7&is=6682e177&hm=5b12ce445fcddcf3981be169152fb20ef944e38eb7cbc62d7fca3b0851b54b5e&

[teal geyser]

"Finding the limit of an undefined integral" seems too vague

[restive shard]

they're called improper integrals

[teal geyser]

Sorry, I should've been more specific. I meant evaluating an integral over an interval with a singularity

[restive shard]

there's not really a term for that specific step

it's pretty much just computing an improper integral

nothing specific for this case

[teal geyser]

Not really, $\int_{-1}^1 \frac{dx}{x}$ doesn't really exist

[wraith dagger]

7aman

[restive shard]

oh yea this one does diverge

but somthing like $\int^{1}_{-1} \frac{dx}{x^2}$ should give you an answer if i remember correctly

[wraith dagger]

890s

[restive shard]

no nvm im just tweaking

[teal geyser]

You are unfortunately

<@&286206848099549185> ?

[cedar kiln]

@teal geyser Has your question been resolved?

[mental trail]

Cauchy principal value

[teal geyser]

Tysm

And is there a name for this one too?

$\int_{-1}^1 \frac{dx}{x} \to \lim_{\epsilon \to 0} \int_{-1}^1 \frac{dx}{x+i\epsilon}$

[wraith dagger]

7aman

[cedar kiln]

@teal geyser Has your question been resolved?

[cedar kiln]

@teal geyser 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.

[visual pasture]

During the proof of Lagrange's Mean Value Theorem we assume a function as F(x) = f(x) + Ax

Why do we assume it only this way? I understand that this form leads us to the proper conclusion of LMVT but why not just f(x), what's the point of also taking Ax?
Does this form or type of a function have some name?

[cedar kiln]

@visual pasture 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.

[stray pilot]

I was wondering how to do this? I don't even know where to start. Do I do the bottom and get the restrictions? It can't = 0 or be -1

[humble karma]

Multiply by conjugate/conjugate

[stray pilot]

Ahh ok my bad

That's what I was thinking but I always doubt myself

[humble karma]

Whenever either the numerator or denominator is a + sqrt(b) it's worth trying

[cedar kiln]

@stray pilot Has your question been resolved?

Channel closed

Closed by @stray 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.

[civic coral]

Furry animal!

I would like to check if there’s a part of my attempt is incorrect that leads me to a wrong answer.

Furry animal! <@&286206848099549185>

[grand moss]

@civic coral not math, but ops on eminem?

Also

Why am I female?? 😭😭

I'm literally male

[alpine knot]

Accidentally clicked the wrong pronouns role probably

[earnest idol]

the slope of the line is 2 not -2/3

[civic coral]

Ahhh

Smart people

[earnest idol]

its making an acute angle with the positive x axis right so how can the slope be negative

[civic coral]

Smart people

The solution provided by khan using calculus to solve it

Smart people

That’s too much, no?

Inefficient

Time-consuming

Exhausted

Furry animal

[earnest idol]

useless, just do what you were doing

you know that the perpendicular is the shortest distance from the origin, they just derive that using calculus

[civic coral]

That’s quite a singular approach

Uncommon

[cedar kiln]

@civic coral 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]

i need help

[crimson sedge]

2.37

let's get to the middle part since it's pretty hard to do type

[nimble mountain]

can u factorise any of the denominators?

[crimson sedge]

\begin{align*}
\frac{2z(2z-1) + 4z - 3(2z-1) + z}{2z^2 - z} &= \frac{2z(2z-1) - 3(2z-1) + 4z + z}{2z^2 - z} \
&= \frac{(2z - 3)(2z - 1) + 5z}{2z^2 - z}
\end{align*}

[wraith dagger]

Gizmo_siz

[nimble mountain]

u didnt have to work it all out from the start

[crimson sedge]

\begin{align*}
\frac{2z(2z-1) + 4z - 3(2z-1) + z}{2z^2 - z} &= \frac{2z(2z-1) - 3(2z-1) + 4z + z}{2z^2 - z} \
&= \frac{(2z - 3)(2z - 1) + 5z}{2z^2 - z} \
&= \frac{(2z - 3)(2z - 1) + 5z}{z(2z - 1)} \
&= \frac{(2z - 3)\cancel{(2z - 1)} + 5z}{z\cancel{(2z - 1)}} \
&= \frac{2z - 3 + 5z}{z} \
&= \frac{7z - 3}{z} \
&= 7 - \frac{3}{z}
\end{align*}

[wraith dagger]

Gizmo_siz

[crimson sedge]

fuck gpt

[nimble mountain]

no u cant cancel that

[crimson sedge]

why?

[nimble mountain]

did u just copy from gpt..

[crimson sedge]

no

that's mine

i telled gpt to do my latex thing

...

i dont know latex at all

oh

wait

i can still factor out

[nimble mountain]

$\frac{2*7+3}{2}$

[wraith dagger]

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

[nimble mountain]

u cant just cancel the twos

[crimson sedge]

2z(2z-1)-3(2z-1)+4z+z/2z^2-z

i can still factor out

4z+z

z(4+1)

\begin{align*}
\frac{(2z-3)(2z-1) + z(4+1)}{z(2z-1)} &= \frac{(2z-3)(2z-1) + 5z}{z(2z-1)} \
&= \frac{(2z-3)\cancel{(2z-1)} + 5z}{z\cancel{(2z-1)}} \
&= \frac{2z-3 + 5z}{z} \
&= \frac{7z-3}{z} \
&= 7 - \frac{3}{z}
\end{align*}

[wraith dagger]

Gizmo_siz

[crimson sedge]

nah damn

this is wrong latex

it's supposed to be like this

(2z-3)(2z-1)+4z+z/2z^2-z

you can still see i can factor out 4z+z right?

so

(2z-3)(2z-1)z(4+1)/z(2z-1)

which cancels the denominator

and I'm left with

(2z-3)(4+1)

I've got 2 minutes before helper

can i ping??

1 minute left

<@&286206848099549185>

[alpine knot]

Tip: if you type it into desmos you can just copy and paste it and it gives you the latex

[crimson sedge]

need help...

[crimson sedge]

there's no fraction thing??

[alpine knot]

$2+\frac{4}{2x-1}+\frac{3}{x}+\frac{x}{2x^{2}-x}$

[wraith dagger]

Max

[alpine knot]

$\frac{8x^{2}-4x}{4x^{2}-2x}+\frac{8x}{4x^{2}-2x}+\frac{3\left(4x-2\right)}{4x^{2}-2x}+\frac{2x}{4x^{2}-2x}$

[wraith dagger]

Max

[alpine knot]

$\frac{\left(8x^{2}-4x+8x+12x-6+2x\right)}{4x^{2}-2x}$

[wraith dagger]

Max

[alpine knot]

$\frac{8x^{2}+18x-6}{4x^{2}-2x}$

[wraith dagger]

Max

[alpine knot]

$\frac{4x^{2}+9x-3}{2x^{2}-x}$

[wraith dagger]

Max

[alpine knot]

Is this what you were looking for?

[crimson sedge]

yes

but i still have doubts

[frigid osprey]

max as a helper you need to help the person get to the answer themselves not answer it for them

[crimson sedge]

2z(2z-1)+4z-3(2z-1)+z/2z^2-z

look

[alpine knot]

oh ok

[crimson sedge]

wait

after that

i rearrange it

[alpine knot]

Oh, I just used the wrong variable

[crimson sedge]

by comm. and assoc.

2z(2z-1)-3(2z-1)4z+z/2z^2-z

this is the part where im freaking confused

because i can factor out 4z+z

(2z-3)(2z-1)z(4+1)/z(2z-1)

[frigid osprey]

max find a common denominator

cross multiply

[crimson sedge]

look i can cancel the denominator because i have z(2z-1) in my numerator

and I'm left with

(2z-3)(5)

= 10z-15

[runic nacelle]

Yes if it's this equation

[crimson sedge]

?

[runic nacelle]

The one you got it right

[crimson sedge]

but

[runic nacelle]

But the latex shows a different equation

[crimson sedge]

if i put it up in Google rn

the answer is different

i really need help with this...

is there anyone??

[runic nacelle]

[4z - 6z + 3 + z / 2z-1(z) ] +2

[crimson sedge]

$[4z - 6z + 3 + z / 2z-1(z) ] +2 $

$[4z - 6z + 3 + z / 2z-1(z) ] +2$

[wraith dagger]

Gizmo_siz

[runic nacelle]

[-3/2z-1] + 2

[crimson sedge]

??

[runic nacelle]

$-3 + 4z - 2 / 2z - 1$

[wraith dagger]

Zc

[runic nacelle]

You can do the rest ig

[crimson sedge]

i dont understand

my doubt haven't still been cleared..

[runic nacelle]

Which step?

[frigid osprey]

ok so listen to me and imma take you from the top

[frigid osprey]

out of the z/2z^2-z what can you factor out of that?

specifically the denominator

[crimson sedge]

z(2z-1)?

[frigid osprey]

great

[runic nacelle]

Oh it seems I made a slight mistake

[frigid osprey]

now you have z/z(2z-1) and you can cancel the z

[crimson sedge]

ah nvm i think i found my error in here

(2z-3)(2z-1)+4z+z

that right?

but there's a plus (+)

[frigid osprey]

theres two terms now that have the same denominator, combine the like terms

[crimson sedge]

in here

[crimson sedge]

yea

[frigid osprey]

so you have

[crimson sedge]

4z^2 - 3z + 3

i found my slightest mistake

💀

[frigid osprey]

imma have to write this in paper cause idk how to use the frac bots

[runic nacelle]

Same

[crimson sedge]

same

[runic nacelle]

They mess it up

[crimson sedge]

clearly if you use gpt

Anyway one last question

about

(2z-3)(2z-1)+4z+z

[frigid osprey]

Right?

[crimson sedge]

you can factor 4z+z

[crimson sedge]

yes

[crimson sedge]

= z(4+1)

[runic nacelle]

Yes you can

[frigid osprey]

Don’t get ahead of yourself, take this step by step

[crimson sedge]

should it be (2z-3)(2z-1)z(4z+1) or should it be (2z-3)(2z-1)+z(4+1)?

[crimson sedge]

...

[runic nacelle]

$2z^2 - z + 5z - 6z + 3 / 2z^2 - z$

[wraith dagger]

Zc

[frigid osprey]

Look so you can make a common denominator by multiplying

[crimson sedge]

yeap

well anyway i alr got my doubts

[crimson sedge]

lemme show you mine

[frigid osprey]

ok

[runic nacelle]

Yes you get the above equation if you solve this

$4z^2 - 2z + 5z - 6z + 3 / 2z^2 - z$

[wraith dagger]

Zc

[crimson sedge]

here

that should be correct right?

[runic nacelle]

Yes

[crimson sedge]

i skipped some few thing in there...

[frigid osprey]

You are close but not exact

[crimson sedge]

?

how?

[frigid osprey]

you have some signs wrong

[crimson sedge]

what sign?

[crimson sedge]

i alr did cross out my mistake

[frigid osprey]

Wait no I messed up ignore me

[crimson sedge]

...

brb I'm gonna take out the trash

[frigid osprey]

Ur correct. Mb I actually had a wrong sign.

[crimson sedge]

hehe that's ok

should i close this channel now?

alr

.close

[cedar kiln]

Channel closed

Closed by @grave sphinx

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]

hello

[crimson sedge]

mb wrong channel

.close

[cedar kiln]

Channel closed

Closed by @grave sphinx

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.

[wooden summit]

Can you help me with a question about linear combination

[cedar kiln]

Please don't occupy multiple help channels.

[wooden summit]

find the unique value of
𝑎 that makes a set not a generator of
𝑅3

[cedar kiln]

@wooden summit Has your question been resolved?

[cedar kiln]

@wooden summit Has your question been resolved?

[upper abyss]

Put into a matrix, row reduce. You want the case with less than 3 pivots.

Remember that you cannot divide by 0, so watch out for specific values of a when dividing.

[wooden summit]

so a value that dividing for a is equal zero?

[deep oriole]

no, just that when you divide by certain numbers involving a, make sure it wont be 0, or at least keep account of what values of a your row reducing doesnt work for when you potentially divide by 0

[cedar kiln]

@wooden summit 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.

[open vine]

can someone explain to me the solution? I dont understand how if gamma is an empty set it can be true?cause its saying gamma proves A but how can it prove A if its empty?

[open vine]

.close

[cedar kiln]

Channel closed

Closed by @open vine

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.

[west scarab]

Hello, this is abstract algebra and I would like help on how to prove why U(16) to itself given by the mapping from x to x^3 is an automorphism

[west scarab]

Here is the question

I tried using the four separate steps of an isomorphism to prove that a group G is isomorphic to a group G bar

Don’t know how to prove why it’s operation preserving

[cedar kiln]

@west scarab Has your question been resolved?

[cedar kiln]

@west scarab Has your question been resolved?

[dawn junco]

@west scarab still here ?

[west scarab]

yeah

I just got back

[dawn junco]

aight

[dawn junco]

what are your four steps ? (just to know what they are)

[dawn junco]

do you have a clear idea what it means for that specific mapping to be operation preserving ?

[west scarab]

first step: prove the mapping of a function phi from G to G bar, second step: to prove how the function phi is injective, third step: to prove how the function phi is surjective

last is pretty much operation preserving

[dawn junco]

ok

[west scarab]

sort of

dont know whether it should be phi(a+b) or phi(a*b) for all a and b in G

[dawn junco]

well what's the operation in the group U(16) ?

[west scarab]

oh its multiplication mod n

so in this case it would be multiplication mod 16 then

i dont know how to prove that based on the mapping from x to x^3

[dawn junco]

say phi is that mapping x -> x^3

what's phi(a*b)

what's phi(a)*phi(b)

[west scarab]

hm okay

phi(a * b)mod16 = phi(a)mod16 * phi(b)mod16 for all a and b in G

forgot to mention the mapping from x to x^3

phi(a^3 * b^3)mod16 = phi(a^3)mod16 * phi(b^3)mod16

[dawn junco]

right, drop the phi's, you already computed it here

[west scarab]

ok

[dawn junco]

and you're going a bit fast

[west scarab]

dont know if i have to show anything else

[dawn junco]

phi(a*b) = a^3 * b^3, that's what you're saying ?

[west scarab]

oh

yeah

[dawn junco]

you're gonna have to justify that a little bit

that doesn't follow straight up from the definition of phi

[west scarab]

would i have to show anything else that its an automorphism

i failed this a year ago so i dont remember too much if there were any properties/steps

[dawn junco]

there's no extra steps in your 4 step list I'm adding all of a sudden

[dawn junco]

I'm just not convinced by that part

again, what's phi(a*b) ? just apply the definition of phi, don't do anything else

[west scarab]

ok

To justify, the operation U(16) is preserved under multiplication from the mapping G to G bar for all a and b in G. Phi in this case would be a function defined as an isomorphism mapping onto itself after verifying the four steps.

i honestly suck at abstract algebra so im not that skilled at this yet

[west scarab]

well anyways thanks for the help

i think i had most things figured out

.close

[cedar kiln]

Channel closed

Closed by @west scarab

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.

[runic river]

I am just starting calculus

Can someone send step by step

I tried conjugate but idk what to do after

[austere hull]

!show

[cedar kiln]

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

[short stratus]

The question should be incorrect

Unless you're trying it in the complex plane

[wraith dagger]

xd_senBugha

[runic river]

I got this after the conjugate

[runic river]

How did you get that conclusion

Is it undefined?

[short stratus]

.

[dusky peak]

you want to approach x=0 right? try for a small x, like x=1

you will get a negative in the sqrt

[earnest idol]

its not uhh -3,3 its -inf to -3 and 3 to inf right?

[dusky peak]

senBugha meant that you have R without (-3,3)

[short stratus]

It's the same thing

[earnest idol]

ye i understand mb

[runic river]

I see that it’s incorrect now

How did you guys get the conclusion

Can you figure it out without finding the domain of the numerator thing

[earnest idol]

basically put 0 and the square root is becoming negative

i know its wrong to do that since the limit is becoming undefined

[short stratus]

Put something else really close to 0

[earnest idol]

yeah works as good

[dusky peak]

it's not about the 0, it's about the values close to 0

,w limit of x/x as x approaches 0

[wraith dagger]

Results provided by WolframAlpha

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

Requested by machmut_

[dusky peak]

here we have an example of how the 0 doesn't really matter

[earnest idol]

i know 0+ and 0- blud didnt know what domain was so i just told him to check with 0

[cedar kiln]

@runic river Has your question been resolved?

Channel closed

Closed by @runic river

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.

[tidal sierra]

Can anyone help me with 3.34 and 3.35?

[austere hull]

,rccw

[tidal sierra]

What is that?

[upper laurel]

command to rotate the last posted image counterclockwise

[austere hull]

just rotating the image

[upper laurel]

it stands for rotate counter clockwise

[tidal sierra]

Oh ok

Can you help me with these 2 questions?

[violet flume]

I could help with 3.34

[violet flume]

.

twhat have you tried

[tidal sierra]

Well i tried finding 9! First

Then dividing it with 3! And 4! And 2

That is where I got stuck

[violet flume]

you have to draw one black ball somewhere

lets say it happens first

so first, you draw a black ball.

how many ways can we draw the remaining 2?

[tidal sierra]

2 ways

[violet flume]

no

[tidal sierra]

Oh sorry

[violet flume]

how many balls are there left after we draw the first black ball

[tidal sierra]

7 ways

Divided by

2!

[violet flume]

no

[tidal sierra]

4!

[violet flume]

how many balls are there to start

[tidal sierra]

9

[violet flume]

before we do anything

yea

okay

now we draw one black ball

8 are left

[tidal sierra]

Yes

[violet flume]

now we need to draw 2 more balls

we can draw any of the 8 for the second draw

and now, 7 are left

we can draw any of the seven

[tidal sierra]

I got the question now

1 min let me solve it to get the answer

[violet flume]

there is only one slightly tricky part to check

we might worry that, if we draw the black ball last, we have to restrict the possibilities of the first 2 draws

to make sure there remains a black ball for us to draw on the 3rd draw

is it a concern?

[tidal sierra]

I wouldnt say so

[violet flume]

yea, me neither

because there are 3 black balls

we could draw black - black - black and be fine

so we dont need to restrict anything

[tidal sierra]

Ya

I would have to divide it with 2!,2!,4! Right?

[violet flume]

why?

[tidal sierra]

There is a repetition of 4 red balls and 2 black balls and 2 white balls

[violet flume]

oh are the implied distinct

[tidal sierra]

No

[violet flume]

lemme think

[tidal sierra]

We might get many permutations in the same order

[violet flume]

right

[tidal sierra]

Soo i will divide now

[violet flume]

is this a concern i get the same answer both ways

ohh sorry we need to use 8c2 dont we

[tidal sierra]

No

I dont think so

I got a decimal as the answer

3.5

[violet flume]

ugh this is turning into more f a nightmare than i thought

because some of the ones between black ball second isnt actually distinct

maybe its easier to enumerate all possible combos

and remove the ones with no black balls

[tidal sierra]

Video of my working

[violet flume]

video

[tidal sierra]

Make that a 3.5

[tidal sierra]

What’s wrong

[violet flume]

unusual

[tidal sierra]

Video or working?

[violet flume]

video

im working on a subproblem

[tidal sierra]

Ok

Is my working correct tho

There is an answer for none of the above

[crimson sedge]

the answer will be 3C1 * 8C2

cuz we want to take 1 ball from 3 black balls

[tidal sierra]

Why 8C2 tho?

[crimson sedge]

there are 8 balls left

in which u should take 2

[tidal sierra]

We can permutate and divide it by the no. Of repetitions factorial

[crimson sedge]

no u should use combination here

so the answer is divisible by 7

[tidal sierra]

Can you explain why

[crimson sedge]

8C2 will be = 8!/2!*(8-2)!

= (8 * 7)/2*1

[tidal sierra]

But why are we using combinations

Ok gotta go

Will see later

[crimson sedge]

When selecting items where the order isn’t important, combinations are the right choice.

[cedar kiln]

@tidal sierra 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.

[covert island]

can someone help me determine what lim x-> -3 |g(x) - f(x)| would be

from my understanding this would be the limit as x-> -3 g(x) which is = 1

and x -> -3 f(x) which is 4

so 1 - 4

[blazing zephyr]

yes

[covert island]

and the absolute value of that which is 3

or am i tweaking

[blazing zephyr]

i think so?

[worldly chasm]

That all looks 100% correct to me

[covert island]

but the solutions provided

or the like multiple choice solutions only have 4, -2 , 6, 0, -3

[worldly chasm]

Can you show the question

?

[covert island]

yeah lemme get it

[worldly chasm]

There might be a part that you missed that we might be able to point out

[covert island]

here we are

[worldly chasm]

It's not abs

[livid hound]

those don't look like abs bars

[worldly chasm]

Just square brackets

[livid hound]

just square brackets

[covert island]

oh my god

my eyes

theyve deceived me

[idle rain]

It is quite small to be misleading

[worldly chasm]

Yeah completely understandable

[blazing zephyr]

why do people even use square brackets smh

[covert island]

lmao wait

but then for this one

[blazing zephyr]

looks right

[covert island]

its the same ish concept except now its the limit as x approaches 1 for both functions

[olive wind]

because it is useful to visually distinguish different brackets

[idle rain]

But if you are working with absolute function, your intuition is correct. To further point out, absolute function is continuous. Therefore, limit of absolute of something is absolute of limit of something.

[worldly chasm]

Approaches -1, not 1.

[covert island]

right

my fault

[worldly chasm]

No worries. Just wanted to make sure it was a typo rather than a reading mistake.

[covert island]

These are my last two can y’all just double check it

i think i got the concept im just worried

i made a careless error yk

[worldly chasm]

Lgtm

[covert island]

awesome! any other second opinions

if not imma full send this hw assignment lol

[idle rain]

Looks good

[covert island]

thanks guys!

i really appreciate it

.close

[cedar kiln]

Channel closed

Closed by @covert island

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.

[warped spear]

Hi, I'm not looking to solve an existing equation but rather need help finding it. Also it might be a bit more rudimentary than what this discord is used to..

I hope that's okay and I drew a diagram if my explanation sucks.

I am intending to engineer a box where a push-solenoid (a small electronic piston) will:
push a door of a known length,
with known distance pushed, and distance of the pushing from point of rotation.

With these I hope to find the angle which the door will swing to, ignoring resistance.

Thank you. In the diagram the red represents the unknown variable.

[forest escarp]

can you clarify what you mean by "distance of push"

[warped spear]

imagine you put your finger on a doorknob of your door. you push forward(assuming the door is unlatched), 3 inches. the door probably opens a small amount.

[forest escarp]

ah i see

i think it's just a trigonometric ratio

let the angle be θ

sin(θ) is the distance pushed divided by the distance of the pushing from point of rotation

so to find θ we use the inverse of sine

$$\theta = \sin^{-1}(\frac{d_\text{pushed}}{d_\text{from rotation point}})$$

[wraith dagger]

aZxc

[warped spear]

I think that's all I need. I appreciate the help @forest escarp

.close

[cedar kiln]

Channel closed

Closed by @warped spear

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.

[eternal rain]

I feel like I'm missing something trivial here, but why is the RHS continuous depending on x?

[eternal rain]

I'm aware of the result that the iterated integral of a continuous function is continuous, but that's only for a compact interval. But here the iterated integral is on all of Rn, so why is it still continuous??

[cedar kiln]

@eternal rain Has your question been resolved?

[eternal rain]

need help 😭

<@&286206848099549185>

[meager river]

I don't know much but did you say its true on a compact interval? You do know that R^n is compact by the Heine Borel Theorem?

[eternal rain]

sorry I meant to say bounded interval

[eternal rain]

nvm I got it

.close

[cedar kiln]

Channel closed

Closed by @eternal rain

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.

[ornate radish]

I found that both A and C are false but the mark scheme says that only C is false, where am I going wrong

[ornate radish]

Is it that the lim x-> 2 approaches the same answer from both sides despite the point (2,1) being defined

[jovial anchor]

Yes essentially

[ornate radish]

Ah okay thank you

.close

[cedar kiln]

Channel closed

Closed by @ornate radish

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.

[marble ermine]

hello