Available help channel!
#help-13
midnight zealot
Isn't length just distance here though? So we would just do velocity multiplied by change in time, which we did in one of the legs. I think I'm getting confused, if you have some time to explain this to me I would really appreciate it.
simple shale
midnight zealot
Yeah but I just don't understand why we need to multiply delta time with the speed of light
Maybe I'm not getting it
olive gazelle
How can I simplify the roots of negative numbers?
cedar kilnBOT
How can I simplify the roots of negative numbers?
olive gazelle
Say, the square root of -52?
This sal khanacademy lesson isn't really doing much justice for me
wind glade
so first you can split the -52 into (-1)(52)
and do you know how to split the products inside a square root
@olive gazelle
or in general for some positive number N
the square root of -N
wraith daggerBOT
please request a new nickname
dire geode
This sal khanacademy lesson isn't really doing much justice for me
What's wrong with their explanation that you don't understand?
cosmic steppe
Say, the square root of -52?
Well you can say that is $\sqrt{-1}\sqrt{52}$
wraith daggerBOT
Umbraleviathan
cosmic steppe
Which is $i\sqrt{52}$
wraith daggerBOT
Umbraleviathan
crystal raptor
Be warned this rule does not apply to two negative numbers
cosmic steppe
Which is uhhhhh
crystal raptor
And be scared
cosmic steppe
**Umbraleviathan**
$= 3i\sqrt{6}$
wraith daggerBOT
Umbraleviathan
crystal raptor
The old 1=-1
cosmic steppe
I guess
I mean
We hate it
We try not to
And normally we should have to put i
crystal raptor
What lol, why do you think this is an English thing
It's a maths thing
And is used a lot
cosmic steppe
Remember when Schrodinger had i in his funny wave function
wind glade
math is a universal language
crystal raptor
Remember when Schrodinger had *i* in his funny wave function
Must've been English
cosmic steppe
Silly Schrödinger
crystal raptor
Also wait till you hear what dirac was up to in his equation
dire geode
bobbyt has to learn Dirac's equation now
olive gazelle
khanacademy says my answer is wrong
however they literally do the same thing...
wind glade
your i
cosmic steppe
Yeah because you put accidentally put the i inside of the root instead of outside
dire geode
,w sqrt(i)
wraith daggerBOT
olive gazelle
Yeah because you put accidentally put the *i* inside of the root instead of outs...
well i mean they're i looks like its in the square root aswell
cosmic steppe
well i mean they're i looks like its in the square root aswell
Theirs is outside
crystal raptor
I guarantee you french mathematicians do it
olive gazelle
cosmic steppe
Yeah the line doesn't extend above the i
olive gazelle
i see, theyre root is not extended
but the thing is, how can i even not do that? lmfao
if i press space
cosmic steppe
Arrow key
olive gazelle
it doesn't do anything between
cosmic steppe
Arrow key.
Probably because you need to convert it to a complex number
Like
0 + 2i
Or
cosmic steppe
Yeah
crystal raptor
When you get older you're allowed to
olive gazelle
seems a bit disingenious from the summary
cosmic steppe
You gotta be a big boy first
olive gazelle
i get how it's right
olive gazelle
but the summary doesn't do it justice
lmfaooooo
when being pedantic would actually help
cosmic steppe
It's like that time they fucked up an entire chemistry question and labeled selenium as a metal
That was funny
mighty drift
Apparently in Galois theory it can be more common to use sqrt(-1) than i because there's no difference between i and -i
dire geode
j has entered the chat
mighty drift
math's j or physics's j ?
dire geode
Electrical engineers' j
crystal raptor
Apparently in Galois theory it can be more common to use sqrt(-1) than i because...
Eh what? That's not true
mighty drift
our teacher quickly said that earlier today: since there's no point in making the difference between i and -i, they allow themselves to use negative sqrts for more generality, like {Q[sqrt(a)] \ a in Q*}
crystal raptor
It depends heavily on your field and field extension, i is definitely not the same as -i all the time in Galois theory
mighty drift
but you can't tell the difference between when you construct C as the algebraic closure of R, you make an arbitrary choice of which one to call i and which one to call -i
crystal raptor
Right but you still have distinct elements you call i and -i
mighty drift
yeah but you allow yourself to write negative square roots
mighty drift
our teacher quickly said that earlier today: since there's no point in making th...
because in a set like Q[sqrt(a)], it doesn't matter whether you consider that to be i sqrt(-a) or -i sqrt(-a)
I'm French so that's that
but I'm also only in first year of undergrad so I wouldn't want to sound like a Galois theory expert
crystal raptor
I understand that adjoining something called i or -i results in the same field, but I do not think its accurate to say i and -i are the same in galois theory, they are not the same element is my point
mighty drift
but structurally it wouldn't change the nature of the sets. That's why I'm saying it doesn't really matter. They're different, but they play the same role as roots of XÂČ+1
MPSI
you ?
where ?
quelle prépa avant ?
j'aurais pu, mais un peu loin, surtout quand comparé au Parc
je suis pas au Parc par contre
mais vu que j'Ă©tais pris lĂ bas j'aurais jamais pris Champollion je pense
Louis le Grand
et t'es oĂč maintenant ?
bien
c'est bien lĂ bas ?
dommage
pas voyager de toute façon, on a l'habitude récemment
D'ailleurs tu dirais qu'elles ont quelle importance les matiĂšres non scientifiques en Ă©cole ?
SHS ?
tant mieux, vu Ă quel point le français peut ĂȘtre passionnant avec les bons profs.....
le problĂšme c'est que c'est l'annĂ©e oĂč les connaissances n'ont pas d'importance mais la mĂ©thodo si, et on a fait que du cours de connaissances
oui, mais un minimum, pas que ça
le pire c'est quand tu as un remplaçant pendant 6 heures et que tu te demande qu'est ce qui t'a apporté le plus
actuellement je suis Monsieur 12: DS 1, 12, chacune des 3 colles de français, 12. Aucune autre note
aucun autre exercice. D'oĂč le manque crucial de mĂ©thodo
ce qui est bien c'est que les profs de maths sont géniaux
surtout la culture qu'ils ont Ă partager est un + trĂšs sympa
cedar kilnBOT
@olive gazelle Has your question been resolved?
urban cipher
i am not sure what this question is asking me to do?
cedar kilnBOT
i am not sure what this question is asking me to do?
urban cipher
could someone please explain what it's asking and how i would do it
cedar kilnBOT
@urban cipher Has your question been resolved?
cedar kilnBOT
@urban cipher Has your question been resolved?
cedar kilnBOT
@urban cipher Has your question been resolved?
tidal yoke
Help
violet flume
crimson sedge
take the 4yd as height
crimson sedge
then use ur formula
vestal bear
The front side is two right triangles
you can find the areas individually, add them up and multiply by height
crimson sedge
you can find the areas individually, add them up and multiply by height
why tho?
vestal bear
what
crimson sedge
why divide into two?
crimson sedge
area = h*b/2?
crimson sedge
6.1?
tidal yoke
Ight so what we got here
crimson sedge
what did u get as the area of the triangle?
tidal yoke
61
crimson sedge
/2
tidal yoke
So itâs 30.5
tidal yoke
Idk
crimson sedge
did u find?
cedar kilnBOT
@tidal yoke Has your question been resolved?
crimson sedge
help
crimson sedge
I thought I did this correctly
but I didn't
long story short the answer is this:
they tell us in the textbook lol
I got that kinda
the 1/5 is in the wrong place and instead of a 1/5 I got a 1/2
I am pretty sure the "u" of this equation is 1+5t
but correct me if I am wrong
wraith daggerBOT
Umbraleviathan
crimson sedge
ohhh so the 5 was supposed to cancel out
I got confused basically
I was scared that the 5 got canceld out completley lmao
static sage
to check you can always differentiate your answer and see if you get the original
crimson sedge
I based my work off of a very similar problem so maybe thats where I got confused
I will send my work so you can correct me where I went wrong to get a 1/2 if you'd like
help lol
rugged wasp
cedar kilnBOT
rugged wasp
Hey guys this is trig derivatives
My teacherâs solution sheet
Can someone show me how he went from the part labelled 1 to 2?
late cloak
Can someone show me how he went from the part labelled 1 to 2?
applied pythagorean identity
$cos^2x + sin^2x =1$
wraith daggerBOT
blushysullyforemoteforryc
rugged wasp
How does that identity apply to the denominator?
late cloak
$cos^2x = 1 - sin^2x$
wraith daggerBOT
blushysullyforemoteforryc
late cloak
đ
boreal hemlock
cedar kilnBOT
south dawn
separate fraction and reduce.
boreal hemlock
once reduced i then find the anti derivative?
south dawn
once reduced i then find the anti derivative?
yes
boreal hemlock
.close
dreamy cedar
Hello, could someone tell me the answer to this? I got 6.0N and 55 degrees, but I'm not sure if that's even right
dreamy cedar
I'm gonna redo it tbh but I'm just lost cos cosine/sine laws are cringe, i prefer using components
With components I got 6.0N and [N 4° W] or 6.0N [W 4° N]
Just rlly confused rn
OH MY GODF
I GOT IT
IM SO HAPPY WTF WTF WTFWW TWTFW TWADJOASOD ITS ALL ABOUT DRAWIG THE DAMN TRIANGLE PROPERLY
.close
hybrid light
cedar kilnBOT
flint plinth
any thoughts?
bitter reef
$$\frac{a^b}{c^b} = \left(\frac{a}{c}\right)^b$$
wraith daggerBOT
Doggo
cedar kilnBOT
@hybrid light Has your question been resolved?
hybrid light
any thoughts?
i honestly dont know
can you walk me through
can someone walk me through this
eager pier
can you not rewrite it as $$7*\left(\frac{-3}{5}\right)^n$$
wraith daggerBOT
Sm3
wraith daggerBOT
Sm3
eager pier
-.6 is inside the domain that proves convergence
cedar kilnBOT
@hybrid light Has your question been resolved?
tranquil anchor
Can anyone please help me understand regularisation in math, especially in infinite series ?
sleek condor
do you want to understand the principle or dig deeper?
tranquil anchor
Both
sleek condor
whats your level of knowledge in series / analysis
tranquil anchor
I know about convergence and divergence of a series, how we can add parameters to the series with limits of that parameters to get to zero after getting final result
sleek condor
yeah so not that much
tranquil anchor
Yeah you can say
sleek condor
So regularization is the task of attributing a value to a diverging series
sleek condor
i will talk about one kind of regularization only (its famoujs aswell) the zeta regularization
tranquil anchor
Ok
sleek condor
If you have a diverging series of the form a1 + a2 + a3+ ......
tranquil anchor
To power?
tranquil anchor
Oh subscript
sleek condor
with an being the general term
tranquil anchor
oh ok
sleek condor
You introduce its zeta function
tranquil anchor
Please write it as a_n for better understanding of mine
tranquil anchor
ok further
sleek condor
this sum converges for large values of Re(s)
and by some trickery we can define it on the whole complex plane (analytic continuation)
sleek condor
it depends on a_n
also there are some (a_n) such that even this does not converge for any value of s
but for many (a_n) this will converge eventually
sleek condor
the classic example is a_n =n
tranquil anchor
Thats divergent right?
sleek condor
the sum of natural numbers is
but the zeta sum or function is convergent for Re(s)>1
and its analytic continuation is
tranquil anchor
But I thought 1+1/2+1/3⊠is divergent
sleek condor
you're right
its a strictly
w/e
it converges for some values of s, and its an analytical function so we can continue it on the whole complex plane
tranquil anchor
What is {t}? in the integral
sleek condor
actually theres a more comprehensive form
heres a functionnal equation
zeta follows it
tranquil anchor
What does lamda represent there?
sleek condor
so you using it you can link values with Re(s)>1 with values with Re(s) <=1
lambda?
gamma you mean?
tranquil anchor
oh sorry
sleek condor
its the gamma function
dire geode
$\Lambda$
wraith daggerBOT
riemann
sleek condor
its an extention of the factorial function over continous values
tranquil anchor
Sorry I mistaken it
tranquil anchor
its an extention of the factorial function over continous values
Can you go in a bit detail
sleek condor
i can give you a formula but i cant teach you all the maths surrounding it
the definition is given by
for values of Re(z)>0
tranquil anchor
Oh ok
tranquil anchor
If you would have to explain regularisation in the most simple words how would it be?
sleek condor
its a way to attributing a value to diverging series, let me finish to explain
actually all those formulas dont mmatter mmuch for your understanding
zeta(s) = 1/(a_1)^s + 1/(a_2)^s + 1/(a_3)^s + ......
all you have to see
is that for s =-1
this sum is just the orginial sum
a_1 +a_2+a_3
but obviously this series diverges
and zeta(s) is not defined for Re(s)<=1
but we define an continuation
over the whole complex plane
(unique)
so we can access a value
for zeta(-1)
so what u need to understand is that the continuation is not the same as actually doing the sum
but its the only function that has good properties (such as differentiable etc....) that continues the zeta function
so in a sense zeta(-1) has a value
so in a sense the diverging sum can be attributed a value
tranquil anchor
How is this attributed value used practically?
sleek condor
wym? does it have real world applications?
tranquil anchor
Like I know $\sum {n=1}{\infinity} {n} =\frac{-1}{12} $ and this is used to explain forces in the Casmir effect
sleek condor
yeah
tranquil anchor
Wait I have a formula
sleek condor
so if u want to understand deeply what is zeta regulariuzation (and other regularizations) i suggest you pursue complex analysis
tranquil anchor
so if u want to understand deeply what is zeta regulariuzation (and other regula...
I would once I get into college for my undergraduate
tranquil anchor
regularization does not mean that 1 +2 +3+4+5 =-1/12
Yeah ik its just the part
If it is part of pure mathematics then why do we have to assign values to this divergent series?
The pictures are not in order I an sorry
sleek condor
The pictures are not in order I an sorry
didnt read themm dont worry
sleek condor
If it is part of pure mathematics then why do we have to assign values to this d...
we dont have to do anything
we just noticed we could
tranquil anchor
Would it make more sense to write it as 1+2+3+âŠ=infinity -1/12
sleek condor
no it wouldnt
tranquil anchor
Why?
sick ruin
Iâm jumping into this conversation so forgive me if youâve already covered some of this
But you need some context when you talk about infinite series and the notion of equality
With the normal idea of equality, taking the limit of partial sums as they approach infinity, the series 1+2+3+⊠(which is really the limit of the sequence 1,1+2,1+2+3, âŠ) simply diverges
But if you want to have some systematic way to assign a finite value to divergent series, there are methods to do that
Ramanujan summation, Cesaro summation, Borel summation, etc
Letâs be clear though: if you want to do such a thing, you must specify which system youâre operating under, or else everyone will be confused
tranquil anchor
Does the answer after using this different summations come different or are they for different types of divergent serieses?
sick ruin
I assume the methods work a little differently for different series
I donât have experience with it tho
But I have heard that this particular series (1+2+3+âŠ) somehow comes to the same answer, -1/12, under many different methods
And the coincidence with physics is another interesting thing
tranquil anchor
But I have heard that this particular series (1+2+3+âŠ) somehow comes to the same...
Yeah it does
dire geode
What am I reading
tranquil anchor
And the coincidence with physics is another interesting thing
Please let us also talk about it
tranquil anchor
Oh ok
tranquil anchor
dire geode
PBS spacetime on YouTube has some nice videos explaining the questionable infinite sum in quantum field theory
tranquil anchor
crystal raptor
Physicists be like, what's a divergent series lol
dire geode
At least now I know about as much about physics as they know about math
tranquil anchor
Well I do not know anything much of physics stuff and interested in pure mathematics used
crystal shell
How would I go about doing part b? Not really sure where to start
crystal shell
I have been able to do all the other parts but I'm still uncertain of b
crimson sedge
Rate of flow is the derivative of the graph at that particular point from what I understand
So you have you estimate the gradient of the graph at t=200
Do that by looking at the point t=200 taking a very small step from it across the graph in either direction and then connecting the tree points with a line
Find the slope of that line
crystal shell
no, no equation is given
crimson sedge
Then yes just estimate a tangent line
crystal shell
How would I do that if you don't mind?
Like I understand the idea but just a bit unsure of how to actually do it
bitter reef
from t = 200 to t = 300 it looks kinda like a line, I guess you use that..?
crystal shell
Could use like (6,200) and (8,300) ?
bitter reef
I don't see any other way
bitter reef
I think it's 1/50
crystal shell
oh
XD
wait but we go up by 100, and across by 2
Am i misunderstanding this?
oh
the scale is flipped...
bitter reef
we go from V = 6 to V = 8, so up by 2 and t = 200 to t = 300 so go across by 100
crystal shell
Yep you're right
So if gradient is 1/50 what do I do with that then to find the rate of flow
crimson sedge
It is the rate of flow
crystal shell
Here's from textbook answers
But obviously I could look and copy but that won't help me learn
That's why I came here
crimson sedge
What is the rate of flow?
What do you think?
I think the answers may be wrong
For the gradient
crimson sedge
Check the non-worked solutions
crystal shell
so perhaps they got their estimate in a different way
bitter reef
it's like double our approximate
crystal shell
Same thing, 430,000
crystal shell
What did I get wrong?
crimson sedge
No the other guy
He calculated the gradiet by doing x2-x1/y2-y1
Itâs the other way around
crimson sedge
The answer is correct
bitter reef
crystal shell
^
bitter reef
so you took the x intercept on this right?
what I don't understand is why does (250, 8) or (300, 8) not work?
bitter reef
yeah
crystal shell
It was kinda my bad i didn't look properly
crimson sedge
bitter reef
oh right yea
crimson sedge
@crystal shell you got it?
crimson sedge
Ok cool
cedar kilnBOT
cedar kilnBOT
Available help channel!
bright sorrel
cedar kilnBOT
bright sorrel
"In isosceles trapezoid, AB= 18 cm, the height DQ = 5 cm. Find the middle segment"
somehow I struggle with this
although I know the theorem
(a+b)/2=middle sedment
I've already added every other detail
to the model
ohh DQ = AQ
muted ocean
Yrs
bright sorrel
not AD=CD
lemme see if I solve it (which I'm confident I can)
AQ=(a-b)/2
5=(18-b)/2
10=18-b
28=-b
-28=b
hmm
oh wait
10=18-b
-8=-b
b=8
which makes
(18+8)/2=13
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
spiral surge
how did they arrive at the first equality in last sentence??
spiral surge
like $ah = (aha^{-1})a$
wraith daggerBOT
RĆmer
spiral surge
how did they get that
crimson delta
just multiply by 1=a^(-1) a and then place convenient brackets
analog wind
cedar kilnBOT
analog wind
need help with part 2
3(ii) answer is given ^
i cannot seem to brute force d2y/dx2 using quotient rule
i got dydx=( T*lnT +T)/T+1
Wait i cannot brute force it cuz dy/dx is in terms of t lol
do i take derivative from dy/dx
then divide by dt/dx
nvm
.close
still echo
Meow
still echo
đ
crystal raptor
?
cedar kilnBOT
@still echo Has your question been resolved?
crimson sedge
<@&268886789983436800>
calm sierra
cedar kilnBOT
cedar kilnBOT
Available help channel!
dull anchor
$\int\frac{1}{\sin^2(x)}dx$
cedar kilnBOT
$\int\frac{1}{\sin^2(x)}dx$
dull anchor
i need help solving this integral
wraith daggerBOT
Big xdddd
wraith daggerBOT
Big xdddd
reef venture
what is cosx/sinx
reef venture
what is the antiderivative of cot^2(x)
dull anchor
but how can i integrate this one?
dull anchor
what is the antiderivative of cot^2(x)
hmm idk this
reef venture
its a standard formula
dull anchor
antiderivate means integral?
reef venture
yes
dull anchor
its a standard formula
i dont really know
reef venture
do you know the derivative of cotx?
dull anchor
its cos(x)/sin(x)
reef venture
derivative
reef venture
yes
dull anchor
subistute sin^2(x) ?
reef venture
no need to subsitute
reef venture
if the derivative of cotx is -cosec^2x, then the integral of cosec^2x is -cotx
not a rule as such, its just the definition of the intergal
dull anchor
ok
wraith daggerBOT
crimson sedge
$\int 1+\frac{cos^2(x)}{sin^2(x)}dx = x + \int_{}^{} cot^2(x) dx$
wraith daggerBOT
Pi Creature
crimson sedge
and also this
@dull anchor
Bruv
1+cotÂČx = cosecÂČx
Integral of cosecÂČx is -cotx
cedar kilnBOT
@dull anchor Has your question been resolved?
trim spear
Is a matrix hermitian conjugate the same as a transposition
cedar kilnBOT
Is a matrix hermitian conjugate the same as a transposition
trim spear
Right, just a transposition with an additional step then (application of conjugate function across non diagonal entries)?
leaden snow
i think you need to take the conjugate of all entries
reef venture
Right, just a transposition with an additional step then (application of conjuga...
I remember taking all entries
dapper dawn
please help, I don't understand the question and what it wants
cedar kilnBOT
please help, I don't understand the question and what it wants
@dapper dawn Has your question been resolved?
dapper dawn
<@&286206848099549185>
crimson sedge
From how the problem phrases it n represents number of parts. So weâre told that at maximum the factory can sell 5000 so which of the 3 makes profit or maximum profit if they sell the maximum amount of 5000 parts
dapper dawn
oo so just substitute n by 5000 then?
crimson sedge
No Iâm wrong I think you have to use calculus and optimize the profit cause they make a maximum profit somewhere between 1000 and 5000 parts
normal tide
How do I reduce 4â3/8
cedar kilnBOT
How do I reduce 4â3/8
normal tide
If it's 4/8 i can just divide by 4/4 and get 1/2
wraith daggerBOT
Chunkin
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fair hare
If it's 4/8 i can just divide by 4/4 and get 1/2
basically that
normal tide
what abt the â3
fair hare
$\frac{4\sqrt3}{8}=\frac{1\sqrt3}{2}$
wraith daggerBOT
Chunkin
normal tide
oh i just ignore the â3 for a bit then add it later after dividing by 4/4
fair hare
yeah it's the distributive property
normal tide
Ok thanks
normal tide
Does it also work if it's the opposite
wraith daggerBOT
umbral sparrow
cedar kilnBOT
umbral sparrow
Hi, i dont know how to do this
i tried doing it by using the z chart but it didnt work
modern compass
What Z-scores correspond to the upper 25% and lower 15%?
umbral sparrow
What Z-scores correspond to the upper 25% and lower 15%?
thats what im trying to figure out
upper abyss
You'll need to use the chart backwards to do this
umbral sparrow
so i tried that before and i got, 5.668
but the teacher got 5.672
then for the lower 15 percent i got 4.84 and she got 4.996
modern compass
sounds like you're just using different z-scores
umbral sparrow
sounds like you're just using different z-scores
oh, so am i using the wrong one or are both allowed, i used the one closest to 25 and 15
modern compass
the first one, .25 is almost directly in between. It'd be better to use .675 instead of .67 or .68
in the second one .15 is closer to the -1.04 z-score than -1.03
umbral sparrow
oh alright, thanks
gentle yacht
The following picture shows two overlapping circle inside a rectangle with a length of 12 cm and a height of 9 cm. Prove that the distanse between G and H is equal to 3.
I've written my approach below, and I wonder if it's really convincing enough
We know that the diameter of each circle is equal to 9, considering that the diameter equals the rectangles height. With that in mind, if we would to line up the two circles next to each other, the distance between the two radii in the cirlcles would also be equal to the lenght of their diameters, and that the lenght of the circles would in total be 2*d = 18
However, the following picture shows that the circles had been overlapped on top of eachother in a rectangle with a length of 12 cm, meaning that the overlap between the circles is equal to 18-12 = 6. With that in mind, the only thing we're required to do in order to find the distance between the two radii would be to substract the length of the overlap from the intial lenght of the two radii
9 - 6 = 3
The distance between point G and H is equal to 3.
cedar kilnBOT
The following picture shows two overlapping circle inside a rectangle with a len...
@gentle yacht Has your question been resolved?
deep wind
in the example if there is no light, i cannot see what is the truth table for q implies p
deep wind
p implies q would be
if there is no light and i cannot see then P implies Q is true
if there is no light and i can see then P implies Q is false
if there is light and I cannot see, then P implies Q is still true
if there is light and you can see, P implies Q is true as well
austere heath
what
wait
oh
so its
visibility P Q
wait there are 3 variables?
just light, visibility
L V
F F T
F T F
T F T
TT T
cedar kilnBOT
@deep wind Has your question been resolved?
cosmic herald
How can I do this, My year 8 end of year exam is tomorrow and I am extremely stressed out I done most of the paper just a few questions that I wish I listen when my teacher explained.
https://cdn.discordapp.com/attachments/238956921581862913/976901850039193690/IMG_0938.jpg
north juniper
Banger picture
cosmic herald
is it unclear
cosmic herald
I know the square
what about circle and triangle
if possible could u explain in year 8 (7th grade) terms
north juniper
Yea, divided by 2 for the semicircle
north juniper
so since square is an equilateral
6ÂČ
cosmic herald
then 6 x 6 = 36 x pi
cosmic herald
yeah so
6 x 6 = 36 x pi divided by 2
same thing right cuz radius is always half the circumference
modern compass
same thing right cuz radius is always half the circumference
*diameter
And no, you need to find the radius first
cosmic herald
same
cosmic herald
Okay so I half 6 by 2 first
north juniper
Yes
modern compass
for the semicircle, yes
north juniper
(bh)/2
cosmic herald
oh
base x height divided by 2
okay
but um how do i find out height, is it 2.5 but it says not drawn accurately so how do i know
how much of the 11cm the triangle is
idk if i can say 2.5 since not drawn to scale
modern compass
you know the height of the square is 6, and the radius of the semicircle is 3
north juniper
11 - (6+3)
cosmic herald
in idiot terms
north juniper
cosmic herald
like really stupid idiot terms
modern compass
distance from the center of the circle, to the edge of the circle
or half the diameter
north juniper
but can u define radius
Diameter /2
cosmic herald
right
and circumference is space around it
and diameter is distance from start to end point of the shape
one side to the other
north juniper
That means the base of the triangle is 6 and the height is 2
north juniper
No, (bh)/2
cosmic herald
The square
6 x 6 = 36cm squared
The circle
6 divided by 2 = 3 x 3 = 9 x pi = 9đż
The triangle
6 x 2 = 12 divided by 2 = 6
Now how do I add all of those together to get the area?
<@&286206848099549185>
cedar kilnBOT
@cosmic herald Has your question been resolved?
cosmic herald
help
tribal pier
Now how do I add all of those together to get the area?
you're looking at the combination shape up at the top?
cosmic herald
you're looking at the combination shape up at the top?
hm?
I found the area of all 3 separate shapes
I just need to know how to add them all together when there's a 9pi in there
tribal pier
9pi? is it a circle or a semi-circle?
cosmic herald
semi
that's why i used radius rather than diamater
(divided length of the equilateral in the middle by 2)
tribal pier
the area of a circle is pi(r^2)
tribal pier
so you found the full circle with that radius, right?
tribal pier
what's a semicircle?
tribal pier
describe it
tribal pier
so if you have the full circle, how do you find the semicircle?
cosmic herald
divide by 2
tribal pier
good
cosmic herald
i divided 6 by 2
tribal pier
yes, but that got you the radius
tribal pier
the area of a circle uses the radius
cosmic herald
Yeah it wants the area
tribal pier
the area of a semicircle, not a full circle
cosmic herald
Yeah the full circle
would be 6
Cuz the thing only shows a semi circle
it doesn't show a full one
tribal pier
the full circle has an area of 6?
tribal pier
the area of a circle is pi(r^2), the area of a semicircle is pi(r^2)/2
what's the radius
cosmic herald
the radius is the equilateral in the middle divided by 2 right
that's how i get the radius correct?
tribal pier
the radius is half the diameter, and the diameter is the same length as the square's side, right?
tribal pier
there you go
cosmic herald
or do i divie by 2 before squaring
tribal pier
nope, after squaring
tribal pier
do you have the triangle's area and the square's area?
cosmic herald
The square
6 x 6 = 36cm squared
The circle
6 divided by 2 = 3 x 3 = 9 divided by 2 = 4.5 x pi = 9đż
The triangle
6 x 2 = 12 divided by 2 = 6
tribal pier
alright, now do you need an exact answer or an approximate answer?
cosmic herald
I much prefer exact lmao
my parents r going to kill me if i don't do good on this exam
tmrw
(this is revision paper not cheating btw)
tribal pier
then add up all the things without pi first
crimson sedge
I much prefer exact lmao
actually impossible to solve
tribal pier
actually impossible to solve
no, you just have to express it as a binomial
cosmic herald
Should this be on a year 8 paper lmao
crimson sedge
set of solutions
cosmic herald
sir said it will be on the exam though
crimson sedge
oh wait it said square mb
tribal pier
so the stuff without pi is 42 cm^2, and you have a leftover 4.5pi, which has an irrational number attached (pi) so you can't reduce it to a nice decimal
so you just have to leave it by itself, giving you 42+4.5pi cm^2
that should end up being approximately ~56.17 cm^2 ish, going to only 2 decimal places
(using a slide rule, not digital arithmetic, so that last digit is approximate)
tribal pier
you're stuck because there's a pi in there, right?
you have the square: 6x6=36, the triangle: 6x2/2=6, and the semicircle: 4.5pi, and you need to add them up to get one big shape, right?
add up all the terms that you can (the areas of the square and triangle), and then leave any parts that you can't add in their own terms (the semicircle)
that should give you 36+6+4.5pi=42+4.5pi
cosmic herald
you have the square: 6x6=36, the triangle: 6x2/2=6, and the semicircle: 4.5pi, a...
so i write that as an answer?
42 + 4.5pi
tribal pier
why not? it has all the pieces, right?
cosmic herald
or if it's a calculator paper
I do 4.5xpi
and i add that to my answer?
so if it was a calculator paper my answer would be 50.1
(if i was rounding)
tribal pier
that's a way to do it, yeah, though I got a different answer
cosmic herald
that's a way to do it, yeah, though I got a different answer
What is it?
tribal pier
about 56.14
cosmic herald
Oh rounding
well i imagined it only wants one decimal place
but i won't ay dream ab it lolk
tribal pier
then you would put 56.1
cosmic herald
also would u mind helping me with a few easier questions if that's okay
b4 i close
tribal pier
not at all
cosmic herald
not at all
sorry my brain froze
not sure why it took me 4 mins to pull up a pic
Is it clear enough/
?
tribal pier
not quite, but you can type out the A and B parts, and we can walk through them
sorry, B and C, I'm not familiar with part A
looking at the examples in the table, I think you add up the score in the column with the score in the row to get that particular box's value
tribal pier
not bad
I can do graphs good
so let's look through some of these. What's the equation for the first blank?
cosmic herald
so let's look through some of these. What's the equation for the first blank?
Graph [input] shows the equation y = 2x - 6
I have 0 idea of how to do these
I know absolutely nothing ab them
tribal pier
alright, so have you used graphs before?
tribal pier
so should this equation be a straight line or wiggly?
cosmic herald
wiggly
tribal pier
why?
cosmic herald
cuz
wait
oh wait
straight
cuz it going straight down
no going back up
but they all like that
hmhmhmhmhmhmhmhmhhm
tribal pier
so can you guess which graph it might be?
tribal pier
so do you know the equation for a straight line?
cosmic herald
uhh
tribal pier
does it look kinda the same?
cosmic herald
i'm still really confused with gradients and stuff so i think it would help a ton if we did
the question above this one first
and would help lots with this one too
tribal pier
sure
cosmic herald
tribal pier
what is a gradient?
cosmic herald
idk
tribal pier
it's also called the "slope" of the graph. It's the angle of the graph
cosmic herald
what's that supposed to mean
tribal pier
look back down at the lower problem, at graph B
do you see how it's a straight line that is angled down as you go from left to right?
cosmic herald
yeah
tribal pier
that's what the gradient is. it's how fast the graph goes up or down as you go from left to right
cosmic herald
wdym by "how fast"?
tribal pier
well, a graph with a gradient of 0 is a flat line, right?
cosmic herald
sure
tribal pier
y=0x+1
y=1
it'll be at the same height everywhere
BUT if we have a slope of 1
y=x+1
will it be flat, or will it go up or down?
cosmic herald
it will go up 1
tribal pier
(try putting in some values for x to see if it changes)
so now if we have y=-x+1, will it go up, down, or be flat?
cosmic herald
be flat
tribal pier
what is y when x is 0?
tribal pier
y=-0+1
y=1
now what if x is 10?
y=-10+1
y=-9
is y getting bigger (going up) or smaller (going down) as x gets bigger?
cosmic herald
smaller
tribal pier
so is the graph going up, down, or not moving?
cosmic herald
down
tribal pier
exactly
so the only thing else we have to talk about is when it's not 1 or -1. as the numbers get bigger than 1, they get steeper and steeper, becoming almost vertical as you get WAYYY bigger. as the numbers go down below -1, they go down steeper and steeper, until they're almost vertical too
tribal pier
so let's look at y=2x-6
is it going to go up, down, or be flat?
tribal pier
why?
cosmic herald
uhm
I forgot what mx + c means
man i'm failing that exam tomorrow
it's 9:50 alrdy i got 2 hours and 10 mins
tribal pier
that's the form. does y=2x-6 look kinda like y=mx+c?
cosmic herald
no
tribal pier
sure it does, you just have numbers instead of letters in a couple spots
cosmic herald
1 is -
tribal pier
that's ok, we'll just call all of (-6) c
tribal pier
we're kind of in the middle of a math puzzle of our own
crimson sedge
oh sorry
tribal pier
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