now same idea for the green region
#help-36
misty sequoia
9/2 - (9/2 - 9/8) = 9/8
final tangle
yes
misty sequoia
You mean 9/8 + 9/8 = 9/4
Well, you're right
@final tangle Thank you a lot for your help
.close
tranquil pine
Is there a simpler solution to this ODE: \
$(1+x)dy=(1+xy-x)dx$ \
Here's what I did:
Evaluate $\frac{dy}{dx}$ \
express the numerator as $(1+x)(y-1)-y+2$ \
Seperate the terms \
Assume $y-1=y_1$ and $x+1=x_1$ \
Assume $(1-y_1)=vx_1$ \
Then we have a L.D.E. which can be solved easily \
The values are substitited and the final solution is obtained: \
$y(1+x)=x+Ce^x$
final saddleBOT
Is there a simpler solution to this ODE: \\
$(1+x)dy=(1+xy-x)dx$ \\
Here's what...
soft zealotBOT
meow
tranquil pine
(please ping me if you have any ideas)
final saddleBOT
@tranquil pine Has your question been resolved?
ruby lake
final saddleBOT
ruby lake
can someone tell me where this is coming from
i saw somehwere from bayes formula but i dont get how
tranquil pine
Not yet
ruby lake
what
tranquil pine
<@456226577798135808> Has your question been resolved?
mb lol I replied to this but the message was late
ruby lake
.close
final saddleBOT
final saddleBOT
Available help channel!
trail river
how did we go from the first to the second?
final saddleBOT
how did we go from the first to the second?
wide sedge
factoring out tan2x
on the right side theres a tan2x in both before and after the munis sign
so they pull it out
final saddleBOT
final saddleBOT
Available help channel!
oak kraken
final saddleBOT
oak kraken
Do I wanna start with RREF on this? Or is that not gonna help
It’s asking to write the vector as a linear combination of the other 4 vectors
Does that mean augmented matrix? The first vector becomes the 5th (augmented) column?
Like this? Or still wrong
vital surge
your augmented matrix should be transposed
oak kraken
your augmented matrix should be transposed
How so?
oak kraken
Yes
vital surge
then transpose it and your setup will be correct
vital surge
sorry i mean the A matrix only
oak kraken
sorry i mean the A matrix only
That’s why I asked
Why does it need the transpose tho?
vital surge
because you need to recall what the process of solving an augmented matrix actually does
vital surge
yw
i feel like there's an easier way to do this problem because of the specific choice of the vectors
though the gauss jordan elimination approach is not bad i suppose
oak kraken
oak kraken
though the gauss jordan elimination approach is not bad i suppose
I solved with RREF but is this the actual answer?
Or does it want it written differently
The question asks to write the vector (column 5 of augmented matrix) as a linear combination of the 4 vectors
vital surge
yeah what you have is that 1, 1, 0, 1 are the weights
so you can write c1x1 + c2x2 + c3x3 + c4x4 and plug in the 4 vectors and their weights
final saddleBOT
@oak kraken Has your question been resolved?
devout cairn
Hello guys, my teacher asked this question in the exam and it was among the choices and he said: that none of you will be able to solve it until you reach the university. I tried to solve it, but I could not. I was curious about this question. I hope to solve this question with an explanation with pictures and I will be very grateful.
final saddleBOT
Hello guys, my teacher asked this question in the exam and it was among the choi...
@devout cairn Has your question been resolved?
devout cairn
<@&286206848099549185>
final saddleBOT
@devout cairn Has your question been resolved?
devout cairn
<@&286206848099549185>
devout cairn
Hello guys, my teacher asked this question in the exam and it was among the choi...
This
tranquil pine
Hm gimme a sec
devout cairn
Did you made it
No my teacher gave it to me in the exam
devout cairn
Ok
devout cairn
Bro are you sure itz it
Yeah he said, there are many mathematics teachers who could not solve it
sharp goblet
Bro imma student too *
devout cairn
Coz you have squared the inner terms and a root too
I don't know man, I tried a lot but I couldn't
devout cairn
What does ypu mean
sharp goblet
How long will you be on discord
devout cairn
How long will you be on discord
For 3 years
devout cairn
I will do it bro
I will be very grateful to you
final saddleBOT
@devout cairn Has your question been resolved?
devout cairn
.close
final saddleBOT
final saddleBOT
Available help channel!
open shore
final saddleBOT
open shore
im quite stuck on d), i tried to do P(a+ib)+P(a-ib)=0 but that gave me the results a^3-3ab^2+ca+d=0
oblique turret
im quite stuck on d), i tried to do P(a+ib)+P(a-ib)=0 but that gave me the resul...
Use Vieta's formula instead
open shore
ah true that always slips my mind
im sturglging on e) too
i tried using product of roots but that got me something else
oblique turret
i tried using product of roots but that got me something else
Use that with the other two formulas
Sum of roots and sum of products of two roots
final saddleBOT
open shore
.reopen
final saddleBOT
✅
open shore
Sum of roots and sum of products of two roots
I got an answer of 8a^3-2ac, and i tried multiple times and kept getting this answer
humble marlin
final saddleBOT
humble marlin
Im completely stumped
I tried rearranging y'' to the left side and y^3 to the right then taking the integral
hybrid heath
A very useful identity for differential equations: $$y''=\frac{dy'}{dx}=\frac{dy'}{dy}\frac{dy}{dx}=y'\frac{dy'}{dy}$$
soft zealotBOT
SWR
hybrid heath
No. It should not.
atomic moss
No. It should not.
dont the dy 's cancel?
hybrid heath
I explicitly added them and turned dy/dx into y'
atomic moss
oh yh i see
humble marlin
would it be y'' = dy''/dx =... or is it y'' = dy'/dx
hybrid heath
would it be y'' = dy''/dx =... or is it y'' = dy'/dx
The former makes no sense. You're saying y''=y'''. The latter is true by definition
final saddleBOT
@humble marlin Has your question been resolved?
humble marlin
now I'm stuck at this part:
lusty pecan
An orchestra of 140 players take 70 minutes to paint a fence. How long would it take for 70 players to paint the fence, assuming all of them paint at the same rate?
honestly forgot how to set up these rate questions
final saddleBOT
An orchestra of 140 players take 70 minutes to paint a fence. How long would it ...
lusty pecan
this is literally my channel
fair dragon
Oooops that’s my bad I thought I clicked another channel 💀
lusty pecan
all good
safe terrace
hello
safe terrace
no
lusty pecan
bruh
digital osprey
You should first find out how long it will take 1 orchestra to paint.
Multiply the time for 1 orchestra by 70
lusty pecan
You should first find out how long it will take 1 orchestra to paint.
Multiply ...
you mean..divide?
sorry
not sure why its multiply since i get pretty big numbers
safe terrace
im not sure how to help you
digital osprey
If they take 70mins to paint a fence share the 70 minutes among each of them. That's the time it takes for 1 orchestra to paint. When you find the time it takes for 1 orchestra. Multiply that one time for 70 orchestras
Or just do this.
140/70 =70/t
Find t
lusty pecan
so t is 35
but that makes no sense
how do they paint the same fence in a faster time with less people
safe terrace
Or just do this.
140/70 =70/t
Find t
hes right how do they paint faster with less people??
<@&286206848099549185> i dont understand how it is 35
safe terrace
its just a simple rate problem in alg
i dont know how to help
<@&286206848099549185> ???
lusty pecan
yo chill
lusty pecan
i dont know how to help
its ok
safe terrace
An orchestra of 140 players take 70 minutes to paint a fence. How long would it ...
<@&286206848099549185> idont understand?? is this possible
lusty pecan
dude stop pinging them
pallid spoke
<@&286206848099549185> idont understand?? is this possible
its just replacing it with a variable we dont know
let me help please
lusty pecan
ouch
digital osprey
The rate at which they paint does not depend on the number of people. Say if 2 people run 100m and finish in 1 min. Then 1 person should not be using double the time to finish the same 100m
lusty pecan
but if theres less people does the fence not take longer to paint
pallid spoke
but if theres less people does the fence not take longer to paint
i got it now
so we can say that 1 person takes 0.5 parts of the fence
lusty pecan
0.5 minutes?
pallid spoke
eh doesnt matter
it should double is what i'm trying to say
logically speaking
i still need to make the thing
pallid spoke
you sure this is the correct question
because ive read one similiar
but it was with a song
lusty pecan
well either way the situation makes sense logically
pallid spoke
this question isnt a ratio one well from what im looking at
lusty pecan
im not sure why it is so hard to set up
pallid spoke
its more like algebra
lusty pecan
it seems like a rate problem though
pallid spoke
it would need to be equivalent tho
and that would make it less
time
you cant use a fence in this context
lusty pecan
but how though
pallid spoke
well the same
pallid spoke
but how though
the fence is the same but takes a shorter time despite having less people
lusty pecan
wait so is the answer 140 minutes
pallid spoke
yea
lusty pecan
how would we solve this with algebra then
like thinking about it logically, if the players paint at the same rate in both problems then it would just be half as fast and therefore twice as long but theres no rate for some reason
pallid spoke
like thinking about it logically, if the players paint at the same rate in both ...
the fence is the same in this situation
so we would need to first account for that
like splitting it into 70 parts
one part each minute for two people
give me a sec
i need a pen and paper
digital osprey
It's 140 minutes. It's an indirect proportion. 140(70) = 70t
pallid spoke
huh
digital osprey
I just looked up and this is the correct one
pallid spoke
FINALLY
lusty pecan
wait how
pallid spoke
It's 140 minutes. It's an indirect proportion. 140(70) = 70t
it places time as a variable
digital osprey
Indirect proportion
pallid spoke
yeah that too
lusty pecan
like
pallid spoke
Or just do this.
140/70 =70/t
Find t
it was multiplicaton
not division
thats where we got wrong
lusty pecan
wait
lusty pecan
can you explain it conceptually in the siutation
digital osprey
Okay, say from the first one where you get 140/70 =70/t which you'll get 2t = 70. But the time is 70.
pallid spoke
2(1)=1/70f
2 is people 1 is time
so we can say it took 70(t)=1/70f
so divide 70 from both
waitwait wait
lusty pecan
wait 70t = f/70?
pallid spoke
its still a variable
mb
ok so basically
you cant seperate the two
140(70) = 70(t)
Bro why is this so hard to explain
digital osprey
If 140 orchestras use 70 minutes. Then 70 orchestras which are half of which will use double the time.
lusty pecan
140/t = 1 fence 😭
what
pallid spoke
OK GOT IT FRFR THIS TIME
digital osprey
Using indirect proportion is much simpler.
People 140, 70
Time 70, x
People * people = time * time
140*70 = 70 * x and find x
pallid spoke
basically theres this formula
that i finally remembered
its the inverse proportion formula
basically y = k/x
lusty pecan
Using indirect proportion is much simpler.
People 140, 70
Time 70, x
People * ...
wait how does that work though in terms of the situation
digital osprey
wait how does that work though in terms of the situation
https://youtu.be/K7h4l4OGr8I?si=WCLkXNhUU3WEE0Rr
This will better your understanding
lusty pecan
140 = k/70
so k is 70*140 and then what
lusty pecan
what
pallid spoke
Sorry oklet me actually do it fr this time
140 = k/70 <time btw
140(70) = k
9800 = k
place it into the formula again
70 = 9800/t
70(t)
= 9800
t = 9800/70
t = 140!!!!
LETS GOO
Whoo wee finally
lusty pecan
ohhh
you use the equation of y = k/t, use a known solution set to find k, plug in to find t
lusty pecan
thank you guys so much
im sorry this problem turned out to take so long
@digital osprey thanks to you too
pallid spoke
honestly kinda my fault dude
dude i literally have it in my book
and i just couldn't find it
final saddleBOT
final saddleBOT
Available help channel!
limber isle
final saddleBOT
limber isle
why is this so?
spice depot
A good question to ask is why wouldn't it be so?
limber isle
oh a question to my question
spoken like a true tutor..
well i know very little about this topic
but
i kind of thought it would be c
since -5.50..
final saddleBOT
@limber isle Has your question been resolved?
zenith sierra
How?
zenith sierra
I haven't done these type of questions in a few years and now I'm stumped.
long wraith
Gauss series?
long wraith
Yeah
4640?
Its been so long since I did Gauss series, do u have the answer sheet and confirm its D 4640?
silver roost
I saw a mathstacks post on this same exact topic earlier today but already forgot
Stackexgange wheyever it’s called
zenith sierra
Nah I don't have an answer sheet.
silver roost
pseudo knot
How?
It's a quadratic series so
You can basically right nth term = an²+bn+c
And then check 3 different terms to find a, b and c
After that u can use the standard summation
final saddleBOT
final saddleBOT
Available help channel!
pseudo slate
this is the question and here is my work
final saddleBOT
this is the question and here is my work
shadow aspen
Use original equation to get a system of equations with unknowns a and b
What youve done so far looks right and gets you the necessary 2nd equation
pseudo slate
how do i do that? do i just rewrite the equation?
shadow aspen
how do i do that? do i just rewrite the equation?
Just plug in the numbers they gave you
pseudo slate
i did
shadow aspen
Yeah but also do it for the original equation
You have the original and the derivative equations
These are your two equations that will make up your system of equations
final saddleBOT
final saddleBOT
Available help channel!
verbal steppe
In what points for the constant d has the ellipsoid \
$2x^2+3y^2+3z^2=41$ \
and the plane \
$2x+6y+9z=d$ \
a common tangent point?
final saddleBOT
In what points for the constant d has the ellipsoid \\
$2x^2+3y^2+3z^2=41$ \\
an...
soft zealotBOT
Merineth
verbal steppe
My assumption was that if i find the gradient for the ellipsoide
And then use that's normal vector combined with the normal vector for the plane, i could create an equation which would solve to find the common values?
My gradient came out to be \
$\nabla f(x,y,z) = [4x,6y,6z]^T$
soft zealotBOT
Merineth
soft zealotBOT
Merineth
verbal steppe
@pliant shore Sorry for the ping. We were talking yesterday about this question and i just wanted to confirm if this was what you meant?
pliant shore
**Merineth**
Yes
Just note that the d you're using is not the same as the d in the question
verbal steppe
Oh, it isn't?
pliant shore
So if we use t
pliant shore
Oh, it isn't?
No
We have 4x = 2t, 6y = 6t, and 6z = 9t
Or (x, y, z) = (t/2, t, 3t/2)
Which is a line of course
So now you have to substitute this (x, y, z) = (t/2, t, 3t/2) back into 2x^2 + 3y^2 + 3z^2 = 41 to find t
And then find the point (x, y, z)
And then substitute (x, y, z) into 2x + 6y + 9z
That's your d, the one in the question
verbal steppe
We have 4x = 2t, 6y = 6t, and 6z = 9t
Can i solve for t here?
pliant shore
Can i solve for t here?
No it's impossible
verbal steppe
$4x=2t \implies t = 2x \ 6y = 6t \implies t = y \ 6z = 9t \implies t = \frac{2}{3}z$
soft zealotBOT
Merineth
pliant shore
$4x=2t \implies t = 2x \\ 6y = 6t \implies t = y \\ 6z = 9t \implies t = \frac{2...
Oh that's what you mean ok
Well yes you can do that, but it's not very useful
Doing that gives you the Cartesian form of the line
It's more useful to have x, y, z all in terms of t
verbal steppe
This is very complex
I found a similar example online
But this one was easy since c had to be -1
because of the -1 in the LHS
But now t can be any infinite number?
<@&286206848099549185>
pliant shore
But now t can be any infinite number?
Yes, t can be any real number
verbal steppe
But that means there can be an infinite amount of solutions?
pliant shore
So that means the possible (x, y, z) all lie on a straight line
pliant shore
But that means there can be an infinite amount of solutions?
Exactly
verbal steppe
But they are asking for what specific points
pliant shore
But the key is that the line can only intersect the ellipse once
A line on a tangent plane
verbal steppe
This is very confusing, i thought it was a plane that was intersecting with a ellipse?
Not a line intersecting with an ellipse
pliant shore
This is very confusing, i thought it was a plane that was intersecting with a el...
Well the line comes from the fact that you equate the gradients to each other
pliant shore
**Merineth**
This
If we didn't have something with x^2, y^2, z^2, that wouldn't differentiate to some multiple of x, y, z
And so we wouldn't have a line
verbal steppe
I'm so sorry but i honestly don't understand what you are talking about
pliant shore
It kind of is a miracle that we get a line
pliant shore
**Merineth**
It comes from this
verbal steppe
I've sat on this question for nearly 3 days now and deadline is today while having to do 4 more questions before 12:00 AM. Would it be possible to get a solution?
I just clearly don't understand 😞
I sadly don't know what line you are talking about
final saddleBOT
@verbal steppe Has your question been resolved?
verbal steppe
ÅPO¨KS awpäodskapwo dkl'äåpwokl d'awåpld aw'påokdkasoäp kdiöäoplazksnf jökasnäödfiop jkmaewäpoi dk'awepå kld'¨åwa odwaolpp'äo dkoawkd oäp'awkl d'åpawkldä pålwapå' dolpaåä'wold på'awl d osakd mlköjaw mdnäoöliawk jdoaåw'kda0å
wp' odlaw
pliant shore
I've sat on this question for nearly 3 days now and deadline is today while havi...
Yes and I've outlined the solution process above
pliant shore
https://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx
If you don't know what parametric equations and parametric lines are, read this
final saddleBOT
@verbal steppe Has your question been resolved?
verbal steppe
It's easy for you
but in have no idea what to do
I would've never come up with this equatsiooin on my own
or that i'm supposed to use gradients
But it's ok i'll watch a tutorial from math.lamar and i'll understand everything hahahahaha
verbal steppe
.close
final saddleBOT
final saddleBOT
Available help channel!
fallen patrol
final saddleBOT
fallen patrol
please tell me a row operation which can simplify the expansion of this determinant
tranquil pine
first split the determinant
fallen patrol
@tranquil pine what next?
tranquil pine
apply row operations
autumn oracle
yeah do this step
fallen patrol
@steep tulip lol u saved me
steep tulip
<@952833974890295316> lol u saved me
yeah
you can apply direct formula from her
steep tulip
yes now
tranquil pine
now?
steep tulip
you can hack this question from a direct formual
fallen patrol
??
steep tulip
it's the answer of the determinant
a b and c are not equal
so 1+ abc has to be 0
got it?
steep tulip
fallen patrol
because I proved it long ago
yea i did too but i didnt memorize the results
steep tulip
yea i did too but i didnt memorize the results
I do memorise a few
it makes it way easier for me
fallen patrol
but cant do it in exam tho
steep tulip
fallen patrol
it's a direct method
steep tulip
but cant do it in exam tho
yeah
I mean
I am technically preparing for an mcq exam
so it works for me
fallen patrol
lol dont tell me if it's JEE or nEET
steep tulip
but again sometimes
memorising results
or having a rough figure helps me
prove them faster as well
steep tulip
lol dont tell me if it's JEE or nEET
JEE obviously
you don't need math for NEET
steep tulip
this equation is formed
And I think something like a b and c are not equal should be given in the question
fallen patrol
hhow does that work
tranquil pine
would have been easy if these type of questions were given in JEE
steep tulip
would have been easy if these type of questions were given in JEE
exactly
steep tulip
hhow does that work
okay so imagine
fallen patrol
would have been easy if these type of questions were given in JEE
i cant even solve these bro
steep tulip
if
tranquil pine
tese?
fallen patrol
is there another way that doesn't use logic
steep tulip
Idk
that's how my brain worked
steep tulip
11th grade
steep tulip
fallen patrol
💀
tranquil pine
xD
steep tulip
yes
fallen patrol
and what do i ave to do
steep tulip
it's literally an identical question
tranquil pine
find the zeros of X which are distinct
fallen patrol
to solve this
fallen patrol
it's literally an identical question
do u have a written solution
steep tulip
no I'll have to solve it
fallen patrol
leave it that shit looks way too difficult
have you doneyour 11th yet
@steep tulip
steep tulip
have you doneyour 11th yet
done with my 12th as well
steep tulip
leave it that shit looks way too difficult
jee advanced 2016
fallen patrol
done with my 12th as well
did they give you such questions in 11th too
steep tulip
did they give you such questions in 11th too
no
matrix and determinants are taught in 12th
final saddleBOT
steep tulip
yeah bye
autumn oracle
2?
final saddleBOT
Available help channel!
final saddleBOT
that was an adv question?
final saddleBOT
final saddleBOT
Available help channel!
fickle sinew
final saddleBOT
final saddleBOT
@fickle sinew Has your question been resolved?
final saddleBOT
@fickle sinew Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
silver roost
final saddleBOT
silver roost
hi, i dont know if im understanding this correctly
the only surface integrals ive done have been dot products
my best guess rn is every region being 0 besides S4 which is positive
formal trail
it's a surface integral of a vector field (see https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx), which makes it slightly different
for a planar surface like this, it comes out to be essentially the same as a double integral
formal trail
well I1 is essentially the double integral of x over a square in the xy-plane
formal trail
yes. normally they teach this first but idk. it's similar to line integrals where the integrand can either be a scalar field or a vector field using the dot product
silver roost
yea that vaguely makes sense
all the formulas here are so similar they start to get blurry
thanks for the help
.close
green oak
can someone help me with a pretty easy math that I don't under stand what is 9x> or equal to 3
final saddleBOT
can someone help me with a pretty easy math that I don't under stand what is 9x>...
blissful meadow
You mean you want to solve $9x \ge 3$ ?
soft zealotBOT
Azyrashacorki
green oak
yep
final saddleBOT
@green oak Has your question been resolved?
pearl lion
I want to find the volume of a hyper sphere
final saddleBOT
I want to find the volume of a hyper sphere
pearl lion
I started with trying to find the volume of a sphere of radius R
and you can break that into disks
with width dx and radius r
so you get the integral from -R to R of pi * r^2 dx
if you look at the cross section of a plain and the sphere you get that x^2 + r^2 = R^2
r=sqrt(R^2-x^2)
so you get
$\int_{-R}^{R}\pi\left(R^{2}-x^{2}\right)dx$ which is easy to solve
soft zealotBOT
TimesZeroed
pearl lion
for a hyper sphere I had two ideas
I've seen some visualizations where the hyper sphere 3d cross section becomes a sphere that gets larger then smaller
the volume of each sphere would be 4r^3pi/3
times dx
But Idk how to relate the radius to dx
I thought it would still be
r=sqrt(R^2-x^2)
because if you track the 4d spheres cross sections height in 3d if seems to be a semi circle
Anyway I got $\int_{-R}^{R}\pi\left(\sqrt{R^{2}-x^{2}}\right)^{3}dx$
soft zealotBOT
TimesZeroed
final saddleBOT
@pearl lion Has your question been resolved?
final saddleBOT
@pearl lion Has your question been resolved?
zenith pollen
yea that's correct https://en.wikipedia.org/wiki/Volume_of_an_n-ball
final saddleBOT
final saddleBOT
Available help channel!
marble spade
final saddleBOT
marble spade
Hi could someone help me figure out what tests would work best to test the intervals for convergence?
static plinth
to test for the endpoints?
marble spade
Yeah
My understanding is that once we test and if it converges we say that it is included with the bracket?
static plinth
yep
so lets just plug in the endpoints back into the original series and see what we can do
soft zealotBOT
y0shi
$\sum_{n=1}^{\infty}(-1)^n n 4^n (\frac{-1}{4})^n$
marble spade
Could the 4^n cancel each other?
static plinth
yep
soft zealotBOT
y0shi
static plinth
we can simplify a little bit more here
marble spade
We just get n right after the -1^n multiply
static plinth
yep
soft zealotBOT
y0shi
static plinth
you can actually use a lot of different tests here
marble spade
Ah so it diverges right
static plinth
yep
and what test did you use
although it makes sense why it must diverge intuitively
marble spade
Hm honestly I can’t tell,what test this was
static plinth
we can just use the divergence test
marble spade
Ohhh I see
static plinth
take the limit as n approaches infinity
and it wont be equal to 0, so it will diverge
marble spade
Forgot about that one lol so many tests to remember
static plinth
yep
marble spade
For it to converge it has to decrease and test for limit = 0 if I remember
marble spade
No its increasing I believe
static plinth
yw!
marble spade
.close
final saddleBOT
final saddleBOT
Available help channel!
rotund goblet
Can someone help me with this? I don't know why the answer in the blank is incorrect even though i watched multiple videos/read documentations. Like its supposed to be simple but I don't know wut I am missing.
final saddleBOT
Can someone help me with this? I don't know why the answer in the blank is incor...
mellow axle
they're taking the determinant
not just the real and imaginary parts as the entries
oh nvm im brain lag
candid hull
are you certain the way you type the matrix is what the software expects ?
@rotund goblet
candid hull
turns out you can also have a+ib represented as [[a, b], [-b, a]]
the operations also work out fine (if you compare it to what you get from complex number addition and product)
it's 2 different conventions you can take
rotund goblet
thats
so
i guess in this case like
OHHH
right im stupid
its because J is like that
bruh i thought it was completely unrelated kms
but thanks thooo
.close
final saddleBOT
final saddleBOT
Available help channel!
dim hull
final saddleBOT
dim hull
I don't really know how to find the other leg or the hypotenuse
or the angles
Maybe the question is more simple and asking what point she needs to aim at without knowing the angles or any of the hypotuneses
<@&286206848099549185>
final saddleBOT
@dim hull Has your question been resolved?
zenith pollen
you can do it with similar triangles but a cool way is to mirror it across
which should tell you the slope of the line
viscid frigate
I need help with this question
final saddleBOT
I need help with this question
viscid frigate
<@&286206848099549185>
long wraith
Isnt it obvious?
viscid frigate
Isnt it obvious?
no
long wraith
Let say I want to print 10 books, which company offers the best price?
@viscid frigate
viscid frigate
is it a
long wraith
Yes, how's abt 100 books
long wraith
Here's the key question: Is there any amount of books such that company B offers the better deal than company A
viscid frigate
but here their saying under what conditions should the school choose b and whatsoever i don't understand the question
long wraith
Here's the key question: Is there any amount of books such that company B offers...
Just answer this @viscid frigate
viscid frigate
Here's the key question: Is there any amount of books such that company B offers...
no
there is 100
only
viscid frigate
is it because of the cost
viscid frigate
but why would they chose b.....a is cheaper
long wraith
but why would they chose b.....a is cheaper
Yeah
viscid frigate
Is this Algebra?
idk
long wraith
but why would they chose b.....a is cheaper
So answer must be "Under no condition, the school SHOULD choose B over A"
Well except company B could bribe the headmaster to choose it lmao
long wraith
it's ... point of intersection of two lines
Is it? A and B seem parallel?
viscid frigate
Is it? A and B seem parallel?
it is but idk they gave us this question for homework
long wraith
Is this Algebra?
Well, I ask this cause in certain branch of math, parallel lines could intersect at infinity
viscid frigate
so what's the answer
long wraith
But Im pretty sure you're just a middle schooler
long wraith
So answer must be "Under no condition, the school SHOULD choose B over A"
@viscid frigate
You lowkey answer it yourself
viscid frigate
oh
viscid frigate
You lowkey answer it yourself
i'm not answering
tom is a test
and i want to understand these type of questions
viscid frigate
But Im pretty sure you're just a middle schooler
grade 9
long wraith
Good
@viscid frigate Phrase the answer like this
Since A's price is always better then B, thus under no conditions should the school choose B over A
long wraith
You should do it yourself
viscid frigate
could u explain at least
final saddleBOT
@viscid frigate Has your question been resolved?
subtle elbow
I need help
final saddleBOT
I need help
subtle elbow
<@&286206848099549185>
wheat flower
!status
final saddleBOT
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
1
stray rose
have you learnt u-substitution
rustic sandal
you probably use u-substitution
subtle elbow
yes i have and I don't know which one i should put for "u"
wet thicket
you probably use u-substitution
it looks like ibp i wont lie
cuz integral of 1/x = ln(x)
so then youll get a 1/x^2 and a ln(x)^2
stray rose
actually yea i think its ibp
stray rose
i thought usub would cancel an x
rustic sandal
i thought you just do u=lnx then du is 1/x dx
wet thicket
let me get some paper
subtle elbow
thank you!
stray rose
no its u sub im silly again
stray rose
why nuke the door if it's unlocked
rustic sandal
itll prolly work if you do it enough times
subtle elbow
actually i think i got it!
wet thicket
goodgood
subtle elbow
thank you guys! I just put the answer as it is
lethal bronze
so-called “free-willed” mathematicians when they see single-variable integral calculus:
subtle elbow
stray rose
so-called “free-willed” mathematicians when they see single-variable integral ca...
what does this mean
wet thicket
okay now we can close this
subtle elbow
.close
final saddleBOT
wet thicket
what does this mean
probably means how everyone just defaults to u sub or something along those lines
final saddleBOT
Available help channel!
lament tulip
final saddleBOT
lament tulip
b
wet thicket
i absolutely love the scale they gave
lament tulip
?
wet thicket
ad=dc but the scale is so off
wet thicket
no it just screws with your mind
final saddleBOT
lament tulip
.reopen
final saddleBOT
✅
lethal bronze
try dividing equation by x^2
brittle mesa
final saddleBOT
brittle mesa
Why can u set 2k simply into a 2?
Yes the rate of change of x is constant, but like what if the rate of change x was 2? Then wouldn’t dy/dx=4?
Got me confused
versed crater
Is this your working out?
proud plover
send whole question since without context it doesnt make sense to let 2k=2
brittle mesa
Is this your working out?
No that’s an answer I found on internet
Yes that’s it
They didn’t give extra context
proud plover
yeah but whats the question?
brittle mesa
This
proud plover
oh
versed crater
No that’s an answer I found on internet
Have you tried doing the question
brittle mesa
Yes
And I was stuck
Since I assumed I needed to find the rate of change x
and I couldn’t
proud plover
well there is no way u can allow 2k=2 as a complete solution
proud plover
the complete solution would require u to express the answer in terms of k
the rest of it is fine
brittle mesa
Wait if I understood correctly
Dx/dy is the rate of change x right?
So if I do 1/dy/dx =k
And then I do a simultaneous equation with dy/dx=2k
Does that work?
proud plover
that works
but the question is ambigious in the sense that
nvm it isnt ambiguous
since it defines p(x,y)
brittle mesa
What p(x,y) btw
I’ve been reading this
Never understood the point of mentioning it?
Doesn’t it just mean a point moving along that curve?
proud plover
it says that there exists a function that is expressed in terms of 2 variables x and y
proud plover
yes
brittle mesa
What
proud plover
blud
proud plover
p(x,y) is just a function
brittle mesa
I was making shit up
proud plover
multivariable functions
proud plover
no
brittle mesa
Oh
proud plover
thats a single variable
wise veldt
final saddleBOT
wise veldt
How do i get angle acb and cba
I got angle bac=70
And acm=40
But idk what do to now
ivory vessel
is M the center of the circle?
wise veldt
Yes
cunning warren
How did you got angle bac=70?
wise veldt
M=2a
feral shard
Acb + Cba = 360-140 = 220( circles are 360)
BMC is a triangle with 2 equal sides(it's made of 2 radiuses)
So mbc=mcb=180-140=40
Cba=40+30=70
2Acb = arc BC(big one) - arc AC = 220-140=80 => abc = 80/2= 40
@wise veldt
cunning warren
Acb + Cba = 360-140 = 220( circles are 360)
What kind of theory is that?
feral shard
Acb + Cba = 360-140 = 220( circles are 360)
What kind of theory is that?
The circle is 360 degrees
feral shard
Acb + Cba = 360-140 = 220( circles are 360)
What kind of theory is that?
Arc BC is 140 degrees (equals to angle bmc)
wise veldt
Acb + Cba = 360-140 = 220( circles are 360)
BMC is a triangle with 2 equal sides...
Thanks
I get it
.close
final saddleBOT
cunning warren
It's wrong
cunning warren
angle ACM and ABM is not same
final saddleBOT
Available help channel!
cunning warren
if acb + cba = 220 , then larger than 180?
final saddleBOT
if acb + cba = 220 , then larger than 180?
feral shard
Ohh i miswrote
feral shard
Acb + Cba = 360-140 = 220( circles are 360)
BMC is a triangle with 2 equal sides...
Acb
Not abc
cunning warren
but
cunning warren
I misunderstand
feral shard
cunning warren
so?
wise veldt
Yo isnt mbc=mcb=20
wise veldt
Yeah i get it now
cunning warren
year
feral shard
Acb + Cba = 360-140 = 220( circles are 360)
BMC is a triangle with 2 equal sides...
Then cba will be 30+20=50
And Acb will be (220-100)/2=120/2=60
final saddleBOT
@cunning warren Has your question been resolved?
gusty slate
final saddleBOT
gusty slate
for this is the probability of T=5 1/18?
since prob of getting 3 and 2 is 2/6*1/6
but in the answer key it says 1/9
sleek quartz
if you want to be sure, make a table like this and count maybe
gusty slate
if you want to be sure, make a table like this and count maybe
this doesnt give the total added up
can u just explain what is wrong with my thinking
but in the answer key it says 1/9
but you could get 2 first then 3
but order doesnt matter for independent events?
right?
how would the roll of one dice affect the roll of another?
white tiger
hmm lemme think about this
gusty slate
@white tiger any ideas?
sleek quartz
order does matter
sleek quartz
if you want to be sure, make a table like this and count maybe
e.x. in this table 1+2 and 2+1 are distinct events
sleek quartz
there are 6^2 = 36 possible outcomes right
gusty slate
yes
sleek quartz
so we consider all 36 outcomes in our probability
have you seen the cartesian product before
gusty slate
have you seen the cartesian product before
what?
why are you talking about cartesion
sleek quartz
it's a way to list out every possible dice roll
you'll notice both (2,3) and (3,2) are there
sleek quartz
in this case there are no cases where both (a,b) and its "flipped" (b,a) are present in the outcomes
so it's a little less confusing
gusty slate
so order doesnt matter?