help-17

[vocal sleet]

Channel closed

Closed by @rough zenith

Use .reopen if this was a mistake.

[vocal sleet]

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.

[bleak prawn]

!status

[vocal sleet]

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

[bleak prawn]

4

I just want to know if my method is correct:

First sub in x(5) and y(5) to get the coords of a point on the tangent line

Then get y'(5)/x'(5) to get the slope (lets call it 'm') of the tangent line

Then y(5) = (m)(x(5)) + c gives us the y intercept 'c'

Then rearrange y = mx+c into the form they want and thats my answer?

[paper depot]

yes the method is correct

[bleak prawn]

Awesome! Thanks

❤️

.close

[vocal sleet]

Channel closed

Closed by @bleak prawn

Use .reopen if this was a mistake.

[oblique bobcat]

guys

i have finals in a week

i have to cover integration, differential equations, probability

and idk shit

bout them

what to do

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[final parcel]

quick question -- isn't a generator/equalizer the same thing, likewise a cogenerator/coequalizer?

[versed bane]

what is a generator in this context

[final parcel]

well, our teacher uses it kinda ambiguously in this context in his notes (on module theory), as if we're already supposed to know

from what i was looking for, it could also mean separator but idk. Language difference may play a role :/

[versed bane]

okay, do you have any notion of what a generator is? also, does your teacher use the term “cogenerator” ever?

[final parcel]

i was actually looking for meaning of generator because he uses cogenerator

[versed bane]

just checked out the nlab, i think a generator here is supposed to be analogous to a basis, yes generators are separators

[final parcel]

he proves that Q/Z is s cogenerator in Ab, that is, for u,v:A->B morphisms in Ab there exists a f:B->Q/Z s.t. fu!=fv

doesn't that just mean it's a coequalizer diagram?

i mean it's not the same, but it's an object in a coequalizer diagram, is what I'm asking

[versed bane]

is it just a “coequalizer diagram” in the sense that u and v are distinct parallel morphisms and Q/Z on the right? we are saying that there is some f such that f isn’t the coequalizer of u and v right?

[final parcel]

wait I'm dumb

lmaooooooo

coequalizer Equalizes

o diós mio

Anyway, thank you

sorry for wasting your time

[versed bane]

but the parallel morphism diagram is a test diagram

it’s not a waste of time

[final parcel]

it's basically the opposite, right?

[versed bane]

like you’re testing every morphism to Q/Z from B and if u and v are distinct morphisms then there is gonna be some f such that fu neq fv

idk the idea is that there’s an initial object in the coequalizer cat for a particular morphism in C to be a coequalizer

so it’s related to this diagram

[final parcel]

this is helpful, thanks

also now I'm sure he means separators and coseparators so i can read up on them

[versed bane]

yep, again nlab is kind of accessible here

[final parcel]

i love the internet

thanks smay

.close

[vocal sleet]

Channel closed

Closed by @final parcel

Use .reopen if this was a mistake.

[vocal sleet]

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.

[atomic shell]

integration of e^x -1/(e^x +1)

[knotty lynx]

Split it up

I mean, split it into two terms

[atomic shell]

yehh i understood

i splitted it into e^x/(e^x+1) and 1/e^x+1 and if i put y=e^x and derivative it dy=e^x.dx this way i can get the integration of the first part what about the second part?

[wary hull]

$\int\frac{e^x-1}{e^x+1}dx=\overbrace{\int\frac{u-1}{(u+1)u}du}^{u=e^x}=\int\frac{2}{u+1}-\frac{1}{u}du=2\ln|u+1|-\ln|u|+C=2\ln|e^x+1|-x+C$

[twin meteor]

mathisfun

[atomic shell]

waht now?

how do i integrate the second term?

[leaden ingot]

E

[atomic shell]

@knotty lynx how do i integrate the second term?

[leaden ingot]

THIS IS THE SOLUTION

[atomic shell]

i want to do it by substitution method

not like that

[leaden ingot]

THAT IS SUBSTITUTION WDYM

[atomic shell]

nothing

[atomic shell]

do you know what after this?

@leaden ingot

[leaden ingot]

both the first and 2nd part are done the same way

it's e^x so its very convenient here

[atomic shell]

in second part there is 1/e^x+1

[leaden ingot]

so?

[atomic shell]

what value should i put in y?

y= waht?

e^x?

[leaden ingot]

y = e^x
or even more convenient, y = e^x + 1

[atomic shell]

then for which value do i substitue on the original problem i.e 1/e^x+1

[leaden ingot]

If y = e^x + 1, dy = e^x dx and dy/(y-1) = dx
If y = e^x, dy = e^x dx and dy/y = dx

[atomic shell]

kool but now listen try to get what i am telling to you

in second part there is 1/e^x +1 right ? if i take y=e^x +1 then dy=e^x.dx then how do i substitute it in the second part

[leaden ingot]

...

[atomic shell]

that's my question

[leaden ingot]

did you not see what am i showing?

or you are avoiding it because it's "uncool"?

you blinded yourselves in front of me 3 times and i am not very happy about it

"cool but-" like, why the but? i have shown it very clearly

because dx = dy/y, you can just replace "dx" with "dy/y"

is that not clear?

[atomic shell]

wauu where do you live?

it's 8:25 there?

[leaden ingot]

does it even matter anymore

[atomic shell]

here its 7:14

i think it does

i think you are kool enough to be my friend

so will you?

be my friend?

[leaden ingot]

look, just tell me you are understanding or not and i will forget what just happened

[atomic shell]

mr targetvn

[atomic shell]

i didn't really got it

[leaden ingot]

there we go

wait a sec, lemme go get my whiteboard

[atomic shell]

yess yesss

hello @leaden ingot ?

[leaden ingot]

replace any instance of e^x with y
replace dx with dy/y

[atomic shell]

okayy

heyy but don't you want to be my friend lad?

[leaden ingot]

i bet you will unfriend me even before friending me

[atomic shell]

no wayy

i think you aree a chill guyy

cmon let's me friends

[leaden ingot]

i don't

[atomic shell]

will you?\

[leaden ingot]

sorry

[atomic shell]

no way man

[leaden ingot]

you are nice but i can't

[atomic shell]

there you go

you seemed pretty cool

but now tell

will you?

[leaden ingot]

... fine, ig

i hope you withstand my anger issue

[atomic shell]

😂

what should i call you then?

[leaden ingot]

just call me target

[atomic shell]

okayy

call me kaustuv

[leaden ingot]

k

[atomic shell]

well atleast i found one npc like me so asking this question was worth it😂

[nimble spindle]

lets be respectful

[atomic shell]

.close

[vocal sleet]

Channel closed

Closed by @atomic shell

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

[mild trench]

i need help here:

[mild trench]

for part b

ms says "to the left"

but

why isnt it to the right

coz i is positive

[vocal sleet]

@mild trench Has your question been resolved?

[vocal sleet]

@mild trench Has your question been resolved?

[mild trench]

pls anyone

.solved

[vocal sleet]

Channel closed

Closed by @mild trench

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.

[uneven mango]

Quick question: how to find the equation of a bisector AB in ABC, I know all 3 points and the middle of AB M. Do I find it by using C and M

[uneven mango]

Bcus it's not working

[paper depot]

"bisector AB"?

!xy

[vocal sleet]

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

[uneven mango]

Sorry the bisector of AB

[leaden ingot]

what

there's only "bisector of angles"

or "bisector of a triangle starting from a vertex"

[uneven mango]

This

Bisector of the line AB

Idk if the translation wrong

[leaden ingot]

give me the whole problem

[uneven mango]

It's not in english

[mild flower]

that's okay

[uneven mango]

Oh it's a perpendicular bisector

[mild flower]

ok yeah

do you know the slope of the line AB?

[uneven mango]

-4

So the k*k=-1

[mild flower]

yep

[uneven mango]

Yeah I forgot what

[uneven mango]

This is

[mild flower]

so the new slope will be $\f{-1}{\blue{-4}}$

[twin meteor]

hayley is NOT BRITISH

[paper depot]

"bisector" на английски обикновено се използва за ъглополовяща

[uneven mango]

Ok

Не съм решавал задачи със симетрали много и се обръках

.close

[vocal sleet]

Channel closed

Closed by @uneven mango

Use .reopen if this was a mistake.

[vocal sleet]

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.

[twilit needle]

Determine exactly for which point c the conclusion of the Mean Value Theorem holds on the interval [1, √3].

[oak magnet]

Is the 5/20 not meant to be here ?

[twilit needle]

sorry fixed it

[oak magnet]

Well so x positive

You had that this function strict monotonic

[twilit needle]

1. f is continuous on R \ {0}, [1,√3] subset R \ {0}. So it is continuous on the interval
2. f is differentiable on R \ {0} , (1,√3) subset R \ {0}. So it is differentiable on the interval.
3. f'(c) = (f(root(3)) - f(1)) /(root(3) - 1))

[twilit needle]

true

but how can I solve f(root(3)) - f(1) ?

cuz i suppose i must use that to equal it to the derivative ?

[oak magnet]

You can calculate it

[twilit needle]

I only know the unit circle ;-;

[oak magnet]

Its arctan(1/sqrt(3)) - arctan(1)

[twilit needle]

So arctan 1 is pi/4

i know that one

[oak magnet]

No tan value in mind?

The other one is pi/6

I give it

[twilit needle]

1/sqrt(3) must be also equal to (1/2)/((1/2)sqrt(3))?

[gritty sage]

If you know the unit circle, you should get 1/sqrt(3) in a form like the tangent values on the unit circle.

[twilit needle]

sin(1/2) / cos(1/2 * sqrt(3)) = arctan(x)

[gritty sage]

Presumably, you have something like sqrt(3)/3.

[twilit needle]

aaah i might figured it out

sin(x) = 1/2
cos(x) = 1/2 * sqrt(3)

And then divide sin(x) / cos(x)?

[gritty sage]

That's not how arctan works.

[twilit needle]

wait ill show my work i might just typed it worng

[gritty sage]

I don't need to see the work. That's just wrong.

[twilit needle]

i got pi/6 tho

[oak magnet]

Tan(pi/6) = sqrt(3)/3

[twilit needle]

doing it like this isnt allowed?

[wary hull]

You can, if you know your angles.

[twilit needle]

well I only know the unit circle for sin and cos

[wary hull]

Though, you should probably draw a triangle along with it to be demonstrative.

[twilit needle]

if you guys have any better idea please tell me

cuz this will probably give a lot of struggles later in further maths

[wary hull]

Draw a triangle with opposite side 1 and adjacent side rt(3). Then compute the hypotenuse, and it will make it easier.

[twilit needle]

2?

aah and then i can use sine for example

[gritty sage]

You can also remember the tangent values on the unit circle:

[twilit needle]

hmmm

that would save the most time tho

but i feel like the triangle one will like always work and this one i must do some adjustments

imma just write it down though

[wary hull]

Yep.

[twilit needle]

why did I never learn this ;-;

[wary hull]

It's not a conventional technique.

[twilit needle]

Aaah

well it is really useful!

okay so now i have

f'(c) = (-pi/12) / (sqrt(3) - 1)

i know that f'(c)= -1/(c²+1)

just solve for c?

[wary hull]

Is this an equation in c?

[twilit needle]

huh?

[wary hull]

What were you doing originally?

[twilit needle]

Determine exactly for which point c the conclusion of the Mean Value Theorem holds on the interval [1, √3].

1. f is continuous on R \ {0}, [1,√3] subset R \ {0}. So it is continuous on the interval
2. f is differentiable on R \ {0} , (1,√3) subset R \ {0}. So it is differentiable on the interval.
3. f'(c) = (f(root(3)) - f(1)) /(root(3) - 1))

Now i know 3) f'(c) = (-pi/12)/(sqrt(3)-1)

and i know f'(c) for c>0 f'(c)= -1/(c²+1)

[wary hull]

Yeah then solve for c

[twilit needle]

alright

it is really ugly tho

[wary hull]

It is differentiation

You did simplify it to arccot(|x|) right?

[twilit needle]

not allowed to use anything other then sine cosine and tan and their inverses

so sadly not ;-;

[wary hull]

Ok.

[twilit needle]

i get c=sqrt((sqrt(3)-1)*12/(pi) -1)

[flat whale]

plug this into arctan(1/x) and use a calc to verify

[twilit needle]

Aaah okay just to check now right

cuz on my exam i cant sadly

alright thank you guys

have a good day/night

.close

[vocal sleet]

Channel closed

Closed by @twilit needle

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.

[viral slate]

Can anyone help me with this??

[vocal sleet]

@viral slate Has your question been resolved?

[viral slate]

<@&286206848099549185>

[vocal sleet]

@viral slate Has your question been resolved?

[vocal sleet]

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.

[turbid snow]

what does it mean for a system of equations to be linearly independent?

[oak magnet]

It means that the systeme = 0 implies that the unique solution is 0

Do you have a specific example ?

[vocal sleet]

@turbid snow Has your question been resolved?

Channel closed

Closed by @turbid snow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[wet halo]

for a) There are no solutions to this system if k ~= -1

for b) No unique solutions

c) Infinitely many solutions when k = -1

that's what I got can someone verify this

Im sure there are errors in my row operations for part b/c but I still believe what I say holds true

[vocal sleet]

@wet halo Has your question been resolved?

[vocal sleet]

@wet halo Has your question been resolved?

Channel closed

Closed by @wet halo

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.

[vast shale]

the domain of both of them would be R? and the range for first would be set {1, 5} and for second it would be irrational U {1}

am i right

U is for union

[tawny hollow]

Yes

[vast shale]

Cool

thanks

.close

[vocal sleet]

Channel closed

Closed by @rugged heron

Use .reopen if this was a mistake.

[vocal sleet]

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.

[wary hound]

i cannot do this for the life of m,e

[vast shale]

!status

[vocal sleet]

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

[wary hound]

1

[vast shale]

have you ever calculated an inverse of a matrix before

[wary hound]

no it just came up on the last question of my matrix questions and i havent been taught it yet

[rancid kelp]

What is det(tA) being t number ?

[wary hound]

5?

[rancid kelp]

Hein ?

[wary hound]

what

[rancid kelp]

Ok if you know M is a 2x2 matrix, such as det(M) = 4

What is det(3M) for example ?

[wary hound]

36

[rancid kelp]

Good

Now apply that to det(5(A^-1)(B^t)) ... How do you get the 5 out of the determinant ?

[wary hound]

im not sure

[rancid kelp]

It's the same as what you did in the simpler example :

det(5(A^-1)(B^t)) = 5² det [(A^-1)(B^t)]

Do you agree ?

[wary hound]

ahhh

i see now

[rancid kelp]

Ok, now det(MN) = ?

What is the determinant of a product of matrices

[wary hound]

(det M)(det N)

?

[rancid kelp]

Good

Now use that to develop this further : det(5(A^-1)(B^t)) = 5² det [(A^-1)(B^t)] = ...

[wary hound]

[det(a^-1)][det(b^t)]

[rancid kelp]

Ok

What is det(A^-1)

[wary hound]

3x-24?

[rancid kelp]

No that's det A

I'm asking about det (A^-1)

[wary hound]

is it just (3x-24)^-1

[rancid kelp]

Yes, but only if 3x-24 is not 0

The determinant of the inverse of a matrix (when it exists) is just the inverse of the determinant

Now last step

What is det(B^t)

[wary hound]

26^t

[rancid kelp]

Have you ever transposed a number ?

[wary hound]

no sorry

[rancid kelp]

Ok

So det (B^t) = det (B)

The transpose of a matrix has the same determinant as the matrix itself

So

det(5(A^-1)(B^t)) = 5² det(A)^-1 . det(B) = 25.26/(3x-24)

[wary hound]

ohhh

[rancid kelp]

remember the determinant of products is the product of determinants

the determinant of an inverse is the inverse of a determinant

transpose doesn't change the determinant

And for M nxn matrix, and "a" a number : det(aM) = a^n . det(M)

[wary hound]

okay?

so then what

[rancid kelp]

I just gave you the answer

det(5(A^-1)(B^t)) = 5² det(A)^-1 . det(B) = 25.26/(3x-24)

Now solve for x

[wary hound]

okay thanks

.close

[vocal sleet]

Channel closed

Closed by @wary hound

Use .reopen if this was a mistake.

[vocal sleet]

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.

[floral crystal]

can someone tell me how to do part c

[floral crystal]

for some reason, i struggle with the graphs a lot...

[flat whale]

absolute minimum is the most negative y value

which one is the "lowest"

[floral crystal]

oh

how to find that value

[flat whale]

find all the y-values of your graph

then take the minimum of them

[golden frost]

it says to find it for the function g, which you have an integral

[flat whale]

do you know how to find a y-value

oh oops

[golden frost]

so solve what the function g is first

[floral crystal]

oh

i jsut do that area thing rihgt ???

like g(x) = antideriv from -2 to 2 f(t)dt and i get -8

is that how i find the y value

[olive stag]

at x=10, we see that g(x) is 0. If we go a lil bit after 10, it starts to decrease, if we go a litle before 10, it starts to increase, so i think its neither, or saddle point

that is my understanding of it

not sure if i explained myself well

[floral crystal]

i knwo that

im asking about c)

[olive stag]

ah

mb

[floral crystal]

oh wait so g'(x)=f(x)

[floral crystal]

is ok

g'(x) change sign at -2 and 6

so io nly check those 2 points?

[flat whale]

extrema occurs when g'(x) = 0 or when the derivative isn't defined or the boundaries.

[floral crystal]

okay

how do i solve for y 😭

[flat whale]

you don't need the exact y value

oh yes you do

[flat whale]

find the x value from here

and plug it into g(x)

[olive stag]

i feel u can just make a quick sketch of the g(x) graph

and just literally look at the min maxs from there

[floral crystal]

i know that the value of 6 is 8 becausearea is 1/2(4)(2)+1/2(4)(2)

[olive stag]

g(x) is just the net area

[floral crystal]

but i dont know why on earth -2 is -8 thats what the answer sheet says

[floral crystal]

i dont know how to sketch a graph

[olive stag]

like, g(-4) is 8

[floral crystal]

i only know how to draw the lines

[olive stag]

lemme show u what i mean

[floral crystal]

um

its not 8

aint it -4...

[manic bay]

what does ur name mean?

no father?

or like a father

[floral crystal]

what ru even talking about

[manic bay]

ur name

[floral crystal]

it's waterflower

[manic bay]

whattttt

[floral crystal]

its not arabic or wahatever

[manic bay]

OHHH

i thought it was arabic LOL

[floral crystal]

oh yes i got that

[olive stag]

g(-4) is just asking what is the area from 2 to -4

[floral crystal]

but when i go from -2 to 2

i do not get -8

i get what u mean

like on the answer sheet it says that g(-2) is equal to -8? but when i do that net area thing, i get 8

[olive stag]

here u are going from 2 -> -2, so ur going right to left, which makes the area negative

[floral crystal]

ah

[olive stag]

remember the rule that if u switch the places of the limits of integration u get a sign flip

[floral crystal]

my teacher only said that its negative if its below the graph

oh

oH

ohhh

[floral crystal]

I FORGOT ABOUT THAT

OHHH

OKAY

OKAY

THANK YOU

😭

[olive stag]

ye

[floral crystal]

tytyty

thats all i needed help with

tysm

.close

[vocal sleet]

Channel closed

Closed by @floral crystal

Use .reopen if this was a mistake.

[vocal sleet]

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.

[buoyant veldt]

how do i solve 'a'

for 'b', when i have value of k, i just integrate the gradient and then that'll be the equation of the curve. I can solve the constant "+C" using the origin point (0, 0)

I just odnt understand how the tangent can help to find the value of 'k'

[leaden ingot]

You can write a linear function given just 2 points

here we have (1,e²) and (0,0) so what is the equation of the line passing through these points?

[vocal sleet]

@buoyant veldt Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[strange charm]

is this nonsense

[hexed needle]

it's not nonsense, just maybe a little sloppy

all of your logic seems sound but some parts are confusing...

Like in your first part, you say let (xn) converge to x0, but you don't mention f(xn) anywhere, which you should by the definition

[hexed needle]

i think you meant to say it here

[vocal sleet]

@strange charm Has your question been resolved?

[hexed needle]

I would just make sure you mention f(xn) anywhere you're doing continuity proofs for readability :p

and for the part where you're disproving continuity at 1, I would reword it like:

Define xn = 1 + 1/n. (xn) converges to 1, but f(xn) converges to 1 =/= f(1), so f is not continuous at x = 1

the main confusing part about the last thing you said was f(xn) = 1 as n goes to infinity, and ik what you mean but you'd probably get docked for it

[strange charm]

ahhh

[hexed needle]

you got all the logic correct, the hard part is just formalizing :)

you have all the intuition

[strange charm]

yep :) its my first offical proof class so i feel like i have the idea but whenever i try to formalize it, it becomes very sloppy

[hexed needle]

well you're honestly doing very well for a first proofs class lol, most people take at least a couple other proof based courses before real analysis...

[strange charm]

i took discrete but i feel like the proofs in that class were kinda brain dead / very formulaic

[hexed needle]

yeah i would agree with that, there isn't much variation in those. this class you have to think a lotttt more

[strange charm]

ye defintely :)

[strange charm]

this makes alot of sense ! so thanks for reviewing

[hexed needle]

ofc! helps me review real analysis so helps me too lol

[vocal sleet]

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.

[dull sable]

help

[vocal sleet]

@dull sable Has your question been resolved?

[vocal sleet]

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.

[west harbor]

can i use mesh analysis without using the supermesh?

[vocal sleet]

@west harbor Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[languid venture]

Question 29

Why is the correct answer d?

Shouldn’t it be c?

[olive stag]

should be c

[languid venture]

Ok

How to do 36, 37

I’m lost

😞

[olive stag]

can it be rotated

i know there is a command in this server to do that idk what it is tho

,cw

,ccw

.cw

,rotate cw

[olive stag]

oooo

found it

[languid venture]

Oh

There we go

[olive stag]

,rotate cw

[olive stag]

hehe

[languid venture]

Hahah

[olive stag]

,rotate cw

[olive stag]

ok enough fun lol

[languid venture]

Imao

[edgy sapphire]

it's d

[languid venture]

How

[edgy sapphire]

you have to look at it as f(-(x+2))

like you have to shift the x before you do the -1 scale

[languid venture]

Yup shouldn’t it be (1/2x)^2 +2?

Ok but how did u get the answer though

How did u like plug it in

The answer key said the correct answer is b

[olive stag]

it's b

not d

[languid venture]

Plz help

How

[olive stag]

ok so

lets just look at vertical and horizontal stretches first

Af(Bx) so it looks like this

[languid venture]

I know it should be like -(1/2x)^2+2 right

[olive stag]

if A is larger than 1, then it gets stretched

[languid venture]

Because horizontally factor of 2 is 1/2 and 2 down is +2

[olive stag]

but if B is larger than 1, it shrinks

stuff u do to x is somehow reversed to what u expect

at least thats how i remember it

so if u strecth the x by 2

u actually are dividing x by 2

so you replace every x that you see with (x/2)

[languid venture]

I just figure it out today, what my idea is just do what u do to b

When u got equation that’s not f(x)

[olive stag]

and since u r moving the hwole thing down by 2 u just subtract the final answer by 2

$y=\sqrt{16-(x/2)^2}-2$

hmm

[languid venture]

Is that good thought though

Should I think about that way?

[olive stag]

1 sec

[languid venture]

Okk

[twin meteor]

IronVoltage

[olive stag]

ok perfect

uhhhhhhh ur idea?

wdym

[languid venture]

So how I think is

When u do question like this right, is not y=f(x), u just do the opposite way

Like factor or 2 right

Just 1/2

2 down just +2

[olive stag]

uhhhh i dont follow

nono so u have to see the general form of a transformation

let's say you have your original function called

$f(x)$

[twin meteor]

IronVoltage

[olive stag]

and you wana create a new function, that is just a transformation of f

so

$g(x)=Af(Bx+C)+D$

[twin meteor]

IronVoltage

[olive stag]

remember that whatever f is, its just poops out the value of the original function

so if you multiply the final output by some number A

you are scaling the output

this is why A stretched or shrinks vertically

you are scalling the final number

if you add or remove from the final number, you are moving the final number up and down

this is why D moves it up and down

if u add D, you move the whole thing up

cause everything gets bigger

[languid venture]

Oh oh oh

[olive stag]

nothice how both A and D have to do with u fing around with the output

[languid venture]

So like when u do horizontally u do what b does

[olive stag]

however, B and C are numbers used to f'k around with the input

[languid venture]

And when u do vertically u do what a does

And up down just what d does and right left is what c does

[olive stag]

yes

yes

[languid venture]

Okok

So is like -2 here

[olive stag]

u can remember it by seeing what A B C and D are attached to

[languid venture]

Because d is not affect by b and c

Yeah okokt

[olive stag]

both A and D are outside the function f(x)

but B and C are inside f(x)

[languid venture]

Yeah 👍

[olive stag]

they are messing around with the input

x

[languid venture]

Okok

So we know now is like (1/2x)^2 -2

[olive stag]

and for somereason that is a bit hard to wrap your head around, big numbers for B and C actually shrink/move left the graph

for the +C it kinda makes sense

as to why positive numbers makes it move to the left

cause like

by adding to the input, ur esentially making whatever output to come out sooner

like

imagine the x axis is time

and you are like 3 hours ahead

ur entire graph shifts left cause it happens sooner

does that make a lil sense?

[languid venture]

🤨

[olive stag]

guess not

its weird

[languid venture]

Make me more confused lol

[olive stag]

lmao

[languid venture]

But I think I get it

[olive stag]

then in that case just know that smaller numbers for x means up and stretch

[languid venture]

I know how abcd work, but just not know they connected like this

[olive stag]

a stretch in x is a division in x

[languid venture]

👍

[olive stag]

B and C are confusing to understand but im glad it helped a lil bit

anyhow the problem

$y=\sqrt{16-(x/2)^2}-2$

[twin meteor]

IronVoltage

[olive stag]

so u understand here?

[languid venture]

Tub

Yup

[olive stag]

ye, then just expand the x/2 and try to factor out a denominator

[languid venture]

1/4

[olive stag]

ye

[languid venture]

And square root out is 1/2

[olive stag]

pop it out of the radical

yep

u got it

[languid venture]

I don’t get how the 64

[olive stag]

oh

nwnw

ok so

$\sqrt{16-x^2/4}-2$

[twin meteor]

IronVoltage

[olive stag]

we want to combine the 16 and the x^2/4 as a single fraction

but they have different denominators

I want the denominator on 16 to be 4

[languid venture]

Ohhhhhh

[olive stag]

so I multiply and divide by 4

[languid venture]

So is 64-x square and u get it 4 out

I c

[olive stag]

$\sqrt{16\times4/4-x^2/4}-2$

[twin meteor]

IronVoltage

[languid venture]

Ok I get it

[olive stag]

$\sqrt{64/4-x^2/4}-2$

ye

[twin meteor]

IronVoltage

[languid venture]

Tyty and can u also explain 37

[olive stag]

ye lemme just see it again

[languid venture]

🙏🙏🙏

[olive stag]

hmm

ig we plugin -n for x and see what we can do

$1-1/(-n)$

[twin meteor]

IronVoltage

[languid venture]

1+1/n?

[olive stag]

$1+1/n$

ye

[twin meteor]

IronVoltage

[olive stag]

hmm

maybe we should do the prblem in reverse

like we start with each answer and we see if it matches with 1+1/n

[languid venture]

Oh

[olive stag]

f(n) def wont be it, nothing changd

1/f(n)

well since

$f(n)=1-1/n$

[twin meteor]

IronVoltage

[olive stag]

i can rewrite it as a single fraction

$f(n)=(n-1)/n$

[twin meteor]

IronVoltage

[olive stag]

so 1/f(n) is just the inverse of that fraction, which doesnt seem to match with what we want

[languid venture]

So b is like n/(n-1)

[olive stag]

ye

and that doesnt simplify to what we want

so c

lets try it

$f(-1/n)=1-1/(-1/n)$

[twin meteor]

IronVoltage

[olive stag]

eww

[languid venture]

N/(-n+1)?

[olive stag]

how do i make the fraction prettier

$\frac{a}{a}$

[twin meteor]

IronVoltage

[olive stag]

oooo ok

$f(-\frac{1}{n})=1-\frac{1}{-1/n}$

[twin meteor]

IronVoltage

[olive stag]

so gross but better

the negatives cancel and the inverse of an inverse is the original number

so it becomes

$1+n$

[twin meteor]

IronVoltage

[olive stag]

which isnt what we want

so we try the last one ig

[languid venture]

Yeah

[olive stag]

i am not used to writing in latex so bare with me lol

[languid venture]

Hhhh

[olive stag]

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

[twin meteor]

IronVoltage

[olive stag]

uhhh is that write uhhh

ye

so gross lol

[languid venture]

So it ? The 1 is under ?

[olive stag]

huh?

wdym

[languid venture]

I mean is it?

[olive stag]

oh yeah

cause

[languid venture]

Ohohoh

My bad

😬

[olive stag]

its just the inverse of f(n+1)
since f(n+1) = 1-1/(n+1)

we just slap that under a 1

yee nwnw

its alot going on

[languid venture]

So is d

[olive stag]

now we simplify x.x

[languid venture]

I got it

[olive stag]

dang taht was quick

u simplified?

[languid venture]

Kinda messy

[olive stag]

uhh

im guessint thats right LMAO

lots of lines

and n's

lol

[languid venture]

But is like 1/n/n+1

So like n+1/n? I guess?

[olive stag]

ahhh no guessing >:I

[languid venture]

Hahaha yeah

[olive stag]

1 sec ima simplify as well

[languid venture]

It is !

: )

[olive stag]

yeah its d

i simplified it to get 1+ 1/n

[languid venture]

Do u have time : )

Mind doing other question ?

[olive stag]

ill die in like 30 years so sure

[languid venture]

Hahahaha

[olive stag]

lmao

[olive stag]

sure i can do more

,rotate cw

[languid venture]

I don’t get the question for 42

[olive stag]

ahh hold on my eyes r not eying

1 sec

[languid venture]

Oh Okok

[olive stag]

back

[languid venture]

🫡

Do u plug the f(x) in the y

[olive stag]

ok so the y intercept is just the point on the graph that it intercepts the y axis (surprise)
BUT this only can occur when x = 0, cuz thats the x coord of the y axis

so what we do is that we first transform the given function

and slap a 0 for x and see what gets pooped out

[languid venture]

So like (x+2)^2-9?

X=0?

[olive stag]

so lets actually SEE what our new function looks like first

yes

escatly that

[languid venture]

So -5?

[olive stag]

but dont forget the absolute value

[languid venture]

Ohhh

[olive stag]

abs value

[languid venture]

So is 5

[olive stag]

ye

[languid venture]

44 and 45: )

[olive stag]

ye

,rotate ccw

i can never get it the first try

[olive stag]

hmm ok a lil trickier

[languid venture]

45 is a

I get it

X=0 so negative value in front of X

[olive stag]

so x intercept is just when y = 0 cause that is where the x axis is

so we gotta find at what x's y is 0

[languid venture]

For d, like x=y is switch them, what happen to y=-x do we switch then and plug negative?

[olive stag]

so we solve for x for 0=(x+1)(x-2)

wait huh

[languid venture]

Sry

Keep going

[olive stag]

r u talking about 45?

[languid venture]

I was like what’s the difference between c and b

C is like switch X and y right

What about d

[olive stag]

ahhh ic

hmm, my method was seeing what the zeros are for each of the answers but i feel like that is very tedious and isnt what the problem wants u to do. Like i feel like there is a rule about transforms thats like "oh if u translate it this way using A or something, it doesnt efect where the intercepts are!" type thing

if there is one i dont know it so im just gon run through the list

the x intercepts of the original function are when x = -1 and 2

[languid venture]

Ok

[olive stag]

so let's see y = f(-2x)=((-2x)+1)((-2x)-2)

$y = f(-2x)=((-2x)+1)((-2x)-2)$

[twin meteor]

IronVoltage

[olive stag]

set it to zero to find its x intercepts $(-2x+1)(-2x-2)=0$

[languid venture]

I don’t think is a and c then

[twin meteor]

IronVoltage

[olive stag]

doesnt seem like it, it will give fractions for the x's

OHHHHH its b

and i c why

[languid venture]

For b idk cuz like did the -2 affect?

And can’t be d

[olive stag]

nono it issssssss

cause look

[languid venture]

Set

Sry

I try to said d

Not b

[olive stag]

$y=-2f(x)$ then you set $y=0$ to find the x intercept

[twin meteor]

IronVoltage

[languid venture]

-2 won’t affect what happen inside cuz if you plug the same thing

U still gonna get 0 at the end

[olive stag]

$0=-2f(x)$

[twin meteor]

IronVoltage

[olive stag]

THEN DIVIDE BY -2!!!!!

$0=f(x)$

[twin meteor]

IronVoltage

[languid venture]

Yeah that’s what I thought

[olive stag]

zero divided by anything is zero

[languid venture]

-2 won’t affect what happen inside

[olive stag]

then u solve for x and its the same

ye

[languid venture]

👍👍👍

For 45 I get it cuz a

[olive stag]

that was a cool revelation for me lmao

[languid venture]

U just add negative in front of x

[languid venture]

Haha

[olive stag]

wait what answer did u get for 45?

[languid venture]

Can u explain what the difference of c and d, did d juts switch x and y and add negative in front of x?
And for b as u explain to me before is -y right

I got a

For the answer

[olive stag]

dont think its that

ill explain the difference between c and d

lemme look at them rq

[languid venture]

The answer key said is a though

[olive stag]

ok so in c. you literally replace any x's with y's and any y's with x's

[languid venture]

Switch x and y

What happen to d? Switch x and y and add negative sign in front of x ?

[olive stag]

so since f(x) = (x+1)(x-2)
x=f(y)
x=(y+1)(y-2)

for d u r just slapping everything under a 1/

so 1/((x+1)(x-2))

[languid venture]

Wait

[olive stag]

$\frac{1}{(x+1)(x-2)}$

[twin meteor]

IronVoltage

[languid venture]

What question are we?

[olive stag]

44

[languid venture]

Answer is b

Right ?

[olive stag]

yes

[languid venture]

Oh

I mean 45 d

My bad

[olive stag]

ohhh

[languid venture]

😣

[olive stag]

lemme see what the answer for 45 is first

[languid venture]

Okok

[olive stag]

45 is a were righbt mb

[languid venture]

And I just a little bit confuse

[olive stag]

wait what was ur qurestion about 45 c and d?

[languid venture]

For 45 b as u taught me before is -y right

[languid venture]

For c is like x and y switch what happen on d then, did they switch and add a negative sign in front of x?

[languid venture]

Did I understand correct for this btw?

[olive stag]

oh nonono, those equations are not saying that

[languid venture]

🫢

[olive stag]

read the question again, those are equations for lines

ur not switching anything

x=0 is the line that is the y axis

y=0 is the x axis

x=y is just a diagonal line (think of y=mx+b)

and x=-y is the same thing but with the opposite slope

like literally they are just y=mx+b equations

[languid venture]

Can you do each of the option

Like a

[olive stag]

wdym

[languid venture]

Is add a negative sign in X right

So like 2(-x)^2

[olive stag]

huh, i dont follow

[languid venture]

+3(-x)

So the answer is a because of that

[languid venture]

Did u get what I mean

😢

[olive stag]

i dont follow

i think ur misinterpretting the question?

[languid venture]

Ok, let said why is a correct

Because u plug in - in x because is reflect y axis so like 2(-x)^2-3(-x)

Right so u get g(x)

😐

[olive stag]

oh thats what u mean ic

ye thats why

x=0 is literally the y axis

and reflection across the y-axis is just u slapping a negative on any x u see

[languid venture]

Then what happen to b then

What answer will u get

[olive stag]

y=0 is literally the x-axis

[languid venture]

I don’t know how cuz I only know how to do a

Imao

[olive stag]

so reflection across the x axis is just slapping a negative on any y u see

[languid venture]

A is the only option I know how to do and is correct

Like ohhh

Wait

Like this?

[olive stag]

ye

like that :>

and reflection along the lines y=x and y=-x

i have no clue how to do

[languid venture]

I think just switch x and y right?

[olive stag]

🤷‍♂️

i legit dont remember how to reflect a function along any arbitrary axes

[languid venture]

Alr alr ty so much that all my question 😘😘😘

[olive stag]

sorry mate ;-;

[languid venture]

No is fine

Don’t feel sry

U help me so much

🥰🥰🥰🥰🥰🥰🥰

Thank you so so much

[olive stag]

glad I could help!

np!

[languid venture]

.close

[vocal sleet]

Channel closed

Closed by @languid venture

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[quaint jetty]

hi could anyone help with this

[quaint jetty]

i found my bounds

but im not sure what to put as my R(x)

At first I thought its only (4x-3sqrt(3))^2 but i think im missing smth

[deft oar]

why don't you graph it

[quaint jetty]

yeah used desmos

[deft oar]

also, this would be a height not a radius, I don't if you're using R(x) to mean radius or just as a general function

[quaint jetty]

as my radius

could you elaborate please

[deft oar]

look at the axis you're rotating around

[quaint jetty]

alright so the y axis

[deft oar]

(4x-3sqrt(x)) would be the height of the cylinder

[quaint jetty]

ohhh

[deft oar]

you'd have to dy to do washer method, I actually recommend sticking with shell method

[quaint jetty]

ah ic ok i got it thank you

[deft oar]

!done

[vocal sleet]

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

[quaint jetty]

.close

[vocal sleet]

Channel closed

Closed by @quaint jetty

Use .reopen if this was a mistake.

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

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

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

Channel closed

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

[vocal sleet]

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.

[modest wharf]

idk where to go from here

or if I even did it right

[vast shale]

hello

|| denotes?

[tidal dock]

absolute value of a complex number

[vast shale]

oh

[tidal dock]

i don't know if you can

give me a sec

[willow pike]

whats the question

[modest wharf]

sketch each of the following

so I’m just trying to find the circle equation

[willow pike]

yeah you almost did it

now you know center and radius

[modest wharf]

oh ok

[tidal dock]

yeah it's correct

[willow pike]

r² = 4

and position is (0, 2)

[modest wharf]

ok thanks

[willow pike]

from x and y - 2

[modest wharf]

ohhh ok ok

and then the sides are just

2+2i

-2+2i

[willow pike]

sides?

[modest wharf]

uhhh nvm

can u pls help me with this

for part i

what does it mean

[willow pike]

plot the center first

oh

it means that distance from 3 is less than or equal to distance from -3i

[modest wharf]

wat do i do with that info

[willow pike]

or you can once again convert z to x + yi

and form inequality

[modest wharf]

i plotted -3i and 3

[willow pike]

now

in the perpendicular bisector of them

|z - 3| = |z + 3i|

ok wait

before I go on

did you have any problem using any idea like this?