#help-42 | Mathematics | Page 115

west horizon Dec 4, 2024, 6:36 AM

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drifting seal Dec 4, 2024, 6:36 AM

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this because we can do this

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hold on

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$x^2+y^2 = 400-2xy \geq 2xy \implies 400\geq 4xy$

potent lotusBOT Dec 4, 2024, 6:37 AM

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knief

drifting seal Dec 4, 2024, 6:37 AM

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so 100 >= xy

west horizon Dec 4, 2024, 6:38 AM

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drifting seal Dec 4, 2024, 6:38 AM

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hence how we get the x,y = 10

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because

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x + y = 20

west horizon Dec 4, 2024, 6:38 AM

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drifting seal Dec 4, 2024, 6:38 AM

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wdym

west horizon Dec 4, 2024, 6:38 AM

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drifting seal Dec 4, 2024, 6:39 AM

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i already did

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it’s easy asf

west horizon Dec 4, 2024, 6:39 AM

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drifting seal Dec 4, 2024, 6:39 AM

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alright

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wait

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lemme show you the other way

west horizon Dec 4, 2024, 6:39 AM

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potent lotusBOT Dec 4, 2024, 6:40 AM

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Kenzo

drifting seal Dec 4, 2024, 6:40 AM

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$f(x,y) = x^2+y^2 \quad g(x,y) = x+y$

potent lotusBOT Dec 4, 2024, 6:40 AM

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knief

drifting seal Dec 4, 2024, 6:40 AM

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$\nabla f = \langle 2x, 2y \rangle \quad \nabla g = \langle 1, 1\rangle$

potent lotusBOT Dec 4, 2024, 6:41 AM

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knief

drifting seal Dec 4, 2024, 6:41 AM

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$\langle 2x,2y \rangle = \lambda \langle 1, 1\rangle$

potent lotusBOT Dec 4, 2024, 6:41 AM

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knief

drifting seal Dec 4, 2024, 6:41 AM

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2x = lambda

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2y = lambda

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x = y

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x + y = 2x = 20 hence

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x = 10

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x = y = 10

west horizon Dec 4, 2024, 6:42 AM

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drifting seal Dec 4, 2024, 6:42 AM

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west horizon One message removed from a suspended account.

lagrange optimization

west horizon Dec 4, 2024, 6:42 AM

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drifting seal Dec 4, 2024, 6:43 AM

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west horizon One message removed from a suspended account.

$\lambda$

west horizon Dec 4, 2024, 6:43 AM

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potent lotusBOT Dec 4, 2024, 6:43 AM

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knief

drifting seal Dec 4, 2024, 6:43 AM

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west horizon One message removed from a suspended account.

you won’t unless you take calc 3

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partial derivatives

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i think i might’ve shown you those

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like when we did implicit

west horizon Dec 4, 2024, 6:43 AM

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drifting seal Dec 4, 2024, 6:43 AM

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remember my implicit differentiation trick

west horizon Dec 4, 2024, 6:44 AM

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drifting seal Dec 4, 2024, 6:44 AM

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$\frac{dy}{dx} = \frac{-\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}$

west horizon Dec 4, 2024, 6:44 AM

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potent lotusBOT Dec 4, 2024, 6:45 AM

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knief

drifting seal Dec 4, 2024, 6:45 AM

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where $F(x,y) = c$

potent lotusBOT Dec 4, 2024, 6:45 AM

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knief

drifting seal Dec 4, 2024, 6:45 AM

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i definitely showed you

west horizon Dec 4, 2024, 6:45 AM

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drifting seal Dec 4, 2024, 6:45 AM

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west horizon One message removed from a suspended account.

partial derivative

drifting seal Dec 4, 2024, 6:45 AM

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west horizon One message removed from a suspended account.

nah

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implicit function theorem

west horizon Dec 4, 2024, 6:46 AM

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drifting seal Dec 4, 2024, 6:47 AM

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$\frac{\partial F}{\partial x} dx + \frac{\partial F}{\partial y} dy = 0$

potent lotusBOT Dec 4, 2024, 6:47 AM

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knief

drifting seal Dec 4, 2024, 6:47 AM

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west horizon One message removed from a suspended account.

fun

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bprp videos

west horizon Dec 4, 2024, 6:48 AM

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drifting seal Dec 4, 2024, 6:48 AM

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black pen red pen

west horizon Dec 4, 2024, 6:48 AM

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drifting seal Dec 4, 2024, 6:49 AM

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they’re good too

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but you’re missing out

drifting seal Dec 4, 2024, 6:49 AM

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west horizon One message removed from a suspended account.

they really did do a good job on the ap calc khan course

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like the most effort they ever put into it

west horizon Dec 4, 2024, 6:49 AM

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drifting seal Dec 4, 2024, 6:49 AM

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the differential equations course on the other hand….

west horizon Dec 4, 2024, 6:49 AM

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drifting seal Dec 4, 2024, 6:49 AM

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not the differential equations in ap calc

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like

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further differential equations

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more advanced

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wasn’t so good

west horizon Dec 4, 2024, 6:50 AM

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drifting seal Dec 4, 2024, 6:50 AM

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needs a lot of work

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multivariable was good on khan academy actually

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because 3b1b did it

west horizon Dec 4, 2024, 6:50 AM

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drifting seal Dec 4, 2024, 6:50 AM

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3blue1brown

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goat math youtuber

west horizon Dec 4, 2024, 6:50 AM

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drifting seal Dec 4, 2024, 6:51 AM

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you might’ve seen his essence of calc series

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he’s probably the most popular math youtuber

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makes all those sick animations

west horizon Dec 4, 2024, 6:51 AM

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drifting seal Dec 4, 2024, 6:51 AM

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alright

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see ya

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.close

calm coralBOT Dec 4, 2024, 6:52 AM

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mossy wigeon Dec 4, 2024, 7:07 AM

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b right?

calm coralBOT Dec 4, 2024, 7:08 AM

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mossy wigeon b right?

slender gate Dec 4, 2024, 7:09 AM

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mossy wigeon b right?

yep

unreal rose Dec 4, 2024, 7:09 AM

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i think its a simply cuz its heavier

swift laurel Dec 4, 2024, 7:10 AM

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they have the same mass

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we have to consider their moment of inertia

unreal rose Dec 4, 2024, 7:10 AM

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oh same mass

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then yeah b

mossy wigeon Dec 4, 2024, 7:10 AM

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ok ty

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.close

calm coralBOT Dec 4, 2024, 7:10 AM

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calm coralBOT Dec 4, 2024, 12:46 PM

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obsidian swan Dec 4, 2024, 1:17 PM

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calm coralBOT Dec 4, 2024, 1:17 PM

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obsidian swan

obsidian swan Dec 4, 2024, 1:17 PM

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Help pls

torn gorge Dec 4, 2024, 1:19 PM

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jovial gyro Dec 4, 2024, 1:22 PM

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which part are you exactly confused with?

calm coralBOT Dec 4, 2024, 1:32 PM

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@obsidian swan Has your question been resolved?

obsidian swan Dec 4, 2024, 1:43 PM

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jovial gyro which part are you exactly confused with?

For a, what does it mean about y intercept equals to 8 and for b, it says through point 0,-3 what does it mean and how should I apply in the equation?

jovial gyro Dec 4, 2024, 1:44 PM

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y intercept means that the function intersects y-axis at -8

obsidian swan Dec 4, 2024, 1:44 PM

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How should I apply it in the equation

jovial gyro Dec 4, 2024, 1:44 PM

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remember that if a function passes through that point it is a solution of that equation

obsidian swan Dec 4, 2024, 1:44 PM

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Alright

jovial gyro Dec 4, 2024, 1:45 PM

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so, if a function passes through (0, -3) then it has a solution x=0 and f(x)=-3

obsidian swan Dec 4, 2024, 1:46 PM

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I see

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Ty

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.close

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barren sand Dec 4, 2024, 2:57 PM

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I have no idea what to do here

calm coralBOT Dec 4, 2024, 2:57 PM

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barren sand I have no idea what to do here

umbral sinew Dec 4, 2024, 2:57 PM

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what are you even trying to do

barren sand Dec 4, 2024, 2:57 PM

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Completing squares with fractions trip me out

barren sand Dec 4, 2024, 2:57 PM

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umbral sinew what are you even trying to do

Convert to vertex form so I’m tryna complete da square

umbral sinew Dec 4, 2024, 2:58 PM

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this is the problem

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barren sand Dec 4, 2024, 2:59 PM

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How’d you get that?

umbral sinew Dec 4, 2024, 2:59 PM

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from your working

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you are not supposed to expand it again

barren sand Dec 4, 2024, 2:59 PM

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I know that’s correct, but how do we reach dat conclusion bc the fraction within the parameters is tripping me out

umbral sinew Dec 4, 2024, 2:59 PM

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barren sand I have no idea what to do here

this is just going in endless circles

umbral sinew Dec 4, 2024, 3:00 PM

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barren sand I know that’s correct, but how do we reach dat conclusion bc the fraction within...

???

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what parameters

barren sand Dec 4, 2024, 3:00 PM

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Bro

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Ok

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Let's look at this

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This so far is correct right?

umbral sinew Dec 4, 2024, 3:00 PM

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yes but no

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correct as in the number is correct

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but wrong as in the wrong step to take from the previous line

barren sand Dec 4, 2024, 3:01 PM

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I should have left it as (3/2)^2?

umbral sinew Dec 4, 2024, 3:01 PM

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barren sand I should have left it as (3/2)^2?

yes

umbral sinew Dec 4, 2024, 3:01 PM

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barren sand

cuz what are you gonna do with this

barren sand Dec 4, 2024, 3:01 PM

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Okay

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So I leave it at 3/2 squared, and then what do I do from that?

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I just hug it with brackets n make it (x +3/2)^2 n we good?

umbral sinew Dec 4, 2024, 3:03 PM

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barren sand I just hug it with brackets n make it (x +3/2)^2 n we good?

yes

barren sand Dec 4, 2024, 3:03 PM

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Ok so

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I understand

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Now

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Is this something I apply with all completing the square procedures that involve fractions?

That is, getting the (b/2)^2 n hugging dat + squaring it n eliminating da real b variable?

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Ik how to complete squares yfm, it's just when they fractions it tweaks me out a bit

umbral sinew Dec 4, 2024, 3:04 PM

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barren sand Is this something I apply with all completing the square procedures that involve...

yes

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treat a fraction like a regular number

barren sand Dec 4, 2024, 3:05 PM

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Ok ty

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.solved

calm coralBOT Dec 4, 2024, 3:05 PM

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calm coralBOT Dec 4, 2024, 3:20 PM

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calm coralBOT Dec 4, 2024, 3:44 PM

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calm coralBOT Dec 4, 2024, 3:59 PM

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@sinful oak Has your question been resolved?

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simple musk Dec 4, 2024, 4:32 PM

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calm coralBOT Dec 4, 2024, 4:32 PM

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simple musk

simple musk Dec 4, 2024, 4:36 PM

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4.- Let $B = {(0,1,1), (2,0,1), v}$ and $B' = {(-3,1,0), v, (0,0,1)}$ be bases of $\mathbb{R}^3$. Find, if possible, $v$ and $w$ in $\mathbb{R}^3$ such that the coordinates of $w$ in the basis $B$ are $(w)B = (3,-4,1)$ and the coordinates of $3w$ in the basis $B'$ are $(3w){B'} = (7,2,-4)$.

potent lotusBOT Dec 4, 2024, 4:36 PM

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xbz

simple musk Dec 4, 2024, 4:44 PM

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w = 3(0,1,1) -4(2,0,1) + v

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3w = 7(-3,1,0)+2v-4(0,0,1)

calm coralBOT Dec 4, 2024, 5:00 PM

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@simple musk Has your question been resolved?

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simple musk Dec 4, 2024, 5:00 PM

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.reopen

calm coralBOT Dec 4, 2024, 5:00 PM

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✅

simple musk Dec 4, 2024, 5:00 PM

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I miss clicked

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9(0,1,1)-12(2,0,1) +3v = 7(-3,1,0)+2v-4(0,0,1)

onyx berry Dec 4, 2024, 5:04 PM

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good

simple musk Dec 4, 2024, 5:04 PM

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,av @onyx berry

potent lotusBOT Dec 4, 2024, 5:04 PM

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simple musk Dec 4, 2024, 5:05 PM

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9(0,1,1)-12(2,0,1) +3v = 7(-3,1,0)+2v-4(0,0,1)
3v - 2v = 7(-3,1,0) -4(0,0,1) + 12(2,0,1) - 9(0,1,1)

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,w 7(-3,1,0) -4(0,0,1) + 12(2,0,1) - 9(0,1,1)

potent lotusBOT Dec 4, 2024, 5:06 PM

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simple musk Dec 4, 2024, 5:06 PM

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v = (3,-2,-1)

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w = 3(0,1,1) -4(2,0,1) + v

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w = 3(0,1,1) -4(2,0,1) + (3,-2,-1)

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,w 3(0,1,1) -4(2,0,1) + (3,-2,-1)

potent lotusBOT Dec 4, 2024, 5:07 PM

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simple musk Dec 4, 2024, 5:07 PM

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w = (-5,1,-2)

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too easy

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@onyx berry

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💖❤️

onyx berry Dec 4, 2024, 5:08 PM

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good that I could help

simple musk Dec 4, 2024, 5:08 PM

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,av @onyx berry

potent lotusBOT Dec 4, 2024, 5:08 PM

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simple musk Dec 4, 2024, 5:09 PM

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.solved

calm coralBOT Dec 4, 2024, 5:09 PM

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calm coralBOT Dec 4, 2024, 5:24 PM

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wheat owl Dec 4, 2024, 5:31 PM

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I need to solve for x

calm coralBOT Dec 4, 2024, 5:31 PM

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wheat owl I need to solve for x

glad parrot Dec 4, 2024, 5:32 PM

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try to write left side as (x-1)^smth

wheat owl Dec 4, 2024, 5:33 PM

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Wdym

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Btw if y^y^2 = 2
Then we can start from there

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@glad parrot

glad parrot Dec 4, 2024, 5:40 PM

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well you can also write 8/4(x-1) as 2/(x-1)

wheat owl Dec 4, 2024, 5:40 PM

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Yeah

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That's the first step

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What now

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@glad parrot

manic sandal Dec 4, 2024, 5:42 PM

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(2/(x -1))^(1/x) looks promising

wheat owl Dec 4, 2024, 5:42 PM

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Did that

manic sandal Dec 4, 2024, 5:42 PM

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assuming it’s xth root and not multiplied by x

wheat owl Dec 4, 2024, 5:43 PM

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We can raise both sides to the power of x

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And do some other stuff

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And substitute

manic sandal Dec 4, 2024, 5:43 PM

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okay so where are you getting stuck?

wheat owl Dec 4, 2024, 5:43 PM

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And finally get y^y^2 = 2

manic sandal Dec 4, 2024, 5:43 PM

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can i see all your work

wheat owl Dec 4, 2024, 5:43 PM

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Y = x-1

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Lemme write again

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Hold on

manic sandal Dec 4, 2024, 5:44 PM

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holding

wheat owl Dec 4, 2024, 5:44 PM

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I was solving it with someone here but I didnt really like the solve

manic sandal Dec 4, 2024, 5:45 PM

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all fine

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just hard to know where you are without all the work

wheat owl Dec 4, 2024, 5:47 PM

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Here

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@manic sandal

manic sandal Dec 4, 2024, 5:49 PM

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sorry i got class rn someone else gon help

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i would usually just plug into desmos or smth to find it quickly

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but an exact answer can’t give right now

wheat owl Dec 4, 2024, 5:49 PM

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Its pre differentiation

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And I can't use a calculator

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Also idk what desmos is

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Anyways

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It's alright

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Good luck

manic sandal Dec 4, 2024, 5:50 PM

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graphing calculator

manic sandal Dec 4, 2024, 5:50 PM

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wheat owl Good luck

ty

wheat owl Dec 4, 2024, 5:50 PM

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Npnp

calm coralBOT Dec 4, 2024, 6:05 PM

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@wheat owl Has your question been resolved?

frail yacht Dec 4, 2024, 6:19 PM

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wheat owl I need to solve for x

Try let a be x-1

wheat owl Dec 4, 2024, 6:21 PM

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Hey @frail yacht

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Sorry didn't see that

wheat owl Dec 4, 2024, 6:21 PM

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frail yacht Try let a be x-1

Look

wheat owl Dec 4, 2024, 6:21 PM

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wheat owl

.

frail yacht Dec 4, 2024, 6:22 PM

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rn_image_picker_lib_temp_673bcb82-4292-414b-a5c7-f21b7f2ac187.jpg

wheat owl Dec 4, 2024, 6:22 PM

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Or are you thinking of a different approach

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Hold on

frail yacht Dec 4, 2024, 6:23 PM

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Do u see?

wheat owl Dec 4, 2024, 6:24 PM

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Wait...

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X

frail yacht Dec 4, 2024, 6:25 PM

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You only get one real solution x =0

wheat owl Dec 4, 2024, 6:25 PM

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Is part of the root

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Not like x multiplied by the root

frail yacht Dec 4, 2024, 6:26 PM

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U can substitute I to Original equation to see

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If its valid

wheat owl Dec 4, 2024, 6:26 PM

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It's the xth root of the mentioned thing

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Not X . The square root

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So what you did is wrong

frail yacht Dec 4, 2024, 6:30 PM

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Ifk then

wheat owl Dec 4, 2024, 6:30 PM

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Okay

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Appreciate your help tho !

calm coralBOT Dec 4, 2024, 7:01 PM

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@wheat owl Has your question been resolved?

wheat owl Dec 4, 2024, 7:07 PM

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Ima head to bed now

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I'd appreciate if someone solves this by the time I wake up

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Good night!

calm coralBOT Dec 4, 2024, 8:08 PM

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@wheat owl Has your question been resolved?

calm coralBOT Dec 4, 2024, 9:08 PM

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Channel closed

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calm coralBOT Dec 4, 2024, 10:40 PM

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rapid lion Dec 4, 2024, 10:45 PM

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Evaluate the function ƒ(x) = −x^2 − 1 and simplify at the indicated value: ƒ(−a) = ?

calm coralBOT Dec 4, 2024, 10:45 PM

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rapid lion 3. Evaluate the function ƒ(x) = −x^2 − 1 and simplify at the indicated value: ƒ...

rapid lion Dec 4, 2024, 10:46 PM

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I got f(-a) = a^2 - 1 but it says its wrong

pallid halo Dec 4, 2024, 10:46 PM

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be careful about order of operations

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-x^2 means first compute x^2, then multiply the result by -1

rapid lion Dec 4, 2024, 10:48 PM

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so lets say x = 1 -(1)^2 you do 1 * 1 = 1 then mulitply it by a negative to get -1?

rapid lion Dec 4, 2024, 10:48 PM

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pallid halo -x^2 means first compute x^2, then multiply the result by -1

^

pallid halo Dec 4, 2024, 10:49 PM

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yes that's right

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1 - (1)^2 would be 1 - 1 = 0

rapid lion Dec 4, 2024, 10:49 PM

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ok that makes sense ty

calm coralBOT Dec 4, 2024, 11:04 PM

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@rapid lion Has your question been resolved?

calm coralBOT Dec 4, 2024, 11:19 PM

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Channel closed

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viral abyss Dec 4, 2024, 11:29 PM

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calm coralBOT Dec 4, 2024, 11:29 PM

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viral abyss

viral abyss Dec 4, 2024, 11:29 PM

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got 4.5 but it was wrong :p

wet urchin Dec 4, 2024, 11:30 PM

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so

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the midpoint of maple street

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is 0.45 miles

viral abyss Dec 4, 2024, 11:30 PM

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yes

wet urchin Dec 4, 2024, 11:30 PM

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and the midpoint of walnut street is 0.9 miles

viral abyss Dec 4, 2024, 11:30 PM

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yes

wet urchin Dec 4, 2024, 11:31 PM

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so

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0.9

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plus

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did u solve for oak street

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if so what did u get

viral abyss Dec 4, 2024, 11:32 PM

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isnt it 0.9

wet urchin Dec 4, 2024, 11:32 PM

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idk

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you have to use the pythrageon theroum

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to solve for it

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i didnt do it

viral abyss Dec 4, 2024, 11:33 PM

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its the midsegment so its half of spruce street what

wet urchin Dec 4, 2024, 11:33 PM

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what

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walk me through your thought process of why you think that

viral abyss Dec 4, 2024, 11:34 PM

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triangle midsegment theorem "the segment connecting the midpoints of two sides of a triangle is paralle to the third side and is half as long as that side"

light acorn Dec 4, 2024, 11:34 PM

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wet urchin you have to use the pythrageon theroum

none of these are right triangles right

wet urchin Dec 4, 2024, 11:34 PM

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light acorn none of these are right triangles right

yea im slow

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sorry

viral abyss Dec 4, 2024, 11:35 PM

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Cat_BruhXD

wet urchin Dec 4, 2024, 11:35 PM

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well

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if ur right

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and its 0.9

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0.9 + 0.9 + 0.45 + 1.8

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miles

viral abyss Dec 4, 2024, 11:38 PM

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yep we got it TP_Cat_dance

wet urchin Dec 4, 2024, 11:38 PM

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viral abyss yep we got it <a:TP_Cat_dance:1060722523836252220>

woo hoo

viral abyss Dec 4, 2024, 11:38 PM

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.close

calm coralBOT Dec 4, 2024, 11:38 PM

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fleet cairn Dec 5, 2024, 12:15 AM

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hi i need help on a stats question

calm coralBOT Dec 5, 2024, 12:15 AM

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fleet cairn hi i need help on a stats question

fleet cairn Dec 5, 2024, 12:15 AM

#

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im just confused on what the

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7% is used for

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actually idek what formula to use

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i think its the

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n = z^2 ( p(p-1)) / e^2

calm coralBOT Dec 5, 2024, 12:32 AM

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@fleet cairn Has your question been resolved?

fleet cairn Dec 5, 2024, 12:32 AM

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<@&286206848099549185>

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ok so

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i found the solution for it

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but

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im still confused

#

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they said e = .07

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so WHYYY in the bottom right is it .03?

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.close

calm coralBOT Dec 5, 2024, 12:36 AM

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Channel closed

Closed by @fleet cairn

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calm coralBOT Dec 5, 2024, 1:57 AM

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west horizon Dec 5, 2024, 2:10 AM

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calm coralBOT Dec 5, 2024, 2:10 AM

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west horizon One message removed from a suspended account.

west horizon Dec 5, 2024, 2:10 AM

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manic sandal Dec 5, 2024, 2:22 AM

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lets use area formula

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volume*

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what’s the volume of a cone

west horizon Dec 5, 2024, 2:22 AM

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manic sandal Dec 5, 2024, 2:22 AM

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formula

west horizon Dec 5, 2024, 2:22 AM

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manic sandal Dec 5, 2024, 2:22 AM

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cool cool

west horizon Dec 5, 2024, 2:22 AM

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potent lotusBOT Dec 5, 2024, 2:22 AM

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Kenzo

manic sandal Dec 5, 2024, 2:23 AM

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it’s alright

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i understand what it means

west horizon Dec 5, 2024, 2:23 AM

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manic sandal Dec 5, 2024, 2:23 AM

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uhm

west horizon Dec 5, 2024, 2:23 AM

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manic sandal Dec 5, 2024, 2:24 AM

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what i think you needa do

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is use differentiation

west horizon Dec 5, 2024, 2:24 AM

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manic sandal Dec 5, 2024, 2:24 AM

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dV/dt = -50

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which will be useful

manic sandal Dec 5, 2024, 2:25 AM

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west horizon One message removed from a suspended account.

uhm

west horizon Dec 5, 2024, 2:25 AM

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potent lotusBOT Dec 5, 2024, 2:25 AM

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Kenzo

manic sandal Dec 5, 2024, 2:25 AM

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you see the problem is we don’t know r’

west horizon Dec 5, 2024, 2:26 AM

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manic sandal Dec 5, 2024, 2:26 AM

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uhhh

manic sandal Dec 5, 2024, 2:26 AM

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west horizon One message removed from a suspended account.

yes i know

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water level

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which is height no?

west horizon Dec 5, 2024, 2:26 AM

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manic sandal Dec 5, 2024, 2:26 AM

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so i’m thinking more like

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uhh

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i wanna say plug in r before differentiating but it isn’t constant

west horizon Dec 5, 2024, 2:27 AM

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manic sandal Dec 5, 2024, 2:28 AM

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yea

west horizon Dec 5, 2024, 2:28 AM

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manic sandal Dec 5, 2024, 2:28 AM

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we know h tho

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we don’t know h’

west horizon Dec 5, 2024, 2:28 AM

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manic sandal Dec 5, 2024, 2:29 AM

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west horizon One message removed from a suspended account.

i believe is it asking what is dh/dt when h = 5

west horizon Dec 5, 2024, 2:29 AM

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potent lotusBOT Dec 5, 2024, 2:30 AM

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Kenzo

manic sandal Dec 5, 2024, 2:30 AM

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oh

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wait

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you need to find r in terms of h using similar triangles

west horizon Dec 5, 2024, 2:30 AM

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manic sandal Dec 5, 2024, 2:31 AM

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or else you have 2 variables to work with which doesn’t work

manic sandal Dec 5, 2024, 2:31 AM

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west horizon One message removed from a suspended account.

this one is really easy man

west horizon Dec 5, 2024, 2:31 AM

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manic sandal Dec 5, 2024, 2:31 AM

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i don’t have a pencil

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one second

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yoy agree that the radius and the height wit change in proportion to one another

west horizon Dec 5, 2024, 2:32 AM

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manic sandal Dec 5, 2024, 2:32 AM

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nope

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very white

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irish/jewish

west horizon Dec 5, 2024, 2:33 AM

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manic sandal Dec 5, 2024, 2:33 AM

#

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we could make something like this

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then h/6 = r/45

west horizon Dec 5, 2024, 2:33 AM

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manic sandal Dec 5, 2024, 2:33 AM

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so r = 45h/6

west horizon Dec 5, 2024, 2:33 AM

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manic sandal Dec 5, 2024, 2:33 AM

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plug thag back in

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THEN differentiate with respect to h

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and you win

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gg ez

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(i am also doing related rates in calc rn 😜)

west horizon Dec 5, 2024, 2:34 AM

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manic sandal Dec 5, 2024, 2:34 AM

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west horizon One message removed from a suspended account.

i’m a sophomore in our calc 1 advanced clas

west horizon Dec 5, 2024, 2:35 AM

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manic sandal Dec 5, 2024, 2:36 AM

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n

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no

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i’m 16 in high school

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i just mess w math

west horizon Dec 5, 2024, 2:36 AM

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manic sandal Dec 5, 2024, 2:36 AM

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😭😭

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it’s all good

west horizon Dec 5, 2024, 2:37 AM

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manic sandal Dec 5, 2024, 2:37 AM

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anyways u got the rest of the problem or any more questions

potent lotusBOT Dec 5, 2024, 2:37 AM

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Kenzo

manic sandal Dec 5, 2024, 2:37 AM

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nonono

west horizon Dec 5, 2024, 2:37 AM

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manic sandal Dec 5, 2024, 2:37 AM

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too early

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plug r back into ur volume equation

west horizon Dec 5, 2024, 2:37 AM

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manic sandal Dec 5, 2024, 2:37 AM

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wait i’m tripping

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how do you spell

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silly

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solly

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like

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huh

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😭

west horizon Dec 5, 2024, 2:38 AM

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manic sandal Dec 5, 2024, 2:38 AM

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no like

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idk

west horizon Dec 5, 2024, 2:38 AM

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manic sandal Dec 5, 2024, 2:38 AM

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it doesn’t t matter

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anyways

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V = whatever in term of h

west horizon Dec 5, 2024, 2:39 AM

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manic sandal Dec 5, 2024, 2:39 AM

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h not h’

west horizon Dec 5, 2024, 2:39 AM

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manic sandal Dec 5, 2024, 2:39 AM

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not yet

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fix that latex

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😔

potent lotusBOT Dec 5, 2024, 2:39 AM

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Kenzo

manic sandal Dec 5, 2024, 2:39 AM

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combine terms???

west horizon Dec 5, 2024, 2:39 AM

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manic sandal Dec 5, 2024, 2:39 AM

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…

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u wanna product rule

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instead of combine terms

west horizon Dec 5, 2024, 2:40 AM

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manic sandal Dec 5, 2024, 2:40 AM

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225h^2/4 * h/3
75h^3 * pi =V

west horizon Dec 5, 2024, 2:41 AM

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manic sandal Dec 5, 2024, 2:41 AM

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now

west horizon Dec 5, 2024, 2:41 AM

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manic sandal Dec 5, 2024, 2:41 AM

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(15h/2)^2

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15*15 =225

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🤯

west horizon Dec 5, 2024, 2:42 AM

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manic sandal Dec 5, 2024, 2:42 AM

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2^2

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is what

west horizon Dec 5, 2024, 2:42 AM

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manic sandal Dec 5, 2024, 2:42 AM

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WOAH

west horizon Dec 5, 2024, 2:42 AM

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manic sandal Dec 5, 2024, 2:42 AM

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im on my phone watching arcane eating famous amos cookies

west horizon Dec 5, 2024, 2:43 AM

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manic sandal Dec 5, 2024, 2:43 AM

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oki

west horizon Dec 5, 2024, 2:43 AM

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manic sandal Dec 5, 2024, 2:43 AM

#

2

west horizon Dec 5, 2024, 2:43 AM

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manic sandal Dec 5, 2024, 2:43 AM

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just started

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watched 1 a while go

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ago

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anyway

west horizon Dec 5, 2024, 2:43 AM

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manic sandal Dec 5, 2024, 2:43 AM

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V = 75h^3*pi

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then differentiate

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wait

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oop

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i forgot

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V = 75/4 * h^3 * pi

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not differentiate

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now

west horizon Dec 5, 2024, 2:44 AM

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manic sandal Dec 5, 2024, 2:44 AM

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…

west horizon Dec 5, 2024, 2:44 AM

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manic sandal Dec 5, 2024, 2:45 AM

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okay

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i will write it out

west horizon Dec 5, 2024, 2:45 AM

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manic sandal Dec 5, 2024, 2:45 AM

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3 minutes

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😭

#

#

back to my show

west horizon Dec 5, 2024, 2:49 AM

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manic sandal Dec 5, 2024, 2:50 AM

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i combined???

west horizon Dec 5, 2024, 2:50 AM

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manic sandal Dec 5, 2024, 2:50 AM

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okay

west horizon Dec 5, 2024, 2:50 AM

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manic sandal Dec 5, 2024, 2:50 AM

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do we understand

west horizon Dec 5, 2024, 2:50 AM

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manic sandal Dec 5, 2024, 2:50 AM

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now

#

DIFFERENTIATE

west horizon Dec 5, 2024, 2:51 AM

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potent lotusBOT Dec 5, 2024, 2:51 AM

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Kenzo

manic sandal Dec 5, 2024, 2:51 AM

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???

west horizon Dec 5, 2024, 2:51 AM

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manic sandal Dec 5, 2024, 2:52 AM

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dV/dt = 75pi/4 * 3h^2 * dh/dt

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yes yes???

west horizon Dec 5, 2024, 2:52 AM

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manic sandal dV/dt = 75pi/4 * 3h^2 * dh/dt

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manic sandal Dec 5, 2024, 2:52 AM

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yes

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but it’s like

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product rule

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or chain rule

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idk

west horizon Dec 5, 2024, 2:53 AM

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manic sandal Dec 5, 2024, 2:53 AM

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Okay

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if you product rule

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and you differentiate anything but h^3

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you’ll have 0

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so like

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yes

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do i needa restate

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what’s the derivative of a•x^n

west horizon Dec 5, 2024, 2:54 AM

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manic sandal Dec 5, 2024, 2:54 AM

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n•a•x^(n - 1)

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in this case a = all the constants

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n is 3

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and x is h

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yay’

west horizon Dec 5, 2024, 2:55 AM

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manic sandal Dec 5, 2024, 2:55 AM

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yea

west horizon Dec 5, 2024, 2:55 AM

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manic sandal Dec 5, 2024, 2:55 AM

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😭

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a just like

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stays there

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🙏🙏🙏

west horizon Dec 5, 2024, 2:56 AM

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manic sandal Dec 5, 2024, 2:56 AM

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okay

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now

manic sandal Dec 5, 2024, 2:56 AM

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manic sandal dV/dt = 75pi/4 * 3h^2 * dh/dt

.

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do i needa latex or u got it

west horizon Dec 5, 2024, 2:57 AM

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manic sandal Dec 5, 2024, 2:57 AM

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okay

#

so

#

dV/dt = -50
h = 5

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then isolate dh/dt and you win

west horizon Dec 5, 2024, 2:58 AM

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manic sandal Dec 5, 2024, 2:59 AM

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😭😭

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do i needa pull out the paper

west horizon Dec 5, 2024, 2:59 AM

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manic sandal Dec 5, 2024, 2:59 AM

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okay

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yayes

west horizon Dec 5, 2024, 2:59 AM

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calm coralBOT Dec 5, 2024, 2:59 AM

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Channel closed

Closed by @west horizon

Use .reopen if this was a mistake.

manic sandal Dec 5, 2024, 3:00 AM

#

gotchu

#

same process for next step btw

calm coralBOT Dec 5, 2024, 3:14 AM

#

Available help channel!

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west horizon Dec 5, 2024, 3:14 AM

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calm coralBOT Dec 5, 2024, 3:15 AM

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west horizon One message removed from a suspended account.

west horizon Dec 5, 2024, 3:15 AM

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potent lotusBOT Dec 5, 2024, 3:16 AM

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Kenzo

potent igloo Dec 5, 2024, 3:16 AM

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Looks good so far

west horizon Dec 5, 2024, 3:16 AM

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potent lotusBOT Dec 5, 2024, 3:16 AM

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Kenzo

west horizon Dec 5, 2024, 3:16 AM

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potent lotusBOT Dec 5, 2024, 3:16 AM

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Kenzo

west horizon Dec 5, 2024, 3:17 AM

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potent igloo Dec 5, 2024, 3:17 AM

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west horizon One message removed from a suspended account.

Think hard on this answer

west horizon Dec 5, 2024, 3:17 AM

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potent igloo Dec 5, 2024, 3:17 AM

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west horizon One message removed from a suspended account.

correct

west horizon Dec 5, 2024, 3:17 AM

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potent igloo Dec 5, 2024, 3:18 AM

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But +12 (don't forget your units) is still the correct answer to (a), btw

west horizon Dec 5, 2024, 3:18 AM

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potent lotusBOT Dec 5, 2024, 3:20 AM

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Kenzo

west horizon Dec 5, 2024, 3:20 AM

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potent igloo Dec 5, 2024, 3:20 AM

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west horizon One message removed from a suspended account.

Wait, how did you get 12 for part a? thonk

west horizon Dec 5, 2024, 3:20 AM

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potent igloo Dec 5, 2024, 3:21 AM

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potent lotus **Kenzo**

This is incorrect, but y=5 is correct. I presume you mean minus here

west horizon Dec 5, 2024, 3:21 AM

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potent lotusBOT Dec 5, 2024, 3:21 AM

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Kenzo

west horizon Dec 5, 2024, 3:22 AM

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potent igloo This is incorrect, but y=5 is correct. I presume you mean minus here

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west horizon Dec 5, 2024, 3:22 AM

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potent lotus **Kenzo**

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potent igloo Dec 5, 2024, 3:22 AM

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oh yea

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you are correct

west horizon Dec 5, 2024, 3:22 AM

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potent igloo Dec 5, 2024, 3:22 AM

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I was doing dy/dx derp

potent lotusBOT Dec 5, 2024, 3:22 AM

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Kenzo

west horizon Dec 5, 2024, 3:22 AM

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potent igloo Dec 5, 2024, 3:23 AM

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yeah 12 ft/s is the rate at which the ladder falls

west horizon Dec 5, 2024, 3:23 AM

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potent igloo Dec 5, 2024, 3:23 AM

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naw area is $A=\frac12xy$

potent lotusBOT Dec 5, 2024, 3:23 AM

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SWR

west horizon Dec 5, 2024, 3:23 AM

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potent igloo Dec 5, 2024, 3:23 AM

#

and $\dot{A}=\frac12(x\dot{y}+y\dot{x})$

potent lotusBOT Dec 5, 2024, 3:23 AM

#

SWR

west horizon Dec 5, 2024, 3:23 AM

#

One message removed from a suspended account.

potent igloo Dec 5, 2024, 3:24 AM

#

,calc (12*(-12)+5*5)/2

potent lotusBOT Dec 5, 2024, 3:24 AM

#

Result:

-59.5

west horizon Dec 5, 2024, 3:24 AM

#

One message removed from a suspended account.

potent igloo Dec 5, 2024, 3:24 AM

#

discord hid the asterisks

west horizon Dec 5, 2024, 3:24 AM

#

One message removed from a suspended account.

#

One message removed from a suspended account.

potent igloo Dec 5, 2024, 3:25 AM

#

west horizon One message removed from a suspended account.

you multiplied by 2

potent lotusBOT Dec 5, 2024, 3:25 AM

#

Result:

-59.5

west horizon Dec 5, 2024, 3:25 AM

#

One message removed from a suspended account.

#

One message removed from a suspended account.

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One message removed from a suspended account.

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One message removed from a suspended account.

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One message removed from a suspended account.

#

One message removed from a suspended account.

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One message removed from a suspended account.

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One message removed from a suspended account.

calm coralBOT Dec 5, 2024, 3:25 AM

#

Channel closed

Closed by @west horizon

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potent igloo Dec 5, 2024, 3:28 AM

#

west horizon One message removed from a suspended account.

fr tho you had it all along. Just calculator mistakes

calm coralBOT Dec 5, 2024, 3:40 AM

#

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tired locust Dec 5, 2024, 4:04 AM

#

calm coralBOT Dec 5, 2024, 4:04 AM

#

tired locust

#

Please don't occupy multiple help channels.

tired locust Dec 5, 2024, 4:04 AM

#

.close

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odd heart Dec 5, 2024, 4:21 AM

#

how does it go from line 1 to line 2, more specifically the derivatives?

calm coralBOT Dec 5, 2024, 4:21 AM

#

odd heart how does it go from line 1 to line 2, more specifically the derivatives?

#

@odd heart Has your question been resolved?

odd heart Dec 5, 2024, 4:37 AM

#

<@&286206848099549185>

unkempt drift Dec 5, 2024, 4:39 AM

#

odd heart how does it go from line 1 to line 2, more specifically the derivatives?

if you try simplifying the second line you get the derivative of $kp^k$ or $k^2 p^{k - 1}$, then multiply by $q$

potent lotusBOT Dec 5, 2024, 4:39 AM

#

south

unkempt drift Dec 5, 2024, 4:39 AM

#

so yeah you can interchange the derivative and the summation like that

#

also for the second summation just swap p and q everywhere that they appear
so instead of d/dp, you do d/dq and so on

odd heart Dec 5, 2024, 4:41 AM

#

unkempt drift if you try simplifying the second line you get the derivative of $kp^k$ or $k^2 ...

i still don't get it

#

what keeps it equal?

#

oh nvm

unkempt drift Dec 5, 2024, 4:45 AM

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odd heart i still don't get it

I don't know what you mean

#

oh ok

odd heart Dec 5, 2024, 4:45 AM

#

yeah it's just weird

#

so it's because of this right $k^2p^{k-1}=k\frac{\mathrm{d}}{\mathrm{d}p}p^k$?

potent lotusBOT Dec 5, 2024, 4:49 AM

#

jacky

unkempt drift Dec 5, 2024, 4:49 AM

#

potent lotus **jacky**

yeah

odd heart Dec 5, 2024, 4:49 AM

#

ok makes sense thanks

#

you just have to do the process again to fully get rid of the k right

unkempt drift Dec 5, 2024, 4:50 AM

#

potent lotus **jacky**

yeah so that's $\frac{d}{dp} \left(p \frac{d}{dp} p^k \right)$

odd heart Dec 5, 2024, 4:51 AM

#

yup makes perfect sense now

#

man it seems so simple now but thanks again

#

.close

calm coralBOT Dec 5, 2024, 4:51 AM

#

Channel closed

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potent lotusBOT Dec 5, 2024, 4:52 AM

#

south

calm coralBOT Dec 5, 2024, 5:21 AM

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strange crown Dec 5, 2024, 5:35 AM

#

if I were to look at the left branch of this graph, so when x < 4, what's an intuitive way to see if the slope is negative & increasing or negative & decreasing at, when glancing at it.

My first assumption was negative & increasing but turns out it's negative & decreasing

calm coralBOT Dec 5, 2024, 5:35 AM

#

strange crown if I were to look at the left branch of this graph, so when x < 4, what's an int...

cursive tartan Dec 5, 2024, 5:37 AM

#

strange crown if I were to look at the left branch of this graph, so when x < 4, what's an int...

Which side ?

latent pelican Dec 5, 2024, 5:37 AM

#

strange crown if I were to look at the left branch of this graph, so when x < 4, what's an int...

the best way i'd like take a look is graphs go from left to right

as i go from negative infinity to approach 4 i am rapidly exponentially decreasing and becomign negative

cursive tartan Dec 5, 2024, 5:37 AM

#

^

strange crown Dec 5, 2024, 5:38 AM

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cursive tartan Which side ?

left side

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and oo I see

cursive tartan Dec 5, 2024, 5:38 AM

#

strange crown if I were to look at the left branch of this graph, so when x < 4, what's an int...

When you got from left to right in x axis you should get increase in y for a increasing function

strange crown Dec 5, 2024, 5:41 AM

#

latent pelican the best way i'd like take a look is graphs go from left to right as i go from ...

I guess my assumption was based on the fact that it's getting steeper, so the slope was "Increasing" but It's decreasing in value at a rapid rate, so the slope is "decreasing at a rapid/increasing rate"

latent pelican Dec 5, 2024, 5:43 AM

#

strange crown I guess my assumption was based on the fact that it's getting steeper, so the sl...

That's if you were going from right to left, however graphs as you can see go left to right,

The tangent line compared to the exponential is rapidly at a decreasing rate

cursive tartan Dec 5, 2024, 5:44 AM

#

strange crown I guess my assumption was based on the fact that it's getting steeper, so the sl...

The best way is to get two points and see the slope

latent pelican Dec 5, 2024, 5:44 AM

#

if you were to say x > 4 if you were to analyze that then it would be increasing, positive as the slope never goes below 0 and just flattens out

potent smelt Dec 5, 2024, 5:46 AM

#

Its slope is negative because it's going down. And it's decreasing because it's going more and more down (becoming larger negative values)

simple cave Dec 5, 2024, 5:46 AM

#

always direction is left to right.

strange crown Dec 5, 2024, 5:46 AM

#

latent pelican if you were to say x > 4 if you were to analyze that then it would be increasing...

hmm well the way my class analyzed the the right side was that It's also negative slope, negative m value, except it's increasing

strange crown Dec 5, 2024, 5:50 AM

#

potent smelt Its slope is negative because it's going down. And it's decreasing because it's ...

ahh I see but for the right branch, when x>4, the slope is negative as well, but couldn't you say it's decreasing since the y-values are getting closer to 0, when they initially started out bigger while being closer to the asymptote

potent smelt Dec 5, 2024, 5:55 AM

#

A negative number decreasing means that the magnitude is increasing

#

So -3 decreases to -4 and so on

#

On the other hand a negative number increasing means its magnitude is decreasing, -3 increases to -2

calm coralBOT Dec 5, 2024, 6:05 AM

#

@strange crown Has your question been resolved?

calm coralBOT Dec 5, 2024, 6:20 AM

#

Channel closed

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topaz raft Dec 5, 2024, 6:27 AM

#

I’m confused, shouldn’t it be n-3 as the power not n-2?

calm coralBOT Dec 5, 2024, 6:27 AM

#

topaz raft I’m confused, shouldn’t it be n-3 as the power not n-2?

pallid halo Dec 5, 2024, 6:28 AM

#

topaz raft I’m confused, shouldn’t it be n-3 as the power not n-2?

what's the derivative of sec theta?

topaz raft Dec 5, 2024, 6:28 AM

#

secxtanx

pallid halo Dec 5, 2024, 6:29 AM

#

yep...

topaz raft Dec 5, 2024, 6:29 AM

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ohhhhh

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ok that makes sense

#

thanks bungo

pallid halo Dec 5, 2024, 6:29 AM

#

sure, yw

topaz raft Dec 5, 2024, 6:29 AM

#

catking sotrue

#

.close

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calm coralBOT Dec 5, 2024, 6:44 AM

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potent totem Dec 5, 2024, 7:04 AM

#

Okay, so solving part a) is pretty much just plugging in number into the formula. 2pi * integral (g(y)+2) * \sqrt(1+(5y^4)^2)dy. Probably typed something in wrong (not sure how to do latex on discord).

But for part b, rotating around the x-axis, I'm not sure what I need to do.

The formula is basically the same, but do I need to change my limits of integration? Do I still use g(y) in my equation?

To be clear, this is an old exam. I'm going back over it in preparation for finals and this is one that I wasn't sure how to do.

calm coralBOT Dec 5, 2024, 7:04 AM

#

potent totem Okay, so solving part a) is pretty much just plugging in number into the formula...

cursive tartan Dec 5, 2024, 7:05 AM

#

potent totem Okay, so solving part a) is pretty much just plugging in number into the formula...

You gotta integrate x in terms of y with the limits

#

So just [y^6/6]

potent totem Dec 5, 2024, 7:10 AM

#

Sorry, I think I'm being dense and missing what you're saying. I can see how integrating x would give us y^6/6, but I'm not seeing why that's the solution to rotating around the x-axis.

'I'm not doubting you, just trying to understand.

cursive tartan Dec 5, 2024, 7:11 AM

#

potent totem Sorry, I think I'm being dense and missing what you're saying. I can see how int...

Ok so there is 2 ways to understand this

#

1 way : they gave limits for y (which for lower cases means you gotta integrate in terms of y)

#

If you gonna ask can't you get x from y , you can't here

cursive tartan Dec 5, 2024, 7:15 AM

#

potent totem Sorry, I think I'm being dense and missing what you're saying. I can see how int...

The 2nd is trying it out

See when the rotation axis is x axis

And we gotta find an area between the two x axis line (y=a)

Which is only possible if we integrate the y axis

potent totem Dec 5, 2024, 7:17 AM

#

Okay, this is helpful. I feel like I need to draw the diagrams myself and work on some more problems. This was useful. Thank you.

#

.close

calm coralBOT Dec 5, 2024, 7:17 AM

#

Channel closed

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calm coralBOT Dec 5, 2024, 7:32 AM

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subtle palm Dec 5, 2024, 10:57 AM

#

how to do these types of questions? i never understand how they just know

calm coralBOT Dec 5, 2024, 10:57 AM

#

subtle palm how to do these types of questions? i never understand how they just know

finite oasis Dec 5, 2024, 10:59 AM

#

subtle palm how to do these types of questions? i never understand how they just know

do you know binomial expansion

subtle palm Dec 5, 2024, 10:59 AM

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yeah to some extent

#

i can do normal binomial expansion but doing that wastes too much time in an exam

#

so they do the binomial expansion with combinatorics and algebra

finite oasis Dec 5, 2024, 10:59 AM

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Yes you shouldnt actually expand it

subtle palm Dec 5, 2024, 10:59 AM

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andi dont get the shortcutted combinatorics version

lapis oracle Dec 5, 2024, 11:00 AM

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need help with this

lapis oracle Dec 5, 2024, 11:03 AM

#

subtle palm how to do these types of questions? i never understand how they just know

use this formula Tr+1 = nCr x^n-r y^r

finite oasis Dec 5, 2024, 11:03 AM

#

subtle palm andi dont get the shortcutted combinatorics version

Basically, for a binomial of the form $(a+b)^n$ the $k$-th general term of its expansion is given by [
T_k = \binom nk \cdot a^{n-k} b^{k}
]
Thus, for your binomial, the $k$-th general term can be represented as[
T_k = \binom 6k \cdot \left(\frac{3}{x^2}\right)^{6-k} \cdot \left(-\frac{x}{2}\right)^k
]
Your objective is to simplify the above expression, and find under what conditions is the exponent of $x$ equal to 0

gray smelt Dec 5, 2024, 11:04 AM

#

lapis oracle need help with this

#❓how-to-get-help check here

potent lotusBOT Dec 5, 2024, 11:05 AM

#

Aero

subtle palm Dec 5, 2024, 11:05 AM

#

oh, i see so from here it kind of is like guess and check to see what makes x's power = 0

Screenshot_2024-12-05_at_10.05.40_pm.png

finite oasis Dec 5, 2024, 11:06 AM

#

You needn't guess

#

it is algebra

#

Try to simplify first

#

distribute the powers, group like terms, etc.

subtle palm Dec 5, 2024, 11:06 AM

#

yep okay
thank you!

#

.close

calm coralBOT Dec 5, 2024, 11:07 AM

#

Channel closed

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calm coralBOT Dec 5, 2024, 11:22 AM

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pallid coral Dec 5, 2024, 12:19 PM

#

In high school, does yall teacher make quizzes?

calm coralBOT Dec 5, 2024, 12:19 PM

#

pallid coral In high school, does yall teacher make quizzes?

atomic quarry Dec 5, 2024, 12:20 PM

#

pallid coral In high school, does yall teacher make quizzes?

gray smelt Dec 5, 2024, 12:20 PM

#

why do you ask

pallid coral Dec 5, 2024, 12:20 PM

#

.close

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Channel closed

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remote mural Dec 5, 2024, 12:41 PM

#

WhatsApp_Image_2024-12-05_at_18.11.18_1439f7a5.jpg

calm coralBOT Dec 5, 2024, 12:41 PM

#

remote mural

remote mural Dec 5, 2024, 12:43 PM

#

In need of dire help, the answer sheet (very unreliable) tells that it is option (B).

amber bolt Dec 5, 2024, 12:44 PM

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doesn't make sense

#

even the unit doesn't make sense

#

wtf

remote mural Dec 5, 2024, 12:46 PM

#

It should be 1500Pa right?

amber bolt Dec 5, 2024, 12:47 PM

#

it should be 0 because there's only atmospheric pressure in those points

#

like yeah, it will flow to the right, so there's a pressure difference, i'm just really confused

gray smelt Dec 5, 2024, 12:56 PM

#

https://byjus.com/question-answer/a-siphon-in-use-is-demonstrated-in-the-following-figure-the-density-of-the-liquid-8/

A siphon in use is demonstrated in the following figure. The densit...

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm / cc. The pressure difference between the point P and S will beA. ZeroB. 105 N / MC. InfinityD. 2 × 105 N / M

remote mural Dec 5, 2024, 12:59 PM

#

Thank you

#

I have another question

#

WhatsApp_Image_2024-12-05_at_18.29.24_466a098b.jpg

#

How can we even approach finding it?

amber bolt Dec 5, 2024, 1:03 PM

#

remote mural It should be 1500Pa right?

yeah if i pretend the tube is 1m² in section there's 150 kg difference

#

so 1500 Pa

calm coralBOT Dec 5, 2024, 1:15 PM

#

@remote mural Has your question been resolved?

remote mural Dec 5, 2024, 1:16 PM

#

<@&286206848099549185>

dire gulch Dec 5, 2024, 1:18 PM

#

ok

#

firstly, wlog, let us assume A>B

#

yes?

#

ping me when you are there

remote mural Dec 5, 2024, 1:23 PM

#

yes

dire gulch Dec 5, 2024, 1:29 PM

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ok are u here now?

#

pls ping me when u r

#

anyway

#

you agree we can just cut of the length b from both of the parralel sides, withouth changing the distance we want to find?

remote mural Dec 5, 2024, 1:31 PM

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yes

#

@dire gulch

dire gulch Dec 5, 2024, 1:33 PM

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yes

#

so now we have a traingle

#

with the top angle 90*

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and the bottom length a-b

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and we want to find the median length

remote mural Dec 5, 2024, 1:34 PM

#

can you show the diagram?

dire gulch Dec 5, 2024, 1:34 PM

#

sry, i am doing this mentally, you can imagine what i am saying tho?

#

oh

remote mural Dec 5, 2024, 1:36 PM

#

dire gulch Dec 5, 2024, 1:36 PM

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yes

#

now you contract CD around the center by length AB

#

can you do that?

#

just make the midline first

#

#

do you get this?

#

@remote mural

remote mural Dec 5, 2024, 1:38 PM

#

oh

#

dire gulch Dec 5, 2024, 1:38 PM

#

yeh

#

E i midpoint of AB

#

H is midpoint of CD

remote mural Dec 5, 2024, 1:39 PM

#

Oh so AE = DF?

dire gulch Dec 5, 2024, 1:39 PM

#

yes

#

and we know that FEG = 90*

#

right?

remote mural Dec 5, 2024, 1:40 PM

#

yes

dire gulch Dec 5, 2024, 1:40 PM

#

and you know that the median length of a rightangle triangle is half the hypotenuse

#

since

#

if one side is a, and the other sidelngth is b

remote mural Dec 5, 2024, 1:40 PM

#

I know this

dire gulch Dec 5, 2024, 1:40 PM

#

yeh

#

so you are done?

remote mural Dec 5, 2024, 1:41 PM

#

oh yes

#

thanks

#

.close

calm coralBOT Dec 5, 2024, 1:41 PM

#

Channel closed

Closed by @honest stream

Use .reopen if this was a mistake.

dire gulch Dec 5, 2024, 1:42 PM

#

welcome

calm coralBOT Dec 5, 2024, 3:58 PM

#

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prisma wyvern Dec 5, 2024, 4:04 PM

#

If $F(x)=\int^x_1 e^x+e^t dt$, then $F'(x)=2e^x$ is this correct?

calm coralBOT Dec 5, 2024, 4:04 PM

#

prisma wyvern If $F(x)=\int^x_1 e^x+e^t dt$, then $F'(x)=2e^x$ is this correct?

potent lotusBOT Dec 5, 2024, 4:04 PM

#

Volas

noble lynx Dec 5, 2024, 4:06 PM

#

yes.

prisma wyvern Dec 5, 2024, 4:06 PM

#

ok thx

#

.close

calm coralBOT Dec 5, 2024, 4:07 PM

#

Channel closed

Closed by @prisma wyvern

Use .reopen if this was a mistake.

mortal orbit Dec 5, 2024, 4:07 PM

#

prisma wyvern If $F(x)=\int^x_1 e^x+e^t dt$, then $F'(x)=2e^x$ is this correct?

wait

#

the way you wrote it

#

$F(x) = (x-1)e^x + e^x - 1$

potent lotusBOT Dec 5, 2024, 4:07 PM

#

rafilou is not not born in 2003

mortal orbit Dec 5, 2024, 4:08 PM

#

so $F'(x) = (x+1)e^x$

potent lotusBOT Dec 5, 2024, 4:08 PM

#

rafilou is not not born in 2003

prisma wyvern Dec 5, 2024, 4:08 PM

#

oh i should add the parenthesis

#

(e^x+e^t)

mortal orbit Dec 5, 2024, 4:08 PM

#

you can only use FTC if you have $F(x) = \int_a^x f(t)dt$

potent lotusBOT Dec 5, 2024, 4:08 PM

#

rafilou is not not born in 2003

mortal orbit Dec 5, 2024, 4:09 PM

#

potent lotus **Volas**

the problem here

#

is that f also depends on x

#

so no FTC

prisma wyvern Dec 5, 2024, 4:09 PM

#

okay

#

.reopen

calm coralBOT Dec 5, 2024, 4:11 PM

#

✅

prisma wyvern Dec 5, 2024, 4:14 PM

#

wait no

#

hmm

#

ok

#

.close

calm coralBOT Dec 5, 2024, 4:17 PM

#

Channel closed

Closed by @prisma wyvern

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fleet cairn Dec 5, 2024, 5:02 PM

#

calm coralBOT Dec 5, 2024, 5:02 PM

#

fleet cairn

fleet cairn Dec 5, 2024, 5:02 PM

#

so i split this into 2 integrals

#

and when im solving the left integral

#

im using x = 2tan(theta)

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but when im using photomath to double check its saying the answer is ln something

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how to do

calm coralBOT Dec 5, 2024, 5:18 PM

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@fleet cairn Has your question been resolved?

vagrant oak Dec 5, 2024, 5:18 PM

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fleet cairn im using x = 2tan(theta)

this should work

vagrant oak Dec 5, 2024, 5:19 PM

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fleet cairn but when im using photomath to double check its saying the answer is ln somethin...

the answer is gonna be a hyperbolic function, which can be also written through lns

vagrant oak Dec 5, 2024, 5:19 PM

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fleet cairn

btw there is a simpler approach

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of what "degree" is the first fraction? Of what degree is the second one?

calm coralBOT Dec 5, 2024, 5:33 PM

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weary cape Dec 5, 2024, 6:06 PM

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Let V be a finite set with at least two elements. Does the structure of a Q-vector space exist on V?

calm coralBOT Dec 5, 2024, 6:06 PM

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weary cape > Let V be a finite set with at least two elements. Does the structure of a Q-ve...

weary cape Dec 5, 2024, 6:07 PM

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how would I go about showing or disproving this?

calm coralBOT Dec 5, 2024, 6:22 PM

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@weary cape Has your question been resolved?

weary cape Dec 5, 2024, 6:24 PM

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<@&286206848099549185>

calm coralBOT Dec 5, 2024, 6:54 PM

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@weary cape Has your question been resolved?

weary cape Dec 5, 2024, 7:07 PM

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<@&286206848099549185>

mortal orbit Dec 5, 2024, 7:26 PM

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weary cape > Let V be a finite set with at least two elements. Does the structure of a Q-ve...

if by absurd you could create such a structure

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call v1 the element that would correspond to the 0 vector

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and v2 a different element

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Can you explain why there must exist different p,q in Q such that p * v2 = q * v2?

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then conclude as to the existence of such a structure

weary cape Dec 5, 2024, 7:34 PM

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$\mathbb{Q}$ is infinite right?

potent lotusBOT Dec 5, 2024, 7:34 PM

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aName

weary cape Dec 5, 2024, 7:36 PM

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now I am honestly already confused at what it means for a Q-Vectorspace to exist on a set.

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because if I take any element/vector in V and use scalar multiplication to multiply it with a rational number then it might not exist in V anymore

mortal orbit Dec 5, 2024, 7:55 PM

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weary cape because if I take any element/vector in V and use scalar multiplication to multi...

well it literally should

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if you have a Q-vectorspace structure

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it means that you have

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an addition operation

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meaning for v,w in V

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v+w in V

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so (V,+) is a commutative group

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and a scalar multiplication operation

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meaning that for q in Q, v in V

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q * v is in V

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and it satisfies (pq) * v = p * (q * v), 1 * v = v and distributivity

mortal orbit Dec 5, 2024, 7:58 PM

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weary cape $\mathbb{Q}$ is infinite right?

so yes, Q is infinite

weary cape Dec 5, 2024, 8:01 PM

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mortal orbit Can you explain why there must exist different p,q in Q such that p * v2 = q * v...

hm if v2 is the only other vector existing in V aside from the 0 vector then multiplying it can't do anything to it right?

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cuz if p*v2 ≠ v2 it can only be v1

mortal orbit Dec 5, 2024, 8:15 PM

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weary cape hm if v2 is the only other vector existing in V aside from the 0 vector then mul...

well for example

mortal orbit Dec 5, 2024, 8:15 PM

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weary cape cuz if p*v2 ≠ v2 it can only be v1

that would only be possible when p = 0

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in a vector space, if p * v = the zero vector, then p = 0 or v = the zero vector

weary cape Dec 5, 2024, 8:18 PM

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yes but there are no other vectors besides v1 (zero vector) and v2 so scalar multiplication wouldn't work with any elements of Q besides 0

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and therefore it cannot exist?

mortal orbit Dec 5, 2024, 8:19 PM

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?

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you haven't told me why yet

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i could very much have p*v2 = v2 when p is not 0

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why doesn't it work?

weary cape Dec 5, 2024, 8:21 PM

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the neutral element wouldn't be unique?

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i remember a proof we had where if there are two elements having the property of e * v = v = e' * v then e = e'

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but then for all q in Q q*v2 = v2

mortal orbit Dec 5, 2024, 8:24 PM

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well try to apply that

weary cape Dec 5, 2024, 8:25 PM

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okay

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thank you

calm coralBOT Dec 5, 2024, 9:25 PM

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gentle rampart Dec 5, 2024, 9:28 PM

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hi

calm coralBOT Dec 5, 2024, 9:29 PM

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gentle rampart hi

gentle rampart Dec 5, 2024, 9:29 PM

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how can i solve this?\

onyx berry Dec 5, 2024, 9:30 PM

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given an angle and radius, what is the formula for the arc length, and the formula for the area of the sector?

odd moon Dec 5, 2024, 9:31 PM

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$\frac{\theta}{2 \pi} \cdot \pi r^2 = 6\pi$

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oops

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the area of the sector can be described like this

onyx berry Dec 5, 2024, 9:32 PM

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now you are mixing degree and radians

odd moon Dec 5, 2024, 9:32 PM

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potent lotusBOT Dec 5, 2024, 9:33 PM

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tenshi

odd moon Dec 5, 2024, 9:34 PM

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$\frac{\theta}{2 \pi} \cdot 2 \pi r = 2\pi$

potent lotusBOT Dec 5, 2024, 9:34 PM

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tenshi

odd moon Dec 5, 2024, 9:34 PM

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this is the length of the arc

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solve the system for theta and r

gentle rampart Dec 5, 2024, 9:35 PM

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ah

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i was using the equation and using theta/360

odd moon Dec 5, 2024, 9:38 PM

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hm i got r = 6?

glad adder Dec 5, 2024, 9:49 PM

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I got the same radius

calm coralBOT Dec 5, 2024, 9:54 PM

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torpid summit Dec 5, 2024, 11:09 PM

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wait how do you do this again 💀

calm coralBOT Dec 5, 2024, 11:09 PM

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torpid summit wait how do you do this again 💀

torpid summit Dec 5, 2024, 11:09 PM

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kind meteor Dec 5, 2024, 11:10 PM

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just supstitue t to be 60?

torpid summit Dec 5, 2024, 11:10 PM

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damn

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wait what

kind meteor Dec 5, 2024, 11:11 PM

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i think?

torpid summit Dec 5, 2024, 11:11 PM

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not that simple lmao

kind meteor Dec 5, 2024, 11:11 PM

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yea

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nvm