i also have to ask you about this symbol
#help-36
earnest cobalt
next thorn
sand what does it mean
next thorn
this is correct
next thorn
yes, if it works then we're good
earnest cobalt
top is still 0
next thorn
how.
next thorn
i dont think e^(2*0) is 0.
next thorn
its okay
next thorn
you do that and ill be afk for a bit
think about what you can do
back and
im not very sure what to do for the second...?
if there are any helpers spectating
earnest cobalt
first one is 2 right
next thorn
please do interfere
yes it is 2... hopefully
(x+1)^(1/sqrt(x)) sounds like a very interesting function
i wonder how its plotted...
next thorn
seems like i missed it too.
sorry.
@vital crag helo, what can we do for the second limit? OP claims that the exponent here is 1/sqrt(x)
im not sure how i would force this function into inf/inf or 0/0 (for lhopital's)
earnest cobalt
this makes any sense?
loud phoenix
this makes any sense?
Yep, the AI is correct
next thorn
this makes any sense?
seems so... i hate to admit it
but htat means we're getting replaced by the clankers
we shouldnt let that happen 😡
earnest cobalt
okay cause i dont really understand so there is still space to work with
next thorn
i can explain what the ai did.
earnest cobalt
so i guess when we plug in infinity we get infinity^0
next thorn
where did it confuse you
next thorn
so i guess when we plug in infinity we get infinity^0
which is sdly not a form for lhopital's to take place
next thorn
where did it confuse you
.?
earnest cobalt
the step 2
next thorn
ignore step 1
okay
a limit just outputs a number
lim (x^2-4)/(x-2) as x approaches 2 is just-
a number
and any limit is like this
so for this specific limit
the ai said "lets call it soemthing, like L"
and assumed
L = our limit
then he took ln of both ssides
are you familiar with what ln is
or logarithms in general?
earnest cobalt
yea i think this is the problem i dont get it fully
all i know is that its log with e in base
next thorn
have you learned about logarithms?
earnest cobalt
yea
next thorn
and their properties?
earnest cobalt
loga b = c
a^c=b
earnest cobalt
ye
earnest cobalt
ye we can take it outside
next thorn
exactly
next thorn
this makes any sense?
when called
L = our limit
we can see that our limit is rasied to the power of 1/sqrt(x)
so we can take ln of both sides
and drop kick the 1/sqrt(x) outside.
so
Ln( L ) = ln ( (ourlimit) ^1/sqrtx )
we can bring the 1/sqrt(x) down
earnest cobalt
next thorn
yes.
earnest cobalt
awesome i get it now
next thorn
also we can shove the ln inside of a limit because thats one of the properties for a limit
earnest cobalt
alr let me try to use de hospital
next thorn
alr let me try to use de hospital
hope you know how to differentiate logarithmitic functions
earnest cobalt
hope you know how to differentiate logarithmitic functions
1/x?
let me just try i guess
next thorn
so ln inf = inf?
i guess so. (anyone please confirm)
earnest cobalt
derivative?
next thorn
okay so im here
notice, in your denominator, its x+1 so if you were to "derive" that for lhopitals, it would become 1
which confirms that you wont need lhopitals agian if you do it one more time
earnest cobalt
next thorn
mhm.
next thorn
yes and notice smth very important
we're talking about ln(L)
not L itself, which is what we want
so
ln(L)=0
can you solve for L?
earnest cobalt
dam i suck at ln
next thorn
ignore the bot
no no the bot sucks
second of all
if
perhaps
2^x=3
how would you express this in logarithms?
earnest cobalt
a^c=b
a=2
c=x
b=3
loga b = c
log2 3 = x
next thorn
uhm yeah sure
log(2)_3 = x
is the log form
which we can translate back into 2^x=3
so
if
log(a)_b=c
next thorn
log(2)_3 = x
is the log form
wait a damn minute
ok this is a moment where i grief because i dont know latex
next thorn
a^c=b
a=2
c=x
b=3
loga b = c
log2 3 = x
can you rewrite this on paper and send?
earnest cobalt
rocky tusk
log(2)_3 = x
is the log form
🤔
rocky tusk
what you wrote looks like $\log_3(2)$
soft zealotBOT
knief
next thorn
yeah i didnt mean to 😭
rocky tusk
interesting
next thorn
what you wrote looks like $\log_3(2)$
can you latex that
if we have
loga b = c
then c would be smth
rocky tusk
$\log_a b = c \iff a^c = b$
next thorn
yk
soft zealotBOT
knief
next thorn
**knief**
@earnest cobalt remember
we have
ln(L)=0
or log e L = 0
can you try converting that to the exponent form and solving for L?
earnest cobalt
earnest cobalt
nice
next thorn
anything else
earnest cobalt
i think rest of the tasks are fine
next thorn
amazing
earnest cobalt
tysm
next thorn
you can .close the channel and claim another one when you have other questions
next thorn
this
earnest cobalt
bot broke
earnest cobalt
we been here too long
next thorn
.close
oh my god
it wont close
okay just- go on about your exercises until the bot recovers
next thorn
great luck 
mint orbit
final saddleBOT
final saddleBOT
Available help channel!
subtle path
hey I need some help with a physics concept I cant succeed to understand
subtle path
so when we assign a wave a function, we say it is a two function variable
and in my class it says that for any function of x of a wave, it is in the form f(x-ct), where t is a fixed instant)
why is that true
why is it not f(x+ct)
final saddleBOT
@subtle path Has your question been resolved?
subtle path
<@&286206848099549185>
final saddleBOT
@subtle path Has your question been resolved?
upbeat creek
and in my class it says that for any function of x of a wave, it is in the form ...
The plus or minus sign only changes the direction of proportion of wave
Otherwise it is the same
lime crest
Let $p>2$ be a prime and let $n$ be an odd positive integer. Prove that the amount of solutions to [x_1^2 + x_2^2 + ... + x_n^2 \equiv 1 \pmod{p} ] for $x_i \in \mathbb{F}_p$ is exactly [\frac{p^n + ((-1)^{\frac{p-1}{2}}p)n}{2} ]
final saddleBOT
Let $p>2$ be a prime and let $n$ be an odd positive integer. Prove that the amou...
soft zealotBOT
Copter
oak pagoda
lol i came here everytime my exams are close
this sem kinda tough as hell , every 5 subject is maths
lime crest
**Copter**
uhh i dunno how i would even get this form
unless could it be possible by induction on n-2 -> n?
okay i know gpt isnt advised here but what is it cooking ;-;
<@&286206848099549185> bwaaaa
final saddleBOT
@lime crest Has your question been resolved?
white venture
If you want step by step for these types of things, Wolfram Alpha is much more reliable.
covert tree
althoughi don't think the thing it is saying is wrong in this particular instance.
lime crest
If you want step by step for these types of things, Wolfram Alpha is much more r...
doesnt wolfram do only computations and stuff
white venture
Also step by step explanation of the solution.
final saddleBOT
@lime crest Has your question been resolved?
soft zealotBOT
loud sundial
But there's two solutions ($1$ and $2$) in case $\mathbb{F}_3$ for $p=3$, $n=1$
soft zealotBOT
Civil Service Pigeon
loud sundial
I think it should be
,texsp ||$$p^{n-1}+(-1)^{\frac{(p-1)(n-1)}{4}} p^{\frac{n-1}{2}}$$||
soft zealotBOT
Civil Service Pigeon
lime crest
oh
lime crest
**Civil Service Pigeon**
what, where is this from😭
final saddleBOT
@lime crest Has your question been resolved?
timid jasper
Can anyone help me understand what this is asking or how to solve this ?
timid jasper
That says " f'(x) is equal to" at the end btw
final saddleBOT
@timid jasper Has your question been resolved?
final saddleBOT
Available help channel!
timid jasper
Can anyone help me understand what this is asking or how to solve this ?
timid jasper
oops
abstract mango
Is it asking for what’s f’(x) equal?
abstract mango
so use basically chain rule
timid jasper
Also
How's 1/|x| different from 1/x ?
timid jasper
so use basically chain rule
Could u show?
abstract mango
,w plot ln x
soft zealotBOT
abstract mango
Ok before I plot the other one
This is how log functions looks like, notice it’s only defined for positive real numbers
when you write ln x , you assume you only plus positive real numbers. ln(-2) doesn’t make sense in the reals because we are asking what’s a real number such that e^x = -2
so far cool?
,w plot ln|x|
soft zealotBOT
abstract mango
ln |x| is defined for all reals expect zero.
unlike ln
you can write it as piecewise function,
ln |x| = ln(x), x>0 , ln(-x) , x < 0.
timid jasper
This is how log functions looks like, notice it’s only defined for positive real...
What does "defined" mean here?
abstract mango
it’s all reasonable choices for ln
the domain of definition
ask yourself does log_10 (-2) makes sense?
log_10 (-2) is the real number x such that 10^x = -2 right?
Eg. log_10(1) = 0 because 10^0 = 1
or log_10(100) = 2, because 10^2 = 100.
timid jasper
Ok so how do i go about solving it?
abstract mango
you can write it as piecewise function,
ln |x| = ln(x), x>0 , ln(-x) , x < 0...
Basically differentiate piecewise.
timid jasper
Basically differentiate piecewise.
Could you answer this
#help-36 message
thorny otter
timid jasper
Yeah
abstract mango
[
\ln |x| =
\begin{cases}
\ln x & \text{if } x > 0, \
\ln(-x) & \text{if } x < 0.
\end{cases}
]
soft zealotBOT
dotdoc
abstract mango
do you know how to differentiate this function?
what’s the derivative of ln|x| at x when x < 0?
@timid jasper
timid jasper
what’s the derivative of ln|x| at x when x < 0?
-1/x ?
abstract mango
What’s the derivative of ln|x| at x when x> 0?
timid jasper
what about x > 0
1/x or maybe 1/|x| not sure
abstract mango
[
\ln |x|^{'} =
\begin{cases}
\frac{1}{x} & \text{if } x > 0, \
\frac{-1}{x} & \text{if } x < 0.
\end{cases}
]
I tried couldn’t get that
soft zealotBOT
dotdoc
abstract mango
done
abstract mango
Can anyone help me understand what this is asking or how to solve this ?
1/x or -1/x is very poorly written
timid jasper
What?
abstract mango
You should know that derivative is a function that is defined at each point
timid jasper
That's just the q paper
timid jasper
You should know that derivative is a function that is defined at each point
Okay
timid jasper
1/x or -1/x is hand-wavy
What's that mean
timid jasper
better way to write is 1/x if x > 0 and -1/x if x > 0
And could u explain why the modulus is removed
abstract mango
look at here too, right side it’s usual ln x and to left it’s flipped
and the derivative to right should be same as that of lnx which is 1/x
and to left is that of ln(-x) which is -1/x.
abstract mango
[
\ |x| =
\begin{cases}
\ x & \text{if } x \geq 0, \
\ -x & \text{if } x < 0.
\end{cases}
]
what do you think about this?
soft zealotBOT
dotdoc
timid jasper
what do you think about this?
Ok but why does it get removed
timid jasper
So what's the correct answer
abstract mango
notice the second piece, if x< 0 it means your x is negative so multiply with a negative to make it pisitive
abstract mango
So what's the correct answer
I mean I’ve already solved it for you.
timid jasper
If x≠0 it could be either 1/x or -1/x. So is it D?
abstract mango
please don’t expect me to tell answer is option “X”
timid jasper
That's not what i see when i look up the solution to this
abstract mango
**dotdoc**
sorry I made mistake here
What’s the derivative of ln (-x) when x < 0.
It’s 1/(-x) * (-1) = 1/x
it should be 1/x everywhere expect 0.
@timid jasper
final saddleBOT
Available help channel!
peak tapir
Did i miss an important step or am i close
final saddleBOT
Did i miss an important step or am i close
crude rampart
Did i miss an important step or am i close
would u mind sending the original problem?
oh sorry nvm
peak tapir
That is the problem
crude rampart
yeah my apologies, i misread
hmmm
alright i apologize, i find myself unable to assist with this question, originally i thought i could.
plain girder
Did i miss an important step or am i close
I can help if you want.
peak tapir
I can help if you want.
Yeah plz
plain girder
give me a min
crude cairn
everything until second last line is technically correct
peak tapir
Technically?
crude cairn
but you then factorised the numerator wrongly
in the numerator you have cos^3 A, how did that become a cos^2 A in cos^2 A(1-3sinA)
same thing, you have sin^3 A in the numerator, how did that become sin^2 A in sin^2 A (1 - 3cosA)
peak tapir
Uhh
crude cairn
also, piece of advice, when you factorise you want to actively try to fish out the thing in the denominator
from second last line, using sin^2 + cos^2 = 1 in the numerator will help
peak tapir
(A+b)(a^2-ab + b^2)?
plain girder
yes
plain girder
(A+b)(a^2-ab + b^2)?
Then factor out a common factor (sinA+cosA), and you’ll see the denominator cancels out.
all steps is correct but last
crude cairn
do you know factorize? a³+b³？
this does work, but if factorising a^3 + b^3 isnt taught in that syllabus, then an alt method is
sin^3 = sin (sin^2)
cos^3 = cos (cos^2)
then use sin^2 + cos^2 = 1
peak tapir
How do u know its not taught in syllabus
crude cairn
How do u know its not taught in syllabus
i have a feeling that such trig math is taught at a lower level than factorising a^3 + b^3, a^4 + 4b^4, e.t.c.
plain girder
wait can't we use a³+b³?
plain girder
not 2sinAcosA
crude cairn
your a^2 - ab + b^2 shouldnt be
(cos^2 - 2cos sin + sin^2)
plain girder
it is sinA+cosA
peak tapir
Ehy
plain girder
If you know how to factor x³±y³, this becomes easy.
crude cairn
well it does seem like you are indeed unfamiliar with factoring a^3 ± b^3
peak tapir
Ye ive never been taught stuff after polynomial and only used it once for a comp like 2 yrs ago
crude cairn
but even if you struggle with factoring a^3 ± b^3, it is still fairly easy to do with just sin^2 + cos^2 = 1
peak tapir
Ok
plain girder
btw, It looks like you’re pressing really hard on the paper.
plain girder
:p
crude cairn
stress :L
plain girder
your a^2 - ab + b^2 shouldnt be
(cos^2 - **2cos sin** + sin^2)
How did you make your text bold?
crude cairn
yeah
final saddleBOT
final saddleBOT
Available help channel!
split cipher
now who closed my help ticket
final saddleBOT
now who closed my help ticket
next thorn
now who closed my help ticket
resend the question 😭
split cipher
Just be giving anyone the helpful role
ok listen
I need to remember the range of all six inverse trig ratios
The domain is easy but the range is confusing me
latent dragon
…I am affraid that would be you due to a lack of a response in #help-20 when the bot pinged you if your question had beeen resolved. 🙁
vital crag
Just be giving anyone the helpful role
Why are you so butthurt
next thorn
Just be giving anyone the helpful role
girl 😭 🫳
vital crag
Read
rocky tusk
,av iheartfrankocean729
soft zealotBOT
vital crag
Should have learned to read before doing trig
rocky tusk
checks out
split cipher
I need help omg
next thorn
good luck 
worthy wren
I need to remember the range of all six inverse trig ratios
when it comes to inverse functions, if you know the domain and range of the original functions then the inverse function will just flip it so the domain of the original function is the range of the inverse function for example
so just remember the domain and range of the original 6 trig functions
split cipher
when it comes to inverse functions, if you know the domain and range of the orig...
doesn’t that only work when it’s one-to-one?
vital crag
I need help omg
Be less unpleasant
split cipher
I remember using that trick in class but the range was giving me problems
split cipher
Be less unpleasant
sorry!!
worthy wren
yeah f is only invertible if it is one to one and onto. so we define arcsinx on a domain where sinx satisfies both these properties which is why we choose our domain of f(x) = arcsinx from [-1, 1] but then what is the range?
the domain we chose for sinx is [-pi/2, pi/2] so it must be the range of arcsinx!
u can choose any interval where sinx is one to one but -pi/2 to pi/2 is just convention
final saddleBOT
@split cipher Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
covert lodge
im really confused on how to solve these symmetrical problems, i cant understand what to do / how to approach
final saddleBOT
im really confused on how to solve these symmetrical problems, i cant understand...
edgy pulsar
leme try
soft zealotBOT
edgy pulsar
ye
covert lodge
damn cute
edgy pulsar
we did function q yest too
try finding g(1-x)
and then finding f(x) and f(1-x) in terms of g and put it in the equation
covert lodge
g(1-x) = f(1-x) -1
edgy pulsar
ye then put f(1-x) and f(x) values in the other eqn
covert lodge
i get g (1-x) = 1 - f(x)
ye
edgy pulsar
i think then u get
g(x) + g(1-x) = 0
covert lodge
hmm
edgy pulsar
are u aware of any formula for symmetry?
covert lodge
i think then u get
g(x) + g(1-x) = 0
yesi got that too
covert lodge
are u aware of any formula for symmetry?
nope
edgy pulsar
i think then u get
g(x) + g(1-x) = 0
in this equation we are supposed to try replacing and getting something
edgy pulsar
equation in terms of just g(x)
covert lodge
even and odd functions?
covert lodge
i wanna avoid using options
edgy pulsar
fine leme try something else
edgy pulsar
i know one thing i am not sure if u are aware of not
if there is a function f(a+x) + f(a-x) = 0 then that is symmetrical about a,0
covert lodge
yea i didnt know abt this
edgy pulsar
also
odd functions are symmetric about origin and even functions are symmetric about y axis
always
edgy pulsar
i think we need to dive in detail how symmetry works
u are aware of midpoint formula right?
covert lodge
yes
edgy pulsar
so for symmetry , from one point the distance of the graph should be same
if we talk about symmetry about the point
covert lodge
ye
edgy pulsar
m trying to derive something @covert lodge i am not sure exactly if its the besy way
edgy pulsar
so suppose u are finding symmetry about h,k
let the 2 points on graph be x,x* and y,y*
covert lodge
ye
edgy pulsar
we are assuming that they are symmetrycal and tryin to derive
so as they are symmetrical about h,k
their midpoints are h,k
covert lodge
oh
edgy pulsar
so x+x*/2 = h and same for y
covert lodge
ye
tired walrus
so x+x*/2 = h and same for y
brackets
edgy pulsar
like this
covert lodge
ye i got it
so the dist is same either side
as it is symmetric the point shall be the midpoint
edgy pulsar
basically now x* , y*
= (2h-x, 2k-y)
basically what we said is if x,y lies on the graph and the function is symmetrycal about h,k then this should also lie on the graph
edgy pulsar
so if y = f(x), then y* = f(x*)
covert lodge
ye
edgy pulsar
so in this question we have to prove its converse
not really, i think basically u r supposed to knwo the formula to do the q
i think the formula will be easy
covert lodge
ah
edgy pulsar
lets see what we get
covert lodge
aight
covert lodge
hmm
edgy pulsar
f(x) + f(2h-x) = 2k
if any eqn satisfies this then its symmetric about h,k
covert lodge
if any eqn satisfies this then its symmetric about h,k
thats genuinely amazing
now it makes so much sense
tysm
edgy pulsar
our equation was
g(x) + g(1-x) = 0
So ya u can compare it and find h,k
covert lodge
holy hell
1 sec imma lowk take short notes of this
i wanna note down its derivation
edgy pulsar
sure
covert lodge
so basically if a func is symmetric about some point (h,k) , and function gives (x,x*) and (y,y*)
it took the * away
edgy pulsar
np
covert lodge
so x + x*/2 = h
edgy pulsar
so basically if a func is symmetric about some point (h,k) , and function gives...
its more like x,y and x'y'
edgy pulsar
cause a point is both x and y coordinate right ;D
edgy pulsar
btw
u can use the main formula
to also find out symmetry about straight and horizontal lines
covert lodge
whats the main formula
covert lodge
ye
edgy pulsar
and u want to check wether ur function f(x) symmetric about x = h or not
its gonna look something like this
covert lodge
yep
edgy pulsar
basically what u can see from here is, y value is same for all
for all meaning both the symmetrical points
like f(x) = fx*)
so u get f(x) = f(2h-x)
We calculated x* before the same way again
so your condition if f(x) is symmetrical about a line x = h is
f(x) = f(2h-x)
covert lodge
ohhh
edgy pulsar
remmember i told u before even functions are symmetric about y axis
covert lodge
yeah
edgy pulsar
from here it comes ig
basically u understood the idea about it right
so if u get any unique q jjust try to derive something
edgy pulsar
for symmetry about point yes
if u get something like f(x) = f(2h-x) then
U know tht its symmetric about the line x = h
covert lodge
for about a like we input either h or k as 0
edgy pulsar
for about a like we input either h or k as 0
sorry diddnt really get u
covert lodge
to find symmetricity about a line
we have to put x = 0
i mean h = 0
to find for what line k is symmetric
covert lodge
k 1sec
edgy pulsar
this formula is just for verification
like if its symmetrical about a line x = h ( vertical line)
the 2 points must have the same y coordinate
edgy pulsar
my axis are a bit slant but try to understand
edgy pulsar
yes
covert lodge
and the distance of the point from that line is also same
edgy pulsar
y coord of both f(x) and f(x*) is same
edgy pulsar
and the distance of the point from that line is also same
yes
covert lodge
what abt lines with a slope
edgy pulsar
thats too complex
covert lodge
i had a ques saying y = -x
covert lodge
i asked that ques in this srver
he told that x,y after reflection becomes -y.-x
so yea
i understood that 1
edgy pulsar
ye
u can js replace
for lines
like y = x +c
Replace x = y-c and y with x+c
but if ther is a slope m i am not aware
edgy pulsar
like y = x +c
Replace x = y-c and y with x+c
wait leme find a q with symmetry about y = x
ye suppose y = 1/(x-2) + 2
to check if its symmetric about y = x
covert lodge
ye
covert lodge
ye
edgy pulsar
on simplifyin this
if u get the orignal eqn
then u can say it was symmetrical about y = x
covert lodge
so this holds for any line?
edgy pulsar
I cant say for surity with slope m
i am aware if slope is 1 or -1
covert lodge
what abt it haing intersept
covert lodge
ngl my ppl wont ask shi that complex other than 1 or -1
edgy pulsar
and u have some equation
edgy pulsar
suppose the line u want to check symmetry about is y = x + c and u have some function alright
covert lodge
ye
edgy pulsar
then in that function in places of y put y = x+c
and in places of x put x = y - c
if u can land up to the orignal function
then that function is symmetrical about y = x + c
covert lodge
i have a related ques
edgy pulsar
sorry but currently i have to go
covert lodge
covert lodge
les keep it all here
edgy pulsar
will be back in 1-2hr or something
edgy pulsar
sure
covert lodge
tysm for all the help
edgy pulsar
np
I think inverse of a function is symmetric about the line x = y
just use that or something
alr
covert lodge
yes it is
i almost got it
im getting
aight got it
i dont understand that the function even means
why did they give a comma?
small urchin
m replaces x and n replaces y
thus the comma
no wait hold on
yes so basically when u put x= 2x+y/8 and y=2x-y/8 in a certain function, you get xy
so now instead of 2x+y/8 you input m/n and instead of 2x-y/8 you input n/m respectively
covert lodge
what
nah ts too complicated
so if i put
ok so f(x,y)
is this it>
so f(m,n) will give mn
tysm for the help
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opal plume
why is f(X) not continous at those points?
final saddleBOT
why is f(X) not continous at those points?
opal plume
ques
lime crest
why is f(X) not continous at those points?
well the floor(n) is already discontinuous at every integer n
willow tiger
???
hollow iron
Still
willow tiger
well its clearly discontinous
opal plume
oh
plucky rover
well its clearly discontinous
Not helpful
willow tiger
its discontinous when it turns from non-integer to integer
lime crest
well the floor(n) is already discontinuous at every integer n
well from here theyre just taking 3x^2 = n ∈ ℤ
willow tiger
and because the one without the floor is increasing, its discontinous when its an integer
and x^2 is an integer if its a multiple of 1/3
lime crest
let me process T-T
imagine the graph of f(x) = [x]. approach it from the left at an integer n and from the right
opal plume
ohhhhhh
stone flint
and x^2 is an integer if its a multiple of 1/3
did you mean, 3x^2 is an integer if x^2 is a multiple of 1/3? because if x^2 is a multiple of 1/3, how is it going to be an integer generally?
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candid pulsar
i can understand what d/dx (f(g(x))) looks like but i cant make sense of how theres only one point of inflection
final saddleBOT
i can understand what d/dx (f(g(x))) looks like but i cant make sense of how the...
candid pulsar
stupid discord image display ✊
willow tiger
xD
candid pulsar
i feel like theres one point of inflection between every root
final saddleBOT
@candid pulsar Has your question been resolved?
old quarry
i feel like theres one point of inflection between every root
uh why looks like their explanation is pretty clear
old quarry
wait what does point of inflection actually mean
concavity changes
old quarry
just f''(x) = 0 no?
yeah this also
hmm oh wait i kinda see ur point
maybe they only want inflection points which are stationary
candid pulsar
i believe so
theres some more dumb slip ups so im going to believe this is a mistake
thanks for your time
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lime crest
Hello! the question is to show that [ \sum_{d | n}\phi(d) = n]
final saddleBOT
Hello! the question is to show that \[ \sum_{d | n}\phi(d) = n\]
soft zealotBOT
Copter
lime crest
i have a feeling that the way i wrote this is too loosely
from lhs to rhs it should be some expansion stuff but i dont know how to notate that ;-;
still edge
pretty handwriting
lime crest
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@lime crest Has your question been resolved?
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sullen echo
Can anyone help me with these questions from the 2024 JC mock paper.
You can find a PDF of the exam here: https://drive.google.com/file/d/17K12og6nUZqxKLG8OW5ikLbcybbeiuqB/view.
final saddleBOT
Can anyone help me with these questions from the 2024 JC mock paper.
You can fin...
tired walrus
ok, let's try question 5. do you need help with a, b or both?
sullen echo
both
sullen echo
..no
tired walrus
ok then let's go back one step
can you write down an expression for how much Marian will spend on the dress and x shirts?
your expression will have the letter x in it
@sullen echo can you answer with one of "yes"/"no"/"let me try"
sullen echo
..idk how to do it. is it €60 - €36 - x??
tired walrus
you're overthinking it and also i want the expenses and not how much is left anyway
ok
let's forget about the dress for now
sullen echo
okay
tired walrus
if you buy x shirts, each one for 5 euro, how many euros will you spend? (expression in terms of x)
sullen echo
12x?
tired walrus
how did twelve happen
sullen echo
ughh idkkkk
tired walrus
would you like to try again
let me repeat: x shirts, each shirt costs 5 (five) euro; how much do we spend total?
sullen echo
€60
tired walrus
we always spend exactly sixty euro no matter how many shirts?
sullen echo
no
tired walrus
ok then why are you claiming it with your answer of "60"
ok let's just forget even more of the problem
focus on the most basic concept possible
let's say you go to the same shop as marian and you buy, say... 4 shirts of the same kind. and they still cost you €5 each. you buy just those shirts, nothing else.
tell me now: how much do you spend? and most importantly, be prepared to tell me how you got your answer
sullen echo
..€20?
tired walrus
yes, and how did you figure that out? can you explain in words?
sullen echo
4 shirts x €5 = €20
so you buy 4 shirts and they each cost €5, so u just multiply the two numbers
tired walrus
ok, so you multiplied the number of shirts by the price
sullen echo
yeah
tired walrus
you need to be specific about it. "the two numbers" isnt really good enough.
but ok
to figure out the total cost of a number of shirts, you multiplied the number of shirts by the price
let us now come back to this:
x shirts, each shirt costs 5 (five) euro; how much do we spend total?
tired walrus
there we go
...i still wonder what could have led you to say "12x" earlier, but whatever, we got that sorted out.
so marian spends 5x euro on the shirts, and another 36 euro on the dress,
so what's the expression for her total spending?
don't try to do anything more than what i ask
sullen echo
€36 + 5x = €60
tired walrus
...and you just did try to do more than what i asked.
also those € symbols will be obstructions in our inequality (not equation). you should not be putting them.
sullen echo
okay
tired walrus
marian spends 36 + 5x euro on her clothing.
now,
she has a budget of 60 euro.
that means we will need to fill in the blank here:
36 + 5x ___ 60
with an inequality symbol.
but before we do that: do you know what the words "inequality symbol" or "inequality sign" refer to? yes or no
(DO NOT try to do the next step. i am asking you about knowledge.)
sullen echo
but **before** we do that: do you know what the words **"inequality symbol"** or...
yeah its like < and >
sullen echo
yeah its the ones with the lines under them
tired walrus
do you know what those ones mean, in words?
sullen echo
yeah, it means that it includes the number. so like 15 > with the line, means that the number could also include 15
tired walrus
they mean "less than or equal to" and "greater than or equal to" respectively, yes.
if you can't type them on discord, >= and <= are acceptable substitutes.
good.
sullen echo
ohh okay
tired walrus
now, in this blank:
36 + 5x ___ 60
which symbol should we put, from these four?
< > ≤ ≥
keeping in mind that on the left we have spending and on the right we have budget.
sullen echo
hmm is it ≤
tired walrus
yes
so our inequality, now that we have carefully constructed it step by step, reads:
36 + 5x ≤ 60
now, can you solve this inequality carefully and step by step?
sullen echo
no, i never learned how to solve inequalities
tired walrus
what about equations
if we pretend for a moment that it said = instead of ≤ would you know what to do
sullen echo
u have to make it equal to 0?
tired walrus
mmmmmmmmmmmmm no
ok
let me say it more directly
36 + 5x = 60. solve for x. do you know what to do
sullen echo
hmm i think u -x from both sides
tired walrus
i am tempted to just let you execute that step and see what happens
but actually i'd rather tell you it will leave you with 36 + 4x = 60 - x, which is not very helpful.
so uh
youre gonna need to review basic equation solving
linear equations in one variable too
sullen echo
mhmm okay
tired walrus
i dont have a lot of time rn so i cant teach you this from scratch sorry
sullen echo
hmm i think u -x from both sides
sryy i just noticed i ment -36 sryy
tired walrus
blurgh
ok so like can you attempt solving the equation 36+5x=60 on paper and show me what you get
-36 both sides is a good first step
i will then tell you that it works in basically the exact same way for inequalities
the only difference is that if you were multiplying or dividing both sides by a negative number then the ineq sign flips around\
sullen echo
tired walrus
ok so you in fact know the basic algebra i was trying to go for
should i repeat my msg earlier or can you reread and understand it?
sullen echo
should i repeat my msg earlier or can you reread and understand it?
i understand
sullen echo
sullen echo
yayy
tired walrus
now can you show how this would be plotted on a number line
sullen echo
is this correct?
tired walrus
the endpoint is correct but your ray goes the wrong way
x ≤ 4.8 means x is to the LEFT of 4.8
tired walrus
that's better but you should probably stretch it past 0 as well
sullen echo
ohh okay, so up to the end of the number line
sullen echo
Can anyone help me with these questions from the 2024 JC mock paper.
You can fin...
okay i guess we could move on to question 6 now
tired walrus
question 5 took us a full hour and i dont have another hour to spend on q6 sorry 😭
sullen echo
ohh thats okay, so sorry it took me so long to understand
<@&286206848099549185> can anyone else help me out with question 6
south geyser
alright
so they have given us the total surface area of the box
its important to note that we have 4 faces that are rectangles and two faces which are squared
and ofcourse the total surface area is nothing but the addition of the areas of all the faces
so it would kinda be like (2x^2)+(4x*4.5)=140
thats your quadratic
then take x common and solve
for which is correct, you will get one value as 0 and then a finite val
x is obviously not 0 as then its no longer a box
but a 2 dimensional object
sullen echo
ohh okayy
sullen echo
yea so this is what i mean
where did u get 18x from?
south geyser
so one face is 4.5 multiplied by x
since its a rectangle
and then multiply it by 4 since 4 faces
so it becomes 18
into x
sullen echo
ohh
sullen echo
yea so this is what i mean
so am i ment to solve this using the quadratic formula?
sullen echo
i tried it but i got syntax error
south geyser
i tried it but i got syntax error
did you use the quadratic formula to find the roots?
sullen echo
did you use the quadratic formula to find the roots?
no i just put this in my calc
south geyser
no i just put this in my calc
yea cause the roots you get are pretty weird
but
one root is -ve and another +v
so try doing it once without the calc and use the quadratic formula
sullen echo
my teacher never taught me how to do it without the calc
sullen echo
okayy
south geyser
willow tiger
,rccw
soft zealotBOT
south geyser
also what does β mean?
im just showing the two roots with alpha and beta thats it
sullen echo
ohh
south geyser
hmm i dont get it sry, never did this
did you understand the logic tho?
like how to get the quadratic from the box?
south geyser
whats the portions you have?
sullen echo
wdym
sullen echo
hmm well i have a math mock exam tmr. my teacher sent me a math mock exam from 2024. u can find it here: https://drive.google.com/file/d/17K12og6nUZqxKLG8OW5ikLbcybbeiuqB/view. not quite sure what topics are def gonna be on the exam, cus my teacher didnt want to look at the exam, cus she wants it to be a suprise for her too loll. but i think that coordinate geometry, factorising, statistics might be on it. so im just going through the exam and asking yall on discord what i dont understand
south geyser
yea so it looks pretty balanced
and the easiest and fast thing which u could learn is geometry and factorising
sullen echo
yeah, i did coordinate geometry not that long ago in skl, and with my math tutor, so im not quite worried with that. i could go over factorising tho
also i have a feeling that trigenometry might be on it.
south geyser
also i have a feeling that trigenometry might be on it.
a slight bit, but its more of geometry only
like properties of triangles
sullen echo
yeah
south geyser
yeah, i did coordinate geometry not that long ago in skl, and with my math tutor...
factorizing you could watch an online video and it would help a lot
like from khan academy and other places
sullen echo
factorizing you could watch an online video and it would help a lot
yeah i might do that
also for q6 (c) how do u know which is correct?
steady stratus
√361 = 19
So alpha = (-9+19)/2 = 5
beta = (-9-19)/2 = -14
So values of x can be 5 and -14. But x is the length of some of the edges of this cuboid so x can't be negative
Therefore, correct value of x is 5
@sullen echo
final saddleBOT
@sullen echo Has your question been resolved?
sullen echo
<@1406387591594512425>
yeah yeah im here sorry
final saddleBOT
half yacht
<@&268886789983436800>
toxic tusk
Hi this isn’t what the help channels are for. You can chat to users here in #discussion or #chill however
fair zephyr
we have to find number of points of non-differentiability
final saddleBOT
we have to find number of points of non-differentiability
fair zephyr
i managed to simplify f(x) into a composite function but i dont get what g(x) does to f(x)
anyone there?
scarlet sequoia
Imagine we had f(x) = |x| (not the f we have here but as an example)
What g does, is look, for some value of x, all the images between x and x+1, and take the biggest one
If we start looking at x <= -1
Then x+1 <= 0
And so f is decreasing on [x,x+1]
So the max value on that interval has to be on the left
g(x) = |x| = -x for x <= -1
Another easy case is x>=0
Then f is increasing on [x,x+1]
So the max value on the interval has to be on the right
g(x) = |x+1| = x+1
We can then look at other cases, like x = -1/2 for example
from x to x+1, f is decreasing then increasing
The max value is either on the left or right bound
Turns out they're equal
g(-1/2) = |±1/2| = 1/2
In the end, after checking every case, g(x) = |x+1/2| + 1/2
fair zephyr
In the end, after checking every case, g(x) = |x+1/2| + 1/2
ahh ok
so till x=-1/2, the max is always on the left, after -1/2, max is on the right, that switch is the point of non differentiability for g(x)
i think i got it
so for mine, i graph it and move the interval to find where max chnages?
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prisma hawk
Excuse the horrible formatting, I didn't write it. I'm very stuck right now, I asked AI and it's insisting the answer is -9.41*10^-192 but according to the homework that's incorrect
final saddleBOT
Excuse the horrible formatting, I didn't write it. I'm very stuck right now, I a...
prisma hawk
here's the expression not formatted horribly
Update, I must have typed it wrong or something, All set
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severe pike
How can I make a camera "system" using math. I'm a programmer and am making my own engine, and I need to gain a somewhat coherent understanding of linear algebra for said camera system. I have no understanding of how to do this and need help