So it can be anything
#help-33
red mason
smoky plover
yeah
red mason
So it adds up to 1
smoky plover
yeah
turbid mica
but you do know the heights
red mason
1?
turbid mica
you know the sum of all heights is 2
red mason
Hmmm yh I understand now but isnt that like supossing
Actually nvm
How do I now solve it?
red mason
the height of all triangles together is 2
Cant you just make it into a dquare to make it easier?
Okay nvm its 6
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
wraith creek
How do i solve this?
marsh citrusBOT
How do i solve this?
wraith creek
I tried to solve it for like 45 mins, but can't get the proper value
desert dirge
have you actually done the derivatives youve left
marsh citrusBOT
@wraith creek Has your question been resolved?
main mica
Conuses base radius is 5. The conus when spraed out is the second one and its sector angle is 120 need the conus surface area
marsh citrusBOT
Conuses base radius is 5. The conus when spraed out is the second one and its s...
main mica
.close
marsh citrusBOT
worldly lava
Conuses base radius is 5. The conus when spraed out is the second one and its s...
These two lengths are identical
@main mica
marsh citrusBOT
✅
worldly lava
Let the radius of right sector be r, and solve for r by equating two red kines together
worldly lava
circumference of sector = 2 pi r angle
elfin berryBOT
kelvinchan9786
main mica
not rn
worldly lava
You will find that these right red line is derives from the left line
otherwise use imagination lol
winter smelt
**kelvinchan9786**
$l = 2\pi r \cdot \frac{\theta}{360}$ where l is the arc length, and theta is the angle of the sector
elfin berryBOT
lgkoo
main mica
oh so thats equal to l?
winter smelt
oh so thats equal to l?
the 10 pi that you worked out is the l
winter smelt
the 10 pi that you worked out is the l
since unfolding a cone, the circumference of the base circle = length of the arc of the sector
winter smelt
whats the nest step to take?
well what does the area of the sector represent for the cone?
main mica
surface area?
winter smelt
yes, but without the base circle
the sector itself is the area of the curvy part of the cone
which is part of what you need to find
so the question is, how to find area of the sector?
winter smelt
area of unfolding cone is 25pi/3 right?
how did you get that?
winter smelt
what is your r?
winter smelt
oh thats the circles r
correct, but when we can work out the sector's r
winter smelt
**lgkoo**
using this formula
we knew the arc length and the angle of the sector, so you can work the radius of the sector then
hard heron
Umm @winter smelt
I tried to use the same logic here but it was inc9rrcwt
Could u tell me where i went wrong
Plz
winter smelt
I see you tried to use the formula for length of arc $l = \theta r$
elfin berryBOT
lgkoo
hard heron
Yeah
winter smelt
and equal that to the perimeter of the circle
hard heron
Yeah thats what i could come up with
winter smelt
Other than that are there any mistakes?
don't think so, as long as you fixed theta, and find the correct r accordingly. Your method is fine. But don't forget that the sector is only the surface area of the curvy part of the cone
winter smelt
yup
main mica
wait so finding how do we find l
winter smelt
wait so finding how do we find l
we know what l is
hard heron
Im gotta sleep rn
Sorry @main mica if i couldnt help u much
Hopefully @winter smelt can clear stuff up
main mica
ok no you were a lot of help thanks
hard heron
Gn and thank u
main mica
10pi=2pir * 1/3??
winter smelt
10pi=2pir * 1/3??
yup
main mica
r is 30 pi?
winter smelt
no, don't forget to divide by the 2 pi as well
main mica
15
winter smelt
correct
winter smelt
sounds right
winter smelt
<@690217572871831558>
pls don't ping me twice in a row and don't send me friend request. I'm happy to help when I'm free to help, and I'll show up to answer questions. Also, I do not answer questions in private, if you have any question asks here and ask public, not just specifically me
main mica
ok sorry
but i have one more problem its not as complicated i just need to make equation
sorry again
could you help it sjouldnt take more then 2 mins
im just stuck
winter smelt
just post the question here
main mica
on a circle race track there are 2 cars that are moving. they meet each other every 40 mins when they go the same way and they meet in 10 mins when thy move the oppisete way. what time would it take for each car to go around the whole track
ik i have to make a equation or a system just not sure how to
make a correct one
if you could help with this one too it would help a lot
@winter smelt
young helm
for critical points if I solve them and get x = 1 and x=3
marsh citrusBOT
for critical points if I solve them and get x = 1 and x=3
young helm
suppose
would the critical points be [1,3] or do I sub in those roots somewhere else or would it be 1,0 3,0
onyx perch
Um is this where I ask for help with my algebra
Ik it’s basic but I can’t understand when to multiply the units and stuff like that I feels really random
barren summit
help i gotta get the range of f(x) = 1 / (x^2 + 5x + 6) and my teacher said that i gotta solve for Y doing y = 1 / (x^2 + 5x + 6) but im stuck and i cant do it
for domain i got ℝ-{-3,-2}
marsh citrusBOT
help i gotta get the range of f(x) = 1 / (x^2 + 5x + 6) and my teacher said that...
desert dirge
domain is fine, sure
what do you mean by solve for y?
marsh citrusBOT
@barren summit Has your question been resolved?
eternal schooner
help i gotta get the range of f(x) = 1 / (x^2 + 5x + 6) and my teacher said that...
Are they asking for Y-Intercept ?
barren summit
Are they asking for Y-Intercept ?
no, its asking for the range
barren summit
domain is fine, sure
what do you mean by solve for y?
like he told me to replace f(x) with Y and told me to solve it like an equation
eternal schooner
no, its asking for the range
It’s a quadratic with two roots, so find the vertex
eternal schooner
I think
barren summit
how do i find b if its 1 / (x^2 + 5x + 6) tho
i tried doing y(x^2 + 5x + 6) = 1 but idk what to do next
marsh citrusBOT
barren summit
.reopen
marsh citrusBOT
@barren summit Has your question been resolved?
marsh citrusBOT
@barren summit Has your question been resolved?
marsh citrusBOT
@barren summit Has your question been resolved?
spare matrix
suppose 3y⁴ = 9x², is it fair to say derivative of x = derivative of y?
spare matrix
hey
what im asking is
if we have an equation (lhs = rhs) , can we say derivative of lhs = derivative of rhs
serene spoke
Like whenever we differentiate
spare matrix
yeah go on
serene spoke
we differentiate somwthing w.r.t something
Like we can differentiate x w.r.t y or reverse or do partial differentiation
spare matrix
mhm
still temple
if we have an equation (lhs = rhs) , can we say derivative of lhs = derivative o...
I think so it would be the same yess. Because the derivative of y=derivate of x...that would be saying the slope of y=slope of x since LHS=RHS the slope would be same
serene spoke
suppose 3y⁴ = 9x², is it fair to say derivative of x = derivative of y?
If you differentiate this you get 12y³dy = 18x dx
spare matrix
I think so it would be the same yess. Because the derivative of y=derivate of x....
hmm, well i think itll be the reciprocal no?
since dx / dy = 1 / dy/dx
spare matrix
If you differentiate this you get 12y³dy = 18x dx
yeaj nvm i gave a bad example
still temple
hmm, well i think itll be the reciprocal no?
since dx / dy = 1 / dy/dx
You mean to say that the slope would be perpendicular??
strong dagger
It would be equivalent I believe
still temple
You mean to say that the slope would be perpendicular??
It would not if LHS=RHS
serene spoke
are you speaking of symmetric functions
still temple
hmm, well i think itll be the reciprocal no?
since dx / dy = 1 / dy/dx
Wait it's not-1 i misread still wdym
still temple
It would be equivalent I believe
Yes
spare matrix
are you speaking of symmetric functions
i have no idea what this is
so
assume
im finding
dx³ / dx
its obviously 3x²
but what's the logic behind it
still temple
i have no idea what this is
You can graph it...since LHS=RHS the graph would be the same so the slope would be same
spare matrix
can we assume another variable, p = x³ and do dp/dx or what?
spare matrix
You can graph it...since LHS=RHS the graph would be the same so the slope would ...
oh
serene spoke
Yeah
strong dagger
if we have an equation (lhs = rhs) , can we say derivative of lhs = derivative o...
it is a valid operation to take the derivative of both sides and this would still make the equation true so they would be equivalent
still temple
You can graph it...since LHS=RHS the graph would be the same so the slope would ...
And derivative is rate of change or slope so that would be same
spare matrix
it is a valid operation to take the derivative of both sides and this would stil...
i think this is what we often do when we're given question where its related to rate of change
spare matrix
can we assume another variable, p = x³ and do dp/dx or what?
um is this valid?
serene spoke
Yeah bro
But for a eqn to stand LHS = RHS and it is given
If you speaking of that always the function will reduce to x = y
Ignoring some domains of def
spare matrix
ight
serene spoke
Yeah bro
Now consider a function f(x,y) = x³ + y³ , this is a symmetric function coz you can replace x with y and eqn remains same
spare matrix
yep
serene spoke
So was your issue solved ?
spare matrix
yes i get it
serene spoke
marsh citrusBOT
@spare matrix Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
vivid wharf
he alredy found x = -2 . from there how did he conclude that x >= -2
runic temple
you have to go back to the original objective which is to find the values of x which satisfy the inequality
vivid wharf
you have to go back to the original objective which is to find the values of x w...
yh so x = -2 would satisfy. How would values greater than -2 would satisfy too
runic temple
2^x is increasing
so we know that the left side of the inequality is increasing as well
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
Are given: M(1;-2) and vector vMN = (3, 4). How to find N?
marsh citrusBOT
Are given: M(1;-2) and vector vMN = (3, 4). How to find N?
still temple
(idea, or hint)
marsh citrusBOT
@still temple Has your question been resolved?
still temple
.close
upper blade
can someone help me graph
$$-4\sin2\left(x+\frac{\pi}{2}\right)$$
marsh citrusBOT
can someone help me graph
$$-4\sin2\left(x+\frac{\pi}{2}\right)$$
elfin berryBOT
ghiolimer
dim zodiac
Is it $-4 \sin[2 \left(x+\frac{\pi}{2}\right)]$
upper blade
elfin berryBOT
Good
upper blade
question
find the amplitude, period, and horizontal shift of the function, and graph one complete period
okay so i know how to graph -4sinx
but when the period of 2 and this π/2 gets involved i become confuse
i know what to do
but i cant just graph it
lethal bridge
Do you know how to find the phase shift
lethal bridge
You suppose?
upper blade
the thing is i dont exaclty know the names of the terms
thats why im not sure whether i know it or not
lethal bridge
By how many units to the left
lethal bridge
Ye
upper blade
as i said i know what to do but idk why i cant do it
like
the adjusting it specifically makes it hard
lemme share my work
lethal bridge
Give me a few minutes I need to finish something up and then I can help you
upper blade
okay during that time ill show u my work
upper blade
couldnt do anything bth
tbh
im confused
no matter what i do i cant get the 2 period done
or if i do it the π/2 thing
they are not going well together
@lethal bridge
and desmos made me even more confused
check out the blue one its a negative right
-sinx
but the red one is opposite although it is - as well
<@&286206848099549185>
lethal bridge
lets just restart
so tell me,
we found the phase shift to be -pi/2 right
amplitude to be 4
upper blade
yeah
lethal bridge
what is the period?
upper blade
period is 2
lethal bridge
correct
lethal bridge
now a method i like to use when graphing is finding the "x scale" or however you like to call it
its basically just the points on the graph you will use
the x-scale is given by "P/4" where P is the period and 4 is the intervals you will break it into
so whats the x scale we will use?
upper blade
idk
upper blade
π/4?
lethal bridge
yes
upper blade
so we're gonna divide the x scale as π/4
lethal bridge
the reason its divided by 4 is because we will see that it helps us graph exactly one period
upper blade
oh
lethal bridge
we dont divide the x scale, pi/4 is the x scale
do you have a pen a paper near you so you can graph?
upper blade
yeah
lethal bridge
yes to either the left or the right
lethal bridge
here in our case, imagine a sine graph, but moved pi/2 units to the left
lethal bridge
am i right
yeah essentially
so
with this information, can you tell me where this graph will start?
upper blade
not 0 and instead on -π/2
upper blade
done
lethal bridge
cool
lethal bridge
we need it in exact form
if it helps you can convert it into degrees but with trig functions and graph you will likely be asked to keep it in radians
lethal bridge
since i know how this graph will turn out i recommend spacing it a bit more to the left
so you have enough space
upper blade
alr
lethal bridge
so this is where the x scale comes in; it will tell us the distance in between our next points
if the x scale is pi/4 units, it means our next point will be -pi/2 + pi/4
does that make sense?
upper blade
yeah sort of so we're gonna do π/2?
so basically π/4 thing means the gap between them ?
lethal bridge
so basically π/4 thing means the gap between them ?
yeah
upper blade
alr
lethal bridge
so whats -pi/2 + pi/4
upper blade
its -π/4
upper blade
alr
lethal bridge
we want to do this 3 more times since the x scale is divided into 4 bits
lethal bridge
the thing is i mess up this part because idk where to point
wdym?
lethal bridge
how so?
lethal bridge
it doesnt have to be accurate
lethal bridge
just plot it wherever but make sure ur numbers are in the right order
upper blade
i usually dont care abt it as well
lethal bridge
then i always got it wrong tho
does ur teacher say the spacing has to be accurate?
upper blade
but this time since its complicated
upper blade
does ur teacher say the spacing has to be accurate?
no
lethal bridge
just keep the spacing even
upper blade
okay so usually idc about that
but this time since we have complicated things
im confused so to prove it i wanted to be same yk
anyways
lethal bridge
itll make things more confusing
upper blade
because yk otherwise the period of 2 thing is not correct
lethal bridge
because yk otherwise the period of 2 thing is not correct
it will be
upper blade
yeah it does but otherwise when i want to show a period of 2 it doesnt make it correct
when dots are not placed correctly
lethal bridge
does the trigonometric function know if the physical distance between ur points are exact?
no
lethal bridge
when dots are not placed correctly
ur dots will be placed correctly
if you follow what i say
dont worry about the exact details
lethal bridge
if ur so worried you can put 3 boxes in between
lethal bridge
is this thing correct?
yes...
lethal bridge
it doesnt matter the exact spacing like i said, just make the distance even and not ridiculously large lol
lethal bridge
$x:\left{-\frac{\pi}{2},-\frac{\pi}{4},0,\frac{\pi}{4},\frac{\pi}{2}\right}$
elfin berryBOT
شعاع الماء
lethal bridge
these are your points on the x axis which you should have
upper blade
done
lethal bridge
show me
upper blade
alr
lethal bridge
now for ur amplitude u know its going to reach y=4 and y=-4
so put 4 and -4 near the top and bottom of ur y axis
lethal bridge
now we will start connecting the dots
so
can you tell me the behaviour of the sine graph
as in how its curve looks
just the regular y = sinx
upper blade
it passes 0 from the below and reaches to 1 because that is the amplitude
then goes down until -1 and does the same
lethal bridge
yes
so its going to start at the bottom
reach the top
then go back to the bottom
upper blade
our function is negative sinx so we're gonna start at top?
upper blade
yep
lethal bridge
our function is negative sinx so we're gonna start at top?
put an X on -pi/2 thats where itll start
like mark it
upper blade
done
lethal bridge
so regular sine would go up
but we have a minus sign
so its flipped
so its going to go down
upper blade
alr
lethal bridge
where will this point be can you tell me?
upper blade
-π/4
lethal bridge
and the y value?
upper blade
4
lethal bridge
4 or -4?
upper blade
oh for -π/4 its -4
elfin berryBOT
شعاع الماء
lethal bridge
sure
lethal bridge
every pi it completes a period
how many rotations does it complete in the graph you showed me
upper blade
so uhm the second part where its below it should be under π/4 right
upper blade
how many rotations does it complete in the graph you showed me
2?
lethal bridge
**شعاع الماء**
just go back to this part we are almost done
upper blade
alr
lethal bridge
**شعاع الماء**
so you marked a point at this right
upper blade
yes
lethal bridge
now we said that the sine graph
starts on the x axis, goes up, goes to the x axis, goes down, then goes back up
but here its flipped
after reaching the very bottom
it will go back and touch the x axis
at 0
makes sense?
upper blade
yes
lethal bridge
so we have a point marked at 0
lethal bridge
then where will it go?
upper blade
in previous examples i have done 4 and it didnt work and according to the move it shpuld be *4?
-4?
lethal bridge
we just touched -4
upper blade
also to get the period of π
we marked 0
we touched 0 ?
oh okay
my previous work was correct
the amplitude is 4
lethal bridge
yes the amplitude is 4
lethal bridge
upper blade
anyways now i got it
lethal bridge
look
we start at x axis
go down
go back up to x axis
then we will go back up again
upper blade
alr
upper blade
y=4 x = π/4
upper blade
done
lethal bridge
show me
upper blade
upper blade
yep
lethal bridge
so you know how to sketch it now?
upper blade
yeah the part i actually missed before was the x scale thing i guess
lethal bridge
yes the x scale helps a lot
upper blade
its alwyas period/4 thats how we're gonna do?
lethal bridge
yep
always p/4 will get you one period
if you want more you can easily add on points
upper blade
i also found out that i knew period wrong tbh
isnt period the distance between two peaks
in sin thing
upper blade
no uhm
it shows like this
which is correct?
the reason why i got it wrong tons of times is because i tried to make the distance in red equal to 2 :/
upper blade
so i am correct?
lethal bridge
yes
upper blade
ohh
lethal bridge
but the internet is also correct
upper blade
can u pls go to another channel
lethal bridge
the image on the left is what one period looks like
upper blade
the image on the left is what one period looks like
uhuh
lethal bridge
so whats ur confusion?
upper blade
so the thing im saying is yk how period is the distance between peaks
but our graph shows the period isnt π
upper blade
GO FIND ANOTHER CHANNEL
dude are u stupid?
anwyays
ur wasting my time
no ones gonna solve it here
lethal bridge
upper blade
just read the text
damn
READ
THE
DAMN
TEXT
THE ONE SHE OR HE SENT
anwaysy
please ignore them
as i was saying
shouldnt the peak should be on π/4
if the period is π?
lethal bridge
look
upper blade
if period means the distance between peaks
lethal bridge
if period means the distance between peaks
from -pi/2 to 0 it completes half a rotation do you agree
upper blade
yes
upper blade
yep
lethal bridge
if you add both of them together it is one full period
lethal bridge
you can break it into to parts
upper blade
and leave
lethal bridge
<@&268886789983436800> troll
upper blade
i dont need ur help
please leave
@lethal bridge is already helping
go find another channel
leave
how do u know im doing this for an exam so u guarantee that i get low marks?
quaint elm
@still temple take some time to reflect on what happened
lethal bridge
thank you hayley
upper blade
what happened?
lethal bridge
they were trolling thats what happened
abstract isle
You're doing this for an exam?
upper blade
no
i am not
thats why i wrote it lol
i dont have an exam im a 12th grader im in final yearim preparing for uni
ik it isnt allowed
upper blade
they were trolling thats what happened
anyways i got what ur trying to do
lethal bridge
np
lethal bridge
you too
upper blade
.close
marsh citrusBOT
limpid heart
We use the formula but it's not on the choices 😭
still temple
u should probably hide revealing information
marsh citrusBOT
limpid heart
u should probably hide revealing information
Ohh shittttt
I don't know if my answers were right
marsh citrusBOT
Available help channel!
iron tundra
I still don’t know how this one works
marsh citrusBOT
I still don’t know how this one works
iron tundra
Ik v=d/t
So I drew the triangle
But uhh how do I get his displacement
The answers don’t make sense, and I don’t understand how the hypotenuse of this triangle is the displacement
And then what would I do for the direction? I think the root of my problem is the lack of understanding of where the boat ends up, and therefore how displacement makes any sense
calm skiff
So I drew the triangle
i dont think you got the question?
its asking the resultant velocity
iron tundra
Yeah me neither
calm skiff
which will be the vector sum of the velocities of the current and boat
calm skiff
"determine the resultant velocity of the fishing boat"
iron tundra
So I add the velocities!
calm skiff
you have to add the two velocities together
calm skiff
So I add the velocities!
yup
iron tundra
Hang on
Does my teachers working out make any sense?
Because idk if he added vectors
calm skiff
Does my teachers working out make any sense?
yes this is how you do it
the vectors are mutually perpendicular
iron tundra
Mhm
calm skiff
so you can use the pythagoras' theorem
worldly ledge
the hypotenuse is the answer no?
worldly ledge
sqrt(3^2 + 1.5^2) is the resultant velocity no?
worldly ledge
adding the vectors gives the resultant direction and velocity'
the length of it is the velocity
so finding the hyp is the resultant velocity
iron tundra
Ok wait
How does displacement work in a scenario like this it’s hard to explain what I mean when I say I don’t get it.
If the angle from which the dude started was not 90 degrees it would make sense
worldly ledge
the vectors that you have drawn represent the velocity and direction only, for displacement youd have to bring in time
iron tundra
Ok set the time equal to 1
worldly ledge
s=d/t etc
iron tundra
Second
worldly ledge
the question doesnt talk about displacement though, so you shouldnt worry about it
if it did it would tell you it travelled for x amount of time
iron tundra
That’s how I calc the velocity? Through displacement
worldly ledge
no, you have the velocities
so to find the final velocity you use pythagoras, if they werent at right angles youd use cosine rule
iron tundra
But if two forces are acting on him at the same time time, how do I find where he would end up, I add the vectors right, because if I just found the hypo that doesn’t help me
worldly ledge
ok so what im getting is that you dont fully appreciate what a vector is. a vector in general carries a direction and size. for this question you want direction and velocity so when adding them you get the final velocity and direction. if the question was about forces on a body, the vectors when added would show the final force and direction
so in this question adding the vectors gives final velocity and direction of travel, to find the size (and therefore velocity) you use pythagoras
if that doesnt help i hope someone else can word it better
iron tundra
It’s taking a bit to digest this
How
Does
Finding
The
Hypotenuse
Of
The
Triangle
In
The
Question
Give
Me
The
Displacement
Just check my diagram of the question
orchid kiln
The hypotenuse is the magnitude of the final vector
iron tundra
Is that a correct diagram of the question
So in that diagram
How would the hypotenus tell me where this fucking boat has travelled
Im so fed up with this question
But I appreciate all the help thank you
orchid kiln
Revise that topic again maybe you will comprehend it later
worldly ledge
it says find the final velocity
not distance or anything else
you have two velocities acting on the boat as seen in the diagram
iron tundra
Yes
worldly ledge
so adding the vectors gives you where the boat is actually travelling
and at what speed
orchid kiln
Omg
iron tundra
Or is there something with the hypo
worldly ledge
that gives you the direction and final size but is the final size the same as adding the sizes of each vector?
the answer is no
the hypo is the adding of the vectors
orchid kiln
Read what bro has said above he's told you exactly what you need to do, try just doing it then once you get your answer think about it
iron tundra
Yes ok
This might be a dumb question but,
We find the size through pythag
But
The hypo isn’t actually telling you where guy end up, you have to take the length of the hypo and now position from the origin and then you’ll find where he is
I could just b me stupid
worldly ledge
position isnt a part of this problem, its just the velocities, let me try with a drawing
iron tundra
Your a legend thanks so much for helping me
worldly ledge
the boat is travelling at a certain speed and direction, after some time it will still be travelling in the same speed and direction, just in a different place, the hypo still tells us the speed
iron tundra
I think I get it now
worldly ledge
if thats all please close the chat and have a good day
iron tundra
It 10 at night for me lol but tysm
Also queens gambit is the best chess opening and that objective
.close
marsh citrusBOT
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hearty dust
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hearty dust
im not sure how to do part a
tbh im not sure how to approach most questions like this
a general approach would be nice
leaden monolith
P(X|Y’) = P(Y’|X)P(X)/P(Y’)
P(X|Y) = P(Y|X)P(X)/P(Y)
You know that P(Y’) = 1 - P(Y) and P(Y’|X) + P(Y|X) = 1
I think you just need to fiddle around to solve for P(Y)
Clearly this P(X|Y) and P(X|Y’) are related you need to change them to a form you can deal with
cobalt sentinel
brooo u just turned into an algebra problem
hearty dust
is there an easier way?
leaden monolith
Not sure, this is how I would do it
leaden monolith
That’s just bayes theorem
leaden monolith
brooo u just turned into an algebra problem
Is there a better way? Do you know?
cobalt sentinel
nah i was saying u made it too easy lol
leaden monolith
Have you not seen anything like this before?
Bayes theorem is one of the most fundamental theorems you learn for conditional probability
cobalt sentinel
hold on lemme sit down and take a look at this
wait lol
@leaden monolith
this is just law of total probability
Px = Px|y * Py + Px|y’ * Py’
then Py’ = 1 - Py
and theres ur answer
leaden monolith
But you get that identity by rearranging bayes theorem…
cobalt sentinel
Yea i mean u can derive it, but law of total probability is more ‘fundamental’ than bayes so they probably woulda learned it
leaden monolith
Ah I see what you mean
cobalt sentinel
@hearty dust are u familiar with law of total probability
marsh citrusBOT
@hearty dust Has your question been resolved?
marsh citrusBOT
@hearty dust Has your question been resolved?
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winter scarab
is this right???
marsh citrusBOT
is this right???
winter smelt
is this right???
yup that's correct
winter scarab
ok thank you
winter smelt
you could've also checked by simply substituting the 3 points you had back into the function you got at the end
winter scarab
is this right???
it said the graph will have holes
but my graph didn’t turn out with holes in it
golden junco
But you have a hole
In the points 2 and -2
Since you can cancel them out above and under in your function
marsh citrusBOT
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winter scarab
wait i don’t understand
magic sequoia
How to find it.. i know a thing that when this type of question asked.. try to eliminate the parameter in this case its theta.. but i don't know how to exactly do that in this question..
marsh citrusBOT
How to find it.. i know a thing that when this type of question asked.. try to e...
marsh citrusBOT
@magic sequoia Has your question been resolved?
wicked fox
How to find it.. i know a thing that when this type of question asked.. try to e...
Actually can you elaborate? r and θ are independent unless otherwise stated and as such you can't get rid of either without losing information
magic sequoia
Actually can you elaborate? r and θ are independent unless otherwise stated and ...
Hm.. i need to find the conic section to which this equation represents
wicked fox
Can you post the full question?
magic sequoia
Wait..
I can't understand this answer..
@wicked fox sir.. ping me while you reply pls..
wicked fox
You can multiply both sides by r and substitute rcosθ = x, then you get 1 = r/8 + (3/8)x
Oops I forgot to ping @magic sequoia
And also, if r is the distance from origin, then r = sqrt(x^2 + y^2)
marsh citrusBOT
@magic sequoia Has your question been resolved?
celest harbor
im doing part b but idk what they did in the red
marsh citrusBOT
im doing part b but idk what they did in the red
wicked fox
im doing part b but idk what they did in the red
They multiplied by (x-2) and divided by (x-2) on the -7 and -2 so that they could combine the fractions on top and bottom
$-7 = \frac{-7(x-2)}{x-2}$, $-2 = \frac{-2(x-2)}{x-2}$
elfin berryBOT
Leander
celest harbor
They multiplied by (x-2) and divided by (x-2) on the -7 and -2 so that they coul...
youre allowed to do that?
wicked fox
youre allowed to do that?
-7 is the same as -7/1, which is a fraction, and in fractions, you can multiply on top and the bottom with the same number
$\frac{1}{2} = \frac{1 \cdot 2}{2 \cdot 2} = \frac{2}{4}$ for example
elfin berryBOT
Leander
celest harbor
-7 is the same as -7/1, which is a fraction, and in fractions, you can multiply ...
oh ye, i wouldnt think of that without the ms
wicked fox
You can also multiply with the same number on the top and the bottom if that number has a variable
wicked fox
oh ye, i wouldnt think of that without the ms
Think of it like multiplication and division are inverse operations. If you multiply with a number, then divide by the same number, you end up where you started
celest harbor
Think of it like multiplication and division are inverse operations. If you mult...
ight ima blow through some questions before my exams
thanks
wicked fox
No worries
celest harbor
.close
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vocal cloud
can i please get help with this
marsh citrusBOT
can i please get help with this
normal sky
!status
marsh citrusBOT
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
@vocal cloud Has your question been resolved?
still temple
A quadrangle ABCD inscribed in a circle has following parameters: |AB| = 3, |AD| = 9 and angle BAD = 120 degrees. Two remaining sides are both $3\sqrt{13}$. Calculate the field of given quadrangle. (Could be done in analytical geometry with integrals (if possible) or in normal geometry)
marsh citrusBOT
A quadrangle ABCD inscribed in a circle has following parameters: |AB| = 3, |AD...
elfin berryBOT
Hollow Knight Addict
still temple
got to this point, only managed to figure out the BCD angle
marsh citrusBOT
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still temple
I also managed to figure out this, the formulas for linear functions. the problem with the 2 latter is that I only have each of their points ($l_{CD}$ goes through [$-4.5, 4.5\sqrt{3}$] and $l_{BC}$ goes through [3, 0]) and that they create together an angle of $\frac{2\pi}{3}$
elfin berryBOT
Hollow Knight Addict
still temple
they create sth like this
still temple
<@&286206848099549185>
minor tinsel
friend me if ur very good at math
marsh citrusBOT
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marsh citrusBOT
@still temple Has your question been resolved?
dense quest
got to this point, only managed to figure out the BCD angle
One thing I noticed
Try write R in terms of 3
harsh vine
Can someone please help me with question 2b
marsh citrusBOT
Can someone please help me with question 2b
@harsh vine Has your question been resolved?
marsh citrusBOT
@harsh vine Has your question been resolved?
marsh citrusBOT
@harsh vine Has your question been resolved?
marsh citrusBOT
@harsh vine Has your question been resolved?
magic sequoia
You can multiply both sides by r and substitute rcosθ = x, then you get 1 = r/8 ...
sir.. how this helped us to find that the equation is hyperbola?
wicked fox
sir.. how this helped us to find that the equation is hyperbola?
$r=\sqrt{x^2+y^2}$
elfin berryBOT
Leander
wicked fox
So if you put that for r you only have x and y
magic sequoia
oh.. but how we know that $r=\sqrt{x^2+y^2}$?
elfin berryBOT
Mirthun1012
wicked fox
Because r is the distance from the origin to the point, but it is also the hypotenuse of a triangle where the two other sides have length x and y
magic sequoia
@harsh vine and yeah.. sorry to use your channel.. as the bot unfortunately closed the channel before my question resolved..
magic sequoia
Because r is the distance from the origin to the point, but it is also the hypot...
hm.. ok..
magic sequoia
r stands for the radius if that makes sense
yeah.. it making sense.. thank you
wicked fox
yeah.. it making sense.. thank you
No worries, have a good day
magic sequoia
No worries, have a good day
and.. i posted another question sir.. if you wish.. you can check it out #help-42
marsh citrusBOT
@harsh vine Has your question been resolved?
harsh vine
can someone please help me with question 2b
marsh citrusBOT
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limber marsh
What in the economics??
marsh citrusBOT
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hard gull
$$\int^5 _{-1} |x-3|$$ i know we have to split the integral , but i forgot how to do that
marsh citrusBOT
$$\int^5 _{-1} |x-3|$$ i know we have to split the integral , but i forgot how t...
elfin berryBOT
JustToPro
undone bane
check where the function changes its definition
limber marsh
Do you remember piecewise functions?
hard gull
check where the function changes its definition
x = 3?
undone bane
right
hard gull
so something like this ?
$$\int ^5 _{3} |x-3| + \int ^3 _{-1} |x-3|$$
elfin berryBOT
JustToPro
hard gull
Do you remember piecewise functions?
no
undone bane
well that is an issue then
you'll have to revise how to write |x-3| as a piecewise function
undone bane
yup
hard gull
yeah i can write that into that kind of thing
undone bane
try writing |x-3| for those intervals
undone bane
correct
hard gull
now what
undone bane
i think you can do the same thing in those integrals now
hard gull
i cant
elfin berryBOT
Dyssrupt
undone bane
here, x lies between 3 and 5
hard gull
ye
undone bane
and according to your piecewise function, when x >=3, |x-3| = x-3
hard gull
yes
undone bane
now for the second integral?
hard gull
3 to -1
undone bane
-1 to 3, yeah
hard gull
**JustToPro**
so this?
elfin berryBOT
Dyssrupt
undone bane
try doing the same thing here
undone bane
right
elfin berryBOT
JustToPro
hard gull
$$\int ^5 _{3} (x-3) dx - \int ^3 _{-1} (x-3)dx$$
elfin berryBOT
JustToPro
undone bane
marsh citrusBOT
hard gull
**Dyssrupt**
btw here x lies between 3 and -1
so if x lies on 3
shouldnt function be positive?
.reopen
marsh citrusBOT
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hard gull
@undone bane ^
or can x not lie on 3 ? cuz in the original question x is from -1 to 5
cuz when x is greater or equal to 3 , then function is positive
undone bane
or can x not lie on 3 ? cuz in the original question x is from -1 to 5
the endpoints dont really matter in integration
you can think of it as (-1,3) and (3,5)
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cunning fern
i'm confused on how this happens ( a friend sent me this so it might be wrong)
hard gull
$$ x^2 \cdot dx = \ln x \cdot \frac{1}{t} \cdot dt$$
dividing both by $\ln x$
$$\frac{x^2}{\ln x} dx = \frac{1}{t} dt$$
elfin berryBOT
JustToPro
cunning fern
then you can just flip it?
hard gull
and then they took reciprocal on both sides which is wrong
cuz then this is what u will get
$$\frac{\ln x}{x^2 dx} = \frac{t}{dt}$$
elfin berryBOT
JustToPro
hard gull
they didnt flip the dx and dt
proud zealot
marsh citrusBOT