i suck at geometry, i hate similarity
#help-10
obtuse pebbleBOT
@high furnace Has your question been resolved?
high furnace
i uh feel like triangle CEB and triangle CAD are congruent
it just looks congruent to me
<@&286206848099549185>
high furnace
i sincerely need help
<@&286206848099549185>
my questions are always the ignored questions
<@&286206848099549185> i've been waiting for 45min
visual granite
k
high furnace
ping me if you have anything to say
visual granite
ok
high furnace
i've given up and am going to work on other subjects
half dock
i've given up and am going to work on other subjects
I inboxed you long ago
high furnace
wdym inboxed
high furnace
...
wintry swift
i've given up and am going to work on other subjects
then you should close the channel so it can used by other users.
high furnace
...
as in i've given up waiting solely for help
because just now i wasn't doing anything else except waiting for someone to help
high furnace
<@&286206848099549185>
gray remnant
yes sir
high furnace
the question is on top
gray remnant
where
gray remnant
and what do you think that i can do
gray remnant
i can guide you but you need to make one of my wishes real
high furnace
how can i do tha sir
gray remnant
how can i do tha sir
will u be my discord kitten
high furnace
no
gray remnant
warm shaleBOT
gray remnant
@high furnace im just kidding that was a prank
high furnace
it was kinda obvious
gray remnant
good one ha?
high furnace
@gray remnant do you know how to solve
gray remnant
where r u from?
high furnace
asia
high furnace
nope
im 13
i lucked into the best MO class
the question i posted is a 2mark question that doesn't require explanation, there are harder ones in my worksheet 😭
gray remnant
the question i posted is a 2mark question that doesn't require explanation, ther...
oh god damn it
high furnace
why disrespectful though
im really bad at MO but I scored well last semester and barely got into the better class
gray remnant
shame on you@high furnace
high furnace
my worksheet is due tmr 😭
gray remnant
im really bad at MO but I scored well last semester and barely got into the bett...
congrats:)
high furnace
this is 1 out of 8 questions i don't know how to solve 😭
gray remnant
what you gonna do with other 7
high furnace
congrats:)
because right last semester, literally everything in the notes, but now i'm inside a class with literally top 20 in my country
:/
high furnace
what you gonna do with other 7
i solved one but I'm not sure if it's correct
maybe not everyone is top 20
gray remnant
because right last semester, literally everything in the notes, but now i'm insi...
nice, but one question what do you want to do in your life?
high furnace
mm i haven't figured that out yet tbh
gray remnant
cause you are really smart for your age
gray remnant
mm i haven't figured that out yet tbh
do you have any idea
high furnace
cause you are really smart for your age
my school is top maths and science school, the ppl in my MO class are way smarter 😭
like 1/4 of the class solves the questions before the teacher asks us to solve it
high furnace
do you have any idea
nope, none at all
gray remnant
fdfs
high furnace
im from asia 🤣
gray remnant
and?
high furnace
mostly 140+ i doubt the accuracy though
high furnace
most of the questions are very repetitive
high furnace
on chess.com
yeah
gray remnant
whats your nick?
high furnace
do yalls mind looking at the other questions
high furnace
whats your nick?
i stopped playing
cloud igloo
923
gray remnant
lets playu
high furnace
do you want to polay one game?
i want to solve my worksheet 😭
gray remnant
i can solve
high furnace
whyyyy
gray remnant
im not home rn
gray remnant
so do you want to play chess until i dont get homd
high furnace
can yalls stop trolling
gray remnant
when u need to finish your work
cloud igloo
@high furnace what you need help with?
warm shaleBOT
wintry swift
post the whole question, not only parts of it.
clever pier
Reub, if you truly want help, close this channel and get a new one since these guys won't stop trolling. (cofi, david)
high furnace
@cloud igloo are you able to help
gray remnant
no
cloud igloo
<@679370210016493579> are you able to help
Where is the rest?
gray remnant
sorry anger issuses again
high furnace
can yalls stop flooding
@cloud igloo wants to see the question
AND DIAGRAM
BESIDE EACH OTHER
you have 1 minute to try
gray remnant
i told u something
high furnace
i told u something
uh huh
cloud igloo
Make a new channel @high furnace
slim cove
<@531535537362829315>
ping @ moderators next time you'll get a faster response
obtuse pebbleBOT
ping @ moderators next time you'll get a faster response
slim cove
.close
obtuse pebbleBOT
slim cove
do you play chess
stop trolling, if you want to play chess then find people on #chess-go-shogi
oh wait they were already banned
that settles that
cloud igloo
💯💯
obtuse pebbleBOT
Available help channel!
split granite
I'm trying to find F'(t)
the correct answer is given to me, it's the second image, however when I work the problem out, my answer is similar but incorrect, I'm getting
-30[0.6cos(t)-sin(t)] / (0.6cos(t)-sin(t))^2
could it be something to do with the negative sign?
obtuse pebbleBOT
I'm trying to find F'(t)
the correct answer is given to me, it's the second ima...
split granite
this is my work, it's messy though
(Extra context if needed, I'm doing this for Calc 3, although this is a Calc 1-2 review haha)
split granite
isn't the derivative of 0.6sin(t)+cos(t) = to 0.6cos(t)-sin(t)?
hexed gull
You can multiply both terms in the brackets by the - and therefore the numerator is the same
split granite
ohh that makes more sense
ebon remnant
sin x + cos x = √2
sin x - cos x = ?
I don't have any idea to finish it
just found out sin x cos x is 1/2 from that
obtuse pebbleBOT
sin x + cos x = √2
sin x - cos x = ?
I don't have any idea to finish it
just fou...
timid silo
Do you have an interval u r working with
For x
Or are you looking for a general solution
fossil crag
this is supposed to be always true I think
tender stratus
yeah
ebon remnant
um I'm on 11th
cinder lintel
whole square it and replace value
tender stratus
$\frac{1}{\sqrt{2}}\sin{x} + \frac{1}{\sqrt{2}}\cos{x} = 1$
warm shaleBOT
nebula40
fossil crag
do you know what happens when you know the value of a+b and ab?
fossil crag
yes
tender stratus
or you could use this $\sin{(x + \pi/4)} = 1$
warm shaleBOT
nebula40
fossil crag
or you could use this $\sin{(x + \pi/4)} = 1$
only use parentheses
cinder lintel
its a formula
fossil crag
develop sin(x+45)
cinder lintel
sin a +b
ebon remnant
which means cos(x+45) = 1 too?
ebon remnant
but sin((90-(x+45))
ebon remnant
eh sry i mean yeah
tender stratus
$\frac{1}{\sqrt{2}}\sin{x} + \frac{1}{\sqrt{2}}\cos{x} = \cos{(\pi/4)}\sin{x} + \sin{(\pi/4)}\cos{x} = \sin(x+\pi/4)$
warm shaleBOT
nebula40
tender stratus
**nebula40**
this was what I was going at
or just use the method rafilou mentioned if you're still not comfortable with trig identities
its more straighforward
ebon remnant
or just use the method rafilou mentioned if you're still not comfortable with tr...
I'm quite new for this
ebon remnant
this was what I was going at
alright thx alot
got 1 more question tho
sry about blur, its square root of 3
do i just power all of it by 3?
fossil crag
sry about blur, its square root of 3
this looks like I've consumed too much of the good stuff
ebon remnant
hehe
ebon remnant
this one better
tender stratus
you can cube it, its not as bad as it looks lol
make sure to use (a+b) = 2^(1/3) in the 3ab(a+b) term
tender stratus
$\sin^4x + \cos^4x = 1 - 2\sin^2x\cos^2x$
warm shaleBOT
nebula40
tender stratus
you'll need this
tender stratus
(sin^2 A)^x +(cos^2 A)^x = ?
I dont think there's any special expansion for this
ebon remnant
I dont think there's any special expansion for this
oh alright
ebon remnant
**nebula40**
how do you develop this?
tender stratus
split the sin^4 into sin^2 times sin^2. then make it (sin^2)(1-cos^2)
similar for cos^4
compact shadow
obtuse pebbleBOT
compact shadow
.close
compact shadow
this one better
obtuse pebbleBOT
compact shadow
$not \frac{1}{3\sqrt{2}} but \frac{1}{3(2^{\frac{1}{3}})}$ my bad
warm shaleBOT
Cogwheels of the mind
ebon remnant
but thanks alot for the better explanation
compact shadow
I see
ebon remnant
Appreciate it
ebon remnant
obtuse pebbleBOT
Available help channel!
distant rampart
I've come across a mathematical problem that I've been trying to wrap my head around, and I could use some help verifying my solution. The problem involves demonstrating that P(n, n) = P(n, n-1), and I'd like to confirm whether my approach is correct. Here's what I've done so far:
The problem at hand is to demonstrate the equality P(n, n) = P(n, n-1) and provide a proof for it using two approaches:
a) Simplify both sides of the equation and show that they are equal.
b) Use the multiplication principle to establish the equality between the two expressions.
a) To begin with, I tried simplifying both sides of the equation. After some manipulation, I managed to express both P(n, n) and P(n, n-1) in terms of factorials, leading me to believe that they are indeed equal. However, I'm not entirely confident in my simplification and would appreciate it if someone could take a look and offer their input.
b) Additionally, I thought about using the multiplication principle to further substantiate the equation. My intuition tells me that there might be a way to connect the two expressions using this principle, but I'm struggling to find the precise steps to do so.
obtuse pebbleBOT
I've come across a mathematical problem that I've been trying to wrap my head ar...
kind hawk
what is P(n,n) supposed to be?
distant rampart
(P(n,n)) refers to permutations of (n) objects taken (n) at a time. Permutations represent the arrangements of objects in a specific order, and (P(n,n)) refers to the number of ways to arrange (n) objects in (n) positions.
warm shaleBOT
dgh
kind hawk
ok and now with two different letters so it would be clear which is the first input and which the second
distant rampart
(P(n, r)) represents permutations of (n) objects taken (r) at a time. So, (P(n, r)) would stand for the number of ways to arrange (n) objects in (r) positions, where (n) is the total number of objects and (r) is the number of positions.
warm shaleBOT
dgh
compact shadow
P(n,m) is number of arranging m objects on n positions?
For m=n-1, arranging n-1 objects on n position, you can view the empty position, as it’s taken by an imaginary object
Since there is only one empty position you can do that
(Actually r many empty positions you just divide by r! in the end)
distant rampart
So, we divide by (n - 1) factorial ((n - 1)!)?
warm shaleBOT
dgh
fossil crag
What he meant is that we know that P(n,n) = n!
distant rampart
And what'd P(n, n-1) be?
fossil crag
The idea if you want to arrange n-1 elements into n boxes, you can consider "emptiness" as your missing nth element
distant rampart
n! -1?
fossil crag
No, n! too
distant rampart
Or (n-1)!
fossil crag
n!/1!
distant rampart
So for each less empty spot means we add by 1 in the denominator?
fossil crag
Yeah, P(n,n-m) = n!/m!
The idea for P(n,n-1) is that "void" is your nth element, and so you're left with arranging n objects (including void) in n positions
obtuse pebbleBOT
@distant rampart Has your question been resolved?
ocean swift
lim x -> 1 (1 - x ^ 2)/(sin pi*x)
obtuse pebbleBOT
lim x -> 1 (1 - x ^ 2)/(sin pi*x)
ocean swift
,help
warm shaleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
ocean swift
$lim x -> 1 (1 - x ^ 2)/(sin pi*x)$
warm shaleBOT
I_am_Success_51
ocean swift
$lim x -> 1 (1 - x ^ 2)/(sin pi*x)$
compact shadow
Hopital’s rule
warm shaleBOT
I_am_Success_51
ocean swift
Hopital’s rule
I want without it
We havent studied L hopital rule from our syllabus
So the tracher doesnot allow us to do advanced techniques
ocean swift
Nice handwriting
harsh remnant
Why can't we just substitute right away?
harsh remnant
Nice handwriting
Trust me he's the best
ocean swift
Why can't we just substitute right away?
I also thought that
I think it will take me around 5 minutes to understand this handwriting
But thanks
I was wondering the ans since 1 hr
compact shadow
I think you can recognize it in one min, just ignore those ugly “lim”
ocean swift
I think you can recognize it in one min, just ignore those ugly “lim”
I cant
I cant i cant i cant
ocean swift
Bro u here ?
compact shadow
Yeah writing in tex
$\frac{1-x^{2}}{\sin(\pi x)}=(\frac{1+x}{2\sin(\frac{\pi x}{2})})(\frac{1-x}{\cos(\frac{\pi x}{2})})=\frac{x-1}{\sin(\frac{\pi}{2}(x-1))}=(\frac{2}{\pi})(\frac{\frac{\pi}{2}(x-1)}{\sin(\frac{\pi}{2}(x-1))})=\frac{2}{\pi}$
warm shaleBOT
Cogwheels of the mind
compact shadow
With all “lim” omitted
compact shadow
Np
ocean swift
I dont underatand the third one
compact shadow
Now the second term
Is product of two fractions right
The left fraction has limit 1
So only the right fraction left
This becomes the third term, with cos(πx/2) replaced with -sin(πx/2-π/2)
?
zinc stirrup
(x-2)(3x-3)
obtuse pebbleBOT
(x-2)(3x-3)
rigid ermine
zinc stirrup
how do i calculate this (x-2)(3x-3)
rigid ermine
the solution at the bottom is supposed to be the answer
but how do we get that answer
zinc stirrup
we just need help making it make sense
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
zinc stirrup
<@&286206848099549185>
obtuse pebbleBOT
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.
royal basin
!nosols
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
rigid ermine
how do we get the 9x
rose snow
As a helper, please do not give out answers that could be copied as a homework s...
whats the question?
royal basin
also just don't give google's auto solutions.
zinc stirrup
can u help us in call lmao like we dont understand
rose snow
question pls
zinc stirrup
(x-2)(3x-3)
rigid ermine
he just open the channel
zinc stirrup
we are pondering on how we can get to the final solution
rose snow
just this multiplication?
rose snow
Already Wait a min I'll share it with steps
rigid ermine
from that question
zinc stirrup
ok but if were to slow to get it, can u like join our voice call and explain it with paint or something
rose snow
What I can do right now is type the steps and if you dont understand ill join it
harsh remnant
Voice channels are obsolete here
zinc stirrup
yeah were in a private call but we can try the steps first
rose snow
(X-2)(3X-3)
(x multiplied with 3x and -3 indivialy and then -2 multipled with 3x and -3
so thats
3x square -3x -6x +6
3x sq -9x +6
got it?
zinc stirrup
wait
let me read
3x square
whats that mean
were not english native
or is it the same as ^
rose snow
the first term here
rigid ermine
we just need to know like how to make it 3x^2 - 9x + 6
rose snow
the exponent
rose snow
yeah
zinc stirrup
ok ok
rose snow
so in the answer its 3x^2
zinc stirrup
were gonna try and understand it give us a minute
rigid ermine
so in the answer its 3x^2
but why is it -9x after
rose snow
Like youre both 17 years old?
zinc stirrup
yeah
rose snow
-2 multipled by 3x
are you guys on insta by any chance? I could write this on a piece of paper and send you
rigid ermine
Kristoffer_Brandsoy
zinc stirrup
dm me
rigid ermine
can make group chat
rose snow
you guys make and add me
zinc stirrup
whats ur insta?
rose snow
yeah i judt did
rose snow
did
rose snow
am
rigid ermine
we need help from someone that can join discord and explain on video
<@&286206848099549185>
zinc stirrup
shristii couldnt explain it to our dumb heads
can someone help us in call <@&286206848099549185>
obtuse pebbleBOT
@zinc stirrup Has your question been resolved?
neat orchid
i dont understand how to solve this problem. do i set the 2 equal to one another and solve for x?
obtuse pebbleBOT
i dont understand how to solve this problem. do i set the 2 equal to one another...
tardy epoch
this question sure is confusing
sage geode
I think it is asking for the solutions to f(x) = 1/x
warm shaleBOT
riemann
neat orchid
then do i plug the 1/x into the firrst equation?
tardy epoch
then do i plug the 1/x into the firrst equation?
what do you mean "plug the 1/x"
write out a couple steps
obtuse pebbleBOT
@neat orchid Has your question been resolved?
neat orchid
I'm confused
tardy epoch
when you plug in x=c to f(x), you get f(c) = c / (2-c)
tardy epoch
**riemann**
i'll ask again, do you understand this
neat orchid
I think. Ur just replacing x with c?
tardy epoch
yes
x is a variable
c is a specific solution to what the question is asking for
like x^2 = 4, then x=2 or x=-2. but instead of 2, x=c
obtuse pebbleBOT
@neat orchid Has your question been resolved?
neat orchid
So then ur just essentially plugging the second equation into thr first?
obtuse pebbleBOT
@neat orchid Has your question been resolved?
woeful gyro
need help
woeful gyro
<@&286206848099549185> need help please
tardy epoch
<@&286206848099549185> need help please
!15m
obtuse pebbleBOT
<@&286206848099549185> need help please
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.
woeful gyro
what exactly is the question?
its solvin for x and the length of zt
tardy epoch
its solvin for x and the length of zt
is this a test?
woeful gyro
no it's jus on a goggle form
hollow dove
that's also a different question from the original picture
which do you want help with
woeful gyro
the second one i posted
hollow dove
okay, have you tried drawing a diagram?
woeful gyro
yes
hollow dove
can you show us
balmy mortar
Please remove the undegrad role if you are not
#advanced-lounge is definitely not for posting stuff at this level, note. See the channel description
woeful gyro
can you show us
woeful gyro
oh did i label the wrong ones
hollow dove
no, your diagram is fine
you just haven't labelled any distances on it
I mean like, write 3x+7 above the line between Z and S
woeful gyro
like this
woeful gyro
so do i do 3x+7=-5x+23 to solve for x
hollow dove
yep!
woeful gyro
i got 8 is that right?
woeful gyro
hollow dove
remember it's a -5x on the right side
not 5x
so subtracting 3 from both sides gives 7 = -8x + 23
hollow dove
yep!
woeful gyro
so now how i determine the lenth of zt
woeful gyro
what i did is i plugged in x which is 2 and i got 13 the i multiplied them by 2 and got 26
did i do it right?
hollow dove
what do you have to find for this question?
woeful gyro
the same thing and x and the length
woeful gyro
yes
hollow dove
okay, have you drawn a diagram for this one?
woeful gyro
yes
hollow dove
L is the midpoint of WB, so you should be able to write down something that relates WL to WB
woeful gyro
woeful gyro
i did solve for x and i got -2/3 whixh is not an answer on the answers
hollow dove
what was the initial equation you wrote down?
woeful gyro
3x+8=1/2+12
hollow dove
3x+8 is the length from W to B, not W to L, so those lengths are not equal
woeful gyro
so what do i do
woeful gyro
so i don't use 3x+8?
hollow dove
we have the full length WB is 3x+8
we have half the length is (1/2)x+12
so we can add up two copies of these half lengths to get the full length
so 3x+8 = 2*( (1/2)x + 12 )
woeful gyro
i got 8
hollow dove
looks good
woeful gyro
i plugged it i got 32 and 16
hollow dove
remember that 3x+8 is already the distance WB
(1/2)x+12 is half the distance
so you can either plug x=8 into 3x+8 and take that
or plug x=8 into (1/2)x+12 and double it
hollow dove
yes
woeful gyro
thank youi got one more question
hollow dove
not sure how you're supposed to input the answer to the first question
but the other parts are exactly the same as the questions we just did
woeful gyro
but which i equations i do to get x theres alot of them
hollow dove
it's in the same form as this
the question tells you the length of a full line and also the length of one of the halves
woeful gyro
like this
hollow dove
the top equation isn't right
remember 24x -12 is the full line
10x-2 is half of the line
hollow dove
we can't use the second one
because we don't know if TR = RM
we only have that SK is bisected at R
not that MT is bisected as well
so these two parts are not necessarily equal
so, if 24x - 12 is the full line
and 10x - 2 is half of the line
how do we get from half of the line to the full line
woeful gyro
do we make multiply?
hollow dove
multiply what by what?
woeful gyro
the 10x and 12 im not rlly sure
hollow dove
say you have a stick, and you know half of that stick measures 30cm
how long is the full stick
woeful gyro
60
hollow dove
so how did you get to that result from the given information
woeful gyro
cause the halves would have to be equal
hollow dove
so 30 + 30, right?
so in our question, one half of the line is given by 10x -2
so we can get the full line with (10x - 2) + (10x - 2)
or more compactly, as 2(10x - 2)
and we also know what the full line should be; 24x-12
woeful gyro
so i would have to add 10x-2 and 10x-2?
hollow dove
yes
woeful gyro
i got 20x-4
hollow dove
so that's the length of WB
but we're also given that WB has length 24x - 12
so you can set these equal
woeful gyro
what does that eqaution look like its not an answer
hollow dove
you just found WB = 20x -4
and we have WB = 24x-12
so 20x-4 = 24x-12
you can solve this for x
woeful gyro
i got 2
hollow dove
now you can find all the lengths
woeful gyro
for 4(2)+ 5 i got 13 which is not an answer
hollow dove
that's the length of TR
look at which lengths you are asked for and check your formulas again
hollow dove
but MT is made up of other lines that you do have formulas for
woeful gyro
so what do i plug 2 in any number?
hollow dove
look at the line MT
can you break it up into two smaller lines
perhaps lines that you are given equations for in the question
woeful gyro
8x-5? or 4x+5 only ones i haven't use
woeful gyro
got 44x-5
oh i multipled i got 12x now
does that mean tr+rm are congruent to each other
hollow dove
what lengths do you have for all the lines
woeful gyro
only length i had to solve for was rk and mt now i have to find out which line segments are congruent to each other
hollow dove
yes, but line segments are congruent if they have the same length
so you want the length of each of the lines segments to compare them
woeful gyro
the length are 18 and 12
hollow dove
they're not the same so those two lines are not congruent
MT bisects SK, so you know the two lines that make up SK are equal
you can just take those two lines
woeful gyro
so the lines that are congruent are mt and sk
hollow dove
no
SK is being bisected
that means the two sides that it is divided into are equal, because they are each one half
woeful gyro
so sk and and tr or sr
hollow dove
it's SR and RK
hollow dove
RK is the same thing as KR
woeful gyro
thank youvery much you have been verry helpful !!!
obtuse pebbleBOT
@woeful gyro Has your question been resolved?
keen garnet
I proved that the first and the third are wrong but for the tree remaining I don’t know
warm shaleBOT
Joseph.P
obtuse pebbleBOT
@keen garnet Has your question been resolved?
keen garnet
<@&286206848099549185>
keen garnet
Anyone ?
tardy epoch
Hmmm. Maybe try #elementary-number-theory or #groups-rings-fields
sharp anchor
I need help on something
obtuse pebbleBOT
I need help on something
shadow tangle
would it be possible for you to send a clearer image?
sharp anchor
0 to 5 and 0 to 3
(a) Describe and sketch the curve given parametrically by
{
x = 5 sin (3t)
y = 3 cos (3t) for 0 $\le$ t $< $ 2$\pi$
3 .
What happens if we instead allow t to vary between 0 and 2$\pi$?
(b) Set up, but do not evaluate an integral that calculates the arc length of the curve described in part
warm shaleBOT
DeRainMan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sharp anchor
(a) Describe and sketch the curve given parametrically by
{
x = 5 sin (3t)
y = 3 cos (3t) for 0 $\le t \ < $ 2\pi$
3 .
What happens if we instead allow t to vary between 0 and 2$\pi$?
(b) Set up, but do not evaluate an integral that calculates the arc length of the curve described in part
warm shaleBOT
DeRainMan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
sharp anchor
I put S = 4$\int_0^3{\int_0^5{\sqrt{x^2 + y^2}}}dxdy$
timid silo
pretty sure thats wrong
warm shaleBOT
DeRainMan
timid silo
do u know the formula?
sharp anchor
yes
timid silo
its not even a double integral
sharp anchor
I was wondering if it could work this way.
timid silo
nono u need the differece of the xs and ys
timid silo
nonono
sharp anchor
sqrt of
timid silo
ill type it out
sharp anchor
ok ty
timid silo
Integral sqrt((dy/dt)² + (dx/dt)²) dt
sharp anchor
ik that 1
timid silo
yep
sharp anchor
I want to know it in terms of "x" and "y"
timid silo
of a function of y?
sharp anchor
like x and y inside of an integral.
timid silo
dont think what youre trying will work
timid silo
Integral sqrt((dy/dt)² + (dx/dt)²) dt
thats the closest youll get
maybe somebody else can help tho
obtuse pebbleBOT
@sharp anchor Has your question been resolved?
proper sable
how do we translate the following words into inequalities?
https://cdn.discordapp.com/attachments/689915677431169069/1144059345680740353/image.png
obtuse pebbleBOT
how do we translate the following words into inequalities?
https://cdn.discorda...
@proper sable Has your question been resolved?
polar fossil
I'd probably start by drawing the second two equations on the yz plane
like draw a yz plane on paper and plot the two equations
and then figure out where that first equation, the x + y + z = 8, where it intersects the yz axis, maybe draw a dashed line or something to figure out the bounds on x
tepid mountain
I don't understand how
X + Y + Z = 8 is a plane
Isn't it a 3d shape like?
polar fossil
I don't understand how
X + Y + Z = 8 is a plane
Isn't it a 3d shape like?
it's a plane, yeah - it is at a 45º angle from every axis
tepid mountain
it's a plane, yeah - it is at a 45º angle from every axis
Oh yes
Is that what it called solid geometry
Combined with inequalities ?
polar fossil
i would call this analytic geometry
proper sable
I'd probably start by drawing the second two equations on the yz plane
how can we translate the words "behind" and "in front" into inequalities?
polar fossil
good question; I suspect that the three surfaces will enclose an area
but i haven't graphed them
proper sable
a volume*
polar fossil
graph in your head 
i mean you could try points right
like find the intersections
drawing a sketch of at least the second two equations is a very good idea though
tepid mountain
graph in your head <:sungl:1107693832272883772>
That would be like hell to graph 4 functions in a 3d dimension in your head
polar fossil
yeah... graphing 3d functions is hard enough
it's okay to get a machine to do it for you but you should try some on your own, again at least do the 2d bit
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
round wing
yo
hot sonnet
b² = 3/4 has 2 solutions
round wing
b² = 3/4 has 2 solutions
?
hot sonnet
?
It's a quadratic equation, so there are 2 solutions. Notice that b is not restricted 👀
It can be positive, negative too
hot sonnet
This is Pearson platform (?
round wing
yes
hot sonnet
also squareroot cant be negative irrc
Yes, but this is not a square root
hot sonnet
You have b²=4/3, not b=√(4/3). The first equation is solved as b = ±√(4/3)
Ok great 👍🏽
round wing
You have b²=4/3, not b=√(4/3). The first equation is solved as b = ±√(4/3)
I see, but isnt that the same
b=√(4/3) can be written as b^2 = 4/3 if u just square both sides
hot sonnet
(oh sry it was 3/4, but let's leave it like that)
hot sonnet
b=√(4/3) can be written as b^2 = 4/3 if u just square both sides
Yes, b = √(4/3) implies b² = 4/3 as you already have the value for b, which is positive. If you get to b² = 4/3 in a different way and there are no restrictions for b, then the correct way is considering it to be a quadratic equation
As any quadratic equation, it has 2 solutions
round wing
Ah I see, if we just have b=√(4/3), then we dont do anyting as we already have the answer, but if its b^2 then its a quadratic eq and has 2 solutions
hot sonnet
Yess
sage dagger
Is the derivative of arcsin(x^2) = 2x/sqrt(1-x^4)
obtuse pebbleBOT
Is the derivative of arcsin(x^2) = 2x/sqrt(1-x^4)
sage dagger
did I do anything wrong there
flat roost
did I do anything wrong there
nope , its correct
flat roost
And for arccos(e^x) is that just -e^x/sqrt(1-(e^x)^2)
yep
tardy epoch
Is the derivative of arcsin(x^2) = 2x/sqrt(1-x^4)
,w diff arcsin(x^2)
warm shaleBOT
tardy epoch
And for arccos(e^x) is that just -e^x/sqrt(1-(e^x)^2)
,w diff arccos(e^x)
warm shaleBOT
sage dagger
2x?
tardy epoch
Do you know exponent rules
sage dagger
Oh yeah I thought you couldn’t do that because of e^x idk
tardy epoch
I don't know what your confusion is
royal basin
Oh yeah I thought you couldn’t do that because of e^x idk
you were wrong to think that
tardy epoch
Oh yeah I thought you couldn’t do that because of e^x idk
Read this live channel
#help-9 message
royal basin
$(e^x)^2$ is still equal to $e^{x \cdot 2}$ and $x \cdot 2$ still equals $2x$ and the presence of the number $e$ changes absolutely nothing about that
warm shaleBOT
Ann
tardy epoch
Might apply to your problems too
sage dagger
I thought e^x would like not apply to exponent rules
royal basin
why not
sage dagger
e^x different
sage dagger
if dy/dx can’t change it then why should exponent rules 
royal basin
you are just painting yourself into unreasonable corners with alarming determination
sage dagger
What shall I do with this
(Differentiating)
2ln(arcsinx)
What do I do from there because ln(arcsinx) is one whole function
timid silo
What do I do from there because ln(arcsinx) is one whole function
huh
just use chainrule xD
sage dagger
what I do first
timid silo
(f(g(x)))’ = f’(g(x)) * g’(x)
sage dagger
That notation don’t help
royal basin
hold up.
this feels ambiguous
do you mean $\ln[ (\arcsin(x))^2]$ or $[\ln(\arcsin(x))]^2$
warm shaleBOT
Ann
royal basin
yes there is a difference between them no they aren't the same
if you cannot tell then you should not do this problem at all no matter what
timid silo
seems to be first since he used log law
timid silo
ye
royal basin
ok alright
so yeah that equals 2 ln(arcsin(x))
which is a good move since it relieves some of the headache
royal basin
What do I do from there because ln(arcsinx) is one whole function
it is a composition of two functions
ln and arcsin
royal basin
no
you've successfully bamboozled yourself into putting the square in the wrong place.
royal basin
you treated this as $\mathrm{sq} \circ \ln \circ \arcsin$ when it was written for you UNAMBIGUOUSLY as $\ln \circ \mathrm{sq} \circ \arcsin$
warm shaleBOT
Ann
sage dagger
I don’t follow
polar fossil
$[\ln(\sin\inv x)^2]' = [2\ln(\sin\inv x)]'$ so you won't see $2\ln(\sin\inv x)$ show up in the derivative
warm shaleBOT
hayley!
timid silo
(f(g(x)))’ = f’(g(x)) * g’(x)
^
obtuse pebbleBOT
@sage dagger Has your question been resolved?
timid silo
Find number of divisors of N which are less than $\sqrt{N}$.
obtuse pebbleBOT
Find number of divisors of N which are less than $\sqrt{N}$.
warm shaleBOT
Feynmann
timid silo
Where $N=2^{10}×3^{15}$
warm shaleBOT
Feynmann
timid silo
Why does my method not work?
$\sqrt{N}=2^{5}.3^{7}.\sqrt{3}$
Number of divisors greater than √N would be 5×8=40, so number of divisors less than √N =176-40
warm shaleBOT
Feynmann
timid silo
Divisors greater than √N =2^6 onwards ×3^8 onwards
spice citrus
Because for example 3^7 * 2^9 is also a divisor greater sqrt(N)
timid silo
Because for example 3^7 * 2^9 is also a divisor greater sqrt(N)
So divisors less than $\sqrt{N}$ would be $\prod_{n=0}^{4}2^{n}× \prod_{k=0}^{8}3^{k}$ ?
warm shaleBOT
Feynmann
timid silo
I didn't mean to put all of that together
spice citrus
There's an easier way actually, notice all divisors come in pairs
If d | n, then (n / d) is also a divisor
*this doesn't have to be the case if N was a perfect square. Then d and n / d can be the same
timid silo
How should i proceed?
timid silo
Gcd=1 ?
spice citrus
No, about their size
timid silo
Like?
spice citrus
One being bigger then sqrt(N) and one being smaller
timid silo
I can do this question with that method, in that case it would be 176/2
But how should i proceed with my method?
Or does my method not make any sense?
spice citrus
It makes it way more difficult and time consuming since there will be a lot of cases to consider
Would 2^2 * 3^9 be bigger? You would need to do that for multiple numbers
timid silo
If √N =2^5×3^7 (approx), so why can't the divisors less than √N be (5+1)(7+1)?
Since sqrtN also has a √3 in it's factor
spice citrus
Because we already found it was 88 and not 48
and one exponent can be below the threshold if the other one is sufficiently large
scenic surge
what happened here?
obtuse pebbleBOT
what happened here?
undone quest
What is value of x when line l,m are l//m and there's ∠35 over the line l and there's ∠x under line l and there's ∠50 over line m
obtuse pebbleBOT
What is value of x when line l,m are l//m and there's ∠35 over the line l and t...
undone quest
undone quest
???
hardy ginkgo
@timid silo help him
tender stratus
x = red angle + blue angle
you should be able to find those two
apologies for the not so straight line
obtuse pebbleBOT
@undone quest Has your question been resolved?
undone quest
There's no values for 2 angles
tender stratus
the red angle is 35 degrees, and the blue one is 50 degrees
from the properties of parallel lines
corresponding angles, and interior opposite angles respectively. you might have used different terminology but the concept is the same
obtuse pebbleBOT
@undone quest Has your question been resolved?
harsh remnant
이해 되셨을까요?
grizzled shore
What’s the difference between assume and suppose, and where would you choose 1 over the other?
obtuse pebbleBOT
What’s the difference between assume and suppose, and where would you choose 1 o...
sage geode
I think I would use "suppose" more when considering cases, but I don't think there is any difference between those terms
timid silo
maybe the same thing
maybe when you are taking a quiz it's more common to find "suppose" in first paragraph of an exercise, and "now assume" with paragraphs derived from it?
for example, 1) A) suppose y = 5/x, what is the domain of x? B) Now assume x =2, whats the value of y ?
idk they have the same meaning
grizzled shore
Here’s what I think:
You can’t be wrong with suppose.
You could be wrong with assume.
What I mean is when you say suppose you’re considering a subset of possible cases. In this sense, “Suppose we have…” and “Consider…” has the same meaning. We consider only the cases under which my supposition is true.
This is different to “Assume…” where we kinda go out on a limb or hunch, we don’t really know if it’s true or not.
Which makes me think that suppose and assume are different starts to proof by contradiction
Suppose feels more like, if P then Q implies P is impossible. And it doesn’t say my supposition is wrong
But if I start with assume then we say the assumption was wrong
obtuse pebbleBOT
@grizzled shore Has your question been resolved?
balmy mortar
This is all natural language anyways, the differences aren't necessarily clearcut
Here's how I use them, but it may differ for other ppl
===============
Let this be that for assignment
Assume not Q for a contradiction to show P => Q
Suppose P for a direct proof P => Q
Hmm for contrapositive
I think I would write Suppose not Q
and make it clear Im proving the contrapositive
balmy mortar
Thats just how I use them
Suppose this for a contradiction is perfectly reasonable
Assume P. ... . Therefore Q. is also reasonable
Just assume you will see the 2 words used interchangeably in texts you read
Although it does make sense to me at least to not treat them as exact synonyms in my own writing to be more systematic.
timid silo
Can you represent an iff statement as "if and also"? As in
"I wont get banned if I don't break the rules and also don't annoy a mod"
obtuse pebbleBOT
Can you represent an iff statement as "if and also"? As in
"I wont get banned if...
tacit scarab
I don't think that's how it works
gleaming ridge
Iff is a shorthand for if and only if
So I don't think you're allowed to do that
Plus if and also don't seem like iff
It's more of an if and an &
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
merry vault
When is a sup or inf of a set an element in the set?
obtuse pebbleBOT
When is a sup or inf of a set an element in the set?
merry vault
for example M := {x in R | x < 2}, sup M = 2 right?
grizzled shore
Yes
merry vault
there is a sentence in my script that confuses me
it says
let A subset R. If A has an upper bound (english?) and when sup A in A, then A has a maximum and it's max A = sup A
royal basin
yes, "upper bound" is the correct word
sup(A) is a number that may belong to A but also may not.
when it does, it is A's greatest element.
grizzled shore
for example M := {x in R | x < 2}, sup M = 2 right?
There’s no max M
It doesn’t exist in this set
merry vault
ohhhh
grizzled shore
But if it did exist then it’s also the sup of the set
Max is a stronger thing than sup
If something is the max of a set it is also the sup of the set
merry vault
is a limit similar to a sup/inf in that it could be in the set too but doesn't have to?
grizzled shore
Because the definition of a max also satisfies the definition of the supremum
Wdym a limit is in the set
merry vault
umm
you can take the limit of a set right
lim x->inf (M)
is 2
= sup M
I assume
is there a set M where the limit is an element of M
royal basin
you can take the limit of a set right
no
merry vault
o
grizzled shore
What the heck is the limit of a set lol
royal basin
that notion does not exist and won't exist for a while
merry vault
LMAO
royal basin
unless you do probability theory and even THEN it's niche as shit
just forget that "limit of a set" can ever be a thing
merry vault
ok wait ... I had an exercise where we were given a sequeence
grizzled shore
Don’t we use sup in probability as well
merry vault
I proved that the sequence has a lower bound and is monotonous decreasing
grizzled shore
At least from my limited knowledge we do
grizzled shore
I proved that the sequence has a lower bound and is monotonous decreasing
What’s the sequence defined as?
royal basin
Don’t we use sup in probability as well
sure sup might come up but did you mean for that to contradict my point?