,tex $\sin^3(x) + \cos^3(x) = 1$
#help-43
cursive harbor
boreal girderBOT
Xavier 🌺
cursive harbor
Well are you familiar with the factorization of a³ + b³
dawn briar
How do you make a canonical form of a matrix?
cursive harbor
What do you have currenrly
bleak dock
How do you make a canonical form of a matrix?
please don't spam
cursive harbor
How do you make a canonical form of a matrix?
!occupied, use an available channel pls
compact pewterBOT
How do you make a canonical form of a matrix?
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).
cursive harbor
but im stuck after replacing the squares with 1
Would help me if you showed what you currently have
thick shore
,tex $(sinx+cosx)(1−sinxcosx)=1$
cursive harbor
Well
boreal girderBOT
JustBrutal
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cursive harbor
There's obvious answers here without any further simplification
thick shore
yeha but how do u prove with algebra that this equation leads to sinx=1 and cosx=0
or sinx=0 and cosx=1
tired bear
yeha but how do u prove with algebra that this equation leads to sinx=1 and cosx...
check maxima
thick shore
check maxima
maximal?
cursive harbor
Are you familiar with differentiation
tired bear
maximum value the function $f(x) = \sin^3(x) + \cos^3(x)$ can obtain
boreal girderBOT
thick shore
i dont study maths in eng so no
cursive harbor
Derivatives?
cursive harbor
I see
thick shore
any way of directly proving it?
thick shore
maximum value the function $f(x) = \sin^3(x) + \cos^3(x)$ can obtain
yeah im not familiar with that
cursive harbor
I'm sure there is, but I'm also very bad at trig
thick shore
oh okay
cursive harbor
So I'm gonna let a more capable helper help you
thick shore
<@&286206848099549185>
thick shore
,tex $\sin^3(x) + \cos^3(x) = 1$
boreal girderBOT
JustBrutal
thick shore
@thorny heath find the sols without derivatives
thick shore
bruh
thorny heath
whole question
thorny heath
k
thick shore
<@&286206848099549185>
thorny heath
hmm..
sin(x) max = cos(x) max =1
you can say one of the terms should be 1,
or put sinx + cosx = t
thorny heath
**JustBrutal**
Compile Error! Click the <:errors:504266556054962196> reaction fo...
and solve this in terms of t
define t : $-\sqrt{2}<=t<=\sqrt{2}$
boreal girderBOT
heisenberg
tired bear
oh wait oh boy
i got a funny one
$\sin^3(x) + \cos^3(x) = 1 = \sin^2(x) + \cos^2(x)$
boreal girderBOT
tired bear
$\implies \sin^2(x) \cdot (\sin(x) - 1) + \cos^2(x) \cdot (\cos(x) - 1) = 0$
boreal girderBOT
tired bear
can you see where this is going
tired bear
$\implies (1 - \cos(x))(1 + \cos(x))(\sin(x) - 1) + (1 - \sin(x))(1 + \sin(x))(\cos(x) - 1) = 0$
boreal girderBOT
bleak dock
$\implies (1 - \cos(x))(1 + \cos(x))(\sin(x) - 1) + (1 - \sin(x))(1 + \sin(x))(\...
bruh, #help-28
thorny heath
bruh, <#903486480985489478>
brodie just close this channel
bleak dock
.close
compact pewterBOT
compact pewterBOT
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icy nymph
so this is the question
$\begin{tikzpicture}
\draw[->,ultra thick] (-4,0)--(4,0) node[right]{$x$};
\draw[->,ultra thick] (0,-4)--(0,4) node[above]{$y$};
\draw[domain=-1.6:1.6, smooth, samples=200, very thick, <->] plot({\x},{(\x*\x - 1)^3});
\end{tikzpicture}$
compact pewterBOT
so this is the question
$\begin{tikzpicture}
\draw[->,ultra thick] (-4,0)--(4,0)...
boreal girderBOT
Flatus
icy nymph
if the question asks when this graph is parallel to the x-axis,
is it 1 or 3?
-# ||or is it just very poorly worded||
runic creek
-# ||or is it just very poorly worded||
Quite this one
runic creek
if the question asks when this graph is parallel to the x-axis,
I think they meant the tangent?
runic creek
If it's the tangent then 0 is also included
runic creek
**Flatus**
Anyways there aren't any numbers in the graph here so we don't know where 1 and 3 are 💀
icy nymph
when the tangent to the graph is parallel to the x-axis
implying
when is the gradient = 0
so would those stationary points lying at y=0 count as "parallel to the x-axis"?
@runic creek
runic creek
so would those stationary points lying at y=0 count as "parallel to the x-axis"?
Seems so
runic creek
Yes
icy nymph
.close
compact pewterBOT
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pastel ice
compact pewterBOT
pastel ice
is it valid to confirm the integral converges first
open girder
Not even an equation. Sloppy slop
pastel ice
then say since the function is odd splitting the integral up from -infinity to 0 and from 0 to +infinity both integrals will then be equal and will cancel each other out giving you 0
open girder
Yes
compact pewterBOT
open girder
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hollow kettle
what. do i do. how do i plot (exponential functions)
compact pewterBOT
what. do i do. how do i plot (exponential functions)
hollow kettle
i had MASSIVE brain fog and was somehow the most bored i have been in my math class today so i think half the info went through my ears
rotund sphinx
i had MASSIVE brain fog and was somehow the most bored i have been in my math cl...
pick x values, get the corresponding y value, and plot the corresponding point
Ex. If $x=1$, then $y=3^1-5=3-5=-2$, so you'd plot the point $(1,-2)$
boreal girderBOT
Civil Service Pigeon
wary mulch
compact pewterBOT
upper bane
no
the table clearly separates all four categories. there's no risk of double counting here
wary mulch
whats with the double counting in the additional rule
upper bane
wdym? there is no such thing, esp. not with the setup in this pic
there is no such thing in this pic
mb
kind viper
whats with the double counting in the additional rule
it's when you count the exact same objects twice
it's not about them fulfilling both conditions in an or
here is what it would look like if you overcounted:
total guilty = 11+72 = 83
total who did it = 72+9 = 81
and then you would add 83+81
but then the ones who are guilty AND did it (72) get counted twice
also, addition rule, no -al
compact pewterBOT
@wary mulch Has your question been resolved?
compact pewterBOT
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high shadow
guys when doing functions table, what happens if i get an ERROR?
compact pewterBOT
guys when doing functions table, what happens if i get an ERROR?
compact pewterBOT
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.
high shadow
what...
cursive harbor
The plot you do depends on what exactly your function looks like
More specifically what exactly was divided by zero
Just show the original question please
high shadow
fine shawty
past ginkgo
fine shawty
cursive harbor
Let's think about what happens when x is close to -1
Let's say -0.9 for example
Since you're using a calculator anyway
upper bane
you can do it manually
upper bane
type $\frac{2}{(-0.9)+1}$
boreal girderBOT
Hanako(x, y); ∂(fox)/∂x
high shadow
ugh so i have to delete it..
upper bane
if the calculator gives you lemons, find ways to work around it
high shadow
okay then
sullen merlin
fine shawty
Please don't use nicknames like "shawty", or for example "babe", etc to refer to people you don't know, it can make people uncomfortable
high shadow
that was a joke..
sullen merlin
yeah but jokes can make ppl uncomfortable, the important thing is to just avoid doing it in the future
compact pewterBOT
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dull heron
Hello everyone! I had an exam today and I am not sure if I got a question right and it’s really bugging me that I can’t remember/answer it correctly. If I am not mistaken we were required to find mean squared error MLE theta.hat of theta for the Bernoulli distribution. I wrote theta(1-theta). Was that correct? Thank you so much in advance
compact pewterBOT
Hello everyone! I had an exam today and I am not sure if I got a question right ...
@dull heron Has your question been resolved?
dull heron
No
pseudo rapids
could you first find the Likelihood fnction of the bernoulli distribution?
please open ur own channel king
This ones tamaras
close
not 1.1
wheat pasture
It was a one hour mute for trolling in someone else's help channel 
dull heron
could you first find the Likelihood fnction of the bernoulli distribution?
I went by logic p(1-p) so it could be the same for theta but some said theta^2 or my answer over n
pseudo rapids
correct answer is your answer over n
do you understand why?
or are you too tired
which is fair
dull heron
It was 20 statistics questions in 90 minutes
I am really exhausted but thank you very much
.close
compact pewterBOT
winged lion
compact pewterBOT
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cursive warren
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drifting flax
compact pewterBOT
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peak stratus
compact pewterBOT
peak stratus
is it correct
keen granite
trying to sketch f'(x)?
thorny urchin
seems ok
thorny urchin
yes
compact pewterBOT
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Available help channel!
woven prairie
compact pewterBOT
woven prairie
Can someone help with the second one
Would it converg or diverge ans why
And
Also this is in french sorry
lusty sequoia
Can someone help with the second one
could you translate
woven prairie
could you translate
Im only intrested in the second serie of the first exercise
It says
Study the nature oc the numerical series :
gilded dirge
1/(n+1)^(1+(1/n^2)) Is that correct
woven prairie
1/(n+1)^(1+(1/n^2)) Is that correct
Yeah the sum from n= 1 to infinity
Of
1/(n+1)^(1+1/n²)
gilded dirge
It seems to be a geometric series
woven prairie
Nah
For me it looks like a reiman thing
Smthn like 1/n^æ
Cuz like
n+1 is the same as n when n approches infinity
So it really depends on weather u call 1+1/n² > 1 or u just say it is equal to 1 when n approches infinity
Im not sure about it
gilded dirge
Maybe try replacing the sigma with an integral
Integrate over n to get the value
If it keeps increasing, it will diverge to infinity
or else it will converge on a number
open lotus
i need help on part a. isnt a vertical tangent line an undefined slope?
compact pewterBOT
i need help on part a. isnt a vertical tangent line an undefined slope?
open lotus
do you have an equation for dy/dx
both are given so i js put dx/dt as y1 in my calculator anf dy/dt as y2 in my calculator
and put y3 = y2/y1
kind crane
Idk what y1 and y2 are supposed to be
open lotus
Idk what y1 and y2 are supposed to be
kind crane
No idea what your calculator model is doing
open lotus
open lotus
No idea what your calculator model is doing
Y3 is my dy/dx
kind crane
You don't need to graph at all to do a)
Graphing wouldn't give you an exact answer anyway
open lotus
alright
but what about dy/dx? i have it stored in the calculator as Y3 but how do i set it equal to an undefined value?
kind crane
finite / 0 = vertical tangent
open lotus
finite / 0 = vertical tangent
dy/dx = ?/0 to get a vertical tangent right?
from t=0 to t=1.5 there’s a point where the tangent line of the particle is ?/0
how should i set that up in my calculator?
kind crane
Use math, not calculator
kind crane
i should be taking a look at (dy/dt)/(dx/dt) right
And use
open lotus
Use math, not calculator
it’s question two on the ap exam it’s a calculator active question
the first section of the ap frq is always calculator active
kind crane
i should be taking a look at (dy/dt)/(dx/dt) right
Then just use this
What's the denominator equal to?
distant path
.
kind crane
finite / 0 = vertical tangent
verify the numerator is finite for all 0<t<1.5
open lotus
What's the denominator equal to?
it should be equal to zero
and sine of 0 should be 0
at t = 0 and pi, dy/dt is 0
and then dx/dt should equal a finite number, and if we plug t = 0 into it, we should get a real finite number
wait i got it
at t=0, the line tangent to the particle is vertical
we don’t use pi bc 3.14 is not in the 0 to 1.5 interval
open lotus
oh my days i did dx/dy instead
dx/dt has to equal 0 in between 0 and 1.5
while dy/dt has to be finite
theres two times dx/dt is equal to zero
and where dy/dt is not zero
t = 1.145
and at t = 1.253
that blue line represents dx/dt while the red one is dy/dt
at both points when the blue line is at 0, dy/dt on that same t is a real nonzero value
at these two points dy is a real number while dx is 0, satisfying the conditions that dy/dx needs to be equal to finite/0
kind crane
,calc log(pi)
boreal girderBOT
Result:
1.1447298858494
,calc sqrt(pi/2)
boreal girderBOT
Result:
1.2533141373155
Both look right
open lotus
that’s crazy
wait that’s so cool
i take it i got the right answer, so im going to sleep
tyy
.close
abstract agate
why is this matrix not diagnolizable?
compact pewterBOT
why is this matrix not diagnolizable?
rigid perch
what do you get for the eigenvalues and eigenvectors?
kind viper
why is this matrix not diagnolizable?
have you calculated its eigenstuff?
compact pewterBOT
@abstract agate Has your question been resolved?
wintry knot
here, we are trying to find out if the conclusions of both I1 and I2 are true or not by making all the premises true and the conclusions false. in I2, we took ~R as true so R would be false, then does ~C not have two possible values (both true and false)? why did we only take one possible value (true), here?
compact pewterBOT
here, we are trying to find out if the conclusions of both I1 and I2 are true or...
wintry knot
because taking ~C as false would make C true and hence I2 would be valid, right?
please ping if responding
compact pewterBOT
@wintry knot Has your question been resolved?
wintry knot
in this example as well, for (b), we took ~C as true so for the first premise (C -> ~E), does E, again, not have two choices?
woeful schooner
here, we are trying to find out if the conclusions of both I1 and I2 are true or...
I2 is invalid because if it didn't rain, thne the inference of whether the match was played or not can't be made
Citing wikipedia
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
wintry knot
okay so we kinda always take the case where an argument can be invalid?
woeful schooner
okay so we kinda always take the case where an argument *can* be invalid?
It's not about taking a case, it's about that case existing. In an implication, that case shouldn't exist.
To give you a slightly more digestible peice of data which is easier to understand
$$x + 3 = 4 \implies x = 1$$
Look at the implication here, given that the first statement ($x + 3 = 4$) is true the consequence ($x = 1$) can not be false.
@woeful schooner
woeful schooner
You're welcome :)
thorny heath
in this example as well, for (b), we took ~C as true so for the first premise (C...
If one is corrupt they cannot be elected
woeful schooner
!done
compact pewterBOT
If you are done with this channel, please mark your problem as solved by typing .close
wintry knot
If one is corrupt they cannot be elected
no, i get that. i am just having a hard time with such kind of questions where there's multiple inferences, so drawing a valid conclusion is a little troublesome for me
but well yeah, it makes sense
anyway, thanks again
.close
compact pewterBOT
compact pewterBOT
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safe raptor
how to solve this integral
I have to use U sub
compact pewterBOT
how to solve this integral
I have to use U sub
tired bear
how to solve this integral
I have to use U sub
look at the bottom line on your answer
$\int 2^u \cdot \frac{3}{2} du$
boreal girderBOT
tired bear
how did that become $\int \frac{6^u}{2} du$
boreal girderBOT
safe raptor
can i not do 6^2/2 which would be 3^u?
so i can take 3/2 out of integral but how do i take the integral of 2^u du?
tired bear
so i can take 3/2 out of integral but how do i take the integral of 2^u du?
this is correct
$\int{a^x dx} = \frac{a^x}{ln(a)} + C$
boreal girderBOT
tired bear
a is a constant
safe raptor
how do you get to that or is it just something I just have to know to solve this integral?
tired bear
how do you get to that or is it just something I just have to know to solve this...
differential of $a^x$ is $a^x ln(a)$
boreal girderBOT
tired bear
you can use some method like logarithmic differentiation to prove this
tired bear
how do you get to that or is it just something I just have to know to solve this...
and you can easily see how differentiating the integral we get here gives us back a^x
but its mostly a common integral
safe raptor
i didnt have differentials yet
but i will chekc this out
so once i use this i just resub back to X?
thank you
.close
compact pewterBOT
tired bear
so once i use this i just resub back to X?
yeah
compact pewterBOT
Available help channel!
young tinsel
What is the area, in square units, of the region enclosed by y= |x-20| and y=10?
compact pewterBOT
What is the area, in square units, of the region enclosed by y= |x-20| and y=10?
potent berry
!status
compact pewterBOT
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
junior saddle
What is the area, in square units, of the region enclosed by y= |x-20| and y=10?
What have you tried?
young tinsel
What have you tried?
I saw the solution to the problem, and it said something about the function having a vertex at (20,0 ) and that it created an isosceles triangle, but i have no idea where they got any of that info from
i know that x=30 or 10 but that's it
daring axle
I saw the solution to the problem, and it said something about the function havi...
abs(x) has a vertex at (0,0)
junior saddle
I saw the solution to the problem, and it said something about the function havi...
I think you should try graphing it out.
Or try calculating the intersection point.
daring axle
translating 20 units to the right gets you to (20,0)
since abs(x -20) means translating abs(x) 20 units to the right
young tinsel
how does the absolute value of x have a vertex at the origin
daring axle
,w graph |x|
boreal girderBOT
daring axle
those are two lines
namely, y = -x and y = x
plotted for y >= 0
the two lines intersect at (0,0)
compact pewterBOT
compact pewterBOT
Available help channel!
robust flicker
how do i solve this? i am unable to approach it
compact pewterBOT
how do i solve this? i am unable to approach it
short ferry
have u drawn a diagram?
random mica
if the horse travels x km along the circle, what angle has it made to the centre of the circle
robust flicker
yes
robust flicker
if the horse travels x km along the circle, what angle has it made to the centre...
pi/4
some guy told me to find the speed of shadow as a function of time
but i dont get how to do that
random mica
what is the definition of angles in radians
robust flicker
ok so what next
robust flicker
so theta = x/r
yep
random mica
now, from our diagram, how can we get the distance travelled by the shadow from this
robust flicker
hiow?
random mica
pull up the diagram
robust flicker
ye
random mica
(hint: trigonometry)
robust flicker
then?
random mica
so distance travelled by the shadow = r * tan (x/r)
random mica
now take the time derivative of both sides
robust flicker
k
random mica
(r is constant and x changes with time
random mica
how?
robust flicker
tan x derivative is sec square x right
random mica
yeah
robust flicker
so 1/r is constant anyway
tan(x/r) to 1/r(sec square x/r)
and 1/r from before too
sec square x/r whole by r square
random mica
close
$\frac{dy}{dt} = \frac{1}{r} \sec^2\left(\frac{x}{r}\right) \frac{dx}{dt}$
dx/dt is left
robust flicker
oh
boreal girderBOT
CherryMan
random mica
(chain rule)
random mica
so do we know x
random mica
speed times time is x
thats only when its a linear function
but read the question carefully
we are explicitly given everything
they said the horse covers 1/8 of the circle
random mica
so 1/8 * 2pi r
robust flicker
ye
random mica
welcome
robust flicker
.close
gray crest
Kinda stuck? Don't know where to go from here, my brain just stopped
compact pewterBOT
Kinda stuck? Don't know where to go from here, my brain just stopped
primal drift
Kinda stuck? Don't know where to go from here, my brain just stopped
If you have solved it correctly, why don't you take tan inverse omega and 1/root2ln[t-root2/t+root2] as general formulas?
gray crest
If you have solved it correctly, why don't you take tan inverse omega and 1/root...
uh what?
primal drift
Wait
primal drift
I am a highschool student i don't know what a tan inversa omega is
...
And you can solve integration...
gray crest
And you can solve integration...
Yeah we take that, 17 years old is not a kid?
😭
you got any simpler solutions man?
primal drift
you got any simpler solutions man?
gray crest
okay let me try that
primal drift
gray crest
but that's if it's 1+? and here it's 2 ?
gray crest
so the a^2 is basically (root2)^2
gray crest
i don't get this part
gray crest
okay i am done with this one
gray crest
not really
primal drift
gray crest
okay can you wait a minute and check if i am right?
primal drift
Ok
primal drift
I think you are correct
gray crest
LETS GOO
gray crest
thank youu i would've never found those
i kept searching and found some stuff called tanh^-1 or smth
primal drift
thank youu i would've never found those
Those are basic integrals..
Ok, welcome nvm
compact pewterBOT
compact pewterBOT
Available help channel!
azure edge
struggling with an rref algorithm, this matrix ends up as an identity matrix, but if I parallel its operations onto an identity matrix I don't get its inverse
compact pewterBOT
struggling with an rref algorithm, this matrix ends up as an identity matrix, bu...
azure edge
I think it's a math issue not a programming bug
bc I wrote this memory, where to get ref I
{go through each row, if nonzero element, choose it as your next pivot row, swap it with the row beneath your previous pivot row, multiply it so the lead is 1, weighted sum it on every row below to make every entry below the pivot 0}```then to get rref
{find the leading nonzero element, weighted sum this row on every row above so every element above the lead is 0}```the error I get is that after this is all said and done, A * (my calculated A inverse, where I do parallel rref on A and identity matrix), = not identity matrix
and yes the matrix is invertible
kind crane
can you print your matrix at every operation to debug
azure edge
probably, let me check
lambda functions sometimes resist the use of external variables
(colored text bc my prints are extremely long, and I need an easy way to find which one I care about)
I show the output matrices from each operation, the input is the matrix directly above (all operations shown)
hushed magnet
bc I wrote this memory, where to get ref I
```go through each column
{go throug...
when you say nonzero, I hope you check that you dont get numerical inaccuracies somewhere?
(havent checked your code)
say the entry is 1e-12, thats nonzero but certainly should never be your pivot
azure edge
yup that is in fact what I was just checking
specifically the third row, matrix 1E-40 or whatnot
I do have built in functions to cancel out numbers when summing (a, -a) (I check if the ratio is close enough to -1)
istg
that was it
thank you! I have been tearing my hair out over this.
I was calling a function that does not check when doing a += b if (a ~= -b)
kind crane
i love when RREF makes me get numbers on the order of 10^45
azure edge
i love when RREF makes me get numbers on the order of 10^45
tbf I saw that exact case in a different matrix and there it was valid 💀
it multiplied by 10^-60 and all was well
I also do get numbers also on the order of 10E45
because sometimes my newton raphson diverges horribly
and I have to calculate e^(10^15)
or, sometimes, more reasonably, just e^150 or so
kind crane
wow. dafuq is your machine epsilon
azure edge
amusingly, even with these terrible errors, I can still do euler stepping + newton raphson for simulation purposes so long as I add a dampening factor into NR and limit the maximum change between NR iterations to like norm ≤ 0.1
azure edge
wow. dafuq is your machine epsilon
64 bit IEEE double precision float, only precise to 1 + 1E-15 though iirc
azure edge
the range of a double precision float is 1E-308 to 1E308 iirc
the precision is 15-17 orders of magnitude
doubles do well with multiplication that doesn't need to be exactly correct
kind crane
oh nice
azure edge
so if I multiply the whole row with 1E40, the exponent in the double just gets + 40 (in binary), that's not a problem
oh well thanks again!!
this has been haunting me
.close
compact pewterBOT
compact pewterBOT
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chrome quail
simultaneous elimination method
compact pewterBOT
simultaneous elimination method
slate sand
What have you tried
quiet sentinel
you want to make one term the same in each equation so it can be eliminated through subtraction
in this case that is already done
drifting flax
i got 4
Yes
Well on the paper it says x =
Don't know where the 4 went
But notice your system of equations has two unknowns, x and y
You got the x
You need the y still
chrome quail
i got -3y
lusty sequoia
i got -3y
you got x = 4, right?
plug that in to 7x + 2y = 22
then
28 + 2y = 22
2y = -6
y = -3
if thats what u meant
drifting flax
Ah I see
chrome quail
well i plugged it into equation 1 instead
chrome quail
ye
how do i do this
a cup and a soacer cost $3.15 together. a cup and 2 soacers cost $4.50. Find the cost of a cup and of a soacer
lusty sequoia
a cup and a soacer cost $3.15 together. a cup and 2 soacers cost $4.50. Find the...
if C represents the cost of a cup and S the cost of a soacer, how would you represent this an an equation?
*two equations
lusty sequoia
yeah
so now you can solve with elimination
you get
0c + s = $1.35
s = $1.35
c + $1.35 = $3.15
c = $1.80
drifting flax
you get
0c + s = $1.35
s = $1.35
c + $1.35 = $3.15
c = $1.80
Just a tip, try not to solve the entire thing for them, but guide them through the steps and explain the reasoning behind them 🙂
While making them actually do the steps or give their approach etc.
chrome quail
you get
0c + s = $1.35
s = $1.35
c + $1.35 = $3.15
c = $1.80
i dont get it
lusty sequoia
i dont get it
you understand elimination, where you subtract one equation from another to cancel out a variable, correct?
you have
c + s = $3.15
c + 2s = $4.50
and you can subtract the first equation from the second to cancel out c
chrome quail
wym by cancel out tho
lusty sequoia
like when you subtract c + s = 3.15 from c + 2s = 4.50 you get
(c - c) + (2s - s) = (4.50 - 3.15)
s = 1.35
you are "eliminating" c since you subtract c in the first equation from c in the second equation
compact pewterBOT
@chrome quail Has your question been resolved?
compact pewterBOT
@chrome quail Has your question been resolved?
novel wagon
where would I plot this?
compact pewterBOT
where would I plot this?
grizzled ember
On the complex plane.
grizzled ember
Do you have any formulas which relate the modulus and the argument of a complex number to the x +iy form?
hint: e
spark folio
other way you could do that is you already know that the magnitude is 4, so it is gonna lie on a circle of radius 4, which should be easy enough to plot
near crown
Idk if that's the problem if they're asking how to plot
spark folio
and from there you figure out the angle and how to place that in the plane
viscid canopy
consider searching polar coordinates
grizzled ember
other way you could do that is you already know that the magnitude is 4, so it i...
That's identical to what I said
near crown
No it isn't
spark folio
same end result does not mean same order of steps
novel wagon
Do you have any formulas which relate the modulus and the argument of a complex ...
Im not sure
novel wagon
other way you could do that is you already know that the magnitude is 4, so it i...
yes I know its in quad 4 but nothing else
grizzled ember
I think to use the perspective that z lies on a circle of some radius is implicitly using euler
spark folio
yes I know its in quad 4 but nothing else
do you know how to measure the angle? that should get you specific location
novel wagon
What fraction of a circle is the angle?
5pi/3
grizzled ember
Note that without the multiplication between complex numbers, the structure is identical to vectors in R^2. If you've done linear algebra then this is just finding the tail of a vector with this magnitude and angle
lusty sequoia
Note that without the multiplication between complex numbers, the structure is i...
for precalculus they just want you to know x = r cos(theta) and y = r sin(theta)
you are overcomplicating it
grizzled ember
I don't know what level this guy is at.
near crown
Look at the problem then
grizzled ember
I didn't come across complex numbers in precalc so i just assumed it was university
near crown
Do you think they've done linear algebra?
grizzled ember
Uh, yes.
lusty sequoia
@novel wagon but yes the intuition is thinking about it as in polar coordinates, where the point lies on a circle of radius 4 and at the angle 5pi/3
and to find that coordinate you use trigonomtery to get (r cos(theta), r sin(theta)) = (4cos(5pi/3), 4sin(5pi/3))
novel wagon
and to find that coordinate you use trigonomtery to get (r cos(theta), r sin(the...
why 3?
grizzled ember
If you have this information (modulus and angle) and still don't know what to do, then it indicates to me that they just don't know the definitions.
novel wagon
wdym 3? 4 and 5pi/3 are given
OH sorry nevermind I see what you mean
novel wagon
and to find that coordinate you use trigonomtery to get (r cos(theta), r sin(the...
I get -2√3
lusty sequoia
yeah (2, -2sqrt(3))
compact pewterBOT
@novel wagon Has your question been resolved?
novel wagon
.close
compact pewterBOT
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brave tusk
i dont understand Polynomial long division
compact pewterBOT
i dont understand Polynomial long division
chilly basalt
I have two approaches for you
One fulfills your need, long division
the other requires a bit prerequisite knowledge
Let's begin with the former, do you have a paper and a pen with you?
or a pad
@brave tusk
compact pewterBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
brave tusk
Can you draw a line for me?
Done
brave tusk
done
chilly basalt
Right, what the value of 2a^2 divided by a?
brave tusk
Right, what the value of 2a^2 divided by a?
2a
chilly basalt
correct, right it above 2a^2 and the line
brave tusk
Like this?
chilly basalt
let's speed up the process, what's 2a times a
Write it below 2a^2
and 2a times 1
write it below -4a
brave tusk
let's speed up the process, what's 2a times a
Write it below 2a^2
2a^2
chilly basalt
Alright, finish it and share the progress after that
brave tusk
Alright, finish it and share the progress after that
Is that correct
chilly basalt
-6a divided by a
brave tusk
-6a divided by a
-6
chilly basalt
Alright so now i am here
becareful
brave tusk
and 2a times 1
write it below -4a
oh wait
chilly basalt
there is a small mistake in your last step
chilly basalt
,calc (-8)-(-6)
boreal girderBOT
Result:
-2
i should do -8+6
brave tusk
,calc (-8)-(-6)
alright whats the last step
chilly basalt
that's everything
time to collect the result
2a-6 is the quotient
-2 is the remainder
brave tusk
alright thanks man
chilly basalt
anything else?
I can provide you an alternative
a slightly more advanced approach
brave tusk
I can provide you an alternative
sure tell me
chilly basalt
sure tell me
Let's observe the division $8\div 3 = 2...2$
boreal girderBOT
VerifiedCrank
chilly basalt
We can write their relationship as the following
$8 = 3\times 2 + 2$
boreal girderBOT
VerifiedCrank
chilly basalt
Do you agree so far?
brave tusk
Do you agree so far?
yes
chilly basalt
So we got the equation\
$2a^2-4a-8 = (a+1)Q + R$ where Q is the quotient and R is the remainder
boreal girderBOT
VerifiedCrank
twilit schooner
I think I should mention that you don't need to think of "polynomial divison" as some magical algorithm, it's just algebra:
(2a^2-4a-8) / (a + 1) = (2a(a - 2) - 8) / (a + 1) = (2a(a+1-1-2) - 8) / (a+1) = (2a(a+1) + 2a(-3) - 8) / (a+1) = 2a + (-6a - 8) / (a+1) = 2a + (-6(a + 1) - 2) / (a+1) = (2a - 6) - 2/(a+1)
... If I didn't screw up algebra
chilly basalt
Let's plug in a = -1 to find out the remainder
brave tusk
alright
chilly basalt
$-2 = (0)$Q + R
boreal girderBOT
VerifiedCrank
brave tusk
sure
chilly basalt
If we move -2 to the left, we get $2a^2-4a-6 = (a+1)$Q
boreal girderBOT
VerifiedCrank
chilly basalt
We know that Q must have the leading coefficient of 2, because the leader coefficient of $2a^2-4a-6$ is 2
brave tusk
alright
boreal girderBOT
VerifiedCrank
chilly basalt
So we have the equation
$a^2-2a-3 = (a+1)(\frac{Q}{2})$
boreal girderBOT
VerifiedCrank
chilly basalt
do you know how to factorize?
brave tusk
do you know how to factorize?
no
twilit schooner
do you know how to solve quadratic eqs?
chilly basalt
ah I see, then just take this approach as a show as it would take a lot of time to teach this
chilly basalt
Alright, can you factorize a^2-2a-3?
twilit schooner
i think 3, -1?
brave tusk
yes my bad
chilly basalt
Right, so you got
$(a-3)(a+1) = (a+1)(\frac{Q}{2})$
boreal girderBOT
VerifiedCrank
brave tusk
mhm
chilly basalt
So $\frac{Q}{2} = (a-3)$
boreal girderBOT
VerifiedCrank
chilly basalt
pretty sure you know what to do next 
This approach is slightly more complicated but beneficial in the long run
brave tusk
times 2 on the both sides to remove the 2
chilly basalt
and I actually have the third approach
brave tusk
This approach is slightly more complicated but beneficial in the long run
is there a way to get better in maths ?
chilly basalt
is there a way to get better in maths ?
Just do more questions honestly
brave tusk
Just do more questions honestly
i see
chilly basalt
improve your pattern recognition skill
brave tusk
improve your pattern recognition skill
how
brave tusk
i see
brave tusk
Alright, anything else?
nah thx
brave tusk
I gotta go studying if it's alright for now
good luck
brave tusk
u too
chilly basalt
.solved
maiden geode
compact pewterBOT
maiden geode
I don’t how to find that sin 2theta is negative when I am finding it’s positive, in interval -pi to 0
I multiplied the interval by 2 to -pi/2 - theta- 0 and got -pi - 2theta. - 0
I drawed the graph and I see it’s positive
Am I doing something stupid
<@&286206848099549185>
noble sorrel
can u tell which question are u talking about?
rancid mason
For a you just need to proof that the radius r is negative
maiden geode
Yup
rancid mason
You can do that by arguing that sine is negativ
noble sorrel
I don’t how to find that sin 2theta is negative when I am finding it’s positive,...
yes
ur correct because its supposed to pe positive
maiden geode
But should be negative
noble sorrel
read the question again
noble sorrel
But should be negative
for the equation to be true but if u have to prove that it is false
and since ur sin2theta can only be posit
rancid mason
But should be negative
The graph of ur sine is wrong
noble sorrel
so there is no part of C in those region
compact pewterBOT
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Available help channel!
open lance
can someone help me with geometry
compact pewterBOT
can someone help me with geometry
open lance
circles
strange ermine
open lance
The vertex of the angle is outside the circle, its sides represent the sides of the triangle, and the angle is equal to the measure (in degrees) of the smallest circle inscribed in its sides. Find this angle.
i have to draw it myself cuz its just the question in the book
ok well how about this one
find the angles of abc triangle, <ACM=50
<BCN=70
jade nymph
ok well how about this one
Angle ACB would be 60
open lance
why
jade nymph
All the angles would be 60
@open lance
open lance
in the answers it says 70 , 60 , 50
toxic cipher
Linear angle axiom
*you may know this as "sum of angles on a straight line is 180"
jade nymph
in the answers it says 70 , 60 , 50
Sorry my bad I didn’t see the figure accusations
open lance
so whats the formula
i cant just write the answer the teacher will ask me how i got it
jade nymph
i cant just write the answer the teacher will ask me how i got it
So u tell that MF that for a straight line the sum of all the angles subtending through it is 180 so by basic arithmetic 180-(50+70)=60 for angle ACB
And there is the application of exterior angle theorem as well
jade nymph
And there is the application of exterior angle theorem as well
@open lance
open lance
So u tell that MF that for a straight line the sum of all the angles subtending ...
ok i wrote this
but what abt the other angles
jade nymph
<@1279217526621999167>
For other angles
jade nymph
can u help me with some more stuff
Like?
open lance
From a given point on a circle, a diameter and a chord equal to the radius are drawn. Find the angle between them
jade nymph
From a given point on a circle, a diameter and a chord equal to the radius are d...
Can u give me a min?
open lance
ok
jade nymph
From a given point on a circle, a diameter and a chord equal to the radius are d...
Answ is 60 ig do u know the answer
open lance
how do u solve it
jade nymph
@open lance btw can i ask which standard or course u are taking ?
jade nymph
how do u solve it
It’s pretty elaborate but I can explain over voice chat if u want
open lance
idk im being tutored in math and i use 2 books 1 geometry 1 algebra
and theyre in my native language so u wouldnt understand
open lance
georgia
open lance
is there like a formula
simple maple
and theyre in my native language so u wouldnt understand
i'm pretty sure you're not the only one that speaks your native language
open lance
i'm pretty sure you're not the only one that speaks your native language
well idk how to find someone in here that does and can help me
cuz its even more difficult to try and understand when the words r in english
simple maple
you dont need to. But if someone DOES speak it, they will identify so when the original is posted
open lance
im trying to use chatgpt as well but its not good at explaining
jade nymph
im trying to use chatgpt as well but its not good at explaining
Do u know about a equilateral triangle
jade nymph
I’m sorry I’m unable to help u
sacred snow
Hello I need help
brazen quiver
@sacred snow do you know the Pythagorean theorem?
sacred snow
Yes
brazen quiver
Can you set up the equation in the pythagorean theorem to solve this right triangle?
brazen quiver
Well, what is the equation?
sacred snow
A squared plus b squared = c squared
brazen quiver
Ok, now in that equation, which letter represents the hypotenuse?
brazen quiver
Angle? You mean side length yes?
brazen quiver
Ok, now assume you have a^2 + b^2 = c^2
We know that c is the largest side, which side in the 6b) triangle is the largest?
sacred snow
9 root 3
brazen quiver
So we have a^2 + b^2 = (9√3)^2
We know another side length, let's call it b. Can you replace b into this equation?
sacred snow
Yes
brazen quiver
Go ahead and do that if you would
sacred snow
With 4root6
brazen quiver
So what is your equation now?
sacred snow
A squared plus 4 root 6 =9root3 squared
sacred snow
Four root 6 squared
brazen quiver
Ok. So now we can simplify and solve for a.
sacred snow
Yes
brazen quiver
Both (4√6)^2 and (9√3)^2 are integers, what are their values?
sacred snow
Not sure
brazen quiver
Well, I'll do an example: (5√7)^2 = 5^2 * (√7)^2 = 25 * 7 = 175
Can you simplify yours?
brazen quiver
Show your work please
brazen quiver
Similar problem with 81 x 9
sacred snow
Prime factorize
sacred snow
Equals 7 root 3
brazen quiver
You did it!
brazen quiver
I can, but I cannot promise I'll be available.
compact pewterBOT
compact pewterBOT
Available help channel!
drifting drum
compact pewterBOT
drifting drum
why is it important that a and b have no common factors?
daring axle
why is it important that a and b have no common factors?
it's not
you didn't use the fact that gcd(a,b) = 1 in the proof
fathom crest
Say we have a common term 2, for the equation $$(5^b)^2=(10^a)^2$$ we could have positive and negative "solutions". Say a arbitrary number x, we can solve b for $$5^b=x \implies b=\log_5x$$ with the same logic, then we will get $$-5^b=x \implies b\log(-5)=\log_5x$$ which is not doable.
boreal girderBOT
Good
fathom crest
I think I've seen something similar before, but I'm not sure if this was the explanation that "works".
daring axle
Say we have a common term 2, for the equation $$(5^b)^2=(10^a)^2$$ we could have...
but there's no case where there's a "negative solution" tho
5^b = -10^a
the proof they posted doesn't use gcd(a,b) = 1 even if it was (2a)/(2b) like you wrote out
their argument of comparing the parity between the left and right side is structurally the same
also don't we usually consider the simplest form so that we don't have to spend more time on an infinite descent argument
compact pewterBOT
@drifting drum Has your question been resolved?
drifting drum
the proof they posted doesn't use gcd(a,b) = 1 even if it was (2a)/(2b) like you...
ok
yeah i was confused about that, good to know
daring axle
yeah i was confused about that, good to know
tldr; it's a good thing to have
like some proofs of sqrt(2) being irrational
use the fact that a/b is in simplified form
but you can do it without the gcd(a,b) = 1 requirement
and even if you use the proof that rests on the gcd(a,b) = 1
u just have to use infinite descent on that to make it workable without gcd(a,b) = 1
drifting drum
u just have to use infinite descent on that to make it workable without gcd(a,b)...
idk what that means lol
drifting drum
Say we have a common term 2, for the equation $$(5^b)^2=(10^a)^2$$ we could have...
but we say that a and b are positive integers right?
fathom crest
Yes, since logarithms can't be negative.
drifting drum
Yes, since logarithms can't be negative.
okay
i just don't see how if we have a common term 2, this means that we could also have negative solutions like -5^b = x
fathom crest
I didn't know what I though there, but you can do $$5^{2b}=2b=\log_5x$$
boreal girderBOT
Good
daring axle
idk what that means lol
i guess it doesn't matter then
what i was getting at was
if a/b = sqrt(2) where a and b are even
then you can imagine continuously dividing both the numerator and denominator repeatedly by 2
and then you have a cycle of "infinite divisions"
drifting drum
and then you have a cycle of "infinite divisions"
i mean
you can do this with any numbers?
daring axle
eventually you may reach an odd number and then that makes no sense cuz we supposed that a/b was even
drifting drum
eventually you may reach an odd number and then that makes no sense cuz we suppo...
okay that makes sense
drifting drum
if a/b = sqrt(2) where a and b are even
what if they were both odd, would it be the opposite?
and what if one was odd and the other even