PLEASE HELP DUE TOMORROW MORN ONLY HAVE 2 QUESTIONS LEFT ITS CALCULUS | Mathematics | Page 1

native pathBOT Dec 3, 2023, 8:36 AM

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queen hamlet Dec 3, 2023, 8:38 AM

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@fast wyvern

balmy wren Dec 3, 2023, 8:40 AM

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where did the random multiply by 2 come from

queen hamlet Dec 3, 2023, 8:41 AM

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i did this like a week a go with the help of my teacher I couldnt even tell you, I've had some time of sick and then been slammed with this im so confused

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i might've just made an error im not sure it was hard enough to get to that stage

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i assume for part 1 b I just use the volume formula of a rectangle box

queen hamlet Dec 3, 2023, 9:22 AM

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can anyone help me ive been trying to watch youtube videos on it and I just do not understand

balmy wren Dec 3, 2023, 9:35 AM

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so which part do you need help on

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B?

queen hamlet Dec 3, 2023, 9:35 AM

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im up to part 1 b

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we only just started learning it in class and I missed a fair few lessons due to sickness

balmy wren Dec 3, 2023, 9:36 AM

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queen hamlet i assume for part 1 b I just use the volume formula of a rectangle box

well yes

queen hamlet Dec 3, 2023, 9:38 AM

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yes Im not entirely sure on how to plug it in I assume the smaller squares would relate to width

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be like 2x or something maybe im not sure

balmy wren Dec 3, 2023, 9:38 AM

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what is the width of the folded up sides

queen hamlet Dec 3, 2023, 9:39 AM

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wdym

balmy wren Dec 3, 2023, 9:39 AM

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you cut off 2 squares of side length x, what does that leave the formerly a-long side as?

queen hamlet Dec 3, 2023, 9:40 AM

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im sorry im confused

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is that what you mean?

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for b would it be 30 x 13 x 2x

balmy wren Dec 3, 2023, 9:48 AM

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queen hamlet for b would it be 30 x 13 x 2x

no, the box when folded up is not 30 long

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the sheet started with a side of 30

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but you can see the box is smaller than that

queen hamlet Dec 3, 2023, 9:49 AM

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its not to scale im not getting what you mean what im thinking is

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390 x 2x

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and then make x the subject

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maybe

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but I haven't been taught any of this our teacher wants us to figure it out

balmy wren Dec 3, 2023, 9:50 AM

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queen hamlet 390 x 2x

no

queen hamlet Dec 3, 2023, 9:50 AM

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no?

balmy wren Dec 3, 2023, 9:50 AM

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the box is not 30 long

queen hamlet Dec 3, 2023, 9:50 AM

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explain

balmy wren Dec 3, 2023, 9:50 AM

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the sheet of paper is 30 long

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correct?

queen hamlet Dec 3, 2023, 9:50 AM

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yes

balmy wren Dec 3, 2023, 9:50 AM

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the base of the box is a rectangle inside the 30x13 rectangle

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it must be smaller in both dimensions

queen hamlet Dec 3, 2023, 9:51 AM

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im so confused its okay

balmy wren Dec 3, 2023, 9:51 AM

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?

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would cutting a piece of paper help

queen hamlet Dec 3, 2023, 9:52 AM

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honestly I dont know I just dont get it

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its hard for me to learn like this ig i have learning

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dissabilites

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id prefer a vc but i dont want to if ohter people arent comfortable with it

balmy wren Dec 3, 2023, 9:54 AM

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visualiziation i guess

queen hamlet Dec 3, 2023, 9:55 AM

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I think I know what you mean

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but isnt it meant to be a rectangle

balmy wren Dec 3, 2023, 9:55 AM

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yeah

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the point is the part of the 30x13 rectangle that ends up being the base, is not the whole rectangle

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otherwise

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there would be no sides

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it is smaller

queen hamlet Dec 3, 2023, 9:56 AM

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right

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so we need to cut the sides out?

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or find the starts

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sides

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balmy wren Dec 3, 2023, 9:56 AM

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you would like to find the dimensions of the inner rectangle

queen hamlet Dec 3, 2023, 9:56 AM

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so like

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looking at it like this

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the inner rectangle

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thats what I need to find

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before I found the whole sheet

balmy wren Dec 3, 2023, 9:58 AM

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mhm

queen hamlet Dec 3, 2023, 9:58 AM

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im sorry im a bit spesh

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is there a specific formula I can plug into

balmy wren Dec 3, 2023, 9:59 AM

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hmm

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look at the top horizontal line

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its total length is 30

queen hamlet Dec 3, 2023, 9:59 AM

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yes

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i see that

balmy wren Dec 3, 2023, 9:59 AM

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then you should subtract off the 2 end parts

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to find the middle part length

queen hamlet Dec 3, 2023, 10:00 AM

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how would I find what to subtract?

balmy wren Dec 3, 2023, 10:02 AM

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this segment is what to subtract

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and also the one on the other side

queen hamlet Dec 3, 2023, 10:02 AM

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yeah but i dont have the values

balmy wren Dec 3, 2023, 10:02 AM

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you do

queen hamlet Dec 3, 2023, 10:02 AM

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i do?

balmy wren Dec 3, 2023, 10:02 AM

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that segment is also on one of the cut-out squares

queen hamlet Dec 3, 2023, 10:03 AM

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you've lost me again

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im attempting to find that top bit

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with the side segments gone

balmy wren Dec 3, 2023, 10:05 AM

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yes

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each side segment is on a cut-out square, which you know how big they are

queen hamlet Dec 3, 2023, 10:10 AM

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so how do i know the values

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all I see is x

balmy wren Dec 3, 2023, 10:21 AM

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yes, that's right

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x is the length of each of those segments

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you have x + middle + x = 30

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can you find middle now, in terms of x

queen hamlet Dec 4, 2023, 5:42 AM

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i did. it sorry went to sleep and been at school

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ive graphed it etc

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up to using calculus to prove the max point using the quadratic formula

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queen hamlet Dec 4, 2023, 6:04 AM

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i’m now stumped as i’ve put it in the quadratic formula and tried to put it in a calculus calculator and i’m not getting the estimated value

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@balmy wren

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this is the formula i tried but i’m not sure i got it right

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i think i got it i think the one on the right is the correct answer

queen hamlet Dec 4, 2023, 7:09 AM

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nevermind

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i need to get the derivate of the volume equation i got

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i’m just confused how like do i use product rule

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i haven’t done it for a while

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@fast wyvern @balmy wren

balmy wren Dec 4, 2023, 7:37 AM

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queen hamlet i’m just confused how like do i use product rule

you can also multiply out the polynomial and take power rule

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generally the way to do product rule is for example (abc)' = a'bc + ab'c + abc'

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(abcd)' = a'bcd + ab'cd + abc'd + abcd'

queen hamlet Dec 4, 2023, 7:55 AM

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i think im meant to use the power rule

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much simpler

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is this correct? have I ordered it correctly?

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theres an x next to the 3600 btw

balmy wren Dec 4, 2023, 8:15 AM

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queen hamlet

i don't think that -60x^2 is right

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once you correct that:
remember the power rule, that (a*x^n)' = a*n*x^(n-1)

queen hamlet Dec 4, 2023, 8:16 AM

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im tarded its meant to be -86

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^2

balmy wren Dec 4, 2023, 8:16 AM

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indeed

queen hamlet Dec 4, 2023, 8:16 AM

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i think

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its a = 12 b = -172 and c = 390

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correct me if im wrong plssss

balmy wren Dec 4, 2023, 8:17 AM

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uh no i think b = -86 like you said

queen hamlet Dec 4, 2023, 8:17 AM

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but dont I need to derive it first before I put it into the quadratic equation?

balmy wren Dec 4, 2023, 8:17 AM

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oh mb

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yes that's right

queen hamlet Dec 4, 2023, 8:18 AM

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like that I believe

balmy wren Dec 4, 2023, 8:19 AM

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yees

queen hamlet Dec 4, 2023, 8:25 AM

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would that be correct

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and then I just test both plus and minus of it

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over 24

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like 172+104/24 and 172-104/24

balmy wren Dec 4, 2023, 8:25 AM

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,calc (172^2 - 4(12)(390))^0.5

void ravineBOT Dec 4, 2023, 8:25 AM

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Result:

104.23051376636

balmy wren Dec 4, 2023, 8:25 AM

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well so its not exactly 104

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close enough i guess

queen hamlet Dec 4, 2023, 8:26 AM

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yeah its estimated

balmy wren Dec 4, 2023, 8:26 AM

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queen hamlet and then I just test both plus and minus of it

well one of them doesn't make sense if you go back to the original problem

queen hamlet Dec 4, 2023, 8:26 AM

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??

balmy wren Dec 4, 2023, 8:27 AM

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just find approximate values and then you'll see

queen hamlet Dec 4, 2023, 8:27 AM

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alright

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i got 11.5 for the +

balmy wren Dec 4, 2023, 8:28 AM

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remember that one of the box lengths is 13 - 2x

queen hamlet Dec 4, 2023, 8:30 AM

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I still need to find the second derivative

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of

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-172 + 24x

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im confused now

balmy wren Dec 4, 2023, 8:32 AM

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balmy wren remember that one of the box lengths is 13 - 2x

if x = 11.5, this is a negative number
boxes don't have negative lengths

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... or you can use second derivative test yeah

queen hamlet Dec 4, 2023, 8:32 AM

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yeah I know what you nean but yeah

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Im pre sure I ned to use the second derivative tesrt

balmy wren Dec 4, 2023, 8:33 AM

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queen hamlet -172 + 24x

that's right, anyway

queen hamlet Dec 4, 2023, 8:36 AM

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would that be correct i’m not too confident with min and max

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but i’ve just been watching a shit ton of youtube vids

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i’m not sure what to do from here

balmy wren Dec 4, 2023, 8:50 AM

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queen hamlet

one thing, -172 + 24(11.5) is 104 > 0
they should be the same, due to symmetry of cubic equations
but beyond that, it's correct

queen hamlet Dec 4, 2023, 8:59 AM

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im confused with e now

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I dont know what to dop

balmy wren Dec 4, 2023, 9:00 AM

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queen hamlet

minimum volume?

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min volume is 0

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right?

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to get the material, plug values of x you found into the formula from part A probably

queen hamlet Dec 4, 2023, 9:02 AM

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cheers

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like that?

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or plug 188 in instead of 11.5

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because i got that for min

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i got 59.375 it doesnt seem right

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because I got 390 for the area in part A it just doesnt make sense

balmy wren Dec 4, 2023, 9:14 AM

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queen hamlet

11.5 is not a possible value for x

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probably 2.83 or whatever it was

queen hamlet Dec 4, 2023, 9:14 AM

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please explain how to plug it in

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yeah I used that

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and got

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369.9310278

balmy wren Dec 4, 2023, 9:16 AM

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don't use so much precision (unless you didnt round in any previous step)

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remember you rounded 104.23 to 104

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that is correct to the nearest integer

queen hamlet Dec 4, 2023, 9:17 AM

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would that be correct though

balmy wren Dec 4, 2023, 9:17 AM

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i mean if you answer it as 369.9310278

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then rhrhrhhr uhhhh

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i would say no

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too much precision

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the actual value is slightly higher than 370

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but for all intents and purposes in real life

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its right

queen hamlet Dec 4, 2023, 9:19 AM

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would you consider hopping in a vc with me and giving me a hand all g if not though just thought id asked im pretty confused

balmy wren Dec 4, 2023, 9:19 AM

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sorry, cant

queen hamlet Dec 4, 2023, 9:19 AM

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thats all g ]

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I just dont understand how the surface area of it could be lower than the area I got earlier for part a

balmy wren Dec 4, 2023, 9:20 AM

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balmy wren the actual value is slightly higher than 370

do you not understand why this is the case

queen hamlet Dec 4, 2023, 9:20 AM

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and if so what I did wronhg

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does the min matter

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should I have more than one asnwer for at as the min and max

balmy wren Dec 4, 2023, 9:21 AM

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min volume should be when x = 0 i guess

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so 2 answers

queen hamlet Dec 4, 2023, 9:21 AM

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so min is just when x = 0

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I dont need to do anything else?

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im so confused

balmy wren Dec 4, 2023, 9:26 AM

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queen hamlet I dont need to do anything else?

not for e i guess

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then for f who knows what they're saying

queen hamlet Dec 4, 2023, 9:26 AM

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not me aha Im so confused for e

balmy wren Dec 4, 2023, 9:26 AM

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is it like best volume to area ratio? is it best volume?

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for e, just plug in x = 0 (minimum) and x = 2.8 (maximum) i think

queen hamlet Dec 4, 2023, 9:26 AM

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i cant even think about f

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but how does it = 2.8 I thought it was the sa

balmy wren Dec 4, 2023, 9:27 AM

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what

queen hamlet Dec 4, 2023, 9:27 AM

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im confused

balmy wren Dec 4, 2023, 9:27 AM

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the maximum volume is when x is 2.8, right?

queen hamlet Dec 4, 2023, 9:27 AM

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wait sorry

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so I plug it into the part 1 A formula I made

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make x 0

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for min

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and make max 2.8

balmy wren Dec 4, 2023, 9:28 AM

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that's what i think

queen hamlet Dec 4, 2023, 9:28 AM

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ill give it a go

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i got 369.93 for max

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I didnt plug min in properly

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IS THAT RIGHT

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OR HAVE I GOT MY HOPES UP

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@balmy wren

balmy wren Dec 4, 2023, 9:34 AM

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you wrote 390 on both of them

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wasn't it 370

queen hamlet Dec 4, 2023, 9:34 AM

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i think i plugged it in wrong the first time

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I did it again and thats whjat I got

balmy wren Dec 4, 2023, 9:35 AM

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the first one is right

queen hamlet Dec 4, 2023, 9:35 AM

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is the second one not?

balmy wren Dec 4, 2023, 9:35 AM

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queen hamlet Dec 4, 2023, 9:35 AM

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i’m confused again where do i go wrong

balmy wren Dec 4, 2023, 9:36 AM

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it cant possibly be more than 390, anyway

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that's 390 - 2.5x^2

queen hamlet Dec 4, 2023, 9:36 AM

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huh

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i don’t get it

balmy wren Dec 4, 2023, 9:38 AM

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you started with a sheet of area 390 and cut some parts from the corners away

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it's going to be less than 390

queen hamlet Dec 4, 2023, 9:40 AM

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so 370 was correct

balmy wren Dec 4, 2023, 9:44 AM

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yes

queen hamlet Dec 4, 2023, 9:45 AM

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ah okay thank you

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i dont understand f at all

queen hamlet Dec 4, 2023, 10:50 AM

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hi @here i dont understand part 1 f and part 2 e can anyone help me?

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#PLEASE HELP DUE TOMORROW MORN ONLY HAVE 2 QUESTIONS LEFT ITS CALCULUS