TOA, tan is opposite over adjacent
#help-4
hazy lily
what I was able to get this question earlier but this one is literally so confusing
stark wedge
please do not call me "dude"!
stark wedge
can you edit your message to not have the word "dude" in it
hazy lily
ya
stark wedge
or anything else masculine for that matter
stark wedge
you got lucky in the 45° one.
hazy lily
luck is my speciality
stark wedge
you got the right answer by the wrong method.
no such luck in the last 58° case
idk really how else to tell you:
opposite = 52.1
adjacent = x
o/a = 52.1/x
i actually do not see what is stopping you from grasping it other than a bad case of brain freeze
stark wedge
a what now
stark wedge
why are you doing math while high
stark wedge
i mean this in the kindest way possible but you're not erdős
hazy lily
thanks for the advice
hazy lily
i mean this in the kindest way possible but you're not erdős
I could care less if u meant it in the worst way possible
no offence
but ya
hazy lily
i mean this in the kindest way possible but you're not erdős
I got it
Ann
I got it
Are u proud of me
you have helped me pass my exam
you will not be forgotten
.close
pallid smelt
vale dockBOT
pallid smelt
this is my first attempt
this is my 2nd, switching u and v’
<@&286206848099549185>
vale dockBOT
@pallid smelt Has your question been resolved?
ionic pebble
<@&286206848099549185>
i can give it a shot if you need
pallid smelt
please that would be greatly appreciated
ionic pebble
please that would be greatly appreciated
sure but technically im not a helper so take whatever i do with a grain of salt
pallid smelt
i'm not a helper either but i js helped someone
but i also had that question from my gcse paper so yk
noble anvil
Yeah theres no assigned helpers lol its just on you if u wanna help or not
ionic pebble
ok
noble anvil
this is my 2nd, switching u and v’
I suggest taking an x separate from the last integral you got and applying by parts
I'm not completely sure but that seems to be a way to try since you can take x^3=t after that, resulting in dt*t in the numerator
pallid smelt
just x or 3x?
pallid smelt
bc i took 3x separate and had to differentiate(x^2)(1+x^3)^(-1/2)
that
that's not very pretty
i did it and it looked horrible considering i'm multiplying that by v and then having to integrate it
unless u want me to integrate it using reverse chain rule?
noble anvil
? I'm saying take x out so you'll be left with x^5 in num and x^3 in denom now take 1+x^3 as t, resulting in dt being 3x^2 so num would become some constant* t-1*dt
pallid smelt
my mistake
noble anvil
Nw
pallid smelt
idk
it's a cambridge sixth term examination paper
so end of year 13?
or grade 12
typically 17-18 yr olds
pallid smelt
no it's ridiculously difficult apparently
ionic pebble
oh ok
pallid smelt
like sadistic
ionic pebble
yeah that really is awful
and you havent been taught like trig sub and stuff yet right
so its only ibp
noble anvil
Did you try
storm perch
This is from Cambridge, isn’t it
pallid smelt
yes
storm perch
I did this one before
pallid smelt
Did you try
i did an idk if i'm good enough at calculus to do that
like i tried and i only got a worse integral
storm perch
And yes, I would recommend by parts on the first integral (figure out what would be suitable for integration/differentiation)
storm perch
And yes, I would recommend by parts on the first integral (figure out what would...
After that it gets really easy :)
pallid smelt
wait on the integral of 2(1+x^3)^(-1/2)
noble anvil
Ooh true you can also do it on the first integral
pallid smelt
i kinda forgot it was there
the question literally says on either one
but i also have a question
like i looked at the markscheme
pallid smelt
this is my first attempt
how did i get this wrong?
noble anvil
I'll check
storm perch
wait on the integral of 2(1+x^3)^(-1/2)
no, on $2\sqrt{1+x^3}$
rocky lotusBOT
;(
noble anvil
this is my first attempt
Um what the hell is that
How did you do /3x^2
Thats not a thing
pallid smelt
How did you do /3x^2
also before u roast me i uhh was never taught this, this is me going off intuition kinda
noble anvil
Oh
Well pog try then
Even i used to use chain rule in integration 
But it doesnt work like that sadly
pallid smelt
wait i got /3x^2 because thats chain rule no?
or reverse chain rule?
i let a = 1+x^3
now i have an integral for a
needed to change dx to da
noble anvil
I dont understand i might be wrong
Ive never been taught reverse chain rule
But ik integration pretty well and afaik thats not a thing
storm perch
wait i got /3x^2 because thats chain rule no?
You can't take a function out of the integral.
x is a function of a.
Very common mistake.
noble anvil
Yea
noble anvil
My 11th grade was just full of doing stuff like this lmao
storm perch
Both work nicely.
noble anvil
Even I'll try to solve it lol I'm intrigued now
storm perch
I love how when I put this into GPT its going in loops lol
Its so funny just watching it fail horribly 💀
noble anvil
Yeah i wouldnt even try
Gpt has betrayed me every time
Past like 10th grade it's just useless for math
noble anvil
I got my answer
Idek what I've done
Cause i didnt read the qn properly
But i got this
pallid smelt
thats the answer
storm perch
I can explain.
noble anvil
tf u taking a double integral for?
Thats just the integration by parts thing
I skipped a few steps
pallid smelt
oh
storm perch
What you essentially want to do here is integrate the 2 and differentiate $\sqrt{1+x^3}$.
rocky lotusBOT
;(
storm perch
$\begin{matrix}\quad&\mathrm{D}&\mathrm{I}\+&\sqrt{1+x^3}&2\-&\frac{3x^3}{2\sqrt{1+x^3}}&2x\end{matrix}$
rocky lotusBOT
;(
pallid smelt
yup
noble anvil
Idek what I've done
Like i know but i didnt read what we had to find
storm perch
So then we get, if we let $I=\int\frac{3x^3}{\sqrt{1+x^3}}dx$, that our desired integral is $2x\sqrt{1+x^3}-I+I=\boxed{2x\sqrt{1+x^3}}$.
rocky lotusBOT
;(
storm perch
I'm actually laughing that GPT couldn't solve this
noble anvil
Fr that was like 2 lines 
Imagine praising ai when it cant do shit like this
@pallid smelt after you read this explanation and solve it yourself read my working
Thats what you should aim for to minimise the extra stuff
Speed is what matters most
pallid smelt
i mean i get it sort of but i'm in the dilemma of (3x^2)(1+x^3)^(-1/2)
when i differentiate u
pallid smelt
What you essentially want to do here is integrate the 2 and differentiate $\sqrt...
but he did it with
idk if it's a he
they
mb
noble anvil
Should i just walk u through this
storm perch
but he did it with
With what?
pallid smelt
the root
storm perch
Differentiate it?
storm perch
Yeah, it was easier for me.
pallid smelt
i don't rlly get urs ngl
noble anvil
I always prefer not to take powers into my variables
Ok wait ill write it out properly
pallid smelt
thank you
storm perch
I always prefer not to take powers into my variables
I mean, it’s a more direct application of chain rule.
noble anvil
Hope it's clearer
noble anvil
I mean, it’s a more direct application of chain rule.
Eh i always say math is expression do what you want as long as it gets you the answer
Just do it quickk
Cause thats been like drilled into me
If i cant do something under 10 mins i just ditch it
noble anvil
Hope it's clearer
@pallid smelt
pallid smelt
am currently working through it
why can we just take the x out of the integral like that?
noble anvil
Lmk if you're having difficulty I'll try to help you through it
noble anvil
Pog pog
pallid smelt
oh right
noble anvil
I just like taking it like this it's personal preference
pallid smelt
oh thats sexy
noble anvil
Nice about me
pallid smelt
i see that
nono i see taking 3x^2#
bc the inside of (1+x^3) differentiates to that
which is rlly nice
noble anvil
Yeah
Trained eyes spot that shii
You'll get there in like a month if you work even halfass decent
noble anvil
Nice about me
But i was just saying this in general
The god equation for your about me
pallid smelt
ofc ofc
genius using the taylor expansion of sin and cos and knowing to use i for sin
to compose e^itheta
mental
noble anvil
Its 4 am lmao why tf am i doing integration im supposed to be on vacation rn 
noble anvil
Yes i do
Do you have any more similar qns youre having a problem with
I might be able to help
noble anvil
Sure
I know just a tiny bit of every high school topic so if nothing i can atleast give tips
A decent bit actually but not enough, nothing is ever enough
pallid smelt
idk in all honesty where my knowledge is up to
noble anvil
If you can do this
pallid smelt
only basic stuff ik
noble anvil
Then its good
pallid smelt
i'm only 11th grade i believe
i'm 16
anyways now that i get it
thanks for all the help to u and ;)
.close
vale dockBOT
dry trail
noble anvil
Pog
vale dockBOT
Available help channel!
half wind
how do u do this?
vale dockBOT
how do u do this?
unborn python
do you know how to solve a quadratic?
tepid wind
how do u do this?
The equations must be equal to each other for intersection:
$$\begin{aligned}
y &= y \
x + 8 &= x^2 + 16x + 8 \end{aligned}$$
We can subtract $(x + 8)$ from both sides:
$$\begin{aligned}x + 8 - (x + 8) &= x^2 + 16x + 8 - (x + 8) \
0 &= x^2 + 16x + 8 - (x + 8) \end{aligned}$$
Simplify this and solve it like a new Quadratic.
rocky lotusBOT
@tepid wind
vale dockBOT
lilac scarab
for part b specifically
vale dockBOT
@lilac scarab Has your question been resolved?
vale dockBOT
@lilac scarab Has your question been resolved?
ebon gulch
vale dockBOT
ebon gulch
From my understanding, all non-planar graphs contain K3,3 or K5.
The answer says it is not planar, but I can't find the K3,3 or K5 graph.
I also can't find a way to draw it so that it is planar, so now I'm, confused.
(Please ignore the colours this question has a part b where I also answered the chromatic colours)
vale dockBOT
@ebon gulch Has your question been resolved?
proper nest
From my understanding, all non-planar graphs contain K3,3 or K5.
The answer say...
well they must contain a subdivision of K3,3 or K5
vale dockBOT
proper nest
i.e., K3,3 or K5 but you can introduce intermediate vertices along edges
vale dockBOT
Available help channel!
weak juniper
hi i need help 😦
vale dockBOT
hi i need help 😦
weak juniper
- (-sqrt(6),0) WRONG
- (-sqrt(6),9/2)
- (-sqrt(6),9) WRONG
- (0,0)
- (0,9)
- (sqrt(6),0) WRONG
- (sqrt(6), 9/2)
- (sqrt(6),9) WRONG
i said fx = (x^2-6)(9y-y^2)
and fy = (1/3x^2-6x)(9-2y)
idk what im doing wrong tbh
fierce vector
i said fx = (x^2-6)(9y-y^2)
yeah your f_x and f_y looks good to me
weak juniper
yeah i think theyre correct
fierce vector
not sure how you got something like $(\sqrt{6}, 0)$ from there though
rocky lotusBOT
mmmm7
weak juniper
my next step was finding (x,y) values for them to be 0
yeah i think its wrong, but i was struggling w finding the legit values
$(x^2-6)(9-2y)$
rocky lotusBOT
pais
fierce vector
yes that = 0
weak juniper
x could be equal to root36?
fierce vector
that gives you $x = \pm \sqrt{6}$
rocky lotusBOT
mmmm7
fierce vector
x could be equal to root36?
hmm
weak juniper
yeah
fierce vector
okay so you just need to make one of the terms = 0 for f_x and f_y
fierce vector
and fy = (1/3x^2-6x)(9-2y)
now use the values $\pm \sqrt{6}$ here
rocky lotusBOT
mmmm7
weak juniper
$(1/3yx^3-6x)(9-2y)$
rocky lotusBOT
pais
fierce vector
yes
fierce vector
i mean without the typo
weak juniper
lmao yeah
fierce vector
yes so for f_y = 0
either the first term
or the second term has to be 0
the first term can't be 0 because
,w 1/3 x^3 - 6x when x = [sqrt(6), -sqrt(6)]
rocky lotusBOT
weak juniper
(1/3(6)-6root6)(9-2y)=0?
weak juniper
so y = 9/2
rocky lotusBOT
mmmm7
weak juniper
7) (sqrt(6), 9/2)
i had that here and in #2
fierce vector
yep
rocky lotusBOT
pais
fierce vector
now consider the case where 9y -y^2 = 0
weak juniper
so 1/3x^2-6x = 0
fierce vector
so 1/3x^2-6x = 0
no no
weak juniper
and 9y-y^2=0
fierce vector
we have f_x and f_y
f_x = ab where a and b are each their own "terms"
for f_x = 0 you need a = 0 or b = 0 or both
we did the case for a = 0
weak juniper
yeah i think i was doing the fy case
rocky lotusBOT
mmmm7
weak juniper
9y-y^2 = 0, y = 0 or 9
fierce vector
yes
so those are your two remaining cases to work with
consider these two values of y for equation 2 and see what values of x makes the second equation 0
fierce vector
well you want to solve for f_y = 0 with the fact that y = 0
fierce vector
and solve 1/3x^2-6x for 0?
yes
that's only because 9 - 2y for y = 0 isn't 0
so for f_y to be equal to 0
weak juniper
x(1/3x-6) so x = 0, 18
fierce vector
you need the first term (aka the 1/3 x^2 - 6x bit) to be 0
fierce vector
x(1/3x-6) so x = 0, 18
uhh not really
weak juniper
wait why isn't it 18
fierce vector
because like you changed your expression for f_y
rocky lotusBOT
pais
fierce vector
oh nvm i see your flaw
weak juniper
i typed it wrong earlier
fierce vector
$f_y = \qty(\frac 13 x^3 - 6x)( 9 - 2y)$
weak juniper
my fault
rocky lotusBOT
mmmm7
fierce vector
not 1/3 x^2 😭
weak juniper
x(1/3x^2-6) = 0
fierce vector
yes
weak juniper
so x = 0, sqrt18, -sqrt18
fierce vector
yes
weak juniper
wait so are the answers
fierce vector
9y-y^2 = 0, y = 0 or 9
^
weak juniper
oh
fierce vector
y = 9 is your last case
fierce vector
well we initially had f_x = 0 -> x = +- sqrt(6), y = 0, and y = 9
for these values of x and y
we want to find the corresponding values of x or y
that makes f_y = 0
we did that for the x values
and y = 0
weak juniper
and now y=9
fierce vector
yes
weak juniper
so, (x^2-6)(9-18)=0
fierce vector
well yeah
in your work
u want to again show that 9 - 2y isn't 0 for y = 9
which is why we set the 1/3 x^3 - 6x = 0 instead
weak juniper
yeah which is 0, -sqrt18, and sqrt18
weak juniper
x(1/3x^2-6)
fierce vector
so yeah those are your 8
weak juniper
okay so (-sqrt6,0) and (sqrt6,0) are wrong
weak juniper
wait, we solved for fx for +/- sqrt 6
but the corresponding y value i thought was 0
i also have +/-sqrt(6), 9/2 as an answer
fierce vector
but the corresponding y value i thought was 0
why?
critical points occur when both f_x and f_y = 0
so we started off by setting f_x = 0
for those values of x (or) y
weak juniper
because when x = sqrt6, fx = 0 and when y = 0, fy = 0
fierce vector
we found each corresponding pair so that f_y = 0 is also true
weak juniper
oh wait thats not true
fierce vector
because when x = sqrt6, fx = 0 and when y = 0, fy = 0
x = sqrt(6) then f_x = 0 yes
but f_y is not 0
for y = 0 and x = sqrt(6)
weak juniper
no wait (9y-y^2) = y(9-y)
fierce vector
it's (9 - 2y)
weak juniper
oh never mind its 9/2
fierce vector
in the second equation
fierce vector
1)$(x^2 - 6)(9y - y^2) = 0\\\\$
2) $(\frac 13 x^3 - 6x)( 9 - 2y) = 0$
mmmm7
fierce vector
yes
weak juniper
$\left(-\sqrt{6},0\right),\ \left(-\sqrt{6},\frac{9}{2}\right),\ \left(-\sqrt{18},9\right),\ \left(0,0\right),\ \left(0,9\right),\ \left(\sqrt{6},0\right),\ \left(\sqrt{6},\frac{9}{2}\right),\ \left(\sqrt{18},9\right)/$
fierce vector
same logic for x = -sqrt(6)
rocky lotusBOT
pais
weak juniper
these were the answers listed
weak juniper
yeah ik
6 is also wrong
do i need to plug y as 0 into fx?
thats what i did
$fx = (x^2-6)(9y-y^2)$
rocky lotusBOT
pais
weak juniper
plugging in y as 0, so (x^2-6)(0) = 0
fierce vector
plugging in y as 0, so (x^2-6)(0) = 0
consider the case where y = 9
it's the last case we were doing
and the case which gets you the two right answers
(the ones u missed)
y = 9 gets you that f_x = 0
what about the x value when f_y = 0 and y = 9?
vale dockBOT
@weak juniper Has your question been resolved?
desert basalt
hello all, my name is scott im 46, i need help with math in order to take my GED test.
vale dockBOT
hello all, my name is scott im 46, i need help with math in order to take my GED...
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
desert basalt
sorry i feel so stupid being here im sorry, ty
plush crater
vale dockBOT
@desert basalt Has your question been resolved?
echo hearth
Yo guys, what the equation for combinations
vale dockBOT
Yo guys, what the equation for combinations
echo hearth
Let’s say that there is a burger
A burger can have between zero and six ingredients
There are 12 different ingredients
How many possible combinations are there?
odd jackal
!status
vale dockBOT
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
ebon glade
can an ingredient be used more than once?
echo hearth
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
What does this mean?
echo hearth
can an ingredient be used more than once?
Yes
shrewd hinge
Is 0 and 6 included?
echo hearth
Is 0 and 6 included?
Wdym
shrewd hinge
you said the ingredients is between 0 and 6. so, Is 0 and 6 inluded?
echo hearth
No, it would be [0…6]
shrewd hinge
I mean can a burger has 0 ingredients?
shrewd hinge
I see
ebon glade
!nosols
vale dockBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
ebon glade
in particular also not false solutions
shrewd hinge
mb
ebon glade
does the order of the ingredients matter?
shrewd hinge
I suppose not
ebon glade
not a question for you to answer
shrewd hinge
You may ping him!
ebon glade
@echo hearth
ebon glade
does the order of the ingredients matter?
.
ebon glade
that does not compute what you think it does
anyway. lets start slow
how many burgers are there with 0 ingredients?
echo hearth
1
ebon glade
how many are there with 1 ingredient
echo hearth
12
ebon glade
how many with 2 ingredients
lets first do two same ingredients
then two different ones
echo hearth
how many with 2 ingredients
I would assume 24
ebon glade
no
ebon glade
lets first do two same ingredients
how many like this
shrewd hinge
how many like this
Are you trying to explain the intuition of combinations?
ebon glade
random formula here we go
stark wedge
number smoothie
echo hearth
So do you guys know the equation
ebon glade
this is not about knowing an equation. this is about understanding the thought process
but well I have to go. luffy or ann can hopefully take over
shrewd hinge
but well I have to go. luffy or ann can hopefully take over
But I don't know how to explain the intuition btw
well @echo hearth do you know how combinations work?
echo hearth
Yeah, I know
shrewd hinge
I mean what does $^{m}C_{n}$
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
mean
echo hearth
Let’s say that there is
0 and 1
And they can take up two spaces
00
10
01
11
that 4 combinations
shrewd hinge
It's permutations where order matters not combinations
Here you have 12 ingredients
like denascite said with 0 ingredients there is $^{12}C_{0}=1$ burgers
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
with 1 ingredients there is $^{12}C_{1}=12$ burgers
@echo hearth Are you following?
rocky lotusBOT
Monkey•D•Luffy
echo hearth
What? I’m here. I’m here. I’m here.
echo hearth
Yeah, I understand. I understand one sec.
shrewd hinge
you may do it tell me what ans do you get
echo hearth
Desmos is a little wonky
Yeah, I’m actually kind of confused a little bit
Usually, when I tell people, I’m confused, they get angry
shrewd hinge
Don't use some formula for finding ans in perm and comb
You should apply your knowledge in doing perm and comb
see my explanation
Are you able to get that?
echo hearth
Yeah, I think so
shrewd hinge
\begin{itemize}\item with 0 ingredients there is $^{12}C_{0}=1$ burgers \item with 1 ingredients there is $^{12}C_{1}=12$ burgers \item with 2 ingredients there is $^{12}C_{2}=66$ burgers\end{itemize} and so on
Do you know why is this like this?
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
Do you know the $^{n}C_{r}=\frac{n!}{r!(n-r)!}?$
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
@echo hearth
shrewd hinge
I’m sorry for being stupid
no worries!
shrewd hinge
**Monkey•D•Luffy**
Do you know this?
echo hearth
Do you know this?
Unfamiliar with that territory no
shrewd hinge
Do you know the ans?
echo hearth
The ans?
shrewd hinge
yeah
echo hearth
What is ans?
echo hearth
**Monkey•D•Luffy**
Wait a minute
The cogs in my brain
They’re turning
My brain is doing the math
shrewd hinge
shrewd hinge
https://youtu.be/0NAASclUm4k?si=zTMlUvVJZXZp3KP9
@echo hearth You should learn what perm and comb first?
echo hearth
Wowsers
I’m still a little bit of a short shortcuting
I kind of understand I think
There is one burger buns
Oh, my fucking God
It’s working. I’m doing it.
shrewd hinge
Do you understand now @echo hearth ?
echo hearth
I don’t really know, but I’ll try
shrewd hinge
Do you understand comb and perm now?
echo hearth
echo hearth
Do you understand comb and perm now?
A little bit
shrewd hinge
12C1 means selecting one ingredients from 12 ingredients
12C2 means selection two ingredients from 12 ingredients
we need to select it upto 6 ingredients
echo hearth
Can you show that an equation form so I can understand?
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
,, ^{12}C_{1}
rocky lotusBOT
Monkey•D•Luffy
shrewd hinge
we are selecting the no. of ingredients from 12 ingredients using combinations
echo hearth
What does C stand for?
shrewd hinge
https://youtu.be/0NAASclUm4k?si=zTMlUvVJZXZp3KP9
Did you even see this?
@echo hearth If you're studying counting use https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:permutations-and-combinations-ncert-new/xea4762213f311c5e:untitled-908
It'd help you a lot
shrewd hinge
even for fun You should learn fundamental principles of counting, permutations and combinations to do this
shrewd hinge
use Khan Academy
echo hearth
I a slow learner
shrewd hinge
They will teach you from scratch
shrewd hinge
<@1269024659358351450> If you're studying counting use https://www.khanacademy.o...
Use this!
shrewd hinge
it's nah 
echo hearth
What do you mean?
shrewd hinge
you're are wrong i mean
I can see you aren't willing to do this as soon as you know you have to learn more lol!
you may close the channel, If you don't want help!
vale dockBOT
@echo hearth Has your question been resolved?
echo hearth
I can see you aren't willing to do this as soon as you know you have to learn mo...
You’re right
I should learn to well learn
I’ll come back more and
vale dockBOT
shrewd hinge
Have a great day, wusan!
vale dockBOT
Available help channel!
dusk mauve
12 raised to the pwr 6
vale dockBOT
12 raised to the pwr 6
ebon glade
is a big number
rocky lotusBOT
noble anvil
Um you could have done this yourself lmao
vale dockBOT
@dusk mauve Has your question been resolved?
vale dockBOT
vale dockBOT
Available help channel!
noble sonnet
How can I use the Pythagorean theorem to check if this triangle is a right triangle?
odd jackal
IS PQRS a rectangle
stark wedge
ok then figure out PT and TQ
noble sonnet
How do i do that?
Ohhhh
I figured it out
Okay let me calculate it rq
Okay i got it
So do i just calculate the lenght of all sides and see if a+b=c?
<@&286206848099549185>
static birch
yes?
earnest citrus
Looks like it
vale dockBOT
forest skiff
midnight pier
Im just getting started w/ condition probability here so i wanna get some intuitive understand of it , ( im getting a bit confused)
so example problem
Tossing 3 coins
what is the probability of occurance of exactly two heads if first coin shows tail ( i hope this is how the wording is done , for example the teacher didnt start us up w/ fully worded question , instead he just gave us two events like event A and event B , event A is occurance of exactly two heads and event B is first coin shows tail
( and he told us that first coins tail occurance is the condition)
so what im trying to make sense of here
by classical probability
there is one case where the first coin is Tails and the rest are heads , THH , so it should be 1/8 right the probability
but in condition probability its 1/4 , ik its the right answer , but im not able to make intuitive sense of it
noble anvil
Im just getting started w/ condition probability here so i wanna get some intui...
yes, by taking the HHH HHT HTH etc you will get 1/8
however, for independent events
we take each case individually
since none of the cases are dependent on each other
for the first coin, there is a tail. however, that does not affect any other coin
i.e.
midnight pier
yes, by taking the HHH HHT HTH etc you will get 1/8
is that a dependant event
noble anvil
for both the second and the third coins, the chance of it being head would be 1/2 and 1/2
noble anvil
is that a dependant event
well no, we take those 8 cases for when we want to analyse specific outcomes such as ORDER of the coins tossed
in this case all 3 coins are tossed together
midnight pier
and it does say first coin shows tail
noble anvil
yes, however the other coins do not form a sequence (ie, we are not analysing the probability of a specific sequence of events happening such as H after H after T)
midnight pier
but there is only one sequence where it occurs THH , because it says the first coin lands tails
im sorry if im confusing you
noble anvil
oh wait i might have misled you a bit
when we take the 8 cases
we are just looking at the sample space
midnight pier
yea
noble anvil
not the probability of something from that sample space happenin
midnight pier
ok
noble anvil
oh wait i might have misled you a bit
nm, the sequence thing is also applicable i thought about it
noble anvil
for both the second and the third coins, the chance of it being head would be 1/...
you understood this?
midnight pier
yea
noble anvil
ok so you understood that, and the probability of them both being heads would just be 1/2*1/2
midnight pier
yea
noble anvil
which is 1/4
midnight pier
mhm
noble anvil
now for the 8 cases thing, thats just our sample space used for counting favourable outcomes
it isnt used for simultaneous coin tosses, since in simultaneous coin tosses there is no sequence
eg
For sequential coin tosses
HHT, HTH, THH
are all different
however for simultaneous coin tosses
they are all the same
do you understand why?
midnight pier
yea but , here its a sequential coin toss right
noble anvil
no it isnt mentioned anywhere in the question that its sequential
it just says that one coin was observed to be tails
midnight pier
thank you for help ill come some time later maybe ive got something to do rn 😭
noble anvil
doesnt mean it was tossed before the rest
midnight pier
it just says that one coin was observed to be tails
first coin
i did mention that in the question
noble anvil
thank you for help ill come some time later maybe ive got something to do rn 😭
oh alr
cya
noble anvil
explain it to me
oh
another way to explain through the sample space could be
since we've gotten tails first already,
we will eliminate HHH
and also HTH
and HTT
and HHT
do you get why?
midnight pier
and we need the next two to be heads
so for the first coin to be heads , the probability is 1/2 and the 2nd to be heads is again 1/2 , so 1/2*1/2 = 1/4
we are kind of ignoring calculations with the occurance of tails first ( i mean i just totally ignored it here) , because it doesnt matter , cuz we already know tails has occured first and from there on we have to calculate the rest
midnight pier
do you get why?
yea yea
noble anvil
another way to explain through the sample space could be
(if we consider seq order)
midnight pier
and we get 1 case where is THH
yep
thank you so much , have a great day ahead :D
noble anvil
i confused you a bit before sorry 😂 was pretty straightforward
noble anvil
thank you so much , have a great day ahead :D
you too cya
midnight pier
.close
sturdy kelp
I've been looking for a while and can't seem to find how I integrated the cone part of the question wrong...It's meant to be 18 pi
sturdy kelp
everytime i integrate i make a mistake ☹️
timber chasm
When integrating between two curves I believe it is
int (top curve - bottom curve) d(var)
Since this is the area of a circular disks the equation (pi)r^2 squared is relavent which you seen to know
manic igloo
When squaring in the integral (-2)^2 = 4
timber chasm
if r is the integrand, the (top curve - bottom curve) is squared itself if I remember correctly, so (top - bottom)^2
sturdy kelp
yeah
I squared it i thought tho and then expanded it
oh and then the bottom
like the blah blah blah/-2 squared
and thne i didnt square the minus 2
ahhhh
timber chasm
R is also bounded to x >= 0 I believe
sturdy kelp
let me see if that fixes it
timber chasm
Why is your integral from 7 to 13?
sturdy kelp
im working out the cone
yeah i could use the cone formula
but it says to use vol by integration
noble anvil
I've been looking for a while and can't seem to find how I integrated the cone p...
wait is R not integral of sqrt y+2 from -2 to +7 added to integral of (13-y)/2 from 7 to 13?
timber chasm
R is bounded by the y-axis and the two equations given, I don't think 7 to 13 is an enclosed space (as exact points are not given)
noble anvil
When integrating between two curves I believe it is
int (top curve - bottom curv...
this isnt applicable here btw
sturdy kelp
bottom part that i got
disregard the part with 36 pi that was my incorrect first integral
this is correct according to the markscheme
manic igloo
That all looks good, just that small error when squaring the fraction.
noble anvil
bottom part that i got
its sqrt y+2
timber chasm
this isnt applicable here btw
Cause it's in terms of y, so it is outer - inner?
manic igloo
its sqrt y+2
(sqrt(y+2))^2
noble anvil
Cause it's in terms of y, so it is outer - inner?
there is no outer inner curve here, the region can be clearly divided into area covered by the parabola on y axis and area covered by the line on y axis
sturdy kelp
i just split the cont part and the curve part
noble anvil
(sqrt(y+2))^2
??
timber chasm
there is no outer inner curve here, the region can be clearly divided into area ...
not for points above y = 13
sturdy kelp
because I wasn't comfortable integrating the area around the axis
not really sure how you do that
noble anvil
not for points above y = 13
points above y 13 are not enclosed by the parabola
noble anvil
points above y 13 are not enclosed by the parabola
its just infinite area there
sturdy kelp
Do you know how to calculate bodies of revolution?
yep
manic igloo
Sorry, that was for Executor, you are doing fine!
timber chasm
points above y 13 are not enclosed by the parabola
Oh my bad that's in x < 0 area
noble anvil
Do you know how to calculate bodies of revolution?
No, i thought we just had to find the area so said we should do x=sqrt y+2 and integrate from 7 to 13. idk what a body of revolution calculation is, so i must be wrong
manic igloo
Like I said. Good work!
manic igloo
np
vale dockBOT
noble anvil
oh i understand now its the area of the discs lol
i didnt see the pi before
sorry @manic igloo
manic igloo
No problem.
vale dockBOT
Available help channel!
solemn cave
Hey
solemn cave
This is what we are doing in class (stochiometry) , and my teacher said we're gonna have a test tomorrow on the combustion reaction of ethane. But how can there be grams of oxygen in a combustion reaction?
Like wouldn't there have to be grams above oxygen? But that's not possible?
violet nimbus
tech number of moles is measured in grams
like in the reaction of ethane there's like 224 g of oxygen reacting
solemn cave
tech number of moles is measured in grams
What is tech numbers
solemn cave
like in the reaction of ethane there's like 224 g of oxygen reacting
So they give oxygen grams?
violet nimbus
techinically=tech( my bad)
violet nimbus
So they give oxygen grams?
yeah
number of moles = given wt of the compound/ gram molecular weight
vale dockBOT
@solemn cave Has your question been resolved?
solemn cave
yeah
But on a YouTube video they didn't
Also does anyone know if I did this correct or not?
Bro I'm gonna combust
wraith heart
Bro I'm gonna combust
try chem server in #old-network
you're asking for chem help in a math server
solemn cave
you're asking for chem help in a math server
Its stoichiometry
Like dimensional analysis
marsh forge
Also does anyone know if I did this correct or not?
where'd you get 60g/mol of co2?
solemn cave
Its basically just math
marsh forge
(i might be wrong since i dont usually do stoichiometry this way)
viscid sedge
But on a YouTube video they didn't
in air means endless supply of oxygen
your limiting reagent is C3H8
viscid sedge
(i might be wrong since i dont usually do stoichiometry this way)
ikr
wraith heart
Its stoichiometry
solemn cave
(i might be wrong since i dont usually do stoichiometry this way)
My teacher found the worst was possible did he 😔
wraith heart
sounds like chemistry
solemn cave
Yeah but the process is like pure math 😭
wraith heart
yes lots of sciences use math
solemn cave
To find the chemical thing you gotta do this math
wraith heart
#old-network has a few science servers
marsh forge
My teacher found the worst was possible did he 😔
its mostly not, its just really hard to sight read
wraith heart
solemn cave
<#406129911992942593> has a few science servers
Ok pluh thanks
solemn cave
where'd you get 60g/mol of co2?
I have no idea. It's 44.01 grams now that i recalculated
Is it correct now?
I got it correct thank you to the alphas excluding the guy with the attitude
marsh forge
Is it correct now?
i think so yea
vale dockBOT
@solemn cave Has your question been resolved?
next moss
hey there, long time no seen
can someone please confirm for me if i have done it correctly? im not a fan of chat gpt and the final results might change anyway from person to the other... appriciated a lot < 3
next moss
nvm i think i have a mistake with the 1, it should be -1
next moss
yeee... damn- thanks
stark wedge
you can't drop the brackets in cos(60+2x) btw.
in fact i personally recommend NEVER dropping the brackets, even when it's just one letter or one number.
next moss
ok i hope it's better now
stark wedge
yeah looks ok now
could also have gone straight to cos(30+x) = 0 though no need for the double angle identity
fallow sparrow
yo
stark wedge
you need to find the angle between i-2j and j
fallow sparrow
you need to find the angle between i-2j and j
okay
the question is worded so weirdly
how do you know that's what they want me to find?
stark wedge
R is parallel to i-2j
tbh there's some ambiguity as to whether it's facing the same way or the opposite way
fallow sparrow
R is parallel to i-2j
and the resultant of the two forces
stark wedge
resultant is an old-timey physics-y way to say vector sum
fallow sparrow
resultant is an old-timey physics-y way to say vector sum
i know
so
resultant is R
and i need to know what the angle between vector j and R is
but i don't know p and q
so i cant even calculate the resultant force
stark wedge
so i cant even calculate the resultant force
you dont need R itself
any vector parallel to it will do
vale dockBOT
@fallow sparrow Has your question been resolved?
vale dockBOT
@fallow sparrow Has your question been resolved?
fallow sparrow
.close
livid gull
Hii im new here and really need some help (a lot of help) cuz i have a pretty important maths exam tomorrow and for personal reasons i haven't been able to pay attention and focus in class properly for months and now matter how i tried to study id either get distracted or i would just forget it the next day
ivory valley
hi, do you have a specific problem/question?
livid gull
The overall topic is parables and all the sub topics are the quadratic function y=x²+c, the quadratic funktion y=ax²+c, the vertex form y=(x-d)²+, the normal form y=x²+bx+c, intersections, zeros and mathematical modeling (im not sure if all of those are translatef correctly cuz like english is not my first language and i have no idea about mathematic terms in english)
ivory valley
Do you happen to speak German?
livid gull
Yep
livid gull
Tbh ich hab halt wie gesagt seit monaten nicht richtig im Unterricht aufgepasst ich weiß so ungefähr die basics aber den rest check ich einfach nicht
livid gull
Nullstellen, quadratische Ergänzung, ...?
Warte eine sekunde muss selber genau kucken was ich insbesonders nicht verstanden hab
echo spear
viscid sedge
i can't understand everything but i can understand a lot
echo spear
💀
viscid sedge
(i happen to know a bit of german)
livid gull
Warte eine sekunde muss selber genau kucken was ich insbesonders nicht verstande...
Ich hab schnittpunkte und modellieren insbesonders nicht gecheckt
ivory valley
Modellieren im Sinne wie man Parabelgleichungen aufstellt?
Also Schnittpunkte, da setzt man die Parabelgleichungen gleich und löst für x.
livid gull
Modellieren im Sinne wie man Parabelgleichungen aufstellt?
Keine ahnung das wo man so sachen von der echten welt nehmen muss und das "übersetzen muss"
livid gull
Also Schnittpunkte, da setzt man die Parabelgleichungen gleich und löst für x.
Aber wie mach ich das 😭
livid gull
Hast du ein konkretes Beispiel?
Von modellieren?
ivory valley
Dafür musst du Gleichungen umstellen können.
ivory valley
Von modellieren?
Ja.
Also im Prinzip bei Schnittpunkten setzt du die beiden gleich. Dann bringst du alles auf eine Seite und benutzt anschließend die Mitternachtsformel.
livid gull
Ja.
Ja wir haben so 3 arbeitsblätter paar tage her bekommen da sind aufgaben drauf (to be honest hab ich aber garnix von den blättern gecheckt)
Ich schick bild warte
ivory valley
Zum Beispiel: 2x²+3x+5 = x²+x+4 dann kriegst du x²+2x+1 = 0
ivory valley
Ok.
livid gull
(Ich weiß ich bin mies dumm aber ich check eif nicht und ich will nicht 9te wiederholen)
ivory valley
Ok also den Boden den kannst du dir wie die x-Achse vorstellen.
Also der Boden hat Höhe 0.
So kannst du das dir vorstellen, wie man es am Geschicktesten angeht.
So soll das Ding aussehen, die nächste Frage, die du dir stellst ist, welche Informationen sind dir gegeben.
Was kannst du rauslesen aus dem Text?
livid gull
Das ist 192m hoch und breit
ivory valley
Ja!
Jetzt stell dir vor, du hast den Nullpunkt in der Mitte
Wie weit voneinander sind dann die grünen Nullstellen?
Wenn es 192m breit ist insgesamt.
livid gull
Also von einander sind die ja 192m entfernt
ivory valley
Ja, und von der 0 aus, dann?
livid gull
achso
ivory valley
(Die Parabel ist achsenssymetrisch)
livid gull
96 m
livid gull
Uhh 192 meter? (Ich weiß ned ob ich die frage richtig verstanden hab)
ivory valley
Ja, das wäre die y Koordinate.
Was ist mit x?
Ein Punkt (x,y) hat die Koordinaten x und y.
ivory valley
Wenn du das Bild anschaust, der grüne Punkt oben, was hätte der für einen x-Wert?
livid gull
96 glaub ich
ivory valley
Das wäre dann rechts.
Aber wir wollen nicht diesen Punkt.
Der Punkt ist ja weiter links, genau genommen in der Mitte, im Ursprung.
livid gull
Achso
ivory valley
Der Hochpunkt ist ja genau auf der y-Achse, also hat der die x-Koordinate?
livid gull
Ja null
ivory valley
Ja.
So würde man es ungefähr modellieren.
Du fängst am Besten immer an, das Koordinatensystem möglichst so zu zeichen, sodass die Parabel achsensymmetrisch. Dann kann man Nullstellen und Hoch/Tiefpunkt leichter zeichnen und rechnen.
Jetzt hast du alles an Informationen, um die Funktionsgleichung aufzustellen, am Besten Scheitelpunktform.
rocky lotusBOT
ivory valley
Was wäre der Scheitelpunkt hier?
ivory valley
Aus dem Bild.
livid gull
(0|192)
ivory valley
Ja.
ivory valley
So jetzt können wir das hier einsetzen. Was würdest du dann kriegen?
livid gull
Uhh warte lass mich nachdenken
ivory valley
Musst eigentlich nur d und e einsetzen.