Does this set have a name in English. I was interested in reading more about it but I couldn't find anything on it. Perhaps related to p-adic?
#help-33
weary temple
marsh citrusBOT
Does this set have a name in English. I was interested in reading more about it ...
stoic saddle
"fractions between 0 and 1 with denominator equal to a power of 3"
weary temple
"fractions between 0 and 1 with denominator equal to a power of 3"
So no real name to it? In Dutch triadische getallen was used
stoic saddle
well you could call them triadic fractions by analogy with dyadic fractions ig
marsh citrusBOT
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sharp whale
Is this sketch correct for the complex plane?
marsh citrusBOT
Is this sketch correct for the complex plane?
@sharp whale Has your question been resolved?
marsh citrusBOT
@sharp whale Has your question been resolved?
sharp whale
<@&286206848099549185>
marsh citrusBOT
@sharp whale Has your question been resolved?
static orchid
@sharp whale Yes it is.
sharp whale
thanks
so lets say it was just mod(z-i) for example
would it be the same circle
just with an origin of (1,1) instead right
marsh citrusBOT
@sharp whale Has your question been resolved?
still temple
Is the answer b or a?
marsh citrusBOT
Is the answer b or a?
still temple
nova totem
still temple
Im not asking for answer i think its a but theres a chance its b too
Im asking if b or a is correct
velvet cairn
R u seeing any similar triangles ?
still temple
R u seeing any similar triangles ?
BDA and CBA
I think b is right but a might be right too
velvet cairn
Yes
still temple
its b?
marsh citrusBOT
@still temple Has your question been resolved?
sly thunder
marsh citrusBOT
tribal panther
Correct
marsh citrusBOT
marsh citrusBOT
✅
sly thunder
yay
Help me the last question
Wait I show
If the r=1,2kohm
How calculate probability
Do resistance change when mean change?
upper briar
If the r=1,2kohm
wait wdym r=
did u mean the standard deviation?
like are u asking abt 6.4
upper briar
oh
well
u kinda repeat the same thing
but u find a calculator with normal distribution
with mean of 10k, std of 1.2k
std is standard deviation
sly thunder
Because my friends, they are said I wrong
If I only choose 9,6-9,7 for question a
I ask but they don't explain
sly thunder
std is standard deviation
So in question a, which resistor are less than 9,8
I will know all if I know this
upper briar
oh
6.4 u ignore the stuff previously said
it says suppose that it follows normal distribution
so all prev stuff is irrelavent
upper briar
but u find a calculator with normal distribution
so this
alternatively use the normal distribution formula
marsh citrusBOT
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void patio
Using Linear Equations system, how would I solve this?
Fe^7 + O^2 -> Fe^3 O^2 + S O^2
marsh citrusBOT
Using Linear Equations system, how would I solve this?
Fe^7 + O^2 -> Fe^3 O^2 +...
void patio
The answer is (0,0,0)
drowsy bronze
lmaoo
brave spire
Cus..like I dont think u can call ur variables Fe
marsh citrusBOT
@void patio Has your question been resolved?
ornate silo
marsh citrusBOT
brave spire
Risolvere means solve ig?
drowsy bronze
yup
brave spire
K
brave spire
@ornate silo U there?
brave spire
Okay, can u send ur work?
brave spire
Hmm..Well, just take log(base3)x common (In the numerator)
that would become 2/3 * log(base 3) x
then transpose 2/3 to the other side
drowsy bronze
@brave spire final answer?
brave spire
<@717652530061901855> final answer?
Let him do the calculation
drowsy bronze
i want to confirm
ornate silo
let me try one sec
brave spire
i want to confirm
wait pls
brave spire
yes
brave spire
Np bud
ornate silo
.close
tender ocean
marsh citrusBOT
tender ocean
ok so the solution states $\sin \frac {1} {x}$ tends to $\lambda$ as x tends to 0, where lambda is [-1,1]
i dont understand how that makes sense
elfin berryBOT
sho
glass silo
Do you have the solution as it appears like that?
tender ocean
tender ocean
Do you have the solution as it appears like that?
this is the first half of the solution, i left out the rest
glass silo
I don't get what they meant by that tbh, but at least otherwise I can kinda see that... [they divided numerator and denom by x in aim of working out the limits of them both, which can be done]
tender ocean
this is the first half of the solution, i left out the rest
they said the "x sin (1/x)" term becomes zero. as its 0 into a finite number. my question was how is sin (1/x) a finite number
glass silo
Ohhhh alright I get what they're saying now 🥪
The sin(1/x) is bounded between -1 and 1, and as x tends to zero, you must have that x * sin(1/x) tends to zero too, as it's sandwiched
A weird way of saying that, and the fact that they used lambda in the question as well as the solution 
tender ocean
The sin(1/x) is bounded between -1 and 1, and as x tends to zero, you must have ...
wait so sin (1/x) exists, its not undefined
glass silo
The limit of it doesn't exist by itself no
However it is bounded
,w plot y = abs(x), y = -abs(x), y = x * sin(1/x)
elfin berryBOT
tender ocean
The sin(1/x) is bounded between -1 and 1, and as x tends to zero, you must have ...
ok i kind of get it
does this work for other trig functions too?
what about x tan (1/x) or x cos(1/x)
glass silo
For x * cos(1/x), it's a similar picture, cos is bounded between -1 and 1
,w plot y = abs(x), y = -abs(x), y = x * cos(1/x)
elfin berryBOT
tender ocean
so cos (1/x) x is also zero
glass silo
For tan I'm not too sure because it's not necessarily bounded, so you can't really sandwich it
,w plot y = abs(x), y = -abs(x), y = x * tan(1/x)
elfin berryBOT
tender ocean
interesting
glass silo
(as you can see, the bounds I used before for sin and cos don't work, so at the very least you'd need to find new ones, but the image suggests they don't exist...)
,w lim x * tan(1/x), x to zero
elfin berryBOT
tender ocean
The limit of it doesn't exist by itself no
so if something that is technically "undefined" gets multiplied by zero, can i assume its equal to zero
glass silo
It's the boundedness which is the crucial property we're using
tender ocean
It's the *boundedness* which is the crucial property we're using
is there a specific name for it? i mean i kinda get it, but a video explanation about it would be nice
glass silo
Because sin and cos were bounded, we were able to create "sandwich/squeeze" functions that those products had to be in between
tender ocean
Because sin and cos were bounded, we were able to create "sandwich/squeeze" func...
oh yea i get it
glass silo
is there a specific name for it? i mean i kinda get it, but a video explanation ...
Erm, try sandwich theorem/squeeze theorem, something like that
,w sandwich theorem
elfin berryBOT
glass silo
tender ocean
Erm, try sandwich theorem/squeeze theorem, something like that
yea squeeze theorem sounded familiar i was wondering if this was that. havent learned it tho
glass silo
Aha, fair enough, well now you've seen an application of it 
weird cause it seems like that's what they're trying to use there 
marsh citrusBOT
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fathom hawk
marsh citrusBOT
fathom hawk
<@&286206848099549185>
pallid pine
!15m
marsh citrusBOT
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pallid pine
if -6< y < 2
then
-18 < 3y < 6
well acc i dont even know why i typed
lmao my brain has just stopped at this part
mystic walrus
I personally would calculate the amount of possible values, then see how many can be answered like that?
Sorry I'm also really tired so there's probably a much better way to do it KFHS
fathom hawk
what is it
pallid pine
since -18 < 3y < 6, and -4<= x < 6
they overlap at the numbers
where 3y and x are
-4 -3 -2 -1 0 1 2 3 4 5
and since youre minusing these two together
this is almost exactly
like when you add two dice rolls together
marsh citrusBOT
Available help channel!
jagged turret
can you translate to english
marsh citrusBOT
can you translate to english
jagged turret
is the limit the ratio of leading coefficients?
lucid zenith
yes
jagged turret
what does that mean
lucid zenith
that's what is written
if you have a function which is the ratio of two polynomial functions of the same degree, the limit as x tends to +- infinity is the ratio of the leading coefficients of the two polynomials
fluid yarrow
leading coefficient is the coefficient of the term with the highest degree
jagged turret
i understand
you take the highest equal coefficients
but what does that "ratio" mean?
lucid zenith
the two polynomials have to be of the same degree
knotty trellis
but what does that "ratio" mean?
Ratio of a and b means a/b
jagged turret
a/b is horizontal asymptote not a limit though
lucid zenith
then the limit of the function is the limit of a/b (considering a and b to be the coefficients of the terms with the highest power of x in the numerator and denominator, respectively)
knotty trellis
a/b is horizontal asymptote not a limit though
horizontal asymptote is the limit as x approaches infinity
stoic saddle
a/b is horizontal asymptote not a limit though
the horizontal asymptote('s y-coordinate) is the limit at infinity (of your function).
lucid zenith
for example, you have $\lim_{x\to\pm\infty} \frac{4x^2+3x-9}{5x^2+8x-10} = \frac{4}{5}$
jagged turret
thought u need a small hole for it to be the limit
elfin berryBOT
kheerii
jagged turret
ok
the limit of that would be whatever equals 0 in the denominator
not 4/5?
which is a horizontal asymptote
jagged turret
limit means
it gets close to it
but never touches
4/5 is an x value
that has a y value
if i plug in 4/5 it wont be undefined
jagged turret
oh?
lucid zenith
x is tending to +-infinity isn't it?
lucid zenith
what do you mean
lucid zenith
,w graph (4x^2+3x-9)/(5x^2+8x-10)
elfin berryBOT
jagged turret
at 4/5
lucid zenith
you're calculating the limit as x tends to +- infinity
what do you understand from that?
lucid zenith
in relation to this graph
lucid zenith
you're calculating the limit as x tends to +- infinity
.
lucid zenith
what do you understand from that?
.
jagged turret
ur finding holes
lucid zenith
let's say
you have a function
f(x)
when I ask you what the limit of f(x) is as x tends to +infinity
what does that mean?
lucid zenith
what do you mean "holes"
jagged turret
gaps
where x doesnt touch
it has to skip over
like a constant is 5x
but cant equal 1
for example
then u have a hole
at x =1
a limit at x=1
for example
lucid zenith
that is a different kind of limit
well
not a different kind of limit
but
it represents a different thing
when x tends to infinity, it literally means x tends to infinity.
lucid zenith
when I ask you what the limit of f(x) is as x tends to +infinity
i.e this means "what value does f(x) approach as the value of x gets larger and larger?"
jagged turret
ohok
so
a horizontal
asymtote
needs to be there
in order for
x-> infinity
lucid zenith
yup
lucid zenith
this graph isn't a great example
jagged turret
whats a better one
jagged turret
looks like an octopus
elfin berryBOT
lucid zenith
yes
but
as x tends to infinity (as x gets larger)
what happens to the value of the function
do you see how the waves get closer and closer to 0
,w graph sin(x)/x for x from 0 to 1000
elfin berryBOT
lucid zenith
notice the downward bend in the graph
jagged turret
looks like something else tbh
but yes
it gets closer
to 0
can we use
a non sin graph
im religious
i dont sin
elfin berryBOT
jagged turret
**kheerii**
4/5 is the limit? not 0?
lucid zenith
yes
jagged turret
ty
lucid zenith
that's what the theorem states
you can think of it as the lower powers of x "fading away" as x gets larger and larger, leaving only 4x^2/5x^2 inside the limit, which evaluates to 4/5
abstract coyote
marsh citrusBOT
abstract coyote
I understand how the coordinates for a,b,c,d,and j were fource
But how were the coordinates for e,f,g,h determined
For example, F is not in the same y position as O is, but how do i know how far to go down to reach F
marsh citrusBOT
@abstract coyote Has your question been resolved?
marsh citrusBOT
@abstract coyote Has your question been resolved?
marsh citrusBOT
@abstract coyote Has your question been resolved?
abstract coyote
<@&286206848099549185>
marsh citrusBOT
@abstract coyote Has your question been resolved?
marsh citrusBOT
@abstract coyote Has your question been resolved?
sand garden
<@&286206848099549185>
still temple
But how were the coordinates for e,f,g,h determined
Using trigonimetry
marsh citrusBOT
Using trigonimetry
still temple
.close
alpine basalt
In mathematical logic/proofs, are $\iff$ and $\text{iff}$ interchangeable?
elfin berryBOT
normalAtmosphericPa=101,325
stoic saddle
yes
alpine basalt
yes
so does "if and only if" always mean a two directional implication?
i.e., if I use "iff" in my statement to restrict some claim of mine, will I then need to go on to show a proof in both directions?
I often don't see people doing so though
devout mauve
yes both directions
sometimes one direction is obvious
or the proof goes the same in both directions
alpine basalt
or the proof goes the same in both directions
thank you!
p => q is equivalent to (~p)vq. The implication p=>q is true provided either p is false or q is true.
^^ why is this statement true/?
stoic saddle
so does "if and only if" always mean a two directional implication?
yes it does
alpine basalt
i.e., "if x=5, then x^2=25", is equivalent to "if x≠5, then x^2=25???"
alpine basalt
either (~p) or q is true right?
devout mauve
"or" doesnt mean exclusive or
if p is false then ~p is true and it doesnt matter what q is
if p is true then ~p is false and q has to be true for (~p or q) to be true
alpine basalt
I should really comb through a basic proofs book aye
I think they contain logic
is there a difference between propositional and predicate logic?
alpine basalt
if p is true then ~p is false and q has to be true for (~p or q) to be true
thank you=
marsh citrusBOT
@alpine basalt Has your question been resolved?
marsh citrusBOT
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random sphinx
ivory laurel
Just to quickly check,suppose in an ODE, the complimentary solution is e^x(sin(x)+cos(x))
marsh citrusBOT
Just to quickly check,suppose in an ODE, the complimentary solution is e^x(sin(x...
still temple
yes?
ivory laurel
For my particular solution can I use Ae^x as my Ansatz
still temple
it depends on the inhomogeneous function
i.e. the function on the RHS
the complementary solution tells you nothing
ivory laurel
Yes the inhomogeneous functions is a linear combination of e^x
still temple
show me the problem
ivory laurel
I just mean is the Ansatz allowed since if it is then then the problem is solved
still temple
If we have a linear combination of $e^x$ on the RHS. That is, $c_1e^{bx} + \hdots + c_re^{rx}$ then the Ansatz is going to be $Ae^{bx} + \hdots + Ne^{rx}$.
elfin berryBOT
Nika
lethal shell
Yes I believe so, it doesn’t affect the complimentary function you stated hence making it valid
still temple
where A, ...., N are coefficients to be discovered
(if you are using the method of undetermined coefficients)
marsh citrusBOT
@ivory laurel Has your question been resolved?
smoky marsh
if i had the sum start at n=0 would it then be (-1/8)^n-3?
marsh citrusBOT
if i had the sum start at n=0 would it then be (-1/8)^n-3?
smoky marsh
or n+3
high pine
n+3
smoky marsh
so as i take away from n, the exponent increases right
devout mauve
it might help to make the substitution very explicitly. set $k=n-3$. then $k$ starts at $0$. also $n=k+3$ so you can exchange the exponent using that. so $\sum_{k=0}^\infty (-\frac18)^{k+3}$
elfin berryBOT
Denascite
smoky marsh
ah yea that makes sense, i tried setting up a formula like that but this one is much neater
thanks! .close
.close
still temple
Hey ! I do not understand how this is right.
1 + (yz/(1+yz)) • x = (1 + yz + yx + zx)/(1 +yz)
On the right side of the equality, where do we get the yz from ?
marsh citrusBOT
Hey ! I do not understand how this is right.
1 + (yz/(1+yz)) • x = (1 + yz + yx ...
burnt oxide
hi
lean flame
Because when we add 1 and .../yz, we take yz as common denominator
1+yz as common denominator*
So 1 * (1+yz)/(1+yz) + .../(1+yz)
still temple
@lean flame oh it get it ! Thank you very much
woeful glade
marsh citrusBOT
woeful glade
could sm1 help me for IBP
for this
u=n+3
du = 1
dv = 1/(-5)^n
idk how to get v
ik u take the antidervative
but how do u take the antidervative of it
marsh citrusBOT
@woeful glade Has your question been resolved?
tight furnace
first simplify it
marsh citrusBOT
marsh citrusBOT
✅
tight furnace
writing 1 as 1^n might help
or wait 
tf are they doing bringing a negative to the power of n when n varies across a continuum
there's going to be complex values involved whenever n isn't an integer
tight furnace
is this your NA then
doesn't look like the function is in the realm of what you should be dealing with integrating
woeful glade
is this your NA then
how is it Na?
because it oscillates betweeen neg and positive values?
elfin berryBOT
tight furnace
complex valued function is the problem
it could be integrated still, over the complex numbers
but since that isn't in the scope of calc 1 at all I'd say it means not integrable
glass silo
It's worth remembering the conditions for integral test tho
[could tell that there probably was some other problem behind this 
]
woeful glade
but since that isn't in the scope of calc 1 at all I'd say it means not integrab...
calc 2
tight furnace
ah well still
tight furnace
[could tell that there probably was some other problem behind this <:lolDog:5430...
Yeah the dn should have tipped me off lol
marsh citrusBOT
@woeful glade Has your question been resolved?
woeful glade
daam what am i doing wrong here
tight furnace
did you try just putting NA?
or is it the other problems
2 of the other answers are also outlined in red
marsh citrusBOT
@woeful glade Has your question been resolved?
dreamy trench
does there exist a closed form for the arithmetic geometric mean?
marsh citrusBOT
does there exist a closed form for the arithmetic geometric mean?
dreamy trench
as in not a recurrence
still temple
what do you mean by "ideal"
dreamy trench
i just want something reasonably accurate and computationally simple
still temple
what is the original question that you want to answer, before we get too deep into the xy rabbit hole
dreamy trench
i want to make a function on my calculator for the agm but it's really slow so i don't want to have to resort to integral expressions
so now i'm just wondering how many iterations of the sequence defn are required to be reasonably close (maybe to 3 decimals or so)
still temple
I doubt doing the integral numerically would converge much faster than the recursion
https://en.wikipedia.org/wiki/Arithmetic–geometric_mean#Example
The number of digits in which an and gn agree (underlined) approximately doubles with each iteration.
there's a siam paper for this lmao
main idol
SIAM -> NIAM -> NIAP -> PAIN
still temple
<https://epubs.siam.org/doi/abs/10.1137/1026073>
seems like they give some error bounds there
convergence rates for their computation of pi are pretty good
main idol
wow 2788 digits correct just in 10 iterations
marsh citrusBOT
@dreamy trench Has your question been resolved?
still temple
damn
3 iterations already convinces python
a = [np.sqrt(2)]
b = [0.]
p = [2.+np.sqrt(2)]
for i in range(3):
a.append((a[-1]**.5+a[-1]**-.5 )/2.)
b.append((a[-2]**.5)* ((b[-1]+1)/(b[-1]+a[-2])))
p.append(p[-1]*b[-1]*((1+a[-1])/(1+b[-1])))
print(p[-1], p[-1]==np.pi)```
dire dawn
tried this a few times and I'm always way off, I don't know what to do.
marsh citrusBOT
tried this a few times and I'm always way off, I don't know what to do.
@dire dawn Has your question been resolved?
dire dawn
honestly i had no idea what I was doing and I kept erasing things so it might not all be on there
marsh citrusBOT
@dire dawn Has your question been resolved?
dire dawn
.close
long arch
yes
yes
you need to write 512 as a power of 8
then you can cancel with the log
probably
idk my powers of 8
write sqrt(125) as a power of 5
yes
yes
marsh citrusBOT
Available help channel!
jagged turret
How does the bottom question, answer C make sense
marsh citrusBOT
How does the bottom question, answer C make sense
jagged turret
Shouldnt it be 415 not 405?
it says "interpret A'6 = 405" then it talks about a(7)
a(7) if we were to go there, is = 8514
a(6) = 8099
a(7)-a(6) = 415
not 405
a'(7) = 425
knotty trellis
Interpreting A'(6) like that indeed doesnt make sense. A'(6) means that the instantenous rate of change is 405. But 1 month later it will be greater, so using that you can just aproximate A(7)
jagged turret
Interpreting A'(6) like that indeed doesnt make sense. A'(6) means that the inst...
it says "it will be"
not "approximately will be"
knotty trellis
Yeah, and that's why I think it's incorrect
jagged turret
the instantaneous rate of change is 425
not 405
but yes i agree with you
I was told last night though
that it made sense
something about
a'(7)-a'(6) = a'(7-6) * a'(6)
or something like that
found it
is this true
jagged turret
well thats baloney
because the question
answer c*
is saying "it is x value"
not "approximately"
knotty trellis
thats weird
jagged turret
well
what would it be
then
really
would i be taking
a'(7)-a'(6)
or a(7)-a(6)
jagged turret
a(7)-a(6) = 415
here, down
knotty trellis
I feel like none of the answers is correct interpretation of A'(6)=405, C) is a decent approximation
jagged turret
ok so just f this problem then
thanks mathisalwaysright
in this case guess "mathway" isnt always right
.close
marsh citrusBOT
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Available help channel!
rocky pilot
marsh citrusBOT
rocky pilot
Did I do these one's right?
marsh citrusBOT
@rocky pilot Has your question been resolved?
rocky pilot
<@&286206848099549185> ?
marsh citrusBOT
@rocky pilot Has your question been resolved?
marsh citrusBOT
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Available help channel!
bitter tulip
Hello. Any ideas on how to solve this?
marsh citrusBOT
Hello. Any ideas on how to solve this?
bitter tulip
I tried taking ln and then differentiating but I don’t think that gives anything useful
worn nimbus
looks very difficult
bitter tulip
You’re supposed to solve this in 3 minutes apparently
worn nimbus
bruh lmao
marsh citrusBOT
@bitter tulip Has your question been resolved?
marsh citrusBOT
@bitter tulip Has your question been resolved?
austere steppe
need help
austere steppe
why is it positioned there
i dont get how graphing works
y= -2x+1
why is it not in 2?
still temple
you don't understand how/why the line y = -2x+1 is graphed like that?
well the best way to see why is to pick 3 x values, say x = 0, 1, 2 and plot them on the graph
austere steppe
yess i think im struggling the teacher didnt provide a video lesson for us anymore 😭 so the handout given is straightforward
still temple
and then try to extend the line to infinity
so like,
lets try it
get a piece of paper or something
draw the coordinates
austere steppe
okey
still temple
okay so did u do it
austere steppe
austere steppe
Yess
still temple
lets try taking some x values
lets start with x = 0
in that equation, what would y be for this x value
austere steppe
1??
austere steppe
points?
still temple
wait gtg sorry 😭 but just basically try to draw the points and connect them then u will see the patttern of the line
austere steppe
wait gtg sorry 😭 but just basically try to draw the points and connect them the...
okie
still temple
is this correct?
yepp
austere steppe
i have to
still temple
okie kinda back
still temple
the idea is like
plot a few points
then connect those dots in a line
and then
just extend that line
forever in both sides
thats lke
like
the easiest way to go about it
hexed sparrow
I am not sure what I did wrong here. Green is what the actual answer is and red is my answer
nimble mason
marsh citrusBOT
I am not sure what I did wrong here. Green is what the actual answer is and red ...
proper zodiac
I am not sure what I did wrong here. Green is what the actual answer is and red ...
The answers are the same, use log rules
brittle sun
I solved it but am not sure if my way is correct
marsh citrusBOT
I solved it but am not sure if my way is correct
brittle sun
i did 12-x+x/2 = 6
then
18-x+x/2 = 9
then did 9+6 = 15
i am not sure if this way is correct tho
sturdy plank
im not sure i follow.. this is what i would do:
sturdy plank
im not sure i follow.. this is what i would do:
@brittle sun (forgot to enable ping)
trim quest
im not sure i follow.. this is what i would do:
shouldn't the midpoints be (D+C)/2 and (B+A)/2 ?
rather than minus
sturdy plank
oh the averages, yeah mb
he can fix up my calculations xD (yeah 15's correct, you're good JoRe)
marsh citrusBOT
@brittle sun Has your question been resolved?
trim quest
then did 9+6 = 15
Yeah 15 is right but I don't quite understand what you did here to get it
marsh citrusBOT
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barren tangle
Any idea what I did wrong?
marsh citrusBOT
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barren tangle
.close
marsh citrusBOT
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dusky turret
marsh citrusBOT
dusky turret
i need help finding the interest paid
fading plank
How would i do this
marsh citrusBOT
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uneven wraith
not sure why U turns into and because i thought it turned into or
marsh citrusBOT
not sure why U turns into and because i thought it turned into or
uneven wraith
elfin berryBOT
heavy
high pine
de Morgan
worn nimbus
so $x \in \bar{A} \cap \bar{B} \iff x \notin A \cup B$
elfin berryBOT
heavy
whole sleet
If x is not in A U B, then it had better be the case that x is not in A, and that x is not in B.
For example, if x were in A, then x would also be in A U B.
uneven wraith
so if it was x is not in A intersection B would it turn into x is in A union B?
whole sleet
If x is not in A n B
Then x is not in A, or x is not in B.
In other words, if x is not in both, then it has to be missing from one of them.
marsh citrusBOT
@uneven wraith Has your question been resolved?
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earnest rain
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undone kindle
marsh citrusBOT
undone kindle
Pretty sure what I did is illegal
Can I get some help on the proper way to do this?
marsh citrusBOT
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fair cove
how can i solve this question with no initial condition
marsh citrusBOT
how can i solve this question with no initial condition
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orchid scarab
how do i answerthis?
marsh citrusBOT
how do i answerthis?
willow plinth
how do i answerthis?
Do you know what a summation is
willow plinth
yea i just need help w the square
You plug in 0 for i
n = 19
i = 0
you start from 0
and end at 19
so (0+3)^2 + (1+3)^2 + (2+3)^2 .... (19+3)^2
up until the nth term
which is 19
orchid scarab
yea im doing double summation to make it easier for me doe + brute forcing isnt allowed
ik how to do the first summation
and teh second i just dk what to do with the square
orchid scarab
double summation
using double summation so i dont have to brute force substituting the i values and adding it
pallid pine
@orchid scarab wdym by double
im pretty sure
double summation
is when you have two summations with different letters
at the same time
like this
pallid pine
how do i answerthis?
for your one
what you can do is
expand that bracket
then you can use the rules
for i^2
i
and constant
marsh citrusBOT
@orchid scarab Has your question been resolved?
long cape
marsh citrusBOT
long cape
would the second line be equal or am I not allowed to distribute into unequal powers?
if I consider - as (-1)^1
1 and -1 would not match powers
so therefor should I just use (x+3)^-1 instead?
converting -(factor) to + (-1)(factor) is like changing the subtraction operator - into a power 1 factor, ya? always power 1
cobalt sentinel
Is this wat ur talking about?
elfin berryBOT
Stephen
cobalt sentinel
Sorry it goes to the next line and looks bad
U have a sign error at the end
O ur talking abt the powers
long cape
O ur talking abt the powers
ya, the powers
cobalt sentinel
converting -(factor) to + (-1)(factor) is like changing the subtraction operator...
I think what ur saying here is correct
long cape
OK
cobalt sentinel
so therefor should I just use (x+3)^-1 instead?
Looks better
cobalt sentinel
**Stephen**
But this is still correct
cobalt sentinel
Correct no issues
long cape
what I don't get, is when I distribute - into (1/(x+3))
top version
I can decide on distributing the - into the numerator *or * the denominator
but when it's written like (x+3)^-1 I can't distribute the - operator into it at all
I may be confusing this with multiplication, not subtraction
but same thing applies
actually nvm, subtraction too
I can change - into + (-1) for subtraction
cobalt sentinel
but when it's written like (x+3)^-1 I can't distribute the - operator into it at...
So like if we had -5(2x+2)^-1 it wouldn’t be (-10x -10)^-1 right? That’s what ur saying?
long cape
yeah exactly
but if it's written -5(1/(2x+2)) I could make it -5/(2x+2) **or ** 5/(-2x-2)
cobalt sentinel
Yes that’s correct
long cape
it's like deciding do I want the negative for 5 to be -5/1 or 5/-1
cobalt sentinel
Yep
long cape
but I lose that ability when the power is negative, right?
cobalt sentinel
Example?
long cape
-5(2x+2)^-1
cobalt sentinel
I mean even if it was -5(2x+2)^2 u couldn’t distribute in
long cape
true, but -5(1/(2x+2)) is the same thing as -5(2x+2)^-1, just different notation.. or so I thought
so basically, negative exponent can cause issue for stuff like this? .. I guess it depends on what I need to do with them?
cobalt sentinel
true, but `-5(1/(2x+2))` is the same thing as `-5(2x+2)^-1`, just different nota...
Yea same just different notation
cobalt sentinel
so basically, negative exponent can cause issue for stuff like this? .. I guess...
I guess
Could also do something like this
elfin berryBOT
Stephen
cobalt sentinel
its because when you distribute the -1 you are distributing 1/-1
Lol yea I was legit about to say this
Is that musashi’s friend?
In ur pfp
cobalt sentinel
yea
Controversial take: I’m happy the author went on hiatus (hope they feel better tho or whatever happened)
Cuz I didn’t want kojiro and him to fight
cobalt sentinel
ah
marsh citrusBOT
@long cape Has your question been resolved?
white brook
Stuck on:
white brook
What I've tried
marsh citrusBOT
@white brook Has your question been resolved?
fallow arrow
fallow arrow
does anyone k what they mean by this thing
why would u ever subtract the omitted term from the 8th term
usually you would ifnd the summation of 8 terms and subtract and add the 9th
fallow arrow
it might be a bit difficult tho
because this is a complicated question since ur using the partial sum notation to get it
pallid pine
remember that the error cannot be bigger than the next term of the series
so if we choose S8
the error cant be bigger than a9
fallow arrow
the error is always the omitted term
pallid pine
and since a9 = S9 - S8
fallow arrow
how does a9=S9-S8
pallid pine
remember
fallow arrow
i didnt understand that part
paper venture
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 43 months and a standard deviation of 8 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 19 and 27 months?
marsh citrusBOT
A company has a policy of retiring company cars; this policy looks at number of ...
whole hazel
!status
marsh citrusBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Do you know how to use the 68 95 99.7 rule
paper venture
no this is my first time coming across a problem like this and I am stuck
i have no idea what I am supposed to do
paper venture
2.35%?
pallid pine
@paper venture is that your final answer
pallid pine
@paper venture it shows you the %
for areas
that are certain standard deviation
from the mean
paper venture
since the standard deviation is 8 months it would be 3 standard deviations correct?
pallid pine
since the standard deviation is 8 months it would be 3 standard deviations corre...
yh
how much is 27
away from the mean
interms of standard deviation
pallid pine
like 3.2/3.2 interms of standard deviation since 3 interms is 24 right
what is 43 - 27
pallid pine
yh
so from 2 to 3 standard deviations below the mean
what is the probability
using the graph
i sent
paper venture
95% is 2 standard deviations and 99.7% is 3 standard deviations
pallid pine
95% is 2 standard deviations and 99.7% is 3 standard deviations
well those are
from both ends
you only want to go less than
so half it
paper venture
you said half of 95%
paper venture
sorry😓
pallid pine
half of 99.7%
paper venture
ok
pallid pine
and then take them away from each other
or
you could skip all that
and
just
use
the
graph
paper venture
so its 2.35%
pallid pine
yh
paper venture
ok so that is the percentage of cars that have remained in service between 19 and 27 months