I don’t get what you mean but thanks
#help-36
compact saddle
I don’t get what you mean but thanks
gritty flume
what about the 3rd and forth quadrant
compact saddle
the theta should be the angle that the curved arrow is showing, not the one under the line
gritty flume
the theta should be the angle that the curved arrow is showing, not the one unde...
what’s a theta
and what’s the
tae
gritty flume
the theta should be the angle that the curved arrow is showing, not the one unde...
kinda like coordinate lines
like making a straight line
gritty flume
the theta should be the angle that the curved arrow is showing, not the one unde...
.
tae
compact saddle
theta is how θ is pronounced
warped perch
but what about the theta
It's the angle between the x-axis and the line
'The reference angle'
compact saddle
yea, positive x axis to be more precise
gritty flume
oh ok ok
warped perch
oh I’m learning the cetesian plane rn
Oh Cartesian plane
compact saddle
the b) question here, tey wanted to know how they should represent it and apparently they needed to use the coordinate system to represent is and not just a trangle
warped perch
If Tan and Sin both are +ve it means we're talking about the first quadrant
gritty flume
If Tan and Sin both are +ve it means we're talking about the first quadrant
what’s ve
gritty flume
oh ok ok
gritty flume
i only understand it as the y and x are positive so the first quadrant
y is ve and x is negative so second
both y and x and negative so third
warped perch
- Sin^2 x + Cos^2 x = 1
This will be the line y=x
gritty flume
2) Sin^2 x + Cos^2 x = 1
This will be the line y=x
I don’t get this
warped perch
So which grade are you in right now
warped perch
I don’t get this
Do you understand what the slope of a line is?
warped perch
Do you understand what the slope of a line is?
It's used in coordinate maths
gritty flume
So which grade are you in right now
10
gritty flume
Do you understand what the slope of a line is?
yes
compact saddle
2) Sin^2 x + Cos^2 x = 1
This will be the line y=x
huh?
warped perch
How much do you understand trigonometry?
Like do you know that trigonometric ratios?
compact saddle
thats not a graph for line
gritty flume
Like do you know that trigonometric ratios?
idk the name but maybe i do know it
ik the formulas
how fo ind th enable
and side
angle
warped perch
thats not a graph for line
Yes pls elaborate
gritty flume
and side
compact saddle
Yes pls elaborate
i mean Sin^2 x + Cos^2 x=y would be 1=y so the graph would be the same as y=1
i dont get where you got y=x from
warped perch
Yes you're right
compact saddle
Sin^2 x + Cos^2 x=1 would even be a graph thechically since you would need x and y
warped perch
Idk why I went to tan 🤦🏻
compact saddle
anyw skittlx u can ignore what weve been going on abtw
compact saddle
i only understand it as the y and x are positive so the first quadrant
once sec
a vid would probably help
gritty flume
anyw skittlx u can ignore what weve been going on abtw
ok
warped perch
btw were you thought about angles using radians
I don't think so
You don't learn that in 10 grade
gritty flume
btw were you thought about angles using radians
I’m not sure what radians are
i learn just for learning sake, I don’t learn like the terms or like the topic names with my learning
compact saddle
You don't learn that in 10 grade
yea i was confused cuz i learnt about the coordinates and radians in 11th, and only triagles with angles below 90 in 10th
warped perch
yea i was confused cuz i learnt about the coordinates and radians in 11th, and ...
Yea same
warped perch
i learn just for learning sake, I don’t learn like the terms or like the topic n...
Do you know how to find out the value of the trigonometric ratios if any one of them is given?
You must have learnt that in school
gritty flume
Do you know how to find out the value of the trigonometric ratios if any one of ...
what exactly is a trigonometric ratio
is it the sine rule
cosine rule?
warped perch
Right, so all the 6 ratios let me name them
Sine
Cosine
Tan
Cot
Sec
Cosec
These all are the trigonometric ratios
warped perch
Right, so all the 6 ratios let me name them
Sine
Cosine
Tan
Cot
Sec
Cosec
These...
Heard of them? @gritty flume
gritty flume
Right, so all the 6 ratios let me name them
Sine
Cosine
Tan
Cot
Sec
Cosec
These...
ig so
i just found out what the cot, scs and sec meant
gritty flume
We deal with the Right-Angled Triangle with these 6 ratios.
oh yes
and the triangles without is the other two
warped perch
and the triangles without is the other two
?
warped perch
sine rule and cosine rule
What do you know about them?
gritty flume
What do you know about them?
the formula
idk when to exactly use the cosine rule tho
ill be closing the channel after an hour bc ill learn something else and relearn math
gritty flume
Do you know the names of the three sides of the Right-Angled Triangle
I don’t think so
unless your referring to the opposite side
adjacent and hypetenuns
warped perch
adjacent and hypetenuns
Yes talking about them
gritty flume
oh ok
compact saddle
and 4th y is positive and x isn’t
do you know how sin and cos
are defined
in the coordinate system
gritty flume
I don’t think so
compact saddle
I don’t think so
yea, thats probably hwy you cant understand why its negative
gritty flume
isn’t it bc the x is negative
compact saddle
the way sine and cos are actually defined is by considering a circle of radius r centered at the origin
then if you draw a radius making a angle θ with the positive x axis
warped perch
the way sine and cos are actually defined is by considering a circle of radius r...
Showing her the visual illustration would be better
compact saddle
sin=y/r
cos=x/r
warped perch
sin=y/r
cos=x/r
School teaches it with a Right angled triangle😭😭
gritty flume
this?
gritty flume
i kind of get it in a way
compact saddle
Showing her the visual illustration would be better
i was trying to find a vid but they all had radians
😭
gritty flume
yea i was confused cuz i learnt about the coordinates and radians in 11th, and ...
what are radians
compact saddle
what are radians
i mean its easy to understad i can send you a vid one sec
gritty flume
yeah
warped perch
Just know that
180° = π radian
You can convert any angle into radian with this relation
gritty flume
oh ok ok
compact saddle
what are radians
they way i would explain it: basically, its a way we define angles so that we can use pure real numbers instead of degrees
we consider a unit circle, if a given arc of a=the unit circle(radius=1) subtends a angle of θ at the centre, we say the angle is (arc length) radians, so 360 degrees (the arc is the entire circumference)=2pi radians
https://www.youtube.com/watch?v=e7QjCL7lQM4&t=1091s, you can look at the "why radians" part of this vid
also you can look up about radians on chrome or yt for more vids
ignore the later half of the vid, you dont really need those formulas rn
compact saddle
looks like he would slap me
LOL
compact saddle
Man I personally needed help with Ray Optics🥀😔
ncert?
compact saddle
You see i am preparing for JEE
idk if i can help much cuz im in chapter cuz my coaching is currently in that chap
LOL
we can crack our heads togeather in dms if u want
warped perch
Lol you in the same boat you mean?
compact saddle
Lol you in the same boat you mean?
i mean i can understand it
but the chap isnt finished yet
warped perch
I haven't really started with it tbh, but I know the 10th part well
compact saddle
I haven't really started with it tbh, but I know the 10th part well
i mean i studied the ncert part for a exam and did well
warped perch
i mean i studied the ncert part for a exam and did well
Cool
warped perch
Where u from
compact saddle
Where u from
pretty obvious which country im from but i dont wanna talk about where exctly in a help channel here 😭
we can move to dms if u wanna talk
warped perch
pretty obvious which country im from but i dont wanna talk about where exctly in...
I understand 😭
compact saddle
or not no pressure
warped perch
Sure idm
compact saddle
dang the close up
btw if you want problem sheets related to radians you should be able to find them by searching online
gritty flume
btw if you want problem sheets related to radians you should be able to find the...
sure thanks
are you free
compact saddle
sry about us lmao
gritty flume
yea, you can ping or dm me
mmh I’ll, ping
unlesss the channel gets taken by another person then ill dm
compact saddle
sounds good
!!
idk much about how the help channels here work im not 100% sure if your alowed to just keep it up
i think it closes itself after a period of inactivity
you can reopen one later and ping me if that happens
gritty flume
idk much about how the help channels here work im not 100% sure if your alowed t...
Thanks
chrome hemlock
final saddleBOT
severe canyon
The rays are how far apart? How many degrees? Can you recognise that?
tired walrus
wym red or blue
chrome hemlock
tired walrus
does your class take arguments from 0 to 2pi or from -pi to pi
severe canyon
is it 5pi/12
Btw this would be an angle in the first quadrant, whereas z2 lives in the 4th
chrome hemlock
Btw this would be an angle in the first quadrant, whereas z2 lives in the 4th
-5pi/12…?
chrome hemlock
does your class take arguments from 0 to 2pi or from -pi to pi
im not sure
this is how they calculated iz2
severe canyon
does your class take arguments from 0 to 2pi or from -pi to pi
You have to be sure about this though
tired walrus
do you have any class materials from when you were introduced to argument
chrome hemlock
ok thanks
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Available help channel!
hollow needle
its obviously just yes right?
final saddleBOT
its obviously just yes right?
hollow needle
its obviously just yes right?
actually maybe not
hasty mist
its obviously just yes right?
Yes.
hasty mist
Intuitively?
hasty mist
im having a hard time understand why it must be trhe
When you intersect more sets, you get something smaller or equal because you’re imposing more conditions for membership. Since I includes all of J, the intersection over I includes more sets in the intersection, so it can only get smaller or equal to the intersection over J
versed crater
Pick something from the left
Then it is in every A_I
If you then pick a subset of these I’s all of them should (and does) still have the something
final saddleBOT
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Available help channel!
worthy radish
With quadric equations, I’m finding “x” using the delta solutions because the whole equation isn’t solvable otherwise using the regular algebra rules?
final saddleBOT
With quadric equations, I’m finding “x” using the delta solutions because the wh...
compact saddle
With quadric equations, I’m finding “x” using the delta solutions because the wh...
by "finding x using the delta solutions" do you mean the quadiatic equation?
worthy radish
For example here what method would you guys use here?
compact saddle
Yea
well the quadratic equasions can be derrived using the rules of algebra
but somewhere along the derrivation you end up assuming b^2-4ac isnt negative if x is a real number
however, when we consider complex numbers, the quadratic formula can give you the answer for any equasion, just that the equations where b^2-4ac is negative have complex solutions
compact saddle
For example here what method would you guys use here?
x(x-4)=0
so x=0 or x-4=0 which implies x=4
so x=0 or x=4
the derrivation of the quadratic quasion uses a method called "completing the square" which can also be done on any quadratic
since the square root function is only defined when the thing inside it is positive, then you can see how the derrivation assumes (b^2-4ac)/4a^2 is positive, but since 4a^2 is always positive, we only need b^2-4c to be positive
for square roots to be defined for negative values, you need the coples numbers
worthy radish
x(x-4)=0
so x=0 or x-4=0 which implies x=4
so x=0 or x=4
But I can’t use delta method here
Because I don’t have “c”
Here once again I need to use another method of solving cause i don’t have “b”….
So there are 3 ways of solving quadric equations
compact saddle
Here once again I need to use another method of solving cause i don’t have “b”….
b=0
compact saddle
But I can’t use delta method here
you can, c=0
compact saddle
I can’t use bracket method if abc
yes, not directly, you have to do something called "completing the square"
remember a^2+b^2+2ab=(a+b)^2?
worthy radish
But what’s the ultimate goal for quadric equations? To know what the x is that leads to 0?
compact saddle
But what’s the ultimate goal for quadric equations? To know what the x is that l...
consider a quadratic expression ax^2+bx+c
different values of x give you different answers, (you can use desmos to see its graph)
the quadratic equation tells you when this equals 0 (or graphically, when the graph touches the x axis)
so yes, it is to find out what x implies ax^2+bx+c equates to 0
compact saddle
I can’t use bracket method if abc
do you want to try using completing the square on one of your problems where a,b,c !=0?
its actually quite useful to know
allows you to express the quadratic in a more useful way in some contexts
(like solving integrals for example, but you dont have to worry about that for now)
worthy radish
But why can’t we solve x?
worthy radish
How
compact saddle
you have to use, a^2+b^2+2ab=(a+b)^2
to bring your equasion in the from of kx^2+n=0
compact saddle
you have to use, a^2+b^2+2ab=(a+b)^2
to bring your equasion in the from of kx^2...
though how exactly you do this is usually directly just told to you, you can try to give it some thought atleast
clue is that you try to add and subtract a number
its the same this as adding a 0
or just tell me u just want the method
final saddleBOT
@worthy radish Has your question been resolved?
final saddleBOT
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dense garnet
Let $(Y_n)$ be a sequence of i.i.d. real random variables with a symmetric distribution (i.e. $Y_n$ has the same law as $-Y_n$). Assume that $\frac1{n}(Y_1+\cdots+Y_n)$ has the same distribution as $Y_1$, for every $n$. Show that $Y_n$ follows a Cauchy distribution.\
Using properties of characteristic functions (cf), where $\phi$ is the cf of $Y_i$, I arrive at the functional equation $$[\phi(t/n)]^n = \phi(t)\quad\forall t\in\mathbb{R}$$Clearly $e^{|t|}$ satisfies this, which is the cf of the standard Cauchy distribution. But is it the only one? (Also, $\phi$ is a real-valued function.)
final saddleBOT
Let $(Y_n)$ be a sequence of i.i.d. real random variables with a symmetric distr...
soft zealotBOT
psie
final saddleBOT
@dense garnet Has your question been resolved?
final saddleBOT
@dense garnet Has your question been resolved?
sturdy badge
need help with this
final saddleBOT
need help with this
atomic moon
Why e on top?
atomic moon
When its sum a*r^n
Here you have e^cn which is (e^c)^n
"a" would be 1
in fact a is the first term of the sum which is 1 here
echo carbon
hi
atomic moon
Except this it should work
polar spruce
<@&268886789983436800> castrate this guy
final saddleBOT
polar spruce
thank you
final saddleBOT
Available help channel!
peak owl
hi im stuck where do i start with this
final saddleBOT
hi im stuck where do i start with this
gray vortex
hi im stuck where do i start with this
use equations to describe the problem:
- what does P being on the curve y=sqrt(x) mean in terms of its coordinates
- closest implies you want to minimise the distance
peak owl
use equations to describe the problem:
- what does P being on the curve y=sqrt(x...
yea i understand that part
im just stuck on the approach
i feel like its smth to do with a triangle
gray vortex
what have you done so far
gray vortex
do you know pythagorean theorem
gray vortex
well it's the same
peak owl
well it's the same
do u just extend a line downwards and then conntect p to 4,0 to make a rat?
gray vortex
yes
final saddleBOT
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Available help channel!
twin wing
can you check if i math this correctly
final saddleBOT
can you check if i math this correctly
@twin wing Has your question been resolved?
hasty mist
can you check if i math this correctly
I mean 0.00031 m is a lot smaller than 1 cm, so I doubt this is correct.
final saddleBOT
@twin wing Has your question been resolved?
serene panther
From what I know of physics, Intensity is inversely proportional to square of distance between point source to that point
In this case
But youve taken it to be directly proportional
@twin wing
deft terrace
final saddleBOT
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drowsy juniper
I'm trying to understand a Pythagorean Triangle problem using the Speed of Light in one second (299792458m) as leg A, and the Plank Length (1.61 * 10^-35m) as leg B. Every time I calculate it in C++ using boost there's no difference in the hypotenuse and leg A. Does the triangle break at one point at certain lengths?
final saddleBOT
I'm trying to understand a Pythagorean Triangle problem using the Speed of Light...
mint orbit
I'm trying to understand a Pythagorean Triangle problem using the Speed of Light...
no, pythagorean always holds true
you're hitting the limits of precision though
how much comp sci do you know
drowsy juniper
Not much, just getting started in community college.
mint orbit
to answer your question directly, math on a computer with very small and very big numbers is usually error-prone
you might look into how a computer stores numbers
idk what types youre using here
drowsy juniper
Okay, I'll try something else. Also taking the inverse cosines of the angles posits one angle to be 90 degrees in at the end of the B side. I think I found something but just want to actually test it.
So it becomes a 90, 90, really small degree angle.
mint orbit
youre bumping against a common problem in computing so its probably worth exploring if youre curious
drowsy juniper
Okay, thanks man. Just seeing if I was losing my mind about the triangle always holding.
.close
final saddleBOT
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twin wing
From what I know of physics, Intensity is inversely proportional to square of di...
omg i never responded to this. thats why my math seems wrong.
final saddleBOT
omg i never responded to this. thats why my math seems wrong.
@twin wing Has your question been resolved?
rotund parrot
for part b, how am i supposed to find the two vectors that i need to find the angle between?
final saddleBOT
for part b, how am i supposed to find the two vectors that i need to find the an...
odd seal
i dont know how they got there
from the position vector r
the only time dependent component gives you the velocity here (v = dr/dt)
and that has a vector direction of [40, -100, 0]
and while descending, you know the z component is additionally -16km/h, so the new vector becomes
original velocity + [0, 0, -16]
final saddleBOT
@rotund parrot Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
fair sigil
midpoint of OH , right
final saddleBOT
midpoint of OH , right
severe verge
correct
severe verge
only takes 3 days to respond sadly
final saddleBOT
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Available help channel!
severe robin
trying to solve using mathematical induction. I know this isn't the way to do it however I think I'm still proving it (?). I'm asking for help on how to properly use inductions to prove this
final saddleBOT
trying to solve using mathematical induction. I know this isn't the way to do it...
thorny canyon
trying to solve using mathematical induction. I know this isn't the way to do it...
take base case n=1
assume it holds for n=k
use that to prove that it must hold for n=k+1
$6^{n+1}-1 = 6^{n+1}-6+5=6[6^n-1]+5$
soft zealotBOT
Donkey
severe robin
$6^{n+1}-1 = 6^{n+1}-6+5=6[6^n-1]+5$
honestly I see how to get to the second part after the first = but I'm unsure how the -6+5 becomes the last thing there
thorny canyon
honestly I see how to get to the second part after the first = but I'm unsure ho...
you take 6 common from the first two terms
factor out 6 from 6^{n+1}-6, leave 5 untouched
severe robin
factor out 6 from 6^{n+1}-6, leave 5 untouched
ohh omg that makes sense sorry if that's dumb I really didn't know how to get there but after I do get there how do I match it w the hypothesis?
thorny canyon
ohh omg that makes sense sorry if that's dumb I really didn't know how to get th...
ok, what's your induction hypothesis?
severe robin
ok, what's your induction hypothesis?
$6^{k}-1=5t
not sure how to use the image bot
soft zealotBOT
⃟
thorny canyon
so you js substitute that in the last part of this expression
$6[6^k-1]+5 = 6(5t)+5$
soft zealotBOT
Donkey
thorny canyon
and that's done
severe robin
and that's done
can I know how the that above 6(5t)+5 is proving?
thorny canyon
the core idea of induction is that you prove a base case, make an assumption abt it holding for some random integer k, and prove that if it holds for k, it must hold for k+1
so the thing where we substituted $6^k-1=5t$ is us implementing the "if it holds for k" condition
soft zealotBOT
Donkey
thorny canyon
the remaining part is js taking 5 common, so $6(5t)+5=5(6t+1)$ which is clearly divisible by 5
soft zealotBOT
Donkey
severe robin
the remaining part is js taking 5 common, so $6(5t)+5=5(6t+1)$ which is clearly ...
how is $6(5t)+5$ resulting in that? or is that the other side of the equation originally?
soft zealotBOT
⃟
thorny canyon
how is $6(5t)+5$ resulting in that? or is that the other side of the equation or...
factor out 5 from both terms
severe robin
factor out 5 from both terms
ohh I see it now thank you sm for your help with this
thorny canyon
np
severe robin
I'm a hs senior
oh I see you seem very good at it
thorny canyon
thanks
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mystic patio
In EDA should you do analysis first and then clean the data or the other way around
final saddleBOT
In EDA should you do analysis first and then clean the data or the other way aro...
@mystic patio Has your question been resolved?
final saddleBOT
@mystic patio Has your question been resolved?
bronze grove
hola
abstract bramble
maybe you should start by finding the solutions to those inequalities
bronze grove
maybe you should start by finding the solutions to those inequalities
got the intervals of x yes
true escarp
got the intervals of x yes
what are those intervals
bronze grove
what are those intervals
9/4 to 25/4
true escarp
okay
so just transform the middle part of that expression to |x - 4|
what do you think the first step is?
bronze grove
so just transform the middle part of that expression to |x - 4|
we need to use inf and lamda that minimizes it
i need to understand in this form
steep hatch
A general tip I'd suggest for something like this is try to find an equality relating |x-4| to |\sqrt{x}-2|
bronze grove
A general tip I'd suggest for something like this is try to find an **equality**...
and then using restriction on lambda to find x?
steep hatch
I mean okay, first can you find the equality I hinted at
bronze grove
yes wair
bronze grove
I mean okay, first can you find the equality I hinted at
i think i should read the chapter once
steep hatch
okay so that's not what I was thinking
what I'm thinking is
[ |x-4|= |\sqrt{x}+2| |\sqrt{x}-2|]
soft zealotBOT
lance lance
steep hatch
So like do you know geometrically @bronze grove what |x-4| represents?
steep hatch
what is it?
steep hatch
no like not as a shape
what is the geometric interpretation of the number |x-4|
if I fix a value of x
bronze grove
like on a graph?
steep hatch
no
bronze grove
what is the geometric interpretation of the number |x-4|
i don't understand what u want me to do 😭
bronze grove
yes
steep hatch
if I tell you a value of x
bronze grove
like if x is 1
steep hatch
what does |x-4| mean
bronze grove
then its 3
steep hatch
Okay and what does that 3 mean
bronze grove
what does |x-4| mean
mod of the number?
steep hatch
mod of the number?
almost
the point is that |x-4| is the distance between x and 4 right
bronze grove
Okay and what does that 3 mean
a number? 😭
steep hatch
So if I tell you |x-4|<1, that means the distance between x and 4 is at most 1
so what values can x be then?
bronze grove
3 and 5
steep hatch
well between 3 and 5
steep hatch
**lance lance**
so circling back to this
you then know that sqrt{x} is between what two numbers?
steep hatch
And basically the game we play here is we go
bronze grove
steep hatch
\begin{align*}
|\sqrt{x}-2| &<\varepsilon \
\implies |\sqrt{x}-2| \cdot |\sqrt{x}+2| &< \varepsilon \cdot |\sqrt{x}+2| \
\implies |x-4| &< \varepsilon |\sqrt{x}+2|
\end{align*}
and what you need to convince yourself of is
we can go backwards
soft zealotBOT
lance lance
steep hatch
So if we start off by already saying |x-4| < 1, then we know that |\sqrt{x}+2|< \sqrt{5}+2, which we'll round to 5
So we can then say that
our condition will be $ |x-4| < \mathrm{min}( 5\varepsilon, 1)$
huh
anyway
bronze grove
our condition will be $|x-4| < \mathrm{min}( 5\varepsilon, 1)$
soft zealotBOT
vie
steep hatch
convince yourself now that using this we can go backwards to get |\sqrt{x}-2|<\varepsilon
bronze grove
convince yourself now that using this we can go backwards to get |\sqrt{x}-2|<\v...
gotcha
steep hatch
wait here did the 5e come from
Because if |x-4|<1 then
$|\sqrt{x}+2|<5$
soft zealotBOT
lance lance
steep hatch
No worries :)
bronze grove
Because if |x-4|<1 then
$|\sqrt{x}+2|<5$
i think i will try to conclude myself
tysmm
.close
final saddleBOT
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fierce timber
Hi im a 9th grader can someone help me explain how do i get the 8 in front of the (y-2) photomath gives me that buti dont understand tbst step
final saddleBOT
Hi im a 9th grader can someone help me explain how do i get the 8 in front of th...
craggy plank
,rccw
soft zealotBOT
magic meteor
Got that math teachwr handwriting already, keep it up.
Think of it this way, what did we factor out of the first parenthesis
pliant shore
$2y - 4 = 2(y - 2)$ and $4y^2 + 8y + 16 = 4(y^2 + 2y + 4)$
soft zealotBOT
south
fierce timber
Think of it this way, what did we factor out of the first parenthesis
im new to this terminology what does factor out mean
smoky bramble
Hi im a 9th grader can someone help me explain how do i get the 8 in front of th...
8(y³-8)
or (2y-4)(4y²+8y+16)
(2y-4) can take out 2, and (4y²+8y+16) you can take out 4
magic meteor
im new to this terminology what does factor out mean
Ok, how much of the problem do you understand?
fierce timber
oh so basically i divide the first one by 2 and the second one by 4 and thats like multiplying both by 8?
magic meteor
Walk be through your steps
fierce timber
Ok, how much of the problem do you understand?
to the part where i get 8 in front
fierce timber
and so basically thats like multiplying everything by 8?
magic meteor
Yes, we factor out 2 and 4, and since the parentheses are being multiplied we just multiply the factors and we get 8
fierce timber
it all makes sense now, thanks
magic meteor
Np
fierce timber
Got that math teachwr handwriting already, keep it up.
is that supposed to be good or bad
because my actual notebook is way worse
everything is so messy
magic meteor
Uhh, dont even worry about it, my physics homework is terrible
vestal crest
the only nitpick I can see about the handwriting is the possibility of misreading the 4 for an a, but that should be highly unlikely.
magic meteor
Terrible
vestal crest
this is new - writing in mixed case.
pliant shore
I'd cry if I were your TA
magic meteor
this is new - writing in mixed case.
I genuinely could not read what i wrote myself
magic meteor
I'd cry if I were your TA
There is 20 more pages
pliant shore
it is readable but it's just annoying to read
fierce timber
does someone understand 18.b we wrote a pop quiz that wasnt for grade and i got 0/10 from this part
pliant shore
does someone understand 18.b we wrote a pop quiz that wasnt for grade and i got ...
ah, it's a difference of two squares
because $2^2 (ab + 1)^2 = [2(ab + 1)]^2$
soft zealotBOT
south
magic meteor
because $2^2 (ab + 1)^2 = [2(ab + 1)]^2$
I really need to learn latex goddamn
pliant shore
in the exercise the solution should be (2a-1)(2a+1)(b-2)(b+2)
can you first write it as a product of two brackets?
fierce timber
and it has quite a few steps i believe
fierce timber
can you first write it as a product of two brackets?
you mean am i smart enough to do it?
magic meteor
Smart≠good at math
pliant shore
or you could write $x^2 - y^2$ first and factor that
fierce timber
im sorry i dont understand the question
soft zealotBOT
south
pliant shore
im sorry i dont understand the question
I believe it's to fully factorise all these expressions
so you keep factorising until there's nothing left to factorise
pliant shore
right! so the idea is with $[2(ab + 1)]^2 - (4a + b)^2$
soft zealotBOT
south
pliant shore
we use $x = 2(ab + 1)$ and $y = 4a + b$
soft zealotBOT
south
pliant shore
sub those in
fierce timber
wait i dont understand what text should i look at
magic meteor
Its a bit unintuitive to go straight to factors when youre new to it. I reckon we should expand the squares
magic meteor
8ab
fierce timber
like doesnt it square the whole thing?
pliant shore
if i square the first part, doesnt that make it 4 a2b2+ 2ab+1?
that's going in the wrong direction
because what you're doing is trying to expand that
magic meteor
that's going in the wrong direction
I mean its more intuitive for ninth graders
Expand the squares, sum them, factor
pliant shore
if i square the first part, doesnt that make it 4 a2b2+ 2ab+1?
you're missing brackets but 4(a^2 b^2 + 2ab + 1) is correct
fierce timber
i think i should learn english math terminology so i can understand what yall saying
pliant shore
I mean its more intuitive for ninth graders
no, that's even harder
this is absolutely a difference of 2 squares exercise
magic meteor
no, that's even harder
Just expanding the squares, summing like terms, and ABC formula?
pliant shore
Just expanding the squares, summing like terms, and ABC formula?
yes
fierce timber
oh wait i think i understand, im supposed to make it have 2 parts so i can do the x-y) (x+y
leaden moon
pliant shore
I bet they haven't learned how to factorise 4uv - 16u - v - 4 as (2u + ...)(2v - ..) or (4u + ...)(v - ..)
pliant shore
oh wait i think i understand, im supposed to make it have 2 parts so i can do th...
yep!
fierce timber
does someone understand 18.b we wrote a pop quiz that wasnt for grade and i got ...
can you help me with 18.3
pliant shore
you want to get the multiplication of some brackets
because the parts in each bracket are simpler
fierce timber
but like dont give the answer immediately i mean its fine if you do
fierce timber
because the parts in each bracket are simpler
makes sense
pliant shore
can you help me with 18.3
if you can do 18.2 you can do 18.3
fierce timber
imma try
magic meteor
A^2-B^2=(A-B)(A+B)
magic meteor
You remember the double negative rules?
pliant shore
your factorisation should be using a and b
fierce timber
You remember the double negative rules?
like a-(-b)= a+b
magic meteor
like a-(-b)= a+b
++=+, +-=-, -+=-, —=+
pliant shore
like a-(-b)= a+b
actually you just need this
but it helps to be aware of similar rules
magic meteor
Odd number of lines and its negative, even number and its positive
fierce timber
i get to the step the first one where i have (x-y) squared (x+y) squared - (x+y) squared
magic meteor
Is this 18.3?
fierce timber
yeah
pliant shore
by 'sub', I mean find x, and replace it with 2(ab + 1)
every time you see x, replace it with 2(ab + 1)
magic meteor
no they're still on 18.2
I mean its the same problem essentially
Just different numbers
fierce timber
how do yall se that as the same thing
pliant shore
how do yall se that as the same thing
those 4 problems are all difference of squares problems
you use (x + y)(x - y) for all of them
pliant shore
what are you getting now?
pliant shore
imma send pic rq
you were close with your first idea
it's $[2(ab + 1) + (4a + b)][2(ab + 1) - (4a + b)]$
soft zealotBOT
south
pliant shore
again, you should use brackets surrounding the y first (cause you need to subtract it)
then you can drop them later
magic meteor
Important to define what x and y is in this context
pliant shore
x = 2(ab + 1) and y = 4a + b to remind you
yeah, I see you're getting the idea for 18.3 too, but you're further off
fierce timber
imma try doing it again with the info you just gave me
to see if i get any closer or actually solve it
pliant shore
do not try and expand x^2 - y^2 or factor it just yet
pliant shore
it's substitute first then factor
fierce timber
i got it right but i pretty much guessed
like i didnt get it right because i completely understood it
magic meteor
Ok so think of it this way. We have two squares right?
We call one x and the other y.
If we want to find the difference between them, we have to do x^2 - y^2=(x+y)*(x-y)
First of all, lets do 18.3. What is x and y in that context?
fierce timber
youre asking me to compare it to 18.2?
pliant shore
do you see how you can get $(x^2 - y^2 + x + y)(x^2 - y^2 - x - y)$?
soft zealotBOT
south
fierce timber
what should i answer first
fierce timber
What is x and y in 18.3
x- x2 (btw when i put the 2 its because i cant find the squared) so basically x= (x2-y2)2 and y is -(x+y)2 if thats what you meant
actually without the squared at the end
magic meteor
Last page of your special symbols there should be ^
we use that to denote squared
So x^2
fierce timber
how to type it
magic meteor
Phone or pc?
fierce timber
pc
magic meteor
Look carefully on your keyboard for the upwards arrow, it varies with region
For me its next to enter
fierce timber
how is the szmbol called so i can google it
pliant shore
try 'caret'
fierce timber
no wait actually i have better solution
alr so is this correct
in 18.3
x- (x^2-y^2)
y- -(x+y)
pliant shore
alr so is this correct
in 18.3
x- (x^2-y^2)
y- -(x+y)
no, the new y is (x + y)
no minus sign
fierce timber
oh yeah mb
pliant shore
otherwise that's correct
magic meteor
I hate how the names for the squares are the same as the factors
Just stick with a and b😭
pliant shore
yeah it's an abuse of notation to say that
fierce timber
so should i try to replace x with a and y with b and solve it like that
pliant shore
you'd need to say X = x^2 - y^2 and Y = x + y
pliant shore
so should i try to replace x with a and y with b and solve it like that
yes
magic meteor
Write the equation now
magic meteor
Yup,
fierce timber
so im on the right track?
pliant shore
now you can expand the brackets, yes
fierce timber
wdym by expand
does that mean that you want the first part of the first bracket (a^2-b^2) to make it (a-b) (a+b)
pliant shore
does that mean that you want the first part of the first bracket (a^2-b^2) to ma...
that's what we need, yes!
so (a - b)(a + b) + (a + b)
fierce timber
and i do that for both parts or just the first
pliant shore
and i do that for both parts or just the first
both parts
magic meteor
We do the first first and the second second
pliant shore
you need to factor both brackets
fierce timber
like this?
magic meteor
We should prolly collect like terms to avoid confusion before expanding tbh
fierce timber
yeah cuz from 1st to 8th grade everything was in italian and now 9th grade everything is in croatian so my terminology that i know is like split in half with italian and croatian and i know a bit of it in english
magic meteor
Math is math, the symbols may change but the methods stay the same
We usually do everything in the english alphabet, since its more international
fierce timber
wait so am i on the right track if you look at the last thing i wrote
pliant shore
like this?
correct, but you need to keep factoring both brackets
fierce timber
and how do i do that
pliant shore
(a + b)(a - b) + (a + b)(1), that's the same as the first, do you agree?
fierce timber
wait what
yeah thats the same
cuz anything multiplied by 1 is 1
i mean
that
by 1
is that
like x by 1 is x
magic meteor
Correct
fierce timber
my bad my fingers are faster than my brain
pliant shore
(a + b)(a - b) + (a + b)(1), that's the same as the first, do you agree?
so you can factor this with (a + b) in common
fierce timber
wait i think i see what you mean
magic meteor
Ok, lets start with the first bracket step by step, [(a^2-b^2)+(a+b)]=[a^2-b^2+a+b] right?
fierce timber
yes
magic meteor
If we wanted to collect all the as together and the bs together how would we do that
With parenthesis
fierce timber
wait but then my last step was useless?
fierce timber
yeah but my step and the one he showed me go in diffeent directions
i feel like his is more simple
magic meteor
Theyre both right
fierce timber
imma go with yours
magic meteor
I just prefer to collect like terms before expanding
What do we do next then?
If we want to collect as together and bs separate?
fierce timber
if i do that i get (a^2-b^2+a+b) (a^2-b^2-a-b)
fierce timber
Ok, lets start with the first bracket step by step, [(a^2-b^2)+(a+b)]=[a^2-b^2+a...
, we cancel out the parenthesis?
magic meteor
But we want to keep them in brackets for now
magic meteor
if i do that i get (a^2-b^2+a+b) (a^2-b^2-a-b)
(a^2-b^2+a+b) now what?
Dont dissolve the parenthesis
fierce timber
but thats what you did here
fierce timber
Ok, lets start with the first bracket step by step, [(a^2-b^2)+(a+b)]=[a^2-b^2+a...
.
magic meteor
Yes, correct, its just better to do them separate😭
Since it avoids confusion
Lets start with grouping terms, (a^2-b^2+a+b) =[(a^2+a)-(b^2-b)] right?
fierce timber
yes
magic meteor
So now we have two parts. What can we do?
pliant shore
Lets start with grouping terms, (a^2-b^2+a+b) =[(a^2+a)-(b^2-b)] right?
that's not how you fully factor it though
fierce timber
i can send u the way my teacher did it its way shorter but like way more complex
magic meteor
that's not how you fully factor it though
I mean we can just multiply after
fierce timber
So now we have two parts. What can we do?
i really have no idea dawg
pliant shore
a(a + 1) - b(b - 1) is not a valid factorisation
magic meteor
a(a + 1) - b(b - 1) is not a valid factorisation
No, but a(a + 1) - b(b - 1) can be factored further
pliant shore
fair
fierce timber
i can send u the way my teacher did it its way shorter but like way more complex
should i?
magic meteor
Wait are we going for a linear system or a factored system??
fierce timber
i have no idea waht you just said
the exercise says
rastavi na faktore which means decompose into factors
magic meteor
Classic vague maths
fierce timber
hopefully you understand it
its just the way my professor did it i sent it here so maybe this is the way i should do it too
fierce timber
can you explain why he adds the -1^2 in the bracket?
pliant shore
cause $(a - b)^2 - (1)^2$ is another difference of squares
soft zealotBOT
south
pliant shore
oh wait before that
magic meteor
Should be -(1^2) tbh
pliant shore
if you divide $(a - b)^2 (a + b)^2$ by $(a +b)^2$, you get $(a - b)^2$
soft zealotBOT
south
pliant shore
now if you divide $(a + b)^2$ by $(a + b)^2$...
soft zealotBOT
south
fierce timber
thats just 1?
magic meteor
@pliant shore Are we going for [a(a - 1) - b(b + 1)] * [a(a + 1) - b(b - 1)] or the linear form😭
Theyre both fully factored technically
pliant shore
<@1151031274413228043> Are we going for [a(a - 1) - b(b + 1)] * [a(a + 1) - b(b ...
no, a(a - 1) - b(b + 1) is not fully factored
cause that's not a product of brackets
pliant shore
thats just 1?
indeed
magic meteor
Alr fair, only linear factors
fierce timber
i kinda understand now
magic meteor
I mean what your professor wrote is the solution 🙂
fierce timber
basically we got that for homework 2 weeks ago and someone asked if he could explain it which he didnt do he just solved the exercise without explaining
magic meteor
I do think that it should be -(1^2) rather than -1^2 but i guess its just semantics
magic meteor
basically we got that for homework 2 weeks ago and someone asked if he could exp...
Unfortunately it be like that, factorizing is just finding common factors and pulling them out
Its hard to explain
fierce timber
and even harder to understand
magic meteor
Pretty much, if it helps, consider factors to be a polynomial just divided up, whenever you have a group of factors you can go backwards and create a polynomial.
@pliant shore Gotta go, freezing my hands off writing this so imma go inside
fierce timber
yall so nice ty guys
fierce timber
.close
final saddleBOT
final saddleBOT
Available help channel!
plain rain
if a sequence diverges does that mean that every subsequence of it also diverges?
final saddleBOT
if a sequence diverges does that mean that every subsequence of it also diverges...
half raptor
lethal totem
Think!
tired walrus
if a sequence diverges does that mean that every subsequence of it also diverges...
1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, ...
lethal totem
(-1)^n
final saddleBOT
rocky tusk
this doesnt diverge
wut
plain rain
.reopen
final saddleBOT
✅ Original question: #help-36 message
bleak granite
it's bounded but not convergent
plain rain
yeah but also not divergent
rocky tusk
dawg
plain rain
look
bleak granite
we define divergent by not convergent
plain rain
| a_n | < 2
bleak granite
yes
plain rain
we define divergent by not convergent
rlly?
bleak granite
it's bounded
plain rain
but divergence means a_n > M for every positive M in R. or -M
rocky tusk
no it doesn't
plain rain
huhhhh
bleak granite
that's just the opposite of bounded
rocky tusk
thats unbounded
plain rain
oh i see
bleak granite
a sequence being bounded is not a sufficient condition of it converging
plain rain
im not talking abt convergence
rocky tusk
there is no such thing as a sequence neither converging or diverging
divergence is the literal negation of convergence
plain rain
divergence. i thought if it doesnt converge to a point, but also doesnt diverge to infty, it doesnt diverge
rocky tusk
no
final saddleBOT
formal trail
if it doesn't converge to a point, then it diverges, full stop
lethal totem
maybe wed have to mention its monotonous too
So you're looking for a monotone divergent sequence with convergent subsequence?
plain rain
nono i was just asking
lethal totem
That's actually an interesting question though
plain rain
.reopen
final saddleBOT
✅ Original question: #help-36 message
lethal totem
Yeah that makes sense
plain rain
.close
gritty flume
Can I get help w question 3
final saddleBOT
Can I get help w question 3
tired walrus
ok, that's definitely a lot of threes running around
how far did you get on your own thus far
tired walrus
show your attempt and we can diagnose it
gritty flume
I don’t understand why
tired walrus
show your attempt so that we can see where and how you went wrong
gritty flume
tired walrus
ok i see two mistakes
the second of which is that 3x^(3+3+3) somehow had its x completely evaporate into nothing
actually no i see more mistakes
gritty flume
I multiplied
tired walrus
on the bottom, you have:
3 * x^3 * 3 * x^3 * 3 * x^3
there are three 3's in the product
those become 27, not just a single 3
tired walrus
why what
gritty flume
those become 27, not just a single 3
Does it multiply
tired walrus
remember that when a number and a letter stand next to each other in algebra, it means multiplication
$3x^3$ is really $3 \cdot x^3$, agree or disagree?
gritty flume
Yes
soft zealotBOT
Ann
tired walrus
on the bottom, you have:
3 * x^3 * 3 * x^3 * 3 * x^3
or
3 * 3 * 3 * x^3 * x^3 * x^3
do you understand now what went on in the denominator
gritty flume
I still don’t get it
tired walrus
ok lets try to forget about that for a bit
here is a different expression
i want you to simplify this for me:
2a * 4a
gritty flume
Idk how to do it
tired walrus
again,
when two things are next to each other,
it means multiplication,
so 2a * 4a breaks down into 2 * a * 4 * a
understand?
gritty flume
Yes
tired walrus
multiplication is commutative,
so these factors can be written in any order you like,
for example as 2 * 4 * a * a
understand?
tired walrus
there's no kinda, you either understand what im talking about or you dont
gritty flume
Does it become 8a^2?
tired walrus
yes 8a^2 is correct
gritty flume
Ic
tired walrus
now can you do the same thing to 3x^3 * 3x^3 * 3x^3
tired walrus
x^3
don't miscopy the 3 exponents as 2's
you did that all three times 
also your fraction bar is way way too short and those x's are very sad in the rain
gritty flume
I’m sorry
gritty flume
gritty flume
I don’t know how to do the x
Ohh
So the 3 multiply
And the card
Add
X
Tysm
I still need help
tired walrus
ok, so what did you get in the denominator then
gritty flume
I got 27x^9
Can you tell me the rules for this
Bc it’s way different form what Ik
tired walrus
the rules for... what exactly
gritty flume
The question you helped me w
What Ik is same base and it’s multiplying means you add
tired walrus
i dont really know what "rules" i could possibly give you
tired walrus
What Ik is same base and it’s multiplying means you add
that's the law a^x * a^y = a^(x+y)
but phrased in a wonky way
gritty flume
I don’t get it
tired walrus
i am taking the thing you're saying and rephrasing it with more proper wording.
im struggling to think of any rules that i could give you to memorize as mantras
cause like, idk
when a number and a letter stand next to each other in algebra, it means multiplication
thats the closest i can give you
you maybe need to go back to easier questions to repractice
gritty flume
I don’t have time
I have an exam tomorrow
And other thing to study
What about question 4
The guy in the video did 4.4^x as the denominator
tired walrus
when you add four of the same thing together, it is the same as multiplying that thing by 4
granite ivy
Yes
tired walrus
$a+a+a+a=4a$
soft zealotBOT
Ann
tired walrus
no deep magic or mystery or arcane rule here