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#help-17
vocal sleetBOT
Available help channel!
simple basin
I have a simple question, why are r=sintheta and r=costheta grahs are circles?
meager shoal
by conversion from cartesian coor?
or u can interpret sin as the y-value of a unit circle
same goes for cos
vocal sleetBOT
@simple basin Has your question been resolved?
simple basin
or u can interpret sin as the y-value of a unit circle
okay that makes a lot of sense
thanks
raw sage
I somehow missed 1 x intercept and idk how to get it. The intercept I’m missing is -5piover12
vocal sleetBOT
I somehow missed 1 x intercept and idk how to get it. The intercept I’m missing ...
raw sage
I feel like I went wrong here but idk
vocal sleetBOT
@raw sage Has your question been resolved?
strong isle
I somehow missed 1 x intercept and idk how to get it. The intercept I’m missing ...
First of all, the last two solutions for x + π/4 are incorrect. You cannot - π or + π to π/6 and 2π - π/6. Luckily with the second last solution thanks to the domain restriction you eliminated that one, but the last one did satisfy the domain restriction despite being incorrect which is why got an incorrect answer of 7π/12. And you also forgot to consider from the more negative end in the beginning, like for example x + π/4 = π/6 - 2π or x + π/4 = - π/6 or x + π/4 = -π/6 - 2π. Clearly the last one doesn’t satisfy the domain restriction, neither would the first one, but the second one does fit the domain restriction which becomes your missing -5π/12. So your x intercepts should look like { -5π/12, -π/12, 19π/12, 23π/12 }
raw sage
But because I wanted to fit in the left end of the domain (the -pi) I though I can just minus pi like I did with the 3rd and 4th one
You know how I just plus 2pi
How do I get -pi then
If I wanted to do it that way instead of the 2npi method
strong isle
But because I wanted to fit in the left end of the domain (the -pi) I though I c...
Uh wdym. In the third and fourth one you either added or subtracted 2π which is the correct thing to do. Adding or subtracting π to the trivial solutions does not work however. And you can’t do what you said btw
strong isle
If I wanted to do it that way instead of the 2npi method
You have to do the 2kπ method. There’s not really any shortcut
raw sage
Oh ok
So not even minus 2pi if the domain was [-2pi,2pi]
Only if it’s [0,2pi]
I can add 2pi
strong isle
So not even minus 2pi if the domain was [-2pi,2pi]
I’m sorry, I’m bit confused as to what you mean here
strong isle
Only if it’s [0,2pi]
What you do is find the trivial angles within this domain instead. Then next thing is to use the 2kπ method to find solutions in general and find which k for each trivial solution works within the domain restriction that you had in the problem
strong isle
So not even minus 2pi if the domain was [-2pi,2pi]
Like say if this was your domain in the problem instead
strong isle
Only if it’s [0,2pi]
And you found your trivial angles from this domain
strong isle
I can add 2pi
You can then only subtract 2π from your trivial angles.
raw sage
Subtract?
strong isle
Subtract?
Because the domain in the new problem is from [-2π, 2π]. You find your trivial angles from [0, 2π]. If you add 2π or anything greater to your trivial solutions, it’s out of the original domain. If you subtract 2π from your trivial solutions it has to be within [-2π, 2π] which works. If you subtract anything more though then it doesn’t work.
This is all using the 2kπ method btw
strong isle
But I can’t do that with -pi or anything greater than -2pi
Sorry, what do you mean? What can’t you do?
raw sage
Like if the domain was [-pi,2pi] I can’t subtract pi
Only if it’s [-2pi,2pi] then I can subtract 2pi
strong isle
Like if the domain was [-pi,2pi] I can’t subtract pi
From what though? It depends on what trivial angles you find within [0, 2π]. And you cannot subtract π to begin with, it doesn’t really work like that. I think it’s much easier finding your trivial angles and then using the 2kπ method
strong isle
Only if it’s [-2pi,2pi] then I can subtract 2pi
Yes that’s true
Sorry if I might be confusing you
raw sage
Ok I’ll try and use 2kpi method. But i get confused sometimes when i use it, like idk when i should keep the 2 in 2kpi or when i need to remove it
And sometimes it gets changed when I have expressions I need to bring to the right
Or I somehow get it wrong
I dunno I’ll see how I go with my next question
Oh and deciding what numbers to use as k gets annoying
strong isle
Ok I’ll try and use 2kpi method. But i get confused sometimes when i use it, lik...
You always use the 2kπ method. It works all the time. The only time it doesn’t work is when it doesn’t fit the domain restriction, otherwise it always satisfies the equation no matter what.
raw sage
Because I do all that working out just to find out it doesn’t fit
strong isle
I dunno I’ll see how I go with my next question
Okay
strong isle
Oh and deciding what numbers to use as k gets annoying
Yeah it is indeed annoying and exhaustive
raw sage
And time consuming esp in an exam
strong isle
Because I do all that working out just to find out it doesn’t fit
Lol. That’s what happened to be the first time, but the more problems I did the better I got at making mistakes
raw sage
So was just trying to find easier way
strong isle
And time consuming esp in an exam
That’s why I kinda despise those questions. Too much working out needed
raw sage
Yea I’m trying to do as many problems as I can now so hopefully I’ll figure it out the more I do
I literally have an exam on monday so im lowk cooked
Anyway thank you for your help
strong isle
Yea I’m trying to do as many problems as I can now so hopefully I’ll figure it o...
That’s good.
strong isle
I literally have an exam on monday so im lowk cooked
Best of luck on the exam. And you’re not cooked, I’m sure you will do well. You just made tiny errors that can easily be prevented
strong isle
Anyway thank you for your help
No problem. And btw I’m also pretty bad at trig, I really need to brush up too
raw sage
Thank you! I hope so, I’ve been drowning myself in problems to get a hang of it
strong isle
Thank you! I hope so, I’ve been drowning myself in problems to get a hang of it
All good. And maybe don’t do too many problems. It just gets way too frustrating and you might make mistakes the more problems you do. Just do an adequate number of problems
Yeah that’s true
raw sage
lol
strong isle
Have a look at this table for future reference. It is indeed very useful
strong isle
Thanks again
No problem
raw sage
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
fiery path
oh okay okay , but how do i reduce the overcounted one ?
vocal sleetBOT
oh okay okay , but how do i reduce the overcounted one ?
@fiery path Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
daring panther
I Just finished an Applied Mathematics Exam for WJEC As level, and there was a 2 mark question “Using V=u+at and S=1/2(u+v)t, show S = ut + 1/2 at^2” and the method your meant to do is substitute one into the other, but what i did was integrated v=u+at, with respect to t to get, S= ut+1/2at^2 + C, then set it equal to 1/2(u+v)t and solved to find C and showed that C was 0. Was what I did mathematically correct?
vocal sleetBOT
I Just finished an Applied Mathematics Exam for WJEC As level, and there was a 2...
edgy kayak
well did the question say "use substitution"
vocal sleetBOT
@daring panther Has your question been resolved?
candid magnet
vocal sleetBOT
candid magnet
If i have a way to i tegrate just the denominator without the ln2x being there
Thats also fine
pure marten
,w integrate 1/(sqrt(x(x+1)(2x+1))
twin meteorBOT
jewels!
pure marten
I'm trying to see if there's some sort of similarity
,w integrate ln(2x)/sqrt(x(x+1)(2x+1)) from 0 to infinity
twin meteorBOT
candid magnet
<@583225537288208394> does it have a closed form answer
[ln2 /4√2pi] gamma 1/4 ^ 2
candid magnet
**jewels!**
can u share the sol for this one ?
candid magnet
this one also im pretty sure first step is x->1/2x
pure marten
$\frac 18 \int_0^{\infty} \frac{\ln x}{x^2 + x + 1} + \frac{\ln 2}{8}\int_0^{\infty} \frac{\dd{x}}{1 + x + x^2}$
twin meteorBOT
jewels!
pure marten
The left integral is 0, if you sub x --> 1/x
And the right integral is just an arctan
pure marten
this one also im pretty sure first step is x->1/2x
You know how it's done?
candid magnet
You know how it's done?
if u do that ln x gets cancelled and u just left witht he denominator im stuck after that
pure marten
Hmm
candid magnet
int 1/√x√x+1√2x+1 *ln2/2
pure marten
$\frac{\ln 2}{2} \int_0^{\infty} \frac{\dd{x}}{\sqrt{x(x+1)(2x+1)}}$
why is this typesetting so shitty
anyways
Maybe you should complete the cube
twin meteorBOT
jewels!
pure marten
,w expand x(x + 1)(2x + 1)
twin meteorBOT
candid magnet
Maybe you should complete the cube
i couldnt get anythign useful 
pure marten
you already tried it?
Since there is a lemniscate constant it is tempting to somehow relate this to its equation
candid magnet
you already tried it?
ye but i couldnt get anything i was familiar
pure marten
I see
candid magnet
idk lemniscate constant
pure marten
$\varpi = \frac{\Gamma (1/4)^2}{2\sqrt{2\pi}}$
twin meteorBOT
jewels!
pure marten
it is the ratio of the perimeter to the diameter of a figure called bernoulli's lemniscate
So if you somehow convert this into an integral the represents this length, you're done
vocal sleetBOT
@candid magnet Has your question been resolved?
vocal sleetBOT
autumn chasm
@candid magnet reopen it this a good question imma try it
vocal sleetBOT
Available help channel!
willow quiver
once again! no idea where to start 💔 the only force i know is weight force pulling them down
willow quiver
they say other 2 forces but i only know weight
tawny nacelle
normal force, kinetic friction
tawny nacelle
if there was just weight (gravity), the car would be accelerating into the ramp
tawny nacelle
the force pointing perpendicularly out of the ramp is called the normal force
tawny nacelle
the car is also experiencing friction to keep it from sliding down the ramp
which points up the ramp, as depicted in the diagram
tawny nacelle
mhm
short bone
short bone
Pls ping me if anyone got anytg I will see it after my classes
vocal sleetBOT
@short bone Has your question been resolved?
pure marten
Did you solve for x and y in terms of s, t, and r?
willow quiver
i need a video recommendation on how to draw vectors
vocal sleetBOT
i need a video recommendation on how to draw vectors
willow quiver
this is the question
and i just cant wrap my head around on how to draw the vectors!
this is the answer for it btw
like why is there no angle over there?
vocal sleetBOT
@willow quiver Has your question been resolved?
rapid grotto
Can anyone help?
vocal sleetBOT
Can anyone help?
golden herald
What have you tried
rapid grotto
I tried to plug all the value applicable for the given interval
But i keep getting many solutions
But ans is only one solution
By Given interval
Gif x would be 0,1,2 right
golden herald
Yeah
rapid grotto
But i am missing something 😭
rapid grotto
I got x is 0 and 4 by plugging x is 0
And
Other
4 solution by plugging x as 1 and 2
golden herald
Well what are those 4 other solutions
Are you sure they're valid
Also
"$x$ is 0 and 4" however the question specifies that $x\in [0,2]$
Keep that in mind
twin meteorBOT
rapid grotto
"$x$ is 0 and 4" however the question specifies that $x\in [0,2]$
Ouu I forgot that part
To check
golden herald
Yeah, if you do that you should get only 1 valid solution
rapid grotto
Welp
Now i understood
The only one that follows is x=0
And hence sols no is 1
All other outside the range
Are*
.close
vocal sleetBOT
rapid grotto
Yeah, if you do that you should get only 1 valid solution
Tq for help I forgot considering the range in the output
I thought it only applied for input gif x
golden herald
Tq for help I forgot considering the range in the output
I thought it only appl...
Yeah nice gjob
rapid grotto
Yeah nice gjob
Bruh I am quit ashamed to miss such little fact
I was thinking all other things except that
golden herald
Bruh I am quit ashamed to miss such little fact
I was thinking all other things ...
Yeah it happens a lot. I always tell myself to make sure I reread the question multiple times to make sure I'm not missing something 😅
vocal sleetBOT
Available help channel!
tulip temple
I was trying to understand the radical axis of two circles. Putting the definition aside, radical axis is a straight line. It is obtained by substracting two circles. But the circle formula is essentially just the distance formula. So we are substracting the squares of distances. But why does subtracting the squares of two distances give a straight line. I tried to understand it as a difference of areas of two squares. But after substracting, how is the leftover area a straight line?
vocal sleetBOT
I was trying to understand the radical axis of two circles. Putting the definiti...
tulip temple
And finally, why does every point on this line have equal tangents to both circles
slim birch
I was trying to understand the radical axis of two circles. Putting the definiti...
one way is to imagine finding the points of intersection as usual
subtracting both circle equations is similar to elimination
and the result is a linear equation
which means it's the equation of the line which contains all the points of intersection
slim birch
I was trying to understand the radical axis of two circles. Putting the definiti...
and if you want to imagine it as subtracting the squares of distances
in this case it's slightly different
cuz the point is not just one
it's a set of points
atomic pine
I was trying to understand the radical axis of two circles. Putting the definiti...
"subtacting circles" is ambiguous. It is specifically, when you write two circles into the form of
$$(x-a_1)^2+(y-b_1)^2=c_1\quad\text{and}\quad (x-a_2)^2+(y-b_2)^2=c_2$$
then the radical axis is
$$(x-a_1)^2+(y-b_1)^2-(x-a_2)^2-(y-b_2)^2=c_1-c_2$$
This works if we write the formula in this form.
slim birch
it's a set of points
which forms a circle
twin meteorBOT
qwertytrewq
slim birch
which forms a circle
(x, y)
atomic pine
**qwertytrewq**
and you can check that all the x^2, y^2 terms cancels out so you are left with an equation of a line.
valid palm
**qwertytrewq**
but why is substracting squares of distances giving out a line?
atomic pine
but why is substracting squares of distances giving out a line?
i don't really get what you mean by subtractive squares of distances.
its just that x^2 terms and y^2 terms cancels out so you have no degree 2 terms
thus a line
valid palm
alright so
isnt the circle formula just a distance formula?
it is the distance from the center to a variable point such that the distance is the raidus
therefor we get a circle
now substracting the equations
we are essentially substracting the squares
of distances
Now why is THIS a line?
atomic pine
**qwertytrewq**
I want to emphasize that we need to specifically pick equations of those form
atomic pine
I understand that
if you model the first circle using $$(x-a_1)^2+(y-b_1)^2=c_1$$
and write the second circle as $$\frac{1}{2}(x-a_2)^2+\frac{1}{2}(y-b_2)^2=\frac{1}{2}c_2$$
IF you subtract the two equations, you no longer get a line
twin meteorBOT
qwertytrewq
atomic pine
Now why is THIS a line?
it is because we pick a particular way to represent it that we get a line
specifically choosing a way to represent it, so that after we subtract the two equations, x^2 and y^2 vanishes
valid palm
So are you trying to say that the radical axis is not a line?
atomic pine
So are you trying to say that the radical axis is not a line?
no im saying "subtracting two circle" is ambiguous
valid palm
but substracting two circles is just the radical axis
atomic pine
but substracting two circles is just the radical axis
again "subtracting two circles" is ambiguous, it should really be "subtracting the equation of two circles in this particular way" gets you the radical axis
as you see, I gave you two different ways to subtract two circles
they give very different results
valid palm
but whyyyy
atomic pine
but whyyyy
the explanation is solely algebraic: its nothing more than x^2 and y^2 cancels out
atomic pine
**qwertytrewq**
you look at the difference equation there
and you look at whether there is a $x^2$ term, you would realize that there are none, the one $x^2$ term in $(x-a_1)^2$ gets canceled out with $(x-a_2)^2$.
twin meteorBOT
qwertytrewq
atomic pine
**qwertytrewq**
but you look at the second difference
you realize that the x^2 term DOES NOT cancel out
valid palm
yeah yeah i understood the reason why straight line comes
still i dont understand why is it a straight line tho
hehe
atomic pine
it really comes down to picking a specific way to represent the circle. becuase representing the circle in this way forces x^2 term to dissapear and y^2 term to dissapear
valid palm
im kind of getting why substracting two equations isnt the same as substracting the distances
Well how does representing
atomic pine
im kind of getting why substracting two equations isnt the same as substracting ...
can you be a bit precise with what you mean by "subtracting the distances"?
valid palm
completely change the result tho
valid palm
**qwertytrewq**
ok so look at the right hand side
that is just the square of radius of first circle
minus the square of
radius of second circle
radius is just a geometric line segemnt
so substracting two distances, will eventually give you a distance
But then again, substracting two equations isnt same as substracting the actaul distances
that is what i understood from your explanation
atomic pine
radius is just a geometric line segemnt
i don't get this: "radius is just a geometric line segment"
distance is a measure of the length of a line segment, it is not the same as a line segment
valid palm
here
bigger line minus smaller line
the part left is c2-c1
not exactly because its the difference of squares of distances
so it is something like
atomic pine
right, but by reducing to this, you lose all info about where the points in the 2D graph should lie
you are just talking about a number
valid palm
atomic pine
distance does not contain any information about where point lies: so you cannot deduce information about whether the ending result is a line or not
valid palm
im thinking its like a vector from some point
atomic pine
im thinking its like a vector from some point
then you have to specify from where?
atomic pine
to which direction?
atomic pine
idk man:c
im under the impression it is these small imprecise notions without justification and evetually led to some erroneous intuition
valid palm
yeah definitely
atomic pine
like if you have a circle of radius 3, and a circle of radius 2
valid palm
well then why is it a line
atomic pine
how do you meaninfully represent the value "3^2-2^2=5" on the graph?
valid palm
lets try the think that
atomic pine
**qwertytrewq**
do you get why subtracting the two equation there gives you a line?
valid palm
nah thats the whole point
what in that 2d space are we actually substracting when we susbtract one equation from the other tho?
atomic pine
nah thats the whole point
I mean, do you get my argument that proves that it is a line?
you just expand and subtract the equation
you get something like cx+dy=e which is a line
valid palm
well yeah thats the algebraic way
but what does it mean geometrically?
substracting two circles
what is that
atomic pine
how do you meaninfully represent the value "3^2-2^2=5" on the graph?
but then to speak of "geometric way" of viewing this "subtraction of circle" i want you tell me what you mean byt those?
valid palm
because isnt that what it is
equation of a circle
so when you substract equations
you substract circles
atomic pine
substracting two circles
honestly, I don't think there is much intuitive way of viewing "subtraction of circles"
valid palm
that is what im afraid is true
atomic pine
it is algebraic in nature: you subtract the circle equations
paper depot
i think there might be a way to phrase it geometrically, but "subtracting two circles" is not it
valid palm
somehow substracting two lines gives you a new line ig
atomic pine
because i dont know what it means to even substract two lines
yeah subtracting two lines wouldn't make much sense either, unless you are talking about vectors
valid palm
but then it does give you a line
paper depot
you have two circles with centers O_1, O_2 and radii r_1, r_2.
valid palm
if it isnt the same line. If it is that is just 0=0
valid palm
you have two circles with centers O_1, O_2 and radii r_1, r_2.
mhm
atomic pine
somehow substracting two lines gives you a new line ig
i don't get this? wdym by subtracting two lines gives you a new line
paper depot
their equations, in terms of the variable point $X=(x,y)$, are: $$XO_1^2 = r_1^2 \quad\mbox{and}\quad XO_2^2 = r_2^2$$
twin meteorBOT
Ann
valid palm
i don't get this? wdym by subtracting two lines gives you a new line
like 3x + 2y = 5, 2x = y = 6 substract them. you get x = y = -1
that is a line
paper depot
subtracting these gets you $$XO_1^2 - XO_2^2 = r_1^2 - r_2^2$$
twin meteorBOT
Ann
atomic pine
like 3x + 2y = 5, 2x = y = 6 substract them. you get x = y = -1
you mean 2x+y=6?
valid palm
you mean 2x+y=6?
yeah yeah mb
atomic pine
2x=y=6 is not a line
paper depot
now hm how do i explain that XO1^2 - XO2^2 is a "linear" function of the coords of x...
atomic pine
yeah yeah mb
again, subtracting here is ambiguous: 1.5x+1y=2.5 represents the same line as 3x+2y=5, but yields completely different result when you subtract with 2x+y=6
atomic pine
no it does not?
$(1.5x+1y=2.5)-(2x+y=6)$ gets you $-0.5x=3.5$
meawhile $(3x+2y=5)-(2x+y=6)$ gives you $x+y=-1$
twin meteorBOT
qwertytrewq
atomic pine
you are subtracting the same lines, but you get different results. So your definition of "subtract two lines" is inherently ambiguous
you can't subtract lines
you can't subtract circles
valid palm
damn
atomic pine
should be the takeaway here
atomic pine
understood
only "subtracting the equations" makes sense
atomic pine
only "subtracting the equations" makes sense
but there are many equations that may represent the same thing so you need to be careful, and fix a way to represent the line/circle
atomic pine
np
atomic pine
.close
bronze vapor
is the rank of the matrix 3?
0 0 0 0
1 2 3 4
0 0 1 0
0 3 5 2
vocal sleetBOT
is the rank of the matrix 3?
0 0 0 0
1 2 3 4
0 0 1 0
0 3 5 2
bronze vapor
if having a row of 0's in the top doesn't matter to the rank of the matrix i mean
flat lava
same
bronze vapor
so it is 3?
heavy yoke
the simplest way to tell is to put it into row echelon form
vocal sleetBOT
@bronze vapor Has your question been resolved?
oak magnet
if having a row of 0's in the top doesn't matter to the rank of the matrix i mea...
Its the number of non nul element on the diagonal
So if you swap the rows
You will have what you found indeed
vocal sleetBOT
vocal sleetBOT
Available help channel!
elder tangle
Illustrate the representation of irrational numbers on number line
Can someone show me how to do this
paper depot
Illustrate the representation of irrational numbers on number line
Can someone ...
that is kind of an odd question...
like you could try and draw something like an interval but dotted with holes or something
but i personally actually dont know what kind of picture is expected of you
elder tangle
I don't know myself 
paper depot
can you post a screenshot of the question
and maybe the other questions on your homework
elder tangle
Alr
little ivy
Illustrate the representation of irrational numbers on number line
Can someone ...
U can do this with help of right angle triangle
Like it depends what irrational no. U want to on no. Line
vocal timber
Well i remember there is a procedure you have to follow in order to show any rational number on number line for example √2,√5etc
elder tangle
can you post a screenshot of the question
There are actually no pics
little ivy
If u want to ✓2
Take 1 unit isorightangle triangle
paper depot
send a pic of the questions themselves
elder tangle
send a pic _of the questions themselves_
Why tho
vocal timber
Consider a unit square with any name OABC lets say, with each side one unit in length then you can see by the Pythagoras theorem that OB = √(1²+1²) = √2.
Now you can transfer this onto no. Line
Smh like this
Make sure that the vertex O coincides with zero
You may use a compass with centre and radius OB and draw an arc intersecting the number line at the point P then P corresponds to root 2 on the number line
hope this helps
Similar for more irr nos
Just add them on top of this right triangle as considering base
elder tangle
Just tell bro
Tasks:
line and app
in solving real-life mathematical problems.
Explore the concept of real numbers by explaining their classification, properties and decimal representation.
➤ Illustrate the representation of irrational numbers on number line. > Rationalisation of irrational numbers.
Analyse the significance of Real Numbers in real-life situations.
Assignment 2:
Objective: To construct a square root spiral visually representing square roots from √1 to√20 using geometric methods such as right angled triangles. The aim is to provide a clear understanding of irrational numbers and the Pythagorean theorem.
Task:
› Construct a square root spiral to represent the square roots from √1 to √20. Highlight the perfect squares like √1, √4, √9 and √16.
There is one more but I don't need any help with jt
It
vocal timber
For root spiral consider √2 as base and other two sides of 1 unit and repeat till √20 ig
paper depot
Assignment 2:
Objective: To construct a square root spiral visually representing square roots from √1 to√20 using geometric methods such as right angled triangles. The aim is to provide a clear understanding of irrational numbers and the Pythagorean theorem.
ok so it's not irrational numbers in general but specifically square roots of whole numbers that you need help constructing?
little ivy
ok so it's not _irrational numbers in general_ but specifically _square roots of...
It's clearly says do all ✓1 to ✓20 and highlight those
paper depot
It's clearly says do all ✓1 to ✓20 and highlight those
yeah i was confused by the wording that OP sent first
i was thinking that he might have been expected to sketch the set of all irrational numbers
vocal timber
yeah i was confused by the wording that OP sent first
Why my name is OP?
paper depot
I have seen you taking this name for me indirectly...
when it's your question
then you are the original poster
little ivy
Owner of problem
paper depot
Owner of problem
Original Poster. it stands for Original Poster.
little ivy
Original Poster. it stands for Original Poster.
Not in my dictionary
bitter pilot
Not in my dictionary
bad dictionary
little ivy
bad dictionary
It is
bitter pilot
my condolescenes
little ivy
my condolescenes
Thanks
vocal sleetBOT
@elder tangle Has your question been resolved?
chilly widget
Consider a unit square with any name OABC lets say, with each side one unit in l...
Is that ncert?
elder tangle
OP means Original Poster, in this case <@1093938130740051999>
Oki
elder tangle
Is that ncert?
Yeah
chilly widget
Hehe
hidden turret
elder tangle
Wait
vocal sleetBOT
@elder tangle Has your question been resolved?
vocal sleetBOT
@elder tangle Has your question been resolved?
vocal sleetBOT
@elder tangle Has your question been resolved?
sharp pilot
Google it and you will get it
vocal sleetBOT
@elder tangle Has your question been resolved?
dusty galleon
Let $f: A \to B$
My book says B is the codomain and $R={f(x) | x \in A}$ is the range
Is there a difference between codomain and range beyond $R \subset B$ but $R=B$ is not nessecarily true?
vocal sleetBOT
Let $f: A \to B$
My book says B is the codomain and $R=\{f(x) | x \in A\}$ is th...
twin meteorBOT
Player_X_YT
dusty galleon
my book keeps stressing the differences but I don't get why
heavy yoke
the difference is as you said that the range is a subset of the codomain
it's useful to use the codomain when defining a function since the range tends to be harder to pin down
hard atlas
take a function like f(x)=e^arctan(sqrt(x-cos(x)))/(x^2-13 sin(x)) or something. that obviously looks hideous and who knows what the range is. but its easy to just write down R as the codomain
the point of the codomain is just to tell you what kind of outputs you are expecting
real numbers, integers, complex numbers, ...
dusty galleon
so for $f(x)=\frac{1}{x}$ and $A=\mathbb{Z}$ then $R=\mathbb{Q}$ but you could say $B=\mathbb{R}$ or $B=\mathbb{C}$?
twin meteorBOT
Player_X_YT
dusty galleon
for x != 0
silk osprey
range isn’t Q
heavy yoke
but R is not Q here, 2/3 is not included for example
but that's a good example of where it would be easier to set B = Q since that's the sort of number you're expecting
hard atlas
tho of course there would be nothing wrong with having B=R or B=C or some other set
dusty galleon
ok i get it
hard atlas
the codomain is often far from unique
nimble heath
How do they do this?
vocal sleetBOT
How do they do this?
pallid zenith
nimble heath
Yeah here is the whole problem
I also havbe no idea how they go from log to ln in the last step
oak magnet
2x*log(6) = log(60/7)
2*log6 = log36
Log and ln are probably two names for the same thing no ?
lone dock
Yeah here is the whole problem
doesnt really matter both ln and log will give the same thing
nimble heath
That was never the case before
lone dock
Log and ln are probably two names for the same thing no ?
log is usually for base 10
oak magnet
log is usually for base 10
Sure but some use it for ln
lone dock
ye sometimes
nimble heath
@lone dock yes that was always the case
lone dock
doesnt really matter both ln and log will give the same thing
.
both are the same thing
the base doesnt matter
nimble heath
@oak magnet where did you get "2*log6 = log36"?
nimble heath
@oak magnet right, but where was the term log(6^2)?
nimble heath
Exponents
nimble heath
O
nimble heath
I am on pc shrug
civic otter
Use Windows + .
nimble heath
O thats spiffy, but I have to go through it
civic otter
Use Windows + .
With this you get access to a huge amount of characters, including emojis, math symbols, greek and other languages letters and many other things, also phonetic symbols iirc
nimble heath
OK tysm guys ho do I close?
oak magnet
!done
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
nimble heath
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
left portal
how is it possible that a basis of R^2[X] is dim 3 and consecuently R^n[X] is dim n+1 for n < infty
vocal sleetBOT
how is it possible that a basis of R^2[X] is dim 3 and consecuently R^n[X] is di...
left portal
if you are asken to prove a basis of R^n[X] is dim n+1 how would u do it
hybrid flicker
if you are asken to prove a basis of R^n[X] is dim n+1 how would u do it
what do elements of R^n[X] look like
left portal
{1, x, . . . x^n}
hybrid flicker
{1, x, . . . x^n}
well it's a combination of those polynomials yeah
they make a basis
how many of them are there
hybrid flicker
cardinality is n + 1 of the basis
So the dimension of R^n[X] is n+1 @left portal
left portal
yes, I get the general rationale, what about putting it into a proof?
hybrid flicker
well it's all about showing {1,x,...,x^n} is a basis of R^n[X]
and isn't that basically the definition of that space?
left portal
I think so, ye
oak magnet
Its just independant vectors and by definition of polynome can generate any n-th degrees polynome so its a basis
left portal
I think its fine
bitter pilot
well it's all about showing {1,x,...,x^n} is a basis of R^n[X]
wouldn't this assume the dimension of R^n[x] already?
oak magnet
Showing basis don't neccessarly require the dim
bitter pilot
i see
oak magnet
D'accord
opaque shell
vocal sleetBOT
gritty sage
vocal sleetBOT
@opaque shell Has your question been resolved?
versed raft
question what do they use theta, alpha, beta, and phi for in precalculus trigonometry
vocal sleetBOT
question what do they use theta, alpha, beta, and phi for in precalculus trigono...
vocal sleetBOT
@versed raft Has your question been resolved?
kind light
question what do they use theta, alpha, beta, and phi for in precalculus trigono...
because it usually becomes easier to distinguish variables of length and angles
vocal sleetBOT
vocal sleetBOT
Available help channel!
frigid nexus
Anyone know what I can do from here to prove that last line for question iii coz I put it into my calc and it’s true but I don’t know how to prove that
vocal sleetBOT
Anyone know what I can do from here to prove that last line for question iii coz...
@frigid nexus Has your question been resolved?
chilly widget
Anyone know what I can do from here to prove that last line for question iii coz...
Make cos25π/9 cos 7π/9
frigid nexus
Make cos25π/9 cos 7π/9
oh ok and then do i like do like sum to products or osme
chilly widget
Yea
frigid nexus
is there a way to know which two i choose to turn into products or should it work either way
chilly widget
Yea cos5π/9 and cos7π/9 will work
Because one of the terms is cosπ/9 .
And you can talk that out common and proceed
frigid nexus
ah ok
uh btw why are we able to convert cos 25pi/9 into cos 7pi/9
oh wait did we just subtract 2pi and make it within the domain of cos
chilly widget
25π/9 = (18+7)π/9 = 2π + 7π/9
chilly widget
oh wait did we just subtract 2pi and make it within the domain of cos
Yea
frigid nexus
yea ok thanks
twilit ocean
you can also ||note that certain combinations of the original sin^2 angles sum into convenient angles, then you might just need sum of angles formulas||
vocal sleetBOT
frigid nexus
.reopen
vocal sleetBOT
✅
frigid nexus
you can also ||note that certain combinations of the original sin^2 angles sum i...
what sum of angles formula are you talking abt?
also i got to like cos 2pi/3 = -1/2 can i just say thats true or do i have to prove that if so how
wait nvm ty for ur help yall
.close
vocal sleetBOT
silk osprey
@frigid nexus nice name bro
vocal sleetBOT
Available help channel!
silk sparrow
solve : dy/dx+ysinx=e^cosx
vocal sleetBOT
solve : dy/dx+ysinx=e^cosx
pure marten
Have you made a start?
graceful abyss
solve : dy/dx+ysinx=e^cosx
!status
vocal sleetBOT
solve : dy/dx+ysinx=e^cosx
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
@silk sparrow Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
winged agate
in the first picture s(t) is shown along with íts formular, idk how to write it in discord so i just used the images, and in the second picture its sA(t),sB(t),sC(t),sD(t).
s(t) is just all of them combined.
i figured that a0 is 10 since the average in s(t) is 5 and that w = 125 "2pi/0.05"
how can i calculate a1..an and b1..bn?
i cant find the formular used here with w anywhere on youtube they always use something different.
vocal sleetBOT
in the first picture s(t) is shown along with íts formular, idk how to write it ...
@winged agate Has your question been resolved?
winged agate
<@&286206848099549185>
prisma fjord
winged agate
lmao
winged agate
find a1, b1 etc i cant find any youtube video or anything at all explaining it
ill close the channel, if anyone can help me please tag in discussion and ill reopen this. thanks in advance
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
tawny bramble
Hello, I'm a french student and I'm making an oral exam but as I was trying to make it I bump into this. Can you help me to understand it please? Thank you.
vocal sleetBOT
Hello, I'm a french student and I'm making an oral exam but as I was trying to m...
knotty lynx
What's the problem
simple basin
Hello, I'm a french student and I'm making an oral exam but as I was trying to m...
you know the usual square root? imagine that but 6 times lol
tawny bramble
can't we write it just 6*square root of 2?
simple basin
noo
knotty lynx
It's not 6 × sqrt(2)
meager shoal
It’s square rooting smth 6 times
knotty lynx
It's the sqrt applied 6
meager shoal
Not multiplying square root by 6
simple basin
well square root means number^1/2
i dont know how to use texit i cant show it properly..
cunning yew
,, 2^\frac{1}{12}
twin meteorBOT
<rajel />
tawny bramble
it's an non-real number right?
meager shoal
Square root is defined as something to the power of 1/2, ya?
This thing is something to the power of 1/12
meager shoal
you know the usual square root? imagine that but 6 times lol
I think that we might be wrong 🥀
1/12 is a combination of applying 2 square roots and one cube root
tawny bramble
i need to go back to highschool..
I'm not doing this sort of calculation in highschool
meager shoal
this article should clarify a lot of thing
tawny bramble
yeah ok so it's just 12 times the sqrt?
meager shoal
yeah ok so it's just 12 times the sqrt?
no
simple basin
maybe this will help visualisation
tawny bramble
yeah that's what I meant sorry...
meager shoal
${\sqrt[n]{r} = r^{\frac{1}{n}}}$ for ${n > 0}$
twin meteorBOT
k
meager shoal
do u agree with this
tawny bramble
You can just put 12 sqrt in front of it right?
tawny bramble
I mean instead of applying a 1/3 and two 1/2 we could directly apply one 1/12?
meager shoal
I mean instead of applying a 1/3 and two 1/2 we could directly apply one 1/12?
yes
in fact the former is an application of exponential properties
tawny bramble
yeah I understood but it was just to clarify it for me.
meager shoal
evidently
tawny bramble
Thank you so much
meager shoal
${\sqrt{r} = \sqrt[2]{r}}$
twin meteorBOT
k
meager shoal
alright
so
deifnition of the principal square root
is to output the positive number that when multiplied togehter is the same as our output
observe that
The expression ${r^\frac{1}{2}}$ has this property. Therefore, ${\sqrt{r} = r^\frac{1}{2}}$. Using the provided notation, ${r^\frac{1}{2} = \sqrt[2]{r}}$. Thus, ${\sqrt{r} = \sqrt[2]{r}}$.
twin meteorBOT
k
tawny bramble
So basically, the "normal" formula of the sqrt this?
quick plinth
\frac{dy}{dx}
twin meteorBOT
type.arc
${\frac{dy}{dx}}$
vocal sleetBOT
silk sparrow
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
.reopen
tawny bramble
.reopen
vocal sleetBOT
✅
tawny bramble
Hello once more. I bump into something new. Can you help me to understand whhy is there so many letters and what do they mean (if they have a meaning)? thank you
pearl wadi
😂
paper depot
yeah pretty massive jump there
at the very least you need to go through like
enough calculus to talk about integration and infinite series
before that equation starts being remotely relevant
graceful abyss
Hello once more. I bump into something new. Can you help me to understand whhy i...
All you need to kknow that the RHS is a summation
tawny bramble
RHS?
graceful abyss
right hand side of the equation
tawny bramble
I need it for my oral so do you have any idea how could I make it simpler for me to explain? (I'm in 12th grade)
paper depot
LHS and RHS are common abbreviations in english for left-hand side & right-hand side
paper depot
I need it for my oral so do you have any idea how could I make it simpler for me...
you need complex fourier series for your oral exam?
like they test you on things you never studied?
💀
tawny bramble
No it's for my baccalaureate
graceful abyss
I need it for my oral so do you have any idea how could I make it simpler for me...
It's a way to represent a function as a sum of trigonometric waves
tawny bramble
They ask me to do a math oral and a physic one
graceful abyss
You'd need to use a bit of euler's formula for ts
Aka $e^{ix} = cos{x} + i sin{x}$
twin meteorBOT
pix
paper depot
$e^{ix} = \cos(x) + i \sin(x)$
twin meteorBOT
Ann
tawny bramble
i is a constant?
graceful abyss
i is a constant?
i is an imaginary value
meager shoal
Square root of -1…
paper depot
well it is sqrt(-1) [if that's a thing you talk about at all]
im still a bit confused cause you seem to be getting examined on things that are definitely out of your depth
tawny bramble
I thought we couldn't do a sqrt of a negative number
paper depot
in the real numbers you can't.
graceful abyss
I thought we couldn't do a sqrt of a negative number
This branches out to soooooo many topics of math
You usually learn this after you master the form of quadratic equations
meager shoal
And physics 🥀
simple basin
Hello once more. I bump into something new. Can you help me to understand whhy i...
are you 100% sure you will be examined with this
graceful abyss
And then there's number theory, with complex numbers, imaginary numbers, rational/irrational numbers, real numbers, integers, etc
paper depot
homeboy is getting tested on complex number shit when he didnt even know what a 12th root was until recently 
graceful abyss
Argand's diagram, anything that has to do with Euler, and so on
paper depot
there is no possible way for any of us to teach you all of this higher math in a fucking discord chat
tawny bramble
No I gotta make my own oral on a subject that I choose by my own
graceful abyss
Welll.....
pearl wadi
I need it for my oral so do you have any idea how could I make it simpler for me...
u are in 12th u say?
simple basin
No I gotta make my own oral on a subject that I choose by my own
dont choose that 💔
graceful abyss
meager shoal
LOL
paper depot
No I gotta make my own oral on a subject that I choose by my own
then don't choose a topic that's way out of your depth lmfao...
tawny bramble
My subject is the math in music
pearl wadi
ig france is more advanced than other countries cause im in 12th and ive never seen this before
paper depot
do they give you a choice of subjects
tawny bramble
No
paper depot
bruh
ok well i have no idea how to advise you on choice of subject other than maybe pick something else or maybe don't go into as much depth
graceful abyss
ig france is more advanced than other countries cause im in 12th and ive never s...
I understand how functions and summation works but what the hell is the use of c_n and omega in this series??
paper depot
I understand how functions and summation works but what the hell is the use of c...
if you wanna know we could go off to #calculus or you could open your own help channel and talk there?
pearl wadi
I understand how functions and summation works but what the hell is the use of c...
same lmao...dk what fourier series is but ive seen a lot of questions on it here
graceful abyss
if you wanna know we could go off to <#326138772477575180> or you could open you...
Nah it's fine
tawny bramble
I was doing lately the fibonacci's series which was way easier but my professor said that it was a bad subject...
graceful abyss
I was doing lately the fibonacci's series which was way easier but my professor ...
You can try..
Uhh
Discrete maths
tawny bramble
I understood it all but couldn't make it
graceful abyss
It's way simpler than Fourier Series.. at least that's what I think it should be
graceful abyss
Discrete maths
The ones with set theory, number theory, and the weird one with the stuff with bunch of weird ass symbols
Oh it's called mathematical logic
meager shoal
Sizes of infinity or construction of number systems are interesting imo
lusty briar
No clue on how to do this and find the values 😭😭 studying for my exams
paper depot
,rccw
twin meteorBOT
lusty briar
ignore my writing their like 100% incorrect
paper depot
@lusty briar a, b or c? or all of them in order?
lusty briar
all of them but mainly a first cause ive been stuck on this lol
paper depot
ok let's see
lusty briar
i was watching youtube vidoes to help but it didnt help 😞
lusty briar
yeah
late oyster
1 + 3 + 5 + 7 +a,mean = 5,what is the value of a here?
paper depot
1 + 3 + 5 + 7 +a,mean = 5,what is the value of a here?
!occupied
vocal sleetBOT
1 + 3 + 5 + 7 +a,mean = 5,what is the value of a here?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
lusty briar
times the numbers with freq all respectively and add them up above the freq altogether iirc ☹️
lusty briar
HELP i feel like its wrong
paper depot
i was helping you
pretty sure you weren't bc it's not relevant to OP's question
paper depot
HELP i feel like its wrong
you didn't do what i said
(explain how to find the mean from a frequency table in words)
lusty briar
times the numbers with freq all respectively and add them up above the freq alto...
This
In the context of the question times the number of students each with their respective number of devices and add them altogether above/divided by number of devices added tgt
paper depot
oh mb
lusty briar
Still feel like i got it wrong ☹️
paper depot
yes, you sum up each value * its frequency and divide it by the total frequency.
ok so we're good (i hope) on planning.
lusty briar
Im in the worst class in the entire grade for maths lol
late oyster
pretty sure you weren't bc it's not relevant to OP's question
my bad,i thought you was the op
paper depot
now show your work.
lusty briar
ok so we're good (i hope) on planning.
I hope 🙏
paper depot
show your work so we can catch arithmetic or algebra errors.
lusty briar
like find the mean first without the unknown?
paper depot
find the mean in terms of a.
you're gonna have a fraction which has the letter a both on the top and on the bottom.
this is ok and intended.
write down the equation that says mean = 2.6 and send a photo of it here.
DO NOT SIMPLIFY ANYTHING YET.
also do not proceed with the algebra until i tell you so.
lusty briar
mhm
paper depot
so let's go over it one thing at a time.
lusty briar
im afraid your equation is wrong in several ways.
💀
lusty briar
number of smart devices
paper depot
incorrect.
times the numbers with freq all respectively and add them up above the freq altogether iirc ☹️
you said this before
the denominator should be the total frequency.
you might have heard this phrased as $\bar{x} = \frac{\sum fx}{\sum f}$ --- the denominator is $\sum f$, the total frequency.
twin meteorBOT
Ann
lusty briar
are you rewriting the equation
not yet
lusty briar
cause we weren't done yet
right 😞
lusty briar
Mhm
paper depot
ok so this is your freq table.
look at your table here. which row gives the frequencies --- the top row, or the bottom row?
lusty briar
Bottom
paper depot
right.
ok, now write down the expression for the total frequency.
do it in Discord and leave it unsimplified.
lusty briar
9x1 + 2x16 + 3x14 + 4x18 + 5xa ?
lusty briar
😞
paper depot
i'm asking you for Σf and not Σxf.
paper depot
yes, correct.
paper depot
9x1 + 2x16 + 3x14 + 4x18 + 5xa ?
now, this thing actually goes in the numerator of the fraction.
paper depot
9+16+14+8+a
while this goes in the denominator.
now write down the correct equation.
lusty briar
The photos so blurry
paper depot
do not forget the =2.6 also
also strongly recommend making your 9 and a not look like each other somehow.
lusty briar
Its on the left side lol
lusty briar
also strongly recommend making your _9_ and _a_ not look like each other somehow...
😞
Alr
lusty briar
Do i factorize it
lusty briar
you cropped it out so i didn't see it
Cause i drew on that side 😭
paper depot
factorize what and where
lusty briar
The equation rn
paper depot
this is a fractional equation. idk which part of it you were trying to factorize.
but it is not a quadratic.
my first course of action would be to multiply both sides by (47+a) so as to get rid of that fraction.
ah crap.
these mistakes keep slipping past me.
$\frac{9 + 36 + 42 + 32 + 5a}{47 + a} = 2.6$
twin meteorBOT
Ann
lusty briar
I think i skipped ahead
paper depot
,rccw
twin meteorBOT
lusty briar
And its wrong
paper depot
yes you did by a long shot
lusty briar
hel
paper depot
also why did the (47+a) get cancelled out
that wasn't supposed to happen
$\frac{9 + 36 + 42 + 32 + 5a}{47 + a} = 2.6$
twin meteorBOT
Ann
paper depot
,calc 9+36+42+32
twin meteorBOT
Result:
119
$\frac{119+5a}{47+a} = 2.6$
and then multiplying by $(47+a)$ gets you:
$119 + 5a = 2.6(47+a)$
twin meteorBOT
Ann
lusty briar
Im crying HELPPP im whiteoutinf this rq
paper depot
are you actually in tears or was that hyperbole
lusty briar
Mhm
paper depot
k
lusty briar
Im a surcivor
lusty briar
do you understand this so far
Yes
paper depot
ok
lusty briar
Writing it down
paper depot
do you see how to continue
lusty briar
Ill try
Nvm it proves that i dont
I did for like two liens
Then i went too far
😭
paper depot
ok first of all can you name the type of equation that 119 + 5a = 2.6(47+a) is
looking for a word here
lusty briar
no 😭🙏
Id catrgorize it as quadratic equation cause its the only one i remember but u mentioned thag it wasnt
paper depot
do you know what a quadratic equation is
lusty briar
Ik one when its given…
paper depot
like imagine i'm a classmate of yours who's way behind and i ask you: "hey so what the fuck is a quadratic equation"
what would you answer?
lusty briar
“Idk ask the teacher or smt”
lone dock
blud
paper depot
ok so you don't know
lusty briar
😿
paper depot
a quadratic equation is one that involves the unknown being raised to the 2nd power, i.e. squared.
(but no other higher powers)
here though you won't see any a^2 at all
lusty briar
Ill attempt to rememebe that
paper depot
from $119 + 5a = 2.6(47+a)$, first \textbf{expand} on the right to get: $$119 + 5a = 2.6 \cdot 47 + 2.6a$$
twin meteorBOT
Ann
paper depot
Ill attempt to rememebe that
this is something you really should know now that you're doing stats stuff
lusty briar
Im moving on the grade 11 in less than rwo months and by then there will be no worst class for me to thrive in
Cause immactually soing pretty good in my class cause its the worst one
paper depot
,calc 2.6 * 47
twin meteorBOT
Result:
122.2
what did you do
paper depot
no wait hold on
the execution is the exact same as how i would have imagined it to play out
lusty briar
But the fractions negative rn
paper depot
time to go back and see if there's any arithmetic error neither of us caught
paper depot
But the fractions negative rn
not the issue
the issue is that a = 1.5 which isn't an integer
paper depot
Cant be negative in the table
a negative divided by a negative gives you positive
lusty briar
a negative divided by a negative gives you positive
Yeah
paper depot
so the sign is not the issue at all
lusty briar
Ik that
But it gave like
1.1
Or smt
And there cant be 1.1 students unless that one student has an extra limb
lusty briar
Arithmetic mistake i made
paper depot
my bad for not catching it but honestly i was also trying to patch the huge gaps in your algebra knowledge
lusty briar
Stop help
paper depot
you have to be extremely careful about arithmetic
paper depot
mmmkay
lusty briar
That kinda