#help-36 | Mathematics | Page 119

remote island Apr 22, 2024, 7:25 AM

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which problem are you erferrign to

midnight sparrow Apr 22, 2024, 7:25 AM

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The 1 you send

remote island Apr 22, 2024, 7:26 AM

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there's no transpose in

midnight sparrow Apr 22, 2024, 7:26 AM

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Here

remote island Apr 22, 2024, 7:26 AM

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wdym by "unchange"?

midnight sparrow Apr 22, 2024, 7:26 AM

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I will let ten duce continue I think

remote island Apr 22, 2024, 7:26 AM

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midnight sparrow I will let ten duce continue I think

no, you're also helping

midnight sparrow Apr 22, 2024, 7:26 AM

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Like multiply by the Identity do nothing

remote island Apr 22, 2024, 7:26 AM

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so both of you can help me

midnight sparrow Apr 22, 2024, 7:27 AM

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If I multiply a Matrix by the Identity it will be thé same as befofe

remote island Apr 22, 2024, 7:27 AM

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okay, but you're multiplyign it by A^-1

remote island Apr 22, 2024, 7:27 AM

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midnight sparrow If I multiply a Matrix by the Identity it will be thé same as befofe

i know

midnight sparrow Apr 22, 2024, 7:27 AM

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midnight sparrow I will let ten duce continue I think

I Say that because I will go in 10 min also

nocturne vale Apr 22, 2024, 7:28 AM

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yo

remote island Apr 22, 2024, 7:28 AM

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midnight sparrow I Say that because I will go in 10 min also

just be fast

nocturne vale Apr 22, 2024, 7:28 AM

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XA=C

midnight sparrow Apr 22, 2024, 7:28 AM

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So by multiplying by thé inverse on each side you get the Identity multiply by X

nocturne vale Apr 22, 2024, 7:28 AM

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XAA^-1=CA^-1

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XI=CA^-1

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X=CA^-1

remote island Apr 22, 2024, 7:29 AM

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ok gothca

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what do you do with this tho

midnight sparrow Apr 22, 2024, 7:29 AM

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But you need to make sure A is invertible

nocturne vale Apr 22, 2024, 7:29 AM

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Sorry this is my topic pre midterm so I almost forgot

nocturne vale Apr 22, 2024, 7:29 AM

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midnight sparrow But you need to make sure A is invertible

yes

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so take the given matrix on LHS

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and take transpost

midnight sparrow Apr 22, 2024, 7:30 AM

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The set of invertible matrices is a group so AA-1 gives you the identity

remote island Apr 22, 2024, 7:31 AM

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yeah ok got it

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now let's do

nocturne vale Apr 22, 2024, 7:32 AM

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sorry one sec

remote island Apr 22, 2024, 7:32 AM

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how would you do it without setting up a system

nocturne vale Apr 22, 2024, 7:32 AM

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let me just make sure

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one sec

midnight sparrow Apr 22, 2024, 7:34 AM

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Sry I need to go GL 👍

remote island Apr 22, 2024, 7:34 AM

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ty, bye

remote island Apr 22, 2024, 7:55 AM

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@nocturne vale ynou there?

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or could sm1 else please come and help me with these 3

remote island Apr 22, 2024, 8:11 AM

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X^-1 != X^T tho

final saddleBOT Apr 22, 2024, 8:41 AM

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@remote island Has your question been resolved?

nocturne vale Apr 22, 2024, 8:43 AM

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remote island <@772109046412214285> ynou there?

the last one evaluate to $\mathcal{I}$

soft zealotBOT Apr 22, 2024, 8:44 AM

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Ten-Duce

nocturne vale Apr 22, 2024, 8:45 AM

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@remote island yo

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still there?

remote island Apr 22, 2024, 8:52 AM

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yea @nocturne vale

remote island Apr 22, 2024, 8:52 AM

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nocturne vale the last one evaluate to $\mathcal{I}$

how did you calculate it

nocturne vale Apr 22, 2024, 8:54 AM

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the inside evaluate to (I) so (I)^2001

remote island Apr 22, 2024, 8:55 AM

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nocturne vale the inside evaluate to (I) so (I)^2001

you're referring to this, right

nocturne vale Apr 22, 2024, 8:55 AM

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yeah

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I felt like these usully wont be too hard u know

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they are really testing the concept of matrix power

remote island Apr 22, 2024, 8:56 AM

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i think you're wrong

nocturne vale Apr 22, 2024, 8:56 AM

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ok let me ck

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right?

remote island Apr 22, 2024, 9:03 AM

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oh yeah

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wha about the other two

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for the 2nd just multilpy and subtarct

nocturne vale Apr 22, 2024, 9:04 AM

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the transpose one is fucking weird

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the other one I haven't try

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like what did you guy learned recently?

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might be some theorem I forgot

remote island Apr 22, 2024, 9:06 AM

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it's from an old problem sets o idk

nocturne vale Apr 22, 2024, 9:06 AM

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let me try the other one

final saddleBOT Apr 22, 2024, 9:11 AM

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Channel closed

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remote island Apr 22, 2024, 9:11 AM

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.reopen

final saddleBOT Apr 22, 2024, 9:11 AM

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✅

nocturne vale Apr 22, 2024, 9:17 AM

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YO

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The second one $4IX-2IX=2IX=2X=A$

soft zealotBOT Apr 22, 2024, 9:18 AM

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Ten-Duce

remote island Apr 22, 2024, 9:18 AM

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how did you figure it out

nocturne vale Apr 22, 2024, 9:19 AM

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see the first and 4th term on the lhs is just scaler times identity matrix

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you see that?

remote island Apr 22, 2024, 9:19 AM

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yea

nocturne vale Apr 22, 2024, 9:20 AM

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the other one let me have another try

remote island Apr 22, 2024, 9:21 AM

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nocturne vale you see that?

is the solution>?

nocturne vale Apr 22, 2024, 9:21 AM

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Si

remote island Apr 22, 2024, 9:30 AM

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@nocturne vale i have to go in 5min

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can you do it till then

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gotta go

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bye and thanks

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.close

final saddleBOT Apr 22, 2024, 9:36 AM

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final saddleBOT Apr 22, 2024, 10:06 AM

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modern dome Apr 22, 2024, 10:17 AM

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#help-36

final saddleBOT Apr 22, 2024, 10:17 AM

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modern dome <#908076393198419988>

modern dome Apr 22, 2024, 10:18 AM

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Integration using U substitution

modern dome Apr 22, 2024, 10:19 AM

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modern dome

I just gota ask is it always 1 when you move the derivative u and why 1?

final saddleBOT Apr 22, 2024, 10:34 AM

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@modern dome Has your question been resolved?

shadow tinsel Apr 22, 2024, 10:43 AM

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modern dome I just gota ask is it always 1 when you move the derivative u and why 1?

where is the 1?

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or which 1 are u referring to

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modern dome Apr 22, 2024, 10:56 AM

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#help-36

final saddleBOT Apr 22, 2024, 10:56 AM

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modern dome <#908076393198419988>

modern dome Apr 22, 2024, 10:56 AM

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shadow tinsel where is the 1?

The 1/3

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Du/3 to 1/3

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Sorry it took me long to reply I was cooking

shadow tinsel Apr 22, 2024, 10:58 AM

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it wont always be 1

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du/3 is just 1/3 * du

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so thats how they get the 1/3

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it wont always be 1/3 tho, it can be 2/3 it can be pretty much any number rly

final saddleBOT Apr 22, 2024, 11:12 AM

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@modern dome Has your question been resolved?

modern dome Apr 22, 2024, 11:26 AM

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I'm confused cause the video I watch just said 1 and no explanation

modern dome Apr 22, 2024, 11:26 AM

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shadow tinsel du/3 is just 1/3 * du

Do you have any other explanation on it?

final saddleBOT Apr 22, 2024, 11:26 AM

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mystic zenith Apr 22, 2024, 12:09 PM

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hey quick question. Number 1, what does the weird brackets mean? And how to solve a)

final saddleBOT Apr 22, 2024, 12:09 PM

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mystic zenith hey quick question. Number 1, what does the weird brackets mean? And how to solv...

final tangle Apr 22, 2024, 12:12 PM

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are you referring to the
]a,b[

mystic zenith Apr 22, 2024, 12:12 PM

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Yes

final tangle Apr 22, 2024, 12:13 PM

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that's old interval notation still used in some places
other places use (a,b)
to represent the set of values between a and b exlcuding a and b

mystic zenith Apr 22, 2024, 12:13 PM

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So a and b does not work in function? But numbers between them do?

final tangle Apr 22, 2024, 12:14 PM

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well here the words say except for ]a,b[

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so stuff between are the values that don't work

mystic zenith Apr 22, 2024, 12:15 PM

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Oh ok so a and b does but not in between

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And how would one solve the a question?

final saddleBOT Apr 22, 2024, 12:30 PM

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@mystic zenith Has your question been resolved?

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charred warren Apr 22, 2024, 2:18 PM

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i need guidance to answer this

final saddleBOT Apr 22, 2024, 2:18 PM

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charred warren i need guidance to answer this

cloud cloud Apr 22, 2024, 2:20 PM

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charred warren i need guidance to answer this

I would say start by solving the two angles of p

charred warren Apr 22, 2024, 2:21 PM

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180 - 104 - 21

cloud cloud Apr 22, 2024, 2:21 PM

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Yes

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,calc 180-104-21

soft zealotBOT Apr 22, 2024, 2:21 PM

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Result:

cloud cloud Apr 22, 2024, 2:22 PM

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Then you know that b is 1/2(O) bc of arcs

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And solve for w from there

tranquil pine Apr 22, 2024, 2:23 PM

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cloud cloud Then you know that b is 1/2(O) bc of arcs

how ?

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nvm

final saddleBOT Apr 22, 2024, 2:36 PM

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@charred warren Has your question been resolved?

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keen turret Apr 22, 2024, 2:56 PM

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final saddleBOT Apr 22, 2024, 2:56 PM

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keen turret

keen turret Apr 22, 2024, 2:57 PM

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What did I do wrong for my answer to be wrong

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The second calculation is the actual answer

silver roost Apr 22, 2024, 3:00 PM

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You forgot to change bounds back

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Once you went back to x

keen turret Apr 22, 2024, 3:03 PM

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Oh

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I actually didn’t know that

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Or forgot

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Thank you

silver roost Apr 22, 2024, 3:03 PM

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Np

final saddleBOT Apr 22, 2024, 3:18 PM

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thorn minnow Apr 22, 2024, 3:46 PM

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R is integrityring need to show those sets are equal, any ideas? 🥺

final saddleBOT Apr 22, 2024, 3:46 PM

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thorn minnow R is integrityring need to show those sets are equal, any ideas? 🥺

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@thorn minnow Has your question been resolved?

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vale reef Apr 22, 2024, 4:30 PM

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final saddleBOT Apr 22, 2024, 4:30 PM

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vale reef

vale reef Apr 22, 2024, 4:30 PM

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What does symbol on second line mean

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I thing

desert mantle Apr 22, 2024, 4:32 PM

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I thing?

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do you mean $\Phi$?

soft zealotBOT Apr 22, 2024, 4:32 PM

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Denascite

long wraith Apr 22, 2024, 4:33 PM

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soft zealot **Denascite**

Is that the capitalized one?

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$\phi$

soft zealotBOT Apr 22, 2024, 4:33 PM

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Blues

long wraith Apr 22, 2024, 4:33 PM

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Oh yeah

past hedge Apr 22, 2024, 4:34 PM

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.reopen

vale reef Apr 22, 2024, 4:35 PM

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Yeah

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Idk why that’s here

long wraith Apr 22, 2024, 4:37 PM

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Your teacher just named it phi thats all

vale reef Apr 22, 2024, 4:41 PM

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Oh ok lol

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Thx

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.close

final saddleBOT Apr 22, 2024, 4:41 PM

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final saddleBOT Apr 22, 2024, 4:56 PM

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tranquil pine Apr 22, 2024, 5:05 PM

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253.52 apples, 5 is 5/10 of 1 apple, 2 is 2/100 of 1 apple (if the whole appks gets divided into 100 equal parts) , 2/100 of one apple is 10 smaller than 5/10 of 1 apple, as , 2/10x 1/10 right guys?

final saddleBOT Apr 22, 2024, 5:05 PM

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tranquil pine 253.52 apples, 5 is 5/10 of 1 apple, 2 is 2/100 of 1 apple (if the whole appks g...

hidden oriole Apr 22, 2024, 5:06 PM

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tranquil pine 253.52 apples, 5 is 5/10 of 1 apple, 2 is 2/100 of 1 apple (if the whole appks g...

send the problem

tranquil pine Apr 22, 2024, 5:06 PM

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hidden oriole send the problem

bro

tranquil pine Apr 22, 2024, 5:06 PM

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hidden oriole send the problem

im askin if my understanding is right

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is it riht

hidden oriole Apr 22, 2024, 5:07 PM

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send the actual problem idk what ur saying

crisp ridge Apr 22, 2024, 5:08 PM

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tranquil pine 253.52 apples, 5 is 5/10 of 1 apple, 2 is 2/100 of 1 apple (if the whole appks g...

ye that sounds right

tranquil pine Apr 22, 2024, 5:09 PM

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guys

tranquil pine Apr 22, 2024, 5:11 PM

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crisp ridge ye that sounds right

2/100 is the same as 1/50 coz same proportions right? but they aint exactly equal tho right?

hidden oriole Apr 22, 2024, 5:11 PM

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tranquil pine 2/100 is the same as 1/50 coz same proportions right? but they aint exactly equa...

no they are equal

tranquil pine Apr 22, 2024, 5:15 PM

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.close

final saddleBOT Apr 22, 2024, 5:15 PM

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final saddleBOT Apr 22, 2024, 5:30 PM

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frail girder Apr 22, 2024, 5:37 PM

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WhatsApp_Image_2024-04-22_at_22.35.00_fa84a840.jpg

final saddleBOT Apr 22, 2024, 5:37 PM

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frail girder

frail girder Apr 22, 2024, 5:37 PM

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d option?

cold gorge Apr 22, 2024, 5:38 PM

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Assuming A, G and H are arithmetic geometric and harmonic means, yeah.

frail girder Apr 22, 2024, 5:40 PM

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yup

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o my god dude you got a trippy profile

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.close

final saddleBOT Apr 22, 2024, 5:40 PM

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final saddleBOT Apr 22, 2024, 5:55 PM

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hidden oriole Apr 22, 2024, 5:56 PM

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final saddleBOT Apr 22, 2024, 5:56 PM

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hidden oriole

hidden oriole Apr 22, 2024, 5:56 PM

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help

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i used the IBP but i got an answer way off

thick breach Apr 22, 2024, 5:56 PM

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there's no need for that

hidden oriole Apr 22, 2024, 5:56 PM

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there isnt?

thick breach Apr 22, 2024, 5:57 PM

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$take lnx = t => x = e^{t}$

soft zealotBOT Apr 22, 2024, 5:57 PM

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penguin

hidden oriole Apr 22, 2024, 5:57 PM

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OH

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substitution

errant crane Apr 22, 2024, 5:57 PM

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what are the chances of getting 5.5% 3x in a row?

thick breach Apr 22, 2024, 5:57 PM

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yeah, no need for IBP

hidden oriole Apr 22, 2024, 5:57 PM

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errant crane what are the chances of getting 5.5% 3x in a row?

this channel is occupied rn

errant crane Apr 22, 2024, 5:58 PM

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sorry, idk what im doing tbh

hidden oriole Apr 22, 2024, 5:58 PM

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hidden oriole

so we have integral of t/? dt

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because e^t isnt in the function

hidden oriole Apr 22, 2024, 6:00 PM

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errant crane sorry, idk what im doing tbh

see #help-6

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its available

lethal bronze Apr 22, 2024, 6:00 PM

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hidden oriole because e^t isnt in the function

(e^t)^3…

thick breach Apr 22, 2024, 6:01 PM

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ah the integral should come out to be
\newline
$\int \frac{t}{e^{2t}}dt$

soft zealotBOT Apr 22, 2024, 6:01 PM

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penguin

hidden oriole Apr 22, 2024, 6:01 PM

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OH because they are inverse

thick breach Apr 22, 2024, 6:01 PM

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soft zealot **penguin**

now use IBP

lethal bronze Apr 22, 2024, 6:01 PM

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isn’t the denominator e^3t

thick breach Apr 22, 2024, 6:01 PM

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lethal bronze isn’t the denominator e^3t

we substituted lnx = t so it 1/x dx is dt

lethal bronze Apr 22, 2024, 6:02 PM

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I am stupid carry on

hidden oriole Apr 22, 2024, 6:02 PM

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ok i get it

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so then we have u = t

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and v' = 1/e^2t

thick breach Apr 22, 2024, 6:04 PM

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no point in taking u = t mate

hidden oriole Apr 22, 2024, 6:04 PM

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i am not that great with IBP so it helps me remember

thick breach Apr 22, 2024, 6:04 PM

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oh my bad you meant the u and v right?

hidden oriole Apr 22, 2024, 6:04 PM

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yeah

thick breach Apr 22, 2024, 6:05 PM

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yeah you're right, v'= e^{-2t}

hidden oriole Apr 22, 2024, 6:06 PM

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so we have
\newline
$ t * \int e^-2t

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for the first term

thick breach Apr 22, 2024, 6:06 PM

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correct

hidden oriole Apr 22, 2024, 6:07 PM

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which is t * -0.5e^-2t

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and for the second term we have the integral of e^-2t

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which is -0.5e^-2t

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so its -0.5e^-2t(t + 1)

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and we just sub in ln(x)?

thick breach Apr 22, 2024, 6:09 PM

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yeah just substitute the original variables

hidden oriole Apr 22, 2024, 6:09 PM

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0.5e^-2lnx(lnx + 1)

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and evaluating for e gives us e^-2

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and evaluating for 1 gives hs

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0.5(ln(1) + 1))

thick breach Apr 22, 2024, 6:12 PM

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$\frac{-2lnx+1}{4x^{2}} + C$

soft zealotBOT Apr 22, 2024, 6:13 PM

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penguin

hidden oriole Apr 22, 2024, 6:13 PM

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ty

thick breach Apr 22, 2024, 6:13 PM

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anytime!

hidden oriole Apr 22, 2024, 6:13 PM

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.clised

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.closed

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.solved

final saddleBOT Apr 22, 2024, 6:13 PM

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Channel closed

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final saddleBOT Apr 22, 2024, 6:28 PM

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tranquil pine Apr 22, 2024, 7:01 PM

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yo

final saddleBOT Apr 22, 2024, 7:01 PM

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tranquil pine yo

tranquil pine Apr 22, 2024, 7:02 PM

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hi@yoo

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alr so

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a) 1/2 represwnts half of a sandwich

small linden Apr 22, 2024, 7:04 PM

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what

hidden oriole Apr 22, 2024, 7:07 PM

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what

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i guess

tranquil pine Apr 22, 2024, 7:14 PM

#

situation 1:
1:2, ratio representing a scenerio where one over 2 ppl/ one to two ppl, got 1/2 of a sandwhich so one person got half of a sandwhich
situation 2

3:4
3 dogs per 4 cats got got their legs taken away
so
0.75 of their legs got taken away? like what is the decimal representing here?

marble agate Apr 22, 2024, 7:17 PM

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is this your hw question or what?

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i dont get what youre asking

tranquil pine Apr 22, 2024, 7:17 PM

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im trying to understand decimals

tranquil pine Apr 22, 2024, 7:17 PM

#

tranquil pine situation 1: 1:2, ratio representing a scenerio where one over 2 ppl/ one to two...

the queation is there

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.close

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verbal wren Apr 22, 2024, 8:08 PM

#

final saddleBOT Apr 22, 2024, 8:08 PM

#

verbal wren

agile coral Apr 22, 2024, 8:11 PM

#

!status

final saddleBOT Apr 22, 2024, 8:11 PM

#

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

vapid basalt Apr 22, 2024, 8:13 PM

#

verbal wren

hint: complete the square

whole pecan Apr 22, 2024, 8:17 PM

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Ignore the 4

final saddleBOT Apr 22, 2024, 8:23 PM

#

@verbal wren Has your question been resolved?

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fossil widget Apr 22, 2024, 8:41 PM

#

halo guys this is discrete, um, my understanding of vertices are they are like the joints and connect the edges together and edges are just the lines, however im a little confused on how to find the degree of each vertex, and how to identify a pendant, (i assume isolated means a vertex has no edges connected to it)

final saddleBOT Apr 22, 2024, 8:41 PM

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fossil widget halo guys this is discrete, um, my understanding of vertices are they are like t...

fossil widget Apr 22, 2024, 8:46 PM

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nvm got it ty guys

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cyan shoal Apr 22, 2024, 9:16 PM

#

final saddleBOT Apr 22, 2024, 9:16 PM

#

cyan shoal

cyan shoal Apr 22, 2024, 9:20 PM

#

A country's trade balance, in a given period, is the difference between the total value of exports and imports, in that order. What was the percentage growth rate of the trade balance from 2023 to 2024 for this country?

#

#

and this

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A country's trade balance, in a given period, is the difference between the total value of exports and imports, in that order. What was the percentage growth rate of the trade balance from 2022 to 2023 for this country?

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<@&286206848099549185> pls?

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20%?

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ohhh ok

cyan shoal Apr 22, 2024, 9:41 PM

#

cyan shoal

and this is 25% right ?

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tysm bro

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<3

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trail river Apr 23, 2024, 12:21 AM

#

how do I simplify this?

final saddleBOT Apr 23, 2024, 12:21 AM

#

trail river how do I simplify this?

trail river Apr 23, 2024, 12:21 AM

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further

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I want to prove its equal

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to

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whole pecan Apr 23, 2024, 12:22 AM

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the top

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you can factor

trail river Apr 23, 2024, 12:22 AM

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whole pecan you can factor

but 1

whole pecan Apr 23, 2024, 12:22 AM

#

waht

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well

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let k=cosx

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k^2 -2k + 1

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factor!

trail river Apr 23, 2024, 12:23 AM

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ah

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it wasn't obvious

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?

trail river Apr 23, 2024, 12:25 AM

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whole pecan factor!

(cosx-1)(cosx-1)

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what now

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still can't simplify

lethal bronze Apr 23, 2024, 12:27 AM

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factor the denominator

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difference of squares

trail river Apr 23, 2024, 12:28 AM

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lethal bronze difference of squares

oh

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nice thakns

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got it

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.close

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tranquil pine Apr 23, 2024, 1:14 AM

#

I just dont even know where to start

final saddleBOT Apr 23, 2024, 1:14 AM

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tranquil pine I just dont even know where to start

tranquil pine Apr 23, 2024, 1:14 AM

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if anyone can help

rustic sinew Apr 23, 2024, 1:18 AM

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tranquil pine if anyone can help

If you read example 6.4.4, does that help?
https://math.libretexts.org/Bookshelves/Calculus/Map%3A_University_Calculus_(Hass_et_al)/6%3A_Applications_of_Definite_Integrals/6.4%3A_Areas_of_Surfaces_of_Revolution

tulip coyote Apr 23, 2024, 1:20 AM

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y axis sadcat

tranquil pine Apr 23, 2024, 1:20 AM

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ok i'd be wrong to say i dont know anything

tulip coyote Apr 23, 2024, 1:20 AM

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Do you have that example 3 they refer to?

tranquil pine Apr 23, 2024, 1:21 AM

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yea hold on

tulip coyote Apr 23, 2024, 1:21 AM

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rustic sinew If you read example 6.4.4, does that help? <https://math.libretexts.org/Bookshel...

(example 6.4.5 more relevant sadCatThumbsUp )

tranquil pine Apr 23, 2024, 1:23 AM

#

#

#

so i know $:f'\left(x\right)=\frac{ln\left(x\right)}{x\sqrt{ln^2\left(x\right)-1}}$ if im not wrong

soft zealotBOT Apr 23, 2024, 1:26 AM

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Draco

tulip coyote Apr 23, 2024, 1:27 AM

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That would be the second derivative of f

tranquil pine Apr 23, 2024, 1:27 AM

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$2\pi \int _e^{e^3}x\sqrt{1+\left(f'\left(x\right)\right)^2}dx$

soft zealotBOT Apr 23, 2024, 1:27 AM

#

Draco

tulip coyote Apr 23, 2024, 1:27 AM

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First derivative is as per here via FTC catThumbsUp

tranquil pine Apr 23, 2024, 1:28 AM

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oops

tulip coyote Apr 23, 2024, 1:28 AM

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Anyways how do you even rearrange an integral function NervousSweat

tranquil pine Apr 23, 2024, 1:29 AM

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ummm

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So this is what i have rn $2\pi \int _e^{e^3}x\sqrt{1+\left(\sqrt{ln\left(x\right)^2}-1\right)^2}dx$

soft zealotBOT Apr 23, 2024, 1:30 AM

#

Draco

tranquil pine Apr 23, 2024, 1:30 AM

#

then this $:S=2\pi :\int _e^{e^3}x\sqrt{1+\sqrt{ln\left(x\right)^2-1}}$

soft zealotBOT Apr 23, 2024, 1:30 AM

#

Draco

tranquil pine Apr 23, 2024, 1:30 AM

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wait no

tulip coyote Apr 23, 2024, 1:30 AM

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Wouldn't it be dy though, if you're revolving about the y axis sadcat

tranquil pine Apr 23, 2024, 1:30 AM

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$S=2\pi :\int _e^{e^3}x\sqrt{1+ln\left(x\right)^2-1}$

soft zealotBOT Apr 23, 2024, 1:30 AM

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Draco

tranquil pine Apr 23, 2024, 1:31 AM

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hmm true

tulip coyote Apr 23, 2024, 1:31 AM

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Also isn't it supposed to be f(x) instead of x on that inside bcaForgiveBeg3

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Nasty FumizukiCross

tranquil pine Apr 23, 2024, 1:35 AM

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idk

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imma just show what i got

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$2\pi \int _e^{e^3}x\sqrt{1+\left(\sqrt{ln\left(x\right)^2}-1\right)^2}dx$
$S=2\pi :\int _e^{e^3}x\sqrt{1+ln\left(x\right)^2-1}$
$S=2\pi :\int _e^{e^3}x\left|ln\left(x\right)\right|dx$

soft zealotBOT Apr 23, 2024, 1:36 AM

#

Draco

tulip coyote Apr 23, 2024, 1:37 AM

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I mean, taking that as is, and noting that cause x > 1 for all the values under consideration, you can get rid of the absolute values catThumbsUp

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For which it becomes by parts, I'm just gonna assume they messed up and meant x axis tbh catGiggle

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If it were y axis, I'd give up life HangMyself

tranquil pine Apr 23, 2024, 1:38 AM

#

$\int :xln\left(x\right)dx:=:\frac{x^2}{2}ln\left(x\right)-\frac{x^2}{4}+C$

soft zealotBOT Apr 23, 2024, 1:38 AM

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Draco

tranquil pine Apr 23, 2024, 1:38 AM

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tulip coyote For which it becomes by parts, I'm just gonna assume they messed up and meant x ...

yea i cant think of how to do it

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what do u think of the last thing i posted

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i think i just plug in e and e^3 into the last part of the problem

tulip coyote Apr 23, 2024, 1:39 AM

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Yep seems about right happyCat put the limits in and all

tranquil pine Apr 23, 2024, 1:42 AM

#

$2\pi \left(\frac{e^6}{2}ln\left(e^3\right)-\frac{e^6}{4}-\frac{e^2}{2}ln\left(e\right)+\frac{e^2}{4}\right)$

soft zealotBOT Apr 23, 2024, 1:42 AM

#

Draco

tranquil pine Apr 23, 2024, 1:42 AM

#

$2\pi \left(\frac{5e^6}{4}-\frac{e^2}{4}\right)$

soft zealotBOT Apr 23, 2024, 1:42 AM

#

Draco

tranquil pine Apr 23, 2024, 1:42 AM

#

$\frac{\pi }{2}\left(5e^6-e^2\right)$

soft zealotBOT Apr 23, 2024, 1:42 AM

#

Draco

tranquil pine Apr 23, 2024, 1:43 AM

#

how is this looking @tulip coyote

tulip coyote Apr 23, 2024, 1:48 AM

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Looks good to me I think happyCat

tranquil pine Apr 23, 2024, 1:48 AM

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ty ty

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and uhhh

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i think thats all

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i put the absolute values on the constants u said last tie so i dont think more questions

tulip coyote Apr 23, 2024, 1:51 AM

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happyCat perfect SCgoodjob2

tranquil pine Apr 23, 2024, 1:51 AM

#

https://tenor.com/view/they-didnt-believe-in-us-but-god-did-dj-khaled-gif-26564481

Tenor

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have a goodnight gang

#

.close

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wheat hamlet Apr 23, 2024, 2:34 AM

#

final saddleBOT Apr 23, 2024, 2:34 AM

#

wheat hamlet

wheat hamlet Apr 23, 2024, 2:34 AM

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anyone know what this is

faint monolith Apr 23, 2024, 2:35 AM

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double angle trigonometry

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basically change tan to sin/cos and use sin/cos double angle formula

wheat hamlet Apr 23, 2024, 2:42 AM

#

.close

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tranquil pine Apr 23, 2024, 3:30 AM

#

Screen_Shot_2024-04-22_at_11.30.32_PM.png

final saddleBOT Apr 23, 2024, 3:30 AM

#

tranquil pine

tranquil pine Apr 23, 2024, 3:31 AM

#

trying to understand why b is S14W

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I'm getting S14E

timid pollen Apr 23, 2024, 3:35 AM

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tranquil pine I'm getting S14E

Wind from the east means its traveling westward

tranquil pine Apr 23, 2024, 3:36 AM

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oh ok thx

#

.close

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young verge Apr 23, 2024, 3:53 AM

#

Would this be y = 9 and x = 4?

final saddleBOT Apr 23, 2024, 3:53 AM

#

young verge Would this be y = 9 and x = 4?

white sphinx Apr 23, 2024, 3:55 AM

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no

wanton pine Apr 23, 2024, 3:56 AM

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it never specified integers

faint monolith Apr 23, 2024, 3:57 AM

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what does it mean its a minimum

white sphinx Apr 23, 2024, 3:57 AM

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minima

wanton pine Apr 23, 2024, 3:57 AM

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as small as possible

white sphinx Apr 23, 2024, 3:58 AM

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write the second equation (x+4y) in terms of one variable then find the minima

young verge Apr 23, 2024, 3:58 AM

#

white sphinx write the second equation (x+4y) in terms of one variable then find the minima

can it be 36/y + 4y?

wanton pine Apr 23, 2024, 3:59 AM

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yeah

young verge Apr 23, 2024, 3:59 AM

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oh i see what i did wrong

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i frogot the squared

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so should it be 3 and 12

white sphinx Apr 23, 2024, 3:59 AM

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young verge can it be 36/y + 4y?

yes

white sphinx Apr 23, 2024, 3:59 AM

#

young verge so should it be 3 and 12

yes

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x = 12 and y = 3

young verge Apr 23, 2024, 4:00 AM

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white sphinx x = 12 and y = 3

would it matter if it was the other way around ?

white sphinx Apr 23, 2024, 4:00 AM

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yes

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it says first number + 4 times of second number

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if you take second number as 12

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it isnt really minima

white sphinx Apr 23, 2024, 4:01 AM

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young verge can it be 36/y + 4y?

you'll get y = 3 automatically when u find minima of this

#

so x must be 12

young verge Apr 23, 2024, 4:01 AM

#

alr

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thanks

#

.close

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#

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young verge Apr 23, 2024, 4:21 AM

#

A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?

final saddleBOT Apr 23, 2024, 4:21 AM

#

young verge A manufacturer wants to design an open box having a square base and a surface ar...

young verge Apr 23, 2024, 4:21 AM

#

Can someone walk me through this

#

im having trouble with the set up

wanton pine Apr 23, 2024, 4:23 AM

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aight

#

just a question first? the box mentions having a square base but i assume it doesnt have the same length height?

young verge Apr 23, 2024, 4:24 AM

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wanton pine just a question first? the box mentions having a square base but i assume it doe...

i would assume the height isnt the same, yes

wanton pine Apr 23, 2024, 4:25 AM

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aight well our first goal should be to setup an equation for the surface area of the box since we are given what it should equal

young verge Apr 23, 2024, 4:25 AM

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would the surface area be

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the base and the top * the sides?

wanton pine Apr 23, 2024, 4:25 AM

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if we let x equal the base length of the box and y equal the height what could u create?

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just the base and the sides

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its an 'open' box

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meaning it has no top

young verge Apr 23, 2024, 4:26 AM

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wanton pine just the base and the sides

4xh + x^2

wanton pine Apr 23, 2024, 4:27 AM

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right

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and that equates to 108

young verge Apr 23, 2024, 4:27 AM

#

yes

wanton pine Apr 23, 2024, 4:27 AM

#

now we should setup our function to find the maximum for

#

since we want to find the maximum volume we should create a function for the volume of the open box

young verge Apr 23, 2024, 4:28 AM

#

because the height isnt the same, the volume would be x^2 * h right

wanton pine Apr 23, 2024, 4:28 AM

#

correct

#

but this creates a problem as we have 2 variables which we dont want

young verge Apr 23, 2024, 4:30 AM

#

yaeh

#

How ould i seperate this

wanton pine Apr 23, 2024, 4:30 AM

#

but since we know that 4xh+x^2=108 we are able to find the value of either x or h in terms of the other variable

young verge Apr 23, 2024, 4:32 AM

#

would it be easier to make it in terms of x or h?

wanton pine Apr 23, 2024, 4:33 AM

#

h

#

make h in terms of x

young verge Apr 23, 2024, 4:33 AM

#

so 108/4x - x/4 = h?

#

by moving the x^2 to the other side

#

and dividng by 4x

wanton pine Apr 23, 2024, 4:34 AM

#

right

#

just for simplification sake 108/4x = 27/x

young verge Apr 23, 2024, 4:35 AM

#

yea

wanton pine Apr 23, 2024, 4:35 AM

#

now we can just sub in the values for h into our volume function

young verge Apr 23, 2024, 4:37 AM

#

ok so v = x^2 (27/x - x/4)

wanton pine Apr 23, 2024, 4:37 AM

#

right and i'd expand that to make finding its derivative easier

young verge Apr 23, 2024, 4:37 AM

#

27x - x^3/4

wanton pine Apr 23, 2024, 4:37 AM

#

yep

young verge Apr 23, 2024, 4:37 AM

#

derive?

wanton pine Apr 23, 2024, 4:39 AM

#

yeah since we have a function we are able to find out its Minima and Maxima, to do that we take the derivative of the function and set that equal to 0 to find 'stationary points' which relate to points that have a slope of 0 which are Minima, Maxima and Horizontal Points of Inflection

young verge Apr 23, 2024, 4:40 AM

#

so would the max value be 6?

wanton pine Apr 23, 2024, 4:41 AM

#

not the max value, but a max when x=6

#

actually

young verge Apr 23, 2024, 4:41 AM

#

wanton pine not the max value, but a max when x=6

wdym?

wanton pine Apr 23, 2024, 4:42 AM

#

well we have 27-3x^2/4 =0 right?

#

108=3x^2

#

x^2=36

young verge Apr 23, 2024, 4:42 AM

#

wait whered 2/4 come from?

#

oh 3/4

wanton pine Apr 23, 2024, 4:42 AM

#

oh sorry its the notation

young verge Apr 23, 2024, 4:42 AM

#

Yeah

wanton pine Apr 23, 2024, 4:42 AM

#

x=+6 or -6

young verge Apr 23, 2024, 4:43 AM

#

oh and now do i have to find the max / min using second derivative?

wanton pine Apr 23, 2024, 4:43 AM

#

yeah

young verge Apr 23, 2024, 4:43 AM

#

so max at -6

wanton pine Apr 23, 2024, 4:44 AM

#

correct

young verge Apr 23, 2024, 4:44 AM

#

young verge so 108/4x - x/4 = h?

and i plug in my x here to find h ?

wanton pine Apr 23, 2024, 4:44 AM

#

yep

young verge Apr 23, 2024, 4:45 AM

#

wanton pine correct

wait but how can the side be negative

wanton pine Apr 23, 2024, 4:45 AM

#

oh wait im mistaken its 6

#

yeah was bout to say mb

#

second derivative needs to be negative for a maximum

young verge Apr 23, 2024, 4:46 AM

#

so would h then be 23/6

wanton pine Apr 23, 2024, 4:48 AM

#

,calc 27/6-6/4

soft zealotBOT Apr 23, 2024, 4:48 AM

#

Result:

wanton pine Apr 23, 2024, 4:48 AM

#

,calc 108-36

soft zealotBOT Apr 23, 2024, 4:48 AM

#

Result:

young verge Apr 23, 2024, 4:48 AM

#

oh

wanton pine Apr 23, 2024, 4:48 AM

#

yeah its 3

young verge Apr 23, 2024, 4:48 AM

#

wanton pine ,calc 108-36

wait whyd u do this?

wanton pine Apr 23, 2024, 4:49 AM

#

just checking if it calculated correctly

young verge Apr 23, 2024, 4:49 AM

#

ah alr

#

thanks

final saddleBOT Apr 23, 2024, 5:04 AM

#

@young verge Has your question been resolved?

#

Channel closed

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teal robin Apr 23, 2024, 8:35 AM

#

I understand the process of this question but I am unsure how to know which one the average is? why is it v_x = 4/3 and not the v_y or the v_z?

final saddleBOT Apr 23, 2024, 8:35 AM

#

teal robin I understand the process of this question but I am unsure how to know which one ...

teal robin Apr 23, 2024, 8:36 AM

#

Here is the introduction to the question, before the parts come into play : )

final saddleBOT Apr 23, 2024, 8:51 AM

#

@teal robin Has your question been resolved?

final saddleBOT Apr 23, 2024, 9:06 AM

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teal robin Apr 23, 2024, 9:07 AM

#

.reopen

final saddleBOT Apr 23, 2024, 9:07 AM

#

✅

#

@teal robin Has your question been resolved?

final saddleBOT Apr 23, 2024, 9:52 AM

#

@teal robin Has your question been resolved?

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haughty moth Apr 23, 2024, 3:02 PM

#

Show that any rational complex function can be expanded into a power series within any disk where it is defined

final saddleBOT Apr 23, 2024, 3:02 PM

#

haughty moth Show that any rational complex function can be expanded into a power series with...

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real mesa Apr 23, 2024, 3:40 PM

#

why he did that 1 x i frac i x i

final saddleBOT Apr 23, 2024, 3:40 PM

#

real mesa why he did that 1 x i frac i x i

candid hull Apr 23, 2024, 3:50 PM

#

C'est un trick pour rendre le dénominateur réel

final saddleBOT Apr 23, 2024, 3:55 PM

#

@real mesa Has your question been resolved?

real mesa Apr 23, 2024, 4:05 PM

#

candid hull C'est un trick pour rendre le dénominateur réel

Ahh merci beaucoup

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tawny nest Apr 23, 2024, 4:07 PM

#

final saddleBOT Apr 23, 2024, 4:07 PM

#

tawny nest

tawny nest Apr 23, 2024, 4:07 PM

#

F2 is a sub vectorial space, how can I determine its base?

midnight sparrow Apr 23, 2024, 4:08 PM

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Resolve this system in parametric form

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It will gives you 2 vector

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Show there are not colinear and it's your basis

tawny nest Apr 23, 2024, 4:09 PM

#

#

I didn't understand the solution either.

midnight sparrow Apr 23, 2024, 4:09 PM

#

T'es français

tawny nest Apr 23, 2024, 4:09 PM

#

midnight sparrow T'es français

System Français mais pas français.

midnight sparrow Apr 23, 2024, 4:09 PM

#

Ah

last palm Apr 23, 2024, 4:09 PM

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Can I use integration by parts with more than 3 functions

midnight sparrow Apr 23, 2024, 4:10 PM

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Yes it's basicaly that I forgot the z

tawny nest Apr 23, 2024, 4:10 PM

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But like how to solve it? How to get those vectors?

midnight sparrow Apr 23, 2024, 4:11 PM

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Do you know how to have the nulle space of a matrix

tawny nest Apr 23, 2024, 4:11 PM

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Suppose that la combinaison linéaire =0?

tawny nest Apr 23, 2024, 4:11 PM

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midnight sparrow Do you know how to have the nulle space of a matrix

Using Gauss Algorithm?

midnight sparrow Apr 23, 2024, 4:11 PM

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Yeah

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It's basically the same thing

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Here t IS the unknown with 3 parameters x,y and z

tawny nest Apr 23, 2024, 4:12 PM

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The issue for me is, everything is a variable, there is no constants, Idk how to that...

midnight sparrow Apr 23, 2024, 4:12 PM

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Just write t with parameters

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Make F2 in parametric form

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And it will gives you the vectors

tawny nest Apr 23, 2024, 4:13 PM

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Picture of the beginning of the solution would be helpful...

midnight sparrow Apr 23, 2024, 4:13 PM

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tawny nest Picture of the beginning of the solution would be helpful...

Wdym

#

Do you understand french or not ?

terse dagger Apr 23, 2024, 4:14 PM

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they write t as a function of x and y

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this means that the subspace only has 3 degrees of freedom

tawny nest Apr 23, 2024, 4:15 PM

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You didn't get the issue I'm facing...

terse dagger Apr 23, 2024, 4:16 PM

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oh ok

tawny nest Apr 23, 2024, 4:16 PM

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rn_image_picker_lib_temp_0e7104e7-cbad-4ec6-a85b-8532bedc8e24.jpg

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How is it useful to apply the algorithm since everything is a variable?

terse dagger Apr 23, 2024, 4:16 PM

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,rotate

soft zealotBOT Apr 23, 2024, 4:16 PM

#

terse dagger Apr 23, 2024, 4:17 PM

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i'm not entirely sure what algorithm you're using

midnight sparrow Apr 23, 2024, 4:17 PM

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What do you want

tawny nest Apr 23, 2024, 4:17 PM

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Gauss Algorithm to simplify such matrices.

tawny nest Apr 23, 2024, 4:17 PM

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midnight sparrow What do you want

Find the base of F2.

midnight sparrow Apr 23, 2024, 4:17 PM

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Your matrices refer to what ?

tawny nest Apr 23, 2024, 4:18 PM

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I think la combinaison linear de F2.

midnight sparrow Apr 23, 2024, 4:18 PM

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F2 IS the nullspace of this row matrice A= (1 -2 0 1)

honest lily Apr 23, 2024, 4:18 PM

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What does this even mean? "You need to provide information about your population and what subset of the population your sample was taken for your study."

tawny nest Apr 23, 2024, 4:19 PM

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I made this matrix to find a base by using (famille génératrice et libre).

#

Propriété.*

midnight sparrow Apr 23, 2024, 4:19 PM

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Une famille génératrice tu l'as avec ton ensemble

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Ensuite il faut montrer que cette famille est libre

tawny nest Apr 23, 2024, 4:21 PM

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Pour montrer "libre" il faut faire l'algorithme du Gauss, mais comment je faire ça avec tout ces variable....

midnight sparrow Apr 23, 2024, 4:22 PM

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Déjà quelle famille veut tu montrer la liberté

tawny nest Apr 23, 2024, 4:22 PM

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tawny nest

^ alors:

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Xvect + Yvect2 + Zvect3 + Tvect4.

midnight sparrow Apr 23, 2024, 4:25 PM

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Vect 1 2 3 et 4 c'est quoi, quelle est la famille

tawny nest Apr 23, 2024, 4:26 PM

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Idk, F2?

midnight sparrow Apr 23, 2024, 4:27 PM

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Do you understand how WE pass from F2 to its parametric form ?

tawny nest Apr 23, 2024, 4:27 PM

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Using combinaison linéaire.

tawny nest Apr 23, 2024, 4:27 PM

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tawny nest Xvect + Yvect2 + Zvect3 + Tvect4.

V =

midnight sparrow Apr 23, 2024, 4:28 PM

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Yeah it's really simple, WE write t with all parameters

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So F2 = Vect ( v1,v2,V3 ) right

tawny nest Apr 23, 2024, 4:30 PM

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I know, I specified my problem earlier, my problem is how to find the values of each vector so la famille doit être génératrice et libre.

midnight sparrow Apr 23, 2024, 4:30 PM

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So it's how they find v1, v2 and V3 ?

tawny nest Apr 23, 2024, 4:31 PM

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Exactly.

midnight sparrow Apr 23, 2024, 4:31 PM

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Ok

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So do you understand thé first Line of the proof ?

tawny nest Apr 23, 2024, 4:32 PM

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We talked about it earlier.

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The line where it showed each vector components is confusing me.

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Is the problem.

midnight sparrow Apr 23, 2024, 4:33 PM

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So you understand Line 1 and 2 but not the third

tawny nest Apr 23, 2024, 4:33 PM

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2nd line and 3rd.

midnight sparrow Apr 23, 2024, 4:33 PM

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Ok

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So AT the end of thé first Line WE write F2 in a parametric form

tawny nest Apr 23, 2024, 4:34 PM

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Show me how.

midnight sparrow Apr 23, 2024, 4:34 PM

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So you don't understand also the 1 st Line

tawny nest Apr 23, 2024, 4:36 PM

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Bro

midnight sparrow Apr 23, 2024, 4:36 PM

#

Screenshot_2024-04-23-18-36-05-946_com.discord.jpg

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IS this clear

tawny nest Apr 23, 2024, 4:36 PM

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You have (X,y,z,2y-x) it is normal.

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How to go to the 2nd step?

midnight sparrow Apr 23, 2024, 4:37 PM

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Do you know that (a,3a,4a) = a(1,3,4) ?

tawny nest Apr 23, 2024, 4:38 PM

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Okey?

midnight sparrow Apr 23, 2024, 4:38 PM

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So do you understand thé 2nd Line now ?

tawny nest Apr 23, 2024, 4:38 PM

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No.

#

#

Look at the solution....

midnight sparrow Apr 23, 2024, 4:39 PM

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tawny nest Look at the solution....

And ?

tawny nest Apr 23, 2024, 4:39 PM

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Exactly, how the did he reach the 2nd line?

midnight sparrow Apr 23, 2024, 4:40 PM

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midnight sparrow Do you know that (a,3a,4a) = a(1,3,4) ?

Look again this message

#

Can't you see

#

Just factorise by X, y and z

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(x,y,z,-x+2y) = x(1,0,0,-1) + (0,y,z,2y) right ?

tawny nest Apr 23, 2024, 4:42 PM

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oH

midnight sparrow Apr 23, 2024, 4:42 PM

#

Factorise by y and Z after

tawny nest Apr 23, 2024, 4:42 PM

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But how is that possible and X,y,z are vectors not scalaires?

midnight sparrow Apr 23, 2024, 4:43 PM

#

tawny nest But how is that possible and X,y,z are vectors not scalaires?

?????

#

Look again what is x,y,Z and t

tawny nest Apr 23, 2024, 4:43 PM

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It belongs to R^4

midnight sparrow Apr 23, 2024, 4:44 PM

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So what is x

#

What is y

#

What is z

#

And what is t

tawny nest Apr 23, 2024, 4:44 PM

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Oh

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Vectors.

midnight sparrow Apr 23, 2024, 4:44 PM

#

No🥲

tawny nest Apr 23, 2024, 4:44 PM

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lol jk

midnight sparrow Apr 23, 2024, 4:44 PM

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They are reals, scalars

tawny nest Apr 23, 2024, 4:44 PM

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They are scalaires since they are multiplied to a vector components.

midnight sparrow Apr 23, 2024, 4:44 PM

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You said it belongs to R 4

#

Yesssssss

tawny nest Apr 23, 2024, 4:45 PM

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Lmao

midnight sparrow Apr 23, 2024, 4:45 PM

#

😂

#

So 2 nd Line IS ok ?

tawny nest Apr 23, 2024, 4:45 PM

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Everything is ok lol.

midnight sparrow Apr 23, 2024, 4:45 PM

#

👍

tawny nest Apr 23, 2024, 4:45 PM

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Thanks mate.

#

,close

#

.close

final saddleBOT Apr 23, 2024, 4:45 PM

#

Channel closed

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final saddleBOT Apr 23, 2024, 5:00 PM

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brittle sail Apr 23, 2024, 5:16 PM

#

rn_image_picker_lib_temp_ef1e5c0c-e8d8-45da-b74c-91c664d9b504.jpg

final saddleBOT Apr 23, 2024, 5:16 PM

#

brittle sail

brittle sail Apr 23, 2024, 5:17 PM

#

Can someone please help me solve number B or C of number 8

hybrid heath Apr 23, 2024, 5:21 PM

#

,rccw

soft zealotBOT Apr 23, 2024, 5:21 PM

#

midnight sparrow Apr 23, 2024, 5:24 PM

#

Just developp for B

#

And use the fact that cos ^2 + sin ^2 = 1

#

For c, Idk what is cosec

final saddleBOT Apr 23, 2024, 5:32 PM

#

@brittle sail Has your question been resolved?

azure trellis Apr 23, 2024, 5:32 PM

#

Cosec is 1/sin

#

There are rules you can derive from the base trig equation by dividing by sin^2 or cos^2

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#

tawny vault Apr 23, 2024, 6:04 PM

#

what have you tried so far? can you send your working?

#

ok i found y pretty easily so there must be something you have done wrong :0

#

we can say e^5y = x and 4ln(x) = 7 - y

#

for the second equation, we can isolate 'x' by dividing both sides by 4 and raising both sides to 'e'

#

x = e^(1/4(7-y))

#

then sub x = e^(1/4(7-y)) into e^5y = x

#

does this help you progress further?

#

:) good luck

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#

final saddleBOT Apr 23, 2024, 6:44 PM

#

@crisp epoch Has your question been resolved?

final saddleBOT Apr 23, 2024, 7:16 PM

#

@crisp epoch Has your question been resolved?

crisp epoch Apr 23, 2024, 7:51 PM

#

.close

final saddleBOT Apr 23, 2024, 7:51 PM

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coral prawn Apr 23, 2024, 9:11 PM

#

In #help-28 , some other people concluded that this function is not continuous at x=0.

However, if you write e^x as k then you get (1+xk^n)/(1+k^n)

= (1/k^n + x k^n) / (1/k^n + 1)

final saddleBOT Apr 23, 2024, 9:11 PM

#

coral prawn In <#903486480985489478> , some other people concluded that this function is not...

coral prawn Apr 23, 2024, 9:12 PM

#

and as far as I can see, for negative x<0, k<1 and thus by the original expression you get (1+0)/(1+0) = 1

#

oh yeah nevermind lol

#

.close

final saddleBOT Apr 23, 2024, 9:13 PM

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final saddleBOT Apr 23, 2024, 9:28 PM

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naive shoal Apr 23, 2024, 10:06 PM

#

final saddleBOT Apr 23, 2024, 10:06 PM

#

naive shoal

naive shoal Apr 23, 2024, 10:06 PM

#

x^2-14x+40

#

symbollab says thats wron

#

but isnt what i did correct?

#

NVM

#

.close

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remote ingot Apr 23, 2024, 10:24 PM

#

how would i go about finding the derivative of this?

final saddleBOT Apr 23, 2024, 10:24 PM

#

remote ingot how would i go about finding the derivative of this?

coral prawn Apr 23, 2024, 10:26 PM

#

chain rule

#

(cos(2x))^2

#

2(cos(2x)) times the derivative of the inner function

final saddleBOT Apr 23, 2024, 10:40 PM

#

@remote ingot Has your question been resolved?

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remote ingot Apr 23, 2024, 10:50 PM

#

thank you!

final saddleBOT Apr 23, 2024, 10:51 PM

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sacred lynx Apr 23, 2024, 11:00 PM

#

Need to find m every values sum so that (2m,0,4) vectors length is less then (sqrt3 *m,3sqrtm,2sqrt13) vector length

final saddleBOT Apr 23, 2024, 11:00 PM

#

sacred lynx Need to find m every values sum so that (2m,0,4) vectors length is less then (sq...

#

@sacred lynx Has your question been resolved?

sacred lynx Apr 23, 2024, 11:26 PM

#

<@&286206848099549185>

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@sacred lynx Has your question been resolved?

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peak kernel Apr 24, 2024, 12:37 AM

#

final saddleBOT Apr 24, 2024, 12:37 AM

#

peak kernel

peak kernel Apr 24, 2024, 12:37 AM

#

why is part a not differentibale at x = 0 but part b is

nocturne ravine Apr 24, 2024, 12:38 AM

#

is it continuous at 0

#

u could ask urself that

peak kernel Apr 24, 2024, 12:38 AM

#

ahh and if discontinuous then its not differentiable?

nocturne ravine Apr 24, 2024, 12:38 AM

#

yes

peak kernel Apr 24, 2024, 12:39 AM

#

im just struggling to wrap my mind around the function

#

am i meant to try and visualise it?

nocturne ravine Apr 24, 2024, 12:40 AM

#

umm i guess it would be hard to visualize it

#

take derivative

#

of each

#

compare the two for each question

peak kernel Apr 24, 2024, 12:42 AM

#

ok

#

im still confused

nocturne ravine Apr 24, 2024, 12:44 AM

#

what dont u get

peak kernel Apr 24, 2024, 12:45 AM

#

after i get derivative

#

how does that help me with the question?

nocturne ravine Apr 24, 2024, 12:46 AM

#

what makes a function differentiable at x = 0

#

or at x = a

peak kernel Apr 24, 2024, 12:49 AM

#

continuous and doesnt have a sudden change in gradient

nocturne ravine Apr 24, 2024, 12:49 AM

#

like a corner or cusp?

peak kernel Apr 24, 2024, 12:49 AM

#

ye

#

ohh

nocturne ravine Apr 24, 2024, 12:50 AM

#

peak kernel Apr 24, 2024, 12:51 AM

#

ah so part a has a sudden change in gradient

nocturne ravine Apr 24, 2024, 12:51 AM

#

Sure

#

how do you know?

peak kernel Apr 24, 2024, 12:51 AM

#

is that cuz the powers differ by alot

#

on the limit

nocturne ravine Apr 24, 2024, 12:52 AM

#

Honestly i dont think u can use that explanation here

#

My approach would be determining the derivative of each part of the piecewise function

#

and determining fi they are equal or not

final saddleBOT Apr 24, 2024, 1:06 AM

#

@peak kernel Has your question been resolved?

#

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midnight trellis Apr 24, 2024, 1:28 AM

#

Ik this is physics but I trying to figure out if the algebra is off

final saddleBOT Apr 24, 2024, 1:28 AM

#

midnight trellis Ik this is physics but I trying to figure out if the algebra is off

midnight trellis Apr 24, 2024, 1:29 AM

#

find v_af and v_bf

#

Just need someone to tell me this algebraically correct

zenith pollen Apr 24, 2024, 1:32 AM

#

uh which equations did you start with

midnight trellis Apr 24, 2024, 1:32 AM

#

I’m solving for v_bf

#

As of now

zenith pollen Apr 24, 2024, 1:45 AM

#

like the 2 starting equations

#

you can plug into something like wolframalpha to verify the algebra

final saddleBOT Apr 24, 2024, 1:51 AM

#

@midnight trellis Has your question been resolved?

midnight trellis Apr 24, 2024, 2:17 AM

#

missed a negative

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.close

final saddleBOT Apr 24, 2024, 2:17 AM

#

Channel closed

Closed by @midnight trellis

Use .reopen if this was a mistake.

final saddleBOT Apr 24, 2024, 2:48 AM

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waxen jay Apr 24, 2024, 2:57 AM

#

how is the derivative of $e^t=e^t$?

final saddleBOT Apr 24, 2024, 2:57 AM

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waxen jay how is the derivative of $e^t=e^t$?

soft zealotBOT Apr 24, 2024, 2:57 AM

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guy

long wraith Apr 24, 2024, 2:58 AM

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2 things

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First: d(e^t)/dt = e^t

waxen jay Apr 24, 2024, 2:59 AM

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Ok

long wraith Apr 24, 2024, 2:59 AM

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Second, e is define as the value such that when the rate of change of a^x = x itself

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When this happen

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a somehow = 2.718281..

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We call this special value e

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Thats all

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So d(e^x)/dx = e^x

waxen jay Apr 24, 2024, 3:00 AM

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ok i see

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thank you

#

.close

final saddleBOT Apr 24, 2024, 3:00 AM

#

Channel closed

Closed by @waxen jay

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final saddleBOT Apr 24, 2024, 3:29 AM

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#

waxen jay Apr 24, 2024, 3:35 AM

#

is it the derivative of the deriviative? lmao

tranquil pine Apr 24, 2024, 3:37 AM

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yes

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you can keep taking derivatives infinitely

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i mean eventually you'll hit 0

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doesn't mean you can't take the derivative of it

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lmao

waxen jay Apr 24, 2024, 3:37 AM

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ok thank you, haha

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good to know

fathom walrus Apr 24, 2024, 3:38 AM

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@waxen jay if f(x) = -7, find f’’’’(x)

waxen jay Apr 24, 2024, 3:38 AM

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0?

fathom walrus Apr 24, 2024, 3:38 AM

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yes

waxen jay Apr 24, 2024, 3:38 AM

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yeye, cause the deriviative of -7 is 0 and the deriviative of 0 is 0

fathom walrus Apr 24, 2024, 3:39 AM

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if f(x) = e^x, find f^(1000000)(x)

tranquil pine Apr 24, 2024, 3:39 AM

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oh yeah

fathom walrus Apr 24, 2024, 3:39 AM

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@waxen jay

waxen jay Apr 24, 2024, 3:39 AM

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fathom walrus if f(x) = e^x, find f^(1000000)(x)

e^x? right

tranquil pine Apr 24, 2024, 3:39 AM

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forgot abt e^x and the sin and cos functions

fathom walrus Apr 24, 2024, 3:39 AM

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correct

tulip coyote Apr 24, 2024, 3:40 AM

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tranquil pine forgot abt e^x and the sin and cos functions

[which even appears in the very example here catGiggle ]

tranquil pine Apr 24, 2024, 3:40 AM

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yup

fathom walrus Apr 24, 2024, 3:40 AM

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tranquil pine forgot abt e^x and the sin and cos functions

theres a lot more than that haha

tranquil pine Apr 24, 2024, 3:40 AM

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you can still take them infinitely tho

fathom walrus Apr 24, 2024, 3:41 AM

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are there more functions for which lim n-> inf f^(n)(x) = 0 or lim n -> inf f^(n)(x) != 0?

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@tulip coyote

tranquil pine Apr 24, 2024, 3:41 AM

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there's by extension ae^x

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and e^-x will alternate between -e^-x and e^-x

tulip coyote Apr 24, 2024, 3:42 AM

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fathom walrus are there more functions for which lim n-> inf f^(n)(x) = 0 or lim n -> inf f^(n...

Can't think of any examples atm catGiggle

fathom walrus Apr 24, 2024, 3:42 AM

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no im saying like

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how many functions exist such that they fulfill that property 1

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compared to the number of functions that fulfill the second property

tranquil pine Apr 24, 2024, 3:43 AM

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don't all functions eventually bottom out to some repeating pattern

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well ig not e^ax

waxen jay Apr 24, 2024, 3:44 AM

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would it be correct to say if i take the derivative of e^x an infinite amount of times, it will always be e^x

fathom walrus Apr 24, 2024, 3:46 AM

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are there more functions that satisfy lim n-> inf f^(n)(x) = 0 or more functions that satisfy lim n -> inf f^(n)(x) != 0? Or do they have the same cardinality? @tulip coyote this is what i meant, sorry its badly worded

fathom walrus Apr 24, 2024, 3:46 AM

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waxen jay would it be correct to say if i take the derivative of e^x an infinite amount of...

yes

waxen jay Apr 24, 2024, 3:46 AM

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ok thanks guys

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.close

final saddleBOT Apr 24, 2024, 3:46 AM

#

Channel closed

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final saddleBOT Apr 24, 2024, 4:01 AM

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heavy tundra Apr 24, 2024, 4:10 AM

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Need help please

final saddleBOT Apr 24, 2024, 4:10 AM

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heavy tundra Need help please

#

@heavy tundra Has your question been resolved?

final saddleBOT Apr 24, 2024, 4:40 AM

#

Channel closed

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waxen jay Apr 24, 2024, 4:54 AM

#

Do I need the product rule to find the derivative for $-2x^4\sqrt{x}$

final saddleBOT Apr 24, 2024, 4:54 AM

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waxen jay Do I need the product rule to find the derivative for $-2x^4\sqrt{x}$

soft zealotBOT Apr 24, 2024, 4:54 AM

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guy

rustic sandal Apr 24, 2024, 4:55 AM

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no you do not

waxen jay Apr 24, 2024, 4:56 AM

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why?

signal shell Apr 24, 2024, 4:56 AM

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What is sqrt(x)?

waxen jay Apr 24, 2024, 4:56 AM

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x^1/2

rustic sandal Apr 24, 2024, 4:56 AM

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you can rewrite $\sqrt(x)$ as $x^{\frac{1}{2}}$

soft zealotBOT Apr 24, 2024, 4:56 AM

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Brennenberg

waxen jay Apr 24, 2024, 4:56 AM

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but if two things are multiplying, you need the product rule dont you?

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such as $-2x^4 \cdot \sqrt{x}$?

soft zealotBOT Apr 24, 2024, 4:57 AM

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guy

waxen jay Apr 24, 2024, 4:57 AM

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isnt the first part f(x) and the second part g(x)

rustic sandal Apr 24, 2024, 4:57 AM

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you can also do that

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yes

signal shell Apr 24, 2024, 4:57 AM

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You can definitely use product rule but you don’t strictly need it ^

waxen jay Apr 24, 2024, 4:57 AM

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ok i see, thank you

#

.close

final saddleBOT Apr 24, 2024, 4:57 AM

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Channel closed

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final saddleBOT Apr 24, 2024, 5:12 AM

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snow temple Apr 24, 2024, 5:33 AM

#

Hey! Just wondering what the variable “k” is in this equation

final saddleBOT Apr 24, 2024, 5:33 AM

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snow temple Hey! Just wondering what the variable “k” is in this equation

snow temple Apr 24, 2024, 5:34 AM

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And how we would find the half life based on the polynomial

final saddleBOT Apr 24, 2024, 5:49 AM

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@snow temple Has your question been resolved?

zenith pollen Apr 24, 2024, 6:01 AM

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snow temple Hey! Just wondering what the variable “k” is in this equation

k is the exponent in the equation Ae^-kt

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idk why there's a polynomial in this question

snow temple Apr 24, 2024, 6:02 AM

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What the heck

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Okay thank you

#

.close

final saddleBOT Apr 24, 2024, 6:02 AM

#

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final saddleBOT Apr 24, 2024, 1:53 PM

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wind bough Apr 24, 2024, 2:05 PM

#

I tried using the pythagorean theorem to solve this and ended up with 40.5(sqr3) and i dont know if i did something wrong or if i am missing a step or if im not even supposed to use the pythagorean theorem 😭 help please

final saddleBOT Apr 24, 2024, 2:05 PM

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wind bough I tried using the pythagorean theorem to solve this and ended up with 40.5(sqr3)...

magic rampart Apr 24, 2024, 2:07 PM

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cant use pythagoras

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not a right angled triangle

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use area of hexagon

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formula

wind bough Apr 24, 2024, 2:08 PM

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the only explanation i was provided for this was a hexagon inscribed in a circle

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i couldnt find the formula

magic rampart Apr 24, 2024, 2:09 PM

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#

regular hexagon yes

magic rampart Apr 24, 2024, 2:12 PM

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magic rampart

so just input r here

wind bough Apr 24, 2024, 2:12 PM

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magic rampart

oh, so it would be 94 yards, right?

magic rampart Apr 24, 2024, 2:12 PM

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yes

wind bough Apr 24, 2024, 2:12 PM

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okay, thank you very much 🙂

magic rampart Apr 24, 2024, 2:12 PM

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this works too simplifying it will give the area of a hexagon formula though

magic rampart Apr 24, 2024, 2:12 PM

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wind bough okay, thank you very much 🙂

no worries

wind bough Apr 24, 2024, 2:14 PM

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i did have one more thing i was confused on if you dont mind, i think its just because they dont organize the formulas well and i cant find them 😭

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how do i find the area of a pentagon or hexagon from the apothem?

magic rampart Apr 24, 2024, 2:15 PM

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what's the apothem

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is that the centre of the shape

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oh

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line drawn to midpoint from the side

wind bough Apr 24, 2024, 2:16 PM

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yes

magic rampart Apr 24, 2024, 2:16 PM

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yeah so with the hexagon formula for example

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do u know the formula for an equilateral triangle

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a regular hexagon can be divided into 6 equilateral triangles

wind bough Apr 24, 2024, 2:17 PM

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this?

magic rampart Apr 24, 2024, 2:17 PM

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yes that

#

#

u have 6 equilateral triangles

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wtf

soft zealotBOT Apr 24, 2024, 2:19 PM

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taro

so its simplify \$\frac{6\sqrt{3}}{4}$
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.49 so its simplify \$\frac{6\sqrt{3}}{4}
                                          $
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

LaTeX Font Info:    Trying to load font information for OT1+lmr on input line 4
9.
(/usr/local/texlive/2023/texmf-dist/tex/latex/lm/ot1lmr.fd```

magic rampart Apr 24, 2024, 2:19 PM

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so its simplify $\frac{6\sqrt{3}}{4}}a^2$

soft zealotBOT Apr 24, 2024, 2:19 PM

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

magic rampart Apr 24, 2024, 2:19 PM

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ok give me a sec

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$\frac{6\sqrt{3}}{4} \cdot a^2$

soft zealotBOT Apr 24, 2024, 2:20 PM

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taro

magic rampart Apr 24, 2024, 2:20 PM

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then u reduce that

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$\frac{3\sqrt{3}}{2} \cdot a^2$

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which is the formula for area of a hexagon

soft zealotBOT Apr 24, 2024, 2:22 PM

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taro

magic rampart Apr 24, 2024, 2:22 PM

#

simply put, its the area of an equilateral triangle * 6

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beacuse you have 6 equilateral triangles in the hexagon

wind bough Apr 24, 2024, 2:24 PM

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ohh

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but for the pentagon would it no longer be the equalateral

magic rampart Apr 24, 2024, 2:25 PM

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for a pengaton the area formula i think is

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ap/2

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where a is the apothem

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and p is the perimeter

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i dont think its possible to work out the area of a pentagon with just the apothem

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since as you said if u were to cut it into triangles they wouldnt be equilateral

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it would be isoceles

wind bough Apr 24, 2024, 2:27 PM

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thats all they give me 😭

magic rampart Apr 24, 2024, 2:27 PM

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a stop sign has 8 sides though

wind bough Apr 24, 2024, 2:31 PM

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ohh

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so iot would be like the hexagon but *8 right?

magic rampart Apr 24, 2024, 2:33 PM

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hold on give me a moment

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i think youd need trig to solve this

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hmmm ok @wind bough do u know simple trig?

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i cant think of an easier way to solve this with just the apothem

wind bough Apr 24, 2024, 2:38 PM

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yes a little but i may need to be reminded i havent done it in like 6 months

magic rampart Apr 24, 2024, 2:38 PM

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alr

#

#

so the way we're gonna do it

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is using the ap/2 forumla

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but we need to find the perimeter

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we're given the apothem

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which is 39.5

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yes?

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ok wait im ac gonna redraw that give me a second

#

magic rampart Apr 24, 2024, 2:41 PM

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wind bough yes a little but i may need to be reminded i havent done it in like 6 months

okay heres the diagram

wind bough Apr 24, 2024, 2:42 PM

#

magic rampart yes?

yes

magic rampart Apr 24, 2024, 2:42 PM

#

does that diagram somewhat make sense

wind bough Apr 24, 2024, 2:42 PM

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yes it does

magic rampart Apr 24, 2024, 2:42 PM

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okay

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knowing that all sides of the octagon are equal

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do u think theres a way we could figure out what that angle is

wind bough Apr 24, 2024, 2:44 PM

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do we use tanjent

magic rampart Apr 24, 2024, 2:44 PM

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if you had this for example

I4i4R3-Qft1J8wp6n8L7yjFwaRyWW6tAEFAuQ-jgTZZe4xSknslsiLaqPHP8OJD9B7HBpldGivZdnaYp5kV9jgu0kp7QzfLGtq3jn-QKMeglNEX-2R8bLnJAtJTECJvLiIKdS28IphI.png

magic rampart Apr 24, 2024, 2:44 PM

#

wind bough do we use tanjent

wed still need the angle

#

each triangle is the same

#

#

and since those angles add up to 360 (its a revolution) and each angle is the same

#

u can work out what each angle is equal to

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which is?

wind bough Apr 24, 2024, 2:46 PM

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45

magic rampart Apr 24, 2024, 2:47 PM

#

yes

magic rampart Apr 24, 2024, 2:47 PM

#

magic rampart

now referring back to this

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what would this angle be

wind bough Apr 24, 2024, 2:49 PM

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would it not be 45? I'm sorry im confused

magic rampart Apr 24, 2024, 2:50 PM

#

#

the isoceles triangle (in the photo angle O) overall is 45 degrees

#

but in our diagram

#

ours is cut in half

#

to make a right angled triangle

wind bough Apr 24, 2024, 2:51 PM

#

so it would be 22.5?

magic rampart Apr 24, 2024, 2:51 PM

#

yes

#

almost there

#

now

#

#

we have the angle

#

we have adjacent

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and we're looking for opposite

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which means we're using which trig function?

wind bough Apr 24, 2024, 2:53 PM

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tan

magic rampart Apr 24, 2024, 2:53 PM

#

yep

#

so setup ur equation and solve for x

wind bough Apr 24, 2024, 2:55 PM

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i forgot how to set up the equation 😰

magic rampart Apr 24, 2024, 2:55 PM

#

tan theta = o/a

#

whats our angle

wind bough Apr 24, 2024, 2:56 PM

#

22.5

magic rampart Apr 24, 2024, 2:56 PM

#

whats our o and a

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tan22.5 = o/a

wind bough Apr 24, 2024, 2:56 PM

#

ohh

magic rampart Apr 24, 2024, 2:56 PM

#

then isolate x

#

it should look like tan22.5 = x/39.5

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then bring 39.5 over

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x = ?

wind bough Apr 24, 2024, 2:58 PM

#

when i bring 39.5 over am i not supposed to subtract it

magic rampart Apr 24, 2024, 2:58 PM

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multiply

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because its x divided by 39.5

wind bough Apr 24, 2024, 2:59 PM

#

ohh

magic rampart Apr 24, 2024, 2:59 PM

#

so u gotta do the reverse which is multiply by 39.5

#

x = ?

wind bough Apr 24, 2024, 3:01 PM

#

tan888.75

magic rampart Apr 24, 2024, 3:01 PM

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nono

#

ur doing 39.5 * tan(22.5)

wind bough Apr 24, 2024, 3:01 PM

#

ohh

magic rampart Apr 24, 2024, 3:02 PM

#

so put that into ur calc

wind bough Apr 24, 2024, 3:02 PM

#

16.36

magic rampart Apr 24, 2024, 3:02 PM

#

39.5 * tan(22.5) isnt the same as tan(22.5 * 39.5)

#

okay so u found x

magic rampart Apr 24, 2024, 3:02 PM

#

magic rampart

u can see that x is half of the side length

#

so the side length is 2 * 16.36

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= 31.72

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which is ur side length

#

now the formula for area is ap/2

#

again where a is apothem

#

and p is perimeter