#help-10
frail tulip
Remember to state that we're letting x_1, x_2 in R SUCH THAT x_1 ≠ x_2 AND f(x_1) = f(x_2)
what we've done here is find a contradiction
Hope this helps
dim nacelle
Thank you it really did!
obtuse pebbleBOT
Available help channel!
dire umbra
Question: Solve the following system of equations using an inverse matrix.
dire umbra
I don't know where to begin with it
Should I first get the inverse of the first matrix
tame narwhal
yes
tame narwhal
yes, that's what you're asked to do
dire umbra
I thought maybe first multiply
and than do that
Wait does that mean I also need to get the inverse for the 1x3?
tame narwhal
there is no inverse for the vector
dire umbra
Why not?
tame narwhal
inverse is only defined for square matrices
dire umbra
so 1x1 2x2 3x3 4x4 etc?
tame narwhal
yes
dire umbra
I see well I am going to find the inverse first than
Another question on that
on a inverse of 2x2 you can use the formule 1/ad-bc etc
Why isn't there a formula for a 3x3?
wet moss
There is
winter timber
it is quite a long process without a calculator
dire umbra
I have a calculator?
tame narwhal
you can do it by row reduction
dire umbra
you can do it by row reduction
Yes but that method takes a bit time
winter timber
well with your calculator just find the inverse?
dire umbra
I thought maybe there is a way faster than that because the 2x2 matrix is also fast
tame narwhal
any method will take time unless you just use a calculator
dire umbra
well with your calculator just find the inverse?
It is a normal calc though
dire umbra
any method will take time unless you just use a calculator
Well the formula for 2x2 is quite fast less than a minute
wet moss
The shortest method I can think of is like a 5 step process but even then it takes about 5 mins to do it by hand
dire umbra
row reducing a 3x3 shouldn't take too long
Well I find it quite "hard"
I keep getting like strangled up with it
tame narwhal
Well I find it quite "hard"
well yea, it's not necessarily easy, it just takes practice
wet moss
But it is what you are expected to do in this question I think
dire umbra
How do you guys like do the row reduction
is there like some steps you need to follow
wet moss
There are different methods to doing it
dire umbra
There are different methods to doing it
Like? I normally just go with what looks alright
tame narwhal
you start with $\begin{pmatrix} 2 & 1 & 0 & | & 1 & 0 & 0 \ 0 & -1 & 3 & | & 0 & 1 & 0 \ -1 & 0 & 2 & | & 0 & 0 & 1 \end{pmatrix}$. you want to row-reduce so you get the identity to the left of the "|" vertical bars
wet moss
Personally I don’t know the row reduction method but that may be easiest
warm shaleBOT
cwatson
tame narwhal
then the matrix to the right of the vertical bars will be the inverse
dire umbra
No I know how to do it
I meant as in are there steps like first complete the 1st row and then the 2nd than the 3rd?
Is there like "rule" to do it
tame narwhal
I would do it column-by-column
first "clear" the first column, make the (1,1) entry equal to 1. then go to the second column, etc.
dire umbra
Alright
you know when you do c1 - c2
if you do c3 - c1 can you apply that to column 1?
or do you need to apply that to column3?
tame narwhal
you do row operations. and you can for example apply r1 - r3 to r1, or to r3
tame narwhal
you could, but you shouldn't
dire umbra
why not?
tame narwhal
because then you'll have -3 -1 2 as your first row
(plus whatever will be to the right of the vertical bar)
dire umbra
Yeah makes sense thanks I do that first and see if it works out
tame narwhal
I recommend doing r1 + 2r3 and applying it to r3, see if that works out
dire umbra
first "clear" the first column, make the (1,1) entry equal to 1. then go to the ...
btw when you said this. you mean as in the first row needs to be 1,0,0 than do the next?
dire umbra
I recommend doing r1 + 2r3 and applying it to r3, see if that works out
let me try that out
dire umbra
so first get a 1 in the first row and 2nd and then 3rd?
tame narwhal
yes, once your first column is [1 0 0]^T, you move to the second and get it to be [0 1 0]^T
and so on
tame narwhal
yes of course
dire umbra
Got it just making sure thanks
dire umbra
you do *row* operations. and you can for example apply r1 - r3 to r1, or to r3
seems to give 0,1,4 on r3 too big
tame narwhal
too big?
tame narwhal
no, I said do it column by column
tame narwhal
if you want to, yes
dire umbra
got it thanks
obtuse pebbleBOT
@dire umbra Has your question been resolved?
dire umbra
not yet
dire umbra
if you want to, yes
Can you also do 0r1 - r2?
tame narwhal
I don't remember if you can multiply a row by 0, but why would you?
dire umbra
I got like right now this
1 4 -2
3 1 3
1 -1 1
I want to multiply the first row by 0 than add the row 3 to row 1
tame narwhal
for what purpose?
tame narwhal
actually you can't multiply by 0: https://math.stackexchange.com/a/2911891
dire umbra
actually you can't multiply by 0: https://math.stackexchange.com/a/2911891
Interesting thanks
Can you just do 1 row?
so like 2r2?
tame narwhal
if you want, yes
dire umbra
Other question
It looks you can looks switch the rows
so a11 can go to a12
Is that really a possibility?
tame narwhal
yes
obtuse pebbleBOT
@dire umbra Has your question been resolved?
obtuse pebbleBOT
@dire umbra Has your question been resolved?
torpid dagger
obtuse pebbleBOT
torpid dagger
how do i find the size of a right triangle with just this information
i have three degrees and one side
is this possible?
thin pawn
using trigonometry probably
thin pawn
yeah, in this case, if you call the side opposite to 47 degrees h:
$cot(47) = 550 / h$
warm shaleBOT
imTyp0
thin pawn
and then you can do the same with 22 degrees
and find both pieces and add them up to get x :)
Is this clear enough?
torpid dagger
yes
thin pawn
:L
thin pawn
Should be yeah
altough you shouldn't write hyp as it's not the hypothenuse but that doesn't matter
torpid dagger
altough you shouldn't write hyp as it's not the hypothenuse but that doesn't mat...
i had one more question
im trying to solve for theta
but idk what to do algebraically here
thin pawn
er, there is a way to solve it algebraicly, but I don't think that's what you meant. Here you can use literally any trigonometric function since you have all 3 sides
thin pawn
why did you use sin(2theta)?
that angle is just theta. I'd understand if it was 2theta, but now I really don't
torpid dagger
My homework said i was solving for sin(2theta)
thin pawn
Ah, okay
well, you probably have seen this identity then: $\newline sin(2\theta) = 2sin\theta cos\theta$
warm shaleBOT
imTyp0
thin pawn
well, if we're not using that, I don't see what else to use. With that, you went from having an angle of 2theta, to it being in terms of just theta. And you know sin and cos of theta
thin pawn
?
torpid dagger
im p certain this is the answer
i found a practice problem and that was how it was done
warm shaleBOT
Result:
0.5376
i believe it is correct
thin pawn
576/625?
torpid dagger
ye
thin pawn
do you have any way to make sure it's correct? Because I don't understand where it comes from
torpid dagger
cuz on a practice problem it had the same question
thin pawn
because that's sine of 2theta, not sine square of theta
I think you did sine square
if the question was:
$sin^{2}\theta$
warm shaleBOT
imTyp0
thin pawn
then yes it would be your answer
thin pawn
where do those numbers even come from?
torpid dagger
A practice problem
thin pawn
can I see said problem please?
thin pawn
Yeah and? It's doing it the way I told you
torpid dagger
Oh haha
thin pawn
$sin(2\theta) = 2sin\theta cos\theta \newline sin\theta = 15/17, cos\theta = 8/17 \newline sin(2\theta) = 2(15/17)(8/17)$
warm shaleBOT
imTyp0
thin pawn
and if you put it in your calculator, you'll see that this is, indeed, 250/289
thin pawn
So yeah, whenever you have sine(2theta) or cos(2theta), you want to change it back into things that only have theta. That's where trigonometric identities come in handy
thin pawn
thank you :)
no worries :D
torpid dagger
.close
whole plaza
help lol
obtuse pebbleBOT
@whole plaza Has your question been resolved?
whole plaza
<@&286206848099549185>
limber umbra
whole plaza
this is what the mark scheme says
This is the mark scheme
obtuse pebbleBOT
@whole plaza Has your question been resolved?
glossy nest
obtuse pebbleBOT
glossy nest
Not sure where to begin. I believe I need to convert the line equation to parametrized equations, but I'm not sure how to do so without a vector
I could be totally wrong
glass dagger
If you have an equation of the form ax+by+cz+d=0 then are you aware what the coefficients a, b and c represent geometrically?
@glossy nest
glossy nest
I believe the coefficients rotate the plane around the x, y, and z axis?
glass dagger
well it turns out that if you form the vector [a b c]^T then the direction it points towards is normal to the plane
and that's super helpful because it means that if you know what direction the plane is facing (its normal vector) and one point on the plane then you can easily figure out an equation whose solutions make up that plane
If you knew, for example, that a plane was normal to the vector [1 1 1]^T, then you would know that its equation would be of the form x+y+z+d=0
if you additionally knew that the point (1, 1, 1) was on the plane then you'd know that 1+1+1+d=0 <=> d=-3
so if you knew a vector that was normal to your plane then you'd be golden. Do you have any ideas on how you might find one?
glossy nest
I think we could rearrange the plane's equation to be 2x - y - 1 = 0, which would then give us the normal vector [2, -1, 0]^T?
glass dagger
y=2x-1 isn't the plane's equation, it's the equation of a line
glossy nest
ur right nvm
glass dagger
if we had the plane's equation then we'd already be done :^)
glossy nest
lol true
It seems like a vector that is normal to the given line wouldn't tell us anything, and the point cant give us a vector so i'm not sure
glass dagger
alright I gave it some more thought and it's actually not quite as easy as I'd originally thought but we're definitely on the right track. So you can definitely find one vector that rests on the plane by just following the line y=2x-1, right? alright. Well, if you had a second vector resting on the plane that pointed in a different direction then you could take the cross product between these two vectors and then we'd get a normal vector, right
so, is there a way to get a second vector that rests on the plane?
I'll give you a hint. The plane goes through the point (1, 1, 0)
and also through the point (3, 2, -2)
fathom flicker
I'll just add on and probably reiterate in a different way what Stipendi just said: The plane contains the line y=2x-1, and the point (3, 2, -2). Since a plane is just made up of 2 different independent lines, you need to find a line that could take you from somewhere on y=2x-1 to (3, 2, -2). So, take a point on the line, like (1, 1, 0) and take yourself to the point you want, (3, 2, -2). The vector that does this, can serve as your new line that makes up the plane. And then to express a plane, we don't use 2 independent lines that make it up, because for any plane there are infinitely many different ways that we could do that. So instead, we express the line that is normal to the plane (perpendicular). We know that taking the cross product of two vectors will give us a new vector that is perpendicular to the beginning two, so take the two lines you found already and cross them to find the normal vector for the plane. @glossy nest
obtuse pebbleBOT
@glossy nest Has your question been resolved?
glossy nest
Ok so I have one vector a = <2, -1, 0> that was formed from the equation of the line. I find one more point on this line like (1, 1, 0) and create a second vector b = <2, 1, -2> using points P(1, 1, 0) and the given Q(3, 2, -2), then take the cross product of these two vectors to create a perpendicular vector to both a and b. The result of the cross product of a and b is the normal vector for the plane?
glass dagger
alright I gave it some more thought and it's actually not quite as easy as I'd o...
One thing I'll add is that sometimes vectors should be thought of as points, other times vectors should be thought of as arrows with no position, indicating direction. Here they should be thought of as having no position and merely indicating direction
glass dagger
Ok so I have one vector a = <2, -1, 0> that was formed from the equation of the ...
Note that the vector <2, -1, 0> is not a point on the line
glossy nest
What direction is the vector <2, -1, 0> in relation to the line?
glass dagger
I don't know, how did you come up with it?
unique lodge
hello, i do not know how to start solving this problem every answer ive come to was wrong
obtuse pebbleBOT
hello, i do not know how to start solving this problem every answer ive come to ...
unique lodge
i thought the problem im solving would be 60=1/2 (140-12x-8) but doing that brought me to a negative answer
.close
timid silo
i do not understand much about this concept, ive gotten a few naswers right but a majority of them wrong
obtuse pebbleBOT
i do not understand much about this concept, ive gotten a few naswers right but ...
native inlet
i do not understand much about this concept, ive gotten a few naswers right but ...
do you know how to solve linear equations?
timid silo
do you know how to solve linear equations?
yeah im pretty sure i can
the left side is x >= -7 and the right is x < -12
native inlet
check the second again
timid silo
okay
native inlet
but yes that is almost right, gj!
timid silo
ou yeah its 12
ive asked like ai and stuff but i never really understood the stuff that slike "satisfy both questions" or something like that
native inlet
well that's AI is very bad and you really shouldn't use it understand subject matter but rather use it to assist you in solving problems
when you have two linear inequalities, which you do
you are looking for a value x that is both greater than or equal to -7 OR less than -12
so that means 69 is a correct value or x because it is greater than -7
also a value like -69 works because it is less than -12
but something like -6.9 will NOT work because it is neither less than -12 nor greater -7
native inlet
so basically all values of x can be is a solution or
no, -8 is not a solution
timid silo
;_; idk thats what i got when i got one of the answers wrong
native inlet
It's a lot better to see this graphically
native inlet
relaly bad drawing
but hope you get a kinda general idea
of what this means geometrically
native inlet
it means that if put in x=-9 looks what we get -9 >= -7
this is saying that -9 is greater than -7
it is not
that makes no sense
so it doesn't "satisfy" that equation
just a verb
that mathematicians like to use
timid silo
so something like mathematically correct
native inlet
if a value of "x" satisfies an equation then it makes it true
ig "satisfied" is used bcz equations want to be true
like -9>=x wants to be true, but if we put x=-7 then the equation isn't true
and hence isn't satisfied
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tight pond
how do i manipulate this to remove the 2 ?
obtuse pebbleBOT
how do i manipulate this to remove the 2 ?
tight pond
ps ( i converted e^i2p/3 to this and need to remove the 2 so i can finish finding the answer for an exercise in complex numbers)
tardy epoch
Just show the original question
tight pond
2)
R(B)= C
figured its : Zc-D (centre) = (e^i2p/3)(Zb-D)
the exp part is supposed to turn into:
cos(the angle) + i sin (the angle)
so i can be able to find C=-4
hope this is detailed enough
obtuse pebbleBOT
@tight pond Has your question been resolved?
tight pond
guess everyone is busy
obtuse pebbleBOT
@tight pond Has your question been resolved?
tight pond
no bot
obtuse pebbleBOT
@tight pond Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
thick crystal
hi
thick crystal
how do I find the inverse derivative of f(X) =-x^3-5x-2
i am also given the point (1,-8) and told to find the value of g(x) which is f inverse of x
dense zodiac
can u elaborate what u mean by inverse derivative
thick crystal
can u elaborate what u mean by inverse derivative
i showed
dense zodiac
ohhh
dense zodiac
how do I find the inverse derivative of f(X) =-x^3-5x-2
so we need to diffn this and reciprocal right?
dense zodiac
well i mean acc to your ques thats what it means
inverse derivative of f(x)
is reciprocal of the derivative
obtuse pebbleBOT
@thick crystal Has your question been resolved?
cloud egret
can yall help me with this
obtuse pebbleBOT
can yall help me with this
Please read #❓how-to-get-help
Available help channel!
calm panther
I'm getting brain issues with this. I have to get momentum having as reference point C and then point A
obtuse pebbleBOT
I'm getting brain issues with this. I have to get momentum having as reference p...
terse bane
the A point is fixed, correct me if im wrong?
like there's no way the entire system can move?
terse bane
ok so its only rotational motion that it undergoes right
calm panther
mhm
terse bane
you know that Torque would be equal to the Force x Perpendicular Distance correct?
terse bane
so with that resolve the forces to be perpendicular to the surfaces and equate it as such
tired sierra
wait a minute, this is physics
calm panther
you know that Torque would be equal to the Force x Perpendicular Distance correc...
oh wait, yeye
calm panther
so with that resolve the forces to be perpendicular to the surfaces and equate i...
but how 
terse bane
but how <:despair3:945967642886410240>
vectors u can translate into perpendiculars by trig
calm panther
Do i translate it to F(x) or F(y) ? Is it the same ?
terse bane
more or less
calm panther
Probably F(y) better (?)
calm panther
ye
terse bane
so take both components of force figure out torque for each and add/subtract as such
calm panther
F(y) should be 5√3, right ?
terse bane
cos60 or sin60?
calm panther
Should be sin(60°) 
terse bane
is the angle btw vertical or horizontal
obtuse pebbleBOT
@calm panther Has your question been resolved?
calm panther
No :P
obtuse pebbleBOT
@calm panther Has your question been resolved?
calm panther
hybrid gull
I'm getting brain issues with this. I have to get momentum having as reference p...
Angular momentum about point A? Is there no text/question associated with the diagram?
hybrid gull
That’s the moment
calm panther
Determine the moment of the 10N force about points A and C
hybrid gull
Not momentum
hybrid gull
you know that Torque would be equal to the Force x Perpendicular Distance correc...
Basically just compute this
calm panther
Basically just compute this
Well, if I could i would have already solved it, wouldn't i ?
:P
hybrid gull
I’m just making sure you know what your goal is
Here’s how I’d do this problem: split the force into horizontal and vertical components (left and up).
For the force going left, multiply that by the vertical distance from C to where the force is applied.
For the force going down, multiply that by the horizontal distance from C to where the force is applied
obtuse pebbleBOT
@calm panther Has your question been resolved?
rotund flare
what is the meaning of this?
obtuse pebbleBOT
what is the meaning of this?
rotund flare
can give me the example question?
untold flax
yeah
say you have numbers 1 - 9
and you want to find the amount of 3 digit numbers
wait no
bad example
royal basin
can give me the example question?
how many ways are there to arrange r cards in a row face up from a deck of n cards
rotund flare
untold flax
and you want to find the amount of 3 digit numbers
with different digits
it would be 9x8x7
or 9!/(9-3)!
cus 9 options for first digit, 8 options for second digit, 7 for third
untold flax
yeah I did mention with different digits
otherwise the amount of possibilities would be 9^3
obtuse pebbleBOT
Available help channel!
signal sinew
obtuse pebbleBOT
signal sinew
Trying to solve e) but not sure how to start. Distribution of d) is Exp(2)
Anyone have any advice?
minor arch
Just wanted to check my answer is right
(Goddam book doesn't give answers for this chapter
lean dew
Just wanted to check my answer is right
Send in one of the available help channels
signal sinew
Trying to solve e) but not sure how to start. Distribution of d) is Exp(2)
Anyone have any advice?
obtuse pebbleBOT
@signal sinew Has your question been resolved?
signal sinew
<@&286206848099549185>
obtuse pebbleBOT
@signal sinew Has your question been resolved?
obtuse pebbleBOT
@signal sinew Has your question been resolved?
obtuse pebbleBOT
@signal sinew Has your question been resolved?
shadow lava
Why are you allowed to do this in Gaussian Elimination?
-2R1 + R2 -> R2
obtuse pebbleBOT
Why are you allowed to do this in Gaussian Elimination?
-2R1 + R2 -> R2
shadow lava
wouldn't it change the equation?
I understand swapping rows, and multiplying rows by a scalar
but this one is tricky for me to wrap my head around
-2R1 + R2 -> R2
timid silo
This notation is nonstandard afaik
Can you give an example of how this affects the matrix?
shadow lava
This notation is nonstandard afaik
do you mean with the first row getting modified, and the arrow +R# -> R# at the end?
it's the notation we are taught in class, what notation would you use instead?
warm canopy
Are you trying to notate "row 2 is replaced with row2 minus two lots of row 1"
tame narwhal
yes they are
shadow lava
like let's say the augmented matrix is
1 2 3 4 | 5 2 3 4 5 | 6
we wanna get the r2,c1 to be 0
so we do this operation -2R1 + R2 -> R2
tame narwhal
it's allowed because it doesn't change the solutions. you can convince yourself of this but it's tedious IMO
dark stirrup
I'll give you a simpler example
shadow lava
Are you trying to notate "row 2 is replaced with row2 minus two lots of row 1"
I'm confused why my operation is not clear? -2R1 + R2 -> R2
am I using wrong notation?
tame narwhal
See here: https://math.stackexchange.com/a/509143
tame narwhal
I'm confused why my operation is not clear? `-2R1 + R2 -> R2`
I understood it FYI
dark stirrup
1 1 | 3
1 -1 | -1
warm canopy
I'm confused why my operation is not clear? `-2R1 + R2 -> R2`
Just a less common way to write it i would say, to me atleast
shadow lava
See here: https://math.stackexchange.com/a/509143
interesting! still the same point
shadow lava
Just a less common way to write it i would say, to me atleast
how would you write it instead?
warm canopy
Just with it flipped: R2 -> -2R1 + R2
timid silo
^
shadow lava
it's basically the same thing imo
warm canopy
I am not debating whether they carry the same info, just which is more common
shadow lava
I am not debating whether they carry the same info, just which is more common
I think I picked up the habit from this video (in timestamp) https://youtu.be/W95p0E-CB_s?t=1600
probably more specific here: https://youtu.be/W95p0E-CB_s?t=2591
dark stirrup
This is augmented form of
x+y=3
x-y=-1
When I add row 2 to row 1, I am first going to take advantage of the algebra property that if a=b, then a+c=b+c.
a is x+y, b is 3, and c is going to be -1.
(x+y)+(-1)=(3)+(-1).
Next, I'll replace -1 with (x-y) on the left side since they are equal.
(x+y)+(x-y)=(3)+(-1)
And just like that, I have added row 2 to row 1
upbeat plinth
the bottom half of the SE post is probably the best algebraic way to explain why the solution set doesnt change
shadow lava
the bottom half of the SE post is probably the best algebraic way to explain why...
this answer?
upbeat plinth
cwatson's link
shadow lava
cwatson's link
the screenshot is taken from the same link
which bottom half are you referring to?
it's a pretty big post
upbeat plinth
thats a different reply in the thread...
shadow lava
oh you mean bottom half of the first reply
as a quick aside, do we still have an issue on StackExchange with AI generated responses? or that has been resolved for the most part now?
upbeat plinth
try to stay focused
tardy epoch
try to stay focused
@shadow lava i encourage this as well.
warm canopy
I don't, I wonder if they did resolve the AI problem 
shadow lava
@upbeat plinth and @tardy epoch are AI bots
they don't want us asking these questions 😄
upbeat plinth
cut it out
shadow lava
.close
timid silo
A bit confused on the last 2
obtuse pebbleBOT
A bit confused on the last 2
warm canopy
What's 1 - 1/2?
timid silo
Half
warm canopy
So the first step is dividing by 1/2
obtuse pebbleBOT
timid silo
.reopen
obtuse pebbleBOT
✅
timid silo
Is what im doing now ok
<@&286206848099549185>
Well i hope i figure it out one day
.close
rugged notch
What is the minimum value of the magnitude of the sum of two vectors? I assume it’s the zero vector as they could cancel each other out but idk
obtuse pebbleBOT
What is the minimum value of the magnitude of the sum of two vectors? I assume i...
haughty coyote
In general yes
|u + v| >= | |u| - |v||
Can be deduced from the triangle inequality, and gives a reachable lower bound
regal jewel
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl number 2 there are 11 balls where 8 are yellow and 3 are black. In bowl number 3 there are a total of 10 balls where 5 are green and 5 are black. What is the chance of drawing 3 balls of different colors
obtuse pebbleBOT
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl n...
lime phoenix
Can someone give me a function/ algorithm that can calculate a circle and a rectangles collision?
I badly need it in my project
regal jewel
lime phoenix
oh sorry
regal jewel
np
lime phoenix
didn't see it's occupied
regal jewel
it was a coincidence
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl number 2 there are 11 balls where 8 are yellow and 3 are black. In bowl number 3 there are a total of 10 balls where 5 are green and 5 are black. What is the chance of drawing 3 balls of different colors
ancient jacinth
consider the chance of picking black in the first bowl, and then the chances of not picking black in the other 2 bowls
regal jewel
but there is a chance to get red in the first bowl
ancient jacinth
you can look at this case by case
if you pick black first
you could pick yellow and green in the other two bowls
if you pick red first
regal jewel
$2/8$
ancient jacinth
you have to either pick yellow and then green
or black and then green
Or yellow and then black
warm shaleBOT
紅卫兵，周
regal jewel
so do i look after how many combinations?
ancient jacinth
what do you mean?
ancient jacinth
4
regal jewel
so how should i proceed?
regal jewel
it didnt specify, but lets say the order doesn't matter
ancient jacinth
hmm
regal jewel
ok if its easier if the order matters, then lets proceed on that path
ancient jacinth
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl n...
1 2 3
regal jewel
what?
regal jewel
it didn't
ancient jacinth
i am more of a 123 then a 213 guy ykwim
ancient jacinth
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl n...
ya they did
bowl 1
regal jewel
,
ancient jacinth
they said bowl number 1 right
regal jewel
in the task, there were 3 pictures of bbowls
and the marbles laying inside
and i counted them
regal jewel
lmao
but anyways if the matters do matter, how should we proceed?
its possible to get $6/88/115/10$
warm shaleBOT
紅卫兵，周
regal jewel
and $2/88/115/10$
warm shaleBOT
紅卫兵，周
ancient jacinth
ancient jacinth
In bowl number 1 there are 8 balls, 6 of them are red and 2 are black. In bowl n...
consider the case where you choose black
find the probability of getting three different coloured balls
then consider the case where you choose red
regal jewel
which i have done above
ancient jacinth
the red part
regal jewel
why the red part?
regal jewel
that is the red part
ancient jacinth
the red part itself has 3 different cases
regal jewel
what?
ancient jacinth
no
regal jewel
what
ancient jacinth
R-> Y -> G
R -> B -> G
R-> Y -> B
calculate these probabilities and add
regal jewel
scrub?
ancient jacinth
dont forget the case in which you choose black
regal jewel
so for red it will be, $\frac{6]{8}*\frac{3}{11}*frac{5}{10} $
wait
chill
dont bully me
nope
ancient jacinth
regal jewel
.
ancient jacinth
warm shaleBOT
紅卫兵，周
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
regal jewel
ancient jacinth
$frac{6}[8}\* \frac{3}{11}$
$\frac{6}{8} * \frac{3}{11}$
warm shaleBOT
Blighter
regal jewel
wow
regal jewel
$\frac{6}{8} * \frac{8}{11}*\frac{5}{10}$
warm shaleBOT
紅卫兵，周
ancient jacinth
next case
wait which one is this
R-> Y -> G
or R -> Y -> B
you are adding these two right
regal jewel
wait a sec
ancient jacinth
B->Y-> G
R-> Y -> G
R -> B -> G
R-> Y -> B
solve for the probabilities of each of these cases and add
ancient jacinth
good job
"I dream of you almost every night
Hopefully i won't wake up this time"
ed sheeran ahh lyric
@regal jewel you gonna close the channel or.....
obtuse pebbleBOT
@regal jewel Has your question been resolved?
regal jewel
https://tenor.com/view/skeleton-smoking-skeleton-smoking-mk11-gif-24716013
so is the answer the red part and the black part added together?
ancient jacinth
ye
regal jewel
thanks
ancient jacinth
i think
regal jewel
so what did you get?
ancient jacinth
solve
ancient jacinth
think bro
obtuse pebbleBOT
@regal jewel Has your question been resolved?
warm shaleBOT
Result:
0.29545454545455
true talon
calc 3
robust sleet
What have u tried.
obtuse pebbleBOT
robust sleet
💀
obtuse pebbleBOT
Available help channel!
surreal estuary
if we know f(a)/f(b) for every a>b can we find what just f(x) is
obtuse pebbleBOT
if we know f(a)/f(b) for every a>b can we find what just f(x) is
civic zealot
you could probably define a piecewise function. Fix a particular value of b then get f(x) based on x>b and x<b
boreal light
what does this mean?
obtuse pebbleBOT
what does this mean?
boreal light
knotty crow
obtuse pebbleBOT
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Available help channel!
half pecan
obtuse pebbleBOT
half pecan
so i proved that T is linear
but P(x) is in PnR
but the transofrmation is P(x)x
which is in Pn+1(R) right
so does this mean it's not an operator?
warm canopy
what space are they wanting you to show it is an operator on
half pecan
what space are they wanting you to show it is an operator on
doesn't say
or sorry
vector space of polynomials
so i'm assuming Pn(R)?
warm canopy
do all polynomials live in Pn(R)?
half pecan
do all polynomials live in Pn(R)?
of n degrees or less
warm canopy
so Pn(R) is not the space of all polynomials
half pecan
so Pn(R) is not the space of *all* polynomials
P(R)?
warm canopy
that is a fine notation for the space of all polynomials sure
half pecan
that is a fine notation for the space of all polynomials sure
so then to prove that T is indeed an operator from P(R) to P(R)
do I just say that xP(x) + P'(x) is still contained in the vector space of all polynomials
wide star
What is the least optimal packing for 3 squares?
obtuse pebbleBOT
What is the *least* optimal packing for 3 squares?
tranquil sonnet
Wdym packing?
wide star
for some orientation of 3 squares take the smallest box it can fit in
the least optimal would be "what orientation of 3 squares need the biggest box"
tranquil sonnet
Area wise?
wide star
(the box also needs to be some square)
native inlet
the least optimal would be "what orientation of 3 squares need the biggest box"
well technically infinity 
do the boxes have to be touching?
proud trout
least packing of 17 squares for example
tranquil sonnet
So the sum of 3 diagonals of a square
wide star
least packing of 17 squares for example
(that's the most optimal)
tranquil sonnet
Anyways just lay out the three smaller squares so that their diagonals are collinear
native inlet
yes
My guesstimate would be to form an equilateral triangle with three of the edges then form a square on the outside
wide star
Anyways just lay out the three smaller squares so that their diagonals are colli...
thats boring
would it be like that for any amount of squares?
tranquil sonnet
Yes
wide star
so it would be?
1 square = side length 1
2 squares = side length 2root2
3 squares = side length 3root2
4 squares = side length 4*root2
etc?
tranquil sonnet
Yea
wide star
thats boring lol
proud trout
least packing of 17 squares for example
not in this case but this isnt definitively the most optimal, just the best representation out now
tranquil sonnet
Yea, that’s why the most optimal case is more discussed
tranquil sonnet
Maybe let the squares be in a rectangle? (greatest and least is defined with area)
wide star
how about if the squares have to be touching all 4 sides
tranquil sonnet
That could work
wide star
1 square = 1
2 squares = 2
3 squares = 2?
4 squares = ?
wait no
1 square = 1
2 squares = 2
3 squares = 2*root2
4 squares = ?
tranquil sonnet
I think I messed up but for 3 squares I got 2 sqrt6
wide star
I think I messed up but for 3 squares I got 2 sqrt6
how?
wide star
that was not what i was expecting
tranquil sonnet
if the sidelength of the small square is 1, the sidelenght of the big square is sqrt6 i think
wide star
the sidelength of small square is 1
tranquil sonnet
sorry typo
tranquil sonnet
oops i didnt see it had to be touching all 4 sides
obtuse pebbleBOT
@wide star Has your question been resolved?
lilac parcel
The question here was to find the radius of convergence, which i understand how they did it. However I was wondering if the answer of the limit (here its |x|) is always <1, every time we use the ratio test or how do we determine what the answer of the limit is inferior to
obtuse pebbleBOT
The question here was to find the radius of convergence, which i understand how ...
crystal solstice
The question here was to find the radius of convergence, which i understand how ...
The ratio test tells you you series converges if the value of the limit is less than 1. Here the only way it converges is if $|x|< 1$
But you can get other answers. For example the ratio test applied to the alternating harmonic series has a limit of 1, so it's inconclusive.
For the geometric series $\sum 2^n$ the limit is 2, so it diverges
warm shaleBOT
catGPT
wooden sparrow
.close
obtuse pebbleBOT
Available help channel!
wind panther
]
wind panther
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
soft terrace
How is the pension worked out in this question?
obtuse pebbleBOT
How is the pension worked out in this question?
wind panther
did you figure it out?
yes
obtuse pebbleBOT
@soft terrace Has your question been resolved?
soft terrace
<@&286206848099549185>
tardy epoch
How is the pension worked out in this question?
If 609.30 is what they each get, how much do they get combined?
soft terrace
If 609.30 is what they each get, how much do they get combined?
But that's the full pension, but since they earn over $292 don't they get less than full?
obtuse pebbleBOT
@soft terrace Has your question been resolved?
obtuse pebbleBOT
@soft terrace Has your question been resolved?
soft terrace
<@&286206848099549185>
obtuse pebbleBOT
@soft terrace Has your question been resolved?
obtuse pebbleBOT
@soft terrace Has your question been resolved?
soft terrace
<@&286206848099549185>
candid yarrow
Can you send the steps you tried?
soft terrace
Well I tried doing 609.3 x 2 and then minus that from half of 453 since it says 50 cents in the dollar, but that doesn't get me the right answer
I don't really understand this table and I can't find anywhere else that really uses it
@candid yarrow
candid yarrow
I don't really understand this table and I can't find anywhere else that really ...
What course is this from
soft terrace
What course is this from
Like what year? Year 11
candid yarrow
Like what year? Year 11
I’m guessing it’s an algebra problem and you don’t know anything beyond what the question tells you about pensions and personal income?
soft terrace
I’m guessing it’s an algebra problem and you don’t know anything beyond what the...
I believe this is all the information we have
candid yarrow
I believe this is all the information we have
Have you solved questions 19 to 21 yet?
soft terrace
They aren't about pension
candid yarrow
How is the pension worked out in this question?
It says here you can use the table to answer questions 18 to 21, so I was hoping you might get a clue from there
soft terrace
Oh the ones after yeah
soft terrace
It says here you can use the table to answer questions 18 to 21, so I was hoping...
Well it's not actually my textbook I'm helping someone else but I don't understand and haven't seen one like thus
candid yarrow
Have they solved questions 19 to 21 yet? If they have, hopefully question 18 is similar or contains similar terms
soft terrace
I'll ask thanks for the suggestion
timid silo
hybrid gull
?
vagrant wraith
what for
upbeat lantern
bro 😭
obtuse pebbleBOT
@soft terrace Has your question been resolved?
wicked bluff
Not to criticise but your 2 looks like the partial derivative sign, I couldn’t understand your notation however you can check your calculations with these:
V = Pi x (r)^2 x h
(r: radius, h: height)
SA = 2(pi x r^2) + 2Pi x r x h
zinc plaza
Yeah my bad, I write a lot of my numbers weird
wicked bluff
All good, it’s unique I guess 😁
wind panther
oh shi u do Jac plus too?
yeds
wooden anchor
same
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
uneven night
obtuse pebbleBOT
slow phoenix
Hello there!
obtuse pebbleBOT
Hello there!
warm shaleBOT
slow phoenix
the eqn of two circle are r = 4 cos (theta) & r = 4 sin (theta)
what im unsure is how are the "boundaries" determined here?
like i am not really sure how i shld come with the boundaries hehe i cant seem to visualise it correctly (hope i make sense)
urban ether
Do you have an answer for this?
slow phoenix
yep the 2nd pic attached is the answer sheet but theres no working which makes it a bitt difficult
slow phoenix
qns
slow phoenix
ans
slow phoenix
Do you have an answer for this?
if the answer pic is blur i can retake btw -
urban ether
Ah ok I got it, so I used x and y instead of theta which makes the boundaries 0 to 2
slow phoenix
ooh
how do u do that btw?
cld u show me the working hehe ^^
cus im not really sure based on what i shld get the boundaries or how exactly its derived lol
urban ether
So the area is bounded by the yellow circle and straight line. Do you know how to determine equation of the yellow circle first?
I can help u with the steps if u not sure
slow phoenix
So the area is bounded by the yellow circle and straight line. Do you know how t...
its given as 4 cos theta rite?
straightline is hmm
also apologies for late reply < 3
y=x?
slow phoenix
r^2=x^2+y^2 is the general form for a circle
ooh so we must place it in this way
urban ether
also apologies for late reply < 3
Don’t sweat it 👍
slow phoenix
haha ^w^ tyty so wait how do i change the r = 4 cos theta to the way u said it?
urban ether
ooh so we must place it in this way
Yeah, but since it’s moved to the right, we have to minus 2, making equation (x-2)^2+y^2=r^2,
slow phoenix
And then integrate
cld u write it out?
if its not too troublesome!
like i still dont get how i can get the boundaries " v "
@urban ether ^
urban ether
Ya sure give me a sec
slow phoenix
okii
urban ether
slow phoenix
but this doesnt involve double integral rite? How cld i do it with double integral
urban ether
Yeah it does, so I took the line integral from the circle integral
I could also write it like this
slow phoenix
but then u saw the ans sheet how they wrote right? if i wanna use that method how wld it be possible
urban ether
Waittttt nvm I see what you mean
obtuse pebbleBOT
@slow phoenix Has your question been resolved?
novel crystal
can someone explain i dont really understand
obtuse pebbleBOT
can someone explain i dont really understand
novel crystal
what happens to cos(x/4)?
plain stag
novel crystal
.close
obtuse pebbleBOT
Available help channel!
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
the first triangle isn't a right angle triangle
you should try finding the height of it using pythagoras
royal basin
could find the angle between the two 2-length sides with the law of cosines
timid silo
yup, you are correct
the area of the big triangle is already less than 1
,calc sqrt(7)/4
warm shaleBOT
Result:
0.66143782776615
alternatively, you can bound the larger triangle area by 2 since two legs are already given
so area is bounded by 2-1
yeah
ig that doesnt help
yeah
timid silo
Result:
```
0.66143782776615
```
I guess calculating the area of the big triangle is necessary
np
wooden belfry
aaaaa how is this not 39?
obtuse pebbleBOT
aaaaa how is this not 39?
wooden belfry
is it 129 then?
timid silo
S __ E means the bearing is taken from South towards East
wooden belfry
so?
timid silo
so it should be the angle between south and A
wooden belfry
the angle between south and a is 39
wooden belfry
i just guessed the answer and i got it correct
it was 51
but idk why its 51
cus like
timid silo
find the angle between south and A as marked
wooden belfry
cus on this question i put 41 and it said correct
wooden belfry
cus on this question i put 41 and it said correct
this a diff question btw
so idk why that one is different
timid silo
since S comes first, the angle is taken wrt to the south axis
S 41 W means 41 degrees west of south
wooden belfry
what is wrt
timid silo
with respect to
timid silo
find the angle between south and A as marked
S 51 E means 51 degrees east of south
wooden belfry
sorry i am confused
candid yarrow
sorry i am confused
which part are you confused about?
wooden belfry
cus on this question i put 41 and it said correct
and on this question it is 41 degrees so what is it that makes that other question different like ykwim
candid yarrow
and on this question it is 41 degrees so what is it that makes that other questi...
Because you start from south in the 41° question, but in the other one you start from east
candid yarrow
and on this question it is 41 degrees so what is it that makes that other questi...
doing another question or three might help you see the difference
wooden belfry
Because you start from south in the 41° question, but in the other one you start...
so how do i know when to use a diff technique
candid yarrow
so how do i know when to use a diff technique
wooden belfry
so if it were at the blue line do we use the same technique for the 51 degrees one?
wooden belfry
and if it were at north west do we use the original angle given? like the 41 degrees one
ohhh okay
candid yarrow
aaaaa how is this not 39?
do you understand how to do this type of question now?
wooden belfry
kind of
candid yarrow
kind of
if you’re not sure, you should do some more questions to test your understanding
wooden belfry
yes thank you for helping me
candid yarrow
yes thank you for helping me
you can .close this channel and .reopen it if you have any more questions
wooden belfry
yes ill leave it open for now in case i run into more problems
obtuse pebbleBOT
@wooden belfry Has your question been resolved?
hoary onyx
A bisector drawn to one side of an isosceles triangle divides the perimeter of the triangle into parts of length 12 cm and 9 cm. Calculate the length of the base of the triangle if it is known that it is greater than the length of the lateral side.
obtuse pebbleBOT
A bisector drawn to one side of an isosceles triangle divides the perimeter of t...
crimson breach
A bisector drawn to one side of an isosceles triangle divides the perimeter of t...
you can use bisector theorem
as if AD is the bisector of angle A and D is on BC (BD/CD =AB/AC)
hoary onyx
A2B2 = 10cm. How long are the other slats? A1B1 = ?cm, A3B3 = ?cm, A4B4 = ?cm.
The median line of a triangle is parallel to one side of the triangle and equal to its half.
oak bear
You can use variables to solve that
name first all the line segments that are the same
like a2 - a1 = x
so all of the same sides are also x
Like this
And just apply proportionality theorem
so a1-b1 = 5
and just do the rest
hoary onyx
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ruby elm
I have started and got an answer but its wrong.
obtuse pebbleBOT
I have started and got an answer but its wrong.
ruby elm
