#help-10

1 messages · Page 81 of 1

timid silo
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it should be sec

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idk how ot explain it just 1 sec

drifting loom
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you wanna find derivative of this

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#
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timid silo
#

.reopen

obtuse pebbleBOT
#

timid silo
#

okay sowe need

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function horizontal and vertical asymptote

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and function local min and max

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i hope google translated it right

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local min max f'(x) and asymptote

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

timid silo
#

For horizontal asymptotes: what happens to f(x) when $x \to \pm \infty$

warm shaleBOT
obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#
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primal river
#

I was wondering if there are word problems for power series I have a project to make a situation involving power series but I cant find any exampels

drifting loom
#

what is power series?

primal river
#

a infinite series

drifting loom
#

ohh

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of infinite series

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lemme give you an example

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@primal river

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see this if it help you

primal river
#

I think I was supposed to think of something like a word problem

drifting loom
#

you can create a word problem of this

zenith raft
#

also that's not a power series and it's not totally clear what the pattern is but it doesn't seem to equal 1

final thunder
#

1/10

obtuse pebbleBOT
#

@primal river Has your question been resolved?

obtuse pebbleBOT
#
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nocturne quail
obtuse pebbleBOT
royal basin
#

distinct positive integers b, c, d

hot hazel
#

apologies for the disruption.

neon eagle
#

ok so you do realise the question boils down to $c^3=d^4$

warm shaleBOT
royal basin
#

to reiterate what i said that got purged,

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a needs to be a cube and a fourth power at the same time

neon eagle
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where c and d are integers and you're trying to minimise the values of c and d

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yes what ann said

sharp pecan
neon eagle
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jigglyproff be quiet.

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@nocturne quail use fundamental theorem of algebra

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every positive integer can be written as a unique factorisation of prime factors

nocturne quail
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Yes, I think I got it. It's a = 4096

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Thanks a lot all of you.

zenith raft
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i think that's the wrong FTA

neon eagle
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wait is it

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shit

zenith raft
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arithmetic haha

neon eagle
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OOPS

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same thing.

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wait im so bad at math

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why am i helping people i need help.

zenith raft
#

same

neon eagle
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mood

sharp pecan
neon eagle
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dude

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he might not even know FTA

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also its obvious why its the correct approach

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thats how math is

#

once a solution is presented its hard to forget

nocturne quail
#

.close

obtuse pebbleBOT
#
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obtuse pebbleBOT
#
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obtuse pebbleBOT
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royal basin
#

are you sure that this inequality is in the right direction

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bc as-is it feels like a contradiction is about to surface

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or maybe not a contradiction but the problem might become a little too trivial

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can you show your proof?

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it's strange that your proof would depend on a_2 itself being nonnegative as opposed to say the difference between a_2 and a_1

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$a_n = (n-1)a_2 - a_1$?

warm shaleBOT
royal basin
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er

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≥ not =

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that looks odd to me though

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you could say $a_n - a_1 \geq (n-1)(a_2 - a_1)$

warm shaleBOT
royal basin
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are you sure though

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sorry, got distracted

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Using this I managed to get
a(n)>=(n-1)a(2)-a(1)
i think this is nonsense, but given how you jump from the givens to this with nothing inbetween i can't really comment on where you went wrong

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here's how i would've done this: let $d = a_2 - a_1$, then for all $n$ you have $a_{n+1} \geq a_n + d$, and from this it is transparent that $a_n \geq a_1 + (n-1)d$

warm shaleBOT
royal basin
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from this you can conclude that if d > 0 then the sequence is unbounded, so d has to be ≤0

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because $a_{n+1} - a_n \geq d$

warm shaleBOT
lethal cloud
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are you sure the inequality at the top is right?

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If the sequence is monotonically increasing, then we have $\lvert a_{2} - a_{1} \rvert \leq \lvert a_{n+1} - a_n \rvert$. Hence we have some $\varepsilon$ so that $\varepsilon < \lvert a_{2} - a_{1} \rvert \leq \lvert a_{n+1} - a_n \rvert$` for any n, therefore it is not cauchy, and cannot converge.

royal basin
#

let $b_n = a_{n+1} - a_n$, then you're told that $(b_n)$ is an increasing sequence

warm shaleBOT
obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
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heady tendon
#

can anyone help with this

obtuse pebbleBOT
heady tendon
faint prism
#

Calculate every surface area and add them together.

heady tendon
#

yh ik but i keep getting it wrong

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can u help me

faint prism
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Calculate for each figure. Rectangle, 2 of 4x6, 4 of 15x4. And do it the same way with the triangle.

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Take your time and calculate each side of the figures.

heady tendon
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i still dont understand D

faint prism
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Do you know what surface area is?

heady tendon
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i not very goof with it D:

faint prism
#

Like it is, the area of the surface. You got a table that is 4cm long and 6cm wide, the areal of the surface is 24cm^2.

heady tendon
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6x4 ok

faint prism
heady tendon
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ok

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so the answer is 174

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so the answer is 174????

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umm @faint prism

faint prism
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How you got it?

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answer:||4* 6 + 4(15* 4)+(3* 4)+5* 6+3*6||

heady tendon
#

that 3798 right

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@faint prism its was wrong

warm shaleBOT
#

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

faint prism
#

324 dosen't work?

heady tendon
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yes

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and now i'm in recovery

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doing this

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thanks alot

faint prism
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Ah, I saw my mistake. It should be ||4* 6 + 2(15* 4)+2(15* 6)+(3* 4)+5* 6+3*6||

heady tendon
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i already failed u goota help me with recovery pls man

faint prism
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I mean, does the question just ask for surface area of one pyramid?

heady tendon
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like 20 questions

of this but it gets harder

faint prism
void swift
#

no..?

heady tendon
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no

void swift
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hi you need help?

faint prism
#

Alright, I'm in a doubt. You should probably find other helpers.

heady tendon
void swift
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how can you break them up into

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(smaller shapes)

heady tendon
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u mean this

void swift
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yes

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what are the shapes you can see?

heady tendon
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pyramid\

void swift
heady tendon
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yes and fyi cool pffp

void swift
#

and four other triangles that connects the square?

void swift
heady tendon
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yh

void swift
#

okay now what you need to do is, in order to calculate the entire surface area, you calculate the surface areas of the smaller shapes (square, triangle), and add them up

#

make sense?

heady tendon
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not at all

void swift
#

gimme a sec

heady tendon
#

ok

void swift
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see how the larger shape's surface area is just the combination of the smaller ones

heady tendon
#

nice drawing mine is ass

heady tendon
#

yh i think

void swift
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alright

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so we just find the area of each individual shapes that we just got

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tell me how do we find the surfacd area of a square?

heady tendon
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is the answer 5`

void swift
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nonono

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tell me

heady tendon
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51

void swift
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yep

heady tendon
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is it 51?

void swift
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how did you get it?

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you break them up into smaller shapes

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so we calculate the small shape's area and sum it up

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for the square, its 9inches squared

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for one of the triangles, its 10.5 inches squared

heady tendon
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bruh i just did 7 x 3 / 2 and times it by 4 and i did 3 x 3 and added it

void swift
#

yep its the same thing as what im doing

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its just a breakdown of it

heady tendon
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ok ty pls dont just go

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i will need later pls pls pls dont go

void swift
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i have things to do, if i can ill come back but no guarantees..

heady tendon
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D:

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pls can u come back at 3

void swift
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how old are you btw?

void swift
heady tendon
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whats ur time

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@void swift

heady tendon
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i'm 13

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<@&286206848099549185>

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<@&286206848099549185>

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<@&286206848099549185>

obtuse pebbleBOT
#

@heady tendon Has your question been resolved?

heady tendon
#

<@&286206848099549185>

timid silo
#

@heady tendon wait let me see

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@heady tendon @heady tendon @heady tendon @timid silo

heady tendon
#

hi

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srrry

timid silo
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@heady tendon

heady tendon
#

done with that

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i need help with this

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wait pls try and solve it with me pls pls

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is the answer 314

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is 489.84 @timid silo

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umm pls can I get another <@&286206848099549185>

timid silo
#

@heady tendon come in vc?

heady tendon
#

srry its very very loud

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so i cant chat

#

which one

timid silo
heady tendon
#

i have to watch a 15 min vid

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before i can do anything

timid silo
#

@heady tendon so can't come in vc

heady tendon
#

i think i can

timid silo
#

?

heady tendon
#

what vc?

timid silo
#

@heady tendon

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@heady tendon come in 384kbps

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@heady tendon

#

@heady tendon fast

heady tendon
#

ook

#

hi

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i cant chat

timid silo
#

@heady tendon why?

heady tendon
#

@timid silo

timid silo
#

@timid silo why?

heady tendon
#

like is aid real loud

#

hi

#

ok

#

hold on a sec still in a vid

heady tendon
#

do u know surface area of composition figures

timid silo
#

Yes

heady tendon
#

ty

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nah already done that

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too easy

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i need to do 7 question

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@timid silo

timid silo
#

Yes

heady tendon
#

i need to do 7 questions

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🥺 help

#

@timid silo u here

timid silo
#

@heady tendon it is the same type of sum I helped you now try on your own

heady tendon
#

54?

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is the total?

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@timid silo

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📚

timid silo
#

@heady tendon donno

heady tendon
#

I manage to finish that one but an even harder one

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<@&286206848099549185>

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pls can anyone help me

proven lotus
#

stop

drowsy cosmos
#

no one will help you if you behave like that

timid silo
#

its only the green part right

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2 x base x height + 5x4^2

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so 2 x 5 x 4 + 5 x 16

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if i am not mistaken

light geyser
#

poor @jaunty stream

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Please don't spam the helpers

#

It does the opposite of the desired effect

timid silo
#

,, 3(12\times3)+2(3\times4)+13\times4+2(5\times12)+5\times4

warm shaleBOT
#

Vortism

timid silo
#

@heady tendon

balmy mortar
#

<@&268886789983436800> . And i got a random ghost ping here

upbeat plinth
#

.close

obtuse pebbleBOT
#
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vital frost
#

hey

obtuse pebbleBOT
#

Please don't occupy multiple help channels.

vital frost
#

.close

obtuse pebbleBOT
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hollow grail
#

How?

obtuse pebbleBOT
hollow grail
#

how is cos/sin^2 = -1/sin

distant moth
solar trellis
hollow grail
#

its question 4

#

i dont get it

hollow grail
#

ok i got it now

#

.close

obtuse pebbleBOT
#
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loud tangle
#

having some issues with this problem

in the center figure, ABC is a right triangle with BC = 2AB, BCD is a right isoceles triangle right in D and E is on AC s.t AE = AB.

i need help with b) prove BDE is equilateral

loud tangle
#

i got 1 60° angle down but i just cant see what to do to get the 2nd

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or prove 2 sides are congruent

#

cube people i am hereby reaching outto any of you

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<@&286206848099549185>

#

been 15 minutes

#

i counted

#

come onnnnn 😭

vital bramble
#

if im not mistaken abc should be a 30 60 90 triangle

loud tangle
#

yeah ik

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did that already

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i tried messing with the angles a whole lot and all i got was ebd is 60

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anything else involves proving edc is isosceles

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which idrk how to do cause all i can rly compute is bec to be 135

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if anyone finds a solution ping me

#

ill be skipping and doing the next problems

vital bramble
#

ACB = 30, BEC = 135, (solve for third angle of triangle BEC) 180 - 135 + 30 = 15, DBE = CBE + DBC, DBE = 15 + 45, DBE = 60

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isoceles right triangles are 45-45-90 triangles so DBC = 45

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so thats one angle of the equilateral triangle if that helps @loud tangle

loud tangle
#

its just 1 anglei

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angle

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i already did that

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i need to find a 2nd one

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just cause 1 angle's 60 doesnt mean its equilateral

#

ebd is dbe

loud tangle
obtuse pebbleBOT
#

@loud tangle Has your question been resolved?

obtuse pebbleBOT
#

@loud tangle Has your question been resolved?

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stark hollow
obtuse pebbleBOT
stark hollow
#

the answer has to be 84, but i didn't understand how to get that

proud haven
#

I mean I got 36 so if anyone else can pitch in and verify before i give out any misleading info that'd be great

stark hollow
#

oh have u drawn the altitude from the vertex A? i also did that and got 36 as well, but it is only part of it

obtuse pebbleBOT
#

@stark hollow Has your question been resolved?

stark hollow
#

PLS HELPPP

obtuse pebbleBOT
#

@stark hollow Has your question been resolved?

obtuse pebbleBOT
#

@stark hollow Has your question been resolved?

obtuse pebbleBOT
#

@stark hollow Has your question been resolved?

obtuse pebbleBOT
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real cobalt
#

how did they solve this,?

obtuse pebbleBOT
smoky slate
#

It's written there

real cobalt
#

ik

#

but its not helpful

#

its ixl, ixl scks

cedar lichen
#

What do you mean it's not helpful

#

It says exactly what they did

real cobalt
#

it says subtract 14x, but from where?

cedar lichen
#

From both sides of the equation

real cobalt
#

wait nvm

#

now i get it

#

.close

obtuse pebbleBOT
#
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clear leaf
obtuse pebbleBOT
#

@clear leaf Has your question been resolved?

real cobalt
clear leaf
real cobalt
#

ok

#

idk how to this

clear leaf
#

i hate savvas sm

real cobalt
#

same

#

type "<@&286206848099549185>"

clear leaf
#

oh alr

#

<@&286206848099549185>

obtuse pebbleBOT
#

@clear leaf Has your question been resolved?

obtuse pebbleBOT
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jagged edge
obtuse pebbleBOT
jagged edge
#

how did they know it was x and y?

#

randomly?

tardy epoch
jagged edge
#

wait wdym

tardy epoch
#
jagged edge
#

Ohh

#

the formula

#

i see it now

#

xd

tardy epoch
obtuse pebbleBOT
#

@jagged edge Has your question been resolved?

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static glacier
obtuse pebbleBOT
static glacier
#

can anyone help with the last part

#

answer is x+2y+3z=d

obtuse pebbleBOT
#

@static glacier Has your question been resolved?

obtuse pebbleBOT
#

@static glacier Has your question been resolved?

obtuse pebbleBOT
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obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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stone flint
#

Hello

obtuse pebbleBOT
stone flint
#

A+b=10
Ab= 36

#

How to get a and b

gilded needle
#

well the first one gives you b = 10 - a, try substituting that into the second equation

stone flint
#

A×10-a=36
10a - A^2 = 36

gilded needle
#

so far so good

stone flint
#

LOL.

#

But nau what

timid silo
#

Quad quad

copper spade
#

Ye quadratic formula

stone flint
#

I don't get what I need

copper spade
#

Ya applied formula

#

Or better way ya know how to take factors and split 10a?

stone flint
#

Where

copper spade
#

Like that equation is 10a-a²=36
a²-10a+36=0

#

Split 10a

#

Ya know how to?

stone flint
#

A(a-10)

#

?

copper spade
#

Nah wait ig you can't split here

#

Use quadratic formula

stone flint
#

I keep getting wrong numbers ffs

obtuse pebbleBOT
#

@stone flint Has your question been resolved?

copper spade
#

Send me your working

#

(Ping me if u do send me the workin)

obtuse pebbleBOT
#

@stone flint Has your question been resolved?

stone flint
#

@copper spade

copper spade
#

Slide

stone flint
#

Can u tell me precisely what are a b and c as numbers

#

C 36

#

A is 1

#

B is -10

#

Am I right or wrong about it

#

<@&286206848099549185>

obtuse pebbleBOT
#
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timid silo
#

What can I do for this

obtuse pebbleBOT
timid silo
#

$x^{2009} + 2009x + 1=0$

warm shaleBOT
#

beijing

timid silo
#

Prove it only has one solution in [-1, 0]

sharp pecan
timid silo
#

Calculus

sharp pecan
#

I see

timid silo
#

I think I’m supposed to use derivatives or something related

sharp pecan
timid silo
#

Yes

#

I think youre supposed to use differential proving method

sharp pecan
#

you can use derivatives

#

it has something to do with minimum and maximum

timid silo
#

Yea yea

sharp pecan
#

I just have a hard time explaining that without telling the answer right away ;-;

sharp pecan
timid silo
#

The derivative is 2009x^2008 + 2009

sharp pecan
#

mhm yes but do you already know what to do with that information?

timid silo
#

I know how to prove its always growing but I can’t prove the solution is exactly in interval-1,0

sharp pecan
timid silo
#

Do you know first and second order derivatives? Or how fo calculate maxima and minima and input interval values on the derivative?

sharp pecan
#

since its basically required to have no min or max inside that interval then

sharp pecan
timid silo
#

Second order derivative is 4034072x^2007

#

Odd power

#

Idrk but try rolle's theorem or other ways to find.. wish i could help

sharp pecan
#

I think they already figured out there is no extreme locality in that interval though...

#

since thats required for steady growth

novel knoll
#

Is your function continious? Do you have a theorem that says smth about what points a continious function attains? You have shown its increasing so it has at most 1 solution

#

Figure out what theorem gives you it has 1 solution

timid silo
#

Bro what are u doing

stone flint
#

@sharp pecan help

sharp pecan
obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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quaint finch
obtuse pebbleBOT
quaint finch
#

I feel like generalised pigeonhole principle is required

#

ans is 225

sharp pecan
# quaint finch ans is 225

is there more to the task?
if I get it right, you may have level 1 with 29 people, then the other levels have 0 and its still true

quaint finch
#

I don't understand what ur tryin to say

sharp pecan
# quaint finch

I don't quite know how to interpret the task.
there are a total of n objects and 8 containers
One of the containers must have at least 29 objects

is that correct?

quaint finch
#

yes

sharp pecan
#

so, the minimum n is 29 right?

quaint finch
#

yes

sharp pecan
#

since one object has 29, the other 7 all have 0

#

so how 225?

quaint finch
#

the others have to be more than 29

sharp pecan
quaint finch
#

cuz it says at least 29

#

so 29 or more

sharp pecan
#

yes, but ONE level has to have 29 or more, not all of them

#

right?

quaint finch
#

yes

sharp pecan
#

so if level 1 has 29 people the condition is fullfilled.
how do you know the other levels need 29 too?

quaint finch
#

I get you

sharp pecan
#

at least 29 people in at least one level I think that really means that ONE level needs to be 29+

quaint finch
#

yh ur right

#

meaning that the other 7 can have 0?

sharp pecan
#

I think

#

something like {29 ,0 ,0 ,0 ,0 ,0 ,0 ,0} could be a distribution over the levels

#

since you have at least 29 people in at least one level

#

so min(n)=29

#

so the function for n(x) could be n(x)=29+x, x is a natural number

quaint finch
sharp pecan
#

do we?

#

in practice yes, but there is nothing said that you cannot have infinite people in a single level

#

and you have 8 levels

#

something like {12321321312312321 ,12312321321312, ...} would be possible

quaint finch
#

so there are many possible answers but the lowest it can get to is 29

sharp pecan
#

yes

#

to formulate n you could say
${n=29+x|x\in \mathbb{N}}$

warm shaleBOT
#

Jigglyproff

quaint finch
#

alright, that helps, thx

sharp pecan
#

yw

quaint finch
#

do u go to uni

sharp pecan
#

yes

quaint finch
#

no wonder

sharp pecan
#

im here to prognosticate on my own math tasks XD

quaint finch
#

ha

#

.close

obtuse pebbleBOT
#
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tribal iris
obtuse pebbleBOT
tribal iris
#

Am currently stuck at example A the last part

#

How did we get that( -xe^-x )+(-e^-x) | 0 to infinity equals 1

mighty geyser
#

take limits as x -> 0 and x -> inf

tribal iris
#

What do i do for the lim at infinity

mighty geyser
#

might be easier if you write as a fraction

tribal iris
#

How

obtuse pebbleBOT
#

@tribal iris Has your question been resolved?

mighty geyser
#

(-x-1)/e^x

tribal iris
#

Ohhhhhhhhhh

#

Then i do Lhopital

#

1/e^x

#

So =0

#

So [0] - [-1] =1

tribal iris
obtuse pebbleBOT
#
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balmy scaffold
#

wait

#

yes

#

(3; -2) (4; -2) (3; -4)

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
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balmy scaffold
#

|x-1|+|x-2|+|x-3|+...|x-n|>=59

obtuse pebbleBOT
#

Please don't occupy multiple help channels.

balmy scaffold
#

n is the smallest possible natural number
to find n
and x is any real number

timid silo
#

Wat

balmy scaffold
#

|x-1|+|x-2|+|x-3|+...|x-n|>=59

timid silo
#

send screenshot

balmy scaffold
#

how do i calculate it?

timid silo
#

I dont understand you writing send pic

balmy scaffold
#

no its in another language

timid silo
#

Send idc

balmy scaffold
#

waht 1

#

@timid silo

#

?

timid silo
#

Idk 1

mighty geyser
#

consider |x-1|+|x-n|, what's the minimum value of this

balmy scaffold
#

nonono sorry its

#

smallest possible natural value

mighty geyser
#

in terms of n, if x can vary

balmy scaffold
#

x is any real number

#

pls help

loud tangle
#

so what do you plan to acomplish with this?

#

like find an n that follows this rule

balmy scaffold
#

ye

loud tangle
#

well it has to at least be bigger than the middle term of the sum

#

so its at the very least positive

#

no wait

#

its mod anyway

ebon remnant
#

n?

balmy scaffold
#

i think its 16 but i cant prove it without a graph

balmy scaffold
ebon remnant
#

is there any specific things for n?

loud tangle
#

can you set x to say 0

#

since youre finding the smallest value

balmy scaffold
#

its natural number

balmy scaffold
loud tangle
#

yeah but you wanna find the min value of n

balmy scaffold
#

umm so

loud tangle
#

which would require the min value of x

#

and in mod its 0

ebon remnant
#

nvm wait

#

wait

loud tangle
#

not really

ebon remnant
#

<59

#

wait

balmy scaffold
loud tangle
#

so set x to 0

#

then work out the sum

balmy scaffold
loud tangle
#

do u wanna prove the inequality for all x

#

for all x and with the smallest n

#

?

balmy scaffold
loud tangle
#

for all x?

#

like for every value x can have you wanna find n?

#

or just the smallest n

balmy scaffold
#

x is any real number

loud tangle
#

arbitrary from x

#

so for all values of x

balmy scaffold
#

yes

loud tangle
#

alr then

#

the graph idea was good tbh

#

thats what i thought of first

balmy scaffold
#

but i was set to like

#

prove it without graph

loud tangle
#

honestly it try induction

#

set x to like the minimum value then see if u notice anything that is the same for x is 0 and 1

#

then by induction works for all x

balmy scaffold
#

i think it is induction

#

x is like

#

one number right

loud tangle
#

yes

balmy scaffold
#

yea i think so

ebon remnant
#

hmm

ebon remnant
#

cuz we need to find smalled n natural number to get it right

balmy scaffold
#

yea

ebon remnant
#

sry nvm

#

the number of the sum can;t be 59

#

like 60 something

loud tangle
#

wouldnt do anything

#

if were doing induction you kinda have it be in inequality form

balmy scaffold
#

but if its =59 and if n has to be natural number it wont be possible

loud tangle
#

if x is 0 it would just be 1 + 2 + 3 + ... + n >= 59 => ((n)(n+1))/2 >= 59
=> n(n+1)>=118

if x = 1 => 1 + 2 + 3 + ... + n-1 >= 59
=> n(n-1) >= 59 => n²-n >= 118
.
.
.
meaning for all x the series reduces to 1 + 2 + ... n-x>= 59 => (n-x)(n-x+1)>=118
maybe that general formula does something

#

x is real right?

#

meaning it can be irrational

balmy scaffold
#

yea

balmy scaffold
loud tangle
#

gauss' formula for sums

#

for sums of n terms and ration 1

balmy scaffold
#

ohhhh

#

i get it now

ebon remnant
#

idk about that

loud tangle
#

(n-1)(n-1+1) = n(n-1)

ebon remnant
#

@balmy scaffold can u give me the question pic?

balmy scaffold
#

umm sure but

#

its in another language

ebon remnant
#

um can u copy paste it?

#

can u translate it with google translate?

#

or u may copy the question

balmy scaffold
#

sure

#

For any real number x, find the smallest natural number n such that |x-1|+|x-2|+|x-3|+...|x-n|>=59 is satisfied.

#

@ebon remnant

ebon remnant
#

thanks

loud tangle
#

n is natural right?

#

meaning it cant be negative

ebon remnant
#

ye

balmy scaffold
#

ye

ebon remnant
#

start from 1

loud tangle
#

working on that final equation and assuming its 118 cause its minunum

balmy scaffold
#

man my brain goin real smooth ngl

#

118?

loud tangle
#

i got $n = \frac{2x \pm \sqrt{437}}{2}$

warm shaleBOT
#

Kel.plush

loud tangle
#

by me i mean symbolav

#

symbolab

ebon remnant
#

the n can't be decimal

balmy scaffold
#

how did u got the 437?

ebon remnant
#

its -b +- thingy

balmy scaffold
#

oh

loud tangle
#

i dont really think there is a minimum value that satisfies all values of x

#

cause x is dependent on n

#

so if we have to define n automatically x gets restrained

#

hold on i fucked up

#

i realized i did

balmy scaffold
#

where

loud tangle
#

but its in mod

#

so its always +

balmy scaffold
#

ye

loud tangle
#

ok so u can split it in 2 sums

#

1 for x>n and one for the opposite

#

and if x=n its 0 anyway

balmy scaffold
#

and?

loud tangle
#

and that may partlemy be why it resulted that goofy ahh result

#

oh you literally just put a - in front of the first bit

balmy scaffold
#

fisrt bit?

loud tangle
#

hold on

#

ok so the first half of the sum is solely dependant on x

balmy scaffold
#

yes?

loud tangle
#

lemme write it out in latex

#

if x is 0 it would just be $1 + 2 + 3 + ... + n \ge 59 => \frac{n(n+1)}{2} \ge 59
=> (n)(n+1)\ge 118 =>n²+n \ge 118\\vdot\
\vdot\
\vdot\$
if x is 2, it would mean $|2-1|+|2
-2|+|2-3|+...+|2-n| = 1 + 0 + 1 + 2 + 3 + ... + |3-n| = 1 + \frac{|3-n|(|3-n|+1)}{2}\
\vdot\
\vdot\
\vdot\$
for a general scenario, it could be interpreted as 2 sums, one of x-1 terms and one of n-x+1 terms (the +1 being the case where x = 0)

therefore, a general formula would be:
$|x-1|+|x-2|+...+|x-n| = \frac{x(x-1)}{2} + \frac{|x-n|(|x-n|+2)}{2}$

#

im still editing hold on

balmy scaffold
#

oke

warm shaleBOT
#

Kel.plush

balmy scaffold
#

still editing?

loud tangle
#

if x is 0 it would just be $1 + 2 + 3 + ... + n \ge 59 => \frac{0(0-1)}{2}+\frac{n(n+1)}{2} \ge 59
=> (n)(n+1)\ge 118 =>n²+n \ge 118\\vdot\
\vdot\
\vdot\$
if x is 2, it would mean $|2-1|+|2
-2|+|2-3|+...+|2-n| = 1 + 0 + 1 + 2 + 3 + ... + |3-n| = \frac{2(2-1)}{2} + \frac{|3-n|(|3-n|+1)}{2}\
\vdot\
\vdot\
\vdot\$
for a general scenario, it could be interpreted as 2 sums, one of x-1 terms and one of n-x+1 terms (the +1 being the case where x = 0)

therefore, a general formula would be:
$|x-1|+|x-2|+...+|x-n| = \frac{x(x-1)}{2} + \frac{|x-n|(|x-n|+2)}{2}=\frac{x(x-1)+|x-n|(|x-n|+1)}{2}$

#

i think thats it

#

i think

#

this is very confusing tbh

balmy scaffold
#

it is

loud tangle
#

wait lemme write the first sum in a clearer way in the first 2 examples

warm shaleBOT
#

Kel.plush

loud tangle
#

there

#

phew

#

done

#

@balmy scaffold

balmy scaffold
#

umm

loud tangle
#

i might have fucked up somewhere

balmy scaffold
#

so the general formula right

loud tangle
#

yeah i think thats it

#

thats the sum rewritten for all x and n

balmy scaffold
#

$\frac{x(x-1)+|x-n|(|x-n|+1)}{2}$

warm shaleBOT
#

water bottle

loud tangle
#

yes

balmy scaffold
#

is it equal to 0?

#

or 59

loud tangle
#

its equal to the sum

balmy scaffold
#

on

loud tangle
#

if were taking the minimum its 59

balmy scaffold
#

ohh

#

as you were saying

#

n is directly Proportional to x

#

?

ebon remnant
#

its from other server

#

i don't understand the whole thing (I'm on grade 10)

#

why theres sigma

balmy scaffold
ebon remnant
loud tangle
#

is that the same exercise?

balmy scaffold
#

but still getting the grasp of it

loud tangle
#

cause idk where the floor came from

ebon remnant
#

i asked the same question

#

Anonymous

I'd probably approach the problem by finding the value of x for which the sum is minimal, which is x=(n+1)/2
then I'd split the summation into two parts, one for k less than (n+1)/2 and one for the rest
then I'd make the second summation negative and remove the absolute values
we have summation formulas that would apply to this scenario
and then you should be able to solve for n

#

wait that's actually almost right
but the minimal value of n for which this is true is 15
but it should be 16

balmy scaffold
#

what server did u ask tho

ebon remnant
#

its a mathematics server too

balmy scaffold
#

can u like inv me

ebon remnant
#

sure

ebon remnant
balmy scaffold
#

hm

#

also this problem is from 10th olympiad

#

but i think thats it

#

thank you for your time

#

.close

obtuse pebbleBOT
#
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wintry sundial
#

Why am I getting p = .5

obtuse pebbleBOT
wintry sundial
#

P is supposed to be .125

#

idk what i did wrong

#

in the 2nd question

obtuse pebbleBOT
#

@wintry sundial Has your question been resolved?

wintry sundial
#

<@&286206848099549185>

storm tapir
wintry sundial
#

I just expanded

storm tapir
#

should be $\frac{1}{2}(y+4) = (x-2)^2$

warm shaleBOT
#

asakura_akio

wintry sundial
#

and got this

storm tapir
#

and then $4p = \frac{1}{2}$

#

wait

#

om

warm shaleBOT
#

asakura_akio

storm tapir
#

did you forget the 4 part

wintry sundial
#

no

#

(y+4)=2(x-2)²

#

4p=2

#

p=.5

#

what did i do wrong

#

how did 4p=1/2

storm tapir
#

yeah the 2 is supposed to go to the other side

#

you should have nothing except (x-2)^2 on the right side

#

you're in this form because you have x^2 not y^2 so 4p is on the y-k side

wintry sundial
#

Is (y+4)/2=(x-2)² same as 1/2(y+4)=(x-2)²

storm tapir
#

yes

wintry sundial
#

Im really sorry but can you explain why it is the same

storm tapir
#

yeah, you just divided by 2 on both sides of the equation

#

1/2 times something is the same as dividing that something by 2

#

it's just a different way to write it

#

its like saying 1/2 times 2 is the same as 2/2

#

or 1/2 times 5 is the same as 5/2

#

you just have y+4 here instead of a number

wintry sundial
#

omg yeah i wrote it down and got it

#

thank you so much

storm tapir
#

np

wintry sundial
#

.close

obtuse pebbleBOT
#
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vestal niche
#

Where does the 1/11 and 11 infront of the e come from

fierce lagoon
#

Application of reversing the chain rule

#

Basically the direct result of a u-sub

#

If you let u = 11x

#

then du = 11 dx
=> dx = 1/11 du

#

But they instead wanted to keep dx so they rather split 1 = 11 • 1/11

vestal niche
#

Wait what?

#

I have a formula sheet with integration of e and derivative of e, but neither show or explain why that is done

#

Same thing with like sin1/7 x, idk why it’s -7cos1/7x

fierce lagoon
#

$$\begin{align*}
\int e^{11x}dx &= \frac{1}{11}\int e^u du \
&= \frac{1}{11}e^u \
&= \frac{1}{11}e^{11x}
\end{align*}$$

warm shaleBOT
#

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

fierce lagoon
#

They basically did this but in one step

vestal niche
#

Okay but the very first step, why is there a 1/11 infront of the integral

fierce lagoon
#

If you're familiar with the chain rule, deriving e^(11x) gets you 11e^(11x). They manipulated so that you're only integrating 11e^(11x) -> e^(11x) + C, but you need to balance out that 11 with a 1/11

vestal niche
#

I thought i was familiar with chain rule but I guess not

fierce lagoon
warm shaleBOT
#

Umbraleviathan

vestal niche
#

Okay but it’s an e not an x, does that not change anythjnf?

#

Anything

fierce lagoon
#

Doesn't change anything

vestal niche
#

Okay

fierce lagoon
#

$$e^{11x}dx \rightarrow \frac{1}{11}e^udu$$

warm shaleBOT
#

Umbraleviathan

vestal niche
#

So e^ what ever just stays the same but because we have a dx we need to have a value for the dx

fierce lagoon
#

Wdym a value for dx

vestal niche
#

Like you’re taking the derivative of 11x to get du/dx = 11, then multiplying 11 by dx to get du = 11dx, then dividing du by 11 to get du/11 = dx

fierce lagoon
#

Yeah

vestal niche
#

So the value of dx is du/11 which is the same as the 1/11 x du

fierce lagoon
#

You could say that yeah

#

dx is just equivalent to du/11 if you let u = 11x

vestal niche
#

Right so when we have the formula of integral e^u du = e^u + c

#

We actually need to re arrange what ever were taking the integral of to have a du there as well

fierce lagoon
#

well you can't just forget about the 1/11

#

You're integrating 1/11 • e^u du

#

That becomes 1/11 e^u + C

#

You had let u = 11x so just place it back in

vestal niche
#

Right but what I meant was like we’re integrating e^11x dx

#

There initially is no 1/11 there

#

But that dx has a value of du/11, so we take the 1/11 out infront, but idk why we keep the dx, unless it’s because we’re also putting an 11 infront of the e

fierce lagoon
#

Well what they're doing is similar. You would agree that $e^{11x} = 1 \cdot e^{11x}$?

warm shaleBOT
#

Umbraleviathan

fierce lagoon
#

Because what they basically said is "let's do a u-sub but fuck showing any of that"

fierce lagoon
vestal niche
#

Rofl yes

fierce lagoon
#

Their logic is similar to u-sub. The only reason why I'm showing you the u-sub is to show their logic behind doing that (basically expanding a step)

vestal niche
#

I agree 11/11 is 1, it’s just dumb to make it complicated for no reason but I guess there is a reason.

fierce lagoon
#

And 11 • 1/11 = 1

vestal niche
#

Okay

fierce lagoon
#

So split that 1

#

And then what they did was this

vestal niche
#

So they split the 1 into 11 x 1/11 to do a u sub randomly

fierce lagoon
#

They understand that if you were to derive e^(11x), you would get 11e^(11x) right

vestal niche
#

Right cause it’s e^u x u prime

fierce lagoon
#

But the integrand is e^(11x), not 11e^(11x)

vestal niche
#

Which would be 11e^11x

fierce lagoon
#

So they slapped a 1/11 to match the integrand

vestal niche
#

Right right right okay

fierce lagoon
#

But the same intuition is used for u-sub

vestal niche
#

Same as integral of 6x^2 is 2x^3

fierce lagoon
#

Yeah

vestal niche
#

Okay so even with e

#

It’s going to be the same integration rules as anything else like x

#

You need to cancel out the constant if there’s one there

#

Okay

#

That makes sense

#

So the formula I have for e^ du, I need to plug a du value in before

fierce lagoon
#

If need be yeah

vestal niche
#

Kk

#

Thank you

#

Appreciate you dumbing it down for me lol

fierce lagoon
#

Lol np

vestal niche
#

Have a nice Christmas man haha

#

.close

obtuse pebbleBOT
#
Channel closed

Closed by @vestal niche

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obtuse pebbleBOT
#
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winged jacinth
obtuse pebbleBOT
#

Please don't occupy multiple help channels.

#

@winged jacinth Has your question been resolved?

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timid silo
#

How would I rationalize the numerator

obtuse pebbleBOT
timid silo
#

Rationalise the Numerator? There is not much else you can or should do to that tbh

#

Ok

#

Maybe provide context on what you're trying to do

#

thats all

#

but that the answer

#

I got it wrong

#

You can multiply with (sqrt(r)-sqrt(7))/(sqrt(r)-sqrt(7)) if you want to make the thing be rational ib the numerator then

#

Oh hm

#

how about this one

#

Yeah idk should be right, maybe expand the thing

fierce lagoon
#

Multiply by the conjugate

timid silo
#

conjugate is sqrt (x^2+3) +x

#

@fierce lagoon

fierce lagoon
#

That ain't the conjugate

#

Where did the 2 come from

#

Also the conjugate is a fraction

timid silo
#

thats what I meant

fierce lagoon
#

Multiply by $\frac{\sqrt{x^2 + 3} + x}{\sqrt{x^2 + 3} + x}$

warm shaleBOT
#

Umbraleviathan

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

#
Channel closed

Closed by @dawn lotus

Use .reopen if this was a mistake.

#
Available help channel!

Send your question here to claim the channel.

Remember:
Ask your math question in a clear, concise manner.
Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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hybrid tartan
#

yo

obtuse pebbleBOT
hybrid tartan
#

Can anyone correct me if im wrong

#

(i) == 0.00604
(ii) == 0.00035
(iii) == 3

hybrid tartan
timid silo
hybrid tartan
#

Are you referring too the chance of a server being busy?

open raven
#

(i) and (iii) seem to be correct

#

but on the (ii) is giving me another answer

hybrid tartan
#

for part (ii) i just done .6^3 * .4^7

open raven
#

no, my logic was "less that 4 busy" = 0 busy + 1 busy + 2 busy + 3 busy

hybrid tartan
#

Aight give me a min, ill try it again

open raven
#

and im assuming order doesn't matter, right?

hybrid tartan
#

no

#

would it be 0.01229

#

For (ii)

#

wait

open raven
#

i dont think so

brazen jungle
#

bro?

hybrid tartan
#

.05476

open raven
#

it didn't give me that value, what was your way to thinking, i may be forgetting something

hybrid tartan
open raven
#

oh yeah, okay, i forgot the binomials

hybrid tartan
#

but instead of <= i done <

open raven
#

you are write if you did from x=0 to x=3

hybrid tartan
#

yes

open raven
#

its been a while since i have done this 😅

hybrid tartan
#

Well i think im right

open raven
#

yeah, i agree!

hybrid tartan
#

.close

obtuse pebbleBOT
#
Channel closed

Closed by @hybrid tartan

Use .reopen if this was a mistake.

solemn crypt
#

.reopen

#

🧍🏿‍♂️

hybrid tartan
#

.reopen

obtuse pebbleBOT
#

hybrid tartan
#

.close

obtuse pebbleBOT
#
Channel closed

Closed by @hybrid tartan

Use .reopen if this was a mistake.

solemn crypt
#

☹️

#

🦌

obtuse pebbleBOT
#
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Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
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hybrid tartan
#

yo

obtuse pebbleBOT
hybrid tartan
#

Can some correct me if im wrong

broken dove
#

Yeah

hybrid tartan
#

(i) == 1/5
(ii) == 1/25
(iii) == 1/625
(iv) == 24/625
(v) == 11/25
(vi) == 1/25

broken dove
#

give me a sec

rigid lintel
#

ii is wrong

#

1/5

#

iii correct

#

iv is wrong

#

v is correct

hybrid tartan
#

idk what i done wrong

rigid lintel
#

vi is correct

#

well if theres no balls of the same colour

#

then theres 5 possible colours for the first ball

#

4 possible for the second

#

3 2 1

#

5 * 4 * 3 * 2 * 1

#

= 120

#

1/120

broken dove
#

isnt iv like 0

#

or am i trippin

rigid lintel
#

you have 5 spots for 5 different colours

#

so they can all hjave different colours

#

so not 0

broken dove
#

bro i got
1

1000000

#

is my math off

rigid lintel
#

how did tyou get that

#

wait actually

#

oh you cant type that lmao

#

,calc 1 * 4/5 * 3/5 * 2/5 * 1/5

warm shaleBOT
#

Result:

0.0384
rigid lintel
#

,calc 1/120

warm shaleBOT
#

Result:

0.0083333333333333
rigid lintel
#

ohhhhhhhhhhhhhhhhhhhhhhhhhhhh

#

,calc 24/625

warm shaleBOT
#

Result:

0.0384
rigid lintel
#

you were right

#

lol

#

iv correct

#

my bad

hybrid tartan
rigid lintel
#

yeah

rigid lintel
hybrid tartan
#

I also got another question, how would I be able to approach this

#

These questions are also not homework, they are past exam papers which im doing as revision

#

Can anyone give me a hint?

solemn crypt
#

12

hybrid tartan
#

.close

obtuse pebbleBOT
#
Channel closed

Closed by @hybrid tartan

Use .reopen if this was a mistake.

#
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Ask your math question in a clear, concise manner.
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timid silo
#

hi my teacher sent us this for a task and i’m confused by the task like what am i suppose to do and how if you could give hints

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
#

@timid silo Has your question been resolved?