#help-41
amber waspBOT
@tough mica Has your question been resolved?
split sail
Hey
Here you need to find distance of point E from AD not AB
tough mica
yeah
split sail
You can try drawing a line parallel to AB passing through point E
Since it's parallel to AB, it would be perpendicular to AD and CB
split sail
You can try drawing a line parallel to AB passing through point E
let's say this line intersects AD at point P and CB at point Q, so we need to find distance EP
do u now see how we can solve it?
tough mica
let's say this line intersects AD at point P and CB at point Q, so we need to f...
yeah
tough mica
do u now see how we can solve it?
no
split sail
If u draw the figure things would be clear, now say distance EP =x so EQ = 13-x
there are 2 right triangles one including EP and other EQ....so we just form 2 equations using pythagoras theorem and equate them to find value of x
tough mica
there are 2 right triangles one including EP and other EQ....so we just form 2 e...
after understanding everything I got stuck at the Pythagoras step
is my drawing accurate? let me indicate the right angle
tough mica
there are 2 right triangles one including EP and other EQ....so we just form 2 e...
we dont know AP or BQ
split sail
yeah, this is perfect!
split sail
we dont know AP or BQ
see you don't need to know that, just know that they both are equal, say you denote them with "a", and now try forming both the equations
tough mica
25 = x^2 + a^2
split sail
a^2
tough mica
144 = (13-x)^2 + a^2
split sail
gr8!
tough mica
144 - 25 = (13-x)^2 - x^2
split sail
exactly! yeahhh
tough mica
119 = 169 -26x^2 - x^2 - x^2
split sail
nah...you didn't open (13-x)^2 correctly
tough mica
,w expand (13-x)^2
grizzled pagodaBOT
split sail
26x=50
split sail
you solved it!
tough mica
,w 50/26
amber waspBOT
amber waspBOT
amber waspBOT
Available help channel!
shell talon
amber waspBOT
shell talon
How do I make it a piecewise function so that I can differentiate it
shell talon
Yea
grizzled pagodaBOT
artemetra
crisp stratus
in your case, 🐟 = x^2 - 4
amber waspBOT
amber waspBOT
Available help channel!
river brook
hi
if i want to prove something by induction, here i want to prove that in a sequence a pattern repeats for indices modulo 3
river brook
if i prove that xn+1=xn+4
xn+2=xn+5
xn+3=xn+6
is that sufficient to say x3k+1=x1
x3k+2=x2
x3k+3=x3
winged panther
if i prove that xn+1=xn+4
xn+2=xn+5
xn+3=xn+6
Yes. If you have proved this, it suffices to say that $x_m = x_{m-3}$
grizzled pagodaBOT
Arya
amber waspBOT
@river brook Has your question been resolved?
zenith galleon
how do i do this
you have to express a, the amount owed, in an expression that uses the original loan l, the interest rate i and the number n of years passed, for example:
a = l + i * n
This is a false formula, but you need the right one.
zenith galleon
simple interest or compound interest
what formula should i use
zenith galleon
nono what type of interest did they specify
it doesnt say lol
i found this
try a general formula that forks for any interest rate and any initial loan.
frank radish
where did you find this
zenith galleon
where did you find this
my teacher wrote it in my book lol
frank radish
still
frank radish
simple interest or compound interest
first of all do you know what these are
zenith galleon
first of all do you know what these are
compound interest is when the amount owed changes higher
right
than the usual rate
frank radish
compound interest is when the rate exponentially increases over time
zenith galleon
k
zenith galleon
simple interest or compound interest
i think its compound interest then
frank radish
did they tell you how many times the rate updates in a year
actually ill assume its simple interest
zenith galleon
did they tell you how many times the rate updates in a year
once
frank radish
they didnt mention anything about time
zenith galleon
actually ill assume its simple interest
k
frank radish
do you know how simple interest works
zenith galleon
its without interest adding up over time
frank radish
interest stilla dds up over time
honest galleon
interest is generally $P(t)=P_i\left(1+\frac{r}{n}\right)^{tn}$, where $P_i$ is initial amount, r is rate, and n is amount compounded. yearly would be when n=1 and monthly, n=12, etc. the interest rate does not change
zenith galleon
k
honest galleon
nevermind, simple interest is linear (it's been years since i've looked at this)
grizzled pagodaBOT
fish
honest galleon
yes
the initial incorrect formula in the question would be simple interest, so it wants you to use compound interest
honest galleon
nevermind, actually it does want you to use simple interest (i did not look at the formula)
zenith galleon
k
honest galleon
well, simple interest is $P_0+P_0(i\cdot n)$, since simple just adds $P_0\cdot i$ for each n
grizzled pagodaBOT
fish
zenith galleon
well, simple interest is $P_0+P_0(i\cdot n)$, since simple just adds $P_0\cdot i...
so if the initial amount was $2 with an interest rate of 0.5% it would be 4 (0.5 * 4) in 4 years
honest galleon
yes
zenith galleon
kk tysm
night sundial
amber waspBOT
night sundial
ill try to explain where im at
i begin with determining whether B is a bsis of V
first of all it holds that p(1) = 0
so we can continue
then i looked and saw B was independent, so it has only the trivial solution with coefficients = 0
idk what to do further
verbal jewel
assume q is in V, can you express q as a(1-t^2)+b(1-t)?
night sundial
assume q is in V, can you express q as a(1-t^2)+b(1-t)?
q = c1 + c2 x t + c3 x t^2
is this correct
night sundial
we can write (1-t^2)+b(1-t) = (a+b)1 - b(t) , a(t^2)
this is indeed in the form q
so we can write q as the linear combinations of the vectors in B
am i saying correct things? @verbal jewel
verbal jewel
if you have q = c1+c2t+c3t^2, and you should express q as a(1-t^2)+b(1-t), then i would (as proof) express c1, c2, c3 in terms of a and b.
night sundial
if you have q = c1+c2t+c3t^2, and you should express q as a(1-t^2)+b(1-t), then ...
i dont know how to do this
verbal jewel
whats the problem? c1+c2t+c3t^2=a(1-t^2)+b(1-t).
then compare the coeffizients of t^2, t and the constant term
and use q(1) = 0
night sundial
and use q(1) = 0
using this we get c1 + c2 + c3 = 0
night sundial
whats the problem? c1+c2t+c3t^2=a(1-t^2)+b(1-t).
i really have no clue
ohh
i get it
night sundial
if you have q = c1+c2t+c3t^2, and you should express q as a(1-t^2)+b(1-t), then ...
okay i have done this
what to do after?
amber waspBOT
@night sundial Has your question been resolved?
amber waspBOT
@night sundial Has your question been resolved?
verbal jewel
what to do after?
whats the question? what to do after what?
night sundial
after i have expressed c1 c2 and c3 in terms of a and b
verbal jewel
why do you want to do something after that?
night sundial
oh thats it?
verbal jewel
do you know what a basis is?
night sundial
do you know what a basis is?
a linear combination of independant sets?
ohh
we just proved they are linearly indepedant
so we can just take the basis
yes B is a basis
thank you
amber waspBOT
@night sundial Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
half rover
is this legit and legal
amber waspBOT
is this legit and legal
outer hull
the fact that you got a function is already wrong
outer hull
sub u = 2n - 1
as n approaches infty, so does u
thus you would have $\lim_{u\to\infty}\left(1-\frac1u\right)^u$
stupid keyboard
grizzled pagodaBOT
outer hull
which i'm sure you are familiar with
outer hull
yes, and you're done
half rover
o
oh wait does (1 - 1/thing)^thing always equal to 1/e
no matter what monstrosity "thing" is?
amber waspBOT
amber waspBOT
Available help channel!
shy sage
Anybody can explain how to solve this?
amber waspBOT
Anybody can explain how to solve this?
shrewd elm
is it true if x=0?
grizzled plume
winged panther
Bring all terms to left side and factorize: $x^2(2x^2 - 3x - 5) \leq 0$
grizzled pagodaBOT
Arya
winged panther
Anybody can explain how to solve this?
What difficulty are you facing with this?
shrewd elm
seems OP disappeared
amber waspBOT
@shy sage Has your question been resolved?
keen pawn
Let $(a_n)$ and $(b_n)$ be Cauchy Seqeunce, determine if $c_n = \abs{a_n - b_n}$ is a Cauchy sequence. As $(a_n)$ and $(b_n)$ are Cauchy , it follows that $\abs{a_n - a_m} + \abs{b_n - b_m} < \varepsilon$. From this it follows that $\abs{a_n+b_n - ( a_m + b_m)} < \varepsilon$
grizzled pagodaBOT
What a wonderful world!
wet breach
|a_n - b_n| is a distance formula.
wet breach
How can you ruin the Cauchyness of it by choosing a and b?
keen pawn
chose a_n to be positive and b_n to be negative
Let a be a seqeunce of 1s
b be the seqeunce of -2s
wet breach
I haven't done much Cauchy stuff, but what if the distance was constant?
wet breach
Oh, I get it.
keen pawn
So is the example fine?
wet breach
Yes, I think so. I'm new to Cauchy sequences, but you can't get it below an arbitrary epsilon if the sequence is a nonzero constant.
amber waspBOT
amber waspBOT
Available help channel!
tough mica
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
signal furnace
Start by angle chasing. (Like the last question)
tough mica
ACE = 180-(60 + 90)
prime gate
its a bunch of 30-60-90s
signal furnace
its a bunch of 30-60-90s
||EBC is a 15-75-90 triangle, which is what you need to actually do the question||
tough mica
ABD = 30
prime gate
||EBC is a 15-75-90 triangle, which is what you need to actually do the question...
oh yea
but just special triangles
tough mica
||EBC is a 15-75-90 triangle, which is what you need to actually do the question...
how so?
prime gate
angle chase
in triangle DBC we have angle BDC=90, angle DCE = 30
and the problem gives angle DBC = 3 *angle ECB
so angle DBC + angle ECB = 60 too
those who know 💀 💀 💀
tough mica
tough mica
dbc = 3ecb
prime gate
and they add up to 60
tough mica
and they add up to 60
tough mica
so dbc = 3k
tough mica
so now u have triangle EBC as 15-75-90
prime gate
yes then solve using 15-75-90 triangle ratios
tough mica
yes then solve using 15-75-90 triangle ratios
what ratio
prime gate
or use trig
prime gate
Ratio of the sides=(2− sqrt(3)):(2+ sqrt(3)): 4 btw
short leg : long leg : hypotenus
trig is easier
sin (angle EBC) = EC/BC
tough mica
prime gate
yea u would use sin if u use 75, cos if u use 15
tough mica
night snow
yea figure out the hypotenuse, adjacent and all
prime gate
and btw sin 75 = cos 15 = (√6 + √2)/4
night snow
name the triangle first ig
prime gate
yes
tough mica
EC = a(sqrt(b) + sqrt(c))
prime gate
they give in the problem
prime gate
wait
use what i gave u
and btw sin 75 = cos 15 = (√6 + √2)/4
this is the square root form of the trig value
since the problem asks for this format EC = a(sqrt(b) + sqrt(c))
tough mica
and btw sin 75 = cos 15 = (√6 + √2)/4
? how
prime gate
its just trig values
u can find 30,45, 60, 90, 120, 150 etc. easily
then use half and double angle formulas to find 15 and 75
or just memorize like i did
u kinda need to learn trig to know why
like basic analytic trig
tough mica
, w cos(15)
grizzled pagodaBOT
prime gate
yea see
tough mica
,w simplify (1+sqrt(3))/(2sqrt(2))
grizzled pagodaBOT
tough mica
u kinda need to learn trig to know why
prime gate
ok lets not get into trig identities
prime gate
use this
tough mica
sin(75)=cos(90-75)
prime gate
oh ok
prime gate
this gave u correct value of cos 15 u can use
the exact result
just rationalize the demoniator
?
tough mica
prime gate
just use sin 75 = cos 15 = (√6 + √2)/4
night snow
what are u getting as the sum
tough mica
,w 1/4 + 2 + 6
grizzled pagodaBOT
prime gate
???
prime gate
i told him
night snow
CE= BC cos 15
prime gate
that
tough mica
a+b+c
night snow
ye and now plug in them values
prime gate
its just 12 * (√6 + √2)/4
night snow
yea
tough mica
a(sqrt(b) + sqrt(c))
prime gate
factor the 3
night snow
3(√6 + √2)
grizzled pagodaBOT
Result:
11
floral vessel
How do I derive this:
amber waspBOT
How do I derive this:
floral vessel
floral vessel
How can I learn chain rule? I have trouble with it constantly. Help me?
native stag
$\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)$ is the chain rule.
grizzled pagodaBOT
Percy
native stag
here $f(x) = x^2$ and $g(x) = -2 +x$, for instance.
grizzled pagodaBOT
Percy
native stag
No
vernal bobcat
Ah but you want to write down f’(g(x)) as the first thing
native stag
what's $\frac{d}{dx} x^2$?
vernal bobcat
You wrote f’(x) as the first thing
grizzled pagodaBOT
Percy
native stag
...right
floral vessel
no idea @native stag and @vernal bobcat
native stag
what's $(x^2)'$ if you're more comfortable with lagrangian notation for some reason
floral vessel
2x
grizzled pagodaBOT
Percy
floral vessel
2x
grizzled pagodaBOT
Percy
so the point is that $f(x)^2 '$ is then $2f(x) f'(x)$
```Compilation error:```! Double superscript.
<recently read> ^
l.49 so the point is that $f(x)^2 '
$ is then $2f(x) f'(x)$
I treat `x^1^2' essentially like `x^1{}^2'.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l
ocal/texlive/2023/texmf-dist/fonts/enc/dvips/lm/lm-ec.enc}{/usr/local/texlive/2
023/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/local/texlive/2023/texmf-```
native stag
looks fine
floral vessel
Can you give me a few more tests?
floral vessel
yes
native stag
i mean if you wanna get nice differentiation practice you can always just do this
some are kinda hard so just do what you feel comfy with
floral vessel
i mean if you wanna get nice differentiation practice you can always just do thi...
Thanks @native stag
.solved
amber waspBOT
amber waspBOT
Available help channel!
split sail
amber waspBOT
split sail
I don't understand the hint
amber waspBOT
@split sail Has your question been resolved?
zenith heron
I don't understand the hint
It means you need to create a function of x meaning you should have an equation y=(expression in terms of x only)
split sail
It means you need to create a function of x meaning you should have an equation ...
so y=x
Then it becomes a cubic
Then solve
By first order differentiation
For the x values of stationary points
Then sub back into the unaltered equation and rearrange to get the corresponding y values for each?
That didn't work
Gonna try x^2
zenith heron
wait I think you need to try to get the partial derivatives
then equate to 0?
then solve the linear equations
and I think those are the points
zenith heron
tbh same I didnt really try to understand the question haahahha
zenith heron
The hint threw me off
I think it meant after getting the system of linear equations you should substitute whatever y you get to x then get the roots
split sail
I think it meant after getting the system of linear equations you should substit...
I still don't get it, here's the solutin though hopefully you can interpret it
zenith heron
can I see the partial derivatives you got?
split sail
can I see the partial derivatives you got?
“x only” “y only”
I don’t remember the proper notation but it’s there
zenith heron
its fx or dz/dx anyway, after that, you have to equate then to 0 so that we can determine their stationary points
split sail
its fx or dz/dx anyway, after that, you have to equate then to 0 so that we can ...
But there is still a mix of x and y terms in each
zenith heron
so itll be 3x^2+2yx-4 = 0 and x^2 -6y^2 + 4 = 0
split sail
Yup
zenith heron
But there is still a mix of x and y terms in each
yess but since we have 2 unknown variable and 2 equations, we'll be able to know their exact values
so you can use substitution or elimination method
I rather suggest u do substitution method
split sail
Ahh ok I’ll try that now, so I rearrange the rhs equation for x, then sub in
zenith heron
As hinted, I think it'll be best if we get an equation of y in terms of x
zenith heron
yess
split sail
.close
amber waspBOT
amber waspBOT
Available help channel!
wide kelp
what method is this? it looks like integration by parts but im not sure, for how many problems does it work? and can i use it on exams?
lusty pine
its integration by parts, dont know, dont know but probably depends on your teacher weather they allow it or not
fast badger
Tabular integration is just integration by parts for dummies (best way)
wide kelp
if i have more complex expressions can i just work through them with this recursively?
fast badger
I’m pretty certain i’ve used it in my exams and not been marked wrong
But I would check with your prof
wide kelp
Tabular integration is just integration by parts for dummies (best way)
so its safe to use yeah? cause my professor has never talked about this and it looks sketchy lmao
but ill practice a bit and see how i feel about it
amber waspBOT
amber waspBOT
Available help channel!
split sail
amber waspBOT
split sail
Meant to do with partial differentiation
No idea how this would be related
if you have a function $f(x, y, z...)$ where $x, y, z...$ are the arguments of the function, the error in the function would be:
$$\Delta f(x, y, z, \ldots) = \sqrt{\left( \frac{\partial f}{\partial x} \cdot \Delta x \right)^2 + \left( \frac{\partial f}{\partial y} \cdot \Delta y \right)^2 + \left( \frac{\partial f}{\partial z} \cdot \Delta z \right)^2}$$
grizzled pagodaBOT
Edmund Cloudsley
split sail
create a function for height in terms of the two variables for heigh of the mast
amber waspBOT
@split sail Has your question been resolved?
keen pawn
A sequence is said to be quasi increasing , if $\forall \varepsilon >0$, there exists an $N$, such that whenever $n>m \geq N$, it follows that $a_n>_m - \varepsilon$.
\
\
From this it follows that $a_m>a_n$.
\
\
Give an example of a quasi increasing sequence that;s not monotone or eventually monotone.
\
Would $ a_n = e^{-n}$ work?
grizzled pagodaBOT
What a wonderful world!
gloomy tide
A sequence is said to be quasi increasing , if $\forall \varepsilon >0$, there ...
what do you think i'm going to ask you?
keen pawn
Why is this quasi increasing?
gloomy tide
dunno but that looks monotone to me
keen pawn
Oh right , it is
😭
thanks
If it's not monotone or eventually monotone the only example I can think of are seqeunces defined by trignometric functions
gloomy tide
define it then
keen pawn
$a_n = -\abs{tan(n)}+n$ intutively feels like it should work, but I think proving it's quasi increasing will be very hard
grizzled pagodaBOT
What a wonderful world!
gloomy tide
why does that feel like it should work?
keen pawn
because it feels like a seqeunce that , overall, decreases
There's probably a simple example I'm missing
An alternating series should probably do the trick
gloomy tide
because it feels like a seqeunce that , overall, decreases
shouldn't you want it to increase?
anyway tan(n) jumps all around right
gloomy tide
what does quasi-increasing mean?
keen pawn
Beyond a certain point in the seqeunce if n>m, then a_ n>a_m
But unless I'm missing something then it will be eventually monotone
nvm, eventually monotone just means it's bounded
forgot that
so $a_n = (n-3)^2$ should work It's neither monotone nor eventually monotone
grizzled pagodaBOT
What a wonderful world!
keen pawn
Does this work?
keen pawn
a_m>a_n
keen pawn
whenever n>m \geq N , then a_n>a_m - \varepsilon
gloomy tide
so $a_n = (n-3)^2$ should work It's neither monotone nor eventually monotone
this is eventually monotone
keen pawn
Unless I'm mistaken eventually monotones means that it's eventually bounded
gloomy tide
where are you seeing that?
gloomy tide
probably!
keen pawn
so eventually monotone means for large enough N, the function is monotone?
gloomy tide
yes
keen pawn
so I take a monotone function and then add to it a vibrating term
That feels wrong, I did consider that
but maybe I'm not understanding the defn
violet blaze
why does it feel wrong?
violet blaze
but maybe I'm not understanding the defn
why do you say so?
keen pawn
why does it feel wrong?
I feel like the function has to be monotone
violet blaze
I feel like the function has to be monotone
why do you think so?
violet blaze
one nice way to find a counter example is to try to prove there is no counter example, and see where your proof fails
keen pawn
so $a_n= \abs{n} e^ {\abs{\sin(n)}}$ shoudl work
grizzled pagodaBOT
What a wonderful world!
keen pawn
Idk, It just felt right that way
keen pawn
as there exist certain n, m, such that n>m \implies a_n > a_m
violet blaze
that is not the defn?
keen pawn
yea?
violet blaze
A sequence is said to be quasi increasing , if $\forall \varepsilon >0$, there ...
also, how can you say the second line in this?
keen pawn
well, a_m-a_n is less than every positive real
keen pawn
for all epsilon>0
violet blaze
no?
for all positive reals we have there exists N, such that if m>n>N, am-an is less than that positive real
violet blaze
its fine
gloomy tide
it's similar to the limit defn
in that your qualifiers are backwards in your brain
so yes revisit it tomorrow
amber waspBOT
amber waspBOT
Available help channel!
obsidian shoal
$4x^2 - 9 - (2x+3)$
amber waspBOT
$4x^2 - 9 - (2x+3)$
grizzled pagodaBOT
Simon James B
obsidian shoal
is we say 4x^2 = (2x)^2 and 9 = 3^2
would this give us a diffrence of squares to help us solve this? because i think i did something wrong
or we just distribute the -
summer temple
move the identity to zero thatll fix it no need to thank me
obsidian shoal
move the identity to zero thatll fix it no need to thank me
that will do nothing
split sail
or we just distribute the -
Is the question just to factorize
obsidian shoal
Is the question just to factorize
Yes!
split sail
Then just distribute the negative
summer temple
that will do nothing
thats rude lil bro
obsidian shoal
thats rude lil bro
I am sorry if i sounded rude i did not mean that<3
split sail
4x^2 -2x -12
obsidian shoal
$4x^2 -2x -12$
grizzled pagodaBOT
Simon James B
obsidian shoal
no
split sail
(x-2)(2x+3)
obsidian shoal
$4x^2 -9 -2x -3$
summer temple
I am sorry if i sounded rude i did not mean that<3
heart react (not sure how to heart react)
grizzled pagodaBOT
Simon James B
obsidian shoal
ok so distributed the minus
grizzled pagodaBOT
Simon James B
split sail
No
obsidian shoal
why
split sail
You're multiplying them with the rest of the equation
They're just subtracted from it
4x^2 -2x -9 -3
-9-3 = -12
obsidian shoal
$4x^2 -2x -9 -3$
split sail
So 4x^2 - 2x - 12
grizzled pagodaBOT
Simon James B
obsidian shoal
$2x(2x-1) -12$
grizzled pagodaBOT
Simon James B
obsidian shoal
now?
split sail
Well that is right but it can be simplified in a better way
obsidian shoal
how
split sail
Take 2 as a common factor from all the equation
obsidian shoal
2(2x^2 -x)-12
obsidian shoal
$2(2x^2-x -6)$
grizzled pagodaBOT
Simon James B
split sail
Are you allowed to use calculators or not
obsidian shoal
no
obsidian shoal
So it'll be 2((2x^2 - x -6))
why -2x if we have 2x and factor 2 from it we are left with x
split sail
why -2x if we have 2x and factor 2 from it we are left with x
Oops-x
obsidian shoal
cunning birch
wait
cunning birch
$4x^2 - 9 - (2x+3)$
you didn't have to distribute the -
obsidian shoal
?????
cunning birch
it's much easier keeping the -(2x+3) aside
and interesting yourself at 4x^2 - 9
any identities we can use?
grizzled pagodaBOT
Simon James B
cunning birch
uhhuh
obsidian shoal
no?
cunning birch
yeah
obsidian shoal
$(2x-3)(2x+3) - (2x+3)$
grizzled pagodaBOT
Simon James B
obsidian shoal
ok and now?
grizzled pagodaBOT
Simon James B
cunning birch
you have a common factor
cunning birch
**Simon James B**
idk what happened here
obsidian shoal
me neither 
cunning birch
**Simon James B**
go back from this
obsidian shoal
you have a common factor
it's 2x+3?
obsidian shoal
(2x+3)(2x-3 )
cunning birch
**Simon James B**
the whole thing
you have to rewrite the whole thing as (2x+3)(...)
obsidian shoal
$(2x+3)(2x-3 -1)$?
grizzled pagodaBOT
Simon James B
obsidian shoal
idkk
obsidian shoal
(2x+3)(2x-4)
obsidian shoal
2x common factor?
cunning birch
no
obsidian shoal
awh
grizzled pagodaBOT
Simon James B
cunning birch
there we go
obsidian shoal
why this feels so hard omg
cunning birch
just remember that if the expression is written in a weird way, like not developed yet
to factor, maybe there is something to do before developing
like in this case
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cloud brook
A Graduated cylinder has a mass of 80g when empty. When 20mL (1ml =1g for water) of water is added, the graduated cylinder has a mass of 100g. If a stone is added to the graduated cylinder, the water level rises to 45mL and the total mass is now 156 g. What is the density of the stone?
winged panther
!status
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
I understand the formula mass divided by volume will give me density but I’m stuck on what my other variable specifically volume is
Because I know the total mass ends up to 156g minus 145g (Water + weight of cylinder) leaves 11g of stone
winged panther
For the volume of the stone, if completely submerged (which we'll assume), is equivalent to the volume of water displaced
winged panther
Because I know the total mass ends up to 156g minus 145g (Water + weight of cyli...
? No. Water is not being created
The mass of water + cylinder is still 100g. It was a stone that was added
cloud brook
Ohhh
winged panther
Why would adding a stone change the mass of water present in graduating cylinder
cloud brook
So the stone would be 56g and the Volume of the stone is 45?
tired girder
45 ml
cloud brook
Ty ty
tired girder
Huh?
cloud brook
1.24g/ml
tired girder
Hey
20 ml of water was already there
It says the volume rises to 45 , and not rises by 45
winged panther
Volume of stone is 25ml?
tired girder
It should be so !
cloud brook
I did 56 divided by 45
winged panther
Why 45?
cloud brook
Isn’t that the volume?
winged panther
When Volume of Water + Volume of stone = 45ml
And volume of water initially was given 20ml
What volume was added?
cloud brook
Im getting confused now so the formula in this case for Density would be 25g (from rock) divided by 45?
Wait no it would be 56 divided by 25 because we are excluding the water and just adding the stones weight
And volume right?
winged panther
Yes
cloud brook
Ahhh okay that makes sense I would adding the water as well
My answer is 2.24g/ml
For the density of the stone
winged panther
,calc 56/25
grizzled pagodaBOT
Result:
2.24
Yep
winged panther
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twilit dove
That's not a polynomial?
amber waspBOT
That's not a polynomial?
quick ridge
why would you think sin y makes it a polynomial
crisp stratus
it is a polynomial if you make a substitution t=sin(y)
honest dagger
That's not a polynomial?
It's a polynomial of sin y
twilit dove
Yes
winged panther
Look into the definition of polynomial
twilit dove
In fact, the variables of a polynomial are never functions
Like sin y
Can you explain to me pls
covert vine
just sustitute sin(y) into any variable, then solve as a quadratic equation
finally you take inverse sine of the solutions and you should obtain 4 solutions for y
twilit dove
finally you take inverse sine of the solutions and you should obtain 4 solutions...
Yes, I did it
I just wanted to understand the fact that this isn't a polynomial
covert vine
because it can't be written in the form of a finite sum of ax^1 + bx^2 ...
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vernal sphinx
Hi guys, trying to find the centre of the circle. I tried using two midpoints and getting the perpendicular gradient then finding where they intersect. Upon getting frustrated I looked at the actual answer and they used the much simple way... WHOOPS! that being said, as far as im aware my method should work... but I can not get the right answer by getting the two midpoints and then finding where they intersect... any help? the first 2 images are my attempt (dont laugh please) and the last image is the example answer. the question is in the first image. its question number B
vernal sphinx
Have I just done something stupid?
Again yes I just did not think about the easy way... my bad, again this other way should work afaik
The drawing is a sketch, I am aware that DFs midpoint is the centre as there is a right angle in the triangle where all edges on the triangle touch the circles perimeter meaning the line opposite the right angle is obviously the diameter. ignore the drawing being shit please
brb btw as ive already spotted one mistake
haha, all that and I simply used the wrong sign... let this be a reminder to make sure you dont forget to use the correct signs (+ or -)
Okay my biggest trouble now is finding y
Despite the fact that I have equations where y is the subject, I can not substitute in x to find y where y would end up being equal to -3 like the example answer, this is where I now need help
okay ive managed to get it now 🤦♂️ wish i didnt overcomplicate that
.close
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noble plume
How is the sum not 1?
amber waspBOT
How is the sum not 1?
winged panther
,w 2x(x - 1) = 3/2
grizzled pagodaBOT
winged panther
idk how it's not 1
What's the condition for infinite GP sum = a/(1-r)?
noble plume
What's the condition for infinite GP sum = a/(1-r)?
-1<r<1
OH
so the answer is just -1/2
winged panther
Yeah -1 < 3/2 < 1 ✓✓
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past pawn
Is anyone here good with probabilities and integration in probabilities
wet breach
Is anyone here good with probabilities and integration in probabilities
I'm not, but people won't know for sure whether they can help you with it unless they see the problem you're having trouble with.
past pawn
So
I have a project where I'll discuss one of the integration applications
And I picked probabilities
Since we used Integration in them
And because we haven't studied them yet
I wanna make sure that I have all the required concepts to discuss it
So I need someone to tell me if I am missing something
sterile nymph
This is still not a form of a question that can be answered.
past pawn
I Know
But I first need someone to tell me they do
So I don't waste all that time explaining what I have studied since it'll take a while
And I have a test along with the project
So time is tight
sterile nymph
But I first need someone to tell me they do
So I don't waste all that time expl...
So in other words, you want someone to commit to taking the time to help you before you commit to taking the time to actually ask your question?
past pawn
Yes because I have a test coming up as they said
Stop trying to argue for no reason
Be chill
sterile nymph
lusty saffron
probably there is at least one person in this server of 240,000 people who knows enough about probability to answer your question and who might show up once you actually ask it
lusty saffron
if that doesn't happen, then just take the fully-written-out question and copy+paste it to whoever else you're going to ask
past pawn
I have studied basic probability rules
Like the probability of heads or tails and such
The probability density and cumulative distribution functions
And how to use integration with them
But I still need to improve my understanding in pdfs and cdfs
So what else am I missing
🙏.
pallid canopy
https://probabilitycourse.com/ or go pick a book
past pawn
https://probabilitycourse.com/ or go pick a book
If I had enough time I would've dived into great details but I really don't
sterile nymph
Integration can be used to find means and higher moments (like variance, skew, and kurtosis)
Integration can be used to find the characteristic functions of probability distributions
Integration can be used to find the sum of two random variables via convolution.
There are many other examples
past pawn
Integration can be used to find means and higher moments (like variance, skew, a...
Can I please DM you
sterile nymph
I would rather not in this case, as I'm touch and go this evening
past pawn
Just answer me when you can
sterile nymph
So I wouldn't want to disappoint you because I'm unlikely to be available much this evening
past pawn
I have to finish this part before 2 am for me and then I'll see what else I can do for the project
sterile nymph
Especially because it seems you are seeking tutoring of some kind?
past pawn
Yes but I don't need you to answer me today
Since I'm currently studying the subject I have a test about
sterile nymph
Well, feel free to DM me, but I cannot make promises that I'll be able to answer in a timely manner
past pawn
Tism and it's alright
sterile nymph
But you realize, that there are many people on this server who are more experienced than I am in probability
So if you take the time to formulate your question in a focused way, you'll probably get more, better helpers than I.
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@past pawn Has your question been resolved?
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tough mica
can someone explain drinkers paradox
amber waspBOT
can someone explain drinkers paradox
torn furnace
just reading on wikipedia, it seems like it just depends on vacuous truth?
Do you have any specific issue with this explanation
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@tough mica Has your question been resolved?
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solemn escarp
Let $a$ be an integer that makes the smallest integer value of $x$ satisfying the inequality
$ax < 1728$ equal to -17. Find how many values $a$ can take
grizzled pagodaBOT
Copter
solemn escarp
i have absolutely no idea where to begin
im so cooked for the exam😭
<@&286206848099549185>
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@solemn escarp Has your question been resolved?
sterile swan
you have an inequality and equality?
solemn escarp
the minimum of x is -17
im probably overcomplicating here, but then this means for every $x_0 < -17$, $ax_0 > 1728$
grizzled pagodaBOT
Copter
solemn escarp
maybe i could do something with that?
sterile swan
if $x_0<-17$ then $ax_0<-17a$
grizzled pagodaBOT
Bonk
solemn escarp
yes
sterile swan
and we know that $ax_0>1728$
grizzled pagodaBOT
Bonk
sterile swan
thus $-17a>1728$
grizzled pagodaBOT
Bonk
solemn escarp
then a< -101.something
sterile swan
yep
solemn escarp
$-17a < 1728 \leq -18a$
grizzled pagodaBOT
Copter
sterile swan
?
sterile swan
huh?
sterile swan
im just confused where all this is coming from
sterile swan
**Copter**
from what is this?
sterile swan
then -101 <= a <= -96
and this?
sterile swan
so itd be 6
6?
solemn escarp
from what is this?
since -17a < -18a we can do that since the minimum is -17
sterile swan
from -17a < 1728 and -18a >= 1728
but why take -18? why not smth like -25? or -100?
solemn escarp
no, since x is an integer as well
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fierce edge
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fierce edge
I don't have an answer key for this so i need osme confirmation
each roll is independent
the firs tthree is a binomial trial
so 3 * (1/6)^2 * 5/6
for the last three rolls, it's just 8/6^3
the first three rolls are independent from the last three rolls
so you multiply those two
my final answer is then 3 * (1/6)^2 * (5/6) * 8/6^3
formal harbor
my final answer is then 3 * (1/6)^2 * (5/6) * 8/6^3
i think that should be right
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tough mica
What is the largest number, with its digits all different, whose digits add up to $16$?
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
winged panther
What is the largest number, with its digits all different, whose digits add up t...
You're basically looking to maximize the number of digits of N, because more digits = larger number
Also, when you get all digits, the number with all digits arranged in descending order is largest ✓
So, starting with units digit, you can accomodate 0 + 1 + 2 + 3 + 4 + (5 + 1) = 16 but for all digits to be equal, you cannot have another 1 in the number
So, it's 643210
tough mica
why use 0
naive pivot
winged panther
Yes that's the gist
tough mica
.solved
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ebon rock
(\sum_{n=1}^{\infty} (e^{1/n^2} - 1))
amber waspBOT
\(\sum_{n=1}^{\infty} (e^{1/n^2} - 1)\)
grizzled pagodaBOT
Chrome
ebon rock
by expansion of e^x i got something like
1/n^2+1/2n^4+....
How can I check convergence of it?
solar gust
So you have something like 1/(n^2n * n!)
formal harbor
by expansion of e^x i got something like
1/n^2+1/2n^4+....
ratio test
amber waspBOT
@ebon rock Has your question been resolved?
ebon rock
I found by ratio test is 0 so convergent
Thanks both of you
@solar gust @formal harbor
.close
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copper nest
Find limit as n approaches infinity
amber waspBOT
Find limit as n approaches infinity
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shadow shell
Hello you great math fellows.
I have a kind of stupid question.
So I'm an undergrad math student, and recently I got permitted by my prof to start study and work on an idea regarding set theory where there is no application at-all, and it's all because curiosity.
My question is what if (later) I publish this study as apepr later? I believe it won't get any love, but I'm asking if these kind of works good later when I apply for graduate school? or it's bad idea, and I shall not do that?
celest cove
wouldnt harm you, if anything it shows your ability to think and work on it which is quite valuable
beyond that, it could be something that is found to be very important much later on even if not currently
maths is just like that
shadow shell
wouldnt harm you, if anything it shows your ability to think and work on it whic...
Thank you for your answer, yes I was thinking about the same thing. Now I have a great peace in mind, wonderful.
honest dagger
Hello you great math fellows.
I have a kind of stupid question.
So I'm an underg...
Even if its bad, you can learn from it, and make a much better "first" paper in college
It can only help you to try
You gain a very valuable experience in the process of research
shadow shell
You gain a very valuable experience in the process of research
Great point and advice. Really appreciate for sharing that.
honest dagger
Great point and advice. Really appreciate for sharing that.
poverty?
amber waspBOT
@shadow shell Has your question been resolved?
unborn plaza
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amber waspBOT
@unborn plaza Has your question been resolved?
willow hull
I think those are right, though on the RHS of those arrows that's supposed to be the group that the subgroup is isomorphic to yeah?
Is {(0,0)} -> Z_4 x Z_4 right?
unborn plaza
Not the subgroup but the factor group
willow hull
AH okay yeah that makes more sense
Well I might be more out of practice with group theory than I thought, but ultimately I think those are all right 👍
unborn plaza
thank you! 🙏
willow hull
Depending on how nitpicky your grader is maybe double check the order of the terms in the factor groups for order 2
Like, Z_2 x Z_4 is obviously iso to Z_4 x Z_2 so it shouldn't matter, but some graders can be real sticklers about that sorta thing
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tough mica
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tough mica
2 -b + b = -2
fuckk
like if you plug in (x1,x2,x3,x4) =(2,1,0,1) we get a value for A but for B we dont
first of all what does it mean that system S1 has infinitely many solutions?
that we have at least one free variable
whats with this?
x1 + (1-b)x2 + (b-3)x3 + (b-3)x4 = 0
2 + (1-b) + (b-3) = 0
whatever
let me find a first
a(2) + 1 + 3(0) + 2(1) = 1
2a + 3 = 1
a = (1 -3)/2
a = -1
now
if a = -1 plug it in S1
and make it satisfy s2
if you plug in (2,1,0,1) you can't get b
okay
,w rref {{1,0,-2,-2,0},{-1,1,3,2,1}}
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