#help-10 | Mathematics | Page 460

tacit root Oct 29, 2021, 12:07 PM

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if you get (f(-x) = f(x)), then the function is even

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otherwise, it is neither

warm shaleBOT Oct 29, 2021, 12:07 PM

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ricey

tacit root Oct 29, 2021, 12:08 PM

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so evaluate ( \dfrac{(-x)^2 - 9}{(-x)-5} ) and check if it is equal to (- \left(\dfrac{x^2 - 9}{x-5} \right))

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@karmic plover as above

karmic plover Oct 29, 2021, 12:09 PM

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tacit root <@!896517328261488730> as above

yyeah, on my end it turned out odd

warm shaleBOT Oct 29, 2021, 12:09 PM

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ricey

tacit root Oct 29, 2021, 12:09 PM

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great, so are you able to sketch the curve?

karmic plover Oct 29, 2021, 12:09 PM

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siince the negative on the denom x moves out

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oh yeah i did it, and confirmed with the help of desmos

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.close

obtuse pebbleBOT Oct 29, 2021, 12:09 PM

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obtuse pebbleBOT Oct 29, 2021, 12:55 PM

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sonic coyote Oct 29, 2021, 1:08 PM

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a+b+c=0 also means that a^3 + b^3 + c^3 = 3abc ?

obtuse pebbleBOT Oct 29, 2021, 1:08 PM

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sonic coyote a+b+c=0 also means that a^3 + b^3 + c^3 = 3abc ?

fervent cradle Oct 29, 2021, 1:10 PM

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no

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wait

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maybe

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no

stuck owl Oct 29, 2021, 1:11 PM

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expanding (a+b+c)^3 we get a bunch of terms so probably not

fervent cradle Oct 29, 2021, 1:11 PM

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because let a = 1, b = 0, c = -1

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then you get 1 + -1

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and 3 * -1

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so it doesn't work

stuck owl Oct 29, 2021, 1:11 PM

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b = 0

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RHS becomes 0 so try like b = 1

fervent cradle Oct 29, 2021, 1:12 PM

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what

stuck owl Oct 29, 2021, 1:12 PM

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and c = -2

fervent cradle Oct 29, 2021, 1:12 PM

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what are you on about

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wait fuck

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yes

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you're right

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ok

sonic coyote Oct 29, 2021, 1:13 PM

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thanks

fervent cradle Oct 29, 2021, 1:13 PM

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wait

sonic coyote Oct 29, 2021, 1:13 PM

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.close

obtuse pebbleBOT Oct 29, 2021, 1:13 PM

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stuck owl Oct 29, 2021, 1:14 PM

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rip (a,b,c) = (1, 1, -2) doesn't work

obtuse pebbleBOT Oct 29, 2021, 1:45 PM

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stuck owl Oct 29, 2021, 1:48 PM

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if anyone was wondering about the previous problem

obtuse pebbleBOT Oct 29, 2021, 1:48 PM

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stuck owl if anyone was wondering about the previous problem

stuck owl Oct 29, 2021, 1:48 PM

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.close

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wise holly Oct 29, 2021, 1:58 PM

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how do I know if they specify a function

obtuse pebbleBOT Oct 29, 2021, 1:58 PM

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wise holly how do I know if they specify a function

cold thistle Oct 29, 2021, 2:03 PM

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There’s a neat trick called the vertical line test

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If you can draw a vertical line at any point and it touches the curve more than once, it is NOT a function

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Because every input in a function has exactly one output

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So in 16. for example, you can draw a vertical line anywhere and it will only ever touch that line once

wise holly Oct 29, 2021, 2:07 PM

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so if I understand that correctly, then only 17 and 18 don't specify functions

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is that correct?

cold thistle Oct 29, 2021, 2:07 PM

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Mhm

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If you plug 0 into the function in 17, you get three answers

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Which violates intergalactic law or someth

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It’s because the way functions are defined, each input can only have one output

stray cave Oct 29, 2021, 2:09 PM

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sonic coyote a+b+c=0 also means that a^3 + b^3 + c^3 = 3abc ?

no

cold thistle Oct 29, 2021, 2:10 PM

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Aleph this channel is being used for a different question

wise holly Oct 29, 2021, 2:10 PM

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thanks for your answer

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.close

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sick mantle Oct 29, 2021, 2:14 PM

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Is 4 a multiple of 4?

obtuse pebbleBOT Oct 29, 2021, 2:14 PM

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sick mantle Is 4 a multiple of 4?

rugged kite Oct 29, 2021, 2:14 PM

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yes

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4 = 4*1

sick mantle Oct 29, 2021, 2:14 PM

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Alright, thanks, that's it! :D

timid silo Oct 29, 2021, 2:14 PM

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are adjacent angles supplementry?

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yes rite

cold thistle Oct 29, 2021, 2:15 PM

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Angles are supplementary when their measures add up to 180°

timid silo Oct 29, 2021, 2:15 PM

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cold thistle Angles are supplementary when their measures add up to 180°

ok thnks

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https://tenor.com/view/reject-modernity-return-to-monke-monke-gif-19167526

Tenor

covert river Oct 29, 2021, 2:27 PM

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f(x)=1/x differentiated is -1/x^2?

obtuse pebbleBOT Oct 29, 2021, 2:32 PM

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@sick mantle Has your question been resolved?

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obtuse pebbleBOT Oct 29, 2021, 3:06 PM

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@steady marsh Has your question been resolved?

obtuse pebbleBOT Oct 29, 2021, 3:21 PM

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ebon agate Oct 29, 2021, 3:27 PM

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what does taking a linearization of a function mean?
same as differentiating a function?

obtuse pebbleBOT Oct 29, 2021, 3:27 PM

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ebon agate what does taking a linearization of a function mean? same as differentiating a f...

ebon agate Oct 29, 2021, 3:27 PM

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num 1.

obtuse pebbleBOT Oct 29, 2021, 3:42 PM

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@ebon agate Has your question been resolved?

ebon agate Oct 29, 2021, 3:44 PM

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<@&286206848099549185>

obtuse pebbleBOT Oct 29, 2021, 4:14 PM

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@ebon agate Has your question been resolved?

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obtuse pebbleBOT Oct 29, 2021, 4:48 PM

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austere folio Oct 29, 2021, 4:57 PM

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?

obtuse pebbleBOT Oct 29, 2021, 4:57 PM

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austere folio ?

austere folio Oct 29, 2021, 4:57 PM

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.close

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austere folio Oct 29, 2021, 4:57 PM

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lol

obtuse pebbleBOT Oct 29, 2021, 5:07 PM

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steady marsh Oct 29, 2021, 5:20 PM

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For this function, is there no easier way to find any Inflection Points? I found the second derivative, and I'm not sure if I'm doing this correctly...

obtuse pebbleBOT Oct 29, 2021, 5:20 PM

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steady marsh For this function, is there no easier way to find any Inflection Points? I found...

steady marsh Oct 29, 2021, 5:20 PM

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#

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This is the work I've done
and I'm not sure how to proceed... since the denominator goes to 0 at x=0, am I allowed to just see when the numerator is 0?
and so I guess there are no points of inflection since x=0 and x=6 are both disallowed in the denominator
I'm not sure

obtuse pebbleBOT Oct 29, 2021, 5:35 PM

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@steady marsh Has your question been resolved?

steady marsh Oct 29, 2021, 5:56 PM

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.close

obtuse pebbleBOT Oct 29, 2021, 5:56 PM

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timid silo Oct 29, 2021, 6:03 PM

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The vector k · v → has a length of 1.
Calculate the length v → and the number k, if v → = (6, 8)

obtuse pebbleBOT Oct 29, 2021, 6:03 PM

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timid silo The vector k · v → has a length of 1. Calculate the length v → and the number k,...

timid silo Oct 29, 2021, 6:04 PM

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<@&286206848099549185>

atomic hemlock Oct 29, 2021, 6:04 PM

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hey i might look dumb but is √108 + √12 is √130 right?

steady marsh Oct 29, 2021, 6:05 PM

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atomic hemlock hey i might look dumb but is √108 + √12 is √130 right?

Channel's occupied

steady marsh Oct 29, 2021, 6:05 PM

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timid silo The vector k · v → has a length of 1. Calculate the length v → and the number k,...

Do you know how to calculate a unit vector?

timid silo Oct 29, 2021, 6:05 PM

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not really

steady marsh Oct 29, 2021, 6:05 PM

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Okay, so imagine you're going to the store

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and you see a 6 pack of eggs for 12 dollars

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How much would you be paying for one egg?

timid silo Oct 29, 2021, 6:06 PM

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12 dollars

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wai no

steady marsh Oct 29, 2021, 6:06 PM

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one egg

timid silo Oct 29, 2021, 6:06 PM

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i pay 12 dollar*6

steady marsh Oct 29, 2021, 6:06 PM

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it's a 6 pack

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6 eggs for 12 dollars

timid silo Oct 29, 2021, 6:06 PM

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ahaaaaa

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XDD

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wait

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so for 1 egg its 2 dollars

steady marsh Oct 29, 2021, 6:07 PM

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yeah, and how did you find that out?

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what calculation did you do?

timid silo Oct 29, 2021, 6:07 PM

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i did

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wait

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i like

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took a amout of eggs

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and did this

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egg/price

steady marsh Oct 29, 2021, 6:08 PM

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Well, egg/price or price/egg?

timid silo Oct 29, 2021, 6:08 PM

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price/egg

steady marsh Oct 29, 2021, 6:08 PM

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yeah! and you found out that one egg costs 2 dollars by doing 12/6, right?

timid silo Oct 29, 2021, 6:08 PM

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yes

steady marsh Oct 29, 2021, 6:08 PM

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so calculating a unit vector is the same idea, really

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you take a vector and divide it by it's own magnitude

timid silo Oct 29, 2021, 6:09 PM

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but how im supposed to divaide this The vector k · v → has a length of 1.
Calculate the length v → and the number k, if v → = (6, 8)

steady marsh Oct 29, 2021, 6:09 PM

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so if I had a vector of length 6, and I divided it by its own length, then I'd be doing 6/6

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which would give me a length of 1, right?

timid silo Oct 29, 2021, 6:09 PM

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yea

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so i do 6/6 and 8/6

steady marsh Oct 29, 2021, 6:09 PM

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Not quite

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How do you calculate the magnitude of a vector?

timid silo Oct 29, 2021, 6:10 PM

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wait

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a=(a1,a2)

steady marsh Oct 29, 2021, 6:10 PM

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the magnitude is a single number

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it's a scalar

timid silo Oct 29, 2021, 6:10 PM

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yes

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so

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wait i still dont get it

steady marsh Oct 29, 2021, 6:12 PM

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okay, so the magnitude of a vector is given by

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$\sqrt{a^{2}+b^{2}}$

warm shaleBOT Oct 29, 2021, 6:12 PM

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QLightningWolf44

timid silo Oct 29, 2021, 6:12 PM

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aaa

steady marsh Oct 29, 2021, 6:12 PM

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where a, and b, are the components of the vector

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so how would you calculate the magnitude

timid silo Oct 29, 2021, 6:13 PM

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wait now im lost

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in school we use

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$\sqrt{x^{2}+y^{2}}$

warm shaleBOT Oct 29, 2021, 6:13 PM

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Amon

steady marsh Oct 29, 2021, 6:13 PM

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yeah yeah it's the same thing!

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(x, y) and (a, b) are just different variables that are the same idea

timid silo Oct 29, 2021, 6:14 PM

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aha

steady marsh Oct 29, 2021, 6:14 PM

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warm shale **Amon**

this is correct

timid silo Oct 29, 2021, 6:14 PM

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i just got a little bit lost sorry

steady marsh Oct 29, 2021, 6:14 PM

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no worries!

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so what's the magnitude then?

timid silo Oct 29, 2021, 6:14 PM

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steady marsh where a, and b, are the components of the vector

so 6 is a^2

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and 8 is y^2

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?

steady marsh Oct 29, 2021, 6:15 PM

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not quite, a is 6 and b is 8

timid silo Oct 29, 2021, 6:15 PM

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aha

steady marsh Oct 29, 2021, 6:15 PM

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you must square them and take the square root of them added together

timid silo Oct 29, 2021, 6:15 PM

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wait

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3.74165738677

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so we can basically say 3.74

steady marsh Oct 29, 2021, 6:16 PM

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what

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how are you getting that?

timid silo Oct 29, 2021, 6:16 PM

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wait

steady marsh Oct 29, 2021, 6:16 PM

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6^2 + 8^2 is 100

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and the square root of 100 is 10

timid silo Oct 29, 2021, 6:16 PM

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ytes

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yes

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it is

steady marsh Oct 29, 2021, 6:17 PM

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so the unit vector would be (6/10, 8/10)

timid silo Oct 29, 2021, 6:17 PM

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aha

steady marsh Oct 29, 2021, 6:17 PM

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because remember, you're dividing the vector by its own magnitude

timid silo Oct 29, 2021, 6:17 PM

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yea

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so its 0,6 and 0,8?

steady marsh Oct 29, 2021, 6:18 PM

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yep

timid silo Oct 29, 2021, 6:19 PM

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so what now

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that is all?

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but wait

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its wrong

steady marsh Oct 29, 2021, 6:20 PM

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k is 1/10

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that should be it

timid silo Oct 29, 2021, 6:20 PM

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its not wrong

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u are right

steady marsh Oct 29, 2021, 6:20 PM

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the unit vector is 1/10 (6, 8)

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1/10 is a scalar

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it scales the vector

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hence, scalar

timid silo Oct 29, 2021, 6:20 PM

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oki doki

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thanks for help

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how do i close it?

steady marsh Oct 29, 2021, 6:22 PM

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.close

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just type that

timid silo Oct 29, 2021, 6:22 PM

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oki

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thanks

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.close

obtuse pebbleBOT Oct 29, 2021, 6:22 PM

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Channel closed

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obtuse pebbleBOT Oct 29, 2021, 7:35 PM

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topaz forge Oct 29, 2021, 7:38 PM

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I don’t understand

obtuse pebbleBOT Oct 29, 2021, 7:38 PM

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topaz forge I don’t understand

topaz forge Oct 29, 2021, 7:38 PM

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I don’t under stand this**

forest sinew Oct 29, 2021, 7:50 PM

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do you have any idea about part a?

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i mean how to start or any thinking about it

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can you think of a way given some amount of money how many things you can buy?

obtuse pebbleBOT Oct 29, 2021, 7:56 PM

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@topaz forge Has your question been resolved?

topaz forge Oct 29, 2021, 8:00 PM

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forest sinew can you think of a way given some amount of money how many things you can buy?

I started by sorting them but I got stumped

obtuse pebbleBOT Oct 29, 2021, 8:00 PM

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timid silo Oct 29, 2021, 8:06 PM

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$$\begin{aligned}xy'=2y\ y=x^{2}\end{aligned}$$

obtuse pebbleBOT Oct 29, 2021, 8:06 PM

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timid silo $$\begin{aligned}xy'=2y\\ y=x^{2}\end{aligned}$$

warm shaleBOT Oct 29, 2021, 8:06 PM

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BadBanana

timid silo Oct 29, 2021, 8:06 PM

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so why is the bottom expression not a solution to the differential equation at x = 0

spiral maple Oct 29, 2021, 8:09 PM

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because y=0 is the equilibrium solution

timid silo Oct 29, 2021, 8:09 PM

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The book I'm using says "Be sure to state the common interval for which the solution and diffeq make sense"

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what does that mean

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sorry if thats a dumb question the book hasnt used that term

spiral maple Oct 29, 2021, 8:10 PM

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if y=0, y'=0 so 0=0 means it's a solution for initial condition y(0)=0

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equilibrium solutions are constant solutions.

timid silo Oct 29, 2021, 8:11 PM

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if its a constant solution why is it excluded from the interval

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im not following

spiral maple Oct 29, 2021, 8:11 PM

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cause you start on an equilibrium, so you stay on the equilbrium

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instead of following a curved path

timid silo Oct 29, 2021, 8:14 PM

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sorry you need to dumb this down more. Is it similar to how in a piecewise function there can be a solution to both "parts" of the function but a discontinuity still exists?

spiral maple Oct 29, 2021, 8:14 PM

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alternatively when you actually solve the DE you have to divide by x, so you remove the fact x=0 from the y=x^2 solution

spiral maple Oct 29, 2021, 8:15 PM

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timid silo sorry you need to dumb this down more. Is it similar to how in a piecewise funct...

no, DE has solutions depending on the initial condition

ie depending on where you start dictates what curve is the solution

timid silo Oct 29, 2021, 8:16 PM

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do you have a visual example?

spiral maple Oct 29, 2021, 8:16 PM

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sure

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$xy'=2y$

warm shaleBOT Oct 29, 2021, 8:16 PM

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Mosh

spiral maple Oct 29, 2021, 8:17 PM

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if y=0, then you can easily check it's a solution. and this solution has y(0)=0, so if the IVP had y(0)=0 as the condition, then you know the solution is just y=0

timid silo Oct 29, 2021, 8:19 PM

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okay what is the IVP

spiral maple Oct 29, 2021, 8:19 PM

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initial value problem

timid silo Oct 29, 2021, 8:20 PM

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so the y = x^2

spiral maple Oct 29, 2021, 8:20 PM

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no

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that's a solution.

timid silo Oct 29, 2021, 8:20 PM

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y = 0 then?

spiral maple Oct 29, 2021, 8:20 PM

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y=0 is also a solution.

timid silo Oct 29, 2021, 8:20 PM

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oh man

spiral maple Oct 29, 2021, 8:20 PM

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IVP is the DE and initial condition...

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$f(x,y,y')=g(x,y,y') \ y(0)=y_0$

warm shaleBOT Oct 29, 2021, 8:20 PM

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Mosh

spiral maple Oct 29, 2021, 8:21 PM

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or whatever initial condition you have

timid silo Oct 29, 2021, 8:22 PM

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hmm I havent seen any of this yet in the book. I might need to plug away and return when I have more of the vocabulary down.

spiral maple Oct 29, 2021, 8:22 PM

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Ok

timid silo Oct 29, 2021, 8:23 PM

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I have a note on the some of the term you used so when they come up all have something to refer back to

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thank though

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.close

obtuse pebbleBOT Oct 29, 2021, 8:23 PM

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Channel closed

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raven plume Oct 29, 2021, 8:28 PM

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''Find the probability of different numbers' fall when a pair of standard dice is thrown twice repeatedly ''
I apologize for my poor language, can someone explain me how can I solve that problem?

obtuse pebbleBOT Oct 29, 2021, 8:28 PM

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raven plume ''Find the probability of different numbers' fall when a pair of standard dice ...

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@raven plume Has your question been resolved?

tired shell Oct 29, 2021, 8:44 PM

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go through it one dice at a time

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if you want the different* numbers on the dice, what numbers can the first one be?

#

once you've answered that question and picked a number, do the same for the other dice

raven plume Oct 29, 2021, 8:55 PM

#

$\frac{6}{6}\frac{5}{6}=\frac{5}{6}$ and for the second time, $\frac{5}{6}\frac{4*3}{36}$

warm shaleBOT Oct 29, 2021, 8:55 PM

#

tired shell Oct 29, 2021, 8:56 PM

#

yup!

raven plume Oct 29, 2021, 8:56 PM

#

thanks for help mate

#

I appraciate that

#

.close

obtuse pebbleBOT Oct 29, 2021, 8:58 PM

#

Channel closed

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austere drum Oct 29, 2021, 9:06 PM

#

Hi, could somebody please help me with the following problem?

Where I am right now is I think the recurrence relation could be something like: a(n) = a(n-2) + a(n-1) because a(n-2)-1 would be all the steps needed to turn off the light at position n (-1 because you don't have to turn off the first light in this case) plus 1 (because you do have to turn off the light at position n)

obtuse pebbleBOT Oct 29, 2021, 9:06 PM

#

austere drum Hi, could somebody please help me with the following problem? Where I am right ...

austere drum Oct 29, 2021, 9:06 PM

#

#

But I think I am going in the wrong direction and am quite lost

unique solstice Oct 29, 2021, 9:14 PM

#

Say that each light if its on or off is just represented as a 0 or 1

#

So this is the five lights initially

#

11111

#

So just thinking about how many turns itd take to turn off light n and all before assuming theyre all on

#

n=1
11111
01111
One switch

#

n=2
11111
00111
Two switches

#

n=3
11111
01111
01011
11011
10011
00011
Six switches

obtuse pebbleBOT Oct 29, 2021, 9:27 PM

#

@austere drum Has your question been resolved?

unique solstice Oct 29, 2021, 9:27 PM

#

n=4
11111
10111
00111
00101
10101
11101
01101
01001
11001
10001
00001
Eleven switches

#

It kinda looks like it adds on 2 more to the rate each time

austere drum Oct 29, 2021, 9:33 PM

#

So because the rate of change was 5 switches when n=4 when n=5 the rate of change will be 7 switches and so
n=5
Eighteen switches?

unique solstice Oct 29, 2021, 9:34 PM

#

Thats my thinking

austere drum Oct 29, 2021, 9:36 PM

#

So could the recurrence relation be described as something like:
a(n) = [a(n-1) - a(n-2)] + 2 ?

#

Wait

#

I think it would be a(n) = a(n-1) + [a(n-1) - a(n-2)] + 2

#

YEAH THATS IT

#

THANK YOU

unique solstice Oct 29, 2021, 9:39 PM

#

Epic

austere drum Oct 29, 2021, 9:39 PM

#

.close

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#

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terse yoke Oct 29, 2021, 9:42 PM

#

can someone please tell me if the cross product would satisfy the cartesian equation?

obtuse pebbleBOT Oct 29, 2021, 9:42 PM

#

terse yoke can someone please tell me if the cross product would satisfy the cartesian equa...

#

@terse yoke Has your question been resolved?

terse yoke Oct 29, 2021, 9:57 PM

#

<@&286206848099549185>

terse yoke Oct 29, 2021, 10:24 PM

#

.close

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dense stone Oct 29, 2021, 10:31 PM

#

.reopen

#

obtuse pebbleBOT Oct 29, 2021, 10:31 PM

#

dense stone

dense stone Oct 29, 2021, 10:31 PM

#

help i don’t understand

#

i did 38+90

#

which is 128

#

then did 180-128 and got 52

#

and it’s wrong

#

idk how to do it

brave bramble Oct 29, 2021, 10:33 PM

#

Why 38 + 90?

#

Remember the angles in a triangle sum to 180.

slender badge Oct 29, 2021, 10:33 PM

#

52 is the interior angle, x is the exterior

dense stone Oct 29, 2021, 10:34 PM

#

oh

#

so how do i get the exterior

#

like how do i set it up

jagged marsh Oct 29, 2021, 10:35 PM

#

dense stone like how do i set it up

A straight line always forms a 180° angle

dense stone Oct 29, 2021, 10:35 PM

#

yeah

slender badge Oct 29, 2021, 10:35 PM

#

52+x = 180

jagged marsh Oct 29, 2021, 10:35 PM

#

So if the sum of all interior angles is 180°, x interior would be 52°

brave bramble Oct 29, 2021, 10:35 PM

#

Well, you'll want the interior angle first. The interior angles in a triangle sum to 180.

dense stone Oct 29, 2021, 10:36 PM

#

how do i find c

#

X

#

**

slender badge Oct 29, 2021, 10:37 PM

#

dense stone how do i find c

52+x = 180

brave bramble Oct 29, 2021, 10:37 PM

#

Before finding x, you should find the interior angle

#

Gotta take more than one step on this one

dense stone Oct 29, 2021, 10:37 PM

#

ok so the interior is 128

#

right?

jagged marsh Oct 29, 2021, 10:37 PM

#

dense stone ok so the interior is 128

How much is left to 180?

brave bramble Oct 29, 2021, 10:37 PM

#

The interior angles in a triangle sum to 180.

dense stone Oct 29, 2021, 10:37 PM

#

oh

#

ok

dense stone Oct 29, 2021, 10:37 PM

#

jagged marsh How much is left to 180?

uh

brave bramble Oct 29, 2021, 10:38 PM

#

So, consider calling that angle "c" or something, and write an equation

dense stone Oct 29, 2021, 10:38 PM

#

ok

#

so

#

x+52=180? and x would be 128 i’m so confused

#

??

jagged marsh Oct 29, 2021, 10:39 PM

#

yup

dense stone Oct 29, 2021, 10:39 PM

#

oh woah

#

so is 128 the answer or?-

jagged marsh Oct 29, 2021, 10:39 PM

#

yup

dense stone Oct 29, 2021, 10:39 PM

#

tysm!!

jagged marsh Oct 29, 2021, 10:39 PM

#

It’s the exterior angle

dense stone Oct 29, 2021, 10:39 PM

#

this rlly helped

#

.close

obtuse pebbleBOT Oct 29, 2021, 10:39 PM

#

Channel closed

Closed by @dense stone

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obtuse pebbleBOT Oct 29, 2021, 11:00 PM

#

Available help channel!

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dim cairn Oct 29, 2021, 11:01 PM

#

how would i solve this quickly?

obtuse pebbleBOT Oct 29, 2021, 11:01 PM

#

dim cairn how would i solve this quickly?

whole scroll Oct 29, 2021, 11:15 PM

#

dim cairn how would i solve this quickly?

Are you familiar with logarithms?

obtuse pebbleBOT Oct 29, 2021, 11:20 PM

#

@dim cairn Has your question been resolved?

obtuse pebbleBOT Oct 29, 2021, 11:35 PM

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ruby minnow Oct 29, 2021, 11:38 PM

#

Sorry for asking too many questions
Prove that equation 3x^5 -x^3 =1 has at least one solution

Sorry someone told me to use IVT

So I decided to set interval as [0,2]

f(0)=0
f(2)= 88

obtuse pebbleBOT Oct 29, 2021, 11:38 PM

#

ruby minnow Sorry for asking too many questions Prove that equation 3x^5 -x^3 =1 has at lea...

ruby minnow Oct 29, 2021, 11:39 PM

#

What should I do next? I'm confused pls help

spiral maple Oct 29, 2021, 11:40 PM

#

so not sure how you got f(0)=0...

#

$f(x):=3x^5-x^3-1$

warm shaleBOT Oct 29, 2021, 11:40 PM

#

Mosh

ruby minnow Oct 29, 2021, 11:40 PM

#

Oh

#

I ignored that -1

#

Because I thought

#

Something else

#

Okay

#

-1 and 87

#

But

#

Why did I take interval as 0 and2

spiral maple Oct 29, 2021, 11:42 PM

#

idk

ruby minnow Oct 29, 2021, 11:42 PM

#

Oh

spiral maple Oct 29, 2021, 11:42 PM

#

you just provided me with an interval

ruby minnow Oct 29, 2021, 11:42 PM

#

Nope I thought I can use 0 and 2 because there was 1 on the RHS

#

How else can i prove it?

spiral maple Oct 29, 2021, 11:42 PM

#

you just find any interval that works for IVT

#

it's an odd degree polynomial, so it has at least 1 R root

ruby minnow Oct 29, 2021, 11:43 PM

#

spiral maple you just find any interval that works for IVT

Um how can I find it, sorry

#

I watched YouTube video but in that they had interval specified

#

Already in the questions

#

And my teacher didnt teach this ;-;

spiral maple Oct 29, 2021, 11:44 PM

#

trial and error

ruby minnow Oct 29, 2021, 11:45 PM

#

Oh okay, I just need to find the values of x that make the equation equal to zero

#

Sorry if I sound dumb

spiral maple Oct 29, 2021, 11:46 PM

#

No, you're showing that there's at least one solution

#

you're never asked to find the solution ~~cause you likely cant algebraically~~

ruby minnow Oct 29, 2021, 11:47 PM

#

Oh

#

Ok

#

Thank you so muchh!

#

.close

obtuse pebbleBOT Oct 29, 2021, 11:47 PM

#

Channel closed

Closed by @ruby minnow

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• Be polite and have a nice day!

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leaden bay Oct 29, 2021, 11:56 PM

#

obtuse pebbleBOT Oct 29, 2021, 11:56 PM

#

leaden bay

leaden bay Oct 29, 2021, 11:57 PM

#

how should I approach proving this?

leaden bay Oct 29, 2021, 11:59 PM

#

spiral maple you're never asked to find the solution ~~cause you likely cant algebraically~~

bolzano epic

#

i have tried squeeze theorem but i a stuck, i think i need to make an epsilon somwóehow

#

<@&286206848099549185>

sour mortar Oct 30, 2021, 12:26 AM

#

well, to proof, you'd need to investigate the properties of the functions you don't even know

#

but there is a way to calculate it

#

if f, g are continuous and well behaved

#

blobsweat

sour mortar Oct 30, 2021, 12:27 AM

#

leaden bay <@&286206848099549185>

sully

upbeat plinth Oct 30, 2021, 12:29 AM

#

f,g are sequences not functions on R

sour mortar Oct 30, 2021, 12:29 AM

#

upbeat plinth f,g are sequences not functions on R

bleak

leaden bay Oct 30, 2021, 12:33 AM

#

I am certain that this holds true

#

But i can't show it properly

#

Math prof: homework is going to be easy

#

Homework 1st exercise: prove the Riemann hypothesis

#

opencry

sour mortar Oct 30, 2021, 12:44 AM

#

leaden bay Homework 1st exercise: prove the Riemann hypothesis

isleep

#

2nd exercise: solve the Navier Stokes problem

#

realshit

leaden bay Oct 30, 2021, 12:47 AM

#

Hilbert's twenty-fourth problem is a mathematical problem that was not published as part of the list of 23 problems known as Hilbert's problems but was included in David Hilbert's original notes. The problem asks for a criterion of simplicity in mathematical proofs and the development of a proof theory with the power to prove that a given proof is the simplest possible.[1

sour mortar Oct 30, 2021, 12:47 AM

#

so, if you still want to solve that question

#

then I can try help you

#

I'm just not sure if it'll be the correct way

leaden bay Oct 30, 2021, 12:47 AM

#

I made like

#

Cooked up proofs lmao

#

But they're far from academically correct omes

sour mortar Oct 30, 2021, 12:48 AM

#

I see

#

try #proofs-and-logic and see if someone can help you there

#

I mean, most likely this questions is not just to show the limit evaluates to e^k algebraically

dim cairn Oct 30, 2021, 12:50 AM

#

whole scroll Are you familiar with logarithms?

yeah

#

wait. what do i do now KEK

leaden bay Oct 30, 2021, 12:52 AM

#

Yeah i eill do that thank!

#

.close

obtuse pebbleBOT Oct 30, 2021, 12:52 AM

#

Channel closed

Closed by @leaden bay

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#

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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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.

astral siren Oct 30, 2021, 1:16 AM

#

Hi

obtuse pebbleBOT Oct 30, 2021, 1:16 AM

#

astral siren Hi

astral siren Oct 30, 2021, 1:16 AM

#

clear inlet Oct 30, 2021, 1:17 AM

#

what have you tried ? what do you want help with? show your work

astral siren Oct 30, 2021, 1:18 AM

#

clear inlet what have you tried ? what do you want help with? show your work

I have doubt how to do HD

clear inlet Oct 30, 2021, 1:18 AM

#

have you learned matrix multiplication

astral siren Oct 30, 2021, 1:18 AM

#

Is it juts to 2,2 or while matrices

#

Yes

#

I got 1/4g

#

But not sure how to do hd

#

@clear inlet

#

Is -15/8

#

?

clear inlet Oct 30, 2021, 1:27 AM

#

don't ping me

astral siren Oct 30, 2021, 1:27 AM

#

?

#

Is it correct or

#

Not

#

Hello??

spiral maple Oct 30, 2021, 1:34 AM

#

astral siren Hello??

You gonna post your working like you were asked to or...?

astral siren Oct 30, 2021, 1:35 AM

#

But is it correct

spiral maple Oct 30, 2021, 1:35 AM

#

idk how you expect to get help without giving everything that's relevant.

astral siren Oct 30, 2021, 1:35 AM

#

spiral maple idk how you expect to get help without giving everything that's relevant.

I did the working and I got that value is it right or not

spiral maple Oct 30, 2021, 1:35 AM

#

can I see the working?

#

cause that's what is being asked by the people trying to help you

#

If you dont want help that's less work for me to do, so I'm fine with not helping.

astral siren Oct 30, 2021, 1:41 AM

#

I figured nvm

spiral maple Oct 30, 2021, 1:41 AM

#

ok...

astral siren Oct 30, 2021, 1:42 AM

#

I have another question

#

I don’t get how to do

#

#

Can u help

spiral maple Oct 30, 2021, 1:43 AM

#

is it a test..?

astral siren Oct 30, 2021, 1:44 AM

#

No

spiral maple Oct 30, 2021, 1:45 AM

#

ok... what have you tried then?

timid silo Oct 30, 2021, 1:47 AM

#

astral siren Can u help

what's the simplest case you can think of to use for matrix A

spiral maple Oct 30, 2021, 1:47 AM

#

???

timid silo Oct 30, 2021, 1:48 AM

#

if they can't abstractly think about the question, then try using some defined matrix

spiral maple Oct 30, 2021, 1:48 AM

#

I mean sure, but that wont answer the question

#

also I was waiting for a response from them instead of talking to the void...

timid silo Oct 30, 2021, 1:49 AM

#

there was a guy like that last night 😔

spiral maple Oct 30, 2021, 1:49 AM

#

Cool

astral siren Oct 30, 2021, 1:50 AM

#

What

spiral maple Oct 30, 2021, 1:50 AM

#

spiral maple ok... what have you tried then?

.

astral siren Oct 30, 2021, 1:50 AM

#

I don’t get it

spiral maple Oct 30, 2021, 1:50 AM

#

What have you attempted?

astral siren Oct 30, 2021, 1:50 AM

#

I don’t understand what to do

spiral maple Oct 30, 2021, 1:50 AM

#

Find A^(-1) if it exists.

astral siren Oct 30, 2021, 1:59 AM

#

Ok

#

Then

obtuse pebbleBOT Oct 30, 2021, 2:14 AM

#

@astral siren Has your question been resolved?

astral siren Oct 30, 2021, 2:23 AM

#

@spiral maple

#

Is it option 2?

spiral maple Oct 30, 2021, 2:23 AM

#

no.

plain owl Oct 30, 2021, 2:25 AM

#

It isn’t unique right?

astral siren Oct 30, 2021, 2:28 AM

#

spiral maple no.

Then?

#

4?

spiral maple Oct 30, 2021, 2:29 AM

#

Yes..

obtuse pebbleBOT Oct 30, 2021, 2:29 AM

#

Channel closed

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• Be polite and have a nice day!

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timid silo Oct 30, 2021, 2:46 AM

#

obtuse pebbleBOT Oct 30, 2021, 2:46 AM

#

timid silo

timid silo Oct 30, 2021, 2:47 AM

#

I'm tryna learn induction before I actually learn it in class so I understand it better then, so I'm not entirely sure how to start this

#

How would I get the LHS?

#

do I use the sums of arithemtic formula?

#

i know i substitute (1) in

obtuse pebbleBOT Oct 30, 2021, 3:07 AM

#

@timid silo Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 3:22 AM

#

Channel closed

Closed due to timeout

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timid silo Oct 30, 2021, 3:24 AM

#

.reopen

obtuse pebbleBOT Oct 30, 2021, 3:24 AM

#

✅

timid silo Oct 30, 2021, 3:27 AM

#

<@&286206848099549185>

sour mortar Oct 30, 2021, 3:28 AM

#

timid silo How would I get the LHS?

just sub n = 1

#

on both sides and you find they're indeed equal

timid silo Oct 30, 2021, 3:29 AM

#

yeah but just in the (2n-1) part?

#

@sour mortar

#

sorry for the ping idk how to get your attention

sour mortar Oct 30, 2021, 3:30 AM

#

timid silo yeah but just in the (2n-1) part?

this is the LHS

sour mortar Oct 30, 2021, 3:30 AM

#

timid silo sorry for the ping idk how to get your attention

you can reply directly to my message

timid silo Oct 30, 2021, 3:31 AM

#

yeah i got the RHS

#

just (1)^2

#

but im confused on the LHS

sour mortar Oct 30, 2021, 3:31 AM

#

oh, I messed up

#

LHS indeed on the 2n -1 part

#

then it will be equal to 1

timid silo Oct 30, 2021, 3:31 AM

#

ty

sour mortar Oct 30, 2021, 3:32 AM

#

the thing is, when n = 1, then the 3, 5 kinda DNE

#

because they appear when n assumes greater values

#

it is just a form of representing the sum

timid silo Oct 30, 2021, 3:32 AM

#

tysm that makes sense

#

appreciate you

obtuse pebbleBOT Oct 30, 2021, 3:47 AM

#

@timid silo Has your question been resolved?

#

Channel closed

Closed by @junior barn

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Remember:
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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.

ember glacier Oct 30, 2021, 4:11 AM

#

need help on what to do on this question

obtuse pebbleBOT Oct 30, 2021, 4:11 AM

#

ember glacier need help on what to do on this question

ember glacier Oct 30, 2021, 4:11 AM

#

#

<@&286206848099549185>

sour mortar Oct 30, 2021, 4:26 AM

#

ember glacier

do you remember chain rule for partial differentiation?

ember glacier Oct 30, 2021, 4:26 AM

#

no i don't think i know it

sour mortar Oct 30, 2021, 4:28 AM

#

so, I recommend you doing it like a tree

#

#

then you can use the values given by the table and solve the question

ember glacier Oct 30, 2021, 4:31 AM

#

ok im going to attempt it

#

@sour mortar

#

i got 3p+rd

#

is that correct?

sour mortar Oct 30, 2021, 4:37 AM

#

ember glacier is that correct?

I didn't calculate anything

#

but I can try

ember glacier Oct 30, 2021, 4:38 AM

#

can you check to see if i did it correct

sour mortar Oct 30, 2021, 4:39 AM

#

ember glacier i got 3p+rd

#

it is correct

ember glacier Oct 30, 2021, 4:40 AM

#

oh sweet

#

is it ok for me to ask u another similar question or do i have to go into a different channel

#

its a question i already did but i have doubts if my answer is correct or not

sour mortar Oct 30, 2021, 4:41 AM

#

I need to sleep now

#

but you can post on this same channel since it is still ocuppied by you

#

maybe use .close and .reopen

#

https://tenor.com/view/joaquin-phoenix-laughing-pain-unhappy-sad-gif-16287601

Tenor

ember glacier Oct 30, 2021, 4:42 AM

#

.close

obtuse pebbleBOT Oct 30, 2021, 4:42 AM

#

Channel closed

Closed by @ember glacier

Use .reopen if this was a mistake.

ember glacier Oct 30, 2021, 4:42 AM

#

.reopen

obtuse pebbleBOT Oct 30, 2021, 4:42 AM

#

✅

sour mortar Oct 30, 2021, 4:42 AM

#

now post the question

#

wait for someone to answer

ember glacier Oct 30, 2021, 4:43 AM

#

sour mortar Oct 30, 2021, 4:43 AM

#

ping helpers if not answered in 15 minutes

ember glacier Oct 30, 2021, 4:43 AM

#

alright thanks

sour mortar Oct 30, 2021, 4:43 AM

#

ember glacier

oh, this is implicit differentiation

#

calc 1 thing

ember glacier Oct 30, 2021, 4:43 AM

#

yeah so i was really worried because my answer is negative

sour mortar Oct 30, 2021, 4:44 AM

#

ember glacier yeah so i was really worried because my answer is negative

not exactly a problem

#

since when you find a negative rate, it means the volume is decreasing

ember glacier Oct 30, 2021, 4:44 AM

#

This is my work

sour mortar Oct 30, 2021, 4:44 AM

#

I'll just help you with that one

ember glacier Oct 30, 2021, 4:44 AM

#

sour mortar Oct 30, 2021, 4:50 AM

#

ember glacier

everything is okay then

#

pepepray

ember glacier Oct 30, 2021, 4:51 AM

#

oh ok and since we're on implicit differentiation

#

can u just check 1 more question for me please xD

#

@sour mortar

#

.close

obtuse pebbleBOT Oct 30, 2021, 4:56 AM

#

Channel closed

Closed by @ember glacier

Use .reopen if this was a mistake.

ember glacier Oct 30, 2021, 4:56 AM

#

.reopen

obtuse pebbleBOT Oct 30, 2021, 4:56 AM

#

✅

ember glacier Oct 30, 2021, 4:57 AM

#

is my implicit differentiation correct?

#

obtuse pebbleBOT Oct 30, 2021, 5:12 AM

#

@ember glacier Has your question been resolved?

ember glacier Oct 30, 2021, 5:18 AM

#

<@&286206848099549185>

ember glacier Oct 30, 2021, 5:35 AM

#

<@&286206848099549185>

plain owl Oct 30, 2021, 5:40 AM

#

ember glacier is my implicit differentiation correct?

Looks correct…

ember glacier Oct 30, 2021, 5:40 AM

#

hey euclid!

#

yo i was wondering if u could check another answer i had

plain owl Oct 30, 2021, 5:41 AM

#

I’ll try

ember glacier Oct 30, 2021, 5:42 AM

#

#

i got that as my answer

#

but im not sure if i did it correctly tbh

#

did u get an answer like that?

plain owl Oct 30, 2021, 5:48 AM

#

What did you try though?

ember glacier Oct 30, 2021, 5:49 AM

#

#

this is what i did

plain owl Oct 30, 2021, 5:50 AM

#

Ok did the same so far. I’ll try to evaluate

#

I am getting something like $\frac{\sqrt{73^3}-1}{6}$

warm shaleBOT Oct 30, 2021, 5:56 AM

#

Euclid31415

ember glacier Oct 30, 2021, 5:56 AM

#

hmm ok

plain owl Oct 30, 2021, 5:57 AM

#

Substituted the entire thing under sqrt =u

ember glacier Oct 30, 2021, 5:57 AM

#

are u sure

#

that it should be that

plain owl Oct 30, 2021, 5:58 AM

#

ember glacier are u sure

Umm yeah. Unless I made a mistake

#

I think I did it properly

ember glacier Oct 30, 2021, 5:58 AM

#

alright thanks man i appreciate it

#

also btw

#

i couldn't respond to your dm

#

the one u sent

plain owl Oct 30, 2021, 5:59 AM

#

It’s no problem

plain owl Oct 30, 2021, 6:00 AM

#

ember glacier

The square root should be multiplied by entire of (18t+36t^3) here… I think that’s what led you to the answer 66.2339

ember glacier Oct 30, 2021, 6:03 AM

#

ah i see

#

thanks

plain owl Oct 30, 2021, 6:06 AM

#

Type .close when you are finished @ember glacier

ember glacier Oct 30, 2021, 6:14 AM

#

.close

obtuse pebbleBOT Oct 30, 2021, 6:14 AM

#

Channel closed

Closed by @ember glacier

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ember glacier Oct 30, 2021, 6:14 AM

#

oops haha forgot to

obtuse pebbleBOT Oct 30, 2021, 6:53 AM

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#

timid silo Oct 30, 2021, 6:55 AM

#

whenever there is -ve in power, in order to make in positive, we reciprocate the fraction.

#

that's correct

obtuse pebbleBOT Oct 30, 2021, 7:04 AM

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quartz jacinth Oct 30, 2021, 7:06 AM

#

obtuse pebbleBOT Oct 30, 2021, 7:06 AM

#

quartz jacinth

quartz jacinth Oct 30, 2021, 7:06 AM

#

can somone pls help me

rocky schooner Oct 30, 2021, 7:07 AM

#

Hint: join AB.

quartz jacinth Oct 30, 2021, 7:07 AM

#

what do you mean by join

#

sry im new to this topic

rocky schooner Oct 30, 2021, 7:08 AM

#

Draw a straight line from A to B

quartz jacinth Oct 30, 2021, 7:08 AM

#

ok

rocky schooner Oct 30, 2021, 7:08 AM

#

What can you tell about angle CAB

quartz jacinth Oct 30, 2021, 7:09 AM

#

umm

#

idk

rocky schooner Oct 30, 2021, 7:09 AM

#

Something related to CB is the diameter?

#

So that it forms a semi circle?

#

Any theorem related to semicircle?

quartz jacinth Oct 30, 2021, 7:11 AM

#

yeah im prett sure there is one but i still didnt learn the theorems

#

our teacher didnt teach us the theorems but she is giving us homework about it

#

soo

#

is a 90 degrees?

rocky schooner Oct 30, 2021, 7:13 AM

#

Yep it's 90°

#

Your good! Even your teacher didn't teach you you can figure it out!

#

Next consider angle ACB and angle BAT

quartz jacinth Oct 30, 2021, 7:16 AM

#

ok

rocky schooner Oct 30, 2021, 7:16 AM

#

Hint: something about tangent

#

Something like alternate segments

quartz jacinth Oct 30, 2021, 7:17 AM

#

ok

#

i couldnt do it

rocky schooner Oct 30, 2021, 7:21 AM

#

It's okay, lemme grab something online real quick

quartz jacinth Oct 30, 2021, 7:22 AM

#

is bat 29

#

?

rocky schooner Oct 30, 2021, 7:22 AM

#

https://www.cuemath.com/geometry/alternate-segment-theorem/

Alternate Segment Theorem is also known as tangent-chord theorem. Explore "why" it is so, with concepts, proof, examples, questions, and solutions.

rocky schooner Oct 30, 2021, 7:22 AM

#

quartz jacinth is bat 29

Yes, 29°

quartz jacinth Oct 30, 2021, 7:22 AM

#

than cat is 119

rocky schooner Oct 30, 2021, 7:24 AM

#

Yep

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And then x is easy

quartz jacinth Oct 30, 2021, 7:25 AM

#

is x 32

#

?

rocky schooner Oct 30, 2021, 7:26 AM

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I didn't calculate ,lemme get it the answer with my calculator

#

Yea

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32

#

Very good!

quartz jacinth Oct 30, 2021, 7:30 AM

#

btw

#

#

what do the lines mean on ce and oc

#

yk theres a small line

#

#

@rocky schooner

rocky schooner Oct 30, 2021, 7:31 AM

#

They mean those two lines are equal in length

quartz jacinth Oct 30, 2021, 7:31 AM

#

ok thanks

rocky schooner Oct 30, 2021, 7:34 AM

#

Good luck and have a nice day!

quartz jacinth Oct 30, 2021, 7:35 AM

#

u too!

night igloo Oct 30, 2021, 7:37 AM

#

.close

obtuse pebbleBOT Oct 30, 2021, 7:37 AM

#

Channel closed

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obtuse pebbleBOT Oct 30, 2021, 12:08 PM

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timid silo Oct 30, 2021, 12:52 PM

#

How many ovens are needed to bake 6 million loaves of bread if it takes 2 hours to bake bread and you only have the ovens for 4 years? Aka 6 million Jews

obtuse pebbleBOT Oct 30, 2021, 12:52 PM

#

timid silo How many ovens are needed to bake 6 million loaves of bread if it takes 2 hours ...

#

@hexed oak Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 1:22 PM

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Channel closed

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modern sierra Oct 30, 2021, 1:34 PM

#

If we’re talking sets, does A/B and A-B mean the same thing?

obtuse pebbleBOT Oct 30, 2021, 1:34 PM

#

modern sierra If we’re talking sets, does A/B and A-B mean the same thing?

rugged kite Oct 30, 2021, 1:34 PM

#

If you meant to write A\B then yes

#

they're two notations for the same thing

#

A/B is very different however

modern sierra Oct 30, 2021, 1:36 PM

#

rugged kite A/B is very different however

Oh then what’s that?

rugged kite Oct 30, 2021, 1:36 PM

#

There are multiple ways to see it

#

The easiest example is the integers modulo n. Ever heard of that?

modern sierra Oct 30, 2021, 1:37 PM

#

Nope

rugged kite Oct 30, 2021, 1:37 PM

#

It's like the numbers on a clock

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You can add or multiply them, but it always wraps back around to be less than 12

modern sierra Oct 30, 2021, 1:37 PM

#

Okay

rugged kite Oct 30, 2021, 1:38 PM

#

(well, technically on a clock you have all numbers from 1 to 12 inclusive, but usually in math it makes more sense to consider all the numbers from 0 to 12 or 11 inclusive, 0 is important to have)

modern sierra Oct 30, 2021, 1:38 PM

#

Alright

rugged kite Oct 30, 2021, 1:38 PM

#

So for example the integers modulo 12 are 0 through 11

modern sierra Oct 30, 2021, 1:39 PM

#

Oh okay

rugged kite Oct 30, 2021, 1:39 PM

#

And if I write 6+6, that's 12 usually

#

But in modular arithmetic, we always loop back around

#

So 6+6=0 mod 12

#

Another way to say this is that the remainder of dividing 6+6 by 12 is 0

#

That remainder is also called the modulus, hence "mod" and "modular"

modern sierra Oct 30, 2021, 1:39 PM

#

Oh okay

#

Yeah I think I get it

#

Thanks

rugged kite Oct 30, 2021, 1:40 PM

#

Well, that's the first part

#

You asked about A/B

#

For example, the set of all integers modulo 12 might be written as ℤ/12ℤ

modern sierra Oct 30, 2021, 1:41 PM

#

Yeah but I think this is above what I’m studying right now, I was just curious because I thought it might be related to what I’m doing lol

rugged kite Oct 30, 2021, 1:41 PM

#

I see

modern sierra Oct 30, 2021, 1:41 PM

#

But thanks anyways

rugged kite Oct 30, 2021, 1:41 PM

#

This notation comes when studying group theory, which, who knows, you might do some day

modern sierra Oct 30, 2021, 1:41 PM

#

Yeah I probably will

#

But thanks I’m gonna close this now

#

.close

obtuse pebbleBOT Oct 30, 2021, 1:42 PM

#

Channel closed

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long yoke Oct 30, 2021, 1:46 PM

#

How do i solve this??

Screen_Shot_2021-10-31_at_12.46.24_am.png

obtuse pebbleBOT Oct 30, 2021, 1:46 PM

#

long yoke How do i solve this??

unique solstice Oct 30, 2021, 1:49 PM

#

Do you know how to calculate that at 1 second?

#

So like if the question read

#

"It starts with 1200 g and is reduced by 12% each second, whats the mass after 1 second"

#

So just a normal question asking you to make a number 12% less than its original self

timid silo Oct 30, 2021, 1:50 PM

#

exactly

obtuse pebbleBOT Oct 30, 2021, 2:01 PM

#

@long yoke Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 2:16 PM

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Channel closed

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hearty estuary Oct 30, 2021, 2:22 PM

#

obtuse pebbleBOT Oct 30, 2021, 2:22 PM

#

hearty estuary

hearty estuary Oct 30, 2021, 2:22 PM

#

#

Is this working correct

#

I am a bit confused by the trapezium

#

Oh wait I see the trapezium

#

But I didn’t do it that way

obtuse pebbleBOT Oct 30, 2021, 2:38 PM

#

@hearty estuary Has your question been resolved?

pallid summit Oct 30, 2021, 2:42 PM

#

hearty estuary

This looks like an active test

hearty estuary Oct 30, 2021, 2:49 PM

#

It’s printed out dr frost

#

And I wouldn’t be doing a test at home lol

obtuse pebbleBOT Oct 30, 2021, 3:20 PM

#

@hearty estuary Has your question been resolved?

ripe carbon Oct 30, 2021, 3:37 PM

#

How to find a natural number n such that n mod x = y mod n ?

fervent cradle Oct 30, 2021, 3:42 PM

#

ax+n = bn + y

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ax - y = bn - n

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n = (ax-y)/(b-1)

#

for some a and b

#

ok that's non-trivial

#

idk

rugged kite Oct 30, 2021, 3:45 PM

#

that's not quite right

#

you have n=px+r and y=qn+r'

#

We're interested in n such that r=r'

#

i.e n-px=y-qn i.e n(1+q)=px+y i.e n=(px+y)/(q+1) for some q and p

ripe carbon Oct 30, 2021, 3:47 PM

#

rugged kite i.e n-px=y-qn i.e n(1+q)=px+y i.e n=(px+y)/(q+1) for some q and p

then how to choose p, q such that n is always correct?

rugged kite Oct 30, 2021, 3:48 PM

#

yeah that's the thing, there need to be some extra conditions on n

ripe carbon Oct 30, 2021, 3:48 PM

#

x, y are even

rugged kite Oct 30, 2021, 3:48 PM

#

for example, if you try x=5,y=2,p=q=0, you'll get the invalid solution n=2

#

which doesn't work because 2 mod 5 = 2 ≠ 0 = 2 mod 2

ripe carbon Oct 30, 2021, 3:49 PM

#

x=4 , y=8, then n can be 4

ripe carbon Oct 30, 2021, 3:49 PM

#

rugged kite which doesn't work because 2 mod 5 = 2 ≠ 0 = 2 mod 2

yes

obtuse pebbleBOT Oct 30, 2021, 3:50 PM

#

Channel closed

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ripe carbon Oct 30, 2021, 3:50 PM

#

.reopen

obtuse pebbleBOT Oct 30, 2021, 4:14 PM

#

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toxic elm Oct 30, 2021, 4:18 PM

#

is my calculation for this question correct?

obtuse pebbleBOT Oct 30, 2021, 4:18 PM

#

toxic elm is my calculation for this question correct?

brisk grove Oct 30, 2021, 4:19 PM

#

It seems correct yes

obtuse pebbleBOT Oct 30, 2021, 4:33 PM

#

@toxic elm Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 4:48 PM

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obtuse pebbleBOT Oct 30, 2021, 7:22 PM

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timid silo Oct 30, 2021, 7:25 PM

#

hey i dont need math help, but theres this really cute girl in class and i was wondering how would i go around to asking her out

obtuse pebbleBOT Oct 30, 2021, 7:25 PM

#

timid silo hey i dont need math help, but theres this really cute girl in class and i was w...

nocturne minnow Oct 30, 2021, 7:33 PM

#

timid silo hey i dont need math help, but theres this really cute girl in class and i was w...

Don't use a help channel for this kind of stuff. Help channels is used specifically for math related help. You can have discussion related stuff in #discussion or #serious-discussion or #chill

#

Go ahead and close this channel
.close

timid silo Oct 30, 2021, 7:33 PM

#

but its math class bro

#

.close

obtuse pebbleBOT Oct 30, 2021, 7:34 PM

#

Channel closed

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meager osprey Oct 30, 2021, 7:49 PM

#

How come in this inequation, the teacher doesn't simplify the m's? so it's x >= 3m. Time and time again I see them doing it this way (they leave the m and the m^2 factors), for what reason?

obtuse pebbleBOT Oct 30, 2021, 7:49 PM

#

meager osprey How come in this inequation, the teacher doesn't simplify the m's? so it's x >= ...

meager osprey Oct 30, 2021, 7:58 PM

#

Another question, for the same inequality. So the sign depends on m. But why is this true?

#

#

If mx >= 3m^2, then mx will be a negative quantity and 3m^2 will always be positive so why are there solutions at all?

#

I assume that it's because then x >= 3m^2/m, so x>= an overall negative quantity but then why do we flip the sign? If we flip the sign then shouldn't it then become -x >= -3m^2/m ? :(

obtuse pebbleBOT Oct 30, 2021, 8:16 PM

#

@meager osprey Has your question been resolved?

meager osprey Oct 30, 2021, 8:16 PM

#

<@&286206848099549185>

#

anyone? is there something about the question that makes it difficult to solve? Can I provide more info?

meager osprey Oct 30, 2021, 8:46 PM

#

Ahh merci, vous me sauvez là

#

certes, mais si on change pas les signes de l'équation elle-même? Je comprends pas comment on peut changer les signes si on change pas l'équation. On "suppose" que x est négatif mais...

#

oui...

#

🤔

#

mais je vois toujours pas

#

car ici y a les - qui s'ajoutent

#

en gros, ce qui me gène c'est qu'on ne modifie pas l'équation

#

Ah merde

#

yes

#

c'est vrai

#

j'ai fait ça aussi au premier coup

#

#

un truc du genre

#

Je sais pas si on peut raisonner comme j'ai fait

#

En gros je comprends pas vraiment, je m'embrouille toujours avec les notations

#

mais est-ce qu'on peut simplement substitioner des trucs au bol et après voir quelle égalité tient la route?

#

en gros -1 n'est pas superieur à 3 donc ça doit être de l'autre sens, l'égalité

obtuse pebbleBOT Oct 30, 2021, 9:24 PM

#

@meager osprey Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 10:24 PM

#

@meager osprey Has your question been resolved?

obtuse pebbleBOT Oct 30, 2021, 11:24 PM

#

Channel closed

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terse yoke Oct 30, 2021, 11:33 PM

#

can i please get help on A

obtuse pebbleBOT Oct 30, 2021, 11:33 PM

#

terse yoke can i please get help on A

nocturne minnow Oct 30, 2021, 11:36 PM

#

terse yoke can i please get help on A

What exactly are you stuck on?

terse yoke Oct 30, 2021, 11:41 PM

#

i dont really know how to solve the question

#

@nocturne minnow

nocturne minnow Oct 30, 2021, 11:41 PM

#

So you know w, correct?

terse yoke Oct 30, 2021, 11:41 PM

#

yeah

#

sqrt3+i/2

nocturne minnow Oct 30, 2021, 11:41 PM

#

It just wants powers of w

terse yoke Oct 30, 2021, 11:42 PM

#

so do i just

#

power w?

nocturne minnow Oct 30, 2021, 11:42 PM

#

Think about it like this, if w = 2, what is w^2?

terse yoke Oct 30, 2021, 11:42 PM

#

4

nocturne minnow Oct 30, 2021, 11:42 PM

#

Or 2^2?

#

Right?

terse yoke Oct 30, 2021, 11:42 PM

#

yea

#

so i basically power it

nocturne minnow Oct 30, 2021, 11:42 PM

#

What about w^3

terse yoke Oct 30, 2021, 11:42 PM

#

okay ty

nocturne minnow Oct 30, 2021, 11:43 PM

#

It'd be 2^3

#

And so on

terse yoke Oct 30, 2021, 11:43 PM

#

ahh

#

okay ty

nocturne minnow Oct 30, 2021, 11:43 PM

#

But you're given sqrt3+i/2

#

As w

#

Just do the same process

terse yoke Oct 30, 2021, 11:44 PM

#

how about this

#

?

nocturne minnow Oct 30, 2021, 11:45 PM

#

Looks complicated, wish I could help sorry

terse yoke Oct 30, 2021, 11:48 PM

#

ahh so you know w^4

terse yoke Oct 30, 2021, 11:48 PM

#

terse yoke can i please get help on A

for this

#

since it is a reflection of w^2 in the imaginary axis

#

would that mean it would be

#

1-sqrt(3)i/2

nocturne minnow Oct 30, 2021, 11:49 PM

#

Looks like it

#

I could be wrong though

terse yoke Oct 30, 2021, 11:50 PM

#

yeah all good

#

ty anyways

#

.close

obtuse pebbleBOT Oct 30, 2021, 11:50 PM

#

Channel closed

Closed by @terse yoke

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obtuse pebbleBOT Oct 31, 2021, 2:07 AM

#

Available help channel!

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wicked wigeon Oct 31, 2021, 2:08 AM

#

obtuse pebbleBOT Oct 31, 2021, 2:08 AM

#

wicked wigeon

spiral maple Oct 31, 2021, 2:09 AM

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wicked wigeon

pick 1 channel and stick to it.

nocturne minnow Oct 31, 2021, 2:09 AM

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wicked wigeon

Don't use multiple channels

wicked wigeon Oct 31, 2021, 2:09 AM

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im trying but no ones helped for my past 5 questions lol

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ill remove the other

spiral maple Oct 31, 2021, 2:10 AM

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yeah cause you havent posted what you've tried

wicked wigeon Oct 31, 2021, 2:10 AM

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i posted this

obtuse pebbleBOT Oct 31, 2021, 2:25 AM

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@wicked wigeon Has your question been resolved?

wicked wigeon Oct 31, 2021, 2:41 AM

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.close

obtuse pebbleBOT Oct 31, 2021, 2:41 AM

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Channel closed

Closed by @wicked wigeon

Use .reopen if this was a mistake.

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violet sentinel Oct 31, 2021, 2:52 AM

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I can't remember, how do I find the max distance between any two pairs of points between two functions?
For example, I have f(x) = x^3 and g(x)=x/2.
I want to find at what points do f(x) and g(x) create the maximum distance between the two functions? And where is the point on f(x) and on g(x) respectively?

obtuse pebbleBOT Oct 31, 2021, 2:52 AM

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violet sentinel I can't remember, how do I find the max distance between any two pairs of points...

violet sentinel Oct 31, 2021, 2:52 AM

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example here:

unique solstice Oct 31, 2021, 2:54 AM

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Just use Pythagorean theorem

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Then derivate it and find the critical points epicly

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Then see which ones a max

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And bam

drifting wraith Oct 31, 2021, 2:54 AM

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epicness is optional, it still works if you do it mediocrily

unique solstice Oct 31, 2021, 2:55 AM

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Optional but highly recommended*

violet sentinel Oct 31, 2021, 2:57 AM

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unique solstice Just use Pythagorean theorem

sorry my brain is a bit slow tonight.
Do you mean something like sqrt(f(x)^2 + g(x)^2)?

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I'm gonna feel dumb once you I understand what you mean haha

unique solstice Oct 31, 2021, 2:59 AM

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More like

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sqrt((x_2-x_1)^2 + (g(x_2)-f(x_1))^2)

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I think

violet sentinel Oct 31, 2021, 3:01 AM

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I'll give it a shot!

unique solstice Oct 31, 2021, 3:01 AM

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I might be a bit wrong on my process

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But its along those lines

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I mean I would personally use like dot product or something

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Solely because the second function is a straight line

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But thats by absolutely no means a "general solution"

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Well actually

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Does the problem go into more detail?

violet sentinel Oct 31, 2021, 3:07 AM

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oh no it's just me experimenting

unique solstice Oct 31, 2021, 3:07 AM

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Oh

violet sentinel Oct 31, 2021, 3:07 AM

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I'm messing with Chebyshev polynomials

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and for the equation above it states that the maximum error between them is 1/2

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so I was verifying that!

unique solstice Oct 31, 2021, 3:08 AM

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So youre looking only for vertical error?

violet sentinel Oct 31, 2021, 3:08 AM

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oh I'm an idiot... I just need the vertical error

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yeah

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derp

unique solstice Oct 31, 2021, 3:08 AM

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Yeah thats way easier

violet sentinel Oct 31, 2021, 3:08 AM

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haha

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yeah it is

unique solstice Oct 31, 2021, 3:08 AM

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Do you know how to do it?

violet sentinel Oct 31, 2021, 3:09 AM

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iirc it should be f(x)-g(x)
then you find the derivative to find critical points

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similar process

unique solstice Oct 31, 2021, 3:10 AM

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Ye

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Youd prob want |f(x)-g(x)| technically ig

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Which throws a small wrench into things

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But it shouldnt be that bad

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Just split it into two functions

violet sentinel Oct 31, 2021, 3:14 AM

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yep!
So it'd be a(x)=|x^3 - (1/2)x|
a'(x) = { 3x^2 - (1/2) if x > 0
{ -3x^2 + 1/2 if x <0
?

unique solstice Oct 31, 2021, 3:14 AM

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Yeah

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Or wait

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Check your bounds

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Its a bit nastier than I thought

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You have to find exactly where the specific function is negative

violet sentinel Oct 31, 2021, 3:17 AM

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oh I see

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the bounds will be the critical points it looks like?

unique solstice Oct 31, 2021, 3:18 AM

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Itll be the zeroes of the original function

violet sentinel Oct 31, 2021, 3:18 AM

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oh yeah my b that's right

unique solstice Oct 31, 2021, 3:18 AM

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And depending if its positive or negative between the zeroes is whether or not its reversed

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Ye its all confusing

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With all the different zeroes meaning all kinds of stuff

violet sentinel Oct 31, 2021, 3:18 AM

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well damn this became more complicated than I assumed 😮

unique solstice Oct 31, 2021, 3:18 AM

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Yeah

violet sentinel Oct 31, 2021, 3:18 AM

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*first assumed

unique solstice Oct 31, 2021, 3:19 AM

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Well after you figured out it was vertical distance

violet sentinel Oct 31, 2021, 3:19 AM

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that's fine tho

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this is part of a numerical analysis course

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so it seems this is on par with how this section of math goes

unique solstice Oct 31, 2021, 3:19 AM

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Reasonable

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I learned the way to do it in precalc by plotting the zeroes on a number line

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And testing values between all of the zeroes if its positive or negative

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Its really simplistic but oftentimes thats whats useful

violet sentinel Oct 31, 2021, 3:21 AM

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oh yeah I remember that too, that made it fairly easy!

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well thank you for the help, I appreciate it!

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.close

obtuse pebbleBOT Oct 31, 2021, 3:23 AM

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Channel closed

Closed by @violet sentinel

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unique solstice Oct 31, 2021, 3:23 AM

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Np

obtuse pebbleBOT Oct 31, 2021, 3:24 AM

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Available help channel!

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hallow cedar Oct 31, 2021, 5:05 AM

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obtuse pebbleBOT Oct 31, 2021, 5:05 AM

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hallow cedar

hallow cedar Oct 31, 2021, 5:05 AM

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i have a brainfart

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may someone guide me through the steps o_O

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is this good so far @_@

craggy flame Oct 31, 2021, 5:11 AM

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Call ab = W.
Then Right side = W

hallow cedar Oct 31, 2021, 5:11 AM

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hm yea just another constant really

craggy flame Oct 31, 2021, 5:11 AM

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That is ... sqrt(...) = x + W

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square the thing...

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cancel stuff

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... do you see?

hallow cedar Oct 31, 2021, 5:12 AM

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uh

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sqrt(x^2 + 1) = ab + x

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hm

craggy flame Oct 31, 2021, 5:13 AM

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yup.. now, square both sides...

hallow cedar Oct 31, 2021, 5:13 AM

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x^2 + 1 = (ab)^2 + 2(ab)(x) + x^2

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oh there's a remaining x

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thanks

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weird

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when I would keep the other x on the left side i wouldnt find it

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o_O

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.close

obtuse pebbleBOT Oct 31, 2021, 5:13 AM

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Channel closed

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obtuse pebbleBOT Oct 31, 2021, 5:31 AM

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Channel closed

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obtuse pebbleBOT Oct 31, 2021, 9:13 AM

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toxic elm Oct 31, 2021, 10:02 AM

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is my calculation correct?

obtuse pebbleBOT Oct 31, 2021, 10:02 AM

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toxic elm is my calculation correct?

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@toxic elm Has your question been resolved?

obtuse pebbleBOT Oct 31, 2021, 10:32 AM

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lilac grove Oct 31, 2021, 11:02 AM

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how will I factor this, its so hard
\
$(a + b)(p + q + r) + (b + c)(p + q + r) + (c + a)(p + q + r)$

obtuse pebbleBOT Oct 31, 2021, 11:02 AM

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lilac grove how will I factor this, its so hard \\ $(a + b)(p + q + r) + (b + c)(p + q + r) ...

warm shaleBOT Oct 31, 2021, 11:05 AM

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JUGisMUG🎃

timid silo Oct 31, 2021, 11:17 AM

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lilac grove how will I factor this, its so hard \\ $(a + b)(p + q + r) + (b + c)(p + q + r) ...

take (p + q + r) as common

obtuse pebbleBOT Oct 31, 2021, 11:22 AM

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@lilac grove Has your question been resolved?

obtuse pebbleBOT Oct 31, 2021, 11:37 AM

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Channel closed

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glad sleet Oct 31, 2021, 11:40 AM

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L = 0.5((A1 -Y)^2) -> Y = constant
A1 = σ(P1) -> sigma = sigmoid function
P1 = X.W1 + B1

∂L/∂B1 = (∂L/∂A1) * (∂A1/∂P1) * (∂P1/∂B1)
(this is correct right?)

if this is correct I get that ∂L/∂B1 = (A1-Y) * A1(1-A1) * 1
now, every variable except sigma are matrices, but the result I get from the final partial gives me a 6x20 matrix in my example whilst I should get a 1x20 matrix
so I must have done something wrong

obtuse pebbleBOT Oct 31, 2021, 11:40 AM

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glad sleet L = 0.5((A1 -Y)^2) -> Y = constant A1 = σ(P1) -> sigma = sigmoid function P1 = X...

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@glad sleet Has your question been resolved?

obtuse pebbleBOT Oct 31, 2021, 12:26 PM

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@glad sleet Has your question been resolved?

obtuse pebbleBOT Oct 31, 2021, 1:30 PM

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@glad sleet Has your question been resolved?

glad sleet Oct 31, 2021, 2:39 PM

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Still waiting btw

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pls

fiery venture Oct 31, 2021, 4:23 PM

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maybe write it out a little more clearly @glad sleet . I'm assuming you're trying to do something with neural networks, and I know how backprop works pretty well, but I can't make heads or tails of your question at all.

glad sleet Oct 31, 2021, 4:24 PM

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so I have a simple network with an input matrix X and that propagates to the output Y

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I just wanted to find ∂L/∂B1 since I want to initialize my bias' and update them after each cycle

fiery venture Oct 31, 2021, 4:25 PM

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how many layers are in your network?

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and what loss function are you using?

glad sleet Oct 31, 2021, 4:27 PM

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just 1 hidden layer

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loss function is 0.5((A1 -Y)^2)

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sorry

fiery venture Oct 31, 2021, 4:28 PM

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and A1 is your target?

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or your output layer?

glad sleet Oct 31, 2021, 4:28 PM

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A1 is the output

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Y is the target

fiery venture Oct 31, 2021, 4:29 PM

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hmm

glad sleet Oct 31, 2021, 4:31 PM

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granted I just summed all my weights so it becomes a (1,20) matrix as desired

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but I guess that's not really a good way

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cuz it works perfectly

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I'm just curious to what I might have missed

fiery venture Oct 31, 2021, 4:32 PM

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the full equation for the loss of your network will be $L(y; \theta) = L(W_{2} \sigma(W_{1} x + b_{1}) + b_{2}$ right?

warm shaleBOT Oct 31, 2021, 4:32 PM

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yoohoo

glad sleet Oct 31, 2021, 4:33 PM

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I don't have the second weight/bias

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but yes