@void steeple Has your question been resolved?
#help-41
amber waspBOT
pallid canopy
What's x? Arbitrary?
void steeple
What's x? Arbitrary?
just a generic input function
amber waspBOT
@void steeple Has your question been resolved?
dense geode
lim inf sin(n^2)/n = 0
so you can get -1/n < sin(n^2)/n < 1/n then use squeeze theorem to get
lim sin(n^2)/n = 0 but is that enough to say lim inf sin(n^2)/n = 0?
viscid swan
yup because if the limit exists then limit equals liminf equals limsup
verbal lark
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amber waspBOT
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verbal lark
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pallid canopy
$A= \pi r^2$, and $C = 2\pi r$
grizzled pagodaBOT
riemann
verbal lark
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verbal lark
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verbal lark
solve for r in circumference, then plug it into A
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pallid canopy
yea you can simplify further
verbal lark
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amber waspBOT
amber waspBOT
Available help channel!
woven trellis
I can't solve this obscenely easy math problem
amber waspBOT
I can't solve this obscenely easy math problem
woven trellis
That's the formula for change in consumer surplus
P2 remains fixed at 5
P1 goes down from 10 to 5
And m is income m
pallid canopy
Can you solve the integral if x=P1 and c=P2
empty dome
@pallid canopy
woven trellis
And then take p1 =10 and subtract it from p1=5?
Did I do that right
Or was it supposed to be
In(p1)
grizzled pagodaBOT
woven trellis
P2=5 here
grizzled pagodaBOT
riemann
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
woven trellis
What's happens to m
So it becomes log|p1+5| +C
I'm not sure what becomes of the constant either
Ah
It's integration not derivative
Sorry
So does m drop out
And it's just log(p1+p2) +c
And then it just becomes essentially
Log(10+5) - log(5+5)?
With maybe + c - c canceling out
@pallid canopy
I got
Rather
m*ln(|x+c|)+c
And then evaluating
(In(15)-In(10))m
Or m*In(3/2) in other words
@pallid canopy can you please confirm if I did that right
amber waspBOT
@woven trellis Has your question been resolved?
white fog
white fog
yup
quick ridge
@slow pelican how’d you accidentally do that
white fog
and area of ebd is 1/3 of acde area
slow pelican
<@800739623839858688> how’d you accidentally do that
uh I am bad with planes && jets
quick ridge
uh I am bad with planes && jets
ahh happened to a buddy of mine not too long ago actually
slow pelican
ahh happened to a buddy of mine not too long ago actually
yeah its pretty common
idle light
they're similar triangles
idle light
as well as ABC and EBD
white fog
the same
idle light
working on it but I hate geometry
white fog
who does love geometry
idle light
who does love geometry
are you sure that it's 1/3 the area of acde instead of abc
white fog
i don't know bec it is on my book
myabe there is something wrong
where did you stop at
amber waspBOT
@white fog Has your question been resolved?
white fog
noooooooooooooooooooo
amber waspBOT
@white fog Has your question been resolved?
boreal panther
can any one solve my math thing
Was it solved
amber waspBOT
split kraken
amber waspBOT
Available help channel!
fierce quiver
can someone
amber waspBOT
can someone
fierce quiver
help me figure out
this is what i have so far and i’ve seen on math forms it has to do with divisibility between consecutive numbers which i don’t really understand
molten shale
for n-1, n, and n+1 theres always a multiple of 2 amongst two consecutive numbers and a multiple of three amongst three consecutive numbers
so the expression is divisible by 6 because 2*3
and now u prove that it is divisible by 5
amber waspBOT
@fierce quiver Has your question been resolved?
void steeple
$$C \cdot \int^{\infty}_{-\infty} e^{\frac{-|x-a|}{b}}dx = 1$$
C is a constant which depends on values a and b, not sure how to start deducing appropriate vals of a/b
grizzled pagodaBOT
jack
tulip tapir
yes
amber waspBOT
@void steeple Has your question been resolved?
vocal hearth
how is the derivative of f(x)/g(x) f'(x)g(x)=f(x)g'(x)
amber waspBOT
how is the derivative of f(x)/g(x) f'(x)g(x)...
stiff jetty
how is the derivative of f(x)/g(x) f'(x)g(x)...
its not
assuming u meant $\frac{d}{dx} \frac{f(x)}{g(x)}$
grizzled pagodaBOT
Dootud
vocal hearth
what
stiff jetty
its just an expression
it doesnt mean anything outside of the context of f(x) and g(x) being defined
indigo cloud
!original
amber waspBOT
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.
vocal hearth
to find the local maximum of the function at the median values of the domain (\left[\frac{3\pi}{2},\frac{7\pi}{2}\right]). To do that we know from theory that to find the local maximum of a quotient function of the form:
[\frac{f(x)}{g(x)}]
we just solve for the values of (x) that satisfy the equation
[f'(x)g(x)=f(x)g'(x)]
grizzled pagodaBOT
LiSA
vocal hearth
i dont understand why they used f'(x)g(x)=f(x)g'(x)
vocal hearth
so this is not the derivative set to 0?
indigo cloud
it results from setting the derivative equal to 0
amber waspBOT
amber waspBOT
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tranquil summit
If you have the formula f(x) = 2x^2, and you want to fill in point x = -3, do you calculate it as f(x) = 2 * (-3)^2 or f(x) = 2 * -3^2
shadow stump
the first one
amber waspBOT
amber waspBOT
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scenic moon
amber waspBOT
scenic moon
ive no idea how to solve this
twin helm
Divide both sides
scenic moon
but rhs is already 0
timid vault
It's in factored form. You can read the two solutions are -13/2 and +13/2
twin helm
Yes
spare belfry
positive
scenic moon
So the answer is 2?
but how
gilded nymph
It is in form of (a-b) (a+b)
gilded nymph
The formula is (a+b)(a-b) = (a^2-b^2). Substitute the values. You will get (plus or minus) 13/2
scenic moon
Have you realized that it's a quadratic equation?
yeah
gilded nymph
But the answer is real solutions and hence it is 2 solutions
scenic moon
How you typically get something (x-4)(x+4)=0
a^2+b^2=2ab ?
gilded nymph
Can anyone tell if I am right?
midnight jackal
are u guys from 10th grade
gilded nymph
I'll take it as that I'm wrong :/
midnight jackal
u are talkig abt this silly prblm
gilded nymph
are u guys from 10th grade
Nope.
scenic moon
After you factor it but yes
i still didnt got it
gilded nymph
i still didnt got it
WHich problem?
scenic moon
.
midnight jackal
WHich problem?
whats ur grade speak up bro
scenic moon
can you actually help me understand or just keep defaming ?
gilded nymph
.
Scroll up a bit and see my response. If You can't understand ask again
The question is in the form of (a+b)(a-b) which is equal to a²-b². (Or just multiply it!). Then you get x = 13/2 and -13/2
Or another solution:
scenic moon
The formula is (a+b)(a-b) = (a^2-b^2). Substitute the values. You will get (plus...
so a=(x+13/2) and b=(x-13/2) here right ?
gilded nymph
It is in form of (x+a) (x-b) = 0. That means either x+a or x-b is must and should equal to 0.
gilded nymph
so a=(x+13/2) and b=(x-13/2) here right ?
Yes
So the no of solutions is 2
got it?
scenic moon
so first ive to square the bracket and then substitute ?
scenic moon
can you please do it and show
amber waspBOT
@scenic moon Has your question been resolved?
slate gale
Guys, am i doing it right? (The blue writing)
amber waspBOT
Guys, am i doing it right? (The blue writing)
patent raptor
Guys, am i doing it right? (The blue writing)
To me it looks right
patent raptor
Are you using the formula for conditional probability?
slate gale
Are you using the formula for conditional probability?
Yes!
patent raptor
I think you need law of total probability for P(B')
acoustic falcon
When a complex contour integral "vanishes," does that mean that the sum of its residues equal zero?
amber waspBOT
When a complex contour integral "vanishes," does that mean that the sum of its r...
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.
acoustic falcon
<@&286206848099549185>
topaz token
When a complex contour integral is equal to zero, it means that the sum of the residues of the singularities inside the contour is zero
acoustic falcon
And what I said and what you said are the same thing right?
topaz token
Yes, what you said and what I said mean the same thing.
When a complex contour integral is equal to zero, it means that the singularities inside the contour have residues that cancel each other out. This is because, according to the Residue Theorem, the value of the integral depends on the sum of those residues. If the sum is zero, then the integral is also zero, indicating that there is no net contribution from the singularities.
acoustic falcon
Okay cool. I thought so, but my class doesn't explain this stuff very well. Thank you @topaz token
topaz token
Okay cool. I thought so, but my class doesn't explain this stuff very well. Than...
Keep learning, stay motivated, you can do it, wishing you much success!
sonic kindle
Can i get some help with this exercise?
amber waspBOT
Can i get some help with this exercise?
sonic kindle
I need to demonstrate that that fraction is in between 6 and 12
amber waspBOT
@sonic kindle Has your question been resolved?
craggy sundial
simplify the logs and use the change of base formula
sonic kindle
I did that
grizzled plume
Whats your working?
sonic kindle
But i get stuck
grizzled plume
!show
amber waspBOT
Show your work, and if possible, explain where you are stuck.
sonic kindle
I dont have it on me, but i got somewhere like log base 7 out of 2 + log base 2 out of 7
grizzled plume
Hm
Then let log base (2) (7) be x
Then get an expression for x i think and then probably solve
Or use a bound since this interval is wide
sonic kindle
Yeah i was thinking about estimating but idk to what to estimate
grizzled plume
Try setting a bound which has a known value
sonic kindle
Like what? I guess for log base 2of 7 i can say that its less than 3 but for log base 7 of 2?
craggy sundial
use the $\frac{1}{log_2(7)}$ instead
grizzled pagodaBOT
Sepdron
sonic kindle
Could work since i can aproximate this one to .33 and the other to 3 but i think the interval is too small for the problem to be solved with estimations
craggy sundial
you could do 2 estimations
one where you replace both with a smaller value
and one where you replace both with a larger value
craggy sundial
Could work since i can aproximate this one to .33 and the other to 3 but i think...
replacing it with 1/3 + 3 isn't a good argument btw
bc 1/3 < 1/log2(7) and 3 > log2(7)
you want them both to be in the same direction
amber waspBOT
amber waspBOT
Available help channel!
split sail
is d/dx (x+a) = d/dx (x) + d/dx (a)
amber waspBOT
is d/dx (x+a) = d/dx (x) + d/dx (a)
unique flare
yeah
split sail
if a=b, is d/dx a = d/dx b?
ofc
now
see
this
sec^2 x = tan^2 x + 1
d/dx sec^2 x = d/dx (tan^2 x+ 1) = d/dx sec^2 x = d/dx tan^2 x + d/dx (1) = d/dx tan^2 x
therefore d/dx sec^2 x = d/dx tan^2 x
is this true?
covert onyx
if a=b, is d/dx a = d/dx b?
Yes
covert onyx
is this true?
Yes
grizzled pagodaBOT
split sail
,w d/dx sec^2 x
grizzled pagodaBOT
covert onyx
hooray!
split sail
.close
amber waspBOT
split sail
hooray hoo
amber waspBOT
Available help channel!
woeful dirge
help:
patent raptor
y = 1 the horizontal line where the function is equidistant, that way you can figure a
unique flare
should we take derivative
patent raptor
b = 2π/p
woeful dirge
a is clearly 2
how
rocky tendon
how
take the distance between the highest value and the lowest value than devide it by 2
unique flare
a is clearly 2
is a height?
rocky tendon
is a height?
yes but from the symytrical axe
rocky tendon
a stretches the it vertically, b horizontally
yeah b is called the pulsation if i'm not wrong
b = 2PI / 90
amber waspBOT
@woeful dirge Has your question been resolved?
grizzled pagodaBOT
RulzerFly
rocky tendon
@woeful dirge
slate gale
hi guys pls help. for letter a, how do i know that the event is dependent, instead of independent?? 😭
slate gale
the guy at youtube did it this way
but i don't understand why he considers it as dependent
quick ridge
because 0.28≠0.3
thorny terrace
We have that:
P(A) = 0.3
P(B) = 0.7
P(A,B) = 0.28
Is P(A)*P(B) = P(A,B) ?
quick ridge
because 0.28≠0.3
meaning P(A and B) ≠ P(A) * P(B) so they are not independent
slate gale
meaning P(A and B) ≠ P(A) * P(B) so they are not independent
yes but how do i know this by only reading the question?
slate gale
We have that:
P(A) = 0.3
P(B) = 0.7
P(A,B) = 0.28
Is P(A)*P(B) = P(A,B) ?
the guy did the 0.28 as part of the answer
slate gale
hi guys pls help. for letter a, how do i know that the event is dependent, inste...
this is the original question
quick ridge
P(A|B) ≠ P(A)
since the probability of event A occurring is different given that event B occurred, A is dependent on B
slate gale
alright thank youuu!
slate gale
We have that:
P(A) = 0.3
P(B) = 0.7
P(A,B) = 0.28
Is P(A)*P(B) = P(A,B) ?
thank youuuu!
thank you sm guys
quick ridge
you’re welcome
slate gale
.close
amber waspBOT
amber waspBOT
Available help channel!
rocky tendon
amber waspBOT
amber waspBOT
@rocky tendon Has your question been resolved?
meager gale
amber waspBOT
mint nacelle
,calc (4/3)/(1 - 1/3)
mint nacelle
I was trying to see if 4/3 + 4/9 + 4/27 + ..... did anything
meager gale
also why
meager gale
I was trying to see if 4/3 + 4/9 + 4/27 + ..... did anything
oh
mint nacelle
wait not 1
meager gale
fair enough
grizzled pagodaBOT
Result:
2
that's interesting
mint nacelle
I think they mean it's 0 - (4/3 + 4/9 + 4/27 + ....) = -2
yeah it's BS
you don't have the proper tools to make sense of the principal value of a divergent sequence
there's no reason why adding infinitely many terms can be negative
cunning birch
I think that they were trying to say that, if S_infinity = 1/(1-x) only works for |x| < 1, the function 1/(1-x) can be extended to any x != 1
cunning birch
So we could technically attribute a finite value to an infinite sum even if said sum doesn't converge, even diverges to +infinity
cunning birch
whats the x!=1 part mean?
x not equal to 1
cunning birch
So we could technically attribute a finite value to an infinite sum even if said...
So be very careful with this
cunning birch
There is a very important distinction between
"Attributing an arbitrary value"
And
"Converging to said value"
The same distinction
That so many 1+2+3+4+... = -1/12 believers fail to grasp
mint nacelle
nicely said
cunning birch
who believes that???
Trust me, some people do
amber waspBOT
crystal cloak
How do we do this problem?
I know combinatorics but only have a very basic understanding of probability
Baye's Theorem is all I know
mint nacelle
- you can't have 0 as any of the numbers
- there must be either 5, 3, or 1 positive numbers
wait
amber waspBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
crystal cloak
ask in a new help channel please
mint nacelle
scroll down
crystal cloak
mint nacelle
wait what the how are there no open channels
crystal cloak
wait what the how are there no open channels
¯_(ツ)_/¯
mint nacelle
¯\_(ツ)_/¯
ask in #prealg-and-algebra then
amber waspBOT
Available help channel!
rapid oasis
For my homework I need to find the best upper and lower bound on (x^2+y^2)/(2^x+3^y), lower bound is trivial and I think the upper bound is 10/11, but I couldn't prove that is the case even though it makes sense intuitively. I need help with this
rapid oasis
x,y natural >=1
mint nacelle
For my homework I need to find the best upper and lower bound on (x^2+y^2)/(2^x+...
if you're allowed calculus, show that f(y) = (k^2 + y^2) / (2^k + 3^y) and g(x) = (x^2 + m^2) / (2^x + 3^m) are both decreasing functions for constants k, m
rapid oasis
I'm not
mint nacelle
oh okay
rapid oasis
Ive only just learned induction
mint nacelle
I mean they are decreasing in the long run
they're not decreasing for all naturals I checked
rapid oasis
yeah
mint nacelle
maybe you can try induction then, so given that (k^2 + (y + 1)^2) / (2^k + 3^(y + 1)) - (k^2 + y^2) / (2^k + 3^y) < 0
show (k^2 + (y + 2)^2) / (2^k + 3^(y + 2)) - (k^2 + (y + 1)^2) / (2^k + 3^(y + 1)) < 0 for y >= 2?
that would be nasty though
this might help
amber waspBOT
@rapid oasis Has your question been resolved?
amber waspBOT
@rapid oasis Has your question been resolved?
rapid oasis
okay I used induction to prove for m and n separately after multiplying out and on m>=8 and n>=1 and I'll check the values m<8 and it works
.close
dapper falcon
hep
quick estuary
Try starting with tan(2theta+2theta)?
dapper falcon
Try starting with tan(2theta+2theta)?
chat how to do this
quick estuary
Wait lemme pull out the addition formula
quick estuary
dapper falcon
but idk how to simplify
dapper falcon
i get tan4theta/1-tan^2 4 theta
when i somplify
chartbit
wait
im getting it lowkey
quick estuary
you got it?
quick estuary
nice
amber waspBOT
@dapper falcon Has your question been resolved?
dapper falcon
h..........help..........
amber waspBOT
dark rover
.close
amber waspBOT
amber waspBOT
Available help channel!
strong orbit
Is $f(2)$ considered a hole in this function? $f(x)=\frac{x-2}{x^2-4}$
grizzled pagodaBOT
Mai
mighty lagoon
is this defined at x=2?
abstract canopy
it is technically a removable discontinuity
strong orbit
is this defined at x=2?
yes
mighty lagoon
as it is now
strong orbit
is this defined at x=2?
sorry, I misread your question. the function isn't defined at x=2
hearty inlet
yeah so there's a hole at x=2
mighty lagoon
you might call that a hole 🕳️
strong orbit
I am asking it's considered a hole since x=2 approaches both infinity and -infinity, and I couldn't find a formal definition of hole
inner zenith
I am asking it's considered a hole since x=2 approaches both infinity and -infin...
basically a hole is a input value that doesnt work cause like divide by 0
amber waspBOT
strong orbit
.reopen
amber waspBOT
✅
strong orbit
it is technically a removable discontinuity
actually wait, can it be if the limits from both directions aren't equal
abstract canopy
actually wait, can it be if the limits from both directions aren't equal
if the limits aren't equal, then it's not, but in this case they are
strong orbit
are they?
tawdry lintel
abstract canopy
i mean non-removable
strong orbit
so a jump/step discontinuity
or is it considered an essential discontinuity because infinity is out of domain?
floral nexus
pearl fractal
I gotchu
rugged edge
amber waspBOT
rugged edge
so far i have
∠AOC = 180-70=110 (supplementary angle theorem)
∠AED = 90 (two points on diameter in a triangle)
∠ACD = 90 (same as above)
∠OAB = 180-110=70 (c pattern)
amber waspBOT
@rugged edge Has your question been resolved?
rugged edge
<@&286206848099549185>
split sail
It's an isosceles triangle and you know that the angles opposite to the equals sides are equal
rugged edge
FUCK Im dumb
this is what i miss about a lot of these questions
all radii are the same length
so triangles with center and 2 points on circle are all isosceles
split sail
Angle ACD
rugged edge
alright
i think i have all of them
∠AOC = 180-70=110 (supplementary angle theorem)
∠AED = 90 (two points on diameter in a triangle)
∠ACD = 90 (same as above)
∠OAB = 180-110=70 (c pattern)
∠OAC = 70/2 =35
∠OCA = ∠OAC = 35
∠CAB = ∠OCA = 35
∠OCD = 90 - ∠OCA = 55
∠ODC = 180-70-∠OCD= 55
∠ADC=∠OCD=55
split sail
ADC AND ODC represent the same angle
split sail
🤨
amber waspBOT
amber waspBOT
Available help channel!
coral jackal
amber waspBOT
coral jackal
so is the green box ok?
coral jackal
outer hull
this is still wrong
coral jackal
ohh
outer hull
you are differentiating -x^2sinx
amber waspBOT
If you are done with this channel, please mark your problem as solved by typing .close
coral jackal
.close
amber waspBOT
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solemn escarp
"From the image, ABCD is a square with sidelength 40sqrt(7), O is the center of a circle inscribed in other circles, as in the image. Find the shaded area"
solemn escarp
i have no idea how to start
amber waspBOT
@solemn escarp Has your question been resolved?
solemn escarp
<@&286206848099549185>
covert dock
I’m sorry I’m only really good at mod math I also have absolutely no idea where to start so
That doesn’t mean I can’t try
That just means I’m unreliable. I’m sorry.
covert dock
<@&286206848099549185>
I’m sorry I cannot offer assistance for I do not know how to start either
Good luck,
solemn escarp
awh poo
amber waspBOT
@solemn escarp Has your question been resolved?
amber waspBOT
@solemn escarp Has your question been resolved?
solemn escarp
anyone?
amber waspBOT
@solemn escarp Has your question been resolved?
remote fable
Let C a convex set in Rm then int(C) is a convex set
amber waspBOT
Let C a convex set in Rm then int(C) is a convex set
remote fable
So, let x,y in Int(C)
Then there exists epsilon_{1} & epsilon_{2}
Such that B(x;epsilon_{1}) is contained in C (the same with y)
Now, let c=x+t(y-x) with 0≤t≤1
In this moment i dont know how to continue. I know i have to find a epsilon such that B(c;epsilon) is contained in C
I also drew some convexs sets (with the wish that an idea can appear) and now im thinking that min(epsilon_{1};epsilon_{2}) works
amber waspBOT
@remote fable Has your question been resolved?
remote fable
<@&286206848099549185>
glad mantle
<@&286206848099549185>
Yes
amber waspBOT
@remote fable Has your question been resolved?
exotic marsh
i need help with my calculator can anyone help dm
amber waspBOT
i need help with my calculator can anyone help dm
spiral zealot
just ask here
amber waspBOT
@exotic marsh Has your question been resolved?
unreal tusk
hello
unreal tusk
I was revising linear algebra notes and I found that my prof wrote this note
it seems that 2 statements in red squares are contradicting each other. cuz for example if Ax=0 then according to the statement on the left then it is infinitely many sol. But according to the other the one on the right it can be zero or infinitely many
Can anyone please explain ?
amber waspBOT
@unreal tusk Has your question been resolved?
unreal tusk
<@&286206848099549185>
lost mantle
Does that Ax=0 mean "Zero solution" i.e. where x = 0 ?
unreal tusk
Does that Ax=0 mean "Zero solution" i.e. where x = 0 ?
it means when it's in echelon form [a1,..|0]
lost mantle
I mean the "has Zero solution" written in notes
if Ax=0 then x=0 is a solution for it
unreal tusk
yeah look at the right side (*if there are n leading entries)
it's written like that
and on the left it says infelnely many solutions by looking at last row that all zeros
lost mantle
If echelon for has n leading entries then and Ax=0 then x=0 would be a unique solution (unless I'm misunderstanding something here)
unreal tusk
idk I am confused
lost mantle
the a part on left side says
last row in echolon form = [0 ... m | n] where m != 0
but n could be 0
lost mantle
Yes, if there less than n leading entries in echelon form of nXn matrix then last row must be [0 ... 0 | k] form
unreal tusk
Also there's smth else not clear if u can help me
This should be an example if these 2 remarks
at the end when we got echelon form prof represented x3 =k but why x3 not x1 or x2 for example
lost mantle
Its just a way of saying we have infinitely many solution (you can substitute k with any real number and get corresponding x1 and x2)
you could also say x2=p and then derive x1 and x3 in-terms of p - which would also show that you have infinitely many solution. (you can substitute p with any real number to get corresponding x1 and x3)
it is just easier to take x3=k because we have things in echelon form
unreal tusk
it is just easier to take x3=k because we have things in echelon form
can u elaborate ? why it is easier to take x3 compared to the rest ?
lost mantle
i mean when you have a echelon form you usually solve for x3 first then x2 then x1
unreal tusk
i mean when you have a echelon form you usually solve for x3 first then x2 then ...
I see .. we use last variable usually
lost mantle
unreal tusk
<:catthumbsup:614540188747563008>
I see great
one last thing
I didn't understand it actually
we have infintely many solutions, right ? That mean we have ∞ solutions which we can't list them
how in below we defined a solution space
lost mantle
Solution space represent a set of all possible solutions
A solution space is set that can contain infinitely many solutions
we are representing it with mathematical notation
its like saying ${x | x \in \mathbb{R}}$ is a set of all real numbers - we know there are infinite real numbers but we are defining it with notation
grizzled pagodaBOT
delta
unreal tusk
its like saying $\{x | x \in \mathbb{R}\}$ is a set of all real numbers - we kno...
I see
pretty cool
thanks alot
lost mantle
unreal tusk
have a good day/night
amber waspBOT
@unreal tusk Has your question been resolved?
slate gale
Hi guys, i don’t understand how to do this (esp the yellow part, i don’t know what to do)
little dagger
see in the ques its given that the 4 digits number we chose must be b/w 4.5k and 5k
how did they even got 501
slate gale
how did they even got 501
I wrote it 😀
little dagger
aha
slate gale
how did they even got 501
I thought 5000-4500
little dagger
I thought 5000-4500
yeah but no letters/digits can be repeated
little dagger
yeah so first digit must be 4
in 4 digit number
it cannot be 5 as it would exceed 5000
slate gale
Oooh
little dagger
so first digit must be 4
now we come to 2nd digit
the 2nd digit must be greater than or equal to 5
so it exceeds 4500
slate gale
Yess
little dagger
now we come to 3rd digit
it can be anything except first and 2nd digit
so 7-2 = i.e 5 possible digits
and last one will have 4 possible digits
slate gale
so 7-2 = i.e 5 possible digits
Is 7-2 only an example?
slate gale
and last one will have 4 possible digits
Okkk i will try it first
little dagger
7 is possible digits overall
2 is count of first two digits which we have already chosen
slate gale
7 is possible digits overall
How to get 7?
slate gale
Ohhh yess ure right
little dagger
Ohhh yess ure right
u sure, you're clear abt it?
little dagger
yes
about letters D & E is already given
just tell me possible outcomes and favourable outcome
slate gale
1/5 * 1/4 for D and E!
little dagger
yes and of digits?
slate gale
Holdon is will think first
little dagger
ok
slate gale
1/7 x 3/6 x 5/5 x 4/4 for the four digits
amber waspBOT
slate gale
.reopen
amber waspBOT
✅
slate gale
Wait guys
little dagger
sup
slate gale
“Between” means the number can’t be that right
little dagger
aha grammar
slate gale
Like between 4500 and 5000, means it cannot be 4500 or 5000
slate gale
aha grammar
Yes i recently forgot many grammar
little dagger
well technically doesnt matter whatever it means
as the no. of combinations will always be greater than 4500
ancient jolt
hehehe
little dagger
and 4500 is not possible as set doesn't include 0
ancient jolt
who's pretty good at math here
inland pulsar
ohh
little dagger
who's pretty good at math here
!occupied
amber waspBOT
who's pretty good at math here
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
ancient jolt
i have a doubt
little dagger
Yes i recently forgot many grammar
u got what i mean?
slate gale
and 4500 is not possible as set doesn't include 0
Ohhhh
Yes yess
Wait how about for other questions
What does between mean
For example, between number 1 and 9
Is 1 and 9 included?
I think so
little dagger
uhm
good ques
they will mention exclusively and inclusively maybe
yeah
doesnt include ig
so b/w 1 & 9 = 2...8
amber waspBOT
amber waspBOT
Available help channel!
chilly kindle
amber waspBOT
chilly kindle
The problem is part a don't understand how to conceptually pick values to make inequalities of
's what the mark scheme says
amber waspBOT
@chilly kindle Has your question been resolved?
amber waspBOT
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vapid creek
just have a quick question.. can trigonometric functions be used in any triangle? or only 90 degree ones
quasi dirge
just have a quick question.. can trigonometric functions be used in any triangle...
any triangle
sinful sapphire
it has to be 90°
quasi dirge
what
sinful sapphire
you can use it with any angle
but when you say sin(x) you're always talking about a triangle where one angle is 90° and one angle is x
sinful sapphire
no wait
quasi dirge
it doesnt have to be
vapid creek
is it that you can only use like sin, cos, tan in a right triangle. and in any triangle you can only use the sine theorem,cosine theorem ...
quasi dirge
@sinful sapphire did i defend your position?
quasi dirge
yes, that was my mistake
nope you're good happens to the best of us
quasi dirge
thank you both
happy to help
vapid creek
.close
amber waspBOT
sinful sapphire
cus of this?
yes, and there's no right triangle you can draw like this if x is already 90°+
so what i'm saying doesn't make sense
hearty inlet
happy to help
who's in ur pfp btw
quasi dirge
who's in ur pfp btw
freesciencelessons dude
quasi dirge
yes, and there's no right triangle you can draw like this if x is already 90°+
isnt it a unit circle tho
hearty inlet
freesciencelessons dude
damn
hearty inlet
whats in your pfp
gamma function
quasi dirge
ainnoway somone drew that
amber waspBOT
Available help channel!
neat dagger
why does k=0 in the binomial theorem
amber waspBOT
why does k=0 in the binomial theorem
neat dagger
under the sigma notation
indigo cloud
do you know what the sigma notation means?
neat dagger
no lmfao im dumb asf
i was learning the binomial theorem
i was js wondering why k=0
indigo cloud
I am not sure what to answer you. you need that term, otherwise its false
neat dagger
I am not sure what to answer you. you need that term, otherwise its false
the theorem?
indigo cloud
if k starts at 1 for example then you dont have one of the terms you need
neat dagger
if k starts at 1 for example then you dont have one of the terms you need
it will be diff
indigo cloud
which is from k=0
neat dagger
ok can i ask a dumb question
what does the sigma notatoin mean
i looked through the wiki page and kinda got it but
indigo cloud
well its notation for a sum. just like you did it in the example
indigo cloud
you can see it as a for loop if you know programming
k starts at 0 and increases in steps of 1 until it hits the upper bound n
indigo cloud
and each time the formula is evaluated in terms of k and then everything is added up
neat dagger
yea i programmed before a bunch
neat dagger
and each time the formula is evaluated in terms of k and then everything is adde...
alrr
bro tysm
can i close this now
indigo cloud
sure. its your channel
amber waspBOT
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Available help channel!
analog bobcat
The answer is 679
amber waspBOT
The answer is 679
analog bobcat
I it's fluid force
reef kraken
First if all physics
reef kraken
I it's fluid force
Pressure * Area
Or is the cylinder placed horizontally and we need the force on the horizontal face?
mint nacelle
The answer is 679
yes and you also need density = mass/volume
actually you don't need pressure * area then
so can you find the volume first?
oh wait that's weird
mint nacelle
seems like you need integration to find the volume
analog bobcat
Yea
mint nacelle
The answer is 679
you don't actually need integration though
but I don't know if your teacher wants you to use integration
analog bobcat
He prob does
I'm confused on wht the integral is though
Inegral 0 to 3 (50y * pir^2 *3-y) i think
Still wrong 😭
amber waspBOT
@analog bobcat Has your question been resolved?
analog bobcat
Yes
rose mica
is this algebra correct?
amber waspBOT
is this algebra correct?
solar gust
Not quite
The last term is not wrong
But i advice you to use (a-b)² formula, it avoid a bit of algebra like this
-e^-pi/2 * -e^-pi/2 = e^(-pi/2 -pi/2) = e^-2pi/2 = e^-pi
But with formula it gives just (e^-pi/2)^2 = e^-pi quickly, you see ?
solar gust
You're welcome !
rose mica
You're welcome !
just wanted to confirm before closing, is this correct?
solar gust
just wanted to confirm before closing, is this correct?
All good
amber waspBOT
amber waspBOT
Available help channel!
opaque goblet
this is the equation i'm trying to solve for the derivative.
opaque goblet
This is the answer i got, but it isn't correct after i tried to graph
celest cove
show your method
opaque goblet
okay give me a sec
opaque goblet
show your method
i used quotient rule, the x^2 derivative is 2x and the bottom graph derivative i got was shown in the pic i sent
and then doing the quotient rule, i got this, then i simplified to the answer i got above
but even plugging this into desmos it was wrong, so i'm confused on what i did wrong
celest cove
,w differentiate [(x^3+1)^2]^(1/3)
grizzled pagodaBOT
celest cove
1-4/3=-1/3
so 2x^2/(x^3+1)^1/3
opaque goblet
1-4/3=-1/3
where did you get this?
celest cove
i was just doing the exponents of x^3+1
numerator: 1
denominator 2*2/3=4/3
1-4/3
opaque goblet
oh ok
celest cove
i used quotient rule, the x^2 derivative is 2x and the bottom graph derivative i...
may want to check this again
opaque goblet
may want to check this again
the pic i sent?
celest cove
1-4/3=-1/3
so 2x^2/(x^3+1)^1/3
yeah this is the derivative of the denominator
you at the very least have a sign issue
opaque goblet
okay for the denominator i switched that to (x^3+1)^-2/3
then i tried to take the derivative of it that way
opaque goblet
ohhh wow i can't believe i missed that
i think that solves my problem then... thanks 😂 can't believe i made that mistake
amber waspBOT
Available help channel!
jaunty viper
How can I find the closed form formula for this without assuming directly it is -(n+1)/n ? Like, no induction too.
coral wigeon
amber waspBOT
@jaunty viper Has your question been resolved?
amber waspBOT
U1 i meant
jaunty viper
.reopen
amber waspBOT
@jaunty viper Has your question been resolved?
jaunty viper
@minor trellis pls
amber waspBOT
@jaunty viper Has your question been resolved?
gritty lark
Does the question specifically asks for you to not use induction?
plain hare
i think the question is how to derive the -(n+1)/n in the first place
amber waspBOT
@jaunty viper Has your question been resolved?
jaunty viper
Does the question specifically asks for you to not use induction?
no
but
i want to know
jaunty viper
i think the question is how to derive the -(n+1)/n in the first place
yea
how
like
i could see the pattern
i could use induction
but how to derive it rigorously?
plain hare
i believe equations like this are called difference equations
its like differential equations, but the variable is an integer
there are specific ways to solve them ig
amber waspBOT
@jaunty viper Has your question been resolved?
split sail
\textbf{Problem:} Consider the heat equation in $\R^n$:\[
\pdv[u]t - \Delta u = 0, \q (x,t) \in \R^n \by (0,\infty)
\]
with the initial condition \[
\6u{x,0}=\6fx, \q x\in\R^n
\]
Show that the solution to the PDE can be written as \[
\6u{x,t} = \41{(4\pi t)^{\5n2}}\int_{\R^n}\6\exp{-\4{\abs{x-y}^2}{4t}}\6fy\dd y
\]
\textbf{My current progress:} So we need to use Fourier transform here, and I did some tinkering to get the equation \[
\dv[\hat u]t+\abs{\xi}^2\hat u = 0
\]
And from that you get $\6{\hat u}{\xi, t} = \6{\hat f}\xi\6\exp{-\abs{\xi}^2t}$. But I am kinda stuck on how to compute the inverse Fourier transform of this now
amber waspBOT
@split sail Has your question been resolved?
split sail
no idea about how to solve but cant u plug the expression of u in the equation and see that it works ?
split sail
no idea about how to solve but cant u plug the expression of u in the equation a...
thats not u
thats u hat
aka the fourier transform of u
to "undo" the fourier transform you have to do something called the inverse fourier transform
i talked about the first equation written
but idk anyway
amber waspBOT
@split sail Has your question been resolved?
split sail
if root(ab) is rational, is root(a/b) rational?
amber waspBOT
if root(ab) is rational, is root(a/b) rational?
split sail
hi
split sail
if root(ab) is rational, is root(a/b) rational?
well a and b both are rational
tawny herald
$\sqrt{ab}=\frac{x}{y}$ so $ab=\frac{x^2}{y^2}\implies a=\frac{x^2}{b\cdot y^2}$
Hence, $\sqrt{\frac{a}{b}}=\sqrt{\frac{x^2}{b^2y^2}}=\frac{x}{by}$
grizzled pagodaBOT
PajamaMamaLlama
tropic atlas
opal aurora
Hey