help-49

[robust isle]

for all a in A, [a]_R is included in [a]_S (A is Z in the context of our congruence relations)

[last slate]

We take R = S

I'm tripping

Oh, equivalence classes come in the equation?

[robust isle]

well you can use them

they provide two equivalent definitions for refinement in the intro section

[last slate]

R is a "subset" of S

Subset notation

Don't know how to class this

Meaning S has all the characteristics R has, but can have more

Is that what you're referring to

[robust isle]

yeah an actual subset

not a "subset"

[last slate]

Ok

[robust isle]

that makes it even easier tbh

[last slate]

I thought there was another term for this

[last slate]

Don't know, am still quite confused

[robust isle]

you want to show "R refines R" for any relation R

but "R refines R" just means "R is a subset of R"

the latter is obviously true

you have R=R after all

so R is a subset of R

done

that's why I said everything rests on set inclusion

[last slate]

Oh, okay, got it

That's simple indeed

[robust isle]

and the two other arguments will also boil down to "set inclusion is antisymmetric" and "set inclusion is transitive"

we used set inclusion to define refinements after all

[last slate]

That's true

Okay

Way more straightforward than expected

And this would work for whatever C

[robust isle]

also

even if the relations in C aren't equivalence relations, you can still talk about refinements

you'd want these relations to be defined on the same set at least

but that's pretty much the only requirement

[last slate]

Got you

Understood

Now that I see we can use sets

Makes things way easier

This is the following part

I mean, at first glance, seems pretty okay

[robust isle]

yeah now is the fun part

[last slate]

Would say that yes

For the first question

No for the second

Am not sure if the refinement relation respects the Law of Trichotomy, for it to be a total order

[robust isle]

ok and ok

[robust isle]

well it's time to investigate =_2 and =_3 then

[last slate]

Yup

Well

[last slate]

Mod 3 refines mod 2

Oh no actually no

Not always

[robust isle]

well I kinda spoiled you earlier with my drawings

it doesn't indeed

[last slate]

I have this as definition of total order

How can 2 relations be ≤_t comparable?

Oh, should I just say that this isn't a total order

Because mod 2 doesn't refine mod 3, mod 3 doesn't refine mod 2, and mod 3 is not equal to mod 2

(Counter-example I guess)

[robust isle]

indeed

[last slate]

I'm not too sure how to justify

[robust isle]

well just find counter-examples to each of these statements

[last slate]

Okay, got it, will do

[robust isle]

if =_2 doesn't refine =_3, then there has to be a pair (a, b) in =_2 that's not in =_3

[last slate]

Got you

[robust isle]

refinement is set inclusion yadayada...

[last slate]

Yup

I'll manage

Thanks so much for helping by the way

This is the rest of the problem

I think a lattice diagram is a vertical drawing

[robust isle]

well you're drawing the relation yes

vertical drawing is a bit of stretch, refinement isn't a total order

[last slate]

Well, mod relations aren't comparable

They're either equal, or not

So how can I represent that?

[robust isle]

you can compare some of them

[last slate]

Using subset notation?

[robust isle]

well you know how a lattice diagram looks like for the set inclusion relation

[last slate]

Oh yeah

[robust isle]

even if it's not a total order, you can still draw the possible comparisons

well here it's the same thing

except the objects are "congruence mod n" relations, and the links represent refinement

[last slate]

Does mod 1 refine everything?

[robust isle]

yeah

wait no nvm

it's the least refined relation of them all

[last slate]

Oof

[robust isle]

you have a=b mod 1 for any a, b

it tells you nothing about a and b

[last slate]

Oh, right

This is very confusing 😭

[robust isle]

so ok =1 is the least refined one

after that, what do you think are the relations directly refining =1 ?

(as in R refines =1 and there's no other relation S such that R refines S and S refines =1)

[last slate]

I don't understand your question

[robust isle]

here's a diagram that looks a bit more like the "set inclusion" one

so =1 is refined by any other congruence relation sure

but you're not gonna draw a line between =1 any every other relation it would be barely readable

so you only draw "direct refinements" as I defined above

but I can rephrase that question in a more graphical way

[robust isle]

what relations would end up in the first layer (just below =1) ?

@last slate

[midnight plank]

@last slate Has your question been resolved?

[last slate]

Primes

Right?

Sorry, was AFK for a minute

[robust isle]

yeah primes

[last slate]

I need to urgently go somewhere, I'll try finishing this up tonight, do you mind if I get back to you (and ping/DM you) if I need more help? Really appreciate you guiding me through everything up to this point

[robust isle]

I'll prolly be asleep by then

someone else could continue

@last slate

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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.

[tiny gate]

What is the difference between Gaussian elimination and gauss Jordan elimination

[tiny gate]

Do they both require augmented matrix to reduce something to echelon form

Even if you’re not solving a system

[hexed birch]

you can literally type this question on google

in gauss-jordan there are zeroes above the 1's

[tiny gate]

.close

[midnight plank]

Channel closed

Closed by @tiny gate

Use .reopen if this was a mistake.

[midnight plank]

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.

[tiny gate]

Bit lost on part 2

[midnight plank]

@tiny gate Has your question been resolved?

[midnight plank]

@tiny gate Has your question been resolved?

[tribal temple]

x is a 3 x 1 vector

[stray mist]

I see

What is a 3 vector btw

X y z?

[tribal temple]

3 dimensional vector, three components

[stray mist]

Oh

[midnight plank]

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.

[neat lily]

I am trying to prove the formula for angles between two vectors.

The angle between two vectors $v$ and $w$ is given by the formula $\cos(\theta) = \frac{v \cdot w}{|v| |w|}$. Let $v$ and $w$ be two unit vectors. $v=(\cos(\theta), \sin(\theta))$ and $w=(\cos(\phi), \sin(\phi))$. Then, $v \cdot w = \cos(\theta) \cos(\phi) + \sin(\theta) \sin(\phi) = \cos(\theta - \phi)$.

[grand pond]

what7todo

[neat lily]

I am not sure what happen if $\phi >\theta$.

[grand pond]

what7todo

[neat lily]

I understand now

https://math.stackexchange.com/questions/741255/why-cos-theta-gives-positive-values-while-in-case-of-sine-it-is-negative

[midnight plank]

@neat lily Has your question been resolved?

Channel closed

Closed by @neat lily

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.

[obtuse totem]

hold up

I do not agree with this answer

equality also holds if v is a zero vector

[twilit rampart]

how are the norms defined?

[obtuse totem]

well, ||v|E is the euclidean norm

square root of all entries squared

and ||v|m is max norm so the max of all absolute value of the entries

[twilit rampart]

i agree with you

it should say at most one of the v_i is non zero

[obtuse totem]

ye

ok

thank you!

[twilit rampart]

youre welcome

[obtuse totem]

same with b

also at most one is non zero

same hereee

[midnight plank]

@obtuse totem Has your question been resolved?

[midnight plank]

@obtuse totem Has your question been resolved?

[midnight plank]

@obtuse totem Has your question been resolved?

[obtuse totem]

no questions yet..

[obtuse totem]

ok I got a question

not really sure what operator norms are..

In my notes, ||A| is an operator norm

not sure what it means

I dont understand their answer

ahh I see

[obtuse totem]

but I still dont get what ||.| is

[obtuse totem]

<@&286206848099549185>

nvm got it

[midnight plank]

@obtuse totem Has your question been resolved?

[midnight plank]

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.

[last slate]

what do you mean?

are you sure that's the full question? if so then I am not much of a help then

can you show full question to see if i can help

[drowsy pewter]

Consider using trigonometry using the angles and side lengths of the rectangle

As you have right-angled triangles everywhere

AH = Lcos(x)

Because AH is adjacent to the angle

If it was AE then it would be sin

So do that for all 4 sides you asked about

And you'll see that the things you asked about are equal

one sec

I guess there probably is just an immediate symmetry / similar triangle argument

Like AEH and FCG both have the same length hypotenuse and angles and hence are identical

And likewise for HDG and EBF

So both triangles have a right angle and an angle x yeah? And therefore their other angle must be 90-x

So they have all 3 angles the same

Also they both have hypotenuse of L

Since it's a rectangle

So they are identical triangles, since they have the same size and angles

[stray mist]

There is a chapter called congruency of triangles iirc in that chapter it teaches how to proof one triangle is equal to other i think this would help you

[drowsy pewter]

You know more than one angle

They both have right-angles also

[stray mist]

What is your question now i will try to help

[drowsy pewter]

It all boils down to the fact that you have ASA

So you have that the triangles are congruent

So the side lengths are equal

Basically just that if you flipped the rectangle, the diagram would look identical. But you don't need to worry about it, it's just a different way of thinking about it.

By symmetry. Like imagine if you rotated the image 180 degrees. Then it would be identical except the box would be slanted the other way

Rotating doesn't change the shape/size/angles

To formally prove it, it's going to be a lot easier to just use the congruent triangles ASA approach

Or the trigonometry approach

More of an understanding of the properties of rotation

Actually nah. To be honest I think that the rotational argument still assumes the congruent triangles part

I could be wrong on that, geometry is not my strong suit. But basically with the rotational argument I believe I'm still assuming that the triangles are identical

So you may as well just ignore rotation and just use congruent triangles

somewhat yeah

[midnight plank]

Channel closed

Closed by @fresh blade

Use .reopen if this was a mistake.

[midnight plank]

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.

[vital tide]

Hello !
I'd like to ask how you get angle 0 and angle a using sin, cos or tan !

I get that the missing side is 11.49 (Using pythagorean theorem)

[vital tide]

herp me

[wanton quest]

do you know about the inverse trig functions

[vital tide]

kinda yeah

[wanton quest]

alright, so given the sides 14 and 8

which trig function should we use

lets make theta our reference angle for now

[vital tide]

errr

oh ok

[wanton quest]

its obvious that the hypotenuse will be 14 right?

how about the 8

is it the adjacent or the opposite side?

[vital tide]

adjecent i think

[wanton quest]

correct

now we have an hypotenuse and an adjacent

which function should we use from
SOH CAH TOA

we have A and H

[vital tide]

UH

CAH??

[wanton quest]

yes

we gonna use cosine

now how can you set the equation up

,,\cos(\theta)=\frac{A}{H}

[grand pond]

Renz

[vital tide]

oooo

oke

slowly learning B)

so how do i get the angles of 0 and a

[wanton quest]

what do you get here

when you substituted the length of the adjacent and hypotenuse

[vital tide]

you get 8/14

[wanton quest]

yea

you get

,,\cos(\theta)=\frac{8}{14}

[grand pond]

Renz

[wanton quest]

but you want theta right

[vital tide]

yeah

[wanton quest]

so what we can do is, apply the inverse cosine function to both sides

so that the cosine will get cancelled, leaving you with theta

the inverse of cosine will "undo" the cosine function

giving you back theta as those two functions are inverses of each other

,,cos^{-1}(cos(\theta)) = \theta

[grand pond]

Renz

[wanton quest]

like that

so we have:

,,cos^{-1}(cos(\theta))=cos^{-1}(\frac{8}{14})

[grand pond]

Renz

[wanton quest]

,,\implies \theta=cos^{-1}(\frac{8}{14})

[grand pond]

Renz

[wanton quest]

where the right hand side can be evaluated using a calculator

[vital tide]

AHhhhhh ok ok i get it now by a bit

[wanton quest]

lets just use wolfram

,w arccos(8/14)

[grand pond]

Results provided by WolframAlpha

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

Requested by reenziee

[wanton quest]

wait its in radians

[vital tide]

wha

[wanton quest]

,w arccos(8/14 degrees)

[grand pond]

Results provided by WolframAlpha

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

Requested by reenziee

[wanton quest]

uhh

[vital tide]

uh

wuz happenign

[wanton quest]

but you should be getting this

[vital tide]

yaa i got it

[wanton quest]

$arccos(x)$ or $acos(x)$ is another way to rewrite $cos^{-1}(x)$

btw

[grand pond]

Renz

[vital tide]

oh ok

[wanton quest]

so now we know theta is 55.15 degrees

to find a

we just subtract theta from 90

since they are complementary angles

or in other words, theta + a should equal 90

[vital tide]

so 35

ye

oo ok i think i know how to do this properly know

eyyy thanks for ur help man

!!

.close

[midnight plank]

Channel closed

Closed by @vital tide

Use .reopen if this was a mistake.

[wanton quest]

dont forget to use some decimal places

[vital tide]

oh yea h

[wanton quest]

2 decimals should be enough

theta will be 55.15 while a will be 34.85

[vital tide]

i forgot about the decimals

oop

is there anything else i missed or need to learn?

[wanton quest]

just keep on practicing SOHCAHTOA

know what to do if you are given a length and an angle, or 2 lengths of a right triangle

but to generalize, if 2 lengths are given and the problem asks you to find the angles, then inverse trig functions will be involved

just like what we did earlier

[vital tide]

yeaa i kinda get how to use it now

ill keep it in mind

[midnight plank]

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.

[astral moon]

yo

[astral moon]

can u help

need help with the whole of question 4

[obsidian horizon]

do you think you could take a closer photo of the question?

[astral moon]

yep

[wet pollen]

,rotate ccw

[midnight plank]

@astral moon Has your question been resolved?

[astral moon]

no

[ember furnace]

dilation from x-axis by factor n means multiply x by n

y is the same

multiply y by n

reflection in x-axis means inverse y

reflection in y-axis means inverse x

translation m units left (x-m), right (x+m)

translation m units down (y-m), up (y+m)

[midnight plank]

@astral moon Has your question been resolved?

Channel closed

Closed by @astral moon

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.

[topaz wolf]

how do ik that theres is values for k that makes A row equivelant to the other matrix

and if there r what r they

how do i figure em out

btw det(A)=2(4-k)

[midnight plank]

@topaz wolf Has your question been resolved?

[heavy wagon]

There are a few ways you could approach this:
1.) You could perform some elementary row operations to try and get A to equal your left matrix and get k by inspection, which can be a long process
2.) You can use the fact that 2 matrices A,B are row equivilent if they share the same row space.
3.) Suppose instead that these two matricies are part of a homogenous system, i.e. $A\vec{x} = \vec{0}$, the two matrices are row-equivalent iff they share the same null-space.

Those are some strategies I suggest...

[grand pond]

TomB

[midnight plank]

@topaz wolf Has your question been resolved?

[topaz wolf]

wdym by same null space

[midnight plank]

Channel closed

Closed by @topaz wolf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[heavy wagon]

It's essentially the set of vectors which maps to the null (all-zero) vector

[heavy wagon]

.close

[midnight plank]

Channel closed

Closed by @heavy wagon

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[keen seal]

if n goes to infinity here

nume or deno grows faster

[severe cloud]

Factorial grows much faster than square. Try it out, 6^2 vs 6!

And they‘re both increasing functions

[keen seal]

what about cube?

or ^4

[severe cloud]

They might be bigger than factorial for small values, but factorial absolutely crushes after like 10 units

I said 10 but it‘s obviously going to vary from function to function.

,calc 10^4

[grand pond]

Result:

10000

[severe cloud]

,calc 10!

[grand pond]

Result:

3.6288e+6

[severe cloud]

See how ginormous that is? xD

[keen seal]

oh

damn

yeah i see

big asf

okay tysm!

.close

[midnight plank]

Channel closed

Closed by @keen seal

Use .reopen if this was a mistake.

[midnight plank]

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.

[tiny gate]

Kinda stuck

[severe cloud]

<@&268886789983436800>

[tiny gate]

?

I closed the other channel

[last slate]

there was a troll

[tiny gate]

Oh

[atomic jolt]

Try to write out the expression x^T A x

Maybe first think about what Ax looks like

and then multiply by x^T on the left

Might be helpful to keep in mind that matrix multiplication is distributive

[tiny gate]

Yeah i think i kind of get it

Let me just send working though cause I don’t think the working is the most logical lol

When i try and do that I just get a 1x1 matrix = (Ax1^2 + Ax2 ^2 )

I’m just confused because i changed the LHS to matrix form and that was the answer but I don’t get why

Feels wrong

[tribal temple]

It's worth writing $A$ out as per the entries, $A = \pmqty{a & b \ b & d}$ (noting $A$ is said to be symmetric)

[grand pond]

@tribal temple

[tribal temple]

Then work out these products in terms of the a, b, d's

[tiny gate]

Oh my god

[midnight plank]

@tiny gate Has your question been resolved?

[midnight plank]

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.

[frail oar]

Any help with part d?

this shit's fuckin impossible

[midnight plank]

@frail oar Has your question been resolved?

[tribal temple]

So FD is both $\mathbf{a} + \qty(6 - \frac{12}{m + 1})\mathbf{c}$ and also $\mathbf{a} + 3 \mathbf{c}$

[grand pond]

@tribal temple

[frail oar]

FD being equal to a +3c is info for the next part, part e

so i can't use that info for part d

[frail oar]

$\text{For part d, I need to derive}\vec{FD} = a +6c -(\frac{12}{m+1})c$

[grand pond]

hoax

[frail oar]

<@&286206848099549185>

[midnight plank]

@frail oar Has your question been resolved?

[last raft]

i tried but got -6c instead of +6c and (12c)m/(m+1) instead of 12c/(m+1)

[midnight plank]

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.

[tiny gate]

If i want to check if a symmetric 3x3 matrix is positive definite/semidefinite etc etc is it best to change it to quadratic form?

[tiny gate]

Like is that the only way

[tribal temple]

You can e.g. check eigenvalues too

[tiny gate]

Heard of that but don’t know what it is

This is an intro class i think the people who do it throughout the year learn it

Is there any other way or nah

[tribal temple]

Oh

[tiny gate]

It seems like for the quadratic method u just complete the square lol and then see what it sits

[tribal temple]

Well I can't think of any other ways from those to suggest

Probably easiest to check from quadratic form then

[tiny gate]

Only thing is how do you differentiate something being positive definite vs positive semidefinite

Oh the semidefinite has the >= whereas definite has to be > 0?

And im assuming vice versa for negative

[tribal temple]

Yep, strict against non-strict

[tiny gate]

Ok thanks

How do u even complete the square for three variables

Looks weird

[tribal temple]

Ewww

[tiny gate]

There’s no straightforward way for this example is there

[midnight plank]

@tiny gate Has your question been resolved?

[tribal temple]

I doubt it, at least not that way

[midnight plank]

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.

[granite sphinx]

hi

[granite sphinx]

This is thé question : For 20 years, each time at the end of the year, Piet puts

€ 3,000.00 at an interest rate of 3.00%. One year after the last deposit, he takes out €6,000.00 for 10 years.

What amount will Piet have left if he withdraws € 6,000.00 for the 10th time?

this is what i have and its correct but i have to do it in a shorter way

[runic python]

pretty sure you find the future value of the deposits and the present value of the withdrawals and then net them

[granite sphinx]

i can do A20*1.03^10 but then i need the debt of 6000 from it

.close

[midnight plank]

Channel closed

Closed by @granite sphinx

Use .reopen if this was a mistake.

[runic python]

did you get it

[granite sphinx]

yea

[runic python]

aight

[midnight plank]

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.

[bitter wagon]

help. need to simplify this expression, dont even know where to start. work shown but i think im started in the completely wrong direction. i have the identities im using listed for convenience, dont even know if theyre applicable to this problem

[queen ermine]

what can you rewrite csc(theta) as?

[bitter wagon]

1/sin(theta)

[queen ermine]

Right

Oh god

What is this?

[bitter wagon]

help I DONT KNOW

im so lost dude

like i said i am started... in the complete wrong direction

[queen ermine]

Here's a nudge

[bitter wagon]

so like i have a vague idea of the fact that i was supposed to get here by multiplying by a common denominator and then adding ? i think???

i got confused bc i tried multiplying by sin(t) and then that just got me here and then i gave up on that bc the denominators are still wrong

😔 my head hurts, ill just get the question wrong so i can see the explanation video and risk having to do review... ty for the help

.close

[midnight plank]

Channel closed

Closed by @bitter wagon

Use .reopen if this was a mistake.

[midnight plank]

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.

[coral bobcat]

Hii i cant tell whats wrong 😭

[tribal temple]

Think you meant pi/5 rather than 5/pi

Remember testing the points and everything

[coral bobcat]

Wait but if you do 2pi x 5/pi then youd get 10 and rhats the period

[queen ermine]

Not reading the question again?

[coral bobcat]

Noooo i swear im pressing my eyeballs onto the question 😭

[queen ermine]

You should also read the answer you typed in

very important step

[coral bobcat]

😭

[tribal temple]

Well, are you sure you're supposed to be multiplying those?

e.g. sin(2pi * x) has period 1, quite clearly...

[coral bobcat]

Arent you supposed to multiply to get the period

[queen ermine]

Are you allowed to use a graphing calculator?

[tribal temple]

Can you clarify what you mean please?

[coral bobcat]

No😔

[tribal temple]

(the answer is "not like that" but I wanna see where you got that from )

[queen ermine]

You're so close too

[coral bobcat]

Lile when ur trying to find the period arent u supposed to multiply 2pi by the coefficient of x

[tribal temple]

No

[coral bobcat]

Oh 😭

[queen ermine]

So do you know what the period of this function is?

Given the 2 points you have

[coral bobcat]

10

[queen ermine]

Good

So now do the opposite of the thing you said you did

[coral bobcat]

Huh

2pi/10

Oh

OH

WHAT

[queen ermine]

[coral bobcat]

OH

[queen ermine]

You were probably thinking of frequency

remember frequency = 1/T

1/period that is

The frequency is multiplied, the period is divided

[coral bobcat]

[queen ermine]

2pi stays where it is

[coral bobcat]

Ohhhh 😭

[queen ermine]

Also, I have to say again

NeGaTiVe aMpLiTuDe

[coral bobcat]

I KNOW THAT PART I REREAD THE QUESTION 😭😭

[queen ermine]

Does it work now?

[coral bobcat]

YES

IT WORKED

THX GUYS 🥹

🫶

.close

[midnight plank]

Channel closed

Closed by @coral bobcat

Use .reopen if this was a mistake.

[midnight plank]

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.

[coral bobcat]

Hii how do i know if an equation like this is sin or cos 😭

[tribal temple]

Well, this one is easier to choose cos for, considering you start at a minimum (similar for maximums)

If you "start" at the midline, you'd prefer to use sin, knowing the behaviour of sin and cos

[coral bobcat]

OHHHH

😭

OK TY

ALSO WOULD THE PERIOD BE 3

Cos minimum is 0 and the midline is 1 and then next point is 2 and then fjnal point would be 3?

[tribal temple]

The midline would be 1, what type of point do you think 2 is?

[coral bobcat]

Minimum?

[tribal temple]

Not minimum, but...?

[coral bobcat]

Max?

[tribal temple]

Yep, and remember you want to get back to where you started, that "minimum"

so what kind of point is the 3?

[coral bobcat]

Its like

It has the same y coordinate

As the minimum

So wouldnt it be 3?

[tribal temple]

It doesn't

[coral bobcat]

What 😭

[tribal temple]

To go from the maximum to the minimum, you have to pass through something, after all...

[coral bobcat]

Midline?

Wait so if its a cosine graph

Wouldnt it start at the minimum

And then go to midline

And then go back to midline

And go back to minimum

?

Or wait

No

Idk im confused now 😭

[tribal temple]

You start at the minimum, sure, then midline, then maximum, then from the maximum you wanna go down...

[coral bobcat]

To the midline?

And then minimum!

[tribal temple]

There you go

So, from that, what's the period?

[coral bobcat]

4?

Omg :DDD

Thank you!! 💗💗💗

Lol but actually tho tysm for always helping me 🥹💕

https://tenor.com/view/hug-virtualhug-hugsent-gif-7170588153364811748

[tribal temple]

It's a pleasure, you're wonderful to work with

[coral bobcat]

Awww tyyy 🥹🥹💕🫶💗

And U TOO

OKK CYA LATER :DDDD

LOL

.close

[midnight plank]

Channel closed

Closed by @coral bobcat

Use .reopen if this was a mistake.

[midnight plank]

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.

[ionic lance]

Stuck on the final part of 3

[ionic lance]

I have shown everything up to the π²/8 integral. The sum is also π²/8 but idk how to prove it

<@&286206848099549185>

[atomic jolt]

I'm gonna be 100% honest (just because you specifically asked me to help you), I don't know where to really start with any of those

[ionic lance]

Fair enough

I have them all done up to the end of 3

[atomic jolt]

like idk if the taylor series of 1/sqrt(1-x^2) comes from a partial fraction decomposition? and I certainly don't know where arcsin comes into play

[ionic lance]

The fact that arcsine differentiates to 1/sqrt(1-x^2) has seemed to be the basis of most of this question so far

[atomic jolt]

oh yeah right

did not have that memorized tbh

[ionic lance]

Lol all good

Just confused how to go from the integrals to the sum

[ionic lance]

<@&286206848099549185>

[atomic jolt]

something's kinda sus here because what's a_1

[ionic lance]

1/2

The binomial expansion is

[atomic jolt]

a_(0+1)=((-1/2)+0)/0 * a_0

[ionic lance]

$1 + \frac{x^2}{2} + \frac{3x^4}{8} + \frac{5x^6}{16}+\frac{35x^8}{256}+...$

[grand pond]

Josh ♘

[ionic lance]

Yeah n should say (n+1)

On the bottom

[atomic jolt]

Like I'm not trying to be pedantic I'm just really tired and can't think for myself

a0 = 1
a1 = -1/2 ?

[ionic lance]

$a_{n+1}=\frac{a_{n}(\frac{-1}{2}+n)}{n+1}$

[grand pond]

Josh ♘

[ionic lance]

1, 1/2, 3/8, 5/16, 35/256...

Starting at n=0

[atomic jolt]

doesn't that give a1 = -1/2

[ionic lance]

Wait hang on I typed it wrong

Yes

The -1/2

Should be positive

[atomic jolt]

I can't help you with anything productive but I can torture my brain by trying to understand what's going on and be really unintentionally pedantic as a result

[ionic lance]

$a_{n+1}=\frac{a_{n}(\frac{1}{2}+n)}{n+1}$

[grand pond]

Josh ♘

[ionic lance]

This is correct, I believe

Anyways back to the point

How do any of the integrals help with the summation

[atomic jolt]

Not gonna lie I don't even see the pattern here or understand where this series comes from

but that's just my personal skill issue

and probably also my cue to go to bed

[ionic lance]

Fair enough, gn

[atomic jolt]

you too

[ionic lance]

( <@&286206848099549185> )

[atomic jolt]

I'm sure the helpers love being pinged twice from the same channel in a 15 minute timespan

[ionic lance]

Probably 👍

Lol idk I can't go to sleep with a half completed problem on my board

[atomic jolt]

I used to have the helper role but then I got rid of it because it got pretty annoying pretty quickly

[ionic lance]

It's like 1am I just wanna finish the question and go to sleep

[ionic lance]

Fair enough

[atomic jolt]

haha I know that feeling. Good luck

btw you seem to have a mistake in your taylor series

just a small one

I know this isn't really helping but 😂

I do wish I knew how to form that series though, because I don't think you get it by differentiation

the assignment sheet says to use the binomial theorem but maybe I'm just stupid but I don't see it

[ionic lance]

(1+(-x^2))^-0.5 @atomic jolt

[ionic lance]

Also those coefficients are obtained by this sequence I put 64 not 128 by accident

[atomic jolt]

I don't get it 😭😂 but good night, and good luck. Hopefully someone manages to help you out

[midnight plank]

@ionic lance Has your question been resolved?

[midnight plank]

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.

[coral bobcat]

😭

[tribal temple]

Well, any ideas so far?

[coral bobcat]

The period is 15?

No? 😭

Wait

75?

[tribal temple]

Rather coincidentally, it's a clock you're working with...

[coral bobcat]

OH

15

Oh

Nvm

Um

What does it mean by “peaks”

[tribal temple]

Take that as "maximum"

[coral bobcat]

Oooh okk

[tribal temple]

So at [hh]:15 you're at the max and at [hh]:45 you're at the min

[coral bobcat]

Ohh okk

So the midline is 30

Amp is 15

HUH

[tribal temple]

The function is supposed to describe the torque as the output

What are the maximum and minimum torque levels given?

[coral bobcat]

Max is 15 and min is 45?

[tribal temple]

Well, those are when they occur, but not their actual values

[coral bobcat]

Huh

[tribal temple]

Methinks it's reading time

[coral bobcat]

Noo 😔

So

Max is 3?

And min is -3?

Omg :DD

Ok so

Midline is 0

Anp is 3

[tribal temple]

They're also really annoying here

But more on that later, you have a and b

[coral bobcat]

Yay :))

Okok so

Would it be

A sin graph?

[tribal temple]

A sin graph would be nicer to choose here, sure

[coral bobcat]

:DD

Would the period be 12?

[tribal temple]

Again, remember it's a clock...

What do you know about clocks

[coral bobcat]

Ah

So

[tribal temple]

Actually let me make myself a bit clearer-

[coral bobcat]

Are we going by minutes

[tribal temple]

Yep, that's it, it's the minute hand you're thinking of, not the hour hand

[coral bobcat]

So the period would be 60?

So the answer is 3sin(pi/30)x

?

[tribal temple]

here's where my earlier comment comes in

The weight gets tied on at 11:55

[coral bobcat]

Huh 😭

So

By tied

Wait

What does it mean

Like ik thats when the weight gets put on

But how does it affect it

[tribal temple]

Well, remember that your equation is going to be in terms of how long after the weight was tied on

So at 12am, the torque should be 0Nm, right?

[coral bobcat]

Yeahhh

Huh 😭

[tribal temple]

Remember, at 12:15am you reach a max torque of 3Nm, and at 12:45am, you reach a min torque of -3Nm

[coral bobcat]

Wait how does the 11:55 affect it

[tribal temple]

Because you're going to be shifted because of it

[coral bobcat]

So does the min and max change

[tribal temple]

Writing now $\tau = 3\sin(bt + c)$ (we found that $a = 3$ and $d = 0$ already) you know that when $t = 5$, then $\tau = 0$

[grand pond]

@tribal temple

[tribal temple]

Because 5 minutes after 11:55, at 12am, that's when you reach the midline

[coral bobcat]

Ohh

So rn we hafta find c?

[tribal temple]

Yep, oh, and find b too

[tribal temple]

Finding b should be easier to do first

[coral bobcat]

Ohh yeah

Okkk :DD

Wait

Is b

Pi/30

[tribal temple]

Yep

Now, as for that c, note that when t = 5, we want to get tau as 0

I'm sure you know what to do now, with the value of b

[coral bobcat]

Wait would i use t instead of x in this case?

(Pi/30)t?

[tribal temple]

Yep, because they tell you that they want tau as the output and t as the input

[coral bobcat]

So we put in 5 for t?

So would c be -6pi?

[tribal temple]

Almost, not quite

[coral bobcat]

😔

Oh wait

Pi/6?

I see my mistake

[tribal temple]

-pi/6 but yep

[coral bobcat]

Okk :DD

So like this?

[tribal temple]

Yep

[coral bobcat]

Yay :DDD

TYSMMMMM

[tribal temple]

A pleasure

[coral bobcat]

:DDDDDD

.close

[midnight plank]

Channel closed

Closed by @coral bobcat

Use .reopen if this was a mistake.

[midnight plank]

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.

[toxic pecan]

Guys is there a way to integrate sqrt(1-x^a)

[keen sleet]

hmmm

[toxic pecan]

cant really procceed with this as im not the best with integrals

[keen sleet]

same, better with derivatives

[toxic pecan]

it tends to turn into a square ( if you include the bottom area) when a goes to infinity, is a circle when a =2

[keen sleet]

sorry for late replies i am helping someone else simultaneously

[toxic pecan]

k

[keen sleet]

ok back

[toxic pecan]

k

[keen sleet]

is this homework or

[toxic pecan]

no

[keen sleet]

math for fun?

[toxic pecan]

kinda more like math for suffering

[keen sleet]

most importantly, did you do this to yourself or

[toxic pecan]

do what ,create the question,

if so yes

i did do it

[keen sleet]

ah

big chance for no then

trust me i've done this to myself more times then i'd like to admit

for example, trying to compute the infinite sum of shrinking cylinders to find the formula for the volume of a cone... yeah not my proudest moment, spent a month on it in 5th grade

thinking chain rule

[toxic pecan]

chain rule? yea maybe

lemme try

ill close for now

[keen sleet]

i mean reverse chain rule mb

[toxic pecan]

ik

.close

[midnight plank]

Channel closed

Closed by @toxic pecan

Use .reopen if this was a mistake.

[keen sleet]

bye

[midnight plank]

Available help channel!

Send your question here to claim the channel.

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

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

[wanton shore]

(fogoh)^(-1)(x) = h^(-1) o g^(-1) o f^(-1) (x)

[wanton shore]

Is this valid for n functions?

Also is proof of this very hard ?

[midnight plank]

@wanton shore Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[wanton shore]

.reopen

[midnight plank]

✅

[wanton shore]

<@&286206848099549185>

[midnight plank]

@wanton shore Has your question been resolved?

[midnight plank]

@wanton shore Has your question been resolved?

[midnight plank]

@wanton shore Has your question been resolved?

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[wanton shore]

.reopen

[midnight plank]

✅

[wanton shore]

<@&286206848099549185>

[midnight plank]

@wanton shore Has your question been resolved?

[wanton shore]

<@&286206848099549185>

[midnight plank]

@wanton shore Has your question been resolved?

[winged elbow]

I think it should be valid, if the domains and ranges of the functions, correspond correctly

[wanton shore]

Ok

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[fossil locust]

Hi, could anyone please help with this? "The numbers 1 to 9 are arranged in a line (uniformly at random). What is the probability that the first number and last number are both at most 3?". I tried doing this so far but the answer seems wildly wrong. Thanks!

[warped folio]

sooo

the first number and last number are both at most 3

what do u think this means ?

[fossil locust]

Well I guess it means that the first number has to be an element of the set {1,2,3} and the last number has to be an element of the set {1,2,3}

Basically the first and last numbers must be between 1 and 3 inclusive I guess

I think

[warped folio]

mmmm

doesnt it mean the probability of the first number being 3 and the last number being 3 ?

[fossil locust]

I thought it meant that the maximum they could be is 3

Because it says "at most 3"

Not 100% sure though

[warped folio]

i think

that means

the probability of the first number being 3 combined with the probability of the last number being 3

[fossil locust]

But then why would they put "at most 3"

[warped folio]

that means

mmmm

im not sure

[last raft]

i agree with this tho

i also interpreted it like that

[warped folio]

mmm

[fossil locust]

But this is not possible right, because if 3 is the first number then it's knocked out and can't be the last number

[last raft]

at most 3, so it could be 1, 2 or 3

[fossil locust]

Because numbers from 1 to 9 are lined up

[warped folio]

yes those 2 actions cant happen at the same time

[last raft]

i got 1/12

but i feel like im wrong

[fossil locust]

I know almost for a fact that my answer is wrong because it seems so ridiculous

So it definitely will be smaller numbers

[loud geyser]

we need to find the number of ways to arrange the digits such that both the first and last digits are at most 3.

• we have 3 choices for the first digit (1, 2, 3)
• for the last digit, after choosing the first digit, we have 2 remaining choices (from the digits 1, 2, or 3 that have not been used as the first digit)
• for the remaining 7 digits, there are 7! ways to arrange the remaining seven digits (those that are not chosen as the first or last digit)

probability is favourable outcomes divided by total possible outcomes

[last raft]

true tho, the denominator is uncomfortably large lmao

[loud geyser]

favourable outcomes here is thus 3 x 2 x 7!

total possible outcomes is simply 9!

and i arrive at the answer 1/12

[last raft]

oh i did it right then yay

[fossil locust]

So (3x2x7!)/(9!)?

Which is 1/12

Thanks so much everyone, I really appreciate it. Have a great day, I need to revise this topic a lot more. Thanks!

.close

[midnight plank]

Channel closed

Closed by @fossil locust

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.

[past heron]

Hey I solved this particular question but I feel like I made a mistake even though, my final answer is correct. Please point out my mistake.

[past heron]

Question 42

[lethal path]

Your final answer is not correct

Should be x < 3 union 4 <= x

Cause the denominator can't be zero so $[x] \ne 3 \implies 3 \le x < 4$ is not in the domain

[grand pond]

south

[lethal path]

Furthermore, for g(x) = (x - 2)/(x - 3), g(2) = 0
g(x) is negative only when 2 < x < 3

So for these values of x, [x] = 2 and all is good for the square root

[midnight plank]

@past heron Has your question been resolved?

Channel closed

Closed by @past heron

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.

[midnight plank]

@graceful elk Has your question been resolved?

[midnight plank]

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.

[plain zealot]

Can someone spot a mistake

I have to calculate integral of (ln(x+3))^3

<@&286206848099549185>

[midnight plank]

@plain zealot Has your question been resolved?

[midnight plank]

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.

[ripe sandal]

y-y1=m(x-x1)

[ripe sandal]

i have a problem solving a question

[midnight plank]

@ripe sandal Has your question been resolved?

[bold oak]

Yes, so for tangent line, your $m = \frac{dy}{dx}$.

[grand pond]

poypoyan

[bold oak]

Then for implicit diff, since you want dy/dx, you differentiate both sides of the eqn. of circle w.r.t. dx. Chain rule helps here.

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[midnight plank]

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.

[nimble hazel]

hey I cant fully understand related rates i understand the concept and how it works but cant get the right answer

[nimble hazel]

any tips

[midnight plank]

@nimble hazel Has your question been resolved?

[midnight plank]

@nimble hazel Has your question been resolved?

[midnight plank]

@nimble hazel Has your question been resolved?

[midnight plank]

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.

[last slate]

How do I find the probability of the shaded region?
It’s the probability that a randomly chosen point in the figure lies in the shaded region

[hexed elbow]

area of shaded region/ area of total region

[last slate]

i got 4 pi / 25 pi

[hexed elbow]

what are the radii given

[last slate]

5 for total and 2 for shaded

[hexed elbow]

is the centre white portion suposoed to be part of the shaded region or?

[last slate]

no

[hexed elbow]

cancel out the pi

[hexed elbow]

oh

then shouldnt you account for that too

[last slate]

wdym?

[hexed elbow]

like the shaded portion as per the image youve sent

isnt a full circle

[last slate]

oh

so u subtract?

[hexed elbow]

yeha but whats the radius for the tiny circle

[last slate]

tiny circle is 1

[hexed elbow]

is this the data given to you?

[last slate]

yes

[hexed elbow]

then yeah

youd subtract

[last slate]

3/25

[hexed elbow]

mhm

[last slate]

so thats the answer?

[hexed elbow]

i should hope so

[last slate]

okay, thank you for your help

.close

[midnight plank]

Channel closed

Closed by @worthy heron

Use .reopen if this was a mistake.

[midnight plank]

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.

[valid wind]

anyone know how to format this better in notion

[valid wind]

\begin{pmatrix}
1&1&0&0&0&\big |&0\\
1&1&1&0&0&\big |&1\\
0&1&1&1&0&\big |&0\\
0&0&1&1&1&\big |&1\\
0&0&0&1&1&\big |&0\\
\end{pmatrix}
\\

\begin{pmatrix}
1&1&0&0&0&\big |&0\\
0&0&1&0&0&\big |&1\\
0&1&1&1&0&\big |&0\\
0&0&1&0&0&\big |&1\\
0&0&0&1&1&\big |&0\\
\end{pmatrix}
\tag{R2=R2+R1, R4=R4+R5}
\\

\begin{pmatrix}
1&1&0&0&0&\big |&0\\
0&0&1&0&0&\big |&1\\
0&1&0&1&0&\big |&1\\
0&0&0&0&0&\big |&0\\
0&0&0&1&1&\big |&0\\
\end{pmatrix}
\tag{R3=R3+R2, R4=R4+R2}
\\

\begin{pmatrix}
1&0&0&1&0&\big |&1\\
0&0&1&0&0&\big |&1\\
0&1&0&1&0&\big |&1\\
0&0&0&0&0&\big |&0\\
0&0&0&1&1&\big |&0\\
\end{pmatrix}
\tag{R1=R1+R3}
\\

\begin{pmatrix}
1&0&0&0&0&\big |&1\\
0&0&1&0&0&\big |&1\\
0&1&0&0&0&\big |&1\\
0&0&0&0&0&\big |&0\\
0&0&0&1&1&\big |&0\\
\end{pmatrix}
\tag{R1=R1+R5, R3=R3+R5}
\\

\begin{pmatrix}
1&0&0&0&0&\big |&1\\
0&1&0&0&0&\big |&1\\
0&0&1&0&0&\big |&1\\
0&0&0&1&1&\big |&0\\
0&0&0&0&0&\big |&0\\
\end{pmatrix}
\tag{Swap R2 R3, R4 R5}

\end{align*}```

[polar mortar]

using array instead of pmatrix if you need to make an augmented matrix,
You can also use the amsmath package with xrightarrow to put text over arrows if that's your prefered style

[midnight plank]

@valid wind Has your question been resolved?

Channel closed

Closed by @valid wind

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.

[hybrid grail]

can someone explain my mistake plz

[sharp coral]

the derivative of sin(x) is not -cos(x)

[hybrid grail]

oh no way

okay i also have a question on this one

[sharp coral]

the same strategy should work

[hybrid grail]

what do i break up

[sharp coral]

either one will work, but cos(x) may be easier

[hybrid grail]

like this

?

[sharp coral]

yes, but it is a definite integral

[hybrid grail]

oh yea

but is the answer right

ik i have to plug in and eval

[sharp coral]

yes

[valid wind]

With definite integrals though you don't have to substitute u=sin(x) back, you can adjust the terminals according and evaluate the integral with respect to u

[hybrid grail]

can u guys help me w this one

idik why this is wronf

[valid wind]

Top curve - bottom curve = (-y^2+2y) - (y^2-4y) = -2y^2+6y

I think you just negated your integral

[hybrid grail]

wdym

.close

[midnight plank]

Channel closed

Closed by @hybrid grail

Use .reopen if this was a mistake.

[midnight plank]

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.

[cosmic river]

Can I get some help with this please

[low moon]

Sure

$F'(x) = sin(x^2)e^(sin(x^2))$

[grand pond]

Akira

[low moon]

What's the ans anyway ?

Ig i m wrong

[low moon]

Oh right

Forgot to differentiate x^2

Sin(x^2) *

[cosmic river]

First I evaluate the definite integral right

[low moon]

No

[cosmic river]

get its antiderivatve*

[low moon]

Yes

[cosmic river]

what do I do if its functions multiplying

[low moon]

Hold on

Whenever we diff both sides... The integral would get strike off

In simple words

So only the limits would get placed in that "part" inside the integeal

I.e. sinx^2

Plus the derivative of the limit

To conclude:

$the sin(x^2) will be inserted into xe^x multiplied by the derivative of it$

[grand pond]

Akira

[cosmic river]

I am confused

😭

pls walk me thru from step one

[last slate]

dude

do you know byparts