help-43

[karmic stirrup]

and what are precipitate reactions

[tacit robin]

Silver chloride for example

Take any inorganic salt of Ag

[karmic stirrup]

(please speak in letters, my english vocab for chemistry is non-existant)

[tacit robin]

Silver is Ag

AgCl

[covert creek]

From what have learnt NaCl or any salt dissolve become Na+ and Cl-. So in solution NaCl or HCl are basically Na+, Cl-,H+ and Cl-

[tacit robin]

Not every

[covert creek]

ik

[karmic stirrup]

oh tis means the material on hte bottom thing...

[tacit robin]

But yes it's true for Na

[covert creek]

If for example, NaSO4 + Ba(OH)2 in solution it has Na+, SO4-, Ba2+, and OH-

[karmic stirrup]

so- this applies for soluable salts and doesn't when reacting with insoluables

[karmic stirrup]

im assumingthis is insoluable btw

[upper bane]

yes, and also applies only to acids in aqueous form ofc

[tacit robin]

Insoluble in water yes

[covert creek]

you see Ba2+ and SO4- make BaSO4 which doesn't dissolve in water and that's why NaSO4 and Ba(OH)2 has reaction

[karmic stirrup]

okay! I got what i wanted... Fionna, ping me when you're done and ill close the channel.

[covert creek]

that's what I think

[plush lichen]

what chem yall in

[covert creek]

why it form as solution lol, because like in NaSO4 + Ba(OH)2

[karmic stirrup]

||senior highschool, both of us||

[plush lichen]

ap chem?

[covert creek]

Na+ and (OH)- basically have no react it just floating in the solution

[covert creek]

yk I can close your channel too

[karmic stirrup]

wait no you cant

you dont have helper role

[covert creek]

Not this me

other me

[karmic stirrup]

sure.

[karmic stirrup]

I dont understand your concern

[covert creek]

basically, in reaction for example: Na2SO4 + BaCl2 -> 2NaCl + BaSO4

Na2SO4 -> Na+ and SO4(-2)

BaCL2 -> Ba2+ and Cl-

these ions just bond and unboud with each other in the solution as if it get dissolved in water

But the thing is

Ba2+ and SO4(2-) form BaSO4 which can be dissolved

can't

So all the Ba and SO4 form BaSO4 and sink to the bottom

[covert creek]

left the solution with only Na+ and Cl- which as we call NaCl in this reaction

so ig the same thing happens with the reaction you asked

[karmic stirrup]

https://tenor.com/view/i-think-quinn-harlem-maybe-probably-gif-24065899

I dont fully get it but- yeah i do understand what you're trying to say

but rn i have to go back to electricity

[covert creek]

[karmic stirrup]

bye fie!

[covert creek]

cya

[karmic stirrup]

.close

[compact pewter]

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[zenith barn]

how do you get alpha in the formula to the right,, im starting to forget all of my trigonometry worksheets

[grizzled geyser]

Letting $r = \sqrt{a^2+b^2}$, you know that $r \sin (\theta + \alpha) = r \sin \theta \cos \alpha + r \cos \theta \sin \alpha$

[boreal girder]

Xwtek

[grizzled geyser]

You then have to solve for $a = r \cos \alpha$ and $b = r \sin \alpha$

[boreal girder]

Xwtek

[zenith barn]

ah,, so cosalpha = sinalpha where x = pi/4,,, i think

i found the sheet i was looking for let me relearn

[grizzled geyser]

You mean alpha = pi / 4, but close enough

[zenith barn]

i miss when i understood this

ah, take the radius then divide it from sinx + cosx to extract r from both of them

managed to solve it 🎉

[worldly snow]

omg that takes like an hour to solve bro

[zenith barn]

ouh wdym?

[worldly snow]

We did that in university dorm it was hard for us

[zenith barn]

thats true..the way our tutor worksheets did it is like seperate them into simpler pieces and explore those fundamentals before teaching you how to integrate them together

[bleak dock]

you could also note that that's the area for half a period

[boreal girder]

south

[zenith barn]

ouh,, its similar to int_0-2pi sin(x-a) dx = 0

[bleak dock]

yeah!

[zenith barn]

hm,, if a function f(x) repeats at a period a and is integrated as F(x) from ma to na where m and n are integers, the result of F(c+k) equals F(c) ,i assume

[compact pewter]

@zenith barn Has your question been resolved?

[compact pewter]

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[floral kelp]

guys does anyone understand this notes?

[floral kelp]

why is there 2 different formulas for standard deviation?

the “s” and σ

[upper bane]

you mean why the population and sample SD have different formulas?

[floral kelp]

yes

[upper bane]

a sample is a subset (or a portion) of the whole population. the difference in formulas accounts for the fact that by choosing an arbitrary sample, we may have biased the sample

the -1 attempts to correct for this bias

[floral kelp]

ohhhhh

so “sample” is “biased”?

like we consider it as a biased estimate?

[upper bane]

not all samples are biased, but by picking a sample, we consider it to be biased, yes

you may be interested in studying Bessel's correction, which is exactly this.

[floral kelp]

if the question states “20 randomly chosen”

does this mean it is unbiased since it is random?

[upper bane]

normally if the question says "sample" or "chosen", then use the sample formulas

[upper bane]

conceptual error here

randomness is not the same as fairness

something that is random is not necessarily fair or uniform

[floral kelp]

oooooo

[upper bane]

just ask any gacha player

[floral kelp]

so we can only use the population formula if it is “fair”?

[upper bane]

well, the population represents the whole picture

there's no contest about fair or unfair because you have the whole picture. if the population is biased towards one side, then it's the nature of that population

you can't say a population is biased, because there's nothing to compare against

[floral kelp]

ohhhh i get it

[upper bane]

if you have something bigger to compare against, then your population is really just a larger sample.

[floral kelp]

i have another questionn

for confidence interval of normal distribution, why do we use sigma in the formula?

is it bcs normal distribution is not biased?

[floral kelp]

but aren't we supposed to use s for sample?

not sigma

[upper bane]

oh, but look carefully

the variance is coming from the population

only the mean is from the sample

[floral kelp]

ohhh

what about confidence interval for large samples

wait lemme take pic of the box

oh wait this is actually obvious already

it uses s because it is a sample rightt?

i think i get itt already

[floral kelp]

thank youuu so so much!

[upper bane]

nps

[floral kelp]

.close

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[compact pewter]

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[ornate sable]

I simplified sinx and x. I feel like it could be clear to say that sin x < x based on this but also I feel like it could be too big of an assumption but I don't know how I would actually go about it

[short lantern]

what is the area of the sector?

[ornate sable]

idk all we have defined is the area of a circle of radius 1

[short lantern]

you also have the angle is x

[ornate sable]

yes?

[short lantern]

do you know the formula for area of a sector given radius and angle?

[ornate sable]

well I guess xr^2

[short lantern]

close

the area of a circle is pi*r^2

[ornate sable]

how? isn't it just swiching variables in our first equation?

[short lantern]

the angle is x/(2pi) of a full circle

so you want x/(2pi) of the area

i.e. (x/(2pi))*(pi*r^2)

which is (x*r^2)/2

what is the area of the triangle OPA?

[ornate sable]

im not seeing this why?

[ornate sable]

1/2 sinx cosx

[short lantern]

i gave you the full derivation

[short lantern]

P goes all the way to the end, so no

A goes*

[ornate sable]

for the anglel though?

oh wait but that isn't a triangle

oh outside teh circle

[short lantern]

yes, a sector is a part of a circle, like a pizza slice

[ornate sable]

1/2 sinx

[short lantern]

what does that signify

[ornate sable]

half the height

[short lantern]

what exactly are you looking for

[ornate sable]

the relation between x and sinx

[short lantern]

and how can we show this relationship?

[ornate sable]

ok so what I think what your saying is that x represents the circular sector that we are looking at in our case and 1/2sinx is the area of the triangle which is already bigger than that circular sector and then if we multiply by 2 to obtain sin x it will most definitely be bigger

[short lantern]

draw the triangle

[short lantern]

are those three points O, P, and A

[ornate sable]

yes

oh wait no

not p

wait I ddint' draw this right

[ornate sable]

I don't see why that matters

[short lantern]

the entire point of this hinges on knowing exactly what you are looking at

[ornate sable]

ok but the triangle outside of the circle could not have p as a point

oh wait

I think I see

nvm

regarding what you said early are you saying that I set up the image incorrectly?

[short lantern]

yes

the triangle is not correct

[ornate sable]

ok

ok so we want to find the area of opa but if oa is cosx and pa is sinx how can it not be 1/2sinxcosx?

wait that is opa not OPA

[short lantern]

the triangle does not have to be a right triangle

[ornate sable]

\

[short lantern]

yes

that is your triangle

what is the area of this triangle

[ornate sable]

ok so for the base I will make a smaller triangle and then (1-cosx)^2 +sin^2x = b^2 and then I can find the height by h = 1 - (b/2)^2 so area is 1/2 [sqrt (1-cosx)^2 +sin^2x ] * [(1- sqrt (1-cosx)^2 +sin^2x/2)^2 ]

[short lantern]

theres a much easier method

what is the base at the bottom of this triangle?

[ornate sable]

the one from purple and blue?

[short lantern]

OA

what is OA

[ornate sable]

oh I misread it as triangle sorry OA is 1

[short lantern]

what is the height from P to OA

[ornate sable]

sinx

[short lantern]

ok so what is the area of the triangle OAP

[ornate sable]

I don't see how it can be sinx

[short lantern]

its not

[ornate sable]

ok I thought that was going to be the natural concllusion becsause 1 and sinx

but still that doens't tell us about the base or the height the only things they do is let us calculalte it which is what I did above

[short lantern]

use the formula for area of a triangle

[ornate sable]

wait your looking at the triangle differenlty I see now

but then teh area is sinx the base we found is 1 and the height is sinx

[short lantern]

what is the formula for area of a triangle

[ornate sable]

oh 1/2sinx

[short lantern]

thank you

now real quick before we continue, which area is bigger, the sector or the triangle?

[ornate sable]

the sector

[short lantern]

ok good

moving on

i said earlier the area of a sector is (x*r^2)/2, would you like me to show you how we got that again?

[ornate sable]

no I see it

[short lantern]

ok, what is the radius of our circle

[ornate sable]

1

[short lantern]

ok plug that in for r

what do you get for the area of the sector

[ornate sable]

yes x/2

mutlilpllying both by 2 then?

[short lantern]

ok, now we know the sector is bigger, so what will an inequality look like

yes

then you multiply bu 2

and it shows what you wanated

[ornate sable]

yes and then I am assuming what I sent the first time does not because it is not explicitly easy to see

[short lantern]

it also operates on a wrong assumption of what triangle OAP is

[ornate sable]

wait im referring to this one

I don't use triangles here

[short lantern]

imma be completely honest i have no idea what youre doing here

[ornate sable]

all this was was plugging in for r in then isolating for sinx

also for the second part could you not just say apply the same method because anything in an absolute value is positive so wouldn't it just be doing the same thing but rewritten with |sinx| and |x|

[compact pewter]

@ornate sable Has your question been resolved?

[compact pewter]

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[kind viper]

,rccw

[wet vine]

How do you do a problem like this? And if i get a problem similar to it in the future how would i do it myself

/ how would i identify it

[kind viper]

find the areas of the white triangles (AXY, YDC, CXB)

you can find them as fractions of the rectangle

[wet vine]

Ye ik

But idk how

[kind viper]

do you know how to find the area of a right triangle in general

[wet vine]

But the quetion doesnt show or say its a like 1/4 or 1/2 or whatever the empty spaces are

[wet vine]

Yes

Oh wait

They're mid points

Hol up

Lemme try smthing rq

Wait nvm i got the anwser

😭

[bleak dock]

oh lmao this is PSLE

[wet vine]

I over complicated it for myself

[wet vine]

Whats that?

[bleak dock]

it's not PSLE? damn

[wet vine]

Whats psle?

[bleak dock]

yeah no you're across the border in Malaysia I guess

[bleak dock]

primary school leaving exam, grade 6

[wet vine]

💀 nah lmao

Aint this hard in year 6

Eh

[bleak dock]

some of the challenge problems on the PSLE are, anyways

[wet vine]

Idk im js dumb

Anyways imma go

Cus i found the anwser

🔥

.close

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[wet vine]

Uhhhh how to do this

[bleak dock]

,rccw

[bleak dock]

hint: you can make a rectangle by combining 2 of the J pieces

[covert grove]

اه

hi

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@wet vine Has your question been resolved?

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[wet vine]

I already did that and got 27 as the awnser

[wet vine]

But anwser is 6

[bleak dock]

okay, how did you get 27?

hopefully you're on the same page as me, where you have 2 J pieces= 4 cm x 3 cm rectangle

[wet vine]

Yea 2J pieces = 4 x 3 cm

Since it wants a 10 x 15

I made a

12 x 9 square

Then left with one side which is 3 x 15

And one side which is 1 x 12

[bleak dock]

12 is already out of bounds

[wet vine]

No like 9 x 12

Its under 10 x 15

[bleak dock]

ohhhh okay, then yeah, keep going

[wet vine]

Then for the 3 x 15 i could only fit like

[bleak dock]

,calc 10 * 15 - 9 * 12

[boreal girder]

Result:

42

[bleak dock]

okay hmm

[wet vine]

Like 5 of em

Which leaves 3 empty space each time

Making it 15

Then add the 1 x 12

Cus u cant rly put the j there

So 27

[bleak dock]

yeah the packing is not obvious then

[wet vine]

Ye

Is it that we have to surround the 10 x 15 square with the 3 x 4 square first so theres more space in the middle?

[bleak dock]

this seems to be the best configuration

oh yeah, so notice how I rotated the 3 by 4 rectangle the other way, in the bottom right corner

you can fill the empty space at the top with the 4 by 3 rectangles

yes I also get 6 this way

[wet vine]

Ohhhh

I understand it now

Ty

.close

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[compact pewter]

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[wet vine]

Wouldn't the awnser to this be 52?

My anwser sheet says 51

But 51 only makes it so theres one of each ball colour left

It has to be 52 so all colours of 1 sack will be picked

[junior mantle]

.rotate

[junior mantle]

rotate

[covert creek]

,rccw

[junior mantle]

!show

[compact pewter]

Show your work, and if possible, explain where you are stuck.

[wet vine]

._.

7 , 8 ,9 ,10 ,11 , 12

Each represent a bag

With the respective number of balls

Worst case scenario

U pick every single colour expect for one

Make its so u now picked 6 + 7 + 8 + 9 + 10 + 11 balls

So 51

So now each bag has only 1 ball left

So u need to pick 1 more ball so u have a complete set

So its 51 + 1

= 52

But my awnser sheet says 51

Am i missing something

[junior mantle]

Why 6+

There is no group of 6 balls?

[compact pewter]

@wet vine Has your question been resolved?

[compact pewter]

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[low pulsar]

im so confused with this

[low pulsar]

if you need me to translate english i can

[noble sorrel]

yes

[low pulsar]

Pure water is added to 50 mL of a 30% acid solution. The rule C(x)= (15)/(x+50)
​ represente the acid concentration as a function of the quantity
x of water added to the solution. All quantities are in milliliters.

a) In the Cartesian plane opposite, draw the graph of this function for values of
x
x up to 150 mL.

b) What is the y-intercept of this function?

c) How much water must be added for the concentration to be less than 1%?

d) What rule allows calculating the concentration of 80 mL of a 40% acid solution if
x milliliters of water are added?

[toxic cipher]

Part a:
Draw a table of at least three values of x and their corresponding C(x) values.

Choose an appropriate scale for the horizontal and vertical axes, and plot the points

then draw a straight line through those points

also label the axes

[low pulsar]

why at least 3

is there a reason or nahh

[toxic cipher]

you need 3 values at least for straight line graph

[low pulsar]

aleight

so can i pick like x = 130

and find C(x)

[toxic cipher]

yes

[low pulsar]

kk

[toxic cipher]

x = 150 has to be one of the values in the table though

[low pulsar]

alright also

when i do 130

it gives a really small number of y

1/12

bit hard to place that on the graph

[toxic cipher]

hmm

notice that we're dealing with percentage concentration here

[low pulsar]

yeahj

[toxic cipher]

At x = 0, C(x) = 0.3

the question states that x = 0, the percentage concentration is 30%

so you can convert everything to percentage

(at least i think)

but you will need to label your vertical axis appropriately

[low pulsar]

so i convert the ml into percentage?

[toxic cipher]

nono like you convert your 1/12 into percentage

[low pulsar]

its 8.33^

8.33%

[toxic cipher]

yup

[low pulsar]

what do i do with that

[toxic cipher]

i would just choose something like x = 0, x = 50, x = 100, and x = 150

cause those give nice numbers

[toxic cipher]

can i see your table?

[low pulsar]

its empty because i got lost there but do i put in the 8.33% in the table

like x = 130

y = 8.33

[toxic cipher]

draw a table like this (wait a sec)

[low pulsar]

i got it like this

[toxic cipher]

,tex \begin{table}[]
\begin{tabular}{l|l|l|l|l}
x & 0 & 50 & 100 & 150 \ \hline
C(x) & ? & ? & ? & ?
\end{tabular}
\end{table}

[low pulsar]

oh ok

so x 130 and 8,33

[low pulsar]

we dont have a x =0 y =?

right?

[toxic cipher]

youre supposed to calculate the value of C(x) in percentage and replace '?'

the '?' is a placeholder

[low pulsar]

ah alright

30%

[toxic cipher]

and then?

[low pulsar]

then i have 130

which is 8.33%

now ill calculate 150

which is the max

[toxic cipher]

why did you choose 130 btw lol

[low pulsar]

no clue

[toxic cipher]

it'll give such a weird value of C(x)

next time you should choose something that'll be easier to calculate and wont require rounding

[low pulsar]

alright my fault there

when its 150

its 7.5%

thats 3 values right

[toxic cipher]

okay

yup

[low pulsar]

alright

in the graph

[toxic cipher]

now look at your grid

[low pulsar]

in the y axe

[toxic cipher]

yeah?

[low pulsar]

is it like %

like 5%

then 10%

15%

[toxic cipher]

lemme check

[low pulsar]

in the y axe i probably gotta jump by 20

so like 0 20 40 60 80 100

[toxic cipher]

no an increase of 5% per square would be too small

[low pulsar]

10%

[toxic cipher]

look at the range of values you got for C(x)

[low pulsar]

i got

30 8.33 and 7.5

[toxic cipher]

you have at x = 0, C(x) = 30% and at x = 150, C(x) = 7.5

so the maximum will be when x = 0

and the range for C(x) is 30 - 7.5 = 22.5%

[low pulsar]

wait il lshow u osmething

[toxic cipher]

so ideally you would want 30% to be near the top of the graph

[low pulsar]

i meant this

[low pulsar]

oh 30 to the top?

[toxic cipher]

yea ik

[low pulsar]

to make it accurate?

we should do 2.5 then

[toxic cipher]

well at least above half of the vertical axis

that's what i was thinking

[low pulsar]

yeah

also w cant do 10

because it doesnt reach 105

150

[toxic cipher]

yup

[low pulsar]

so we should do 15?

[toxic cipher]

i think 15 would work

[low pulsar]

alright

yeah it does

did my line

[toxic cipher]

can i see it?

[low pulsar]

looks like this

[low pulsar]

yeah

[toxic cipher]

uh no that shouldnt be how it looks

can you mark out the vertical and horizontal axes first?

[low pulsar]

a;rogjt

[toxic cipher]

and then plot out the points

[low pulsar]

wait

its a rational function

has to look like this

[toxic cipher]

hm

i think you need to record more values of x and C(x) in your table

[low pulsar]

alright

[toxic cipher]

like x = 50 and x = 100

[low pulsar]

i did 75 is that ok?

[toxic cipher]

btw i was wrong in saying you only needed 3 values just now, sorry

[low pulsar]

no worries dude

[toxic cipher]

it's alright ig

[low pulsar]

y is 12

when its 75

[toxic cipher]

yh

[low pulsar]

now it looks ike this

wait forgot one

[toxic cipher]

right

so you should be able to draw a line through that

it'll be a curve

[low pulsar]

yes

drew

[toxic cipher]

you want to do all the markings for your horizontal and vertical axes

for your vertical axis you stopped at 20 for some reason

[low pulsar]

i didnt

its just for that screenshot idid

but on my paper i wrote it all

[toxic cipher]

oh ok

anyways the last step (which should have been the first step) is to label the axes

[low pulsar]

whats label

wdym

[toxic cipher]

like

your vertical axis will be "percentage concentration"

you can write that at the side of the grid

and then your horizontal axis will be "x"

[low pulsar]

oh alr

[toxic cipher]

you can write that at the bottom of the grid

[low pulsar]

got u

thanks for ur help

[toxic cipher]

and that should be part a'

[low pulsar]

yeah

part b is 30

right

[toxic cipher]

30%

the percentage sign is important

[low pulsar]

ah

[toxic cipher]

part c is reading off the graph when y = 1%

[low pulsar]

we have to do

1% divided by 100

then replace C(x) by 0.01

[toxic cipher]

oh yeah you can do that too

they didnt say "using the graph"

actually your method is better

[low pulsar]

yeah

0.01 = (15)/(x+50)

[toxic cipher]

wait a sec

[low pulsar]

do we do (x+50) both sides

[toxic cipher]

@low pulsar sorry i was doing smth just now

[low pulsar]

dw

i found it tho

i did (x+50) both sides

[toxic cipher]

so this is actually a very common mistake that students make

[low pulsar]

ah

[toxic cipher]

the question states "how much water must be added for the concentration to be less than 1%"

so you want to make an inequality not an equality

[low pulsar]

but how do we know its inequality

what if it said to be 1%

then its >= ?

or =

[toxic cipher]

huh

if it said to be 1% then it would be an equality

[low pulsar]

oh

[toxic cipher]

it says less than 1% so it's an inequality

[low pulsar]

alr

what if it said more

[toxic cipher]

well then you would do >

it's less than so it's '<'

[low pulsar]

alright i see

[toxic cipher]

yeah

i made this mistake like some time ago

so i remember it ;(

[low pulsar]

😭

damn

i've obtained 0.01 < (15)/(x+50)

[toxic cipher]

nono it's $C(x) < 0.01$

[toxic cipher]

meaning $\frac{15}{x + 50} < 0.01$

[low pulsar]

oh wait yeah we want to know how much will be less than 0.01

mb

usually what i do here

wait i dont think we can do what i was gonna do

but i can tell u

[toxic cipher]

ok

[low pulsar]

so what i was gonna say

we do -0.01 both sides

to put it 0

then we put the -0.01 on the same denomiantor

as x+50

[toxic cipher]

uhh

[low pulsar]

then we do

the curve method

like this

might be wrong tho

[toxic cipher]

that seems overly complicated

you can multiply (x + 50) to both sides

[low pulsar]

alright

sorry

@toxic cipher back

aslright

[toxic cipher]

aight

[low pulsar]

0.01x + 0.5 > 15

[toxic cipher]

okay

[low pulsar]

now

0.5 bothj sides

wait

we cant

its not an equality

?

[toxic cipher]

wdym

[low pulsar]

we can do -.05?

[toxic cipher]

yes

[low pulsar]

ah alr

1450 = x

[toxic cipher]

we're not doing an equality

we're doing an inequality

[low pulsar]

mb

x > 1450

[toxic cipher]

yup

[low pulsar]

so x has to be

1451

for it to be below 1%

[toxic cipher]

nono x doesnt have to be an integer

[low pulsar]

what do i write for c then

only x > 1450

[toxic cipher]

You can just write a statement saying "For the percentage concentration of water to be less than 1%, the amount of water added must be greater than 1450 ml"

[low pulsar]

alright i see

[toxic cipher]

honestly part c is written badly cause there isnt any one answer that satisfies it

but a range of answers

[low pulsar]

yeah exactlyt

for d)

pretty sure its

0.4 = (15)/(80+50)

nvm im wrong

its only asking for the equation

[toxic cipher]

idk about that

we have 80 ml of a 40% acid solution so we cant use back C(x)

[low pulsar]

80 ml of a 40% solution

[toxic cipher]

first you want to calculate the amount of acid in ml initially

[low pulsar]

so y is 0.4 and x is 80

[low pulsar]

alright

[toxic cipher]

nono i think they're asking for an equation which describes the concentration of the solution as a function of x

[low pulsar]

1 ml how much % acid solution

hm

wait we cant use the rational equation like last time?

C(x) = (?)/(x+?)

?

[toxic cipher]

wdym

like we want a new function to describe the concentration given the amount of water added

we cant use back the previous one because the initial parameters are different

[low pulsar]

i know but without the numbers like 15 and 50

can we use that format

[toxic cipher]

yes

[low pulsar]

alright

its gonna be

im actually not sur

[toxic cipher]

well

i think it would be nice if you understood what C(x) actually means and how it derived

So in the original scenario, we have 30% concentration of a 50 ml acid solution initially

what would be the volume of acid present initially?

[low pulsar]

it means the % right

[low pulsar]

50

[toxic cipher]

the concentration

[toxic cipher]

no..

do you know how to calculate concentration?

[low pulsar]

like in ml then we put into %?

[toxic cipher]

like in general

okay so concentration of acid in a solution is $\frac{\text{volume of acid}}{\text{total volume of solution}}$

[low pulsar]

ah

initially it was 15 no?

[toxic cipher]

yes

[low pulsar]

alright

so this time

we dont know

this is what i wrote for now

80/? = ?/0.4

[toxic cipher]

okay wait

what is the volume of acid initially? will it change?
what is the total volume of the solution initially? will it change?

[low pulsar]

15 it wont change

yes it can change because its x+50

we can change x

[toxic cipher]

right

so what would be the concentration?

[low pulsar]

the %

[toxic cipher]

in terms of the fraction here

[low pulsar]

we gotta know x

for that

[toxic cipher]

i mean like

you know the total volume and you know the volume of acid

the concentration would be $\frac{\text{volume of acid}}{\text{total volume}} = \frac{15}{x + 50}$

[toxic cipher]

do you understand?

[low pulsar]

x+80 is total volume

[low pulsar]

yeah

[toxic cipher]

and the initial volume of acid for the second case?

[low pulsar]

it doesnt give that information

[toxic cipher]

yes it does

you know the total volume initially, and you know the concentration initially

[low pulsar]

but i only have 80 ml solution acide

at 40%

[low pulsar]

yes

[toxic cipher]

so you can find the volume of acid initially

[low pulsar]

oh

its 32

[toxic cipher]

yeah

[low pulsar]

i see

c(x) = 32/x+80

[toxic cipher]

yes

that's it

[low pulsar]

oo

alright i see

well ty for ur help dude

[toxic cipher]

no problem

[low pulsar]

.close

.close

[compact pewter]

Channel closed

Closed by @low pulsar

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

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[compact pewter]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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[cursive harbor]

.close

[compact pewter]

Channel closed

Closed by @cursive harbor

Use .reopen if this was a mistake.

[cursive harbor]

.reopen

[mild sky]

Xavier the tester

[cursive harbor]

Why did it work last time

[verbal kiln]

[cursive harbor]

What

[viscid canopy]

!xy

[compact pewter]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[mild sky]

!nogpt

[compact pewter]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[native shard]

!status

[compact pewter]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[cursive harbor]

Lmfao

[strange pendant]

!done

[compact pewter]

If you are done with this channel, please mark your problem as solved by typing .close

[cursive harbor]

.reopen

Why did it work last fime

[mild sky]

.reopen

[cursive harbor]

Am I hallucinating

[verbal kiln]

People bombarding this poor guy

[viscid canopy]

what are u talking about

[cursive harbor]

It's classic helpful behaviour

[strange pendant]

its already open

[cursive harbor]

.close

[verbal kiln]

Maybe I’m not fit out for GREN infinium then

[cursive harbor]

No it's not

[viscid canopy]

.close

[weak cobalt]

It's clopen

[mild sky]

.close

[verbal kiln]

Is the bot borken?

[strange pendant]

seems broken to me

[verbal kiln]

*borken you mean?

[unique lynx]

It's some kind of broken -- it's spamming lots of error messages to its internal log channel.

[cursive harbor]

Ah interesting

[verbal kiln]

Xavier do you have any comment on this?

[cursive harbor]

Are the errors related to what I'm doing or is the bot just buggy rn

[mild sky]

You have access to the logs

[strange pendant]

how do you see the logs?

[cursive harbor]

They're an admin lmao

[verbal kiln]

[mild sky]

If the logs are not in 5 different colors I am going to be sad

[strange pendant]

would be useful if the users with the bot enthusiast role have access to the logs

[unique lynx]

Access to the log channel comes with being a seniormod on indefinite break.

[strange pendant]

so they can fix this mess

[cursive harbor]

Would reveal too much sensitive info

[verbal kiln]

Why would they?

[mild sky]

Because colored text is fun

[verbal kiln]

Sensitive info? What would be there anyway?

[paper anchor]

Well this help channel looks fun

[digital lark]

Hello

[verbal kiln]

Mini dicussion while the bit is being fixed

[paper anchor]

Fun stuff man

[cursive harbor]

Bot logs can have a lot of information lol

.close

[strange pendant]

yeah I guess is better than the bot remains broken for who knows how much time (?

[verbal kiln]

“Closed channel. Open channel. Open channel. Closed channel. Open channel. Closed channel.”

[cursive harbor]

.reopen

[paper anchor]

OMG it's still not working

[cursive harbor]

I doubt the bot logs are only for help channels

[verbal kiln]

!bnuuy?

[compact pewter]

[verbal kiln]

Oops

[paper anchor]

never knew that

[cursive harbor]

The bot is only broken in this channel I think

It seems to be working in other places

[paper anchor]

Maybe wait 15 minutes

[verbal kiln]

Probably didn’t like the clopen and the msg delete

[cursive harbor]

Yes

I thought I found a vulnerability and I did

[paper anchor]

It'd ask whether your question has been answered and you could just tick it

[cursive harbor]

The channel is closed lol

[paper anchor]

Oh whoops

[cursive harbor]

^^

It worked when I tried to close it

And then died when I tried to open it back after deleting my original message

[paper anchor]

Ahhh I see, but it's not reopening right

[cursive harbor]

Yeah

It should become available or hidden soon enough ig

[compact pewter]

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.
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[pale ocean]

Not really math, but how should I think abt this?

[signal goblet]

is this the full question?

[compact pewter]

@pale ocean Has your question been resolved?

Channel closed

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Available help channel!

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Remember:
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[flint wing]

i dont understand why the last three rows are true?

[old mica]

vacuous truths

since p ^ (p -> q) is false, the entire implication (p ^ (p -> q)) -> q is true

[flint wing]

hello higher, im looking at the wiki and it shows this but i dont think i understand what is happening here

[old mica]

what's the confusing part?

if you have an implication P => Q, then it's true when P is false

that's all the sentence is saying

[flint wing]

ohh ok can you give an example like in words for me please

[old mica]

I like to think about vacuous truths in terms of lying

[rigid perch]

"if it rains tomorrow then i'll take the bus"
if it's sunny tomorrow i might walk or take the bus, but either way I didn't lie to you, my statement was true

[old mica]

let's raise the stakes

let's say P is "if I quit mathcord tomorrow", and Q is "then I will die"

when am I lying to you?

if I quit mathcord tomorrow and I die, I told the truth and you couldn't call me a liar (implication is true)

if I quit mathcord tomorrow but I surivive, then I lied to your face and you can call me a liar (implication is false)

now if I don't quit mathcord tomorrow and die, then you can't call me a liar still

for all you know, I was gonna die either way

so the implication is true

likewise, if I don't quit mathcord tomorrow and I still survive, you also cannot call me a liar

so P is false means the entire implication is true

note to any onlookers: I will not be quitting mathcord tomorrow, and I will probably not die tomorrow either

[flint wing]

ohhhhhh okay so i was assuming if P then Q meant like Q happens only if P happens but the whole statement is true if P is false. so if we have P =>Q then the statement doesnt promise anything if P is false essentially?

[old mica]

yeah!

I didn't tell you what might happen if I didn't leave the mathcord

so you can't call me a liar

and as it happens, my life force is bound to this server

[flint wing]

ohhh okay i think i get it now

thank u both

[flint wing]

.solved

[compact pewter]

Channel closed

Closed by @flint wing

Use .reopen if this was a mistake.

[compact pewter]

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

[rotund moth]

i need help with this question

[rotund moth]

i understand the formula

but idk where to start

i thought i had to find the roots but

'its about the y-axis

so im not sure

[glass oracle]

okay, have you done solids of revolution around the y axis before?

[rotund moth]

ye

do i need to write the equation in terms of y?

[glass oracle]

ah right, can you rewrite the equation as a function of y

yeah

[rotund moth]

ok

[glass oracle]

you also need to find bounds in terms of y

so that's probably 0 and the y coordinate of the maxima

[rotund moth]

what does that mean

oh like

oh yeyeok

[glass oracle]

the integration bounds yea

oh wait i might be dumb sorry

this is probably gonna find the volume left of the curve

[rotund moth]

heh?

i have the solution but i js dont know where everythihng came from

[glass oracle]

like this part

[rotund moth]

rught

right

[glass oracle]

i haven't done solids in a while, i think you need volume by shells for this (?)

one sec lemme check my notes

[rotund moth]

thats what they did

where did 81 come from....

[glass oracle]

oh wait that's still volume by washers

[glass oracle]

okay so they're using the original method, calculating the full volume from the y axis then subtracting the volume i highlighted here

81 is the y coordinate of the maxima when a=18

so your integrating between 0 and 18 along the y axis

you find the volume by rotating the blue region around the y axis then subtracting the volume of the red region rotated around the y axis

[compact pewter]

@rotund moth Has your question been resolved?

[rotund moth]

huh? wdym isnt y=0 when x=18

[glass oracle]

yup

[rotund moth]

but 81?

[glass oracle]

so the maxima is halfway between the roots x=0 and x=18

[rotund moth]

omg right

ok

so when x=9?

[glass oracle]

yaya

[rotund moth]

ohhhh

omg

thank you

SJSJS I LITERALLY HAVE A TEST LIKE

IN LIKE 30 MINS

[glass oracle]

np! sorry for being confusing before haha

[rotund moth]

RAH IM COOKED

[rotund moth]

nononono tysmmm

[glass oracle]

rahhh lock in you got this

[rotund moth]

at least i got it in the end

[rotund moth]

tytytytyy

[compact pewter]

Channel closed

Closed due to timeout

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Available help channel!

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Remember:
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[quartz sorrel]

Nontrivial combinatorics
How many of these are there as the number of let's say legs grows (symmetry reduced and not)
The leg connectors can only be at either edge, the spike on each of the connectors has to exist either inside or outside aka both variables are xor
n*90deg rotation, 4 lines of symmetry of the square or a combination of the two are counted

[quartz sorrel]

Without the spike swappability it should be

[boreal girder]

tomka700

[quartz sorrel]

And

[boreal girder]

tomka700

[quartz sorrel]

Respectively

It can be mapped to a 2x(2n-1) or (2n-1)x2 matrix where there is exactly one nonzero (1 or 2 depending on spike) in every even row/col eg
00
10
00
02
00

<@&286206848099549185>

[compact pewter]

@quartz sorrel Has your question been resolved?

[quartz sorrel]

I don't know whether or not there is a closed formula as this is a result of a pet project but it doesn't feel that complicated

[compact pewter]

@quartz sorrel Has your question been resolved?

[boreal girder]

tomka700

[compact pewter]

@quartz sorrel Has your question been resolved?

[worldly snow]

help

The Philippine eagle is one of the largest and rarest birds in the world. Its powerful wings spread to about 2.4 m. What is the measurement of its wingspan in feet?
A metric ton, abbreviated as “t”, is a unit of measurement used for large masses such as those of cars, planes or heavy construction equipment. The weight of a compact excavator is 1.893 t. If 1 t = 1000 kg, what is the weight of the compact excavator in kilograms?
A kilogram of carrots costs 60 pesos. How much does 750 g of carrots cost?
!help

[compact pewter]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[compact pewter]

@quartz sorrel Has your question been resolved?

[compact pewter]

Channel closed

Closed due to timeout

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Available help channel!

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Remember:
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[floral kelp]

guys for this question, i noticced that they use CLT in 12a. why do they use CLT if the distribution is already normal?

[floral kelp]

i was thinking that this is probably because it will be asked in the following subquestion but the first time i did it, i did not apply CLT at all, so the answer is wrong

[upper bane]

they did not though?

that's the z-score calculation, not a CLT application

[floral kelp]

for the variance, they divide it by n (which is 40)

[upper bane]

that's a z-test

[floral kelp]

whats that

[upper bane]

hm, I might not be the best person to explain the diff between z-score and z-test

[floral kelp]

hmmm

but if questions like that appear, am i just supposed to apply CLT

i would not know they would apply CLT if i didnt see the mark scheme

[upper bane]

I wouldn't call this an application of a CLT, but I also am not sure how to start explaining z-tests, so

[floral kelp]

oooooo

okok

[floral kelp]

thankyouuu

[upper bane]

i did nothing this time

[floral kelp]

btw for letter c

[floral kelp]

15c

does anyone know how CLT is used 😂

why does it says CLT is necessary but at the same time i cant spot any working that applies CLT

[compact pewter]

@floral kelp Has your question been resolved?

[compact pewter]

@floral kelp Has your question been resolved?

[limber plover]

I think as you make inference about population which is normal distribution using the random sample, when the no. of sacks gets large (n -> infinity), the random sample follows normal distribution. And that is the statement of Central limit theorem.

[odd pewter]

,help

[boreal girder]

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!

[floral kelp]

Oooh so we can’t actually see how CLT is applied in the question?

Like is it invisible

[limber plover]

That's my intuition, it may be wrong. I'm yet to study theory of estimation in depth 🙂

@floral kelp It turns out my statement was little imprecise. Here's what GPT says and answer your questions also:

[floral kelp]

yess i think i get it

it’s approximated and not changed

[floral kelp]

but i don’t understand in letter c, they said it’s necessary to use CLT for part b. But in part B, they did not use CLT at all

[upper bane]

try not to use AI when helping others

!noai

[compact pewter]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[limber plover]

ok sorry

[upper bane]

nps

[floral kelp]

btww thank youuu!

[limber plover]

You haven't directly used it but CLT makes possible to use sampling distribution for the estimation (confidence interval in your case) of population. So it turns out You've used it indirectly. I suggest you to read Theory of Estimation 🙂

[limber plover]

My pleasure to know I've helped you.

[floral kelp]

alrightt thank you so much once again

will close the channel

.close

[compact pewter]

Channel closed

Closed by @floral kelp

Use .reopen if this was a mistake.

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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.

[fallow coral]

Can somebody explain how Σ(sin^2B-sin^2C) is expanded here?

[grim adder]

they just opened the summation and wrote all possible elements in it

[grim adder]

if you're confused with what i just said expand the first summation and do what you did, with each of them separately .

[fallow coral]

shouldn't there be lower limit and upper limit ? How do I expand?

[fallow coral]

How do I expand with no starting and ending point?

[grim adder]

it's a symmetric expansion

[grim adder]

so like aSin(B-C) + bSin(C-A) + cSin(A-B)

thats what you have to prove to 0

since theres no real way to express this in a general summation without getting it too clustered they just leave it out

[grim adder]

you get me now ??

[fringe granite]

Omaxe

[grim adder]

uh huh

what now

[fallow coral]

I didn't know about this

[grim adder]

no worries

[fallow coral]

thanks

.close

[compact pewter]

Channel closed

Closed by @fallow coral

Use .reopen if this was a mistake.

[grim adder]

wlcm

[compact pewter]

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[polar laurel]

HELP

[polar laurel]

I need someone to check my work

and answers

i think i did it correct

but i wanted to backcheck with a professional

[verbal kiln]

Just for future reference, can you please post the image/question as your first message so the bot doesn’t pin greetings or requests for help? This way, if the conversation continues for long, helpers don’t have to dig backwards to find the problem you are having trouble with.

[polar laurel]

yes srry

[grim adder]

just put the value's you found back into the original equation

if the result is 0

then it's correct

if welp, try again

[verbal kiln]

please try to be kinder when dealing with questions and the helpee.

[grim adder]

I see

[compact pewter]

@polar laurel Has your question been resolved?

Channel closed

Closed by @polar laurel

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
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• Be polite and have a nice day!

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[clever stratus]

how many of the first 10,000 positive integers contain the digit-pair 43 in that order

[clever stratus]

i got like

xx43 as 100
x43x as another 100
43xx as another 100

but answer says its 299

[tired bear]

4343

[clever stratus]

that js counts as 1

[tired bear]

in two cases

[clever stratus]

oh

[grim adder]

xx43 is 90 cases btw

[noble sorrel]

100?

u can't put 0 in front

[grim adder]

ohh nvm it can be multi digits

[clever stratus]

wait how? 0-99

[grim adder]

dont mind me heh