help-10

[obtuse pebble]

Channel closed

Closed by @iron edge

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[dusk pelican]

how to find the integral of this

[dusk pelican]

i tried

[royal basin]

why did the 2 factor become 2x

also why is there an x at all in the first place

[dusk pelican]

oh i just work from outside to inside

[royal basin]

you kinda walked into that one

this is like integrating 10x^2 as (10x)(x^3/3)+C

integral of product generally is NOT the same as product of integrals

the 2 should have stayed as 2

also the theta should have stayed as theta throughout

[dusk pelican]

oh

[royal basin]

also at the step where you actually take the integral you shouldn't have dtheta anymore

[dusk pelican]

idk why i replaced x lol

[royal basin]

and before that, you should keep the integral sign

you should write $\int x^2\dd{x}$, never $\int x^2$ and never $x^2\dd{x}$

[warm shale]

Ann

[dusk pelican]

here is my new

do i have to include a parenthesis before my 2 ?

[royal basin]

also at the step where you actually take the integral you shouldn't have dtheta anymore

[dusk pelican]

so the last step

i should get rid of dtheta

[royal basin]

you should obliterate it yes

erase it

[dusk pelican]

alr here

[obtuse pebble]

@dusk pelican Has your question been resolved?

Channel closed

Closed by @dusk pelican

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 elk]

Need help on 27

I'm confused if this is asking for only the first derivative or the second

do I set the first derivative to 0?

[livid glade]

i mean they all are part of the same theme, like you have to do the same thing for each question, can you show me how you did the questions from 21-26

the question wants you to
find the global max min values
graph the function
and then writing the value of x at which the extrema occured

[topaz elk]

I was only assigned 27 lol

[livid glade]

ic, can you tell me how you can find the functions global maxima or minima

[topaz elk]

Its where the first derivative = 0 right?

[livid glade]

partially correct, thats for the local maximas and minimas
im guesing the "absolute" maxima minima reffers to the global maxima minima
so you also have to check the given domains boundaries ( here its -1 and 8 )

so yeah can you proceed to find the first derivative

set it to zero

[topaz elk]

well cube root of x doesn't have a global maxima

because its constant

at x= 0 its undefined

but its not a maxima

[livid glade]

asertion is correct
reason is wrong

but the thing is we have restricted the domain

so asertion for this context is also wrong

its gonna have a global maxima and minima

for the given domain

[topaz elk]

OK lets see

Still confused

[livid glade]

though its not advised to look at a graphing calculator while doing a question which is asking you to graph yourself
notice in the question you are given a specific domain

[topaz elk]

ye

[soft hazel]

Hi Guys

I wanna ask some questions id anyone free here?

[topaz elk]

Go above

this one is taken

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[soft hazel]

K

[topaz elk]

Right but is this for the function, the derivative or second derivative?

[livid glade]

? what

can you define domain

like what does a domain means to you

[topaz elk]

the set of x values

*real x values

[livid glade]

for which

[topaz elk]

the function/

?

[livid glade]

just a set of values of x for which the function is defined right?

[topaz elk]

right

[livid glade]

so like when you graph the function, you are only gonna take those values

now here you noticed there are no local maximas or minimas

yeah?

[topaz elk]

ye

[livid glade]

so the next step is checking the bounderies
as notice the nature of f'(x)
can you check if f'(x) is positive or negative

[topaz elk]

it will be postive

[livid glade]

for all x?

what can i conclude from that information

[topaz elk]

that the function has no relative mins or maxs because it never changes direction

dont kill me

[livid glade]

that can be said if f'(x) is either positve or negative yeah
but what can we conclude if its positive

[topaz elk]

uhhhh

[livid glade]

if f'(x) >0 for a specific domain
then we can conclude f(x) is increasing in that specific domain
here f'(x) > 0 for all x
hence f(x) is increasing for all values of x

remember doing anything like this?

[topaz elk]

kinda

[livid glade]

i would suggest you do all the questions from 21-26 (atleast till you get the hang of it)

[topaz elk]

ye

but whats the points?

its asking for them

or is there no points because there are no maxes and mins?

[livid glade]

so what do you think will be the maximum value of the function for -1<x<8

like if the function increases at what point will it have the maximum for the given domain
-1<x<8

[topaz elk]

the graph says 2

because the y value at 8 is 2

but that doesn't seem right

because how is that a max?

[livid glade]

because after the 8 we are not fetching any values of y

your graph looks like this:

y = (x)^(1/3) {-1<x<8}

graph this

[topaz elk]

ok

[livid glade]

thats whats known as a restricted domain

we are only looking at the values of y given by the x where x belongs to [-1,8]

[topaz elk]

so would the min be -1?

and the max 2?

because its restricted at that domain

?

[livid glade]

almost there

the function has a minima at -1, maxima at 8 , because the function is increasing and we have restricted the domain
and the minimum value of the function is -1, and the maximum value of the function is 2

note that the function might also have critical points in the given domain ( not here just giving and example) so you might have to check all the critical points you get and the boundaries

[topaz elk]

got it

[livid glade]

like for example for this function
if you set the derivative to zero you will get the points circled in white
thoese are the local maxima's and minimas
but if the question asks for global/absolute maxima and minima
you also have to check for the bounderies ( the domain's boundaries)
as you can see from the graph the actual maximum and minimum value of the function are located at the boundaries( its not nessasary that it happens hence we have to check each values manually by puting it in the function)

try to do questions from 21 to 26

[obtuse pebble]

@topaz elk Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[peak shuttle]

does anyone know how to plot functions (x=t, y=t, t) in MATLAB?

[peak shuttle]

so x and y is dependent on t

and the horizontal axis is t

.close

[obtuse pebble]

Channel closed

Closed by @peak shuttle

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[gritty dirge]

can somene help? i keep messing up the sum

[royal basin]

what's the goal here?

what does m(θ) mean

[gritty dirge]

number of inversions

[royal basin]

ok right

so it's the number of pairs of entries in the bottom row where the bigger one is on the left

2 pairs with 1
4 pairs with 1 and 3
6 pairs with 1, 3 and 5

... 2n pairs with a total of n entries -- all of the right half

[gritty dirge]

so the sum is equal to?

thats where i keep messing up

so 2 has 1
4 has 2
6 has 3
....
n has n
so its n(n+1)/2 right?

[obtuse pebble]

@gritty dirge Has your question been resolved?

Channel closed

Closed by @gritty dirge

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[gray trail]

hello what would i do with the deposit in this question

[obtuse pebble]

@gray trail Has your question been resolved?

[obtuse pebble]

@gray trail Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[manic yarrow]

help with #55 please

a. find gradient via ([f_x(4,4,8)],[f_y(4,4,8)]) I assume

idk how to do b or c

[obtuse pebble]

@manic yarrow Has your question been resolved?

[manic yarrow]

<@&286206848099549185>

[forest lion]

What is the vector that points in the direction of steepest descent

[manic yarrow]

<-1,0>

forgot to mention it's - up there

opposite of gradient

[forest lion]

Yep

[manic yarrow]

I'm looking in my book rn

part a description is so confusing I feel like so many things are left out

can you help walk me through either the practice problem #55 above or example 7?

[last ore]

what university textbook is this if I may ask

[last ore]

Ty

[forest lion]

To make the other parts easier, I would find the gradient in terms of x and y

[manic yarrow]

how?

[forest lion]

But in the case of problem 55 it’s the same (may be different for other problems)

[manic yarrow]

yeah

do you just mean [f_x(x,y,z)],[f_y(x,y,z)]

[forest lion]

Yeah

[manic yarrow]

okay well yeah it's the same then

how does that help us though

[forest lion]

The tangent vector to the curve would point opposite the gradient vector

[manic yarrow]

okay makes sense

now what

[forest lion]

For b the slope y’(x) would be -f_y(x,y)/-f_x(x,y)

The above statement would help more with part c

As we have equations for x’(t) and y’(t)

[manic yarrow]

yeah I'm still lost ngl

I'm lacking a lot conceptually

[forest lion]

Maybe we can base our solution off the textbook solution

[manic yarrow]

sure

[forest lion]

We have that the vector pointing in the direction of steepest descent is {-1,0}

[manic yarrow]

idk where the initial point (3,4) came from

[manic yarrow]

oh

[forest lion]

It comes from the fact we are solving a differential equation, and need an initial point ( I believe)

[manic yarrow]

okay

so dy/dx = -6y/2x = 3y/x

makes sense

[forest lion]

In our case we have dy/dx= 0/-1

[manic yarrow]

okay yeah

so we gotta use initial point I assume

[forest lion]

Certainly

[manic yarrow]

to make x(t) and y(t)?

[forest lion]

That is for part c

Which also uses the initial point

As for right now, we can determine a general solution for y from dy/dx = 0

And use the initial point

[manic yarrow]

so slope = 0

?

[forest lion]

So y is constant

[manic yarrow]

oh

[forest lion]

Based on our initial point (4,4,8), y must be?

[manic yarrow]

4

[forest lion]

So we have that y=4 as our equation (remember it’s on the xy plane)

[manic yarrow]

okay cool

so for c now we need x(t) and y(t) using initial point?

[forest lion]

Yes

[manic yarrow]

so to undo derivative we take integral?

[forest lion]

For the path of greatest descent, use x’(t)=-f_x(x,y) and y’(t)=-f_y(x,y)

[forest lion]

Yes

[manic yarrow]

okay so integral -1 dt, integral 0 dt

-t + C and C respectively

initial condition x and y are 4

[forest lion]

Mhm

[manic yarrow]

so C = 4 in both situations

[forest lion]

Yes

[manic yarrow]

x(t)=-t+4

y(t)=4

?

[forest lion]

I believe so

[manic yarrow]

okay so now what

what about z component?

[forest lion]

For z, just plug into f(x(t),y(t))

[manic yarrow]

4+(-t+4)?

so 8-t?

[forest lion]

You got it

[manic yarrow]

dang okay

cool

I guess that wasn't too bad then

so the final answer is just (4-t,4,8-t) right

[forest lion]

For part c, yes

[manic yarrow]

okay cool I think I understand enough of it

I'll try out the rest, thanks for the help!

.close

[obtuse pebble]

Channel closed

Closed by @manic yarrow

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[latent walrus]

undefined

.close

[obtuse pebble]

Channel closed

Closed by @latent walrus

Use .reopen if this was a mistake.

[tardy epoch]

<@&268886789983436800> troll

[timid silo]

I’m in 9th grade can anyone explain calculus?

What it is and what formulas I need to learn to fully do calculus equations

[sweet gulch]

Try resending this question in a channel that is fully ready for a new topic

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[warped latch]

Heyyyy I need some help with this geometry question I don’t understand this at all plssss help here’s the work I did in desmos and stuff but I need to find n and m

[topaz tusk]

do you see a right isosceles triangle?

[warped latch]

Do u mean the one inside of the bigger one

[topaz tusk]

yep

what are the angles in a right isoceles triangle

[warped latch]

90 degrees

[topaz tusk]

and what are the other two angles equal to?

[warped latch]

Ummmm well since it has 2 dashed lines on the inner triangle does that mean it’s also 90 degrees?

[topaz tusk]

no

[warped latch]

Oof sorry

[topaz tusk]

it only means the two sides have the same length

[warped latch]

Oh ok

[topaz tusk]

actually do you know a special property in isoceles triangles?

[warped latch]

Umm 🤔 isocelise means it has 2 equal line right

[vapid lake]

basically because it’s isoceles you can make a system of equations and solve for m and n

the right angle only matters because it tells you what that angle equals

[warped latch]

Like m+n=180?

[vapid lake]

well all 3 angles added would equal 180

[topaz tusk]

????

[vapid lake]

This is all you need to know

[topaz tusk]

you're explaining in a terribly vague way

[vapid lake]

Isoceles triangle has 2 equal angles and 2 equal sides

one always implies the other

[vapid lake]

so for example 90 + 2n = 180

[warped latch]

Ooooo so like 189-90 then 2 divided

[vapid lake]

yes

[warped latch]

Oki

How do I figure out M

[hollow pine]

m+n = 65 !

[vapid lake]

yes

[hollow pine]

Try using same tactic you used to find n

[warped latch]

So 50+m2 =180?

[hollow pine]

but instead with the bigger iscoceles triangle with the 50 degree angle

[vapid lake]

you forgot the n but yes

[hollow pine]

close, but you need to include "n" as well because that is part of the angle

[warped latch]

So 50 + n+ m = 180?

[hollow pine]

how many of those (n+m) angles are there in the big triangle?

[warped latch]

2 I think

[hollow pine]

yeah, so you need to include (n+m) 2 times in your equation

[warped latch]

So like n+m+n+m + 50 =180 ?

[hollow pine]

yes

[warped latch]

Oooooo ok thank u

Thank u all for helping I better understand this now 😊

. close

.close

[obtuse pebble]

Channel closed

Closed by @warped latch

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[slate zealot]

I've just put my question in the forum but I was hoping to get some help quicker I just have a simple algebra equation (or it might be calculus I can't remember) and I just need some help so i cant remember the equation for my exam coming up :)

[ember frost]

what have you tried?

[slate zealot]

uhhh ive done equations like this before and im pretty sure i just have to gather the like variables

but im not sure if thats right

im just trying to find x

[hybrid brook]

that would be the first step done separately in the numerator and denominator, yes. but here there doesn't seem to be any like terms, which is an indicator you should look elsewhere.

[dim yacht]

Also, this isn't quite your goal. There is no equation given to help you find x, only an expression that you are asked to simplify.

[slate zealot]

ah ok

yeah im just really lost because i dont know where to start

[dim yacht]

Do you recall learning about factoring expressions?

[slate zealot]

not really...

[dim yacht]

Alright well that's pretty much all this problem is

I'll send you a video explaining the concept if you'd like

[slate zealot]

YES PLZ

[dim yacht]

https://www.youtube.com/watch?v=9MUDAr1PnlE

Also one important fact that you'll need for this problem (that might show up in this video, idk) is the difference of squares

which states that a^2 - b^2 = (a+b)(a-b)

Which you should note looks very similar to your bottom expression

[ember frost]

in general if you need to simplify a rational expression with polynomial numerator and denominator, your first instinct should be factorizing the numerator and denominator

[obtuse pebble]

@slate zealot Has your question been resolved?

Channel closed

Closed by @slate zealot

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[timber plover]

can someone please explain this to me? Im looking at the key and I still dont understand this at all

[fallen pine]

Average rate of change of $f$ on $[a,b]$ is given by
$$\frac{f(b) - f(a)}{b-a}$$

[warm shale]

Ari

[fallen pine]

the question is basically an application of this ^

[timber plover]

I have no idea what that is

Is that a rendition of y2 - y1 over x2 - x1

[fallen pine]

Yes that's basically what it is

[timber plover]

im still so confused

why is there so much plugging in

[fallen pine]

wdym

[timber plover]

I just dont understand the certain parts where the numbers are plugged in

[fallen pine]

ok first do you get where the formula comes from

for average rate of change

[timber plover]

yeah I think

wait slope right yes

[fallen pine]

It's not exactly slope because the function itself isn't a line

so the rate of change varies

but if you want to know the average rate of change, you can imagine the function as a line

[timber plover]

yes

[fallen pine]

Anyways, let's look at the sphere first

we're on the interval [0.5, 2]

what is the surface area of the sphere at x=0.5 and x=2?

using the formula they gave (which is wrong lol but whatever)

[timber plover]

uhh give me a second

im gonna be honest, I dont know 😓😓💔 is it the (.5,1) and (2,16)

[fallen pine]

yes exactly

Because the sphere surface area is given by $f(x) = 4x^2$. So $f(0.5) = 4(0.5)^2 = 1$ and $f(2) = 4(2)^2 = 16$.

[warm shale]

Ari

[fallen pine]

So now what would the average rate of change be?

[timber plover]

16-1/2-.5 ?

10?

[fallen pine]

correct

Now try it for the cube

[timber plover]

OH

I SEE IT NOW

I THINK

6-.375/2-.5

3.75??

[fallen pine]

yessss

[timber plover]

If its just plugging in why is it worded like that omg

Making my life difficult for what

Thank u sm

[fallen pine]

[obtuse pebble]

@timber plover Has your question been resolved?

[sonic comet]

Hallo

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[raven ore]

Hello

[raven ore]

May I have help with a question

[dense yoke]

hi, welcome to the server! you always have permission to ask, so don't hesitate to just send your question!

[obtuse pebble]

@raven ore Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[atomic merlin]

I need some help with factoring
I got only 4 problems left

[atomic merlin]

First one\$$81 - 192r^6$$\This is supposed to be diff of cubes

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[atomic merlin]

The rest are mixed meaning they could apply to any of the factoring rules
Here they are:

[hybrid brook]

this one should be a diff of squares instead.

[atomic merlin]

$$p^6 - 64$$\$$20k^4 + 3k^2 -2$$\$$8r^6 + 47r^3 - 6$$

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[atomic merlin]

I had thought that
Probably shouldn't have destroyed the folded format
Could you walk me through it regardless please?

[hybrid brook]

it would probably help if you can first factor out any common factors between the coefficients.

one quick scan reveals that 81 and 192 has a common factor. try to factor that out first.

[hybrid brook]

I stand corrected after factoring. it indeed seems to be a difference of cubes.

[hybrid brook]

but either way, the first step is to do this.

[atomic merlin]

Still trying to find that 😅

Is there some sort of trick to find it quickly or do I keep plugging

[hybrid brook]

well, all I will tell you is that the common factor is very small. don't overthink it.

like, single-digit levels of small.

[atomic merlin]

oh wait
I was plugging in 82 instead of 81 💀

The answer is 3

[hybrid brook]

oh. 😅

yes it is!

so what do you have left after factoring a 3 out?

[atomic merlin]

$$3(27 - 64r^6)$$

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[atomic merlin]

Still need to reduce that to r^3 🤔

[hybrid brook]

excellent. now, can you rewrite everything here as cubes?

[atomic merlin]

Oh wait

[hybrid brook]

for the r, consider using the power rule of exponents.

[atomic merlin]

cube root 27

3

$$3^3 - 64r^2$$

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[hybrid brook]

what happened to the r^6?

[atomic merlin]

cube rooted it

it became r^6/3 = r^2

[hybrid brook]

don't cube root it first! or if you want to, wrap it in a cube, like you did with the 3^3.

you can't just poof the r^6 out of existence by cube rooting it, but not the other parts.

the idea is to express everything in cubes, so that you get a^3 - b^3.

[atomic merlin]

Can I cube root one of them and square root the other?

[hybrid brook]

no.

and you don't need to do that anyway.

64 is also a perfect cube.

[atomic merlin]

well I am worried about the r^6 part
Don't I need to lower it to r^3?

[hybrid brook]

no. your job is to express $r^6$ as a cube, so you will get $(r^x)^3$, where $x$ is your job to find.

[warm shale]

Hyacine

[atomic merlin]

x = 2

[hybrid brook]

so write it as $(r^2)^3$, like you did with your $3^3$.

[warm shale]

Hyacine

[hybrid brook]

then move on to the 64.

[atomic merlin]

Is the answer\$$3^3 - (4r^2)^3$$

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[hybrid brook]

yes! now don't forget the 3 you originally factored out.

since you now have this, you can then apply the difference of two cubes on this expression.

[atomic merlin]

$$9^3 - (12r^2)^3?$$

[warm shale]

لبيك يا حسين ٣١٣- Servant Azadar

[regal carbon]

3³ = 3×3×3
3×3³ = 3×3×3×3 = 9×3² so kinda kills the fun. same for (4r²)³

[atomic merlin]

I'm not looking for fun
I am just looking to complete this painful assignment

I was about to just use ai, but I thought I'd try to understand it

[hybrid brook]

no, keep it like this.

don't multiply the 3 back in.

[hybrid brook]

then do the difference of cubes on this.

I only reminded you of the 3 you factored out in case you forgot we originally factored out a 3.

[atomic merlin]

Okay I think I got it

Alas

3 problems remain

😭

[dense yoke]

the first one is a straightforward diff. of two cubes, much like the one you just did

the last two are just quadratics in disguise

[atomic merlin]

Well I can't use quad formula here so what should I do

[dense yoke]

why not?

the quadratic formula works for any quadratic

[atomic merlin]

Well I am not finding x's

I am factoring

[regal carbon]

they need to prove that they are difference of cubes

or scalar×(diff of cubes)

[dense yoke]

OP replied to my last message, which is about the two quads at the bottom

[dense yoke]

aha, but finding the roots of a quadratic allows you to factor them!

[regal carbon]

lol youre right sorry

[atomic merlin]

That would be nice except my teacher prob will hate me more than she already does for that

[dense yoke]

...and why would that be? if the question never said you can't use the formula?

[atomic merlin]

We did similar problems in class and she said no when I asked if I can use it

[dense yoke]

I guess you could do it by completing the square or using Vieta? but honestly for numbers this big, why.

[atomic merlin]

idk I give up on this assignment

[regal carbon]

using Vietta is like solving a quadratic but making your life harder with numbers like that

idk what your teacher wants

[obtuse pebble]

@atomic merlin Has your question been resolved?

Channel closed

Closed by @atomic merlin

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[inland juniper]

Stuck on c

[inland juniper]

Lowk have no clue how to grt point d

[fast cliff]

what do you know about parrelelgrams

[inland juniper]

ohhh shoot

nvm im so dumb

.close

[obtuse pebble]

Channel closed

Closed by @inland juniper

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[dark orbit]

whats f''(x)? Whats the difference between f'(x)? I dont get it

[sage flax]

f'(x) is the derivative of f, or one way of writing it anyway

f''(x) is the derivative of the derivative

$f(x) = x^3$

$f'(x) = 3x^2$

$f''(x) = 6x$

and you can keep going

$f'''(x) = 6$

$f''''(x) = 0$

[warm shale]

Karma

[dark orbit]

Oooo

Ty

[royal basin]

typically btw

when we talk about derivatives of high order (4th, 5th etc) we dont put that many prime symbols

instead we put the order in brackets as a superscript

i.e. the 7th derivative would typically be written $f^{(7)}(x)$ rather than $f'''''''(x)$

[warm shale]

Ann

[royal basin]

primes are used up to like... 3rd, i think

also obv you need this in order to be able to speak about the n'th derivative

i.e. $f^{(n)}(x)$

[warm shale]

Ann

[obtuse pebble]

@dark orbit Has your question been resolved?

Channel closed

Closed by @dark orbit

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[minor venture]

hello gng can I get a hint for 25 😭

[minor venture]

This is my attempt ... 😔

[sage flax]

do you know law of sines

[minor venture]

Oh my

Yes...

Uh huh

[sage flax]

have you tried that

[minor venture]

Trying rn thx

[sage flax]

my fault, i read the problem wrong and thought it was asking about the angle for some reason instead of the area. you dont need law of sines for this

[minor venture]

Ok was about to ask

[sage flax]

you just need to relate area to two sides & one angle

which theres a formula for

[minor venture]

Oh ....

I know this one...

Wait do i

[minor venture]

👀

[sage flax]

$A = ab\frac{sin\theta}{2}$

[warm shale]

Karma

[minor venture]

Hmmm I will use this

would this formula be required for an ap calc course tho? Unless I missed smth

[sage flax]

its what i know off the top of my head, i don't know if you are expected to know it tbh

[minor venture]

Hmm bc I have not been introduced yet..

[upbeat condor]

it's usually learnt in trig/precalc courses

[obtuse pebble]

@minor venture Has your question been resolved?

[upbeat condor]

it's probably useful to know here that if you could let a be the base of the triangle and then b*sin(theta) will be the height

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[minor venture]

Yes I had that! I can follow it now thank you!!

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[twilit pendant]

Question and solution.

I don't get second step

[twilit pendant]

Like how changing coefficients a and b changes the equation

[rose scroll]

you are applying the function on a new value. Insteaf of x, you substitute it with 1/x

[rose scroll]

Imagine using x = c and x = 1/c to evaluate the equation two times separately. Thats what they did here

[twilit pendant]

Ok, thank you. I was thinking of swapping coefficients lol.

.close

[obtuse pebble]

Channel closed

Closed by @twilit pendant

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[tardy plume]

Hey! Can someone help me out with this question? I've never been good with probability and the way it's worded is confusing me 😅

[tame thistle]

essentially what is the probability that a multiple of 2 (2,4,6,8) is directly across from a multiple of 3 (3,6)

[tardy plume]

Ok I've figured it out

.close

[obtuse pebble]

Channel closed

Closed by @tardy plume

Use .reopen if this was a mistake.

[fast cliff]

4/7 * 3/5

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[sick thicket]

Hii

[sick thicket]

Could you help me

How do I find if a decimal is rational when it doesn’t have a repeating number

[worn yoke]

,rccw

[worn yoke]

i think the dot is supposed to denote the repeating part

but for the ones that 'arent repeating', you can think of it as just being that number followed by repeated zeros

[sick thicket]

But how do I do that

Finding the ratio I mean

[worn yoke]

what method do you use for finding the ratio of repeating decimals?

[sick thicket]

Uh the x= the original

Then 10x or 100x

Idk the formula

I just know how to find repeating numbers

But the 0,15 isn’t reacting

That’s the one I wanna know how to make it rational

[worn yoke]

,, 0.15 = 0,15000000000000\ldots

[warm shale]

cloud ☁

[sick thicket]

Pls explain

I’m sorry

[worn yoke]

do you agree that these two numbers are equal?

[sick thicket]

Ig

I’m not sure tho

[worn yoke]

0 = 0.00000000000....

if you add that to your number that's what you get

[sick thicket]

Ic

But another question

How many 0’s should Ik to use

Pls

[worn yoke]

it doesn't matter really

[sick thicket]

And do I multiply all non repeating number decimals by 0.0000

[worn yoke]

just 1 is fine

[coral yew]

0.15 = 15/100

You could also just do that and simplify

[sick thicket]

Oh

When I used it for the a2)

I got a diff answer tho

[coral yew]

It's 825/1000

Not 0,825/1000

[sick thicket]

Oh

Tysm both of you

[sick thicket]

Question

When number are I between two recurring numbers

Does that mean the ALL the numbers are recurring

[coral yew]

Can you explain what you meant

[sick thicket]

For the number 12

Two and four are recurring

And the are numbers inveterate

In between

[coral yew]

Usually that notation means 0.124124124 and so on

[sick thicket]

No no for question 12

A12

[coral yew]

Oh

Yes, all of the numbers between 2 and 4 repeat

[sick thicket]

Dang

Ok

Tyyy

[coral yew]

You can type ".close" if you don't have any more questions

[sick thicket]

Could you help me

[coral yew]

Send your question

[sick thicket]

It’s the question 12

[coral yew]

No that's not how you do it

Find 1000000x - x

It will be an integer

[sick thicket]

Wdym

[coral yew]

Tell me what 1000000x is

Then what is x

Find their difference

[sick thicket]

Ok wait

[sick thicket]

Tysm

.close

[obtuse pebble]

Channel closed

Closed by @sick thicket

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[sick thicket]

Can someone explain solution a

[inner sierra]

the question asked to find the common denominator between the fractions?

[sick thicket]

yes

but I don’t understand why x^3 is the common

[royal basin]

you consider the raw-numbers, the x's and the y's separately

[sick thicket]

cant it be x

[royal basin]

no bc then your x^2 and x^3 dont get coverage

[inner sierra]

your denominators are $4x^2$, $3x^3$ and $2xy$?

[warm shale]

1 divided by 0 equals Infinity

[inner sierra]

so to find the common denominator, you gotta find the commons between the variables

[sick thicket]

so the highest value is the common

[obtuse pebble]

@sick thicket Has your question been resolved?

[sick thicket]

Can someone help me

[willow drift]

you don't need to multiply by 3x inside the brackets, you can directly expand it

[sick thicket]

ok

[sick thicket]

Like this?

[willow drift]

yep

[sick thicket]

But the answer is diff

[willow drift]

you can cancel the x in the 2x/3x term

[sick thicket]

Why

[willow drift]

you get 2/3 and when you subtract 1 you get -1/3

[willow drift]

x is being multiplied both in the numerator and denominator

if something is being multiplied both top and bottom you can remove it

[sick thicket]

So I cancel the x?

[sick thicket]

.

[willow drift]

yes

[sick thicket]

tysm

Could u help w this too

Oh or do I do the last term

Using difference of two cubes

[limber ginkgo]

the final line incorrect add an extra “–1”

[sick thicket]

Wdym?

[limber ginkgo]

the formula is
(a+b)2=a2+2ab+b2

[sick thicket]

Uhuh

[sick thicket]

Idk how to do the right side

[willow drift]

try squaring the first equation

[sick thicket]

Which

[willow drift]

i mean the first in the question
x+1/x=4

remember to cancel if you get x in both the numerator and denominator

[sick thicket]

Could you further explain

I don’t get why I need to square it

Not in a rude way

[willow drift]

not sure how to explain without giving the answer
if you square it, the equation you'll get will help you do the right side

[sick thicket]

So I don’t use the differenc eor cube method then

[willow drift]

no I mean (x+1/3x)(x²-x/3x+1/9x²) is correct

[willow drift]

if you square the first equation, you'll get an equation that will let you do (x²-x/3x+1/9x²)

also you can cancel x in x/3x

[sick thicket]

Tyyy

[hushed narwhal]

very easy

[obtuse pebble]

@sick thicket Has your question been resolved?

Channel closed

Closed by @sick thicket

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hasty swan]

hi what's a dot product again? idk why i can't think rn

[hasty swan]

idk what's going on with me

[royal basin]

given $\bd{u} = (u_1,u_2,u_3), \bd{v} = (v_1,v_2,v_3) \in \bR^3$, the dot product is defined as $$\bd{u} \cdot \bd{v} = u_1v_1 + u_2v_2 + u_3v_3$$

[hasty swan]

i remember talking to someone about inner and outer products earlier today but i can't access anything rn

[warm shale]

Ann

[royal basin]

dot product is inner

[hasty swan]

thank you

[old lily]

do u see outer products in ml

[hasty swan]

i was reading the paper on (forgot topic) earlier today about

what

idk whats happening to me

[old lily]

an ml paper?

[hasty swan]

i dont remember anything and im scared

[old lily]

ok calm down

[hasty swan]

i think i need to take a break, this isn't normal

sorry

.close

[obtuse pebble]

Channel closed

Closed by @hasty swan

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[wide gulch]

why lim x → 0 sinx/x=1?

[serene elk]

Great philosophical question

[native inlet]

https://math.stackexchange.com/a/75151

[obtuse pebble]

@wide gulch Has your question been resolved?

[obtuse pebble]

@wide gulch Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[autumn shore]

how do i calculate the range of this rational function

[obtuse pebble]

@autumn shore Has your question been resolved?

[serene elk]

Well you need to think about what values of x could I realistically put into this function

And see what y values they tend to spit out

Then you need to consider where y and X may be asymptotic

[serene elk]

Tell me if this helps or if you'd want a more step by step kind of guide

[obtuse pebble]

@autumn shore Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[mortal garden]

not sure how to solve this terrible with this topic

[wary badger]

which one

[mortal garden]

well the whole question 4 so a and b

[wary badger]

ok do you know the proper definitions for injective and surjective

[mortal garden]

yes

[wary badger]

let’s start with injective

ok so you haven’t tried assuming f(x_1) = f(x_2)?

[mortal garden]

not sure what this it

[wary badger]

ok so you don’t know the proper definitions

[mortal garden]

I know definition based on the coordinate planes way, like what's supposed to happen there otherwise no not really

[wary badger]

$f \colon A \to B$ is said to be injective if for all $x_1, x_2 \in A,$ [f(x_1) = f(x_2) \implies x_1 = x_2]

[warm shale]

knief

[wary badger]

here is your definition

now if you’re familiar with proving implications you’d know that to show this implication holds we assume that f(x_1) = f(x_2) and try to show that we must have x_1 = x_2

yes?

[mortal garden]

yes

[wary badger]

ok so let’s apply that same reasoning here

take x_1, x_2 in R and assume that f(x_1) = f(x_2)

what do we get?

rewrite the last equation i wrote based on the rule for f

[mortal garden]

I'm not sure what to do here, do I apply 2x to both?

[wary badger]

sure

not sure that’s how i’d phrase it but let’s see what you meant

[mortal garden]

I'm not sure myself 😭

[wary badger]

🤔🤔🤔

[wary badger]

what was confusing here

[mortal garden]

all of it..? sorryy

[wary badger]

rewrite f(x_1) = f(x_2)

using f(x) = 2x

[mortal garden]

2x1 = 2x2

[wary badger]

yes

and can you simplify this

remember what our goal is

[wary badger]

^

[mortal garden]

well we can reverse it by divdiing both side by 2

[wary badger]

yes

which gives…

[mortal garden]

x1 = x2

[wary badger]

right so this proves f is injective

x_1 = x_2 is the conclusion of the implication

so we’ve showed the implication holds for arbitrary x_1 and x_2

now we move on to surjective

do you have a working definition of surjective

[mortal garden]

all elements of codomains are in at least 1 input?

[wary badger]

have at least one input is a better way to say it but yes

$f \colon A \to B$ is said to be surjective if for all $b \in B$ there exists $a \in A$ such that $f(a) = b$

[warm shale]

knief

[wary badger]

so we begin by taking an arbitrary real number

call it y

now we need to find a real number x such that f(x) = y

can you do this for me?

using the rule for f

[mortal garden]

would this be where x and y is the same number?

[wary badger]

i don’t know what you mean

why are they the same number?

f isn’t the identity function

[mortal garden]

sorry not sure what II need to do there thats all

[wary badger]

we need to find a real number x so that f(x) = y

in other words

find x such that 2x = y

just solve for x

[mortal garden]

x= 2y?

[wary badger]

no not quite

please review algebra

[mortal garden]

oh sorry x= y/2

[wary badger]

yes

[mortal garden]

I mixed it up with what I did with another question

[wary badger]

so corresponding to each real number y we found a real number x such that f(x) = y

namely

x = y/2

hence f is surjective

so f is injective and surjective

meaning f is

…

[mortal garden]

bijective too

[wary badger]

yep

so the inverse exists

what is it?

[mortal garden]

is it just replacing x and y?

so y=x/2

[wary badger]

yep

probably better to write f^-1(x) = x/2 though

[mortal garden]

oh yeah I was just lazy to write it properly

[wary badger]

try b now

[mortal garden]

do I do the same thing since it's also 2x?

[wary badger]

but its a function from Z to Z

so you can't just do the exact same thing

see where it fails

[mortal garden]

what do I do instead?

\

[wary badger]

well, does the same work for injective?

lets start there

retrace our steps

[mortal garden]

okay

[wary badger]

what do you think

if we take two integers m and n and assume f(m) = f(n)

what do we get?

does the same logic still apply?

[mortal garden]

no it's different

[wary badger]

why?

[mortal garden]

wait nvm you just made them into letters instead

then yeah it does apply

[wary badger]

mhm

we do get 2m = 2n --> m = n

so its injective still

but how about surjective?

is it true that for any integer n, there is some integer m such that n = 2m

if not, find a counterexample

i.e. find some integer n such that n \neq 2m for all integers m

[mortal garden]

no I think

[wary badger]

^

[mortal garden]

Im trying hold on

well m would have to be even

it cant be true for all n

[wary badger]

m?

or n?

why would m have to be even?

maybe you mean n?

[mortal garden]

oh sorry yeah

[wary badger]

yes

so just pick any odd integer

and you're done

[mortal garden]

n would have to be even since its a result in 2m thats always even

ahh

okay thank you

[wary badger]

you're welcome

[mortal garden]

can you give me a short description on what to do to test out each time I'm met with these type of problems?

[wary badger]

these problems always amount to working the definition

[wary badger]

here is injective

[wary badger]

here is surjective

you first want to have a rough idea if you think its injective/surjective or not of course

and if you think its not then try and find a counterexample

if it is injective then you just work the definition by showing the implication holds and to show an implication holds you generally assume the hypothesis and show the conclusion follows from that

if it is surjective then you take some arbitrary element in the codomain and solve for x essentially, like you would when solving for the inverse

solve for x to find a corresponding domain element whose image is the arbitrary element in the codomain

i.e. find x such that f(x) = y

just means take y to be arbitrary and rewrite f(x) = y using the rule for f and then try to solve for x

[mortal garden]

is the rule of f you're referring to like what the equation asks?

[wary badger]

the "rule for f" is just how f assigns an element in the codomain to each element x in the domain

so in the above examples its f(x) = 2x

the rule here is doubling the input

[mortal garden]

ohh

after the equal sight is the rule

gotcha

.close

[obtuse pebble]

Channel closed

Closed by @mortal garden

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[mortal blade]

Don't mind me, just testing smth

[obtuse pebble]

Please don't occupy multiple help channels.

[mortal blade]

.close

[obtuse pebble]

Channel closed

Closed by @mortal blade

Use .reopen if this was a mistake.

[mortal blade]

.reopen

[obtuse pebble]

✅ Original question: #help-10 message

[mortal blade]

Interesting

.close

[obtuse pebble]

Channel closed

Closed by @mortal blade

Use .reopen if this was a mistake.

[unreal musk]

Oi, one channel at a time

[mortal blade]

Lmao I was testing if there's a way to bypass it by closing and reopening

[unreal musk]

Also what's your question

[unreal musk]

Ohhhh I see gotcha

[mortal blade]

Uh show that $\lor$ is associative in minimal logic

[warm shale]

Xavier 🌺

[lament tapir]

42 :3 👍

[mortal blade]

You got it!

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[radiant scarab]

! status

[obtuse pebble]

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

[radiant scarab]

also this is multiple choice

[wooden cipher]

are we assuming g=10m/s^2?

[radiant scarab]

Yes

most probably 10 m/s²

[ancient berry]

Brodie ts no phy discord

[mortal blade]

It's fine, chill

[jolly sable]

Check help-8 👀

[jolly sable]

Well it’s a math discord, physics is somewhat math

[ancient berry]

K lemme try

[jolly sable]

Try my question at help-8, it’s harder than this students question ngl. The hard part is just finding the right numbers then computing is very simple

[radiant scarab]

both topics are distinct but yeah it is

[ancient berry]

A and b?

No all correct ig?

[obtuse pebble]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

@radiant scarab Has your question been resolved?

[ancient berry]

@radiant scarab had to fetch my note lol

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lyric knot]

!nosol

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[wise echo]

what is the absolute minimum and maximum of f(x) = 1/(x-1)^2 (even just helping me find d/dx of this would help, I think I am doing it wrong, tysm!)

[daring ravine]

what is d/dx 1/(x^2)

can you write it without a fraction?

[wise echo]

Can I write it like
(X-1)^-2?

And then

-2(x-1)
-2x +2?

[atomic marsh]

Wrong usage of power rule

Otherwise its fine

[obtuse pebble]

@wise echo Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 sparrow]

Probability theory question: \
$P(B | A) > P(B | A^c)$ \
$P(C | B) = 1$ \

Does it follow that $P(C | A) > P(C | A^c)$?

[warm shale]

! See my about me

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[neat sparrow]

Could you prove it? Using accepted laws of probability theory such as the law of total probability and the definition of conditional probability and the complement rule?

That it follows I mean

[ancient berry]

So we can't deduce?

[formal island]

Oh, thinking about it, i dont think we can really conclude that, lmao

my bad

[ancient berry]

What does the answer say yes/no

[formal island]

im usually inclined to think about probability theory from the set theoretic standpoint of the sample space

for P(C|B) to be = 1, C has to be a subset of B in the sample space. For a venn diagram, C is completely inside B
Assume C = B, then both statements are equal to each other, there isnt nothing to prove
So, assume C ⊂ B (so C is a proper subset in the whole sample space)

[neat sparrow]

I am wondering whether the conclusion follows from the premises.

[ancient berry]

Yeh helps, sometimes venn diagrams

[neat sparrow]

I am asking for a proof or a counterexample

[formal island]

We just know C (either empty, equal or smaller than B) is inside it, nothing more.
We cant conclude where in the set B its situated, so C might be completely closed off inside the set A^c will still being completely closed off inside B.

Or, fun enough, be the empty set.

[ancient berry]

Idk if its opposite, b to be a subset of c is a case

[formal island]

Completely raw concept

But yeah, we cant conclude nothing on C

[wooden cipher]

P(C|B)=1, meaning C contains B

[formal island]

im tryna think of an example

[formal island]

Opposite, C is contained by B

[ancient berry]

Nope

[formal island]

am i going crazy

[wooden cipher]

this region should do the trick

[ancient berry]

P(B intersection C) = P(B) which means c completely overlaps B but it can extend beyond b

[formal island]

Gang we have C|B not B|C

[wooden cipher]

probability of C given B is true

[ancient berry]

So new sample space is b

[wooden cipher]

thus wherever there is a B, a C must also be

[formal island]

This wouldnt be C|B = 1

i feel like im going crazy here

[wooden cipher]

if i drew it right

yes it would

[ancient berry]

Jus swap b and c idk lemme brain my thinkin

[wooden cipher]

|B means you are in the circle with B

[formal island]

You cant swap em 🥀

Do we all agree that $P(A|B)$ is read as "Probability of A given B"

[warm shale]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[wooden cipher]

yes

[formal island]

Then the only thing we can conclude from P(C|B) = 1 is that C is a subset of B in sample space.

[wooden cipher]

its the other way around

if C is a strict subset of B, this implies there is some element of B not in C

[formal island]

we cant even conclude C is a strict subset

[ancient berry]

Ts what i feel

[wooden cipher]

if we think of B as a box of items, and we are given the box of items, there will be an object we can pick from the box not in C

[wooden cipher]

if we assume, by way of contradiction C is a strict subset of B

we get a contradiction

thus C is a (not strict) superset of B

[formal island]

So we dont agree that P(C|B) = 1 implies that C is a subset of B. That you saying?

[wooden cipher]

yes, i am saying C is a superset of B

[formal island]

my bad on notation on that one

[wooden cipher]

=1*

[ancient berry]

Yes

[formal island]

Give an example of P(C|B) where

1. B implies C always happens
2. C is a superset of B

[wooden cipher]

P(mult of 2|mult of 6)

[ancient berry]

Brodie imma show some venn

[wooden cipher]

out of some finite set of integers

[ancient berry]

This if c is subset of b

[obtuse pebble]

@neat sparrow Has your question been resolved?

[neat sparrow]

is this a counterexample?

[wooden cipher]

this red region

P(C|A)<P(C|A')=1

[ancient berry]

it reprensents p(C/B)!= 1 if c is a subset of b

[ancient berry]

Ts counter example

No wait

[wooden cipher]

just maximize C|A' while minimizing C|A

[ancient berry]

yh,

satisfies conditions

ig this solves it

[obtuse pebble]

@neat sparrow Has your question been resolved?

[obtuse pebble]

@neat sparrow Has your question been resolved?

[obtuse pebble]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[velvet radish]

I’m getting 40/40 ? 🤩🤩🤩

[lyric knot]

congrats

[coral yew]

This is a help channel fyi

Not a chatting channel

[solemn burrow]

So.. what do you need help with?

[velvet radish]

Check it