💀
#help-38
verbal idol
dense breach
snow would solve this in 2 minutes using complex numbers
tulip vapor
fr?
dense breach
probably
tulip vapor
but thats cheating fr
frozen plover
snow would take one look at this and decide its not worth anyones time
wet dragon
snow would solve this in 2 minutes using complex numbers
you can use complex numbers for this?
frozen plover
don't ping them...
dense breach
idk I can't
verbal idol
you can use complex numbers for this?
use de moivre?
frozen plover
you can use complex numbers for this?
if there is trig there is probably complex numbers
tulip vapor
havent yall studied complex numbers
wet dragon
use de moivre?
why you putting a question mark like me asking that is bizarre af?
anyway
worldly wing
Isn’t the first bracket equal to 21
worldly wing
Yeah I remember that result
verbal idol
in this question
verbal idol
Yeah I remember that result
same
tulip vapor
could be, then the second must simplify to 5 to make final answer 105
verbal idol
but proving it is hard
dense breach
$\tan(x) = \f{e^{-ix}-e^{ix}}{e^{ix}+e^{-ix}}i$ or something
solid kilnBOT
thewizardofOU
tulip vapor
Yeah I remember that result
then write it down
tulip vapor
**thewizardofOU**
oh fk
wet dragon
tulip vapor
8 of my neurons died just by looking at this
wet dragon
i was trying something
verbal idol
$\tan(x) = \f{e^{-ix}-e^{ix}}{e^{ix}+e^{-ix}}i$ or something
no wait
tulip vapor
woa
verbal idol
(cosx+isinx)^n= cos(nx)+ isin(nx)
tulip vapor
,w $$\left(\tan^2 \frac{\pi}{7} + \tan^2 \frac{2\pi}{7} + \tan^2 \frac{3\pi}{7}\right) \cdot \left(\cot^2 \frac{\pi}{7} + \cot^2 \frac{2\pi}{7} + \cot^2 \frac{3\pi}{7}\right)$$
solid kilnBOT
worldly wing
(cosx+isinx)^n= cos(nx)+ isin(nx)
Ah yeah this works
amber python
snow would solve this in 2 minutes using complex numbers
nah wtf
verbal idol
Ah yeah this works
yepp
tulip vapor
,w explanation $$\left(\tan^2 \frac{\pi}{7} + \tan^2 \frac{2\pi}{7} + \tan^2 \frac{3\pi}{7}\right) \cdot \left(\cot^2 \frac{\pi}{7} + \cot^2 \frac{2\pi}{7} + \cot^2 \frac{3\pi}{7}\right)$$
fkin give the stepss
worldly wing
That’s not how wolframalpha works…
tulip vapor
WHAT THE F
verbal idol
wow
tulip vapor
IM TRAUMATIZED
tulip vapor
but i dont wanna use some random ass identities i dont even know
even if i get the solution now, theres no point
because using this method wont click in my mind ever
verbal idol
but i dont wanna use some random ass identities i dont even know
bro you gotta learn the tan (nx)
it is useful for jee
tulip vapor
bro you gotta learn the tan (nx)
what chapter is that
verbal idol
what chapter is that
you can learn it in trig and prove it in complex numbers
tulip vapor
both my trig functons and equations is done but i havent been taught that tan(nx) thing
marsh forum
was about to suggest using complex numbers
verbal idol
you can see the pattern
tan2x = 2tanx / 1- tan^2x
tan 3x = 3tanx - tan^3x/ 1 - 3tan^2 x
tulip vapor
was about to suggest using complex numbers
this question is from topics you learn before complex numbers
verbal idol
if you see the pattern
tan (2x) = S1/S0 - S2
where Sn is sum of tan(x) taken n at a time
tulip vapor
whaaaaaa
verbal idol
(this was taught to us im not lying)
tulip vapor
hold on
verbal idol
yes
tulip vapor
lemme use normal identities
$$\left(\tan^2 \frac{\pi}{7} + \tan^2 \frac{2\pi}{7} + \tan^2 \frac{3\pi}{7}\right) \cdot \left(\cot^2 \frac{\pi}{7} + \cot^2 \frac{2\pi}{7} + \cot^2 \frac{3\pi}{7}\right)$$
solid kilnBOT
Aryan07
frozen plover
tan(nx) is a neat pattern
tulip vapor
yeah so
verbal idol
tan 3x = S1 - S3/ S0 - S2
verbal idol
tan(nx) is a neat pattern
IKR
tulip vapor
taking pie/7 as theta
verbal idol
its soo good
verbal idol
no other way
worldly wing
you can try finding an equation which has roots tan(pi/7), ...
verbal idol
you can try finding an equation which has roots tan(pi/7), ...
yeah that's what the solutions says
but bro wont listen
worldly wing
ah, I see
that seems to be the easiest way other than like
expanding everything out
verbal idol
yeah
wet dragon
but bro wont listen
@tulip vapor he is little broing you
verbal idol
mb gotta go
worldly wing
$4\theta=\pi-3\theta$ and take tan on both sides
tulip vapor
<@702134769420599347> he is little broing you
im a lil bro fr tho
solid kilnBOT
kheerii
worldly wing
should work
tulip vapor
but wheres 4theta in the question 💀
worldly wing
but wheres 4theta in the question 💀
let $\theta=\frac{\pi}{7}$ then $7\theta=\pi$
solid kilnBOT
kheerii
tulip vapor
yeah
wet dragon
but wheres 4theta in the question 💀
let theta = pi/7
worldly wing
also, $\tan(4\theta)=\tan(\pi-3\theta)$ has roots $\frac{\pi}{7},\frac{2\pi}{7},\frac{3\pi}{7}$
solid kilnBOT
kheerii
tulip vapor
**kheerii**
how on earth is this gonna come in my mind bruv
worldly wing
how on earth is this gonna come in my mind bruv
that's the point of practicing questions, to build up your thought processes while solving questions
tulip vapor
😭
worldly wing
theta=pi/7 is an obvious step, from where you have 7theta=pi
dense breach
it was really more of a slow build up
worldly wing
after this 4theta=pi-3theta should also not be too hard to think of
tulip vapor
theta=pi/7 is an obvious step, from where you have 7theta=pi
till there is fine, after it just blows me off
worldly wing
whenever you have this kind of form you need to split your theta into two parts
it's a similar method to how we find $\cos\left(\frac{\pi}{5}\right)$ and the other trig ratios
solid kilnBOT
kheerii
worldly wing
$5\theta=\pi\implies 3\theta=\pi-2\theta$
solid kilnBOT
kheerii
tulip vapor
i have memorized pie/5 and other important ratios tho
worldly wing
i have memorized pie/5 and other important ratios tho
you should still know how they are found
tulip vapor
hmm
tulip vapor
**kheerii**
instead of this, 3A + 2A = pie would come into my mind
worldly wing
instead of this, 3A + 2A = pie would come into my mind
it's the same
tulip vapor
and I would be doing tan(A+B) 💀
hold on let me write it down
but
why are we bothered with 4theta here
tulip vapor
but out of so many different ways why only 4theta = pie-3theta
worldly wing
It’s the easiest
If you did it as 5theta=pi-2theta you would need to find tan(5theta)
Although this approach will work as well
tulip vapor
but I would have to find 4theta too and i dont know that formula
worldly wing
but I would have to find 4theta too and i dont know that formula
You should learn I
The formula for tan(nx)
It’s pretty handy
frozen plover
real for that
worldly wing
If you refuse to learn any approach which will help you solve this question, nobody can help you.
tulip vapor
The formula for tan(nx)
I dont know basic concepts of complex numbers
worldly wing
Who says this involves complex numbers…?
tulip vapor
the people earlier
so whats the formula for tan(nx)?
the general formula
@worldly wing
...
tulip vapor
what am i supposed to look for in this'
tulip vapor
whats k
frozen plover
index variable for the summation
delicate pagoda
tan(nx) is equal to a sum of things from 0 to n
divided by another such sum
that's just an identity of the tan function
frozen plover
am i supposed to know what that means
yes?
[ \sum_{k = 1}^{10} k ]
Do you know what this means
tulip vapor
nope
solid kilnBOT
Bob l'éponge
frozen plover
oh boy
tulip vapor
i dont know what this summation function upper and buttom thing means
frozen plover
It means you put the value that it starts from
in this case 1
up to the value on top
in this case 10
tulip vapor
oh
frozen plover
so this sum is just 1 + 2 + 3 + 4 ... 10
tulip vapor
ahh
delicate pagoda
**Bob l'éponge**
=1+2+3+4+5+6+7+8+9+10=55
tulip vapor
yeah whats the next step now
frozen plover
Do you know what [ \binom nk ] means
solid kilnBOT
Bob l'éponge
tulip vapor
no
tulip vapor
thats from binomial theorem ig, that chapter we'll study in future
delicate pagoda
the binomial coefficient describes how many ways there are to choose k of n elements
solid kilnBOT
Bob l'éponge
frozen plover
thats from binomial theorem ig, that chapter we'll study in future
yeah
tulip vapor
so in short im cooked
frozen plover
ask your teacher about the problem
i doubt you'll be assigned something you haven't been taught the tools for
tulip vapor
after doing theory of my trig function and eqn chapters i decide to hit some cengage or other modules, but internet decides to hit me up with this question
tulip vapor
i doubt you'll be assigned something you haven't been taught the tools for
i havent been assigned this from my teacher, apparently this topic is from trigo compound angles, but almost all methods require some other tools from later chapters
tulip vapor
usually 11 out of 10 people in help section are indians prepping for jee
idk why they abandon me today
frozen plover
sure but the whole point of your exam is to get as much in as little time as possible
you're no superhero for doing something anyone else can't
tulip vapor
sure but the whole point of your exam is to get as much in as little time as pos...
exactly, thats why I refuse to learn those extra long methods
frozen plover
¯_(ツ)_/¯
frozen plover
you said you aren't to spend more than 5 minutes, this channel's been open for an hour
tulip vapor
fr
lol
but
its like a challenge
first time is always a longer time period
@frozen ploverhow to find range of sqrt(9tan^2 A+ 4cot^2 A + 13)
frozen plover
AM > GM probably
tulip vapor
so I did 9tan^2 + 4cot^2 >= 12
frozen plover
for positive reals
tulip vapor
I mean can you find range of ANY function with this?
frozen plover
I mean can you find range of ANY function with this?
not really
it's only useful in certain cases
frozen plover
is it only for reciprocal functions
like this sure
but the condition for it to be true is positive real
earnest frigate
im lost please
trim joltBOT
im lost please
trim joltBOT
@earnest frigate Has your question been resolved?
trim joltBOT
@earnest frigate Has your question been resolved?
earnest frigate
.close
trim joltBOT
rotund grove
,w derivatives
solid kilnBOT
rotund grove
,w integrals
solid kilnBOT
rotund grove
,w limits
solid kilnBOT
trim joltBOT
Available help channel!
pallid cedar
ok so this is a question on a practice quiz i narrowed it down between 2x^2+5x+2 and 6x^2-x-2 but i can't figure out which one of them is right because both of them interset the quartic function twice at y=0
knotty quest
Just divide as u normally do?
pallid cedar
what do you mean?
knotty quest
Did u ever divide quadratic or cubic with linear?
pallid cedar
it's just polynomial divison right?
knotty quest
Yes
pallid cedar
why would it be with linear?
knotty quest
No i mean like
pallid cedar
isn't it quartic division by quadratic?
knotty quest
That process
U have 2 options
Try diving the thing with ur options
Remainder is zero then that is the answer
pallid cedar
ok give me a min to do that for both factors
knotty quest
Ok
pallid cedar
ok so this is the point where i was at with my first factir
knotty quest
Yes
pallid cedar
wait nvm i realize my mistake
the first factor divides evenly
both divide evenly
(6x^4+23x^5+18x^2-12x-8)/(2x^2+5x+2) = 3x^2+4x-4
and the other factor gives (x^2+4x+4)
would i just pick the first factor bc x^2 + 4x + 4 can be factored further into (x+2)(x+2)
trim joltBOT
@pallid cedar Has your question been resolved?
trim joltBOT
dense breach
I would start by taking the log of the whole thing
since log is continuous you can move it inside the limit
trim joltBOT
slate barn
slate barn
notice that you can bound the top part by pi/2
please continue in https://discord.com/channels/268882317391429632/903430333096132618
delicate bobcat
since arctan(inf) --> +pi/2
slate barn
since arctan(inf) --> +pi/2
and yea you are right
delicate bobcat
but ugh ^(1/n) makes me think about taking ln or doing e^(...)
trim joltBOT
Available help channel!
woeful totem
trim joltBOT
woeful totem
Are there ways to define functions that are piecewise functions kind of like this, but in non piecewise form, like an actual function
woeful totem
Sign just gives the sign of the number correct
lusty delta
yes
woeful totem
Could you explain the floor function, is it describing the periods of the function, and counting what "piece" it's on
lusty delta
plot the graph or individual components to see how it looks
tall prawn
Hey friends. I've been struggling with something in writing Mathematics: how to start a list of biconditional statements. It's something I come up against quite a lot, but I can't figure out the right way to go about it. Please can someone look at the two images I've posted, and tell me if Version 1 or Version 2 is correct? 🙂
trim joltBOT
Hey friends. I've been struggling with something in writing Mathematics: how to ...
@tall prawn Has your question been resolved?
trail ingot
what is ‘the series’
tall prawn
Hey, thanks for the reply. Ah yeah sorry, I should have included that in the post. (Although, I don't think it really matters to my question. I'm interested in the writing, in the parts of the images I've highlighted) 🙂
rugged harness
Hey, thanks for the reply. Ah yeah sorry, I should have included that in the pos...
would you be able to continue this on your own?
tall prawn
Hey Xene, thanks for the reply. My question is not about how to solve this specific problem. My issue is, I am trying to understand how to correctly write a situation like I've highlighted in the images I've posted: how to start a series of biconditional statements. I think my pictures explain it better than I can in words!
tall prawn
.close
trim joltBOT
@tall prawn Has your question been resolved?
simple haven
@tall prawn please forgive me, other than the text at the top indicating the version number, and very minor differences in how the words are written (n.b. literally how, as they appear to be all the same words), I am unable to spot the difference between your original two images.
Can you highlight the difference for me? Because apparently I am bad at reading.
Actually I think I found a difference being the text "the following equations hold" being included in the second and omitted in the first.
If this is the only difference, I don't see a significant problem with either including or excluding that phrase.
flat spruce
why is this not diagonalizable over R, the eigenvalue of 3 has equal algebraic multiplicity and geometric multiplicity, no?
flat spruce
char. poly.
unique minnow
I mean the diagonalization would mean that you get a diagonal 3x3 matrix of the eigenvalues, but 2 of them are complex
flat spruce
oh shit yeah that was stupid of me, I was going purely off the definition
unique minnow
So even if one of them fills its eigenspace, you`re still missing two
trim joltBOT
unique minnow
Nw
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Available help channel!
marsh forum
$\exists x\forall y(x<y)$
trim joltBOT
$\exists x\forall y(x<y)$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
Trying to figure out why this statement is false
We're dsiscussing over W btw
so this means there exists x for all y such that y>x
ooh
say y is 0
there's no smaller number belonging to W
right?
vagrant marsh
whats W
amber python
whole numbers?
exotic jetty
TIL whole numbers are non negative
marsh forum
whole numbers?
yes
marsh forum
there exists x, for all y, such that $y>x$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
vagrant marsh
try saying it without using exists or for all
marsh forum
how? $\forall$ means forall, right?
solid kilnBOT
ƒ(Why am. I here)=I don't Know
vagrant marsh
yes
marsh forum
ok, there is a x for every y such that y>x
exotic jetty
there is a whole number such that any other whole number is greater than it?
vagrant marsh
there is a whole number such that any other whole number is greater than it?
something like this yeah
marsh forum
oh, right.
marsh forum
there is a whole number such that any other whole number is greater than it?
thanks
vagrant marsh
i.e. there is a smallest element of W
trim joltBOT
trim joltBOT
Available help channel!
latent axle
Is there something more to part a in question 13 other than just cancelling the xs?
latent axle
Uh
knotty locust
So you have to show that it agrees with sin(x) in both cases
latent axle
Wdym
knotty locust
What is sin(x) when x is 0?
latent axle
0
knotty locust
And what is xf(x) when x is 0?
latent axle
0
knotty locust
🔠
latent axle
What
latent axle
So I’m just proving continuity
knotty locust
No you’re proving that they’re equivalent functions
knotty locust
In part a there is no integration
latent axle
Yeah
knotty locust
Part a helps with part b
latent axle
Sure but how does that like
Solve it
I guess
because it’s only sinx when x is not 0
knotty locust
No, both are 0
latent axle
Wha
latent axle
Sure
knotty locust
Sure or yes?
knotty locust
So when x is 0, x*f(x) = ?
latent axle
0
knotty locust
No
There’s no division going on
Anywhere
Its x multiplied by f(x)
f(x) is 1
And x is 0
So it’s just 0*1
No division
x * f(x)
Equals
x * 1 (When x=0, f(x)=1 is why we make this replacement)
So
0 * 1
=0
So ignoring the top half of the function, for other values of x
All we’ve shown is that
latent axle
Okay
knotty locust
But how does that help us in (x)(sinx/x)
In the other case, x is always greater than 0, so you can cancel the xs
latent axle
So I can revolve it without it being defined at that point
latent axle
Yes
knotty locust
Okay
And so we can simplify the top case, since x is not 0, they cancel
and we can simplify the bottom case, its x, which is 0
so
solid kilnBOT
Austin
knotty locust
So do you then also agree with this?
knotty locust
Yes
So if we want to show xf(x) = sin(x)
We have to show it for both cases
If 0<x<=pi
We’re already done, because it is sin(x)
Right?
latent axle
Okay yeah
knotty locust
and we want to show its equal to sin(x)
latent axle
Yes
knotty locust
maybe it makes more sense to write this
$$xf(x)=\begin{cases} \sin(x) \quad 0<x\leq \pi \ 0 \quad x=0\end{cases} ?= \begin{cases} \sin(x) \quad 0<x\leq \pi \ \sin(x) \quad x=0 \end{cases}$$
solid kilnBOT
Austin
knotty locust
because the thing on the right is just sin(x), yes?
just written case-wise, so you can compare them more directly
latent axle
Okay
knotty locust
Does it make sense to write it like that or not?
latent axle
Yeah I guess
knotty locust
If it doesn't make sense, what is confusing you
knotty locust
Okay, so now we want to show that they're actually equal not just "?="
we will go case by case
starting with the top case
Are they equal for 0<x<= pi?
latent axle
The top and bottom to each other?
latent axle
the left hand side is xf(x)
Oh
knotty locust
consider first when 0<x<=pi
latent axle
yes
knotty locust
this means showing that the top lines of both sides
are equal
which of course they're
since they're both the same thing
Then consider when x=0
latent axle
Then consider when x=0
Uhm
latent axle
yeah x times sin(0) is 0
latent axle
what is the left
xsin(x)
latent axle
for x is 0
latent axle
it’s just the 0?
knotty locust
yes its just the 0
latent axle
Okay
knotty locust
We showed that earlier
latent axle
well yes x*f(x) is 0 for x is 0
latent axle
So it’s true for both upper and lower case
knotty locust
what is it when x=0?
latent axle
what is it when x=0?
which case
knotty locust
I said "when x=0"
latent axle
It’s 0
knotty locust
because 0*1=0 and sin(0)=0
trim joltBOT
@latent axle Has your question been resolved?
royal escarp
i need help understanding how completing the square can be used to find the vertex of parabolic equation
sick onyx
u know the genral form of the parabola?
u have to compare the genral form with the final eq
main sigil
Completing the square converts the parabola from standard form (ax^2 + bx + c) to vertex form (x-h)^2 + k. And in vertex form the coordinates can be found simply as (h, k)
trim joltBOT
@royal escarp Has your question been resolved?
royal escarp
<@&286206848099549185>
wraith hinge
hey
you pinged helpers ?
@royal escarp i saw your ping i js was helping another guy with potential energy
took ages having to explain it
hey mate u there ?
wraith hinge
yeah
ppl ask for chemistry
physics
and other stuff commonly
may i ask what your inquiry was ?
id love to help
btw sry for the wait
royal escarp
i need help understanding what k is algebraically in vector form
wraith hinge
may i ask for what level
is this o levels or a levels
if so what type of vectors ? do you mean the vectors in triangles
in further mathamatics
wraith hinge
i have some notes on this
just gotta ask
what level of studies are you attending
is this for 16-18
or 14-16
wraith hinge
because vectors change drastically
wraith hinge
the class is calc 1
sorry im not sure what that is exactly
vectors are in both pre calc and calc
royal escarp
pre calc
wraith hinge
im just rusty
makes sence but what system do you attend
royal escarp
correct
wraith hinge
may i ask for the question you wish to have help with ?
royal escarp
i want help with the general idea
wraith hinge
pardon ?
royal escarp
but i can provide a question if that would help
wraith hinge
nah its no problem
royal escarp
vertex
royal escarp
not vector
wraith hinge
i thought i had to do vectors of a parabola
ight so u know how there are quadratic functions right
the general graph is something called a parabola
a parabola graph is a graph which is used when dealing with quadratic functions as it has 2 x values
so look
wraith hinge
the parabola has the axis of symetry the vertex and the y intersept
wraith hinge
its the highest or lowest point depending on which side the parabola is on
royal escarp
ax^2 + bx + c
wraith hinge
but if i want to find that numerically
hmmm could you provide an example question
ahh makes sence
wraith hinge
yeah
royal escarp
(x-h)^2 + k
wraith hinge
to find the vertex from the two points right ?
royal escarp
where h and k are the vertex
wraith hinge
sorry what ?
wraith hinge
k
wraith hinge
$(x - h)^2 = x^2 - 2hx + h^2$ do you mean this ?
solid kilnBOT
Exornion
wraith hinge
mate
you got it all wrong
when they tell you to graph it
they mean to draw the parabola
royal escarp
I'm aware
wraith hinge
there cant be 2 vertexes though
royal escarp
But you need certain information to graph it don't you?
wraith hinge
you get that from the equation
wraith hinge
ahh makes sence
royal escarp
Since that's what I'm having trouble grasping
wraith hinge
but let me help you here
all the points of the graph can be found
i have quite a lot of notes from my gcses
on this self same subject
first off
the parabola opens upwards
because the coefficent is positive
royal escarp
royal escarp
How
wraith hinge
$x = -\frac{b}{2a}$
solid kilnBOT
Exornion
wraith hinge
for the given formula
a is 2
and b is 4
so x is -1
the parabola starts at -1
it intersects the 2 points
royal escarp
what about the y value
wraith hinge
wait let me find the other thingy
ill do it rn
so look
you Substitute x = -1 back into the function to find the y-coordinate of the vertex:
f(-1) = 2(-1)^2 + 4(-1) + 3 = 2(1) - 4 + 3 = 1
see this
i tried to write it well
but it isnt so neat
but its equal to 1
so the vertex is at (-1,1)
@royal escarp
is this good enough ?
i could clarrify more
if you need me to
royal escarp
its -2,1
wraith hinge
;-;
sry mb
i miscalculated
i went a bit fast
havent done 2d quadratic functions in a while
wraith hinge
look u want the steps to graph a quadratic function
i can send an image of my past notes
royal escarp
**Exornion**
this is a gbig help
royal escarp
actually no
wraith hinge
royal escarp
its suppossed to be -2,-1
wraith hinge
oh mb i alr sent
but there are the steps
sry for the mistake
have a good one mate !
also use .close when you are done
royal escarp
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torn shale
Not only did my teacher tell me that this function (x^2+y^2=y) is not implicit
torn shale
He also said that we cant simplify it and turn it to non-implicit using quadratic formula
I need clarifications 🤨
torn shale
Not only did my teacher tell me that this function (x^2+y^2=y) is not implicit
Y is a function of x btw
hallow kite
how are you defining implicit and explicit?
i believe explicit is when you can algebraically rearrange for y to equal only a function of x
and implicit is anything else
torn shale
how are you defining implicit and explicit?
Explicit: you can seperate y from x without having y in the product
Implicit is everything else
torn shale
Explicit: you can seperate y from x without having y in the product
Like y=2+3x is explicit
Y=2+3xy^4 is implicit
torn shale
i believe explicit is when you can algebraically rearrange for y to equal only a...
Idk if thats the same thing 😭
torn shale
Explicit: you can seperate y from x without having y in the product
But here
formal sage
It is the same thing
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@torn shale Has your question been resolved?
torn shale
It is the same thing
That means my teacher was wrong yeah?
wraith hinge
Not only did my teacher tell me that this function (x^2+y^2=y) is not implicit
it is implicit
torn shale
it is implicit
What abt it being simplifiable with quadratic
wraith hinge
but it's defined a bit differently (more generally) than the way you defined it
wraith hinge
What abt it being simplifiable with quadratic
and how exactly would you do that?
torn shale
and how exactly would you do that?
Ah
wraith hinge
yeah, you can't
wraith hinge
you'd need -2xy for this to be a perfect square
and you have -y
also the quadratic formula doesn't apply here
torn shale
you'd need -2xy for this to be a perfect square
Idk how to perfect square studd
wraith hinge
well it's not a quadratic is it?
torn shale
well it's not a quadratic is it?
Isnt it 😭
But like
Isnt c is the coefiicent of y^0
Whats wrong eith applying it there
wraith hinge
well it's not a quadratic is it?
in one variable, that is
torn shale
in one variable, that is
Why cant we consider x^2 as c
wraith hinge
I mean, you could technically factorize this but
I don't see why you would want to
you get a very very messy answer
also it'll only be defined for a specific domain
torn shale
Why cant we consider x^2 as c
.?
torn shale
also it'll only be defined for a specific domain
Oh hmm
wraith hinge
Oh hmm
$\left( y - \frac{1 + \sqrt{1 - 4x^2}}{2} \right) \left( y - \frac{1 - \sqrt{1 - 4x^2}}{2} \right) = 0$
solid kilnBOT
45
wraith hinge
no this is the factorization of y^2 + x^2 - y as two binomials
wraith hinge
But it follows the same steps as this and gives the same answer
you can consider x^2 as c yeah
as a constant
however
note that
for the solutions of this to be real
we need a non-negative discriminant
torn shale
1-4x^2 is equal to or bigger than 0
wraith hinge
so the factorization is only valid for $x \in \left[-\frac{1}{2}, \frac{1}{2}\right]$
solid kilnBOT
45
wraith hinge
1-4x^2 is equal to or bigger than 0
yeah
torn shale
yeah
Ok so the answers for my questions are: yes the function is implicit and it we can factorize but with a certain domian
Would it be explicit
After we factorized it
wraith hinge
Would it be explicit
$y$ would be expressed directly as a function without having it set to zero, if it were explicit
solid kilnBOT
45
wraith hinge
so no, it's implicit
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quartz cave
Im not sure where i'm going wrong for part b
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Im not sure where i'm going wrong for part b
proper kernel
19.62s = 0???
this is telling you "if you go up in the air then go back down, you end up back where you started"
if the ball is at its highest point, what would its velocity be
(its velocity wouldnt be -5)
quartz cave
omg im so stupid
quartz cave
(its velocity wouldnt be -5)
0
proper kernel
yea
proper kernel
np
quartz cave
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regal roost
Hi, is there any difference in way this is solved (i mean is my calculation correct?) second photo is another example solved by professor
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Hi, is there any difference in way this is solved (i mean is my calculation corr...
@regal roost Has your question been resolved?
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@regal roost Has your question been resolved?
low mountain
Goofing up a bit with that question 7
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Goofing up a bit with that question 7
low mountain
I think I'm supposed to use an inverse trig substitution but what exactly
oblique valley
Have you ever learned about separable equations?
marsh forum
hint:- if $\frac{dy}{dx}= f(x$, it's the same as $dy = f(x) dx$
shy nacelle
Goofing up a bit with that question 7
dy/√9-y² = xe^x dx
solid kilnBOT
ƒ(Why am. I here)=I don't Know
low mountain
dy/√9-y² = xe^x dx
Yeah I got past that
marsh forum
for DEs
shy nacelle
Yeah I got past that
Bi parts integration
marsh forum
oh, x= 3 __ should work
shy nacelle
And dy part one step
marsh forum
what do you think x should be ?
low mountain
I'm struggling with the integral of dy/root(9-y^2)
shy nacelle
1/√(a²-x²) = sin^-1 x/a
low mountain
I think Im getting somewhere
shy nacelle
1/√(a²-x²) = sin^-1 x/a
This is formula
marsh forum
1/√(a²-x²) = sin^-1 x/a
!nosols
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1/√(a²-x²) = sin^-1 x/a
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
shy nacelle
You can derive by assuming x = 3sinø
marsh forum
this isn't a formula everywhere
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candid aurora
oh sec i see i did some minor errors in the 2nd line. THis is the correct one:
here the correct one
rapid horizon
Can anyone explain fifth euclid postulate?
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Can anyone explain fifth euclid postulate?
bold gulch
Hello i need help with ona radicals
lyric ether
Hello i need help with ona radicals
This is ciup's help channel, you need to open your own
bold gulch
Ok sorry
lyric ether
Can anyone explain fifth euclid postulate?
Which is the fifth one?
rapid horizon
Ohh i understood
lyric ether
wikipedia seems to have a decent article with a picture: https://en.wikipedia.org/wiki/Parallel_postulate
rapid horizon
So the fifth one says we extends lines on the side which those sum of interior is less than 180°
They will intersect each other after some time
lyric ether
So the fifth one says we extends lines on the side which those sum of interior i...
The important bit is that they will intersect to the side where the angles add up to less than 180°
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severe stump
I just for the life of me cannot wrap my head around this.
severe stump
I know that the rref is 1s down the diagonal, but how do I pull scalars from a bunch of 1s???
Any prompt assistance greatly appreciated. Test in 10 minutes.
severe stump
Right
shy nacelle
So they can be linearly independent
severe stump
I don't know how to get the scalars.
shy nacelle
You know
severe stump
I really don't. I wouldn't have asked the question if I did.
severe stump
Doesn't that defeat the purpose of using matrices if I'm going to solve it algebraicly?
shy nacelle
You need fast answer ?
shy nacelle
Doesn't that defeat the purpose of using matrices if I'm going to solve it algeb...
Bro What :
shy nacelle
Doesn't that defeat the purpose of using matrices if I'm going to solve it algeb...
I think its done that way
severe stump
What's the point of rref'ing if I don't even use the matrix?
That's the entire point of this class.
shy nacelle
you see we get trivial solution if we try solve using matrix method
severe stump
Right.
But how can I use a matrix to get the scalars
Just seems insanely backwards if they're teaching us all these things specifically to find scalars, then you can't use those tools to find these specific scalars.
severe stump
I think its done that way
I did it this way and just got a bunch of 0s.
Cuz 3x1+2x2=0 and -x1-x2=0
So (3x1+2x2)+3(-x1-x2)=0, and -x2=0
Which then gives me x1=0, and x3=0
Test time. Rip me
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plush igloo
Doesn't that defeat the purpose of using matrices if I'm going to solve it algeb...
if you want to do it more matrix-y, you can rewrite the additions as multiplications of 2 matrices, and then used methods like row echelon form or finding its determinant to find out if they're linearly independent or not
but there's nothing wrong with writing a system of equations and simply solving them for the unknown variables
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rapid horizon
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marsh forum
what's the question?
marsh forum
ah
ocean latch
hindi 💀 , btw this is like a 4th grade ques
rapid horizon
Did you read my explanation?
ocean latch
what explanation?
ocean latch
2 lines x axis
this shit ain't no explanation
ocean latch
bro what standard? your english broken asf
rapid horizon
bro what standard? your english broken asf
Good more than your average english
ocean latch
bro why you getting riled up? 💀, you can type in hindi, I understand
ocean latch
Good more than your average english
...
bro why yall Indians get all riled up & defensive? like yall straight up start hurling curses or some zesty ahh replies, this is a math server tho, so I wouldn't respond further, good luck
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rustic nest
Sketch the graph of a function on [-1, 2] that has a local maximum but no absolute maximum
lofty walrus
!status
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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
you know what local and absolute maximums are yes?
rustic nest
kind of but not really,,, here's' what i think i know..
local max and min are beginning and endpoints if closed [], and if there is a point on the graph it can be a local min or max, also if there are dips or waves then that is also a local min/max
absolute im not certain
tepid hamlet
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
rustic nest
the question i wrote is the origina;
lofty walrus
do you know of a function on some interval that has no absolute maximum?
rustic nest
no
tepid hamlet
the question i wrote is the origina;
then there is no such function
tepid hamlet
the function doesn't need to be continuous
ah sorry you're right
lofty walrus
here is an example of a function that has no absolute maximum: 1/x on the interval (0, 1]
rustic nest
Sketch the graph of a function on [-1, 2] that has a local maximum but no absolute maximum
this is my question.
tardy hemlock
Also, since it only asks you to sketch it, I'd assume it doesn't want you to give an algebraic expression for it.
So you can just "draw anything" that fits the description
rustic nest
yeahh
but idk how not to draw an absolute max
my TA said theres always an absolute max
he is obviously wrong
lofty walrus
not when the function isn't continous
tepid hamlet
only if you assume continuous like belabutter said
rustic nest
ok what would that look like on a grapph then lol
tepid hamlet
here's a simple example
