help-26

[carmine marten]

yes

sorry

for scalars $\alpha_1,\alpha_2$, any matrices $A_1,A_2$ show that $T(\alpha_1A_1+\alpha_2A_2) = \alpha_1T(A_1)+\alpha_2T(A_2)$? as usual? (maybe you were taught to do it in a few steps, but fundamentally the same)

[thorny flame]

Edward II

[proud idol]

ok, I know this one
This is additivity property of any matrix

No sorry
I meant Linear transformation*

I know i am asking for too much but can you provide me with the written solutions to these questions?
I will grasp it better then... and you'll be really doing me a lot of favor @carmine marten

[carmine marten]

!noans

[topaz sinew]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[proud idol]

Sorry

Well, just explain me how to do it on my own then

[carmine marten]

the part of question 1 I don't really know what else to really say, it's literally just filling in[B(\alpha_1A_1+\alpha_2A_2)B^{-1} = (B\alpha_1A_1+B\alpha_2A_2)B^{-1}=\dots=\alpha_1(BA_1B^{-1})+\alpha_2(BA_2B^{-1})]

[thorny flame]

Edward II

[carmine marten]

using basic properties of matrix addition and multiplication

[proud idol]

Ohhh

[carmine marten]

you might have had this separated into two properties T(A1 + A2) = T(A1+A2) and T(cA) = cT(A) idk, but the two can be combined like this

[proud idol]

So since you could write T(A +B) as alpha T(A) + beta T(B)
So this is closed under additivity and homogeneity right?
That means this is a valid linear transformation correct?

[carmine marten]

yes

[proud idol]

Yes
We were taught the separate way of doing this

[carmine marten]

(up to you forgetting the scalars in one of those)

[carmine marten]

do be careful with notation, because B is already used

[proud idol]

wait,that means the 3rd part of 1 b)
That is not a linear transformation correct?
Since A² + B² != (A+B)²

[carmine marten]

for q3, all the linear maps are given by matrices

[carmine marten]

yes

I would provide a specific counterexample

[proud idol]

Ok, that is clear to me
Please explain the 3rd one now
You said I can use a matrix with n entries to denote n vectors

Where do I go from here @carmine marten

[carmine marten]

I'm saying you can use a matrix (other way around, 1 row n columns) to represent the linear transformation

the entries you find (like in questions 4, 6) by seeing what happens to basis vectors

[proud idol]

can you please write that down?
I didn't quite get what you're trying to say?

[carmine marten]

$\begin{pmatrix} T(v_1) & T(v_2) & \dots & T(v_n)\end{pmatrix}$

[thorny flame]

Edward II

[carmine marten]

where v1, ..., vn is a basis of R^n

oh

and the obvious basis of just (1) for R

[proud idol]

So the basis of R is...?

[carmine marten]

the single vector 1

it is very confusing to write

[proud idol]

Ah right

[carmine marten]

but the number 1

spans R

[proud idol]

yes, I got you now

But how will I write all transformations from this?

[carmine marten]

They're all given by matrices

And all matrices give a linear transformation

[proud idol]

but this matrix has only 1 row?

[carmine marten]

and we're only asked about transformations R^n to R

the transformation is explicitly left multiplying by this / taking the dot product with this, or can be written not as a matrix as

[proud idol]

I lost track.... what do you even mean by this?

[carmine marten]

if you're confused by why matrices is enough

[proud idol]

no like..
What matrix are you even talking about...?
How will it describe all linear transformations?

[carmine marten]

I mean that to any such matrix $A = \begin{pmatrix}a_1 & \dots & a_n\end{pmatrix}$ in the reals, we can associate the linear transformation taking a (column) vector $\vec x = (x_1,\dots,x_n)^T$ to $A\vec x$

[thorny flame]

Edward II

[carmine marten]

what I'm saying is that every linear transformation is of this form

[proud idol]

yes,
That much I know
But what's it got to do with every transformation out there

[carmine marten]

"Find all linear transformations R^n to R"

multiplying by nx1 matrices gives all these transformations

[proud idol]

multiplying what exactly?

[carmine marten]

(column) vectors in R^n

the map $T(x) = Ax$ is linear for each matrix $A$, and the claim is that all linear maps $T:\bR^n\to\bR$ are like this

[thorny flame]

Edward II

[carmine marten]

I have found all the linear transformations from R^n to R: they are given by nx1 matrices in the above way

[carmine marten]

note: I have jumped from any basis to standard basis because that's the one that is nice and obvious and by q4 this gives the same matrix directly

[topaz sinew]

@proud idol Has your question been resolved?

[thorn elk]

i need to ask few questions about syllabus

[topaz sinew]

@proud idol Has your question been resolved?

[proud idol]

Okay, I finally got it now

@carmine marten can you explain me q8 too?

[carmine marten]

I honestly need some time to think about it, but this should be equivalent to showing that if C is invertible if and only the columns of C are linearly independent

the columns 'represent' the basis vectors, and there are n of them so they are linearly independent if and only if they are a basis

[topaz sinew]

@proud idol Has your question been resolved?

[topaz sinew]

@proud idol Has your question been resolved?

[proud idol]

yes
No worries
I got this now

.close

[topaz sinew]

Channel closed

Closed by @proud idol

Use .reopen if this was a mistake.

[topaz sinew]

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[topaz sinew]

@neon iron Has your question been resolved?

[gusty terrace]

@neon iron
a=64 ar^2-ar=20
64r^2-64=20

then go from there

This is because a number in a sequence is a(n)=k (r^n-1) where k is the first term and r is common ration.

[topaz sinew]

Channel closed

Closed by @zealous osprey

Use .reopen if this was a mistake.

[topaz sinew]

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 agate]

Hii, I have a very quick question of functions. If I were to try to write a quadratic equation to calculate when a ball hits the floor when someone tosses it up, can I write:

F(h) = 3 + 14t - 5t^2

[visual badge]

what seems to be the problem?

[wicked agate]

Just wanted to check whether its correct

[abstract wadi]

If h is your height and originally you're tossing it from 3 metres with speed 14m/s upwards, then the expression for h is correct. (notice how you failed to provide all those details)

[visual badge]

i was wondering where the details were

[abstract wadi]

[wicked agate]

Oh, whoops!! Sorry about that

Would I be able to check something else for my understanding?

In the case above, I throw it from 3m with an upwards velocity of 15 m/s

To work on the question, can I write f(h) as f(0) = -5t^2 + 14t + 3

Since I want the function when h = 0?

[abstract wadi]

a. It should be 15t if you're projecting it with 15m/s upwards velocity.
b. you have h = f(t) = 0, yes.

[wicked agate]

yes 15t is what I meant. Thanks!

For b, is f(h) = -5t^2 + 14t + 3 incorrect then?

[topaz sinew]

@wicked agate Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[sweet shadow]

I keep getting the wrong answer. The answer sheet says the answer is 9/2 but I keep getting something else

[sweet shard]

!show

[topaz sinew]

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

[sweet shadow]

I know the integral is wrong in this one. I was just changing the number in desmos

[glacial adder]

it should be +x^2/2

[sweet shadow]

its [-1,2]

oh

would you mind exlpainnig

[glacial adder]

you have to distribute the negative

to the terms inside the parenthesis

so -(3-x) would become -3+x

and then we can integrate

[sweet shadow]

oh okay

what a bout the x values. Would 5 become 5x?

[glacial adder]

or you can keep it as is and just make sure you have the two terms still in the parenthesis

[glacial adder]

everything else looks correct yeah

[sweet shadow]

and 3 into 3x?

[glacial adder]

yep

inverse power rule

[sweet shadow]

gotcha

so I just plugged in the integral and got 11/2

which is what i've been getting but on the answer sheet it says 9/2

[glacial adder]

can you show your work

[glacial adder]

-1 should be in parenthesis

since most calculators take -1^2 as -(1^2)

[sweet shadow]

OMG

LOL

thank you so much

[glacial adder]

ywyw

[sweet shadow]

now quick question about another problem

if you don't mind

[glacial adder]

go ahead

[sweet shadow]

so for this one

I've been trying to figure out what i've done wrong but I haven't been able to get past the first couple steps

lemme get the work

[glacial adder]

what did you do at first

alright

[glacial adder]

you separated the fractions

but you didn’t integrate it

[sweet shadow]

right

[glacial adder]

the second line should still be in the integral

and then you can take the anti derivative

[sweet shadow]

so it would just be the integral from 1 to 2. 6/t^3- 1/t^2?

[glacial adder]

yep

[sweet shadow]

and then i just integrate?

[glacial adder]

exactly

[sweet shadow]

is it first integration - second?

or in a sense. f(2) - f(1)

[glacial adder]

well just integrate it first

term by term

and then plug it in

and yes it’s the upper minus lower

[sweet shadow]

alright just one sec to work it out

hmm maybe im just being daft. but I got -9/2 and the answer sheet says 7/4

[glacial adder]

from here

integrate each term before plugging in

you didn’t integrate yet and plugged it in

[sweet shadow]

so it'd be something along the lines of 6x^4/4-x^3/3?

no. nvm

not that

would you mind just helping me out with that one. I think im going crazy

[glacial adder]

alright so 6/t^3 can be rewritten as what using negative exponents

[sweet shadow]

woudl it be x^n+1?

so it'd be like

t^-2?

[glacial adder]

sort of

so it would be 6t^-3

if we bring it from the denominator to the numerator

we just negate the exponent

and then we can use the power rule

which would give us something with t^-2

but with a constant in the front

[sweet shadow]

right

[glacial adder]

we can also do the same to 1/t^2

[sweet shadow]

over -2 right

[glacial adder]

yep

[sweet shadow]

right so t^-1

[glacial adder]

negative

don’t forget to divide it by negative 1

[sweet shadow]

so t^-1/-1?

[glacial adder]

yep

[sweet shadow]

alrighty

[glacial adder]

which is just -t^-1

[sweet shadow]

right

[glacial adder]

now we can substitute

[sweet shadow]

so it'd be 6(2)^-2/-2 - (-(2)^-1)?

[glacial adder]

yep

then minus when you plug in 1

[sweet shadow]

frick yes

I really appreciate you

[glacial adder]

you’re welcome

[sweet shadow]

.close

[topaz sinew]

Channel closed

Closed by @sweet shadow

Use .reopen if this was a mistake.

[topaz sinew]

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.

[burnt pumice]

Hi is it possible to turn 9pisqrt2 to become 9sqrt2pi?

[neon iron]

,, 9\pi\32=9\3{2\pi}

[neon iron]

is this what you mean

[burnt pumice]

Yes

Is it possible to manipulate it to do that

[neon iron]

uh it's not true

!xy

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[burnt pumice]

Okay cause I’m trying to find surface area of this rotated on the y axis and I get that instead

But the answer is supposed to be 9*sqrt2pi so I’m assuming I did something wrong

[lost thunder]

rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeerrrrrrrrrrrr

Hola

[burnt pumice]

Hello

.close

[topaz sinew]

Channel closed

Closed by @burnt pumice

Use .reopen if this was a mistake.

[topaz sinew]

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 pond]

Can someone jelp 2B and C bruh

I dont get it jow are they right angled??

[potent lark]

Can someone solve this puzzle?
Hint.: Scott Pearly

[wooden osprey]

OA is perpendicular to the plane ODE

therefore OA is perpendicular to all lines belonging to ODE

[ocean terrace]

this is a help channel..

[topaz sinew]

@carmine pond Has your question been resolved?

[wooden osprey]

h yeah bot is back

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[granite rampart]

How

[neon iron]

shouldnt the answer be 9C5 since every card has 1,2 or 3

[cursive patrol]

108 is correct

[granite rampart]

I don't know the solution process

[cursive patrol]

ik u said that

i was talking to other person who say they think answer is 126

[neon iron]

but the question said at least 1 card tho

[granite rampart]

oh ok

[neon iron]

you can choose anything and its valid

[cursive patrol]

i would consider this problem by using cases…

you are picking 5 cards, and you need to pick at least a card of 1, 2, and 3

then, you can count the number of ways by adding the cases (spoilered hint) ||card number combinations can be 11123, 12223, 12333, 11223, 11233, or 12233||

alternatively you can do this problem using complementary counting but still the answer is achieved using a very similar method (i.e. similar style of casework)

[neon iron]

??

[cursive patrol]

Lion 1, Rabbit 1, Tiger 1, Lion 2, Rabbit 2

is not a valid combination

for example

[neon iron]

it said one card

[cursive patrol]

at least one card each is what the problem means

this is evident because the condition would make zero sense otherwise

[neon iron]

ok then

[granite rampart]

Cards with numbers 1 2 3 must come together. The pattern doesn't matter

[neon iron]

i think the best way is to consider the cases where you dont pick all 3 numbers : which is 9C5 - 3 * 6C5

9C5 is the total number

3 is which number to exclude : so (1,2) , (2,3) , (1,3)

[neon iron]

and 6C5 comes from picking numbers that arent excluded

@granite rampart

[topaz sinew]

@granite rampart Has your question been resolved?

Channel closed

Closed by @granite rampart

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.

[wild tapir]

Got this correct but I just wanted to think about it more, does anyone know how I can find this domain of integration as a multi-variabled function so I could plot it? I have an idea of how it looks but I would like to confirm my understanding

[topaz sinew]

@wild tapir Has your question been resolved?

[topaz sinew]

@wild tapir Has your question been resolved?

[desert peak]

The integration set is:

$D={ (x,y,z) \in \mathbb{R}^3 : x \in [-1,1],-\sqrt{1-x^2}\leq y \leq \sqrt{1-x^2}, 0 \leq z \leq \sqrt{x^2+y^2}}$

[thorny flame]

cristorenzo99

[desert peak]

It should be the same as:

$D={(x,y,z)\in \mathbb{R}^3 : -1 \leq x \leq 1, y^2 \leq 1-x^2, z^2 \leq x^2 +y^2}$

[thorny flame]

cristorenzo99

[desert peak]

You could plot it using Geogebra maybe

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[mild hearth]

what is the median, in terms of F_X

can you say it more algebraically though

[sweet shard]

the data you gave is discrete. you need the definition for continuous

[mild hearth]

look up how to define the median in terms of F_X

[sweet shard]

https://brilliant.org/wiki/continuous-random-variables-cumulative/

[topaz sinew]

Channel closed

Closed by @dark pond

Use .reopen if this was a mistake.

[topaz sinew]

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.

[noble totem]

How to integrate the following

[noble totem]

2sin(5x) sin (3x)

[sweet shard]

,tex .prod2sum

[thorny flame]

riemann

[noble totem]

Oh

Wierd this wasn't on my math book formulas

Quite annoying to be honest

[noble totem]

Thx

[sweet shard]

it's in most trig/precalc books, taught before calculus

[topaz sinew]

@noble totem Has your question been resolved?

Channel closed

Closed by @noble totem

Use .reopen if this was a mistake.

[noble totem]

.reopen

[topaz sinew]

✅

[noble totem]

Well there's too many trig formulas to be entirely fair

[sweet shard]

ok???

[noble totem]

K

Thx

.close

[topaz sinew]

Channel closed

Closed by @noble totem

Use .reopen if this was a mistake.

[crystal goblet]

You should also remember the proofs if that helps

[noble totem]

Hmm ill go check that

Thanks anyways

[crystal goblet]

It did personally for me

[topaz sinew]

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.

[rough axle]

Looking for my solution to be verified

[mild hearth]

,rotate

[mild hearth]

looks right

wait no

-90 should be -105

but the rest is right

[rough axle]

on the cast diagram?

oh the x value

I see now

not sure how I managed that

. close

.close

[topaz sinew]

Channel closed

Closed by @rough axle

Use .reopen if this was a mistake.

[topaz sinew]

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.

[lunar creek]

The question says this is a parallelogram. Therefore can I do distanceBA=distanceDC and distanceBD=distanceAC to get two equations and then isolate the unknown terms?

[lunar creek]

I know that there's a different way to solve this, but I came up with this possible resolution and wanted to know if it makes sense

since its a parallelogram the distance of the vertices of the opposite sides (which are equal) should be the same? right?

[topaz sinew]

@lunar creek Has your question been resolved?

[rigid ivy]

What do you mean exactly?

Here's an easier-to-read graphic

[lunar creek]

so, BD = AC

and DC = BA

cause it's a parallelogram, right?

[rigid ivy]

correct

[lunar creek]

therefore the distance from the points B,D and A,C must be the same; Just like the distance from the points D,C and B,A right?

[rigid ivy]

The length BD is, by definition, the distance between the points B and D, yes

[lunar creek]

With that being said, I can use that to come up with two equations and then find A and B, right?

[rigid ivy]

yeah sounds good

[lunar creek]

that was my doubt, thanks

.close

[topaz sinew]

Channel closed

Closed by @lunar creek

Use .reopen if this was a mistake.

[rigid ivy]

@lunar creek there is a much easier way to find point A though

DC is parallel to BA, so they have the same rise over run

[lunar creek]

you mean the same angular coefficient?

[rigid ivy]

not even that

just the same rise over run

From D to C, the change in x coordinates will be the same as from B to A, and same with y coordinates

[lunar creek]

ah, this?

[rigid ivy]

yes

But I should've said "same rise and same run"

[lunar creek]

Nice, didn't know this way of solving this

[rigid ivy]

the slopes are indeed the same for both lines, but because the lines have the length, the change in y and change in x is the same for both lines

[topaz sinew]

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.

[static jacinth]

When building a completion of $\mathbb{Q}$, it can employ Cauchy sequences. Call $C$ the ring of Cauchy sequences over $\mathbb{Q}$ and call $N$ the ideal of sequences that tend to zero. $N$ is maximal, so then the quotient $C/N$ is a field. Now, some of the proofs I'm reading usually say someting among the lines "Let $\lambda \in C/N$ and let it be represented by $(x_n) \in C$". Does this depend on the axiom of choice when saying this for uncountably many lambdas?

[static jacinth]

I think it can be avoided by working with lambda directly, but invoking a representative for each lambda seems choice-y, but it also lets me work over rational sequences instead

[thorny flame]

Casiel368

[topaz sinew]

@static jacinth Has your question been resolved?

[static jacinth]

<@&286206848099549185>

[mild hearth]

probably you should try one of the more advanced channels like #groups-rings-fields

[odd pagoda]

yeah I think that should need axiom of choice. just like for example picking a set of representatives of the quotient group R/Q requires AC. but I am no expert on that kinda stuff

I never thought about this construction being a factor ring. thanks for that

[static jacinth]

It's kind of disappointing that the proof of existence of these things relies on AC

[odd pagoda]

well the thing still exists

or which specific thing do you mean right now

when would you ever care about having a set of representatives of C/N

[static jacinth]

Here the construction is meant for p-adics, so no Dedekind cuts will avoid AC

[static jacinth]

To prove that it's unique up to unique isomorphism

I need a function that maps elements from one field to another, and so it is necessary to have a representative for each element in the quotient

I don't mean to xy by any means though, I felt like somehow a choice function can be found in these kind of cases

[odd pagoda]

maybe but I wouldnt know how a choice function could look like. as noted before, better to go into the advanced channels with this

[static jacinth]

Got it. Thank you

.close

[topaz sinew]

Channel closed

Closed by @static jacinth

Use .reopen if this was a mistake.

[topaz sinew]

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.

[royal sky]

i did b-a/n

and multiply that by -42 -37-25-6+15+36 for the lower estimate

im not sure what i did wrong

[topaz sinew]

@royal sky Has your question been resolved?

[weary crystal]

almost, just ignore the 36

you need to look at each interval and determine which value is lower on each

[royal sky]

yes sorry 36 ignored

[weary crystal]

oh i see

[royal sky]

the answer i gave did ignore 36

and its wrong

[weary crystal]

I just plugged it in and got -475

what was your (b-a)/n?

[royal sky]

yeah mb i put 6/25 instead of 5/25

.close

[topaz sinew]

Channel closed

Closed by @royal sky

Use .reopen if this was a mistake.

[topaz sinew]

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.

[rotund gust]

how to set up this question?

[topaz sinew]

@rotund gust Has your question been resolved?

[topaz sinew]

@rotund gust Has your question been resolved?

[steady quarry]

here's a diagram

theta is the angle subtended, theta1 is the angle from horizontal to the line between the eye and the bottom of the picture, and theta2 is the angle between horizontal to the line between the eye and the top of the picture

theta = theta2 - theta1

derive expressions for theta1 and theta2 using trig

then its a straightforward optimization problem

[rotund gust]

thank you

[topaz sinew]

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.

[ember glade]

can someone help with this

[neon iron]

what have you tried

use the definition of modulus

[gusty bane]

are you allowed to use the triangle inequality?

[ember glade]

u mean |x| = |root(x^2)| ?

[neon iron]

$|x| = \sqrt{x^2}$

[thorny flame]

45

[ember glade]

not sure bc its not even in the textbook im using

[ember glade]

when u do proofs do u start off with one side to get the other side of the equation or what

[topaz sinew]

@ember glade Has your question been resolved?

[sweet shard]

What has the textbook covered then

[ember glade]

its covered the definition of modulus

and also

these properties

[topaz sinew]

@ember glade Has your question been resolved?

[cursive patrol]

ah that third one is the triangle inequality

[ember glade]

ah ok yeh mb

how do u use it to prove the statement?

[cursive patrol]

you notice that what you’re trying to prove is extremely similar to the triangle inequality

[topaz sinew]

@ember glade Has your question been resolved?

[topaz sinew]

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.

[desert dagger]

whats the method of doing this?

[crystal goblet]

What would a general term of the expansion look like?

Hint:||use the binomial theorem||

[desert dagger]

Tr+1 = (nr) (8x^3)^n-r(-1/2x)^r

[desert dagger]

is it this^

[crystal goblet]

Right, and you want to have a constant term in the expansion

So what would the exponent of x be in a constant term?

[desert dagger]

can you give an example of a nonzero constant term

[crystal goblet]

6

[desert dagger]

like ax^2 + bx + c where c is a non zero constant term right?

[desert dagger]

0 i think

[crystal goblet]

Yes c will be a nonzero constant term as long as c≠0

[crystal goblet]

Yes

So make the exponent of x =0

[desert dagger]

3n-3r=0?

[crystal goblet]

No,3(n-r)-r=0

You forgot to take into account the (-1/(2x))^r

[desert dagger]

,rotate

[desert dagger]

Isn’t it this?

[crystal goblet]

It is

[desert dagger]

How do we equate exponent of x to 0

[crystal goblet]

3n-3r-r=0

[desert dagger]

Okay

3n-4r=0

[crystal goblet]

Now you want to find integer solutions to this, and n≥r≥0

[desert dagger]

But we have to variables

[crystal goblet]

Calm down

[desert dagger]

2 variables *

3n=4r

N=4r/3

[crystal goblet]

N=4 and r=3 satisfies this

[desert dagger]

Yes

[crystal goblet]

From this, you can see N=4k and r=3k , k≥1also satisfies the equation

[desert dagger]

How do we get this?

[crystal goblet]

3(4k)=4(3k)

[desert dagger]

Ok yes got it

[crystal goblet]

So you have a set of values of n which have nonzero constant term

The set S={n | n=4k, k≥1, k integer}

[desert dagger]

But all possible values

This is the set for n

Got it

[crystal goblet]

So all possible values would be {4,8,12,...}

[desert dagger]

But this goes till infinite right

[crystal goblet]

Yes

[desert dagger]

So it’s better if we give the answer in the set format

[crystal goblet]

Yes that's why I wrote this

[desert dagger]

Okay ty for the help

.close

[topaz sinew]

Channel closed

Closed by @desert dagger

Use .reopen if this was a mistake.

[topaz sinew]

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[dim panther]

https://www.toppr.com/ask/question/if-the-middle-points-of-the-sides-of-a-triangle-are-1123-and-32-find/

[dim panther]

How come they r finding the centroid from the middle points?

Don't we use the coordinates of vertices to find the centroid?

[loud oasis]

the triangle formed from the midpoints has the same centroid as the larger triangle

[topaz sinew]

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.

[neon iron]

anyone help me

[wooden osprey]

,rccw

[neon iron]

according to the diagram i gave AB is parrallel to CD and AB is parrallel to EF . Find the measure of DAE

,rccw

woow

,rccw

,rccw

[wooden osprey]

sir

[neon iron]

,rccw

[neon iron]

Dont call me sir

How to do 😦

https://tenor.com/view/miserable-crying-sad-tears-black-guy-gif-12326280655494835815

<@&286206848099549185> Ayooooo help me

[wooden osprey]

!15min

[topaz sinew]

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.

[neon iron]

https://tenor.com/view/sad-gif-13261737358986789359

[neon iron]

seb help meee

,rccw

[neon iron]

<@&286206848099549185>

this question is super easy but i was absent when maam teach this

[restive birch]

DAE = DAB - EAB

DAB = 80 (alternate angles on parallel lines)

you could construct a line at like FB

then the shape would be 4 sided polygon meaning the interior angle sum is 360

90 + 90 + 125 + EAB = 360

[neon iron]

hmm

[restive birch]

EAB = 55

so DAE = 80 - 55

= 15?

[neon iron]

idk

[restive birch]

or easier

since EF and AB are parallel lines

FEA + BAE = 180

since they are co-interior angles

[neon iron]

i unDerstand

[restive birch]

125 + BAE = 180

alr

[neon iron]

o

/close

/lose

/close

[swift hinge]

.close

[restive inlet]

!done

[topaz sinew]

If you are done with this channel, please mark your problem as solved by typing .close

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[weary wagon]

Hey guys, my weak mind can't figure out how to calculate something:

So, George comes to me and gives me 50.000 fake bananas, i tell him that i can turn these fake bananas into real bananas but i will take a percentage of these bananas as a payment.
So i take his 50.000 fake bananas, in the meantime, on my own, i harvest 100,000 fake bananas, so now in total i have 150.000 fake bananas, 50.000 of which are George's.
I finally decide to turn these bananas into real ones, so i go to Mr. Cool. Mr. Cool is capable of turning fake bananas into real bananas but he will keep the 50%.
After finally converting the fake bananas into real ones, first i keep the remaining amount of MY bananas that i harvested, so now the remaining bananas are George's.
I go to George with the real bananas, but before giving them to him, i take 20% of his remaining bananas as payment as i said before.
So, how many real bananas did I and George get?

[fair thorn]

@weary wagon

you mean 50,000 right

not 50 = 50.000

[weary wagon]

50,000 yes

[fair thorn]

okay

so mr cool takes 50% of the fake bananas?

so u have 75k left

[weary wagon]

Yes

[fair thorn]

that's less than 100,000

[weary wagon]

Like, how many bananas remain of my previous 100,000 ones

I hand to Mr.Cool 150,000 fake bananas

100,000 of which are mine, and 50,000 are George's

Percentages are my weak point

Wait maybe my mind had a realisation

So, 66.67% of 150,000 is 100,000

66.67% of 75,000 is around 50,000

Oh my god wait am i that stupid

Ok...

.close

[topaz sinew]

Channel closed

Closed by @weary wagon

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.

[final wren]

Hello,
I need to prove that all checkerboard matrices are diagnoalizable.
(checkerboard matrix = aij = 1 if i-j is even, aij = 0 otherwise)
So, for instance, This is a 5x5 checkerboard matrix:
$\begin{pmatrix}1&0&1&0&1\ :0&1&0&1&0\ :1&0&1&0&1\ :0&1&0&1&0\ :1&0&1&0&1\end{pmatrix}$

[thorny flame]

sloppymope

[final wren]

I tried finding eigenvalues and eigenvectors but I couldnt really see where it was going

[woeful stone]

Why don't you use matrixcalc?

[final wren]

wdym?

I want to prove for a general checkerboard matrix

[woeful stone]

Ahh I see

Have you considered mathematical induction?

[final wren]

I thought about that , base is easy but I couldnt really complete the step.
I can show my full work but in a nutshell what I tried to do was to assume for n, prove for n+1.
So given B nxn matrix we know its diagonalizable so we take the P such that PBP^1 is diagnoal then we try to do smth to P to create an n+1xn+1 matrix that will diagonalize an n+1 x n+1 matrix but I didnt really know how to do that

[topaz sinew]

@final wren Has your question been resolved?

Channel closed

Closed by @final wren

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.

[quaint mesa]

How was the chain rule historically proven?

I.e-

$\frac{d}{dx}[f(g(x))]=f'(g(x)) \cdot g'(x)$

Where f' and g' represent the derivative of f and g respectively.

[thorny flame]

The Prophet Of The Damned

[outer portal]

https://hsm.stackexchange.com/questions/762/when-how-were-the-product-and-chain-rules-first-proved

[quaint mesa]

alright thank you

.close

[topaz sinew]

Channel closed

Closed by @quaint mesa

Use .reopen if this was a mistake.

[quaint mesa]

how do I close

fuck

.close

.close

[topaz sinew]

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.

[neon iron]

Hey how do I do these?

[craggy haven]

(f + g)(x) is f(x) + g(x)

plot each point, so plot a point at x = -5, x = -4, x = -3, x = -2, etc

[neon iron]

So pick a bunch of points, input them, get an output and plot the outputs?

[craggy haven]

yes

you should plot more points than you think you need

[clear lodge]

they generously made the functions be lines, which change on the same points

[craggy haven]

until you understand which ones are unnecessary

[neon iron]

Will I be fine if I only pick the exact points? Ex : 5, 2 , 3

Or do I need to do like the fraction (half,Quarter) points as well?

[clear lodge]

you will need x=-3, x=0, x=3, and at least two more points to the left and right

[neon iron]

Am I doing this right?

[craggy haven]

i don't understand the last column

[neon iron]

When x is -3, f is 3 and g is -2

[craggy haven]

yeah so you add them and get 1

why did you write down (-3, -2)?

[neon iron]

That’s an error, oops

Oh.. what have I done

I always make silly mistakes like this

Idk how

I know what I’m doing tho

Hold up

[craggy haven]

i don't understand the first part of those ordered pairs either

particularly the last three rows

[neon iron]

I just noticed that as well….

It should be 3,4,5 the last three ordered pairs (x vals)

I’m so stupid idk how I keep making all these silly mistakes

[craggy haven]

that's okay, you're learning

once you get comfortable with it you'll find that you need the chart less and less

but for now it's good to be explicit so you can retrace your steps

[neon iron]

Ok… so are these ordered pairs I have enough.. I picked the exact points that I saw since I’d rather not have to plot/deal with fractions… but do you think I need more x values to the left and right of -3 and 3?

[craggy haven]

you should do one to the left of -3 yeah

[neon iron]

Okay I’ll do -4.5

Ok I think these are enough points, one more to right is unnecessary…..

Ok… so I now just plot these and I get my (f+g)(x) line yeah?

[craggy haven]

yeah (except that's not -8/2)

[neon iron]

-9/2

[craggy haven]

i think you mean -9/2 but honestly just write -4.5

[neon iron]

Okay

Idk how I making all these stupid silly mistakes

[neon iron]

.

[craggy haven]

yeah go ahead

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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.

[clear knot]

i need a savior

[sweet shard]

!show

[topaz sinew]

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

[clear knot]

(a) Bernouii(0.10) since Bob TikTok chance 10%
(b) The total # of viral Tiktoks out of the n=100 posted ones since its basically adding the X's up based on if X=0 (not viral) or X=1 (viral)
(c): ????? What does sample distribution even mean? I know intuitively the meaning but adding algebra makes it so much harder, why is it so much letters? Need to find example of same problem or else I am lost

[sweet shard]

https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/what-is-sampling-distribution/v/introduction-to-sampling-distributions

https://online.stat.psu.edu/stat500/lesson/4

[topaz sinew]

@clear knot Has your question been resolved?

[clear knot]

so this will look like a normal distribution since there are enough observations n=100 to make it look towards normal by the central limit theorem ? the thing now is I am not sure what the mean and standard deviation of this normal distribution will be;

[clear knot]

<@&286206848099549185>

how do i find sampling distribution of sum of Xi ?

each Xi is bernoulli(0.1)

[topaz sinew]

@clear knot Has your question been resolved?

[crude anchor]

I’m pretty sure that the sampling distribution is binomial

Since Y is essentially the sum of n Bernoulli random variables

Meaning Y should be binomially distributed

You can’t really invoke CLT since that would be an approximation and it ask for the exact sampling distribution

At least that’s how I read the question

So I believe that Y has a binomial distribution with n = 100 and p=0.1

Or I guess you would leave n as is, but when you estimate p in part d you set n = 100

[clear knot]

Would final answer for c be something like this then?
Sampling Dist: nXbar = Y ~ Bin(100,0.1).
PMF: P(nXbar = Y = v) = (100 choose v) (0.1)^v (0.9)^(100-v)

[crude anchor]

I believe

[clear knot]

Can u check my work on the rest?

(d) (X1+X2+...+X100)/100
(e)
{p hat > u} = percent of viral tiktoks that are more than u
{n X bar > v} = number of viral tiktoks more than v
(f) u = v/n
(g) p hat > 0.20, or v > 20
(h) Sum from 21 to 100 of (100 choose v)(0.1)^v(0.9)^(100-v) ~= 0.00081

or can a <@&286206848099549185> check it* to not put you on the spot

[sweet shard]

Google "sum of Bernoulli random variables"

[clear knot]

bin(100,0.1)

[clear knot]

helllo?

<@&286206848099549185>
p hat is (X1+X2+...+X100)/100

[clear knot]

<@&286206848099549185>

.close

[topaz sinew]

Channel closed

Closed by @clear knot

Use .reopen if this was a mistake.

[clear knot]

.reopen

[topaz sinew]

✅

[clear knot]

is p hat equal to X bar in statistics?

<@&286206848099549185>

[topaz sinew]

@clear knot Has your question been resolved?

[topaz sinew]

@clear knot Has your question been resolved?

[clear knot]

<@&286206848099549185> let X1, X2, ..., Xn ~ N(0,1) what's the sampling distribution of X bar?

my friends say it is different answer than N(0, 1/n)

N(0, 1/sqrt(n))

[opal vault]

N(0,x) where x is the variance or std?

[clear knot]

The two main parameters of a (normal) distribution are the mean and standard deviation

[opal vault]

so the thing on the right is std

and not variance

correct?

[clear knot]

so we can choose whether it's std/variance?

then my professor just sucks then

[opal vault]

nonono

the usual thing

is that x is the variance

and NOT the std

[clear knot]

the o^2 is the variance i believe

and the o is the std

[opal vault]

exactly

[clear knot]

yep

but in this case it doesn't matter, right?

[opal vault]

so 1/n is your variance correct?

[opal vault]

it DOES

because i want to know if your 1/n represents variance or std

[clear knot]

ok since o^2=1/n

then yes it is variance

[opal vault]

then it's correct

[clear knot]

which?

1/n or 1/sqrt(n)

[opal vault]

yours

1/n

[clear knot]

also, tbh, i forgot how to even start this problem

i only have the answer but i didnt remember the process LOL

Because Now i am looking

[opal vault]

X1 + X2 ... + Xn ~ N(0,n)

[clear knot]

in this case then it looks like the answer should be 1+1+...+1 n times

[opal vault]

so dividing by n divides the variance by n^2

[clear knot]

(0, n/n) = (0,1)

[opal vault]

:(

[clear knot]

is that just a property to memorize?

[opal vault]

of course

$\mathbb{V}[aX+b] = a^2\mathbb{V}[X]$

[thorny flame]

rafilou2003

[clear knot]

im going to fail this class bro

[opal vault]

you can find this again

you use that the expectation (mean) is linear

and the def of variance

[clear knot]

Ah yes i know that

But variance is different

right

Var(aX+bY)=a^2Var(X)+b^2Var(Y)

[opal vault]

only for X and Y independent

otherwise there's some 2abCov(X,Y)

but it's pretty easy to see right?

like a^2 + 2ab + b^2

acts almost like trinomial

[clear knot]

Nah, it's not obvious at all

I'll just memorize it though

Ok so in our case (1/n) Var(X)

[opal vault]

huh

X1 + X2 ... + Xn ~ N(0,n)

so Var(X1 + X2 ... + Xn) = n

we want Xbar

[opal vault]

like Var(X1)?

in that case I would say yes

[clear knot]

X1 + X2 ... + Xn ~ N(0,n <- [since we add the variances of X's which is 1 up to n] )
so Var(X1 + X2 ... + Xn) = n <- {showed before}

to find X bar's variance we divide the stuff inside the variance by n but by rule it needs to divide by n^2 since Var(aX) = a^2Var(X)

Then final answere is N(0, 1/n)

[opal vault]

Yes

[clear knot]

.close

[topaz sinew]

Channel closed

Closed by @clear knot

Use .reopen if this was a mistake.

[topaz sinew]

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.

[muted temple]

,rccw

[muted temple]

try substituting 5^x with a

[prime forum]

so like a^2-12a+35=0

then solve?

[muted temple]

yea

[prime forum]

ok got it ty

[muted temple]

after solving for a, substitute 5^x again

[topaz sinew]

@prime forum Has your question been resolved?

Channel closed

Closed by @prime forum

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.

[placid drum]

\

[acoustic plover]

just take e^bx common from denominator

[placid drum]

wait what

[acoustic plover]

sorry english is not my first language we call it taking common here

taking common as in:
e^bx(Ae^-bx+1)

do you get why A has the coeffecient e^-bx?

[placid drum]

so $L(x)=\frac{600e^{bx}}{A+e^{bx}}\cdot\frac{\frac{1}{e^{bx}}}{\frac{1}{e^{bx}}}$

[thorny flame]

Jash

[acoustic plover]

yea exactly

[placid drum]

oh the top cancels out

in the bottom u can distribute it into each term

so u get A/e^bx+1

[acoustic plover]

yup

[acoustic plover]

Ae^-bx+1

[placid drum]

ok ty

.close

[topaz sinew]

Channel closed

Closed by @placid drum

Use .reopen if this was a mistake.

[topaz sinew]

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.

[humble chasm]

So i have 2 reasonings and i get two answers, the one i posted is my second reasoning. I just want to confirm my understanding of the problem and why one way is the correct way. I first explain my 2nd reasoning which is what you see above. So my reasoning is given i have 2 temps and it takes 11 minutes to go from one to another i just use algebra and plug it into the equation i derived in the 4th image where ln[t-70] is on the left side. and then i pull out k and plug t2-t1= 11minutes and divide it to get my K. This makes sense since i dont have the rate it cools at.
My next reasoning makes sense but i believe i doesnt yield the correct answer in part b: My reasoning behind it is i assume the rate is (85.7 - 81.3)/11 = 4.4/11 is my rate thus all i did was i took 98.6 - 4.4 and said at T(11) = 94.2 and solved for K after i solved for C using T(0) = 98.6
My question is which reasoning is correct here? my curent assumptions i the 2nd reasoning since in reality the 11minutes might not be some rate?

[mild hearth]

don't post in someone else's channel

[humble chasm]

he fixed it

we happend to post at same time

[mild hearth]

ok

[humble chasm]

you able to help with the my reasoning

[mild hearth]

i'm looking at it

[humble chasm]

oh thank you very much

[mild hearth]

i think the problem is you using (T_2 - T_1)/(t_2 - t_1) to get the rate K

because this assumes that the rate of cooling is constant

it's assuming a linear thing

but you want an exponential thing

so what you should do is assume like T(t) = a + be^-Kt

[topaz tulip]

i have a simple problem, anyone care to take a look at it?

[mild hearth]

and then plug in T(0) = 98.6, T(c) = 85.7, T(c+11) = 81.3

and that should give you a, b, K

[humble chasm]

i see

interesting

yea what i did was, T(t1) = 85.7 - T(t2)=81.3

i wonder if that yields same resutls

i'll try it

because it sounds like the same thing

i'll give it a try

thank you

[topaz sinew]

@humble chasm Has your question been resolved?

Channel closed

Closed by @humble chasm

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.

[green sierra]

how come can i say that $\text{If } \mathbf{x} = \mathbf{x}(q^i)\text{, then }\dfrac{d}{dt}\dfrac{\partial \mathbf{x}}{\partial q^i} = \dfrac{\partial \dot{\mathbf{x}}}{\partial q^i}$

[thorny flame]

tannhaus

[steady quarry]

one is taking the derivative with respect to qi then with respect to t, the other is taking the derivative with respect to t then with respect to qi

but order of differentiation does not matter

so they're equal

[green sierra]

why the order doesn't matter tho?

i know partial derivatives usually commute

but it's weird that partial and total derivatives are commuting

[sweet shard]

Depends on the assumptions of x, q_i

If x doesn't depend on d/dt ( q_i) then you can prove it by taking the total derivative of x wrt to t, then partial derivative wrt to q_i. If x does depend on d/dt(q_i), then it's also true, just the proof is longer

https://math.stackexchange.com/questions/3830737/when-do-total-and-partial-derivatives-commute

[topaz sinew]

@green sierra Has your question been resolved?

Channel closed

Closed by @green sierra

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.

[shut obsidian]

Why does $\int e^{-\frac{x^2}{2}}\dd x$ look like this?

[shut obsidian]

Why does it not go up on the left again

[noble laurel]

What kind of explanation are you looking for?

[shut obsidian]

After all the oriented area under the function is positive there

[mild hearth]

e^(-x^2/2) is positive everywhere

so if you go more and more left

you're taking away more and more positive area

so it's decreasing

[odd pagoda]

well desmos decided to choose a constant of integration so that the integral can be negative

hopefully if you actually asked it $\int_{-\infty}^x f dx$ then it wouldnt look like that

[thorny flame]

Denascite

[shut obsidian]

Oh

[chilly walrus]

it helps to rewrite the integral as $F(x)=\int_0^x e^{-\frac{t^2}{2}}dt$

[thorny flame]

artemetra

[chilly walrus]

as x grows the integral 'accumulates' more area

going in the other direction, the area is taken away

[shut obsidian]

Is there any way we can determine the zero

It looks like it's at -c

And it looks like that's always the case

Is there a better justification?

[chilly walrus]

doesn't work when c = 50

[odd pagoda]

if c is big enough then it has no zero. so thats definitely false

[shut obsidian]

Oh

c has to be between -sqrt(pi/2) and sqrt(pi/2)

According to WA's limit

[mild hearth]

let an indefinite integral of a function f(x) be F(x)

integral from -infinity to x of f(t) dt = F(x) - F(-infinity)

you want to know when F(x) = 0

so that's when integral from -infinity to x of f(t) dt = -F(-infinity)

so it's dependent on what -F(-infinity) is

[pastel salmon]

the function is classical cdf of N(0,1) adn it shu dlook this way:

[shut obsidian]

What's cdf

[chilly walrus]

you'll need https://mathworld.wolfram.com/InverseErf.html

[pastel salmon]

dystrybuanta rokladu normalnego

[shut obsidian]

cumulative density function I guess?

[pastel salmon]

yes correct

[shut obsidian]

Thanks

.close

[topaz sinew]

Channel closed

Closed by @shut obsidian

Use .reopen if this was a mistake.

[shut obsidian]

Oh wait

.reopen

[topaz sinew]

✅

[chilly walrus]

essentially you need to solve
$\sqrt{\pi}\frac{\erf(\frac{1}{2}\sqrt{2}x)}{\sqrt{2}}+C = 0$

[thorny flame]

artemetra

[chilly walrus]

which transforms to $\erf(\frac{1}{2}\sqrt{2}x) = -C\frac{\sqrt{2}}{\sqrt{\pi}}$

[thorny flame]

artemetra

[chilly walrus]

which transforms to $x = \frac{2}{\sqrt{2}x}\erf^{-1}({-C\frac{\sqrt{2}}{\sqrt{\pi}}})$

[thorny flame]

artemetra

[chilly walrus]

ta-da @shut obsidian

good luck evaluating that tho lol

[shut obsidian]

Lol, thanks

So here, we had $J_u$

That means the integral function with lower bound u

[shut obsidian]

And we had an upper bound of x I guess, right?

[chilly walrus]

what's J ?

[shut obsidian]

integral function

$J_u(x) = \int_u^x f(t) \dd t$

[chilly walrus]

otherwise erf is defined for all reals

[shut obsidian]

We had $J_u(x)$ with $f$ defined as $f(t) = e^{- \frac{t^2}{2}}$

Right?

[chilly walrus]

i see

yea

[shut obsidian]

Now the exercise asks how $J_u(-u)$ would look like

E.g. is it strictly monotonic increasing etc.

Should be yes, right

Just like J_u(x)

[chilly walrus]

so $J_u(-u) = \int_u^{-u} f(t) \dd t$

[thorny flame]

artemetra

[shut obsidian]

Yes

Wait sry

I meant J_{-u}(u)

So -u and u is changed there

[chilly walrus]

so $J_{-u}(u) = \int_{-u}^{u} f(t) \dd t$

[thorny flame]

artemetra

[chilly walrus]

this is nicer

[shut obsidian]

Yes

[shut obsidian]

How can we imagine that though

f being the function from before

[chilly walrus]

well i know how that function would look like

[shut obsidian]

$f(t) = e^{- \frac{t^2}{2}}$

[shut obsidian]

How?

[chilly walrus]

almost like the integral you had already

it needs to be odd

right?

[shut obsidian]

What needs to be odd

[shut obsidian]

It'll be symmetrical to the origin apparently

So yes

[chilly walrus]

what is the original task

[shut obsidian]

Can you plot the original function next to it

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[shut obsidian]

It's just to examine this function, is it strictly monotonic increasing, if so, argue why, is it symmetrical to the origin, if so, argue why

[shut obsidian]

I meant the integral of that

[chilly walrus]

what?

[shut obsidian]

Of e^(...)

[chilly walrus]

i plotted the integral and the original

[chilly walrus]

yeah it's there

in blue

and the integral is red

[shut obsidian]

But that's the integral from -x to x?

Not the indefinite one?

[chilly walrus]

same thing as from -u to u

[shut obsidian]

Or are they the same

[chilly walrus]

no

[pastel salmon]

integral cant be negative if function is positive here

[chilly walrus]

i was plotting this

[pastel salmon]

you mstmove this cmd up

[chilly walrus]

it can be

[pastel salmon]

no

[chilly walrus]

check the bounds

[pastel salmon]

i said

and it is > 0

[chilly walrus]

yes those are different bounds

[pastel salmon]

do noto discuss with it

[chilly walrus]

it's not what i have

[shut obsidian]

Can you also insert $\int e^{-\frac{x^2}{2}} \dd x$ there

[pastel salmon]

it is worth mentioning that there is a slight but subtle difference between the error function and the cumulative distribution function of the standardized normal distribution, their relationship can be given

where:

[chilly walrus]

one sec

[chilly walrus]

desmos doesn't support indefinite integrals but this is as close as i can get it to be

[shut obsidian]

Ok well that's the same

[chilly walrus]

the J thingy is twice the other integral

why? f(t) is even, so $\int_{-u}^{u} f(t) \dd t = \int_{0}^{2u} f(t) \dd t$

[shut obsidian]

How would we argue that the J thing is strictly monotonic increasing

[pastel salmon]

derivative is posotive

[shut obsidian]

Ah, I guess just say the original function is pos

What about it being symmetrical to the origin

How do we argue that

[chilly walrus]

integral of even function is odd

[shut obsidian]

Oh

Thank you!

[chilly walrus]

no problem

[shut obsidian]

Wait, if we didn't know that

Could we still argue

[chilly walrus]

mm

yes

[thorny flame]

artemetra

[chilly walrus]

use this fact

[shut obsidian]

Ah, true

Thanks

.close

[topaz sinew]

Channel closed

Closed by @shut obsidian

Use .reopen if this was a mistake.

[topaz sinew]

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.

[feral tapir]

Hello

[feral tapir]

.claim

I need assistance with this

please

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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

[feral tapir]

1

I am probably overthinking this a lot

.close

[topaz sinew]

Channel closed

Closed by @feral tapir

Use .reopen if this was a mistake.

[topaz sinew]

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.

[next aspen]

hey, can someone tell me how we got this step?

[next aspen]

idk i think im forgetting basic ln/log rules

[wild tapir]

log rules, ln(A) - ln(B) = ln(A/B)

[craggy haven]

missing set of parentheses in ln (x+h)

[next aspen]

yea ik that part

[wild tapir]

good way to remember them is they always take an operation to the next most powerful operation

so addition -> multiplication, subtraction -> division, multiplication -> exponentiation

that sort of stuff

[next aspen]

ye i rmmbr the rules now

but

i still cant wrap my head around it for some reason lol

[wild tapir]

which part in particular