it's not about the visuals at all though, it's about geometry
#help-23
trail lotus
the line segment of AB would show a vector of (−5, 3, 0) once you subtract B from A
same thing with line segment BC
by doing this math, you would see that they already aren't perpendicular, meaning no equal length
errant ravine
same thing with line segment BC
wait is Bc not longer?
turbid ore
an the point D lies on the line 3x-4y=-4
you can make two equations and solve for x an y
errant ravine
by doing this math, you would see that they already aren't perpendicular, meanin...
yes becuse bc is a dagonal? calculate distance from A-b
to A-C (i belive)
errant ravine
the line segment of AB would show a vector of (−5, 3, 0) once you subtract B fro...
okay so lets calculate A to b
its (5,3)
and then A to c
is (3, -5)
turbid ore
let D(x,y) and find distance of bc = ad
trail lotus
wait is Bc not longer?
wtf r we doing to AC line segment bro 💀
errant ravine
wtf r we doing to AC line segment bro 💀
BECAUSE A is the red DOT...
A(4,0,2), B(-1,3,2), C(1,-5,2),
trail lotus
okay so lets calculate A to b
its (5,3)
and then A to c
is (3, -5)
(-5, 3) 😭 😭
errant ravine
BECAUSE A is the red DOT...
please just calculate distance A to b
and then A to C and they would be equaly
errant ravine
(-5, 3) 😭 😭
yes that is equal distance just rotated by 90 degrees-
errant ravine
am i going insane? 😭
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Available help channel!
sonic phoenix
open.
sonic phoenix
yo
opaque fern
yo
sonic phoenix
why is wrong?,
The question is
Q1; Simplify the equation using law of logarithms.
Not sure why but my sir wants us to find log and anti-log too , pretty sure i founded the log correctly though
ts is 9th maths for reference
opaque fern
to begin with
sonic phoenix
🥀
broken pewter
Antilog is a new term for me, isn't that just the exponent
sonic phoenix
antilog is just inverse of log
upbeat swan
antilog is crazy
sonic phoenix
like waht was the original value of log
sonic phoenix
why is ur setup log(x) = (expression)^5
idk my sir did it not sure , hes a weirdooo
broken pewter
like waht was the original value of log
Yeah that's some weird name for what is known as the exponent
opaque fern
y = f(x) -> log(y) = log(f(x))
upbeat swan
opaque fern
what you (or apparently your 'sir') did is
y = f(x) -> log(y) = f(x)
sonic phoenix
where did FUNCTIONS come from
opaque fern
it was just a way to showcase what was wrong lol
sonic phoenix
pretty sure he supposed the base of log to be x , like a variable
sonic phoenix
let me send his guide
opaque fern
!nopdf
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Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.
prisma karma
why is wrong?,
The question is
Q1; Simplify the equation using law of logarithm...
For example if i write
Let
\begin{align*}
\log(x)&=2\
&=\log(2)
\end{align*}
should this be correct?
flat frigateBOT
qwertytrewq
sonic phoenix
this is the most similar i could find to the question
its from his holy grail of a guide
prisma karma
this is saying that log(x)=2=log(2)
This is essentially what u did in your solution
sonic phoenix
the thing is the teacher doesnt explain , i once even wrote a complain </3
silent nova
its from his holy grail of a guide
see the second step thats where you went wrong
sonic phoenix
see the second step thats where you went wrong
thats my sir's holy grail guide
silent nova
thats my sir's holy grail guide
nah i mean in your solution
sonic phoenix
what
silent nova
why is wrong?,
The question is
Q1; Simplify the equation using law of logarithm...
this
sonic phoenix
how
prisma karma
how
Ive noted above how saying log(x)=2
=log(2) is incorrect
same applies in your case
sonic phoenix
what?
sonic phoenix
Ive noted above how saying log(x)=2
=log(2) is incorrect
i didnt write this equation
teh thing is if i dont write he will get mad
but he wont explain whats its for either
silent nova
what your first step should've been is assume the answer of the problem is x and then take log on both sides and then simply find x
prisma karma
i didnt write this equation
u wrote let
log(x)=expression^5
=log(expression)^5
prisma karma
it is not correct that expression^5=log(expression)^5
sonic phoenix
x = expression^5
logx =log( expression^5
silent nova
yeah then you apply log rules
sonic phoenix
oh okay that makes sense , but the question he marked correct had a different answer
saying strictly focusing on the working / answer
prisma karma
x = expression^5
logx =log( expression^5
log(x)=log(expression^5) I assume that is a typo
prisma karma
saying strictly focusing on the working / answer
yeah ur solution was also wrong
sonic phoenix
🥀
prisma karma
You have put log(x)=log(expression)^5
prisma karma
x = question
logx = log(question)
sure but why is ^5 outside
lets do an example: put on your calc log(10)^5 and log(10^5), ull see that they are not the same
in general you cant say log(expression^5)=log(expression)^5
sonic phoenix
hmm
sonic phoenix
sure but why is ^5 outside
its the question
silent nova
in general you cant say log(expression^5)=log(expression)^5
you can treat the bracket as y and then after taking log it will be 5log y
sonic phoenix
prisma karma
its the question
i meant why is it outside when u took log
sonic phoenix
that matters?
prisma karma
that matters?
yeah as i said log(10^5) is not the same as log(10)^5
u can try some example if you want
silent nova
indeed but that is not what you did in the solution
prisma karma
but isnt it like if its log(10)^5 , 5log10
wdym
sonic phoenix
law of logartihm
prisma karma
thats where its confusing: they should add bracket atound m^k
it is not (loga m)^k
it is loga (m^k)
silent nova
in the first one,m is 10 while k is one
and in the second one,m is 10 and k is 5
flat frigateBOT
qwertytrewq
sonic phoenix
a is a base like 10 ,, e? right
prisma karma
oh the left hand side they were taking log of the whole m^k
sonic phoenix
ye
silent nova
a is a base like 10 ,, e? right
10
sonic phoenix
we are basci ally taking the log of the whole equation
like evaluating it
im tryna see where i messed up evaluating i
flat frigateBOT
qwertytrewq
prisma karma
but isnt it like if its log(10)^5 , 5log10
so when u said this the formula dont apply
log(10)^5 is not 5log(10)
silent nova
and that is not $\log_a (m)^k$
so we first take the log of m and then raise it to the power k,right?
prisma karma
on the other hand,
log(10^5) is 5log(10)
prisma karma
so we first take the log of m and then raise it to the power k,right?
in the power rule they are taking log of (m^k), in the img u quoted yeah I did that
prisma karma
they should add brackets dude
they should
sonic phoenix
oh welp , better luck next time to me lol
prisma karma
especially when it is obviously ambiguous
sonic phoenix
nah its okay
prisma karma
aight
sonic phoenix
.close
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Available help channel!
ionic gale
What is the value of x?
safe radishBOT
What is the value of x?
brave wolf
What is the value of x?
notice that all those angles add up to a full angle (360°)
can you use that to create an equation?
ionic gale
i had subtracted 30 from 360, which gave me 330. Therefore, I set up an equation where 10x = 330, which resulted in 33, and that worked out for me. However, when talking to my teacher, he argues that x could be 39; he subtracts 3x - 30 first because he says the 30-degree angle is extra.
He basically calculates 39 times 10 and then subtracts the 30 degrees from the extra angle at the end
grave sand
Looks like the 30° angle is overlapping with 3x
safe radishBOT
@ionic gale Has your question been resolved?
upper forge
@ionic gale notice both 3x overlaps with 30
so the actual angle is 30,4x, 3x-30 and 3x-30
empty gyro
That is a pretty crappy diagram.
upper forge
That is a pretty crappy diagram.
um. sorta
empty gyro
It's misleading
upper forge
the overlapping part could be clearer
empty gyro
Yes
OP your logic was sound. You just made an understandable mistake because the angles are a little hard to read
ionic gale
Hmm
I dont get it
if we have to subtract the 30° because it's 'extra,' does that mean the total drawing actually measures 420°? Because 10(39) + 30 = 420. Where did the extra 60 degrees come from?
upper forge
I dont get it
do you see the three lines in the triangle thingy with 30 degree?
upper forge
if we have to subtract the 30° because it's 'extra,' does that mean the total dr...
if you add 3x + 30 + 3x + 40 , you will get extra 60. because both the 3x overlaps with 30
but if you only add the red 3x's and 30 and 4x
you will get 360
coz none of them overlap
burnt nymph
coz none of them overlap
How bro feels after multitasking
upper forge
How bro feels after multitasking
lmao
burnt nymph
ionic gale
Ahhhh, i see what you mean with the red lines now, i was taking the original black printed arcs super literally, which is why I was stuck on 33 but if the intention of the problem is that they overlap, then 39 makes total sense.... thanks for taking the time to draw it out and explain it to me 🫡
.close
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desert juniper
<@&268886789983436800>
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Available help channel!
fresh phoenix
can anyone tell me how to use a cast diagram when doing trig equations I rlly don't understand that whole topic
safe radishBOT
can anyone tell me how to use a cast diagram when doing trig equations I rlly do...
radiant ice
u can remember cast diagram with “all students take calculus”
safe radishBOT
@fresh phoenix Has your question been resolved?
fresh phoenix
It tells you which quadrants each trig function is positive in
ion get it
im slow sry
mortal sandal
is there a specific word you don't know the meaning of?
fresh phoenix
like yo how is says which thing= positive/negative
2tanx⁰ +5 =-4
for, 0≤ x ≤360
that was the question but I genuinely dk what to do at all
mortal sandal
well first you have to figure out what tan(x) is
fresh phoenix
how
do you do the opposite of what's there, like -5 the ÷2
mortal sandal
yeah
eager junco
Hi, may I know how the mobius function was derived to be helpful on combinatoric problems? So far, the definition seems random to me
safe radishBOT
Hi, may I know how the mobius function was derived to be helpful on combinatoric...
plucky elk
You just want the historical discovery?
eager junco
Like, I want to know why someone defined something like this
plucky elk
that's not a math question at all
eager junco
Mainly I don’t get why it is useful
eager junco
If you could provide an example on how it can be used, it would be helpful
plucky elk
eager junco
I am learning how to solve a problem related to gcd. I’m still not sure how the möbius function helps. Is it possible I can learn how to use it if I don’t know what the dirichlet convolution is?
<@&286206848099549185>
plucky elk
I am learning how to solve a problem related to gcd. I’m still not sure how the ...
!original
safe radishBOT
I am learning how to solve a problem related to gcd. I’m still not sure how the ...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
eager junco
This is the original problem: https://spoj.com/problems/GCDEX
plucky elk
just screenshot the problem here
eager junco
Basically, it wants us to simplify the following function: f(n) = \sum_{i=1}^n \sum_{j=i+1}^n gcd(i, j)
<@&286206848099549185> I think it is related to the totient function, but I am not sure how that works here
crystal olive
<@&286206848099549185> I think it is related to the totient function, but I am n...
i think are they all coprime to uh whats the series of numbers again
to 9 right?
or wait no n
eager junco
Wdym 9
crystal olive
wait wait no no no wrong thing to reply to forget that
eager junco
Ok
crystal olive
i think so
loud wren
<@&286206848099549185> I think it is related to the totient function, but I am n...
the thing is that totient gives you coprime, so you'd have to exclude the phi(n) that are coprime, i.e. there are n-phi(n) non-comprime numbers to n
other than that I don't see anything...
eager junco
Oh ok, I will work on something else, and get back to it some other time. Thanks all!
.close
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lilac relic
Hey, is the intercept an indication of a confidence interval?
safe radishBOT
Hey, is the intercept an indication of a confidence interval?
lilac relic
For example if you're trying to work out the 90% confidence interval with confint(sample,level=0.90).
pallid magnet
nope
lilac relic
.close
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Available help channel!
polar cave
How does Φ work
safe radishBOT
How does Φ work
arctic raven
How does Φ work
who?
polar cave
What
arctic raven
when where and why?
polar cave
arctic raven
How does Φ work
could you phrase your query with more elegance?
polar cave
In what mathematical way does the elegant symbol Φ work in arithmetic?
arctic raven
from where does this phi originate? what kind of object is phi?
you asked how it works in arithmetic; does that mean phi is a number?
polar cave
I do not know 
median vigil
phi is just a greek letter
it can be used in the same way other letters are used in math
more details require more context
versed wave
In what mathematical way does the elegant symbol Φ work in arithmetic?
where did you encounter this symbol?
the first instance i think of is the cdf of standard normal
polar cave
where did you encounter this symbol?
Well, in the standard model of course.
versed wave
well it's the cumulative distribution function of the standard normal distribution
more specifically, if you have a random variable $X \sim \mathcal N(0, 1)$, then the function $\Phi(z)$ is defined as $P(X \le z)$
flat frigateBOT
versed wave
was that clear enough?
polar cave
Uh
arctic raven
I was more inclined to think phi is the golden ratio
versed wave
i did a quick search and see that standard model is physics
versed wave
I was more inclined to think phi is the golden ratio
that's lowercase phi
arctic raven
that would mean my inclination was wrong
astral glacier
How does Φ work
!original
safe radishBOT
How does Φ work
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
astral glacier
I'm gonna. Ask every single person in this channel to notice that OP has the pre-uni math role. As such, standard normal is probably going a bit far
My best guess is they refer to its usage as the empty set symbol?
Some books use ϕ instead of ∅
versed wave
blasphemy
astral glacier
<@&268886789983436800> troll
polar cave
?
radiant isle
hmmm
polar cave
<@&268886789983436800> troll
Im tryna learn math here man 
radiant isle
Im tryna learn math here man <:blobcry:971797574916907028>
i doubt you have the background to get an answer that will satisfy you
but i also believe youve been told this already
polar cave
When
modest ivy
sounds like hes just attention seeking ig
polar cave
solar hazel
sounds like hes just attention seeking ig
as an attention seeker i can confirm
astral glacier
This dude is trolling while I actually need help
!noadvert please be patient
safe radishBOT
This dude is trolling while I actually need help
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
radiant isle
anyway
modest ivy
This dude is trolling while I actually need help
lmao im ug and i dont have a monkeys when it comes to venn diagrams
radiant isle
im going to close this channel
radiant isle
@polar cave i cant be certain whether youre trolling or not but try to stick to math at your level for now
.close
ancient spindle
An airplane is flying at 150 km/h on a heading of 070 degrees. The wind is blowing at 40 km/h from a bearing of 130 degrres. Find the groundspeed (the magnitude of the ground velocity) of the airplane
modest ivy
calculate using trig the forces/ speeds on the x and y axis
Sum them up
And pythag it
ig
i dont remember jackshit about mechanics ngl
trail rune
An airplane is flying at 150 km/h on a heading of 070 degrees. The wind is blow...
which tools have you learned to deal with this kind of question? vector math or law of cosines?
ancient spindle
which tools have you learned to deal with this kind of question? vector math or ...
vector
trail rune
then convert both velocities to vectors
ancient spindle
i just dont know how to find that center angle im tryna use cosine to find the resultant but its tripping me out
trail rune
you don't need the center angle to convert to vectors
ancient spindle
wym
trail rune
which vector is the wind speed?
ancient spindle
this is my updated drawing mb
ancient spindle
which vector is the wind speed?
the arrow going northwest
trail rune
what are its coordinates
do you know how to convert speed and bearing to xy coordinates?
ancient spindle
nvm i got it
i just subtracted 130 from 70 to that angle between the wind vector and plane vector and since theta was an opposite angle i made it equal to 60 and used cosine law to find the resultant
trail rune
that works too
safe radishBOT
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Available help channel!
somber cape
Im having trouble grasping a concept
safe radishBOT
Im having trouble grasping a concept
somber cape
Im struggling with the base 3 representations
They say that the elements in G_1 have 1 in the first digit after the decimal point, but why does this imply for those numbers with 2 representations that they both have 1 in the first digit after the decimal point
astral glacier
They don't need to
Cantor set is just, they have a base 3 rep which doesn't use 1
solar hazel
i think he's talking about something said earlier in the excerpt
astral glacier
Nvm I can't read
Yeah I realized sorry lemme read
Oh okay it's because G_1 is precisely the points between 0.1 and 0.2
solar hazel
is 0.1222... in G_1?
somber cape
my lack of understanding might be coming from base 3 decimal representation in general
astral glacier
is 0.1222... in G_1?
Wrong way around
Isn't saying it contains all points
Says that all points it contains start with 1
astral glacier
Oh okay it's because G_1 is precisely the points between 0.1 and 0.2
Do you see this
solar hazel
Wrong way around
uhh that wasn't a question for you
somber cape
excluding 0.1 and 0.2 right
astral glacier
Oh sorry I thought you were thinking out loud
We are talking over each other, all yours layla 
solar hazel
no i'm not that interested, all yours
astral glacier
We could play ping pong for a while now
astral glacier
excluding 0.1 and 0.2 right
Yes
Now think of it this way
Take the open interval (0,1)
Divide it by 3
Translate it right by 1/3
This gives you precisely G_1 correct?
somber cape
yeah
astral glacier
Now look at this in base 3
Divide by 10, translate right by 0.1
Now pick any base 3 representation in (0,1)
What does it look like after the transformation
somber cape
when you mention looking at it in base 3, is dividing by 10 and translating it by 0.1 converting it from base 10 to base 3?
astral glacier
Okay let's ignore base 3 for a minute and write it as what it really is
A base 3 representation is you expressing a number as
A sum of multiples of powers of 3
somber cape
yeah
astral glacier
I realised latexing it is too much work 
somber cape
lol
astral glacier
In the interval (0,1) the only powers we have are the negative ones
somber cape
yeah
astral glacier
A sum of multiples of powers of 3
Now let's write a number as this
And then let's do the operations I said
We divide it by 3, and then add 1/3
Now, the first digit in a base 3 representation (after the decimal point) is the coefficient of 1/3
astral glacier
Now, the first digit in a base 3 representation (after the decimal point) is the...
Do you agree with this
astral glacier
Are you familiar with binary
somber cape
yeah
somber cape
yeah
astral glacier
So in base 3
The first digit after the decimal point
Is the coefficient of 3^(-1)
somber cape
Now let's write a number as this
when you said a number here is that a number from (0,1)
astral glacier
Yes
Any number between (0,1)
And then we do the map that I said
Wait before we do that
Do you realize that the mapping that I said is a bijection
somber cape
yeah
astral glacier
Good
astral glacier
Any number between (0,1)
Now let's do this
Let's express this number as a sum of multiples of powers of 3 (the coefficients are only allowed to be 0,1,2)
After you do those operations, what is the coefficient of 1/3
somber cape
after you divide by 3, the coefficient that was at 3^0 becomes the coefficient for 3^-1 and when you add 3^-1 wouldnt it be adding 1 to that coefficient?
astral glacier
Correct but you're missing one thing
What's the coefficient for 3^0
Remember we are in (0,1)
astral glacier
So what's the coefficient of 1/3 for any point in G_1
somber cape
1
astral glacier
And does it depend on the representation we started with?
somber cape
no since we just took an arbitrary one right
astral glacier
Yup
somber cape
ook I see it all makes sense now
astral glacier
I hate that Cantor set proofs just throw base 3 at you lol
somber cape
yeah I always struggle dealing with other bases, but hopefully going through this can help me get better with them
astral glacier
Good luck
somber cape
thanks for the help Xavier ill try to get through the rest
astral glacier
And ofc, feel free to ask whenever you're stuck
safe radishBOT
@somber cape Has your question been resolved?
snow sable
What is a rule of three?
safe radishBOT
What is a rule of three?
snow sable
minimum common multiple and the other one
i really don't understand it, and it appears everywhere
light shoal
can you show a reference/screenshot of what you're talking about?
opaque fern
Grey on grey communication
tawdry plover
~~Grey on grey communication~~
i got confused and thought OP was talking with himself lol
didnt realize the goat bungo was speaking
grand basin
these are 2 different things
snow sable
different in which topic?
light shoal
hmm, never seen this called "rule of three" before, seems like "do the obvious thing to solve for the variable you want"
grand basin
first one is in number theory, second one is just pure algebra
light shoal
and yeah, the first screenshot isn't related to the second
snow sable
Well, they're very comum in my school books
grand basin
lets see
rule of 3 is easy
lets say you know that 4 bags of rice cost 12 dollars
and you want to buy 6 bags
whats the total price?
grand basin
no, that's too much, don't you think?
4 bags is 12
2 more bags can't possibly be 30/40 more dollars
light shoal
could be if you're ordering from some crazy amazon seller 😂
jk jk
snow sable
4/12=3x6=18
grand basin
very good thinking, (actually its 12/4 not 4/12)
thats exactly the rule of 3
it tells you how proportionality works
snow sable
ohhhh
grand basin
price of 6 = price of one unit * 6
price of one unit is just 12/4
so you get price of 6 = 12*6/4
which is the same as A = C*B/D
snow sable
and the lcm?
snow sable
no
grand basin
we say that A divides B if B/A is a clean number
for example, 2 divides 4
why?
4/2 = 2
you can divide 4 dollars over 2 children equally, can't you?
10 divides a 100, because 100/10 = 10
but 10 does not divide 25
why? 25/10 = 2.5 (not a clean number)
do you get this much?
snow sable
So, if we deal with natural numbers, we need this to find the better way in solving the problem, is that right?
grand basin
we are always dealing with natural numbers
LCM is a bit complicated, but no problem
if you understand what "A divides B" mean, we can proceed
snow sable
hmmm
grand basin
does 5 divide 9?
snow sable
No
grand basin
does 5 divide 10?
snow sable
yes
grand basin
how did you know?
snow sable
because learned that, in somewhere
grand basin
okay
question for you
can you give me some numbers that 3 divides?
give me one example
snow sable
3,6,9,12,15
grand basin
great
we call these numbers multiples of 3
a multiple of A is just a number that A divides
can you give me multiples of 10, for example?
snow sable
1, 2, 3, 4, 5
quick tundra
LCM?
grand basin
1, 2, 3, 4, 5
that is not correct!
multiples of 10 are numbers that 10 divides
10 does not divide 5
quick tundra
So numbers that when multiplied with some other number that give 10
snow sable
so, who are they multiples?
grand basin
ok let me give you an example
multiples of 2 are = 2; 4; 6 ;8 ; 10 ....
multiples of 10 are = 10; 20; 30; 40 ....
do you notice the pattern?
quick tundra
multiples of 2 are = 2; 4; 6 ;8 ; 10 ....
Like numbers that when multiplied with some numbers and 2 give some other number
quick tundra
Those are multiples of ten yeah
snow sable
10, 15, 20, 25, 30
grand basin
excellent
okay
quick question
is 11 a multiple of 5?
is 29 a multiple of 7?
is 30 a multple of 6?
snow sable
no no yes
grand basin
is 12 a multiple of 24?
snow sable
no
grand basin
great
quick tundra
Correct
grand basin
okay, now you understand what multiples are
let's talk about common multiplis
common = shared
quick question
can you give me the first 5 multiples of 3
and the first 5 multiples of 4?
snow sable
6,9,12,15,18. 8,12,16,20,24
grand basin
excellent
now let's play a quick game
you have 2 lists
a list for 3
and a list for 4
do you notice one number appearing in both lists?
snow sable
twelve
grand basin
great
twelve is cheeky
is it a multiple of 3
and a multiple of 4
isn't that interesting?
do you know what we call 12?
we call 12 a common multiple of 3 and 4
they both share 12 as a multiple
another try
give me the first 7 multiples of 5
the first 7 multiples of 6
snow sable
and the higher comum divisor?
grand basin
and the higher comum divisor?
i will get to it, but first we need to understand common multiple
we're not done yet
snow sable
10,15,20,25,30,35,40. 12,18,24,30,36,42,48
grand basin
now give me a common multiple of 5 and 6?
snow sable
30
grand basin
perfect
now you understand what common multiples are
okay, almost done
give me the first 9 multiples of 2
the first 9 multples of 3
snow sable
4,6,8,10,12,14,16,18,20. 6,9,12,15,18,21,24,27,30
grand basin
common multiple of 2 and 3?
snow sable
12,
grand basin
what about 6?
snow sable
you dont ask for it all
snow sable
yes
grand basin
what about 30?
snow sable
yes
grand basin
do you notice something?
snow sable
15x2=30
grand basin
ok ok i get it
but i mean
2 numbers have MANY common multiples
common multiple of 3 and 4? not just 12, but 24 and 36 and 72 ...
common multiples of 5 and 6 = not just 30, 60, 90 ...
snow sable
i was supossed to do other type of operation?
grand basin
no, so far you are correct
i have an idea
if i ask you for common multiple of A and B, how many answer can you find?
snow sable
No one, since i dont know their values, but if it is not, maybe
grand basin
ok lets say you know A and B, can you find just one common multiple
or many many common multiples?
snow sable
a lot of them, but not if it has a zero
grand basin
ok good
a lot of them
so let's fix this problem
how about we start taking the smallest one
snow sable
no
grand basin
for example CM of 5 and 6 are 30; 60; 90; 120; 300; 3000 .... and many many more
can give me the smallest CM of 5 and 6?
go to #help-14
snow sable
30
grand basin
excellent
do you know what 30 is?
30 is the LCM of 5 and 6!!
this is the LCM
least common multiple
least = smallest
example
CM of 2 and 3 are 6, 60, 12, 450, 6000 ..... and many many more
whats the LCM (2; 3) ?
snow sable
6
grand basin
perfect
now one last question to make sure you understand
give me 5 common multiples of 5 and 4
THEN, tell me whats the LCM (4; 5)
snow sable
10,15,20,25,30. 4x2,3,4,5,6
grand basin
hmm?
snow sable
8,12,16,20,24
grand basin
ok, these are multiples of 4, and multiples of 5
I asked for COMMON multiples of 4 and 5
snow sable
10,15,20,25,30. 4x2,3,4,5,6
snow sable
20
grand basin
excellent
20 is CM of 5 and 4
but earlier, we agreed that there are many many CMs
so my question
give me 5 CMs
not just 1
give me more numbers that appear in both lists
snow sable
there are some other logical i can use to take this more easily?
grand basin
what do you mean
snow sable
like 2x2=4 3x3=9 8,12,16,20,24,28,32,36 9,18,27, 36, 45
the 36 of the two has appeared on different times
how d i calculate the time by time?
in the relation about the mcs of the two numbers
grand basin
just follow the steps
step 1 = write the list of multiples of A
step 2 = write the list of multiples of B
step 3 = take the numbers that appear in both lists
step 4 = choose the smallest number from the last list
thats how you find the LCM
snow sable
and the proportion about like 100 cms of the two?
36 was the 4° ordinal of 4, the 36 of 9 was the fourth
grand basin
if you want more CMs, make bigger lists
snow sable
but i can't just multiple the mcs of them
it would give a almost exaclty number but not all exactly
grand basin
step 1 = write the list of multiples of A
step 2 = write the list of multiples o...
Step 1
Go
In this case, we have 5 an 4
We want LCM of 4 and 5
GO step 1
snow sable
8,12,16,20,24. 5,10,15,20,25
snow sable
I already get it, please lets to the divisors?
snow sable
5,10,15,20,25,30,35,40. 8,12,16,20,24,28,32,36,40. 20,30,40. lmc=20, the lowest mc
grand basin
Sounds good
Now, the GCD is very similar
You know multiples, now let's talk divisors
Divisors are the opposite
Take all the numbers that divide your numbers
For example, divisors of 20 are 1, 2, 4, 5, 10 and 20
Divisors of 9 are 1, 3, and 9
Does that make sense?
snow sable
the numbers that the product don't results in a unpaired
snow sable
24,12,8,6,4,3,2,1
grand basin
Divisors of 20?
snow sable
10,5,4,2,1
grand basin
30?
snow sable
30,15,10,6,5,3,2,1
snow sable
thats harder
snow sable
5
grand basin
good luck
safe radishBOT
@snow sable Has your question been resolved?
echo marlin
Suppose p and q are real numbers which do not simulateneously take the values p = 0, q = 1. Suppose the equation
( 1-q+ (p^2/2))x^2 + p(1+q)x + q(q-1) + (p^2/2) = 0 has two equal roots. Prove that p^2 = 4q
safe radishBOT
Suppose p and q are real numbers which do not simulateneously take the values p ...
brave wedge
$\left(1-q+ \frac{p^2}{2}\right)x^2 + p(1+q)x + q(q-1) +\frac{p^2}{2} = 0$
flat frigateBOT
Defy logic guy
brave wedge
is this correct?
echo marlin
**Defy logic guy**
Yep
astral glacier
Well, do you see that this is a quadratic in x
echo marlin
Well, do you see that this is a quadratic in x
Yeah, and since the roots are equal, it's clear that the discriminant will be 0, so b^2 - 4ac = 0
But then after that, solving the equation gets hard
And it gets kinda confusing because there are so many terms
astral glacier
I mean yeah but unfortunately there's nothing you can meaningfully do about that
safe radishBOT
Available help channel!
spiral pewter
stop spamming @fleet tulip
dense dove
what to write if there is no mode
safe radishBOT
what to write if there is no mode
dusk halo
why are you in such a rush?
agile scaffold
use these definitions
echo marlin
use these definitions
Except that for finding the mode, each of the data appears only once
dusk halo
no? digestive is 9 times, custard cream is 15 and shortbread is 16
agile scaffold
Except that for finding the mode, each of the data appears only once
huh?
dense dove
so whats the answer
agile scaffold
yeah because 9 appears once, 15 appears once too, and so does 16
youre trolling with me arent you
round egret
yeah because 9 appears once, 15 appears once too, and so does 16
digestive appears 9 times, custard cream appears 15 times and shortbread 16 times
that's their frequency
agile scaffold
so whats the answer
mode is defined as the value that appears most often in a dataset so here, another way of saying it is the most frequent data
echo marlin
huh what
dusk halo
Kzryze we arent meant to just give the answer
you wont learn if you are just told what it is
dense dove
ok
dense dove
i think the answer is 0 or no mode
agile scaffold
mode is defined as the value that appears most often in a dataset so here, anoth...
this should immediately show you what the answer is
dense dove
so which item has the most frequency?
shortbread
dusk halo
i think the answer is 0 or no mode
look again at the frequencies, which one is highest?
yes
agile scaffold
mode does not necessarily need to be strictly numerical, it can also be categorical
in this case, finding the mode is the equivalent of asking in the set {a, b, a, a, c, d, b}, what is the letter that appears most frequently, in contrast to asking what is the number of times the letter appears
i could also represent this using a tally
number of appearances in the set
a: 3
b: 2
c: 1
d: 1
dense dove
.close
safe radishBOT
safe radishBOT
Available help channel!
glass edge
A square based pyramid has coordinates A(4,0,2), B(-1,3,2), C(1,-5,2), and D. The apes lies directly above the center of the base, and the pyramid has surface area 210 units square.
a) Find the coordinates of D.
b) Find the height of the pyramid, correct to 1 decimal place.
c) Hence find the volume of the pyramid.
safe radishBOT
A square based pyramid has coordinates A(4,0,2), B(-1,3,2), C(1,-5,2), and D. Th...
exotic anvil
Already been handled
timid ridge
its done
glass edge
can you help pls .^.
covert yoke
It's a common spam/scam
exotic anvil
Usually the account has been hacked. If you see the messages deleted its bc the user was banned
covert yoke
Do you know how to find the center of the base? Which version of center is being used here?
glass edge
i dont understand how if its a square based pyramid, it has different sides
glass edge
Do you know how to find the center of the base? Which version of center is being...
if im correct, you find the distance between the diagonals
midpoint
covert yoke
Oh, D is part of the base, my bad
glass edge
i dont understand how if its a square based pyramid, it has different sides
like for example, AC has the distance sqrt38, but AC has the distance sqrt34
if its a "square base", then all angles/sides should in theory be equivalent to each other
timid ridge
maybe abc isnt part of the square base
covert yoke
So leading questions:
If you have a square based pyramid, the surface area is the sum of what shapes?
Are all of the faces except the base equal?
How much surface area is in each triangle?
Can you find the area of an isosceles triangle with an unknown height and known base? Will this help you solve for the area required?
,w sqrt((4- (-1))^2 + (0-3)^2 + (2-2)^2))
flat frigateBOT
covert yoke
,w sqrt((4- (1))^2 + (0-(-5))^2 + (2-2)^2))
flat frigateBOT
glass edge
So leading questions:
If you have a square based pyramid, the surface area is t...
- Surface Area = Area of base multiplied by the area of 4 triangular faces
- In theory they should be because it is a square base, however since I have calculated the distances to not be equivalent, they should not.
3)Distance between base points and slant height divided by 2 - I do not believe you can
covert yoke
Sides seem the same, AB and AC
glass edge
oh
covert yoke
1) Surface Area = Area of base multiplied by the area of 4 triangular faces
2) I...
- you definitely can
glass edge
4) you definitely can
oh, then I am not aware how to do so
can you use latex to draw 3d shapes for visualization?
because i want to show something
covert yoke
For 3) what I'm driving at here is there is a base and 4 slanted triangles, so the area of a single triangle is 1/4 of the remaining area after subtracting the base from the total
covert yoke
can you use latex to draw 3d shapes for visualization?
You can but it is a bit clunky
glass edge
You can but it is a bit clunky
oh
covert yoke
You might as well use something like desmos instead
glass edge
$A(4,0,2), B(-1,3,2), C(1,-5,2)$
flat frigateBOT
Tan
covert yoke
You'll need to make a tikz diagram and handle all of the perspective and coordinate transformations yourself
glass edge
You might as well use something like desmos instead
okay, what i found out is that AC is parallel to BD, so if i found out the translation of C to A, then maybe I can use that translation and do it for B in order to get to D
glass edge
but, when i tried it the other day, i got an incorrect answer
covert yoke
!show
safe radishBOT
Show your work, and if possible, explain where you are stuck.
timid ridge
okay, what i found out is that AC is parallel to BD, so if i found out the trans...
wait why is AC parallel to BD
glass edge
wait why is AC parallel to BD
i drew it in my notebook and it looked like it
glass edge
glass edge
green is B red is A
covert yoke
And BC should be a diagonal
covert yoke
To prove it you would need to prove that AB and AC are perpendicular.
And to do that you'd just compute the dot product
covert yoke
AB = <4-(-1), 0-3, 2-2> = <5, -3, 0>
AC = <4-1, 0-(-5), 2-2> = <3, 5, 0>
AB . AC = 5*3 + -3*5 + 0*0 = 15-15 = 0 = cos(α) => α = 90°
So the base truly can be square.
glass edge
okay, i verified using the formula
and i got sqrt34
now, the height of the pyramid..
hm
i cant really use the surface area
errant ravine
i cant really use the surface area
why not?
glass edge
why not?
-# hey whats up im back doing the same question
because when calculating area of triangle, we use the slant height, not the real one
errant ravine
but, when i tried it the other day, i got an incorrect answer
(actualyl u were really close u just misculacluted a 1 and a -1)
glass edge
(actualyl u were really close u just misculacluted a 1 and a -1)
i got it now
i was being dumb earlier
errant ravine
no no worries u just needed some rest!
covert yoke
-# hey whats up im back doing the same question
because when calculating area of...
You can get the real height from the slant height
glass edge
You can get the real height from the slant height
yeah, but i dont know the slant height either
covert yoke
You find the slant height by figuring out how much area each triangle ought to have
glass edge
to find out the slant height, i need the real height in order to calculate the distance between midpoint AC and height
glass edge
You find the slant height by figuring out how much area each triangle ought to h...
hmm
how would we know the z value of the apex though?
it could be literally any positive integer
covert yoke
Ok, let's take this step by step:
First, what is the total surface area of the pyramid?
glass edge
34+ area of 4 triangular faces
covert yoke
But what is the total area? It's given in the problem statement
glass edge
210
covert yoke
Ok, so next question, are all of the triangle faces the same?
glass edge
oh, since all sides are same, can i just do 210-34/4
glass edge
Ok, so next question, are all of the triangle faces the same?
yes
because all sider are same
covert yoke
So how much area for each triangle?
glass edge
44 units squared
covert yoke
Alright, now we have each triangle is an isosceles triangle with area 44. And we know that the base of this triangle is sqrt(34). What is the height?
covert yoke
You'll want to clean that up a bit
covert yoke
44√(34)/17
glass edge
$1/2(sqrt34)h=44
sqrt34h=88
h=88/sqrt34$
covert yoke
Anyway, now consider the three points: the apex of the pyramid, the middle of one side of the base, and the middle of the base.
flat frigateBOT
Tan
glass edge
Anyway, now consider the three points: the apex of the pyramid, the middle of on...
okay
covert yoke
These points form a right triangle
You know two sides of this right triangle
But you want the third, which is the height
What are these side values? And which one is the hypotenuse?
errant ravine
well done tan!
glass edge
.close
safe radishBOT
safe radishBOT
Available help channel!
safe cobalt
Could anyone check my work for 4a and help me out with 4b? I'm not too sure what I'm supposed to do for that one since what I'm supposed to show is just one of the given Laplace transform
safe radishBOT
Could anyone check my work for 4a and help me out with 4b? I'm not too sure what...
@safe cobalt Has your question been resolved?
tardy mango
Could anyone check my work for 4a and help me out with 4b? I'm not too sure what...
4a is fine
For part (b), note that
$$t\mathcal{L}^{-1} \left(\int^{\infty}_{s} F(u) \dd{u} \right)=f(t)$$
flat frigateBOT
Civil Service Pigeon
safe radishBOT
safe cobalt
.reopen
safe radishBOT
✅ Original question: #help-23 message
safe cobalt
**Civil Service Pigeon**
Ohhh I see, I guess I was overthinking it haha
Thank you so much!
safe radishBOT
red fjord
Why do we find y
safe radishBOT
red fjord
Wait
fiery remnant
please open a new channel if you still want help, this one has been closed and cannot be reopened
red fjord
red fjord
please open a new channel if you still want help, this one has been closed and c...
Oh
Ok
.close
It’s not working
rustic goblet
it’s already closed :p
fiery remnant
(it's already closed dw just occupy a new channel)
safe radishBOT
Available help channel!
supple basin
is this proof correct?and like x E B and x not E B. so it means the set is empty?
safe radishBOT
is this proof correct?and like x E B and x not E B. so it means the set is empty...
supple basin
i tried to prove by using element method but i dont think i did right. if someone can tell me what i missed. it'd be helpful
tardy mango
is the original statement even true
supple basin
is the original statement even true
no
tardy mango
What if A={1,2}, B={3}, and C={4}
supple basin
is the original statement even true
you have to figure if it's true
tardy mango
ah so you're doing a prove/disprove
ok that's helpful context
it looks like you're trying to use an equal sign to connect your propositions .. ?
honestly I'm not entirety sure what I'm reading
there's definitely some kind of right intuition and you correctly found that the left hand side is the empty set
but instead of noticing that you have an always empty left hand side and a potentially non-empty right hand side, you tried to force these steps into some kind of "proof" of an untrue statement?
supple basin
but instead of noticing that you have an always empty left hand side and a poten...
yes
i wanna learn to write proofs but defniitly i dont know how
what should i improve?
tardy mango
For the left-hand side,
\begin{align*}
x \in (A-B) \cap (B-C) & \iff x \in (A-B) \land x \in (B-C) \
& \iff (x \in A \land x \notin B) \land (x \in B \land x \notin C)
& \iff \text{False}
\end{align*}
For the right-hand side,
\begin{align*}
x \in (A-B)-C & \iff x \in (A-B) \land x \notin C \
& \iff x \in A \land x \notin B \land x \notin C
\end{align*}
Comparing the two sides yields
$$\text{False} \iff (x \in A \land x \notin B \land x \notin C)$$
Since the right hand side is not universally false, the two sides are not equivalent and the original equation is false.
flat frigateBOT
Civil Service Pigeon
tardy mango
Here's a rough first draft of how I'd write it
The key point I'm seeing here is to not abuse notation (especially with the equal signs). Once that is fixed, it might be easier to parse, though I can't promise anything ofc. Also don't be afraid of splitting things into parts - you don't need to clump everything together at once.
don't think of writing proofs as some completely foreign task
really it's just writing up your arguments coherently
sure there's some things you'll have to pick up like verbiage and certain notational symbols
but a lot of "regular" writing skills transfer over
supple basin
**Civil Service Pigeon**
wdym the left side is false
tardy mango
wdym the left side is false
$\iff$ false is the same as saying "contradiction" or "impossible". So this is saying that no element can ever be in $(A-B) \cap (B-C)$. Aka $(A-B) \cap (B-C)=\emptyset$.
flat frigateBOT
Civil Service Pigeon
supple basin
so i dont have to use equal sign instead i have to use if and only if sign?
tardy mango
lemme write that with more detail actually
you can use an equals sign when two sets are equal
tardy mango
**Civil Service Pigeon**
Like with $(A-B) \cap (B-C)=\emptyset$ here
flat frigateBOT
Civil Service Pigeon
tardy mango
that's saying that the set $(A-B) \cap (B-C)$ is the same as the empty set
flat frigateBOT
Civil Service Pigeon
tardy mango
But when you're connecting logical statements/propositions
like here with "an element in the set" translates to "it meets these specific conditions"
you use the biconditional/"if and only if" symbol $\iff$
flat frigateBOT
Civil Service Pigeon
tardy mango
tldr equals signs for comparing sets/objects, biconditional arrows for connecting logical truths
<@&268886789983436800>
tardy mango
tldr equals signs for comparing sets/objects, biconditional arrows for connectin...
Hello?
supple basin
thank you
primal bone
**Civil Service Pigeon**
@supple basin I'm acc gonna double down on suggesting you take a look at this and similar proofs (e.g. from textbooks or lecture notes)
Specifically to get an understanding on how to lay proofs out - as 🐦⬛ has mentioned, proofs don't have to be done in one go, so to speak
A (reasonable) breakdown of what it is you want to prove can make both understanding what's needed of a proof (or disproof, considering the nature of this specific question) and writing a proof much easier
safe radishBOT
@supple basin Has your question been resolved?
brazen nimbus
can someone explain me what i did wrong? im trying to find the intersection point of both lines
shut aspen
So you have 1 point (-2,-,4) with normal vector (3,2,-1) and 1 point (3,2,5) with normal vector(1,2,-4)
Yes, so you want to find a point, where, if you choose t and s, g intersection with f exists
brazen nimbus
You seem to understand the method though
yeah but
im kinda stuck
on the last thing
did you see?
shut aspen
Once you find t, you can find s
Check if all conditions satisfy
plug in any s or t to get your point of intersection
shut aspen
Very important to check both s and t to have the same outcome!