help-4

[stable parcel]

That's a bit off.

[undone crane]

oh crap

I'm using (P+1)-(E+O1+O2+O3) as my equation from part a

[stable parcel]

It should be I instead of 1.

[nimble crypt]

I got -3879 cfs

[undone crane]

I mistyped, I used I not 1

[stable parcel]

,calc 2250 + 2050 - 1769 - 4100 - 1270 - 1040

[rocky lotus]

Result:

-3879

[stable parcel]

Then you convert ft^3/s to mi^3/(7 days).

[nimble crypt]

Than divide with the area of the lake to get how much does that water level drop

[vale dock]

@undone crane Has your question been resolved?

[undone crane]

Ok I got -1.38 in loss

[vale dock]

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.

[merry jasper]

Is this correct?

We haven't discussed the rules of derivatives yet, so this is what we were asked to do

[hardy coral]

No, that makes little sense

Is the goal to compute f'(x)?

If so, why the lim {x -> 0} ?

And what is h?

[safe fulcrum]

yes, it should be $\lim_{h \to 0}$

[rocky lotus]

south

[safe fulcrum]

your answer isn't correct so there must be something wrong in the intermediate steps

[hardy coral]

Ok well that's what I didn't want to say but sure

[safe fulcrum]

probably some arithmetic

[merry jasper]

oops

yeah it shoyuld be

[safe fulcrum]

you better just tell them so that they know what they did wrong

[merry jasper]

h approaches 0

my bad

thanks for noticing

[merry jasper]

which part

[hardy coral]

I just believe it's better to catch your own mistakes yourself once you know where to look

[hardy coral]

Should be 6x at the end, not 8x

[safe fulcrum]

here

[hardy coral]

So somewhere along the way you have a 2x surplus

[safe fulcrum]

oh the arrow started from the wrong place but yes

[safe fulcrum]

fair

[merry jasper]

wait, i don'

[safe fulcrum]

yeah you added a +2x out of nowhere

[merry jasper]

which 2x

[safe fulcrum]

in the 3rd line

[merry jasper]

this?

[safe fulcrum]

no, before that

should read $6hx^2 + 6h^2 x + 2h^3$

[rocky lotus]

south

[merry jasper]

ohhh

cause it was

the

h and x

are

together

[safe fulcrum]

yeah seems like you misread your own work

[merry jasper]

yep

i didnt notice that

so the final answer is

$6x^2 + 6x - 6$

[rocky lotus]

Sakurora

[safe fulcrum]

yep!

once you learn the power rule you'll know why

[merry jasper]

wait so, what happens to the

6hx

why does it become 6x

[safe fulcrum]

you just use the limit definition on x^n instead and it's some binomial theorem

[safe fulcrum]

you divided by h remember

[merry jasper]

ohhhh yeah

wait, let me re write it

Ohh so the 6hx disappears right cause times 0

and then the 6x comes from the 6xh

[hardy coral]

Basically once you've completely expanded the f(x+h)-f(x) expression in the numerator, all the terms that don't have an h should cancel out, all the terms that have an h^2 or higher become insignificant and you're left with all the terms that have a single h, which cancel with the denominator

[safe fulcrum]

that looks so much like cos x....

but yes, I see, (0)

[vale dock]

@merry jasper Has your question been resolved?

[merry jasper]

ok thanks, last check for this one

This is number 4

[hardy coral]

Looks correct

[merry jasper]

okay thanks for the help guys, appreciate it

im closing it

.close

[vale dock]

Channel closed

Closed by @merry jasper

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.

[fresh warren]

how do I solve this differential equation man im lost

[fresh warren]

nevermind 👅

.close

[vale dock]

Channel closed

Closed by @fresh warren

Use .reopen if this was a mistake.

[vale dock]

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.

[gray hill]

hi can someone help explain this to me? im very confused about the rule lnx and e^x cancelling out each other. Thanks!

[jaunty path]

So e^x and lnx are inverse functions

They’re like multiplication and division

x * a / a gets you x

[gray hill]

i see and how can that apply to this quesiton?

this question is really confusing me

[oblique gazelle]

Suppose x=2, and e^2 = 7.389, ln(7.389) = 2, so ln(e^2) = 2

[jaunty path]

Likewise if you take the inverse function of the function, it just gets you the number itself back

[oblique gazelle]

just an example

[jaunty path]

So logarithms are the inverse of exponentials

So if you take the log of an exponential, for example, it undoes it

The natural log, ln, undoes exponentials with the base e

[oblique gazelle]

The natural log (ln) and the exponential function (e^x) undo each other basically

[gray hill]

im confused about how they go from lne^ln(3+pi) = ln(3+pi) to ln(3+pi)lne = ln(3+pi) and then how does lne just magically cancel out in the last step?

[jaunty path]

So because they’re inverses, if you have a log or an exponential you want to get rid of, you can apply the corresponding inverse

[oblique gazelle]

theres a log rule that says ln(ab)=b⋅ln(a)

apply it and youll see

[jaunty path]

So taking the log of its base gets you 1

[oblique gazelle]

ln(e^ln(3+pi)) = ln(3+pi)* ln(e)

[jaunty path]

e is the base of ln by definition

so if you undo it, you just get the exponent of e

e=e^1

and br definition, ln(e^x)=x

[gray hill]

then shouldnt it just become ln(3+pi)e = ln(3+pi)? why does the e still have ln behind it?

[oblique gazelle]

No it becomes ln(3+pi)*ln(e)

we're applying a log rule not an exponent rule

[jaunty path]

If you bave ln(a^b) it becomes bln(a)

In this case b=ln(3+pi)

and a=e

[oblique gazelle]

we're not multiplying by e, we're multiplying by ln(e)

so the ln stays

[gray hill]

ohhh ok i understand and then lne equals 1?

[jaunty path]

Yes

[gray hill]

ok ok i understand now thanks

[jaunty path]

Exactly

[oblique gazelle]

👍

[gray hill]

i was missing the ln(a^b) can become bln(a)

thanks so much

[jaunty path]

But what exactly was the question asking for

[gray hill]

it said to simplify

[jaunty path]

Oh ok

Cuz it was all circular

There’s a faster way to do it

[gray hill]

really?

[jaunty path]

Tan the example

btw

Yeah

[oblique gazelle]

bruh i need to learn how to use LaTex

[jaunty path]

so $$\e^{lnx} = x$$

[rocky lotus]

a sad pet walker
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[jaunty path]

Wair one sec

$$e^{lnx} = x$$

[rocky lotus]

a sad pet walker

[jaunty path]

Yeah

So using that you can just cancel out ln and e

Getting 3+pi =3+pi

[stark wedge]

$e^{\ln(x)} = x$

[rocky lotus]

Ann

[gray hill]

ohh so if it was like a question asking the answer i could js do that?

is that what u mean?

thats a useful rule

not sure why they havent taught it

[jaunty path]

Yeah

[jaunty path]

They’ll get to it

[gray hill]

alr thanks so much i really appreciate the help :D

.close

[vale dock]

Channel closed

Closed by @gray hill

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.

[daring rover]

#i am pretty confused right now

[stark wedge]

send your question(s)

[daring rover]

ok

here u go

[stark wedge]

uh what.

thats an open problem.

do you have an actual homework/whatever question you need help with or did you come here to troll?

yknow what <@&268886789983436800> we got a navier-stokes in here

[wooden frigate]

please don’t troll in the help channels

.close

[vale dock]

Channel closed

Closed by @wooden frigate

Use .reopen if this was a mistake.

[daring rover]

ok, no

[vale dock]

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.

[lament vortex]

FInd the integral of 2xdx (5 on top, 0 on the bottom)
I'm wondering if this is right: I found the antiderivative of x^2, then proceeded to do F(5^2)-F(0) = C*25 - C0 = 25C. I feel like this is wrong, but I was taught to use Cx and not x + c

[jaunty path]

Cx isn’t right

C is the constant of integration

[lament vortex]

That's the equation

[jaunty path]

Also for definite integrals, integrals with bounds, you don’t add c

[lament vortex]

okay, so i was taught integrals/derivives in 30 minutes by my physics teacher

[jaunty path]

It would just be the integral of 2x, which is x^2, from 5 to 0

[tidal swift]

wth whatever

[jaunty path]

Ah ok

Understandable

[lament vortex]

and so

ill paste my notes in

because they use Cx

not x+c

[jaunty path]

So when you have integrals without bounds, you use +c

Cuz they’re anti derivatives as well

[lament vortex]

Weird integral symbol (a and b) f(x)dx= F(x) | (atop b bottom) = F(b)-F(a) where F(x) is the antiderivative of f(x)
F(x) is the reverse of finding a derivative
The vertical line is the a value between b and a (b is upper, a is limit)
How to find anti-derivative
If f(x) = Cx^n, n=/ -1
Then, F(x) = (Cx^(n+1))/(n+1)
(n+1)Cx^n/(n+1) = F(x) = Cx^n
Cx^1dx
Cx^2/2 |1,0 ½c - 0 = ½c

Okay, so when you say "with/out bounds" i have no idea what you mean

does that mean the 5,0 thingy

[jaunty path]

But cuz the derivative of a constant is 0, the constant of integration is added so if you take the derivative you get the integrals

[jaunty path]

Yeah

[lament vortex]

is that yes bounds or no bounds

[jaunty path]

Yes bounds

[tidal swift]

5,0 are the bounds, yes

[jaunty path]

Bounds are where the integral starts and ends

[lament vortex]

so because we have bounds, we use Cx^2 as the antiderivative, correct?

or is that where I'm wrong

[jaunty path]

Ok so this is a specific function where C is a variable

Unrelated to integrals

[lament vortex]

okay that makes sense. this specific function is the only type of integrals ive learned

[jaunty path]

You’re integrating 2x right?

[lament vortex]

Yeah

[jaunty path]

Integrating it gets you x^2

[lament vortex]

with 5,0

[stark wedge]

F(5^2)-F(0)
this notation is wrong for sure

what do you mean by "i was taught to use Cx" though

[jaunty path]

And because it’s a definite integral, you don’t add +C

[lament vortex]

idk chat gpt says to use +c

[stark wedge]

!nogpt

[vale dock]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[jaunty path]

Did you give it the bounds

Cuz it shouldn’t say that

[jaunty path]

So x^2 from 0 to 5 is 5^2-0^2 which is js 25

[lament vortex]

wait

isn't it

5 on the top

0 on the bottom

[jaunty path]

If it were js asking for the integral of 2x then it would be x^2

[jaunty path]

Yeah

[lament vortex]

yeah but it's evaluate the followign definite integrals

thats what my homework says

[jaunty path]

Yes

25 is what you get when you evaluate it

[lament vortex]

okay, so

let me explain my process

and then guide me to 25

cuz i got c25 not c = 25

so i start with getting x^2

[jaunty path]

What is c

[lament vortex]

the constant

idk

😭

[jaunty path]

there is no constant twin 🥀💔

[lament vortex]

so we start with Cx^2 with bounds of 5 and 0

[jaunty path]

It’s a definite integral

[lament vortex]

okay

[jaunty path]

Ok yea go on

[lament vortex]

then because we have those bounds

we use C(5)^2 - C(0)^2

= C(25) - 0

= C(25) or 25C

that was how i ended it

[stark wedge]

why Cx^2

[jaunty path]

Ok so in the notes your physics tutor sent, C is js for tjay function

[stark wedge]

the derivative of Cx^2 would be 2Cx and not 2x

[lament vortex]

because we were given to evaluate the defnite integrals of 2xdx

[jaunty path]

It doesn’t have to do with anything for the actual integral

[stark wedge]

yeah but the antiderivative is not Cx^2 it is just x^2.

[jaunty path]

So just ignore C for now cuz it’s only for that example

[stark wedge]

what is that C multiplier doing in there?

[lament vortex]

idk my physics notes from my teacher told me to use it

[stark wedge]

show those notes!

i want to see exactly what was said and whether there was any miscommunication or misinformation or not.

[jaunty path]

^

[lament vortex]

i have a writing disability so i type my notes thats why it can get really weird but this is what i wrote

theres a few graphs

[jaunty path]

What exactly is your integral

2x right?

[lament vortex]

yeah

so wait

what do i do about the whole

25c thing

[jaunty path]

Ok so the integral of that is x^2

[lament vortex]

cuz its supposed to cancel out

[jaunty path]

Ignore the c’s twin idk what it is

[stark wedge]

i think i know what the issue is

[jaunty path]

There are no c multipliers in integrals

Only constants

Tjay are added

[stark wedge]

@lament vortex in your notes you used C as an arbitrary coefficient on the x^n but you're now confusing it with the constant of integration

these are not the same

[lament vortex]

okay

makes a bit more sense

[jaunty path]

You only use it for indefinite integrals

Integrals without bounds

[lament vortex]

and then

i solved this

[jaunty path]

or the numbers at the top and bottom of the integral

[lament vortex]

Cx^2dx = Cx^3/3 = C/3 - 0 = ⅓c

as well

so basically just

[jaunty path]

Ok where did c come from

[lament vortex]

ending with c is okay?

[jaunty path]

Is it 2Cx or 2x

[lament vortex]

the question my teacher wrote on the board 😭

[lament vortex]

the question says jsut 2xdx 😭

[jaunty path]

Ok so then there’s no C

Integrating 2x gets x^2, and applying the bounds gets (5)^2-(0)^2

[jaunty path]

If the integral has the c in it then you keep it there

[lament vortex]

okay so then it just goes to 25 no c

[jaunty path]

But you don’t just add it all the time

[jaunty path]

Yes

[lament vortex]

and lets try one more question

[jaunty path]

Also if C is being used in your equation use a different symbol for constant of integration

Like k

[lament vortex]

oh makes sense

alr

the integral symbol bounds = 5,2
(5x^2+3x)dx

[jaunty path]

Ok so now you use power rule

[lament vortex]

that integrates to 5/3x^3 + 3x^2/2 right?

[jaunty path]

Yes that’s right

[lament vortex]

5/3 * x^3 + 3/2 * x^2

ok so now

we plug in the values

with F(5)-F(2)

correct?

[jaunty path]

Yes

[lament vortex]

lemme solve it rq

and let me know if im right

[jaunty path]

Ok

[lament vortex]

= 226.5?

[jaunty path]

Yeah that’s right

[lament vortex]

TUFF

and hold on

theres 2 last questions

i can solve them

just let me know if i integrate them rq

[jaunty path]

Ok yeah do you need help

Ok

[lament vortex]

3x^3+4

is also equal to

3x^3 + 4(x^0)

correct?

so that goes to 4x

[jaunty path]

Yeah

[lament vortex]

and then the last one... is sqrt(3x)

which is just

3x^1/2 correct?

so then it goes to 3x^3/2?

[jaunty path]

The 3x^3 goes to 3/4 x^4

[lament vortex]

sosqrt( 3x^3)

[lament vortex]

yeah and that

[jaunty path]

Yeah

[lament vortex]

ok thanksso much

i got it now

[jaunty path]

Btw

sqrt(3x) can be written as sqrt(3) * sqrt(x)

[lament vortex]

yeah

[jaunty path]

And cuz it’s a constant you can js ignore sqrt(3) and integrate sqrt(x) by itself

Which can make it easier

[lament vortex]

WHAT?!?!!!

THATS SO COOL

i dont think my teacher wants me to do that

but

noted for exams

[jaunty path]

Yeah ik

[lament vortex]

can u just check my sqrt(3x) question when i do it

the bounds are 3,1

[jaunty path]

It makes it way easier

[jaunty path]

Ok

[lament vortex]

and the other ones bounds were 8,2

but im finihing it rn

[jaunty path]

Also if you ever wanna double check you can js plug in the integral into wolframalpha

Btw

[lament vortex]

whats that

[jaunty path]

the greatest thing to bless this earth

wolframalpha is a math website ai

I’m not sure if it’s an ai acc

[lament vortex]

wait hold up

can u also do the 3x^3+4 one LOL

[jaunty path]

But it basically can do math for you

Simple ones

[lament vortex]

alr ill try it

[jaunty path]

Yeah

Ok

What are the bounds

[lament vortex]

bounds for that are 8,2

i got 3084

which idk if right

WHAT WOLFRAMALPHA IS SO TUFF

[jaunty path]

Yeah that’s right

[jaunty path]

Ye

Ik

[lament vortex]

ok

i got sqrt(3x)

to 2x^(3/2)

is that right

ok final result was 8.39

so i am apparently so wrong

my integral is wrong

so its 3x^1/2

then goes to 3x^3/2

then divide by that

so its now 3x/1.5^3/2

so then 2x^3/2?

[jaunty path]

Where’d the 2 come from

[lament vortex]

3/(3/2) = 2

oh wait

i still need to divide x? or no

wait no i dont

[jaunty path]

sqrt(3) * sqrt(x) integral is sqrt(3) * x * sqrt(x) * 2/3

Yeah ts

[lament vortex]

ok

so the gpt AND wolfram say sqrt(3x) goes to 2*x^3/2 / sqrt(3)

where does the /sqrt(3) come from

cuz i got the top half

[jaunty path]

Cuz sqrt(3)/3= 1/sqrt(3)

But don’t leave it like that

It’s not simplified

[lament vortex]

wait huh

hold on

just

is the integral

2x^3/2

or is that wrong

[jaunty path]

You’re forgetting to multiply by sqrt(3)/3

From before

[lament vortex]

wait so

is that integral right

or no

so we have 3x^1/2

add + 1 to the exponent

so now 3x^3/2

then divide by the new exponent

[jaunty path]

the 3 is in the root as well remember

[lament vortex]

which is 3/2

[jaunty path]

Ok forget allat

[lament vortex]

yeah?

[jaunty path]

sqrt(3) * sqrt(c)

x not c mb

[jaunty path]

The integral of ts is sqrt(3) * 2/3 * x^1.5

Right

[lament vortex]

the integral

of sqrt(3x)?

or

[jaunty path]

Yes

[lament vortex]

idk i dont see why

the power rule doesnt work here

for 3x^1/2

just go to 3x^3/2

then divide?

[jaunty path]

It does work here

But you’re forgetting the fact that 3 is in the radical as well

[lament vortex]

3 is in the radical as well...

OHHH
so its

3^1/2 * x^1/2

so basically

i just have to multiply the final result by sqrt(3)

not 3

lets see now

[jaunty path]

Yes

[lament vortex]

so then

its

sqrt(3)*x^3/2

all divided by 3/2

[jaunty path]

Yes

[lament vortex]

so

4.27

[jaunty path]

Yeah prolly

What are the bounds

[lament vortex]

wolfram says 4.84

oh

its cuz i forgot to divide

i got 4.84

😎

thanks so much goat

[jaunty path]

No problem twin 🥀💔

Good luck with your physics tutor

[vale dock]

@lament vortex Has your question been resolved?

[vale dock]

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.

[ebon wharf]

I need help with this: if the above inequality has one unique solution, find the parameter a.

I was thinking of rewriting the logs as lns(to have the same base), but I don't think that works.

[stark wedge]

why do you think it doesn't work

[ebon wharf]

If I do it that way, I get this:

From here, I don't know what to do.

[stark wedge]

ok right so it just does you no good

here's an idea

you want this inequality to be true for exactly one value of x, yeah?

[ebon wharf]

Yes

[stark wedge]

for that unique x, it'll have to be an equality

[ebon wharf]

So the product must equal -log_a {3}

[stark wedge]

yeah sure

you can also, i believe, claim that the one x value will have to be -a/2

bc the entire thing is expressible in terms of x^2+ax

[ebon wharf]

I would have to prove that the product of logs(call it f(x)) is monotonic, right?

[stark wedge]

mm i guess so but that's a bit tangential to my point

or rather itll come in later

[ebon wharf]

For x=-a/2, the inequality holds.

So i think that, since a function of x is less than or equal to a constant, it needs to be monotonic, such that a horizontal line can intersect it at most once.

.close

[vale dock]

Channel closed

Closed by @ebon wharf

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.

[stark wedge]

[c, ∞] 💀

but ok,

!status

[vale dock]

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

[silver osprey]

the answer is 2.5

[silver osprey]

3

[hazy pivot]

Show us what you did then

[hazy pivot]

Lmaoooo

[silver osprey]

i got
[0,1] U [3/2,3] , [3,∞) u {-2}

but it should be
[0,1] U [3/2,∞) U {-2}

so that the answer comes out as 2.5

[hazy pivot]

What is [3/2,3] ∪ [3, ∞]

[stark wedge]

[3/2,3] ∪ [3,∞]
you can combine these

[silver osprey]

oh right

that makes it

[3/2, ∞)

[hazy pivot]

Yes

[silver osprey]

thanks

.close

[vale dock]

Channel closed

Closed by @silver osprey

Use .reopen if this was a mistake.

[vale dock]

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.

[lyric bloom]

Just want some starting ideas

[lyric bloom]

Did try trig substitution but couldn't make anything solid

Did try PMI

Maybe works

Didn't explore much

I'll try again

Probably doesn't work

[stark wedge]

given that your sequence is defined recursively, some kind of induction is going to be necessary.

[lyric bloom]

Makes sense

Ohk got it

.close

[vale dock]

Channel closed

Closed by @lyric bloom

Use .reopen if this was a mistake.

[vale dock]

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.

[sterile mauve]

in a pattern like 2 6 12 20 , why we are so sure about the next term will be 30
is this a general acceptance or next term possibly be every number

[sterile mauve]

if i take n^2 + n as general equation next will be 30 but if i take that as n^2 + n + (n-1)(n-2)(n-3)(n-4) next terms gonna be 54

[heady pawn]

there is actually a proof that such a sequence gives ANY real number

there is an equation for any real number

[sterile mauve]

so theres no such as thing called pattern

''right'' patern actually

[heady pawn]

this is more theological talk, patterns happen in math and all over the world

[sterile mauve]

ja there are pattern

but is there ''right'' patern

i mean i just saw that in a intelligence test

[heady pawn]

usually the simpelest pattern is the correct one

but mathematically, the question is super dumb

[sterile mauve]

is this a general acceptance

oh ok

cause of the lack of information?

[heady pawn]

yes

[native rover]

there's a pattern for ts, right? and do you see it?

[sterile mauve]

yea yea i saw smthng like that before

[vale dock]

@sterile mauve Has your question been resolved?

Channel closed

Closed by @sterile mauve

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.

[carmine willow]

hi, i am solving dif. equations, is this a valid move, if i want to get rid of fractions?

[carmine willow]

to mutliply both sides by 2, i was told its not since it will change the whole outcome

[stark wedge]

you were told that multiplying both sides by 2 is illegal?

[carmine willow]

i guess not going to jail type of illegal, i was just told not to do it

[stark wedge]

frankly i have no idea who said that or why

[carmine willow]

it changes the result so idk

[stark wedge]

who told you not to do it

what change, exactly, does it result in

[carmine willow]

they are essential to keep the derivative correc

correct

[midnight pier]

tbh, people who multiply both sides by 0 and call it a day should really go to jail

[carmine willow]

the fractions

[carmine willow]

might just do that on exam honestly

[midnight pier]

your prof will send you to jail

[stark wedge]

this... does not answer my question

[carmine willow]

i cant say who told me that, ill get banned from the server

[stark wedge]

why will you get banned from the server???

[carmine willow]

i asked the internet

last time i got shouted at on here for telling chatgpt told me otherwise

[stark wedge]

well you'll get !nogpt

hardly a shout and more of a sign-tap

[carmine willow]

yeah so i am here just to consult, i have 3 days to prepare differential equations...

[stark wedge]

i dont think multiplying both sides by 2 is ever invalid

nor does it actually change anything

[carmine willow]

You are right, sorry for dumb question

[stark wedge]

if it does not change anything in algebraic equations why would it do that in differential equations

[carmine willow]

thank you, i agree

.close

[vale dock]

Channel closed

Closed by @carmine willow

Use .reopen if this was a mistake.

[vale dock]

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.

[hasty sinew]

hey, i need to prove the red equality

[hasty sinew]

i can use lhopitals rule ^

any hint will be cool

no full answer tho

[stark wedge]

$\lim_{x \to (\pi/2)^-} \cos(x)^{\tan(x)} \overset?= 0$

[brisk fjord]

I can't really read that

[rocky lotus]

Ann

[stark wedge]

this?

[brisk fjord]

Ah I see

[hasty sinew]

yep

[stark wedge]

consider the logarithm of this function

[hasty sinew]

ok

@stark wedge thx i think it worked

.close

[vale dock]

Channel closed

Closed by @hasty sinew

Use .reopen if this was a mistake.

[vale dock]

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.

[vocal fossil]

Guys help me with q9

[tidal swift]

no question statement provided

[vocal fossil]

Find the derivative

!

[stark wedge]

(x+sin^5(x))^6?

what's troubling you with this one?

[vocal fossil]

Sorry

My bad

[north olive]

I think he meant xi

[vocal fossil]

Q11

[stark wedge]

xi means 11 in roman numerals

[vocal fossil]

Yess

[stark wedge]

sin[(sin^7(x^7)+1)^7]

this one?

[north olive]

Chain rule(repeatedly)

[vocal fossil]

Yeah

[stark wedge]

my question will remain the same: what is troubling you?

[vocal fossil]

See my work

[stark wedge]

uploading?

[stark wedge]

the { } will need to have the derivative of sin^7(x^7)+1

[vocal fossil]

How am I supposed to find a derivative of sine to the power 7

[stark wedge]

btw you misplaced the 7 coefficient

[stark wedge]

chain rule again

[vocal fossil]

Yeah

[stark wedge]

also don't be afraid to break the question down into smaller steps

cause rn it looks like you are trying to swallow it all in one go

[vocal fossil]

Oo

That’s my habit

[stark wedge]

a habit that deserves breaking!

[vocal fossil]

But I will try it from nxt q

[vocal fossil]

Ok

[stark wedge]

no try it from this one

[vocal fossil]

Fine

Lemme upload

[stark wedge]

this is what i mean by breaking down chain rule stuff

you don't try to take the derivative of every single component all at once but leave these intermediate results with the prime symbol that you then work out step by step

[vocal fossil]

Ooo

That’s make things clear

[stark wedge]

yeah keep going now

now you need to work out the derivative of sin^7(x^7)

[vocal fossil]

And how am I supposed to do that

[stark wedge]

that's still a composition (of three functions)

so once again chain rule

remember sin^7(t) really means [sin(t)]^7

sin^7(x^7) is the composition of x^7, sin, and x^7 again

[vocal fossil]

Ooo

[vocal fossil]

See !!

[stark wedge]

all this times dt/dx

another 7x^6 factor

[vocal fossil]

What do you mean, I didn’t got it?

Ooo

I got it

Thanks @stark wedge

[stark wedge]

this is how the full working would look

[vocal fossil]

Yeahhh

.close

[vale dock]

Channel closed

Closed by @vocal fossil

Use .reopen if this was a mistake.

[vale dock]

Available help channel!

Send your question here to claim the channel.

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

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

[last comet]

Apparently I'm supposed to factorise

[severe verge]

Have you tried that

[last comet]

Yah, not getting anything of not

Note*

[thin valley]

And what have you tried?

[last comet]

Not sure exactly where to start

Tried taking x-y as a, and xy as b

Then u get a(a^2 +3b) =61+b

No follow up

Should I try to make it in the form a^3 + b^3 +c^3 -3abc

With some constant c

[thin valley]

I would divide x³-y³ by x-y to see what happens

But there is not a method, you know

I mean this is a random diophantine equation

[last comet]

Ya, but in this section I'm supposed to use factorization

[thin valley]

Yes, that is factoring

Well, it's factoring one side only

If you need to factor the whole polynomial that is different

[tight oxide]

I have a feeling it's something like:
x³-xy+y³=61
(A)(B)(C)=61
where only 1 value can be 61, and the other must be 1

the goal is to find A, B, C

and its probably some snide identity stuff going on

[last comet]

True, but factorization is not rly possible directly

[tight oxide]

yup, you'll have to add a constant value after doing some work

[thin valley]

(x-y)(x²+xy+y²)=xy+61

[last comet]

Yes I see it

[last comet]

This idea works

1646= a^3 + b^3+c^3-3abc=1646

Where a=3x, b=-3y and c=-1

Ok bye

.close

[vale dock]

Channel closed

Closed by @last comet

Use .reopen if this was a mistake.

[vale dock]

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.

[river hare]

If x^3 - x - 1 = 0, find the value of sum(a,b,c) (x+1)/(x-1), where the expression of the sum is evaluated at a, b and c and the evaluations are then added

[river hare]

Note: a, b and c are the roots of x^3 - x - 1 = 0.

If I evaluate 1/(a-1) + 1/(b-1) + 1/(c-1), then I can do the question.

How may I evaluate 1/(a-1) + 1/(b-1) + 1/(c-1)?

[lapis agate]

I think you should make another equation with roots as the denominators

[noble raft]

,, \frac{(a+b+c)(x+1)}{(x-1}

,, \frac{(a+b+c)(x+1)}{(x-1}

[rocky lotus]

AnitaG

[noble raft]

is this what ur trying to find?

[river hare]

No.

(a+1)/(a-1) + ...

[noble raft]

okay I'm confused by the wording of the question

[noble raft]

okay got u

[river hare]

I rewrote the question

[river hare]

great

[noble raft]

,, 3 - 2\left(\frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}\right)

no thats wrong hang on

,, 3 + 2\left(\frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}\right)

[rocky lotus]

AnitaG

[noble raft]

thats what ur trying to find I take it?

[noble raft]

so yeah do what this guy says

[lapis agate]

You can do this by Vieta’s formula. Do you know Vieta’s formula?

[river hare]

Yes.

[noble raft]

u want to find the polynomial with roots 1/a-1 etc..

[lapis agate]

Okay can you compute what a+b+c ab+bc+ac and abc are?

[lapis agate]

That’s one way. Another way I found is to actually just simplify the sum as an entire fraction and then use Vieta’s

Either way you use Vieta’s formula

[noble raft]

if thats what the sum simplifies to then yeah that method would work

[noble raft]

if u wanted to do this tho u could let u=1/x-1, rearrange for x and plug into ur original polynomal, then find the sum of roots of the polynomial u end up with

[river hare]

This is worse

[lapis agate]

This should be correct. Then use the equation that you had before and sub all the values in

[river hare]

Got it.ThankYou.

.close

[vale dock]

Channel closed

Closed by @river hare

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.

[thin meadow]

Hello, I want to learn calculus online but it's kinda hard trying to find the exact online course I want. I know Khan Academy and The Organic Chemistry Tutor (if you were about to mention it), but I don't really enjoy having to watch someone writing things everytime. It's kinda boring to me. And, their playlist kind of overwhelms me since they tend to have like 100+ vids in it. I prefer visuals videos but I think I could work with bulky playlists.

[jovial edge]

There are some visual videos for calculus concepts like the 3blue1brown fundamental of calculus but if you want to be able to do complex problems you will have to watch videos like those in The Organic Chemistry Tutor or do problems in books

[stark wedge]

i mean KA isn't just videos now is it

if you go to their website they got practice problems aplenty

[vale dock]

@thin meadow Has your question been resolved?

Channel closed

Closed by @thin meadow

Use .reopen if this was a mistake.

[vale dock]

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.

[cobalt crow]

guys can it be said a level curves is an special case of a trace but the case where an xy plane at an z height intersects a surface?

[cobalt crow]

while a trace, is a more general case of an level curve, for example y = 1, so the xz plane intersecting the surface at y = 1

[turbid valve]

No?

A level curve is the intersection of a surface with a plane of the form z = c

A trace is the intersection of a surface with the axis-defined planes

[cobalt crow]

parallel to, not necessarily the axis defined planes

[turbid valve]

I think then this depends on the definition at play

Note then that these are going to vary from author to author

[cobalt crow]

where did you get your def from ?

[turbid valve]

From a worksheet I found from UC Davis

[turbid valve]

By this definition then ig yes that would be correct to say that a level curve is a type of trace

[cobalt crow]

https://web.ma.utexas.edu/users/m408m/Display12-6-2.shtml

[cobalt crow]

this one is also fairly similsr to level curves

[turbid valve]

i.e. a level curve is a trace which is so graphed in some plane z = k for some k a constant

[cobalt crow]

they are very similar concepts, but idk

[cobalt crow]

can you elaborate please?

[turbid valve]

dafuq is there to elaborate on

[cobalt crow]

Notice the critical difference between a level curve C
of value c
and the trace on the plane z=c
: a level curve C
always lies in the xy
-plane, and is the set C
of points in the xy
-plane on which f(x,y)=c
, whereas the trace lies in the plane z=c
, and is the set of points (x,y,c)
with (x,y)
in C
.

[ivory valley]

Waes is saying this basically

[shut cobalt]

Level curves are traces but where the planes are just constant values of z

[cobalt crow]

.solved

[vale dock]

Channel closed

Closed by @cobalt crow

Use .reopen if this was a mistake.

[vale dock]

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 zenith]

hi i have a question about a lesson in my book. specifically the part w/ the blue arrows using the distributive property. why doesn't the right side of the equation's numerator have the distributive property applied to it as well? why just the left side (2x and 3) ? i hope i explained my question clearly

[sharp whale]

distributive property applies to things that are being added
A(B + C) = AB + AC
that isnt present on the right side, so it doesnt happen

a bigger reason is that its dividing by (x-4)(x+2) then multiplying by (x-4)(x+2), two opposite actions, so this simplifies to x^2 + 14

[buoyant zenith]

okay, but the left side is also getting divided by x-4 and x+2, so why doesn't the two opposite actions cancel on the left side?

[sharp whale]

if you have

5 * 3 * (1/5 + 1/3)

you wouldnt say this is 2, right

if you use distributive property, this is 5 * 3 * 1/5 + 5 * 3 * 1/3

or 3 + 5

[sharp whale]

distributive property shows that the 1/5 and 1/3 arent "together"

[buoyant zenith]

oh so the minus sign in betwenn the fractions on the left separate them

[sharp whale]

yes

[buoyant zenith]

so the denominators aren't the same, cause if they were the left side would be written as (x-4)(x+2)

could the right side be rewritten as x2/(x-4) + 14/(x+2)?

[sharp whale]

you might need a refresher on fractions

[buoyant zenith]

yes

[sharp whale]

1/6 is not 1/3 + 0/2

you dont add across to combine fractions together

you definitely dont add across and multiply across, thats stranger

[sharp whale]

so no, you cant do this

[buoyant zenith]

okay, i'll relearn my fraction rules

[vale dock]

@buoyant zenith Has your question been resolved?

Channel closed

Closed by @buoyant zenith

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.

[tall shale]

why would the first column be 3,2,2 when that would map 1,0,0 to 3,2,2 instead of 0,0,1 or is it bc its hyperbolic space? i cant find this in my notes but i thought the third column would need to be 3,2,2

[tall shale]

i feel like this is a stupid question for some reason so im sure the reason why is clear

does it have to be 3,2,2 because <(3,2,2),(3,2,2)>_{L} = -1

because i dont get how it maps 0,0,1 still but i also get that

this is the matrix you end up with and that process makes perfect sense to me

[vale dock]

@tall shale Has your question been resolved?

[tall shale]

<@&286206848099549185> is there a different channel i should ask this where i could get a response faster maybe

unless one of yall can help me :3

[vale dock]

@tall shale Has your question been resolved?

[tall shale]

cooked

[bright vector]

what's the problem @tall shale ?

[tall shale]

i dont get why the first column being 3,2,2 works here

to move 0,0,1 to 3,2,2

or am i thinking about it wrong

bc its hyperbolic

[scarlet silo]

The first column of a matrix does not represent the vector I want to map, but rather the image of the first vector of the canonical basis (1,0,0). For this reason (3,2,2) can work. Indeed, (1,0,0) has Lorentz norm plus one and (3,2,2) also has norm plus one, so the condition is satisfied. Lorentz matrices belong to the group O(2,1) and are characterized by the fact that their columns form an orthogonal basis with respect to the Lorentz metric. This means that each column must have the same norm as the vector it comes from, and the columns must be mutually orthogonal in the Lorentzian sense.

[tall shale]

how does it actually map 0,0,1 tho

whats the operation here

Ax would just give something else

with x the column vector (0,0,1)

also doesnt 1,0,0 have lorentz norm -1

or i actually

holy fuck its a typo

i hate everything

!close

is that not how u close it

.close

[vale dock]

Channel closed

Closed by @tall shale

Use .reopen if this was a mistake.

[vale dock]

Available help channel!

Send your question here to claim the channel.

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

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

[neat lynx]

Sorry for the bad photo. I need help with this question I’ve tried calculating the 3 transformation matrices then picking a single point and going through all 3! possible options to try and move the original point to one of the image points but none of them have lined up. I’m so confused

[hardy coral]

Which of the Bs is actually A?

[neat lynx]

That’s the thing it doesn’t even specify so I tried mapping both but i still can’t get an answer

[hardy coral]

Alright let me try to find the solution...

Yea that doesn't add up

[vale dock]

@neat lynx Has your question been resolved?

[neat lynx]

Okay thank you

[vale dock]

Channel closed

Closed by @neat lynx

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.

[olive ocean]

How exactly does he get 0.333?? I don't really understand derivatives so I keep doing it "normally" and getting 1

[hardy coral]

,calc log(2*3.001)

[rocky lotus]

Result:

1.7920927470182

[hardy coral]

,calc (log(23.001)-log(23))/0.001

[rocky lotus]

Result:

0.33327779012038

[hardy coral]

I mean, that checks out

How do you get something different?

[olive ocean]

It's my first calc class and I missed the first 2 weeks so I didn't even know what log was

So all I have to go over is the notes he posted

[hardy coral]

It's one of the functions your calculator surely has

[olive ocean]

Yeah it does I just did it

Thank u

.close

[vale dock]

Channel closed

Closed by @olive ocean

Use .reopen if this was a mistake.

[vale dock]

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.

[crystal gulch]

my teacher taught it in class but i didn't really understand

(he used bezout theorem to prove $y_1+a_1+ y_2a_2+..y_ka_k = 1$ (for $y_1;y_2;...;y_k$ be interger)

[vale dock]

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.

[crystal gulch]

I need to solve this theorem

For numbers $a_1, .a_2, ..., a_k$ being natrual numbers and $GCD(a_1, a_2, a_3, ..., a_k)=1$. Prove that for x $\geq$ g (g is a number), $x = y_1a_1 + y_2a_2 + ... + y_ka_k$ ($y_i$ are natrual numbers)
so basically i need to prove that there is a finite amount of numbers that can't be expressed like that
my teacher taught it in class but i didn't really understand
(he used bezout theorem to prove $y_1+a_1+ y_2a_2+..y_ka_k = 1$ (for $y_1;y_2;...;y_k$ be interger)

[rocky lotus]

shio6695

[crystal gulch]

I need to solve this theorem

For numbers $a_1, .a_2, ..., a_k$ being natrual numbers and $GCD(a_1, a_2, a_3, ..., a_k)=1$. Prove that for x $\geq$ g (g is a number), $x = y_1a_1 + y_2a_2 + ... + y_ka_k$ ($y_i$ are natrual numbers)

so basically i need to prove that there is a finite amount of numbers that can't be expressed like that

my teacher taught it in class but i didn't really understand

(he used bezout theorem to prove $y_1a_1+ y_2a_2+..y_ka_k = 1$ (for $y_1;y_2;...;y_k$ be interger)

[rocky lotus]

shio6695

[crystal gulch]

repost btw to fix some typo

[vale dock]

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.

[north scarab]

guys I need help with the first quesiton

[hardy coral]

!status

[vale dock]

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

[north scarab]

1

[hardy coral]

Can you express V in terms of x and y?

[north scarab]

well

what does that mean

make x and y the subject?

[fading dock]

V = some expression that includes x and y

[north scarab]

well they given us v in terms of x

[hardy coral]

No

That's what you need to show, it's not given

[north scarab]

oh ok so

why did u say in terms of x and y

they dont have y

[hardy coral]

I don't care what they have

Can you answer my question

[fading dock]

We need to start somewhere - this is the first step to solving the question

[north scarab]

volume and SA are not the same

I dont remember the SA formula

[fading dock]

The SA formula is irrelevant for this step.

[hardy coral]

Why are you bringing SA into this? I'm asking for V

[pliant wedge]

The question gives you a answer of surface area of this cuboid. The write the equation of total surface area and subject the y term. After that write the equation of volume and replace y value with that .

[north scarab]

so I can solve simultataneous equations which is common in min max problems

[fading dock]

is this a min max problem?

part a specifically

[hardy coral]

Yet you still haven't shown that you're capable of expressing the volume of a cuboid in terms of its side length

[north scarab]

part a isnt a min max problem

[hardy coral]

I can't help you if you don't answer my questions

[north scarab]

your questions werent clear, could you repeat that again

[hardy coral]

.

[tawny moon]

then why are you bringing up minmaxing here

[hardy coral]

I can't really make that clearer

[tawny moon]

you haven't gotten to the minmaxing part, so don't minimize your understanding by maximizing your confusion

[marble arch]

Do you know the formula of the volume of a cuboid?

[north scarab]

what is a cuboid?

[marble arch]

The figure shown

A box basically

[north scarab]

2xxy

[marble arch]

Thank you

[hardy coral]

Alright, second part now, can you express the SA in terms of x and y?

[north scarab]

yeah I prob could but before I do, why express it in terms of y

if the question is expressing v in terms of x

[marble arch]

So that you have two variables, you'll need that while differentiating

As of now just state what you know, the formulae

Then work with them

[hardy coral]

When asked, you said you didn't know where to begin

[fading dock]

You will find y in terms of x and substitute that in eventually

[hardy coral]

I'm giving you steps to solve your question

[north scarab]

but we arent in part b

we are in pat a

[fading dock]

.

[north scarab]

part*

[fading dock]

^

[marble arch]

Alright, we'll get on that later mate

As of now, what's the formula for TSA of cuboid, include y for now

[north scarab]

okay

hmm

[north scarab]

didnt I say it already

2xxy

[marble arch]

That's volume

lbh

[marble arch]

Yes

so basically, 4x^2 + 6xy

[north scarab]

yep

[marble arch]

Now they've given you the TSA

600 sq.cm

[north scarab]

now we just sub

[fading dock]

no, you haven't solved for y yet

[north scarab]

we need to manipulate

first

yea ik

do we equate 4x^2+6xy=0

or

4x^2+6xy=SA

[marble arch]

This

[north scarab]

alr

correct?

[marble arch]

Yes

Now you have y in terms of x

[fading dock]

Now sub this into the expression for volume you found earlier.

and simplify

[north scarab]

kk

but

there isny y value to sub in

[marble arch]

See, trust the process, list all that you know and use them to solve the question

[marble arch]

2xxy

[north scarab]

I thought I need to sub in the volume function they given

[fading dock]

...no, you have to ignore that, since you dont know if its true yet

[marble arch]

yes, let f(x) = V

that'll help you

[north scarab]

how will that help

[marble arch]

Trust the process

You'll differentiate it later, this form will be more convenient

[north scarab]

oh now we sub in value of SA?

[marble arch]

Yes

And break it into 2, separate it

[north scarab]

if I do sub in the value of SA in, il be introducing the variable y

[marble arch]

It was 600 mate

[north scarab]

ah

[lavish rune]

SA=2x2z+4xy

[marble arch]

what

There's no z

[lavish rune]

hm

[marble arch]

They're correct BTW, there's nothing wrong with the function

[marble arch]

Exactly, you got one part

[marble arch]

And now for (b), we differentiate the function

[tawny moon]

!occupied

[vale dock]

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

[tawny moon]

and holy shit format your question without all the extra lines

[lavish rune]

dang okay

[marble arch]

Insane

[tawny moon]

though in this case, i suggest removing the message because it's taking up like the entire screen

and is not relevant here

[lavish rune]

well i dont want to delete

[tawny moon]

ok then, still not your channel though

[north scarab]

this guy

[lavish rune]

never said it was

[tawny moon]

cool. OP, continue

[lavish rune]

?

[north scarab]

is the working out correct?

wait

Im getting a negative volume

[jovial scarab]

-4x^2 + 200 = 0

everything is good up to and including here

do you see the error next

[tawny moon]

zoomed in for your reference

[wild linden]

!help @lavish rune

[vale dock]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[lavish rune]

what......

[vale dock]

@north scarab Has your question been resolved?

[marble arch]

@north scarab , you got the error?