flat roost
thank you
#help-0
dawn crest
Is this a correct way to use asymptotic comparison to find the convergence of an integral?
dawn crest
the answer i got is right but i dont know about the actual process
lone heartBOT
@dawn crest Has your question been resolved?
lone heartBOT
@dawn crest Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
patent lotus
In standard normal distribution, P[Z <= 3] gives what value?
tacit arch
In standard normal distribution, P[Z <= 3] gives what value?
this isn't unique to normal. P(Z <= 3) is the probability
vapid steppe
if you get a 0/0 when u do direct substitution on a limit, does that guarantee that the limit exists?
vale wigeon
no
echo socket
Nope
weary wyvern
$\lim_{x\to0} \frac{x}{x^4}$
ocean sealBOT
giannis_money
wild umbra
can someone pls cross check this note if ive written anything wrong
nimble fern
I'm totally unsure about the non real part, but how would D>0 or D<0 for complex coefficients?
wild umbra
like
for example
x^2-2ix-2=0
this eq has, a complex coefficient
and when you calculate its
discriminant
its coming 4
that is >0
this is how
old guy
help
lone heartBOT
@wild umbra Has your question been resolved?
lone heartBOT
@wild umbra Has your question been resolved?
wild umbra
.close
late moss
lone heartBOT
late moss
What mistake M i doing in 4th question
My foot of perpendicular coordinates are coming same as acos^3 theta, a sin^3 theta
near apex
So, what's the issue? (acos^3 theta, asin^3 theta) lies on the line.
late moss
Si then line should be xsec theta+ y cosec theta = a itself right?
@near apex
But that isn't the answer
near apex
Si then line should be xsec theta+ y cosec theta = a itself right?
No.
Line required is perpendicular to the given line.
near apex
My foot of perpendicular coordinates are coming same as acos^3 theta, a sin^3 th...
That doesn't mean anything. You are dropping a perpendicular from a point on the line to line itself, of course it'll give that point only.
late moss
But the cordinates of foot of perpendicular are coming same as the given points
late moss
That doesn't mean anything. You are dropping a perpendicular from a point on the...
But I am finding the foot
Check my diagram
I found x not and y not
near apex
But I am finding the foot
Yeah. I know.
Gosh. Listen.
In general, you have a point which doesn't lie on the line.
Here, your point lies on the line.
late moss
Which point u talking bout
near apex
When you have a point which doesn't lie on the line, you drop a perpendicular and foot of perpendicular are the coordinates where that perpendicular cuts the line.
near apex
Which point u talking bout
(acos^3 theta, asin^3 theta)
late moss
When you have a point which doesn't lie on the line, you drop a perpendicular an...
Yes
That's what I did
But here it lies on the line
near apex
(acos^3 theta, asin^3 theta)
But this point lies on the line.
late moss
Yes
near apex
But here it lies on the line
Yes, so it doesn't give you a separate foot of perpendicular.
late moss
Yes
near apex
It itself is the foot of perpendicular.
near apex
Exactly
late moss
The. Use one point form
near apex
Yes
fierce willow
I have no idea what to do here and my textbook explained nothing
tacit arch
I have no idea what to do here and my textbook explained nothing
does your book give demoivre's theorem
fierce willow
yes, but I was having trouble applying it to the problem
tacit arch
correct you're supposed to use it
fierce willow
whenever i use it tho i only get one answer
tacit arch
show work
fierce willow
ok one sec
sorry i'm on my computer so i had to find my phone to use as a camera
needless to say, I know i messed up, but I just dont know how
fierce willow
i took the cosine and sine of 5pi/18
and rounded to threee decimal places
the value for cos was 0.999885... so it rounded to 1
tacit arch
,calc cos (5pi/18)
ocean sealBOT
Result:
0.64278760968654
hmm...my calculator lied...
tacit arch
don't think you're in radians mode
lone heartBOT
@fierce willow Has your question been resolved?
dry matrix
i dont understand why im wrong
lone heartBOT
i dont understand why im wrong
worn fox
what does bimodal mean to you
dry matrix
multiple modes
worn fox
do you see multiple modes
dry matrix
there is one moe
mode
but this would also be considered bimodal even though theres one mode
tacit arch
bimodal means there are two modes
dry matrix
oh okay
my educator provided this diagram
but in the bimodal it shows only 1 mode
tacit arch
okay i'm wrong
Data distributions in statistics can have one peak, or they can have several peaks. The type of distribution you might be familiar with seeing is the normal distribution, or bell curve, which has one peak. The bimodal distribution has two peaks.
fallen verge
If you roughly fit a curve on the graph, it would look like a left skewed bell
worn fox
yeah i think the small sample size is stopping this being considered bimodal
dry matrix
oh okay
thank u sm 😭 i didnt consider the sample size and justl okoed at the graph
.close
meager plinth
\
meager plinth
Where did they get '1'?
near apex
What is derivative of t?
meager plinth
lone heartBOT
meager plinth
instead of pi/3
I get 1.047197551 (if in radians)
I get 60 (if in degrees)
with my calculator
ocean sealBOT
Result:
3.141592653
,calc pi
ocean sealBOT
Result:
3.1415926535898
meager plinth
math is so hard
tacit arch
use the definition of csc in terms of sin
meager plinth
1/sin
ocean sealBOT
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
meager plinth
final wont let me
meager plinth
ohh so its (1/sin(45))^2
meager plinth
ohh so its (1/sin(45))^2
this gives me 1.3811
but the answesr is -2
oh
i was in raidan
tacit arch
pi/4 is in radians
meager plinth
oh ium
ocean sealBOT
riemann
meager plinth
stupid
lone heartBOT
@meager plinth Has your question been resolved?
meager plinth
,tex \.point slope
hey
tacit arch
?
meager plinth
for -cos(pi/4)
my calculator gives me -.707106....
when I need an exact answer
of -1/sqrt(2)
meager plinth
math is shit
ocean sealBOT
riemann
tacit arch
you really just need the first quadrant
tacit arch
math is shit
mystic nebula
lone heartBOT
mystic nebula
i chose B cause it made the most sense
it reached its peak at 10ms
why is it D
wary stream
it reached its peak at 10ms
Yes it's true but if you read the wording of the given info, it states that a hammer hits it once every p seconds, meaning that it is periodic
mystic nebula
Yes it's true but if you read the wording of the given info, it states that a ha...
damn i just need to read these problems really well
lone heartBOT
Available help channel!
spring condor
Hello
wary stream
You understand that it's not asking for the value of a
It's asking for the x coordinate of where it intersects
mental flame
Look at the point on your graph
spring condor
No like how am I supposed to find the value of a
wary stream
No like how am I supposed to find the value of a
Set the equations equal to each other, then move the terms so it equals zero, then use the discriminant
mental flame
Are you in calc or algebra? There is an easier alternative to solving this if you know a lil bit of calc
lone heartBOT
Available help channel!
blissful radish
The Eurovision Song Contest attracted performers from 100 countries, one from each country.
one from each country. Each performer sings a song of three verses and leaves immediately. The organisers, after reading the lyrics, have worked out that each verse is offensive to exactly one participating country. Prove that it is possible to schedule the performances so that each performer listens to no more than 3 insults.
blissful radish
<@&286206848099549185>
cinder rover
blissful radish
tvt?
prime badge
i don't get it
blissful radish
i too,that's why I asked
prime badge
like no you can't
like ok if there is in fact 3 offensive verses per country, then you maybe can, they don;t make this promise though
maybe 289 verses are about norway and the rest is about france
and scheduling isn;t defined
it's just nonsense idk
strong rampart
Hello
strong rampart
Id like to know how question 1 works
I tried to solve it but the answer i got is √2xy/y²
Is that correct?
naive crystal
Isn't the denominator already rationalised?
strong rampart
I dont get rationalization rolules🥹
ocean sealBOT
_basudev
naive crystal
If denominatior is already rationalised then why would you even touch the question?
naive crystal
**\_basudev**
If your question means this
naive crystal
So it should be √2xy/y ?
Then this is correct...
strong rampart
How to know if the denominator is rationalized
naive crystal
What does rationalisation means?
wary stream
I dont know🥹
Google things you don't know
strong rampart
Removing exponents on the denominator?
strong rampart
But why do i have to multiply it by √y/y
naive crystal
naive crystal
But why do i have to multiply it by √y/y
You've to multiply by root(y)/root(y)
Not root(y)/y
ocean sealBOT
_basudev
naive crystal
**\_basudev**
It has some restrictions... be careful while using it, y >= 0
naive crystal
Den and num both will be affected when you rationalise that's but upon simplifying you'll get the same ans
lone heartBOT
lone heartBOT
Available help channel!
gilded pawn
idk how to do this
carmine bronze
I got a) onto b) neither c) onto. Am I tripping?
lone heartBOT
I got a) onto b) neither c) onto. Am I tripping?
carmine bronze
a) f(0,0)=f(-1,1)=1
b) no integers such f(m,n)=2 and f(0,0)=f(1,1)=0
c) f(0,0)=f(1,1)=0
mystic vortex
what does onto mean?
carmine bronze
means that it needs to cover the entire domain
worn fox
looks fine
sweet pecan
Hello! I’m having a hard time solving the rest of this question. For the first 2 I have -2^3 and 3, aside from that I’m not sure what else to do.
median arrow
You should probably distribute f(x) first (multiply each piece of the first part by each piece in the second)
lone heartBOT
@sweet pecan Has your question been resolved?
median arrow
The sign of the leading coefficient (the number multiplied by x to the highest exponent) would be either +/- depending on what you get after distributing. The degree is the value of the highest exponent after distributing. Maximum number of turning points is the degree - 1. Maximum number of zeros is equal to the degree.
Refer to this for end behavior^
sweet pecan
Refer to this for end behavior^
Than you!
Okay I went back to my lessons and I did it kinda like how the teacher instructed us
There was no mention of distribution before finding the degree and leading coefficient
This is what I got
pallid glade
to find the degree you need to imagine a single equation, not the factorised one. so you need to open the brackets which will give you a maximum degree of 5.
sweet pecan
to find the degree you need to imagine a single equation, not the factorised one...
Thank you! Is this okay?
lone heartBOT
@sweet pecan Has your question been resolved?
shut vessel
Three dice are thrown, find the possibility of
getting a prime number on the first dice, composite
number on the second dice and odd number on the
third dice?
shut vessel
i am doing like 14/216 ,is this right?
tardy stag
can you show your work? that's not the answer i got to
shut vessel
can you show your work? that's not the answer i got to
favourable outcome i got like - 321+221+221 = 14
frozen tiger
i am doing like 14/216 ,is this right?
Multiplication rule right?
probability of A outcome x probability of B outcome
shut vessel
Multiplication rule right?
yeah like when i fix last
shut vessel
probability of A outcome x probability of B outcome
the answer i am getting is right?
frozen tiger
the answer i am getting is right?
what's a composite number
shut vessel
what's a composite number
4 and 6
frozen tiger
Three dice are thrown, find the possibility of
getting a prime number on the fi...
chance 1 x chance 2 x chance 3
tardy stag
what's a composite number
number that isn't a prime and isn't 1
tardy stag
yes they're called composite numbers because they can be decomposed into smaller numbers that are multiplied together like 15 = 3 x 5
shut vessel
chance 1 x chance 2 x chance 3
i don't understand what you are trying to say
shut vessel
chance 1 x chance 2 x chance 3
can you solve it?
frozen tiger
i don't understand what you are trying to say
multiplication rule
The probability of chance A AND chance B to happen is equal to the probability of chance A times the probability of chance B
shut vessel
multiplication rule
The probability of chance A AND chance B to happen is equal ...
you are saying (3 * 2* 3)/216
?
frozen tiger
you are saying (3 * 2* 3)/216
Yes
isn't 1 a prime though
depends on the teacher tbh
shut vessel
it is not a prime
frozen tiger
it is not a prime
fair enough, 1 is a mysterious number
frozen tiger
you are saying (3 * 2* 3)/216
You can do something like 3/6 * 2/6 * 3/6 to make simplifying easier
frozen tiger
but is it not wrong?
it shouldn't be
shut vessel
2 number 3 and 5 are repeated 2 times
shut vessel
there's three dice right?
yeah
frozen tiger
I'm not sure
shut vessel
but when there is 5 on last die you cant get 3 possible outcome in 1st die
you can only get 2 or 3 in first die if there is 5 on last
shut vessel
then the other two don't matter for the respective dice
oh my bad man
just confused
now got clear
individual outcome does not affect other
thanks
.close
lone heartBOT
lone heartBOT
Available help channel!
dusty gull
Hello! Less of a question here and more just that I wan't to make sure I'm doing the elementary part of my matrices correct here. The question i'm working on is this
dusty gull
\begin{enumerate}
\item Find the inverse of the square matrix, if it exists
\item Express each invertible matrix as a produce of elementary matrices
\end{enumerate}
$$\begin{bmatrix} 3 & 6 \ 3 & 8 \end{bmatrix}$$
ocean sealBOT
April | Koi of Mahjong
dusty gull
Finding the inverse is simple, so no questions on that
for the second part though
would the elementary matrices be $E_{1} = \begin{bmatrix} 1 & 0 \ -1 & 1 \end{bmatrix}$
ocean sealBOT
April | Koi of Mahjong
dusty gull
$E_{2} = \begin{bmatrix} 1 & -3 \ 0 & 1 \end{bmatrix}$
ocean sealBOT
April | Koi of Mahjong
dusty gull
$E_{3} = \begin{bmatrix} \frac{1}{3} & 0 \ 0 & 1 \end{bmatrix}$
ocean sealBOT
April | Koi of Mahjong
dusty gull
$E_{4} = \begin{bmatrix} 1 & 0 \ 0 & \frac{1}{2} \end{bmatrix}$
ocean sealBOT
April | Koi of Mahjong
dusty gull
?
the book words it confusingly, so i want to make sure that I'm doing it correctly.
We perform the same row operation we performed on our augmented matrix when finding the inverse to the identity matrix to find that elemetary step right?
What I mean by that is if the first thing that I do to the matrix $$\left[ \begin{array}{cc|cc} 3 & 6 & 1 & 0 \ 3 & 8 & 0 & 1 \end{array} \right]$$ is $R_{2}\rightarrow R_{2} - R_{1}$ I subtract $R_{2} \rightarrow R_{2} - R_{1}$ from the identity matrix to find the first elementary matrix?
ocean sealBOT
April | Koi of Mahjong
strange meadow
the inverse is just the product of the inverse of the elementary matrices you left multiplied to reduce it to I2 right
In the reverse order if that makes sense
dusty gull
are you referring to $A = E_{1}^{-1} E_{2}^{-1} \cdots E_{k}^{-1}$?
ocean sealBOT
April | Koi of Mahjong
dusty gull
As far as i understand, two is asking us to express each step that we took in finding the inverse, as an elementary matrix
inland edge
i dont mean to interrupt, but if your book doesnt explain this well, a video may be able to fill in the gaps or present it in a smoother manner, such as this video i found after seeing this: https://m.youtube.com/watch?v=5SUVnKRbJFM
tight locust
dusty gull
Honestly the book doesn't really explain it at all. All the book says is write in left-to-right order the inverses of the elementary matrices corresponding to successsive row operations that reduce A to I. Which i'm not really understanding
strange meadow
What part is confusing
dusty gull
okay so in order the steps I took in row reduction are
$$\begin{enumerate}
\item R_{2} \rightarrow R_{2} - R_{1} \
\item R_{1} \rightarrow R_{1} - 3R_{2} \
\item R_{1} \rightarrow \frac{1}{3}R_{1} \
\item R_{2} \rightarrow \frac{1}{2}R_{2} \
\end{enumerate}$$
strange meadow
**April \| Koi of Mahjong**
This is literally it!
strange meadow
This is literally it!
Isn’t this what 2 is asking
write A as the product of elementary matrices
ocean sealBOT
April | Koi of Mahjong
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
strange meadow
The inverse of an elementary matrix is elementary so yeah?
Yes each row reduction step corresponds to a matrix
dusty gull
Yes the inverse of an elementary matrix is elementary. But when it asks for the invertible matrices I'm assuming its talking about $\begin{bmatrix} 3 & 6 \ 3 & 8 \end{bmatrix}$, so we need to express this as a product of elementary matrices
ocean sealBOT
April | Koi of Mahjong
strange meadow
then you take the inverse to rearrange for A
You do this
Multiply by the inverse of a matrix
Do that 4 times
And you’re done
dusty gull
so I find the elementary matrices (as above) and then find the inverse of those and multiply them?
strange meadow
Yes
dusty gull
and this should give me A?
strange meadow
Remember doing a row operation is left multiplication of the elementary matrix associated with what you did
write E_k, …E_2, E_1 A = I
Then rearrange
strange meadow
and this should give me A?
So yes
dusty gull
Give me a second
So, this should be the answer I think $$A = \begin{bmatrix} 1 & 0 \ 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & 0 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 \ 0 & 2 \end{bmatrix}$$ ?
ocean sealBOT
April | Koi of Mahjong
strange meadow
i haven't done linalg for a long time hold up
yeha seems right
that's it i believe
i think you were overthinking it
dusty gull
Alright, I think I understand now. Thank you
I think it was just me trying to understand the book which confused me
dusty gull
.close
copper aspen
hi hi
lone heartBOT
@copper aspen Has your question been resolved?
copper aspen
<@&286206848099549185> hi hi
dusty gull
is there a specific reason youre using $\tan \theta$ as a subtitution to start?
ocean sealBOT
April | Koi of Mahjong
dusty gull
I would recommend a u-sub
copper aspen
oh that's because tanx^2 + 1 = sec^2
copper aspen
I would recommend a u-sub
sry but im trying to use trig sub
dusty gull
No problem, I'm rusty on my trig, so I probably wont be the best along that route
dusty gull
No problem, just a heads up I don't think the answer in the book used a trig sub, so you may get a different answer with both of them being correct, I'm pretty certain negative would come from a partial fraction decomposition after the u-sub
copper aspen
sry i didn't mentioned that this exercise was from the trig sub chapter 
so i guess i have to stick on to it
copper aspen
No problem, just a heads up I don't think the answer in the book used a trig sub...
(tho i'll try that too
copper aspen
.close
tame flume
the sides of a triangle are 3 consecutive integers, a perpendicular is drawn on the second largest side . if it divides the second largest side into two parts of lengths p and q respectively, then find the value of (p-q)^2
lone heartBOT
the sides of a triangle are 3 consecutive integers, a perpendicular is drawn on ...
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@tame flume Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
I still can't solve this question after three days
I uhh did what it is basically
,rotate
ocean sealBOT
vapid shuttle
!15mins
lone heartBOT
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.
near apex
How did they go from that to this?
Have you tried seeing further solution? Maybe it's a typo.
alpine sable
Have you tried seeing further solution? Maybe it's a typo.
I did
It's not
They then just use the cosx + cos nx to make it into product
near apex
,w solve sin(nx)/(cos(x) + cos(2nx)) = sin(nx)/(cos(x) + cos(nx))
ocean sealBOT
alpine sable
Okay that may not be correct I get it, can't believe too much on the source , Doubtnut
alpine sable
Maybe try finding another solution.
I did not get any except this, this one was given by my friend 😭
near apex
I myself have no idea yet. I had given it a try the other day.
alpine sable
Can anyone help me in this directly
alpine sable
I myself have no idea yet. I had given it a try the other day.
Yeahhh
near apex
I did not get any except this, this one was given by my friend 😭
maybe ask your friend.
alpine sable
maybe ask your friend.
He didn't know how to either
But he was happy that he got the video and was like okay, (cos nx = cos x) , I told him it Wass wrong but he wouldn't listen
Man this question will take my life ☠️
near apex
Wolfram doesn't have an answer either. Just try MSE once.
alpine sable
It is not possible to use computers
Cuz
It's a series
Where two variables are changing
Till another variable
And there's one term that stays constant all throughout
I haven't seen any calculator do that yet 😭
I did
Try in symbolabs to no avail
<@&286206848099549185> please please pleaseeee 😭😭😭
<@&286206848099549185> dm me if you get something too anytime anyday 😭
shy flare
what is the question
shy flare
sin(x)/cos(x)+cos(2n*x)?
shy flare
then to infinity?
alpine sable
Basic form for n = [1,n]
alpine sable
then to infinity?
You got something man?
alpine sable
Ikr
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185> help
high mortar
@alpine sable not disturning u but is my answer right or wrong
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
is this the answer : (n^2+2n)/4
Oh oh oh right right can be can be
Idk the answer I wanted the whole steps but ye
That's a good method
alpine sable
<@456226577798135808> not disturning u but is my answer right or wrong
It can be used , unless in the actual solution somehow this x = π/2 set gets excluded
So I can't say for sure if it's correct but yes that's a way I use in exams
Thanks a lot tho
I would still like the steps tho for proving for all values of x
lone heartBOT
@alpine sable Has your question been resolved?
blissful elbow
help 🥵
blissful elbow
i need to find the area of the square, but all i can work out are unnecessary obvious angles. these are all the information given
blissful elbow
i tried making a trapezium with the square plus the triangles on either side
mellow grail
i tried making a trapezium with the square plus the triangles on either side
that wont help much
blissful elbow
i can tell
mellow grail
do you know calculus?
blissful elbow
no (year 9) he expects us to know to solve this
mellow grail
no (year 9) he expects us to know to solve this
Must be some geometric trick
blissful elbow
he gives a question like this every now and then and gives a few days
mellow grail
no (year 9) he expects us to know to solve this
do you know trignometry?
i dont think so but just to be sure
blissful elbow
basic trigonometry, + sin rule and cos rule
mellow grail
basic trigonometry, + sin rule and cos rule
I am assuming its construction shenanigan + trig/geometry crap
blissful elbow
im guessing the exact same part, with a lot more crap on it
mellow grail
in terms of trig functions
blissful elbow
i cannot find the side of the square because a simple 10-x wont work
mellow grail
i cannot find the side of the square because a simple 10-x wont work
label the centre of the circle O and the square ABCD starting from the bottom-left corner
can u find BC in terms of sin/cos and OC?
blissful elbow
A bottom left, B is above or wat
mellow grail
A bottom left, B is above or wat
lemme label it
blissful elbow
area of entire sector is 50 pi / 3 (with the area of sector formula)
blissful elbow
i cant find BC till i know OC or OB
or i can hold any one of them as a pronumeral
mellow grail
i cant find BC till i know OC or OB
bruh its sin(60deg)*OC = BC
mellow grail
or i can hold any one of them as a pronumeral
wtf is pronumeral
mellow grail
bruh those are called variables
mellow grail
kk
blissful elbow
in that case yes sin 60
mellow grail
tan(60deg) = BC/OB
OC = sin(60deg)/BC
BC^2 + OB^2 = OC^2
use the numeral values of sin, and tan to find OC and OB in terms of BC, and substitute
this might work
@blissful elbow
mellow grail
yes
blissful elbow
will that work here
mellow grail
its an application of sine rule right
blissful elbow
if i call BC as x
and OC as 10-x because of the radius
and the top angle is 30 degrees
just look at this part at the top of the drawing
mellow grail
OC + CY (consider the point colinear with O and C as Y) = 10. but CY is not x
blissful elbow
it can be a smaller sector itself, the centre being C
mellow grail
wait no
blissful elbow
then the side of the square can be the same radius as that top one
which is x
so then OC can be 10-x
mellow grail
just look at this part at the top of the drawing
its not equal. u can see it by construction its not equal
blissful elbow
if its not to scale, thats a curved side with 2 lines meeting at a point.
forming a sector with 2 radii
mellow grail
if its not to scale, thats a curved side with 2 lines meeting at a point.
formin...
but they first have to be equal
blissful elbow
i see what you mean
mellow grail
that forms an eliptical sector (unsure if thats what its called)
not the usual circular sector we call sector
blissful elbow
have you worked it out yet?
mellow grail
have you worked it out yet?
no am doing some other work side by side, lemme try now tho
blissful elbow
im going to get the solutions on monday if i can, and compare answers and if u want ill check back with u then
because this is taking up too much unnecessary time for me now
mellow grail
im going to get the solutions on monday if i can, and compare answers and if u w...
aight
mellow grail
because this is taking up too much unnecessary time for me now
i will dm ya if i can find a solution
blissful elbow
im just going to send a msg there to keep you in the dm list and then close this channel
.close
cerulean folio
In the sequence 1/4, 4/27, 7/256, 2/625 what r the next 3 fractions, i cant find the pattern help i get that the denominators r like 2 squared 3 cubed but i still dont get it
cerulean folio
I thought the 4th one should have a denominator of 3125 but my teacher said it doesnt
gray isle
2^2
3^3
what comes next
cerulean folio
Its 4^4
gray isle
what's after that
cerulean folio
5^4
gray isle
no
cerulean folio
What how
gray isle
why are yuo keeping the power as 4
wanton pebble
cause it is
cerulean folio
In the sequence 1/4, 4/27, 7/256, 2/625 what r the next 3 fractions, i cant find...
Cos in the sequence the power is 4
wanton pebble
it is given
gray isle
i'm only after the pattern
these fractions are simplified
i want you to consider the unsimplified fractions
wanton pebble
ohh
gray isle
following the pattern being outlined
wanton pebble
got it
cerulean folio
I dont get it
gray isle
forget about the rest of the question
cerulean folio
Wdym?
gray isle
focusing on just what i'm asking for
gray isle
giving me more than what i asked but ok.
cerulean folio
Oh
gray isle
the denominator is 5^5 right?
cerulean folio
Yep
gray isle
so what would be the denominator of the unsimplified fraction of the next term?
cerulean folio
6^6?
gray isle
yes
cerulean folio
But it doesnt follow the pattern given...
gray isle
now note the numerators of the unsimplified fractions would be
1,4,7,10, what comes next?
cerulean folio
13
gray isle
thus the next term would be 13/6^6
cerulean folio
In the sequence 1/4, 4/27, 7/256, 2/625 what r the next 3 fractions, i cant find...
But the next term isnt that
cerulean folio
In the sequence 1/4, 4/27, 7/256, 2/625 what r the next 3 fractions, i cant find...
The 4th fraction is 2/5^4 instead of 13/6^6
cerulean folio
Ahhhh i dont get it
gray isle
consider the unsimplified fractions
cerulean folio
Wdym by that
gray isle
you acknowledge taht 2/625 = 10/3125 right?
cerulean folio
What how
gray isle
you said that yourself
cerulean folio
Wait what
gray isle
(or implied it)
gray isle
Its 10/3125
.
cerulean folio
Its 10/3125
What no this isnt the 4th fraction
gray isle
,w 2/625 = 10/3125
cerulean folio
The 4th fraction is alr given i have to find the 5th 6th and 7th fraction
ocean sealBOT
cerulean folio
Whaaaa
gray isle
i'm aware of what the question is saying
and you seem to have been ignoring everything i've been saying
cerulean folio
I dont get it
cerulean folio
How is 2/625 equal to that
cerulean folio
OHHHHHHH
gray isle
likewise 10/3125 simplies to 2/625
cerulean folio
I didnt see that :0
gray isle
by cancelling the common factor of 5
hence why i asked you to consider the unsimplfied fraction
cerulean folio
Wow
gray isle
$\frac 1{2^2} ,\frac{4}{3^3},\frac{7}{4^4}, \underbrace{\frac{10}{5^5}}_{\frac{2}{625}}, \dots$
ocean sealBOT
ℝam()n()v
cerulean folio
Would the 5th term be the same as the 4th one?
gray isle
no
the main line shows the unsimplified fractions
observe the pattern in the numerator
cerulean folio
Yep what about them
cerulean folio
13
cerulean folio
So its 6^6 next then itll be simplified?
gray isle
thus the next term would be 13/6^6
cerulean folio
Then it will be simplified?
gray isle
whehter that can be simplied further is a different matter
that's just how you'd get the value of the next term
same idea for finding terms after that
cerulean folio
> thus the next term would be 13/6^6
Wait so the 5th term is just this?
gray isle
yes
cerulean folio
If it can be simplified i should simplify it?
gray isle
yes
they may not like exponents in which case you'd evaluate that 6^6 to 46656 giving you
13/46656
cerulean folio
Oh
lone heartBOT
Available help channel!
lime sluice
lone heartBOT
lime sluice
My answer c
tardy stag
what's your reasoning?
vale wigeon
@lime sluice then what is sup(A)
vale wigeon
do you want to redo the problem or is your answer still c
vale wigeon
so you claim sup(A) = 2?
lime sluice
Yes
vale wigeon
are you sure?
lime sluice
A supermumim can be out of the set
vale wigeon
the supremum of a set is its least upper bound.
the supremum of A doesn't need to belong to A, yes. but that isn't my issue with it.
2 is an upper bound for A...
but there are many better ones
1.9 is also an upper bound for A
lime sluice
Yes there are many
vale wigeon
do you see what is wrong with your answer now?
lime sluice
Not yet
vale wigeon
it's true that every element in A is less than 2
but it is also true that every element in A is less than 1.9
lime sluice
We can't decide then
vale wigeon
❌
summer dirge
We can't decide then
you can
lime sluice
I can then only 2
summer dirge
I can then only 2
why 2?
vale wigeon
note that the way i am pointing out the wrongness of your answer isn't actually indicative of how to get to the right answer.
that's on purpose.
tardy stag
do you know the definition of supremum?
lime sluice
Least upper bound
Which can be out of the set
So here 2,3,4,5
Minimum will be 2
So square root √2
Every point next to it will exceed >2
I meant greater than √2 will suprpass 2
vale wigeon
So here 2,3,4,5
Minimum will be 2
no
2 is not the minimum
upper bounds exist that are smaller
lime sluice
√2 is
vale wigeon
for future reference, "surpass" only has one P.
and your wording is rapidly getting worse and worse.
lime sluice
Every number greater than (√2+.......1) square will be greater than 2
So the supremum i can see here is only √2
No clue then
vale wigeon
supermumim
supremum
as i said,
sup(A) = sqrt(2) is almost correct but not quite.
you didn't let me elaborate.
instead you went off on your badly worded rambles.
lime sluice
you didn't let me elaborate.
Yes please
vale wigeon
sup(A) = sqrt(2) would be true if we were working in the real numbers instead of the rational numbers.
however you can show that when restricting to only rational numbers (as the question tells us),
any rational upper bound can always be improved
maybe by a little bit, but it still counts -- so there will not be any LEAST upper bound.
in fact this is what distinguishes Q from R
tardy stag
oh I didn't even see the "in Q" part
lime sluice
Ohh got it
vale wigeon
in R, this sort of thing never happens -- any bounded-above set always has a supremum
lime sluice
There will be many rational numbers
vale wigeon
axiom of completeness
lime sluice
So the answer is complicated
C or d?
√2 is the answer for real numbers
Ohh then D
Doesn't exist
Because rational numbers
C is incorrect it doesn't exist
.close
restive chasm
lone heartBOT
restive chasm
wind cloak
what have you tried
restive chasm
I tried to think using the options so as to get the integral done, but could not.
somber eagle
what integration method did you use?
wind cloak
Lol that only really works with indefinite integration
@restive chasm is that all you've done?
restive chasm
Yes.
restive chasm
Ok.
wind cloak
Can you think of the term to be integrated, and the one to be differentiated?
restive chasm
Yes, integrate the 1/ (x+2)^2
wind cloak
perfect
restive chasm
I actually got it. Tnx.
tardy stag
<@&268886789983436800>
restive chasm
.close
molten oak
lone heartBOT
molten oak
What do those lines mean
mental flame
sides with single markings are equivalent to each other, sides with double markings are equivalent to each other, and sides with triple markings are equivalent to each other. for example, side RQ is equivalent to side ON.
alpine sable
lone heartBOT
alpine sable
I am having trouble understanding the third line of the answer
I do understand that we are trying to isolate the C
alpine sable
I do understand that we are trying to isolate the C
Cuz it says show there’s no value of C
i get that
but where did we get 1 over 12 from
I feel like it could be a simple factoring problem
I understand the question
just not how the isolation was done
<@&286206848099549185>
nimble fern
but where did we get 1 over 12 from
that's 1² not 12
alpine sable
well
i still dont understand that part of the solution.
regardless
thank you for your help
.close
mental flame
send a picture
you dont have a work sheet?
this should explain what you need to know assuming you learned factoring
vale wigeon
you want someone to give you practice problems for solving quadratics via factorization? @alpine sable
tardy stag
wait i have a command for this
vale wigeon
how many?
tardy stag
\newcount\cA \cA\pdfuniformdeviate5\relax
\newcount\cB \cB\pdfuniformdeviate10\relax
\newcount\cC \cC\pdfuniformdeviate5\relax
\newcount\cD \cD\pdfuniformdeviate10\relax
${\the\numexpr\cA*\cC}x^2 + {\the\numexpr \cB*\cC + \cA*\cD}x + {\the\numexpr \cB*\cD} = 0$
Hayley
vale wigeon
well you also fucked up the formula by the looks of it
also even if you DO get decimals,
never drop the zero at the front
it's 0.562 and not .562
sure is, but the form is different
it's better to write the leading zero
so that you know for sure you don't lose the decimal point
tardy stag
but also the solution to these will be rational numbers; they're factorable
vale wigeon
anyway im generating a list of 10 problems in ROUGHLY increasing order of difficulty by hand rn
Solve the following equations using the factorization method.
[I] x^2 - 8x + 15 = 0
[II] z^2 + 10z + 21 = 0
[III] t^2 - 5t - 14 = 0
[IV] w^2 + w - 6 = 0
[V] r^2 - 4r = -3
[VI] 10s^2 + 90s - 100 = 0
[VII] p^2 + 2p - 15 = 33
[VIII] -d^2 + 10d - 25 = 0
[IX] y^2 - 10y - 24 = 0
[*X] v^3 + 10v^2 + 16v = 0
Hey you still here? Sorry I got smth to do
Sub 1 in f(x) to get f(1) = 1/4
Sub 4 into f(x) to get f(4) = 1
Let c = x
Sub the values in f(4) - f(1) = f’(x)(4-1)
You’ll get (x-3)^3 + 8
Then find the value of x
tardy stag
@alpine sable this isn't your channel or sara's anymore
alpine sable
<@456226577798135808> this isn't your channel or sara's anymore
Wdym
alpine sable
Sub 1 in f(x) to get f(1) = 1/4
Sub 4 into f(x) to get f(4) = 1
Let c = x
Su...
Thank you for your help
alpine sable
Ah I’m new to this
Don’t worry
vale wigeon
@alpine sable @alpine sable please move to a different channel if you want to continue your convo.
you are clogging up this channel.
alpine sable
I apologize
vale wigeon
well i could but you're 100% going to complain about the black magic i'm gonna pull
so probably not otherwise
ok then here's how i would do, by factorization, problem [I] from my list:
x^2 - 8x + 15 = 0
=> x^2 - 3x - 5x + 15 = 0
=> x(x-3) - 5(x-3) = 0
=> (x-5)(x-3) = 0
=> [x-5 = 0 OR x-3 = 0]
=> [x = 5 OR x = 3]
answer: x = 5, x = 3.
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
lone heartBOT
tardy tapir
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
2
sick lintel
1
tardy tapir
send us your working
alpine sable
i can tell you what i did
i wrote it as e^(whole thing)
cause ik that whenever 1^infinity form is there
doing so will make it easy
what next ?
tardy tapir
yes
lethal belfry
1
please vist #❓how-to-get-help to learn how to get help
tardy tapir
do you know how to evaluate 1^infinity form?
alpine sable
do you know how to evaluate 1^infinity form?
yeah i can do it if the equation gets simplified
winter light
First I would try a substitution. For example, let t = x - e
tardy tapir
if you just know the direct way, it will be much easier imo
alpine sable
what next then ?
tardy tapir
form the expression first
alpine sable
tardy tapir
let the expression in the exponent as some variable
alpine sable
alr
tardy tapir
now, do you know LH rule?
tardy tapir
then you are done
alpine sable
yeah got it
i was stuck at this step
doing very crazy things
never thought of lh
anyways yeah
done
thanks
tardy tapir
np
lone heartBOT
lone heartBOT
Available help channel!
ruby elbow
how what huh where what
lone heartBOT
how what huh where what
lethal belfry
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Draw a horizontal line on y=2. Where does h(x) intercept that line?
ruby elbow
i know what they mean about h(x) = 2
lethal belfry
how what huh where what
look at the y axis (or as I like to call it , the output axis), see which x value (input axis), gives you the required answer
ruby elbow
look at the y axis (or as I like to call it , the output axis), see which x valu...
hm
so h(x) = 2 is required answer
and
ok
hm
lethal belfry
no, 4
lethal belfry
look at the X axis, and see which input gives 2 as the output
ruby elbow
then it would be 6
ruby elbow
look at the X axis, and see which input gives 2 as the output
4
x = 4
gives
y -2
y = 2
ruby elbow
look at the X axis, and see which input gives 2 as the output
so 4 is the input?
x = 4
makes y = 2
and x = 6
makes y = 4
x = 0
makes y = -2
lethal belfry
yeah, correct
ruby elbow
yeah, correct
so
ruby elbow
yeah, correct
is it 4 and 6
i dont get what we are suppose to be finding
aren't we suppose to find this
tardy tapir
y = h(x)
ruby elbow
but what do i do with this exact info "= 2"
lethal belfry
x is the input
lethal belfry
yeah, that's why they gave you that info
ruby elbow
yeah, that's why they gave you that info
they gave the info h(x)
ruby elbow
yeah, that's why they gave you that info
what do i do with the other half, "= 2"