@uncut ginkgo Has your question been resolved?
#help-13
cedar kilnBOT
cedar kilnBOT
@uncut ginkgo Has your question been resolved?
blissful stag
blissful stag
<@&286206848099549185>
cedar kilnBOT
@blissful stag Has your question been resolved?
cedar kilnBOT
@blissful stag Has your question been resolved?
proven vale
| P(P(P(A))) |
cedar kilnBOT
| P(P(P(A))) |
proven vale
would it be 2^2^2^(n_A)
sick bough
what is this power set?
sick bough
what doubts do you have
mighty summit
would it be $2^2^2^(n_A)$
cedar kilnBOT
wraith daggerBOT
eurgene114514
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cedar kilnBOT
Available help channel!
raw yoke
new question dropped ;-;
S2 = {6 to 13}
s6 - {11 to 17}
Image
Image
The symbol is a union so that means all of the elements?
however the answer is saying 2^8 + 2^7 - 2^3.
( i looked through all my lectures, this question has never come up)
raw yoke
clear umbra
what does the square mean
silk stratus
probably number of possible subsets
clear umbra
then just seems like principle of inclusion-exclusion
solid juniper
yea it's power set
not that it's a standard symbol loll i just know from helping her on another question
cedar kilnBOT
@raw yoke Has your question been resolved?
raw yoke
a little confused why this doesnt work
cedar kilnBOT
a little confused why this doesnt work
hollow minnow
solid juniper
trim valve
a little confused why this doesnt work
you cannot deduce injectivity from examining just one value from the codomain
hollow minnow
yo that's pure
Hello my dear desciple
trim valve
truly a help channel
hollow minnow
one of the help channels of all time
solid juniper
May Rishi Sunak take the world
cedar kilnBOT
@raw yoke Has your question been resolved?
crimson sedge
Hello my dear desciple
🥺
crimson sedge
hello yajat and pure
hello layla
crimson sedge
guess im ready for whatever comes next 🙏😭
solid juniper
you turned reply ping off
trim valve
mr sweatyballs_123
wtf it's really sir sweatyballs_123...
solid juniper
YOU TURNED REPLY PING OFF TOO
crimson sedge
you turned reply ping off
just tryna be lowkey 🙏
crimson sedge
wtf it's really sir sweatyballs_123...
yes
solid juniper
you aren’t lowkey sir sweatyballs_123
cedar kilnBOT
solid juniper
try all you want
crimson sedge
you aren’t lowkey sir sweatyballs_123
i guess im not very good at it
cedar kilnBOT
Available help channel!
old fiber
how do i subject k
cedar kilnBOT
how do i subject k
past wave
Do you know this property of log that
2^(log(base 2) a) is just a
Basically exponent and log cut each other
But the base of log and exponent have to be the same
@old fiber ?
cedar kilnBOT
past wave
Wlcm 
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Available help channel!
crisp gale
cedar kilnBOT
pastel vault
first thing would probably be convert those conditions into angles
so $\tan \theta < 0$ implies $\theta$ is in the 2nd or 4th quadrants
and $\frac{4 \pi}{3} < \theta < \frac{5 \pi}{3}$
wraith daggerBOT
higher's secret twin brother
nova snow
first thing would probably be convert those conditions into angles
so $\tan \th...
qhigher
pastel vault
first thing would probably be convert those conditions into angles
so $\tan \th...
ah so $\frac{3 \pi}{2} < \theta < \frac{5 \pi}{3}$ overall
wraith daggerBOT
higher's secret twin brother
crisp gale
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cedar kilnBOT
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azure stone
heya i posted a doubt on integration a couple of hours ago, but i gave up.
azure stone
pastel vault
use the formula $(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$
wraith daggerBOT
higher's secret twin brother
azure stone
use the formula $(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$
hey, i tried to use the trigonometric expansions
i mean it isnt expansions
pastel vault
pastel vault
yeah?
azure stone
yeah?
i dont know how the correct terminology.
like sin(alpha) + sin(alpha+beta) and so on….
such that it forms an AP.
pastel vault
ok so what have you tried from here?
azure stone
so sinx would be
sin(n(a.b))/2 sin(first angle . last angle /2)/whole by sin(first angle)
pastel vault
you don't need APs
azure stone
n is the amount of terms in the series
a-first angle
b-second angle
azure stone
you don't need APs
wait i dont know what its called.
pastel vault
wait i dont know what its called.
I would call them (arithmetic) sin and cos series
azure stone
azure stone
https://math.stackexchange.com/questions/17966/how-can-we-sum-up-sin-and-cos-ser...
yes.
pastel vault
how are you going to integrate $\frac{\sin(3x/2)}{\sin(x/2)}$ though
azure stone
after simplifying i got sin3x/sinx
wraith daggerBOT
higher's secret twin brother
azure stone
how are you going to integrate $\frac{\sin(3x/2)}{\sin(x/2)}$ though
i assumed x/2 as z
pastel vault
after simplifying i got sin3x/sinx
wait for real?
azure stone
and differentiated.
pastel vault
great now use the fact that sin 3x = 3 sin x - 4 sin^3 x
you can get it from sin(2x + x)
pastel vault
but from this you should get (sin(3x/2) / sin(x/2) * sin(2x))^2
so I think you're integrating the wrong thing
azure stone
4cos^2x-1
azure stone
yea common
azure stone
but from this you should get (sin(3x/2) / sin(x/2) * sin(2x))^2
sin3(x/2)/sin(x/2) and then cos^2(2x) and sin^2(2x) grt added and equal one
then the root cancels
azure stone
great now use the fact that sin 3x = 3 sin x - 4 sin^3 x
thanks for the clutch.
i got it.
pastel vault
oh wow
pastel vault
okay I see that's clever
never would have guessed to use the AP series
I'm not Indian
azure stone
I'm not Indian
haha
its okay i mean its not necessary you know
i forgot a much simpler formula
i forgot sin3x bro lol
Well the answer is 2pie.
tysm again.
.close
crimson sedge
Hii
pastel vault
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
quick flume
cedar kilnBOT
quick flume
How do I even start
grand shale
bash
quick flume
bish bash bosh
outer nova
you want to simplify?
quick flume
yes
outer nova
Manipulate the latter two terms to get a common denominator of x^2 and y^2
weary ingot
$$\frac{x^4-y^4}{x^2y^2} \div [(1+\frac{y^2}{x^2})\cdot (1-\frac{2x}{y}+\frac{x^2}{y^2})] =$$
wraith daggerBOT
woomy
weary ingot
Is this correct?
quick flume
Indeed
wraith daggerBOT
woomy
wraith daggerBOT
woomy
weary ingot
try to find the "a" and "b"
quick flume
x and y
quick flume
y2 and x2
weary ingot
yep
try to write x^4 instead as (x^2)^2
cause by properties of exponents thats just x^4
from there we quickly get $\frac{(x^2)^2 - (y^2)^2}{x^2y^2}$
wraith daggerBOT
woomy
quick flume
(x^2-y^2)x(x^2+y^2)
weary ingot
yep
outer nova
Denominator:
$$\frac{x^2 + y^2}{x^2} \cdot \frac{y^2 - 2xy + x^2}{y^2} = \frac{ (x^2 + y^2) \cdot (x-y)^2 }{x^2 y^2} $$
weary ingot
i think you mean \cdot
outer nova
yup missed it
weary ingot
also in the next eq
wraith daggerBOT
RadMeerkat62445
weary ingot
but try not to give out the answer directly maybe
outer nova
hmm alr sorry
weary ingot
(x^2-y^2)x(x^2+y^2)
notice how the first one
(x^2-y^2)
is in the form a^2-b^2
so you can apply the simplification again
reposting so i dont have to scroll up
quick flume
weary ingot
you are not showing a lot of steps
show as many steps as possible
for your teacher and also for us to understand what you're doing
quick flume
weary ingot
,rotate
wraith daggerBOT
weary ingot
there are a quite a few steps you arent showing though
ohh wait
sorry i understood
no no we are only solving the fraction now
not the whole exercise
we will do piece by piece
right now we are focusing on $\frac{x^4-y^4}{x^2y^2}$
wraith daggerBOT
woomy
wraith daggerBOT
woomy
weary ingot
now lets look back at the whole equation
so so far
, \begin{align*}
&\frac{x^4-y^4}{x^2y^2} \div [(1+\frac{y^2}{x^2})\cdot (1-\frac{2x}{y}+\frac{x^2}{y^2})] \
= &\frac{(x^2-y^2)(x^2+y^2)}{x^2y^2} \div [(1+\frac{y^2}{x^2})\cdot (1-\frac{2x}{y}+\frac{x^2}{y^2})] \
= &\frac{(x-y)(x+y)(x^2+y^2)}{(xy)^2} \div [(1+\frac{y^2}{x^2})\cdot (1-\frac{2x}{y}+\frac{x^2}{y^2})]
\end{align*}
wraith daggerBOT
woomy
weary ingot
okay
now we simplified the fraction
lets look at whats inside the braces
so
$$\left[\left(1+\frac{y^2}{x^2}\right)\cdot \left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)\right]$$
wraith daggerBOT
woomy
weary ingot
which one do you want to focus on first?
quick flume
one on the left
weary ingot
okay
so we cant really do necessarily much
but maybe y^2/x^2
we can turn into (y/x)^2
although its not certain that it helps, but might aswell try
quick flume
and what about the 1
weary ingot
maybe we can simplify it
bring it all under the same fraction
so note that we have 1+y^2/x^2 right?
but we can make a single fraction by finding the common denominator
quick flume
weary ingot
yes!
if you want you can write (xy)^2 as x^2 y^2 again
since i dont think thats necessary
weary ingot
$\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} \div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)\right]$
sorry i just rewrote everything so i see where we are at
wraith daggerBOT
woomy
weary ingot
Okay lets look at the last brackets
so
$\left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)$
wraith daggerBOT
woomy
quick flume
weary ingot
not quite
maybe rewriting it like this rings a bell: \
$\left((1)^2-2\left(\frac{x}{y}\right)+\left(\frac{x}{y}\right)^2\right)$
wraith daggerBOT
woomy
weary ingot
remember $(a-b)^2 = a^2 - 2ab + b^2$
wraith daggerBOT
woomy
weary ingot
what would "a" and "b" be?
weary ingot
\begin{align*}
&(1)^2-2\left(1 \cdot \frac{x}{y}\right)+\left(\frac{x}{y}\right)^2 \[5 pt]
&a^2\quad - 2ab\quad \ + b^2
\end{align*}
how about now?
quick flume
aha
weary ingot
i added the 1 so it makes more sense
wraith daggerBOT
woomy
weary ingot
yep
quick flume
(a+b)^2
quick flume
(a-b)^2
weary ingot
right
so in this case?
maybe lets set a = x/y and b = 1, the outcome is the same but this is easier to understand
quick flume
(x/y-1)
weary ingot
yes
now you can find the common denominator
oh wait
u are forgetting the power
so
(x/y - 1)^2
weary ingot
what would be the commond denominator then?
weary ingot
righr
right*
so putting everything togheter
\begin{align*}
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(1-\frac{x}{y}\right)^2\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{y-x}{y}\right)^2\right]
\end{align*}
wraith daggerBOT
woomy
weary ingot
does this look right? is there maybe anything you dont really understand?
quick flume
Nope
weary ingot
oh ill add this step, notice that $(\frac{a}{b})^2 = \frac{a^2}{b^2}$ so we have
\begin{align*}
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{x}{y} - 1\right)^2\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{x-y}{y}\right)^2\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{(x-y)^2}{y^2}\right)\right]
\end{align*}
okay sorry im just in the middle of something
wraith daggerBOT
woomy
weary ingot
yep
so
(a/b)^2 = a^2/b^2
like you can take the power of 2 and give it to the numerator and denominator
weary ingot
perfecg
so lets just multiply the fractions within the brackets
$$\left[\frac{x^2 + y^2}{x^2}\cdot \frac{(x-y)^2}{y^2}\right]$$
wraith daggerBOT
woomy
weary ingot
multiply but dont expand everything
so this just becomes
$$\frac{(x^2+y^2)(x-y)^2}{x^2y^2}$$
wraith daggerBOT
woomy
weary ingot
right?
quick flume
so the denominator will be x^2*y^2
weary ingot
yes
quick flume
I can use the formula on the second bracket
weary ingot
not really
we already simplified everything
so there is no need to now expand again
weary ingot
theres no real need to expand anything cause we just did all this effort to simplify
lets first right down what we reached so far
so
oh ill add this step, notice that $(\frac{a}{b})^2 = \frac{a^2}{b^2}$ so we have
\begin{align*}
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(1-\frac{2x}{y}+\frac{x^2}{y^2}\right)\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{x}{y} - 1\right)^2\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{x-y}{y}\right)^2\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\left(\frac{x^2 + y^2}{x^2}\right)\cdot \left(\frac{(x-y)^2}{y^2}\right)\right] \
\frac{(x-y)(x+y)(x^2+y^2)}{x^2y^2} &\div \left[\frac{(x^2 + y^2)(x-y)^2}{x^2y^2}\right]
\end{align*}
wraith daggerBOT
woomy
weary ingot
we are trying to go from the right to the left by simplifying
not left to right by expanding
weary ingot
**woomy**
we are just 2 steps away from finishing
and i have to go aaa
remember that $\div \frac{a}{b} = \cdot \frac{b}{a}$
wraith daggerBOT
woomy
weary ingot
and then try to cancel stuff out
i have to go now, you can try finishing it on your own
but ill message you back afterwards incase u didnt
quick flume
okay thanks 🙂
hot crag
@quick flume close either this or your other channel
quick flume
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
small nymph
IN the figure below AE and EB are equally long and DE is double the length of EF. How much of BCDE is gray?
hot crag
lemme see
small nymph
What is the area of the gray part of BCDE
tender jewel
there is no gray part?
small nymph
EFCA is highlighted as gray
small nymph
ah I see
tender jewel
All corners are 45 degrees except the 90 degree ones
all of the triangles are the same but in different scales
if that helps
what is the chapter called, like what is this type of math called?
visual socket
I need help with this question. The question is to graph the piecewise function given the information.
visual socket
All the information is given in blue at the top and the domain in pencil. This is my first attempt and the teacher says my graph is incorrect.
errant pecan
$54 \cdot 3^{2x} \leq 36 \cdot 4^x$
cedar kilnBOT
$54 \cdot 3^{2x} \leq 36 \cdot 4^x$
wraith daggerBOT
JustANormalTeo
errant pecan
hi guys, i need help with this exponential inequality
now i will show you my work, its not correct tho... the result should be $$x \leq \frac{1}{2}$$
wraith daggerBOT
JustANormalTeo
errant pecan
my work
blissful pumice
hmm
blissful pumice
i dont think i can help you on that one
i thought i could
hold on
walk me thru your thought process
wraith daggerBOT
JustANormalTeo
blissful pumice
i have $\frac{3^{3+2x}}{2^{2+2x}} \leq \frac{3^2}{2^1}$
yeah sorry idk if i cna help you there
you might need to wait for someone else
errant pecan
dont worry
errant pecan
.close
cedar kilnBOT
errant pecan
.reopen
cedar kilnBOT
✅
green plaza
Open another
crimson sedge
how?
crimson sedge
i did
errant pecan
yes
crimson sedge
thanks
green plaza
Np
errant pecan
and x > 1
wraith daggerBOT
JustANormalTeo
errant pecan
shouldnt work like that? if $3^{3+2x} \leq 3^2$ then $3+2x \leq 2$?
wraith daggerBOT
JustANormalTeo
green plaza
It should
green plaza
It should be -1/2
errant pecan
it should be only x<=1/2
green plaza
Not that x>1 though, you can't equate it like that they are exponents of diff bases so need to be operated seperately
errant pecan
Not that x>1 though, you can't equate it like that they are exponents of diff ba...
so whats the problem in that...?
green plaza
I just told you that x<=-1/2 is the answer of that eqn and what you've done to solve for x>1 is wrong as there are two different bases so you can't just do it as a whole like that.
errant pecan
I just told you that x<=-1/2 is the answer of that eqn and what you've done to s...
x<=-1/2 is wrong
my textbook answer is x<=1/2
green plaza
my textbook answer is x<=1/2
It could be an error too
Recheck with your teacher
For your own confirmation
There are many instances of the answer being misprinted
errant pecan
hope to do well
green plaza
You cannot do anything in maths a day before test
errant pecan
hate exponentials
green plaza
It ain't no history
errant pecan
You cannot do anything in maths a day before test
a day before?
man i studied for a week these things
green plaza
You did it alright
green plaza
Did you understand why I said x>1 is not the solution ?
errant pecan
cause the bases are differents and you cannot work them like that
green plaza
if it was like this $\frac{3^{3+2x}}{3^{2+2x}} \leq \frac{3^2}{3^1}$ we could have got that x>1
wraith daggerBOT
FlexO
errant pecan
ohhh
green plaza
This is what I mean by different base
It's 2 in denominator right
Not 3
So you have to do it separately
errant pecan
can i type here another problem i have?
green plaza
Sure
errant pecan
$2^{\sqrt{6x-x^2}} < 2^{3-2x}$
wraith daggerBOT
JustANormalTeo
green plaza
Same
errant pecan
i have to do $\sqrt{6x-x^2} < 3-2x$
wraith daggerBOT
JustANormalTeo
green plaza
Yes
errant pecan
and then i have to square both sides to remove the square root?
green plaza
Yes
wraith daggerBOT
JustANormalTeo
errant pecan
so it becomes $-5x^2 +6x -9 < 0$
wraith daggerBOT
JustANormalTeo
errant pecan
but then the $\Delta$ is negative so the equation does not exist in $\mathbb{R}$
wraith daggerBOT
JustANormalTeo
green plaza
**JustANormalTeo**
No
errant pecan
oh...
green plaza
$6x - x^2 < 9 + 4x^2 -12x$
wraith daggerBOT
FlexO
errant pecan
DAMNNNN
green plaza
errant pecan
RIGHT
OH MY GOSH
IM SO BLIND
why am i that stupid...
ugh...
well guess i have to thank you^-^
green plaza
You are just anxious
errant pecan
i am.
green plaza
Chill out
errant pecan
last test i got 10/10
errant pecan
thank you!
errant pecan
have a nice day!
green plaza
Have a nice day too
errant pecan
.close
hollow spoke
cedar kilnBOT
hollow spoke
How do i integrate this
hollow spoke
Wanna integrate sqrt(1+4x) ?
I have to integrate the sqrt(1+ dy/dx^2) part
Oop
If i combine the inside is it possible to do partial fraction decomp
No bc its only one cx
X
dire geode
unrelated to your integral, but your dy is incorrect
cedar kilnBOT
@hollow spoke Has your question been resolved?
rose narwhal
how can i simulate this through code?
cedar kilnBOT
how can i simulate this through code?
rose narwhal
<@&286206848099549185>
cedar kilnBOT
@rose narwhal Has your question been resolved?
rose narwhal
<@&286206848099549185>
fair geyser
from each mark you send a ray towrds the camera, advance the stick, advance the rays, make more rays from the new position
then at the end check what rays are at the camera (they can go through, and they don't count)
at that moment the camera will see the mark for each ray at its original position
idk if that's what you meant
rose narwhal
from each mark you send a ray towrds the camera, advance the stick, advance the ...
by each mark do you mean the meter stick ticks?
fair geyser
yeah
rose narwhal
clarifying again, are the black lines the camera angle at which it sees the ruler?
fair geyser
like a particular green dot would say "mark #4 at this location"
rose narwhal
what do the red and green marks mean
fair geyser
and you would have like 5000 green dots
green dots are images, they travel along the line
you track each one, and make more and more from each location of the stick
rose narwhal
what about the light rays?
rose narwhal
ohh are the light rays the same as when the camera takes the image?
fair geyser
the camera is like blind, it can only see the dots
there's no time for dots to travel
but some dots are already inside the camera and haven't passed through
rose narwhal
why dots instead of like a blurred rectangle?
fair geyser
incredibly short time
there's no blurring, we magically get a crisp but bright image
rose narwhal
in this context, let's say we could modify our velocity, but no matter how fast the meter stick goes, it always takes the same amount of perceived time. does that impact anything?
fair geyser
i don't understand
rose narwhal
the ruler always moves the at the same time frame no matter how fast it is
fair geyser
no idea
rose narwhal
did you create this as a drawing or did you code it? if it’s coded, could you share the code with me? curious to know how it works
fair geyser
no that's just paint
rose narwhal
ohh ok
can you describe what the movement would look like for the ruler besides the images? also what are the red dots?
fair geyser
it would be like an hour to code, i'm pretty slow
rose narwhal
chatgpt
fair geyser
if you remind me in ~13 hours, maybe i'll be in the mood
i would have to learn chatgpt that's not even time, then it would take effort
rose narwhal
gotcha
rose narwhal
can you describe what the movement would look like for the ruler besides the ima...
^^
fair geyser
the red dots are the ticks obviously
the sources of the images
the ruler would just teleport a bit to the left, it's all discrete
rose narwhal
i had included light rays in my code. are the dots better than the varied-length "rays"?
fair geyser
i don't know, it's just an idea how i would try to do it
i literally didn't study physics
rose narwhal
ok
can you confirm if the tick marks change when the ruler moves at the speed of light
fair geyser
of course
i can't picture it exactly, but it should be weird
the ruler probably lengthens
maybe the marks even swap?
or double up
rose narwhal
is this right for the tick marks to move this way?
rose narwhal
it's showing that it's on a finite speed of light
cedar kilnBOT
@rose narwhal Has your question been resolved?
cedar kilnBOT
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inner pendant
😵💫
inner pendant
!status
cedar kilnBOT
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
2
cedar kilnBOT
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narrow dagger
How do I find the domain of the fraction x4^2+x-3/12x^2-9x
cedar kilnBOT
How do I find the domain of the fraction x4^2+x-3/12x^2-9x
summer otter
How do I find the domain of the fraction x4^2+x-3/12x^2-9x
Find the values where there denominatior is not 0
narrow dagger
Find the values where there denominatior is not 0
I cant figure out how to get it to the final answer, x=0 x=3/4
I tried factoring out 3 to get 3(4x^2-3) but i dont know if its right to do
summer otter
I tried factoring out 3 to get 3(4x^2-3) but i dont know if its right to do
Complete the square method on the denominator
cedar kilnBOT
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hoary light
cedar kilnBOT
hoary light
how do you find the vertical asymptotes for this?
infinite limits i can understand how to solve the other problems
the problem is when it incorporates trig i dont know where to start
glacial field
Do you know what a vertical asymptote is
In reference to the function itself, not the graph
hoary light
it is where the limit approaches infinity or negative infinity from the left and right side?
glacial field
it is where the limit approaches infinity or negative infinity from the left and...
There is a vertical asymptote when the function is undefined
Otherwise, the x value simply does not exist
Like 1/0
What is csc in terms of sin?
hoary light
1/sin
glacial field
So what are you looking for
hoary light
Right
glacial field
Sin wont be undefined, but since it is in the denominator, and sin can yield 0, that is what you will look for
Sin is a periodic function which means there will be infinitely many x values that will yield 0
hoary light
I see so every pi value it will end up as 1/0
odd sierra
cedar kilnBOT
odd sierra
Bro
How is this not 4.8x10^3
i did sig figs all week just to get it wrong
😭😭😭😭
ignore those random writings i was panicking
I hope its right fr
cedar kilnBOT
@odd sierra Has your question been resolved?
odd sierra
o i gotta send it tmrw
supple shell
dont worry im a very good expert(am not)
supple shell
o i gotta send it tmrw
yep just send me the question, if i can solve it than I’ll explain the steps
blud?
odd sierra
ok thanks
supple shell
before you get instantly killed by your teacher
soft lark
cedar kilnBOT
soft lark
So if I were to solve this using the quadratic formula
I start with this
Then they would turn into
And then I can't actually solve for x since I don't a sqaure root that I can't solve right?
So is this the answer?
cedar kilnBOT
@soft lark Has your question been resolved?
slate lintel
you could simplify √60 a bit but you won't be able to get rid of the square root entirely
dire geode
,w roots 3x^2-6x-2
wraith daggerBOT
river estuary
The question is
After being painted, a solid wooden cube whose edge 4cm long is cut into 64 small cubes. How many of these small cubes have at least two painted faces?
river estuary
I do not understand what it means by "at least two painted faces"
idle crystal
if it was cut into 64 cubes (4^3) then youd have a big cube with side length 4 small cubes
"atleast 2 painted faces" means youd count faces with 2, 3
river estuary
"atleast 2 painted faces" means youd count faces with 2, 3
?
idle crystal
try to think about why there wouldnt be 4,5 and so on
you're painting the outside of a cube though
river estuary
oh
idle crystal
when you paint something, only the surface would be painted
river estuary
okay
so i came to understand
there are 12 edges so in total of 24 can be colored in
2 faces
but i don't know how 3 faces can be painted in
<@&286206848099549185>
idle crystal
but i don't know how 3 faces can be painted in
on the corners
wispy drum
hi
soft lark
Example 6: What are the roots of - 2x ^ 2 - 3x + 7 = 0 ?
cedar kilnBOT
Example 6: What are the roots of - 2x ^ 2 - 3x + 7 = 0 ?
soft lark
Example 6: What are the roots of - 2x ^ 2 - 3x + 7 = 0 ?
I want to solve by completing the sqaure
( - 2x ^ 2 - 3x )+ 7
Okay so half of 3 is 3/6
If I sqaure 3/6 that's
9/36?
violet lagoon
half of 3 is not 3/6
remote trail
I would probably first divide everything by -2
or at least factorise the x^2 and x terms
soft lark
K wtf let me restart
remote trail
it's not necessary but makes it clearer how to complete the square
soft lark
x ^ 2 - 3x/-2 + 7/-2
soft lark
it's not necessary but makes it clearer how to complete the square
So this?
remote trail
x ^ 2 - 3x/-2 + 7/-2
yeah and then simplify and set equal to 0
soft lark
yeah and then simplify and set equal to 0
x ^ 2 + 3x/2 + 7/-2 =0
Let me start doing work
So 3x/2 half of this would be
3/4?
soft lark
yeah and then simplify and set equal to 0
?
viral drum
you can get rid of the fractions if you don't like them
soft lark
you can get rid of the fractions if you don't like them
I need to
But is 3/4 right?
Then I need to swaure it
(x ^ 2 + 3x/2 +9/16)-9/16 + 7
.close
cedar kilnBOT
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knotty harness
how can u 100% know this has more than 1 solution
cedar kilnBOT
how can u 100% know this has more than 1 solution
knotty harness
without using like desmos
brazen dagger
how can u 100% know this has more than 1 solution
Because the number of solutions will be equal to the highest power of x if you simplify the equation unless it's a perfect square which isn't the case for your question
knotty harness
Because the number of solutions will be equal to the highest power of x if you s...
?
U could have (x+3)(x-3)(x+2) + 50
Which only has 1 solution
And isnt a perfect square
knotty harness
U could have (x+3)(x-3)(x+2) + 50
And the highest power in this is x^3
brazen dagger
Which only has 1 solution
How do you know it has one solution?
It has 3 solutions, 1 real 2 imaginary
knotty harness
Bruh but look at the domain and codomain
Its real numbers
Its only asking for real solutions
brazen dagger
Bruh but look at the domain and codomain
Yes for your question all 3 will be real
brazen dagger
Its only asking for real solutions
The second question you asked for that I am saying
knotty harness
U could have (x+3)(x-3)(x+2) + 50
How can u definitively know this has 1 real solution
brazen dagger
How can u definitively know this has 1 real solution
Because I calculated all 3 roots
brazen dagger
U literally can't 💀
Yeah for cubic I am also not sure
outer stag
brazen dagger
.close another channel is open
cedar kilnBOT
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undone star
if $\omega$ is the cube root of unity with the smallest positive argument, solve for $z$ in the equation $z^{6}+\omega z^{5}+\omega^{2}z^{4}+z^{3}+\omega z^{2}+\omega^{2}z + 1 = 0$
wraith daggerBOT
Dootud
undone star
i was told my solution si worng but idk why, it is highly possible im just really stupid
i generated 3 equations
hot crag
"cube root of unity"?
dreamy void
i generated 3 equations
damn i wouldn't even generate 1
hot crag
you mean third root of unity?
dusk finch
cube root of unity is fine
hot crag
huh, never heard it being said that way
undone star
$z^{6}+\omega z^{5}+\omega^{2}z^{4}+z^{3}+\omega z^{2}+\omega^{2}z + 1 = 0$ \
$\omega[z^{6}+\omega z^{5}+\omega^{2}z^{4}+z^{3}+\omega z^{2}+\omega^{2}z + 1]= 0$ \
$ \omega^{2}[$z^{6}+\omega z^{5}+\omega^{2}z^{4}+z^{3}+\omega z^{2}+\omega^{2}z + 1]= 0$
wraith daggerBOT
Dootud
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
undone star
and then i summed all 3
hot crag
looks to be binomial with coeffs = 1
crimson sedge
**Dootud**
coefficients of omega and omega^2 equals 1 ?
undone star
to yield that z are all the 7th root of unity besides z=1
mental trail
if $\omega$ is the cube root of unity with the smallest positive argument, solve...
hint : z^7 - w^7
undone star
but i was told that was wrong
undone star
hint : z^7 - w^7
okie let me try
hot crag
hint : z^7 - w^7
damn, rafi, that was fast
undone star
hint : z^7 - w^7
is $z= cis(\frac{2\pi + 6k\pi}{21}), k \in {1,2,3,4,5,6}$
wraith daggerBOT
Dootud
mental trail
not sure but
if you wanna check your answer
it should be z = w*exp(i2kpi/7) with k = 1,...,6
undone star
its z^7 = w but z=/=w
mental trail
its z^7 = w but z=/=w
z^7 = w^7
mental trail
well it makes things kinda easier
undone star
i made a booboo somewhere then
uno momento
oh hmm
your solution is 6kpi +12pi/21 instead of 2pi + 6kpi/21 (which is what i got)
so i got it wrong
ok thx rafilou
.close
cunning prawn
cedar kilnBOT
cunning prawn
i dont understand how to find the mean but i think i know what to do with it after to find the variance
dude
nvm
i was just being stupid
.close
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leaden flare
can anybody explain me how i can find CEG (they ask for the circumference of CEG)
leaden flare
with the help of pythagoras
leaden flare
✅
leaden flare
little goten
can you help with the question?
vast pike
I am not seeing any criconference
leaden flare
I am not seeing any criconference
we need to find it from CEG
what it is
and we know the edges are 3 cm
undone star
a little google translate seems to suggest that if this is dutch, omtrekken also means outline = perimeter perhaps?
leaden flare
a little google translate seems to suggest that if this is dutch, omtrekken also...
YES
thats what i mean
i think
vast pike
for the circumference that contains the triangle you knwo that they ray is half of CE as the triangle has a right angle at G
leaden flare
for the circumference that contains the triangle you knwo that they ray is half...
yeah
cedar kilnBOT
@leaden flare Has your question been resolved?
cedar kilnBOT
frigid kernel
I got to x^2.5 = 32 What do i do now
i know i have to move the ^2.5
to the other side
not quite suyre
burnt vapor
i know i have to move the ^2.5
Yes
To do it you can ^p both sides for some p so that 2.5 goes away
(x^2.5)^p = 32^p
So that (x^2.5)^p = x
frigid kernel
wait whats p?
frigid kernel
x^2.5p?
burnt vapor
Yes
frigid kernel
thats the answer?
frigid kernel
2/5?
cedar kilnBOT
@frigid kernel Has your question been resolved?
cedar kilnBOT
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near quiver
Got an issue with b)
cedar kilnBOT
Got an issue with b)
near quiver
There's this associative law of composition and I got no idea what to do other than doing the cube root of negative numbers being -cbrt of the number
near quiver
And since it is associative I can write N as (-cbrt(n) * cbrt(n) ) * (-cbrt(n-1) * cbrt(n-1) ) * ... * 0
Sure, one sec
past wave
Bruh moment lmao
near quiver
That's what I thought of
Welp..
I got -2x^2 + 15 actually
Since x+(-x) is 0
6 * 0 is 0
OH
Yeah mb
-2x^2 + 21
Yes
Still, can't see a pattern when I move the terms
Yeah thought there might have been some killer term
Like in multiplication
Since it's associative there must BE something
A term out of those 4047
That cancels out the whole thing
-2 * 2 ?
Or the cbrt from -2 to 2?
Let me give it a shot
Not the prettiest stuff
-2(cbrt(4)) + 21 * 19 * 0 ?
Yup.
near quiver
But 0 isn't natural
Also for the sake of conversation despite it being a hot topic 0 is a natural number taught in schools
cedar kilnBOT
@near quiver Has your question been resolved?
near quiver
<@&286206848099549185>
Since it is quite up there I'll make a checkpoint
There is this law of composition and I need to prove N is a natural number.
Okay that was weird
Glad the promoter withered away
past wave
Also for the sake of conversation despite it being a hot topic 0 is a natural nu...
We were taught that 0 is not a natural number, it is a whole number tho
But ok
Doesn't matter
near quiver
We were taught that 0 is not a natural number, it is a whole number tho
Well here we got problems where they say "x is a non-zero natural number" which implies the set of natural number N consists of the natural numbers from 0 to infinity
near quiver
Doesn't matter
Yeah dw, I like to yap about math
past wave
0 to inf as in (0, inf) or [0, inf)
past wave
Yeah dw, I like to yap about math
yap battle nice
near quiver
0 to inf as in (0, inf) or [0, inf)
For every n greater or equal to 0, obviously
So, [0, inf)
past wave
Btw what does whole numbers mean for y'all?
near quiver
Z
past wave
Does it include negative numbers?
near quiver
Yes
past wave
past wave
b part is done?
near quiver
Despite it being associative, and searching for a value for x * (-x) which is -2x^2 + 21, there is no pattern I could find for this whole set to somehow simplify to 0, 1 or whatever
past wave
@near quiver
near quiver
I assume it is 0 since its associativity MAY work like multiplication in my intuition, but no way to prove it mathematically from my side
near quiver
b part is done?
No.
past wave
What question are you taking about?
near quiver
b.
near quiver
How old are you?
near quiver
You are the same age as me. I assume you never heard of the laws of composition?
steep badge
near quiver
Romanian. I assume the terms were similar to english, especially b)