help-27

[fluid rampart]

Isn't it suppose to be au+bv+cw = 0 with a,b,c = 0 for linearly independent?

[left robin]

nope

au+bv+cw=/=0 for all a,b,c=/=0
is lienar independency

[fluid rampart]

Wait I learnt the opposite: if au+bv+cw = 0 for all a,b,c ≠ 0 then it's dependent, but if au+bv+cw = 0 and a,b,c = 0 then it's independent (trivial solution as unique solution)

[left robin]

for a,b,c=0 we always get that the whole equals 0

so we kinda ignore

[fluid rampart]

if the vecteur is null then a,b,c can be different from zero

[left robin]

oh wait

i think i get what you mean

[fluid rampart]

but still gives zero as an answer

[left robin]

u,v,w are linearly independent if
au+bv+cw=0
ONLY if a,b,c=0

which is equivalent to saying:
u,v,w are linearly independent if
au+bv+cw≠0 for all a,b,c such that not all a,b,c equal 0

[fluid rampart]

Yes now we need to prove u+v, v+w and u+w are independent but I'm struggling to get from au+bv+cw=0 for all a,b,c = 0 to a(u+v)+b(v+w)+c(u+w)=0 for all a,b,c = 0

[fluid rampart]

This makes sense ty man!

.close

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[fallen wind]

hi its me again..

[fallen wind]

i cant tell what im doing wrong

heres the answer i was supposed to get for f'

[pseudo basin]

s', not f'

[fallen wind]

same thing

[pseudo basin]

no, not the same thing. you don't have a function named f.

also there's the issue that your handwriting makes it kind of hard to tell apart y and 4.

[fallen wind]

sorry

[pseudo basin]

oh and you differentiated $-4y^{2/5}$ incorrectly

[woven radish]

Ann

[pseudo basin]

it should be $-\frac{8}{5} y^{-3/5}$ and not $-\frac{4}{5} y^{-3/5}$ as you wrote

[woven radish]

Ann

[pseudo basin]

so that's at least one algebraic screwup spotted

[fallen wind]

youre right

[pseudo basin]

that and also tbh i would not have gone about differentiating s this way in the first place, unless you're under explicit instructions from your teacher to Use The Product Rule Or Else, or something.

[fallen wind]

how else would i differentiate it

but also i dont know what i did wrong with product rule aside from that algebra

[pseudo basin]

i would have first expanded $-4y^{2/5}(y^2 - 54)$ as $-4y^{12/5} + 216y^{2/5}$ and then i would apply the power rule

[woven radish]

Ann

[pseudo basin]

much less headache

[pseudo basin]

well like... that alone is already enough to get a wrong answer, so.

[fallen wind]

but if i fixed my algebra its still off

[pseudo basin]

have you actually redone the algebra yet

[fallen wind]

yes

[pseudo basin]

ok, show me

maybe you screwed up again but somewhere else this time

also by doing this you will acknowledge that you actually deliberately want to cause yourself headache

[grim burrow]

If you have decided to bring the negative sign in together with the term 4y^(2/5), this here would have been a + sign instead

[pseudo basin]

you were not done...

[fallen wind]

i understand that later i should expand. but i also wanna make sure i know how to do power rule

what am i not done with

[pseudo basin]

you are not done with redoing your work w/ the product rule

[fallen wind]

you mean like the two negatives cancel out?

[pseudo basin]

the second term just disappeared

you thanos-snapped it

leaving a lone minus sign with nothing to its right

why did you do that

[grim burrow]

No, i meant your product rule is wrong

[fallen wind]

i dont understand

i dont see what disappeared

and i dont see what was wrong with product rule

[grim burrow]

There would have been a - sign there if your you didnt choose u to be -4y^(2/5)

[fallen wind]

oh i just never wrote that in cause it already wasnt looking right

[pseudo basin]

you claim to have redone your work and then submit unfinished work

[fallen wind]

.close

[devout snow]

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[pseudo basin]

??

.reopen

[devout snow]

✅

[pseudo basin]

could've at least said "i don't need any more help from y'all" if that's the case, rather than just closing the channel in our faces.

[fallen wind]

its not that i dont need help its just that im tired of the attitude

[pseudo basin]

and that you could also have communicated.

instead, you are displaying "attitude" of your own.

[fallen wind]

why are you making such a big deal out of it

move on

[pseudo basin]

imagine slamming shut a physical door in front of someone. they will make a big deal out of it.

[patent tartan]

"tired of the attitude" while people try to help you

[devout snow]

@fallen wind Has your question been resolved?

[devout snow]

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[devout snow]

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[raw briar]

where do I go to get quick math help?

[raw briar]

I'm in math in society and need help with sets

[pseudo basin]

post the problem(s) you need help with

[raw briar]

eh...it's not that simple

if something is asking me for the compliment and the set is A=(xIx is even and x>6)

I don't know how to write the compliment, A'

[devout snow]

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[devout snow]

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[winged torrent]

Anyone can teach me how to do this?

[devout snow]

@winged torrent Has your question been resolved?

[patent tartan]

You can use the equation ax + bx + cz = S to eliminate one of the variables in P = xyz

Then for example you have P(x,y), and you can use standard methods to find stationary points (ie max/min)

[winged torrent]

Ah okay ty

.close

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[neon folio]

@brittle raven

[neon folio]

case 1 is [-1:3/2[

[brittle raven]

ye

[neon folio]

case 2 is R intersected with x<1

no

cuz x can be positive

like 0.8

[brittle raven]

ye ye

[neon folio]

so whats the solution

[brittle raven]

[-1:3/2[ in case 1
]-infinity ; 1 [ in case 2

[neon folio]

without ( )

[brittle raven]

finally

[neon folio]

edit it

and with ] at -inf

good

now we need to reunite those solutions

form the 2 cases

le reunion

i guess

[brittle raven]

ye

[neon folio]

so

[brittle raven]

union & reunion

[neon folio]

whats the reunion

yes

[neon folio]

?

[brittle raven]

we use it in intervals

[neon folio]

yes

tell me the reunion

[brittle raven]

of those solutions ?

[neon folio]

yes

we have 2 cases

we need to reunite the solutions

to get the answer

[brittle raven]

]-infinity ; -1 ] ∪ [- 1 ; 1 ]

]-infinity;1] ?

[neon folio]

no

case 1 was [-1:3/2[

case 2 was ]-infinity ; 1 [

[brittle raven]

]-infinity; 1 ] ∪ [ 1 ; 3/2 [

[neon folio]

reunite those

[neon folio]

yes

[brittle raven]

yaay

[neon folio]

wait

in case 2 the 1 has [

[brittle raven]

ahh ye ye

so

]-infinity; 1 [ 😐

[neon folio]

yes

case 1 was [-1:3/2[
case 2 was ]-infinity ; 1 [

reunite these

[brittle raven]

]-infinity ; 1[

[neon folio]

?

[brittle raven]

3/2 > 1

[neon folio]

whats that

[-1:3/2) ∪ (-infinity ; 1)

use )

it's so confusing to use [ and ]

[brittle raven]

3/2 > 1

[neon folio]

no

do you know how to reunite?

it means to combine the solutions of both cases into a single interval

[brittle raven]

in first case we have x < 1 and in the second case we have -1<x<3/2

the combine of the solution is ]-infinity ; 1 ]

cuz 1 < 3/2

is that false ?

[neon folio]

3/2 is 1.5

so you need to include 3/2 into the new interval too

[brittle raven]

1 < 1.5

[neon folio]

yes

[brittle raven]

x < 1

why we need to include it ??

[neon folio]

and on the right side of the interval you write the biggest possible value it can have

here the biggest value is 3/2

not 1

[brittle raven]

for example

it gonna works ?

[brittle raven]

so if we test 1.2
for example
it gonna works ?

[neon folio]

yes

[brittle raven]

oh ok

[woven radish]

Results provided by WolframAlpha

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Requested by Master Oogway#0599

[neon folio]

see?

if we use 1.2 the inequality is true

if we use 1.6

[woven radish]

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[neon folio]

it's false

because 3/2 < 1.6

@brittle raven

[brittle raven]

oh ok

ty

[neon folio]

so whats the final answer

[brittle raven]

[-1;3/2( ∪ )-infinity ; 1 )

[neon folio]

no

thats not final

final answer is a single interval

[brittle raven]

ah

(-infinity;3/2(

[neon folio]

)

[brittle raven]

i forget hh

[neon folio]

BUT

we didnt finish

we still have 1 more thing to do

[brittle raven]

what ?

what it is

[neon folio]

what was the first step we did

in this problem

?

[brittle raven]

solve inequality

to know the restricted values

[neon folio]

yes

[brittle raven]

(2;3)

[neon folio]

now we have to check

if our final answer

contains a restricted value

so we do the intersection

of our final answer

with the restricted values

[brittle raven]

nop

3/2 < (3,2)

[neon folio]

(-infinity;3/2) intersected with (2,3)

(3,2) isnt an interval

in an interval the bigger number is on the right

and a number cant be smaller than an interval

it can only be smaller than a value from the interval

[brittle raven]

what that means ?

[neon folio]

thats what we need to do

to see if our final answer and the restriced values have something in common

if they dont

then our final answer is correct

if they do

we have to change our final answer

[brittle raven]

they dont

[neon folio]

why

[brittle raven]

we don't have any number from this set (2,3) in our intervale

[neon folio]

in other words

3/2 < 2

right?

[brittle raven]

yep

[neon folio]

good

so whats our final answer

[brittle raven]

)-infinity;3/2(

[neon folio]

]

and [

[brittle raven]

]-infinity;3/2[

[neon folio]

good

so

how was the problem?

hard?

or easy

[brittle raven]

nqh

nah

easy

[neon folio]

nic

e

[brittle raven]

If you were a teacher, how many points would you give for this question?

[neon folio]

idk

depends on how many questions there are in total

this is preety hard

so i guess more than the rest

[brittle raven]

3 pts HHHH

[neon folio]

3 pts out of what?

[brittle raven]

20

[neon folio]

hm

ok

whats the exercise with the most points?

[neon folio]

3.5

lol

[brittle raven]

i hate logic

hard 😢

[neon folio]

i know how to do this

[brittle raven]

lets do it

:3

[neon folio]

1 sec

to check if i know

i forgot 😭

[brittle raven]

rip

check dm

u can close this channel

[neon folio]

.close

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[stuck axle]

In the rectangle ABCD, |AB| = 60. The point M is the middle of the side [AD]. The point N is on [AD] with |AN| = 20, what is the length of [AD] if the triangle MNC is right in N

[stuck axle]

I don’t know where I should start lol

And I should make them equal right ?

With the Pythagorean theorem right ?

Never mind I don’t need help lol

.close

[devout snow]

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[stuck axle]

.reopen

[devout snow]

✅

[stuck axle]

I’ve made a mistake somehow

Oh never mind I’m really dumb I can’t read a question

It’s |AD| that we want not |ND|

So it’s 110

.close

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[tiny flume]

using the shoelace method

[tiny flume]

i have my answer

but im not sure if im correct

[midnight dirge]

um

send ur working n ans

[devout snow]

@tiny flume Has your question been resolved?

[tiny flume]

my ans is 49

.close

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[devout snow]

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[cunning fern]

Hi ,can someone help me with the Fourier transform of "Λ(t/T)signum(t)" ?

[devout snow]

@cunning fern Has your question been resolved?

[devout snow]

@cunning fern Has your question been resolved?

[devout snow]

@cunning fern Has your question been resolved?

[devout snow]

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[summer dune]

hello! i’m stuck on part ii

how would i find the domain restrictions on this function?

i looked it up on desmos and it seems to be (0,120) but how would i get to this answer through an equation?

[manic zinc]

Do you know how to draw a quadratic graph?

[summer dune]

i think so

but this one has a negative in front of the x^2 so would my parabola be flipped?

[manic zinc]

Yep, it's upside down

What are the roots?

[summer dune]

my graph on desmos says it’s right side up

[manic zinc]

What are you plotting?

What is the equation that you put into desmos?

[summer dune]

i put the p(x) équation

[manic zinc]

Try putting it without p(x)

[summer dune]

so like a y instead?

[manic zinc]

Yep

[summer dune]

ok!

hmm i’m getting the same result

[manic zinc]

It's still upside down u shaped

[summer dune]

it’s u shaped

[manic zinc]

It looks more like n than u?

[summer dune]

oh wait im-

im an idiot

NVM yeah it’s shaped as an n

sorry

sorry sorry

[manic zinc]

Do you get it now?

[summer dune]

i’m still confused on how would i find my domain?

[manic zinc]

So for what x values is the y value bigger than zero?

[summer dune]

would i have to split it in half?

[manic zinc]

That part is the graph is positive y values

For what x values do we get those y values?

[summer dune]

120? right

[manic zinc]

When x=120 y=0

So y is not positive

[summer dune]

so i’d half to put parentheses on them?

[manic zinc]

The parentheses represent a range of values

[summer dune]

wait i’m a little confused

[manic zinc]

(a,b) means a<x<b

[summer dune]

if the second half of the parabola has a negative slope, i would have to ignore that part right?

[manic zinc]

No, because y is still positive

[summer dune]

but if the slope is negative then wouldn’t i leave that out of the domain?

[manic zinc]

We are not looking at gradient

[summer dune]

wait wait

this is the question im working on

[manic zinc]

Ohh I see

Sorry about that

Yeah so you only want when the slope is positive

[summer dune]

sorry i should have been more clearer

im still confused how would i find this through an equation

math is so harddhifhfi

[manic zinc]

I thought you were asking for what range of x is p(x) positive?

But you are asking for what x is p'(x) positive?

[summer dune]

i was thinking the same thing until i reread the question

what’s p’(x)?

[manic zinc]

The derivative

Do you know what that is?

[summer dune]

yeahh

[manic zinc]

Basically you had the right idea here

When is the slope positive?

Like for what x values?

[summer dune]

so i would have to find the max point? and set my restriction based on that?

[manic zinc]

Yeo

Yep*

[summer dune]

(0,60)

is that right

[manic zinc]

Is that a coordinate?

[summer dune]

oh

those are intervals

the domain

[manic zinc]

Is the gradient positive when x is less than zero

[summer dune]

im not sure what gradient means

[manic zinc]

Sorry slope

[summer dune]

oh

yeah it would be

[manic zinc]

Is the slope positive when x is less than zero?

[summer dune]

i think

[manic zinc]

Yep so you need to include that part in your values too

[summer dune]

okayyy

wait would that make sense with my equation?

what do the negatives represent?

[manic zinc]

Oh in your question you are only interested in x being positive because it represents sales of an item?

I see

[manic zinc]

Then this is correct

[summer dune]

ohh okayy thank you

wait

how would i solve this equation-wise?

[manic zinc]

Using the equation, you can draw the graph yourself instead of using desmos

Then everything else is the same

[summer dune]

is there any other way

like would i be able to find the derivative and do something with it?

[manic zinc]

Yep you can, so what is the derivative in this case?

[summer dune]

would it be 10?

[manic zinc]

Not quite

[summer dune]

ohh

[manic zinc]

Have you seen differentiation before?

Like x^a differentiates to ax^(a-1)

[summer dune]

i have, but my teacher didn’t tell us to use it for these questions

so i would have to do it the long way right?

[manic zinc]

In that case drawing the graph is the easiest way

[summer dune]

alright :))

if i were to find the derivative, how would it help solve the answer?

like how do i use it to solve the question?

[manic zinc]

So in this case the derivative is 120-2x

This is positive means 120-2x>0 so x<60

Did that make sense?

[summer dune]

ohh i think so

thanks so much for the help!

[manic zinc]

No problem

[summer dune]

i really appreciate it!

.close

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[zealous spruce]

8.5
the inflection point is 1/2

why is it considered the maximum gradient?

[sonic smelt]

Because the maximum gradients occurs at the point where the derivative of the gradient (aka the second derivative) is 0

Which is also the inflation point

[zealous spruce]

so max gradient is always the 2nd derivative = 0

[winter patrol]

not always

[zealous spruce]

pls explain

[winter patrol]

second derivative can be used to tell you locations of stationary points of the first derivative,
which could be local max/min or inflection

generally it doesn't give you the location of the absolute max gradient

[zealous spruce]

thanks

.close

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[hollow onyx]

can anyone explain to me how this works?

[hollow onyx]

i forgot how to do the quadratic formula

:<

[small nymph]

this should explain it

[hollow onyx]

substitute?

im still kinda confused

[hollow onyx]

is the denominator p?

[small nymph]

https://opentextbc.ca/intermediatealgebraberg/chapter/10-5-solving-quadratic-equations-substitution/ if you never saw it before

then im using the reduced quadratic equation https://en.wikipedia.org/wiki/Quadratic_equation

[small nymph]

last line is my prefered formula for quadratic equations 🙂

[hollow onyx]

ic

ill process it

[small nymph]

quick paint scribble sorry haha

[hollow onyx]

yep i drawing a blank hahha

[devout snow]

@hollow onyx Has your question been resolved?

[devout snow]

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[devout snow]

@kindred mango Has your question been resolved?

[devout snow]

@kindred mango Has your question been resolved?

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[turbid sphinx]

How do I simplify this?

[tranquil light]

what was the original question?

[turbid sphinx]

find the derivative of x/2-tanx

[devout snow]

@turbid sphinx Has your question been resolved?

[shadow breach]

for starters, the - needs to become a + because of the -tanx turning into -1/cos²x

[shadow breach]

in here i mean

[turbid sphinx]

I thought the derivative of tan was sec^2?

[shadow breach]

you're working with -tan

not tan

the minus stays

[turbid sphinx]

oh

[turbid sphinx]

how would I find the derivative of -tan?

[shadow breach]

the derivative of -anything is the same as the derivative of anything except you add the minus

because you can write - as -1 x f(x)

and a if you have a function multiplied by a constant

the constant stays as it is when you derive constant * f(x)

[turbid sphinx]

ok i see

[turbid sphinx]

.close

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[restive river]

can someone help me out here

[restive river]

its a practice test (non-graded)

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

[elfin hill]

Use Rienman

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[short iron]

[\tan = \frac{1}{3\sqrt{7}} * \frac{\sqrt{7}}{\sqrt{7}}= \frac{\sqrt{7}}{21}]

[woven radish]

dopediscorduser

[short iron]

Where's my mistake?

[dense jay]

it would just be $3\sqrt{7}$

[woven radish]

Azo

[devout snow]

@short iron Has your question been resolved?

[short iron]

Oh

I must have mixed up my opposite and adjacent values

.close

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[vivid wren]

Tc f = 5 + 12
A manufacturer shipped units of a certain product to
two locations. The equation above shows the total
shipping cost T, in dollars, for shipping c units to the
closer location and shipping f units to the farther
location. If the total shipping cost was $47,000 and
3000 units were shipped to the farther location, how
many units were shipped to the closer location?

[vivid wren]

need help someone

[devout snow]

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[restive river]

hey i have a question

[restive river]

im struggling with this issue

the question is in spanish which makes it worse

but i can translate it to english

for context this is it in englihs

it basically says

Perian Herring inserts announcements into her envelopes for extra income during her spare time. Her initial cost for obtaining the cost information was £200.00. Every envelope is £0.2 and she is paid £.04 per ready-made envelope. Consider that x represents the number of envelopes already prepared.

Perian does a job. She makes 50% value from what she spends to do the job (40p). She has already spent £200.

The question is to find out how many envelopes have already been prepared.

[devout snow]

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@restive river Has your question been resolved?

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[devout snow]

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[spiral shell]

not sure where to start

[trim vine]

In plain English, that’s inverse prime equals one over prime inverse. U can see a pattern in English

[devout snow]

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[patent marsh]

whoops lol

okay so for this your u is right

but also consider that $u = 10 - x \implies x = 10 - u$

[woven radish]

MellowDramaLlama

[patent marsh]

make an extra substitution 🙂

[dusky adder]

u mad man

thank you

[patent marsh]

https://tenor.com/view/extreme-gif-8818707

[patent marsh]

yep! now just solve like you normally would with the power rule

[dusky adder]

I think exponents can be combined here?

or no

[patent marsh]

nah not with + and -

mulitplication yeah

[dusky adder]

oooh, ok

ty

[patent marsh]

np

[dusky adder]

program is telling me this is wrong

i gotta rest though so I'll bbl

.close

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[teal goblet]

what does log e evaluate to?

[teal goblet]

is it one?

[pseudo basin]

when you say log do you mean the natural log?

[solid spire]

When you just say log base 10 is in implied

Then it's 0.434 something

[winter patrol]

When you just say log base 10 is in implied
no, the base depends on context

[teal goblet]

log(log(e-x))

would it be

1/log(e-x)

[solid spire]

Very true. But if you just write log(x) base 10 would be the most common. Hence why it would be implied

[grim agate]

no, wolfram says otherwise, so do many. context is necessary

[winter patrol]

no, i mean what i said

[grim agate]

,w log 10

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by deep.#7373

[teal goblet]

^

the derivitive i mean

[grim agate]

uh i’m confused

[pseudo basin]

got a feeling that my question of "When you say log, do you mean natural log?" went unanswered.

[teal goblet]

bruh

[pseudo basin]

whether that was by carelessness or by deliberate decision, i do not know.

[winter patrol]

regardless the derivative is incorrect

[teal goblet]

so

[solid spire]

Turns out it's an engineering thing

[teal goblet]

would it be 0?

because e is a constant right

[winter patrol]

would it be 0?
depends of you're differentiating with respect to x or something related to x

[teal goblet]

with respect to x

[winter patrol]

then no, the derivative isn't 0

as log(log(e-x)) isn't a constant

[teal goblet]

sorry

x is 0

so it would be 0 right

[winter patrol]

can you show the original question...

where's x is 0 coming from

wdym by "it"

[pseudo basin]

how could i forget that i am not the kind of person who deserves answers to their questions.

[teal goblet]

ye x is 0 mb

[winter patrol]

differentiate first, plug in 0 after

you do NOT plug in 0 first

[teal goblet]

ye ik

i got to the log part and im not sure what to do next

[winter patrol]

where's the double log coming from...

[teal goblet]

the bottom

logarithmic differentiation

[winter patrol]

can you show your work

[pseudo basin]

ok so log means natural log

it wouldve been hella nice to know this by explicit confirmation and not by contextual inference alone ngl

[teal goblet]

im not sure if 1/log(e-x) should be d/dx (log(e-x)/log(e-x)

[winter patrol]

bad notation and sign screw up

[teal goblet]

???

[winter patrol]

note that you have actually differentiated in your first step,
writing f'(x) there is highly inappropriate / wrong

[teal goblet]

im supposed to be d/dx first right

[winter patrol]

you're supposed to have ln(f(x)) = there

[teal goblet]

we cant use ln lmao

[winter patrol]

why not

i'm just using ln here to unambiguously refer to natural log

if your using log for the natural log just write log whenever i use ln

log(f(x)) =
if you insist

[teal goblet]

alrigh

[winter patrol]

you also miswrote cos as cot in the numerator when copying down the question

[teal goblet]

im tired lmao

[winter patrol]

as for the part involving the derivative of log(log(e-x))
you're missing a - sign from the derivative or from distribution,
it is unclear which

[teal goblet]

how?

[winter patrol]

start by showing your work for the derivative of

log(log(e-x))
, with adequate application of chain rule

[teal goblet]

im not following

did i not do that?

[devout snow]

@teal goblet Has your question been resolved?

[devout snow]

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[acoustic mountain]

maybe im just dumb …

Jake drops his piece of cake off his porch and half a second later it hits the ground. Find the instantaneous velocity of the cake when it hits the ground. how do u find the instantaneous velocity??? 🤠

[winter hound]

Instantaneous velocity is the velocity recorded at a specific point of time

[acoustic mountain]

what would the equation be tho 🧍🏻‍♀️

v = gt?

[winter hound]

I’m not an expert in that but all I can give is an example

since this was not taught in my school and I had to google it in order to find the answer

imagine yourself

and let’s say you have a bf or gf shouting for help from a far place

[acoustic mountain]

yes

[winter hound]

so you run to them, and your velocity is not constant

so at some point, your velocity will be slow

and at some point, it will be fast

It’s like you’re running and getting tired so you’re slowing down

Once you get enough energy you start to get back to your original speed

[acoustic mountain]

mhm

[winter hound]

Let’s say I want to know what’s the velocity at a specific point of time when I’m running

That’s called instantaneous velocity

[acoustic mountain]

yes

OHHHH

[winter hound]

let’s say at the 5th second of running, my velocity is 2ms^-1

[acoustic mountain]

OK

[winter hound]

is my instantaneous velocity at 5th second is 2ms^-1

You can search up for more, this is what my memory told me

maybe searching is better since it’s been a while I’ve dealt with these questions

[acoustic mountain]

i think its dealing with free fall

so it would be like

(9.8m/s^2) (.5s)

RIGHT

RIGHT

i think im rigt

HHANK YOU

.close

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[fathom rivet]

anyone know how to do these

[devout snow]

@fathom rivet Has your question been resolved?

[fathom rivet]

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[restive river]

how do do this - 10 to the power 2 route -2

[pseudo basin]

the first step would be to write it in a way that can actually be understood by someone other than you

[restive river]

i am in myp1

[pseudo basin]

maybe write it on paper

[restive river]

i cant

[pseudo basin]

why not?

[restive river]

let me try

how do i send it

[pseudo basin]

writing it with the keyboard so far has produced 10 to the power 2 route -2, which i can't say i understand.

but yes, send a photo here.

[midnight dirge]

route?

root?

wot

i too think

[pseudo basin]

let us not riddle ourselves.

[pseudo basin]

it is OP's responsibility to make their question understandable.

[pseudo basin]

okay, so 10^(2 sqrt(-2))

...have you had any encounters with complex numbers before?

[restive river]

yees

[pseudo basin]

right...

[midnight dirge]

OH THIS PERSON WASNT OP LOL

[pseudo basin]

and have you also encountered complex exponentials?

[restive river]

niet

[pseudo basin]

namely, are you familiar with the formula e^(ix) = cos(x) + i sin(x)?

[restive river]

no

[midnight dirge]

hey this looks fun

[pseudo basin]

well. yikes, i guess

[midnight dirge]

we can use

[pseudo basin]

ok @midnight dirge you can take over from here

[midnight dirge]

$z^s = e^{s \log (z)}$

[midnight dirge]

and

$\log (z) = \log |z| + i arg(z)$

[midnight dirge]

T.T that arg

welp

[restive river]

10^2i

[midnight dirge]

errrr

[restive river]

that does'nt meke sense

[midnight dirge]

u didnt eval the top properly

anyway

first

[restive river]

i knoow

[midnight dirge]

$10 ^ {2 \sqrt{-2}}$

[restive river]

exactly

[restive river]

exactly

[midnight dirge]

$2 \sqrt{-2}$

[restive river]

this

[midnight dirge]

what happens to this

how would u simplify this

im not asking u

...

[restive river]

2o

2i

[midnight dirge]

no

its 2i if we had

[proud mural]

Kekw

just leave

[midnight dirge]

$2 \sqrt{-1} = 2i$

[midnight dirge]

but here its sqrt 2

so what would it be instead

...

[restive river]

my mind - ...

[midnight dirge]

wot

[winter hound]

let me add more chaos

imaginary number

[midnight dirge]

$2 \sqrt{-1} = 2i$

[midnight dirge]

$2 \sqrt{-2} = ?$

[restive river]

idk

[winter hound]

Separate sqrt of -2

[midnight dirge]

so

[winter hound]

And make it so that it has sqrt -1

And you’ll see it

[midnight dirge]

notice u can take out 2 from the sqrt cuz its real

or arg 0

like

[restive river]

2i root 2

[midnight dirge]

yep

$10 ^ {2i \sqrt{2}}$

[restive river]

ok

[midnight dirge]

so rewriting it we get

$e^{2i \sqrt2 \log (10)}$

[midnight dirge]

idk thats about it?

what exactly do u want anw

[restive river]

im just solving some problems

and found this one hard

thanks

[midnight dirge]

um

idk i just

rewrote it

but we arent exactly solving for anything?

[restive river]

true

i was simplifying it

*wanted to

bye

.close

[devout snow]

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[gusty merlin]

Hi

[gusty merlin]

How many times would 0.86 go in 100

[hollow pollen]

use division

[gusty merlin]

How?

[spare zealot]

Here let's start with a simpler problem, how many times would, say, 2 go into 100?

[hollow pollen]

3 divided by 2 is how many times 2 goes in 3

so you can apply the same concept

[gusty merlin]

50

[gusty merlin]

1.5?

[spare zealot]

Yup, you got both of those

The same concept applies with decimal numbers

[gusty merlin]

So basically 30/0.86?

[heavy terrace]

multiply both by 100 to get rid of the decimal. You're not changing the result

[spare zealot]

Where did the 30 come from?

[heavy terrace]

that will help ya

then use long division formula

[gusty merlin]

I’m confused

Okay so

Basically

[heavy terrace]

10000/86 and use long division formula

[gusty merlin]

I’m figuring out how many coffee cups (0.86cm2) would go into a 30 metre room

How do I do that

[heavy terrace]

[spare zealot]

30 square metre?

Like setting them side by side on the floor?

[gusty merlin]

Like we’re filling the whole classroom

[spare zealot]

Or 30 cubic meter

[gusty merlin]

Up to the top

Cube

[gusty merlin]

Sorryyy

[heavy terrace]

all good

[spare zealot]

It's the same process as the simpler problem I gave before

When you wanted to know how many times 2 goes into 100, you divided 100 by 2

Yup

Just like that

[gusty merlin]

Oh

[spare zealot]

You deleted it but I saw it

[gusty merlin]

That equals 34.88

[spare zealot]

,w 30/0.86

[coral token]

pstttt he has to convert to same units

[gusty merlin]

Yea I did coz I thought it was wrong

If it has to be the same unit then we can add another 0

[spare zealot]

Not sure how to convert the cups to cubic when I'm not sure what 0.86 cm^2 is even measuring

[coral token]

i think he means 0.86 cm^3 but idk man

[spare zealot]

That's what I assumed

[coral token]

even so 30/0.86 would not make much sense

[gusty merlin]

How many coffee cups - 0.0086m would fit into a 30m room

[hollow pollen]

30m?

[spare zealot]

Assuming both units are cm^3, you would be correct with your 34.something answer

[hollow pollen]

do you mean 30m^2 or 30m^3

[spare zealot]

They mean 30cm^3

We're not sure about the cups tho

[gusty merlin]

What is happening

Y’all

[hollow pollen]

what kind of room is 30cm^3 lol

[gusty merlin]

I’m confused now why are there so many people here

We don’t know we got given that

[pseudo basin]

if you were given a poorly worded problem then it is not your responsibility to untangle the wording

[gusty merlin]

I’ll start from the start

I need to figure out the volume of a coffee cup - I will paste the picture below

This coffee cup - I need to find out how many of these would fit into a 30m^3 room. Firstly, I need to find out the perimeter and the volume for this in order to find out how many would fit in the room

Can someone please help me finding out the volume of the coffee cup - like edges etc

I need to fill the whole room to the top

That’s the room below

[gusty merlin]

I need to figure out how many of these cups would fit into that room

Can someone please help?

[pseudo basin]

are those cups empty? like, are we stacking cups inside each other for this?

or are we treating them as solid, filled-in objects

[gusty merlin]

Yes they’re empty

[pseudo basin]

right...

that kind of complicates matters, i think

[pseudo basin]

because then we need to know the thickness of the paper they're made of, to know how high a stack of n such cups will be

@devout lichen channel occupied please move

[gusty merlin]

No basically they’re solids

[pseudo basin]

...

so are they empty or are they filled in

[gusty merlin]

Like they’re trash and we need to figure out how many would fit in the room

They are empty tho

[pseudo basin]

so we can stack them inside each other

[gusty merlin]

However it will fit in the room

Inside eachother, randomly stack, just throw them in etc

So how would I do that- firstly I would have to calculate the cup

[pseudo basin]

well it does kind of matter. are we looking to maximize the number of cups filling the room?

[gusty merlin]

Yes

The room has to be FULL of cups

[pseudo basin]

right

well ok like

some assumptions may need to be made

[gusty merlin]

I’m hearing

[pseudo basin]

like, how thick is the lip of the cup? i.e. the ring at the top of it

i imagine it can't be more than a few millimeters

[gusty merlin]

I’m not sure

That’s all I have

[pseudo basin]

hm.

[gusty merlin]

12oz (360ml)

[pseudo basin]

yes, you've sent that here already

[gusty merlin]

Yea that’s all I have

Omg I found something else that may help

[pseudo basin]

i mean, we could just naïvely divide the volume of the room by the volume of one cup, and get an estimate on how many cups will fill the room if we just toss them in haphazardly.

but i believe we can do better.

ah wait hold on! the diagram DOES tell us the thickness of the lip, even though it's indirect

110 - (97+10) = 3mm

[gusty merlin]

Oh

OMG

UR A GOENUS

[pseudo basin]

right, so then a stack of n cups would have height 110 + 3(n-1)
(the full height of the bottommost cup plus n-1 lip thicknesses)

and the cross section of the stack is of course a circle of radius 89mm

[gusty merlin]

What’s n?

Like why did u add n

[pseudo basin]

n is the number of cups in the stack

[gusty merlin]

Ohhh

[pseudo basin]

we don't know how big our stacks will be, as it will matter what orientation we place them in the room

the room is 4m by 3m by 2.5m, yes?

[gusty merlin]

Correct

[pseudo basin]

right

so then

[pseudo basin]

let's consider three orientations: heightwise, lengthwise and widthwise

[gusty merlin]

Sure

[pseudo basin]

in each case, we will find the number of cups in one stack, and then we will approximate the number of stacks using the area of the corresponding wall or floor of the room

[gusty merlin]

Don’t we need to find out the volume of the cup first?

[pseudo basin]

no actually, we don't

[gusty merlin]

Oh

[pseudo basin]

we are stacking cups inside each other anyway. their volumes overlap a lot.

[gusty merlin]

OHHHH

Okay we’re on the same page now

[pseudo basin]

circles of identical size packed optimally on the plane have a packing density of about 91% - this is the ratio of a circle's area to that of a regular hexagon circumscribed around it. you can calculate the exact value of that on your own time, but for now we can just roll with it.

[gusty merlin]

It wants me to find out the volume tho

[pseudo basin]

what this means is that, for example, when putting stacks in height-wise, we will have only 91% of the area of the floor be covered by the circles that are the cups viewed from the top

[pseudo basin]

we can do that separately. it will not be necessary for our cup stacking calculations.

[gusty merlin]

Perfect

So what I do now

[pseudo basin]

do you follow this?

[gusty merlin]

Yes I do

[pseudo basin]

right

ok

so the top-down area of a single cup (and also a stack of cups) is the area of a circle with radius 89mm

er

diameter 89mm, sorry

so in square millimeters that will be

,calc 89 * 89 * pi/4

...why is the bot not responding

whatever, i calculated that on my own calculator.

6221 mm^2 give or take

and the floor is 4000 mm * 3000 mm, before adjusting for packing density

[gusty merlin]

Yup

I think we’re on the same page

[pseudo basin]

so that gives us the number of stacks as (4000 * 3000 * 0.91)/6221 = 1755 (rounded down)

and to find the number of cups in a stack inserted height-wise, remember n cups give a height of 107+3n mm

thus, 2500mm ceiling height gives us (2500-107)/3 = 797 (rounded down) cups in a stack

[gusty merlin]

our room is in metres tho - will we have to convert it at the end?

[pseudo basin]

i have already converted all lengths into millimeters.

the results of my calculations are dimensionless anyway bc they are counts

[gusty merlin]

OHHHHH

Yup got ya

[pseudo basin]

anyway, 797 * 1755 = about 1.4 million cups in the room.

1,398,735 is the exact value from the calculator but we are not being infinitely precise anyway

[gusty merlin]

so that

's

how many cups i need

to fill the room?

[pseudo basin]

well that's if we are putting them in vertical stacks

let's see what happens if we try to arrange the stacks horizontally instead.

there are two ways to do that: lengthwise or widthwise

[gusty merlin]

no thank you, I just needed one way

[pseudo basin]

maybe we can do more cups tho

this still gives you a ballpark though i suppose

[gusty merlin]

just to make sure this is how many cups u can stack in verticle order?

[pseudo basin]

yes

also i just checked

putting them in widthwise you can squeeze in about 2% more cups

[gusty merlin]

Omg thank you so much.

you are the best honestly

[pseudo basin]

oh yeah btw just for comparison purposes

the cup is approximately a truncated cone

[gusty merlin]

whats the volume of each one tho?

[pseudo basin]

,w conical frustum volume

[gusty merlin]

oh... thank you so much

[pseudo basin]

...okay, the bot is unresponsive again

[gusty merlin]

Haahahhaha

[pseudo basin]

and i am getting a volume that is like three times bigger than it's supposed to be...

oh wait no

i'm using diameters as radii again

right ok so

480 ish ml from those dimensions

,calc 400 * 300 * 250/0.48

[gusty merlin]

62500000

[pseudo basin]

er wait no

480 not 0.48 my bad

i did it in cm this time

so only 62,500 cups that way

[woven radish]

Result:

6.25e+7

[gusty merlin]

the volume of one cup is 62,500cm?

[pseudo basin]

no

cm are not a unit of volume anyway and i did not say the output of my calculations was measured in cm