help-23

[nova creek]

If an example is necessary, construct one

You can do that with an example other than the literal question given

[earnest pond]

Guys please dont fight, im watching youtube for me to understand more of this lesson. I appreciate all the help, but dw i will figure out all the answers by solving it on my own.

[rigid inlet]

you can't just hold their hand the entire way.
you're doing the work for them, you're the only one holding hands

getting them to think for themselves, and providing only enough guidance to ensure their thinking is on the right track, is how you actually help someone learn

you don't learn how to do something by just looking at it

[toxic stratus]

bruh how is giving away the answer an example

[nova creek]

This isn't really up for debate. This server's teaching philosophy is against just giving away answers

If you want free answers, use chegg

[rigid inlet]

source, please

[nova creek]

A Socratic method esque teaching style has been shown consistently to provide good results

[rigid inlet]

I'm actually quite aware of various teaching methods, there is data explicitly suggesting that just looking at something is the most inefficient way to learn

[nova creek]

Ah yes the greatest source

[toxic stratus]

apply your personal experiences to yourself then

[rigid inlet]

"just trust me bro"

[toxic stratus]

then go do that on your own

that's not what this server does

it's explicitly stated in the rules

[rigid inlet]

"an example" is not the questions they're given

you've robbed them of the chance to figure things out themselves

christ you're dense

[toxic stratus]

well as it turns out you aren't geiko so what's your point

[nova creek]

The objective isn't to just memorize how to get the answer to a particular question. It's to understand the logic behind the answer, to understand the justification for why were doing what were doing

Having a deeper understanding to why we're doing something is much better than just memorizing what steps to do when

And such memorization doesn't even work in higher mathematics, where a conceptual understanding of the concepts is required

No, that's how you memorize the steps to get to the solution

Not why those steps work

[rigid inlet]

see a problem start to finish, and then apply it to another problem to confirm that you understand the process

[nova creek]

Or why we're doing those steps

[rigid inlet]

most people will get the answer right if you give them the answer, yes

the problems they're given on the test will not be the same

hence why they need to do it themselves to confirm they understand

source: trust me bro

[nova creek]

Intelligent people will prefer a conceptual understanding of the material than a mechanical one

(Not universal)

[rigid inlet]

you learn by doing the problems

we've said that a handful of times

[nova creek]

By doing probing questions, giving tips, guiding the person to the answer. That's how we teach

[rigid inlet]

notice how, after you gave them the answers, they said they were going to youtube. Your method is demonstrably horrible

[nova creek]

This server operates on a Socratic method esque teaching style

[rigid inlet]

along with it being against the rules, the fact that you're still arguing is incredibly asinine

[toxic stratus]

subreddit

[nova creek]

Fuck

[toxic stratus]

LOL

[rigid inlet]

they said "wait i'm trying to solve it"

they were in the middle of thinking, then you decided to cut the process short

you have 0 way of knowing whether or not they would have made headway, because "this works for me"

if they don't get it, they ask questions. Perhaps with another nugget of information, they get an idea of what to do

[nova creek]

Why do you think it'd take them 4 hours

Is it hard for you to believe that some people have critical thinking skills and can solve problems on their own

With a bit of guidance

This is literally not even debatable. This is clearly specified directly in #rules and #❓how-to-get-help

Then get banned because that's against the rules

If they don't want to learn, they shouldn't ask in this server

[rigid inlet]

the will was that they posted it in a server dedicated to learning

if they didn't care, they wouldn't post

[nova creek]

This is not the server to just get answers to questions

[toxic stratus]

everyone participating in this server should have read the rules before posting

if not that's on them

[rigid inlet]

we're not forcing anyone to do anything. If they no longer care, they can close the channel at any time

you, on the other hand, are removing the chance to learn, because they no longer have a means through which to demonstrate any understanding they may have

[warped roost]

.close

[safe radish]

Channel closed

Closed by @warped roost

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.

[marsh granite]

is there a way to factor out the denomator?

[thin bridge]

well yeh.

both terms have a common factor of 1/(x+6) and you can factor that out

[marsh granite]

how about just factoring x+6 out

i just want x+6 out

[thin bridge]

wdym

[marsh granite]

i dont want to factor out 1/x+6

i just wanna factor x+6

[thin bridge]

well (x+6) isn't a factor of the numerators

to forcible factor out (x+6) will result in stuff like

[marsh granite]

i remember that there was a way to factor out the denominator

[dense tiger]

1/x+6(x+9x^2+6x+3)??

[thin bridge]

$(x+6) \cdot\br{ \frac{x}{(x+6)^2} + \frac{(9x^2+6x+3)}{(x+6)^2}}$

[marsh granite]

oo

[thin bridge]

is what you're implying you want when you're saying you want to factor out (x+6)

[marsh granite]

how about like this?

[flat frigate]

ℝamonov

[marsh granite]

something same like yours

[thin bridge]

yeh.

[marsh granite]

i forget to add parentheses to the x+6

[thin bridge]

i mean its valid, but its not very meaningful and doubt that it helps you do anything

[marsh granite]

ye cause i was doing this. I wondered if there was a way to factor out the same denominators and cancel them out

[thin bridge]

what's the original problem

[marsh granite]

idk what to do now

hmm conjugate?

[thin bridge]

might work.

pretty sure there should be something more elgant

[marsh granite]

ow

ill try plugging in 0 first to see if it works before multiplying conjugate

ye its still in indeterminate form ill do conjugate

[safe radish]

@marsh granite Has your question been resolved?

Channel closed

Closed by @marsh granite

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.

[slender reef]

how to factor 2x^2+4

[slender reef]

find zeros

[safe radish]

@slender reef Has your question been resolved?

[safe radish]

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.

@bitter oak Has your question been resolved?

Channel closed

Closed due to the original message being deleted

[safe radish]

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.

[coarse heron]

Can someone pls explain how i derive the homo solution and particular pls

[safe radish]

@coarse heron Has your question been resolved?

[coarse heron]

@sonic wadi

<@&286206848099549185>

[white umbra]

for which question?

[coarse heron]

can start with v

how do you derive the characteristic equation from y''

because wouldnt that be r^2=0?

[crimson field]

r = 0 would give you y_c = c_1 + c_2 t.

[coarse heron]

u use repeated roots gen solution

cos r1, r2 = 0

hang on

[crimson field]

We require two linearly independent solutuons to obtain it's general solution so r = 0 twice gives us y_c above.

[coarse heron]

yeah beacause e^0 is just one

[crimson field]

Yes.

[coarse heron]

oh its that easy

ok so can u pls explain good ways in doing the undetermind coefficent?

[crimson field]

You can use the method of undetermined coefficients on the RHS which in effect here means the linear combination of the linearly independent derivatives of t^2. But since some of them are contained in y_c you need not include them.

y_p = At^2 (+ Bt + C).

[coarse heron]

so you need y'' to be in a similar format to the RHS, thus why you have more powers starting with yp

[crimson field]

My book makes usage of linear independence in the section on this*

[coarse heron]

by more powers, you can see yp is to the power 4 and so on

so when we derive twice we get same format as the RHS of equation. Which makes it easy to find coefficents>

?

[crimson field]

There's three cases for the method. They all start with the RHS which is Q(t) = At^2 + Bt + C.
The trial solutions changes if Q(t) contained terms t^k (terms of y_c).

Oh. It does include terms like that here doesn't it.

[coarse heron]

ok thank you, i think i understand it a little better now

[crimson field]

Due to y_c having the constant term we need to multiply our guess my t^2.

We can use any term of Q(t) and see that y_c contains a term t^2(a term of y_c) so we need to guess the linear combination of t^4 and it's linearly independent derivatives like you have.

[coarse heron]

ok, so then when we find y'' and sub it into yc, we can easilt find the undetermined coeffieicnets of the RHS

[crimson field]

Yes.

Just have to be careful when you substitute it in you don't make any errors.

[safe radish]

@coarse heron Has your question been resolved?

[safe radish]

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.

[chrome sorrel]

Can anyone tell me is E(Y|X=1) = 0(0.042/0.249) + 1(0.207/0.249) ?

[safe radish]

@chrome sorrel Has your question been resolved?

[chrome sorrel]

<@&286206848099549185>

[rigid inlet]

yes

[chrome sorrel]

Thanks

.close

[safe radish]

Channel closed

Closed by @chrome sorrel

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.

[raw pebble]

not sure how to solve c

[safe radish]

@raw pebble Has your question been resolved?

[safe radish]

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.

[devout harbor]

How does that simplification to 1-sin^2 t come about?

[thin bridge]

expand and simplify?

[devout harbor]

yes I get 4 sin t + 1 - sin^2 t

[thin bridge]

show work

[devout harbor]

4(sint + 2) - 3 - (sint + 2)^2

4sint + 8 - 3 - sin^2t -4

4sint +1 - sin^2t

[thin bridge]

you didn't square (sin(t) + 2) properly

[devout harbor]

ah fuk

I see

lemme try again haha

yrah it simplifies to 1 - sin^2 t

thank you fellas

.close

[safe radish]

Channel closed

Closed by @devout harbor

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.

[dapper sinew]

How is (n+1)! expanded

[split ether]

(n+1)! = (n+1)*n!

If you want to expand it to the fullest then just use the definition of a factorial

[safe radish]

@dapper sinew Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[cedar lance]

We have this math problem:
"A ball is dropped from a height of 8 feet. If every time it bounces 60% of its previous height, what is the total distance traveled by the ball?"

And we were given this example earlier. The teacher told us that a_1 was "2(4)" because 'tossing' a ball meant it would double the distance. Does that mean I won't multiply the a_1 in my new problem with 2 because I will only be dropping it? Or am I not understanding?

[buoyant shadow]

what teacher said doesn't make sense to me

you add the height to the travelled distance sure, it's not called "doubling"

[cedar lance]

Ah I see.

[buoyant shadow]

maybe it makes sense though

with the way formula works, i don't get it

[cedar lance]

Me neither mans.

[buoyant shadow]

i think they messed up

[cedar lance]

Okay so I don't know if I got it or not but what I did was use the "infinite geometric series" formula:

My "a_1" is "8"
My "r" is "0.6"

Idk if this is right.

[buoyant shadow]

ok I see, you double it when it's tossed

the whole thing

2(a/(1-r))

this makes sense, every stretch down has an up stretch of the same height

and if it's dropped, you subtract from that

[cedar lance]

I think I kind of get it, but I'm unsure by what you mean in subtracting?

[buoyant shadow]

like if it's dropped from 4 meters, you do 2(4/(1-r)) - 4

just because it did not go 4 meters up

doubling happens in both cases

[cedar lance]

I'm very confused.

[buoyant shadow]

the geometric series gives you the sum of the black part

the yellow part is identical so you double

if the ball is dropped, it's not identical it starts from the second arrow

[cedar lance]

Oh, but the 4th yellow part shouldn't exist right?

[buoyant shadow]

yes but it doesn't change the answer because it's always inifinitely small

you'd just subtract 0 to correct for it

[cedar lance]

Ahh.

Hmm I think I kind of got it, thanks for your help!

.close

[safe radish]

Channel closed

Closed by @cedar lance

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.

[fickle trail]

Why is this showing absolute value of a?

Why not just a rather than |a|

[quasi bison]

to cover both positive and negative values of a

with the unstated proviso that negative values yield a reflection in addition to the stretch/compression as specified.

[fickle trail]

Just a bit later it mentions the reflection

[fickle trail]

OK thanks

So it just covers positive and negative values. It is NOT suggesting that a negative value would turn positive

I get messed up when I see the absolute value in formulas, domain, range, etc thinking that it won’t accept negative values or something

[fickle trail]

Couldn’t the bottom right also be written ±a rather than |a| ?

Wait nvm

That wouldn’t make sense, -a > 1

OK thanks. Only thing positive or negative indicates is upward or downward direction

.close

[safe radish]

Channel closed

Closed by @fickle trail

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[coral pendant]

how do i get help

[idle parrot]

You just ask ur question directly

[coral pendant]

here it is

[foggy salmon]

lol by asking what u need help with

so

[coral pendant]

are you a mathematics genius

how do you do it cute little goddess?

[foggy salmon]

u can consider 2 rectangles

that pink bit

and the bigger one

which is the pink bit + the original part

[coral pendant]

can you do it and ill see if i get the same

[foggy salmon]

so u first find the bigger one

[coral pendant]

yes

[foggy salmon]

um no im supposed to

guide u to the ans

[coral pendant]

do you do 3(8x+8)

[foggy salmon]

so whats the expression that

as in how to multiply it?

[coral pendant]

and simplified?

[obtuse jackal]

It's also quite obvious you're in a test here, so that's very sus behavior

[coral pendant]

im not in a test

its homework

and i don't understand

[foggy salmon]

eh its ok

u cant rly tell

unless they

[coral pendant]

wdym test

[foggy salmon]

actually say hey im in a test

[coral pendant]

like and exam

im not

[foggy salmon]

i need help rn

[coral pendant]

its my homework

[foggy salmon]

yes

anyway

so whats the expression that would give u the

big rectangles area

[coral pendant]

i don't know

[foggy salmon]

whats the formula for a rectangles area

[coral pendant]

i don't know

[foggy salmon]

i was expecting that to be known

:c

[coral pendant]

oh

[foggy salmon]

the area of a rectangle is its

base * height

so

like with this diagram

its those 2 stuff they show

get it?

[coral pendant]

ok

can you give me your answer

[foggy salmon]

um no

[coral pendant]

what

[foggy salmon]

uve to work it out

[coral pendant]

why not

[plucky elk]

can't give answers here. it's against the rules

[coral pendant]

fr?

thats brazy

[foggy salmon]

ikr

[final halo]

so brazy

[coral pendant]

crazy

[plucky elk]

yea insane that we want people to learn instead of copying down answers

[foggy salmon]

braZY!

[plucky elk]

i'm going brazy, brazy, brazy, brazy just thinking about you

[foggy salmon]

ok anyway

back to the Q

[plucky elk]

https://www.youtube.com/watch?v=qi-KCd0guJI

[foggy salmon]

what would the width and length of the big rectangle be

[coral pendant]

base times height

[foggy salmon]

i like this diagram more

yes

[coral pendant]

how do i find that

[foggy salmon]

and what is base and height here?

[coral pendant]

3

8x+8

[foggy salmon]

how did u get

3

and

no the

oops lemme

[coral pendant]

its the bottom isn't it

[foggy salmon]

this rectangle

whats the base and height

[coral pendant]

8x+8

5x+4

[final halo]

this song is as old as some of the kids on this server

[foggy salmon]

ok and

the formula wants u to multiply those 2 to get the area

so what happens when u multiply then

[coral pendant]

im working here 😠

[foggy salmon]

its ok chill

[coral pendant]

8x+8 x 5x+4

[foggy salmon]

we also do a bit of trollin sometimes

[coral pendant]

im joking

obv

im doing it on purpose

[foggy salmon]

ok have u heard of

order of operations

[coral pendant]

anyway

[foggy salmon]

u need brackets

[coral pendant]

whats that

[foggy salmon]

else its totally different

so

like

1 + 1

multiplied by

1+ 1

we write it as

(1+1) * (1+1)

if we wrote

1+1 * 1+1

that

• normally is handled first

so it becomes 3

[obtuse jackal]

Sorry to tell you they're not kids anymore

[coral pendant]

(8x+8) (5x+4)

[foggy salmon]

ok then what happens when u expand that

distribute the terms

[final halo]

hey, groot is working here😠

[foggy salmon]

LOL

[coral pendant]

tiems it

[plucky elk]

me irl 🧓🏻

[coral pendant]

so

we times it

[foggy salmon]

yes and

what expression do we get

[final halo]

ok well i stand corrected, its as old as me

[plucky elk]

YOU ARE KID

[foggy salmon]

groot disappeared :c

[safe radish]

@coral pendant Has your question been resolved?

[plucky elk]

*:b

[foggy salmon]

i think

groot didnt actually wanna stydy lol

[plucky elk]

i think so

[foggy salmon]

:c

[safe radish]

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.

[safe radish]

Channel closed

Closed due to the original message being deleted

[crude prism]

.close

[safe radish]

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.

[nova arch]

I got a question

[safe radish]

Please don't occupy multiple help channels.

[foggy salmon]

can u type it out

its bit hard to read :c

[steep dove]

,rotate

[steep dove]

that looks so nasty

[nova arch]

idk how to type it here in latex

[nova arch]

yeaa thanks

[foggy salmon]

i too am bad at latex

u can just say like

lim(from x to 9)

just put approriate brackets n stuf

[nova arch]

with the sum and fraction it will look worse

if p is odd this will be 0

[steep dove]

yep

[nova arch]

what if p is even ?

[steep dove]

use l'hopital's

[foggy salmon]

hm i think

[nova arch]

I'm not allowed to use it

[foggy salmon]

rewrite the bottom as a geometric sum

i mean

its a geometric series

[nova arch]

it will be

[foggy salmon]

use the formula on it

[steep dove]

^

[nova arch]

[1-(-1)^p]/[2]

1-1/2 then another 0

but it will be (x+1)/0

[steep dove]

dont evaluate it

just expand the geometric series in terms of x

[nova arch]

1+x+x^2+......+x^(p-1)=[1-x^p]/[1-x]

[steep dove]

ok you can simplify the original now a little

[foggy salmon]

lol low response rate

:c

[nova arch]

huhhh

(1-x^2)/(1-x^p)

[nova arch]

lol

[steep dove]

honestly i still dont know why you arent allowed to use l'hopitals

but basically it will approach the ratio of the powers

i dont know how to explain that without rates of change tho

[nova arch]

lhopitals is used after highschool still we don't use it all the time to know really what's the function we're dealing with

[foggy salmon]

its just

sometimes they want certain methods used

just gotta follow that ig

[nova arch]

yes

thanks a lot

.close

[safe radish]

Channel closed

Closed by @nova arch

Use .reopen if this was a mistake.

[safe radish]

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.

[split cypress]

An investigator has a spreadsheet showing family incomes for 100 subjects in a certain study. These range from $5,800 a year to $98,600 a year. By accident, the lowest income in the spreadsheet gets changed to $58.
Does this affect the average? Enter the amount that this error changes the average, or 0 if there is no change.

To find the percentage change i did 5800-58/100 = 5742/100 = 57.42 . I'm not sure if im doing this incorrectly or not, but my homework is marking it wrong

[safe radish]

@split cypress Has your question been resolved?

[split cypress]

<@&286206848099549185>

[light shoal]

maybe it's expecting -57.42? (the average decreases, not increases)

also, that's an absolute change, not a percentage change

i.e. the average changes by -57.42, not by -57.42 percent

[split cypress]

thank you T_T it's correct. i thought we couldn't because there was a dollar sign in front of it

[safe radish]

@split cypress Has your question been resolved?

[safe radish]

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.

[lean otter]

Hey I'm still having trouble with part b

I know part a is 0 -1, 1 0

how would I reflect it?

I see this for a similar problem

but I don't understand what's happening here

is this literally just assigning the x2 column to -x1 column?

[safe radish]

@lean otter Has your question been resolved?

[thick sparrow]

https://math.stackexchange.com/a/525112

This post should offer a good enough explaination on your problem 🙂

[toxic stratus]

nono dont do that

thats too much work for a simple problem

you just need to figure out where the basis vectors are sent

you can do that with just a diagram

draw a cartesian plane and follow where (1, 0) and (0, 1) get sent after the rotation/reflection

it shouldnt be too hard

[safe radish]

@lean otter Has your question been resolved?

[foggy salmon]

lol

[safe radish]

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.

[lean otter]

This worked, I appreciate it. I think I was overthinking the problem and not doing it geometrically

[lean otter]

.close

[safe radish]

Channel closed

Closed by @dire raptor

Use .reopen if this was a mistake.

[safe radish]

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.

[snow robin]

When i have $\frac{\partial}{\partial \theta}\dot{\theta}^2$ what do i do?

[flat frigate]

Katharine

[foggy salmon]

whats the dot

[snow robin]

derivative to time

it's angular position and angular velocity

[foggy salmon]

oh

[snow robin]

$\frac{\partial}{\partial \theta}{\left(\frac{\partial \theta}{\partial t}\right)}^2$

[foggy salmon]

u r so good at latex

[flat frigate]

Katharine

[foggy salmon]

yea i was about to do that but ok

i woulda taken awhile to

[snow robin]

i genuinely don't know what to do

i'm trying to figure out lagrange mechanics for a pendulum

but the person whose notes i'm looking at didn't write all steps down

[foggy salmon]

yea im not sure exactly what u can do with partial derivatives :c im not the best here sorry

[snow robin]

wolfram says that it is 0 if i use x for theta

[wind stream]

well it would still be 2dtheta/dt * par(dtheta/dt)

where par is the partial operator wrt theta

[stark cloud]

wdym?

do you not know how to take the partial derivative?

[snow robin]

i do but i don't know how to take a partial derivative like this

[stark cloud]

or is the notation confusing or smth

[snow robin]

i don't understand what d/dx (dx/dt)^2

is

[stark cloud]

im still not quite sure what u mean...

ohh i get what u mean i think

pretend taht $\dot{\theta}(t)=\phi(\theta(t))$

where phi some function

[flat frigate]

rockpaperscissors

[stark cloud]

if ur studying pendulums

i assume uve studied simple harmonic motion and the differentail equation defining it

there u exress the double derivative in terms of the original funciton

the situation is the same here

[snow robin]

what is d/dx of dx/dt?

[stark cloud]

try to use cahin rule

[wind stream]

you just need to ignore that theta depends on t for now

[stark cloud]

$\frac{\dfrac{dy}{dx}}{\dfrac{dt}{dx}}=\frac{dy}{dt}$

[flat frigate]

rockpaperscissors

[wind stream]

tho im a bit curious, why are you taking the partials of theta wrt theta? Iirc, we should be taking the partials of the lagrangian wrt theta?

[snow robin]

it's the lagrangian but i left out the constants

this is the lagrangian of a pendulum according to the guys notes

[wind stream]

yeah should be what you have

taking that wrt theta

like just ignore that theta is a funciton of t, imagine it as a variable

and then differentiate

[snow robin]

i know what mglcos() is

[stark cloud]

its theta dot squared

[snow robin]

differentiated to theta

[stark cloud]

thats why katherine havign problem

[snow robin]

but theta dot

[stark cloud]

its shm

ofc thers a second derivative term

[wind stream]

no, there is no second derivative here

[stark cloud]

anyway use this

??

[wind stream]

again, we are taking the partials derivative wrt theta

[stark cloud]

there ahs to be an accelration term

[wind stream]

not the derivative

[stark cloud]

dude ur not understanding

$\frac{1}{2}ml^2\dot{\theta}^2}$

[flat frigate]

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

[wind stream]

i dont want to spoil the answer but technically after taking the partial, you should have $\frac{\partial L}{\partial \theta} = -mgl\sin (\theta)$

[flat frigate]

waler

[wind stream]

it has nothing to do with second derivative and stuff

[snow robin]

but why

[wind stream]

this is because the partial of theta dot is 0

[snow robin]

why is d/dx of dx/dt 0

[wind stream]

again, note that this is the partials derivative

meaning we are taking the other variables as constant

and theta as our only variable

theta dot is a function of t, hence the partials of theta dot is 0

because t is a constant wrt theta

[snow robin]

ok

[wind stream]

and this also has nothign to do with the implicit differentiation too

it's jsut how partial differentiation works

i think michael van bezen has a video on the lagrangian of the pendulum iirc, if you are unsure of something, you could check him out

he also does langrangian for other mechanics too

[snow robin]

ok thanks for the reference, this guys' notes are terrible for learning XD

[wind stream]

sure np, lagrangian is not too hard after some exercises, good luck with it

[snow robin]

ty

.close

[safe radish]

Channel closed

Closed by @snow robin

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.

[robust sonnet]

what are the answers

p.s some of these answers are wrong

[foggy salmon]

u can try

graphing it and connecting the points on the graph

[robust sonnet]

then

[cedar rover]

then.. answer the questions?
If you don't want to graph it you can use the intermediate value theorem

[robust sonnet]

thats whats our lesson about and its so confusing 😭

the intermediate value thm

[cedar rover]

Mh ok, what's confusing you exactly?

[robust sonnet]

everything about it the prof didnt explain it well at all

[cedar rover]

Ok, I suggest checking this video out, it looks awesome
https://www.youtube.com/watch?v=BNLu4_3Okuk
This video contains a proof too, but if you are not interested in that just ignore it

[robust sonnet]

ok ty

[cedar rover]

I found this one too, this is more practical

https://www.youtube.com/watch?v=j3tPwgqS4ns
I haven't seen this one specifically, but usually RobBob does a good job at explaining

[safe radish]

@robust sonnet Has your question been resolved?

Channel closed

Closed by @robust sonnet

Use .reopen if this was a mistake.

[safe radish]

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.

[dire crypt]

how do i find lim x tends to infinity (2x^2 - sin3x)/(x^2+10) with the help of LH rule

[split ether]

What are you having troubles with?

[dire crypt]

i double derivated num and denom to get, (4+9sin3x)/2

what do i do next

[halcyon carbon]

differentiated I think

[dire crypt]

ok

[split ether]

You can't apply LH rule twice here

After applying it once you get this

Which isn't an inf/inf situation

Are you sure you're supposed to use LH rule btw?

Because the limits don't match

Before and after applying it

Perhaps you should use the squeeze theorem and LH rule only after that

[safe radish]

@dire crypt Has your question been resolved?

[safe radish]

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.

[languid shadow]

I am certainly getting messed up for the set up of this problem

I first want to sketch the graph and when I do, then I want to find the points of intersection so I set x^2 + 2 = 1

and I end up getting x^2 = -1 but I feel that I'm wrong for finding the intersections

[crimson field]

Well y = x^2 + 2 intersects x = 1 at x = 1.

Just sketch all three curves and you should see what the bounded region is meant to be.

[languid shadow]

Yeah, when I graph that, I notice they intersect at two points

[pulsar hull]

do you know integral

[crimson field]

Sounds impossible. Can you show your graph.

[languid shadow]

well actually, only once

they only intersect at x=1

Integral of?

[languid shadow]

so when I wanted to find the area, I plugged in 0 & 1 as the bounds,

[pulsar hull]

no it is integral but because it is a parabole

you simply can divide area by 3

1 remains in the drawn area

and 2 in the other one

2/3 and 1/3 actually

is to find the center x point of the drawn area a lil bit complicated integral

[languid shadow]

so in this instance, since I'm dealing with a Parabola, I find the area then divide by 3 and that gives me what?

I think I'm a bit more confused but thanks for trying to help!

.close

[safe radish]

Channel closed

Closed by @languid shadow

Use .reopen if this was a mistake.

[pulsar hull]

it is just a formula I dont remember what was the name of it @languid shadow

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

[topaz rivet]

Show that $y(x)=2 x^2+\frac{1}{x^2}$ is an explicit and unique solution to the initial value problem $x^2 y^{\prime \prime}+x y^{\prime}=4 y, \quad y(1)=3, \quad y^{\prime}(1)=2$ on the interval $(0, \infty)$

kinda confuse on the interval, i think the only time it does not satisfies the equation is when x=0

[flat frigate]

Ji

[topaz rivet]

I've shown that y(x) is a solution but the interval (0, infinity)

kind of confuses me

[halcyon carbon]

x=0 is not included in the interval

[topaz rivet]

yes but how about x<0

i think that should be included

[toxic stratus]

your question doesnt care about x<0

and if your y really is the solution to the IVP

then the solution over x<0 cannot be determined

[topaz rivet]

why?

[toxic stratus]

y is discontinuous at x=0

[topaz rivet]

ohhh

[toxic stratus]

the initial values are in the region x>0

so the domain becomes disconnected

[topaz rivet]

ah now i get it

thanks

.close

[safe radish]

Channel closed

Closed by @topaz rivet

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.

[pseudo nimbus]

I'm stuck on how I would solve this. The last tutor I went to told me to look up the commission formula online (since my professor didn't provide it), and I found it, but I'm still stuck, as my professor didn't show us a problem like this in the lectures. I'm unsure of even where to start

[pseudo nimbus]

For context: This is college level alegebra

[safe radish]

@pseudo nimbus Has your question been resolved?

[pseudo nimbus]

<@&286206848099549185>

[nova creek]

What have you tried

[pseudo nimbus]

I'm not sure where to plug in each value in the formula as I dont know which part goes where

I know that commission = Saleprice x Commission rate but Im not sure how it relates

[nova creek]

Well, we're trying to find the sales level that makes both options equal

So let's call that x

[pseudo nimbus]

Alright

[nova creek]

So if the sales level is x, how much money do you make per month with the first option?

[pseudo nimbus]

3300 plus that 5% of sales

[nova creek]

What is that as a mathematical equation?

[pseudo nimbus]

3300 + 0.05?

[nova creek]

There's no x in the equation?

So how much you make doesn't depend on the sales level?

[pseudo nimbus]

I guess it could

So would it be 3300+0.05x?

[nova creek]

Yes

What about the second option?

[pseudo nimbus]

3700+0.04(x), but it says its commission, not sales

[nova creek]

The commission is how much of the sales you get

[pseudo nimbus]

Oh they mean the same?

[nova creek]

Well, not the same as sales

The commission is the fraction of the sales you get

If your sales were $100, you'd get to keep $5 as per the first option

[pseudo nimbus]

Ah alright

[nova creek]

Now, we want to find the value of x that makes both options equal

How can we do that?

[pseudo nimbus]

Im not really sure

Oh wait

Can we set them equal to eachother then solve for x?

[nova creek]

Yes

[pseudo nimbus]

ok I got x=40,000

Alright that was the right answer

Thank you so much

.close

[safe radish]

Channel closed

Closed by @pseudo nimbus

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.

[real geyser]

So we have a clock that isn't working properly.

[stray socket]

A broken clock is always right twice a day

[real geyser]

Hahahah

Clicked to quickly on enter XD

[bold ferry]

[real geyser]

Havent finished the problem

Alright so one of the hands of the clock goes in the opposite direction. (counter clockwise)

So from the 0 point one goes to the left and the other to the right.

Create a formula that will calculate the distance apart from each other of one of the hands.

We should take the right "hand" by the way. the one that is going clockwise

The clock is btw also broken in times and minutes.

Am I overthinking this?

<@&286206848099549185>

[safe radish]

@real geyser Has your question been resolved?

[dire crypt]

it would be 4x in numerator

[dire crypt]

@plucky elk

[split ether]

mb

[safe radish]

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.

[polar knot]

heres what i have so far

i dont know what to do next tho

i need a hint

[safe radish]

@polar knot Has your question been resolved?

[white umbra]

what is the highest possible the y-intercept of S could be?

and what is the lowest possible?

once you know those, you know the answer

[polar knot]

it would be 8 and lowest would be 1

but no the

answer is 33 i know from anyswe key but how the hell did they get 33

[white umbra]

highest is correct

lowest isn't

[polar knot]

why

nvm

ik why

to find the lowest i just find where the perpendicular line

intersects (-15, 0) right

[white umbra]

yup :) figure out the y-intercept of that line

[polar knot]

bruhr how

[white umbra]

and then the y-intercept of S has to be > that

[polar knot]

well

i know the slope of that line mustbe

-5/3

right

[white umbra]

yup!

[polar knot]

wait

0 = -5/3(-15) + b

find b

[white umbra]

yup :)

you can also use point-slope form

[polar knot]

aha

wait ik it

let me think

dont tell me

[white umbra]

yay! :D

[polar knot]

shittt what is it

y2-y1 = m(x2-x1)

FCK

0-y = -5/3(-15-x)??????

or is it the other way

[white umbra]

you can write it like that, or y-0 = -5/3(x-(-15))

they're both correct

[white umbra]

but yeah once you solve this equation, then you basically know the answer :)

[polar knot]

so know

now*

i set the 0

in the eqution to 0

so

y = -5/3(15)

right

[white umbra]

yup

so y = what

[polar knot]

uhhhhhhhhh

uhhh

why am i not getting this

nvm

[white umbra]

what's 15 / 3

[polar knot]

y = -25

[white umbra]

yea!

so now you know

the y-intercept has to be what

[polar knot]

it must be

-24 to 8

which means there are

because it says

it doesnt count when u touch the axis

[white umbra]

yep :))

so how many numbers are there in -24, -23, -22, ..., 6, 7, 8?

[polar knot]

wait then my teacher made a mistake

[white umbra]

how?

[polar knot]

32

[white umbra]

how did you get that

[polar knot]

33*

[white umbra]

yea

33

[polar knot]

i forgot about 0 xd

[white umbra]

haha

[polar knot]

ty

i have another question

i know how to solve this with algebra

but how do solve this with graph?

i will try myself first

if it doesnt work u hint me

[white umbra]

how did you solve it with algebra

[polar knot]

welll

lets say egg is x

and toast is y

2x = 1.5

x + y = 0.9

[white umbra]

do you mean 2x + y = 1.5

[polar knot]

huh

o yea

[white umbra]

okay yea

[polar knot]

2x + y = 1.5

[white umbra]

by graphically it just means

[polar knot]

x + y = 0.9

[white umbra]

plot those two lines

and then

[polar knot]

so now i just have to do this

[white umbra]

based on that graph, how would you be able to tell the answer?

[polar knot]

y = 0.9-x

so now i can do

2x + (0.9 - x) = 1.5

and then solve for x

[white umbra]

yeah that's correct

[polar knot]

where they intersect

yea ok ik now but

[white umbra]

yea

[polar knot]

can you explain to me

WHY when they intersect

it works?

[white umbra]

okay

[polar knot]

i want to know WHY that works like how and why

[white umbra]

you want to find x,y such that both the equations are true right?

so like

[polar knot]

i brb 5 mins

[polar knot]

yea

sorry i brb for 3 mins

sorry

brb

[white umbra]

both x+y = 0.9 and 2x+y = 1.5 are true

well

a point (x,y) satisfies x+y = 0.9 if it's on the line when you graph x+y = 0.9

and similarly, a point (x,y) satisfies 2x+y = 1.5 if it's on the line when you graph 2x+y = 1.5

so the solution has to be on both lines AKA the intersection

[polar knot]

wait

can u graph it

no ill graph it

[polar knot]

bac

back

x + y = 0.9

2x + y = 1.5

y = -x + 0.9

y = -2x + 1.5

now i set them equal

cuz its hard to graph

[white umbra]

I thought you were trying to figure out how to do it graphically

[polar knot]

BUTS HARD TO

i invted a new word

but's

xd

it means but its

too hard to graph decimals precise

[white umbra]

Lol

[polar knot]

argh i messed up my graph

[polar knot]

is this correct atleast

[white umbra]

Yes

[polar knot]

sorry im really stupid ):

ok i graphed it

[white umbra]

No you're not!

[polar knot]

i am xd

i dont even know how I made

extended maths

with my idiocracy

[white umbra]

You are not!

[polar knot]

i graphed it but i cant find

how am i suppose tofind the exact value with a pencil graph

...

nvm i AM STUPID

i got it

i just need to sharpen my pencil xd

i just hand drew grid paper

I FOUND IT

30, 60

with a graph

(60, 30)

@white umbra i have a question how do i know which one is egg and which one is toast

[white umbra]

^

[polar knot]

oh

tysm

last one!

adult = a

child = c

5a + 2c = 2345

a + c = 568?

[white umbra]

yup

make sure to be precise though when you're defining your variables

a = number of adults

c = number of children

for more complicated problems, this can trip you up if you don't know exactly what your variables mean

[polar knot]

5a + 2c = 2345

a + c = 568

c = 568 - a

5a + 2(568 - a) = 2345

3a + 2(568) = 3245

3a = 1209

a = 403 (tickets sold)

c = 165 then since total is 568

price (a)(403) + 2(165) = 3554

403a = 3554 - 330

a = 8

the new price is 8$

right

[white umbra]

wait what is a in this equation?

[polar knot]

a is the price of the new adult ticket

since child ticket and sales dont change

and we know the new total is 3554

we can find a

[white umbra]

okay

my advice is don't use the same letter to mean two different things

or else it'll get confusing

and whenever you introduce a new variable, define what it is

you're correct that it's $8 tho

[polar knot]

ok thx

.close

[safe radish]

Channel closed

Closed by @polar knot

Use .reopen if this was a mistake.

[white umbra]

np

[safe radish]

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.

[vivid pewter]

Can someone give an idea on how to solve this sommation

[vivid pewter]

Though I would really appreciate it if I am not given the answer

[obtuse jackal]

The usual trick for these of a^k * (k+1) that it equals d/dx(x^(k+1))(a). Here use the derivative trick twice.

The second trick is how to slightly adjust the k^2 to make it work with the double derivative trick

[vivid pewter]

Thank you very much

[safe radish]

@vivid pewter Has your question been resolved?

[vivid pewter]

I give up

Can someone please teach me how to do them step by step

<@&286206848099549185>

<@&286206848099549185>

.close

[safe radish]

Channel closed

Closed by @vivid pewter

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[gritty lotus]

i dont get the second last step

how did they move $x^(-2/3)$ to the top?

[flat frigate]

Arm

[gritty lotus]

<@&286206848099549185>

[tardy mango]

!15m

[safe radish]

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

[gritty lotus]

ah shoot forgot its 15mins!

[halcyon carbon]

Exponent rules

$a^{-m} = \frac{1}{a^m}$

[pure agate]

a^{-m}

[gritty lotus]

so wouldnt it be

[flat frigate]

Pure

[gritty lotus]

$x^2 - x^-2/3$

[flat frigate]

Arm

[gritty lotus]

since b^x/b^y = b^x-y

[halcyon carbon]

Why would there be a minus sign?

[pure agate]

--> x^{2} - x^{-\frac{2}{3}}

[gritty lotus]

using these rules

[unreal pasture]

$x^m*\frac1{x^{-n}}=x^m*x^n$

[flat frigate]

𝙲𝚊𝚜𝚝𝚟𝚕𝚎

[halcyon carbon]

Use the second rule you would get $$x^{2-(-\frac{2}{3}})$$

[gritty lotus]

ah right

[flat frigate]

Pure

[gritty lotus]

so what rule do we aply?

for the second last step?

[halcyon carbon]

You can think of it two ways

One

$$ \frac{1}{x^{-n}} = x^n$$

[flat frigate]

Pure

[halcyon carbon]

And so $$\frac{8x^2}{16x^{-\frac{2}{3}} = \frac{x^2\cdot x^{\frac{2}{3}}$$

[flat frigate]

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

[gritty lotus]

like this right?

[halcyon carbon]

Ah

2^-2 is not -4

And 1/-4 is not 4

1/2^-2 = 2^2 = 4 is the correct steps

[unreal pasture]

Think of rule 2, but x=0

[halcyon carbon]

That works too

[unreal pasture]

Yea

[halcyon carbon]

But the point is

If you have a negative power at the bottom

You can bring it to the top and change the sign

Or any power at the bottom

Bring it up to the top and flip the sign

[gritty lotus]

so i can bring a variable with a power to the top, so long i switch the sign?

[halcyon carbon]

Yeah

[gritty lotus]

interesting

thank you very much 🙂

[halcyon carbon]

Np

[gritty lotus]

.close

[safe radish]

Channel closed

Closed by @gritty lotus

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.

[fierce gust]

Find Domain:

[tardy mango]

note that the denominator cannot equal 0, since dividing by zero causes an undefined result.
Also, the radicand must be non-negative

[pure agate]

There is also a limitation of the square root as well.

[tardy mango]

edited 🙂