#help-27 | Mathematics | Page 469

fervent jewel May 3, 2022, 5:22 AM

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Screen_Shot_2022-05-03_at_1.20.33_AM.png

steel sage May 3, 2022, 5:24 AM

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And you did correctly

torn vessel May 3, 2022, 5:24 AM

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looks good

fervent jewel May 3, 2022, 5:24 AM

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🥳

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ty

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vague obsidian May 3, 2022, 5:48 AM

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Quick question: why do I get a different answers when I multiply the whole equation by 9 and when I just simplify 5/9 and 18?

devout snowBOT May 3, 2022, 5:48 AM

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vague obsidian Quick question: why do I get a different answers when I multiply the whole equat...

main gull May 3, 2022, 5:49 AM

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Because if you multiply the right side by 9, you also have to do it on the left side

vague obsidian May 3, 2022, 5:49 AM

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Oh

main gull May 3, 2022, 5:49 AM

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So you'd end up with 9c = 5 * 18

vague obsidian May 3, 2022, 5:50 AM

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wait is not 9c = 5 * (18*9)

main gull May 3, 2022, 5:50 AM

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No

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Because 5/9 * 18 * 9, the 9s cancel

vague obsidian May 3, 2022, 5:51 AM

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OHHHHHHH

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that make sense

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thank you

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analog trellis May 3, 2022, 7:00 AM

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I'm stuck on finding the Mobius map...could anyone help? In class we showed how to construct a mobius map that takes three points to another three points, but how to do this problem?

devout snowBOT May 3, 2022, 7:00 AM

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analog trellis I'm stuck on finding the Mobius map...could anyone help? In class we showed how ...

analog trellis May 3, 2022, 7:07 AM

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<@&286206848099549185>

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pls

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🥺

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river trout May 3, 2022, 7:31 AM

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yo g's need help with a question:
2 × √3 × (sin(2x))=3 ; 0<x<2pi
Need to determine all the possible solutions

devout snowBOT May 3, 2022, 7:31 AM

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river trout yo g's need help with a question: 2 × √3 × (sin(2x))=3 ; 0<x<2pi Need to determ...

magic galleon May 3, 2022, 7:40 AM

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,tex $2 $\sqrt{3} \sin 2x = 3, 0<x<2 \pi$

river trout May 3, 2022, 7:41 AM

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uhm not quite

pallid vector May 3, 2022, 7:42 AM

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$2 \sqrt{3} \cdot sin(2x) = 3 ; 0 < x < 2\pi$

woven radishBOT May 3, 2022, 7:42 AM

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Si Arya

river trout May 3, 2022, 7:42 AM

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👍

magic galleon May 3, 2022, 7:43 AM

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so what have you done?

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pls show us your working

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or any thoughts

river trout May 3, 2022, 7:43 AM

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aight

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so

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2 × (sin(2x))= 3 x 3^2
(sin(2x))= 27/2
(sin(2x)) = 13.5

magic galleon May 3, 2022, 7:45 AM

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river trout 2 × (sin(2x))= 3 x 3^2 (sin(2x))= 27/2 (sin(2x)) = 13.5

why is this 3^2

river trout May 3, 2022, 7:45 AM

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uhm cause it was √3 so it goes to the other side yk and now its power of 2 instead of square root

magic galleon May 3, 2022, 7:46 AM

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river trout uhm cause it was √3 so it goes to the other side yk and now its power of 2 inst...

not really

river trout May 3, 2022, 7:46 AM

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nah chill

magic galleon May 3, 2022, 7:46 AM

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river trout nah chill

wdym

river trout May 3, 2022, 7:46 AM

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ong thats what i remember

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so what would it be then?

magic galleon May 3, 2022, 7:46 AM

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3^-1/2

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not 3^2

woven radishBOT May 3, 2022, 7:47 AM

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||𝓚𝓪𝓼𝓹𝓮𝓻||

magic galleon May 3, 2022, 7:47 AM

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@river trout

river trout May 3, 2022, 7:48 AM

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ahhhh

magic galleon May 3, 2022, 7:48 AM

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just treat sqrt(3)

river trout May 3, 2022, 7:48 AM

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that makes more sense

magic galleon May 3, 2022, 7:48 AM

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as a regular number

river trout May 3, 2022, 7:48 AM

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alr cool

magic galleon May 3, 2022, 7:48 AM

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cool so can we continue

river trout May 3, 2022, 7:48 AM

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yessir

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this is non calc, let me do the calculation rq

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1 sec

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so 1/√3 x 3 = √3

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so then sin(2x) = √3/2

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and i know what to do from here

woven radishBOT May 3, 2022, 7:52 AM

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||𝓚𝓪𝓼𝓹𝓮𝓻||

river trout May 3, 2022, 7:52 AM

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nah that aint right

magic galleon May 3, 2022, 7:52 AM

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why?

magic galleon May 3, 2022, 7:52 AM

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woven radish **Si Arya**

2 sqrt 3 here

river trout May 3, 2022, 7:52 AM

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its √3/2

charred bolt May 3, 2022, 7:52 AM

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same thing lol

magic galleon May 3, 2022, 7:52 AM

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yea

pallid vector May 3, 2022, 7:52 AM

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river trout nah that aint right

It is right

magic galleon May 3, 2022, 7:53 AM

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if you do the rationalise

river trout May 3, 2022, 7:53 AM

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nah but idk why you do it like that

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when it clearer when its √3/2

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as √3/2 is a clear sin value of 60

magic galleon May 3, 2022, 7:53 AM

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fine

river trout May 3, 2022, 7:53 AM

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anyways thats all

magic galleon May 3, 2022, 7:53 AM

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but you skipped the step bro

river trout May 3, 2022, 7:53 AM

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thanks for the help 👍

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ik what to do

magic galleon May 3, 2022, 7:54 AM

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I'm just doing division

river trout May 3, 2022, 7:54 AM

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trust

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yeh ik only thing i was having trouble with was rearranging it

magic galleon May 3, 2022, 7:54 AM

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Yea if that's what you want

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I respect your opinions

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restive river May 3, 2022, 8:14 AM

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Hello! I'd like to compute this beauty. Does anyone have an idea ? I guess it is impossible to find an analytic solution

devout snowBOT May 3, 2022, 8:14 AM

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restive river Hello! I'd like to compute this beauty. Does anyone have an idea ? I guess it is...

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@restive river Has your question been resolved?

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near shoal May 3, 2022, 10:08 AM

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help

devout snowBOT May 3, 2022, 10:08 AM

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near shoal help

near shoal May 3, 2022, 10:08 AM

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i dont get why (f f)=(0,4)

supple trench May 3, 2022, 10:18 AM

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near shoal i dont get why (f f)=(0,4)

(0,4) is different from {0,4}
the order of matters in the former, but not the later

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because order of elements doesn't matter in a set

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i.e. {0,4} = {4,0}

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but $(0,4) \ne (4,0)$

woven radishBOT May 3, 2022, 10:19 AM

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vin100

near shoal May 3, 2022, 10:19 AM

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is this like

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graph coordinates?

supple trench May 3, 2022, 10:21 AM

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i would say graph coordinates use this $(?,?,?,\dots)$ structure

woven radishBOT May 3, 2022, 10:21 AM

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vin100

supple trench May 3, 2022, 10:21 AM

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because each axis is supposed to have a different role to play\

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say in the 2D case, using the Cartesian coordinates

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the $x$-axis and the $y$-axis are the independent and dependent variables respectively.

woven radishBOT May 3, 2022, 10:22 AM

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vin100

near shoal May 3, 2022, 10:23 AM

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so why is range the of (f f) = set {0,4}?

winter patrol May 3, 2022, 10:24 AM

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the range of f is {-2,0,2,4}
if you plug those values into f again, it'll come out as 0 or 4

near shoal May 3, 2022, 10:24 AM

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ah

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im stupid

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didnt notice that

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thanks for the help

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amber dock May 3, 2022, 10:27 AM

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help

devout snowBOT May 3, 2022, 10:27 AM

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amber dock help

amber dock May 3, 2022, 10:28 AM

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Im Confused on the median and mode

devout snowBOT May 3, 2022, 10:43 AM

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@amber dock Has your question been resolved?

amber dock May 3, 2022, 10:44 AM

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<@&286206848099549185>

devout snowBOT May 3, 2022, 11:14 AM

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@amber dock Has your question been resolved?

amber dock May 3, 2022, 11:17 AM

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.close

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devout snowBOT May 3, 2022, 3:39 PM

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worn crystal May 3, 2022, 3:42 PM

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i need to find the height of the container, i dont know how. any help?

devout snowBOT May 3, 2022, 3:42 PM

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worn crystal i need to find the height of the container, i dont know how. any help?

small field May 3, 2022, 3:42 PM

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I think it wants you to assume you got a right angle

worn crystal May 3, 2022, 3:43 PM

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im sorry i dont understand 😦

small field May 3, 2022, 3:44 PM

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worn crystal im sorry i dont understand 😦

do you know what trig is

sonic spruce May 3, 2022, 3:44 PM

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worn crystal i need to find the height of the container, i dont know how. any help?

200cm

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h=200cm ..

worn crystal May 3, 2022, 3:45 PM

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small field do you know what trig is

no lol

worn crystal May 3, 2022, 3:45 PM

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sonic spruce 200cm

ty

small field May 3, 2022, 3:46 PM

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sonic spruce 200cm

monkey

worn crystal May 3, 2022, 3:46 PM

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but i need to write how i got the answer 🙂

sonic spruce May 3, 2022, 3:47 PM

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ah yes

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h =√(250²-150²)

worn crystal May 3, 2022, 3:47 PM

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ah ty

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small field May 3, 2022, 3:48 PM

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my g doesn't know trig

worn crystal May 3, 2022, 3:48 PM

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look i hate math okay😂

devout snowBOT May 3, 2022, 4:46 PM

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craggy quiver May 3, 2022, 5:08 PM

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devout snowBOT May 3, 2022, 5:08 PM

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craggy quiver

craggy quiver May 3, 2022, 5:08 PM

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why doesn't order matter?

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i thought because theres 6 possible answers that are wrong and your choosing 3

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you would multiply that by 5C3

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but you dont?? why?

weak tundra May 3, 2022, 5:21 PM

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craggy quiver but you dont?? why?

The answers which are correct are fixed. There are exactly 5 wrong answers. So it's 5C3/8C3 oe MS method

craggy quiver May 3, 2022, 5:22 PM

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weak tundra The answers which are correct are fixed. There are exactly 5 wrong answers. So i...

i dont understand

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i did this x 5c3

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weak tundra May 3, 2022, 5:23 PM

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craggy quiver i thought because theres 6 possible answers that are wrong and your choosing 3

6 possible wrong ans
No. There are 5 wrong answers. The question has 3 fixed correct answers.

craggy quiver May 3, 2022, 5:23 PM

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yh and p=0 is probability they choose all 3 incorrect answers, right?

weak tundra May 3, 2022, 5:23 PM

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craggy quiver

The 5 wrong answers are fixed. You can't change the 3 correct answers to the question

weak tundra May 3, 2022, 5:23 PM

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craggy quiver yh and p=0 is probability they choose all 3 incorrect answers, right?

Yes

craggy quiver May 3, 2022, 5:23 PM

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i dont understand what fixed means

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you cant answer them in a different order?

weak tundra May 3, 2022, 5:25 PM

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craggy quiver i dont understand what fixed means

Fixed means doesn't change.
You just have to choose 3 answers.

Say the question had options:
1 2 3 4 5 6 7 8
and 2,3,4 are correct. [This is fixed. Suppose the question was "Please choose 2,3,4". The correct answers are 2,3,4 and 2,3,4 only. This is fixed, because the question is fixed. Fixed means doesn't change.]
Then the probability of getting none correct is choosing something out of 1,5,6,7,8. There are 5C3 choices you can make out of a total of 8C3, so 5C3/8C3 is the ans.
Or 5/8 * blabla as ms did

craggy quiver May 3, 2022, 5:26 PM

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i dont understand how there are 5c3 choices you can make out of 8c3

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can we do it in terms of probabilities first?

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ok so 12345678, 234 are correct

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which means probability of someone picking 167 is 5/28? yes or no?

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ohhh wait a second

weak tundra May 3, 2022, 5:27 PM

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craggy quiver which means probability of someone picking 167 is 5/28? yes or no?

No.

craggy quiver May 3, 2022, 5:27 PM

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i think i just realized fixed

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your saying

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order dont matter

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123 is same as 231 because they are all picked at once?

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i understand the 5c3 now

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however i dont understand why 8c3 is total

weak tundra May 3, 2022, 5:28 PM

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craggy quiver 123 is same as 231 because they are all picked at once?

Yes. Both give X=2.

weak tundra May 3, 2022, 5:28 PM

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craggy quiver however i dont understand why 8c3 is total

8 numbers. Choose 3.

craggy quiver May 3, 2022, 5:29 PM

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hmmmmmm i thiiink i get it maybe

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yes, yes i get it.

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now i just need to make sure it sticks.

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ahh, ok thanks for the help appreciate it

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agile narwhal May 3, 2022, 6:07 PM

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devout snowBOT May 3, 2022, 6:07 PM

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agile narwhal

agile narwhal May 3, 2022, 6:07 PM

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Is this correct

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?

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restive river May 3, 2022, 6:20 PM

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I'm supposed to prove this identity

I've tried multiplying the right side's first term with 1 + tanA/1 + tanA

devout snowBOT May 3, 2022, 6:20 PM

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restive river I'm supposed to prove this identity I've tried multiplying the right side's fi...

restive river May 3, 2022, 6:22 PM

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I've also tried doing something similar with the right side's second term
but I can never get them to make sin A + cos A

turbid locust May 3, 2022, 6:22 PM

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restive river I'm supposed to prove this identity I've tried multiplying the right side's fi...

try expressing tan on the RHS as sin/cos and then getting rid of the /cos

restive river May 3, 2022, 6:24 PM

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would I get sinA.cosA/ 1 - cos A?

turbid locust May 3, 2022, 6:24 PM

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uhm i dont think so

restive river May 3, 2022, 6:25 PM

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turbid locust May 3, 2022, 6:25 PM

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$$\frac{\cos A}{1-\frac{\sin A}{\cos A}} - \frac{\sin^2 A}{\cos A - \sin A}$$

woven radishBOT May 3, 2022, 6:25 PM

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Nathan_

turbid locust May 3, 2022, 6:26 PM

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them multiply the left fraction by cos/cos

restive river May 3, 2022, 6:26 PM

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wouldn't the sin A at the bottom multiply with the cos A?

turbid locust May 3, 2022, 6:26 PM

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$$\frac{\cos^2 A}{\cos A -\sin A} - \frac{\sin^2 A}{\cos A - \sin A}$$

woven radishBOT May 3, 2022, 6:26 PM

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Nathan_

turbid locust May 3, 2022, 6:27 PM

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restive river wouldn't the sin A at the bottom multiply with the cos A?

wdym?

restive river May 3, 2022, 6:27 PM

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I mean wouldn't the sinA that's underneath the cosA go to the top?

turbid locust May 3, 2022, 6:28 PM

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there is no sin A underneath a cos A
tan = sin/cos so its the cos that is underneath

restive river May 3, 2022, 6:28 PM

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it's a random example
just checking if my math is right
I understand how to prove the identity tho thks

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this is what I meant

turbid locust May 3, 2022, 6:31 PM

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where have you got that from though?

restive river May 3, 2022, 6:33 PM

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restive river it's a random example just checking if my math is right I understand how to pr...

sorry
I edited a message instead of replying

turbid locust May 3, 2022, 6:34 PM

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oh right lol

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1/(1+tan) = cos/(cos+sin)

restive river May 3, 2022, 6:36 PM

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turbid locust 1/(1+tan) = cos/(cos+sin)

so what I did is completely wrong ye?
thks

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turbid locust May 3, 2022, 6:37 PM

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restive river so what I did is completely wrong ye? thks

uhm ye...

devout snowBOT May 3, 2022, 10:47 PM

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stoic crystal May 3, 2022, 11:02 PM

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What is the complement of the intersection between two sets when the sets are disjoint

devout snowBOT May 3, 2022, 11:02 PM

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stoic crystal What is the complement of the intersection between two sets when the sets are di...

distant harbor May 3, 2022, 11:03 PM

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U

stoic crystal May 3, 2022, 11:04 PM

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$(P\cap Q)'$

woven radishBOT May 3, 2022, 11:04 PM

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JUGisMUG

stoic crystal May 3, 2022, 11:04 PM

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P and Q are disjoint

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Oh wait

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The universal?

distant harbor May 3, 2022, 11:05 PM

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ye

stoic crystal May 3, 2022, 11:05 PM

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Ok so a set being disjoint does not affect anything about (P int Q)'

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Thanks

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.close

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devout snowBOT May 5, 2022, 1:31 AM

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dreamy pine May 5, 2022, 1:59 AM

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how do I do c. ii?

devout snowBOT May 5, 2022, 1:59 AM

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dreamy pine how do I do c. ii?

dreamy pine May 5, 2022, 2:00 AM

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cuz theres no values so I dunno if area is possible

devout snowBOT May 5, 2022, 2:15 AM

#

@dreamy pine Has your question been resolved?

devout snowBOT May 5, 2022, 2:45 AM

#

@dreamy pine Has your question been resolved?

devout snowBOT May 5, 2022, 3:57 AM

#

@dreamy pine Has your question been resolved?

devout snowBOT May 5, 2022, 4:57 AM

#

Channel closed

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devout snowBOT May 5, 2022, 1:46 PM

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indigo abyss May 5, 2022, 1:50 PM

#

can someone please explain how to solve this?

devout snowBOT May 5, 2022, 1:50 PM

#

indigo abyss can someone please explain how to solve this?

supple trench May 5, 2022, 1:56 PM

#

symmetry is great sosad u cant use that

west pulsar May 5, 2022, 1:57 PM

#

3*Pi/2 is the only number thats coming to me rn

supple trench May 5, 2022, 1:59 PM

#

think about the period of $r(\theta)$

woven radishBOT May 5, 2022, 1:59 PM

#

vin100

supple trench May 5, 2022, 2:00 PM

#

when 1 is added to $\sin(\theta)$, what are the roots of $r(\theta) = 0$?

woven radishBOT May 5, 2022, 2:00 PM

#

vin100

devout snowBOT May 5, 2022, 2:05 PM

#

@indigo abyss Has your question been resolved?

devout snowBOT May 5, 2022, 2:20 PM

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Channel closed

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tawny horizon May 5, 2022, 2:22 PM

#

yo

devout snowBOT May 5, 2022, 2:22 PM

#

tawny horizon yo

#

Please don't occupy multiple help channels.

main gull May 5, 2022, 2:23 PM

#

tawny horizon yo

Someone was literally helping you in your other channel you had, and asked for your work, if you are still doing that problem

tawny horizon May 5, 2022, 2:23 PM

#

i know how to solve it but how is answer 79.6

tawny horizon May 5, 2022, 2:24 PM

#

main gull Someone was literally helping you in your other channel you had, and asked for y...

my phone aint with me

#

#

thats the problem

main gull May 5, 2022, 2:24 PM

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Show your work on what you did

#

Write it out

#

Paint or something

tawny horizon May 5, 2022, 2:24 PM

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okay

restive river May 5, 2022, 2:24 PM

#

Or @woven radish

tawny horizon May 5, 2022, 2:24 PM

#

i will

#

so

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16400 x 4/100 x 3 /100

main gull May 5, 2022, 2:25 PM

#

restive river Or <@510789298321096704>

Not a lot of users know latex, but if the OP does, that'll be good

tawny horizon May 5, 2022, 2:25 PM

#

=19.68 + 16400

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and compound interest

main gull May 5, 2022, 2:25 PM

#

tawny horizon 16400 x 4/100 x 3 /100

Horribly formatting, need parentheses

tawny horizon May 5, 2022, 2:26 PM

#

16400(1 + 4/100)to the power of 3

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16400

#

how is the answer 79.6

pseudo basin May 5, 2022, 2:28 PM

#

tawny horizon 16400(1 + 4/100)to the power of 3

use ^ for exponents

pseudo basin May 5, 2022, 2:28 PM

#

tawny horizon 16400 x 4/100 x 3 /100

why 3/100?

#

did the investment only last 0.03 years, i.e. eleven or so days?

tawny horizon May 5, 2022, 2:29 PM

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no

pseudo basin May 5, 2022, 2:29 PM

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no, of course not. it lasted 3 years and your calculation should reflect that.

tawny horizon May 5, 2022, 2:29 PM

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its a fraction

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it lasted 3 years

pseudo basin May 5, 2022, 2:30 PM

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yes, but there is no reason to divide the duration by 100.

tawny horizon May 5, 2022, 2:30 PM

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pseudo basin use `^` for exponents

yea forgot ^ ^

pseudo basin May 5, 2022, 2:30 PM

#

also, you calculated the total for one plan, but only the interest for the other. so of course you get bullshit if you try to subtract them.

tawny horizon May 5, 2022, 2:31 PM

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i was doing without adding and subtracting but the ms was telling me otherwise

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@pseudo basin

pseudo basin May 5, 2022, 2:34 PM

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??

tawny horizon May 5, 2022, 2:34 PM

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you just disappeared

pseudo basin May 5, 2022, 2:34 PM

#

wym disappeared

tawny horizon May 5, 2022, 2:34 PM

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are you a helper

pseudo basin May 5, 2022, 2:35 PM

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i never went anywhere

tawny horizon May 5, 2022, 2:35 PM

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?

pseudo basin May 5, 2022, 2:35 PM

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no, i don't have the helper role

#

will you now tell me to fuck off on those grounds?

tawny horizon May 5, 2022, 2:35 PM

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nah

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can you help

pseudo basin May 5, 2022, 2:35 PM

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tawny horizon i was doing without adding and subtracting but the ms was telling me otherwise

i don't know what you mean by this

tawny horizon May 5, 2022, 2:35 PM

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lol

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if you dont mind

pseudo basin May 5, 2022, 2:36 PM

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both because you are being cryptic in showing your work and because i haven't seen your mark scheme

tawny horizon May 5, 2022, 2:36 PM

#

okay i will solve again

#

one sec

#

how do you even draw the answers out on paint

#

can you solve it

#

.close

devout snowBOT May 5, 2022, 2:38 PM

#

Channel closed

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obtuse slate May 5, 2022, 3:18 PM

#

devout snowBOT May 5, 2022, 3:18 PM

#

obtuse slate

obtuse slate May 5, 2022, 3:18 PM

#

lilac heath May 5, 2022, 3:19 PM

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it resembles your pfp

obtuse slate May 5, 2022, 3:20 PM

#

wdym

wooden zodiac May 5, 2022, 3:21 PM

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egg

lilac heath May 5, 2022, 3:21 PM

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oh did i offend you

obtuse slate May 5, 2022, 3:22 PM

#

oh you mean my profile picture?

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i didn't know what pfp means

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lol

#

ellipses = egg

#

<@&286206848099549185>

buoyant coyote May 5, 2022, 3:35 PM

#

obtuse slate

your answer is off by a number

#

you might have calculated something wrong

obtuse slate May 5, 2022, 3:36 PM

#

the major vertices = 4
the minor vertices = 6
Center = (-3,2)

#

is this right?

buoyant coyote May 5, 2022, 3:38 PM

#

obtuse slate the major vertices = 4 the minor vertices = 6 Center = (-3,2)

somethings off

obtuse slate May 5, 2022, 3:38 PM

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did i miscount on the graph?

buoyant coyote May 5, 2022, 3:38 PM

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perhaps

#

count again

buoyant coyote May 5, 2022, 3:40 PM

#

obtuse slate

or you can try graphing your answer and see whats off

obtuse slate May 5, 2022, 3:40 PM

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i think the minor vertices is 12.

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Is the minor vertices the entire length of the ellipse or just the center to the end?

buoyant coyote May 5, 2022, 3:47 PM

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obtuse slate Is the minor vertices the entire length of the ellipse or just the center to the...

pretty sure vertices are points

obtuse slate May 5, 2022, 3:47 PM

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yes but they are ___ amount of spaces away from the center

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im pretty sure I did not miscount

buoyant coyote May 5, 2022, 3:47 PM

#

then try graphing your answer

obtuse slate May 5, 2022, 3:52 PM

#

It looks shorter than the graph given

#

.close

devout snowBOT May 5, 2022, 3:58 PM

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Channel closed

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peak lark May 5, 2022, 4:11 PM

#

https://www.chegg.com/homework-help/questions-and-answers/213-find-sketch-even-odd-parts-following-signals-x-t-xln-1-4-c-x-t-sin-a01-3--e-xn-n-21-d--q29605291

devout snowBOT May 5, 2022, 4:11 PM

#

peak lark https://www.chegg.com/homework-help/questions-and-answers/213-find-sketch-even-o...

peak lark May 5, 2022, 4:11 PM

#

https://www.chegg.com/homework-help/questions-and-answers/124-determine-sketch-even-odd-parts-signals-depicted-figure-p124-label-sketches-carefully--q35161933

devout snowBOT May 5, 2022, 4:26 PM

#

@peak lark Has your question been resolved?

weak tundra May 5, 2022, 4:47 PM

#

peak lark https://www.chegg.com/homework-help/questions-and-answers/124-determine-sketch-e...

• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.```

devout snowBOT May 5, 2022, 4:57 PM

#

@peak lark Has your question been resolved?

devout snowBOT May 5, 2022, 5:57 PM

#

@peak lark Has your question been resolved?

devout snowBOT May 5, 2022, 6:57 PM

#

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restive river May 5, 2022, 7:15 PM

#

devout snowBOT May 5, 2022, 7:15 PM

#

restive river

restive river May 5, 2022, 7:15 PM

#

#

can someone explain this solution

#

for a!=0

#

how do they say that b/a = 0

torn vessel May 5, 2022, 7:21 PM

#

Once you have 1 in the bottom right, do roe operations to make the top right =0

torn vessel May 5, 2022, 7:23 PM

#

restive river how do they say that b/a = 0

Basically, they don’t say b/a = 0, they do row operations to get 0 in that position

restive river May 5, 2022, 7:29 PM

#

torn vessel Basically, they don’t say b/a = 0, they do row operations to get 0 in that posit...

what how

#

what row operation

torn vessel May 5, 2022, 7:30 PM

#

-b/a*R_2 + R_1 —> R_1

restive river May 5, 2022, 7:31 PM

#

whats R_2

#

and R_1

torn vessel May 5, 2022, 7:35 PM

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row 2

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row 1

restive river May 5, 2022, 7:40 PM

#

torn vessel row 2

im still confused

#

so its

torn vessel May 5, 2022, 7:40 PM

#

multiply the second row by -b/a

#

add it to the first row

restive river May 5, 2022, 7:41 PM

#

why is it

#

-b*a

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b/a

torn vessel May 5, 2022, 7:41 PM

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to get 0 in the top right

restive river May 5, 2022, 7:41 PM

#

im so confused

#

if you multiply the second row by -b/a

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wouldn't u get

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0, -b/a

torn vessel May 5, 2022, 7:42 PM

#

yes

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now add that to the first row

restive river May 5, 2022, 7:42 PM

#

but then

#

the second row is still

#

0, -b/a

torn vessel May 5, 2022, 7:42 PM

#

so multiply it by -a/b

restive river May 5, 2022, 7:42 PM

#

oh ok

#

its clicking

#

man thanks a lot

#

u've helped me with at least like 10 problems so far I think

#

much appreciated

#

.close

devout snowBOT May 5, 2022, 7:43 PM

#

Channel closed

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devout snowBOT May 6, 2022, 4:52 AM

#

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mystic dew May 6, 2022, 4:56 AM

#

how would you get started with this?

devout snowBOT May 6, 2022, 4:56 AM

#

mystic dew how would you get started with this?

mystic dew May 6, 2022, 4:57 AM

#

so far I have pulled the n out and make it (2^p/3)^n but I'm not sure what to do from there

crystal rune May 6, 2022, 4:57 AM

#

Maybe some case work

#

p=0, p=1, 0 < p < 1, p > 1

#

(I think)

mystic dew May 6, 2022, 4:58 AM

#

oh so would it just be sort of guess and check?

crystal rune May 6, 2022, 4:59 AM

#

Not really, we're considering all values that p could take

#

Once you do the positive cases, you can do the negative ones similarly

mystic dew May 6, 2022, 5:00 AM

#

ok i'll try that out, ty :)

#

.close

devout snowBOT May 6, 2022, 5:14 AM

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Channel closed

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devout snowBOT May 6, 2022, 4:22 PM

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devout snowBOT May 6, 2022, 4:50 PM

#

orchid sierra May 6, 2022, 4:53 PM

#

What is your question?

#

Do you not know what equation to use?

#

Are you unable to explain your choice?

#

Are you having trouble using the equation?

#

The function takes horizontal distance, d, as an input
And outputs height

#

d is distance from the ramp

#

All stated in the problem, I am just repeating

#

Yes, but use d instead of x

#

Ok. Why did you pick that equation?

#

Since the assignment asks

#

You would do that in both equations

#

But do you mean to say

#

The first two terms become zero immediately and you just read off the third constant term?

#

goo

#

~

#

Ok, what has you stuck though, you were gonna say something

devout snowBOT May 6, 2022, 5:00 PM

#

Channel closed

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solemn onyx May 6, 2022, 5:03 PM

#

The sum of the sides of two squares is 21 cm and the sum of their areas is 225 cm2.
Find the length of a side of the smaller square.

devout snowBOT May 6, 2022, 5:03 PM

#

solemn onyx The sum of the sides of two squares is 21 cm and the sum of their areas is 225 c...

winter patrol May 6, 2022, 5:03 PM

#

what ahve you tried

solemn onyx May 6, 2022, 5:04 PM

#

idk how to form an equation

restive river May 6, 2022, 5:05 PM

#

did u draw

solemn onyx May 6, 2022, 5:05 PM

#

o wait i got it

devout snowBOT May 6, 2022, 5:20 PM

#

@solemn onyx Has your question been resolved?

devout snowBOT May 6, 2022, 5:35 PM

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Channel closed

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oak forum May 6, 2022, 6:03 PM

#

devout snowBOT May 6, 2022, 6:03 PM

#

oak forum

oak forum May 6, 2022, 6:03 PM

#

this is what i've done so far

#

I'm still confused how to manipulate what I've got into the RHS

patent tartan May 6, 2022, 6:07 PM

#

try also writing the RHS in sin/cos form

oak forum May 6, 2022, 6:08 PM

#

ahh okay is the reason I'm struggling because I'm approaching it from the more difficult side?

patent tartan May 6, 2022, 6:09 PM

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nah looks solid so far

#

one way to prove this is to manipulate both LHS and RHS into their basic parts consisting only of sin and cos and then trying to manipulate the resulting fractions

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so leave the LHS as is right now and play around with the RHS

near fern May 6, 2022, 6:13 PM

#

Whats on the LHS side

#

@oak forum

oak forum May 6, 2022, 6:16 PM

#

near fern <@921012659388809237>

tan (A+B).

#

then I've manipulated it

near fern May 6, 2022, 6:16 PM

#

as in whats the question a the paper thing

oak forum May 6, 2022, 6:18 PM

#

near fern as in whats the question a the paper thing

the question is in a booklet, i wrote the question down in the 1st image

near fern May 6, 2022, 6:19 PM

#

can u take a photo?

oak forum May 6, 2022, 6:21 PM

#

near fern can u take a photo?

why the question is in the 1st image, besides theres load of other questions in the booklet on that page that would complicate it.

near fern May 6, 2022, 6:21 PM

#

oh found it k

patent tartan May 6, 2022, 6:36 PM

#

@oak forum did you solve?

oak forum May 6, 2022, 6:37 PM

#

patent tartan <@921012659388809237> did you solve?

nahh i'm still crunching. I think I've hit a brick wall

patent tartan May 6, 2022, 6:38 PM

#

Write the RHS as
$$\frac{\frac{\sin A}{\cos A} + \frac{\sin B}{\cos B}}{1 - \frac{\sin A}{\cos A} \cdot \frac{\sin B}{\cos B}}$$

woven radishBOT May 6, 2022, 6:38 PM

#

nvx

patent tartan May 6, 2022, 6:39 PM

#

Now you only need to multiply and divide the fraction by a specific term to get exactly the LHS

oak forum May 6, 2022, 6:40 PM

#

woven radish **nvx**

I've got to that stage but my brains not working to get over the final hurdle

patent tartan May 6, 2022, 6:40 PM

#

Hint: You want to clear the nested fractions

#

What would you need to multiply the numerator with to clear the nested fractions?

#

if you have something like 1/x + 2/y = 0 what would multiply that equation with to make the denominators disappear?

oak forum May 6, 2022, 6:52 PM

#

am I simply just flipping the nest fraction (denominator) and multiplying the numerator (top fractions ?

devout snowBOT May 6, 2022, 7:07 PM

#

@oak forum Has your question been resolved?

oak forum May 6, 2022, 7:07 PM

#

patent tartan if you have something like 1/x + 2/y = 0 what would multiply that equation with ...

am i multiplying by the denominator ?

#

@patent tartan is this correct ?

#

<@&286206848099549185>

patent tartan May 6, 2022, 7:25 PM

#

Multiply both numerator and denominator by cos(A)cos(B)

#

@oak forum

oak forum May 6, 2022, 7:34 PM

#

patent tartan Multiply both numerator and denominator by cos(A)cos(B)

I still don't understand

#

is my most recent image i sent wrong

oak forum May 6, 2022, 7:38 PM

#

woven radish **nvx**

is it at this step I multiply both the numerator and denominator by cos(A)cos(B) ?

#

@nvx I've finally done it, sorry my severely handicapped brain wasted your time lol

patent tartan May 6, 2022, 7:55 PM

#

@oak forum gj!

devout snowBOT May 6, 2022, 8:18 PM

#

@oak forum Has your question been resolved?

devout snowBOT May 6, 2022, 8:48 PM

#

Channel closed

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• Be polite and have a nice day!

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

silk hull May 6, 2022, 9:54 PM

#

two questions

devout snowBOT May 6, 2022, 9:54 PM

#

silk hull two questions

silk hull May 6, 2022, 9:54 PM

#

firstly

#

e^(3lnx) can be simplified to x^3

#

but e^(3lnx) cannot take some values that x^3 can

#

how does that work

#

secondly

#

i am having trouble rearranging x=(3y-5)/(y+1) to get y

tiny carbon May 6, 2022, 9:55 PM

#

silk hull but e^(3lnx) cannot take some values that x^3 can

Give an example of a value

silk hull May 6, 2022, 9:56 PM

#

-1

tiny carbon May 6, 2022, 9:56 PM

#

-1^(3 * ln(-1)) = -1

silk hull May 6, 2022, 9:56 PM

#

you cant ln a negative

#

or am wrong

magic thicket May 6, 2022, 9:56 PM

#

The constraints stay, so x > 0

silk hull May 6, 2022, 9:56 PM

#

what constraints

silk hull May 6, 2022, 9:57 PM

#

tiny carbon -1^(3 * ln(-1)) = -1

it shouldnt be -1 to the power of it should be e

magic thicket May 6, 2022, 9:57 PM

#

That ln must be defined. As assuming you're studying a function for instance

silk hull May 6, 2022, 9:57 PM

#

so when dealing with lns there must be a domain?

#

and yes this has to do with functions but i was asking about this as an independent equation

#

how does that work when its impossible to have a natural log take a negative value?

tiny carbon May 6, 2022, 9:59 PM

#

It's not impossible..?

silk hull May 6, 2022, 9:59 PM

#

it should be undefined no?

tiny carbon May 6, 2022, 9:59 PM

#

It's just a complex solution

silk hull May 6, 2022, 9:59 PM

#

like dividing by zero?

tiny carbon May 6, 2022, 9:59 PM

#

It is just pi * i

#

I believe

silk hull May 6, 2022, 9:59 PM

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but i is imaginary

tiny carbon May 6, 2022, 9:59 PM

#

So?

#

That doesn't make it impossible

silk hull May 6, 2022, 9:59 PM

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im talking about real answers

magic thicket May 6, 2022, 9:59 PM

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silk hull so when dealing with lns there must be a domain?

The function you're studying has a predetermined domain, and your stick to it normally

silk hull May 6, 2022, 10:00 PM

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x^3 will have a real answer but the e wont

tiny carbon May 6, 2022, 10:00 PM

#

silk hull x^3 will have a real answer but the e wont

It will

#

$e^{3 * ln(x)}$

woven radishBOT May 6, 2022, 10:00 PM

#

Breeziboi

silk hull May 6, 2022, 10:00 PM

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e^(3ln-1) has a real value?

tiny carbon May 6, 2022, 10:00 PM

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Plug in -1

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Yes

silk hull May 6, 2022, 10:00 PM

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my calculator wont compute it

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says math error

tiny carbon May 6, 2022, 10:00 PM

#

silk hull May 6, 2022, 10:01 PM

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it wont compute anything to do with lns that have negative values

tiny carbon May 6, 2022, 10:01 PM

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silk hull it wont compute anything to do with lns that have negative values

You might have imaginary disabled

#

Or something

silk hull May 6, 2022, 10:01 PM

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but thats imaginary i mean

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-1^3 will have a real answer

#

and thats just a simplification of the original right

tiny carbon May 6, 2022, 10:01 PM

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3 * ln(-1) = 3pi * i

silk hull May 6, 2022, 10:02 PM

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how come they give two different answers for the same value

#

if x^3 is just the original equation simplified

tiny carbon May 6, 2022, 10:02 PM

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silk hull how come they give two different answers for the same value

I just said... they have the same answer

tiny carbon May 6, 2022, 10:02 PM

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silk hull if x^3 is just the original equation simplified

It is

silk hull May 6, 2022, 10:02 PM

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no -1^3 is -1

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real answer

tiny carbon May 6, 2022, 10:02 PM

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e^ln(x) = x

silk hull May 6, 2022, 10:02 PM

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e^(3ln-1) has an imaginary answer right

tiny carbon May 6, 2022, 10:02 PM

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Use exponent laws

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Since there is a 3 in the exponent

#

Just take it out like so:

silk hull May 6, 2022, 10:03 PM

#

#

natural logs cannot take negative values and give real answers

#

what am i missing here

tiny carbon May 6, 2022, 10:04 PM

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silk hull natural logs cannot take negative values and give real answers

Complex is not the same as undefined

silk hull May 6, 2022, 10:04 PM

#

but what i dont understand is

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how come the answer for the same input (-1) is different depending on whether u input it into the simplified equation or the original one

#

shouldnt both give the same answers since theyre just the same equation one is just simplified?

tiny carbon May 6, 2022, 10:05 PM

#

silk hull how come the answer for the same input (-1) is different depending on whether u ...

I don't think you understand, they give the exact same answers

silk hull May 6, 2022, 10:05 PM

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no one gives a complex the other gives a real answer

#

thats not the same?

tiny carbon May 6, 2022, 10:05 PM

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silk hull no one gives a complex the other gives a real answer

Complex exponent, the answer is real

silk hull May 6, 2022, 10:05 PM

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but -1^3 is just -1

tiny carbon May 6, 2022, 10:06 PM

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silk hull but -1^3 is just -1

So is e^(3ln(-1))

silk hull May 6, 2022, 10:06 PM

#

is the exponent not part of the answer?

magic thicket May 6, 2022, 10:06 PM

#

silk hull no one gives a complex the other gives a real answer

e^(3ln(-1)) = e^3(i pi) = e^pi i = -1

silk hull May 6, 2022, 10:06 PM

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no it isnt

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wait

#

how

tiny carbon May 6, 2022, 10:06 PM

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Theres a proof

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Somewhere

silk hull May 6, 2022, 10:06 PM

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how is e^pi i equal to minus 1

tiny carbon May 6, 2022, 10:06 PM

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for e^(pi * i) = -1

silk hull May 6, 2022, 10:06 PM

#

are you sure?

tiny carbon May 6, 2022, 10:06 PM

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Yes

silk hull May 6, 2022, 10:07 PM

#

wtf

magic thicket May 6, 2022, 10:07 PM

#

ln -1 = i pi (1+2n) for any n. You can take any n because they're all valid

silk hull May 6, 2022, 10:07 PM

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is that just something youre supposed to know?

magic thicket May 6, 2022, 10:07 PM

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silk hull is that just something youre supposed to know?

That's basic complex numbers

tiny carbon May 6, 2022, 10:07 PM

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silk hull is that just something youre supposed to know?

It's one of the more famous things in math I guess

silk hull May 6, 2022, 10:07 PM

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magic thicket ln -1 = i pi (1+2n) for any n. You can take any n because they're all valid

so no matter what n is the answer will always be -1?

magic thicket May 6, 2022, 10:08 PM

#

Because x -> e^ix is 2pi periodic

silk hull May 6, 2022, 10:08 PM

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what does periodic mean

magic thicket May 6, 2022, 10:10 PM

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f is T periodic iff for all x in its domain, x+T is also in the domain and f(x) = f(x+T)

silk hull May 6, 2022, 10:10 PM

#

ok

#

now on to my second question

#

should be less theoretical im just stuck on rearranging an equation

#

i am having trouble rearranging x=(3y-5)/(y+1) to get y

#

i brought y+1 to the left side

#

so now i have x(y+1) = 3y-5

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but im stuck with ys on both sides

magic thicket May 6, 2022, 10:12 PM

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y depends on x, that's to be expected

silk hull May 6, 2022, 10:12 PM

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i need to isolate y tho

#

and i dunno how to get rid of the xy and 3y

#

to get just y

#

ive literally been staring at xy+x = 3y-5 for ten minutes

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all ive done in ten minutes is expand x(y+1) and im not sure thats brought me any closer

magic thicket May 6, 2022, 10:13 PM

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silk hull all ive done in ten minutes is expand x(y+1) and im not sure thats brought me an...

It has

silk hull May 6, 2022, 10:13 PM

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my problem is the xy and the 3y

magic thicket May 6, 2022, 10:13 PM

#

Then you can write (x-3)y and there is only one y

silk hull May 6, 2022, 10:14 PM

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where did you get (x-3)y from

magic thicket May 6, 2022, 10:14 PM

#

Just move the 3y to the other side and factor y out

tiny carbon May 6, 2022, 10:15 PM

#

https://www.youtube.com/watch?v=v0YEaeIClKY

YouTube

3Blue1Brown

e^(iπ) in 3.14 minutes, using dynamics | DE5

Euler's formula about e to the i pi, explained with velocities to positions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://www.3blue1brown.com

Not familiar with the calculus referenced in this video? Try takin...

▶ Play video

silk hull May 6, 2022, 10:15 PM

#

ill watch that

#

trying to figure out (x-3)y tho even if u move it to the other sid

#

side*

#

u still have an x

#

u didnt account for

#

did u move that too

magic thicket May 6, 2022, 10:17 PM

#

silk hull ive literally been staring at xy+x = 3y-5 for ten minutes

xy-3y = 5-x
(x-3)y = 5-x
y = (5-x)/(x-3)

silk hull May 6, 2022, 10:17 PM

#

u moved the lone x to the right hand side right?

#

the x that was on the left side of the equation

magic thicket May 6, 2022, 10:17 PM

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Yes of course

silk hull May 6, 2022, 10:17 PM

#

and then divided by the (x-3)

#

ok i see

#

didnt see it before

#

might be braindead

#

thanks for the help

magic thicket May 6, 2022, 10:18 PM

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Just consider both x and y as constants. It's a little extra abstraction but the math is the same

silk hull May 6, 2022, 10:18 PM

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got it

silk hull May 6, 2022, 10:28 PM

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magic thicket xy-3y = 5-x (x-3)y = 5-x y = (5-x)/(x-3)

its y=(-5-x)/(x-3) right?

#

i think u missed a minus

magic thicket May 6, 2022, 10:28 PM

#

Yes

silk hull May 6, 2022, 10:28 PM

#

ok thank you

devout snowBOT May 6, 2022, 10:44 PM

#

@silk hull Has your question been resolved?

devout snowBOT May 6, 2022, 10:59 PM

#

Channel closed

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devout snowBOT May 7, 2022, 3:07 PM

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restive river May 7, 2022, 3:21 PM

#

<@&286206848099549185>

devout snowBOT May 7, 2022, 3:21 PM

#

restive river <@&286206848099549185>

restive river May 7, 2022, 3:30 PM

#

could it be 10km/h + 2km/h = 12 km/h, t= s/v= 18/12= 1,5 - answer for the 2nd one?

cold bough May 7, 2022, 3:30 PM

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yes you got it

restive river May 7, 2022, 3:30 PM

#

thank you so much!

cold bough May 7, 2022, 3:30 PM

#

restive river thank you so much!

no problem

devout snowBOT May 7, 2022, 3:45 PM

#

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runic turtle May 7, 2022, 4:02 PM

#

ive got a question

devout snowBOT May 7, 2022, 4:02 PM

#

runic turtle ive got a question

runic turtle May 7, 2022, 4:02 PM

#

#

how would you solve this

magic thicket May 7, 2022, 4:09 PM

#

this is not an equation, what do you mean by "solve"

runic turtle May 7, 2022, 4:12 PM

#

it says write equation in simplest form

restive river May 7, 2022, 4:21 PM

#

make them both have the same denom

solid vapor May 7, 2022, 4:21 PM

#

multiply top and bottom by 4 - root 3

runic turtle May 7, 2022, 4:23 PM

#

oh mb i found it already

#

.close

devout snowBOT May 7, 2022, 4:23 PM

#

Channel closed

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pliant gyro May 7, 2022, 4:30 PM

#

Hi there

devout snowBOT May 7, 2022, 4:30 PM

#

pliant gyro Hi there

pliant gyro May 7, 2022, 4:30 PM

#

#

I am asking about (b)

#

I am first considering the absolute value of it and I get that it is equal to sum (1 / |a^ln(n)|)
Can I just say here that it is like 1/q^n which converges?
or is it different because ln(n) tends to inf slower than n?

pseudo basin May 7, 2022, 4:34 PM

#

a^ln(n) is not exponential in n so yes your argument falls apart

#

in fact it is equal to n^ln(a)

pliant gyro May 7, 2022, 4:40 PM

#

I see

pliant gyro May 7, 2022, 4:40 PM

#

pseudo basin in fact it is equal to n^ln(a)

How do you get there exactly?

pseudo basin May 7, 2022, 4:41 PM

#

$a^{\ln(n)} = e^{\ln(a)\ln(n)} = e^{\ln(n)\ln(a)} = n^{\ln(a)}$

woven radishBOT May 7, 2022, 4:41 PM

#

Ann

pliant gyro May 7, 2022, 4:41 PM

#

hmmm

#

e^ln

#

yeah

#

that's a good trick.

#

Thanks Ann

pliant gyro May 7, 2022, 4:44 PM

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pseudo basin in fact it is equal to n^ln(a)

In that case, using the fact than a > 1 we can see that ln(a) > 0

pseudo basin May 7, 2022, 4:44 PM

#

yes

pliant gyro May 7, 2022, 4:44 PM

#

But that does not help right?

#

I mean it does

pseudo basin May 7, 2022, 4:45 PM

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it does

pliant gyro May 7, 2022, 4:45 PM

#

but does not say if it converges or not

#

since we don't know if it is smaller than 1 or bigger

pseudo basin May 7, 2022, 4:45 PM

#

well you have absolute convergence for a>e

pliant gyro May 7, 2022, 4:46 PM

#

which is 1 yeah

#

But if a < e it does not

#

So in that case I need to split into cases?

pseudo basin May 7, 2022, 4:48 PM

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you have an alternating series

#

and the sequence 1/n^ln(a) goes to 0, and monotonically at that, no matter what a is (so long as it's above 1)

pliant gyro May 7, 2022, 4:53 PM

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But you can not assure it is above 1

#

We already learned in class that for a exponent > 1 it converges.

pseudo basin May 7, 2022, 5:02 PM

#

pliant gyro But you can not assure it is above 1

a>1 is given

#

and a being above 1 is what i was referring to

pliant gyro May 7, 2022, 5:04 PM

#

I think I do understand what you're saying

#

Let me send something

#

pliant gyro May 7, 2022, 5:05 PM

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pseudo basin well you have absolute convergence for a>e

As you said before, it depends if a > e of not

#

Is that correct?

pseudo basin May 7, 2022, 5:06 PM

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...................

#

the ratio of adjacent terms tends to 1 regardless of the value of a

#

and the limit of b_n is 0 for all a > 1 regardless of whether or not a > e

pliant gyro May 7, 2022, 5:08 PM

#

pliant gyro

I meant to write > 1 or < 1, mb

pliant gyro May 7, 2022, 5:08 PM

#

pseudo basin the ratio of adjacent terms tends to 1 regardless of the value of a

Yeah I know

#

But we learned that the sequence must be decreasing

pseudo basin May 7, 2022, 5:09 PM

#

$1/n^p$ is a decreasing sequence for all positive $p$

woven radishBOT May 7, 2022, 5:09 PM

#

Ann

pseudo basin May 7, 2022, 5:09 PM

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yes even when 0<p<1

#

ive repeated this like three times already

pliant gyro May 7, 2022, 5:10 PM

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Oh yeah

#

it decreases anyways.

#

Sorry... my bad here..

#

To sum it up:
The series is converging absolutely if a > e and converging conditionally if a <= e?

pseudo basin May 7, 2022, 5:17 PM

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yes

#

and my energy has converged to zero

pliant gyro May 7, 2022, 5:20 PM

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pseudo basin and my energy has converged to zero

lol

#

Then I am done asking you for today

#

cya tomorrow 🙂

#

Thanks for the help

#

.clsoe

#

.close

devout snowBOT May 7, 2022, 5:20 PM

#

Channel closed

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tall dawn May 7, 2022, 5:25 PM

#

hi, can aynone tell me what how to solve this

devout snowBOT May 7, 2022, 5:25 PM

#

tall dawn hi, can aynone tell me what how to solve this

tall dawn May 7, 2022, 5:34 PM

#

which role

mighty harness May 7, 2022, 5:34 PM

#

tall dawn hi, can aynone tell me what how to solve this

Feels like overkill with L'hospital. Just note that the numerator is larger than $\sqrt{ h}$ for positive $h$

tall dawn May 7, 2022, 5:35 PM

#

you mean this. no i don't

woven radishBOT May 7, 2022, 5:35 PM

#

GUNILLA62

mighty harness May 7, 2022, 5:36 PM

#

Sure but the expression is always negative for negative h

tall dawn May 7, 2022, 5:36 PM

#

they gave us hint. wait a sec

#

Determine the limit value by first simplifying and then extending the rational expression so that you can use the conjugate rule.

mighty harness May 7, 2022, 5:37 PM

#

Sorry I got a sign wrong

#

Dont mind me

tall dawn May 7, 2022, 5:38 PM

#

mighty harness Sorry I got a sign wrong

its fine. 🙂

#

ok, but how

#

ok

hybrid snow May 7, 2022, 5:45 PM

#

When in doubt with an indeterminate form, use L'Hopital

tall dawn May 7, 2022, 5:56 PM

#

oooh, the picture disappeared

devout snowBOT May 7, 2022, 6:11 PM

#

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devout snowBOT May 8, 2022, 11:14 AM

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nimble narwhal May 8, 2022, 11:19 AM

#

A restaurant receives 8 cartons of milk daily. On a random day, the number of cartons with a defective screw cap among them is equal to 2. One of the employees picks up 2 cartons.
a) What is the probability that the employee receives more than 1 milk carton with the defect?
b) What is the probability that the employee receives exactly 0 defective milk cartons if the employee receives 1 or fewer milk cartons with the defect?
c) What is the expected number of cartons with the defect?
d) Calculate the variance of the number of defective milk cartons.

devout snowBOT May 8, 2022, 11:19 AM

#

nimble narwhal A restaurant receives 8 cartons of milk daily. On a random day, the number of ca...

nimble narwhal May 8, 2022, 11:20 AM

#

No idea how to come any closer to the answer. previous task asked about the p of 0 defected cartons, I got it correct, 0,536

devout snowBOT May 8, 2022, 11:35 AM

#

@nimble narwhal Has your question been resolved?

nimble narwhal May 8, 2022, 11:41 AM

#

<@&286206848099549185>

marsh linden May 8, 2022, 11:59 AM

#

mighty harness Feels like overkill with L'hospital. Just note that the numerator is larger than...

lhopitals. it’s a 0/0 situation.
you’ll get -1/2 I think

marsh linden May 8, 2022, 12:01 PM

#

nimble narwhal A restaurant receives 8 cartons of milk daily. On a random day, the number of ca...

so for n = 2
it’s 2/8 * 1/7

#

b) for n = 1
it’s 2/8 * 6/7 = 3/14 = 6/28
for n = 0
it’s 6/8 * 5/7 = 15/28
so total probability of clause is 21/28 = 3/4
answer is 15/28 divided by 3/4 (bayes theorem)

#

c) 1/4 * 2 + 3/14 * 1 = 5/7 . so almost 1

#

d)use your calc or the formula for variance

#

@nimble narwhal

mighty harness May 8, 2022, 12:12 PM

#

marsh linden lhopitals. it’s a 0/0 situation. you’ll get -1/2 I think

Yeah that works. A first degree Taylor expansion of sqrt(2+x) works as well

marsh linden May 8, 2022, 12:13 PM

#

mighty harness Yeah that works. A first degree Taylor expansion of sqrt(2+x) works as well

did you mean mac expansion (taylor expansion with fn(0) ) ?

#

but I feel like expansions for 0/0 or infinite /infinite limits are a bit of an overkill

#

but hey, if it works, it works

nimble narwhal May 8, 2022, 12:20 PM

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I didn't really got c. b is also saying wrong (it is a homework where I get if the answer is correct right away)

nimble narwhal May 8, 2022, 12:36 PM

#

@marsh linden

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<@&286206848099549185>

tiny carbon May 8, 2022, 12:55 PM

#

.close

devout snowBOT May 8, 2022, 12:55 PM

#

Channel closed

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tiny carbon May 8, 2022, 12:55 PM

#

You have a much more recent channel

devout snowBOT May 8, 2022, 12:56 PM

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#

wooden veldt May 8, 2022, 1:15 PM

#

Take the standard parameterization of a cone

#

And mess with it to get it to look like the one you want

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dense trout May 8, 2022, 1:36 PM

#

I have a question, does the converse of the power rule true for all natural numbers n?

devout snowBOT May 8, 2022, 1:36 PM

#

dense trout I have a question, does the converse of the power rule true for all natural numb...

dense trout May 8, 2022, 1:37 PM

#

<@&286206848099549185>

#

.close

devout snowBOT May 8, 2022, 1:40 PM

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Channel closed

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normal sleet May 8, 2022, 2:31 PM

#

Could someone check if it’s right

devout snowBOT May 8, 2022, 2:31 PM

#

normal sleet Could someone check if it’s right

normal sleet May 8, 2022, 2:32 PM

#

#

Just rough sketch

#

Don’t mind the extra lines

twin flame May 8, 2022, 2:37 PM

#

This looks good, I would just mark on the maximum turning point coordinates and the point at x=4 where it has a root

normal sleet May 8, 2022, 2:41 PM

#

Ok tysm

#

.close

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mighty harness May 8, 2022, 2:46 PM

#

marsh linden did you mean mac expansion (taylor expansion with fn(0) ) ?

Didn't think I would need to specify it since there is no other natural choice of point to do the expansion around. I personally prefer using Taylor over l'hopitals when I can since Taylor expansions are more useful in other parts of analysis

devout snowBOT May 8, 2022, 2:46 PM

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mighty harness Didn't think I would need to specify it since there is no other natural choice o...

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@mighty harness Has your question been resolved?

devout snowBOT May 8, 2022, 3:16 PM

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craggy quiver May 8, 2022, 3:26 PM

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uh

devout snowBOT May 8, 2022, 3:26 PM

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craggy quiver uh

craggy quiver May 8, 2022, 3:26 PM

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if cos(x) = cos(-x)

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why does cos(a-x) not equal cos(a+x)

green inlet May 8, 2022, 3:27 PM

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I think it might be because the cos(a-x) starts at a minus going to a plus while cos(a+x) starts with a plus going to a minus

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Or vice versa

winter patrol May 8, 2022, 3:28 PM

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-(a-x) isn't a+x

placid narwhal May 8, 2022, 3:28 PM

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Let $a - x = s$
$cos(s) = cos(-s)$
Substitite back

woven radishBOT May 8, 2022, 3:28 PM

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Pluton

craggy quiver May 8, 2022, 3:33 PM

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winter patrol -(a-x) isn't a+x

oh whops

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how did i mess that up lol

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thank

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s

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.close

devout snowBOT May 8, 2022, 3:33 PM

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Channel closed

Closed by @craggy quiver

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bitter night May 8, 2022, 3:53 PM

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Hello I need help

devout snowBOT May 8, 2022, 3:53 PM

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bitter night

bitter night May 8, 2022, 3:54 PM

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I got

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32 1/8 as my answer

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But it says A is the answer

shrewd dock May 8, 2022, 3:55 PM

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subtract 8 7/8 from 23 1/4

bitter night May 8, 2022, 3:55 PM

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Sir I did

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I got 257/8

shrewd dock May 8, 2022, 3:55 PM

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start with whole numbers first

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23-8

main gull May 8, 2022, 3:55 PM

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bitter night 32 1/8 as my answer

Provide work

bitter night May 8, 2022, 3:55 PM

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15

shrewd dock May 8, 2022, 3:56 PM

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1/4 - 7/8

bitter night May 8, 2022, 3:56 PM

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5/8

bitter night May 8, 2022, 3:56 PM

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main gull Provide work

Alright look

shrewd dock May 8, 2022, 3:58 PM

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okay so break 1 off 23

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to get 4/4

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it would be 22 4/4+1/4

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22 5/4

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now you go from there

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22 5/4 - 8 7/8

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now 22 - 8

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14

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now you do 5/4 - 7/8

main gull May 8, 2022, 4:00 PM

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shrewd dock now 22 - 8

Don't do the work for people

main gull May 8, 2022, 4:01 PM

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shrewd dock 22 5/4 - 8 7/8

This was sufficient

bitter night May 8, 2022, 4:01 PM

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Welp

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8 7/8 - 23 1/4 = 71/8 -182/8= 13 7/8

shrewd dock May 8, 2022, 4:01 PM

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he already tried it himself and i think he knows 22-8

bitter night May 8, 2022, 4:01 PM

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That's what I got

bitter night May 8, 2022, 4:01 PM

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shrewd dock he already tried it himself and i think he knows 22-8

14

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But it's 23

shrewd dock May 8, 2022, 4:01 PM

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no

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you're subtracting 8 from 23

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not 23 from 8

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its 23 1/4 - 8 7/8

bitter night May 8, 2022, 4:02 PM

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WhT

bitter night May 8, 2022, 4:02 PM

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shrewd dock its 23 1/4 - 8 7/8

Yes

shrewd dock May 8, 2022, 4:02 PM

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so why this 8 7/8 - 23 1/4

bitter night May 8, 2022, 4:03 PM

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Wdym why this

shrewd dock May 8, 2022, 4:03 PM

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is this your old work?

bitter night May 8, 2022, 4:03 PM

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No

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I look

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I solved the mixed numbers

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Then

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Found a LCM

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And subtracted them

shrewd dock May 8, 2022, 4:03 PM

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do constants first

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then fractions

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dont mix right away

bitter night May 8, 2022, 4:04 PM

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Hmmm

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So

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1/4 - 7/8

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First

shrewd dock May 8, 2022, 4:04 PM

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sure

bitter night May 8, 2022, 4:04 PM

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?

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Alright

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So

shrewd dock May 8, 2022, 4:04 PM

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but you dont want a negative

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because you cant have negative rope

bitter night May 8, 2022, 4:05 PM

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Right

shrewd dock May 8, 2022, 4:05 PM

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so you need to take one from 23

bitter night May 8, 2022, 4:05 PM

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So other way around

shrewd dock May 8, 2022, 4:05 PM

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no

bitter night May 8, 2022, 4:05 PM

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Okay

shrewd dock May 8, 2022, 4:05 PM

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you need to take one from 23

bitter night May 8, 2022, 4:05 PM

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One from 23

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Then

shrewd dock May 8, 2022, 4:05 PM

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1/4

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so

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4/4 = 1 yes

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?

bitter night May 8, 2022, 4:05 PM

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Ye

shrewd dock May 8, 2022, 4:05 PM

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so does 1/4 belong to 23 or 8

bitter night May 8, 2022, 4:06 PM

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23 ig

shrewd dock May 8, 2022, 4:06 PM

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yep

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so take one from 23

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23-1

bitter night May 8, 2022, 4:06 PM

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22

shrewd dock May 8, 2022, 4:06 PM

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that 1 just equals 4/4 now okay

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so give me the full equation now

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with the 22 and 4/4

bitter night May 8, 2022, 4:07 PM

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22 4/4 - 8 7/8

shrewd dock May 8, 2022, 4:07 PM

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whered the 1/4 go

bitter night May 8, 2022, 4:07 PM

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Wha

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You said 4/4

shrewd dock May 8, 2022, 4:08 PM

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1 = 4/4 correct

bitter night May 8, 2022, 4:08 PM

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Yes

shrewd dock May 8, 2022, 4:08 PM

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but we started with 23 1/4

bitter night May 8, 2022, 4:08 PM

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Right

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Alright

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23 1/4 - 8 7/8

shrewd dock May 8, 2022, 4:08 PM

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now should be (22 1/4 + 4/4) - (8 7/8)

bitter night May 8, 2022, 4:09 PM

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Alright

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So

shrewd dock May 8, 2022, 4:09 PM

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you cant just get rid of the 1/4 understand?

bitter night May 8, 2022, 4:09 PM

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Got it

shrewd dock May 8, 2022, 4:09 PM

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so subtract the constants now and tell me what you get

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when I say constants i mean non fraction numbers

bitter night May 8, 2022, 4:10 PM

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10/8 - 7/8 = 3/8

bitter night May 8, 2022, 4:10 PM

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shrewd dock when I say constants i mean non fraction numbers

💀💀💀

shrewd dock May 8, 2022, 4:10 PM

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well yes that is correct for the fractions

bitter night May 8, 2022, 4:10 PM

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Welp

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My bad

shrewd dock May 8, 2022, 4:10 PM

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thats correct now do the whole numbers

bitter night May 8, 2022, 4:10 PM

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22-8 = 14

shrewd dock May 8, 2022, 4:10 PM

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now combine those two solutions

bitter night May 8, 2022, 4:10 PM

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14 3/8

shrewd dock May 8, 2022, 4:10 PM

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there it is

bitter night May 8, 2022, 4:11 PM

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Wow

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We got A

shrewd dock May 8, 2022, 4:11 PM

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do you understand it though

bitter night May 8, 2022, 4:11 PM

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Kind off

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One thing I didn't understood is

shrewd dock May 8, 2022, 4:11 PM

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you need to take one away from the constants because you cannot find a negative fraction without having negative rope as well

bitter night May 8, 2022, 4:11 PM

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Why did we take One from 23

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And how the whole 4/4

shrewd dock May 8, 2022, 4:11 PM

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because 4 divided by 4 equals 1

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4/4 = 1

bitter night May 8, 2022, 4:12 PM

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Yeah so

shrewd dock May 8, 2022, 4:12 PM

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so we turn one into its fraction form

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we are given its fraction form with 1/4

bitter night May 8, 2022, 4:12 PM

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Hmmm

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I see

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Tysm

shrewd dock May 8, 2022, 4:12 PM

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yes any further qs?

bitter night May 8, 2022, 4:12 PM

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Nah that's it

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You can close this channel now

shrewd dock May 8, 2022, 4:12 PM

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okay best of luck with the rest

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.close

devout snowBOT May 8, 2022, 4:12 PM

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Channel closed

Closed by @shrewd dock

Use .reopen if this was a mistake.

bitter night May 8, 2022, 4:12 PM

#

Tysm

devout snowBOT May 8, 2022, 4:13 PM

#

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dull flax May 8, 2022, 4:15 PM

#

I'm trying to find the coefficient of x^5 in the expansion of (1 + x + x^2)^8 and I think I've reduced it to finding the number of natural number solutions to y_0 + 2y_1 + 3y_2 = 13, but I'm not sure how to do that. Could someone give me a hint?

devout snowBOT May 8, 2022, 4:15 PM

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dull flax I'm trying to find the coefficient of x^5 in the expansion of (1 + x + x^2)^8 an...

placid narwhal May 8, 2022, 4:18 PM

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Well id treat it as binom

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$$(x^2 + (1 + x))^8$$
So we get
$$x^{16} + {8 \choose 1}x^{14}(1 + x) + {8 \choose 2}x^{12}(1 + x)^2 ... + (1 + x)^8$$

woven radishBOT May 8, 2022, 4:22 PM

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Pluton

placid narwhal May 8, 2022, 4:23 PM

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Maybe it helped maybe it didnt

restive river May 8, 2022, 4:24 PM

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if i'm right you can consider the polynom f(x) = 1 + x + x^2 as a 3-vector (1,1,1), let A be (1,1,1) then we can consider the vector associated with f(x)^2 as the convolution between A and A.
So the vector associated with f(x)^8 would be foundd by making A = convolution(A,A) 3 times in a row (because 8 = 2^3) then the sixth value of the final vector A would be the coefficient of x^5 in the expanded polynom

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it's been only 24 hour i know what is a convulotion so maybe i'm wrong though xd

placid narwhal May 8, 2022, 4:26 PM

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We ignore first few so we focus only on
$$(1 + x)^8 + {8 \choose 1}x^2(1 + x)^7 + {8 \choose 2}x^4(1 + x)^6$$

woven radishBOT May 8, 2022, 4:26 PM

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Pluton

placid narwhal May 8, 2022, 4:28 PM

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$$(1 + x)^8$$ has coefficient of $x^5$ as ${8 \choose 5}$

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Now just calculate for other ones

woven radishBOT May 8, 2022, 4:28 PM

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Pluton

devout snowBOT May 8, 2022, 4:33 PM

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@dull flax Has your question been resolved?

restive river May 8, 2022, 4:35 PM

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>>> import numpy as np
>>> a = np.array([1,1,1])
>>> for i in range(3) :
...     a = np.convolve(a,a)
>>> print(a)
[   1    8   36  112  266  504  784 1016 1107 1016  784  504  266  112
   36    8    1]```

restive river May 8, 2022, 4:35 PM

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restive river ```py >>> import numpy as np >>> a = np.array([1,1,1]) >>> for i in range(3) : ....

well i guess that works

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i'm responding to the guy that want a way to calculate the coefficient of x^5 :(

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so sorry

marsh linden May 8, 2022, 4:52 PM

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mighty harness Didn't think I would need to specify it since there is no other natural choice o...

fairs

devout snowBOT May 8, 2022, 5:03 PM

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@dull flax Has your question been resolved?

devout snowBOT May 8, 2022, 6:03 PM

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@dull flax Has your question been resolved?

dull flax May 8, 2022, 6:27 PM

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<@&286206848099549185>

dull flax May 8, 2022, 6:28 PM

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dull flax I'm trying to find the coefficient of x^5 in the expansion of (1 + x + x^2)^8 an...

this is the question

devout snowBOT May 8, 2022, 8:28 PM

#

@dull flax Has your question been resolved?

devout snowBOT May 8, 2022, 10:28 PM

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Channel closed

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devout snowBOT May 9, 2022, 2:28 AM

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devout snowBOT May 9, 2022, 3:14 AM

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atomic river May 9, 2022, 3:14 AM

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oops

devout snowBOT May 9, 2022, 3:14 AM

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Channel closed

Closed due to the original message being deleted

atomic river May 9, 2022, 3:14 AM

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ok

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this

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didn’t mean to send the second pic, only the frost

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anyways i thought that you just do the integral from 2 to 6, which gives you choice A

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but that’s wrong, and the right answer is C and i’m confused why

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<@&286206848099549185>

crimson drift May 9, 2022, 3:17 AM

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dont @ helpers until no one responds for 15 mins

atomic river May 9, 2022, 3:17 AM

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it’s 11:17 at night

zealous oyster May 9, 2022, 3:18 AM

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So

atomic river May 9, 2022, 3:18 AM

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nobody’s on

zealous oyster May 9, 2022, 3:19 AM

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The integral from 2 to 6 seems right conceptually. Maybe double check your work?

proper lark May 9, 2022, 3:19 AM

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Total difference takes into account the negative area as well.

crimson drift May 9, 2022, 3:19 AM

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that doesnt mean you can do that, theres rules for a reason

atomic river May 9, 2022, 3:19 AM

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it’s a calculator question

crimson drift May 9, 2022, 3:19 AM

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then use symbolab lol

atomic river May 9, 2022, 3:19 AM

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wdym mmao

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it’s not abt plugging it in

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like doing integral from 2 to 6 is wrong

zealous oyster May 9, 2022, 3:19 AM

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Are you using radians

atomic river May 9, 2022, 3:19 AM

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yes

proper lark May 9, 2022, 3:19 AM

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Doing the integral from 2 to 6 is wrong yes.

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Because there are roots in between 2 to 6

atomic river May 9, 2022, 3:20 AM

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proper lark Total difference takes into account the negative area as well.

wait idk what this means

proper lark May 9, 2022, 3:20 AM

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that you need to account for

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Look at the roots between 2 to 6

atomic river May 9, 2022, 3:20 AM

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the roots?

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should i graph it

proper lark May 9, 2022, 3:20 AM

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Screen_Shot_2022-05-08_at_11.20.39_PM.png

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precisely

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From 2 to 6

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it has 3 roots

atomic river May 9, 2022, 3:21 AM

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i see but how does that

proper lark May 9, 2022, 3:21 AM

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Take the absolute value

atomic river May 9, 2022, 3:21 AM

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of

zealous oyster May 9, 2022, 3:21 AM

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Ohhhh distance and not displacement

proper lark May 9, 2022, 3:21 AM

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yes

zealous oyster May 9, 2022, 3:21 AM

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I get it now

proper lark May 9, 2022, 3:21 AM

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total distance

zealous oyster May 9, 2022, 3:21 AM

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Right

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Yeah listen to this guy

atomic river May 9, 2022, 3:21 AM

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wait i’m not like

zealous oyster May 9, 2022, 3:22 AM

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The velocity is changing from negative to positive to negative to positive so the displacement will be around 0. Hence why you got a small number for A

proper lark May 9, 2022, 3:22 AM

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When you graph the velocity of an object, the area is considered the amount of distance traveled. Seeing as he is moving right to left, -

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yes what he said.

atomic river May 9, 2022, 3:23 AM

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ohhh i understand

zealous oyster May 9, 2022, 3:23 AM

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So to get total distance you need to do absolute value so the negative adds to the distance instead of subtract

atomic river May 9, 2022, 3:24 AM

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ok ok ima do that

devout snowBOT May 9, 2022, 3:24 AM

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gleaming grove May 9, 2022, 3:40 AM

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hiya, the problem is finding the extrema of $$f(x,y,z)=\abs{2x+y+z-2}$$ subject to the constraints $$y^2-xz=1$$ and $$z^2-xy=1$$ using lagrange multipliers

devout snowBOT May 9, 2022, 3:40 AM

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gleaming grove hiya, the problem is finding the extrema of $$f(x,y,z)=\abs{2x+y+z-2}$$ subject ...

woven radishBOT May 9, 2022, 3:40 AM

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dino