No it shouldn’t
#help-0
vapid shuttle
Ah yes because
Yes
But
The undefined piece
As in part(a)
We can cancel (x-2)/(x-2)
Unless
x=2
Right? Can’t divide by zero… but that point of discontinuity is exactly what we are limiting to
Limit don’t care about the point the limit is at
They only care about near that point
So it doesn’t matter if we have that removable discontinuity or not, because we aren’t really considering x=2 exactly
And if we were, the fact that it is a removable discontinuity tells you something special
That the limit approaching that point exists
Otherwise it would be a jump/infinite discontinuity
Which it’s not
lone heartBOT
@alpine sable Has your question been resolved?
opal sphinx
lone heartBOT
opal sphinx
I'm confused
isn't 13 ft/sec^2 just 13x expressed as a function, so we can take the integral and find the velocity function 13x^2/2 and then just solve for x at 51mph?
prime badge
if the units don't match proly no
opal sphinx
if the units don't match proly no
I'm pretty sure they do
51mph is exactly 74.8 ft/sec
opal sphinx
Why not?
prime badge
you're just ganing speed
prime badge
yep
gritty pond
What day of the week is 9 September 2046?
lone heartBOT
What day of the week is 9 September 2046?
tacit arch
What day of the week is 9 September 2046?
is this a hw question
gritty pond
is this a hw question
yes
gritty pond
i think we need to use mod arithmetic
saturday
saturday?
approx 52
just looked it up sept 9 next year is monday
not saturday
and sep 9 2046 day is sunday???
then, how do we solve it?
stark crater
How many days are there left this year?
How many days are there in the next 22 years (assume every year has 365 days)?
subtract the amount of leap years there are now.
How many days are there in the first 8 months of a year (assume every month has 31 days)?
subtract 3 for feb, 1 for april, and 1 for june
add 9 for 9th day of the month
You can mod 7 every step to do w/o calc
lone heartBOT
@gritty pond Has your question been resolved?
winter crescent
i figured it out
lone heartBOT
Available help channel!
tight locust
Prove that:
2^(2n) - 2^(2(n-1)) divisible by 3
lone heartBOT
Prove that:
2^(2n) - 2^(2(n-1)) divisible by 3
tight locust
So like 16 - 4 = 12
proven leaf
may I suggest first rewriting $4^{n}-4^{n-1}|3$ then here a good old proof by induction should suffice :)
ocean sealBOT
PajamaMamaLlama
tight locust
I want to show it algebraically
tight locust
Ah
(2^n - 2^n-1)(2^n + 2^(n-1)
2^(n-1) (2-1) (2+1) = 3 × 2^(n-1)
Oh shit yeah
Makes complete sense
Because it's exactly halfway
sour verge
I mean you could also just factor out 2^{2(n-1)} straight out of the original equation.
Also works, but easier to work out with difference of square.
lone heartBOT
@tight locust Has your question been resolved?
austere compass
The exponential map for matrices is defined by
$$
\exp : \mathbb{R}^{n,n} \rightarrow \mathbb{R}^{n,n}, \quad \quad A \mapsto \sum^{\infty}{k=0} \frac {A^k}{k!}.
$$
We consider $\mathbb{R}^{n,n}$ with the norm
$$
|A|{op} = \sup_{x\in \mathbb {R}^n\setminus{0}} \frac{|Ax|_2}{|x|_2},
$$
where $| \cdot |2$ is the Euclidean norm on $\mathbb{R}^n$.\
\
(a) Show that $\exp$ is well-defined, i.e. $\left(\sum^n{k=0} \frac{A^k}{k!}\right)_n$ is a Cauchy sequence and converges for all $A \in \mathbb{R}^{n,n}$.
ocean sealBOT
Levens
lone heartBOT
@austere compass Has your question been resolved?
austere compass
<@&286206848099549185>
lone heartBOT
@austere compass Has your question been resolved?
austere compass
can someone help lol
lone heartBOT
@austere compass Has your question been resolved?
opal sphinx
Any good concept videos on the fundemental theorem of calculus
opal sphinx
so I can better understand integrals
When I say concepts I mean those types of videos where you get the concept behind something, not really the specifics and shit
opal sphinx
3blue1brown essence of calculus
I'll check it out thx
hushed locust
opal sphinx
.close
lone heartBOT
Available help channel!
visual flume
lone heartBOT
visual flume
Use the disk method to find volume problem.
I understand that I am supposed to get x in terms of y, but I don't know how to do that with these kinds of problems.
It doesn't make sense to me tbh.
All of the examples my teacher gave didn't have these kind of problems with mismatched values.
Not without a simple way to convert them.
lone heartBOT
@visual flume Has your question been resolved?
visual flume
nope
visual flume
.close
median vessel
lone heartBOT
median vessel
how do I get this
finite flax
how do I get this
using FTC 1, iirc
when you integrate g(x) from a to b, you get G(b) - G(a).
when you integrate a constant "c" with respect to x (since our function g is a function of x) from a to b, you get c(b - a).
the thing is, since these are definite integrals (we are integrating from a lower bound to a higher bound, a and b, respectively, we are really doing
$\int_a^b g(x) = G(b) - G(a)$
ocean sealBOT
Disorganized
finite flax
this is FTC 1
("Fundamental Theorem of Caluclus Part 1")
@median vessel
let me know you're alive and I'll continue
finite flax
alright, so even though we don't know what g(x) is, we can use the definition, get a system of equations, and end up with what we need
hm, I might have made a mistake
let's go through it
the first integral:
integration is a linear operator, which means we can split the terms into two integrals.
Another property of linear operators is that we can pull out the constant coefficients.
so the first integral is
$\int_{-1}^{3} 2g(x) + 4 dx = 2\int_{-1}^{3} g(x) dx + 4\int_{-1}^{3} dx$
median vessel
k that makes sense
ocean sealBOT
Disorganized
ocean sealBOT
Disorganized
ocean sealBOT
Disorganized
median vessel
**Disorganized**
wait how
finite flax
what algebra
I told you we were going to rearrange the equation so we had the g's on one side
ok
now, when we do the next one, we will get another linear equation involving g(-1) and g(10).
Let's do that
$\int_{10}^{-1} g(x) dx = 12$
ocean sealBOT
Disorganized
finite flax
here's where I messed it up
notice that the "lower bound" and "upper bound" are backwards here
I mean, this is allowed
but (I guess) for us to use our integration rules as we know them, we need to reorganize the upper and lower limits to match properly
and there is a formula for that
median vessel
and there is a formula for that
it's the negative right?
ocean sealBOT
Disorganized
ocean sealBOT
Disorganized
finite flax
$-G(10) + G(-1) = 12$
ocean sealBOT
Disorganized
finite flax
ok, now we can make a system of two linear equations
G(3) - G(-1) = 3
-G(10) + G(-1) = 12
ugh
I'll figure out the LaTeX formatting later
notice that if we add these together, the G(-1) will cancel
G(3) - G(10) = -9
G(10) - G(3) = 9
using FTC 1 again, this is
$\int_{3}^{10} g(x) dx = 9$
ocean sealBOT
Disorganized
finite flax
@median vessel
also, earlier, I fogot to uppercase the fuction g(x) after integration
I hope that pattern is clear to you
integrated functions are capitalized
median vessel
sorry I'm copying down the equaltions rn
median vessel
I hope that pattern is clear to you
nah dw about it, it was very clear
Thank you so much for your help!!
finite flax
np
lone heartBOT
@median vessel Has your question been resolved?
jade viper
Why does 1/1^2 + 1/2^2 + 1/3^2 .... converge to pi^2/6?
lone heartBOT
Why does 1/1^2 + 1/2^2 + 1/3^2 .... converge to pi^2/6?
wise spruce
Many videos online about it
lone heartBOT
@jade viper Has your question been resolved?
exotic canopy
Why does 1/1^2 + 1/2^2 + 1/3^2 .... converge to pi^2/6?
look up basel problem
alpine sable
Why does 1/1^2 + 1/2^2 + 1/3^2 .... converge to pi^2/6?
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.
prime seal
What did I do wrong here?
lone heartBOT
What did I do wrong here?
prime seal
Why can I use that substitution I used
lone heartBOT
@prime seal Has your question been resolved?
north perch
U assumed tanx/2 as' u' but u substituted it in place of tan^3(x) as u^3 which is incorrect
@prime seal
prime seal
U assumed tanx/2 as' u' but u substituted it in place of tan^3(x) as u^3 which ...
Ah I see thanks
north perch
Wc
honest folio
Why do the «du» part disappear?
lone heartBOT
Why do the «du» part disappear?
still ibex
Like 4 is incorrect
Line 3 reads “the integral of the square root of u with respect to u”
And your workings in the box in the top right
The second line in the box should read du = 3x^2 dx
alpine sable
Why do the «du» part disappear?
the correct way to write it is: [
\dd u = 3x^2 \dd x
]
ocean sealBOT
honest folio
Like 4 is incorrect
Ahhh true, thanks!
honest folio
the correct way to write it is: \[
\dd u = 3x^2 \dd x
\]
Thanks!
lone heartBOT
@honest folio Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
slender scaffold
How do I do B
lone heartBOT
How do I do B
slender scaffold
How do I do B
For maximum height I know it is m g h
But energy is not given
So how do I find out h
alpine sable
what is "the green"
slender scaffold
what is "the green"
Ground Level I think
Basically x level 0
No
Y level 0 yes
lament wyvern
yeah the green = the golf course
slender scaffold
Yeah, so velocity is given but im confused because kinetic energy cannot equal gravitational potential energy
@alpine sable @lament wyvern anything?
<@&286206848099549185>
leaden scroll
I got a ping but can't see anything
slender scaffold
How do I do B
@leaden scroll
lone heartBOT
@slender scaffold Has your question been resolved?
worn fox
You know the speed of the ball at max height
lone heartBOT
lone heartBOT
Available help channel!
stable grotto
lone heartBOT
lone heartBOT
@stable grotto Has your question been resolved?
rigid smelt
for part b, consider that you have proved if $\lim_{x\to \infty} a_{n} = L$, then $f(L) = L$. Hence, here you get that $\cos(L) = L$
ocean sealBOT
waler
rigid smelt
the value of a should not be a concern here
stable grotto
i don't get this
rigid smelt
alright, so for part a, everything is clear for you, yes?
just need you to agree with me on part a
stable grotto
alright, so for part a, everything is clear for you, yes?
yes
rigid smelt
great, so now consider the sequence $a_{n+1} = cos(a_{n})$, such that $\lim_{n\to\infty} a_{n} = L$, then we have that $\cos(L) = L$
ocean sealBOT
waler
rigid smelt
i'm basically just restating part a, where I know f(x) = cos(x)
rigid smelt
hmm?
stable grotto
and why are you using cos(L)=L formula in the first place?
rigid smelt
we jnow that A=>B but we di mot kniw that B =A ?
what exactly do you mean by this?
stable grotto
if limit of a_n is L then cos L = L but reverse might bot be true
rigid smelt
yes, but I'm not saying that is cos(L) = L then the limit exists
I'm assuming that the limit exists, and thus, cos(L) = L
stable grotto
ok
rigid smelt
I haven't entirely proved that the limit converges at all, I'm just assuming that it does
stable grotto
idk how to solve that
rigid smelt
one common approach to estimate this by hand is newton's method
which also is the most straight-foward way
stable grotto
ok but is it even solvable ?
rigid smelt
solvable as in does a solution exist? Yes
Solvable as in is there a closed form? Also yes, it's called the dottie number
stable grotto
simple looking equation and so complicated lol
ok i understood everything but
we assumed that limit exists
and we are saying that if limit exists than it is that D number
but what if that limit dne at all
how we know that limit exists
rigid smelt
well in this context, it doesn't really matter since the question assumes it.
Out of topic, the limit actually exists, a proof is done through the use of banach fixed-point theorem
I don't remember the full proof, but idea was that f(x) is a contraction mapping, hence for each iteration of applying f, the distances between each value of applying f onto itself gets closer and closer to 0
hence it implies after some point of applying f onto itself, it will converge to some value
midnight ingot
I asked this question previously. However, I want to verify if what I did here is correct
midnight ingot
Can I use =? In this case?
lone heartBOT
@midnight ingot Has your question been resolved?
wraith marlin
help
north perch
Do u know what is inflection point
It's the midpoint of maxima and minima
@wraith marlin
wraith marlin
yea
wraith marlin
It's the midpoint of maxima and minima
but how’d they get -7
as an inflection point
where did that come from?
north perch
-7 is y cordinate of the point
north perch
Do u know how they got 1?
north perch
Oh ok so a point on a graph is written as (x,y) where x is x cordinate and y is y cordinate. Here y=x^3-3x^2-9x+4 so if x is 1 , y would be -7
wraith marlin
what-
north perch
It's given
wraith marlin
hold on
north perch
In the question
north perch
Is it done
north perch
Wc
north perch
lone heartBOT
vernal prawn
Just assume a moving point and chuck in those conditions
north perch
I did and got a eqn of degree 4
north perch
Assume MBA as 2alpha and mab as alpha
Then tan alpha=(y)/(x+1)
Tan 2alpha=(y)/(x-2)
Then I used the formula for tan2alpha
Nvm i got it
.close
normal trail
Hi how do you determine the number of roots by just look at it?
normal trail
Do you multiply the first variable to the exponent outside the parenthesis?
swift thorn
first you expand
gray isle
you'd first want to factorise the quadratic expressions 9x^2 - 16
and (2x^2 + x - 3)
just to make it easier to make sure you're not double counting certain roots
ocean whale
you'd first want to factorise the quadratic expressions 9x^2 - 16
and (2x^2 + x ...
But do you need that? The question is how to know total number of roots, so don't you just look at the leading power of the factor and the exponent?
gray isle
depends if you care about uniqueness/multiplicity
normal trail
I only need the total number of roots not the actual ones where you need to solve it
normal trail
But do you need that? The question is how to know total number of roots, so don'...
Can you please elaborate? Thanks
I'm kinda confused if there are 8 roots or 5 roots
ocean whale
Do you multiply the first variable to the exponent outside the parenthesis?
It's almost what you said here, except more specifically, it's the leading power, not just the first variable. For example, (4x - x^2)^2 would have 4 roots because the leading term is x^2 but then you have the exponent so (x^2)^2 = x^4 so 4 roots
The first variable in my example would technically be 4x but not the leading power
normal trail
Wait so in (4x-3)^2, there are 3 roots? Cuz you said the leading power should be multiplied to the exponent
So like (x^1)^2
Is that correct?
ocean whale
Not quite 3
gray isle
what's the exact wording of the question
normal trail
Not quite 3
Why? I thought x raised to nothing is automatically x^1
ocean whale
So like (x^1)^2
That's not raised to nothing
It's raise to 2
Oh you meant x
Yeah, x = x^1
But (x^1)^2 is not x^3
You don't add the powers
gray isle
I'm kinda confused if there are 8 roots or 5 roots
depends if you care about uniqueness/multiplicity
and that depends on
exact wording of the question
normal trail
Wait so (9x^2-16)^2 has 4 roots? You just multiply the leading exponent to the exponent outside the parenthesis? Not add?
normal trail
Wdym by unique roots?
ocean whale
Well, (9x^2-16)^2 = (9x^2-16)(9x^2-16) so that root repeats twice, meaning that (9x^2-16) is a root that will repeat
normal trail
Ohh okayy
normal trail
Hi how do you determine the number of roots by just look at it?
So in this equation there are 8 roots?
ocean whale
> I'm kinda confused if there are 8 roots or 5 roots
>
> depends if you care ab...
.
That's what ramonov meant
normal trail
Oh i need the multiplicity one
ocean whale
Are you asking for total or uniqueness/multiplicity?
normal trail
That's what ramonov meant
Ohh i get it sorry i was kinda confused earlier
normal trail
Are you asking for *total* or *uniqueness/multiplicity*?
Total one like with the duplicated roots
ocean whale
Total means you don't care about uniqueness, all you want is the overall amount of roots
ocean whale
Wait so (9x^2-16)^2 has 4 roots? You just multiply the leading exponent to the e...
Like with this, again, it has 4 total roots but 2 unique ones
normal trail
Total means you don't care about uniqueness, all you want is the overall amount ...
Oh
ocean whale
To make life less confusing, can you send the full question taht you are working on?
Including the instructions that comes with it
normal trail
Wait so there are 5 roots if its based on the multiplicity and there are 8 roots if its based on the total number of roots?
ocean whale
Wait so there are 5 roots if its based on the multiplicity and there are 8 roots...
Yes, in your equation given, there are 8 total roots but only 5 unique ones
normal trail
Ohh okay that made sense ,, We were always asked to just find the roots and they didn't specify if its total or unique thats why I am also new to those terms
Okay thanks guys :))
.close
strange fractal
How come on my calculator
lone heartBOT
How come on my calculator
pseudo ice
Can you show the full input you're putting in? Like scroll right a bit?
strange fractal
Its solve (log(1.022) 1000000/720500
pseudo ice
Maybe try it without solve?
ocean whale
I'm pretty sure solve tries to find an unknown solution set
pseudo ice
After all, you haven't really given anything to "solve" as such, you just want to calculate the value
ocean whale
Not evaluating
pseudo ice
What I'd assume 
golden nebula
2 * x=10 , x is NOT 5 (aka a question I got on my math exam)
pseudo ice
My exams tomorrow
Awww 
hopefully it goes well 
strange fractal
Awww <a:SChug:767629974353608717> hopefully it goes well <:catlove:9206987629329...
Ikkk its my last exam too
ocean whale
It's asking for a box and whisker plot so I don't know if that calculator can draw that
strange fractal
It's asking for a box and whisker plot so I don't know if that calculator can dr...
Oh it can
ocean whale
Then yes, put the values in the table and make a box and whisker plot
ocean whale
The calculator should automatically do that
strange fractal
ocean whale
Then that, you should look up that manual for
To see how to find the scale
But it might be the 4th item on the top, the one with the box and 4 arrows pointing to each side
strange fractal
Whats the difference beteeen sample standard deviation and population standard deviation
lone heartBOT
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).
ocean whale
And please don't troll
ocean whale
Whats the difference beteeen sample standard deviation and population standard d...
This one I'm not sure
Maybe @pseudo ice can answer it
pseudo ice
Maybe <@788085606483361802> can answer it
not sure either tbh, me no stats 
strange fractal
I hate stats
This is the most boring thing in my life
Thats why im doing calculus next yr
.close
icy notch
hi i need help with this question, i have no idea how on how to plot it cuz i cant i dont know the variables
lone heartBOT
hi i need help with this question, i have no idea how on how to plot it cuz i ca...
@icy notch Has your question been resolved?
jovial relic
who can help
pine bridge
well thats simple : imagine a square
wild umbra
who can help
"angle between line KM", this statement sounds kinda incorrect to me
pine bridge
you see that every angle is 90 degrees or 45 (it depend of which points you choose)
wild umbra
oh okay it continued in the second line
gaunt turret
how do i divide polynomial functions
lone heartBOT
how do i divide polynomial functions
gaunt turret
2x+4 ÷ 8x^2+12x-8
how am i gonna start dividing this
carmine reef
did you write them in the wrong order?
carmine reef
that's okay
gaunt turret
its 12am and im cramming aaa
carmine reef
8x^2+12x-8 / 2x+4
so for long division it starts like
How many "times" does 2x+4 go into 8x^2+12x-8
which means dividing the leading coefficients by each other
gaunt turret
4x??
carmine reef
Yeah
So if we look at (2x+4)(4x), that's 8x^2+16x
Which is a good start
Our first term is right
carmine reef
nah ur not
gaunt turret
thank youuuuuuuuuu , i get it now
i can finally sleep
SO LIEK MY ANSWER IS 4X-2
is it wrong]
gaunt turret
.close
misty kraken
Can someone help me with N and O
lone heartBOT
Can someone help me with N and O
misty kraken
What have you done so far ?
for number O
I tried subtracting the square from circle
pie x 2.5^2 - 5^2
answer doesnt match
it's supposed to be 72.7
half vapor
so basically
alpine sable
can u provide complete info of the Q
half vapor
for number O
did u solve question n?
alpine sable
n is solved, it's just that info for o is incomplete...
misty kraken
did u solve question n?
yes
Q doesnt have anymore info than what is provided
Ig we gotta assume it is square
worldly sail
Hey there, senior here ... What's the problem here ...
alpine sable
Ig we gotta assume it is square
yes sir
half vapor
what abt next one
misty kraken
Hey there, senior here ... What's the problem here ...
need help with umber O
alpine sable
well if we gonna assume the shape inside the circle is square so then it is solved
worldly sail
Number o seems like it has incomplete info... Just given one side, we can't determine the anything...
misty kraken
Number o seems like it has incomplete info... Just given one side, we can't dete...
assume it's square
half vapor
it should be 2.5
misty kraken
yes
alpine sable
half vapor
l^2 =d^2(pythogaras)
5^2=d^2
25=d^2
d=5
r=d/2
r=5/2
r=2.5
worldly sail
Well, considering it's a square, @senn800 you might be correct...
worldly sail
But I have an idea... It might just solve it...
Do you have any idea of the Pythagorean triplets...
half vapor
ok its not a square then
worldly sail
Try doing a Pythagorean triplets for 5...
Where the base is 5...
Nvm, it doesn't work...
misty kraken
the area of the shaded part is 72.7
alpine sable
brah what type of pythogras therom is this
half vapor
question should be wrong
alpine sable
true
misty kraken
answer is 72.7
half vapor
answer is 72.7
what book is tht
misty kraken
what book is tht
not book
worksheet
a worksheet given by my teacher
if u use pythagorean triplet
and u assume it is a rectangl
diamater is hypo
radius comes
6.5
pie x 6.5^2 - 5 x 12 comes 72.7
which is the correct answer
might have been printing mistake for not including that it is a rectangle
lone heartBOT
@misty kraken Has your question been resolved?
desert fractal
Is this correct?
lone heartBOT
Is this correct?
honest folio
Is this correct?
Lemme check, Ill get back to you in 2-3 work days.
desert fractal
2-3 days?? But this only took me 7 hours to write down. Shouldnt take you that long to check
Smh
pseudo ice
Is this correct?
desert fractal
.. oh no
pseudo ice
I will make the comment that you could have simplified that a bit more
desert fractal
Wait, how?
pseudo ice
That you could have written that as $\frac12 \ln(3x + x^2) =\frac12\pqty{\ln(x) + \ln(x + 3)}$
ocean sealBOT
@pseudo ice
void nymph
$\frac12$
ocean sealBOT
Percy
pseudo ice
,w diff ( sqrt(3x + x^2) * (4x^3 + 3) ) / (2x^2 + 1) wrt x
ocean sealBOT
void nymph
ooh now this is interesting lmao
pseudo ice
Is this correct?
Seems like your final answer is good tho 
pseudo ice
Or if there were any, they cancelled each other out 
But gonna guess it’s all good I think 
gritty pond
What day of the week is 6 September 2045?
lone heartBOT
What day of the week is 6 September 2045?
keen pasture
I think google can figure it out faster
tacit arch
What day of the week is 6 September 2045?
you've asked this question multiple times with multiplre responses already. what more are you hoping for
gritty pond
gritty pond
you've asked this question multiple times with multiplre responses already. what...
My answer is never right for random dates and i dont know how this solution works
tacit arch
yea you've been presented with multiple responses already
gritty pond
is there any video that I can watch that is like "date arithmetic"?
cuz i memorized this already
but still after doing it it dont work
and the solution in the book makes zero sense
tacit arch
Why does it make 0 sense
gritty pond
how do we get wednesday from this
and how do we even get the answer from one date
i thought we need a reference
where did 7 jan 1998 come from
ik leap years are multiples of 4 but not 400
366 days in those
tacit arch
where did 7 jan 1998 come from
Like I said before, it's just an arbitrary starting date
You pick any year
Do 2023 and the solution will look similar, just numbers will be different
gritty pond
Do 2023 and the solution will look similar, just numbers will be different
so what is sol for 2023
how do we pick any year
i thought we need to have a day of the week associated
tacit arch
Just follow this. Calculate leap years, then remaining first
tacit arch
how do we pick any year
You just do
Pick a year where you know the day of week
Do you know what day of week is Jan 1 2023?
tacit arch
i thought we need to have a day of the week associated
That can come later
tacit arch
The important part is working how many days are between your chosen start date and Sep 6 2045
gritty pond
Do you know what day of week is Jan 1 2023?
Jan 1 2023 is Sunday
gritty pond
The important part is working how many days are between your chosen start date a...
The sol up there doesn't make sense cuz it doesn't even specify a chosen start date
tacit arch
The sol up there doesn't make sense cuz it doesn't even specify a chosen start d...
It does
You have to read the whole thing
gritty pond
The chosen start date is 7 January 1998?
tacit arch
They worked that out yes
gritty pond
it doesnt even include the time between January 1998 and beginning of next year 1999
tacit arch
The important part is working how many days are between your chosen start date a...
Once you do this and figure out the residue mod 7, then you can change Jan 1 2023 to another date that week
,w day of week Sep 6 2045
ocean sealBOT
tacit arch
,w day of week Jan 1 2023
ocean sealBOT
tacit arch
,w days between Jan 1 2023 and Sep 6 2045
ocean sealBOT
tacit arch
Should be 3, not 4
tacit arch
Shouldn't be 6 no
You have to understand what it's counting
31(5) is correct do you know why?
gritty pond
31(5) is correct do you know why?
everything else is correct yes?
366(6) is the leap years and 365(16) are the regular years (total - leap )
total is 22 years
from Jan 1 2023 to Jan 1 2045
which is this
So we are now at sept 1 2045
so add 6 get sept 7 2045
mod all of it to get 4
which is 4 days after Sunday
wich is thursday
gritty pond
31(5) is correct do you know why?
oh so i think its sghould add 5 instead
cuz from Sept 1 2045 we should add 5 days to get to sep 6 2045?
then its good?
tacit arch
Yes
tacit arch
Should be 3, not 4
4-1 = 3 and you're done
lone heartBOT
@gritty pond Has your question been resolved?
lyric pulsar
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fickle mesa
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mellow frigate
this double integral should give me area right
lone heartBOT
this double integral should give me area right
celest stump
Doesn't 1 integral give u area
olive oar
If k=1, then $$A(D) = \iint_D k dxdy.$$
ocean sealBOT
Zander
jagged cobalt
you cant cancel like that, whatever it is you were doing
im not entirely sure
id recommend perhaps factorising the numerator of the first fraction first
expanding the denom was unnecessary
lone heartBOT
cinder egret
sorry for that
mint ruin
mint ruin
oh
thick lynx
(you can't)
mint ruin
ok
cinder egret
open a channel
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tardy fern
how do you show this
lone heartBOT
how do you show this
tardy fern
?
tall topaz
,, \sqrt{\left(\sqrt 2 \right)^2 +2\sqrt{2}\sqrt{3} + \left(\sqrt 3 \right)^2}
ocean sealBOT
Pure
tardy fern
ohhh
i should've squared both sides
and then saw the connection
ok ty guys
.close
lone heartBOT
tall topaz
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rich timber
hi
rich timber
so this is my question
im struggling on both really
my issue is wording of the question
maybe someone else can help reexplain it to me?
i just dont understand what its purely asking me to do
my first step would be to multiply the x variable by a multiplier of 1/4
then
talk about adding the cos?
pseudo ice
Basically you can write $4\cos(2x) + 3\sin(2x)$ as some set of transformations of $\sin(x)$
ocean sealBOT
@pseudo ice
pseudo ice
So for example you could transform sin(x) to sin(2x) and that's one part, but there are some more transformations you'd need to do
Expressing that 4cos(2x) + 3sin(2x) as some scalar multiple of sin("sonething") may be a good idea
rich timber
please elaborate on that further
i am understanding that i need to scale up my sinx to sin2x
but how would i able to imply that while being respective to cos?
lavish holly
sorry to barge in, but is it not sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
pseudo ice
Are you familiar that given constants $a, b$, you can write $a\sin(y) + b\cos(y) = R\sin(y + \alpha)$ for some $R$ and $\alpha$ depending on $a$ and $b$
ocean sealBOT
@pseudo ice
pseudo ice
sorry to barge in, but is it not sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
tl;dr use this and the above
rich timber
could i do sinx as sin(x/2 + x/2)?
then i can get 2sinx/2cosx/2?
actually no
dont work
so our first transformation would be by dividng the collective of x coordinates by 4?
our second
is applying the rule of sin(a+b)
and our third is multiplying the y coordinates
by a number that shows 4 and 3 on their respective coeffecients?
and for b?
what does it suggest by range?
.close
cold zephyr
Is it possible to solve for x and y?
lone heartBOT
Is it possible to solve for x and y?
cold zephyr
im assuming it isnt
dim oasis
Sure is, know much trigonometry?
cold zephyr
i know a bit
i drew that bad the 51 is out side of the rectangle
i tried to draw a straight line
dim oasis
There are some trig ratios you can use with the angle and hypotenuse length to identify them
Oh that's that angle
cold zephyr
yeah
dim oasis
Hm 🧠
cold zephyr
yeah i know how to do it if it was inside
lone heartBOT
@cold zephyr Has your question been resolved?
hushed locust
we would need some information about the interior angles of the triangle, so the 51° is pretty much useless unless we know some other angle that horizontal line makes (e.g. if it was perpendicular or parallel to some other line in the figure)
cold zephyr
we would need some information about the interior angles of the triangle, so the...
this wouldnt help would it
i dont think this problem is possible
cold zephyr
this wouldnt help would it
assume this is like straight btw
and connects to that corner of the rectangle
hushed locust
not really, no. you could draw the same figure that even if we swapped 51° for any other acute angle
hushed locust
not without more information, no
jovial herald
lone heartBOT
jovial herald
i’m completely lost i know the basic formulas for arithmetic sequences but the teacher didn’t teach anything like this
6th term is 4 20th term is 46 find first term and common difference
i can find the formula once i get those two
lone heartBOT
@jovial herald Has your question been resolved?
peak stag
how do I show this?
lone heartBOT
how do I show this?
peak stag
I draw this, but have no idea how to continue
i was thinking to apply the sine law here somewhere
.close
crude hawk
Hii! I hope you are having a nice evening. I am having some trouble understanding this exercise.
"Simplify each expression. Suppose that
the literals represent positive real numbers."
crude hawk
When I simplify the expression, I am left with it being = xy^2. Then the original expression is equal to xy^2.
long axle
Uh
tall topaz
youre right
long axle
What do u need help w
tall topaz
crude hawk
I wanted to check with wolfram alpha and it tells me that this is true if x and y are positive, why? I tried to evaluate both expressions with x = -2, y = -3, x = 2, y = 3 and its always true
Then why does it only work with positive numbers?
Yeah, sorry, I was typing hahaha
How do I find a case where it is not true if x or y are not positive?
open marten
tall topaz
I wanted to check with wolfram alpha and it tells me that this is true if x and ...
wolfy said that?
,w cbrt{x^3y^6} = xy^2
lol thats a weird output
tall topaz
open marten
Then why does it only work with positive numbers?
Hmm ?
For Something like x³y⁶= -6 it's (-6)^(1/3) = +1.something
Which is can use negative numbers (-6 is negative)
open marten
I wanted to check with wolfram alpha and it tells me that this is true if x and ...
Yea it's will always give values
crude hawk
Yes, sorry. Maybe it was a dumb question. I'm confused that the calculator clarifies that it works assuming x and y are positive, when it also works with all the negative numbers I'm testing.
Thank you guys
tall topaz
crude hawk
.close
cloud wing
Hey everyone, I need help with one probability problem: Suppose that you perform the following experiment. First you roll a fair 6-sided die and its outcome is o1. If o1<3, you roll a second six-sided die. If o2>3, you roll a fair 12-sided die. Let R(o1,o2)=o1+o2. What is E(R|o1<6)?
strange meadow
Did you mistype the question?
tribal haven
break it down into cases
cloud wing
lone heartBOT
@cloud wing Has your question been resolved?
lone heartBOT
@cloud wing Has your question been resolved?
lone heartBOT
@cloud wing Has your question been resolved?
stiff orchid
lone heartBOT
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Available help channel!
wary spear
lone heartBOT
wary spear
i have no clue how to do this
snow cobalt
okay
if the monkey keeps "x" percentage of his bananas each day
then how many bananas does he have the next day before eating one?
plucky tree
lone heartBOT
plucky tree
Trying to help my cousin with his algebra homework, before showing him, would this be correct?
vapid shuttle
it isn't clear
one of the lines should be a dashed line
to indicate that it is not included in the region
and the other line should be solid
and I can't tell what you have
plucky tree
one of the lines should be a dashed line
Y int +2 line is dashed
vapid shuttle
okay, then it's fine
plucky tree
I’m confused on how to know which region to shade
vapid shuttle
well
if it says greater than
then you shade above the line
if it says less than
you shade below the line
if it is less than or equal to (or greater than or equal to) then the line is included, since you can be equal to the line
otherwise, the line is dashed
plucky tree
if it is less than or equal to (or greater than or equal to) then the line is in...
Is this correct?
vapid shuttle
looks good
plucky tree
So less than or equal to or less than = shade below
Then greater than or equal to or greater than = above
vapid shuttle
yes, it is asking you to shade the region that is less than (below) that line
compared to greater than (above) the line
plucky tree
Ah okay thank you
vapid shuttle
np
vapid shuttle
Ah okay thank you
!done
lone heartBOT
Ah okay thank you
If you are done with this channel, please mark your problem as solved by typing .close
vapid shuttle
yes, but not sure why you didn't shade the little tiny triangle u missed
plucky tree
Just didn’t get down there
vapid shuttle
looks good
plucky tree
vapid shuttle
!1q
lone heartBOT
It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.
plucky tree
!done
lone heartBOT
If you are done with this channel, please mark your problem as solved by typing .close
plucky tree
.close
lone heartBOT
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mighty cliff
Find the radius of the sphere circumscribed around a triangular pyramid, the three edges of which are perpendicular in pairs and have lengths a, b, c (how to solve this problem? Otherwise I'm in a stupor
)
lone heartBOT
Find the radius of the sphere circumscribed around a triangular pyramid, the thr...
@mighty cliff Has your question been resolved?
mighty cliff
<@&286206848099549185>
wise spruce
does that line go through the centre of the sphere
it looks like it does to me
if not idk how to solve
jagged sigil
Yes, if it is 90 degree, just use Pythagoras and easy solution
I mean, if it's going through the centre, the angle BAC1 will be a right angle.
mighty cliff
I think not, since the center lies approximately above the middle of AB
jagged sigil
Then, the question is incomplete.
lone heartBOT
@mighty cliff Has your question been resolved?
grim olive
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pseudo ice
Note that $\log_a(x)$ is a decreasing function when $0<a<1$, which is what I'm assuming the question is going to be
ocean sealBOT
@pseudo ice
pseudo ice
Alternatively if you make use of change of base to, say, the natural log, note that $\log_{0.5}(x^2 + x) = \frac{\ln(x^2 + x)}{\ln(0.5)}$ but that $\ln(0.5) = -\ln(2)$ is negative, so multiplying it out reverses the inequaltity
ocean sealBOT
@pseudo ice
pseudo ice
Similar for base 10 too 
grim olive
shall I firstly establish range of acceptable values?
pseudo ice
That might be a good idea to do 
mind you, do you want help solving it from the start?
alpine sable
lone heartBOT
summer quarry
lone heartBOT
summer quarry
,rotate
ocean sealBOT
tall topaz
thougths?
tall topaz
you can try rationalising the denominator
summer quarry
Hm
tall topaz
,, \lim_{x \to 3} \frac{\left( x^3 - 9\sqrt{x+6} \right)\left( x^3 + 9\sqrt{x+6} \right)}{(x^2 -9)\left( x^3 + 9\sqrt{x+6} \right)}
ocean sealBOT
Pure
ocean sealBOT
summer quarry
Uhm this?
tall topaz
should be ( x^6 -81x - 486 )
ocean sealBOT
Pure
summer quarry
Ohh I forgot about 81x
I was afraid of x⁶ is too big so I kept it as (x³)² instead
Same with 81.6
summer quarry
Same with 81.6
And should be -
summer quarry
should be \( x^6 -81x - 486 \)
What to do with the x⁶ now 
are we going to do the Hoocner thingy?
tall topaz
notice that ( (3)^6 -81\cdot 3 - 486 = 0 )
ocean sealBOT
Pure
